LMFDB - Embedded newform 2002.2.c.a.1847.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2002,2,Mod(1847,2002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2002.1847");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2002 = 2 \cdot 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2002.c (of order $2$, degree $1$, 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:	$15.9860504847$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1847.3
Character	$\chi$	$=$	2002.1847
Dual form			2002.2.c.a.1847.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -2.80296i q^{3} -1.00000 q^{4} -3.66969i q^{5} -2.80296 q^{6} +(-1.34713 - 2.27711i) q^{7} +1.00000i q^{8} -4.85657 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -2.80296i q^{3} -1.00000 q^{4} -3.66969i q^{5} -2.80296 q^{6} +(-1.34713 - 2.27711i) q^{7} +1.00000i q^{8} -4.85657 q^{9} -3.66969 q^{10} +(2.39918 - 2.28997i) q^{11} +2.80296i q^{12} -1.00000 q^{13} +(-2.27711 + 1.34713i) q^{14} -10.2860 q^{15} +1.00000 q^{16} +5.13228 q^{17} +4.85657i q^{18} +2.77101 q^{19} +3.66969i q^{20} +(-6.38265 + 3.77595i) q^{21} +(-2.28997 - 2.39918i) q^{22} -5.13498 q^{23} +2.80296 q^{24} -8.46663 q^{25} +1.00000i q^{26} +5.20388i q^{27} +(1.34713 + 2.27711i) q^{28} +1.93789i q^{29} +10.2860i q^{30} -8.63265i q^{31} -1.00000i q^{32} +(-6.41868 - 6.72479i) q^{33} -5.13228i q^{34} +(-8.35630 + 4.94356i) q^{35} +4.85657 q^{36} -8.99776 q^{37} -2.77101i q^{38} +2.80296i q^{39} +3.66969 q^{40} +12.0216 q^{41} +(3.77595 + 6.38265i) q^{42} +0.841340i q^{43} +(-2.39918 + 2.28997i) q^{44} +17.8221i q^{45} +5.13498i q^{46} +6.07678i q^{47} -2.80296i q^{48} +(-3.37047 + 6.13514i) q^{49} +8.46663i q^{50} -14.3856i q^{51} +1.00000 q^{52} +9.66179 q^{53} +5.20388 q^{54} +(-8.40347 - 8.80424i) q^{55} +(2.27711 - 1.34713i) q^{56} -7.76703i q^{57} +1.93789 q^{58} -3.16644i q^{59} +10.2860 q^{60} +4.39436 q^{61} -8.63265 q^{62} +(6.54244 + 11.0589i) q^{63} -1.00000 q^{64} +3.66969i q^{65} +(-6.72479 + 6.41868i) q^{66} +10.7949 q^{67} -5.13228 q^{68} +14.3931i q^{69} +(4.94356 + 8.35630i) q^{70} +1.03883 q^{71} -4.85657i q^{72} +15.7817 q^{73} +8.99776i q^{74} +23.7316i q^{75} -2.77101 q^{76} +(-8.44652 - 2.37831i) q^{77} +2.80296 q^{78} -0.0681048i q^{79} -3.66969i q^{80} +0.0165472 q^{81} -12.0216i q^{82} +3.65253 q^{83} +(6.38265 - 3.77595i) q^{84} -18.8339i q^{85} +0.841340 q^{86} +5.43182 q^{87} +(2.28997 + 2.39918i) q^{88} -15.6169i q^{89} +17.8221 q^{90} +(1.34713 + 2.27711i) q^{91} +5.13498 q^{92} -24.1969 q^{93} +6.07678 q^{94} -10.1688i q^{95} -2.80296 q^{96} +12.1836i q^{97} +(6.13514 + 3.37047i) q^{98} +(-11.6518 + 11.1214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{7} - 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^7 - 48 * q^9	$ 48 q - 48 q^{4} - 8 q^{7} - 48 q^{9} - 4 q^{11} - 48 q^{13} - 2 q^{14} + 8 q^{15} + 48 q^{16} - 4 q^{17} + 20 q^{21} + 2 q^{22} - 32 q^{23} - 56 q^{25} + 8 q^{28} + 20 q^{33} - 10 q^{35} + 48 q^{36} - 16 q^{37} + 16 q^{42} + 4 q^{44} - 38 q^{49} + 48 q^{52} + 4 q^{53} - 60 q^{55} + 2 q^{56} + 24 q^{58} - 8 q^{60} - 28 q^{61} - 28 q^{62} + 32 q^{63} - 48 q^{64} + 46 q^{66} - 8 q^{67} + 4 q^{68} - 20 q^{70} + 16 q^{73} - 14 q^{77} + 16 q^{81} + 40 q^{83} - 20 q^{84} - 24 q^{87} - 2 q^{88} + 20 q^{90} + 8 q^{91} + 32 q^{92} - 48 q^{93} - 44 q^{94} + 92 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^7 - 48 * q^9 - 4 * q^11 - 48 * q^13 - 2 * q^14 + 8 * q^15 + 48 * q^16 - 4 * q^17 + 20 * q^21 + 2 * q^22 - 32 * q^23 - 56 * q^25 + 8 * q^28 + 20 * q^33 - 10 * q^35 + 48 * q^36 - 16 * q^37 + 16 * q^42 + 4 * q^44 - 38 * q^49 + 48 * q^52 + 4 * q^53 - 60 * q^55 + 2 * q^56 + 24 * q^58 - 8 * q^60 - 28 * q^61 - 28 * q^62 + 32 * q^63 - 48 * q^64 + 46 * q^66 - 8 * q^67 + 4 * q^68 - 20 * q^70 + 16 * q^73 - 14 * q^77 + 16 * q^81 + 40 * q^83 - 20 * q^84 - 24 * q^87 - 2 * q^88 + 20 * q^90 + 8 * q^91 + 32 * q^92 - 48 * q^93 - 44 * q^94 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2002\mathbb{Z}\right)^\times$.

$n$	$365$	$925$	$1431$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	2.80296i		−	1.61829i	−0.587610	−	0.809144i	$-0.699931\pi$
$3$		−	2.80296i		−	1.61829i	0.587610	−	0.809144i	$-0.300069\pi$
$4$	−1.00000			−0.500000
$5$		−	3.66969i		−	1.64114i	−0.571549	−	0.820568i	$-0.693657\pi$
$5$		−	3.66969i		−	1.64114i	0.571549	−	0.820568i	$-0.306343\pi$
$6$	−2.80296			−1.14430
$7$	−1.34713	−	2.27711i	−0.509168	−	0.860667i
$7$	−1.34713	−	2.27711i	−0.509168	−	0.860667i
$8$			1.00000i			0.353553i
$9$	−4.85657			−1.61886
$10$	−3.66969			−1.16046
$11$	2.39918	−	2.28997i	0.723379	−	0.690451i
$11$	2.39918	−	2.28997i	0.723379	−	0.690451i
$12$			2.80296i			0.809144i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.27711	+	1.34713i	−0.608584	+	0.360036i
$15$	−10.2860			−2.65583
$16$	1.00000			0.250000
$17$	5.13228			1.24476			0.622380	−	0.782715i	$-0.286166\pi$
$17$	5.13228			1.24476			0.622380	+	0.782715i	$0.286166\pi$
$18$			4.85657i			1.14470i
$19$	2.77101			0.635714			0.317857	−	0.948139i	$-0.397037\pi$
$19$	2.77101			0.635714			0.317857	+	0.948139i	$0.397037\pi$
$20$			3.66969i			0.820568i
$21$	−6.38265	+	3.77595i	−1.39281	+	0.823980i
$22$	−2.28997	−	2.39918i	−0.488223	−	0.511506i
$23$	−5.13498			−1.07072			−0.535358	−	0.844625i	$-0.679823\pi$
$23$	−5.13498			−1.07072			−0.535358	+	0.844625i	$0.679823\pi$
$24$	2.80296			0.572151
$25$	−8.46663			−1.69333
$26$			1.00000i			0.196116i
$27$			5.20388i			1.00149i
$28$	1.34713	+	2.27711i	0.254584	+	0.430334i
$29$			1.93789i			0.359857i	0.983680	+	0.179928i	$0.0575866\pi$
$29$			1.93789i			0.359857i	−0.983680	+	0.179928i	$0.942413\pi$
$30$			10.2860i			1.87796i
$31$		−	8.63265i		−	1.55047i	−0.631673	−	0.775235i	$-0.717632\pi$
$31$		−	8.63265i		−	1.55047i	0.631673	−	0.775235i	$-0.282368\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.41868	−	6.72479i	−1.11735	−	1.17064i
$34$		−	5.13228i		−	0.880179i
$35$	−8.35630	+	4.94356i	−1.41247	+	0.835614i
$36$	4.85657			0.809428
$37$	−8.99776			−1.47922			−0.739611	−	0.673035i	$-0.764990\pi$
$37$	−8.99776			−1.47922			−0.739611	+	0.673035i	$0.764990\pi$
$38$		−	2.77101i		−	0.449518i
$39$			2.80296i			0.448832i
$40$	3.66969			0.580229
$41$	12.0216			1.87746			0.938729	−	0.344657i	$-0.112005\pi$
$41$	12.0216			1.87746			0.938729	+	0.344657i	$0.112005\pi$
$42$	3.77595	+	6.38265i	0.582642	+	0.984864i
$43$			0.841340i			0.128303i	0.997940	+	0.0641516i	$0.0204341\pi$
$43$			0.841340i			0.128303i	−0.997940	+	0.0641516i	$0.979566\pi$
$44$	−2.39918	+	2.28997i	−0.361689	+	0.345226i
$45$			17.8221i			2.65676i
$46$			5.13498i			0.757111i
$47$			6.07678i			0.886389i	0.896425	+	0.443195i	$0.146155\pi$
$47$			6.07678i			0.886389i	−0.896425	+	0.443195i	$0.853845\pi$
$48$		−	2.80296i		−	0.404572i
$49$	−3.37047	+	6.13514i	−0.481496	+	0.876448i
$50$			8.46663i			1.19736i
$51$		−	14.3856i		−	2.01438i
$52$	1.00000			0.138675
$53$	9.66179			1.32715			0.663574	−	0.748111i	$-0.269039\pi$
$53$	9.66179			1.32715			0.663574	+	0.748111i	$0.269039\pi$
$54$	5.20388			0.708158
$55$	−8.40347	−	8.80424i	−1.13312	−	1.18716i
$56$	2.27711	−	1.34713i	0.304292	−	0.180018i
$57$		−	7.76703i		−	1.02877i
$58$	1.93789			0.254457
$59$		−	3.16644i		−	0.412236i	−0.978527	−	0.206118i	$-0.933917\pi$
$59$		−	3.16644i		−	0.412236i	0.978527	−	0.206118i	$-0.0660830\pi$
$60$	10.2860			1.32792
$61$	4.39436			0.562640			0.281320	−	0.959614i	$-0.409228\pi$
$61$	4.39436			0.562640			0.281320	+	0.959614i	$0.409228\pi$
$62$	−8.63265			−1.09635
$63$	6.54244	+	11.0589i	0.824269	+	1.39330i
$64$	−1.00000			−0.125000
$65$			3.66969i			0.455169i
$66$	−6.72479	+	6.41868i	−0.827764	+	0.790085i
$67$	10.7949			1.31881			0.659403	−	0.751790i	$-0.270809\pi$
$67$	10.7949			1.31881			0.659403	+	0.751790i	$0.270809\pi$
$68$	−5.13228			−0.622380
$69$			14.3931i			1.73273i
$70$	4.94356	+	8.35630i	0.590868	+	0.998768i
$71$	1.03883			0.123286			0.0616429	−	0.998098i	$-0.480366\pi$
$71$	1.03883			0.123286			0.0616429	+	0.998098i	$0.480366\pi$
$72$		−	4.85657i		−	0.572352i
$73$	15.7817			1.84710			0.923552	−	0.383473i	$-0.125272\pi$
$73$	15.7817			1.84710			0.923552	+	0.383473i	$0.125272\pi$
$74$			8.99776i			1.04597i
$75$			23.7316i			2.74029i
$76$	−2.77101			−0.317857
$77$	−8.44652	−	2.37831i	−0.962570	−	0.271033i
$78$	2.80296			0.317372
$79$		−	0.0681048i		−	0.00766239i	−0.999993	−	0.00383120i	$-0.998780\pi$
$79$		−	0.0681048i		−	0.00766239i	0.999993	−	0.00383120i	$-0.00121951\pi$
$80$		−	3.66969i		−	0.410284i
$81$	0.0165472			0.00183858
$82$		−	12.0216i		−	1.32756i
$83$	3.65253			0.400918			0.200459	−	0.979702i	$-0.435757\pi$
$83$	3.65253			0.400918			0.200459	+	0.979702i	$0.435757\pi$
$84$	6.38265	−	3.77595i	0.696404	−	0.411990i
$85$		−	18.8339i		−	2.04282i
$86$	0.841340			0.0907240
$87$	5.43182			0.582352
$88$	2.28997	+	2.39918i	0.244111	+	0.255753i
$89$		−	15.6169i		−	1.65539i	−0.561180	−	0.827694i	$-0.689652\pi$
$89$		−	15.6169i		−	1.65539i	0.561180	−	0.827694i	$-0.310348\pi$
$90$	17.8221			1.87861
$91$	1.34713	+	2.27711i	0.141218	+	0.238706i
$92$	5.13498			0.535358
$93$	−24.1969			−2.50911
$94$	6.07678			0.626772
$95$		−	10.1688i		−	1.04329i
$96$	−2.80296			−0.286076
$97$			12.1836i			1.23706i	0.785761	+	0.618530i	$0.212272\pi$
$97$			12.1836i			1.23706i	−0.785761	+	0.618530i	$0.787728\pi$
$98$	6.13514	+	3.37047i	0.619742	+	0.340469i
$99$	−11.6518	+	11.1214i	−1.17105	+	1.11774i
$100$	8.46663			0.846663
$101$	−14.0868			−1.40169			−0.700846	−	0.713313i	$-0.747194\pi$
$101$	−14.0868			−1.40169			−0.700846	+	0.713313i	$0.747194\pi$
$102$	−14.3856			−1.42438
$103$		−	14.7845i		−	1.45676i	−0.685173	−	0.728380i	$-0.740273\pi$
$103$		−	14.7845i		−	1.45676i	0.685173	−	0.728380i	$-0.259727\pi$
$104$		−	1.00000i		−	0.0980581i
$105$	13.8566	+	23.4223i	1.35226	+	2.28579i
$106$		−	9.66179i		−	0.938436i
$107$			3.27614i			0.316716i	0.987382	+	0.158358i	$0.0506201\pi$
$107$			3.27614i			0.316716i	−0.987382	+	0.158358i	$0.949380\pi$
$108$		−	5.20388i		−	0.500744i
$109$		−	5.92460i		−	0.567474i	−0.958902	−	0.283737i	$-0.908426\pi$
$109$		−	5.92460i		−	0.567474i	0.958902	−	0.283737i	$-0.0915742\pi$
$110$	−8.80424	+	8.40347i	−0.839451	+	0.801240i
$111$			25.2203i			2.39381i
$112$	−1.34713	−	2.27711i	−0.127292	−	0.215167i
$113$	14.7381			1.38644			0.693220	−	0.720726i	$-0.256191\pi$
$113$	14.7381			1.38644			0.693220	+	0.720726i	$0.256191\pi$
$114$	−7.76703			−0.727449
$115$			18.8438i			1.75719i
$116$		−	1.93789i		−	0.179928i
$117$	4.85657			0.448990
$118$	−3.16644			−0.291495
$119$	−6.91386	−	11.6868i	−0.633792	−	1.07132i
$120$		−	10.2860i		−	0.938978i
$121$	0.512097	−	10.9881i	0.0465543	−	0.998916i
$122$		−	4.39436i		−	0.397847i
$123$		−	33.6960i		−	3.03827i
$124$			8.63265i			0.775235i
$125$			12.7215i			1.13784i
$126$	11.0589	−	6.54244i	0.985209	−	0.582847i
$127$		−	0.530947i		−	0.0471139i	−0.999722	−	0.0235570i	$-0.992501\pi$
$127$		−	0.530947i		−	0.0471139i	0.999722	−	0.0235570i	$-0.00749910\pi$
$128$			1.00000i			0.0883883i
$129$	2.35824			0.207631
$130$	3.66969			0.321853
$131$	−2.20035			−0.192245			−0.0961226	−	0.995370i	$-0.530644\pi$
$131$	−2.20035			−0.192245			−0.0961226	+	0.995370i	$0.530644\pi$
$132$	6.41868	+	6.72479i	0.558674	+	0.585318i
$133$	−3.73292	−	6.30991i	−0.323685	−	0.547138i
$134$		−	10.7949i		−	0.932537i
$135$	19.0966			1.64358
$136$			5.13228i			0.440089i
$137$	14.1394			1.20801			0.604007	−	0.796979i	$-0.293570\pi$
$137$	14.1394			1.20801			0.604007	+	0.796979i	$0.293570\pi$
$138$	14.3931			1.22522
$139$	19.4965			1.65368			0.826838	−	0.562441i	$-0.190138\pi$
$139$	19.4965			1.65368			0.826838	+	0.562441i	$0.190138\pi$
$140$	8.35630	−	4.94356i	0.706236	−	0.417807i
$141$	17.0330			1.43443
$142$		−	1.03883i		−	0.0871763i
$143$	−2.39918	+	2.28997i	−0.200629	+	0.191497i
$144$	−4.85657			−0.404714
$145$	7.11145			0.590574
$146$		−	15.7817i		−	1.30610i
$147$	17.1965	+	9.44729i	1.41835	+	0.779199i
$148$	8.99776			0.739611
$149$			17.3215i			1.41903i	0.704691	+	0.709514i	$0.251086\pi$
$149$			17.3215i			1.41903i	−0.704691	+	0.709514i	$0.748914\pi$
$150$	23.7316			1.93768
$151$		−	1.70260i		−	0.138555i	−0.997597	−	0.0692777i	$-0.977931\pi$
$151$		−	1.70260i		−	0.138555i	0.997597	−	0.0692777i	$-0.0220695\pi$
$152$			2.77101i			0.224759i
$153$	−24.9253			−2.01509
$154$	−2.37831	+	8.44652i	−0.191649	+	0.680640i
$155$	−31.6791			−2.54453
$156$		−	2.80296i		−	0.224416i
$157$			10.3114i			0.822936i	0.911424	+	0.411468i	$0.134984\pi$
$157$			10.3114i			0.822936i	−0.911424	+	0.411468i	$0.865016\pi$
$158$	−0.0681048			−0.00541813
$159$		−	27.0816i		−	2.14771i
$160$	−3.66969			−0.290115
$161$	6.91749	+	11.6929i	0.545175	+	0.921531i
$162$		−	0.0165472i		−	0.00130007i
$163$	−7.30778			−0.572389			−0.286195	−	0.958171i	$-0.592390\pi$
$163$	−7.30778			−0.572389			−0.286195	+	0.958171i	$0.592390\pi$
$164$	−12.0216			−0.938729
$165$	−24.6779	+	23.5546i	−1.92117	+	1.83372i
$166$		−	3.65253i		−	0.283492i
$167$	0.915824			0.0708686			0.0354343	−	0.999372i	$-0.488719\pi$
$167$	0.915824			0.0708686			0.0354343	+	0.999372i	$0.488719\pi$
$168$	−3.77595	−	6.38265i	−0.291321	−	0.492432i
$169$	1.00000			0.0769231
$170$	−18.8339			−1.44449
$171$	−13.4576			−1.02913
$172$		−	0.841340i		−	0.0641516i
$173$	−18.3425			−1.39456			−0.697279	−	0.716800i	$-0.745606\pi$
$173$	−18.3425			−1.39456			−0.697279	+	0.716800i	$0.745606\pi$
$174$		−	5.43182i		−	0.411785i
$175$	11.4057	+	19.2795i	0.862187	+	1.45739i
$176$	2.39918	−	2.28997i	0.180845	−	0.172613i
$177$	−8.87540			−0.667116
$178$	−15.6169			−1.17054
$179$	−12.3591			−0.923764			−0.461882	−	0.886941i	$-0.652826\pi$
$179$	−12.3591			−0.923764			−0.461882	+	0.886941i	$0.652826\pi$
$180$		−	17.8221i		−	1.32838i
$181$		−	7.92365i		−	0.588960i	−0.955658	−	0.294480i	$-0.904854\pi$
$181$		−	7.92365i		−	0.588960i	0.955658	−	0.294480i	$-0.0951464\pi$
$182$	2.27711	−	1.34713i	0.168791	−	0.0998560i
$183$		−	12.3172i		−	0.910514i
$184$		−	5.13498i		−	0.378555i
$185$			33.0190i			2.42760i
$186$			24.1969i			1.77421i
$187$	12.3132	−	11.7528i	0.900434	−	0.859446i
$188$		−	6.07678i		−	0.443195i
$189$	11.8498	−	7.01031i	0.861947	−	0.509925i
$190$	−10.1688			−0.737720
$191$	12.7866			0.925203			0.462601	−	0.886566i	$-0.346916\pi$
$191$	12.7866			0.925203			0.462601	+	0.886566i	$0.346916\pi$
$192$			2.80296i			0.202286i
$193$			12.2196i			0.879586i	0.898099	+	0.439793i	$0.144948\pi$
$193$			12.2196i			0.879586i	−0.898099	+	0.439793i	$0.855052\pi$
$194$	12.1836			0.874734
$195$	10.2860			0.736595
$196$	3.37047	−	6.13514i	0.240748	−	0.438224i
$197$			15.7548i			1.12249i	0.827651	+	0.561243i	$0.189677\pi$
$197$			15.7548i			1.12249i	−0.827651	+	0.561243i	$0.810323\pi$
$198$	11.1214	+	11.6518i	0.790362	+	0.828055i
$199$			19.9465i			1.41397i	0.707227	+	0.706987i	$0.249946\pi$
$199$			19.9465i			1.41397i	−0.707227	+	0.706987i	$0.750054\pi$
$200$		−	8.46663i		−	0.598681i
$201$		−	30.2576i		−	2.13421i
$202$			14.0868i			0.991146i
$203$	4.41279	−	2.61059i	0.309717	−	0.183227i
$204$			14.3856i			1.00719i
$205$		−	44.1155i		−	3.08116i
$206$	−14.7845			−1.03009
$207$	24.9384			1.73334
$208$	−1.00000			−0.0693375
$209$	6.64815	−	6.34553i	0.459862	−	0.438930i
$210$	23.4223	−	13.8566i	1.61629	−	0.956195i
$211$			2.52634i			0.173920i	0.996212	+	0.0869601i	$0.0277153\pi$
$211$			2.52634i			0.173920i	−0.996212	+	0.0869601i	$0.972285\pi$
$212$	−9.66179			−0.663574
$213$		−	2.91178i		−	0.199512i
$214$	3.27614			0.223952
$215$	3.08746			0.210563
$216$	−5.20388			−0.354079
$217$	−19.6575	+	11.6293i	−1.33444	+	0.789449i
$218$	−5.92460			−0.401264
$219$		−	44.2353i		−	2.98915i
$220$	8.40347	+	8.80424i	0.566562	+	0.593582i
$221$	−5.13228			−0.345234
$222$	25.2203			1.69268
$223$		−	13.3805i		−	0.896026i	−0.894027	−	0.448013i	$-0.852132\pi$
$223$		−	13.3805i		−	0.896026i	0.894027	−	0.448013i	$-0.147868\pi$
$224$	−2.27711	+	1.34713i	−0.152146	+	0.0900090i
$225$	41.1188			2.74125
$226$		−	14.7381i		−	0.980361i
$227$	−19.2279			−1.27620			−0.638099	−	0.769954i	$-0.720279\pi$
$227$	−19.2279			−1.27620			−0.638099	+	0.769954i	$0.720279\pi$
$228$			7.76703i			0.514384i
$229$			1.10489i			0.0730131i	0.999333	+	0.0365066i	$0.0116230\pi$
$229$			1.10489i			0.0730131i	−0.999333	+	0.0365066i	$0.988377\pi$
$230$	18.8438			1.24252
$231$	−6.66629	+	23.6752i	−0.438609	+	1.55772i
$232$	−1.93789			−0.127229
$233$			14.2561i			0.933949i	0.884271	+	0.466974i	$0.154656\pi$
$233$			14.2561i			0.933949i	−0.884271	+	0.466974i	$0.845344\pi$
$234$		−	4.85657i		−	0.317484i
$235$	22.2999			1.45469
$236$			3.16644i			0.206118i
$237$	−0.190895			−0.0124000
$238$	−11.6868	+	6.91386i	−0.757541	+	0.448159i
$239$			7.03614i			0.455130i	0.973763	+	0.227565i	$0.0730765\pi$
$239$			7.03614i			0.455130i	−0.973763	+	0.227565i	$0.926924\pi$
$240$	−10.2860			−0.663958
$241$	−18.1083			−1.16646			−0.583230	−	0.812307i	$-0.698212\pi$
$241$	−18.1083			−1.16646			−0.583230	+	0.812307i	$0.698212\pi$
$242$	−10.9881	−	0.512097i	−0.706340	−	0.0329189i
$243$			15.5653i			0.998512i
$244$	−4.39436			−0.281320
$245$	22.5141	+	12.3686i	1.43837	+	0.790200i
$246$	−33.6960			−2.14838
$247$	−2.77101			−0.176315
$248$	8.63265			0.548174
$249$		−	10.2379i		−	0.648800i
$250$	12.7215			0.804576
$251$		−	20.1509i		−	1.27191i	−0.771725	−	0.635956i	$-0.780606\pi$
$251$		−	20.1509i		−	1.27191i	0.771725	−	0.635956i	$-0.219394\pi$
$252$	−6.54244	−	11.0589i	−0.412135	−	0.696648i
$253$	−12.3197	+	11.7589i	−0.774534	+	0.739278i
$254$	−0.530947			−0.0333146
$255$	−52.7906			−3.30587
$256$	1.00000			0.0625000
$257$			8.73710i			0.545005i	0.962155	+	0.272503i	$0.0878513\pi$
$257$			8.73710i			0.545005i	−0.962155	+	0.272503i	$0.912149\pi$
$258$		−	2.35824i		−	0.146818i
$259$	12.1212	+	20.4889i	0.753172	+	1.27312i
$260$		−	3.66969i		−	0.227585i
$261$		−	9.41148i		−	0.582556i
$262$			2.20035i			0.135938i
$263$			23.5162i			1.45007i	0.688710	+	0.725037i	$0.258177\pi$
$263$			23.5162i			1.45007i	−0.688710	+	0.725037i	$0.741823\pi$
$264$	6.72479	−	6.41868i	0.413882	−	0.395042i
$265$		−	35.4558i		−	2.17803i
$266$	−6.30991	+	3.73292i	−0.386885	+	0.228880i
$267$	−43.7735			−2.67889
$268$	−10.7949			−0.659403
$269$			6.24824i			0.380962i	0.981691	+	0.190481i	$0.0610047\pi$
$269$			6.24824i			0.380962i	−0.981691	+	0.190481i	$0.938995\pi$
$270$		−	19.0966i		−	1.16218i
$271$	27.2079			1.65276			0.826381	−	0.563111i	$-0.190396\pi$
$271$	27.2079			1.65276			0.826381	+	0.563111i	$0.190396\pi$
$272$	5.13228			0.311190
$273$	6.38265	−	3.77595i	0.386295	−	0.228531i
$274$		−	14.1394i		−	0.854195i
$275$	−20.3129	+	19.3883i	−1.22492	+	1.16916i
$276$		−	14.3931i		−	0.866364i
$277$			28.8058i			1.73077i	0.501106	+	0.865386i	$0.332927\pi$
$277$			28.8058i			1.73077i	−0.501106	+	0.865386i	$0.667073\pi$
$278$		−	19.4965i		−	1.16932i
$279$			41.9250i			2.50999i
$280$	−4.94356	−	8.35630i	−0.295434	−	0.499384i
$281$		−	24.7299i		−	1.47526i	−0.675204	−	0.737631i	$-0.735944\pi$
$281$		−	24.7299i		−	1.47526i	0.675204	−	0.737631i	$-0.264056\pi$
$282$		−	17.0330i		−	1.01430i
$283$	−10.6559			−0.633428			−0.316714	−	0.948521i	$-0.602580\pi$
$283$	−10.6559			−0.633428			−0.316714	+	0.948521i	$0.602580\pi$
$284$	−1.03883			−0.0616429
$285$	−28.5026			−1.68835
$286$	2.28997	+	2.39918i	0.135409	+	0.141866i
$287$	−16.1947	−	27.3745i	−0.955941	−	1.61587i
$288$			4.85657i			0.286176i
$289$	9.34029			0.549429
$290$		−	7.11145i		−	0.417599i
$291$	34.1502			2.00192
$292$	−15.7817			−0.923552
$293$	−2.34402			−0.136939			−0.0684696	−	0.997653i	$-0.521812\pi$
$293$	−2.34402			−0.136939			−0.0684696	+	0.997653i	$0.521812\pi$
$294$	9.44729	−	17.1965i	0.550977	−	1.00292i
$295$	−11.6199			−0.676535
$296$		−	8.99776i		−	0.522984i
$297$	11.9167	+	12.4850i	0.691478	+	0.724455i
$298$	17.3215			1.00340
$299$	5.13498			0.296963
$300$		−	23.7316i		−	1.37014i
$301$	1.91582	−	1.13340i	0.110426	−	0.0653278i
$302$	−1.70260			−0.0979735
$303$			39.4848i			2.26834i
$304$	2.77101			0.158929
$305$		−	16.1260i		−	0.923369i
$306$			24.9253i			1.42488i
$307$	7.00258			0.399658			0.199829	−	0.979831i	$-0.435961\pi$
$307$	7.00258			0.399658			0.199829	+	0.979831i	$0.435961\pi$
$308$	8.44652	+	2.37831i	0.481285	+	0.135517i
$309$	−41.4403			−2.35746
$310$			31.6791i			1.79925i
$311$			8.32828i			0.472254i	0.971722	+	0.236127i	$0.0758781\pi$
$311$			8.32828i			0.472254i	−0.971722	+	0.236127i	$0.924122\pi$
$312$	−2.80296			−0.158686
$313$		−	7.99184i		−	0.451725i	−0.974159	−	0.225863i	$-0.927480\pi$
$313$		−	7.99184i		−	0.451725i	0.974159	−	0.225863i	$-0.0725201\pi$
$314$	10.3114			0.581904
$315$	40.5829	−	24.0087i	2.28659	−	1.35274i
$316$			0.0681048i			0.00383120i
$317$	−19.5414			−1.09756			−0.548778	−	0.835968i	$-0.684907\pi$
$317$	−19.5414			−1.09756			−0.548778	+	0.835968i	$0.684907\pi$
$318$	−27.0816			−1.51866
$319$	4.43770	+	4.64933i	0.248463	+	0.260313i
$320$			3.66969i			0.205142i
$321$	9.18288			0.512538
$322$	11.6929	−	6.91749i	0.651621	−	0.385497i
$323$	14.2216			0.791312
$324$	−0.0165472			−0.000919288
$325$	8.46663			0.469644
$326$			7.30778i			0.404740i
$327$	−16.6064			−0.918336
$328$			12.0216i			0.663781i
$329$	13.8375	−	8.18622i	0.762886	−	0.451321i
$330$	23.5546	+	24.6779i	1.29664	+	1.35847i
$331$	−9.95811			−0.547347			−0.273674	−	0.961823i	$-0.588239\pi$
$331$	−9.95811			−0.547347			−0.273674	+	0.961823i	$0.588239\pi$
$332$	−3.65253			−0.200459
$333$	43.6982			2.39465
$334$		−	0.915824i		−	0.0501117i
$335$		−	39.6139i		−	2.16434i
$336$	−6.38265	+	3.77595i	−0.348202	+	0.205995i
$337$			26.4785i			1.44238i	0.692740	+	0.721188i	$0.256403\pi$
$337$			26.4785i			1.44238i	−0.692740	+	0.721188i	$0.743597\pi$
$338$		−	1.00000i		−	0.0543928i
$339$		−	41.3102i		−	2.24366i
$340$			18.8339i			1.02141i
$341$	−19.7685	−	20.7112i	−1.07052	−	1.12158i
$342$			13.4576i			0.727705i
$343$	18.5109	−	0.589895i	0.999493	−	0.0318513i
$344$	−0.841340			−0.0453620
$345$	52.8183			2.84364
$346$			18.3425i			0.986101i
$347$			0.660075i			0.0354347i	0.999843	+	0.0177173i	$0.00563990\pi$
$347$			0.660075i			0.0354347i	−0.999843	+	0.0177173i	$0.994360\pi$
$348$	−5.43182			−0.291176
$349$	−10.1681			−0.544288			−0.272144	−	0.962257i	$-0.587733\pi$
$349$	−10.1681			−0.544288			−0.272144	+	0.962257i	$0.587733\pi$
$350$	19.2795	−	11.4057i	1.03053	−	0.609659i
$351$		−	5.20388i		−	0.277763i
$352$	−2.28997	−	2.39918i	−0.122056	−	0.127877i
$353$			8.67403i			0.461672i	0.972993	+	0.230836i	$0.0741461\pi$
$353$			8.67403i			0.461672i	−0.972993	+	0.230836i	$0.925854\pi$
$354$			8.87540i			0.471722i
$355$		−	3.81217i		−	0.202329i
$356$			15.6169i			0.827694i
$357$	−32.7575	+	19.3792i	−1.73371	+	1.02566i
$358$			12.3591i			0.653200i
$359$			19.4370i			1.02585i	0.858435	+	0.512923i	$0.171437\pi$
$359$			19.4370i			1.02585i	−0.858435	+	0.512923i	$0.828563\pi$
$360$	−17.8221			−0.939307
$361$	−11.3215			−0.595867
$362$	−7.92365			−0.416458
$363$	−30.7991	−	1.43539i	−1.61653	−	0.0753383i
$364$	−1.34713	−	2.27711i	−0.0706089	−	0.119353i
$365$		−	57.9138i		−	3.03135i
$366$	−12.3172			−0.643831
$367$		−	13.4868i		−	0.704003i	−0.935999	−	0.352001i	$-0.885501\pi$
$367$		−	13.4868i		−	0.704003i	0.935999	−	0.352001i	$-0.114499\pi$
$368$	−5.13498			−0.267679
$369$	−58.3837			−3.03933
$370$	33.0190			1.71658
$371$	−13.0157	−	22.0010i	−0.675741	−	1.14223i
$372$	24.1969			1.25455
$373$		−	12.2451i		−	0.634025i	−0.948421	−	0.317012i	$-0.897320\pi$
$373$		−	12.2451i		−	0.634025i	0.948421	−	0.317012i	$-0.102680\pi$
$374$	−11.7528	−	12.3132i	−0.607720	−	0.636703i
$375$	35.6577			1.84136
$376$	−6.07678			−0.313386
$377$		−	1.93789i		−	0.0998063i
$378$	−7.01031	−	11.8498i	−0.360571	−	0.609489i
$379$	30.5025			1.56681			0.783404	−	0.621512i	$-0.213481\pi$
$379$	30.5025			1.56681			0.783404	+	0.621512i	$0.213481\pi$
$380$			10.1688i			0.521647i
$381$	−1.48822			−0.0762439
$382$		−	12.7866i		−	0.654217i
$383$			24.1492i			1.23397i	0.786975	+	0.616984i	$0.211646\pi$
$383$			24.1492i			1.23397i	−0.786975	+	0.616984i	$0.788354\pi$
$384$	2.80296			0.143038
$385$	−8.72764	+	30.9961i	−0.444802	+	1.57971i
$386$	12.2196			0.621961
$387$		−	4.08602i		−	0.207704i
$388$		−	12.1836i		−	0.618530i
$389$	14.4295			0.731606			0.365803	−	0.930692i	$-0.380794\pi$
$389$	14.4295			0.731606			0.365803	+	0.930692i	$0.380794\pi$
$390$		−	10.2860i		−	0.520851i
$391$	−26.3541			−1.33279
$392$	−6.13514	−	3.37047i	−0.309871	−	0.170235i
$393$			6.16748i			0.311108i
$394$	15.7548			0.793717
$395$	−0.249924			−0.0125750
$396$	11.6518	−	11.1214i	0.585523	−	0.558870i
$397$			23.7305i			1.19100i	0.803356	+	0.595499i	$0.203046\pi$
$397$			23.7305i			1.19100i	−0.803356	+	0.595499i	$0.796954\pi$
$398$	19.9465			0.999830
$399$	−17.6864	+	10.4632i	−0.885428	+	0.523816i
$400$	−8.46663			−0.423332
$401$	−13.0436			−0.651365			−0.325683	−	0.945479i	$-0.605594\pi$
$401$	−13.0436			−0.651365			−0.325683	+	0.945479i	$0.605594\pi$
$402$	−30.2576			−1.50911
$403$			8.63265i			0.430023i
$404$	14.0868			0.700846
$405$		−	0.0607230i		−	0.00301735i
$406$	−2.61059	−	4.41279i	−0.129561	−	0.219003i
$407$	−21.5872	+	20.6046i	−1.07004	+	1.02133i
$408$	14.3856			0.712191
$409$	−7.37336			−0.364589			−0.182295	−	0.983244i	$-0.558352\pi$
$409$	−7.37336			−0.364589			−0.182295	+	0.983244i	$0.558352\pi$
$410$	−44.1155			−2.17871
$411$		−	39.6323i		−	1.95492i
$412$			14.7845i			0.728380i
$413$	−7.21034	+	4.26561i	−0.354798	+	0.209897i
$414$		−	24.9384i		−	1.22565i
$415$		−	13.4037i		−	0.657960i
$416$			1.00000i			0.0490290i
$417$		−	54.6480i		−	2.67612i
$418$	−6.34553	−	6.64815i	−0.310370	−	0.325172i
$419$		−	22.3434i		−	1.09155i	−0.837932	−	0.545774i	$-0.816236\pi$
$419$		−	22.3434i		−	1.09155i	0.837932	−	0.545774i	$-0.183764\pi$
$420$	−13.8566	−	23.4223i	−0.676132	−	1.14289i
$421$	−5.67014			−0.276346			−0.138173	−	0.990408i	$-0.544123\pi$
$421$	−5.67014			−0.276346			−0.138173	+	0.990408i	$0.544123\pi$
$422$	2.52634			0.122980
$423$		−	29.5123i		−	1.43494i
$424$			9.66179i			0.469218i
$425$	−43.4531			−2.10779
$426$	−2.91178			−0.141076
$427$	−5.91978	−	10.0065i	−0.286478	−	0.484246i
$428$		−	3.27614i		−	0.158358i
$429$	6.41868	+	6.72479i	0.309897	+	0.324676i
$430$		−	3.08746i		−	0.148890i
$431$		−	28.3827i		−	1.36715i	−0.729882	−	0.683573i	$-0.760425\pi$
$431$		−	28.3827i		−	1.36715i	0.729882	−	0.683573i	$-0.239575\pi$
$432$			5.20388i			0.250372i
$433$			13.0366i			0.626499i	0.949671	+	0.313249i	$0.101418\pi$
$433$			13.0366i			0.626499i	−0.949671	+	0.313249i	$0.898582\pi$
$434$	11.6293	+	19.6575i	0.558225	+	0.943590i
$435$		−	19.9331i		−	0.955718i
$436$			5.92460i			0.283737i
$437$	−14.2291			−0.680670
$438$	−44.2353			−2.11365
$439$	18.8916			0.901645			0.450822	−	0.892614i	$-0.351131\pi$
$439$	18.8916			0.901645			0.450822	+	0.892614i	$0.351131\pi$
$440$	8.80424	−	8.40347i	0.419726	−	0.400620i
$441$	16.3689	−	29.7957i	0.779473	−	1.41884i
$442$			5.13228i			0.244118i
$443$	−26.0533			−1.23783			−0.618914	−	0.785459i	$-0.712427\pi$
$443$	−26.0533			−1.23783			−0.618914	+	0.785459i	$0.712427\pi$
$444$		−	25.2203i		−	1.19690i
$445$	−57.3092			−2.71672
$446$	−13.3805			−0.633586
$447$	48.5513			2.29640
$448$	1.34713	+	2.27711i	0.0636460	+	0.107583i
$449$	3.06370			0.144585			0.0722925	−	0.997383i	$-0.476968\pi$
$449$	3.06370			0.144585			0.0722925	+	0.997383i	$0.476968\pi$
$450$		−	41.1188i		−	1.93836i
$451$	28.8419	−	27.5291i	1.35811	−	1.29629i
$452$	−14.7381			−0.693220
$453$	−4.77231			−0.224223
$454$			19.2279i			0.902409i
$455$	8.35630	−	4.94356i	0.391749	−	0.231758i
$456$	7.76703			0.363725
$457$			17.3459i			0.811405i	0.914005	+	0.405702i	$0.132973\pi$
$457$			17.3459i			0.811405i	−0.914005	+	0.405702i	$0.867027\pi$
$458$	1.10489			0.0516281
$459$			26.7078i			1.24661i
$460$		−	18.8438i		−	0.878596i
$461$	−6.50454			−0.302947			−0.151473	−	0.988461i	$-0.548402\pi$
$461$	−6.50454			−0.302947			−0.151473	+	0.988461i	$0.548402\pi$
$462$	23.6752	+	6.66629i	1.10147	+	0.310144i
$463$	−30.9453			−1.43815			−0.719075	−	0.694933i	$-0.755434\pi$
$463$	−30.9453			−1.43815			−0.719075	+	0.694933i	$0.755434\pi$
$464$			1.93789i			0.0899642i
$465$			88.7953i			4.11778i
$466$	14.2561			0.660401
$467$		−	35.4509i		−	1.64047i	−0.572024	−	0.820237i	$-0.693842\pi$
$467$		−	35.4509i		−	1.64047i	0.572024	−	0.820237i	$-0.306158\pi$
$468$	−4.85657			−0.224495
$469$	−14.5421	−	24.5812i	−0.671494	−	1.13505i
$470$		−	22.2999i		−	1.02862i
$471$	28.9023			1.33175
$472$	3.16644			0.145747
$473$	1.92664	+	2.01852i	0.0885870	+	0.0928118i
$474$			0.190895i			0.00876810i
$475$	−23.4612			−1.07647
$476$	6.91386	+	11.6868i	0.316896	+	0.535662i
$477$	−46.9231			−2.14846
$478$	7.03614			0.321826
$479$	7.15430			0.326888			0.163444	−	0.986553i	$-0.447740\pi$
$479$	7.15430			0.326888			0.163444	+	0.986553i	$0.447740\pi$
$480$			10.2860i			0.469489i
$481$	8.99776			0.410262
$482$			18.1083i			0.824812i
$483$	32.7747	−	19.3894i	1.49130	−	0.882249i
$484$	−0.512097	+	10.9881i	−0.0232772	+	0.499458i
$485$	44.7102			2.03018
$486$	15.5653			0.706054
$487$	21.8726			0.991142			0.495571	−	0.868568i	$-0.334959\pi$
$487$	21.8726			0.991142			0.495571	+	0.868568i	$0.334959\pi$
$488$			4.39436i			0.198923i
$489$			20.4834i			0.926291i
$490$	12.3686	−	22.5141i	0.558756	−	1.01708i
$491$		−	22.5588i		−	1.01807i	−0.860747	−	0.509033i	$-0.830003\pi$
$491$		−	22.5588i		−	1.01807i	0.860747	−	0.509033i	$-0.169997\pi$
$492$			33.6960i			1.51913i
$493$			9.94578i			0.447935i
$494$			2.77101i			0.124674i
$495$	40.8120	+	42.7584i	1.83436	+	1.92185i
$496$		−	8.63265i		−	0.387617i
$497$	−1.39943	−	2.36552i	−0.0627732	−	0.106108i
$498$	−10.2379			−0.458771
$499$	−23.5389			−1.05375			−0.526874	−	0.849943i	$-0.676636\pi$
$499$	−23.5389			−1.05375			−0.526874	+	0.849943i	$0.676636\pi$
$500$		−	12.7215i		−	0.568921i
$501$		−	2.56702i		−	0.114686i
$502$	−20.1509			−0.899378
$503$	1.09095			0.0486431			0.0243215	−	0.999704i	$-0.492257\pi$
$503$	1.09095			0.0486431			0.0243215	+	0.999704i	$0.492257\pi$
$504$	−11.0589	+	6.54244i	−0.492605	+	0.291423i
$505$			51.6943i			2.30037i
$506$	11.7589	+	12.3197i	0.522748	+	0.547678i
$507$		−	2.80296i		−	0.124484i
$508$			0.530947i			0.0235570i
$509$			36.5658i			1.62075i	0.585910	+	0.810376i	$0.300737\pi$
$509$			36.5658i			1.62075i	−0.585910	+	0.810376i	$0.699263\pi$
$510$			52.7906i			2.33760i
$511$	−21.2600	−	35.9366i	−0.940486	−	1.58974i
$512$		−	1.00000i		−	0.0441942i
$513$			14.4200i			0.636660i
$514$	8.73710			0.385377
$515$	−54.2546			−2.39074
$516$	−2.35824			−0.103816
$517$	13.9156	+	14.5793i	0.612009	+	0.641195i
$518$	20.4889	−	12.1212i	0.900230	−	0.532573i
$519$			51.4134i			2.25680i
$520$	−3.66969			−0.160927
$521$			4.37822i			0.191813i	0.995390	+	0.0959065i	$0.0305750\pi$
$521$			4.37822i			0.191813i	−0.995390	+	0.0959065i	$0.969425\pi$
$522$	−9.41148			−0.411929
$523$	2.97144			0.129932			0.0649659	−	0.997887i	$-0.479306\pi$
$523$	2.97144			0.129932			0.0649659	+	0.997887i	$0.479306\pi$
$524$	2.20035			0.0961226
$525$	54.0395	−	31.9696i	2.35848	−	1.39527i
$526$	23.5162			1.02536
$527$		−	44.3052i		−	1.92996i
$528$	−6.41868	−	6.72479i	−0.279337	−	0.292659i
$529$	3.36798			0.146434
$530$	−35.4558			−1.54010
$531$			15.3780i			0.667350i
$532$	3.73292	+	6.30991i	0.161843	+	0.273569i
$533$	−12.0216			−0.520713
$534$			43.7735i			1.89426i
$535$	12.0224			0.519775
$536$			10.7949i			0.466268i
$537$			34.6421i			1.49492i
$538$	6.24824			0.269381
$539$	5.96291	+	22.4376i	0.256841	+	0.966454i
$540$	−19.0966			−0.821788
$541$		−	14.2462i		−	0.612491i	−0.951953	−	0.306245i	$-0.900927\pi$
$541$		−	14.2462i		−	0.612491i	0.951953	−	0.306245i	$-0.0990728\pi$
$542$		−	27.2079i		−	1.16868i
$543$	−22.2096			−0.953107
$544$		−	5.13228i		−	0.220045i
$545$	−21.7414			−0.931301
$546$	−3.77595	−	6.38265i	−0.161596	−	0.273152i
$547$		−	16.8944i		−	0.722352i	−0.932498	−	0.361176i	$-0.882375\pi$
$547$		−	16.8944i		−	0.722352i	0.932498	−	0.361176i	$-0.117625\pi$
$548$	−14.1394			−0.604007
$549$	−21.3415			−0.910834
$550$	19.3883	+	20.3129i	0.826720	+	0.866147i
$551$			5.36991i			0.228766i
$552$	−14.3931			−0.612612
$553$	−0.155082	+	0.0917462i	−0.00659477	+	0.00390144i
$554$	28.8058			1.22384
$555$	92.5508			3.92856
$556$	−19.4965			−0.826838
$557$			27.4230i			1.16195i	0.813922	+	0.580974i	$0.197328\pi$
$557$			27.4230i			1.16195i	−0.813922	+	0.580974i	$0.802672\pi$
$558$	41.9250			1.77483
$559$		−	0.841340i		−	0.0355849i
$560$	−8.35630	+	4.94356i	−0.353118	+	0.208903i
$561$	−32.9425	−	34.5135i	−1.39083	−	1.45716i
$562$	−24.7299			−1.04317
$563$	−13.5156			−0.569613			−0.284807	−	0.958585i	$-0.591929\pi$
$563$	−13.5156			−0.569613			−0.284807	+	0.958585i	$0.591929\pi$
$564$	−17.0330			−0.717217
$565$		−	54.0841i		−	2.27534i
$566$			10.6559i			0.447901i
$567$	−0.0222912	−	0.0376798i	−0.000936144	−	0.00158240i
$568$			1.03883i			0.0435881i
$569$		−	21.3313i		−	0.894255i	−0.894470	−	0.447127i	$-0.852447\pi$
$569$		−	21.3313i		−	0.894255i	0.894470	−	0.447127i	$-0.147553\pi$
$570$			28.5026i			1.19384i
$571$			8.47573i			0.354698i	0.984148	+	0.177349i	$0.0567522\pi$
$571$			8.47573i			0.354698i	−0.984148	+	0.177349i	$0.943248\pi$
$572$	2.39918	−	2.28997i	0.100315	−	0.0957484i
$573$		−	35.8402i		−	1.49724i
$574$	−27.3745	+	16.1947i	−1.14259	+	0.675952i
$575$	43.4760			1.81307
$576$	4.85657			0.202357
$577$			13.8458i			0.576410i	0.957569	+	0.288205i	$0.0930585\pi$
$577$			13.8458i			0.576410i	−0.957569	+	0.288205i	$0.906942\pi$
$578$		−	9.34029i		−	0.388505i
$579$	34.2510			1.42342
$580$	−7.11145			−0.295287
$581$	−4.92045	−	8.31723i	−0.204134	−	0.345057i
$582$		−	34.1502i		−	1.41557i
$583$	23.1803	−	22.1252i	0.960031	−	0.916331i
$584$			15.7817i			0.653050i
$585$		−	17.8221i		−	0.736853i
$586$			2.34402i			0.0968307i
$587$		−	26.5326i		−	1.09512i	−0.836767	−	0.547559i	$-0.815557\pi$
$587$		−	26.5326i		−	1.09512i	0.836767	−	0.547559i	$-0.184443\pi$
$588$	−17.1965	−	9.44729i	−0.709173	−	0.389600i
$589$		−	23.9212i		−	0.985655i
$590$			11.6199i			0.478382i
$591$	44.1601			1.81650
$592$	−8.99776			−0.369806
$593$	−28.6695			−1.17731			−0.588657	−	0.808383i	$-0.700343\pi$
$593$	−28.6695			−1.17731			−0.588657	+	0.808383i	$0.700343\pi$
$594$	12.4850	−	11.9167i	0.512267	−	0.488949i
$595$	−42.8868	+	25.3717i	−1.75819	+	1.04014i
$596$		−	17.3215i		−	0.709514i
$597$	55.9093			2.28822
$598$		−	5.13498i		−	0.209985i
$599$	30.8324			1.25978			0.629888	−	0.776686i	$-0.283101\pi$
$599$	30.8324			1.25978			0.629888	+	0.776686i	$0.283101\pi$
$600$	−23.7316			−0.968839
$601$	28.1337			1.14760			0.573799	−	0.818996i	$-0.305469\pi$
$601$	28.1337			1.14760			0.573799	+	0.818996i	$0.305469\pi$
$602$	−1.13340	−	1.91582i	−0.0461938	−	0.0780832i
$603$	−52.4261			−2.13496
$604$			1.70260i			0.0692777i
$605$	−40.3228	−	1.87924i	−1.63936	−	0.0764019i
$606$	39.4848			1.60396
$607$	35.2523			1.43085			0.715423	−	0.698691i	$-0.246234\pi$
$607$	35.2523			1.43085			0.715423	+	0.698691i	$0.246234\pi$
$608$		−	2.77101i		−	0.112379i
$609$	−7.31737	−	12.3688i	−0.296515	−	0.501211i
$610$	−16.1260			−0.652921
$611$		−	6.07678i		−	0.245840i
$612$	24.9253			1.00754
$613$			4.57698i			0.184862i	0.995719	+	0.0924312i	$0.0294638\pi$
$613$			4.57698i			0.184862i	−0.995719	+	0.0924312i	$0.970536\pi$
$614$		−	7.00258i		−	0.282601i
$615$	−123.654			−4.98621
$616$	2.37831	−	8.44652i	0.0958246	−	0.340320i
$617$	24.8817			1.00170			0.500851	−	0.865534i	$-0.333021\pi$
$617$	24.8817			1.00170			0.500851	+	0.865534i	$0.333021\pi$
$618$			41.4403i			1.66698i
$619$			22.7147i			0.912982i	0.889728	+	0.456491i	$0.150894\pi$
$619$			22.7147i			0.912982i	−0.889728	+	0.456491i	$0.849106\pi$
$620$	31.6791			1.27227
$621$		−	26.7218i		−	1.07231i
$622$	8.32828			0.333934
$623$	−35.5614	+	21.0380i	−1.42474	+	0.842870i
$624$			2.80296i			0.112208i
$625$	4.35069			0.174028
$626$	−7.99184			−0.319418
$627$	−17.7863	−	18.6345i	−0.710315	−	0.744190i
$628$		−	10.3114i		−	0.411468i
$629$	−46.1790			−1.84128
$630$	−24.0087	−	40.5829i	−0.956530	−	1.61686i
$631$	6.97695			0.277748			0.138874	−	0.990310i	$-0.455652\pi$
$631$	6.97695			0.277748			0.138874	+	0.990310i	$0.455652\pi$
$632$	0.0681048			0.00270907
$633$	7.08121			0.281453
$634$			19.5414i			0.776090i
$635$	−1.94841			−0.0773203
$636$			27.0816i			1.07385i
$637$	3.37047	−	6.13514i	0.133543	−	0.243083i
$638$	4.64933	−	4.43770i	0.184069	−	0.175690i
$639$	−5.04513			−0.199582
$640$	3.66969			0.145057
$641$	−16.9540			−0.669644			−0.334822	−	0.942281i	$-0.608676\pi$
$641$	−16.9540			−0.669644			−0.334822	+	0.942281i	$0.608676\pi$
$642$		−	9.18288i		−	0.362419i
$643$			2.75669i			0.108713i	0.998522	+	0.0543567i	$0.0173108\pi$
$643$			2.75669i			0.108713i	−0.998522	+	0.0543567i	$0.982689\pi$
$644$	−6.91749	−	11.6929i	−0.272587	−	0.460765i
$645$		−	8.65401i		−	0.340751i
$646$		−	14.2216i		−	0.559542i
$647$		−	20.1497i		−	0.792168i	−0.918214	−	0.396084i	$-0.870369\pi$
$647$		−	20.1497i		−	0.792168i	0.918214	−	0.396084i	$-0.129631\pi$
$648$			0.0165472i			0.000650035i
$649$	−7.25105	−	7.59685i	−0.284629	−	0.298203i
$650$		−	8.46663i		−	0.332089i
$651$	32.5965	+	55.0991i	1.27756	+	2.15950i
$652$	7.30778			0.286195
$653$	−46.6365			−1.82503			−0.912514	−	0.409045i	$-0.865862\pi$
$653$	−46.6365			−1.82503			−0.912514	+	0.409045i	$0.865862\pi$
$654$			16.6064i			0.649361i
$655$			8.07459i			0.315500i
$656$	12.0216			0.469364
$657$	−76.6447			−2.99020
$658$	−8.18622	−	13.8375i	−0.319132	−	0.539442i
$659$		−	3.94225i		−	0.153568i	−0.997048	−	0.0767841i	$-0.975535\pi$
$659$		−	3.94225i		−	0.153568i	0.997048	−	0.0767841i	$-0.0244652\pi$
$660$	24.6779	−	23.5546i	0.960586	−	0.916861i
$661$		−	0.0718953i		−	0.00279640i	−0.999999	−	0.00139820i	$-0.999555\pi$
$661$		−	0.0718953i		−	0.00279640i	0.999999	−	0.00139820i	$-0.000445062\pi$
$662$			9.95811i			0.387033i
$663$			14.3856i			0.558689i
$664$			3.65253i			0.141746i
$665$	−23.1554	+	13.6987i	−0.897928	+	0.531211i
$666$		−	43.6982i		−	1.69327i
$667$		−	9.95101i		−	0.385305i
$668$	−0.915824			−0.0354343
$669$	−37.5050			−1.45003
$670$	−39.6139			−1.53042
$671$	10.5429	−	10.0629i	0.407002	−	0.388476i
$672$	3.77595	+	6.38265i	0.145661	+	0.246216i
$673$			31.1588i			1.20108i	0.799593	+	0.600542i	$0.205049\pi$
$673$			31.1588i			1.20108i	−0.799593	+	0.600542i	$0.794951\pi$
$674$	26.4785			1.01991
$675$		−	44.0593i		−	1.69584i
$676$	−1.00000			−0.0384615
$677$	26.1273			1.00415			0.502076	−	0.864824i	$-0.332570\pi$
$677$	26.1273			1.00415			0.502076	+	0.864824i	$0.332570\pi$
$678$	−41.3102			−1.58651
$679$	27.7435	−	16.4130i	1.06470	−	0.629871i
$680$	18.8339			0.722246
$681$			53.8949i			2.06526i
$682$	−20.7112	+	19.7685i	−0.793075	+	0.756974i
$683$	38.5430			1.47481			0.737404	−	0.675452i	$-0.236051\pi$
$683$	38.5430			1.47481			0.737404	+	0.675452i	$0.236051\pi$
$684$	13.4576			0.514565
$685$		−	51.8874i		−	1.98252i
$686$	−0.589895	−	18.5109i	−0.0225223	−	0.706748i
$687$	3.09696			0.118156
$688$			0.841340i			0.0320758i
$689$	−9.66179			−0.368085
$690$		−	52.8183i		−	2.01076i
$691$		−	21.7195i		−	0.826249i	−0.910675	−	0.413124i	$-0.864437\pi$
$691$		−	21.7195i		−	0.826249i	0.910675	−	0.413124i	$-0.135563\pi$
$692$	18.3425			0.697279
$693$	41.0211	+	11.5504i	1.55826	+	0.438763i
$694$	0.660075			0.0250561
$695$		−	71.5463i		−	2.71391i
$696$			5.43182i			0.205892i
$697$	61.6982			2.33698
$698$			10.1681i			0.384870i
$699$	39.9593			1.51140
$700$	−11.4057	−	19.2795i	−0.431094	−	0.728695i
$701$		−	12.5975i		−	0.475803i	−0.971289	−	0.237901i	$-0.923540\pi$
$701$		−	12.5975i		−	0.475803i	0.971289	−	0.237901i	$-0.0764595\pi$
$702$	−5.20388			−0.196408
$703$	−24.9329			−0.940363
$704$	−2.39918	+	2.28997i	−0.0904224	+	0.0863064i
$705$		−	62.5057i		−	2.35410i
$706$	8.67403			0.326452
$707$	18.9768	+	32.0773i	0.713697	+	1.20639i
$708$	8.87540			0.333558
$709$	6.67654			0.250743			0.125371	−	0.992110i	$-0.459988\pi$
$709$	6.67654			0.250743			0.125371	+	0.992110i	$0.459988\pi$
$710$	−3.81217			−0.143068
$711$			0.330756i			0.0124043i
$712$	15.6169			0.585268
$713$			44.3284i			1.66011i
$714$	19.3792	+	32.7575i	0.725250	+	1.22592i
$715$	8.40347	+	8.80424i	0.314272	+	0.329260i
$716$	12.3591			0.461882
$717$	19.7220			0.736532
$718$	19.4370			0.725382
$719$		−	14.4354i		−	0.538351i	−0.963091	−	0.269175i	$-0.913249\pi$
$719$		−	14.4354i		−	0.538351i	0.963091	−	0.269175i	$-0.0867511\pi$
$720$			17.8221i			0.664191i
$721$	−33.6660	+	19.9167i	−1.25379	+	0.741736i
$722$			11.3215i			0.421342i
$723$			50.7569i			1.88767i
$724$			7.92365i			0.294480i
$725$		−	16.4074i		−	0.609355i
$726$	−1.43539	+	30.7991i	−0.0532722	+	1.14306i
$727$		−	40.0421i		−	1.48508i	−0.669802	−	0.742540i	$-0.733621\pi$
$727$		−	40.0421i		−	1.48508i	0.669802	−	0.742540i	$-0.266379\pi$
$728$	−2.27711	+	1.34713i	−0.0843954	+	0.0499280i
$729$	43.6784			1.61772
$730$	−57.9138			−2.14349
$731$			4.31799i			0.159707i
$732$			12.3172i			0.455257i
$733$	25.8157			0.953525			0.476763	−	0.879032i	$-0.341810\pi$
$733$	25.8157			0.953525			0.476763	+	0.879032i	$0.341810\pi$
$734$	−13.4868			−0.497805
$735$	34.6686	−	63.1059i	1.27877	−	2.32770i
$736$			5.13498i			0.189278i
$737$	25.8989	−	24.7200i	0.953997	−	0.910571i
$738$			58.3837i			2.14913i
$739$			21.3556i			0.785578i	0.919629	+	0.392789i	$0.128490\pi$
$739$			21.3556i			0.785578i	−0.919629	+	0.392789i	$0.871510\pi$
$740$		−	33.0190i		−	1.21380i
$741$			7.76703i			0.285329i
$742$	−22.0010	+	13.0157i	−0.807681	+	0.477821i
$743$		−	14.5876i		−	0.535168i	−0.963535	−	0.267584i	$-0.913775\pi$
$743$		−	14.5876i		−	0.535168i	0.963535	−	0.267584i	$-0.0862253\pi$
$744$		−	24.1969i		−	0.887103i
$745$	63.5644			2.32882
$746$	−12.2451			−0.448323
$747$	−17.7388			−0.649028
$748$	−12.3132	+	11.7528i	−0.450217	+	0.429723i
$749$	7.46014	−	4.41339i	0.272587	−	0.161262i
$750$		−	35.6577i		−	1.30204i
$751$	34.4309			1.25640			0.628201	−	0.778051i	$-0.283792\pi$
$751$	34.4309			1.25640			0.628201	+	0.778051i	$0.283792\pi$
$752$			6.07678i			0.221597i
$753$	−56.4820			−2.05832
$754$	−1.93789			−0.0705737
$755$	−6.24801			−0.227388
$756$	−11.8498	+	7.01031i	−0.430974	+	0.254963i
$757$	34.7137			1.26169			0.630846	−	0.775908i	$-0.282708\pi$
$757$	34.7137			1.26169			0.630846	+	0.775908i	$0.282708\pi$
$758$		−	30.5025i		−	1.10790i
$759$	32.9598	+	34.5316i	1.19636	+	1.25342i
$760$	10.1688			0.368860
$761$	−14.3807			−0.521300			−0.260650	−	0.965433i	$-0.583937\pi$
$761$	−14.3807			−0.521300			−0.260650	+	0.965433i	$0.583937\pi$
$762$			1.48822i			0.0539125i
$763$	−13.4910	+	7.98121i	−0.488406	+	0.288939i
$764$	−12.7866			−0.462601
$765$			91.4680i			3.30703i
$766$	24.1492			0.872548
$767$			3.16644i			0.114334i
$768$		−	2.80296i		−	0.101143i
$769$	−28.0764			−1.01246			−0.506231	−	0.862398i	$-0.668962\pi$
$769$	−28.0764			−1.01246			−0.506231	+	0.862398i	$0.668962\pi$
$770$	30.9961	+	8.72764i	1.11702	+	0.314522i
$771$	24.4897			0.881975
$772$		−	12.2196i		−	0.439793i
$773$		−	43.4463i		−	1.56266i	−0.624120	−	0.781328i	$-0.714543\pi$
$773$		−	43.4463i		−	1.56266i	0.624120	−	0.781328i	$-0.285457\pi$
$774$	−4.08602			−0.146869
$775$			73.0894i			2.62545i
$776$	−12.1836			−0.437367
$777$	57.4295	−	33.9751i	2.06027	−	1.21885i
$778$		−	14.4295i		−	0.517324i
$779$	33.3120			1.19353
$780$	−10.2860			−0.368297
$781$	2.49233	−	2.37888i	0.0891824	−	0.0851229i
$782$			26.3541i			0.942422i
$783$	−10.0845			−0.360392
$784$	−3.37047	+	6.13514i	−0.120374	+	0.219112i
$785$	37.8395			1.35055
$786$	6.16748			0.219987
$787$	−1.57856			−0.0562695			−0.0281347	−	0.999604i	$-0.508957\pi$
$787$	−1.57856			−0.0562695			−0.0281347	+	0.999604i	$0.508957\pi$
$788$		−	15.7548i		−	0.561243i
$789$	65.9150			2.34664
$790$			0.249924i			0.00889189i
$791$	−19.8541	−	33.5602i	−0.705931	−	1.19326i
$792$	−11.1214	−	11.6518i	−0.395181	−	0.414027i
$793$	−4.39436			−0.156048
$794$	23.7305			0.842162
$795$	−99.3810			−3.52468
$796$		−	19.9465i		−	0.706987i
$797$		−	25.6976i		−	0.910254i	−0.890426	−	0.455127i	$-0.849594\pi$
$797$		−	25.6976i		−	0.910254i	0.890426	−	0.455127i	$-0.150406\pi$
$798$	10.4632	+	17.6864i	0.370394	+	0.626092i
$799$			31.1877i			1.10334i
$800$			8.46663i			0.299341i
$801$			75.8445i			2.67983i
$802$			13.0436i			0.460585i
$803$	37.8630	−	36.1395i	1.33616	−	1.27534i
$804$			30.2576i			1.06710i
$805$	42.9094	−	25.3850i	1.51236	−	0.894705i
$806$	8.63265			0.304072
$807$	17.5135			0.616506
$808$		−	14.0868i		−	0.495573i
$809$		−	23.8545i		−	0.838679i	−0.907829	−	0.419340i	$-0.862262\pi$
$809$		−	23.8545i		−	0.838679i	0.907829	−	0.419340i	$-0.137738\pi$
$810$	−0.0607230			−0.00213359
$811$	30.0782			1.05619			0.528095	−	0.849185i	$-0.322907\pi$
$811$	30.0782			1.05619			0.528095	+	0.849185i	$0.322907\pi$
$812$	−4.41279	+	2.61059i	−0.154858	+	0.0916137i
$813$		−	76.2626i		−	2.67464i
$814$	20.6046	+	21.5872i	0.722190	+	0.756631i
$815$			26.8173i			0.939369i
$816$		−	14.3856i		−	0.503595i
$817$			2.33136i			0.0815641i
$818$			7.37336i			0.257804i
$819$	−6.54244	−	11.0589i	−0.228611	−	0.386431i
$820$			44.1155i			1.54058i
$821$			9.32486i			0.325440i	0.986672	+	0.162720i	$0.0520267\pi$
$821$			9.32486i			0.325440i	−0.986672	+	0.162720i	$0.947973\pi$
$822$	−39.6323			−1.38233
$823$	−32.6862			−1.13937			−0.569685	−	0.821863i	$-0.692935\pi$
$823$	−32.6862			−1.13937			−0.569685	+	0.821863i	$0.692935\pi$
$824$	14.7845			0.515043
$825$	54.3446	+	56.9363i	1.89204	+	1.98227i
$826$	4.26561	+	7.21034i	0.148420	+	0.250880i
$827$			37.2643i			1.29581i	0.761723	+	0.647903i	$0.224354\pi$
$827$			37.2643i			1.29581i	−0.761723	+	0.647903i	$0.775646\pi$
$828$	−24.9384			−0.866668
$829$		−	9.21642i		−	0.320100i	−0.987109	−	0.160050i	$-0.948835\pi$
$829$		−	9.21642i		−	0.320100i	0.987109	−	0.160050i	$-0.0511655\pi$
$830$	−13.4037			−0.465248
$831$	80.7414			2.80089
$832$	1.00000			0.0346688
$833$	−17.2982	+	31.4872i	−0.599347	+	1.09097i
$834$	−54.6480			−1.89230
$835$		−	3.36079i		−	0.116305i
$836$	−6.64815	+	6.34553i	−0.229931	+	0.219465i
$837$	44.9233			1.55277
$838$	−22.3434			−0.771842
$839$			35.4799i			1.22490i	0.790508	+	0.612452i	$0.209817\pi$
$839$			35.4799i			1.22490i	−0.790508	+	0.612452i	$0.790183\pi$
$840$	−23.4223	+	13.8566i	−0.808147	+	0.478097i
$841$	25.2446			0.870503
$842$			5.67014i			0.195406i
$843$	−69.3169			−2.38740
$844$		−	2.52634i		−	0.0869601i
$845$		−	3.66969i		−	0.126241i
$846$	−29.5123			−1.01465
$847$	−25.7109	+	13.6363i	−0.883438	+	0.468548i
$848$	9.66179			0.331787
$849$			29.8681i			1.02507i
$850$			43.4531i			1.49043i
$851$	46.2033			1.58383
$852$			2.91178i			0.0997560i
$853$	−4.17582			−0.142977			−0.0714887	−	0.997441i	$-0.522775\pi$
$853$	−4.17582			−0.142977			−0.0714887	+	0.997441i	$0.522775\pi$
$854$	−10.0065	+	5.91978i	−0.342414	+	0.202571i
$855$			49.3853i			1.68894i
$856$	−3.27614			−0.111976
$857$	−40.0505			−1.36810			−0.684050	−	0.729435i	$-0.739783\pi$
$857$	−40.0505			−1.36810			−0.684050	+	0.729435i	$0.739783\pi$
$858$	6.72479	−	6.41868i	0.229581	−	0.219130i
$859$		−	20.0570i		−	0.684337i	−0.939639	−	0.342169i	$-0.888839\pi$
$859$		−	20.0570i		−	0.684337i	0.939639	−	0.342169i	$-0.111161\pi$
$860$	−3.08746			−0.105281
$861$	−76.7296	+	45.3930i	−2.61494	+	1.54699i
$862$	−28.3827			−0.966719
$863$	38.8483			1.32241			0.661207	−	0.750204i	$-0.270045\pi$
$863$	38.8483			1.32241			0.661207	+	0.750204i	$0.270045\pi$
$864$	5.20388			0.177040
$865$			67.3115i			2.28866i
$866$	13.0366			0.443001
$867$		−	26.1804i		−	0.889134i
$868$	19.6575	−	11.6293i	0.667219	−	0.394725i
$869$	−0.155958	−	0.163396i	−0.00529051	−	0.00554281i
$870$	−19.9331			−0.675795
$871$	−10.7949			−0.365771
$872$	5.92460			0.200632
$873$		−	59.1706i		−	2.00262i
$874$			14.2291i			0.481306i
$875$	28.9682	−	17.1375i	0.979304	−	0.579353i
$876$			44.2353i			1.49457i
$877$			8.16547i			0.275728i	0.990451	+	0.137864i	$0.0440237\pi$
$877$			8.16547i			0.275728i	−0.990451	+	0.137864i	$0.955976\pi$
$878$		−	18.8916i		−	0.637559i
$879$			6.57019i			0.221607i
$880$	−8.40347	−	8.80424i	−0.283281	−	0.296791i
$881$			18.8827i			0.636175i	0.948061	+	0.318088i	$0.103041\pi$
$881$			18.8827i			0.636175i	−0.948061	+	0.318088i	$0.896959\pi$
$882$	−29.7957	−	16.3689i	−1.00327	−	0.551171i
$883$	18.1581			0.611070			0.305535	−	0.952181i	$-0.401165\pi$
$883$	18.1581			0.611070			0.305535	+	0.952181i	$0.401165\pi$
$884$	5.13228			0.172617
$885$			32.5700i			1.09483i
$886$			26.0533i			0.875277i
$887$	7.10255			0.238480			0.119240	−	0.992865i	$-0.461954\pi$
$887$	7.10255			0.238480			0.119240	+	0.992865i	$0.461954\pi$
$888$	−25.2203			−0.846339
$889$	−1.20902	+	0.715255i	−0.0405494	+	0.0239889i
$890$			57.3092i			1.92101i
$891$	0.0396996	−	0.0378925i	0.00132999	−	0.00126945i
$892$			13.3805i			0.448013i
$893$			16.8388i			0.563490i
$894$		−	48.5513i		−	1.62380i
$895$			45.3541i			1.51602i
$896$	2.27711	−	1.34713i	0.0760730	−	0.0450045i
$897$		−	14.3931i		−	0.480572i
$898$		−	3.06370i		−	0.102237i
$899$	16.7291			0.557947
$900$	−41.1188			−1.37063
$901$	49.5870			1.65198
$902$	−27.5291	−	28.8419i	−0.916617	−	0.960331i
$903$	−3.17686	−	5.36997i	−0.105719	−	0.178702i
$904$			14.7381i			0.490181i
$905$	−29.0773			−0.966563
$906$			4.77231i			0.158549i
$907$	15.1617			0.503435			0.251718	−	0.967801i	$-0.419005\pi$
$907$	15.1617			0.503435			0.251718	+	0.967801i	$0.419005\pi$
$908$	19.2279			0.638099
$909$	68.4136			2.26914
$910$	−4.94356	−	8.35630i	−0.163877	−	0.277008i
$911$	−50.0298			−1.65756			−0.828780	−	0.559574i	$-0.810965\pi$
$911$	−50.0298			−1.65756			−0.828780	+	0.559574i	$0.810965\pi$
$912$		−	7.76703i		−	0.257192i
$913$	8.76308	−	8.36419i	0.290016	−	0.276814i
$914$	17.3459			0.573750
$915$	−45.2003			−1.49428
$916$		−	1.10489i		−	0.0365066i
$917$	2.96416	+	5.01044i	0.0978851	+	0.165459i
$918$	26.7078			0.881488
$919$			20.2432i			0.667762i	0.942615	+	0.333881i	$0.108358\pi$
$919$			20.2432i			0.667762i	−0.942615	+	0.333881i	$0.891642\pi$
$920$	−18.8438			−0.621261
$921$		−	19.6279i		−	0.646762i
$922$			6.50454i			0.214216i
$923$	−1.03883			−0.0341933
$924$	6.66629	−	23.6752i	0.219305	−	0.778858i
$925$	76.1807			2.50481
$926$			30.9453i			1.01692i
$927$			71.8020i			2.35829i
$928$	1.93789			0.0636143
$929$		−	12.9777i		−	0.425785i	−0.977076	−	0.212893i	$-0.931712\pi$
$929$		−	12.9777i		−	0.425785i	0.977076	−	0.212893i	$-0.0682885\pi$
$930$	88.7953			2.91171
$931$	−9.33963	+	17.0006i	−0.306094	+	0.557171i
$932$		−	14.2561i		−	0.466974i
$933$	23.3438			0.764242
$934$	−35.4509			−1.15999
$935$	−43.1290	−	45.1858i	−1.41047	−	1.47773i
$936$			4.85657i			0.158742i
$937$	−14.2134			−0.464332			−0.232166	−	0.972676i	$-0.574581\pi$
$937$	−14.2134			−0.464332			−0.232166	+	0.972676i	$0.574581\pi$
$938$	−24.5812	+	14.5421i	−0.802604	+	0.474818i
$939$	−22.4008			−0.731022
$940$	−22.2999			−0.727343
$941$	44.7032			1.45728			0.728641	−	0.684896i	$-0.240152\pi$
$941$	44.7032			1.45728			0.728641	+	0.684896i	$0.240152\pi$
$942$		−	28.9023i		−	0.941688i
$943$	−61.7306			−2.01022
$944$		−	3.16644i		−	0.103059i
$945$	−25.7257	−	43.4852i	−0.836856	−	1.41457i
$946$	2.01852	−	1.92664i	0.0656278	−	0.0626405i
$947$	−47.6867			−1.54961			−0.774804	−	0.632201i	$-0.782151\pi$
$947$	−47.6867			−1.54961			−0.774804	+	0.632201i	$0.782151\pi$
$948$	0.190895			0.00619998
$949$	−15.7817			−0.512295
$950$			23.4612i			0.761180i
$951$			54.7738i			1.77616i
$952$	11.6868	−	6.91386i	0.378770	−	0.224079i
$953$			22.3327i			0.723427i	0.932289	+	0.361714i	$0.117808\pi$
$953$			22.3327i			0.723427i	−0.932289	+	0.361714i	$0.882192\pi$
$954$			46.9231i			1.51919i
$955$		−	46.9227i		−	1.51838i
$956$		−	7.03614i		−	0.227565i
$957$	13.0319	−	12.4387i	0.421261	−	0.402085i
$958$		−	7.15430i		−	0.231145i
$959$	−19.0477	−	32.1971i	−0.615082	−	1.03970i
$960$	10.2860			0.331979
$961$	−43.5226			−1.40395
$962$		−	8.99776i		−	0.290099i
$963$		−	15.9108i		−	0.512718i
$964$	18.1083			0.583230
$965$	44.8421			1.44352
$966$	−19.3894	−	32.7747i	−0.623844	−	1.05451i
$967$			5.82258i			0.187241i	0.995608	+	0.0936207i	$0.0298441\pi$
$967$			5.82258i			0.187241i	−0.995608	+	0.0936207i	$0.970156\pi$
$968$	10.9881	+	0.512097i	0.353170	+	0.0164594i
$969$		−	39.8626i		−	1.28057i
$970$		−	44.7102i		−	1.43556i
$971$		−	21.4648i		−	0.688839i	−0.938816	−	0.344419i	$-0.888076\pi$
$971$		−	21.4648i		−	0.688839i	0.938816	−	0.344419i	$-0.111924\pi$
$972$		−	15.5653i		−	0.499256i
$973$	−26.2644	−	44.3958i	−0.841998	−	1.42326i
$974$		−	21.8726i		−	0.700843i
$975$		−	23.7316i		−	0.760020i
$976$	4.39436			0.140660
$977$	−9.39669			−0.300627			−0.150313	−	0.988638i	$-0.548028\pi$
$977$	−9.39669			−0.300627			−0.150313	+	0.988638i	$0.548028\pi$
$978$	20.4834			0.654986
$979$	−35.7622	−	37.4677i	−1.14296	−	1.19747i
$980$	−22.5141	−	12.3686i	−0.719185	−	0.395100i
$981$			28.7732i			0.918658i
$982$	−22.5588			−0.719881
$983$			37.1379i			1.18451i	0.805749	+	0.592257i	$0.201763\pi$
$983$			37.1379i			1.18451i	−0.805749	+	0.592257i	$0.798237\pi$
$984$	33.6960			1.07419
$985$	57.8154			1.84215
$986$	9.94578			0.316738
$987$	−22.9456	−	38.7859i	−0.730367	−	1.23457i
$988$	2.77101			0.0881577
$989$		−	4.32026i		−	0.137376i
$990$	42.7584	−	40.8120i	1.35895	−	1.29709i
$991$	−24.3096			−0.772221			−0.386111	−	0.922453i	$-0.626182\pi$
$991$	−24.3096			−0.772221			−0.386111	+	0.922453i	$0.626182\pi$
$992$	−8.63265			−0.274087
$993$			27.9121i			0.885765i
$994$	−2.36552	+	1.39943i	−0.0750298	+	0.0443874i
$995$	73.1977			2.32052
$996$			10.2379i			0.324400i
$997$	−35.9564			−1.13875			−0.569375	−	0.822078i	$-0.692815\pi$
$997$	−35.9564			−1.13875			−0.569375	+	0.822078i	$0.692815\pi$
$998$			23.5389i			0.745112i
$999$		−	46.8232i		−	1.48142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2002.2.c.a.1847.3	✓	48
7.6	odd	2		2002.2.c.b.1847.22	yes	48
11.10	odd	2		2002.2.c.b.1847.27	yes	48
77.76	even	2	inner	2002.2.c.a.1847.46	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2002.2.c.a.1847.3	✓	48	1.1	even	1	trivial
2002.2.c.a.1847.46	yes	48	77.76	even	2	inner
2002.2.c.b.1847.22	yes	48	7.6	odd	2
2002.2.c.b.1847.27	yes	48	11.10	odd	2

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:	\( N \)	\(=\)	\( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2002.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -2.80296i q^{3} -1.00000 q^{4} -3.66969i q^{5} -2.80296 q^{6} +(-1.34713 - 2.27711i) q^{7} +1.00000i q^{8} -4.85657 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -2.80296i q^{3} -1.00000 q^{4} -3.66969i q^{5} -2.80296 q^{6} +(-1.34713 - 2.27711i) q^{7} +1.00000i q^{8} -4.85657 q^{9} -3.66969 q^{10} +(2.39918 - 2.28997i) q^{11} +2.80296i q^{12} -1.00000 q^{13} +(-2.27711 + 1.34713i) q^{14} -10.2860 q^{15} +1.00000 q^{16} +5.13228 q^{17} +4.85657i q^{18} +2.77101 q^{19} +3.66969i q^{20} +(-6.38265 + 3.77595i) q^{21} +(-2.28997 - 2.39918i) q^{22} -5.13498 q^{23} +2.80296 q^{24} -8.46663 q^{25} +1.00000i q^{26} +5.20388i q^{27} +(1.34713 + 2.27711i) q^{28} +1.93789i q^{29} +10.2860i q^{30} -8.63265i q^{31} -1.00000i q^{32} +(-6.41868 - 6.72479i) q^{33} -5.13228i q^{34} +(-8.35630 + 4.94356i) q^{35} +4.85657 q^{36} -8.99776 q^{37} -2.77101i q^{38} +2.80296i q^{39} +3.66969 q^{40} +12.0216 q^{41} +(3.77595 + 6.38265i) q^{42} +0.841340i q^{43} +(-2.39918 + 2.28997i) q^{44} +17.8221i q^{45} +5.13498i q^{46} +6.07678i q^{47} -2.80296i q^{48} +(-3.37047 + 6.13514i) q^{49} +8.46663i q^{50} -14.3856i q^{51} +1.00000 q^{52} +9.66179 q^{53} +5.20388 q^{54} +(-8.40347 - 8.80424i) q^{55} +(2.27711 - 1.34713i) q^{56} -7.76703i q^{57} +1.93789 q^{58} -3.16644i q^{59} +10.2860 q^{60} +4.39436 q^{61} -8.63265 q^{62} +(6.54244 + 11.0589i) q^{63} -1.00000 q^{64} +3.66969i q^{65} +(-6.72479 + 6.41868i) q^{66} +10.7949 q^{67} -5.13228 q^{68} +14.3931i q^{69} +(4.94356 + 8.35630i) q^{70} +1.03883 q^{71} -4.85657i q^{72} +15.7817 q^{73} +8.99776i q^{74} +23.7316i q^{75} -2.77101 q^{76} +(-8.44652 - 2.37831i) q^{77} +2.80296 q^{78} -0.0681048i q^{79} -3.66969i q^{80} +0.0165472 q^{81} -12.0216i q^{82} +3.65253 q^{83} +(6.38265 - 3.77595i) q^{84} -18.8339i q^{85} +0.841340 q^{86} +5.43182 q^{87} +(2.28997 + 2.39918i) q^{88} -15.6169i q^{89} +17.8221 q^{90} +(1.34713 + 2.27711i) q^{91} +5.13498 q^{92} -24.1969 q^{93} +6.07678 q^{94} -10.1688i q^{95} -2.80296 q^{96} +12.1836i q^{97} +(6.13514 + 3.37047i) q^{98} +(-11.6518 + 11.1214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{7} - 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^7 - 48 * q^9	\( 48 q - 48 q^{4} - 8 q^{7} - 48 q^{9} - 4 q^{11} - 48 q^{13} - 2 q^{14} + 8 q^{15} + 48 q^{16} - 4 q^{17} + 20 q^{21} + 2 q^{22} - 32 q^{23} - 56 q^{25} + 8 q^{28} + 20 q^{33} - 10 q^{35} + 48 q^{36} - 16 q^{37} + 16 q^{42} + 4 q^{44} - 38 q^{49} + 48 q^{52} + 4 q^{53} - 60 q^{55} + 2 q^{56} + 24 q^{58} - 8 q^{60} - 28 q^{61} - 28 q^{62} + 32 q^{63} - 48 q^{64} + 46 q^{66} - 8 q^{67} + 4 q^{68} - 20 q^{70} + 16 q^{73} - 14 q^{77} + 16 q^{81} + 40 q^{83} - 20 q^{84} - 24 q^{87} - 2 q^{88} + 20 q^{90} + 8 q^{91} + 32 q^{92} - 48 q^{93} - 44 q^{94} + 92 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^7 - 48 * q^9 - 4 * q^11 - 48 * q^13 - 2 * q^14 + 8 * q^15 + 48 * q^16 - 4 * q^17 + 20 * q^21 + 2 * q^22 - 32 * q^23 - 56 * q^25 + 8 * q^28 + 20 * q^33 - 10 * q^35 + 48 * q^36 - 16 * q^37 + 16 * q^42 + 4 * q^44 - 38 * q^49 + 48 * q^52 + 4 * q^53 - 60 * q^55 + 2 * q^56 + 24 * q^58 - 8 * q^60 - 28 * q^61 - 28 * q^62 + 32 * q^63 - 48 * q^64 + 46 * q^66 - 8 * q^67 + 4 * q^68 - 20 * q^70 + 16 * q^73 - 14 * q^77 + 16 * q^81 + 40 * q^83 - 20 * q^84 - 24 * q^87 - 2 * q^88 + 20 * q^90 + 8 * q^91 + 32 * q^92 - 48 * q^93 - 44 * q^94 + 92 * q^99

Introduction

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