LMFDB - Embedded newform 432.2.be.b.335.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.4
Character	$\chi$	$=$	432.335
Dual form			432.2.be.b.383.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +O(q^{10})$	\(q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +(-5.69507 + 2.07284i) q^{11} +(-2.30399 + 1.93328i) q^{13} +(6.46883 + 2.68182i) q^{15} +(-2.73425 + 1.57862i) q^{17} +(3.28561 + 1.89695i) q^{19} +(0.415234 - 1.87026i) q^{21} +(-0.347216 - 1.96916i) q^{23} +(-8.69152 - 7.29305i) q^{25} +(-0.683011 + 5.15107i) q^{27} +(2.14987 - 2.56211i) q^{29} +(3.05409 - 0.538519i) q^{31} +(3.15348 + 10.0123i) q^{33} +(-2.23597 + 3.87281i) q^{35} +(4.96790 + 8.60465i) q^{37} +(3.17000 + 4.13387i) q^{39} +(5.58989 + 6.66177i) q^{41} +(-1.77028 - 4.86379i) q^{43} +(5.13275 - 10.9895i) q^{45} +(-0.132939 + 0.753937i) q^{47} +(-5.42820 - 1.97570i) q^{49} +(2.52358 + 4.85141i) q^{51} +3.19332i q^{53} -24.5030i q^{55} +(3.53243 - 5.54102i) q^{57} +(7.48972 + 2.72603i) q^{59} +(-1.13739 + 6.45044i) q^{61} +(-3.20467 - 0.860813i) q^{63} +(-4.15895 - 11.4266i) q^{65} +(-3.17844 - 3.78791i) q^{67} +(-3.43381 + 0.450990i) q^{69} +(-4.30646 - 7.45900i) q^{71} +(4.12714 - 7.14841i) q^{73} +(-13.2810 + 14.4847i) q^{75} +(-6.60169 + 1.16406i) q^{77} +(-4.29080 + 5.11358i) q^{79} +(8.86133 + 1.57379i) q^{81} +(-9.12222 - 7.65445i) q^{83} +(-2.21658 - 12.5709i) q^{85} +(-4.26985 - 3.91503i) q^{87} +(10.9332 + 6.31231i) q^{89} +(-2.88103 + 1.66336i) q^{91} +(-0.699469 - 5.32571i) q^{93} +(-11.7502 + 9.85957i) q^{95} +(-6.13725 + 2.23378i) q^{97} +(17.5651 - 4.69491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0760859	−	1.73038i	0.0439282	−	0.999035i
$3$	0.0760859	−	1.73038i	0.0439282	−	0.999035i
$4$		0			0
$5$	−1.38279	+	3.79919i	−0.618404	+	1.69905i	0.0924566	+	0.995717i	$0.470528\pi$
$5$	−1.38279	+	3.79919i	−0.618404	+	1.69905i	−0.710860	+	0.703333i	$0.751694\pi$
$6$		0			0
$7$	1.08929	+	0.192071i	0.411711	+	0.0725958i	0.375668	−	0.926754i	$-0.377413\pi$
$7$	1.08929	+	0.192071i	0.411711	+	0.0725958i	0.0360436	+	0.999350i	$0.488524\pi$
$8$		0			0
$9$	−2.98842	−	0.263315i	−0.996141	−	0.0877716i
$10$		0			0
$11$	−5.69507	+	2.07284i	−1.71713	+	0.624984i	−0.997585	−	0.0694631i	$-0.977871\pi$
$11$	−5.69507	+	2.07284i	−1.71713	+	0.624984i	−0.719544	+	0.694447i	$0.755649\pi$
$12$		0			0
$13$	−2.30399	+	1.93328i	−0.639011	+	0.536194i	−0.903714	−	0.428136i	$-0.859170\pi$
$13$	−2.30399	+	1.93328i	−0.639011	+	0.536194i	0.264703	+	0.964330i	$0.414726\pi$
$14$		0			0
$15$	6.46883	+	2.68182i	1.67024	+	0.692443i
$16$		0			0
$17$	−2.73425	+	1.57862i	−0.663154	+	0.382872i	−0.793478	−	0.608599i	$-0.791732\pi$
$17$	−2.73425	+	1.57862i	−0.663154	+	0.382872i	0.130324	+	0.991472i	$0.458398\pi$
$18$		0			0
$19$	3.28561	+	1.89695i	0.753770	+	0.435190i	0.827055	−	0.562122i	$-0.190015\pi$
$19$	3.28561	+	1.89695i	0.753770	+	0.435190i	−0.0732842	+	0.997311i	$0.523348\pi$
$20$		0			0
$21$	0.415234	−	1.87026i	0.0906115	−	0.408125i
$22$		0			0
$23$	−0.347216	−	1.96916i	−0.0723995	−	0.410598i	−0.999371	−	0.0354658i	$-0.988709\pi$
$23$	−0.347216	−	1.96916i	−0.0723995	−	0.410598i	0.926971	−	0.375132i	$-0.122403\pi$
$24$		0			0
$25$	−8.69152	−	7.29305i	−1.73830	−	1.45861i
$26$		0			0
$27$	−0.683011	+	5.15107i	−0.131445	+	0.991323i
$28$		0			0
$29$	2.14987	−	2.56211i	0.399220	−	0.475772i	−0.528562	−	0.848895i	$-0.677268\pi$
$29$	2.14987	−	2.56211i	0.399220	−	0.475772i	0.927782	+	0.373123i	$0.121713\pi$
$30$		0			0
$31$	3.05409	−	0.538519i	0.548531	−	0.0967209i	0.107488	−	0.994206i	$-0.465719\pi$
$31$	3.05409	−	0.538519i	0.548531	−	0.0967209i	0.441044	+	0.897486i	$0.354608\pi$
$32$		0			0
$33$	3.15348	+	10.0123i	0.548950	+	1.74293i
$34$		0			0
$35$	−2.23597	+	3.87281i	−0.377948	+	0.654625i
$36$		0			0
$37$	4.96790	+	8.60465i	0.816717	+	1.41460i	0.908088	+	0.418779i	$0.137542\pi$
$37$	4.96790	+	8.60465i	0.816717	+	1.41460i	−0.0913713	+	0.995817i	$0.529125\pi$
$38$		0			0
$39$	3.17000	+	4.13387i	0.507606	+	0.661949i
$40$		0			0
$41$	5.58989	+	6.66177i	0.872994	+	1.04039i	0.998831	+	0.0483427i	$0.0153940\pi$
$41$	5.58989	+	6.66177i	0.872994	+	1.04039i	−0.125837	+	0.992051i	$0.540162\pi$
$42$		0			0
$43$	−1.77028	−	4.86379i	−0.269965	−	0.741722i	−0.998397	−	0.0566037i	$-0.981973\pi$
$43$	−1.77028	−	4.86379i	−0.269965	−	0.741722i	0.728432	−	0.685118i	$-0.240249\pi$
$44$		0			0
$45$	5.13275	−	10.9895i	0.765145	−	1.63821i
$46$		0			0
$47$	−0.132939	+	0.753937i	−0.0193912	+	0.109973i	−0.992967	−	0.118391i	$-0.962226\pi$
$47$	−0.132939	+	0.753937i	−0.0193912	+	0.109973i	0.973576	+	0.228364i	$0.0733376\pi$
$48$		0			0
$49$	−5.42820	−	1.97570i	−0.775457	−	0.282243i
$50$		0			0
$51$	2.52358	+	4.85141i	0.353371	+	0.679333i
$52$		0			0
$53$			3.19332i			0.438636i	0.975653	+	0.219318i	$0.0703832\pi$
$53$			3.19332i			0.438636i	−0.975653	+	0.219318i	$0.929617\pi$
$54$		0			0
$55$		−	24.5030i		−	3.30398i
$56$		0			0
$57$	3.53243	−	5.54102i	0.467881	−	0.733926i
$58$		0			0
$59$	7.48972	+	2.72603i	0.975078	+	0.354899i	0.779925	−	0.625873i	$-0.215257\pi$
$59$	7.48972	+	2.72603i	0.975078	+	0.354899i	0.195153	+	0.980773i	$0.437480\pi$
$60$		0			0
$61$	−1.13739	+	6.45044i	−0.145627	+	0.825894i	0.821234	+	0.570592i	$0.193286\pi$
$61$	−1.13739	+	6.45044i	−0.145627	+	0.825894i	−0.966861	+	0.255302i	$0.917825\pi$
$62$		0			0
$63$	−3.20467	−	0.860813i	−0.403751	−	0.108452i
$64$		0			0
$65$	−4.15895	−	11.4266i	−0.515854	−	1.41730i
$66$		0			0
$67$	−3.17844	−	3.78791i	−0.388308	−	0.462767i	0.536110	−	0.844148i	$-0.319893\pi$
$67$	−3.17844	−	3.78791i	−0.388308	−	0.462767i	−0.924418	+	0.381381i	$0.875449\pi$
$68$		0			0
$69$	−3.43381	+	0.450990i	−0.413382	+	0.0542928i
$70$		0			0
$71$	−4.30646	−	7.45900i	−0.511082	−	0.885220i	−0.999918	−	0.0128443i	$-0.995911\pi$
$71$	−4.30646	−	7.45900i	−0.511082	−	0.885220i	0.488835	−	0.872376i	$-0.337422\pi$
$72$		0			0
$73$	4.12714	−	7.14841i	0.483045	−	0.836658i	−0.516766	−	0.856127i	$-0.672864\pi$
$73$	4.12714	−	7.14841i	0.483045	−	0.836658i	0.999810	+	0.0194687i	$0.00619746\pi$
$74$		0			0
$75$	−13.2810	+	14.4847i	−1.53356	+	1.67255i
$76$		0			0
$77$	−6.60169	+	1.16406i	−0.752333	+	0.132657i
$78$		0			0
$79$	−4.29080	+	5.11358i	−0.482753	+	0.575322i	−0.951359	−	0.308085i	$-0.900312\pi$
$79$	−4.29080	+	5.11358i	−0.482753	+	0.575322i	0.468606	+	0.883407i	$0.344756\pi$
$80$		0			0
$81$	8.86133	+	1.57379i	0.984592	+	0.174866i
$82$		0			0
$83$	−9.12222	−	7.65445i	−1.00129	−	0.840185i	−0.0141306	−	0.999900i	$-0.504498\pi$
$83$	−9.12222	−	7.65445i	−1.00129	−	0.840185i	−0.987163	+	0.159715i	$0.948943\pi$
$84$		0			0
$85$	−2.21658	−	12.5709i	−0.240422	−	1.36350i
$86$		0			0
$87$	−4.26985	−	3.91503i	−0.457776	−	0.419735i
$88$		0			0
$89$	10.9332	+	6.31231i	1.15892	+	0.669104i	0.951045	−	0.309051i	$-0.100012\pi$
$89$	10.9332	+	6.31231i	1.15892	+	0.669104i	0.207876	+	0.978155i	$0.433345\pi$
$90$		0			0
$91$	−2.88103	+	1.66336i	−0.302014	+	0.174368i
$92$		0			0
$93$	−0.699469	−	5.32571i	−0.0725315	−	0.552251i
$94$		0			0
$95$	−11.7502	+	9.85957i	−1.20554	+	1.01157i
$96$		0			0
$97$	−6.13725	+	2.23378i	−0.623144	+	0.226806i	−0.634244	−	0.773133i	$-0.718689\pi$
$97$	−6.13725	+	2.23378i	−0.623144	+	0.226806i	0.0111006	+	0.999938i	$0.496466\pi$
$98$		0			0
$99$	17.5651	−	4.69491i	1.76536	−	0.471857i
$100$		0			0
$101$	−0.0682784	−	0.0120393i	−0.00679396	−	0.00119796i	0.170250	−	0.985401i	$-0.445542\pi$
$101$	−0.0682784	−	0.0120393i	−0.00679396	−	0.00119796i	−0.177044	+	0.984203i	$0.556654\pi$
$102$		0			0
$103$	2.61896	−	7.19554i	0.258054	−	0.708998i	−0.741233	−	0.671248i	$-0.765759\pi$
$103$	2.61896	−	7.19554i	0.258054	−	0.708998i	0.999287	−	0.0377502i	$-0.0120191\pi$
$104$		0			0
$105$	6.53131	+	4.16374i	0.637390	+	0.406339i
$106$		0			0
$107$	−8.77523			−0.848333			−0.424167	−	0.905584i	$-0.639433\pi$
$107$	−8.77523			−0.848333			−0.424167	+	0.905584i	$0.639433\pi$
$108$		0			0
$109$	−7.10766			−0.680790			−0.340395	−	0.940283i	$-0.610561\pi$
$109$	−7.10766			−0.680790			−0.340395	+	0.940283i	$0.610561\pi$
$110$		0			0
$111$	15.2673	−	7.94165i	1.44911	−	0.753788i
$112$		0			0
$113$	−1.52252	+	4.18309i	−0.143227	+	0.393512i	−0.990476	−	0.137683i	$-0.956035\pi$
$113$	−1.52252	+	4.18309i	−0.143227	+	0.393512i	0.847250	+	0.531195i	$0.178257\pi$
$114$		0			0
$115$	7.96133	+	1.40380i	0.742398	+	0.130905i
$116$		0			0
$117$	7.39435	−	5.17077i	0.683608	−	0.478038i
$118$		0			0
$119$	−3.28159	+	1.19440i	−0.300823	+	0.109491i
$120$		0			0
$121$	19.7107	−	16.5392i	1.79188	−	1.50357i
$122$		0			0
$123$	11.9527	−	9.16576i	1.07774	−	0.826449i
$124$		0			0
$125$	22.2195	−	12.8284i	1.98737	−	1.14741i
$126$		0			0
$127$	18.8491	+	10.8825i	1.67259	+	0.965668i	0.966183	+	0.257859i	$0.0830170\pi$
$127$	18.8491	+	10.8825i	1.67259	+	0.965668i	0.706404	+	0.707809i	$0.250316\pi$
$128$		0			0
$129$	−8.55090	+	2.69318i	−0.752865	+	0.237122i
$130$		0			0
$131$	−0.293030	−	1.66185i	−0.0256021	−	0.145197i	0.969327	−	0.245774i	$-0.0790422\pi$
$131$	−0.293030	−	1.66185i	−0.0256021	−	0.145197i	−0.994929	+	0.100577i	$0.967931\pi$
$132$		0			0
$133$	3.21462	+	2.69739i	0.278743	+	0.233893i
$134$		0			0
$135$	−18.6254	−	9.71775i	−1.60302	−	0.836370i
$136$		0			0
$137$	−7.85456	+	9.36070i	−0.671060	+	0.799738i	−0.988928	−	0.148397i	$-0.952589\pi$
$137$	−7.85456	+	9.36070i	−0.671060	+	0.799738i	0.317868	+	0.948135i	$0.397033\pi$
$138$		0			0
$139$	−18.6597	+	3.29020i	−1.58269	+	0.279071i	−0.894707	−	0.446654i	$-0.852616\pi$
$139$	−18.6597	+	3.29020i	−1.58269	+	0.279071i	−0.687985	+	0.725725i	$0.741504\pi$
$140$		0			0
$141$	1.29448	+	0.287399i	0.109015	+	0.0242034i
$142$		0			0
$143$	9.11401	−	15.7859i	0.762152	−	1.32009i
$144$		0			0
$145$	6.76113	+	11.7106i	0.561482	+	0.972515i
$146$		0			0
$147$	−3.83172	+	9.24251i	−0.316035	+	0.762310i
$148$		0			0
$149$	2.05041	+	2.44358i	0.167976	+	0.200186i	0.843465	−	0.537184i	$-0.180512\pi$
$149$	2.05041	+	2.44358i	0.167976	+	0.200186i	−0.675489	+	0.737370i	$0.736067\pi$
$150$		0			0
$151$	7.21676	+	19.8279i	0.587291	+	1.61357i	0.775434	+	0.631428i	$0.217531\pi$
$151$	7.21676	+	19.8279i	0.587291	+	1.61357i	−0.188143	+	0.982142i	$0.560247\pi$
$152$		0			0
$153$	8.58678	−	3.99762i	0.694200	−	0.323189i
$154$		0			0
$155$	−2.17724	+	12.3477i	−0.174880	+	0.991795i
$156$		0			0
$157$	10.1291	+	3.68669i	0.808390	+	0.294230i	0.712959	−	0.701206i	$-0.247355\pi$
$157$	10.1291	+	3.68669i	0.808390	+	0.294230i	0.0954313	+	0.995436i	$0.469577\pi$
$158$		0			0
$159$	5.52565	+	0.242966i	0.438213	+	0.0192685i
$160$		0			0
$161$		−	2.21167i		−	0.174304i
$162$		0			0
$163$			9.46792i			0.741585i	0.928716	+	0.370792i	$0.120914\pi$
$163$			9.46792i			0.741585i	−0.928716	+	0.370792i	$0.879086\pi$
$164$		0			0
$165$	−42.3994	−	1.86433i	−3.30079	−	0.145138i
$166$		0			0
$167$	4.31832	+	1.57174i	0.334161	+	0.121625i	0.503651	−	0.863907i	$-0.331990\pi$
$167$	4.31832	+	1.57174i	0.334161	+	0.121625i	−0.169490	+	0.985532i	$0.554212\pi$
$168$		0			0
$169$	−0.686620	+	3.89401i	−0.0528169	+	0.299539i
$170$		0			0
$171$	−9.31929	−	6.53403i	−0.712664	−	0.499670i
$172$		0			0
$173$	−1.18374	−	3.25230i	−0.0899981	−	0.247268i	0.886525	−	0.462681i	$-0.153112\pi$
$173$	−1.18374	−	3.25230i	−0.0899981	−	0.247268i	−0.976523	+	0.215413i	$0.930890\pi$
$174$		0			0
$175$	−8.06677	−	9.61360i	−0.609790	−	0.726720i
$176$		0			0
$177$	5.28693	−	12.7526i	0.397390	−	0.958547i
$178$		0			0
$179$	−0.297137	−	0.514656i	−0.0222090	−	0.0384672i	0.854707	−	0.519110i	$-0.173737\pi$
$179$	−0.297137	−	0.514656i	−0.0222090	−	0.0384672i	−0.876916	+	0.480643i	$0.840403\pi$
$180$		0			0
$181$	−3.23404	+	5.60152i	−0.240384	+	0.416358i	−0.960824	−	0.277160i	$-0.910607\pi$
$181$	−3.23404	+	5.60152i	−0.240384	+	0.416358i	0.720439	+	0.693518i	$0.243940\pi$
$182$		0			0
$183$	11.0752	+	2.45890i	0.818700	+	0.181767i
$184$		0			0
$185$	−39.5603	+	6.97554i	−2.90853	+	0.512852i
$186$		0			0
$187$	12.2995	−	14.6580i	0.899432	−	1.07190i
$188$		0			0
$189$	−1.73336	+	5.47980i	−0.126084	+	0.398597i
$190$		0			0
$191$	17.0734	+	14.3263i	1.23539	+	1.03661i	0.997870	+	0.0652317i	$0.0207786\pi$
$191$	17.0734	+	14.3263i	1.23539	+	1.03661i	0.237519	+	0.971383i	$0.423666\pi$
$192$		0			0
$193$	−1.58626	−	8.99614i	−0.114182	−	0.647557i	−0.987152	−	0.159783i	$-0.948920\pi$
$193$	−1.58626	−	8.99614i	−0.114182	−	0.647557i	0.872970	−	0.487773i	$-0.162191\pi$
$194$		0			0
$195$	−20.0888	+	6.32715i	−1.43859	+	0.453097i
$196$		0			0
$197$	16.9561	+	9.78961i	1.20807	+	0.697481i	0.962338	−	0.271856i	$-0.0876375\pi$
$197$	16.9561	+	9.78961i	1.20807	+	0.697481i	0.245735	+	0.969337i	$0.420971\pi$
$198$		0			0
$199$	−11.3321	+	6.54259i	−0.803311	+	0.463792i	−0.844627	−	0.535355i	$-0.820178\pi$
$199$	−11.3321	+	6.54259i	−0.803311	+	0.463792i	0.0413169	+	0.999146i	$0.486845\pi$
$200$		0			0
$201$	−6.79636	+	5.21169i	−0.479378	+	0.367605i
$202$		0			0
$203$	2.83393	−	2.37795i	0.198903	−	0.166899i
$204$		0			0
$205$	−33.0390	+	12.0252i	−2.30754	+	0.839877i
$206$		0			0
$207$	0.519119	+	5.97610i	0.0360812	+	0.415368i
$208$		0			0
$209$	−22.6438	−	3.99272i	−1.56631	−	0.276182i
$210$		0			0
$211$	−2.90364	+	7.97769i	−0.199895	+	0.549207i	−0.998622	−	0.0524872i	$-0.983285\pi$
$211$	−2.90364	+	7.97769i	−0.199895	+	0.549207i	0.798727	+	0.601694i	$0.205507\pi$
$212$		0			0
$213$	−13.2346	+	6.88428i	−0.906817	+	0.471703i
$214$		0			0
$215$	20.9264			1.42717
$216$		0			0
$217$	3.43021			0.232858
$218$		0			0
$219$	−12.0554	−	7.68540i	−0.814631	−	0.519331i
$220$		0			0
$221$	3.24778	−	8.92320i	0.218469	−	0.600239i
$222$		0			0
$223$	−4.40925	−	0.777470i	−0.295265	−	0.0520633i	0.0240532	−	0.999711i	$-0.492343\pi$
$223$	−4.40925	−	0.777470i	−0.295265	−	0.0520633i	−0.319319	+	0.947647i	$0.603454\pi$
$224$		0			0
$225$	24.0536	+	24.0833i	1.60357	+	1.60555i
$226$		0			0
$227$	−4.95239	+	1.80252i	−0.328702	+	0.119638i	−0.501099	−	0.865390i	$-0.667071\pi$
$227$	−4.95239	+	1.80252i	−0.328702	+	0.119638i	0.172397	+	0.985027i	$0.444849\pi$
$228$		0			0
$229$	−3.50504	+	2.94107i	−0.231619	+	0.194352i	−0.751209	−	0.660064i	$-0.770529\pi$
$229$	−3.50504	+	2.94107i	−0.231619	+	0.194352i	0.519590	+	0.854416i	$0.326085\pi$
$230$		0			0
$231$	1.51196	+	11.5120i	0.0994799	+	0.757434i
$232$		0			0
$233$	7.68478	−	4.43681i	0.503447	−	0.290665i	−0.226689	−	0.973967i	$-0.572790\pi$
$233$	7.68478	−	4.43681i	0.503447	−	0.290665i	0.730136	+	0.683302i	$0.239457\pi$
$234$		0			0
$235$	−2.68052	−	1.54760i	−0.174858	−	0.100954i
$236$		0			0
$237$	8.52196	+	7.81378i	0.553561	+	0.507560i
$238$		0			0
$239$	−2.00688	−	11.3816i	−0.129815	−	0.736215i	−0.978331	−	0.207046i	$-0.933615\pi$
$239$	−2.00688	−	11.3816i	−0.129815	−	0.736215i	0.848517	−	0.529169i	$-0.177496\pi$
$240$		0			0
$241$	13.7462	+	11.5344i	0.885471	+	0.742998i	0.967296	−	0.253649i	$-0.0816307\pi$
$241$	13.7462	+	11.5344i	0.885471	+	0.742998i	−0.0818259	+	0.996647i	$0.526075\pi$
$242$		0			0
$243$	3.39748	−	15.2137i	0.217948	−	0.975960i
$244$		0			0
$245$	15.0121	−	17.8908i	0.959090	−	1.14300i
$246$		0			0
$247$	−11.2373	+	1.98144i	−0.715014	+	0.126076i
$248$		0			0
$249$	−13.9392	+	15.2025i	−0.883359	+	0.963419i
$250$		0			0
$251$	11.4327	−	19.8020i	0.721625	−	1.24989i	−0.238724	−	0.971088i	$-0.576729\pi$
$251$	11.4327	−	19.8020i	0.721625	−	1.24989i	0.960348	−	0.278803i	$-0.0899377\pi$
$252$		0			0
$253$	6.05916	+	10.4948i	0.380936	+	0.659801i
$254$		0			0
$255$	−21.9210	+	2.87906i	−1.37275	+	0.180294i
$256$		0			0
$257$	−3.51480	−	4.18877i	−0.219247	−	0.261288i	0.645198	−	0.764015i	$-0.276775\pi$
$257$	−3.51480	−	4.18877i	−0.219247	−	0.261288i	−0.864445	+	0.502727i	$0.832330\pi$
$258$		0			0
$259$	3.75876	+	10.3271i	0.233558	+	0.641695i
$260$		0			0
$261$	−7.09935	+	7.09058i	−0.439439	+	0.438896i
$262$		0			0
$263$	2.70605	−	15.3468i	0.166862	−	0.946324i	−0.780261	−	0.625454i	$-0.784914\pi$
$263$	2.70605	−	15.3468i	0.166862	−	0.946324i	0.947123	−	0.320870i	$-0.103975\pi$
$264$		0			0
$265$	−12.1320	−	4.41570i	−0.745264	−	0.271254i
$266$		0			0
$267$	11.7546	−	18.4384i	0.719367	−	1.12841i
$268$		0			0
$269$		−	3.32950i		−	0.203003i	−0.994835	−	0.101502i	$-0.967635\pi$
$269$		−	3.32950i		−	0.203003i	0.994835	−	0.101502i	$-0.0323647\pi$
$270$		0			0
$271$		−	7.46821i		−	0.453661i	−0.973934	−	0.226831i	$-0.927164\pi$
$271$		−	7.46821i		−	0.453661i	0.973934	−	0.226831i	$-0.0728364\pi$
$272$		0			0
$273$	2.65904	+	5.11183i	0.160932	+	0.309382i
$274$		0			0
$275$	64.6161	+	23.5183i	3.89650	+	1.41821i
$276$		0			0
$277$	−0.0646551	+	0.366677i	−0.00388475	+	0.0220315i	−0.986689	−	0.162622i	$-0.948005\pi$
$277$	−0.0646551	+	0.366677i	−0.00388475	+	0.0220315i	0.982804	+	0.184653i	$0.0591161\pi$
$278$		0			0
$279$	−9.26872	+	0.805134i	−0.554904	+	0.0482021i
$280$		0			0
$281$	−0.756825	−	2.07936i	−0.0451484	−	0.124044i	0.915069	−	0.403296i	$-0.132136\pi$
$281$	−0.756825	−	2.07936i	−0.0451484	−	0.124044i	−0.960218	+	0.279252i	$0.909913\pi$
$282$		0			0
$283$	8.02980	+	9.56954i	0.477322	+	0.568850i	0.949946	−	0.312414i	$-0.101138\pi$
$283$	8.02980	+	9.56954i	0.477322	+	0.568850i	−0.472624	+	0.881264i	$0.656693\pi$
$284$		0			0
$285$	16.1668	+	21.0824i	0.957637	+	1.24882i
$286$		0			0
$287$	4.80946	+	8.33023i	0.283893	+	0.491718i
$288$		0			0
$289$	−3.51590	+	6.08972i	−0.206818	+	0.358219i
$290$		0			0
$291$	3.39832	+	10.7897i	0.199213	+	0.632505i
$292$		0			0
$293$	17.2687	−	3.04493i	1.00885	−	0.177887i	0.355283	−	0.934759i	$-0.384384\pi$
$293$	17.2687	−	3.04493i	1.00885	−	0.177887i	0.653563	+	0.756872i	$0.273273\pi$
$294$		0			0
$295$	−20.7134	+	24.6853i	−1.20598	+	1.43724i
$296$		0			0
$297$	−6.78753	−	30.7515i	−0.393852	−	1.78438i
$298$		0			0
$299$	4.60690	+	3.86565i	0.266424	+	0.223556i
$300$		0			0
$301$	−0.994146	−	5.63808i	−0.0573016	−	0.324974i
$302$		0			0
$303$	−0.0260276	+	0.117232i	−0.00149525	+	0.00673477i
$304$		0			0
$305$	−22.9337	−	13.2408i	−1.31318	−	0.758164i
$306$		0			0
$307$	8.25491	−	4.76598i	0.471133	−	0.272009i	−0.245581	−	0.969376i	$-0.578979\pi$
$307$	8.25491	−	4.76598i	0.471133	−	0.272009i	0.716714	+	0.697367i	$0.245645\pi$
$308$		0			0
$309$	−12.2518	−	5.07928i	−0.696978	−	0.288950i
$310$		0			0
$311$	−24.6382	+	20.6739i	−1.39711	+	1.17231i	−0.434741	+	0.900556i	$0.643160\pi$
$311$	−24.6382	+	20.6739i	−1.39711	+	1.17231i	−0.962366	+	0.271756i	$0.912396\pi$
$312$		0			0
$313$	2.99538	−	1.09023i	0.169309	−	0.0616234i	−0.255975	−	0.966683i	$-0.582396\pi$
$313$	2.99538	−	1.09023i	0.169309	−	0.0616234i	0.425284	+	0.905060i	$0.360174\pi$
$314$		0			0
$315$	7.70179	−	10.9848i	0.433947	−	0.618925i
$316$		0			0
$317$	−6.86086	−	1.20975i	−0.385344	−	0.0679466i	−0.0223797	−	0.999750i	$-0.507124\pi$
$317$	−6.86086	−	1.20975i	−0.385344	−	0.0679466i	−0.362965	+	0.931803i	$0.618235\pi$
$318$		0			0
$319$	−6.93281	+	19.0477i	−0.388163	+	1.06647i
$320$		0			0
$321$	−0.667671	+	15.1845i	−0.0372657	+	0.847515i
$322$		0			0
$323$	−11.9783			−0.666488
$324$		0			0
$325$	34.1246			1.89289
$326$		0			0
$327$	−0.540792	+	12.2989i	−0.0299059	+	0.680133i
$328$		0			0
$329$	−0.289618	+	0.795719i	−0.0159672	+	0.0438694i
$330$		0			0
$331$	−16.2725	−	2.86928i	−0.894419	−	0.157710i	−0.292498	−	0.956266i	$-0.594487\pi$
$331$	−16.2725	−	2.86928i	−0.894419	−	0.157710i	−0.601921	+	0.798556i	$0.705598\pi$
$332$		0			0
$333$	−12.5804	−	27.0224i	−0.689404	−	1.48082i
$334$		0			0
$335$	18.7861	−	6.83759i	1.02640	−	0.373578i
$336$		0			0
$337$	17.6769	−	14.8327i	0.962925	−	0.807990i	−0.0185019	−	0.999829i	$-0.505890\pi$
$337$	17.6769	−	14.8327i	0.962925	−	0.807990i	0.981426	+	0.191839i	$0.0614452\pi$
$338$		0			0
$339$	7.12249	+	2.95281i	0.386840	+	0.160375i
$340$		0			0
$341$	−16.2770	+	9.39754i	−0.881450	+	0.508905i
$342$		0			0
$343$	−12.2387	−	7.06602i	−0.660828	−	0.381529i
$344$		0			0
$345$	3.03485	−	13.6693i	0.163391	−	0.735931i
$346$		0			0
$347$	−5.24439	−	29.7424i	−0.281534	−	1.59666i	−0.717411	−	0.696650i	$-0.754673\pi$
$347$	−5.24439	−	29.7424i	−0.281534	−	1.59666i	0.435878	−	0.900006i	$-0.356438\pi$
$348$		0			0
$349$	−6.03314	−	5.06240i	−0.322946	−	0.270984i	0.466872	−	0.884325i	$-0.345381\pi$
$349$	−6.03314	−	5.06240i	−0.322946	−	0.270984i	−0.789819	+	0.613341i	$0.789825\pi$
$350$		0			0
$351$	−8.38478	−	13.1884i	−0.447547	−	0.703947i
$352$		0			0
$353$	7.94108	−	9.46381i	0.422661	−	0.503708i	−0.512129	−	0.858909i	$-0.671143\pi$
$353$	7.94108	−	9.46381i	0.422661	−	0.503708i	0.934790	+	0.355201i	$0.115587\pi$
$354$		0			0
$355$	34.2931	−	6.04680i	1.82009	−	0.320931i
$356$		0			0
$357$	1.81708	+	5.76927i	0.0961703	+	0.305342i
$358$		0			0
$359$	−17.4551	+	30.2332i	−0.921247	+	1.59565i	−0.123760	+	0.992312i	$0.539495\pi$
$359$	−17.4551	+	30.2332i	−0.921247	+	1.59565i	−0.797488	+	0.603335i	$0.793838\pi$
$360$		0			0
$361$	−2.30318	−	3.98923i	−0.121220	−	0.209959i
$362$		0			0
$363$	−27.1194	−	35.3654i	−1.42340	−	1.85620i
$364$		0			0
$365$	21.4512	+	25.5646i	1.12281	+	1.33811i
$366$		0			0
$367$	4.42147	+	12.1479i	0.230799	+	0.634114i	0.999988	−	0.00490680i	$-0.00156189\pi$
$367$	4.42147	+	12.1479i	0.230799	+	0.634114i	−0.769189	+	0.639021i	$0.779340\pi$
$368$		0			0
$369$	−14.9508	−	21.3801i	−0.778308	−	1.11300i
$370$		0			0
$371$	−0.613342	+	3.47844i	−0.0318431	+	0.180591i
$372$		0			0
$373$	25.1002	+	9.13573i	1.29964	+	0.473030i	0.896879	−	0.442275i	$-0.145828\pi$
$373$	25.1002	+	9.13573i	1.29964	+	0.473030i	0.402761	+	0.915305i	$0.368051\pi$
$374$		0			0
$375$	−20.5075	−	39.4242i	−1.05900	−	2.03586i
$376$		0			0
$377$			10.0594i			0.518083i
$378$		0			0
$379$			25.2149i			1.29520i	0.761980	+	0.647600i	$0.224227\pi$
$379$			25.2149i			1.29520i	−0.761980	+	0.647600i	$0.775773\pi$
$380$		0			0
$381$	20.2650	−	31.7881i	1.03821	−	1.62855i
$382$		0			0
$383$	7.57778	+	2.75809i	0.387206	+	0.140932i	0.528286	−	0.849067i	$-0.322835\pi$
$383$	7.57778	+	2.75809i	0.387206	+	0.140932i	−0.141079	+	0.989998i	$0.545057\pi$
$384$		0			0
$385$	4.70630	−	26.6907i	0.239855	−	1.36029i
$386$		0			0
$387$	4.00962	+	15.0012i	0.203821	+	0.762554i
$388$		0			0
$389$	−9.34231	−	25.6678i	−0.473674	−	1.30141i	−0.914780	−	0.403953i	$-0.867636\pi$
$389$	−9.34231	−	25.6678i	−0.473674	−	1.30141i	0.441106	−	0.897455i	$-0.354586\pi$
$390$		0			0
$391$	4.05793	+	4.83606i	0.205218	+	0.244570i
$392$		0			0
$393$	−2.89793	+	0.380609i	−0.146181	+	0.0191992i
$394$		0			0
$395$	−13.4942	−	23.3726i	−0.678965	−	1.17600i
$396$		0			0
$397$	−0.561110	+	0.971871i	−0.0281613	+	0.0487768i	−0.879763	−	0.475413i	$-0.842299\pi$
$397$	−0.561110	+	0.971871i	−0.0281613	+	0.0487768i	0.851601	+	0.524190i	$0.175632\pi$
$398$		0			0
$399$	4.91209	−	5.35728i	0.245912	−	0.268199i
$400$		0			0
$401$	−3.05033	+	0.537855i	−0.152326	+	0.0268592i	−0.249291	−	0.968429i	$-0.580198\pi$
$401$	−3.05033	+	0.537855i	−0.152326	+	0.0268592i	0.0969651	+	0.995288i	$0.469086\pi$
$402$		0			0
$403$	−5.99549	+	7.14515i	−0.298657	+	0.355925i
$404$		0			0
$405$	−18.2325	+	31.4897i	−0.905981	+	1.56473i
$406$		0			0
$407$	−46.1285	−	38.7064i	−2.28651	−	1.91861i
$408$		0			0
$409$	3.12881	+	17.7443i	0.154710	+	0.877402i	0.959051	+	0.283234i	$0.0914073\pi$
$409$	3.12881	+	17.7443i	0.154710	+	0.877402i	−0.804341	+	0.594168i	$0.797482\pi$
$410$		0			0
$411$	15.5999	+	14.3036i	0.769488	+	0.705543i
$412$		0			0
$413$	7.63485	+	4.40798i	0.375687	+	0.216903i
$414$		0			0
$415$	41.6949	−	24.0725i	2.04672	−	1.18167i
$416$		0			0
$417$	4.27356	+	32.5386i	0.209277	+	1.59342i
$418$		0			0
$419$	7.33380	−	6.15379i	0.358279	−	0.300632i	−0.445825	−	0.895120i	$-0.647090\pi$
$419$	7.33380	−	6.15379i	0.358279	−	0.300632i	0.804105	+	0.594488i	$0.202645\pi$
$420$		0			0
$421$	27.5246	−	10.0181i	1.34147	−	0.488254i	0.431193	−	0.902260i	$-0.358093\pi$
$421$	27.5246	−	10.0181i	1.34147	−	0.488254i	0.910275	+	0.414005i	$0.135870\pi$
$422$		0			0
$423$	0.595802	−	2.21808i	0.0289689	−	0.107847i
$424$		0			0
$425$	35.2778	+	6.22043i	1.71122	+	0.301735i
$426$		0			0
$427$	−2.47788	+	6.80791i	−0.119913	+	0.329458i
$428$		0			0
$429$	−26.6222	−	16.9718i	−1.28533	−	0.819405i
$430$		0			0
$431$	4.22604			0.203561			0.101781	−	0.994807i	$-0.467546\pi$
$431$	4.22604			0.203561			0.101781	+	0.994807i	$0.467546\pi$
$432$		0			0
$433$	24.7833			1.19101			0.595504	−	0.803352i	$-0.296952\pi$
$433$	24.7833			1.19101			0.595504	+	0.803352i	$0.296952\pi$
$434$		0			0
$435$	20.7782	−	10.8083i	0.996241	−	0.518219i
$436$		0			0
$437$	2.59457	−	7.12853i	0.124115	−	0.341004i
$438$		0			0
$439$	7.08050	+	1.24848i	0.337934	+	0.0595868i	0.340040	−	0.940411i	$-0.389559\pi$
$439$	7.08050	+	1.24848i	0.337934	+	0.0595868i	−0.00210632	+	0.999998i	$0.500670\pi$
$440$		0			0
$441$	15.7015	+	7.33355i	0.747691	+	0.349217i
$442$		0			0
$443$	−13.4625	+	4.89994i	−0.639621	+	0.232803i	−0.641414	−	0.767195i	$-0.721652\pi$
$443$	−13.4625	+	4.89994i	−0.639621	+	0.232803i	0.00179224	+	0.999998i	$0.499430\pi$
$444$		0			0
$445$	−39.1001	+	32.8089i	−1.85352	+	1.55529i
$446$		0			0
$447$	4.38433	−	3.36207i	0.207372	−	0.159020i
$448$		0			0
$449$	1.65721	−	0.956788i	0.0782084	−	0.0451536i	−0.460386	−	0.887719i	$-0.652289\pi$
$449$	1.65721	−	0.956788i	0.0782084	−	0.0451536i	0.538594	+	0.842565i	$0.318956\pi$
$450$		0			0
$451$	−45.6436	−	26.3523i	−2.14927	−	1.24088i
$452$		0			0
$453$	34.8588	−	10.9791i	1.63781	−	0.515843i
$454$		0			0
$455$	−2.33557	−	13.2457i	−0.109493	−	0.620966i
$456$		0			0
$457$	−25.4947	−	21.3926i	−1.19259	−	1.00070i	−0.999811	−	0.0194611i	$-0.993805\pi$
$457$	−25.4947	−	21.3926i	−1.19259	−	1.00070i	−0.192781	−	0.981242i	$-0.561751\pi$
$458$		0			0
$459$	−6.26407	−	15.1625i	−0.292382	−	0.707727i
$460$		0			0
$461$	8.78283	−	10.4670i	0.409057	−	0.487495i	−0.521702	−	0.853128i	$-0.674703\pi$
$461$	8.78283	−	10.4670i	0.409057	−	0.487495i	0.930759	+	0.365632i	$0.119147\pi$
$462$		0			0
$463$	−26.9189	+	4.74653i	−1.25103	+	0.220590i	−0.759636	−	0.650349i	$-0.774623\pi$
$463$	−26.9189	+	4.74653i	−1.25103	+	0.220590i	−0.491392	+	0.870939i	$0.663512\pi$
$464$		0			0
$465$	21.2006	+	4.70694i	0.983155	+	0.218279i
$466$		0			0
$467$	3.55751	−	6.16179i	0.164622	−	0.285134i	−0.771899	−	0.635745i	$-0.780693\pi$
$467$	3.55751	−	6.16179i	0.164622	−	0.285134i	0.936521	+	0.350612i	$0.114026\pi$
$468$		0			0
$469$	−2.73468	−	4.73661i	−0.126276	−	0.218716i
$470$		0			0
$471$	7.15005	−	17.2467i	0.329457	−	0.794684i
$472$		0			0
$473$	20.1637	+	24.0302i	0.927128	+	1.10491i
$474$		0			0
$475$	−14.7224	−	40.4495i	−0.675510	−	1.85595i
$476$		0			0
$477$	0.840847	−	9.54298i	0.0384998	−	0.436943i
$478$		0			0
$479$	−4.10239	+	23.2658i	−0.187443	+	1.06304i	0.735334	+	0.677705i	$0.237026\pi$
$479$	−4.10239	+	23.2658i	−0.187443	+	1.06304i	−0.922776	+	0.385336i	$0.874086\pi$
$480$		0			0
$481$	−28.0811	−	10.2207i	−1.28039	−	0.466024i
$482$		0			0
$483$	−3.82702	−	0.168276i	−0.174135	−	0.00765684i
$484$		0			0
$485$		−	26.4055i		−	1.19901i
$486$		0			0
$487$			32.5422i			1.47463i	0.675551	+	0.737314i	$0.263906\pi$
$487$			32.5422i			1.47463i	−0.675551	+	0.737314i	$0.736094\pi$
$488$		0			0
$489$	16.3831	+	0.720375i	0.740869	+	0.0325765i
$490$		0			0
$491$	−24.0124	−	8.73980i	−1.08366	−	0.394422i	−0.262394	−	0.964961i	$-0.584512\pi$
$491$	−24.0124	−	8.73980i	−1.08366	−	0.394422i	−0.821270	+	0.570539i	$0.806734\pi$
$492$		0			0
$493$	−1.83368	+	10.3993i	−0.0825846	+	0.468361i
$494$		0			0
$495$	−6.45199	+	73.2252i	−0.289995	+	3.29123i
$496$		0			0
$497$	−3.25831	−	8.95213i	−0.146155	−	0.401558i
$498$		0			0
$499$	3.15334	+	3.75800i	0.141163	+	0.168231i	0.831994	−	0.554785i	$-0.187200\pi$
$499$	3.15334	+	3.75800i	0.141163	+	0.168231i	−0.690831	+	0.723016i	$0.742755\pi$
$500$		0			0
$501$	3.04827	−	7.35274i	0.136187	−	0.328496i
$502$		0			0
$503$	17.7556	+	30.7537i	0.791685	+	1.37124i	0.924923	+	0.380155i	$0.124129\pi$
$503$	17.7556	+	30.7537i	0.791685	+	1.37124i	−0.133238	+	0.991084i	$0.542537\pi$
$504$		0			0
$505$	0.140155	−	0.242755i	0.00623680	−	0.0108025i
$506$		0			0
$507$	6.68588	+	1.48439i	0.296930	+	0.0659241i
$508$		0			0
$509$	−31.5798	+	5.56837i	−1.39975	+	0.246814i	−0.822040	−	0.569429i	$-0.807164\pi$
$509$	−31.5798	+	5.56837i	−1.39975	+	0.246814i	−0.577709	+	0.816243i	$0.696053\pi$
$510$		0			0
$511$	5.86863	−	6.99396i	0.259613	−	0.309395i
$512$		0			0
$513$	−12.0154	+	15.6288i	−0.530493	+	0.690027i
$514$		0			0
$515$	23.7158	+	19.8999i	1.04504	+	0.876894i
$516$		0			0
$517$	−0.805688	−	4.56929i	−0.0354341	−	0.200957i
$518$		0			0
$519$	−5.71777	+	1.80086i	−0.250982	+	0.0790492i
$520$		0			0
$521$	−0.881959	−	0.509200i	−0.0386393	−	0.0223084i	0.480556	−	0.876964i	$-0.340435\pi$
$521$	−0.881959	−	0.509200i	−0.0386393	−	0.0223084i	−0.519195	+	0.854656i	$0.673768\pi$
$522$		0			0
$523$	2.29961	−	1.32768i	0.100555	−	0.0580555i	−0.448879	−	0.893592i	$-0.648177\pi$
$523$	2.29961	−	1.32768i	0.100555	−	0.0580555i	0.549434	+	0.835537i	$0.314843\pi$
$524$		0			0
$525$	−17.2489	+	13.2271i	−0.752805	+	0.577278i
$526$		0			0
$527$	−7.50055	+	6.29371i	−0.326729	+	0.274158i
$528$		0			0
$529$	17.8559	−	6.49902i	0.776344	−	0.282566i
$530$		0			0
$531$	−21.6646	−	10.1187i	−0.940165	−	0.439114i
$532$		0			0
$533$	−25.7581	−	4.54184i	−1.11571	−	0.196729i
$534$		0			0
$535$	12.1343	−	33.3388i	0.524612	−	1.44136i
$536$		0			0
$537$	−0.913157	+	0.475001i	−0.0394057	+	0.0204978i
$538$		0			0
$539$	35.0093			1.50796
$540$		0			0
$541$	−9.39810			−0.404056			−0.202028	−	0.979380i	$-0.564753\pi$
$541$	−9.39810			−0.404056			−0.202028	+	0.979380i	$0.564753\pi$
$542$		0			0
$543$	9.44669	+	6.02231i	0.405396	+	0.258442i
$544$		0			0
$545$	9.82842	−	27.0034i	0.421003	−	1.15670i
$546$		0			0
$547$	18.0711	+	3.18642i	0.772663	+	0.136241i	0.546060	−	0.837746i	$-0.316127\pi$
$547$	18.0711	+	3.18642i	0.772663	+	0.136241i	0.226603	+	0.973987i	$0.427238\pi$
$548$		0			0
$549$	5.09749	−	18.9771i	0.217555	−	0.809925i
$550$		0			0
$551$	11.9238	−	4.33991i	0.507972	−	0.184887i
$552$		0			0
$553$	−5.65608	+	4.74601i	−0.240521	+	0.201821i
$554$		0			0
$555$	9.06036	+	68.9850i	0.384591	+	2.92825i
$556$		0			0
$557$	−22.3343	+	12.8947i	−0.946334	+	0.546366i	−0.891940	−	0.452153i	$-0.850656\pi$
$557$	−22.3343	+	12.8947i	−0.946334	+	0.546366i	−0.0543940	+	0.998520i	$0.517323\pi$
$558$		0			0
$559$	13.4818	+	7.78369i	0.570217	+	0.329215i
$560$		0			0
$561$	−24.4281	−	22.3981i	−1.03136	−	0.945651i
$562$		0			0
$563$	−4.51280	−	25.5933i	−0.190192	−	1.07863i	−0.919102	−	0.394021i	$-0.871084\pi$
$563$	−4.51280	−	25.5933i	−0.190192	−	1.07863i	0.728910	−	0.684610i	$-0.240027\pi$
$564$		0			0
$565$	−13.7870	−	11.5687i	−0.580025	−	0.486699i
$566$		0			0
$567$	9.35024	+	3.41631i	0.392673	+	0.143471i
$568$		0			0
$569$	−22.4714	+	26.7804i	−0.942050	+	1.12269i	0.0502374	+	0.998737i	$0.484002\pi$
$569$	−22.4714	+	26.7804i	−0.942050	+	1.12269i	−0.992288	+	0.123955i	$0.960442\pi$
$570$		0			0
$571$	16.7380	−	2.95137i	0.700466	−	0.123511i	0.187937	−	0.982181i	$-0.439820\pi$
$571$	16.7380	−	2.95137i	0.700466	−	0.123511i	0.512529	+	0.858670i	$0.328709\pi$
$572$		0			0
$573$	26.0890	−	28.4535i	1.08988	−	1.18866i
$574$		0			0
$575$	−11.3433	+	19.6472i	−0.473050	+	0.819346i
$576$		0			0
$577$	−22.4525	−	38.8889i	−0.934711	−	1.61897i	−0.775149	−	0.631779i	$-0.782325\pi$
$577$	−22.4525	−	38.8889i	−0.934711	−	1.61897i	−0.159562	−	0.987188i	$-0.551008\pi$
$578$		0			0
$579$	−15.6874	+	2.06036i	−0.651947	+	0.0856255i
$580$		0			0
$581$	−8.46651	−	10.0900i	−0.351250	−	0.418604i
$582$		0			0
$583$	−6.61923	−	18.1862i	−0.274140	−	0.753194i
$584$		0			0
$585$	9.41989	+	35.2426i	0.389465	+	1.45710i
$586$		0			0
$587$	−0.297968	+	1.68986i	−0.0122985	+	0.0697481i	−0.990339	−	0.138665i	$-0.955719\pi$
$587$	−0.297968	+	1.68986i	−0.0122985	+	0.0697481i	0.978041	+	0.208413i	$0.0668299\pi$
$588$		0			0
$589$	11.0561	+	4.02409i	0.455559	+	0.165810i
$590$		0			0
$591$	18.2299	−	28.5956i	0.749876	−	1.17627i
$592$		0			0
$593$			6.04981i			0.248436i	0.992255	+	0.124218i	$0.0396422\pi$
$593$			6.04981i			0.248436i	−0.992255	+	0.124218i	$0.960358\pi$
$594$		0			0
$595$		−	14.1190i		−	0.578823i
$596$		0			0
$597$	10.4589	+	20.1066i	0.428056	+	0.822909i
$598$		0			0
$599$	24.8844	+	9.05720i	1.01675	+	0.370067i	0.796022	−	0.605268i	$-0.206934\pi$
$599$	24.8844	+	9.05720i	1.01675	+	0.370067i	0.220729	+	0.975335i	$0.429156\pi$
$600$		0			0
$601$	−5.02900	+	28.5209i	−0.205137	+	1.16339i	0.692086	+	0.721815i	$0.256692\pi$
$601$	−5.02900	+	28.5209i	−0.205137	+	1.16339i	−0.897224	+	0.441577i	$0.854419\pi$
$602$		0			0
$603$	8.50110	+	12.1568i	0.346191	+	0.495064i
$604$		0			0
$605$	35.5799	+	97.7550i	1.44653	+	3.97431i
$606$		0			0
$607$	−31.4425	−	37.4717i	−1.27621	−	1.52093i	−0.730394	−	0.683026i	$-0.760663\pi$
$607$	−31.4425	−	37.4717i	−1.27621	−	1.52093i	−0.545818	−	0.837904i	$-0.683781\pi$
$608$		0			0
$609$	−3.89913	−	5.08469i	−0.158001	−	0.206042i
$610$		0			0
$611$	−1.15128	−	1.99407i	−0.0465757	−	0.0806714i
$612$		0			0
$613$	−16.3748	+	28.3620i	−0.661371	+	1.14553i	0.318884	+	0.947794i	$0.396692\pi$
$613$	−16.3748	+	28.3620i	−0.661371	+	1.14553i	−0.980255	+	0.197735i	$0.936641\pi$
$614$		0			0
$615$	18.2944	+	58.0849i	0.737700	+	2.34221i
$616$		0			0
$617$	21.7419	−	3.83369i	0.875296	−	0.154338i	0.282089	−	0.959388i	$-0.408973\pi$
$617$	21.7419	−	3.83369i	0.875296	−	0.154338i	0.593207	+	0.805050i	$0.297861\pi$
$618$		0			0
$619$	13.2926	−	15.8415i	0.534276	−	0.636725i	−0.429618	−	0.903011i	$-0.641352\pi$
$619$	13.2926	−	15.8415i	0.534276	−	0.636725i	0.963894	+	0.266285i	$0.0857964\pi$
$620$		0			0
$621$	10.3804	−	0.443575i	0.416552	−	0.0178001i
$622$		0			0
$623$	10.6970	+	8.97587i	0.428567	+	0.359610i
$624$		0			0
$625$	8.16167	+	46.2871i	0.326467	+	1.85149i
$626$		0			0
$627$	−8.63179	+	38.8786i	−0.344721	+	1.55266i
$628$		0			0
$629$	−27.1670	−	15.6849i	−1.08322	−	0.625397i
$630$		0			0
$631$	17.6889	−	10.2127i	0.704182	−	0.406560i	−0.104721	−	0.994502i	$-0.533395\pi$
$631$	17.6889	−	10.2127i	0.704182	−	0.406560i	0.808903	+	0.587942i	$0.200062\pi$
$632$		0			0
$633$	13.5835	+	5.63139i	0.539896	+	0.223828i
$634$		0			0
$635$	−67.4092	+	56.5630i	−2.67505	+	2.24464i
$636$		0			0
$637$	16.3261	−	5.94220i	0.646863	−	0.235439i
$638$		0			0
$639$	10.9054	+	23.4246i	0.431413	+	0.926663i
$640$		0			0
$641$	28.5691	+	5.03751i	1.12841	+	0.198970i	0.706532	−	0.707681i	$-0.250259\pi$
$641$	28.5691	+	5.03751i	1.12841	+	0.198970i	0.421882	+	0.906651i	$0.361370\pi$
$642$		0			0
$643$	9.33983	−	25.6610i	0.368327	−	1.01197i	−0.607671	−	0.794189i	$-0.707896\pi$
$643$	9.33983	−	25.6610i	0.368327	−	1.01197i	0.975998	−	0.217781i	$-0.0698818\pi$
$644$		0			0
$645$	1.59220	−	36.2106i	0.0626930	−	1.42579i
$646$		0			0
$647$	−30.2231			−1.18819			−0.594096	−	0.804394i	$-0.702490\pi$
$647$	−30.2231			−1.18819			−0.594096	+	0.804394i	$0.702490\pi$
$648$		0			0
$649$	−48.3051			−1.89614
$650$		0			0
$651$	0.260991	−	5.93557i	0.0102290	−	0.232633i
$652$		0			0
$653$	8.57540	−	23.5607i	0.335581	−	0.922002i	−0.651050	−	0.759035i	$-0.725671\pi$
$653$	8.57540	−	23.5607i	0.335581	−	0.922002i	0.986631	−	0.162968i	$-0.0521066\pi$
$654$		0			0
$655$	6.71890	+	1.18472i	0.262529	+	0.0462910i
$656$		0			0
$657$	−14.2159	+	20.2757i	−0.554615	+	0.791032i
$658$		0			0
$659$	−4.97059	+	1.80915i	−0.193627	+	0.0704744i	−0.437013	−	0.899455i	$-0.643964\pi$
$659$	−4.97059	+	1.80915i	−0.193627	+	0.0704744i	0.243387	+	0.969929i	$0.421742\pi$
$660$		0			0
$661$	6.96047	−	5.84053i	0.270731	−	0.227170i	−0.497307	−	0.867575i	$-0.665678\pi$
$661$	6.96047	−	5.84053i	0.270731	−	0.227170i	0.768038	+	0.640405i	$0.221233\pi$
$662$		0			0
$663$	−15.1934	−	6.29881i	−0.590063	−	0.244626i
$664$		0			0
$665$	−14.6930	+	8.48303i	−0.569772	+	0.328958i
$666$		0			0
$667$	−5.79167	−	3.34382i	−0.224254	−	0.129473i
$668$		0			0
$669$	−1.68080	+	7.57052i	−0.0649835	+	0.292693i
$670$		0			0
$671$	−6.89321	−	39.0933i	−0.266109	−	1.50918i
$672$		0			0
$673$	21.6889	+	18.1991i	0.836045	+	0.701525i	0.956670	−	0.291173i	$-0.0940456\pi$
$673$	21.6889	+	18.1991i	0.836045	+	0.701525i	−0.120626	+	0.992698i	$0.538490\pi$
$674$		0			0
$675$	43.5034	−	39.7894i	1.67445	−	1.53149i
$676$		0			0
$677$	−13.8249	+	16.4759i	−0.531335	+	0.633221i	−0.963222	−	0.268707i	$-0.913404\pi$
$677$	−13.8249	+	16.4759i	−0.531335	+	0.633221i	0.431887	+	0.901928i	$0.357848\pi$
$678$		0			0
$679$	−7.11427	+	1.25444i	−0.273021	+	0.0481409i
$680$		0			0
$681$	2.74224	+	8.70667i	0.105083	+	0.333640i
$682$		0			0
$683$	−1.83973	+	3.18651i	−0.0703953	+	0.121928i	−0.899075	−	0.437795i	$-0.855759\pi$
$683$	−1.83973	+	3.18651i	−0.0703953	+	0.121928i	0.828679	+	0.559724i	$0.189093\pi$
$684$		0			0
$685$	−24.7019	−	42.7849i	−0.943809	−	1.63473i
$686$		0			0
$687$	4.82249	+	6.28881i	0.183989	+	0.239933i
$688$		0			0
$689$	−6.17356	−	7.35737i	−0.235194	−	0.280293i
$690$		0			0
$691$	0.481097	+	1.32180i	0.0183018	+	0.0502837i	0.948507	−	0.316756i	$-0.102594\pi$
$691$	0.481097	+	1.32180i	0.0183018	+	0.0502837i	−0.930205	+	0.367040i	$0.880371\pi$
$692$		0			0
$693$	20.0352	−	1.74037i	0.761073	−	0.0661112i
$694$		0			0
$695$	13.3023	−	75.4413i	0.504586	−	2.86165i
$696$		0			0
$697$	−25.8006	−	9.39065i	−0.977267	−	0.355696i
$698$		0			0
$699$	−7.09266	−	13.6352i	−0.268269	−	0.515729i
$700$		0			0
$701$			26.9701i			1.01865i	0.860575	+	0.509323i	$0.170104\pi$
$701$			26.9701i			1.01865i	−0.860575	+	0.509323i	$0.829896\pi$
$702$		0			0
$703$			37.6953i			1.42171i
$704$		0			0
$705$	−2.88188	+	4.52057i	−0.108538	+	0.170254i
$706$		0			0
$707$	−0.0720623	−	0.0262285i	−0.00271018	−	0.000986426i
$708$		0			0
$709$	−5.47277	+	31.0376i	−0.205534	+	1.16564i	0.691063	+	0.722795i	$0.257143\pi$
$709$	−5.47277	+	31.0376i	−0.205534	+	1.16564i	−0.896597	+	0.442847i	$0.853968\pi$
$710$		0			0
$711$	14.1692	−	14.1517i	0.531387	−	0.530730i
$712$		0			0
$713$	−2.12086	−	5.82701i	−0.0794267	−	0.218223i
$714$		0			0
$715$	47.3710	+	56.4545i	1.77157	+	2.11128i
$716$		0			0
$717$	−19.8472	+	2.60669i	−0.741207	+	0.0973486i
$718$		0			0
$719$	−3.71854	−	6.44071i	−0.138678	−	0.240198i	0.788318	−	0.615268i	$-0.210952\pi$
$719$	−3.71854	−	6.44071i	−0.138678	−	0.240198i	−0.926997	+	0.375070i	$0.877619\pi$
$720$		0			0
$721$	4.23485	−	7.33498i	0.157714	−	0.273169i
$722$		0			0
$723$	21.0048	−	22.9085i	0.781178	−	0.851977i
$724$		0			0
$725$	−37.3712	+	6.58955i	−1.38793	+	0.244730i
$726$		0			0
$727$	24.3792	−	29.0539i	0.904173	−	1.07755i	−0.0924731	−	0.995715i	$-0.529477\pi$
$727$	24.3792	−	29.0539i	0.904173	−	1.07755i	0.996646	−	0.0818359i	$-0.0260784\pi$
$728$		0			0
$729$	−26.0670	−	7.03647i	−0.965444	−	0.260610i
$730$		0			0
$731$	12.5185	+	10.5043i	0.463013	+	0.388514i
$732$		0			0
$733$	−7.08394	−	40.1750i	−0.261651	−	1.48390i	−0.778404	−	0.627764i	$-0.783970\pi$
$733$	−7.08394	−	40.1750i	−0.261651	−	1.48390i	0.516752	−	0.856135i	$-0.327141\pi$
$734$		0			0
$735$	−29.8156	−	27.3379i	−1.09976	−	1.00837i
$736$		0			0
$737$	25.9532	+	14.9841i	0.955997	+	0.551945i
$738$		0			0
$739$	−37.5716	+	21.6920i	−1.38210	+	0.797953i	−0.992407	−	0.122994i	$-0.960750\pi$
$739$	−37.5716	+	21.6920i	−1.38210	+	0.797953i	−0.389688	+	0.920947i	$0.627417\pi$
$740$		0			0
$741$	2.57365	+	19.5956i	0.0945453	+	0.719862i
$742$		0			0
$743$	−23.6176	+	19.8175i	−0.866444	+	0.727033i	−0.963346	−	0.268261i	$-0.913551\pi$
$743$	−23.6176	+	19.8175i	−0.866444	+	0.727033i	0.0969021	+	0.995294i	$0.469107\pi$
$744$		0			0
$745$	−12.1189	+	4.41093i	−0.444003	+	0.161604i
$746$		0			0
$747$	25.2455	+	25.2767i	0.923685	+	0.924828i
$748$		0			0
$749$	−9.55873	−	1.68546i	−0.349269	−	0.0615855i
$750$		0			0
$751$	−6.94105	+	19.0704i	−0.253283	+	0.695888i	0.746260	+	0.665654i	$0.231847\pi$
$751$	−6.94105	+	19.0704i	−0.253283	+	0.695888i	−0.999543	+	0.0302340i	$0.990375\pi$
$752$		0			0
$753$	−33.3951	−	21.2895i	−1.21698	−	0.775834i
$754$		0			0
$755$	−85.3092			−3.10472
$756$		0			0
$757$	−45.5588			−1.65586			−0.827931	−	0.560830i	$-0.810482\pi$
$757$	−45.5588			−1.65586			−0.827931	+	0.560830i	$0.810482\pi$
$758$		0			0
$759$	18.6209	−	9.68614i	0.675898	−	0.351585i
$760$		0			0
$761$	12.2329	−	33.6096i	0.443443	−	1.21835i	−0.493771	−	0.869592i	$-0.664382\pi$
$761$	12.2329	−	33.6096i	0.443443	−	1.21835i	0.937213	−	0.348756i	$-0.113396\pi$
$762$		0			0
$763$	−7.74227	−	1.36517i	−0.280289	−	0.0494225i
$764$		0			0
$765$	3.31399	+	38.1507i	0.119818	+	1.37934i
$766$		0			0
$767$	−22.5264	+	8.19894i	−0.813381	+	0.296046i
$768$		0			0
$769$	8.79701	−	7.38157i	0.317228	−	0.266186i	−0.470244	−	0.882537i	$-0.655834\pi$
$769$	8.79701	−	7.38157i	0.317228	−	0.266186i	0.787472	+	0.616350i	$0.211390\pi$
$770$		0			0
$771$	−7.51559	+	5.76322i	−0.270667	+	0.207557i
$772$		0			0
$773$	31.0680	−	17.9371i	1.11744	−	0.645153i	0.176693	−	0.984266i	$-0.443460\pi$
$773$	31.0680	−	17.9371i	1.11744	−	0.645153i	0.940746	+	0.339113i	$0.110127\pi$
$774$		0			0
$775$	−30.4722	−	17.5931i	−1.09459	−	0.631963i
$776$		0			0
$777$	18.1558	−	5.71833i	0.651336	−	0.205144i
$778$		0			0
$779$	5.72916	+	32.4917i	0.205269	+	1.16414i
$780$		0			0
$781$	39.9869	+	33.5530i	1.43084	+	1.20062i
$782$		0			0
$783$	11.7292	+	12.8241i	0.419168	+	0.458295i
$784$		0			0
$785$	−28.0129	+	33.3844i	−0.999822	+	1.19154i
$786$		0			0
$787$	53.8788	−	9.50029i	1.92057	−	0.338649i	0.921778	−	0.387719i	$-0.126737\pi$
$787$	53.8788	−	9.50029i	1.92057	−	0.338649i	0.998795	+	0.0490696i	$0.0156256\pi$
$788$		0			0
$789$	−26.3499	−	5.85017i	−0.938080	−	0.208272i
$790$		0			0
$791$	−2.46191	+	4.26415i	−0.0875354	+	0.151616i
$792$		0			0
$793$	−9.84995	−	17.0606i	−0.349782	−	0.605840i
$794$		0			0
$795$	−8.56390	+	20.6570i	−0.303730	+	0.732629i
$796$		0			0
$797$	10.5979	+	12.6301i	0.375397	+	0.447380i	0.920356	−	0.391082i	$-0.127899\pi$
$797$	10.5979	+	12.6301i	0.375397	+	0.447380i	−0.544959	+	0.838463i	$0.683455\pi$
$798$		0			0
$799$	−0.826692	−	2.27132i	−0.0292462	−	0.0803534i
$800$		0			0
$801$	−31.0110	−	21.7427i	−1.09572	−	0.768242i
$802$		0			0
$803$	−8.68685	+	49.2656i	−0.306552	+	1.73854i
$804$		0			0
$805$	8.40254	+	3.05827i	0.296151	+	0.107790i
$806$		0			0
$807$	−5.76130	−	0.253328i	−0.202807	−	0.00891756i
$808$		0			0
$809$			24.3400i			0.855747i	0.903839	+	0.427874i	$0.140737\pi$
$809$			24.3400i			0.855747i	−0.903839	+	0.427874i	$0.859263\pi$
$810$		0			0
$811$		−	12.6690i		−	0.444869i	−0.974948	−	0.222434i	$-0.928600\pi$
$811$		−	12.6690i		−	0.444869i	0.974948	−	0.222434i	$-0.0714003\pi$
$812$		0			0
$813$	−12.9228	−	0.568225i	−0.453224	−	0.0199285i
$814$		0			0
$815$	−35.9704	−	13.0922i	−1.25999	−	0.458599i
$816$		0			0
$817$	3.40993	−	19.3386i	0.119298	−	0.676574i
$818$		0			0
$819$	9.04771	−	4.21221i	0.316153	−	0.147187i
$820$		0			0
$821$	9.52718	+	26.1757i	0.332501	+	0.913539i	0.987459	+	0.157874i	$0.0504640\pi$
$821$	9.52718	+	26.1757i	0.332501	+	0.913539i	−0.654958	+	0.755665i	$0.727314\pi$
$822$		0			0
$823$	−3.07252	−	3.66168i	−0.107101	−	0.127638i	0.709831	−	0.704372i	$-0.248771\pi$
$823$	−3.07252	−	3.66168i	−0.107101	−	0.127638i	−0.816932	+	0.576734i	$0.804327\pi$
$824$		0			0
$825$	45.6120	−	110.021i	1.58801	−	3.83044i
$826$		0			0
$827$	−19.2477	−	33.3380i	−0.669309	−	1.15928i	−0.978098	−	0.208146i	$-0.933257\pi$
$827$	−19.2477	−	33.3380i	−0.669309	−	1.15928i	0.308789	−	0.951131i	$-0.400076\pi$
$828$		0			0
$829$	5.97867	−	10.3554i	0.207648	−	0.359657i	−0.743325	−	0.668930i	$-0.766753\pi$
$829$	5.97867	−	10.3554i	0.207648	−	0.359657i	0.950973	+	0.309274i	$0.100086\pi$
$830$		0			0
$831$	0.629571	+	0.139777i	0.0218396	+	0.00484880i
$832$		0			0
$833$	17.9610	−	3.16700i	0.622310	−	0.109730i
$834$		0			0
$835$	−11.9427	+	14.2327i	−0.413293	+	0.492544i
$836$		0			0
$837$	0.687969	+	16.0997i	0.0237797	+	0.556485i
$838$		0			0
$839$	8.53864	+	7.16477i	0.294787	+	0.247355i	0.778170	−	0.628053i	$-0.216148\pi$
$839$	8.53864	+	7.16477i	0.294787	+	0.247355i	−0.483384	+	0.875409i	$0.660592\pi$
$840$		0			0
$841$	3.09331	+	17.5430i	0.106666	+	0.604932i
$842$		0			0
$843$	−3.65566	+	1.15138i	−0.125908	+	0.0396558i
$844$		0			0
$845$	−13.8446	−	7.99321i	−0.476270	−	0.274975i
$846$		0			0
$847$	24.6473	−	14.2301i	0.846891	−	0.488953i
$848$		0			0
$849$	17.1699	−	13.1665i	0.589269	−	0.451873i
$850$		0			0
$851$	15.2190	−	12.7702i	0.521700	−	0.437758i
$852$		0			0
$853$	41.1723	−	14.9855i	1.40971	−	0.513093i	0.478667	−	0.877997i	$-0.341120\pi$
$853$	41.1723	−	14.9855i	1.40971	−	0.513093i	0.931045	+	0.364903i	$0.118898\pi$
$854$		0			0
$855$	37.7107	−	26.3706i	1.28968	−	0.901854i
$856$		0			0
$857$	20.1732	+	3.55708i	0.689104	+	0.121508i	0.507225	−	0.861813i	$-0.330671\pi$
$857$	20.1732	+	3.55708i	0.689104	+	0.121508i	0.181878	+	0.983321i	$0.441782\pi$
$858$		0			0
$859$	3.78049	−	10.3868i	0.128989	−	0.354393i	−0.858340	−	0.513081i	$-0.828504\pi$
$859$	3.78049	−	10.3868i	0.128989	−	0.354393i	0.987329	+	0.158688i	$0.0507263\pi$
$860$		0			0
$861$	14.7804	−	7.68837i	0.503714	−	0.262019i
$862$		0			0
$863$	33.2458			1.13170			0.565851	−	0.824508i	$-0.308548\pi$
$863$	33.2458			1.13170			0.565851	+	0.824508i	$0.308548\pi$
$864$		0			0
$865$	13.9930			0.475775
$866$		0			0
$867$	10.2700	+	6.54718i	0.348788	+	0.222354i
$868$		0			0
$869$	13.8368	−	38.0163i	0.469382	−	1.28962i
$870$		0			0
$871$	14.6462	+	2.58251i	0.496266	+	0.0875051i
$872$		0			0
$873$	18.9289	−	5.05944i	0.640646	−	0.171236i
$874$		0			0
$875$	26.6673	−	9.70612i	0.901521	−	0.328127i
$876$		0			0
$877$	13.6667	−	11.4677i	0.461491	−	0.387237i	−0.382188	−	0.924085i	$-0.624829\pi$
$877$	13.6667	−	11.4677i	0.461491	−	0.387237i	0.843679	+	0.536847i	$0.180385\pi$
$878$		0			0
$879$	−3.95499	−	30.1130i	−0.133398	−	1.01569i
$880$		0			0
$881$	−24.4208	+	14.0993i	−0.822756	+	0.475019i	−0.851366	−	0.524572i	$-0.824225\pi$
$881$	−24.4208	+	14.0993i	−0.822756	+	0.475019i	0.0286097	+	0.999591i	$0.490892\pi$
$882$		0			0
$883$	25.3714	+	14.6482i	0.853815	+	0.492950i	0.861936	−	0.507017i	$-0.169252\pi$
$883$	25.3714	+	14.6482i	0.853815	+	0.492950i	−0.00812108	+	0.999967i	$0.502585\pi$
$884$		0			0
$885$	41.1390	+	37.7203i	1.38287	+	1.26795i
$886$		0			0
$887$	−5.29796	−	30.0463i	−0.177888	−	1.00885i	−0.934757	−	0.355288i	$-0.884383\pi$
$887$	−5.29796	−	30.0463i	−0.177888	−	1.00885i	0.756869	−	0.653567i	$-0.226728\pi$
$888$		0			0
$889$	18.4418	+	15.4745i	0.618519	+	0.518999i
$890$		0			0
$891$	−53.7281	+	9.40524i	−1.79996	+	0.315087i
$892$		0			0
$893$	−1.86697	+	2.22496i	−0.0624756	+	0.0744555i
$894$		0			0
$895$	2.36615	−	0.417217i	0.0790918	−	0.0139460i
$896$		0			0
$897$	7.03956	−	7.67757i	0.235044	−	0.256347i
$898$		0			0
$899$	5.18615	−	8.98267i	0.172968	−	0.299589i
$900$		0			0
$901$	−5.04104	−	8.73134i	−0.167942	−	0.290883i
$902$		0			0
$903$	−9.83166	+	1.29127i	−0.327177	+	0.0429708i
$904$		0			0
$905$	−16.8093	−	20.0325i	−0.558758	−	0.665902i
$906$		0			0
$907$	−14.8367	−	40.7636i	−0.492646	−	1.35353i	−0.898250	−	0.439485i	$-0.855161\pi$
$907$	−14.8367	−	40.7636i	−0.492646	−	1.35353i	0.405604	−	0.914049i	$-0.367061\pi$
$908$		0			0
$909$	0.200875	+	0.0539573i	0.00666259	+	0.00178965i
$910$		0			0
$911$	4.10884	−	23.3024i	0.136132	−	0.772042i	−0.837933	−	0.545773i	$-0.816236\pi$
$911$	4.10884	−	23.3024i	0.136132	−	0.772042i	0.974065	−	0.226269i	$-0.0726529\pi$
$912$		0			0
$913$	67.8181	+	24.6838i	2.24445	+	0.816914i
$914$		0			0
$915$	−24.6565	+	38.6765i	−0.815118	+	1.27861i
$916$		0			0
$917$		−	1.86652i		−	0.0616378i
$918$		0			0
$919$		−	11.1644i		−	0.368278i	−0.982900	−	0.184139i	$-0.941050\pi$
$919$		−	11.1644i		−	0.368278i	0.982900	−	0.184139i	$-0.0589497\pi$
$920$		0			0
$921$	−7.61886	−	14.6467i	−0.251050	−	0.482627i
$922$		0			0
$923$	24.3423	+	8.85988i	0.801237	+	0.291627i
$924$		0			0
$925$	19.5756	−	111.019i	0.643641	−	3.65027i
$926$		0			0
$927$	−9.72126	+	20.8137i	−0.319288	+	0.683612i
$928$		0			0
$929$	−3.45084	−	9.48112i	−0.113219	−	0.311065i	0.870123	−	0.492835i	$-0.164040\pi$
$929$	−3.45084	−	9.48112i	−0.113219	−	0.311065i	−0.983341	+	0.181770i	$0.941817\pi$
$930$		0			0
$931$	−14.0871	−	16.7884i	−0.461687	−	0.550217i
$932$		0			0
$933$	33.8991	+	44.2065i	1.10981	+	1.44726i
$934$		0			0
$935$	38.6809	+	66.9974i	1.26500	+	2.19105i
$936$		0			0
$937$	−10.6352	+	18.4207i	−0.347437	+	0.601779i	−0.985793	−	0.167962i	$-0.946281\pi$
$937$	−10.6352	+	18.4207i	−0.347437	+	0.601779i	0.638356	+	0.769741i	$0.279615\pi$
$938$		0			0
$939$	−1.65860	−	5.26609i	−0.0541265	−	0.171852i
$940$		0			0
$941$	46.7214	−	8.23825i	1.52308	−	0.268559i	0.651435	−	0.758705i	$-0.274167\pi$
$941$	46.7214	−	8.23825i	1.52308	−	0.268559i	0.871641	+	0.490145i	$0.163056\pi$
$942$		0			0
$943$	11.1772	−	13.3204i	0.363979	−	0.433773i
$944$		0			0
$945$	−18.4219	−	14.1628i	−0.599265	−	0.460716i
$946$		0			0
$947$	−6.99920	−	5.87302i	−0.227443	−	0.190848i	0.521944	−	0.852980i	$-0.325207\pi$
$947$	−6.99920	−	5.87302i	−0.227443	−	0.190848i	−0.749387	+	0.662132i	$0.769652\pi$
$948$		0			0
$949$	4.31097	+	24.4487i	0.139940	+	0.793640i
$950$		0			0
$951$	−2.61535	+	11.7798i	−0.0848085	+	0.381987i
$952$		0			0
$953$	−31.4382	−	18.1509i	−1.01838	−	0.587964i	−0.104748	−	0.994499i	$-0.533404\pi$
$953$	−31.4382	−	18.1509i	−1.01838	−	0.587964i	−0.913635	+	0.406535i	$0.866737\pi$
$954$		0			0
$955$	−78.0373	+	45.0549i	−2.52523	+	1.45794i
$956$		0			0
$957$	32.4323	+	13.4456i	1.04839	+	0.434636i
$958$		0			0
$959$	−10.3538	+	8.68785i	−0.334341	+	0.280545i
$960$		0			0
$961$	−20.0930	+	7.31325i	−0.648161	+	0.235911i
$962$		0			0
$963$	26.2241	+	2.31065i	0.845059	+	0.0744596i
$964$		0			0
$965$	36.3715	+	6.41329i	1.17084	+	0.206451i
$966$		0			0
$967$	6.23041	−	17.1179i	0.200357	−	0.550475i	−0.798302	−	0.602258i	$-0.794268\pi$
$967$	6.23041	−	17.1179i	0.200357	−	0.550475i	0.998658	+	0.0517824i	$0.0164902\pi$
$968$		0			0
$969$	−0.911376	+	20.7269i	−0.0292776	+	0.665845i
$970$		0			0
$971$	21.3471			0.685062			0.342531	−	0.939507i	$-0.388716\pi$
$971$	21.3471			0.685062			0.342531	+	0.939507i	$0.388716\pi$
$972$		0			0
$973$	−20.9577			−0.671872
$974$		0			0
$975$	2.59640	−	59.0485i	0.0831514	−	1.89107i
$976$		0			0
$977$	−4.60332	+	12.6475i	−0.147273	+	0.404630i	−0.991292	−	0.131684i	$-0.957962\pi$
$977$	−4.60332	+	12.6475i	−0.147273	+	0.404630i	0.844018	+	0.536314i	$0.180184\pi$
$978$		0			0
$979$	−75.3500	−	13.2862i	−2.40820	−	0.424630i
$980$		0			0
$981$	21.2407	+	1.87155i	0.678163	+	0.0597540i
$982$		0			0
$983$	46.5988	−	16.9606i	1.48627	−	0.540959i	0.533807	−	0.845606i	$-0.320761\pi$
$983$	46.5988	−	16.9606i	1.48627	−	0.540959i	0.952465	+	0.304647i	$0.0985386\pi$
$984$		0			0
$985$	−60.6394	+	50.8825i	−1.93213	+	1.62125i
$986$		0			0
$987$	1.35486	+	0.561692i	0.0431257	+	0.0178789i
$988$		0			0
$989$	−8.96291	+	5.17474i	−0.285004	+	0.164547i
$990$		0			0
$991$	35.6190	+	20.5647i	1.13148	+	0.653258i	0.944306	−	0.329070i	$-0.106735\pi$
$991$	35.6190	+	20.5647i	1.13148	+	0.653258i	0.187170	+	0.982328i	$0.440068\pi$
$992$		0			0
$993$	−6.20306	+	27.9393i	−0.196848	+	0.886627i
$994$		0			0
$995$	−9.18660	−	52.0998i	−0.291235	−	1.65168i
$996$		0			0
$997$	−19.4258	−	16.3002i	−0.615221	−	0.516232i	0.281076	−	0.959686i	$-0.409309\pi$
$997$	−19.4258	−	16.3002i	−0.615221	−	0.516232i	−0.896297	+	0.443453i	$0.853753\pi$
$998$		0			0
$999$	−47.7163	+	19.7129i	−1.50968	+	0.623689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.335.4	✓	36
4.3	odd	2		432.2.be.c.335.3	yes	36
27.5	odd	18		432.2.be.c.383.3	yes	36
108.59	even	18	inner	432.2.be.b.383.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.4	✓	36	1.1	even	1	trivial
432.2.be.b.383.4	yes	36	108.59	even	18	inner
432.2.be.c.335.3	yes	36	4.3	odd	2
432.2.be.c.383.3	yes	36	27.5	odd	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +O(q^{10})\)	\(q+(0.0760859 - 1.73038i) q^{3} +(-1.38279 + 3.79919i) q^{5} +(1.08929 + 0.192071i) q^{7} +(-2.98842 - 0.263315i) q^{9} +(-5.69507 + 2.07284i) q^{11} +(-2.30399 + 1.93328i) q^{13} +(6.46883 + 2.68182i) q^{15} +(-2.73425 + 1.57862i) q^{17} +(3.28561 + 1.89695i) q^{19} +(0.415234 - 1.87026i) q^{21} +(-0.347216 - 1.96916i) q^{23} +(-8.69152 - 7.29305i) q^{25} +(-0.683011 + 5.15107i) q^{27} +(2.14987 - 2.56211i) q^{29} +(3.05409 - 0.538519i) q^{31} +(3.15348 + 10.0123i) q^{33} +(-2.23597 + 3.87281i) q^{35} +(4.96790 + 8.60465i) q^{37} +(3.17000 + 4.13387i) q^{39} +(5.58989 + 6.66177i) q^{41} +(-1.77028 - 4.86379i) q^{43} +(5.13275 - 10.9895i) q^{45} +(-0.132939 + 0.753937i) q^{47} +(-5.42820 - 1.97570i) q^{49} +(2.52358 + 4.85141i) q^{51} +3.19332i q^{53} -24.5030i q^{55} +(3.53243 - 5.54102i) q^{57} +(7.48972 + 2.72603i) q^{59} +(-1.13739 + 6.45044i) q^{61} +(-3.20467 - 0.860813i) q^{63} +(-4.15895 - 11.4266i) q^{65} +(-3.17844 - 3.78791i) q^{67} +(-3.43381 + 0.450990i) q^{69} +(-4.30646 - 7.45900i) q^{71} +(4.12714 - 7.14841i) q^{73} +(-13.2810 + 14.4847i) q^{75} +(-6.60169 + 1.16406i) q^{77} +(-4.29080 + 5.11358i) q^{79} +(8.86133 + 1.57379i) q^{81} +(-9.12222 - 7.65445i) q^{83} +(-2.21658 - 12.5709i) q^{85} +(-4.26985 - 3.91503i) q^{87} +(10.9332 + 6.31231i) q^{89} +(-2.88103 + 1.66336i) q^{91} +(-0.699469 - 5.32571i) q^{93} +(-11.7502 + 9.85957i) q^{95} +(-6.13725 + 2.23378i) q^{97} +(17.5651 - 4.69491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 - 18 * q^11 + 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 + 27 * q^31 + 27 * q^33 + 27 * q^35 - 45 * q^39 + 18 * q^41 + 27 * q^45 + 45 * q^47 - 63 * q^51 - 9 * q^57 + 54 * q^59 - 63 * q^63 - 57 * q^65 - 63 * q^69 + 36 * q^71 + 9 * q^73 - 45 * q^75 - 81 * q^77 - 54 * q^81 - 27 * q^83 - 36 * q^85 + 45 * q^87 - 63 * q^89 + 27 * q^91 - 63 * q^93 - 72 * q^95 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more