LMFDB - Embedded newform 1260.2.c.d.811.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.11
Root			$-0.449546 - 1.34086i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.d.811.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.449546 - 1.34086i) q^{2} +(-1.59582 - 1.20556i) q^{4} -1.00000i q^{5} +(1.40015 + 2.24490i) q^{7} +(-2.33388 + 1.59781i) q^{8} +O(q^{10})$	\(q+(0.449546 - 1.34086i) q^{2} +(-1.59582 - 1.20556i) q^{4} -1.00000i q^{5} +(1.40015 + 2.24490i) q^{7} +(-2.33388 + 1.59781i) q^{8} +(-1.34086 - 0.449546i) q^{10} -3.99156i q^{11} -2.50547i q^{13} +(3.63953 - 0.868219i) q^{14} +(1.09326 + 3.84770i) q^{16} +1.07705i q^{17} -7.78975 q^{19} +(-1.20556 + 1.59582i) q^{20} +(-5.35213 - 1.79439i) q^{22} -8.10651i q^{23} -1.00000 q^{25} +(-3.35948 - 1.12632i) q^{26} +(0.471978 - 5.27041i) q^{28} +5.99783 q^{29} -6.32559 q^{31} +(5.65070 + 0.263812i) q^{32} +(1.44417 + 0.484184i) q^{34} +(2.24490 - 1.40015i) q^{35} +3.05357 q^{37} +(-3.50185 + 10.4450i) q^{38} +(1.59781 + 2.33388i) q^{40} -9.32685i q^{41} -8.13000i q^{43} +(-4.81206 + 6.36980i) q^{44} +(-10.8697 - 3.64425i) q^{46} -9.01476 q^{47} +(-3.07916 + 6.28639i) q^{49} +(-0.449546 + 1.34086i) q^{50} +(-3.02049 + 3.99827i) q^{52} -2.86521 q^{53} -3.99156 q^{55} +(-6.85471 - 3.00215i) q^{56} +(2.69630 - 8.04226i) q^{58} -9.68276 q^{59} +3.21235i q^{61} +(-2.84365 + 8.48173i) q^{62} +(2.89399 - 7.45821i) q^{64} -2.50547 q^{65} +7.79060i q^{67} +(1.29845 - 1.71877i) q^{68} +(-0.868219 - 3.63953i) q^{70} +5.84987i q^{71} -5.73252i q^{73} +(1.37272 - 4.09441i) q^{74} +(12.4310 + 9.39100i) q^{76} +(8.96067 - 5.58879i) q^{77} +2.81801i q^{79} +(3.84770 - 1.09326i) q^{80} +(-12.5060 - 4.19285i) q^{82} +12.5103 q^{83} +1.07705 q^{85} +(-10.9012 - 3.65481i) q^{86} +(6.37777 + 9.31583i) q^{88} -3.51385i q^{89} +(5.62453 - 3.50803i) q^{91} +(-9.77288 + 12.9365i) q^{92} +(-4.05255 + 12.0875i) q^{94} +7.78975i q^{95} +12.0136i q^{97} +(7.04495 + 6.95475i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8 + 2 * q^14 + 6 * q^16 - 24 * q^19 - 12 * q^22 - 16 * q^25 + 12 * q^26 + 14 * q^28 - 16 * q^29 + 8 * q^31 + 18 * q^32 + 24 * q^34 + 24 * q^37 - 28 * q^38 + 12 * q^40 + 8 * q^44 - 20 * q^46 - 16 * q^47 - 16 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 - 2 * q^56 - 32 * q^58 - 8 * q^59 - 16 * q^62 - 2 * q^64 + 8 * q^65 - 4 * q^68 + 4 * q^74 + 16 * q^76 + 8 * q^77 + 16 * q^80 - 4 * q^82 - 8 * q^83 - 64 * q^86 - 52 * q^88 + 16 * q^91 - 64 * q^92 + 16 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	0.449546	−	1.34086i	0.317877	−	0.948132i
$2$	0.449546	−	1.34086i	0.317877	−	0.948132i
$3$		0			0
$3$		0			0
$4$	−1.59582	−	1.20556i	−0.797908	−	0.602779i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	1.40015	+	2.24490i	0.529207	+	0.848493i
$7$	1.40015	+	2.24490i	0.529207	+	0.848493i
$8$	−2.33388	+	1.59781i	−0.825151	+	0.564912i
$9$		0			0
$10$	−1.34086	−	0.449546i	−0.424017	−	0.142159i
$11$		−	3.99156i		−	1.20350i	−0.798684	−	0.601751i	$-0.794470\pi$
$11$		−	3.99156i		−	1.20350i	0.798684	−	0.601751i	$-0.205530\pi$
$12$		0			0
$13$		−	2.50547i		−	0.694892i	−0.937700	−	0.347446i	$-0.887049\pi$
$13$		−	2.50547i		−	0.694892i	0.937700	−	0.347446i	$-0.112951\pi$
$14$	3.63953	−	0.868219i	0.972706	−	0.232041i
$15$		0			0
$16$	1.09326	+	3.84770i	0.273315	+	0.961925i
$17$			1.07705i			0.261223i	0.991434	+	0.130611i	$0.0416940\pi$
$17$			1.07705i			0.261223i	−0.991434	+	0.130611i	$0.958306\pi$
$18$		0			0
$19$	−7.78975			−1.78709			−0.893546	−	0.448973i	$-0.851790\pi$
$19$	−7.78975			−1.78709			−0.893546	+	0.448973i	$0.851790\pi$
$20$	−1.20556	+	1.59582i	−0.269571	+	0.356835i
$21$		0			0
$22$	−5.35213	−	1.79439i	−1.14108	−	0.382566i
$23$		−	8.10651i		−	1.69033i	−0.534509	−	0.845163i	$-0.679504\pi$
$23$		−	8.10651i		−	1.69033i	0.534509	−	0.845163i	$-0.320496\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.35948	−	1.12632i	−0.658849	−	0.220890i
$27$		0			0
$28$	0.471978	−	5.27041i	0.0891955	−	0.996014i
$29$	5.99783			1.11377			0.556885	−	0.830590i	$-0.311997\pi$
$29$	5.99783			1.11377			0.556885	+	0.830590i	$0.311997\pi$
$30$		0			0
$31$	−6.32559			−1.13611			−0.568055	−	0.822991i	$-0.692304\pi$
$31$	−6.32559			−1.13611			−0.568055	+	0.822991i	$0.692304\pi$
$32$	5.65070	+	0.263812i	0.998912	+	0.0466358i
$33$		0			0
$34$	1.44417	+	0.484184i	0.247674	+	0.0830368i
$35$	2.24490	−	1.40015i	0.379458	−	0.236668i
$36$		0			0
$37$	3.05357			0.502003			0.251002	−	0.967987i	$-0.419240\pi$
$37$	3.05357			0.502003			0.251002	+	0.967987i	$0.419240\pi$
$38$	−3.50185	+	10.4450i	−0.568076	+	1.69440i
$39$		0			0
$40$	1.59781	+	2.33388i	0.252636	+	0.369019i
$41$		−	9.32685i		−	1.45661i	−0.685254	−	0.728305i	$-0.740309\pi$
$41$		−	9.32685i		−	1.45661i	0.685254	−	0.728305i	$-0.259691\pi$
$42$		0			0
$43$		−	8.13000i		−	1.23981i	−0.784676	−	0.619906i	$-0.787171\pi$
$43$		−	8.13000i		−	1.23981i	0.784676	−	0.619906i	$-0.212829\pi$
$44$	−4.81206	+	6.36980i	−0.725446	+	0.960284i
$45$		0			0
$46$	−10.8697	−	3.64425i	−1.60265	−	0.537316i
$47$	−9.01476			−1.31494			−0.657469	−	0.753482i	$-0.728373\pi$
$47$	−9.01476			−1.31494			−0.657469	+	0.753482i	$0.728373\pi$
$48$		0			0
$49$	−3.07916	+	6.28639i	−0.439880	+	0.898056i
$50$	−0.449546	+	1.34086i	−0.0635755	+	0.189626i
$51$		0			0
$52$	−3.02049	+	3.99827i	−0.418866	+	0.554460i
$53$	−2.86521			−0.393566			−0.196783	−	0.980447i	$-0.563049\pi$
$53$	−2.86521			−0.393566			−0.196783	+	0.980447i	$0.563049\pi$
$54$		0			0
$55$	−3.99156			−0.538222
$56$	−6.85471	−	3.00215i	−0.916000	−	0.401179i
$57$		0			0
$58$	2.69630	−	8.04226i	0.354042	−	1.05600i
$59$	−9.68276			−1.26059			−0.630294	−	0.776356i	$-0.717066\pi$
$59$	−9.68276			−1.26059			−0.630294	+	0.776356i	$0.717066\pi$
$60$		0			0
$61$			3.21235i			0.411299i	0.978626	+	0.205649i	$0.0659307\pi$
$61$			3.21235i			0.411299i	−0.978626	+	0.205649i	$0.934069\pi$
$62$	−2.84365	+	8.48173i	−0.361143	+	1.07718i
$63$		0			0
$64$	2.89399	−	7.45821i	0.361748	−	0.932276i
$65$	−2.50547			−0.310765
$66$		0			0
$67$			7.79060i			0.951773i	0.879507	+	0.475887i	$0.157873\pi$
$67$			7.79060i			0.951773i	−0.879507	+	0.475887i	$0.842127\pi$
$68$	1.29845	−	1.71877i	0.157460	−	0.208432i
$69$		0			0
$70$	−0.868219	−	3.63953i	−0.103772	−	0.435007i
$71$			5.84987i			0.694252i	0.937819	+	0.347126i	$0.112842\pi$
$71$			5.84987i			0.694252i	−0.937819	+	0.347126i	$0.887158\pi$
$72$		0			0
$73$		−	5.73252i		−	0.670941i	−0.942051	−	0.335470i	$-0.891105\pi$
$73$		−	5.73252i		−	0.670941i	0.942051	−	0.335470i	$-0.108895\pi$
$74$	1.37272	−	4.09441i	0.159575	−	0.475965i
$75$		0			0
$76$	12.4310	+	9.39100i	1.42593	+	1.07722i
$77$	8.96067	−	5.58879i	1.02116	−	0.636901i
$78$		0			0
$79$			2.81801i			0.317050i	0.987355	+	0.158525i	$0.0506739\pi$
$79$			2.81801i			0.317050i	−0.987355	+	0.158525i	$0.949326\pi$
$80$	3.84770	−	1.09326i	0.430186	−	0.122230i
$81$		0			0
$82$	−12.5060	−	4.19285i	−1.38106	−	0.463023i
$83$	12.5103			1.37318			0.686590	−	0.727045i	$-0.259107\pi$
$83$	12.5103			1.37318			0.686590	+	0.727045i	$0.259107\pi$
$84$		0			0
$85$	1.07705			0.116822
$86$	−10.9012	−	3.65481i	−1.17551	−	0.394108i
$87$		0			0
$88$	6.37777	+	9.31583i	0.679873	+	0.993071i
$89$		−	3.51385i		−	0.372467i	−0.982505	−	0.186234i	$-0.940372\pi$
$89$		−	3.51385i		−	0.372467i	0.982505	−	0.186234i	$-0.0596282\pi$
$90$		0			0
$91$	5.62453	−	3.50803i	0.589611	−	0.367741i
$92$	−9.77288	+	12.9365i	−1.01889	+	1.34872i
$93$		0			0
$94$	−4.05255	+	12.0875i	−0.417989	+	1.24673i
$95$			7.78975i			0.799211i
$96$		0			0
$97$			12.0136i			1.21980i	0.792479	+	0.609899i	$0.208790\pi$
$97$			12.0136i			1.21980i	−0.792479	+	0.609899i	$0.791210\pi$
$98$	7.04495	+	6.95475i	0.711648	+	0.702536i
$99$		0			0
$100$	1.59582	+	1.20556i	0.159582	+	0.120556i
$101$		−	0.260498i		−	0.0259205i	−0.999916	−	0.0129602i	$-0.995875\pi$
$101$		−	0.260498i		−	0.0259205i	0.999916	−	0.0129602i	$-0.00412549\pi$
$102$		0			0
$103$	1.76484			0.173895			0.0869475	−	0.996213i	$-0.472289\pi$
$103$	1.76484			0.173895			0.0869475	+	0.996213i	$0.472289\pi$
$104$	4.00327	+	5.84746i	0.392553	+	0.573391i
$105$		0			0
$106$	−1.28804	+	3.84184i	−0.125106	+	0.373153i
$107$		−	6.10229i		−	0.589930i	−0.955508	−	0.294965i	$-0.904692\pi$
$107$		−	6.10229i		−	0.589930i	0.955508	−	0.294965i	$-0.0953081\pi$
$108$		0			0
$109$	14.9561			1.43253			0.716265	−	0.697828i	$-0.245850\pi$
$109$	14.9561			1.43253			0.716265	+	0.697828i	$0.245850\pi$
$110$	−1.79439	+	5.35213i	−0.171089	+	0.510306i
$111$		0			0
$112$	−7.10698	+	7.84161i	−0.671546	+	0.740963i
$113$	−11.8448			−1.11427			−0.557133	−	0.830423i	$-0.688099\pi$
$113$	−11.8448			−1.11427			−0.557133	+	0.830423i	$0.688099\pi$
$114$		0			0
$115$	−8.10651			−0.755936
$116$	−9.57144	−	7.23074i	−0.888686	−	0.671357i
$117$		0			0
$118$	−4.35285	+	12.9832i	−0.400712	+	1.19520i
$119$	−2.41787	+	1.50803i	−0.221646	+	0.138241i
$120$		0			0
$121$	−4.93258			−0.448416
$122$	4.30731	+	1.44410i	0.389966	+	0.130743i
$123$		0			0
$124$	10.0945	+	7.62587i	0.906511	+	0.684823i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	5.49406i		−	0.487519i	−0.969836	−	0.243760i	$-0.921619\pi$
$127$		−	5.49406i		−	0.487519i	0.969836	−	0.243760i	$-0.0783808\pi$
$128$	−8.69944	−	7.23324i	−0.768929	−	0.639334i
$129$		0			0
$130$	−1.12632	+	3.35948i	−0.0987852	+	0.294646i
$131$	9.93971			0.868436			0.434218	−	0.900808i	$-0.357025\pi$
$131$	9.93971			0.868436			0.434218	+	0.900808i	$0.357025\pi$
$132$		0			0
$133$	−10.9068	−	17.4872i	−0.945741	−	1.51633i
$134$	10.4461	+	3.50224i	0.902407	+	0.302547i
$135$		0			0
$136$	−1.72092	−	2.51370i	−0.147568	−	0.215548i
$137$	−16.4345			−1.40409			−0.702046	−	0.712132i	$-0.747730\pi$
$137$	−16.4345			−1.40409			−0.702046	+	0.712132i	$0.747730\pi$
$138$		0			0
$139$	17.8065			1.51033			0.755164	−	0.655535i	$-0.227557\pi$
$139$	17.8065			1.51033			0.755164	+	0.655535i	$0.227557\pi$
$140$	−5.27041	−	0.471978i	−0.445431	−	0.0398894i
$141$		0			0
$142$	7.84386	+	2.62979i	0.658242	+	0.220687i
$143$	−10.0007			−0.836303
$144$		0			0
$145$		−	5.99783i		−	0.498093i
$146$	−7.68651	−	2.57703i	−0.636140	−	0.213277i
$147$		0			0
$148$	−4.87293	−	3.68125i	−0.400553	−	0.302597i
$149$	19.6876			1.61287			0.806434	−	0.591324i	$-0.201395\pi$
$149$	19.6876			1.61287			0.806434	+	0.591324i	$0.201395\pi$
$150$		0			0
$151$		−	13.2712i		−	1.08000i	−0.841666	−	0.539998i	$-0.818425\pi$
$151$		−	13.2712i		−	1.08000i	0.841666	−	0.539998i	$-0.181575\pi$
$152$	18.1803	−	12.4466i	1.47462	−	1.00955i
$153$		0			0
$154$	−3.46555	−	14.5274i	−0.279262	−	1.17065i
$155$			6.32559i			0.508083i
$156$		0			0
$157$		−	19.3395i		−	1.54346i	−0.635951	−	0.771730i	$-0.719392\pi$
$157$		−	19.3395i		−	1.54346i	0.635951	−	0.771730i	$-0.280608\pi$
$158$	3.77855	+	1.26682i	0.300606	+	0.100783i
$159$		0			0
$160$	0.263812	−	5.65070i	0.0208562	−	0.446727i
$161$	18.1983	−	11.3503i	1.43423	−	0.894531i
$162$		0			0
$163$			2.74676i			0.215143i	0.994197	+	0.107572i	$0.0343075\pi$
$163$			2.74676i			0.215143i	−0.994197	+	0.107572i	$0.965693\pi$
$164$	−11.2441	+	14.8839i	−0.878014	+	1.16224i
$165$		0			0
$166$	5.62394	−	16.7745i	0.436502	−	1.30196i
$167$	−5.82171			−0.450498			−0.225249	−	0.974301i	$-0.572320\pi$
$167$	−5.82171			−0.450498			−0.225249	+	0.974301i	$0.572320\pi$
$168$		0			0
$169$	6.72263			0.517125
$170$	0.484184	−	1.44417i	0.0371352	−	0.110763i
$171$		0			0
$172$	−9.80118	+	12.9740i	−0.747333	+	0.989257i
$173$		−	10.5651i		−	0.803253i	−0.915804	−	0.401626i	$-0.868445\pi$
$173$		−	10.5651i		−	0.803253i	0.915804	−	0.401626i	$-0.131555\pi$
$174$		0			0
$175$	−1.40015	−	2.24490i	−0.105841	−	0.169699i
$176$	15.3583	−	4.36381i	1.15768	−	0.328935i
$177$		0			0
$178$	−4.71158	−	1.57964i	−0.353148	−	0.118399i
$179$			4.59887i			0.343736i	0.985120	+	0.171868i	$0.0549802\pi$
$179$			4.59887i			0.343736i	−0.985120	+	0.171868i	$0.945020\pi$
$180$		0			0
$181$			9.42719i			0.700717i	0.936616	+	0.350359i	$0.113940\pi$
$181$			9.42719i			0.700717i	−0.936616	+	0.350359i	$0.886060\pi$
$182$	−2.17529	−	9.11873i	−0.161244	−	0.675925i
$183$		0			0
$184$	12.9527	+	18.9196i	0.954885	+	1.39477i
$185$		−	3.05357i		−	0.224503i
$186$		0			0
$187$	4.29911			0.314382
$188$	14.3859	+	10.8678i	1.04920	+	0.792617i
$189$		0			0
$190$	10.4450	+	3.50185i	0.757758	+	0.254051i
$191$		−	5.02689i		−	0.363733i	−0.983323	−	0.181866i	$-0.941786\pi$
$191$		−	5.02689i		−	0.363733i	0.983323	−	0.181866i	$-0.0582139\pi$
$192$		0			0
$193$	15.8775			1.14288			0.571442	−	0.820642i	$-0.306384\pi$
$193$	15.8775			1.14288			0.571442	+	0.820642i	$0.306384\pi$
$194$	16.1086	+	5.40068i	1.15653	+	0.387746i
$195$		0			0
$196$	12.4924	−	6.31982i	0.892314	−	0.451416i
$197$	10.1289			0.721651			0.360826	−	0.932633i	$-0.382495\pi$
$197$	10.1289			0.721651			0.360826	+	0.932633i	$0.382495\pi$
$198$		0			0
$199$	1.13945			0.0807737			0.0403869	−	0.999184i	$-0.487141\pi$
$199$	1.13945			0.0807737			0.0403869	+	0.999184i	$0.487141\pi$
$200$	2.33388	−	1.59781i	0.165030	−	0.112982i
$201$		0			0
$202$	−0.349291	−	0.117106i	−0.0245760	−	0.00823953i
$203$	8.39786	+	13.4645i	0.589414	+	0.945025i
$204$		0			0
$205$	−9.32685			−0.651415
$206$	0.793378	−	2.36641i	0.0552773	−	0.164875i
$207$		0			0
$208$	9.64029	−	2.73912i	0.668434	−	0.189924i
$209$			31.0933i			2.15077i
$210$		0			0
$211$		−	16.8644i		−	1.16099i	−0.814263	−	0.580497i	$-0.802858\pi$
$211$		−	16.8644i		−	1.16099i	0.814263	−	0.580497i	$-0.197142\pi$
$212$	4.57234	+	3.45417i	0.314030	+	0.237233i
$213$		0			0
$214$	−8.18232	−	2.74326i	−0.559332	−	0.187525i
$215$	−8.13000			−0.554461
$216$		0			0
$217$	−8.85677	−	14.2003i	−0.601237	−	0.963981i
$218$	6.72344	−	20.0540i	0.455369	−	1.35823i
$219$		0			0
$220$	6.36980	+	4.81206i	0.429452	+	0.324429i
$221$	2.69851			0.181522
$222$		0			0
$223$	1.84769			0.123730			0.0618652	−	0.998085i	$-0.480295\pi$
$223$	1.84769			0.123730			0.0618652	+	0.998085i	$0.480295\pi$
$224$	7.31959	+	13.0546i	0.489061	+	0.872250i
$225$		0			0
$226$	−5.32479	+	15.8822i	−0.354200	+	1.05647i
$227$	−26.0109			−1.72640			−0.863201	−	0.504861i	$-0.831544\pi$
$227$	−26.0109			−1.72640			−0.863201	+	0.504861i	$0.831544\pi$
$228$		0			0
$229$		−	14.8172i		−	0.979146i	−0.871962	−	0.489573i	$-0.837153\pi$
$229$		−	14.8172i		−	0.979146i	0.871962	−	0.489573i	$-0.162847\pi$
$230$	−3.64425	+	10.8697i	−0.240295	+	0.716727i
$231$		0			0
$232$	−13.9982	+	9.58342i	−0.919028	+	0.629182i
$233$	3.41871			0.223967			0.111983	−	0.993710i	$-0.464280\pi$
$233$	3.41871			0.223967			0.111983	+	0.993710i	$0.464280\pi$
$234$		0			0
$235$			9.01476i			0.588058i
$236$	15.4519	+	11.6731i	1.00583	+	0.759856i
$237$		0			0
$238$	0.935114	+	3.91996i	0.0606144	+	0.254093i
$239$		−	2.84316i		−	0.183909i	−0.995763	−	0.0919544i	$-0.970689\pi$
$239$		−	2.84316i		−	0.183909i	0.995763	−	0.0919544i	$-0.0293114\pi$
$240$		0			0
$241$			20.0977i			1.29461i	0.762233	+	0.647303i	$0.224103\pi$
$241$			20.0977i			1.29461i	−0.762233	+	0.647303i	$0.775897\pi$
$242$	−2.21742	+	6.61390i	−0.142541	+	0.425158i
$243$		0			0
$244$	3.87267	−	5.12632i	0.247922	−	0.328179i
$245$	6.28639	+	3.07916i	0.401623	+	0.196720i
$246$		0			0
$247$			19.5170i			1.24183i
$248$	14.7632	−	10.1071i	0.937462	−	0.641802i
$249$		0			0
$250$	1.34086	+	0.449546i	0.0848035	+	0.0284318i
$251$	15.7417			0.993607			0.496803	−	0.867863i	$-0.334507\pi$
$251$	15.7417			0.993607			0.496803	+	0.867863i	$0.334507\pi$
$252$		0			0
$253$	−32.3577			−2.03431
$254$	−7.36677	−	2.46983i	−0.462232	−	0.154971i
$255$		0			0
$256$	−13.6096	+	8.41306i	−0.850598	+	0.525816i
$257$		−	7.43670i		−	0.463889i	−0.972729	−	0.231944i	$-0.925491\pi$
$257$		−	7.43670i		−	0.463889i	0.972729	−	0.231944i	$-0.0745087\pi$
$258$		0			0
$259$	4.27545	+	6.85496i	0.265664	+	0.425946i
$260$	3.99827	+	3.02049i	0.247962	+	0.187323i
$261$		0			0
$262$	4.46836	−	13.3278i	0.276056	−	0.823392i
$263$		−	8.49327i		−	0.523718i	−0.965106	−	0.261859i	$-0.915665\pi$
$263$		−	8.49327i		−	0.523718i	0.965106	−	0.261859i	$-0.0843355\pi$
$264$		0			0
$265$			2.86521i			0.176008i
$266$	−28.3510	+	6.76321i	−1.73831	+	0.414679i
$267$		0			0
$268$	9.39202	−	12.4324i	0.573709	−	0.759428i
$269$		−	5.94512i		−	0.362480i	−0.983439	−	0.181240i	$-0.941989\pi$
$269$		−	5.94512i		−	0.362480i	0.983439	−	0.181240i	$-0.0580111\pi$
$270$		0			0
$271$	−11.2023			−0.680490			−0.340245	−	0.940337i	$-0.610510\pi$
$271$	−11.2023			−0.680490			−0.340245	+	0.940337i	$0.610510\pi$
$272$	−4.14416	+	1.17749i	−0.251277	+	0.0713960i
$273$		0			0
$274$	−7.38806	+	22.0363i	−0.446329	+	1.33126i
$275$			3.99156i			0.240700i
$276$		0			0
$277$	2.17155			0.130476			0.0652378	−	0.997870i	$-0.479219\pi$
$277$	2.17155			0.130476			0.0652378	+	0.997870i	$0.479219\pi$
$278$	8.00485	−	23.8761i	0.480099	−	1.43199i
$279$		0			0
$280$	−3.00215	+	6.85471i	−0.179413	+	0.409647i
$281$	−1.72189			−0.102720			−0.0513598	−	0.998680i	$-0.516356\pi$
$281$	−1.72189			−0.102720			−0.0513598	+	0.998680i	$0.516356\pi$
$282$		0			0
$283$	6.51271			0.387140			0.193570	−	0.981086i	$-0.437993\pi$
$283$	6.51271			0.387140			0.193570	+	0.981086i	$0.437993\pi$
$284$	7.05236	−	9.33532i	0.418481	−	0.553949i
$285$		0			0
$286$	−4.49579	+	13.4096i	−0.265842	+	0.792926i
$287$	20.9379	−	13.0590i	1.23592	−	0.770847i
$288$		0			0
$289$	15.8400			0.931763
$290$	−8.04226	−	2.69630i	−0.472258	−	0.158332i
$291$		0			0
$292$	−6.91089	+	9.14805i	−0.404429	+	0.535349i
$293$		−	9.20381i		−	0.537692i	−0.963183	−	0.268846i	$-0.913358\pi$
$293$		−	9.20381i		−	0.537692i	0.963183	−	0.268846i	$-0.0866423\pi$
$294$		0			0
$295$			9.68276i			0.563752i
$296$	−7.12666	+	4.87903i	−0.414229	+	0.283588i
$297$		0			0
$298$	8.85047	−	26.3983i	0.512694	−	1.52921i
$299$	−20.3106			−1.17459
$300$		0			0
$301$	18.2510	−	11.3832i	1.05197	−	0.656117i
$302$	−17.7949	−	5.96603i	−1.02398	−	0.343306i
$303$		0			0
$304$	−8.51621	−	29.9726i	−0.488438	−	1.71905i
$305$	3.21235			0.183938
$306$		0			0
$307$	32.5750			1.85916			0.929578	−	0.368626i	$-0.120172\pi$
$307$	32.5750			1.85916			0.929578	+	0.368626i	$0.120172\pi$
$308$	−21.0372	−	1.88393i	−1.19870	−	0.107347i
$309$		0			0
$310$	8.48173	+	2.84365i	0.481730	+	0.161508i
$311$	27.3621			1.55156			0.775781	−	0.631002i	$-0.217356\pi$
$311$	27.3621			1.55156			0.775781	+	0.631002i	$0.217356\pi$
$312$		0			0
$313$			19.7088i			1.11401i	0.830510	+	0.557004i	$0.188049\pi$
$313$			19.7088i			1.11401i	−0.830510	+	0.557004i	$0.811951\pi$
$314$	−25.9316	−	8.69400i	−1.46340	−	0.490631i
$315$		0			0
$316$	3.39727	−	4.49702i	0.191111	−	0.252977i
$317$	0.854973			0.0480201			0.0240100	−	0.999712i	$-0.492357\pi$
$317$	0.854973			0.0480201			0.0240100	+	0.999712i	$0.492357\pi$
$318$		0			0
$319$		−	23.9407i		−	1.34042i
$320$	−7.45821	−	2.89399i	−0.416926	−	0.161779i
$321$		0			0
$322$	−7.03823	−	29.5039i	−0.392225	−	1.64419i
$323$		−	8.38994i		−	0.466829i
$324$		0			0
$325$			2.50547i			0.138978i
$326$	3.68303	+	1.23480i	0.203984	+	0.0683891i
$327$		0			0
$328$	14.9026	+	21.7677i	0.822856	+	1.20192i
$329$	−12.6220	−	20.2372i	−0.695874	−	1.11572i
$330$		0			0
$331$			4.23740i			0.232909i	0.993196	+	0.116454i	$0.0371529\pi$
$331$			4.23740i			0.232909i	−0.993196	+	0.116454i	$0.962847\pi$
$332$	−19.9641	−	15.0818i	−1.09567	−	0.827724i
$333$		0			0
$334$	−2.61713	+	7.80611i	−0.143203	+	0.427131i
$335$	7.79060			0.425646
$336$		0			0
$337$	20.5956			1.12191			0.560956	−	0.827846i	$-0.310434\pi$
$337$	20.5956			1.12191			0.560956	+	0.827846i	$0.310434\pi$
$338$	3.02213	−	9.01411i	0.164382	−	0.490303i
$339$		0			0
$340$	−1.71877	−	1.29845i	−0.0932135	−	0.0704181i
$341$			25.2490i			1.36731i
$342$		0			0
$343$	−18.4236	+	1.88948i	−0.994782	+	0.102022i
$344$	12.9902	+	18.9744i	0.700385	+	1.02303i
$345$		0			0
$346$	−14.1664	−	4.74952i	−0.761590	−	0.255336i
$347$			13.8257i			0.742200i	0.928593	+	0.371100i	$0.121019\pi$
$347$			13.8257i			0.742200i	−0.928593	+	0.371100i	$0.878981\pi$
$348$		0			0
$349$			8.06666i			0.431798i	0.976416	+	0.215899i	$0.0692683\pi$
$349$			8.06666i			0.431798i	−0.976416	+	0.215899i	$0.930732\pi$
$350$	−3.63953	+	0.868219i	−0.194541	+	0.0464082i
$351$		0			0
$352$	1.05302	−	22.5551i	0.0561262	−	1.20219i
$353$		−	7.67694i		−	0.408602i	−0.978908	−	0.204301i	$-0.934508\pi$
$353$		−	7.67694i		−	0.408602i	0.978908	−	0.204301i	$-0.0654922\pi$
$354$		0			0
$355$	5.84987			0.310479
$356$	−4.23615	+	5.60746i	−0.224516	+	0.297195i
$357$		0			0
$358$	6.16645	+	2.06741i	0.325907	+	0.109266i
$359$			21.6267i			1.14141i	0.821154	+	0.570706i	$0.193330\pi$
$359$			21.6267i			1.14141i	−0.821154	+	0.570706i	$0.806670\pi$
$360$		0			0
$361$	41.6802			2.19369
$362$	12.6405	+	4.23796i	0.664372	+	0.222742i
$363$		0			0
$364$	−13.2048	−	1.18253i	−0.692122	−	0.0619812i
$365$	−5.73252			−0.300054
$366$		0			0
$367$	−6.62228			−0.345680			−0.172840	−	0.984950i	$-0.555294\pi$
$367$	−6.62228			−0.345680			−0.172840	+	0.984950i	$0.555294\pi$
$368$	31.1914	−	8.86251i	1.62597	−	0.461990i
$369$		0			0
$370$	−4.09441	−	1.37272i	−0.212858	−	0.0713643i
$371$	−4.01172	−	6.43210i	−0.208278	−	0.333938i
$372$		0			0
$373$	−31.1585			−1.61332			−0.806662	−	0.591013i	$-0.798728\pi$
$373$	−31.1585			−1.61332			−0.806662	+	0.591013i	$0.798728\pi$
$374$	1.93265	−	5.76451i	0.0999349	−	0.298076i
$375$		0			0
$376$	21.0394	−	14.4039i	1.08502	−	0.742825i
$377$		−	15.0274i		−	0.773949i
$378$		0			0
$379$			31.1885i			1.60204i	0.598635	+	0.801022i	$0.295710\pi$
$379$			31.1885i			1.60204i	−0.598635	+	0.801022i	$0.704290\pi$
$380$	9.39100	−	12.4310i	0.481748	−	0.637697i
$381$		0			0
$382$	−6.74036	−	2.25982i	−0.344867	−	0.115622i
$383$	−27.9907			−1.43026			−0.715128	−	0.698993i	$-0.753632\pi$
$383$	−27.9907			−1.43026			−0.715128	+	0.698993i	$0.753632\pi$
$384$		0			0
$385$	−5.58879	−	8.96067i	−0.284831	−	0.456678i
$386$	7.13766	−	21.2895i	0.363297	−	1.08361i
$387$		0			0
$388$	14.4831	−	19.1715i	0.735269	−	0.973286i
$389$	−15.7502			−0.798568			−0.399284	−	0.916827i	$-0.630741\pi$
$389$	−15.7502			−0.798568			−0.399284	+	0.916827i	$0.630741\pi$
$390$		0			0
$391$	8.73111			0.441551
$392$	−2.85809	−	19.5916i	−0.144355	−	0.989526i
$393$		0			0
$394$	4.55339	−	13.5814i	0.229397	−	0.684221i
$395$	2.81801			0.141789
$396$		0			0
$397$			11.3689i			0.570589i	0.958440	+	0.285294i	$0.0920914\pi$
$397$			11.3689i			0.570589i	−0.958440	+	0.285294i	$0.907909\pi$
$398$	0.512237	−	1.52785i	0.0256761	−	0.0765841i
$399$		0			0
$400$	−1.09326	−	3.84770i	−0.0546629	−	0.192385i
$401$	−12.7623			−0.637319			−0.318659	−	0.947869i	$-0.603233\pi$
$401$	−12.7623			−0.637319			−0.318659	+	0.947869i	$0.603233\pi$
$402$		0			0
$403$			15.8486i			0.789473i
$404$	−0.314045	+	0.415706i	−0.0156243	+	0.0206822i
$405$		0			0
$406$	21.8293	−	5.20743i	1.08337	−	0.258440i
$407$		−	12.1885i		−	0.604162i
$408$		0			0
$409$			1.91649i			0.0947643i	0.998877	+	0.0473822i	$0.0150879\pi$
$409$			1.91649i			0.0947643i	−0.998877	+	0.0473822i	$0.984912\pi$
$410$	−4.19285	+	12.5060i	−0.207070	+	0.617628i
$411$		0			0
$412$	−2.81636	−	2.12762i	−0.138752	−	0.104820i
$413$	−13.5573	−	21.7368i	−0.667112	−	1.06960i
$414$		0			0
$415$		−	12.5103i		−	0.614104i
$416$	0.660972	−	14.1576i	0.0324068	−	0.694136i
$417$		0			0
$418$	41.6918	+	13.9779i	2.03921	+	0.683680i
$419$	13.7105			0.669800			0.334900	−	0.942254i	$-0.391297\pi$
$419$	13.7105			0.669800			0.334900	+	0.942254i	$0.391297\pi$
$420$		0			0
$421$	7.87629			0.383867			0.191933	−	0.981408i	$-0.438524\pi$
$421$	7.87629			0.383867			0.191933	+	0.981408i	$0.438524\pi$
$422$	−22.6128	−	7.58133i	−1.10077	−	0.369053i
$423$		0			0
$424$	6.68704	−	4.57806i	0.324752	−	0.222330i
$425$		−	1.07705i		−	0.0522446i
$426$		0			0
$427$	−7.21140	+	4.49777i	−0.348984	+	0.217662i
$428$	−7.35666	+	9.73813i	−0.355598	+	0.470710i
$429$		0			0
$430$	−3.65481	+	10.9012i	−0.176251	+	0.525702i
$431$			22.3788i			1.07795i	0.842322	+	0.538974i	$0.181188\pi$
$431$			22.3788i			1.07795i	−0.842322	+	0.538974i	$0.818812\pi$
$432$		0			0
$433$		−	33.9772i		−	1.63284i	−0.577460	−	0.816419i	$-0.695956\pi$
$433$		−	33.9772i		−	1.63284i	0.577460	−	0.816419i	$-0.304044\pi$
$434$	−23.0222	+	5.49199i	−1.10510	+	0.263624i
$435$		0			0
$436$	−23.8671	−	18.0304i	−1.14303	−	0.863499i
$437$			63.1477i			3.02076i
$438$		0			0
$439$	−2.97475			−0.141977			−0.0709886	−	0.997477i	$-0.522615\pi$
$439$	−2.97475			−0.141977			−0.0709886	+	0.997477i	$0.522615\pi$
$440$	9.31583	−	6.37777i	0.444115	−	0.304048i
$441$		0			0
$442$	1.21311	−	3.61833i	0.0577016	−	0.172106i
$443$		−	20.4095i		−	0.969684i	−0.874602	−	0.484842i	$-0.838877\pi$
$443$		−	20.4095i		−	0.969684i	0.874602	−	0.484842i	$-0.161123\pi$
$444$		0			0
$445$	−3.51385			−0.166572
$446$	0.830622	−	2.47750i	0.0393311	−	0.117313i
$447$		0			0
$448$	20.7949	−	3.94589i	0.982469	−	0.186426i
$449$	11.0234			0.520226			0.260113	−	0.965578i	$-0.416240\pi$
$449$	11.0234			0.520226			0.260113	+	0.965578i	$0.416240\pi$
$450$		0			0
$451$	−37.2287			−1.75303
$452$	18.9021	+	14.2796i	0.889082	+	0.671656i
$453$		0			0
$454$	−11.6931	+	34.8769i	−0.548784	+	1.63686i
$455$	−3.50803	−	5.62453i	−0.164459	−	0.263682i
$456$		0			0
$457$	0.409340			0.0191481			0.00957406	−	0.999954i	$-0.496952\pi$
$457$	0.409340			0.0191481			0.00957406	+	0.999954i	$0.496952\pi$
$458$	−19.8678	−	6.66101i	−0.928360	−	0.311248i
$459$		0			0
$460$	12.9365	+	9.77288i	0.603168	+	0.455663i
$461$			23.9577i			1.11582i	0.829901	+	0.557910i	$0.188397\pi$
$461$			23.9577i			1.11582i	−0.829901	+	0.557910i	$0.811603\pi$
$462$		0			0
$463$			10.1008i			0.469424i	0.972065	+	0.234712i	$0.0754147\pi$
$463$			10.1008i			0.469424i	−0.972065	+	0.234712i	$0.924585\pi$
$464$	6.55718	+	23.0779i	0.304409	+	1.07136i
$465$		0			0
$466$	1.53687	−	4.58401i	0.0711940	−	0.212350i
$467$	38.6883			1.79028			0.895140	−	0.445785i	$-0.147076\pi$
$467$	38.6883			1.79028			0.895140	+	0.445785i	$0.147076\pi$
$468$		0			0
$469$	−17.4891	+	10.9080i	−0.807573	+	0.503685i
$470$	12.0875	+	4.05255i	0.557557	+	0.186930i
$471$		0			0
$472$	22.5984	−	15.4712i	1.04018	−	0.712122i
$473$	−32.4514			−1.49212
$474$		0			0
$475$	7.78975			0.357418
$476$	5.67649	+	0.508344i	0.260182	+	0.0232999i
$477$		0			0
$478$	−3.81228	−	1.27813i	−0.174370	−	0.0584604i
$479$	−7.91710			−0.361742			−0.180871	−	0.983507i	$-0.557892\pi$
$479$	−7.91710			−0.361742			−0.180871	+	0.983507i	$0.557892\pi$
$480$		0			0
$481$		−	7.65062i		−	0.348838i
$482$	26.9482	+	9.03484i	1.22746	+	0.411526i
$483$		0			0
$484$	7.87149	+	5.94651i	0.357795	+	0.270296i
$485$	12.0136			0.545510
$486$		0			0
$487$		−	28.5984i		−	1.29592i	−0.761676	−	0.647958i	$-0.775623\pi$
$487$		−	28.5984i		−	1.29592i	0.761676	−	0.647958i	$-0.224377\pi$
$488$	−5.13273	−	7.49723i	−0.232348	−	0.339384i
$489$		0			0
$490$	6.95475	−	7.04495i	0.314184	−	0.318259i
$491$		−	23.6318i		−	1.06649i	−0.845961	−	0.533244i	$-0.820973\pi$
$491$		−	23.6318i		−	1.06649i	0.845961	−	0.533244i	$-0.179027\pi$
$492$		0			0
$493$			6.45996i			0.290942i
$494$	26.1695	+	8.77378i	1.17742	+	0.394751i
$495$		0			0
$496$	−6.91550	−	24.3390i	−0.310515	−	1.09285i
$497$	−13.1324	+	8.19069i	−0.589068	+	0.367403i
$498$		0			0
$499$			0.663011i			0.0296805i	0.999890	+	0.0148402i	$0.00472397\pi$
$499$			0.663011i			0.0296805i	−0.999890	+	0.0148402i	$0.995276\pi$
$500$	1.20556	−	1.59582i	0.0539142	−	0.0713671i
$501$		0			0
$502$	7.07662	−	21.1074i	0.315845	−	0.942070i
$503$	19.7450			0.880385			0.440192	−	0.897904i	$-0.354910\pi$
$503$	19.7450			0.880385			0.440192	+	0.897904i	$0.354910\pi$
$504$		0			0
$505$	−0.260498			−0.0115920
$506$	−14.5463	+	43.3871i	−0.646661	+	1.92879i
$507$		0			0
$508$	−6.62341	+	8.76751i	−0.293866	+	0.388995i
$509$			24.6928i			1.09449i	0.836972	+	0.547245i	$0.184324\pi$
$509$			24.6928i			1.09449i	−0.836972	+	0.547245i	$0.815676\pi$
$510$		0			0
$511$	12.8689	−	8.02639i	0.569288	−	0.355066i
$512$	5.16261	+	22.0306i	0.228157	+	0.973624i
$513$		0			0
$514$	−9.97158	−	3.34314i	−0.439828	−	0.147460i
$515$		−	1.76484i		−	0.0777682i
$516$		0			0
$517$			35.9830i			1.58253i
$518$	11.1136	−	2.65116i	0.488302	−	0.116485i
$519$		0			0
$520$	5.84746	−	4.00327i	0.256428	−	0.175555i
$521$		−	13.0343i		−	0.571042i	−0.958372	−	0.285521i	$-0.907833\pi$
$521$		−	13.0343i		−	0.571042i	0.958372	−	0.285521i	$-0.0921666\pi$
$522$		0			0
$523$	21.5279			0.941348			0.470674	−	0.882307i	$-0.344011\pi$
$523$	21.5279			0.941348			0.470674	+	0.882307i	$0.344011\pi$
$524$	−15.8619	−	11.9829i	−0.692932	−	0.523475i
$525$		0			0
$526$	−11.3883	−	3.81812i	−0.496553	−	0.166478i
$527$		−	6.81297i		−	0.296778i
$528$		0			0
$529$	−42.7156			−1.85720
$530$	3.84184	+	1.28804i	0.166879	+	0.0559490i
$531$		0			0
$532$	−3.67659	+	41.0552i	−0.159400	+	1.77997i
$533$	−23.3681			−1.01219
$534$		0			0
$535$	−6.10229			−0.263825
$536$	−12.4479	−	18.1823i	−0.537668	−	0.785357i
$537$		0			0
$538$	−7.97158	−	2.67261i	−0.343679	−	0.115224i
$539$	25.0925	+	12.2907i	1.08081	+	0.529397i
$540$		0			0
$541$	−17.3274			−0.744965			−0.372482	−	0.928039i	$-0.621493\pi$
$541$	−17.3274			−0.744965			−0.372482	+	0.928039i	$0.621493\pi$
$542$	−5.03595	+	15.0207i	−0.216312	+	0.645195i
$543$		0			0
$544$	−0.284138	+	6.08608i	−0.0121823	+	0.260939i
$545$		−	14.9561i		−	0.640647i
$546$		0			0
$547$		−	5.19581i		−	0.222157i	−0.993812	−	0.111079i	$-0.964569\pi$
$547$		−	5.19581i		−	0.222157i	0.993812	−	0.111079i	$-0.0354305\pi$
$548$	26.2264	+	19.8127i	1.12034	+	0.846357i
$549$		0			0
$550$	5.35213	+	1.79439i	0.228216	+	0.0765132i
$551$	−46.7216			−1.99041
$552$		0			0
$553$	−6.32615	+	3.94563i	−0.269015	+	0.167785i
$554$	0.976211	−	2.91174i	0.0414752	−	0.123708i
$555$		0			0
$556$	−28.4159	−	21.4668i	−1.20510	−	0.910395i
$557$	−10.4597			−0.443190			−0.221595	−	0.975139i	$-0.571126\pi$
$557$	−10.4597			−0.443190			−0.221595	+	0.975139i	$0.571126\pi$
$558$		0			0
$559$	−20.3694			−0.861536
$560$	7.84161	+	7.10698i	0.331369	+	0.300325i
$561$		0			0
$562$	−0.774071	+	2.30882i	−0.0326522	+	0.0973917i
$563$	−1.94438			−0.0819459			−0.0409730	−	0.999160i	$-0.513046\pi$
$563$	−1.94438			−0.0819459			−0.0409730	+	0.999160i	$0.513046\pi$
$564$		0			0
$565$			11.8448i			0.498315i
$566$	2.92777	−	8.73264i	0.123063	−	0.367060i
$567$		0			0
$568$	−9.34700	−	13.6529i	−0.392191	−	0.572863i
$569$	5.72219			0.239887			0.119943	−	0.992781i	$-0.461729\pi$
$569$	5.72219			0.239887			0.119943	+	0.992781i	$0.461729\pi$
$570$		0			0
$571$			42.2732i			1.76908i	0.466466	+	0.884539i	$0.345527\pi$
$571$			42.2732i			1.76908i	−0.466466	+	0.884539i	$0.654473\pi$
$572$	15.9593	+	12.0565i	0.667293	+	0.504106i
$573$		0			0
$574$	−8.09774	−	33.9454i	−0.337993	−	1.41685i
$575$			8.10651i			0.338065i
$576$		0			0
$577$		−	0.216956i		−	0.00903200i	−0.999990	−	0.00451600i	$-0.998563\pi$
$577$		−	0.216956i		−	0.00903200i	0.999990	−	0.00451600i	$-0.00143749\pi$
$578$	7.12080	−	21.2392i	0.296186	−	0.883434i
$579$		0			0
$580$	−7.23074	+	9.57144i	−0.300240	+	0.397432i
$581$	17.5162	+	28.0843i	0.726696	+	1.16513i
$582$		0			0
$583$			11.4366i			0.473658i
$584$	9.15950	+	13.3790i	0.379023	+	0.553627i
$585$		0			0
$586$	−12.3410	−	4.13754i	−0.509803	−	0.170920i
$587$	6.61005			0.272826			0.136413	−	0.990652i	$-0.456443\pi$
$587$	6.61005			0.272826			0.136413	+	0.990652i	$0.456443\pi$
$588$		0			0
$589$	49.2747			2.03033
$590$	12.9832	+	4.35285i	0.534511	+	0.179204i
$591$		0			0
$592$	3.33834	+	11.7492i	0.137205	+	0.482889i
$593$			19.2223i			0.789365i	0.918818	+	0.394682i	$0.129145\pi$
$593$			19.2223i			0.789365i	−0.918818	+	0.394682i	$0.870855\pi$
$594$		0			0
$595$	1.50803	+	2.41787i	0.0618232	+	0.0991230i
$596$	−31.4177	−	23.7345i	−1.28692	−	0.972203i
$597$		0			0
$598$	−9.13056	+	27.2337i	−0.373376	+	1.11367i
$599$		−	29.5976i		−	1.20933i	−0.796481	−	0.604663i	$-0.793308\pi$
$599$		−	29.5976i		−	1.20933i	0.796481	−	0.604663i	$-0.206692\pi$
$600$		0			0
$601$			42.7644i			1.74440i	0.489154	+	0.872198i	$0.337306\pi$
$601$			42.7644i			1.74440i	−0.489154	+	0.872198i	$0.662694\pi$
$602$	−7.05861	−	29.5894i	−0.287688	−	1.20597i
$603$		0			0
$604$	−15.9992	+	21.1784i	−0.650999	+	0.861738i
$605$			4.93258i			0.200538i
$606$		0			0
$607$	−43.6339			−1.77104			−0.885522	−	0.464598i	$-0.846199\pi$
$607$	−43.6339			−1.77104			−0.885522	+	0.464598i	$0.846199\pi$
$608$	−44.0175	−	2.05503i	−1.78515	−	0.0833424i
$609$		0			0
$610$	1.44410	−	4.30731i	0.0584699	−	0.174398i
$611$			22.5862i			0.913740i
$612$		0			0
$613$	−41.2984			−1.66803			−0.834013	−	0.551744i	$-0.813963\pi$
$613$	−41.2984			−1.66803			−0.834013	+	0.551744i	$0.813963\pi$
$614$	14.6440	−	43.6786i	0.590983	−	1.76272i
$615$		0			0
$616$	−11.9833	+	27.3610i	−0.482820	+	1.10241i
$617$	2.12487			0.0855439			0.0427719	−	0.999085i	$-0.486381\pi$
$617$	2.12487			0.0855439			0.0427719	+	0.999085i	$0.486381\pi$
$618$		0			0
$619$	21.1221			0.848970			0.424485	−	0.905435i	$-0.360455\pi$
$619$	21.1221			0.848970			0.424485	+	0.905435i	$0.360455\pi$
$620$	7.62587	−	10.0945i	0.306262	−	0.405404i
$621$		0			0
$622$	12.3005	−	36.6888i	0.493206	−	1.47109i
$623$	7.88825	−	4.91992i	0.316036	−	0.197112i
$624$		0			0
$625$	1.00000			0.0400000
$626$	26.4268	+	8.86002i	1.05623	+	0.354118i
$627$		0			0
$628$	−23.3149	+	30.8623i	−0.930365	+	1.23154i
$629$			3.28884i			0.131135i
$630$		0			0
$631$		−	3.20820i		−	0.127716i	−0.997959	−	0.0638582i	$-0.979659\pi$
$631$		−	3.20820i		−	0.127716i	0.997959	−	0.0638582i	$-0.0203406\pi$
$632$	−4.50265	−	6.57689i	−0.179106	−	0.261615i
$633$		0			0
$634$	0.384350	−	1.14640i	0.0152645	−	0.0455294i
$635$	−5.49406			−0.218025
$636$		0			0
$637$	15.7504	+	7.71474i	0.624052	+	0.305669i
$638$	−32.1012	−	10.7625i	−1.27090	−	0.426090i
$639$		0			0
$640$	−7.23324	+	8.69944i	−0.285919	+	0.343875i
$641$	14.2121			0.561345			0.280673	−	0.959804i	$-0.409442\pi$
$641$	14.2121			0.561345			0.280673	+	0.959804i	$0.409442\pi$
$642$		0			0
$643$	−7.89830			−0.311479			−0.155739	−	0.987798i	$-0.549776\pi$
$643$	−7.89830			−0.311479			−0.155739	+	0.987798i	$0.549776\pi$
$644$	−42.7247	−	3.82610i	−1.68359	−	0.150769i
$645$		0			0
$646$	−11.2497	−	3.77167i	−0.442615	−	0.148394i
$647$	−0.910960			−0.0358135			−0.0179068	−	0.999840i	$-0.505700\pi$
$647$	−0.910960			−0.0358135			−0.0179068	+	0.999840i	$0.505700\pi$
$648$		0			0
$649$			38.6494i			1.51712i
$650$	3.35948	+	1.12632i	0.131770	+	0.0441781i
$651$		0			0
$652$	3.31138	−	4.38333i	0.129684	−	0.171664i
$653$	−1.82376			−0.0713691			−0.0356846	−	0.999363i	$-0.511361\pi$
$653$	−1.82376			−0.0713691			−0.0356846	+	0.999363i	$0.511361\pi$
$654$		0			0
$655$		−	9.93971i		−	0.388377i
$656$	35.8869	−	10.1967i	1.40115	−	0.398113i
$657$		0			0
$658$	−32.8095	+	7.82678i	−1.27905	+	0.305120i
$659$			6.38815i			0.248847i	0.992229	+	0.124423i	$0.0397081\pi$
$659$			6.38815i			0.248847i	−0.992229	+	0.124423i	$0.960292\pi$
$660$		0			0
$661$		−	16.7429i		−	0.651222i	−0.945504	−	0.325611i	$-0.894430\pi$
$661$		−	16.7429i		−	0.651222i	0.945504	−	0.325611i	$-0.105570\pi$
$662$	5.68177	+	1.90491i	0.220828	+	0.0740364i
$663$		0			0
$664$	−29.1974	+	19.9891i	−1.13308	+	0.775726i
$665$	−17.4872	+	10.9068i	−0.678125	+	0.422948i
$666$		0			0
$667$		−	48.6215i		−	1.88263i
$668$	9.29038	+	7.01841i	0.359456	+	0.271551i
$669$		0			0
$670$	3.50224	−	10.4461i	0.135303	−	0.403569i
$671$	12.8223			0.494999
$672$		0			0
$673$	−35.5295			−1.36956			−0.684782	−	0.728748i	$-0.740102\pi$
$673$	−35.5295			−1.36956			−0.684782	+	0.728748i	$0.740102\pi$
$674$	9.25866	−	27.6158i	0.356630	−	1.06372i
$675$		0			0
$676$	−10.7281	−	8.10452i	−0.412619	−	0.311712i
$677$			12.3173i			0.473391i	0.971584	+	0.236696i	$0.0760644\pi$
$677$			12.3173i			0.473391i	−0.971584	+	0.236696i	$0.923936\pi$
$678$		0			0
$679$	−26.9694	+	16.8209i	−1.03499	+	0.645525i
$680$	−2.51370	+	1.72092i	−0.0963961	+	0.0659944i
$681$		0			0
$682$	33.8554	+	11.3506i	1.29639	+	0.434637i
$683$		−	5.01785i		−	0.192003i	−0.995381	−	0.0960014i	$-0.969395\pi$
$683$		−	5.01785i		−	0.192003i	0.995381	−	0.0960014i	$-0.0306053\pi$
$684$		0			0
$685$			16.4345i			0.627929i
$686$	−5.74875	+	25.5529i	−0.219488	+	0.975615i
$687$		0			0
$688$	31.2818	−	8.88819i	1.19261	−	0.338859i
$689$			7.17868i			0.273486i
$690$		0			0
$691$	31.8714			1.21245			0.606224	−	0.795294i	$-0.292684\pi$
$691$	31.8714			1.21245			0.606224	+	0.795294i	$0.292684\pi$
$692$	−12.7369	+	16.8600i	−0.484184	+	0.640922i
$693$		0			0
$694$	18.5383	+	6.21527i	0.703703	+	0.235928i
$695$		−	17.8065i		−	0.675440i
$696$		0			0
$697$	10.0455			0.380500
$698$	10.8163	+	3.62634i	0.409402	+	0.137259i
$699$		0			0
$700$	−0.471978	+	5.27041i	−0.0178391	+	0.199203i
$701$	−20.4325			−0.771725			−0.385862	−	0.922556i	$-0.626096\pi$
$701$	−20.4325			−0.771725			−0.385862	+	0.922556i	$0.626096\pi$
$702$		0			0
$703$	−23.7865			−0.897126
$704$	−29.7699	−	11.5515i	−1.12200	−	0.435365i
$705$		0			0
$706$	−10.2937	−	3.45114i	−0.387409	−	0.129885i
$707$	0.584791	−	0.364735i	0.0219933	−	0.0137173i
$708$		0			0
$709$	−42.4953			−1.59594			−0.797972	−	0.602695i	$-0.794094\pi$
$709$	−42.4953			−1.59594			−0.797972	+	0.602695i	$0.794094\pi$
$710$	2.62979	−	7.84386i	0.0986942	−	0.294375i
$711$		0			0
$712$	5.61448	+	8.20090i	0.210411	+	0.307342i
$713$			51.2785i			1.92039i
$714$		0			0
$715$			10.0007i			0.374006i
$716$	5.54421	−	7.33895i	0.207197	−	0.274270i
$717$		0			0
$718$	28.9984	+	9.72219i	1.08221	+	0.362829i
$719$	3.58392			0.133658			0.0668289	−	0.997764i	$-0.478712\pi$
$719$	3.58392			0.133658			0.0668289	+	0.997764i	$0.478712\pi$
$720$		0			0
$721$	2.47104	+	3.96190i	0.0920264	+	0.147549i
$722$	18.7372	−	55.8873i	0.697326	−	2.07991i
$723$		0			0
$724$	11.3650	−	15.0441i	0.422378	−	0.559108i
$725$	−5.99783			−0.222754
$726$		0			0
$727$	21.1835			0.785652			0.392826	−	0.919613i	$-0.371497\pi$
$727$	21.1835			0.785652			0.392826	+	0.919613i	$0.371497\pi$
$728$	−7.52179	+	17.1743i	−0.278776	+	0.636521i
$729$		0			0
$730$	−2.57703	+	7.68651i	−0.0953803	+	0.284491i
$731$	8.75641			0.323867
$732$		0			0
$733$		−	27.6118i		−	1.01986i	−0.860215	−	0.509932i	$-0.829670\pi$
$733$		−	27.6118i		−	1.01986i	0.860215	−	0.509932i	$-0.170330\pi$
$734$	−2.97702	+	8.87956i	−0.109884	+	0.327751i
$735$		0			0
$736$	2.13859	−	45.8075i	0.0788296	−	1.68849i
$737$	31.0967			1.14546
$738$		0			0
$739$		−	18.3419i		−	0.674716i	−0.941376	−	0.337358i	$-0.890467\pi$
$739$		−	18.3419i		−	0.674716i	0.941376	−	0.337358i	$-0.109533\pi$
$740$	−3.68125	+	4.87293i	−0.135326	+	0.179133i
$741$		0			0
$742$	−10.4280	+	2.48762i	−0.382824	+	0.0913236i
$743$			47.9531i			1.75923i	0.475688	+	0.879614i	$0.342199\pi$
$743$			47.9531i			1.75923i	−0.475688	+	0.879614i	$0.657801\pi$
$744$		0			0
$745$		−	19.6876i		−	0.721296i
$746$	−14.0072	+	41.7792i	−0.512839	+	1.52964i
$747$		0			0
$748$	−6.86059	−	5.18283i	−0.250848	−	0.189503i
$749$	13.6990	−	8.54411i	0.500552	−	0.312195i
$750$		0			0
$751$		−	51.3906i		−	1.87527i	−0.347624	−	0.937634i	$-0.613011\pi$
$751$		−	51.3906i		−	1.87527i	0.347624	−	0.937634i	$-0.386989\pi$
$752$	−9.85546	−	34.6861i	−0.359392	−	1.26487i
$753$		0			0
$754$	−20.1496	−	6.75550i	−0.733806	−	0.246021i
$755$	−13.2712			−0.482989
$756$		0			0
$757$	−7.69109			−0.279537			−0.139769	−	0.990184i	$-0.544636\pi$
$757$	−7.69109			−0.279537			−0.139769	+	0.990184i	$0.544636\pi$
$758$	41.8194	+	14.0207i	1.51895	+	0.509253i
$759$		0			0
$760$	−12.4466	−	18.1803i	−0.451484	−	0.659470i
$761$			48.0926i			1.74336i	0.490080	+	0.871678i	$0.336968\pi$
$761$			48.0926i			1.74336i	−0.490080	+	0.871678i	$0.663032\pi$
$762$		0			0
$763$	20.9407	+	33.5749i	0.758105	+	1.21549i
$764$	−6.06021	+	8.02199i	−0.219251	+	0.290225i
$765$		0			0
$766$	−12.5831	+	37.5316i	−0.454646	+	1.35607i
$767$			24.2599i			0.875973i
$768$		0			0
$769$		−	46.2666i		−	1.66842i	−0.551449	−	0.834209i	$-0.685925\pi$
$769$		−	46.2666i		−	1.66842i	0.551449	−	0.834209i	$-0.314075\pi$
$770$	−14.5274	+	3.46555i	−0.523532	+	0.124890i
$771$		0			0
$772$	−25.3375	−	19.1412i	−0.911917	−	0.688907i
$773$		−	37.7785i		−	1.35880i	−0.733768	−	0.679400i	$-0.762240\pi$
$773$		−	37.7785i		−	1.35880i	0.733768	−	0.679400i	$-0.237760\pi$
$774$		0			0
$775$	6.32559			0.227222
$776$	−19.1955	−	28.0383i	−0.689079	−	1.00652i
$777$		0			0
$778$	−7.08046	+	21.1189i	−0.253847	+	0.757148i
$779$			72.6538i			2.60309i
$780$		0			0
$781$	23.3501			0.835533
$782$	3.92504	−	11.7072i	0.140359	−	0.418649i
$783$		0			0
$784$	−27.5545	−	4.97504i	−0.984088	−	0.177680i
$785$	−19.3395			−0.690256
$786$		0			0
$787$	11.0579			0.394172			0.197086	−	0.980386i	$-0.436852\pi$
$787$	11.0579			0.394172			0.197086	+	0.980386i	$0.436852\pi$
$788$	−16.1638	−	12.2109i	−0.575811	−	0.434996i
$789$		0			0
$790$	1.26682	−	3.77855i	0.0450716	−	0.134435i
$791$	−16.5845	−	26.5904i	−0.589677	−	0.945447i
$792$		0			0
$793$	8.04843			0.285808
$794$	15.2441	+	5.11085i	0.540993	+	0.181377i
$795$		0			0
$796$	−1.81836	−	1.37368i	−0.0644500	−	0.0486887i
$797$		−	35.7434i		−	1.26610i	−0.774113	−	0.633048i	$-0.781804\pi$
$797$		−	35.7434i		−	1.26610i	0.774113	−	0.633048i	$-0.218196\pi$
$798$		0			0
$799$		−	9.70934i		−	0.343492i
$800$	−5.65070	−	0.263812i	−0.199782	−	0.00932715i
$801$		0			0
$802$	−5.73725	+	17.1125i	−0.202589	+	0.604262i
$803$	−22.8817			−0.807478
$804$		0			0
$805$	−11.3503	−	18.1983i	−0.400047	−	0.641407i
$806$	21.2507	+	7.12466i	0.748524	+	0.250956i
$807$		0			0
$808$	0.416226	+	0.607970i	0.0146428	+	0.0213883i
$809$	7.42802			0.261155			0.130578	−	0.991438i	$-0.458317\pi$
$809$	7.42802			0.261155			0.130578	+	0.991438i	$0.458317\pi$
$810$		0			0
$811$	49.8603			1.75083			0.875416	−	0.483370i	$-0.160587\pi$
$811$	49.8603			1.75083			0.875416	+	0.483370i	$0.160587\pi$
$812$	2.83085	−	31.6110i	0.0993432	−	1.10933i
$813$		0			0
$814$	−16.3431	−	5.47930i	−0.572825	−	0.192049i
$815$	2.74676			0.0962149
$816$		0			0
$817$			63.3306i			2.21566i
$818$	2.56975	+	0.861551i	0.0898491	+	0.0301234i
$819$		0			0
$820$	14.8839	+	11.2441i	0.519770	+	0.392660i
$821$	−32.6401			−1.13915			−0.569574	−	0.821940i	$-0.692892\pi$
$821$	−32.6401			−1.13915			−0.569574	+	0.821940i	$0.692892\pi$
$822$		0			0
$823$		−	35.2404i		−	1.22840i	−0.789150	−	0.614201i	$-0.789478\pi$
$823$		−	35.2404i		−	1.22840i	0.789150	−	0.614201i	$-0.210522\pi$
$824$	−4.11893	+	2.81989i	−0.143490	+	0.0982354i
$825$		0			0
$826$	−35.2407	+	8.40676i	−1.22618	+	0.292508i
$827$			16.9100i			0.588019i	0.955802	+	0.294010i	$0.0949898\pi$
$827$			16.9100i			0.588019i	−0.955802	+	0.294010i	$0.905010\pi$
$828$		0			0
$829$			6.01900i			0.209049i	0.994522	+	0.104524i	$0.0333320\pi$
$829$			6.01900i			0.209049i	−0.994522	+	0.104524i	$0.966668\pi$
$830$	−16.7745	−	5.62394i	−0.582252	−	0.195210i
$831$		0			0
$832$	−18.6863	−	7.25079i	−0.647831	−	0.251376i
$833$	−6.77076	−	3.31641i	−0.234593	−	0.114907i
$834$		0			0
$835$			5.82171i			0.201469i
$836$	37.4848	−	49.6192i	1.29644	−	1.71611i
$837$		0			0
$838$	6.16349	−	18.3838i	0.212914	−	0.635059i
$839$	28.4981			0.983864			0.491932	−	0.870634i	$-0.336291\pi$
$839$	28.4981			0.983864			0.491932	+	0.870634i	$0.336291\pi$
$840$		0			0
$841$	6.97399			0.240482
$842$	3.54076	−	10.5610i	0.122023	−	0.363956i
$843$		0			0
$844$	−20.3310	+	26.9125i	−0.699822	+	0.926366i
$845$		−	6.72263i		−	0.231265i
$846$		0			0
$847$	−6.90635	−	11.0732i	−0.237305	−	0.380478i
$848$	−3.13241	−	11.0244i	−0.107567	−	0.378581i
$849$		0			0
$850$	−1.44417	−	0.484184i	−0.0495347	−	0.0166074i
$851$		−	24.7538i		−	0.848549i
$852$		0			0
$853$			19.8203i			0.678635i	0.940672	+	0.339317i	$0.110196\pi$
$853$			19.8203i			0.678635i	−0.940672	+	0.339317i	$0.889804\pi$
$854$	2.78902	+	11.6914i	0.0954383	+	0.400073i
$855$		0			0
$856$	9.75031	+	14.2420i	0.333259	+	0.486782i
$857$		−	28.1486i		−	0.961539i	−0.876847	−	0.480769i	$-0.840357\pi$
$857$		−	28.1486i		−	0.961539i	0.876847	−	0.480769i	$-0.159643\pi$
$858$		0			0
$859$	−47.6978			−1.62743			−0.813715	−	0.581265i	$-0.802558\pi$
$859$	−47.6978			−1.62743			−0.813715	+	0.581265i	$0.802558\pi$
$860$	12.9740	+	9.80118i	0.442409	+	0.334218i
$861$		0			0
$862$	30.0068	+	10.0603i	1.02204	+	0.342655i
$863$			4.53008i			0.154206i	0.997023	+	0.0771028i	$0.0245670\pi$
$863$			4.53008i			0.154206i	−0.997023	+	0.0771028i	$0.975433\pi$
$864$		0			0
$865$	−10.5651			−0.359226
$866$	−45.5586	−	15.2743i	−1.54815	−	0.519042i
$867$		0			0
$868$	−2.98554	+	33.3385i	−0.101336	+	1.13158i
$869$	11.2483			0.381571
$870$		0			0
$871$	19.5191			0.661379
$872$	−34.9056	+	23.8970i	−1.18205	+	0.809254i
$873$		0			0
$874$	84.6723	+	28.3878i	2.86408	+	0.960232i
$875$	−2.24490	+	1.40015i	−0.0758915	+	0.0473337i
$876$		0			0
$877$	45.2414			1.52769			0.763847	−	0.645397i	$-0.223308\pi$
$877$	45.2414			1.52769			0.763847	+	0.645397i	$0.223308\pi$
$878$	−1.33729	+	3.98873i	−0.0451313	+	0.134613i
$879$		0			0
$880$	−4.36381	−	15.3583i	−0.147104	−	0.517729i
$881$		−	6.77716i		−	0.228328i	−0.993462	−	0.114164i	$-0.963581\pi$
$881$		−	6.77716i		−	0.228328i	0.993462	−	0.114164i	$-0.0364190\pi$
$882$		0			0
$883$		−	16.8172i		−	0.565943i	−0.959128	−	0.282971i	$-0.908680\pi$
$883$		−	16.8172i		−	0.565943i	0.959128	−	0.282971i	$-0.0913202\pi$
$884$	−4.30633	−	3.25321i	−0.144838	−	0.109417i
$885$		0			0
$886$	−27.3663	−	9.17501i	−0.919388	−	0.308240i
$887$	−43.9171			−1.47459			−0.737296	−	0.675570i	$-0.763898\pi$
$887$	−43.9171			−1.47459			−0.737296	+	0.675570i	$0.763898\pi$
$888$		0			0
$889$	12.3336	−	7.69251i	0.413656	−	0.257998i
$890$	−1.57964	+	4.71158i	−0.0529496	+	0.157933i
$891$		0			0
$892$	−2.94857	−	2.22750i	−0.0987255	−	0.0745822i
$893$	70.2227			2.34991
$894$		0			0
$895$	4.59887			0.153723
$896$	4.05740	−	29.6570i	0.135548	−	0.990771i
$897$		0			0
$898$	4.95552	−	14.7808i	0.165368	−	0.493242i
$899$	−37.9398			−1.26536
$900$		0			0
$901$		−	3.08597i		−	0.102808i
$902$	−16.7360	+	49.9185i	−0.557249	+	1.66211i
$903$		0			0
$904$	27.6444	−	18.9258i	0.919438	−	0.629463i
$905$	9.42719			0.313370
$906$		0			0
$907$			1.93060i			0.0641044i	0.999486	+	0.0320522i	$0.0102043\pi$
$907$			1.93060i			0.0641044i	−0.999486	+	0.0320522i	$0.989796\pi$
$908$	41.5085	+	31.3576i	1.37751	+	1.04064i
$909$		0			0
$910$	−9.11873	+	2.17529i	−0.302283	+	0.0721103i
$911$			2.73855i			0.0907323i	0.998970	+	0.0453661i	$0.0144454\pi$
$911$			2.73855i			0.0907323i	−0.998970	+	0.0453661i	$0.985555\pi$
$912$		0			0
$913$		−	49.9355i		−	1.65262i
$914$	0.184017	−	0.548868i	0.00608675	−	0.0181549i
$915$		0			0
$916$	−17.8630	+	23.6455i	−0.590209	+	0.781269i
$917$	13.9171	+	22.3137i	0.459582	+	0.736862i
$918$		0			0
$919$			23.3016i			0.768648i	0.923198	+	0.384324i	$0.125565\pi$
$919$			23.3016i			0.768648i	−0.923198	+	0.384324i	$0.874435\pi$
$920$	18.9196	−	12.9527i	0.623762	−	0.427038i
$921$		0			0
$922$	32.1239	+	10.7701i	1.05795	+	0.354694i
$923$	14.6567			0.482430
$924$		0			0
$925$	−3.05357			−0.100401
$926$	13.5438	+	4.54077i	0.445076	+	0.149219i
$927$		0			0
$928$	33.8919	+	1.58230i	1.11256	+	0.0519415i
$929$			27.8007i			0.912110i	0.889952	+	0.456055i	$0.150738\pi$
$929$			27.8007i			0.912110i	−0.889952	+	0.456055i	$0.849262\pi$
$930$		0			0
$931$	23.9859	−	48.9694i	0.786106	−	1.60491i
$932$	−5.45563	−	4.12145i	−0.178705	−	0.135003i
$933$		0			0
$934$	17.3922	−	51.8756i	0.569089	−	1.69742i
$935$		−	4.29911i		−	0.140596i
$936$		0			0
$937$			8.85962i			0.289431i	0.989473	+	0.144716i	$0.0462267\pi$
$937$			8.85962i			0.289431i	−0.989473	+	0.144716i	$0.953773\pi$
$938$	6.76394	+	28.3541i	0.220851	+	0.925796i
$939$		0			0
$940$	10.8678	−	14.3859i	0.354469	−	0.469216i
$941$		−	53.7586i		−	1.75248i	−0.481873	−	0.876241i	$-0.660043\pi$
$941$		−	53.7586i		−	1.75248i	0.481873	−	0.876241i	$-0.339957\pi$
$942$		0			0
$943$	−75.6082			−2.46214
$944$	−10.5858	−	37.2564i	−0.344537	−	1.21259i
$945$		0			0
$946$	−14.5884	+	43.5128i	−0.474310	+	1.41472i
$947$			16.1410i			0.524513i	0.964998	+	0.262257i	$0.0844667\pi$
$947$			16.1410i			0.524513i	−0.964998	+	0.262257i	$0.915533\pi$
$948$		0			0
$949$	−14.3626			−0.466231
$950$	3.50185	−	10.4450i	0.113615	−	0.338880i
$951$		0			0
$952$	3.23346	−	7.38286i	0.104797	−	0.239280i
$953$	−31.2699			−1.01293			−0.506466	−	0.862260i	$-0.669048\pi$
$953$	−31.2699			−1.01293			−0.506466	+	0.862260i	$0.669048\pi$
$954$		0			0
$955$	−5.02689			−0.162666
$956$	−3.42760	+	4.53716i	−0.110856	+	0.146742i
$957$		0			0
$958$	−3.55911	+	10.6157i	−0.114989	+	0.342979i
$959$	−23.0107	−	36.8938i	−0.743055	−	1.19136i
$960$		0			0
$961$	9.01306			0.290744
$962$	−10.2584	−	3.43931i	−0.330744	−	0.110888i
$963$		0			0
$964$	24.2289	−	32.0722i	0.780361	−	1.03298i
$965$		−	15.8775i		−	0.511114i
$966$		0			0
$967$		−	29.6531i		−	0.953581i	−0.879017	−	0.476791i	$-0.841800\pi$
$967$		−	29.6531i		−	0.953581i	0.879017	−	0.476791i	$-0.158200\pi$
$968$	11.5120	−	7.88134i	0.370011	−	0.253316i
$969$		0			0
$970$	5.40068	−	16.1086i	0.173405	−	0.517215i
$971$	−50.3454			−1.61566			−0.807831	−	0.589414i	$-0.799359\pi$
$971$	−50.3454			−1.61566			−0.807831	+	0.589414i	$0.799359\pi$
$972$		0			0
$973$	24.9318	+	39.9739i	0.799276	+	1.28150i
$974$	−38.3464	−	12.8563i	−1.22870	−	0.411942i
$975$		0			0
$976$	−12.3601	+	3.51193i	−0.395639	+	0.112414i
$977$	40.8268			1.30617			0.653083	−	0.757286i	$-0.273475\pi$
$977$	40.8268			1.30617			0.653083	+	0.757286i	$0.273475\pi$
$978$		0			0
$979$	−14.0258			−0.448265
$980$	−6.31982	−	12.4924i	−0.201879	−	0.399055i
$981$		0			0
$982$	−31.6870	−	10.6236i	−1.01117	−	0.339012i
$983$	−18.2294			−0.581427			−0.290713	−	0.956810i	$-0.593893\pi$
$983$	−18.2294			−0.581427			−0.290713	+	0.956810i	$0.593893\pi$
$984$		0			0
$985$		−	10.1289i		−	0.322732i
$986$	8.66191	+	2.90405i	0.275851	+	0.0924838i
$987$		0			0
$988$	23.5288	−	31.1455i	0.748552	−	0.990870i
$989$	−65.9059			−2.09569
$990$		0			0
$991$			58.5653i			1.86039i	0.367070	+	0.930193i	$0.380361\pi$
$991$			58.5653i			1.86039i	−0.367070	+	0.930193i	$0.619639\pi$
$992$	−35.7440	−	1.66876i	−1.13487	−	0.0529833i
$993$		0			0
$994$	5.07897	+	21.2908i	0.161095	+	0.675303i
$995$		−	1.13945i		−	0.0361231i
$996$		0			0
$997$		−	61.3384i		−	1.94261i	−0.237846	−	0.971303i	$-0.576441\pi$
$997$		−	61.3384i		−	1.94261i	0.237846	−	0.971303i	$-0.423559\pi$
$998$	0.889006	+	0.298054i	0.0281410	+	0.00943475i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.d.811.11		16
3.2	odd	2		420.2.c.a.391.6	yes	16
4.3	odd	2		1260.2.c.e.811.12		16
7.6	odd	2		1260.2.c.e.811.11		16
12.11	even	2		420.2.c.b.391.5	yes	16
21.20	even	2		420.2.c.b.391.6	yes	16
28.27	even	2	inner	1260.2.c.d.811.12		16
84.83	odd	2		420.2.c.a.391.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.5	✓	16	84.83	odd	2
420.2.c.a.391.6	yes	16	3.2	odd	2
420.2.c.b.391.5	yes	16	12.11	even	2
420.2.c.b.391.6	yes	16	21.20	even	2
1260.2.c.d.811.11		16	1.1	even	1	trivial
1260.2.c.d.811.12		16	28.27	even	2	inner
1260.2.c.e.811.11		16	7.6	odd	2
1260.2.c.e.811.12		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.449546 - 1.34086i) q^{2} +(-1.59582 - 1.20556i) q^{4} -1.00000i q^{5} +(1.40015 + 2.24490i) q^{7} +(-2.33388 + 1.59781i) q^{8} +O(q^{10})\)	\(q+(0.449546 - 1.34086i) q^{2} +(-1.59582 - 1.20556i) q^{4} -1.00000i q^{5} +(1.40015 + 2.24490i) q^{7} +(-2.33388 + 1.59781i) q^{8} +(-1.34086 - 0.449546i) q^{10} -3.99156i q^{11} -2.50547i q^{13} +(3.63953 - 0.868219i) q^{14} +(1.09326 + 3.84770i) q^{16} +1.07705i q^{17} -7.78975 q^{19} +(-1.20556 + 1.59582i) q^{20} +(-5.35213 - 1.79439i) q^{22} -8.10651i q^{23} -1.00000 q^{25} +(-3.35948 - 1.12632i) q^{26} +(0.471978 - 5.27041i) q^{28} +5.99783 q^{29} -6.32559 q^{31} +(5.65070 + 0.263812i) q^{32} +(1.44417 + 0.484184i) q^{34} +(2.24490 - 1.40015i) q^{35} +3.05357 q^{37} +(-3.50185 + 10.4450i) q^{38} +(1.59781 + 2.33388i) q^{40} -9.32685i q^{41} -8.13000i q^{43} +(-4.81206 + 6.36980i) q^{44} +(-10.8697 - 3.64425i) q^{46} -9.01476 q^{47} +(-3.07916 + 6.28639i) q^{49} +(-0.449546 + 1.34086i) q^{50} +(-3.02049 + 3.99827i) q^{52} -2.86521 q^{53} -3.99156 q^{55} +(-6.85471 - 3.00215i) q^{56} +(2.69630 - 8.04226i) q^{58} -9.68276 q^{59} +3.21235i q^{61} +(-2.84365 + 8.48173i) q^{62} +(2.89399 - 7.45821i) q^{64} -2.50547 q^{65} +7.79060i q^{67} +(1.29845 - 1.71877i) q^{68} +(-0.868219 - 3.63953i) q^{70} +5.84987i q^{71} -5.73252i q^{73} +(1.37272 - 4.09441i) q^{74} +(12.4310 + 9.39100i) q^{76} +(8.96067 - 5.58879i) q^{77} +2.81801i q^{79} +(3.84770 - 1.09326i) q^{80} +(-12.5060 - 4.19285i) q^{82} +12.5103 q^{83} +1.07705 q^{85} +(-10.9012 - 3.65481i) q^{86} +(6.37777 + 9.31583i) q^{88} -3.51385i q^{89} +(5.62453 - 3.50803i) q^{91} +(-9.77288 + 12.9365i) q^{92} +(-4.05255 + 12.0875i) q^{94} +7.78975i q^{95} +12.0136i q^{97} +(7.04495 + 6.95475i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 2 * q^8 + 2 * q^14 + 6 * q^16 - 24 * q^19 - 12 * q^22 - 16 * q^25 + 12 * q^26 + 14 * q^28 - 16 * q^29 + 8 * q^31 + 18 * q^32 + 24 * q^34 + 24 * q^37 - 28 * q^38 + 12 * q^40 + 8 * q^44 - 20 * q^46 - 16 * q^47 - 16 * q^49 + 2 * q^50 - 20 * q^52 + 32 * q^53 - 2 * q^56 - 32 * q^58 - 8 * q^59 - 16 * q^62 - 2 * q^64 + 8 * q^65 - 4 * q^68 + 4 * q^74 + 16 * q^76 + 8 * q^77 + 16 * q^80 - 4 * q^82 - 8 * q^83 - 64 * q^86 - 52 * q^88 + 16 * q^91 - 64 * q^92 + 16 * q^94 + 86 * q^98

Introduction

L-functions

Modular forms

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