LMFDB - Embedded newform 1380.2.r.c.737.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (of order $4$, degree $2$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.14
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795128 + 1.53876i) q^{3} +(-1.56652 + 1.59562i) q^{5} +(0.769646 + 0.769646i) q^{7} +(-1.73554 - 2.44702i) q^{9} +O(q^{10})$	\(q+(-0.795128 + 1.53876i) q^{3} +(-1.56652 + 1.59562i) q^{5} +(0.769646 + 0.769646i) q^{7} +(-1.73554 - 2.44702i) q^{9} -2.12034i q^{11} +(3.53512 - 3.53512i) q^{13} +(-1.20969 - 3.67922i) q^{15} +(1.63046 - 1.63046i) q^{17} -3.93859i q^{19} +(-1.79626 + 0.572331i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(-0.0920108 - 4.99915i) q^{25} +(5.14534 - 0.724887i) q^{27} +1.04476 q^{29} -0.661930 q^{31} +(3.26269 + 1.68594i) q^{33} +(-2.43373 + 0.0223949i) q^{35} +(2.26541 + 2.26541i) q^{37} +(2.62881 + 8.25055i) q^{39} +5.31675i q^{41} +(1.28783 - 1.28783i) q^{43} +(6.62328 + 1.06404i) q^{45} +(0.204904 - 0.204904i) q^{47} -5.81529i q^{49} +(1.21245 + 3.80530i) q^{51} +(0.488959 + 0.488959i) q^{53} +(3.38326 + 3.32156i) q^{55} +(6.06053 + 3.13168i) q^{57} +0.286614 q^{59} +4.92347 q^{61} +(0.547582 - 3.21909i) q^{63} +(0.102863 + 11.1785i) q^{65} +(1.93068 + 1.93068i) q^{67} +(1.65031 - 0.525825i) q^{69} +13.5645i q^{71} +(8.71007 - 8.71007i) q^{73} +(7.76564 + 3.83338i) q^{75} +(1.63191 - 1.63191i) q^{77} +4.33841i q^{79} +(-2.97578 + 8.49381i) q^{81} +(-12.5210 - 12.5210i) q^{83} +(0.0474424 + 5.15574i) q^{85} +(-0.830720 + 1.60764i) q^{87} -4.39452 q^{89} +5.44157 q^{91} +(0.526319 - 1.01855i) q^{93} +(6.28449 + 6.16989i) q^{95} +(7.43748 + 7.43748i) q^{97} +(-5.18851 + 3.67994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.795128	+	1.53876i	−0.459067	+	0.888401i
$3$	−0.795128	+	1.53876i	−0.459067	+	0.888401i
$4$		0			0
$5$	−1.56652	+	1.59562i	−0.700570	+	0.713583i
$5$	−1.56652	+	1.59562i	−0.700570	+	0.713583i
$6$		0			0
$7$	0.769646	+	0.769646i	0.290899	+	0.290899i	0.837435	−	0.546537i	$-0.184054\pi$
$7$	0.769646	+	0.769646i	0.290899	+	0.290899i	−0.546537	+	0.837435i	$0.684054\pi$
$8$		0			0
$9$	−1.73554	−	2.44702i	−0.578514	−	0.815672i
$10$		0			0
$11$		−	2.12034i		−	0.639307i	−0.947534	−	0.319654i	$-0.896433\pi$
$11$		−	2.12034i		−	0.639307i	0.947534	−	0.319654i	$-0.103567\pi$
$12$		0			0
$13$	3.53512	−	3.53512i	0.980465	−	0.980465i	−0.0193482	−	0.999813i	$-0.506159\pi$
$13$	3.53512	−	3.53512i	0.980465	−	0.980465i	0.999813	+	0.0193482i	$0.00615911\pi$
$14$		0			0
$15$	−1.20969	−	3.67922i	−0.312339	−	0.949971i
$16$		0			0
$17$	1.63046	−	1.63046i	0.395444	−	0.395444i	−0.481179	−	0.876623i	$-0.659791\pi$
$17$	1.63046	−	1.63046i	0.395444	−	0.395444i	0.876623	+	0.481179i	$0.159791\pi$
$18$		0			0
$19$		−	3.93859i		−	0.903574i	−0.892126	−	0.451787i	$-0.850787\pi$
$19$		−	3.93859i		−	0.903574i	0.892126	−	0.451787i	$-0.149213\pi$
$20$		0			0
$21$	−1.79626	+	0.572331i	−0.391977	+	0.124893i
$22$		0			0
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	−0.0920108	−	4.99915i	−0.0184022	−	0.999831i
$26$		0			0
$27$	5.14534	−	0.724887i	0.990221	−	0.139505i
$28$		0			0
$29$	1.04476			0.194008			0.0970038	−	0.995284i	$-0.469074\pi$
$29$	1.04476			0.194008			0.0970038	+	0.995284i	$0.469074\pi$
$30$		0			0
$31$	−0.661930			−0.118886			−0.0594430	−	0.998232i	$-0.518932\pi$
$31$	−0.661930			−0.118886			−0.0594430	+	0.998232i	$0.518932\pi$
$32$		0			0
$33$	3.26269	+	1.68594i	0.567961	+	0.293485i
$34$		0			0
$35$	−2.43373	+	0.0223949i	−0.411376	+	0.00378542i
$36$		0			0
$37$	2.26541	+	2.26541i	0.372431	+	0.372431i	0.868362	−	0.495931i	$-0.165173\pi$
$37$	2.26541	+	2.26541i	0.372431	+	0.372431i	−0.495931	+	0.868362i	$0.665173\pi$
$38$		0			0
$39$	2.62881	+	8.25055i	0.420947	+	1.32115i
$40$		0			0
$41$			5.31675i			0.830337i	0.909745	+	0.415168i	$0.136277\pi$
$41$			5.31675i			0.830337i	−0.909745	+	0.415168i	$0.863723\pi$
$42$		0			0
$43$	1.28783	−	1.28783i	0.196392	−	0.196392i	−0.602059	−	0.798451i	$-0.705653\pi$
$43$	1.28783	−	1.28783i	0.196392	−	0.196392i	0.798451	+	0.602059i	$0.205653\pi$
$44$		0			0
$45$	6.62328	+	1.06404i	0.987340	+	0.158618i
$46$		0			0
$47$	0.204904	−	0.204904i	0.0298882	−	0.0298882i	−0.692005	−	0.721893i	$-0.743272\pi$
$47$	0.204904	−	0.204904i	0.0298882	−	0.0298882i	0.721893	+	0.692005i	$0.243272\pi$
$48$		0			0
$49$		−	5.81529i		−	0.830756i
$50$		0			0
$51$	1.21245	+	3.80530i	0.169778	+	0.532849i
$52$		0			0
$53$	0.488959	+	0.488959i	0.0671636	+	0.0671636i	0.739891	−	0.672727i	$-0.234877\pi$
$53$	0.488959	+	0.488959i	0.0671636	+	0.0671636i	−0.672727	+	0.739891i	$0.734877\pi$
$54$		0			0
$55$	3.38326	+	3.32156i	0.456199	+	0.447880i
$56$		0			0
$57$	6.06053	+	3.13168i	0.802736	+	0.414801i
$58$		0			0
$59$	0.286614			0.0373140			0.0186570	−	0.999826i	$-0.494061\pi$
$59$	0.286614			0.0373140			0.0186570	+	0.999826i	$0.494061\pi$
$60$		0			0
$61$	4.92347			0.630386			0.315193	−	0.949028i	$-0.397931\pi$
$61$	4.92347			0.630386			0.315193	+	0.949028i	$0.397931\pi$
$62$		0			0
$63$	0.547582	−	3.21909i	0.0689889	−	0.405567i
$64$		0			0
$65$	0.102863	+	11.1785i	0.0127586	+	1.38653i
$66$		0			0
$67$	1.93068	+	1.93068i	0.235871	+	0.235871i	0.815138	−	0.579267i	$-0.196661\pi$
$67$	1.93068	+	1.93068i	0.235871	+	0.235871i	−0.579267	+	0.815138i	$0.696661\pi$
$68$		0			0
$69$	1.65031	−	0.525825i	0.198673	−	0.0633019i
$70$		0			0
$71$			13.5645i			1.60981i	0.593401	+	0.804907i	$0.297785\pi$
$71$			13.5645i			1.60981i	−0.593401	+	0.804907i	$0.702215\pi$
$72$		0			0
$73$	8.71007	−	8.71007i	1.01944	−	1.01944i	0.0196298	−	0.999807i	$-0.493751\pi$
$73$	8.71007	−	8.71007i	1.01944	−	1.01944i	0.999807	−	0.0196298i	$-0.00624877\pi$
$74$		0			0
$75$	7.76564	+	3.83338i	0.896699	+	0.442641i
$76$		0			0
$77$	1.63191	−	1.63191i	0.185974	−	0.185974i
$78$		0			0
$79$			4.33841i			0.488110i	0.969761	+	0.244055i	$0.0784777\pi$
$79$			4.33841i			0.488110i	−0.969761	+	0.244055i	$0.921522\pi$
$80$		0			0
$81$	−2.97578	+	8.49381i	−0.330642	+	0.943756i
$82$		0			0
$83$	−12.5210	−	12.5210i	−1.37435	−	1.37435i	−0.853873	−	0.520482i	$-0.825752\pi$
$83$	−12.5210	−	12.5210i	−1.37435	−	1.37435i	−0.520482	−	0.853873i	$-0.674248\pi$
$84$		0			0
$85$	0.0474424	+	5.15574i	0.00514585	+	0.559219i
$86$		0			0
$87$	−0.830720	+	1.60764i	−0.0890626	+	0.172357i
$88$		0			0
$89$	−4.39452			−0.465818			−0.232909	−	0.972499i	$-0.574824\pi$
$89$	−4.39452			−0.465818			−0.232909	+	0.972499i	$0.574824\pi$
$90$		0			0
$91$	5.44157			0.570432
$92$		0			0
$93$	0.526319	−	1.01855i	0.0545767	−	0.105619i
$94$		0			0
$95$	6.28449	+	6.16989i	0.644775	+	0.633017i
$96$		0			0
$97$	7.43748	+	7.43748i	0.755161	+	0.755161i	0.975438	−	0.220276i	$-0.0706958\pi$
$97$	7.43748	+	7.43748i	0.755161	+	0.755161i	−0.220276	+	0.975438i	$0.570696\pi$
$98$		0			0
$99$	−5.18851	+	3.67994i	−0.521465	+	0.369848i
$100$		0			0
$101$		−	9.81667i		−	0.976795i	−0.872621	−	0.488397i	$-0.837582\pi$
$101$		−	9.81667i		−	0.976795i	0.872621	−	0.488397i	$-0.162418\pi$
$102$		0			0
$103$	9.88737	−	9.88737i	0.974232	−	0.974232i	−0.0254446	−	0.999676i	$-0.508100\pi$
$103$	9.88737	−	9.88737i	0.974232	−	0.974232i	0.999676	+	0.0254446i	$0.00810013\pi$
$104$		0			0
$105$	1.90067	−	3.76273i	0.185486	−	0.367204i
$106$		0			0
$107$	1.08163	−	1.08163i	0.104565	−	0.104565i	−0.652889	−	0.757454i	$-0.726443\pi$
$107$	1.08163	−	1.08163i	0.104565	−	0.104565i	0.757454	+	0.652889i	$0.226443\pi$
$108$		0			0
$109$		−	12.1672i		−	1.16540i	−0.812686	−	0.582702i	$-0.801995\pi$
$109$		−	12.1672i		−	1.16540i	0.812686	−	0.582702i	$-0.198005\pi$
$110$		0			0
$111$	−5.28720	+	1.68462i	−0.501839	+	0.159897i
$112$		0			0
$113$	−5.79146	−	5.79146i	−0.544815	−	0.544815i	0.380122	−	0.924936i	$-0.375882\pi$
$113$	−5.79146	−	5.79146i	−0.544815	−	0.544815i	−0.924936	+	0.380122i	$0.875882\pi$
$114$		0			0
$115$	2.23597	−	0.0205751i	0.208506	−	0.00191864i
$116$		0			0
$117$	−14.7858	−	2.51514i	−1.36695	−	0.232525i
$118$		0			0
$119$	2.50975			0.230068
$120$		0			0
$121$	6.50415			0.591286
$122$		0			0
$123$	−8.18118	−	4.22750i	−0.737673	−	0.381181i
$124$		0			0
$125$	8.12089	+	7.68447i	0.726354	+	0.687320i
$126$		0			0
$127$	1.61722	+	1.61722i	0.143505	+	0.143505i	0.775209	−	0.631705i	$-0.217644\pi$
$127$	1.61722	+	1.61722i	0.143505	+	0.143505i	−0.631705	+	0.775209i	$0.717644\pi$
$128$		0			0
$129$	0.957665	+	3.00564i	0.0843177	+	0.264632i
$130$		0			0
$131$			21.8392i			1.90810i	0.299642	+	0.954052i	$0.403133\pi$
$131$			21.8392i			1.90810i	−0.299642	+	0.954052i	$0.596867\pi$
$132$		0			0
$133$	3.03132	−	3.03132i	0.262849	−	0.262849i
$134$		0			0
$135$	−6.90365	+	9.34557i	−0.594172	+	0.804338i
$136$		0			0
$137$	13.6170	−	13.6170i	1.16338	−	1.16338i	0.179645	−	0.983732i	$-0.442505\pi$
$137$	13.6170	−	13.6170i	1.16338	−	1.16338i	0.983732	−	0.179645i	$-0.0574948\pi$
$138$		0			0
$139$		−	2.56281i		−	0.217375i	−0.994076	−	0.108688i	$-0.965335\pi$
$139$		−	2.56281i		−	0.217375i	0.994076	−	0.108688i	$-0.0346648\pi$
$140$		0			0
$141$	0.152372	+	0.478221i	0.0128320	+	0.0402735i
$142$		0			0
$143$	−7.49565	−	7.49565i	−0.626818	−	0.626818i
$144$		0			0
$145$	−1.63665	+	1.66705i	−0.135916	+	0.138441i
$146$		0			0
$147$	8.94832	+	4.62390i	0.738045	+	0.381373i
$148$		0			0
$149$	4.66617			0.382268			0.191134	−	0.981564i	$-0.438784\pi$
$149$	4.66617			0.382268			0.191134	+	0.981564i	$0.438784\pi$
$150$		0			0
$151$	15.8647			1.29105			0.645527	−	0.763738i	$-0.276638\pi$
$151$	15.8647			1.29105			0.645527	+	0.763738i	$0.276638\pi$
$152$		0			0
$153$	−6.81949	−	1.16003i	−0.551323	−	0.0937826i
$154$		0			0
$155$	1.03693	−	1.05619i	0.0832881	−	0.0848351i
$156$		0			0
$157$	−5.96043	−	5.96043i	−0.475694	−	0.475694i	0.428057	−	0.903752i	$-0.359198\pi$
$157$	−5.96043	−	5.96043i	−0.475694	−	0.475694i	−0.903752	+	0.428057i	$0.859198\pi$
$158$		0			0
$159$	−1.14117	+	0.363604i	−0.0905009	+	0.0288356i
$160$		0			0
$161$		−	1.08844i		−	0.0857814i
$162$		0			0
$163$	−1.40360	+	1.40360i	−0.109939	+	0.109939i	−0.759936	−	0.649998i	$-0.774770\pi$
$163$	−1.40360	+	1.40360i	−0.109939	+	0.109939i	0.649998	+	0.759936i	$0.274770\pi$
$164$		0			0
$165$	−7.80120	+	2.56495i	−0.607323	+	0.199681i
$166$		0			0
$167$	−4.10670	+	4.10670i	−0.317786	+	0.317786i	−0.847916	−	0.530130i	$-0.822143\pi$
$167$	−4.10670	+	4.10670i	−0.317786	+	0.317786i	0.530130	+	0.847916i	$0.322143\pi$
$168$		0			0
$169$		−	11.9941i		−	0.922622i
$170$		0			0
$171$	−9.63779	+	6.83559i	−0.737020	+	0.522731i
$172$		0			0
$173$	−6.90766	−	6.90766i	−0.525180	−	0.525180i	0.393951	−	0.919131i	$-0.371108\pi$
$173$	−6.90766	−	6.90766i	−0.525180	−	0.525180i	−0.919131	+	0.393951i	$0.871108\pi$
$174$		0			0
$175$	3.77676	−	3.91839i	0.285496	−	0.296203i
$176$		0			0
$177$	−0.227895	+	0.441030i	−0.0171296	+	0.0331498i
$178$		0			0
$179$	3.17936			0.237637			0.118818	−	0.992916i	$-0.462089\pi$
$179$	3.17936			0.237637			0.118818	+	0.992916i	$0.462089\pi$
$180$		0			0
$181$	−16.3431			−1.21477			−0.607387	−	0.794406i	$-0.707782\pi$
$181$	−16.3431			−1.21477			−0.607387	+	0.794406i	$0.707782\pi$
$182$		0			0
$183$	−3.91479	+	7.57603i	−0.289390	+	0.560036i
$184$		0			0
$185$	−7.16354	+	0.0659179i	−0.526674	+	0.00484638i
$186$		0			0
$187$	−3.45713	−	3.45713i	−0.252810	−	0.252810i
$188$		0			0
$189$	4.51800	+	3.40218i	0.328636	+	0.247472i
$190$		0			0
$191$			2.34094i			0.169385i	0.996407	+	0.0846923i	$0.0269907\pi$
$191$			2.34094i			0.169385i	−0.996407	+	0.0846923i	$0.973009\pi$
$192$		0			0
$193$	14.9377	−	14.9377i	1.07524	−	1.07524i	0.0783090	−	0.996929i	$-0.475048\pi$
$193$	14.9377	−	14.9377i	1.07524	−	1.07524i	0.996929	−	0.0783090i	$-0.0249521\pi$
$194$		0			0
$195$	−17.2828	−	8.73009i	−1.23765	−	0.625175i
$196$		0			0
$197$	19.1550	−	19.1550i	1.36473	−	1.36473i	0.496961	−	0.867773i	$-0.334449\pi$
$197$	19.1550	−	19.1550i	1.36473	−	1.36473i	0.867773	−	0.496961i	$-0.165551\pi$
$198$		0			0
$199$			17.1982i			1.21915i	0.792730	+	0.609573i	$0.208659\pi$
$199$			17.1982i			1.21915i	−0.792730	+	0.609573i	$0.791341\pi$
$200$		0			0
$201$	−4.50600	+	1.43571i	−0.317828	+	0.101267i
$202$		0			0
$203$	0.804097	+	0.804097i	0.0564366	+	0.0564366i
$204$		0			0
$205$	−8.48352	−	8.32881i	−0.592514	−	0.581709i
$206$		0			0
$207$	−0.503088	+	2.95752i	−0.0349670	+	0.205562i
$208$		0			0
$209$	−8.35115			−0.577661
$210$		0			0
$211$	−21.0643			−1.45013			−0.725065	−	0.688681i	$-0.758190\pi$
$211$	−21.0643			−1.45013			−0.725065	+	0.688681i	$0.758190\pi$
$212$		0			0
$213$	−20.8725	−	10.7855i	−1.43016	−	0.739013i
$214$		0			0
$215$	0.0374727	+	4.07229i	0.00255562	+	0.277728i
$216$		0			0
$217$	−0.509451	−	0.509451i	−0.0345838	−	0.0345838i
$218$		0			0
$219$	6.47706	+	20.3283i	0.437679	+	1.37366i
$220$		0			0
$221$		−	11.5277i		−	0.775438i
$222$		0			0
$223$	−18.9227	+	18.9227i	−1.26716	+	1.26716i	−0.319610	+	0.947549i	$0.603552\pi$
$223$	−18.9227	+	18.9227i	−1.26716	+	1.26716i	−0.947549	+	0.319610i	$0.896448\pi$
$224$		0			0
$225$	−12.0733	+	8.90140i	−0.804888	+	0.593427i
$226$		0			0
$227$	3.93255	−	3.93255i	0.261013	−	0.261013i	−0.564453	−	0.825465i	$-0.690913\pi$
$227$	3.93255	−	3.93255i	0.261013	−	0.261013i	0.825465	+	0.564453i	$0.190913\pi$
$228$		0			0
$229$		−	13.3913i		−	0.884920i	−0.896788	−	0.442460i	$-0.854106\pi$
$229$		−	13.3913i		−	0.884920i	0.896788	−	0.442460i	$-0.145894\pi$
$230$		0			0
$231$	1.21354	+	3.80869i	0.0798448	+	0.250594i
$232$		0			0
$233$	6.28261	+	6.28261i	0.411588	+	0.411588i	0.882291	−	0.470704i	$-0.156000\pi$
$233$	6.28261	+	6.28261i	0.411588	+	0.411588i	−0.470704	+	0.882291i	$0.656000\pi$
$234$		0			0
$235$	0.00596220	+	0.647934i	0.000388931	+	0.0422666i
$236$		0			0
$237$	−6.67576	−	3.44959i	−0.433637	−	0.224075i
$238$		0			0
$239$	20.0871			1.29933			0.649664	−	0.760221i	$-0.274909\pi$
$239$	20.0871			1.29933			0.649664	+	0.760221i	$0.274909\pi$
$240$		0			0
$241$	−6.89303			−0.444019			−0.222010	−	0.975044i	$-0.571262\pi$
$241$	−6.89303			−0.444019			−0.222010	+	0.975044i	$0.571262\pi$
$242$		0			0
$243$	−10.7038	−	11.3327i	−0.686647	−	0.726991i
$244$		0			0
$245$	9.27900	+	9.10979i	0.592813	+	0.582003i
$246$		0			0
$247$	−13.9234	−	13.9234i	−0.885922	−	0.885922i
$248$		0			0
$249$	29.2225	−	9.31095i	1.85190	−	0.590057i
$250$		0			0
$251$		−	3.26055i		−	0.205804i	−0.994692	−	0.102902i	$-0.967187\pi$
$251$		−	3.26055i		−	0.205804i	0.994692	−	0.102902i	$-0.0328128\pi$
$252$		0			0
$253$	−1.49931	+	1.49931i	−0.0942607	+	0.0942607i
$254$		0			0
$255$	−7.97115	−	4.02647i	−0.499173	−	0.252147i
$256$		0			0
$257$	−10.1328	+	10.1328i	−0.632067	+	0.632067i	−0.948586	−	0.316519i	$-0.897486\pi$
$257$	−10.1328	+	10.1328i	−0.632067	+	0.632067i	0.316519	+	0.948586i	$0.397486\pi$
$258$		0			0
$259$			3.48712i			0.216679i
$260$		0			0
$261$	−1.81323	−	2.55655i	−0.112236	−	0.158247i
$262$		0			0
$263$	3.16925	+	3.16925i	0.195424	+	0.195424i	0.798035	−	0.602611i	$-0.205873\pi$
$263$	3.16925	+	3.16925i	0.195424	+	0.195424i	−0.602611	+	0.798035i	$0.705873\pi$
$264$		0			0
$265$	−1.54616	+	0.0142275i	−0.0949797	+	0.000873990i
$266$		0			0
$267$	3.49420	−	6.76209i	0.213842	−	0.413833i
$268$		0			0
$269$	19.6487			1.19801			0.599003	−	0.800747i	$-0.295564\pi$
$269$	19.6487			1.19801			0.599003	+	0.800747i	$0.295564\pi$
$270$		0			0
$271$	2.83702			0.172337			0.0861684	−	0.996281i	$-0.472538\pi$
$271$	2.83702			0.172337			0.0861684	+	0.996281i	$0.472538\pi$
$272$		0			0
$273$	−4.32675	+	8.37326i	−0.261867	+	0.506772i
$274$		0			0
$275$	−10.5999	+	0.195094i	−0.639199	+	0.0117646i
$276$		0			0
$277$	−14.0664	−	14.0664i	−0.845167	−	0.845167i	0.144359	−	0.989525i	$-0.453888\pi$
$277$	−14.0664	−	14.0664i	−0.845167	−	0.845167i	−0.989525	+	0.144359i	$0.953888\pi$
$278$		0			0
$279$	1.14881	+	1.61975i	0.0687773	+	0.0969721i
$280$		0			0
$281$		−	18.4661i		−	1.10159i	−0.834640	−	0.550796i	$-0.814324\pi$
$281$		−	18.4661i		−	1.10159i	0.834640	−	0.550796i	$-0.185676\pi$
$282$		0			0
$283$	−3.79021	+	3.79021i	−0.225304	+	0.225304i	−0.810728	−	0.585423i	$-0.800928\pi$
$283$	−3.79021	+	3.79021i	−0.225304	+	0.225304i	0.585423	+	0.810728i	$0.300928\pi$
$284$		0			0
$285$	−14.4909	+	4.76445i	−0.858369	+	0.282222i
$286$		0			0
$287$	−4.09201	+	4.09201i	−0.241544	+	0.241544i
$288$		0			0
$289$			11.6832i			0.687248i
$290$		0			0
$291$	−17.3582	+	5.53072i	−1.01756	+	0.324217i
$292$		0			0
$293$	−8.15261	−	8.15261i	−0.476280	−	0.476280i	0.427660	−	0.903940i	$-0.359338\pi$
$293$	−8.15261	−	8.15261i	−0.476280	−	0.476280i	−0.903940	+	0.427660i	$0.859338\pi$
$294$		0			0
$295$	−0.448988	+	0.457328i	−0.0261411	+	0.0266267i
$296$		0			0
$297$	−1.53701	−	10.9099i	−0.0891863	−	0.633056i
$298$		0			0
$299$	−4.99941			−0.289123
$300$		0			0
$301$	1.98234			0.114260
$302$		0			0
$303$	15.1055	+	7.80551i	0.867786	+	0.448415i
$304$		0			0
$305$	−7.71273	+	7.85600i	−0.441630	+	0.449833i
$306$		0			0
$307$	2.78701	+	2.78701i	0.159063	+	0.159063i	0.782151	−	0.623088i	$-0.214122\pi$
$307$	2.78701	+	2.78701i	0.159063	+	0.159063i	−0.623088	+	0.782151i	$0.714122\pi$
$308$		0			0
$309$	7.35253	+	23.0760i	0.418271	+	1.31275i
$310$		0			0
$311$		−	17.2686i		−	0.979210i	−0.871944	−	0.489605i	$-0.837141\pi$
$311$		−	17.2686i		−	0.979210i	0.871944	−	0.489605i	$-0.162859\pi$
$312$		0			0
$313$	8.96358	−	8.96358i	0.506652	−	0.506652i	−0.406845	−	0.913497i	$-0.633371\pi$
$313$	8.96358	−	8.96358i	0.506652	−	0.506652i	0.913497	+	0.406845i	$0.133371\pi$
$314$		0			0
$315$	4.27864	+	5.91651i	0.241074	+	0.333358i
$316$		0			0
$317$	0.525557	−	0.525557i	0.0295182	−	0.0295182i	−0.692194	−	0.721712i	$-0.743356\pi$
$317$	0.525557	−	0.525557i	0.0295182	−	0.0295182i	0.721712	+	0.692194i	$0.243356\pi$
$318$		0			0
$319$		−	2.21525i		−	0.124030i
$320$		0			0
$321$	0.804330	+	2.52440i	0.0448933	+	0.140898i
$322$		0			0
$323$	−6.42170	−	6.42170i	−0.357313	−	0.357313i
$324$		0			0
$325$	−17.9979	−	17.3473i	−0.998341	−	0.962256i
$326$		0			0
$327$	18.7223	+	9.67446i	1.03535	+	0.534999i
$328$		0			0
$329$	0.315406			0.0173889
$330$		0			0
$331$	−35.1031			−1.92944			−0.964720	−	0.263278i	$-0.915196\pi$
$331$	−35.1031			−1.92944			−0.964720	+	0.263278i	$0.915196\pi$
$332$		0			0
$333$	1.61178	−	9.47520i	0.0883248	−	0.519238i
$334$		0			0
$335$	−6.10510	+	0.0561783i	−0.333557	+	0.00306935i
$336$		0			0
$337$	24.2986	+	24.2986i	1.32363	+	1.32363i	0.910814	+	0.412817i	$0.135455\pi$
$337$	24.2986	+	24.2986i	1.32363	+	1.32363i	0.412817	+	0.910814i	$0.364545\pi$
$338$		0			0
$339$	13.5166	−	4.30669i	0.734121	−	0.233908i
$340$		0			0
$341$			1.40352i			0.0760047i
$342$		0			0
$343$	9.86323	−	9.86323i	0.532565	−	0.532565i
$344$		0			0
$345$	−1.74622	+	3.45698i	−0.0940136	+	0.186117i
$346$		0			0
$347$	15.0302	−	15.0302i	0.806865	−	0.806865i	−0.177293	−	0.984158i	$-0.556734\pi$
$347$	15.0302	−	15.0302i	0.806865	−	0.806865i	0.984158	+	0.177293i	$0.0567341\pi$
$348$		0			0
$349$			4.66694i			0.249815i	0.992168	+	0.124908i	$0.0398635\pi$
$349$			4.66694i			0.249815i	−0.992168	+	0.124908i	$0.960137\pi$
$350$		0			0
$351$	15.6268	−	20.7519i	0.834098	−	1.10766i
$352$		0			0
$353$	−7.42229	−	7.42229i	−0.395049	−	0.395049i	0.481434	−	0.876482i	$-0.340116\pi$
$353$	−7.42229	−	7.42229i	−0.395049	−	0.395049i	−0.876482	+	0.481434i	$0.840116\pi$
$354$		0			0
$355$	−21.6438	−	21.2492i	−1.14874	−	1.12779i
$356$		0			0
$357$	−1.99557	+	3.86189i	−0.105617	+	0.204393i
$358$		0			0
$359$	−21.7363			−1.14720			−0.573599	−	0.819136i	$-0.694453\pi$
$359$	−21.7363			−1.14720			−0.573599	+	0.819136i	$0.694453\pi$
$360$		0			0
$361$	3.48753			0.183554
$362$		0			0
$363$	−5.17163	+	10.0083i	−0.271440	+	0.525300i
$364$		0			0
$365$	0.253442	+	27.5425i	0.0132658	+	1.44164i
$366$		0			0
$367$	−3.54200	−	3.54200i	−0.184891	−	0.184891i	0.608592	−	0.793483i	$-0.291735\pi$
$367$	−3.54200	−	3.54200i	−0.184891	−	0.184891i	−0.793483	+	0.608592i	$0.791735\pi$
$368$		0			0
$369$	13.0102	−	9.22745i	0.677283	−	0.480362i
$370$		0			0
$371$			0.752650i			0.0390756i
$372$		0			0
$373$	−7.88620	+	7.88620i	−0.408332	+	0.408332i	−0.881157	−	0.472825i	$-0.843234\pi$
$373$	−7.88620	+	7.88620i	−0.408332	+	0.408332i	0.472825	+	0.881157i	$0.343234\pi$
$374$		0			0
$375$	−18.2817	+	6.38593i	−0.944062	+	0.329768i
$376$		0			0
$377$	3.69336	−	3.69336i	0.190218	−	0.190218i
$378$		0			0
$379$		−	11.8176i		−	0.607031i	−0.952826	−	0.303516i	$-0.901840\pi$
$379$		−	11.8176i		−	0.607031i	0.952826	−	0.303516i	$-0.0981605\pi$
$380$		0			0
$381$	−3.77440	+	1.20261i	−0.193368	+	0.0616115i
$382$		0			0
$383$	19.3566	+	19.3566i	0.989074	+	0.989074i	0.999941	−	0.0108666i	$-0.00345902\pi$
$383$	19.3566	+	19.3566i	0.989074	+	0.989074i	−0.0108666	+	0.999941i	$0.503459\pi$
$384$		0			0
$385$	0.0474847	+	5.16034i	0.00242005	+	0.262995i
$386$		0			0
$387$	−5.38641	−	0.916254i	−0.273807	−	0.0465758i
$388$		0			0
$389$	−11.0231			−0.558894			−0.279447	−	0.960161i	$-0.590151\pi$
$389$	−11.0231			−0.558894			−0.279447	+	0.960161i	$0.590151\pi$
$390$		0			0
$391$	−2.30582			−0.116610
$392$		0			0
$393$	−33.6053	−	17.3650i	−1.69516	−	0.875948i
$394$		0			0
$395$	−6.92246	−	6.79622i	−0.348307	−	0.341955i
$396$		0			0
$397$	5.53780	+	5.53780i	0.277934	+	0.277934i	0.832284	−	0.554350i	$-0.187033\pi$
$397$	5.53780	+	5.53780i	0.277934	+	0.277934i	−0.554350	+	0.832284i	$0.687033\pi$
$398$		0			0
$399$	2.25417	+	7.07474i	0.112850	+	0.354180i
$400$		0			0
$401$			12.0757i			0.603030i	0.953461	+	0.301515i	$0.0974924\pi$
$401$			12.0757i			0.603030i	−0.953461	+	0.301515i	$0.902508\pi$
$402$		0			0
$403$	−2.34000	+	2.34000i	−0.116564	+	0.116564i
$404$		0			0
$405$	−8.89126	−	18.0540i	−0.441810	−	0.897108i
$406$		0			0
$407$	4.80344	−	4.80344i	0.238098	−	0.238098i
$408$		0			0
$409$			31.6986i			1.56740i	0.621142	+	0.783698i	$0.286669\pi$
$409$			31.6986i			1.56740i	−0.621142	+	0.783698i	$0.713331\pi$
$410$		0			0
$411$	10.1260	+	31.7804i	0.499477	+	1.56761i
$412$		0			0
$413$	0.220591	+	0.220591i	0.0108546	+	0.0108546i
$414$		0			0
$415$	39.5931	−	0.364330i	1.94355	−	0.0178843i
$416$		0			0
$417$	3.94355	+	2.03776i	0.193116	+	0.0997898i
$418$		0			0
$419$	−23.9071			−1.16794			−0.583968	−	0.811776i	$-0.698501\pi$
$419$	−23.9071			−1.16794			−0.583968	+	0.811776i	$0.698501\pi$
$420$		0			0
$421$	−1.08958			−0.0531030			−0.0265515	−	0.999647i	$-0.508453\pi$
$421$	−1.08958			−0.0531030			−0.0265515	+	0.999647i	$0.508453\pi$
$422$		0			0
$423$	−0.857021	−	0.145783i	−0.0416698	−	0.00708823i
$424$		0			0
$425$	−8.30093	−	8.00089i	−0.402654	−	0.388100i
$426$		0			0
$427$	3.78933	+	3.78933i	0.183379	+	0.183379i
$428$		0			0
$429$	17.4940	−	5.57398i	0.844618	−	0.269114i
$430$		0			0
$431$			13.0880i			0.630426i	0.949021	+	0.315213i	$0.102076\pi$
$431$			13.0880i			0.630426i	−0.949021	+	0.315213i	$0.897924\pi$
$432$		0			0
$433$	−13.2741	+	13.2741i	−0.637912	+	0.637912i	−0.950040	−	0.312128i	$-0.898958\pi$
$433$	−13.2741	+	13.2741i	−0.637912	+	0.637912i	0.312128	+	0.950040i	$0.398958\pi$
$434$		0			0
$435$	−1.26383	−	3.84391i	−0.0605962	−	0.184302i
$436$		0			0
$437$	−2.78500	+	2.78500i	−0.133225	+	0.133225i
$438$		0			0
$439$			14.4167i			0.688074i	0.938956	+	0.344037i	$0.111794\pi$
$439$			14.4167i			0.688074i	−0.938956	+	0.344037i	$0.888206\pi$
$440$		0			0
$441$	−14.2301	+	10.0927i	−0.677624	+	0.480604i
$442$		0			0
$443$	−21.7602	−	21.7602i	−1.03386	−	1.03386i	−0.999406	−	0.0344525i	$-0.989031\pi$
$443$	−21.7602	−	21.7602i	−1.03386	−	1.03386i	−0.0344525	−	0.999406i	$-0.510969\pi$
$444$		0			0
$445$	6.88411	−	7.01198i	0.326338	−	0.332400i
$446$		0			0
$447$	−3.71020	+	7.18010i	−0.175487	+	0.339607i
$448$		0			0
$449$	−39.2206			−1.85093			−0.925467	−	0.378827i	$-0.876328\pi$
$449$	−39.2206			−1.85093			−0.925467	+	0.378827i	$0.876328\pi$
$450$		0			0
$451$	11.2733			0.530840
$452$		0			0
$453$	−12.6145	+	24.4120i	−0.592681	+	1.14697i
$454$		0			0
$455$	−8.52435	+	8.68269i	−0.399628	+	0.407051i
$456$		0			0
$457$	−20.6764	−	20.6764i	−0.967202	−	0.967202i	0.0322771	−	0.999479i	$-0.489724\pi$
$457$	−20.6764	−	20.6764i	−0.967202	−	0.967202i	−0.999479	+	0.0322771i	$0.989724\pi$
$458$		0			0
$459$	7.20736	−	9.57116i	0.336411	−	0.446743i
$460$		0			0
$461$		−	32.1416i		−	1.49699i	−0.663143	−	0.748493i	$-0.730778\pi$
$461$		−	32.1416i		−	1.49699i	0.663143	−	0.748493i	$-0.269222\pi$
$462$		0			0
$463$	13.9312	−	13.9312i	0.647436	−	0.647436i	−0.304937	−	0.952373i	$-0.598635\pi$
$463$	13.9312	−	13.9312i	0.647436	−	0.647436i	0.952373	+	0.304937i	$0.0986354\pi$
$464$		0			0
$465$	0.800727	+	2.43539i	0.0371328	+	0.112938i
$466$		0			0
$467$	6.16367	−	6.16367i	0.285221	−	0.285221i	−0.549966	−	0.835187i	$-0.685359\pi$
$467$	6.16367	−	6.16367i	0.285221	−	0.285221i	0.835187	+	0.549966i	$0.185359\pi$
$468$		0			0
$469$			2.97189i			0.137229i
$470$		0			0
$471$	13.9110	−	4.43235i	0.640983	−	0.204232i
$472$		0			0
$473$	−2.73063	−	2.73063i	−0.125555	−	0.125555i
$474$		0			0
$475$	−19.6896	+	0.362393i	−0.903421	+	0.0166277i
$476$		0			0
$477$	0.347881	−	2.04510i	0.0159284	−	0.0936386i
$478$		0			0
$479$	19.2812			0.880979			0.440489	−	0.897758i	$-0.354805\pi$
$479$	19.2812			0.880979			0.440489	+	0.897758i	$0.354805\pi$
$480$		0			0
$481$	16.0169			0.730310
$482$		0			0
$483$	1.67485	+	0.865452i	0.0762083	+	0.0393794i
$484$		0			0
$485$	−23.5184	+	0.216413i	−1.06791	+	0.00982680i
$486$		0			0
$487$	14.8022	+	14.8022i	0.670752	+	0.670752i	0.957889	−	0.287137i	$-0.0927037\pi$
$487$	14.8022	+	14.8022i	0.670752	+	0.670752i	−0.287137	+	0.957889i	$0.592704\pi$
$488$		0			0
$489$	−1.04376	−	3.27585i	−0.0472005	−	0.148139i
$490$		0			0
$491$			4.44013i			0.200380i	0.994968	+	0.100190i	$0.0319451\pi$
$491$			4.44013i			0.200380i	−0.994968	+	0.100190i	$0.968055\pi$
$492$		0			0
$493$	1.70344	−	1.70344i	0.0767192	−	0.0767192i
$494$		0			0
$495$	2.25613	−	14.0436i	0.101405	−	0.631214i
$496$		0			0
$497$	−10.4399	+	10.4399i	−0.468293	+	0.468293i
$498$		0			0
$499$			1.94637i			0.0871317i	0.999051	+	0.0435658i	$0.0138718\pi$
$499$			1.94637i			0.0871317i	−0.999051	+	0.0435658i	$0.986128\pi$
$500$		0			0
$501$	−3.05386	−	9.58457i	−0.136436	−	0.428207i
$502$		0			0
$503$	17.4060	+	17.4060i	0.776093	+	0.776093i	0.979164	−	0.203071i	$-0.0650921\pi$
$503$	17.4060	+	17.4060i	0.776093	+	0.776093i	−0.203071	+	0.979164i	$0.565092\pi$
$504$		0			0
$505$	15.6637	+	15.3780i	0.697024	+	0.684314i
$506$		0			0
$507$	18.4560	+	9.53683i	0.819658	+	0.423545i
$508$		0			0
$509$	6.50231			0.288210			0.144105	−	0.989562i	$-0.453970\pi$
$509$	6.50231			0.288210			0.144105	+	0.989562i	$0.453970\pi$
$510$		0			0
$511$	13.4073			0.593106
$512$		0			0
$513$	−2.85503	−	20.2654i	−0.126053	−	0.894738i
$514$		0			0
$515$	0.287699	+	31.2653i	0.0126775	+	1.37771i
$516$		0			0
$517$	−0.434465	−	0.434465i	−0.0191078	−	0.0191078i
$518$		0			0
$519$	16.1217	−	5.13674i	0.707664	−	0.225478i
$520$		0			0
$521$			17.6022i			0.771167i	0.922673	+	0.385584i	$0.126000\pi$
$521$			17.6022i			0.771167i	−0.922673	+	0.385584i	$0.874000\pi$
$522$		0			0
$523$	−5.02681	+	5.02681i	−0.219807	+	0.219807i	−0.808417	−	0.588610i	$-0.799675\pi$
$523$	−5.02681	+	5.02681i	−0.219807	+	0.219807i	0.588610	+	0.808417i	$0.299675\pi$
$524$		0			0
$525$	3.02644	+	8.92714i	0.132085	+	0.389612i
$526$		0			0
$527$	−1.07925	+	1.07925i	−0.0470128	+	0.0470128i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	−0.497432	−	0.701350i	−0.0215867	−	0.0304360i
$532$		0			0
$533$	18.7953	+	18.7953i	0.814116	+	0.814116i
$534$		0			0
$535$	0.0314728	+	3.42026i	0.00136069	+	0.147871i
$536$		0			0
$537$	−2.52800	+	4.89227i	−0.109091	+	0.211117i
$538$		0			0
$539$	−12.3304			−0.531108
$540$		0			0
$541$	36.4650			1.56775			0.783875	−	0.620918i	$-0.213240\pi$
$541$	36.4650			1.56775			0.783875	+	0.620918i	$0.213240\pi$
$542$		0			0
$543$	12.9949	−	25.1481i	0.557663	−	1.07921i
$544$		0			0
$545$	19.4142	+	19.0602i	0.831613	+	0.816448i
$546$		0			0
$547$	9.82950	+	9.82950i	0.420279	+	0.420279i	0.885300	−	0.465021i	$-0.153953\pi$
$547$	9.82950	+	9.82950i	0.420279	+	0.420279i	−0.465021	+	0.885300i	$0.653953\pi$
$548$		0			0
$549$	−8.54490	−	12.0478i	−0.364687	−	0.514188i
$550$		0			0
$551$		−	4.11489i		−	0.175300i
$552$		0			0
$553$	−3.33904	+	3.33904i	−0.141990	+	0.141990i
$554$		0			0
$555$	5.59450	−	11.0754i	0.237473	−	0.470123i
$556$		0			0
$557$	23.2811	−	23.2811i	0.986454	−	0.986454i	−0.0134559	−	0.999909i	$-0.504283\pi$
$557$	23.2811	−	23.2811i	0.986454	−	0.986454i	0.999909	+	0.0134559i	$0.00428327\pi$
$558$		0			0
$559$		−	9.10523i		−	0.385110i
$560$		0			0
$561$	8.06854	−	2.57082i	0.340654	−	0.108540i
$562$		0			0
$563$	−15.5149	−	15.5149i	−0.653877	−	0.653877i	0.300048	−	0.953924i	$-0.402997\pi$
$563$	−15.5149	−	15.5149i	−0.653877	−	0.653877i	−0.953924	+	0.300048i	$0.902997\pi$
$564$		0			0
$565$	18.3134	−	0.168518i	0.770452	−	0.00708959i
$566$		0			0
$567$	−8.82752	+	4.24692i	−0.370721	+	0.178354i
$568$		0			0
$569$	6.39226			0.267977			0.133989	−	0.990983i	$-0.457221\pi$
$569$	6.39226			0.267977			0.133989	+	0.990983i	$0.457221\pi$
$570$		0			0
$571$	−23.6929			−0.991519			−0.495759	−	0.868460i	$-0.665110\pi$
$571$	−23.6929			−0.991519			−0.495759	+	0.868460i	$0.665110\pi$
$572$		0			0
$573$	−3.60214	−	1.86135i	−0.150482	−	0.0777590i
$574$		0			0
$575$	−3.46987	+	3.60000i	−0.144704	+	0.150130i
$576$		0			0
$577$	6.36275	+	6.36275i	0.264885	+	0.264885i	0.827035	−	0.562150i	$-0.190026\pi$
$577$	6.36275	+	6.36275i	0.264885	+	0.264885i	−0.562150	+	0.827035i	$0.690026\pi$
$578$		0			0
$579$	11.1081	+	34.8628i	0.461636	+	1.44885i
$580$		0			0
$581$		−	19.2734i		−	0.799596i
$582$		0			0
$583$	1.03676	−	1.03676i	0.0429382	−	0.0429382i
$584$		0			0
$585$	27.1756	−	19.6526i	1.12357	−	0.812533i
$586$		0			0
$587$	23.9023	−	23.9023i	0.986553	−	0.986553i	−0.0133579	−	0.999911i	$-0.504252\pi$
$587$	23.9023	−	23.9023i	0.986553	−	0.986553i	0.999911	+	0.0133579i	$0.00425207\pi$
$588$		0			0
$589$			2.60707i			0.107422i
$590$		0			0
$591$	14.2442	+	44.7055i	0.585927	+	1.83894i
$592$		0			0
$593$	24.7761	+	24.7761i	1.01743	+	1.01743i	0.999845	+	0.0175869i	$0.00559836\pi$
$593$	24.7761	+	24.7761i	1.01743	+	1.01743i	0.0175869	+	0.999845i	$0.494402\pi$
$594$		0			0
$595$	−3.93158	+	4.00461i	−0.161179	+	0.164173i
$596$		0			0
$597$	−26.4638	−	13.6747i	−1.08309	−	0.559670i
$598$		0			0
$599$	27.6005			1.12773			0.563864	−	0.825868i	$-0.309314\pi$
$599$	27.6005			1.12773			0.563864	+	0.825868i	$0.309314\pi$
$600$		0			0
$601$	9.94916			0.405835			0.202917	−	0.979196i	$-0.434958\pi$
$601$	9.94916			0.405835			0.202917	+	0.979196i	$0.434958\pi$
$602$		0			0
$603$	1.37363	−	8.07520i	0.0559386	−	0.328848i
$604$		0			0
$605$	−10.1889	+	10.3782i	−0.414238	+	0.421932i
$606$		0			0
$607$	0.0925441	+	0.0925441i	0.00375625	+	0.00375625i	0.708982	−	0.705226i	$-0.249155\pi$
$607$	0.0925441	+	0.0925441i	0.00375625	+	0.00375625i	−0.705226	+	0.708982i	$0.749155\pi$
$608$		0			0
$609$	−1.87667	+	0.597950i	−0.0760465	+	0.0242301i
$610$		0			0
$611$		−	1.44872i		−	0.0586087i
$612$		0			0
$613$	11.0136	−	11.0136i	0.444834	−	0.444834i	−0.448799	−	0.893633i	$-0.648148\pi$
$613$	11.0136	−	11.0136i	0.444834	−	0.444834i	0.893633	+	0.448799i	$0.148148\pi$
$614$		0			0
$615$	19.5615	−	6.43160i	0.788796	−	0.259347i
$616$		0			0
$617$	−23.1932	+	23.1932i	−0.933722	+	0.933722i	−0.997936	−	0.0642143i	$-0.979546\pi$
$617$	−23.1932	+	23.1932i	−0.933722	+	0.933722i	0.0642143	+	0.997936i	$0.479546\pi$
$618$		0			0
$619$		−	19.8708i		−	0.798675i	−0.916804	−	0.399338i	$-0.869240\pi$
$619$		−	19.8708i		−	0.798675i	0.916804	−	0.399338i	$-0.130760\pi$
$620$		0			0
$621$	−4.15088	−	3.12573i	−0.166569	−	0.125431i
$622$		0			0
$623$	−3.38222	−	3.38222i	−0.135506	−	0.135506i
$624$		0			0
$625$	−24.9831	+	0.919953i	−0.999323	+	0.0367981i
$626$		0			0
$627$	6.64023	−	12.8504i	0.265185	−	0.513195i
$628$		0			0
$629$	7.38730			0.294551
$630$		0			0
$631$	−14.9354			−0.594567			−0.297284	−	0.954789i	$-0.596081\pi$
$631$	−14.9354			−0.594567			−0.297284	+	0.954789i	$0.596081\pi$
$632$		0			0
$633$	16.7488	−	32.4129i	0.665707	−	1.28830i
$634$		0			0
$635$	−5.11387	+	0.0470571i	−0.202938	+	0.00186741i
$636$		0			0
$637$	−20.5577	−	20.5577i	−0.814527	−	0.814527i
$638$		0			0
$639$	33.1926	−	23.5418i	1.31308	−	0.931300i
$640$		0			0
$641$			2.26909i			0.0896238i	0.998995	+	0.0448119i	$0.0142688\pi$
$641$			2.26909i			0.0896238i	−0.998995	+	0.0448119i	$0.985731\pi$
$642$		0			0
$643$	−29.5042	+	29.5042i	−1.16353	+	1.16353i	−0.179835	+	0.983697i	$0.557556\pi$
$643$	−29.5042	+	29.5042i	−1.16353	+	1.16353i	−0.983697	+	0.179835i	$0.942444\pi$
$644$		0			0
$645$	−6.29606	−	3.18033i	−0.247907	−	0.125225i
$646$		0			0
$647$	27.6539	−	27.6539i	1.08719	−	1.08719i	0.0913696	−	0.995817i	$-0.470876\pi$
$647$	27.6539	−	27.6539i	1.08719	−	1.08719i	0.995817	−	0.0913696i	$-0.0291245\pi$
$648$		0			0
$649$		−	0.607720i		−	0.0238551i
$650$		0			0
$651$	1.18900	−	0.378843i	0.0466006	−	0.0148480i
$652$		0			0
$653$	29.1124	+	29.1124i	1.13926	+	1.13926i	0.988583	+	0.150674i	$0.0481444\pi$
$653$	29.1124	+	29.1124i	1.13926	+	1.13926i	0.150674	+	0.988583i	$0.451856\pi$
$654$		0			0
$655$	−34.8471	−	34.2117i	−1.36159	−	1.33676i
$656$		0			0
$657$	−36.4304	−	6.19699i	−1.42129	−	0.241767i
$658$		0			0
$659$	31.0210			1.20841			0.604204	−	0.796830i	$-0.293491\pi$
$659$	31.0210			1.20841			0.604204	+	0.796830i	$0.293491\pi$
$660$		0			0
$661$	20.2767			0.788671			0.394335	−	0.918967i	$-0.370975\pi$
$661$	20.2767			0.788671			0.394335	+	0.918967i	$0.370975\pi$
$662$		0			0
$663$	17.7383	+	9.16601i	0.688900	+	0.355978i
$664$		0			0
$665$	0.0882041	+	9.58546i	0.00342041	+	0.371708i
$666$		0			0
$667$	−0.738759	−	0.738759i	−0.0286049	−	0.0286049i
$668$		0			0
$669$	−14.0715	−	44.1635i	−0.544035	−	1.70746i
$670$		0			0
$671$		−	10.4394i		−	0.403010i
$672$		0			0
$673$	0.338766	−	0.338766i	0.0130585	−	0.0130585i	−0.700547	−	0.713606i	$-0.747061\pi$
$673$	0.338766	−	0.338766i	0.0130585	−	0.0130585i	0.713606	+	0.700547i	$0.247061\pi$
$674$		0			0
$675$	−4.09725	−	25.6557i	−0.157703	−	0.987487i
$676$		0			0
$677$	−12.1120	+	12.1120i	−0.465501	+	0.465501i	−0.900453	−	0.434952i	$-0.856765\pi$
$677$	−12.1120	+	12.1120i	−0.465501	+	0.465501i	0.434952	+	0.900453i	$0.356765\pi$
$678$		0			0
$679$			11.4484i			0.439351i
$680$		0			0
$681$	2.92436	+	9.17812i	0.112062	+	0.351706i
$682$		0			0
$683$	19.6497	+	19.6497i	0.751877	+	0.751877i	0.974829	−	0.222953i	$-0.0715695\pi$
$683$	19.6497	+	19.6497i	0.751877	+	0.751877i	−0.222953	+	0.974829i	$0.571570\pi$
$684$		0			0
$685$	0.396221	+	43.0588i	0.0151388	+	1.64519i
$686$		0			0
$687$	20.6059	+	10.6478i	0.786164	+	0.406238i
$688$		0			0
$689$	3.45705			0.131703
$690$		0			0
$691$	−11.8202			−0.449661			−0.224831	−	0.974398i	$-0.572183\pi$
$691$	−11.8202			−0.449661			−0.224831	+	0.974398i	$0.572183\pi$
$692$		0			0
$693$	−6.82557	−	1.16106i	−0.259282	−	0.0441051i
$694$		0			0
$695$	4.08928	+	4.01471i	0.155115	+	0.152287i
$696$		0			0
$697$	8.66874	+	8.66874i	0.328352	+	0.328352i
$698$		0			0
$699$	−14.6629	+	4.67193i	−0.554602	+	0.176709i
$700$		0			0
$701$		−	31.9281i		−	1.20591i	−0.797776	−	0.602953i	$-0.793991\pi$
$701$		−	31.9281i		−	1.20591i	0.797776	−	0.602953i	$-0.206009\pi$
$702$		0			0
$703$	8.92250	−	8.92250i	0.336519	−	0.336519i
$704$		0			0
$705$	−1.00175	−	0.506016i	−0.0377282	−	0.0190577i
$706$		0			0
$707$	7.55536	−	7.55536i	0.284148	−	0.284148i
$708$		0			0
$709$		−	27.1129i		−	1.01825i	−0.860694	−	0.509123i	$-0.829970\pi$
$709$		−	27.1129i		−	1.01825i	0.860694	−	0.509123i	$-0.170030\pi$
$710$		0			0
$711$	10.6162	−	7.52950i	0.398137	−	0.282378i
$712$		0			0
$713$	0.468055	+	0.468055i	0.0175288	+	0.0175288i
$714$		0			0
$715$	23.7023	−	0.218106i	0.886417	−	0.00815669i
$716$		0			0
$717$	−15.9718	+	30.9092i	−0.596479	+	1.15433i
$718$		0			0
$719$	−37.5274			−1.39954			−0.699768	−	0.714370i	$-0.746713\pi$
$719$	−37.5274			−1.39954			−0.699768	+	0.714370i	$0.746713\pi$
$720$		0			0
$721$	15.2195			0.566806
$722$		0			0
$723$	5.48084	−	10.6067i	0.203835	−	0.394467i
$724$		0			0
$725$	−0.0961295	−	5.22293i	−0.00357016	−	0.193975i
$726$		0			0
$727$	−21.4537	−	21.4537i	−0.795675	−	0.795675i	0.186735	−	0.982410i	$-0.440209\pi$
$727$	−21.4537	−	21.4537i	−0.795675	−	0.795675i	−0.982410	+	0.186735i	$0.940209\pi$
$728$		0			0
$729$	25.9491	−	7.45958i	0.961077	−	0.276281i
$730$		0			0
$731$		−	4.19949i		−	0.155324i
$732$		0			0
$733$	−17.4671	+	17.4671i	−0.645164	+	0.645164i	−0.951820	−	0.306657i	$-0.900790\pi$
$733$	−17.4671	+	17.4671i	−0.645164	+	0.645164i	0.306657	+	0.951820i	$0.400790\pi$
$734$		0			0
$735$	−21.3957	+	7.03467i	−0.789194	+	0.259478i
$736$		0			0
$737$	4.09371	−	4.09371i	0.150794	−	0.150794i
$738$		0			0
$739$			47.3324i			1.74115i	0.492035	+	0.870575i	$0.336253\pi$
$739$			47.3324i			1.74115i	−0.492035	+	0.870575i	$0.663747\pi$
$740$		0			0
$741$	32.4955	−	10.3538i	1.19375	−	0.380357i
$742$		0			0
$743$	−21.2979	−	21.2979i	−0.781345	−	0.781345i	0.198713	−	0.980058i	$-0.436324\pi$
$743$	−21.2979	−	21.2979i	−0.781345	−	0.781345i	−0.980058	+	0.198713i	$0.936324\pi$
$744$		0			0
$745$	−7.30966	+	7.44544i	−0.267805	+	0.272780i
$746$		0			0
$747$	−8.90833	+	52.3697i	−0.325939	+	1.91611i
$748$		0			0
$749$	1.66494			0.0608356
$750$		0			0
$751$	0.520366			0.0189884			0.00949422	−	0.999955i	$-0.496978\pi$
$751$	0.520366			0.0189884			0.00949422	+	0.999955i	$0.496978\pi$
$752$		0			0
$753$	5.01719	+	2.59255i	0.182837	+	0.0944779i
$754$		0			0
$755$	−24.8525	+	25.3141i	−0.904474	+	0.921274i
$756$		0			0
$757$	27.0141	+	27.0141i	0.981843	+	0.981843i	0.999838	−	0.0179948i	$-0.00572822\pi$
$757$	27.0141	+	27.0141i	0.981843	+	0.981843i	−0.0179948	+	0.999838i	$0.505728\pi$
$758$		0			0
$759$	−1.11493	−	3.49921i	−0.0404693	−	0.127013i
$760$		0			0
$761$		−	29.2267i		−	1.05947i	−0.848165	−	0.529733i	$-0.822292\pi$
$761$		−	29.2267i		−	1.05947i	0.848165	−	0.529733i	$-0.177708\pi$
$762$		0			0
$763$	9.36442	−	9.36442i	0.339015	−	0.339015i
$764$		0			0
$765$	12.5338	−	9.06410i	0.453162	−	0.327713i
$766$		0			0
$767$	1.01321	−	1.01321i	0.0365851	−	0.0365851i
$768$		0			0
$769$			35.7070i			1.28763i	0.765183	+	0.643813i	$0.222649\pi$
$769$			35.7070i			1.28763i	−0.765183	+	0.643813i	$0.777351\pi$
$770$		0			0
$771$	−7.53505	−	23.6488i	−0.271368	−	0.851691i
$772$		0			0
$773$	−30.1187	−	30.1187i	−1.08329	−	1.08329i	−0.996200	−	0.0870940i	$-0.972242\pi$
$773$	−30.1187	−	30.1187i	−1.08329	−	1.08329i	−0.0870940	−	0.996200i	$-0.527758\pi$
$774$		0			0
$775$	0.0609047	+	3.30909i	0.00218776	+	0.118866i
$776$		0			0
$777$	−5.36583	−	2.77271i	−0.192498	−	0.0994703i
$778$		0			0
$779$	20.9405			0.750271
$780$		0			0
$781$	28.7614			1.02917
$782$		0			0
$783$	5.37566	−	0.757335i	0.192111	−	0.0270650i
$784$		0			0
$785$	18.8477	−	0.173434i	0.672705	−	0.00619014i
$786$		0			0
$787$	−21.4014	−	21.4014i	−0.762878	−	0.762878i	0.213964	−	0.976842i	$-0.431363\pi$
$787$	−21.4014	−	21.4014i	−0.762878	−	0.762878i	−0.976842	+	0.213964i	$0.931363\pi$
$788$		0			0
$789$	−7.39666	+	2.35675i	−0.263328	+	0.0839024i
$790$		0			0
$791$		−	8.91474i		−	0.316972i
$792$		0			0
$793$	17.4050	−	17.4050i	0.618071	−	0.618071i
$794$		0			0
$795$	1.20750	−	2.39047i	0.0428256	−	0.0847813i
$796$		0			0
$797$	0.786685	−	0.786685i	0.0278658	−	0.0278658i	−0.693037	−	0.720902i	$-0.743728\pi$
$797$	0.786685	−	0.786685i	0.0278658	−	0.0278658i	0.720902	+	0.693037i	$0.243728\pi$
$798$		0			0
$799$		−	0.668173i		−	0.0236383i
$800$		0			0
$801$	7.62687	+	10.7535i	0.269482	+	0.379955i
$802$		0			0
$803$	−18.4683	−	18.4683i	−0.651733	−	0.651733i
$804$		0			0
$805$	1.73674	+	1.70507i	0.0612121	+	0.0600959i
$806$		0			0
$807$	−15.6233	+	30.2346i	−0.549965	+	1.06431i
$808$		0			0
$809$	6.42050			0.225733			0.112866	−	0.993610i	$-0.463997\pi$
$809$	6.42050			0.225733			0.112866	+	0.993610i	$0.463997\pi$
$810$		0			0
$811$	20.4432			0.717859			0.358930	−	0.933365i	$-0.383142\pi$
$811$	20.4432			0.717859			0.358930	+	0.933365i	$0.383142\pi$
$812$		0			0
$813$	−2.25580	+	4.36549i	−0.0791142	+	0.153104i
$814$		0			0
$815$	−0.0408416	−	4.43840i	−0.00143062	−	0.155470i
$816$		0			0
$817$	−5.07222	−	5.07222i	−0.177454	−	0.177454i
$818$		0			0
$819$	−9.44408	−	13.3156i	−0.330003	−	0.465285i
$820$		0			0
$821$			46.2281i			1.61337i	0.590981	+	0.806686i	$0.298741\pi$
$821$			46.2281i			1.61337i	−0.590981	+	0.806686i	$0.701259\pi$
$822$		0			0
$823$	28.1291	−	28.1291i	0.980520	−	0.980520i	−0.0192940	−	0.999814i	$-0.506142\pi$
$823$	28.1291	−	28.1291i	0.980520	−	0.980520i	0.999814	+	0.0192940i	$0.00614184\pi$
$824$		0			0
$825$	8.12808	−	16.4658i	0.282984	−	0.573266i
$826$		0			0
$827$	11.6229	−	11.6229i	0.404168	−	0.404168i	−0.475531	−	0.879699i	$-0.657744\pi$
$827$	11.6229	−	11.6229i	0.404168	−	0.404168i	0.879699	+	0.475531i	$0.157744\pi$
$828$		0			0
$829$			37.1278i			1.28950i	0.764393	+	0.644751i	$0.223039\pi$
$829$			37.1278i			1.28950i	−0.764393	+	0.644751i	$0.776961\pi$
$830$		0			0
$831$	32.8293	−	10.4602i	1.13884	−	0.362859i
$832$		0			0
$833$	−9.48159	−	9.48159i	−0.328517	−	0.328517i
$834$		0			0
$835$	−0.119495	−	12.9860i	−0.00413530	−	0.449399i
$836$		0			0
$837$	−3.40585	+	0.479824i	−0.117724	+	0.0165852i
$838$		0			0
$839$	−48.5834			−1.67729			−0.838643	−	0.544682i	$-0.816651\pi$
$839$	−48.5834			−1.67729			−0.838643	+	0.544682i	$0.816651\pi$
$840$		0			0
$841$	−27.9085			−0.962361
$842$		0			0
$843$	28.4148	+	14.6829i	0.978656	+	0.505705i
$844$		0			0
$845$	19.1380	+	18.7890i	0.658367	+	0.646361i
$846$		0			0
$847$	5.00589	+	5.00589i	0.172004	+	0.172004i
$848$		0			0
$849$	−2.81851	−	8.84590i	−0.0967309	−	0.303591i
$850$		0			0
$851$		−	3.20377i		−	0.109824i
$852$		0			0
$853$	2.19911	−	2.19911i	0.0752962	−	0.0752962i	−0.668456	−	0.743752i	$-0.733044\pi$
$853$	2.19911	−	2.19911i	0.0752962	−	0.0752962i	0.743752	+	0.668456i	$0.233044\pi$
$854$		0			0
$855$	4.19081	−	26.0864i	0.143323	−	0.892135i
$856$		0			0
$857$	−14.8471	+	14.8471i	−0.507169	+	0.507169i	−0.913656	−	0.406488i	$-0.866753\pi$
$857$	−14.8471	+	14.8471i	−0.507169	+	0.507169i	0.406488	+	0.913656i	$0.366753\pi$
$858$		0			0
$859$			0.455728i			0.0155492i	0.999970	+	0.00777462i	$0.00247476\pi$
$859$			0.455728i			0.0155492i	−0.999970	+	0.00777462i	$0.997525\pi$
$860$		0			0
$861$	−3.04294	−	9.55029i	−0.103703	−	0.325473i
$862$		0			0
$863$	3.62428	+	3.62428i	0.123372	+	0.123372i	0.766097	−	0.642725i	$-0.222196\pi$
$863$	3.62428	+	3.62428i	0.123372	+	0.123372i	−0.642725	+	0.766097i	$0.722196\pi$
$864$		0			0
$865$	21.8430	−	0.200997i	0.742685	−	0.00683409i
$866$		0			0
$867$	−17.9776	−	9.28965i	−0.610552	−	0.315493i
$868$		0			0
$869$	9.19892			0.312052
$870$		0			0
$871$	13.6504			0.462526
$872$		0			0
$873$	5.29157	−	31.1077i	0.179092	−	1.05284i
$874$		0			0
$875$	0.335885	+	12.1645i	0.0113550	+	0.411236i
$876$		0			0
$877$	4.70945	+	4.70945i	0.159027	+	0.159027i	0.782135	−	0.623109i	$-0.214131\pi$
$877$	4.70945	+	4.70945i	0.159027	+	0.159027i	−0.623109	+	0.782135i	$0.714131\pi$
$878$		0			0
$879$	19.0272	−	6.06251i	0.641773	−	0.204483i
$880$		0			0
$881$		−	17.4607i		−	0.588266i	−0.955764	−	0.294133i	$-0.904969\pi$
$881$		−	17.4607i		−	0.588266i	0.955764	−	0.294133i	$-0.0950309\pi$
$882$		0			0
$883$	−17.5302	+	17.5302i	−0.589938	+	0.589938i	−0.937615	−	0.347676i	$-0.886971\pi$
$883$	−17.5302	+	17.5302i	−0.589938	+	0.589938i	0.347676	+	0.937615i	$0.386971\pi$
$884$		0			0
$885$	−0.346713	−	1.05452i	−0.0116546	−	0.0354472i
$886$		0			0
$887$	−10.8924	+	10.8924i	−0.365732	+	0.365732i	−0.865918	−	0.500186i	$-0.833265\pi$
$887$	−10.8924	+	10.8924i	−0.365732	+	0.365732i	0.500186	+	0.865918i	$0.333265\pi$
$888$		0			0
$889$			2.48937i			0.0834907i
$890$		0			0
$891$	18.0098	+	6.30967i	0.603350	+	0.211382i
$892$		0			0
$893$	−0.807030	−	0.807030i	−0.0270062	−	0.0270062i
$894$		0			0
$895$	−4.98055	+	5.07306i	−0.166481	+	0.169574i
$896$		0			0
$897$	3.97517	−	7.69287i	0.132727	−	0.256858i
$898$		0			0
$899$	−0.691560			−0.0230648
$900$		0			0
$901$	1.59445			0.0531189
$902$		0			0
$903$	−1.57621	+	3.05034i	−0.0524531	+	0.101509i
$904$		0			0
$905$	25.6019	−	26.0774i	0.851035	−	0.866842i
$906$		0			0
$907$	−12.4788	−	12.4788i	−0.414352	−	0.414352i	0.468899	−	0.883252i	$-0.344651\pi$
$907$	−12.4788	−	12.4788i	−0.414352	−	0.414352i	−0.883252	+	0.468899i	$0.844651\pi$
$908$		0			0
$909$	−24.0215	+	17.0372i	−0.796744	+	0.565090i
$910$		0			0
$911$			11.4011i			0.377736i	0.982002	+	0.188868i	$0.0604819\pi$
$911$			11.4011i			0.377736i	−0.982002	+	0.188868i	$0.939518\pi$
$912$		0			0
$913$	−26.5487	+	26.5487i	−0.878635	+	0.878635i
$914$		0			0
$915$	−5.95585	−	18.1145i	−0.196894	−	0.598848i
$916$		0			0
$917$	−16.8085	+	16.8085i	−0.555065	+	0.555065i
$918$		0			0
$919$		−	41.7932i		−	1.37863i	−0.724461	−	0.689316i	$-0.757911\pi$
$919$		−	41.7932i		−	1.37863i	0.724461	−	0.689316i	$-0.242089\pi$
$920$		0			0
$921$	−6.50456	+	2.07250i	−0.214332	+	0.0682912i
$922$		0			0
$923$	47.9522	+	47.9522i	1.57837	+	1.57837i
$924$		0			0
$925$	11.1167	−	11.5336i	0.365514	−	0.379221i
$926$		0			0
$927$	−41.3545	−	7.03460i	−1.35826	−	0.231047i
$928$		0			0
$929$	−20.4189			−0.669922			−0.334961	−	0.942232i	$-0.608723\pi$
$929$	−20.4189			−0.669922			−0.334961	+	0.942232i	$0.608723\pi$
$930$		0			0
$931$	−22.9040			−0.750649
$932$		0			0
$933$	26.5721	+	13.7307i	0.869932	+	0.449523i
$934$		0			0
$935$	10.9319	−	0.100594i	0.357512	−	0.00328978i
$936$		0			0
$937$	17.2594	+	17.2594i	0.563839	+	0.563839i	0.930396	−	0.366557i	$-0.119463\pi$
$937$	17.2594	+	17.2594i	0.563839	+	0.563839i	−0.366557	+	0.930396i	$0.619463\pi$
$938$		0			0
$939$	6.66558	+	20.9200i	0.217523	+	0.682697i
$940$		0			0
$941$		−	45.2803i		−	1.47609i	−0.674749	−	0.738047i	$-0.735748\pi$
$941$		−	45.2803i		−	1.47609i	0.674749	−	0.738047i	$-0.264252\pi$
$942$		0			0
$943$	3.75951	−	3.75951i	0.122426	−	0.122426i
$944$		0			0
$945$	−12.5061	+	1.87941i	−0.406825	+	0.0611372i
$946$		0			0
$947$	22.1761	−	22.1761i	0.720628	−	0.720628i	−0.248105	−	0.968733i	$-0.579808\pi$
$947$	22.1761	−	22.1761i	0.720628	−	0.720628i	0.968733	+	0.248105i	$0.0798079\pi$
$948$		0			0
$949$		−	61.5822i		−	1.99904i
$950$		0			0
$951$	0.390819	+	1.22659i	0.0126732	+	0.0397749i
$952$		0			0
$953$	35.0491	+	35.0491i	1.13535	+	1.13535i	0.989273	+	0.146077i	$0.0466647\pi$
$953$	35.0491	+	35.0491i	1.13535	+	1.13535i	0.146077	+	0.989273i	$0.453335\pi$
$954$		0			0
$955$	−3.73526	−	3.66714i	−0.120870	−	0.118666i
$956$		0			0
$957$	3.40874	+	1.76141i	0.110189	+	0.0569383i
$958$		0			0
$959$	20.9605			0.676849
$960$		0			0
$961$	−30.5618			−0.985866
$962$		0			0
$963$	−4.52398	−	0.769550i	−0.145783	−	0.0247984i
$964$		0			0
$965$	0.434651	+	47.2351i	0.0139919	+	1.52055i
$966$		0			0
$967$	−2.54533	−	2.54533i	−0.0818523	−	0.0818523i	0.664995	−	0.746848i	$-0.268434\pi$
$967$	−2.54533	−	2.54533i	−0.0818523	−	0.0818523i	−0.746848	+	0.664995i	$0.768434\pi$
$968$		0			0
$969$	14.9875	−	4.77536i	0.481468	−	0.153407i
$970$		0			0
$971$			53.6724i			1.72243i	0.508242	+	0.861214i	$0.330296\pi$
$971$			53.6724i			1.72243i	−0.508242	+	0.861214i	$0.669704\pi$
$972$		0			0
$973$	1.97246	−	1.97246i	0.0632341	−	0.0632341i
$974$		0			0
$975$	41.0039	−	13.9010i	1.31318	−	0.445188i
$976$		0			0
$977$	2.97649	−	2.97649i	0.0952264	−	0.0952264i	−0.657889	−	0.753115i	$-0.728550\pi$
$977$	2.97649	−	2.97649i	0.0952264	−	0.0952264i	0.753115	+	0.657889i	$0.228550\pi$
$978$		0			0
$979$			9.31787i			0.297801i
$980$		0			0
$981$	−29.7733	+	21.1167i	−0.950588	+	0.674203i
$982$		0			0
$983$	−28.1628	−	28.1628i	−0.898254	−	0.898254i	0.0970278	−	0.995282i	$-0.469066\pi$
$983$	−28.1628	−	28.1628i	−0.898254	−	0.898254i	−0.995282	+	0.0970278i	$0.969066\pi$
$984$		0			0
$985$	0.557363	+	60.5707i	0.0177591	+	1.92994i
$986$		0			0
$987$	−0.250788	+	0.485333i	−0.00798268	+	0.0154483i
$988$		0			0
$989$	−1.82126			−0.0579128
$990$		0			0
$991$	8.52755			0.270886			0.135443	−	0.990785i	$-0.456754\pi$
$991$	8.52755			0.270886			0.135443	+	0.990785i	$0.456754\pi$
$992$		0			0
$993$	27.9114	−	54.0151i	0.885743	−	1.71412i
$994$		0			0
$995$	−27.4417	−	26.9413i	−0.869962	−	0.854097i
$996$		0			0
$997$	39.7830	+	39.7830i	1.25994	+	1.25994i	0.951121	+	0.308818i	$0.0999335\pi$
$997$	39.7830	+	39.7830i	1.25994	+	1.25994i	0.308818	+	0.951121i	$0.400066\pi$
$998$		0			0
$999$	13.2985	+	10.0141i	0.420745	+	0.316833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.14	yes	80
3.2	odd	2	inner	1380.2.r.c.737.5	✓	80
5.3	odd	4	inner	1380.2.r.c.1013.5	yes	80
15.8	even	4	inner	1380.2.r.c.1013.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.5	✓	80	3.2	odd	2	inner
1380.2.r.c.737.14	yes	80	1.1	even	1	trivial
1380.2.r.c.1013.5	yes	80	5.3	odd	4	inner
1380.2.r.c.1013.14	yes	80	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795128 + 1.53876i) q^{3} +(-1.56652 + 1.59562i) q^{5} +(0.769646 + 0.769646i) q^{7} +(-1.73554 - 2.44702i) q^{9} +O(q^{10})\)	\(q+(-0.795128 + 1.53876i) q^{3} +(-1.56652 + 1.59562i) q^{5} +(0.769646 + 0.769646i) q^{7} +(-1.73554 - 2.44702i) q^{9} -2.12034i q^{11} +(3.53512 - 3.53512i) q^{13} +(-1.20969 - 3.67922i) q^{15} +(1.63046 - 1.63046i) q^{17} -3.93859i q^{19} +(-1.79626 + 0.572331i) q^{21} +(-0.707107 - 0.707107i) q^{23} +(-0.0920108 - 4.99915i) q^{25} +(5.14534 - 0.724887i) q^{27} +1.04476 q^{29} -0.661930 q^{31} +(3.26269 + 1.68594i) q^{33} +(-2.43373 + 0.0223949i) q^{35} +(2.26541 + 2.26541i) q^{37} +(2.62881 + 8.25055i) q^{39} +5.31675i q^{41} +(1.28783 - 1.28783i) q^{43} +(6.62328 + 1.06404i) q^{45} +(0.204904 - 0.204904i) q^{47} -5.81529i q^{49} +(1.21245 + 3.80530i) q^{51} +(0.488959 + 0.488959i) q^{53} +(3.38326 + 3.32156i) q^{55} +(6.06053 + 3.13168i) q^{57} +0.286614 q^{59} +4.92347 q^{61} +(0.547582 - 3.21909i) q^{63} +(0.102863 + 11.1785i) q^{65} +(1.93068 + 1.93068i) q^{67} +(1.65031 - 0.525825i) q^{69} +13.5645i q^{71} +(8.71007 - 8.71007i) q^{73} +(7.76564 + 3.83338i) q^{75} +(1.63191 - 1.63191i) q^{77} +4.33841i q^{79} +(-2.97578 + 8.49381i) q^{81} +(-12.5210 - 12.5210i) q^{83} +(0.0474424 + 5.15574i) q^{85} +(-0.830720 + 1.60764i) q^{87} -4.39452 q^{89} +5.44157 q^{91} +(0.526319 - 1.01855i) q^{93} +(6.28449 + 6.16989i) q^{95} +(7.43748 + 7.43748i) q^{97} +(-5.18851 + 3.67994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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