LMFDB - Embedded newform 1008.2.t.k.961.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.6
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.k.193.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.371921 + 1.69165i) q^{3} +1.68316 q^{5} +(-0.960133 + 2.46539i) q^{7} +(-2.72335 - 1.25832i) q^{9} +O(q^{10})$	\(q+(-0.371921 + 1.69165i) q^{3} +1.68316 q^{5} +(-0.960133 + 2.46539i) q^{7} +(-2.72335 - 1.25832i) q^{9} -1.24498 q^{11} +(1.96039 + 3.39550i) q^{13} +(-0.626001 + 2.84731i) q^{15} +(-1.62691 - 2.81788i) q^{17} +(-2.36192 + 4.09097i) q^{19} +(-3.81348 - 2.54114i) q^{21} +0.398135 q^{23} -2.16699 q^{25} +(3.14150 - 4.13895i) q^{27} +(-3.19896 + 5.54076i) q^{29} +(-0.289184 + 0.500881i) q^{31} +(0.463034 - 2.10607i) q^{33} +(-1.61605 + 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-6.47311 + 2.05344i) q^{39} +(4.20216 + 7.27836i) q^{41} +(-2.46299 + 4.26603i) q^{43} +(-4.58382 - 2.11795i) q^{45} +(-0.212595 - 0.368225i) q^{47} +(-5.15629 - 4.73420i) q^{49} +(5.37195 - 1.70412i) q^{51} +(-0.466315 - 0.807681i) q^{53} -2.09550 q^{55} +(-6.04204 - 5.51707i) q^{57} +(3.02527 - 5.23992i) q^{59} +(-5.10459 - 8.84140i) q^{61} +(5.71702 - 5.50596i) q^{63} +(3.29965 + 5.71516i) q^{65} +(-4.70976 + 8.15754i) q^{67} +(-0.148075 + 0.673505i) q^{69} -8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(0.805948 - 3.66578i) q^{75} +(1.19535 - 3.06936i) q^{77} +(-2.76670 - 4.79207i) q^{79} +(5.83327 + 6.85369i) q^{81} +(8.03669 - 13.9199i) q^{83} +(-2.73833 - 4.74293i) q^{85} +(-8.18325 - 7.47224i) q^{87} +(-6.03776 + 10.4577i) q^{89} +(-10.2535 + 1.57300i) q^{91} +(-0.739760 - 0.675485i) q^{93} +(-3.97549 + 6.88575i) q^{95} +(-5.86046 + 10.1506i) q^{97} +(3.39052 + 1.56658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9	$ 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9} - 6 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 15 q^{21} + 4 q^{23} + 20 q^{25} + 4 q^{27} + 9 q^{29} + 4 q^{31} - 31 q^{33} - 14 q^{35} + 2 q^{37} - 8 q^{39} + 16 q^{41} + 22 q^{45} - 5 q^{47} - 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} + 19 q^{59} - 13 q^{61} - 21 q^{63} + 13 q^{65} - 26 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 8 q^{75} - 4 q^{77} - 10 q^{79} - 8 q^{81} + 28 q^{83} - 20 q^{85} - 9 q^{87} + 6 q^{89} + 37 q^{91} - 32 q^{93} - 12 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9 - 6 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 15 * q^21 + 4 * q^23 + 20 * q^25 + 4 * q^27 + 9 * q^29 + 4 * q^31 - 31 * q^33 - 14 * q^35 + 2 * q^37 - 8 * q^39 + 16 * q^41 + 22 * q^45 - 5 * q^47 - 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 + 19 * q^59 - 13 * q^61 - 21 * q^63 + 13 * q^65 - 26 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 8 * q^75 - 4 * q^77 - 10 * q^79 - 8 * q^81 + 28 * q^83 - 20 * q^85 - 9 * q^87 + 6 * q^89 + 37 * q^91 - 32 * q^93 - 12 * q^95 - 29 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.371921	+	1.69165i	−0.214729	+	0.976674i
$3$	−0.371921	+	1.69165i	−0.214729	+	0.976674i
$4$		0			0
$5$	1.68316			0.752730			0.376365	−	0.926471i	$-0.377174\pi$
$5$	1.68316			0.752730			0.376365	+	0.926471i	$0.377174\pi$
$6$		0			0
$7$	−0.960133	+	2.46539i	−0.362896	+	0.931830i
$7$	−0.960133	+	2.46539i	−0.362896	+	0.931830i
$8$		0			0
$9$	−2.72335	−	1.25832i	−0.907783	−	0.419440i
$10$		0			0
$11$	−1.24498			−0.375376			−0.187688	−	0.982229i	$-0.560099\pi$
$11$	−1.24498			−0.375376			−0.187688	+	0.982229i	$0.560099\pi$
$12$		0			0
$13$	1.96039	+	3.39550i	0.543715	+	0.941743i	0.998687	+	0.0512366i	$0.0163162\pi$
$13$	1.96039	+	3.39550i	0.543715	+	0.941743i	−0.454971	+	0.890506i	$0.650350\pi$
$14$		0			0
$15$	−0.626001	+	2.84731i	−0.161633	+	0.735172i
$16$		0			0
$17$	−1.62691	−	2.81788i	−0.394582	−	0.683437i	0.598465	−	0.801149i	$-0.295777\pi$
$17$	−1.62691	−	2.81788i	−0.394582	−	0.683437i	−0.993048	+	0.117712i	$0.962444\pi$
$18$		0			0
$19$	−2.36192	+	4.09097i	−0.541863	+	0.938534i	0.456935	+	0.889500i	$0.348947\pi$
$19$	−2.36192	+	4.09097i	−0.541863	+	0.938534i	−0.998797	+	0.0490333i	$0.984386\pi$
$20$		0			0
$21$	−3.81348	−	2.54114i	−0.832169	−	0.554522i
$22$		0			0
$23$	0.398135			0.0830170			0.0415085	−	0.999138i	$-0.486784\pi$
$23$	0.398135			0.0830170			0.0415085	+	0.999138i	$0.486784\pi$
$24$		0			0
$25$	−2.16699			−0.433397
$26$		0			0
$27$	3.14150	−	4.13895i	0.604583	−	0.796542i
$28$		0			0
$29$	−3.19896	+	5.54076i	−0.594032	+	1.02889i	0.399651	+	0.916667i	$0.369131\pi$
$29$	−3.19896	+	5.54076i	−0.594032	+	1.02889i	−0.993683	+	0.112226i	$0.964202\pi$
$30$		0			0
$31$	−0.289184	+	0.500881i	−0.0519389	+	0.0899608i	−0.890826	−	0.454345i	$-0.849873\pi$
$31$	−0.289184	+	0.500881i	−0.0519389	+	0.0899608i	0.838887	+	0.544306i	$0.183207\pi$
$32$		0			0
$33$	0.463034	−	2.10607i	0.0806039	−	0.366620i
$34$		0			0
$35$	−1.61605	+	4.14963i	−0.273163	+	0.701416i
$36$		0			0
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	−0.550811	−	0.834630i	$-0.685682\pi$
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	0.998216	+	0.0597015i	$0.0190149\pi$
$38$		0			0
$39$	−6.47311	+	2.05344i	−1.03653	+	0.328813i
$40$		0			0
$41$	4.20216	+	7.27836i	0.656267	+	1.13669i	0.981574	+	0.191080i	$0.0611990\pi$
$41$	4.20216	+	7.27836i	0.656267	+	1.13669i	−0.325307	+	0.945608i	$0.605468\pi$
$42$		0			0
$43$	−2.46299	+	4.26603i	−0.375603	+	0.650563i	−0.990417	−	0.138109i	$-0.955898\pi$
$43$	−2.46299	+	4.26603i	−0.375603	+	0.650563i	0.614814	+	0.788672i	$0.289231\pi$
$44$		0			0
$45$	−4.58382	−	2.11795i	−0.683316	−	0.315725i
$46$		0			0
$47$	−0.212595	−	0.368225i	−0.0310101	−	0.0537112i	0.850104	−	0.526615i	$-0.176539\pi$
$47$	−0.212595	−	0.368225i	−0.0310101	−	0.0537112i	−0.881114	+	0.472904i	$0.843206\pi$
$48$		0			0
$49$	−5.15629	−	4.73420i	−0.736613	−	0.676315i
$50$		0			0
$51$	5.37195	−	1.70412i	0.752223	−	0.238625i
$52$		0			0
$53$	−0.466315	−	0.807681i	−0.0640533	−	0.110944i	0.832220	−	0.554445i	$-0.187069\pi$
$53$	−0.466315	−	0.807681i	−0.0640533	−	0.110944i	−0.896274	+	0.443501i	$0.853736\pi$
$54$		0			0
$55$	−2.09550			−0.282557
$56$		0			0
$57$	−6.04204	−	5.51707i	−0.800288	−	0.730753i
$58$		0			0
$59$	3.02527	−	5.23992i	0.393856	−	0.682179i	−0.599098	−	0.800676i	$-0.704474\pi$
$59$	3.02527	−	5.23992i	0.393856	−	0.682179i	0.992954	+	0.118496i	$0.0378074\pi$
$60$		0			0
$61$	−5.10459	−	8.84140i	−0.653575	−	1.13203i	−0.982249	−	0.187582i	$-0.939935\pi$
$61$	−5.10459	−	8.84140i	−0.653575	−	1.13203i	0.328674	−	0.944444i	$-0.393398\pi$
$62$		0			0
$63$	5.71702	−	5.50596i	0.720277	−	0.693686i
$64$		0			0
$65$	3.29965	+	5.71516i	0.409271	+	0.708878i
$66$		0			0
$67$	−4.70976	+	8.15754i	−0.575389	+	0.996602i	0.420611	+	0.907241i	$0.361816\pi$
$67$	−4.70976	+	8.15754i	−0.575389	+	0.996602i	−0.995999	+	0.0893612i	$0.971517\pi$
$68$		0			0
$69$	−0.148075	+	0.673505i	−0.0178261	+	0.0810805i
$70$		0			0
$71$	−8.46617			−1.00475			−0.502375	−	0.864650i	$-0.667540\pi$
$71$	−8.46617			−1.00475			−0.502375	+	0.864650i	$0.667540\pi$
$72$		0			0
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	0.920516	+	0.390705i	$0.127769\pi$
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	−0.121897	+	0.992543i	$0.538898\pi$
$74$		0			0
$75$	0.805948	−	3.66578i	0.0930628	−	0.423288i
$76$		0			0
$77$	1.19535	−	3.06936i	0.136222	−	0.349786i
$78$		0			0
$79$	−2.76670	−	4.79207i	−0.311278	−	0.539149i	0.667361	−	0.744734i	$-0.267424\pi$
$79$	−2.76670	−	4.79207i	−0.311278	−	0.539149i	−0.978639	+	0.205585i	$0.934090\pi$
$80$		0			0
$81$	5.83327	+	6.85369i	0.648141	+	0.761521i
$82$		0			0
$83$	8.03669	−	13.9199i	0.882141	−	1.52791i	0.0331848	−	0.999449i	$-0.489435\pi$
$83$	8.03669	−	13.9199i	0.882141	−	1.52791i	0.848956	−	0.528463i	$-0.177232\pi$
$84$		0			0
$85$	−2.73833	−	4.74293i	−0.297014	−	0.514444i
$86$		0			0
$87$	−8.18325	−	7.47224i	−0.877337	−	0.801108i
$88$		0			0
$89$	−6.03776	+	10.4577i	−0.640001	+	1.10851i	0.345431	+	0.938444i	$0.387733\pi$
$89$	−6.03776	+	10.4577i	−0.640001	+	1.10851i	−0.985432	+	0.170070i	$0.945601\pi$
$90$		0			0
$91$	−10.2535	+	1.57300i	−1.07486	+	0.164895i
$92$		0			0
$93$	−0.739760	−	0.675485i	−0.0767096	−	0.0700445i
$94$		0			0
$95$	−3.97549	+	6.88575i	−0.407876	+	0.706463i
$96$		0			0
$97$	−5.86046	+	10.1506i	−0.595040	+	1.03064i	0.398501	+	0.917168i	$0.369530\pi$
$97$	−5.86046	+	10.1506i	−0.595040	+	1.03064i	−0.993541	+	0.113472i	$0.963803\pi$
$98$		0			0
$99$	3.39052	+	1.56658i	0.340760	+	0.157447i
$100$		0			0
$101$	5.40605			0.537922			0.268961	−	0.963151i	$-0.413320\pi$
$101$	5.40605			0.537922			0.268961	+	0.963151i	$0.413320\pi$
$102$		0			0
$103$	−14.6204			−1.44059			−0.720294	−	0.693669i	$-0.755993\pi$
$103$	−14.6204			−1.44059			−0.720294	+	0.693669i	$0.755993\pi$
$104$		0			0
$105$	−6.41868	−	4.27713i	−0.626399	−	0.417405i
$106$		0			0
$107$	3.40209	−	5.89259i	0.328892	−	0.569658i	−0.653400	−	0.757013i	$-0.726658\pi$
$107$	3.40209	−	5.89259i	0.328892	−	0.569658i	0.982292	+	0.187354i	$0.0599913\pi$
$108$		0			0
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	0.918092	+	0.396367i	$0.129729\pi$
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	−0.115783	+	0.993275i	$0.536938\pi$
$110$		0			0
$111$	6.96176	+	6.35688i	0.660781	+	0.603368i
$112$		0			0
$113$	6.77154	+	11.7287i	0.637013	+	1.10334i	0.986085	+	0.166243i	$0.0531636\pi$
$113$	6.77154	+	11.7287i	0.637013	+	1.10334i	−0.349072	+	0.937096i	$0.613503\pi$
$114$		0			0
$115$	0.670124			0.0624894
$116$		0			0
$117$	−1.06621	−	11.7139i	−0.0985714	−	1.08295i
$118$		0			0
$119$	8.50922	−	1.30541i	0.780039	−	0.119667i
$120$		0			0
$121$	−9.45002			−0.859093
$122$		0			0
$123$	−13.8753	+	4.40161i	−1.25109	+	0.396880i
$124$		0			0
$125$	−12.0632			−1.07896
$126$		0			0
$127$	−10.5904			−0.939748			−0.469874	−	0.882734i	$-0.655701\pi$
$127$	−10.5904			−0.939748			−0.469874	+	0.882734i	$0.655701\pi$
$128$		0			0
$129$	−6.30058	−	5.75314i	−0.554735	−	0.506536i
$130$		0			0
$131$	22.3638			1.95394			0.976968	−	0.213387i	$-0.0684495\pi$
$131$	22.3638			1.95394			0.976968	+	0.213387i	$0.0684495\pi$
$132$		0			0
$133$	−7.81808	−	9.75094i	−0.677914	−	0.845514i
$134$		0			0
$135$	5.28764	−	6.96651i	0.455088	−	0.599581i
$136$		0			0
$137$	17.9540			1.53391			0.766957	−	0.641699i	$-0.221770\pi$
$137$	17.9540			1.53391			0.766957	+	0.641699i	$0.221770\pi$
$138$		0			0
$139$	−0.570825	−	0.988699i	−0.0484168	−	0.0838603i	0.840801	−	0.541344i	$-0.182084\pi$
$139$	−0.570825	−	0.988699i	−0.0484168	−	0.0838603i	−0.889218	+	0.457483i	$0.848751\pi$
$140$		0			0
$141$	0.701976	−	0.222685i	0.0591170	−	0.0187535i
$142$		0			0
$143$	−2.44065	−	4.22733i	−0.204098	−	0.353507i
$144$		0			0
$145$	−5.38434	+	9.32596i	−0.447145	+	0.774479i
$146$		0			0
$147$	9.92634	−	6.96188i	0.818711	−	0.574206i
$148$		0			0
$149$	17.6583			1.44663			0.723313	−	0.690521i	$-0.242619\pi$
$149$	17.6583			1.44663			0.723313	+	0.690521i	$0.242619\pi$
$150$		0			0
$151$	15.2354			1.23984			0.619919	−	0.784666i	$-0.287166\pi$
$151$	15.2354			1.23984			0.619919	+	0.784666i	$0.287166\pi$
$152$		0			0
$153$	0.884835	+	9.72124i	0.0715347	+	0.785916i
$154$		0			0
$155$	−0.486741	+	0.843060i	−0.0390960	+	0.0677162i
$156$		0			0
$157$	6.81439	−	11.8029i	0.543847	−	0.941971i	−0.454831	−	0.890578i	$-0.650300\pi$
$157$	6.81439	−	11.8029i	0.543847	−	0.941971i	0.998678	−	0.0513933i	$-0.0163662\pi$
$158$		0			0
$159$	1.53974	−	0.488447i	0.122110	−	0.0387364i
$160$		0			0
$161$	−0.382263	+	0.981559i	−0.0301265	+	0.0773577i
$162$		0			0
$163$	4.04726	−	7.01005i	0.317006	−	0.549070i	−0.662856	−	0.748747i	$-0.730656\pi$
$163$	4.04726	−	7.01005i	0.317006	−	0.549070i	0.979862	+	0.199677i	$0.0639893\pi$
$164$		0			0
$165$	0.779359	−	3.54484i	0.0606730	−	0.275966i
$166$		0			0
$167$	2.07739	+	3.59814i	0.160753	+	0.278433i	0.935139	−	0.354281i	$-0.115274\pi$
$167$	2.07739	+	3.59814i	0.160753	+	0.278433i	−0.774386	+	0.632714i	$0.781941\pi$
$168$		0			0
$169$	−1.18629	+	2.05471i	−0.0912529	+	0.158055i
$170$		0			0
$171$	11.5801	−	8.16909i	0.885552	−	0.624706i
$172$		0			0
$173$	−6.91730	−	11.9811i	−0.525913	−	0.910907i	−0.999544	−	0.0301845i	$-0.990391\pi$
$173$	−6.91730	−	11.9811i	−0.525913	−	0.910907i	0.473632	−	0.880723i	$-0.342943\pi$
$174$		0			0
$175$	2.08059	−	5.34247i	0.157278	−	0.403852i
$176$		0			0
$177$	7.73894	+	7.06653i	0.581694	+	0.531153i
$178$		0			0
$179$	4.71167	+	8.16084i	0.352166	+	0.609970i	0.986629	−	0.162984i	$-0.0521118\pi$
$179$	4.71167	+	8.16084i	0.352166	+	0.609970i	−0.634462	+	0.772954i	$0.718778\pi$
$180$		0			0
$181$	1.32133			0.0982136			0.0491068	−	0.998794i	$-0.484363\pi$
$181$	1.32133			0.0982136			0.0491068	+	0.998794i	$0.484363\pi$
$182$		0			0
$183$	16.8550	−	5.34686i	1.24596	−	0.395251i
$184$		0			0
$185$	4.58064	−	7.93390i	0.336775	−	0.583312i
$186$		0			0
$187$	2.02546	+	3.50821i	0.148117	+	0.256546i
$188$		0			0
$189$	7.18787	+	11.7190i	0.522841	+	0.852430i
$190$		0			0
$191$	8.14271	+	14.1036i	0.589186	+	1.02050i	0.994339	+	0.106251i	$0.0338848\pi$
$191$	8.14271	+	14.1036i	0.589186	+	1.02050i	−0.405153	+	0.914249i	$0.632782\pi$
$192$		0			0
$193$	−1.28077	+	2.21837i	−0.0921921	+	0.159681i	−0.908433	−	0.418030i	$-0.862721\pi$
$193$	−1.28077	+	2.21837i	−0.0921921	+	0.159681i	0.816241	+	0.577711i	$0.196054\pi$
$194$		0			0
$195$	−10.8952	+	3.45626i	−0.780225	+	0.247508i
$196$		0			0
$197$	21.6916			1.54546			0.772730	−	0.634735i	$-0.218891\pi$
$197$	21.6916			1.54546			0.772730	+	0.634735i	$0.218891\pi$
$198$		0			0
$199$	5.59684	+	9.69402i	0.396750	+	0.687191i	0.993323	−	0.115368i	$-0.0368047\pi$
$199$	5.59684	+	9.69402i	0.396750	+	0.687191i	−0.596573	+	0.802559i	$0.703471\pi$
$200$		0			0
$201$	−12.0480	−	11.0012i	−0.849803	−	0.775966i
$202$		0			0
$203$	−10.5887	−	13.2065i	−0.743181	−	0.926917i
$204$		0			0
$205$	7.07289	+	12.2506i	0.493992	+	0.855620i
$206$		0			0
$207$	−1.08426	−	0.500981i	−0.0753614	−	0.0348206i
$208$		0			0
$209$	2.94055	−	5.09318i	0.203402	−	0.352303i
$210$		0			0
$211$	14.1807	+	24.5616i	0.976237	+	1.69089i	0.675793	+	0.737092i	$0.263801\pi$
$211$	14.1807	+	24.5616i	0.976237	+	1.69089i	0.300444	+	0.953799i	$0.402865\pi$
$212$		0			0
$213$	3.14875	−	14.3218i	0.215749	−	0.981313i
$214$		0			0
$215$	−4.14560	+	7.18039i	−0.282728	+	0.489699i
$216$		0			0
$217$	−0.957211	−	1.19386i	−0.0649797	−	0.0810446i
$218$		0			0
$219$	−22.5305	+	7.14726i	−1.52247	+	0.482967i
$220$		0			0
$221$	6.37875	−	11.0483i	0.429081	−	0.743190i
$222$		0			0
$223$	12.6962	−	21.9905i	0.850202	−	1.47259i	−0.0308242	−	0.999525i	$-0.509813\pi$
$223$	12.6962	−	21.9905i	0.850202	−	1.47259i	0.881026	−	0.473068i	$-0.156853\pi$
$224$		0			0
$225$	5.90146	+	2.72676i	0.393431	+	0.181784i
$226$		0			0
$227$	−4.62860			−0.307211			−0.153606	−	0.988132i	$-0.549089\pi$
$227$	−4.62860			−0.307211			−0.153606	+	0.988132i	$0.549089\pi$
$228$		0			0
$229$	2.32592			0.153701			0.0768506	−	0.997043i	$-0.475514\pi$
$229$	2.32592			0.153701			0.0768506	+	0.997043i	$0.475514\pi$
$230$		0			0
$231$	4.74771	+	3.16367i	0.312376	+	0.208154i
$232$		0			0
$233$	−6.37989	+	11.0503i	−0.417960	+	0.723929i	−0.995734	−	0.0922683i	$-0.970588\pi$
$233$	−6.37989	+	11.0503i	−0.417960	+	0.723929i	0.577774	+	0.816197i	$0.303922\pi$
$234$		0			0
$235$	−0.357830	−	0.619780i	−0.0233423	−	0.0404300i
$236$		0			0
$237$	9.13548	−	2.89801i	0.593413	−	0.188246i
$238$		0			0
$239$	11.0492	+	19.1378i	0.714714	+	1.23792i	0.963070	+	0.269252i	$0.0867766\pi$
$239$	11.0492	+	19.1378i	0.714714	+	1.23792i	−0.248355	+	0.968669i	$0.579890\pi$
$240$		0			0
$241$	20.0177			1.28945			0.644726	−	0.764414i	$-0.276972\pi$
$241$	20.0177			1.28945			0.644726	+	0.764414i	$0.276972\pi$
$242$		0			0
$243$	−13.7635	+	7.31880i	−0.882932	+	0.469502i
$244$		0			0
$245$	−8.67884	−	7.96840i	−0.554471	−	0.509082i
$246$		0			0
$247$	−18.5212			−1.17848
$248$		0			0
$249$	20.5586	+	18.7724i	1.30285	+	1.18965i
$250$		0			0
$251$	2.12390			0.134059			0.0670297	−	0.997751i	$-0.478648\pi$
$251$	2.12390			0.134059			0.0670297	+	0.997751i	$0.478648\pi$
$252$		0			0
$253$	−0.495671			−0.0311625
$254$		0			0
$255$	9.04182	−	2.86830i	0.566221	−	0.179620i
$256$		0			0
$257$	−12.7630			−0.796134			−0.398067	−	0.917356i	$-0.630319\pi$
$257$	−12.7630			−0.796134			−0.398067	+	0.917356i	$0.630319\pi$
$258$		0			0
$259$	9.00816	+	11.2352i	0.559740	+	0.698124i
$260$		0			0
$261$	15.6839	−	11.0641i	0.970810	−	0.684851i
$262$		0			0
$263$	11.0686			0.682522			0.341261	−	0.939969i	$-0.389146\pi$
$263$	11.0686			0.682522			0.341261	+	0.939969i	$0.389146\pi$
$264$		0			0
$265$	−0.784881	−	1.35945i	−0.0482148	−	0.0835105i
$266$		0			0
$267$	−15.4452	−	14.1032i	−0.945230	−	0.863102i
$268$		0			0
$269$	−1.77479	−	3.07403i	−0.108211	−	0.187427i	0.806835	−	0.590777i	$-0.201179\pi$
$269$	−1.77479	−	3.07403i	−0.108211	−	0.187427i	−0.915046	+	0.403351i	$0.867846\pi$
$270$		0			0
$271$	0.687666	−	1.19107i	0.0417727	−	0.0723525i	−0.844383	−	0.535740i	$-0.820033\pi$
$271$	0.687666	−	1.19107i	0.0417727	−	0.0723525i	0.886156	+	0.463387i	$0.153366\pi$
$272$		0			0
$273$	1.15252	−	17.9303i	0.0697534	−	1.08519i
$274$		0			0
$275$	2.69786			0.162687
$276$		0			0
$277$	−29.1617			−1.75216			−0.876079	−	0.482168i	$-0.839849\pi$
$277$	−29.1617			−1.75216			−0.876079	+	0.482168i	$0.839849\pi$
$278$		0			0
$279$	1.41782	−	1.00019i	0.0848824	−	0.0598797i
$280$		0			0
$281$	6.29603	−	10.9050i	0.375590	−	0.650540i	−0.614826	−	0.788663i	$-0.710774\pi$
$281$	6.29603	−	10.9050i	0.375590	−	0.650540i	0.990415	+	0.138123i	$0.0441069\pi$
$282$		0			0
$283$	−4.73028	+	8.19309i	−0.281186	+	0.487029i	−0.971677	−	0.236312i	$-0.924061\pi$
$283$	−4.73028	+	8.19309i	−0.281186	+	0.487029i	0.690491	+	0.723341i	$0.257394\pi$
$284$		0			0
$285$	−10.1697	−	9.28608i	−0.602401	−	0.550060i
$286$		0			0
$287$	−21.9786	+	3.37178i	−1.29736	+	0.199030i
$288$		0			0
$289$	3.20636	−	5.55358i	0.188609	−	0.326681i
$290$		0			0
$291$	−14.9917	−	13.6891i	−0.878826	−	0.802468i
$292$		0			0
$293$	−8.32726	−	14.4232i	−0.486484	−	0.842614i	0.513396	−	0.858152i	$-0.328387\pi$
$293$	−8.32726	−	14.4232i	−0.486484	−	0.842614i	−0.999879	+	0.0155376i	$0.995054\pi$
$294$		0			0
$295$	5.09200	−	8.81960i	0.296468	−	0.513497i
$296$		0			0
$297$	−3.91111	+	5.15292i	−0.226946	+	0.299003i
$298$		0			0
$299$	0.780502	+	1.35187i	0.0451376	+	0.0781806i
$300$		0			0
$301$	−8.15262	−	10.1682i	−0.469909	−	0.586085i
$302$		0			0
$303$	−2.01062	+	9.14513i	−0.115507	+	0.525374i
$304$		0			0
$305$	−8.59181	−	14.8815i	−0.491966	−	0.852110i
$306$		0			0
$307$	9.55966			0.545599			0.272799	−	0.962071i	$-0.412051\pi$
$307$	9.55966			0.545599			0.272799	+	0.962071i	$0.412051\pi$
$308$		0			0
$309$	5.43762	−	24.7325i	0.309335	−	1.40698i
$310$		0			0
$311$	13.1851	−	22.8373i	0.747658	−	1.29498i	−0.201284	−	0.979533i	$-0.564512\pi$
$311$	13.1851	−	22.8373i	0.747658	−	1.29498i	0.948943	−	0.315449i	$-0.102155\pi$
$312$		0			0
$313$	6.35091	+	11.0001i	0.358975	+	0.621762i	0.987790	−	0.155792i	$-0.0497931\pi$
$313$	6.35091	+	11.0001i	0.358975	+	0.621762i	−0.628815	+	0.777555i	$0.716460\pi$
$314$		0			0
$315$	9.62264	−	9.26739i	0.542174	−	0.522159i
$316$		0			0
$317$	−0.0165768	−	0.0287119i	−0.000931047	−	0.00161262i	0.865560	−	0.500806i	$-0.166963\pi$
$317$	−0.0165768	−	0.0287119i	−0.000931047	−	0.00161262i	−0.866491	+	0.499193i	$0.833630\pi$
$318$		0			0
$319$	3.98264	−	6.89813i	0.222985	−	0.386221i
$320$		0			0
$321$	8.70289	+	7.94672i	0.485748	+	0.443543i
$322$		0			0
$323$	15.3705			0.855238
$324$		0			0
$325$	−4.24815	−	7.35801i	−0.235645	−	0.408149i
$326$		0			0
$327$	−27.6583	+	8.77392i	−1.52951	+	0.485199i
$328$		0			0
$329$	1.11194	−	0.170584i	0.0613031	−	0.00940461i
$330$		0			0
$331$	−2.42694	−	4.20358i	−0.133397	−	0.231050i	0.791587	−	0.611056i	$-0.209255\pi$
$331$	−2.42694	−	4.20358i	−0.133397	−	0.231050i	−0.924984	+	0.380006i	$0.875922\pi$
$332$		0			0
$333$	−13.3428	+	9.41260i	−0.731183	+	0.515807i
$334$		0			0
$335$	−7.92726	+	13.7304i	−0.433112	+	0.750173i
$336$		0			0
$337$	−4.32200	−	7.48592i	−0.235434	−	0.407784i	0.723965	−	0.689837i	$-0.242318\pi$
$337$	−4.32200	−	7.48592i	−0.235434	−	0.407784i	−0.959399	+	0.282053i	$0.908985\pi$
$338$		0			0
$339$	−22.3592	+	7.09293i	−1.21439	+	0.385235i
$340$		0			0
$341$	0.360028	−	0.623586i	0.0194966	−	0.0337691i
$342$		0			0
$343$	16.6224	−	8.16680i	0.897524	−	0.440966i
$344$		0			0
$345$	−0.249233	+	1.13361i	−0.0134183	+	0.0610317i
$346$		0			0
$347$	−11.6116	+	20.1119i	−0.623344	+	1.07966i	0.365515	+	0.930806i	$0.380893\pi$
$347$	−11.6116	+	20.1119i	−0.623344	+	1.07966i	−0.988859	+	0.148858i	$0.952440\pi$
$348$		0			0
$349$	−3.76025	+	6.51295i	−0.201282	+	0.348630i	−0.948942	−	0.315452i	$-0.897844\pi$
$349$	−3.76025	+	6.51295i	−0.201282	+	0.348630i	0.747660	+	0.664082i	$0.231177\pi$
$350$		0			0
$351$	20.2124	+	2.55300i	1.07886	+	0.136269i
$352$		0			0
$353$	−0.919056			−0.0489164			−0.0244582	−	0.999701i	$-0.507786\pi$
$353$	−0.919056			−0.0489164			−0.0244582	+	0.999701i	$0.507786\pi$
$354$		0			0
$355$	−14.2499			−0.756306
$356$		0			0
$357$	−0.956458	+	14.8801i	−0.0506211	+	0.787540i
$358$		0			0
$359$	−8.24300	+	14.2773i	−0.435049	+	0.753527i	−0.997300	−	0.0734398i	$-0.976602\pi$
$359$	−8.24300	+	14.2773i	−0.435049	+	0.753527i	0.562251	+	0.826967i	$0.309936\pi$
$360$		0			0
$361$	−1.65737	−	2.87066i	−0.0872302	−	0.151087i
$362$		0			0
$363$	3.51466	−	15.9861i	0.184472	−	0.839054i
$364$		0			0
$365$	11.4848	+	19.8923i	0.601144	+	1.04121i
$366$		0			0
$367$	12.6784			0.661808			0.330904	−	0.943664i	$-0.392646\pi$
$367$	12.6784			0.661808			0.330904	+	0.943664i	$0.392646\pi$
$368$		0			0
$369$	−2.28546	−	25.1092i	−0.118976	−	1.30713i
$370$		0			0
$371$	2.43897	−	0.374167i	0.126625	−	0.0194258i
$372$		0			0
$373$	22.6821			1.17443			0.587217	−	0.809430i	$-0.300224\pi$
$373$	22.6821			1.17443			0.587217	+	0.809430i	$0.300224\pi$
$374$		0			0
$375$	4.48654	−	20.4066i	0.231684	−	1.05379i
$376$		0			0
$377$	−25.0849			−1.29194
$378$		0			0
$379$	−19.0925			−0.980717			−0.490358	−	0.871521i	$-0.663134\pi$
$379$	−19.0925			−0.980717			−0.490358	+	0.871521i	$0.663134\pi$
$380$		0			0
$381$	3.93880	−	17.9153i	0.201791	−	0.917827i
$382$		0			0
$383$	6.07925			0.310635			0.155318	−	0.987865i	$-0.450360\pi$
$383$	6.07925			0.310635			0.155318	+	0.987865i	$0.450360\pi$
$384$		0			0
$385$	2.01195	−	5.16621i	0.102539	−	0.263295i
$386$		0			0
$387$	12.0756	−	8.51865i	0.613838	−	0.433028i
$388$		0			0
$389$	−0.631562			−0.0320214			−0.0160107	−	0.999872i	$-0.505097\pi$
$389$	−0.631562			−0.0320214			−0.0160107	+	0.999872i	$0.505097\pi$
$390$		0			0
$391$	−0.647728	−	1.12190i	−0.0327570	−	0.0567368i
$392$		0			0
$393$	−8.31757	+	37.8317i	−0.419566	+	1.90836i
$394$		0			0
$395$	−4.65679	−	8.06579i	−0.234308	−	0.405834i
$396$		0			0
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.102170	+	0.994767i	$0.532579\pi$
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.810408	+	0.585865i	$0.800755\pi$
$398$		0			0
$399$	19.4029	−	9.59887i	0.971359	−	0.480544i
$400$		0			0
$401$	−31.6137			−1.57871			−0.789357	−	0.613934i	$-0.789586\pi$
$401$	−31.6137			−1.57871			−0.789357	+	0.613934i	$0.789586\pi$
$402$		0			0
$403$	−2.26765			−0.112960
$404$		0			0
$405$	9.81829	+	11.5358i	0.487875	+	0.573220i
$406$		0			0
$407$	−3.38816	+	5.86847i	−0.167945	+	0.290889i
$408$		0			0
$409$	−10.0906	+	17.4774i	−0.498948	+	0.864203i	−0.999999	−	0.00121422i	$-0.999614\pi$
$409$	−10.0906	+	17.4774i	−0.498948	+	0.864203i	0.501051	+	0.865418i	$0.332947\pi$
$410$		0			0
$411$	−6.67747	+	30.3718i	−0.329375	+	1.49813i
$412$		0			0
$413$	10.0138	+	12.4895i	0.492746	+	0.614567i
$414$		0			0
$415$	13.5270	−	23.4294i	0.664014	−	1.15011i
$416$		0			0
$417$	1.88483	−	0.597918i	0.0923006	−	0.0292802i
$418$		0			0
$419$	12.4159	+	21.5049i	0.606555	+	1.05058i	0.991804	+	0.127772i	$0.0407825\pi$
$419$	12.4159	+	21.5049i	0.606555	+	1.05058i	−0.385248	+	0.922813i	$0.625884\pi$
$420$		0			0
$421$	−5.71841	+	9.90458i	−0.278698	+	0.482720i	−0.971062	−	0.238829i	$-0.923236\pi$
$421$	−5.71841	+	9.90458i	−0.278698	+	0.482720i	0.692363	+	0.721549i	$0.256570\pi$
$422$		0			0
$423$	0.115625	+	1.27032i	0.00562190	+	0.0617650i
$424$		0			0
$425$	3.52548	+	6.10631i	0.171011	+	0.296200i
$426$		0			0
$427$	26.6986	−	4.09587i	1.29203	−	0.198213i
$428$		0			0
$429$	8.05889	−	2.55649i	0.389087	−	0.123429i
$430$		0			0
$431$	−2.80157	−	4.85246i	−0.134947	−	0.233735i	0.790630	−	0.612294i	$-0.209753\pi$
$431$	−2.80157	−	4.85246i	−0.134947	−	0.233735i	−0.925577	+	0.378559i	$0.876420\pi$
$432$		0			0
$433$	−4.22555			−0.203067			−0.101534	−	0.994832i	$-0.532375\pi$
$433$	−4.22555			−0.203067			−0.101534	+	0.994832i	$0.532375\pi$
$434$		0			0
$435$	−13.7737	−	12.5769i	−0.660398	−	0.603018i
$436$		0			0
$437$	−0.940366	+	1.62876i	−0.0449838	+	0.0779142i
$438$		0			0
$439$	−17.7316	−	30.7120i	−0.846281	−	1.46580i	−0.884504	−	0.466532i	$-0.845503\pi$
$439$	−17.7316	−	30.7120i	−0.846281	−	1.46580i	0.0382233	−	0.999269i	$-0.487830\pi$
$440$		0			0
$441$	8.08524	+	19.3811i	0.385012	+	0.922912i
$442$		0			0
$443$	−11.4658	−	19.8593i	−0.544755	−	0.943543i	−0.998622	−	0.0524740i	$-0.983289\pi$
$443$	−11.4658	−	19.8593i	−0.544755	−	0.943543i	0.453867	−	0.891069i	$-0.350044\pi$
$444$		0			0
$445$	−10.1625	+	17.6019i	−0.481748	+	0.834412i
$446$		0			0
$447$	−6.56750	+	29.8717i	−0.310632	+	1.41288i
$448$		0			0
$449$	20.4850			0.966747			0.483373	−	0.875414i	$-0.339411\pi$
$449$	20.4850			0.966747			0.483373	+	0.875414i	$0.339411\pi$
$450$		0			0
$451$	−5.23161	−	9.06141i	−0.246347	−	0.426685i
$452$		0			0
$453$	−5.66636	+	25.7729i	−0.266229	+	1.21092i
$454$		0			0
$455$	−17.2582	+	2.64761i	−0.809076	+	0.124122i
$456$		0			0
$457$	−7.72677	−	13.3832i	−0.361443	−	0.626038i	0.626755	−	0.779216i	$-0.284383\pi$
$457$	−7.72677	−	13.3832i	−0.361443	−	0.626038i	−0.988199	+	0.153178i	$0.951049\pi$
$458$		0			0
$459$	−16.7740	−	2.11870i	−0.782944	−	0.0988927i
$460$		0			0
$461$	14.0815	−	24.3898i	0.655839	−	1.13595i	−0.325844	−	0.945424i	$-0.605648\pi$
$461$	14.0815	−	24.3898i	0.655839	−	1.13595i	0.981683	−	0.190523i	$-0.0610183\pi$
$462$		0			0
$463$	15.3193	+	26.5338i	0.711948	+	1.23313i	0.964125	+	0.265449i	$0.0855202\pi$
$463$	15.3193	+	26.5338i	0.711948	+	1.23313i	−0.252177	+	0.967681i	$0.581146\pi$
$464$		0			0
$465$	−1.24513	−	1.13695i	−0.0577416	−	0.0527246i
$466$		0			0
$467$	6.61798	−	11.4627i	0.306244	−	0.530429i	−0.671294	−	0.741191i	$-0.734261\pi$
$467$	6.61798	−	11.4627i	0.306244	−	0.530429i	0.977537	+	0.210762i	$0.0675945\pi$
$468$		0			0
$469$	−15.5895	−	19.4437i	−0.719857	−	0.897827i
$470$		0			0
$471$	17.4319	+	15.9173i	0.803219	+	0.733429i
$472$		0			0
$473$	3.06638	−	5.31112i	0.140992	−	0.244206i
$474$		0			0
$475$	5.11826	−	8.86508i	0.234842	−	0.406758i
$476$		0			0
$477$	0.253618	+	2.78637i	0.0116124	+	0.127579i
$478$		0			0
$479$	−14.0872			−0.643658			−0.321829	−	0.946798i	$-0.604298\pi$
$479$	−14.0872			−0.643658			−0.321829	+	0.946798i	$0.604298\pi$
$480$		0			0
$481$	21.3405			0.973044
$482$		0			0
$483$	−1.51828	−	1.01172i	−0.0690842	−	0.0460347i
$484$		0			0
$485$	−9.86407	+	17.0851i	−0.447904	+	0.775793i
$486$		0			0
$487$	−3.45654	−	5.98690i	−0.156631	−	0.271292i	0.777021	−	0.629475i	$-0.216730\pi$
$487$	−3.45654	−	5.98690i	−0.156631	−	0.271292i	−0.933652	+	0.358183i	$0.883397\pi$
$488$		0			0
$489$	10.3533	+	9.45372i	0.468192	+	0.427512i
$490$		0			0
$491$	15.3481	+	26.5837i	0.692651	+	1.19971i	0.970966	+	0.239217i	$0.0768909\pi$
$491$	15.3481	+	26.5837i	0.692651	+	1.19971i	−0.278315	+	0.960490i	$0.589776\pi$
$492$		0			0
$493$	20.8176			0.937578
$494$		0			0
$495$	5.70677	+	2.63680i	0.256500	+	0.118515i
$496$		0			0
$497$	8.12865	−	20.8724i	0.364620	−	0.936256i
$498$		0			0
$499$	22.0371			0.986518			0.493259	−	0.869882i	$-0.335805\pi$
$499$	22.0371			0.986518			0.493259	+	0.869882i	$0.335805\pi$
$500$		0			0
$501$	−6.85942	+	2.17599i	−0.306456	+	0.0972159i
$502$		0			0
$503$	−38.9653			−1.73737			−0.868687	−	0.495361i	$-0.835036\pi$
$503$	−38.9653			−1.73737			−0.868687	+	0.495361i	$0.835036\pi$
$504$		0			0
$505$	9.09922			0.404910
$506$		0			0
$507$	−3.03464	−	2.77097i	−0.134773	−	0.123063i
$508$		0			0
$509$	−28.2941			−1.25412			−0.627058	−	0.778973i	$-0.715741\pi$
$509$	−28.2941			−1.25412			−0.627058	+	0.778973i	$0.715741\pi$
$510$		0			0
$511$	−35.6885	+	5.47503i	−1.57877	+	0.242201i
$512$		0			0
$513$	9.51236	+	22.6277i	0.419981	+	0.999038i
$514$		0			0
$515$	−24.6084			−1.08437
$516$		0			0
$517$	0.264676	+	0.458433i	0.0116405	+	0.0201619i
$518$		0			0
$519$	22.8405	−	7.24561i	1.00259	−	0.318047i
$520$		0			0
$521$	−5.98150	−	10.3603i	−0.262054	−	0.453892i	0.704733	−	0.709472i	$-0.251067\pi$
$521$	−5.98150	−	10.3603i	−0.262054	−	0.453892i	−0.966788	+	0.255581i	$0.917733\pi$
$522$		0			0
$523$	3.15056	−	5.45693i	0.137764	−	0.238615i	−0.788886	−	0.614540i	$-0.789342\pi$
$523$	3.15056	−	5.45693i	0.137764	−	0.238615i	0.926650	+	0.375925i	$0.122675\pi$
$524$		0			0
$525$	8.26376	+	5.50661i	0.360660	+	0.240328i
$526$		0			0
$527$	1.88190			0.0819767
$528$		0			0
$529$	−22.8415			−0.993108
$530$		0			0
$531$	−14.8324	+	10.4634i	−0.643669	+	0.454072i
$532$		0			0
$533$	−16.4758	+	28.5369i	−0.713645	+	1.23607i
$534$		0			0
$535$	5.72625	−	9.91815i	0.247567	−	0.428799i
$536$		0			0
$537$	−15.5576	+	4.93529i	−0.671362	+	0.212974i
$538$		0			0
$539$	6.41948	+	5.89399i	0.276507	+	0.253872i
$540$		0			0
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	−0.571550	−	0.820567i	$-0.693658\pi$
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	0.996407	+	0.0846937i	$0.0269912\pi$
$542$		0			0
$543$	−0.491430	+	2.23522i	−0.0210893	+	0.0959227i
$544$		0			0
$545$	14.0987	+	24.4197i	0.603923	+	1.04602i
$546$		0			0
$547$	−21.6125	+	37.4340i	−0.924085	+	1.60056i	−0.131059	+	0.991375i	$0.541838\pi$
$547$	−21.6125	+	37.4340i	−0.924085	+	1.60056i	−0.793026	+	0.609188i	$0.791496\pi$
$548$		0			0
$549$	2.77626	+	30.5014i	0.118488	+	1.30177i
$550$		0			0
$551$	−15.1114	−	26.1737i	−0.643767	−	1.11504i
$552$		0			0
$553$	14.4707	−	2.21997i	0.615357	−	0.0944029i
$554$		0			0
$555$	11.7177	+	10.6996i	0.497390	+	0.454173i
$556$		0			0
$557$	−14.0838	−	24.3938i	−0.596748	−	1.03360i	−0.993298	−	0.115584i	$-0.963126\pi$
$557$	−14.0838	−	24.3938i	−0.596748	−	1.03360i	0.396550	−	0.918013i	$-0.370207\pi$
$558$		0			0
$559$	−19.3137			−0.816884
$560$		0			0
$561$	−6.68797	+	2.12160i	−0.282366	+	0.0895739i
$562$		0			0
$563$	12.8472	−	22.2520i	0.541445	−	0.937810i	−0.457377	−	0.889273i	$-0.651211\pi$
$563$	12.8472	−	22.2520i	0.541445	−	0.937810i	0.998821	−	0.0485366i	$-0.0154558\pi$
$564$		0			0
$565$	11.3976	+	19.7411i	0.479499	+	0.830516i
$566$		0			0
$567$	−22.4977	+	7.80082i	−0.944815	+	0.327604i
$568$		0			0
$569$	−17.7441	−	30.7336i	−0.743870	−	1.28842i	−0.950721	−	0.310048i	$-0.899655\pi$
$569$	−17.7441	−	30.7336i	−0.743870	−	1.28842i	0.206851	−	0.978373i	$-0.433679\pi$
$570$		0			0
$571$	10.8412	−	18.7775i	0.453689	−	0.785813i	−0.544923	−	0.838486i	$-0.683441\pi$
$571$	10.8412	−	18.7775i	0.453689	−	0.785813i	0.998612	+	0.0526737i	$0.0167743\pi$
$572$		0			0
$573$	−26.8868	+	8.52919i	−1.12321	+	0.356312i
$574$		0			0
$575$	−0.862754			−0.0359793
$576$		0			0
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	0.663102	−	0.748529i	$-0.269240\pi$
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	−0.979796	+	0.199998i	$0.935906\pi$
$578$		0			0
$579$	−3.27635	−	2.99168i	−0.136160	−	0.124330i
$580$		0			0
$581$	26.6018	+	33.1786i	1.10363	+	1.37648i
$582$		0			0
$583$	0.580553	+	1.00555i	0.0240440	+	0.0416455i
$584$		0			0
$585$	−1.79460	−	19.7164i	−0.0741976	−	0.815172i
$586$		0			0
$587$	19.1924	−	33.2423i	0.792157	−	1.37206i	−0.132472	−	0.991187i	$-0.542292\pi$
$587$	19.1924	−	33.2423i	0.792157	−	1.37206i	0.924629	−	0.380869i	$-0.124375\pi$
$588$		0			0
$589$	−1.36606	−	2.36608i	−0.0562875	−	0.0974928i
$590$		0			0
$591$	−8.06754	+	36.6945i	−0.331854	+	1.50941i
$592$		0			0
$593$	−9.25559	+	16.0311i	−0.380081	+	0.658320i	−0.991074	−	0.133316i	$-0.957437\pi$
$593$	−9.25559	+	16.0311i	−0.380081	+	0.658320i	0.610992	+	0.791637i	$0.290771\pi$
$594$		0			0
$595$	14.3223	−	2.19721i	0.587159	−	0.0900770i
$596$		0			0
$597$	−18.4805	+	5.86248i	−0.756355	+	0.239935i
$598$		0			0
$599$	−10.8413	+	18.7776i	−0.442962	+	0.767233i	−0.997908	−	0.0646536i	$-0.979406\pi$
$599$	−10.8413	+	18.7776i	−0.442962	+	0.767233i	0.554946	+	0.831887i	$0.312739\pi$
$600$		0			0
$601$	3.95776	−	6.85505i	0.161441	−	0.279623i	−0.773945	−	0.633253i	$-0.781719\pi$
$601$	3.95776	−	6.85505i	0.161441	−	0.279623i	0.935386	+	0.353630i	$0.115053\pi$
$602$		0			0
$603$	23.0911	−	16.2895i	0.940343	−	0.663358i
$604$		0			0
$605$	−15.9059			−0.646665
$606$		0			0
$607$	−35.9247			−1.45814			−0.729068	−	0.684441i	$-0.760046\pi$
$607$	−35.9247			−1.45814			−0.729068	+	0.684441i	$0.760046\pi$
$608$		0			0
$609$	26.2790	−	13.0006i	1.06488	−	0.526810i
$610$		0			0
$611$	0.833539	−	1.44373i	0.0337214	−	0.0584072i
$612$		0			0
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	0.831847	−	0.555005i	$-0.187284\pi$
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	−0.896572	+	0.442898i	$0.853950\pi$
$614$		0			0
$615$	−23.3543	+	7.40859i	−0.941736	+	0.298743i
$616$		0			0
$617$	15.9357	+	27.6015i	0.641549	+	1.11120i	0.985087	+	0.172056i	$0.0550411\pi$
$617$	15.9357	+	27.6015i	0.641549	+	1.11120i	−0.343538	+	0.939139i	$0.611626\pi$
$618$		0			0
$619$	20.9726			0.842959			0.421480	−	0.906838i	$-0.361511\pi$
$619$	20.9726			0.842959			0.421480	+	0.906838i	$0.361511\pi$
$620$		0			0
$621$	1.25074	−	1.64786i	0.0501906	−	0.0661265i
$622$		0			0
$623$	−19.9853	−	24.9262i	−0.800692	−	0.998647i
$624$		0			0
$625$	−9.46924			−0.378769
$626$		0			0
$627$	7.52222	+	6.86864i	0.300409	+	0.274307i
$628$		0			0
$629$	−17.7102			−0.706153
$630$		0			0
$631$	−26.4435			−1.05270			−0.526349	−	0.850268i	$-0.676440\pi$
$631$	−26.4435			−1.05270			−0.526349	+	0.850268i	$0.676440\pi$
$632$		0			0
$633$	−46.8237	+	14.8537i	−1.86108	+	0.590382i
$634$		0			0
$635$	−17.8253			−0.707377
$636$		0			0
$637$	5.96663	−	26.7891i	0.236407	−	1.06142i
$638$		0			0
$639$	23.0564	+	10.6532i	0.912095	+	0.421432i
$640$		0			0
$641$	−27.9618			−1.10443			−0.552213	−	0.833703i	$-0.686217\pi$
$641$	−27.9618			−1.10443			−0.552213	+	0.833703i	$0.686217\pi$
$642$		0			0
$643$	6.12936	+	10.6164i	0.241718	+	0.418669i	0.961204	−	0.275839i	$-0.0889556\pi$
$643$	6.12936	+	10.6164i	0.241718	+	0.418669i	−0.719485	+	0.694508i	$0.755622\pi$
$644$		0			0
$645$	−10.6049	−	9.68344i	−0.417566	−	0.381285i
$646$		0			0
$647$	−4.49923	−	7.79290i	−0.176883	−	0.306371i	0.763928	−	0.645301i	$-0.223268\pi$
$647$	−4.49923	−	7.79290i	−0.176883	−	0.306371i	−0.940811	+	0.338931i	$0.889935\pi$
$648$		0			0
$649$	−3.76640	+	6.52360i	−0.147844	+	0.256074i
$650$		0			0
$651$	2.37560	−	1.17524i	0.0931072	−	0.0460614i
$652$		0			0
$653$	−22.7901			−0.891844			−0.445922	−	0.895072i	$-0.647124\pi$
$653$	−22.7901			−0.891844			−0.445922	+	0.895072i	$0.647124\pi$
$654$		0			0
$655$	37.6418			1.47079
$656$		0			0
$657$	−3.71109	−	40.7719i	−0.144783	−	1.59066i
$658$		0			0
$659$	19.3311	−	33.4824i	0.753033	−	1.30429i	−0.193314	−	0.981137i	$-0.561924\pi$
$659$	19.3311	−	33.4824i	0.753033	−	1.30429i	0.946347	−	0.323154i	$-0.104743\pi$
$660$		0			0
$661$	5.75399	−	9.96621i	0.223804	−	0.387641i	−0.732156	−	0.681137i	$-0.761486\pi$
$661$	5.75399	−	9.96621i	0.223804	−	0.387641i	0.955960	+	0.293497i	$0.0948190\pi$
$662$		0			0
$663$	16.3175	+	14.8997i	0.633718	+	0.578657i
$664$		0			0
$665$	−13.1590	−	16.4124i	−0.510286	−	0.636444i
$666$		0			0
$667$	−1.27362	+	2.20597i	−0.0493147	+	0.0854156i
$668$		0			0
$669$	32.4782	+	29.6563i	1.25568	+	1.14658i
$670$		0			0
$671$	6.35511	+	11.0074i	0.245336	+	0.424935i
$672$		0			0
$673$	−10.6642	+	18.4709i	−0.411075	+	0.712002i	−0.995008	−	0.0997997i	$-0.968180\pi$
$673$	−10.6642	+	18.4709i	−0.411075	+	0.712002i	0.583933	+	0.811802i	$0.301513\pi$
$674$		0			0
$675$	−6.80760	+	8.96906i	−0.262025	+	0.345219i
$676$		0			0
$677$	−13.8799	−	24.0407i	−0.533449	−	0.923961i	−0.999237	−	0.0390641i	$-0.987562\pi$
$677$	−13.8799	−	24.0407i	−0.533449	−	0.923961i	0.465788	−	0.884896i	$-0.345771\pi$
$678$		0			0
$679$	−19.3984	−	24.1943i	−0.744443	−	0.928491i
$680$		0			0
$681$	1.72147	−	7.82997i	0.0659670	−	0.300045i
$682$		0			0
$683$	8.66854	+	15.0143i	0.331692	+	0.574508i	0.982844	−	0.184440i	$-0.0590471\pi$
$683$	8.66854	+	15.0143i	0.331692	+	0.574508i	−0.651151	+	0.758948i	$0.725714\pi$
$684$		0			0
$685$	30.2194			1.15462
$686$		0			0
$687$	−0.865059	+	3.93464i	−0.0330041	+	0.150116i
$688$		0			0
$689$	1.82832	−	3.16675i	0.0696535	−	0.120643i
$690$		0			0
$691$	19.8023	+	34.2986i	0.753315	+	1.30478i	0.946207	+	0.323560i	$0.104880\pi$
$691$	19.8023	+	34.2986i	0.753315	+	1.30478i	−0.192892	+	0.981220i	$0.561787\pi$
$692$		0			0
$693$	−7.11758	+	6.85482i	−0.270375	+	0.260393i
$694$		0			0
$695$	−0.960788	−	1.66413i	−0.0364448	−	0.0631242i
$696$		0			0
$697$	13.6730	−	23.6824i	0.517903	−	0.897035i
$698$		0			0
$699$	−16.3204	−	14.9024i	−0.617294	−	0.563659i
$700$		0			0
$701$	7.28469			0.275139			0.137570	−	0.990492i	$-0.456071\pi$
$701$	7.28469			0.275139			0.137570	+	0.990492i	$0.456071\pi$
$702$		0			0
$703$	12.8558	+	22.2668i	0.484864	+	0.839809i
$704$		0			0
$705$	1.18153	−	0.374814i	0.0444992	−	0.0141163i
$706$		0			0
$707$	−5.19052	+	13.3280i	−0.195210	+	0.501251i
$708$		0			0
$709$	−6.00541	−	10.4017i	−0.225538	−	0.390643i	0.730943	−	0.682439i	$-0.239081\pi$
$709$	−6.00541	−	10.4017i	−0.225538	−	0.390643i	−0.956481	+	0.291796i	$0.905747\pi$
$710$		0			0
$711$	1.50474	+	16.5319i	0.0564323	+	0.619993i
$712$		0			0
$713$	−0.115134	+	0.199418i	−0.00431181	+	0.00746827i
$714$		0			0
$715$	−4.10800	−	7.11526i	−0.153630	−	0.266096i
$716$		0			0
$717$	−36.4839	+	11.5736i	−1.36252	+	0.432225i
$718$		0			0
$719$	2.15819	−	3.73809i	0.0804868	−	0.139407i	−0.822972	−	0.568081i	$-0.807686\pi$
$719$	2.15819	−	3.73809i	0.0804868	−	0.139407i	0.903459	+	0.428674i	$0.141019\pi$
$720$		0			0
$721$	14.0375	−	36.0449i	0.522783	−	1.34238i
$722$		0			0
$723$	−7.44499	+	33.8629i	−0.276882	+	1.25937i
$724$		0			0
$725$	6.93210	−	12.0067i	0.257452	−	0.445919i
$726$		0			0
$727$	−10.2483	+	17.7506i	−0.380090	+	0.658334i	−0.991075	−	0.133308i	$-0.957440\pi$
$727$	−10.2483	+	17.7506i	−0.380090	+	0.658334i	0.610985	+	0.791642i	$0.290774\pi$
$728$		0			0
$729$	−7.26189	−	26.0051i	−0.268959	−	0.963152i
$730$		0			0
$731$	16.0282			0.592825
$732$		0			0
$733$	25.3322			0.935666			0.467833	−	0.883817i	$-0.345035\pi$
$733$	25.3322			0.935666			0.467833	+	0.883817i	$0.345035\pi$
$734$		0			0
$735$	16.7076	−	11.7179i	0.616268	−	0.432222i
$736$		0			0
$737$	5.86356	−	10.1560i	0.215987	−	0.374100i
$738$		0			0
$739$	6.63391	+	11.4903i	0.244032	+	0.422676i	0.961859	−	0.273545i	$-0.0881964\pi$
$739$	6.63391	+	11.4903i	0.244032	+	0.422676i	−0.717827	+	0.696222i	$0.754863\pi$
$740$		0			0
$741$	6.88843	−	31.3314i	0.253053	−	1.15099i
$742$		0			0
$743$	−22.6116	−	39.1644i	−0.829538	−	1.43680i	−0.898401	−	0.439176i	$-0.855270\pi$
$743$	−22.6116	−	39.1644i	−0.829538	−	1.43680i	0.0688624	−	0.997626i	$-0.478063\pi$
$744$		0			0
$745$	29.7217			1.08892
$746$		0			0
$747$	−39.4024	+	27.7962i	−1.44166	+	1.01701i
$748$		0			0
$749$	11.2611	+	14.0451i	0.411471	+	0.513199i
$750$		0			0
$751$	28.3797			1.03559			0.517795	−	0.855505i	$-0.326753\pi$
$751$	28.3797			1.03559			0.517795	+	0.855505i	$0.326753\pi$
$752$		0			0
$753$	−0.789924	+	3.59289i	−0.0287864	+	0.130932i
$754$		0			0
$755$	25.6435			0.933263
$756$		0			0
$757$	5.08483			0.184811			0.0924056	−	0.995721i	$-0.470544\pi$
$757$	5.08483			0.184811			0.0924056	+	0.995721i	$0.470544\pi$
$758$		0			0
$759$	0.184350	−	0.838500i	0.00669149	−	0.0304356i
$760$		0			0
$761$	37.7225			1.36744			0.683720	−	0.729745i	$-0.260361\pi$
$761$	37.7225			1.36744			0.683720	+	0.729745i	$0.260361\pi$
$762$		0			0
$763$	−43.8110	+	6.72111i	−1.58606	+	0.243321i
$764$		0			0
$765$	1.48932	+	16.3624i	0.0538463	+	0.591583i
$766$		0			0
$767$	23.7229			0.856583
$768$		0			0
$769$	11.8729	+	20.5644i	0.428147	+	0.741572i	0.996709	−	0.0810688i	$-0.0258333\pi$
$769$	11.8729	+	20.5644i	0.428147	+	0.741572i	−0.568562	+	0.822641i	$0.692500\pi$
$770$		0			0
$771$	4.74683	−	21.5905i	0.170953	−	0.777563i
$772$		0			0
$773$	19.5347	+	33.8351i	0.702614	+	1.21696i	0.967546	+	0.252696i	$0.0813172\pi$
$773$	19.5347	+	33.8351i	0.702614	+	1.21696i	−0.264932	+	0.964267i	$0.585350\pi$
$774$		0			0
$775$	0.626657	−	1.08540i	0.0225102	−	0.0389888i
$776$		0			0
$777$	−22.3564	+	11.0600i	−0.802031	+	0.396776i
$778$		0			0
$779$	−39.7008			−1.42243
$780$		0			0
$781$	10.5402			0.377159
$782$		0			0
$783$	12.8834	+	30.6467i	0.460415	+	1.09522i
$784$		0			0
$785$	11.4697	−	19.8661i	0.409370	−	0.709050i
$786$		0			0
$787$	1.90458	−	3.29882i	0.0678908	−	0.117590i	−0.830082	−	0.557642i	$-0.811706\pi$
$787$	1.90458	−	3.29882i	0.0678908	−	0.117590i	0.897973	+	0.440051i	$0.145040\pi$
$788$		0			0
$789$	−4.11666	+	18.7242i	−0.146557	+	0.666601i
$790$		0			0
$791$	−35.4173	+	5.43342i	−1.25929	+	0.193190i
$792$		0			0
$793$	20.0140	−	34.6653i	0.710718	−	1.23100i
$794$		0			0
$795$	2.59163	−	0.822133i	0.0919157	−	0.0291581i
$796$		0			0
$797$	−10.8239	−	18.7476i	−0.383404	−	0.664075i	0.608143	−	0.793828i	$-0.291915\pi$
$797$	−10.8239	−	18.7476i	−0.383404	−	0.664075i	−0.991546	+	0.129753i	$0.958582\pi$
$798$		0			0
$799$	−0.691743	+	1.19813i	−0.0244721	+	0.0423870i
$800$		0			0
$801$	29.6020	−	20.8825i	1.04594	−	0.737848i
$802$		0			0
$803$	−8.49500	−	14.7138i	−0.299782	−	0.519238i
$804$		0			0
$805$	−0.643408	+	1.65212i	−0.0226771	+	0.0582294i
$806$		0			0
$807$	5.86026	−	1.85903i	0.206291	−	0.0654408i
$808$		0			0
$809$	−18.5128	−	32.0652i	−0.650877	−	1.12735i	−0.982910	−	0.184084i	$-0.941068\pi$
$809$	−18.5128	−	32.0652i	−0.650877	−	1.12735i	0.332034	−	0.943268i	$-0.392265\pi$
$810$		0			0
$811$	−5.37416			−0.188712			−0.0943561	−	0.995539i	$-0.530079\pi$
$811$	−5.37416			−0.188712			−0.0943561	+	0.995539i	$0.530079\pi$
$812$		0			0
$813$	1.75912	+	1.60627i	0.0616950	+	0.0563345i
$814$		0			0
$815$	6.81216	−	11.7990i	0.238620	−	0.413301i
$816$		0			0
$817$	−11.6348	−	20.1521i	−0.407050	−	0.705032i
$818$		0			0
$819$	29.9031	+	8.61831i	1.04490	+	0.301148i
$820$		0			0
$821$	−1.11119	−	1.92464i	−0.0387809	−	0.0671706i	0.845983	−	0.533209i	$-0.179014\pi$
$821$	−1.11119	−	1.92464i	−0.0387809	−	0.0671706i	−0.884764	+	0.466039i	$0.845681\pi$
$822$		0			0
$823$	18.5537	−	32.1359i	0.646740	−	1.12019i	−0.337157	−	0.941449i	$-0.609465\pi$
$823$	18.5537	−	32.1359i	0.646740	−	1.12019i	0.983897	−	0.178738i	$-0.0572015\pi$
$824$		0			0
$825$	−1.00339	+	4.56382i	−0.0349335	+	0.158892i
$826$		0			0
$827$	−19.4790			−0.677351			−0.338676	−	0.940903i	$-0.609979\pi$
$827$	−19.4790			−0.677351			−0.338676	+	0.940903i	$0.609979\pi$
$828$		0			0
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	0.868397	−	0.495870i	$-0.165151\pi$
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	−0.863634	+	0.504119i	$0.831817\pi$
$830$		0			0
$831$	10.8459	−	49.3314i	0.376238	−	1.71129i
$832$		0			0
$833$	−4.95163	+	22.2319i	−0.171564	+	0.770290i
$834$		0			0
$835$	3.49657	+	6.05623i	0.121004	+	0.209585i
$836$		0			0
$837$	1.16465	+	2.77044i	0.0402562	+	0.0957603i
$838$		0			0
$839$	−21.0711	+	36.4962i	−0.727455	+	1.25999i	0.230501	+	0.973072i	$0.425964\pi$
$839$	−21.0711	+	36.4962i	−0.727455	+	1.25999i	−0.957956	+	0.286917i	$0.907370\pi$
$840$		0			0
$841$	−5.96666	−	10.3346i	−0.205747	−	0.356364i
$842$		0			0
$843$	16.1059	+	14.7065i	0.554716	+	0.506518i
$844$		0			0
$845$	−1.99671	+	3.45840i	−0.0686888	+	0.118973i
$846$		0			0
$847$	9.07328	−	23.2980i	0.311762	−	0.800528i
$848$		0			0
$849$	−12.1005	−	11.0492i	−0.415289	−	0.379206i
$850$		0			0
$851$	1.08351	−	1.87669i	0.0371422	−	0.0643322i
$852$		0			0
$853$	22.3086	−	38.6397i	0.763833	−	1.32300i	−0.177029	−	0.984206i	$-0.556649\pi$
$853$	22.3086	−	38.6397i	0.763833	−	1.32300i	0.940862	−	0.338791i	$-0.110018\pi$
$854$		0			0
$855$	19.4911	−	13.7499i	0.666582	−	0.470235i
$856$		0			0
$857$	−7.33227			−0.250466			−0.125233	−	0.992127i	$-0.539968\pi$
$857$	−7.33227			−0.250466			−0.125233	+	0.992127i	$0.539968\pi$
$858$		0			0
$859$	2.70146			0.0921725			0.0460863	−	0.998937i	$-0.485325\pi$
$859$	2.70146			0.0921725			0.0460863	+	0.998937i	$0.485325\pi$
$860$		0			0
$861$	2.47045	−	38.4341i	0.0841928	−	1.30983i
$862$		0			0
$863$	−7.40188	+	12.8204i	−0.251963	+	0.436413i	−0.964066	−	0.265662i	$-0.914409\pi$
$863$	−7.40188	+	12.8204i	−0.251963	+	0.436413i	0.712103	+	0.702075i	$0.247743\pi$
$864$		0			0
$865$	−11.6429	−	20.1661i	−0.395870	−	0.685668i
$866$		0			0
$867$	8.20219	+	7.48953i	0.278561	+	0.254358i
$868$		0			0
$869$	3.44449	+	5.96603i	0.116846	+	0.202384i
$870$		0			0
$871$	−36.9319			−1.25139
$872$		0			0
$873$	28.7328	−	20.2694i	0.972458	−	0.686014i
$874$		0			0
$875$	11.5822	−	29.7404i	0.391551	−	1.00541i
$876$		0			0
$877$	−11.0961			−0.374690			−0.187345	−	0.982294i	$-0.559988\pi$
$877$	−11.0961			−0.374690			−0.187345	+	0.982294i	$0.559988\pi$
$878$		0			0
$879$	27.4961	−	8.72249i	0.927421	−	0.294202i
$880$		0			0
$881$	15.0536			0.507168			0.253584	−	0.967313i	$-0.418391\pi$
$881$	15.0536			0.507168			0.253584	+	0.967313i	$0.418391\pi$
$882$		0			0
$883$	−2.39418			−0.0805704			−0.0402852	−	0.999188i	$-0.512827\pi$
$883$	−2.39418			−0.0805704			−0.0402852	+	0.999188i	$0.512827\pi$
$884$		0			0
$885$	13.0258	+	11.8941i	0.437859	+	0.399815i
$886$		0			0
$887$	4.93394			0.165666			0.0828328	−	0.996563i	$-0.473603\pi$
$887$	4.93394			0.165666			0.0828328	+	0.996563i	$0.473603\pi$
$888$		0			0
$889$	10.1682	−	26.1095i	0.341031	−	0.875685i
$890$		0			0
$891$	−7.26230	−	8.53270i	−0.243296	−	0.285856i
$892$		0			0
$893$	2.00853			0.0672130
$894$		0			0
$895$	7.93047	+	13.7360i	0.265086	+	0.459143i
$896$		0			0
$897$	−2.57717	+	0.817547i	−0.0860493	+	0.0272971i
$898$		0			0
$899$	−1.85017	−	3.20459i	−0.0617067	−	0.106879i
$900$		0			0
$901$	−1.51730	+	2.62804i	−0.0505486	+	0.0875527i
$902$		0			0
$903$	20.2331	−	10.0096i	0.673316	−	0.333099i
$904$		0			0
$905$	2.22400			0.0739284
$906$		0			0
$907$	3.39631			0.112773			0.0563863	−	0.998409i	$-0.482042\pi$
$907$	3.39631			0.112773			0.0563863	+	0.998409i	$0.482042\pi$
$908$		0			0
$909$	−14.7226	−	6.80253i	−0.488316	−	0.225626i
$910$		0			0
$911$	−4.65142	+	8.05649i	−0.154108	+	0.266924i	−0.932734	−	0.360565i	$-0.882584\pi$
$911$	−4.65142	+	8.05649i	−0.154108	+	0.266924i	0.778626	+	0.627489i	$0.215917\pi$
$912$		0			0
$913$	−10.0055	+	17.3301i	−0.331134	+	0.573541i
$914$		0			0
$915$	28.3697	−	8.99960i	0.937872	−	0.297518i
$916$		0			0
$917$	−21.4722	+	55.1355i	−0.709076	+	1.82073i
$918$		0			0
$919$	−8.92656	+	15.4613i	−0.294460	+	0.510020i	−0.974859	−	0.222822i	$-0.928473\pi$
$919$	−8.92656	+	15.4613i	−0.294460	+	0.510020i	0.680399	+	0.732842i	$0.261806\pi$
$920$		0			0
$921$	−3.55544	+	16.1716i	−0.117156	+	0.532872i
$922$		0			0
$923$	−16.5970	−	28.7469i	−0.546298	−	0.946216i
$924$		0			0
$925$	−5.89737	+	10.2145i	−0.193904	+	0.335852i
$926$		0			0
$927$	39.8164	+	18.3971i	1.30774	+	0.604240i
$928$		0			0
$929$	23.6430	+	40.9510i	0.775703	+	1.34356i	0.934398	+	0.356230i	$0.115938\pi$
$929$	23.6430	+	40.9510i	0.775703	+	1.34356i	−0.158695	+	0.987328i	$0.550729\pi$
$930$		0			0
$931$	31.5463	−	9.91242i	1.03389	−	0.324866i
$932$		0			0
$933$	33.7288	+	30.7982i	1.10423	+	1.00829i
$934$		0			0
$935$	3.40917	+	5.90486i	0.111492	+	0.193110i
$936$		0			0
$937$	21.2493			0.694183			0.347092	−	0.937831i	$-0.387169\pi$
$937$	21.2493			0.694183			0.347092	+	0.937831i	$0.387169\pi$
$938$		0			0
$939$	−20.9703	+	6.65234i	−0.684341	+	0.217091i
$940$		0			0
$941$	30.0405	−	52.0316i	0.979292	−	1.69618i	0.314315	−	0.949319i	$-0.398225\pi$
$941$	30.0405	−	52.0316i	0.979292	−	1.69618i	0.664977	−	0.746864i	$-0.268441\pi$
$942$		0			0
$943$	1.67303	+	2.89777i	0.0544813	+	0.0943644i
$944$		0			0
$945$	12.0983	+	19.7249i	0.393558	+	0.641650i
$946$		0			0
$947$	1.83468	+	3.17775i	0.0596189	+	0.103263i	0.894294	−	0.447479i	$-0.147678\pi$
$947$	1.83468	+	3.17775i	0.0596189	+	0.103263i	−0.834675	+	0.550742i	$0.814345\pi$
$948$		0			0
$949$	−26.7531	+	46.3377i	−0.868442	+	1.50419i
$950$		0			0
$951$	0.0547357	−	0.0173636i	0.00177493	−	0.000563053i
$952$		0			0
$953$	0.837421			0.0271267			0.0135634	−	0.999908i	$-0.495683\pi$
$953$	0.837421			0.0271267			0.0135634	+	0.999908i	$0.495683\pi$
$954$		0			0
$955$	13.7055	+	23.7385i	0.443498	+	0.768161i
$956$		0			0
$957$	10.1880	+	9.30279i	0.329331	+	0.300716i
$958$		0			0
$959$	−17.2382	+	44.2636i	−0.556651	+	1.42935i
$960$		0			0
$961$	15.3327	+	26.5571i	0.494605	+	0.856680i
$962$		0			0
$963$	−16.6798	+	11.7667i	−0.537500	+	0.379176i
$964$		0			0
$965$	−2.15574	+	3.73386i	−0.0693958	+	0.120197i
$966$		0			0
$967$	−21.8856	−	37.9070i	−0.703795	−	1.21901i	−0.967125	−	0.254302i	$-0.918154\pi$
$967$	−21.8856	−	37.9070i	−0.703795	−	1.21901i	0.263330	−	0.964706i	$-0.415179\pi$
$968$		0			0
$969$	−5.71661	+	26.0015i	−0.183644	+	0.835288i
$970$		0			0
$971$	20.3059	−	35.1709i	0.651648	−	1.12869i	−0.331075	−	0.943605i	$-0.607411\pi$
$971$	20.3059	−	35.1709i	0.651648	−	1.12869i	0.982723	−	0.185083i	$-0.0592554\pi$
$972$		0			0
$973$	2.98560	−	0.458025i	0.0957138	−	0.0146836i
$974$		0			0
$975$	14.0271	−	4.44977i	0.449228	−	0.142507i
$976$		0			0
$977$	−28.7479	+	49.7929i	−0.919728	+	1.59302i	−0.119901	+	0.992786i	$0.538258\pi$
$977$	−28.7479	+	49.7929i	−0.919728	+	1.59302i	−0.799827	+	0.600230i	$0.795076\pi$
$978$		0			0
$979$	7.51689	−	13.0196i	0.240241	−	0.416109i
$980$		0			0
$981$	−4.55571	−	50.0513i	−0.145452	−	1.59801i
$982$		0			0
$983$	13.4594			0.429289			0.214644	−	0.976692i	$-0.431141\pi$
$983$	13.4594			0.429289			0.214644	+	0.976692i	$0.431141\pi$
$984$		0			0
$985$	36.5103			1.16331
$986$		0			0
$987$	−0.124985	+	1.94445i	−0.00397830	+	0.0618926i
$988$		0			0
$989$	−0.980604	+	1.69846i	−0.0311814	+	0.0540078i
$990$		0			0
$991$	17.7821	+	30.7995i	0.564867	+	0.978379i	0.997062	+	0.0765983i	$0.0244059\pi$
$991$	17.7821	+	30.7995i	0.564867	+	0.978379i	−0.432195	+	0.901780i	$0.642261\pi$
$992$		0			0
$993$	8.01362	−	2.54213i	0.254304	−	0.0806720i
$994$		0			0
$995$	9.42036	+	16.3165i	0.298645	+	0.517269i
$996$		0			0
$997$	32.7289			1.03653			0.518267	−	0.855219i	$-0.326577\pi$
$997$	32.7289			1.03653			0.518267	+	0.855219i	$0.326577\pi$
$998$		0			0
$999$	−10.9603	−	26.0721i	−0.346770	−	0.824885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.k.961.6		22
3.2	odd	2		3024.2.t.l.289.4		22
4.3	odd	2		504.2.t.d.457.6	yes	22
7.4	even	3		1008.2.q.k.529.11		22
9.4	even	3		1008.2.q.k.625.11		22
9.5	odd	6		3024.2.q.k.2305.8		22
12.11	even	2		1512.2.t.d.289.4		22
21.11	odd	6		3024.2.q.k.2881.8		22
28.11	odd	6		504.2.q.d.25.1	✓	22
36.23	even	6		1512.2.q.c.793.8		22
36.31	odd	6		504.2.q.d.121.1	yes	22
63.4	even	3	inner	1008.2.t.k.193.6		22
63.32	odd	6		3024.2.t.l.1873.4		22
84.11	even	6		1512.2.q.c.1369.8		22
252.67	odd	6		504.2.t.d.193.6	yes	22
252.95	even	6		1512.2.t.d.361.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.1	✓	22	28.11	odd	6
504.2.q.d.121.1	yes	22	36.31	odd	6
504.2.t.d.193.6	yes	22	252.67	odd	6
504.2.t.d.457.6	yes	22	4.3	odd	2
1008.2.q.k.529.11		22	7.4	even	3
1008.2.q.k.625.11		22	9.4	even	3
1008.2.t.k.193.6		22	63.4	even	3	inner
1008.2.t.k.961.6		22	1.1	even	1	trivial
1512.2.q.c.793.8		22	36.23	even	6
1512.2.q.c.1369.8		22	84.11	even	6
1512.2.t.d.289.4		22	12.11	even	2
1512.2.t.d.361.4		22	252.95	even	6
3024.2.q.k.2305.8		22	9.5	odd	6
3024.2.q.k.2881.8		22	21.11	odd	6
3024.2.t.l.289.4		22	3.2	odd	2
3024.2.t.l.1873.4		22	63.32	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.371921 + 1.69165i) q^{3} +1.68316 q^{5} +(-0.960133 + 2.46539i) q^{7} +(-2.72335 - 1.25832i) q^{9} +O(q^{10})\)	\(q+(-0.371921 + 1.69165i) q^{3} +1.68316 q^{5} +(-0.960133 + 2.46539i) q^{7} +(-2.72335 - 1.25832i) q^{9} -1.24498 q^{11} +(1.96039 + 3.39550i) q^{13} +(-0.626001 + 2.84731i) q^{15} +(-1.62691 - 2.81788i) q^{17} +(-2.36192 + 4.09097i) q^{19} +(-3.81348 - 2.54114i) q^{21} +0.398135 q^{23} -2.16699 q^{25} +(3.14150 - 4.13895i) q^{27} +(-3.19896 + 5.54076i) q^{29} +(-0.289184 + 0.500881i) q^{31} +(0.463034 - 2.10607i) q^{33} +(-1.61605 + 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-6.47311 + 2.05344i) q^{39} +(4.20216 + 7.27836i) q^{41} +(-2.46299 + 4.26603i) q^{43} +(-4.58382 - 2.11795i) q^{45} +(-0.212595 - 0.368225i) q^{47} +(-5.15629 - 4.73420i) q^{49} +(5.37195 - 1.70412i) q^{51} +(-0.466315 - 0.807681i) q^{53} -2.09550 q^{55} +(-6.04204 - 5.51707i) q^{57} +(3.02527 - 5.23992i) q^{59} +(-5.10459 - 8.84140i) q^{61} +(5.71702 - 5.50596i) q^{63} +(3.29965 + 5.71516i) q^{65} +(-4.70976 + 8.15754i) q^{67} +(-0.148075 + 0.673505i) q^{69} -8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(0.805948 - 3.66578i) q^{75} +(1.19535 - 3.06936i) q^{77} +(-2.76670 - 4.79207i) q^{79} +(5.83327 + 6.85369i) q^{81} +(8.03669 - 13.9199i) q^{83} +(-2.73833 - 4.74293i) q^{85} +(-8.18325 - 7.47224i) q^{87} +(-6.03776 + 10.4577i) q^{89} +(-10.2535 + 1.57300i) q^{91} +(-0.739760 - 0.675485i) q^{93} +(-3.97549 + 6.88575i) q^{95} +(-5.86046 + 10.1506i) q^{97} +(3.39052 + 1.56658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9	\( 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9} - 6 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 15 q^{21} + 4 q^{23} + 20 q^{25} + 4 q^{27} + 9 q^{29} + 4 q^{31} - 31 q^{33} - 14 q^{35} + 2 q^{37} - 8 q^{39} + 16 q^{41} + 22 q^{45} - 5 q^{47} - 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} + 19 q^{59} - 13 q^{61} - 21 q^{63} + 13 q^{65} - 26 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 8 q^{75} - 4 q^{77} - 10 q^{79} - 8 q^{81} + 28 q^{83} - 20 q^{85} - 9 q^{87} + 6 q^{89} + 37 q^{91} - 32 q^{93} - 12 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9 - 6 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 15 * q^21 + 4 * q^23 + 20 * q^25 + 4 * q^27 + 9 * q^29 + 4 * q^31 - 31 * q^33 - 14 * q^35 + 2 * q^37 - 8 * q^39 + 16 * q^41 + 22 * q^45 - 5 * q^47 - 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 + 19 * q^59 - 13 * q^61 - 21 * q^63 + 13 * q^65 - 26 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 8 * q^75 - 4 * q^77 - 10 * q^79 - 8 * q^81 + 28 * q^83 - 20 * q^85 - 9 * q^87 + 6 * q^89 + 37 * q^91 - 32 * q^93 - 12 * q^95 - 29 * q^97 + 56 * q^99

Introduction

L-functions

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