LMFDB - Embedded newform 1122.2.l.e.727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.1
Root			$1.08335 + 1.08335i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.e.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.65785 + 2.65785i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.65785 + 2.65785i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +4.33340 q^{13} +(-2.65785 - 2.65785i) q^{14} +1.41421i q^{15} +1.00000 q^{16} +(-4.06418 + 0.694593i) q^{17} -1.00000 q^{18} -3.75877i q^{19} +(1.00000 + 1.00000i) q^{20} +3.75877 q^{21} +(-0.707107 - 0.707107i) q^{22} +(1.10092 - 1.10092i) q^{23} +(-0.707107 + 0.707107i) q^{24} -3.00000i q^{25} +4.33340i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.65785 - 2.65785i) q^{28} +(-0.963259 - 0.963259i) q^{29} -1.41421 q^{30} +(6.18087 + 6.18087i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(-0.694593 - 4.06418i) q^{34} +5.31570 q^{35} -1.00000i q^{36} +(-6.72203 - 6.72203i) q^{37} +3.75877 q^{38} +(-3.06418 - 3.06418i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(5.74107 - 5.74107i) q^{41} +3.75877i q^{42} +2.94612i q^{43} +(0.707107 - 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(1.10092 + 1.10092i) q^{46} +10.0568 q^{47} +(-0.707107 - 0.707107i) q^{48} -7.12836i q^{49} +3.00000 q^{50} +(3.36496 + 2.38266i) q^{51} -4.33340 q^{52} -8.60107i q^{53} +(0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +(2.65785 + 2.65785i) q^{56} +(-2.65785 + 2.65785i) q^{57} +(0.963259 - 0.963259i) q^{58} -10.3696i q^{59} -1.41421i q^{60} +(7.09217 - 7.09217i) q^{61} +(-6.18087 + 6.18087i) q^{62} +(-2.65785 - 2.65785i) q^{63} -1.00000 q^{64} +(-4.33340 - 4.33340i) q^{65} +1.00000i q^{66} +14.8686 q^{67} +(4.06418 - 0.694593i) q^{68} -1.55693 q^{69} +5.31570i q^{70} +(-6.99125 - 6.99125i) q^{71} +1.00000 q^{72} +(3.60589 + 3.60589i) q^{73} +(6.72203 - 6.72203i) q^{74} +(-2.12132 + 2.12132i) q^{75} +3.75877i q^{76} -3.75877i q^{77} +(3.06418 - 3.06418i) q^{78} +(0.118616 - 0.118616i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(5.74107 + 5.74107i) q^{82} +0.648901i q^{83} -3.75877 q^{84} +(4.75877 + 3.36959i) q^{85} -2.94612 q^{86} +1.36225i q^{87} +(0.707107 + 0.707107i) q^{88} -11.4441 q^{89} +(1.00000 + 1.00000i) q^{90} +(-11.5175 + 11.5175i) q^{91} +(-1.10092 + 1.10092i) q^{92} -8.74107i q^{93} +10.0568i q^{94} +(-3.75877 + 3.75877i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-0.0176976 - 0.0176976i) q^{97} +7.12836 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 12 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 12 * q^5	$ 12 q - 12 q^{4} - 12 q^{5} + 12 q^{10} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 12 q^{20} + 12 q^{29} + 12 q^{33} - 12 q^{37} - 12 q^{40} + 12 q^{41} + 12 q^{45} + 36 q^{50} - 12 q^{58} - 12 q^{61} - 12 q^{64} + 48 q^{67} + 12 q^{68} + 12 q^{72} + 12 q^{73} + 12 q^{74} - 12 q^{80} - 12 q^{81} + 12 q^{82} + 12 q^{85} + 12 q^{90} - 48 q^{91} - 12 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 12 * q^5 + 12 * q^10 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 12 * q^20 + 12 * q^29 + 12 * q^33 - 12 * q^37 - 12 * q^40 + 12 * q^41 + 12 * q^45 + 36 * q^50 - 12 * q^58 - 12 * q^61 - 12 * q^64 + 48 * q^67 + 12 * q^68 + 12 * q^72 + 12 * q^73 + 12 * q^74 - 12 * q^80 - 12 * q^81 + 12 * q^82 + 12 * q^85 + 12 * q^90 - 48 * q^91 - 12 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	0.447214	−	0.894427i	$-0.352416\pi$
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	−0.894427	+	0.447214i	$0.852416\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.65785	+	2.65785i	−1.00457	+	1.00457i	−0.00458417	+	0.999989i	$0.501459\pi$
$7$	−2.65785	+	2.65785i	−1.00457	+	1.00457i	−0.999989	+	0.00458417i	$0.998541\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	1.00000	−	1.00000i	0.316228	−	0.316228i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	4.33340			1.20187			0.600935	−	0.799298i	$-0.294795\pi$
$13$	4.33340			1.20187			0.600935	+	0.799298i	$0.294795\pi$
$14$	−2.65785	−	2.65785i	−0.710341	−	0.710341i
$15$			1.41421i			0.365148i
$16$	1.00000			0.250000
$17$	−4.06418	+	0.694593i	−0.985708	+	0.168463i
$17$	−4.06418	+	0.694593i	−0.985708	+	0.168463i
$18$	−1.00000			−0.235702
$19$		−	3.75877i		−	0.862321i	−0.902275	−	0.431161i	$-0.858104\pi$
$19$		−	3.75877i		−	0.862321i	0.902275	−	0.431161i	$-0.141896\pi$
$20$	1.00000	+	1.00000i	0.223607	+	0.223607i
$21$	3.75877			0.820231
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	1.10092	−	1.10092i	0.229557	−	0.229557i	−0.582950	−	0.812508i	$-0.698102\pi$
$23$	1.10092	−	1.10092i	0.229557	−	0.229557i	0.812508	+	0.582950i	$0.198102\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$		−	3.00000i		−	0.600000i
$26$			4.33340i			0.849850i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.65785	−	2.65785i	0.502287	−	0.502287i
$29$	−0.963259	−	0.963259i	−0.178873	−	0.178873i	0.611992	−	0.790864i	$-0.290369\pi$
$29$	−0.963259	−	0.963259i	−0.178873	−	0.178873i	−0.790864	+	0.611992i	$0.790369\pi$
$30$	−1.41421			−0.258199
$31$	6.18087	+	6.18087i	1.11012	+	1.11012i	0.993134	+	0.116984i	$0.0373225\pi$
$31$	6.18087	+	6.18087i	1.11012	+	1.11012i	0.116984	+	0.993134i	$0.462678\pi$
$32$			1.00000i			0.176777i
$33$	1.00000			0.174078
$34$	−0.694593	−	4.06418i	−0.119122	−	0.697001i
$35$	5.31570			0.898518
$36$		−	1.00000i		−	0.166667i
$37$	−6.72203	−	6.72203i	−1.10509	−	1.10509i	−0.993786	−	0.111309i	$-0.964496\pi$
$37$	−6.72203	−	6.72203i	−1.10509	−	1.10509i	−0.111309	−	0.993786i	$-0.535504\pi$
$38$	3.75877			0.609753
$39$	−3.06418	−	3.06418i	−0.490661	−	0.490661i
$40$	−1.00000	+	1.00000i	−0.158114	+	0.158114i
$41$	5.74107	−	5.74107i	0.896605	−	0.896605i	−0.0985292	−	0.995134i	$-0.531414\pi$
$41$	5.74107	−	5.74107i	0.896605	−	0.896605i	0.995134	+	0.0985292i	$0.0314138\pi$
$42$			3.75877i			0.579991i
$43$			2.94612i			0.449279i	0.974442	+	0.224639i	$0.0721204\pi$
$43$			2.94612i			0.449279i	−0.974442	+	0.224639i	$0.927880\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	1.00000	−	1.00000i	0.149071	−	0.149071i
$46$	1.10092	+	1.10092i	0.162322	+	0.162322i
$47$	10.0568			1.46693			0.733466	−	0.679726i	$-0.237901\pi$
$47$	10.0568			1.46693			0.733466	+	0.679726i	$0.237901\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	7.12836i		−	1.01834i
$50$	3.00000			0.424264
$51$	3.36496	+	2.38266i	0.471188	+	0.333639i
$52$	−4.33340			−0.600935
$53$		−	8.60107i		−	1.18145i	−0.806874	−	0.590724i	$-0.798842\pi$
$53$		−	8.60107i		−	1.18145i	0.806874	−	0.590724i	$-0.201158\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	1.41421			0.190693
$56$	2.65785	+	2.65785i	0.355170	+	0.355170i
$57$	−2.65785	+	2.65785i	−0.352041	+	0.352041i
$58$	0.963259	−	0.963259i	0.126482	−	0.126482i
$59$		−	10.3696i		−	1.35000i	−0.737815	−	0.675002i	$-0.764143\pi$
$59$		−	10.3696i		−	1.35000i	0.737815	−	0.675002i	$-0.235857\pi$
$60$		−	1.41421i		−	0.182574i
$61$	7.09217	−	7.09217i	0.908060	−	0.908060i	−0.0880559	−	0.996116i	$-0.528065\pi$
$61$	7.09217	−	7.09217i	0.908060	−	0.908060i	0.996116	+	0.0880559i	$0.0280654\pi$
$62$	−6.18087	+	6.18087i	−0.784972	+	0.784972i
$63$	−2.65785	−	2.65785i	−0.334858	−	0.334858i
$64$	−1.00000			−0.125000
$65$	−4.33340	−	4.33340i	−0.537492	−	0.537492i
$66$			1.00000i			0.123091i
$67$	14.8686			1.81649			0.908247	−	0.418435i	$-0.137421\pi$
$67$	14.8686			1.81649			0.908247	+	0.418435i	$0.137421\pi$
$68$	4.06418	−	0.694593i	0.492854	−	0.0842317i
$69$	−1.55693			−0.187433
$70$			5.31570i			0.635348i
$71$	−6.99125	−	6.99125i	−0.829709	−	0.829709i	0.157767	−	0.987476i	$-0.449570\pi$
$71$	−6.99125	−	6.99125i	−0.829709	−	0.829709i	−0.987476	+	0.157767i	$0.949570\pi$
$72$	1.00000			0.117851
$73$	3.60589	+	3.60589i	0.422038	+	0.422038i	0.885905	−	0.463867i	$-0.153538\pi$
$73$	3.60589	+	3.60589i	0.422038	+	0.422038i	−0.463867	+	0.885905i	$0.653538\pi$
$74$	6.72203	−	6.72203i	0.781420	−	0.781420i
$75$	−2.12132	+	2.12132i	−0.244949	+	0.244949i
$76$			3.75877i			0.431161i
$77$		−	3.75877i		−	0.428352i
$78$	3.06418	−	3.06418i	0.346950	−	0.346950i
$79$	0.118616	−	0.118616i	0.0133453	−	0.0133453i	−0.700403	−	0.713748i	$-0.746996\pi$
$79$	0.118616	−	0.118616i	0.0133453	−	0.0133453i	0.713748	+	0.700403i	$0.246996\pi$
$80$	−1.00000	−	1.00000i	−0.111803	−	0.111803i
$81$	−1.00000			−0.111111
$82$	5.74107	+	5.74107i	0.633995	+	0.633995i
$83$			0.648901i			0.0712261i	0.999366	+	0.0356131i	$0.0113384\pi$
$83$			0.648901i			0.0712261i	−0.999366	+	0.0356131i	$0.988662\pi$
$84$	−3.75877			−0.410115
$85$	4.75877	+	3.36959i	0.516161	+	0.365483i
$86$	−2.94612			−0.317688
$87$			1.36225i			0.146049i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	−11.4441			−1.21307			−0.606534	−	0.795058i	$-0.707441\pi$
$89$	−11.4441			−1.21307			−0.606534	+	0.795058i	$0.707441\pi$
$90$	1.00000	+	1.00000i	0.105409	+	0.105409i
$91$	−11.5175	+	11.5175i	−1.20737	+	1.20737i
$92$	−1.10092	+	1.10092i	−0.114779	+	0.114779i
$93$		−	8.74107i		−	0.906407i
$94$			10.0568i			1.03728i
$95$	−3.75877	+	3.75877i	−0.385642	+	0.385642i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−0.0176976	−	0.0176976i	−0.00179692	−	0.00179692i	0.706208	−	0.708005i	$-0.250404\pi$
$97$	−0.0176976	−	0.0176976i	−0.00179692	−	0.00179692i	−0.708005	+	0.706208i	$0.750404\pi$
$98$	7.12836			0.720073
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$			3.00000i			0.300000i
$101$	7.45502			0.741802			0.370901	−	0.928672i	$-0.379049\pi$
$101$	7.45502			0.741802			0.370901	+	0.928672i	$0.379049\pi$
$102$	−2.38266	+	3.36496i	−0.235918	+	0.333181i
$103$	−2.77726			−0.273651			−0.136826	−	0.990595i	$-0.543690\pi$
$103$	−2.77726			−0.273651			−0.136826	+	0.990595i	$0.543690\pi$
$104$		−	4.33340i		−	0.424925i
$105$	−3.75877	−	3.75877i	−0.366818	−	0.366818i
$106$	8.60107			0.835410
$107$	−3.40306	−	3.40306i	−0.328986	−	0.328986i	0.523215	−	0.852201i	$-0.324733\pi$
$107$	−3.40306	−	3.40306i	−0.328986	−	0.328986i	−0.852201	+	0.523215i	$0.824733\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	8.07447	−	8.07447i	0.773394	−	0.773394i	−0.205304	−	0.978698i	$-0.565818\pi$
$109$	8.07447	−	8.07447i	0.773394	−	0.773394i	0.978698	+	0.205304i	$0.0658183\pi$
$110$			1.41421i			0.134840i
$111$			9.50639i			0.902306i
$112$	−2.65785	+	2.65785i	−0.251143	+	0.251143i
$113$	−5.50398	+	5.50398i	−0.517771	+	0.517771i	−0.916896	−	0.399126i	$-0.869314\pi$
$113$	−5.50398	+	5.50398i	−0.517771	+	0.517771i	0.399126	+	0.916896i	$0.369314\pi$
$114$	−2.65785	−	2.65785i	−0.248931	−	0.248931i
$115$	−2.20184			−0.205322
$116$	0.963259	+	0.963259i	0.0894364	+	0.0894364i
$117$			4.33340i			0.400623i
$118$	10.3696			0.954598
$119$	8.95586	−	12.6481i	0.820982	−	1.15945i
$120$	1.41421			0.129099
$121$		−	1.00000i		−	0.0909091i
$122$	7.09217	+	7.09217i	0.642095	+	0.642095i
$123$	−8.11910			−0.732075
$124$	−6.18087	−	6.18087i	−0.555059	−	0.555059i
$125$	−8.00000	+	8.00000i	−0.715542	+	0.715542i
$126$	2.65785	−	2.65785i	0.236780	−	0.236780i
$127$			5.98330i			0.530932i	0.964120	+	0.265466i	$0.0855257\pi$
$127$			5.98330i			0.530932i	−0.964120	+	0.265466i	$0.914474\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.08322	−	2.08322i	0.183417	−	0.183417i
$130$	4.33340	−	4.33340i	0.380064	−	0.380064i
$131$	−12.3098	−	12.3098i	−1.07551	−	1.07551i	−0.996906	−	0.0786051i	$-0.974953\pi$
$131$	−12.3098	−	12.3098i	−1.07551	−	1.07551i	−0.0786051	−	0.996906i	$-0.525047\pi$
$132$	−1.00000			−0.0870388
$133$	9.99026	+	9.99026i	0.866265	+	0.866265i
$134$			14.8686i			1.28445i
$135$	−1.41421			−0.121716
$136$	0.694593	+	4.06418i	0.0595608	+	0.348500i
$137$	−9.00795			−0.769601			−0.384801	−	0.923000i	$-0.625730\pi$
$137$	−9.00795			−0.769601			−0.384801	+	0.923000i	$0.625730\pi$
$138$		−	1.55693i		−	0.132535i
$139$	16.0667	+	16.0667i	1.36276	+	1.36276i	0.870386	+	0.492369i	$0.163869\pi$
$139$	16.0667	+	16.0667i	1.36276	+	1.36276i	0.492369	+	0.870386i	$0.336131\pi$
$140$	−5.31570			−0.449259
$141$	−7.11122	−	7.11122i	−0.598872	−	0.598872i
$142$	6.99125	−	6.99125i	0.586693	−	0.586693i
$143$	−3.06418	+	3.06418i	−0.256239	+	0.256239i
$144$			1.00000i			0.0833333i
$145$			1.92652i			0.159989i
$146$	−3.60589	+	3.60589i	−0.298426	+	0.298426i
$147$	−5.04051	+	5.04051i	−0.415734	+	0.415734i
$148$	6.72203	+	6.72203i	0.552547	+	0.552547i
$149$	23.1950			1.90021			0.950104	−	0.311934i	$-0.100977\pi$
$149$	23.1950			1.90021			0.950104	+	0.311934i	$0.100977\pi$
$150$	−2.12132	−	2.12132i	−0.173205	−	0.173205i
$151$			18.8694i			1.53557i	0.640706	+	0.767786i	$0.278642\pi$
$151$			18.8694i			1.53557i	−0.640706	+	0.767786i	$0.721358\pi$
$152$	−3.75877			−0.304877
$153$	−0.694593	−	4.06418i	−0.0561545	−	0.328569i
$154$	3.75877			0.302890
$155$		−	12.3617i		−	0.992919i
$156$	3.06418	+	3.06418i	0.245331	+	0.245331i
$157$	−5.10291			−0.407257			−0.203628	−	0.979048i	$-0.565273\pi$
$157$	−5.10291			−0.407257			−0.203628	+	0.979048i	$0.565273\pi$
$158$	0.118616	+	0.118616i	0.00943658	+	0.00943658i
$159$	−6.08188	+	6.08188i	−0.482324	+	0.482324i
$160$	1.00000	−	1.00000i	0.0790569	−	0.0790569i
$161$			5.85216i			0.461215i
$162$		−	1.00000i		−	0.0785674i
$163$	3.87456	−	3.87456i	0.303479	−	0.303479i	−0.538894	−	0.842373i	$-0.681158\pi$
$163$	3.87456	−	3.87456i	0.303479	−	0.303479i	0.842373	+	0.538894i	$0.181158\pi$
$164$	−5.74107	+	5.74107i	−0.448302	+	0.448302i
$165$	−1.00000	−	1.00000i	−0.0778499	−	0.0778499i
$166$	−0.648901			−0.0503645
$167$	2.42020	+	2.42020i	0.187281	+	0.187281i	0.794519	−	0.607239i	$-0.207723\pi$
$167$	2.42020	+	2.42020i	0.187281	+	0.187281i	−0.607239	+	0.794519i	$0.707723\pi$
$168$		−	3.75877i		−	0.289995i
$169$	5.77837			0.444490
$170$	−3.36959	+	4.75877i	−0.258435	+	0.364981i
$171$	3.75877			0.287440
$172$		−	2.94612i		−	0.224639i
$173$	−12.8142	−	12.8142i	−0.974246	−	0.974246i	0.0254308	−	0.999677i	$-0.491904\pi$
$173$	−12.8142	−	12.8142i	−0.974246	−	0.974246i	−0.999677	+	0.0254308i	$0.991904\pi$
$174$	−1.36225			−0.103272
$175$	7.97356	+	7.97356i	0.602744	+	0.602744i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	−7.33240	+	7.33240i	−0.551137	+	0.551137i
$178$		−	11.4441i		−	0.857769i
$179$		−	9.07447i		−	0.678258i	−0.940740	−	0.339129i	$-0.889868\pi$
$179$		−	9.07447i		−	0.678258i	0.940740	−	0.339129i	$-0.110132\pi$
$180$	−1.00000	+	1.00000i	−0.0745356	+	0.0745356i
$181$	−3.94477	+	3.94477i	−0.293213	+	0.293213i	−0.838348	−	0.545135i	$-0.816478\pi$
$181$	−3.94477	+	3.94477i	−0.293213	+	0.293213i	0.545135	+	0.838348i	$0.316478\pi$
$182$	−11.5175	−	11.5175i	−0.853737	−	0.853737i
$183$	−10.0298			−0.741428
$184$	−1.10092	−	1.10092i	−0.0811608	−	0.0811608i
$185$			13.4441i			0.988427i
$186$	8.74107			0.640927
$187$	2.38266	−	3.36496i	0.174237	−	0.246070i
$188$	−10.0568			−0.733466
$189$			3.75877i			0.273410i
$190$	−3.75877	−	3.75877i	−0.272690	−	0.272690i
$191$	9.38997			0.679435			0.339717	−	0.940528i	$-0.389669\pi$
$191$	9.38997			0.679435			0.339717	+	0.940528i	$0.389669\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−7.23710	+	7.23710i	−0.520938	+	0.520938i	−0.917855	−	0.396917i	$-0.870080\pi$
$193$	−7.23710	+	7.23710i	−0.520938	+	0.520938i	0.396917	+	0.917855i	$0.370080\pi$
$194$	0.0176976	−	0.0176976i	0.00127061	−	0.00127061i
$195$			6.12836i			0.438861i
$196$			7.12836i			0.509168i
$197$	−9.29345	+	9.29345i	−0.662131	+	0.662131i	−0.955882	−	0.293751i	$-0.905096\pi$
$197$	−9.29345	+	9.29345i	−0.662131	+	0.662131i	0.293751	+	0.955882i	$0.405096\pi$
$198$	0.707107	−	0.707107i	0.0502519	−	0.0502519i
$199$	−11.0600	−	11.0600i	−0.784026	−	0.784026i	0.196482	−	0.980507i	$-0.437048\pi$
$199$	−11.0600	−	11.0600i	−0.784026	−	0.784026i	−0.980507	+	0.196482i	$0.937048\pi$
$200$	−3.00000			−0.212132
$201$	−10.5137	−	10.5137i	−0.741580	−	0.741580i
$202$			7.45502i			0.524533i
$203$	5.12040			0.359382
$204$	−3.36496	−	2.38266i	−0.235594	−	0.166819i
$205$	−11.4821			−0.801948
$206$		−	2.77726i		−	0.193501i
$207$	1.10092	+	1.10092i	0.0765191	+	0.0765191i
$208$	4.33340			0.300467
$209$	2.65785	+	2.65785i	0.183847	+	0.183847i
$210$	3.75877	−	3.75877i	0.259380	−	0.259380i
$211$	−6.18222	+	6.18222i	−0.425601	+	0.425601i	−0.887127	−	0.461526i	$-0.847302\pi$
$211$	−6.18222	+	6.18222i	−0.425601	+	0.425601i	0.461526	+	0.887127i	$0.347302\pi$
$212$			8.60107i			0.590724i
$213$			9.88713i			0.677455i
$214$	3.40306	−	3.40306i	0.232628	−	0.232628i
$215$	2.94612	−	2.94612i	0.200924	−	0.200924i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−32.8557			−2.23039
$218$	8.07447	+	8.07447i	0.546872	+	0.546872i
$219$		−	5.09950i		−	0.344592i
$220$	−1.41421			−0.0953463
$221$	−17.6117	+	3.00995i	−1.18469	+	0.202471i
$222$	−9.50639			−0.638027
$223$			11.4441i			0.766351i	0.923676	+	0.383175i	$0.125170\pi$
$223$			11.4441i			0.766351i	−0.923676	+	0.383175i	$0.874830\pi$
$224$	−2.65785	−	2.65785i	−0.177585	−	0.177585i
$225$	3.00000			0.200000
$226$	−5.50398	−	5.50398i	−0.366119	−	0.366119i
$227$	−7.81394	+	7.81394i	−0.518629	+	0.518629i	−0.917157	−	0.398527i	$-0.869521\pi$
$227$	−7.81394	+	7.81394i	−0.518629	+	0.518629i	0.398527	+	0.917157i	$0.369521\pi$
$228$	2.65785	−	2.65785i	0.176021	−	0.176021i
$229$		−	26.5990i		−	1.75771i	−0.477089	−	0.878855i	$-0.658308\pi$
$229$		−	26.5990i		−	1.75771i	0.477089	−	0.878855i	$-0.341692\pi$
$230$		−	2.20184i		−	0.145185i
$231$	−2.65785	+	2.65785i	−0.174874	+	0.174874i
$232$	−0.963259	+	0.963259i	−0.0632411	+	0.0632411i
$233$	10.6097	+	10.6097i	0.695065	+	0.695065i	0.963342	−	0.268277i	$-0.0864541\pi$
$233$	10.6097	+	10.6097i	0.695065	+	0.695065i	−0.268277	+	0.963342i	$0.586454\pi$
$234$	−4.33340			−0.283283
$235$	−10.0568	−	10.0568i	−0.656032	−	0.656032i
$236$			10.3696i			0.675002i
$237$	−0.167748			−0.0108964
$238$	12.6481	+	8.95586i	0.819855	+	0.580522i
$239$	22.9932			1.48730			0.743652	−	0.668567i	$-0.233092\pi$
$239$	22.9932			1.48730			0.743652	+	0.668567i	$0.233092\pi$
$240$			1.41421i			0.0912871i
$241$	1.57825	+	1.57825i	0.101664	+	0.101664i	0.756109	−	0.654445i	$-0.227098\pi$
$241$	1.57825	+	1.57825i	0.101664	+	0.101664i	−0.654445	+	0.756109i	$0.727098\pi$
$242$	1.00000			0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−7.09217	+	7.09217i	−0.454030	+	0.454030i
$245$	−7.12836	+	7.12836i	−0.455414	+	0.455414i
$246$		−	8.11910i		−	0.517655i
$247$		−	16.2883i		−	1.03640i
$248$	6.18087	−	6.18087i	0.392486	−	0.392486i
$249$	0.458842	−	0.458842i	0.0290779	−	0.0290779i
$250$	−8.00000	−	8.00000i	−0.505964	−	0.505964i
$251$	−1.79232			−0.113130			−0.0565650	−	0.998399i	$-0.518015\pi$
$251$	−1.79232			−0.113130			−0.0565650	+	0.998399i	$0.518015\pi$
$252$	2.65785	+	2.65785i	0.167429	+	0.167429i
$253$			1.55693i			0.0978836i
$254$	−5.98330			−0.375425
$255$	−0.982302	−	5.74762i	−0.0615142	−	0.359930i
$256$	1.00000			0.0625000
$257$		−	15.6820i		−	0.978215i	−0.872223	−	0.489108i	$-0.837322\pi$
$257$		−	15.6820i		−	0.978215i	0.872223	−	0.489108i	$-0.162678\pi$
$258$	2.08322	+	2.08322i	0.129696	+	0.129696i
$259$	35.7323			2.22030
$260$	4.33340	+	4.33340i	0.268746	+	0.268746i
$261$	0.963259	−	0.963259i	0.0596243	−	0.0596243i
$262$	12.3098	−	12.3098i	0.760501	−	0.760501i
$263$		−	21.5110i		−	1.32643i	−0.748431	−	0.663213i	$-0.769192\pi$
$263$		−	21.5110i		−	1.32643i	0.748431	−	0.663213i	$-0.230808\pi$
$264$		−	1.00000i		−	0.0615457i
$265$	−8.60107	+	8.60107i	−0.528360	+	0.528360i
$266$	−9.99026	+	9.99026i	−0.612542	+	0.612542i
$267$	8.09217	+	8.09217i	0.495233	+	0.495233i
$268$	−14.8686			−0.908247
$269$	−13.4264	−	13.4264i	−0.818620	−	0.818620i	0.167288	−	0.985908i	$-0.446499\pi$
$269$	−13.4264	−	13.4264i	−0.818620	−	0.818620i	−0.985908	+	0.167288i	$0.946499\pi$
$270$		−	1.41421i		−	0.0860663i
$271$	−26.8222			−1.62933			−0.814666	−	0.579930i	$-0.803080\pi$
$271$	−26.8222			−1.62933			−0.814666	+	0.579930i	$0.803080\pi$
$272$	−4.06418	+	0.694593i	−0.246427	+	0.0421159i
$273$	16.2883			0.985811
$274$		−	9.00795i		−	0.544190i
$275$	2.12132	+	2.12132i	0.127920	+	0.127920i
$276$	1.55693			0.0937164
$277$	−8.24597	−	8.24597i	−0.495453	−	0.495453i	0.414566	−	0.910019i	$-0.363933\pi$
$277$	−8.24597	−	8.24597i	−0.495453	−	0.495453i	−0.910019	+	0.414566i	$0.863933\pi$
$278$	−16.0667	+	16.0667i	−0.963614	+	0.963614i
$279$	−6.18087	+	6.18087i	−0.370039	+	0.370039i
$280$		−	5.31570i		−	0.317674i
$281$		−	32.8511i		−	1.95974i	−0.199648	−	0.979868i	$-0.563980\pi$
$281$		−	32.8511i		−	1.95974i	0.199648	−	0.979868i	$-0.436020\pi$
$282$	7.11122	−	7.11122i	0.423467	−	0.423467i
$283$	2.17953	−	2.17953i	0.129559	−	0.129559i	−0.639354	−	0.768913i	$-0.720798\pi$
$283$	2.17953	−	2.17953i	0.129559	−	0.129559i	0.768913	+	0.639354i	$0.220798\pi$
$284$	6.99125	+	6.99125i	0.414855	+	0.414855i
$285$	5.31570			0.314875
$286$	−3.06418	−	3.06418i	−0.181189	−	0.181189i
$287$			30.5178i			1.80141i
$288$	−1.00000			−0.0589256
$289$	16.0351	−	5.64590i	0.943240	−	0.332112i
$290$	−1.92652			−0.113129
$291$			0.0250281i			0.00146718i
$292$	−3.60589	−	3.60589i	−0.211019	−	0.211019i
$293$	21.1059			1.23302			0.616509	−	0.787348i	$-0.288546\pi$
$293$	21.1059			1.23302			0.616509	+	0.787348i	$0.288546\pi$
$294$	−5.04051	−	5.04051i	−0.293968	−	0.293968i
$295$	−10.3696	+	10.3696i	−0.603741	+	0.603741i
$296$	−6.72203	+	6.72203i	−0.390710	+	0.390710i
$297$			1.00000i			0.0580259i
$298$			23.1950i			1.34365i
$299$	4.77072	−	4.77072i	0.275898	−	0.275898i
$300$	2.12132	−	2.12132i	0.122474	−	0.122474i
$301$	−7.83035	−	7.83035i	−0.451334	−	0.451334i
$302$	−18.8694			−1.08581
$303$	−5.27149	−	5.27149i	−0.302839	−	0.302839i
$304$		−	3.75877i		−	0.215580i
$305$	−14.1843			−0.812193
$306$	4.06418	−	0.694593i	0.232334	−	0.0397072i
$307$	20.0459			1.14408			0.572040	−	0.820225i	$-0.306152\pi$
$307$	20.0459			1.14408			0.572040	+	0.820225i	$0.306152\pi$
$308$			3.75877i			0.214176i
$309$	1.96382	+	1.96382i	0.111718	+	0.111718i
$310$	12.3617			0.702100
$311$	6.82935	+	6.82935i	0.387257	+	0.387257i	0.873708	−	0.486451i	$-0.161709\pi$
$311$	6.82935	+	6.82935i	0.387257	+	0.387257i	−0.486451	+	0.873708i	$0.661709\pi$
$312$	−3.06418	+	3.06418i	−0.173475	+	0.173475i
$313$	0.187349	−	0.187349i	0.0105896	−	0.0105896i	−0.701792	−	0.712382i	$-0.747616\pi$
$313$	0.187349	−	0.187349i	0.0105896	−	0.0105896i	0.712382	+	0.701792i	$0.247616\pi$
$314$		−	5.10291i		−	0.287974i
$315$			5.31570i			0.299506i
$316$	−0.118616	+	0.118616i	−0.00667267	+	0.00667267i
$317$	1.47471	−	1.47471i	0.0828280	−	0.0828280i	−0.664479	−	0.747307i	$-0.731346\pi$
$317$	1.47471	−	1.47471i	0.0828280	−	0.0828280i	0.747307	+	0.664479i	$0.231346\pi$
$318$	−6.08188	−	6.08188i	−0.341055	−	0.341055i
$319$	1.36225			0.0762716
$320$	1.00000	+	1.00000i	0.0559017	+	0.0559017i
$321$			4.81265i			0.268616i
$322$	−5.85216			−0.326128
$323$	2.61081	+	15.2763i	0.145270	+	0.849997i
$324$	1.00000			0.0555556
$325$		−	13.0002i		−	0.721122i
$326$	3.87456	+	3.87456i	0.214592	+	0.214592i
$327$	−11.4190			−0.631474
$328$	−5.74107	−	5.74107i	−0.316998	−	0.316998i
$329$	−26.7294	+	26.7294i	−1.47364	+	1.47364i
$330$	1.00000	−	1.00000i	0.0550482	−	0.0550482i
$331$			5.27431i			0.289902i	0.989439	+	0.144951i	$0.0463025\pi$
$331$			5.27431i			0.289902i	−0.989439	+	0.144951i	$0.953698\pi$
$332$		−	0.648901i		−	0.0356131i
$333$	6.72203	−	6.72203i	0.368365	−	0.368365i
$334$	−2.42020	+	2.42020i	−0.132427	+	0.132427i
$335$	−14.8686	−	14.8686i	−0.812361	−	0.812361i
$336$	3.75877			0.205058
$337$	22.4392	+	22.4392i	1.22234	+	1.22234i	0.966797	+	0.255546i	$0.0822553\pi$
$337$	22.4392	+	22.4392i	1.22234	+	1.22234i	0.255546	+	0.966797i	$0.417745\pi$
$338$			5.77837i			0.314302i
$339$	7.78380			0.422758
$340$	−4.75877	−	3.36959i	−0.258081	−	0.182741i
$341$	−8.74107			−0.473356
$342$			3.75877i			0.203251i
$343$	0.341150	+	0.341150i	0.0184204	+	0.0184204i
$344$	2.94612			0.158844
$345$	1.55693	+	1.55693i	0.0838225	+	0.0838225i
$346$	12.8142	−	12.8142i	0.688896	−	0.688896i
$347$	−0.114483	+	0.114483i	−0.00614575	+	0.00614575i	−0.710173	−	0.704027i	$-0.751383\pi$
$347$	−0.114483	+	0.114483i	−0.00614575	+	0.00614575i	0.704027	+	0.710173i	$0.251383\pi$
$348$		−	1.36225i		−	0.0730245i
$349$		−	21.3395i		−	1.14228i	−0.820853	−	0.571139i	$-0.806502\pi$
$349$		−	21.3395i		−	1.14228i	0.820853	−	0.571139i	$-0.193498\pi$
$350$	−7.97356	+	7.97356i	−0.426205	+	0.426205i
$351$	3.06418	−	3.06418i	0.163554	−	0.163554i
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	−31.8813			−1.69687			−0.848435	−	0.529300i	$-0.822455\pi$
$353$	−31.8813			−1.69687			−0.848435	+	0.529300i	$0.822455\pi$
$354$	−7.33240	−	7.33240i	−0.389713	−	0.389713i
$355$			13.9825i			0.742114i
$356$	11.4441			0.606534
$357$	−15.2763	+	2.61081i	−0.808508	+	0.138179i
$358$	9.07447			0.479601
$359$		−	22.9036i		−	1.20881i	−0.796679	−	0.604403i	$-0.793412\pi$
$359$		−	22.9036i		−	1.20881i	0.796679	−	0.604403i	$-0.206588\pi$
$360$	−1.00000	−	1.00000i	−0.0527046	−	0.0527046i
$361$	4.87164			0.256402
$362$	−3.94477	−	3.94477i	−0.207333	−	0.207333i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	11.5175	−	11.5175i	0.603683	−	0.603683i
$365$		−	7.21179i		−	0.377482i
$366$		−	10.0298i		−	0.524268i
$367$	19.5591	−	19.5591i	1.02098	−	1.02098i	0.0212015	−	0.999775i	$-0.493251\pi$
$367$	19.5591	−	19.5591i	1.02098	−	1.02098i	0.999775	−	0.0212015i	$-0.00674914\pi$
$368$	1.10092	−	1.10092i	0.0573893	−	0.0573893i
$369$	5.74107	+	5.74107i	0.298868	+	0.298868i
$370$	−13.4441			−0.698923
$371$	22.8604	+	22.8604i	1.18685	+	1.18685i
$372$			8.74107i			0.453204i
$373$	2.99979			0.155323			0.0776617	−	0.996980i	$-0.475255\pi$
$373$	2.99979			0.155323			0.0776617	+	0.996980i	$0.475255\pi$
$374$	3.36496	+	2.38266i	0.173998	+	0.123204i
$375$	11.3137			0.584237
$376$		−	10.0568i		−	0.518639i
$377$	−4.17419	−	4.17419i	−0.214982	−	0.214982i
$378$	−3.75877			−0.193330
$379$	−7.63654	−	7.63654i	−0.392263	−	0.392263i	0.483230	−	0.875493i	$-0.339463\pi$
$379$	−7.63654	−	7.63654i	−0.392263	−	0.392263i	−0.875493	+	0.483230i	$0.839463\pi$
$380$	3.75877	−	3.75877i	0.192821	−	0.192821i
$381$	4.23083	−	4.23083i	0.216752	−	0.216752i
$382$			9.38997i			0.480433i
$383$			6.71394i			0.343067i	0.985178	+	0.171533i	$0.0548721\pi$
$383$			6.71394i			0.343067i	−0.985178	+	0.171533i	$0.945128\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−3.75877	+	3.75877i	−0.191565	+	0.191565i
$386$	−7.23710	−	7.23710i	−0.368358	−	0.368358i
$387$	−2.94612			−0.149760
$388$	0.0176976	+	0.0176976i	0.000898458	+	0.000898458i
$389$		−	3.00874i		−	0.152549i	−0.997087	−	0.0762745i	$-0.975697\pi$
$389$		−	3.00874i		−	0.152549i	0.997087	−	0.0762745i	$-0.0243025\pi$
$390$	−6.12836			−0.310321
$391$	−3.70964	+	5.23902i	−0.187604	+	0.264949i
$392$	−7.12836			−0.360036
$393$			17.4087i			0.878151i
$394$	−9.29345	−	9.29345i	−0.468197	−	0.468197i
$395$	−0.237232			−0.0119364
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−19.3605	+	19.3605i	−0.971675	+	0.971675i	−0.999610	−	0.0279345i	$-0.991107\pi$
$397$	−19.3605	+	19.3605i	−0.971675	+	0.971675i	0.0279345	+	0.999610i	$0.491107\pi$
$398$	11.0600	−	11.0600i	0.554390	−	0.554390i
$399$		−	14.1284i		−	0.707302i
$400$		−	3.00000i		−	0.150000i
$401$	2.16063	−	2.16063i	0.107897	−	0.107897i	−0.651098	−	0.758994i	$-0.725691\pi$
$401$	2.16063	−	2.16063i	0.107897	−	0.107897i	0.758994	+	0.651098i	$0.225691\pi$
$402$	10.5137	−	10.5137i	0.524377	−	0.524377i
$403$	26.7842	+	26.7842i	1.33422	+	1.33422i
$404$	−7.45502			−0.370901
$405$	1.00000	+	1.00000i	0.0496904	+	0.0496904i
$406$			5.12040i			0.254121i
$407$	9.50639			0.471214
$408$	2.38266	−	3.36496i	0.117959	−	0.166590i
$409$	7.62457			0.377011			0.188505	−	0.982072i	$-0.439636\pi$
$409$	7.62457			0.377011			0.188505	+	0.982072i	$0.439636\pi$
$410$		−	11.4821i		−	0.567063i
$411$	6.36959	+	6.36959i	0.314188	+	0.314188i
$412$	2.77726			0.136826
$413$	27.5608	+	27.5608i	1.35618	+	1.35618i
$414$	−1.10092	+	1.10092i	−0.0541072	+	0.0541072i
$415$	0.648901	−	0.648901i	0.0318533	−	0.0318533i
$416$			4.33340i			0.212463i
$417$		−	22.7217i		−	1.11269i
$418$	−2.65785	+	2.65785i	−0.130000	+	0.130000i
$419$	−24.3272	+	24.3272i	−1.18846	+	1.18846i	−0.210967	+	0.977493i	$0.567661\pi$
$419$	−24.3272	+	24.3272i	−1.18846	+	1.18846i	−0.977493	+	0.210967i	$0.932339\pi$
$420$	3.75877	+	3.75877i	0.183409	+	0.183409i
$421$	20.9860			1.02280			0.511398	−	0.859344i	$-0.329128\pi$
$421$	20.9860			1.02280			0.511398	+	0.859344i	$0.329128\pi$
$422$	−6.18222	−	6.18222i	−0.300946	−	0.300946i
$423$			10.0568i			0.488977i
$424$	−8.60107			−0.417705
$425$	2.08378	+	12.1925i	0.101078	+	0.591425i
$426$	−9.88713			−0.479033
$427$			37.6999i			1.82443i
$428$	3.40306	+	3.40306i	0.164493	+	0.164493i
$429$	4.33340			0.209219
$430$	2.94612	+	2.94612i	0.142074	+	0.142074i
$431$	−5.92095	+	5.92095i	−0.285202	+	0.285202i	−0.835180	−	0.549977i	$-0.814636\pi$
$431$	−5.92095	+	5.92095i	−0.285202	+	0.285202i	0.549977	+	0.835180i	$0.314636\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	29.9097i		−	1.43737i	−0.695336	−	0.718685i	$-0.744744\pi$
$433$		−	29.9097i		−	1.43737i	0.695336	−	0.718685i	$-0.255256\pi$
$434$		−	32.8557i		−	1.57712i
$435$	1.36225	−	1.36225i	0.0653151	−	0.0653151i
$436$	−8.07447	+	8.07447i	−0.386697	+	0.386697i
$437$	−4.13810	−	4.13810i	−0.197952	−	0.197952i
$438$	5.09950			0.243664
$439$	−5.50215	−	5.50215i	−0.262603	−	0.262603i	0.563508	−	0.826111i	$-0.309452\pi$
$439$	−5.50215	−	5.50215i	−0.262603	−	0.262603i	−0.826111	+	0.563508i	$0.809452\pi$
$440$		−	1.41421i		−	0.0674200i
$441$	7.12836			0.339446
$442$	−3.00995	−	17.6117i	−0.143169	−	0.837704i
$443$	16.6921			0.793067			0.396533	−	0.918020i	$-0.370213\pi$
$443$	16.6921			0.793067			0.396533	+	0.918020i	$0.370213\pi$
$444$		−	9.50639i		−	0.451153i
$445$	11.4441	+	11.4441i	0.542500	+	0.542500i
$446$	−11.4441			−0.541892
$447$	−16.4013	−	16.4013i	−0.775756	−	0.775756i
$448$	2.65785	−	2.65785i	0.125572	−	0.125572i
$449$	14.8519	−	14.8519i	0.700903	−	0.700903i	−0.263701	−	0.964604i	$-0.584943\pi$
$449$	14.8519	−	14.8519i	0.700903	−	0.700903i	0.964604	+	0.263701i	$0.0849434\pi$
$450$			3.00000i			0.141421i
$451$			8.11910i			0.382314i
$452$	5.50398	−	5.50398i	0.258885	−	0.258885i
$453$	13.3427	−	13.3427i	0.626895	−	0.626895i
$454$	−7.81394	−	7.81394i	−0.366726	−	0.366726i
$455$	23.0351			1.07990
$456$	2.65785	+	2.65785i	0.124465	+	0.124465i
$457$		−	29.7502i		−	1.39166i	−0.718208	−	0.695828i	$-0.755037\pi$
$457$		−	29.7502i		−	1.39166i	0.718208	−	0.695828i	$-0.244963\pi$
$458$	26.5990			1.24289
$459$	−2.38266	+	3.36496i	−0.111213	+	0.157063i
$460$	2.20184			0.102661
$461$		−	2.44419i		−	0.113837i	−0.998379	−	0.0569186i	$-0.981872\pi$
$461$		−	2.44419i		−	0.113837i	0.998379	−	0.0569186i	$-0.0181275\pi$
$462$	−2.65785	−	2.65785i	−0.123654	−	0.123654i
$463$	−39.9928			−1.85862			−0.929312	−	0.369294i	$-0.879599\pi$
$463$	−39.9928			−1.85862			−0.929312	+	0.369294i	$0.879599\pi$
$464$	−0.963259	−	0.963259i	−0.0447182	−	0.0447182i
$465$	−8.74107	+	8.74107i	−0.405358	+	0.405358i
$466$	−10.6097	+	10.6097i	−0.491485	+	0.491485i
$467$			22.9603i			1.06248i	0.847223	+	0.531238i	$0.178273\pi$
$467$			22.9603i			1.06248i	−0.847223	+	0.531238i	$0.821727\pi$
$468$		−	4.33340i		−	0.200312i
$469$	−39.5186	+	39.5186i	−1.82480	+	1.82480i
$470$	10.0568	−	10.0568i	0.463885	−	0.463885i
$471$	3.60830	+	3.60830i	0.166262	+	0.166262i
$472$	−10.3696			−0.477299
$473$	−2.08322	−	2.08322i	−0.0957866	−	0.0957866i
$474$		−	0.167748i		−	0.00770493i
$475$	−11.2763			−0.517393
$476$	−8.95586	+	12.6481i	−0.410491	+	0.579725i
$477$	8.60107			0.393816
$478$			22.9932i			1.05168i
$479$	−7.26040	−	7.26040i	−0.331736	−	0.331736i	0.521509	−	0.853246i	$-0.325369\pi$
$479$	−7.26040	−	7.26040i	−0.331736	−	0.331736i	−0.853246	+	0.521509i	$0.825369\pi$
$480$	−1.41421			−0.0645497
$481$	−29.1293	−	29.1293i	−1.32818	−	1.32818i
$482$	−1.57825	+	1.57825i	−0.0718871	+	0.0718871i
$483$	4.13810	−	4.13810i	0.188290	−	0.188290i
$484$			1.00000i			0.0454545i
$485$			0.0353951i			0.00160721i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	20.5395	−	20.5395i	0.930734	−	0.930734i	−0.0670182	−	0.997752i	$-0.521349\pi$
$487$	20.5395	−	20.5395i	0.930734	−	0.930734i	0.997752	+	0.0670182i	$0.0213486\pi$
$488$	−7.09217	−	7.09217i	−0.321048	−	0.321048i
$489$	−5.47945			−0.247790
$490$	−7.12836	−	7.12836i	−0.322026	−	0.322026i
$491$			10.6176i			0.479165i	0.970876	+	0.239582i	$0.0770105\pi$
$491$			10.6176i			0.479165i	−0.970876	+	0.239582i	$0.922989\pi$
$492$	8.11910			0.366037
$493$	4.58393	+	3.24578i	0.206450	+	0.146183i
$494$	16.2883			0.732844
$495$			1.41421i			0.0635642i
$496$	6.18087	+	6.18087i	0.277529	+	0.277529i
$497$	37.1634			1.66701
$498$	0.458842	+	0.458842i	0.0205612	+	0.0205612i
$499$	10.5105	−	10.5105i	0.470515	−	0.470515i	−0.431566	−	0.902081i	$-0.642039\pi$
$499$	10.5105	−	10.5105i	0.470515	−	0.470515i	0.902081	+	0.431566i	$0.142039\pi$
$500$	8.00000	−	8.00000i	0.357771	−	0.357771i
$501$		−	3.42268i		−	0.152914i
$502$		−	1.79232i		−	0.0799951i
$503$	4.21436	−	4.21436i	0.187909	−	0.187909i	−0.606882	−	0.794792i	$-0.707580\pi$
$503$	4.21436	−	4.21436i	0.187909	−	0.187909i	0.794792	+	0.606882i	$0.207580\pi$
$504$	−2.65785	+	2.65785i	−0.118390	+	0.118390i
$505$	−7.45502	−	7.45502i	−0.331744	−	0.331744i
$506$	−1.55693			−0.0692141
$507$	−4.08593	−	4.08593i	−0.181462	−	0.181462i
$508$		−	5.98330i		−	0.265466i
$509$	−21.5654			−0.955868			−0.477934	−	0.878396i	$-0.658614\pi$
$509$	−21.5654			−0.955868			−0.477934	+	0.878396i	$0.658614\pi$
$510$	5.74762	−	0.982302i	0.254509	−	0.0434971i
$511$	−19.1679			−0.847936
$512$			1.00000i			0.0441942i
$513$	−2.65785	−	2.65785i	−0.117347	−	0.117347i
$514$	15.6820			0.691703
$515$	2.77726	+	2.77726i	0.122381	+	0.122381i
$516$	−2.08322	+	2.08322i	−0.0917087	+	0.0917087i
$517$	−7.11122	+	7.11122i	−0.312751	+	0.312751i
$518$			35.7323i			1.56999i
$519$			18.1220i			0.795468i
$520$	−4.33340	+	4.33340i	−0.190032	+	0.190032i
$521$	3.98522	−	3.98522i	0.174596	−	0.174596i	−0.614399	−	0.788995i	$-0.710602\pi$
$521$	3.98522	−	3.98522i	0.174596	−	0.174596i	0.788995	+	0.614399i	$0.210602\pi$
$522$	0.963259	+	0.963259i	0.0421607	+	0.0421607i
$523$	18.3741			0.803444			0.401722	−	0.915762i	$-0.368412\pi$
$523$	18.3741			0.803444			0.401722	+	0.915762i	$0.368412\pi$
$524$	12.3098	+	12.3098i	0.537755	+	0.537755i
$525$		−	11.2763i		−	0.492139i
$526$	21.5110			0.937924
$527$	−29.4134	−	20.8270i	−1.28127	−	0.907237i
$528$	1.00000			0.0435194
$529$			20.5760i			0.894607i
$530$	−8.60107	−	8.60107i	−0.373607	−	0.373607i
$531$	10.3696			0.450002
$532$	−9.99026	−	9.99026i	−0.433133	−	0.433133i
$533$	24.8784	−	24.8784i	1.07760	−	1.07760i
$534$	−8.09217	+	8.09217i	−0.350183	+	0.350183i
$535$			6.80612i			0.294254i
$536$		−	14.8686i		−	0.642227i
$537$	−6.41662	+	6.41662i	−0.276898	+	0.276898i
$538$	13.4264	−	13.4264i	0.578852	−	0.578852i
$539$	5.04051	+	5.04051i	0.217110	+	0.217110i
$540$	1.41421			0.0608581
$541$	17.4888	+	17.4888i	0.751902	+	0.751902i	0.974834	−	0.222932i	$-0.0715628\pi$
$541$	17.4888	+	17.4888i	0.751902	+	0.751902i	−0.222932	+	0.974834i	$0.571563\pi$
$542$		−	26.8222i		−	1.15211i
$543$	5.57875			0.239407
$544$	−0.694593	−	4.06418i	−0.0297804	−	0.174250i
$545$	−16.1489			−0.691745
$546$			16.2883i			0.697073i
$547$	28.8304	+	28.8304i	1.23270	+	1.23270i	0.962923	+	0.269777i	$0.0869498\pi$
$547$	28.8304	+	28.8304i	1.23270	+	1.23270i	0.269777	+	0.962923i	$0.413050\pi$
$548$	9.00795			0.384801
$549$	7.09217	+	7.09217i	0.302687	+	0.302687i
$550$	−2.12132	+	2.12132i	−0.0904534	+	0.0904534i
$551$	−3.62067	+	3.62067i	−0.154246	+	0.154246i
$552$			1.55693i			0.0662675i
$553$			0.630527i			0.0268127i
$554$	8.24597	−	8.24597i	0.350338	−	0.350338i
$555$	9.50639	−	9.50639i	0.403524	−	0.403524i
$556$	−16.0667	−	16.0667i	−0.681378	−	0.681378i
$557$	20.2493			0.857990			0.428995	−	0.903307i	$-0.358868\pi$
$557$	20.2493			0.857990			0.428995	+	0.903307i	$0.358868\pi$
$558$	−6.18087	−	6.18087i	−0.261657	−	0.261657i
$559$			12.7667i			0.539975i
$560$	5.31570			0.224630
$561$	−4.06418	+	0.694593i	−0.171590	+	0.0293257i
$562$	32.8511			1.38574
$563$			21.1977i			0.893376i	0.894690	+	0.446688i	$0.147397\pi$
$563$			21.1977i			0.893376i	−0.894690	+	0.446688i	$0.852603\pi$
$564$	7.11122	+	7.11122i	0.299436	+	0.299436i
$565$	11.0080			0.463108
$566$	2.17953	+	2.17953i	0.0916123	+	0.0916123i
$567$	2.65785	−	2.65785i	0.111619	−	0.111619i
$568$	−6.99125	+	6.99125i	−0.293346	+	0.293346i
$569$		−	21.6822i		−	0.908964i	−0.890756	−	0.454482i	$-0.849824\pi$
$569$		−	21.6822i		−	0.908964i	0.890756	−	0.454482i	$-0.150176\pi$
$570$			5.31570i			0.222650i
$571$	6.78992	−	6.78992i	0.284149	−	0.284149i	−0.550612	−	0.834761i	$-0.685606\pi$
$571$	6.78992	−	6.78992i	0.284149	−	0.284149i	0.834761	+	0.550612i	$0.185606\pi$
$572$	3.06418	−	3.06418i	0.128120	−	0.128120i
$573$	−6.63971	−	6.63971i	−0.277378	−	0.277378i
$574$	−30.5178			−1.27379
$575$	−3.30276	−	3.30276i	−0.137734	−	0.137734i
$576$		−	1.00000i		−	0.0416667i
$577$	34.9488			1.45494			0.727469	−	0.686141i	$-0.240697\pi$
$577$	34.9488			1.45494			0.727469	+	0.686141i	$0.240697\pi$
$578$	5.64590	+	16.0351i	0.234838	+	0.666971i
$579$	10.2348			0.425344
$580$		−	1.92652i		−	0.0799943i
$581$	−1.72468	−	1.72468i	−0.0715519	−	0.0715519i
$582$	−0.0250281			−0.00103745
$583$	6.08188	+	6.08188i	0.251886	+	0.251886i
$584$	3.60589	−	3.60589i	0.149213	−	0.149213i
$585$	4.33340	−	4.33340i	0.179164	−	0.179164i
$586$			21.1059i			0.871876i
$587$			43.4013i			1.79137i	0.444694	+	0.895683i	$0.353313\pi$
$587$			43.4013i			1.79137i	−0.444694	+	0.895683i	$0.646687\pi$
$588$	5.04051	−	5.04051i	0.207867	−	0.207867i
$589$	23.2325	−	23.2325i	0.957278	−	0.957278i
$590$	−10.3696	−	10.3696i	−0.426909	−	0.426909i
$591$	13.1429			0.540628
$592$	−6.72203	−	6.72203i	−0.276274	−	0.276274i
$593$			9.58522i			0.393618i	0.980442	+	0.196809i	$0.0630579\pi$
$593$			9.58522i			0.393618i	−0.980442	+	0.196809i	$0.936942\pi$
$594$	−1.00000			−0.0410305
$595$	−21.6040	+	3.69225i	−0.885676	+	0.151367i
$596$	−23.1950			−0.950104
$597$			15.6413i			0.640154i
$598$	4.77072	+	4.77072i	0.195089	+	0.195089i
$599$	46.4960			1.89977			0.949887	−	0.312593i	$-0.101198\pi$
$599$	46.4960			1.89977			0.949887	+	0.312593i	$0.101198\pi$
$600$	2.12132	+	2.12132i	0.0866025	+	0.0866025i
$601$	3.65877	−	3.65877i	0.149244	−	0.149244i	−0.628536	−	0.777780i	$-0.716346\pi$
$601$	3.65877	−	3.65877i	0.149244	−	0.149244i	0.777780	+	0.628536i	$0.216346\pi$
$602$	7.83035	−	7.83035i	0.319141	−	0.319141i
$603$			14.8686i			0.605498i
$604$		−	18.8694i		−	0.767786i
$605$	−1.00000	+	1.00000i	−0.0406558	+	0.0406558i
$606$	5.27149	−	5.27149i	0.214140	−	0.214140i
$607$	−14.4244	−	14.4244i	−0.585467	−	0.585467i	0.350933	−	0.936400i	$-0.385864\pi$
$607$	−14.4244	−	14.4244i	−0.585467	−	0.585467i	−0.936400	+	0.350933i	$0.885864\pi$
$608$	3.75877			0.152438
$609$	−3.62067	−	3.62067i	−0.146717	−	0.146717i
$610$		−	14.1843i		−	0.574307i
$611$	43.5801			1.76306
$612$	0.694593	+	4.06418i	0.0280772	+	0.164285i
$613$	−9.83545			−0.397250			−0.198625	−	0.980076i	$-0.563648\pi$
$613$	−9.83545			−0.397250			−0.198625	+	0.980076i	$0.563648\pi$
$614$			20.0459i			0.808987i
$615$	8.11910	+	8.11910i	0.327394	+	0.327394i
$616$	−3.75877			−0.151445
$617$	20.4048	+	20.4048i	0.821466	+	0.821466i	0.986318	−	0.164852i	$-0.0527146\pi$
$617$	20.4048	+	20.4048i	0.821466	+	0.821466i	−0.164852	+	0.986318i	$0.552715\pi$
$618$	−1.96382	+	1.96382i	−0.0789963	+	0.0789963i
$619$	−15.2470	+	15.2470i	−0.612830	+	0.612830i	−0.943683	−	0.330852i	$-0.892664\pi$
$619$	−15.2470	+	15.2470i	−0.612830	+	0.612830i	0.330852	+	0.943683i	$0.392664\pi$
$620$			12.3617i			0.496460i
$621$		−	1.55693i		−	0.0624776i
$622$	−6.82935	+	6.82935i	−0.273832	+	0.273832i
$623$	30.4166	−	30.4166i	1.21862	−	1.21862i
$624$	−3.06418	−	3.06418i	−0.122665	−	0.122665i
$625$	1.00000			0.0400000
$626$	0.187349	+	0.187349i	0.00748796	+	0.00748796i
$627$		−	3.75877i		−	0.150111i
$628$	5.10291			0.203628
$629$	31.9886	+	22.6505i	1.27547	+	0.903133i
$630$	−5.31570			−0.211783
$631$		−	33.3892i		−	1.32920i	−0.747198	−	0.664601i	$-0.768602\pi$
$631$		−	33.3892i		−	1.32920i	0.747198	−	0.664601i	$-0.231398\pi$
$632$	−0.118616	−	0.118616i	−0.00471829	−	0.00471829i
$633$	8.74298			0.347502
$634$	1.47471	+	1.47471i	0.0585682	+	0.0585682i
$635$	5.98330	−	5.98330i	0.237440	−	0.237440i
$636$	6.08188	−	6.08188i	0.241162	−	0.241162i
$637$		−	30.8900i		−	1.22391i
$638$			1.36225i			0.0539322i
$639$	6.99125	−	6.99125i	0.276570	−	0.276570i
$640$	−1.00000	+	1.00000i	−0.0395285	+	0.0395285i
$641$	9.32727	+	9.32727i	0.368405	+	0.368405i	0.866895	−	0.498490i	$-0.166112\pi$
$641$	9.32727	+	9.32727i	0.368405	+	0.368405i	−0.498490	+	0.866895i	$0.666112\pi$
$642$	−4.81265			−0.189940
$643$	15.3341	+	15.3341i	0.604719	+	0.604719i	0.941561	−	0.336843i	$-0.109359\pi$
$643$	15.3341	+	15.3341i	0.604719	+	0.604719i	−0.336843	+	0.941561i	$0.609359\pi$
$644$		−	5.85216i		−	0.230607i
$645$	−4.16644			−0.164053
$646$	−15.2763	+	2.61081i	−0.601038	+	0.102721i
$647$	−23.6706			−0.930587			−0.465293	−	0.885157i	$-0.654051\pi$
$647$	−23.6706			−0.930587			−0.465293	+	0.885157i	$0.654051\pi$
$648$			1.00000i			0.0392837i
$649$	7.33240	+	7.33240i	0.287822	+	0.287822i
$650$	13.0002			0.509910
$651$	23.2325	+	23.2325i	0.910553	+	0.910553i
$652$	−3.87456	+	3.87456i	−0.151739	+	0.151739i
$653$	−18.7607	+	18.7607i	−0.734162	+	0.734162i	−0.971441	−	0.237280i	$-0.923744\pi$
$653$	−18.7607	+	18.7607i	−0.734162	+	0.734162i	0.237280	+	0.971441i	$0.423744\pi$
$654$		−	11.4190i		−	0.446519i
$655$			24.6196i			0.961966i
$656$	5.74107	−	5.74107i	0.224151	−	0.224151i
$657$	−3.60589	+	3.60589i	−0.140679	+	0.140679i
$658$	−26.7294	−	26.7294i	−1.04202	−	1.04202i
$659$	−5.51154			−0.214699			−0.107350	−	0.994221i	$-0.534236\pi$
$659$	−5.51154			−0.214699			−0.107350	+	0.994221i	$0.534236\pi$
$660$	1.00000	+	1.00000i	0.0389249	+	0.0389249i
$661$		−	28.7224i		−	1.11717i	−0.829447	−	0.558585i	$-0.811344\pi$
$661$		−	28.7224i		−	1.11717i	0.829447	−	0.558585i	$-0.188656\pi$
$662$	−5.27431			−0.204992
$663$	14.5817	+	10.3250i	0.566307	+	0.400990i
$664$	0.648901			0.0251822
$665$		−	19.9805i		−	0.774811i
$666$	6.72203	+	6.72203i	0.260473	+	0.260473i
$667$	−2.12094			−0.0821231
$668$	−2.42020	−	2.42020i	−0.0936403	−	0.0936403i
$669$	8.09217	−	8.09217i	0.312861	−	0.312861i
$670$	14.8686	−	14.8686i	0.574426	−	0.574426i
$671$			10.0298i			0.387198i
$672$			3.75877i			0.144998i
$673$	−21.3589	+	21.3589i	−0.823326	+	0.823326i	−0.986583	−	0.163258i	$-0.947800\pi$
$673$	−21.3589	+	21.3589i	−0.823326	+	0.823326i	0.163258	+	0.986583i	$0.447800\pi$
$674$	−22.4392	+	22.4392i	−0.864327	+	0.864327i
$675$	−2.12132	−	2.12132i	−0.0816497	−	0.0816497i
$676$	−5.77837			−0.222245
$677$	−11.7280	−	11.7280i	−0.450743	−	0.450743i	0.444858	−	0.895601i	$-0.353254\pi$
$677$	−11.7280	−	11.7280i	−0.450743	−	0.450743i	−0.895601	+	0.444858i	$0.853254\pi$
$678$			7.78380i			0.298935i
$679$	0.0940750			0.00361027
$680$	3.36959	−	4.75877i	0.129218	−	0.182491i
$681$	11.0506			0.423459
$682$		−	8.74107i		−	0.334713i
$683$	−4.69876	−	4.69876i	−0.179793	−	0.179793i	0.611472	−	0.791266i	$-0.290578\pi$
$683$	−4.69876	−	4.69876i	−0.179793	−	0.179793i	−0.791266	+	0.611472i	$0.790578\pi$
$684$	−3.75877			−0.143720
$685$	9.00795	+	9.00795i	0.344176	+	0.344176i
$686$	−0.341150	+	0.341150i	−0.0130252	+	0.0130252i
$687$	−18.8083	+	18.8083i	−0.717582	+	0.717582i
$688$			2.94612i			0.112320i
$689$		−	37.2719i		−	1.41995i
$690$	−1.55693	+	1.55693i	−0.0592715	+	0.0592715i
$691$	−2.53937	+	2.53937i	−0.0966021	+	0.0966021i	−0.753756	−	0.657154i	$-0.771760\pi$
$691$	−2.53937	+	2.53937i	−0.0966021	+	0.0966021i	0.657154	+	0.753756i	$0.271760\pi$
$692$	12.8142	+	12.8142i	0.487123	+	0.487123i
$693$	3.75877			0.142784
$694$	−0.114483	−	0.114483i	−0.00434570	−	0.00434570i
$695$		−	32.1333i		−	1.21889i
$696$	1.36225			0.0516361
$697$	−19.3450	+	27.3204i	−0.732745	+	1.03484i
$698$	21.3395			0.807712
$699$		−	15.0044i		−	0.567519i
$700$	−7.97356	−	7.97356i	−0.301372	−	0.301372i
$701$	36.1832			1.36662			0.683311	−	0.730128i	$-0.260539\pi$
$701$	36.1832			1.36662			0.683311	+	0.730128i	$0.260539\pi$
$702$	3.06418	+	3.06418i	0.115650	+	0.115650i
$703$	−25.2666	+	25.2666i	−0.952947	+	0.952947i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$			14.2224i			0.535648i
$706$		−	31.8813i		−	1.19987i
$707$	−19.8143	+	19.8143i	−0.745195	+	0.745195i
$708$	7.33240	−	7.33240i	0.275569	−	0.275569i
$709$	−30.6278	−	30.6278i	−1.15025	−	1.15025i	−0.986502	−	0.163751i	$-0.947641\pi$
$709$	−30.6278	−	30.6278i	−1.15025	−	1.15025i	−0.163751	−	0.986502i	$-0.552359\pi$
$710$	−13.9825			−0.524754
$711$	0.118616	+	0.118616i	0.00444845	+	0.00444845i
$712$			11.4441i			0.428884i
$713$	13.6093			0.509671
$714$	−2.61081	−	15.2763i	−0.0977073	−	0.571702i
$715$	6.12836			0.229188
$716$			9.07447i			0.339129i
$717$	−16.2586	−	16.2586i	−0.607189	−	0.607189i
$718$	22.9036			0.854755
$719$	−12.7140	−	12.7140i	−0.474153	−	0.474153i	0.429102	−	0.903256i	$-0.358830\pi$
$719$	−12.7140	−	12.7140i	−0.474153	−	0.474153i	−0.903256	+	0.429102i	$0.858830\pi$
$720$	1.00000	−	1.00000i	0.0372678	−	0.0372678i
$721$	7.38154	−	7.38154i	0.274903	−	0.274903i
$722$			4.87164i			0.181304i
$723$		−	2.23198i		−	0.0830081i
$724$	3.94477	−	3.94477i	0.146606	−	0.146606i
$725$	−2.88978	+	2.88978i	−0.107324	+	0.107324i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−15.7767			−0.585125			−0.292562	−	0.956246i	$-0.594508\pi$
$727$	−15.7767			−0.585125			−0.292562	+	0.956246i	$0.594508\pi$
$728$	11.5175	+	11.5175i	0.426868	+	0.426868i
$729$		−	1.00000i		−	0.0370370i
$730$	7.21179			0.266920
$731$	−2.04635	−	11.9736i	−0.0756871	−	0.442858i
$732$	10.0298			0.370714
$733$			26.2721i			0.970382i	0.874408	+	0.485191i	$0.161250\pi$
$733$			26.2721i			0.970382i	−0.874408	+	0.485191i	$0.838750\pi$
$734$	19.5591	+	19.5591i	0.721940	+	0.721940i
$735$	10.0810			0.371844
$736$	1.10092	+	1.10092i	0.0405804	+	0.0405804i
$737$	−10.5137	+	10.5137i	−0.387278	+	0.387278i
$738$	−5.74107	+	5.74107i	−0.211332	+	0.211332i
$739$		−	44.4758i		−	1.63607i	−0.575168	−	0.818035i	$-0.695063\pi$
$739$		−	44.4758i		−	1.63607i	0.575168	−	0.818035i	$-0.304937\pi$
$740$		−	13.4441i		−	0.494213i
$741$	−11.5175	+	11.5175i	−0.423107	+	0.423107i
$742$	−22.8604	+	22.8604i	−0.839231	+	0.839231i
$743$	−18.1801	−	18.1801i	−0.666963	−	0.666963i	0.290049	−	0.957012i	$-0.406328\pi$
$743$	−18.1801	−	18.1801i	−0.666963	−	0.666963i	−0.957012	+	0.290049i	$0.906328\pi$
$744$	−8.74107			−0.320463
$745$	−23.1950	−	23.1950i	−0.849799	−	0.849799i
$746$			2.99979i			0.109830i
$747$	−0.648901			−0.0237420
$748$	−2.38266	+	3.36496i	−0.0871185	+	0.123035i
$749$	18.0897			0.660981
$750$			11.3137i			0.413118i
$751$	−8.92788	−	8.92788i	−0.325783	−	0.325783i	0.525197	−	0.850980i	$-0.323991\pi$
$751$	−8.92788	−	8.92788i	−0.325783	−	0.325783i	−0.850980	+	0.525197i	$0.823991\pi$
$752$	10.0568			0.366733
$753$	1.26736	+	1.26736i	0.0461852	+	0.0461852i
$754$	4.17419	−	4.17419i	0.152015	−	0.152015i
$755$	18.8694	−	18.8694i	0.686729	−	0.686729i
$756$		−	3.75877i		−	0.136705i
$757$		−	51.9077i		−	1.88662i	−0.331916	−	0.943309i	$-0.607695\pi$
$757$		−	51.9077i		−	1.88662i	0.331916	−	0.943309i	$-0.392305\pi$
$758$	7.63654	−	7.63654i	0.277372	−	0.277372i
$759$	1.10092	−	1.10092i	0.0399608	−	0.0399608i
$760$	3.75877	+	3.75877i	0.136345	+	0.136345i
$761$	−3.20683			−0.116247			−0.0581237	−	0.998309i	$-0.518512\pi$
$761$	−3.20683			−0.116247			−0.0581237	+	0.998309i	$0.518512\pi$
$762$	4.23083	+	4.23083i	0.153267	+	0.153267i
$763$			42.9215i			1.55386i
$764$	−9.38997			−0.339717
$765$	−3.36959	+	4.75877i	−0.121828	+	0.172054i
$766$	−6.71394			−0.242585
$767$		−	44.9356i		−	1.62253i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−21.4645			−0.774030			−0.387015	−	0.922073i	$-0.626494\pi$
$769$	−21.4645			−0.774030			−0.387015	+	0.922073i	$0.626494\pi$
$770$	−3.75877	−	3.75877i	−0.135457	−	0.135457i
$771$	−11.0888	+	11.0888i	−0.399355	+	0.399355i
$772$	7.23710	−	7.23710i	0.260469	−	0.260469i
$773$			41.3422i			1.48698i	0.668749	+	0.743488i	$0.266830\pi$
$773$			41.3422i			1.48698i	−0.668749	+	0.743488i	$0.733170\pi$
$774$		−	2.94612i		−	0.105896i
$775$	18.5426	−	18.5426i	0.666070	−	0.666070i
$776$	−0.0176976	+	0.0176976i	−0.000635306	+	0.000635306i
$777$	−25.2666	−	25.2666i	−0.906433	−	0.906433i
$778$	3.00874			0.107868
$779$	−21.5794	−	21.5794i	−0.773161	−	0.773161i
$780$		−	6.12836i		−	0.219430i
$781$	9.88713			0.353789
$782$	−5.23902	−	3.70964i	−0.187347	−	0.132656i
$783$	−1.36225			−0.0486830
$784$		−	7.12836i		−	0.254584i
$785$	5.10291	+	5.10291i	0.182131	+	0.182131i
$786$	−17.4087			−0.620947
$787$	−34.4619	−	34.4619i	−1.22844	−	1.22844i	−0.964555	−	0.263880i	$-0.914998\pi$
$787$	−34.4619	−	34.4619i	−1.22844	−	1.22844i	−0.263880	−	0.964555i	$-0.585002\pi$
$788$	9.29345	−	9.29345i	0.331066	−	0.331066i
$789$	−15.2106	+	15.2106i	−0.541511	+	0.541511i
$790$		−	0.237232i		−	0.00844033i
$791$		−	29.2575i		−	1.04028i
$792$	−0.707107	+	0.707107i	−0.0251259	+	0.0251259i
$793$	30.7332	−	30.7332i	1.09137	−	1.09137i
$794$	−19.3605	−	19.3605i	−0.687078	−	0.687078i
$795$	12.1638			0.431404
$796$	11.0600	+	11.0600i	0.392013	+	0.392013i
$797$			37.7282i			1.33640i	0.743981	+	0.668201i	$0.232935\pi$
$797$			37.7282i			1.33640i	−0.743981	+	0.668201i	$0.767065\pi$
$798$	14.1284			0.500138
$799$	−40.8725	+	6.98536i	−1.44597	+	0.247124i
$800$	3.00000			0.106066
$801$		−	11.4441i		−	0.404356i
$802$	2.16063	+	2.16063i	0.0762943	+	0.0762943i
$803$	−5.09950			−0.179958
$804$	10.5137	+	10.5137i	0.370790	+	0.370790i
$805$	5.85216	−	5.85216i	0.206261	−	0.206261i
$806$	−26.7842	+	26.7842i	−0.943433	+	0.943433i
$807$			18.9877i			0.668400i
$808$		−	7.45502i		−	0.262267i
$809$	3.06062	−	3.06062i	0.107606	−	0.107606i	−0.651254	−	0.758860i	$-0.725757\pi$
$809$	3.06062	−	3.06062i	0.107606	−	0.107606i	0.758860	+	0.651254i	$0.225757\pi$
$810$	−1.00000	+	1.00000i	−0.0351364	+	0.0351364i
$811$	−3.29139	−	3.29139i	−0.115576	−	0.115576i	0.646953	−	0.762530i	$-0.276043\pi$
$811$	−3.29139	−	3.29139i	−0.115576	−	0.115576i	−0.762530	+	0.646953i	$0.776043\pi$
$812$	−5.12040			−0.179691
$813$	18.9662	+	18.9662i	0.665172	+	0.665172i
$814$			9.50639i			0.333199i
$815$	−7.74912			−0.271440
$816$	3.36496	+	2.38266i	0.117797	+	0.0834097i
$817$	11.0738			0.387423
$818$			7.62457i			0.266587i
$819$	−11.5175	−	11.5175i	−0.402455	−	0.402455i
$820$	11.4821			0.400974
$821$	−34.5659	−	34.5659i	−1.20636	−	1.20636i	−0.972198	−	0.234159i	$-0.924767\pi$
$821$	−34.5659	−	34.5659i	−1.20636	−	1.20636i	−0.234159	−	0.972198i	$-0.575233\pi$
$822$	−6.36959	+	6.36959i	−0.222165	+	0.222165i
$823$	7.90879	−	7.90879i	0.275683	−	0.275683i	−0.555700	−	0.831383i	$-0.687550\pi$
$823$	7.90879	−	7.90879i	0.275683	−	0.275683i	0.831383	+	0.555700i	$0.187550\pi$
$824$			2.77726i			0.0967503i
$825$		−	3.00000i		−	0.104447i
$826$	−27.5608	+	27.5608i	−0.958964	+	0.958964i
$827$	−6.92139	+	6.92139i	−0.240680	+	0.240680i	−0.817132	−	0.576451i	$-0.804437\pi$
$827$	−6.92139	+	6.92139i	−0.240680	+	0.240680i	0.576451	+	0.817132i	$0.304437\pi$
$828$	−1.10092	−	1.10092i	−0.0382596	−	0.0382596i
$829$	−35.5989			−1.23640			−0.618200	−	0.786021i	$-0.712138\pi$
$829$	−35.5989			−1.23640			−0.618200	+	0.786021i	$0.712138\pi$
$830$	0.648901	+	0.648901i	0.0225237	+	0.0225237i
$831$			11.6616i			0.404535i
$832$	−4.33340			−0.150234
$833$	4.95130	+	28.9709i	0.171553	+	1.00378i
$834$	22.7217			0.786787
$835$		−	4.84040i		−	0.167509i
$836$	−2.65785	−	2.65785i	−0.0919237	−	0.0919237i
$837$	8.74107			0.302136
$838$	−24.3272	−	24.3272i	−0.840368	−	0.840368i
$839$	−26.8496	+	26.8496i	−0.926952	+	0.926952i	−0.997508	−	0.0705560i	$-0.977523\pi$
$839$	−26.8496	+	26.8496i	−0.926952	+	0.926952i	0.0705560	+	0.997508i	$0.477523\pi$
$840$	−3.75877	+	3.75877i	−0.129690	+	0.129690i
$841$		−	27.1443i		−	0.936009i
$842$			20.9860i			0.723227i
$843$	−23.2293	+	23.2293i	−0.800059	+	0.800059i
$844$	6.18222	−	6.18222i	0.212801	−	0.212801i
$845$	−5.77837	−	5.77837i	−0.198782	−	0.198782i
$846$	−10.0568			−0.345759
$847$	2.65785	+	2.65785i	0.0913249	+	0.0913249i
$848$		−	8.60107i		−	0.295362i
$849$	−3.08232			−0.105785
$850$	−12.1925	+	2.08378i	−0.418200	+	0.0714730i
$851$	−14.8008			−0.507365
$852$		−	9.88713i		−	0.338727i
$853$	10.5731	+	10.5731i	0.362016	+	0.362016i	0.864555	−	0.502539i	$-0.167601\pi$
$853$	10.5731	+	10.5731i	0.362016	+	0.362016i	−0.502539	+	0.864555i	$0.667601\pi$
$854$	−37.6999			−1.29006
$855$	−3.75877	−	3.75877i	−0.128547	−	0.128547i
$856$	−3.40306	+	3.40306i	−0.116314	+	0.116314i
$857$	−0.764709	+	0.764709i	−0.0261220	+	0.0261220i	−0.720047	−	0.693925i	$-0.755880\pi$
$857$	−0.764709	+	0.764709i	−0.0261220	+	0.0261220i	0.693925	+	0.720047i	$0.255880\pi$
$858$			4.33340i			0.147940i
$859$			12.6694i			0.432275i	0.976363	+	0.216137i	$0.0693459\pi$
$859$			12.6694i			0.432275i	−0.976363	+	0.216137i	$0.930654\pi$
$860$	−2.94612	+	2.94612i	−0.100462	+	0.100462i
$861$	21.5794	−	21.5794i	0.735423	−	0.735423i
$862$	−5.92095	−	5.92095i	−0.201668	−	0.201668i
$863$	32.9725			1.12240			0.561198	−	0.827682i	$-0.310341\pi$
$863$	32.9725			1.12240			0.561198	+	0.827682i	$0.310341\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$			25.6284i			0.871392i
$866$	29.9097			1.01637
$867$	−15.3308	−	7.34626i	−0.520660	−	0.249492i
$868$	32.8557			1.11519
$869$			0.167748i			0.00569047i
$870$	1.36225	+	1.36225i	0.0461848	+	0.0461848i
$871$	64.4318			2.18319
$872$	−8.07447	−	8.07447i	−0.273436	−	0.273436i
$873$	0.0176976	−	0.0176976i	0.000598972	−	0.000598972i
$874$	4.13810	−	4.13810i	0.139973	−	0.139973i
$875$		−	42.5256i		−	1.43763i
$876$			5.09950i			0.172296i
$877$	18.0324	−	18.0324i	0.608912	−	0.608912i	−0.333749	−	0.942662i	$-0.608314\pi$
$877$	18.0324	−	18.0324i	0.608912	−	0.608912i	0.942662	+	0.333749i	$0.108314\pi$
$878$	5.50215	−	5.50215i	0.185688	−	0.185688i
$879$	−14.9241	−	14.9241i	−0.503378	−	0.503378i
$880$	1.41421			0.0476731
$881$	9.89027	+	9.89027i	0.333212	+	0.333212i	0.853805	−	0.520593i	$-0.174289\pi$
$881$	9.89027	+	9.89027i	0.333212	+	0.333212i	−0.520593	+	0.853805i	$0.674289\pi$
$882$			7.12836i			0.240024i
$883$	−48.4758			−1.63134			−0.815671	−	0.578516i	$-0.803632\pi$
$883$	−48.4758			−1.63134			−0.815671	+	0.578516i	$0.803632\pi$
$884$	17.6117	−	3.00995i	0.592346	−	0.101236i
$885$	14.6648			0.492952
$886$			16.6921i			0.560783i
$887$	1.86806	+	1.86806i	0.0627234	+	0.0627234i	0.737773	−	0.675049i	$-0.235878\pi$
$887$	1.86806	+	1.86806i	0.0627234	+	0.0627234i	−0.675049	+	0.737773i	$0.735878\pi$
$888$	9.50639			0.319013
$889$	−15.9027	−	15.9027i	−0.533360	−	0.533360i
$890$	−11.4441	+	11.4441i	−0.383606	+	0.383606i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$		−	11.4441i		−	0.383175i
$893$		−	37.8011i		−	1.26497i
$894$	16.4013	−	16.4013i	0.548543	−	0.548543i
$895$	−9.07447	+	9.07447i	−0.303326	+	0.303326i
$896$	2.65785	+	2.65785i	0.0887926	+	0.0887926i
$897$	−6.74682			−0.225270
$898$	14.8519	+	14.8519i	0.495613	+	0.495613i
$899$		−	11.9076i		−	0.397140i
$900$	−3.00000			−0.100000
$901$	5.97424	+	34.9563i	0.199031	+	1.16456i
$902$	−8.11910			−0.270337
$903$			11.0738i			0.368513i
$904$	5.50398	+	5.50398i	0.183060	+	0.183060i
$905$	7.88955			0.262257
$906$	13.3427	+	13.3427i	0.443282	+	0.443282i
$907$	−6.42154	+	6.42154i	−0.213224	+	0.213224i	−0.805635	−	0.592412i	$-0.798176\pi$
$907$	−6.42154	+	6.42154i	−0.213224	+	0.213224i	0.592412	+	0.805635i	$0.298176\pi$
$908$	7.81394	−	7.81394i	0.259315	−	0.259315i
$909$			7.45502i			0.247267i
$910$			23.0351i			0.763606i
$911$	−7.80121	+	7.80121i	−0.258466	+	0.258466i	−0.824430	−	0.565964i	$-0.808504\pi$
$911$	−7.80121	+	7.80121i	−0.258466	+	0.258466i	0.565964	+	0.824430i	$0.308504\pi$
$912$	−2.65785	+	2.65785i	−0.0880103	+	0.0880103i
$913$	−0.458842	−	0.458842i	−0.0151855	−	0.0151855i
$914$	29.7502			0.984050
$915$	10.0298	+	10.0298i	0.331576	+	0.331576i
$916$			26.5990i			0.878855i
$917$	65.4352			2.16086
$918$	−3.36496	−	2.38266i	−0.111060	−	0.0786394i
$919$	−39.7045			−1.30973			−0.654866	−	0.755745i	$-0.727275\pi$
$919$	−39.7045			−1.30973			−0.654866	+	0.755745i	$0.727275\pi$
$920$			2.20184i			0.0725924i
$921$	−14.1746	−	14.1746i	−0.467069	−	0.467069i
$922$	2.44419			0.0804950
$923$	−30.2959	−	30.2959i	−0.997202	−	0.997202i
$924$	2.65785	−	2.65785i	0.0874369	−	0.0874369i
$925$	−20.1661	+	20.1661i	−0.663057	+	0.663057i
$926$		−	39.9928i		−	1.31425i
$927$		−	2.77726i		−	0.0912171i
$928$	0.963259	−	0.963259i	0.0316205	−	0.0316205i
$929$	13.0950	−	13.0950i	0.429633	−	0.429633i	−0.458870	−	0.888503i	$-0.651746\pi$
$929$	13.0950	−	13.0950i	0.429633	−	0.429633i	0.888503	+	0.458870i	$0.151746\pi$
$930$	−8.74107	−	8.74107i	−0.286631	−	0.286631i
$931$	−26.7939			−0.878133
$932$	−10.6097	−	10.6097i	−0.347533	−	0.347533i
$933$		−	9.65816i		−	0.316194i
$934$	−22.9603			−0.751284
$935$	−5.74762	+	0.982302i	−0.187967	+	0.0321247i
$936$	4.33340			0.141642
$937$		−	0.134157i		−	0.00438271i	−0.999998	−	0.00219136i	$-0.999302\pi$
$937$		−	0.134157i		−	0.00438271i	0.999998	−	0.00219136i	$-0.000697531\pi$
$938$	−39.5186	−	39.5186i	−1.29033	−	1.29033i
$939$	−0.264951			−0.00864635
$940$	10.0568	+	10.0568i	0.328016	+	0.328016i
$941$	9.18890	−	9.18890i	0.299550	−	0.299550i	−0.541288	−	0.840837i	$-0.682063\pi$
$941$	9.18890	−	9.18890i	0.299550	−	0.299550i	0.840837	+	0.541288i	$0.182063\pi$
$942$	−3.60830	+	3.60830i	−0.117565	+	0.117565i
$943$		−	12.6409i		−	0.411645i
$944$		−	10.3696i		−	0.337501i
$945$	3.75877	−	3.75877i	0.122273	−	0.122273i
$946$	2.08322	−	2.08322i	0.0677314	−	0.0677314i
$947$	25.3559	+	25.3559i	0.823957	+	0.823957i	0.986673	−	0.162716i	$-0.0520255\pi$
$947$	25.3559	+	25.3559i	0.823957	+	0.823957i	−0.162716	+	0.986673i	$0.552025\pi$
$948$	0.167748			0.00544821
$949$	15.6258	+	15.6258i	0.507234	+	0.507234i
$950$		−	11.2763i		−	0.365852i
$951$	−2.08556			−0.0676288
$952$	−12.6481	−	8.95586i	−0.409928	−	0.290261i
$953$	−38.0910			−1.23389			−0.616944	−	0.787007i	$-0.711629\pi$
$953$	−38.0910			−1.23389			−0.616944	+	0.787007i	$0.711629\pi$
$954$			8.60107i			0.278470i
$955$	−9.38997	−	9.38997i	−0.303852	−	0.303852i
$956$	−22.9932			−0.743652
$957$	−0.963259	−	0.963259i	−0.0311378	−	0.0311378i
$958$	7.26040	−	7.26040i	0.234573	−	0.234573i
$959$	23.9418	−	23.9418i	0.773121	−	0.773121i
$960$		−	1.41421i		−	0.0456435i
$961$			45.4064i			1.46472i
$962$	29.1293	−	29.1293i	0.939165	−	0.939165i
$963$	3.40306	−	3.40306i	0.109662	−	0.109662i
$964$	−1.57825	−	1.57825i	−0.0508319	−	0.0508319i
$965$	14.4742			0.465941
$966$	4.13810	+	4.13810i	0.133141	+	0.133141i
$967$		−	1.10543i		−	0.0355482i	−0.999842	−	0.0177741i	$-0.994342\pi$
$967$		−	1.10543i		−	0.0355482i	0.999842	−	0.0177741i	$-0.00565798\pi$
$968$	−1.00000			−0.0321412
$969$	8.95586	−	12.6481i	0.287704	−	0.406316i
$970$	−0.0353951			−0.00113647
$971$		−	17.6147i		−	0.565284i	−0.959226	−	0.282642i	$-0.908789\pi$
$971$		−	17.6147i		−	0.565284i	0.959226	−	0.282642i	$-0.0912108\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−85.4056			−2.73798
$974$	20.5395	+	20.5395i	0.658128	+	0.658128i
$975$	−9.19253	+	9.19253i	−0.294397	+	0.294397i
$976$	7.09217	−	7.09217i	0.227015	−	0.227015i
$977$			41.2452i			1.31955i	0.751463	+	0.659775i	$0.229348\pi$
$977$			41.2452i			1.31955i	−0.751463	+	0.659775i	$0.770652\pi$
$978$		−	5.47945i		−	0.175214i
$979$	8.09217	−	8.09217i	0.258627	−	0.258627i
$980$	7.12836	−	7.12836i	0.227707	−	0.227707i
$981$	8.07447	+	8.07447i	0.257798	+	0.257798i
$982$	−10.6176			−0.338821
$983$	−22.6055	−	22.6055i	−0.721004	−	0.721004i	0.247806	−	0.968810i	$-0.420290\pi$
$983$	−22.6055	−	22.6055i	−0.721004	−	0.721004i	−0.968810	+	0.247806i	$0.920290\pi$
$984$			8.11910i			0.258828i
$985$	18.5869			0.592228
$986$	−3.24578	+	4.58393i	−0.103367	+	0.145982i
$987$	37.8011			1.20322
$988$			16.2883i			0.518199i
$989$	3.24344	+	3.24344i	0.103135	+	0.103135i
$990$	−1.41421			−0.0449467
$991$	24.1220	+	24.1220i	0.766260	+	0.766260i	0.977446	−	0.211186i	$-0.0677325\pi$
$991$	24.1220	+	24.1220i	0.766260	+	0.766260i	−0.211186	+	0.977446i	$0.567732\pi$
$992$	−6.18087	+	6.18087i	−0.196243	+	0.196243i
$993$	3.72950	−	3.72950i	0.118352	−	0.118352i
$994$			37.1634i			1.17875i
$995$			22.1201i			0.701254i
$996$	−0.458842	+	0.458842i	−0.0145390	+	0.0145390i
$997$	29.3991	−	29.3991i	0.931080	−	0.931080i	−0.0666934	−	0.997774i	$-0.521245\pi$
$997$	29.3991	−	29.3991i	0.931080	−	0.931080i	0.997774	+	0.0666934i	$0.0212449\pi$
$998$	10.5105	+	10.5105i	0.332704	+	0.332704i
$999$	−9.50639			−0.300769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.e.727.1	yes	12
17.4	even	4	inner	1122.2.l.e.463.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.e.463.1	✓	12	17.4	even	4	inner
1122.2.l.e.727.1	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.65785 + 2.65785i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.65785 + 2.65785i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.00000 - 1.00000i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +4.33340 q^{13} +(-2.65785 - 2.65785i) q^{14} +1.41421i q^{15} +1.00000 q^{16} +(-4.06418 + 0.694593i) q^{17} -1.00000 q^{18} -3.75877i q^{19} +(1.00000 + 1.00000i) q^{20} +3.75877 q^{21} +(-0.707107 - 0.707107i) q^{22} +(1.10092 - 1.10092i) q^{23} +(-0.707107 + 0.707107i) q^{24} -3.00000i q^{25} +4.33340i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.65785 - 2.65785i) q^{28} +(-0.963259 - 0.963259i) q^{29} -1.41421 q^{30} +(6.18087 + 6.18087i) q^{31} +1.00000i q^{32} +1.00000 q^{33} +(-0.694593 - 4.06418i) q^{34} +5.31570 q^{35} -1.00000i q^{36} +(-6.72203 - 6.72203i) q^{37} +3.75877 q^{38} +(-3.06418 - 3.06418i) q^{39} +(-1.00000 + 1.00000i) q^{40} +(5.74107 - 5.74107i) q^{41} +3.75877i q^{42} +2.94612i q^{43} +(0.707107 - 0.707107i) q^{44} +(1.00000 - 1.00000i) q^{45} +(1.10092 + 1.10092i) q^{46} +10.0568 q^{47} +(-0.707107 - 0.707107i) q^{48} -7.12836i q^{49} +3.00000 q^{50} +(3.36496 + 2.38266i) q^{51} -4.33340 q^{52} -8.60107i q^{53} +(0.707107 + 0.707107i) q^{54} +1.41421 q^{55} +(2.65785 + 2.65785i) q^{56} +(-2.65785 + 2.65785i) q^{57} +(0.963259 - 0.963259i) q^{58} -10.3696i q^{59} -1.41421i q^{60} +(7.09217 - 7.09217i) q^{61} +(-6.18087 + 6.18087i) q^{62} +(-2.65785 - 2.65785i) q^{63} -1.00000 q^{64} +(-4.33340 - 4.33340i) q^{65} +1.00000i q^{66} +14.8686 q^{67} +(4.06418 - 0.694593i) q^{68} -1.55693 q^{69} +5.31570i q^{70} +(-6.99125 - 6.99125i) q^{71} +1.00000 q^{72} +(3.60589 + 3.60589i) q^{73} +(6.72203 - 6.72203i) q^{74} +(-2.12132 + 2.12132i) q^{75} +3.75877i q^{76} -3.75877i q^{77} +(3.06418 - 3.06418i) q^{78} +(0.118616 - 0.118616i) q^{79} +(-1.00000 - 1.00000i) q^{80} -1.00000 q^{81} +(5.74107 + 5.74107i) q^{82} +0.648901i q^{83} -3.75877 q^{84} +(4.75877 + 3.36959i) q^{85} -2.94612 q^{86} +1.36225i q^{87} +(0.707107 + 0.707107i) q^{88} -11.4441 q^{89} +(1.00000 + 1.00000i) q^{90} +(-11.5175 + 11.5175i) q^{91} +(-1.10092 + 1.10092i) q^{92} -8.74107i q^{93} +10.0568i q^{94} +(-3.75877 + 3.75877i) q^{95} +(0.707107 - 0.707107i) q^{96} +(-0.0176976 - 0.0176976i) q^{97} +7.12836 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 12 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 12 * q^5	\( 12 q - 12 q^{4} - 12 q^{5} + 12 q^{10} + 12 q^{16} - 12 q^{17} - 12 q^{18} + 12 q^{20} + 12 q^{29} + 12 q^{33} - 12 q^{37} - 12 q^{40} + 12 q^{41} + 12 q^{45} + 36 q^{50} - 12 q^{58} - 12 q^{61} - 12 q^{64} + 48 q^{67} + 12 q^{68} + 12 q^{72} + 12 q^{73} + 12 q^{74} - 12 q^{80} - 12 q^{81} + 12 q^{82} + 12 q^{85} + 12 q^{90} - 48 q^{91} - 12 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 12 * q^5 + 12 * q^10 + 12 * q^16 - 12 * q^17 - 12 * q^18 + 12 * q^20 + 12 * q^29 + 12 * q^33 - 12 * q^37 - 12 * q^40 + 12 * q^41 + 12 * q^45 + 36 * q^50 - 12 * q^58 - 12 * q^61 - 12 * q^64 + 48 * q^67 + 12 * q^68 + 12 * q^72 + 12 * q^73 + 12 * q^74 - 12 * q^80 - 12 * q^81 + 12 * q^82 + 12 * q^85 + 12 * q^90 - 48 * q^91 - 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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