LMFDB - Embedded newform 225.4.f.c.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(107,225)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			143.1
Root			$-3.78139 - 0.0336790i$ of defining polynomial
Character	$\chi$	$=$	225.143
Dual form			225.4.f.c.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.74771 - 3.74771i) q^{2} +20.0907i q^{4} +(-1.80948 + 1.80948i) q^{7} +(45.3126 - 45.3126i) q^{8} +O(q^{10})$	\(q+(-3.74771 - 3.74771i) q^{2} +20.0907i q^{4} +(-1.80948 + 1.80948i) q^{7} +(45.3126 - 45.3126i) q^{8} -46.0907i q^{11} +(-18.6099 - 18.6099i) q^{13} +13.5628 q^{14} -178.911 q^{16} +(14.5793 + 14.5793i) q^{17} +74.4577i q^{19} +(-172.735 + 172.735i) q^{22} +(-59.6003 + 59.6003i) q^{23} +139.489i q^{26} +(-36.3538 - 36.3538i) q^{28} -202.168 q^{29} -49.5423 q^{31} +(308.008 + 308.008i) q^{32} -109.278i q^{34} +(45.0594 - 45.0594i) q^{37} +(279.046 - 279.046i) q^{38} +306.253i q^{41} +(230.784 + 230.784i) q^{43} +925.996 q^{44} +446.730 q^{46} +(-176.943 - 176.943i) q^{47} +336.452i q^{49} +(373.886 - 373.886i) q^{52} +(-85.1290 + 85.1290i) q^{53} +163.985i q^{56} +(757.669 + 757.669i) q^{58} -330.873 q^{59} +678.639 q^{61} +(185.670 + 185.670i) q^{62} -877.361i q^{64} +(-756.373 + 756.373i) q^{67} +(-292.909 + 292.909i) q^{68} +100.264i q^{71} +(-586.919 - 586.919i) q^{73} -337.739 q^{74} -1495.91 q^{76} +(83.4004 + 83.4004i) q^{77} -286.986i q^{79} +(1147.75 - 1147.75i) q^{82} +(-947.796 + 947.796i) q^{83} -1729.83i q^{86} +(-2088.49 - 2088.49i) q^{88} -688.442 q^{89} +67.3485 q^{91} +(-1197.41 - 1197.41i) q^{92} +1326.26i q^{94} +(-920.676 + 920.676i) q^{97} +(1260.92 - 1260.92i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−3.74771	−	3.74771i	−1.32502	−	1.32502i	−0.909657	−	0.415360i	$-0.863656\pi$
$2$	−3.74771	−	3.74771i	−1.32502	−	1.32502i	−0.415360	−	0.909657i	$-0.636344\pi$
$3$		0			0
$3$		0			0
$4$			20.0907i			2.51134i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.80948	+	1.80948i	−0.0977029	+	0.0977029i	−0.754269	−	0.656566i	$-0.772008\pi$
$7$	−1.80948	+	1.80948i	−0.0977029	+	0.0977029i	0.656566	+	0.754269i	$0.272008\pi$
$8$	45.3126	−	45.3126i	2.00255	−	2.00255i
$9$		0			0
$10$		0			0
$11$		−	46.0907i		−	1.26335i	−0.775232	−	0.631676i	$-0.782367\pi$
$11$		−	46.0907i		−	1.26335i	0.775232	−	0.631676i	$-0.217633\pi$
$12$		0			0
$13$	−18.6099	−	18.6099i	−0.397035	−	0.397035i	0.480151	−	0.877186i	$-0.340582\pi$
$13$	−18.6099	−	18.6099i	−0.397035	−	0.397035i	−0.877186	+	0.480151i	$0.840582\pi$
$14$	13.5628			0.258916
$15$		0			0
$16$	−178.911			−2.79549
$17$	14.5793	+	14.5793i	0.208000	+	0.208000i	0.803417	−	0.595417i	$-0.203013\pi$
$17$	14.5793	+	14.5793i	0.208000	+	0.208000i	−0.595417	+	0.803417i	$0.703013\pi$
$18$		0			0
$19$			74.4577i			0.899041i	0.893270	+	0.449520i	$0.148405\pi$
$19$			74.4577i			0.899041i	−0.893270	+	0.449520i	$0.851595\pi$
$20$		0			0
$21$		0			0
$22$	−172.735	+	172.735i	−1.67396	+	1.67396i
$23$	−59.6003	+	59.6003i	−0.540327	+	0.540327i	−0.923625	−	0.383298i	$-0.874788\pi$
$23$	−59.6003	+	59.6003i	−0.540327	+	0.540327i	0.383298	+	0.923625i	$0.374788\pi$
$24$		0			0
$25$		0			0
$26$			139.489i			1.05216i
$27$		0			0
$28$	−36.3538	−	36.3538i	−0.245365	−	0.245365i
$29$	−202.168			−1.29454			−0.647271	−	0.762260i	$-0.724090\pi$
$29$	−202.168			−1.29454			−0.647271	+	0.762260i	$0.724090\pi$
$30$		0			0
$31$	−49.5423			−0.287034			−0.143517	−	0.989648i	$-0.545841\pi$
$31$	−49.5423			−0.287034			−0.143517	+	0.989648i	$0.545841\pi$
$32$	308.008	+	308.008i	1.70152	+	1.70152i
$33$		0			0
$34$		−	109.278i		−	0.551208i
$35$		0			0
$36$		0			0
$37$	45.0594	−	45.0594i	0.200209	−	0.200209i	−0.599881	−	0.800089i	$-0.704785\pi$
$37$	45.0594	−	45.0594i	0.200209	−	0.200209i	0.800089	+	0.599881i	$0.204785\pi$
$38$	279.046	−	279.046i	1.19124	−	1.19124i
$39$		0			0
$40$		0			0
$41$			306.253i			1.16655i	0.812274	+	0.583276i	$0.198229\pi$
$41$			306.253i			1.16655i	−0.812274	+	0.583276i	$0.801771\pi$
$42$		0			0
$43$	230.784	+	230.784i	0.818472	+	0.818472i	0.985887	−	0.167415i	$-0.0535420\pi$
$43$	230.784	+	230.784i	0.818472	+	0.818472i	−0.167415	+	0.985887i	$0.553542\pi$
$44$	925.996			3.17271
$45$		0			0
$46$	446.730			1.43189
$47$	−176.943	−	176.943i	−0.549143	−	0.549143i	0.377050	−	0.926193i	$-0.376938\pi$
$47$	−176.943	−	176.943i	−0.549143	−	0.549143i	−0.926193	+	0.377050i	$0.876938\pi$
$48$		0			0
$49$			336.452i			0.980908i
$50$		0			0
$51$		0			0
$52$	373.886	−	373.886i	0.997090	−	0.997090i
$53$	−85.1290	+	85.1290i	−0.220630	+	0.220630i	−0.808764	−	0.588134i	$-0.799863\pi$
$53$	−85.1290	+	85.1290i	−0.220630	+	0.220630i	0.588134	+	0.808764i	$0.299863\pi$
$54$		0			0
$55$		0			0
$56$			163.985i			0.391310i
$57$		0			0
$58$	757.669	+	757.669i	1.71529	+	1.71529i
$59$	−330.873			−0.730103			−0.365051	−	0.930987i	$-0.618949\pi$
$59$	−330.873			−0.730103			−0.365051	+	0.930987i	$0.618949\pi$
$60$		0			0
$61$	678.639			1.42444			0.712220	−	0.701956i	$-0.247690\pi$
$61$	678.639			1.42444			0.712220	+	0.701956i	$0.247690\pi$
$62$	185.670	+	185.670i	0.380325	+	0.380325i
$63$		0			0
$64$		−	877.361i		−	1.71360i
$65$		0			0
$66$		0			0
$67$	−756.373	+	756.373i	−1.37919	+	1.37919i	−0.533199	+	0.845990i	$0.679010\pi$
$67$	−756.373	+	756.373i	−1.37919	+	1.37919i	−0.845990	+	0.533199i	$0.820990\pi$
$68$	−292.909	+	292.909i	−0.522360	+	0.522360i
$69$		0			0
$70$		0			0
$71$			100.264i			0.167594i	0.996483	+	0.0837972i	$0.0267048\pi$
$71$			100.264i			0.167594i	−0.996483	+	0.0837972i	$0.973295\pi$
$72$		0			0
$73$	−586.919	−	586.919i	−0.941010	−	0.941010i	0.0573449	−	0.998354i	$-0.481737\pi$
$73$	−586.919	−	586.919i	−0.941010	−	0.941010i	−0.998354	+	0.0573449i	$0.981737\pi$
$74$	−337.739			−0.530560
$75$		0			0
$76$	−1495.91			−2.25780
$77$	83.4004	+	83.4004i	0.123433	+	0.123433i
$78$		0			0
$79$		−	286.986i		−	0.408714i	−0.978896	−	0.204357i	$-0.934490\pi$
$79$		−	286.986i		−	0.408714i	0.978896	−	0.204357i	$-0.0655103\pi$
$80$		0			0
$81$		0			0
$82$	1147.75	−	1147.75i	1.54570	−	1.54570i
$83$	−947.796	+	947.796i	−1.25342	+	1.25342i	−0.299248	+	0.954175i	$0.596736\pi$
$83$	−947.796	+	947.796i	−1.25342	+	1.25342i	−0.954175	+	0.299248i	$0.903264\pi$
$84$		0			0
$85$		0			0
$86$		−	1729.83i		−	2.16898i
$87$		0			0
$88$	−2088.49	−	2088.49i	−2.52993	−	2.52993i
$89$	−688.442			−0.819941			−0.409970	−	0.912099i	$-0.634461\pi$
$89$	−688.442			−0.819941			−0.409970	+	0.912099i	$0.634461\pi$
$90$		0			0
$91$	67.3485			0.0775829
$92$	−1197.41	−	1197.41i	−1.35695	−	1.35695i
$93$		0			0
$94$			1326.26i			1.45525i
$95$		0			0
$96$		0			0
$97$	−920.676	+	920.676i	−0.963716	+	0.963716i	−0.999364	−	0.0356483i	$-0.988650\pi$
$97$	−920.676	+	920.676i	−0.963716	+	0.963716i	0.0356483	+	0.999364i	$0.488650\pi$
$98$	1260.92	−	1260.92i	1.29972	−	1.29972i
$99$		0			0
$100$		0			0
$101$			1018.42i			1.00333i	0.865061	+	0.501667i	$0.167280\pi$
$101$			1018.42i			1.00333i	−0.865061	+	0.501667i	$0.832720\pi$
$102$		0			0
$103$	381.856	+	381.856i	0.365295	+	0.365295i	0.865758	−	0.500463i	$-0.166837\pi$
$103$	381.856	+	381.856i	0.365295	+	0.365295i	−0.500463	+	0.865758i	$0.666837\pi$
$104$	−1686.52			−1.59017
$105$		0			0
$106$	638.078			0.584676
$107$	11.6954	+	11.6954i	0.0105667	+	0.0105667i	0.712370	−	0.701804i	$-0.247622\pi$
$107$	11.6954	+	11.6954i	0.0105667	+	0.0105667i	−0.701804	+	0.712370i	$0.747622\pi$
$108$		0			0
$109$			1346.99i			1.18366i	0.806064	+	0.591828i	$0.201594\pi$
$109$			1346.99i			1.18366i	−0.806064	+	0.591828i	$0.798406\pi$
$110$		0			0
$111$		0			0
$112$	323.737	−	323.737i	0.273127	−	0.273127i
$113$	677.607	−	677.607i	0.564105	−	0.564105i	−0.366366	−	0.930471i	$-0.619398\pi$
$113$	677.607	−	677.607i	0.564105	−	0.564105i	0.930471	+	0.366366i	$0.119398\pi$
$114$		0			0
$115$		0			0
$116$		−	4061.71i		−	3.25104i
$117$		0			0
$118$	1240.02	+	1240.02i	0.967398	+	0.967398i
$119$	−52.7621			−0.0406445
$120$		0			0
$121$	−793.355			−0.596059
$122$	−2543.35	−	2543.35i	−1.88741	−	1.88741i
$123$		0			0
$124$		−	995.340i		−	0.720840i
$125$		0			0
$126$		0			0
$127$	1220.98	−	1220.98i	0.853107	−	0.853107i	−0.137408	−	0.990515i	$-0.543877\pi$
$127$	1220.98	−	1220.98i	0.853107	−	0.853107i	0.990515	+	0.137408i	$0.0438771\pi$
$128$	−824.034	+	824.034i	−0.569023	+	0.569023i
$129$		0			0
$130$		0			0
$131$			215.023i			0.143409i	0.997426	+	0.0717046i	$0.0228439\pi$
$131$			215.023i			0.143409i	−0.997426	+	0.0717046i	$0.977156\pi$
$132$		0			0
$133$	−134.730	−	134.730i	−0.0878389	−	0.0878389i
$134$	5669.34			3.65490
$135$		0			0
$136$	1321.25			0.833063
$137$	877.965	+	877.965i	0.547516	+	0.547516i	0.925721	−	0.378206i	$-0.123459\pi$
$137$	877.965	+	877.965i	0.547516	+	0.547516i	−0.378206	+	0.925721i	$0.623459\pi$
$138$		0			0
$139$		−	2489.62i		−	1.51918i	−0.650400	−	0.759592i	$-0.725399\pi$
$139$		−	2489.62i		−	1.51918i	0.650400	−	0.759592i	$-0.274601\pi$
$140$		0			0
$141$		0			0
$142$	375.762	−	375.762i	0.222065	−	0.222065i
$143$	−857.743	+	857.743i	−0.501595	+	0.501595i
$144$		0			0
$145$		0			0
$146$			4399.21i			2.49371i
$147$		0			0
$148$	905.276	+	905.276i	0.502792	+	0.502792i
$149$	−1497.94			−0.823596			−0.411798	−	0.911275i	$-0.635099\pi$
$149$	−1497.94			−0.823596			−0.411798	+	0.911275i	$0.635099\pi$
$150$		0			0
$151$	−1614.69			−0.870209			−0.435104	−	0.900380i	$-0.643289\pi$
$151$	−1614.69			−0.870209			−0.435104	+	0.900380i	$0.643289\pi$
$152$	3373.87	+	3373.87i	1.80038	+	1.80038i
$153$		0			0
$154$		−	625.121i		−	0.327102i
$155$		0			0
$156$		0			0
$157$	456.938	−	456.938i	0.232278	−	0.232278i	−0.581365	−	0.813643i	$-0.697481\pi$
$157$	456.938	−	456.938i	0.232278	−	0.232278i	0.813643	+	0.581365i	$0.197481\pi$
$158$	−1075.54	+	1075.54i	−0.541553	+	0.541553i
$159$		0			0
$160$		0			0
$161$		−	215.691i		−	0.105583i
$162$		0			0
$163$	−1434.13	−	1434.13i	−0.689140	−	0.689140i	0.272902	−	0.962042i	$-0.412017\pi$
$163$	−1434.13	−	1434.13i	−0.689140	−	0.689140i	−0.962042	+	0.272902i	$0.912017\pi$
$164$	−6152.83			−2.92961
$165$		0			0
$166$	7104.14			3.32162
$167$	1129.18	+	1129.18i	0.523226	+	0.523226i	0.918544	−	0.395318i	$-0.129366\pi$
$167$	1129.18	+	1129.18i	0.523226	+	0.523226i	−0.395318	+	0.918544i	$0.629366\pi$
$168$		0			0
$169$		−	1504.34i		−	0.684726i
$170$		0			0
$171$		0			0
$172$	−4636.62	+	4636.62i	−2.05546	+	2.05546i
$173$	−1656.73	+	1656.73i	−0.728084	+	0.728084i	−0.970238	−	0.242154i	$-0.922146\pi$
$173$	−1656.73	+	1656.73i	−0.728084	+	0.728084i	0.242154	+	0.970238i	$0.422146\pi$
$174$		0			0
$175$		0			0
$176$			8246.15i			3.53169i
$177$		0			0
$178$	2580.08	+	2580.08i	1.08644	+	1.08644i
$179$	1449.32			0.605180			0.302590	−	0.953121i	$-0.402149\pi$
$179$	1449.32			0.605180			0.302590	+	0.953121i	$0.402149\pi$
$180$		0			0
$181$	−1120.24			−0.460037			−0.230019	−	0.973186i	$-0.573879\pi$
$181$	−1120.24			−0.460037			−0.230019	+	0.973186i	$0.573879\pi$
$182$	−252.403	−	252.403i	−0.102799	−	0.102799i
$183$		0			0
$184$			5401.29i			2.16407i
$185$		0			0
$186$		0			0
$187$	671.972	−	671.972i	0.262778	−	0.262778i
$188$	3554.90	−	3554.90i	1.37908	−	1.37908i
$189$		0			0
$190$		0			0
$191$		−	3827.59i		−	1.45002i	−0.688737	−	0.725012i	$-0.741834\pi$
$191$		−	3827.59i		−	1.45002i	0.688737	−	0.725012i	$-0.258166\pi$
$192$		0			0
$193$	−1792.85	−	1792.85i	−0.668665	−	0.668665i	0.288742	−	0.957407i	$-0.406763\pi$
$193$	−1792.85	−	1792.85i	−0.668665	−	0.668665i	−0.957407	+	0.288742i	$0.906763\pi$
$194$	6900.86			2.55388
$195$		0			0
$196$	−6759.55			−2.46339
$197$	2222.09	+	2222.09i	0.803640	+	0.803640i	0.983663	−	0.180022i	$-0.0576169\pi$
$197$	2222.09	+	2222.09i	0.803640	+	0.803640i	−0.180022	+	0.983663i	$0.557617\pi$
$198$		0			0
$199$		−	1421.45i		−	0.506352i	−0.967420	−	0.253176i	$-0.918525\pi$
$199$		−	1421.45i		−	0.506352i	0.967420	−	0.253176i	$-0.0814752\pi$
$200$		0			0
$201$		0			0
$202$	3816.75	−	3816.75i	1.32943	−	1.32943i
$203$	365.820	−	365.820i	0.126481	−	0.126481i
$204$		0			0
$205$		0			0
$206$		−	2862.17i		−	0.968043i
$207$		0			0
$208$	3329.52	+	3329.52i	1.10991	+	1.10991i
$209$	3431.81			1.13580
$210$		0			0
$211$	1133.67			0.369883			0.184942	−	0.982749i	$-0.440790\pi$
$211$	1133.67			0.369883			0.184942	+	0.982749i	$0.440790\pi$
$212$	−1710.30	−	1710.30i	−0.554076	−	0.554076i
$213$		0			0
$214$		−	87.6623i		−	0.0280022i
$215$		0			0
$216$		0			0
$217$	89.6459	−	89.6459i	0.0280441	−	0.0280441i
$218$	5048.15	−	5048.15i	1.56837	−	1.56837i
$219$		0			0
$220$		0			0
$221$		−	542.639i		−	0.165167i
$222$		0			0
$223$	−666.458	−	666.458i	−0.200131	−	0.200131i	0.599925	−	0.800056i	$-0.295197\pi$
$223$	−666.458	−	666.458i	−0.200131	−	0.200131i	−0.800056	+	0.599925i	$0.795197\pi$
$224$	−1114.67			−0.332487
$225$		0			0
$226$	−5078.95			−1.49490
$227$	−2292.99	−	2292.99i	−0.670446	−	0.670446i	0.287373	−	0.957819i	$-0.407218\pi$
$227$	−2292.99	−	2292.99i	−0.670446	−	0.670446i	−0.957819	+	0.287373i	$0.907218\pi$
$228$		0			0
$229$		−	2535.40i		−	0.731634i	−0.930687	−	0.365817i	$-0.880790\pi$
$229$		−	2535.40i		−	0.731634i	0.930687	−	0.365817i	$-0.119210\pi$
$230$		0			0
$231$		0			0
$232$	−9160.77	+	9160.77i	−2.59239	+	2.59239i
$233$	1699.70	−	1699.70i	0.477902	−	0.477902i	−0.426558	−	0.904460i	$-0.640274\pi$
$233$	1699.70	−	1699.70i	0.477902	−	0.477902i	0.904460	+	0.426558i	$0.140274\pi$
$234$		0			0
$235$		0			0
$236$		−	6647.49i		−	1.83354i
$237$		0			0
$238$	197.737	+	197.737i	0.0538546	+	0.0538546i
$239$	−3948.41			−1.06863			−0.534313	−	0.845287i	$-0.679430\pi$
$239$	−3948.41			−1.06863			−0.534313	+	0.845287i	$0.679430\pi$
$240$		0			0
$241$	−2447.20			−0.654101			−0.327050	−	0.945007i	$-0.606055\pi$
$241$	−2447.20			−0.654101			−0.327050	+	0.945007i	$0.606055\pi$
$242$	2973.27	+	2973.27i	0.789788	+	0.789788i
$243$		0			0
$244$			13634.3i			3.57725i
$245$		0			0
$246$		0			0
$247$	1385.65	−	1385.65i	0.356951	−	0.356951i
$248$	−2244.89	+	2244.89i	−0.574801	+	0.574801i
$249$		0			0
$250$		0			0
$251$			4755.75i			1.19594i	0.801519	+	0.597969i	$0.204025\pi$
$251$			4755.75i			1.19594i	−0.801519	+	0.597969i	$0.795975\pi$
$252$		0			0
$253$	2747.02	+	2747.02i	0.682624	+	0.682624i
$254$	−9151.78			−2.26076
$255$		0			0
$256$	−842.400			−0.205664
$257$	−1127.34	−	1127.34i	−0.273624	−	0.273624i	0.556933	−	0.830557i	$-0.311978\pi$
$257$	−1127.34	−	1127.34i	−0.273624	−	0.273624i	−0.830557	+	0.556933i	$0.811978\pi$
$258$		0			0
$259$			163.068i			0.0391219i
$260$		0			0
$261$		0			0
$262$	805.843	−	805.843i	0.190020	−	0.190020i
$263$	−358.621	+	358.621i	−0.0840817	+	0.0840817i	−0.747897	−	0.663815i	$-0.768936\pi$
$263$	−358.621	+	358.621i	−0.0840817	+	0.0840817i	0.663815	+	0.747897i	$0.268936\pi$
$264$		0			0
$265$		0			0
$266$			1009.86i			0.232776i
$267$		0			0
$268$	−15196.1	−	15196.1i	−3.46361	−	3.46361i
$269$	3824.41			0.866834			0.433417	−	0.901193i	$-0.357308\pi$
$269$	3824.41			0.866834			0.433417	+	0.901193i	$0.357308\pi$
$270$		0			0
$271$	535.546			0.120045			0.0600223	−	0.998197i	$-0.480883\pi$
$271$	535.546			0.120045			0.0600223	+	0.998197i	$0.480883\pi$
$272$	−2608.41	−	2608.41i	−0.581463	−	0.581463i
$273$		0			0
$274$		−	6580.72i		−	1.45093i
$275$		0			0
$276$		0			0
$277$	−1108.08	+	1108.08i	−0.240354	+	0.240354i	−0.816996	−	0.576643i	$-0.804362\pi$
$277$	−1108.08	+	1108.08i	−0.240354	+	0.240354i	0.576643	+	0.816996i	$0.304362\pi$
$278$	−9330.37	+	9330.37i	−2.01294	+	2.01294i
$279$		0			0
$280$		0			0
$281$			3439.91i			0.730277i	0.930953	+	0.365139i	$0.118978\pi$
$281$			3439.91i			0.730277i	−0.930953	+	0.365139i	$0.881022\pi$
$282$		0			0
$283$	−2726.08	−	2726.08i	−0.572610	−	0.572610i	0.360247	−	0.932857i	$-0.382693\pi$
$283$	−2726.08	−	2726.08i	−0.572610	−	0.572610i	−0.932857	+	0.360247i	$0.882693\pi$
$284$	−2014.38			−0.420886
$285$		0			0
$286$	6429.15			1.32924
$287$	−554.159	−	554.159i	−0.113975	−	0.113975i
$288$		0			0
$289$		−	4487.89i		−	0.913472i
$290$		0			0
$291$		0			0
$292$	11791.6	−	11791.6i	2.36320	−	2.36320i
$293$	4347.55	−	4347.55i	0.866849	−	0.866849i	−0.125273	−	0.992122i	$-0.539981\pi$
$293$	4347.55	−	4347.55i	0.866849	−	0.866849i	0.992122	+	0.125273i	$0.0399808\pi$
$294$		0			0
$295$		0			0
$296$		−	4083.51i		−	0.801856i
$297$		0			0
$298$	5613.84	+	5613.84i	1.09128	+	1.09128i
$299$	2218.31			0.429058
$300$		0			0
$301$	−835.200			−0.159934
$302$	6051.39	+	6051.39i	1.15304	+	1.15304i
$303$		0			0
$304$		−	13321.3i		−	2.51326i
$305$		0			0
$306$		0			0
$307$	−3137.18	+	3137.18i	−0.583220	+	0.583220i	−0.935787	−	0.352567i	$-0.885309\pi$
$307$	−3137.18	+	3137.18i	−0.583220	+	0.583220i	0.352567	+	0.935787i	$0.385309\pi$
$308$	−1675.57	+	1675.57i	−0.309983	+	0.309983i
$309$		0			0
$310$		0			0
$311$		−	8268.00i		−	1.50751i	−0.657157	−	0.753754i	$-0.728241\pi$
$311$		−	8268.00i		−	1.50751i	0.657157	−	0.753754i	$-0.271759\pi$
$312$		0			0
$313$	4673.46	+	4673.46i	0.843959	+	0.843959i	0.989371	−	0.145412i	$-0.0464507\pi$
$313$	4673.46	+	4673.46i	0.843959	+	0.843959i	−0.145412	+	0.989371i	$0.546451\pi$
$314$	−3424.95			−0.615544
$315$		0			0
$316$	5765.75			1.02642
$317$	3271.78	+	3271.78i	0.579690	+	0.579690i	0.934818	−	0.355128i	$-0.115563\pi$
$317$	3271.78	+	3271.78i	0.579690	+	0.579690i	−0.355128	+	0.934818i	$0.615563\pi$
$318$		0			0
$319$			9318.09i			1.63546i
$320$		0			0
$321$		0			0
$322$	−808.350	+	808.350i	−0.139899	+	0.139899i
$323$	−1085.54	+	1085.54i	−0.187001	+	0.187001i
$324$		0			0
$325$		0			0
$326$			10749.4i			1.82624i
$327$		0			0
$328$	13877.1	+	13877.1i	2.33608	+	2.33608i
$329$	640.349			0.107306
$330$		0			0
$331$	9665.06			1.60495			0.802477	−	0.596684i	$-0.203515\pi$
$331$	9665.06			1.60495			0.802477	+	0.596684i	$0.203515\pi$
$332$	−19041.9	−	19041.9i	−3.14777	−	3.14777i
$333$		0			0
$334$		−	8463.70i		−	1.38657i
$335$		0			0
$336$		0			0
$337$	−1911.95	+	1911.95i	−0.309053	+	0.309053i	−0.844542	−	0.535489i	$-0.820127\pi$
$337$	−1911.95	+	1911.95i	−0.309053	+	0.309053i	0.535489	+	0.844542i	$0.320127\pi$
$338$	−5637.85	+	5637.85i	−0.907274	+	0.907274i
$339$		0			0
$340$		0			0
$341$			2283.44i			0.362625i
$342$		0			0
$343$	−1229.46	−	1229.46i	−0.193540	−	0.193540i
$344$	20914.9			3.27806
$345$		0			0
$346$	12417.9			1.92945
$347$	−7023.71	−	7023.71i	−1.08661	−	1.08661i	−0.995875	−	0.0907318i	$-0.971079\pi$
$347$	−7023.71	−	7023.71i	−1.08661	−	1.08661i	−0.0907318	−	0.995875i	$-0.528921\pi$
$348$		0			0
$349$			9259.70i			1.42023i	0.704085	+	0.710115i	$0.251357\pi$
$349$			9259.70i			1.42023i	−0.704085	+	0.710115i	$0.748643\pi$
$350$		0			0
$351$		0			0
$352$	14196.3	−	14196.3i	2.14962	−	2.14962i
$353$	−4338.33	+	4338.33i	−0.654125	+	0.654125i	−0.953984	−	0.299859i	$-0.903060\pi$
$353$	−4338.33	+	4338.33i	−0.654125	+	0.654125i	0.299859	+	0.953984i	$0.403060\pi$
$354$		0			0
$355$		0			0
$356$		−	13831.3i		−	2.05915i
$357$		0			0
$358$	−5431.64	−	5431.64i	−0.801874	−	0.801874i
$359$	−5949.44			−0.874650			−0.437325	−	0.899304i	$-0.644074\pi$
$359$	−5949.44			−0.874650			−0.437325	+	0.899304i	$0.644074\pi$
$360$		0			0
$361$	1315.05			0.191726
$362$	4198.34	+	4198.34i	0.609557	+	0.609557i
$363$		0			0
$364$			1353.08i			0.194837i
$365$		0			0
$366$		0			0
$367$	9153.79	−	9153.79i	1.30197	−	1.30197i	0.374912	−	0.927061i	$-0.377673\pi$
$367$	9153.79	−	9153.79i	1.30197	−	1.30197i	0.927061	−	0.374912i	$-0.122327\pi$
$368$	10663.2	−	10663.2i	1.51048	−	1.51048i
$369$		0			0
$370$		0			0
$371$		−	308.079i		−	0.0431123i
$372$		0			0
$373$	6473.68	+	6473.68i	0.898644	+	0.898644i	0.995316	−	0.0966723i	$-0.0308199\pi$
$373$	6473.68	+	6473.68i	0.898644	+	0.898644i	−0.0966723	+	0.995316i	$0.530820\pi$
$374$	−5036.72			−0.696370
$375$		0			0
$376$	−16035.4			−2.19937
$377$	3762.33	+	3762.33i	0.513979	+	0.513979i
$378$		0			0
$379$		−	245.031i		−	0.0332094i	−0.999862	−	0.0166047i	$-0.994714\pi$
$379$		−	245.031i		−	0.0332094i	0.999862	−	0.0166047i	$-0.00528569\pi$
$380$		0			0
$381$		0			0
$382$	−14344.7	+	14344.7i	−1.92131	+	1.92131i
$383$	4476.48	−	4476.48i	0.597225	−	0.597225i	−0.342348	−	0.939573i	$-0.611222\pi$
$383$	4476.48	−	4476.48i	0.597225	−	0.597225i	0.939573	+	0.342348i	$0.111222\pi$
$384$		0			0
$385$		0			0
$386$			13438.2i			1.77199i
$387$		0			0
$388$	−18497.0	−	18497.0i	−2.42022	−	2.42022i
$389$	4429.26			0.577307			0.288654	−	0.957434i	$-0.406792\pi$
$389$	4429.26			0.577307			0.288654	+	0.957434i	$0.406792\pi$
$390$		0			0
$391$	−1737.87			−0.224777
$392$	15245.5	+	15245.5i	1.96432	+	1.96432i
$393$		0			0
$394$		−	16655.5i		−	2.12967i
$395$		0			0
$396$		0			0
$397$	−4786.16	+	4786.16i	−0.605065	+	0.605065i	−0.941652	−	0.336588i	$-0.890727\pi$
$397$	−4786.16	+	4786.16i	−0.605065	+	0.605065i	0.336588	+	0.941652i	$0.390727\pi$
$398$	−5327.19	+	5327.19i	−0.670925	+	0.670925i
$399$		0			0
$400$		0			0
$401$		−	4521.85i		−	0.563119i	−0.959544	−	0.281559i	$-0.909148\pi$
$401$		−	4521.85i		−	0.563119i	0.959544	−	0.281559i	$-0.0908516\pi$
$402$		0			0
$403$	921.977	+	921.977i	0.113963	+	0.113963i
$404$	−20460.8			−2.51971
$405$		0			0
$406$	−2741.98			−0.335178
$407$	−2076.82	−	2076.82i	−0.252934	−	0.252934i
$408$		0			0
$409$			10162.9i			1.22866i	0.789048	+	0.614331i	$0.210574\pi$
$409$			10162.9i			1.22866i	−0.789048	+	0.614331i	$0.789426\pi$
$410$		0			0
$411$		0			0
$412$	−7671.76	+	7671.76i	−0.917379	+	0.917379i
$413$	598.710	−	598.710i	0.0713331	−	0.0713331i
$414$		0			0
$415$		0			0
$416$		−	11464.0i		−	1.35113i
$417$		0			0
$418$	−12861.4	−	12861.4i	−1.50496	−	1.50496i
$419$	−13243.2			−1.54409			−0.772044	−	0.635569i	$-0.780766\pi$
$419$	−13243.2			−1.54409			−0.772044	+	0.635569i	$0.780766\pi$
$420$		0			0
$421$	−7488.37			−0.866891			−0.433445	−	0.901180i	$-0.642702\pi$
$421$	−7488.37			−0.866891			−0.433445	+	0.901180i	$0.642702\pi$
$422$	−4248.69	−	4248.69i	−0.490102	−	0.490102i
$423$		0			0
$424$			7714.83i			0.883644i
$425$		0			0
$426$		0			0
$427$	−1227.99	+	1227.99i	−0.139172	+	0.139172i
$428$	−234.970	+	234.970i	−0.0265367	+	0.0265367i
$429$		0			0
$430$		0			0
$431$			5842.63i			0.652969i	0.945202	+	0.326485i	$0.105864\pi$
$431$			5842.63i			0.652969i	−0.945202	+	0.326485i	$0.894136\pi$
$432$		0			0
$433$	5310.04	+	5310.04i	0.589340	+	0.589340i	0.937453	−	0.348112i	$-0.113177\pi$
$433$	5310.04	+	5310.04i	0.589340	+	0.589340i	−0.348112	+	0.937453i	$0.613177\pi$
$434$	−671.934			−0.0743177
$435$		0			0
$436$	−27062.1			−2.97257
$437$	−4437.70	−	4437.70i	−0.485776	−	0.485776i
$438$		0			0
$439$			10440.4i			1.13506i	0.823352	+	0.567530i	$0.192101\pi$
$439$			10440.4i			1.13506i	−0.823352	+	0.567530i	$0.807899\pi$
$440$		0			0
$441$		0			0
$442$	−2033.66	+	2033.66i	−0.218849	+	0.218849i
$443$	2729.46	−	2729.46i	0.292732	−	0.292732i	−0.545426	−	0.838159i	$-0.683632\pi$
$443$	2729.46	−	2729.46i	0.292732	−	0.292732i	0.838159	+	0.545426i	$0.183632\pi$
$444$		0			0
$445$		0			0
$446$			4995.38i			0.530355i
$447$		0			0
$448$	1587.57	+	1587.57i	0.167423	+	0.167423i
$449$	2227.63			0.234139			0.117070	−	0.993124i	$-0.462650\pi$
$449$	2227.63			0.234139			0.117070	+	0.993124i	$0.462650\pi$
$450$		0			0
$451$	14115.4			1.47377
$452$	13613.6	+	13613.6i	1.41666	+	1.41666i
$453$		0			0
$454$			17187.0i			1.77670i
$455$		0			0
$456$		0			0
$457$	−4328.64	+	4328.64i	−0.443075	+	0.443075i	−0.893044	−	0.449969i	$-0.851435\pi$
$457$	−4328.64	+	4328.64i	−0.443075	+	0.443075i	0.449969	+	0.893044i	$0.351435\pi$
$458$	−9501.96	+	9501.96i	−0.969427	+	0.969427i
$459$		0			0
$460$		0			0
$461$			8223.98i			0.830865i	0.909624	+	0.415433i	$0.136370\pi$
$461$			8223.98i			0.830865i	−0.909624	+	0.415433i	$0.863630\pi$
$462$		0			0
$463$	2611.01	+	2611.01i	0.262082	+	0.262082i	0.825899	−	0.563817i	$-0.190668\pi$
$463$	2611.01	+	2611.01i	0.262082	+	0.262082i	−0.563817	+	0.825899i	$0.690668\pi$
$464$	36170.2			3.61888
$465$		0			0
$466$	−12740.0			−1.26646
$467$	−12010.6	−	12010.6i	−1.19012	−	1.19012i	−0.977034	−	0.213085i	$-0.931649\pi$
$467$	−12010.6	−	12010.6i	−1.19012	−	1.19012i	−0.213085	−	0.977034i	$-0.568351\pi$
$468$		0			0
$469$		−	2737.29i		−	0.269501i
$470$		0			0
$471$		0			0
$472$	−14992.7	+	14992.7i	−1.46207	+	1.46207i
$473$	10637.0	−	10637.0i	1.03402	−	1.03402i
$474$		0			0
$475$		0			0
$476$		−	1060.03i		−	0.102072i
$477$		0			0
$478$	14797.5	+	14797.5i	1.41595	+	1.41595i
$479$	6186.30			0.590103			0.295051	−	0.955481i	$-0.404663\pi$
$479$	6186.30			0.590103			0.295051	+	0.955481i	$0.404663\pi$
$480$		0			0
$481$	−1677.10			−0.158980
$482$	9171.42	+	9171.42i	0.866694	+	0.866694i
$483$		0			0
$484$		−	15939.1i		−	1.49691i
$485$		0			0
$486$		0			0
$487$	12791.1	−	12791.1i	1.19019	−	1.19019i	0.213173	−	0.977015i	$-0.431620\pi$
$487$	12791.1	−	12791.1i	1.19019	−	1.19019i	0.977015	−	0.213173i	$-0.0683797\pi$
$488$	30750.9	−	30750.9i	2.85251	−	2.85251i
$489$		0			0
$490$		0			0
$491$		−	13622.3i		−	1.25207i	−0.779796	−	0.626034i	$-0.784677\pi$
$491$		−	13622.3i		−	1.25207i	0.779796	−	0.626034i	$-0.215323\pi$
$492$		0			0
$493$	−2947.48	−	2947.48i	−0.269265	−	0.269265i
$494$	−10386.0			−0.945931
$495$		0			0
$496$	8863.68			0.802401
$497$	−181.427	−	181.427i	−0.0163744	−	0.0163744i
$498$		0			0
$499$		−	15358.5i		−	1.37784i	−0.724837	−	0.688920i	$-0.758085\pi$
$499$		−	15358.5i		−	1.37784i	0.724837	−	0.688920i	$-0.241915\pi$
$500$		0			0
$501$		0			0
$502$	17823.2	−	17823.2i	1.58464	−	1.58464i
$503$	−9784.44	+	9784.44i	−0.867329	+	0.867329i	−0.992176	−	0.124847i	$-0.960156\pi$
$503$	−9784.44	+	9784.44i	−0.867329	+	0.867329i	0.124847	+	0.992176i	$0.460156\pi$
$504$		0			0
$505$		0			0
$506$		−	20590.1i		−	1.80898i
$507$		0			0
$508$	24530.4	+	24530.4i	2.14244	+	2.14244i
$509$	5300.61			0.461583			0.230791	−	0.973003i	$-0.425869\pi$
$509$	5300.61			0.461583			0.230791	+	0.973003i	$0.425869\pi$
$510$		0			0
$511$	2124.04			0.183879
$512$	9749.34	+	9749.34i	0.841532	+	0.841532i
$513$		0			0
$514$			8449.89i			0.725114i
$515$		0			0
$516$		0			0
$517$	−8155.41	+	8155.41i	−0.693761	+	0.693761i
$518$	611.134	−	611.134i	0.0518372	−	0.0518372i
$519$		0			0
$520$		0			0
$521$			8512.67i			0.715829i	0.933754	+	0.357915i	$0.116512\pi$
$521$			8512.67i			0.715829i	−0.933754	+	0.357915i	$0.883488\pi$
$522$		0			0
$523$	−7880.88	−	7880.88i	−0.658904	−	0.658904i	0.296217	−	0.955121i	$-0.404275\pi$
$523$	−7880.88	−	7880.88i	−0.658904	−	0.658904i	−0.955121	+	0.296217i	$0.904275\pi$
$524$	−4319.96			−0.360149
$525$		0			0
$526$	2688.02			0.222819
$527$	−722.293	−	722.293i	−0.0597032	−	0.0597032i
$528$		0			0
$529$			5062.61i			0.416093i
$530$		0			0
$531$		0			0
$532$	2706.82	−	2706.82i	0.220593	−	0.220593i
$533$	5699.33	−	5699.33i	0.463162	−	0.463162i
$534$		0			0
$535$		0			0
$536$			68546.4i			5.52379i
$537$		0			0
$538$	−14332.8	−	14332.8i	−1.14857	−	1.14857i
$539$	15507.3			1.23923
$540$		0			0
$541$	8961.43			0.712166			0.356083	−	0.934454i	$-0.384112\pi$
$541$	8961.43			0.712166			0.356083	+	0.934454i	$0.384112\pi$
$542$	−2007.07	−	2007.07i	−0.159061	−	0.159061i
$543$		0			0
$544$			8981.10i			0.707833i
$545$		0			0
$546$		0			0
$547$	−13458.8	+	13458.8i	−1.05203	+	1.05203i	−0.0534553	+	0.998570i	$0.517023\pi$
$547$	−13458.8	+	13458.8i	−1.05203	+	1.05203i	−0.998570	+	0.0534553i	$0.982977\pi$
$548$	−17639.0	+	17639.0i	−1.37500	+	1.37500i
$549$		0			0
$550$		0			0
$551$		−	15053.0i		−	1.16385i
$552$		0			0
$553$	519.296	+	519.296i	0.0399325	+	0.0399325i
$554$	8305.52			0.636946
$555$		0			0
$556$	50018.2			3.81519
$557$	12265.3	+	12265.3i	0.933031	+	0.933031i	0.997894	−	0.0648635i	$-0.0206612\pi$
$557$	12265.3	+	12265.3i	0.933031	+	0.933031i	−0.0648635	+	0.997894i	$0.520661\pi$
$558$		0			0
$559$		−	8589.74i		−	0.649924i
$560$		0			0
$561$		0			0
$562$	12891.8	−	12891.8i	0.967630	−	0.967630i
$563$	−10874.1	+	10874.1i	−0.814011	+	0.814011i	−0.985233	−	0.171222i	$-0.945229\pi$
$563$	−10874.1	+	10874.1i	−0.814011	+	0.814011i	0.171222	+	0.985233i	$0.445229\pi$
$564$		0			0
$565$		0			0
$566$			20433.2i			1.51744i
$567$		0			0
$568$	4543.24	+	4543.24i	0.335616	+	0.335616i
$569$	−5162.54			−0.380360			−0.190180	−	0.981749i	$-0.560907\pi$
$569$	−5162.54			−0.380360			−0.190180	+	0.981749i	$0.560907\pi$
$570$		0			0
$571$	6356.12			0.465842			0.232921	−	0.972496i	$-0.425172\pi$
$571$	6356.12			0.465842			0.232921	+	0.972496i	$0.425172\pi$
$572$	−17232.7	−	17232.7i	−1.25968	−	1.25968i
$573$		0			0
$574$			4153.66i			0.302039i
$575$		0			0
$576$		0			0
$577$	7183.63	−	7183.63i	0.518299	−	0.518299i	−0.398758	−	0.917056i	$-0.630559\pi$
$577$	7183.63	−	7183.63i	0.518299	−	0.518299i	0.917056	+	0.398758i	$0.130559\pi$
$578$	−16819.3	+	16819.3i	−1.21037	+	1.21037i
$579$		0			0
$580$		0			0
$581$		−	3430.04i		−	0.244926i
$582$		0			0
$583$	3923.66	+	3923.66i	0.278733	+	0.278733i
$584$	−53189.6			−3.76884
$585$		0			0
$586$	−32586.8			−2.29718
$587$	6007.01	+	6007.01i	0.422378	+	0.422378i	0.886022	−	0.463644i	$-0.153458\pi$
$587$	6007.01	+	6007.01i	0.422378	+	0.422378i	−0.463644	+	0.886022i	$0.653458\pi$
$588$		0			0
$589$		−	3688.81i		−	0.258055i
$590$		0			0
$591$		0			0
$592$	−8061.64	+	8061.64i	−0.559681	+	0.559681i
$593$	0.276387	−	0.276387i	1.91397e−5	−	1.91397e-5i	−0.707097	−	0.707116i	$-0.749996\pi$
$593$	0.276387	−	0.276387i	1.91397e−5	−	1.91397e-5i	0.707116	+	0.707097i	$0.249996\pi$
$594$		0			0
$595$		0			0
$596$		−	30094.7i		−	2.06833i
$597$		0			0
$598$	−8313.59	−	8313.59i	−0.568509	−	0.568509i
$599$	792.766			0.0540761			0.0270380	−	0.999634i	$-0.491392\pi$
$599$	792.766			0.0540761			0.0270380	+	0.999634i	$0.491392\pi$
$600$		0			0
$601$	−6779.60			−0.460142			−0.230071	−	0.973174i	$-0.573896\pi$
$601$	−6779.60			−0.460142			−0.230071	+	0.973174i	$0.573896\pi$
$602$	3130.09	+	3130.09i	0.211915	+	0.211915i
$603$		0			0
$604$		−	32440.3i		−	2.18539i
$605$		0			0
$606$		0			0
$607$	14598.9	−	14598.9i	0.976194	−	0.976194i	−0.0235289	−	0.999723i	$-0.507490\pi$
$607$	14598.9	−	14598.9i	0.976194	−	0.976194i	0.999723	+	0.0235289i	$0.00749016\pi$
$608$	−22933.6	+	22933.6i	−1.52974	+	1.52974i
$609$		0			0
$610$		0			0
$611$			6585.76i			0.436058i
$612$		0			0
$613$	−9862.97	−	9862.97i	−0.649856	−	0.649856i	0.303102	−	0.952958i	$-0.401978\pi$
$613$	−9862.97	−	9862.97i	−0.649856	−	0.649856i	−0.952958	+	0.303102i	$0.901978\pi$
$614$	23514.5			1.54555
$615$		0			0
$616$	7558.17			0.494363
$617$	10135.5	+	10135.5i	0.661329	+	0.661329i	0.955693	−	0.294364i	$-0.0951078\pi$
$617$	10135.5	+	10135.5i	0.661329	+	0.661329i	−0.294364	+	0.955693i	$0.595108\pi$
$618$		0			0
$619$		−	27282.6i		−	1.77153i	−0.464132	−	0.885766i	$-0.653634\pi$
$619$		−	27282.6i		−	1.77153i	0.464132	−	0.885766i	$-0.346366\pi$
$620$		0			0
$621$		0			0
$622$	−30986.1	+	30986.1i	−1.99747	+	1.99747i
$623$	1245.72	−	1245.72i	0.0801106	−	0.0801106i
$624$		0			0
$625$		0			0
$626$		−	35029.5i		−	2.23652i
$627$		0			0
$628$	9180.22	+	9180.22i	0.583329	+	0.583329i
$629$	1313.87			0.0832869
$630$		0			0
$631$	−28414.9			−1.79268			−0.896340	−	0.443368i	$-0.853783\pi$
$631$	−28414.9			−1.79268			−0.896340	+	0.443368i	$0.853783\pi$
$632$	−13004.1	−	13004.1i	−0.818471	−	0.818471i
$633$		0			0
$634$		−	24523.4i		−	1.53620i
$635$		0			0
$636$		0			0
$637$	6261.33	−	6261.33i	0.389455	−	0.389455i
$638$	34921.5	−	34921.5i	2.16702	−	2.16702i
$639$		0			0
$640$		0			0
$641$			26402.3i			1.62688i	0.581650	+	0.813439i	$0.302407\pi$
$641$			26402.3i			1.62688i	−0.581650	+	0.813439i	$0.697593\pi$
$642$		0			0
$643$	2361.97	+	2361.97i	0.144863	+	0.144863i	0.775819	−	0.630956i	$-0.217337\pi$
$643$	2361.97	+	2361.97i	0.144863	+	0.144863i	−0.630956	+	0.775819i	$0.717337\pi$
$644$	4333.40			0.265155
$645$		0			0
$646$	8136.61			0.495558
$647$	−11204.5	−	11204.5i	−0.680826	−	0.680826i	0.279360	−	0.960186i	$-0.409878\pi$
$647$	−11204.5	−	11204.5i	−0.680826	−	0.680826i	−0.960186	+	0.279360i	$0.909878\pi$
$648$		0			0
$649$			15250.2i			0.922377i
$650$		0			0
$651$		0			0
$652$	28812.7	−	28812.7i	1.73066	−	1.73066i
$653$	18407.7	−	18407.7i	1.10314	−	1.10314i	0.109108	−	0.994030i	$-0.465201\pi$
$653$	18407.7	−	18407.7i	1.10314	−	1.10314i	0.994030	−	0.109108i	$-0.0347995\pi$
$654$		0			0
$655$		0			0
$656$		−	54792.0i		−	3.26108i
$657$		0			0
$658$	−2399.84	−	2399.84i	−0.142182	−	0.142182i
$659$	−8165.28			−0.482662			−0.241331	−	0.970443i	$-0.577584\pi$
$659$	−8165.28			−0.482662			−0.241331	+	0.970443i	$0.577584\pi$
$660$		0			0
$661$	−16725.1			−0.984163			−0.492082	−	0.870549i	$-0.663764\pi$
$661$	−16725.1			−0.984163			−0.492082	+	0.870549i	$0.663764\pi$
$662$	−36221.9	−	36221.9i	−2.12659	−	2.12659i
$663$		0			0
$664$			85894.2i			5.02009i
$665$		0			0
$666$		0			0
$667$	12049.3	−	12049.3i	0.699476	−	0.699476i
$668$	−22686.1	+	22686.1i	−1.31400	+	1.31400i
$669$		0			0
$670$		0			0
$671$		−	31279.0i		−	1.79957i
$672$		0			0
$673$	−321.610	−	321.610i	−0.0184208	−	0.0184208i	0.697836	−	0.716257i	$-0.254146\pi$
$673$	−321.610	−	321.610i	−0.0184208	−	0.0184208i	−0.716257	+	0.697836i	$0.754146\pi$
$674$	14330.9			0.819000
$675$		0			0
$676$	30223.4			1.71958
$677$	4497.58	+	4497.58i	0.255326	+	0.255326i	0.823150	−	0.567824i	$-0.192215\pi$
$677$	4497.58	+	4497.58i	0.255326	+	0.255326i	−0.567824	+	0.823150i	$0.692215\pi$
$678$		0			0
$679$		−	3331.89i		−	0.188316i
$680$		0			0
$681$		0			0
$682$	8557.68	−	8557.68i	0.480485	−	0.480485i
$683$	−7479.00	+	7479.00i	−0.418999	+	0.418999i	−0.884859	−	0.465860i	$-0.845745\pi$
$683$	−7479.00	+	7479.00i	−0.418999	+	0.418999i	0.465860	+	0.884859i	$0.345745\pi$
$684$		0			0
$685$		0			0
$686$			9215.30i			0.512889i
$687$		0			0
$688$	−41289.9	−	41289.9i	−2.28803	−	2.28803i
$689$	3168.48			0.175195
$690$		0			0
$691$	−22650.6			−1.24699			−0.623496	−	0.781827i	$-0.714288\pi$
$691$	−22650.6			−1.24699			−0.623496	+	0.781827i	$0.714288\pi$
$692$	−33284.8	−	33284.8i	−1.82847	−	1.82847i
$693$		0			0
$694$			52645.7i			2.87955i
$695$		0			0
$696$		0			0
$697$	−4464.96	+	4464.96i	−0.242643	+	0.242643i
$698$	34702.7	−	34702.7i	1.88183	−	1.88183i
$699$		0			0
$700$		0			0
$701$		−	1858.50i		−	0.100135i	−0.998746	−	0.0500676i	$-0.984056\pi$
$701$		−	1858.50i		−	0.100135i	0.998746	−	0.0500676i	$-0.0159437\pi$
$702$		0			0
$703$	3355.02	+	3355.02i	0.179996	+	0.179996i
$704$	−40438.2			−2.16487
$705$		0			0
$706$	32517.6			1.73345
$707$	−1842.82	−	1842.82i	−0.0980286	−	0.0980286i
$708$		0			0
$709$		−	14344.6i		−	0.759836i	−0.925020	−	0.379918i	$-0.875952\pi$
$709$		−	14344.6i		−	0.759836i	0.925020	−	0.379918i	$-0.124048\pi$
$710$		0			0
$711$		0			0
$712$	−31195.1	+	31195.1i	−1.64197	+	1.64197i
$713$	2952.74	−	2952.74i	0.155092	−	0.155092i
$714$		0			0
$715$		0			0
$716$			29117.9i			1.51981i
$717$		0			0
$718$	22296.8	+	22296.8i	1.15893	+	1.15893i
$719$	10128.2			0.525337			0.262669	−	0.964886i	$-0.415397\pi$
$719$	10128.2			0.525337			0.262669	+	0.964886i	$0.415397\pi$
$720$		0			0
$721$	−1381.92			−0.0713807
$722$	−4928.43	−	4928.43i	−0.254040	−	0.254040i
$723$		0			0
$724$		−	22506.4i		−	1.15531i
$725$		0			0
$726$		0			0
$727$	−15769.7	+	15769.7i	−0.804490	+	0.804490i	−0.983794	−	0.179304i	$-0.942615\pi$
$727$	−15769.7	+	15769.7i	−0.804490	+	0.804490i	0.179304	+	0.983794i	$0.442615\pi$
$728$	3051.74	−	3051.74i	0.155364	−	0.155364i
$729$		0			0
$730$		0			0
$731$			6729.36i			0.340485i
$732$		0			0
$733$	−22982.0	−	22982.0i	−1.15806	−	1.15806i	−0.984892	−	0.173169i	$-0.944599\pi$
$733$	−22982.0	−	22982.0i	−1.15806	−	1.15806i	−0.173169	−	0.984892i	$-0.555401\pi$
$734$	−68611.5			−3.45027
$735$		0			0
$736$	−36714.7			−1.83875
$737$	34861.8	+	34861.8i	1.74240	+	1.74240i
$738$		0			0
$739$			1989.79i			0.0990467i	0.998773	+	0.0495234i	$0.0157702\pi$
$739$			1989.79i			0.0990467i	−0.998773	+	0.0495234i	$0.984230\pi$
$740$		0			0
$741$		0			0
$742$	−1154.59	+	1154.59i	−0.0571245	+	0.0571245i
$743$	−4460.57	+	4460.57i	−0.220246	+	0.220246i	−0.808602	−	0.588356i	$-0.799775\pi$
$743$	−4460.57	+	4460.57i	−0.220246	+	0.220246i	0.588356	+	0.808602i	$0.299775\pi$
$744$		0			0
$745$		0			0
$746$		−	48523.0i		−	2.38144i
$747$		0			0
$748$	13500.4	+	13500.4i	0.659924	+	0.659924i
$749$	−42.3254			−0.00206480
$750$		0			0
$751$	7038.34			0.341988			0.170994	−	0.985272i	$-0.445302\pi$
$751$	7038.34			0.341988			0.170994	+	0.985272i	$0.445302\pi$
$752$	31657.0	+	31657.0i	1.53512	+	1.53512i
$753$		0			0
$754$		−	28200.3i		−	1.36206i
$755$		0			0
$756$		0			0
$757$	8036.02	−	8036.02i	0.385831	−	0.385831i	−0.487366	−	0.873198i	$-0.662042\pi$
$757$	8036.02	−	8036.02i	0.385831	−	0.385831i	0.873198	+	0.487366i	$0.162042\pi$
$758$	−918.304	+	918.304i	−0.0440031	+	0.0440031i
$759$		0			0
$760$		0			0
$761$		−	11486.5i		−	0.547154i	−0.961850	−	0.273577i	$-0.911793\pi$
$761$		−	11486.5i		−	0.547154i	0.961850	−	0.273577i	$-0.0882068\pi$
$762$		0			0
$763$	−2437.36	−	2437.36i	−0.115647	−	0.115647i
$764$	76899.0			3.64150
$765$		0			0
$766$	−33553.1			−1.58267
$767$	6157.52	+	6157.52i	0.289876	+	0.289876i
$768$		0			0
$769$		−	11244.4i		−	0.527289i	−0.964620	−	0.263644i	$-0.915075\pi$
$769$		−	11244.4i		−	0.527289i	0.964620	−	0.263644i	$-0.0849245\pi$
$770$		0			0
$771$		0			0
$772$	36019.7	−	36019.7i	1.67925	−	1.67925i
$773$	−21176.6	+	21176.6i	−0.985341	+	0.985341i	−0.999894	−	0.0145529i	$-0.995367\pi$
$773$	−21176.6	+	21176.6i	−0.985341	+	0.985341i	0.0145529	+	0.999894i	$0.495367\pi$
$774$		0			0
$775$		0			0
$776$			83436.4i			3.85978i
$777$		0			0
$778$	−16599.6	−	16599.6i	−0.764942	−	0.764942i
$779$	−22802.9			−1.04878
$780$		0			0
$781$	4621.26			0.211731
$782$	6513.02	+	6513.02i	0.297833	+	0.297833i
$783$		0			0
$784$		−	60195.0i		−	2.74212i
$785$		0			0
$786$		0			0
$787$	1608.25	−	1608.25i	0.0728437	−	0.0728437i	−0.669746	−	0.742590i	$-0.733597\pi$
$787$	1608.25	−	1608.25i	0.0728437	−	0.0728437i	0.742590	+	0.669746i	$0.233597\pi$
$788$	−44643.3	+	44643.3i	−2.01821	+	2.01821i
$789$		0			0
$790$		0			0
$791$			2452.24i			0.110229i
$792$		0			0
$793$	−12629.4	−	12629.4i	−0.565553	−	0.565553i
$794$	35874.3			1.60344
$795$		0			0
$796$	28558.0			1.27162
$797$	−7418.34	−	7418.34i	−0.329700	−	0.329700i	0.522772	−	0.852472i	$-0.324898\pi$
$797$	−7418.34	−	7418.34i	−0.329700	−	0.329700i	−0.852472	+	0.522772i	$0.824898\pi$
$798$		0			0
$799$		−	5159.41i		−	0.228444i
$800$		0			0
$801$		0			0
$802$	−16946.6	+	16946.6i	−0.746142	+	0.746142i
$803$	−27051.5	+	27051.5i	−1.18883	+	1.18883i
$804$		0			0
$805$		0			0
$806$		−	6910.61i		−	0.302005i
$807$		0			0
$808$	46147.3	+	46147.3i	2.00923	+	2.00923i
$809$	1490.14			0.0647595			0.0323797	−	0.999476i	$-0.489691\pi$
$809$	1490.14			0.0647595			0.0323797	+	0.999476i	$0.489691\pi$
$810$		0			0
$811$	26161.5			1.13274			0.566371	−	0.824150i	$-0.308347\pi$
$811$	26161.5			1.13274			0.566371	+	0.824150i	$0.308347\pi$
$812$	7349.59	+	7349.59i	0.317636	+	0.317636i
$813$		0			0
$814$			15566.7i			0.670284i
$815$		0			0
$816$		0			0
$817$	−17183.7	+	17183.7i	−0.735839	+	0.735839i
$818$	38087.7	−	38087.7i	1.62800	−	1.62800i
$819$		0			0
$820$		0			0
$821$			21056.4i			0.895095i	0.894260	+	0.447548i	$0.147702\pi$
$821$			21056.4i			0.895095i	−0.894260	+	0.447548i	$0.852298\pi$
$822$		0			0
$823$	−187.614	−	187.614i	−0.00794631	−	0.00794631i	0.703122	−	0.711069i	$-0.251789\pi$
$823$	−187.614	−	187.614i	−0.00794631	−	0.00794631i	−0.711069	+	0.703122i	$0.751789\pi$
$824$	34605.7			1.46304
$825$		0			0
$826$	−4487.59			−0.189035
$827$	−10888.3	−	10888.3i	−0.457827	−	0.457827i	0.440114	−	0.897942i	$-0.354938\pi$
$827$	−10888.3	−	10888.3i	−0.457827	−	0.457827i	−0.897942	+	0.440114i	$0.854938\pi$
$828$		0			0
$829$			9441.85i			0.395572i	0.980245	+	0.197786i	$0.0633751\pi$
$829$			9441.85i			0.395572i	−0.980245	+	0.197786i	$0.936625\pi$
$830$		0			0
$831$		0			0
$832$	−16327.6	+	16327.6i	−0.680357	+	0.680357i
$833$	−4905.24	+	4905.24i	−0.204029	+	0.204029i
$834$		0			0
$835$		0			0
$836$			68947.5i			2.85239i
$837$		0			0
$838$	49631.8	+	49631.8i	2.04594	+	2.04594i
$839$	−25744.3			−1.05935			−0.529673	−	0.848202i	$-0.677685\pi$
$839$	−25744.3			−1.05935			−0.529673	+	0.848202i	$0.677685\pi$
$840$		0			0
$841$	16483.1			0.675840
$842$	28064.3	+	28064.3i	1.14865	+	1.14865i
$843$		0			0
$844$			22776.3i			0.928903i
$845$		0			0
$846$		0			0
$847$	1435.56	−	1435.56i	0.0582367	−	0.0582367i
$848$	15230.5	−	15230.5i	0.616768	−	0.616768i
$849$		0			0
$850$		0			0
$851$			5371.11i			0.216356i
$852$		0			0
$853$	32181.0	+	32181.0i	1.29174	+	1.29174i	0.933709	+	0.358033i	$0.116552\pi$
$853$	32181.0	+	32181.0i	1.29174	+	1.29174i	0.358033	+	0.933709i	$0.383448\pi$
$854$	9204.28			0.368810
$855$		0			0
$856$	1059.90			0.0423208
$857$	−15272.0	−	15272.0i	−0.608729	−	0.608729i	0.333885	−	0.942614i	$-0.391640\pi$
$857$	−15272.0	−	15272.0i	−0.608729	−	0.608729i	−0.942614	+	0.333885i	$0.891640\pi$
$858$		0			0
$859$			11140.0i			0.442484i	0.975219	+	0.221242i	$0.0710110\pi$
$859$			11140.0i			0.442484i	−0.975219	+	0.221242i	$0.928989\pi$
$860$		0			0
$861$		0			0
$862$	21896.5	−	21896.5i	0.865196	−	0.865196i
$863$	2425.86	−	2425.86i	0.0956863	−	0.0956863i	−0.657643	−	0.753330i	$-0.728447\pi$
$863$	2425.86	−	2425.86i	0.0956863	−	0.0956863i	0.753330	+	0.657643i	$0.228447\pi$
$864$		0			0
$865$		0			0
$866$		−	39801.0i		−	1.56177i
$867$		0			0
$868$	1801.05	+	1801.05i	0.0704282	+	0.0704282i
$869$	−13227.4			−0.516350
$870$		0			0
$871$	28152.0			1.09517
$872$	61035.7	+	61035.7i	2.37033	+	2.37033i
$873$		0			0
$874$			33262.5i			1.28732i
$875$		0			0
$876$		0			0
$877$	−28777.5	+	28777.5i	−1.10803	+	1.10803i	−0.114625	+	0.993409i	$0.536567\pi$
$877$	−28777.5	+	28777.5i	−1.10803	+	1.10803i	−0.993409	+	0.114625i	$0.963433\pi$
$878$	39127.5	−	39127.5i	1.50397	−	1.50397i
$879$		0			0
$880$		0			0
$881$			3701.33i			0.141545i	0.997492	+	0.0707724i	$0.0225464\pi$
$881$			3701.33i			0.141545i	−0.997492	+	0.0707724i	$0.977454\pi$
$882$		0			0
$883$	−30772.1	−	30772.1i	−1.17278	−	1.17278i	−0.981544	−	0.191236i	$-0.938751\pi$
$883$	−30772.1	−	30772.1i	−1.17278	−	1.17278i	−0.191236	−	0.981544i	$-0.561249\pi$
$884$	10902.0			0.414790
$885$		0			0
$886$	−20458.4			−0.775750
$887$	−12139.6	−	12139.6i	−0.459536	−	0.459536i	0.438967	−	0.898503i	$-0.355344\pi$
$887$	−12139.6	−	12139.6i	−0.459536	−	0.459536i	−0.898503	+	0.438967i	$0.855344\pi$
$888$		0			0
$889$			4418.69i			0.166702i
$890$		0			0
$891$		0			0
$892$	13389.6	−	13389.6i	0.502598	−	0.502598i
$893$	13174.7	−	13174.7i	0.493702	−	0.493702i
$894$		0			0
$895$		0			0
$896$		−	2982.15i		−	0.111190i
$897$		0			0
$898$	−8348.53	−	8348.53i	−0.310238	−	0.310238i
$899$	10015.9			0.371578
$900$		0			0
$901$	−2482.25			−0.0917821
$902$	−52900.5	−	52900.5i	−1.95276	−	1.95276i
$903$		0			0
$904$		−	61408.2i		−	2.25930i
$905$		0			0
$906$		0			0
$907$	316.892	−	316.892i	0.0116011	−	0.0116011i	−0.701282	−	0.712884i	$-0.747389\pi$
$907$	316.892	−	316.892i	0.0116011	−	0.0116011i	0.712884	+	0.701282i	$0.247389\pi$
$908$	46067.8	−	46067.8i	1.68372	−	1.68372i
$909$		0			0
$910$		0			0
$911$			15635.7i			0.568643i	0.958729	+	0.284321i	$0.0917683\pi$
$911$			15635.7i			0.568643i	−0.958729	+	0.284321i	$0.908232\pi$
$912$		0			0
$913$	43684.6	+	43684.6i	1.58352	+	1.58352i
$914$	32445.0			1.17416
$915$		0			0
$916$	50938.1			1.83738
$917$	−389.080	−	389.080i	−0.0140115	−	0.0140115i
$918$		0			0
$919$		−	7430.80i		−	0.266724i	−0.991067	−	0.133362i	$-0.957423\pi$
$919$		−	7430.80i		−	0.266724i	0.991067	−	0.133362i	$-0.0425773\pi$
$920$		0			0
$921$		0			0
$922$	30821.1	−	30821.1i	1.10091	−	1.10091i
$923$	1865.91	−	1865.91i	0.0665408	−	0.0665408i
$924$		0			0
$925$		0			0
$926$		−	19570.6i		−	0.694526i
$927$		0			0
$928$	−62269.5	−	62269.5i	−2.20269	−	2.20269i
$929$	889.629			0.0314185			0.0157092	−	0.999877i	$-0.494999\pi$
$929$	889.629			0.0314185			0.0157092	+	0.999877i	$0.494999\pi$
$930$		0			0
$931$	−25051.4			−0.881876
$932$	34148.2	+	34148.2i	1.20017	+	1.20017i
$933$		0			0
$934$			90024.8i			3.15386i
$935$		0			0
$936$		0			0
$937$	4028.44	−	4028.44i	0.140452	−	0.140452i	−0.633385	−	0.773837i	$-0.718335\pi$
$937$	4028.44	−	4028.44i	0.140452	−	0.140452i	0.773837	+	0.633385i	$0.218335\pi$
$938$	−10258.6	+	10258.6i	−0.357094	+	0.357094i
$939$		0			0
$940$		0			0
$941$			14232.9i			0.493072i	0.969134	+	0.246536i	$0.0792924\pi$
$941$			14232.9i			0.493072i	−0.969134	+	0.246536i	$0.920708\pi$
$942$		0			0
$943$	−18252.7	−	18252.7i	−0.630319	−	0.630319i
$944$	59197.0			2.04099
$945$		0			0
$946$	−79729.0			−2.74018
$947$	13637.1	+	13637.1i	0.467947	+	0.467947i	0.901249	−	0.433302i	$-0.142652\pi$
$947$	13637.1	+	13637.1i	0.467947	+	0.467947i	−0.433302	+	0.901249i	$0.642652\pi$
$948$		0			0
$949$			21845.0i			0.747227i
$950$		0			0
$951$		0			0
$952$	−2390.79	+	2390.79i	−0.0813927	+	0.0813927i
$953$	−10234.2	+	10234.2i	−0.347869	+	0.347869i	−0.859315	−	0.511446i	$-0.829110\pi$
$953$	−10234.2	+	10234.2i	−0.347869	+	0.347869i	0.511446	+	0.859315i	$0.329110\pi$
$954$		0			0
$955$		0			0
$956$		−	79326.5i		−	2.68368i
$957$		0			0
$958$	−23184.5	−	23184.5i	−0.781896	−	0.781896i
$959$	−3177.33			−0.106988
$960$		0			0
$961$	−27336.6			−0.917611
$962$	6285.29	+	6285.29i	0.210651	+	0.210651i
$963$		0			0
$964$		−	49166.1i		−	1.64267i
$965$		0			0
$966$		0			0
$967$	−7178.73	+	7178.73i	−0.238731	+	0.238731i	−0.816324	−	0.577594i	$-0.803992\pi$
$967$	−7178.73	+	7178.73i	−0.238731	+	0.238731i	0.577594	+	0.816324i	$0.303992\pi$
$968$	−35948.9	+	35948.9i	−1.19364	+	1.19364i
$969$		0			0
$970$		0			0
$971$			43718.0i			1.44488i	0.691434	+	0.722440i	$0.256979\pi$
$971$			43718.0i			1.44488i	−0.691434	+	0.722440i	$0.743021\pi$
$972$		0			0
$973$	4504.92	+	4504.92i	0.148429	+	0.148429i
$974$	−95875.0			−3.15404
$975$		0			0
$976$	−121416.			−3.98201
$977$	−36446.0	−	36446.0i	−1.19346	−	1.19346i	−0.976089	−	0.217371i	$-0.930252\pi$
$977$	−36446.0	−	36446.0i	−1.19346	−	1.19346i	−0.217371	−	0.976089i	$-0.569748\pi$
$978$		0			0
$979$			31730.8i			1.03587i
$980$		0			0
$981$		0			0
$982$	−51052.5	+	51052.5i	−1.65901	+	1.65901i
$983$	28612.6	−	28612.6i	0.928382	−	0.928382i	−0.0692194	−	0.997601i	$-0.522051\pi$
$983$	28612.6	−	28612.6i	0.928382	−	0.928382i	0.997601	+	0.0692194i	$0.0220508\pi$
$984$		0			0
$985$		0			0
$986$			22092.6i			0.713562i
$987$		0			0
$988$	27838.7	+	27838.7i	0.896424	+	0.896424i
$989$	−27509.6			−0.884485
$990$		0			0
$991$	56452.4			1.80956			0.904778	−	0.425884i	$-0.140037\pi$
$991$	56452.4			1.80956			0.904778	+	0.425884i	$0.140037\pi$
$992$	−15259.4	−	15259.4i	−0.488394	−	0.488394i
$993$		0			0
$994$			1359.87i			0.0433928i
$995$		0			0
$996$		0			0
$997$	−19121.4	+	19121.4i	−0.607402	+	0.607402i	−0.942266	−	0.334864i	$-0.891310\pi$
$997$	−19121.4	+	19121.4i	−0.607402	+	0.607402i	0.334864	+	0.942266i	$0.391310\pi$
$998$	−57559.4	+	57559.4i	−1.82566	+	1.82566i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.f.c.143.1		12
3.2	odd	2	inner	225.4.f.c.143.6		12
5.2	odd	4	inner	225.4.f.c.107.6		12
5.3	odd	4		45.4.f.a.17.1	yes	12
5.4	even	2		45.4.f.a.8.6	yes	12
15.2	even	4	inner	225.4.f.c.107.1		12
15.8	even	4		45.4.f.a.17.6	yes	12
15.14	odd	2		45.4.f.a.8.1	✓	12
20.3	even	4		720.4.w.d.17.3		12
20.19	odd	2		720.4.w.d.593.4		12
60.23	odd	4		720.4.w.d.17.4		12
60.59	even	2		720.4.w.d.593.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.f.a.8.1	✓	12	15.14	odd	2
45.4.f.a.8.6	yes	12	5.4	even	2
45.4.f.a.17.1	yes	12	5.3	odd	4
45.4.f.a.17.6	yes	12	15.8	even	4
225.4.f.c.107.1		12	15.2	even	4	inner
225.4.f.c.107.6		12	5.2	odd	4	inner
225.4.f.c.143.1		12	1.1	even	1	trivial
225.4.f.c.143.6		12	3.2	odd	2	inner
720.4.w.d.17.3		12	20.3	even	4
720.4.w.d.17.4		12	60.23	odd	4
720.4.w.d.593.3		12	60.59	even	2
720.4.w.d.593.4		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-3.74771 - 3.74771i) q^{2} +20.0907i q^{4} +(-1.80948 + 1.80948i) q^{7} +(45.3126 - 45.3126i) q^{8} +O(q^{10})\)	\(q+(-3.74771 - 3.74771i) q^{2} +20.0907i q^{4} +(-1.80948 + 1.80948i) q^{7} +(45.3126 - 45.3126i) q^{8} -46.0907i q^{11} +(-18.6099 - 18.6099i) q^{13} +13.5628 q^{14} -178.911 q^{16} +(14.5793 + 14.5793i) q^{17} +74.4577i q^{19} +(-172.735 + 172.735i) q^{22} +(-59.6003 + 59.6003i) q^{23} +139.489i q^{26} +(-36.3538 - 36.3538i) q^{28} -202.168 q^{29} -49.5423 q^{31} +(308.008 + 308.008i) q^{32} -109.278i q^{34} +(45.0594 - 45.0594i) q^{37} +(279.046 - 279.046i) q^{38} +306.253i q^{41} +(230.784 + 230.784i) q^{43} +925.996 q^{44} +446.730 q^{46} +(-176.943 - 176.943i) q^{47} +336.452i q^{49} +(373.886 - 373.886i) q^{52} +(-85.1290 + 85.1290i) q^{53} +163.985i q^{56} +(757.669 + 757.669i) q^{58} -330.873 q^{59} +678.639 q^{61} +(185.670 + 185.670i) q^{62} -877.361i q^{64} +(-756.373 + 756.373i) q^{67} +(-292.909 + 292.909i) q^{68} +100.264i q^{71} +(-586.919 - 586.919i) q^{73} -337.739 q^{74} -1495.91 q^{76} +(83.4004 + 83.4004i) q^{77} -286.986i q^{79} +(1147.75 - 1147.75i) q^{82} +(-947.796 + 947.796i) q^{83} -1729.83i q^{86} +(-2088.49 - 2088.49i) q^{88} -688.442 q^{89} +67.3485 q^{91} +(-1197.41 - 1197.41i) q^{92} +1326.26i q^{94} +(-920.676 + 920.676i) q^{97} +(1260.92 - 1260.92i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) \) 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

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