LMFDB - Embedded newform 441.4.e.b.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +(-27.0000 - 46.7654i) q^{10} +(-18.0000 - 31.1769i) q^{11} -34.0000 q^{13} +(35.5000 - 61.4878i) q^{16} +(21.0000 + 36.3731i) q^{17} +(62.0000 - 107.387i) q^{19} +18.0000 q^{20} +108.000 q^{22} +(-99.5000 - 172.339i) q^{25} +(51.0000 - 88.3346i) q^{26} -102.000 q^{29} +(80.0000 + 138.564i) q^{31} +(22.5000 + 38.9711i) q^{32} -126.000 q^{34} +(-199.000 + 344.678i) q^{37} +(186.000 + 322.161i) q^{38} +(189.000 - 327.358i) q^{40} +318.000 q^{41} -268.000 q^{43} +(-18.0000 + 31.1769i) q^{44} +(120.000 - 207.846i) q^{47} +597.000 q^{50} +(17.0000 + 29.4449i) q^{52} +(-249.000 - 431.281i) q^{53} +648.000 q^{55} +(153.000 - 265.004i) q^{58} +(-66.0000 - 114.315i) q^{59} +(-199.000 + 344.678i) q^{61} -480.000 q^{62} +433.000 q^{64} +(306.000 - 530.008i) q^{65} +(-46.0000 - 79.6743i) q^{67} +(21.0000 - 36.3731i) q^{68} +720.000 q^{71} +(251.000 + 434.745i) q^{73} +(-597.000 - 1034.03i) q^{74} -124.000 q^{76} +(512.000 - 886.810i) q^{79} +(639.000 + 1106.78i) q^{80} +(-477.000 + 826.188i) q^{82} +204.000 q^{83} -756.000 q^{85} +(402.000 - 696.284i) q^{86} +(378.000 + 654.715i) q^{88} +(177.000 - 306.573i) q^{89} +(360.000 + 623.538i) q^{94} +(1116.00 + 1932.97i) q^{95} -286.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - q^{4} - 18 q^{5} - 42 q^{8} - 54 q^{10} - 36 q^{11} - 68 q^{13} + 71 q^{16} + 42 q^{17} + 124 q^{19} + 36 q^{20} + 216 q^{22} - 199 q^{25} + 102 q^{26} - 204 q^{29} + 160 q^{31} + 45 q^{32}+ \cdots - 572 q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 - q^4 - 18 * q^5 - 42 * q^8 - 54 * q^10 - 36 * q^11 - 68 * q^13 + 71 * q^16 + 42 * q^17 + 124 * q^19 + 36 * q^20 + 216 * q^22 - 199 * q^25 + 102 * q^26 - 204 * q^29 + 160 * q^31 + 45 * q^32 - 252 * q^34 - 398 * q^37 + 372 * q^38 + 378 * q^40 + 636 * q^41 - 536 * q^43 - 36 * q^44 + 240 * q^47 + 1194 * q^50 + 34 * q^52 - 498 * q^53 + 1296 * q^55 + 306 * q^58 - 132 * q^59 - 398 * q^61 - 960 * q^62 + 866 * q^64 + 612 * q^65 - 92 * q^67 + 42 * q^68 + 1440 * q^71 + 502 * q^73 - 1194 * q^74 - 248 * q^76 + 1024 * q^79 + 1278 * q^80 - 954 * q^82 + 408 * q^83 - 1512 * q^85 + 804 * q^86 + 756 * q^88 + 354 * q^89 + 720 * q^94 + 2232 * q^95 - 572 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.50000	+	2.59808i	−0.530330	+	0.918559i	0.469044	+	0.883175i	$0.344599\pi$
$2$	−1.50000	+	2.59808i	−0.530330	+	0.918559i	−0.999374	+	0.0353837i	$0.988735\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$5$	−9.00000	+	15.5885i	−0.804984	+	1.39427i	0.111317	+	0.993785i	$0.464493\pi$
$5$	−9.00000	+	15.5885i	−0.804984	+	1.39427i	−0.916302	+	0.400489i	$0.868840\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−21.0000			−0.928078
$9$		0			0
$10$	−27.0000	−	46.7654i	−0.853815	−	1.47885i
$11$	−18.0000	−	31.1769i	−0.493382	−	0.854563i	0.506589	−	0.862188i	$-0.330906\pi$
$11$	−18.0000	−	31.1769i	−0.493382	−	0.854563i	−0.999971	+	0.00762479i	$0.997573\pi$
$12$		0			0
$13$	−34.0000			−0.725377			−0.362689	−	0.931910i	$-0.618141\pi$
$13$	−34.0000			−0.725377			−0.362689	+	0.931910i	$0.618141\pi$
$14$		0			0
$15$		0			0
$16$	35.5000	−	61.4878i	0.554688	−	0.960747i
$17$	21.0000	+	36.3731i	0.299603	+	0.518927i	0.976045	−	0.217568i	$-0.0698125\pi$
$17$	21.0000	+	36.3731i	0.299603	+	0.518927i	−0.676442	+	0.736496i	$0.736479\pi$
$18$		0			0
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	−0.199865	−	0.979824i	$-0.564050\pi$
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	0.948484	−	0.316824i	$-0.102616\pi$
$20$	18.0000			0.201246
$21$		0			0
$22$	108.000			1.04662
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−99.5000	−	172.339i	−0.796000	−	1.37871i
$26$	51.0000	−	88.3346i	0.384689	−	0.666301i
$27$		0			0
$28$		0			0
$29$	−102.000			−0.653135			−0.326568	−	0.945174i	$-0.605892\pi$
$29$	−102.000			−0.653135			−0.326568	+	0.945174i	$0.605892\pi$
$30$		0			0
$31$	80.0000	+	138.564i	0.463498	+	0.802801i	0.999132	−	0.0416484i	$-0.0132609\pi$
$31$	80.0000	+	138.564i	0.463498	+	0.802801i	−0.535635	+	0.844450i	$0.679928\pi$
$32$	22.5000	+	38.9711i	0.124296	+	0.215287i
$33$		0			0
$34$	−126.000			−0.635554
$35$		0			0
$36$		0			0
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.0375721	+	0.999294i	$0.511962\pi$
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.846628	+	0.532185i	$0.821371\pi$
$38$	186.000	+	322.161i	0.794031	+	1.37530i
$39$		0			0
$40$	189.000	−	327.358i	0.747088	−	1.29399i
$41$	318.000			1.21130			0.605649	−	0.795732i	$-0.292913\pi$
$41$	318.000			1.21130			0.605649	+	0.795732i	$0.292913\pi$
$42$		0			0
$43$	−268.000			−0.950456			−0.475228	−	0.879863i	$-0.657634\pi$
$43$	−268.000			−0.950456			−0.475228	+	0.879863i	$0.657634\pi$
$44$	−18.0000	+	31.1769i	−0.0616728	+	0.106820i
$45$		0			0
$46$		0			0
$47$	120.000	−	207.846i	0.372421	−	0.645053i	−0.617516	−	0.786558i	$-0.711861\pi$
$47$	120.000	−	207.846i	0.372421	−	0.645053i	0.989937	+	0.141506i	$0.0451943\pi$
$48$		0			0
$49$		0			0
$50$	597.000			1.68857
$51$		0			0
$52$	17.0000	+	29.4449i	0.0453361	+	0.0785244i
$53$	−249.000	−	431.281i	−0.645335	−	1.11775i	−0.984224	−	0.176927i	$-0.943384\pi$
$53$	−249.000	−	431.281i	−0.645335	−	1.11775i	0.338888	−	0.940827i	$-0.389949\pi$
$54$		0			0
$55$	648.000			1.58866
$56$		0			0
$57$		0			0
$58$	153.000	−	265.004i	0.346377	−	0.599943i
$59$	−66.0000	−	114.315i	−0.145635	−	0.252247i	0.783975	−	0.620793i	$-0.213189\pi$
$59$	−66.0000	−	114.315i	−0.145635	−	0.252247i	−0.929610	+	0.368546i	$0.879856\pi$
$60$		0			0
$61$	−199.000	+	344.678i	−0.417694	+	0.723467i	−0.995707	−	0.0925602i	$-0.970495\pi$
$61$	−199.000	+	344.678i	−0.417694	+	0.723467i	0.578013	+	0.816028i	$0.303828\pi$
$62$	−480.000			−0.983227
$63$		0			0
$64$	433.000			0.845703
$65$	306.000	−	530.008i	0.583917	−	1.01137i
$66$		0			0
$67$	−46.0000	−	79.6743i	−0.0838775	−	0.145280i	0.821035	−	0.570878i	$-0.193397\pi$
$67$	−46.0000	−	79.6743i	−0.0838775	−	0.145280i	−0.904912	+	0.425598i	$0.860064\pi$
$68$	21.0000	−	36.3731i	0.0374504	−	0.0648659i
$69$		0			0
$70$		0			0
$71$	720.000			1.20350			0.601748	−	0.798686i	$-0.294471\pi$
$71$	720.000			1.20350			0.601748	+	0.798686i	$0.294471\pi$
$72$		0			0
$73$	251.000	+	434.745i	0.402429	+	0.697028i	0.994019	−	0.109212i	$-0.0348326\pi$
$73$	251.000	+	434.745i	0.402429	+	0.697028i	−0.591589	+	0.806239i	$0.701499\pi$
$74$	−597.000	−	1034.03i	−0.937836	−	1.62438i
$75$		0			0
$76$	−124.000			−0.187155
$77$		0			0
$78$		0			0
$79$	512.000	−	886.810i	0.729171	−	1.26296i	−0.228063	−	0.973646i	$-0.573239\pi$
$79$	512.000	−	886.810i	0.729171	−	1.26296i	0.957234	−	0.289315i	$-0.0934274\pi$
$80$	639.000	+	1106.78i	0.893030	+	1.54677i
$81$		0			0
$82$	−477.000	+	826.188i	−0.642388	+	1.11265i
$83$	204.000			0.269782			0.134891	−	0.990860i	$-0.456932\pi$
$83$	204.000			0.269782			0.134891	+	0.990860i	$0.456932\pi$
$84$		0			0
$85$	−756.000			−0.964703
$86$	402.000	−	696.284i	0.504056	−	0.873050i
$87$		0			0
$88$	378.000	+	654.715i	0.457897	+	0.793101i
$89$	177.000	−	306.573i	0.210809	−	0.365131i	−0.741159	−	0.671329i	$-0.765724\pi$
$89$	177.000	−	306.573i	0.210809	−	0.365131i	0.951968	+	0.306198i	$0.0990570\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	360.000	+	623.538i	0.395012	+	0.684182i
$95$	1116.00	+	1932.97i	1.20525	+	2.08756i
$96$		0			0
$97$	−286.000			−0.299370			−0.149685	−	0.988734i	$-0.547826\pi$
$97$	−286.000			−0.299370			−0.149685	+	0.988734i	$0.547826\pi$
$98$		0			0
$99$		0			0
$100$	−99.5000	+	172.339i	−0.0995000	+	0.172339i
$101$	207.000	+	358.535i	0.203933	+	0.353223i	0.949792	−	0.312881i	$-0.101294\pi$
$101$	207.000	+	358.535i	0.203933	+	0.353223i	−0.745859	+	0.666104i	$0.767961\pi$
$102$		0			0
$103$	−28.0000	+	48.4974i	−0.0267857	+	0.0463941i	−0.879107	−	0.476624i	$-0.841860\pi$
$103$	−28.0000	+	48.4974i	−0.0267857	+	0.0463941i	0.852322	+	0.523018i	$0.175194\pi$
$104$	714.000			0.673206
$105$		0			0
$106$	1494.00			1.36896
$107$	6.00000	−	10.3923i	0.00542095	−	0.00938936i	−0.863302	−	0.504687i	$-0.831608\pi$
$107$	6.00000	−	10.3923i	0.00542095	−	0.00938936i	0.868723	+	0.495298i	$0.164941\pi$
$108$		0			0
$109$	−739.000	−	1279.99i	−0.649389	−	1.12477i	−0.983269	−	0.182159i	$-0.941692\pi$
$109$	−739.000	−	1279.99i	−0.649389	−	1.12477i	0.333880	−	0.942615i	$-0.391642\pi$
$110$	−972.000	+	1683.55i	−0.842514	+	1.45928i
$111$		0			0
$112$		0			0
$113$	−402.000			−0.334664			−0.167332	−	0.985901i	$-0.553515\pi$
$113$	−402.000			−0.334664			−0.167332	+	0.985901i	$0.553515\pi$
$114$		0			0
$115$		0			0
$116$	51.0000	+	88.3346i	0.0408210	+	0.0707040i
$117$		0			0
$118$	396.000			0.308939
$119$		0			0
$120$		0			0
$121$	17.5000	−	30.3109i	0.0131480	−	0.0227730i
$122$	−597.000	−	1034.03i	−0.443031	−	0.767353i
$123$		0			0
$124$	80.0000	−	138.564i	0.0579372	−	0.100350i
$125$	1332.00			0.953102
$126$		0			0
$127$	1280.00			0.894344			0.447172	−	0.894448i	$-0.352431\pi$
$127$	1280.00			0.894344			0.447172	+	0.894448i	$0.352431\pi$
$128$	−829.500	+	1436.74i	−0.572798	+	0.992115i
$129$		0			0
$130$	918.000	+	1590.02i	0.619338	+	1.07272i
$131$	882.000	−	1527.67i	0.588250	−	1.01888i	−0.406212	−	0.913779i	$-0.633151\pi$
$131$	882.000	−	1527.67i	0.588250	−	1.01888i	0.994462	−	0.105099i	$-0.0335161\pi$
$132$		0			0
$133$		0			0
$134$	276.000			0.177931
$135$		0			0
$136$	−441.000	−	763.834i	−0.278055	−	0.481605i
$137$	−1179.00	−	2042.09i	−0.735246	−	1.27348i	−0.954615	−	0.297842i	$-0.903733\pi$
$137$	−1179.00	−	2042.09i	−0.735246	−	1.27348i	0.219369	−	0.975642i	$-0.429600\pi$
$138$		0			0
$139$	−52.0000			−0.0317308			−0.0158654	−	0.999874i	$-0.505050\pi$
$139$	−52.0000			−0.0317308			−0.0158654	+	0.999874i	$0.505050\pi$
$140$		0			0
$141$		0			0
$142$	−1080.00	+	1870.61i	−0.638251	+	1.10548i
$143$	612.000	+	1060.02i	0.357888	+	0.619881i
$144$		0			0
$145$	918.000	−	1590.02i	0.525764	−	0.910650i
$146$	−1506.00			−0.853681
$147$		0			0
$148$	398.000			0.221050
$149$	−873.000	+	1512.08i	−0.479993	+	0.831372i	−0.999737	−	0.0229501i	$-0.992694\pi$
$149$	−873.000	+	1512.08i	−0.479993	+	0.831372i	0.519744	+	0.854322i	$0.326027\pi$
$150$		0			0
$151$	116.000	+	200.918i	0.0625162	+	0.108281i	0.895590	−	0.444881i	$-0.146754\pi$
$151$	116.000	+	200.918i	0.0625162	+	0.108281i	−0.833073	+	0.553163i	$0.813421\pi$
$152$	−1302.00	+	2255.13i	−0.694777	+	1.20339i
$153$		0			0
$154$		0			0
$155$	−2880.00			−1.49243
$156$		0			0
$157$	−847.000	−	1467.05i	−0.430560	−	0.745752i	0.566361	−	0.824157i	$-0.308351\pi$
$157$	−847.000	−	1467.05i	−0.430560	−	0.745752i	−0.996922	+	0.0784048i	$0.975017\pi$
$158$	1536.00	+	2660.43i	0.773403	+	1.33957i
$159$		0			0
$160$	−810.000			−0.400226
$161$		0			0
$162$		0			0
$163$	1466.00	−	2539.19i	0.704454	−	1.22015i	−0.262434	−	0.964950i	$-0.584525\pi$
$163$	1466.00	−	2539.19i	0.704454	−	1.22015i	0.966888	−	0.255200i	$-0.0821413\pi$
$164$	−159.000	−	275.396i	−0.0757062	−	0.131127i
$165$		0			0
$166$	−306.000	+	530.008i	−0.143074	+	0.247811i
$167$	−1176.00			−0.544920			−0.272460	−	0.962167i	$-0.587837\pi$
$167$	−1176.00			−0.544920			−0.272460	+	0.962167i	$0.587837\pi$
$168$		0			0
$169$	−1041.00			−0.473828
$170$	1134.00	−	1964.15i	0.511611	−	0.886136i
$171$		0			0
$172$	134.000	+	232.095i	0.0594035	+	0.102890i
$173$	435.000	−	753.442i	0.191170	−	0.331116i	−0.754468	−	0.656337i	$-0.772105\pi$
$173$	435.000	−	753.442i	0.191170	−	0.331116i	0.945638	+	0.325220i	$0.105438\pi$
$174$		0			0
$175$		0			0
$176$	−2556.00			−1.09469
$177$		0			0
$178$	531.000	+	919.719i	0.223596	+	0.387280i
$179$	−1158.00	−	2005.71i	−0.483536	−	0.837509i	0.516285	−	0.856417i	$-0.327315\pi$
$179$	−1158.00	−	2005.71i	−0.483536	−	0.837509i	−0.999821	+	0.0189075i	$0.993981\pi$
$180$		0			0
$181$	−106.000			−0.0435299			−0.0217650	−	0.999763i	$-0.506929\pi$
$181$	−106.000			−0.0435299			−0.0217650	+	0.999763i	$0.506929\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3582.00	−	6204.21i	−1.42353	−	2.46563i
$186$		0			0
$187$	756.000	−	1309.43i	0.295637	−	0.512059i
$188$	−240.000			−0.0931053
$189$		0			0
$190$	−6696.00			−2.55673
$191$	−564.000	+	976.877i	−0.213663	+	0.370075i	−0.952858	−	0.303416i	$-0.901873\pi$
$191$	−564.000	+	976.877i	−0.213663	+	0.370075i	0.739195	+	0.673491i	$0.235206\pi$
$192$		0			0
$193$	−2017.00	−	3493.55i	−0.752263	−	1.30296i	−0.946723	−	0.322048i	$-0.895629\pi$
$193$	−2017.00	−	3493.55i	−0.752263	−	1.30296i	0.194460	−	0.980910i	$-0.437705\pi$
$194$	429.000	−	743.050i	0.158765	−	0.274989i
$195$		0			0
$196$		0			0
$197$	1314.00			0.475221			0.237611	−	0.971360i	$-0.423636\pi$
$197$	1314.00			0.475221			0.237611	+	0.971360i	$0.423636\pi$
$198$		0			0
$199$	−2548.00	−	4413.27i	−0.907653	−	1.57210i	−0.817316	−	0.576190i	$-0.804539\pi$
$199$	−2548.00	−	4413.27i	−0.907653	−	1.57210i	−0.0903369	−	0.995911i	$-0.528794\pi$
$200$	2089.50	+	3619.12i	0.738750	+	1.27955i
$201$		0			0
$202$	−1242.00			−0.432608
$203$		0			0
$204$		0			0
$205$	−2862.00	+	4957.13i	−0.975077	+	1.68888i
$206$	−84.0000	−	145.492i	−0.0284105	−	0.0492084i
$207$		0			0
$208$	−1207.00	+	2090.59i	−0.402358	+	0.696904i
$209$	−4464.00			−1.47742
$210$		0			0
$211$	−3076.00			−1.00360			−0.501802	−	0.864982i	$-0.667330\pi$
$211$	−3076.00			−1.00360			−0.501802	+	0.864982i	$0.667330\pi$
$212$	−249.000	+	431.281i	−0.0806669	+	0.139719i
$213$		0			0
$214$	18.0000	+	31.1769i	0.00574979	+	0.00995893i
$215$	2412.00	−	4177.71i	0.765102	−	1.32520i
$216$		0			0
$217$		0			0
$218$	4434.00			1.37756
$219$		0			0
$220$	−324.000	−	561.184i	−0.0992913	−	0.171977i
$221$	−714.000	−	1236.68i	−0.217325	−	0.376418i
$222$		0			0
$223$	−1888.00			−0.566950			−0.283475	−	0.958980i	$-0.591487\pi$
$223$	−1888.00			−0.566950			−0.283475	+	0.958980i	$0.591487\pi$
$224$		0			0
$225$		0			0
$226$	603.000	−	1044.43i	0.177482	−	0.307408i
$227$	−2358.00	−	4084.18i	−0.689454	−	1.19417i	−0.972015	−	0.234919i	$-0.924517\pi$
$227$	−2358.00	−	4084.18i	−0.689454	−	1.19417i	0.282561	−	0.959249i	$-0.408816\pi$
$228$		0			0
$229$	845.000	−	1463.58i	0.243839	−	0.422342i	−0.717965	−	0.696079i	$-0.754926\pi$
$229$	845.000	−	1463.58i	0.243839	−	0.422342i	0.961805	+	0.273737i	$0.0882598\pi$
$230$		0			0
$231$		0			0
$232$	2142.00			0.606160
$233$	69.0000	−	119.512i	0.0194006	−	0.0336028i	−0.856162	−	0.516707i	$-0.827158\pi$
$233$	69.0000	−	119.512i	0.0194006	−	0.0336028i	0.875563	+	0.483104i	$0.160491\pi$
$234$		0			0
$235$	2160.00	+	3741.23i	0.599587	+	1.03851i
$236$	−66.0000	+	114.315i	−0.0182044	+	0.0315309i
$237$		0			0
$238$		0			0
$239$	−1896.00			−0.513147			−0.256573	−	0.966525i	$-0.582594\pi$
$239$	−1896.00			−0.513147			−0.256573	+	0.966525i	$0.582594\pi$
$240$		0			0
$241$	1799.00	+	3115.96i	0.480846	+	0.832849i	0.999758	−	0.0219782i	$-0.00699644\pi$
$241$	1799.00	+	3115.96i	0.480846	+	0.832849i	−0.518913	+	0.854827i	$0.673663\pi$
$242$	52.5000	+	90.9327i	0.0139456	+	0.0241544i
$243$		0			0
$244$	398.000			0.104424
$245$		0			0
$246$		0			0
$247$	−2108.00	+	3651.16i	−0.543032	+	0.940558i
$248$	−1680.00	−	2909.85i	−0.430162	−	0.745062i
$249$		0			0
$250$	−1998.00	+	3460.64i	−0.505458	+	0.875480i
$251$	3060.00			0.769504			0.384752	−	0.923020i	$-0.374287\pi$
$251$	3060.00			0.769504			0.384752	+	0.923020i	$0.374287\pi$
$252$		0			0
$253$		0			0
$254$	−1920.00	+	3325.54i	−0.474297	+	0.821507i
$255$		0			0
$256$	−756.500	−	1310.30i	−0.184692	−	0.319897i
$257$	−3411.00	+	5908.03i	−0.827908	+	1.43398i	0.0717686	+	0.997421i	$0.477136\pi$
$257$	−3411.00	+	5908.03i	−0.827908	+	1.43398i	−0.899676	+	0.436557i	$0.856198\pi$
$258$		0			0
$259$		0			0
$260$	−612.000			−0.145979
$261$		0			0
$262$	2646.00	+	4583.01i	0.623933	+	1.08068i
$263$	1296.00	+	2244.74i	0.303858	+	0.526298i	0.977007	−	0.213209i	$-0.0683917\pi$
$263$	1296.00	+	2244.74i	0.303858	+	0.526298i	−0.673148	+	0.739508i	$0.735058\pi$
$264$		0			0
$265$	8964.00			2.07794
$266$		0			0
$267$		0			0
$268$	−46.0000	+	79.6743i	−0.0104847	+	0.0181600i
$269$	4107.00	+	7113.53i	0.930886	+	1.61234i	0.781811	+	0.623515i	$0.214296\pi$
$269$	4107.00	+	7113.53i	0.930886	+	1.61234i	0.149074	+	0.988826i	$0.452371\pi$
$270$		0			0
$271$	2672.00	−	4628.04i	0.598939	−	1.03739i	−0.394039	−	0.919094i	$-0.628923\pi$
$271$	2672.00	−	4628.04i	0.598939	−	1.03739i	0.992978	−	0.118299i	$-0.0377441\pi$
$272$	2982.00			0.664744
$273$		0			0
$274$	7074.00			1.55969
$275$	−3582.00	+	6204.21i	−0.785464	+	1.36046i
$276$		0			0
$277$	3257.00	+	5641.29i	0.706477	+	1.22365i	0.966156	+	0.257959i	$0.0830500\pi$
$277$	3257.00	+	5641.29i	0.706477	+	1.22365i	−0.259679	+	0.965695i	$0.583617\pi$
$278$	78.0000	−	135.100i	0.0168278	−	0.0291466i
$279$		0			0
$280$		0			0
$281$	−6618.00			−1.40497			−0.702485	−	0.711698i	$-0.747926\pi$
$281$	−6618.00			−1.40497			−0.702485	+	0.711698i	$0.747926\pi$
$282$		0			0
$283$	−1630.00	−	2823.24i	−0.342380	−	0.593019i	0.642494	−	0.766290i	$-0.277900\pi$
$283$	−1630.00	−	2823.24i	−0.342380	−	0.593019i	−0.984874	+	0.173271i	$0.944566\pi$
$284$	−360.000	−	623.538i	−0.0752186	−	0.130282i
$285$		0			0
$286$	−3672.00			−0.759195
$287$		0			0
$288$		0			0
$289$	1574.50	−	2727.11i	0.320476	−	0.555081i
$290$	2754.00	+	4770.07i	0.557657	+	0.965890i
$291$		0			0
$292$	251.000	−	434.745i	0.0503036	−	0.0871285i
$293$	−5118.00			−1.02047			−0.510233	−	0.860036i	$-0.670441\pi$
$293$	−5118.00			−1.02047			−0.510233	+	0.860036i	$0.670441\pi$
$294$		0			0
$295$	2376.00			0.468936
$296$	4179.00	−	7238.24i	0.820606	−	1.42133i
$297$		0			0
$298$	−2619.00	−	4536.24i	−0.509109	−	0.881803i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−696.000			−0.132617
$303$		0			0
$304$	−4402.00	−	7624.49i	−0.830500	−	1.43847i
$305$	−3582.00	−	6204.21i	−0.672475	−	1.16476i
$306$		0			0
$307$	452.000			0.0840293			0.0420147	−	0.999117i	$-0.486622\pi$
$307$	452.000			0.0840293			0.0420147	+	0.999117i	$0.486622\pi$
$308$		0			0
$309$		0			0
$310$	4320.00	−	7482.46i	0.791482	−	1.37089i
$311$	2508.00	+	4343.98i	0.457285	+	0.792041i	0.998816	−	0.0486397i	$-0.0154886\pi$
$311$	2508.00	+	4343.98i	0.457285	+	0.792041i	−0.541531	+	0.840681i	$0.682155\pi$
$312$		0			0
$313$	−2701.00	+	4678.27i	−0.487762	+	0.844829i	−0.999901	−	0.0140739i	$-0.995520\pi$
$313$	−2701.00	+	4678.27i	−0.487762	+	0.844829i	0.512139	+	0.858903i	$0.328853\pi$
$314$	5082.00			0.913356
$315$		0			0
$316$	−1024.00			−0.182293
$317$	5043.00	−	8734.73i	0.893511	−	1.54761i	0.0578751	−	0.998324i	$-0.481567\pi$
$317$	5043.00	−	8734.73i	0.893511	−	1.54761i	0.835636	−	0.549283i	$-0.185099\pi$
$318$		0			0
$319$	1836.00	+	3180.05i	0.322245	+	0.558145i
$320$	−3897.00	+	6749.80i	−0.680778	+	1.17914i
$321$		0			0
$322$		0			0
$323$	5208.00			0.897154
$324$		0			0
$325$	3383.00	+	5859.53i	0.577400	+	1.00009i
$326$	4398.00	+	7617.56i	0.747186	+	1.29416i
$327$		0			0
$328$	−6678.00			−1.12418
$329$		0			0
$330$		0			0
$331$	4022.00	−	6966.31i	0.667883	−	1.15681i	−0.310613	−	0.950537i	$-0.600534\pi$
$331$	4022.00	−	6966.31i	0.667883	−	1.15681i	0.978495	−	0.206270i	$-0.0661325\pi$
$332$	−102.000	−	176.669i	−0.0168614	−	0.0292048i
$333$		0			0
$334$	1764.00	−	3055.34i	0.288987	−	0.500541i
$335$	1656.00			0.270080
$336$		0			0
$337$	4178.00			0.675342			0.337671	−	0.941264i	$-0.390361\pi$
$337$	4178.00			0.675342			0.337671	+	0.941264i	$0.390361\pi$
$338$	1561.50	−	2704.60i	0.251285	−	0.435239i
$339$		0			0
$340$	378.000	+	654.715i	0.0602939	+	0.104432i
$341$	2880.00	−	4988.31i	0.457363	−	0.792176i
$342$		0			0
$343$		0			0
$344$	5628.00			0.882097
$345$		0			0
$346$	1305.00	+	2260.33i	0.202767	+	0.351202i
$347$	78.0000	+	135.100i	0.0120670	+	0.0209007i	0.871996	−	0.489513i	$-0.162826\pi$
$347$	78.0000	+	135.100i	0.0120670	+	0.0209007i	−0.859929	+	0.510414i	$0.829492\pi$
$348$		0			0
$349$	−12418.0			−1.90464			−0.952321	−	0.305097i	$-0.901311\pi$
$349$	−12418.0			−1.90464			−0.952321	+	0.305097i	$0.901311\pi$
$350$		0			0
$351$		0			0
$352$	810.000	−	1402.96i	0.122651	−	0.212438i
$353$	−3915.00	−	6780.98i	−0.590296	−	1.02242i	−0.994192	−	0.107618i	$-0.965678\pi$
$353$	−3915.00	−	6780.98i	−0.590296	−	1.02242i	0.403897	−	0.914805i	$-0.367656\pi$
$354$		0			0
$355$	−6480.00	+	11223.7i	−0.968796	+	1.67800i
$356$	−354.000			−0.0527021
$357$		0			0
$358$	6948.00			1.02574
$359$	−4656.00	+	8064.43i	−0.684497	+	1.18558i	0.289098	+	0.957299i	$0.406645\pi$
$359$	−4656.00	+	8064.43i	−0.684497	+	1.18558i	−0.973595	+	0.228283i	$0.926689\pi$
$360$		0			0
$361$	−4258.50	−	7375.94i	−0.620863	−	1.07537i
$362$	159.000	−	275.396i	0.0230852	−	0.0399848i
$363$		0			0
$364$		0			0
$365$	−9036.00			−1.29580
$366$		0			0
$367$	1880.00	+	3256.26i	0.267398	+	0.463148i	0.968189	−	0.250219i	$-0.0805027\pi$
$367$	1880.00	+	3256.26i	0.267398	+	0.463148i	−0.700791	+	0.713367i	$0.747169\pi$
$368$		0			0
$369$		0			0
$370$	21492.0			3.01977
$371$		0			0
$372$		0			0
$373$	−2935.00	+	5083.57i	−0.407422	+	0.705676i	−0.994600	−	0.103782i	$-0.966906\pi$
$373$	−2935.00	+	5083.57i	−0.407422	+	0.705676i	0.587178	+	0.809458i	$0.300239\pi$
$374$	2268.00	+	3928.29i	0.313571	+	0.543121i
$375$		0			0
$376$	−2520.00	+	4364.77i	−0.345636	+	0.598659i
$377$	3468.00			0.473769
$378$		0			0
$379$	−1852.00			−0.251005			−0.125502	−	0.992093i	$-0.540054\pi$
$379$	−1852.00			−0.251005			−0.125502	+	0.992093i	$0.540054\pi$
$380$	1116.00	−	1932.97i	0.150657	−	0.260945i
$381$		0			0
$382$	−1692.00	−	2930.63i	−0.226624	−	0.392524i
$383$	1080.00	−	1870.61i	0.144087	−	0.249566i	−0.784945	−	0.619566i	$-0.787309\pi$
$383$	1080.00	−	1870.61i	0.144087	−	0.249566i	0.929032	+	0.369999i	$0.120642\pi$
$384$		0			0
$385$		0			0
$386$	12102.0			1.59579
$387$		0			0
$388$	143.000	+	247.683i	0.0187106	+	0.0324078i
$389$	−3393.00	−	5876.85i	−0.442241	−	0.765985i	0.555614	−	0.831440i	$-0.312483\pi$
$389$	−3393.00	−	5876.85i	−0.442241	−	0.765985i	−0.997855	+	0.0654557i	$0.979150\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−1971.00	+	3413.87i	−0.252024	+	0.436519i
$395$	9216.00	+	15962.6i	1.17394	+	2.03333i
$396$		0			0
$397$	3257.00	−	5641.29i	0.411748	−	0.713169i	−0.583333	−	0.812233i	$-0.698252\pi$
$397$	3257.00	−	5641.29i	0.411748	−	0.713169i	0.995081	+	0.0990641i	$0.0315849\pi$
$398$	15288.0			1.92542
$399$		0			0
$400$	−14129.0			−1.76612
$401$	1665.00	−	2883.86i	0.207347	−	0.359135i	−0.743531	−	0.668701i	$-0.766850\pi$
$401$	1665.00	−	2883.86i	0.207347	−	0.359135i	0.950878	+	0.309566i	$0.100184\pi$
$402$		0			0
$403$	−2720.00	−	4711.18i	−0.336211	−	0.582334i
$404$	207.000	−	358.535i	0.0254917	−	0.0441529i
$405$		0			0
$406$		0			0
$407$	14328.0			1.74499
$408$		0			0
$409$	2699.00	+	4674.81i	0.326301	+	0.565169i	0.981775	−	0.190048i	$-0.0608645\pi$
$409$	2699.00	+	4674.81i	0.326301	+	0.565169i	−0.655474	+	0.755218i	$0.727531\pi$
$410$	−8586.00	−	14871.4i	−1.03423	−	1.79133i
$411$		0			0
$412$	56.0000			0.00669641
$413$		0			0
$414$		0			0
$415$	−1836.00	+	3180.05i	−0.217170	+	0.376150i
$416$	−765.000	−	1325.02i	−0.0901616	−	0.156164i
$417$		0			0
$418$	6696.00	−	11597.8i	0.783522	−	1.35710i
$419$	−13092.0			−1.52646			−0.763229	−	0.646128i	$-0.776387\pi$
$419$	−13092.0			−1.52646			−0.763229	+	0.646128i	$0.776387\pi$
$420$		0			0
$421$	−322.000			−0.0372763			−0.0186381	−	0.999826i	$-0.505933\pi$
$421$	−322.000			−0.0372763			−0.0186381	+	0.999826i	$0.505933\pi$
$422$	4614.00	−	7991.68i	0.532242	−	0.921870i
$423$		0			0
$424$	5229.00	+	9056.89i	0.598921	+	1.03736i
$425$	4179.00	−	7238.24i	0.476968	−	0.826132i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.00135524
$429$		0			0
$430$	7236.00	+	12533.1i	0.811514	+	1.40558i
$431$	1308.00	+	2265.52i	0.146181	+	0.253193i	0.929813	−	0.368032i	$-0.119968\pi$
$431$	1308.00	+	2265.52i	0.146181	+	0.253193i	−0.783632	+	0.621226i	$0.786635\pi$
$432$		0			0
$433$	4322.00			0.479681			0.239841	−	0.970812i	$-0.422905\pi$
$433$	4322.00			0.479681			0.239841	+	0.970812i	$0.422905\pi$
$434$		0			0
$435$		0			0
$436$	−739.000	+	1279.99i	−0.0811736	+	0.140597i
$437$		0			0
$438$		0			0
$439$	4508.00	−	7808.09i	0.490103	−	0.848883i	−0.509832	−	0.860274i	$-0.670293\pi$
$439$	4508.00	−	7808.09i	0.490103	−	0.848883i	0.999935	+	0.0113909i	$0.00362592\pi$
$440$	−13608.0			−1.47440
$441$		0			0
$442$	4284.00			0.461016
$443$	−2634.00	+	4562.22i	−0.282495	+	0.489295i	−0.971999	−	0.234987i	$-0.924495\pi$
$443$	−2634.00	+	4562.22i	−0.282495	+	0.489295i	0.689504	+	0.724282i	$0.257829\pi$
$444$		0			0
$445$	3186.00	+	5518.31i	0.339395	+	0.587850i
$446$	2832.00	−	4905.17i	0.300671	−	0.520777i
$447$		0			0
$448$		0			0
$449$	5310.00			0.558117			0.279058	−	0.960274i	$-0.409978\pi$
$449$	5310.00			0.558117			0.279058	+	0.960274i	$0.409978\pi$
$450$		0			0
$451$	−5724.00	−	9914.26i	−0.597633	−	1.03513i
$452$	201.000	+	348.142i	0.0209165	+	0.0362284i
$453$		0			0
$454$	14148.0			1.46255
$455$		0			0
$456$		0			0
$457$	−7885.00	+	13657.2i	−0.807100	+	1.39794i	0.107764	+	0.994177i	$0.465631\pi$
$457$	−7885.00	+	13657.2i	−0.807100	+	1.39794i	−0.914864	+	0.403762i	$0.867702\pi$
$458$	2535.00	+	4390.75i	0.258631	+	0.447961i
$459$		0			0
$460$		0			0
$461$	5370.00			0.542529			0.271264	−	0.962505i	$-0.412558\pi$
$461$	5370.00			0.542529			0.271264	+	0.962505i	$0.412558\pi$
$462$		0			0
$463$	−3328.00			−0.334050			−0.167025	−	0.985953i	$-0.553416\pi$
$463$	−3328.00			−0.334050			−0.167025	+	0.985953i	$0.553416\pi$
$464$	−3621.00	+	6271.76i	−0.362286	+	0.627498i
$465$		0			0
$466$	207.000	+	358.535i	0.0205774	+	0.0356412i
$467$	2274.00	−	3938.68i	0.225328	−	0.390280i	−0.731090	−	0.682281i	$-0.760988\pi$
$467$	2274.00	−	3938.68i	0.225328	−	0.390280i	0.956418	+	0.292002i	$0.0943213\pi$
$468$		0			0
$469$		0			0
$470$	−12960.0			−1.27192
$471$		0			0
$472$	1386.00	+	2400.62i	0.135161	+	0.234105i
$473$	4824.00	+	8355.41i	0.468938	+	0.812225i
$474$		0			0
$475$	−24676.0			−2.38361
$476$		0			0
$477$		0			0
$478$	2844.00	−	4925.95i	0.272137	−	0.471355i
$479$	−4032.00	−	6983.63i	−0.384607	−	0.666159i	0.607108	−	0.794620i	$-0.292330\pi$
$479$	−4032.00	−	6983.63i	−0.384607	−	0.666159i	−0.991715	+	0.128461i	$0.958996\pi$
$480$		0			0
$481$	6766.00	−	11719.1i	0.641378	−	1.11090i
$482$	−10794.0			−1.02003
$483$		0			0
$484$	−35.0000			−0.00328700
$485$	2574.00	−	4458.30i	0.240988	−	0.417404i
$486$		0			0
$487$	−8308.00	−	14389.9i	−0.773042	−	1.33895i	−0.935888	−	0.352296i	$-0.885401\pi$
$487$	−8308.00	−	14389.9i	−0.773042	−	1.33895i	0.162847	−	0.986651i	$-0.447932\pi$
$488$	4179.00	−	7238.24i	0.387653	−	0.671434i
$489$		0			0
$490$		0			0
$491$	7140.00			0.656260			0.328130	−	0.944633i	$-0.393582\pi$
$491$	7140.00			0.656260			0.328130	+	0.944633i	$0.393582\pi$
$492$		0			0
$493$	−2142.00	−	3710.05i	−0.195681	−	0.338930i
$494$	−6324.00	−	10953.5i	−0.575972	−	0.997613i
$495$		0			0
$496$	11360.0			1.02839
$497$		0			0
$498$		0			0
$499$	4562.00	−	7901.62i	0.409265	−	0.708868i	−0.585543	−	0.810642i	$-0.699119\pi$
$499$	4562.00	−	7901.62i	0.409265	−	0.708868i	0.994808	+	0.101774i	$0.0324519\pi$
$500$	−666.000	−	1153.55i	−0.0595689	−	0.103176i
$501$		0			0
$502$	−4590.00	+	7950.11i	−0.408091	+	0.706834i
$503$	6552.00			0.580794			0.290397	−	0.956906i	$-0.406213\pi$
$503$	6552.00			0.580794			0.290397	+	0.956906i	$0.406213\pi$
$504$		0			0
$505$	−7452.00			−0.656653
$506$		0			0
$507$		0			0
$508$	−640.000	−	1108.51i	−0.0558965	−	0.0968155i
$509$	1395.00	−	2416.21i	0.121478	−	0.210406i	−0.798873	−	0.601500i	$-0.794570\pi$
$509$	1395.00	−	2416.21i	0.121478	−	0.210406i	0.920351	+	0.391094i	$0.127903\pi$
$510$		0			0
$511$		0			0
$512$	−8733.00			−0.753804
$513$		0			0
$514$	−10233.0	−	17724.1i	−0.878129	−	1.52096i
$515$	−504.000	−	872.954i	−0.0431241	−	0.0746931i
$516$		0			0
$517$	−8640.00			−0.734984
$518$		0			0
$519$		0			0
$520$	−6426.00	+	11130.2i	−0.541921	+	0.938634i
$521$	−7431.00	−	12870.9i	−0.624871	−	1.08231i	−0.988566	−	0.150791i	$-0.951818\pi$
$521$	−7431.00	−	12870.9i	−0.624871	−	1.08231i	0.363694	−	0.931518i	$-0.381515\pi$
$522$		0			0
$523$	−8830.00	+	15294.0i	−0.738258	+	1.27870i	0.215021	+	0.976609i	$0.431018\pi$
$523$	−8830.00	+	15294.0i	−0.738258	+	1.27870i	−0.953279	+	0.302091i	$0.902315\pi$
$524$	−1764.00			−0.147062
$525$		0			0
$526$	−7776.00			−0.644581
$527$	−3360.00	+	5819.69i	−0.277730	+	0.481043i
$528$		0			0
$529$	6083.50	+	10536.9i	0.500000	+	0.866025i
$530$	−13446.0	+	23289.2i	−1.10199	+	1.90871i
$531$		0			0
$532$		0			0
$533$	−10812.0			−0.878649
$534$		0			0
$535$	108.000	+	187.061i	0.00872756	+	0.0151166i
$536$	966.000	+	1673.16i	0.0778449	+	0.134831i
$537$		0			0
$538$	−24642.0			−1.97471
$539$		0			0
$540$		0			0
$541$	9917.00	−	17176.7i	0.788106	−	1.36504i	−0.139021	−	0.990290i	$-0.544395\pi$
$541$	9917.00	−	17176.7i	0.788106	−	1.36504i	0.927126	−	0.374749i	$-0.122271\pi$
$542$	8016.00	+	13884.1i	0.635271	+	1.10032i
$543$		0			0
$544$	−945.000	+	1636.79i	−0.0744789	+	0.129001i
$545$	26604.0			2.09099
$546$		0			0
$547$	20972.0			1.63930			0.819651	−	0.572863i	$-0.194167\pi$
$547$	20972.0			1.63930			0.819651	+	0.572863i	$0.194167\pi$
$548$	−1179.00	+	2042.09i	−0.0919058	+	0.159186i
$549$		0			0
$550$	−10746.0	−	18612.6i	−0.833111	−	1.44299i
$551$	−6324.00	+	10953.5i	−0.488950	+	0.846886i
$552$		0			0
$553$		0			0
$554$	−19542.0			−1.49866
$555$		0			0
$556$	26.0000	+	45.0333i	0.00198318	+	0.00343496i
$557$	10587.0	+	18337.2i	0.805360	+	1.39492i	0.916048	+	0.401069i	$0.131361\pi$
$557$	10587.0	+	18337.2i	0.805360	+	1.39492i	−0.110688	+	0.993855i	$0.535305\pi$
$558$		0			0
$559$	9112.00			0.689439
$560$		0			0
$561$		0			0
$562$	9927.00	−	17194.1i	0.745098	−	1.29055i
$563$	−8886.00	−	15391.0i	−0.665187	−	1.15214i	−0.979235	−	0.202730i	$-0.935019\pi$
$563$	−8886.00	−	15391.0i	−0.665187	−	1.15214i	0.314048	−	0.949407i	$-0.398315\pi$
$564$		0			0
$565$	3618.00	−	6266.56i	0.269399	−	0.466613i
$566$	9780.00			0.726297
$567$		0			0
$568$	−15120.0			−1.11694
$569$	4125.00	−	7144.71i	0.303917	−	0.526400i	−0.673102	−	0.739549i	$-0.735039\pi$
$569$	4125.00	−	7144.71i	0.303917	−	0.526400i	0.977020	+	0.213149i	$0.0683720\pi$
$570$		0			0
$571$	−10378.0	−	17975.2i	−0.760606	−	1.31741i	−0.942539	−	0.334097i	$-0.891569\pi$
$571$	−10378.0	−	17975.2i	−0.760606	−	1.31741i	0.181933	−	0.983311i	$-0.441765\pi$
$572$	612.000	−	1060.02i	0.0447360	−	0.0774851i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.00000	−	1.73205i	−7.21500e−5	−	0.000124967i	0.865989	−	0.500062i	$-0.166690\pi$
$577$	−1.00000	−	1.73205i	−7.21500e−5	−	0.000124967i	−0.866061	+	0.499938i	$0.833356\pi$
$578$	4723.50	+	8181.34i	0.339916	+	0.588753i
$579$		0			0
$580$	−1836.00			−0.131441
$581$		0			0
$582$		0			0
$583$	−8964.00	+	15526.1i	−0.636794	+	1.10296i
$584$	−5271.00	−	9129.64i	−0.373485	−	0.646896i
$585$		0			0
$586$	7677.00	−	13297.0i	0.541184	−	0.937359i
$587$	−26364.0			−1.85376			−0.926881	−	0.375354i	$-0.877521\pi$
$587$	−26364.0			−1.85376			−0.926881	+	0.375354i	$0.877521\pi$
$588$		0			0
$589$	19840.0			1.38793
$590$	−3564.00	+	6173.03i	−0.248691	+	0.430745i
$591$		0			0
$592$	14129.0	+	24472.1i	0.980909	+	1.69898i
$593$	1149.00	−	1990.13i	0.0795679	−	0.137816i	−0.823496	−	0.567323i	$-0.807979\pi$
$593$	1149.00	−	1990.13i	0.0795679	−	0.137816i	0.903064	+	0.429507i	$0.141313\pi$
$594$		0			0
$595$		0			0
$596$	1746.00			0.119998
$597$		0			0
$598$		0			0
$599$	1536.00	+	2660.43i	0.104773	+	0.181473i	0.913646	−	0.406512i	$-0.133255\pi$
$599$	1536.00	+	2660.43i	0.104773	+	0.181473i	−0.808872	+	0.587984i	$0.799922\pi$
$600$		0			0
$601$	24554.0			1.66652			0.833260	−	0.552881i	$-0.186472\pi$
$601$	24554.0			1.66652			0.833260	+	0.552881i	$0.186472\pi$
$602$		0			0
$603$		0			0
$604$	116.000	−	200.918i	0.00781452	−	0.0135352i
$605$	315.000	+	545.596i	0.0211679	+	0.0366639i
$606$		0			0
$607$	−8416.00	+	14576.9i	−0.562759	+	0.974728i	0.434495	+	0.900674i	$0.356927\pi$
$607$	−8416.00	+	14576.9i	−0.562759	+	0.974728i	−0.997254	+	0.0740535i	$0.976406\pi$
$608$	5580.00			0.372202
$609$		0			0
$610$	21492.0			1.42653
$611$	−4080.00	+	7066.77i	−0.270146	+	0.467906i
$612$		0			0
$613$	1241.00	+	2149.48i	0.0817676	+	0.141626i	0.904009	−	0.427513i	$-0.140610\pi$
$613$	1241.00	+	2149.48i	0.0817676	+	0.141626i	−0.822242	+	0.569139i	$0.807277\pi$
$614$	−678.000	+	1174.33i	−0.0445633	+	0.0771859i
$615$		0			0
$616$		0			0
$617$	15798.0			1.03080			0.515400	−	0.856950i	$-0.327643\pi$
$617$	15798.0			1.03080			0.515400	+	0.856950i	$0.327643\pi$
$618$		0			0
$619$	7730.00	+	13388.8i	0.501930	+	0.869369i	0.999998	+	0.00223050i	$0.000709990\pi$
$619$	7730.00	+	13388.8i	0.501930	+	0.869369i	−0.498067	+	0.867138i	$0.665957\pi$
$620$	1440.00	+	2494.15i	0.0932771	+	0.161561i
$621$		0			0
$622$	−15048.0			−0.970048
$623$		0			0
$624$		0			0
$625$	449.500	−	778.557i	0.0287680	−	0.0498276i
$626$	−8103.00	−	14034.8i	−0.517350	−	0.896076i
$627$		0			0
$628$	−847.000	+	1467.05i	−0.0538200	+	0.0932190i
$629$	−16716.0			−1.05964
$630$		0			0
$631$	−7720.00			−0.487050			−0.243525	−	0.969895i	$-0.578304\pi$
$631$	−7720.00			−0.487050			−0.243525	+	0.969895i	$0.578304\pi$
$632$	−10752.0	+	18623.0i	−0.676727	+	1.17213i
$633$		0			0
$634$	15129.0	+	26204.2i	0.947712	+	1.64149i
$635$	−11520.0	+	19953.2i	−0.719933	+	1.24696i
$636$		0			0
$637$		0			0
$638$	−11016.0			−0.683586
$639$		0			0
$640$	−14931.0	−	25861.3i	−0.922187	−	1.59727i
$641$	−8631.00	−	14949.3i	−0.531832	−	0.921159i	−0.999310	−	0.0371545i	$-0.988171\pi$
$641$	−8631.00	−	14949.3i	−0.531832	−	0.921159i	0.467478	−	0.884005i	$-0.345163\pi$
$642$		0			0
$643$	−12220.0			−0.749471			−0.374735	−	0.927132i	$-0.622266\pi$
$643$	−12220.0			−0.749471			−0.374735	+	0.927132i	$0.622266\pi$
$644$		0			0
$645$		0			0
$646$	−7812.00	+	13530.8i	−0.475788	+	0.824089i
$647$	6780.00	+	11743.3i	0.411977	+	0.713566i	0.995106	−	0.0988143i	$-0.0315050\pi$
$647$	6780.00	+	11743.3i	0.411977	+	0.713566i	−0.583129	+	0.812380i	$0.698172\pi$
$648$		0			0
$649$	−2376.00	+	4115.35i	−0.143707	+	0.248909i
$650$	−20298.0			−1.22485
$651$		0			0
$652$	−2932.00			−0.176113
$653$	11547.0	−	20000.0i	0.691989	−	1.19856i	−0.279196	−	0.960234i	$-0.590068\pi$
$653$	11547.0	−	20000.0i	0.691989	−	1.19856i	0.971185	−	0.238326i	$-0.0765988\pi$
$654$		0			0
$655$	15876.0	+	27498.0i	0.947064	+	1.64036i
$656$	11289.0	−	19553.1i	0.671892	−	1.16375i
$657$		0			0
$658$		0			0
$659$	−22548.0			−1.33285			−0.666423	−	0.745574i	$-0.732175\pi$
$659$	−22548.0			−1.33285			−0.666423	+	0.745574i	$0.732175\pi$
$660$		0			0
$661$	−8731.00	−	15122.5i	−0.513762	−	0.889862i	−0.999873	−	0.0159643i	$-0.994918\pi$
$661$	−8731.00	−	15122.5i	−0.513762	−	0.889862i	0.486111	−	0.873897i	$-0.338415\pi$
$662$	12066.0	+	20898.9i	0.708396	+	1.22698i
$663$		0			0
$664$	−4284.00			−0.250379
$665$		0			0
$666$		0			0
$667$		0			0
$668$	588.000	+	1018.45i	0.0340575	+	0.0589893i
$669$		0			0
$670$	−2484.00	+	4302.41i	−0.143232	+	0.248085i
$671$	14328.0			0.824331
$672$		0			0
$673$	−22462.0			−1.28655			−0.643274	−	0.765636i	$-0.722424\pi$
$673$	−22462.0			−1.28655			−0.643274	+	0.765636i	$0.722424\pi$
$674$	−6267.00	+	10854.8i	−0.358154	+	0.620341i
$675$		0			0
$676$	520.500	+	901.532i	0.0296142	+	0.0512934i
$677$	−12777.0	+	22130.4i	−0.725347	+	1.25634i	0.233484	+	0.972361i	$0.424987\pi$
$677$	−12777.0	+	22130.4i	−0.725347	+	1.25634i	−0.958831	+	0.283977i	$0.908346\pi$
$678$		0			0
$679$		0			0
$680$	15876.0			0.895319
$681$		0			0
$682$	8640.00	+	14964.9i	0.485107	+	0.840229i
$683$	4638.00	+	8033.25i	0.259836	+	0.450050i	0.966198	−	0.257802i	$-0.0829981\pi$
$683$	4638.00	+	8033.25i	0.259836	+	0.450050i	−0.706362	+	0.707851i	$0.749665\pi$
$684$		0			0
$685$	42444.0			2.36745
$686$		0			0
$687$		0			0
$688$	−9514.00	+	16478.7i	−0.527206	+	0.913148i
$689$	8466.00	+	14663.5i	0.468112	+	0.810793i
$690$		0			0
$691$	−13690.0	+	23711.8i	−0.753679	+	1.30541i	0.192349	+	0.981326i	$0.438389\pi$
$691$	−13690.0	+	23711.8i	−0.753679	+	1.30541i	−0.946028	+	0.324084i	$0.894944\pi$
$692$	−870.000			−0.0477925
$693$		0			0
$694$	−468.000			−0.0255980
$695$	468.000	−	810.600i	0.0255428	−	0.0442414i
$696$		0			0
$697$	6678.00	+	11566.6i	0.362909	+	0.628576i
$698$	18627.0	−	32262.9i	1.01009	−	1.74953i
$699$		0			0
$700$		0			0
$701$	−25830.0			−1.39171			−0.695853	−	0.718184i	$-0.744973\pi$
$701$	−25830.0			−1.39171			−0.695853	+	0.718184i	$0.744973\pi$
$702$		0			0
$703$	24676.0	+	42740.1i	1.32386	+	2.29299i
$704$	−7794.00	−	13499.6i	−0.417255	−	0.722707i
$705$		0			0
$706$	23490.0			1.25221
$707$		0			0
$708$		0			0
$709$	3113.00	−	5391.87i	0.164896	−	0.285608i	−0.771722	−	0.635959i	$-0.780605\pi$
$709$	3113.00	−	5391.87i	0.164896	−	0.285608i	0.936618	+	0.350351i	$0.113938\pi$
$710$	−19440.0	−	33671.1i	−1.02756	−	1.77979i
$711$		0			0
$712$	−3717.00	+	6438.03i	−0.195647	+	0.338870i
$713$		0			0
$714$		0			0
$715$	−22032.0			−1.15238
$716$	−1158.00	+	2005.71i	−0.0604420	+	0.104689i
$717$		0			0
$718$	−13968.0	−	24193.3i	−0.726018	−	1.25750i
$719$	−7536.00	+	13052.7i	−0.390884	+	0.677030i	−0.992566	−	0.121705i	$-0.961164\pi$
$719$	−7536.00	+	13052.7i	−0.390884	+	0.677030i	0.601683	+	0.798735i	$0.294497\pi$
$720$		0			0
$721$		0			0
$722$	25551.0			1.31705
$723$		0			0
$724$	53.0000	+	91.7987i	0.00272062	+	0.00471225i
$725$	10149.0	+	17578.6i	0.519896	+	0.900486i
$726$		0			0
$727$	−32920.0			−1.67942			−0.839708	−	0.543038i	$-0.817274\pi$
$727$	−32920.0			−1.67942			−0.839708	+	0.543038i	$0.817274\pi$
$728$		0			0
$729$		0			0
$730$	13554.0	−	23476.2i	0.687200	−	1.19027i
$731$	−5628.00	−	9747.98i	−0.284759	−	0.493218i
$732$		0			0
$733$	3473.00	−	6015.41i	0.175004	−	0.303116i	−0.765158	−	0.643842i	$-0.777339\pi$
$733$	3473.00	−	6015.41i	0.175004	−	0.303116i	0.940163	+	0.340726i	$0.110673\pi$
$734$	−11280.0			−0.567238
$735$		0			0
$736$		0			0
$737$	−1656.00	+	2868.28i	−0.0827674	+	0.143357i
$738$		0			0
$739$	1178.00	+	2040.36i	0.0586379	+	0.101564i	0.893854	−	0.448358i	$-0.147991\pi$
$739$	1178.00	+	2040.36i	0.0586379	+	0.101564i	−0.835216	+	0.549922i	$0.814658\pi$
$740$	−3582.00	+	6204.21i	−0.177942	+	0.308204i
$741$		0			0
$742$		0			0
$743$	23520.0			1.16133			0.580663	−	0.814144i	$-0.302793\pi$
$743$	23520.0			1.16133			0.580663	+	0.814144i	$0.302793\pi$
$744$		0			0
$745$	−15714.0	−	27217.4i	−0.772774	−	1.33848i
$746$	−8805.00	−	15250.7i	−0.432137	−	0.748483i
$747$		0			0
$748$	−1512.00			−0.0739094
$749$		0			0
$750$		0			0
$751$	−1504.00	+	2605.00i	−0.0730782	+	0.126575i	−0.900249	−	0.435376i	$-0.856616\pi$
$751$	−1504.00	+	2605.00i	−0.0730782	+	0.126575i	0.827171	+	0.561951i	$0.189949\pi$
$752$	−8520.00	−	14757.1i	−0.413155	−	0.715605i
$753$		0			0
$754$	−5202.00	+	9010.13i	−0.251254	+	0.435185i
$755$	−4176.00			−0.201298
$756$		0			0
$757$	−20770.0			−0.997224			−0.498612	−	0.866825i	$-0.666157\pi$
$757$	−20770.0			−0.997224			−0.498612	+	0.866825i	$0.666157\pi$
$758$	2778.00	−	4811.64i	0.133115	−	0.230563i
$759$		0			0
$760$	−23436.0	−	40592.3i	−1.11857	−	1.93742i
$761$	5769.00	−	9992.20i	0.274804	−	0.475975i	−0.695281	−	0.718738i	$-0.744720\pi$
$761$	5769.00	−	9992.20i	0.274804	−	0.475975i	0.970086	+	0.242763i	$0.0780536\pi$
$762$		0			0
$763$		0			0
$764$	1128.00			0.0534157
$765$		0			0
$766$	3240.00	+	5611.84i	0.152828	+	0.264705i
$767$	2244.00	+	3886.72i	0.105640	+	0.182974i
$768$		0			0
$769$	8498.00			0.398499			0.199249	−	0.979949i	$-0.436150\pi$
$769$	8498.00			0.398499			0.199249	+	0.979949i	$0.436150\pi$
$770$		0			0
$771$		0			0
$772$	−2017.00	+	3493.55i	−0.0940329	+	0.162870i
$773$	−16161.0	−	27991.7i	−0.751967	−	1.30245i	−0.946868	−	0.321623i	$-0.895772\pi$
$773$	−16161.0	−	27991.7i	−0.751967	−	1.30245i	0.194901	−	0.980823i	$-0.437562\pi$
$774$		0			0
$775$	15920.0	−	27574.2i	0.737888	−	1.27806i
$776$	6006.00			0.277839
$777$		0			0
$778$	20358.0			0.938136
$779$	19716.0	−	34149.1i	0.906802	−	1.57063i
$780$		0			0
$781$	−12960.0	−	22447.4i	−0.593784	−	1.02846i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30492.0			1.38638
$786$		0			0
$787$	−13114.0	−	22714.1i	−0.593982	−	1.02881i	−0.993690	−	0.112164i	$-0.964222\pi$
$787$	−13114.0	−	22714.1i	−0.593982	−	1.02881i	0.399708	−	0.916643i	$-0.369112\pi$
$788$	−657.000	−	1137.96i	−0.0297013	−	0.0514442i
$789$		0			0
$790$	−55296.0			−2.49031
$791$		0			0
$792$		0			0
$793$	6766.00	−	11719.1i	0.302986	−	0.524787i
$794$	9771.00	+	16923.9i	0.436725	+	0.756430i
$795$		0			0
$796$	−2548.00	+	4413.27i	−0.113457	+	0.196513i
$797$	43338.0			1.92611			0.963056	−	0.269302i	$-0.0867931\pi$
$797$	43338.0			1.92611			0.963056	+	0.269302i	$0.0867931\pi$
$798$		0			0
$799$	10080.0			0.446314
$800$	4477.50	−	7755.26i	0.197879	−	0.342737i
$801$		0			0
$802$	4995.00	+	8651.59i	0.219925	+	0.380921i
$803$	9036.00	−	15650.8i	0.397103	−	0.687802i
$804$		0			0
$805$		0			0
$806$	16320.0			0.713210
$807$		0			0
$808$	−4347.00	−	7529.22i	−0.189266	−	0.327818i
$809$	−14451.0	−	25029.9i	−0.628022	−	1.08777i	−0.987948	−	0.154786i	$-0.950531\pi$
$809$	−14451.0	−	25029.9i	−0.628022	−	1.08777i	0.359926	−	0.932981i	$-0.382802\pi$
$810$		0			0
$811$	27164.0			1.17615			0.588075	−	0.808807i	$-0.299886\pi$
$811$	27164.0			1.17615			0.588075	+	0.808807i	$0.299886\pi$
$812$		0			0
$813$		0			0
$814$	−21492.0	+	37225.2i	−0.925423	+	1.60288i
$815$	26388.0	+	45705.4i	1.13415	+	1.96440i
$816$		0			0
$817$	−16616.0	+	28779.8i	−0.711530	+	1.23241i
$818$	−16194.0			−0.692188
$819$		0			0
$820$	5724.00			0.243769
$821$	−8601.00	+	14897.4i	−0.365624	+	0.633279i	−0.988876	−	0.148742i	$-0.952478\pi$
$821$	−8601.00	+	14897.4i	−0.365624	+	0.633279i	0.623252	+	0.782021i	$0.285811\pi$
$822$		0			0
$823$	2996.00	+	5189.22i	0.126894	+	0.219787i	0.922472	−	0.386064i	$-0.126166\pi$
$823$	2996.00	+	5189.22i	0.126894	+	0.219787i	−0.795578	+	0.605852i	$0.792832\pi$
$824$	588.000	−	1018.45i	0.0248592	−	0.0430573i
$825$		0			0
$826$		0			0
$827$	−25884.0			−1.08836			−0.544181	−	0.838968i	$-0.683159\pi$
$827$	−25884.0			−1.08836			−0.544181	+	0.838968i	$0.683159\pi$
$828$		0			0
$829$	737.000	+	1276.52i	0.0308770	+	0.0534806i	0.881051	−	0.473021i	$-0.156837\pi$
$829$	737.000	+	1276.52i	0.0308770	+	0.0534806i	−0.850174	+	0.526502i	$0.823503\pi$
$830$	−5508.00	−	9540.14i	−0.230344	−	0.398967i
$831$		0			0
$832$	−14722.0			−0.613454
$833$		0			0
$834$		0			0
$835$	10584.0	−	18332.0i	0.438652	−	0.759768i
$836$	2232.00	+	3865.94i	0.0923389	+	0.159936i
$837$		0			0
$838$	19638.0	−	34014.0i	0.809527	−	1.40214i
$839$	−33528.0			−1.37964			−0.689818	−	0.723983i	$-0.742310\pi$
$839$	−33528.0			−1.37964			−0.689818	+	0.723983i	$0.742310\pi$
$840$		0			0
$841$	−13985.0			−0.573414
$842$	483.000	−	836.581i	0.0197687	−	0.0342405i
$843$		0			0
$844$	1538.00	+	2663.89i	0.0627253	+	0.108643i
$845$	9369.00	−	16227.6i	0.381424	−	0.660646i
$846$		0			0
$847$		0			0
$848$	−35358.0			−1.43184
$849$		0			0
$850$	12537.0	+	21714.7i	0.505901	+	0.876246i
$851$		0			0
$852$		0			0
$853$	1190.00			0.0477665			0.0238832	−	0.999715i	$-0.492397\pi$
$853$	1190.00			0.0477665			0.0238832	+	0.999715i	$0.492397\pi$
$854$		0			0
$855$		0			0
$856$	−126.000	+	218.238i	−0.00503106	+	0.00871406i
$857$	17289.0	+	29945.4i	0.689126	+	1.19360i	0.972121	+	0.234480i	$0.0753387\pi$
$857$	17289.0	+	29945.4i	0.689126	+	1.19360i	−0.282995	+	0.959121i	$0.591328\pi$
$858$		0			0
$859$	22202.0	−	38455.0i	0.881865	−	1.52744i	0.0326009	−	0.999468i	$-0.489621\pi$
$859$	22202.0	−	38455.0i	0.881865	−	1.52744i	0.849265	−	0.527967i	$-0.177046\pi$
$860$	−4824.00			−0.191276
$861$		0			0
$862$	−7848.00			−0.310097
$863$	−19164.0	+	33193.0i	−0.755910	+	1.30927i	0.189011	+	0.981975i	$0.439472\pi$
$863$	−19164.0	+	33193.0i	−0.755910	+	1.30927i	−0.944921	+	0.327299i	$0.893862\pi$
$864$		0			0
$865$	7830.00	+	13562.0i	0.307778	+	0.533087i
$866$	−6483.00	+	11228.9i	−0.254390	+	0.440616i
$867$		0			0
$868$		0			0
$869$	−36864.0			−1.43904
$870$		0			0
$871$	1564.00	+	2708.93i	0.0608428	+	0.105383i
$872$	15519.0	+	26879.7i	0.602683	+	1.04388i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19421.0	−	33638.2i	0.747777	−	1.29519i	−0.201109	−	0.979569i	$-0.564454\pi$
$877$	19421.0	−	33638.2i	0.747777	−	1.29519i	0.948886	−	0.315619i	$-0.102212\pi$
$878$	13524.0	+	23424.3i	0.519832	+	0.900376i
$879$		0			0
$880$	23004.0	−	39844.1i	0.881210	−	1.52630i
$881$	35046.0			1.34022			0.670108	−	0.742264i	$-0.266248\pi$
$881$	35046.0			1.34022			0.670108	+	0.742264i	$0.266248\pi$
$882$		0			0
$883$	14204.0			0.541339			0.270670	−	0.962672i	$-0.412755\pi$
$883$	14204.0			0.541339			0.270670	+	0.962672i	$0.412755\pi$
$884$	−714.000	+	1236.68i	−0.0271656	+	0.0470523i
$885$		0			0
$886$	−7902.00	−	13686.7i	−0.299631	−	0.518976i
$887$	−13068.0	+	22634.4i	−0.494679	+	0.856810i	−0.999981	−	0.00613301i	$-0.998048\pi$
$887$	−13068.0	+	22634.4i	−0.494679	+	0.856810i	0.505302	+	0.862943i	$0.331381\pi$
$888$		0			0
$889$		0			0
$890$	−19116.0			−0.719966
$891$		0			0
$892$	944.000	+	1635.06i	0.0354344	+	0.0613741i
$893$	−14880.0	−	25772.9i	−0.557604	−	0.965798i
$894$		0			0
$895$	41688.0			1.55696
$896$		0			0
$897$		0			0
$898$	−7965.00	+	13795.8i	−0.295986	+	0.512663i
$899$	−8160.00	−	14133.5i	−0.302727	−	0.524338i
$900$		0			0
$901$	10458.0	−	18113.8i	0.386689	−	0.669764i
$902$	34344.0			1.26777
$903$		0			0
$904$	8442.00			0.310594
$905$	954.000	−	1652.38i	0.0350409	−	0.0606927i
$906$		0			0
$907$	4526.00	+	7839.26i	0.165693	+	0.286988i	0.936901	−	0.349595i	$-0.113681\pi$
$907$	4526.00	+	7839.26i	0.165693	+	0.286988i	−0.771208	+	0.636583i	$0.780347\pi$
$908$	−2358.00	+	4084.18i	−0.0861817	+	0.149271i
$909$		0			0
$910$		0			0
$911$	−5016.00			−0.182423			−0.0912116	−	0.995832i	$-0.529074\pi$
$911$	−5016.00			−0.182423			−0.0912116	+	0.995832i	$0.529074\pi$
$912$		0			0
$913$	−3672.00	−	6360.09i	−0.133106	−	0.230546i
$914$	−23655.0	−	40971.7i	−0.856059	−	1.48274i
$915$		0			0
$916$	−1690.00			−0.0609598
$917$		0			0
$918$		0			0
$919$	−22276.0	+	38583.2i	−0.799584	+	1.38492i	0.120304	+	0.992737i	$0.461613\pi$
$919$	−22276.0	+	38583.2i	−0.799584	+	1.38492i	−0.919887	+	0.392182i	$0.871720\pi$
$920$		0			0
$921$		0			0
$922$	−8055.00	+	13951.7i	−0.287719	+	0.498345i
$923$	−24480.0			−0.872989
$924$		0			0
$925$	79202.0			2.81529
$926$	4992.00	−	8646.40i	0.177157	−	0.306845i
$927$		0			0
$928$	−2295.00	−	3975.06i	−0.0811822	−	0.140612i
$929$	12117.0	−	20987.3i	0.427929	−	0.741194i	−0.568760	−	0.822503i	$-0.692577\pi$
$929$	12117.0	−	20987.3i	0.427929	−	0.741194i	0.996689	+	0.0813090i	$0.0259101\pi$
$930$		0			0
$931$		0			0
$932$	−138.000			−0.00485015
$933$		0			0
$934$	6822.00	+	11816.1i	0.238996	+	0.413954i
$935$	13608.0	+	23569.7i	0.475967	+	0.824399i
$936$		0			0
$937$	−13894.0			−0.484415			−0.242208	−	0.970224i	$-0.577872\pi$
$937$	−13894.0			−0.484415			−0.242208	+	0.970224i	$0.577872\pi$
$938$		0			0
$939$		0			0
$940$	2160.00	−	3741.23i	0.0749483	−	0.129814i
$941$	23379.0	+	40493.6i	0.809919	+	1.40282i	0.912920	+	0.408139i	$0.133822\pi$
$941$	23379.0	+	40493.6i	0.809919	+	1.40282i	−0.103001	+	0.994681i	$0.532844\pi$
$942$		0			0
$943$		0			0
$944$	−9372.00			−0.323128
$945$		0			0
$946$	−28944.0			−0.994768
$947$	6906.00	−	11961.5i	0.236974	−	0.410452i	−0.722870	−	0.690984i	$-0.757178\pi$
$947$	6906.00	−	11961.5i	0.236974	−	0.410452i	0.959845	+	0.280532i	$0.0905109\pi$
$948$		0			0
$949$	−8534.00	−	14781.3i	−0.291913	−	0.505608i
$950$	37014.0	−	64110.1i	1.26410	−	2.18948i
$951$		0			0
$952$		0			0
$953$	58518.0			1.98907			0.994535	−	0.104402i	$-0.0332930\pi$
$953$	58518.0			1.98907			0.994535	+	0.104402i	$0.0332930\pi$
$954$		0			0
$955$	−10152.0	−	17583.8i	−0.343991	−	0.595809i
$956$	948.000	+	1641.98i	0.0320717	+	0.0555498i
$957$		0			0
$958$	24192.0			0.815875
$959$		0			0
$960$		0			0
$961$	2095.50	−	3629.51i	0.0703400	−	0.121833i
$962$	20298.0	+	35157.2i	0.680285	+	1.17829i
$963$		0			0
$964$	1799.00	−	3115.96i	0.0601057	−	0.104106i
$965$	72612.0			2.42224
$966$		0			0
$967$	19640.0			0.653133			0.326567	−	0.945174i	$-0.394108\pi$
$967$	19640.0			0.653133			0.326567	+	0.945174i	$0.394108\pi$
$968$	−367.500	+	636.529i	−0.0122024	+	0.0211351i
$969$		0			0
$970$	7722.00	+	13374.9i	0.255607	+	0.442724i
$971$	−29154.0	+	50496.2i	−0.963539	+	1.66890i	−0.250049	+	0.968233i	$0.580447\pi$
$971$	−29154.0	+	50496.2i	−0.963539	+	1.66890i	−0.713490	+	0.700665i	$0.752887\pi$
$972$		0			0
$973$		0			0
$974$	49848.0			1.63987
$975$		0			0
$976$	14129.0	+	24472.1i	0.463379	+	0.802597i
$977$	−11775.0	−	20394.9i	−0.385584	−	0.667851i	0.606266	−	0.795262i	$-0.292667\pi$
$977$	−11775.0	−	20394.9i	−0.385584	−	0.667851i	−0.991850	+	0.127411i	$0.959333\pi$
$978$		0			0
$979$	−12744.0			−0.416037
$980$		0			0
$981$		0			0
$982$	−10710.0	+	18550.3i	−0.348034	+	0.602813i
$983$	7884.00	+	13655.5i	0.255809	+	0.443075i	0.965115	−	0.261826i	$-0.0843247\pi$
$983$	7884.00	+	13655.5i	0.255809	+	0.443075i	−0.709306	+	0.704901i	$0.750991\pi$
$984$		0			0
$985$	−11826.0	+	20483.2i	−0.382546	+	0.662589i
$986$	12852.0			0.415102
$987$		0			0
$988$	4216.00			0.135758
$989$		0			0
$990$		0			0
$991$	−17632.0	−	30539.5i	−0.565186	−	0.978930i	−0.997032	−	0.0769832i	$-0.975471\pi$
$991$	−17632.0	−	30539.5i	−0.565186	−	0.978930i	0.431847	−	0.901947i	$-0.357862\pi$
$992$	−3600.00	+	6235.38i	−0.115222	+	0.199570i
$993$		0			0
$994$		0			0
$995$	91728.0			2.92259
$996$		0			0
$997$	14669.0	+	25407.5i	0.465970	+	0.807083i	0.999245	−	0.0388586i	$-0.0123722\pi$
$997$	14669.0	+	25407.5i	0.465970	+	0.807083i	−0.533275	+	0.845942i	$0.679039\pi$
$998$	13686.0	+	23704.8i	0.434091	+	0.751868i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.b.226.1		2
3.2	odd	2		147.4.e.i.79.1		2
7.2	even	3		63.4.a.c.1.1		1
7.3	odd	6		441.4.e.d.361.1		2
7.4	even	3	inner	441.4.e.b.361.1		2
7.5	odd	6		441.4.a.j.1.1		1
7.6	odd	2		441.4.e.d.226.1		2
21.2	odd	6		21.4.a.a.1.1	✓	1
21.5	even	6		147.4.a.c.1.1		1
21.11	odd	6		147.4.e.i.67.1		2
21.17	even	6		147.4.e.g.67.1		2
21.20	even	2		147.4.e.g.79.1		2
28.23	odd	6		1008.4.a.v.1.1		1
35.9	even	6		1575.4.a.b.1.1		1
84.23	even	6		336.4.a.f.1.1		1
84.47	odd	6		2352.4.a.r.1.1		1
105.2	even	12		525.4.d.c.274.1		2
105.23	even	12		525.4.d.c.274.2		2
105.44	odd	6		525.4.a.g.1.1		1
168.107	even	6		1344.4.a.n.1.1		1
168.149	odd	6		1344.4.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.a.1.1	✓	1	21.2	odd	6
63.4.a.c.1.1		1	7.2	even	3
147.4.a.c.1.1		1	21.5	even	6
147.4.e.g.67.1		2	21.17	even	6
147.4.e.g.79.1		2	21.20	even	2
147.4.e.i.67.1		2	21.11	odd	6
147.4.e.i.79.1		2	3.2	odd	2
336.4.a.f.1.1		1	84.23	even	6
441.4.a.j.1.1		1	7.5	odd	6
441.4.e.b.226.1		2	1.1	even	1	trivial
441.4.e.b.361.1		2	7.4	even	3	inner
441.4.e.d.226.1		2	7.6	odd	2
441.4.e.d.361.1		2	7.3	odd	6
525.4.a.g.1.1		1	105.44	odd	6
525.4.d.c.274.1		2	105.2	even	12
525.4.d.c.274.2		2	105.23	even	12
1008.4.a.v.1.1		1	28.23	odd	6
1344.4.a.n.1.1		1	168.107	even	6
1344.4.a.ba.1.1		1	168.149	odd	6
1575.4.a.b.1.1		1	35.9	even	6
2352.4.a.r.1.1		1	84.47	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +(-27.0000 - 46.7654i) q^{10} +(-18.0000 - 31.1769i) q^{11} -34.0000 q^{13} +(35.5000 - 61.4878i) q^{16} +(21.0000 + 36.3731i) q^{17} +(62.0000 - 107.387i) q^{19} +18.0000 q^{20} +108.000 q^{22} +(-99.5000 - 172.339i) q^{25} +(51.0000 - 88.3346i) q^{26} -102.000 q^{29} +(80.0000 + 138.564i) q^{31} +(22.5000 + 38.9711i) q^{32} -126.000 q^{34} +(-199.000 + 344.678i) q^{37} +(186.000 + 322.161i) q^{38} +(189.000 - 327.358i) q^{40} +318.000 q^{41} -268.000 q^{43} +(-18.0000 + 31.1769i) q^{44} +(120.000 - 207.846i) q^{47} +597.000 q^{50} +(17.0000 + 29.4449i) q^{52} +(-249.000 - 431.281i) q^{53} +648.000 q^{55} +(153.000 - 265.004i) q^{58} +(-66.0000 - 114.315i) q^{59} +(-199.000 + 344.678i) q^{61} -480.000 q^{62} +433.000 q^{64} +(306.000 - 530.008i) q^{65} +(-46.0000 - 79.6743i) q^{67} +(21.0000 - 36.3731i) q^{68} +720.000 q^{71} +(251.000 + 434.745i) q^{73} +(-597.000 - 1034.03i) q^{74} -124.000 q^{76} +(512.000 - 886.810i) q^{79} +(639.000 + 1106.78i) q^{80} +(-477.000 + 826.188i) q^{82} +204.000 q^{83} -756.000 q^{85} +(402.000 - 696.284i) q^{86} +(378.000 + 654.715i) q^{88} +(177.000 - 306.573i) q^{89} +(360.000 + 623.538i) q^{94} +(1116.00 + 1932.97i) q^{95} -286.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - q^{4} - 18 q^{5} - 42 q^{8} - 54 q^{10} - 36 q^{11} - 68 q^{13} + 71 q^{16} + 42 q^{17} + 124 q^{19} + 36 q^{20} + 216 q^{22} - 199 q^{25} + 102 q^{26} - 204 q^{29} + 160 q^{31} + 45 q^{32}+ \cdots - 572 q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 - q^4 - 18 * q^5 - 42 * q^8 - 54 * q^10 - 36 * q^11 - 68 * q^13 + 71 * q^16 + 42 * q^17 + 124 * q^19 + 36 * q^20 + 216 * q^22 - 199 * q^25 + 102 * q^26 - 204 * q^29 + 160 * q^31 + 45 * q^32 - 252 * q^34 - 398 * q^37 + 372 * q^38 + 378 * q^40 + 636 * q^41 - 536 * q^43 - 36 * q^44 + 240 * q^47 + 1194 * q^50 + 34 * q^52 - 498 * q^53 + 1296 * q^55 + 306 * q^58 - 132 * q^59 - 398 * q^61 - 960 * q^62 + 866 * q^64 + 612 * q^65 - 92 * q^67 + 42 * q^68 + 1440 * q^71 + 502 * q^73 - 1194 * q^74 - 248 * q^76 + 1024 * q^79 + 1278 * q^80 - 954 * q^82 + 408 * q^83 - 1512 * q^85 + 804 * q^86 + 756 * q^88 + 354 * q^89 + 720 * q^94 + 2232 * q^95 - 572 * q^97

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