LMFDB - Embedded newform 588.2.e.f.491.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.8
Character	$\chi$	$=$	588.491
Dual form			588.2.e.f.491.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05533 + 0.941421i) q^{2} +(0.406768 - 1.68361i) q^{3} +(0.227452 - 1.98702i) q^{4} +1.25365i q^{5} +(1.15571 + 2.15971i) q^{6} +(1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +(-1.18022 - 1.32302i) q^{10} -5.05827 q^{11} +(-3.25285 - 1.19120i) q^{12} -4.41798 q^{13} +(2.11066 + 0.509947i) q^{15} +(-3.89653 - 0.903905i) q^{16} +5.85341i q^{17} +(4.10621 - 1.06726i) q^{18} +1.53176i q^{19} +(2.49104 + 0.285146i) q^{20} +(5.33816 - 4.76197i) q^{22} -0.313570 q^{23} +(4.55426 - 1.80519i) q^{24} +3.42835 q^{25} +(4.66244 - 4.15918i) q^{26} +(-3.39170 + 3.93654i) q^{27} -5.53862i q^{29} +(-2.70753 + 1.44886i) q^{30} +4.89898i q^{31} +(4.96309 - 2.71436i) q^{32} +(-2.05755 + 8.51615i) q^{33} +(-5.51053 - 6.17729i) q^{34} +(-3.32867 + 4.99199i) q^{36} -5.33816 q^{37} +(-1.44203 - 1.61652i) q^{38} +(-1.79709 + 7.43815i) q^{39} +(-2.89732 + 2.04420i) q^{40} +1.97938i q^{41} -3.18613i q^{43} +(-1.15051 + 10.0509i) q^{44} +(1.71710 - 3.34610i) q^{45} +(0.330921 - 0.295202i) q^{46} -11.4963 q^{47} +(-3.10681 + 6.19256i) q^{48} +(-3.61805 + 3.22752i) q^{50} +(9.85486 + 2.38098i) q^{51} +(-1.00488 + 8.77863i) q^{52} +12.7903i q^{53} +(-0.126578 - 7.34738i) q^{54} -6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(5.21417 + 5.84508i) q^{58} -7.96701 q^{59} +(1.49335 - 4.07795i) q^{60} +0.302889 q^{61} +(-4.61200 - 5.17005i) q^{62} +(-2.68236 + 7.53691i) q^{64} -5.53862i q^{65} +(-5.84589 - 10.9244i) q^{66} -10.5438i q^{67} +(11.6309 + 1.33137i) q^{68} +(-0.127550 + 0.527930i) q^{69} -4.53490 q^{71} +(-1.18671 - 8.40189i) q^{72} -1.41421 q^{73} +(5.63353 - 5.02546i) q^{74} +(1.39454 - 5.77200i) q^{75} +(3.04365 + 0.348402i) q^{76} +(-5.10590 - 9.54154i) q^{78} -6.92820i q^{79} +(1.13319 - 4.88490i) q^{80} +(5.24797 + 7.31156i) q^{81} +(-1.86343 - 2.08890i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(2.99949 + 3.36243i) q^{86} +(-9.32487 - 2.25294i) q^{87} +(-8.24797 - 11.6902i) q^{88} -4.79755i q^{89} +(1.33798 + 5.14777i) q^{90} +(-0.0713222 + 0.623072i) q^{92} +(8.24797 + 1.99275i) q^{93} +(12.1324 - 10.8228i) q^{94} -1.92030 q^{95} +(-2.55109 - 9.46002i) q^{96} +13.6844 q^{97} +(13.5009 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) $ 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.05533	+	0.941421i	−0.746233	+	0.665685i
$2$	−1.05533	+	0.941421i	−0.746233	+	0.665685i
$3$	0.406768	−	1.68361i	0.234848	−	0.972032i
$3$	0.406768	−	1.68361i	0.234848	−	0.972032i
$4$	0.227452	−	1.98702i	0.113726	−	0.993512i
$5$			1.25365i			0.560651i	0.959905	+	0.280326i	$0.0904425\pi$
$5$			1.25365i			0.560651i	−0.959905	+	0.280326i	$0.909558\pi$
$6$	1.15571	+	2.15971i	0.471817	+	0.881697i
$7$		0			0
$7$		0			0
$8$	1.63059	+	2.31110i	0.576500	+	0.817097i
$9$	−2.66908	−	1.36968i	−0.889693	−	0.456559i
$10$	−1.18022	−	1.32302i	−0.373217	−	0.418376i
$11$	−5.05827			−1.52513			−0.762563	−	0.646914i	$-0.776059\pi$
$11$	−5.05827			−1.52513			−0.762563	+	0.646914i	$0.776059\pi$
$12$	−3.25285	−	1.19120i	−0.939017	−	0.343869i
$13$	−4.41798			−1.22533			−0.612664	−	0.790344i	$-0.709902\pi$
$13$	−4.41798			−1.22533			−0.612664	+	0.790344i	$0.709902\pi$
$14$		0			0
$15$	2.11066	+	0.509947i	0.544971	+	0.131668i
$16$	−3.89653	−	0.903905i	−0.974133	−	0.225976i
$17$			5.85341i			1.41966i	0.704372	+	0.709831i	$0.251229\pi$
$17$			5.85341i			1.41966i	−0.704372	+	0.709831i	$0.748771\pi$
$18$	4.10621	−	1.06726i	0.967843	−	0.251556i
$19$			1.53176i			0.351410i	0.984443	+	0.175705i	$0.0562205\pi$
$19$			1.53176i			0.351410i	−0.984443	+	0.175705i	$0.943779\pi$
$20$	2.49104	+	0.285146i	0.557014	+	0.0637607i
$21$		0			0
$22$	5.33816	−	4.76197i	1.13810	−	1.01525i
$23$	−0.313570			−0.0653839			−0.0326920	−	0.999465i	$-0.510408\pi$
$23$	−0.313570			−0.0653839			−0.0326920	+	0.999465i	$0.510408\pi$
$24$	4.55426	−	1.80519i	0.929634	−	0.368484i
$25$	3.42835			0.685670
$26$	4.66244	−	4.15918i	0.914379	−	0.815682i
$27$	−3.39170	+	3.93654i	−0.652733	+	0.757588i
$28$		0			0
$29$		−	5.53862i		−	1.02850i	−0.857642	−	0.514248i	$-0.828071\pi$
$29$		−	5.53862i		−	1.02850i	0.857642	−	0.514248i	$-0.171929\pi$
$30$	−2.70753	+	1.44886i	−0.494325	+	0.264525i
$31$			4.89898i			0.879883i	0.898027	+	0.439941i	$0.145001\pi$
$31$			4.89898i			0.879883i	−0.898027	+	0.439941i	$0.854999\pi$
$32$	4.96309	−	2.71436i	0.877359	−	0.479835i
$33$	−2.05755	+	8.51615i	−0.358173	+	1.48247i
$34$	−5.51053	−	6.17729i	−0.945048	−	1.05940i
$35$		0			0
$36$	−3.32867	+	4.99199i	−0.554778	+	0.831998i
$37$	−5.33816			−0.877588			−0.438794	−	0.898588i	$-0.644594\pi$
$37$	−5.33816			−0.877588			−0.438794	+	0.898588i	$0.644594\pi$
$38$	−1.44203	−	1.61652i	−0.233929	−	0.262234i
$39$	−1.79709	+	7.43815i	−0.287765	+	1.19106i
$40$	−2.89732	+	2.04420i	−0.458106	+	0.323216i
$41$			1.97938i			0.309127i	0.987983	+	0.154564i	$0.0493971\pi$
$41$			1.97938i			0.309127i	−0.987983	+	0.154564i	$0.950603\pi$
$42$		0			0
$43$		−	3.18613i		−	0.485881i	−0.970041	−	0.242940i	$-0.921888\pi$
$43$		−	3.18613i		−	0.485881i	0.970041	−	0.242940i	$-0.0781119\pi$
$44$	−1.15051	+	10.0509i	−0.173447	+	1.51523i
$45$	1.71710	−	3.34610i	0.255971	−	0.498808i
$46$	0.330921	−	0.295202i	0.0487916	−	0.0435251i
$47$	−11.4963			−1.67690			−0.838451	−	0.544977i	$-0.816539\pi$
$47$	−11.4963			−1.67690			−0.838451	+	0.544977i	$0.816539\pi$
$48$	−3.10681	+	6.19256i	−0.448429	+	0.893818i
$49$		0			0
$50$	−3.61805	+	3.22752i	−0.511669	+	0.456440i
$51$	9.85486	+	2.38098i	1.37996	+	0.333404i
$52$	−1.00488	+	8.77863i	−0.139352	+	1.21738i
$53$			12.7903i			1.75688i	0.477854	+	0.878439i	$0.341415\pi$
$53$			12.7903i			1.75688i	−0.477854	+	0.878439i	$0.658585\pi$
$54$	−0.126578	−	7.34738i	−0.0172251	−	0.999852i
$55$		−	6.34133i		−	0.855064i
$56$		0			0
$57$	2.57889	+	0.623072i	0.341582	+	0.0825279i
$58$	5.21417	+	5.84508i	0.684655	+	0.767497i
$59$	−7.96701			−1.03722			−0.518608	−	0.855012i	$-0.673550\pi$
$59$	−7.96701			−1.03722			−0.518608	+	0.855012i	$0.673550\pi$
$60$	1.49335	−	4.07795i	0.192791	−	0.526461i
$61$	0.302889			0.0387810			0.0193905	−	0.999812i	$-0.493827\pi$
$61$	0.302889			0.0387810			0.0193905	+	0.999812i	$0.493827\pi$
$62$	−4.61200	−	5.17005i	−0.585725	−	0.656597i
$63$		0			0
$64$	−2.68236	+	7.53691i	−0.335295	+	0.942113i
$65$		−	5.53862i		−	0.686981i
$66$	−5.84589	−	10.9244i	−0.719580	−	1.34470i
$67$		−	10.5438i		−	1.28813i	−0.764969	−	0.644067i	$-0.777246\pi$
$67$		−	10.5438i		−	1.28813i	0.764969	−	0.644067i	$-0.222754\pi$
$68$	11.6309	+	1.33137i	1.41045	+	0.161452i
$69$	−0.127550	+	0.527930i	−0.0153553	+	0.0635553i
$70$		0			0
$71$	−4.53490			−0.538194			−0.269097	−	0.963113i	$-0.586725\pi$
$71$	−4.53490			−0.538194			−0.269097	+	0.963113i	$0.586725\pi$
$72$	−1.18671	−	8.40189i	−0.139855	−	0.990172i
$73$	−1.41421			−0.165521			−0.0827606	−	0.996569i	$-0.526374\pi$
$73$	−1.41421			−0.165521			−0.0827606	+	0.996569i	$0.526374\pi$
$74$	5.63353	−	5.02546i	0.654885	−	0.584197i
$75$	1.39454	−	5.77200i	0.161028	−	0.666493i
$76$	3.04365	+	0.348402i	0.349130	+	0.0399645i
$77$		0			0
$78$	−5.10590	−	9.54154i	−0.578130	−	1.08037i
$79$		−	6.92820i		−	0.779484i	−0.920924	−	0.389742i	$-0.872564\pi$
$79$		−	6.92820i		−	0.779484i	0.920924	−	0.389742i	$-0.127436\pi$
$80$	1.13319	−	4.88490i	0.126694	−	0.546149i
$81$	5.24797	+	7.31156i	0.583107	+	0.812395i
$82$	−1.86343	−	2.08890i	−0.205781	−	0.230681i
$83$	6.78340			0.744575			0.372287	−	0.928118i	$-0.378574\pi$
$83$	6.78340			0.744575			0.372287	+	0.928118i	$0.378574\pi$
$84$		0			0
$85$	−7.33816			−0.795935
$86$	2.99949	+	3.36243i	0.323444	+	0.362580i
$87$	−9.32487	−	2.25294i	−0.999731	−	0.241540i
$88$	−8.24797	−	11.6902i	−0.879236	−	1.24618i
$89$		−	4.79755i		−	0.508540i	−0.967133	−	0.254270i	$-0.918165\pi$
$89$		−	4.79755i		−	0.508540i	0.967133	−	0.254270i	$-0.0818351\pi$
$90$	1.33798	+	5.14777i	0.141035	+	0.542622i
$91$		0			0
$92$	−0.0713222	+	0.623072i	−0.00743586	+	0.0649597i
$93$	8.24797	+	1.99275i	0.855274	+	0.206639i
$94$	12.1324	−	10.8228i	1.25136	−	1.11629i
$95$	−1.92030			−0.197019
$96$	−2.55109	−	9.46002i	−0.260369	−	0.965509i
$97$	13.6844			1.38944			0.694719	−	0.719281i	$-0.255529\pi$
$97$	13.6844			1.38944			0.694719	+	0.719281i	$0.255529\pi$
$98$		0			0
$99$	13.5009	+	6.92820i	1.35689	+	0.696311i
$100$	0.779785	−	6.81221i	0.0779785	−	0.681221i
$101$			4.07183i			0.405162i	0.979266	+	0.202581i	$0.0649329\pi$
$101$			4.07183i			0.405162i	−0.979266	+	0.202581i	$0.935067\pi$
$102$	−12.6417	+	6.76485i	−1.25171	+	0.669820i
$103$			13.0758i			1.28839i	0.764860	+	0.644197i	$0.222808\pi$
$103$			13.0758i			1.28839i	−0.764860	+	0.644197i	$0.777192\pi$
$104$	−7.20391	−	10.2104i	−0.706402	−	1.00121i
$105$		0			0
$106$	−12.0410	−	13.4980i	−1.16953	−	1.31104i
$107$	−3.90776			−0.377777			−0.188889	−	0.981999i	$-0.560489\pi$
$107$	−3.90776			−0.377777			−0.188889	+	0.981999i	$0.560489\pi$
$108$	7.05056	+	7.63476i	0.678441	+	0.734655i
$109$	−8.24797			−0.790012			−0.395006	−	0.918679i	$-0.629257\pi$
$109$	−8.24797			−0.790012			−0.395006	+	0.918679i	$0.629257\pi$
$110$	5.96986	+	6.69221i	0.569204	+	0.638077i
$111$	−2.17139	+	8.98737i	−0.206100	+	0.853044i
$112$		0			0
$113$		−	6.72485i		−	0.632621i	−0.948656	−	0.316311i	$-0.897556\pi$
$113$		−	6.72485i		−	0.632621i	0.948656	−	0.316311i	$-0.102444\pi$
$114$	−3.30816	+	1.77027i	−0.309837	+	0.165801i
$115$		−	0.393109i		−	0.0366576i
$116$	−11.0054	−	1.25977i	−1.02182	−	0.116967i
$117$	11.7919	+	6.05121i	1.09016	+	0.559434i
$118$	8.40785	−	7.50032i	0.774005	−	0.690460i
$119$		0			0
$120$	2.26309	+	5.70947i	0.206591	+	0.521201i
$121$	14.5861			1.32601
$122$	−0.319649	+	0.285146i	−0.0289396	+	0.0258159i
$123$	3.33250	+	0.805149i	0.300482	+	0.0725978i
$124$	9.73439	+	1.11428i	0.874174	+	0.100066i
$125$			10.5662i			0.945073i
$126$		0			0
$127$		−	8.50404i		−	0.754611i	−0.926089	−	0.377306i	$-0.876851\pi$
$127$		−	8.50404i		−	0.754611i	0.926089	−	0.377306i	$-0.123149\pi$
$128$	−4.26463	−	10.4792i	−0.376943	−	0.926236i
$129$	−5.36420	−	1.29602i	−0.472291	−	0.114108i
$130$	5.21417	+	5.84508i	0.457313	+	0.512648i
$131$	−8.41047			−0.734826			−0.367413	−	0.930058i	$-0.619756\pi$
$131$	−8.41047			−0.734826			−0.367413	+	0.930058i	$0.619756\pi$
$132$	16.4538	+	6.02541i	1.43212	+	0.524445i
$133$		0			0
$134$	9.92618	+	11.1272i	0.857491	+	0.961247i
$135$	−4.93507	−	4.25202i	−0.424743	−	0.365955i
$136$	−13.5278	+	9.54451i	−1.16000	+	0.818435i
$137$		−	13.7567i		−	1.17531i	−0.809111	−	0.587657i	$-0.800051\pi$
$137$		−	13.7567i		−	1.17531i	0.809111	−	0.587657i	$-0.199949\pi$
$138$	−0.362396	−	0.677220i	−0.0308492	−	0.0576488i
$139$		−	13.1652i		−	1.11666i	−0.829620	−	0.558328i	$-0.811443\pi$
$139$		−	13.1652i		−	1.11666i	0.829620	−	0.558328i	$-0.188557\pi$
$140$		0			0
$141$	−4.67632	+	19.3552i	−0.393817	+	1.63000i
$142$	4.78583	−	4.26925i	0.401618	−	0.358268i
$143$	22.3473			1.86878
$144$	9.16209	+	7.74959i	0.763508	+	0.645799i
$145$	6.94352			0.576628
$146$	1.49247	−	1.33137i	0.123517	−	0.110185i
$147$		0			0
$148$	−1.21417	+	10.6071i	−0.0998046	+	0.871894i
$149$		−	11.2971i		−	0.925491i	−0.886491	−	0.462745i	$-0.846864\pi$
$149$		−	11.2971i		−	0.925491i	0.886491	−	0.462745i	$-0.153136\pi$
$150$	3.96218	+	7.40423i	0.323510	+	0.604553i
$151$			11.0998i			0.903286i	0.892199	+	0.451643i	$0.149162\pi$
$151$			11.0998i			0.903286i	−0.892199	+	0.451643i	$0.850838\pi$
$152$	−3.54005	+	2.49767i	−0.287136	+	0.202588i
$153$	8.01729	−	15.6232i	0.648159	−	1.26306i
$154$		0			0
$155$	−6.14163			−0.493307
$156$	14.3710	+	5.26269i	1.15060	+	0.421353i
$157$	14.7957			1.18083			0.590413	−	0.807101i	$-0.298965\pi$
$157$	14.7957			1.18083			0.590413	+	0.807101i	$0.298965\pi$
$158$	6.52236	+	7.31156i	0.518891	+	0.581676i
$159$	21.5338	+	5.20268i	1.70774	+	0.412599i
$160$	3.40287	+	6.22200i	0.269020	+	0.491892i
$161$		0			0
$162$	−12.4216	−	2.77557i	−0.975933	−	0.218070i
$163$			13.2660i			1.03907i	0.854448	+	0.519537i	$0.173895\pi$
$163$			13.2660i			1.03907i	−0.854448	+	0.519537i	$0.826105\pi$
$164$	3.93307	+	0.450214i	0.307122	+	0.0351558i
$165$	−10.6763	−	2.57945i	−0.831150	−	0.200810i
$166$	−7.15874	+	6.38603i	−0.555626	+	0.495652i
$167$	4.78624			0.370371			0.185185	−	0.982704i	$-0.440711\pi$
$167$	4.78624			0.370371			0.185185	+	0.982704i	$0.440711\pi$
$168$		0			0
$169$	6.51854			0.501426
$170$	7.74419	−	6.90830i	0.593953	−	0.529842i
$171$	2.09802	−	4.08839i	0.160440	−	0.312647i
$172$	−6.33092	−	0.724692i	−0.482728	−	0.0552573i
$173$		−	14.4119i		−	1.09572i	−0.836570	−	0.547859i	$-0.815443\pi$
$173$		−	14.4119i		−	1.09572i	0.836570	−	0.547859i	$-0.184557\pi$
$174$	11.9618	−	6.40104i	0.906822	−	0.485261i
$175$		0			0
$176$	19.7097	+	4.57220i	1.48568	+	0.344643i
$177$	−3.24073	+	13.4133i	−0.243588	+	1.00821i
$178$	4.51652	+	5.06301i	0.338527	+	0.379489i
$179$	−0.694300			−0.0518944			−0.0259472	−	0.999663i	$-0.508260\pi$
$179$	−0.694300			−0.0518944			−0.0259472	+	0.999663i	$0.508260\pi$
$180$	−6.25823	−	4.17300i	−0.466461	−	0.311037i
$181$	−6.31042			−0.469050			−0.234525	−	0.972110i	$-0.575353\pi$
$181$	−6.31042			−0.469050			−0.234525	+	0.972110i	$0.575353\pi$
$182$		0			0
$183$	0.123206	−	0.509947i	0.00910763	−	0.0376964i
$184$	−0.511305	−	0.724692i	−0.0376939	−	0.0534250i
$185$		−	6.69221i		−	0.492021i
$186$	−10.5804	+	5.66180i	−0.775790	+	0.415143i
$187$		−	29.6082i		−	2.16516i
$188$	−2.61485	+	22.8434i	−0.190707	+	1.66602i
$189$		0			0
$190$	2.02655	−	1.80781i	0.147022	−	0.131152i
$191$	−3.90776			−0.282755			−0.141378	−	0.989956i	$-0.545153\pi$
$191$	−3.90776			−0.282755			−0.141378	+	0.989956i	$0.545153\pi$
$192$	11.5981	+	7.58181i	0.837021	+	0.547170i
$193$	1.57165			0.113130			0.0565649	−	0.998399i	$-0.481985\pi$
$193$	1.57165			0.113130			0.0565649	+	0.998399i	$0.481985\pi$
$194$	−14.4416	+	12.8828i	−1.03684	+	0.924929i
$195$	−9.32487	−	2.25294i	−0.667768	−	0.161336i
$196$		0			0
$197$		−	1.83285i		−	0.130585i	−0.997866	−	0.0652924i	$-0.979202\pi$
$197$		−	1.83285i		−	0.130585i	0.997866	−	0.0652924i	$-0.0207980\pi$
$198$	−20.7703	+	5.39851i	−1.47608	+	0.383655i
$199$			3.67091i			0.260224i	0.991499	+	0.130112i	$0.0415337\pi$
$199$			3.67091i			0.260224i	−0.991499	+	0.130112i	$0.958466\pi$
$200$	5.59023	+	7.92326i	0.395289	+	0.560259i
$201$	−17.7517	−	4.28889i	−1.25211	−	0.302515i
$202$	−3.83331	−	4.29713i	−0.269710	−	0.302345i
$203$		0			0
$204$	6.97258	−	19.0403i	0.488178	−	1.33309i
$205$	−2.48146			−0.173313
$206$	−12.3098	−	13.7993i	−0.857665	−	0.961441i
$207$	0.836944	+	0.429490i	0.0581716	+	0.0298516i
$208$	17.2148	+	3.99344i	1.19363	+	0.276895i
$209$		−	7.74807i		−	0.535945i
$210$		0			0
$211$			14.8763i			1.02413i	0.858948	+	0.512063i	$0.171119\pi$
$211$			14.8763i			1.02413i	−0.858948	+	0.512063i	$0.828881\pi$
$212$	25.4146	+	2.90917i	1.74548	+	0.199803i
$213$	−1.84465	+	7.63500i	−0.126394	+	0.523141i
$214$	4.12398	−	3.67885i	0.281910	−	0.251481i
$215$	3.99431			0.272410
$216$	−14.6282	−	1.41966i	−0.995324	−	0.0965958i
$217$		0			0
$218$	8.70434	−	7.76481i	0.589533	−	0.525899i
$219$	−0.575257	+	2.38098i	−0.0388723	+	0.160892i
$220$	−12.6004	−	1.44235i	−0.849517	−	0.0972431i
$221$		−	25.8603i		−	1.73955i
$222$	−6.16936	−	11.5289i	−0.414060	−	0.773766i
$223$			19.4171i			1.30026i	0.759821	+	0.650132i	$0.225287\pi$
$223$			19.4171i			1.30026i	−0.759821	+	0.650132i	$0.774713\pi$
$224$		0			0
$225$	−9.15054	−	4.69573i	−0.610036	−	0.313049i
$226$	6.33092	+	7.09696i	0.421127	+	0.472082i
$227$	10.6827			0.709038			0.354519	−	0.935049i	$-0.384645\pi$
$227$	10.6827			0.709038			0.354519	+	0.935049i	$0.384645\pi$
$228$	1.82463	−	4.98259i	0.120839	−	0.329980i
$229$	−7.50151			−0.495714			−0.247857	−	0.968797i	$-0.579726\pi$
$229$	−7.50151			−0.495714			−0.247857	+	0.968797i	$0.579726\pi$
$230$	0.370081	+	0.414861i	0.0244024	+	0.0273551i
$231$		0			0
$232$	12.8003	−	9.03122i	0.840381	−	0.592928i
$233$			2.79927i			0.183386i	0.995787	+	0.0916930i	$0.0292278\pi$
$233$			2.79927i			0.183386i	−0.995787	+	0.0916930i	$0.970772\pi$
$234$	−18.1411	+	4.71515i	−1.18592	+	0.308239i
$235$		−	14.4123i		−	0.940158i
$236$	−1.81211	+	15.8307i	−0.117959	+	1.03049i
$237$	−11.6644	−	2.81817i	−0.757683	−	0.183060i
$238$		0			0
$239$	−20.5467			−1.32905			−0.664527	−	0.747265i	$-0.731367\pi$
$239$	−20.5467			−1.32905			−0.664527	+	0.747265i	$0.731367\pi$
$240$	−7.76333	−	3.89487i	−0.501121	−	0.251412i
$241$	−18.0546			−1.16300			−0.581499	−	0.813547i	$-0.697533\pi$
$241$	−18.0546			−1.16300			−0.581499	+	0.813547i	$0.697533\pi$
$242$	−15.3932	+	13.7317i	−0.989513	+	0.882706i
$243$	14.4445	−	5.86141i	0.926616	−	0.376010i
$244$	0.0688928	−	0.601848i	0.00441041	−	0.0385294i
$245$		0			0
$246$	−4.27488	+	2.28759i	−0.272556	+	0.145851i
$247$		−	6.76729i		−	0.430592i
$248$	−11.3220	+	7.98822i	−0.718949	+	0.507253i
$249$	2.75927	−	11.4206i	0.174862	−	0.723750i
$250$	−9.94728	−	11.1509i	−0.629121	−	0.705244i
$251$	−10.4810			−0.661555			−0.330777	−	0.943709i	$-0.607311\pi$
$251$	−10.4810			−0.661555			−0.330777	+	0.943709i	$0.607311\pi$
$252$		0			0
$253$	1.58612			0.0997188
$254$	8.00588	+	8.97458i	0.502334	+	0.563115i
$255$	−2.98493	+	12.3546i	−0.186924	+	0.773674i
$256$	14.3659	+	7.04419i	0.897869	+	0.440262i
$257$		−	8.36072i		−	0.521528i	−0.965403	−	0.260764i	$-0.916026\pi$
$257$		−	8.36072i		−	0.521528i	0.965403	−	0.260764i	$-0.0839744\pi$
$258$	6.88111	−	3.68224i	0.428399	−	0.229246i
$259$		0			0
$260$	−11.0054	−	1.25977i	−0.682524	−	0.0781277i
$261$	−7.58612	+	14.7830i	−0.469569	+	0.915046i
$262$	8.87584	−	7.91780i	0.548351	−	0.489163i
$263$	29.3700			1.81103			0.905517	−	0.424309i	$-0.139483\pi$
$263$	29.3700			1.81103			0.905517	+	0.424309i	$0.139483\pi$
$264$	−23.0367	+	9.13116i	−1.41781	+	0.561984i
$265$	−16.0346			−0.984996
$266$		0			0
$267$	−8.07720	−	1.95149i	−0.494317	−	0.119429i
$268$	−20.9508	−	2.39821i	−1.27978	−	0.146494i
$269$		−	20.3977i		−	1.24367i	−0.783149	−	0.621834i	$-0.786388\pi$
$269$		−	20.3977i		−	1.24367i	0.783149	−	0.621834i	$-0.213612\pi$
$270$	9.21108	−	0.158685i	0.560568	−	0.00965726i
$271$			20.5964i			1.25114i	0.780167	+	0.625572i	$0.215134\pi$
$271$			20.5964i			1.25114i	−0.780167	+	0.625572i	$0.784866\pi$
$272$	5.29093	−	22.8080i	0.320810	−	1.38294i
$273$		0			0
$274$	12.9508	+	14.5179i	0.782389	+	0.877057i
$275$	−17.3415			−1.04573
$276$	1.02000	+	0.373525i	0.0613967	+	0.0224835i
$277$	−3.94689			−0.237146			−0.118573	−	0.992945i	$-0.537832\pi$
$277$	−3.94689			−0.237146			−0.118573	+	0.992945i	$0.537832\pi$
$278$	12.3940	+	13.8936i	0.743341	+	0.833285i
$279$	6.71002	−	13.0758i	0.401719	−	0.782825i
$280$		0			0
$281$		−	1.18623i		−	0.0707648i	−0.999374	−	0.0353824i	$-0.988735\pi$
$281$		−	1.18623i		−	0.0707648i	0.999374	−	0.0353824i	$-0.0112649\pi$
$282$	−13.2863	−	24.8286i	−0.791190	−	1.47852i
$283$		−	27.6833i		−	1.64560i	−0.568331	−	0.822800i	$-0.692410\pi$
$283$		−	27.6833i		−	1.64560i	0.568331	−	0.822800i	$-0.307590\pi$
$284$	−1.03147	+	9.01095i	−0.0612066	+	0.534702i
$285$	−0.781117	+	3.23303i	−0.0462694	+	0.191508i
$286$	−23.5839	+	21.0383i	−1.39454	+	1.24402i
$287$		0			0
$288$	−16.9647	+	0.446999i	−0.999653	+	0.0263396i
$289$	−17.2624			−1.01544
$290$	−7.32772	+	6.53677i	−0.430298	+	0.383853i
$291$	5.56637	−	23.0391i	0.326306	−	1.35058i
$292$	−0.321666	+	2.81008i	−0.0188241	+	0.164447i
$293$			0.197795i			0.0115553i	0.999983	+	0.00577765i	$0.00183909\pi$
$293$			0.197795i			0.0115553i	−0.999983	+	0.00577765i	$0.998161\pi$
$294$		0			0
$295$		−	9.98789i		−	0.581517i
$296$	−8.70434	−	12.3370i	−0.505930	−	0.717074i
$297$	17.1561	−	19.9121i	0.995500	−	1.15542i
$298$	10.6353	+	11.9221i	0.616086	+	0.690631i
$299$	1.38535			0.0801167
$300$	−11.1519	−	4.08385i	−0.643856	−	0.235781i
$301$		0			0
$302$	−10.4496	−	11.7139i	−0.601304	−	0.674061i
$303$	6.85537	+	1.65629i	0.393831	+	0.0951514i
$304$	1.38457	−	5.96856i	0.0794104	−	0.342320i
$305$			0.379718i			0.0217426i
$306$	6.24713	+	24.0353i	0.357125	+	1.37401i
$307$			16.6218i			0.948657i	0.880348	+	0.474328i	$0.157309\pi$
$307$			16.6218i			0.948657i	−0.880348	+	0.474328i	$0.842691\pi$
$308$		0			0
$309$	22.0145	+	5.31881i	1.25236	+	0.302576i
$310$	6.48146	−	5.78186i	0.368122	−	0.328388i
$311$	−10.7561			−0.609923			−0.304961	−	0.952365i	$-0.598644\pi$
$311$	−10.7561			−0.609923			−0.304961	+	0.952365i	$0.598644\pi$
$312$	−20.1206	+	7.97531i	−1.13911	+	0.451513i
$313$	−4.94400			−0.279451			−0.139726	−	0.990190i	$-0.544622\pi$
$313$	−4.94400			−0.279451			−0.139726	+	0.990190i	$0.544622\pi$
$314$	−15.6144	+	13.9290i	−0.881170	+	0.786058i
$315$		0			0
$316$	−13.7665	−	1.57583i	−0.774427	−	0.0886476i
$317$			21.9347i			1.23197i	0.787756	+	0.615987i	$0.211243\pi$
$317$			21.9347i			1.23197i	−0.787756	+	0.615987i	$0.788757\pi$
$318$	−27.6232	+	14.7818i	−1.54903	+	0.828924i
$319$			28.0159i			1.56859i
$320$	−9.44868	−	3.36275i	−0.528197	−	0.187983i
$321$	−1.58955	+	6.57914i	−0.0887202	+	0.367212i
$322$		0			0
$323$	−8.96603			−0.498883
$324$	15.7219	−	8.76481i	0.873439	−	0.486934i
$325$	−15.1464			−0.840170
$326$	−12.4889	−	14.0000i	−0.691696	−	0.775390i
$327$	−3.35501	+	13.8864i	−0.185533	+	0.767917i
$328$	−4.57454	+	3.22756i	−0.252587	+	0.178212i
$329$		0			0
$330$	13.6954	−	7.32873i	0.753908	−	0.403433i
$331$		−	3.74207i		−	0.205683i	−0.994698	−	0.102841i	$-0.967207\pi$
$331$		−	3.74207i		−	0.205683i	0.994698	−	0.102841i	$-0.0327934\pi$
$332$	1.54290	−	13.4788i	0.0846775	−	0.739744i
$333$	14.2480	+	7.31156i	0.780784	+	0.400671i
$334$	−5.05108	+	4.50587i	−0.276383	+	0.246550i
$335$	13.2183			0.722194
$336$		0			0
$337$	22.9774			1.25166			0.625829	−	0.779960i	$-0.284761\pi$
$337$	22.9774			1.25166			0.625829	+	0.779960i	$0.284761\pi$
$338$	−6.87923	+	6.13669i	−0.374181	+	0.333792i
$339$	−11.3220	−	2.73546i	−0.614928	−	0.148570i
$340$	−1.66908	+	14.5811i	−0.0905185	+	0.790771i
$341$		−	24.7804i		−	1.34193i
$342$	1.63479	+	6.28973i	0.0883994	+	0.340110i
$343$		0			0
$344$	7.36347	−	5.19527i	0.397011	−	0.280110i
$345$	−0.661842	−	0.159904i	−0.0356324	−	0.00860896i
$346$	13.5677	+	15.2094i	0.729404	+	0.817661i
$347$	2.13010			0.114350			0.0571750	−	0.998364i	$-0.481791\pi$
$347$	2.13010			0.114350			0.0571750	+	0.998364i	$0.481791\pi$
$348$	−6.59760	+	18.0163i	−0.353668	+	0.965776i
$349$	3.55710			0.190407			0.0952036	−	0.995458i	$-0.469650\pi$
$349$	3.55710			0.190407			0.0952036	+	0.995458i	$0.469650\pi$
$350$		0			0
$351$	14.9845	−	17.3916i	0.799811	−	0.928293i
$352$	−25.1047	+	13.7300i	−1.33808	+	0.731809i
$353$			18.9270i			1.00738i	0.863884	+	0.503690i	$0.168025\pi$
$353$			18.9270i			1.00738i	−0.863884	+	0.503690i	$0.831975\pi$
$354$	−9.20756	−	17.2064i	−0.489376	−	0.914511i
$355$		−	5.68520i		−	0.301739i
$356$	−9.53285	−	1.09121i	−0.505240	−	0.0578342i
$357$		0			0
$358$	0.732717	−	0.653628i	0.0387253	−	0.0345453i
$359$	1.22600			0.0647058			0.0323529	−	0.999477i	$-0.489700\pi$
$359$	1.22600			0.0647058			0.0323529	+	0.999477i	$0.489700\pi$
$360$	10.5331	−	1.48773i	0.555141	−	0.0784101i
$361$	16.6537			0.876511
$362$	6.65959	−	5.94076i	0.350020	−	0.312240i
$363$	5.93317	−	24.5573i	0.311411	−	1.28893i
$364$		0			0
$365$		−	1.77294i		−	0.0927997i
$366$	0.350052	+	0.654152i	0.0182975	+	0.0341931i
$367$			20.2033i			1.05460i	0.849678	+	0.527302i	$0.176796\pi$
$367$			20.2033i			1.05460i	−0.849678	+	0.527302i	$0.823204\pi$
$368$	1.22184	+	0.283438i	0.0636926	+	0.0147752i
$369$	2.71111	−	5.28312i	0.141135	−	0.275028i
$370$	6.30019	+	7.06250i	0.327531	+	0.367162i
$371$		0			0
$372$	5.83566	−	15.9357i	0.302565	−	0.826225i
$373$	−8.18038			−0.423564			−0.211782	−	0.977317i	$-0.567927\pi$
$373$	−8.18038			−0.423564			−0.211782	+	0.977317i	$0.567927\pi$
$374$	27.8738	+	31.2464i	1.44132	+	1.61572i
$375$	17.7894	+	4.29801i	0.918642	+	0.221948i
$376$	−18.7457	−	26.5690i	−0.966735	−	1.37019i
$377$			24.4695i			1.26024i
$378$		0			0
$379$			31.2020i			1.60274i	0.598170	+	0.801369i	$0.295895\pi$
$379$			31.2020i			1.60274i	−0.598170	+	0.801369i	$0.704105\pi$
$380$	−0.436776	+	3.81568i	−0.0224061	+	0.195740i
$381$	−14.3175	−	3.45917i	−0.733506	−	0.177219i
$382$	4.12398	−	3.67885i	0.211001	−	0.188226i
$383$	24.4179			1.24770			0.623848	−	0.781546i	$-0.285569\pi$
$383$	24.4179			1.24770			0.623848	+	0.781546i	$0.285569\pi$
$384$	−19.3775	+	2.91737i	−0.988856	+	0.148877i
$385$		0			0
$386$	−1.65861	+	1.47958i	−0.0844212	+	0.0753089i
$387$	−4.36397	+	8.50404i	−0.221833	+	0.432285i
$388$	3.11254	−	27.1912i	0.158015	−	1.38042i
$389$			9.08449i			0.460602i	0.973119	+	0.230301i	$0.0739711\pi$
$389$			9.08449i			0.460602i	−0.973119	+	0.230301i	$0.926029\pi$
$390$	11.9618	−	6.40104i	0.605709	−	0.324129i
$391$		−	1.83546i		−	0.0928230i
$392$		0			0
$393$	−3.42111	+	14.1599i	−0.172572	+	0.714275i
$394$	1.72548	+	1.93426i	0.0869284	+	0.0974466i
$395$	8.68557			0.437019
$396$	16.8373	−	25.2508i	0.846107	−	1.26890i
$397$	−23.2810			−1.16844			−0.584220	−	0.811596i	$-0.698599\pi$
$397$	−23.2810			−1.16844			−0.584220	+	0.811596i	$0.698599\pi$
$398$	−3.45588	−	3.87403i	−0.173227	−	0.194188i
$399$		0			0
$400$	−13.3587	−	3.09890i	−0.667934	−	0.154945i
$401$		−	7.59128i		−	0.379090i	−0.981872	−	0.189545i	$-0.939299\pi$
$401$		−	7.59128i		−	0.379090i	0.981872	−	0.189545i	$-0.0607014\pi$
$402$	22.7716	−	12.1856i	1.13574	−	0.607763i
$403$		−	21.6436i		−	1.07814i
$404$	8.09082	+	0.926146i	0.402533	+	0.0460775i
$405$	−9.16617	+	6.57914i	−0.455470	+	0.326920i
$406$		0			0
$407$	27.0019			1.33843
$408$	10.5665	+	26.6580i	0.523122	+	1.31977i
$409$	6.39018			0.315974			0.157987	−	0.987441i	$-0.449500\pi$
$409$	6.39018			0.315974			0.157987	+	0.987441i	$0.449500\pi$
$410$	2.61876	−	2.33610i	0.129331	−	0.115372i
$411$	−23.1609	−	5.59578i	−1.14244	−	0.276020i
$412$	25.9819	+	2.97411i	1.28003	+	0.146524i
$413$		0			0
$414$	−1.28759	+	0.334662i	−0.0632814	+	0.0164477i
$415$			8.50404i			0.417447i
$416$	−21.9268	+	11.9920i	−1.07505	+	0.587955i
$417$	−22.1650	−	5.35518i	−1.08543	−	0.262244i
$418$	7.29419	+	8.17678i	0.356771	+	0.399940i
$419$	29.1307			1.42313			0.711565	−	0.702620i	$-0.247987\pi$
$419$	29.1307			1.42313			0.711565	+	0.702620i	$0.247987\pi$
$420$		0			0
$421$	−32.0821			−1.56358			−0.781792	−	0.623539i	$-0.785694\pi$
$421$	−32.0821			−1.56358			−0.781792	+	0.623539i	$0.785694\pi$
$422$	−14.0049	−	15.6994i	−0.681746	−	0.764237i
$423$	30.6844	+	15.7462i	1.49193	+	0.765605i
$424$	−29.5596	+	20.8557i	−1.43554	+	1.01284i
$425$			20.0675i			0.973419i
$426$	−5.24103	−	9.79405i	−0.253929	−	0.474523i
$427$		0			0
$428$	−0.888828	+	7.76481i	−0.0429631	+	0.375326i
$429$	9.09019	−	37.6242i	0.438879	−	1.81651i
$430$	−4.21532	+	3.76033i	−0.203281	+	0.181339i
$431$	−18.2456			−0.878861			−0.439431	−	0.898277i	$-0.644820\pi$
$431$	−18.2456			−0.878861			−0.439431	+	0.898277i	$0.644820\pi$
$432$	16.7741	−	12.2731i	0.807045	−	0.590489i
$433$	−4.84842			−0.233000			−0.116500	−	0.993191i	$-0.537168\pi$
$433$	−4.84842			−0.233000			−0.116500	+	0.993191i	$0.537168\pi$
$434$		0			0
$435$	2.82440	−	11.6902i	0.135420	−	0.560501i
$436$	−1.87602	+	16.3889i	−0.0898449	+	0.784886i
$437$		−	0.480315i		−	0.0229766i
$438$	−1.63442	−	3.05429i	−0.0780956	−	0.145939i
$439$		−	20.2520i		−	0.966578i	−0.875461	−	0.483289i	$-0.839442\pi$
$439$		−	20.2520i		−	0.966578i	0.875461	−	0.483289i	$-0.160558\pi$
$440$	14.6554	−	10.3401i	0.698670	−	0.492945i
$441$		0			0
$442$	24.3454	+	27.2912i	1.15799	+	1.29811i
$443$	22.4670			1.06744			0.533719	−	0.845662i	$-0.320794\pi$
$443$	22.4670			1.06744			0.533719	+	0.845662i	$0.320794\pi$
$444$	17.3642	+	6.35881i	0.824070	+	0.301776i
$445$	6.01447			0.285113
$446$	−18.2797	−	20.4915i	−0.865567	−	0.970300i
$447$	−19.0198	−	4.59528i	−0.899607	−	0.217349i
$448$		0			0
$449$			29.5660i			1.39531i	0.716435	+	0.697654i	$0.245773\pi$
$449$			29.5660i			1.39531i	−0.716435	+	0.697654i	$0.754227\pi$
$450$	14.0775	−	3.65895i	0.663621	−	0.172485i
$451$		−	10.0122i		−	0.471458i
$452$	−13.3624	−	1.52958i	−0.628517	−	0.0719455i
$453$	18.6877	+	4.51503i	0.878023	+	0.212135i
$454$	−11.2738	+	10.0569i	−0.529107	+	0.471996i
$455$		0			0
$456$	2.76513	+	6.97604i	0.129489	+	0.326683i
$457$	18.1949			0.851120			0.425560	−	0.904930i	$-0.360077\pi$
$457$	18.1949			0.851120			0.425560	+	0.904930i	$0.360077\pi$
$458$	7.91658	−	7.06208i	0.369918	−	0.329989i
$459$	−23.0422	−	19.8530i	−1.07552	−	0.926659i
$460$	−0.781117	−	0.0894134i	−0.0364198	−	0.00416892i
$461$		−	24.9782i		−	1.16335i	−0.813422	−	0.581675i	$-0.802398\pi$
$461$		−	24.9782i		−	1.16335i	0.813422	−	0.581675i	$-0.197602\pi$
$462$		0			0
$463$			6.37226i			0.296144i	0.988977	+	0.148072i	$0.0473068\pi$
$463$			6.37226i			0.296144i	−0.988977	+	0.148072i	$0.952693\pi$
$464$	−5.00639	+	21.5814i	−0.232416	+	1.00189i
$465$	−2.49822	+	10.3401i	−0.115852	+	0.479511i
$466$	−2.63529	−	2.95415i	−0.122077	−	0.136849i
$467$	−27.3569			−1.26593			−0.632964	−	0.774182i	$-0.718162\pi$
$467$	−27.3569			−1.26593			−0.632964	+	0.774182i	$0.718162\pi$
$468$	14.7060	−	22.0545i	0.679785	−	1.01947i
$469$		0			0
$470$	13.5681	+	15.2098i	0.625849	+	0.701576i
$471$	6.01842	−	24.9102i	0.277314	−	1.14780i
$472$	−12.9909	−	18.4126i	−0.597956	−	0.847507i
$473$			16.1163i			0.741029i
$474$	14.9629	−	8.00699i	0.687268	−	0.367773i
$475$			5.25141i			0.240951i
$476$		0			0
$477$	17.5185	−	34.1382i	0.802119	−	1.56308i
$478$	21.6836	−	19.3431i	0.991783	−	0.884731i
$479$	−19.8334			−0.906209			−0.453105	−	0.891457i	$-0.649684\pi$
$479$	−19.8334			−0.906209			−0.453105	+	0.891457i	$0.649684\pi$
$480$	11.8596	−	3.19818i	0.541314	−	0.145976i
$481$	23.5839			1.07533
$482$	19.0536	−	16.9970i	0.867866	−	0.774190i
$483$		0			0
$484$	3.31764	−	28.9830i	0.150802	−	1.31741i
$485$			17.1555i			0.778990i
$486$	−9.72569	+	19.7841i	−0.441166	+	0.897425i
$487$			40.8524i			1.85120i	0.378506	+	0.925599i	$0.376438\pi$
$487$			40.8524i			1.85120i	−0.378506	+	0.925599i	$0.623562\pi$
$488$	0.493888	+	0.700007i	0.0223573	+	0.0316878i
$489$	22.3348	+	5.39619i	1.01001	+	0.244024i
$490$		0			0
$491$	20.3003			0.916137			0.458069	−	0.888917i	$-0.348541\pi$
$491$	20.3003			0.916137			0.458069	+	0.888917i	$0.348541\pi$
$492$	2.35783	−	6.43863i	0.106299	−	0.290276i
$493$	32.4198			1.46012
$494$	6.37087	+	7.14174i	0.286639	+	0.321322i
$495$	−8.68557	+	16.9255i	−0.390388	+	0.760745i
$496$	4.42821	−	19.0890i	0.198833	−	0.857123i
$497$		0			0
$498$	7.83964	+	14.6502i	0.351303	+	0.656489i
$499$			34.2272i			1.53222i	0.642709	+	0.766110i	$0.277810\pi$
$499$			34.2272i			1.53222i	−0.642709	+	0.766110i	$0.722190\pi$
$500$	20.9954	+	2.40331i	0.938942	+	0.107479i
$501$	1.94689	−	8.05816i	0.0869807	−	0.360012i
$502$	11.0609	−	9.86704i	0.493674	−	0.440387i
$503$	−31.1279			−1.38792			−0.693962	−	0.720011i	$-0.744137\pi$
$503$	−31.1279			−1.38792			−0.693962	+	0.720011i	$0.744137\pi$
$504$		0			0
$505$	−5.10467			−0.227155
$506$	−1.67389	+	1.49321i	−0.0744134	+	0.0663813i
$507$	2.65154	−	10.9747i	0.117759	−	0.487402i
$508$	−16.8977	−	1.93426i	−0.749715	−	0.0858189i
$509$			39.5032i			1.75095i	0.483266	+	0.875474i	$0.339450\pi$
$509$			39.5032i			1.75095i	−0.483266	+	0.875474i	$0.660550\pi$
$510$	−8.48078	−	15.8483i	−0.375535	−	0.701773i
$511$		0			0
$512$	−21.7924	+	6.09041i	−0.963095	+	0.269161i
$513$	−6.02985	−	5.19527i	−0.266224	−	0.229377i
$514$	7.87096	+	8.82334i	0.347173	+	0.389181i
$515$	−16.3925			−0.722340
$516$	−3.79532	+	10.3640i	−0.167079	+	0.456250i
$517$	58.1512			2.55749
$518$		0			0
$519$	−24.2641	−	5.86232i	−1.06507	−	0.257327i
$520$	12.8003	−	9.03122i	0.561330	−	0.396045i
$521$			24.1110i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$521$			24.1110i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$522$	−5.91116	−	22.7427i	−0.258725	−	0.995422i
$523$		−	9.26670i		−	0.405204i	−0.979261	−	0.202602i	$-0.935060\pi$
$523$		−	9.26670i		−	0.405204i	0.979261	−	0.202602i	$-0.0649398\pi$
$524$	−1.91298	+	16.7118i	−0.0835689	+	0.730059i
$525$		0			0
$526$	−30.9952	+	27.6496i	−1.35145	+	1.20558i
$527$	−28.6757			−1.24914
$528$	15.7151	−	31.3236i	0.683911	−	1.36319i
$529$	−22.9017			−0.995725
$530$	16.9218	−	15.0953i	0.735036	−	0.655698i
$531$	21.2646	+	10.9122i	0.922805	+	0.473551i
$532$		0			0
$533$		−	8.74486i		−	0.378782i
$534$	10.3613	−	5.54458i	0.448378	−	0.239937i
$535$		−	4.89898i		−	0.211801i
$536$	24.3678	−	17.1926i	1.05253	−	0.742609i
$537$	−0.282419	+	1.16893i	−0.0121873	+	0.0504430i
$538$	19.2028	+	21.5263i	0.827892	+	0.928066i
$539$		0			0
$540$	−9.57136	+	8.83897i	−0.411886	+	0.380369i
$541$	25.9017			1.11360			0.556800	−	0.830647i	$-0.312029\pi$
$541$	25.9017			1.11360			0.556800	+	0.830647i	$0.312029\pi$
$542$	−19.3899	−	21.7361i	−0.832868	−	0.933644i
$543$	−2.56688	+	10.6243i	−0.110155	+	0.455932i
$544$	15.8882	+	29.0510i	0.681203	+	1.24555i
$545$		−	10.3401i		−	0.442921i
$546$		0			0
$547$		−	32.9387i		−	1.40836i	−0.710022	−	0.704179i	$-0.751315\pi$
$547$		−	32.9387i		−	1.40836i	0.710022	−	0.704179i	$-0.248685\pi$
$548$	−27.3349	−	3.12899i	−1.16769	−	0.133664i
$549$	−0.808435	−	0.414861i	−0.0345032	−	0.0177058i
$550$	18.3011	−	16.3257i	0.780360	−	0.696130i
$551$	8.48384			0.361424
$552$	−1.42808	+	0.566055i	−0.0607832	+	0.0240929i
$553$		0			0
$554$	4.16528	−	3.71569i	0.176966	−	0.157864i
$555$	−11.2671	−	2.72218i	−0.478260	−	0.115550i
$556$	−26.1595	−	2.99445i	−1.10941	−	0.126993i
$557$			29.9057i			1.26714i	0.773684	+	0.633572i	$0.218412\pi$
$557$			29.9057i			1.26714i	−0.773684	+	0.633572i	$0.781588\pi$
$558$	5.22850	+	20.1162i	0.221340	+	0.851588i
$559$			14.0763i			0.595363i
$560$		0			0
$561$	−49.8486	−	12.0437i	−2.10461	−	0.508484i
$562$	1.11675	+	1.25187i	0.0471071	+	0.0528070i
$563$	−31.1063			−1.31097			−0.655487	−	0.755206i	$-0.727537\pi$
$563$	−31.1063			−1.31097			−0.655487	+	0.755206i	$0.727537\pi$
$564$	37.3956	+	13.6943i	1.57464	+	0.576636i
$565$	8.43065			0.354680
$566$	26.0616	+	29.2151i	1.09545	+	1.22800i
$567$		0			0
$568$	−7.39456	−	10.4806i	−0.310269	−	0.439756i
$569$		−	17.6694i		−	0.740742i	−0.928884	−	0.370371i	$-0.879231\pi$
$569$		−	17.6694i		−	0.740742i	0.928884	−	0.370371i	$-0.120769\pi$
$570$	−2.21931	−	4.14729i	−0.0929566	−	0.173711i
$571$			7.51861i			0.314644i	0.987547	+	0.157322i	$0.0502860\pi$
$571$			7.51861i			0.314644i	−0.987547	+	0.157322i	$0.949714\pi$
$572$	5.08295	−	44.4047i	0.212529	−	1.85665i
$573$	−1.58955	+	6.57914i	−0.0664045	+	0.274847i
$574$		0			0
$575$	−1.07503			−0.0448318
$576$	17.4826	−	16.4426i	0.728440	−	0.685110i
$577$	4.26311			0.177476			0.0887378	−	0.996055i	$-0.471717\pi$
$577$	4.26311			0.177476			0.0887378	+	0.996055i	$0.471717\pi$
$578$	18.2176	−	16.2512i	0.757753	−	0.675962i
$579$	0.639297	−	2.64604i	0.0265683	−	0.109966i
$580$	1.57932	−	13.7969i	0.0655776	−	0.572887i
$581$		0			0
$582$	15.8152	+	29.5542i	0.655560	+	1.22506i
$583$		−	64.6967i		−	2.67946i
$584$	−2.30600	−	3.26839i	−0.0954230	−	0.135247i
$585$	−7.58612	+	14.7830i	−0.313648	+	0.611202i
$586$	−0.186208	−	0.208739i	−0.00769219	−	0.00862294i
$587$	−43.2909			−1.78681			−0.893404	−	0.449253i	$-0.851690\pi$
$587$	−43.2909			−1.78681			−0.893404	+	0.449253i	$0.851690\pi$
$588$		0			0
$589$	−7.50407			−0.309200
$590$	9.40281	+	10.5405i	0.387107	+	0.433947i
$591$	−3.08580	−	0.745543i	−0.126933	−	0.0306676i
$592$	20.8003	+	4.82519i	0.854887	+	0.198314i
$593$		−	5.76869i		−	0.236892i	−0.992961	−	0.118446i	$-0.962209\pi$
$593$		−	5.76869i		−	0.236892i	0.992961	−	0.118446i	$-0.0377912\pi$
$594$	0.640266	+	37.1650i	0.0262704	+	1.52490i
$595$		0			0
$596$	−22.4475	−	2.56954i	−0.919486	−	0.105252i
$597$	6.18038	+	1.49321i	0.252946	+	0.0611131i
$598$	−1.46200	+	1.30420i	−0.0597857	+	0.0533325i
$599$	−35.7970			−1.46262			−0.731312	−	0.682043i	$-0.761092\pi$
$599$	−35.7970			−1.46262			−0.731312	+	0.682043i	$0.761092\pi$
$600$	15.6136	−	6.18883i	0.637422	−	0.252658i
$601$	−42.3193			−1.72624			−0.863121	−	0.504998i	$-0.831493\pi$
$601$	−42.3193			−1.72624			−0.863121	+	0.504998i	$0.831493\pi$
$602$		0			0
$603$	−14.4416	+	28.1423i	−0.588109	+	1.14604i
$604$	22.0555	+	2.52466i	0.897426	+	0.102727i
$605$			18.2860i			0.743430i
$606$	−8.79396	+	4.70585i	−0.357230	+	0.191162i
$607$			47.3686i			1.92263i	0.275446	+	0.961316i	$0.411174\pi$
$607$			47.3686i			1.92263i	−0.275446	+	0.961316i	$0.588826\pi$
$608$	4.15775	+	7.60227i	0.168619	+	0.308313i
$609$		0			0
$610$	−0.357475	−	0.400729i	−0.0144737	−	0.0162250i
$611$	50.7903			2.05475
$612$	−29.2202	−	19.4841i	−1.18116	−	0.787597i
$613$	2.78912			0.112651			0.0563257	−	0.998412i	$-0.482061\pi$
$613$	2.78912			0.112651			0.0563257	+	0.998412i	$0.482061\pi$
$614$	−15.6481	−	17.5415i	−0.631507	−	0.707919i
$615$	−1.00938	+	4.17781i	−0.0407021	+	0.168465i
$616$		0			0
$617$		−	21.6549i		−	0.871795i	−0.899996	−	0.435898i	$-0.856431\pi$
$617$		−	21.6549i		−	0.871795i	0.899996	−	0.435898i	$-0.143569\pi$
$618$	−28.2398	+	15.1118i	−1.13597	+	0.607885i
$619$			5.64452i			0.226873i	0.993545	+	0.113436i	$0.0361858\pi$
$619$			5.64452i			0.226873i	−0.993545	+	0.113436i	$0.963814\pi$
$620$	−1.39693	+	12.2036i	−0.0561019	+	0.490107i
$621$	1.06354	−	1.23438i	0.0426782	−	0.0495341i
$622$	11.3513	−	10.1260i	0.455144	−	0.406017i
$623$		0			0
$624$	13.7258	−	27.3586i	0.549472	−	1.09522i
$625$	3.89533			0.155813
$626$	5.21756	−	4.65438i	0.208536	−	0.186027i
$627$	−13.0447	−	3.15167i	−0.520956	−	0.125865i
$628$	3.36531	−	29.3994i	0.134291	−	1.17316i
$629$		−	31.2464i		−	1.24588i
$630$		0			0
$631$			6.37226i			0.253676i	0.991923	+	0.126838i	$0.0404828\pi$
$631$			6.37226i			0.253676i	−0.991923	+	0.126838i	$0.959517\pi$
$632$	16.0118	−	11.2971i	0.636914	−	0.449373i
$633$	25.0459	+	6.05121i	0.995484	+	0.240514i
$634$	−20.6498	−	23.1484i	−0.820107	−	0.919339i
$635$	10.6611			0.423074
$636$	15.2358	−	41.6048i	0.604137	−	1.64974i
$637$		0			0
$638$	−26.3747	−	29.5660i	−1.04419	−	1.17053i
$639$	12.1040	+	6.21135i	0.478827	+	0.245717i
$640$	13.1373	−	5.34637i	0.519296	−	0.211334i
$641$			16.4960i			0.651554i	0.945447	+	0.325777i	$0.105626\pi$
$641$			16.4960i			0.651554i	−0.945447	+	0.325777i	$0.894374\pi$
$642$	−4.51623	−	8.43961i	−0.178242	−	0.333085i
$643$		−	2.36672i		−	0.0933343i	−0.998910	−	0.0466671i	$-0.985140\pi$
$643$		−	2.36672i		−	0.0933343i	0.998910	−	0.0466671i	$-0.0148600\pi$
$644$		0			0
$645$	1.62476	−	6.72485i	0.0639748	−	0.264791i
$646$	9.46214	−	8.44081i	0.372283	−	0.332099i
$647$	−11.3495			−0.446196			−0.223098	−	0.974796i	$-0.571617\pi$
$647$	−11.3495			−0.446196			−0.223098	+	0.974796i	$0.571617\pi$
$648$	−8.34045	+	24.0507i	−0.327644	+	0.944801i
$649$	40.2993			1.58189
$650$	15.9845	−	14.2591i	0.626962	−	0.559289i
$651$		0			0
$652$	26.3599	+	3.01738i	1.03233	+	0.118170i
$653$		−	44.5689i		−	1.74411i	−0.489404	−	0.872057i	$-0.662786\pi$
$653$		−	44.5689i		−	1.74411i	0.489404	−	0.872057i	$-0.337214\pi$
$654$	−9.53225	−	17.8132i	−0.372741	−	0.696551i
$655$		−	10.5438i		−	0.411981i
$656$	1.78917	−	7.71271i	0.0698554	−	0.301131i
$657$	3.77465	+	1.93702i	0.147263	+	0.0755702i
$658$		0			0
$659$	−0.590533			−0.0230039			−0.0115019	−	0.999934i	$-0.503661\pi$
$659$	−0.590533			−0.0230039			−0.0115019	+	0.999934i	$0.503661\pi$
$660$	−7.55378	+	20.6274i	−0.294031	+	0.802920i
$661$	−43.1004			−1.67641			−0.838206	−	0.545353i	$-0.816396\pi$
$661$	−43.1004			−1.67641			−0.838206	+	0.545353i	$0.816396\pi$
$662$	3.52287	+	3.94913i	0.136920	+	0.153487i
$663$	−43.5386	−	10.5191i	−1.69090	−	0.408529i
$664$	11.0609	+	15.6771i	0.429248	+	0.608390i
$665$		0			0
$666$	−21.9196	+	5.69722i	−0.849367	+	0.220763i
$667$			1.73675i			0.0672471i
$668$	1.08864	−	9.51038i	0.0421208	−	0.367968i
$669$	32.6908	+	7.89826i	1.26390	+	0.305364i
$670$	−13.9497	+	12.4440i	−0.538924	+	0.480754i
$671$	−1.53210			−0.0591459
$672$		0			0
$673$	15.2706			0.588637			0.294319	−	0.955707i	$-0.404907\pi$
$673$	15.2706			0.588637			0.294319	+	0.955707i	$0.404907\pi$
$674$	−24.2488	+	21.6314i	−0.934028	+	0.833211i
$675$	−11.6279	+	13.4959i	−0.447559	+	0.519456i
$676$	1.48266	−	12.9525i	0.0570252	−	0.498173i
$677$			41.3887i			1.59070i	0.606151	+	0.795349i	$0.292713\pi$
$677$			41.3887i			1.59070i	−0.606151	+	0.795349i	$0.707287\pi$
$678$	14.5237	−	7.77198i	0.557780	−	0.298481i
$679$		0			0
$680$	−11.9655	−	16.9592i	−0.458857	−	0.650356i
$681$	4.34540	−	17.9855i	0.166516	−	0.689207i
$682$	23.3288	+	26.1515i	0.893305	+	1.00139i
$683$	4.53490			0.173523			0.0867615	−	0.996229i	$-0.472348\pi$
$683$	4.53490			0.173523			0.0867615	+	0.996229i	$0.472348\pi$
$684$	−7.64654	−	5.09873i	−0.292373	−	0.194955i
$685$	17.2461			0.658941
$686$		0			0
$687$	−3.05138	+	12.6296i	−0.116417	+	0.481850i
$688$	−2.87996	+	12.4149i	−0.109798	+	0.473312i
$689$		−	56.5071i		−	2.15275i
$690$	0.849000	−	0.454320i	0.0323209	−	0.0172957i
$691$		−	27.2902i		−	1.03817i	−0.854723	−	0.519084i	$-0.826273\pi$
$691$		−	27.2902i		−	1.03817i	0.854723	−	0.519084i	$-0.173727\pi$
$692$	−28.6369	−	3.27802i	−1.08861	−	0.124612i
$693$		0			0
$694$	−2.24797	+	2.00532i	−0.0853316	+	0.0761211i
$695$	16.5046			0.626055
$696$	−9.99828	−	25.2243i	−0.378984	−	0.956125i
$697$	−11.5861			−0.438856
$698$	−3.75392	+	3.34873i	−0.142088	+	0.126751i
$699$	4.71287	+	1.13865i	0.178257	+	0.0430678i
$700$		0			0
$701$			9.20431i			0.347642i	0.984777	+	0.173821i	$0.0556114\pi$
$701$			9.20431i			0.347642i	−0.984777	+	0.173821i	$0.944389\pi$
$702$	0.559219	+	32.4606i	0.0211063	+	1.22515i
$703$		−	8.17678i		−	0.308393i
$704$	13.5681	−	38.1237i	0.511367	−	1.43684i
$705$	−24.2648	−	5.86249i	−0.913864	−	0.220794i
$706$	−17.8182	−	19.9742i	−0.670598	−	0.751740i
$707$		0			0
$708$	25.9155	+	9.49030i	0.973965	+	0.356667i
$709$	−29.6006			−1.11167			−0.555837	−	0.831291i	$-0.687602\pi$
$709$	−29.6006			−1.11167			−0.555837	+	0.831291i	$0.687602\pi$
$710$	5.35217	+	5.99977i	0.200863	+	0.225167i
$711$	−9.48941	+	18.4919i	−0.355880	+	0.693501i
$712$	11.0876	−	7.82284i	0.415526	−	0.293173i
$713$		−	1.53617i		−	0.0575302i
$714$		0			0
$715$			28.0159i			1.04773i
$716$	−0.157920	+	1.37959i	−0.00590174	+	0.0515577i
$717$	−8.35773	+	34.5925i	−0.312125	+	1.29188i
$718$	−1.29384	+	1.15418i	−0.0482856	+	0.0430737i
$719$	−2.71571			−0.101279			−0.0506395	−	0.998717i	$-0.516126\pi$
$719$	−2.71571			−0.101279			−0.0506395	+	0.998717i	$0.516126\pi$
$720$	−9.71531	+	11.4861i	−0.362068	+	0.428062i
$721$		0			0
$722$	−17.5752	+	15.6782i	−0.654081	+	0.583480i
$723$	−7.34403	+	30.3968i	−0.273127	+	1.13047i
$724$	−1.43532	+	12.5390i	−0.0533432	+	0.466007i
$725$		−	18.9883i		−	0.705209i
$726$	16.8573	+	31.5018i	0.625634	+	1.16914i
$727$		−	18.9752i		−	0.703753i	−0.936046	−	0.351876i	$-0.885544\pi$
$727$		−	18.9752i		−	0.703753i	0.936046	−	0.351876i	$-0.114456\pi$
$728$		0			0
$729$	−3.99276	−	26.7031i	−0.147880	−	0.989005i
$730$	1.66908	+	1.87104i	0.0617754	+	0.0692501i
$731$	18.6497			0.689786
$732$	−0.985254	−	0.360801i	−0.0364160	−	0.0133356i
$733$	−15.3059			−0.565336			−0.282668	−	0.959218i	$-0.591220\pi$
$733$	−15.3059			−0.565336			−0.282668	+	0.959218i	$0.591220\pi$
$734$	−19.0198	−	21.3212i	−0.702035	−	0.786980i
$735$		0			0
$736$	−1.55628	+	0.851142i	−0.0573652	+	0.0313735i
$737$			53.3335i			1.96457i
$738$	2.11252	+	8.12774i	0.0777629	+	0.299186i
$739$		−	26.8695i		−	0.988411i	−0.869345	−	0.494205i	$-0.835459\pi$
$739$		−	26.8695i		−	0.988411i	0.869345	−	0.494205i	$-0.164541\pi$
$740$	−13.2976	−	1.52216i	−0.488829	−	0.0559556i
$741$	−11.3935	−	2.75272i	−0.418550	−	0.101124i
$742$		0			0
$743$	23.4748			0.861208			0.430604	−	0.902541i	$-0.358301\pi$
$743$	23.4748			0.861208			0.430604	+	0.902541i	$0.358301\pi$
$744$	8.84361	+	22.3112i	0.324222	+	0.817969i
$745$	14.1626			0.518878
$746$	8.63302	−	7.70119i	0.316077	−	0.281960i
$747$	−18.1054	−	9.29107i	−0.662443	−	0.339942i
$748$	−58.8321	−	6.73444i	−2.15112	−	0.246235i
$749$		0			0
$750$	−22.8200	+	12.2115i	−0.833268	+	0.445901i
$751$			35.9640i			1.31234i	0.754612	+	0.656172i	$0.227825\pi$
$751$			35.9640i			1.31234i	−0.754612	+	0.656172i	$0.772175\pi$
$752$	44.7956	+	10.3915i	1.63353	+	0.378940i
$753$	−4.26334	+	17.6459i	−0.155365	+	0.643053i
$754$	−23.0361	−	25.8235i	−0.838926	−	0.940435i
$755$	−13.9153			−0.506429
$756$		0			0
$757$	23.4202			0.851222			0.425611	−	0.904906i	$-0.360059\pi$
$757$	23.4202			0.851222			0.425611	+	0.904906i	$0.360059\pi$
$758$	−29.3742	−	32.9285i	−1.06692	−	1.19602i
$759$	0.645185	−	2.67041i	0.0234187	−	0.0969299i
$760$	−3.13122	−	4.43800i	−0.113581	−	0.160983i
$761$			40.3136i			1.46137i	0.682716	+	0.730684i	$0.260799\pi$
$761$			40.3136i			1.46137i	−0.682716	+	0.730684i	$0.739201\pi$
$762$	18.3662	−	9.82820i	0.665338	−	0.356038i
$763$		0			0
$764$	−0.888828	+	7.76481i	−0.0321567	+	0.280921i
$765$	19.5861	+	10.0509i	0.708138	+	0.363391i
$766$	−25.7690	+	22.9875i	−0.931071	+	0.830572i
$767$	35.1981			1.27093
$768$	17.7033	−	21.3212i	0.638811	−	0.769363i
$769$	−20.6279			−0.743861			−0.371930	−	0.928261i	$-0.621304\pi$
$769$	−20.6279			−0.743861			−0.371930	+	0.928261i	$0.621304\pi$
$770$		0			0
$771$	−14.0762	−	3.40088i	−0.506942	−	0.122480i
$772$	0.357475	−	3.12291i	0.0128658	−	0.112396i
$773$			23.3006i			0.838064i	0.907972	+	0.419032i	$0.137630\pi$
$773$			23.3006i			0.838064i	−0.907972	+	0.419032i	$0.862370\pi$
$774$	−3.40044	−	13.0829i	−0.122226	−	0.470256i
$775$			16.7954i			0.603309i
$776$	22.3136	+	31.6260i	0.801012	+	1.13531i
$777$		0			0
$778$	−8.55233	−	9.58716i	−0.306616	−	0.343716i
$779$	−3.03194			−0.108630
$780$	−6.59760	+	18.0163i	−0.236232	+	0.645087i
$781$	22.9388			0.820813
$782$	1.72794	+	1.93702i	0.0617909	+	0.0692676i
$783$	21.8030	+	18.7853i	0.779177	+	0.671333i
$784$		0			0
$785$			18.5487i			0.662032i
$786$	−9.72006	−	18.1642i	−0.346703	−	0.647894i
$787$			3.18839i			0.113654i	0.998384	+	0.0568269i	$0.0180983\pi$
$787$			3.18839i			0.113654i	−0.998384	+	0.0568269i	$0.981902\pi$
$788$	−3.64191	−	0.416884i	−0.129738	−	0.0148509i
$789$	11.9468	−	49.4477i	0.425318	−	1.76038i
$790$	−9.16617	+	8.17678i	−0.326118	+	0.290917i
$791$		0			0
$792$	6.00271	+	42.4990i	0.213297	+	1.51014i
$793$	−1.33816			−0.0475194
$794$	24.5692	−	21.9172i	0.871927	−	0.777813i
$795$	−6.52236	+	26.9960i	−0.231324	+	0.957448i
$796$	7.29419	+	0.834957i	0.258536	+	0.0295943i
$797$			55.9985i			1.98357i	0.127925	+	0.991784i	$0.459168\pi$
$797$			55.9985i			1.98357i	−0.127925	+	0.991784i	$0.540832\pi$
$798$		0			0
$799$		−	67.2924i		−	2.38063i
$800$	17.0152	−	9.30576i	0.601579	−	0.329008i
$801$	−6.57110	+	12.8050i	−0.232178	+	0.452444i
$802$	7.14659	+	8.01132i	0.252355	+	0.282890i
$803$	7.15348			0.252441
$804$	−12.5598	+	34.2975i	−0.442950	+	1.20958i
$805$		0			0
$806$	20.3757	+	22.8412i	0.717705	+	0.804546i
$807$	−34.3417	−	8.29713i	−1.20889	−	0.292073i
$808$	−9.41040	+	6.63948i	−0.331057	+	0.233576i
$809$			21.3480i			0.750555i	0.926913	+	0.375277i	$0.122453\pi$
$809$			21.3480i			0.750555i	−0.926913	+	0.375277i	$0.877547\pi$
$810$	3.47961	−	15.5724i	0.122261	−	0.547158i
$811$		−	52.7856i		−	1.85355i	−0.375614	−	0.926776i	$-0.622568\pi$
$811$		−	52.7856i		−	1.85355i	0.375614	−	0.926776i	$-0.377432\pi$
$812$		0			0
$813$	34.6763	+	8.37797i	1.21615	+	0.293828i
$814$	−28.4959	+	25.4201i	−0.998782	+	0.890975i
$815$	−16.6310			−0.582558
$816$	−36.2476	−	18.1854i	−1.26892	−	0.636618i
$817$	4.88039			0.170743
$818$	−6.74377	+	6.01585i	−0.235790	+	0.210339i
$819$		0			0
$820$	−0.564413	+	4.93072i	−0.0197101	+	0.172188i
$821$			5.81834i			0.203062i	0.994832	+	0.101531i	$0.0323740\pi$
$821$			5.81834i			0.203062i	−0.994832	+	0.101531i	$0.967626\pi$
$822$	29.7104	−	15.8987i	1.03627	−	0.554532i
$823$		−	10.1488i		−	0.353765i	−0.984232	−	0.176882i	$-0.943399\pi$
$823$		−	10.1488i		−	0.353765i	0.984232	−	0.176882i	$-0.0566012\pi$
$824$	−30.2194	+	21.3212i	−1.05274	+	0.742759i
$825$	−7.05398	+	29.1964i	−0.245588	+	1.01649i
$826$		0			0
$827$	53.0241			1.84383			0.921915	−	0.387393i	$-0.126624\pi$
$827$	53.0241			1.84383			0.921915	+	0.387393i	$0.126624\pi$
$828$	1.04377	−	1.56534i	0.0362736	−	0.0543993i
$829$	32.7023			1.13580			0.567898	−	0.823099i	$-0.307757\pi$
$829$	32.7023			1.13580			0.567898	+	0.823099i	$0.307757\pi$
$830$	−8.00588	−	8.97458i	−0.277888	−	0.311512i
$831$	−1.60547	+	6.64502i	−0.0556932	+	0.230513i
$832$	11.8506	−	33.2979i	0.410845	−	1.15440i
$833$		0			0
$834$	28.4329	−	15.2151i	0.984552	−	0.526857i
$835$			6.00030i			0.207649i
$836$	−15.3956	−	1.76231i	−0.532468	−	0.0609509i
$837$	−19.2850	−	16.6159i	−0.666589	−	0.574328i
$838$	−30.7426	+	27.4243i	−1.06199	+	0.947357i
$839$	37.5962			1.29796			0.648982	−	0.760803i	$-0.275195\pi$
$839$	37.5962			1.29796			0.648982	+	0.760803i	$0.275195\pi$
$840$		0			0
$841$	−1.67632			−0.0578040
$842$	33.8572	−	30.2027i	1.16680	−	1.04085i
$843$	−1.99715	−	0.482522i	−0.0687857	−	0.0166190i
$844$	29.5596	+	3.38364i	1.01748	+	0.116470i
$845$			8.17200i			0.281125i
$846$	−47.2061	+	12.2695i	−1.62298	+	0.421835i
$847$		0			0
$848$	11.5612	−	49.8377i	0.397013	−	1.71143i
$849$	−46.6078	−	11.2607i	−1.59958	−	0.386466i
$850$	−18.8920	−	21.1779i	−0.647991	−	0.726397i
$851$	1.67389			0.0573802
$852$	14.7514	+	5.40197i	0.505373	+	0.185068i
$853$	5.68417			0.194622			0.0973112	−	0.995254i	$-0.468976\pi$
$853$	5.68417			0.194622			0.0973112	+	0.995254i	$0.468976\pi$
$854$		0			0
$855$	5.12543	+	2.63019i	0.175286	+	0.0899507i
$856$	−6.37195	−	9.03122i	−0.217789	−	0.308681i
$857$		−	31.6896i		−	1.08250i	−0.840862	−	0.541249i	$-0.817952\pi$
$857$		−	31.6896i		−	1.08250i	0.840862	−	0.541249i	$-0.182048\pi$
$858$	25.8270	+	48.2637i	0.881721	+	1.64770i
$859$			6.03763i			0.206001i	0.994681	+	0.103001i	$0.0328444\pi$
$859$			6.03763i			0.206001i	−0.994681	+	0.103001i	$0.967156\pi$
$860$	0.908514	−	7.93679i	0.0309801	−	0.270642i
$861$		0			0
$862$	19.2552	−	17.1768i	0.655835	−	0.585045i
$863$	40.1137			1.36549			0.682744	−	0.730658i	$-0.260787\pi$
$863$	40.1137			1.36549			0.682744	+	0.730658i	$0.260787\pi$
$864$	−6.14812	+	28.7437i	−0.209163	+	0.977881i
$865$	18.0676			0.614316
$866$	5.11669	−	4.56440i	0.173872	−	0.155105i
$867$	−7.02181	+	29.0632i	−0.238473	+	0.987038i
$868$		0			0
$869$			35.0447i			1.18881i
$870$	8.02469	+	14.9960i	0.272062	+	0.508411i
$871$			46.5824i			1.57838i
$872$	−13.4490	−	19.0619i	−0.455442	−	0.645516i
$873$	−36.5247	−	18.7432i	−1.23617	−	0.634361i
$874$	0.452179	+	0.506892i	0.0152952	+	0.0171459i
$875$		0			0
$876$	4.60023	+	1.68461i	0.155427	+	0.0569177i
$877$	−43.8872			−1.48197			−0.740983	−	0.671524i	$-0.765640\pi$
$877$	−43.8872			−1.48197			−0.740983	+	0.671524i	$0.765640\pi$
$878$	19.0657	+	21.3726i	0.643436	+	0.721292i
$879$	0.333009	+	0.0804567i	0.0112321	+	0.00271374i
$880$	−5.73196	+	24.7092i	−0.193224	+	0.832946i
$881$			1.27293i			0.0428860i	0.999770	+	0.0214430i	$0.00682603\pi$
$881$			1.27293i			0.0428860i	−0.999770	+	0.0214430i	$0.993174\pi$
$882$		0			0
$883$		−	19.5118i		−	0.656625i	−0.944569	−	0.328312i	$-0.893520\pi$
$883$		−	19.5118i		−	0.656625i	0.944569	−	0.328312i	$-0.106480\pi$
$884$	−51.3850	−	5.88197i	−1.72826	−	0.197832i
$885$	−16.8157	−	4.06276i	−0.565253	−	0.136568i
$886$	−23.7101	+	21.1509i	−0.796557	+	0.710578i
$887$	26.8919			0.902940			0.451470	−	0.892286i	$-0.350900\pi$
$887$	26.8919			0.902940			0.451470	+	0.892286i	$0.350900\pi$
$888$	−24.3114	+	9.63641i	−0.815836	+	0.323377i
$889$		0			0
$890$	−6.34727	+	5.66215i	−0.212761	+	0.189796i
$891$	−26.5456	−	36.9838i	−0.889313	−	1.23901i
$892$	38.5822	+	4.41646i	1.29183	+	0.147874i
$893$		−	17.6095i		−	0.589281i
$894$	24.3983	−	13.0561i	0.816002	−	0.436662i
$895$		−	0.870412i		−	0.0290947i
$896$		0			0
$897$	0.563515	−	2.33238i	0.0188152	−	0.0778760i
$898$	−27.8341	−	31.2020i	−0.928836	−	1.04122i
$899$	27.1336			0.904956
$900$	−11.4118	+	17.1143i	−0.380395	+	0.570476i
$901$	−74.8667			−2.49417
$902$	9.42574	+	10.5662i	0.313843	+	0.351817i
$903$		0			0
$904$	15.5418	−	10.9655i	0.516913	−	0.364706i
$905$		−	7.91109i		−	0.262973i
$906$	−23.9722	+	12.8281i	−0.796424	+	0.426185i
$907$		−	18.6528i		−	0.619357i	−0.950841	−	0.309679i	$-0.899779\pi$
$907$		−	18.6528i		−	0.619357i	0.950841	−	0.309679i	$-0.100221\pi$
$908$	2.42981	−	21.2268i	0.0806360	−	0.704437i
$909$	5.57709	−	10.8680i	0.184980	−	0.360470i
$910$		0			0
$911$	−8.12909			−0.269329			−0.134664	−	0.990891i	$-0.542996\pi$
$911$	−8.12909			−0.269329			−0.134664	+	0.990891i	$0.542996\pi$
$912$	−9.48552	−	4.75889i	−0.314097	−	0.157583i
$913$	−34.3123			−1.13557
$914$	−19.2016	+	17.1290i	−0.635133	+	0.566578i
$915$	0.639297	+	0.154457i	0.0211345	+	0.00510621i
$916$	−1.70623	+	14.9057i	−0.0563755	+	0.492497i
$917$		0			0
$918$	43.0072	−	0.740913i	1.41945	−	0.0244538i
$919$		−	17.5640i		−	0.579383i	−0.957120	−	0.289692i	$-0.906447\pi$
$919$		−	17.5640i		−	0.579383i	0.957120	−	0.289692i	$-0.0935528\pi$
$920$	0.908514	−	0.640999i	0.0299528	−	0.0211331i
$921$	27.9846	+	6.76123i	0.922125	+	0.222790i
$922$	23.5150	+	26.3603i	0.774425	+	0.868129i
$923$	20.0351			0.659463
$924$		0			0
$925$	−18.3011			−0.601736
$926$	−5.99898	−	6.72485i	−0.197139	−	0.220992i
$927$	17.9096	−	34.9002i	0.588228	−	1.14627i
$928$	−15.0338	−	27.4887i	−0.493508	−	0.902360i
$929$		−	38.9854i		−	1.27907i	−0.768762	−	0.639535i	$-0.779127\pi$
$929$		−	38.9854i		−	1.27907i	0.768762	−	0.639535i	$-0.220873\pi$
$930$	−7.09794	−	13.2641i	−0.232751	−	0.434948i
$931$		0			0
$932$	5.56221	+	0.636699i	0.182196	+	0.0208558i
$933$	−4.37524	+	18.1091i	−0.143239	+	0.592864i
$934$	28.8706	−	25.7544i	0.944676	−	0.842709i
$935$	37.1184			1.21390
$936$	5.24287	+	37.1194i	0.171368	+	1.21328i
$937$	−23.7865			−0.777072			−0.388536	−	0.921434i	$-0.627019\pi$
$937$	−23.7865			−0.777072			−0.388536	+	0.921434i	$0.627019\pi$
$938$		0			0
$939$	−2.01106	+	8.32376i	−0.0656285	+	0.271636i
$940$	−28.6377	−	3.27812i	−0.934058	−	0.106920i
$941$		−	30.6145i		−	0.998005i	−0.866601	−	0.499002i	$-0.833700\pi$
$941$		−	30.6145i		−	0.998005i	0.866601	−	0.499002i	$-0.166300\pi$
$942$	17.0995	+	31.9544i	0.557133	+	1.04113i
$943$		−	0.620675i		−	0.0202120i
$944$	31.0437	+	7.20143i	1.01039	+	0.234387i
$945$		0			0
$946$	−15.1722	−	17.0081i	−0.493292	−	0.552980i
$947$	−15.4601			−0.502386			−0.251193	−	0.967937i	$-0.580823\pi$
$947$	−15.4601			−0.502386			−0.251193	+	0.967937i	$0.580823\pi$
$948$	−8.25287	+	22.5364i	−0.268041	+	0.731949i
$949$	6.24797			0.202818
$950$	−4.94379	−	5.54199i	−0.160398	−	0.179806i
$951$	36.9294	+	8.92233i	1.19752	+	0.289326i
$952$		0			0
$953$			13.4497i			0.435679i	0.975985	+	0.217839i	$0.0699009\pi$
$953$			13.4497i			0.435679i	−0.975985	+	0.217839i	$0.930099\pi$
$954$	13.6506	+	52.5195i	0.441954	+	1.70038i
$955$		−	4.89898i		−	0.158527i
$956$	−4.67338	+	40.8267i	−0.151148	+	1.32043i
$957$	47.1677	+	11.3960i	1.52472	+	0.368379i
$958$	20.9308	−	18.6715i	0.676243	−	0.603250i
$959$		0			0
$960$	−9.50498	+	14.5400i	−0.306772	+	0.469277i
$961$	7.00000			0.225806
$962$	−24.8888	+	22.2024i	−0.802448	+	0.715833i
$963$	10.4301	+	5.35237i	0.336106	+	0.172478i
$964$	−4.10655	+	35.8749i	−0.132263	+	1.15545i
$965$			1.97031i			0.0634264i
$966$		0			0
$967$			41.1554i			1.32347i	0.749738	+	0.661734i	$0.230179\pi$
$967$			41.1554i			1.32347i	−0.749738	+	0.661734i	$0.769821\pi$
$968$	23.7840	+	33.7100i	0.764446	+	1.08348i
$969$	−3.64710	+	15.0953i	−0.117162	+	0.484931i
$970$	−16.1505	−	18.1047i	−0.518562	−	0.581308i
$971$	28.8890			0.927093			0.463546	−	0.886073i	$-0.346577\pi$
$971$	28.8890			0.927093			0.463546	+	0.886073i	$0.346577\pi$
$972$	−8.36134	−	30.0348i	−0.268190	−	0.963366i
$973$		0			0
$974$	−38.4593	−	43.1128i	−1.23232	−	1.38142i
$975$	−6.16107	+	25.5006i	−0.197312	+	0.816672i
$976$	−1.18022	−	0.273783i	−0.0377778	−	0.00876359i
$977$		−	46.9884i		−	1.50329i	−0.659567	−	0.751646i	$-0.729260\pi$
$977$		−	46.9884i		−	1.50329i	0.659567	−	0.751646i	$-0.270740\pi$
$978$	−28.6507	+	15.3316i	−0.916148	+	0.490252i
$979$			24.2673i			0.775587i
$980$		0			0
$981$	22.0145	+	11.2971i	0.702868	+	0.360687i
$982$	−21.4235	+	19.1111i	−0.683652	+	0.609859i
$983$	27.3353			0.871861			0.435931	−	0.899980i	$-0.356419\pi$
$983$	27.3353			0.871861			0.435931	+	0.899980i	$0.356419\pi$
$984$	3.57316	+	9.01461i	0.113908	+	0.287375i
$985$	2.29776			0.0732126
$986$	−34.2137	+	30.5207i	−1.08959	+	0.971978i
$987$		0			0
$988$	−13.4468	−	1.53923i	−0.427799	−	0.0489696i
$989$			0.999076i			0.0317688i
$990$	−6.76786	−	26.0388i	−0.215097	−	0.827568i
$991$		−	20.7846i		−	0.660245i	−0.943938	−	0.330122i	$-0.892910\pi$
$991$		−	20.7846i		−	0.660245i	0.943938	−	0.330122i	$-0.107090\pi$
$992$	13.2976	+	24.3141i	0.422199	+	0.771973i
$993$	−6.30019	−	1.52216i	−0.199930	−	0.0483042i
$994$		0			0
$995$	−4.60206			−0.145895
$996$	−22.0654	−	8.08037i	−0.699168	−	0.256036i
$997$	12.0424			0.381386			0.190693	−	0.981650i	$-0.438926\pi$
$997$	12.0424			0.381386			0.190693	+	0.981650i	$0.438926\pi$
$998$	−32.2222	−	36.1211i	−1.01998	−	1.14339i
$999$	18.1054	−	21.0139i	0.572830	−	0.664850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.f.491.8	yes	24
3.2	odd	2	inner	588.2.e.f.491.17	yes	24
4.3	odd	2	inner	588.2.e.f.491.19	yes	24
7.2	even	3		588.2.n.h.263.10		24
7.3	odd	6		588.2.n.d.275.6		24
7.4	even	3		588.2.n.d.275.5		24
7.5	odd	6		588.2.n.h.263.9		24
7.6	odd	2	inner	588.2.e.f.491.7	yes	24
12.11	even	2	inner	588.2.e.f.491.6	yes	24
21.2	odd	6		588.2.n.h.263.4		24
21.5	even	6		588.2.n.h.263.3		24
21.11	odd	6		588.2.n.d.275.7		24
21.17	even	6		588.2.n.d.275.8		24
21.20	even	2	inner	588.2.e.f.491.18	yes	24
28.3	even	6		588.2.n.h.275.3		24
28.11	odd	6		588.2.n.h.275.4		24
28.19	even	6		588.2.n.d.263.8		24
28.23	odd	6		588.2.n.d.263.7		24
28.27	even	2	inner	588.2.e.f.491.20	yes	24
84.11	even	6		588.2.n.h.275.10		24
84.23	even	6		588.2.n.d.263.5		24
84.47	odd	6		588.2.n.d.263.6		24
84.59	odd	6		588.2.n.h.275.9		24
84.83	odd	2	inner	588.2.e.f.491.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.5	✓	24	84.83	odd	2	inner
588.2.e.f.491.6	yes	24	12.11	even	2	inner
588.2.e.f.491.7	yes	24	7.6	odd	2	inner
588.2.e.f.491.8	yes	24	1.1	even	1	trivial
588.2.e.f.491.17	yes	24	3.2	odd	2	inner
588.2.e.f.491.18	yes	24	21.20	even	2	inner
588.2.e.f.491.19	yes	24	4.3	odd	2	inner
588.2.e.f.491.20	yes	24	28.27	even	2	inner
588.2.n.d.263.5		24	84.23	even	6
588.2.n.d.263.6		24	84.47	odd	6
588.2.n.d.263.7		24	28.23	odd	6
588.2.n.d.263.8		24	28.19	even	6
588.2.n.d.275.5		24	7.4	even	3
588.2.n.d.275.6		24	7.3	odd	6
588.2.n.d.275.7		24	21.11	odd	6
588.2.n.d.275.8		24	21.17	even	6
588.2.n.h.263.3		24	21.5	even	6
588.2.n.h.263.4		24	21.2	odd	6
588.2.n.h.263.9		24	7.5	odd	6
588.2.n.h.263.10		24	7.2	even	3
588.2.n.h.275.3		24	28.3	even	6
588.2.n.h.275.4		24	28.11	odd	6
588.2.n.h.275.9		24	84.59	odd	6
588.2.n.h.275.10		24	84.11	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05533 + 0.941421i) q^{2} +(0.406768 - 1.68361i) q^{3} +(0.227452 - 1.98702i) q^{4} +1.25365i q^{5} +(1.15571 + 2.15971i) q^{6} +(1.63059 + 2.31110i) q^{8} +(-2.66908 - 1.36968i) q^{9} +(-1.18022 - 1.32302i) q^{10} -5.05827 q^{11} +(-3.25285 - 1.19120i) q^{12} -4.41798 q^{13} +(2.11066 + 0.509947i) q^{15} +(-3.89653 - 0.903905i) q^{16} +5.85341i q^{17} +(4.10621 - 1.06726i) q^{18} +1.53176i q^{19} +(2.49104 + 0.285146i) q^{20} +(5.33816 - 4.76197i) q^{22} -0.313570 q^{23} +(4.55426 - 1.80519i) q^{24} +3.42835 q^{25} +(4.66244 - 4.15918i) q^{26} +(-3.39170 + 3.93654i) q^{27} -5.53862i q^{29} +(-2.70753 + 1.44886i) q^{30} +4.89898i q^{31} +(4.96309 - 2.71436i) q^{32} +(-2.05755 + 8.51615i) q^{33} +(-5.51053 - 6.17729i) q^{34} +(-3.32867 + 4.99199i) q^{36} -5.33816 q^{37} +(-1.44203 - 1.61652i) q^{38} +(-1.79709 + 7.43815i) q^{39} +(-2.89732 + 2.04420i) q^{40} +1.97938i q^{41} -3.18613i q^{43} +(-1.15051 + 10.0509i) q^{44} +(1.71710 - 3.34610i) q^{45} +(0.330921 - 0.295202i) q^{46} -11.4963 q^{47} +(-3.10681 + 6.19256i) q^{48} +(-3.61805 + 3.22752i) q^{50} +(9.85486 + 2.38098i) q^{51} +(-1.00488 + 8.77863i) q^{52} +12.7903i q^{53} +(-0.126578 - 7.34738i) q^{54} -6.34133i q^{55} +(2.57889 + 0.623072i) q^{57} +(5.21417 + 5.84508i) q^{58} -7.96701 q^{59} +(1.49335 - 4.07795i) q^{60} +0.302889 q^{61} +(-4.61200 - 5.17005i) q^{62} +(-2.68236 + 7.53691i) q^{64} -5.53862i q^{65} +(-5.84589 - 10.9244i) q^{66} -10.5438i q^{67} +(11.6309 + 1.33137i) q^{68} +(-0.127550 + 0.527930i) q^{69} -4.53490 q^{71} +(-1.18671 - 8.40189i) q^{72} -1.41421 q^{73} +(5.63353 - 5.02546i) q^{74} +(1.39454 - 5.77200i) q^{75} +(3.04365 + 0.348402i) q^{76} +(-5.10590 - 9.54154i) q^{78} -6.92820i q^{79} +(1.13319 - 4.88490i) q^{80} +(5.24797 + 7.31156i) q^{81} +(-1.86343 - 2.08890i) q^{82} +6.78340 q^{83} -7.33816 q^{85} +(2.99949 + 3.36243i) q^{86} +(-9.32487 - 2.25294i) q^{87} +(-8.24797 - 11.6902i) q^{88} -4.79755i q^{89} +(1.33798 + 5.14777i) q^{90} +(-0.0713222 + 0.623072i) q^{92} +(8.24797 + 1.99275i) q^{93} +(12.1324 - 10.8228i) q^{94} -1.92030 q^{95} +(-2.55109 - 9.46002i) q^{96} +13.6844 q^{97} +(13.5009 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) \) 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

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