LMFDB - Embedded newform 1045.2.b.e.419.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.4
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39831i q^{2} -0.881728i q^{3} -3.75187 q^{4} +(-0.259771 - 2.22093i) q^{5} -2.11465 q^{6} -2.42713i q^{7} +4.20151i q^{8} +2.22256 q^{9} +O(q^{10})$	\(q-2.39831i q^{2} -0.881728i q^{3} -3.75187 q^{4} +(-0.259771 - 2.22093i) q^{5} -2.11465 q^{6} -2.42713i q^{7} +4.20151i q^{8} +2.22256 q^{9} +(-5.32646 + 0.623010i) q^{10} +1.00000 q^{11} +3.30813i q^{12} -3.61900i q^{13} -5.82099 q^{14} +(-1.95825 + 0.229047i) q^{15} +2.57278 q^{16} -6.97796i q^{17} -5.33037i q^{18} -1.00000 q^{19} +(0.974627 + 8.33263i) q^{20} -2.14006 q^{21} -2.39831i q^{22} +8.41688i q^{23} +3.70459 q^{24} +(-4.86504 + 1.15387i) q^{25} -8.67947 q^{26} -4.60487i q^{27} +9.10626i q^{28} +5.07297 q^{29} +(0.549325 + 4.69649i) q^{30} -0.478941 q^{31} +2.23272i q^{32} -0.881728i q^{33} -16.7353 q^{34} +(-5.39047 + 0.630497i) q^{35} -8.33874 q^{36} +3.19619i q^{37} +2.39831i q^{38} -3.19097 q^{39} +(9.33126 - 1.09143i) q^{40} +10.7701 q^{41} +5.13253i q^{42} +2.14239i q^{43} -3.75187 q^{44} +(-0.577356 - 4.93614i) q^{45} +20.1862 q^{46} -3.37631i q^{47} -2.26849i q^{48} +1.10906 q^{49} +(2.76732 + 11.6678i) q^{50} -6.15266 q^{51} +13.5780i q^{52} +6.23113i q^{53} -11.0439 q^{54} +(-0.259771 - 2.22093i) q^{55} +10.1976 q^{56} +0.881728i q^{57} -12.1665i q^{58} +1.66947 q^{59} +(7.34711 - 0.859356i) q^{60} +10.3069 q^{61} +1.14865i q^{62} -5.39443i q^{63} +10.5003 q^{64} +(-8.03754 + 0.940112i) q^{65} -2.11465 q^{66} +6.57029i q^{67} +26.1804i q^{68} +7.42140 q^{69} +(1.51213 + 12.9280i) q^{70} +3.86707 q^{71} +9.33810i q^{72} +6.54942i q^{73} +7.66544 q^{74} +(1.01740 + 4.28964i) q^{75} +3.75187 q^{76} -2.42713i q^{77} +7.65293i q^{78} -7.07840 q^{79} +(-0.668334 - 5.71396i) q^{80} +2.60743 q^{81} -25.8299i q^{82} +0.498408i q^{83} +8.02924 q^{84} +(-15.4976 + 1.81267i) q^{85} +5.13811 q^{86} -4.47298i q^{87} +4.20151i q^{88} -13.8117 q^{89} +(-11.8384 + 1.38468i) q^{90} -8.78377 q^{91} -31.5790i q^{92} +0.422296i q^{93} -8.09742 q^{94} +(0.259771 + 2.22093i) q^{95} +1.96865 q^{96} -9.39315i q^{97} -2.65985i q^{98} +2.22256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.39831i		−	1.69586i	−0.530110	−	0.847929i	$-0.677849\pi$
$2$		−	2.39831i		−	1.69586i	0.530110	−	0.847929i	$-0.322151\pi$
$3$		−	0.881728i		−	0.509066i	−0.967064	−	0.254533i	$-0.918078\pi$
$3$		−	0.881728i		−	0.509066i	0.967064	−	0.254533i	$-0.0819217\pi$
$4$	−3.75187			−1.87593
$5$	−0.259771	−	2.22093i	−0.116173	−	0.993229i
$5$	−0.259771	−	2.22093i	−0.116173	−	0.993229i
$6$	−2.11465			−0.863303
$7$		−	2.42713i		−	0.917368i	−0.888600	−	0.458684i	$-0.848321\pi$
$7$		−	2.42713i		−	0.917368i	0.888600	−	0.458684i	$-0.151679\pi$
$8$			4.20151i			1.48546i
$9$	2.22256			0.740852
$10$	−5.32646	+	0.623010i	−1.68438	+	0.197013i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			3.30813i			0.954974i
$13$		−	3.61900i		−	1.00373i	−0.864946	−	0.501865i	$-0.832647\pi$
$13$		−	3.61900i		−	1.00373i	0.864946	−	0.501865i	$-0.167353\pi$
$14$	−5.82099			−1.55573
$15$	−1.95825	+	0.229047i	−0.505619	+	0.0591398i
$16$	2.57278			0.643195
$17$		−	6.97796i		−	1.69240i	−0.532862	−	0.846202i	$-0.678883\pi$
$17$		−	6.97796i		−	1.69240i	0.532862	−	0.846202i	$-0.321117\pi$
$18$		−	5.33037i		−	1.25638i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.974627	+	8.33263i	0.217933	+	1.86323i
$21$	−2.14006			−0.467000
$22$		−	2.39831i		−	0.511320i
$23$			8.41688i			1.75504i	0.479539	+	0.877520i	$0.340804\pi$
$23$			8.41688i			1.75504i	−0.479539	+	0.877520i	$0.659196\pi$
$24$	3.70459			0.756197
$25$	−4.86504	+	1.15387i	−0.973008	+	0.230773i
$26$	−8.67947			−1.70218
$27$		−	4.60487i		−	0.886208i
$28$			9.10626i			1.72092i
$29$	5.07297			0.942027			0.471014	−	0.882126i	$-0.343888\pi$
$29$	5.07297			0.942027			0.471014	+	0.882126i	$0.343888\pi$
$30$	0.549325	+	4.69649i	0.100293	+	0.857458i
$31$	−0.478941			−0.0860204			−0.0430102	−	0.999075i	$-0.513695\pi$
$31$	−0.478941			−0.0860204			−0.0430102	+	0.999075i	$0.513695\pi$
$32$			2.23272i			0.394693i
$33$		−	0.881728i		−	0.153489i
$34$	−16.7353			−2.87008
$35$	−5.39047	+	0.630497i	−0.911156	+	0.106574i
$36$	−8.33874			−1.38979
$37$			3.19619i			0.525451i	0.964871	+	0.262725i	$0.0846213\pi$
$37$			3.19619i			0.525451i	−0.964871	+	0.262725i	$0.915379\pi$
$38$			2.39831i			0.389056i
$39$	−3.19097			−0.510964
$40$	9.33126	−	1.09143i	1.47540	−	0.172571i
$41$	10.7701			1.68200			0.841000	−	0.541036i	$-0.181968\pi$
$41$	10.7701			1.68200			0.841000	+	0.541036i	$0.181968\pi$
$42$			5.13253i			0.791966i
$43$			2.14239i			0.326712i	0.986567	+	0.163356i	$0.0522318\pi$
$43$			2.14239i			0.326712i	−0.986567	+	0.163356i	$0.947768\pi$
$44$	−3.75187			−0.565615
$45$	−0.577356	−	4.93614i	−0.0860671	−	0.735836i
$46$	20.1862			2.97630
$47$		−	3.37631i		−	0.492485i	−0.969208	−	0.246243i	$-0.920804\pi$
$47$		−	3.37631i		−	0.492485i	0.969208	−	0.246243i	$-0.0791960\pi$
$48$		−	2.26849i		−	0.327428i
$49$	1.10906			0.158436
$50$	2.76732	+	11.6678i	0.391358	+	1.65008i
$51$	−6.15266			−0.861545
$52$			13.5780i			1.88293i
$53$			6.23113i			0.855912i	0.903800	+	0.427956i	$0.140766\pi$
$53$			6.23113i			0.855912i	−0.903800	+	0.427956i	$0.859234\pi$
$54$	−11.0439			−1.50288
$55$	−0.259771	−	2.22093i	−0.0350275	−	0.299470i
$56$	10.1976			1.36271
$57$			0.881728i			0.116788i
$58$		−	12.1665i		−	1.59754i
$59$	1.66947			0.217346			0.108673	−	0.994078i	$-0.465340\pi$
$59$	1.66947			0.217346			0.108673	+	0.994078i	$0.465340\pi$
$60$	7.34711	−	0.859356i	0.948507	−	0.110942i
$61$	10.3069			1.31966			0.659830	−	0.751415i	$-0.270628\pi$
$61$	10.3069			1.31966			0.659830	+	0.751415i	$0.270628\pi$
$62$			1.14865i			0.145878i
$63$		−	5.39443i		−	0.679634i
$64$	10.5003			1.31254
$65$	−8.03754	+	0.940112i	−0.996934	+	0.116607i
$66$	−2.11465			−0.260296
$67$			6.57029i			0.802689i	0.915927	+	0.401345i	$0.131457\pi$
$67$			6.57029i			0.802689i	−0.915927	+	0.401345i	$0.868543\pi$
$68$			26.1804i			3.17484i
$69$	7.42140			0.893431
$70$	1.51213	+	12.9280i	0.180734	+	1.54519i
$71$	3.86707			0.458937			0.229469	−	0.973316i	$-0.426301\pi$
$71$	3.86707			0.458937			0.229469	+	0.973316i	$0.426301\pi$
$72$			9.33810i			1.10051i
$73$			6.54942i			0.766552i	0.923634	+	0.383276i	$0.125204\pi$
$73$			6.54942i			0.766552i	−0.923634	+	0.383276i	$0.874796\pi$
$74$	7.66544			0.891090
$75$	1.01740	+	4.28964i	0.117479	+	0.495325i
$76$	3.75187			0.430369
$77$		−	2.42713i		−	0.276597i
$78$			7.65293i			0.866523i
$79$	−7.07840			−0.796383			−0.398191	−	0.917302i	$-0.630362\pi$
$79$	−7.07840			−0.796383			−0.398191	+	0.917302i	$0.630362\pi$
$80$	−0.668334	−	5.71396i	−0.0747220	−	0.638840i
$81$	2.60743			0.289714
$82$		−	25.8299i		−	2.85243i
$83$			0.498408i			0.0547073i	0.999626	+	0.0273537i	$0.00870803\pi$
$83$			0.498408i			0.0547073i	−0.999626	+	0.0273537i	$0.991292\pi$
$84$	8.02924			0.876062
$85$	−15.4976	+	1.81267i	−1.68095	+	0.196612i
$86$	5.13811			0.554056
$87$		−	4.47298i		−	0.479554i
$88$			4.20151i			0.447883i
$89$	−13.8117			−1.46403			−0.732017	−	0.681286i	$-0.761421\pi$
$89$	−13.8117			−1.46403			−0.732017	+	0.681286i	$0.761421\pi$
$90$	−11.8384	+	1.38468i	−1.24787	+	0.145958i
$91$	−8.78377			−0.920790
$92$		−	31.5790i		−	3.29234i
$93$			0.422296i			0.0437900i
$94$	−8.09742			−0.835185
$95$	0.259771	+	2.22093i	0.0266520	+	0.227862i
$96$	1.96865			0.200925
$97$		−	9.39315i		−	0.953730i	−0.878977	−	0.476865i	$-0.841773\pi$
$97$		−	9.39315i		−	0.953730i	0.878977	−	0.476865i	$-0.158227\pi$
$98$		−	2.65985i		−	0.268686i
$99$	2.22256			0.223375
$100$	18.2530	−	4.32915i	1.82530	−	0.432915i
$101$	−10.5232			−1.04710			−0.523551	−	0.851994i	$-0.675393\pi$
$101$	−10.5232			−1.04710			−0.523551	+	0.851994i	$0.675393\pi$
$102$			14.7560i			1.46106i
$103$		−	8.48659i		−	0.836209i	−0.908399	−	0.418104i	$-0.862695\pi$
$103$		−	8.48659i		−	0.836209i	0.908399	−	0.418104i	$-0.137305\pi$
$104$	15.2053			1.49100
$105$	0.555927	+	4.75293i	0.0542529	+	0.463838i
$106$	14.9442			1.45151
$107$			3.05355i			0.295198i	0.989047	+	0.147599i	$0.0471545\pi$
$107$			3.05355i			0.295198i	−0.989047	+	0.147599i	$0.952845\pi$
$108$			17.2769i			1.66247i
$109$	7.05740			0.675976			0.337988	−	0.941150i	$-0.390254\pi$
$109$	7.05740			0.675976			0.337988	+	0.941150i	$0.390254\pi$
$110$	−5.32646	+	0.623010i	−0.507858	+	0.0594017i
$111$	2.81817			0.267489
$112$		−	6.24446i		−	0.590046i
$113$			2.60969i			0.245499i	0.992438	+	0.122749i	$0.0391711\pi$
$113$			2.60969i			0.245499i	−0.992438	+	0.122749i	$0.960829\pi$
$114$	2.11465			0.198055
$115$	18.6933	−	2.18646i	1.74316	−	0.203889i
$116$	−19.0331			−1.76718
$117$		−	8.04343i		−	0.743616i
$118$		−	4.00389i		−	0.368588i
$119$	−16.9364			−1.55256
$120$	−0.962346	−	8.22763i	−0.0878498	−	0.751076i
$121$	1.00000			0.0909091
$122$		−	24.7190i		−	2.23796i
$123$		−	9.49625i		−	0.856248i
$124$	1.79693			0.161369
$125$	3.82645	+	10.5052i	0.342248	+	0.939610i
$126$	−12.9375			−1.15256
$127$			9.94390i			0.882379i	0.897414	+	0.441189i	$0.145443\pi$
$127$			9.94390i			0.882379i	−0.897414	+	0.441189i	$0.854557\pi$
$128$		−	20.7175i		−	1.83118i
$129$	1.88901			0.166318
$130$	2.25467	+	19.2765i	0.197748	+	1.69066i
$131$	−11.2666			−0.984366			−0.492183	−	0.870492i	$-0.663801\pi$
$131$	−11.2666			−0.984366			−0.492183	+	0.870492i	$0.663801\pi$
$132$			3.30813i			0.287935i
$133$			2.42713i			0.210459i
$134$	15.7576			1.36125
$135$	−10.2271	+	1.19621i	−0.880208	+	0.102954i
$136$	29.3180			2.51400
$137$			4.81798i			0.411628i	0.978591	+	0.205814i	$0.0659841\pi$
$137$			4.81798i			0.411628i	−0.978591	+	0.205814i	$0.934016\pi$
$138$		−	17.7988i		−	1.51513i
$139$	4.76257			0.403956			0.201978	−	0.979390i	$-0.435263\pi$
$139$	4.76257			0.403956			0.201978	+	0.979390i	$0.435263\pi$
$140$	20.2243	−	2.36554i	1.70927	−	0.199925i
$141$	−2.97698			−0.250707
$142$		−	9.27443i		−	0.778293i
$143$		−	3.61900i		−	0.302636i
$144$	5.71815			0.476512
$145$	−1.31781	−	11.2667i	−0.109438	−	0.935649i
$146$	15.7075			1.29996
$147$		−	0.977885i		−	0.0806546i
$148$		−	11.9917i		−	0.985711i
$149$	−20.7718			−1.70169			−0.850847	−	0.525414i	$-0.823911\pi$
$149$	−20.7718			−1.70169			−0.850847	+	0.525414i	$0.823911\pi$
$150$	10.2879	−	2.44002i	0.840000	−	0.199227i
$151$	23.7180			1.93014			0.965072	−	0.261985i	$-0.0843772\pi$
$151$	23.7180			1.93014			0.965072	+	0.261985i	$0.0843772\pi$
$152$		−	4.20151i		−	0.340788i
$153$		−	15.5089i		−	1.25382i
$154$	−5.82099			−0.469069
$155$	0.124415	+	1.06369i	0.00999327	+	0.0854380i
$156$	11.9721			0.958536
$157$		−	12.7166i		−	1.01490i	−0.861682	−	0.507448i	$-0.830589\pi$
$157$		−	12.7166i		−	1.01490i	0.861682	−	0.507448i	$-0.169411\pi$
$158$			16.9762i			1.35055i
$159$	5.49416			0.435715
$160$	4.95871	−	0.579996i	0.392020	−	0.0458527i
$161$	20.4288			1.61002
$162$		−	6.25341i		−	0.491314i
$163$		−	6.43013i		−	0.503647i	−0.967773	−	0.251823i	$-0.918970\pi$
$163$		−	6.43013i		−	0.503647i	0.967773	−	0.251823i	$-0.0810302\pi$
$164$	−40.4078			−3.15532
$165$	−1.95825	+	0.229047i	−0.152450	+	0.0178313i
$166$	1.19533			0.0927759
$167$			20.8661i			1.61467i	0.590093	+	0.807335i	$0.299091\pi$
$167$			20.8661i			1.61467i	−0.590093	+	0.807335i	$0.700909\pi$
$168$		−	8.99151i		−	0.693710i
$169$	−0.0971613			−0.00747395
$170$	4.34734	+	37.1679i	0.333426	+	2.85064i
$171$	−2.22256			−0.169963
$172$		−	8.03797i		−	0.612889i
$173$		−	20.5992i		−	1.56613i	−0.621942	−	0.783063i	$-0.713656\pi$
$173$		−	20.5992i		−	1.56613i	0.621942	−	0.783063i	$-0.286344\pi$
$174$	−10.7276			−0.813255
$175$	2.80058	+	11.8081i	0.211704	+	0.892606i
$176$	2.57278			0.193931
$177$		−	1.47201i		−	0.110643i
$178$			33.1246i			2.48280i
$179$	−13.6177			−1.01784			−0.508918	−	0.860815i	$-0.669954\pi$
$179$	−13.6177			−1.01784			−0.508918	+	0.860815i	$0.669954\pi$
$180$	2.16616	+	18.5197i	0.161456	+	1.38038i
$181$	−13.4839			−1.00225			−0.501124	−	0.865375i	$-0.667080\pi$
$181$	−13.4839			−1.00225			−0.501124	+	0.865375i	$0.667080\pi$
$182$			21.0662i			1.56153i
$183$		−	9.08785i		−	0.671794i
$184$	−35.3636			−2.60704
$185$	7.09851	−	0.830278i	0.521893	−	0.0610433i
$186$	1.01279			0.0742617
$187$		−	6.97796i		−	0.510279i
$188$			12.6675i			0.923870i
$189$	−11.1766			−0.812979
$190$	5.32646	−	0.623010i	0.386422	−	0.0451979i
$191$	1.65754			0.119935			0.0599676	−	0.998200i	$-0.480900\pi$
$191$	1.65754			0.119935			0.0599676	+	0.998200i	$0.480900\pi$
$192$		−	9.25841i		−	0.668168i
$193$		−	17.3014i		−	1.24538i	−0.782469	−	0.622690i	$-0.786040\pi$
$193$		−	17.3014i		−	1.24538i	0.782469	−	0.622690i	$-0.213960\pi$
$194$	−22.5276			−1.61739
$195$	0.828922	+	7.08692i	0.0593604	+	0.507505i
$196$	−4.16103			−0.297216
$197$		−	11.9926i		−	0.854441i	−0.904147	−	0.427220i	$-0.859493\pi$
$197$		−	11.9926i		−	0.854441i	0.904147	−	0.427220i	$-0.140507\pi$
$198$		−	5.33037i		−	0.378813i
$199$	24.0453			1.70453			0.852265	−	0.523111i	$-0.175229\pi$
$199$	24.0453			1.70453			0.852265	+	0.523111i	$0.175229\pi$
$200$	−4.84798	−	20.4405i	−0.342804	−	1.44536i
$201$	5.79321			0.408621
$202$			25.2379i			1.77574i
$203$		−	12.3127i		−	0.864185i
$204$	23.0840			1.61620
$205$	−2.79775	−	23.9195i	−0.195403	−	1.67061i
$206$	−20.3534			−1.41809
$207$			18.7070i			1.30023i
$208$		−	9.31089i		−	0.645594i
$209$	−1.00000			−0.0691714
$210$	11.3990	−	1.33328i	0.786604	−	0.0920052i
$211$	20.3764			1.40277			0.701384	−	0.712784i	$-0.252566\pi$
$211$	20.3764			1.40277			0.701384	+	0.712784i	$0.252566\pi$
$212$		−	23.3784i		−	1.60563i
$213$		−	3.40971i		−	0.233629i
$214$	7.32335			0.500614
$215$	4.75810	−	0.556531i	0.324499	−	0.0379551i
$216$	19.3474			1.31643
$217$			1.16245i			0.0789124i
$218$		−	16.9258i		−	1.14636i
$219$	5.77481			0.390225
$220$	0.974627	+	8.33263i	0.0657093	+	0.561786i
$221$	−25.2533			−1.69872
$222$		−	6.75883i		−	0.453623i
$223$			5.05921i			0.338790i	0.985548	+	0.169395i	$0.0541813\pi$
$223$			5.05921i			0.338790i	−0.985548	+	0.169395i	$0.945819\pi$
$224$	5.41910			0.362079
$225$	−10.8128	+	2.56453i	−0.720855	+	0.170969i
$226$	6.25883			0.416331
$227$		−	13.7792i		−	0.914556i	−0.889324	−	0.457278i	$-0.848824\pi$
$227$		−	13.7792i		−	0.914556i	0.889324	−	0.457278i	$-0.151176\pi$
$228$		−	3.30813i		−	0.219086i
$229$	−13.8678			−0.916411			−0.458206	−	0.888846i	$-0.651508\pi$
$229$	−13.8678			−0.916411			−0.458206	+	0.888846i	$0.651508\pi$
$230$	−5.24380	−	44.8322i	−0.345766	−	2.95615i
$231$	−2.14006			−0.140806
$232$			21.3142i			1.39934i
$233$			17.7021i			1.15970i	0.814723	+	0.579851i	$0.196889\pi$
$233$			17.7021i			1.15970i	−0.814723	+	0.579851i	$0.803111\pi$
$234$	−19.2906			−1.26107
$235$	−7.49854	+	0.877067i	−0.489151	+	0.0572136i
$236$	−6.26362			−0.407727
$237$			6.24122i			0.405411i
$238$			40.6187i			2.63292i
$239$	−14.3572			−0.928691			−0.464346	−	0.885654i	$-0.653710\pi$
$239$	−14.3572			−0.928691			−0.464346	+	0.885654i	$0.653710\pi$
$240$	−5.03815	+	0.589288i	−0.325211	+	0.0380384i
$241$	−2.56931			−0.165504			−0.0827519	−	0.996570i	$-0.526371\pi$
$241$	−2.56931			−0.165504			−0.0827519	+	0.996570i	$0.526371\pi$
$242$		−	2.39831i		−	0.154169i
$243$		−	16.1137i		−	1.03369i
$244$	−38.6700			−2.47560
$245$	−0.288101	−	2.46313i	−0.0184061	−	0.157364i
$246$	−22.7749			−1.45208
$247$			3.61900i			0.230271i
$248$		−	2.01228i		−	0.127780i
$249$	0.439460			0.0278496
$250$	25.1946	−	9.17699i	1.59344	−	0.580404i
$251$	−18.1347			−1.14465			−0.572326	−	0.820026i	$-0.693959\pi$
$251$	−18.1347			−1.14465			−0.572326	+	0.820026i	$0.693959\pi$
$252$			20.2392i			1.27495i
$253$			8.41688i			0.529165i
$254$	23.8485			1.49639
$255$	1.59828	+	13.6646i	0.100088	+	0.855712i
$256$	−28.6863			−1.79289
$257$		−	18.4185i		−	1.14891i	−0.818534	−	0.574457i	$-0.805213\pi$
$257$		−	18.4185i		−	1.14891i	0.818534	−	0.574457i	$-0.194787\pi$
$258$		−	4.53041i		−	0.282051i
$259$	7.75756			0.482031
$260$	30.1558	−	3.52718i	1.87018	−	0.218746i
$261$	11.2750			0.697903
$262$			27.0207i			1.66935i
$263$			18.2132i			1.12308i	0.827451	+	0.561538i	$0.189790\pi$
$263$			18.2132i			1.12308i	−0.827451	+	0.561538i	$0.810210\pi$
$264$	3.70459			0.228002
$265$	13.8389	−	1.61867i	0.850117	−	0.0994340i
$266$	5.82099			0.356908
$267$			12.1781i			0.745290i
$268$		−	24.6509i		−	1.50579i
$269$	19.5373			1.19121			0.595605	−	0.803277i	$-0.296912\pi$
$269$	19.5373			1.19121			0.595605	+	0.803277i	$0.296912\pi$
$270$	2.86888	+	24.5277i	0.174595	+	1.49271i
$271$	−13.1552			−0.799123			−0.399562	−	0.916706i	$-0.630838\pi$
$271$	−13.1552			−0.799123			−0.399562	+	0.916706i	$0.630838\pi$
$272$		−	17.9528i		−	1.08855i
$273$			7.74489i			0.468742i
$274$	11.5550			0.698062
$275$	−4.86504	+	1.15387i	−0.293373	+	0.0695807i
$276$	−27.8441			−1.67602
$277$			16.3129i			0.980147i	0.871681	+	0.490073i	$0.163030\pi$
$277$			16.3129i			0.980147i	−0.871681	+	0.490073i	$0.836970\pi$
$278$		−	11.4221i		−	0.685052i
$279$	−1.06447			−0.0637284
$280$	−2.64904	−	22.6482i	−0.158311	−	1.35349i
$281$	−6.93123			−0.413483			−0.206741	−	0.978396i	$-0.566286\pi$
$281$	−6.93123			−0.413483			−0.206741	+	0.978396i	$0.566286\pi$
$282$			7.13972i			0.425164i
$283$		−	29.0804i		−	1.72865i	−0.502932	−	0.864326i	$-0.667745\pi$
$283$		−	29.0804i		−	1.72865i	0.502932	−	0.864326i	$-0.332255\pi$
$284$	−14.5088			−0.860936
$285$	1.95825	−	0.229047i	0.115997	−	0.0135676i
$286$	−8.67947			−0.513228
$287$		−	26.1403i		−	1.54301i
$288$			4.96235i			0.292409i
$289$	−31.6920			−1.86423
$290$	−27.0210	+	3.16051i	−1.58673	+	0.185592i
$291$	−8.28220			−0.485511
$292$		−	24.5726i		−	1.43800i
$293$			14.2567i			0.832884i	0.909162	+	0.416442i	$0.136723\pi$
$293$			14.2567i			0.832884i	−0.909162	+	0.416442i	$0.863277\pi$
$294$	−2.34527			−0.136779
$295$	−0.433679	−	3.70776i	−0.0252498	−	0.215874i
$296$	−13.4288			−0.780536
$297$		−	4.60487i		−	0.267202i
$298$			49.8172i			2.88583i
$299$	30.4607			1.76159
$300$	−3.81713	−	16.0942i	−0.220382	−	0.929197i
$301$	5.19985			0.299715
$302$		−	56.8830i		−	3.27325i
$303$			9.27863i			0.533044i
$304$	−2.57278			−0.147559
$305$	−2.67743	−	22.8908i	−0.153309	−	1.31072i
$306$	−37.1951			−2.12630
$307$			33.5768i			1.91633i	0.286221	+	0.958164i	$0.407601\pi$
$307$			33.5768i			1.91633i	−0.286221	+	0.958164i	$0.592399\pi$
$308$			9.10626i			0.518877i
$309$	−7.48286			−0.425685
$310$	2.55106	−	0.298386i	0.144891	−	0.0169472i
$311$	−16.2193			−0.919710			−0.459855	−	0.887994i	$-0.652099\pi$
$311$	−16.2193			−0.919710			−0.459855	+	0.887994i	$0.652099\pi$
$312$		−	13.4069i		−	0.759017i
$313$		−	21.3775i		−	1.20833i	−0.796861	−	0.604163i	$-0.793508\pi$
$313$		−	21.3775i		−	1.20833i	0.796861	−	0.604163i	$-0.206492\pi$
$314$	−30.4983			−1.72112
$315$	−11.9806	+	1.40132i	−0.675032	+	0.0789552i
$316$	26.5572			1.49396
$317$		−	0.682827i		−	0.0383514i	−0.999816	−	0.0191757i	$-0.993896\pi$
$317$		−	0.682827i		−	0.0383514i	0.999816	−	0.0191757i	$-0.00610419\pi$
$318$		−	13.1767i		−	0.738912i
$319$	5.07297			0.284032
$320$	−2.72768	−	23.3204i	−0.152482	−	1.30365i
$321$	2.69240			0.150275
$322$		−	48.9946i		−	2.73036i
$323$			6.97796i			0.388264i
$324$	−9.78272			−0.543485
$325$	4.17584	+	17.6066i	0.231634	+	0.976637i
$326$	−15.4214			−0.854113
$327$		−	6.22270i		−	0.344116i
$328$			45.2505i			2.49854i
$329$	−8.19473			−0.451790
$330$	0.549325	+	4.69649i	0.0302394	+	0.258533i
$331$	−7.30286			−0.401401			−0.200701	−	0.979653i	$-0.564322\pi$
$331$	−7.30286			−0.401401			−0.200701	+	0.979653i	$0.564322\pi$
$332$		−	1.86996i		−	0.102627i
$333$			7.10372i			0.389281i
$334$	50.0434			2.73825
$335$	14.5921	−	1.70677i	0.797254	−	0.0932509i
$336$	−5.50591			−0.300372
$337$			17.1865i			0.936210i	0.883673	+	0.468105i	$0.155063\pi$
$337$			17.1865i			0.936210i	−0.883673	+	0.468105i	$0.844937\pi$
$338$			0.233023i			0.0126748i
$339$	2.30103			0.124975
$340$	58.1448	−	6.80091i	3.15334	−	0.368831i
$341$	−0.478941			−0.0259361
$342$			5.33037i			0.288233i
$343$		−	19.6817i		−	1.06271i
$344$	−9.00129			−0.485317
$345$	−1.92786	−	16.4824i	−0.103793	−	0.887382i
$346$	−49.4031			−2.65593
$347$		−	3.39517i		−	0.182262i	−0.995839	−	0.0911310i	$-0.970952\pi$
$347$		−	3.39517i		−	0.182262i	0.995839	−	0.0911310i	$-0.0290482\pi$
$348$			16.7820i			0.899611i
$349$	11.7063			0.626626			0.313313	−	0.949650i	$-0.398561\pi$
$349$	11.7063			0.626626			0.313313	+	0.949650i	$0.398561\pi$
$350$	28.3193	−	6.71664i	1.51373	−	0.359020i
$351$	−16.6650			−0.889514
$352$			2.23272i			0.119004i
$353$		−	3.94711i		−	0.210083i	−0.994468	−	0.105042i	$-0.966502\pi$
$353$		−	3.94711i		−	0.210083i	0.994468	−	0.105042i	$-0.0334976\pi$
$354$	−3.53034			−0.187635
$355$	−1.00455	−	8.58849i	−0.0533162	−	0.455830i
$356$	51.8196			2.74643
$357$			14.9333i			0.790354i
$358$			32.6595i			1.72611i
$359$	−4.61575			−0.243610			−0.121805	−	0.992554i	$-0.538868\pi$
$359$	−4.61575			−0.243610			−0.121805	+	0.992554i	$0.538868\pi$
$360$	20.7393	−	2.42577i	1.09305	−	0.127849i
$361$	1.00000			0.0526316
$362$			32.3385i			1.69967i
$363$		−	0.881728i		−	0.0462787i
$364$	32.9556			1.72734
$365$	14.5458	−	1.70135i	0.761362	−	0.0890528i
$366$	−21.7955			−1.13927
$367$		−	10.4291i		−	0.544396i	−0.962241	−	0.272198i	$-0.912249\pi$
$367$		−	10.4291i		−	0.544396i	0.962241	−	0.272198i	$-0.0877505\pi$
$368$			21.6548i			1.12883i
$369$	23.9370			1.24611
$370$	−1.99126	−	17.0244i	−0.103521	−	0.885056i
$371$	15.1238			0.785186
$372$		−	1.58440i		−	0.0821472i
$373$		−	29.1916i		−	1.51148i	−0.654870	−	0.755742i	$-0.727276\pi$
$373$		−	29.1916i		−	1.51148i	0.654870	−	0.755742i	$-0.272724\pi$
$374$	−16.7353			−0.865361
$375$	9.26269	−	3.37388i	0.478323	−	0.174227i
$376$	14.1856			0.731567
$377$		−	18.3591i		−	0.945541i
$378$			26.8049i			1.37870i
$379$	11.8935			0.610927			0.305464	−	0.952204i	$-0.401189\pi$
$379$	11.8935			0.610927			0.305464	+	0.952204i	$0.401189\pi$
$380$	−0.974627	−	8.33263i	−0.0499973	−	0.427455i
$381$	8.76781			0.449189
$382$		−	3.97528i		−	0.203393i
$383$			11.0496i			0.564610i	0.959325	+	0.282305i	$0.0910991\pi$
$383$			11.0496i			0.564610i	−0.959325	+	0.282305i	$0.908901\pi$
$384$	−18.2672			−0.932193
$385$	−5.39047	+	0.630497i	−0.274724	+	0.0321331i
$386$	−41.4940			−2.11199
$387$			4.76159i			0.242045i
$388$			35.2419i			1.78913i
$389$	4.87229			0.247035			0.123517	−	0.992342i	$-0.460583\pi$
$389$	4.87229			0.247035			0.123517	+	0.992342i	$0.460583\pi$
$390$	16.9966	−	1.98801i	0.860656	−	0.100667i
$391$	58.7327			2.97024
$392$			4.65971i			0.235351i
$393$			9.93406i			0.501107i
$394$	−28.7620			−1.44901
$395$	1.83876	+	15.7206i	0.0925183	+	0.790990i
$396$	−8.33874			−0.419037
$397$			28.7888i			1.44487i	0.691438	+	0.722435i	$0.256977\pi$
$397$			28.7888i			1.44487i	−0.691438	+	0.722435i	$0.743023\pi$
$398$		−	57.6681i		−	2.89064i
$399$	2.14006			0.107137
$400$	−12.5167	+	2.96864i	−0.625833	+	0.148432i
$401$	14.8413			0.741141			0.370571	−	0.928804i	$-0.379162\pi$
$401$	14.8413			0.741141			0.370571	+	0.928804i	$0.379162\pi$
$402$		−	13.8939i		−	0.692964i
$403$			1.73329i			0.0863413i
$404$	39.4818			1.96429
$405$	−0.677334	−	5.79091i	−0.0336570	−	0.287752i
$406$	−29.5297			−1.46554
$407$			3.19619i			0.158429i
$408$		−	25.8505i		−	1.27979i
$409$	1.79225			0.0886209			0.0443105	−	0.999018i	$-0.485891\pi$
$409$	1.79225			0.0886209			0.0443105	+	0.999018i	$0.485891\pi$
$410$	−57.3663	+	6.70985i	−2.83312	+	0.331376i
$411$	4.24815			0.209546
$412$			31.8406i			1.56867i
$413$		−	4.05201i		−	0.199386i
$414$	44.8651			2.20500
$415$	1.10693	−	0.129472i	0.0543369	−	0.00635553i
$416$	8.08022			0.396165
$417$		−	4.19929i		−	0.205640i
$418$			2.39831i			0.117305i
$419$	−26.4590			−1.29261			−0.646304	−	0.763080i	$-0.723686\pi$
$419$	−26.4590			−1.29261			−0.646304	+	0.763080i	$0.723686\pi$
$420$	−2.08576	−	17.8324i	−0.101775	−	0.870130i
$421$	25.1482			1.22565			0.612825	−	0.790219i	$-0.290033\pi$
$421$	25.1482			1.22565			0.612825	+	0.790219i	$0.290033\pi$
$422$		−	48.8688i		−	2.37889i
$423$		−	7.50404i		−	0.364859i
$424$	−26.1802			−1.27142
$425$	8.05163	+	33.9481i	0.390562	+	1.64672i
$426$	−8.17752			−0.396202
$427$		−	25.0161i		−	1.21061i
$428$		−	11.4565i		−	0.553772i
$429$	−3.19097			−0.154062
$430$	−1.33473	−	11.4114i	−0.0643665	−	0.550305i
$431$	27.9253			1.34511			0.672557	−	0.740045i	$-0.265196\pi$
$431$	27.9253			1.34511			0.672557	+	0.740045i	$0.265196\pi$
$432$		−	11.8473i		−	0.570004i
$433$		−	13.1923i		−	0.633984i	−0.948428	−	0.316992i	$-0.897327\pi$
$433$		−	13.1923i		−	0.633984i	0.948428	−	0.316992i	$-0.102673\pi$
$434$	2.78791			0.133824
$435$	−9.93416	+	1.16195i	−0.476307	+	0.0557113i
$436$	−26.4784			−1.26809
$437$		−	8.41688i		−	0.402634i
$438$		−	13.8498i		−	0.661767i
$439$	33.3084			1.58972			0.794861	−	0.606792i	$-0.207544\pi$
$439$	33.3084			1.58972			0.794861	+	0.606792i	$0.207544\pi$
$440$	9.33126	−	1.09143i	0.444850	−	0.0520320i
$441$	2.46494			0.117378
$442$			60.5650i			2.88078i
$443$		−	21.1149i		−	1.00320i	−0.865100	−	0.501599i	$-0.832745\pi$
$443$		−	21.1149i		−	1.00320i	0.865100	−	0.501599i	$-0.167255\pi$
$444$	−10.5734			−0.501791
$445$	3.58788	+	30.6747i	0.170082	+	1.45412i
$446$	12.1335			0.574539
$447$			18.3151i			0.866274i
$448$		−	25.4856i		−	1.20408i
$449$	18.7173			0.883326			0.441663	−	0.897181i	$-0.354389\pi$
$449$	18.7173			0.883326			0.441663	+	0.897181i	$0.354389\pi$
$450$	6.15053	+	25.9324i	0.289939	+	1.22247i
$451$	10.7701			0.507142
$452$		−	9.79120i		−	0.460539i
$453$		−	20.9128i		−	0.982570i
$454$	−33.0467			−1.55096
$455$	2.28177	+	19.5081i	0.106971	+	0.914555i
$456$	−3.70459			−0.173483
$457$		−	17.7899i		−	0.832178i	−0.909324	−	0.416089i	$-0.863400\pi$
$457$		−	17.7899i		−	0.832178i	0.909324	−	0.416089i	$-0.136600\pi$
$458$			33.2593i			1.55410i
$459$	−32.1326			−1.49982
$460$	−70.1347	+	8.20332i	−3.27005	+	0.382482i
$461$	37.8470			1.76271			0.881356	−	0.472452i	$-0.156631\pi$
$461$	37.8470			1.76271			0.881356	+	0.472452i	$0.156631\pi$
$462$			5.13253i			0.238787i
$463$			32.3807i			1.50486i	0.658672	+	0.752430i	$0.271119\pi$
$463$			32.3807i			1.50486i	−0.658672	+	0.752430i	$0.728881\pi$
$464$	13.0516			0.605907
$465$	0.937889	−	0.109700i	0.0434935	−	0.00508723i
$466$	42.4550			1.96669
$467$			35.0214i			1.62060i	0.586017	+	0.810298i	$0.300695\pi$
$467$			35.0214i			1.62060i	−0.586017	+	0.810298i	$0.699305\pi$
$468$			30.1779i			1.39497i
$469$	15.9469			0.736361
$470$	2.10348	+	17.9838i	0.0970261	+	0.829530i
$471$	−11.2126			−0.516649
$472$			7.01429i			0.322859i
$473$			2.14239i			0.0985072i
$474$	14.9684			0.687520
$475$	4.86504	−	1.15387i	0.223223	−	0.0529430i
$476$	63.5432			2.91250
$477$			13.8490i			0.634104i
$478$			34.4330i			1.57493i
$479$	−21.1526			−0.966489			−0.483245	−	0.875485i	$-0.660542\pi$
$479$	−21.1526			−0.966489			−0.483245	+	0.875485i	$0.660542\pi$
$480$	−0.511399	−	4.37223i	−0.0233421	−	0.199564i
$481$	11.5670			0.527411
$482$			6.16199i			0.280671i
$483$		−	18.0127i		−	0.819605i
$484$	−3.75187			−0.170539
$485$	−20.8615	+	2.44007i	−0.947272	+	0.110798i
$486$	−38.6455			−1.75299
$487$		−	4.46076i		−	0.202136i	−0.994880	−	0.101068i	$-0.967774\pi$
$487$		−	4.46076i		−	0.202136i	0.994880	−	0.101068i	$-0.0322260\pi$
$488$			43.3045i			1.96030i
$489$	−5.66962			−0.256389
$490$	−5.90734	+	0.690953i	−0.266867	+	0.0312141i
$491$	−11.9343			−0.538586			−0.269293	−	0.963058i	$-0.586790\pi$
$491$	−11.9343			−0.538586			−0.269293	+	0.963058i	$0.586790\pi$
$492$			35.6287i			1.60626i
$493$		−	35.3990i		−	1.59429i
$494$	8.67947			0.390508
$495$	−0.577356	−	4.93614i	−0.0259502	−	0.221863i
$496$	−1.23221			−0.0553279
$497$		−	9.38588i		−	0.421014i
$498$		−	1.05396i		−	0.0472290i
$499$	8.02905			0.359429			0.179715	−	0.983719i	$-0.442483\pi$
$499$	8.02905			0.359429			0.179715	+	0.983719i	$0.442483\pi$
$500$	−14.3563	−	39.4140i	−0.642035	−	1.76265i
$501$	18.3983			0.821973
$502$			43.4925i			1.94117i
$503$			42.8719i			1.91156i	0.294077	+	0.955782i	$0.404988\pi$
$503$			42.8719i			1.91156i	−0.294077	+	0.955782i	$0.595012\pi$
$504$	22.6648			1.00957
$505$	2.73363	+	23.3714i	0.121645	+	1.04001i
$506$	20.1862			0.897388
$507$			0.0856698i			0.00380473i
$508$		−	37.3082i		−	1.65528i
$509$	−5.15439			−0.228464			−0.114232	−	0.993454i	$-0.536441\pi$
$509$	−5.15439			−0.228464			−0.114232	+	0.993454i	$0.536441\pi$
$510$	32.7719	−	3.83317i	1.45117	−	0.169736i
$511$	15.8963			0.703210
$512$			27.3634i			1.20930i
$513$			4.60487i			0.203310i
$514$	−44.1732			−1.94840
$515$	−18.8481	+	2.20457i	−0.830547	+	0.0971450i
$516$	−7.08730			−0.312001
$517$		−	3.37631i		−	0.148490i
$518$		−	18.6050i		−	0.817457i
$519$	−18.1629			−0.797261
$520$	−3.94989	−	33.7698i	−0.173214	−	1.48091i
$521$	−15.9569			−0.699084			−0.349542	−	0.936921i	$-0.613663\pi$
$521$	−15.9569			−0.699084			−0.349542	+	0.936921i	$0.613663\pi$
$522$		−	27.0408i		−	1.18354i
$523$		−	16.8367i		−	0.736217i	−0.929783	−	0.368109i	$-0.880005\pi$
$523$		−	16.8367i		−	0.736217i	0.929783	−	0.368109i	$-0.119995\pi$
$524$	42.2707			1.84661
$525$	10.4115	−	2.46935i	0.454395	−	0.107771i
$526$	43.6809			1.90458
$527$			3.34204i			0.145581i
$528$		−	2.26849i		−	0.0987234i
$529$	−47.8439			−2.08017
$530$	−3.88206	−	33.1899i	−0.168626	−	1.44168i
$531$	3.71048			0.161021
$532$		−	9.10626i		−	0.394806i
$533$		−	38.9768i		−	1.68827i
$534$	29.2069			1.26391
$535$	6.78172	−	0.793225i	0.293199	−	0.0342941i
$536$	−27.6052			−1.19236
$537$			12.0071i			0.518146i
$538$		−	46.8564i		−	2.02012i
$539$	1.10906			0.0477704
$540$	38.3707	−	4.48803i	1.65121	−	0.193134i
$541$	22.3452			0.960693			0.480347	−	0.877079i	$-0.340511\pi$
$541$	22.3452			0.960693			0.480347	+	0.877079i	$0.340511\pi$
$542$			31.5503i			1.35520i
$543$			11.8891i			0.510211i
$544$	15.5798			0.667980
$545$	−1.83331	−	15.6740i	−0.0785303	−	0.671399i
$546$	18.5746			0.794920
$547$		−	31.9594i		−	1.36649i	−0.730191	−	0.683243i	$-0.760569\pi$
$547$		−	31.9594i		−	1.36649i	0.730191	−	0.683243i	$-0.239431\pi$
$548$		−	18.0764i		−	0.772187i
$549$	22.9076			0.977673
$550$	2.76732	+	11.6678i	0.117999	+	0.497519i
$551$	−5.07297			−0.216116
$552$			31.1811i			1.32716i
$553$			17.1802i			0.730576i
$554$	39.1233			1.66219
$555$	−0.732079	−	6.25895i	−0.0310750	−	0.265678i
$556$	−17.8685			−0.757795
$557$			27.5927i			1.16914i	0.811343	+	0.584570i	$0.198737\pi$
$557$			27.5927i			1.16914i	−0.811343	+	0.584570i	$0.801263\pi$
$558$			2.55293i			0.108074i
$559$	7.75331			0.327930
$560$	−13.8685	+	1.62213i	−0.586051	+	0.0685475i
$561$	−6.15266			−0.259766
$562$			16.6232i			0.701208i
$563$		−	13.1484i		−	0.554141i	−0.960850	−	0.277070i	$-0.910636\pi$
$563$		−	13.1484i		−	0.554141i	0.960850	−	0.277070i	$-0.0893635\pi$
$564$	11.1693			0.470310
$565$	5.79593	−	0.677921i	0.243836	−	0.0285204i
$566$	−69.7437			−2.93155
$567$		−	6.32856i		−	0.265774i
$568$			16.2476i			0.681733i
$569$	23.0070			0.964505			0.482252	−	0.876032i	$-0.339819\pi$
$569$	23.0070			0.964505			0.482252	+	0.876032i	$0.339819\pi$
$570$	−0.549325	−	4.69649i	−0.0230087	−	0.196714i
$571$	−25.2924			−1.05845			−0.529227	−	0.848480i	$-0.677518\pi$
$571$	−25.2924			−1.05845			−0.529227	+	0.848480i	$0.677518\pi$
$572$			13.5780i			0.567725i
$573$		−	1.46150i		−	0.0610549i
$574$	−62.6924			−2.61673
$575$	−9.71195	−	40.9484i	−0.405016	−	1.70767i
$576$	23.3375			0.972397
$577$			23.2447i			0.967689i	0.875154	+	0.483845i	$0.160760\pi$
$577$			23.2447i			0.967689i	−0.875154	+	0.483845i	$0.839240\pi$
$578$			76.0070i			3.16148i
$579$	−15.2551			−0.633980
$580$	4.94426	+	42.2712i	0.205299	+	1.75522i
$581$	1.20970			0.0501868
$582$			19.8632i			0.823358i
$583$			6.23113i			0.258067i
$584$	−27.5175			−1.13868
$585$	−17.8639	+	2.08945i	−0.738581	+	0.0863882i
$586$	34.1919			1.41245
$587$			3.22113i			0.132950i	0.997788	+	0.0664750i	$0.0211753\pi$
$587$			3.22113i			0.132950i	−0.997788	+	0.0664750i	$0.978825\pi$
$588$			3.66889i			0.151303i
$589$	0.478941			0.0197344
$590$	−8.89235	+	1.04009i	−0.366092	+	0.0428200i
$591$	−10.5742			−0.434967
$592$			8.22309i			0.337967i
$593$			15.4786i			0.635628i	0.948153	+	0.317814i	$0.102949\pi$
$593$			15.4786i			0.635628i	−0.948153	+	0.317814i	$0.897051\pi$
$594$	−11.0439			−0.453136
$595$	4.39959	+	37.6145i	0.180366	+	1.54205i
$596$	77.9331			3.19227
$597$		−	21.2014i		−	0.867717i
$598$		−	73.0540i		−	2.98740i
$599$	33.1111			1.35288			0.676441	−	0.736497i	$-0.263521\pi$
$599$	33.1111			1.35288			0.676441	+	0.736497i	$0.263521\pi$
$600$	−18.0230	+	4.27460i	−0.735785	+	0.174510i
$601$	−29.0826			−1.18630			−0.593151	−	0.805091i	$-0.702116\pi$
$601$	−29.0826			−1.18630			−0.593151	+	0.805091i	$0.702116\pi$
$602$		−	12.4708i		−	0.508273i
$603$			14.6028i			0.594674i
$604$	−88.9868			−3.62082
$605$	−0.259771	−	2.22093i	−0.0105612	−	0.0902935i
$606$	22.2530			0.903966
$607$			31.2259i			1.26742i	0.773570	+	0.633711i	$0.218469\pi$
$607$			31.2259i			1.26742i	−0.773570	+	0.633711i	$0.781531\pi$
$608$		−	2.23272i		−	0.0905488i
$609$	−10.8565			−0.439927
$610$	−54.8992	+	6.42129i	−2.22280	+	0.259990i
$611$	−12.2189			−0.494322
$612$			58.1874i			2.35209i
$613$			28.3645i			1.14563i	0.819685	+	0.572815i	$0.194149\pi$
$613$			28.3645i			1.14563i	−0.819685	+	0.572815i	$0.805851\pi$
$614$	80.5273			3.24982
$615$	−21.0905	+	2.46685i	−0.850450	+	0.0994731i
$616$	10.1976			0.410873
$617$		−	6.34748i		−	0.255540i	−0.991804	−	0.127770i	$-0.959218\pi$
$617$		−	6.34748i		−	0.255540i	0.991804	−	0.127770i	$-0.0407819\pi$
$618$			17.9462i			0.721901i
$619$	−41.7475			−1.67797			−0.838987	−	0.544152i	$-0.816852\pi$
$619$	−41.7475			−1.67797			−0.838987	+	0.544152i	$0.816852\pi$
$620$	−0.466789	−	3.99084i	−0.0187467	−	0.160276i
$621$	38.7587			1.55533
$622$			38.8987i			1.55970i
$623$			33.5227i			1.34306i
$624$	−8.20967			−0.328650
$625$	22.3372	−	11.2272i	0.893488	−	0.449088i
$626$	−51.2697			−2.04915
$627$			0.881728i			0.0352128i
$628$			47.7111i			1.90388i
$629$	22.3029			0.889275
$630$	3.36078	+	28.7332i	0.133897	+	1.14476i
$631$	12.8808			0.512775			0.256388	−	0.966574i	$-0.417468\pi$
$631$	12.8808			0.512775			0.256388	+	0.966574i	$0.417468\pi$
$632$		−	29.7400i		−	1.18299i
$633$		−	17.9664i		−	0.714101i
$634$	−1.63763			−0.0650385
$635$	22.0847	−	2.58314i	0.876404	−	0.102509i
$636$	−20.6134			−0.817374
$637$		−	4.01367i		−	0.159027i
$638$		−	12.1665i		−	0.481678i
$639$	8.59479			0.340005
$640$	−46.0120	+	5.38181i	−1.81879	+	0.212735i
$641$	2.77014			0.109414			0.0547070	−	0.998502i	$-0.482578\pi$
$641$	2.77014			0.109414			0.0547070	+	0.998502i	$0.482578\pi$
$642$		−	6.45720i		−	0.254845i
$643$			16.8712i			0.665335i	0.943044	+	0.332667i	$0.107949\pi$
$643$			16.8712i			0.665335i	−0.943044	+	0.332667i	$0.892051\pi$
$644$	−76.6463			−3.02029
$645$	−0.490709	−	4.19534i	−0.0193216	−	0.165191i
$646$	16.7353			0.658441
$647$			32.9371i			1.29489i	0.762111	+	0.647446i	$0.224163\pi$
$647$			32.9371i			1.29489i	−0.762111	+	0.647446i	$0.775837\pi$
$648$			10.9551i			0.430359i
$649$	1.66947			0.0655323
$650$	42.2259	−	10.0149i	1.65624	−	0.392818i
$651$	1.02497			0.0401716
$652$			24.1250i			0.944808i
$653$		−	36.2654i		−	1.41917i	−0.704618	−	0.709587i	$-0.748881\pi$
$653$		−	36.2654i		−	1.41917i	0.704618	−	0.709587i	$-0.251119\pi$
$654$	−14.9239			−0.583572
$655$	2.92673	+	25.0223i	0.114357	+	0.977701i
$656$	27.7090			1.08185
$657$			14.5565i			0.567902i
$658$			19.6535i			0.766172i
$659$	32.7584			1.27609			0.638044	−	0.770000i	$-0.279744\pi$
$659$	32.7584			1.27609			0.638044	+	0.770000i	$0.279744\pi$
$660$	7.34711	−	0.859356i	0.285986	−	0.0334504i
$661$	−36.5425			−1.42134			−0.710669	−	0.703526i	$-0.751608\pi$
$661$	−36.5425			−1.42134			−0.710669	+	0.703526i	$0.751608\pi$
$662$			17.5145i			0.680720i
$663$			22.2665i			0.864759i
$664$	−2.09407			−0.0812656
$665$	5.39047	−	0.630497i	0.209034	−	0.0244496i
$666$	17.0369			0.660166
$667$			42.6986i			1.65330i
$668$		−	78.2870i		−	3.02902i
$669$	4.46084			0.172466
$670$	−4.09336	−	34.9964i	−0.158140	−	1.35203i
$671$	10.3069			0.397892
$672$		−	4.77817i		−	0.184322i
$673$		−	45.4842i		−	1.75329i	−0.481141	−	0.876643i	$-0.659778\pi$
$673$		−	45.4842i		−	1.75329i	0.481141	−	0.876643i	$-0.340222\pi$
$674$	41.2185			1.58768
$675$	5.31340	+	22.4029i	0.204513	+	0.862287i
$676$	0.364537			0.0140206
$677$			28.5739i			1.09818i	0.835762	+	0.549092i	$0.185027\pi$
$677$			28.5739i			1.09818i	−0.835762	+	0.549092i	$0.814973\pi$
$678$		−	5.51858i		−	0.211940i
$679$	−22.7984			−0.874921
$680$	−7.61597	−	65.1132i	−0.292059	−	2.49698i
$681$	−12.1495			−0.465569
$682$			1.14865i			0.0439840i
$683$		−	21.3120i		−	0.815483i	−0.913097	−	0.407741i	$-0.866316\pi$
$683$		−	21.3120i		−	0.815483i	0.913097	−	0.407741i	$-0.133684\pi$
$684$	8.33874			0.318840
$685$	10.7004	−	1.25157i	0.408841	−	0.0478201i
$686$	−47.2027			−1.80221
$687$			12.2276i			0.466513i
$688$			5.51190i			0.210139i
$689$	22.5505			0.859105
$690$	−39.5298	+	4.62361i	−1.50487	+	0.176018i
$691$	14.4436			0.549462			0.274731	−	0.961521i	$-0.411411\pi$
$691$	14.4436			0.549462			0.274731	+	0.961521i	$0.411411\pi$
$692$			77.2854i			2.93795i
$693$		−	5.39443i		−	0.204917i
$694$	−8.14264			−0.309090
$695$	−1.23718	−	10.5773i	−0.0469289	−	0.401221i
$696$	18.7933			0.712358
$697$		−	75.1530i		−	2.84662i
$698$		−	28.0754i		−	1.06267i
$699$	15.6084			0.590364
$700$	−10.5074	−	44.3023i	−0.397142	−	1.67447i
$701$	25.1962			0.951647			0.475823	−	0.879541i	$-0.342150\pi$
$701$	25.1962			0.951647			0.475823	+	0.879541i	$0.342150\pi$
$702$			39.9678i			1.50849i
$703$		−	3.19619i		−	0.120547i
$704$	10.5003			0.395745
$705$	0.773335	+	6.61167i	0.0291255	+	0.249010i
$706$	−9.46637			−0.356272
$707$			25.5412i			0.960577i
$708$			5.52280i			0.207560i
$709$	−28.5121			−1.07079			−0.535397	−	0.844600i	$-0.679838\pi$
$709$	−28.5121			−1.07079			−0.535397	+	0.844600i	$0.679838\pi$
$710$	−20.5978	+	2.40923i	−0.773023	+	0.0904167i
$711$	−15.7322			−0.590002
$712$		−	58.0300i		−	2.17477i
$713$		−	4.03119i		−	0.150969i
$714$	35.8146			1.34033
$715$	−8.03754	+	0.940112i	−0.300587	+	0.0351582i
$716$	51.0919			1.90939
$717$			12.6592i			0.472765i
$718$			11.0700i			0.413128i
$719$	−36.2670			−1.35253			−0.676265	−	0.736658i	$-0.736403\pi$
$719$	−36.2670			−1.35253			−0.676265	+	0.736658i	$0.736403\pi$
$720$	−1.48541	−	12.6996i	−0.0553579	−	0.473286i
$721$	−20.5980			−0.767111
$722$		−	2.39831i		−	0.0892557i
$723$			2.26543i			0.0842523i
$724$	50.5897			1.88015
$725$	−24.6802	+	5.85353i	−0.916600	+	0.217395i
$726$	−2.11465			−0.0784821
$727$			45.1687i			1.67521i	0.546273	+	0.837607i	$0.316046\pi$
$727$			45.1687i			1.67521i	−0.546273	+	0.837607i	$0.683954\pi$
$728$		−	36.9051i		−	1.36780i
$729$	−6.38557			−0.236503
$730$	−4.08036	−	34.8853i	−0.151021	−	1.29116i
$731$	14.9495			0.552928
$732$			34.0964i			1.26024i
$733$		−	47.5104i		−	1.75484i	−0.479727	−	0.877418i	$-0.659264\pi$
$733$		−	47.5104i		−	1.75484i	0.479727	−	0.877418i	$-0.340736\pi$
$734$	−25.0122			−0.923218
$735$	−2.17181	+	0.254026i	−0.0801085	+	0.00936990i
$736$	−18.7925			−0.692702
$737$			6.57029i			0.242020i
$738$		−	57.4083i		−	2.11323i
$739$	−18.3467			−0.674894			−0.337447	−	0.941344i	$-0.609563\pi$
$739$	−18.3467			−0.674894			−0.337447	+	0.941344i	$0.609563\pi$
$740$	−26.6327	+	3.11509i	−0.979036	+	0.114513i
$741$	3.19097			0.117223
$742$		−	36.2714i		−	1.33156i
$743$		−	10.1542i		−	0.372522i	−0.982500	−	0.186261i	$-0.940363\pi$
$743$		−	10.1542i		−	0.372522i	0.982500	−	0.186261i	$-0.0596370\pi$
$744$	−1.77428			−0.0650484
$745$	5.39592	+	46.1327i	0.197691	+	1.69017i
$746$	−70.0104			−2.56326
$747$			1.10774i			0.0405301i
$748$			26.1804i			0.957250i
$749$	7.41136			0.270805
$750$	−8.09161	−	22.2147i	−0.295464	−	0.811168i
$751$	40.9167			1.49307			0.746535	−	0.665346i	$-0.231716\pi$
$751$	40.9167			1.49307			0.746535	+	0.665346i	$0.231716\pi$
$752$		−	8.68650i		−	0.316764i
$753$			15.9899i			0.582703i
$754$	−44.0307			−1.60350
$755$	−6.16125	−	52.6760i	−0.224231	−	1.91707i
$756$	41.9332			1.52509
$757$		−	47.6130i		−	1.73053i	−0.501319	−	0.865263i	$-0.667152\pi$
$757$		−	47.6130i		−	1.73053i	0.501319	−	0.865263i	$-0.332848\pi$
$758$		−	28.5242i		−	1.03605i
$759$	7.42140			0.269380
$760$	−9.33126	+	1.09143i	−0.338480	+	0.0395904i
$761$	0.701613			0.0254335			0.0127167	−	0.999919i	$-0.495952\pi$
$761$	0.701613			0.0254335			0.0127167	+	0.999919i	$0.495952\pi$
$762$		−	21.0279i		−	0.761760i
$763$		−	17.1292i		−	0.620119i
$764$	−6.21886			−0.224990
$765$	−34.4442	+	4.02877i	−1.24533	+	0.145660i
$766$	26.5004			0.957499
$767$		−	6.04180i		−	0.218157i
$768$			25.2935i			0.912699i
$769$	11.1424			0.401806			0.200903	−	0.979611i	$-0.435612\pi$
$769$	11.1424			0.401806			0.200903	+	0.979611i	$0.435612\pi$
$770$	1.51213	+	12.9280i	0.0544932	+	0.465893i
$771$	−16.2401			−0.584873
$772$			64.9125i			2.33625i
$773$			5.07851i			0.182661i	0.995821	+	0.0913306i	$0.0291120\pi$
$773$			5.07851i			0.182661i	−0.995821	+	0.0913306i	$0.970888\pi$
$774$	11.4197			0.410474
$775$	2.33007	−	0.552634i	0.0836985	−	0.0198512i
$776$	39.4655			1.41673
$777$		−	6.84006i		−	0.245386i
$778$		−	11.6852i		−	0.418936i
$779$	−10.7701			−0.385877
$780$	−3.11001	−	26.5892i	−0.111356	−	0.952045i
$781$	3.86707			0.138375
$782$		−	140.859i		−	5.03710i
$783$		−	23.3604i		−	0.834832i
$784$	2.85335			0.101906
$785$	−28.2427	+	3.30341i	−1.00802	+	0.117904i
$786$	23.8249			0.849806
$787$		−	14.9335i		−	0.532322i	−0.963929	−	0.266161i	$-0.914245\pi$
$787$		−	14.9335i		−	0.532322i	0.963929	−	0.266161i	$-0.0857554\pi$
$788$			44.9948i			1.60287i
$789$	16.0591			0.571720
$790$	37.7029	−	4.40992i	1.34141	−	0.156898i
$791$	6.33404			0.225213
$792$			9.33810i			0.331815i
$793$		−	37.3006i		−	1.32458i
$794$	69.0444			2.45030
$795$	−1.42722	−	12.2021i	−0.0506185	−	0.432765i
$796$	−90.2150			−3.19759
$797$			21.9700i			0.778218i	0.921192	+	0.389109i	$0.127217\pi$
$797$			21.9700i			0.778218i	−0.921192	+	0.389109i	$0.872783\pi$
$798$		−	5.13253i		−	0.181690i
$799$	−23.5598			−0.833484
$800$	−2.57626	−	10.8623i	−0.0910845	−	0.384039i
$801$	−30.6972			−1.08463
$802$		−	35.5941i		−	1.25687i
$803$			6.54942i			0.231124i
$804$	−21.7354			−0.766547
$805$	−5.30682	−	45.3710i	−0.187041	−	1.59912i
$806$	4.15696			0.146423
$807$		−	17.2266i		−	0.606404i
$808$		−	44.2136i		−	1.55543i
$809$	34.2895			1.20555			0.602777	−	0.797910i	$-0.294061\pi$
$809$	34.2895			1.20555			0.602777	+	0.797910i	$0.294061\pi$
$810$	−13.8884	+	1.62445i	−0.487987	+	0.0570775i
$811$	29.3319			1.02998			0.514992	−	0.857195i	$-0.327795\pi$
$811$	29.3319			1.02998			0.514992	+	0.857195i	$0.327795\pi$
$812$			46.1958i			1.62115i
$813$			11.5993i			0.406806i
$814$	7.66544			0.268674
$815$	−14.2809	+	1.67036i	−0.500236	+	0.0585102i
$816$	−15.8294			−0.554141
$817$		−	2.14239i		−	0.0749528i
$818$		−	4.29836i		−	0.150288i
$819$	−19.5224			−0.682169
$820$	10.4968	+	89.7428i	0.366564	+	3.13396i
$821$	−45.6628			−1.59364			−0.796822	−	0.604214i	$-0.793487\pi$
$821$	−45.6628			−1.59364			−0.796822	+	0.604214i	$0.793487\pi$
$822$		−	10.1883i		−	0.355359i
$823$			8.33710i			0.290613i	0.989387	+	0.145306i	$0.0464168\pi$
$823$			8.33710i			0.290613i	−0.989387	+	0.145306i	$0.953583\pi$
$824$	35.6565			1.24215
$825$	1.01740	+	4.28964i	0.0354212	+	0.149346i
$826$	−9.71795			−0.338131
$827$		−	21.3910i		−	0.743837i	−0.928265	−	0.371918i	$-0.878700\pi$
$827$		−	21.3910i		−	0.743837i	0.928265	−	0.371918i	$-0.121300\pi$
$828$		−	70.1862i		−	2.43914i
$829$	−31.3777			−1.08979			−0.544895	−	0.838504i	$-0.683431\pi$
$829$	−31.3777			−1.08979			−0.544895	+	0.838504i	$0.683431\pi$
$830$	−0.310513	−	2.65475i	−0.0107781	−	0.0921477i
$831$	14.3835			0.498959
$832$		−	38.0006i		−	1.31743i
$833$		−	7.73895i		−	0.268139i
$834$	−10.0712			−0.348737
$835$	46.3422	−	5.42042i	1.60374	−	0.187581i
$836$	3.75187			0.129761
$837$			2.20546i			0.0762320i
$838$			63.4568i			2.19208i
$839$	−22.4365			−0.774594			−0.387297	−	0.921955i	$-0.626591\pi$
$839$	−22.4365			−0.774594			−0.387297	+	0.921955i	$0.626591\pi$
$840$	−19.9695	+	2.33574i	−0.689013	+	0.0805905i
$841$	−3.26496			−0.112585
$842$		−	60.3131i		−	2.07853i
$843$			6.11146i			0.210490i
$844$	−76.4495			−2.63150
$845$	0.0252397	+	0.215788i	0.000868272	+	0.00742334i
$846$	−17.9970			−0.618749
$847$		−	2.42713i		−	0.0833971i
$848$			16.0313i			0.550518i
$849$	−25.6410			−0.879997
$850$	81.4178	−	19.3103i	2.79261	−	0.662337i
$851$	−26.9020			−0.922187
$852$			12.7928i			0.438273i
$853$			17.2099i			0.589254i	0.955612	+	0.294627i	$0.0951955\pi$
$853$			17.2099i			0.589254i	−0.955612	+	0.294627i	$0.904805\pi$
$854$	−59.9962			−2.05303
$855$	0.577356	+	4.93614i	0.0197452	+	0.168812i
$856$	−12.8295			−0.438505
$857$			37.0827i			1.26672i	0.773857	+	0.633360i	$0.218325\pi$
$857$			37.0827i			1.26672i	−0.773857	+	0.633360i	$0.781675\pi$
$858$			7.65293i			0.261267i
$859$	−50.3098			−1.71655			−0.858274	−	0.513191i	$-0.828463\pi$
$859$	−50.3098			−1.71655			−0.858274	+	0.513191i	$0.828463\pi$
$860$	−17.8517	+	2.08803i	−0.608740	+	0.0712013i
$861$	−23.0486			−0.785494
$862$		−	66.9734i		−	2.28112i
$863$			34.3964i			1.17087i	0.810720	+	0.585434i	$0.199076\pi$
$863$			34.3964i			1.17087i	−0.810720	+	0.585434i	$0.800924\pi$
$864$	10.2814			0.349780
$865$	−45.7493	+	5.35107i	−1.55552	+	0.181942i
$866$	−31.6393			−1.07515
$867$			27.9437i			0.949017i
$868$		−	4.36137i		−	0.148034i
$869$	−7.07840			−0.240118
$870$	2.78671	+	23.8252i	0.0944784	+	0.807748i
$871$	23.7779			0.805683
$872$			29.6518i			1.00414i
$873$		−	20.8768i		−	0.706573i
$874$	−20.1862			−0.682810
$875$	25.4973	−	9.28728i	0.861968	−	0.313967i
$876$	−21.6663			−0.732037
$877$			44.8126i			1.51321i	0.653870	+	0.756607i	$0.273144\pi$
$877$			44.8126i			1.51321i	−0.653870	+	0.756607i	$0.726856\pi$
$878$		−	79.8836i		−	2.69594i
$879$	12.5705			0.423992
$880$	−0.668334	−	5.71396i	−0.0225295	−	0.192617i
$881$	−15.3024			−0.515550			−0.257775	−	0.966205i	$-0.582989\pi$
$881$	−15.3024			−0.515550			−0.257775	+	0.966205i	$0.582989\pi$
$882$		−	5.91167i		−	0.199056i
$883$		−	8.49905i		−	0.286016i	−0.989722	−	0.143008i	$-0.954323\pi$
$883$		−	8.49905i		−	0.286016i	0.989722	−	0.143008i	$-0.0456775\pi$
$884$	94.7469			3.18668
$885$	−3.26924	+	0.382387i	−0.109894	+	0.0128538i
$886$	−50.6399			−1.70128
$887$			22.9800i			0.771593i	0.922584	+	0.385796i	$0.126073\pi$
$887$			22.9800i			0.771593i	−0.922584	+	0.385796i	$0.873927\pi$
$888$			11.8406i			0.397344i
$889$	24.1351			0.809466
$890$	73.5674	−	8.60482i	2.46598	−	0.288434i
$891$	2.60743			0.0873521
$892$		−	18.9815i		−	0.635547i
$893$			3.37631i			0.112984i
$894$	43.9252			1.46908
$895$	3.53749	+	30.2440i	0.118245	+	1.01094i
$896$	−50.2840			−1.67987
$897$		−	26.8580i		−	0.896763i
$898$		−	44.8899i		−	1.49800i
$899$	−2.42966			−0.0810336
$900$	40.5683	−	9.62178i	1.35228	−	0.320726i
$901$	43.4806			1.44855
$902$		−	25.8299i		−	0.860041i
$903$		−	4.58486i		−	0.152574i
$904$	−10.9646			−0.364678
$905$	3.50272	+	29.9467i	0.116434	+	0.995463i
$906$	−50.1553			−1.66630
$907$			45.6766i			1.51667i	0.651866	+	0.758334i	$0.273986\pi$
$907$			45.6766i			1.51667i	−0.651866	+	0.758334i	$0.726014\pi$
$908$			51.6976i			1.71565i
$909$	−23.3885			−0.775748
$910$	46.7864	−	5.47238i	1.55096	−	0.181408i
$911$	42.6676			1.41364			0.706820	−	0.707393i	$-0.250129\pi$
$911$	42.6676			1.41364			0.706820	+	0.707393i	$0.250129\pi$
$912$			2.26849i			0.0751172i
$913$			0.498408i			0.0164949i
$914$	−42.6657			−1.41126
$915$	−20.1835	+	2.36076i	−0.667245	+	0.0780444i
$916$	52.0302			1.71913
$917$			27.3454i			0.903026i
$918$			77.0639i			2.54349i
$919$	35.2065			1.16135			0.580677	−	0.814134i	$-0.302788\pi$
$919$	35.2065			1.16135			0.580677	+	0.814134i	$0.302788\pi$
$920$	9.18645	+	78.5401i	0.302868	+	2.58939i
$921$	29.6056			0.975536
$922$		−	90.7688i		−	2.98931i
$923$		−	13.9949i		−	0.460649i
$924$	8.02924			0.264143
$925$	−3.68798	−	15.5496i	−0.121260	−	0.511267i
$926$	77.6589			2.55203
$927$		−	18.8619i		−	0.619507i
$928$			11.3265i			0.371812i
$929$	10.1969			0.334551			0.167275	−	0.985910i	$-0.446503\pi$
$929$	10.1969			0.334551			0.167275	+	0.985910i	$0.446503\pi$
$930$	−0.263095	−	2.24934i	−0.00862722	−	0.0737589i
$931$	−1.10906			−0.0363478
$932$		−	66.4159i		−	2.17552i
$933$			14.3010i			0.468193i
$934$	83.9920			2.74830
$935$	−15.4976	+	1.81267i	−0.506824	+	0.0592808i
$936$	33.7946			1.10461
$937$		−	17.2852i		−	0.564684i	−0.959314	−	0.282342i	$-0.908889\pi$
$937$		−	17.2852i		−	0.564684i	0.959314	−	0.282342i	$-0.0911112\pi$
$938$		−	38.2456i		−	1.24876i
$939$	−18.8491			−0.615117
$940$	28.1335	−	3.29064i	0.917614	−	0.107329i
$941$	−26.6527			−0.868853			−0.434427	−	0.900707i	$-0.643049\pi$
$941$	−26.6527			−0.868853			−0.434427	+	0.900707i	$0.643049\pi$
$942$			26.8912i			0.876163i
$943$			90.6502i			2.95198i
$944$	4.29517			0.139796
$945$	2.90336	+	24.8224i	0.0944463	+	0.807474i
$946$	5.13811			0.167054
$947$		−	6.36411i		−	0.206806i	−0.994640	−	0.103403i	$-0.967027\pi$
$947$		−	6.36411i		−	0.206806i	0.994640	−	0.103403i	$-0.0329731\pi$
$948$		−	23.4163i		−	0.760524i
$949$	23.7024			0.769411
$950$	−2.76732	−	11.6678i	−0.0897838	−	0.378555i
$951$	−0.602067			−0.0195234
$952$		−	71.1585i		−	2.30626i
$953$		−	43.9993i		−	1.42528i	−0.701532	−	0.712638i	$-0.747500\pi$
$953$		−	43.9993i		−	1.42528i	0.701532	−	0.712638i	$-0.252500\pi$
$954$	33.2142			1.07535
$955$	−0.430580	−	3.68127i	−0.0139332	−	0.119123i
$956$	53.8664			1.74216
$957$		−	4.47298i		−	0.144591i
$958$			50.7305i			1.63903i
$959$	11.6938			0.377614
$960$	−20.5623	+	2.40507i	−0.663644	+	0.0776232i
$961$	−30.7706			−0.992600
$962$		−	27.7412i		−	0.894413i
$963$			6.78669i			0.218698i
$964$	9.63971			0.310474
$965$	−38.4251	+	4.49440i	−1.23695	+	0.144680i
$966$	−43.1999			−1.38993
$967$			34.0102i			1.09370i	0.837232	+	0.546848i	$0.184172\pi$
$967$			34.0102i			1.09370i	−0.837232	+	0.546848i	$0.815828\pi$
$968$			4.20151i			0.135042i
$969$	6.15266			0.197652
$970$	5.85203	+	50.0323i	0.187897	+	1.60644i
$971$	−12.6084			−0.404623			−0.202312	−	0.979321i	$-0.564845\pi$
$971$	−12.6084			−0.404623			−0.202312	+	0.979321i	$0.564845\pi$
$972$			60.4563i			1.93914i
$973$		−	11.5594i		−	0.370576i
$974$	−10.6983			−0.342794
$975$	15.5242	−	3.68195i	0.497172	−	0.117917i
$976$	26.5173			0.848798
$977$			12.1967i			0.390206i	0.980783	+	0.195103i	$0.0625041\pi$
$977$			12.1967i			0.390206i	−0.980783	+	0.195103i	$0.937496\pi$
$978$			13.5975i			0.434800i
$979$	−13.8117			−0.441423
$980$	1.08092	+	9.24135i	0.0345286	+	0.295204i
$981$	15.6855			0.500798
$982$			28.6220i			0.913365i
$983$			14.4664i			0.461407i	0.973024	+	0.230703i	$0.0741027\pi$
$983$			14.4664i			0.461407i	−0.973024	+	0.230703i	$0.925897\pi$
$984$	39.8986			1.27192
$985$	−26.6348	+	3.11534i	−0.848655	+	0.0992631i
$986$	−84.8976			−2.70369
$987$			7.22552i			0.229991i
$988$		−	13.5780i		−	0.431974i
$989$	−18.0322			−0.573392
$990$	−11.8384	+	1.38468i	−0.376248	+	0.0440079i
$991$	−0.197926			−0.00628733			−0.00314367	−	0.999995i	$-0.501001\pi$
$991$	−0.197926			−0.00628733			−0.00314367	+	0.999995i	$0.501001\pi$
$992$		−	1.06934i		−	0.0339517i
$993$			6.43913i			0.204340i
$994$	−22.5102			−0.713980
$995$	−6.24629	−	53.4030i	−0.198021	−	1.69299i
$996$	−1.64880			−0.0522441
$997$			18.6791i			0.591572i	0.955254	+	0.295786i	$0.0955815\pi$
$997$			18.6791i			0.591572i	−0.955254	+	0.295786i	$0.904418\pi$
$998$		−	19.2561i		−	0.609541i
$999$	14.7181			0.465659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.4	✓	30
5.2	odd	4		5225.2.a.bc.1.27		30
5.3	odd	4		5225.2.a.bc.1.4		30
5.4	even	2	inner	1045.2.b.e.419.27	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.4	✓	30	1.1	even	1	trivial
1045.2.b.e.419.27	yes	30	5.4	even	2	inner
5225.2.a.bc.1.4		30	5.3	odd	4
5225.2.a.bc.1.27		30	5.2	odd	4

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.39831i q^{2} -0.881728i q^{3} -3.75187 q^{4} +(-0.259771 - 2.22093i) q^{5} -2.11465 q^{6} -2.42713i q^{7} +4.20151i q^{8} +2.22256 q^{9} +O(q^{10})\)	\(q-2.39831i q^{2} -0.881728i q^{3} -3.75187 q^{4} +(-0.259771 - 2.22093i) q^{5} -2.11465 q^{6} -2.42713i q^{7} +4.20151i q^{8} +2.22256 q^{9} +(-5.32646 + 0.623010i) q^{10} +1.00000 q^{11} +3.30813i q^{12} -3.61900i q^{13} -5.82099 q^{14} +(-1.95825 + 0.229047i) q^{15} +2.57278 q^{16} -6.97796i q^{17} -5.33037i q^{18} -1.00000 q^{19} +(0.974627 + 8.33263i) q^{20} -2.14006 q^{21} -2.39831i q^{22} +8.41688i q^{23} +3.70459 q^{24} +(-4.86504 + 1.15387i) q^{25} -8.67947 q^{26} -4.60487i q^{27} +9.10626i q^{28} +5.07297 q^{29} +(0.549325 + 4.69649i) q^{30} -0.478941 q^{31} +2.23272i q^{32} -0.881728i q^{33} -16.7353 q^{34} +(-5.39047 + 0.630497i) q^{35} -8.33874 q^{36} +3.19619i q^{37} +2.39831i q^{38} -3.19097 q^{39} +(9.33126 - 1.09143i) q^{40} +10.7701 q^{41} +5.13253i q^{42} +2.14239i q^{43} -3.75187 q^{44} +(-0.577356 - 4.93614i) q^{45} +20.1862 q^{46} -3.37631i q^{47} -2.26849i q^{48} +1.10906 q^{49} +(2.76732 + 11.6678i) q^{50} -6.15266 q^{51} +13.5780i q^{52} +6.23113i q^{53} -11.0439 q^{54} +(-0.259771 - 2.22093i) q^{55} +10.1976 q^{56} +0.881728i q^{57} -12.1665i q^{58} +1.66947 q^{59} +(7.34711 - 0.859356i) q^{60} +10.3069 q^{61} +1.14865i q^{62} -5.39443i q^{63} +10.5003 q^{64} +(-8.03754 + 0.940112i) q^{65} -2.11465 q^{66} +6.57029i q^{67} +26.1804i q^{68} +7.42140 q^{69} +(1.51213 + 12.9280i) q^{70} +3.86707 q^{71} +9.33810i q^{72} +6.54942i q^{73} +7.66544 q^{74} +(1.01740 + 4.28964i) q^{75} +3.75187 q^{76} -2.42713i q^{77} +7.65293i q^{78} -7.07840 q^{79} +(-0.668334 - 5.71396i) q^{80} +2.60743 q^{81} -25.8299i q^{82} +0.498408i q^{83} +8.02924 q^{84} +(-15.4976 + 1.81267i) q^{85} +5.13811 q^{86} -4.47298i q^{87} +4.20151i q^{88} -13.8117 q^{89} +(-11.8384 + 1.38468i) q^{90} -8.78377 q^{91} -31.5790i q^{92} +0.422296i q^{93} -8.09742 q^{94} +(0.259771 + 2.22093i) q^{95} +1.96865 q^{96} -9.39315i q^{97} -2.65985i q^{98} +2.22256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more