LMFDB - Embedded newform 1045.2.b.c.419.7

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + \cdots + 4 $ x^20 + 26x^18 + 281x^16 + 1640x^14 + 5623x^12 + 11551x^10 + 13894x^8 + 9095x^6 + 2753x^4 + 276*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.7
Root			$-1.22468i$ of defining polynomial
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.c.419.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22468i q^{2} +1.51450i q^{3} +0.500160 q^{4} +(-1.12399 + 1.93304i) q^{5} +1.85478 q^{6} +0.966830i q^{7} -3.06189i q^{8} +0.706295 q^{9} +O(q^{10})$	\(q-1.22468i q^{2} +1.51450i q^{3} +0.500160 q^{4} +(-1.12399 + 1.93304i) q^{5} +1.85478 q^{6} +0.966830i q^{7} -3.06189i q^{8} +0.706295 q^{9} +(2.36736 + 1.37652i) q^{10} +1.00000 q^{11} +0.757491i q^{12} +3.72985i q^{13} +1.18406 q^{14} +(-2.92759 - 1.70227i) q^{15} -2.74952 q^{16} +2.85383i q^{17} -0.864985i q^{18} +1.00000 q^{19} +(-0.562172 + 0.966830i) q^{20} -1.46426 q^{21} -1.22468i q^{22} +1.26493i q^{23} +4.63723 q^{24} +(-2.47331 - 4.34542i) q^{25} +4.56788 q^{26} +5.61318i q^{27} +0.483570i q^{28} -2.66677 q^{29} +(-2.08474 + 3.58536i) q^{30} -0.0694967 q^{31} -2.75651i q^{32} +1.51450i q^{33} +3.49502 q^{34} +(-1.86893 - 1.08670i) q^{35} +0.353260 q^{36} -0.887066i q^{37} -1.22468i q^{38} -5.64886 q^{39} +(5.91878 + 3.44152i) q^{40} -7.73545 q^{41} +1.79325i q^{42} -5.48663i q^{43} +0.500160 q^{44} +(-0.793865 + 1.36530i) q^{45} +1.54913 q^{46} +11.2850i q^{47} -4.16414i q^{48} +6.06524 q^{49} +(-5.32175 + 3.02902i) q^{50} -4.32211 q^{51} +1.86552i q^{52} +12.5557i q^{53} +6.87434 q^{54} +(-1.12399 + 1.93304i) q^{55} +2.96033 q^{56} +1.51450i q^{57} +3.26594i q^{58} +10.0125 q^{59} +(-1.46426 - 0.851409i) q^{60} +9.57033 q^{61} +0.0851112i q^{62} +0.682867i q^{63} -8.87488 q^{64} +(-7.20997 - 4.19230i) q^{65} +1.85478 q^{66} +13.5976i q^{67} +1.42737i q^{68} -1.91573 q^{69} +(-1.33086 + 2.28883i) q^{70} -14.9834 q^{71} -2.16260i q^{72} +2.93685i q^{73} -1.08637 q^{74} +(6.58114 - 3.74583i) q^{75} +0.500160 q^{76} +0.966830i q^{77} +6.91804i q^{78} +14.8054 q^{79} +(3.09042 - 5.31494i) q^{80} -6.38226 q^{81} +9.47344i q^{82} -10.1575i q^{83} -0.732365 q^{84} +(-5.51657 - 3.20766i) q^{85} -6.71937 q^{86} -4.03881i q^{87} -3.06189i q^{88} -9.46175 q^{89} +(1.67205 + 0.972230i) q^{90} -3.60614 q^{91} +0.632666i q^{92} -0.105253i q^{93} +13.8205 q^{94} +(-1.12399 + 1.93304i) q^{95} +4.17473 q^{96} +2.98734i q^{97} -7.42797i q^{98} +0.706295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) $ 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9	$ 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) $ 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9 - 6 * q^10 + 20 * q^11 + 24 * q^14 - 6 * q^15 - 4 * q^16 + 20 * q^19 - 6 * q^20 - 30 * q^21 + 38 * q^24 + 2 * q^25 + 8 * q^26 + 50 * q^29 - 20 * q^30 - 50 * q^31 + 28 * q^34 + 6 * q^35 - 12 * q^36 + 48 * q^39 + 12 * q^40 - 34 * q^41 - 12 * q^44 - 18 * q^45 - 36 * q^46 - 6 * q^49 + 26 * q^50 - 40 * q^51 - 6 * q^54 - 40 * q^56 + 30 * q^59 - 30 * q^60 - 14 * q^61 + 36 * q^64 + 30 * q^65 - 8 * q^66 - 12 * q^69 - 54 * q^70 - 40 * q^71 + 50 * q^74 - 8 * q^75 - 12 * q^76 + 106 * q^79 + 8 * q^80 - 30 * q^84 - 22 * q^85 + 56 * q^86 + 36 * q^89 - 64 * q^90 - 56 * q^91 + 28 * q^94 + 66 * q^96 - 10 * 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 $

$2$		−	1.22468i		−	0.865979i	−0.901399	−	0.432990i	$-0.857459\pi$
$2$		−	1.22468i		−	0.865979i	0.901399	−	0.432990i	$-0.142541\pi$
$3$			1.51450i			0.874396i	0.899365	+	0.437198i	$0.144029\pi$
$3$			1.51450i			0.874396i	−0.899365	+	0.437198i	$0.855971\pi$
$4$	0.500160			0.250080
$5$	−1.12399	+	1.93304i	−0.502661	+	0.864483i
$5$	−1.12399	+	1.93304i	−0.502661	+	0.864483i
$6$	1.85478			0.757209
$7$			0.966830i			0.365428i	0.983166	+	0.182714i	$0.0584882\pi$
$7$			0.966830i			0.365428i	−0.983166	+	0.182714i	$0.941512\pi$
$8$		−	3.06189i		−	1.08254i
$9$	0.706295			0.235432
$10$	2.36736	+	1.37652i	0.748625	+	0.435294i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			0.757491i			0.218669i
$13$			3.72985i			1.03448i	0.855842	+	0.517238i	$0.173040\pi$
$13$			3.72985i			1.03448i	−0.855842	+	0.517238i	$0.826960\pi$
$14$	1.18406			0.316453
$15$	−2.92759	−	1.70227i	−0.755901	−	0.439525i
$16$	−2.74952			−0.687380
$17$			2.85383i			0.692154i	0.938206	+	0.346077i	$0.112486\pi$
$17$			2.85383i			0.692154i	−0.938206	+	0.346077i	$0.887514\pi$
$18$		−	0.864985i		−	0.203879i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.562172	+	0.966830i	−0.125706	+	0.216190i
$21$	−1.46426			−0.319528
$22$		−	1.22468i		−	0.261103i
$23$			1.26493i			0.263756i	0.991266	+	0.131878i	$0.0421006\pi$
$23$			1.26493i			0.263756i	−0.991266	+	0.131878i	$0.957899\pi$
$24$	4.63723			0.946572
$25$	−2.47331	−	4.34542i	−0.494663	−	0.869085i
$26$	4.56788			0.895834
$27$			5.61318i			1.08026i
$28$			0.483570i			0.0913861i
$29$	−2.66677			−0.495206			−0.247603	−	0.968862i	$-0.579643\pi$
$29$	−2.66677			−0.495206			−0.247603	+	0.968862i	$0.579643\pi$
$30$	−2.08474	+	3.58536i	−0.380620	+	0.654594i
$31$	−0.0694967			−0.0124820			−0.00624099	−	0.999981i	$-0.501987\pi$
$31$	−0.0694967			−0.0124820			−0.00624099	+	0.999981i	$0.501987\pi$
$32$		−	2.75651i		−	0.487286i
$33$			1.51450i			0.263640i
$34$	3.49502			0.599391
$35$	−1.86893	−	1.08670i	−0.315906	−	0.183686i
$36$	0.353260			0.0588767
$37$		−	0.887066i		−	0.145833i	−0.997338	−	0.0729164i	$-0.976769\pi$
$37$		−	0.887066i		−	0.145833i	0.997338	−	0.0729164i	$-0.0232306\pi$
$38$		−	1.22468i		−	0.198669i
$39$	−5.64886			−0.904541
$40$	5.91878	+	3.44152i	0.935841	+	0.544153i
$41$	−7.73545			−1.20807			−0.604037	−	0.796956i	$-0.706442\pi$
$41$	−7.73545			−1.20807			−0.604037	+	0.796956i	$0.706442\pi$
$42$			1.79325i			0.276705i
$43$		−	5.48663i		−	0.836704i	−0.908285	−	0.418352i	$-0.862608\pi$
$43$		−	5.48663i		−	0.836704i	0.908285	−	0.418352i	$-0.137392\pi$
$44$	0.500160			0.0754019
$45$	−0.793865	+	1.36530i	−0.118342	+	0.203527i
$46$	1.54913			0.228407
$47$			11.2850i			1.64609i	0.567977	+	0.823044i	$0.307726\pi$
$47$			11.2850i			1.64609i	−0.567977	+	0.823044i	$0.692274\pi$
$48$		−	4.16414i		−	0.601043i
$49$	6.06524			0.866463
$50$	−5.32175	+	3.02902i	−0.752610	+	0.428368i
$51$	−4.32211			−0.605217
$52$			1.86552i			0.258701i
$53$			12.5557i			1.72466i	0.506347	+	0.862330i	$0.330996\pi$
$53$			12.5557i			1.72466i	−0.506347	+	0.862330i	$0.669004\pi$
$54$	6.87434			0.935480
$55$	−1.12399	+	1.93304i	−0.151558	+	0.260652i
$56$	2.96033			0.395591
$57$			1.51450i			0.200600i
$58$			3.26594i			0.428838i
$59$	10.0125			1.30352			0.651761	−	0.758425i	$-0.274031\pi$
$59$	10.0125			1.30352			0.651761	+	0.758425i	$0.274031\pi$
$60$	−1.46426	−	0.851409i	−0.189036	−	0.109916i
$61$	9.57033			1.22536			0.612678	−	0.790333i	$-0.290092\pi$
$61$	9.57033			1.22536			0.612678	+	0.790333i	$0.290092\pi$
$62$			0.0851112i			0.0108091i
$63$			0.682867i			0.0860332i
$64$	−8.87488			−1.10936
$65$	−7.20997	−	4.19230i	−0.894287	−	0.519991i
$66$	1.85478			0.228307
$67$			13.5976i			1.66121i	0.556862	+	0.830605i	$0.312005\pi$
$67$			13.5976i			1.66121i	−0.556862	+	0.830605i	$0.687995\pi$
$68$			1.42737i			0.173094i
$69$	−1.91573			−0.230627
$70$	−1.33086	+	2.28883i	−0.159069	+	0.273568i
$71$	−14.9834			−1.77820			−0.889100	−	0.457712i	$-0.848669\pi$
$71$	−14.9834			−1.77820			−0.889100	+	0.457712i	$0.848669\pi$
$72$		−	2.16260i		−	0.254865i
$73$			2.93685i			0.343733i	0.985120	+	0.171866i	$0.0549797\pi$
$73$			2.93685i			0.343733i	−0.985120	+	0.171866i	$0.945020\pi$
$74$	−1.08637			−0.126288
$75$	6.58114	−	3.74583i	0.759924	−	0.432531i
$76$	0.500160			0.0573723
$77$			0.966830i			0.110181i
$78$			6.91804i			0.783314i
$79$	14.8054			1.66573			0.832867	−	0.553473i	$-0.186698\pi$
$79$	14.8054			1.66573			0.832867	+	0.553473i	$0.186698\pi$
$80$	3.09042	−	5.31494i	0.345520	−	0.594229i
$81$	−6.38226			−0.709140
$82$			9.47344i			1.04617i
$83$		−	10.1575i		−	1.11493i	−0.830199	−	0.557466i	$-0.811774\pi$
$83$		−	10.1575i		−	1.11493i	0.830199	−	0.557466i	$-0.188226\pi$
$84$	−0.732365			−0.0799076
$85$	−5.51657	−	3.20766i	−0.598356	−	0.347919i
$86$	−6.71937			−0.724568
$87$		−	4.03881i		−	0.433006i
$88$		−	3.06189i		−	0.326399i
$89$	−9.46175			−1.00294			−0.501472	−	0.865174i	$-0.667208\pi$
$89$	−9.46175			−1.00294			−0.501472	+	0.865174i	$0.667208\pi$
$90$	1.67205	+	0.972230i	0.176250	+	0.102482i
$91$	−3.60614			−0.378026
$92$			0.632666i			0.0659599i
$93$		−	0.105253i		−	0.0109142i
$94$	13.8205			1.42548
$95$	−1.12399	+	1.93304i	−0.115318	+	0.198326i
$96$	4.17473			0.426081
$97$			2.98734i			0.303319i	0.988433	+	0.151659i	$0.0484617\pi$
$97$			2.98734i			0.303319i	−0.988433	+	0.151659i	$0.951538\pi$
$98$		−	7.42797i		−	0.750339i
$99$	0.706295			0.0709853
$100$	−1.23705	−	2.17341i	−0.123705	−	0.217341i
$101$	6.38909			0.635738			0.317869	−	0.948135i	$-0.397033\pi$
$101$	6.38909			0.635738			0.317869	+	0.948135i	$0.397033\pi$
$102$			5.29320i			0.524105i
$103$		−	13.9414i		−	1.37369i	−0.726803	−	0.686846i	$-0.758995\pi$
$103$		−	13.9414i		−	1.37369i	0.726803	−	0.686846i	$-0.241005\pi$
$104$	11.4204			1.11986
$105$	1.64581	−	2.83048i	0.160615	−	0.276227i
$106$	15.3767			1.49352
$107$		−	7.92964i		−	0.766587i	−0.923627	−	0.383294i	$-0.874790\pi$
$107$		−	7.92964i		−	0.766587i	0.923627	−	0.383294i	$-0.125210\pi$
$108$			2.80749i			0.270150i
$109$	−7.15662			−0.685480			−0.342740	−	0.939430i	$-0.611355\pi$
$109$	−7.15662			−0.685480			−0.342740	+	0.939430i	$0.611355\pi$
$110$	2.36736	+	1.37652i	0.225719	+	0.131246i
$111$	1.34346			0.127516
$112$		−	2.65832i		−	0.251188i
$113$		−	13.9228i		−	1.30974i	−0.755740	−	0.654872i	$-0.772723\pi$
$113$		−	13.9228i		−	1.30974i	0.755740	−	0.654872i	$-0.227277\pi$
$114$	1.85478			0.173716
$115$	−2.44516	−	1.42176i	−0.228012	−	0.132580i
$116$	−1.33381			−0.123841
$117$			2.63438i			0.243548i
$118$		−	12.2622i		−	1.12882i
$119$	−2.75917			−0.252932
$120$	−5.21218	+	8.96398i	−0.475805	+	0.818295i
$121$	1.00000			0.0909091
$122$		−	11.7206i		−	1.06113i
$123$		−	11.7153i		−	1.05633i
$124$	−0.0347595			−0.00312149
$125$	11.1799	+	0.103169i	0.999957	+	0.00922775i
$126$	0.836294			0.0745030
$127$			16.7799i			1.48897i	0.667638	+	0.744486i	$0.267305\pi$
$127$			16.7799i			1.48897i	−0.667638	+	0.744486i	$0.732695\pi$
$128$			5.35587i			0.473397i
$129$	8.30950			0.731610
$130$	−5.13423	+	8.82990i	−0.450301	+	0.774434i
$131$	−0.908620			−0.0793865			−0.0396932	−	0.999212i	$-0.512638\pi$
$131$	−0.908620			−0.0793865			−0.0396932	+	0.999212i	$0.512638\pi$
$132$			0.757491i			0.0659311i
$133$			0.966830i			0.0838348i
$134$	16.6527			1.43857
$135$	−10.8505	−	6.30913i	−0.933864	−	0.543003i
$136$	8.73811			0.749287
$137$		−	10.2206i		−	0.873201i	−0.899655	−	0.436601i	$-0.856182\pi$
$137$		−	10.2206i		−	0.873201i	0.899655	−	0.436601i	$-0.143818\pi$
$138$			2.34616i			0.199718i
$139$	14.2820			1.21138			0.605692	−	0.795699i	$-0.292896\pi$
$139$	14.2820			1.21138			0.605692	+	0.795699i	$0.292896\pi$
$140$	−0.934761	−	0.543525i	−0.0790017	−	0.0459363i
$141$	−17.0911			−1.43933
$142$			18.3498i			1.53988i
$143$			3.72985i			0.311906i
$144$	−1.94197			−0.161831
$145$	2.99741	−	5.15498i	0.248921	−	0.428097i
$146$	3.59670			0.297665
$147$			9.18579i			0.757632i
$148$		−	0.443675i		−	0.0364698i
$149$	5.64141			0.462163			0.231081	−	0.972934i	$-0.425774\pi$
$149$	5.64141			0.462163			0.231081	+	0.972934i	$0.425774\pi$
$150$	−4.58744	−	8.05979i	−0.374563	−	0.658079i
$151$	22.3439			1.81832			0.909159	−	0.416449i	$-0.136726\pi$
$151$	22.3439			1.81832			0.909159	+	0.416449i	$0.136726\pi$
$152$		−	3.06189i		−	0.248352i
$153$			2.01564i			0.162955i
$154$	1.18406			0.0954141
$155$	0.0781133	−	0.134340i	0.00627421	−	0.0107905i
$156$	−2.82533			−0.226208
$157$		−	21.7579i		−	1.73647i	−0.496157	−	0.868233i	$-0.665256\pi$
$157$		−	21.7579i		−	1.73647i	0.496157	−	0.868233i	$-0.334744\pi$
$158$		−	18.1318i		−	1.44249i
$159$	−19.0156			−1.50804
$160$	5.32845	+	3.09827i	0.421251	+	0.244940i
$161$	−1.22297			−0.0963835
$162$			7.81623i			0.614101i
$163$		−	6.46294i		−	0.506216i	−0.967438	−	0.253108i	$-0.918547\pi$
$163$		−	6.46294i		−	0.506216i	0.967438	−	0.253108i	$-0.0814528\pi$
$164$	−3.86896			−0.302115
$165$	−2.92759	−	1.70227i	−0.227913	−	0.132522i
$166$	−12.4397			−0.965509
$167$		−	14.6819i		−	1.13612i	−0.822987	−	0.568060i	$-0.807694\pi$
$167$		−	14.6819i		−	1.13612i	0.822987	−	0.568060i	$-0.192306\pi$
$168$			4.48342i			0.345903i
$169$	−0.911812			−0.0701394
$170$	−3.92835	+	6.75603i	−0.301291	+	0.518164i
$171$	0.706295			0.0540117
$172$		−	2.74419i		−	0.209243i
$173$		−	22.3021i		−	1.69560i	−0.530319	−	0.847798i	$-0.677928\pi$
$173$		−	22.3021i		−	1.69560i	0.530319	−	0.847798i	$-0.322072\pi$
$174$	−4.94625			−0.374974
$175$	4.20129	−	2.39128i	0.317588	−	0.180763i
$176$	−2.74952			−0.207253
$177$			15.1640i			1.13979i
$178$			11.5876i			0.868528i
$179$	−13.9910			−1.04573			−0.522867	−	0.852414i	$-0.675138\pi$
$179$	−13.9910			−1.04573			−0.522867	+	0.852414i	$0.675138\pi$
$180$	−0.397059	+	0.682867i	−0.0295950	+	0.0508979i
$181$	4.24540			0.315558			0.157779	−	0.987474i	$-0.449567\pi$
$181$	4.24540			0.315558			0.157779	+	0.987474i	$0.449567\pi$
$182$			4.41636i			0.327363i
$183$			14.4943i			1.07145i
$184$	3.87307			0.285527
$185$	1.71474	+	0.997049i	0.126070	+	0.0733045i
$186$	−0.128901			−0.00945146
$187$			2.85383i			0.208692i
$188$			5.64431i			0.411654i
$189$	−5.42699			−0.394756
$190$	2.36736	+	1.37652i	0.171746	+	0.0998634i
$191$	8.28343			0.599368			0.299684	−	0.954038i	$-0.403119\pi$
$191$	8.28343			0.599368			0.299684	+	0.954038i	$0.403119\pi$
$192$		−	13.4410i		−	0.970020i
$193$		−	10.7790i		−	0.775890i	−0.921683	−	0.387945i	$-0.873185\pi$
$193$		−	10.7790i		−	0.775890i	0.921683	−	0.387945i	$-0.126815\pi$
$194$	3.65854			0.262668
$195$	6.34923	−	10.9195i	0.454678	−	0.781961i
$196$	3.03359			0.216685
$197$			4.69665i			0.334623i	0.985904	+	0.167311i	$0.0535085\pi$
$197$			4.69665i			0.334623i	−0.985904	+	0.167311i	$0.946492\pi$
$198$		−	0.864985i		−	0.0614718i
$199$	−16.1492			−1.14479			−0.572394	−	0.819978i	$-0.693985\pi$
$199$	−16.1492			−1.14479			−0.572394	+	0.819978i	$0.693985\pi$
$200$	−13.3052	+	7.57303i	−0.940822	+	0.535494i
$201$	−20.5935			−1.45256
$202$		−	7.82459i		−	0.550536i
$203$		−	2.57831i		−	0.180962i
$204$	−2.16175			−0.151353
$205$	8.69453	−	14.9530i	0.607252	−	1.04436i
$206$	−17.0738			−1.18959
$207$			0.893411i			0.0620964i
$208$		−	10.2553i		−	0.711078i
$209$	1.00000			0.0691714
$210$	−3.46644	−	2.01559i	−0.239207	−	0.139089i
$211$	−18.5002			−1.27360			−0.636802	−	0.771027i	$-0.719743\pi$
$211$	−18.5002			−1.27360			−0.636802	+	0.771027i	$0.719743\pi$
$212$			6.27986i			0.431303i
$213$		−	22.6923i		−	1.55485i
$214$	−9.71127			−0.663849
$215$	10.6059	+	6.16689i	0.723316	+	0.420579i
$216$	17.1870			1.16942
$217$		−	0.0671915i		−	0.00456126i
$218$			8.76457i			0.593611i
$219$	−4.44786			−0.300558
$220$	−0.562172	+	0.966830i	−0.0379016	+	0.0651837i
$221$	−10.6444			−0.716017
$222$		−	1.64531i		−	0.110426i
$223$			23.7411i			1.58982i	0.606724	+	0.794912i	$0.292483\pi$
$223$			23.7411i			1.58982i	−0.606724	+	0.794912i	$0.707517\pi$
$224$	2.66508			0.178068
$225$	−1.74689	−	3.06915i	−0.116459	−	0.204610i
$226$	−17.0509			−1.13421
$227$		−	11.2958i		−	0.749727i	−0.927080	−	0.374864i	$-0.877689\pi$
$227$		−	11.2958i		−	0.749727i	0.927080	−	0.374864i	$-0.122311\pi$
$228$			0.757491i			0.0501661i
$229$	20.7759			1.37291			0.686456	−	0.727171i	$-0.259165\pi$
$229$	20.7759			1.37291			0.686456	+	0.727171i	$0.259165\pi$
$230$	−1.74120	+	2.99454i	−0.114811	+	0.197454i
$231$	−1.46426			−0.0963414
$232$			8.16536i			0.536082i
$233$		−	15.7293i		−	1.03046i	−0.857051	−	0.515231i	$-0.827706\pi$
$233$		−	15.7293i		−	1.03046i	0.857051	−	0.515231i	$-0.172294\pi$
$234$	3.22627			0.210908
$235$	−21.8144	−	12.6842i	−1.42302	−	0.827425i
$236$	5.00787			0.325984
$237$			22.4227i			1.45651i
$238$			3.37909i			0.219034i
$239$	4.60384			0.297798			0.148899	−	0.988852i	$-0.452427\pi$
$239$	4.60384			0.297798			0.148899	+	0.988852i	$0.452427\pi$
$240$	8.04947	+	4.68044i	0.519591	+	0.302121i
$241$	−16.7257			−1.07740			−0.538699	−	0.842498i	$-0.681084\pi$
$241$	−16.7257			−1.07740			−0.538699	+	0.842498i	$0.681084\pi$
$242$		−	1.22468i		−	0.0787254i
$243$			7.17360i			0.460187i
$244$	4.78669			0.306437
$245$	−6.81724	+	11.7244i	−0.435537	+	0.749043i
$246$	−14.3475			−0.914764
$247$			3.72985i			0.237325i
$248$			0.212792i			0.0135123i
$249$	15.3836			0.974893
$250$	0.126349	−	13.6918i	0.00799104	−	0.865942i
$251$	4.04538			0.255342			0.127671	−	0.991817i	$-0.459250\pi$
$251$	4.04538			0.255342			0.127671	+	0.991817i	$0.459250\pi$
$252$			0.341543i			0.0215152i
$253$			1.26493i			0.0795253i
$254$	20.5500			1.28942
$255$	4.85799	−	8.35483i	0.304219	−	0.523200i
$256$	−11.1905			−0.699408
$257$		−	12.9559i		−	0.808169i	−0.914722	−	0.404085i	$-0.867590\pi$
$257$		−	12.9559i		−	0.808169i	0.914722	−	0.404085i	$-0.132410\pi$
$258$		−	10.1765i		−	0.633559i
$259$	0.857642			0.0532913
$260$	−3.60614	−	2.09682i	−0.223643	−	0.130039i
$261$	−1.88352			−0.116587
$262$			1.11277i			0.0687471i
$263$			1.14335i			0.0705021i	0.999378	+	0.0352510i	$0.0112231\pi$
$263$			1.14335i			0.0705021i	−0.999378	+	0.0352510i	$0.988777\pi$
$264$	4.63723			0.285402
$265$	−24.2707	−	14.1124i	−1.49094	−	0.866920i
$266$	1.18406			0.0725992
$267$		−	14.3298i		−	0.876970i
$268$			6.80097i			0.415435i
$269$	17.0669			1.04059			0.520293	−	0.853988i	$-0.325823\pi$
$269$	17.0669			1.04059			0.520293	+	0.853988i	$0.325823\pi$
$270$	−7.72666	+	13.2884i	−0.470230	+	0.808707i
$271$	18.3874			1.11695			0.558477	−	0.829520i	$-0.311386\pi$
$271$	18.3874			1.11695			0.558477	+	0.829520i	$0.311386\pi$
$272$		−	7.84665i		−	0.475773i
$273$		−	5.46149i		−	0.330544i
$274$	−12.5169			−0.756174
$275$	−2.47331	−	4.34542i	−0.149146	−	0.262039i
$276$	−0.958171			−0.0576751
$277$		−	17.5351i		−	1.05358i	−0.849994	−	0.526792i	$-0.823395\pi$
$277$		−	17.5351i		−	1.05358i	0.849994	−	0.526792i	$-0.176605\pi$
$278$		−	17.4909i		−	1.04903i
$279$	−0.0490852			−0.00293865
$280$	−3.32737	+	5.72245i	−0.198848	+	0.341982i
$281$	16.6245			0.991734			0.495867	−	0.868399i	$-0.334850\pi$
$281$	16.6245			0.991734			0.495867	+	0.868399i	$0.334850\pi$
$282$			20.9312i			1.24643i
$283$		−	4.90030i		−	0.291293i	−0.989337	−	0.145646i	$-0.953474\pi$
$283$		−	4.90030i		−	0.291293i	0.989337	−	0.145646i	$-0.0465262\pi$
$284$	−7.49409			−0.444692
$285$	−2.92759	−	1.70227i	−0.173416	−	0.100834i
$286$	4.56788			0.270104
$287$		−	7.47887i		−	0.441463i
$288$		−	1.94691i		−	0.114723i
$289$	8.85568			0.520922
$290$	−6.31319	−	3.67086i	−0.370724	−	0.215560i
$291$	−4.52432			−0.265221
$292$			1.46890i			0.0859606i
$293$			20.0181i			1.16947i	0.811224	+	0.584736i	$0.198802\pi$
$293$			20.0181i			1.16947i	−0.811224	+	0.584736i	$0.801198\pi$
$294$	11.2497			0.656093
$295$	−11.2539	+	19.3547i	−0.655230	+	1.12687i
$296$	−2.71610			−0.157870
$297$			5.61318i			0.325710i
$298$		−	6.90892i		−	0.400223i
$299$	−4.71799			−0.272849
$300$	3.29162	−	1.87351i	0.190042	−	0.108167i
$301$	5.30464			0.305755
$302$		−	27.3641i		−	1.57463i
$303$			9.67626i			0.555887i
$304$	−2.74952			−0.157696
$305$	−10.7569	+	18.4999i	−0.615939	+	1.05930i
$306$	2.46852			0.141116
$307$			9.38081i			0.535391i	0.963504	+	0.267696i	$0.0862621\pi$
$307$			9.38081i			0.535391i	−0.963504	+	0.267696i	$0.913738\pi$
$308$			0.483570i			0.0275539i
$309$	21.1143			1.20115
$310$	−0.164524	−	0.0956637i	−0.00934432	−	0.00543334i
$311$	−15.1624			−0.859784			−0.429892	−	0.902880i	$-0.641448\pi$
$311$	−15.1624			−0.859784			−0.429892	+	0.902880i	$0.641448\pi$
$312$			17.2962i			0.979205i
$313$			24.1447i			1.36474i	0.731008	+	0.682369i	$0.239050\pi$
$313$			24.1447i			1.36474i	−0.731008	+	0.682369i	$0.760950\pi$
$314$	−26.6464			−1.50374
$315$	−1.32001	−	0.767533i	−0.0743743	−	0.0432456i
$316$	7.40505			0.416567
$317$		−	4.99774i		−	0.280701i	−0.990102	−	0.140350i	$-0.955177\pi$
$317$		−	4.99774i		−	0.280701i	0.990102	−	0.140350i	$-0.0448229\pi$
$318$			23.2880i			1.30593i
$319$	−2.66677			−0.149310
$320$	9.97523	−	17.1555i	0.557633	−	0.959023i
$321$	12.0094			0.670301
$322$			1.49775i			0.0834662i
$323$			2.85383i			0.158791i
$324$	−3.19215			−0.177342
$325$	16.2078	−	9.22510i	0.899047	−	0.511717i
$326$	−7.91503			−0.438373
$327$		−	10.8387i		−	0.599381i
$328$			23.6851i			1.30779i
$329$	−10.9107			−0.601526
$330$	−2.08474	+	3.58536i	−0.114761	+	0.197368i
$331$	−27.6346			−1.51894			−0.759468	−	0.650544i	$-0.774541\pi$
$331$	−27.6346			−1.51894			−0.759468	+	0.650544i	$0.774541\pi$
$332$		−	5.08038i		−	0.278822i
$333$		−	0.626530i		−	0.0343336i
$334$	−17.9806			−0.983856
$335$	−26.2847	−	15.2835i	−1.43609	−	0.835026i
$336$	4.02602			0.219638
$337$		−	27.2883i		−	1.48649i	−0.669020	−	0.743244i	$-0.733286\pi$
$337$		−	27.2883i		−	1.48649i	0.669020	−	0.743244i	$-0.266714\pi$
$338$			1.11668i			0.0607393i
$339$	21.0860			1.14523
$340$	−2.75917	−	1.60434i	−0.149637	−	0.0870076i
$341$	−0.0694967			−0.00376346
$342$		−	0.864985i		−	0.0467730i
$343$			12.6319i			0.682057i
$344$	−16.7995			−0.905768
$345$	2.15325	−	3.70319i	0.115927	−	0.199373i
$346$	−27.3129			−1.46835
$347$		−	0.209435i		−	0.0112431i	−0.999984	−	0.00562154i	$-0.998211\pi$
$347$		−	0.209435i		−	0.0112431i	0.999984	−	0.00562154i	$-0.00178940\pi$
$348$		−	2.02005i		−	0.108286i
$349$	15.4247			0.825665			0.412833	−	0.910807i	$-0.364539\pi$
$349$	15.4247			0.825665			0.412833	+	0.910807i	$0.364539\pi$
$350$	−2.92855	−	5.14523i	−0.156537	−	0.275024i
$351$	−20.9363			−1.11750
$352$		−	2.75651i		−	0.146922i
$353$			7.00575i			0.372879i	0.982466	+	0.186439i	$0.0596948\pi$
$353$			7.00575i			0.372879i	−0.982466	+	0.186439i	$0.940305\pi$
$354$	18.5710			0.987038
$355$	16.8411	−	28.9635i	0.893833	−	1.53722i
$356$	−4.73238			−0.250816
$357$		−	4.17875i		−	0.221163i
$358$			17.1345i			0.905585i
$359$	−18.7163			−0.987810			−0.493905	−	0.869516i	$-0.664431\pi$
$359$	−18.7163			−0.987810			−0.493905	+	0.869516i	$0.664431\pi$
$360$	4.18040	+	2.43073i	0.220326	+	0.128111i
$361$	1.00000			0.0526316
$362$		−	5.19925i		−	0.273266i
$363$			1.51450i			0.0794905i
$364$	−1.80364			−0.0945367
$365$	−5.67706	−	3.30098i	−0.297151	−	0.172781i
$366$	17.7508			0.927850
$367$			8.78006i			0.458315i	0.973389	+	0.229158i	$0.0735972\pi$
$367$			8.78006i			0.458315i	−0.973389	+	0.229158i	$0.926403\pi$
$368$		−	3.47794i		−	0.181300i
$369$	−5.46351			−0.284419
$370$	1.22107	−	2.10000i	0.0634802	−	0.109174i
$371$	−12.1392			−0.630238
$372$		−	0.0526431i		−	0.00272942i
$373$		−	15.2111i		−	0.787600i	−0.919196	−	0.393800i	$-0.871160\pi$
$373$		−	15.2111i		−	0.787600i	0.919196	−	0.393800i	$-0.128840\pi$
$374$	3.49502			0.180723
$375$	−0.156250	+	16.9319i	−0.00806871	+	0.874359i
$376$	34.5535			1.78196
$377$		−	9.94665i		−	0.512279i
$378$			6.64633i			0.341850i
$379$	33.5270			1.72217			0.861084	−	0.508463i	$-0.169786\pi$
$379$	33.5270			1.72217			0.861084	+	0.508463i	$0.169786\pi$
$380$	−0.562172	+	0.966830i	−0.0288388	+	0.0495974i
$381$	−25.4131			−1.30195
$382$		−	10.1446i		−	0.519040i
$383$			23.0339i			1.17698i	0.808506	+	0.588488i	$0.200277\pi$
$383$			23.0339i			1.17698i	−0.808506	+	0.588488i	$0.799723\pi$
$384$	−8.11146			−0.413936
$385$	−1.86893	−	1.08670i	−0.0952493	−	0.0553835i
$386$	−13.2008			−0.671904
$387$		−	3.87518i		−	0.196986i
$388$			1.49415i			0.0758539i
$389$	−10.7475			−0.544917			−0.272459	−	0.962167i	$-0.587837\pi$
$389$	−10.7475			−0.544917			−0.272459	+	0.962167i	$0.587837\pi$
$390$	−13.3729	−	7.77578i	−0.677162	−	0.393742i
$391$	−3.60988			−0.182560
$392$		−	18.5711i		−	0.937983i
$393$		−	1.37610i		−	0.0694152i
$394$	5.75189			0.289776
$395$	−16.6410	+	28.6194i	−0.837301	+	1.44000i
$396$	0.353260			0.0177520
$397$		−	31.2539i		−	1.56859i	−0.620390	−	0.784293i	$-0.713026\pi$
$397$		−	31.2539i		−	1.56859i	0.620390	−	0.784293i	$-0.286974\pi$
$398$			19.7776i			0.991363i
$399$	−1.46426			−0.0733048
$400$	6.80043	+	11.9478i	0.340021	+	0.597392i
$401$	13.7437			0.686328			0.343164	−	0.939275i	$-0.388501\pi$
$401$	13.7437			0.686328			0.343164	+	0.939275i	$0.388501\pi$
$402$			25.2205i			1.25788i
$403$		−	0.259213i		−	0.0129123i
$404$	3.19556			0.158985
$405$	7.17357	−	12.3372i	0.356458	−	0.613040i
$406$	−3.15761			−0.156709
$407$		−	0.887066i		−	0.0439702i
$408$			13.2339i			0.655174i
$409$	−2.14094			−0.105863			−0.0529314	−	0.998598i	$-0.516856\pi$
$409$	−2.14094			−0.105863			−0.0529314	+	0.998598i	$0.516856\pi$
$410$	−18.3126	−	10.6480i	−0.904394	−	0.525868i
$411$	15.4790			0.763524
$412$		−	6.97295i		−	0.343533i
$413$			9.68043i			0.476343i
$414$	1.09414			0.0537742
$415$	19.6349	+	11.4169i	0.963841	+	0.560434i
$416$	10.2814			0.504086
$417$			21.6301i			1.05923i
$418$		−	1.22468i		−	0.0599010i
$419$	6.05609			0.295859			0.147930	−	0.988998i	$-0.452739\pi$
$419$	6.05609			0.295859			0.147930	+	0.988998i	$0.452739\pi$
$420$	0.823168	−	1.41569i	0.0401665	−	0.0690788i
$421$	23.9793			1.16868			0.584339	−	0.811510i	$-0.301354\pi$
$421$	23.9793			1.16868			0.584339	+	0.811510i	$0.301354\pi$
$422$			22.6568i			1.10291i
$423$			7.97055i			0.387541i
$424$	38.4443			1.86702
$425$	12.4011	−	7.05841i	0.601541	−	0.342383i
$426$	−27.7908			−1.34647
$427$			9.25289i			0.447779i
$428$		−	3.96609i		−	0.191708i
$429$	−5.64886			−0.272729
$430$	7.55247	−	12.9888i	0.364212	−	0.626377i
$431$	−17.1882			−0.827928			−0.413964	−	0.910293i	$-0.635856\pi$
$431$	−17.1882			−0.827928			−0.413964	+	0.910293i	$0.635856\pi$
$432$		−	15.4335i		−	0.742547i
$433$		−	5.34686i		−	0.256954i	−0.991713	−	0.128477i	$-0.958991\pi$
$433$		−	5.34686i		−	0.256954i	0.991713	−	0.128477i	$-0.0410088\pi$
$434$	−0.0822881			−0.00394996
$435$	7.80720	+	4.53957i	0.374327	+	0.217656i
$436$	−3.57945			−0.171425
$437$			1.26493i			0.0605097i
$438$			5.44720i			0.260277i
$439$	32.0112			1.52781			0.763907	−	0.645327i	$-0.223279\pi$
$439$	32.0112			1.52781			0.763907	+	0.645327i	$0.223279\pi$
$440$	5.91878	+	3.44152i	0.282167	+	0.164068i
$441$	4.28385			0.203993
$442$			13.0359i			0.620056i
$443$			12.5754i			0.597474i	0.954336	+	0.298737i	$0.0965653\pi$
$443$			12.5754i			0.597474i	−0.954336	+	0.298737i	$0.903435\pi$
$444$	0.671944			0.0318891
$445$	10.6349	−	18.2900i	0.504141	−	0.867028i
$446$	29.0753			1.37676
$447$			8.54391i			0.404113i
$448$		−	8.58050i		−	0.405391i
$449$	−15.7096			−0.741382			−0.370691	−	0.928756i	$-0.620879\pi$
$449$	−15.7096			−0.741382			−0.370691	+	0.928756i	$0.620879\pi$
$450$	−3.75873	+	2.13938i	−0.177188	+	0.100851i
$451$	−7.73545			−0.364248
$452$		−	6.96361i		−	0.327540i
$453$			33.8398i			1.58993i
$454$	−13.8337			−0.649248
$455$	4.05324	−	6.97082i	0.190019	−	0.326797i
$456$	4.63723			0.217158
$457$			15.9751i			0.747285i	0.927573	+	0.373643i	$0.121891\pi$
$457$			15.9751i			0.747285i	−0.927573	+	0.373643i	$0.878109\pi$
$458$		−	25.4439i		−	1.18891i
$459$	−16.0190			−0.747704
$460$	−1.22297	−	0.711107i	−0.0570213	−	0.0331555i
$461$	−10.7322			−0.499850			−0.249925	−	0.968265i	$-0.580406\pi$
$461$	−10.7322			−0.499850			−0.249925	+	0.968265i	$0.580406\pi$
$462$			1.79325i			0.0834297i
$463$			26.5162i			1.23231i	0.787623	+	0.616157i	$0.211311\pi$
$463$			26.5162i			1.23231i	−0.787623	+	0.616157i	$0.788689\pi$
$464$	7.33233			0.340395
$465$	0.203458	+	0.118302i	0.00943514	+	0.00548614i
$466$	−19.2634			−0.892359
$467$		−	0.0862962i		−	0.00399331i	−0.999998	−	0.00199666i	$-0.999364\pi$
$467$		−	0.0862962i		−	0.00399331i	0.999998	−	0.00199666i	$-0.000635555\pi$
$468$			1.31761i			0.0609065i
$469$	−13.1466			−0.607052
$470$	−15.5341	+	26.7157i	−0.716533	+	1.23230i
$471$	32.9522			1.51836
$472$		−	30.6573i		−	1.41112i
$473$		−	5.48663i		−	0.252276i
$474$	27.4606			1.26131
$475$	−2.47331	−	4.34542i	−0.113483	−	0.199382i
$476$	−1.38002			−0.0632533
$477$			8.86804i			0.406039i
$478$		−	5.63823i		−	0.257887i
$479$	7.33976			0.335362			0.167681	−	0.985841i	$-0.446372\pi$
$479$	7.33976			0.335362			0.167681	+	0.985841i	$0.446372\pi$
$480$	−4.69233	+	8.06993i	−0.214175	+	0.368340i
$481$	3.30863			0.150860
$482$			20.4836i			0.933004i
$483$		−	1.85219i		−	0.0842774i
$484$	0.500160			0.0227345
$485$	−5.77466	−	3.35773i	−0.262214	−	0.152467i
$486$	8.78537			0.398512
$487$		−	32.7787i		−	1.48534i	−0.669655	−	0.742672i	$-0.733558\pi$
$487$		−	32.7787i		−	1.48534i	0.669655	−	0.742672i	$-0.266442\pi$
$488$		−	29.3034i		−	1.32650i
$489$	9.78811			0.442634
$490$	14.3586	+	8.34893i	0.648655	+	0.377166i
$491$	38.8581			1.75364			0.876820	−	0.480819i	$-0.159661\pi$
$491$	38.8581			1.75364			0.876820	+	0.480819i	$0.159661\pi$
$492$		−	5.85953i		−	0.264168i
$493$		−	7.61049i		−	0.342759i
$494$	4.56788			0.205518
$495$	−0.793865	+	1.36530i	−0.0356816	+	0.0613656i
$496$	0.191083			0.00857986
$497$		−	14.4864i		−	0.649804i
$498$		−	18.8399i		−	0.844237i
$499$	36.0334			1.61308			0.806538	−	0.591183i	$-0.201339\pi$
$499$	36.0334			1.61308			0.806538	+	0.591183i	$0.201339\pi$
$500$	5.59172	+	0.0516012i	0.250069	+	0.00230767i
$501$	22.2357			0.993418
$502$		−	4.95429i		−	0.221121i
$503$			14.8954i			0.664151i	0.943253	+	0.332076i	$0.107749\pi$
$503$			14.8954i			0.664151i	−0.943253	+	0.332076i	$0.892251\pi$
$504$	2.09087			0.0931347
$505$	−7.18124	+	12.3504i	−0.319561	+	0.549585i
$506$	1.54913			0.0688673
$507$		−	1.38094i		−	0.0613296i
$508$			8.39261i			0.372362i
$509$	−15.5077			−0.687365			−0.343682	−	0.939086i	$-0.611674\pi$
$509$	−15.5077			−0.687365			−0.343682	+	0.939086i	$0.611674\pi$
$510$	−10.2320	−	5.94948i	−0.453080	−	0.263448i
$511$	−2.83944			−0.125609
$512$			24.4166i			1.07907i
$513$			5.61318i			0.247828i
$514$	−15.8669			−0.699858
$515$	26.9494	+	15.6700i	1.18753	+	0.690502i
$516$	4.15608			0.182961
$517$			11.2850i			0.496314i
$518$		−	1.05034i		−	0.0461492i
$519$	33.7765			1.48262
$520$	−12.8364	+	22.0762i	−0.562913	+	0.968104i
$521$	−5.68991			−0.249279			−0.124640	−	0.992202i	$-0.539777\pi$
$521$	−5.68991			−0.249279			−0.124640	+	0.992202i	$0.539777\pi$
$522$			2.30671i			0.100962i
$523$			14.0692i			0.615203i	0.951515	+	0.307601i	$0.0995263\pi$
$523$			14.0692i			0.615203i	−0.951515	+	0.307601i	$0.900474\pi$
$524$	−0.454455			−0.0198530
$525$	3.62158	+	6.36285i	0.158059	+	0.277697i
$526$	1.40024			0.0610533
$527$		−	0.198331i		−	0.00863945i
$528$		−	4.16414i		−	0.181221i
$529$	21.4000			0.930433
$530$	−17.2832	+	29.7239i	−0.750735	+	1.29112i
$531$	7.07180			0.306890
$532$			0.483570i			0.0209654i
$533$		−	28.8521i		−	1.24972i
$534$	−17.5494			−0.759437
$535$	15.3283	+	8.91280i	0.662702	+	0.385334i
$536$	41.6344			1.79833
$537$		−	21.1893i		−	0.914386i
$538$		−	20.9015i		−	0.901126i
$539$	6.06524			0.261248
$540$	−5.42699	−	3.15557i	−0.233541	−	0.135794i
$541$	−3.13164			−0.134640			−0.0673198	−	0.997731i	$-0.521445\pi$
$541$	−3.13164			−0.134640			−0.0673198	+	0.997731i	$0.521445\pi$
$542$		−	22.5186i		−	0.967258i
$543$			6.42964i			0.275922i
$544$	7.86659			0.337277
$545$	8.04394	−	13.8341i	0.344564	−	0.592586i
$546$	−6.68857			−0.286245
$547$		−	28.6581i		−	1.22533i	−0.790341	−	0.612667i	$-0.790097\pi$
$547$		−	28.6581i		−	1.22533i	0.790341	−	0.612667i	$-0.209903\pi$
$548$		−	5.11191i		−	0.218370i
$549$	6.75948			0.288487
$550$	−5.32175	+	3.02902i	−0.226920	+	0.129158i
$551$	−2.66677			−0.113608
$552$			5.86576i			0.249663i
$553$			14.3143i			0.608705i
$554$	−21.4749			−0.912382
$555$	−1.51003	+	2.59697i	−0.0640972	+	0.110235i
$556$	7.14329			0.302943
$557$			21.3194i			0.903332i	0.892187	+	0.451666i	$0.149170\pi$
$557$			21.3194i			0.903332i	−0.892187	+	0.451666i	$0.850830\pi$
$558$			0.0601136i			0.00254481i
$559$	20.4643			0.865549
$560$	5.13865	+	2.98791i	0.217148	+	0.126262i
$561$	−4.32211			−0.182480
$562$		−	20.3597i		−	0.858821i
$563$			10.9764i			0.462600i	0.972883	+	0.231300i	$0.0742978\pi$
$563$			10.9764i			0.462600i	−0.972883	+	0.231300i	$0.925702\pi$
$564$	−8.54830			−0.359948
$565$	26.9133	+	15.6490i	1.13225	+	0.658358i
$566$	−6.00130			−0.252254
$567$		−	6.17057i		−	0.259139i
$568$			45.8775i			1.92498i
$569$	−29.7270			−1.24622			−0.623109	−	0.782135i	$-0.714131\pi$
$569$	−29.7270			−1.24622			−0.623109	+	0.782135i	$0.714131\pi$
$570$	−2.08474	+	3.58536i	−0.0873202	+	0.150174i
$571$	−5.72566			−0.239611			−0.119806	−	0.992797i	$-0.538227\pi$
$571$	−5.72566			−0.239611			−0.119806	+	0.992797i	$0.538227\pi$
$572$			1.86552i			0.0780014i
$573$			12.5452i			0.524085i
$574$	−9.15922			−0.382298
$575$	5.49665	−	3.12856i	0.229226	−	0.130470i
$576$	−6.26828			−0.261178
$577$			9.21100i			0.383459i	0.981448	+	0.191729i	$0.0614096\pi$
$577$			9.21100i			0.383459i	−0.981448	+	0.191729i	$0.938590\pi$
$578$		−	10.8454i		−	0.451108i
$579$	16.3248			0.678435
$580$	1.49918	−	2.57831i	0.0622501	−	0.107059i
$581$	9.82060			0.407427
$582$			5.54085i			0.229676i
$583$			12.5557i			0.520005i
$584$	8.99234			0.372105
$585$	−5.09236	−	2.96100i	−0.210543	−	0.122422i
$586$	24.5158			1.01274
$587$			19.5062i			0.805108i	0.915396	+	0.402554i	$0.131877\pi$
$587$			19.5062i			0.805108i	−0.915396	+	0.402554i	$0.868123\pi$
$588$			4.59436i			0.189468i
$589$	−0.0694967			−0.00286356
$590$	23.7033	+	13.7825i	0.975848	+	0.567416i
$591$	−7.11307			−0.292593
$592$			2.43901i			0.100243i
$593$		−	15.0231i		−	0.616923i	−0.951237	−	0.308462i	$-0.900186\pi$
$593$		−	15.0231i		−	0.616923i	0.951237	−	0.308462i	$-0.0998141\pi$
$594$	6.87434			0.282058
$595$	3.10126	−	5.33359i	0.127139	−	0.218656i
$596$	2.82161			0.115578
$597$		−	24.4580i		−	1.00100i
$598$			5.77803i			0.236281i
$599$	41.9974			1.71597			0.857983	−	0.513678i	$-0.171718\pi$
$599$	41.9974			1.71597			0.857983	+	0.513678i	$0.171718\pi$
$600$	−11.4693	−	20.1508i	−0.468234	−	0.822651i
$601$	−27.3856			−1.11708			−0.558541	−	0.829477i	$-0.688639\pi$
$601$	−27.3856			−1.11708			−0.558541	+	0.829477i	$0.688639\pi$
$602$		−	6.49649i		−	0.264777i
$603$			9.60391i			0.391101i
$604$	11.1755			0.454725
$605$	−1.12399	+	1.93304i	−0.0456965	+	0.0785894i
$606$	11.8503			0.481386
$607$		−	9.13370i		−	0.370726i	−0.982670	−	0.185363i	$-0.940654\pi$
$607$		−	9.13370i		−	0.370726i	0.982670	−	0.185363i	$-0.0593460\pi$
$608$		−	2.75651i		−	0.111791i
$609$	3.90485			0.158232
$610$	22.6564	+	13.1738i	0.917331	+	0.533390i
$611$	−42.0915			−1.70284
$612$			1.00814i			0.0407518i
$613$		−	5.28122i		−	0.213306i	−0.994296	−	0.106653i	$-0.965987\pi$
$613$		−	5.28122i		−	0.213306i	0.994296	−	0.106653i	$-0.0340135\pi$
$614$	11.4885			0.463638
$615$	22.6462	+	13.1678i	0.913184	+	0.530979i
$616$	2.96033			0.119275
$617$			6.43064i			0.258888i	0.991587	+	0.129444i	$0.0413192\pi$
$617$			6.43064i			0.258888i	−0.991587	+	0.129444i	$0.958681\pi$
$618$		−	25.8583i		−	1.04017i
$619$	−36.5217			−1.46793			−0.733966	−	0.679186i	$-0.762333\pi$
$619$	−36.5217			−1.46793			−0.733966	+	0.679186i	$0.762333\pi$
$620$	0.0390691	−	0.0671915i	0.00156905	−	0.00269848i
$621$	−7.10026			−0.284924
$622$			18.5691i			0.744555i
$623$		−	9.14791i		−	0.366503i
$624$	15.5317			0.621764
$625$	−12.7654	+	21.4952i	−0.510617	+	0.859808i
$626$	29.5695			1.18183
$627$			1.51450i			0.0604832i
$628$		−	10.8824i		−	0.434255i
$629$	2.53153			0.100939
$630$	−0.939982	+	1.61659i	−0.0374498	+	0.0644066i
$631$	−29.6182			−1.17908			−0.589540	−	0.807739i	$-0.700691\pi$
$631$	−29.6182			−1.17908			−0.589540	+	0.807739i	$0.700691\pi$
$632$		−	45.3325i		−	1.80323i
$633$		−	28.0185i		−	1.11363i
$634$	−6.12063			−0.243081
$635$	−32.4362	−	18.8603i	−1.28719	−	0.748449i
$636$	−9.51084			−0.377129
$637$			22.6225i			0.896334i
$638$			3.26594i			0.129300i
$639$	−10.5827			−0.418645
$640$	−10.3531	−	6.01992i	−0.409243	−	0.237958i
$641$	−23.6994			−0.936069			−0.468035	−	0.883710i	$-0.655038\pi$
$641$	−23.6994			−0.936069			−0.468035	+	0.883710i	$0.655038\pi$
$642$		−	14.7077i		−	0.580467i
$643$		−	0.184997i		−	0.00729555i	−0.999993	−	0.00364778i	$-0.998839\pi$
$643$		−	0.184997i		−	0.00729555i	0.999993	−	0.00364778i	$-0.00116113\pi$
$644$	−0.611680			−0.0241036
$645$	−9.33975	+	16.0626i	−0.367752	+	0.632465i
$646$	3.49502			0.137510
$647$			7.04719i			0.277054i	0.990359	+	0.138527i	$0.0442367\pi$
$647$			7.04719i			0.277054i	−0.990359	+	0.138527i	$0.955763\pi$
$648$			19.5418i			0.767675i
$649$	10.0125			0.393027
$650$	−11.2978	−	19.8494i	−0.443136	−	0.778556i
$651$	0.101761			0.00398835
$652$		−	3.23250i		−	0.126594i
$653$		−	24.9123i		−	0.974893i	−0.873153	−	0.487446i	$-0.837928\pi$
$653$		−	24.9123i		−	0.974893i	0.873153	−	0.487446i	$-0.162072\pi$
$654$	−13.2739			−0.519052
$655$	1.02128	−	1.75640i	0.0399045	−	0.0686283i
$656$	21.2688			0.830406
$657$			2.07428i			0.0809255i
$658$			13.3621i			0.520909i
$659$	41.2108			1.60534			0.802672	−	0.596421i	$-0.203411\pi$
$659$	41.2108			1.60534			0.802672	+	0.596421i	$0.203411\pi$
$660$	−1.46426	−	0.851409i	−0.0569964	−	0.0331410i
$661$	−2.05438			−0.0799061			−0.0399530	−	0.999202i	$-0.512721\pi$
$661$	−2.05438			−0.0799061			−0.0399530	+	0.999202i	$0.512721\pi$
$662$			33.8436i			1.31537i
$663$		−	16.1209i		−	0.626082i
$664$	−31.1013			−1.20696
$665$	−1.86893	−	1.08670i	−0.0724738	−	0.0421405i
$666$	−0.767299			−0.0297322
$667$		−	3.37327i		−	0.130613i
$668$		−	7.34330i		−	0.284121i
$669$	−35.9559			−1.39014
$670$	−18.7174	+	32.1904i	−0.723115	+	1.24362i
$671$	9.57033			0.369459
$672$			4.03625i			0.155702i
$673$		−	20.4855i		−	0.789657i	−0.918755	−	0.394829i	$-0.870804\pi$
$673$		−	20.4855i		−	0.789657i	0.918755	−	0.394829i	$-0.129196\pi$
$674$	−33.4194			−1.28727
$675$	24.3916	−	13.8832i	0.938835	−	0.534363i
$676$	−0.456052			−0.0175405
$677$		−	9.79899i		−	0.376606i	−0.982111	−	0.188303i	$-0.939701\pi$
$677$		−	9.79899i		−	0.376606i	0.982111	−	0.188303i	$-0.0602986\pi$
$678$		−	25.8236i		−	0.991749i
$679$	−2.88825			−0.110841
$680$	−9.82151	+	16.8912i	−0.376638	+	0.647746i
$681$	17.1074			0.655559
$682$			0.0851112i			0.00325908i
$683$		−	21.2343i		−	0.812509i	−0.913760	−	0.406255i	$-0.866835\pi$
$683$		−	21.2343i		−	0.812509i	0.913760	−	0.406255i	$-0.133165\pi$
$684$	0.353260			0.0135072
$685$	19.7568	+	11.4878i	0.754868	+	0.438925i
$686$	15.4700			0.590647
$687$			31.4651i			1.20047i
$688$			15.0856i			0.575134i
$689$	−46.8310			−1.78412
$690$	−4.53522	−	2.63704i	−0.172653	−	0.100391i
$691$	23.7535			0.903627			0.451814	−	0.892112i	$-0.350777\pi$
$691$	23.7535			0.903627			0.451814	+	0.892112i	$0.350777\pi$
$692$		−	11.1546i		−	0.424034i
$693$			0.682867i			0.0259400i
$694$	−0.256491			−0.00973628
$695$	−16.0528	+	27.6078i	−0.608917	+	1.04722i
$696$	−12.3664			−0.468748
$697$		−	22.0756i		−	0.836174i
$698$		−	18.8903i		−	0.715009i
$699$	23.8220			0.901032
$700$	2.10132	−	1.19602i	0.0794223	−	0.0452053i
$701$	−23.9793			−0.905685			−0.452843	−	0.891590i	$-0.649590\pi$
$701$	−23.9793			−0.905685			−0.452843	+	0.891590i	$0.649590\pi$
$702$			25.6403i			0.967731i
$703$		−	0.887066i		−	0.0334563i
$704$	−8.87488			−0.334485
$705$	19.2102	−	33.0379i	0.723497	−	1.24428i
$706$	8.57980			0.322905
$707$			6.17716i			0.232316i
$708$			7.58441i			0.285040i
$709$	−46.9292			−1.76246			−0.881231	−	0.472686i	$-0.843284\pi$
$709$	−46.9292			−1.76246			−0.881231	+	0.472686i	$0.843284\pi$
$710$	−35.4711	−	20.6250i	−1.33120	−	0.774041i
$711$	10.4570			0.392167
$712$			28.9709i			1.08573i
$713$		−	0.0879083i		−	0.00329219i
$714$	−5.11763			−0.191523
$715$	−7.20997	−	4.19230i	−0.269638	−	0.156783i
$716$	−6.99772			−0.261517
$717$			6.97252i			0.260393i
$718$			22.9215i			0.855423i
$719$	−6.70665			−0.250116			−0.125058	−	0.992149i	$-0.539912\pi$
$719$	−6.70665			−0.250116			−0.125058	+	0.992149i	$0.539912\pi$
$720$	2.18275	−	3.75392i	0.0813462	−	0.139900i
$721$	13.4790			0.501985
$722$		−	1.22468i		−	0.0455779i
$723$		−	25.3311i		−	0.942072i
$724$	2.12338			0.0789146
$725$	6.59575	+	11.5882i	0.244960	+	0.430376i
$726$	1.85478			0.0688372
$727$			44.1042i			1.63573i	0.575408	+	0.817866i	$0.304843\pi$
$727$			44.1042i			1.63573i	−0.575408	+	0.817866i	$0.695157\pi$
$728$			11.0416i			0.409229i
$729$	−30.0112			−1.11153
$730$	−4.04264	+	6.95259i	−0.149625	+	0.257327i
$731$	15.6579			0.579128
$732$			7.24944i			0.267947i
$733$		−	41.1629i		−	1.52039i	−0.649697	−	0.760193i	$-0.725104\pi$
$733$		−	41.1629i		−	1.52039i	0.649697	−	0.760193i	$-0.274896\pi$
$734$	10.7528			0.396892
$735$	−17.7565	−	10.3247i	−0.654960	−	0.380832i
$736$	3.48678			0.128524
$737$			13.5976i			0.500874i
$738$			6.69104i			0.246301i
$739$	−16.4325			−0.604479			−0.302240	−	0.953232i	$-0.597734\pi$
$739$	−16.4325			−0.604479			−0.302240	+	0.953232i	$0.597734\pi$
$740$	0.857642	+	0.498684i	0.0315276	+	0.0183320i
$741$	−5.64886			−0.207516
$742$			14.8667i			0.545773i
$743$			53.2160i			1.95231i	0.217084	+	0.976153i	$0.430346\pi$
$743$			53.2160i			1.95231i	−0.217084	+	0.976153i	$0.569654\pi$
$744$	−0.322273			−0.0118151
$745$	−6.34087	+	10.9051i	−0.232311	+	0.399532i
$746$	−18.6287			−0.682045
$747$		−	7.17421i		−	0.262490i
$748$			1.42737i			0.0521898i
$749$	7.66662			0.280132
$750$	20.7361	+	0.191356i	0.757177	+	0.00698733i
$751$	−22.2837			−0.813145			−0.406573	−	0.913618i	$-0.633276\pi$
$751$	−22.2837			−0.813145			−0.406573	+	0.913618i	$0.633276\pi$
$752$		−	31.0284i		−	1.13149i
$753$			6.12672i			0.223270i
$754$	−12.1815			−0.443623
$755$	−25.1142	+	43.1917i	−0.913999	+	1.57191i
$756$	−2.71436			−0.0987204
$757$		−	36.2525i		−	1.31762i	−0.752310	−	0.658809i	$-0.771061\pi$
$757$		−	36.2525i		−	1.31762i	0.752310	−	0.658809i	$-0.228939\pi$
$758$		−	41.0599i		−	1.49136i
$759$	−1.91573			−0.0695366
$760$	5.91878	+	3.44152i	0.214697	+	0.124837i
$761$	−31.4541			−1.14021			−0.570105	−	0.821572i	$-0.693097\pi$
$761$	−31.4541			−1.14021			−0.570105	+	0.821572i	$0.693097\pi$
$762$			31.1229i			1.12746i
$763$		−	6.91924i		−	0.250493i
$764$	4.14304			0.149890
$765$	−3.89632	−	2.26555i	−0.140872	−	0.0819112i
$766$	28.2091			1.01924
$767$			37.3453i			1.34846i
$768$		−	16.9480i		−	0.611560i
$769$	8.51028			0.306888			0.153444	−	0.988157i	$-0.450963\pi$
$769$	8.51028			0.306888			0.153444	+	0.988157i	$0.450963\pi$
$770$	−1.33086	+	2.28883i	−0.0479610	+	0.0824839i
$771$	19.6217			0.706660
$772$		−	5.39122i		−	0.194034i
$773$			13.2514i			0.476621i	0.971189	+	0.238311i	$0.0765937\pi$
$773$			13.2514i			0.476621i	−0.971189	+	0.238311i	$0.923406\pi$
$774$	−4.74585			−0.170586
$775$	0.171887	+	0.301993i	0.00617437	+	0.0108479i
$776$	9.14693			0.328356
$777$			1.29890i			0.0465977i
$778$			13.1622i			0.471887i
$779$	−7.73545			−0.277151
$780$	3.17563	−	5.46149i	0.113706	−	0.195553i
$781$	−14.9834			−0.536148
$782$			4.42095i			0.158093i
$783$		−	14.9690i		−	0.534950i
$784$	−16.6765			−0.595589
$785$	42.0589	+	24.4555i	1.50115	+	0.872854i
$786$	−1.68529			−0.0601122
$787$			23.5128i			0.838142i	0.907953	+	0.419071i	$0.137644\pi$
$787$			23.5128i			0.838142i	−0.907953	+	0.419071i	$0.862356\pi$
$788$			2.34908i			0.0836824i
$789$	−1.73160			−0.0616467
$790$	35.0496	+	20.3799i	1.24701	+	0.725085i
$791$	13.4610			0.478616
$792$		−	2.16260i		−	0.0768447i
$793$			35.6959i			1.26760i
$794$	−38.2760			−1.35836
$795$	21.3733	−	36.7580i	0.758032	−	1.30367i
$796$	−8.07720			−0.286289
$797$		−	1.73400i		−	0.0614216i	−0.999528	−	0.0307108i	$-0.990223\pi$
$797$		−	1.73400i		−	0.0614216i	0.999528	−	0.0307108i	$-0.00977709\pi$
$798$			1.79325i			0.0634805i
$799$	−32.2055			−1.13935
$800$	−11.9782	+	6.81771i	−0.423493	+	0.241042i
$801$	−6.68278			−0.236125
$802$		−	16.8316i		−	0.594346i
$803$			2.93685i			0.103639i
$804$	−10.3001			−0.363255
$805$	1.37460	−	2.36405i	0.0484483	−	0.0833220i
$806$	−0.317452			−0.0111818
$807$			25.8478i			0.909884i
$808$		−	19.5627i		−	0.688214i
$809$	47.2481			1.66115			0.830577	−	0.556903i	$-0.188011\pi$
$809$	47.2481			1.66115			0.830577	+	0.556903i	$0.188011\pi$
$810$	−15.1091	−	8.78533i	−0.530880	−	0.308685i
$811$	−30.7140			−1.07851			−0.539257	−	0.842141i	$-0.681295\pi$
$811$	−30.7140			−1.07851			−0.539257	+	0.842141i	$0.681295\pi$
$812$		−	1.28957i		−	0.0452549i
$813$			27.8476i			0.976660i
$814$	−1.08637			−0.0380773
$815$	12.4931	+	7.26425i	0.437616	+	0.254455i
$816$	11.8837			0.416014
$817$		−	5.48663i		−	0.191953i
$818$			2.62197i			0.0916749i
$819$	−2.54700			−0.0889992
$820$	4.34865	−	7.47887i	0.151862	−	0.261173i
$821$	10.0585			0.351045			0.175522	−	0.984475i	$-0.443839\pi$
$821$	10.0585			0.351045			0.175522	+	0.984475i	$0.443839\pi$
$822$		−	18.9568i		−	0.661196i
$823$			55.9207i			1.94927i	0.223797	+	0.974636i	$0.428155\pi$
$823$			55.9207i			1.94927i	−0.223797	+	0.974636i	$0.571845\pi$
$824$	−42.6873			−1.48708
$825$	6.58114	−	3.74583i	0.229126	−	0.130413i
$826$	11.8554			0.412503
$827$		−	19.0563i		−	0.662652i	−0.943516	−	0.331326i	$-0.892504\pi$
$827$		−	19.0563i		−	0.662652i	0.943516	−	0.331326i	$-0.107496\pi$
$828$			0.446848i			0.0155291i
$829$	−37.1691			−1.29094			−0.645468	−	0.763787i	$-0.723338\pi$
$829$	−37.1691			−1.29094			−0.645468	+	0.763787i	$0.723338\pi$
$830$	13.9821	−	24.0465i	0.485324	−	0.834666i
$831$	26.5569			0.921250
$832$		−	33.1020i		−	1.14761i
$833$			17.3091i			0.599726i
$834$	26.4899			0.917271
$835$	28.3808	+	16.5022i	0.982156	+	0.571084i
$836$	0.500160			0.0172984
$837$		−	0.390097i		−	0.0134837i
$838$		−	7.41677i		−	0.256208i
$839$	4.23142			0.146085			0.0730423	−	0.997329i	$-0.476729\pi$
$839$	4.23142			0.146085			0.0730423	+	0.997329i	$0.476729\pi$
$840$	−8.66665	−	5.03930i	−0.299028	−	0.173872i
$841$	−21.8884			−0.754771
$842$		−	29.3669i		−	1.01205i
$843$			25.1778i			0.867168i
$844$	−9.25304			−0.318503
$845$	1.02486	−	1.76257i	0.0352564	−	0.0606343i
$846$	9.76137			0.335603
$847$			0.966830i			0.0332207i
$848$		−	34.5222i		−	1.18550i
$849$	7.42150			0.254705
$850$	−8.64429	−	15.1874i	−0.296497	−	0.520922i
$851$	1.12207			0.0384642
$852$		−	11.3498i		−	0.388837i
$853$			17.0221i			0.582827i	0.956597	+	0.291413i	$0.0941255\pi$
$853$			17.0221i			0.582827i	−0.956597	+	0.291413i	$0.905875\pi$
$854$	11.3318			0.387767
$855$	−0.793865	+	1.36530i	−0.0271496	+	0.0466922i
$856$	−24.2797			−0.829864
$857$		−	37.4327i		−	1.27868i	−0.768925	−	0.639339i	$-0.779208\pi$
$857$		−	37.4327i		−	1.27868i	0.768925	−	0.639339i	$-0.220792\pi$
$858$			6.91804i			0.236178i
$859$	1.79225			0.0611508			0.0305754	−	0.999532i	$-0.490266\pi$
$859$	1.79225			0.0611508			0.0305754	+	0.999532i	$0.490266\pi$
$860$	5.30464	+	3.08443i	0.180887	+	0.105178i
$861$	11.3267			0.386014
$862$			21.0501i			0.716969i
$863$			13.0820i			0.445318i	0.974896	+	0.222659i	$0.0714736\pi$
$863$			13.0820i			0.445318i	−0.974896	+	0.222659i	$0.928526\pi$
$864$	15.4728			0.526394
$865$	43.1109	+	25.0672i	1.46581	+	0.852311i
$866$	−6.54819			−0.222516
$867$			13.4119i			0.455492i
$868$		−	0.0336065i		−	0.00114068i
$869$	14.8054			0.502238
$870$	5.55952	−	9.56132i	0.188485	−	0.324159i
$871$	−50.7170			−1.71848
$872$			21.9128i			0.742062i
$873$			2.10994i			0.0714108i
$874$	1.54913			0.0524001
$875$	−0.0997473	+	10.8090i	−0.00337207	+	0.365412i
$876$	−2.22464			−0.0751636
$877$		−	29.1282i		−	0.983588i	−0.870712	−	0.491794i	$-0.836341\pi$
$877$		−	29.1282i		−	0.983588i	0.870712	−	0.491794i	$-0.163659\pi$
$878$		−	39.2035i		−	1.32305i
$879$	−30.3174			−1.02258
$880$	3.09042	−	5.31494i	0.104178	−	0.179167i
$881$	30.9351			1.04223			0.521115	−	0.853486i	$-0.325516\pi$
$881$	30.9351			1.04223			0.521115	+	0.853486i	$0.325516\pi$
$882$		−	5.24634i		−	0.176653i
$883$		−	3.73004i		−	0.125526i	−0.998028	−	0.0627629i	$-0.980009\pi$
$883$		−	3.73004i		−	0.125526i	0.998028	−	0.0627629i	$-0.0199912\pi$
$884$	−5.32388			−0.179061
$885$	−29.3126	−	17.0441i	−0.985333	−	0.572931i
$886$	15.4008			0.517400
$887$			2.56757i			0.0862106i	0.999071	+	0.0431053i	$0.0137251\pi$
$887$			2.56757i			0.0862106i	−0.999071	+	0.0431053i	$0.986275\pi$
$888$		−	4.11353i		−	0.138041i
$889$	−16.2233			−0.544111
$890$	−22.3994	−	13.0243i	−0.750828	−	0.436576i
$891$	−6.38226			−0.213814
$892$			11.8744i			0.397583i
$893$			11.2850i			0.377639i
$894$	10.4636			0.349954
$895$	15.7257	−	27.0452i	0.525651	−	0.904020i
$896$	−5.17822			−0.172992
$897$		−	7.14539i		−	0.238578i
$898$			19.2392i			0.642022i
$899$	0.185332			0.00618115
$900$	−0.873723	−	1.53507i	−0.0291241	−	0.0511689i
$901$	−35.8318			−1.19373
$902$			9.47344i			0.315431i
$903$			8.03387i			0.267351i
$904$	−42.6300			−1.41785
$905$	−4.77176	+	8.20653i	−0.158619	+	0.272794i
$906$	41.4429			1.37685
$907$		−	5.79376i		−	0.192379i	−0.995363	−	0.0961893i	$-0.969335\pi$
$907$		−	5.79376i		−	0.192379i	0.995363	−	0.0961893i	$-0.0306654\pi$
$908$		−	5.64970i		−	0.187492i
$909$	4.51258			0.149673
$910$	−8.53702	−	4.96393i	−0.282999	−	0.164553i
$911$	−13.7537			−0.455681			−0.227840	−	0.973699i	$-0.573166\pi$
$911$	−13.7537			−0.455681			−0.227840	+	0.973699i	$0.573166\pi$
$912$		−	4.16414i		−	0.137889i
$913$		−	10.1575i		−	0.336165i
$914$	19.5644			0.647134
$915$	−28.0180	−	16.2913i	−0.926247	−	0.538575i
$916$	10.3913			0.343338
$917$		−	0.878481i		−	0.0290100i
$918$			19.6182i			0.647496i
$919$	−18.1442			−0.598521			−0.299260	−	0.954172i	$-0.596740\pi$
$919$	−18.1442			−0.598521			−0.299260	+	0.954172i	$0.596740\pi$
$920$	−4.35328	+	7.48682i	−0.143523	+	0.246833i
$921$	−14.2072			−0.468144
$922$			13.1436i			0.432860i
$923$		−	55.8858i		−	1.83950i
$924$	−0.732365			−0.0240931
$925$	−3.85468	+	2.19399i	−0.126741	+	0.0721380i
$926$	32.4739			1.06716
$927$		−	9.84677i		−	0.323410i
$928$			7.35096i			0.241307i
$929$	−6.09545			−0.199985			−0.0999926	−	0.994988i	$-0.531882\pi$
$929$	−6.09545			−0.199985			−0.0999926	+	0.994988i	$0.531882\pi$
$930$	0.144883	−	0.249171i	0.00475089	−	0.00817063i
$931$	6.06524			0.198780
$932$		−	7.86718i		−	0.257698i
$933$		−	22.9635i		−	0.751791i
$934$	−0.105685			−0.00345812
$935$	−5.51657	−	3.20766i	−0.180411	−	0.104902i
$936$	8.06618			0.263651
$937$		−	16.7984i		−	0.548781i	−0.961618	−	0.274390i	$-0.911524\pi$
$937$		−	16.7984i		−	0.548781i	0.961618	−	0.274390i	$-0.0884761\pi$
$938$			16.1003i			0.525694i
$939$	−36.5671			−1.19332
$940$	−10.9107	−	6.34412i	−0.355868	−	0.206922i
$941$	−50.3075			−1.63998			−0.819989	−	0.572379i	$-0.806021\pi$
$941$	−50.3075			−1.63998			−0.819989	+	0.572379i	$0.806021\pi$
$942$		−	40.3559i		−	1.31487i
$943$		−	9.78478i		−	0.318636i
$944$	−27.5297			−0.896015
$945$	6.09986	−	10.4906i	0.198428	−	0.341260i
$946$	−6.71937			−0.218465
$947$			9.22289i			0.299704i	0.988708	+	0.149852i	$0.0478797\pi$
$947$			9.22289i			0.299704i	−0.988708	+	0.149852i	$0.952120\pi$
$948$			11.2149i			0.364244i
$949$	−10.9540			−0.355583
$950$	−5.32175	+	3.02902i	−0.172660	+	0.0982743i
$951$	7.56907			0.245444
$952$			8.44827i			0.273810i
$953$			29.7492i			0.963670i	0.876262	+	0.481835i	$0.160030\pi$
$953$			29.7492i			0.963670i	−0.876262	+	0.481835i	$0.839970\pi$
$954$	10.8605			0.351622
$955$	−9.31046	+	16.0122i	−0.301279	+	0.518144i
$956$	2.30266			0.0744733
$957$		−	4.03881i		−	0.130556i
$958$		−	8.98885i		−	0.290417i
$959$	9.88155			0.319092
$960$	25.9820	+	15.1075i	0.838566	+	0.487592i
$961$	−30.9952			−0.999844
$962$		−	4.05201i		−	0.130642i
$963$		−	5.60066i		−	0.180479i
$964$	−8.36553			−0.269436
$965$	20.8363	+	12.1154i	0.670744	+	0.390010i
$966$	−2.26833			−0.0729825
$967$		−	5.86655i		−	0.188656i	−0.995541	−	0.0943278i	$-0.969930\pi$
$967$		−	5.86655i		−	0.188656i	0.995541	−	0.0943278i	$-0.0300702\pi$
$968$		−	3.06189i		−	0.0984130i
$969$	−4.32211			−0.138846
$970$	−4.11214	+	7.07211i	−0.132033	+	0.227072i
$971$	−14.2880			−0.458523			−0.229261	−	0.973365i	$-0.573631\pi$
$971$	−14.2880			−0.458523			−0.229261	+	0.973365i	$0.573631\pi$
$972$			3.58795i			0.115083i
$973$			13.8083i			0.442673i
$974$	−40.1434			−1.28628
$975$	13.9714	+	24.5467i	0.447443	+	0.786123i
$976$	−26.3138			−0.842285
$977$		−	25.8956i		−	0.828475i	−0.910169	−	0.414237i	$-0.864048\pi$
$977$		−	25.8956i		−	0.828475i	0.910169	−	0.414237i	$-0.135952\pi$
$978$		−	11.9873i		−	0.383311i
$979$	−9.46175			−0.302399
$980$	−3.40971	+	5.86406i	−0.108919	+	0.187320i
$981$	−5.05468			−0.161384
$982$		−	47.5887i		−	1.51862i
$983$		−	26.7680i		−	0.853766i	−0.904307	−	0.426883i	$-0.859612\pi$
$983$		−	26.7680i		−	0.853766i	0.904307	−	0.426883i	$-0.140388\pi$
$984$	−35.8711			−1.14353
$985$	−9.07883	−	5.27897i	−0.289276	−	0.168202i
$986$	−9.32041			−0.296822
$987$		−	16.5242i		−	0.525972i
$988$			1.86552i			0.0593502i
$989$	6.94019			0.220685
$990$	1.67205	+	0.972230i	0.0531413	+	0.0308995i
$991$	−4.25490			−0.135161			−0.0675806	−	0.997714i	$-0.521528\pi$
$991$	−4.25490			−0.135161			−0.0675806	+	0.997714i	$0.521528\pi$
$992$			0.191568i			0.00608230i
$993$		−	41.8526i		−	1.32815i
$994$	−17.7412			−0.562716
$995$	18.1515	−	31.2172i	0.575441	−	0.989651i
$996$	7.69423			0.243801
$997$			29.4931i			0.934057i	0.884242	+	0.467028i	$0.154675\pi$
$997$			29.4931i			0.934057i	−0.884242	+	0.467028i	$0.845325\pi$
$998$		−	44.1293i		−	1.39689i
$999$	4.97926			0.157537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.c.419.7	✓	20
5.2	odd	4		5225.2.a.ba.1.14		20
5.3	odd	4		5225.2.a.ba.1.7		20
5.4	even	2	inner	1045.2.b.c.419.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.c.419.7	✓	20	1.1	even	1	trivial
1045.2.b.c.419.14	yes	20	5.4	even	2	inner
5225.2.a.ba.1.7		20	5.3	odd	4
5225.2.a.ba.1.14		20	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)

\(f(q)\)	\(=\)	\(q-1.22468i q^{2} +1.51450i q^{3} +0.500160 q^{4} +(-1.12399 + 1.93304i) q^{5} +1.85478 q^{6} +0.966830i q^{7} -3.06189i q^{8} +0.706295 q^{9} +O(q^{10})\)	\(q-1.22468i q^{2} +1.51450i q^{3} +0.500160 q^{4} +(-1.12399 + 1.93304i) q^{5} +1.85478 q^{6} +0.966830i q^{7} -3.06189i q^{8} +0.706295 q^{9} +(2.36736 + 1.37652i) q^{10} +1.00000 q^{11} +0.757491i q^{12} +3.72985i q^{13} +1.18406 q^{14} +(-2.92759 - 1.70227i) q^{15} -2.74952 q^{16} +2.85383i q^{17} -0.864985i q^{18} +1.00000 q^{19} +(-0.562172 + 0.966830i) q^{20} -1.46426 q^{21} -1.22468i q^{22} +1.26493i q^{23} +4.63723 q^{24} +(-2.47331 - 4.34542i) q^{25} +4.56788 q^{26} +5.61318i q^{27} +0.483570i q^{28} -2.66677 q^{29} +(-2.08474 + 3.58536i) q^{30} -0.0694967 q^{31} -2.75651i q^{32} +1.51450i q^{33} +3.49502 q^{34} +(-1.86893 - 1.08670i) q^{35} +0.353260 q^{36} -0.887066i q^{37} -1.22468i q^{38} -5.64886 q^{39} +(5.91878 + 3.44152i) q^{40} -7.73545 q^{41} +1.79325i q^{42} -5.48663i q^{43} +0.500160 q^{44} +(-0.793865 + 1.36530i) q^{45} +1.54913 q^{46} +11.2850i q^{47} -4.16414i q^{48} +6.06524 q^{49} +(-5.32175 + 3.02902i) q^{50} -4.32211 q^{51} +1.86552i q^{52} +12.5557i q^{53} +6.87434 q^{54} +(-1.12399 + 1.93304i) q^{55} +2.96033 q^{56} +1.51450i q^{57} +3.26594i q^{58} +10.0125 q^{59} +(-1.46426 - 0.851409i) q^{60} +9.57033 q^{61} +0.0851112i q^{62} +0.682867i q^{63} -8.87488 q^{64} +(-7.20997 - 4.19230i) q^{65} +1.85478 q^{66} +13.5976i q^{67} +1.42737i q^{68} -1.91573 q^{69} +(-1.33086 + 2.28883i) q^{70} -14.9834 q^{71} -2.16260i q^{72} +2.93685i q^{73} -1.08637 q^{74} +(6.58114 - 3.74583i) q^{75} +0.500160 q^{76} +0.966830i q^{77} +6.91804i q^{78} +14.8054 q^{79} +(3.09042 - 5.31494i) q^{80} -6.38226 q^{81} +9.47344i q^{82} -10.1575i q^{83} -0.732365 q^{84} +(-5.51657 - 3.20766i) q^{85} -6.71937 q^{86} -4.03881i q^{87} -3.06189i q^{88} -9.46175 q^{89} +(1.67205 + 0.972230i) q^{90} -3.60614 q^{91} +0.632666i q^{92} -0.105253i q^{93} +13.8205 q^{94} +(-1.12399 + 1.93304i) q^{95} +4.17473 q^{96} +2.98734i q^{97} -7.42797i q^{98} +0.706295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9	\( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) \) 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9 - 6 * q^10 + 20 * q^11 + 24 * q^14 - 6 * q^15 - 4 * q^16 + 20 * q^19 - 6 * q^20 - 30 * q^21 + 38 * q^24 + 2 * q^25 + 8 * q^26 + 50 * q^29 - 20 * q^30 - 50 * q^31 + 28 * q^34 + 6 * q^35 - 12 * q^36 + 48 * q^39 + 12 * q^40 - 34 * q^41 - 12 * q^44 - 18 * q^45 - 36 * q^46 - 6 * q^49 + 26 * q^50 - 40 * q^51 - 6 * q^54 - 40 * q^56 + 30 * q^59 - 30 * q^60 - 14 * q^61 + 36 * q^64 + 30 * q^65 - 8 * q^66 - 12 * q^69 - 54 * q^70 - 40 * q^71 + 50 * q^74 - 8 * q^75 - 12 * q^76 + 106 * q^79 + 8 * q^80 - 30 * q^84 - 22 * q^85 + 56 * q^86 + 36 * q^89 - 64 * q^90 - 56 * q^91 + 28 * q^94 + 66 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

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Database

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