LMFDB - Embedded newform 400.2.u.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.b.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{3} +(-1.80902 - 1.31433i) q^{5} +1.61803 q^{7} +(1.61803 + 1.17557i) q^{9} +(-0.618034 + 0.449028i) q^{11} +(3.92705 + 2.85317i) q^{13} +(1.80902 - 1.31433i) q^{15} +(-0.236068 - 0.726543i) q^{17} +(1.80902 + 5.56758i) q^{19} +(-0.500000 + 1.53884i) q^{21} +(6.66312 - 4.84104i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-4.04508 + 2.93893i) q^{27} +(-0.427051 + 1.31433i) q^{29} +(0.927051 + 2.85317i) q^{31} +(-0.236068 - 0.726543i) q^{33} +(-2.92705 - 2.12663i) q^{35} +(-3.42705 - 2.48990i) q^{37} +(-3.92705 + 2.85317i) q^{39} +(4.23607 + 3.07768i) q^{41} -1.85410 q^{43} +(-1.38197 - 4.25325i) q^{45} +(0.500000 - 1.53884i) q^{47} -4.38197 q^{49} +0.763932 q^{51} +(1.69098 - 5.20431i) q^{53} +1.70820 q^{55} -5.85410 q^{57} +(-3.35410 - 2.43690i) q^{59} +(3.80902 - 2.76741i) q^{61} +(2.61803 + 1.90211i) q^{63} +(-3.35410 - 10.3229i) q^{65} +(-2.85410 - 8.78402i) q^{67} +(2.54508 + 7.83297i) q^{69} +(1.35410 - 4.16750i) q^{71} +(7.28115 - 5.29007i) q^{73} -5.00000 q^{75} +(-1.00000 + 0.726543i) q^{77} +(-0.954915 + 2.93893i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.545085 + 1.67760i) q^{83} +(-0.527864 + 1.62460i) q^{85} +(-1.11803 - 0.812299i) q^{87} +(-7.23607 + 5.25731i) q^{89} +(6.35410 + 4.61653i) q^{91} -3.00000 q^{93} +(4.04508 - 12.4495i) q^{95} +(0.881966 - 2.71441i) q^{97} -1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 + 2 * q^11 + 9 * q^13 + 5 * q^15 + 8 * q^17 + 5 * q^19 - 2 * q^21 + 11 * q^23 - 5 * q^25 - 5 * q^27 + 5 * q^29 - 3 * q^31 + 8 * q^33 - 5 * q^35 - 7 * q^37 - 9 * q^39 + 8 * q^41 + 6 * q^43 - 10 * q^45 + 2 * q^47 - 22 * q^49 + 12 * q^51 + 9 * q^53 - 20 * q^55 - 10 * q^57 + 13 * q^61 + 6 * q^63 + 2 * q^67 - q^69 - 8 * q^71 + 9 * q^73 - 20 * q^75 - 4 * q^77 - 15 * q^79 - q^81 - 9 * q^83 - 20 * q^85 - 20 * q^89 + 12 * q^91 - 12 * q^93 + 5 * q^95 + 8 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$		0			0
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	1.61803			0.611559			0.305780	−	0.952102i	$-0.401083\pi$
$7$	1.61803			0.611559			0.305780	+	0.952102i	$0.401083\pi$
$8$		0			0
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$		0			0
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	−0.677046	−	0.735940i	$-0.736740\pi$
$11$	−0.618034	+	0.449028i	−0.186344	+	0.135387i	0.490702	+	0.871327i	$0.336740\pi$
$12$		0			0
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.979259	−	0.202615i	$-0.0649439\pi$
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.109909	+	0.993942i	$0.464944\pi$
$14$		0			0
$15$	1.80902	−	1.31433i	0.467086	−	0.339358i
$16$		0			0
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	0.918339	−	0.395794i	$-0.129531\pi$
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	−0.975594	+	0.219582i	$0.929531\pi$
$18$		0			0
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	0.912236	+	0.409666i	$0.134355\pi$
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	−0.497219	+	0.867625i	$0.665645\pi$
$20$		0			0
$21$	−0.500000	+	1.53884i	−0.109109	+	0.335803i
$22$		0			0
$23$	6.66312	−	4.84104i	1.38936	−	1.00943i	0.393421	−	0.919359i	$-0.371292\pi$
$23$	6.66312	−	4.84104i	1.38936	−	1.00943i	0.995936	−	0.0900679i	$-0.0287084\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$		0			0
$27$	−4.04508	+	2.93893i	−0.778477	+	0.565597i
$28$		0			0
$29$	−0.427051	+	1.31433i	−0.0793014	+	0.244065i	−0.982846	−	0.184430i	$-0.940956\pi$
$29$	−0.427051	+	1.31433i	−0.0793014	+	0.244065i	0.903544	+	0.428495i	$0.140956\pi$
$30$		0			0
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	0.999144	−	0.0413693i	$-0.0131720\pi$
$31$	0.927051	+	2.85317i	0.166503	+	0.512444i	−0.832641	+	0.553814i	$0.813172\pi$
$32$		0			0
$33$	−0.236068	−	0.726543i	−0.0410942	−	0.126475i
$34$		0			0
$35$	−2.92705	−	2.12663i	−0.494762	−	0.359466i
$36$		0			0
$37$	−3.42705	−	2.48990i	−0.563404	−	0.409337i	0.269299	−	0.963057i	$-0.413208\pi$
$37$	−3.42705	−	2.48990i	−0.563404	−	0.409337i	−0.832703	+	0.553720i	$0.813208\pi$
$38$		0			0
$39$	−3.92705	+	2.85317i	−0.628831	+	0.456873i
$40$		0			0
$41$	4.23607	+	3.07768i	0.661563	+	0.480653i	0.867190	−	0.497977i	$-0.165924\pi$
$41$	4.23607	+	3.07768i	0.661563	+	0.480653i	−0.205628	+	0.978630i	$0.565924\pi$
$42$		0			0
$43$	−1.85410			−0.282748			−0.141374	−	0.989956i	$-0.545152\pi$
$43$	−1.85410			−0.282748			−0.141374	+	0.989956i	$0.545152\pi$
$44$		0			0
$45$	−1.38197	−	4.25325i	−0.206011	−	0.634038i
$46$		0			0
$47$	0.500000	−	1.53884i	0.0729325	−	0.224463i	−0.907945	−	0.419089i	$-0.862349\pi$
$47$	0.500000	−	1.53884i	0.0729325	−	0.224463i	0.980877	+	0.194626i	$0.0623494\pi$
$48$		0			0
$49$	−4.38197			−0.625995
$50$		0			0
$51$	0.763932			0.106972
$52$		0			0
$53$	1.69098	−	5.20431i	0.232274	−	0.714867i	−0.765197	−	0.643796i	$-0.777358\pi$
$53$	1.69098	−	5.20431i	0.232274	−	0.714867i	0.997471	−	0.0710707i	$-0.0226416\pi$
$54$		0			0
$55$	1.70820			0.230334
$56$		0			0
$57$	−5.85410			−0.775395
$58$		0			0
$59$	−3.35410	−	2.43690i	−0.436667	−	0.317257i	0.347642	−	0.937627i	$-0.386982\pi$
$59$	−3.35410	−	2.43690i	−0.436667	−	0.317257i	−0.784309	+	0.620370i	$0.786982\pi$
$60$		0			0
$61$	3.80902	−	2.76741i	0.487695	−	0.354331i	−0.316602	−	0.948558i	$-0.602542\pi$
$61$	3.80902	−	2.76741i	0.487695	−	0.354331i	0.804297	+	0.594227i	$0.202542\pi$
$62$		0			0
$63$	2.61803	+	1.90211i	0.329841	+	0.239644i
$64$		0			0
$65$	−3.35410	−	10.3229i	−0.416025	−	1.28039i
$66$		0			0
$67$	−2.85410	−	8.78402i	−0.348684	−	1.07314i	−0.959582	−	0.281430i	$-0.909191\pi$
$67$	−2.85410	−	8.78402i	−0.348684	−	1.07314i	0.610898	−	0.791709i	$-0.290809\pi$
$68$		0			0
$69$	2.54508	+	7.83297i	0.306392	+	0.942978i
$70$		0			0
$71$	1.35410	−	4.16750i	0.160702	−	0.494591i	−0.837992	−	0.545683i	$-0.816270\pi$
$71$	1.35410	−	4.16750i	0.160702	−	0.494591i	0.998694	+	0.0510922i	$0.0162702\pi$
$72$		0			0
$73$	7.28115	−	5.29007i	0.852194	−	0.619156i	−0.0735557	−	0.997291i	$-0.523435\pi$
$73$	7.28115	−	5.29007i	0.852194	−	0.619156i	0.925750	+	0.378136i	$0.123435\pi$
$74$		0			0
$75$	−5.00000			−0.577350
$76$		0			0
$77$	−1.00000	+	0.726543i	−0.113961	+	0.0827972i
$78$		0			0
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	−0.990295	−	0.138985i	$-0.955616\pi$
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	0.882858	+	0.469640i	$0.155616\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	0.545085	+	1.67760i	0.0598308	+	0.184140i	0.976505	−	0.215495i	$-0.0691366\pi$
$83$	0.545085	+	1.67760i	0.0598308	+	0.184140i	−0.916674	+	0.399636i	$0.869137\pi$
$84$		0			0
$85$	−0.527864	+	1.62460i	−0.0572549	+	0.176212i
$86$		0			0
$87$	−1.11803	−	0.812299i	−0.119866	−	0.0870876i
$88$		0			0
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	−0.901056	−	0.433703i	$-0.857207\pi$
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	0.134034	+	0.990977i	$0.457207\pi$
$90$		0			0
$91$	6.35410	+	4.61653i	0.666091	+	0.483943i
$92$		0			0
$93$	−3.00000			−0.311086
$94$		0			0
$95$	4.04508	−	12.4495i	0.415017	−	1.27729i
$96$		0			0
$97$	0.881966	−	2.71441i	0.0895501	−	0.275607i	−0.896245	−	0.443559i	$-0.853716\pi$
$97$	0.881966	−	2.71441i	0.0895501	−	0.275607i	0.985795	+	0.167953i	$0.0537155\pi$
$98$		0			0
$99$	−1.52786			−0.153556
$100$		0			0
$101$	−7.47214			−0.743505			−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214			−0.743505			−0.371753	+	0.928332i	$0.621243\pi$
$102$		0			0
$103$	3.57295	−	10.9964i	0.352053	−	1.08351i	−0.605645	−	0.795735i	$-0.707085\pi$
$103$	3.57295	−	10.9964i	0.352053	−	1.08351i	0.957699	−	0.287773i	$-0.0929150\pi$
$104$		0			0
$105$	2.92705	−	2.12663i	0.285651	−	0.207538i
$106$		0			0
$107$	−10.4164			−1.00699			−0.503496	−	0.863998i	$-0.667953\pi$
$107$	−10.4164			−1.00699			−0.503496	+	0.863998i	$0.667953\pi$
$108$		0			0
$109$	−8.09017	−	5.87785i	−0.774898	−	0.562996i	0.128546	−	0.991704i	$-0.458969\pi$
$109$	−8.09017	−	5.87785i	−0.774898	−	0.562996i	−0.903443	+	0.428707i	$0.858969\pi$
$110$		0			0
$111$	3.42705	−	2.48990i	0.325281	−	0.236331i
$112$		0			0
$113$	−8.20820	−	5.96361i	−0.772163	−	0.561009i	0.130454	−	0.991454i	$-0.458357\pi$
$113$	−8.20820	−	5.96361i	−0.772163	−	0.561009i	−0.902617	+	0.430445i	$0.858357\pi$
$114$		0			0
$115$	−18.4164			−1.71734
$116$		0			0
$117$	3.00000	+	9.23305i	0.277350	+	0.853596i
$118$		0			0
$119$	−0.381966	−	1.17557i	−0.0350148	−	0.107764i
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$		0			0
$123$	−4.23607	+	3.07768i	−0.381953	+	0.277505i
$124$		0			0
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$		0			0
$127$	−12.8541	+	9.33905i	−1.14062	+	0.828707i	−0.987205	−	0.159455i	$-0.949026\pi$
$127$	−12.8541	+	9.33905i	−1.14062	+	0.828707i	−0.153412	+	0.988162i	$0.549026\pi$
$128$		0			0
$129$	0.572949	−	1.76336i	0.0504453	−	0.155255i
$130$		0			0
$131$	5.50000	+	16.9273i	0.480537	+	1.47894i	0.838342	+	0.545145i	$0.183525\pi$
$131$	5.50000	+	16.9273i	0.480537	+	1.47894i	−0.357805	+	0.933797i	$0.616475\pi$
$132$		0			0
$133$	2.92705	+	9.00854i	0.253808	+	0.781139i
$134$		0			0
$135$	11.1803			0.962250
$136$		0			0
$137$	−4.80902	−	3.49396i	−0.410862	−	0.298509i	0.363089	−	0.931755i	$-0.381722\pi$
$137$	−4.80902	−	3.49396i	−0.410862	−	0.298509i	−0.773951	+	0.633246i	$0.781722\pi$
$138$		0			0
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	−0.402869	−	0.915258i	$-0.631987\pi$
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	0.745968	+	0.665981i	$0.231987\pi$
$140$		0			0
$141$	1.30902	+	0.951057i	0.110239	+	0.0800934i
$142$		0			0
$143$	−3.70820			−0.310096
$144$		0			0
$145$	2.50000	−	1.81636i	0.207614	−	0.150840i
$146$		0			0
$147$	1.35410	−	4.16750i	0.111684	−	0.343729i
$148$		0			0
$149$	13.9443			1.14236			0.571180	−	0.820825i	$-0.306486\pi$
$149$	13.9443			1.14236			0.571180	+	0.820825i	$0.306486\pi$
$150$		0			0
$151$	5.56231			0.452654			0.226327	−	0.974051i	$-0.427328\pi$
$151$	5.56231			0.452654			0.226327	+	0.974051i	$0.427328\pi$
$152$		0			0
$153$	0.472136	−	1.45309i	0.0381699	−	0.117475i
$154$		0			0
$155$	2.07295	−	6.37988i	0.166503	−	0.512444i
$156$		0			0
$157$	−9.18034			−0.732671			−0.366335	−	0.930483i	$-0.619388\pi$
$157$	−9.18034			−0.732671			−0.366335	+	0.930483i	$0.619388\pi$
$158$		0			0
$159$	4.42705	+	3.21644i	0.351088	+	0.255080i
$160$		0			0
$161$	10.7812	−	7.83297i	0.849674	−	0.617324i
$162$		0			0
$163$	8.89919	+	6.46564i	0.697038	+	0.506428i	0.878966	−	0.476884i	$-0.158234\pi$
$163$	8.89919	+	6.46564i	0.697038	+	0.506428i	−0.181928	+	0.983312i	$0.558234\pi$
$164$		0			0
$165$	−0.527864	+	1.62460i	−0.0410942	+	0.126475i
$166$		0			0
$167$	1.71885	+	5.29007i	0.133008	+	0.409358i	0.995275	−	0.0970971i	$-0.0309557\pi$
$167$	1.71885	+	5.29007i	0.133008	+	0.409358i	−0.862267	+	0.506455i	$0.830956\pi$
$168$		0			0
$169$	3.26393	+	10.0453i	0.251072	+	0.772719i
$170$		0			0
$171$	−3.61803	+	11.1352i	−0.276678	+	0.851527i
$172$		0			0
$173$	13.6631	−	9.92684i	1.03879	−	0.754723i	0.0687392	−	0.997635i	$-0.478102\pi$
$173$	13.6631	−	9.92684i	1.03879	−	0.754723i	0.970049	+	0.242911i	$0.0781024\pi$
$174$		0			0
$175$	2.50000	+	7.69421i	0.188982	+	0.581628i
$176$		0			0
$177$	3.35410	−	2.43690i	0.252110	−	0.183168i
$178$		0			0
$179$	2.92705	−	9.00854i	0.218778	−	0.673330i	−0.780086	−	0.625673i	$-0.784825\pi$
$179$	2.92705	−	9.00854i	0.218778	−	0.673330i	0.998864	−	0.0476570i	$-0.0151754\pi$
$180$		0			0
$181$	4.23607	+	13.0373i	0.314864	+	0.969053i	0.975810	+	0.218619i	$0.0701553\pi$
$181$	4.23607	+	13.0373i	0.314864	+	0.969053i	−0.660946	+	0.750434i	$0.729845\pi$
$182$		0			0
$183$	1.45492	+	4.47777i	0.107550	+	0.331006i
$184$		0			0
$185$	2.92705	+	9.00854i	0.215201	+	0.662321i
$186$		0			0
$187$	0.472136	+	0.343027i	0.0345260	+	0.0250846i
$188$		0			0
$189$	−6.54508	+	4.75528i	−0.476085	+	0.345896i
$190$		0			0
$191$	−19.5623	−	14.2128i	−1.41548	−	1.02841i	−0.992497	−	0.122267i	$-0.960984\pi$
$191$	−19.5623	−	14.2128i	−1.41548	−	1.02841i	−0.422982	−	0.906138i	$-0.639016\pi$
$192$		0			0
$193$	−5.70820			−0.410886			−0.205443	−	0.978669i	$-0.565863\pi$
$193$	−5.70820			−0.410886			−0.205443	+	0.978669i	$0.565863\pi$
$194$		0			0
$195$	10.8541			0.777278
$196$		0			0
$197$	−3.00000	+	9.23305i	−0.213741	+	0.657828i	0.785499	+	0.618862i	$0.212406\pi$
$197$	−3.00000	+	9.23305i	−0.213741	+	0.657828i	−0.999241	+	0.0389652i	$0.987594\pi$
$198$		0			0
$199$	−2.56231			−0.181637			−0.0908185	−	0.995867i	$-0.528948\pi$
$199$	−2.56231			−0.181637			−0.0908185	+	0.995867i	$0.528948\pi$
$200$		0			0
$201$	9.23607			0.651462
$202$		0			0
$203$	−0.690983	+	2.12663i	−0.0484975	+	0.149260i
$204$		0			0
$205$	−3.61803	−	11.1352i	−0.252694	−	0.777714i
$206$		0			0
$207$	16.4721			1.14489
$208$		0			0
$209$	−3.61803	−	2.62866i	−0.250265	−	0.181828i
$210$		0			0
$211$	10.6631	−	7.74721i	0.734079	−	0.533340i	−0.156772	−	0.987635i	$-0.550109\pi$
$211$	10.6631	−	7.74721i	0.734079	−	0.533340i	0.890851	+	0.454295i	$0.150109\pi$
$212$		0			0
$213$	3.54508	+	2.57565i	0.242905	+	0.176481i
$214$		0			0
$215$	3.35410	+	2.43690i	0.228748	+	0.166195i
$216$		0			0
$217$	1.50000	+	4.61653i	0.101827	+	0.313390i
$218$		0			0
$219$	2.78115	+	8.55951i	0.187933	+	0.578398i
$220$		0			0
$221$	1.14590	−	3.52671i	0.0770814	−	0.237232i
$222$		0			0
$223$	17.9443	−	13.0373i	1.20164	−	0.873041i	0.207193	−	0.978300i	$-0.433567\pi$
$223$	17.9443	−	13.0373i	1.20164	−	0.873041i	0.994445	+	0.105260i	$0.0335673\pi$
$224$		0			0
$225$	−3.09017	+	9.51057i	−0.206011	+	0.634038i
$226$		0			0
$227$	15.5623	−	11.3067i	1.03291	−	0.750451i	0.0640182	−	0.997949i	$-0.479608\pi$
$227$	15.5623	−	11.3067i	1.03291	−	0.750451i	0.968888	+	0.247498i	$0.0796084\pi$
$228$		0			0
$229$	2.56231	−	7.88597i	0.169322	−	0.521119i	−0.830007	−	0.557753i	$-0.811664\pi$
$229$	2.56231	−	7.88597i	0.169322	−	0.521119i	0.999329	+	0.0366339i	$0.0116635\pi$
$230$		0			0
$231$	−0.381966	−	1.17557i	−0.0251315	−	0.0773469i
$232$		0			0
$233$	4.61803	+	14.2128i	0.302537	+	0.931115i	0.980585	+	0.196096i	$0.0628265\pi$
$233$	4.61803	+	14.2128i	0.302537	+	0.931115i	−0.678047	+	0.735018i	$0.737174\pi$
$234$		0			0
$235$	−2.92705	+	2.12663i	−0.190940	+	0.138726i
$236$		0			0
$237$	−2.50000	−	1.81636i	−0.162392	−	0.117985i
$238$		0			0
$239$	−23.8435	+	17.3233i	−1.54231	+	1.12055i	−0.593436	+	0.804881i	$0.702229\pi$
$239$	−23.8435	+	17.3233i	−1.54231	+	1.12055i	−0.948869	+	0.315669i	$0.897771\pi$
$240$		0			0
$241$	−9.28115	−	6.74315i	−0.597852	−	0.434365i	0.247264	−	0.968948i	$-0.420468\pi$
$241$	−9.28115	−	6.74315i	−0.597852	−	0.434365i	−0.845116	+	0.534584i	$0.820468\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$		0			0
$245$	7.92705	+	5.75934i	0.506441	+	0.367951i
$246$		0			0
$247$	−8.78115	+	27.0256i	−0.558731	+	1.71960i
$248$		0			0
$249$	−1.76393			−0.111785
$250$		0			0
$251$	6.81966			0.430453			0.215227	−	0.976564i	$-0.430951\pi$
$251$	6.81966			0.430453			0.215227	+	0.976564i	$0.430951\pi$
$252$		0			0
$253$	−1.94427	+	5.98385i	−0.122235	+	0.376202i
$254$		0			0
$255$	−1.38197	−	1.00406i	−0.0865421	−	0.0628765i
$256$		0			0
$257$	16.1459			1.00715			0.503577	−	0.863951i	$-0.332017\pi$
$257$	16.1459			1.00715			0.503577	+	0.863951i	$0.332017\pi$
$258$		0			0
$259$	−5.54508	−	4.02874i	−0.344555	−	0.250334i
$260$		0			0
$261$	−2.23607	+	1.62460i	−0.138409	+	0.100560i
$262$		0			0
$263$	−17.8713	−	12.9843i	−1.10199	−	0.800645i	−0.120609	−	0.992700i	$-0.538485\pi$
$263$	−17.8713	−	12.9843i	−1.10199	−	0.800645i	−0.981384	+	0.192055i	$0.938485\pi$
$264$		0			0
$265$	−9.89919	+	7.19218i	−0.608102	+	0.441812i
$266$		0			0
$267$	−2.76393	−	8.50651i	−0.169150	−	0.520590i
$268$		0			0
$269$	−5.32624	−	16.3925i	−0.324746	−	0.999467i	−0.971555	−	0.236814i	$-0.923897\pi$
$269$	−5.32624	−	16.3925i	−0.324746	−	0.999467i	0.646808	−	0.762652i	$-0.276103\pi$
$270$		0			0
$271$	2.47214	−	7.60845i	0.150172	−	0.462181i	−0.847468	−	0.530846i	$-0.821874\pi$
$271$	2.47214	−	7.60845i	0.150172	−	0.462181i	0.997640	+	0.0686657i	$0.0218742\pi$
$272$		0			0
$273$	−6.35410	+	4.61653i	−0.384568	+	0.279405i
$274$		0			0
$275$	−3.09017	−	2.24514i	−0.186344	−	0.135387i
$276$		0			0
$277$	9.13525	−	6.63715i	0.548884	−	0.398788i	−0.278490	−	0.960439i	$-0.589834\pi$
$277$	9.13525	−	6.63715i	0.548884	−	0.398788i	0.827374	+	0.561651i	$0.189834\pi$
$278$		0			0
$279$	−1.85410	+	5.70634i	−0.111002	+	0.341630i
$280$		0			0
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	0.940505	−	0.339779i	$-0.110352\pi$
$281$	−0.336881	−	1.03681i	−0.0200966	−	0.0618511i	−0.960602	+	0.277928i	$0.910352\pi$
$282$		0			0
$283$	7.15248	+	22.0131i	0.425171	+	1.30854i	0.902831	+	0.429996i	$0.141485\pi$
$283$	7.15248	+	22.0131i	0.425171	+	1.30854i	−0.477660	+	0.878545i	$0.658515\pi$
$284$		0			0
$285$	10.5902	+	7.69421i	0.627308	+	0.455766i
$286$		0			0
$287$	6.85410	+	4.97980i	0.404585	+	0.293948i
$288$		0			0
$289$	13.2812	−	9.64932i	0.781244	−	0.567607i
$290$		0			0
$291$	2.30902	+	1.67760i	0.135357	+	0.0983426i
$292$		0			0
$293$	−28.4721			−1.66336			−0.831680	−	0.555255i	$-0.812621\pi$
$293$	−28.4721			−1.66336			−0.831680	+	0.555255i	$0.812621\pi$
$294$		0			0
$295$	2.86475	+	8.81678i	0.166792	+	0.513333i
$296$		0			0
$297$	1.18034	−	3.63271i	0.0684903	−	0.210791i
$298$		0			0
$299$	39.9787			2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$		0			0
$303$	2.30902	−	7.10642i	0.132650	−	0.408253i
$304$		0			0
$305$	−10.5279			−0.602824
$306$		0			0
$307$	−4.76393			−0.271892			−0.135946	−	0.990716i	$-0.543407\pi$
$307$	−4.76393			−0.271892			−0.135946	+	0.990716i	$0.543407\pi$
$308$		0			0
$309$	9.35410	+	6.79615i	0.532136	+	0.386620i
$310$		0			0
$311$	−23.8713	+	17.3435i	−1.35362	+	0.983461i	−0.354796	+	0.934944i	$0.615450\pi$
$311$	−23.8713	+	17.3435i	−1.35362	+	0.983461i	−0.998822	+	0.0485178i	$0.984550\pi$
$312$		0			0
$313$	17.1803	+	12.4822i	0.971090	+	0.705538i	0.955700	−	0.294343i	$-0.0951009\pi$
$313$	17.1803	+	12.4822i	0.971090	+	0.705538i	0.0153904	+	0.999882i	$0.495101\pi$
$314$		0			0
$315$	−2.23607	−	6.88191i	−0.125988	−	0.387752i
$316$		0			0
$317$	−7.30902	−	22.4948i	−0.410515	−	1.26344i	−0.916201	−	0.400719i	$-0.868761\pi$
$317$	−7.30902	−	22.4948i	−0.410515	−	1.26344i	0.505686	−	0.862718i	$-0.331239\pi$
$318$		0			0
$319$	−0.326238	−	1.00406i	−0.0182658	−	0.0562164i
$320$		0			0
$321$	3.21885	−	9.90659i	0.179659	−	0.552932i
$322$		0			0
$323$	3.61803	−	2.62866i	0.201313	−	0.146262i
$324$		0			0
$325$	−7.50000	+	23.0826i	−0.416025	+	1.28039i
$326$		0			0
$327$	8.09017	−	5.87785i	0.447387	−	0.325046i
$328$		0			0
$329$	0.809017	−	2.48990i	0.0446026	−	0.137273i
$330$		0			0
$331$	−5.29180	−	16.2865i	−0.290863	−	0.895186i	−0.984580	−	0.174937i	$-0.944028\pi$
$331$	−5.29180	−	16.2865i	−0.290863	−	0.895186i	0.693716	−	0.720248i	$-0.255972\pi$
$332$		0			0
$333$	−2.61803	−	8.05748i	−0.143467	−	0.441547i
$334$		0			0
$335$	−6.38197	+	19.6417i	−0.348684	+	1.07314i
$336$		0			0
$337$	−0.927051	−	0.673542i	−0.0504997	−	0.0366902i	0.562249	−	0.826968i	$-0.309936\pi$
$337$	−0.927051	−	0.673542i	−0.0504997	−	0.0366902i	−0.612749	+	0.790278i	$0.709936\pi$
$338$		0			0
$339$	8.20820	−	5.96361i	0.445808	−	0.323899i
$340$		0			0
$341$	−1.85410	−	1.34708i	−0.100405	−	0.0729487i
$342$		0			0
$343$	−18.4164			−0.994393
$344$		0			0
$345$	5.69098	−	17.5150i	0.306392	−	0.942978i
$346$		0			0
$347$	9.60739	−	29.5685i	0.515752	−	1.58732i	−0.266158	−	0.963929i	$-0.585754\pi$
$347$	9.60739	−	29.5685i	0.515752	−	1.58732i	0.781910	−	0.623391i	$-0.214246\pi$
$348$		0			0
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$		0			0
$351$	−24.2705			−1.29546
$352$		0			0
$353$	7.44427	−	22.9111i	0.396219	−	1.21944i	−0.531790	−	0.846876i	$-0.678480\pi$
$353$	7.44427	−	22.9111i	0.396219	−	1.21944i	0.928008	−	0.372559i	$-0.121520\pi$
$354$		0			0
$355$	−7.92705	+	5.75934i	−0.420724	+	0.305674i
$356$		0			0
$357$	1.23607			0.0654197
$358$		0			0
$359$	−23.2533	−	16.8945i	−1.22726	−	0.891658i	−0.230580	−	0.973053i	$-0.574062\pi$
$359$	−23.2533	−	16.8945i	−1.22726	−	0.891658i	−0.996682	+	0.0813956i	$0.974062\pi$
$360$		0			0
$361$	−12.3541	+	8.97578i	−0.650216	+	0.472409i
$362$		0			0
$363$	−8.42705	−	6.12261i	−0.442305	−	0.321354i
$364$		0			0
$365$	−20.1246			−1.05337
$366$		0			0
$367$	1.68034	+	5.17155i	0.0877130	+	0.269953i	0.985286	−	0.170913i	$-0.0546716\pi$
$367$	1.68034	+	5.17155i	0.0877130	+	0.269953i	−0.897573	+	0.440866i	$0.854672\pi$
$368$		0			0
$369$	3.23607	+	9.95959i	0.168463	+	0.518476i
$370$		0			0
$371$	2.73607	−	8.42075i	0.142050	−	0.437184i
$372$		0			0
$373$	−4.26393	+	3.09793i	−0.220778	+	0.160405i	−0.692677	−	0.721248i	$-0.743569\pi$
$373$	−4.26393	+	3.09793i	−0.220778	+	0.160405i	0.471899	+	0.881653i	$0.343569\pi$
$374$		0			0
$375$	9.04508	+	6.57164i	0.467086	+	0.339358i
$376$		0			0
$377$	−5.42705	+	3.94298i	−0.279507	+	0.203074i
$378$		0			0
$379$	10.6910	−	32.9035i	0.549159	−	1.69014i	−0.161732	−	0.986835i	$-0.551708\pi$
$379$	10.6910	−	32.9035i	0.549159	−	1.69014i	0.710891	−	0.703303i	$-0.248292\pi$
$380$		0			0
$381$	−4.90983	−	15.1109i	−0.251538	−	0.774155i
$382$		0			0
$383$	3.51064	+	10.8046i	0.179385	+	0.552092i	0.999807	−	0.0196680i	$-0.00626093\pi$
$383$	3.51064	+	10.8046i	0.179385	+	0.552092i	−0.820421	+	0.571760i	$0.806261\pi$
$384$		0			0
$385$	2.76393			0.140863
$386$		0			0
$387$	−3.00000	−	2.17963i	−0.152499	−	0.110797i
$388$		0			0
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	−0.851270	−	0.524727i	$-0.824167\pi$
$389$	−12.1353	+	8.81678i	−0.615282	+	0.447028i	0.235988	+	0.971756i	$0.424167\pi$
$390$		0			0
$391$	−5.09017	−	3.69822i	−0.257421	−	0.187027i
$392$		0			0
$393$	−17.7984			−0.897809
$394$		0			0
$395$	5.59017	−	4.06150i	0.281272	−	0.204356i
$396$		0			0
$397$	−0.0106431	+	0.0327561i	−0.000534163	+	0.00164398i	−0.951323	−	0.308195i	$-0.900275\pi$
$397$	−0.0106431	+	0.0327561i	−0.000534163	+	0.00164398i	0.950789	+	0.309839i	$0.100275\pi$
$398$		0			0
$399$	−9.47214			−0.474200
$400$		0			0
$401$	−22.5967			−1.12843			−0.564214	−	0.825629i	$-0.690821\pi$
$401$	−22.5967			−1.12843			−0.564214	+	0.825629i	$0.690821\pi$
$402$		0			0
$403$	−4.50000	+	13.8496i	−0.224161	+	0.689897i
$404$		0			0
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$		0			0
$407$	3.23607			0.160406
$408$		0			0
$409$	−22.9894	−	16.7027i	−1.13675	−	0.825898i	−0.150087	−	0.988673i	$-0.547955\pi$
$409$	−22.9894	−	16.7027i	−1.13675	−	0.825898i	−0.986663	+	0.162775i	$0.947955\pi$
$410$		0			0
$411$	4.80902	−	3.49396i	0.237211	−	0.172344i
$412$		0			0
$413$	−5.42705	−	3.94298i	−0.267048	−	0.194022i
$414$		0			0
$415$	1.21885	−	3.75123i	0.0598308	−	0.184140i
$416$		0			0
$417$	1.54508	+	4.75528i	0.0756631	+	0.232867i
$418$		0			0
$419$	0.163119	+	0.502029i	0.00796888	+	0.0245257i	0.954962	−	0.296728i	$-0.0958956\pi$
$419$	0.163119	+	0.502029i	0.00796888	+	0.0245257i	−0.946993	+	0.321254i	$0.895896\pi$
$420$		0			0
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	−0.354429	−	0.935083i	$-0.615325\pi$
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	0.836367	−	0.548170i	$-0.184675\pi$
$422$		0			0
$423$	2.61803	−	1.90211i	0.127293	−	0.0924839i
$424$		0			0
$425$	3.09017	−	2.24514i	0.149895	−	0.108905i
$426$		0			0
$427$	6.16312	−	4.47777i	0.298254	−	0.216694i
$428$		0			0
$429$	1.14590	−	3.52671i	0.0553245	−	0.170271i
$430$		0			0
$431$	−7.36475	−	22.6664i	−0.354747	−	1.09180i	−0.956156	−	0.292858i	$-0.905394\pi$
$431$	−7.36475	−	22.6664i	−0.354747	−	1.09180i	0.601409	−	0.798942i	$-0.294606\pi$
$432$		0			0
$433$	6.22542	+	19.1599i	0.299175	+	0.920765i	0.981787	+	0.189985i	$0.0608438\pi$
$433$	6.22542	+	19.1599i	0.299175	+	0.920765i	−0.682612	+	0.730781i	$0.739156\pi$
$434$		0			0
$435$	0.954915	+	2.93893i	0.0457847	+	0.140911i
$436$		0			0
$437$	39.0066	+	28.3399i	1.86594	+	1.35568i
$438$		0			0
$439$	4.83688	−	3.51420i	0.230852	−	0.167724i	−0.466346	−	0.884602i	$-0.654430\pi$
$439$	4.83688	−	3.51420i	0.230852	−	0.167724i	0.697198	+	0.716879i	$0.254430\pi$
$440$		0			0
$441$	−7.09017	−	5.15131i	−0.337627	−	0.245300i
$442$		0			0
$443$	−12.0557			−0.572785			−0.286392	−	0.958112i	$-0.592456\pi$
$443$	−12.0557			−0.572785			−0.286392	+	0.958112i	$0.592456\pi$
$444$		0			0
$445$	20.0000			0.948091
$446$		0			0
$447$	−4.30902	+	13.2618i	−0.203810	+	0.627261i
$448$		0			0
$449$	20.3262			0.959254			0.479627	−	0.877472i	$-0.340772\pi$
$449$	20.3262			0.959254			0.479627	+	0.877472i	$0.340772\pi$
$450$		0			0
$451$	−4.00000			−0.188353
$452$		0			0
$453$	−1.71885	+	5.29007i	−0.0807585	+	0.248549i
$454$		0			0
$455$	−5.42705	−	16.7027i	−0.254424	−	0.783037i
$456$		0			0
$457$	5.41641			0.253369			0.126684	−	0.991943i	$-0.459566\pi$
$457$	5.41641			0.253369			0.126684	+	0.991943i	$0.459566\pi$
$458$		0			0
$459$	3.09017	+	2.24514i	0.144237	+	0.104794i
$460$		0			0
$461$	−18.7533	+	13.6251i	−0.873428	+	0.634582i	−0.931505	−	0.363730i	$-0.881503\pi$
$461$	−18.7533	+	13.6251i	−0.873428	+	0.634582i	0.0580768	+	0.998312i	$0.481503\pi$
$462$		0			0
$463$	13.0451	+	9.47781i	0.606257	+	0.440471i	0.848094	−	0.529846i	$-0.177750\pi$
$463$	13.0451	+	9.47781i	0.606257	+	0.440471i	−0.241838	+	0.970317i	$0.577750\pi$
$464$		0			0
$465$	5.42705	+	3.94298i	0.251673	+	0.182851i
$466$		0			0
$467$	8.79180	+	27.0584i	0.406836	+	1.25211i	0.919353	+	0.393435i	$0.128713\pi$
$467$	8.79180	+	27.0584i	0.406836	+	1.25211i	−0.512517	+	0.858677i	$0.671287\pi$
$468$		0			0
$469$	−4.61803	−	14.2128i	−0.213241	−	0.656288i
$470$		0			0
$471$	2.83688	−	8.73102i	0.130717	−	0.402304i
$472$		0			0
$473$	1.14590	−	0.832544i	0.0526884	−	0.0382804i
$474$		0			0
$475$	−23.6803	+	17.2048i	−1.08653	+	0.789409i
$476$		0			0
$477$	8.85410	−	6.43288i	0.405401	−	0.294541i
$478$		0			0
$479$	1.28115	−	3.94298i	0.0585374	−	0.180160i	−0.917512	−	0.397708i	$-0.869806\pi$
$479$	1.28115	−	3.94298i	0.0585374	−	0.180160i	0.976050	+	0.217548i	$0.0698059\pi$
$480$		0			0
$481$	−6.35410	−	19.5559i	−0.289722	−	0.891673i
$482$		0			0
$483$	4.11803	+	12.6740i	0.187377	+	0.576687i
$484$		0			0
$485$	−5.16312	+	3.75123i	−0.234445	+	0.170334i
$486$		0			0
$487$	−7.75329	−	5.63309i	−0.351335	−	0.255260i	0.398094	−	0.917345i	$-0.369672\pi$
$487$	−7.75329	−	5.63309i	−0.351335	−	0.255260i	−0.749429	+	0.662085i	$0.769672\pi$
$488$		0			0
$489$	−8.89919	+	6.46564i	−0.402435	+	0.292386i
$490$		0			0
$491$	30.1353	+	21.8945i	1.35999	+	0.988087i	0.998446	+	0.0557300i	$0.0177486\pi$
$491$	30.1353	+	21.8945i	1.35999	+	0.988087i	0.361539	+	0.932357i	$0.382251\pi$
$492$		0			0
$493$	1.05573			0.0475476
$494$		0			0
$495$	2.76393	+	2.00811i	0.124230	+	0.0902580i
$496$		0			0
$497$	2.19098	−	6.74315i	0.0982790	−	0.302472i
$498$		0			0
$499$	12.5623			0.562366			0.281183	−	0.959654i	$-0.409273\pi$
$499$	12.5623			0.562366			0.281183	+	0.959654i	$0.409273\pi$
$500$		0			0
$501$	−5.56231			−0.248506
$502$		0			0
$503$	3.27051	−	10.0656i	0.145825	−	0.448803i	−0.851291	−	0.524693i	$-0.824180\pi$
$503$	3.27051	−	10.0656i	0.145825	−	0.448803i	0.997116	+	0.0758907i	$0.0241800\pi$
$504$		0			0
$505$	13.5172	+	9.82084i	0.601508	+	0.437021i
$506$		0			0
$507$	−10.5623			−0.469088
$508$		0			0
$509$	3.78115	+	2.74717i	0.167597	+	0.121766i	0.668422	−	0.743782i	$-0.266970\pi$
$509$	3.78115	+	2.74717i	0.167597	+	0.121766i	−0.500825	+	0.865548i	$0.666970\pi$
$510$		0			0
$511$	11.7812	−	8.55951i	0.521168	−	0.378650i
$512$		0			0
$513$	−23.6803	−	17.2048i	−1.04551	−	0.759609i
$514$		0			0
$515$	−20.9164	+	15.1967i	−0.921687	+	0.669645i
$516$		0			0
$517$	0.381966	+	1.17557i	0.0167988	+	0.0517015i
$518$		0			0
$519$	5.21885	+	16.0620i	0.229082	+	0.705042i
$520$		0			0
$521$	−4.74671	+	14.6089i	−0.207957	+	0.640026i	0.791622	+	0.611011i	$0.209237\pi$
$521$	−4.74671	+	14.6089i	−0.207957	+	0.640026i	−0.999579	+	0.0290150i	$0.990763\pi$
$522$		0			0
$523$	−16.0623	+	11.6699i	−0.702356	+	0.510291i	−0.880699	−	0.473677i	$-0.842926\pi$
$523$	−16.0623	+	11.6699i	−0.702356	+	0.510291i	0.178343	+	0.983968i	$0.442926\pi$
$524$		0			0
$525$	−8.09017			−0.353084
$526$		0			0
$527$	1.85410	−	1.34708i	0.0807660	−	0.0586799i
$528$		0			0
$529$	13.8541	−	42.6385i	0.602352	−	1.85385i
$530$		0			0
$531$	−2.56231	−	7.88597i	−0.111195	−	0.342222i
$532$		0			0
$533$	7.85410	+	24.1724i	0.340199	+	1.04702i
$534$		0			0
$535$	18.8435	+	13.6906i	0.814674	+	0.591895i
$536$		0			0
$537$	7.66312	+	5.56758i	0.330688	+	0.240259i
$538$		0			0
$539$	2.70820	−	1.96763i	0.116651	−	0.0847516i
$540$		0			0
$541$	10.6180	+	7.71445i	0.456505	+	0.331670i	0.792159	−	0.610315i	$-0.208957\pi$
$541$	10.6180	+	7.71445i	0.456505	+	0.331670i	−0.335654	+	0.941985i	$0.608957\pi$
$542$		0			0
$543$	−13.7082			−0.588275
$544$		0			0
$545$	6.90983	+	21.2663i	0.295985	+	0.910947i
$546$		0			0
$547$	10.7254	−	33.0095i	0.458586	−	1.41138i	−0.408287	−	0.912854i	$-0.633874\pi$
$547$	10.7254	−	33.0095i	0.458586	−	1.41138i	0.866873	−	0.498529i	$-0.166126\pi$
$548$		0			0
$549$	9.41641			0.401882
$550$		0			0
$551$	−8.09017			−0.344653
$552$		0			0
$553$	−1.54508	+	4.75528i	−0.0657037	+	0.202215i
$554$		0			0
$555$	−9.47214			−0.402070
$556$		0			0
$557$	9.23607			0.391345			0.195672	−	0.980669i	$-0.437311\pi$
$557$	9.23607			0.391345			0.195672	+	0.980669i	$0.437311\pi$
$558$		0			0
$559$	−7.28115	−	5.29007i	−0.307960	−	0.223746i
$560$		0			0
$561$	−0.472136	+	0.343027i	−0.0199336	+	0.0144826i
$562$		0			0
$563$	7.78115	+	5.65334i	0.327936	+	0.238260i	0.739555	−	0.673097i	$-0.235036\pi$
$563$	7.78115	+	5.65334i	0.327936	+	0.238260i	−0.411618	+	0.911356i	$0.635036\pi$
$564$		0			0
$565$	7.01064	+	21.5765i	0.294940	+	0.907732i
$566$		0			0
$567$	0.500000	+	1.53884i	0.0209980	+	0.0646253i
$568$		0			0
$569$	9.10739	+	28.0297i	0.381802	+	1.17506i	0.938774	+	0.344534i	$0.111963\pi$
$569$	9.10739	+	28.0297i	0.381802	+	1.17506i	−0.556972	+	0.830531i	$0.688037\pi$
$570$		0			0
$571$	−9.92705	+	30.5523i	−0.415434	+	1.27857i	0.496428	+	0.868078i	$0.334645\pi$
$571$	−9.92705	+	30.5523i	−0.415434	+	1.27857i	−0.911862	+	0.410497i	$0.865355\pi$
$572$		0			0
$573$	19.5623	−	14.2128i	0.817227	−	0.593750i
$574$		0			0
$575$	33.3156	+	24.2052i	1.38936	+	1.00943i
$576$		0			0
$577$	−30.5623	+	22.2048i	−1.27233	+	0.924399i	−0.999293	−	0.0376062i	$-0.988027\pi$
$577$	−30.5623	+	22.2048i	−1.27233	+	0.924399i	−0.273033	+	0.962005i	$0.588027\pi$
$578$		0			0
$579$	1.76393	−	5.42882i	0.0733065	−	0.225614i
$580$		0			0
$581$	0.881966	+	2.71441i	0.0365901	+	0.112613i
$582$		0			0
$583$	1.29180	+	3.97574i	0.0535007	+	0.164658i
$584$		0			0
$585$	6.70820	−	20.6457i	0.277350	−	0.853596i
$586$		0			0
$587$	15.1353	+	10.9964i	0.624699	+	0.453870i	0.854560	−	0.519353i	$-0.173827\pi$
$587$	15.1353	+	10.9964i	0.624699	+	0.453870i	−0.229861	+	0.973224i	$0.573827\pi$
$588$		0			0
$589$	−14.2082	+	10.3229i	−0.585439	+	0.425346i
$590$		0			0
$591$	−7.85410	−	5.70634i	−0.323075	−	0.234727i
$592$		0			0
$593$	−22.0902			−0.907135			−0.453567	−	0.891222i	$-0.649849\pi$
$593$	−22.0902			−0.907135			−0.453567	+	0.891222i	$0.649849\pi$
$594$		0			0
$595$	−0.854102	+	2.62866i	−0.0350148	+	0.107764i
$596$		0			0
$597$	0.791796	−	2.43690i	0.0324061	−	0.0997356i
$598$		0			0
$599$	0.527864			0.0215679			0.0107840	−	0.999942i	$-0.496567\pi$
$599$	0.527864			0.0215679			0.0107840	+	0.999942i	$0.496567\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$		0			0
$603$	5.70820	−	17.5680i	0.232456	−	0.715426i
$604$		0			0
$605$	18.8435	−	13.6906i	0.766096	−	0.556601i
$606$		0			0
$607$	15.4377			0.626597			0.313298	−	0.949655i	$-0.398566\pi$
$607$	15.4377			0.626597			0.313298	+	0.949655i	$0.398566\pi$
$608$		0			0
$609$	−1.80902	−	1.31433i	−0.0733051	−	0.0532592i
$610$		0			0
$611$	6.35410	−	4.61653i	0.257059	−	0.186765i
$612$		0			0
$613$	−25.8713	−	18.7966i	−1.04493	−	0.759188i	−0.0736905	−	0.997281i	$-0.523478\pi$
$613$	−25.8713	−	18.7966i	−1.04493	−	0.759188i	−0.971242	+	0.238093i	$0.923478\pi$
$614$		0			0
$615$	11.7082			0.472120
$616$		0			0
$617$	3.01722	+	9.28605i	0.121469	+	0.373842i	0.993241	−	0.116069i	$-0.0370293\pi$
$617$	3.01722	+	9.28605i	0.121469	+	0.373842i	−0.871772	+	0.489911i	$0.837029\pi$
$618$		0			0
$619$	−12.1976	−	37.5402i	−0.490261	−	1.50887i	−0.824213	−	0.566279i	$-0.808382\pi$
$619$	−12.1976	−	37.5402i	−0.490261	−	1.50887i	0.333952	−	0.942590i	$-0.391618\pi$
$620$		0			0
$621$	−12.7254	+	39.1648i	−0.510654	+	1.57163i
$622$		0			0
$623$	−11.7082	+	8.50651i	−0.469079	+	0.340806i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$	3.61803	−	2.62866i	0.144490	−	0.104978i
$628$		0			0
$629$	−1.00000	+	3.07768i	−0.0398726	+	0.122715i
$630$		0			0
$631$	1.78115	+	5.48183i	0.0709066	+	0.218228i	0.980230	−	0.197862i	$-0.0633999\pi$
$631$	1.78115	+	5.48183i	0.0709066	+	0.218228i	−0.909323	+	0.416090i	$0.863400\pi$
$632$		0			0
$633$	4.07295	+	12.5352i	0.161885	+	0.498231i
$634$		0			0
$635$	35.5279			1.40988
$636$		0			0
$637$	−17.2082	−	12.5025i	−0.681814	−	0.495367i
$638$		0			0
$639$	7.09017	−	5.15131i	0.280483	−	0.203783i
$640$		0			0
$641$	−8.16312	−	5.93085i	−0.322424	−	0.234255i	0.414785	−	0.909919i	$-0.363857\pi$
$641$	−8.16312	−	5.93085i	−0.322424	−	0.234255i	−0.737209	+	0.675665i	$0.763857\pi$
$642$		0			0
$643$	−22.8328			−0.900438			−0.450219	−	0.892918i	$-0.648654\pi$
$643$	−22.8328			−0.900438			−0.450219	+	0.892918i	$0.648654\pi$
$644$		0			0
$645$	−3.35410	+	2.43690i	−0.132068	+	0.0959528i
$646$		0			0
$647$	−9.43769	+	29.0462i	−0.371034	+	1.14193i	0.575082	+	0.818096i	$0.304970\pi$
$647$	−9.43769	+	29.0462i	−0.371034	+	1.14193i	−0.946116	+	0.323829i	$0.895030\pi$
$648$		0			0
$649$	3.16718			0.124323
$650$		0			0
$651$	−4.85410			−0.190247
$652$		0			0
$653$	2.44427	−	7.52270i	0.0956518	−	0.294386i	−0.891771	−	0.452487i	$-0.850537\pi$
$653$	2.44427	−	7.52270i	0.0956518	−	0.294386i	0.987423	+	0.158101i	$0.0505371\pi$
$654$		0			0
$655$	12.2984	−	37.8505i	0.480537	−	1.47894i
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	19.7984	+	14.3844i	0.771235	+	0.560335i	0.902336	−	0.431034i	$-0.141851\pi$
$659$	19.7984	+	14.3844i	0.771235	+	0.560335i	−0.131101	+	0.991369i	$0.541851\pi$
$660$		0			0
$661$	32.9164	−	23.9152i	1.28030	−	0.930192i	0.280738	−	0.959784i	$-0.409421\pi$
$661$	32.9164	−	23.9152i	1.28030	−	0.930192i	0.999562	+	0.0295922i	$0.00942086\pi$
$662$		0			0
$663$	3.00000	+	2.17963i	0.116510	+	0.0846497i
$664$		0			0
$665$	6.54508	−	20.1437i	0.253808	−	0.781139i
$666$		0			0
$667$	3.51722	+	10.8249i	0.136187	+	0.419142i
$668$		0			0
$669$	6.85410	+	21.0948i	0.264995	+	0.815570i
$670$		0			0
$671$	−1.11146	+	3.42071i	−0.0429073	+	0.132055i
$672$		0			0
$673$	8.23607	−	5.98385i	0.317477	−	0.230661i	−0.417621	−	0.908621i	$-0.637136\pi$
$673$	8.23607	−	5.98385i	0.317477	−	0.230661i	0.735098	+	0.677961i	$0.237136\pi$
$674$		0			0
$675$	−20.2254	−	14.6946i	−0.778477	−	0.565597i
$676$		0			0
$677$	−6.78115	+	4.92680i	−0.260621	+	0.189352i	−0.710421	−	0.703777i	$-0.751495\pi$
$677$	−6.78115	+	4.92680i	−0.260621	+	0.189352i	0.449800	+	0.893129i	$0.351495\pi$
$678$		0			0
$679$	1.42705	−	4.39201i	0.0547652	−	0.168550i
$680$		0			0
$681$	5.94427	+	18.2946i	0.227785	+	0.701050i
$682$		0			0
$683$	1.39919	+	4.30625i	0.0535384	+	0.164774i	0.974251	−	0.225468i	$-0.0723912\pi$
$683$	1.39919	+	4.30625i	0.0535384	+	0.164774i	−0.920712	+	0.390242i	$0.872391\pi$
$684$		0			0
$685$	4.10739	+	12.6412i	0.156935	+	0.482997i
$686$		0			0
$687$	6.70820	+	4.87380i	0.255934	+	0.185947i
$688$		0			0
$689$	21.4894	−	15.6129i	0.818679	−	0.594805i
$690$		0			0
$691$	2.20820	+	1.60435i	0.0840040	+	0.0610325i	0.628995	−	0.777410i	$-0.283467\pi$
$691$	2.20820	+	1.60435i	0.0840040	+	0.0610325i	−0.544991	+	0.838442i	$0.683467\pi$
$692$		0			0
$693$	−2.47214			−0.0939087
$694$		0			0
$695$	−11.1803			−0.424094
$696$		0			0
$697$	1.23607	−	3.80423i	0.0468194	−	0.144095i
$698$		0			0
$699$	−14.9443			−0.565244
$700$		0			0
$701$	35.0132			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$701$	35.0132			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$702$		0			0
$703$	7.66312	−	23.5847i	0.289020	−	0.889512i
$704$		0			0
$705$	−1.11803	−	3.44095i	−0.0421076	−	0.129594i
$706$		0			0
$707$	−12.0902			−0.454698
$708$		0			0
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.0529906	−	0.998595i	$-0.516875\pi$
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.966095	+	0.258186i	$0.916875\pi$
$710$		0			0
$711$	−5.00000	+	3.63271i	−0.187515	+	0.136237i
$712$		0			0
$713$	19.9894	+	14.5231i	0.748607	+	0.543895i
$714$		0			0
$715$	6.70820	+	4.87380i	0.250873	+	0.182270i
$716$		0			0
$717$	−9.10739	−	28.0297i	−0.340122	−	1.04679i
$718$		0			0
$719$	11.3435	+	34.9116i	0.423040	+	1.30198i	0.904859	+	0.425712i	$0.139976\pi$
$719$	11.3435	+	34.9116i	0.423040	+	1.30198i	−0.481819	+	0.876271i	$0.660024\pi$
$720$		0			0
$721$	5.78115	−	17.7926i	0.215301	−	0.662630i
$722$		0			0
$723$	9.28115	−	6.74315i	0.345170	−	0.250781i
$724$		0			0
$725$	−6.90983			−0.256625
$726$		0			0
$727$	3.59017	−	2.60841i	0.133152	−	0.0967406i	−0.519216	−	0.854643i	$-0.673776\pi$
$727$	3.59017	−	2.60841i	0.133152	−	0.0967406i	0.652368	+	0.757903i	$0.273776\pi$
$728$		0			0
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$		0			0
$731$	0.437694	+	1.34708i	0.0161887	+	0.0498237i
$732$		0			0
$733$	8.33688	+	25.6583i	0.307930	+	0.947710i	0.978568	+	0.205925i	$0.0660204\pi$
$733$	8.33688	+	25.6583i	0.307930	+	0.947710i	−0.670638	+	0.741785i	$0.733980\pi$
$734$		0			0
$735$	−7.92705	+	5.75934i	−0.292394	+	0.212436i
$736$		0			0
$737$	5.70820	+	4.14725i	0.210264	+	0.152766i
$738$		0			0
$739$	−25.0623	+	18.2088i	−0.921932	+	0.669823i	−0.944004	−	0.329934i	$-0.892974\pi$
$739$	−25.0623	+	18.2088i	−0.921932	+	0.669823i	0.0220723	+	0.999756i	$0.492974\pi$
$740$		0			0
$741$	−22.9894	−	16.7027i	−0.844535	−	0.613591i
$742$		0			0
$743$	16.3607			0.600215			0.300108	−	0.953905i	$-0.402977\pi$
$743$	16.3607			0.600215			0.300108	+	0.953905i	$0.402977\pi$
$744$		0			0
$745$	−25.2254	−	18.3273i	−0.924188	−	0.671462i
$746$		0			0
$747$	−1.09017	+	3.35520i	−0.0398872	+	0.122760i
$748$		0			0
$749$	−16.8541			−0.615835
$750$		0			0
$751$	40.8885			1.49204			0.746022	−	0.665921i	$-0.231961\pi$
$751$	40.8885			1.49204			0.746022	+	0.665921i	$0.231961\pi$
$752$		0			0
$753$	−2.10739	+	6.48588i	−0.0767976	+	0.236359i
$754$		0			0
$755$	−10.0623	−	7.31069i	−0.366205	−	0.266063i
$756$		0			0
$757$	3.58359			0.130248			0.0651239	−	0.997877i	$-0.479256\pi$
$757$	3.58359			0.130248			0.0651239	+	0.997877i	$0.479256\pi$
$758$		0			0
$759$	−5.09017	−	3.69822i	−0.184761	−	0.134237i
$760$		0			0
$761$	−30.2984	+	22.0131i	−1.09832	+	0.797973i	−0.980784	−	0.195096i	$-0.937498\pi$
$761$	−30.2984	+	22.0131i	−1.09832	+	0.797973i	−0.117531	+	0.993069i	$0.537498\pi$
$762$		0			0
$763$	−13.0902	−	9.51057i	−0.473896	−	0.344306i
$764$		0			0
$765$	−2.76393	+	2.00811i	−0.0999302	+	0.0726035i
$766$		0			0
$767$	−6.21885	−	19.1396i	−0.224550	−	0.691092i
$768$		0			0
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	0.848058	−	0.529904i	$-0.177772\pi$
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	−0.997563	+	0.0697749i	$0.977772\pi$
$770$		0			0
$771$	−4.98936	+	15.3557i	−0.179687	+	0.553021i
$772$		0			0
$773$	−26.8262	+	19.4904i	−0.964873	+	0.701021i	−0.954277	−	0.298923i	$-0.903373\pi$
$773$	−26.8262	+	19.4904i	−0.964873	+	0.701021i	−0.0105954	+	0.999944i	$0.503373\pi$
$774$		0			0
$775$	−12.1353	+	8.81678i	−0.435911	+	0.316708i
$776$		0			0
$777$	5.54508	−	4.02874i	0.198929	−	0.144530i
$778$		0			0
$779$	−9.47214	+	29.1522i	−0.339374	+	1.04449i
$780$		0			0
$781$	1.03444	+	3.18368i	0.0370152	+	0.113921i
$782$		0			0
$783$	−2.13525	−	6.57164i	−0.0763078	−	0.234851i
$784$		0			0
$785$	16.6074	+	12.0660i	0.592743	+	0.430653i
$786$		0			0
$787$	−27.6525	−	20.0907i	−0.985704	−	0.716156i	−0.0267281	−	0.999643i	$-0.508509\pi$
$787$	−27.6525	−	20.0907i	−0.985704	−	0.716156i	−0.958976	+	0.283487i	$0.908509\pi$
$788$		0			0
$789$	17.8713	−	12.9843i	0.636236	−	0.462252i
$790$		0			0
$791$	−13.2812	−	9.64932i	−0.472223	−	0.343090i
$792$		0			0
$793$	22.8541			0.811573
$794$		0			0
$795$	−3.78115	−	11.6372i	−0.134104	−	0.412729i
$796$		0			0
$797$	4.39919	−	13.5393i	0.155827	−	0.479587i	−0.842417	−	0.538827i	$-0.818868\pi$
$797$	4.39919	−	13.5393i	0.155827	−	0.479587i	0.998244	+	0.0592400i	$0.0188677\pi$
$798$		0			0
$799$	−1.23607			−0.0437289
$800$		0			0
$801$	−17.8885			−0.632061
$802$		0			0
$803$	−2.12461	+	6.53888i	−0.0749759	+	0.230752i
$804$		0			0
$805$	−29.7984			−1.05025
$806$		0			0
$807$	17.2361			0.606738
$808$		0			0
$809$	12.9271	+	9.39205i	0.454491	+	0.330207i	0.791366	−	0.611342i	$-0.209370\pi$
$809$	12.9271	+	9.39205i	0.454491	+	0.330207i	−0.336875	+	0.941549i	$0.609370\pi$
$810$		0			0
$811$	−1.04508	+	0.759299i	−0.0366979	+	0.0266626i	−0.605983	−	0.795478i	$-0.707220\pi$
$811$	−1.04508	+	0.759299i	−0.0366979	+	0.0266626i	0.569285	+	0.822140i	$0.307220\pi$
$812$		0			0
$813$	6.47214	+	4.70228i	0.226988	+	0.164916i
$814$		0			0
$815$	−7.60081	−	23.3929i	−0.266245	−	0.819417i
$816$		0			0
$817$	−3.35410	−	10.3229i	−0.117345	−	0.361151i
$818$		0			0
$819$	4.85410	+	14.9394i	0.169616	+	0.522025i
$820$		0			0
$821$	6.08359	−	18.7234i	0.212319	−	0.653450i	−0.787014	−	0.616935i	$-0.788374\pi$
$821$	6.08359	−	18.7234i	0.212319	−	0.653450i	0.999333	−	0.0365154i	$-0.0116258\pi$
$822$		0			0
$823$	27.7426	−	20.1562i	0.967048	−	0.702601i	0.0122710	−	0.999925i	$-0.496094\pi$
$823$	27.7426	−	20.1562i	0.967048	−	0.702601i	0.954777	+	0.297323i	$0.0960939\pi$
$824$		0			0
$825$	3.09017	−	2.24514i	0.107586	−	0.0781657i
$826$		0			0
$827$	−24.2984	+	17.6538i	−0.844937	+	0.613883i	−0.923745	−	0.383007i	$-0.874889\pi$
$827$	−24.2984	+	17.6538i	−0.844937	+	0.613883i	0.0788082	+	0.996890i	$0.474889\pi$
$828$		0			0
$829$	−9.00658	+	27.7194i	−0.312811	+	0.962734i	0.663835	+	0.747879i	$0.268928\pi$
$829$	−9.00658	+	27.7194i	−0.312811	+	0.962734i	−0.976646	+	0.214855i	$0.931072\pi$
$830$		0			0
$831$	3.48936	+	10.7391i	0.121044	+	0.372537i
$832$		0			0
$833$	1.03444	+	3.18368i	0.0358413	+	0.110308i
$834$		0			0
$835$	3.84346	−	11.8290i	0.133008	−	0.409358i
$836$		0			0
$837$	−12.1353	−	8.81678i	−0.419456	−	0.304752i
$838$		0			0
$839$	3.35410	−	2.43690i	0.115796	−	0.0841311i	−0.528380	−	0.849008i	$-0.677200\pi$
$839$	3.35410	−	2.43690i	0.115796	−	0.0841311i	0.644176	+	0.764877i	$0.277200\pi$
$840$		0			0
$841$	21.9164	+	15.9232i	0.755738	+	0.549076i
$842$		0			0
$843$	1.09017			0.0375474
$844$		0			0
$845$	7.29837	−	22.4621i	0.251072	−	0.772719i
$846$		0			0
$847$	−5.20820	+	16.0292i	−0.178956	+	0.550770i
$848$		0			0
$849$	−23.1459			−0.794365
$850$		0			0
$851$	−34.8885			−1.19596
$852$		0			0
$853$	14.6180	−	44.9897i	0.500512	−	1.54042i	−0.307675	−	0.951491i	$-0.599551\pi$
$853$	14.6180	−	44.9897i	0.500512	−	1.54042i	0.808187	−	0.588926i	$-0.200449\pi$
$854$		0			0
$855$	21.1803	−	15.3884i	0.724352	−	0.526273i
$856$		0			0
$857$	−40.6869			−1.38984			−0.694919	−	0.719088i	$-0.744560\pi$
$857$	−40.6869			−1.38984			−0.694919	+	0.719088i	$0.744560\pi$
$858$		0			0
$859$	−22.9894	−	16.7027i	−0.784387	−	0.569890i	0.121906	−	0.992542i	$-0.461099\pi$
$859$	−22.9894	−	16.7027i	−0.784387	−	0.569890i	−0.906292	+	0.422651i	$0.861099\pi$
$860$		0			0
$861$	−6.85410	+	4.97980i	−0.233587	+	0.169711i
$862$		0			0
$863$	−33.6246	−	24.4297i	−1.14460	−	0.831597i	−0.156842	−	0.987624i	$-0.550131\pi$
$863$	−33.6246	−	24.4297i	−1.14460	−	0.831597i	−0.987753	+	0.156027i	$0.950131\pi$
$864$		0			0
$865$	−37.7639			−1.28401
$866$		0			0
$867$	5.07295	+	15.6129i	0.172286	+	0.530243i
$868$		0			0
$869$	−0.729490	−	2.24514i	−0.0247463	−	0.0761612i
$870$		0			0
$871$	13.8541	−	42.6385i	0.469428	−	1.44475i
$872$		0			0
$873$	4.61803	−	3.35520i	0.156297	−	0.113556i
$874$		0			0
$875$	5.59017	−	17.2048i	0.188982	−	0.581628i
$876$		0			0
$877$	−24.7082	+	17.9516i	−0.834337	+	0.606181i	−0.920783	−	0.390075i	$-0.872449\pi$
$877$	−24.7082	+	17.9516i	−0.834337	+	0.606181i	0.0864462	+	0.996257i	$0.472449\pi$
$878$		0			0
$879$	8.79837	−	27.0786i	0.296762	−	0.913339i
$880$		0			0
$881$	1.34752	+	4.14725i	0.0453992	+	0.139725i	0.971187	−	0.238320i	$-0.0765967\pi$
$881$	1.34752	+	4.14725i	0.0453992	+	0.139725i	−0.925787	+	0.378044i	$0.876597\pi$
$882$		0			0
$883$	14.6525	+	45.0957i	0.493095	+	1.51759i	0.819904	+	0.572500i	$0.194026\pi$
$883$	14.6525	+	45.0957i	0.493095	+	1.51759i	−0.326809	+	0.945090i	$0.605974\pi$
$884$		0			0
$885$	−9.27051			−0.311625
$886$		0			0
$887$	−4.76393	−	3.46120i	−0.159957	−	0.116216i	0.504927	−	0.863162i	$-0.331519\pi$
$887$	−4.76393	−	3.46120i	−0.159957	−	0.116216i	−0.664885	+	0.746946i	$0.731519\pi$
$888$		0			0
$889$	−20.7984	+	15.1109i	−0.697555	+	0.506803i
$890$		0			0
$891$	−0.618034	−	0.449028i	−0.0207049	−	0.0150430i
$892$		0			0
$893$	9.47214			0.316973
$894$		0			0
$895$	−17.1353	+	12.4495i	−0.572768	+	0.416141i
$896$		0			0
$897$	−12.3541	+	38.0220i	−0.412491	+	1.26952i
$898$		0			0
$899$	−4.14590			−0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$		0			0
$903$	0.927051	−	2.85317i	0.0308503	−	0.0949475i
$904$		0			0
$905$	9.47214	−	29.1522i	0.314864	−	0.969053i
$906$		0			0
$907$	−47.2492			−1.56888			−0.784442	−	0.620202i	$-0.787051\pi$
$907$	−47.2492			−1.56888			−0.784442	+	0.620202i	$0.787051\pi$
$908$		0			0
$909$	−12.0902	−	8.78402i	−0.401006	−	0.291348i
$910$		0			0
$911$	−28.9336	+	21.0215i	−0.958614	+	0.696474i	−0.952828	−	0.303510i	$-0.901842\pi$
$911$	−28.9336	+	21.0215i	−0.958614	+	0.696474i	−0.00578548	+	0.999983i	$0.501842\pi$
$912$		0			0
$913$	−1.09017	−	0.792055i	−0.0360794	−	0.0262132i
$914$		0			0
$915$	3.25329	−	10.0126i	0.107550	−	0.331006i
$916$		0			0
$917$	8.89919	+	27.3889i	0.293877	+	0.904461i
$918$		0			0
$919$	0.551663	+	1.69784i	0.0181977	+	0.0560067i	0.959743	−	0.280880i	$-0.0906262\pi$
$919$	0.551663	+	1.69784i	0.0181977	+	0.0560067i	−0.941545	+	0.336886i	$0.890626\pi$
$920$		0			0
$921$	1.47214	−	4.53077i	0.0485085	−	0.149294i
$922$		0			0
$923$	17.2082	−	12.5025i	0.566415	−	0.411525i
$924$		0			0
$925$	6.54508	−	20.1437i	0.215201	−	0.662321i
$926$		0			0
$927$	18.7082	−	13.5923i	0.614458	−	0.446430i
$928$		0			0
$929$	−11.3197	+	34.8383i	−0.371386	+	1.14301i	0.574499	+	0.818506i	$0.305197\pi$
$929$	−11.3197	+	34.8383i	−0.371386	+	1.14301i	−0.945885	+	0.324503i	$0.894803\pi$
$930$		0			0
$931$	−7.92705	−	24.3970i	−0.259799	−	0.799578i
$932$		0			0
$933$	−9.11803	−	28.0624i	−0.298511	−	0.918722i
$934$		0			0
$935$	−0.403252	−	1.24108i	−0.0131878	−	0.0405877i
$936$		0			0
$937$	−41.4787	−	30.1360i	−1.35505	−	0.984502i	−0.998743	−	0.0501333i	$-0.984035\pi$
$937$	−41.4787	−	30.1360i	−1.35505	−	0.984502i	−0.356308	−	0.934369i	$-0.615965\pi$
$938$		0			0
$939$	−17.1803	+	12.4822i	−0.560659	+	0.407343i
$940$		0			0
$941$	15.8435	+	11.5109i	0.516482	+	0.375246i	0.815277	−	0.579071i	$-0.196585\pi$
$941$	15.8435	+	11.5109i	0.516482	+	0.375246i	−0.298795	+	0.954317i	$0.596585\pi$
$942$		0			0
$943$	43.1246			1.40433
$944$		0			0
$945$	18.0902			0.588473
$946$		0			0
$947$	8.85410	−	27.2501i	0.287720	−	0.885510i	−0.697851	−	0.716243i	$-0.745860\pi$
$947$	8.85410	−	27.2501i	0.287720	−	0.885510i	0.985570	−	0.169267i	$-0.0541399\pi$
$948$		0			0
$949$	43.6869			1.41814
$950$		0			0
$951$	23.6525			0.766984
$952$		0			0
$953$	10.7361	−	33.0422i	0.347775	−	1.07034i	−0.612306	−	0.790621i	$-0.709758\pi$
$953$	10.7361	−	33.0422i	0.347775	−	1.07034i	0.960081	−	0.279721i	$-0.0902421\pi$
$954$		0			0
$955$	16.7082	+	51.4226i	0.540665	+	1.66400i
$956$		0			0
$957$	1.05573			0.0341268
$958$		0			0
$959$	−7.78115	−	5.65334i	−0.251267	−	0.182556i
$960$		0			0
$961$	17.7984	−	12.9313i	0.574141	−	0.417138i
$962$		0			0
$963$	−16.8541	−	12.2452i	−0.543116	−	0.394597i
$964$		0			0
$965$	10.3262	+	7.50245i	0.332413	+	0.241512i
$966$		0			0
$967$	−12.3262	−	37.9363i	−0.396385	−	1.21995i	−0.927878	−	0.372885i	$-0.878369\pi$
$967$	−12.3262	−	37.9363i	−0.396385	−	1.21995i	0.531493	−	0.847063i	$-0.321631\pi$
$968$		0			0
$969$	1.38197	+	4.25325i	0.0443951	+	0.136634i
$970$		0			0
$971$	−1.04508	+	3.21644i	−0.0335384	+	0.103220i	−0.966424	−	0.256951i	$-0.917282\pi$
$971$	−1.04508	+	3.21644i	−0.0335384	+	0.103220i	0.932886	+	0.360172i	$0.117282\pi$
$972$		0			0
$973$	6.54508	−	4.75528i	0.209826	−	0.152447i
$974$		0			0
$975$	−19.6353	−	14.2658i	−0.628831	−	0.456873i
$976$		0			0
$977$	27.2254	−	19.7804i	0.871019	−	0.632832i	−0.0598416	−	0.998208i	$-0.519060\pi$
$977$	27.2254	−	19.7804i	0.871019	−	0.632832i	0.930860	+	0.365376i	$0.119060\pi$
$978$		0			0
$979$	2.11146	−	6.49839i	0.0674824	−	0.207690i
$980$		0			0
$981$	−6.18034	−	19.0211i	−0.197323	−	0.607298i
$982$		0			0
$983$	−2.28115	−	7.02067i	−0.0727575	−	0.223924i	0.908064	−	0.418830i	$-0.137560\pi$
$983$	−2.28115	−	7.02067i	−0.0727575	−	0.223924i	−0.980822	+	0.194906i	$0.937560\pi$
$984$		0			0
$985$	17.5623	−	12.7598i	0.559582	−	0.406560i
$986$		0			0
$987$	2.11803	+	1.53884i	0.0674178	+	0.0489819i
$988$		0			0
$989$	−12.3541	+	8.97578i	−0.392838	+	0.285413i
$990$		0			0
$991$	23.7533	+	17.2578i	0.754548	+	0.548211i	0.897233	−	0.441557i	$-0.145574\pi$
$991$	23.7533	+	17.2578i	0.754548	+	0.548211i	−0.142685	+	0.989768i	$0.545574\pi$
$992$		0			0
$993$	17.1246			0.543433
$994$		0			0
$995$	4.63525	+	3.36771i	0.146947	+	0.106764i
$996$		0			0
$997$	−3.36475	+	10.3556i	−0.106563	+	0.327966i	−0.990094	−	0.140406i	$-0.955159\pi$
$997$	−3.36475	+	10.3556i	−0.106563	+	0.327966i	0.883531	+	0.468372i	$0.155159\pi$
$998$		0			0
$999$	21.1803			0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.b.161.1		4
4.3	odd	2		25.2.d.a.11.1	✓	4
12.11	even	2		225.2.h.b.136.1		4
20.3	even	4		125.2.e.a.74.2		8
20.7	even	4		125.2.e.a.74.1		8
20.19	odd	2		125.2.d.a.51.1		4
25.4	even	10		10000.2.a.l.1.1		2
25.16	even	5	inner	400.2.u.b.241.1		4
25.21	even	5		10000.2.a.c.1.2		2
100.3	even	20		625.2.b.a.624.2		4
100.11	odd	10		625.2.d.h.126.1		4
100.19	odd	10		625.2.d.b.501.1		4
100.23	even	20		625.2.e.c.499.2		8
100.27	even	20		625.2.e.c.499.1		8
100.31	odd	10		625.2.d.h.501.1		4
100.39	odd	10		625.2.d.b.126.1		4
100.47	even	20		625.2.b.a.624.3		4
100.59	odd	10		125.2.d.a.76.1		4
100.63	even	20		125.2.e.a.49.1		8
100.67	even	20		625.2.e.c.124.2		8
100.71	odd	10		625.2.a.b.1.2		2
100.79	odd	10		625.2.a.c.1.1		2
100.83	even	20		625.2.e.c.124.1		8
100.87	even	20		125.2.e.a.49.2		8
100.91	odd	10		25.2.d.a.16.1	yes	4
300.71	even	10		5625.2.a.f.1.1		2
300.179	even	10		5625.2.a.d.1.2		2
300.191	even	10		225.2.h.b.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	4.3	odd	2
25.2.d.a.16.1	yes	4	100.91	odd	10
125.2.d.a.51.1		4	20.19	odd	2
125.2.d.a.76.1		4	100.59	odd	10
125.2.e.a.49.1		8	100.63	even	20
125.2.e.a.49.2		8	100.87	even	20
125.2.e.a.74.1		8	20.7	even	4
125.2.e.a.74.2		8	20.3	even	4
225.2.h.b.91.1		4	300.191	even	10
225.2.h.b.136.1		4	12.11	even	2
400.2.u.b.161.1		4	1.1	even	1	trivial
400.2.u.b.241.1		4	25.16	even	5	inner
625.2.a.b.1.2		2	100.71	odd	10
625.2.a.c.1.1		2	100.79	odd	10
625.2.b.a.624.2		4	100.3	even	20
625.2.b.a.624.3		4	100.47	even	20
625.2.d.b.126.1		4	100.39	odd	10
625.2.d.b.501.1		4	100.19	odd	10
625.2.d.h.126.1		4	100.11	odd	10
625.2.d.h.501.1		4	100.31	odd	10
625.2.e.c.124.1		8	100.83	even	20
625.2.e.c.124.2		8	100.67	even	20
625.2.e.c.499.1		8	100.27	even	20
625.2.e.c.499.2		8	100.23	even	20
5625.2.a.d.1.2		2	300.179	even	10
5625.2.a.f.1.1		2	300.71	even	10
10000.2.a.c.1.2		2	25.21	even	5
10000.2.a.l.1.1		2	25.4	even	10

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-1.80902 - 1.31433i) q^{5} +1.61803 q^{7} +(1.61803 + 1.17557i) q^{9} +(-0.618034 + 0.449028i) q^{11} +(3.92705 + 2.85317i) q^{13} +(1.80902 - 1.31433i) q^{15} +(-0.236068 - 0.726543i) q^{17} +(1.80902 + 5.56758i) q^{19} +(-0.500000 + 1.53884i) q^{21} +(6.66312 - 4.84104i) q^{23} +(1.54508 + 4.75528i) q^{25} +(-4.04508 + 2.93893i) q^{27} +(-0.427051 + 1.31433i) q^{29} +(0.927051 + 2.85317i) q^{31} +(-0.236068 - 0.726543i) q^{33} +(-2.92705 - 2.12663i) q^{35} +(-3.42705 - 2.48990i) q^{37} +(-3.92705 + 2.85317i) q^{39} +(4.23607 + 3.07768i) q^{41} -1.85410 q^{43} +(-1.38197 - 4.25325i) q^{45} +(0.500000 - 1.53884i) q^{47} -4.38197 q^{49} +0.763932 q^{51} +(1.69098 - 5.20431i) q^{53} +1.70820 q^{55} -5.85410 q^{57} +(-3.35410 - 2.43690i) q^{59} +(3.80902 - 2.76741i) q^{61} +(2.61803 + 1.90211i) q^{63} +(-3.35410 - 10.3229i) q^{65} +(-2.85410 - 8.78402i) q^{67} +(2.54508 + 7.83297i) q^{69} +(1.35410 - 4.16750i) q^{71} +(7.28115 - 5.29007i) q^{73} -5.00000 q^{75} +(-1.00000 + 0.726543i) q^{77} +(-0.954915 + 2.93893i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.545085 + 1.67760i) q^{83} +(-0.527864 + 1.62460i) q^{85} +(-1.11803 - 0.812299i) q^{87} +(-7.23607 + 5.25731i) q^{89} +(6.35410 + 4.61653i) q^{91} -3.00000 q^{93} +(4.04508 - 12.4495i) q^{95} +(0.881966 - 2.71441i) q^{97} -1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + q^3 - 5 * q^5 + 2 * q^7 + 2 * q^9 + 2 * q^11 + 9 * q^13 + 5 * q^15 + 8 * q^17 + 5 * q^19 - 2 * q^21 + 11 * q^23 - 5 * q^25 - 5 * q^27 + 5 * q^29 - 3 * q^31 + 8 * q^33 - 5 * q^35 - 7 * q^37 - 9 * q^39 + 8 * q^41 + 6 * q^43 - 10 * q^45 + 2 * q^47 - 22 * q^49 + 12 * q^51 + 9 * q^53 - 20 * q^55 - 10 * q^57 + 13 * q^61 + 6 * q^63 + 2 * q^67 - q^69 - 8 * q^71 + 9 * q^73 - 20 * q^75 - 4 * q^77 - 15 * q^79 - q^81 - 9 * q^83 - 20 * q^85 - 20 * q^89 + 12 * q^91 - 12 * q^93 + 5 * q^95 + 8 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more