LMFDB - Embedded newform 225.4.f.c.143.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(107,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.107"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 $ x^12 - 16x^10 - 14x^8 - 512x^6 + 3889x^4 + 126224*x^2 + 506944
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.2
Root			$-0.347140 + 2.27426i$ of defining polynomial
Character	$\chi$	$=$	225.143
Dual form			225.4.f.c.107.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.62140 - 2.62140i) q^{2} +5.74350i q^{4} +(10.8652 - 10.8652i) q^{7} +(-5.91519 + 5.91519i) q^{8} -37.8905i q^{11} +(48.1085 + 48.1085i) q^{13} -56.9640 q^{14} +76.9602 q^{16} +(-60.3458 - 60.3458i) q^{17} -109.678i q^{19} +(-99.3262 + 99.3262i) q^{22} +(39.7660 - 39.7660i) q^{23} -252.224i q^{26} +(62.4042 + 62.4042i) q^{28} -90.3553 q^{29} -233.678 q^{31} +(-154.422 - 154.422i) q^{32} +316.381i q^{34} +(19.0042 - 19.0042i) q^{37} +(-287.509 + 287.509i) q^{38} +260.783i q^{41} +(-176.216 - 176.216i) q^{43} +217.624 q^{44} -208.485 q^{46} +(-145.788 - 145.788i) q^{47} +106.896i q^{49} +(-276.311 + 276.311i) q^{52} +(-183.285 + 183.285i) q^{53} +128.539i q^{56} +(236.858 + 236.858i) q^{58} -279.564 q^{59} -390.267 q^{61} +(612.563 + 612.563i) q^{62} +193.924i q^{64} +(-150.444 + 150.444i) q^{67} +(346.596 - 346.596i) q^{68} -470.042i q^{71} +(-480.765 - 480.765i) q^{73} -99.6355 q^{74} +629.934 q^{76} +(-411.687 - 411.687i) q^{77} -1322.44i q^{79} +(683.618 - 683.618i) q^{82} +(456.192 - 456.192i) q^{83} +923.868i q^{86} +(224.129 + 224.129i) q^{88} +1364.85 q^{89} +1045.41 q^{91} +(228.396 + 228.396i) q^{92} +764.340i q^{94} +(785.308 - 785.308i) q^{97} +(280.218 - 280.218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82}+ \cdots - 2772 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.62140	−	2.62140i	−0.926806	−	0.926806i	0.0706924	−	0.997498i	$-0.477479\pi$
$2$	−2.62140	−	2.62140i	−0.926806	−	0.926806i	−0.997498	+	0.0706924i	$0.977479\pi$
$3$		0			0
$3$		0			0
$4$			5.74350i			0.717938i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	10.8652	−	10.8652i	0.586664	−	0.586664i	−0.350062	−	0.936726i	$-0.613840\pi$
$7$	10.8652	−	10.8652i	0.586664	−	0.586664i	0.936726	+	0.350062i	$0.113840\pi$
$8$	−5.91519	+	5.91519i	−0.261417	+	0.261417i
$9$		0			0
$10$		0			0
$11$		−	37.8905i		−	1.03858i	−0.854597	−	0.519291i	$-0.826196\pi$
$11$		−	37.8905i		−	1.03858i	0.854597	−	0.519291i	$-0.173804\pi$
$12$		0			0
$13$	48.1085	+	48.1085i	1.02638	+	1.02638i	0.999643	+	0.0267344i	$0.00851083\pi$
$13$	48.1085	+	48.1085i	1.02638	+	1.02638i	0.0267344	+	0.999643i	$0.491489\pi$
$14$	−56.9640			−1.08745
$15$		0			0
$16$	76.9602			1.20250
$17$	−60.3458	−	60.3458i	−0.860942	−	0.860942i	0.130506	−	0.991448i	$-0.458340\pi$
$17$	−60.3458	−	60.3458i	−0.860942	−	0.860942i	−0.991448	+	0.130506i	$0.958340\pi$
$18$		0			0
$19$		−	109.678i		−	1.32430i	−0.749369	−	0.662152i	$-0.769643\pi$
$19$		−	109.678i		−	1.32430i	0.749369	−	0.662152i	$-0.230357\pi$
$20$		0			0
$21$		0			0
$22$	−99.3262	+	99.3262i	−0.962564	+	0.962564i
$23$	39.7660	−	39.7660i	0.360512	−	0.360512i	−0.503489	−	0.864002i	$-0.667951\pi$
$23$	39.7660	−	39.7660i	0.360512	−	0.360512i	0.864002	+	0.503489i	$0.167951\pi$
$24$		0			0
$25$		0			0
$26$		−	252.224i		−	1.90250i
$27$		0			0
$28$	62.4042	+	62.4042i	0.421188	+	0.421188i
$29$	−90.3553			−0.578571			−0.289285	−	0.957243i	$-0.593418\pi$
$29$	−90.3553			−0.578571			−0.289285	+	0.957243i	$0.593418\pi$
$30$		0			0
$31$	−233.678			−1.35386			−0.676932	−	0.736046i	$-0.736691\pi$
$31$	−233.678			−1.35386			−0.676932	+	0.736046i	$0.736691\pi$
$32$	−154.422	−	154.422i	−0.853070	−	0.853070i
$33$		0			0
$34$			316.381i			1.59585i
$35$		0			0
$36$		0			0
$37$	19.0042	−	19.0042i	0.0844399	−	0.0844399i	−0.663625	−	0.748065i	$-0.730983\pi$
$37$	19.0042	−	19.0042i	0.0844399	−	0.0844399i	0.748065	+	0.663625i	$0.230983\pi$
$38$	−287.509	+	287.509i	−1.22737	+	1.22737i
$39$		0			0
$40$		0			0
$41$			260.783i			0.993354i	0.867935	+	0.496677i	$0.165447\pi$
$41$			260.783i			0.993354i	−0.867935	+	0.496677i	$0.834553\pi$
$42$		0			0
$43$	−176.216	−	176.216i	−0.624948	−	0.624948i	0.321845	−	0.946792i	$-0.395697\pi$
$43$	−176.216	−	176.216i	−0.624948	−	0.624948i	−0.946792	+	0.321845i	$0.895697\pi$
$44$	217.624			0.745638
$45$		0			0
$46$	−208.485			−0.668250
$47$	−145.788	−	145.788i	−0.452456	−	0.452456i	0.443713	−	0.896169i	$-0.353661\pi$
$47$	−145.788	−	145.788i	−0.452456	−	0.452456i	−0.896169	+	0.443713i	$0.853661\pi$
$48$		0			0
$49$			106.896i			0.311650i
$50$		0			0
$51$		0			0
$52$	−276.311	+	276.311i	−0.736875	+	0.736875i
$53$	−183.285	+	183.285i	−0.475022	+	0.475022i	−0.903535	−	0.428513i	$-0.859038\pi$
$53$	−183.285	+	183.285i	−0.475022	+	0.475022i	0.428513	+	0.903535i	$0.359038\pi$
$54$		0			0
$55$		0			0
$56$			128.539i			0.306728i
$57$		0			0
$58$	236.858	+	236.858i	0.536223	+	0.536223i
$59$	−279.564			−0.616883			−0.308441	−	0.951243i	$-0.599807\pi$
$59$	−279.564			−0.616883			−0.308441	+	0.951243i	$0.599807\pi$
$60$		0			0
$61$	−390.267			−0.819157			−0.409578	−	0.912275i	$-0.634324\pi$
$61$	−390.267			−0.819157			−0.409578	+	0.912275i	$0.634324\pi$
$62$	612.563	+	612.563i	1.25477	+	1.25477i
$63$		0			0
$64$			193.924i			0.378757i
$65$		0			0
$66$		0			0
$67$	−150.444	+	150.444i	−0.274324	+	0.274324i	−0.830838	−	0.556514i	$-0.812139\pi$
$67$	−150.444	+	150.444i	−0.274324	+	0.274324i	0.556514	+	0.830838i	$0.312139\pi$
$68$	346.596	−	346.596i	0.618103	−	0.618103i
$69$		0			0
$70$		0			0
$71$		−	470.042i		−	0.785686i	−0.919605	−	0.392843i	$-0.871492\pi$
$71$		−	470.042i		−	0.785686i	0.919605	−	0.392843i	$-0.128508\pi$
$72$		0			0
$73$	−480.765	−	480.765i	−0.770812	−	0.770812i	0.207436	−	0.978249i	$-0.433488\pi$
$73$	−480.765	−	480.765i	−0.770812	−	0.770812i	−0.978249	+	0.207436i	$0.933488\pi$
$74$	−99.6355			−0.156519
$75$		0			0
$76$	629.934			0.950769
$77$	−411.687	−	411.687i	−0.609299	−	0.609299i
$78$		0			0
$79$		−	1322.44i		−	1.88337i	−0.336497	−	0.941685i	$-0.609242\pi$
$79$		−	1322.44i		−	1.88337i	0.336497	−	0.941685i	$-0.390758\pi$
$80$		0			0
$81$		0			0
$82$	683.618	−	683.618i	0.920646	−	0.920646i
$83$	456.192	−	456.192i	0.603296	−	0.603296i	−0.337890	−	0.941186i	$-0.609713\pi$
$83$	456.192	−	456.192i	0.603296	−	0.603296i	0.941186	+	0.337890i	$0.109713\pi$
$84$		0			0
$85$		0			0
$86$			923.868i			1.15841i
$87$		0			0
$88$	224.129	+	224.129i	0.271503	+	0.271503i
$89$	1364.85			1.62555			0.812774	−	0.582580i	$-0.197957\pi$
$89$	1364.85			1.62555			0.812774	+	0.582580i	$0.197957\pi$
$90$		0			0
$91$	1045.41			1.20428
$92$	228.396	+	228.396i	0.258825	+	0.258825i
$93$		0			0
$94$			764.340i			0.838677i
$95$		0			0
$96$		0			0
$97$	785.308	−	785.308i	0.822020	−	0.822020i	−0.164377	−	0.986398i	$-0.552561\pi$
$97$	785.308	−	785.308i	0.822020	−	0.822020i	0.986398	+	0.164377i	$0.0525614\pi$
$98$	280.218	−	280.218i	0.288839	−	0.288839i
$99$		0			0
$100$		0			0
$101$		−	111.555i		−	0.109902i	−0.998489	−	0.0549510i	$-0.982500\pi$
$101$		−	111.555i		−	0.109902i	0.998489	−	0.0549510i	$-0.0175003\pi$
$102$		0			0
$103$	−13.8820	−	13.8820i	−0.0132800	−	0.0132800i	0.700436	−	0.713716i	$-0.252989\pi$
$103$	−13.8820	−	13.8820i	−0.0132800	−	0.0132800i	−0.713716	+	0.700436i	$0.752989\pi$
$104$	−569.142			−0.536624
$105$		0			0
$106$	960.929			0.880507
$107$	776.165	+	776.165i	0.701259	+	0.701259i	0.964681	−	0.263422i	$-0.0848510\pi$
$107$	776.165	+	776.165i	0.701259	+	0.701259i	−0.263422	+	0.964681i	$0.584851\pi$
$108$		0			0
$109$		−	410.579i		−	0.360792i	−0.983594	−	0.180396i	$-0.942262\pi$
$109$		−	410.579i		−	0.360792i	0.983594	−	0.180396i	$-0.0577379\pi$
$110$		0			0
$111$		0			0
$112$	836.186	−	836.186i	0.705465	−	0.705465i
$113$	521.328	−	521.328i	0.434004	−	0.434004i	−0.455984	−	0.889988i	$-0.650713\pi$
$113$	521.328	−	521.328i	0.434004	−	0.434004i	0.889988	+	0.455984i	$0.150713\pi$
$114$		0			0
$115$		0			0
$116$		−	518.956i		−	0.415378i
$117$		0			0
$118$	732.849	+	732.849i	0.571730	+	0.571730i
$119$	−1311.34			−1.01017
$120$		0			0
$121$	−104.688			−0.0786538
$122$	1023.05	+	1023.05i	0.759199	+	0.759199i
$123$		0			0
$124$		−	1342.13i		−	0.971990i
$125$		0			0
$126$		0			0
$127$	−786.555	+	786.555i	−0.549571	+	0.549571i	−0.926317	−	0.376746i	$-0.877043\pi$
$127$	−786.555	+	786.555i	−0.549571	+	0.549571i	0.376746	+	0.926317i	$0.377043\pi$
$128$	−727.025	+	727.025i	−0.502036	+	0.502036i
$129$		0			0
$130$		0			0
$131$			448.364i			0.299036i	0.988759	+	0.149518i	$0.0477722\pi$
$131$			448.364i			0.299036i	−0.988759	+	0.149518i	$0.952228\pi$
$132$		0			0
$133$	−1191.67	−	1191.67i	−0.776922	−	0.776922i
$134$	788.751			0.508490
$135$		0			0
$136$	713.914			0.450129
$137$	−950.120	−	950.120i	−0.592512	−	0.592512i	0.345797	−	0.938309i	$-0.387609\pi$
$137$	−950.120	−	950.120i	−0.592512	−	0.592512i	−0.938309	+	0.345797i	$0.887609\pi$
$138$		0			0
$139$		−	112.735i		−	0.0687918i	−0.999408	−	0.0343959i	$-0.989049\pi$
$139$		−	112.735i		−	0.0687918i	0.999408	−	0.0343959i	$-0.0109507\pi$
$140$		0			0
$141$		0			0
$142$	−1232.17	+	1232.17i	−0.728179	+	0.728179i
$143$	1822.85	−	1822.85i	1.06598	−	1.06598i
$144$		0			0
$145$		0			0
$146$			2520.56i			1.42879i
$147$		0			0
$148$	109.151	+	109.151i	0.0606226	+	0.0606226i
$149$	1492.95			0.820852			0.410426	−	0.911894i	$-0.365380\pi$
$149$	1492.95			0.820852			0.410426	+	0.911894i	$0.365380\pi$
$150$		0			0
$151$	−2939.54			−1.58422			−0.792108	−	0.610381i	$-0.791016\pi$
$151$	−2939.54			−1.58422			−0.792108	+	0.610381i	$0.791016\pi$
$152$	648.764	+	648.764i	0.346196	+	0.346196i
$153$		0			0
$154$			2158.39i			1.12940i
$155$		0			0
$156$		0			0
$157$	−156.386	+	156.386i	−0.0794967	+	0.0794967i	−0.745737	−	0.666240i	$-0.767902\pi$
$157$	−156.386	+	156.386i	−0.0794967	+	0.0794967i	0.666240	+	0.745737i	$0.267902\pi$
$158$	−3466.65	+	3466.65i	−1.74552	+	1.74552i
$159$		0			0
$160$		0			0
$161$		−	864.129i		−	0.422999i
$162$		0			0
$163$	239.292	+	239.292i	0.114986	+	0.114986i	0.762259	−	0.647272i	$-0.224090\pi$
$163$	239.292	+	239.292i	0.114986	+	0.114986i	−0.647272	+	0.762259i	$0.724090\pi$
$164$	−1497.81			−0.713167
$165$		0			0
$166$	−2391.72			−1.11828
$167$	−677.159	−	677.159i	−0.313773	−	0.313773i	0.532596	−	0.846369i	$-0.321216\pi$
$167$	−677.159	−	677.159i	−0.313773	−	0.313773i	−0.846369	+	0.532596i	$0.821216\pi$
$168$		0			0
$169$			2431.86i			1.10690i
$170$		0			0
$171$		0			0
$172$	1012.10	−	1012.10i	0.448674	−	0.448674i
$173$	−441.523	+	441.523i	−0.194037	+	0.194037i	−0.797438	−	0.603401i	$-0.793812\pi$
$173$	−441.523	+	441.523i	−0.194037	+	0.194037i	0.603401	+	0.797438i	$0.293812\pi$
$174$		0			0
$175$		0			0
$176$		−	2916.06i		−	1.24890i
$177$		0			0
$178$	−3577.82	−	3577.82i	−1.50657	−	1.50657i
$179$	4724.27			1.97267			0.986337	−	0.164737i	$-0.0526776\pi$
$179$	4724.27			1.97267			0.986337	+	0.164737i	$0.0526776\pi$
$180$		0			0
$181$	−1548.35			−0.635847			−0.317923	−	0.948116i	$-0.602985\pi$
$181$	−1548.35			−0.635847			−0.317923	+	0.948116i	$0.602985\pi$
$182$	−2740.45	−	2740.45i	−1.11613	−	1.11613i
$183$		0			0
$184$			470.447i			0.188488i
$185$		0			0
$186$		0			0
$187$	−2286.53	+	2286.53i	−0.894159	+	0.894159i
$188$	837.336	−	837.336i	0.324835	−	0.324835i
$189$		0			0
$190$		0			0
$191$			1090.71i			0.413200i	0.978426	+	0.206600i	$0.0662398\pi$
$191$			1090.71i			0.413200i	−0.978426	+	0.206600i	$0.933760\pi$
$192$		0			0
$193$	2825.69	+	2825.69i	1.05387	+	1.05387i	0.998464	+	0.0554112i	$0.0176470\pi$
$193$	2825.69	+	2825.69i	1.05387	+	1.05387i	0.0554112	+	0.998464i	$0.482353\pi$
$194$	−4117.22			−1.52371
$195$		0			0
$196$	−613.958			−0.223746
$197$	−1163.99	−	1163.99i	−0.420969	−	0.420969i	0.464569	−	0.885537i	$-0.346209\pi$
$197$	−1163.99	−	1163.99i	−0.420969	−	0.420969i	−0.885537	+	0.464569i	$0.846209\pi$
$198$		0			0
$199$			520.257i			0.185327i	0.995697	+	0.0926633i	$0.0295380\pi$
$199$			520.257i			0.185327i	−0.995697	+	0.0926633i	$0.970462\pi$
$200$		0			0
$201$		0			0
$202$	−292.430	+	292.430i	−0.101858	+	0.101858i
$203$	−981.726	+	981.726i	−0.339427	+	0.339427i
$204$		0			0
$205$		0			0
$206$			72.7808i			0.0246159i
$207$		0			0
$208$	3702.44	+	3702.44i	1.23422	+	1.23422i
$209$	−4155.74			−1.37540
$210$		0			0
$211$	5524.38			1.80244			0.901219	−	0.433365i	$-0.142674\pi$
$211$	5524.38			1.80244			0.901219	+	0.433365i	$0.142674\pi$
$212$	−1052.70	−	1052.70i	−0.341036	−	0.341036i
$213$		0			0
$214$		−	4069.28i		−	1.29986i
$215$		0			0
$216$		0			0
$217$	−2538.95	+	2538.95i	−0.794263	+	0.794263i
$218$	−1076.29	+	1076.29i	−0.334384	+	0.334384i
$219$		0			0
$220$		0			0
$221$		−	5806.30i		−	1.76730i
$222$		0			0
$223$	−323.198	−	323.198i	−0.0970537	−	0.0970537i	0.656913	−	0.753967i	$-0.271862\pi$
$223$	−323.198	−	323.198i	−0.0970537	−	0.0970537i	−0.753967	+	0.656913i	$0.771862\pi$
$224$	−3355.65			−1.00093
$225$		0			0
$226$	−2733.22			−0.804474
$227$	2739.76	+	2739.76i	0.801077	+	0.801077i	0.983264	−	0.182187i	$-0.0583177\pi$
$227$	2739.76	+	2739.76i	0.801077	+	0.801077i	−0.182187	+	0.983264i	$0.558318\pi$
$228$		0			0
$229$		−	230.334i		−	0.0664667i	−0.999448	−	0.0332333i	$-0.989420\pi$
$229$		−	230.334i		−	0.0664667i	0.999448	−	0.0332333i	$-0.0105804\pi$
$230$		0			0
$231$		0			0
$232$	534.468	−	534.468i	0.151248	−	0.151248i
$233$	350.156	−	350.156i	0.0984526	−	0.0984526i	−0.656165	−	0.754618i	$-0.727822\pi$
$233$	350.156	−	350.156i	0.0984526	−	0.0984526i	0.754618	+	0.656165i	$0.227822\pi$
$234$		0			0
$235$		0			0
$236$		−	1605.67i		−	0.442883i
$237$		0			0
$238$	3437.54	+	3437.54i	0.936229	+	0.936229i
$239$	1013.20			0.274218			0.137109	−	0.990556i	$-0.456219\pi$
$239$	1013.20			0.274218			0.137109	+	0.990556i	$0.456219\pi$
$240$		0			0
$241$	2584.30			0.690744			0.345372	−	0.938466i	$-0.387753\pi$
$241$	2584.30			0.690744			0.345372	+	0.938466i	$0.387753\pi$
$242$	274.430	+	274.430i	0.0728968	+	0.0728968i
$243$		0			0
$244$		−	2241.50i		−	0.588104i
$245$		0			0
$246$		0			0
$247$	5276.43	−	5276.43i	1.35924	−	1.35924i
$248$	1382.25	−	1382.25i	0.353923	−	0.353923i
$249$		0			0
$250$		0			0
$251$		−	1708.34i		−	0.429599i	−0.976658	−	0.214800i	$-0.931090\pi$
$251$		−	1708.34i		−	0.429599i	0.976658	−	0.214800i	$-0.0689099\pi$
$252$		0			0
$253$	−1506.75	−	1506.75i	−0.374422	−	0.374422i
$254$	4123.76			1.01869
$255$		0			0
$256$	5363.04			1.30934
$257$	−2659.48	−	2659.48i	−0.645500	−	0.645500i	0.306402	−	0.951902i	$-0.400875\pi$
$257$	−2659.48	−	2659.48i	−0.645500	−	0.645500i	−0.951902	+	0.306402i	$0.900875\pi$
$258$		0			0
$259$		−	412.969i		−	0.0990757i
$260$		0			0
$261$		0			0
$262$	1175.34	−	1175.34i	0.277148	−	0.277148i
$263$	2307.03	−	2307.03i	0.540903	−	0.540903i	−0.382891	−	0.923794i	$-0.625071\pi$
$263$	2307.03	−	2307.03i	0.540903	−	0.540903i	0.923794	+	0.382891i	$0.125071\pi$
$264$		0			0
$265$		0			0
$266$			6247.68i			1.44011i
$267$		0			0
$268$	−864.078	−	864.078i	−0.196948	−	0.196948i
$269$	−447.584			−0.101449			−0.0507243	−	0.998713i	$-0.516153\pi$
$269$	−447.584			−0.101449			−0.0507243	+	0.998713i	$0.516153\pi$
$270$		0			0
$271$	1573.15			0.352627			0.176314	−	0.984334i	$-0.443583\pi$
$271$	1573.15			0.352627			0.176314	+	0.984334i	$0.443583\pi$
$272$	−4644.23	−	4644.23i	−1.03529	−	1.03529i
$273$		0			0
$274$			4981.29i			1.09829i
$275$		0			0
$276$		0			0
$277$	−5816.91	+	5816.91i	−1.26175	+	1.26175i	−0.311504	+	0.950245i	$0.600833\pi$
$277$	−5816.91	+	5816.91i	−1.26175	+	1.26175i	−0.950245	+	0.311504i	$0.899167\pi$
$278$	−295.524	+	295.524i	−0.0637566	+	0.0637566i
$279$		0			0
$280$		0			0
$281$			140.032i			0.0297281i	0.999890	+	0.0148640i	$0.00473155\pi$
$281$			140.032i			0.0297281i	−0.999890	+	0.0148640i	$0.995268\pi$
$282$		0			0
$283$	−4431.85	−	4431.85i	−0.930905	−	0.930905i	0.0668572	−	0.997763i	$-0.478703\pi$
$283$	−4431.85	−	4431.85i	−0.930905	−	0.930905i	−0.997763	+	0.0668572i	$0.978703\pi$
$284$	2699.69			0.564074
$285$		0			0
$286$	−9556.87			−1.97591
$287$	2833.46	+	2833.46i	0.582765	+	0.582765i
$288$		0			0
$289$			2370.24i			0.482442i
$290$		0			0
$291$		0			0
$292$	2761.28	−	2761.28i	0.553395	−	0.553395i
$293$	1244.45	−	1244.45i	0.248127	−	0.248127i	−0.572074	−	0.820202i	$-0.693861\pi$
$293$	1244.45	−	1244.45i	0.248127	−	0.248127i	0.820202	+	0.572074i	$0.193861\pi$
$294$		0			0
$295$		0			0
$296$			224.827i			0.0441480i
$297$		0			0
$298$	−3913.61	−	3913.61i	−0.760771	−	0.760771i
$299$	3826.17			0.740043
$300$		0			0
$301$	−3829.24			−0.733269
$302$	7705.73	+	7705.73i	1.46826	+	1.46826i
$303$		0			0
$304$		−	8440.82i		−	1.59248i
$305$		0			0
$306$		0			0
$307$	7327.60	−	7327.60i	1.36224	−	1.36224i	0.491189	−	0.871053i	$-0.336563\pi$
$307$	7327.60	−	7327.60i	1.36224	−	1.36224i	0.871053	−	0.491189i	$-0.163437\pi$
$308$	2364.52	−	2364.52i	0.437439	−	0.437439i
$309$		0			0
$310$		0			0
$311$			7489.38i			1.36554i	0.730632	+	0.682771i	$0.239225\pi$
$311$			7489.38i			1.36554i	−0.730632	+	0.682771i	$0.760775\pi$
$312$		0			0
$313$	2456.04	+	2456.04i	0.443525	+	0.443525i	0.893195	−	0.449670i	$-0.148458\pi$
$313$	2456.04	+	2456.04i	0.443525	+	0.443525i	−0.449670	+	0.893195i	$0.648458\pi$
$314$	819.903			0.147356
$315$		0			0
$316$	7595.44			1.35214
$317$	6724.30	+	6724.30i	1.19140	+	1.19140i	0.976674	+	0.214728i	$0.0688866\pi$
$317$	6724.30	+	6724.30i	1.19140	+	1.19140i	0.214728	+	0.976674i	$0.431113\pi$
$318$		0			0
$319$			3423.60i			0.600894i
$320$		0			0
$321$		0			0
$322$	−2265.23	+	2265.23i	−0.392038	+	0.392038i
$323$	−6618.59	+	6618.59i	−1.14015	+	1.14015i
$324$		0			0
$325$		0			0
$326$		−	1254.56i		−	0.213140i
$327$		0			0
$328$	−1542.58	−	1542.58i	−0.259679	−	0.259679i
$329$	−3168.03			−0.530879
$330$		0			0
$331$	−199.080			−0.0330586			−0.0165293	−	0.999863i	$-0.505262\pi$
$331$	−199.080			−0.0330586			−0.0165293	+	0.999863i	$0.505262\pi$
$332$	2620.14	+	2620.14i	0.433129	+	0.433129i
$333$		0			0
$334$			3550.21i			0.581614i
$335$		0			0
$336$		0			0
$337$	−3308.77	+	3308.77i	−0.534838	+	0.534838i	−0.922008	−	0.387170i	$-0.873453\pi$
$337$	−3308.77	+	3308.77i	−0.534838	+	0.534838i	0.387170	+	0.922008i	$0.373453\pi$
$338$	6374.88	−	6374.88i	1.02588	−	1.02588i
$339$		0			0
$340$		0			0
$341$			8854.16i			1.40610i
$342$		0			0
$343$	4888.20	+	4888.20i	0.769498	+	0.769498i
$344$	2084.71			0.326744
$345$		0			0
$346$	2314.82			0.359669
$347$	−2371.68	−	2371.68i	−0.366912	−	0.366912i	0.499438	−	0.866350i	$-0.333540\pi$
$347$	−2371.68	−	2371.68i	−0.366912	−	0.366912i	−0.866350	+	0.499438i	$0.833540\pi$
$348$		0			0
$349$		−	8208.92i		−	1.25906i	−0.776975	−	0.629532i	$-0.783247\pi$
$349$		−	8208.92i		−	1.25906i	0.776975	−	0.629532i	$-0.216753\pi$
$350$		0			0
$351$		0			0
$352$	−5851.13	+	5851.13i	−0.885984	+	0.885984i
$353$	−6800.98	+	6800.98i	−1.02544	+	1.02544i	−0.0257707	+	0.999668i	$0.508204\pi$
$353$	−6800.98	+	6800.98i	−1.02544	+	1.02544i	−0.999668	+	0.0257707i	$0.991796\pi$
$354$		0			0
$355$		0			0
$356$			7839.01i			1.16704i
$357$		0			0
$358$	−12384.2	−	12384.2i	−1.82829	−	1.82829i
$359$	−1778.14			−0.261411			−0.130705	−	0.991421i	$-0.541724\pi$
$359$	−1778.14			−0.261411			−0.130705	+	0.991421i	$0.541724\pi$
$360$		0			0
$361$	−5170.20			−0.753783
$362$	4058.86	+	4058.86i	0.589306	+	0.589306i
$363$		0			0
$364$			6004.34i			0.864596i
$365$		0			0
$366$		0			0
$367$	4673.56	−	4673.56i	0.664735	−	0.664735i	−0.291757	−	0.956492i	$-0.594240\pi$
$367$	4673.56	−	4673.56i	0.664735	−	0.664735i	0.956492	+	0.291757i	$0.0942400\pi$
$368$	3060.40	−	3060.40i	0.433517	−	0.433517i
$369$		0			0
$370$		0			0
$371$			3982.85i			0.557357i
$372$		0			0
$373$	5729.37	+	5729.37i	0.795323	+	0.795323i	0.982354	−	0.187031i	$-0.0598865\pi$
$373$	5729.37	+	5729.37i	0.795323	+	0.795323i	−0.187031	+	0.982354i	$0.559886\pi$
$374$	11987.8			1.65742
$375$		0			0
$376$	1724.73			0.236559
$377$	−4346.86	−	4346.86i	−0.593832	−	0.593832i
$378$		0			0
$379$		−	153.883i		−	0.0208561i	−0.999946	−	0.0104280i	$-0.996681\pi$
$379$		−	153.883i		−	0.0208561i	0.999946	−	0.0104280i	$-0.00331941\pi$
$380$		0			0
$381$		0			0
$382$	2859.19	−	2859.19i	0.382956	−	0.382956i
$383$	4297.76	−	4297.76i	0.573382	−	0.573382i	−0.359690	−	0.933072i	$-0.617118\pi$
$383$	4297.76	−	4297.76i	0.573382	−	0.573382i	0.933072	+	0.359690i	$0.117118\pi$
$384$		0			0
$385$		0			0
$386$		−	14814.6i		−	1.95347i
$387$		0			0
$388$	4510.42	+	4510.42i	0.590160	+	0.590160i
$389$	−7833.00			−1.02095			−0.510474	−	0.859893i	$-0.670530\pi$
$389$	−7833.00			−1.02095			−0.510474	+	0.859893i	$0.670530\pi$
$390$		0			0
$391$	−4799.42			−0.620760
$392$	−632.310	−	632.310i	−0.0814706	−	0.0814706i
$393$		0			0
$394$			6102.57i			0.780312i
$395$		0			0
$396$		0			0
$397$	10195.4	−	10195.4i	1.28889	−	1.28889i	0.353435	−	0.935459i	$-0.385013\pi$
$397$	10195.4	−	10195.4i	1.28889	−	1.28889i	0.935459	−	0.353435i	$-0.114987\pi$
$398$	1363.80	−	1363.80i	0.171762	−	0.171762i
$399$		0			0
$400$		0			0
$401$		−	10778.3i		−	1.34226i	−0.741341	−	0.671128i	$-0.765810\pi$
$401$		−	10778.3i		−	1.34226i	0.741341	−	0.671128i	$-0.234190\pi$
$402$		0			0
$403$	−11241.9	−	11241.9i	−1.38957	−	1.38957i
$404$	640.714			0.0789028
$405$		0			0
$406$	5147.00			0.629165
$407$	−720.079	−	720.079i	−0.0876978	−	0.0876978i
$408$		0			0
$409$		−	4629.92i		−	0.559743i	−0.960037	−	0.279872i	$-0.909708\pi$
$409$		−	4629.92i		−	0.559743i	0.960037	−	0.279872i	$-0.0902919\pi$
$410$		0			0
$411$		0			0
$412$	79.7315	−	79.7315i	0.00953420	−	0.00953420i
$413$	−3037.51	+	3037.51i	−0.361903	+	0.361903i
$414$		0			0
$415$		0			0
$416$		−	14858.0i		−	1.75114i
$417$		0			0
$418$	10893.9	+	10893.9i	1.27473	+	1.27473i
$419$	−11276.5			−1.31478			−0.657389	−	0.753551i	$-0.728339\pi$
$419$	−11276.5			−1.31478			−0.657389	+	0.753551i	$0.728339\pi$
$420$		0			0
$421$	3387.58			0.392163			0.196082	−	0.980588i	$-0.437178\pi$
$421$	3387.58			0.392163			0.196082	+	0.980588i	$0.437178\pi$
$422$	−14481.6	−	14481.6i	−1.67051	−	1.67051i
$423$		0			0
$424$		−	2168.33i		−	0.248358i
$425$		0			0
$426$		0			0
$427$	−4240.32	+	4240.32i	−0.480570	+	0.480570i
$428$	−4457.91	+	4457.91i	−0.503461	+	0.503461i
$429$		0			0
$430$		0			0
$431$			16161.7i			1.80623i	0.429402	+	0.903113i	$0.358724\pi$
$431$			16161.7i			1.80623i	−0.429402	+	0.903113i	$0.641276\pi$
$432$		0			0
$433$	3808.79	+	3808.79i	0.422722	+	0.422722i	0.886140	−	0.463418i	$-0.153377\pi$
$433$	3808.79	+	3808.79i	0.422722	+	0.422722i	−0.463418	+	0.886140i	$0.653377\pi$
$434$	13311.2			1.47226
$435$		0			0
$436$	2358.16			0.259026
$437$	−4361.44	−	4361.44i	−0.477428	−	0.477428i
$438$		0			0
$439$		−	1607.30i		−	0.174744i	−0.996176	−	0.0873718i	$-0.972153\pi$
$439$		−	1607.30i		−	0.174744i	0.996176	−	0.0873718i	$-0.0278468\pi$
$440$		0			0
$441$		0			0
$442$	−15220.6	+	15220.6i	−1.63795	+	1.63795i
$443$	8296.60	−	8296.60i	0.889805	−	0.889805i	−0.104699	−	0.994504i	$-0.533388\pi$
$443$	8296.60	−	8296.60i	0.889805	−	0.889805i	0.994504	+	0.104699i	$0.0333880\pi$
$444$		0			0
$445$		0			0
$446$			1694.47i			0.179900i
$447$		0			0
$448$	2107.02	+	2107.02i	0.222203	+	0.222203i
$449$	−15061.8			−1.58309			−0.791547	−	0.611108i	$-0.790724\pi$
$449$	−15061.8			−1.58309			−0.791547	+	0.611108i	$0.790724\pi$
$450$		0			0
$451$	9881.20			1.03168
$452$	2994.25	+	2994.25i	0.311588	+	0.311588i
$453$		0			0
$454$		−	14364.0i		−	1.48489i
$455$		0			0
$456$		0			0
$457$	−2671.27	+	2671.27i	−0.273428	+	0.273428i	−0.830479	−	0.557050i	$-0.811933\pi$
$457$	−2671.27	+	2671.27i	−0.273428	+	0.273428i	0.557050	+	0.830479i	$0.311933\pi$
$458$	−603.797	+	603.797i	−0.0616017	+	0.0616017i
$459$		0			0
$460$		0			0
$461$		−	12809.1i		−	1.29410i	−0.762449	−	0.647049i	$-0.776003\pi$
$461$		−	12809.1i		−	1.29410i	0.762449	−	0.647049i	$-0.223997\pi$
$462$		0			0
$463$	11154.1	+	11154.1i	1.11960	+	1.11960i	0.991799	+	0.127804i	$0.0407927\pi$
$463$	11154.1	+	11154.1i	1.11960	+	1.11960i	0.127804	+	0.991799i	$0.459207\pi$
$464$	−6953.76			−0.695733
$465$		0			0
$466$	−1835.80			−0.182493
$467$	7905.44	+	7905.44i	0.783341	+	0.783341i	0.980393	−	0.197052i	$-0.0631368\pi$
$467$	7905.44	+	7905.44i	0.783341	+	0.783341i	−0.197052	+	0.980393i	$0.563137\pi$
$468$		0			0
$469$			3269.21i			0.321872i
$470$		0			0
$471$		0			0
$472$	1653.67	−	1653.67i	0.161263	−	0.161263i
$473$	−6676.92	+	6676.92i	−0.649060	+	0.649060i
$474$		0			0
$475$		0			0
$476$		−	7531.66i		−	0.725238i
$477$		0			0
$478$	−2655.99	−	2655.99i	−0.254147	−	0.254147i
$479$	10715.8			1.02217			0.511085	−	0.859530i	$-0.329244\pi$
$479$	10715.8			1.02217			0.511085	+	0.859530i	$0.329244\pi$
$480$		0			0
$481$	1828.53			0.173334
$482$	−6774.48	−	6774.48i	−0.640185	−	0.640185i
$483$		0			0
$484$		−	601.277i		−	0.0564685i
$485$		0			0
$486$		0			0
$487$	4489.84	−	4489.84i	0.417770	−	0.417770i	−0.466664	−	0.884435i	$-0.654544\pi$
$487$	4489.84	−	4489.84i	0.417770	−	0.417770i	0.884435	+	0.466664i	$0.154544\pi$
$488$	2308.50	−	2308.50i	0.214141	−	0.214141i
$489$		0			0
$490$		0			0
$491$		−	15174.1i		−	1.39470i	−0.716729	−	0.697352i	$-0.754362\pi$
$491$		−	15174.1i		−	1.39470i	0.716729	−	0.697352i	$-0.245638\pi$
$492$		0			0
$493$	5452.56	+	5452.56i	0.498116	+	0.498116i
$494$	−27663.3			−2.51950
$495$		0			0
$496$	−17983.9			−1.62802
$497$	−5107.09	−	5107.09i	−0.460934	−	0.460934i
$498$		0			0
$499$			8887.20i			0.797286i	0.917106	+	0.398643i	$0.130519\pi$
$499$			8887.20i			0.797286i	−0.917106	+	0.398643i	$0.869481\pi$
$500$		0			0
$501$		0			0
$502$	−4478.25	+	4478.25i	−0.398155	+	0.398155i
$503$	−12740.5	+	12740.5i	−1.12936	+	1.12936i	−0.139084	+	0.990281i	$0.544416\pi$
$503$	−12740.5	+	12740.5i	−1.12936	+	1.12936i	−0.990281	+	0.139084i	$0.955584\pi$
$504$		0			0
$505$		0			0
$506$			7899.61i			0.694033i
$507$		0			0
$508$	−4517.58	−	4517.58i	−0.394558	−	0.394558i
$509$	9257.00			0.806108			0.403054	−	0.915176i	$-0.367949\pi$
$509$	9257.00			0.806108			0.403054	+	0.915176i	$0.367949\pi$
$510$		0			0
$511$	−10447.2			−0.904416
$512$	−8242.49	−	8242.49i	−0.711465	−	0.711465i
$513$		0			0
$514$			13943.1i			1.19651i
$515$		0			0
$516$		0			0
$517$	−5523.99	+	5523.99i	−0.469913	+	0.469913i
$518$	−1082.56	+	1082.56i	−0.0918240	+	0.0918240i
$519$		0			0
$520$		0			0
$521$			13563.3i			1.14054i	0.821458	+	0.570268i	$0.193161\pi$
$521$			13563.3i			1.14054i	−0.821458	+	0.570268i	$0.806839\pi$
$522$		0			0
$523$	−11193.8	−	11193.8i	−0.935894	−	0.935894i	0.0621714	−	0.998065i	$-0.480197\pi$
$523$	−11193.8	−	11193.8i	−0.935894	−	0.935894i	−0.998065	+	0.0621714i	$0.980197\pi$
$524$	−2575.18			−0.214689
$525$		0			0
$526$	−12095.3			−1.00262
$527$	14101.5	+	14101.5i	1.16560	+	1.16560i
$528$		0			0
$529$			9004.33i			0.740062i
$530$		0			0
$531$		0			0
$532$	6844.34	−	6844.34i	0.557782	−	0.557782i
$533$	−12545.9	+	12545.9i	−1.01956	+	1.01956i
$534$		0			0
$535$		0			0
$536$		−	1779.81i		−	0.143426i
$537$		0			0
$538$	1173.30	+	1173.30i	0.0940231	+	0.0940231i
$539$	4050.34			0.323675
$540$		0			0
$541$	1383.33			0.109934			0.0549668	−	0.998488i	$-0.482495\pi$
$541$	1383.33			0.109934			0.0549668	+	0.998488i	$0.482495\pi$
$542$	−4123.86	−	4123.86i	−0.326817	−	0.326817i
$543$		0			0
$544$			18637.5i			1.46889i
$545$		0			0
$546$		0			0
$547$	−2181.76	+	2181.76i	−0.170540	+	0.170540i	−0.787217	−	0.616677i	$-0.788479\pi$
$547$	−2181.76	+	2181.76i	−0.170540	+	0.170540i	0.616677	+	0.787217i	$0.288479\pi$
$548$	5457.01	−	5457.01i	0.425387	−	0.425387i
$549$		0			0
$550$		0			0
$551$			9909.96i			0.766204i
$552$		0			0
$553$	−14368.5	−	14368.5i	−1.10491	−	1.10491i
$554$	30496.9			2.33879
$555$		0			0
$556$	647.494			0.0493882
$557$	−15674.9	−	15674.9i	−1.19240	−	1.19240i	−0.976392	−	0.216007i	$-0.930697\pi$
$557$	−15674.9	−	15674.9i	−1.19240	−	1.19240i	−0.216007	−	0.976392i	$-0.569303\pi$
$558$		0			0
$559$		−	16955.0i		−	1.28286i
$560$		0			0
$561$		0			0
$562$	367.080	−	367.080i	0.0275522	−	0.0275522i
$563$	8213.60	−	8213.60i	0.614852	−	0.614852i	−0.329354	−	0.944206i	$-0.606831\pi$
$563$	8213.60	−	8213.60i	0.614852	−	0.614852i	0.944206	+	0.329354i	$0.106831\pi$
$564$		0			0
$565$		0			0
$566$			23235.3i			1.72554i
$567$		0			0
$568$	2780.39	+	2780.39i	0.205392	+	0.205392i
$569$	16902.1			1.24530			0.622648	−	0.782502i	$-0.286057\pi$
$569$	16902.1			1.24530			0.622648	+	0.782502i	$0.286057\pi$
$570$		0			0
$571$	6507.12			0.476908			0.238454	−	0.971154i	$-0.423359\pi$
$571$	6507.12			0.476908			0.238454	+	0.971154i	$0.423359\pi$
$572$	10469.6	+	10469.6i	0.765305	+	0.765305i
$573$		0			0
$574$		−	14855.3i		−	1.08022i
$575$		0			0
$576$		0			0
$577$	−7884.54	+	7884.54i	−0.568870	+	0.568870i	−0.931812	−	0.362942i	$-0.881772\pi$
$577$	−7884.54	+	7884.54i	−0.568870	+	0.568870i	0.362942	+	0.931812i	$0.381772\pi$
$578$	6213.35	−	6213.35i	0.447130	−	0.447130i
$579$		0			0
$580$		0			0
$581$		−	9913.20i		−	0.707864i
$582$		0			0
$583$	6944.77	+	6944.77i	0.493350	+	0.493350i
$584$	5687.63			0.403007
$585$		0			0
$586$	−6524.39			−0.459932
$587$	9548.44	+	9548.44i	0.671390	+	0.671390i	0.958037	−	0.286646i	$-0.0925404\pi$
$587$	9548.44	+	9548.44i	0.671390	+	0.671390i	−0.286646	+	0.958037i	$0.592540\pi$
$588$		0			0
$589$			25629.2i			1.79293i
$590$		0			0
$591$		0			0
$592$	1462.57	−	1462.57i	0.101539	−	0.101539i
$593$	3491.97	−	3491.97i	0.241818	−	0.241818i	−0.575784	−	0.817602i	$-0.695303\pi$
$593$	3491.97	−	3491.97i	0.241818	−	0.241818i	0.817602	+	0.575784i	$0.195303\pi$
$594$		0			0
$595$		0			0
$596$			8574.75i			0.589321i
$597$		0			0
$598$	−10029.9	−	10029.9i	−0.685876	−	0.685876i
$599$	−11203.0			−0.764175			−0.382087	−	0.924126i	$-0.624795\pi$
$599$	−11203.0			−0.764175			−0.382087	+	0.924126i	$0.624795\pi$
$600$		0			0
$601$	−13953.5			−0.947048			−0.473524	−	0.880781i	$-0.657018\pi$
$601$	−13953.5			−0.947048			−0.473524	+	0.880781i	$0.657018\pi$
$602$	10038.0	+	10038.0i	0.679598	+	0.679598i
$603$		0			0
$604$		−	16883.3i		−	1.13737i
$605$		0			0
$606$		0			0
$607$	1292.54	−	1292.54i	0.0864293	−	0.0864293i	−0.662570	−	0.749000i	$-0.730534\pi$
$607$	1292.54	−	1292.54i	0.0864293	−	0.0864293i	0.749000	+	0.662570i	$0.230534\pi$
$608$	−16936.7	+	16936.7i	−1.12972	+	1.12972i
$609$		0			0
$610$		0			0
$611$		−	14027.3i		−	0.928780i
$612$		0			0
$613$	−225.964	−	225.964i	−0.0148884	−	0.0148884i	0.699623	−	0.714512i	$-0.253351\pi$
$613$	−225.964	−	225.964i	−0.0148884	−	0.0148884i	−0.714512	+	0.699623i	$0.753351\pi$
$614$	−38417.2			−2.52507
$615$		0			0
$616$	4870.41			0.318562
$617$	2717.41	+	2717.41i	0.177308	+	0.177308i	0.790181	−	0.612873i	$-0.209986\pi$
$617$	2717.41	+	2717.41i	0.177308	+	0.177308i	−0.612873	+	0.790181i	$0.709986\pi$
$618$		0			0
$619$		−	8870.55i		−	0.575989i	−0.957632	−	0.287995i	$-0.907011\pi$
$619$		−	8870.55i		−	0.575989i	0.957632	−	0.287995i	$-0.0929886\pi$
$620$		0			0
$621$		0			0
$622$	19632.7	−	19632.7i	1.26559	−	1.26559i
$623$	14829.3	−	14829.3i	0.953650	−	0.953650i
$624$		0			0
$625$		0			0
$626$		−	12876.5i		−	0.822123i
$627$		0			0
$628$	−898.205	−	898.205i	−0.0570737	−	0.0570737i
$629$	−2293.65			−0.145396
$630$		0			0
$631$	29762.7			1.87771			0.938853	−	0.344318i	$-0.111890\pi$
$631$	29762.7			1.87771			0.938853	+	0.344318i	$0.111890\pi$
$632$	7822.48	+	7822.48i	0.492344	+	0.492344i
$633$		0			0
$634$		−	35254.2i		−	2.20840i
$635$		0			0
$636$		0			0
$637$	−5142.61	+	5142.61i	−0.319871	+	0.319871i
$638$	8974.65	−	8974.65i	0.556912	−	0.556912i
$639$		0			0
$640$		0			0
$641$			5168.75i			0.318492i	0.987239	+	0.159246i	$0.0509063\pi$
$641$			5168.75i			0.318492i	−0.987239	+	0.159246i	$0.949094\pi$
$642$		0			0
$643$	2078.46	+	2078.46i	0.127475	+	0.127475i	0.767966	−	0.640491i	$-0.221269\pi$
$643$	2078.46	+	2078.46i	0.127475	+	0.127475i	−0.640491	+	0.767966i	$0.721269\pi$
$644$	4963.13			0.303687
$645$		0			0
$646$	34700.0			2.11339
$647$	10765.7	+	10765.7i	0.654164	+	0.654164i	0.953993	−	0.299829i	$-0.0969297\pi$
$647$	10765.7	+	10765.7i	0.654164	+	0.654164i	−0.299829	+	0.953993i	$0.596930\pi$
$648$		0			0
$649$			10592.8i			0.640684i
$650$		0			0
$651$		0			0
$652$	−1374.37	+	1374.37i	−0.0825530	+	0.0825530i
$653$	12815.1	−	12815.1i	0.767984	−	0.767984i	−0.209767	−	0.977751i	$-0.567271\pi$
$653$	12815.1	−	12815.1i	0.767984	−	0.767984i	0.977751	+	0.209767i	$0.0672707\pi$
$654$		0			0
$655$		0			0
$656$			20069.9i			1.19451i
$657$		0			0
$658$	8304.68	+	8304.68i	0.492022	+	0.492022i
$659$	16634.8			0.983307			0.491654	−	0.870791i	$-0.336393\pi$
$659$	16634.8			0.983307			0.491654	+	0.870791i	$0.336393\pi$
$660$		0			0
$661$	−10835.6			−0.637601			−0.318800	−	0.947822i	$-0.603280\pi$
$661$	−10835.6			−0.637601			−0.318800	+	0.947822i	$0.603280\pi$
$662$	521.868	+	521.868i	0.0306389	+	0.0306389i
$663$		0			0
$664$			5396.92i			0.315423i
$665$		0			0
$666$		0			0
$667$	−3593.07	+	3593.07i	−0.208582	+	0.208582i
$668$	3889.27	−	3889.27i	0.225270	−	0.225270i
$669$		0			0
$670$		0			0
$671$			14787.4i			0.850762i
$672$		0			0
$673$	16220.3	+	16220.3i	0.929045	+	0.929045i	0.997644	−	0.0685992i	$-0.0218530\pi$
$673$	16220.3	+	16220.3i	0.929045	+	0.929045i	−0.0685992	+	0.997644i	$0.521853\pi$
$674$	17347.3			0.991382
$675$		0			0
$676$	−13967.4			−0.794685
$677$	−11196.6	−	11196.6i	−0.635626	−	0.635626i	0.313847	−	0.949473i	$-0.398382\pi$
$677$	−11196.6	−	11196.6i	−0.635626	−	0.635626i	−0.949473	+	0.313847i	$0.898382\pi$
$678$		0			0
$679$		−	17065.0i		−	0.964500i
$680$		0			0
$681$		0			0
$682$	23210.3	−	23210.3i	1.30318	−	1.30318i
$683$	15428.1	−	15428.1i	0.864331	−	0.864331i	−0.127507	−	0.991838i	$-0.540697\pi$
$683$	15428.1	−	15428.1i	0.864331	−	0.864331i	0.991838	+	0.127507i	$0.0406975\pi$
$684$		0			0
$685$		0			0
$686$		−	25627.9i		−	1.42635i
$687$		0			0
$688$	−13561.6	−	13561.6i	−0.751501	−	0.751501i
$689$	−17635.2			−0.975104
$690$		0			0
$691$	21858.6			1.20339			0.601693	−	0.798728i	$-0.294493\pi$
$691$	21858.6			1.20339			0.601693	+	0.798728i	$0.294493\pi$
$692$	−2535.89	−	2535.89i	−0.139307	−	0.139307i
$693$		0			0
$694$			12434.2i			0.680112i
$695$		0			0
$696$		0			0
$697$	15737.2	−	15737.2i	0.855220	−	0.855220i
$698$	−21518.9	+	21518.9i	−1.16691	+	1.16691i
$699$		0			0
$700$		0			0
$701$		−	8846.82i		−	0.476662i	−0.971184	−	0.238331i	$-0.923400\pi$
$701$		−	8846.82i		−	0.476662i	0.971184	−	0.238331i	$-0.0766002\pi$
$702$		0			0
$703$	−2084.34	−	2084.34i	−0.111824	−	0.111824i
$704$	7347.86			0.393371
$705$		0			0
$706$	35656.2			1.90076
$707$	−1212.06	−	1212.06i	−0.0644755	−	0.0644755i
$708$		0			0
$709$			23189.8i			1.22837i	0.789163	+	0.614184i	$0.210515\pi$
$709$			23189.8i			1.22837i	−0.789163	+	0.614184i	$0.789485\pi$
$710$		0			0
$711$		0			0
$712$	−8073.34	+	8073.34i	−0.424945	+	0.424945i
$713$	−9292.43	+	9292.43i	−0.488084	+	0.488084i
$714$		0			0
$715$		0			0
$716$			27133.9i			1.41626i
$717$		0			0
$718$	4661.21	+	4661.21i	0.242277	+	0.242277i
$719$	7005.29			0.363356			0.181678	−	0.983358i	$-0.441847\pi$
$719$	7005.29			0.363356			0.181678	+	0.983358i	$0.441847\pi$
$720$		0			0
$721$	−301.661			−0.0155818
$722$	13553.2	+	13553.2i	0.698611	+	0.698611i
$723$		0			0
$724$		−	8892.98i		−	0.456498i
$725$		0			0
$726$		0			0
$727$	16025.7	−	16025.7i	0.817553	−	0.817553i	−0.168200	−	0.985753i	$-0.553795\pi$
$727$	16025.7	−	16025.7i	0.817553	−	0.817553i	0.985753	+	0.168200i	$0.0537954\pi$
$728$	−6183.82	+	6183.82i	−0.314818	+	0.314818i
$729$		0			0
$730$		0			0
$731$			21267.8i			1.07609i
$732$		0			0
$733$	3319.43	+	3319.43i	0.167266	+	0.167266i	0.785777	−	0.618511i	$-0.212264\pi$
$733$	3319.43	+	3319.43i	0.167266	+	0.167266i	−0.618511	+	0.785777i	$0.712264\pi$
$734$	−24502.5			−1.23216
$735$		0			0
$736$	−12281.5			−0.615084
$737$	5700.41	+	5700.41i	0.284908	+	0.284908i
$738$		0			0
$739$		−	19979.4i		−	0.994526i	−0.867600	−	0.497263i	$-0.834338\pi$
$739$		−	19979.4i		−	0.994526i	0.867600	−	0.497263i	$-0.165662\pi$
$740$		0			0
$741$		0			0
$742$	10440.7	−	10440.7i	0.516562	−	0.516562i
$743$	14574.6	−	14574.6i	0.719637	−	0.719637i	−0.248894	−	0.968531i	$-0.580067\pi$
$743$	14574.6	−	14574.6i	0.719637	−	0.719637i	0.968531	+	0.248894i	$0.0800670\pi$
$744$		0			0
$745$		0			0
$746$		−	30038.0i		−	1.47422i
$747$		0			0
$748$	−13132.7	−	13132.7i	−0.641951	−	0.641951i
$749$	16866.3			0.822807
$750$		0			0
$751$	−11620.1			−0.564612			−0.282306	−	0.959324i	$-0.591099\pi$
$751$	−11620.1			−0.564612			−0.282306	+	0.959324i	$0.591099\pi$
$752$	−11219.9	−	11219.9i	−0.544079	−	0.544079i
$753$		0			0
$754$			22789.7i			1.10073i
$755$		0			0
$756$		0			0
$757$	−10502.0	+	10502.0i	−0.504229	+	0.504229i	−0.912749	−	0.408520i	$-0.866045\pi$
$757$	−10502.0	+	10502.0i	−0.504229	+	0.504229i	0.408520	+	0.912749i	$0.366045\pi$
$758$	−403.390	+	403.390i	−0.0193296	+	0.0193296i
$759$		0			0
$760$		0			0
$761$		−	36489.6i		−	1.73817i	−0.494664	−	0.869085i	$-0.664709\pi$
$761$		−	36489.6i		−	1.73817i	0.494664	−	0.869085i	$-0.335291\pi$
$762$		0			0
$763$	−4461.01	−	4461.01i	−0.211664	−	0.211664i
$764$	−6264.50			−0.296652
$765$		0			0
$766$	−22532.3			−1.06283
$767$	−13449.4	−	13449.4i	−0.633154	−	0.633154i
$768$		0			0
$769$		−	30323.9i		−	1.42199i	−0.703198	−	0.710994i	$-0.748245\pi$
$769$		−	30323.9i		−	1.42199i	0.703198	−	0.710994i	$-0.251755\pi$
$770$		0			0
$771$		0			0
$772$	−16229.4	+	16229.4i	−0.756617	+	0.756617i
$773$	10327.2	−	10327.2i	0.480522	−	0.480522i	−0.424777	−	0.905298i	$-0.639647\pi$
$773$	10327.2	−	10327.2i	0.480522	−	0.480522i	0.905298	+	0.424777i	$0.139647\pi$
$774$		0			0
$775$		0			0
$776$			9290.49i			0.429780i
$777$		0			0
$778$	20533.4	+	20533.4i	0.946220	+	0.946220i
$779$	28602.1			1.31550
$780$		0			0
$781$	−17810.1			−0.816000
$782$	12581.2	+	12581.2i	0.575324	+	0.575324i
$783$		0			0
$784$			8226.74i			0.374760i
$785$		0			0
$786$		0			0
$787$	−21521.8	+	21521.8i	−0.974802	+	0.974802i	−0.999690	−	0.0248882i	$-0.992077\pi$
$787$	−21521.8	+	21521.8i	−0.974802	+	0.974802i	0.0248882	+	0.999690i	$0.492077\pi$
$788$	6685.38	−	6685.38i	0.302229	−	0.302229i
$789$		0			0
$790$		0			0
$791$		−	11328.6i		−	0.509229i
$792$		0			0
$793$	−18775.2	−	18775.2i	−0.840764	−	0.840764i
$794$	−53452.3			−2.38911
$795$		0			0
$796$	−2988.10			−0.133053
$797$	−17277.8	−	17277.8i	−0.767895	−	0.767895i	0.209841	−	0.977736i	$-0.432706\pi$
$797$	−17277.8	−	17277.8i	−0.767895	−	0.767895i	−0.977736	+	0.209841i	$0.932706\pi$
$798$		0			0
$799$			17595.4i			0.779076i
$800$		0			0
$801$		0			0
$802$	−28254.4	+	28254.4i	−1.24401	+	1.24401i
$803$	−18216.4	+	18216.4i	−0.800552	+	0.800552i
$804$		0			0
$805$		0			0
$806$			58939.0i			2.57573i
$807$		0			0
$808$	659.866	+	659.866i	0.0287302	+	0.0287302i
$809$	41260.2			1.79312			0.896558	−	0.442926i	$-0.146059\pi$
$809$	41260.2			1.79312			0.896558	+	0.442926i	$0.146059\pi$
$810$		0			0
$811$	−23357.1			−1.01132			−0.505659	−	0.862733i	$-0.668751\pi$
$811$	−23357.1			−1.01132			−0.505659	+	0.862733i	$0.668751\pi$
$812$	−5638.54	−	5638.54i	−0.243687	−	0.243687i
$813$		0			0
$814$			3775.24i			0.162558i
$815$		0			0
$816$		0			0
$817$	−19327.0	+	19327.0i	−0.827621	+	0.827621i
$818$	−12136.9	+	12136.9i	−0.518773	+	0.518773i
$819$		0			0
$820$		0			0
$821$		−	8296.46i		−	0.352678i	−0.984330	−	0.176339i	$-0.943575\pi$
$821$		−	8296.46i		−	0.352678i	0.984330	−	0.176339i	$-0.0564254\pi$
$822$		0			0
$823$	−17980.5	−	17980.5i	−0.761555	−	0.761555i	0.215048	−	0.976603i	$-0.431009\pi$
$823$	−17980.5	−	17980.5i	−0.761555	−	0.761555i	−0.976603	+	0.215048i	$0.931009\pi$
$824$	164.230			0.00694322
$825$		0			0
$826$	15925.1			0.670827
$827$	9128.21	+	9128.21i	0.383820	+	0.383820i	0.872476	−	0.488656i	$-0.162513\pi$
$827$	9128.21	+	9128.21i	0.383820	+	0.383820i	−0.488656	+	0.872476i	$0.662513\pi$
$828$		0			0
$829$		−	24401.3i		−	1.02231i	−0.859489	−	0.511154i	$-0.829218\pi$
$829$		−	24401.3i		−	1.02231i	0.859489	−	0.511154i	$-0.170782\pi$
$830$		0			0
$831$		0			0
$832$	−9329.38	+	9329.38i	−0.388748	+	0.388748i
$833$	6450.73	−	6450.73i	0.268313	−	0.268313i
$834$		0			0
$835$		0			0
$836$		−	23868.5i		−	0.987452i
$837$		0			0
$838$	29560.2	+	29560.2i	1.21854	+	1.21854i
$839$	−38174.8			−1.57084			−0.785422	−	0.618960i	$-0.787554\pi$
$839$	−38174.8			−1.57084			−0.785422	+	0.618960i	$0.787554\pi$
$840$		0			0
$841$	−16224.9			−0.665256
$842$	−8880.22	−	8880.22i	−0.363459	−	0.363459i
$843$		0			0
$844$			31729.3i			1.29404i
$845$		0			0
$846$		0			0
$847$	−1137.45	+	1137.45i	−0.0461433	+	0.0461433i
$848$	−14105.7	+	14105.7i	−0.571216	+	0.571216i
$849$		0			0
$850$		0			0
$851$		−	1511.44i		−	0.0608833i
$852$		0			0
$853$	−1757.73	−	1757.73i	−0.0705550	−	0.0705550i	0.670949	−	0.741504i	$-0.265887\pi$
$853$	−1757.73	−	1757.73i	−0.0705550	−	0.0705550i	−0.741504	+	0.670949i	$0.765887\pi$
$854$	22231.2			0.890790
$855$		0			0
$856$	−9182.33			−0.366642
$857$	−7091.77	−	7091.77i	−0.282672	−	0.282672i	0.551501	−	0.834174i	$-0.314055\pi$
$857$	−7091.77	−	7091.77i	−0.282672	−	0.282672i	−0.834174	+	0.551501i	$0.814055\pi$
$858$		0			0
$859$			16842.4i			0.668982i	0.942399	+	0.334491i	$0.108564\pi$
$859$			16842.4i			0.668982i	−0.942399	+	0.334491i	$0.891436\pi$
$860$		0			0
$861$		0			0
$862$	42366.4	−	42366.4i	1.67402	−	1.67402i
$863$	−33056.1	+	33056.1i	−1.30387	+	1.30387i	−0.378114	+	0.925759i	$0.623427\pi$
$863$	−33056.1	+	33056.1i	−1.30387	+	1.30387i	−0.925759	+	0.378114i	$0.876573\pi$
$864$		0			0
$865$		0			0
$866$		−	19968.7i		−	0.783562i
$867$		0			0
$868$	−14582.5	−	14582.5i	−0.570231	−	0.570231i
$869$	−50107.9			−1.95603
$870$		0			0
$871$	−14475.3			−0.563120
$872$	2428.65	+	2428.65i	0.0943171	+	0.0943171i
$873$		0			0
$874$			22866.2i			0.884966i
$875$		0			0
$876$		0			0
$877$	−1780.97	+	1780.97i	−0.0685738	+	0.0685738i	−0.740562	−	0.671988i	$-0.765441\pi$
$877$	−1780.97	+	1780.97i	−0.0685738	+	0.0685738i	0.671988	+	0.740562i	$0.265441\pi$
$878$	−4213.39	+	4213.39i	−0.161953	+	0.161953i
$879$		0			0
$880$		0			0
$881$			2698.82i			0.103207i	0.998668	+	0.0516036i	$0.0164332\pi$
$881$			2698.82i			0.103207i	−0.998668	+	0.0516036i	$0.983567\pi$
$882$		0			0
$883$	−6744.66	−	6744.66i	−0.257051	−	0.257051i	0.566803	−	0.823854i	$-0.308180\pi$
$883$	−6744.66	−	6744.66i	−0.257051	−	0.257051i	−0.823854	+	0.566803i	$0.808180\pi$
$884$	33348.5			1.26881
$885$		0			0
$886$	−43497.5			−1.64935
$887$	1302.99	+	1302.99i	0.0493238	+	0.0493238i	0.731338	−	0.682015i	$-0.238896\pi$
$887$	1302.99	+	1302.99i	0.0493238	+	0.0493238i	−0.682015	+	0.731338i	$0.738896\pi$
$888$		0			0
$889$			17092.1i			0.644827i
$890$		0			0
$891$		0			0
$892$	1856.29	−	1856.29i	0.0696785	−	0.0696785i
$893$	−15989.7	+	15989.7i	−0.599189	+	0.599189i
$894$		0			0
$895$		0			0
$896$			15798.5i			0.589052i
$897$		0			0
$898$	39483.0	+	39483.0i	1.46722	+	1.46722i
$899$	21114.0			0.783306
$900$		0			0
$901$	22121.0			0.817933
$902$	−25902.6	−	25902.6i	−0.956167	−	0.956167i
$903$		0			0
$904$			6167.50i			0.226912i
$905$		0			0
$906$		0			0
$907$	3070.33	−	3070.33i	0.112402	−	0.112402i	−0.648669	−	0.761071i	$-0.724674\pi$
$907$	3070.33	−	3070.33i	0.112402	−	0.112402i	0.761071	+	0.648669i	$0.224674\pi$
$908$	−15735.8	+	15735.8i	−0.575123	+	0.575123i
$909$		0			0
$910$		0			0
$911$			19102.6i			0.694727i	0.937731	+	0.347364i	$0.112923\pi$
$911$			19102.6i			0.694727i	−0.937731	+	0.347364i	$0.887077\pi$
$912$		0			0
$913$	−17285.3	−	17285.3i	−0.626572	−	0.626572i
$914$	14004.9			0.506830
$915$		0			0
$916$	1322.92			0.0477189
$917$	4871.55	+	4871.55i	0.175434	+	0.175434i
$918$		0			0
$919$			29786.7i			1.06917i	0.845113	+	0.534587i	$0.179533\pi$
$919$			29786.7i			1.06917i	−0.845113	+	0.534587i	$0.820467\pi$
$920$		0			0
$921$		0			0
$922$	−33577.8	+	33577.8i	−1.19938	+	1.19938i
$923$	22613.0	−	22613.0i	0.806410	−	0.806410i
$924$		0			0
$925$		0			0
$926$		−	58478.9i		−	2.07531i
$927$		0			0
$928$	13952.9	+	13952.9i	0.493561	+	0.493561i
$929$	−7724.87			−0.272815			−0.136407	−	0.990653i	$-0.543556\pi$
$929$	−7724.87			−0.272815			−0.136407	+	0.990653i	$0.543556\pi$
$930$		0			0
$931$	11724.1			0.412720
$932$	2011.12	+	2011.12i	0.0706829	+	0.0706829i
$933$		0			0
$934$		−	41446.7i		−	1.45201i
$935$		0			0
$936$		0			0
$937$	20722.5	−	20722.5i	0.722492	−	0.722492i	−0.246620	−	0.969112i	$-0.579320\pi$
$937$	20722.5	−	20722.5i	0.722492	−	0.722492i	0.969112	+	0.246620i	$0.0793199\pi$
$938$	8569.92	−	8569.92i	0.298313	−	0.298313i
$939$		0			0
$940$		0			0
$941$			21780.7i			0.754548i	0.926102	+	0.377274i	$0.123138\pi$
$941$			21780.7i			0.754548i	−0.926102	+	0.377274i	$0.876862\pi$
$942$		0			0
$943$	10370.3	+	10370.3i	0.358116	+	0.358116i
$944$	−21515.3			−0.741803
$945$		0			0
$946$	35005.8			1.20310
$947$	−29938.4	−	29938.4i	−1.02731	−	1.02731i	−0.999616	−	0.0276975i	$-0.991182\pi$
$947$	−29938.4	−	29938.4i	−1.02731	−	1.02731i	−0.0276975	−	0.999616i	$-0.508818\pi$
$948$		0			0
$949$		−	46257.8i		−	1.58229i
$950$		0			0
$951$		0			0
$952$	7756.79	−	7756.79i	0.264075	−	0.264075i
$953$	29572.1	−	29572.1i	1.00518	−	1.00518i	0.00519163	−	0.999987i	$-0.498347\pi$
$953$	29572.1	−	29572.1i	1.00518	−	1.00518i	0.999987	−	0.00519163i	$-0.00165255\pi$
$954$		0			0
$955$		0			0
$956$			5819.29i			0.196872i
$957$		0			0
$958$	−28090.5	−	28090.5i	−0.947353	−	0.947353i
$959$	−20646.4			−0.695212
$960$		0			0
$961$	24814.3			0.832945
$962$	−4793.32	−	4793.32i	−0.160647	−	0.160647i
$963$		0			0
$964$			14842.9i			0.495911i
$965$		0			0
$966$		0			0
$967$	9478.37	−	9478.37i	0.315206	−	0.315206i	−0.531717	−	0.846922i	$-0.678453\pi$
$967$	9478.37	−	9478.37i	0.315206	−	0.315206i	0.846922	+	0.531717i	$0.178453\pi$
$968$	619.250	−	619.250i	0.0205614	−	0.0205614i
$969$		0			0
$970$		0			0
$971$		−	8382.79i		−	0.277051i	−0.990359	−	0.138525i	$-0.955764\pi$
$971$		−	8382.79i		−	0.277051i	0.990359	−	0.138525i	$-0.0442363\pi$
$972$		0			0
$973$	−1224.89	−	1224.89i	−0.0403577	−	0.0403577i
$974$	−23539.4			−0.774384
$975$		0			0
$976$	−30035.0			−0.985039
$977$	−24277.3	−	24277.3i	−0.794986	−	0.794986i	0.187314	−	0.982300i	$-0.440022\pi$
$977$	−24277.3	−	24277.3i	−0.794986	−	0.794986i	−0.982300	+	0.187314i	$0.940022\pi$
$978$		0			0
$979$		−	51714.8i		−	1.68826i
$980$		0			0
$981$		0			0
$982$	−39777.5	+	39777.5i	−1.29262	+	1.29262i
$983$	14666.4	−	14666.4i	0.475876	−	0.475876i	−0.427934	−	0.903810i	$-0.640758\pi$
$983$	14666.4	−	14666.4i	0.475876	−	0.475876i	0.903810	+	0.427934i	$0.140758\pi$
$984$		0			0
$985$		0			0
$986$		−	28586.7i		−	0.923313i
$987$		0			0
$988$	30305.2	+	30305.2i	0.975847	+	0.975847i
$989$	−14014.8			−0.450603
$990$		0			0
$991$	17192.0			0.551080			0.275540	−	0.961290i	$-0.411143\pi$
$991$	17192.0			0.551080			0.275540	+	0.961290i	$0.411143\pi$
$992$	36085.0	+	36085.0i	1.15494	+	1.15494i
$993$		0			0
$994$			26775.5i			0.854393i
$995$		0			0
$996$		0			0
$997$	−13617.4	+	13617.4i	−0.432566	+	0.432566i	−0.889500	−	0.456935i	$-0.848947\pi$
$997$	−13617.4	+	13617.4i	−0.432566	+	0.432566i	0.456935	+	0.889500i	$0.348947\pi$
$998$	23296.9	−	23296.9i	0.738929	−	0.738929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.f.c.143.2		12
3.2	odd	2	inner	225.4.f.c.143.5		12
5.2	odd	4	inner	225.4.f.c.107.5		12
5.3	odd	4		45.4.f.a.17.2	yes	12
5.4	even	2		45.4.f.a.8.5	yes	12
15.2	even	4	inner	225.4.f.c.107.2		12
15.8	even	4		45.4.f.a.17.5	yes	12
15.14	odd	2		45.4.f.a.8.2	✓	12
20.3	even	4		720.4.w.d.17.2		12
20.19	odd	2		720.4.w.d.593.5		12
60.23	odd	4		720.4.w.d.17.5		12
60.59	even	2		720.4.w.d.593.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.f.a.8.2	✓	12	15.14	odd	2
45.4.f.a.8.5	yes	12	5.4	even	2
45.4.f.a.17.2	yes	12	5.3	odd	4
45.4.f.a.17.5	yes	12	15.8	even	4
225.4.f.c.107.2		12	15.2	even	4	inner
225.4.f.c.107.5		12	5.2	odd	4	inner
225.4.f.c.143.2		12	1.1	even	1	trivial
225.4.f.c.143.5		12	3.2	odd	2	inner
720.4.w.d.17.2		12	20.3	even	4
720.4.w.d.17.5		12	60.23	odd	4
720.4.w.d.593.2		12	60.59	even	2
720.4.w.d.593.5		12	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.62140 - 2.62140i) q^{2} +5.74350i q^{4} +(10.8652 - 10.8652i) q^{7} +(-5.91519 + 5.91519i) q^{8} -37.8905i q^{11} +(48.1085 + 48.1085i) q^{13} -56.9640 q^{14} +76.9602 q^{16} +(-60.3458 - 60.3458i) q^{17} -109.678i q^{19} +(-99.3262 + 99.3262i) q^{22} +(39.7660 - 39.7660i) q^{23} -252.224i q^{26} +(62.4042 + 62.4042i) q^{28} -90.3553 q^{29} -233.678 q^{31} +(-154.422 - 154.422i) q^{32} +316.381i q^{34} +(19.0042 - 19.0042i) q^{37} +(-287.509 + 287.509i) q^{38} +260.783i q^{41} +(-176.216 - 176.216i) q^{43} +217.624 q^{44} -208.485 q^{46} +(-145.788 - 145.788i) q^{47} +106.896i q^{49} +(-276.311 + 276.311i) q^{52} +(-183.285 + 183.285i) q^{53} +128.539i q^{56} +(236.858 + 236.858i) q^{58} -279.564 q^{59} -390.267 q^{61} +(612.563 + 612.563i) q^{62} +193.924i q^{64} +(-150.444 + 150.444i) q^{67} +(346.596 - 346.596i) q^{68} -470.042i q^{71} +(-480.765 - 480.765i) q^{73} -99.6355 q^{74} +629.934 q^{76} +(-411.687 - 411.687i) q^{77} -1322.44i q^{79} +(683.618 - 683.618i) q^{82} +(456.192 - 456.192i) q^{83} +923.868i q^{86} +(224.129 + 224.129i) q^{88} +1364.85 q^{89} +1045.41 q^{91} +(228.396 + 228.396i) q^{92} +764.340i q^{94} +(785.308 - 785.308i) q^{97} +(280.218 - 280.218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82}+ \cdots - 2772 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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