LMFDB - Embedded newform 1045.2.b.e.419.18

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			419.18
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.598278i q^{2} +1.31473i q^{3} +1.64206 q^{4} +(1.14673 - 1.91964i) q^{5} -0.786572 q^{6} +0.976473i q^{7} +2.17897i q^{8} +1.27149 q^{9} +O(q^{10})$	\(q+0.598278i q^{2} +1.31473i q^{3} +1.64206 q^{4} +(1.14673 - 1.91964i) q^{5} -0.786572 q^{6} +0.976473i q^{7} +2.17897i q^{8} +1.27149 q^{9} +(1.14848 + 0.686061i) q^{10} +1.00000 q^{11} +2.15887i q^{12} -2.37077i q^{13} -0.584202 q^{14} +(2.52380 + 1.50763i) q^{15} +1.98050 q^{16} +2.72579i q^{17} +0.760706i q^{18} -1.00000 q^{19} +(1.88300 - 3.15217i) q^{20} -1.28380 q^{21} +0.598278i q^{22} -2.63540i q^{23} -2.86475 q^{24} +(-2.37004 - 4.40260i) q^{25} +1.41838 q^{26} +5.61585i q^{27} +1.60343i q^{28} +6.56331 q^{29} +(-0.901983 + 1.50994i) q^{30} -3.93726 q^{31} +5.54282i q^{32} +1.31473i q^{33} -1.63078 q^{34} +(1.87448 + 1.11975i) q^{35} +2.08787 q^{36} -5.08339i q^{37} -0.598278i q^{38} +3.11692 q^{39} +(4.18283 + 2.49868i) q^{40} +3.22774 q^{41} -0.768067i q^{42} +12.0774i q^{43} +1.64206 q^{44} +(1.45805 - 2.44081i) q^{45} +1.57670 q^{46} -9.84617i q^{47} +2.60382i q^{48} +6.04650 q^{49} +(2.63398 - 1.41794i) q^{50} -3.58368 q^{51} -3.89296i q^{52} +0.422971i q^{53} -3.35984 q^{54} +(1.14673 - 1.91964i) q^{55} -2.12770 q^{56} -1.31473i q^{57} +3.92668i q^{58} -15.0655 q^{59} +(4.14425 + 2.47563i) q^{60} +6.89034 q^{61} -2.35558i q^{62} +1.24158i q^{63} +0.644852 q^{64} +(-4.55103 - 2.71862i) q^{65} -0.786572 q^{66} +2.42926i q^{67} +4.47593i q^{68} +3.46483 q^{69} +(-0.669920 + 1.12146i) q^{70} -10.7764 q^{71} +2.77054i q^{72} +8.27959i q^{73} +3.04128 q^{74} +(5.78822 - 3.11596i) q^{75} -1.64206 q^{76} +0.976473i q^{77} +1.86478i q^{78} +0.722096 q^{79} +(2.27109 - 3.80185i) q^{80} -3.56883 q^{81} +1.93109i q^{82} -12.4875i q^{83} -2.10807 q^{84} +(5.23254 + 3.12574i) q^{85} -7.22564 q^{86} +8.62896i q^{87} +2.17897i q^{88} -13.2163 q^{89} +(1.46028 + 0.872321i) q^{90} +2.31499 q^{91} -4.32749i q^{92} -5.17642i q^{93} +5.89074 q^{94} +(-1.14673 + 1.91964i) q^{95} -7.28730 q^{96} +12.9226i q^{97} +3.61749i q^{98} +1.27149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.598278i			0.423046i	0.977373	+	0.211523i	$0.0678424\pi$
$2$			0.598278i			0.423046i	−0.977373	+	0.211523i	$0.932158\pi$
$3$			1.31473i			0.759058i	0.925180	+	0.379529i	$0.123914\pi$
$3$			1.31473i			0.759058i	−0.925180	+	0.379529i	$0.876086\pi$
$4$	1.64206			0.821032
$5$	1.14673	−	1.91964i	0.512831	−	0.858489i
$5$	1.14673	−	1.91964i	0.512831	−	0.858489i
$6$	−0.786572			−0.321117
$7$			0.976473i			0.369072i	0.982826	+	0.184536i	$0.0590783\pi$
$7$			0.976473i			0.369072i	−0.982826	+	0.184536i	$0.940922\pi$
$8$			2.17897i			0.770381i
$9$	1.27149			0.423831
$10$	1.14848	+	0.686061i	0.363181	+	0.216951i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			2.15887i			0.623211i
$13$		−	2.37077i		−	0.657534i	−0.944411	−	0.328767i	$-0.893367\pi$
$13$		−	2.37077i		−	0.657534i	0.944411	−	0.328767i	$-0.106633\pi$
$14$	−0.584202			−0.156135
$15$	2.52380	+	1.50763i	0.651643	+	0.389269i
$16$	1.98050			0.495125
$17$			2.72579i			0.661102i	0.943788	+	0.330551i	$0.107235\pi$
$17$			2.72579i			0.661102i	−0.943788	+	0.330551i	$0.892765\pi$
$18$			0.760706i			0.179300i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	1.88300	−	3.15217i	0.421051	−	0.704847i
$21$	−1.28380			−0.280147
$22$			0.598278i			0.127553i
$23$		−	2.63540i		−	0.549518i	−0.961513	−	0.274759i	$-0.911402\pi$
$23$		−	2.63540i		−	0.549518i	0.961513	−	0.274759i	$-0.0885981\pi$
$24$	−2.86475			−0.584764
$25$	−2.37004	−	4.40260i	−0.474008	−	0.880521i
$26$	1.41838			0.278167
$27$			5.61585i			1.08077i
$28$			1.60343i			0.303020i
$29$	6.56331			1.21878			0.609388	−	0.792872i	$-0.291415\pi$
$29$	6.56331			1.21878			0.609388	+	0.792872i	$0.291415\pi$
$30$	−0.901983	+	1.50994i	−0.164679	+	0.275675i
$31$	−3.93726			−0.707153			−0.353576	−	0.935406i	$-0.615035\pi$
$31$	−3.93726			−0.707153			−0.353576	+	0.935406i	$0.615035\pi$
$32$			5.54282i			0.979842i
$33$			1.31473i			0.228865i
$34$	−1.63078			−0.279677
$35$	1.87448	+	1.11975i	0.316844	+	0.189272i
$36$	2.08787			0.347978
$37$		−	5.08339i		−	0.835705i	−0.908515	−	0.417852i	$-0.862783\pi$
$37$		−	5.08339i		−	0.835705i	0.908515	−	0.417852i	$-0.137217\pi$
$38$		−	0.598278i		−	0.0970535i
$39$	3.11692			0.499106
$40$	4.18283	+	2.49868i	0.661364	+	0.395076i
$41$	3.22774			0.504089			0.252044	−	0.967716i	$-0.418897\pi$
$41$	3.22774			0.504089			0.252044	+	0.967716i	$0.418897\pi$
$42$		−	0.768067i		−	0.118515i
$43$			12.0774i			1.84178i	0.389817	+	0.920892i	$0.372538\pi$
$43$			12.0774i			1.84178i	−0.389817	+	0.920892i	$0.627462\pi$
$44$	1.64206			0.247550
$45$	1.45805	−	2.44081i	0.217354	−	0.363854i
$46$	1.57670			0.232472
$47$		−	9.84617i		−	1.43621i	−0.695934	−	0.718106i	$-0.745010\pi$
$47$		−	9.84617i		−	1.43621i	0.695934	−	0.718106i	$-0.254990\pi$
$48$			2.60382i			0.375829i
$49$	6.04650			0.863786
$50$	2.63398	−	1.41794i	0.372501	−	0.200527i
$51$	−3.58368			−0.501815
$52$		−	3.89296i		−	0.539856i
$53$			0.422971i			0.0580996i	0.999578	+	0.0290498i	$0.00924814\pi$
$53$			0.422971i			0.0580996i	−0.999578	+	0.0290498i	$0.990752\pi$
$54$	−3.35984			−0.457216
$55$	1.14673	−	1.91964i	0.154624	−	0.258844i
$56$	−2.12770			−0.284326
$57$		−	1.31473i		−	0.174140i
$58$			3.92668i			0.515598i
$59$	−15.0655			−1.96137			−0.980684	−	0.195601i	$-0.937334\pi$
$59$	−15.0655			−1.96137			−0.980684	+	0.195601i	$0.937334\pi$
$60$	4.14425	+	2.47563i	0.535020	+	0.319602i
$61$	6.89034			0.882218			0.441109	−	0.897454i	$-0.354585\pi$
$61$	6.89034			0.882218			0.441109	+	0.897454i	$0.354585\pi$
$62$		−	2.35558i		−	0.299158i
$63$			1.24158i			0.156424i
$64$	0.644852			0.0806064
$65$	−4.55103	−	2.71862i	−0.564486	−	0.337204i
$66$	−0.786572			−0.0968204
$67$			2.42926i			0.296781i	0.988929	+	0.148391i	$0.0474093\pi$
$67$			2.42926i			0.296781i	−0.988929	+	0.148391i	$0.952591\pi$
$68$			4.47593i			0.542786i
$69$	3.46483			0.417117
$70$	−0.669920	+	1.12146i	−0.0800707	+	0.134040i
$71$	−10.7764			−1.27892			−0.639461	−	0.768823i	$-0.720843\pi$
$71$	−10.7764			−1.27892			−0.639461	+	0.768823i	$0.720843\pi$
$72$			2.77054i			0.326511i
$73$			8.27959i			0.969053i	0.874777	+	0.484526i	$0.161008\pi$
$73$			8.27959i			0.969053i	−0.874777	+	0.484526i	$0.838992\pi$
$74$	3.04128			0.353542
$75$	5.78822	−	3.11596i	0.668366	−	0.359800i
$76$	−1.64206			−0.188358
$77$			0.976473i			0.111279i
$78$			1.86478i			0.211145i
$79$	0.722096			0.0812422			0.0406211	−	0.999175i	$-0.487066\pi$
$79$	0.722096			0.0812422			0.0406211	+	0.999175i	$0.487066\pi$
$80$	2.27109	−	3.80185i	0.253916	−	0.425059i
$81$	−3.56883			−0.396537
$82$			1.93109i			0.213253i
$83$		−	12.4875i		−	1.37068i	−0.728222	−	0.685341i	$-0.759653\pi$
$83$		−	12.4875i		−	1.37068i	0.728222	−	0.685341i	$-0.240347\pi$
$84$	−2.10807			−0.230010
$85$	5.23254	+	3.12574i	0.567549	+	0.339034i
$86$	−7.22564			−0.779160
$87$			8.62896i			0.925121i
$88$			2.17897i			0.232279i
$89$	−13.2163			−1.40092			−0.700461	−	0.713691i	$-0.747022\pi$
$89$	−13.2163			−1.40092			−0.700461	+	0.713691i	$0.747022\pi$
$90$	1.46028	+	0.872321i	0.153927	+	0.0919507i
$91$	2.31499			0.242677
$92$		−	4.32749i		−	0.451172i
$93$		−	5.17642i		−	0.536770i
$94$	5.89074			0.607584
$95$	−1.14673	+	1.91964i	−0.117652	+	0.196951i
$96$	−7.28730			−0.743757
$97$			12.9226i			1.31209i	0.754722	+	0.656045i	$0.227772\pi$
$97$			12.9226i			1.31209i	−0.754722	+	0.656045i	$0.772228\pi$
$98$			3.61749i			0.365421i
$99$	1.27149			0.127790
$100$	−3.89176	−	7.22935i	−0.389176	−	0.722935i
$101$	2.93375			0.291919			0.145959	−	0.989291i	$-0.453373\pi$
$101$	2.93375			0.291919			0.145959	+	0.989291i	$0.453373\pi$
$102$		−	2.14403i		−	0.212291i
$103$			2.91075i			0.286805i	0.989664	+	0.143402i	$0.0458043\pi$
$103$			2.91075i			0.286805i	−0.989664	+	0.143402i	$0.954196\pi$
$104$	5.16583			0.506551
$105$	−1.47216	+	2.46443i	−0.143668	+	0.240503i
$106$	−0.253054			−0.0245788
$107$			8.10841i			0.783870i	0.919993	+	0.391935i	$0.128194\pi$
$107$			8.10841i			0.783870i	−0.919993	+	0.391935i	$0.871806\pi$
$108$			9.22158i			0.887347i
$109$	−6.38053			−0.611144			−0.305572	−	0.952169i	$-0.598848\pi$
$109$	−6.38053			−0.611144			−0.305572	+	0.952169i	$0.598848\pi$
$110$	1.14848	+	0.686061i	0.109503	+	0.0654133i
$111$	6.68328			0.634349
$112$			1.93390i			0.182737i
$113$		−	7.61377i		−	0.716243i	−0.933675	−	0.358122i	$-0.883417\pi$
$113$		−	7.61377i		−	0.716243i	0.933675	−	0.358122i	$-0.116583\pi$
$114$	0.786572			0.0736693
$115$	−5.05902	−	3.02208i	−0.471756	−	0.281810i
$116$	10.7774			1.00065
$117$		−	3.01442i		−	0.278683i
$118$		−	9.01338i		−	0.829749i
$119$	−2.66166			−0.243994
$120$	−3.28508	+	5.49928i	−0.299885	+	0.502014i
$121$	1.00000			0.0909091
$122$			4.12234i			0.373219i
$123$			4.24360i			0.382633i
$124$	−6.46523			−0.580595
$125$	−11.1692	−	0.498955i	−0.999004	−	0.0446279i
$126$	−0.742808			−0.0661746
$127$			9.28663i			0.824055i	0.911171	+	0.412028i	$0.135179\pi$
$127$			9.28663i			0.824055i	−0.911171	+	0.412028i	$0.864821\pi$
$128$			11.4714i			1.01394i
$129$	−15.8785			−1.39802
$130$	1.62649	−	2.72278i	0.142653	−	0.238804i
$131$	2.43364			0.212628			0.106314	−	0.994333i	$-0.466095\pi$
$131$	2.43364			0.212628			0.106314	+	0.994333i	$0.466095\pi$
$132$			2.15887i			0.187905i
$133$		−	0.976473i		−	0.0846710i
$134$	−1.45337			−0.125552
$135$	10.7804	+	6.43984i	0.927830	+	0.554253i
$136$	−5.93941			−0.509300
$137$		−	5.10010i		−	0.435731i	−0.975979	−	0.217865i	$-0.930091\pi$
$137$		−	5.10010i		−	0.435731i	0.975979	−	0.217865i	$-0.0699094\pi$
$138$			2.07293i			0.176460i
$139$	−22.0692			−1.87189			−0.935943	−	0.352153i	$-0.885450\pi$
$139$	−22.0692			−1.87189			−0.935943	+	0.352153i	$0.885450\pi$
$140$	3.07801	+	1.83870i	0.260139	+	0.155398i
$141$	12.9450			1.09017
$142$		−	6.44728i		−	0.541044i
$143$		−	2.37077i		−	0.198254i
$144$	2.51819			0.209849
$145$	7.52631	−	12.5992i	0.625026	−	1.04631i
$146$	−4.95350			−0.409954
$147$			7.94950i			0.655664i
$148$		−	8.34726i		−	0.686140i
$149$	−13.7468			−1.12618			−0.563091	−	0.826395i	$-0.690388\pi$
$149$	−13.7468			−1.12618			−0.563091	+	0.826395i	$0.690388\pi$
$150$	1.86421	+	3.46297i	0.152212	+	0.282750i
$151$	−4.03825			−0.328628			−0.164314	−	0.986408i	$-0.552541\pi$
$151$	−4.03825			−0.328628			−0.164314	+	0.986408i	$0.552541\pi$
$152$		−	2.17897i		−	0.176737i
$153$			3.46582i			0.280195i
$154$	−0.584202			−0.0470764
$155$	−4.51496	+	7.55813i	−0.362650	+	0.607083i
$156$	5.11818			0.409782
$157$		−	15.4358i		−	1.23191i	−0.787781	−	0.615955i	$-0.788770\pi$
$157$		−	15.4358i		−	1.23191i	0.787781	−	0.615955i	$-0.211230\pi$
$158$			0.432014i			0.0343692i
$159$	−0.556092			−0.0441010
$160$	10.6402	+	6.35610i	0.841184	+	0.502494i
$161$	2.57340			0.202812
$162$		−	2.13515i		−	0.167754i
$163$		−	1.16781i		−	0.0914699i	−0.998954	−	0.0457349i	$-0.985437\pi$
$163$		−	1.16781i		−	0.0914699i	0.998954	−	0.0457349i	$-0.0145630\pi$
$164$	5.30016			0.413873
$165$	2.52380	+	1.50763i	0.196478	+	0.117369i
$166$	7.47100			0.579862
$167$		−	13.5738i		−	1.05038i	−0.850986	−	0.525188i	$-0.823995\pi$
$167$		−	13.5738i		−	1.05038i	0.850986	−	0.525188i	$-0.176005\pi$
$168$		−	2.79735i		−	0.215820i
$169$	7.37944			0.567649
$170$	−1.87006	+	3.13051i	−0.143427	+	0.240100i
$171$	−1.27149			−0.0972334
$172$			19.8318i			1.51216i
$173$		−	16.1495i		−	1.22782i	−0.789375	−	0.613911i	$-0.789595\pi$
$173$		−	16.1495i		−	1.22782i	0.789375	−	0.613911i	$-0.210405\pi$
$174$	−5.16252			−0.391369
$175$	4.29902	−	2.31428i	0.324976	−	0.174943i
$176$	1.98050			0.149286
$177$		−	19.8071i		−	1.48879i
$178$		−	7.90700i		−	0.592655i
$179$	21.7548			1.62603			0.813014	−	0.582244i	$-0.197825\pi$
$179$	21.7548			1.62603			0.813014	+	0.582244i	$0.197825\pi$
$180$	2.39422	−	4.00796i	0.178454	−	0.298736i
$181$	24.1713			1.79664			0.898318	−	0.439345i	$-0.144789\pi$
$181$	24.1713			1.79664			0.898318	+	0.439345i	$0.144789\pi$
$182$			1.38501i			0.102664i
$183$			9.05892i			0.669655i
$184$	5.74244			0.423339
$185$	−9.75829	−	5.82926i	−0.717444	−	0.428576i
$186$	3.09694			0.227079
$187$			2.72579i			0.199330i
$188$		−	16.1680i		−	1.17917i
$189$	−5.48372			−0.398882
$190$	−1.14848	−	0.686061i	−0.0833194	−	0.0497721i
$191$	16.0631			1.16229			0.581144	−	0.813801i	$-0.302605\pi$
$191$	16.0631			1.16229			0.581144	+	0.813801i	$0.302605\pi$
$192$			0.847804i			0.0611850i
$193$			3.14964i			0.226716i	0.993554	+	0.113358i	$0.0361608\pi$
$193$			3.14964i			0.226716i	−0.993554	+	0.113358i	$0.963839\pi$
$194$	−7.73130			−0.555075
$195$	3.57425	−	5.98336i	0.255957	−	0.428477i
$196$	9.92874			0.709196
$197$		−	20.7989i		−	1.48186i	−0.671581	−	0.740931i	$-0.734384\pi$
$197$		−	20.7989i		−	1.48186i	0.671581	−	0.740931i	$-0.265616\pi$
$198$			0.760706i			0.0540610i
$199$	−19.6178			−1.39067			−0.695335	−	0.718685i	$-0.744744\pi$
$199$	−19.6178			−1.39067			−0.695335	+	0.718685i	$0.744744\pi$
$200$	9.59312	−	5.16424i	0.678336	−	0.365167i
$201$	−3.19382			−0.225274
$202$			1.75520i			0.123495i
$203$			6.40889i			0.449816i
$204$	−5.88462			−0.412006
$205$	3.70134	−	6.19610i	0.258512	−	0.432755i
$206$	−1.74144			−0.121332
$207$		−	3.35089i		−	0.232903i
$208$		−	4.69531i		−	0.325561i
$209$	−1.00000			−0.0691714
$210$	−1.47441	−	0.880762i	−0.101744	−	0.0607784i
$211$	−23.2691			−1.60191			−0.800955	−	0.598725i	$-0.795674\pi$
$211$	−23.2691			−1.60191			−0.800955	+	0.598725i	$0.795674\pi$
$212$			0.694546i			0.0477016i
$213$		−	14.1680i		−	0.970777i
$214$	−4.85108			−0.331613
$215$	23.1842	+	13.8495i	1.58115	+	0.944525i
$216$	−12.2367			−0.832605
$217$		−	3.84463i		−	0.260990i
$218$		−	3.81733i		−	0.258542i
$219$	−10.8854			−0.735568
$220$	1.88300	−	3.15217i	0.126952	−	0.212519i
$221$	6.46223			0.434697
$222$			3.99846i			0.268359i
$223$		−	22.4155i		−	1.50105i	−0.660840	−	0.750527i	$-0.729800\pi$
$223$		−	22.4155i		−	1.50105i	0.660840	−	0.750527i	$-0.270200\pi$
$224$	−5.41242			−0.361632
$225$	−3.01349	−	5.59787i	−0.200899	−	0.373192i
$226$	4.55515			0.303004
$227$		−	16.3081i		−	1.08241i	−0.840892	−	0.541203i	$-0.817969\pi$
$227$		−	16.3081i		−	1.08241i	0.840892	−	0.541203i	$-0.182031\pi$
$228$		−	2.15887i		−	0.142974i
$229$	−9.18306			−0.606834			−0.303417	−	0.952858i	$-0.598128\pi$
$229$	−9.18306			−0.606834			−0.303417	+	0.952858i	$0.598128\pi$
$230$	1.80804	−	3.02670i	0.119219	−	0.199575i
$231$	−1.28380			−0.0844676
$232$			14.3012i			0.938921i
$233$		−	8.83281i		−	0.578656i	−0.957230	−	0.289328i	$-0.906568\pi$
$233$		−	8.83281i		−	0.578656i	0.957230	−	0.289328i	$-0.0934319\pi$
$234$	1.80346			0.117896
$235$	−18.9011	−	11.2909i	−1.23297	−	0.736534i
$236$	−24.7386			−1.61034
$237$			0.949360i			0.0616675i
$238$		−	1.59241i		−	0.103221i
$239$	−28.1616			−1.82162			−0.910810	−	0.412825i	$-0.864542\pi$
$239$	−28.1616			−1.82162			−0.910810	+	0.412825i	$0.864542\pi$
$240$	4.99839	+	2.98586i	0.322645	+	0.192737i
$241$	5.19139			0.334407			0.167203	−	0.985922i	$-0.446526\pi$
$241$	5.19139			0.334407			0.167203	+	0.985922i	$0.446526\pi$
$242$			0.598278i			0.0384588i
$243$			12.1555i			0.779776i
$244$	11.3144			0.724329
$245$	6.93368	−	11.6071i	0.442976	−	0.741551i
$246$	−2.53885			−0.161871
$247$			2.37077i			0.150849i
$248$		−	8.57916i		−	0.544777i
$249$	16.4177			1.04043
$250$	0.298514	−	6.68229i	0.0188797	−	0.422625i
$251$	14.4930			0.914791			0.457396	−	0.889263i	$-0.348782\pi$
$251$	14.4930			0.914791			0.457396	+	0.889263i	$0.348782\pi$
$252$			2.03875i			0.128429i
$253$		−	2.63540i		−	0.165686i
$254$	−5.55599			−0.348614
$255$	−4.10949	+	6.87937i	−0.257346	+	0.430803i
$256$	−5.57341			−0.348338
$257$		−	14.4469i		−	0.901174i	−0.892733	−	0.450587i	$-0.851215\pi$
$257$		−	14.4469i		−	0.901174i	0.892733	−	0.450587i	$-0.148785\pi$
$258$		−	9.49974i		−	0.591428i
$259$	4.96380			0.308435
$260$	−7.47308	−	4.46415i	−0.463461	−	0.276855i
$261$	8.34519			0.516554
$262$			1.45599i			0.0899516i
$263$		−	22.0289i		−	1.35836i	−0.733971	−	0.679181i	$-0.762335\pi$
$263$		−	22.0289i		−	1.35836i	0.733971	−	0.679181i	$-0.237665\pi$
$264$	−2.86475			−0.176313
$265$	0.811953	+	0.485032i	0.0498779	+	0.0297953i
$266$	0.584202			0.0358197
$267$		−	17.3758i		−	1.06338i
$268$			3.98900i			0.243667i
$269$	−29.9620			−1.82681			−0.913407	−	0.407047i	$-0.866559\pi$
$269$	−29.9620			−1.82681			−0.913407	+	0.407047i	$0.866559\pi$
$270$	−3.85281	+	6.44968i	−0.234475	+	0.392515i
$271$	29.6807			1.80297			0.901486	−	0.432809i	$-0.142478\pi$
$271$	29.6807			1.80297			0.901486	+	0.432809i	$0.142478\pi$
$272$			5.39843i			0.327328i
$273$			3.04359i			0.184206i
$274$	3.05128			0.184334
$275$	−2.37004	−	4.40260i	−0.142919	−	0.265487i
$276$	5.68947			0.342466
$277$			6.92335i			0.415984i	0.978131	+	0.207992i	$0.0666928\pi$
$277$			6.92335i			0.415984i	−0.978131	+	0.207992i	$0.933307\pi$
$278$		−	13.2035i		−	0.791894i
$279$	−5.00620			−0.299713
$280$	−2.43989	+	4.08442i	−0.145811	+	0.244091i
$281$	−10.3772			−0.619053			−0.309526	−	0.950891i	$-0.600171\pi$
$281$	−10.3772			−0.619053			−0.309526	+	0.950891i	$0.600171\pi$
$282$			7.74472i			0.461192i
$283$			11.7043i			0.695750i	0.937541	+	0.347875i	$0.113097\pi$
$283$			11.7043i			0.695750i	−0.937541	+	0.347875i	$0.886903\pi$
$284$	−17.6955			−1.05004
$285$	−2.52380	−	1.50763i	−0.149497	−	0.0893044i
$286$	1.41838			0.0838706
$287$			3.15180i			0.186045i
$288$			7.04765i			0.415287i
$289$	9.57005			0.562944
$290$	7.53782	+	4.50283i	0.442636	+	0.264415i
$291$	−16.9897			−0.995952
$292$			13.5956i			0.795623i
$293$			22.3674i			1.30672i	0.757048	+	0.653359i	$0.226641\pi$
$293$			22.3674i			1.30672i	−0.757048	+	0.653359i	$0.773359\pi$
$294$	−4.75601			−0.277376
$295$	−17.2761	+	28.9204i	−1.00585	+	1.68381i
$296$	11.0765			0.643811
$297$			5.61585i			0.325865i
$298$		−	8.22440i		−	0.476427i
$299$	−6.24793			−0.361327
$300$	9.50463	−	5.11660i	0.548750	−	0.295407i
$301$	−11.7932			−0.679751
$302$		−	2.41600i		−	0.139025i
$303$			3.85708i			0.221583i
$304$	−1.98050			−0.113589
$305$	7.90133	−	13.2270i	0.452429	−	0.757375i
$306$	−2.07353			−0.118536
$307$			7.33473i			0.418615i	0.977850	+	0.209308i	$0.0671210\pi$
$307$			7.33473i			0.418615i	−0.977850	+	0.209308i	$0.932879\pi$
$308$			1.60343i			0.0913640i
$309$	−3.82684			−0.217701
$310$	−4.52186	−	2.70120i	−0.256824	−	0.153418i
$311$	−4.20987			−0.238720			−0.119360	−	0.992851i	$-0.538084\pi$
$311$	−4.20987			−0.238720			−0.119360	+	0.992851i	$0.538084\pi$
$312$			6.79166i			0.384502i
$313$		−	20.6808i		−	1.16895i	−0.811413	−	0.584473i	$-0.801301\pi$
$313$		−	20.6808i		−	1.16895i	0.811413	−	0.584473i	$-0.198699\pi$
$314$	9.23489			0.521155
$315$	2.38338	+	1.42375i	0.134288	+	0.0802192i
$316$	1.18573			0.0667024
$317$			6.80831i			0.382393i	0.981552	+	0.191197i	$0.0612368\pi$
$317$			6.80831i			0.382393i	−0.981552	+	0.191197i	$0.938763\pi$
$318$		−	0.332698i		−	0.0186568i
$319$	6.56331			0.367475
$320$	0.739468	−	1.23788i	0.0413375	−	0.0691998i
$321$	−10.6604			−0.595003
$322$			1.53961i			0.0857989i
$323$		−	2.72579i		−	0.151667i
$324$	−5.86025			−0.325569
$325$	−10.4376	+	5.61882i	−0.578972	+	0.311676i
$326$	0.698675			0.0386960
$327$		−	8.38866i		−	0.463894i
$328$			7.03314i			0.388340i
$329$	9.61452			0.530065
$330$	−0.901983	+	1.50994i	−0.0496525	+	0.0831193i
$331$	6.22562			0.342191			0.171095	−	0.985254i	$-0.445269\pi$
$331$	6.22562			0.342191			0.171095	+	0.985254i	$0.445269\pi$
$332$		−	20.5053i		−	1.12537i
$333$		−	6.46350i		−	0.354197i
$334$	8.12093			0.444358
$335$	4.66331	+	2.78570i	0.254784	+	0.152199i
$336$	−2.54256			−0.138708
$337$		−	8.52411i		−	0.464338i	−0.972675	−	0.232169i	$-0.925418\pi$
$337$		−	8.52411i		−	0.464338i	0.972675	−	0.232169i	$-0.0745822\pi$
$338$			4.41496i			0.240142i
$339$	10.0100			0.543670
$340$	8.59217	+	5.13266i	0.465976	+	0.278358i
$341$	−3.93726			−0.213215
$342$		−	0.760706i		−	0.0411342i
$343$			12.7396i			0.687871i
$344$	−26.3162			−1.41888
$345$	3.97321	−	6.65123i	0.213910	−	0.358090i
$346$	9.66187			0.519425
$347$		−	7.01388i		−	0.376525i	−0.982119	−	0.188262i	$-0.939714\pi$
$347$		−	7.01388i		−	0.376525i	0.982119	−	0.188262i	$-0.0602856\pi$
$348$			14.1693i			0.759554i
$349$	−31.1886			−1.66949			−0.834744	−	0.550638i	$-0.814385\pi$
$349$	−31.1886			−1.66949			−0.834744	+	0.550638i	$0.814385\pi$
$350$	1.38458	+	2.57201i	0.0740090	+	0.137480i
$351$	13.3139			0.710643
$352$			5.54282i			0.295433i
$353$			24.4538i			1.30155i	0.759272	+	0.650773i	$0.225555\pi$
$353$			24.4538i			1.30155i	−0.759272	+	0.650773i	$0.774445\pi$
$354$	11.8501			0.629828
$355$	−12.3576	+	20.6868i	−0.655872	+	1.09794i
$356$	−21.7019			−1.15020
$357$		−	3.49936i		−	0.185206i
$358$			13.0154i			0.687885i
$359$	18.4749			0.975068			0.487534	−	0.873104i	$-0.337897\pi$
$359$	18.4749			0.975068			0.487534	+	0.873104i	$0.337897\pi$
$360$	5.31844	+	3.17705i	0.280306	+	0.167445i
$361$	1.00000			0.0526316
$362$			14.4611i			0.760061i
$363$			1.31473i			0.0690053i
$364$	3.80137			0.199246
$365$	15.8938	+	9.49442i	0.831922	+	0.496961i
$366$	−5.41975			−0.283295
$367$			7.05618i			0.368329i	0.982895	+	0.184165i	$0.0589580\pi$
$367$			7.05618i			0.368329i	−0.982895	+	0.184165i	$0.941042\pi$
$368$		−	5.21940i		−	0.272080i
$369$	4.10405			0.213648
$370$	3.48752	−	5.83817i	0.181307	−	0.303512i
$371$	−0.413020			−0.0214429
$372$		−	8.50002i		−	0.440705i
$373$			2.88267i			0.149259i	0.997211	+	0.0746294i	$0.0237774\pi$
$373$			2.88267i			0.149259i	−0.997211	+	0.0746294i	$0.976223\pi$
$374$	−1.63078			−0.0843257
$375$	0.655990	−	14.6845i	0.0338752	−	0.758302i
$376$	21.4545			1.10643
$377$		−	15.5601i		−	0.801386i
$378$		−	3.28079i		−	0.168746i
$379$	−3.02948			−0.155614			−0.0778068	−	0.996968i	$-0.524792\pi$
$379$	−3.02948			−0.155614			−0.0778068	+	0.996968i	$0.524792\pi$
$380$	−1.88300	+	3.15217i	−0.0965957	+	0.161703i
$381$	−12.2094			−0.625506
$382$			9.61021i			0.491701i
$383$			24.6706i			1.26061i	0.776348	+	0.630305i	$0.217070\pi$
$383$			24.6706i			1.26061i	−0.776348	+	0.630305i	$0.782930\pi$
$384$	−15.0818			−0.769641
$385$	1.87448	+	1.11975i	0.0955322	+	0.0570676i
$386$	−1.88436			−0.0959115
$387$			15.3563i			0.780605i
$388$			21.2197i			1.07727i
$389$	−5.13847			−0.260531			−0.130265	−	0.991479i	$-0.541583\pi$
$389$	−5.13847			−0.260531			−0.130265	+	0.991479i	$0.541583\pi$
$390$	3.57971	+	2.13840i	0.181266	+	0.108282i
$391$	7.18355			0.363288
$392$			13.1751i			0.665444i
$393$			3.19957i			0.161397i
$394$	12.4435			0.626897
$395$	0.828046	−	1.38616i	0.0416635	−	0.0697455i
$396$	2.08787			0.104919
$397$			0.456104i			0.0228912i	0.999934	+	0.0114456i	$0.00364333\pi$
$397$			0.456104i			0.0228912i	−0.999934	+	0.0114456i	$0.996357\pi$
$398$		−	11.7369i		−	0.588318i
$399$	1.28380			0.0642702
$400$	−4.69386	−	8.71935i	−0.234693	−	0.435968i
$401$	15.5032			0.774191			0.387096	−	0.922040i	$-0.373478\pi$
$401$	15.5032			0.774191			0.387096	+	0.922040i	$0.373478\pi$
$402$		−	1.91079i		−	0.0953015i
$403$			9.33435i			0.464977i
$404$	4.81740			0.239674
$405$	−4.09247	+	6.85088i	−0.203357	+	0.340423i
$406$	−3.83430			−0.190293
$407$		−	5.08339i		−	0.251975i
$408$		−	7.80871i		−	0.386589i
$409$	−22.0228			−1.08896			−0.544480	−	0.838774i	$-0.683273\pi$
$409$	−22.0228			−1.08896			−0.544480	+	0.838774i	$0.683273\pi$
$410$	3.70699	+	2.21443i	0.183075	+	0.109363i
$411$	6.70524			0.330745
$412$			4.77963i			0.235476i
$413$		−	14.7111i		−	0.723886i
$414$	2.00476			0.0985287
$415$	−23.9715	−	14.3197i	−1.17672	−	0.702929i
$416$	13.1408			0.644279
$417$		−	29.0150i		−	1.42087i
$418$		−	0.598278i		−	0.0292627i
$419$	−9.93165			−0.485193			−0.242596	−	0.970127i	$-0.577999\pi$
$419$	−9.93165			−0.485193			−0.242596	+	0.970127i	$0.577999\pi$
$420$	−2.41738	+	4.04675i	−0.117956	+	0.197461i
$421$	3.24871			0.158332			0.0791661	−	0.996861i	$-0.474774\pi$
$421$	3.24871			0.158332			0.0791661	+	0.996861i	$0.474774\pi$
$422$		−	13.9214i		−	0.677682i
$423$		−	12.5193i		−	0.608710i
$424$	−0.921640			−0.0447588
$425$	12.0006	−	6.46024i	0.582114	−	0.313368i
$426$	8.47642			0.410684
$427$			6.72823i			0.325602i
$428$			13.3145i			0.643582i
$429$	3.11692			0.150486
$430$	−8.28582	+	13.8706i	−0.399578	+	0.668901i
$431$	17.9989			0.866975			0.433488	−	0.901160i	$-0.357283\pi$
$431$	17.9989			0.866975			0.433488	+	0.901160i	$0.357283\pi$
$432$			11.1222i			0.535116i
$433$		−	20.5150i		−	0.985888i	−0.870061	−	0.492944i	$-0.835921\pi$
$433$		−	20.5150i		−	0.985888i	0.870061	−	0.492944i	$-0.164079\pi$
$434$	2.30016			0.110411
$435$	16.5645	+	9.89505i	0.794207	+	0.474431i
$436$	−10.4772			−0.501768
$437$			2.63540i			0.126068i
$438$		−	6.51250i		−	0.311179i
$439$	−0.210462			−0.0100448			−0.00502240	−	0.999987i	$-0.501599\pi$
$439$	−0.210462			−0.0100448			−0.00502240	+	0.999987i	$0.501599\pi$
$440$	4.18283	+	2.49868i	0.199409	+	0.119120i
$441$	7.68808			0.366099
$442$			3.86621i			0.183897i
$443$		−	31.6130i		−	1.50198i	−0.660314	−	0.750990i	$-0.729577\pi$
$443$		−	31.6130i		−	1.50198i	0.660314	−	0.750990i	$-0.270423\pi$
$444$	10.9744			0.520820
$445$	−15.1554	+	25.3705i	−0.718436	+	1.20268i
$446$	13.4107			0.635015
$447$		−	18.0733i		−	0.854837i
$448$			0.629680i			0.0297496i
$449$	17.4689			0.824406			0.412203	−	0.911092i	$-0.364759\pi$
$449$	17.4689			0.824406			0.412203	+	0.911092i	$0.364759\pi$
$450$	3.34908	−	1.80290i	0.157877	−	0.0849896i
$451$	3.22774			0.151988
$452$		−	12.5023i		−	0.588059i
$453$		−	5.30920i		−	0.249448i
$454$	9.75677			0.457908
$455$	2.65466	−	4.44396i	0.124453	−	0.208336i
$456$	2.86475			0.134154
$457$			32.0064i			1.49720i	0.663023	+	0.748599i	$0.269273\pi$
$457$			32.0064i			1.49720i	−0.663023	+	0.748599i	$0.730727\pi$
$458$		−	5.49403i		−	0.256719i
$459$	−15.3076			−0.714499
$460$	−8.30723	−	4.96245i	−0.387326	−	0.231375i
$461$	−1.36435			−0.0635443			−0.0317721	−	0.999495i	$-0.510115\pi$
$461$	−1.36435			−0.0635443			−0.0317721	+	0.999495i	$0.510115\pi$
$462$		−	0.768067i		−	0.0357337i
$463$			10.4066i			0.483636i	0.970322	+	0.241818i	$0.0777438\pi$
$463$			10.4066i			0.483636i	−0.970322	+	0.241818i	$0.922256\pi$
$464$	12.9986			0.603446
$465$	−9.93687	−	5.93594i	−0.460812	−	0.275273i
$466$	5.28447			0.244798
$467$			14.6351i			0.677233i	0.940924	+	0.338617i	$0.109959\pi$
$467$			14.6351i			0.677233i	−0.940924	+	0.338617i	$0.890041\pi$
$468$		−	4.94986i		−	0.228808i
$469$	−2.37211			−0.109534
$470$	6.75507	−	11.3081i	0.311588	−	0.521604i
$471$	20.2939			0.935092
$472$		−	32.8273i		−	1.51100i
$473$			12.0774i			0.555319i
$474$	−0.567981			−0.0260882
$475$	2.37004	+	4.40260i	0.108745	+	0.202005i
$476$	−4.37062			−0.200327
$477$			0.537805i			0.0246244i
$478$		−	16.8484i		−	0.770630i
$479$	8.09427			0.369837			0.184918	−	0.982754i	$-0.440798\pi$
$479$	8.09427			0.369837			0.184918	+	0.982754i	$0.440798\pi$
$480$	−8.35654	+	13.9890i	−0.381422	+	0.638507i
$481$	−12.0516			−0.549504
$482$			3.10589i			0.141470i
$483$			3.38331i			0.153946i
$484$	1.64206			0.0746393
$485$	24.8067	+	14.8187i	1.12641	+	0.672881i
$486$	−7.27237			−0.329881
$487$			23.6459i			1.07150i	0.844378	+	0.535748i	$0.179970\pi$
$487$			23.6459i			1.07150i	−0.844378	+	0.535748i	$0.820030\pi$
$488$			15.0138i			0.679644i
$489$	1.53535			0.0694310
$490$	6.94428	+	4.14827i	0.313710	+	0.187400i
$491$	3.41798			0.154251			0.0771256	−	0.997021i	$-0.475426\pi$
$491$	3.41798			0.154251			0.0771256	+	0.997021i	$0.475426\pi$
$492$			6.96826i			0.314153i
$493$			17.8902i			0.805735i
$494$	−1.41838			−0.0638159
$495$	1.45805	−	2.44081i	0.0655346	−	0.109706i
$496$	−7.79774			−0.350129
$497$		−	10.5229i		−	0.472015i
$498$			9.82233i			0.440149i
$499$	21.7819			0.975093			0.487547	−	0.873097i	$-0.337892\pi$
$499$	21.7819			0.975093			0.487547	+	0.873097i	$0.337892\pi$
$500$	−18.3405	−	0.819316i	−0.820214	−	0.0366409i
$501$	17.8459			0.797296
$502$			8.67085i			0.386999i
$503$		−	34.6223i		−	1.54373i	−0.635784	−	0.771867i	$-0.719323\pi$
$503$		−	34.6223i		−	1.54373i	0.635784	−	0.771867i	$-0.280677\pi$
$504$	−2.70536			−0.120506
$505$	3.36420	−	5.63174i	0.149705	−	0.250609i
$506$	1.57670			0.0700929
$507$			9.70196i			0.430879i
$508$			15.2492i			0.676576i
$509$	−27.8358			−1.23380			−0.616900	−	0.787042i	$-0.711612\pi$
$509$	−27.8358			−1.23380			−0.616900	+	0.787042i	$0.711612\pi$
$510$	−4.11577	−	2.45862i	−0.182250	−	0.108869i
$511$	−8.08480			−0.357650
$512$			19.6084i			0.866579i
$513$		−	5.61585i		−	0.247946i
$514$	8.64327			0.381238
$515$	5.58759	+	3.33783i	0.246219	+	0.147082i
$516$	−26.0735			−1.14782
$517$		−	9.84617i		−	0.433034i
$518$			2.96973i			0.130482i
$519$	21.2322			0.931988
$520$	5.92379	−	9.91654i	0.259775	−	0.434869i
$521$	−19.5896			−0.858237			−0.429118	−	0.903248i	$-0.641176\pi$
$521$	−19.5896			−0.858237			−0.429118	+	0.903248i	$0.641176\pi$
$522$			4.99274i			0.218526i
$523$			22.1464i			0.968394i	0.874959	+	0.484197i	$0.160888\pi$
$523$			22.1464i			0.968394i	−0.874959	+	0.484197i	$0.839112\pi$
$524$	3.99619			0.174574
$525$	3.04265	+	5.65204i	0.132792	+	0.246675i
$526$	13.1794			0.574650
$527$		−	10.7322i		−	0.467500i
$528$			2.60382i			0.113317i
$529$	16.0547			0.698029
$530$	−0.290184	+	0.485774i	−0.0126048	+	0.0211007i
$531$	−19.1557			−0.831287
$532$		−	1.60343i		−	0.0695175i
$533$		−	7.65224i		−	0.331455i
$534$	10.3955			0.449859
$535$	15.5652	+	9.29813i	0.672944	+	0.401993i
$536$	−5.29328			−0.228635
$537$			28.6016i			1.23425i
$538$		−	17.9256i		−	0.772827i
$539$	6.04650			0.260441
$540$	17.7021	+	10.5746i	0.761778	+	0.455059i
$541$	−6.70570			−0.288300			−0.144150	−	0.989556i	$-0.546045\pi$
$541$	−6.70570			−0.288300			−0.144150	+	0.989556i	$0.546045\pi$
$542$			17.7573i			0.762740i
$543$			31.7786i			1.36375i
$544$	−15.1086			−0.647775
$545$	−7.31672	+	12.2483i	−0.313414	+	0.524660i
$546$	−1.82091			−0.0779278
$547$		−	17.5914i		−	0.752152i	−0.926589	−	0.376076i	$-0.877273\pi$
$547$		−	17.5914i		−	0.752152i	0.926589	−	0.376076i	$-0.122727\pi$
$548$		−	8.37468i		−	0.357749i
$549$	8.76101			0.373911
$550$	2.63398	−	1.41794i	0.112313	−	0.0604613i
$551$	−6.56331			−0.279606
$552$			7.54975i			0.321339i
$553$			0.705107i			0.0299842i
$554$	−4.14209			−0.175981
$555$	7.66389	−	12.8295i	0.325314	−	0.544582i
$556$	−36.2390			−1.53688
$557$		−	14.5111i		−	0.614855i	−0.951572	−	0.307427i	$-0.900532\pi$
$557$		−	14.5111i		−	0.614855i	0.951572	−	0.307427i	$-0.0994681\pi$
$558$		−	2.99510i		−	0.126793i
$559$	28.6327			1.21104
$560$	3.71240	+	2.21766i	0.156878	+	0.0937132i
$561$	−3.58368			−0.151303
$562$		−	6.20846i		−	0.261888i
$563$		−	3.12905i		−	0.131874i	−0.997824	−	0.0659369i	$-0.978996\pi$
$563$		−	3.12905i		−	0.131874i	0.997824	−	0.0659369i	$-0.0210036\pi$
$564$	21.2566			0.895062
$565$	−14.6157	−	8.73091i	−0.614887	−	0.367312i
$566$	−7.00244			−0.294334
$567$		−	3.48487i		−	0.146351i
$568$		−	23.4814i		−	0.985258i
$569$	−2.22441			−0.0932523			−0.0466262	−	0.998912i	$-0.514847\pi$
$569$	−2.22441			−0.0932523			−0.0466262	+	0.998912i	$0.514847\pi$
$570$	0.901983	−	1.50994i	0.0377799	−	0.0632443i
$571$	1.99201			0.0833629			0.0416814	−	0.999131i	$-0.486729\pi$
$571$	1.99201			0.0833629			0.0416814	+	0.999131i	$0.486729\pi$
$572$		−	3.89296i		−	0.162773i
$573$			21.1186i			0.882244i
$574$	−1.88565			−0.0787057
$575$	−11.6026	+	6.24600i	−0.483862	+	0.260476i
$576$	0.819923			0.0341635
$577$			9.14505i			0.380713i	0.981715	+	0.190357i	$0.0609644\pi$
$577$			9.14505i			0.380713i	−0.981715	+	0.190357i	$0.939036\pi$
$578$			5.72555i			0.238152i
$579$	−4.14092			−0.172091
$580$	12.3587	−	20.6887i	0.513166	−	0.859050i
$581$	12.1937			0.505880
$582$		−	10.1645i		−	0.421334i
$583$			0.422971i			0.0175177i
$584$	−18.0409			−0.746540
$585$	−5.78660	−	3.45671i	−0.239246	−	0.142917i
$586$	−13.3819			−0.552802
$587$			13.1157i			0.541345i	0.962672	+	0.270672i	$0.0872460\pi$
$587$			13.1157i			0.541345i	−0.962672	+	0.270672i	$0.912754\pi$
$588$			13.0536i			0.538321i
$589$	3.93726			0.162232
$590$	−17.3025	−	10.3359i	−0.712331	−	0.425521i
$591$	27.3449			1.12482
$592$		−	10.0677i		−	0.413778i
$593$			32.9263i			1.35212i	0.736847	+	0.676060i	$0.236314\pi$
$593$			32.9263i			1.35212i	−0.736847	+	0.676060i	$0.763686\pi$
$594$	−3.35984			−0.137856
$595$	−3.05220	+	5.10944i	−0.125128	+	0.209467i
$596$	−22.5731			−0.924631
$597$		−	25.7921i		−	1.05560i
$598$		−	3.73800i		−	0.152858i
$599$	−35.6625			−1.45713			−0.728565	−	0.684977i	$-0.759812\pi$
$599$	−35.6625			−1.45713			−0.728565	+	0.684977i	$0.759812\pi$
$600$	6.78956	+	12.6123i	0.277183	+	0.514897i
$601$	5.43358			0.221640			0.110820	−	0.993840i	$-0.464652\pi$
$601$	5.43358			0.221640			0.110820	+	0.993840i	$0.464652\pi$
$602$		−	7.05564i		−	0.287566i
$603$			3.08878i			0.125785i
$604$	−6.63107			−0.269814
$605$	1.14673	−	1.91964i	0.0466210	−	0.0780445i
$606$	−2.30760			−0.0937400
$607$			25.2530i			1.02499i	0.858691	+	0.512494i	$0.171278\pi$
$607$			25.2530i			1.02499i	−0.858691	+	0.512494i	$0.828722\pi$
$608$		−	5.54282i		−	0.224791i
$609$	−8.42595			−0.341437
$610$	7.91341	+	4.72719i	0.320405	+	0.191398i
$611$	−23.3430			−0.944357
$612$			5.69110i			0.230049i
$613$			10.9415i			0.441922i	0.975283	+	0.220961i	$0.0709194\pi$
$613$			10.9415i			0.441922i	−0.975283	+	0.220961i	$0.929081\pi$
$614$	−4.38821			−0.177094
$615$	8.14619	+	4.86625i	0.328486	+	0.196226i
$616$	−2.12770			−0.0857276
$617$			35.4974i			1.42907i	0.699599	+	0.714536i	$0.253362\pi$
$617$			35.4974i			1.42907i	−0.699599	+	0.714536i	$0.746638\pi$
$618$		−	2.28951i		−	0.0920978i
$619$	−40.6629			−1.63438			−0.817190	−	0.576369i	$-0.804469\pi$
$619$	−40.6629			−1.63438			−0.817190	+	0.576369i	$0.804469\pi$
$620$	−7.41385	+	12.4109i	−0.297747	+	0.498435i
$621$	14.8000			0.593903
$622$		−	2.51867i		−	0.100990i
$623$		−	12.9053i		−	0.517041i
$624$	6.17306			0.247120
$625$	−13.7658	+	20.8687i	−0.550633	+	0.834747i
$626$	12.3728			0.494518
$627$		−	1.31473i		−	0.0525052i
$628$		−	25.3466i		−	1.01144i
$629$	13.8563			0.552486
$630$	−0.851798	+	1.42593i	−0.0339364	+	0.0568102i
$631$	29.6633			1.18088			0.590438	−	0.807083i	$-0.298955\pi$
$631$	29.6633			1.18088			0.590438	+	0.807083i	$0.298955\pi$
$632$			1.57342i			0.0625874i
$633$		−	30.5925i		−	1.21594i
$634$	−4.07326			−0.161770
$635$	17.8270	+	10.6492i	0.707443	+	0.422601i
$636$	−0.913138			−0.0362083
$637$		−	14.3349i		−	0.567968i
$638$			3.92668i			0.155459i
$639$	−13.7021			−0.542047
$640$	22.0210	+	13.1546i	0.870458	+	0.519981i
$641$	10.3723			0.409681			0.204840	−	0.978795i	$-0.434332\pi$
$641$	10.3723			0.409681			0.204840	+	0.978795i	$0.434332\pi$
$642$		−	6.37785i		−	0.251714i
$643$		−	34.7762i		−	1.37144i	−0.727867	−	0.685719i	$-0.759488\pi$
$643$		−	34.7762i		−	1.37144i	0.727867	−	0.685719i	$-0.240512\pi$
$644$	4.22568			0.166515
$645$	−18.2083	+	30.4810i	−0.716950	+	1.20019i
$646$	1.63078			0.0641623
$647$			5.32188i			0.209225i	0.994513	+	0.104612i	$0.0333602\pi$
$647$			5.32188i			0.209225i	−0.994513	+	0.104612i	$0.966640\pi$
$648$		−	7.77637i		−	0.305485i
$649$	−15.0655			−0.591374
$650$	−3.36162	−	6.24456i	−0.131853	−	0.244932i
$651$	5.05464			0.198107
$652$		−	1.91762i		−	0.0750997i
$653$			6.47367i			0.253334i	0.991945	+	0.126667i	$0.0404280\pi$
$653$			6.47367i			0.253334i	−0.991945	+	0.126667i	$0.959572\pi$
$654$	5.01875			0.196249
$655$	2.79072	−	4.67172i	0.109042	−	0.182539i
$656$	6.39254			0.249587
$657$			10.5274i			0.410714i
$658$			5.75215i			0.224242i
$659$	17.5436			0.683400			0.341700	−	0.939809i	$-0.388997\pi$
$659$	17.5436			0.683400			0.341700	+	0.939809i	$0.388997\pi$
$660$	4.14425	+	2.47563i	0.161315	+	0.0963637i
$661$	9.32174			0.362574			0.181287	−	0.983430i	$-0.441974\pi$
$661$	9.32174			0.362574			0.181287	+	0.983430i	$0.441974\pi$
$662$			3.72465i			0.144763i
$663$			8.49607i			0.329960i
$664$	27.2098			1.05595
$665$	−1.87448	−	1.11975i	−0.0726891	−	0.0434219i
$666$	3.86697			0.149842
$667$		−	17.2969i		−	0.669740i
$668$		−	22.2891i		−	0.862392i
$669$	29.4703			1.13939
$670$	−1.66662	+	2.78995i	−0.0643872	+	0.107785i
$671$	6.89034			0.265999
$672$		−	7.11585i		−	0.274500i
$673$			35.7637i			1.37859i	0.724482	+	0.689294i	$0.242079\pi$
$673$			35.7637i			1.37859i	−0.724482	+	0.689294i	$0.757921\pi$
$674$	5.09979			0.196437
$675$	24.7243	−	13.3098i	0.951641	−	0.512294i
$676$	12.1175			0.466058
$677$			41.4421i			1.59275i	0.604804	+	0.796375i	$0.293252\pi$
$677$			41.4421i			1.59275i	−0.604804	+	0.796375i	$0.706748\pi$
$678$			5.98878i			0.229998i
$679$	−12.6186			−0.484256
$680$	−6.81088	+	11.4015i	−0.261185	+	0.437229i
$681$	21.4407			0.821609
$682$		−	2.35558i		−	0.0901997i
$683$			18.2208i			0.697201i	0.937271	+	0.348600i	$0.113343\pi$
$683$			18.2208i			0.697201i	−0.937271	+	0.348600i	$0.886657\pi$
$684$	−2.08787			−0.0798317
$685$	−9.79035	−	5.84841i	−0.374070	−	0.223456i
$686$	−7.62180			−0.291001
$687$		−	12.0732i		−	0.460622i
$688$			23.9193i			0.911914i
$689$	1.00277			0.0382024
$690$	3.97928	+	2.37708i	0.151489	+	0.0904940i
$691$	18.8810			0.718266			0.359133	−	0.933286i	$-0.383072\pi$
$691$	18.8810			0.718266			0.359133	+	0.933286i	$0.383072\pi$
$692$		−	26.5185i		−	1.00808i
$693$			1.24158i			0.0471636i
$694$	4.19625			0.159288
$695$	−25.3073	+	42.3649i	−0.959962	+	1.60699i
$696$	−18.8022			−0.712696
$697$			8.79816i			0.333254i
$698$		−	18.6595i		−	0.706271i
$699$	11.6127			0.439234
$700$	7.05927	−	3.80019i	0.266815	−	0.143634i
$701$	−25.9100			−0.978609			−0.489304	−	0.872113i	$-0.662749\pi$
$701$	−25.9100			−0.978609			−0.489304	+	0.872113i	$0.662749\pi$
$702$			7.96541i			0.300635i
$703$			5.08339i			0.191724i
$704$	0.644852			0.0243038
$705$	14.8444	−	24.8498i	0.559072	−	0.935897i
$706$	−14.6302			−0.550615
$707$			2.86472i			0.107739i
$708$		−	32.5245i		−	1.22235i
$709$	45.7434			1.71793			0.858965	−	0.512034i	$-0.171108\pi$
$709$	45.7434			1.71793			0.858965	+	0.512034i	$0.171108\pi$
$710$	−12.3765	−	7.39326i	−0.464480	−	0.277464i
$711$	0.918139			0.0344329
$712$		−	28.7978i		−	1.07924i
$713$			10.3762i			0.388594i
$714$	2.09359			0.0783507
$715$	−4.55103	−	2.71862i	−0.170199	−	0.101671i
$716$	35.7227			1.33502
$717$		−	37.0248i		−	1.38272i
$718$			11.0531i			0.412499i
$719$	14.0014			0.522162			0.261081	−	0.965317i	$-0.415921\pi$
$719$	14.0014			0.522162			0.261081	+	0.965317i	$0.415921\pi$
$720$	2.88767	−	4.83402i	0.107617	−	0.180153i
$721$	−2.84227			−0.105852
$722$			0.598278i			0.0222656i
$723$			6.82526i			0.253834i
$724$	39.6908			1.47510
$725$	−15.5553	−	28.8956i	−0.577709	−	1.07316i
$726$	−0.786572			−0.0291924
$727$			35.2768i			1.30834i	0.756346	+	0.654172i	$0.226983\pi$
$727$			35.2768i			1.30834i	−0.756346	+	0.654172i	$0.773017\pi$
$728$			5.04429i			0.186954i
$729$	−26.6877			−0.988432
$730$	−5.68030	+	9.50893i	−0.210237	+	0.351941i
$731$	−32.9205			−1.21761
$732$			14.8753i			0.549808i
$733$			23.0762i			0.852338i	0.904644	+	0.426169i	$0.140137\pi$
$733$			23.0762i			0.852338i	−0.904644	+	0.426169i	$0.859863\pi$
$734$	−4.22156			−0.155820
$735$	15.2602	+	9.11590i	0.562880	+	0.336245i
$736$	14.6075			0.538441
$737$			2.42926i			0.0894830i
$738$			2.45536i			0.0903831i
$739$	−39.9646			−1.47012			−0.735060	−	0.678002i	$-0.762846\pi$
$739$	−39.9646			−1.47012			−0.735060	+	0.678002i	$0.762846\pi$
$740$	−16.0237	−	9.57202i	−0.589044	−	0.351874i
$741$	−3.11692			−0.114503
$742$		−	0.247101i		−	0.00907136i
$743$			27.3672i			1.00400i	0.864866	+	0.502002i	$0.167403\pi$
$743$			27.3672i			1.00400i	−0.864866	+	0.502002i	$0.832597\pi$
$744$	11.2793			0.413518
$745$	−15.7638	+	26.3889i	−0.577541	+	0.966815i
$746$	−1.72463			−0.0631434
$747$		−	15.8778i		−	0.580937i
$748$			4.47593i			0.163656i
$749$	−7.91765			−0.289305
$750$	8.78538	+	0.392464i	0.320797	+	0.0143308i
$751$	−24.5895			−0.897283			−0.448642	−	0.893712i	$-0.648092\pi$
$751$	−24.5895			−0.897283			−0.448642	+	0.893712i	$0.648092\pi$
$752$		−	19.5003i		−	0.711104i
$753$			19.0544i			0.694380i
$754$	9.30926			0.339023
$755$	−4.63077	+	7.75200i	−0.168531	+	0.282124i
$756$	−9.00462			−0.327495
$757$		−	25.1120i		−	0.912711i	−0.889798	−	0.456355i	$-0.849155\pi$
$757$		−	25.1120i		−	0.912711i	0.889798	−	0.456355i	$-0.150845\pi$
$758$		−	1.81247i		−	0.0658318i
$759$	3.46483			0.125765
$760$	−4.18283	−	2.49868i	−0.151727	−	0.0906365i
$761$	−51.2302			−1.85709			−0.928547	−	0.371214i	$-0.878942\pi$
$761$	−51.2302			−1.85709			−0.928547	+	0.371214i	$0.878942\pi$
$762$		−	7.30461i		−	0.264618i
$763$		−	6.23041i		−	0.225556i
$764$	26.3767			0.954275
$765$	6.65314	+	3.97435i	0.240545	+	0.143693i
$766$	−14.7599			−0.533296
$767$			35.7170i			1.28966i
$768$		−	7.32751i		−	0.264409i
$769$	−30.0314			−1.08296			−0.541480	−	0.840714i	$-0.682136\pi$
$769$	−30.0314			−1.08296			−0.541480	+	0.840714i	$0.682136\pi$
$770$	−0.669920	+	1.12146i	−0.0241422	+	0.0404146i
$771$	18.9938			0.684043
$772$			5.17192i			0.186141i
$773$		−	49.2335i		−	1.77081i	−0.464825	−	0.885403i	$-0.653883\pi$
$773$		−	49.2335i		−	1.77081i	0.464825	−	0.885403i	$-0.346117\pi$
$774$	−9.18734			−0.330232
$775$	9.33146	+	17.3342i	0.335196	+	0.622663i
$776$	−28.1579			−1.01081
$777$			6.52604i			0.234120i
$778$		−	3.07423i		−	0.110217i
$779$	−3.22774			−0.115646
$780$	5.86915	−	9.82506i	0.210149	−	0.351794i
$781$	−10.7764			−0.385610
$782$			4.29776i			0.153688i
$783$			36.8585i			1.31722i
$784$	11.9751			0.427682
$785$	−29.6312	−	17.7006i	−1.05758	−	0.631762i
$786$	−1.91423			−0.0682785
$787$			3.45465i			0.123145i	0.998103	+	0.0615725i	$0.0196115\pi$
$787$			3.45465i			0.123145i	−0.998103	+	0.0615725i	$0.980388\pi$
$788$		−	34.1532i		−	1.21666i
$789$	28.9620			1.03108
$790$	0.829312	+	0.495402i	0.0295056	+	0.0176256i
$791$	7.43464			0.264345
$792$			2.77054i			0.0984468i
$793$		−	16.3354i		−	0.580088i
$794$	−0.272877			−0.00968405
$795$	−0.637685	+	1.06750i	−0.0226164	+	0.0378602i
$796$	−32.2137			−1.14178
$797$		−	39.3034i		−	1.39220i	−0.717947	−	0.696098i	$-0.754918\pi$
$797$		−	39.3034i		−	1.39220i	0.717947	−	0.696098i	$-0.245082\pi$
$798$			0.768067i			0.0271893i
$799$	26.8386			0.949482
$800$	24.4028	−	13.1367i	0.862771	−	0.464453i
$801$	−16.8044			−0.593753
$802$			9.27520i			0.327519i
$803$			8.27959i			0.292180i
$804$	−5.24445			−0.184957
$805$	2.95098	−	4.93999i	0.104008	−	0.174112i
$806$	−5.58453			−0.196707
$807$		−	39.3918i		−	1.38666i
$808$			6.39253i			0.224889i
$809$	20.5600			0.722850			0.361425	−	0.932401i	$-0.382290\pi$
$809$	20.5600			0.722850			0.361425	+	0.932401i	$0.382290\pi$
$810$	−4.09873	−	2.44844i	−0.144015	−	0.0860293i
$811$	36.1760			1.27031			0.635155	−	0.772385i	$-0.280936\pi$
$811$	36.1760			1.27031			0.635155	+	0.772385i	$0.280936\pi$
$812$			10.5238i			0.369313i
$813$			39.0220i			1.36856i
$814$	3.04128			0.106597
$815$	−2.24177	−	1.33916i	−0.0785259	−	0.0469086i
$816$	−7.09747			−0.248461
$817$		−	12.0774i		−	0.422534i
$818$		−	13.1758i		−	0.460680i
$819$	2.94350			0.102854
$820$	6.07783	−	10.1744i	0.212247	−	0.355305i
$821$	−17.6824			−0.617119			−0.308560	−	0.951205i	$-0.599847\pi$
$821$	−17.6824			−0.617119			−0.308560	+	0.951205i	$0.599847\pi$
$822$			4.01160i			0.139920i
$823$			6.26765i			0.218476i	0.994016	+	0.109238i	$0.0348411\pi$
$823$			6.26765i			0.218476i	−0.994016	+	0.109238i	$0.965159\pi$
$824$	−6.34242			−0.220949
$825$	5.78822	−	3.11596i	0.201520	−	0.108484i
$826$	8.80133			0.306237
$827$		−	3.13465i		−	0.109002i	−0.998514	−	0.0545012i	$-0.982643\pi$
$827$		−	3.13465i		−	0.109002i	0.998514	−	0.0545012i	$-0.0173569\pi$
$828$		−	5.50237i		−	0.191221i
$829$	24.7079			0.858142			0.429071	−	0.903271i	$-0.358841\pi$
$829$	24.7079			0.858142			0.429071	+	0.903271i	$0.358841\pi$
$830$	8.56719	−	14.3416i	0.297371	−	0.497805i
$831$	−9.10232			−0.315756
$832$		−	1.52880i		−	0.0530014i
$833$			16.4815i			0.571050i
$834$	17.3590			0.601094
$835$	−26.0569	−	15.5655i	−0.901736	−	0.538666i
$836$	−1.64206			−0.0567920
$837$		−	22.1111i		−	0.764270i
$838$		−	5.94189i		−	0.205259i
$839$	54.3023			1.87472			0.937361	−	0.348358i	$-0.113261\pi$
$839$	54.3023			1.87472			0.937361	+	0.348358i	$0.113261\pi$
$840$	−5.36990	−	3.20779i	−0.185279	−	0.110679i
$841$	14.0770			0.485413
$842$			1.94363i			0.0669819i
$843$		−	13.6432i		−	0.469897i
$844$	−38.2093			−1.31522
$845$	8.46220	−	14.1659i	0.291108	−	0.487321i
$846$	7.49003			0.257513
$847$			0.976473i			0.0335520i
$848$			0.837695i			0.0287666i
$849$	−15.3880			−0.528115
$850$	3.86502	+	7.17969i	0.132569	+	0.246261i
$851$	−13.3968			−0.459235
$852$		−	23.2648i		−	0.797039i
$853$			29.8507i			1.02207i	0.859561	+	0.511034i	$0.170737\pi$
$853$			29.8507i			1.02207i	−0.859561	+	0.511034i	$0.829263\pi$
$854$	−4.02535			−0.137745
$855$	−1.45805	+	2.44081i	−0.0498643	+	0.0834738i
$856$	−17.6680			−0.603878
$857$			38.8694i			1.32775i	0.747841	+	0.663877i	$0.231090\pi$
$857$			38.8694i			1.32775i	−0.747841	+	0.663877i	$0.768910\pi$
$858$			1.86478i			0.0636626i
$859$	9.55664			0.326068			0.163034	−	0.986620i	$-0.447872\pi$
$859$	9.55664			0.326068			0.163034	+	0.986620i	$0.447872\pi$
$860$	38.0700	+	22.7417i	1.29818	+	0.775485i
$861$	−4.14376			−0.141219
$862$			10.7683i			0.366771i
$863$		−	7.48281i		−	0.254718i	−0.991857	−	0.127359i	$-0.959350\pi$
$863$		−	7.48281i		−	0.254718i	0.991857	−	0.127359i	$-0.0406500\pi$
$864$	−31.1276			−1.05898
$865$	−31.0012	−	18.5190i	−1.05407	−	0.629665i
$866$	12.2737			0.417076
$867$			12.5820i			0.427307i
$868$		−	6.31313i		−	0.214281i
$869$	0.722096			0.0244954
$870$	−5.91999	+	9.91017i	−0.200706	+	0.335986i
$871$	5.75922			0.195144
$872$		−	13.9030i		−	0.470813i
$873$			16.4310i			0.556104i
$874$	−1.57670			−0.0533327
$875$	0.487216	−	10.9064i	0.0164709	−	0.368704i
$876$	−17.8745			−0.603924
$877$		−	55.9410i		−	1.88899i	−0.328519	−	0.944497i	$-0.606549\pi$
$877$		−	55.9410i		−	1.88899i	0.328519	−	0.944497i	$-0.393451\pi$
$878$		−	0.125915i		−	0.00424942i
$879$	−29.4070			−0.991875
$880$	2.27109	−	3.80185i	0.0765584	−	0.128160i
$881$	26.6246			0.897006			0.448503	−	0.893781i	$-0.351957\pi$
$881$	26.6246			0.897006			0.448503	+	0.893781i	$0.351957\pi$
$882$			4.59961i			0.154877i
$883$			22.4194i			0.754472i	0.926117	+	0.377236i	$0.123125\pi$
$883$			22.4194i			0.754472i	−0.926117	+	0.377236i	$0.876875\pi$
$884$	10.6114			0.356900
$885$	−38.0225	−	22.7133i	−1.27811	−	0.763499i
$886$	18.9134			0.635407
$887$			15.3620i			0.515806i	0.966171	+	0.257903i	$0.0830315\pi$
$887$			15.3620i			0.515806i	−0.966171	+	0.257903i	$0.916968\pi$
$888$			14.5626i			0.488690i
$889$	−9.06815			−0.304136
$890$	−15.1786	−	9.06716i	−0.508788	−	0.303932i
$891$	−3.56883			−0.119560
$892$		−	36.8077i		−	1.23241i
$893$			9.84617i			0.329489i
$894$	10.8128			0.361636
$895$	24.9468	−	41.7613i	0.833878	−	1.39593i
$896$	−11.2016			−0.374218
$897$		−	8.21432i		−	0.274268i
$898$			10.4512i			0.348762i
$899$	−25.8414			−0.861861
$900$	−4.94834	−	9.19206i	−0.164945	−	0.306402i
$901$	−1.15293			−0.0384097
$902$			1.93109i			0.0642982i
$903$		−	15.5049i		−	0.515971i
$904$	16.5902			0.551780
$905$	27.7178	−	46.4002i	0.921372	−	1.54239i
$906$	3.17638			0.105528
$907$		−	5.41090i		−	0.179666i	−0.995957	−	0.0898329i	$-0.971367\pi$
$907$		−	5.41090i		−	0.179666i	0.995957	−	0.0898329i	$-0.0286333\pi$
$908$		−	26.7789i		−	0.888689i
$909$	3.73023			0.123724
$910$	2.65872	+	1.58823i	0.0881358	+	0.0526492i
$911$	5.78272			0.191590			0.0957951	−	0.995401i	$-0.469461\pi$
$911$	5.78272			0.191590			0.0957951	+	0.995401i	$0.469461\pi$
$912$		−	2.60382i		−	0.0862210i
$913$		−	12.4875i		−	0.413276i
$914$	−19.1487			−0.633384
$915$	17.3899	+	10.3881i	0.574891	+	0.343420i
$916$	−15.0792			−0.498230
$917$			2.37638i			0.0784751i
$918$		−	9.15822i		−	0.302266i
$919$	12.3747			0.408204			0.204102	−	0.978950i	$-0.434573\pi$
$919$	12.3747			0.408204			0.204102	+	0.978950i	$0.434573\pi$
$920$	6.58501	−	11.0234i	0.217101	−	0.363432i
$921$	−9.64317			−0.317753
$922$		−	0.816263i		−	0.0268822i
$923$			25.5484i			0.840935i
$924$	−2.10807			−0.0693506
$925$	−22.3802	+	12.0478i	−0.735855	+	0.396131i
$926$	−6.22605			−0.204601
$927$			3.70099i			0.121557i
$928$			36.3792i			1.19421i
$929$	22.1624			0.727125			0.363562	−	0.931570i	$-0.381560\pi$
$929$	22.1624			0.727125			0.363562	+	0.931570i	$0.381560\pi$
$930$	3.55134	−	5.94501i	0.116453	−	0.194945i
$931$	−6.04650			−0.198166
$932$		−	14.5040i		−	0.475095i
$933$		−	5.53483i		−	0.181202i
$934$	−8.75588			−0.286501
$935$	5.23254	+	3.12574i	0.171122	+	0.102223i
$936$	6.56831			0.214692
$937$		−	37.3094i		−	1.21885i	−0.792845	−	0.609423i	$-0.791401\pi$
$937$		−	37.3094i		−	1.21885i	0.792845	−	0.609423i	$-0.208599\pi$
$938$		−	1.41918i		−	0.0463379i
$939$	27.1896			0.887298
$940$	−31.0368	−	18.5403i	−1.01231	−	0.604718i
$941$	14.0178			0.456967			0.228484	−	0.973548i	$-0.426623\pi$
$941$	14.0178			0.456967			0.228484	+	0.973548i	$0.426623\pi$
$942$			12.1414i			0.395587i
$943$		−	8.50638i		−	0.277006i
$944$	−29.8373			−0.971122
$945$	−6.28833	+	10.5268i	−0.204559	+	0.342436i
$946$	−7.22564			−0.234926
$947$			3.66296i			0.119030i	0.998227	+	0.0595151i	$0.0189555\pi$
$947$			3.66296i			0.119030i	−0.998227	+	0.0595151i	$0.981045\pi$
$948$			1.55891i			0.0506310i
$949$	19.6290			0.637185
$950$	−2.63398	+	1.41794i	−0.0854576	+	0.0460041i
$951$	−8.95108			−0.290259
$952$		−	5.79968i		−	0.187969i
$953$			3.94137i			0.127673i	0.997960	+	0.0638367i	$0.0203337\pi$
$953$			3.94137i			0.127673i	−0.997960	+	0.0638367i	$0.979666\pi$
$954$	−0.321757			−0.0104173
$955$	18.4200	−	30.8354i	0.596057	−	0.997811i
$956$	−46.2431			−1.49561
$957$			8.62896i			0.278935i
$958$			4.84262i			0.156458i
$959$	4.98011			0.160816
$960$	1.62748	+	0.972199i	0.0525267	+	0.0313776i
$961$	−15.4980			−0.499935
$962$		−	7.21019i		−	0.232466i
$963$			10.3098i			0.332228i
$964$	8.52459			0.274559
$965$	6.04618	+	3.61178i	0.194634	+	0.116267i
$966$	−2.02416			−0.0651263
$967$		−	10.7151i		−	0.344574i	−0.985047	−	0.172287i	$-0.944884\pi$
$967$		−	10.7151i		−	0.344574i	0.985047	−	0.172287i	$-0.0551156\pi$
$968$			2.17897i			0.0700346i
$969$	3.58368			0.115124
$970$	−8.86568	+	14.8413i	−0.284660	+	0.476526i
$971$	−38.2751			−1.22831			−0.614154	−	0.789187i	$-0.710502\pi$
$971$	−38.2751			−1.22831			−0.614154	+	0.789187i	$0.710502\pi$
$972$			19.9601i			0.640221i
$973$		−	21.5500i		−	0.690861i
$974$	−14.1468			−0.453293
$975$	−7.38722	−	13.7226i	−0.236580	−	0.439473i
$976$	13.6463			0.436808
$977$			44.3861i			1.42004i	0.704183	+	0.710019i	$0.251314\pi$
$977$			44.3861i			1.42004i	−0.704183	+	0.710019i	$0.748686\pi$
$978$			0.918567i			0.0293725i
$979$	−13.2163			−0.422394
$980$	11.3855	−	19.0596i	0.363698	−	0.608837i
$981$	−8.11279			−0.259021
$982$			2.04490i			0.0652554i
$983$		−	0.139082i		−	0.00443603i	−0.999998	−	0.00221801i	$-0.999294\pi$
$983$		−	0.139082i		−	0.00443603i	0.999998	−	0.00221801i	$-0.000706017\pi$
$984$	−9.24666			−0.294773
$985$	−39.9265	−	23.8507i	−1.27216	−	0.759946i
$986$	−10.7033			−0.340863
$987$			12.6405i			0.402351i
$988$			3.89296i			0.123851i
$989$	31.8287			1.01209
$990$	1.46028	+	0.872321i	0.0464108	+	0.0277242i
$991$	28.5350			0.906443			0.453221	−	0.891398i	$-0.350275\pi$
$991$	28.5350			0.906443			0.453221	+	0.891398i	$0.350275\pi$
$992$		−	21.8235i		−	0.692898i
$993$			8.18499i			0.259743i
$994$	6.29560			0.199684
$995$	−22.4963	+	37.6592i	−0.713180	+	1.19388i
$996$	26.9588			0.854224
$997$		−	3.04076i		−	0.0963018i	−0.998840	−	0.0481509i	$-0.984667\pi$
$997$		−	3.04076i		−	0.0963018i	0.998840	−	0.0481509i	$-0.0153328\pi$
$998$			13.0316i			0.412510i
$999$	28.5476			0.903205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.18	yes	30
5.2	odd	4		5225.2.a.bc.1.13		30
5.3	odd	4		5225.2.a.bc.1.18		30
5.4	even	2	inner	1045.2.b.e.419.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.13	✓	30	5.4	even	2	inner
1045.2.b.e.419.18	yes	30	1.1	even	1	trivial
5225.2.a.bc.1.13		30	5.2	odd	4
5225.2.a.bc.1.18		30	5.3	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)

\(f(q)\)	\(=\)	\(q+0.598278i q^{2} +1.31473i q^{3} +1.64206 q^{4} +(1.14673 - 1.91964i) q^{5} -0.786572 q^{6} +0.976473i q^{7} +2.17897i q^{8} +1.27149 q^{9} +O(q^{10})\)	\(q+0.598278i q^{2} +1.31473i q^{3} +1.64206 q^{4} +(1.14673 - 1.91964i) q^{5} -0.786572 q^{6} +0.976473i q^{7} +2.17897i q^{8} +1.27149 q^{9} +(1.14848 + 0.686061i) q^{10} +1.00000 q^{11} +2.15887i q^{12} -2.37077i q^{13} -0.584202 q^{14} +(2.52380 + 1.50763i) q^{15} +1.98050 q^{16} +2.72579i q^{17} +0.760706i q^{18} -1.00000 q^{19} +(1.88300 - 3.15217i) q^{20} -1.28380 q^{21} +0.598278i q^{22} -2.63540i q^{23} -2.86475 q^{24} +(-2.37004 - 4.40260i) q^{25} +1.41838 q^{26} +5.61585i q^{27} +1.60343i q^{28} +6.56331 q^{29} +(-0.901983 + 1.50994i) q^{30} -3.93726 q^{31} +5.54282i q^{32} +1.31473i q^{33} -1.63078 q^{34} +(1.87448 + 1.11975i) q^{35} +2.08787 q^{36} -5.08339i q^{37} -0.598278i q^{38} +3.11692 q^{39} +(4.18283 + 2.49868i) q^{40} +3.22774 q^{41} -0.768067i q^{42} +12.0774i q^{43} +1.64206 q^{44} +(1.45805 - 2.44081i) q^{45} +1.57670 q^{46} -9.84617i q^{47} +2.60382i q^{48} +6.04650 q^{49} +(2.63398 - 1.41794i) q^{50} -3.58368 q^{51} -3.89296i q^{52} +0.422971i q^{53} -3.35984 q^{54} +(1.14673 - 1.91964i) q^{55} -2.12770 q^{56} -1.31473i q^{57} +3.92668i q^{58} -15.0655 q^{59} +(4.14425 + 2.47563i) q^{60} +6.89034 q^{61} -2.35558i q^{62} +1.24158i q^{63} +0.644852 q^{64} +(-4.55103 - 2.71862i) q^{65} -0.786572 q^{66} +2.42926i q^{67} +4.47593i q^{68} +3.46483 q^{69} +(-0.669920 + 1.12146i) q^{70} -10.7764 q^{71} +2.77054i q^{72} +8.27959i q^{73} +3.04128 q^{74} +(5.78822 - 3.11596i) q^{75} -1.64206 q^{76} +0.976473i q^{77} +1.86478i q^{78} +0.722096 q^{79} +(2.27109 - 3.80185i) q^{80} -3.56883 q^{81} +1.93109i q^{82} -12.4875i q^{83} -2.10807 q^{84} +(5.23254 + 3.12574i) q^{85} -7.22564 q^{86} +8.62896i q^{87} +2.17897i q^{88} -13.2163 q^{89} +(1.46028 + 0.872321i) q^{90} +2.31499 q^{91} -4.32749i q^{92} -5.17642i q^{93} +5.89074 q^{94} +(-1.14673 + 1.91964i) q^{95} -7.28730 q^{96} +12.9226i q^{97} +3.61749i q^{98} +1.27149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 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

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