LMFDB - Embedded newform 2028.2.i.l.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2028,2,Mod(529,2028)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2028, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("2028.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2028 = 2^{2} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2028.i (of order $3$, degree $2$, not 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:	$16.1936615299$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.2
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	2028.529
Dual form			2028.2.i.l.2005.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} -0.554958 q^{5} +(0.524459 + 0.908389i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.45593 + 2.52174i) q^{11} +(-0.277479 + 0.480608i) q^{15} +(-1.37651 - 2.38419i) q^{17} +(-2.31551 - 4.01058i) q^{19} +1.04892 q^{21} +(2.88135 - 4.99065i) q^{23} -4.69202 q^{25} -1.00000 q^{27} +(1.40097 - 2.42655i) q^{29} -4.18598 q^{31} +(1.45593 + 2.52174i) q^{33} +(-0.291053 - 0.504118i) q^{35} +(-0.233406 + 0.404271i) q^{37} +(1.94989 - 3.37730i) q^{41} +(-4.59783 - 7.96368i) q^{43} +(0.277479 + 0.480608i) q^{45} +11.5211 q^{47} +(2.94989 - 5.10935i) q^{49} -2.75302 q^{51} +5.62565 q^{53} +(0.807979 - 1.39946i) q^{55} -4.63102 q^{57} +(-1.55496 - 2.69327i) q^{59} +(-5.45257 - 9.44414i) q^{61} +(0.524459 - 0.908389i) q^{63} +(-4.02446 + 6.97057i) q^{67} +(-2.88135 - 4.99065i) q^{69} +(-6.84601 - 11.8576i) q^{71} +9.36658 q^{73} +(-2.34601 + 4.06341i) q^{75} -3.05429 q^{77} -3.60925 q^{79} +(-0.500000 + 0.866025i) q^{81} +1.65519 q^{83} +(0.763906 + 1.32312i) q^{85} +(-1.40097 - 2.42655i) q^{87} +(-8.98523 + 15.5629i) q^{89} +(-2.09299 + 3.62517i) q^{93} +(1.28501 + 2.22571i) q^{95} +(0.658834 + 1.14113i) q^{97} +2.91185 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 4 q^{5} - 6 q^{7} - 3 q^{9} - 5 q^{11} - 2 q^{15} - 13 q^{17} + q^{19} - 12 q^{21} - 18 q^{25} - 6 q^{27} + 4 q^{29} + 4 q^{31} + 5 q^{33} + 4 q^{35} + 2 q^{37} - 11 q^{41} + 9 q^{43} + 2 q^{45}+ \cdots + 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 4 * q^5 - 6 * q^7 - 3 * q^9 - 5 * q^11 - 2 * q^15 - 13 * q^17 + q^19 - 12 * q^21 - 18 * q^25 - 6 * q^27 + 4 * q^29 + 4 * q^31 + 5 * q^33 + 4 * q^35 + 2 * q^37 - 11 * q^41 + 9 * q^43 + 2 * q^45 + 38 * q^47 - 5 * q^49 - 26 * q^51 + 10 * q^53 + 15 * q^55 + 2 * q^57 - 10 * q^59 - 7 * q^61 - 6 * q^63 - 15 * q^67 - 36 * q^71 + 4 * q^73 - 9 * q^75 + 6 * q^77 + 2 * q^79 - 3 * q^81 + 56 * q^83 + 11 * q^85 - 4 * q^87 - 19 * q^89 + 2 * q^93 - 17 * q^95 - 13 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1861$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.554958			−0.248185			−0.124092	−	0.992271i	$-0.539602\pi$
$5$	−0.554958			−0.248185			−0.124092	+	0.992271i	$0.539602\pi$
$6$		0			0
$7$	0.524459	+	0.908389i	0.198227	+	0.343339i	0.947954	−	0.318409i	$-0.103148\pi$
$7$	0.524459	+	0.908389i	0.198227	+	0.343339i	−0.749727	+	0.661747i	$0.769815\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.45593	+	2.52174i	−0.438979	+	0.760333i	−0.997611	−	0.0690822i	$-0.977993\pi$
$11$	−1.45593	+	2.52174i	−0.438979	+	0.760333i	0.558632	+	0.829415i	$0.311326\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−0.277479	+	0.480608i	−0.0716448	+	0.124092i
$16$		0			0
$17$	−1.37651	−	2.38419i	−0.333853	−	0.578250i	0.649411	−	0.760438i	$-0.275016\pi$
$17$	−1.37651	−	2.38419i	−0.333853	−	0.578250i	−0.983264	+	0.182188i	$0.941682\pi$
$18$		0			0
$19$	−2.31551	−	4.01058i	−0.531215	−	0.920091i	−0.999336	−	0.0364268i	$-0.988402\pi$
$19$	−2.31551	−	4.01058i	−0.531215	−	0.920091i	0.468122	−	0.883664i	$-0.344931\pi$
$20$		0			0
$21$	1.04892			0.228893
$22$		0			0
$23$	2.88135	−	4.99065i	0.600804	−	1.04062i	−0.391896	−	0.920010i	$-0.628181\pi$
$23$	2.88135	−	4.99065i	0.600804	−	1.04062i	0.992700	−	0.120613i	$-0.0384861\pi$
$24$		0			0
$25$	−4.69202			−0.938404
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	1.40097	−	2.42655i	0.260153	−	0.450599i	−0.706129	−	0.708083i	$-0.749560\pi$
$29$	1.40097	−	2.42655i	0.260153	−	0.450599i	0.966283	+	0.257484i	$0.0828935\pi$
$30$		0			0
$31$	−4.18598			−0.751824			−0.375912	−	0.926655i	$-0.622671\pi$
$31$	−4.18598			−0.751824			−0.375912	+	0.926655i	$0.622671\pi$
$32$		0			0
$33$	1.45593	+	2.52174i	0.253444	+	0.438979i
$34$		0			0
$35$	−0.291053	−	0.504118i	−0.0491969	−	0.0852115i
$36$		0			0
$37$	−0.233406	+	0.404271i	−0.0383717	+	0.0664618i	−0.884573	−	0.466401i	$-0.845550\pi$
$37$	−0.233406	+	0.404271i	−0.0383717	+	0.0664618i	0.846202	+	0.532863i	$0.178884\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.94989	−	3.37730i	0.304521	−	0.527446i	−0.672634	−	0.739976i	$-0.734837\pi$
$41$	1.94989	−	3.37730i	0.304521	−	0.527446i	0.977155	+	0.212530i	$0.0681703\pi$
$42$		0			0
$43$	−4.59783	−	7.96368i	−0.701163	−	1.21445i	−0.968058	−	0.250725i	$-0.919331\pi$
$43$	−4.59783	−	7.96368i	−0.701163	−	1.21445i	0.266895	−	0.963726i	$-0.414002\pi$
$44$		0			0
$45$	0.277479	+	0.480608i	0.0413641	+	0.0716448i
$46$		0			0
$47$	11.5211			1.68053			0.840263	−	0.542179i	$-0.182401\pi$
$47$	11.5211			1.68053			0.840263	+	0.542179i	$0.182401\pi$
$48$		0			0
$49$	2.94989	−	5.10935i	0.421412	−	0.729908i
$50$		0			0
$51$	−2.75302			−0.385500
$52$		0			0
$53$	5.62565			0.772742			0.386371	−	0.922343i	$-0.373728\pi$
$53$	5.62565			0.772742			0.386371	+	0.922343i	$0.373728\pi$
$54$		0			0
$55$	0.807979	−	1.39946i	0.108948	−	0.188703i
$56$		0			0
$57$	−4.63102			−0.613394
$58$		0			0
$59$	−1.55496	−	2.69327i	−0.202438	−	0.350633i	0.746875	−	0.664964i	$-0.231553\pi$
$59$	−1.55496	−	2.69327i	−0.202438	−	0.350633i	−0.949314	+	0.314331i	$0.898220\pi$
$60$		0			0
$61$	−5.45257	−	9.44414i	−0.698131	−	1.20920i	−0.969114	−	0.246614i	$-0.920682\pi$
$61$	−5.45257	−	9.44414i	−0.698131	−	1.20920i	0.270983	−	0.962584i	$-0.412651\pi$
$62$		0			0
$63$	0.524459	−	0.908389i	0.0660756	−	0.114446i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.02446	+	6.97057i	−0.491666	+	0.851590i	−0.999954	−	0.00959683i	$-0.996945\pi$
$67$	−4.02446	+	6.97057i	−0.491666	+	0.851590i	0.508288	+	0.861187i	$0.330279\pi$
$68$		0			0
$69$	−2.88135	−	4.99065i	−0.346874	−	0.600804i
$70$		0			0
$71$	−6.84601	−	11.8576i	−0.812472	−	1.40724i	−0.911129	−	0.412121i	$-0.864788\pi$
$71$	−6.84601	−	11.8576i	−0.812472	−	1.40724i	0.0986570	−	0.995121i	$-0.468545\pi$
$72$		0			0
$73$	9.36658			1.09628			0.548138	−	0.836388i	$-0.315337\pi$
$73$	9.36658			1.09628			0.548138	+	0.836388i	$0.315337\pi$
$74$		0			0
$75$	−2.34601	+	4.06341i	−0.270894	+	0.469202i
$76$		0			0
$77$	−3.05429			−0.348069
$78$		0			0
$79$	−3.60925			−0.406073			−0.203036	−	0.979171i	$-0.565081\pi$
$79$	−3.60925			−0.406073			−0.203036	+	0.979171i	$0.565081\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	1.65519			0.181680			0.0908401	−	0.995865i	$-0.471045\pi$
$83$	1.65519			0.181680			0.0908401	+	0.995865i	$0.471045\pi$
$84$		0			0
$85$	0.763906	+	1.32312i	0.0828572	+	0.143513i
$86$		0			0
$87$	−1.40097	−	2.42655i	−0.150200	−	0.260153i
$88$		0			0
$89$	−8.98523	+	15.5629i	−0.952432	+	1.64966i	−0.212295	+	0.977206i	$0.568094\pi$
$89$	−8.98523	+	15.5629i	−0.952432	+	1.64966i	−0.740137	+	0.672456i	$0.765239\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.09299	+	3.62517i	−0.217033	+	0.375912i
$94$		0			0
$95$	1.28501	+	2.22571i	0.131839	+	0.228353i
$96$		0			0
$97$	0.658834	+	1.14113i	0.0668944	+	0.115865i	0.897533	−	0.440948i	$-0.145358\pi$
$97$	0.658834	+	1.14113i	0.0668944	+	0.115865i	−0.830638	+	0.556812i	$0.812024\pi$
$98$		0			0
$99$	2.91185			0.292652
$100$		0			0
$101$	7.51238	−	13.0118i	0.747509	−	1.29472i	−0.201504	−	0.979488i	$-0.564583\pi$
$101$	7.51238	−	13.0118i	0.747509	−	1.29472i	0.949013	−	0.315237i	$-0.102084\pi$
$102$		0			0
$103$	−9.20775			−0.907267			−0.453633	−	0.891188i	$-0.649872\pi$
$103$	−9.20775			−0.907267			−0.453633	+	0.891188i	$0.649872\pi$
$104$		0			0
$105$	−0.582105			−0.0568077
$106$		0			0
$107$	−3.61476	+	6.26095i	−0.349452	+	0.605269i	−0.986152	−	0.165843i	$-0.946966\pi$
$107$	−3.61476	+	6.26095i	−0.349452	+	0.605269i	0.636700	+	0.771112i	$0.280299\pi$
$108$		0			0
$109$	−15.5036			−1.48498			−0.742490	−	0.669857i	$-0.766355\pi$
$109$	−15.5036			−1.48498			−0.742490	+	0.669857i	$0.766355\pi$
$110$		0			0
$111$	0.233406	+	0.404271i	0.0221539	+	0.0383717i
$112$		0			0
$113$	−6.91335	−	11.9743i	−0.650353	−	1.12644i	−0.983037	−	0.183406i	$-0.941288\pi$
$113$	−6.91335	−	11.9743i	−0.650353	−	1.12644i	0.332684	−	0.943038i	$-0.392046\pi$
$114$		0			0
$115$	−1.59903	+	2.76960i	−0.149110	+	0.258267i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.44385	−	2.50081i	0.132357	−	0.229249i
$120$		0			0
$121$	1.26055	+	2.18334i	0.114596	+	0.198486i
$122$		0			0
$123$	−1.94989	−	3.37730i	−0.175815	−	0.304521i
$124$		0			0
$125$	5.37867			0.481083
$126$		0			0
$127$	−3.58815	+	6.21485i	−0.318396	+	0.551479i	−0.980154	−	0.198239i	$-0.936478\pi$
$127$	−3.58815	+	6.21485i	−0.318396	+	0.551479i	0.661757	+	0.749718i	$0.269811\pi$
$128$		0			0
$129$	−9.19567			−0.809634
$130$		0			0
$131$	13.1304			1.14720			0.573602	−	0.819134i	$-0.305545\pi$
$131$	13.1304			1.14720			0.573602	+	0.819134i	$0.305545\pi$
$132$		0			0
$133$	2.42878	−	4.20677i	0.210602	−	0.364773i
$134$		0			0
$135$	0.554958			0.0477632
$136$		0			0
$137$	−10.9058	−	18.8894i	−0.931747	−	1.61383i	−0.780335	−	0.625361i	$-0.784952\pi$
$137$	−10.9058	−	18.8894i	−0.931747	−	1.61383i	−0.151411	−	0.988471i	$-0.548382\pi$
$138$		0			0
$139$	1.48307	+	2.56876i	0.125793	+	0.217879i	0.922043	−	0.387089i	$-0.126519\pi$
$139$	1.48307	+	2.56876i	0.125793	+	0.217879i	−0.796250	+	0.604968i	$0.793186\pi$
$140$		0			0
$141$	5.76055	−	9.97757i	0.485126	−	0.840263i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−0.777479	+	1.34663i	−0.0645661	+	0.111832i
$146$		0			0
$147$	−2.94989	−	5.10935i	−0.243303	−	0.421412i
$148$		0			0
$149$	2.84817	+	4.93317i	0.233331	+	0.404141i	0.958786	−	0.284128i	$-0.0917041\pi$
$149$	2.84817	+	4.93317i	0.233331	+	0.404141i	−0.725455	+	0.688269i	$0.758371\pi$
$150$		0			0
$151$	19.1468			1.55814			0.779070	−	0.626937i	$-0.215691\pi$
$151$	19.1468			1.55814			0.779070	+	0.626937i	$0.215691\pi$
$152$		0			0
$153$	−1.37651	+	2.38419i	−0.111284	+	0.192750i
$154$		0			0
$155$	2.32304			0.186591
$156$		0			0
$157$	−8.38404			−0.669119			−0.334560	−	0.942375i	$-0.608588\pi$
$157$	−8.38404			−0.669119			−0.334560	+	0.942375i	$0.608588\pi$
$158$		0			0
$159$	2.81282	−	4.87195i	0.223071	−	0.386371i
$160$		0			0
$161$	6.04461			0.476382
$162$		0			0
$163$	0.985230	+	1.70647i	0.0771692	+	0.133661i	0.902028	−	0.431679i	$-0.142079\pi$
$163$	0.985230	+	1.70647i	0.0771692	+	0.133661i	−0.824858	+	0.565339i	$0.808745\pi$
$164$		0			0
$165$	−0.807979	−	1.39946i	−0.0629010	−	0.108948i
$166$		0			0
$167$	−12.3998	+	21.4770i	−0.959523	+	1.66194i	−0.235863	+	0.971786i	$0.575792\pi$
$167$	−12.3998	+	21.4770i	−0.959523	+	1.66194i	−0.723660	+	0.690157i	$0.757542\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−2.31551	+	4.01058i	−0.177072	+	0.306697i
$172$		0			0
$173$	1.28568	+	2.22686i	0.0977481	+	0.169305i	0.910752	−	0.412953i	$-0.135503\pi$
$173$	1.28568	+	2.22686i	0.0977481	+	0.169305i	−0.813004	+	0.582258i	$0.802169\pi$
$174$		0			0
$175$	−2.46077	−	4.26218i	−0.186017	−	0.322191i
$176$		0			0
$177$	−3.10992			−0.233756
$178$		0			0
$179$	1.50269	−	2.60273i	0.112316	−	0.194537i	−0.804388	−	0.594105i	$-0.797506\pi$
$179$	1.50269	−	2.60273i	0.112316	−	0.194537i	0.916704	+	0.399568i	$0.130840\pi$
$180$		0			0
$181$	−14.6843			−1.09147			−0.545736	−	0.837957i	$-0.683750\pi$
$181$	−14.6843			−1.09147			−0.545736	+	0.837957i	$0.683750\pi$
$182$		0			0
$183$	−10.9051			−0.806132
$184$		0			0
$185$	0.129531	−	0.224354i	0.00952328	−	0.0164948i
$186$		0			0
$187$	8.01639			0.586217
$188$		0			0
$189$	−0.524459	−	0.908389i	−0.0381488	−	0.0660756i
$190$		0			0
$191$	8.54019	+	14.7920i	0.617946	+	1.07031i	0.989860	+	0.142047i	$0.0453684\pi$
$191$	8.54019	+	14.7920i	0.617946	+	1.07031i	−0.371914	+	0.928267i	$0.621298\pi$
$192$		0			0
$193$	7.48792	−	12.9695i	0.538992	−	0.933562i	−0.459966	−	0.887936i	$-0.652139\pi$
$193$	7.48792	−	12.9695i	0.538992	−	0.933562i	0.998959	−	0.0456255i	$-0.0145281\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.0963427	+	0.166870i	−0.00686414	+	0.0118890i	−0.869437	−	0.494044i	$-0.835518\pi$
$197$	−0.0963427	+	0.166870i	−0.00686414	+	0.0118890i	0.862573	+	0.505933i	$0.168852\pi$
$198$		0			0
$199$	−5.93631	−	10.2820i	−0.420814	−	0.728871i	0.575205	−	0.818009i	$-0.304922\pi$
$199$	−5.93631	−	10.2820i	−0.420814	−	0.728871i	−0.996019	+	0.0891378i	$0.971589\pi$
$200$		0			0
$201$	4.02446	+	6.97057i	0.283863	+	0.491666i
$202$		0			0
$203$	2.93900			0.206277
$204$		0			0
$205$	−1.08211	+	1.87426i	−0.0755775	+	0.130904i
$206$		0			0
$207$	−5.76271			−0.400536
$208$		0			0
$209$	13.4849			0.932767
$210$		0			0
$211$	−3.01693	+	5.22547i	−0.207694	+	0.359736i	−0.950988	−	0.309229i	$-0.899929\pi$
$211$	−3.01693	+	5.22547i	−0.207694	+	0.359736i	0.743294	+	0.668965i	$0.233262\pi$
$212$		0			0
$213$	−13.6920			−0.938162
$214$		0			0
$215$	2.55161	+	4.41951i	0.174018	+	0.301408i
$216$		0			0
$217$	−2.19537	−	3.80250i	−0.149032	−	0.258130i
$218$		0			0
$219$	4.68329	−	8.11170i	0.316468	−	0.548138i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−4.26324	+	7.38415i	−0.285488	+	0.494479i	−0.972727	−	0.231952i	$-0.925489\pi$
$223$	−4.26324	+	7.38415i	−0.285488	+	0.494479i	0.687240	+	0.726431i	$0.258822\pi$
$224$		0			0
$225$	2.34601	+	4.06341i	0.156401	+	0.270894i
$226$		0			0
$227$	−5.50000	−	9.52628i	−0.365048	−	0.632281i	0.623736	−	0.781635i	$-0.285614\pi$
$227$	−5.50000	−	9.52628i	−0.365048	−	0.632281i	−0.988784	+	0.149354i	$0.952281\pi$
$228$		0			0
$229$	−17.9119			−1.18365			−0.591824	−	0.806067i	$-0.701592\pi$
$229$	−17.9119			−1.18365			−0.591824	+	0.806067i	$0.701592\pi$
$230$		0			0
$231$	−1.52715	+	2.64510i	−0.100479	+	0.174035i
$232$		0			0
$233$	22.8159			1.49472			0.747361	−	0.664418i	$-0.231321\pi$
$233$	22.8159			1.49472			0.747361	+	0.664418i	$0.231321\pi$
$234$		0			0
$235$	−6.39373			−0.417081
$236$		0			0
$237$	−1.80463	+	3.12570i	−0.117223	+	0.203036i
$238$		0			0
$239$	8.34481			0.539781			0.269891	−	0.962891i	$-0.413012\pi$
$239$	8.34481			0.539781			0.269891	+	0.962891i	$0.413012\pi$
$240$		0			0
$241$	1.87771	+	3.25228i	0.120954	+	0.209498i	0.920144	−	0.391580i	$-0.128071\pi$
$241$	1.87771	+	3.25228i	0.120954	+	0.209498i	−0.799190	+	0.601078i	$0.794738\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.63706	+	2.83548i	−0.104588	+	0.181152i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.827593	−	1.43343i	0.0524466	−	0.0908401i
$250$		0			0
$251$	15.1543	+	26.2480i	0.956530	+	1.65676i	0.730827	+	0.682562i	$0.239134\pi$
$251$	15.1543	+	26.2480i	0.956530	+	1.65676i	0.225703	+	0.974196i	$0.427532\pi$
$252$		0			0
$253$	8.39008	+	14.5321i	0.527480	+	0.913622i
$254$		0			0
$255$	1.52781			0.0956752
$256$		0			0
$257$	10.4206	−	18.0490i	0.650018	−	1.12586i	−0.333100	−	0.942892i	$-0.608095\pi$
$257$	10.4206	−	18.0490i	0.650018	−	1.12586i	0.983118	−	0.182973i	$-0.0585720\pi$
$258$		0			0
$259$	−0.489647			−0.0304252
$260$		0			0
$261$	−2.80194			−0.173436
$262$		0			0
$263$	−4.29321	+	7.43606i	−0.264731	+	0.458527i	−0.967493	−	0.252898i	$-0.918616\pi$
$263$	−4.29321	+	7.43606i	−0.264731	+	0.458527i	0.702762	+	0.711425i	$0.251950\pi$
$264$		0			0
$265$	−3.12200			−0.191783
$266$		0			0
$267$	8.98523	+	15.5629i	0.549887	+	0.952432i
$268$		0			0
$269$	−7.41335	−	12.8403i	−0.452000	−	0.782886i	0.546510	−	0.837452i	$-0.315956\pi$
$269$	−7.41335	−	12.8403i	−0.452000	−	0.782886i	−0.998510	+	0.0545658i	$0.982623\pi$
$270$		0			0
$271$	3.61745	−	6.26561i	0.219744	−	0.380608i	−0.734985	−	0.678083i	$-0.762811\pi$
$271$	3.61745	−	6.26561i	0.219744	−	0.380608i	0.954730	+	0.297475i	$0.0961443\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.83124	−	11.8321i	0.411939	−	0.713500i
$276$		0			0
$277$	−5.60268	−	9.70412i	−0.336632	−	0.583064i	0.647165	−	0.762350i	$-0.275955\pi$
$277$	−5.60268	−	9.70412i	−0.336632	−	0.583064i	−0.983797	+	0.179286i	$0.942621\pi$
$278$		0			0
$279$	2.09299	+	3.62517i	0.125304	+	0.217033i
$280$		0			0
$281$	−12.3002			−0.733769			−0.366884	−	0.930267i	$-0.619576\pi$
$281$	−12.3002			−0.733769			−0.366884	+	0.930267i	$0.619576\pi$
$282$		0			0
$283$	−12.1761	+	21.0895i	−0.723791	+	1.25364i	0.235678	+	0.971831i	$0.424269\pi$
$283$	−12.1761	+	21.0895i	−0.723791	+	1.25364i	−0.959470	+	0.281812i	$0.909064\pi$
$284$		0			0
$285$	2.57002			0.152235
$286$		0			0
$287$	4.09054			0.241457
$288$		0			0
$289$	4.71044	−	8.15872i	0.277085	−	0.479925i
$290$		0			0
$291$	1.31767			0.0772430
$292$		0			0
$293$	−3.10119	−	5.37141i	−0.181173	−	0.313801i	0.761107	−	0.648626i	$-0.224656\pi$
$293$	−3.10119	−	5.37141i	−0.181173	−	0.313801i	−0.942280	+	0.334825i	$0.891323\pi$
$294$		0			0
$295$	0.862937	+	1.49465i	0.0502421	+	0.0870219i
$296$		0			0
$297$	1.45593	−	2.52174i	0.0844815	−	0.146326i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	4.82275	−	8.35325i	0.277979	−	0.481473i
$302$		0			0
$303$	−7.51238	−	13.0118i	−0.431575	−	0.747509i
$304$		0			0
$305$	3.02595	+	5.24110i	0.173265	+	0.300105i
$306$		0			0
$307$	−26.4795			−1.51126			−0.755632	−	0.654996i	$-0.772670\pi$
$307$	−26.4795			−1.51126			−0.755632	+	0.654996i	$0.772670\pi$
$308$		0			0
$309$	−4.60388	+	7.97415i	−0.261905	+	0.453633i
$310$		0			0
$311$	15.5308			0.880671			0.440335	−	0.897833i	$-0.354860\pi$
$311$	15.5308			0.880671			0.440335	+	0.897833i	$0.354860\pi$
$312$		0			0
$313$	16.9681			0.959092			0.479546	−	0.877517i	$-0.340801\pi$
$313$	16.9681			0.959092			0.479546	+	0.877517i	$0.340801\pi$
$314$		0			0
$315$	−0.291053	+	0.504118i	−0.0163990	+	0.0284038i
$316$		0			0
$317$	25.5066			1.43260			0.716298	−	0.697795i	$-0.245835\pi$
$317$	25.5066			1.43260			0.716298	+	0.697795i	$0.245835\pi$
$318$		0			0
$319$	4.07942	+	7.06576i	0.228403	+	0.395606i
$320$		0			0
$321$	3.61476	+	6.26095i	0.201756	+	0.349452i
$322$		0			0
$323$	−6.37465	+	11.0412i	−0.354695	+	0.614350i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.75182	+	13.4266i	−0.428677	+	0.742490i
$328$		0			0
$329$	6.04234	+	10.4656i	0.333125	+	0.576990i
$330$		0			0
$331$	−5.30678	−	9.19162i	−0.291687	−	0.505217i	0.682522	−	0.730865i	$-0.260883\pi$
$331$	−5.30678	−	9.19162i	−0.291687	−	0.505217i	−0.974209	+	0.225648i	$0.927550\pi$
$332$		0			0
$333$	0.466812			0.0255811
$334$		0			0
$335$	2.23341	−	3.86837i	0.122024	−	0.211352i
$336$		0			0
$337$	29.2717			1.59453			0.797266	−	0.603628i	$-0.206279\pi$
$337$	29.2717			1.59453			0.797266	+	0.603628i	$0.206279\pi$
$338$		0			0
$339$	−13.8267			−0.750963
$340$		0			0
$341$	6.09448	−	10.5560i	0.330035	−	0.571637i
$342$		0			0
$343$	13.5308			0.730594
$344$		0			0
$345$	1.59903	+	2.76960i	0.0860889	+	0.149110i
$346$		0			0
$347$	17.4073	+	30.1503i	0.934473	+	1.61855i	0.775571	+	0.631261i	$0.217462\pi$
$347$	17.4073	+	30.1503i	0.934473	+	1.61855i	0.158902	+	0.987294i	$0.449205\pi$
$348$		0			0
$349$	15.0978	−	26.1502i	0.808169	−	1.39979i	−0.105962	−	0.994370i	$-0.533792\pi$
$349$	15.0978	−	26.1502i	0.808169	−	1.39979i	0.914131	−	0.405419i	$-0.132874\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.4846	−	21.6239i	0.664486	−	1.15092i	−0.314938	−	0.949112i	$-0.601984\pi$
$353$	12.4846	−	21.6239i	0.664486	−	1.15092i	0.979424	−	0.201812i	$-0.0646830\pi$
$354$		0			0
$355$	3.79925	+	6.58049i	0.201643	+	0.349256i
$356$		0			0
$357$	−1.44385	−	2.50081i	−0.0764164	−	0.132357i
$358$		0			0
$359$	−14.1661			−0.747660			−0.373830	−	0.927497i	$-0.621956\pi$
$359$	−14.1661			−0.747660			−0.373830	+	0.927497i	$0.621956\pi$
$360$		0			0
$361$	−1.22318	+	2.11862i	−0.0643782	+	0.111506i
$362$		0			0
$363$	2.52111			0.132324
$364$		0			0
$365$	−5.19806			−0.272079
$366$		0			0
$367$	−4.39344	+	7.60965i	−0.229335	+	0.397221i	−0.957611	−	0.288063i	$-0.906989\pi$
$367$	−4.39344	+	7.60965i	−0.229335	+	0.397221i	0.728276	+	0.685284i	$0.240322\pi$
$368$		0			0
$369$	−3.89977			−0.203014
$370$		0			0
$371$	2.95042	+	5.11028i	0.153178	+	0.265312i
$372$		0			0
$373$	9.16301	+	15.8708i	0.474443	+	0.821759i	0.999572	−	0.0292636i	$-0.00931621\pi$
$373$	9.16301	+	15.8708i	0.474443	+	0.821759i	−0.525129	+	0.851023i	$0.675983\pi$
$374$		0			0
$375$	2.68933	−	4.65806i	0.138877	−	0.240541i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	2.38793	−	4.13601i	0.122660	−	0.212453i	−0.798156	−	0.602451i	$-0.794191\pi$
$379$	2.38793	−	4.13601i	0.122660	−	0.212453i	0.920816	+	0.389998i	$0.127524\pi$
$380$		0			0
$381$	3.58815	+	6.21485i	0.183826	+	0.318396i
$382$		0			0
$383$	−3.09515	−	5.36095i	−0.158155	−	0.273932i	0.776049	−	0.630673i	$-0.217221\pi$
$383$	−3.09515	−	5.36095i	−0.158155	−	0.273932i	−0.934203	+	0.356741i	$0.883888\pi$
$384$		0			0
$385$	1.69501			0.0863855
$386$		0			0
$387$	−4.59783	+	7.96368i	−0.233721	+	0.404817i
$388$		0			0
$389$	24.8780			1.26136			0.630682	−	0.776041i	$-0.282775\pi$
$389$	24.8780			1.26136			0.630682	+	0.776041i	$0.282775\pi$
$390$		0			0
$391$	−15.8649			−0.802320
$392$		0			0
$393$	6.56518	−	11.3712i	0.331169	−	0.573602i
$394$		0			0
$395$	2.00298			0.100781
$396$		0			0
$397$	2.31013	+	4.00127i	0.115942	+	0.200818i	0.918156	−	0.396219i	$-0.129678\pi$
$397$	2.31013	+	4.00127i	0.115942	+	0.200818i	−0.802214	+	0.597037i	$0.796345\pi$
$398$		0			0
$399$	−2.42878	−	4.20677i	−0.121591	−	0.210602i
$400$		0			0
$401$	0.824240	−	1.42763i	0.0411606	−	0.0712923i	−0.844711	−	0.535222i	$-0.820228\pi$
$401$	0.824240	−	1.42763i	0.0411606	−	0.0712923i	0.885872	+	0.463930i	$0.153561\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.277479	−	0.480608i	0.0137880	−	0.0238816i
$406$		0			0
$407$	−0.679644	−	1.17718i	−0.0336887	−	0.0583506i
$408$		0			0
$409$	17.4025	+	30.1419i	0.860496	+	1.49042i	0.871451	+	0.490483i	$0.163180\pi$
$409$	17.4025	+	30.1419i	0.860496	+	1.49042i	−0.0109543	+	0.999940i	$0.503487\pi$
$410$		0			0
$411$	−21.8116			−1.07589
$412$		0			0
$413$	1.63102	−	2.82501i	0.0802574	−	0.139010i
$414$		0			0
$415$	−0.918559			−0.0450903
$416$		0			0
$417$	2.96615			0.145253
$418$		0			0
$419$	−10.8177	+	18.7367i	−0.528478	+	0.915350i	0.470971	+	0.882149i	$0.343904\pi$
$419$	−10.8177	+	18.7367i	−0.528478	+	0.915350i	−0.999449	+	0.0332014i	$0.989430\pi$
$420$		0			0
$421$	−35.1008			−1.71071			−0.855355	−	0.518043i	$-0.826661\pi$
$421$	−35.1008			−1.71071			−0.855355	+	0.518043i	$0.826661\pi$
$422$		0			0
$423$	−5.76055	−	9.97757i	−0.280088	−	0.485126i
$424$		0			0
$425$	6.45862	+	11.1867i	0.313289	+	0.542632i
$426$		0			0
$427$	5.71930	−	9.90612i	0.276776	−	0.479391i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.0462	−	17.4006i	0.483910	−	0.838156i	−0.515919	−	0.856637i	$-0.672550\pi$
$431$	10.0462	−	17.4006i	0.483910	−	0.838156i	0.999829	+	0.0184807i	$0.00588294\pi$
$432$		0			0
$433$	9.34697	+	16.1894i	0.449187	+	0.778014i	0.998333	−	0.0577118i	$-0.0183805\pi$
$433$	9.34697	+	16.1894i	0.449187	+	0.778014i	−0.549147	+	0.835726i	$0.685047\pi$
$434$		0			0
$435$	0.777479	+	1.34663i	0.0372773	+	0.0645661i
$436$		0			0
$437$	−26.6872			−1.27662
$438$		0			0
$439$	−0.675096	+	1.16930i	−0.0322206	+	0.0558076i	−0.881686	−	0.471837i	$-0.843591\pi$
$439$	−0.675096	+	1.16930i	−0.0322206	+	0.0558076i	0.849465	+	0.527644i	$0.176925\pi$
$440$		0			0
$441$	−5.89977			−0.280942
$442$		0			0
$443$	−0.400436			−0.0190253			−0.00951265	−	0.999955i	$-0.503028\pi$
$443$	−0.400436			−0.0190253			−0.00951265	+	0.999955i	$0.503028\pi$
$444$		0			0
$445$	4.98643	−	8.63674i	0.236379	−	0.409421i
$446$		0			0
$447$	5.69633			0.269427
$448$		0			0
$449$	−17.8952	−	30.9954i	−0.844528	−	1.46277i	−0.886031	−	0.463627i	$-0.846548\pi$
$449$	−17.8952	−	30.9954i	−0.844528	−	1.46277i	0.0415028	−	0.999138i	$-0.486785\pi$
$450$		0			0
$451$	5.67778	+	9.83421i	0.267356	+	0.463075i
$452$		0			0
$453$	9.57338	−	16.5816i	0.449796	−	0.779070i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.58546	+	4.47814i	−0.120943	+	0.209479i	−0.920140	−	0.391590i	$-0.871925\pi$
$457$	−2.58546	+	4.47814i	−0.120943	+	0.209479i	0.799197	+	0.601069i	$0.205258\pi$
$458$		0			0
$459$	1.37651	+	2.38419i	0.0642500	+	0.111284i
$460$		0			0
$461$	10.4390	+	18.0809i	0.486193	+	0.842111i	0.999874	−	0.0158705i	$-0.00505196\pi$
$461$	10.4390	+	18.0809i	0.486193	+	0.842111i	−0.513681	+	0.857981i	$0.671719\pi$
$462$		0			0
$463$	−30.7198			−1.42767			−0.713834	−	0.700315i	$-0.753043\pi$
$463$	−30.7198			−1.42767			−0.713834	+	0.700315i	$0.753043\pi$
$464$		0			0
$465$	1.16152	−	2.01182i	0.0538643	−	0.0932957i
$466$		0			0
$467$	15.2741			0.706802			0.353401	−	0.935472i	$-0.385025\pi$
$467$	15.2741			0.706802			0.353401	+	0.935472i	$0.385025\pi$
$468$		0			0
$469$	−8.44265			−0.389845
$470$		0			0
$471$	−4.19202	+	7.26079i	−0.193158	+	0.334560i
$472$		0			0
$473$	26.7764			1.23118
$474$		0			0
$475$	10.8644	+	18.8177i	0.498494	+	0.863417i
$476$		0			0
$477$	−2.81282	−	4.87195i	−0.128790	−	0.223071i
$478$		0			0
$479$	−1.52930	+	2.64883i	−0.0698756	+	0.121028i	−0.898846	−	0.438264i	$-0.855594\pi$
$479$	−1.52930	+	2.64883i	−0.0698756	+	0.121028i	0.828971	+	0.559292i	$0.188927\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	3.02230	−	5.23478i	0.137520	−	0.238191i
$484$		0			0
$485$	−0.365625	−	0.633281i	−0.0166022	−	0.0287558i
$486$		0			0
$487$	−7.57606	−	13.1221i	−0.343304	−	0.594620i	0.641740	−	0.766922i	$-0.278213\pi$
$487$	−7.57606	−	13.1221i	−0.343304	−	0.594620i	−0.985044	+	0.172302i	$0.944880\pi$
$488$		0			0
$489$	1.97046			0.0891073
$490$		0			0
$491$	−11.7397	+	20.3338i	−0.529807	+	0.917653i	0.469588	+	0.882886i	$0.344402\pi$
$491$	−11.7397	+	20.3338i	−0.529807	+	0.917653i	−0.999395	+	0.0347674i	$0.988931\pi$
$492$		0			0
$493$	−7.71379			−0.347412
$494$		0			0
$495$	−1.61596			−0.0726319
$496$		0			0
$497$	7.18090	−	12.4377i	0.322107	−	0.557906i
$498$		0			0
$499$	38.0689			1.70420			0.852099	−	0.523381i	$-0.175330\pi$
$499$	38.0689			1.70420			0.852099	+	0.523381i	$0.175330\pi$
$500$		0			0
$501$	12.3998	+	21.4770i	0.553981	+	0.959523i
$502$		0			0
$503$	5.56369	+	9.63659i	0.248073	+	0.429674i	0.962991	−	0.269534i	$-0.0868695\pi$
$503$	5.56369	+	9.63659i	0.248073	+	0.429674i	−0.714918	+	0.699208i	$0.753536\pi$
$504$		0			0
$505$	−4.16905	+	7.22101i	−0.185521	+	0.321331i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.3817	+	23.1777i	−0.593131	+	1.02733i	0.400676	+	0.916220i	$0.368775\pi$
$509$	−13.3817	+	23.1777i	−0.593131	+	1.02733i	−0.993808	+	0.111114i	$0.964558\pi$
$510$		0			0
$511$	4.91239	+	8.50850i	0.217311	+	0.376394i
$512$		0			0
$513$	2.31551	+	4.01058i	0.102232	+	0.177072i
$514$		0			0
$515$	5.10992			0.225170
$516$		0			0
$517$	−16.7739	+	29.0532i	−0.737715	+	1.27776i
$518$		0			0
$519$	2.57135			0.112870
$520$		0			0
$521$	20.5797			0.901614			0.450807	−	0.892622i	$-0.351136\pi$
$521$	20.5797			0.901614			0.450807	+	0.892622i	$0.351136\pi$
$522$		0			0
$523$	3.38740	−	5.86714i	0.148120	−	0.256552i	−0.782412	−	0.622761i	$-0.786011\pi$
$523$	3.38740	−	5.86714i	0.148120	−	0.256552i	0.930533	+	0.366209i	$0.119344\pi$
$524$		0			0
$525$	−4.92154			−0.214794
$526$		0			0
$527$	5.76205	+	9.98015i	0.250999	+	0.434742i
$528$		0			0
$529$	−5.10441	−	8.84109i	−0.221931	−	0.384395i
$530$		0			0
$531$	−1.55496	+	2.69327i	−0.0674794	+	0.116878i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	2.00604	−	3.47456i	0.0867287	−	0.150219i
$536$		0			0
$537$	−1.50269	−	2.60273i	−0.0648458	−	0.112316i
$538$		0			0
$539$	8.58964	+	14.8777i	0.369982	+	0.640827i
$540$		0			0
$541$	1.94331			0.0835495			0.0417748	−	0.999127i	$-0.486699\pi$
$541$	1.94331			0.0835495			0.0417748	+	0.999127i	$0.486699\pi$
$542$		0			0
$543$	−7.34213	+	12.7169i	−0.315081	+	0.545736i
$544$		0			0
$545$	8.60388			0.368550
$546$		0			0
$547$	−39.1323			−1.67318			−0.836588	−	0.547833i	$-0.815453\pi$
$547$	−39.1323			−1.67318			−0.836588	+	0.547833i	$0.815453\pi$
$548$		0			0
$549$	−5.45257	+	9.44414i	−0.232710	+	0.403066i
$550$		0			0
$551$	−12.9758			−0.552789
$552$		0			0
$553$	−1.89290	−	3.27861i	−0.0804945	−	0.139420i
$554$		0			0
$555$	−0.129531	−	0.224354i	−0.00549827	−	0.00952328i
$556$		0			0
$557$	12.2494	−	21.2166i	0.519025	−	0.898978i	−0.480731	−	0.876868i	$-0.659628\pi$
$557$	12.2494	−	21.2166i	0.519025	−	0.898978i	0.999756	−	0.0221094i	$-0.00703820\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	4.00820	−	6.94240i	0.169226	−	0.293108i
$562$		0			0
$563$	10.9133	+	18.9025i	0.459943	+	0.796644i	0.998957	−	0.0456522i	$-0.0145366\pi$
$563$	10.9133	+	18.9025i	0.459943	+	0.796644i	−0.539015	+	0.842296i	$0.681203\pi$
$564$		0			0
$565$	3.83662	+	6.64522i	0.161408	+	0.279566i
$566$		0			0
$567$	−1.04892			−0.0440504
$568$		0			0
$569$	5.78136	−	10.0136i	0.242367	−	0.419793i	−0.719021	−	0.694989i	$-0.755409\pi$
$569$	5.78136	−	10.0136i	0.242367	−	0.419793i	0.961388	+	0.275196i	$0.0887427\pi$
$570$		0			0
$571$	24.7614			1.03623			0.518116	−	0.855310i	$-0.326634\pi$
$571$	24.7614			1.03623			0.518116	+	0.855310i	$0.326634\pi$
$572$		0			0
$573$	17.0804			0.713543
$574$		0			0
$575$	−13.5194	+	23.4162i	−0.563797	+	0.976525i
$576$		0			0
$577$	13.5090			0.562388			0.281194	−	0.959651i	$-0.409270\pi$
$577$	13.5090			0.562388			0.281194	+	0.959651i	$0.409270\pi$
$578$		0			0
$579$	−7.48792	−	12.9695i	−0.311187	−	0.538992i
$580$		0			0
$581$	0.868076	+	1.50355i	0.0360139	+	0.0623779i
$582$		0			0
$583$	−8.19053	+	14.1864i	−0.339217	+	0.587541i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.35152	−	5.80500i	0.138332	−	0.239598i	−0.788533	−	0.614992i	$-0.789159\pi$
$587$	3.35152	−	5.80500i	0.138332	−	0.239598i	0.926865	+	0.375394i	$0.122493\pi$
$588$		0			0
$589$	9.69269	+	16.7882i	0.399380	+	0.691747i
$590$		0			0
$591$	0.0963427	+	0.166870i	0.00396301	+	0.00686414i
$592$		0			0
$593$	−16.0194			−0.657837			−0.328918	−	0.944358i	$-0.606684\pi$
$593$	−16.0194			−0.657837			−0.328918	+	0.944358i	$0.606684\pi$
$594$		0			0
$595$	−0.801274	+	1.38785i	−0.0328490	+	0.0568962i
$596$		0			0
$597$	−11.8726			−0.485914
$598$		0			0
$599$	19.8243			0.809999			0.404999	−	0.914317i	$-0.367272\pi$
$599$	19.8243			0.809999			0.404999	+	0.914317i	$0.367272\pi$
$600$		0			0
$601$	−14.5954	+	25.2800i	−0.595360	+	1.03119i	0.398135	+	0.917327i	$0.369657\pi$
$601$	−14.5954	+	25.2800i	−0.595360	+	1.03119i	−0.993496	+	0.113868i	$0.963676\pi$
$602$		0			0
$603$	8.04892			0.327777
$604$		0			0
$605$	−0.699554	−	1.21166i	−0.0284409	−	0.0492611i
$606$		0			0
$607$	3.18114	+	5.50989i	0.129118	+	0.223640i	0.923335	−	0.383995i	$-0.125452\pi$
$607$	3.18114	+	5.50989i	0.129118	+	0.223640i	−0.794217	+	0.607634i	$0.792119\pi$
$608$		0			0
$609$	1.46950	−	2.54525i	0.0595472	−	0.103139i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−15.3855	+	26.6485i	−0.621416	+	1.07632i	0.367806	+	0.929902i	$0.380109\pi$
$613$	−15.3855	+	26.6485i	−0.621416	+	1.07632i	−0.989222	+	0.146422i	$0.953224\pi$
$614$		0			0
$615$	1.08211	+	1.87426i	0.0436347	+	0.0755775i
$616$		0			0
$617$	−6.01208	−	10.4132i	−0.242037	−	0.419221i	0.719257	−	0.694744i	$-0.244482\pi$
$617$	−6.01208	−	10.4132i	−0.242037	−	0.419221i	−0.961294	+	0.275523i	$0.911149\pi$
$618$		0			0
$619$	9.02715			0.362832			0.181416	−	0.983406i	$-0.441932\pi$
$619$	9.02715			0.362832			0.181416	+	0.983406i	$0.441932\pi$
$620$		0			0
$621$	−2.88135	+	4.99065i	−0.115625	+	0.200268i
$622$		0			0
$623$	−18.8495			−0.755190
$624$		0			0
$625$	20.4752			0.819007
$626$		0			0
$627$	6.74243	−	11.6782i	0.269267	−	0.466384i
$628$		0			0
$629$	1.28514			0.0512420
$630$		0			0
$631$	−7.77628	−	13.4689i	−0.309569	−	0.536189i	0.668699	−	0.743533i	$-0.266851\pi$
$631$	−7.77628	−	13.4689i	−0.309569	−	0.536189i	−0.978268	+	0.207344i	$0.933518\pi$
$632$		0			0
$633$	3.01693	+	5.22547i	0.119912	+	0.207694i
$634$		0			0
$635$	1.99127	−	3.44898i	0.0790212	−	0.136869i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.84601	+	11.8576i	−0.270824	+	0.469081i
$640$		0			0
$641$	9.71044	+	16.8190i	0.383539	+	0.664310i	0.991565	−	0.129608i	$-0.0413717\pi$
$641$	9.71044	+	16.8190i	0.383539	+	0.664310i	−0.608026	+	0.793917i	$0.708038\pi$
$642$		0			0
$643$	13.4133	+	23.2326i	0.528971	+	0.916204i	0.999429	+	0.0337821i	$0.0107552\pi$
$643$	13.4133	+	23.2326i	0.528971	+	0.916204i	−0.470458	+	0.882422i	$0.655911\pi$
$644$		0			0
$645$	5.10321			0.200939
$646$		0			0
$647$	−2.54407	+	4.40646i	−0.100018	+	0.173236i	−0.911692	−	0.410875i	$-0.865223\pi$
$647$	−2.54407	+	4.40646i	−0.100018	+	0.173236i	0.811674	+	0.584111i	$0.198557\pi$
$648$		0			0
$649$	9.05562			0.355464
$650$		0			0
$651$	−4.39075			−0.172087
$652$		0			0
$653$	9.85786	−	17.0743i	0.385768	−	0.668169i	−0.606108	−	0.795383i	$-0.707270\pi$
$653$	9.85786	−	17.0743i	0.385768	−	0.668169i	0.991875	+	0.127213i	$0.0406033\pi$
$654$		0			0
$655$	−7.28680			−0.284719
$656$		0			0
$657$	−4.68329	−	8.11170i	−0.182713	−	0.316468i
$658$		0			0
$659$	−4.71260	−	8.16245i	−0.183577	−	0.317964i	0.759519	−	0.650485i	$-0.225434\pi$
$659$	−4.71260	−	8.16245i	−0.183577	−	0.317964i	−0.943096	+	0.332521i	$0.892101\pi$
$660$		0			0
$661$	14.9973	−	25.9761i	0.583328	−	1.01035i	−0.411754	−	0.911295i	$-0.635084\pi$
$661$	14.9973	−	25.9761i	0.583328	−	1.01035i	0.995082	−	0.0990583i	$-0.0315830\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.34787	+	2.33458i	−0.0522682	+	0.0905312i
$666$		0			0
$667$	−8.07338	−	13.9835i	−0.312602	−	0.541443i
$668$		0			0
$669$	4.26324	+	7.38415i	0.164826	+	0.285488i
$670$		0			0
$671$	31.7542			1.22586
$672$		0			0
$673$	23.8647	−	41.3349i	0.919918	−	1.59334i	0.120380	−	0.992728i	$-0.461589\pi$
$673$	23.8647	−	41.3349i	0.919918	−	1.59334i	0.799538	−	0.600616i	$-0.205078\pi$
$674$		0			0
$675$	4.69202			0.180596
$676$		0			0
$677$	−42.9124			−1.64926			−0.824630	−	0.565673i	$-0.808616\pi$
$677$	−42.9124			−1.64926			−0.824630	+	0.565673i	$0.808616\pi$
$678$		0			0
$679$	−0.691062	+	1.19695i	−0.0265205	+	0.0459349i
$680$		0			0
$681$	−11.0000			−0.421521
$682$		0			0
$683$	−0.485230	−	0.840443i	−0.0185668	−	0.0321587i	0.856593	−	0.515993i	$-0.172577\pi$
$683$	−0.485230	−	0.840443i	−0.0185668	−	0.0321587i	−0.875160	+	0.483834i	$0.839244\pi$
$684$		0			0
$685$	6.05227	+	10.4828i	0.231245	+	0.400529i
$686$		0			0
$687$	−8.95593	+	15.5121i	−0.341690	+	0.591824i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.583302	+	1.01031i	−0.0221898	+	0.0384339i	−0.876907	−	0.480660i	$-0.840397\pi$
$691$	−0.583302	+	1.01031i	−0.0221898	+	0.0384339i	0.854717	+	0.519094i	$0.173730\pi$
$692$		0			0
$693$	1.52715	+	2.64510i	0.0580115	+	0.100479i
$694$		0			0
$695$	−0.823044	−	1.42555i	−0.0312198	−	0.0540743i
$696$		0			0
$697$	−10.7362			−0.406661
$698$		0			0
$699$	11.4080	−	19.7592i	0.431489	−	0.747361i
$700$		0			0
$701$	−17.3274			−0.654445			−0.327223	−	0.944947i	$-0.606113\pi$
$701$	−17.3274			−0.654445			−0.327223	+	0.944947i	$0.606113\pi$
$702$		0			0
$703$	2.16182			0.0815345
$704$		0			0
$705$	−3.19687	+	5.53713i	−0.120401	+	0.208541i
$706$		0			0
$707$	15.7597			0.592705
$708$		0			0
$709$	−8.23005	−	14.2549i	−0.309086	−	0.535353i	0.669077	−	0.743193i	$-0.266690\pi$
$709$	−8.23005	−	14.2549i	−0.309086	−	0.535353i	−0.978163	+	0.207841i	$0.933356\pi$
$710$		0			0
$711$	1.80463	+	3.12570i	0.0676788	+	0.117223i
$712$		0			0
$713$	−12.0613	+	20.8908i	−0.451699	+	0.782366i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	4.17241	−	7.22682i	0.155821	−	0.269891i
$718$		0			0
$719$	−7.08575	−	12.2729i	−0.264254	−	0.457701i	0.703114	−	0.711077i	$-0.251792\pi$
$719$	−7.08575	−	12.2729i	−0.264254	−	0.457701i	−0.967368	+	0.253376i	$0.918459\pi$
$720$		0			0
$721$	−4.82908	−	8.36422i	−0.179845	−	0.311500i
$722$		0			0
$723$	3.75541			0.139665
$724$		0			0
$725$	−6.57338	+	11.3854i	−0.244129	+	0.422844i
$726$		0			0
$727$	−37.8810			−1.40493			−0.702464	−	0.711719i	$-0.747917\pi$
$727$	−37.8810			−1.40493			−0.702464	+	0.711719i	$0.747917\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.6579	+	21.9242i	−0.468171	+	0.810895i
$732$		0			0
$733$	0.377338			0.0139373			0.00696865	−	0.999976i	$-0.497782\pi$
$733$	0.377338			0.0139373			0.00696865	+	0.999976i	$0.497782\pi$
$734$		0			0
$735$	1.63706	+	2.83548i	0.0603840	+	0.104588i
$736$		0			0
$737$	−11.7186	−	20.2973i	−0.431662	−	0.747660i
$738$		0			0
$739$	−0.563155	+	0.975413i	−0.0207160	+	0.0358811i	−0.876198	−	0.481952i	$-0.839928\pi$
$739$	−0.563155	+	0.975413i	−0.0207160	+	0.0358811i	0.855482	+	0.517833i	$0.173261\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.3523	−	19.6628i	0.416477	−	0.721360i	−0.579105	−	0.815253i	$-0.696598\pi$
$743$	11.3523	−	19.6628i	0.416477	−	0.721360i	0.995582	+	0.0938932i	$0.0299312\pi$
$744$		0			0
$745$	−1.58061	−	2.73770i	−0.0579092	−	0.100302i
$746$		0			0
$747$	−0.827593	−	1.43343i	−0.0302800	−	0.0524466i
$748$		0			0
$749$	−7.58317			−0.277083
$750$		0			0
$751$	−6.96412	+	12.0622i	−0.254124	+	0.440157i	−0.964657	−	0.263508i	$-0.915121\pi$
$751$	−6.96412	+	12.0622i	−0.254124	+	0.440157i	0.710533	+	0.703664i	$0.248454\pi$
$752$		0			0
$753$	30.3086			1.10451
$754$		0			0
$755$	−10.6256			−0.386707
$756$		0			0
$757$	−0.583302	+	1.01031i	−0.0212005	+	0.0367203i	−0.876431	−	0.481527i	$-0.840082\pi$
$757$	−0.583302	+	1.01031i	−0.0212005	+	0.0367203i	0.855231	+	0.518248i	$0.173415\pi$
$758$		0			0
$759$	16.7802			0.609081
$760$		0			0
$761$	−0.410895	−	0.711690i	−0.0148949	−	0.0257987i	0.858482	−	0.512844i	$-0.171408\pi$
$761$	−0.410895	−	0.711690i	−0.0148949	−	0.0257987i	−0.873377	+	0.487045i	$0.838075\pi$
$762$		0			0
$763$	−8.13102	−	14.0833i	−0.294363	−	0.509851i
$764$		0			0
$765$	0.763906	−	1.32312i	0.0276191	−	0.0478376i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	16.8509	−	29.1865i	0.607657	−	1.05249i	−0.383968	−	0.923346i	$-0.625443\pi$
$769$	16.8509	−	29.1865i	0.607657	−	1.05249i	0.991625	−	0.129147i	$-0.0412239\pi$
$770$		0			0
$771$	−10.4206	−	18.0490i	−0.375288	−	0.650018i
$772$		0			0
$773$	0.382019	+	0.661675i	0.0137403	+	0.0237988i	0.872814	−	0.488053i	$-0.162293\pi$
$773$	0.382019	+	0.661675i	0.0137403	+	0.0237988i	−0.859074	+	0.511852i	$0.828960\pi$
$774$		0			0
$775$	19.6407			0.705515
$776$		0			0
$777$	−0.244824	+	0.424047i	−0.00878300	+	0.0152126i
$778$		0			0
$779$	−18.0599			−0.647064
$780$		0			0
$781$	39.8692			1.42663
$782$		0			0
$783$	−1.40097	+	2.42655i	−0.0500665	+	0.0867178i
$784$		0			0
$785$	4.65279			0.166065
$786$		0			0
$787$	−6.08695	−	10.5429i	−0.216976	−	0.375814i	0.736906	−	0.675995i	$-0.236286\pi$
$787$	−6.08695	−	10.5429i	−0.216976	−	0.375814i	−0.953882	+	0.300181i	$0.902953\pi$
$788$		0			0
$789$	4.29321	+	7.43606i	0.152842	+	0.264731i
$790$		0			0
$791$	7.25153	−	12.5600i	0.257835	−	0.446583i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.56100	+	2.70373i	−0.0553629	+	0.0958914i
$796$		0			0
$797$	−19.1444	−	33.1590i	−0.678128	−	1.17455i	−0.975544	−	0.219804i	$-0.929458\pi$
$797$	−19.1444	−	33.1590i	−0.678128	−	1.17455i	0.297416	−	0.954748i	$-0.403875\pi$
$798$		0			0
$799$	−15.8589	−	27.4685i	−0.561048	−	0.971764i
$800$		0			0
$801$	17.9705			0.634955
$802$		0			0
$803$	−13.6371	+	23.6201i	−0.481242	+	0.833535i
$804$		0			0
$805$	−3.35450			−0.118231
$806$		0			0
$807$	−14.8267			−0.521924
$808$		0			0
$809$	14.9819	−	25.9494i	0.526735	−	0.912331i	−0.472780	−	0.881181i	$-0.656749\pi$
$809$	14.9819	−	25.9494i	0.526735	−	0.912331i	0.999515	−	0.0311508i	$-0.00991722\pi$
$810$		0			0
$811$	−46.3521			−1.62764			−0.813821	−	0.581115i	$-0.802617\pi$
$811$	−46.3521			−1.62764			−0.813821	+	0.581115i	$0.802617\pi$
$812$		0			0
$813$	−3.61745	−	6.26561i	−0.126869	−	0.219744i
$814$		0			0
$815$	−0.546761	−	0.947019i	−0.0191522	−	0.0331726i
$816$		0			0
$817$	−21.2927	+	36.8800i	−0.744936	+	1.29027i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.1552	+	41.8381i	−0.843024	+	1.46016i	0.0443025	+	0.999018i	$0.485893\pi$
$821$	−24.1552	+	41.8381i	−0.843024	+	1.46016i	−0.887326	+	0.461142i	$0.847440\pi$
$822$		0			0
$823$	2.65615	+	4.60058i	0.0925874	+	0.160366i	0.908599	−	0.417669i	$-0.137153\pi$
$823$	2.65615	+	4.60058i	0.0925874	+	0.160366i	−0.816012	+	0.578035i	$0.803820\pi$
$824$		0			0
$825$	−6.83124	−	11.8321i	−0.237833	−	0.411939i
$826$		0			0
$827$	22.0968			0.768380			0.384190	−	0.923254i	$-0.374481\pi$
$827$	22.0968			0.768380			0.384190	+	0.923254i	$0.374481\pi$
$828$		0			0
$829$	0.808274	−	1.39997i	0.0280725	−	0.0486230i	−0.851648	−	0.524114i	$-0.824396\pi$
$829$	0.808274	−	1.39997i	0.0280725	−	0.0486230i	0.879720	+	0.475491i	$0.157730\pi$
$830$		0			0
$831$	−11.2054			−0.388710
$832$		0			0
$833$	−16.2422			−0.562759
$834$		0			0
$835$	6.88135	−	11.9189i	0.238139	−	0.412469i
$836$		0			0
$837$	4.18598			0.144689
$838$		0			0
$839$	20.5411	+	35.5783i	0.709159	+	1.22830i	0.965169	+	0.261626i	$0.0842586\pi$
$839$	20.5411	+	35.5783i	0.709159	+	1.22830i	−0.256010	+	0.966674i	$0.582408\pi$
$840$		0			0
$841$	10.5746	+	18.3157i	0.364640	+	0.631576i
$842$		0			0
$843$	−6.15010	+	10.6523i	−0.211821	+	0.366884i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.32222	+	2.29015i	−0.0454319	+	0.0786903i
$848$		0			0
$849$	12.1761	+	21.0895i	0.417881	+	0.723791i
$850$		0			0
$851$	1.34505	+	2.32970i	0.0461078	+	0.0798610i
$852$		0			0
$853$	35.0441			1.19989			0.599944	−	0.800042i	$-0.295189\pi$
$853$	35.0441			1.19989			0.599944	+	0.800042i	$0.295189\pi$
$854$		0			0
$855$	1.28501	−	2.22571i	0.0439465	−	0.0761175i
$856$		0			0
$857$	−3.76079			−0.128466			−0.0642331	−	0.997935i	$-0.520460\pi$
$857$	−3.76079			−0.128466			−0.0642331	+	0.997935i	$0.520460\pi$
$858$		0			0
$859$	7.11662			0.242816			0.121408	−	0.992603i	$-0.461259\pi$
$859$	7.11662			0.242816			0.121408	+	0.992603i	$0.461259\pi$
$860$		0			0
$861$	2.04527	−	3.54251i	0.0697026	−	0.120728i
$862$		0			0
$863$	−57.5900			−1.96039			−0.980193	−	0.198044i	$-0.936541\pi$
$863$	−57.5900			−1.96039			−0.980193	+	0.198044i	$0.936541\pi$
$864$		0			0
$865$	−0.713496	−	1.23581i	−0.0242596	−	0.0420189i
$866$		0			0
$867$	−4.71044	−	8.15872i	−0.159975	−	0.277085i
$868$		0			0
$869$	5.25481	−	9.10159i	0.178257	−	0.308750i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.658834	−	1.14113i	0.0222981	−	0.0386215i
$874$		0			0
$875$	2.82089	+	4.88592i	0.0953634	+	0.165174i
$876$		0			0
$877$	−9.60752	−	16.6407i	−0.324423	−	0.561917i	0.656972	−	0.753915i	$-0.271837\pi$
$877$	−9.60752	−	16.6407i	−0.324423	−	0.561917i	−0.981395	+	0.191997i	$0.938503\pi$
$878$		0			0
$879$	−6.20237			−0.209201
$880$		0			0
$881$	5.57218	−	9.65130i	0.187731	−	0.325160i	−0.756762	−	0.653690i	$-0.773220\pi$
$881$	5.57218	−	9.65130i	0.187731	−	0.325160i	0.944494	+	0.328530i	$0.106553\pi$
$882$		0			0
$883$	−4.28919			−0.144343			−0.0721714	−	0.997392i	$-0.522993\pi$
$883$	−4.28919			−0.144343			−0.0721714	+	0.997392i	$0.522993\pi$
$884$		0			0
$885$	1.72587			0.0580146
$886$		0			0
$887$	16.5869	−	28.7294i	0.556935	−	0.964640i	−0.440815	−	0.897598i	$-0.645310\pi$
$887$	16.5869	−	28.7294i	0.556935	−	0.964640i	0.997750	−	0.0670421i	$-0.0213562\pi$
$888$		0			0
$889$	−7.52734			−0.252459
$890$		0			0
$891$	−1.45593	−	2.52174i	−0.0487754	−	0.0844815i
$892$		0			0
$893$	−26.6773	−	46.2064i	−0.892720	−	1.54624i
$894$		0			0
$895$	−0.833929	+	1.44441i	−0.0278752	+	0.0482812i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.86443	+	10.1575i	−0.195590	+	0.338771i
$900$		0			0
$901$	−7.74376	−	13.4126i	−0.257982	−	0.446838i
$902$		0			0
$903$	−4.82275	−	8.35325i	−0.160491	−	0.277979i
$904$		0			0
$905$	8.14914			0.270887
$906$		0			0
$907$	20.3141	−	35.1850i	0.674518	−	1.16830i	−0.302092	−	0.953279i	$-0.597685\pi$
$907$	20.3141	−	35.1850i	0.674518	−	1.16830i	0.976610	−	0.215020i	$-0.0689818\pi$
$908$		0			0
$909$	−15.0248			−0.498340
$910$		0			0
$911$	46.2731			1.53309			0.766547	−	0.642188i	$-0.221973\pi$
$911$	46.2731			1.53309			0.766547	+	0.642188i	$0.221973\pi$
$912$		0			0
$913$	−2.40983	+	4.17395i	−0.0797537	+	0.138137i
$914$		0			0
$915$	6.05190			0.200070
$916$		0			0
$917$	6.88633	+	11.9275i	0.227407	+	0.393880i
$918$		0			0
$919$	−25.2337	−	43.7061i	−0.832383	−	1.44173i	−0.896143	−	0.443764i	$-0.853643\pi$
$919$	−25.2337	−	43.7061i	−0.832383	−	1.44173i	0.0637605	−	0.997965i	$-0.479691\pi$
$920$		0			0
$921$	−13.2397	+	22.9319i	−0.436264	+	0.755632i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.09515	−	1.89685i	0.0360082	−	0.0623680i
$926$		0			0
$927$	4.60388	+	7.97415i	0.151211	+	0.261905i
$928$		0			0
$929$	−8.96250	−	15.5235i	−0.294050	−	0.509310i	0.680713	−	0.732550i	$-0.261670\pi$
$929$	−8.96250	−	15.5235i	−0.294050	−	0.509310i	−0.974763	+	0.223240i	$0.928337\pi$
$930$		0			0
$931$	−27.3220			−0.895442
$932$		0			0
$933$	7.76540	−	13.4501i	0.254228	−	0.440335i
$934$		0			0
$935$	−4.44876			−0.145490
$936$		0			0
$937$	5.85325			0.191217			0.0956086	−	0.995419i	$-0.469520\pi$
$937$	5.85325			0.191217			0.0956086	+	0.995419i	$0.469520\pi$
$938$		0			0
$939$	8.48403	−	14.6948i	0.276866	−	0.479546i
$940$		0			0
$941$	−56.7958			−1.85149			−0.925745	−	0.378147i	$-0.876561\pi$
$941$	−56.7958			−1.85149			−0.925745	+	0.378147i	$0.876561\pi$
$942$		0			0
$943$	−11.2366	−	19.4624i	−0.365915	−	0.633783i
$944$		0			0
$945$	0.291053	+	0.504118i	0.00946794	+	0.0163990i
$946$		0			0
$947$	3.07487	−	5.32583i	0.0999198	−	0.173066i	−0.811731	−	0.584031i	$-0.801475\pi$
$947$	3.07487	−	5.32583i	0.0999198	−	0.173066i	0.911651	+	0.410965i	$0.134808\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	12.7533	−	22.0894i	0.413555	−	0.716298i
$952$		0			0
$953$	−24.4889	−	42.4160i	−0.793273	−	1.37399i	−0.923930	−	0.382561i	$-0.875042\pi$
$953$	−24.4889	−	42.4160i	−0.793273	−	1.37399i	0.130658	−	0.991428i	$-0.458291\pi$
$954$		0			0
$955$	−4.73945	−	8.20896i	−0.153365	−	0.265636i
$956$		0			0
$957$	8.15883			0.263738
$958$		0			0
$959$	11.4393	−	19.8134i	0.369394	−	0.639809i
$960$		0			0
$961$	−13.4776			−0.434760
$962$		0			0
$963$	7.22952			0.232968
$964$		0			0
$965$	−4.15548	+	7.19750i	−0.133770	+	0.231696i
$966$		0			0
$967$	54.2616			1.74493			0.872467	−	0.488673i	$-0.162519\pi$
$967$	54.2616			1.74493			0.872467	+	0.488673i	$0.162519\pi$
$968$		0			0
$969$	6.37465	+	11.0412i	0.204783	+	0.354695i
$970$		0			0
$971$	18.1571	+	31.4490i	0.582689	+	1.00925i	0.995159	+	0.0982761i	$0.0313328\pi$
$971$	18.1571	+	31.4490i	0.582689	+	1.00925i	−0.412470	+	0.910971i	$0.635334\pi$
$972$		0			0
$973$	−1.55562	+	2.69442i	−0.0498710	+	0.0863790i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−24.8687	+	43.0739i	−0.795621	+	1.37806i	0.126822	+	0.991925i	$0.459522\pi$
$977$	−24.8687	+	43.0739i	−0.795621	+	1.37806i	−0.922444	+	0.386131i	$0.873811\pi$
$978$		0			0
$979$	−26.1637	−	45.3168i	−0.836195	−	1.44833i
$980$		0			0
$981$	7.75182	+	13.4266i	0.247497	+	0.428677i
$982$		0			0
$983$	−10.9981			−0.350784			−0.175392	−	0.984499i	$-0.556119\pi$
$983$	−10.9981			−0.350784			−0.175392	+	0.984499i	$0.556119\pi$
$984$		0			0
$985$	0.0534662	−	0.0926061i	0.00170357	−	0.00295068i
$986$		0			0
$987$	12.0847			0.384660
$988$		0			0
$989$	−52.9920			−1.68505
$990$		0			0
$991$	−3.36539	+	5.82902i	−0.106905	+	0.185165i	−0.914515	−	0.404552i	$-0.867427\pi$
$991$	−3.36539	+	5.82902i	−0.106905	+	0.185165i	0.807610	+	0.589717i	$0.200761\pi$
$992$		0			0
$993$	−10.6136			−0.336811
$994$		0			0
$995$	3.29440	+	5.70608i	0.104440	+	0.180895i
$996$		0			0
$997$	−21.6749	−	37.5420i	−0.686450	−	1.18897i	−0.972979	−	0.230894i	$-0.925835\pi$
$997$	−21.6749	−	37.5420i	−0.686450	−	1.18897i	0.286529	−	0.958072i	$-0.407498\pi$
$998$		0			0
$999$	0.233406	−	0.404271i	0.00738464	−	0.0127906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.i.l.529.2		6
13.2	odd	12		2028.2.q.j.361.4		12
13.3	even	3	inner	2028.2.i.l.2005.2		6
13.4	even	6		2028.2.a.j.1.2	yes	3
13.5	odd	4		2028.2.q.j.1837.4		12
13.6	odd	12		2028.2.b.f.337.4		6
13.7	odd	12		2028.2.b.f.337.3		6
13.8	odd	4		2028.2.q.j.1837.3		12
13.9	even	3		2028.2.a.i.1.2	✓	3
13.10	even	6		2028.2.i.m.2005.2		6
13.11	odd	12		2028.2.q.j.361.3		12
13.12	even	2		2028.2.i.m.529.2		6
39.17	odd	6		6084.2.a.y.1.2		3
39.20	even	12		6084.2.b.r.4393.4		6
39.32	even	12		6084.2.b.r.4393.3		6
39.35	odd	6		6084.2.a.bb.1.2		3
52.35	odd	6		8112.2.a.ch.1.2		3
52.43	odd	6		8112.2.a.co.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2028.2.a.i.1.2	✓	3	13.9	even	3
2028.2.a.j.1.2	yes	3	13.4	even	6
2028.2.b.f.337.3		6	13.7	odd	12
2028.2.b.f.337.4		6	13.6	odd	12
2028.2.i.l.529.2		6	1.1	even	1	trivial
2028.2.i.l.2005.2		6	13.3	even	3	inner
2028.2.i.m.529.2		6	13.12	even	2
2028.2.i.m.2005.2		6	13.10	even	6
2028.2.q.j.361.3		12	13.11	odd	12
2028.2.q.j.361.4		12	13.2	odd	12
2028.2.q.j.1837.3		12	13.8	odd	4
2028.2.q.j.1837.4		12	13.5	odd	4
6084.2.a.y.1.2		3	39.17	odd	6
6084.2.a.bb.1.2		3	39.35	odd	6
6084.2.b.r.4393.3		6	39.32	even	12
6084.2.b.r.4393.4		6	39.20	even	12
8112.2.a.ch.1.2		3	52.35	odd	6
8112.2.a.co.1.2		3	52.43	odd	6

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:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -0.554958 q^{5} +(0.524459 + 0.908389i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.45593 + 2.52174i) q^{11} +(-0.277479 + 0.480608i) q^{15} +(-1.37651 - 2.38419i) q^{17} +(-2.31551 - 4.01058i) q^{19} +1.04892 q^{21} +(2.88135 - 4.99065i) q^{23} -4.69202 q^{25} -1.00000 q^{27} +(1.40097 - 2.42655i) q^{29} -4.18598 q^{31} +(1.45593 + 2.52174i) q^{33} +(-0.291053 - 0.504118i) q^{35} +(-0.233406 + 0.404271i) q^{37} +(1.94989 - 3.37730i) q^{41} +(-4.59783 - 7.96368i) q^{43} +(0.277479 + 0.480608i) q^{45} +11.5211 q^{47} +(2.94989 - 5.10935i) q^{49} -2.75302 q^{51} +5.62565 q^{53} +(0.807979 - 1.39946i) q^{55} -4.63102 q^{57} +(-1.55496 - 2.69327i) q^{59} +(-5.45257 - 9.44414i) q^{61} +(0.524459 - 0.908389i) q^{63} +(-4.02446 + 6.97057i) q^{67} +(-2.88135 - 4.99065i) q^{69} +(-6.84601 - 11.8576i) q^{71} +9.36658 q^{73} +(-2.34601 + 4.06341i) q^{75} -3.05429 q^{77} -3.60925 q^{79} +(-0.500000 + 0.866025i) q^{81} +1.65519 q^{83} +(0.763906 + 1.32312i) q^{85} +(-1.40097 - 2.42655i) q^{87} +(-8.98523 + 15.5629i) q^{89} +(-2.09299 + 3.62517i) q^{93} +(1.28501 + 2.22571i) q^{95} +(0.658834 + 1.14113i) q^{97} +2.91185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 4 q^{5} - 6 q^{7} - 3 q^{9} - 5 q^{11} - 2 q^{15} - 13 q^{17} + q^{19} - 12 q^{21} - 18 q^{25} - 6 q^{27} + 4 q^{29} + 4 q^{31} + 5 q^{33} + 4 q^{35} + 2 q^{37} - 11 q^{41} + 9 q^{43} + 2 q^{45}+ \cdots + 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 4 * q^5 - 6 * q^7 - 3 * q^9 - 5 * q^11 - 2 * q^15 - 13 * q^17 + q^19 - 12 * q^21 - 18 * q^25 - 6 * q^27 + 4 * q^29 + 4 * q^31 + 5 * q^33 + 4 * q^35 + 2 * q^37 - 11 * q^41 + 9 * q^43 + 2 * q^45 + 38 * q^47 - 5 * q^49 - 26 * q^51 + 10 * q^53 + 15 * q^55 + 2 * q^57 - 10 * q^59 - 7 * q^61 - 6 * q^63 - 15 * q^67 - 36 * q^71 + 4 * q^73 - 9 * q^75 + 6 * q^77 + 2 * q^79 - 3 * q^81 + 56 * q^83 + 11 * q^85 - 4 * q^87 - 19 * q^89 + 2 * q^93 - 17 * q^95 - 13 * q^97 + 10 * q^99

Introduction

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