LMFDB - Embedded newform 1260.2.c.e.811.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (of order $2$, degree $1$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.13
Root			$-0.947441 - 1.04993i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} -1.00000i q^{5} +(2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +O(q^{10})$	\(q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} -1.00000i q^{5} +(2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +(-1.04993 - 0.947441i) q^{10} -0.477147i q^{11} -2.96271i q^{13} +(0.796939 - 3.65580i) q^{14} +(-3.91619 + 0.814543i) q^{16} +3.83353i q^{17} +5.31262 q^{19} +(-1.98950 + 0.204711i) q^{20} +(-0.500972 - 0.452069i) q^{22} -7.60808i q^{23} -1.00000 q^{25} +(-3.11064 - 2.80699i) q^{26} +(-3.08329 - 4.30039i) q^{28} -6.17752 q^{29} +3.38789 q^{31} +(-2.85514 + 4.88346i) q^{32} +(4.02494 + 3.63204i) q^{34} +(-1.31346 - 2.29670i) q^{35} -8.62867 q^{37} +(5.03339 - 5.57788i) q^{38} +(-1.67000 + 2.28279i) q^{40} -1.01125i q^{41} +6.85412i q^{43} +(-0.949282 + 0.0976772i) q^{44} +(-7.98796 - 7.20820i) q^{46} -6.21838 q^{47} +(3.54963 - 6.03325i) q^{49} +(-0.947441 + 1.04993i) q^{50} +(-5.89430 + 0.606499i) q^{52} +9.30380 q^{53} -0.477147 q^{55} +(-7.43634 - 0.837125i) q^{56} +(-5.85284 + 6.48597i) q^{58} +4.88854 q^{59} +4.75818i q^{61} +(3.20982 - 3.55705i) q^{62} +(2.42221 + 7.62449i) q^{64} -2.96271 q^{65} -1.30610i q^{67} +(7.62679 - 0.784764i) q^{68} +(-3.65580 - 0.796939i) q^{70} -9.18700i q^{71} -4.49766i q^{73} +(-8.17516 + 9.05951i) q^{74} +(-1.08755 - 10.5694i) q^{76} +(-0.626715 - 1.09586i) q^{77} -8.80833i q^{79} +(0.814543 + 3.91619i) q^{80} +(-1.06174 - 0.958097i) q^{82} +10.9520 q^{83} +3.83353 q^{85} +(7.19635 + 6.49388i) q^{86} +(-0.796835 + 1.08922i) q^{88} +13.1208i q^{89} +(-3.89141 - 6.80445i) q^{91} +(-15.1362 + 1.55746i) q^{92} +(-5.89154 + 6.52887i) q^{94} -5.31262i q^{95} -1.60612i q^{97} +(-2.97143 - 9.44302i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	0.947441	−	1.04993i	0.669942	−	0.742413i
$2$	0.947441	−	1.04993i	0.669942	−	0.742413i
$3$		0			0
$3$		0			0
$4$	−0.204711	−	1.98950i	−0.102355	−	0.994748i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.29670	−	1.31346i	0.868070	−	0.496442i
$7$	2.29670	−	1.31346i	0.868070	−	0.496442i
$8$	−2.28279	−	1.67000i	−0.807086	−	0.590433i
$9$		0			0
$10$	−1.04993	−	0.947441i	−0.332017	−	0.299607i
$11$		−	0.477147i		−	0.143865i	−0.997409	−	0.0719326i	$-0.977083\pi$
$11$		−	0.477147i		−	0.143865i	0.997409	−	0.0719326i	$-0.0229167\pi$
$12$		0			0
$13$		−	2.96271i		−	0.821708i	−0.911701	−	0.410854i	$-0.865231\pi$
$13$		−	2.96271i		−	0.821708i	0.911701	−	0.410854i	$-0.134769\pi$
$14$	0.796939	−	3.65580i	0.212991	−	0.977054i
$15$		0			0
$16$	−3.91619	+	0.814543i	−0.979047	+	0.203636i
$17$			3.83353i			0.929767i	0.885372	+	0.464883i	$0.153904\pi$
$17$			3.83353i			0.929767i	−0.885372	+	0.464883i	$0.846096\pi$
$18$		0			0
$19$	5.31262			1.21880			0.609399	−	0.792864i	$-0.291411\pi$
$19$	5.31262			1.21880			0.609399	+	0.792864i	$0.291411\pi$
$20$	−1.98950	+	0.204711i	−0.444865	+	0.0457747i
$21$		0			0
$22$	−0.500972	−	0.452069i	−0.106808	−	0.0963814i
$23$		−	7.60808i		−	1.58639i	−0.608965	−	0.793197i	$-0.708415\pi$
$23$		−	7.60808i		−	1.58639i	0.608965	−	0.793197i	$-0.291585\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.11064	−	2.80699i	−0.610047	−	0.550497i
$27$		0			0
$28$	−3.08329	−	4.30039i	−0.582687	−	0.812697i
$29$	−6.17752			−1.14714			−0.573569	−	0.819158i	$-0.694441\pi$
$29$	−6.17752			−1.14714			−0.573569	+	0.819158i	$0.694441\pi$
$30$		0			0
$31$	3.38789			0.608482			0.304241	−	0.952595i	$-0.401597\pi$
$31$	3.38789			0.608482			0.304241	+	0.952595i	$0.401597\pi$
$32$	−2.85514	+	4.88346i	−0.504723	+	0.863282i
$33$		0			0
$34$	4.02494	+	3.63204i	0.690271	+	0.622890i
$35$	−1.31346	−	2.29670i	−0.222016	−	0.388213i
$36$		0			0
$37$	−8.62867			−1.41854			−0.709272	−	0.704935i	$-0.750976\pi$
$37$	−8.62867			−1.41854			−0.709272	+	0.704935i	$0.750976\pi$
$38$	5.03339	−	5.57788i	0.816524	−	0.904852i
$39$		0			0
$40$	−1.67000	+	2.28279i	−0.264050	+	0.360940i
$41$		−	1.01125i		−	0.157930i	−0.996877	−	0.0789651i	$-0.974838\pi$
$41$		−	1.01125i		−	0.157930i	0.996877	−	0.0789651i	$-0.0251616\pi$
$42$		0			0
$43$			6.85412i			1.04524i	0.852565	+	0.522622i	$0.175046\pi$
$43$			6.85412i			1.04524i	−0.852565	+	0.522622i	$0.824954\pi$
$44$	−0.949282	+	0.0976772i	−0.143110	+	0.0147254i
$45$		0			0
$46$	−7.98796	−	7.20820i	−1.17776	−	1.06279i
$47$	−6.21838			−0.907043			−0.453522	−	0.891245i	$-0.649833\pi$
$47$	−6.21838			−0.907043			−0.453522	+	0.891245i	$0.649833\pi$
$48$		0			0
$49$	3.54963	−	6.03325i	0.507090	−	0.861893i
$50$	−0.947441	+	1.04993i	−0.133988	+	0.148483i
$51$		0			0
$52$	−5.89430	+	0.606499i	−0.817392	+	0.0841063i
$53$	9.30380			1.27797			0.638987	−	0.769217i	$-0.279354\pi$
$53$	9.30380			1.27797			0.638987	+	0.769217i	$0.279354\pi$
$54$		0			0
$55$	−0.477147			−0.0643385
$56$	−7.43634	−	0.837125i	−0.993723	−	0.111866i
$57$		0			0
$58$	−5.85284	+	6.48597i	−0.768515	+	0.851650i
$59$	4.88854			0.636433			0.318217	−	0.948018i	$-0.396916\pi$
$59$	4.88854			0.636433			0.318217	+	0.948018i	$0.396916\pi$
$60$		0			0
$61$			4.75818i			0.609222i	0.952477	+	0.304611i	$0.0985264\pi$
$61$			4.75818i			0.609222i	−0.952477	+	0.304611i	$0.901474\pi$
$62$	3.20982	−	3.55705i	0.407648	−	0.451745i
$63$		0			0
$64$	2.42221	+	7.62449i	0.302777	+	0.953061i
$65$	−2.96271			−0.367479
$66$		0			0
$67$		−	1.30610i		−	0.159565i	−0.996812	−	0.0797826i	$-0.974577\pi$
$67$		−	1.30610i		−	0.159565i	0.996812	−	0.0797826i	$-0.0254226\pi$
$68$	7.62679	−	0.784764i	0.924884	−	0.0951667i
$69$		0			0
$70$	−3.65580	−	0.796939i	−0.436952	−	0.0952525i
$71$		−	9.18700i		−	1.09030i	−0.838340	−	0.545148i	$-0.816473\pi$
$71$		−	9.18700i		−	1.09030i	0.838340	−	0.545148i	$-0.183527\pi$
$72$		0			0
$73$		−	4.49766i		−	0.526411i	−0.964740	−	0.263206i	$-0.915220\pi$
$73$		−	4.49766i		−	0.526411i	0.964740	−	0.263206i	$-0.0847797\pi$
$74$	−8.17516	+	9.05951i	−0.950343	+	1.05315i
$75$		0			0
$76$	−1.08755	−	10.5694i	−0.124751	−	1.21240i
$77$	−0.626715	−	1.09586i	−0.0714208	−	0.124885i
$78$		0			0
$79$		−	8.80833i		−	0.991015i	−0.868604	−	0.495507i	$-0.834982\pi$
$79$		−	8.80833i		−	0.991015i	0.868604	−	0.495507i	$-0.165018\pi$
$80$	0.814543	+	3.91619i	0.0910686	+	0.437843i
$81$		0			0
$82$	−1.06174	−	0.958097i	−0.117249	−	0.105804i
$83$	10.9520			1.20214			0.601068	−	0.799198i	$-0.294742\pi$
$83$	10.9520			1.20214			0.601068	+	0.799198i	$0.294742\pi$
$84$		0			0
$85$	3.83353			0.415804
$86$	7.19635	+	6.49388i	0.776003	+	0.700253i
$87$		0			0
$88$	−0.796835	+	1.08922i	−0.0849429	+	0.116112i
$89$			13.1208i			1.39080i	0.718621	+	0.695402i	$0.244774\pi$
$89$			13.1208i			1.39080i	−0.718621	+	0.695402i	$0.755226\pi$
$90$		0			0
$91$	−3.89141	−	6.80445i	−0.407931	−	0.713300i
$92$	−15.1362	+	1.55746i	−1.57806	+	0.162376i
$93$		0			0
$94$	−5.89154	+	6.52887i	−0.607666	+	0.673401i
$95$		−	5.31262i		−	0.545063i
$96$		0			0
$97$		−	1.60612i		−	0.163077i	−0.996670	−	0.0815384i	$-0.974017\pi$
$97$		−	1.60612i		−	0.163077i	0.996670	−	0.0815384i	$-0.0259833\pi$
$98$	−2.97143	−	9.44302i	−0.300160	−	0.953889i
$99$		0			0
$100$	0.204711	+	1.98950i	0.0204711	+	0.198950i
$101$			6.17664i			0.614599i	0.951613	+	0.307299i	$0.0994253\pi$
$101$			6.17664i			0.614599i	−0.951613	+	0.307299i	$0.900575\pi$
$102$		0			0
$103$	−16.8145			−1.65678			−0.828390	−	0.560151i	$-0.810743\pi$
$103$	−16.8145			−1.65678			−0.828390	+	0.560151i	$0.810743\pi$
$104$	−4.94772	+	6.76323i	−0.485164	+	0.663189i
$105$		0			0
$106$	8.81480	−	9.76835i	0.856169	−	0.948786i
$107$			9.15824i			0.885360i	0.896680	+	0.442680i	$0.145972\pi$
$107$			9.15824i			0.885360i	−0.896680	+	0.442680i	$0.854028\pi$
$108$		0			0
$109$	−15.2477			−1.46046			−0.730230	−	0.683201i	$-0.760587\pi$
$109$	−15.2477			−1.46046			−0.730230	+	0.683201i	$0.760587\pi$
$110$	−0.452069	+	0.500972i	−0.0431031	+	0.0477658i
$111$		0			0
$112$	−7.92442	+	7.01452i	−0.748788	+	0.662810i
$113$	4.04995			0.380987			0.190493	−	0.981688i	$-0.438991\pi$
$113$	4.04995			0.380987			0.190493	+	0.981688i	$0.438991\pi$
$114$		0			0
$115$	−7.60808			−0.709457
$116$	1.26461	+	12.2902i	0.117416	+	1.14111i
$117$		0			0
$118$	4.63160	−	5.13263i	0.426373	−	0.472496i
$119$	5.03519	+	8.80445i	0.461576	+	0.807102i
$120$		0			0
$121$	10.7723			0.979303
$122$	4.99576	+	4.50809i	0.452295	+	0.408143i
$123$		0			0
$124$	−0.693537	−	6.74018i	−0.0622814	−	0.605286i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	12.9949i		−	1.15311i	−0.817059	−	0.576554i	$-0.804397\pi$
$127$		−	12.9949i		−	1.15311i	0.817059	−	0.576554i	$-0.195603\pi$
$128$	10.3001	+	4.68060i	0.910409	+	0.413710i
$129$		0			0
$130$	−2.80699	+	3.11064i	−0.246190	+	0.272821i
$131$	−1.77552			−0.155128			−0.0775640	−	0.996987i	$-0.524714\pi$
$131$	−1.77552			−0.155128			−0.0775640	+	0.996987i	$0.524714\pi$
$132$		0			0
$133$	12.2015	−	6.97792i	1.05800	−	0.605063i
$134$	−1.37131	−	1.23745i	−0.118463	−	0.106899i
$135$		0			0
$136$	6.40198	−	8.75112i	0.548965	−	0.750402i
$137$	15.1622			1.29539			0.647695	−	0.761900i	$-0.275733\pi$
$137$	15.1622			1.29539			0.647695	+	0.761900i	$0.275733\pi$
$138$		0			0
$139$	18.8544			1.59921			0.799607	−	0.600524i	$-0.205041\pi$
$139$	18.8544			1.59921			0.799607	+	0.600524i	$0.205041\pi$
$140$	−4.30039	+	3.08329i	−0.363449	+	0.260585i
$141$		0			0
$142$	−9.64571	−	8.70414i	−0.809450	−	0.730435i
$143$	−1.41365			−0.118215
$144$		0			0
$145$			6.17752i			0.513015i
$146$	−4.72223	−	4.26127i	−0.390815	−	0.352665i
$147$		0			0
$148$	1.76638	+	17.1667i	0.145196	+	1.41109i
$149$	18.8439			1.54376			0.771878	−	0.635771i	$-0.219318\pi$
$149$	18.8439			1.54376			0.771878	+	0.635771i	$0.219318\pi$
$150$		0			0
$151$			18.6462i			1.51741i	0.651435	+	0.758704i	$0.274167\pi$
$151$			18.6462i			1.51741i	−0.651435	+	0.758704i	$0.725833\pi$
$152$	−12.1276	−	8.87206i	−0.983675	−	0.719619i
$153$		0			0
$154$	−1.74436	−	0.380257i	−0.140564	−	0.0306420i
$155$		−	3.38789i		−	0.272121i
$156$		0			0
$157$			22.6941i			1.81118i	0.424149	+	0.905592i	$0.360573\pi$
$157$			22.6941i			1.81118i	−0.424149	+	0.905592i	$0.639427\pi$
$158$	−9.24814	−	8.34538i	−0.735743	−	0.663922i
$159$		0			0
$160$	4.88346	+	2.85514i	0.386071	+	0.225719i
$161$	−9.99293	−	17.4734i	−0.787553	−	1.37710i
$162$		0			0
$163$		−	9.17980i		−	0.719017i	−0.933142	−	0.359509i	$-0.882944\pi$
$163$		−	9.17980i		−	0.719017i	0.933142	−	0.359509i	$-0.117056\pi$
$164$	−2.01187	+	0.207013i	−0.157101	+	0.0161650i
$165$		0			0
$166$	10.3764	−	11.4988i	0.805362	−	0.892483i
$167$	14.8751			1.15107			0.575535	−	0.817777i	$-0.304794\pi$
$167$	14.8751			1.15107			0.575535	+	0.817777i	$0.304794\pi$
$168$		0			0
$169$	4.22235			0.324796
$170$	3.63204	−	4.02494i	0.278565	−	0.308699i
$171$		0			0
$172$	13.6362	−	1.40311i	1.03975	−	0.106986i
$173$		−	18.2211i		−	1.38532i	−0.721262	−	0.692662i	$-0.756438\pi$
$173$		−	18.2211i		−	1.38532i	0.721262	−	0.692662i	$-0.243562\pi$
$174$		0			0
$175$	−2.29670	+	1.31346i	−0.173614	+	0.0992885i
$176$	0.388657	+	1.86860i	0.0292961	+	0.140851i
$177$		0			0
$178$	13.7760	+	12.4312i	1.03255	+	0.931758i
$179$		−	5.02780i		−	0.375796i	−0.982189	−	0.187898i	$-0.939833\pi$
$179$		−	5.02780i		−	0.375796i	0.982189	−	0.187898i	$-0.0601674\pi$
$180$		0			0
$181$			14.6503i			1.08895i	0.838777	+	0.544476i	$0.183271\pi$
$181$			14.6503i			1.08895i	−0.838777	+	0.544476i	$0.816729\pi$
$182$	−10.8311	−	2.36110i	−0.802853	−	0.175016i
$183$		0			0
$184$	−12.7055	+	17.3676i	−0.936660	+	1.28036i
$185$			8.62867i			0.634393i
$186$		0			0
$187$	1.82916			0.133761
$188$	1.27297	+	12.3714i	0.0928408	+	0.902279i
$189$		0			0
$190$	−5.57788	−	5.03339i	−0.404662	−	0.365161i
$191$			6.84692i			0.495426i	0.968833	+	0.247713i	$0.0796790\pi$
$191$			6.84692i			0.495426i	−0.968833	+	0.247713i	$0.920321\pi$
$192$		0			0
$193$	7.47575			0.538116			0.269058	−	0.963124i	$-0.413288\pi$
$193$	7.47575			0.538116			0.269058	+	0.963124i	$0.413288\pi$
$194$	−1.68632	−	1.52170i	−0.121070	−	0.109252i
$195$		0			0
$196$	−12.7298	−	5.82690i	−0.909270	−	0.416207i
$197$	14.2749			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$197$	14.2749			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$198$		0			0
$199$	−1.60743			−0.113948			−0.0569739	−	0.998376i	$-0.518145\pi$
$199$	−1.60743			−0.113948			−0.0569739	+	0.998376i	$0.518145\pi$
$200$	2.28279	+	1.67000i	0.161417	+	0.118087i
$201$		0			0
$202$	6.48505	+	5.85200i	0.456286	+	0.411745i
$203$	−14.1879	+	8.11395i	−0.995795	+	0.569487i
$204$		0			0
$205$	−1.01125			−0.0706285
$206$	−15.9307	+	17.6541i	−1.10995	+	1.23002i
$207$		0			0
$208$	2.41325	+	11.6025i	0.167329	+	0.804491i
$209$		−	2.53490i		−	0.175343i
$210$		0			0
$211$			1.32588i			0.0912770i	0.998958	+	0.0456385i	$0.0145322\pi$
$211$			1.32588i			0.0912770i	−0.998958	+	0.0456385i	$0.985468\pi$
$212$	−1.90459	−	18.5099i	−0.130808	−	1.27126i
$213$		0			0
$214$	9.61552	+	8.67689i	0.657303	+	0.593140i
$215$	6.85412			0.467447
$216$		0			0
$217$	7.78094	−	4.44986i	0.528205	−	0.302076i
$218$	−14.4463	+	16.0090i	−0.978424	+	1.08427i
$219$		0			0
$220$	0.0976772	+	0.949282i	0.00658539	+	0.0640006i
$221$	11.3576			0.763997
$222$		0			0
$223$	21.5307			1.44180			0.720902	−	0.693037i	$-0.243728\pi$
$223$	21.5307			1.44180			0.720902	+	0.693037i	$0.243728\pi$
$224$	−0.143157	+	14.9659i	−0.00956508	+	0.999954i
$225$		0			0
$226$	3.83709	−	4.25216i	0.255239	−	0.282850i
$227$	−14.0514			−0.932625			−0.466313	−	0.884620i	$-0.654418\pi$
$227$	−14.0514			−0.932625			−0.466313	+	0.884620i	$0.654418\pi$
$228$		0			0
$229$			17.1949i			1.13627i	0.822934	+	0.568136i	$0.192335\pi$
$229$			17.1949i			1.13627i	−0.822934	+	0.568136i	$0.807665\pi$
$230$	−7.20820	+	7.98796i	−0.475295	+	0.526710i
$231$		0			0
$232$	14.1020	+	10.3164i	0.925839	+	0.677308i
$233$	11.5500			0.756668			0.378334	−	0.925669i	$-0.376497\pi$
$233$	11.5500			0.756668			0.378334	+	0.925669i	$0.376497\pi$
$234$		0			0
$235$			6.21838i			0.405642i
$236$	−1.00074	−	9.72572i	−0.0651424	−	0.633091i
$237$		0			0
$238$	14.0146	+	3.05509i	0.908432	+	0.198032i
$239$		−	13.5047i		−	0.873549i	−0.899571	−	0.436774i	$-0.856121\pi$
$239$		−	13.5047i		−	0.873549i	0.899571	−	0.436774i	$-0.143879\pi$
$240$		0			0
$241$		−	6.07807i		−	0.391523i	−0.980652	−	0.195761i	$-0.937282\pi$
$241$		−	6.07807i		−	0.391523i	0.980652	−	0.195761i	$-0.0627178\pi$
$242$	10.2061	−	11.3102i	0.656076	−	0.727048i
$243$		0			0
$244$	9.46637	−	0.974050i	0.606022	−	0.0623572i
$245$	−6.03325	−	3.54963i	−0.385450	−	0.226778i
$246$		0			0
$247$		−	15.7397i		−	1.00150i
$248$	−7.73381	−	5.65776i	−0.491098	−	0.359268i
$249$		0			0
$250$	1.04993	+	0.947441i	0.0664035	+	0.0599214i
$251$	25.9947			1.64077			0.820385	−	0.571812i	$-0.193759\pi$
$251$	25.9947			1.64077			0.820385	+	0.571812i	$0.193759\pi$
$252$		0			0
$253$	−3.63017			−0.228227
$254$	−13.6437	−	12.3119i	−0.856083	−	0.772516i
$255$		0			0
$256$	14.6730	−	6.37980i	0.917065	−	0.398738i
$257$			26.1382i			1.63045i	0.579141	+	0.815227i	$0.303388\pi$
$257$			26.1382i			1.63045i	−0.579141	+	0.815227i	$0.696612\pi$
$258$		0			0
$259$	−19.8174	+	11.3334i	−1.23140	+	0.704226i
$260$	0.606499	+	5.89430i	0.0376135	+	0.365549i
$261$		0			0
$262$	−1.68220	+	1.86417i	−0.103927	+	0.115169i
$263$		−	20.1419i		−	1.24200i	−0.783809	−	0.621001i	$-0.786726\pi$
$263$		−	20.1419i		−	1.24200i	0.783809	−	0.621001i	$-0.213274\pi$
$264$		0			0
$265$		−	9.30380i		−	0.571528i
$266$	4.23383	−	19.4219i	0.259593	−	1.19083i
$267$		0			0
$268$	−2.59848	+	0.267372i	−0.158727	+	0.0163324i
$269$			25.1731i			1.53483i	0.641151	+	0.767415i	$0.278457\pi$
$269$			25.1731i			1.53483i	−0.641151	+	0.767415i	$0.721543\pi$
$270$		0			0
$271$	9.13276			0.554776			0.277388	−	0.960758i	$-0.410531\pi$
$271$	9.13276			0.554776			0.277388	+	0.960758i	$0.410531\pi$
$272$	−3.12257	−	15.0128i	−0.189334	−	0.910285i
$273$		0			0
$274$	14.3652	−	15.9192i	0.867836	−	0.961715i
$275$			0.477147i			0.0287731i
$276$		0			0
$277$	−17.2069			−1.03386			−0.516931	−	0.856027i	$-0.672926\pi$
$277$	−17.2069			−1.03386			−0.516931	+	0.856027i	$0.672926\pi$
$278$	17.8635	−	19.7959i	1.07138	−	1.18728i
$279$		0			0
$280$	−0.837125	+	7.43634i	−0.0500278	+	0.444407i
$281$	−10.6360			−0.634490			−0.317245	−	0.948344i	$-0.602758\pi$
$281$	−10.6360			−0.634490			−0.317245	+	0.948344i	$0.602758\pi$
$282$		0			0
$283$	−19.3615			−1.15092			−0.575462	−	0.817828i	$-0.695178\pi$
$283$	−19.3615			−1.15092			−0.575462	+	0.817828i	$0.695178\pi$
$284$	−18.2775	+	1.88068i	−1.08457	+	0.111598i
$285$		0			0
$286$	−1.33935	+	1.48423i	−0.0791974	+	0.0877646i
$287$	−1.32823	−	2.32253i	−0.0784032	−	0.137094i
$288$		0			0
$289$	2.30407			0.135534
$290$	6.48597	+	5.85284i	0.380869	+	0.343690i
$291$		0			0
$292$	−8.94807	+	0.920719i	−0.523646	+	0.0538810i
$293$		−	24.5856i		−	1.43631i	−0.695885	−	0.718153i	$-0.744988\pi$
$293$		−	24.5856i		−	1.43631i	0.695885	−	0.718153i	$-0.255012\pi$
$294$		0			0
$295$		−	4.88854i		−	0.284622i
$296$	19.6974	+	14.4099i	1.14489	+	0.837556i
$297$		0			0
$298$	17.8535	−	19.7848i	1.03423	−	1.14611i
$299$	−22.5405			−1.30355
$300$		0			0
$301$	9.00263	+	15.7418i	0.518903	+	0.907344i
$302$	19.5773	+	17.6662i	1.12654	+	1.01658i
$303$		0			0
$304$	−20.8052	+	4.32735i	−1.19326	+	0.248191i
$305$	4.75818			0.272452
$306$		0			0
$307$	3.23094			0.184399			0.0921997	−	0.995741i	$-0.470610\pi$
$307$	3.23094			0.184399			0.0921997	+	0.995741i	$0.470610\pi$
$308$	−2.05192	+	1.47118i	−0.116919	+	0.0838284i
$309$		0			0
$310$	−3.55705	−	3.20982i	−0.202027	−	0.182306i
$311$	9.34597			0.529962			0.264981	−	0.964254i	$-0.414634\pi$
$311$	9.34597			0.529962			0.264981	+	0.964254i	$0.414634\pi$
$312$		0			0
$313$		−	16.6495i		−	0.941085i	−0.882377	−	0.470543i	$-0.844058\pi$
$313$		−	16.6495i		−	0.941085i	0.882377	−	0.470543i	$-0.155942\pi$
$314$	23.8272	+	21.5013i	1.34465	+	1.21339i
$315$		0			0
$316$	−17.5241	+	1.80316i	−0.985810	+	0.101436i
$317$	−25.7874			−1.44836			−0.724182	−	0.689609i	$-0.757782\pi$
$317$	−25.7874			−1.44836			−0.724182	+	0.689609i	$0.757782\pi$
$318$		0			0
$319$			2.94759i			0.165033i
$320$	7.62449	−	2.42221i	0.426222	−	0.135406i
$321$		0			0
$322$	−27.8136	−	6.06318i	−1.54999	−	0.337888i
$323$			20.3661i			1.13320i
$324$		0			0
$325$			2.96271i			0.164342i
$326$	−9.63816	−	8.69732i	−0.533808	−	0.481700i
$327$		0			0
$328$	−1.68878	+	2.30846i	−0.0932473	+	0.127463i
$329$	−14.2817	+	8.16760i	−0.787377	+	0.450295i
$330$		0			0
$331$			33.4834i			1.84041i	0.391432	+	0.920207i	$0.371980\pi$
$331$			33.4834i			1.84041i	−0.391432	+	0.920207i	$0.628020\pi$
$332$	−2.24199	−	21.7889i	−0.123045	−	1.19582i
$333$		0			0
$334$	14.0933	−	15.6178i	0.771151	−	0.854571i
$335$	−1.30610			−0.0713598
$336$		0			0
$337$	−4.98366			−0.271477			−0.135739	−	0.990745i	$-0.543341\pi$
$337$	−4.98366			−0.271477			−0.135739	+	0.990745i	$0.543341\pi$
$338$	4.00042	−	4.43317i	0.217594	−	0.241133i
$339$		0			0
$340$	−0.784764	−	7.62679i	−0.0425598	−	0.413620i
$341$		−	1.61652i		−	0.0875395i
$342$		0			0
$343$	0.227975	−	18.5189i	0.0123095	−	0.999924i
$344$	11.4464	−	15.6465i	0.617147	−	0.843602i
$345$		0			0
$346$	−19.1309	−	17.2634i	−1.02848	−	0.928087i
$347$		−	2.96693i		−	0.159273i	−0.996824	−	0.0796367i	$-0.974624\pi$
$347$		−	2.96693i		−	0.159273i	0.996824	−	0.0796367i	$-0.0253760\pi$
$348$		0			0
$349$			15.7698i			0.844139i	0.906563	+	0.422070i	$0.138696\pi$
$349$			15.7698i			0.844139i	−0.906563	+	0.422070i	$0.861304\pi$
$350$	−0.796939	+	3.65580i	−0.0425982	+	0.195411i
$351$		0			0
$352$	2.33013	+	1.36232i	0.124196	+	0.0726121i
$353$		−	9.20491i		−	0.489928i	−0.969532	−	0.244964i	$-0.921224\pi$
$353$		−	9.20491i		−	0.489928i	0.969532	−	0.244964i	$-0.0787761\pi$
$354$		0			0
$355$	−9.18700			−0.487595
$356$	26.1038	−	2.68597i	1.38350	−	0.142356i
$357$		0			0
$358$	−5.27885	−	4.76355i	−0.278996	−	0.251761i
$359$			20.9031i			1.10322i	0.834102	+	0.551611i	$0.185987\pi$
$359$			20.9031i			1.10322i	−0.834102	+	0.551611i	$0.814013\pi$
$360$		0			0
$361$	9.22390			0.485468
$362$	15.3819	+	13.8803i	0.808452	+	0.729534i
$363$		0			0
$364$	−12.7408	+	9.13489i	−0.667800	+	0.478798i
$365$	−4.49766			−0.235418
$366$		0			0
$367$	−4.79845			−0.250477			−0.125239	−	0.992127i	$-0.539970\pi$
$367$	−4.79845			−0.250477			−0.125239	+	0.992127i	$0.539970\pi$
$368$	6.19710	+	29.7947i	0.323046	+	1.55315i
$369$		0			0
$370$	9.05951	+	8.17516i	0.470982	+	0.425006i
$371$	21.3680	−	12.2202i	1.10937	−	0.634441i
$372$		0			0
$373$	28.9408			1.49850			0.749250	−	0.662287i	$-0.230414\pi$
$373$	28.9408			1.49850			0.749250	+	0.662287i	$0.230414\pi$
$374$	1.73302	−	1.92049i	0.0896122	−	0.0993061i
$375$		0			0
$376$	14.1952	+	10.3847i	0.732062	+	0.535549i
$377$			18.3022i			0.942612i
$378$		0			0
$379$			4.73908i			0.243430i	0.992565	+	0.121715i	$0.0388394\pi$
$379$			4.73908i			0.243430i	−0.992565	+	0.121715i	$0.961161\pi$
$380$	−10.5694	+	1.08755i	−0.542200	+	0.0557901i
$381$		0			0
$382$	7.18880	+	6.48706i	0.367811	+	0.331907i
$383$	−11.9795			−0.612125			−0.306063	−	0.952011i	$-0.599012\pi$
$383$	−11.9795			−0.612125			−0.306063	+	0.952011i	$0.599012\pi$
$384$		0			0
$385$	−1.09586	+	0.626715i	−0.0558503	+	0.0319404i
$386$	7.08283	−	7.84902i	0.360507	−	0.399505i
$387$		0			0
$388$	−3.19537	+	0.328790i	−0.162220	+	0.0166918i
$389$	−24.1871			−1.22633			−0.613167	−	0.789953i	$-0.710105\pi$
$389$	−24.1871			−1.22633			−0.613167	+	0.789953i	$0.710105\pi$
$390$		0			0
$391$	29.1658			1.47498
$392$	−18.1786	+	7.84474i	−0.918156	+	0.396219i
$393$		0			0
$394$	13.5246	−	14.9877i	0.681362	−	0.755069i
$395$	−8.80833			−0.443195
$396$		0			0
$397$		−	37.1405i		−	1.86403i	−0.362420	−	0.932015i	$-0.618049\pi$
$397$		−	37.1405i		−	1.86403i	0.362420	−	0.932015i	$-0.381951\pi$
$398$	−1.52295	+	1.68769i	−0.0763384	+	0.0845964i
$399$		0			0
$400$	3.91619	−	0.814543i	0.195809	−	0.0407271i
$401$	−20.4040			−1.01893			−0.509464	−	0.860492i	$-0.670156\pi$
$401$	−20.4040			−1.01893			−0.509464	+	0.860492i	$0.670156\pi$
$402$		0			0
$403$		−	10.0373i		−	0.499995i
$404$	12.2884	−	1.26442i	0.611371	−	0.0629075i
$405$		0			0
$406$	−4.92311	+	22.5838i	−0.244330	+	1.12082i
$407$			4.11715i			0.204079i
$408$		0			0
$409$			4.69204i			0.232007i	0.993249	+	0.116003i	$0.0370083\pi$
$409$			4.69204i			0.232007i	−0.993249	+	0.116003i	$0.962992\pi$
$410$	−0.958097	+	1.06174i	−0.0473170	+	0.0524356i
$411$		0			0
$412$	3.44211	+	33.4523i	0.169580	+	1.64808i
$413$	11.2275	−	6.42091i	0.552468	−	0.315952i
$414$		0			0
$415$		−	10.9520i		−	0.537612i
$416$	14.4683	+	8.45896i	0.709365	+	0.414735i
$417$		0			0
$418$	−2.66147	−	2.40167i	−0.130177	−	0.117469i
$419$	−10.4551			−0.510766			−0.255383	−	0.966840i	$-0.582202\pi$
$419$	−10.4551			−0.510766			−0.255383	+	0.966840i	$0.582202\pi$
$420$		0			0
$421$	−29.0598			−1.41629			−0.708144	−	0.706068i	$-0.750467\pi$
$421$	−29.0598			−1.41629			−0.708144	+	0.706068i	$0.750467\pi$
$422$	1.39208	+	1.25619i	0.0677653	+	0.0611503i
$423$		0			0
$424$	−21.2386	−	15.5373i	−1.03144	−	0.754559i
$425$		−	3.83353i		−	0.185953i
$426$		0			0
$427$	6.24969	+	10.9281i	0.302444	+	0.528847i
$428$	18.2203	−	1.87479i	0.880710	−	0.0906214i
$429$		0			0
$430$	6.49388	−	7.19635i	0.313162	−	0.347039i
$431$		−	11.8497i		−	0.570779i	−0.958412	−	0.285389i	$-0.907877\pi$
$431$		−	11.8497i		−	0.570779i	0.958412	−	0.285389i	$-0.0921229\pi$
$432$		0			0
$433$		−	37.2566i		−	1.79044i	−0.445625	−	0.895220i	$-0.647019\pi$
$433$		−	37.2566i		−	1.79044i	0.445625	−	0.895220i	$-0.352981\pi$
$434$	2.69994	−	12.3854i	0.129601	−	0.594520i
$435$		0			0
$436$	3.12136	+	30.3352i	0.149486	+	1.45279i
$437$		−	40.4188i		−	1.93349i
$438$		0			0
$439$	−2.20068			−0.105033			−0.0525163	−	0.998620i	$-0.516724\pi$
$439$	−2.20068			−0.105033			−0.0525163	+	0.998620i	$0.516724\pi$
$440$	1.08922	+	0.796835i	0.0519267	+	0.0379876i
$441$		0			0
$442$	10.7607	−	11.9247i	0.511834	−	0.567202i
$443$		−	5.86101i		−	0.278465i	−0.990260	−	0.139233i	$-0.955536\pi$
$443$		−	5.86101i		−	0.278465i	0.990260	−	0.139233i	$-0.0444636\pi$
$444$		0			0
$445$	13.1208			0.621987
$446$	20.3991	−	22.6058i	0.965925	−	1.07041i
$447$		0			0
$448$	15.5776	+	14.3297i	0.735971	+	0.677013i
$449$	11.2784			0.532259			0.266129	−	0.963937i	$-0.414255\pi$
$449$	11.2784			0.532259			0.266129	+	0.963937i	$0.414255\pi$
$450$		0			0
$451$	−0.482513			−0.0227207
$452$	−0.829068	−	8.05735i	−0.0389961	−	0.378986i
$453$		0			0
$454$	−13.3129	+	14.7530i	−0.624805	+	0.692394i
$455$	−6.80445	+	3.89141i	−0.318997	+	0.182432i
$456$		0			0
$457$	10.5671			0.494307			0.247153	−	0.968976i	$-0.420505\pi$
$457$	10.5671			0.494307			0.247153	+	0.968976i	$0.420505\pi$
$458$	18.0535	+	16.2912i	0.843584	+	0.761237i
$459$		0			0
$460$	1.55746	+	15.1362i	0.0726167	+	0.705731i
$461$			0.502682i			0.0234122i	0.999931	+	0.0117061i	$0.00372626\pi$
$461$			0.502682i			0.0234122i	−0.999931	+	0.0117061i	$0.996274\pi$
$462$		0			0
$463$		−	16.5694i		−	0.770044i	−0.922907	−	0.385022i	$-0.874194\pi$
$463$		−	16.5694i		−	0.770044i	0.922907	−	0.385022i	$-0.125806\pi$
$464$	24.1923	−	5.03185i	1.12310	−	0.233598i
$465$		0			0
$466$	10.9430	−	12.1267i	0.506924	−	0.561761i
$467$	−17.1182			−0.792137			−0.396069	−	0.918221i	$-0.629626\pi$
$467$	−17.1182			−0.792137			−0.396069	+	0.918221i	$0.629626\pi$
$468$		0			0
$469$	−1.71551	−	2.99971i	−0.0792149	−	0.138514i
$470$	6.52887	+	5.89154i	0.301154	+	0.271757i
$471$		0			0
$472$	−11.1595	−	8.16384i	−0.513657	−	0.375771i
$473$	3.27042			0.150374
$474$		0			0
$475$	−5.31262			−0.243760
$476$	16.4857	−	11.8199i	0.755619	−	0.541763i
$477$		0			0
$478$	−14.1790	−	12.7949i	−0.648534	−	0.585227i
$479$	7.51289			0.343272			0.171636	−	0.985160i	$-0.445095\pi$
$479$	7.51289			0.343272			0.171636	+	0.985160i	$0.445095\pi$
$480$		0			0
$481$			25.5643i			1.16563i
$482$	−6.38155	−	5.75861i	−0.290672	−	0.262298i
$483$		0			0
$484$	−2.20521	−	21.4315i	−0.100237	−	0.974159i
$485$	−1.60612			−0.0729302
$486$		0			0
$487$			18.3725i			0.832537i	0.909242	+	0.416269i	$0.136662\pi$
$487$			18.3725i			0.832537i	−0.909242	+	0.416269i	$0.863338\pi$
$488$	7.94614	−	10.8619i	0.359705	−	0.491695i
$489$		0			0
$490$	−9.44302	+	2.97143i	−0.426592	+	0.134236i
$491$			12.3732i			0.558395i	0.960234	+	0.279197i	$0.0900684\pi$
$491$			12.3732i			0.558395i	−0.960234	+	0.279197i	$0.909932\pi$
$492$		0			0
$493$		−	23.6817i		−	1.06657i
$494$	−16.5257	−	14.9125i	−0.743524	−	0.670944i
$495$		0			0
$496$	−13.2676	+	2.75958i	−0.595732	+	0.123909i
$497$	−12.0668	−	21.0997i	−0.541269	−	0.946453i
$498$		0			0
$499$		−	3.90928i		−	0.175003i	−0.996164	−	0.0875017i	$-0.972112\pi$
$499$		−	3.90928i		−	0.175003i	0.996164	−	0.0875017i	$-0.0278883\pi$
$500$	1.98950	−	0.204711i	0.0889730	−	0.00915495i
$501$		0			0
$502$	24.6284	−	27.2926i	1.09922	−	1.21813i
$503$	−20.7397			−0.924738			−0.462369	−	0.886688i	$-0.653000\pi$
$503$	−20.7397			−0.924738			−0.462369	+	0.886688i	$0.653000\pi$
$504$		0			0
$505$	6.17664			0.274857
$506$	−3.43937	+	3.81143i	−0.152899	+	0.169439i
$507$		0			0
$508$	−25.8532	+	2.66019i	−1.14705	+	0.118027i
$509$			19.9445i			0.884025i	0.897009	+	0.442012i	$0.145735\pi$
$509$			19.9445i			0.884025i	−0.897009	+	0.442012i	$0.854265\pi$
$510$		0			0
$511$	−5.90751	−	10.3298i	−0.261333	−	0.456962i
$512$	7.20349	−	21.4502i	0.318352	−	0.947972i
$513$		0			0
$514$	27.4433	+	24.7644i	1.21047	+	1.09231i
$515$			16.8145i			0.740935i
$516$		0			0
$517$			2.96708i			0.130492i
$518$	−6.87653	+	31.5447i	−0.302137	+	1.38600i
$519$		0			0
$520$	6.76323	+	4.94772i	0.296587	+	0.216972i
$521$			37.8103i			1.65650i	0.560361	+	0.828249i	$0.310662\pi$
$521$			37.8103i			1.65650i	−0.560361	+	0.828249i	$0.689338\pi$
$522$		0			0
$523$	−16.5206			−0.722398			−0.361199	−	0.932489i	$-0.617632\pi$
$523$	−16.5206			−0.722398			−0.361199	+	0.932489i	$0.617632\pi$
$524$	0.363468	+	3.53239i	0.0158782	+	0.154313i
$525$		0			0
$526$	−21.1476	−	19.0833i	−0.922080	−	0.832070i
$527$			12.9875i			0.565746i
$528$		0			0
$529$	−34.8828			−1.51664
$530$	−9.76835	−	8.81480i	−0.424310	−	0.382890i
$531$		0			0
$532$	−16.3803	−	22.8463i	−0.710177	−	0.990513i
$533$	−2.99603			−0.129773
$534$		0			0
$535$	9.15824			0.395945
$536$	−2.18118	+	2.98154i	−0.0942127	+	0.128783i
$537$		0			0
$538$	26.4300	+	23.8500i	1.13948	+	1.02825i
$539$	−2.87875	−	1.69370i	−0.123996	−	0.0729527i
$540$		0			0
$541$	−32.6251			−1.40266			−0.701331	−	0.712836i	$-0.747411\pi$
$541$	−32.6251			−1.40266			−0.701331	+	0.712836i	$0.747411\pi$
$542$	8.65275	−	9.58877i	0.371668	−	0.411873i
$543$		0			0
$544$	−18.7209	−	10.9453i	−0.802650	−	0.469274i
$545$			15.2477i			0.653138i
$546$		0			0
$547$			35.9526i			1.53722i	0.639716	+	0.768612i	$0.279052\pi$
$547$			35.9526i			1.53722i	−0.639716	+	0.768612i	$0.720948\pi$
$548$	−3.10386	−	30.1650i	−0.132590	−	1.28859i
$549$		0			0
$550$	0.500972	+	0.452069i	0.0213615	+	0.0192763i
$551$	−32.8188			−1.39813
$552$		0			0
$553$	−11.5694	−	20.2301i	−0.491982	−	0.860270i
$554$	−16.3025	+	18.0661i	−0.692628	+	0.767553i
$555$		0			0
$556$	−3.85971	−	37.5108i	−0.163688	−	1.59081i
$557$	8.84229			0.374660			0.187330	−	0.982297i	$-0.440017\pi$
$557$	8.84229			0.374660			0.187330	+	0.982297i	$0.440017\pi$
$558$		0			0
$559$	20.3068			0.858885
$560$	7.01452	+	7.92442i	0.296418	+	0.334868i
$561$		0			0
$562$	−10.0770	+	11.1671i	−0.425072	+	0.471054i
$563$	−17.7594			−0.748471			−0.374235	−	0.927334i	$-0.622095\pi$
$563$	−17.7594			−0.748471			−0.374235	+	0.927334i	$0.622095\pi$
$564$		0			0
$565$		−	4.04995i		−	0.170383i
$566$	−18.3439	+	20.3283i	−0.771052	+	0.854462i
$567$		0			0
$568$	−15.3423	+	20.9719i	−0.643747	+	0.879963i
$569$	−36.7269			−1.53967			−0.769835	−	0.638243i	$-0.779661\pi$
$569$	−36.7269			−1.53967			−0.769835	+	0.638243i	$0.779661\pi$
$570$		0			0
$571$			17.1069i			0.715902i	0.933740	+	0.357951i	$0.116524\pi$
$571$			17.1069i			0.715902i	−0.933740	+	0.357951i	$0.883476\pi$
$572$	0.289389	+	2.81245i	0.0121000	+	0.117594i
$573$		0			0
$574$	−3.69692	−	0.805902i	−0.154306	−	0.0336377i
$575$			7.60808i			0.317279i
$576$		0			0
$577$			37.9794i			1.58110i	0.612395	+	0.790552i	$0.290206\pi$
$577$			37.9794i			1.58110i	−0.612395	+	0.790552i	$0.709794\pi$
$578$	2.18297	−	2.41912i	0.0907998	−	0.100622i
$579$		0			0
$580$	12.2902	−	1.26461i	0.510321	−	0.0525099i
$581$	25.1534	−	14.3850i	1.04354	−	0.596792i
$582$		0			0
$583$		−	4.43928i		−	0.183856i
$584$	−7.51108	+	10.2672i	−0.310811	+	0.424859i
$585$		0			0
$586$	−25.8132	−	23.2934i	−1.06633	−	0.962242i
$587$	40.1743			1.65817			0.829085	−	0.559122i	$-0.188862\pi$
$587$	40.1743			1.65817			0.829085	+	0.559122i	$0.188862\pi$
$588$		0			0
$589$	17.9985			0.741617
$590$	−5.13263	−	4.63160i	−0.211307	−	0.190680i
$591$		0			0
$592$	33.7915	−	7.02842i	1.38882	−	0.288866i
$593$			2.80855i			0.115333i	0.998336	+	0.0576667i	$0.0183661\pi$
$593$			2.80855i			0.115333i	−0.998336	+	0.0576667i	$0.981634\pi$
$594$		0			0
$595$	8.80445	−	5.03519i	0.360947	−	0.206423i
$596$	−3.85756	−	37.4899i	−0.158012	−	1.53565i
$597$		0			0
$598$	−21.3558	+	23.6660i	−0.873305	+	0.967775i
$599$			10.0933i			0.412399i	0.978510	+	0.206200i	$0.0661097\pi$
$599$			10.0933i			0.412399i	−0.978510	+	0.206200i	$0.933890\pi$
$600$		0			0
$601$		−	8.17083i		−	0.333295i	−0.986017	−	0.166648i	$-0.946706\pi$
$601$		−	8.17083i		−	0.333295i	0.986017	−	0.166648i	$-0.0532942\pi$
$602$	25.0573	+	5.46232i	1.02126	+	0.222627i
$603$		0			0
$604$	37.0966	−	3.81708i	1.50944	−	0.155315i
$605$		−	10.7723i		−	0.437958i
$606$		0			0
$607$	20.7112			0.840642			0.420321	−	0.907375i	$-0.361917\pi$
$607$	20.7112			0.840642			0.420321	+	0.907375i	$0.361917\pi$
$608$	−15.1683	+	25.9439i	−0.615155	+	1.05217i
$609$		0			0
$610$	4.50809	−	4.99576i	0.182527	−	0.202272i
$611$			18.4232i			0.745325i
$612$		0			0
$613$	4.61369			0.186345			0.0931726	−	0.995650i	$-0.470299\pi$
$613$	4.61369			0.186345			0.0931726	+	0.995650i	$0.470299\pi$
$614$	3.06112	−	3.39226i	0.123537	−	0.136901i
$615$		0			0
$616$	−0.399432	+	3.54823i	−0.0160936	+	0.142962i
$617$	−13.3799			−0.538655			−0.269328	−	0.963049i	$-0.586801\pi$
$617$	−13.3799			−0.538655			−0.269328	+	0.963049i	$0.586801\pi$
$618$		0			0
$619$	−36.4215			−1.46390			−0.731951	−	0.681357i	$-0.761390\pi$
$619$	−36.4215			−1.46390			−0.731951	+	0.681357i	$0.761390\pi$
$620$	−6.74018	+	0.693537i	−0.270692	+	0.0278531i
$621$		0			0
$622$	8.85476	−	9.81263i	0.355044	−	0.393451i
$623$	17.2337	+	30.1345i	0.690454	+	1.20732i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−17.4808	−	15.7744i	−0.698674	−	0.630473i
$627$		0			0
$628$	45.1498	−	4.64572i	1.80167	−	0.185385i
$629$		−	33.0782i		−	1.31892i
$630$		0			0
$631$			23.3976i			0.931442i	0.884932	+	0.465721i	$0.154205\pi$
$631$			23.3976i			0.931442i	−0.884932	+	0.465721i	$0.845795\pi$
$632$	−14.7099	+	20.1075i	−0.585128	+	0.799835i
$633$		0			0
$634$	−24.4320	+	27.0750i	−0.970320	+	1.07528i
$635$	−12.9949			−0.515686
$636$		0			0
$637$	−17.8748	−	10.5165i	−0.708224	−	0.416680i
$638$	3.09476	+	2.79267i	0.122523	+	0.110563i
$639$		0			0
$640$	4.68060	−	10.3001i	0.185017	−	0.407147i
$641$	−14.4482			−0.570668			−0.285334	−	0.958428i	$-0.592104\pi$
$641$	−14.4482			−0.570668			−0.285334	+	0.958428i	$0.592104\pi$
$642$		0			0
$643$	14.1004			0.556065			0.278033	−	0.960572i	$-0.410318\pi$
$643$	14.1004			0.556065			0.278033	+	0.960572i	$0.410318\pi$
$644$	−32.7177	+	23.4579i	−1.28926	+	0.924370i
$645$		0			0
$646$	21.3830	+	19.2956i	0.841301	+	0.759177i
$647$	−13.1557			−0.517205			−0.258602	−	0.965984i	$-0.583262\pi$
$647$	−13.1557			−0.517205			−0.258602	+	0.965984i	$0.583262\pi$
$648$		0			0
$649$		−	2.33255i		−	0.0915606i
$650$	3.11064	+	2.80699i	0.122009	+	0.110099i
$651$		0			0
$652$	−18.2632	+	1.87920i	−0.715241	+	0.0735953i
$653$	−34.5944			−1.35378			−0.676892	−	0.736083i	$-0.736673\pi$
$653$	−34.5944			−1.35378			−0.676892	+	0.736083i	$0.736673\pi$
$654$		0			0
$655$			1.77552i			0.0693753i
$656$	0.823703	+	3.96023i	0.0321602	+	0.154621i
$657$		0			0
$658$	−4.95567	+	22.7331i	−0.193192	+	0.886230i
$659$		−	8.35962i		−	0.325644i	−0.986655	−	0.162822i	$-0.947940\pi$
$659$		−	8.35962i		−	0.325644i	0.986655	−	0.162822i	$-0.0520597\pi$
$660$		0			0
$661$		−	45.6469i		−	1.77546i	−0.460366	−	0.887729i	$-0.652282\pi$
$661$		−	45.6469i		−	1.77546i	0.460366	−	0.887729i	$-0.347718\pi$
$662$	35.1553	+	31.7235i	1.36635	+	1.23297i
$663$		0			0
$664$	−25.0010	−	18.2898i	−0.970228	−	0.709782i
$665$	−6.97792	−	12.2015i	−0.270592	−	0.473153i
$666$		0			0
$667$			46.9991i			1.81981i
$668$	−3.04510	−	29.5940i	−0.117818	−	1.14503i
$669$		0			0
$670$	−1.23745	+	1.37131i	−0.0478069	+	0.0529784i
$671$	2.27035			0.0876459
$672$		0			0
$673$	−39.4155			−1.51936			−0.759678	−	0.650299i	$-0.774644\pi$
$673$	−39.4155			−1.51936			−0.759678	+	0.650299i	$0.774644\pi$
$674$	−4.72173	+	5.23250i	−0.181874	+	0.201548i
$675$		0			0
$676$	−0.864360	−	8.40034i	−0.0332446	−	0.323090i
$677$			19.6704i			0.755995i	0.925807	+	0.377997i	$0.123387\pi$
$677$			19.6704i			0.755995i	−0.925807	+	0.377997i	$0.876613\pi$
$678$		0			0
$679$	−2.10958	−	3.68877i	−0.0809582	−	0.141562i
$680$	−8.75112	−	6.40198i	−0.335590	−	0.245505i
$681$		0			0
$682$	−1.69723	−	1.53156i	−0.0649905	−	0.0586464i
$683$			5.27739i			0.201934i	0.994890	+	0.100967i	$0.0321936\pi$
$683$			5.27739i			0.201934i	−0.994890	+	0.100967i	$0.967806\pi$
$684$		0			0
$685$		−	15.1622i		−	0.579316i
$686$	−19.2275	−	17.7849i	−0.734111	−	0.679030i
$687$		0			0
$688$	−5.58297	−	26.8420i	−0.212849	−	1.02334i
$689$		−	27.5645i		−	1.05012i
$690$		0			0
$691$	8.48775			0.322889			0.161445	−	0.986882i	$-0.448385\pi$
$691$	8.48775			0.322889			0.161445	+	0.986882i	$0.448385\pi$
$692$	−36.2508	+	3.73005i	−1.37805	+	0.141795i
$693$		0			0
$694$	−3.11508	−	2.81100i	−0.118247	−	0.106704i
$695$		−	18.8544i		−	0.715190i
$696$		0			0
$697$	3.87664			0.146838
$698$	16.5572	+	14.9410i	0.626700	+	0.565524i
$699$		0			0
$700$	3.08329	+	4.30039i	0.116537	+	0.162539i
$701$	10.1888			0.384825			0.192412	−	0.981314i	$-0.438369\pi$
$701$	10.1888			0.384825			0.192412	+	0.981314i	$0.438369\pi$
$702$		0			0
$703$	−45.8408			−1.72892
$704$	3.63800	−	1.15575i	0.137112	−	0.0435591i
$705$		0			0
$706$	−9.66452	−	8.72111i	−0.363729	−	0.328223i
$707$	8.11279	+	14.1859i	0.305113	+	0.533514i
$708$		0			0
$709$	3.99960			0.150208			0.0751041	−	0.997176i	$-0.476071\pi$
$709$	3.99960			0.150208			0.0751041	+	0.997176i	$0.476071\pi$
$710$	−8.70414	+	9.64571i	−0.326660	+	0.361997i
$711$		0			0
$712$	21.9117	−	29.9520i	0.821177	−	1.12250i
$713$		−	25.7753i		−	0.965292i
$714$		0			0
$715$			1.41365i			0.0528675i
$716$	−10.0028	+	1.02925i	−0.373822	+	0.0384647i
$717$		0			0
$718$	21.9468	+	19.8044i	0.819046	+	0.739094i
$719$	−8.22659			−0.306800			−0.153400	−	0.988164i	$-0.549022\pi$
$719$	−8.22659			−0.306800			−0.153400	+	0.988164i	$0.549022\pi$
$720$		0			0
$721$	−38.6178	+	22.0852i	−1.43820	+	0.822496i
$722$	8.73910	−	9.68446i	0.325236	−	0.360418i
$723$		0			0
$724$	29.1468	−	2.99908i	1.08323	−	0.111460i
$725$	6.17752			0.229427
$726$		0			0
$727$	−2.05684			−0.0762839			−0.0381419	−	0.999272i	$-0.512144\pi$
$727$	−2.05684			−0.0762839			−0.0381419	+	0.999272i	$0.512144\pi$
$728$	−2.48016	+	22.0317i	−0.0919208	+	0.816551i
$729$		0			0
$730$	−4.26127	+	4.72223i	−0.157717	+	0.174778i
$731$	−26.2755			−0.971833
$732$		0			0
$733$			24.8578i			0.918145i	0.888399	+	0.459072i	$0.151818\pi$
$733$			24.8578i			0.918145i	−0.888399	+	0.459072i	$0.848182\pi$
$734$	−4.54625	+	5.03804i	−0.167805	+	0.185958i
$735$		0			0
$736$	37.1537	+	21.7221i	1.36950	+	0.800689i
$737$	−0.623201			−0.0229559
$738$		0			0
$739$			1.48614i			0.0546686i	0.999626	+	0.0273343i	$0.00870186\pi$
$739$			1.48614i			0.0546686i	−0.999626	+	0.0273343i	$0.991298\pi$
$740$	17.1667	−	1.76638i	0.631061	−	0.0649335i
$741$		0			0
$742$	7.41456	−	34.0128i	0.272197	−	1.24865i
$743$			4.73363i			0.173660i	0.996223	+	0.0868299i	$0.0276737\pi$
$743$			4.73363i			0.173660i	−0.996223	+	0.0868299i	$0.972326\pi$
$744$		0			0
$745$		−	18.8439i		−	0.690389i
$746$	27.4197	−	30.3859i	1.00391	−	1.11251i
$747$		0			0
$748$	−0.374448	−	3.63910i	−0.0136912	−	0.133059i
$749$	12.0290	+	21.0337i	0.439530	+	0.768555i
$750$		0			0
$751$		−	49.1841i		−	1.79475i	−0.441266	−	0.897376i	$-0.645470\pi$
$751$		−	49.1841i		−	1.79475i	0.441266	−	0.897376i	$-0.354530\pi$
$752$	24.3523	−	5.06513i	0.888038	−	0.184706i
$753$		0			0
$754$	19.2161	+	17.3403i	0.699808	+	0.631495i
$755$	18.6462			0.678606
$756$		0			0
$757$	−6.41551			−0.233176			−0.116588	−	0.993180i	$-0.537196\pi$
$757$	−6.41551			−0.233176			−0.116588	+	0.993180i	$0.537196\pi$
$758$	4.97571	+	4.49000i	0.180726	+	0.163084i
$759$		0			0
$760$	−8.87206	+	12.1276i	−0.321823	+	0.439913i
$761$			1.23026i			0.0445970i	0.999751	+	0.0222985i	$0.00709843\pi$
$761$			1.23026i			0.0445970i	−0.999751	+	0.0222985i	$0.992902\pi$
$762$		0			0
$763$	−35.0192	+	20.0272i	−1.26778	+	0.725035i
$764$	13.6219	−	1.40164i	0.492824	−	0.0507095i
$765$		0			0
$766$	−11.3499	+	12.5777i	−0.410088	+	0.454450i
$767$		−	14.4833i		−	0.522962i
$768$		0			0
$769$			28.9327i			1.04334i	0.853147	+	0.521670i	$0.174691\pi$
$769$			28.9327i			1.04334i	−0.853147	+	0.521670i	$0.825309\pi$
$770$	−0.380257	+	1.74436i	−0.0137035	+	0.0628622i
$771$		0			0
$772$	−1.53037	−	14.8730i	−0.0550791	−	0.535290i
$773$		−	12.9773i		−	0.466761i	−0.972385	−	0.233380i	$-0.925021\pi$
$773$		−	12.9773i		−	0.466761i	0.972385	−	0.233380i	$-0.0749788\pi$
$774$		0			0
$775$	−3.38789			−0.121696
$776$	−2.68222	+	3.66643i	−0.0962860	+	0.131617i
$777$		0			0
$778$	−22.9158	+	25.3948i	−0.821573	+	0.910447i
$779$		−	5.37237i		−	0.192485i
$780$		0			0
$781$	−4.38355			−0.156856
$782$	27.6328	−	30.6220i	0.988148	−	1.09504i
$783$		0			0
$784$	−8.98668	+	26.5187i	−0.320953	+	0.947095i
$785$	22.6941			0.809986
$786$		0			0
$787$	16.7024			0.595377			0.297688	−	0.954663i	$-0.403784\pi$
$787$	16.7024			0.595377			0.297688	+	0.954663i	$0.403784\pi$
$788$	−2.92223	−	28.3999i	−0.104100	−	1.01170i
$789$		0			0
$790$	−8.34538	+	9.24814i	−0.296915	+	0.329034i
$791$	9.30150	−	5.31945i	0.330723	−	0.189138i
$792$		0			0
$793$	14.0971			0.500603
$794$	−38.9950	−	35.1885i	−1.38388	−	1.24879i
$795$		0			0
$796$	0.329059	+	3.19798i	0.0116632	+	0.113349i
$797$		−	7.59395i		−	0.268992i	−0.990914	−	0.134496i	$-0.957059\pi$
$797$		−	7.59395i		−	0.268992i	0.990914	−	0.134496i	$-0.0429415\pi$
$798$		0			0
$799$		−	23.8383i		−	0.843339i
$800$	2.85514	−	4.88346i	0.100945	−	0.172656i
$801$		0			0
$802$	−19.3316	+	21.4228i	−0.682622	+	0.756465i
$803$	−2.14604			−0.0757323
$804$		0			0
$805$	−17.4734	+	9.99293i	−0.615858	+	0.352204i
$806$	−10.5385	−	9.50977i	−0.371203	−	0.334967i
$807$		0			0
$808$	10.3150	−	14.0999i	0.362880	−	0.496034i
$809$	−26.4140			−0.928665			−0.464333	−	0.885661i	$-0.653706\pi$
$809$	−26.4140			−0.928665			−0.464333	+	0.885661i	$0.653706\pi$
$810$		0			0
$811$	2.20334			0.0773697			0.0386848	−	0.999251i	$-0.487683\pi$
$811$	2.20334			0.0773697			0.0386848	+	0.999251i	$0.487683\pi$
$812$	19.0471	+	26.5657i	0.668421	+	0.932275i
$813$		0			0
$814$	4.32272	+	3.90075i	0.151511	+	0.136721i
$815$	−9.17980			−0.321554
$816$		0			0
$817$			36.4133i			1.27394i
$818$	4.92632	+	4.44544i	0.172245	+	0.155431i
$819$		0			0
$820$	0.207013	+	2.01187i	0.00722921	+	0.0702576i
$821$	−8.94895			−0.312321			−0.156160	−	0.987732i	$-0.549912\pi$
$821$	−8.94895			−0.312321			−0.156160	+	0.987732i	$0.549912\pi$
$822$		0			0
$823$		−	40.8135i		−	1.42267i	−0.702853	−	0.711335i	$-0.748091\pi$
$823$		−	40.8135i		−	1.42267i	0.702853	−	0.711335i	$-0.251909\pi$
$824$	38.3839	+	28.0802i	1.33716	+	0.978218i
$825$		0			0
$826$	3.89587	−	17.8715i	0.135555	−	0.621830i
$827$		−	4.55874i		−	0.158523i	−0.996854	−	0.0792615i	$-0.974744\pi$
$827$		−	4.55874i		−	0.158523i	0.996854	−	0.0792615i	$-0.0252562\pi$
$828$		0			0
$829$		−	0.872606i		−	0.0303069i	−0.999885	−	0.0151534i	$-0.995176\pi$
$829$		−	0.872606i		−	0.0303069i	0.999885	−	0.0151534i	$-0.00482367\pi$
$830$	−11.4988	−	10.3764i	−0.399130	−	0.360169i
$831$		0			0
$832$	22.5892	−	7.17632i	0.783138	−	0.248794i
$833$	23.1286	+	13.6076i	0.801359	+	0.471476i
$834$		0			0
$835$		−	14.8751i		−	0.514775i
$836$	−5.04317	+	0.518921i	−0.174422	+	0.0179473i
$837$		0			0
$838$	−9.90561	+	10.9772i	−0.342184	+	0.379200i
$839$	48.9005			1.68823			0.844117	−	0.536160i	$-0.180126\pi$
$839$	48.9005			1.68823			0.844117	+	0.536160i	$0.180126\pi$
$840$		0			0
$841$	9.16178			0.315923
$842$	−27.5324	+	30.5108i	−0.948831	+	1.05147i
$843$		0			0
$844$	2.63782	−	0.271421i	0.0907976	−	0.00934270i
$845$		−	4.22235i		−	0.145253i
$846$		0			0
$847$	24.7408	−	14.1491i	0.850103	−	0.486167i
$848$	−36.4354	+	7.57834i	−1.25120	+	0.260241i
$849$		0			0
$850$	−4.02494	−	3.63204i	−0.138054	−	0.124578i
$851$			65.6476i			2.25037i
$852$		0			0
$853$			46.6995i			1.59896i	0.600692	+	0.799480i	$0.294892\pi$
$853$			46.6995i			1.59896i	−0.600692	+	0.799480i	$0.705108\pi$
$854$	17.3949	+	3.79198i	0.595243	+	0.129759i
$855$		0			0
$856$	15.2942	−	20.9063i	0.522746	−	0.714562i
$857$		−	42.6029i		−	1.45529i	−0.685955	−	0.727644i	$-0.740615\pi$
$857$		−	42.6029i		−	1.45529i	0.685955	−	0.727644i	$-0.259385\pi$
$858$		0			0
$859$	−33.0255			−1.12682			−0.563408	−	0.826179i	$-0.690510\pi$
$859$	−33.0255			−1.12682			−0.563408	+	0.826179i	$0.690510\pi$
$860$	−1.40311	−	13.6362i	−0.0478457	−	0.464992i
$861$		0			0
$862$	−12.4413	−	11.2269i	−0.423754	−	0.382389i
$863$		−	50.3282i		−	1.71319i	−0.515989	−	0.856595i	$-0.672575\pi$
$863$		−	50.3282i		−	1.71319i	0.515989	−	0.856595i	$-0.327425\pi$
$864$		0			0
$865$	−18.2211			−0.619536
$866$	−39.1169	−	35.2985i	−1.32925	−	1.19949i
$867$		0			0
$868$	−10.4458	−	14.5692i	−0.354554	−	0.494512i
$869$	−4.20287			−0.142573
$870$		0			0
$871$	−3.86959			−0.131116
$872$	34.8071	+	25.4636i	1.17872	+	0.862305i
$873$		0			0
$874$	−42.4370	−	38.2944i	−1.43545	−	1.29533i
$875$	1.31346	+	2.29670i	0.0444031	+	0.0776425i
$876$		0			0
$877$	18.9157			0.638738			0.319369	−	0.947630i	$-0.396529\pi$
$877$	18.9157			0.638738			0.319369	+	0.947630i	$0.396529\pi$
$878$	−2.08501	+	2.31056i	−0.0703658	+	0.0779776i
$879$		0			0
$880$	1.86860	−	0.388657i	0.0629904	−	0.0131016i
$881$		−	18.9884i		−	0.639736i	−0.947462	−	0.319868i	$-0.896361\pi$
$881$		−	18.9884i		−	0.639736i	0.947462	−	0.319868i	$-0.103639\pi$
$882$		0			0
$883$			35.4843i			1.19414i	0.802188	+	0.597072i	$0.203669\pi$
$883$			35.4843i			1.19414i	−0.802188	+	0.597072i	$0.796331\pi$
$884$	−2.32503	−	22.5960i	−0.0781992	−	0.759984i
$885$		0			0
$886$	−6.15366	−	5.55296i	−0.206736	−	0.186555i
$887$	53.4487			1.79463			0.897315	−	0.441390i	$-0.145515\pi$
$887$	53.4487			1.79463			0.897315	+	0.441390i	$0.145515\pi$
$888$		0			0
$889$	−17.0683	−	29.8453i	−0.572452	−	1.00098i
$890$	12.4312	−	13.7760i	0.416695	−	0.461771i
$891$		0			0
$892$	−4.40757	−	42.8353i	−0.147576	−	1.43423i
$893$	−33.0358			−1.10550
$894$		0			0
$895$	−5.02780			−0.168061
$896$	29.8040	−	2.77888i	0.995681	−	0.0928359i
$897$		0			0
$898$	10.6856	−	11.8415i	0.356583	−	0.395156i
$899$	−20.9287			−0.698012
$900$		0			0
$901$			35.6664i			1.18822i
$902$	−0.457153	+	0.506606i	−0.0152215	+	0.0168681i
$903$		0			0
$904$	−9.24516	−	6.76340i	−0.307489	−	0.224947i
$905$	14.6503			0.486994
$906$		0			0
$907$		−	48.4656i		−	1.60927i	−0.593768	−	0.804636i	$-0.702360\pi$
$907$		−	48.4656i		−	1.60927i	0.593768	−	0.804636i	$-0.297640\pi$
$908$	2.87648	+	27.9552i	0.0954592	+	0.927727i
$909$		0			0
$910$	−2.36110	+	10.8311i	−0.0782697	+	0.359047i
$911$			1.00067i			0.0331538i	0.999863	+	0.0165769i	$0.00527684\pi$
$911$			1.00067i			0.0331538i	−0.999863	+	0.0165769i	$0.994723\pi$
$912$		0			0
$913$		−	5.22571i		−	0.172946i
$914$	10.0117	−	11.0947i	0.331157	−	0.366980i
$915$		0			0
$916$	34.2092	−	3.51999i	1.13030	−	0.116304i
$917$	−4.07783	+	2.33208i	−0.134662	+	0.0770121i
$918$		0			0
$919$			6.71273i			0.221433i	0.993852	+	0.110716i	$0.0353145\pi$
$919$			6.71273i			0.221433i	−0.993852	+	0.110716i	$0.964686\pi$
$920$	17.3676	+	12.7055i	0.572593	+	0.418887i
$921$		0			0
$922$	0.527782	+	0.476262i	0.0173816	+	0.0156848i
$923$	−27.2184			−0.895905
$924$		0			0
$925$	8.62867			0.283709
$926$	−17.3967	−	15.6985i	−0.571691	−	0.515885i
$927$		0			0
$928$	17.6377	−	30.1677i	0.578986	−	0.990302i
$929$			12.9220i			0.423957i	0.977274	+	0.211979i	$0.0679907\pi$
$929$			12.9220i			0.423957i	−0.977274	+	0.211979i	$0.932009\pi$
$930$		0			0
$931$	18.8578	−	32.0524i	0.618040	−	1.05047i
$932$	−2.36442	−	22.9788i	−0.0774491	−	0.752694i
$933$		0			0
$934$	−16.2185	+	17.9730i	−0.530686	+	0.588093i
$935$		−	1.82916i		−	0.0598198i
$936$		0			0
$937$		−	55.1955i		−	1.80316i	−0.432615	−	0.901579i	$-0.642409\pi$
$937$		−	55.1955i		−	1.80316i	0.432615	−	0.901579i	$-0.357591\pi$
$938$	−4.77484	−	1.04088i	−0.155904	−	0.0339860i
$939$		0			0
$940$	12.3714	−	1.27297i	0.403512	−	0.0415197i
$941$			41.8089i			1.36293i	0.731851	+	0.681465i	$0.238657\pi$
$941$			41.8089i			1.36293i	−0.731851	+	0.681465i	$0.761343\pi$
$942$		0			0
$943$	−7.69364			−0.250539
$944$	−19.1444	+	3.98192i	−0.623098	+	0.129600i
$945$		0			0
$946$	3.09853	−	3.43372i	0.100742	−	0.111640i
$947$		−	29.9634i		−	0.973679i	−0.873491	−	0.486839i	$-0.838150\pi$
$947$		−	29.9634i		−	0.973679i	0.873491	−	0.486839i	$-0.161850\pi$
$948$		0			0
$949$	−13.3253			−0.432556
$950$	−5.03339	+	5.57788i	−0.163305	+	0.180970i
$951$		0			0
$952$	3.20914	−	28.5074i	0.104009	−	0.923931i
$953$	−4.49708			−0.145675			−0.0728373	−	0.997344i	$-0.523205\pi$
$953$	−4.49708			−0.145675			−0.0728373	+	0.997344i	$0.523205\pi$
$954$		0			0
$955$	6.84692			0.221561
$956$	−26.8676	+	2.76457i	−0.868961	+	0.0894125i
$957$		0			0
$958$	7.11802	−	7.88801i	0.229973	−	0.254850i
$959$	34.8229	−	19.9149i	1.12449	−	0.643086i
$960$		0			0
$961$	−19.5222			−0.629749
$962$	26.8407	+	24.2206i	0.865379	+	0.780904i
$963$		0			0
$964$	−12.0923	+	1.24425i	−0.389467	+	0.0400745i
$965$		−	7.47575i		−	0.240653i
$966$		0			0
$967$		−	15.3198i		−	0.492651i	−0.969187	−	0.246326i	$-0.920777\pi$
$967$		−	15.3198i		−	0.492651i	0.969187	−	0.246326i	$-0.0792232\pi$
$968$	−24.5909	−	17.9898i	−0.790382	−	0.578213i
$969$		0			0
$970$	−1.52170	+	1.68632i	−0.0488590	+	0.0541443i
$971$	2.95293			0.0947641			0.0473821	−	0.998877i	$-0.484912\pi$
$971$	2.95293			0.0947641			0.0473821	+	0.998877i	$0.484912\pi$
$972$		0			0
$973$	43.3029	−	24.7646i	1.38823	−	0.793917i
$974$	19.2899	+	17.4069i	0.618087	+	0.557752i
$975$		0			0
$976$	−3.87574	−	18.6339i	−0.124059	−	0.596457i
$977$	−32.6707			−1.04523			−0.522615	−	0.852569i	$-0.675043\pi$
$977$	−32.6707			−1.04523			−0.522615	+	0.852569i	$0.675043\pi$
$978$		0			0
$979$	6.26056			0.200088
$980$	−5.82690	+	12.7298i	−0.186134	+	0.406638i
$981$		0			0
$982$	12.9910	+	11.7229i	0.414560	+	0.374092i
$983$	12.7915			0.407986			0.203993	−	0.978972i	$-0.434608\pi$
$983$	12.7915			0.407986			0.203993	+	0.978972i	$0.434608\pi$
$984$		0			0
$985$		−	14.2749i		−	0.454837i
$986$	−24.8641	−	22.4370i	−0.791836	−	0.714540i
$987$		0			0
$988$	−31.3142	+	3.22210i	−0.996236	+	0.102509i
$989$	52.1467			1.65817
$990$		0			0
$991$		−	29.8437i		−	0.948015i	−0.880521	−	0.474008i	$-0.842807\pi$
$991$		−	29.8437i		−	0.948015i	0.880521	−	0.474008i	$-0.157193\pi$
$992$	−9.67290	+	16.5446i	−0.307115	+	0.525291i
$993$		0			0
$994$	−33.5858	−	7.32148i	−1.06528	−	0.232223i
$995$			1.60743i			0.0509590i
$996$		0			0
$997$			16.0457i			0.508172i	0.967182	+	0.254086i	$0.0817746\pi$
$997$			16.0457i			0.508172i	−0.967182	+	0.254086i	$0.918225\pi$
$998$	−4.10448	−	3.70381i	−0.129925	−	0.117242i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.e.811.13		16
3.2	odd	2		420.2.c.b.391.4	yes	16
4.3	odd	2		1260.2.c.d.811.14		16
7.6	odd	2		1260.2.c.d.811.13		16
12.11	even	2		420.2.c.a.391.3	✓	16
21.20	even	2		420.2.c.a.391.4	yes	16
28.27	even	2	inner	1260.2.c.e.811.14		16
84.83	odd	2		420.2.c.b.391.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.3	✓	16	12.11	even	2
420.2.c.a.391.4	yes	16	21.20	even	2
420.2.c.b.391.3	yes	16	84.83	odd	2
420.2.c.b.391.4	yes	16	3.2	odd	2
1260.2.c.d.811.13		16	7.6	odd	2
1260.2.c.d.811.14		16	4.3	odd	2
1260.2.c.e.811.13		16	1.1	even	1	trivial
1260.2.c.e.811.14		16	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} -1.00000i q^{5} +(2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +O(q^{10})\)	\(q+(0.947441 - 1.04993i) q^{2} +(-0.204711 - 1.98950i) q^{4} -1.00000i q^{5} +(2.29670 - 1.31346i) q^{7} +(-2.28279 - 1.67000i) q^{8} +(-1.04993 - 0.947441i) q^{10} -0.477147i q^{11} -2.96271i q^{13} +(0.796939 - 3.65580i) q^{14} +(-3.91619 + 0.814543i) q^{16} +3.83353i q^{17} +5.31262 q^{19} +(-1.98950 + 0.204711i) q^{20} +(-0.500972 - 0.452069i) q^{22} -7.60808i q^{23} -1.00000 q^{25} +(-3.11064 - 2.80699i) q^{26} +(-3.08329 - 4.30039i) q^{28} -6.17752 q^{29} +3.38789 q^{31} +(-2.85514 + 4.88346i) q^{32} +(4.02494 + 3.63204i) q^{34} +(-1.31346 - 2.29670i) q^{35} -8.62867 q^{37} +(5.03339 - 5.57788i) q^{38} +(-1.67000 + 2.28279i) q^{40} -1.01125i q^{41} +6.85412i q^{43} +(-0.949282 + 0.0976772i) q^{44} +(-7.98796 - 7.20820i) q^{46} -6.21838 q^{47} +(3.54963 - 6.03325i) q^{49} +(-0.947441 + 1.04993i) q^{50} +(-5.89430 + 0.606499i) q^{52} +9.30380 q^{53} -0.477147 q^{55} +(-7.43634 - 0.837125i) q^{56} +(-5.85284 + 6.48597i) q^{58} +4.88854 q^{59} +4.75818i q^{61} +(3.20982 - 3.55705i) q^{62} +(2.42221 + 7.62449i) q^{64} -2.96271 q^{65} -1.30610i q^{67} +(7.62679 - 0.784764i) q^{68} +(-3.65580 - 0.796939i) q^{70} -9.18700i q^{71} -4.49766i q^{73} +(-8.17516 + 9.05951i) q^{74} +(-1.08755 - 10.5694i) q^{76} +(-0.626715 - 1.09586i) q^{77} -8.80833i q^{79} +(0.814543 + 3.91619i) q^{80} +(-1.06174 - 0.958097i) q^{82} +10.9520 q^{83} +3.83353 q^{85} +(7.19635 + 6.49388i) q^{86} +(-0.796835 + 1.08922i) q^{88} +13.1208i q^{89} +(-3.89141 - 6.80445i) q^{91} +(-15.1362 + 1.55746i) q^{92} +(-5.89154 + 6.52887i) q^{94} -5.31262i q^{95} -1.60612i q^{97} +(-2.97143 - 9.44302i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Introduction

L-functions

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