LMFDB - Embedded newform 1008.2.q.l.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (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			625.1
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.l.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71918 + 0.210723i) q^{3} +(0.0309846 + 0.0536670i) q^{5} +(0.981674 + 2.45689i) q^{7} +(2.91119 - 0.724543i) q^{9} +O(q^{10})$	\(q+(-1.71918 + 0.210723i) q^{3} +(0.0309846 + 0.0536670i) q^{5} +(0.981674 + 2.45689i) q^{7} +(2.91119 - 0.724543i) q^{9} +(-1.59027 + 2.75442i) q^{11} +(-0.252417 + 0.437198i) q^{13} +(-0.0645772 - 0.0857342i) q^{15} +(-0.554700 - 0.960769i) q^{17} +(-0.933573 + 1.61700i) q^{19} +(-2.20540 - 4.01699i) q^{21} +(-3.10248 - 5.37365i) q^{23} +(2.49808 - 4.32680i) q^{25} +(-4.85220 + 1.85908i) q^{27} +(2.39645 + 4.15077i) q^{29} +2.53716 q^{31} +(2.15354 - 5.07047i) q^{33} +(-0.101437 + 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(0.341823 - 0.804815i) q^{39} +(-4.94516 + 8.56527i) q^{41} +(3.95574 + 6.85154i) q^{43} +(0.129086 + 0.133785i) q^{45} -6.58336 q^{47} +(-5.07263 + 4.82373i) q^{49} +(1.15609 + 1.53485i) q^{51} +(-1.58258 - 2.74112i) q^{53} -0.197095 q^{55} +(1.26425 - 2.97664i) q^{57} -9.01304 q^{59} -13.8819 q^{61} +(4.63796 + 6.44122i) q^{63} -0.0312842 q^{65} -3.33283 q^{67} +(6.46609 + 8.58454i) q^{69} -2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(-3.38291 + 7.96497i) q^{75} +(-8.32844 - 1.20317i) q^{77} +2.97850 q^{79} +(7.95008 - 4.21856i) q^{81} +(-2.17289 - 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(-4.99460 - 6.63096i) q^{87} +(-4.30077 + 7.44915i) q^{89} +(-1.32194 - 0.190974i) q^{91} +(-4.36184 + 0.534636i) q^{93} -0.115706 q^{95} +(-3.27671 - 5.67542i) q^{97} +(-2.63388 + 9.17087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9	$ 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9} - 3 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} - 22 q^{25} + 2 q^{27} - 7 q^{29} + 12 q^{31} - 3 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 3 q^{45} + 34 q^{47} - 25 q^{49} - 53 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} - 42 q^{59} - 62 q^{61} + 22 q^{63} + 6 q^{65} - 52 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} - 53 q^{75} - q^{77} - 32 q^{79} - 6 q^{81} + 36 q^{83} + 28 q^{85} + 5 q^{87} - 2 q^{89} - 15 q^{91} - 11 q^{93} - 48 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9 - 3 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 - 22 * q^25 + 2 * q^27 - 7 * q^29 + 12 * q^31 - 3 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 3 * q^45 + 34 * q^47 - 25 * q^49 - 53 * q^51 + q^53 - 2 * q^55 - 21 * q^57 - 42 * q^59 - 62 * q^61 + 22 * q^63 + 6 * q^65 - 52 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 - 53 * q^75 - q^77 - 32 * q^79 - 6 * q^81 + 36 * q^83 + 28 * q^85 + 5 * q^87 - 2 * q^89 - 15 * q^91 - 11 * q^93 - 48 * q^95 + 19 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.71918	+	0.210723i	−0.992572	+	0.121661i
$3$	−1.71918	+	0.210723i	−0.992572	+	0.121661i
$4$		0			0
$5$	0.0309846	+	0.0536670i	0.0138567	+	0.0240006i	0.872871	−	0.487952i	$-0.162256\pi$
$5$	0.0309846	+	0.0536670i	0.0138567	+	0.0240006i	−0.859014	+	0.511952i	$0.828922\pi$
$6$		0			0
$7$	0.981674	+	2.45689i	0.371038	+	0.928618i
$7$	0.981674	+	2.45689i	0.371038	+	0.928618i
$8$		0			0
$9$	2.91119	−	0.724543i	0.970397	−	0.241514i
$10$		0			0
$11$	−1.59027	+	2.75442i	−0.479483	+	0.830490i	−0.999723	−	0.0235306i	$-0.992509\pi$
$11$	−1.59027	+	2.75442i	−0.479483	+	0.830490i	0.520240	+	0.854020i	$0.325843\pi$
$12$		0			0
$13$	−0.252417	+	0.437198i	−0.0700078	+	0.121257i	−0.898904	−	0.438145i	$-0.855636\pi$
$13$	−0.252417	+	0.437198i	−0.0700078	+	0.121257i	0.828897	+	0.559402i	$0.188969\pi$
$14$		0			0
$15$	−0.0645772	−	0.0857342i	−0.0166737	−	0.0221365i
$16$		0			0
$17$	−0.554700	−	0.960769i	−0.134535	−	0.233021i	0.790885	−	0.611965i	$-0.209621\pi$
$17$	−0.554700	−	0.960769i	−0.134535	−	0.233021i	−0.925420	+	0.378944i	$0.876287\pi$
$18$		0			0
$19$	−0.933573	+	1.61700i	−0.214176	+	0.370964i	−0.953017	−	0.302915i	$-0.902040\pi$
$19$	−0.933573	+	1.61700i	−0.214176	+	0.370964i	0.738841	+	0.673880i	$0.235373\pi$
$20$		0			0
$21$	−2.20540	−	4.01699i	−0.481258	−	0.876579i
$22$		0			0
$23$	−3.10248	−	5.37365i	−0.646912	−	1.12048i	−0.983856	−	0.178960i	$-0.942727\pi$
$23$	−3.10248	−	5.37365i	−0.646912	−	1.12048i	0.336945	−	0.941525i	$-0.390607\pi$
$24$		0			0
$25$	2.49808	−	4.32680i	0.499616	−	0.865360i
$26$		0			0
$27$	−4.85220	+	1.85908i	−0.933806	+	0.357779i
$28$		0			0
$29$	2.39645	+	4.15077i	0.445010	+	0.770779i	0.998053	−	0.0623731i	$-0.0198669\pi$
$29$	2.39645	+	4.15077i	0.445010	+	0.770779i	−0.553043	+	0.833153i	$0.686534\pi$
$30$		0			0
$31$	2.53716			0.455687			0.227843	−	0.973698i	$-0.426833\pi$
$31$	2.53716			0.455687			0.227843	+	0.973698i	$0.426833\pi$
$32$		0			0
$33$	2.15354	−	5.07047i	0.374884	−	0.882655i
$34$		0			0
$35$	−0.101437	+	0.128809i	−0.0171460	+	0.0217728i
$36$		0			0
$37$	−4.26085	+	7.38001i	−0.700479	+	1.21327i	0.267819	+	0.963469i	$0.413697\pi$
$37$	−4.26085	+	7.38001i	−0.700479	+	1.21327i	−0.968298	+	0.249797i	$0.919636\pi$
$38$		0			0
$39$	0.341823	−	0.804815i	0.0547355	−	0.128874i
$40$		0			0
$41$	−4.94516	+	8.56527i	−0.772305	+	1.33767i	0.163992	+	0.986462i	$0.447563\pi$
$41$	−4.94516	+	8.56527i	−0.772305	+	1.33767i	−0.936297	+	0.351210i	$0.885770\pi$
$42$		0			0
$43$	3.95574	+	6.85154i	0.603244	+	1.04485i	0.992326	+	0.123646i	$0.0394589\pi$
$43$	3.95574	+	6.85154i	0.603244	+	1.04485i	−0.389082	+	0.921203i	$0.627208\pi$
$44$		0			0
$45$	0.129086	+	0.133785i	0.0192430	+	0.0199435i
$46$		0			0
$47$	−6.58336			−0.960282			−0.480141	−	0.877191i	$-0.659414\pi$
$47$	−6.58336			−0.960282			−0.480141	+	0.877191i	$0.659414\pi$
$48$		0			0
$49$	−5.07263	+	4.82373i	−0.724662	+	0.689105i
$50$		0			0
$51$	1.15609	+	1.53485i	0.161885	+	0.214922i
$52$		0			0
$53$	−1.58258	−	2.74112i	−0.217385	−	0.376521i	0.736623	−	0.676304i	$-0.236419\pi$
$53$	−1.58258	−	2.74112i	−0.217385	−	0.376521i	−0.954008	+	0.299782i	$0.903086\pi$
$54$		0			0
$55$	−0.197095			−0.0265763
$56$		0			0
$57$	1.26425	−	2.97664i	0.167454	−	0.394266i
$58$		0			0
$59$	−9.01304			−1.17340			−0.586699	−	0.809805i	$-0.699573\pi$
$59$	−9.01304			−1.17340			−0.586699	+	0.809805i	$0.699573\pi$
$60$		0			0
$61$	−13.8819			−1.77739			−0.888697	−	0.458496i	$-0.848388\pi$
$61$	−13.8819			−1.77739			−0.888697	+	0.458496i	$0.848388\pi$
$62$		0			0
$63$	4.63796	+	6.44122i	0.584329	+	0.811517i
$64$		0			0
$65$	−0.0312842			−0.00388032
$66$		0			0
$67$	−3.33283			−0.407170			−0.203585	−	0.979057i	$-0.565259\pi$
$67$	−3.33283			−0.407170			−0.203585	+	0.979057i	$0.565259\pi$
$68$		0			0
$69$	6.46609	+	8.58454i	0.778425	+	1.03346i
$70$		0			0
$71$	−2.25651			−0.267798			−0.133899	−	0.990995i	$-0.542750\pi$
$71$	−2.25651			−0.267798			−0.133899	+	0.990995i	$0.542750\pi$
$72$		0			0
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	0.961529	−	0.274704i	$-0.0885799\pi$
$73$	2.07503	+	3.59406i	0.242864	+	0.420652i	−0.718665	+	0.695356i	$0.755247\pi$
$74$		0			0
$75$	−3.38291	+	7.96497i	−0.390624	+	0.919716i
$76$		0			0
$77$	−8.32844	−	1.20317i	−0.949114	−	0.137114i
$78$		0			0
$79$	2.97850			0.335107			0.167554	−	0.985863i	$-0.446413\pi$
$79$	2.97850			0.335107			0.167554	+	0.985863i	$0.446413\pi$
$80$		0			0
$81$	7.95008	−	4.21856i	0.883342	−	0.468729i
$82$		0			0
$83$	−2.17289	−	3.76355i	−0.238506	−	0.413104i	0.721780	−	0.692122i	$-0.243324\pi$
$83$	−2.17289	−	3.76355i	−0.238506	−	0.413104i	−0.960286	+	0.279019i	$0.909991\pi$
$84$		0			0
$85$	0.0343744	−	0.0595381i	0.00372842	−	0.00645782i
$86$		0			0
$87$	−4.99460	−	6.63096i	−0.535478	−	0.710914i
$88$		0			0
$89$	−4.30077	+	7.44915i	−0.455880	+	0.789608i	−0.998738	−	0.0502166i	$-0.984009\pi$
$89$	−4.30077	+	7.44915i	−0.455880	+	0.789608i	0.542858	+	0.839824i	$0.317342\pi$
$90$		0			0
$91$	−1.32194	−	0.190974i	−0.138577	−	0.0200195i
$92$		0			0
$93$	−4.36184	+	0.534636i	−0.452302	+	0.0554392i
$94$		0			0
$95$	−0.115706			−0.0118712
$96$		0			0
$97$	−3.27671	−	5.67542i	−0.332699	−	0.576252i	0.650341	−	0.759642i	$-0.274626\pi$
$97$	−3.27671	−	5.67542i	−0.332699	−	0.576252i	−0.983040	+	0.183391i	$0.941293\pi$
$98$		0			0
$99$	−2.63388	+	9.17087i	−0.264714	+	0.921707i
$100$		0			0
$101$	−3.25827	+	5.64349i	−0.324210	+	0.561548i	−0.981352	−	0.192219i	$-0.938432\pi$
$101$	−3.25827	+	5.64349i	−0.324210	+	0.561548i	0.657142	+	0.753767i	$0.271765\pi$
$102$		0			0
$103$	8.50978	+	14.7394i	0.838494	+	1.45231i	0.891154	+	0.453701i	$0.149897\pi$
$103$	8.50978	+	14.7394i	0.838494	+	1.45231i	−0.0526599	+	0.998613i	$0.516770\pi$
$104$		0			0
$105$	0.147246	−	0.242822i	0.0143697	−	0.0236970i
$106$		0			0
$107$	8.86075	−	15.3473i	0.856601	−	1.48368i	−0.0185508	−	0.999828i	$-0.505905\pi$
$107$	8.86075	−	15.3473i	0.856601	−	1.48368i	0.875152	−	0.483848i	$-0.160761\pi$
$108$		0			0
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	0.986522	+	0.163631i	$0.0523208\pi$
$109$	6.62928	+	11.4822i	0.634970	+	1.09980i	−0.351552	+	0.936168i	$0.614346\pi$
$110$		0			0
$111$	5.77005	−	13.5855i	0.547669	−	1.28947i
$112$		0			0
$113$	1.10094	−	1.90689i	0.103568	−	0.179385i	−0.809584	−	0.587004i	$-0.800307\pi$
$113$	1.10094	−	1.90689i	0.103568	−	0.179385i	0.913152	+	0.407619i	$0.133641\pi$
$114$		0			0
$115$	0.192258	−	0.333001i	0.0179282	−	0.0310525i
$116$		0			0
$117$	−0.418064	+	1.45566i	−0.0386501	+	0.134575i
$118$		0			0
$119$	1.81597	−	2.30600i	0.166470	−	0.211391i
$120$		0			0
$121$	0.442104	+	0.765746i	0.0401912	+	0.0696133i
$122$		0			0
$123$	6.69675	−	15.7673i	0.603826	−	1.42169i
$124$		0			0
$125$	0.619455			0.0554057
$126$		0			0
$127$	4.61290			0.409329			0.204664	−	0.978832i	$-0.434390\pi$
$127$	4.61290			0.409329			0.204664	+	0.978832i	$0.434390\pi$
$128$		0			0
$129$	−8.24442	−	10.9455i	−0.725880	−	0.963697i
$130$		0			0
$131$	−0.0760695	−	0.131756i	−0.00664623	−	0.0115116i	0.862683	−	0.505745i	$-0.168782\pi$
$131$	−0.0760695	−	0.131756i	−0.00664623	−	0.0115116i	−0.869329	+	0.494233i	$0.835449\pi$
$132$		0			0
$133$	−4.88925	−	0.706325i	−0.423952	−	0.0612461i
$134$		0			0
$135$	−0.250115	−	0.202800i	−0.0215264	−	0.0174542i
$136$		0			0
$137$	1.77770	−	3.07907i	0.151879	−	0.263063i	−0.780039	−	0.625731i	$-0.784801\pi$
$137$	1.77770	−	3.07907i	0.151879	−	0.263063i	0.931918	+	0.362668i	$0.118134\pi$
$138$		0			0
$139$	7.60945	−	13.1800i	0.645425	−	1.11791i	−0.338778	−	0.940866i	$-0.610013\pi$
$139$	7.60945	−	13.1800i	0.645425	−	1.11791i	0.984203	−	0.177043i	$-0.0566532\pi$
$140$		0			0
$141$	11.3180	−	1.38726i	0.953148	−	0.116829i
$142$		0			0
$143$	−0.802820	−	1.39052i	−0.0671352	−	0.116281i
$144$		0			0
$145$	−0.148506	+	0.257220i	−0.0123328	+	0.0213610i
$146$		0			0
$147$	7.70432	−	9.36181i	0.635442	−	0.772149i
$148$		0			0
$149$	−0.183457	−	0.317757i	−0.0150294	−	0.0260317i	0.858413	−	0.512959i	$-0.171451\pi$
$149$	−0.183457	−	0.317757i	−0.0150294	−	0.0260317i	−0.873442	+	0.486928i	$0.838118\pi$
$150$		0			0
$151$	−6.29162	+	10.8974i	−0.512005	+	0.886818i	0.487899	+	0.872900i	$0.337764\pi$
$151$	−6.29162	+	10.8974i	−0.512005	+	0.886818i	−0.999903	+	0.0139176i	$0.995570\pi$
$152$		0			0
$153$	−2.31096	−	2.39508i	−0.186830	−	0.193631i
$154$		0			0
$155$	0.0786128	+	0.136161i	0.00631434	+	0.0109368i
$156$		0			0
$157$	−5.45468			−0.435331			−0.217666	−	0.976023i	$-0.569844\pi$
$157$	−5.45468			−0.435331			−0.217666	+	0.976023i	$0.569844\pi$
$158$		0			0
$159$	3.29837	+	4.37900i	0.261578	+	0.347277i
$160$		0			0
$161$	10.1569	−	12.8976i	0.800473	−	1.01648i
$162$		0			0
$163$	−3.83559	+	6.64343i	−0.300426	+	0.520354i	−0.976233	−	0.216726i	$-0.930462\pi$
$163$	−3.83559	+	6.64343i	−0.300426	+	0.520354i	0.675806	+	0.737079i	$0.263796\pi$
$164$		0			0
$165$	0.338843	−	0.0415325i	0.0263789	−	0.00323330i
$166$		0			0
$167$	9.47493	−	16.4111i	0.733192	−	1.26993i	−0.222320	−	0.974974i	$-0.571363\pi$
$167$	9.47493	−	16.4111i	0.733192	−	1.26993i	0.955512	−	0.294952i	$-0.0953037\pi$
$168$		0			0
$169$	6.37257	+	11.0376i	0.490198	+	0.849048i
$170$		0			0
$171$	−1.54623	+	5.38380i	−0.118243	+	0.411709i
$172$		0			0
$173$	−23.9919			−1.82407			−0.912034	−	0.410115i	$-0.865488\pi$
$173$	−23.9919			−1.82407			−0.912034	+	0.410115i	$0.865488\pi$
$174$		0			0
$175$	13.0828	+	1.89000i	0.988965	+	0.142871i
$176$		0			0
$177$	15.4951	−	1.89925i	1.16468	−	0.142757i
$178$		0			0
$179$	4.27901	+	7.41146i	0.319828	+	0.553959i	0.980452	−	0.196758i	$-0.0630415\pi$
$179$	4.27901	+	7.41146i	0.319828	+	0.553959i	−0.660624	+	0.750717i	$0.729708\pi$
$180$		0			0
$181$	0.632669			0.0470259			0.0235130	−	0.999724i	$-0.492515\pi$
$181$	0.632669			0.0470259			0.0235130	+	0.999724i	$0.492515\pi$
$182$		0			0
$183$	23.8655	−	2.92523i	1.76419	−	0.216239i
$184$		0			0
$185$	−0.528083			−0.0388255
$186$		0			0
$187$	3.52849			0.258028
$188$		0			0
$189$	−9.33083	−	10.0963i	−0.678718	−	0.734399i
$190$		0			0
$191$	−23.5831			−1.70641			−0.853205	−	0.521575i	$-0.825345\pi$
$191$	−23.5831			−1.70641			−0.853205	+	0.521575i	$0.825345\pi$
$192$		0			0
$193$	25.6059			1.84315			0.921577	−	0.388196i	$-0.126902\pi$
$193$	25.6059			1.84315			0.921577	+	0.388196i	$0.126902\pi$
$194$		0			0
$195$	0.0537832	−	0.00659228i	0.00385150	−	0.000472083i
$196$		0			0
$197$	9.45810			0.673862			0.336931	−	0.941529i	$-0.390611\pi$
$197$	9.45810			0.673862			0.336931	+	0.941529i	$0.390611\pi$
$198$		0			0
$199$	−4.15133	−	7.19032i	−0.294280	−	0.509708i	0.680537	−	0.732714i	$-0.261747\pi$
$199$	−4.15133	−	7.19032i	−0.294280	−	0.509708i	−0.974817	+	0.223005i	$0.928413\pi$
$200$		0			0
$201$	5.72975	−	0.702304i	0.404146	−	0.0495367i
$202$		0			0
$203$	−7.84547	+	9.96253i	−0.550644	+	0.699232i
$204$		0			0
$205$	−0.612896			−0.0428065
$206$		0			0
$207$	−12.9254	−	13.3959i	−0.898374	−	0.931076i
$208$		0			0
$209$	−2.96926	−	5.14291i	−0.205388	−	0.355742i
$210$		0			0
$211$	10.1164	−	17.5222i	0.696444	−	1.20628i	−0.273247	−	0.961944i	$-0.588098\pi$
$211$	10.1164	−	17.5222i	0.696444	−	1.20628i	0.969691	−	0.244333i	$-0.0785689\pi$
$212$		0			0
$213$	3.87935	−	0.475497i	0.265809	−	0.0325805i
$214$		0			0
$215$	−0.245134	+	0.424585i	−0.0167180	+	0.0289564i
$216$		0			0
$217$	2.49066	+	6.23352i	0.169077	+	0.423159i
$218$		0			0
$219$	−4.32471	−	5.74159i	−0.292237	−	0.387981i
$220$		0			0
$221$	0.560062			0.0376739
$222$		0			0
$223$	2.41918	+	4.19014i	0.162000	+	0.280593i	0.935586	−	0.353099i	$-0.114872\pi$
$223$	2.41918	+	4.19014i	0.162000	+	0.280593i	−0.773586	+	0.633692i	$0.781539\pi$
$224$		0			0
$225$	4.13744	−	14.4061i	0.275829	−	0.960408i
$226$		0			0
$227$	0.336106	−	0.582153i	0.0223082	−	0.0386389i	−0.854656	−	0.519195i	$-0.826232\pi$
$227$	0.336106	−	0.582153i	0.0223082	−	0.0386389i	0.876964	+	0.480556i	$0.159565\pi$
$228$		0			0
$229$	3.06776	+	5.31352i	0.202724	+	0.351128i	0.949405	−	0.314054i	$-0.101687\pi$
$229$	3.06776	+	5.31352i	0.202724	+	0.351128i	−0.746681	+	0.665182i	$0.768354\pi$
$230$		0			0
$231$	14.5717	+	0.313475i	0.958745	+	0.0206251i
$232$		0			0
$233$	12.1492	−	21.0431i	0.795922	−	1.37858i	−0.126330	−	0.991988i	$-0.540320\pi$
$233$	12.1492	−	21.0431i	0.795922	−	1.37858i	0.922252	−	0.386589i	$-0.126347\pi$
$234$		0			0
$235$	−0.203983	−	0.353309i	−0.0133064	−	0.0230473i
$236$		0			0
$237$	−5.12059	+	0.627637i	−0.332618	+	0.0407694i
$238$		0			0
$239$	−13.5978	+	23.5521i	−0.879569	+	1.52346i	−0.0277545	+	0.999615i	$0.508836\pi$
$239$	−13.5978	+	23.5521i	−0.879569	+	1.52346i	−0.851815	+	0.523843i	$0.824498\pi$
$240$		0			0
$241$	12.9027	−	22.3481i	0.831135	−	1.43957i	−0.0660031	−	0.997819i	$-0.521025\pi$
$241$	12.9027	−	22.3481i	0.831135	−	1.43957i	0.897139	−	0.441749i	$-0.145642\pi$
$242$		0			0
$243$	−12.7787	+	8.92775i	−0.819754	+	0.572716i
$244$		0			0
$245$	−0.416049	−	0.122771i	−0.0265804	−	0.00784356i
$246$		0			0
$247$	−0.471299	−	0.816313i	−0.0299880	−	0.0519408i
$248$		0			0
$249$	4.52866	+	6.01237i	0.286992	+	0.381018i
$250$		0			0
$251$	27.0741			1.70890			0.854450	−	0.519533i	$-0.173894\pi$
$251$	27.0741			1.70890			0.854450	+	0.519533i	$0.173894\pi$
$252$		0			0
$253$	19.7351			1.24073
$254$		0			0
$255$	−0.0465498	+	0.109601i	−0.00291506	+	0.00686345i
$256$		0			0
$257$	6.76073	+	11.7099i	0.421723	+	0.730445i	0.996108	−	0.0881399i	$-0.0280923\pi$
$257$	6.76073	+	11.7099i	0.421723	+	0.730445i	−0.574385	+	0.818585i	$0.694759\pi$
$258$		0			0
$259$	−22.3146	−	3.22368i	−1.38656	−	0.200310i
$260$		0			0
$261$	9.98394	+	10.3474i	0.617990	+	0.640486i
$262$		0			0
$263$	−6.68727	+	11.5827i	−0.412355	+	0.714220i	−0.995147	−	0.0984018i	$-0.968627\pi$
$263$	−6.68727	+	11.5827i	−0.412355	+	0.714220i	0.582792	+	0.812621i	$0.301960\pi$
$264$		0			0
$265$	0.0980716	−	0.169865i	0.00602449	−	0.0104347i
$266$		0			0
$267$	5.82411	−	13.7127i	0.356430	−	0.839205i
$268$		0			0
$269$	3.91594	+	6.78261i	0.238759	+	0.413543i	0.960359	−	0.278768i	$-0.0899260\pi$
$269$	3.91594	+	6.78261i	0.238759	+	0.413543i	−0.721599	+	0.692311i	$0.756593\pi$
$270$		0			0
$271$	−15.1737	+	26.2816i	−0.921735	+	1.59649i	−0.125005	+	0.992156i	$0.539895\pi$
$271$	−15.1737	+	26.2816i	−0.921735	+	1.59649i	−0.796730	+	0.604335i	$0.793439\pi$
$272$		0			0
$273$	2.31290	+	0.0497566i	0.139983	+	0.00301141i
$274$		0			0
$275$	7.94523	+	13.7615i	0.479115	+	0.829852i
$276$		0			0
$277$	11.3462	−	19.6522i	0.681728	−	1.18079i	−0.292725	−	0.956197i	$-0.594562\pi$
$277$	11.3462	−	19.6522i	0.681728	−	1.18079i	0.974453	−	0.224591i	$-0.0721046\pi$
$278$		0			0
$279$	7.38615	−	1.83828i	0.442197	−	0.110055i
$280$		0			0
$281$	−10.0826	−	17.4635i	−0.601475	−	1.04179i	−0.992598	−	0.121447i	$-0.961246\pi$
$281$	−10.0826	−	17.4635i	−0.601475	−	1.04179i	0.391122	−	0.920339i	$-0.372087\pi$
$282$		0			0
$283$	16.9059			1.00495			0.502477	−	0.864591i	$-0.332422\pi$
$283$	16.9059			1.00495			0.502477	+	0.864591i	$0.332422\pi$
$284$		0			0
$285$	0.198919	−	0.0243818i	0.0117830	−	0.00144425i
$286$		0			0
$287$	−25.8985	−	3.74142i	−1.52874	−	0.220849i
$288$		0			0
$289$	7.88462	−	13.6566i	0.463801	−	0.803327i
$290$		0			0
$291$	6.82920	+	9.06662i	0.400335	+	0.531495i
$292$		0			0
$293$	2.40597	−	4.16727i	0.140558	−	0.243454i	−0.787149	−	0.616763i	$-0.788444\pi$
$293$	2.40597	−	4.16727i	0.140558	−	0.243454i	0.927707	+	0.373309i	$0.121777\pi$
$294$		0			0
$295$	−0.279266	−	0.483703i	−0.0162595	−	0.0281623i
$296$		0			0
$297$	2.59561	−	16.3214i	0.150612	−	0.947066i
$298$		0			0
$299$	3.13247			0.181155
$300$		0			0
$301$	−12.9502	+	16.4448i	−0.746439	+	0.947862i
$302$		0			0
$303$	4.41235	−	10.3888i	0.253483	−	0.596820i
$304$		0			0
$305$	−0.430125	−	0.744999i	−0.0246289	−	0.0426585i
$306$		0			0
$307$	−15.9188			−0.908534			−0.454267	−	0.890866i	$-0.650099\pi$
$307$	−15.9188			−0.908534			−0.454267	+	0.890866i	$0.650099\pi$
$308$		0			0
$309$	−17.7358	−	23.5465i	−1.00896	−	1.33951i
$310$		0			0
$311$	0.262869			0.0149059			0.00745297	−	0.999972i	$-0.497628\pi$
$311$	0.262869			0.0149059			0.00745297	+	0.999972i	$0.497628\pi$
$312$		0			0
$313$	−6.25068			−0.353309			−0.176655	−	0.984273i	$-0.556528\pi$
$313$	−6.25068			−0.353309			−0.176655	+	0.984273i	$0.556528\pi$
$314$		0			0
$315$	−0.201975	+	0.448484i	−0.0113800	+	0.0252692i
$316$		0			0
$317$	−19.6792			−1.10530			−0.552648	−	0.833415i	$-0.686382\pi$
$317$	−19.6792			−1.10530			−0.552648	+	0.833415i	$0.686382\pi$
$318$		0			0
$319$	−15.2440			−0.853499
$320$		0			0
$321$	−11.9992	+	28.2519i	−0.669733	+	1.57687i
$322$		0			0
$323$	2.07141			0.115256
$324$		0			0
$325$	1.26111	+	2.18431i	0.0699540	+	0.121164i
$326$		0			0
$327$	−13.8165	−	18.3432i	−0.764056	−	1.01438i
$328$		0			0
$329$	−6.46271	−	16.1746i	−0.356301	−	0.891734i
$330$		0			0
$331$	−24.5338			−1.34850			−0.674249	−	0.738504i	$-0.735533\pi$
$331$	−24.5338			−1.34850			−0.674249	+	0.738504i	$0.735533\pi$
$332$		0			0
$333$	−7.05702	+	24.5718i	−0.386722	+	1.34653i
$334$		0			0
$335$	−0.103267	−	0.178863i	−0.00564206	−	0.00977233i
$336$		0			0
$337$	−6.89471	+	11.9420i	−0.375579	+	0.650521i	−0.990413	−	0.138135i	$-0.955889\pi$
$337$	−6.89471	+	11.9420i	−0.375579	+	0.650521i	0.614835	+	0.788656i	$0.289223\pi$
$338$		0			0
$339$	−1.49090	+	3.51029i	−0.0809746	+	0.190653i
$340$		0			0
$341$	−4.03475	+	6.98840i	−0.218494	+	0.378443i
$342$		0			0
$343$	−16.8311	−	7.72757i	−0.908792	−	0.417250i
$344$		0			0
$345$	−0.260357	+	0.613004i	−0.0140171	+	0.0330030i
$346$		0			0
$347$	19.6957			1.05732			0.528661	−	0.848833i	$-0.322694\pi$
$347$	19.6957			1.05732			0.528661	+	0.848833i	$0.322694\pi$
$348$		0			0
$349$	5.34712	+	9.26149i	0.286225	+	0.495756i	0.972905	−	0.231203i	$-0.0742662\pi$
$349$	5.34712	+	9.26149i	0.286225	+	0.495756i	−0.686681	+	0.726959i	$0.740933\pi$
$350$		0			0
$351$	0.411990	−	2.59064i	0.0219904	−	0.138278i
$352$		0			0
$353$	5.83073	−	10.0991i	0.310338	−	0.537522i	−0.668097	−	0.744074i	$-0.732891\pi$
$353$	5.83073	−	10.0991i	0.310338	−	0.537522i	0.978436	+	0.206552i	$0.0662243\pi$
$354$		0			0
$355$	−0.0699170	−	0.121100i	−0.00371081	−	0.00642731i
$356$		0			0
$357$	−2.63606	+	4.34711i	−0.139515	+	0.230073i
$358$		0			0
$359$	8.82159	−	15.2794i	0.465586	−	0.806418i	−0.533642	−	0.845710i	$-0.679177\pi$
$359$	8.82159	−	15.2794i	0.465586	−	0.806418i	0.999228	+	0.0392925i	$0.0125104\pi$
$360$		0			0
$361$	7.75688	+	13.4353i	0.408257	+	0.707122i
$362$		0			0
$363$	−0.921418	−	1.22330i	−0.0483619	−	0.0642064i
$364$		0			0
$365$	−0.128588	+	0.222721i	−0.00673061	+	0.0116578i
$366$		0			0
$367$	1.69146	−	2.92969i	0.0882934	−	0.152929i	−0.818496	−	0.574512i	$-0.805192\pi$
$367$	1.69146	−	2.92969i	0.0882934	−	0.152929i	0.906790	+	0.421583i	$0.138525\pi$
$368$		0			0
$369$	−8.19041	+	28.5181i	−0.426376	+	1.48460i
$370$		0			0
$371$	5.18104	−	6.57912i	0.268986	−	0.341571i
$372$		0			0
$373$	−6.69511	−	11.5963i	−0.346660	−	0.600433i	0.638994	−	0.769212i	$-0.279351\pi$
$373$	−6.69511	−	11.5963i	−0.346660	−	0.600433i	−0.985654	+	0.168779i	$0.946018\pi$
$374$		0			0
$375$	−1.06496	+	0.130533i	−0.0549941	+	0.00674070i
$376$		0			0
$377$	−2.41962			−0.124617
$378$		0			0
$379$	27.6131			1.41839			0.709194	−	0.705013i	$-0.249059\pi$
$379$	27.6131			1.41839			0.709194	+	0.705013i	$0.249059\pi$
$380$		0			0
$381$	−7.93042	+	0.972042i	−0.406288	+	0.0497992i
$382$		0			0
$383$	12.5020	+	21.6541i	0.638822	+	1.10647i	0.985692	+	0.168559i	$0.0539114\pi$
$383$	12.5020	+	21.6541i	0.638822	+	1.10647i	−0.346869	+	0.937913i	$0.612755\pi$
$384$		0			0
$385$	−0.193483	−	0.484242i	−0.00986083	−	0.0246792i
$386$		0			0
$387$	16.4801	+	17.0800i	0.837732	+	0.868227i
$388$		0			0
$389$	0.0683229	−	0.118339i	0.00346411	−	0.00600001i	−0.864288	−	0.502997i	$-0.832231\pi$
$389$	0.0683229	−	0.118339i	0.00346411	−	0.00600001i	0.867752	+	0.496997i	$0.165564\pi$
$390$		0			0
$391$	−3.44189	+	5.96153i	−0.174064	+	0.301488i
$392$		0			0
$393$	0.158542	+	0.210484i	0.00799737	+	0.0106175i
$394$		0			0
$395$	0.0922877	+	0.159847i	0.00464350	+	0.00804277i
$396$		0			0
$397$	7.91030	−	13.7010i	0.397006	−	0.687635i	−0.596349	−	0.802726i	$-0.703382\pi$
$397$	7.91030	−	13.7010i	0.397006	−	0.687635i	0.993355	+	0.115090i	$0.0367157\pi$
$398$		0			0
$399$	8.55436	+	0.184027i	0.428254	+	0.00921287i
$400$		0			0
$401$	5.52745	+	9.57383i	0.276028	+	0.478094i	0.970394	−	0.241528i	$-0.0776485\pi$
$401$	5.52745	+	9.57383i	0.276028	+	0.478094i	−0.694366	+	0.719622i	$0.744315\pi$
$402$		0			0
$403$	−0.640420	+	1.10924i	−0.0319016	+	0.0552552i
$404$		0			0
$405$	0.472728	+	0.295946i	0.0234900	+	0.0147057i
$406$		0			0
$407$	−13.5518	−	23.4724i	−0.671737	−	1.16348i
$408$		0			0
$409$	−36.0128			−1.78072			−0.890358	−	0.455260i	$-0.849546\pi$
$409$	−36.0128			−1.78072			−0.890358	+	0.455260i	$0.849546\pi$
$410$		0			0
$411$	−2.40737	+	5.66809i	−0.118747	+	0.279586i
$412$		0			0
$413$	−8.84787	−	22.1441i	−0.435375	−	1.08964i
$414$		0			0
$415$	0.134652	−	0.233225i	0.00660982	−	0.0114485i
$416$		0			0
$417$	−10.3047	+	24.2623i	−0.504625	+	1.18813i
$418$		0			0
$419$	−16.4877	+	28.5576i	−0.805477	+	1.39513i	0.110491	+	0.993877i	$0.464758\pi$
$419$	−16.4877	+	28.5576i	−0.805477	+	1.39513i	−0.915968	+	0.401251i	$0.868576\pi$
$420$		0			0
$421$	14.9800	+	25.9461i	0.730080	+	1.26454i	0.956849	+	0.290587i	$0.0938505\pi$
$421$	14.9800	+	25.9461i	0.730080	+	1.26454i	−0.226769	+	0.973949i	$0.572816\pi$
$422$		0			0
$423$	−19.1654	+	4.76992i	−0.931855	+	0.231922i
$424$		0			0
$425$	−5.54274			−0.268862
$426$		0			0
$427$	−13.6275	−	34.1063i	−0.659480	−	1.65052i
$428$		0			0
$429$	1.67321	+	2.22140i	0.0807834	+	0.107250i
$430$		0			0
$431$	12.4021	+	21.4811i	0.597389	+	1.03471i	0.993205	+	0.116379i	$0.0371286\pi$
$431$	12.4021	+	21.4811i	0.597389	+	1.03471i	−0.395816	+	0.918330i	$0.629538\pi$
$432$		0			0
$433$	−5.00906			−0.240720			−0.120360	−	0.992730i	$-0.538405\pi$
$433$	−5.00906			−0.240720			−0.120360	+	0.992730i	$0.538405\pi$
$434$		0			0
$435$	0.201108	−	0.473503i	0.00964237	−	0.0227027i
$436$		0			0
$437$	11.5856			0.554213
$438$		0			0
$439$	40.5836			1.93695			0.968475	−	0.249110i	$-0.0801381\pi$
$439$	40.5836			1.93695			0.968475	+	0.249110i	$0.0801381\pi$
$440$		0			0
$441$	−11.2724	+	17.7182i	−0.536781	+	0.843721i
$442$		0			0
$443$	28.2665			1.34298			0.671490	−	0.741014i	$-0.265655\pi$
$443$	28.2665			1.34298			0.671490	+	0.741014i	$0.265655\pi$
$444$		0			0
$445$	−0.533031			−0.0252681
$446$		0			0
$447$	0.382355	+	0.507624i	0.0180848	+	0.0240098i
$448$		0			0
$449$	36.6443			1.72935			0.864676	−	0.502329i	$-0.167523\pi$
$449$	36.6443			1.72935			0.864676	+	0.502329i	$0.167523\pi$
$450$		0			0
$451$	−15.7283	−	27.2421i	−0.740615	−	1.28278i
$452$		0			0
$453$	8.52012	−	20.0604i	0.400310	−	0.942521i
$454$		0			0
$455$	−0.0307108	−	0.0768618i	−0.00143975	−	0.00360334i
$456$		0			0
$457$	−6.38308			−0.298588			−0.149294	−	0.988793i	$-0.547700\pi$
$457$	−6.38308			−0.298588			−0.149294	+	0.988793i	$0.547700\pi$
$458$		0			0
$459$	4.47766	+	3.63061i	0.208999	+	0.169462i
$460$		0			0
$461$	7.24366	+	12.5464i	0.337371	+	0.584343i	0.983937	−	0.178514i	$-0.0571291\pi$
$461$	7.24366	+	12.5464i	0.337371	+	0.584343i	−0.646567	+	0.762858i	$0.723796\pi$
$462$		0			0
$463$	−13.2527	+	22.9544i	−0.615907	+	1.06678i	0.374317	+	0.927301i	$0.377877\pi$
$463$	−13.2527	+	22.9544i	−0.615907	+	1.06678i	−0.990225	+	0.139482i	$0.955456\pi$
$464$		0			0
$465$	−0.163842	−	0.217521i	−0.00759801	−	0.0100873i
$466$		0			0
$467$	11.6879	−	20.2440i	0.540851	−	0.936782i	−0.458004	−	0.888950i	$-0.651436\pi$
$467$	11.6879	−	20.2440i	0.540851	−	0.936782i	0.998855	−	0.0478318i	$-0.0152311\pi$
$468$		0			0
$469$	−3.27176	−	8.18841i	−0.151076	−	0.378106i
$470$		0			0
$471$	9.37761	−	1.14943i	0.432097	−	0.0529627i
$472$		0			0
$473$	−25.1627			−1.15698
$474$		0			0
$475$	4.66428	+	8.07877i	0.214012	+	0.370679i
$476$		0			0
$477$	−6.59326	−	6.83327i	−0.301885	−	0.312874i
$478$		0			0
$479$	4.64803	−	8.05063i	0.212374	−	0.367842i	−0.740083	−	0.672515i	$-0.765214\pi$
$479$	4.64803	−	8.05063i	0.212374	−	0.367842i	0.952457	+	0.304673i	$0.0985472\pi$
$480$		0			0
$481$	−2.15102	−	3.72567i	−0.0980780	−	0.169876i
$482$		0			0
$483$	−14.7437	+	24.3137i	−0.670861	+	1.10631i
$484$		0			0
$485$	0.203055	−	0.351702i	0.00922026	−	0.0159700i
$486$		0			0
$487$	−2.04947	−	3.54979i	−0.0928704	−	0.160856i	0.815847	−	0.578267i	$-0.196271\pi$
$487$	−2.04947	−	3.54979i	−0.0928704	−	0.160856i	−0.908718	+	0.417411i	$0.862938\pi$
$488$		0			0
$489$	5.19416	−	12.2295i	0.234888	−	0.553038i
$490$		0			0
$491$	−4.98703	+	8.63778i	−0.225061	+	0.389818i	−0.956338	−	0.292264i	$-0.905592\pi$
$491$	−4.98703	+	8.63778i	−0.225061	+	0.389818i	0.731277	+	0.682081i	$0.238925\pi$
$492$		0			0
$493$	2.65862	−	4.60487i	0.119738	−	0.207393i
$494$		0			0
$495$	−0.573782	+	0.142804i	−0.0257896	+	0.00641856i
$496$		0			0
$497$	−2.21515	−	5.54399i	−0.0993632	−	0.248682i
$498$		0			0
$499$	−5.60415	−	9.70667i	−0.250876	−	0.434530i	0.712891	−	0.701275i	$-0.247385\pi$
$499$	−5.60415	−	9.70667i	−0.250876	−	0.434530i	−0.963767	+	0.266744i	$0.914052\pi$
$500$		0			0
$501$	−12.8310	+	30.2102i	−0.573246	+	1.34969i
$502$		0			0
$503$	1.69350			0.0755094			0.0377547	−	0.999287i	$-0.487979\pi$
$503$	1.69350			0.0755094			0.0377547	+	0.999287i	$0.487979\pi$
$504$		0			0
$505$	−0.403825			−0.0179700
$506$		0			0
$507$	−13.2815	−	17.6329i	−0.589852	−	0.783103i
$508$		0			0
$509$	20.4777	+	35.4685i	0.907659	+	1.57211i	0.817307	+	0.576202i	$0.195466\pi$
$509$	20.4777	+	35.4685i	0.907659	+	1.57211i	0.0903524	+	0.995910i	$0.471201\pi$
$510$		0			0
$511$	−6.79320	+	8.62631i	−0.300514	+	0.381606i
$512$		0			0
$513$	1.52376	−	9.58157i	0.0672758	−	0.423037i
$514$		0			0
$515$	−0.527345	+	0.913388i	−0.0232376	+	0.0402487i
$516$		0			0
$517$	10.4693	−	18.1334i	0.460439	−	0.797504i
$518$		0			0
$519$	41.2464	−	5.05563i	1.81052	−	0.221918i
$520$		0			0
$521$	15.5075	+	26.8598i	0.679396	+	1.17675i	0.975163	+	0.221488i	$0.0710914\pi$
$521$	15.5075	+	26.8598i	0.679396	+	1.17675i	−0.295767	+	0.955260i	$0.595575\pi$
$522$		0			0
$523$	3.67840	−	6.37117i	0.160845	−	0.278592i	−0.774327	−	0.632786i	$-0.781911\pi$
$523$	3.67840	−	6.37117i	0.160845	−	0.278592i	0.935172	+	0.354194i	$0.115245\pi$
$524$		0			0
$525$	−22.8900	−	0.492424i	−0.999001	−	0.0214912i
$526$		0			0
$527$	−1.40736	−	2.43762i	−0.0613056	−	0.106184i
$528$		0			0
$529$	−7.75077	+	13.4247i	−0.336990	+	0.583684i
$530$		0			0
$531$	−26.2387	+	6.53033i	−1.13866	+	0.283392i
$532$		0			0
$533$	−2.49648	−	4.32404i	−0.108135	−	0.187295i
$534$		0			0
$535$	1.09819			0.0474788
$536$		0			0
$537$	−8.91817	−	11.8400i	−0.384847	−	0.510933i
$538$		0			0
$539$	−5.21976	−	21.6432i	−0.224831	−	0.932238i
$540$		0			0
$541$	−14.4735	+	25.0688i	−0.622262	+	1.07779i	0.366801	+	0.930299i	$0.380453\pi$
$541$	−14.4735	+	25.0688i	−0.622262	+	1.07779i	−0.989063	+	0.147491i	$0.952880\pi$
$542$		0			0
$543$	−1.08768	+	0.133318i	−0.0466766	+	0.00572121i
$544$		0			0
$545$	−0.410812	+	0.711546i	−0.0175972	+	0.0304793i
$546$		0			0
$547$	−9.34891	−	16.1928i	−0.399731	−	0.692354i	0.593962	−	0.804493i	$-0.297563\pi$
$547$	−9.34891	−	16.1928i	−0.399731	−	0.692354i	−0.993692	+	0.112140i	$0.964230\pi$
$548$		0			0
$549$	−40.4128	+	10.0580i	−1.72478	+	0.429266i
$550$		0			0
$551$	−8.94905			−0.381242
$552$		0			0
$553$	2.92392	+	7.31785i	0.124338	+	0.311187i
$554$		0			0
$555$	0.907873	−	0.111279i	0.0385371	−	0.00472354i
$556$		0			0
$557$	−17.1787	−	29.7544i	−0.727886	−	1.26074i	−0.957775	−	0.287519i	$-0.907170\pi$
$557$	−17.1787	−	29.7544i	−0.727886	−	1.26074i	0.229889	−	0.973217i	$-0.426164\pi$
$558$		0			0
$559$	−3.99397			−0.168927
$560$		0			0
$561$	−6.06612	+	0.743532i	−0.256112	+	0.0313919i
$562$		0			0
$563$	14.7471			0.621516			0.310758	−	0.950489i	$-0.399417\pi$
$563$	14.7471			0.621516			0.310758	+	0.950489i	$0.399417\pi$
$564$		0			0
$565$	0.136449			0.00574047
$566$		0			0
$567$	18.1689	+	15.3912i	0.763024	+	0.646370i
$568$		0			0
$569$	3.33642			0.139870			0.0699349	−	0.997552i	$-0.477721\pi$
$569$	3.33642			0.139870			0.0699349	+	0.997552i	$0.477721\pi$
$570$		0			0
$571$	−18.8072			−0.787057			−0.393528	−	0.919313i	$-0.628746\pi$
$571$	−18.8072			−0.787057			−0.393528	+	0.919313i	$0.628746\pi$
$572$		0			0
$573$	40.5437	−	4.96949i	1.69374	−	0.207603i
$574$		0			0
$575$	−31.0010			−1.29283
$576$		0			0
$577$	−17.6961	−	30.6505i	−0.736697	−	1.27600i	−0.953975	−	0.299887i	$-0.903051\pi$
$577$	−17.6961	−	30.6505i	−0.736697	−	1.27600i	0.217277	−	0.976110i	$-0.430282\pi$
$578$		0			0
$579$	−44.0213	+	5.39575i	−1.82946	+	0.224240i
$580$		0			0
$581$	7.11357	−	9.03313i	0.295121	−	0.374758i
$582$		0			0
$583$	10.0669			0.416930
$584$		0			0
$585$	−0.0910742	+	0.0226667i	−0.00376545	+	0.000937153i
$586$		0			0
$587$	17.2921	+	29.9508i	0.713722	+	1.23620i	0.963450	+	0.267887i	$0.0863256\pi$
$587$	17.2921	+	29.9508i	0.713722	+	1.23620i	−0.249728	+	0.968316i	$0.580341\pi$
$588$		0			0
$589$	−2.36862	+	4.10257i	−0.0975973	+	0.169043i
$590$		0			0
$591$	−16.2602	+	1.99304i	−0.668856	+	0.0819826i
$592$		0			0
$593$	−15.9787	+	27.6759i	−0.656166	+	1.13651i	0.325434	+	0.945565i	$0.394490\pi$
$593$	−15.9787	+	27.6759i	−0.656166	+	1.13651i	−0.981600	+	0.190949i	$0.938844\pi$
$594$		0			0
$595$	0.180023	+	0.0260070i	0.00738023	+	0.00106618i
$596$		0			0
$597$	8.65207	+	11.4867i	0.354106	+	0.470120i
$598$		0			0
$599$	9.84952			0.402440			0.201220	−	0.979546i	$-0.435509\pi$
$599$	9.84952			0.402440			0.201220	+	0.979546i	$0.435509\pi$
$600$		0			0
$601$	−3.77340	−	6.53572i	−0.153920	−	0.266598i	0.778745	−	0.627340i	$-0.215857\pi$
$601$	−3.77340	−	6.53572i	−0.153920	−	0.266598i	−0.932665	+	0.360743i	$0.882523\pi$
$602$		0			0
$603$	−9.70252	+	2.41478i	−0.395117	+	0.0983374i
$604$		0			0
$605$	−0.0273968	+	0.0474527i	−0.00111384	+	0.00192923i
$606$		0			0
$607$	5.42922	+	9.40368i	0.220365	+	0.381683i	0.954919	−	0.296867i	$-0.0959418\pi$
$607$	5.42922	+	9.40368i	0.220365	+	0.381683i	−0.734554	+	0.678550i	$0.762608\pi$
$608$		0			0
$609$	11.3885	−	18.7806i	0.461484	−	0.761030i
$610$		0			0
$611$	1.66175	−	2.87823i	0.0672272	−	0.116441i
$612$		0			0
$613$	−23.8823	−	41.3653i	−0.964596	−	1.67073i	−0.710697	−	0.703499i	$-0.751620\pi$
$613$	−23.8823	−	41.3653i	−0.964596	−	1.67073i	−0.253899	−	0.967231i	$-0.581713\pi$
$614$		0			0
$615$	1.05368	−	0.129151i	0.0424886	−	0.00520788i
$616$		0			0
$617$	−18.7769	+	32.5225i	−0.755929	+	1.30931i	0.188982	+	0.981980i	$0.439481\pi$
$617$	−18.7769	+	32.5225i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$618$		0			0
$619$	17.9829	−	31.1472i	0.722792	−	1.25191i	−0.237084	−	0.971489i	$-0.576192\pi$
$619$	17.9829	−	31.1472i	0.722792	−	1.25191i	0.959876	−	0.280424i	$-0.0904750\pi$
$620$		0			0
$621$	25.0439	+	20.3063i	1.00498	+	0.814863i
$622$		0			0
$623$	−22.5237	−	3.25388i	−0.902393	−	0.130364i
$624$		0			0
$625$	−12.4712	−	21.6008i	−0.498848	−	0.864030i
$626$		0			0
$627$	6.18843	+	8.21592i	0.247142	+	0.328112i
$628$		0			0
$629$	9.45398			0.376955
$630$		0			0
$631$	31.8848			1.26931			0.634656	−	0.772794i	$-0.281142\pi$
$631$	31.8848			1.26931			0.634656	+	0.772794i	$0.281142\pi$
$632$		0			0
$633$	−13.6997	+	32.2556i	−0.544514	+	1.28205i
$634$		0			0
$635$	0.142929	+	0.247560i	0.00567196	+	0.00982413i
$636$		0			0
$637$	−0.828512	−	3.43534i	−0.0328268	−	0.136113i
$638$		0			0
$639$	−6.56912	+	1.63493i	−0.259870	+	0.0646770i
$640$		0			0
$641$	−8.33939	+	14.4442i	−0.329386	+	0.570513i	−0.982390	−	0.186841i	$-0.940175\pi$
$641$	−8.33939	+	14.4442i	−0.329386	+	0.570513i	0.653004	+	0.757354i	$0.273508\pi$
$642$		0			0
$643$	−23.5295	+	40.7544i	−0.927915	+	1.60720i	−0.141109	+	0.989994i	$0.545067\pi$
$643$	−23.5295	+	40.7544i	−0.927915	+	1.60720i	−0.786805	+	0.617201i	$0.788266\pi$
$644$		0			0
$645$	0.331961	−	0.781595i	0.0130710	−	0.0307753i
$646$		0			0
$647$	12.2324	+	21.1872i	0.480906	+	0.832954i	0.999760	−	0.0219091i	$-0.00697444\pi$
$647$	12.2324	+	21.1872i	0.480906	+	0.832954i	−0.518854	+	0.854863i	$0.673641\pi$
$648$		0			0
$649$	14.3331	−	24.8257i	0.562625	−	0.974495i
$650$		0			0
$651$	−5.59545	−	10.1917i	−0.219303	−	0.399445i
$652$		0			0
$653$	5.91306	+	10.2417i	0.231396	+	0.400789i	0.958219	−	0.286035i	$-0.0923374\pi$
$653$	5.91306	+	10.2417i	0.231396	+	0.400789i	−0.726823	+	0.686824i	$0.759004\pi$
$654$		0			0
$655$	0.00471397	−	0.00816484i	0.000184190	−	0.000319027i
$656$		0			0
$657$	8.64486	+	8.95954i	0.337268	+	0.349545i
$658$		0			0
$659$	−3.51539	−	6.08883i	−0.136940	−	0.237187i	0.789397	−	0.613883i	$-0.210393\pi$
$659$	−3.51539	−	6.08883i	−0.136940	−	0.237187i	−0.926337	+	0.376696i	$0.877060\pi$
$660$		0			0
$661$	14.8605			0.578006			0.289003	−	0.957328i	$-0.406676\pi$
$661$	14.8605			0.578006			0.289003	+	0.957328i	$0.406676\pi$
$662$		0			0
$663$	−0.962851	+	0.118018i	−0.0373940	+	0.00458343i
$664$		0			0
$665$	−0.113585	−	0.284276i	−0.00440465	−	0.0110238i
$666$		0			0
$667$	14.8699	−	25.7554i	0.575764	−	0.997253i
$668$		0			0
$669$	−5.04198	−	6.69385i	−0.194934	−	0.258799i
$670$		0			0
$671$	22.0759	−	38.2366i	0.852231	−	1.47611i
$672$		0			0
$673$	7.81679	+	13.5391i	0.301315	+	0.521893i	0.976434	−	0.215816i	$-0.0692411\pi$
$673$	7.81679	+	13.5391i	0.301315	+	0.521893i	−0.675119	+	0.737709i	$0.735908\pi$
$674$		0			0
$675$	−4.07733	+	25.6386i	−0.156936	+	0.986831i
$676$		0			0
$677$	24.7122			0.949767			0.474883	−	0.880049i	$-0.342490\pi$
$677$	24.7122			0.949767			0.474883	+	0.880049i	$0.342490\pi$
$678$		0			0
$679$	10.7272	−	13.6219i	0.411674	−	0.522762i
$680$		0			0
$681$	−0.455156	+	1.07165i	−0.0174416	+	0.0410659i
$682$		0			0
$683$	16.7467	+	29.0061i	0.640794	+	1.10989i	0.985256	+	0.171087i	$0.0547279\pi$
$683$	16.7467	+	29.0061i	0.640794	+	1.10989i	−0.344462	+	0.938800i	$0.611939\pi$
$684$		0			0
$685$	0.220326			0.00841821
$686$		0			0
$687$	−6.39373	−	8.48848i	−0.243936	−	0.323856i
$688$		0			0
$689$	1.59788			0.0608745
$690$		0			0
$691$	2.67672			0.101827			0.0509137	−	0.998703i	$-0.483787\pi$
$691$	2.67672			0.101827			0.0509137	+	0.998703i	$0.483787\pi$
$692$		0			0
$693$	−25.1174	+	2.53166i	−0.954133	+	0.0961698i
$694$		0			0
$695$	0.943104			0.0357740
$696$		0			0
$697$	10.9723			0.415607
$698$		0			0
$699$	−16.4525	+	38.7370i	−0.622291	+	1.46517i
$700$		0			0
$701$	−36.3715			−1.37373			−0.686866	−	0.726784i	$-0.741014\pi$
$701$	−36.3715			−1.37373			−0.686866	+	0.726784i	$0.741014\pi$
$702$		0			0
$703$	−7.95563	−	13.7796i	−0.300052	−	0.519706i
$704$		0			0
$705$	0.425135	+	0.564419i	0.0160115	+	0.0212573i
$706$		0			0
$707$	−17.0640	−	2.46515i	−0.641758	−	0.0927114i
$708$		0			0
$709$	−11.9074			−0.447191			−0.223596	−	0.974682i	$-0.571779\pi$
$709$	−11.9074			−0.447191			−0.223596	+	0.974682i	$0.571779\pi$
$710$		0			0
$711$	8.67098	−	2.15805i	0.325187	−	0.0809332i
$712$		0			0
$713$	−7.87148	−	13.6338i	−0.294789	−	0.510590i
$714$		0			0
$715$	0.0497501	−	0.0861698i	0.00186055	−	0.00322257i
$716$		0			0
$717$	18.4142	−	43.3558i	0.687690	−	1.61915i
$718$		0			0
$719$	−8.44050	+	14.6194i	−0.314778	+	0.545211i	−0.979390	−	0.201977i	$-0.935263\pi$
$719$	−8.44050	+	14.6194i	−0.314778	+	0.545211i	0.664613	+	0.747188i	$0.268597\pi$
$720$		0			0
$721$	−27.8592	+	35.3769i	−1.03753	+	1.31750i
$722$		0			0
$723$	−17.4729	+	41.1394i	−0.649822	+	1.52999i
$724$		0			0
$725$	23.9461			0.889336
$726$		0			0
$727$	−1.24570	−	2.15762i	−0.0462006	−	0.0800218i	0.842000	−	0.539477i	$-0.181378\pi$
$727$	−1.24570	−	2.15762i	−0.0462006	−	0.0800218i	−0.888201	+	0.459455i	$0.848045\pi$
$728$		0			0
$729$	20.0877	−	18.0412i	0.743988	−	0.668193i
$730$		0			0
$731$	4.38850	−	7.60110i	0.162314	−	0.281137i
$732$		0			0
$733$	6.25653	+	10.8366i	0.231090	+	0.400260i	0.958129	−	0.286336i	$-0.0924374\pi$
$733$	6.25653	+	10.8366i	0.231090	+	0.400260i	−0.727039	+	0.686596i	$0.759104\pi$
$734$		0			0
$735$	0.741135	+	0.123395i	0.0273372	+	0.00455150i
$736$		0			0
$737$	5.30009	−	9.18003i	0.195231	−	0.338151i
$738$		0			0
$739$	10.0051	+	17.3294i	0.368044	+	0.637472i	0.989260	−	0.146168i	$-0.0466941\pi$
$739$	10.0051	+	17.3294i	0.368044	+	0.637472i	−0.621215	+	0.783640i	$0.713361\pi$
$740$		0			0
$741$	0.982265	+	1.30408i	0.0360844	+	0.0479066i
$742$		0			0
$743$	−5.49879	+	9.52419i	−0.201731	+	0.349408i	−0.949086	−	0.315016i	$-0.897990\pi$
$743$	−5.49879	+	9.52419i	−0.201731	+	0.349408i	0.747355	+	0.664425i	$0.231323\pi$
$744$		0			0
$745$	0.0113687	−	0.0196912i	0.000416517	−	0.000721428i
$746$		0			0
$747$	−9.05255	−	9.38208i	−0.331215	−	0.343272i
$748$		0			0
$749$	46.4049	+	6.70388i	1.69560	+	0.244955i
$750$		0			0
$751$	14.4335	+	24.9996i	0.526686	+	0.912247i	0.999516	+	0.0310938i	$0.00989905\pi$
$751$	14.4335	+	24.9996i	0.526686	+	0.912247i	−0.472830	+	0.881154i	$0.656768\pi$
$752$		0			0
$753$	−46.5453	+	5.70512i	−1.69621	+	0.207906i
$754$		0			0
$755$	−0.779774			−0.0283789
$756$		0			0
$757$	−17.3626			−0.631053			−0.315527	−	0.948917i	$-0.602181\pi$
$757$	−17.3626			−0.631053			−0.315527	+	0.948917i	$0.602181\pi$
$758$		0			0
$759$	−33.9283	+	4.15863i	−1.23152	+	0.150949i
$760$		0			0
$761$	26.0020	+	45.0367i	0.942571	+	1.63258i	0.760543	+	0.649287i	$0.224933\pi$
$761$	26.0020	+	45.0367i	0.942571	+	1.63258i	0.182027	+	0.983293i	$0.441734\pi$
$762$		0			0
$763$	−21.7028	+	27.5592i	−0.785696	+	0.997712i
$764$		0			0
$765$	0.0569325	−	0.198233i	0.00205840	−	0.00716712i
$766$		0			0
$767$	2.27504	−	3.94049i	0.0821470	−	0.142283i
$768$		0			0
$769$	13.5839	−	23.5280i	0.489849	−	0.848443i	−0.510083	−	0.860125i	$-0.670385\pi$
$769$	13.5839	−	23.5280i	0.489849	−	0.848443i	0.999932	+	0.0116822i	$0.00371865\pi$
$770$		0			0
$771$	−14.0905	−	18.7069i	−0.507457	−	0.673712i
$772$		0			0
$773$	12.2452	+	21.2093i	0.440428	+	0.762845i	0.997721	−	0.0674716i	$-0.0214932\pi$
$773$	12.2452	+	21.2093i	0.440428	+	0.762845i	−0.557293	+	0.830316i	$0.688160\pi$
$774$		0			0
$775$	6.33802	−	10.9778i	0.227668	−	0.394333i
$776$		0			0
$777$	39.0423	+	0.839903i	1.40063	+	0.0301314i
$778$		0			0
$779$	−9.23334	−	15.9926i	−0.330819	−	0.572995i
$780$		0			0
$781$	3.58845	−	6.21537i	0.128405	−	0.222403i
$782$		0			0
$783$	−19.3447	−	15.6852i	−0.691322	−	0.560543i
$784$		0			0
$785$	−0.169011	−	0.292736i	−0.00603227	−	0.0104482i
$786$		0			0
$787$	−1.87862			−0.0669657			−0.0334828	−	0.999439i	$-0.510660\pi$
$787$	−1.87862			−0.0669657			−0.0334828	+	0.999439i	$0.510660\pi$
$788$		0			0
$789$	9.05592	−	21.3220i	0.322399	−	0.759082i
$790$		0			0
$791$	5.76579	+	0.832955i	0.205008	+	0.0296165i
$792$		0			0
$793$	3.50402	−	6.06914i	0.124431	−	0.215521i
$794$		0			0
$795$	−0.132809	+	0.312695i	−0.00471024	+	0.0110902i
$796$		0			0
$797$	17.6067	−	30.4957i	0.623662	−	1.08021i	−0.365137	−	0.930954i	$-0.618978\pi$
$797$	17.6067	−	30.4957i	0.623662	−	1.08021i	0.988798	−	0.149259i	$-0.0476890\pi$
$798$		0			0
$799$	3.65179	+	6.32509i	0.129191	+	0.223765i
$800$		0			0
$801$	−7.12313	+	24.8020i	−0.251684	+	0.876335i
$802$		0			0
$803$	−13.1994			−0.465797
$804$		0			0
$805$	1.00688	+	0.145459i	0.0354880	+	0.00512677i
$806$		0			0
$807$	−8.16148	−	10.8354i	−0.287298	−	0.381424i
$808$		0			0
$809$	1.53614	+	2.66067i	0.0540077	+	0.0935441i	0.891765	−	0.452498i	$-0.149467\pi$
$809$	1.53614	+	2.66067i	0.0540077	+	0.0935441i	−0.837758	+	0.546042i	$0.816134\pi$
$810$		0			0
$811$	14.8034			0.519818			0.259909	−	0.965633i	$-0.416307\pi$
$811$	14.8034			0.519818			0.259909	+	0.965633i	$0.416307\pi$
$812$		0			0
$813$	20.5482	−	48.3803i	0.720657	−	1.69677i
$814$		0			0
$815$	−0.475377			−0.0166517
$816$		0			0
$817$	−14.7719			−0.516802
$818$		0			0
$819$	−3.98679	+	0.401840i	−0.139310	+	0.0140414i
$820$		0			0
$821$	25.0122			0.872933			0.436467	−	0.899720i	$-0.356230\pi$
$821$	25.0122			0.872933			0.436467	+	0.899720i	$0.356230\pi$
$822$		0			0
$823$	−39.4961			−1.37675			−0.688374	−	0.725356i	$-0.741675\pi$
$823$	−39.4961			−1.37675			−0.688374	+	0.725356i	$0.741675\pi$
$824$		0			0
$825$	−16.5592	−	21.9844i	−0.576517	−	0.765398i
$826$		0			0
$827$	−12.4528			−0.433026			−0.216513	−	0.976280i	$-0.569468\pi$
$827$	−12.4528			−0.433026			−0.216513	+	0.976280i	$0.569468\pi$
$828$		0			0
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	0.503350	−	0.864083i	$-0.332101\pi$
$829$	−14.2995	−	24.7675i	−0.496643	−	0.860211i	−0.999993	+	0.00387209i	$0.998767\pi$
$830$		0			0
$831$	−15.3651	+	36.1767i	−0.533008	+	1.25496i
$832$		0			0
$833$	7.44828	+	2.19790i	0.258068	+	0.0761528i
$834$		0			0
$835$	1.17431			0.0406386
$836$		0			0
$837$	−12.3108	+	4.71677i	−0.425523	+	0.163035i
$838$		0			0
$839$	−21.0794	−	36.5107i	−0.727743	−	1.26049i	−0.957835	−	0.287319i	$-0.907236\pi$
$839$	−21.0794	−	36.5107i	−0.727743	−	1.26049i	0.230092	−	0.973169i	$-0.426097\pi$
$840$		0			0
$841$	3.01405	−	5.22048i	0.103933	−	0.180017i
$842$		0			0
$843$	21.0138	+	27.8984i	0.723752	+	0.960871i
$844$		0			0
$845$	−0.394904	+	0.683993i	−0.0135851	+	0.0235301i
$846$		0			0
$847$	−1.44735	+	1.83791i	−0.0497316	+	0.0631514i
$848$		0			0
$849$	−29.0644	+	3.56247i	−0.997489	+	0.122264i
$850$		0			0
$851$	52.8768			1.81259
$852$		0			0
$853$	−25.6206	−	44.3761i	−0.877232	−	1.51941i	−0.854366	−	0.519671i	$-0.826054\pi$
$853$	−25.6206	−	44.3761i	−0.877232	−	1.51941i	−0.0228654	−	0.999739i	$-0.507279\pi$
$854$		0			0
$855$	−0.336841	+	0.0838337i	−0.0115197	+	0.00286705i
$856$		0			0
$857$	18.9029	−	32.7408i	0.645710	−	1.11840i	−0.338427	−	0.940993i	$-0.609895\pi$
$857$	18.9029	−	32.7408i	0.645710	−	1.11840i	0.984137	−	0.177410i	$-0.0567720\pi$
$858$		0			0
$859$	−22.3112	−	38.6442i	−0.761249	−	1.31852i	−0.942207	−	0.335031i	$-0.891253\pi$
$859$	−22.3112	−	38.6442i	−0.761249	−	1.31852i	0.180958	−	0.983491i	$-0.442080\pi$
$860$		0			0
$861$	45.3127	+	0.974796i	1.54425	+	0.0332210i
$862$		0			0
$863$	15.4848	−	26.8205i	0.527109	−	0.912980i	−0.472392	−	0.881389i	$-0.656609\pi$
$863$	15.4848	−	26.8205i	0.527109	−	0.912980i	0.999501	−	0.0315912i	$-0.0100575\pi$
$864$		0			0
$865$	−0.743379	−	1.28757i	−0.0252756	−	0.0437787i
$866$		0			0
$867$	−10.6774	+	25.1396i	−0.362622	+	0.853786i
$868$		0			0
$869$	−4.73661	+	8.20405i	−0.160678	+	0.278303i
$870$		0			0
$871$	0.841263	−	1.45711i	0.0285051	−	0.0493723i
$872$		0			0
$873$	−13.6512	−	14.1481i	−0.462023	−	0.478842i
$874$		0			0
$875$	0.608103	+	1.52193i	0.0205576	+	0.0514507i
$876$		0			0
$877$	−11.5843	−	20.0646i	−0.391174	−	0.677533i	0.601431	−	0.798925i	$-0.294597\pi$
$877$	−11.5843	−	20.0646i	−0.391174	−	0.677533i	−0.992605	+	0.121392i	$0.961264\pi$
$878$		0			0
$879$	−3.25817	+	7.67130i	−0.109896	+	0.258746i
$880$		0			0
$881$	14.0143			0.472155			0.236077	−	0.971734i	$-0.424138\pi$
$881$	14.0143			0.472155			0.236077	+	0.971734i	$0.424138\pi$
$882$		0			0
$883$	39.9269			1.34365			0.671824	−	0.740711i	$-0.265511\pi$
$883$	39.9269			1.34365			0.671824	+	0.740711i	$0.265511\pi$
$884$		0			0
$885$	0.582037	+	0.772726i	0.0195649	+	0.0259749i
$886$		0			0
$887$	−13.4221	−	23.2477i	−0.450669	−	0.780581i	0.547759	−	0.836636i	$-0.315481\pi$
$887$	−13.4221	−	23.2477i	−0.450669	−	0.780581i	−0.998428	+	0.0560549i	$0.982148\pi$
$888$		0			0
$889$	4.52836	+	11.3334i	0.151876	+	0.380110i
$890$		0			0
$891$	−1.02303	+	28.6065i	−0.0342728	+	0.958354i
$892$		0			0
$893$	6.14605	−	10.6453i	0.205670	−	0.356230i
$894$		0			0
$895$	−0.265167	+	0.459283i	−0.00886356	+	0.0153521i
$896$		0			0
$897$	−5.38530	+	0.660083i	−0.179810	+	0.0220395i
$898$		0			0
$899$	6.08017	+	10.5312i	0.202785	+	0.351234i
$900$		0			0
$901$	−1.75572	+	3.04100i	−0.0584915	+	0.101310i
$902$		0			0
$903$	18.7986	−	31.0005i	0.625577	−	1.03163i
$904$		0			0
$905$	0.0196030	+	0.0339534i	0.000651626	+	0.00112865i
$906$		0			0
$907$	18.8808	−	32.7026i	0.626928	−	1.08587i	−0.361237	−	0.932474i	$-0.617645\pi$
$907$	18.8808	−	32.7026i	0.626928	−	1.08587i	0.988165	−	0.153397i	$-0.0490212\pi$
$908$		0			0
$909$	−5.39650	+	18.7900i	−0.178991	+	0.623226i
$910$		0			0
$911$	−7.93650	−	13.7464i	−0.262948	−	0.455439i	0.704076	−	0.710125i	$-0.251361\pi$
$911$	−7.93650	−	13.7464i	−0.262948	−	0.455439i	−0.967024	+	0.254685i	$0.918028\pi$
$912$		0			0
$913$	13.8219			0.457438
$914$		0			0
$915$	0.896453	+	1.19015i	0.0296358	+	0.0393452i
$916$		0			0
$917$	0.249035	−	0.316236i	0.00822388	−	0.0104430i
$918$		0			0
$919$	−5.22203	+	9.04482i	−0.172259	+	0.298361i	−0.939209	−	0.343345i	$-0.888440\pi$
$919$	−5.22203	+	9.04482i	−0.172259	+	0.298361i	0.766950	+	0.641706i	$0.221773\pi$
$920$		0			0
$921$	27.3673	−	3.35445i	0.901785	−	0.110533i
$922$		0			0
$923$	0.569580	−	0.986541i	0.0187479	−	0.0324724i
$924$		0			0
$925$	21.2879	+	36.8717i	0.699941	+	1.21233i
$926$		0			0
$927$	35.4529	+	36.7435i	1.16443	+	1.20681i
$928$		0			0
$929$	−19.1634			−0.628730			−0.314365	−	0.949302i	$-0.601792\pi$
$929$	−19.1634			−0.628730			−0.314365	+	0.949302i	$0.601792\pi$
$930$		0			0
$931$	−3.06428	−	12.7057i	−0.100428	−	0.416414i
$932$		0			0
$933$	−0.451920	+	0.0553925i	−0.0147952	+	0.00181347i
$934$		0			0
$935$	0.109329	+	0.189363i	0.00357543	+	0.00619283i
$936$		0			0
$937$	3.09451			0.101093			0.0505467	−	0.998722i	$-0.483904\pi$
$937$	3.09451			0.101093			0.0505467	+	0.998722i	$0.483904\pi$
$938$		0			0
$939$	10.7461	−	1.31716i	0.350685	−	0.0429839i
$940$		0			0
$941$	15.3113			0.499133			0.249567	−	0.968358i	$-0.419712\pi$
$941$	15.3113			0.499133			0.249567	+	0.968358i	$0.419712\pi$
$942$		0			0
$943$	61.3691			1.99845
$944$		0			0
$945$	0.252726	−	0.813588i	0.00822119	−	0.0264660i
$946$		0			0
$947$	−1.01549			−0.0329991			−0.0164995	−	0.999864i	$-0.505252\pi$
$947$	−1.01549			−0.0329991			−0.0164995	+	0.999864i	$0.505252\pi$
$948$		0			0
$949$	−2.09509			−0.0680094
$950$		0			0
$951$	33.8322	−	4.14686i	1.09708	−	0.134471i
$952$		0			0
$953$	−35.4930			−1.14973			−0.574865	−	0.818248i	$-0.694945\pi$
$953$	−35.4930			−1.14973			−0.574865	+	0.818248i	$0.694945\pi$
$954$		0			0
$955$	−0.730713	−	1.26563i	−0.0236453	−	0.0409549i
$956$		0			0
$957$	26.2072	−	3.21225i	0.847159	−	0.103837i
$958$		0			0
$959$	9.31006	+	1.34498i	0.300638	+	0.0434316i
$960$		0			0
$961$	−24.5628			−0.792350
$962$		0			0
$963$	14.6756	−	51.0988i	0.472914	−	1.64664i
$964$		0			0
$965$	0.793390	+	1.37419i	0.0255401	+	0.0442368i
$966$		0			0
$967$	−6.87762	+	11.9124i	−0.221169	+	0.383077i	−0.955163	−	0.296079i	$-0.904321\pi$
$967$	−6.87762	+	11.9124i	−0.221169	+	0.383077i	0.733994	+	0.679156i	$0.237654\pi$
$968$		0			0
$969$	−3.56114	+	0.436494i	−0.114400	+	0.0140222i
$970$		0			0
$971$	21.6567	−	37.5104i	0.694995	−	1.20377i	−0.275187	−	0.961391i	$-0.588740\pi$
$971$	21.6567	−	37.5104i	0.694995	−	1.20377i	0.970182	−	0.242376i	$-0.0779269\pi$
$972$		0			0
$973$	39.8517	+	5.75718i	1.27759	+	0.184567i
$974$		0			0
$975$	−2.62837	−	3.48949i	−0.0841753	−	0.111753i
$976$		0			0
$977$	−9.56840			−0.306120			−0.153060	−	0.988217i	$-0.548913\pi$
$977$	−9.56840			−0.306120			−0.153060	+	0.988217i	$0.548913\pi$
$978$		0			0
$979$	−13.6787	−	23.6923i	−0.437174	−	0.757208i
$980$		0			0
$981$	27.6185	+	28.6238i	0.881790	+	0.913889i
$982$		0			0
$983$	8.56644	−	14.8375i	0.273227	−	0.473243i	−0.696459	−	0.717596i	$-0.745242\pi$
$983$	8.56644	−	14.8375i	0.273227	−	0.473243i	0.969686	+	0.244353i	$0.0785757\pi$
$984$		0			0
$985$	0.293056	+	0.507587i	0.00933753	+	0.0161731i
$986$		0			0
$987$	14.5190	+	26.4453i	0.462143	+	0.841763i
$988$		0			0
$989$	24.5452	−	42.5135i	0.780492	−	1.35185i
$990$		0			0
$991$	−6.32891	−	10.9620i	−0.201044	−	0.348219i	0.747821	−	0.663901i	$-0.231100\pi$
$991$	−6.32891	−	10.9620i	−0.201044	−	0.348219i	−0.948865	+	0.315682i	$0.897767\pi$
$992$		0			0
$993$	42.1781	−	5.16982i	1.33848	−	0.164059i
$994$		0			0
$995$	0.257255	−	0.445579i	0.00815553	−	0.0141258i
$996$		0			0
$997$	12.8352	−	22.2312i	0.406495	−	0.704069i	−0.588000	−	0.808861i	$-0.700084\pi$
$997$	12.8352	−	22.2312i	0.406495	−	0.704069i	0.994494	+	0.104792i	$0.0334177\pi$
$998$		0			0
$999$	6.95449	−	43.7305i	0.220030	−	1.38357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.l.625.1		22
3.2	odd	2		3024.2.q.l.2305.6		22
4.3	odd	2		504.2.q.c.121.11	yes	22
7.4	even	3		1008.2.t.l.193.8		22
9.2	odd	6		3024.2.t.k.289.6		22
9.7	even	3		1008.2.t.l.961.8		22
12.11	even	2		1512.2.q.d.793.6		22
21.11	odd	6		3024.2.t.k.1873.6		22
28.11	odd	6		504.2.t.c.193.4	yes	22
36.7	odd	6		504.2.t.c.457.4	yes	22
36.11	even	6		1512.2.t.c.289.6		22
63.11	odd	6		3024.2.q.l.2881.6		22
63.25	even	3	inner	1008.2.q.l.529.1		22
84.11	even	6		1512.2.t.c.361.6		22
252.11	even	6		1512.2.q.d.1369.6		22
252.151	odd	6		504.2.q.c.25.11	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.11	✓	22	252.151	odd	6
504.2.q.c.121.11	yes	22	4.3	odd	2
504.2.t.c.193.4	yes	22	28.11	odd	6
504.2.t.c.457.4	yes	22	36.7	odd	6
1008.2.q.l.529.1		22	63.25	even	3	inner
1008.2.q.l.625.1		22	1.1	even	1	trivial
1008.2.t.l.193.8		22	7.4	even	3
1008.2.t.l.961.8		22	9.7	even	3
1512.2.q.d.793.6		22	12.11	even	2
1512.2.q.d.1369.6		22	252.11	even	6
1512.2.t.c.289.6		22	36.11	even	6
1512.2.t.c.361.6		22	84.11	even	6
3024.2.q.l.2305.6		22	3.2	odd	2
3024.2.q.l.2881.6		22	63.11	odd	6
3024.2.t.k.289.6		22	9.2	odd	6
3024.2.t.k.1873.6		22	21.11	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71918 + 0.210723i) q^{3} +(0.0309846 + 0.0536670i) q^{5} +(0.981674 + 2.45689i) q^{7} +(2.91119 - 0.724543i) q^{9} +O(q^{10})\)	\(q+(-1.71918 + 0.210723i) q^{3} +(0.0309846 + 0.0536670i) q^{5} +(0.981674 + 2.45689i) q^{7} +(2.91119 - 0.724543i) q^{9} +(-1.59027 + 2.75442i) q^{11} +(-0.252417 + 0.437198i) q^{13} +(-0.0645772 - 0.0857342i) q^{15} +(-0.554700 - 0.960769i) q^{17} +(-0.933573 + 1.61700i) q^{19} +(-2.20540 - 4.01699i) q^{21} +(-3.10248 - 5.37365i) q^{23} +(2.49808 - 4.32680i) q^{25} +(-4.85220 + 1.85908i) q^{27} +(2.39645 + 4.15077i) q^{29} +2.53716 q^{31} +(2.15354 - 5.07047i) q^{33} +(-0.101437 + 0.128809i) q^{35} +(-4.26085 + 7.38001i) q^{37} +(0.341823 - 0.804815i) q^{39} +(-4.94516 + 8.56527i) q^{41} +(3.95574 + 6.85154i) q^{43} +(0.129086 + 0.133785i) q^{45} -6.58336 q^{47} +(-5.07263 + 4.82373i) q^{49} +(1.15609 + 1.53485i) q^{51} +(-1.58258 - 2.74112i) q^{53} -0.197095 q^{55} +(1.26425 - 2.97664i) q^{57} -9.01304 q^{59} -13.8819 q^{61} +(4.63796 + 6.44122i) q^{63} -0.0312842 q^{65} -3.33283 q^{67} +(6.46609 + 8.58454i) q^{69} -2.25651 q^{71} +(2.07503 + 3.59406i) q^{73} +(-3.38291 + 7.96497i) q^{75} +(-8.32844 - 1.20317i) q^{77} +2.97850 q^{79} +(7.95008 - 4.21856i) q^{81} +(-2.17289 - 3.76355i) q^{83} +(0.0343744 - 0.0595381i) q^{85} +(-4.99460 - 6.63096i) q^{87} +(-4.30077 + 7.44915i) q^{89} +(-1.32194 - 0.190974i) q^{91} +(-4.36184 + 0.534636i) q^{93} -0.115706 q^{95} +(-3.27671 - 5.67542i) q^{97} +(-2.63388 + 9.17087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9	\( 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9} - 3 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} - 22 q^{25} + 2 q^{27} - 7 q^{29} + 12 q^{31} - 3 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 3 q^{45} + 34 q^{47} - 25 q^{49} - 53 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} - 42 q^{59} - 62 q^{61} + 22 q^{63} + 6 q^{65} - 52 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} - 53 q^{75} - q^{77} - 32 q^{79} - 6 q^{81} + 36 q^{83} + 28 q^{85} + 5 q^{87} - 2 q^{89} - 15 q^{91} - 11 q^{93} - 48 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9 - 3 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 - 22 * q^25 + 2 * q^27 - 7 * q^29 + 12 * q^31 - 3 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 3 * q^45 + 34 * q^47 - 25 * q^49 - 53 * q^51 + q^53 - 2 * q^55 - 21 * q^57 - 42 * q^59 - 62 * q^61 + 22 * q^63 + 6 * q^65 - 52 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 - 53 * q^75 - q^77 - 32 * q^79 - 6 * q^81 + 36 * q^83 + 28 * q^85 + 5 * q^87 - 2 * q^89 - 15 * q^91 - 11 * q^93 - 48 * q^95 + 19 * q^97 - 24 * q^99

Introduction

L-functions

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