LMFDB - Embedded newform 1260.2.c.e.811.12

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +O(q^{10})$	\(q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +(1.34086 - 0.449546i) q^{10} +3.99156i q^{11} -2.50547i q^{13} +(2.38067 - 2.88659i) q^{14} +(1.09326 - 3.84770i) q^{16} +1.07705i q^{17} +7.78975 q^{19} +(1.20556 + 1.59582i) q^{20} +(-5.35213 + 1.79439i) q^{22} +8.10651i q^{23} -1.00000 q^{25} +(3.35948 - 1.12632i) q^{26} +(4.94074 + 1.89449i) q^{28} +5.99783 q^{29} +6.32559 q^{31} +(5.65070 - 0.263812i) q^{32} +(-1.44417 + 0.484184i) q^{34} +(-2.24490 + 1.40015i) q^{35} +3.05357 q^{37} +(3.50185 + 10.4450i) q^{38} +(-1.59781 + 2.33388i) q^{40} -9.32685i q^{41} +8.13000i q^{43} +(-4.81206 - 6.36980i) q^{44} +(-10.8697 + 3.64425i) q^{46} +9.01476 q^{47} +(-3.07916 + 6.28639i) q^{49} +(-0.449546 - 1.34086i) q^{50} +(3.02049 + 3.99827i) q^{52} -2.86521 q^{53} +3.99156 q^{55} +(-0.319153 + 7.47651i) q^{56} +(2.69630 + 8.04226i) q^{58} +9.68276 q^{59} +3.21235i q^{61} +(2.84365 + 8.48173i) q^{62} +(2.89399 + 7.45821i) q^{64} -2.50547 q^{65} -7.79060i q^{67} +(-1.29845 - 1.71877i) q^{68} +(-2.88659 - 2.38067i) q^{70} -5.84987i q^{71} -5.73252i q^{73} +(1.37272 + 4.09441i) q^{74} +(-12.4310 + 9.39100i) q^{76} +(8.96067 - 5.58879i) q^{77} -2.81801i q^{79} +(-3.84770 - 1.09326i) q^{80} +(12.5060 - 4.19285i) q^{82} -12.5103 q^{83} +1.07705 q^{85} +(-10.9012 + 3.65481i) q^{86} +(6.37777 - 9.31583i) q^{88} -3.51385i q^{89} +(-5.62453 + 3.50803i) q^{91} +(-9.77288 - 12.9365i) q^{92} +(4.05255 + 12.0875i) q^{94} -7.78975i q^{95} +12.0136i q^{97} +(-9.81341 - 1.30270i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 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} - 20 q^{70} + 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} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * 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 - 20 * q^70 + 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 - 2 * 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	$0.205530\pi$
$11$			3.99156i			1.20350i	−0.798684	+	0.601751i	$0.794470\pi$
$12$		0			0
$13$		−	2.50547i		−	0.694892i	−0.937700	−	0.347446i	$-0.887049\pi$
$13$		−	2.50547i		−	0.694892i	0.937700	−	0.347446i	$-0.112951\pi$
$14$	2.38067	−	2.88659i	0.636260	−	0.771474i
$15$		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	$-0.148210\pi$
$19$	7.78975			1.78709			0.893546	+	0.448973i	$0.148210\pi$
$20$	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	$0.320496\pi$
$23$			8.10651i			1.69033i	−0.534509	+	0.845163i	$0.679504\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	3.35948	−	1.12632i	0.658849	−	0.220890i
$27$		0			0
$28$	4.94074	+	1.89449i	0.933712	+	0.358025i
$29$	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	$-0.307696\pi$
$31$	6.32559			1.13611			0.568055	+	0.822991i	$0.307696\pi$
$32$	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	$0.212829\pi$
$43$			8.13000i			1.23981i	−0.784676	+	0.619906i	$0.787171\pi$
$44$	−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	$-0.271627\pi$
$47$	9.01476			1.31494			0.657469	+	0.753482i	$0.271627\pi$
$48$		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
$56$	−0.319153	+	7.47651i	−0.0426486	+	0.999090i
$57$		0			0
$58$	2.69630	+	8.04226i	0.354042	+	1.05600i
$59$	9.68276			1.26059			0.630294	−	0.776356i	$-0.282934\pi$
$59$	9.68276			1.26059			0.630294	+	0.776356i	$0.282934\pi$
$60$		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	$-0.842127\pi$
$67$		−	7.79060i		−	0.951773i	0.879507	−	0.475887i	$-0.157873\pi$
$68$	−1.29845	−	1.71877i	−0.157460	−	0.208432i
$69$		0			0
$70$	−2.88659	−	2.38067i	−0.345014	−	0.284544i
$71$		−	5.84987i		−	0.694252i	−0.937819	−	0.347126i	$-0.887158\pi$
$71$		−	5.84987i		−	0.694252i	0.937819	−	0.347126i	$-0.112842\pi$
$72$		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	$-0.949326\pi$
$79$		−	2.81801i		−	0.317050i	0.987355	−	0.158525i	$-0.0506739\pi$
$80$	−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	$-0.740893\pi$
$83$	−12.5103			−1.37318			−0.686590	+	0.727045i	$0.740893\pi$
$84$		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	$0.791210\pi$
$98$	−9.81341	−	1.30270i	−0.991304	−	0.131593i
$99$		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	$-0.527711\pi$
$103$	−1.76484			−0.173895			−0.0869475	+	0.996213i	$0.527711\pi$
$104$	−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	$0.0953081\pi$
$107$			6.10229i			0.589930i	−0.955508	+	0.294965i	$0.904692\pi$
$108$		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
$112$	−10.1684	+	2.93310i	−0.960826	+	0.277152i
$113$	−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	$0.0783808\pi$
$127$			5.49406i			0.487519i	−0.969836	+	0.243760i	$0.921619\pi$
$128$	−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	$-0.642975\pi$
$131$	−9.93971			−0.868436			−0.434218	+	0.900808i	$0.642975\pi$
$132$		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	$-0.772443\pi$
$139$	−17.8065			−1.51033			−0.755164	+	0.655535i	$0.772443\pi$
$140$	1.89449	−	4.94074i	0.160113	−	0.417569i
$141$		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	$0.181575\pi$
$151$			13.2712i			1.08000i	−0.841666	+	0.539998i	$0.818425\pi$
$152$	−18.1803	−	12.4466i	−1.47462	−	1.00955i
$153$		0			0
$154$	11.5220	+	9.50259i	0.928471	+	0.765740i
$155$		−	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	$-0.965693\pi$
$163$		−	2.74676i		−	0.215143i	0.994197	−	0.107572i	$-0.0343075\pi$
$164$	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	$-0.427680\pi$
$167$	5.82171			0.450498			0.225249	+	0.974301i	$0.427680\pi$
$168$		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	$-0.945020\pi$
$179$		−	4.59887i		−	0.343736i	0.985120	−	0.171868i	$-0.0549802\pi$
$180$		0			0
$181$			9.42719i			0.700717i	0.936616	+	0.350359i	$0.113940\pi$
$181$			9.42719i			0.700717i	−0.936616	+	0.350359i	$0.886060\pi$
$182$	−7.23227	−	5.96469i	−0.536091	−	0.442132i
$183$		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	$0.0582139\pi$
$191$			5.02689i			0.363733i	−0.983323	+	0.181866i	$0.941786\pi$
$192$		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
$196$	−2.66484	−	13.7440i	−0.190346	−	0.981717i
$197$	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	$-0.512859\pi$
$199$	−1.13945			−0.0807737			−0.0403869	+	0.999184i	$0.512859\pi$
$200$	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	$0.197142\pi$
$211$			16.8644i			1.16099i	−0.814263	+	0.580497i	$0.802858\pi$
$212$	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	$-0.519705\pi$
$223$	−1.84769			−0.123730			−0.0618652	+	0.998085i	$0.519705\pi$
$224$	−8.50406	−	12.3159i	−0.568201	−	0.822890i
$225$		0			0
$226$	−5.32479	−	15.8822i	−0.354200	−	1.05647i
$227$	26.0109			1.72640			0.863201	−	0.504861i	$-0.168456\pi$
$227$	26.0109			1.72640			0.863201	+	0.504861i	$0.168456\pi$
$228$		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
$238$	3.10900	+	2.56410i	0.201527	+	0.166206i
$239$			2.84316i			0.183909i	0.995763	+	0.0919544i	$0.0293114\pi$
$239$			2.84316i			0.183909i	−0.995763	+	0.0919544i	$0.970689\pi$
$240$		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	$-0.665493\pi$
$251$	−15.7417			−0.993607			−0.496803	+	0.867863i	$0.665493\pi$
$252$		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	$0.0843355\pi$
$263$			8.49327i			0.523718i	−0.965106	+	0.261859i	$0.915665\pi$
$264$		0			0
$265$			2.86521i			0.176008i
$266$	18.5448	−	22.4858i	1.13706	−	1.37869i
$267$		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	$-0.389490\pi$
$271$	11.2023			0.680490			0.340245	+	0.940337i	$0.389490\pi$
$272$	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
$280$	7.47651	+	0.319153i	0.446807	+	0.0190730i
$281$	−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	$-0.562007\pi$
$283$	−6.51271			−0.387140			−0.193570	+	0.981086i	$0.562007\pi$
$284$	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	$-0.879828\pi$
$307$	−32.5750			−1.85916			−0.929578	+	0.368626i	$0.879828\pi$
$308$	−7.56197	+	19.7213i	−0.430883	+	1.12372i
$309$		0			0
$310$	8.48173	−	2.84365i	0.481730	−	0.161508i
$311$	−27.3621			−1.55156			−0.775781	−	0.631002i	$-0.782644\pi$
$311$	−27.3621			−1.55156			−0.775781	+	0.631002i	$0.782644\pi$
$312$		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
$322$	23.4002	+	19.2989i	1.30404	+	1.07549i
$323$			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	$-0.962847\pi$
$331$		−	4.23740i		−	0.232909i	0.993196	−	0.116454i	$-0.0371529\pi$
$332$	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	$-0.878981\pi$
$347$		−	13.8257i		−	0.742200i	0.928593	−	0.371100i	$-0.121019\pi$
$348$		0			0
$349$			8.06666i			0.431798i	0.976416	+	0.215899i	$0.0692683\pi$
$349$			8.06666i			0.431798i	−0.976416	+	0.215899i	$0.930732\pi$
$350$	−2.38067	+	2.88659i	−0.127252	+	0.154295i
$351$		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	$-0.806670\pi$
$359$		−	21.6267i		−	1.14141i	0.821154	−	0.570706i	$-0.193330\pi$
$360$		0			0
$361$	41.6802			2.19369
$362$	−12.6405	+	4.23796i	−0.664372	+	0.222742i
$363$		0			0
$364$	4.74658	−	12.3789i	0.248788	−	0.648829i
$365$	−5.73252			−0.300054
$366$		0			0
$367$	6.62228			0.345680			0.172840	−	0.984950i	$-0.444706\pi$
$367$	6.62228			0.345680			0.172840	+	0.984950i	$0.444706\pi$
$368$	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	$-0.704290\pi$
$379$		−	31.1885i		−	1.60204i	0.598635	−	0.801022i	$-0.295710\pi$
$380$	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	$-0.246368\pi$
$383$	27.9907			1.43026			0.715128	+	0.698993i	$0.246368\pi$
$384$		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
$392$	17.2309	−	9.75176i	0.870291	−	0.492538i
$393$		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
$406$	14.2788	−	17.3133i	0.708647	−	0.859245i
$407$			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	$-0.608703\pi$
$419$	−13.7105			−0.669800			−0.334900	+	0.942254i	$0.608703\pi$
$420$		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	$-0.818812\pi$
$431$		−	22.3788i		−	1.07795i	0.842322	−	0.538974i	$-0.181188\pi$
$432$		0			0
$433$		−	33.9772i		−	1.63284i	−0.577460	−	0.816419i	$-0.695956\pi$
$433$		−	33.9772i		−	1.63284i	0.577460	−	0.816419i	$-0.304044\pi$
$434$	15.0591	−	18.2594i	0.722861	−	0.876479i
$435$		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	$-0.477385\pi$
$439$	2.97475			0.141977			0.0709886	+	0.997477i	$0.477385\pi$
$440$	−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	$0.161123\pi$
$443$			20.4095i			0.969684i	−0.874602	+	0.484842i	$0.838877\pi$
$444$		0			0
$445$	−3.51385			−0.166572
$446$	−0.830622	−	2.47750i	−0.0393311	−	0.117313i
$447$		0			0
$448$	12.6909	−	16.9393i	0.599590	−	0.800308i
$449$	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	$-0.924585\pi$
$463$		−	10.1008i		−	0.469424i	0.972065	−	0.234712i	$-0.0754147\pi$
$464$	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	$-0.852924\pi$
$467$	−38.6883			−1.79028			−0.895140	+	0.445785i	$0.852924\pi$
$468$		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
$476$	−2.04046	+	5.32142i	−0.0935242	+	0.243907i
$477$		0			0
$478$	−3.81228	+	1.27813i	−0.174370	+	0.0584604i
$479$	7.91710			0.361742			0.180871	−	0.983507i	$-0.442108\pi$
$479$	7.91710			0.361742			0.180871	+	0.983507i	$0.442108\pi$
$480$		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	$0.224377\pi$
$487$			28.5984i			1.29592i	−0.761676	+	0.647958i	$0.775623\pi$
$488$	5.13273	−	7.49723i	0.232348	−	0.339384i
$489$		0			0
$490$	−1.30270	+	9.81341i	−0.0588501	+	0.443325i
$491$			23.6318i			1.06649i	0.845961	+	0.533244i	$0.179027\pi$
$491$			23.6318i			1.06649i	−0.845961	+	0.533244i	$0.820973\pi$
$492$		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	$-0.995276\pi$
$499$		−	0.663011i		−	0.0296805i	0.999890	−	0.0148402i	$-0.00472397\pi$
$500$	−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	$-0.645090\pi$
$503$	−19.7450			−0.880385			−0.440192	+	0.897904i	$0.645090\pi$
$504$		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
$518$	7.26953	−	8.81441i	0.319405	−	0.387283i
$519$		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	$-0.655989\pi$
$523$	−21.5279			−0.941348			−0.470674	+	0.882307i	$0.655989\pi$
$524$	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
$532$	38.4871	+	14.7576i	1.66863	+	0.639822i
$533$	−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	$0.0354305\pi$
$547$			5.19581i			0.222157i	−0.993812	+	0.111079i	$0.964569\pi$
$548$	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
$560$	2.93310	+	10.1684i	0.123946	+	0.429695i
$561$		0			0
$562$	−0.774071	−	2.30882i	−0.0326522	−	0.0973917i
$563$	1.94438			0.0819459			0.0409730	−	0.999160i	$-0.486954\pi$
$563$	1.94438			0.0819459			0.0409730	+	0.999160i	$0.486954\pi$
$564$		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	$-0.654473\pi$
$571$		−	42.2732i		−	1.76908i	0.466466	−	0.884539i	$-0.345527\pi$
$572$	−15.9593	+	12.0565i	−0.667293	+	0.504106i
$573$		0			0
$574$	−26.9228	−	22.2041i	−1.12374	−	0.926783i
$575$		−	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	$-0.543557\pi$
$587$	−6.61005			−0.272826			−0.136413	+	0.990652i	$0.543557\pi$
$588$		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	$0.206692\pi$
$599$			29.5976i			1.20933i	−0.796481	+	0.604663i	$0.793308\pi$
$600$		0			0
$601$			42.7644i			1.74440i	0.489154	+	0.872198i	$0.337306\pi$
$601$			42.7644i			1.74440i	−0.489154	+	0.872198i	$0.662694\pi$
$602$	23.4680	+	19.3548i	0.956484	+	0.788844i
$603$		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	$-0.153801\pi$
$607$	43.6339			1.77104			0.885522	+	0.464598i	$0.153801\pi$
$608$	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
$616$	−29.8429	−	1.27392i	−1.20241	−	0.0513276i
$617$	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	$-0.639545\pi$
$619$	−21.1221			−0.848970			−0.424485	+	0.905435i	$0.639545\pi$
$620$	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	$0.0203406\pi$
$631$			3.20820i			0.127716i	−0.997959	+	0.0638582i	$0.979659\pi$
$632$	−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	$-0.450224\pi$
$643$	7.89830			0.311479			0.155739	+	0.987798i	$0.450224\pi$
$644$	−15.3577	+	40.0522i	−0.605178	+	1.57828i
$645$		0			0
$646$	−11.2497	+	3.77167i	−0.442615	+	0.148394i
$647$	0.910960			0.0358135			0.0179068	−	0.999840i	$-0.494300\pi$
$647$	0.910960			0.0358135			0.0179068	+	0.999840i	$0.494300\pi$
$648$		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
$658$	21.4612	−	26.0219i	0.836643	−	1.01444i
$659$		−	6.38815i		−	0.248847i	−0.992229	−	0.124423i	$-0.960292\pi$
$659$		−	6.38815i		−	0.248847i	0.992229	−	0.124423i	$-0.0397081\pi$
$660$		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	$0.0306053\pi$
$683$			5.01785i			0.192003i	−0.995381	+	0.0960014i	$0.969395\pi$
$684$		0			0
$685$			16.4345i			0.627929i
$686$	10.8158	+	23.8541i	0.412949	+	0.910754i
$687$		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	$-0.707316\pi$
$691$	−31.8714			−1.21245			−0.606224	+	0.795294i	$0.707316\pi$
$692$	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
$700$	−4.94074	−	1.89449i	−0.186742	−	0.0716049i
$701$	−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	$-0.521288\pi$
$719$	−3.58392			−0.133658			−0.0668289	+	0.997764i	$0.521288\pi$
$720$		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	$-0.628503\pi$
$727$	−21.1835			−0.785652			−0.392826	+	0.919613i	$0.628503\pi$
$728$	18.7321	+	0.799627i	0.694260	+	0.0296361i
$729$		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	$0.109533\pi$
$739$			18.3419i			0.674716i	−0.941376	+	0.337358i	$0.890467\pi$
$740$	3.68125	+	4.87293i	0.135326	+	0.179133i
$741$		0			0
$742$	−6.82110	+	8.27068i	−0.250411	+	0.303626i
$743$		−	47.9531i		−	1.75923i	−0.475688	−	0.879614i	$-0.657801\pi$
$743$		−	47.9531i		−	1.75923i	0.475688	−	0.879614i	$-0.342199\pi$
$744$		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	$0.386989\pi$
$751$			51.3906i			1.87527i	−0.347624	+	0.937634i	$0.613011\pi$
$752$	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	$-0.314075\pi$
$770$	9.50259	−	11.5220i	0.342450	−	0.415225i
$771$		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
$784$	20.8218	+	18.7203i	0.743637	+	0.668584i
$785$	−19.3395			−0.690256
$786$		0			0
$787$	−11.0579			−0.394172			−0.197086	−	0.980386i	$-0.563148\pi$
$787$	−11.0579			−0.394172			−0.197086	+	0.980386i	$0.563148\pi$
$788$	−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	$-0.839413\pi$
$811$	−49.8603			−1.75083			−0.875416	+	0.483370i	$0.839413\pi$
$812$	29.6337	+	11.3628i	1.03994	+	0.398757i
$813$		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	$0.210522\pi$
$823$			35.2404i			1.22840i	−0.789150	+	0.614201i	$0.789478\pi$
$824$	4.11893	+	2.81989i	0.143490	+	0.0982354i
$825$		0			0
$826$	23.0514	−	27.9502i	0.802062	−	0.972512i
$827$		−	16.9100i		−	0.588019i	−0.955802	−	0.294010i	$-0.905010\pi$
$827$		−	16.9100i		−	0.588019i	0.955802	−	0.294010i	$-0.0949898\pi$
$828$		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	$-0.663709\pi$
$839$	−28.4981			−0.983864			−0.491932	+	0.870634i	$0.663709\pi$
$840$		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	$0.889804\pi$
$854$	9.27274	+	7.64753i	0.317307	+	0.261693i
$855$		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	$-0.197442\pi$
$859$	47.6978			1.62743			0.813715	+	0.581265i	$0.197442\pi$
$860$	−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	$-0.975433\pi$
$863$		−	4.53008i		−	0.154206i	0.997023	−	0.0771028i	$-0.0245670\pi$
$864$		0			0
$865$	−10.5651			−0.359226
$866$	45.5586	−	15.2743i	1.54815	−	0.519042i
$867$		0			0
$868$	31.2531	+	11.9837i	1.06080	+	0.406755i
$869$	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	$0.0913202\pi$
$883$			16.8172i			0.565943i	−0.959128	+	0.282971i	$0.908680\pi$
$884$	−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	$-0.236102\pi$
$887$	43.9171			1.47459			0.737296	+	0.675570i	$0.236102\pi$
$888$		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
$896$	28.4184	+	9.40175i	0.949393	+	0.314091i
$897$		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	$-0.989796\pi$
$907$		−	1.93060i		−	0.0641044i	0.999486	−	0.0320522i	$-0.0102043\pi$
$908$	−41.5085	+	31.3576i	−1.37751	+	1.04064i
$909$		0			0
$910$	−5.96469	+	7.23227i	−0.197727	+	0.239747i
$911$		−	2.73855i		−	0.0907323i	−0.998970	−	0.0453661i	$-0.985555\pi$
$911$		−	2.73855i		−	0.0907323i	0.998970	−	0.0453661i	$-0.0144454\pi$
$912$		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	$-0.874435\pi$
$919$		−	23.3016i		−	0.768648i	0.923198	−	0.384324i	$-0.125565\pi$
$920$	−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	$0.953773\pi$
$938$	−22.4883	−	18.5468i	−0.734269	−	0.605576i
$939$		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	$-0.915533\pi$
$947$		−	16.1410i		−	0.524513i	0.964998	−	0.262257i	$-0.0844667\pi$
$948$		0			0
$949$	−14.3626			−0.466231
$950$	−3.50185	−	10.4450i	−0.113615	−	0.338880i
$951$		0			0
$952$	−8.05256	−	0.343743i	−0.260985	−	0.0111408i
$953$	−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	$0.158200\pi$
$967$			29.6531i			0.953581i	−0.879017	+	0.476791i	$0.841800\pi$
$968$	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	$-0.200641\pi$
$971$	50.3454			1.61566			0.807831	+	0.589414i	$0.200641\pi$
$972$		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
$980$	−13.7440	+	2.66484i	−0.439037	+	0.0851251i
$981$		0			0
$982$	−31.6870	+	10.6236i	−1.01117	+	0.339012i
$983$	18.2294			0.581427			0.290713	−	0.956810i	$-0.406107\pi$
$983$	18.2294			0.581427			0.290713	+	0.956810i	$0.406107\pi$
$984$		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	$-0.619639\pi$
$991$		−	58.5653i		−	1.86039i	0.367070	−	0.930193i	$-0.380361\pi$
$992$	35.7440	−	1.66876i	1.13487	−	0.0529833i
$993$		0			0
$994$	−16.8862	−	13.9266i	−0.535598	−	0.441725i
$995$			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.e.811.12		16
3.2	odd	2		420.2.c.b.391.5	yes	16
4.3	odd	2		1260.2.c.d.811.11		16
7.6	odd	2		1260.2.c.d.811.12		16
12.11	even	2		420.2.c.a.391.6	yes	16
21.20	even	2		420.2.c.a.391.5	✓	16
28.27	even	2	inner	1260.2.c.e.811.11		16
84.83	odd	2		420.2.c.b.391.6	yes	16

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

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)

\(f(q)\)	\(=\)	\(q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +O(q^{10})\)	\(q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +(1.34086 - 0.449546i) q^{10} +3.99156i q^{11} -2.50547i q^{13} +(2.38067 - 2.88659i) q^{14} +(1.09326 - 3.84770i) q^{16} +1.07705i q^{17} +7.78975 q^{19} +(1.20556 + 1.59582i) q^{20} +(-5.35213 + 1.79439i) q^{22} +8.10651i q^{23} -1.00000 q^{25} +(3.35948 - 1.12632i) q^{26} +(4.94074 + 1.89449i) q^{28} +5.99783 q^{29} +6.32559 q^{31} +(5.65070 - 0.263812i) q^{32} +(-1.44417 + 0.484184i) q^{34} +(-2.24490 + 1.40015i) q^{35} +3.05357 q^{37} +(3.50185 + 10.4450i) q^{38} +(-1.59781 + 2.33388i) q^{40} -9.32685i q^{41} +8.13000i q^{43} +(-4.81206 - 6.36980i) q^{44} +(-10.8697 + 3.64425i) q^{46} +9.01476 q^{47} +(-3.07916 + 6.28639i) q^{49} +(-0.449546 - 1.34086i) q^{50} +(3.02049 + 3.99827i) q^{52} -2.86521 q^{53} +3.99156 q^{55} +(-0.319153 + 7.47651i) q^{56} +(2.69630 + 8.04226i) q^{58} +9.68276 q^{59} +3.21235i q^{61} +(2.84365 + 8.48173i) q^{62} +(2.89399 + 7.45821i) q^{64} -2.50547 q^{65} -7.79060i q^{67} +(-1.29845 - 1.71877i) q^{68} +(-2.88659 - 2.38067i) q^{70} -5.84987i q^{71} -5.73252i q^{73} +(1.37272 + 4.09441i) q^{74} +(-12.4310 + 9.39100i) q^{76} +(8.96067 - 5.58879i) q^{77} -2.81801i q^{79} +(-3.84770 - 1.09326i) q^{80} +(12.5060 - 4.19285i) q^{82} -12.5103 q^{83} +1.07705 q^{85} +(-10.9012 + 3.65481i) q^{86} +(6.37777 - 9.31583i) q^{88} -3.51385i q^{89} +(-5.62453 + 3.50803i) q^{91} +(-9.77288 - 12.9365i) q^{92} +(4.05255 + 12.0875i) q^{94} -7.78975i q^{95} +12.0136i q^{97} +(-9.81341 - 1.30270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * 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 - 20 * q^70 + 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 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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