LMFDB - Embedded newform 360.2.bi.b.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	360.169
Dual form			360.2.bi.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54437 + 0.784174i) q^{3} +(0.554267 + 2.16628i) q^{5} +(-0.608912 - 0.351555i) q^{7} +(1.77014 - 2.42211i) q^{9} +O(q^{10})$	\(q+(-1.54437 + 0.784174i) q^{3} +(0.554267 + 2.16628i) q^{5} +(-0.608912 - 0.351555i) q^{7} +(1.77014 - 2.42211i) q^{9} +(-1.80274 + 3.12243i) q^{11} +(-1.97952 + 1.14288i) q^{13} +(-2.55474 - 2.91090i) q^{15} +0.471334i q^{17} -5.51095 q^{19} +(1.21606 + 0.0654377i) q^{21} +(-2.68816 + 1.55201i) q^{23} +(-4.38558 + 2.40140i) q^{25} +(-0.834394 + 5.12872i) q^{27} +(0.195925 - 0.339352i) q^{29} +(-3.10681 - 5.38116i) q^{31} +(0.335557 - 6.23584i) q^{33} +(0.424070 - 1.51393i) q^{35} +10.1237i q^{37} +(2.16089 - 3.31731i) q^{39} +(5.18197 + 8.97544i) q^{41} +(0.279206 + 0.161200i) q^{43} +(6.22810 + 2.49214i) q^{45} +(9.51687 + 5.49457i) q^{47} +(-3.25282 - 5.63405i) q^{49} +(-0.369608 - 0.727913i) q^{51} -12.0166i q^{53} +(-7.76328 - 2.17458i) q^{55} +(8.51093 - 4.32154i) q^{57} +(3.13487 + 5.42975i) q^{59} +(1.09437 - 1.89551i) q^{61} +(-1.92936 + 0.852547i) q^{63} +(-3.57297 - 3.65474i) q^{65} +(9.04913 - 5.22452i) q^{67} +(2.93446 - 4.50486i) q^{69} +3.13506 q^{71} -3.39185i q^{73} +(4.88983 - 7.14770i) q^{75} +(2.19542 - 1.26752i) q^{77} +(-1.66578 + 2.88522i) q^{79} +(-2.73320 - 8.57494i) q^{81} +(12.2334 + 7.06296i) q^{83} +(-1.02104 + 0.261245i) q^{85} +(-0.0364690 + 0.677723i) q^{87} -4.11521 q^{89} +1.60714 q^{91} +(9.01783 + 5.87420i) q^{93} +(-3.05453 - 11.9383i) q^{95} +(11.4831 + 6.62975i) q^{97} +(4.37177 + 9.89357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.54437	+	0.784174i	−0.891641	+	0.452743i
$3$	−1.54437	+	0.784174i	−0.891641	+	0.452743i
$4$		0			0
$5$	0.554267	+	2.16628i	0.247876	+	0.968792i
$5$	0.554267	+	2.16628i	0.247876	+	0.968792i
$6$		0			0
$7$	−0.608912	−	0.351555i	−0.230147	−	0.132875i	0.380493	−	0.924784i	$-0.375754\pi$
$7$	−0.608912	−	0.351555i	−0.230147	−	0.132875i	−0.610640	+	0.791908i	$0.709088\pi$
$8$		0			0
$9$	1.77014	−	2.42211i	0.590047	−	0.807369i
$10$		0			0
$11$	−1.80274	+	3.12243i	−0.543546	+	0.941449i	0.455151	+	0.890414i	$0.349585\pi$
$11$	−1.80274	+	3.12243i	−0.543546	+	0.941449i	−0.998697	+	0.0510348i	$0.983748\pi$
$12$		0			0
$13$	−1.97952	+	1.14288i	−0.549020	+	0.316977i	−0.748726	−	0.662879i	$-0.769334\pi$
$13$	−1.97952	+	1.14288i	−0.549020	+	0.316977i	0.199707	+	0.979856i	$0.436001\pi$
$14$		0			0
$15$	−2.55474	−	2.91090i	−0.659630	−	0.751590i
$16$		0			0
$17$			0.471334i			0.114315i	0.998365	+	0.0571576i	$0.0182038\pi$
$17$			0.471334i			0.114315i	−0.998365	+	0.0571576i	$0.981796\pi$
$18$		0			0
$19$	−5.51095			−1.26430			−0.632149	−	0.774847i	$-0.717827\pi$
$19$	−5.51095			−1.26430			−0.632149	+	0.774847i	$0.717827\pi$
$20$		0			0
$21$	1.21606	+	0.0654377i	0.265367	+	0.0142797i
$22$		0			0
$23$	−2.68816	+	1.55201i	−0.560520	+	0.323617i	−0.753354	−	0.657615i	$-0.771565\pi$
$23$	−2.68816	+	1.55201i	−0.560520	+	0.323617i	0.192834	+	0.981231i	$0.438232\pi$
$24$		0			0
$25$	−4.38558	+	2.40140i	−0.877115	+	0.480280i
$26$		0			0
$27$	−0.834394	+	5.12872i	−0.160579	+	0.987023i
$28$		0			0
$29$	0.195925	−	0.339352i	0.0363823	−	0.0630161i	−0.847261	−	0.531177i	$-0.821750\pi$
$29$	0.195925	−	0.339352i	0.0363823	−	0.0630161i	0.883643	+	0.468161i	$0.155083\pi$
$30$		0			0
$31$	−3.10681	−	5.38116i	−0.558000	−	0.966484i	−0.997663	−	0.0683218i	$-0.978236\pi$
$31$	−3.10681	−	5.38116i	−0.558000	−	0.966484i	0.439663	−	0.898163i	$-0.355098\pi$
$32$		0			0
$33$	0.335557	−	6.23584i	0.0584130	−	1.08552i
$34$		0			0
$35$	0.424070	−	1.51393i	0.0716808	−	0.255901i
$36$		0			0
$37$			10.1237i			1.66432i	0.554537	+	0.832159i	$0.312896\pi$
$37$			10.1237i			1.66432i	−0.554537	+	0.832159i	$0.687104\pi$
$38$		0			0
$39$	2.16089	−	3.31731i	0.346019	−	0.531194i
$40$		0			0
$41$	5.18197	+	8.97544i	0.809288	+	1.40173i	0.913358	+	0.407159i	$0.133480\pi$
$41$	5.18197	+	8.97544i	0.809288	+	1.40173i	−0.104069	+	0.994570i	$0.533186\pi$
$42$		0			0
$43$	0.279206	+	0.161200i	0.0425786	+	0.0245827i	0.521138	−	0.853472i	$-0.325508\pi$
$43$	0.279206	+	0.161200i	0.0425786	+	0.0245827i	−0.478560	+	0.878055i	$0.658841\pi$
$44$		0			0
$45$	6.22810	+	2.49214i	0.928431	+	0.371506i
$46$		0			0
$47$	9.51687	+	5.49457i	1.38818	+	0.801465i	0.993110	−	0.117187i	$-0.0373876\pi$
$47$	9.51687	+	5.49457i	1.38818	+	0.801465i	0.395068	+	0.918652i	$0.370721\pi$
$48$		0			0
$49$	−3.25282	−	5.63405i	−0.464688	−	0.804864i
$50$		0			0
$51$	−0.369608	−	0.727913i	−0.0517555	−	0.101928i
$52$		0			0
$53$		−	12.0166i		−	1.65060i	−0.564691	−	0.825302i	$-0.691005\pi$
$53$		−	12.0166i		−	1.65060i	0.564691	−	0.825302i	$-0.308995\pi$
$54$		0			0
$55$	−7.76328	−	2.17458i	−1.04680	−	0.293221i
$56$		0			0
$57$	8.51093	−	4.32154i	1.12730	−	0.572402i
$58$		0			0
$59$	3.13487	+	5.42975i	0.408125	+	0.706893i	0.994680	−	0.103017i	$-0.0328495\pi$
$59$	3.13487	+	5.42975i	0.408125	+	0.706893i	−0.586555	+	0.809910i	$0.699516\pi$
$60$		0			0
$61$	1.09437	−	1.89551i	0.140120	−	0.242695i	−0.787422	−	0.616415i	$-0.788585\pi$
$61$	1.09437	−	1.89551i	0.140120	−	0.242695i	0.927542	+	0.373720i	$0.121918\pi$
$62$		0			0
$63$	−1.92936	+	0.852547i	−0.243077	+	0.107411i
$64$		0			0
$65$	−3.57297	−	3.65474i	−0.443173	−	0.453315i
$66$		0			0
$67$	9.04913	−	5.22452i	1.10553	−	0.638277i	0.167860	−	0.985811i	$-0.446314\pi$
$67$	9.04913	−	5.22452i	1.10553	−	0.638277i	0.937667	+	0.347534i	$0.112981\pi$
$68$		0			0
$69$	2.93446	−	4.50486i	0.353268	−	0.542322i
$70$		0			0
$71$	3.13506			0.372064			0.186032	−	0.982544i	$-0.440437\pi$
$71$	3.13506			0.372064			0.186032	+	0.982544i	$0.440437\pi$
$72$		0			0
$73$		−	3.39185i		−	0.396986i	−0.980102	−	0.198493i	$-0.936395\pi$
$73$		−	3.39185i		−	0.396986i	0.980102	−	0.198493i	$-0.0636047\pi$
$74$		0			0
$75$	4.88983	−	7.14770i	0.564629	−	0.825345i
$76$		0			0
$77$	2.19542	−	1.26752i	0.250191	−	0.144448i
$78$		0			0
$79$	−1.66578	+	2.88522i	−0.187415	+	0.324613i	−0.944388	−	0.328834i	$-0.893344\pi$
$79$	−1.66578	+	2.88522i	−0.187415	+	0.324613i	0.756972	+	0.653447i	$0.226678\pi$
$80$		0			0
$81$	−2.73320	−	8.57494i	−0.303689	−	0.952771i
$82$		0			0
$83$	12.2334	+	7.06296i	1.34279	+	0.775260i	0.987216	−	0.159388i	$-0.0509520\pi$
$83$	12.2334	+	7.06296i	1.34279	+	0.775260i	0.355574	+	0.934648i	$0.384285\pi$
$84$		0			0
$85$	−1.02104	+	0.261245i	−0.110748	+	0.0283360i
$86$		0			0
$87$	−0.0364690	+	0.677723i	−0.00390989	+	0.0726596i
$88$		0			0
$89$	−4.11521			−0.436212			−0.218106	−	0.975925i	$-0.569988\pi$
$89$	−4.11521			−0.436212			−0.218106	+	0.975925i	$0.569988\pi$
$90$		0			0
$91$	1.60714			0.168474
$92$		0			0
$93$	9.01783	+	5.87420i	0.935105	+	0.609126i
$94$		0			0
$95$	−3.05453	−	11.9383i	−0.313389	−	1.22484i
$96$		0			0
$97$	11.4831	+	6.62975i	1.16593	+	0.673149i	0.952718	−	0.303857i	$-0.0982746\pi$
$97$	11.4831	+	6.62975i	1.16593	+	0.673149i	0.213211	+	0.977006i	$0.431608\pi$
$98$		0			0
$99$	4.37177	+	9.89357i	0.439379	+	0.994341i
$100$		0			0
$101$	−5.07080	+	8.78289i	−0.504564	+	0.873930i	0.495422	+	0.868652i	$0.335013\pi$
$101$	−5.07080	+	8.78289i	−0.504564	+	0.873930i	−0.999986	+	0.00527795i	$0.998320\pi$
$102$		0			0
$103$	−3.21663	+	1.85712i	−0.316944	+	0.182988i	−0.650030	−	0.759909i	$-0.725244\pi$
$103$	−3.21663	+	1.85712i	−0.316944	+	0.182988i	0.333085	+	0.942897i	$0.391910\pi$
$104$		0			0
$105$	0.532267	+	2.67061i	0.0519440	+	0.260625i
$106$		0			0
$107$			2.93731i			0.283961i	0.989869	+	0.141980i	$0.0453470\pi$
$107$			2.93731i			0.283961i	−0.989869	+	0.141980i	$0.954653\pi$
$108$		0			0
$109$	−2.21238			−0.211907			−0.105954	−	0.994371i	$-0.533790\pi$
$109$	−2.21238			−0.211907			−0.105954	+	0.994371i	$0.533790\pi$
$110$		0			0
$111$	−7.93871	−	15.6346i	−0.753509	−	1.48397i
$112$		0			0
$113$	−11.4513	+	6.61142i	−1.07725	+	0.621950i	−0.930153	−	0.367172i	$-0.880326\pi$
$113$	−11.4513	+	6.61142i	−1.07725	+	0.621950i	−0.147097	+	0.989122i	$0.546993\pi$
$114$		0			0
$115$	−4.85205	−	4.96309i	−0.452456	−	0.462811i
$116$		0			0
$117$	−0.735861	+	6.81765i	−0.0680303	+	0.630292i
$118$		0			0
$119$	0.165700	−	0.287001i	0.0151897	−	0.0263093i
$120$		0			0
$121$	−0.999726	−	1.73158i	−0.0908842	−	0.157416i
$122$		0			0
$123$	−15.0412	−	9.79781i	−1.35622	−	0.883439i
$124$		0			0
$125$	−7.63289	−	8.16939i	−0.682707	−	0.730693i
$126$		0			0
$127$		−	7.68855i		−	0.682249i	−0.940018	−	0.341124i	$-0.889192\pi$
$127$		−	7.68855i		−	0.682249i	0.940018	−	0.341124i	$-0.110808\pi$
$128$		0			0
$129$	−0.557606	−	0.0300053i	−0.0490945	−	0.00264182i
$130$		0			0
$131$	8.30649	+	14.3873i	0.725741	+	1.25702i	0.958668	+	0.284526i	$0.0918363\pi$
$131$	8.30649	+	14.3873i	0.725741	+	1.25702i	−0.232927	+	0.972494i	$0.574830\pi$
$132$		0			0
$133$	3.35568	+	1.93740i	0.290974	+	0.167994i
$134$		0			0
$135$	−11.5727	+	1.03514i	−0.996023	+	0.0890910i
$136$		0			0
$137$	10.4297	+	6.02160i	0.891071	+	0.514460i	0.874293	−	0.485399i	$-0.161326\pi$
$137$	10.4297	+	6.02160i	0.891071	+	0.514460i	0.0167781	+	0.999859i	$0.494659\pi$
$138$		0			0
$139$	11.0834	+	19.1970i	0.940079	+	1.62827i	0.765316	+	0.643655i	$0.222583\pi$
$139$	11.0834	+	19.1970i	0.940079	+	1.62827i	0.174763	+	0.984610i	$0.444084\pi$
$140$		0			0
$141$	−19.0062	−	1.02275i	−1.60061	−	0.0861307i
$142$		0			0
$143$		−	8.24122i		−	0.689165i
$144$		0			0
$145$	0.843727	+	0.236338i	0.0700678	+	0.0196268i
$146$		0			0
$147$	9.44162	+	6.15026i	0.778732	+	0.507265i
$148$		0			0
$149$	−6.95157	−	12.0405i	−0.569495	−	0.986394i	−0.996616	−	0.0821996i	$-0.973805\pi$
$149$	−6.95157	−	12.0405i	−0.569495	−	0.986394i	0.427121	−	0.904194i	$-0.359528\pi$
$150$		0			0
$151$	11.2513	−	19.4879i	0.915620	−	1.58590i	0.109628	−	0.993973i	$-0.465034\pi$
$151$	11.2513	−	19.4879i	0.915620	−	1.58590i	0.805991	−	0.591927i	$-0.201633\pi$
$152$		0			0
$153$	1.14162	+	0.834327i	0.0922946	+	0.0674514i
$154$		0			0
$155$	9.93512	−	9.71284i	0.798008	−	0.780154i
$156$		0			0
$157$	−17.9128	+	10.3420i	−1.42960	+	0.825380i	−0.997089	−	0.0762487i	$-0.975706\pi$
$157$	−17.9128	+	10.3420i	−1.42960	+	0.825380i	−0.432511	+	0.901629i	$0.642372\pi$
$158$		0			0
$159$	9.42310	+	18.5580i	0.747300	+	1.47175i
$160$		0			0
$161$	2.18247			0.172003
$162$		0			0
$163$		−	13.2797i		−	1.04015i	−0.854121	−	0.520074i	$-0.825904\pi$
$163$		−	13.2797i		−	1.04015i	0.854121	−	0.520074i	$-0.174096\pi$
$164$		0			0
$165$	13.6946	−	2.72941i	1.06612	−	0.212484i
$166$		0			0
$167$	−18.7831	+	10.8444i	−1.45348	+	0.839166i	−0.998677	−	0.0514271i	$-0.983623\pi$
$167$	−18.7831	+	10.8444i	−1.45348	+	0.839166i	−0.454801	+	0.890593i	$0.650290\pi$
$168$		0			0
$169$	−3.88767	+	6.73365i	−0.299052	+	0.517973i
$170$		0			0
$171$	−9.75515	+	13.3481i	−0.745995	+	1.02075i
$172$		0			0
$173$	−6.80171	−	3.92697i	−0.517124	−	0.298562i	0.218633	−	0.975807i	$-0.429840\pi$
$173$	−6.80171	−	3.92697i	−0.517124	−	0.298562i	−0.735757	+	0.677245i	$0.763174\pi$
$174$		0			0
$175$	3.51465	+	0.0795333i	0.265683	+	0.00601216i
$176$		0			0
$177$	−9.09925	−	5.92724i	−0.683942	−	0.445519i
$178$		0			0
$179$	3.01228			0.225149			0.112574	−	0.993643i	$-0.464090\pi$
$179$	3.01228			0.225149			0.112574	+	0.993643i	$0.464090\pi$
$180$		0			0
$181$	23.4261			1.74125			0.870625	−	0.491947i	$-0.163715\pi$
$181$	23.4261			1.74125			0.870625	+	0.491947i	$0.163715\pi$
$182$		0			0
$183$	−0.203704	+	3.78554i	−0.0150582	+	0.279835i
$184$		0			0
$185$	−21.9307	+	5.61120i	−1.61238	+	0.412544i
$186$		0			0
$187$	−1.47171	−	0.849691i	−0.107622	−	0.0621356i
$188$		0			0
$189$	2.31110	−	2.82960i	0.168108	−	0.205823i
$190$		0			0
$191$	4.68264	−	8.11057i	0.338824	−	0.586860i	−0.645388	−	0.763855i	$-0.723304\pi$
$191$	4.68264	−	8.11057i	0.338824	−	0.586860i	0.984212	+	0.176995i	$0.0566376\pi$
$192$		0			0
$193$	−9.14899	+	5.28217i	−0.658559	+	0.380219i	−0.791728	−	0.610874i	$-0.790818\pi$
$193$	−9.14899	+	5.28217i	−0.658559	+	0.380219i	0.133169	+	0.991093i	$0.457485\pi$
$194$		0			0
$195$	8.38394	+	2.84243i	0.600386	+	0.203551i
$196$		0			0
$197$		−	17.8747i		−	1.27352i	−0.771061	−	0.636761i	$-0.780274\pi$
$197$		−	17.8747i		−	1.27352i	0.771061	−	0.636761i	$-0.219726\pi$
$198$		0			0
$199$	−1.91876			−0.136017			−0.0680087	−	0.997685i	$-0.521665\pi$
$199$	−1.91876			−0.136017			−0.0680087	+	0.997685i	$0.521665\pi$
$200$		0			0
$201$	−9.87825	+	15.1647i	−0.696758	+	1.06963i
$202$		0			0
$203$	−0.238602	+	0.137757i	−0.0167466	+	0.00966864i
$204$		0			0
$205$	−16.5712	+	16.2004i	−1.15738	+	1.13149i
$206$		0			0
$207$	−0.999290	+	9.25829i	−0.0694554	+	0.643496i
$208$		0			0
$209$	9.93479	−	17.2076i	0.687204	−	1.19027i
$210$		0			0
$211$	5.17779	+	8.96820i	0.356454	+	0.617396i	0.987366	−	0.158458i	$-0.0506524\pi$
$211$	5.17779	+	8.96820i	0.356454	+	0.617396i	−0.630912	+	0.775855i	$0.717319\pi$
$212$		0			0
$213$	−4.84169	+	2.45844i	−0.331747	+	0.168449i
$214$		0			0
$215$	−0.194450	+	0.694188i	−0.0132614	+	0.0473432i
$216$		0			0
$217$			4.36887i			0.296578i
$218$		0			0
$219$	2.65980	+	5.23826i	0.179733	+	0.353969i
$220$		0			0
$221$	−0.538676	−	0.933014i	−0.0362353	−	0.0627613i
$222$		0			0
$223$	4.82440	+	2.78537i	0.323066	+	0.186522i	0.652758	−	0.757566i	$-0.273612\pi$
$223$	4.82440	+	2.78537i	0.323066	+	0.186522i	−0.329692	+	0.944088i	$0.606945\pi$
$224$		0			0
$225$	−1.94665	+	14.8731i	−0.129776	+	0.991543i
$226$		0			0
$227$	−13.2675	−	7.65998i	−0.880593	−	0.508411i	−0.00973922	−	0.999953i	$-0.503100\pi$
$227$	−13.2675	−	7.65998i	−0.880593	−	0.508411i	−0.870854	+	0.491542i	$0.836433\pi$
$228$		0			0
$229$	−2.77489	−	4.80624i	−0.183370	−	0.317606i	0.759656	−	0.650325i	$-0.225367\pi$
$229$	−2.77489	−	4.80624i	−0.183370	−	0.317606i	−0.943026	+	0.332719i	$0.892034\pi$
$230$		0			0
$231$	−2.39657	+	3.67911i	−0.157683	+	0.242068i
$232$		0			0
$233$			18.1929i			1.19186i	0.803037	+	0.595929i	$0.203216\pi$
$233$			18.1929i			1.19186i	−0.803037	+	0.595929i	$0.796784\pi$
$234$		0			0
$235$	−6.62791	+	23.6617i	−0.432357	+	1.54352i
$236$		0			0
$237$	0.310065	−	5.76211i	0.0201409	−	0.374289i
$238$		0			0
$239$	−5.76278	−	9.98142i	−0.372763	−	0.645644i	0.617226	−	0.786786i	$-0.288256\pi$
$239$	−5.76278	−	9.98142i	−0.372763	−	0.645644i	−0.989989	+	0.141141i	$0.954923\pi$
$240$		0			0
$241$	8.68563	−	15.0440i	0.559491	−	0.969067i	−0.438048	−	0.898952i	$-0.644330\pi$
$241$	8.68563	−	15.0440i	0.559491	−	0.969067i	0.997539	−	0.0701150i	$-0.0223366\pi$
$242$		0			0
$243$	10.9453	+	11.0996i	0.702142	+	0.712037i
$244$		0			0
$245$	10.4020	−	10.1693i	0.664560	−	0.649692i
$246$		0			0
$247$	10.9090	−	6.29832i	0.694124	−	0.400753i
$248$		0			0
$249$	−24.4315	−	1.31468i	−1.54828	−	0.0833146i
$250$		0			0
$251$	−19.8501			−1.25293			−0.626463	−	0.779451i	$-0.715498\pi$
$251$	−19.8501			−1.25293			−0.626463	+	0.779451i	$0.715498\pi$
$252$		0			0
$253$		−	11.1915i		−	0.703602i
$254$		0			0
$255$	1.37200	−	1.20413i	0.0859183	−	0.0754058i
$256$		0			0
$257$	5.78010	−	3.33714i	0.360553	−	0.208165i	−0.308770	−	0.951137i	$-0.599917\pi$
$257$	5.78010	−	3.33714i	0.360553	−	0.208165i	0.669323	+	0.742971i	$0.266584\pi$
$258$		0			0
$259$	3.55903	−	6.16441i	0.221147	−	0.383038i
$260$		0			0
$261$	−0.475132	−	1.07525i	−0.0294099	−	0.0665564i
$262$		0			0
$263$	−2.11719	−	1.22236i	−0.130551	−	0.0753739i	0.433302	−	0.901249i	$-0.357348\pi$
$263$	−2.11719	−	1.22236i	−0.130551	−	0.0753739i	−0.563853	+	0.825875i	$0.690682\pi$
$264$		0			0
$265$	26.0313	−	6.66039i	1.59909	−	0.409145i
$266$		0			0
$267$	6.35540	−	3.22704i	0.388944	−	0.197492i
$268$		0			0
$269$	−10.0675			−0.613828			−0.306914	−	0.951737i	$-0.599296\pi$
$269$	−10.0675			−0.613828			−0.306914	+	0.951737i	$0.599296\pi$
$270$		0			0
$271$	21.5777			1.31075			0.655376	−	0.755303i	$-0.272510\pi$
$271$	21.5777			1.31075			0.655376	+	0.755303i	$0.272510\pi$
$272$		0			0
$273$	−2.48201	+	1.26027i	−0.150218	+	0.0762753i
$274$		0			0
$275$	0.407838	−	18.0228i	0.0245936	−	1.08681i
$276$		0			0
$277$	−25.1935	−	14.5455i	−1.51373	−	0.873954i	−0.999871	−	0.0160814i	$-0.994881\pi$
$277$	−25.1935	−	14.5455i	−1.51373	−	0.873954i	−0.513862	−	0.857873i	$-0.671786\pi$
$278$		0			0
$279$	−18.5332	−	2.00038i	−1.10956	−	0.119759i
$280$		0			0
$281$	−8.84998	+	15.3286i	−0.527946	+	0.914429i	0.471524	+	0.881853i	$0.343704\pi$
$281$	−8.84998	+	15.3286i	−0.527946	+	0.914429i	−0.999469	+	0.0325754i	$0.989629\pi$
$282$		0			0
$283$	−0.936723	+	0.540817i	−0.0556824	+	0.0321482i	−0.527583	−	0.849504i	$-0.676902\pi$
$283$	−0.936723	+	0.540817i	−0.0556824	+	0.0321482i	0.471900	+	0.881652i	$0.343568\pi$
$284$		0			0
$285$	14.0790	+	16.0418i	0.833969	+	0.950234i
$286$		0			0
$287$		−	7.28700i		−	0.430138i
$288$		0			0
$289$	16.7778			0.986932
$290$		0			0
$291$	−22.9329	−	1.23405i	−1.34435	−	0.0723410i
$292$		0			0
$293$	2.96683	−	1.71290i	0.173324	−	0.100069i	−0.410828	−	0.911713i	$-0.634760\pi$
$293$	2.96683	−	1.71290i	0.173324	−	0.100069i	0.584152	+	0.811644i	$0.301427\pi$
$294$		0			0
$295$	−10.0248	+	9.80054i	−0.583668	+	0.570609i
$296$		0			0
$297$	−14.5099	−	11.8511i	−0.841950	−	0.687669i
$298$		0			0
$299$	3.54751	−	6.14447i	0.205158	−	0.355344i
$300$		0			0
$301$	−0.113341	−	0.196313i	−0.00653289	−	0.0113153i
$302$		0			0
$303$	0.943867	−	17.5404i	0.0542237	−	1.00767i
$304$		0			0
$305$	4.71278	+	1.32010i	0.269853	+	0.0755890i
$306$		0			0
$307$		−	6.76092i		−	0.385866i	−0.981212	−	0.192933i	$-0.938200\pi$
$307$		−	6.76092i		−	0.385866i	0.981212	−	0.192933i	$-0.0618000\pi$
$308$		0			0
$309$	3.51136	−	5.39049i	0.199754	−	0.306654i
$310$		0			0
$311$	4.54403	+	7.87049i	0.257668	+	0.446295i	0.965617	−	0.259969i	$-0.0837124\pi$
$311$	4.54403	+	7.87049i	0.257668	+	0.446295i	−0.707948	+	0.706264i	$0.750379\pi$
$312$		0			0
$313$	22.0630	+	12.7381i	1.24707	+	0.719999i	0.970525	−	0.241001i	$-0.0774756\pi$
$313$	22.0630	+	12.7381i	1.24707	+	0.719999i	0.276550	+	0.961000i	$0.410809\pi$
$314$		0			0
$315$	−2.91624	−	3.70701i	−0.164312	−	0.208867i
$316$		0			0
$317$	11.0926	+	6.40430i	0.623021	+	0.359701i	0.778044	−	0.628209i	$-0.216212\pi$
$317$	11.0926	+	6.40430i	0.623021	+	0.359701i	−0.155023	+	0.987911i	$0.549545\pi$
$318$		0			0
$319$	0.706402	+	1.22352i	0.0395509	+	0.0685042i
$320$		0			0
$321$	−2.30337	−	4.53629i	−0.128561	−	0.253191i
$322$		0			0
$323$		−	2.59750i		−	0.144529i
$324$		0			0
$325$	5.93683	−	9.76578i	0.329316	−	0.541708i
$326$		0			0
$327$	3.41672	−	1.73489i	0.188945	−	0.0959396i
$328$		0			0
$329$	−3.86329	−	6.69142i	−0.212990	−	0.368910i
$330$		0			0
$331$	8.63447	−	14.9553i	0.474594	−	0.822020i	−0.524983	−	0.851113i	$-0.675928\pi$
$331$	8.63447	−	14.9553i	0.474594	−	0.822020i	0.999577	+	0.0290924i	$0.00926172\pi$
$332$		0			0
$333$	24.5206	+	17.9203i	1.34372	+	0.982026i
$334$		0			0
$335$	16.3334	+	16.7072i	0.892391	+	0.912813i
$336$		0			0
$337$	26.5275	−	15.3157i	1.44505	−	0.834298i	0.446867	−	0.894600i	$-0.352540\pi$
$337$	26.5275	−	15.3157i	1.44505	−	0.834298i	0.998180	+	0.0603018i	$0.0192063\pi$
$338$		0			0
$339$	12.5005	−	19.1903i	0.678936	−	1.04227i
$340$		0			0
$341$	22.4031			1.21319
$342$		0			0
$343$			9.49596i			0.512734i
$344$		0			0
$345$	11.3853	+	3.85998i	0.612963	+	0.207815i
$346$		0			0
$347$	−13.4143	+	7.74476i	−0.720118	+	0.415760i	−0.814796	−	0.579748i	$-0.803151\pi$
$347$	−13.4143	+	7.74476i	−0.720118	+	0.415760i	0.0946781	+	0.995508i	$0.469818\pi$
$348$		0			0
$349$	−4.70955	+	8.15717i	−0.252096	+	0.436643i	−0.964103	−	0.265529i	$-0.914453\pi$
$349$	−4.70955	+	8.15717i	−0.252096	+	0.436643i	0.712007	+	0.702173i	$0.247787\pi$
$350$		0			0
$351$	−4.20979	−	11.1060i	−0.224702	−	0.592795i
$352$		0			0
$353$	15.1570	+	8.75092i	0.806728	+	0.465765i	0.845818	−	0.533471i	$-0.179113\pi$
$353$	15.1570	+	8.75092i	0.806728	+	0.465765i	−0.0390902	+	0.999236i	$0.512446\pi$
$354$		0			0
$355$	1.73766	+	6.79144i	0.0922255	+	0.360452i
$356$		0			0
$357$	−0.0308430	+	0.573172i	−0.00163238	+	0.0303355i
$358$		0			0
$359$	−8.81160			−0.465059			−0.232529	−	0.972589i	$-0.574700\pi$
$359$	−8.81160			−0.465059			−0.232529	+	0.972589i	$0.574700\pi$
$360$		0			0
$361$	11.3705			0.598449
$362$		0			0
$363$	2.90180	+	1.89023i	0.152305	+	0.0992114i
$364$		0			0
$365$	7.34771	−	1.87999i	0.384597	−	0.0984031i
$366$		0			0
$367$	−16.5888	−	9.57753i	−0.865927	−	0.499943i	6.57031e−5	−	1.00000i	$-0.499979\pi$
$367$	−16.5888	−	9.57753i	−0.865927	−	0.499943i	−0.865993	+	0.500057i	$0.833312\pi$
$368$		0			0
$369$	30.9123	+	3.33651i	1.60923	+	0.173692i
$370$		0			0
$371$	−4.22449	+	7.31704i	−0.219325	+	0.379882i
$372$		0			0
$373$	−1.80045	+	1.03949i	−0.0932237	+	0.0538227i	−0.545887	−	0.837859i	$-0.683807\pi$
$373$	−1.80045	+	1.03949i	−0.0932237	+	0.0538227i	0.452663	+	0.891681i	$0.350474\pi$
$374$		0			0
$375$	18.1942	+	6.63103i	0.939545	+	0.342425i
$376$		0			0
$377$			0.895671i			0.0461294i
$378$		0			0
$379$	−13.8021			−0.708966			−0.354483	−	0.935063i	$-0.615343\pi$
$379$	−13.8021			−0.708966			−0.354483	+	0.935063i	$0.615343\pi$
$380$		0			0
$381$	6.02917	+	11.8739i	0.308884	+	0.608321i
$382$		0			0
$383$	16.4234	−	9.48208i	0.839199	−	0.484512i	−0.0177929	−	0.999842i	$-0.505664\pi$
$383$	16.4234	−	9.48208i	0.839199	−	0.484512i	0.856992	+	0.515330i	$0.172331\pi$
$384$		0			0
$385$	3.96266	+	4.05335i	0.201956	+	0.206578i
$386$		0			0
$387$	0.884678	−	0.390921i	0.0449707	−	0.0198716i
$388$		0			0
$389$	6.71567	−	11.6319i	0.340498	−	0.589760i	−0.644027	−	0.765002i	$-0.722738\pi$
$389$	6.71567	−	11.6319i	0.340498	−	0.589760i	0.984525	+	0.175243i	$0.0560710\pi$
$390$		0			0
$391$	−0.731515	−	1.26702i	−0.0369943	−	0.0640760i
$392$		0			0
$393$	−24.1104	−	15.7055i	−1.21621	−	0.792237i
$394$		0			0
$395$	−7.17350	−	2.00938i	−0.360938	−	0.101103i
$396$		0			0
$397$			9.78992i			0.491342i	0.969353	+	0.245671i	$0.0790083\pi$
$397$			9.78992i			0.491342i	−0.969353	+	0.245671i	$0.920992\pi$
$398$		0			0
$399$	−6.70167	−	0.360623i	−0.335503	−	0.0180538i
$400$		0			0
$401$	4.06224	+	7.03601i	0.202859	+	0.351361i	0.949448	−	0.313923i	$-0.101643\pi$
$401$	4.06224	+	7.03601i	0.202859	+	0.351361i	−0.746590	+	0.665285i	$0.768310\pi$
$402$		0			0
$403$	12.3000	+	7.10140i	0.612706	+	0.353746i
$404$		0			0
$405$	17.0608	−	10.6737i	0.847760	−	0.530380i
$406$		0			0
$407$	−31.6104	−	18.2503i	−1.56687	−	0.904633i
$408$		0			0
$409$	−11.1670	−	19.3418i	−0.552171	−	0.956388i	−0.998118	−	0.0613286i	$-0.980466\pi$
$409$	−11.1670	−	19.3418i	−0.552171	−	0.956388i	0.445947	−	0.895060i	$-0.352867\pi$
$410$		0			0
$411$	−20.8293	−	1.12085i	−1.02743	−	0.0552872i
$412$		0			0
$413$		−	4.40832i		−	0.216919i
$414$		0			0
$415$	−8.51981	+	30.4158i	−0.418221	+	1.49305i
$416$		0			0
$417$	−32.1706	−	20.9559i	−1.57540	−	1.02621i
$418$		0			0
$419$	−6.90806	−	11.9651i	−0.337481	−	0.584534i	0.646477	−	0.762933i	$-0.276241\pi$
$419$	−6.90806	−	11.9651i	−0.337481	−	0.584534i	−0.983958	+	0.178399i	$0.942908\pi$
$420$		0			0
$421$	−4.04704	+	7.00968i	−0.197241	+	0.341631i	−0.947633	−	0.319362i	$-0.896531\pi$
$421$	−4.04704	+	7.00968i	−0.197241	+	0.341631i	0.750392	+	0.660993i	$0.229865\pi$
$422$		0			0
$423$	30.1546	−	13.3247i	1.46617	−	0.647870i
$424$		0			0
$425$	−1.13186	−	2.06707i	−0.0549033	−	0.100268i
$426$		0			0
$427$	−1.33275	+	0.769465i	−0.0644964	+	0.0372370i
$428$		0			0
$429$	6.46255	+	12.7275i	0.312015	+	0.614488i
$430$		0			0
$431$	13.5943			0.654814			0.327407	−	0.944883i	$-0.393825\pi$
$431$	13.5943			0.654814			0.327407	+	0.944883i	$0.393825\pi$
$432$		0			0
$433$		−	37.9830i		−	1.82535i	−0.408688	−	0.912674i	$-0.634014\pi$
$433$		−	37.9830i		−	1.82535i	0.408688	−	0.912674i	$-0.365986\pi$
$434$		0			0
$435$	−1.48836	+	0.296637i	−0.0713612	+	0.0142227i
$436$		0			0
$437$	14.8143	−	8.55305i	0.708665	−	0.409148i
$438$		0			0
$439$	−9.29167	+	16.0936i	−0.443467	+	0.768108i	−0.997944	−	0.0640914i	$-0.979585\pi$
$439$	−9.29167	+	16.0936i	−0.443467	+	0.768108i	0.554477	+	0.832199i	$0.312918\pi$
$440$		0			0
$441$	−19.4042	−	2.09438i	−0.924010	−	0.0997326i
$442$		0			0
$443$	−13.5829	−	7.84211i	−0.645345	−	0.372590i	0.141326	−	0.989963i	$-0.454864\pi$
$443$	−13.5829	−	7.84211i	−0.645345	−	0.372590i	−0.786670	+	0.617373i	$0.788197\pi$
$444$		0			0
$445$	−2.28092	−	8.91472i	−0.108126	−	0.422598i
$446$		0			0
$447$	20.1776	+	13.1437i	0.954368	+	0.621674i
$448$		0			0
$449$	8.59068			0.405419			0.202710	−	0.979239i	$-0.435025\pi$
$449$	8.59068			0.405419			0.202710	+	0.979239i	$0.435025\pi$
$450$		0			0
$451$	−37.3670			−1.75954
$452$		0			0
$453$	−2.09429	+	38.9194i	−0.0983985	+	1.82859i
$454$		0			0
$455$	0.890782	+	3.48151i	0.0417605	+	0.163216i
$456$		0			0
$457$	4.89306	+	2.82501i	0.228888	+	0.132148i	0.610059	−	0.792356i	$-0.291146\pi$
$457$	4.89306	+	2.82501i	0.228888	+	0.132148i	−0.381171	+	0.924505i	$0.624479\pi$
$458$		0			0
$459$	−2.41734	−	0.393278i	−0.112832	−	0.0183567i
$460$		0			0
$461$	−10.6423	+	18.4329i	−0.495659	+	0.858507i	−0.999987	−	0.00500482i	$-0.998407\pi$
$461$	−10.6423	+	18.4329i	−0.495659	+	0.858507i	0.504328	+	0.863512i	$0.331740\pi$
$462$		0			0
$463$	−36.9615	+	21.3397i	−1.71775	+	0.991741i	−0.794743	+	0.606947i	$0.792394\pi$
$463$	−36.9615	+	21.3397i	−1.71775	+	0.991741i	−0.923003	+	0.384794i	$0.874273\pi$
$464$		0			0
$465$	−7.72691	+	22.7911i	−0.358327	+	1.05691i
$466$		0			0
$467$			0.709510i			0.0328322i	0.999865	+	0.0164161i	$0.00522564\pi$
$467$			0.709510i			0.0328322i	−0.999865	+	0.0164161i	$0.994774\pi$
$468$		0			0
$469$	−7.34683			−0.339245
$470$		0			0
$471$	19.5541	−	30.0186i	0.901005	−	1.38318i
$472$		0			0
$473$	−1.00667	+	0.581202i	−0.0462868	+	0.0267237i
$474$		0			0
$475$	24.1687	−	13.2340i	1.10894	−	0.607217i
$476$		0			0
$477$	−29.1054	−	21.2710i	−1.33265	−	0.973934i
$478$		0			0
$479$	−13.5274	+	23.4301i	−0.618083	+	1.07055i	0.371753	+	0.928332i	$0.378757\pi$
$479$	−13.5274	+	23.4301i	−0.618083	+	1.07055i	−0.989835	+	0.142219i	$0.954576\pi$
$480$		0			0
$481$	−11.5701	−	20.0400i	−0.527550	−	0.913743i
$482$		0			0
$483$	−3.37054	+	1.71144i	−0.153365	+	0.0778731i
$484$		0			0
$485$	−7.99724	+	28.5502i	−0.363136	+	1.29640i
$486$		0			0
$487$		−	6.04139i		−	0.273761i	−0.990588	−	0.136881i	$-0.956292\pi$
$487$		−	6.04139i		−	0.273761i	0.990588	−	0.136881i	$-0.0437077\pi$
$488$		0			0
$489$	10.4136	+	20.5088i	0.470920	+	0.927438i
$490$		0			0
$491$	14.0042	+	24.2559i	0.631999	+	1.09465i	0.987143	+	0.159842i	$0.0510986\pi$
$491$	14.0042	+	24.2559i	0.631999	+	1.09465i	−0.355144	+	0.934812i	$0.615568\pi$
$492$		0			0
$493$	0.159948	+	0.0923460i	0.00720370	+	0.00415906i
$494$		0			0
$495$	−19.0092	+	14.9542i	−0.854398	+	0.672140i
$496$		0			0
$497$	−1.90898	−	1.10215i	−0.0856293	−	0.0494381i
$498$		0			0
$499$	−4.67425	−	8.09604i	−0.209248	−	0.362429i	0.742230	−	0.670146i	$-0.233768\pi$
$499$	−4.67425	−	8.09604i	−0.209248	−	0.362429i	−0.951478	+	0.307717i	$0.900435\pi$
$500$		0			0
$501$	20.5041	−	31.4770i	0.916054	−	1.40629i
$502$		0			0
$503$			16.9461i			0.755588i	0.925890	+	0.377794i	$0.123317\pi$
$503$			16.9461i			0.755588i	−0.925890	+	0.377794i	$0.876683\pi$
$504$		0			0
$505$	−21.8368	−	6.11674i	−0.971726	−	0.272191i
$506$		0			0
$507$	0.723642	−	13.4478i	0.0321381	−	0.597239i
$508$		0			0
$509$	15.7973	+	27.3617i	0.700203	+	1.21279i	0.968395	+	0.249422i	$0.0802405\pi$
$509$	15.7973	+	27.3617i	0.700203	+	1.21279i	−0.268192	+	0.963365i	$0.586426\pi$
$510$		0			0
$511$	−1.19242	+	2.06534i	−0.0527497	+	0.0913652i
$512$		0			0
$513$	4.59830	−	28.2641i	0.203020	−	1.24789i
$514$		0			0
$515$	−5.80593	−	5.93880i	−0.255840	−	0.261695i
$516$		0			0
$517$	−34.3128	+	19.8105i	−1.50908	+	0.871266i
$518$		0			0
$519$	13.5838	+	0.730956i	0.596261	+	0.0320854i
$520$		0			0
$521$	17.2592			0.756138			0.378069	−	0.925777i	$-0.376588\pi$
$521$	17.2592			0.756138			0.378069	+	0.925777i	$0.376588\pi$
$522$		0			0
$523$			32.1076i			1.40397i	0.712194	+	0.701983i	$0.247702\pi$
$523$			32.1076i			1.40397i	−0.712194	+	0.701983i	$0.752298\pi$
$524$		0			0
$525$	−5.49029	+	2.63327i	−0.239616	+	0.114925i
$526$		0			0
$527$	2.53632	−	1.46435i	0.110484	−	0.0637879i
$528$		0			0
$529$	−6.68253	+	11.5745i	−0.290545	+	0.503238i
$530$		0			0
$531$	18.7006	+	2.01844i	0.811536	+	0.0875928i
$532$		0			0
$533$	−20.5156	−	11.8447i	−0.888630	−	0.513051i
$534$		0			0
$535$	−6.36305	+	1.62805i	−0.275099	+	0.0703869i
$536$		0			0
$537$	−4.65207	+	2.36215i	−0.200752	+	0.101934i
$538$		0			0
$539$	23.4559			1.01032
$540$		0			0
$541$	−18.7891			−0.807806			−0.403903	−	0.914802i	$-0.632347\pi$
$541$	−18.7891			−0.807806			−0.403903	+	0.914802i	$0.632347\pi$
$542$		0			0
$543$	−36.1785	+	18.3702i	−1.55257	+	0.788339i
$544$		0			0
$545$	−1.22625	−	4.79264i	−0.0525266	−	0.205294i
$546$		0			0
$547$	−33.5936	−	19.3953i	−1.43636	−	0.829283i	−0.438766	−	0.898601i	$-0.644584\pi$
$547$	−33.5936	−	19.3953i	−1.43636	−	0.829283i	−0.997595	+	0.0693181i	$0.977918\pi$
$548$		0			0
$549$	−2.65393	−	6.00600i	−0.113267	−	0.256330i
$550$		0			0
$551$	−1.07973	+	1.87015i	−0.0459981	+	0.0796711i
$552$		0			0
$553$	2.02863	−	1.17123i	0.0862662	−	0.0498058i
$554$		0			0
$555$	29.4689	−	25.8633i	1.25089	−	1.09783i
$556$		0			0
$557$			7.50060i			0.317811i	0.987294	+	0.158905i	$0.0507964\pi$
$557$			7.50060i			0.317811i	−0.987294	+	0.158905i	$0.949204\pi$
$558$		0			0
$559$	−0.736925			−0.0311686
$560$		0			0
$561$	2.93916	+	0.158159i	0.124092	+	0.00667750i
$562$		0			0
$563$	5.47802	−	3.16273i	0.230871	−	0.133293i	−0.380103	−	0.924944i	$-0.624111\pi$
$563$	5.47802	−	3.16273i	0.230871	−	0.133293i	0.610974	+	0.791651i	$0.290778\pi$
$564$		0			0
$565$	−20.6693	−	21.1423i	−0.869564	−	0.889465i
$566$		0			0
$567$	−1.35029	+	6.18225i	−0.0567068	+	0.259630i
$568$		0			0
$569$	−18.3447	+	31.7739i	−0.769049	+	1.33203i	0.169031	+	0.985611i	$0.445936\pi$
$569$	−18.3447	+	31.7739i	−0.769049	+	1.33203i	−0.938079	+	0.346420i	$0.887397\pi$
$570$		0			0
$571$	7.98496	+	13.8304i	0.334160	+	0.578782i	0.983323	−	0.181867i	$-0.0582140\pi$
$571$	7.98496	+	13.8304i	0.334160	+	0.578782i	−0.649163	+	0.760649i	$0.724881\pi$
$572$		0			0
$573$	−0.871615	+	16.1977i	−0.0364122	+	0.676669i
$574$		0			0
$575$	8.06214	−	13.2618i	0.336215	−	0.553056i
$576$		0			0
$577$			17.8972i			0.745071i	0.928018	+	0.372535i	$0.121511\pi$
$577$			17.8972i			0.745071i	−0.928018	+	0.372535i	$0.878489\pi$
$578$		0			0
$579$	9.98726	−	15.3320i	0.415056	−	0.637177i
$580$		0			0
$581$	−4.96604	−	8.60144i	−0.206026	−	0.356848i
$582$		0			0
$583$	37.5210	+	21.6627i	1.55396	+	0.897179i
$584$		0			0
$585$	−15.1768	+	2.18471i	−0.627485	+	0.0903268i
$586$		0			0
$587$	−17.9853	−	10.3838i	−0.742334	−	0.428587i	0.0805831	−	0.996748i	$-0.474322\pi$
$587$	−17.9853	−	10.3838i	−0.742334	−	0.428587i	−0.822917	+	0.568161i	$0.807655\pi$
$588$		0			0
$589$	17.1215	+	29.6553i	0.705478	+	1.22192i
$590$		0			0
$591$	14.0169	+	27.6052i	0.576579	+	1.13552i
$592$		0			0
$593$			37.5422i			1.54167i	0.637032	+	0.770837i	$0.280162\pi$
$593$			37.5422i			1.54167i	−0.637032	+	0.770837i	$0.719838\pi$
$594$		0			0
$595$	0.713567	+	0.199878i	0.0292534	+	0.00819421i
$596$		0			0
$597$	2.96327	−	1.50464i	0.121279	−	0.0615810i
$598$		0			0
$599$	12.6773	+	21.9577i	0.517981	+	0.897169i	0.999782	+	0.0208884i	$0.00664946\pi$
$599$	12.6773	+	21.9577i	0.517981	+	0.897169i	−0.481801	+	0.876281i	$0.660017\pi$
$600$		0			0
$601$	−8.87584	+	15.3734i	−0.362053	+	0.627095i	−0.988299	−	0.152531i	$-0.951257\pi$
$601$	−8.87584	+	15.3734i	−0.362053	+	0.627095i	0.626245	+	0.779626i	$0.284591\pi$
$602$		0			0
$603$	3.36390	−	31.1661i	0.136989	−	1.26918i
$604$		0			0
$605$	3.19697	−	3.12545i	0.129975	−	0.127067i
$606$		0			0
$607$	21.3197	−	12.3090i	0.865342	−	0.499605i	−0.000455621	−	1.00000i	$-0.500145\pi$
$607$	21.3197	−	12.3090i	0.865342	−	0.499605i	0.865798	+	0.500395i	$0.166812\pi$
$608$		0			0
$609$	0.260464	−	0.399853i	0.0105545	−	0.0162029i
$610$		0			0
$611$	−25.1184			−1.01618
$612$		0			0
$613$		−	27.6596i		−	1.11716i	−0.829450	−	0.558580i	$-0.811346\pi$
$613$		−	27.6596i		−	1.11716i	0.829450	−	0.558580i	$-0.188654\pi$
$614$		0			0
$615$	12.8880	−	38.0141i	0.519695	−	1.53288i
$616$		0			0
$617$	14.8187	−	8.55558i	0.596578	−	0.344435i	−0.171116	−	0.985251i	$-0.554737\pi$
$617$	14.8187	−	8.55558i	0.596578	−	0.344435i	0.767694	+	0.640816i	$0.221404\pi$
$618$		0			0
$619$	17.2301	−	29.8435i	0.692538	−	1.19951i	−0.278466	−	0.960446i	$-0.589826\pi$
$619$	17.2301	−	29.8435i	0.692538	−	1.19951i	0.971004	−	0.239064i	$-0.0768407\pi$
$620$		0			0
$621$	−5.71684	−	15.0818i	−0.229409	−	0.605213i
$622$		0			0
$623$	2.50580	+	1.44673i	0.100393	+	0.0579618i
$624$		0			0
$625$	13.4666	−	21.0630i	0.538663	−	0.842521i
$626$		0			0
$627$	−1.84924	+	34.3654i	−0.0738514	+	1.37242i
$628$		0			0
$629$	−4.77162			−0.190257
$630$		0			0
$631$	17.7172			0.705311			0.352655	−	0.935753i	$-0.385279\pi$
$631$	17.7172			0.705311			0.352655	+	0.935753i	$0.385279\pi$
$632$		0			0
$633$	−15.0290	−	9.78990i	−0.597351	−	0.389114i
$634$		0			0
$635$	16.6556	−	4.26151i	0.660957	−	0.169113i
$636$		0			0
$637$	12.8780	+	7.43513i	0.510246	+	0.294591i
$638$		0			0
$639$	5.54950	−	7.59346i	0.219535	−	0.300393i
$640$		0			0
$641$	8.42149	−	14.5864i	0.332629	−	0.576130i	−0.650398	−	0.759594i	$-0.725398\pi$
$641$	8.42149	−	14.5864i	0.332629	−	0.576130i	0.983026	+	0.183464i	$0.0587310\pi$
$642$		0			0
$643$	−30.5655	+	17.6470i	−1.20538	+	0.695929i	−0.961748	−	0.273937i	$-0.911674\pi$
$643$	−30.5655	+	17.6470i	−1.20538	+	0.695929i	−0.243637	+	0.969867i	$0.578341\pi$
$644$		0			0
$645$	−0.244062	−	1.22456i	−0.00960994	−	0.0482172i
$646$		0			0
$647$		−	0.447554i		−	0.0175952i	−0.999961	−	0.00879758i	$-0.997200\pi$
$647$		−	0.447554i		−	0.0175952i	0.999961	−	0.00879758i	$-0.00280039\pi$
$648$		0			0
$649$	−22.6054			−0.887338
$650$		0			0
$651$	−3.42595	−	6.74714i	−0.134274	−	0.264441i
$652$		0			0
$653$	18.5161	−	10.6903i	0.724592	−	0.418343i	−0.0918485	−	0.995773i	$-0.529278\pi$
$653$	18.5161	−	10.6903i	0.724592	−	0.418343i	0.816440	+	0.577430i	$0.195944\pi$
$654$		0			0
$655$	−26.5629	+	25.9686i	−1.03790	+	1.01468i
$656$		0			0
$657$	−8.21542	−	6.00405i	−0.320514	−	0.234240i
$658$		0			0
$659$	−3.20807	+	5.55655i	−0.124969	+	0.216452i	−0.921721	−	0.387854i	$-0.873216\pi$
$659$	−3.20807	+	5.55655i	−0.124969	+	0.216452i	0.796752	+	0.604306i	$0.206550\pi$
$660$		0			0
$661$	−16.8800	−	29.2370i	−0.656555	−	1.13719i	−0.981502	−	0.191454i	$-0.938680\pi$
$661$	−16.8800	−	29.2370i	−0.656555	−	1.13719i	0.324946	−	0.945732i	$-0.394654\pi$
$662$		0			0
$663$	1.56356	+	1.01850i	0.0607236	+	0.0395553i
$664$		0			0
$665$	−2.33702	+	8.34320i	−0.0906259	+	0.323535i
$666$		0			0
$667$			1.21631i			0.0470957i
$668$		0			0
$669$	−9.63487	−	0.518462i	−0.372506	−	0.0200449i
$670$		0			0
$671$	3.94573	+	6.83421i	0.152323	+	0.263832i
$672$		0			0
$673$	−8.28190	−	4.78156i	−0.319244	−	0.184315i	0.331812	−	0.943346i	$-0.392340\pi$
$673$	−8.28190	−	4.78156i	−0.319244	−	0.184315i	−0.651055	+	0.759030i	$0.725673\pi$
$674$		0			0
$675$	−8.65680	−	24.4961i	−0.333201	−	0.942856i
$676$		0			0
$677$	19.0593	+	11.0039i	0.732508	+	0.422914i	0.819339	−	0.573309i	$-0.194341\pi$
$677$	19.0593	+	11.0039i	0.732508	+	0.422914i	−0.0868307	+	0.996223i	$0.527674\pi$
$678$		0			0
$679$	−4.66145	−	8.07387i	−0.178890	−	0.309847i
$680$		0			0
$681$	26.4966	+	1.42581i	1.01535	+	0.0546371i
$682$		0			0
$683$		−	13.1585i		−	0.503497i	−0.967793	−	0.251749i	$-0.918994\pi$
$683$		−	13.1585i		−	0.503497i	0.967793	−	0.251749i	$-0.0810057\pi$
$684$		0			0
$685$	−7.26365	+	25.9313i	−0.277530	+	0.990784i
$686$		0			0
$687$	8.05438	+	5.24661i	0.307294	+	0.200171i
$688$		0			0
$689$	13.7335	+	23.7870i	0.523203	+	0.906214i
$690$		0			0
$691$	1.03103	−	1.78579i	0.0392221	−	0.0679346i	−0.845748	−	0.533583i	$-0.820845\pi$
$691$	1.03103	−	1.78579i	0.0392221	−	0.0679346i	0.884970	+	0.465648i	$0.154179\pi$
$692$		0			0
$693$	0.816118	−	7.56123i	0.0310018	−	0.287227i
$694$		0			0
$695$	−35.4429	+	34.6500i	−1.34443	+	1.31435i
$696$		0			0
$697$	−4.23043	+	2.44244i	−0.160239	+	0.0925140i
$698$		0			0
$699$	−14.2664	−	28.0965i	−0.539606	−	1.06271i
$700$		0			0
$701$	−22.9923			−0.868406			−0.434203	−	0.900815i	$-0.642970\pi$
$701$	−22.9923			−0.868406			−0.434203	+	0.900815i	$0.642970\pi$
$702$		0			0
$703$		−	55.7909i		−	2.10419i
$704$		0			0
$705$	−8.31897	−	41.7398i	−0.313311	−	1.57201i
$706$		0			0
$707$	6.17535	−	3.56534i	0.232248	−	0.134088i
$708$		0			0
$709$	3.82791	−	6.63014i	0.143760	−	0.249000i	−0.785149	−	0.619306i	$-0.787414\pi$
$709$	3.82791	−	6.63014i	0.143760	−	0.249000i	0.928910	+	0.370306i	$0.120747\pi$
$710$		0			0
$711$	4.03964	+	9.14196i	0.151498	+	0.342850i
$712$		0			0
$713$	16.7032	+	9.64361i	0.625541	+	0.361156i
$714$		0			0
$715$	17.8528	−	4.56783i	0.667658	−	0.170827i
$716$		0			0
$717$	16.7270	+	10.8960i	0.624682	+	0.406917i
$718$		0			0
$719$	2.52489			0.0941625			0.0470812	−	0.998891i	$-0.485008\pi$
$719$	2.52489			0.0941625			0.0470812	+	0.998891i	$0.485008\pi$
$720$		0			0
$721$	2.61153			0.0972584
$722$		0			0
$723$	−1.61672	+	30.0444i	−0.0601266	+	1.11737i
$724$		0			0
$725$	−0.0443246	+	1.95875i	−0.00164618	+	0.0727461i
$726$		0			0
$727$	29.1826	+	16.8486i	1.08232	+	0.624880i	0.931522	−	0.363684i	$-0.118481\pi$
$727$	29.1826	+	16.8486i	1.08232	+	0.624880i	0.150802	+	0.988564i	$0.451814\pi$
$728$		0			0
$729$	−25.6076	−	8.55875i	−0.948429	−	0.316991i
$730$		0			0
$731$	−0.0759789	+	0.131599i	−0.00281018	+	0.00486738i
$732$		0			0
$733$	−0.243044	+	0.140321i	−0.00897702	+	0.00518289i	−0.504482	−	0.863422i	$-0.668316\pi$
$733$	−0.243044	+	0.140321i	−0.00897702	+	0.00518289i	0.495505	+	0.868605i	$0.334983\pi$
$734$		0			0
$735$	−8.09004	+	23.8621i	−0.298406	+	0.880167i
$736$		0			0
$737$			37.6738i			1.38773i
$738$		0			0
$739$	−0.119448			−0.00439396			−0.00219698	−	0.999998i	$-0.500699\pi$
$739$	−0.119448			−0.00439396			−0.00219698	+	0.999998i	$0.500699\pi$
$740$		0			0
$741$	−11.9085	+	18.2815i	−0.437471	+	0.671588i
$742$		0			0
$743$	−4.45547	+	2.57237i	−0.163455	+	0.0943711i	−0.579496	−	0.814975i	$-0.696751\pi$
$743$	−4.45547	+	2.57237i	−0.163455	+	0.0943711i	0.416041	+	0.909346i	$0.363417\pi$
$744$		0			0
$745$	22.2301	−	21.7327i	0.814447	−	0.796225i
$746$		0			0
$747$	38.7621	−	17.1282i	1.41823	−	0.626687i
$748$		0			0
$749$	1.03263	−	1.78856i	0.0377314	−	0.0653527i
$750$		0			0
$751$	−3.19703	−	5.53743i	−0.116661	−	0.202064i	0.801781	−	0.597618i	$-0.203886\pi$
$751$	−3.19703	−	5.53743i	−0.116661	−	0.202064i	−0.918443	+	0.395554i	$0.870553\pi$
$752$		0			0
$753$	30.6558	−	15.5659i	1.11716	−	0.567254i
$754$		0			0
$755$	48.4525	+	13.5721i	1.76337	+	0.493939i
$756$		0			0
$757$			11.9405i			0.433985i	0.976173	+	0.216992i	$0.0696247\pi$
$757$			11.9405i			0.433985i	−0.976173	+	0.216992i	$0.930375\pi$
$758$		0			0
$759$	8.77606	+	17.2837i	0.318551	+	0.627360i
$760$		0			0
$761$	−23.7055	−	41.0591i	−0.859323	−	1.48839i	−0.872576	−	0.488479i	$-0.837552\pi$
$761$	−23.7055	−	41.0591i	−0.859323	−	1.48839i	0.0132529	−	0.999912i	$-0.495781\pi$
$762$		0			0
$763$	1.34714	+	0.777773i	0.0487698	+	0.0281573i
$764$		0			0
$765$	−1.17463	+	2.93552i	−0.0424688	+	0.106134i
$766$		0			0
$767$	−12.4110	−	7.16552i	−0.448137	−	0.258732i
$768$		0			0
$769$	0.763036	+	1.32162i	0.0275158	+	0.0476587i	0.879455	−	0.475981i	$-0.157907\pi$
$769$	0.763036	+	1.32162i	0.0275158	+	0.0476587i	−0.851940	+	0.523640i	$0.824574\pi$
$770$		0			0
$771$	−6.30970	+	9.68638i	−0.227238	+	0.348847i
$772$		0			0
$773$		−	33.3154i		−	1.19827i	−0.800648	−	0.599136i	$-0.795511\pi$
$773$		−	33.3154i		−	1.19827i	0.800648	−	0.599136i	$-0.204489\pi$
$774$		0			0
$775$	26.5475	+	16.1388i	0.953613	+	0.579722i
$776$		0			0
$777$	−0.662468	+	12.3110i	−0.0237659	+	0.441655i
$778$		0			0
$779$	−28.5576	−	49.4632i	−1.02318	−	1.77220i
$780$		0			0
$781$	−5.65170	+	9.78902i	−0.202234	+	0.350279i
$782$		0			0
$783$	1.57696	+	1.28800i	0.0563561	+	0.0460293i
$784$		0			0
$785$	−32.3322	−	33.0721i	−1.15398	−	1.18039i
$786$		0			0
$787$	18.3702	−	10.6060i	0.654826	−	0.378064i	−0.135477	−	0.990781i	$-0.543257\pi$
$787$	18.3702	−	10.6060i	0.654826	−	0.378064i	0.790303	+	0.612717i	$0.209923\pi$
$788$		0			0
$789$	4.22826	+	0.227527i	0.150530	+	0.00810017i
$790$		0			0
$791$	9.29713			0.330568
$792$		0			0
$793$			5.00292i			0.177659i
$794$		0			0
$795$	−34.9790	+	30.6992i	−1.24058	+	1.08879i
$796$		0			0
$797$	41.7281	−	24.0917i	1.47809	−	0.853373i	0.478393	−	0.878146i	$-0.341220\pi$
$797$	41.7281	−	24.0917i	1.47809	−	0.853373i	0.999693	+	0.0247730i	$0.00788629\pi$
$798$		0			0
$799$	−2.58978	+	4.48562i	−0.0916197	+	0.158690i
$800$		0			0
$801$	−7.28451	+	9.96748i	−0.257385	+	0.352184i
$802$		0			0
$803$	10.5908	+	6.11462i	0.373742	+	0.215780i
$804$		0			0
$805$	1.20967	+	4.72785i	0.0426353	+	0.166635i
$806$		0			0
$807$	15.5480	−	7.89470i	0.547314	−	0.277907i
$808$		0			0
$809$	4.97117			0.174777			0.0873886	−	0.996174i	$-0.472148\pi$
$809$	4.97117			0.174777			0.0873886	+	0.996174i	$0.472148\pi$
$810$		0			0
$811$	−30.5332			−1.07216			−0.536082	−	0.844166i	$-0.680096\pi$
$811$	−30.5332			−1.07216			−0.536082	+	0.844166i	$0.680096\pi$
$812$		0			0
$813$	−33.3239	+	16.9207i	−1.16872	+	0.593434i
$814$		0			0
$815$	28.7676	−	7.36050i	1.00769	−	0.257827i
$816$		0			0
$817$	−1.53869	−	0.888364i	−0.0538320	−	0.0310799i
$818$		0			0
$819$	2.84486	−	3.89265i	0.0994074	−	0.136020i
$820$		0			0
$821$	0.542675	−	0.939941i	0.0189395	−	0.0328042i	−0.856400	−	0.516312i	$-0.827304\pi$
$821$	0.542675	−	0.939941i	0.0189395	−	0.0328042i	0.875340	+	0.483508i	$0.160638\pi$
$822$		0			0
$823$	18.4886	−	10.6744i	0.644471	−	0.372085i	−0.141864	−	0.989886i	$-0.545310\pi$
$823$	18.4886	−	10.6744i	0.644471	−	0.372085i	0.786335	+	0.617801i	$0.211976\pi$
$824$		0			0
$825$	13.5031	+	28.1536i	0.470119	+	0.980182i
$826$		0			0
$827$			35.1458i			1.22214i	0.791577	+	0.611070i	$0.209260\pi$
$827$			35.1458i			1.22214i	−0.791577	+	0.611070i	$0.790740\pi$
$828$		0			0
$829$	2.53738			0.0881269			0.0440635	−	0.999029i	$-0.485970\pi$
$829$	2.53738			0.0881269			0.0440635	+	0.999029i	$0.485970\pi$
$830$		0			0
$831$	50.3143	+	2.70746i	1.74538	+	0.0939208i
$832$		0			0
$833$	2.65552	−	1.53316i	0.0920082	−	0.0531210i
$834$		0			0
$835$	−33.9029	−	34.6788i	−1.17326	−	1.20011i
$836$		0			0
$837$	30.1908	−	11.4440i	1.04355	−	0.395561i
$838$		0			0
$839$	20.1583	−	34.9153i	0.695943	−	1.20541i	−0.273918	−	0.961753i	$-0.588320\pi$
$839$	20.1583	−	34.9153i	0.695943	−	1.20541i	0.969862	−	0.243656i	$-0.0783469\pi$
$840$		0			0
$841$	14.4232	+	24.9818i	0.497353	+	0.861440i
$842$		0			0
$843$	1.64731	−	30.6130i	0.0567365	−	1.05437i
$844$		0			0
$845$	−16.7418	−	4.68957i	−0.575935	−	0.161326i
$846$		0			0
$847$			1.40584i			0.0483051i
$848$		0			0
$849$	1.02255	−	1.56977i	0.0350938	−	0.0538745i
$850$		0			0
$851$	−15.7120	−	27.2140i	−0.538601	−	0.932884i
$852$		0			0
$853$	49.5861	+	28.6285i	1.69780	+	0.980223i	0.947846	+	0.318728i	$0.103256\pi$
$853$	49.5861	+	28.6285i	1.69780	+	0.980223i	0.749949	+	0.661495i	$0.230078\pi$
$854$		0			0
$855$	−34.3227	−	13.7340i	−1.17381	−	0.469694i
$856$		0			0
$857$	−12.4224	−	7.17208i	−0.424341	−	0.244994i	0.272592	−	0.962130i	$-0.412119\pi$
$857$	−12.4224	−	7.17208i	−0.424341	−	0.244994i	−0.696933	+	0.717136i	$0.745453\pi$
$858$		0			0
$859$	−14.8559	−	25.7312i	−0.506877	−	0.877937i	−0.999968	−	0.00795944i	$-0.997466\pi$
$859$	−14.8559	−	25.7312i	−0.506877	−	0.877937i	0.493091	−	0.869978i	$-0.335867\pi$
$860$		0			0
$861$	5.71428	+	11.2538i	0.194742	+	0.383529i
$862$		0			0
$863$			1.60851i			0.0547544i	0.999625	+	0.0273772i	$0.00871552\pi$
$863$			1.60851i			0.0547544i	−0.999625	+	0.0273772i	$0.991284\pi$
$864$		0			0
$865$	4.73697	−	16.9110i	0.161062	−	0.574992i
$866$		0			0
$867$	−25.9112	+	13.1568i	−0.879989	+	0.446827i
$868$		0			0
$869$	−6.00594	−	10.4026i	−0.203738	−	0.352884i
$870$		0			0
$871$	−11.9419	+	20.6841i	−0.404637	+	0.700853i
$872$		0			0
$873$	36.3846	−	16.0776i	1.23143	−	0.544145i
$874$		0			0
$875$	1.77576	+	7.65782i	0.0600318	+	0.258882i
$876$		0			0
$877$	26.5499	−	15.3286i	0.896525	−	0.517609i	0.0204539	−	0.999791i	$-0.493489\pi$
$877$	26.5499	−	15.3286i	0.896525	−	0.517609i	0.876071	+	0.482182i	$0.160156\pi$
$878$		0			0
$879$	−3.23867	+	4.97187i	−0.109238	+	0.167697i
$880$		0			0
$881$	9.69932			0.326778			0.163389	−	0.986562i	$-0.447757\pi$
$881$	9.69932			0.326778			0.163389	+	0.986562i	$0.447757\pi$
$882$		0			0
$883$		−	15.2156i		−	0.512047i	−0.966671	−	0.256023i	$-0.917588\pi$
$883$		−	15.2156i		−	0.512047i	0.966671	−	0.256023i	$-0.0824124\pi$
$884$		0			0
$885$	7.79668	−	22.9968i	0.262083	−	0.773030i
$886$		0			0
$887$	12.9037	−	7.44993i	0.433262	−	0.250144i	−0.267473	−	0.963565i	$-0.586189\pi$
$887$	12.9037	−	7.44993i	0.433262	−	0.250144i	0.700735	+	0.713421i	$0.252855\pi$
$888$		0			0
$889$	−2.70295	+	4.68165i	−0.0906541	+	0.157018i
$890$		0			0
$891$	31.7019	+	6.92413i	1.06205	+	0.231967i
$892$		0			0
$893$	−52.4470	−	30.2803i	−1.75507	−	1.01329i
$894$		0			0
$895$	1.66961	+	6.52546i	0.0558088	+	0.218122i
$896$		0			0
$897$	−0.660325	+	12.2712i	−0.0220476	+	0.409723i
$898$		0			0
$899$	−2.43481			−0.0812054
$900$		0			0
$901$	5.66382			0.188689
$902$		0			0
$903$	0.328984	+	0.214300i	0.0109479	+	0.00713146i
$904$		0			0
$905$	12.9843	+	50.7477i	0.431613	+	1.68691i
$906$		0			0
$907$	31.9280	+	18.4336i	1.06015	+	0.612078i	0.925474	−	0.378812i	$-0.123667\pi$
$907$	31.9280	+	18.4336i	1.06015	+	0.612078i	0.134676	+	0.990890i	$0.457000\pi$
$908$		0			0
$909$	12.2971	+	27.8290i	0.407868	+	0.923029i
$910$		0			0
$911$	26.6246	−	46.1151i	0.882111	−	1.52786i	0.0331224	−	0.999451i	$-0.489455\pi$
$911$	26.6246	−	46.1151i	0.882111	−	1.52786i	0.848989	−	0.528411i	$-0.177212\pi$
$912$		0			0
$913$	−44.1072	+	25.4653i	−1.45974	+	0.842779i
$914$		0			0
$915$	−8.31346	+	1.65692i	−0.274835	+	0.0547760i
$916$		0			0
$917$		−	11.6808i		−	0.385733i
$918$		0			0
$919$	34.4511			1.13644			0.568218	−	0.822878i	$-0.307633\pi$
$919$	34.4511			1.13644			0.568218	+	0.822878i	$0.307633\pi$
$920$		0			0
$921$	5.30174	+	10.4413i	0.174698	+	0.344054i
$922$		0			0
$923$	−6.20591	+	3.58299i	−0.204270	+	0.117935i
$924$		0			0
$925$	−24.3109	−	44.3981i	−0.799338	−	1.45980i
$926$		0			0
$927$	−1.19574	+	11.0784i	−0.0392733	+	0.363863i
$928$		0			0
$929$	6.25536	−	10.8346i	0.205232	−	0.355472i	−0.744975	−	0.667093i	$-0.767539\pi$
$929$	6.25536	−	10.8346i	0.205232	−	0.355472i	0.950207	+	0.311621i	$0.100872\pi$
$930$		0			0
$931$	17.9261	+	31.0489i	0.587504	+	1.01759i
$932$		0			0
$933$	−13.1895	−	8.59162i	−0.431805	−	0.281277i
$934$		0			0
$935$	1.02495	−	3.65909i	0.0335196	−	0.119665i
$936$		0			0
$937$			23.9334i			0.781870i	0.920418	+	0.390935i	$0.127848\pi$
$937$			23.9334i			0.781870i	−0.920418	+	0.390935i	$0.872152\pi$
$938$		0			0
$939$	−44.0623	−	2.37104i	−1.43792	−	0.0773758i
$940$		0			0
$941$	−21.4502	−	37.1528i	−0.699256	−	1.21115i	−0.968725	−	0.248138i	$-0.920181\pi$
$941$	−21.4502	−	37.1528i	−0.699256	−	1.21115i	0.269469	−	0.963009i	$-0.413152\pi$
$942$		0			0
$943$	−27.8600	−	16.0850i	−0.907245	−	0.523798i
$944$		0			0
$945$	7.41069	+	3.43815i	0.241070	+	0.111843i
$946$		0			0
$947$	34.0803	+	19.6763i	1.10746	+	0.639393i	0.938171	−	0.346173i	$-0.112519\pi$
$947$	34.0803	+	19.6763i	1.10746	+	0.639393i	0.169291	+	0.985566i	$0.445852\pi$
$948$		0			0
$949$	3.87646	+	6.71423i	0.125835	+	0.217953i
$950$		0			0
$951$	−22.1531	−	1.19208i	−0.718364	−	0.0386559i
$952$		0			0
$953$			9.66984i			0.313237i	0.987659	+	0.156618i	$0.0500593\pi$
$953$			9.66984i			0.313237i	−0.987659	+	0.156618i	$0.949941\pi$
$954$		0			0
$955$	20.1652	+	5.64851i	0.652531	+	0.182781i
$956$		0			0
$957$	−2.05040	−	1.33563i	−0.0662801	−	0.0431748i
$958$		0			0
$959$	−4.23385	−	7.33325i	−0.136718	−	0.236803i
$960$		0			0
$961$	−3.80457	+	6.58971i	−0.122728	+	0.212571i
$962$		0			0
$963$	7.11448	+	5.19946i	0.229261	+	0.167550i
$964$		0			0
$965$	−16.5137	−	16.8916i	−0.531594	−	0.543759i
$966$		0			0
$967$	−15.6478	+	9.03427i	−0.503200	+	0.290522i	−0.730034	−	0.683411i	$-0.760496\pi$
$967$	−15.6478	+	9.03427i	−0.503200	+	0.290522i	0.226834	+	0.973933i	$0.427162\pi$
$968$		0			0
$969$	2.03689	+	4.01149i	0.0654343	+	0.128868i
$970$		0			0
$971$	−13.9590			−0.447966			−0.223983	−	0.974593i	$-0.571906\pi$
$971$	−13.9590			−0.447966			−0.223983	+	0.974593i	$0.571906\pi$
$972$		0			0
$973$		−	15.5857i		−	0.499654i
$974$		0			0
$975$	−1.51057	+	19.7375i	−0.0483770	+	0.632105i
$976$		0			0
$977$	−22.2970	+	12.8732i	−0.713344	+	0.411849i	−0.812298	−	0.583243i	$-0.801784\pi$
$977$	−22.2970	+	12.8732i	−0.713344	+	0.411849i	0.0989538	+	0.995092i	$0.468450\pi$
$978$		0			0
$979$	7.41865	−	12.8495i	0.237101	−	0.410671i
$980$		0			0
$981$	−3.91622	+	5.35861i	−0.125035	+	0.171087i
$982$		0			0
$983$	10.7056	+	6.18090i	0.341457	+	0.197140i	0.660916	−	0.750460i	$-0.270168\pi$
$983$	10.7056	+	6.18090i	0.341457	+	0.197140i	−0.319459	+	0.947600i	$0.603501\pi$
$984$		0			0
$985$	38.7218	−	9.90737i	1.23378	−	0.315675i
$986$		0			0
$987$	11.2136	+	7.30451i	0.356932	+	0.232505i
$988$		0			0
$989$	−1.00074			−0.0318215
$990$		0			0
$991$	19.5181			0.620014			0.310007	−	0.950734i	$-0.399669\pi$
$991$	19.5181			0.620014			0.310007	+	0.950734i	$0.399669\pi$
$992$		0			0
$993$	−1.60720	+	29.8675i	−0.0510029	+	0.947816i
$994$		0			0
$995$	−1.06351	−	4.15659i	−0.0337154	−	0.131773i
$996$		0			0
$997$	2.39885	+	1.38497i	0.0759722	+	0.0438626i	0.537505	−	0.843261i	$-0.319367\pi$
$997$	2.39885	+	1.38497i	0.0759722	+	0.0438626i	−0.461533	+	0.887123i	$0.652700\pi$
$998$		0			0
$999$	−51.9214	−	8.44712i	−1.64272	−	0.267255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.169.3	yes	32
3.2	odd	2		1080.2.bi.b.289.8		32
4.3	odd	2		720.2.by.f.529.14		32
5.4	even	2	inner	360.2.bi.b.169.14	yes	32
9.2	odd	6		3240.2.f.i.649.14		16
9.4	even	3	inner	360.2.bi.b.49.14	yes	32
9.5	odd	6		1080.2.bi.b.1009.3		32
9.7	even	3		3240.2.f.k.649.3		16
12.11	even	2		2160.2.by.f.289.8		32
15.14	odd	2		1080.2.bi.b.289.3		32
20.19	odd	2		720.2.by.f.529.3		32
36.23	even	6		2160.2.by.f.1009.3		32
36.31	odd	6		720.2.by.f.49.3		32
45.4	even	6	inner	360.2.bi.b.49.3	✓	32
45.14	odd	6		1080.2.bi.b.1009.8		32
45.29	odd	6		3240.2.f.i.649.13		16
45.34	even	6		3240.2.f.k.649.4		16
60.59	even	2		2160.2.by.f.289.3		32
180.59	even	6		2160.2.by.f.1009.8		32
180.139	odd	6		720.2.by.f.49.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.3	✓	32	45.4	even	6	inner
360.2.bi.b.49.14	yes	32	9.4	even	3	inner
360.2.bi.b.169.3	yes	32	1.1	even	1	trivial
360.2.bi.b.169.14	yes	32	5.4	even	2	inner
720.2.by.f.49.3		32	36.31	odd	6
720.2.by.f.49.14		32	180.139	odd	6
720.2.by.f.529.3		32	20.19	odd	2
720.2.by.f.529.14		32	4.3	odd	2
1080.2.bi.b.289.3		32	15.14	odd	2
1080.2.bi.b.289.8		32	3.2	odd	2
1080.2.bi.b.1009.3		32	9.5	odd	6
1080.2.bi.b.1009.8		32	45.14	odd	6
2160.2.by.f.289.3		32	60.59	even	2
2160.2.by.f.289.8		32	12.11	even	2
2160.2.by.f.1009.3		32	36.23	even	6
2160.2.by.f.1009.8		32	180.59	even	6
3240.2.f.i.649.13		16	45.29	odd	6
3240.2.f.i.649.14		16	9.2	odd	6
3240.2.f.k.649.3		16	9.7	even	3
3240.2.f.k.649.4		16	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54437 + 0.784174i) q^{3} +(0.554267 + 2.16628i) q^{5} +(-0.608912 - 0.351555i) q^{7} +(1.77014 - 2.42211i) q^{9} +O(q^{10})\)	\(q+(-1.54437 + 0.784174i) q^{3} +(0.554267 + 2.16628i) q^{5} +(-0.608912 - 0.351555i) q^{7} +(1.77014 - 2.42211i) q^{9} +(-1.80274 + 3.12243i) q^{11} +(-1.97952 + 1.14288i) q^{13} +(-2.55474 - 2.91090i) q^{15} +0.471334i q^{17} -5.51095 q^{19} +(1.21606 + 0.0654377i) q^{21} +(-2.68816 + 1.55201i) q^{23} +(-4.38558 + 2.40140i) q^{25} +(-0.834394 + 5.12872i) q^{27} +(0.195925 - 0.339352i) q^{29} +(-3.10681 - 5.38116i) q^{31} +(0.335557 - 6.23584i) q^{33} +(0.424070 - 1.51393i) q^{35} +10.1237i q^{37} +(2.16089 - 3.31731i) q^{39} +(5.18197 + 8.97544i) q^{41} +(0.279206 + 0.161200i) q^{43} +(6.22810 + 2.49214i) q^{45} +(9.51687 + 5.49457i) q^{47} +(-3.25282 - 5.63405i) q^{49} +(-0.369608 - 0.727913i) q^{51} -12.0166i q^{53} +(-7.76328 - 2.17458i) q^{55} +(8.51093 - 4.32154i) q^{57} +(3.13487 + 5.42975i) q^{59} +(1.09437 - 1.89551i) q^{61} +(-1.92936 + 0.852547i) q^{63} +(-3.57297 - 3.65474i) q^{65} +(9.04913 - 5.22452i) q^{67} +(2.93446 - 4.50486i) q^{69} +3.13506 q^{71} -3.39185i q^{73} +(4.88983 - 7.14770i) q^{75} +(2.19542 - 1.26752i) q^{77} +(-1.66578 + 2.88522i) q^{79} +(-2.73320 - 8.57494i) q^{81} +(12.2334 + 7.06296i) q^{83} +(-1.02104 + 0.261245i) q^{85} +(-0.0364690 + 0.677723i) q^{87} -4.11521 q^{89} +1.60714 q^{91} +(9.01783 + 5.87420i) q^{93} +(-3.05453 - 11.9383i) q^{95} +(11.4831 + 6.62975i) q^{97} +(4.37177 + 9.89357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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