LMFDB - Embedded newform 390.2.p.d.161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(161,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("390.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.161
Dual form			390.2.p.d.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{10} +(-1.41421 + 1.41421i) q^{11} +(-1.41421 + 1.00000i) q^{12} +(-3.00000 - 2.00000i) q^{13} +(-0.292893 + 1.70711i) q^{15} -1.00000 q^{16} +4.24264 q^{17} +(-2.70711 + 1.29289i) q^{18} +(6.00000 - 6.00000i) q^{19} +(-0.707107 + 0.707107i) q^{20} -2.00000 q^{22} +1.41421 q^{23} +(-1.70711 - 0.292893i) q^{24} +1.00000i q^{25} +(-0.707107 - 3.53553i) q^{26} +(-5.00000 + 1.41421i) q^{27} +1.41421i q^{29} +(-1.41421 + 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.41421 - 0.585786i) q^{33} +(3.00000 + 3.00000i) q^{34} +(-2.82843 - 1.00000i) q^{36} +(5.00000 + 5.00000i) q^{37} +8.48528 q^{38} +(-0.171573 - 6.24264i) q^{39} -1.00000 q^{40} +(-7.07107 - 7.07107i) q^{41} -4.00000i q^{43} +(-1.41421 - 1.41421i) q^{44} +(-2.70711 + 1.29289i) q^{45} +(1.00000 + 1.00000i) q^{46} +(4.24264 - 4.24264i) q^{47} +(-1.00000 - 1.41421i) q^{48} -7.00000i q^{49} +(-0.707107 + 0.707107i) q^{50} +(4.24264 + 6.00000i) q^{51} +(2.00000 - 3.00000i) q^{52} +11.3137i q^{53} +(-4.53553 - 2.53553i) q^{54} -2.00000 q^{55} +(14.4853 + 2.48528i) q^{57} +(-1.00000 + 1.00000i) q^{58} +(2.82843 - 2.82843i) q^{59} +(-1.70711 - 0.292893i) q^{60} +2.00000 q^{61} -4.24264 q^{62} -1.00000i q^{64} +(-0.707107 - 3.53553i) q^{65} +(-2.00000 - 2.82843i) q^{66} +(5.00000 - 5.00000i) q^{67} +4.24264i q^{68} +(1.41421 + 2.00000i) q^{69} +(-5.65685 - 5.65685i) q^{71} +(-1.29289 - 2.70711i) q^{72} +(6.00000 + 6.00000i) q^{73} +7.07107i q^{74} +(-1.41421 + 1.00000i) q^{75} +(6.00000 + 6.00000i) q^{76} +(4.29289 - 4.53553i) q^{78} +8.00000 q^{79} +(-0.707107 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} -10.0000i q^{82} +(-5.65685 - 5.65685i) q^{83} +(3.00000 + 3.00000i) q^{85} +(2.82843 - 2.82843i) q^{86} +(-2.00000 + 1.41421i) q^{87} -2.00000i q^{88} +(-4.24264 + 4.24264i) q^{89} +(-2.82843 - 1.00000i) q^{90} +1.41421i q^{92} +(-7.24264 - 1.24264i) q^{93} +6.00000 q^{94} +8.48528 q^{95} +(0.292893 - 1.70711i) q^{96} +(10.0000 - 10.0000i) q^{97} +(4.94975 - 4.94975i) q^{98} +(-2.58579 - 5.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{19} - 8 q^{22} - 4 q^{24} - 20 q^{27} - 12 q^{31} - 8 q^{33} + 12 q^{34} + 20 q^{37} - 12 q^{39} - 4 q^{40} - 8 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^6 - 4 * q^9 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^19 - 8 * q^22 - 4 * q^24 - 20 * q^27 - 12 * q^31 - 8 * q^33 + 12 * q^34 + 20 * q^37 - 12 * q^39 - 4 * q^40 - 8 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^52 - 4 * q^54 - 8 * q^55 + 24 * q^57 - 4 * q^58 - 4 * q^60 + 8 * q^61 - 8 * q^66 + 20 * q^67 - 8 * q^72 + 24 * q^73 + 24 * q^76 + 20 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^85 - 8 * q^87 - 12 * q^93 + 24 * q^94 + 4 * q^96 + 40 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$			1.00000i			0.500000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−0.292893	+	1.70711i	−0.119573	+	0.696923i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$			1.00000i			0.316228i
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$	−0.292893	+	1.70711i	−0.0756247	+	0.440773i
$16$	−1.00000			−0.250000
$17$	4.24264			1.02899			0.514496	−	0.857493i	$-0.327979\pi$
$17$	4.24264			1.02899			0.514496	+	0.857493i	$0.327979\pi$
$18$	−2.70711	+	1.29289i	−0.638071	+	0.304738i
$19$	6.00000	−	6.00000i	1.37649	−	1.37649i	0.526026	−	0.850469i	$-0.323682\pi$
$19$	6.00000	−	6.00000i	1.37649	−	1.37649i	0.850469	−	0.526026i	$-0.176318\pi$
$20$	−0.707107	+	0.707107i	−0.158114	+	0.158114i
$21$		0			0
$22$	−2.00000			−0.426401
$23$	1.41421			0.294884			0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421			0.294884			0.147442	+	0.989071i	$0.452896\pi$
$24$	−1.70711	−	0.292893i	−0.348462	−	0.0597866i
$25$			1.00000i			0.200000i
$26$	−0.707107	−	3.53553i	−0.138675	−	0.693375i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		0			0
$29$			1.41421i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$29$			1.41421i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$30$	−1.41421	+	1.00000i	−0.258199	+	0.182574i
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	−0.923181	−	0.384365i	$-0.874420\pi$
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	0.384365	+	0.923181i	$0.374420\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.41421	−	0.585786i	−0.594338	−	0.101972i
$34$	3.00000	+	3.00000i	0.514496	+	0.514496i
$35$		0			0
$36$	−2.82843	−	1.00000i	−0.471405	−	0.166667i
$37$	5.00000	+	5.00000i	0.821995	+	0.821995i	0.986394	−	0.164399i	$-0.0525685\pi$
$37$	5.00000	+	5.00000i	0.821995	+	0.821995i	−0.164399	+	0.986394i	$0.552568\pi$
$38$	8.48528			1.37649
$39$	−0.171573	−	6.24264i	−0.0274736	−	0.999623i
$40$	−1.00000			−0.158114
$41$	−7.07107	−	7.07107i	−1.10432	−	1.10432i	−0.993884	−	0.110432i	$-0.964777\pi$
$41$	−7.07107	−	7.07107i	−1.10432	−	1.10432i	−0.110432	−	0.993884i	$-0.535223\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	−1.41421	−	1.41421i	−0.213201	−	0.213201i
$45$	−2.70711	+	1.29289i	−0.403552	+	0.192733i
$46$	1.00000	+	1.00000i	0.147442	+	0.147442i
$47$	4.24264	−	4.24264i	0.618853	−	0.618853i	−0.326384	−	0.945237i	$-0.605830\pi$
$47$	4.24264	−	4.24264i	0.618853	−	0.618853i	0.945237	+	0.326384i	$0.105830\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$		−	7.00000i		−	1.00000i
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	4.24264	+	6.00000i	0.594089	+	0.840168i
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$			11.3137i			1.55406i	0.629465	+	0.777029i	$0.283274\pi$
$53$			11.3137i			1.55406i	−0.629465	+	0.777029i	$0.716726\pi$
$54$	−4.53553	−	2.53553i	−0.617208	−	0.345042i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	14.4853	+	2.48528i	1.91862	+	0.329184i
$58$	−1.00000	+	1.00000i	−0.131306	+	0.131306i
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	−0.498601	−	0.866831i	$-0.666153\pi$
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	0.866831	+	0.498601i	$0.166153\pi$
$60$	−1.70711	−	0.292893i	−0.220387	−	0.0378124i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.24264			−0.538816
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.707107	−	3.53553i	−0.0877058	−	0.438529i
$66$	−2.00000	−	2.82843i	−0.246183	−	0.348155i
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	−0.332320	−	0.943167i	$-0.607831\pi$
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	0.943167	+	0.332320i	$0.107831\pi$
$68$			4.24264i			0.514496i
$69$	1.41421	+	2.00000i	0.170251	+	0.240772i
$70$		0			0
$71$	−5.65685	−	5.65685i	−0.671345	−	0.671345i	0.286681	−	0.958026i	$-0.407448\pi$
$71$	−5.65685	−	5.65685i	−0.671345	−	0.671345i	−0.958026	+	0.286681i	$0.907448\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	0.964892	−	0.262646i	$-0.0845950\pi$
$73$	6.00000	+	6.00000i	0.702247	+	0.702247i	−0.262646	+	0.964892i	$0.584595\pi$
$74$			7.07107i			0.821995i
$75$	−1.41421	+	1.00000i	−0.163299	+	0.115470i
$76$	6.00000	+	6.00000i	0.688247	+	0.688247i
$77$		0			0
$78$	4.29289	−	4.53553i	0.486074	−	0.513548i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−0.707107	−	0.707107i	−0.0790569	−	0.0790569i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		−	10.0000i		−	1.10432i
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$		0			0
$85$	3.00000	+	3.00000i	0.325396	+	0.325396i
$86$	2.82843	−	2.82843i	0.304997	−	0.304997i
$87$	−2.00000	+	1.41421i	−0.214423	+	0.151620i
$88$		−	2.00000i		−	0.213201i
$89$	−4.24264	+	4.24264i	−0.449719	+	0.449719i	−0.895261	−	0.445542i	$-0.853011\pi$
$89$	−4.24264	+	4.24264i	−0.449719	+	0.449719i	0.445542	+	0.895261i	$0.353011\pi$
$90$	−2.82843	−	1.00000i	−0.298142	−	0.105409i
$91$		0			0
$92$			1.41421i			0.147442i
$93$	−7.24264	−	1.24264i	−0.751027	−	0.128856i
$94$	6.00000			0.618853
$95$	8.48528			0.870572
$96$	0.292893	−	1.70711i	0.0298933	−	0.174231i
$97$	10.0000	−	10.0000i	1.01535	−	1.01535i	0.0154658	−	0.999880i	$-0.495077\pi$
$97$	10.0000	−	10.0000i	1.01535	−	1.01535i	0.999880	−	0.0154658i	$-0.00492310\pi$
$98$	4.94975	−	4.94975i	0.500000	−	0.500000i
$99$	−2.58579	−	5.41421i	−0.259881	−	0.544149i
$100$	−1.00000			−0.100000
$101$	−15.5563			−1.54791			−0.773957	−	0.633238i	$-0.781726\pi$
$101$	−15.5563			−1.54791			−0.773957	+	0.633238i	$0.781726\pi$
$102$	−1.24264	+	7.24264i	−0.123040	+	0.717128i
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	3.53553	−	0.707107i	0.346688	−	0.0693375i
$105$		0			0
$106$	−8.00000	+	8.00000i	−0.777029	+	0.777029i
$107$		−	11.3137i		−	1.09374i	−0.837218	−	0.546869i	$-0.815820\pi$
$107$		−	11.3137i		−	1.09374i	0.837218	−	0.546869i	$-0.184180\pi$
$108$	−1.41421	−	5.00000i	−0.136083	−	0.481125i
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	−0.604807	−	0.796372i	$-0.706750\pi$
$109$	2.00000	−	2.00000i	0.191565	−	0.191565i	0.796372	+	0.604807i	$0.206750\pi$
$110$	−1.41421	−	1.41421i	−0.134840	−	0.134840i
$111$	−2.07107	+	12.0711i	−0.196577	+	1.14574i
$112$		0			0
$113$			7.07107i			0.665190i	0.943070	+	0.332595i	$0.107924\pi$
$113$			7.07107i			0.665190i	−0.943070	+	0.332595i	$0.892076\pi$
$114$	8.48528	+	12.0000i	0.794719	+	1.12390i
$115$	1.00000	+	1.00000i	0.0932505	+	0.0932505i
$116$	−1.41421			−0.131306
$117$	8.65685	−	6.48528i	0.800326	−	0.599564i
$118$	4.00000			0.368230
$119$		0			0
$120$	−1.00000	−	1.41421i	−0.0912871	−	0.129099i
$121$			7.00000i			0.636364i
$122$	1.41421	+	1.41421i	0.128037	+	0.128037i
$123$	2.92893	−	17.0711i	0.264093	−	1.53925i
$124$	−3.00000	−	3.00000i	−0.269408	−	0.269408i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.65685	−	4.00000i	0.498058	−	0.352180i
$130$	2.00000	−	3.00000i	0.175412	−	0.263117i
$131$		−	7.07107i		−	0.617802i	−0.951094	−	0.308901i	$-0.900039\pi$
$131$		−	7.07107i		−	0.617802i	0.951094	−	0.308901i	$-0.0999612\pi$
$132$	0.585786	−	3.41421i	0.0509862	−	0.297169i
$133$		0			0
$134$	7.07107			0.610847
$135$	−4.53553	−	2.53553i	−0.390357	−	0.218224i
$136$	−3.00000	+	3.00000i	−0.257248	+	0.257248i
$137$	−14.1421	+	14.1421i	−1.20824	+	1.20824i	−0.236649	+	0.971595i	$0.576049\pi$
$137$	−14.1421	+	14.1421i	−1.20824	+	1.20824i	−0.971595	+	0.236649i	$0.923951\pi$
$138$	−0.414214	+	2.41421i	−0.0352602	+	0.205512i
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$	10.2426	+	1.75736i	0.862586	+	0.147996i
$142$		−	8.00000i		−	0.671345i
$143$	7.07107	−	1.41421i	0.591312	−	0.118262i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$	−1.00000	+	1.00000i	−0.0830455	+	0.0830455i
$146$			8.48528i			0.702247i
$147$	9.89949	−	7.00000i	0.816497	−	0.577350i
$148$	−5.00000	+	5.00000i	−0.410997	+	0.410997i
$149$	−7.07107	−	7.07107i	−0.579284	−	0.579284i	0.355422	−	0.934706i	$-0.384337\pi$
$149$	−7.07107	−	7.07107i	−0.579284	−	0.579284i	−0.934706	+	0.355422i	$0.884337\pi$
$150$	−1.70711	−	0.292893i	−0.139385	−	0.0239146i
$151$	−13.0000	−	13.0000i	−1.05792	−	1.05792i	−0.998216	−	0.0597092i	$-0.980983\pi$
$151$	−13.0000	−	13.0000i	−1.05792	−	1.05792i	−0.0597092	−	0.998216i	$-0.519017\pi$
$152$			8.48528i			0.688247i
$153$	−4.24264	+	12.0000i	−0.342997	+	0.970143i
$154$		0			0
$155$	−4.24264			−0.340777
$156$	6.24264	−	0.171573i	0.499811	−	0.0137368i
$157$	−6.00000			−0.478852			−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000			−0.478852			−0.239426	+	0.970915i	$0.576959\pi$
$158$	5.65685	+	5.65685i	0.450035	+	0.450035i
$159$	−16.0000	+	11.3137i	−1.26888	+	0.897235i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−0.949747	−	8.94975i	−0.0746192	−	0.703159i
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	0.129936	−	0.991522i	$-0.458523\pi$
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	−0.991522	+	0.129936i	$0.958523\pi$
$164$	7.07107	−	7.07107i	0.552158	−	0.552158i
$165$	−2.00000	−	2.82843i	−0.155700	−	0.220193i
$166$		−	8.00000i		−	0.620920i
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	−0.117582	−	0.993063i	$-0.537514\pi$
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	0.993063	+	0.117582i	$0.0375143\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$			4.24264i			0.325396i
$171$	10.9706	+	22.9706i	0.838940	+	1.75660i
$172$	4.00000			0.304997
$173$	2.82843			0.215041			0.107521	−	0.994203i	$-0.465709\pi$
$173$	2.82843			0.215041			0.107521	+	0.994203i	$0.465709\pi$
$174$	−2.41421	−	0.414214i	−0.183021	−	0.0314014i
$175$		0			0
$176$	1.41421	−	1.41421i	0.106600	−	0.106600i
$177$	6.82843	+	1.17157i	0.513256	+	0.0880608i
$178$	−6.00000			−0.449719
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$	−1.29289	−	2.70711i	−0.0963666	−	0.201776i
$181$			18.0000i			1.33793i	0.743294	+	0.668965i	$0.233262\pi$
$181$			18.0000i			1.33793i	−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$	2.00000	+	2.82843i	0.147844	+	0.209083i
$184$	−1.00000	+	1.00000i	−0.0737210	+	0.0737210i
$185$			7.07107i			0.519875i
$186$	−4.24264	−	6.00000i	−0.311086	−	0.439941i
$187$	−6.00000	+	6.00000i	−0.438763	+	0.438763i
$188$	4.24264	+	4.24264i	0.309426	+	0.309426i
$189$		0			0
$190$	6.00000	+	6.00000i	0.435286	+	0.435286i
$191$			19.7990i			1.43260i	0.697790	+	0.716302i	$0.254167\pi$
$191$			19.7990i			1.43260i	−0.697790	+	0.716302i	$0.745833\pi$
$192$	1.41421	−	1.00000i	0.102062	−	0.0721688i
$193$	−6.00000	−	6.00000i	−0.431889	−	0.431889i	0.457381	−	0.889271i	$-0.348787\pi$
$193$	−6.00000	−	6.00000i	−0.431889	−	0.431889i	−0.889271	+	0.457381i	$0.848787\pi$
$194$	14.1421			1.01535
$195$	4.29289	−	4.53553i	0.307420	−	0.324796i
$196$	7.00000			0.500000
$197$	9.89949	+	9.89949i	0.705310	+	0.705310i	0.965545	−	0.260235i	$-0.0838002\pi$
$197$	9.89949	+	9.89949i	0.705310	+	0.705310i	−0.260235	+	0.965545i	$0.583800\pi$
$198$	2.00000	−	5.65685i	0.142134	−	0.402015i
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$	−0.707107	−	0.707107i	−0.0500000	−	0.0500000i
$201$	12.0711	+	2.07107i	0.851427	+	0.146082i
$202$	−11.0000	−	11.0000i	−0.773957	−	0.773957i
$203$		0			0
$204$	−6.00000	+	4.24264i	−0.420084	+	0.297044i
$205$		−	10.0000i		−	0.698430i
$206$	−5.65685	+	5.65685i	−0.394132	+	0.394132i
$207$	−1.41421	+	4.00000i	−0.0982946	+	0.278019i
$208$	3.00000	+	2.00000i	0.208013	+	0.138675i
$209$			16.9706i			1.17388i
$210$		0			0
$211$	−24.0000			−1.65223			−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000			−1.65223			−0.826114	+	0.563503i	$0.809453\pi$
$212$	−11.3137			−0.777029
$213$	2.34315	−	13.6569i	0.160550	−	0.935752i
$214$	8.00000	−	8.00000i	0.546869	−	0.546869i
$215$	2.82843	−	2.82843i	0.192897	−	0.192897i
$216$	2.53553	−	4.53553i	0.172521	−	0.308604i
$217$		0			0
$218$	2.82843			0.191565
$219$	−2.48528	+	14.4853i	−0.167940	+	0.978825i
$220$		−	2.00000i		−	0.134840i
$221$	−12.7279	−	8.48528i	−0.856173	−	0.570782i
$222$	−10.0000	+	7.07107i	−0.671156	+	0.474579i
$223$	−10.0000	+	10.0000i	−0.669650	+	0.669650i	−0.957635	−	0.287985i	$-0.907015\pi$
$223$	−10.0000	+	10.0000i	−0.669650	+	0.669650i	0.287985	+	0.957635i	$0.407015\pi$
$224$		0			0
$225$	−2.82843	−	1.00000i	−0.188562	−	0.0666667i
$226$	−5.00000	+	5.00000i	−0.332595	+	0.332595i
$227$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$227$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$228$	−2.48528	+	14.4853i	−0.164592	+	0.959311i
$229$	6.00000	+	6.00000i	0.396491	+	0.396491i	0.876993	−	0.480502i	$-0.159546\pi$
$229$	6.00000	+	6.00000i	0.396491	+	0.396491i	−0.480502	+	0.876993i	$0.659546\pi$
$230$			1.41421i			0.0932505i
$231$		0			0
$232$	−1.00000	−	1.00000i	−0.0656532	−	0.0656532i
$233$	18.3848			1.20443			0.602213	−	0.798335i	$-0.294286\pi$
$233$	18.3848			1.20443			0.602213	+	0.798335i	$0.294286\pi$
$234$	10.7071	+	1.53553i	0.699945	+	0.100381i
$235$	6.00000			0.391397
$236$	2.82843	+	2.82843i	0.184115	+	0.184115i
$237$	8.00000	+	11.3137i	0.519656	+	0.734904i
$238$		0			0
$239$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$239$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$240$	0.292893	−	1.70711i	0.0189062	−	0.110193i
$241$	−1.00000	−	1.00000i	−0.0644157	−	0.0644157i	0.674165	−	0.738581i	$-0.264504\pi$
$241$	−1.00000	−	1.00000i	−0.0644157	−	0.0644157i	−0.738581	+	0.674165i	$0.764504\pi$
$242$	−4.94975	+	4.94975i	−0.318182	+	0.318182i
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$			2.00000i			0.128037i
$245$	4.94975	−	4.94975i	0.316228	−	0.316228i
$246$	14.1421	−	10.0000i	0.901670	−	0.637577i
$247$	−30.0000	+	6.00000i	−1.90885	+	0.381771i
$248$		−	4.24264i		−	0.269408i
$249$	2.34315	−	13.6569i	0.148491	−	0.865468i
$250$	−1.00000			−0.0632456
$251$	−4.24264			−0.267793			−0.133897	−	0.990995i	$-0.542749\pi$
$251$	−4.24264			−0.267793			−0.133897	+	0.990995i	$0.542749\pi$
$252$		0			0
$253$	−2.00000	+	2.00000i	−0.125739	+	0.125739i
$254$	−2.82843	+	2.82843i	−0.177471	+	0.177471i
$255$	−1.24264	+	7.24264i	−0.0778172	+	0.453552i
$256$	1.00000			0.0625000
$257$	1.41421			0.0882162			0.0441081	−	0.999027i	$-0.485955\pi$
$257$	1.41421			0.0882162			0.0441081	+	0.999027i	$0.485955\pi$
$258$	6.82843	+	1.17157i	0.425119	+	0.0729389i
$259$		0			0
$260$	3.53553	−	0.707107i	0.219265	−	0.0438529i
$261$	−4.00000	−	1.41421i	−0.247594	−	0.0875376i
$262$	5.00000	−	5.00000i	0.308901	−	0.308901i
$263$		−	4.24264i		−	0.261612i	−0.991408	−	0.130806i	$-0.958243\pi$
$263$		−	4.24264i		−	0.261612i	0.991408	−	0.130806i	$-0.0417566\pi$
$264$	2.82843	−	2.00000i	0.174078	−	0.123091i
$265$	−8.00000	+	8.00000i	−0.491436	+	0.491436i
$266$		0			0
$267$	−10.2426	−	1.75736i	−0.626839	−	0.107549i
$268$	5.00000	+	5.00000i	0.305424	+	0.305424i
$269$			1.41421i			0.0862261i	0.999070	+	0.0431131i	$0.0137276\pi$
$269$			1.41421i			0.0862261i	−0.999070	+	0.0431131i	$0.986272\pi$
$270$	−1.41421	−	5.00000i	−0.0860663	−	0.304290i
$271$	−3.00000	−	3.00000i	−0.182237	−	0.182237i	0.610093	−	0.792330i	$-0.291132\pi$
$271$	−3.00000	−	3.00000i	−0.182237	−	0.182237i	−0.792330	+	0.610093i	$0.791132\pi$
$272$	−4.24264			−0.257248
$273$		0			0
$274$	−20.0000			−1.20824
$275$	−1.41421	−	1.41421i	−0.0852803	−	0.0852803i
$276$	−2.00000	+	1.41421i	−0.120386	+	0.0851257i
$277$			28.0000i			1.68236i	0.540758	+	0.841178i	$0.318138\pi$
$277$			28.0000i			1.68236i	−0.540758	+	0.841178i	$0.681862\pi$
$278$	−11.3137	−	11.3137i	−0.678551	−	0.678551i
$279$	−5.48528	−	11.4853i	−0.328395	−	0.687606i
$280$		0			0
$281$	12.7279	−	12.7279i	0.759284	−	0.759284i	−0.216908	−	0.976192i	$-0.569597\pi$
$281$	12.7279	−	12.7279i	0.759284	−	0.759284i	0.976192	+	0.216908i	$0.0695971\pi$
$282$	6.00000	+	8.48528i	0.357295	+	0.505291i
$283$		−	6.00000i		−	0.356663i	−0.983970	−	0.178331i	$-0.942930\pi$
$283$		−	6.00000i		−	0.356663i	0.983970	−	0.178331i	$-0.0570699\pi$
$284$	5.65685	−	5.65685i	0.335673	−	0.335673i
$285$	8.48528	+	12.0000i	0.502625	+	0.710819i
$286$	6.00000	+	4.00000i	0.354787	+	0.236525i
$287$		0			0
$288$	2.70711	−	1.29289i	0.159518	−	0.0761845i
$289$	1.00000			0.0588235
$290$	−1.41421			−0.0830455
$291$	24.1421	+	4.14214i	1.41524	+	0.242816i
$292$	−6.00000	+	6.00000i	−0.351123	+	0.351123i
$293$	−9.89949	+	9.89949i	−0.578335	+	0.578335i	−0.934444	−	0.356110i	$-0.884103\pi$
$293$	−9.89949	+	9.89949i	−0.578335	+	0.578335i	0.356110	+	0.934444i	$0.384103\pi$
$294$	11.9497	+	2.05025i	0.696923	+	0.119573i
$295$	4.00000			0.232889
$296$	−7.07107			−0.410997
$297$	5.07107	−	9.07107i	0.294253	−	0.526357i
$298$		−	10.0000i		−	0.579284i
$299$	−4.24264	−	2.82843i	−0.245358	−	0.163572i
$300$	−1.00000	−	1.41421i	−0.0577350	−	0.0816497i
$301$		0			0
$302$		−	18.3848i		−	1.05792i
$303$	−15.5563	−	22.0000i	−0.893689	−	1.26387i
$304$	−6.00000	+	6.00000i	−0.344124	+	0.344124i
$305$	1.41421	+	1.41421i	0.0809776	+	0.0809776i
$306$	−11.4853	+	5.48528i	−0.656570	+	0.313573i
$307$	23.0000	+	23.0000i	1.31268	+	1.31268i	0.919433	+	0.393246i	$0.128648\pi$
$307$	23.0000	+	23.0000i	1.31268	+	1.31268i	0.393246	+	0.919433i	$0.371352\pi$
$308$		0			0
$309$	−11.3137	+	8.00000i	−0.643614	+	0.455104i
$310$	−3.00000	−	3.00000i	−0.170389	−	0.170389i
$311$	2.82843			0.160385			0.0801927	−	0.996779i	$-0.474446\pi$
$311$	2.82843			0.160385			0.0801927	+	0.996779i	$0.474446\pi$
$312$	4.53553	+	4.29289i	0.256774	+	0.243037i
$313$	26.0000			1.46961			0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000			1.46961			0.734803	+	0.678280i	$0.237274\pi$
$314$	−4.24264	−	4.24264i	−0.239426	−	0.239426i
$315$		0			0
$316$			8.00000i			0.450035i
$317$	−18.3848	−	18.3848i	−1.03259	−	1.03259i	−0.999451	−	0.0331412i	$-0.989449\pi$
$317$	−18.3848	−	18.3848i	−1.03259	−	1.03259i	−0.0331412	−	0.999451i	$-0.510551\pi$
$318$	−19.3137	−	3.31371i	−1.08306	−	0.185824i
$319$	−2.00000	−	2.00000i	−0.111979	−	0.111979i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	16.0000	−	11.3137i	0.893033	−	0.631470i
$322$		0			0
$323$	25.4558	−	25.4558i	1.41640	−	1.41640i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	2.00000	−	3.00000i	0.110940	−	0.166410i
$326$		−	15.5563i		−	0.861586i
$327$	4.82843	+	0.828427i	0.267013	+	0.0458121i
$328$	10.0000			0.552158
$329$		0			0
$330$	0.585786	−	3.41421i	0.0322465	−	0.187946i
$331$	24.0000	−	24.0000i	1.31916	−	1.31916i	0.404718	−	0.914442i	$-0.367370\pi$
$331$	24.0000	−	24.0000i	1.31916	−	1.31916i	0.914442	−	0.404718i	$-0.132630\pi$
$332$	5.65685	−	5.65685i	0.310460	−	0.310460i
$333$	−19.1421	+	9.14214i	−1.04898	+	0.500986i
$334$	16.0000			0.875481
$335$	7.07107			0.386334
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$	−4.94975	+	12.0208i	−0.269231	+	0.653846i
$339$	−10.0000	+	7.07107i	−0.543125	+	0.384048i
$340$	−3.00000	+	3.00000i	−0.162698	+	0.162698i
$341$		−	8.48528i		−	0.459504i
$342$	−8.48528	+	24.0000i	−0.458831	+	1.29777i
$343$		0			0
$344$	2.82843	+	2.82843i	0.152499	+	0.152499i
$345$	−0.414214	+	2.41421i	−0.0223005	+	0.129977i
$346$	2.00000	+	2.00000i	0.107521	+	0.107521i
$347$			11.3137i			0.607352i	0.952775	+	0.303676i	$0.0982140\pi$
$347$			11.3137i			0.607352i	−0.952775	+	0.303676i	$0.901786\pi$
$348$	−1.41421	−	2.00000i	−0.0758098	−	0.107211i
$349$	−12.0000	−	12.0000i	−0.642345	−	0.642345i	0.308786	−	0.951131i	$-0.400077\pi$
$349$	−12.0000	−	12.0000i	−0.642345	−	0.642345i	−0.951131	+	0.308786i	$0.900077\pi$
$350$		0			0
$351$	17.8284	+	5.75736i	0.951611	+	0.307305i
$352$	2.00000			0.106600
$353$	25.4558	+	25.4558i	1.35488	+	1.35488i	0.880112	+	0.474766i	$0.157467\pi$
$353$	25.4558	+	25.4558i	1.35488	+	1.35488i	0.474766	+	0.880112i	$0.342533\pi$
$354$	4.00000	+	5.65685i	0.212598	+	0.300658i
$355$		−	8.00000i		−	0.424596i
$356$	−4.24264	−	4.24264i	−0.224860	−	0.224860i
$357$		0			0
$358$	−13.0000	−	13.0000i	−0.687071	−	0.687071i
$359$	16.9706	−	16.9706i	0.895672	−	0.895672i	−0.0993777	−	0.995050i	$-0.531685\pi$
$359$	16.9706	−	16.9706i	0.895672	−	0.895672i	0.995050	+	0.0993777i	$0.0316852\pi$
$360$	1.00000	−	2.82843i	0.0527046	−	0.149071i
$361$		−	53.0000i		−	2.78947i
$362$	−12.7279	+	12.7279i	−0.668965	+	0.668965i
$363$	−9.89949	+	7.00000i	−0.519589	+	0.367405i
$364$		0			0
$365$			8.48528i			0.444140i
$366$	−0.585786	+	3.41421i	−0.0306195	+	0.178464i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$	−1.41421			−0.0737210
$369$	27.0711	−	12.9289i	1.40926	−	0.673053i
$370$	−5.00000	+	5.00000i	−0.259938	+	0.259938i
$371$		0			0
$372$	1.24264	−	7.24264i	0.0644279	−	0.375513i
$373$	−32.0000			−1.65690			−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000			−1.65690			−0.828449	+	0.560065i	$0.810776\pi$
$374$	−8.48528			−0.438763
$375$	−1.70711	−	0.292893i	−0.0881546	−	0.0151249i
$376$			6.00000i			0.309426i
$377$	2.82843	−	4.24264i	0.145671	−	0.218507i
$378$		0			0
$379$	16.0000	−	16.0000i	0.821865	−	0.821865i	−0.164511	−	0.986375i	$-0.552604\pi$
$379$	16.0000	−	16.0000i	0.821865	−	0.821865i	0.986375	+	0.164511i	$0.0526045\pi$
$380$			8.48528i			0.435286i
$381$	−5.65685	+	4.00000i	−0.289809	+	0.204926i
$382$	−14.0000	+	14.0000i	−0.716302	+	0.716302i
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	0.125001	−	0.992157i	$-0.460106\pi$
$383$	−16.9706	−	16.9706i	−0.867155	−	0.867155i	−0.992157	+	0.125001i	$0.960106\pi$
$384$	1.70711	+	0.292893i	0.0871154	+	0.0149466i
$385$		0			0
$386$		−	8.48528i		−	0.431889i
$387$	11.3137	+	4.00000i	0.575108	+	0.203331i
$388$	10.0000	+	10.0000i	0.507673	+	0.507673i
$389$	−26.8701			−1.36237			−0.681183	−	0.732113i	$-0.738534\pi$
$389$	−26.8701			−1.36237			−0.681183	+	0.732113i	$0.738534\pi$
$390$	6.24264	−	0.171573i	0.316108	−	0.00868793i
$391$	6.00000			0.303433
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$	10.0000	−	7.07107i	0.504433	−	0.356688i
$394$			14.0000i			0.705310i
$395$	5.65685	+	5.65685i	0.284627	+	0.284627i
$396$	5.41421	−	2.58579i	0.272074	−	0.129941i
$397$	3.00000	+	3.00000i	0.150566	+	0.150566i	0.778371	−	0.627805i	$-0.216046\pi$
$397$	3.00000	+	3.00000i	0.150566	+	0.150566i	−0.627805	+	0.778371i	$0.716046\pi$
$398$	−1.41421	+	1.41421i	−0.0708881	+	0.0708881i
$399$		0			0
$400$		−	1.00000i		−	0.0500000i
$401$	4.24264	−	4.24264i	0.211867	−	0.211867i	−0.593193	−	0.805060i	$-0.702133\pi$
$401$	4.24264	−	4.24264i	0.211867	−	0.211867i	0.805060	+	0.593193i	$0.202133\pi$
$402$	7.07107	+	10.0000i	0.352673	+	0.498755i
$403$	15.0000	−	3.00000i	0.747203	−	0.149441i
$404$		−	15.5563i		−	0.773957i
$405$	−0.949747	−	8.94975i	−0.0471933	−	0.444717i
$406$		0			0
$407$	−14.1421			−0.701000
$408$	−7.24264	−	1.24264i	−0.358564	−	0.0615199i
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	−0.777376	−	0.629036i	$-0.783450\pi$
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	0.629036	+	0.777376i	$0.283450\pi$
$410$	7.07107	−	7.07107i	0.349215	−	0.349215i
$411$	−34.1421	−	5.85786i	−1.68411	−	0.288947i
$412$	−8.00000			−0.394132
$413$		0			0
$414$	−3.82843	+	1.82843i	−0.188157	+	0.0898623i
$415$		−	8.00000i		−	0.392705i
$416$	0.707107	+	3.53553i	0.0346688	+	0.173344i
$417$	−16.0000	−	22.6274i	−0.783523	−	1.10807i
$418$	−12.0000	+	12.0000i	−0.586939	+	0.586939i
$419$		−	15.5563i		−	0.759977i	−0.924991	−	0.379989i	$-0.875928\pi$
$419$		−	15.5563i		−	0.759977i	0.924991	−	0.379989i	$-0.124072\pi$
$420$		0			0
$421$	12.0000	−	12.0000i	0.584844	−	0.584844i	−0.351386	−	0.936231i	$-0.614290\pi$
$421$	12.0000	−	12.0000i	0.584844	−	0.584844i	0.936231	+	0.351386i	$0.114290\pi$
$422$	−16.9706	−	16.9706i	−0.826114	−	0.826114i
$423$	7.75736	+	16.2426i	0.377176	+	0.789744i
$424$	−8.00000	−	8.00000i	−0.388514	−	0.388514i
$425$			4.24264i			0.205798i
$426$	11.3137	−	8.00000i	0.548151	−	0.387601i
$427$		0			0
$428$	11.3137			0.546869
$429$	9.07107	+	8.58579i	0.437955	+	0.414526i
$430$	4.00000			0.192897
$431$	25.4558	+	25.4558i	1.22616	+	1.22616i	0.965403	+	0.260762i	$0.0839737\pi$
$431$	25.4558	+	25.4558i	1.22616	+	1.22616i	0.260762	+	0.965403i	$0.416026\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$		0			0
$435$	−2.41421	−	0.414214i	−0.115753	−	0.0198600i
$436$	2.00000	+	2.00000i	0.0957826	+	0.0957826i
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$	−12.0000	+	8.48528i	−0.573382	+	0.405442i
$439$			6.00000i			0.286364i	0.989696	+	0.143182i	$0.0457335\pi$
$439$			6.00000i			0.286364i	−0.989696	+	0.143182i	$0.954267\pi$
$440$	1.41421	−	1.41421i	0.0674200	−	0.0674200i
$441$	19.7990	+	7.00000i	0.942809	+	0.333333i
$442$	−3.00000	−	15.0000i	−0.142695	−	0.713477i
$443$			8.48528i			0.403148i	0.979473	+	0.201574i	$0.0646056\pi$
$443$			8.48528i			0.403148i	−0.979473	+	0.201574i	$0.935394\pi$
$444$	−12.0711	−	2.07107i	−0.572868	−	0.0982885i
$445$	−6.00000			−0.284427
$446$	−14.1421			−0.669650
$447$	2.92893	−	17.0711i	0.138534	−	0.807434i
$448$		0			0
$449$	−12.7279	+	12.7279i	−0.600668	+	0.600668i	−0.940490	−	0.339822i	$-0.889633\pi$
$449$	−12.7279	+	12.7279i	−0.600668	+	0.600668i	0.339822	+	0.940490i	$0.389633\pi$
$450$	−1.29289	−	2.70711i	−0.0609476	−	0.127614i
$451$	20.0000			0.941763
$452$	−7.07107			−0.332595
$453$	5.38478	−	31.3848i	0.252999	−	1.47459i
$454$		0			0
$455$		0			0
$456$	−12.0000	+	8.48528i	−0.561951	+	0.397360i
$457$	6.00000	−	6.00000i	0.280668	−	0.280668i	−0.552707	−	0.833375i	$-0.686405\pi$
$457$	6.00000	−	6.00000i	0.280668	−	0.280668i	0.833375	+	0.552707i	$0.186405\pi$
$458$			8.48528i			0.396491i
$459$	−21.2132	+	6.00000i	−0.990148	+	0.280056i
$460$	−1.00000	+	1.00000i	−0.0466252	+	0.0466252i
$461$	−2.82843	−	2.82843i	−0.131733	−	0.131733i	0.638166	−	0.769899i	$-0.279693\pi$
$461$	−2.82843	−	2.82843i	−0.131733	−	0.131733i	−0.769899	+	0.638166i	$0.779693\pi$
$462$		0			0
$463$	22.0000	+	22.0000i	1.02243	+	1.02243i	0.999743	+	0.0226840i	$0.00722117\pi$
$463$	22.0000	+	22.0000i	1.02243	+	1.02243i	0.0226840	+	0.999743i	$0.492779\pi$
$464$		−	1.41421i		−	0.0656532i
$465$	−4.24264	−	6.00000i	−0.196748	−	0.278243i
$466$	13.0000	+	13.0000i	0.602213	+	0.602213i
$467$	2.82843			0.130884			0.0654420	−	0.997856i	$-0.479154\pi$
$467$	2.82843			0.130884			0.0654420	+	0.997856i	$0.479154\pi$
$468$	6.48528	+	8.65685i	0.299782	+	0.400163i
$469$		0			0
$470$	4.24264	+	4.24264i	0.195698	+	0.195698i
$471$	−6.00000	−	8.48528i	−0.276465	−	0.390981i
$472$			4.00000i			0.184115i
$473$	5.65685	+	5.65685i	0.260102	+	0.260102i
$474$	−2.34315	+	13.6569i	−0.107624	+	0.627280i
$475$	6.00000	+	6.00000i	0.275299	+	0.275299i
$476$		0			0
$477$	−32.0000	−	11.3137i	−1.46518	−	0.518019i
$478$		0			0
$479$	14.1421	−	14.1421i	0.646171	−	0.646171i	−0.305895	−	0.952065i	$-0.598956\pi$
$479$	14.1421	−	14.1421i	0.646171	−	0.646171i	0.952065	+	0.305895i	$0.0989555\pi$
$480$	1.41421	−	1.00000i	0.0645497	−	0.0456435i
$481$	−5.00000	−	25.0000i	−0.227980	−	1.13990i
$482$		−	1.41421i		−	0.0644157i
$483$		0			0
$484$	−7.00000			−0.318182
$485$	14.1421			0.642161
$486$	11.7071	−	10.2929i	0.531045	−	0.466895i
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−1.41421	+	1.41421i	−0.0640184	+	0.0640184i
$489$	4.55635	−	26.5563i	0.206045	−	1.20092i
$490$	7.00000			0.316228
$491$	15.5563			0.702048			0.351024	−	0.936366i	$-0.385834\pi$
$491$	15.5563			0.702048			0.351024	+	0.936366i	$0.385834\pi$
$492$	17.0711	+	2.92893i	0.769623	+	0.132046i
$493$			6.00000i			0.270226i
$494$	−25.4558	−	16.9706i	−1.14531	−	0.763542i
$495$	2.00000	−	5.65685i	0.0898933	−	0.254257i
$496$	3.00000	−	3.00000i	0.134704	−	0.134704i
$497$		0			0
$498$	11.3137	−	8.00000i	0.506979	−	0.358489i
$499$	−18.0000	+	18.0000i	−0.805791	+	0.805791i	−0.983994	−	0.178203i	$-0.942972\pi$
$499$	−18.0000	+	18.0000i	−0.805791	+	0.805791i	0.178203	+	0.983994i	$0.442972\pi$
$500$	−0.707107	−	0.707107i	−0.0316228	−	0.0316228i
$501$	27.3137	+	4.68629i	1.22029	+	0.209368i
$502$	−3.00000	−	3.00000i	−0.133897	−	0.133897i
$503$			9.89949i			0.441397i	0.975342	+	0.220698i	$0.0708336\pi$
$503$			9.89949i			0.441397i	−0.975342	+	0.220698i	$0.929166\pi$
$504$		0			0
$505$	−11.0000	−	11.0000i	−0.489494	−	0.489494i
$506$	−2.82843			−0.125739
$507$	−11.9706	+	19.0711i	−0.531631	+	0.846976i
$508$	−4.00000			−0.177471
$509$	−14.1421	−	14.1421i	−0.626839	−	0.626839i	0.320432	−	0.947271i	$-0.396172\pi$
$509$	−14.1421	−	14.1421i	−0.626839	−	0.626839i	−0.947271	+	0.320432i	$0.896172\pi$
$510$	−6.00000	+	4.24264i	−0.265684	+	0.187867i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−21.5147	+	38.4853i	−0.949898	+	1.69917i
$514$	1.00000	+	1.00000i	0.0441081	+	0.0441081i
$515$	−5.65685	+	5.65685i	−0.249271	+	0.249271i
$516$	4.00000	+	5.65685i	0.176090	+	0.249029i
$517$			12.0000i			0.527759i
$518$		0			0
$519$	2.82843	+	4.00000i	0.124154	+	0.175581i
$520$	3.00000	+	2.00000i	0.131559	+	0.0877058i
$521$			5.65685i			0.247831i	0.992293	+	0.123916i	$0.0395452\pi$
$521$			5.65685i			0.247831i	−0.992293	+	0.123916i	$0.960455\pi$
$522$	−1.82843	−	3.82843i	−0.0800281	−	0.167566i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	7.07107			0.308901
$525$		0			0
$526$	3.00000	−	3.00000i	0.130806	−	0.130806i
$527$	−12.7279	+	12.7279i	−0.554437	+	0.554437i
$528$	3.41421	+	0.585786i	0.148585	+	0.0254931i
$529$	−21.0000			−0.913043
$530$	−11.3137			−0.491436
$531$	5.17157	+	10.8284i	0.224427	+	0.469914i
$532$		0			0
$533$	7.07107	+	35.3553i	0.306282	+	1.53141i
$534$	−6.00000	−	8.48528i	−0.259645	−	0.367194i
$535$	8.00000	−	8.00000i	0.345870	−	0.345870i
$536$			7.07107i			0.305424i
$537$	−18.3848	−	26.0000i	−0.793362	−	1.12198i
$538$	−1.00000	+	1.00000i	−0.0431131	+	0.0431131i
$539$	9.89949	+	9.89949i	0.426401	+	0.426401i
$540$	2.53553	−	4.53553i	0.109112	−	0.195178i
$541$	−8.00000	−	8.00000i	−0.343947	−	0.343947i	0.513902	−	0.857849i	$-0.328199\pi$
$541$	−8.00000	−	8.00000i	−0.343947	−	0.343947i	−0.857849	+	0.513902i	$0.828199\pi$
$542$		−	4.24264i		−	0.182237i
$543$	−25.4558	+	18.0000i	−1.09241	+	0.772454i
$544$	−3.00000	−	3.00000i	−0.128624	−	0.128624i
$545$	2.82843			0.121157
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−14.1421	−	14.1421i	−0.604122	−	0.604122i
$549$	−2.00000	+	5.65685i	−0.0853579	+	0.241429i
$550$		−	2.00000i		−	0.0852803i
$551$	8.48528	+	8.48528i	0.361485	+	0.361485i
$552$	−2.41421	−	0.414214i	−0.102756	−	0.0176301i
$553$		0			0
$554$	−19.7990	+	19.7990i	−0.841178	+	0.841178i
$555$	−10.0000	+	7.07107i	−0.424476	+	0.300150i
$556$		−	16.0000i		−	0.678551i
$557$	−18.3848	+	18.3848i	−0.778988	+	0.778988i	−0.979659	−	0.200671i	$-0.935688\pi$
$557$	−18.3848	+	18.3848i	−0.778988	+	0.778988i	0.200671	+	0.979659i	$0.435688\pi$
$558$	4.24264	−	12.0000i	0.179605	−	0.508001i
$559$	−8.00000	+	12.0000i	−0.338364	+	0.507546i
$560$		0			0
$561$	−14.4853	−	2.48528i	−0.611569	−	0.104929i
$562$	18.0000			0.759284
$563$	19.7990			0.834428			0.417214	−	0.908808i	$-0.363007\pi$
$563$	19.7990			0.834428			0.417214	+	0.908808i	$0.363007\pi$
$564$	−1.75736	+	10.2426i	−0.0739982	+	0.431293i
$565$	−5.00000	+	5.00000i	−0.210352	+	0.210352i
$566$	4.24264	−	4.24264i	0.178331	−	0.178331i
$567$		0			0
$568$	8.00000			0.335673
$569$	45.2548			1.89718			0.948591	−	0.316506i	$-0.102510\pi$
$569$	45.2548			1.89718			0.948591	+	0.316506i	$0.102510\pi$
$570$	−2.48528	+	14.4853i	−0.104097	+	0.606722i
$571$			12.0000i			0.502184i	0.967963	+	0.251092i	$0.0807897\pi$
$571$			12.0000i			0.502184i	−0.967963	+	0.251092i	$0.919210\pi$
$572$	1.41421	+	7.07107i	0.0591312	+	0.295656i
$573$	−28.0000	+	19.7990i	−1.16972	+	0.827115i
$574$		0			0
$575$			1.41421i			0.0589768i
$576$	2.82843	+	1.00000i	0.117851	+	0.0416667i
$577$	26.0000	−	26.0000i	1.08239	−	1.08239i	0.0861084	−	0.996286i	$-0.472557\pi$
$577$	26.0000	−	26.0000i	1.08239	−	1.08239i	0.996286	−	0.0861084i	$-0.0274431\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	2.48528	−	14.4853i	0.103285	−	0.601988i
$580$	−1.00000	−	1.00000i	−0.0415227	−	0.0415227i
$581$		0			0
$582$	14.1421	+	20.0000i	0.586210	+	0.829027i
$583$	−16.0000	−	16.0000i	−0.662652	−	0.662652i
$584$	−8.48528			−0.351123
$585$	10.7071	+	1.53553i	0.442684	+	0.0634865i
$586$	−14.0000			−0.578335
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	0.168508	−	0.985700i	$-0.446105\pi$
$587$	−19.7990	−	19.7990i	−0.817192	−	0.817192i	−0.985700	+	0.168508i	$0.946105\pi$
$588$	7.00000	+	9.89949i	0.288675	+	0.408248i
$589$			36.0000i			1.48335i
$590$	2.82843	+	2.82843i	0.116445	+	0.116445i
$591$	−4.10051	+	23.8995i	−0.168672	+	0.983094i
$592$	−5.00000	−	5.00000i	−0.205499	−	0.205499i
$593$	−25.4558	+	25.4558i	−1.04535	+	1.04535i	−0.0464244	+	0.998922i	$0.514783\pi$
$593$	−25.4558	+	25.4558i	−1.04535	+	1.04535i	−0.998922	+	0.0464244i	$0.985217\pi$
$594$	10.0000	−	2.82843i	0.410305	−	0.116052i
$595$		0			0
$596$	7.07107	−	7.07107i	0.289642	−	0.289642i
$597$	−2.82843	+	2.00000i	−0.115760	+	0.0818546i
$598$	−1.00000	−	5.00000i	−0.0408930	−	0.204465i
$599$			45.2548i			1.84906i	0.381106	+	0.924531i	$0.375543\pi$
$599$			45.2548i			1.84906i	−0.381106	+	0.924531i	$0.624457\pi$
$600$	0.292893	−	1.70711i	0.0119573	−	0.0696923i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		0			0
$603$	9.14214	+	19.1421i	0.372297	+	0.779528i
$604$	13.0000	−	13.0000i	0.528962	−	0.528962i
$605$	−4.94975	+	4.94975i	−0.201236	+	0.201236i
$606$	4.55635	−	26.5563i	0.185089	−	1.07878i
$607$	36.0000			1.46119			0.730597	−	0.682808i	$-0.239242\pi$
$607$	36.0000			1.46119			0.730597	+	0.682808i	$0.239242\pi$
$608$	−8.48528			−0.344124
$609$		0			0
$610$			2.00000i			0.0809776i
$611$	−21.2132	+	4.24264i	−0.858194	+	0.171639i
$612$	−12.0000	−	4.24264i	−0.485071	−	0.171499i
$613$	−9.00000	+	9.00000i	−0.363507	+	0.363507i	−0.865102	−	0.501596i	$-0.832747\pi$
$613$	−9.00000	+	9.00000i	−0.363507	+	0.363507i	0.501596	+	0.865102i	$0.332747\pi$
$614$			32.5269i			1.31268i
$615$	14.1421	−	10.0000i	0.570266	−	0.403239i
$616$		0			0
$617$	7.07107	+	7.07107i	0.284670	+	0.284670i	0.834968	−	0.550298i	$-0.185486\pi$
$617$	7.07107	+	7.07107i	0.284670	+	0.284670i	−0.550298	+	0.834968i	$0.685486\pi$
$618$	−13.6569	−	2.34315i	−0.549359	−	0.0942551i
$619$	32.0000	+	32.0000i	1.28619	+	1.28619i	0.937084	+	0.349105i	$0.113514\pi$
$619$	32.0000	+	32.0000i	1.28619	+	1.28619i	0.349105	+	0.937084i	$0.386486\pi$
$620$		−	4.24264i		−	0.170389i
$621$	−7.07107	+	2.00000i	−0.283752	+	0.0802572i
$622$	2.00000	+	2.00000i	0.0801927	+	0.0801927i
$623$		0			0
$624$	0.171573	+	6.24264i	0.00686841	+	0.249906i
$625$	−1.00000			−0.0400000
$626$	18.3848	+	18.3848i	0.734803	+	0.734803i
$627$	−24.0000	+	16.9706i	−0.958468	+	0.677739i
$628$		−	6.00000i		−	0.239426i
$629$	21.2132	+	21.2132i	0.845826	+	0.845826i
$630$		0			0
$631$	9.00000	+	9.00000i	0.358284	+	0.358284i	0.863180	−	0.504896i	$-0.168469\pi$
$631$	9.00000	+	9.00000i	0.358284	+	0.358284i	−0.504896	+	0.863180i	$0.668469\pi$
$632$	−5.65685	+	5.65685i	−0.225018	+	0.225018i
$633$	−24.0000	−	33.9411i	−0.953914	−	1.34904i
$634$		−	26.0000i		−	1.03259i
$635$	−2.82843	+	2.82843i	−0.112243	+	0.112243i
$636$	−11.3137	−	16.0000i	−0.448618	−	0.634441i
$637$	−14.0000	+	21.0000i	−0.554700	+	0.832050i
$638$		−	2.82843i		−	0.111979i
$639$	21.6569	−	10.3431i	0.856732	−	0.409169i
$640$	1.00000			0.0395285
$641$	−39.5980			−1.56403			−0.782013	−	0.623262i	$-0.785807\pi$
$641$	−39.5980			−1.56403			−0.782013	+	0.623262i	$0.785807\pi$
$642$	19.3137	+	3.31371i	0.762251	+	0.130782i
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	−0.987262	−	0.159103i	$-0.949140\pi$
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	0.159103	+	0.987262i	$0.449140\pi$
$644$		0			0
$645$	6.82843	+	1.17157i	0.268869	+	0.0461306i
$646$	36.0000			1.41640
$647$	7.07107			0.277992			0.138996	−	0.990293i	$-0.455612\pi$
$647$	7.07107			0.277992			0.138996	+	0.990293i	$0.455612\pi$
$648$	8.94975	−	0.949747i	0.351579	−	0.0373096i
$649$			8.00000i			0.314027i
$650$	3.53553	−	0.707107i	0.138675	−	0.0277350i
$651$		0			0
$652$	11.0000	−	11.0000i	0.430793	−	0.430793i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$	2.82843	+	4.00000i	0.110600	+	0.156412i
$655$	5.00000	−	5.00000i	0.195366	−	0.195366i
$656$	7.07107	+	7.07107i	0.276079	+	0.276079i
$657$	−22.9706	+	10.9706i	−0.896167	+	0.428002i
$658$		0			0
$659$			9.89949i			0.385630i	0.981235	+	0.192815i	$0.0617617\pi$
$659$			9.89949i			0.385630i	−0.981235	+	0.192815i	$0.938238\pi$
$660$	2.82843	−	2.00000i	0.110096	−	0.0778499i
$661$	−22.0000	−	22.0000i	−0.855701	−	0.855701i	0.135127	−	0.990828i	$-0.456856\pi$
$661$	−22.0000	−	22.0000i	−0.855701	−	0.855701i	−0.990828	+	0.135127i	$0.956856\pi$
$662$	33.9411			1.31916
$663$	−0.727922	−	26.4853i	−0.0282702	−	1.02860i
$664$	8.00000			0.310460
$665$		0			0
$666$	−20.0000	−	7.07107i	−0.774984	−	0.273998i
$667$			2.00000i			0.0774403i
$668$	11.3137	+	11.3137i	0.437741	+	0.437741i
$669$	−24.1421	−	4.14214i	−0.933389	−	0.160144i
$670$	5.00000	+	5.00000i	0.193167	+	0.193167i
$671$	−2.82843	+	2.82843i	−0.109190	+	0.109190i
$672$		0			0
$673$		−	6.00000i		−	0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$673$		−	6.00000i		−	0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$674$	−9.89949	+	9.89949i	−0.381314	+	0.381314i
$675$	−1.41421	−	5.00000i	−0.0544331	−	0.192450i
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$		−	36.7696i		−	1.41317i	−0.707629	−	0.706584i	$-0.750235\pi$
$677$		−	36.7696i		−	1.41317i	0.707629	−	0.706584i	$-0.249765\pi$
$678$	−12.0711	−	2.07107i	−0.463587	−	0.0795389i
$679$		0			0
$680$	−4.24264			−0.162698
$681$		0			0
$682$	6.00000	−	6.00000i	0.229752	−	0.229752i
$683$	16.9706	−	16.9706i	0.649361	−	0.649361i	−0.303478	−	0.952838i	$-0.598148\pi$
$683$	16.9706	−	16.9706i	0.649361	−	0.649361i	0.952838	+	0.303478i	$0.0981479\pi$
$684$	−22.9706	+	10.9706i	−0.878301	+	0.419470i
$685$	−20.0000			−0.764161
$686$		0			0
$687$	−2.48528	+	14.4853i	−0.0948194	+	0.552648i
$688$			4.00000i			0.152499i
$689$	22.6274	−	33.9411i	0.862036	−	1.29305i
$690$	−2.00000	+	1.41421i	−0.0761387	+	0.0538382i
$691$	−16.0000	+	16.0000i	−0.608669	+	0.608669i	−0.942598	−	0.333929i	$-0.891625\pi$
$691$	−16.0000	+	16.0000i	−0.608669	+	0.608669i	0.333929	+	0.942598i	$0.391625\pi$
$692$			2.82843i			0.107521i
$693$		0			0
$694$	−8.00000	+	8.00000i	−0.303676	+	0.303676i
$695$	−11.3137	−	11.3137i	−0.429153	−	0.429153i
$696$	0.414214	−	2.41421i	0.0157007	−	0.0915105i
$697$	−30.0000	−	30.0000i	−1.13633	−	1.13633i
$698$		−	16.9706i		−	0.642345i
$699$	18.3848	+	26.0000i	0.695376	+	0.983410i
$700$		0			0
$701$	1.41421			0.0534141			0.0267071	−	0.999643i	$-0.491498\pi$
$701$	1.41421			0.0534141			0.0267071	+	0.999643i	$0.491498\pi$
$702$	8.53553	+	16.6777i	0.322153	+	0.629458i
$703$	60.0000			2.26294
$704$	1.41421	+	1.41421i	0.0533002	+	0.0533002i
$705$	6.00000	+	8.48528i	0.225973	+	0.319574i
$706$			36.0000i			1.35488i
$707$		0			0
$708$	−1.17157	+	6.82843i	−0.0440304	+	0.256628i
$709$	−18.0000	−	18.0000i	−0.676004	−	0.676004i	0.283089	−	0.959094i	$-0.408641\pi$
$709$	−18.0000	−	18.0000i	−0.676004	−	0.676004i	−0.959094	+	0.283089i	$0.908641\pi$
$710$	5.65685	−	5.65685i	0.212298	−	0.212298i
$711$	−8.00000	+	22.6274i	−0.300023	+	0.848594i
$712$		−	6.00000i		−	0.224860i
$713$	−4.24264	+	4.24264i	−0.158888	+	0.158888i
$714$		0			0
$715$	6.00000	+	4.00000i	0.224387	+	0.149592i
$716$		−	18.3848i		−	0.687071i
$717$		0			0
$718$	24.0000			0.895672
$719$	45.2548			1.68772			0.843860	−	0.536563i	$-0.180278\pi$
$719$	45.2548			1.68772			0.843860	+	0.536563i	$0.180278\pi$
$720$	2.70711	−	1.29289i	0.100888	−	0.0481833i
$721$		0			0
$722$	37.4767	−	37.4767i	1.39474	−	1.39474i
$723$	0.414214	−	2.41421i	0.0154048	−	0.0897856i
$724$	−18.0000			−0.668965
$725$	−1.41421			−0.0525226
$726$	−11.9497	−	2.05025i	−0.443497	−	0.0760920i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−6.00000	+	6.00000i	−0.222070	+	0.222070i
$731$		−	16.9706i		−	0.627679i
$732$	−2.82843	+	2.00000i	−0.104542	+	0.0739221i
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	−0.853506	−	0.521083i	$-0.825528\pi$
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	0.521083	+	0.853506i	$0.325528\pi$
$734$	−5.65685	−	5.65685i	−0.208798	−	0.208798i
$735$	11.9497	+	2.05025i	0.440773	+	0.0756247i
$736$	−1.00000	−	1.00000i	−0.0368605	−	0.0368605i
$737$			14.1421i			0.520932i
$738$	28.2843	+	10.0000i	1.04116	+	0.368105i
$739$	−12.0000	−	12.0000i	−0.441427	−	0.441427i	0.451064	−	0.892491i	$-0.351045\pi$
$739$	−12.0000	−	12.0000i	−0.441427	−	0.441427i	−0.892491	+	0.451064i	$0.851045\pi$
$740$	−7.07107			−0.259938
$741$	−38.4853	−	36.4264i	−1.41379	−	1.33816i
$742$		0			0
$743$	−18.3848	−	18.3848i	−0.674472	−	0.674472i	0.284272	−	0.958744i	$-0.408248\pi$
$743$	−18.3848	−	18.3848i	−0.674472	−	0.674472i	−0.958744	+	0.284272i	$0.908248\pi$
$744$	6.00000	−	4.24264i	0.219971	−	0.155543i
$745$		−	10.0000i		−	0.366372i
$746$	−22.6274	−	22.6274i	−0.828449	−	0.828449i
$747$	21.6569	−	10.3431i	0.792383	−	0.378436i
$748$	−6.00000	−	6.00000i	−0.219382	−	0.219382i
$749$		0			0
$750$	−1.00000	−	1.41421i	−0.0365148	−	0.0516398i
$751$			10.0000i			0.364905i	0.983215	+	0.182453i	$0.0584036\pi$
$751$			10.0000i			0.364905i	−0.983215	+	0.182453i	$0.941596\pi$
$752$	−4.24264	+	4.24264i	−0.154713	+	0.154713i
$753$	−4.24264	−	6.00000i	−0.154610	−	0.218652i
$754$	5.00000	−	1.00000i	0.182089	−	0.0364179i
$755$		−	18.3848i		−	0.669091i
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	22.6274			0.821865
$759$	−4.82843	−	0.828427i	−0.175261	−	0.0300700i
$760$	−6.00000	+	6.00000i	−0.217643	+	0.217643i
$761$	9.89949	−	9.89949i	0.358856	−	0.358856i	−0.504535	−	0.863391i	$-0.668336\pi$
$761$	9.89949	−	9.89949i	0.358856	−	0.358856i	0.863391	+	0.504535i	$0.168336\pi$
$762$	−6.82843	−	1.17157i	−0.247368	−	0.0424416i
$763$		0			0
$764$	−19.7990			−0.716302
$765$	−11.4853	+	5.48528i	−0.415251	+	0.198321i
$766$		−	24.0000i		−	0.867155i
$767$	−14.1421	+	2.82843i	−0.510643	+	0.102129i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	−21.0000	+	21.0000i	−0.757279	+	0.757279i	−0.975826	−	0.218547i	$-0.929868\pi$
$769$	−21.0000	+	21.0000i	−0.757279	+	0.757279i	0.218547	+	0.975826i	$0.429868\pi$
$770$		0			0
$771$	1.41421	+	2.00000i	0.0509317	+	0.0720282i
$772$	6.00000	−	6.00000i	0.215945	−	0.215945i
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	0.626680	−	0.779277i	$-0.284413\pi$
$773$	−4.24264	−	4.24264i	−0.152597	−	0.152597i	−0.779277	+	0.626680i	$0.784413\pi$
$774$	5.17157	+	10.8284i	0.185888	+	0.389220i
$775$	−3.00000	−	3.00000i	−0.107763	−	0.107763i
$776$			14.1421i			0.507673i
$777$		0			0
$778$	−19.0000	−	19.0000i	−0.681183	−	0.681183i
$779$	−84.8528			−3.04017
$780$	4.53553	+	4.29289i	0.162398	+	0.153710i
$781$	16.0000			0.572525
$782$	4.24264	+	4.24264i	0.151717	+	0.151717i
$783$	−2.00000	−	7.07107i	−0.0714742	−	0.252699i
$784$			7.00000i			0.250000i
$785$	−4.24264	−	4.24264i	−0.151426	−	0.151426i
$786$	12.0711	+	2.07107i	0.430561	+	0.0738725i
$787$	−3.00000	−	3.00000i	−0.106938	−	0.106938i	0.651613	−	0.758552i	$-0.274093\pi$
$787$	−3.00000	−	3.00000i	−0.106938	−	0.106938i	−0.758552	+	0.651613i	$0.774093\pi$
$788$	−9.89949	+	9.89949i	−0.352655	+	0.352655i
$789$	6.00000	−	4.24264i	0.213606	−	0.151042i
$790$			8.00000i			0.284627i
$791$		0			0
$792$	5.65685	+	2.00000i	0.201008	+	0.0710669i
$793$	−6.00000	−	4.00000i	−0.213066	−	0.142044i
$794$			4.24264i			0.150566i
$795$	−19.3137	−	3.31371i	−0.684987	−	0.117525i
$796$	−2.00000			−0.0708881
$797$	45.2548			1.60301			0.801504	−	0.597989i	$-0.204033\pi$
$797$	45.2548			1.60301			0.801504	+	0.597989i	$0.204033\pi$
$798$		0			0
$799$	18.0000	−	18.0000i	0.636794	−	0.636794i
$800$	0.707107	−	0.707107i	0.0250000	−	0.0250000i
$801$	−7.75736	−	16.2426i	−0.274093	−	0.573905i
$802$	6.00000			0.211867
$803$	−16.9706			−0.598878
$804$	−2.07107	+	12.0711i	−0.0730409	+	0.425714i
$805$		0			0
$806$	12.7279	+	8.48528i	0.448322	+	0.298881i
$807$	−2.00000	+	1.41421i	−0.0704033	+	0.0497827i
$808$	11.0000	−	11.0000i	0.386979	−	0.386979i
$809$		−	25.4558i		−	0.894980i	−0.894289	−	0.447490i	$-0.852318\pi$
$809$		−	25.4558i		−	0.894980i	0.894289	−	0.447490i	$-0.147682\pi$
$810$	5.65685	−	7.00000i	0.198762	−	0.245955i
$811$	−26.0000	+	26.0000i	−0.912983	+	0.912983i	−0.996506	−	0.0835224i	$-0.973383\pi$
$811$	−26.0000	+	26.0000i	−0.912983	+	0.912983i	0.0835224	+	0.996506i	$0.473383\pi$
$812$		0			0
$813$	1.24264	−	7.24264i	0.0435813	−	0.254010i
$814$	−10.0000	−	10.0000i	−0.350500	−	0.350500i
$815$		−	15.5563i		−	0.544915i
$816$	−4.24264	−	6.00000i	−0.148522	−	0.210042i
$817$	−24.0000	−	24.0000i	−0.839654	−	0.839654i
$818$	−4.24264			−0.148340
$819$		0			0
$820$	10.0000			0.349215
$821$	−21.2132	−	21.2132i	−0.740346	−	0.740346i	0.232299	−	0.972645i	$-0.425375\pi$
$821$	−21.2132	−	21.2132i	−0.740346	−	0.740346i	−0.972645	+	0.232299i	$0.925375\pi$
$822$	−20.0000	−	28.2843i	−0.697580	−	0.986527i
$823$		−	52.0000i		−	1.81261i	−0.422628	−	0.906303i	$-0.638892\pi$
$823$		−	52.0000i		−	1.81261i	0.422628	−	0.906303i	$-0.361108\pi$
$824$	−5.65685	−	5.65685i	−0.197066	−	0.197066i
$825$	0.585786	−	3.41421i	0.0203945	−	0.118868i
$826$		0			0
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	−0.417093	−	0.908864i	$-0.636951\pi$
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	0.908864	+	0.417093i	$0.136951\pi$
$828$	−4.00000	−	1.41421i	−0.139010	−	0.0491473i
$829$		−	14.0000i		−	0.486240i	−0.969996	−	0.243120i	$-0.921829\pi$
$829$		−	14.0000i		−	0.486240i	0.969996	−	0.243120i	$-0.0781709\pi$
$830$	5.65685	−	5.65685i	0.196352	−	0.196352i
$831$	−39.5980	+	28.0000i	−1.37364	+	0.971309i
$832$	−2.00000	+	3.00000i	−0.0693375	+	0.104006i
$833$		−	29.6985i		−	1.02899i
$834$	4.68629	−	27.3137i	0.162273	−	0.945796i
$835$	16.0000			0.553703
$836$	−16.9706			−0.586939
$837$	10.7574	−	19.2426i	0.371829	−	0.665123i
$838$	11.0000	−	11.0000i	0.379989	−	0.379989i
$839$	31.1127	−	31.1127i	1.07413	−	1.07413i	0.0771068	−	0.997023i	$-0.475432\pi$
$839$	31.1127	−	31.1127i	1.07413	−	1.07413i	0.997023	−	0.0771068i	$-0.0245682\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	16.9706			0.584844
$843$	30.7279	+	5.27208i	1.05833	+	0.181580i
$844$		−	24.0000i		−	0.826114i
$845$	−4.94975	+	12.0208i	−0.170276	+	0.413529i
$846$	−6.00000	+	16.9706i	−0.206284	+	0.583460i
$847$		0			0
$848$		−	11.3137i		−	0.388514i
$849$	8.48528	−	6.00000i	0.291214	−	0.205919i
$850$	−3.00000	+	3.00000i	−0.102899	+	0.102899i
$851$	7.07107	+	7.07107i	0.242393	+	0.242393i
$852$	13.6569	+	2.34315i	0.467876	+	0.0802749i
$853$	39.0000	+	39.0000i	1.33533	+	1.33533i	0.900520	+	0.434815i	$0.143186\pi$
$853$	39.0000	+	39.0000i	1.33533	+	1.33533i	0.434815	+	0.900520i	$0.356814\pi$
$854$		0			0
$855$	−8.48528	+	24.0000i	−0.290191	+	0.820783i
$856$	8.00000	+	8.00000i	0.273434	+	0.273434i
$857$	−49.4975			−1.69080			−0.845401	−	0.534133i	$-0.820638\pi$
$857$	−49.4975			−1.69080			−0.845401	+	0.534133i	$0.820638\pi$
$858$	0.343146	+	12.4853i	0.0117148	+	0.426240i
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$	2.82843	+	2.82843i	0.0964486	+	0.0964486i
$861$		0			0
$862$			36.0000i			1.22616i
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.985460	−	0.169910i	$-0.945652\pi$
$863$	−33.9411	−	33.9411i	−1.15537	−	1.15537i	−0.169910	−	0.985460i	$-0.554348\pi$
$864$	4.53553	+	2.53553i	0.154302	+	0.0862606i
$865$	2.00000	+	2.00000i	0.0680020	+	0.0680020i
$866$	9.89949	−	9.89949i	0.336399	−	0.336399i
$867$	1.00000	+	1.41421i	0.0339618	+	0.0480292i
$868$		0			0
$869$	−11.3137	+	11.3137i	−0.383791	+	0.383791i
$870$	−1.41421	−	2.00000i	−0.0479463	−	0.0678064i
$871$	−25.0000	+	5.00000i	−0.847093	+	0.169419i
$872$			2.82843i			0.0957826i
$873$	18.2843	+	38.2843i	0.618829	+	1.29573i
$874$	12.0000			0.405906
$875$		0			0
$876$	−14.4853	−	2.48528i	−0.489412	−	0.0839699i
$877$	−15.0000	+	15.0000i	−0.506514	+	0.506514i	−0.913455	−	0.406941i	$-0.866596\pi$
$877$	−15.0000	+	15.0000i	−0.506514	+	0.506514i	0.406941	+	0.913455i	$0.366596\pi$
$878$	−4.24264	+	4.24264i	−0.143182	+	0.143182i
$879$	−23.8995	−	4.10051i	−0.806110	−	0.138307i
$880$	2.00000			0.0674200
$881$	56.5685			1.90584			0.952921	−	0.303218i	$-0.0980609\pi$
$881$	56.5685			1.90584			0.952921	+	0.303218i	$0.0980609\pi$
$882$	9.05025	+	18.9497i	0.304738	+	0.638071i
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$	8.48528	−	12.7279i	0.285391	−	0.428086i
$885$	4.00000	+	5.65685i	0.134459	+	0.190153i
$886$	−6.00000	+	6.00000i	−0.201574	+	0.201574i
$887$			38.1838i			1.28209i	0.767505	+	0.641043i	$0.221498\pi$
$887$			38.1838i			1.28209i	−0.767505	+	0.641043i	$0.778502\pi$
$888$	−7.07107	−	10.0000i	−0.237289	−	0.335578i
$889$		0			0
$890$	−4.24264	−	4.24264i	−0.142214	−	0.142214i
$891$	17.8995	−	1.89949i	0.599656	−	0.0636355i
$892$	−10.0000	−	10.0000i	−0.334825	−	0.334825i
$893$		−	50.9117i		−	1.70369i
$894$	14.1421	−	10.0000i	0.472984	−	0.334450i
$895$	−13.0000	−	13.0000i	−0.434542	−	0.434542i
$896$		0			0
$897$	−0.242641	−	8.82843i	−0.00810154	−	0.294773i
$898$	−18.0000			−0.600668
$899$	−4.24264	−	4.24264i	−0.141500	−	0.141500i
$900$	1.00000	−	2.82843i	0.0333333	−	0.0942809i
$901$			48.0000i			1.59911i
$902$	14.1421	+	14.1421i	0.470882	+	0.470882i
$903$		0			0
$904$	−5.00000	−	5.00000i	−0.166298	−	0.166298i
$905$	−12.7279	+	12.7279i	−0.423090	+	0.423090i
$906$	26.0000	−	18.3848i	0.863792	−	0.610793i
$907$		−	14.0000i		−	0.464862i	−0.972613	−	0.232431i	$-0.925332\pi$
$907$		−	14.0000i		−	0.464862i	0.972613	−	0.232431i	$-0.0746680\pi$
$908$		0			0
$909$	15.5563	−	44.0000i	0.515972	−	1.45939i
$910$		0			0
$911$		−	5.65685i		−	0.187420i	−0.995600	−	0.0937100i	$-0.970127\pi$
$911$		−	5.65685i		−	0.187420i	0.995600	−	0.0937100i	$-0.0298726\pi$
$912$	−14.4853	−	2.48528i	−0.479656	−	0.0822959i
$913$	16.0000			0.529523
$914$	8.48528			0.280668
$915$	−0.585786	+	3.41421i	−0.0193655	+	0.112870i
$916$	−6.00000	+	6.00000i	−0.198246	+	0.198246i
$917$		0			0
$918$	−19.2426	−	10.7574i	−0.635102	−	0.355046i
$919$	42.0000			1.38545			0.692726	−	0.721201i	$-0.256409\pi$
$919$	42.0000			1.38545			0.692726	+	0.721201i	$0.256409\pi$
$920$	−1.41421			−0.0466252
$921$	−9.52691	+	55.5269i	−0.313922	+	1.82967i
$922$		−	4.00000i		−	0.131733i
$923$	5.65685	+	28.2843i	0.186198	+	0.930988i
$924$		0			0
$925$	−5.00000	+	5.00000i	−0.164399	+	0.164399i
$926$			31.1127i			1.02243i
$927$	−22.6274	−	8.00000i	−0.743182	−	0.262754i
$928$	1.00000	−	1.00000i	0.0328266	−	0.0328266i
$929$	12.7279	+	12.7279i	0.417590	+	0.417590i	0.884372	−	0.466783i	$-0.154587\pi$
$929$	12.7279	+	12.7279i	0.417590	+	0.417590i	−0.466783	+	0.884372i	$0.654587\pi$
$930$	1.24264	−	7.24264i	0.0407478	−	0.237496i
$931$	−42.0000	−	42.0000i	−1.37649	−	1.37649i
$932$			18.3848i			0.602213i
$933$	2.82843	+	4.00000i	0.0925985	+	0.130954i
$934$	2.00000	+	2.00000i	0.0654420	+	0.0654420i
$935$	−8.48528			−0.277498
$936$	−1.53553	+	10.7071i	−0.0501905	+	0.349973i
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$	26.0000	+	36.7696i	0.848478	+	1.19993i
$940$			6.00000i			0.195698i
$941$	28.2843	+	28.2843i	0.922041	+	0.922041i	0.997174	−	0.0751327i	$-0.0239380\pi$
$941$	28.2843	+	28.2843i	0.922041	+	0.922041i	−0.0751327	+	0.997174i	$0.523938\pi$
$942$	1.75736	−	10.2426i	0.0572579	−	0.333723i
$943$	−10.0000	−	10.0000i	−0.325645	−	0.325645i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$		0			0
$946$			8.00000i			0.260102i
$947$	−5.65685	+	5.65685i	−0.183823	+	0.183823i	−0.793019	−	0.609196i	$-0.791492\pi$
$947$	−5.65685	+	5.65685i	−0.183823	+	0.183823i	0.609196	+	0.793019i	$0.291492\pi$
$948$	−11.3137	+	8.00000i	−0.367452	+	0.259828i
$949$	−6.00000	−	30.0000i	−0.194768	−	0.973841i
$950$			8.48528i			0.275299i
$951$	7.61522	−	44.3848i	0.246941	−	1.43927i
$952$		0			0
$953$	−12.7279			−0.412298			−0.206149	−	0.978521i	$-0.566093\pi$
$953$	−12.7279			−0.412298			−0.206149	+	0.978521i	$0.566093\pi$
$954$	−14.6274	−	30.6274i	−0.473580	−	0.991599i
$955$	−14.0000	+	14.0000i	−0.453029	+	0.453029i
$956$		0			0
$957$	0.828427	−	4.82843i	0.0267792	−	0.156081i
$958$	20.0000			0.646171
$959$		0			0
$960$	1.70711	+	0.292893i	0.0550966	+	0.00945309i
$961$			13.0000i			0.419355i
$962$	14.1421	−	21.2132i	0.455961	−	0.683941i
$963$	32.0000	+	11.3137i	1.03119	+	0.364579i
$964$	1.00000	−	1.00000i	0.0322078	−	0.0322078i
$965$		−	8.48528i		−	0.273151i
$966$		0			0
$967$	−32.0000	+	32.0000i	−1.02905	+	1.02905i	−0.0294854	+	0.999565i	$0.509387\pi$
$967$	−32.0000	+	32.0000i	−1.02905	+	1.02905i	−0.999565	+	0.0294854i	$0.990613\pi$
$968$	−4.94975	−	4.94975i	−0.159091	−	0.159091i
$969$	61.4558	+	10.5442i	1.97425	+	0.338727i
$970$	10.0000	+	10.0000i	0.321081	+	0.321081i
$971$			12.7279i			0.408458i	0.978923	+	0.204229i	$0.0654688\pi$
$971$			12.7279i			0.408458i	−0.978923	+	0.204229i	$0.934531\pi$
$972$	15.5563	+	1.00000i	0.498970	+	0.0320750i
$973$		0			0
$974$		0			0
$975$	6.24264	−	0.171573i	0.199925	−	0.00549473i
$976$	−2.00000			−0.0640184
$977$	−19.7990	−	19.7990i	−0.633426	−	0.633426i	0.315500	−	0.948926i	$-0.397828\pi$
$977$	−19.7990	−	19.7990i	−0.633426	−	0.633426i	−0.948926	+	0.315500i	$0.897828\pi$
$978$	22.0000	−	15.5563i	0.703482	−	0.497437i
$979$		−	12.0000i		−	0.383522i
$980$	4.94975	+	4.94975i	0.158114	+	0.158114i
$981$	3.65685	+	7.65685i	0.116754	+	0.244465i
$982$	11.0000	+	11.0000i	0.351024	+	0.351024i
$983$	24.0416	−	24.0416i	0.766809	−	0.766809i	−0.210734	−	0.977543i	$-0.567586\pi$
$983$	24.0416	−	24.0416i	0.766809	−	0.766809i	0.977543	+	0.210734i	$0.0675855\pi$
$984$	10.0000	+	14.1421i	0.318788	+	0.450835i
$985$			14.0000i			0.446077i
$986$	−4.24264	+	4.24264i	−0.135113	+	0.135113i
$987$		0			0
$988$	−6.00000	−	30.0000i	−0.190885	−	0.954427i
$989$		−	5.65685i		−	0.179878i
$990$	5.41421	−	2.58579i	0.172075	−	0.0821817i
$991$	−50.0000			−1.58830			−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000			−1.58830			−0.794151	+	0.607720i	$0.792084\pi$
$992$	4.24264			0.134704
$993$	57.9411	+	9.94113i	1.83871	+	0.315472i
$994$		0			0
$995$	−1.41421	+	1.41421i	−0.0448336	+	0.0448336i
$996$	13.6569	+	2.34315i	0.432734	+	0.0742454i
$997$	22.0000			0.696747			0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000			0.696747			0.348373	+	0.937356i	$0.386734\pi$
$998$	−25.4558			−0.805791
$999$	−32.0711	−	17.9289i	−1.01468	−	0.567246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.p.d.161.2	yes	4
3.2	odd	2	inner	390.2.p.d.161.1	✓	4
13.8	odd	4	inner	390.2.p.d.281.1	yes	4
39.8	even	4	inner	390.2.p.d.281.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.d.161.1	✓	4	3.2	odd	2	inner
390.2.p.d.161.2	yes	4	1.1	even	1	trivial
390.2.p.d.281.1	yes	4	13.8	odd	4	inner
390.2.p.d.281.2	yes	4	39.8	even	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.292893 + 1.70711i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{10} +(-1.41421 + 1.41421i) q^{11} +(-1.41421 + 1.00000i) q^{12} +(-3.00000 - 2.00000i) q^{13} +(-0.292893 + 1.70711i) q^{15} -1.00000 q^{16} +4.24264 q^{17} +(-2.70711 + 1.29289i) q^{18} +(6.00000 - 6.00000i) q^{19} +(-0.707107 + 0.707107i) q^{20} -2.00000 q^{22} +1.41421 q^{23} +(-1.70711 - 0.292893i) q^{24} +1.00000i q^{25} +(-0.707107 - 3.53553i) q^{26} +(-5.00000 + 1.41421i) q^{27} +1.41421i q^{29} +(-1.41421 + 1.00000i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.41421 - 0.585786i) q^{33} +(3.00000 + 3.00000i) q^{34} +(-2.82843 - 1.00000i) q^{36} +(5.00000 + 5.00000i) q^{37} +8.48528 q^{38} +(-0.171573 - 6.24264i) q^{39} -1.00000 q^{40} +(-7.07107 - 7.07107i) q^{41} -4.00000i q^{43} +(-1.41421 - 1.41421i) q^{44} +(-2.70711 + 1.29289i) q^{45} +(1.00000 + 1.00000i) q^{46} +(4.24264 - 4.24264i) q^{47} +(-1.00000 - 1.41421i) q^{48} -7.00000i q^{49} +(-0.707107 + 0.707107i) q^{50} +(4.24264 + 6.00000i) q^{51} +(2.00000 - 3.00000i) q^{52} +11.3137i q^{53} +(-4.53553 - 2.53553i) q^{54} -2.00000 q^{55} +(14.4853 + 2.48528i) q^{57} +(-1.00000 + 1.00000i) q^{58} +(2.82843 - 2.82843i) q^{59} +(-1.70711 - 0.292893i) q^{60} +2.00000 q^{61} -4.24264 q^{62} -1.00000i q^{64} +(-0.707107 - 3.53553i) q^{65} +(-2.00000 - 2.82843i) q^{66} +(5.00000 - 5.00000i) q^{67} +4.24264i q^{68} +(1.41421 + 2.00000i) q^{69} +(-5.65685 - 5.65685i) q^{71} +(-1.29289 - 2.70711i) q^{72} +(6.00000 + 6.00000i) q^{73} +7.07107i q^{74} +(-1.41421 + 1.00000i) q^{75} +(6.00000 + 6.00000i) q^{76} +(4.29289 - 4.53553i) q^{78} +8.00000 q^{79} +(-0.707107 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} -10.0000i q^{82} +(-5.65685 - 5.65685i) q^{83} +(3.00000 + 3.00000i) q^{85} +(2.82843 - 2.82843i) q^{86} +(-2.00000 + 1.41421i) q^{87} -2.00000i q^{88} +(-4.24264 + 4.24264i) q^{89} +(-2.82843 - 1.00000i) q^{90} +1.41421i q^{92} +(-7.24264 - 1.24264i) q^{93} +6.00000 q^{94} +8.48528 q^{95} +(0.292893 - 1.70711i) q^{96} +(10.0000 - 10.0000i) q^{97} +(4.94975 - 4.94975i) q^{98} +(-2.58579 - 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{6} - 4 q^{9} - 12 q^{13} - 4 q^{15} - 4 q^{16} - 8 q^{18} + 24 q^{19} - 8 q^{22} - 4 q^{24} - 20 q^{27} - 12 q^{31} - 8 q^{33} + 12 q^{34} + 20 q^{37} - 12 q^{39} - 4 q^{40} - 8 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^6 - 4 * q^9 - 12 * q^13 - 4 * q^15 - 4 * q^16 - 8 * q^18 + 24 * q^19 - 8 * q^22 - 4 * q^24 - 20 * q^27 - 12 * q^31 - 8 * q^33 + 12 * q^34 + 20 * q^37 - 12 * q^39 - 4 * q^40 - 8 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^52 - 4 * q^54 - 8 * q^55 + 24 * q^57 - 4 * q^58 - 4 * q^60 + 8 * q^61 - 8 * q^66 + 20 * q^67 - 8 * q^72 + 24 * q^73 + 24 * q^76 + 20 * q^78 + 32 * q^79 - 28 * q^81 + 12 * q^85 - 8 * q^87 - 12 * q^93 + 24 * q^94 + 4 * q^96 + 40 * q^97 - 16 * q^99

Introduction

L-functions

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