LMFDB - Embedded newform 1638.2.cr.b.667.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(361,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("1638.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cr (of order $6$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 56 x^{18} + 1306 x^{16} + 16508 x^{14} + 123139 x^{12} + 552164 x^{10} + 1447090 x^{8} + \cdots + 576 $ x^20 + 56x^18 + 1306x^16 + 16508x^14 + 123139x^12 + 552164x^10 + 1447090x^8 + 2035844x^6 + 1263505x^4 + 215520*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			667.8
Root			$1.05091i$ of defining polynomial
Character	$\chi$	$=$	1638.667
Dual form			1638.2.cr.b.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.910115 - 0.525455i) q^{5} +(2.61575 + 0.397291i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.910115 - 0.525455i) q^{5} +(2.61575 + 0.397291i) q^{7} -1.00000i q^{8} -1.05091 q^{10} -6.56072i q^{11} +(-3.07474 - 1.88307i) q^{13} +(2.46395 - 0.963812i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.31143 + 4.00351i) q^{17} +2.99423i q^{19} +(-0.910115 + 0.525455i) q^{20} +(-3.28036 - 5.68175i) q^{22} +(-1.59836 - 2.76844i) q^{23} +(-1.94779 - 3.37368i) q^{25} +(-3.60434 - 0.0934133i) q^{26} +(1.65194 - 2.06666i) q^{28} +(1.12381 - 1.94650i) q^{29} +(7.58940 - 4.38174i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.62286i q^{34} +(-2.17188 - 1.73604i) q^{35} +(-4.02143 + 2.32178i) q^{37} +(1.49712 + 2.59308i) q^{38} +(-0.525455 + 0.910115i) q^{40} +(-6.65179 - 3.84041i) q^{41} +(0.696225 + 1.20590i) q^{43} +(-5.68175 - 3.28036i) q^{44} +(-2.76844 - 1.59836i) q^{46} +(9.01677 + 5.20584i) q^{47} +(6.68432 + 2.07843i) q^{49} +(-3.37368 - 1.94779i) q^{50} +(-3.16816 + 1.72127i) q^{52} +(-3.40268 - 5.89362i) q^{53} +(-3.44736 + 5.97101i) q^{55} +(0.397291 - 2.61575i) q^{56} -2.24763i q^{58} +(2.16500 + 1.24996i) q^{59} -9.90929 q^{61} +(4.38174 - 7.58940i) q^{62} -1.00000 q^{64} +(1.80890 + 3.32945i) q^{65} -8.98392i q^{67} +(2.31143 + 4.00351i) q^{68} +(-2.74892 - 0.417517i) q^{70} +(-7.13127 + 4.11724i) q^{71} +(8.18302 - 4.72447i) q^{73} +(-2.32178 + 4.02143i) q^{74} +(2.59308 + 1.49712i) q^{76} +(2.60652 - 17.1612i) q^{77} +(1.65111 - 2.85981i) q^{79} +1.05091i q^{80} -7.68082 q^{82} -9.79351i q^{83} +(4.20733 - 2.42910i) q^{85} +(1.20590 + 0.696225i) q^{86} -6.56072 q^{88} +(3.76799 - 2.17545i) q^{89} +(-7.29464 - 6.14721i) q^{91} -3.19672 q^{92} +10.4117 q^{94} +(1.57334 - 2.72510i) q^{95} +(5.83099 - 3.36652i) q^{97} +(6.82801 - 1.54219i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 6 q^{7}+O(q^{10}) $ 20 * q + 10 * q^4 - 6 * q^7	$ 20 q + 10 q^{4} - 6 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{14} - 10 q^{16} - 4 q^{17} - 10 q^{22} - 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 8 q^{29} - 12 q^{31} - 4 q^{35} - 6 q^{38} - 4 q^{40} + 18 q^{41} + 18 q^{43} - 6 q^{44} - 24 q^{46} - 6 q^{47} + 4 q^{49} - 12 q^{50} - 2 q^{52} - 18 q^{53} - 12 q^{55} - 2 q^{56} - 36 q^{59} + 12 q^{61} - 20 q^{64} + 4 q^{68} - 42 q^{70} + 6 q^{71} - 24 q^{73} + 18 q^{74} + 12 q^{76} + 34 q^{77} - 36 q^{82} - 36 q^{86} - 20 q^{88} - 18 q^{89} - 94 q^{91} - 16 q^{92} + 32 q^{94} - 40 q^{95} - 96 q^{97} + 12 q^{98}+O(q^{100}) $ 20 * q + 10 * q^4 - 6 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^14 - 10 * q^16 - 4 * q^17 - 10 * q^22 - 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^35 - 6 * q^38 - 4 * q^40 + 18 * q^41 + 18 * q^43 - 6 * q^44 - 24 * q^46 - 6 * q^47 + 4 * q^49 - 12 * q^50 - 2 * q^52 - 18 * q^53 - 12 * q^55 - 2 * q^56 - 36 * q^59 + 12 * q^61 - 20 * q^64 + 4 * q^68 - 42 * q^70 + 6 * q^71 - 24 * q^73 + 18 * q^74 + 12 * q^76 + 34 * q^77 - 36 * q^82 - 36 * q^86 - 20 * q^88 - 18 * q^89 - 94 * q^91 - 16 * q^92 + 32 * q^94 - 40 * q^95 - 96 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.910115	−	0.525455i	−0.407016	−	0.234991i	0.282491	−	0.959270i	$-0.408839\pi$
$5$	−0.910115	−	0.525455i	−0.407016	−	0.234991i	−0.689507	+	0.724279i	$0.742173\pi$
$6$		0			0
$7$	2.61575	+	0.397291i	0.988661	+	0.150162i
$7$	2.61575	+	0.397291i	0.988661	+	0.150162i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.05091			−0.332327
$11$		−	6.56072i		−	1.97813i	−0.147475	−	0.989066i	$-0.547115\pi$
$11$		−	6.56072i		−	1.97813i	0.147475	−	0.989066i	$-0.452885\pi$
$12$		0			0
$13$	−3.07474	−	1.88307i	−0.852781	−	0.522269i
$13$	−3.07474	−	1.88307i	−0.852781	−	0.522269i
$14$	2.46395	−	0.963812i	0.658519	−	0.257590i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.31143	+	4.00351i	−0.560604	+	0.970994i	0.436840	+	0.899539i	$0.356097\pi$
$17$	−2.31143	+	4.00351i	−0.560604	+	0.970994i	−0.997444	+	0.0714547i	$0.977236\pi$
$18$		0			0
$19$			2.99423i			0.686925i	0.939166	+	0.343462i	$0.111600\pi$
$19$			2.99423i			0.686925i	−0.939166	+	0.343462i	$0.888400\pi$
$20$	−0.910115	+	0.525455i	−0.203508	+	0.117495i
$21$		0			0
$22$	−3.28036	−	5.68175i	−0.699375	−	1.21135i
$23$	−1.59836	−	2.76844i	−0.333281	−	0.577259i	0.649872	−	0.760043i	$-0.274822\pi$
$23$	−1.59836	−	2.76844i	−0.333281	−	0.577259i	−0.983153	+	0.182784i	$0.941489\pi$
$24$		0			0
$25$	−1.94779	−	3.37368i	−0.389559	−	0.674736i
$26$	−3.60434	−	0.0934133i	−0.706869	−	0.0183199i
$27$		0			0
$28$	1.65194	−	2.06666i	0.312187	−	0.390562i
$29$	1.12381	−	1.94650i	0.208687	−	0.361456i	−0.742614	−	0.669719i	$-0.766414\pi$
$29$	1.12381	−	1.94650i	0.208687	−	0.361456i	0.951301	+	0.308263i	$0.0997477\pi$
$30$		0			0
$31$	7.58940	−	4.38174i	1.36310	−	0.786984i	0.373061	−	0.927807i	$-0.378308\pi$
$31$	7.58940	−	4.38174i	1.36310	−	0.786984i	0.990035	+	0.140823i	$0.0449747\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.62286i			0.792813i
$35$	−2.17188	−	1.73604i	−0.367114	−	0.293445i
$36$		0			0
$37$	−4.02143	+	2.32178i	−0.661120	+	0.381698i	−0.792704	−	0.609607i	$-0.791327\pi$
$37$	−4.02143	+	2.32178i	−0.661120	+	0.381698i	0.131584	+	0.991305i	$0.457994\pi$
$38$	1.49712	+	2.59308i	0.242865	+	0.420654i
$39$		0			0
$40$	−0.525455	+	0.910115i	−0.0830818	+	0.143902i
$41$	−6.65179	−	3.84041i	−1.03883	−	0.599771i	−0.119332	−	0.992854i	$-0.538075\pi$
$41$	−6.65179	−	3.84041i	−1.03883	−	0.599771i	−0.919503	+	0.393083i	$0.871408\pi$
$42$		0			0
$43$	0.696225	+	1.20590i	0.106173	+	0.183898i	0.914217	−	0.405225i	$-0.132807\pi$
$43$	0.696225	+	1.20590i	0.106173	+	0.183898i	−0.808044	+	0.589123i	$0.799474\pi$
$44$	−5.68175	−	3.28036i	−0.856556	−	0.494533i
$45$		0			0
$46$	−2.76844	−	1.59836i	−0.408184	−	0.235665i
$47$	9.01677	+	5.20584i	1.31523	+	0.759349i	0.982957	−	0.183834i	$-0.0588508\pi$
$47$	9.01677	+	5.20584i	1.31523	+	0.759349i	0.332274	+	0.943183i	$0.392184\pi$
$48$		0			0
$49$	6.68432	+	2.07843i	0.954903	+	0.296919i
$50$	−3.37368	−	1.94779i	−0.477110	−	0.275460i
$51$		0			0
$52$	−3.16816	+	1.72127i	−0.439344	+	0.238698i
$53$	−3.40268	−	5.89362i	−0.467394	−	0.809551i	0.531912	−	0.846800i	$-0.321474\pi$
$53$	−3.40268	−	5.89362i	−0.467394	−	0.809551i	−0.999306	+	0.0372492i	$0.988140\pi$
$54$		0			0
$55$	−3.44736	+	5.97101i	−0.464842	+	0.805131i
$56$	0.397291	−	2.61575i	0.0530903	−	0.349545i
$57$		0			0
$58$		−	2.24763i		−	0.295128i
$59$	2.16500	+	1.24996i	0.281858	+	0.162731i	0.634264	−	0.773116i	$-0.281303\pi$
$59$	2.16500	+	1.24996i	0.281858	+	0.162731i	−0.352406	+	0.935847i	$0.614636\pi$
$60$		0			0
$61$	−9.90929			−1.26875			−0.634377	−	0.773024i	$-0.718743\pi$
$61$	−9.90929			−1.26875			−0.634377	+	0.773024i	$0.718743\pi$
$62$	4.38174	−	7.58940i	0.556482	−	0.963855i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.80890	+	3.32945i	0.224367	+	0.412967i
$66$		0			0
$67$		−	8.98392i		−	1.09756i	−0.835967	−	0.548780i	$-0.815092\pi$
$67$		−	8.98392i		−	1.09756i	0.835967	−	0.548780i	$-0.184908\pi$
$68$	2.31143	+	4.00351i	0.280302	+	0.485497i
$69$		0			0
$70$	−2.74892	−	0.417517i	−0.328559	−	0.0499029i
$71$	−7.13127	+	4.11724i	−0.846326	+	0.488627i	−0.859410	−	0.511288i	$-0.829169\pi$
$71$	−7.13127	+	4.11724i	−0.846326	+	0.488627i	0.0130832	+	0.999914i	$0.495835\pi$
$72$		0			0
$73$	8.18302	−	4.72447i	0.957750	−	0.552957i	0.0622705	−	0.998059i	$-0.480166\pi$
$73$	8.18302	−	4.72447i	0.957750	−	0.552957i	0.895480	+	0.445102i	$0.146833\pi$
$74$	−2.32178	+	4.02143i	−0.269901	+	0.467482i
$75$		0			0
$76$	2.59308	+	1.49712i	0.297447	+	0.171731i
$77$	2.60652	−	17.1612i	0.297040	−	1.95570i
$78$		0			0
$79$	1.65111	−	2.85981i	0.185765	−	0.321754i	−0.758069	−	0.652174i	$-0.773857\pi$
$79$	1.65111	−	2.85981i	0.185765	−	0.321754i	0.943834	+	0.330420i	$0.107190\pi$
$80$			1.05091i			0.117495i
$81$		0			0
$82$	−7.68082			−0.848205
$83$		−	9.79351i		−	1.07498i	−0.843271	−	0.537489i	$-0.819373\pi$
$83$		−	9.79351i		−	1.07498i	0.843271	−	0.537489i	$-0.180627\pi$
$84$		0			0
$85$	4.20733	−	2.42910i	0.456349	−	0.263473i
$86$	1.20590	+	0.696225i	0.130035	+	0.0750759i
$87$		0			0
$88$	−6.56072			−0.699375
$89$	3.76799	−	2.17545i	0.399407	−	0.230597i	−0.286821	−	0.957984i	$-0.592599\pi$
$89$	3.76799	−	2.17545i	0.399407	−	0.230597i	0.686228	+	0.727387i	$0.259265\pi$
$90$		0			0
$91$	−7.29464	−	6.14721i	−0.764686	−	0.644403i
$92$	−3.19672			−0.333281
$93$		0			0
$94$	10.4117			1.07388
$95$	1.57334	−	2.72510i	0.161421	−	0.279589i
$96$		0			0
$97$	5.83099	−	3.36652i	0.592047	−	0.341819i	−0.173859	−	0.984770i	$-0.555624\pi$
$97$	5.83099	−	3.36652i	0.592047	−	0.341819i	0.765907	+	0.642952i	$0.222290\pi$
$98$	6.82801	−	1.54219i	0.689733	−	0.155784i
$99$		0			0
$100$	−3.89559			−0.389559
$101$	7.15050			0.711501			0.355750	−	0.934581i	$-0.384225\pi$
$101$	7.15050			0.711501			0.355750	+	0.934581i	$0.384225\pi$
$102$		0			0
$103$	0.342585	−	0.593375i	0.0337559	−	0.0584670i	−0.848654	−	0.528949i	$-0.822586\pi$
$103$	0.342585	−	0.593375i	0.0337559	−	0.0584670i	0.882410	+	0.470482i	$0.155920\pi$
$104$	−1.88307	+	3.07474i	−0.184650	+	0.301503i
$105$		0			0
$106$	−5.89362	−	3.40268i	−0.572439	−	0.330498i
$107$	2.46873	+	4.27597i	0.238662	+	0.413374i	0.960330	−	0.278864i	$-0.0899580\pi$
$107$	2.46873	+	4.27597i	0.238662	+	0.413374i	−0.721669	+	0.692238i	$0.756625\pi$
$108$		0			0
$109$	−6.18109	+	3.56865i	−0.592041	+	0.341815i	−0.765904	−	0.642955i	$-0.777708\pi$
$109$	−6.18109	+	3.56865i	−0.592041	+	0.341815i	0.173863	+	0.984770i	$0.444375\pi$
$110$			6.89473i			0.657387i
$111$		0			0
$112$	−0.963812	−	2.46395i	−0.0910717	−	0.232822i
$113$	4.40041	+	7.62173i	0.413955	+	0.716992i	0.995318	−	0.0966527i	$-0.0308136\pi$
$113$	4.40041	+	7.62173i	0.413955	+	0.716992i	−0.581363	+	0.813644i	$0.697480\pi$
$114$		0			0
$115$			3.35946i			0.313271i
$116$	−1.12381	−	1.94650i	−0.104343	−	0.180728i
$117$		0			0
$118$	2.49992			0.230136
$119$	−7.63668	+	9.55388i	−0.700053	+	0.875803i
$120$		0			0
$121$	−32.0430			−2.91300
$122$	−8.58169	+	4.95464i	−0.776950	+	0.448572i
$123$		0			0
$124$		−	8.76348i		−	0.786984i
$125$			9.34846i			0.836152i
$126$		0			0
$127$	10.2765	−	17.7995i	0.911895	−	1.57945i	0.100511	−	0.994936i	$-0.467952\pi$
$127$	10.2765	−	17.7995i	0.911895	−	1.57945i	0.811385	−	0.584513i	$-0.198714\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	3.23128	+	1.97894i	0.283402	+	0.173564i
$131$	−5.07036	+	8.78212i	−0.442999	+	0.767297i	−0.997910	−	0.0646123i	$-0.979419\pi$
$131$	−5.07036	+	8.78212i	−0.442999	+	0.767297i	0.554911	+	0.831910i	$0.312752\pi$
$132$		0			0
$133$	−1.18958	+	7.83218i	−0.103150	+	0.679136i
$134$	−4.49196	−	7.78031i	−0.388046	−	0.672116i
$135$		0			0
$136$	4.00351	+	2.31143i	0.343298	+	0.198203i
$137$	11.3641	+	6.56106i	0.970900	+	0.560549i	0.899511	−	0.436899i	$-0.143923\pi$
$137$	11.3641	+	6.56106i	0.970900	+	0.560549i	0.0713896	+	0.997449i	$0.477257\pi$
$138$		0			0
$139$	−4.82355	−	8.35464i	−0.409129	−	0.708631i	0.585664	−	0.810554i	$-0.300834\pi$
$139$	−4.82355	−	8.35464i	−0.409129	−	0.708631i	−0.994792	+	0.101923i	$0.967501\pi$
$140$	−2.58939	+	1.01288i	−0.218844	+	0.0856040i
$141$		0			0
$142$	−4.11724	+	7.13127i	−0.345511	+	0.598443i
$143$	−12.3543	+	20.1725i	−1.03312	+	1.68691i
$144$		0			0
$145$	−2.04560	+	1.18103i	−0.169878	+	0.0980789i
$146$	4.72447	−	8.18302i	0.391000	−	0.677232i
$147$		0			0
$148$			4.64355i			0.381698i
$149$			18.5203i			1.51724i	0.651532	+	0.758621i	$0.274126\pi$
$149$			18.5203i			1.51724i	−0.651532	+	0.758621i	$0.725874\pi$
$150$		0			0
$151$	−5.07128	+	2.92791i	−0.412695	+	0.238270i	−0.691947	−	0.721948i	$-0.743247\pi$
$151$	−5.07128	+	2.92791i	−0.412695	+	0.238270i	0.279252	+	0.960218i	$0.409914\pi$
$152$	2.99423			0.242865
$153$		0			0
$154$	−6.32330	−	16.1653i	−0.509546	−	1.30264i
$155$	−9.20963			−0.739736
$156$		0			0
$157$	−7.92320	−	13.7234i	−0.632341	−	1.09525i	−0.987072	−	0.160278i	$-0.948761\pi$
$157$	−7.92320	−	13.7234i	−0.632341	−	1.09525i	0.354731	−	0.934968i	$-0.384572\pi$
$158$		−	3.30223i		−	0.262711i
$159$		0			0
$160$	0.525455	+	0.910115i	0.0415409	+	0.0719509i
$161$	−3.08103	−	7.87656i	−0.242819	−	0.620760i
$162$		0			0
$163$		−	6.15647i		−	0.482212i	−0.970499	−	0.241106i	$-0.922490\pi$
$163$		−	6.15647i		−	0.482212i	0.970499	−	0.241106i	$-0.0775102\pi$
$164$	−6.65179	+	3.84041i	−0.519417	+	0.299886i
$165$		0			0
$166$	−4.89676	−	8.48143i	−0.380062	−	0.658287i
$167$	6.82652	+	3.94129i	0.528252	+	0.304986i	0.740304	−	0.672272i	$-0.234681\pi$
$167$	6.82652	+	3.94129i	0.528252	+	0.304986i	−0.212052	+	0.977258i	$0.568015\pi$
$168$		0			0
$169$	5.90810	+	11.5799i	0.454470	+	0.890762i
$170$	2.42910	−	4.20733i	0.186304	−	0.322687i
$171$		0			0
$172$	1.39245			0.106173
$173$	0.726363			0.0552244			0.0276122	−	0.999619i	$-0.491210\pi$
$173$	0.726363			0.0552244			0.0276122	+	0.999619i	$0.491210\pi$
$174$		0			0
$175$	−3.75461	−	9.59855i	−0.283822	−	0.725582i
$176$	−5.68175	+	3.28036i	−0.428278	+	0.247266i
$177$		0			0
$178$	2.17545	−	3.76799i	0.163057	−	0.282423i
$179$	17.1109			1.27893			0.639464	−	0.768821i	$-0.279156\pi$
$179$	17.1109			1.27893			0.639464	+	0.768821i	$0.279156\pi$
$180$		0			0
$181$	15.7454			1.17035			0.585173	−	0.810908i	$-0.301027\pi$
$181$	15.7454			1.17035			0.585173	+	0.810908i	$0.301027\pi$
$182$	−9.39095	−	1.67632i	−0.696104	−	0.124257i
$183$		0			0
$184$	−2.76844	+	1.59836i	−0.204092	+	0.117832i
$185$	4.87996			0.358782
$186$		0			0
$187$	26.2659	+	15.1646i	1.92075	+	1.10895i
$188$	9.01677	−	5.20584i	0.657616	−	0.379675i
$189$		0			0
$190$		−	3.14667i		−	0.228284i
$191$	19.2661			1.39405			0.697024	−	0.717047i	$-0.254507\pi$
$191$	19.2661			1.39405			0.697024	+	0.717047i	$0.254507\pi$
$192$		0			0
$193$			16.0550i			1.15567i	0.816154	+	0.577834i	$0.196102\pi$
$193$			16.0550i			1.15567i	−0.816154	+	0.577834i	$0.803898\pi$
$194$	3.36652	−	5.83099i	0.241702	−	0.418641i
$195$		0			0
$196$	5.14213	−	4.74957i	0.367295	−	0.339255i
$197$	12.4157	+	7.16821i	0.884582	+	0.510714i	0.872166	−	0.489209i	$-0.162715\pi$
$197$	12.4157	+	7.16821i	0.884582	+	0.510714i	0.0124154	+	0.999923i	$0.496048\pi$
$198$		0			0
$199$	−7.95650	+	13.7811i	−0.564022	+	0.976914i	0.433118	+	0.901337i	$0.357413\pi$
$199$	−7.95650	+	13.7811i	−0.564022	+	0.976914i	−0.997140	+	0.0755770i	$0.975920\pi$
$200$	−3.37368	+	1.94779i	−0.238555	+	0.137730i
$201$		0			0
$202$	6.19251	−	3.57525i	0.435704	−	0.251554i
$203$	3.71294	−	4.64508i	0.260598	−	0.326021i
$204$		0			0
$205$	4.03593	+	6.99043i	0.281881	+	0.488233i
$206$		−	0.685170i		−	0.0477381i
$207$		0			0
$208$	−0.0934133	+	3.60434i	−0.00647705	+	0.249916i
$209$	19.6443			1.35883
$210$		0			0
$211$	−10.0909	+	17.4780i	−0.694688	+	1.20323i	0.275598	+	0.961273i	$0.411124\pi$
$211$	−10.0909	+	17.4780i	−0.694688	+	1.20323i	−0.970286	+	0.241961i	$0.922209\pi$
$212$	−6.80536			−0.467394
$213$		0			0
$214$	4.27597	+	2.46873i	0.292299	+	0.168759i
$215$		−	1.46334i		−	0.0997989i
$216$		0			0
$217$	21.5928	−	8.44635i	1.46582	−	0.573375i
$218$	−3.56865	+	6.18109i	−0.241700	+	0.418636i
$219$		0			0
$220$	3.44736	+	5.97101i	0.232421	+	0.402565i
$221$	14.6459	−	7.95719i	0.985192	−	0.535259i
$222$		0			0
$223$	17.2784	+	9.97570i	1.15705	+	0.668022i	0.950595	−	0.310434i	$-0.100475\pi$
$223$	17.2784	+	9.97570i	1.15705	+	0.668022i	0.206453	+	0.978456i	$0.433808\pi$
$224$	−2.06666	−	1.65194i	−0.138085	−	0.110375i
$225$		0			0
$226$	7.62173	+	4.40041i	0.506990	+	0.292711i
$227$	−20.2480	−	11.6902i	−1.34391	−	0.775906i	−0.356529	−	0.934284i	$-0.616040\pi$
$227$	−20.2480	−	11.6902i	−1.34391	−	0.775906i	−0.987378	+	0.158378i	$0.949373\pi$
$228$		0			0
$229$	4.68467	+	2.70470i	0.309572	+	0.178731i	0.646735	−	0.762715i	$-0.276134\pi$
$229$	4.68467	+	2.70470i	0.309572	+	0.178731i	−0.337163	+	0.941446i	$0.609467\pi$
$230$	1.67973	+	2.90938i	0.110758	+	0.191839i
$231$		0			0
$232$	−1.94650	−	1.12381i	−0.127794	−	0.0737819i
$233$	10.7071	−	18.5453i	0.701448	−	1.21494i	−0.266510	−	0.963832i	$-0.585871\pi$
$233$	10.7071	−	18.5453i	0.701448	−	1.21494i	0.967958	−	0.251111i	$-0.0807960\pi$
$234$		0			0
$235$	−5.47087	−	9.47582i	−0.356880	−	0.618134i
$236$	2.16500	−	1.24996i	0.140929	−	0.0813655i
$237$		0			0
$238$	−1.83662	+	12.0922i	−0.119050	+	0.783824i
$239$			8.80379i			0.569470i	0.958606	+	0.284735i	$0.0919056\pi$
$239$			8.80379i			0.569470i	−0.958606	+	0.284735i	$0.908094\pi$
$240$		0			0
$241$	11.6408	+	6.72082i	0.749850	+	0.432926i	0.825640	−	0.564198i	$-0.190814\pi$
$241$	11.6408	+	6.72082i	0.749850	+	0.432926i	−0.0757899	+	0.997124i	$0.524148\pi$
$242$	−27.7501	+	16.0215i	−1.78384	+	1.02990i
$243$		0			0
$244$	−4.95464	+	8.58169i	−0.317189	+	0.549387i
$245$	−4.99138	−	5.40392i	−0.318887	−	0.345244i
$246$		0			0
$247$	5.63835	−	9.20651i	0.358760	−	0.585796i
$248$	−4.38174	−	7.58940i	−0.278241	−	0.481927i
$249$		0			0
$250$	4.67423	+	8.09601i	0.295624	+	0.512036i
$251$	2.16506	+	3.75000i	0.136658	+	0.236698i	0.926229	−	0.376960i	$-0.123031\pi$
$251$	2.16506	+	3.75000i	0.136658	+	0.236698i	−0.789572	+	0.613658i	$0.789697\pi$
$252$		0			0
$253$	−18.1629	+	10.4864i	−1.14189	+	0.659273i
$254$		−	20.5531i		−	1.28961i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.27315	+	2.20516i	0.0794169	+	0.137554i	0.902999	−	0.429644i	$-0.141361\pi$
$257$	1.27315	+	2.20516i	0.0794169	+	0.137554i	−0.823582	+	0.567198i	$0.808027\pi$
$258$		0			0
$259$	−11.4415	+	4.47551i	−0.710940	+	0.278095i
$260$	3.78784	+	0.0981690i	0.234912	+	0.00608818i
$261$		0			0
$262$			10.1407i			0.626496i
$263$	−7.00731			−0.432090			−0.216045	−	0.976383i	$-0.569316\pi$
$263$	−7.00731			−0.432090			−0.216045	+	0.976383i	$0.569316\pi$
$264$		0			0
$265$			7.15183i			0.439333i
$266$	2.88588	+	7.37766i	0.176945	+	0.452353i
$267$		0			0
$268$	−7.78031	−	4.49196i	−0.475258	−	0.274390i
$269$	−0.701117	+	1.21437i	−0.0427479	+	0.0740415i	−0.886608	−	0.462522i	$-0.846945\pi$
$269$	−0.701117	+	1.21437i	−0.0427479	+	0.0740415i	0.843860	+	0.536564i	$0.180278\pi$
$270$		0			0
$271$	0.455960	−	0.263249i	0.0276976	−	0.0159912i	−0.486087	−	0.873910i	$-0.661576\pi$
$271$	0.455960	−	0.263249i	0.0276976	−	0.0159912i	0.513785	+	0.857919i	$0.328243\pi$
$272$	4.62286			0.280302
$273$		0			0
$274$	13.1221			0.792737
$275$	−22.1338	+	12.7789i	−1.33472	+	0.770598i
$276$		0			0
$277$	16.3572	−	28.3315i	0.982810	−	1.70228i	0.331518	−	0.943449i	$-0.392439\pi$
$277$	16.3572	−	28.3315i	0.982810	−	1.70228i	0.651292	−	0.758827i	$-0.274227\pi$
$278$	−8.35464	−	4.82355i	−0.501078	−	0.289298i
$279$		0			0
$280$	−1.73604	+	2.17188i	−0.103748	+	0.129794i
$281$		−	22.6836i		−	1.35319i	−0.736356	−	0.676594i	$-0.763455\pi$
$281$		−	22.6836i		−	1.35319i	0.736356	−	0.676594i	$-0.236545\pi$
$282$		0			0
$283$	5.48461			0.326026			0.163013	−	0.986624i	$-0.447879\pi$
$283$	5.48461			0.326026			0.163013	+	0.986624i	$0.447879\pi$
$284$			8.23449i			0.488627i
$285$		0			0
$286$	−0.612859	+	23.6471i	−0.0362391	+	1.39828i
$287$	−15.8737	−	12.6883i	−0.936993	−	0.748964i
$288$		0			0
$289$	−2.18539	−	3.78521i	−0.128553	−	0.222660i
$290$	−1.18103	+	2.04560i	−0.0693523	+	0.120122i
$291$		0			0
$292$		−	9.44894i		−	0.552957i
$293$	11.5606	−	6.67449i	0.675375	−	0.389928i	−0.122735	−	0.992439i	$-0.539167\pi$
$293$	11.5606	−	6.67449i	0.675375	−	0.389928i	0.798110	+	0.602512i	$0.205833\pi$
$294$		0			0
$295$	−1.31360	−	2.27522i	−0.0764805	−	0.132468i
$296$	2.32178	+	4.02143i	0.134951	+	0.233741i
$297$		0			0
$298$	9.26015	+	16.0390i	0.536426	+	0.929117i
$299$	−0.298616	+	11.5221i	−0.0172694	+	0.666337i
$300$		0			0
$301$	1.34206	+	3.43093i	0.0773550	+	0.197756i
$302$	−2.92791	+	5.07128i	−0.168482	+	0.291820i
$303$		0			0
$304$	2.59308	−	1.49712i	0.148724	−	0.0858656i
$305$	9.01859	+	5.20689i	0.516403	+	0.298145i
$306$		0			0
$307$			16.4170i			0.936969i	0.883472	+	0.468485i	$0.155200\pi$
$307$			16.4170i			0.936969i	−0.883472	+	0.468485i	$0.844800\pi$
$308$	−13.5588	−	10.8379i	−0.772584	−	0.617548i
$309$		0			0
$310$	−7.97578	+	4.60482i	−0.452994	+	0.261536i
$311$	12.4093	+	21.4936i	0.703669	+	1.21879i	0.967170	+	0.254131i	$0.0817895\pi$
$311$	12.4093	+	21.4936i	0.703669	+	1.21879i	−0.263501	+	0.964659i	$0.584877\pi$
$312$		0			0
$313$	−11.2551	+	19.4943i	−0.636174	+	1.10189i	0.350091	+	0.936716i	$0.386151\pi$
$313$	−11.2551	+	19.4943i	−0.636174	+	1.10189i	−0.986265	+	0.165170i	$0.947183\pi$
$314$	−13.7234	−	7.92320i	−0.774456	−	0.447132i
$315$		0			0
$316$	−1.65111	−	2.85981i	−0.0928824	−	0.160877i
$317$	16.0776	+	9.28239i	0.903006	+	0.521351i	0.878174	−	0.478341i	$-0.158762\pi$
$317$	16.0776	+	9.28239i	0.903006	+	0.521351i	0.0248317	+	0.999692i	$0.492095\pi$
$318$		0			0
$319$	−12.7704	−	7.37302i	−0.715008	−	0.412810i
$320$	0.910115	+	0.525455i	0.0508770	+	0.0293738i
$321$		0			0
$322$	−6.60653	−	5.28078i	−0.368168	−	0.294287i
$323$	−11.9874	−	6.92096i	−0.667000	−	0.385092i
$324$		0			0
$325$	−0.363900	+	14.0410i	−0.0201855	+	0.778856i
$326$	−3.07824	−	5.33166i	−0.170488	−	0.295293i
$327$		0			0
$328$	−3.84041	+	6.65179i	−0.212051	+	0.367283i
$329$	21.5174	+	17.1995i	1.18629	+	0.948237i
$330$		0			0
$331$		−	8.40902i		−	0.462202i	−0.972930	−	0.231101i	$-0.925767\pi$
$331$		−	8.40902i		−	0.462202i	0.972930	−	0.231101i	$-0.0742327\pi$
$332$	−8.48143	−	4.89676i	−0.465479	−	0.268744i
$333$		0			0
$334$	7.88258			0.431316
$335$	−4.72065	+	8.17640i	−0.257917	+	0.446725i
$336$		0			0
$337$	4.80038			0.261493			0.130747	−	0.991416i	$-0.458263\pi$
$337$	4.80038			0.261493			0.130747	+	0.991416i	$0.458263\pi$
$338$	10.9065	+	7.07444i	0.593237	+	0.384799i
$339$		0			0
$340$		−	4.85821i		−	0.263473i
$341$	−28.7474	−	49.7919i	−1.55676	−	2.69638i
$342$		0			0
$343$	16.6588	+	8.09228i	0.899490	+	0.436942i
$344$	1.20590	−	0.696225i	0.0650176	−	0.0375379i
$345$		0			0
$346$	0.629049	−	0.363182i	0.0338179	−	0.0195248i
$347$	1.67396	−	2.89939i	0.0898630	−	0.155647i	−0.817590	−	0.575801i	$-0.804690\pi$
$347$	1.67396	−	2.89939i	0.0898630	−	0.155647i	0.907453	+	0.420153i	$0.138024\pi$
$348$		0			0
$349$	12.3261	+	7.11650i	0.659803	+	0.380938i	0.792202	−	0.610259i	$-0.208935\pi$
$349$	12.3261	+	7.11650i	0.659803	+	0.380938i	−0.132399	+	0.991197i	$0.542268\pi$
$350$	−8.05086	−	6.43528i	−0.430337	−	0.343980i
$351$		0			0
$352$	−3.28036	+	5.68175i	−0.174844	+	0.302838i
$353$			29.2083i			1.55460i	0.629130	+	0.777300i	$0.283411\pi$
$353$			29.2083i			1.55460i	−0.629130	+	0.777300i	$0.716589\pi$
$354$		0			0
$355$	8.65371			0.459291
$356$		−	4.35090i		−	0.230597i
$357$		0			0
$358$	14.8185	−	8.55545i	0.783180	−	0.452169i
$359$	−22.2918	−	12.8702i	−1.17652	−	0.679262i	−0.221310	−	0.975204i	$-0.571033\pi$
$359$	−22.2918	−	12.8702i	−1.17652	−	0.679262i	−0.955206	+	0.295942i	$0.904367\pi$
$360$		0			0
$361$	10.0346			0.528135
$362$	13.6359	−	7.87270i	0.716688	−	0.413780i
$363$		0			0
$364$	−8.97096	+	3.24374i	−0.470206	+	0.170018i
$365$	−9.92999			−0.519759
$366$		0			0
$367$	19.5416			1.02006			0.510030	−	0.860156i	$-0.329634\pi$
$367$	19.5416			1.02006			0.510030	+	0.860156i	$0.329634\pi$
$368$	−1.59836	+	2.76844i	−0.0833202	+	0.144315i
$369$		0			0
$370$	4.22617	−	2.43998i	0.219708	−	0.126848i
$371$	−6.55909	−	16.7681i	−0.340531	−	0.870556i
$372$		0			0
$373$	−19.0435			−0.986034			−0.493017	−	0.870020i	$-0.664106\pi$
$373$	−19.0435			−0.986034			−0.493017	+	0.870020i	$0.664106\pi$
$374$	30.3293			1.56829
$375$		0			0
$376$	5.20584	−	9.01677i	0.268471	−	0.465005i
$377$	−7.12083	+	3.86878i	−0.366742	+	0.199252i
$378$		0			0
$379$	−23.8073	−	13.7451i	−1.22290	−	0.706040i	−0.257363	−	0.966315i	$-0.582854\pi$
$379$	−23.8073	−	13.7451i	−1.22290	−	0.706040i	−0.965535	+	0.260274i	$0.916187\pi$
$380$	−1.57334	−	2.72510i	−0.0807104	−	0.139795i
$381$		0			0
$382$	16.6850	−	9.63307i	0.853677	−	0.492871i
$383$			10.1657i			0.519444i	0.965683	+	0.259722i	$0.0836309\pi$
$383$			10.1657i			0.519444i	−0.965683	+	0.259722i	$0.916369\pi$
$384$		0			0
$385$	−11.3897	+	14.2491i	−0.580472	+	0.726200i
$386$	8.02752	+	13.9041i	0.408590	+	0.707699i
$387$		0			0
$388$		−	6.73305i		−	0.341819i
$389$	−11.6154	−	20.1184i	−0.588922	−	1.02004i	−0.994374	−	0.105926i	$-0.966219\pi$
$389$	−11.6154	−	20.1184i	−0.588922	−	1.02004i	0.405452	−	0.914116i	$-0.367114\pi$
$390$		0			0
$391$	14.7780			0.747353
$392$	2.07843	−	6.68432i	0.104977	−	0.337609i
$393$		0			0
$394$	14.3364			0.722258
$395$	−3.00541	+	1.73517i	−0.151218	+	0.0873060i
$396$		0			0
$397$		−	34.1545i		−	1.71417i	−0.515178	−	0.857083i	$-0.672274\pi$
$397$		−	34.1545i		−	1.71417i	0.515178	−	0.857083i	$-0.327726\pi$
$398$			15.9130i			0.797647i
$399$		0			0
$400$	−1.94779	+	3.37368i	−0.0973897	+	0.168684i
$401$	27.2130	−	15.7114i	1.35895	−	0.784590i	0.369468	−	0.929244i	$-0.379540\pi$
$401$	27.2130	−	15.7114i	1.35895	−	0.784590i	0.989482	+	0.144653i	$0.0462067\pi$
$402$		0			0
$403$	−31.5866	−	0.818626i	−1.57344	−	0.0407787i
$404$	3.57525	−	6.19251i	0.177875	−	0.308089i
$405$		0			0
$406$	0.892962	−	5.87923i	0.0443170	−	0.291781i
$407$	15.2325	+	26.3835i	0.755048	+	1.30778i
$408$		0			0
$409$	−1.59937	−	0.923399i	−0.0790839	−	0.0456591i	0.459937	−	0.887952i	$-0.347872\pi$
$409$	−1.59937	−	0.923399i	−0.0790839	−	0.0456591i	−0.539021	+	0.842293i	$0.681205\pi$
$410$	6.99043	+	4.03593i	0.345233	+	0.199320i
$411$		0			0
$412$	−0.342585	−	0.593375i	−0.0168780	−	0.0292335i
$413$	5.16649	+	4.12972i	0.254226	+	0.203210i
$414$		0			0
$415$	−5.14605	+	8.91322i	−0.252610	+	0.437533i
$416$	1.72127	+	3.16816i	0.0843923	+	0.155332i
$417$		0			0
$418$	17.0125	−	9.82217i	0.832108	−	0.480418i
$419$	−14.5391	+	25.1824i	−0.710281	+	1.23024i	0.254470	+	0.967081i	$0.418099\pi$
$419$	−14.5391	+	25.1824i	−0.710281	+	1.23024i	−0.964752	+	0.263162i	$0.915234\pi$
$420$		0			0
$421$			10.0596i			0.490275i	0.969488	+	0.245138i	$0.0788331\pi$
$421$			10.0596i			0.490275i	−0.969488	+	0.245138i	$0.921167\pi$
$422$			20.1818i			0.982437i
$423$		0			0
$424$	−5.89362	+	3.40268i	−0.286219	+	0.165249i
$425$	18.0087			0.873552
$426$		0			0
$427$	−25.9202	−	3.93687i	−1.25437	−	0.190519i
$428$	4.93747			0.238662
$429$		0			0
$430$	−0.731670	−	1.26729i	−0.0352843	−	0.0611141i
$431$		−	15.6490i		−	0.753784i	−0.926257	−	0.376892i	$-0.876993\pi$
$431$		−	15.6490i		−	0.753784i	0.926257	−	0.376892i	$-0.123007\pi$
$432$		0			0
$433$	14.9276	+	25.8553i	0.717373	+	1.24253i	0.962037	+	0.272919i	$0.0879892\pi$
$433$	14.9276	+	25.8553i	0.717373	+	1.24253i	−0.244664	+	0.969608i	$0.578678\pi$
$434$	14.4768	−	18.1112i	0.694906	−	0.869363i
$435$		0			0
$436$			7.13731i			0.341815i
$437$	8.28935	−	4.78586i	0.396533	−	0.228939i
$438$		0			0
$439$	−6.18523	−	10.7131i	−0.295205	−	0.511310i	0.679827	−	0.733372i	$-0.262055\pi$
$439$	−6.18523	−	10.7131i	−0.295205	−	0.511310i	−0.975033	+	0.222062i	$0.928721\pi$
$440$	5.97101	+	3.44736i	0.284657	+	0.164347i
$441$		0			0
$442$	8.70515	−	14.2141i	0.414062	−	0.676096i
$443$	−16.2819	+	28.2010i	−0.773574	+	1.33987i	0.162018	+	0.986788i	$0.448200\pi$
$443$	−16.2819	+	28.2010i	−0.773574	+	1.33987i	−0.935592	+	0.353082i	$0.885134\pi$
$444$		0			0
$445$	−4.57241			−0.216753
$446$	19.9514			0.944726
$447$		0			0
$448$	−2.61575	−	0.397291i	−0.123583	−	0.0187702i
$449$	8.92105	−	5.15057i	0.421010	−	0.243070i	−0.274499	−	0.961587i	$-0.588512\pi$
$449$	8.92105	−	5.15057i	0.421010	−	0.243070i	0.695509	+	0.718517i	$0.255179\pi$
$450$		0			0
$451$	−25.1959	+	43.6405i	−1.18643	+	2.05495i
$452$	8.80081			0.413955
$453$		0			0
$454$	−23.3804			−1.09730
$455$	3.40888	+	9.42768i	0.159811	+	0.441976i
$456$		0			0
$457$	−15.6594	+	9.04098i	−0.732517	+	0.422919i	−0.819342	−	0.573304i	$-0.805661\pi$
$457$	−15.6594	+	9.04098i	−0.732517	+	0.422919i	0.0868250	+	0.996224i	$0.472328\pi$
$458$	5.40940			0.252764
$459$		0			0
$460$	2.90938	+	1.67973i	0.135650	+	0.0783178i
$461$	3.44357	−	1.98814i	0.160383	−	0.0925971i	−0.417660	−	0.908603i	$-0.637150\pi$
$461$	3.44357	−	1.98814i	0.160383	−	0.0925971i	0.578043	+	0.816006i	$0.303816\pi$
$462$		0			0
$463$		−	9.46729i		−	0.439982i	−0.975502	−	0.219991i	$-0.929397\pi$
$463$		−	9.46729i		−	0.439982i	0.975502	−	0.219991i	$-0.0706029\pi$
$464$	−2.24763			−0.104343
$465$		0			0
$466$		−	21.4143i		−	0.991997i
$467$	−5.16932	+	8.95352i	−0.239208	+	0.414320i	−0.960487	−	0.278324i	$-0.910221\pi$
$467$	−5.16932	+	8.95352i	−0.239208	+	0.414320i	0.721280	+	0.692644i	$0.243554\pi$
$468$		0			0
$469$	3.56923	−	23.4997i	0.164812	−	1.08512i
$470$	−9.47582	−	5.47087i	−0.437087	−	0.252352i
$471$		0			0
$472$	1.24996	−	2.16500i	0.0575341	−	0.0996520i
$473$	7.91155	−	4.56774i	0.363774	−	0.210025i
$474$		0			0
$475$	10.1016	−	5.83215i	0.463492	−	0.267597i
$476$	4.45556	+	11.3905i	0.204220	+	0.522083i
$477$		0			0
$478$	4.40190	+	7.62431i	0.201338	+	0.348728i
$479$		−	27.8712i		−	1.27347i	−0.771083	−	0.636735i	$-0.780285\pi$
$479$		−	27.8712i		−	1.27347i	0.771083	−	0.636735i	$-0.219715\pi$
$480$		0			0
$481$	16.7369	+	0.433770i	0.763139	+	0.0197782i
$482$	13.4416			0.612250
$483$		0			0
$484$	−16.0215	+	27.7501i	−0.728251	+	1.26137i
$485$	−7.07583			−0.321297
$486$		0			0
$487$	12.4031	+	7.16092i	0.562037	+	0.324492i	0.753963	−	0.656917i	$-0.228140\pi$
$487$	12.4031	+	7.16092i	0.562037	+	0.324492i	−0.191926	+	0.981409i	$0.561473\pi$
$488$			9.90929i			0.448572i
$489$		0			0
$490$	−7.02462	−	2.18424i	−0.317340	−	0.0986741i
$491$	−3.52525	+	6.10592i	−0.159093	+	0.275556i	−0.934542	−	0.355854i	$-0.884190\pi$
$491$	−3.52525	+	6.10592i	−0.159093	+	0.275556i	0.775449	+	0.631410i	$0.217523\pi$
$492$		0			0
$493$	5.19522	+	8.99839i	0.233981	+	0.405267i
$494$	0.279701	−	10.7922i	0.0125844	−	0.485566i
$495$		0			0
$496$	−7.58940	−	4.38174i	−0.340774	−	0.196746i
$497$	−20.2894	+	7.93649i	−0.910103	+	0.356000i
$498$		0			0
$499$	32.3050	+	18.6513i	1.44617	+	0.834947i	0.998250	−	0.0591270i	$-0.0188317\pi$
$499$	32.3050	+	18.6513i	1.44617	+	0.834947i	0.447920	+	0.894074i	$0.352165\pi$
$500$	8.09601	+	4.67423i	0.362064	+	0.209038i
$501$		0			0
$502$	3.75000	+	2.16506i	0.167371	+	0.0966316i
$503$	1.61562	+	2.79834i	0.0720370	+	0.124772i	0.899794	−	0.436315i	$-0.143717\pi$
$503$	1.61562	+	2.79834i	0.0720370	+	0.124772i	−0.827757	+	0.561087i	$0.810383\pi$
$504$		0			0
$505$	−6.50777	−	3.75726i	−0.289592	−	0.167196i
$506$	−10.4864	+	18.1629i	−0.466176	+	0.807441i
$507$		0			0
$508$	−10.2765	−	17.7995i	−0.455948	−	0.789724i
$509$	−33.6874	+	19.4494i	−1.49317	+	0.862080i	−0.999969	−	0.00783837i	$-0.997505\pi$
$509$	−33.6874	+	19.4494i	−1.49317	+	0.862080i	−0.493196	+	0.869918i	$0.664172\pi$
$510$		0			0
$511$	23.2818	−	9.10700i	1.02992	−	0.402870i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	2.20516	+	1.27315i	0.0972655	+	0.0561562i
$515$	−0.623584	+	0.360026i	−0.0274784	+	0.0158647i
$516$		0			0
$517$	34.1540	−	59.1565i	1.50209	−	2.60170i
$518$	−7.67087	+	9.59666i	−0.337039	+	0.421653i
$519$		0			0
$520$	3.32945	−	1.80890i	0.146006	−	0.0793256i
$521$	1.54776	+	2.68079i	0.0678085	+	0.117448i	0.897936	−	0.440125i	$-0.145066\pi$
$521$	1.54776	+	2.68079i	0.0678085	+	0.117448i	−0.830128	+	0.557573i	$0.811733\pi$
$522$		0			0
$523$	12.0472	+	20.8664i	0.526789	+	0.912425i	0.999513	+	0.0312143i	$0.00993744\pi$
$523$	12.0472	+	20.8664i	0.526789	+	0.912425i	−0.472724	+	0.881211i	$0.656729\pi$
$524$	5.07036	+	8.78212i	0.221500	+	0.383649i
$525$		0			0
$526$	−6.06851	+	3.50366i	−0.264600	+	0.152767i
$527$			40.5123i			1.76474i
$528$		0			0
$529$	6.39051	−	11.0687i	0.277848	−	0.481247i
$530$	3.57591	+	6.19366i	0.155328	+	0.269036i
$531$		0			0
$532$	6.18807	+	4.94630i	0.268287	+	0.214449i
$533$	13.2208	+	24.3341i	0.572656	+	1.05402i
$534$		0			0
$535$		−	5.18884i		−	0.224333i
$536$	−8.98392			−0.388046
$537$		0			0
$538$			1.40223i			0.0604546i
$539$	13.6360	−	43.8539i	0.587344	−	1.88892i
$540$		0			0
$541$	−15.0491	−	8.68860i	−0.647011	−	0.373552i	0.140299	−	0.990109i	$-0.455194\pi$
$541$	−15.0491	−	8.68860i	−0.647011	−	0.373552i	−0.787310	+	0.616557i	$0.788527\pi$
$542$	0.263249	−	0.455960i	0.0113075	−	0.0195851i
$543$		0			0
$544$	4.00351	−	2.31143i	0.171649	−	0.0991016i
$545$	7.50067			0.321293
$546$		0			0
$547$	35.1878			1.50452			0.752262	−	0.658865i	$-0.228963\pi$
$547$	35.1878			1.50452			0.752262	+	0.658865i	$0.228963\pi$
$548$	11.3641	−	6.56106i	0.485450	−	0.280275i
$549$		0			0
$550$	−12.7789	+	22.1338i	−0.544895	+	0.943787i
$551$	5.82828	+	3.36496i	0.248293	+	0.143352i
$552$		0			0
$553$	5.45508	−	6.82459i	0.231974	−	0.290211i
$554$		−	32.7144i		−	1.38990i
$555$		0			0
$556$	−9.64711			−0.409129
$557$		−	28.2088i		−	1.19524i	−0.801778	−	0.597622i	$-0.796112\pi$
$557$		−	28.2088i		−	1.19524i	0.801778	−	0.597622i	$-0.203888\pi$
$558$		0			0
$559$	0.130073	−	5.01886i	0.00550152	−	0.212275i
$560$	−0.417517	+	2.74892i	−0.0176433	+	0.116163i
$561$		0			0
$562$	−11.3418	−	19.6445i	−0.478424	−	0.828655i
$563$	18.8177	−	32.5932i	0.793072	−	1.37364i	−0.130984	−	0.991384i	$-0.541814\pi$
$563$	18.8177	−	32.5932i	0.793072	−	1.37364i	0.924056	−	0.382257i	$-0.124853\pi$
$564$		0			0
$565$		−	9.24886i		−	0.389103i
$566$	4.74981	−	2.74231i	0.199649	−	0.115268i
$567$		0			0
$568$	4.11724	+	7.13127i	0.172756	+	0.299222i
$569$	−14.5293	−	25.1655i	−0.609100	−	1.05499i	−0.991389	−	0.130950i	$-0.958197\pi$
$569$	−14.5293	−	25.1655i	−0.609100	−	1.05499i	0.382289	−	0.924043i	$-0.375136\pi$
$570$		0			0
$571$	−2.09456	−	3.62788i	−0.0876546	−	0.151822i	0.818865	−	0.573987i	$-0.194604\pi$
$571$	−2.09456	−	3.62788i	−0.0876546	−	0.151822i	−0.906519	+	0.422164i	$0.861271\pi$
$572$	11.2928	+	20.7854i	0.472175	+	0.869081i
$573$		0			0
$574$	−20.0911	−	3.05152i	−0.838587	−	0.127368i
$575$	−6.22654	+	10.7847i	−0.259665	+	0.449753i
$576$		0			0
$577$	−32.9451	+	19.0209i	−1.37152	+	0.791848i	−0.991120	−	0.132973i	$-0.957548\pi$
$577$	−32.9451	+	19.0209i	−1.37152	+	0.791848i	−0.380402	+	0.924821i	$0.624214\pi$
$578$	−3.78521	−	2.18539i	−0.157444	−	0.0909004i
$579$		0			0
$580$			2.36205i			0.0980789i
$581$	3.89088	−	25.6174i	0.161421	−	1.06279i
$582$		0			0
$583$	−38.6664	+	22.3240i	−1.60140	+	0.924567i
$584$	−4.72447	−	8.18302i	−0.195500	−	0.338616i
$585$		0			0
$586$	6.67449	−	11.5606i	0.275721	−	0.477562i
$587$	−16.5253	−	9.54089i	−0.682073	−	0.393795i	0.118563	−	0.992947i	$-0.462171\pi$
$587$	−16.5253	−	9.54089i	−0.682073	−	0.393795i	−0.800635	+	0.599152i	$0.795505\pi$
$588$		0			0
$589$	13.1200	+	22.7244i	0.540599	+	0.936344i
$590$	−2.27522	−	1.31360i	−0.0936691	−	0.0540799i
$591$		0			0
$592$	4.02143	+	2.32178i	0.165280	+	0.0954244i
$593$	−41.9869	−	24.2412i	−1.72420	−	0.995466i	−0.909659	−	0.415356i	$-0.863657\pi$
$593$	−41.9869	−	24.2412i	−1.72420	−	0.995466i	−0.814538	−	0.580110i	$-0.803010\pi$
$594$		0			0
$595$	11.9704	−	4.68240i	0.490738	−	0.191960i
$596$	16.0390	+	9.26015i	0.656985	+	0.379310i
$597$		0			0
$598$	5.50242	+	10.1277i	0.225011	+	0.414152i
$599$	4.69140	+	8.12575i	0.191686	+	0.332009i	0.945809	−	0.324724i	$-0.105271\pi$
$599$	4.69140	+	8.12575i	0.191686	+	0.332009i	−0.754123	+	0.656733i	$0.771938\pi$
$600$		0			0
$601$	1.92984	−	3.34259i	0.0787200	−	0.136347i	−0.823978	−	0.566622i	$-0.808250\pi$
$601$	1.92984	−	3.34259i	0.0787200	−	0.136347i	0.902698	+	0.430275i	$0.141583\pi$
$602$	2.87772	+	2.30024i	0.117287	+	0.0937509i
$603$		0			0
$604$			5.85581i			0.238270i
$605$	29.1629	+	16.8372i	1.18564	+	0.684529i
$606$		0			0
$607$	−2.14815			−0.0871907			−0.0435953	−	0.999049i	$-0.513881\pi$
$607$	−2.14815			−0.0871907			−0.0435953	+	0.999049i	$0.513881\pi$
$608$	1.49712	−	2.59308i	0.0607161	−	0.105163i
$609$		0			0
$610$	10.4138			0.421641
$611$	−17.9213	−	32.9858i	−0.725019	−	1.33446i
$612$		0			0
$613$		−	41.6192i		−	1.68099i	−0.541823	−	0.840493i	$-0.682266\pi$
$613$		−	41.6192i		−	1.68099i	0.541823	−	0.840493i	$-0.317734\pi$
$614$	8.20851	+	14.2176i	0.331269	+	0.573774i
$615$		0			0
$616$	−17.1612	−	2.60652i	−0.691445	−	0.105020i
$617$	−6.91756	+	3.99385i	−0.278490	+	0.160786i	−0.632740	−	0.774364i	$-0.718070\pi$
$617$	−6.91756	+	3.99385i	−0.278490	+	0.160786i	0.354249	+	0.935151i	$0.384736\pi$
$618$		0			0
$619$	−20.7319	+	11.9696i	−0.833285	+	0.481098i	−0.854976	−	0.518667i	$-0.826428\pi$
$619$	−20.7319	+	11.9696i	−0.833285	+	0.481098i	0.0216909	+	0.999765i	$0.493095\pi$
$620$	−4.60482	+	7.97578i	−0.184934	+	0.320315i
$621$		0			0
$622$	21.4936	+	12.4093i	0.861815	+	0.497569i
$623$	10.7204	−	4.19345i	0.429505	−	0.168007i
$624$		0			0
$625$	−4.82677	+	8.36021i	−0.193071	+	0.334408i
$626$			22.5101i			0.899686i
$627$		0			0
$628$	−15.8464			−0.632341
$629$		−	21.4665i		−	0.855924i
$630$		0			0
$631$	−30.4945	+	17.6060i	−1.21397	+	0.700885i	−0.963621	−	0.267271i	$-0.913878\pi$
$631$	−30.4945	+	17.6060i	−1.21397	+	0.700885i	−0.250347	+	0.968156i	$0.580545\pi$
$632$	−2.85981	−	1.65111i	−0.113757	−	0.0656778i
$633$		0			0
$634$	18.5648			0.737301
$635$	−18.7057	+	10.7997i	−0.742311	+	0.428574i
$636$		0			0
$637$	−16.6387	−	18.9777i	−0.659251	−	0.751923i
$638$	−14.7460			−0.583801
$639$		0			0
$640$	1.05091			0.0415409
$641$	−10.4211	+	18.0498i	−0.411608	+	0.712926i	−0.995066	−	0.0992178i	$-0.968366\pi$
$641$	−10.4211	+	18.0498i	−0.411608	+	0.712926i	0.583458	+	0.812143i	$0.301699\pi$
$642$		0			0
$643$	−7.74134	+	4.46946i	−0.305289	+	0.176258i	−0.644816	−	0.764338i	$-0.723066\pi$
$643$	−7.74134	+	4.46946i	−0.305289	+	0.176258i	0.339528	+	0.940596i	$0.389733\pi$
$644$	−8.36182	−	1.27003i	−0.329502	−	0.0500461i
$645$		0			0
$646$	−13.8419			−0.544603
$647$	−23.9738			−0.942508			−0.471254	−	0.881997i	$-0.656199\pi$
$647$	−23.9738			−0.942508			−0.471254	+	0.881997i	$0.656199\pi$
$648$		0			0
$649$	8.20064	−	14.2039i	0.321903	−	0.557553i
$650$	6.70537	+	12.3418i	0.263006	+	0.484087i
$651$		0			0
$652$	−5.33166	−	3.07824i	−0.208804	−	0.120553i
$653$	−4.14381	−	7.17729i	−0.162160	−	0.280869i	0.773483	−	0.633817i	$-0.218513\pi$
$653$	−4.14381	−	7.17729i	−0.162160	−	0.280869i	−0.935643	+	0.352948i	$0.885179\pi$
$654$		0			0
$655$	9.22922	−	5.32849i	0.360615	−	0.208201i
$656$			7.68082i			0.299886i
$657$		0			0
$658$	27.2344	+	4.13647i	1.06171	+	0.161256i
$659$	−22.9958	−	39.8298i	−0.895788	−	1.55155i	−0.832827	−	0.553534i	$-0.813279\pi$
$659$	−22.9958	−	39.8298i	−0.895788	−	1.55155i	−0.0629613	−	0.998016i	$-0.520054\pi$
$660$		0			0
$661$			0.691835i			0.0269093i	0.999909	+	0.0134546i	$0.00428287\pi$
$661$			0.691835i			0.0269093i	−0.999909	+	0.0134546i	$0.995717\pi$
$662$	−4.20451	−	7.28243i	−0.163413	−	0.283040i
$663$		0			0
$664$	−9.79351			−0.380062
$665$	5.19812	−	6.50311i	0.201574	−	0.252180i
$666$		0			0
$667$	−7.18502			−0.278205
$668$	6.82652	−	3.94129i	0.264126	−	0.152493i
$669$		0			0
$670$			9.44130i			0.364749i
$671$			65.0121i			2.50976i
$672$		0			0
$673$	8.59837	−	14.8928i	0.331443	−	0.574076i	−0.651352	−	0.758776i	$-0.725798\pi$
$673$	8.59837	−	14.8928i	0.331443	−	0.574076i	0.982795	+	0.184700i	$0.0591313\pi$
$674$	4.15725	−	2.40019i	0.160131	−	0.0924518i
$675$		0			0
$676$	12.9825	+	0.673387i	0.499329	+	0.0258995i
$677$	5.97634	−	10.3513i	0.229689	−	0.397834i	−0.728027	−	0.685549i	$-0.759562\pi$
$677$	5.97634	−	10.3513i	0.229689	−	0.397834i	0.957716	+	0.287715i	$0.0928957\pi$
$678$		0			0
$679$	16.5899	−	6.48939i	0.636662	−	0.249040i
$680$	−2.42910	−	4.20733i	−0.0931518	−	0.161344i
$681$		0			0
$682$	−49.7919	−	28.7474i	−1.90663	−	1.10079i
$683$	17.0585	+	9.84872i	0.652725	+	0.376851i	0.789499	−	0.613751i	$-0.210340\pi$
$683$	17.0585	+	9.84872i	0.652725	+	0.376851i	−0.136775	+	0.990602i	$0.543674\pi$
$684$		0			0
$685$	−6.89509	−	11.9426i	−0.263448	−	0.456305i
$686$	18.4731	−	1.32127i	0.705305	−	0.0504462i
$687$		0			0
$688$	0.696225	−	1.20590i	0.0265433	−	0.0459744i
$689$	−0.635711	+	24.5289i	−0.0242187	+	0.934475i
$690$		0			0
$691$	−19.1933	+	11.0812i	−0.730147	+	0.421551i	−0.818476	−	0.574541i	$-0.805181\pi$
$691$	−19.1933	+	11.0812i	−0.730147	+	0.421551i	0.0883289	+	0.996091i	$0.471847\pi$
$692$	0.363182	−	0.629049i	0.0138061	−	0.0239129i
$693$		0			0
$694$		−	3.34793i		−	0.127086i
$695$			10.1382i			0.384566i
$696$		0			0
$697$	30.7502	−	17.7537i	1.16475	−	0.672468i
$698$	14.2330			0.538727
$699$		0			0
$700$	−10.1899	−	1.54768i	−0.385142	−	0.0584969i
$701$	45.6839			1.72546			0.862728	−	0.505668i	$-0.168754\pi$
$701$	45.6839			1.72546			0.862728	+	0.505668i	$0.168754\pi$
$702$		0			0
$703$	−6.95194	−	12.0411i	−0.262198	−	0.454139i
$704$			6.56072i			0.247266i
$705$		0			0
$706$	14.6041	+	25.2951i	0.549634	+	0.951994i
$707$	18.7039	+	2.84083i	0.703433	+	0.106840i
$708$		0			0
$709$			22.1597i			0.832224i	0.909313	+	0.416112i	$0.136608\pi$
$709$			22.1597i			0.832224i	−0.909313	+	0.416112i	$0.863392\pi$
$710$	7.49433	−	4.32685i	0.281257	−	0.162384i
$711$		0			0
$712$	−2.17545	−	3.76799i	−0.0815285	−	0.141212i
$713$	−24.2611	−	14.0072i	−0.908587	−	0.524573i
$714$		0			0
$715$	21.8436	−	11.8677i	0.816904	−	0.443827i
$716$	8.55545	−	14.8185i	0.319732	−	0.553792i
$717$		0			0
$718$	−25.7403			−0.960621
$719$	6.75191			0.251804			0.125902	−	0.992043i	$-0.459818\pi$
$719$	6.75191			0.251804			0.125902	+	0.992043i	$0.459818\pi$
$720$		0			0
$721$	1.13186	−	1.41602i	0.0421527	−	0.0527352i
$722$	8.69018	−	5.01728i	0.323415	−	0.186724i
$723$		0			0
$724$	7.87270	−	13.6359i	0.292587	−	0.506775i
$725$	−8.75582			−0.325183
$726$		0			0
$727$	1.00891			0.0374184			0.0187092	−	0.999825i	$-0.494044\pi$
$727$	1.00891			0.0374184			0.0187092	+	0.999825i	$0.494044\pi$
$728$	−6.14721	+	7.29464i	−0.227831	+	0.270357i
$729$		0			0
$730$	−8.59962	+	4.96499i	−0.318286	+	0.183763i
$731$	−6.43709			−0.238084
$732$		0			0
$733$	−26.2879	−	15.1773i	−0.970965	−	0.560587i	−0.0714349	−	0.997445i	$-0.522758\pi$
$733$	−26.2879	−	15.1773i	−0.970965	−	0.560587i	−0.899530	+	0.436858i	$0.856091\pi$
$734$	16.9235	−	9.77078i	0.624657	−	0.360646i
$735$		0			0
$736$			3.19672i			0.117832i
$737$	−58.9410			−2.17112
$738$		0			0
$739$		−	14.1058i		−	0.518890i	−0.965758	−	0.259445i	$-0.916460\pi$
$739$		−	14.1058i		−	0.518890i	0.965758	−	0.259445i	$-0.0835397\pi$
$740$	2.43998	−	4.22617i	0.0896954	−	0.155357i
$741$		0			0
$742$	−14.0644	−	11.2421i	−0.516320	−	0.412709i
$743$	−10.5028	−	6.06381i	−0.385311	−	0.222459i	0.294815	−	0.955554i	$-0.404742\pi$
$743$	−10.5028	−	6.06381i	−0.385311	−	0.222459i	−0.680127	+	0.733095i	$0.738075\pi$
$744$		0			0
$745$	9.73158	−	16.8556i	0.356538	−	0.617541i
$746$	−16.4921	+	9.52174i	−0.603820	+	0.348616i
$747$		0			0
$748$	26.2659	−	15.1646i	0.960377	−	0.554474i
$749$	4.75879	+	12.1657i	0.173882	+	0.444525i
$750$		0			0
$751$	−12.4488	−	21.5619i	−0.454263	−	0.786807i	0.544383	−	0.838837i	$-0.316764\pi$
$751$	−12.4488	−	21.5619i	−0.454263	−	0.786807i	−0.998645	+	0.0520306i	$0.983431\pi$
$752$		−	10.4117i		−	0.379675i
$753$		0			0
$754$	−4.23243	+	6.91087i	−0.154136	+	0.251679i
$755$	6.15394			0.223965
$756$		0			0
$757$	17.0830	−	29.5886i	0.620892	−	1.07542i	−0.368428	−	0.929656i	$-0.620104\pi$
$757$	17.0830	−	29.5886i	0.620892	−	1.07542i	0.989320	−	0.145760i	$-0.0465627\pi$
$758$	−27.4903			−0.998492
$759$		0			0
$760$	−2.72510	−	1.57334i	−0.0988497	−	0.0570709i
$761$		−	10.7480i		−	0.389614i	−0.980842	−	0.194807i	$-0.937592\pi$
$761$		−	10.7480i		−	0.389614i	0.980842	−	0.194807i	$-0.0624080\pi$
$762$		0			0
$763$	−17.5860	+	6.87902i	−0.636656	+	0.249037i
$764$	9.63307	−	16.6850i	0.348512	−	0.603641i
$765$		0			0
$766$	5.08286	+	8.80377i	0.183651	+	0.318093i
$767$	−4.30304	−	7.92014i	−0.155374	−	0.285980i
$768$		0			0
$769$	−42.3478	−	24.4495i	−1.52710	−	0.881673i	−0.999482	−	0.0321920i	$-0.989751\pi$
$769$	−42.3478	−	24.4495i	−1.52710	−	0.881673i	−0.527620	−	0.849481i	$-0.676915\pi$
$770$	−2.73922	+	18.0349i	−0.0987145	+	0.649933i
$771$		0			0
$772$	13.9041	+	8.02752i	0.500419	+	0.288917i
$773$	−9.59631	−	5.54043i	−0.345155	−	0.199275i	0.317394	−	0.948294i	$-0.397192\pi$
$773$	−9.59631	−	5.54043i	−0.345155	−	0.199275i	−0.662549	+	0.749018i	$0.730526\pi$
$774$		0			0
$775$	−29.5652	−	17.0695i	−1.06201	−	0.613153i
$776$	−3.36652	−	5.83099i	−0.120851	−	0.209320i
$777$		0			0
$778$	−20.1184	−	11.6154i	−0.721279	−	0.416431i
$779$	11.4991	−	19.9170i	0.411998	−	0.713601i
$780$		0			0
$781$	27.0121	+	46.7863i	0.966568	+	1.67415i
$782$	12.7981	−	7.38898i	0.457658	−	0.264229i
$783$		0			0
$784$	−1.54219	−	6.82801i	−0.0550781	−	0.243857i
$785$			16.6532i			0.594377i
$786$		0			0
$787$	43.6547	+	25.2041i	1.55612	+	0.898428i	0.997622	+	0.0689247i	$0.0219568\pi$
$787$	43.6547	+	25.2041i	1.55612	+	0.898428i	0.558502	+	0.829504i	$0.311376\pi$
$788$	12.4157	−	7.16821i	0.442291	−	0.255357i
$789$		0			0
$790$	−1.73517	+	3.00541i	−0.0617347	+	0.106928i
$791$	8.48233	+	21.6848i	0.301597	+	0.771022i
$792$		0			0
$793$	30.4685	+	18.6599i	1.08197	+	0.662631i
$794$	−17.0773	−	29.5787i	−0.606049	−	1.04971i
$795$		0			0
$796$	7.95650	+	13.7811i	0.282011	+	0.488457i
$797$	−3.24783	−	5.62541i	−0.115044	−	0.199262i	0.802753	−	0.596311i	$-0.203368\pi$
$797$	−3.24783	−	5.62541i	−0.115044	−	0.199262i	−0.917797	+	0.397049i	$0.870034\pi$
$798$		0			0
$799$	−41.6832	+	24.0658i	−1.47465	+	0.851388i
$800$			3.89559i			0.137730i
$801$		0			0
$802$	15.7114	−	27.2130i	0.554789	−	0.960923i
$803$	−30.9959	−	53.6865i	−1.09382	−	1.89456i
$804$		0			0
$805$	−1.33468	+	8.78752i	−0.0470415	+	0.309719i
$806$	−27.7641	+	15.0843i	−0.977948	+	0.531323i
$807$		0			0
$808$		−	7.15050i		−	0.251554i
$809$	18.0493			0.634579			0.317289	−	0.948329i	$-0.397227\pi$
$809$	18.0493			0.634579			0.317289	+	0.948329i	$0.397227\pi$
$810$		0			0
$811$			47.3832i			1.66385i	0.554889	+	0.831924i	$0.312761\pi$
$811$			47.3832i			1.66385i	−0.554889	+	0.831924i	$0.687239\pi$
$812$	−2.16629	−	5.53805i	−0.0760218	−	0.194347i
$813$		0			0
$814$	26.3835	+	15.2325i	0.924742	+	0.533900i
$815$	−3.23495	+	5.60310i	−0.113315	+	0.196268i
$816$		0			0
$817$	−3.61074	+	2.08466i	−0.126324	+	0.0729330i
$818$	−1.84680			−0.0645718
$819$		0			0
$820$	8.07185			0.281881
$821$	5.86148	−	3.38413i	0.204567	−	0.118107i	−0.394217	−	0.919017i	$-0.628984\pi$
$821$	5.86148	−	3.38413i	0.204567	−	0.118107i	0.598784	+	0.800911i	$0.295651\pi$
$822$		0			0
$823$	14.1503	−	24.5090i	0.493247	−	0.854329i	−0.506723	−	0.862109i	$-0.669143\pi$
$823$	14.1503	−	24.5090i	0.493247	−	0.854329i	0.999970	+	0.00778027i	$0.00247656\pi$
$824$	−0.593375	−	0.342585i	−0.0206712	−	0.0119345i
$825$		0			0
$826$	6.53917	+	0.993197i	0.227527	+	0.0345577i
$827$		−	18.4833i		−	0.642726i	−0.946956	−	0.321363i	$-0.895859\pi$
$827$		−	18.4833i		−	0.642726i	0.946956	−	0.321363i	$-0.104141\pi$
$828$		0			0
$829$	2.76426			0.0960068			0.0480034	−	0.998847i	$-0.484714\pi$
$829$	2.76426			0.0960068			0.0480034	+	0.998847i	$0.484714\pi$
$830$			10.2921i			0.357244i
$831$		0			0
$832$	3.07474	+	1.88307i	0.106598	+	0.0652837i
$833$	−23.7713	+	21.9566i	−0.823628	+	0.760751i
$834$		0			0
$835$	−4.14194	−	7.17406i	−0.143338	−	0.248269i
$836$	9.82217	−	17.0125i	0.339707	−	0.588389i
$837$		0			0
$838$			29.0782i			1.00449i
$839$	−28.1152	+	16.2323i	−0.970646	+	0.560403i	−0.899433	−	0.437058i	$-0.856020\pi$
$839$	−28.1152	+	16.2323i	−0.970646	+	0.560403i	−0.0712130	+	0.997461i	$0.522687\pi$
$840$		0			0
$841$	11.9741	+	20.7397i	0.412900	+	0.715163i
$842$	5.02980	+	8.71187i	0.173338	+	0.300231i
$843$		0			0
$844$	10.0909	+	17.4780i	0.347344	+	0.601617i
$845$	0.707669	−	13.6435i	0.0243446	−	0.469350i
$846$		0			0
$847$	−83.8167	−	12.7304i	−2.87998	−	0.437423i
$848$	−3.40268	+	5.89362i	−0.116849	+	0.202388i
$849$		0			0
$850$	15.5960	−	9.00437i	0.534939	−	0.308847i
$851$	12.8554	+	7.42206i	0.440677	+	0.254425i
$852$		0			0
$853$		−	10.6429i		−	0.364404i	−0.983261	−	0.182202i	$-0.941677\pi$
$853$		−	10.6429i		−	0.364404i	0.983261	−	0.182202i	$-0.0583225\pi$
$854$	−24.4160	+	9.55069i	−0.835499	+	0.326818i
$855$		0			0
$856$	4.27597	−	2.46873i	0.146150	−	0.0843796i
$857$	18.2812	+	31.6639i	0.624473	+	1.08162i	0.988642	+	0.150287i	$0.0480197\pi$
$857$	18.2812	+	31.6639i	0.624473	+	1.08162i	−0.364169	+	0.931333i	$0.618647\pi$
$858$		0			0
$859$	1.98873	−	3.44459i	0.0678547	−	0.117528i	−0.830102	−	0.557612i	$-0.811718\pi$
$859$	1.98873	−	3.44459i	0.0678547	−	0.117528i	0.897957	+	0.440084i	$0.145051\pi$
$860$	−1.26729	−	0.731670i	−0.0432142	−	0.0249497i
$861$		0			0
$862$	−7.82448	−	13.5524i	−0.266503	−	0.461596i
$863$	−31.8449	−	18.3857i	−1.08401	−	0.625855i	−0.152037	−	0.988375i	$-0.548583\pi$
$863$	−31.8449	−	18.3857i	−1.08401	−	0.625855i	−0.931976	+	0.362520i	$0.881917\pi$
$864$		0			0
$865$	−0.661074	−	0.381671i	−0.0224772	−	0.0129772i
$866$	25.8553	+	14.9276i	0.878599	+	0.507260i
$867$		0			0
$868$	3.48166	−	22.9231i	0.118175	−	0.778061i
$869$	−18.7624	−	10.8325i	−0.636472	−	0.367467i
$870$		0			0
$871$	−16.9173	+	27.6233i	−0.573222	+	0.935979i
$872$	3.56865	+	6.18109i	0.120850	+	0.209318i
$873$		0			0
$874$	4.78586	−	8.28935i	0.161884	−	0.280391i
$875$	−3.71406	+	24.4533i	−0.125558	+	0.826671i
$876$		0			0
$877$			56.7616i			1.91670i	0.285590	+	0.958352i	$0.407810\pi$
$877$			56.7616i			1.91670i	−0.285590	+	0.958352i	$0.592190\pi$
$878$	−10.7131	−	6.18523i	−0.361551	−	0.208742i
$879$		0			0
$880$	6.89473			0.232421
$881$	12.8086	−	22.1851i	0.431532	−	0.747435i	−0.565474	−	0.824766i	$-0.691307\pi$
$881$	12.8086	−	22.1851i	0.431532	−	0.747435i	0.997005	+	0.0773317i	$0.0246400\pi$
$882$		0			0
$883$	15.7725			0.530785			0.265393	−	0.964140i	$-0.414498\pi$
$883$	15.7725			0.530785			0.265393	+	0.964140i	$0.414498\pi$
$884$	0.431836	−	16.6623i	0.0145242	−	0.560415i
$885$		0			0
$886$			32.5637i			1.09400i
$887$	−2.85218	−	4.94012i	−0.0957667	−	0.165873i	0.814162	−	0.580638i	$-0.197197\pi$
$887$	−2.85218	−	4.94012i	−0.0957667	−	0.165873i	−0.909928	+	0.414765i	$0.863864\pi$
$888$		0			0
$889$	33.9525	−	42.4763i	1.13873	−	1.42461i
$890$	−3.95982	+	2.28620i	−0.132734	+	0.0766338i
$891$		0			0
$892$	17.2784	−	9.97570i	0.578524	−	0.334011i
$893$	−15.5875	+	26.9983i	−0.521616	+	0.903465i
$894$		0			0
$895$	−15.5729	−	8.99101i	−0.520544	−	0.300536i
$896$	−2.46395	+	0.963812i	−0.0823149	+	0.0321987i
$897$		0			0
$898$	5.15057	−	8.92105i	0.171877	−	0.297699i
$899$		−	19.6970i		−	0.656933i
$900$		0			0
$901$	31.4602			1.04809
$902$			50.3917i			1.67786i
$903$		0			0
$904$	7.62173	−	4.40041i	0.253495	−	0.146355i
$905$	−14.3301	−	8.27350i	−0.476349	−	0.275020i
$906$		0			0
$907$	−12.9554			−0.430178			−0.215089	−	0.976594i	$-0.569004\pi$
$907$	−12.9554			−0.430178			−0.215089	+	0.976594i	$0.569004\pi$
$908$	−20.2480	+	11.6902i	−0.671954	+	0.387953i
$909$		0			0
$910$	7.66601	+	6.46017i	0.254126	+	0.214152i
$911$	23.0999			0.765334			0.382667	−	0.923886i	$-0.375006\pi$
$911$	23.0999			0.765334			0.382667	+	0.923886i	$0.375006\pi$
$912$		0			0
$913$	−64.2525			−2.12645
$914$	−9.04098	+	15.6594i	−0.299049	+	0.517968i
$915$		0			0
$916$	4.68467	−	2.70470i	0.154786	−	0.0893657i
$917$	−16.7519	+	20.9574i	−0.553195	+	0.692076i
$918$		0			0
$919$	−34.1883			−1.12777			−0.563883	−	0.825854i	$-0.690693\pi$
$919$	−34.1883			−1.12777			−0.563883	+	0.825854i	$0.690693\pi$
$920$	3.35946			0.110758
$921$		0			0
$922$	1.98814	−	3.44357i	0.0654760	−	0.113408i
$923$	29.6799	+	0.769210i	0.976926	+	0.0253189i
$924$		0			0
$925$	15.6659	+	9.04468i	0.515090	+	0.297387i
$926$	−4.73365	−	8.19892i	−0.155557	−	0.269433i
$927$		0			0
$928$	−1.94650	+	1.12381i	−0.0638970	+	0.0368910i
$929$			33.4666i			1.09800i	0.835822	+	0.549001i	$0.184992\pi$
$929$			33.4666i			1.09800i	−0.835822	+	0.549001i	$0.815008\pi$
$930$		0			0
$931$	−6.22331	+	20.0144i	−0.203961	+	0.655946i
$932$	−10.7071	−	18.5453i	−0.350724	−	0.607472i
$933$		0			0
$934$			10.3386i			0.338291i
$935$	−15.9367	−	27.6031i	−0.521185	−	0.902718i
$936$		0			0
$937$	4.42393			0.144523			0.0722617	−	0.997386i	$-0.476978\pi$
$937$	4.42393			0.144523			0.0722617	+	0.997386i	$0.476978\pi$
$938$	−8.65881	−	22.1360i	−0.282720	−	0.722765i
$939$		0			0
$940$	−10.9417			−0.356880
$941$	−9.59182	+	5.53784i	−0.312684	+	0.180528i	−0.648127	−	0.761532i	$-0.724447\pi$
$941$	−9.59182	+	5.53784i	−0.312684	+	0.180528i	0.335443	+	0.942061i	$0.391114\pi$
$942$		0			0
$943$			24.5534i			0.799569i
$944$		−	2.49992i		−	0.0813655i
$945$		0			0
$946$	4.56774	−	7.91155i	0.148510	−	0.257227i
$947$	−25.8388	+	14.9180i	−0.839648	+	0.484771i	−0.857145	−	0.515076i	$-0.827764\pi$
$947$	−25.8388	+	14.9180i	−0.839648	+	0.484771i	0.0174964	+	0.999847i	$0.494430\pi$
$948$		0			0
$949$	−34.0572	−	0.882657i	−1.10554	−	0.0286523i
$950$	5.83215	−	10.1016i	0.189220	−	0.327739i
$951$		0			0
$952$	9.55388	+	7.63668i	0.309643	+	0.247506i
$953$	−9.34420	−	16.1846i	−0.302688	−	0.524272i	0.674056	−	0.738681i	$-0.264551\pi$
$953$	−9.34420	−	16.1846i	−0.302688	−	0.524272i	−0.976744	+	0.214409i	$0.931217\pi$
$954$		0			0
$955$	−17.5344	−	10.1235i	−0.567400	−	0.327588i
$956$	7.62431	+	4.40190i	0.246588	+	0.142368i
$957$		0			0
$958$	−13.9356	−	24.1372i	−0.450239	−	0.779837i
$959$	27.1190	+	21.6770i	0.875718	+	0.699986i
$960$		0			0
$961$	22.8993	−	39.6628i	0.738688	−	1.27944i
$962$	14.7115	−	7.99282i	0.474318	−	0.257699i
$963$		0			0
$964$	11.6408	−	6.72082i	0.374925	−	0.216463i
$965$	8.43621	−	14.6119i	0.271571	−	0.470375i
$966$		0			0
$967$		−	0.591853i		−	0.0190327i	−0.999955	−	0.00951636i	$-0.996971\pi$
$967$		−	0.591853i		−	0.0190327i	0.999955	−	0.00951636i	$-0.00302920\pi$
$968$			32.0430i			1.02990i
$969$		0			0
$970$	−6.12785	+	3.53791i	−0.196753	+	0.113596i
$971$	19.8952			0.638468			0.319234	−	0.947676i	$-0.396574\pi$
$971$	19.8952			0.638468			0.319234	+	0.947676i	$0.396574\pi$
$972$		0			0
$973$	−9.29800	−	23.7700i	−0.298080	−	0.762032i
$974$	14.3218			0.458901
$975$		0			0
$976$	4.95464	+	8.58169i	0.158594	+	0.274693i
$977$		−	35.1242i		−	1.12372i	−0.827231	−	0.561862i	$-0.810085\pi$
$977$		−	35.1242i		−	1.12372i	0.827231	−	0.561862i	$-0.189915\pi$
$978$		0			0
$979$	−14.2725	−	24.7208i	−0.456152	−	0.790079i
$980$	−7.17562	+	1.62070i	−0.229217	+	0.0517713i
$981$		0			0
$982$			7.05051i			0.224991i
$983$	25.2058	−	14.5526i	0.803941	−	0.464156i	−0.0409061	−	0.999163i	$-0.513024\pi$
$983$	25.2058	−	14.5526i	0.803941	−	0.464156i	0.844847	+	0.535007i	$0.179691\pi$
$984$		0			0
$985$	−7.53314	−	13.0478i	−0.240026	−	0.415737i
$986$	8.99839	+	5.19522i	0.286567	+	0.165450i
$987$		0			0
$988$	−5.15389	−	9.48621i	−0.163967	−	0.301796i
$989$	2.22563	−	3.85491i	0.0707710	−	0.122579i
$990$		0			0
$991$	−8.36093			−0.265594			−0.132797	−	0.991143i	$-0.542396\pi$
$991$	−8.36093			−0.265594			−0.132797	+	0.991143i	$0.542396\pi$
$992$	−8.76348			−0.278241
$993$		0			0
$994$	−13.6029	+	17.0179i	−0.431457	+	0.539775i
$995$	14.4827	−	8.36157i	0.459131	−	0.265080i
$996$		0			0
$997$	17.6607	−	30.5892i	0.559320	−	0.968770i	−0.438234	−	0.898861i	$-0.644396\pi$
$997$	17.6607	−	30.5892i	0.559320	−	0.968770i	0.997553	−	0.0699089i	$-0.0222709\pi$
$998$	37.3026			1.18079
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cr.b.667.8		20
3.2	odd	2		546.2.bd.b.121.3	✓	20
7.4	even	3		1638.2.dt.b.1369.8		20
13.10	even	6		1638.2.dt.b.1297.3		20
21.11	odd	6		546.2.bm.b.277.3	yes	20
39.23	odd	6		546.2.bm.b.205.8	yes	20
91.88	even	6	inner	1638.2.cr.b.361.8		20
273.179	odd	6		546.2.bd.b.361.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.b.121.3	✓	20	3.2	odd	2
546.2.bd.b.361.3	yes	20	273.179	odd	6
546.2.bm.b.205.8	yes	20	39.23	odd	6
546.2.bm.b.277.3	yes	20	21.11	odd	6
1638.2.cr.b.361.8		20	91.88	even	6	inner
1638.2.cr.b.667.8		20	1.1	even	1	trivial
1638.2.dt.b.1297.3		20	13.10	even	6
1638.2.dt.b.1369.8		20	7.4	even	3

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cr (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.910115 - 0.525455i) q^{5} +(2.61575 + 0.397291i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.910115 - 0.525455i) q^{5} +(2.61575 + 0.397291i) q^{7} -1.00000i q^{8} -1.05091 q^{10} -6.56072i q^{11} +(-3.07474 - 1.88307i) q^{13} +(2.46395 - 0.963812i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.31143 + 4.00351i) q^{17} +2.99423i q^{19} +(-0.910115 + 0.525455i) q^{20} +(-3.28036 - 5.68175i) q^{22} +(-1.59836 - 2.76844i) q^{23} +(-1.94779 - 3.37368i) q^{25} +(-3.60434 - 0.0934133i) q^{26} +(1.65194 - 2.06666i) q^{28} +(1.12381 - 1.94650i) q^{29} +(7.58940 - 4.38174i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.62286i q^{34} +(-2.17188 - 1.73604i) q^{35} +(-4.02143 + 2.32178i) q^{37} +(1.49712 + 2.59308i) q^{38} +(-0.525455 + 0.910115i) q^{40} +(-6.65179 - 3.84041i) q^{41} +(0.696225 + 1.20590i) q^{43} +(-5.68175 - 3.28036i) q^{44} +(-2.76844 - 1.59836i) q^{46} +(9.01677 + 5.20584i) q^{47} +(6.68432 + 2.07843i) q^{49} +(-3.37368 - 1.94779i) q^{50} +(-3.16816 + 1.72127i) q^{52} +(-3.40268 - 5.89362i) q^{53} +(-3.44736 + 5.97101i) q^{55} +(0.397291 - 2.61575i) q^{56} -2.24763i q^{58} +(2.16500 + 1.24996i) q^{59} -9.90929 q^{61} +(4.38174 - 7.58940i) q^{62} -1.00000 q^{64} +(1.80890 + 3.32945i) q^{65} -8.98392i q^{67} +(2.31143 + 4.00351i) q^{68} +(-2.74892 - 0.417517i) q^{70} +(-7.13127 + 4.11724i) q^{71} +(8.18302 - 4.72447i) q^{73} +(-2.32178 + 4.02143i) q^{74} +(2.59308 + 1.49712i) q^{76} +(2.60652 - 17.1612i) q^{77} +(1.65111 - 2.85981i) q^{79} +1.05091i q^{80} -7.68082 q^{82} -9.79351i q^{83} +(4.20733 - 2.42910i) q^{85} +(1.20590 + 0.696225i) q^{86} -6.56072 q^{88} +(3.76799 - 2.17545i) q^{89} +(-7.29464 - 6.14721i) q^{91} -3.19672 q^{92} +10.4117 q^{94} +(1.57334 - 2.72510i) q^{95} +(5.83099 - 3.36652i) q^{97} +(6.82801 - 1.54219i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 6 q^{7}+O(q^{10}) \) 20 * q + 10 * q^4 - 6 * q^7	\( 20 q + 10 q^{4} - 6 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{14} - 10 q^{16} - 4 q^{17} - 10 q^{22} - 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 8 q^{29} - 12 q^{31} - 4 q^{35} - 6 q^{38} - 4 q^{40} + 18 q^{41} + 18 q^{43} - 6 q^{44} - 24 q^{46} - 6 q^{47} + 4 q^{49} - 12 q^{50} - 2 q^{52} - 18 q^{53} - 12 q^{55} - 2 q^{56} - 36 q^{59} + 12 q^{61} - 20 q^{64} + 4 q^{68} - 42 q^{70} + 6 q^{71} - 24 q^{73} + 18 q^{74} + 12 q^{76} + 34 q^{77} - 36 q^{82} - 36 q^{86} - 20 q^{88} - 18 q^{89} - 94 q^{91} - 16 q^{92} + 32 q^{94} - 40 q^{95} - 96 q^{97} + 12 q^{98}+O(q^{100}) \) 20 * q + 10 * q^4 - 6 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^14 - 10 * q^16 - 4 * q^17 - 10 * q^22 - 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 8 * q^29 - 12 * q^31 - 4 * q^35 - 6 * q^38 - 4 * q^40 + 18 * q^41 + 18 * q^43 - 6 * q^44 - 24 * q^46 - 6 * q^47 + 4 * q^49 - 12 * q^50 - 2 * q^52 - 18 * q^53 - 12 * q^55 - 2 * q^56 - 36 * q^59 + 12 * q^61 - 20 * q^64 + 4 * q^68 - 42 * q^70 + 6 * q^71 - 24 * q^73 + 18 * q^74 + 12 * q^76 + 34 * q^77 - 36 * q^82 - 36 * q^86 - 20 * q^88 - 18 * q^89 - 94 * q^91 - 16 * q^92 + 32 * q^94 - 40 * q^95 - 96 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more