LMFDB - Embedded newform 1045.2.b.e.419.13

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

$q$-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	$-0.932158\pi$
$2$		−	0.598278i		−	0.423046i	0.977373	−	0.211523i	$-0.0678424\pi$
$3$		−	1.31473i		−	0.759058i	−0.925180	−	0.379529i	$-0.876086\pi$
$3$		−	1.31473i		−	0.759058i	0.925180	−	0.379529i	$-0.123914\pi$
$4$	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	$-0.940922\pi$
$7$		−	0.976473i		−	0.369072i	0.982826	−	0.184536i	$-0.0590783\pi$
$8$		−	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	$0.106633\pi$
$13$			2.37077i			0.657534i	−0.944411	+	0.328767i	$0.893367\pi$
$14$	−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	$-0.892765\pi$
$17$		−	2.72579i		−	0.661102i	0.943788	−	0.330551i	$-0.107235\pi$
$18$		−	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	$0.0885981\pi$
$23$			2.63540i			0.549518i	−0.961513	+	0.274759i	$0.911402\pi$
$24$	−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	$0.137217\pi$
$37$			5.08339i			0.835705i	−0.908515	+	0.417852i	$0.862783\pi$
$38$			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	$-0.627462\pi$
$43$		−	12.0774i		−	1.84178i	0.389817	−	0.920892i	$-0.372538\pi$
$44$	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	$0.254990\pi$
$47$			9.84617i			1.43621i	−0.695934	+	0.718106i	$0.745010\pi$
$48$		−	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	$-0.990752\pi$
$53$		−	0.422971i		−	0.0580996i	0.999578	−	0.0290498i	$-0.00924814\pi$
$54$	−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	$-0.952591\pi$
$67$		−	2.42926i		−	0.296781i	0.988929	−	0.148391i	$-0.0474093\pi$
$68$		−	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	$-0.838992\pi$
$73$		−	8.27959i		−	0.969053i	0.874777	−	0.484526i	$-0.161008\pi$
$74$	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	$0.240347\pi$
$83$			12.4875i			1.37068i	−0.728222	+	0.685341i	$0.759653\pi$
$84$	−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	$-0.772228\pi$
$97$		−	12.9226i		−	1.31209i	0.754722	−	0.656045i	$-0.227772\pi$
$98$		−	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	$-0.954196\pi$
$103$		−	2.91075i		−	0.286805i	0.989664	−	0.143402i	$-0.0458043\pi$
$104$	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	$-0.871806\pi$
$107$		−	8.10841i		−	0.783870i	0.919993	−	0.391935i	$-0.128194\pi$
$108$		−	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	$0.116583\pi$
$113$			7.61377i			0.716243i	−0.933675	+	0.358122i	$0.883417\pi$
$114$	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	$-0.864821\pi$
$127$		−	9.28663i		−	0.824055i	0.911171	−	0.412028i	$-0.135179\pi$
$128$		−	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	$0.0699094\pi$
$137$			5.10010i			0.435731i	−0.975979	+	0.217865i	$0.930091\pi$
$138$		−	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	$0.211230\pi$
$157$			15.4358i			1.23191i	−0.787781	+	0.615955i	$0.788770\pi$
$158$		−	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	$0.0145630\pi$
$163$			1.16781i			0.0914699i	−0.998954	+	0.0457349i	$0.985437\pi$
$164$	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	$0.176005\pi$
$167$			13.5738i			1.05038i	−0.850986	+	0.525188i	$0.823995\pi$
$168$			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	$0.210405\pi$
$173$			16.1495i			1.22782i	−0.789375	+	0.613911i	$0.789595\pi$
$174$	−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	$-0.963839\pi$
$193$		−	3.14964i		−	0.226716i	0.993554	−	0.113358i	$-0.0361608\pi$
$194$	−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	$0.265616\pi$
$197$			20.7989i			1.48186i	−0.671581	+	0.740931i	$0.734384\pi$
$198$		−	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	$0.270200\pi$
$223$			22.4155i			1.50105i	−0.660840	+	0.750527i	$0.729800\pi$
$224$	−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	$0.182031\pi$
$227$			16.3081i			1.08241i	−0.840892	+	0.541203i	$0.817969\pi$
$228$			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	$0.0934319\pi$
$233$			8.83281i			0.578656i	−0.957230	+	0.289328i	$0.906568\pi$
$234$	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	$0.148785\pi$
$257$			14.4469i			0.901174i	−0.892733	+	0.450587i	$0.851215\pi$
$258$			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	$0.237665\pi$
$263$			22.0289i			1.35836i	−0.733971	+	0.679181i	$0.762335\pi$
$264$	−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	$-0.933307\pi$
$277$		−	6.92335i		−	0.415984i	0.978131	−	0.207992i	$-0.0666928\pi$
$278$			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	$-0.886903\pi$
$283$		−	11.7043i		−	0.695750i	0.937541	−	0.347875i	$-0.113097\pi$
$284$	−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	$-0.773359\pi$
$293$		−	22.3674i		−	1.30672i	0.757048	−	0.653359i	$-0.226641\pi$
$294$	−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	$-0.932879\pi$
$307$		−	7.33473i		−	0.418615i	0.977850	−	0.209308i	$-0.0671210\pi$
$308$		−	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	$0.198699\pi$
$313$			20.6808i			1.16895i	−0.811413	+	0.584473i	$0.801301\pi$
$314$	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	$-0.938763\pi$
$317$		−	6.80831i		−	0.382393i	0.981552	−	0.191197i	$-0.0612368\pi$
$318$			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	$0.0745822\pi$
$337$			8.52411i			0.464338i	−0.972675	+	0.232169i	$0.925418\pi$
$338$		−	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	$0.0602856\pi$
$347$			7.01388i			0.376525i	−0.982119	+	0.188262i	$0.939714\pi$
$348$		−	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	$-0.774445\pi$
$353$		−	24.4538i		−	1.30155i	0.759272	−	0.650773i	$-0.225555\pi$
$354$	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	$-0.941042\pi$
$367$		−	7.05618i		−	0.368329i	0.982895	−	0.184165i	$-0.0589580\pi$
$368$			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	$-0.976223\pi$
$373$		−	2.88267i		−	0.149259i	0.997211	−	0.0746294i	$-0.0237774\pi$
$374$	−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	$-0.782930\pi$
$383$		−	24.6706i		−	1.26061i	0.776348	−	0.630305i	$-0.217070\pi$
$384$	−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	$-0.996357\pi$
$397$		−	0.456104i		−	0.0228912i	0.999934	−	0.0114456i	$-0.00364333\pi$
$398$			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	$0.164079\pi$
$433$			20.5150i			0.985888i	−0.870061	+	0.492944i	$0.835921\pi$
$434$	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	$0.270423\pi$
$443$			31.6130i			1.50198i	−0.660314	+	0.750990i	$0.729577\pi$
$444$	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	$-0.730727\pi$
$457$		−	32.0064i		−	1.49720i	0.663023	−	0.748599i	$-0.269273\pi$
$458$			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	$-0.922256\pi$
$463$		−	10.4066i		−	0.483636i	0.970322	−	0.241818i	$-0.0777438\pi$
$464$	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	$-0.890041\pi$
$467$		−	14.6351i		−	0.677233i	0.940924	−	0.338617i	$-0.109959\pi$
$468$			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	$-0.820030\pi$
$487$		−	23.6459i		−	1.07150i	0.844378	−	0.535748i	$-0.179970\pi$
$488$		−	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	$0.280677\pi$
$503$			34.6223i			1.54373i	−0.635784	+	0.771867i	$0.719323\pi$
$504$	−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	$-0.839112\pi$
$523$		−	22.1464i		−	0.968394i	0.874959	−	0.484197i	$-0.160888\pi$
$524$	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	$0.122727\pi$
$547$			17.5914i			0.752152i	−0.926589	+	0.376076i	$0.877273\pi$
$548$			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	$0.0994681\pi$
$557$			14.5111i			0.614855i	−0.951572	+	0.307427i	$0.900532\pi$
$558$			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	$0.0210036\pi$
$563$			3.12905i			0.131874i	−0.997824	+	0.0659369i	$0.978996\pi$
$564$	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	$-0.939036\pi$
$577$		−	9.14505i		−	0.380713i	0.981715	−	0.190357i	$-0.0609644\pi$
$578$		−	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	$-0.912754\pi$
$587$		−	13.1157i		−	0.541345i	0.962672	−	0.270672i	$-0.0872460\pi$
$588$		−	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	$-0.763686\pi$
$593$		−	32.9263i		−	1.35212i	0.736847	−	0.676060i	$-0.236314\pi$
$594$	−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	$-0.828722\pi$
$607$		−	25.2530i		−	1.02499i	0.858691	−	0.512494i	$-0.171278\pi$
$608$			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	$-0.929081\pi$
$613$		−	10.9415i		−	0.441922i	0.975283	−	0.220961i	$-0.0709194\pi$
$614$	−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	$-0.746638\pi$
$617$		−	35.4974i		−	1.42907i	0.699599	−	0.714536i	$-0.253362\pi$
$618$			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	$0.240512\pi$
$643$			34.7762i			1.37144i	−0.727867	+	0.685719i	$0.759488\pi$
$644$	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	$-0.966640\pi$
$647$		−	5.32188i		−	0.209225i	0.994513	−	0.104612i	$-0.0333602\pi$
$648$			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	$-0.959572\pi$
$653$		−	6.47367i		−	0.253334i	0.991945	−	0.126667i	$-0.0404280\pi$
$654$	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	$-0.757921\pi$
$673$		−	35.7637i		−	1.37859i	0.724482	−	0.689294i	$-0.242079\pi$
$674$	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	$-0.706748\pi$
$677$		−	41.4421i		−	1.59275i	0.604804	−	0.796375i	$-0.293252\pi$
$678$		−	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	$-0.886657\pi$
$683$		−	18.2208i		−	0.697201i	0.937271	−	0.348600i	$-0.113343\pi$
$684$	−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	$-0.773017\pi$
$727$		−	35.2768i		−	1.30834i	0.756346	−	0.654172i	$-0.226983\pi$
$728$		−	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	$-0.859863\pi$
$733$		−	23.0762i		−	0.852338i	0.904644	−	0.426169i	$-0.140137\pi$
$734$	−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	$-0.832597\pi$
$743$		−	27.3672i		−	1.00400i	0.864866	−	0.502002i	$-0.167403\pi$
$744$	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	$0.150845\pi$
$757$			25.1120i			0.912711i	−0.889798	+	0.456355i	$0.849155\pi$
$758$			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	$0.346117\pi$
$773$			49.2335i			1.77081i	−0.464825	+	0.885403i	$0.653883\pi$
$774$	−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	$-0.980388\pi$
$787$		−	3.45465i		−	0.123145i	0.998103	−	0.0615725i	$-0.0196115\pi$
$788$			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	$0.245082\pi$
$797$			39.3034i			1.39220i	−0.717947	+	0.696098i	$0.754918\pi$
$798$		−	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	$-0.965159\pi$
$823$		−	6.26765i		−	0.218476i	0.994016	−	0.109238i	$-0.0348411\pi$
$824$	−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	$0.0173569\pi$
$827$			3.13465i			0.109002i	−0.998514	+	0.0545012i	$0.982643\pi$
$828$			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	$-0.829263\pi$
$853$		−	29.8507i		−	1.02207i	0.859561	−	0.511034i	$-0.170737\pi$
$854$	−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	$-0.768910\pi$
$857$		−	38.8694i		−	1.32775i	0.747841	−	0.663877i	$-0.231090\pi$
$858$		−	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	$0.0406500\pi$
$863$			7.48281i			0.254718i	−0.991857	+	0.127359i	$0.959350\pi$
$864$	−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	$0.393451\pi$
$877$			55.9410i			1.88899i	−0.328519	+	0.944497i	$0.606549\pi$
$878$			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	$-0.876875\pi$
$883$		−	22.4194i		−	0.754472i	0.926117	−	0.377236i	$-0.123125\pi$
$884$	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	$-0.916968\pi$
$887$		−	15.3620i		−	0.515806i	0.966171	−	0.257903i	$-0.0830315\pi$
$888$		−	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	$0.0286333\pi$
$907$			5.41090i			0.179666i	−0.995957	+	0.0898329i	$0.971367\pi$
$908$			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	$0.208599\pi$
$937$			37.3094i			1.21885i	−0.792845	+	0.609423i	$0.791401\pi$
$938$			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	$-0.981045\pi$
$947$		−	3.66296i		−	0.119030i	0.998227	−	0.0595151i	$-0.0189555\pi$
$948$		−	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	$-0.979666\pi$
$953$		−	3.94137i		−	0.127673i	0.997960	−	0.0638367i	$-0.0203337\pi$
$954$	−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	$0.0551156\pi$
$967$			10.7151i			0.344574i	−0.985047	+	0.172287i	$0.944884\pi$
$968$		−	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	$-0.748686\pi$
$977$		−	44.3861i		−	1.42004i	0.704183	−	0.710019i	$-0.251314\pi$
$978$		−	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	$0.000706017\pi$
$983$			0.139082i			0.00443603i	−0.999998	+	0.00221801i	$0.999294\pi$
$984$	−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	$0.0153328\pi$
$997$			3.04076i			0.0963018i	−0.998840	+	0.0481509i	$0.984667\pi$
$998$		−	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.419.13	✓	30
5.2	odd	4		5225.2.a.bc.1.18		30
5.3	odd	4		5225.2.a.bc.1.13		30
5.4	even	2	inner	1045.2.b.e.419.18	yes	30

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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