LMFDB - Embedded newform 1380.2.r.c.737.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.16
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.136960 - 1.72663i) q^{3} +(-2.01176 - 0.976134i) q^{5} +(-0.818985 - 0.818985i) q^{7} +(-2.96248 + 0.472958i) q^{9} +O(q^{10})$	\(q+(-0.136960 - 1.72663i) q^{3} +(-2.01176 - 0.976134i) q^{5} +(-0.818985 - 0.818985i) q^{7} +(-2.96248 + 0.472958i) q^{9} -4.64173i q^{11} +(1.65679 - 1.65679i) q^{13} +(-1.40989 + 3.60724i) q^{15} +(5.49751 - 5.49751i) q^{17} +1.07783i q^{19} +(-1.30191 + 1.52625i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(3.09433 + 3.92749i) q^{25} +(1.22236 + 5.05033i) q^{27} -8.03222 q^{29} -3.08833 q^{31} +(-8.01454 + 0.635731i) q^{33} +(0.848160 + 2.44704i) q^{35} +(-2.77607 - 2.77607i) q^{37} +(-3.08758 - 2.63375i) q^{39} +11.8391i q^{41} +(-6.17071 + 6.17071i) q^{43} +(6.42147 + 1.94030i) q^{45} +(-5.23937 + 5.23937i) q^{47} -5.65853i q^{49} +(-10.2451 - 8.73922i) q^{51} +(-1.39767 - 1.39767i) q^{53} +(-4.53095 + 9.33803i) q^{55} +(1.86101 - 0.147620i) q^{57} -4.09918 q^{59} +8.47597 q^{61} +(2.81358 + 2.03889i) q^{63} +(-4.95031 + 1.71581i) q^{65} +(1.89161 + 1.89161i) q^{67} +(-1.12406 + 1.31776i) q^{69} +0.766555i q^{71} +(0.976885 - 0.976885i) q^{73} +(6.35751 - 5.88066i) q^{75} +(-3.80151 + 3.80151i) q^{77} -4.42798i q^{79} +(8.55262 - 2.80226i) q^{81} +(3.24062 + 3.24062i) q^{83} +(-16.4260 + 5.69335i) q^{85} +(1.10009 + 13.8687i) q^{87} +10.8779 q^{89} -2.71378 q^{91} +(0.422978 + 5.33240i) q^{93} +(1.05211 - 2.16833i) q^{95} +(-1.81549 - 1.81549i) q^{97} +(2.19534 + 13.7510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.136960	−	1.72663i	−0.0790739	−	0.996869i
$3$	−0.136960	−	1.72663i	−0.0790739	−	0.996869i
$4$		0			0
$5$	−2.01176	−	0.976134i	−0.899685	−	0.436540i
$5$	−2.01176	−	0.976134i	−0.899685	−	0.436540i
$6$		0			0
$7$	−0.818985	−	0.818985i	−0.309547	−	0.309547i	0.535187	−	0.844734i	$-0.320241\pi$
$7$	−0.818985	−	0.818985i	−0.309547	−	0.309547i	−0.844734	+	0.535187i	$0.820241\pi$
$8$		0			0
$9$	−2.96248	+	0.472958i	−0.987495	+	0.157653i
$10$		0			0
$11$		−	4.64173i		−	1.39953i	−0.714371	−	0.699767i	$-0.753287\pi$
$11$		−	4.64173i		−	1.39953i	0.714371	−	0.699767i	$-0.246713\pi$
$12$		0			0
$13$	1.65679	−	1.65679i	0.459511	−	0.459511i	−0.438984	−	0.898495i	$-0.644661\pi$
$13$	1.65679	−	1.65679i	0.459511	−	0.459511i	0.898495	+	0.438984i	$0.144661\pi$
$14$		0			0
$15$	−1.40989	+	3.60724i	−0.364032	+	0.931387i
$16$		0			0
$17$	5.49751	−	5.49751i	1.33334	−	1.33334i	0.430983	−	0.902360i	$-0.358167\pi$
$17$	5.49751	−	5.49751i	1.33334	−	1.33334i	0.902360	−	0.430983i	$-0.141833\pi$
$18$		0			0
$19$			1.07783i			0.247271i	0.992328	+	0.123636i	$0.0394554\pi$
$19$			1.07783i			0.247271i	−0.992328	+	0.123636i	$0.960545\pi$
$20$		0			0
$21$	−1.30191	+	1.52625i	−0.284101	+	0.333055i
$22$		0			0
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	3.09433	+	3.92749i	0.618865	+	0.785497i
$26$		0			0
$27$	1.22236	+	5.05033i	0.235244	+	0.971936i
$28$		0			0
$29$	−8.03222			−1.49155			−0.745773	−	0.666200i	$-0.767920\pi$
$29$	−8.03222			−1.49155			−0.745773	+	0.666200i	$0.767920\pi$
$30$		0			0
$31$	−3.08833			−0.554681			−0.277341	−	0.960772i	$-0.589453\pi$
$31$	−3.08833			−0.554681			−0.277341	+	0.960772i	$0.589453\pi$
$32$		0			0
$33$	−8.01454	+	0.635731i	−1.39515	+	0.110667i
$34$		0			0
$35$	0.848160	+	2.44704i	0.143365	+	0.413625i
$36$		0			0
$37$	−2.77607	−	2.77607i	−0.456382	−	0.456382i	0.441084	−	0.897466i	$-0.354594\pi$
$37$	−2.77607	−	2.77607i	−0.456382	−	0.456382i	−0.897466	+	0.441084i	$0.854594\pi$
$38$		0			0
$39$	−3.08758	−	2.63375i	−0.494408	−	0.421737i
$40$		0			0
$41$			11.8391i			1.84896i	0.381229	+	0.924481i	$0.375501\pi$
$41$			11.8391i			1.84896i	−0.381229	+	0.924481i	$0.624499\pi$
$42$		0			0
$43$	−6.17071	+	6.17071i	−0.941024	+	0.941024i	−0.998355	−	0.0573315i	$-0.981741\pi$
$43$	−6.17071	+	6.17071i	−0.941024	+	0.941024i	0.0573315	+	0.998355i	$0.481741\pi$
$44$		0			0
$45$	6.42147	+	1.94030i	0.957256	+	0.289244i
$46$		0			0
$47$	−5.23937	+	5.23937i	−0.764241	+	0.764241i	−0.977086	−	0.212845i	$-0.931727\pi$
$47$	−5.23937	+	5.23937i	−0.764241	+	0.764241i	0.212845	+	0.977086i	$0.431727\pi$
$48$		0			0
$49$		−	5.65853i		−	0.808361i
$50$		0			0
$51$	−10.2451	−	8.73922i	−1.43460	−	1.22374i
$52$		0			0
$53$	−1.39767	−	1.39767i	−0.191984	−	0.191984i	0.604569	−	0.796553i	$-0.293345\pi$
$53$	−1.39767	−	1.39767i	−0.191984	−	0.191984i	−0.796553	+	0.604569i	$0.793345\pi$
$54$		0			0
$55$	−4.53095	+	9.33803i	−0.610953	+	1.25914i
$56$		0			0
$57$	1.86101	−	0.147620i	0.246497	−	0.0195527i
$58$		0			0
$59$	−4.09918			−0.533667			−0.266834	−	0.963743i	$-0.585977\pi$
$59$	−4.09918			−0.533667			−0.266834	+	0.963743i	$0.585977\pi$
$60$		0			0
$61$	8.47597			1.08524			0.542618	−	0.839979i	$-0.317433\pi$
$61$	8.47597			1.08524			0.542618	+	0.839979i	$0.317433\pi$
$62$		0			0
$63$	2.81358	+	2.03889i	0.354477	+	0.256875i
$64$		0			0
$65$	−4.95031	+	1.71581i	−0.614010	+	0.212820i
$66$		0			0
$67$	1.89161	+	1.89161i	0.231096	+	0.231096i	0.813150	−	0.582054i	$-0.197751\pi$
$67$	1.89161	+	1.89161i	0.231096	+	0.231096i	−0.582054	+	0.813150i	$0.697751\pi$
$68$		0			0
$69$	−1.12406	+	1.31776i	−0.135321	+	0.158639i
$70$		0			0
$71$			0.766555i			0.0909733i	0.998965	+	0.0454867i	$0.0144838\pi$
$71$			0.766555i			0.0909733i	−0.998965	+	0.0454867i	$0.985516\pi$
$72$		0			0
$73$	0.976885	−	0.976885i	0.114336	−	0.114336i	−0.647624	−	0.761960i	$-0.724237\pi$
$73$	0.976885	−	0.976885i	0.114336	−	0.114336i	0.761960	+	0.647624i	$0.224237\pi$
$74$		0			0
$75$	6.35751	−	5.88066i	0.734102	−	0.679040i
$76$		0			0
$77$	−3.80151	+	3.80151i	−0.433222	+	0.433222i
$78$		0			0
$79$		−	4.42798i		−	0.498186i	−0.968480	−	0.249093i	$-0.919867\pi$
$79$		−	4.42798i		−	0.498186i	0.968480	−	0.249093i	$-0.0801325\pi$
$80$		0			0
$81$	8.55262	−	2.80226i	0.950291	−	0.311362i
$82$		0			0
$83$	3.24062	+	3.24062i	0.355705	+	0.355705i	0.862227	−	0.506522i	$-0.169069\pi$
$83$	3.24062	+	3.24062i	0.355705	+	0.355705i	−0.506522	+	0.862227i	$0.669069\pi$
$84$		0			0
$85$	−16.4260	+	5.69335i	−1.78165	+	0.617530i
$86$		0			0
$87$	1.10009	+	13.8687i	0.117942	+	1.48688i
$88$		0			0
$89$	10.8779			1.15306			0.576528	−	0.817077i	$-0.304407\pi$
$89$	10.8779			1.15306			0.576528	+	0.817077i	$0.304407\pi$
$90$		0			0
$91$	−2.71378			−0.284481
$92$		0			0
$93$	0.422978	+	5.33240i	0.0438608	+	0.552944i
$94$		0			0
$95$	1.05211	−	2.16833i	0.107944	−	0.222466i
$96$		0			0
$97$	−1.81549	−	1.81549i	−0.184335	−	0.184335i	0.608907	−	0.793242i	$-0.291608\pi$
$97$	−1.81549	−	1.81549i	−0.184335	−	0.184335i	−0.793242	+	0.608907i	$0.791608\pi$
$98$		0			0
$99$	2.19534	+	13.7510i	0.220640	+	1.38203i
$100$		0			0
$101$		−	5.31484i		−	0.528847i	−0.964407	−	0.264423i	$-0.914818\pi$
$101$		−	5.31484i		−	0.528847i	0.964407	−	0.264423i	$-0.0851816\pi$
$102$		0			0
$103$	−5.54157	+	5.54157i	−0.546027	+	0.546027i	−0.925289	−	0.379262i	$-0.876178\pi$
$103$	−5.54157	+	5.54157i	−0.546027	+	0.546027i	0.379262	+	0.925289i	$0.376178\pi$
$104$		0			0
$105$	4.10896	−	1.79960i	0.400993	−	0.175623i
$106$		0			0
$107$	−1.27792	+	1.27792i	−0.123541	+	0.123541i	−0.766174	−	0.642633i	$-0.777842\pi$
$107$	−1.27792	+	1.27792i	−0.123541	+	0.123541i	0.642633	+	0.766174i	$0.277842\pi$
$108$		0			0
$109$		−	16.8548i		−	1.61440i	−0.590277	−	0.807201i	$-0.700982\pi$
$109$		−	16.8548i		−	1.61440i	0.590277	−	0.807201i	$-0.299018\pi$
$110$		0			0
$111$	−4.41302	+	5.17344i	−0.418865	+	0.491041i
$112$		0			0
$113$	12.3189	+	12.3189i	1.15886	+	1.15886i	0.984721	+	0.174140i	$0.0557145\pi$
$113$	12.3189	+	12.3189i	1.15886	+	1.15886i	0.174140	+	0.984721i	$0.444285\pi$
$114$		0			0
$115$	0.732296	+	2.11276i	0.0682869	+	0.197016i
$116$		0			0
$117$	−4.12463	+	5.69181i	−0.381322	+	0.526208i
$118$		0			0
$119$	−9.00477			−0.825466
$120$		0			0
$121$	−10.5456			−0.958695
$122$		0			0
$123$	20.4418	−	1.62149i	1.84317	−	0.146205i
$124$		0			0
$125$	−2.39128	−	10.9216i	−0.213882	−	0.976859i
$126$		0			0
$127$	−3.95997	−	3.95997i	−0.351390	−	0.351390i	0.509236	−	0.860627i	$-0.329928\pi$
$127$	−3.95997	−	3.95997i	−0.351390	−	0.351390i	−0.860627	+	0.509236i	$0.829928\pi$
$128$		0			0
$129$	11.4996	+	9.80937i	1.01249	+	0.863667i
$130$		0			0
$131$		−	17.2941i		−	1.51099i	−0.655154	−	0.755495i	$-0.727396\pi$
$131$		−	17.2941i		−	1.51099i	0.655154	−	0.755495i	$-0.272604\pi$
$132$		0			0
$133$	0.882727	−	0.882727i	0.0765421	−	0.0765421i
$134$		0			0
$135$	2.47070	−	11.3532i	0.212644	−	0.977130i
$136$		0			0
$137$	−8.34377	+	8.34377i	−0.712857	+	0.712857i	−0.967132	−	0.254275i	$-0.918163\pi$
$137$	−8.34377	+	8.34377i	−0.712857	+	0.712857i	0.254275	+	0.967132i	$0.418163\pi$
$138$		0			0
$139$		−	15.3856i		−	1.30499i	−0.757795	−	0.652493i	$-0.773723\pi$
$139$		−	15.3856i		−	1.30499i	0.757795	−	0.652493i	$-0.226277\pi$
$140$		0			0
$141$	9.76403	+	8.32886i	0.822279	+	0.701416i
$142$		0			0
$143$	−7.69038	−	7.69038i	−0.643101	−	0.643101i
$144$		0			0
$145$	16.1589	+	7.84052i	1.34192	+	0.651120i
$146$		0			0
$147$	−9.77017	+	0.774992i	−0.805830	+	0.0639202i
$148$		0			0
$149$	−13.9315			−1.14132			−0.570658	−	0.821188i	$-0.693312\pi$
$149$	−13.9315			−1.14132			−0.570658	+	0.821188i	$0.693312\pi$
$150$		0			0
$151$	−7.88187			−0.641417			−0.320709	−	0.947178i	$-0.603921\pi$
$151$	−7.88187			−0.641417			−0.320709	+	0.947178i	$0.603921\pi$
$152$		0			0
$153$	−13.6862	+	18.8864i	−1.10646	+	1.52687i
$154$		0			0
$155$	6.21297	+	3.01463i	0.499038	+	0.242141i
$156$		0			0
$157$	13.9278	+	13.9278i	1.11156	+	1.11156i	0.992939	+	0.118623i	$0.0378480\pi$
$157$	13.9278	+	13.9278i	1.11156	+	1.11156i	0.118623	+	0.992939i	$0.462152\pi$
$158$		0			0
$159$	−2.22182	+	2.60467i	−0.176202	+	0.206564i
$160$		0			0
$161$			1.15822i			0.0912805i
$162$		0			0
$163$	7.40789	−	7.40789i	0.580231	−	0.580231i	−0.354736	−	0.934967i	$-0.615429\pi$
$163$	7.40789	−	7.40789i	0.580231	−	0.580231i	0.934967	+	0.354736i	$0.115429\pi$
$164$		0			0
$165$	16.7438	+	6.54432i	1.30351	+	0.509475i
$166$		0			0
$167$	12.0344	−	12.0344i	0.931250	−	0.931250i	−0.0665339	−	0.997784i	$-0.521194\pi$
$167$	12.0344	−	12.0344i	0.931250	−	0.931250i	0.997784	+	0.0665339i	$0.0211941\pi$
$168$		0			0
$169$			7.51009i			0.577699i
$170$		0			0
$171$	−0.509768	−	3.19305i	−0.0389829	−	0.244179i
$172$		0			0
$173$	−2.67284	−	2.67284i	−0.203212	−	0.203212i	0.598163	−	0.801375i	$-0.295898\pi$
$173$	−2.67284	−	2.67284i	−0.203212	−	0.203212i	−0.801375	+	0.598163i	$0.795898\pi$
$174$		0			0
$175$	0.682346	−	5.75076i	0.0515805	−	0.434717i
$176$		0			0
$177$	0.561423	+	7.07775i	0.0421991	+	0.531996i
$178$		0			0
$179$	−17.6346			−1.31807			−0.659035	−	0.752112i	$-0.729035\pi$
$179$	−17.6346			−1.31807			−0.659035	+	0.752112i	$0.729035\pi$
$180$		0			0
$181$	−14.0816			−1.04668			−0.523340	−	0.852124i	$-0.675314\pi$
$181$	−14.0816			−1.04668			−0.523340	+	0.852124i	$0.675314\pi$
$182$		0			0
$183$	−1.16087	−	14.6348i	−0.0858139	−	1.08184i
$184$		0			0
$185$	2.87496	+	8.29458i	0.211371	+	0.609830i
$186$		0			0
$187$	−25.5180	−	25.5180i	−1.86606	−	1.86606i
$188$		0			0
$189$	3.13505	−	5.13724i	0.228041	−	0.373680i
$190$		0			0
$191$		−	10.2736i		−	0.743371i	−0.928359	−	0.371685i	$-0.878780\pi$
$191$		−	10.2736i		−	0.743371i	0.928359	−	0.371685i	$-0.121220\pi$
$192$		0			0
$193$	7.94625	−	7.94625i	0.571984	−	0.571984i	−0.360699	−	0.932682i	$-0.617462\pi$
$193$	7.94625	−	7.94625i	0.571984	−	0.571984i	0.932682	+	0.360699i	$0.117462\pi$
$194$		0			0
$195$	3.64056	+	8.31234i	0.260706	+	0.595259i
$196$		0			0
$197$	5.62730	−	5.62730i	0.400929	−	0.400929i	−0.477632	−	0.878560i	$-0.658505\pi$
$197$	5.62730	−	5.62730i	0.400929	−	0.400929i	0.878560	+	0.477632i	$0.158505\pi$
$198$		0			0
$199$		−	22.0362i		−	1.56210i	−0.624466	−	0.781052i	$-0.714684\pi$
$199$		−	22.0362i		−	1.56210i	0.624466	−	0.781052i	$-0.285316\pi$
$200$		0			0
$201$	3.00702	−	3.52517i	0.212099	−	0.248646i
$202$		0			0
$203$	6.57827	+	6.57827i	0.461704	+	0.461704i
$204$		0			0
$205$	11.5566	−	23.8174i	0.807146	−	1.66348i
$206$		0			0
$207$	2.42922	+	1.76036i	0.168843	+	0.122354i
$208$		0			0
$209$	5.00299			0.346064
$210$		0			0
$211$	−5.47434			−0.376869			−0.188435	−	0.982086i	$-0.560341\pi$
$211$	−5.47434			−0.376869			−0.188435	+	0.982086i	$0.560341\pi$
$212$		0			0
$213$	1.32355	−	0.104987i	0.0906884	−	0.00719361i
$214$		0			0
$215$	18.4374	−	6.39052i	1.25742	−	0.435830i
$216$		0			0
$217$	2.52930	+	2.52930i	0.171700	+	0.171700i
$218$		0			0
$219$	−1.82051	−	1.55292i	−0.123019	−	0.104937i
$220$		0			0
$221$		−	18.2165i		−	1.22537i
$222$		0			0
$223$	−16.7499	+	16.7499i	−1.12166	+	1.12166i	−0.130167	+	0.991492i	$0.541551\pi$
$223$	−16.7499	+	16.7499i	−1.12166	+	1.12166i	−0.991492	+	0.130167i	$0.958449\pi$
$224$		0			0
$225$	−11.0244	−	10.1716i	−0.734962	−	0.678109i
$226$		0			0
$227$	−14.4091	+	14.4091i	−0.956364	+	0.956364i	−0.999087	−	0.0427229i	$-0.986397\pi$
$227$	−14.4091	+	14.4091i	−0.956364	+	0.956364i	0.0427229	+	0.999087i	$0.486397\pi$
$228$		0			0
$229$		−	0.385393i		−	0.0254675i	−0.999919	−	0.0127337i	$-0.995947\pi$
$229$		−	0.385393i		−	0.0254675i	0.999919	−	0.0127337i	$-0.00405338\pi$
$230$		0			0
$231$	7.08444	+	6.04313i	0.466122	+	0.397609i
$232$		0			0
$233$	13.7690	+	13.7690i	0.902035	+	0.902035i	0.995612	−	0.0935768i	$-0.0298301\pi$
$233$	13.7690	+	13.7690i	0.902035	+	0.902035i	−0.0935768	+	0.995612i	$0.529830\pi$
$234$		0			0
$235$	15.6547	−	5.42601i	1.02120	−	0.353954i
$236$		0			0
$237$	−7.64547	+	0.606456i	−0.496626	+	0.0393935i
$238$		0			0
$239$	9.48073			0.613257			0.306629	−	0.951829i	$-0.400799\pi$
$239$	9.48073			0.613257			0.306629	+	0.951829i	$0.400799\pi$
$240$		0			0
$241$	3.18465			0.205141			0.102571	−	0.994726i	$-0.467293\pi$
$241$	3.18465			0.205141			0.102571	+	0.994726i	$0.467293\pi$
$242$		0			0
$243$	−6.00983	−	14.3834i	−0.385530	−	0.922695i
$244$		0			0
$245$	−5.52348	+	11.3836i	−0.352882	+	0.727270i
$246$		0			0
$247$	1.78574	+	1.78574i	0.113624	+	0.113624i
$248$		0			0
$249$	5.15151	−	6.03918i	0.326464	−	0.382718i
$250$		0			0
$251$		−	12.4714i		−	0.787191i	−0.919284	−	0.393595i	$-0.871231\pi$
$251$		−	12.4714i		−	0.787191i	0.919284	−	0.393595i	$-0.128769\pi$
$252$		0			0
$253$	−3.28220	+	3.28220i	−0.206350	+	0.206350i
$254$		0			0
$255$	12.0800	+	27.5818i	0.756478	+	1.72724i
$256$		0			0
$257$	−2.24440	+	2.24440i	−0.140002	+	0.140002i	−0.773634	−	0.633632i	$-0.781563\pi$
$257$	−2.24440	+	2.24440i	−0.140002	+	0.140002i	0.633632	+	0.773634i	$0.281563\pi$
$258$		0			0
$259$			4.54711i			0.282544i
$260$		0			0
$261$	23.7953	−	3.79890i	1.47289	−	0.235146i
$262$		0			0
$263$	9.03572	+	9.03572i	0.557167	+	0.557167i	0.928500	−	0.371333i	$-0.121099\pi$
$263$	9.03572	+	9.03572i	0.557167	+	0.557167i	−0.371333	+	0.928500i	$0.621099\pi$
$264$		0			0
$265$	1.44745	+	4.17607i	0.0889164	+	0.256534i
$266$		0			0
$267$	−1.48984	−	18.7821i	−0.0911767	−	1.14945i
$268$		0			0
$269$	−29.0574			−1.77166			−0.885829	−	0.464011i	$-0.846410\pi$
$269$	−29.0574			−1.77166			−0.885829	+	0.464011i	$0.846410\pi$
$270$		0			0
$271$	−19.0260			−1.15575			−0.577874	−	0.816126i	$-0.696117\pi$
$271$	−19.0260			−1.15575			−0.577874	+	0.816126i	$0.696117\pi$
$272$		0			0
$273$	0.371679	+	4.68568i	0.0224950	+	0.283590i
$274$		0			0
$275$	18.2303	−	14.3630i	1.09933	−	0.866123i
$276$		0			0
$277$	−5.71086	−	5.71086i	−0.343132	−	0.343132i	0.514411	−	0.857544i	$-0.328011\pi$
$277$	−5.71086	−	5.71086i	−0.343132	−	0.343132i	−0.857544	+	0.514411i	$0.828011\pi$
$278$		0			0
$279$	9.14914	−	1.46065i	0.547745	−	0.0874469i
$280$		0			0
$281$			20.1498i			1.20204i	0.799235	+	0.601019i	$0.205238\pi$
$281$			20.1498i			1.20204i	−0.799235	+	0.601019i	$0.794762\pi$
$282$		0			0
$283$	−11.9189	+	11.9189i	−0.708503	+	0.708503i	−0.966220	−	0.257718i	$-0.917030\pi$
$283$	−11.9189	+	11.9189i	−0.708503	+	0.708503i	0.257718	+	0.966220i	$0.417030\pi$
$284$		0			0
$285$	−3.88800	−	1.51962i	−0.230305	−	0.0900145i
$286$		0			0
$287$	9.69607	−	9.69607i	0.572341	−	0.572341i
$288$		0			0
$289$		−	43.4453i		−	2.55561i
$290$		0			0
$291$	−2.88603	+	3.38333i	−0.169182	+	0.198334i
$292$		0			0
$293$	17.8189	+	17.8189i	1.04099	+	1.04099i	0.999123	+	0.0418702i	$0.0133316\pi$
$293$	17.8189	+	17.8189i	1.04099	+	1.04099i	0.0418702	+	0.999123i	$0.486668\pi$
$294$		0			0
$295$	8.24654	+	4.00134i	0.480132	+	0.232967i
$296$		0			0
$297$	23.4423	−	5.67388i	1.36026	−	0.329232i
$298$		0			0
$299$	−2.34306			−0.135502
$300$		0			0
$301$	10.1074			0.582583
$302$		0			0
$303$	−9.17675	+	0.727921i	−0.527191	+	0.0418180i
$304$		0			0
$305$	−17.0516	−	8.27368i	−0.976371	−	0.473750i
$306$		0			0
$307$	−18.7101	−	18.7101i	−1.06784	−	1.06784i	−0.997524	−	0.0703199i	$-0.977598\pi$
$307$	−18.7101	−	18.7101i	−1.06784	−	1.06784i	−0.0703199	−	0.997524i	$-0.522402\pi$
$308$		0			0
$309$	10.3272	+	8.80925i	0.587493	+	0.501140i
$310$		0			0
$311$		−	7.01991i		−	0.398063i	−0.979993	−	0.199031i	$-0.936220\pi$
$311$		−	7.01991i		−	0.398063i	0.979993	−	0.199031i	$-0.0637795\pi$
$312$		0			0
$313$	0.0613853	−	0.0613853i	0.00346970	−	0.00346970i	−0.705370	−	0.708840i	$-0.749219\pi$
$313$	0.0613853	−	0.0613853i	0.00346970	−	0.00346970i	0.708840	+	0.705370i	$0.249219\pi$
$314$		0			0
$315$	−3.67000	−	6.84817i	−0.206781	−	0.385851i
$316$		0			0
$317$	10.7707	−	10.7707i	0.604940	−	0.604940i	−0.336679	−	0.941619i	$-0.609304\pi$
$317$	10.7707	−	10.7707i	0.604940	−	0.604940i	0.941619	+	0.336679i	$0.109304\pi$
$318$		0			0
$319$			37.2834i			2.08747i
$320$		0			0
$321$	2.38151	+	2.03146i	0.132923	+	0.113385i
$322$		0			0
$323$	5.92538	+	5.92538i	0.329697	+	0.329697i
$324$		0			0
$325$	11.6337	+	1.38037i	0.645320	+	0.0765693i
$326$		0			0
$327$	−29.1020	+	2.30844i	−1.60935	+	0.127657i
$328$		0			0
$329$	8.58194			0.473137
$330$		0			0
$331$	18.1511			0.997676			0.498838	−	0.866695i	$-0.333760\pi$
$331$	18.1511			0.997676			0.498838	+	0.866695i	$0.333760\pi$
$332$		0			0
$333$	9.53701	+	6.91109i	0.522625	+	0.378725i
$334$		0			0
$335$	−1.95899	−	5.65191i	−0.107031	−	0.308797i
$336$		0			0
$337$	−23.2826	−	23.2826i	−1.26829	−	1.26829i	−0.946973	−	0.321314i	$-0.895875\pi$
$337$	−23.2826	−	23.2826i	−1.26829	−	1.26829i	−0.321314	−	0.946973i	$-0.604125\pi$
$338$		0			0
$339$	19.5829	−	22.9573i	1.06360	−	1.24687i
$340$		0			0
$341$			14.3352i			0.776295i
$342$		0			0
$343$	−10.3671	+	10.3671i	−0.559773	+	0.559773i
$344$		0			0
$345$	3.54765	−	1.55376i	0.190999	−	0.0836519i
$346$		0			0
$347$	21.0772	−	21.0772i	1.13148	−	1.13148i	0.141554	−	0.989930i	$-0.454790\pi$
$347$	21.0772	−	21.0772i	1.13148	−	1.13148i	0.989930	−	0.141554i	$-0.0452100\pi$
$348$		0			0
$349$		−	14.2313i		−	0.761784i	−0.924619	−	0.380892i	$-0.875617\pi$
$349$		−	14.2313i		−	0.761784i	0.924619	−	0.380892i	$-0.124383\pi$
$350$		0			0
$351$	10.3925	+	6.34214i	0.554713	+	0.338518i
$352$		0			0
$353$	−0.0881192	−	0.0881192i	−0.00469011	−	0.00469011i	0.704758	−	0.709448i	$-0.251056\pi$
$353$	−0.0881192	−	0.0881192i	−0.00469011	−	0.00469011i	−0.709448	+	0.704758i	$0.751056\pi$
$354$		0			0
$355$	0.748260	−	1.54212i	0.0397135	−	0.0818473i
$356$		0			0
$357$	1.23329	+	15.5479i	0.0652728	+	0.822881i
$358$		0			0
$359$	9.59320			0.506310			0.253155	−	0.967426i	$-0.418532\pi$
$359$	9.59320			0.506310			0.253155	+	0.967426i	$0.418532\pi$
$360$		0			0
$361$	17.8383			0.938857
$362$		0			0
$363$	1.44433	+	18.2084i	0.0758077	+	0.955693i
$364$		0			0
$365$	−2.91883	+	1.01168i	−0.152778	+	0.0529540i
$366$		0			0
$367$	−13.4758	−	13.4758i	−0.703432	−	0.703432i	0.261714	−	0.965146i	$-0.415712\pi$
$367$	−13.4758	−	13.4758i	−0.703432	−	0.703432i	−0.965146	+	0.261714i	$0.915712\pi$
$368$		0			0
$369$	−5.59941	−	35.0732i	−0.291494	−	1.82584i
$370$		0			0
$371$			2.28934i			0.118856i
$372$		0			0
$373$	7.52935	−	7.52935i	0.389855	−	0.389855i	−0.484781	−	0.874636i	$-0.661101\pi$
$373$	7.52935	−	7.52935i	0.389855	−	0.389855i	0.874636	+	0.484781i	$0.161101\pi$
$374$		0			0
$375$	−18.5301	+	5.62467i	−0.956888	+	0.290457i
$376$		0			0
$377$	−13.3077	+	13.3077i	−0.685382	+	0.685382i
$378$		0			0
$379$		−	19.9050i		−	1.02245i	−0.859446	−	0.511227i	$-0.829191\pi$
$379$		−	19.9050i		−	1.02245i	0.859446	−	0.511227i	$-0.170809\pi$
$380$		0			0
$381$	−6.29503	+	7.37975i	−0.322504	+	0.378076i
$382$		0			0
$383$	−24.0127	−	24.0127i	−1.22699	−	1.22699i	−0.965097	−	0.261894i	$-0.915653\pi$
$383$	−24.0127	−	24.0127i	−1.22699	−	1.22699i	−0.261894	−	0.965097i	$-0.584347\pi$
$384$		0			0
$385$	11.3585	−	3.93693i	0.578882	−	0.200644i
$386$		0			0
$387$	15.3621	−	21.1991i	0.780901	−	1.07761i
$388$		0			0
$389$	18.5736			0.941721			0.470860	−	0.882208i	$-0.343944\pi$
$389$	18.5736			0.941721			0.470860	+	0.882208i	$0.343944\pi$
$390$		0			0
$391$	−7.77466			−0.393181
$392$		0			0
$393$	−29.8604	+	2.36860i	−1.50626	+	0.119480i
$394$		0			0
$395$	−4.32230	+	8.90801i	−0.217478	+	0.448211i
$396$		0			0
$397$	16.2110	+	16.2110i	0.813606	+	0.813606i	0.985172	−	0.171567i	$-0.0548830\pi$
$397$	16.2110	+	16.2110i	0.813606	+	0.813606i	−0.171567	+	0.985172i	$0.554883\pi$
$398$		0			0
$399$	−1.64504	−	1.40324i	−0.0823549	−	0.0702500i
$400$		0			0
$401$			23.9274i			1.19488i	0.801914	+	0.597440i	$0.203815\pi$
$401$			23.9274i			1.19488i	−0.801914	+	0.597440i	$0.796185\pi$
$402$		0			0
$403$	−5.11672	+	5.11672i	−0.254882	+	0.254882i
$404$		0			0
$405$	−19.9412	−	2.71104i	−0.990885	−	0.134713i
$406$		0			0
$407$	−12.8857	+	12.8857i	−0.638723	+	0.638723i
$408$		0			0
$409$		−	10.9274i		−	0.540325i	−0.962815	−	0.270162i	$-0.912923\pi$
$409$		−	10.9274i		−	0.540325i	0.962815	−	0.270162i	$-0.0870774\pi$
$410$		0			0
$411$	15.5493	+	13.2638i	0.766993	+	0.654256i
$412$		0			0
$413$	3.35716	+	3.35716i	0.165195	+	0.165195i
$414$		0			0
$415$	−3.35606	−	9.68262i	−0.164743	−	0.475301i
$416$		0			0
$417$	−26.5651	+	2.10721i	−1.30090	+	0.103190i
$418$		0			0
$419$	−0.210640			−0.0102904			−0.00514522	−	0.999987i	$-0.501638\pi$
$419$	−0.210640			−0.0102904			−0.00514522	+	0.999987i	$0.501638\pi$
$420$		0			0
$421$	27.3257			1.33177			0.665886	−	0.746053i	$-0.268054\pi$
$421$	27.3257			1.33177			0.665886	+	0.746053i	$0.268054\pi$
$422$		0			0
$423$	13.0436	−	17.9996i	0.634199	−	0.875168i
$424$		0			0
$425$	38.6025	+	4.58031i	1.87250	+	0.222178i
$426$		0			0
$427$	−6.94169	−	6.94169i	−0.335932	−	0.335932i
$428$		0			0
$429$	−12.2251	+	14.3317i	−0.590235	+	0.691940i
$430$		0			0
$431$			21.8893i			1.05437i	0.849750	+	0.527185i	$0.176753\pi$
$431$			21.8893i			1.05437i	−0.849750	+	0.527185i	$0.823247\pi$
$432$		0			0
$433$	4.84190	−	4.84190i	0.232687	−	0.232687i	−0.581126	−	0.813813i	$-0.697388\pi$
$433$	4.84190	−	4.84190i	0.232687	−	0.232687i	0.813813	+	0.581126i	$0.197388\pi$
$434$		0			0
$435$	11.3245	−	28.9742i	0.542970	−	1.38921i
$436$		0			0
$437$	0.762141	−	0.762141i	0.0364581	−	0.0364581i
$438$		0			0
$439$			27.8794i			1.33061i	0.746571	+	0.665306i	$0.231699\pi$
$439$			27.8794i			1.33061i	−0.746571	+	0.665306i	$0.768301\pi$
$440$		0			0
$441$	2.67624	+	16.7633i	0.127440	+	0.798252i
$442$		0			0
$443$	16.9122	+	16.9122i	0.803524	+	0.803524i	0.983645	−	0.180121i	$-0.0576489\pi$
$443$	16.9122	+	16.9122i	0.803524	+	0.803524i	−0.180121	+	0.983645i	$0.557649\pi$
$444$		0			0
$445$	−21.8837	−	10.6183i	−1.03739	−	0.503355i
$446$		0			0
$447$	1.90806	+	24.0546i	0.0902483	+	1.13774i
$448$		0			0
$449$	6.46468			0.305087			0.152544	−	0.988297i	$-0.451254\pi$
$449$	6.46468			0.305087			0.152544	+	0.988297i	$0.451254\pi$
$450$		0			0
$451$	54.9540			2.58768
$452$		0			0
$453$	1.07950	+	13.6090i	0.0507194	+	0.639409i
$454$		0			0
$455$	5.45945	+	2.64901i	0.255943	+	0.124187i
$456$		0			0
$457$	3.48566	+	3.48566i	0.163052	+	0.163052i	0.783917	−	0.620865i	$-0.213219\pi$
$457$	3.48566	+	3.48566i	0.163052	+	0.163052i	−0.620865	+	0.783917i	$0.713219\pi$
$458$		0			0
$459$	34.4842	+	21.0443i	1.60959	+	0.982263i
$460$		0			0
$461$		−	15.5040i		−	0.722095i	−0.932547	−	0.361048i	$-0.882419\pi$
$461$		−	15.5040i		−	0.722095i	0.932547	−	0.361048i	$-0.117581\pi$
$462$		0			0
$463$	11.6721	−	11.6721i	0.542449	−	0.542449i	−0.381797	−	0.924246i	$-0.624695\pi$
$463$	11.6721	−	11.6721i	0.542449	−	0.542449i	0.924246	+	0.381797i	$0.124695\pi$
$464$		0			0
$465$	4.35421	−	11.1404i	0.201922	−	0.516623i
$466$		0			0
$467$	22.0317	−	22.0317i	1.01951	−	1.01951i	0.0197009	−	0.999806i	$-0.493729\pi$
$467$	22.0317	−	22.0317i	1.01951	−	1.01951i	0.999806	−	0.0197009i	$-0.00627140\pi$
$468$		0			0
$469$		−	3.09839i		−	0.143071i
$470$		0			0
$471$	22.1406	−	25.9557i	1.02019	−	1.19598i
$472$		0			0
$473$	28.6427	+	28.6427i	1.31699	+	1.31699i
$474$		0			0
$475$	−4.23316	+	3.33516i	−0.194231	+	0.153027i
$476$		0			0
$477$	4.80160	+	3.47952i	0.219850	+	0.159316i
$478$		0			0
$479$	−26.9596			−1.23182			−0.615908	−	0.787818i	$-0.711211\pi$
$479$	−26.9596			−1.23182			−0.615908	+	0.787818i	$0.711211\pi$
$480$		0			0
$481$	−9.19872			−0.419426
$482$		0			0
$483$	1.99981	−	0.158630i	0.0909947	−	0.00721791i
$484$		0			0
$485$	1.88016	+	5.42449i	0.0853739	+	0.246313i
$486$		0			0
$487$	−6.24238	−	6.24238i	−0.282869	−	0.282869i	0.551383	−	0.834252i	$-0.314100\pi$
$487$	−6.24238	−	6.24238i	−0.282869	−	0.282869i	−0.834252	+	0.551383i	$0.814100\pi$
$488$		0			0
$489$	−13.8052	−	11.7761i	−0.624295	−	0.532533i
$490$		0			0
$491$		−	41.1212i		−	1.85577i	−0.372864	−	0.927886i	$-0.621624\pi$
$491$		−	41.1212i		−	1.85577i	0.372864	−	0.927886i	$-0.378376\pi$
$492$		0			0
$493$	−44.1572	+	44.1572i	−1.98874	+	1.98874i
$494$		0			0
$495$	9.00637	−	29.8067i	0.404806	−	1.33971i
$496$		0			0
$497$	0.627797	−	0.627797i	0.0281605	−	0.0281605i
$498$		0			0
$499$			36.4294i			1.63081i	0.578894	+	0.815403i	$0.303485\pi$
$499$			36.4294i			1.63081i	−0.578894	+	0.815403i	$0.696515\pi$
$500$		0			0
$501$	−22.4272	−	19.1307i	−1.00197	−	0.854697i
$502$		0			0
$503$	8.67747	+	8.67747i	0.386909	+	0.386909i	0.873584	−	0.486674i	$-0.161790\pi$
$503$	8.67747	+	8.67747i	0.386909	+	0.386909i	−0.486674	+	0.873584i	$0.661790\pi$
$504$		0			0
$505$	−5.18800	+	10.6922i	−0.230863	+	0.475795i
$506$		0			0
$507$	12.9671	−	1.02858i	0.575890	−	0.0456809i
$508$		0			0
$509$	−17.0114			−0.754016			−0.377008	−	0.926210i	$-0.623047\pi$
$509$	−17.0114			−0.754016			−0.377008	+	0.926210i	$0.623047\pi$
$510$		0			0
$511$	−1.60011			−0.0707847
$512$		0			0
$513$	−5.44340	+	1.31750i	−0.240332	+	0.0581690i
$514$		0			0
$515$	16.5576	−	5.73897i	0.729615	−	0.252889i
$516$		0			0
$517$	24.3197	+	24.3197i	1.06958	+	1.06958i
$518$		0			0
$519$	−4.24893	+	4.98107i	−0.186507	+	0.218645i
$520$		0			0
$521$		−	26.0175i		−	1.13985i	−0.821698	−	0.569923i	$-0.806973\pi$
$521$		−	26.0175i		−	1.13985i	0.821698	−	0.569923i	$-0.193027\pi$
$522$		0			0
$523$	−3.04305	+	3.04305i	−0.133063	+	0.133063i	−0.770501	−	0.637438i	$-0.779994\pi$
$523$	−3.04305	+	3.04305i	−0.133063	+	0.133063i	0.637438	+	0.770501i	$0.279994\pi$
$524$		0			0
$525$	−10.0229	−	0.390533i	−0.437434	−	0.0170443i
$526$		0			0
$527$	−16.9782	+	16.9782i	−0.739580	+	0.739580i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	12.1437	−	1.93874i	0.526993	−	0.0841340i
$532$		0			0
$533$	19.6150	+	19.6150i	0.849618	+	0.849618i
$534$		0			0
$535$	3.81827	−	1.32344i	0.165078	−	0.0572172i
$536$		0			0
$537$	2.41523	+	30.4483i	0.104225	+	1.31394i
$538$		0			0
$539$	−26.2653			−1.13133
$540$		0			0
$541$	10.7056			0.460271			0.230135	−	0.973159i	$-0.426083\pi$
$541$	10.7056			0.460271			0.230135	+	0.973159i	$0.426083\pi$
$542$		0			0
$543$	1.92862	+	24.3137i	0.0827650	+	1.04340i
$544$		0			0
$545$	−16.4526	+	33.9078i	−0.704751	+	1.45245i
$546$		0			0
$547$	−28.5079	−	28.5079i	−1.21891	−	1.21891i	−0.968014	−	0.250895i	$-0.919275\pi$
$547$	−28.5079	−	28.5079i	−1.21891	−	1.21891i	−0.250895	−	0.968014i	$-0.580725\pi$
$548$		0			0
$549$	−25.1099	+	4.00878i	−1.07167	+	0.171090i
$550$		0			0
$551$		−	8.65737i		−	0.368816i
$552$		0			0
$553$	−3.62645	+	3.62645i	−0.154212	+	0.154212i
$554$		0			0
$555$	13.9279	−	6.10000i	0.591206	−	0.258931i
$556$		0			0
$557$	6.76594	−	6.76594i	0.286682	−	0.286682i	−0.549085	−	0.835767i	$-0.685024\pi$
$557$	6.76594	−	6.76594i	0.286682	−	0.286682i	0.835767	+	0.549085i	$0.185024\pi$
$558$		0			0
$559$			20.4471i			0.864822i
$560$		0			0
$561$	−40.5651	+	47.5550i	−1.71266	+	2.00777i
$562$		0			0
$563$	16.0908	+	16.0908i	0.678147	+	0.678147i	0.959581	−	0.281434i	$-0.0908101\pi$
$563$	16.0908	+	16.0908i	0.678147	+	0.678147i	−0.281434	+	0.959581i	$0.590810\pi$
$564$		0			0
$565$	−12.7577	−	36.8074i	−0.536720	−	1.54850i
$566$		0			0
$567$	−9.29948	−	4.70946i	−0.390542	−	0.197779i
$568$		0			0
$569$	−42.5344			−1.78313			−0.891567	−	0.452889i	$-0.850393\pi$
$569$	−42.5344			−1.78313			−0.891567	+	0.452889i	$0.850393\pi$
$570$		0			0
$571$	−23.8309			−0.997291			−0.498645	−	0.866806i	$-0.666169\pi$
$571$	−23.8309			−0.997291			−0.498645	+	0.866806i	$0.666169\pi$
$572$		0			0
$573$	−17.7387	+	1.40707i	−0.741043	+	0.0587812i
$574$		0			0
$575$	0.589133	−	4.96517i	0.0245686	−	0.207062i
$576$		0			0
$577$	7.97434	+	7.97434i	0.331976	+	0.331976i	0.853336	−	0.521361i	$-0.174575\pi$
$577$	7.97434	+	7.97434i	0.331976	+	0.331976i	−0.521361	+	0.853336i	$0.674575\pi$
$578$		0			0
$579$	−14.8085	−	12.6319i	−0.615422	−	0.524964i
$580$		0			0
$581$		−	5.30805i		−	0.220215i
$582$		0			0
$583$	−6.48758	+	6.48758i	−0.268688	+	0.268688i
$584$		0			0
$585$	13.8537	−	7.42435i	0.572780	−	0.306959i
$586$		0			0
$587$	−0.650199	+	0.650199i	−0.0268366	+	0.0268366i	−0.720398	−	0.693561i	$-0.756041\pi$
$587$	−0.650199	+	0.650199i	−0.0268366	+	0.0268366i	0.693561	+	0.720398i	$0.256041\pi$
$588$		0			0
$589$		−	3.32870i		−	0.137157i
$590$		0			0
$591$	−10.4870	−	8.94554i	−0.431376	−	0.367970i
$592$		0			0
$593$	−21.1061	−	21.1061i	−0.866722	−	0.866722i	0.125386	−	0.992108i	$-0.459983\pi$
$593$	−21.1061	−	21.1061i	−0.866722	−	0.866722i	−0.992108	+	0.125386i	$0.959983\pi$
$594$		0			0
$595$	18.1154	+	8.78986i	0.742659	+	0.360349i
$596$		0			0
$597$	−38.0483	+	3.01808i	−1.55721	+	0.123522i
$598$		0			0
$599$	−5.58395			−0.228154			−0.114077	−	0.993472i	$-0.536391\pi$
$599$	−5.58395			−0.228154			−0.114077	+	0.993472i	$0.536391\pi$
$600$		0			0
$601$	−21.1171			−0.861383			−0.430691	−	0.902499i	$-0.641730\pi$
$601$	−21.1171			−0.861383			−0.430691	+	0.902499i	$0.641730\pi$
$602$		0			0
$603$	−6.49850	−	4.70920i	−0.264639	−	0.191774i
$604$		0			0
$605$	21.2153	+	10.2940i	0.862523	+	0.418509i
$606$		0			0
$607$	−26.0428	−	26.0428i	−1.05704	−	1.05704i	−0.998271	−	0.0587734i	$-0.981281\pi$
$607$	−26.0428	−	26.0428i	−1.05704	−	1.05704i	−0.0587734	−	0.998271i	$-0.518719\pi$
$608$		0			0
$609$	10.4573	−	12.2592i	0.423750	−	0.496767i
$610$		0			0
$611$			17.3611i			0.702354i
$612$		0			0
$613$	11.3672	−	11.3672i	0.459119	−	0.459119i	−0.439247	−	0.898366i	$-0.644755\pi$
$613$	11.3672	−	11.3672i	0.459119	−	0.459119i	0.898366	+	0.439247i	$0.144755\pi$
$614$		0			0
$615$	−42.7066	−	16.6919i	−1.72210	−	0.673081i
$616$		0			0
$617$	11.9594	−	11.9594i	0.481465	−	0.481465i	−0.424134	−	0.905599i	$-0.639421\pi$
$617$	11.9594	−	11.9594i	0.481465	−	0.481465i	0.905599	+	0.424134i	$0.139421\pi$
$618$		0			0
$619$			22.3866i			0.899793i	0.893081	+	0.449896i	$0.148539\pi$
$619$			22.3866i			0.899793i	−0.893081	+	0.449896i	$0.851461\pi$
$620$		0			0
$621$	2.70678	−	4.43546i	0.108619	−	0.177989i
$622$		0			0
$623$	−8.90885	−	8.90885i	−0.356926	−	0.356926i
$624$		0			0
$625$	−5.85030	+	24.3058i	−0.234012	+	0.972234i
$626$		0			0
$627$	−0.685210	−	8.63830i	−0.0273647	−	0.344981i
$628$		0			0
$629$	−30.5229			−1.21703
$630$		0			0
$631$	14.8795			0.592342			0.296171	−	0.955135i	$-0.404290\pi$
$631$	14.8795			0.592342			0.296171	+	0.955135i	$0.404290\pi$
$632$		0			0
$633$	0.749766	+	9.45215i	0.0298005	+	0.375689i
$634$		0			0
$635$	4.10103	+	11.8319i	0.162744	+	0.469537i
$636$		0			0
$637$	−9.37500	−	9.37500i	−0.371451	−	0.371451i
$638$		0			0
$639$	−0.362548	−	2.27091i	−0.0143422	−	0.0898357i
$640$		0			0
$641$		−	49.1536i		−	1.94145i	−0.240193	−	0.970725i	$-0.577211\pi$
$641$		−	49.1536i		−	1.94145i	0.240193	−	0.970725i	$-0.422789\pi$
$642$		0			0
$643$	24.6592	−	24.6592i	0.972466	−	0.972466i	−0.0271654	−	0.999631i	$-0.508648\pi$
$643$	24.6592	−	24.6592i	0.972466	−	0.972466i	0.999631	+	0.0271654i	$0.00864807\pi$
$644$		0			0
$645$	−13.5592	−	30.9593i	−0.533894	−	1.21902i
$646$		0			0
$647$	−16.7231	+	16.7231i	−0.657452	+	0.657452i	−0.954777	−	0.297324i	$-0.903906\pi$
$647$	−16.7231	+	16.7231i	−0.657452	+	0.657452i	0.297324	+	0.954777i	$0.403906\pi$
$648$		0			0
$649$			19.0273i			0.746885i
$650$		0			0
$651$	4.02075	−	4.71357i	0.157585	−	0.184739i
$652$		0			0
$653$	−32.7491	−	32.7491i	−1.28157	−	1.28157i	−0.939773	−	0.341800i	$-0.888964\pi$
$653$	−32.7491	−	32.7491i	−1.28157	−	1.28157i	−0.341800	−	0.939773i	$-0.611036\pi$
$654$		0			0
$655$	−16.8813	+	34.7915i	−0.659608	+	1.35941i
$656$		0			0
$657$	−2.43198	+	3.35603i	−0.0948806	+	0.130931i
$658$		0			0
$659$	−15.6170			−0.608354			−0.304177	−	0.952616i	$-0.598381\pi$
$659$	−15.6170			−0.608354			−0.304177	+	0.952616i	$0.598381\pi$
$660$		0			0
$661$	20.2341			0.787017			0.393508	−	0.919321i	$-0.371261\pi$
$661$	20.2341			0.787017			0.393508	+	0.919321i	$0.371261\pi$
$662$		0			0
$663$	−31.4530	+	2.49493i	−1.22154	+	0.0968949i
$664$		0			0
$665$	−2.63749	+	0.914172i	−0.102277	+	0.0354501i
$666$		0			0
$667$	5.67964	+	5.67964i	0.219916	+	0.219916i
$668$		0			0
$669$	31.2150	+	26.6268i	1.20684	+	1.02945i
$670$		0			0
$671$		−	39.3431i		−	1.51883i
$672$		0			0
$673$	−9.98815	+	9.98815i	−0.385015	+	0.385015i	−0.872905	−	0.487890i	$-0.837767\pi$
$673$	−9.98815	+	9.98815i	−0.385015	+	0.385015i	0.487890	+	0.872905i	$0.337767\pi$
$674$		0			0
$675$	−16.0527	+	20.4282i	−0.617869	+	0.786281i
$676$		0			0
$677$	1.22889	−	1.22889i	0.0472302	−	0.0472302i	−0.683097	−	0.730327i	$-0.739367\pi$
$677$	1.22889	−	1.22889i	0.0472302	−	0.0472302i	0.730327	+	0.683097i	$0.239367\pi$
$678$		0			0
$679$			2.97372i			0.114121i
$680$		0			0
$681$	26.8526	+	22.9056i	1.02899	+	0.877746i
$682$		0			0
$683$	−3.59562	−	3.59562i	−0.137583	−	0.137583i	0.634961	−	0.772544i	$-0.281016\pi$
$683$	−3.59562	−	3.59562i	−0.137583	−	0.137583i	−0.772544	+	0.634961i	$0.781016\pi$
$684$		0			0
$685$	24.9303	−	8.64100i	0.952537	−	0.330156i
$686$		0			0
$687$	−0.665429	+	0.0527834i	−0.0253877	+	0.00201381i
$688$		0			0
$689$	−4.63128			−0.176438
$690$		0			0
$691$	−11.3212			−0.430680			−0.215340	−	0.976539i	$-0.569086\pi$
$691$	−11.3212			−0.430680			−0.215340	+	0.976539i	$0.569086\pi$
$692$		0			0
$693$	9.46395	−	13.0599i	0.359506	−	0.496103i
$694$		0			0
$695$	−15.0184	+	30.9520i	−0.569679	+	1.17408i
$696$		0			0
$697$	65.0858	+	65.0858i	2.46530	+	2.46530i
$698$		0			0
$699$	21.8881	−	25.6597i	0.827883	−	0.970538i
$700$		0			0
$701$		−	14.5830i		−	0.550792i	−0.961331	−	0.275396i	$-0.911191\pi$
$701$		−	14.5830i		−	0.550792i	0.961331	−	0.275396i	$-0.0888090\pi$
$702$		0			0
$703$	2.99213	−	2.99213i	0.112850	−	0.112850i
$704$		0			0
$705$	−11.5128	−	26.2866i	−0.433596	−	0.990012i
$706$		0			0
$707$	−4.35278	+	4.35278i	−0.163703	+	0.163703i
$708$		0			0
$709$			2.17171i			0.0815602i	0.999168	+	0.0407801i	$0.0129843\pi$
$709$			2.17171i			0.0815602i	−0.999168	+	0.0407801i	$0.987016\pi$
$710$		0			0
$711$	2.09425	+	13.1178i	0.0785404	+	0.491956i
$712$		0			0
$713$	2.18378	+	2.18378i	0.0817833	+	0.0817833i
$714$		0			0
$715$	7.96433	+	22.9780i	0.297849	+	0.859328i
$716$		0			0
$717$	−1.29848	−	16.3697i	−0.0484926	−	0.611337i
$718$		0			0
$719$	9.16538			0.341811			0.170906	−	0.985287i	$-0.445331\pi$
$719$	9.16538			0.341811			0.170906	+	0.985287i	$0.445331\pi$
$720$		0			0
$721$	9.07692			0.338042
$722$		0			0
$723$	−0.436170	−	5.49870i	−0.0162213	−	0.204499i
$724$		0			0
$725$	−24.8543	−	31.5464i	−0.923066	−	1.17161i
$726$		0			0
$727$	31.6354	+	31.6354i	1.17329	+	1.17329i	0.981420	+	0.191872i	$0.0614559\pi$
$727$	31.6354	+	31.6354i	1.17329	+	1.17329i	0.191872	+	0.981420i	$0.438544\pi$
$728$		0			0
$729$	−24.0117	+	12.3467i	−0.889321	+	0.457284i
$730$		0			0
$731$			67.8471i			2.50941i
$732$		0			0
$733$	−11.2496	+	11.2496i	−0.415515	+	0.415515i	−0.883655	−	0.468139i	$-0.844925\pi$
$733$	−11.2496	+	11.2496i	−0.415515	+	0.415515i	0.468139	+	0.883655i	$0.344925\pi$
$734$		0			0
$735$	20.4117	+	7.97789i	0.752896	+	0.294269i
$736$		0			0
$737$	8.78032	−	8.78032i	0.323427	−	0.323427i
$738$		0			0
$739$			37.9128i			1.39464i	0.716758	+	0.697322i	$0.245625\pi$
$739$			37.9128i			1.39464i	−0.716758	+	0.697322i	$0.754375\pi$
$740$		0			0
$741$	2.83873	−	3.32788i	0.104283	−	0.122253i
$742$		0			0
$743$	−27.1452	−	27.1452i	−0.995861	−	0.995861i	0.00413027	−	0.999991i	$-0.498685\pi$
$743$	−27.1452	−	27.1452i	−0.995861	−	0.995861i	−0.999991	+	0.00413027i	$0.998685\pi$
$744$		0			0
$745$	28.0269	+	13.5990i	1.02682	+	0.498231i
$746$		0			0
$747$	−11.1330	−	8.06761i	−0.407334	−	0.295179i
$748$		0			0
$749$	2.09319			0.0764834
$750$		0			0
$751$	−36.4107			−1.32865			−0.664323	−	0.747446i	$-0.731280\pi$
$751$	−36.4107			−1.32865			−0.664323	+	0.747446i	$0.731280\pi$
$752$		0			0
$753$	−21.5335	+	1.70809i	−0.784726	+	0.0622462i
$754$		0			0
$755$	15.8564	+	7.69376i	0.577073	+	0.280004i
$756$		0			0
$757$	−1.48255	−	1.48255i	−0.0538841	−	0.0538841i	0.679651	−	0.733535i	$-0.262131\pi$
$757$	−1.48255	−	1.48255i	−0.0538841	−	0.0538841i	−0.733535	+	0.679651i	$0.762131\pi$
$758$		0			0
$759$	6.11666	+	5.21760i	0.222021	+	0.189387i
$760$		0			0
$761$		−	47.6544i		−	1.72747i	−0.503946	−	0.863735i	$-0.668119\pi$
$761$		−	47.6544i		−	1.72747i	0.503946	−	0.863735i	$-0.331881\pi$
$762$		0			0
$763$	−13.8039	+	13.8039i	−0.499734	+	0.499734i
$764$		0			0
$765$	45.9689	−	24.6352i	1.66201	−	0.890689i
$766$		0			0
$767$	−6.79148	+	6.79148i	−0.245226	+	0.245226i
$768$		0			0
$769$		−	1.75549i		−	0.0633044i	−0.999499	−	0.0316522i	$-0.989923\pi$
$769$		−	1.75549i		−	0.0633044i	0.999499	−	0.0316522i	$-0.0100769\pi$
$770$		0			0
$771$	4.18264	+	3.56785i	0.150634	+	0.128493i
$772$		0			0
$773$	−17.0246	−	17.0246i	−0.612333	−	0.612333i	0.331221	−	0.943553i	$-0.392540\pi$
$773$	−17.0246	−	17.0246i	−0.612333	−	0.612333i	−0.943553	+	0.331221i	$0.892540\pi$
$774$		0			0
$775$	−9.55631	−	12.1294i	−0.343273	−	0.435701i
$776$		0			0
$777$	7.85117	−	0.622773i	0.281659	−	0.0223419i
$778$		0			0
$779$	−12.7606			−0.457195
$780$		0			0
$781$	3.55814			0.127320
$782$		0			0
$783$	−9.81830	−	40.5654i	−0.350877	−	1.44969i
$784$		0			0
$785$	−14.4240	−	41.6148i	−0.514814	−	1.48530i
$786$		0			0
$787$	−0.190642	−	0.190642i	−0.00679565	−	0.00679565i	0.703701	−	0.710496i	$-0.251530\pi$
$787$	−0.190642	−	0.190642i	−0.00679565	−	0.00679565i	−0.710496	+	0.703701i	$0.751530\pi$
$788$		0			0
$789$	14.3638	−	16.8389i	0.511365	−	0.599479i
$790$		0			0
$791$		−	20.1779i		−	0.717445i
$792$		0			0
$793$	14.0429	−	14.0429i	0.498678	−	0.498678i
$794$		0			0
$795$	7.01227	−	3.07117i	0.248700	−	0.108923i
$796$		0			0
$797$	−32.8922	+	32.8922i	−1.16510	+	1.16510i	−0.181760	+	0.983343i	$0.558179\pi$
$797$	−32.8922	+	32.8922i	−1.16510	+	1.16510i	−0.983343	+	0.181760i	$0.941821\pi$
$798$		0			0
$799$			57.6070i			2.03799i
$800$		0			0
$801$	−32.2256	+	5.14479i	−1.13864	+	0.181782i
$802$		0			0
$803$	−4.53444	−	4.53444i	−0.160017	−	0.160017i
$804$		0			0
$805$	1.13058	−	2.33006i	0.0398476	−	0.0821237i
$806$		0			0
$807$	3.97970	+	50.1712i	0.140092	+	1.76611i
$808$		0			0
$809$	−26.7894			−0.941866			−0.470933	−	0.882169i	$-0.656083\pi$
$809$	−26.7894			−0.941866			−0.470933	+	0.882169i	$0.656083\pi$
$810$		0			0
$811$	36.6442			1.28675			0.643376	−	0.765550i	$-0.277533\pi$
$811$	36.6442			1.28675			0.643376	+	0.765550i	$0.277533\pi$
$812$		0			0
$813$	2.60580	+	32.8508i	0.0913894	+	1.15213i
$814$		0			0
$815$	−22.1340	+	7.67178i	−0.775319	+	0.268731i
$816$		0			0
$817$	−6.65097	−	6.65097i	−0.232688	−	0.232688i
$818$		0			0
$819$	8.03952	−	1.28350i	0.280923	−	0.0448492i
$820$		0			0
$821$			42.6560i			1.48871i	0.667787	+	0.744353i	$0.267242\pi$
$821$			42.6560i			1.48871i	−0.667787	+	0.744353i	$0.732758\pi$
$822$		0			0
$823$	5.92246	−	5.92246i	0.206444	−	0.206444i	−0.596310	−	0.802754i	$-0.703367\pi$
$823$	5.92246	−	5.92246i	0.206444	−	0.206444i	0.802754	+	0.596310i	$0.203367\pi$
$824$		0			0
$825$	−27.2964	−	29.5098i	−0.950339	−	1.02740i
$826$		0			0
$827$	12.7878	−	12.7878i	0.444677	−	0.444677i	−0.448903	−	0.893580i	$-0.648185\pi$
$827$	12.7878	−	12.7878i	0.444677	−	0.444677i	0.893580	+	0.448903i	$0.148185\pi$
$828$		0			0
$829$		−	51.8490i		−	1.80079i	−0.435072	−	0.900396i	$-0.643277\pi$
$829$		−	51.8490i		−	1.80079i	0.435072	−	0.900396i	$-0.356723\pi$
$830$		0			0
$831$	−9.07837	+	10.6427i	−0.314925	+	0.369191i
$832$		0			0
$833$	−31.1078	−	31.1078i	−1.07782	−	1.07782i
$834$		0			0
$835$	−35.9575	+	12.4631i	−1.24436	+	0.431303i
$836$		0			0
$837$	−3.77507	−	15.5971i	−0.130485	−	0.539115i
$838$		0			0
$839$	−33.5279			−1.15751			−0.578757	−	0.815500i	$-0.696462\pi$
$839$	−33.5279			−1.15751			−0.578757	+	0.815500i	$0.696462\pi$
$840$		0			0
$841$	35.5166			1.22471
$842$		0			0
$843$	34.7912	−	2.75972i	1.19827	−	0.0950498i
$844$		0			0
$845$	7.33085	−	15.1085i	0.252189	−	0.519747i
$846$		0			0
$847$	8.63673	+	8.63673i	0.296761	+	0.296761i
$848$		0			0
$849$	22.2118	+	18.9470i	0.762308	+	0.650260i
$850$		0			0
$851$			3.92595i			0.134580i
$852$		0			0
$853$	−10.7310	+	10.7310i	−0.367423	+	0.367423i	−0.866536	−	0.499114i	$-0.833659\pi$
$853$	−10.7310	+	10.7310i	−0.367423	+	0.367423i	0.499114	+	0.866536i	$0.333659\pi$
$854$		0			0
$855$	−2.09132	+	6.92125i	−0.0715216	+	0.236702i
$856$		0			0
$857$	25.8167	−	25.8167i	0.881880	−	0.881880i	−0.111846	−	0.993726i	$-0.535676\pi$
$857$	25.8167	−	25.8167i	0.881880	−	0.881880i	0.993726	+	0.111846i	$0.0356762\pi$
$858$		0			0
$859$		−	49.6389i		−	1.69366i	−0.531865	−	0.846829i	$-0.678509\pi$
$859$		−	49.6389i		−	1.69366i	0.531865	−	0.846829i	$-0.321491\pi$
$860$		0			0
$861$	−18.0695	−	15.4135i	−0.615806	−	0.525292i
$862$		0			0
$863$	8.23448	+	8.23448i	0.280305	+	0.280305i	0.833231	−	0.552926i	$-0.186489\pi$
$863$	8.23448	+	8.23448i	0.280305	+	0.280305i	−0.552926	+	0.833231i	$0.686489\pi$
$864$		0			0
$865$	2.76805	+	7.98615i	0.0941166	+	0.271537i
$866$		0			0
$867$	−75.0139	+	5.95027i	−2.54760	+	0.202082i
$868$		0			0
$869$	−20.5535			−0.697229
$870$		0			0
$871$	6.26799			0.212383
$872$		0			0
$873$	6.23702	+	4.51971i	0.211091	+	0.152969i
$874$		0			0
$875$	−6.98623	+	10.9031i	−0.236178	+	0.368591i
$876$		0			0
$877$	−16.7536	−	16.7536i	−0.565729	−	0.565729i	0.365200	−	0.930929i	$-0.381001\pi$
$877$	−16.7536	−	16.7536i	−0.565729	−	0.565729i	−0.930929	+	0.365200i	$0.881001\pi$
$878$		0			0
$879$	28.3262	−	33.2071i	0.955418	−	1.12005i
$880$		0			0
$881$			18.3448i			0.618050i	0.951054	+	0.309025i	$0.100003\pi$
$881$			18.3448i			0.618050i	−0.951054	+	0.309025i	$0.899997\pi$
$882$		0			0
$883$	−6.92619	+	6.92619i	−0.233085	+	0.233085i	−0.813979	−	0.580894i	$-0.802703\pi$
$883$	−6.92619	+	6.92619i	−0.233085	+	0.233085i	0.580894	+	0.813979i	$0.302703\pi$
$884$		0			0
$885$	5.77938	−	14.7867i	0.194272	−	0.497050i
$886$		0			0
$887$	−24.1497	+	24.1497i	−0.810869	+	0.810869i	−0.984764	−	0.173895i	$-0.944365\pi$
$887$	−24.1497	+	24.1497i	−0.810869	+	0.810869i	0.173895	+	0.984764i	$0.444365\pi$
$888$		0			0
$889$			6.48631i			0.217544i
$890$		0			0
$891$	−13.0073	−	39.6989i	−0.435762	−	1.32996i
$892$		0			0
$893$	−5.64715	−	5.64715i	−0.188975	−	0.188975i
$894$		0			0
$895$	35.4765	+	17.2137i	1.18585	+	0.575391i
$896$		0			0
$897$	0.320905	+	4.04559i	0.0107147	+	0.135078i
$898$		0			0
$899$	24.8062			0.827333
$900$		0			0
$901$	−15.3674			−0.511961
$902$		0			0
$903$	−1.38431	−	17.4518i	−0.0460671	−	0.580759i
$904$		0			0
$905$	28.3288	+	13.7456i	0.941682	+	0.456918i
$906$		0			0
$907$	23.7752	+	23.7752i	0.789444	+	0.789444i	0.981403	−	0.191959i	$-0.0614841\pi$
$907$	23.7752	+	23.7752i	0.789444	+	0.789444i	−0.191959	+	0.981403i	$0.561484\pi$
$908$		0			0
$909$	2.51370	+	15.7451i	0.0833740	+	0.522233i
$910$		0			0
$911$		−	2.03327i		−	0.0673653i	−0.999433	−	0.0336826i	$-0.989276\pi$
$911$		−	2.03327i		−	0.0673653i	0.999433	−	0.0336826i	$-0.0107235\pi$
$912$		0			0
$913$	15.0421	−	15.0421i	0.497821	−	0.497821i
$914$		0			0
$915$	−11.9502	+	30.5749i	−0.395061	+	1.01077i
$916$		0			0
$917$	−14.1636	+	14.1636i	−0.467723	+	0.467723i
$918$		0			0
$919$		−	0.951166i		−	0.0313761i	−0.999877	−	0.0156880i	$-0.995006\pi$
$919$		−	0.951166i		−	0.0313761i	0.999877	−	0.0156880i	$-0.00499386\pi$
$920$		0			0
$921$	−29.7429	+	34.8680i	−0.980062	+	1.14894i
$922$		0			0
$923$	1.27002	+	1.27002i	0.0418033	+	0.0418033i
$924$		0			0
$925$	2.31291	−	19.4930i	0.0760480	−	0.640926i
$926$		0			0
$927$	13.7959	−	19.0377i	0.453116	−	0.625281i
$928$		0			0
$929$	36.5132			1.19796			0.598979	−	0.800765i	$-0.295573\pi$
$929$	36.5132			1.19796			0.598979	+	0.800765i	$0.295573\pi$
$930$		0			0
$931$	6.09893			0.199884
$932$		0			0
$933$	−12.1208	+	0.961447i	−0.396816	+	0.0314764i
$934$		0			0
$935$	26.4270	+	76.2449i	0.864255	+	2.49347i
$936$		0			0
$937$	−4.68273	−	4.68273i	−0.152978	−	0.152978i	0.626469	−	0.779447i	$-0.284500\pi$
$937$	−4.68273	−	4.68273i	−0.152978	−	0.152978i	−0.779447	+	0.626469i	$0.784500\pi$
$938$		0			0
$939$	−0.114397	−	0.0975822i	−0.00373320	−	0.00318447i
$940$		0			0
$941$			9.36113i			0.305164i	0.988291	+	0.152582i	$0.0487588\pi$
$941$			9.36113i			0.305164i	−0.988291	+	0.152582i	$0.951241\pi$
$942$		0			0
$943$	8.37153	−	8.37153i	0.272614	−	0.272614i
$944$		0			0
$945$	−11.3216	+	7.27466i	−0.368291	+	0.236645i
$946$		0			0
$947$	−2.01272	+	2.01272i	−0.0654046	+	0.0654046i	−0.739052	−	0.673648i	$-0.764726\pi$
$947$	−2.01272	+	2.01272i	−0.0654046	+	0.0654046i	0.673648	+	0.739052i	$0.264726\pi$
$948$		0			0
$949$		−	3.23699i		−	0.105077i
$950$		0			0
$951$	−20.0720	−	17.1218i	−0.650881	−	0.555211i
$952$		0			0
$953$	29.3281	+	29.3281i	0.950030	+	0.950030i	0.998810	−	0.0487796i	$-0.0155332\pi$
$953$	29.3281	+	29.3281i	0.950030	+	0.950030i	−0.0487796	+	0.998810i	$0.515533\pi$
$954$		0			0
$955$	−10.0284	+	20.6679i	−0.324511	+	0.668799i
$956$		0			0
$957$	64.3745	−	5.10633i	2.08093	−	0.165064i
$958$		0			0
$959$	13.6669			0.441326
$960$		0			0
$961$	−21.4622			−0.692329
$962$		0			0
$963$	3.18140	−	4.39020i	0.102519	−	0.141472i
$964$		0			0
$965$	−23.7425	+	8.22932i	−0.764299	+	0.264911i
$966$		0			0
$967$	34.7275	+	34.7275i	1.11676	+	1.11676i	0.992214	+	0.124548i	$0.0397482\pi$
$967$	34.7275	+	34.7275i	1.11676	+	1.11676i	0.124548	+	0.992214i	$0.460252\pi$
$968$		0			0
$969$	9.41939	−	11.0425i	0.302594	−	0.354735i
$970$		0			0
$971$			4.55288i			0.146109i	0.997328	+	0.0730544i	$0.0232747\pi$
$971$			4.55288i			0.146109i	−0.997328	+	0.0730544i	$0.976725\pi$
$972$		0			0
$973$	−12.6005	+	12.6005i	−0.403955	+	0.403955i
$974$		0			0
$975$	0.790041	−	20.2761i	0.0253016	−	0.649354i
$976$		0			0
$977$	38.3911	−	38.3911i	1.22824	−	1.22824i	0.263611	−	0.964629i	$-0.415086\pi$
$977$	38.3911	−	38.3911i	1.22824	−	1.22824i	0.964629	−	0.263611i	$-0.0849136\pi$
$978$		0			0
$979$		−	50.4923i		−	1.61374i
$980$		0			0
$981$	7.97163	+	49.9322i	0.254515	+	1.59421i
$982$		0			0
$983$	−25.3476	−	25.3476i	−0.808463	−	0.808463i	0.175938	−	0.984401i	$-0.443704\pi$
$983$	−25.3476	−	25.3476i	−0.808463	−	0.808463i	−0.984401	+	0.175938i	$0.943704\pi$
$984$		0			0
$985$	−16.8138	+	5.82776i	−0.535731	+	0.185688i
$986$		0			0
$987$	−1.17538	−	14.8178i	−0.0374128	−	0.471656i
$988$		0			0
$989$	8.72669			0.277493
$990$		0			0
$991$	47.5932			1.51185			0.755923	−	0.654660i	$-0.227188\pi$
$991$	47.5932			1.51185			0.755923	+	0.654660i	$0.227188\pi$
$992$		0			0
$993$	−2.48598	−	31.3402i	−0.0788901	−	0.994552i
$994$		0			0
$995$	−21.5103	+	44.3314i	−0.681921	+	1.40540i
$996$		0			0
$997$	34.4430	+	34.4430i	1.09082	+	1.09082i	0.995441	+	0.0953811i	$0.0304070\pi$
$997$	34.4430	+	34.4430i	1.09082	+	1.09082i	0.0953811	+	0.995441i	$0.469593\pi$
$998$		0			0
$999$	10.6267	−	17.4134i	0.336213	−	0.550936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.16	✓	80
3.2	odd	2	inner	1380.2.r.c.737.38	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.38	yes	80
15.8	even	4	inner	1380.2.r.c.1013.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.16	✓	80	1.1	even	1	trivial
1380.2.r.c.737.38	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.16	yes	80	15.8	even	4	inner
1380.2.r.c.1013.38	yes	80	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.136960 - 1.72663i) q^{3} +(-2.01176 - 0.976134i) q^{5} +(-0.818985 - 0.818985i) q^{7} +(-2.96248 + 0.472958i) q^{9} +O(q^{10})\)	\(q+(-0.136960 - 1.72663i) q^{3} +(-2.01176 - 0.976134i) q^{5} +(-0.818985 - 0.818985i) q^{7} +(-2.96248 + 0.472958i) q^{9} -4.64173i q^{11} +(1.65679 - 1.65679i) q^{13} +(-1.40989 + 3.60724i) q^{15} +(5.49751 - 5.49751i) q^{17} +1.07783i q^{19} +(-1.30191 + 1.52625i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(3.09433 + 3.92749i) q^{25} +(1.22236 + 5.05033i) q^{27} -8.03222 q^{29} -3.08833 q^{31} +(-8.01454 + 0.635731i) q^{33} +(0.848160 + 2.44704i) q^{35} +(-2.77607 - 2.77607i) q^{37} +(-3.08758 - 2.63375i) q^{39} +11.8391i q^{41} +(-6.17071 + 6.17071i) q^{43} +(6.42147 + 1.94030i) q^{45} +(-5.23937 + 5.23937i) q^{47} -5.65853i q^{49} +(-10.2451 - 8.73922i) q^{51} +(-1.39767 - 1.39767i) q^{53} +(-4.53095 + 9.33803i) q^{55} +(1.86101 - 0.147620i) q^{57} -4.09918 q^{59} +8.47597 q^{61} +(2.81358 + 2.03889i) q^{63} +(-4.95031 + 1.71581i) q^{65} +(1.89161 + 1.89161i) q^{67} +(-1.12406 + 1.31776i) q^{69} +0.766555i q^{71} +(0.976885 - 0.976885i) q^{73} +(6.35751 - 5.88066i) q^{75} +(-3.80151 + 3.80151i) q^{77} -4.42798i q^{79} +(8.55262 - 2.80226i) q^{81} +(3.24062 + 3.24062i) q^{83} +(-16.4260 + 5.69335i) q^{85} +(1.10009 + 13.8687i) q^{87} +10.8779 q^{89} -2.71378 q^{91} +(0.422978 + 5.33240i) q^{93} +(1.05211 - 2.16833i) q^{95} +(-1.81549 - 1.81549i) q^{97} +(2.19534 + 13.7510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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