LMFDB - Embedded newform 504.2.t.c.457.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.3
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07968 - 1.35436i) q^{3} +3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +(-0.668594 + 2.92455i) q^{9} +O(q^{10})$	\(q+(-1.07968 - 1.35436i) q^{3} +3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +(-0.668594 + 2.92455i) q^{9} +5.39638 q^{11} +(1.89598 + 3.28393i) q^{13} +(-3.67885 - 4.61480i) q^{15} +(0.411976 + 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +(4.47365 + 0.993210i) q^{21} -5.49899 q^{23} +6.61011 q^{25} +(4.68276 - 2.25205i) q^{27} +(0.400332 - 0.693396i) q^{29} +(4.95366 - 8.57999i) q^{31} +(-5.82635 - 7.30865i) q^{33} +(-7.01378 + 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(2.40059 - 6.11343i) q^{39} +(1.84467 + 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(-2.27814 + 9.96499i) q^{45} +(5.24957 + 9.09252i) q^{47} +(1.47420 - 6.84301i) q^{49} +(0.521623 - 1.32838i) q^{51} +(-4.71820 - 8.17217i) q^{53} +18.3874 q^{55} +(-0.800234 + 0.120472i) q^{57} +(0.830344 - 1.43820i) q^{59} +(-0.474405 - 0.821694i) q^{61} +(-3.48493 - 7.13129i) q^{63} +(6.46029 + 11.1896i) q^{65} +(-0.269592 + 0.466947i) q^{67} +(5.93714 + 7.44762i) q^{69} -3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(-7.13679 - 8.95248i) q^{75} +(-11.1080 + 8.96985i) q^{77} +(-3.91449 - 6.78010i) q^{79} +(-8.10597 - 3.91067i) q^{81} +(-3.79623 + 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(-1.37134 + 0.206449i) q^{87} +(-3.73498 + 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +(-16.9688 + 2.55457i) q^{93} +(0.795996 - 1.37871i) q^{95} +(-3.22500 + 5.58587i) q^{97} +(-3.60798 + 15.7820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.07968	−	1.35436i	−0.623352	−	0.781941i
$3$	−1.07968	−	1.35436i	−0.623352	−	0.781941i
$4$		0			0
$5$	3.40736			1.52382			0.761909	−	0.647684i	$-0.224262\pi$
$5$	3.40736			1.52382			0.761909	+	0.647684i	$0.224262\pi$
$6$		0			0
$7$	−2.05842	+	1.66220i	−0.778010	+	0.628252i
$7$	−2.05842	+	1.66220i	−0.778010	+	0.628252i
$8$		0			0
$9$	−0.668594	+	2.92455i	−0.222865	+	0.974849i
$10$		0			0
$11$	5.39638			1.62707			0.813535	−	0.581516i	$-0.197540\pi$
$11$	5.39638			1.62707			0.813535	+	0.581516i	$0.197540\pi$
$12$		0			0
$13$	1.89598	+	3.28393i	0.525850	+	0.910800i	0.999547	+	0.0301113i	$0.00958618\pi$
$13$	1.89598	+	3.28393i	0.525850	+	0.910800i	−0.473696	+	0.880688i	$0.657080\pi$
$14$		0			0
$15$	−3.67885	−	4.61480i	−0.949875	−	1.19154i
$16$		0			0
$17$	0.411976	+	0.713564i	0.0999190	+	0.173065i	0.911651	−	0.410965i	$-0.134808\pi$
$17$	0.411976	+	0.713564i	0.0999190	+	0.173065i	−0.811732	+	0.584030i	$0.801475\pi$
$18$		0			0
$19$	0.233611	−	0.404626i	0.0535940	−	0.0928275i	−0.837984	−	0.545695i	$-0.816266\pi$
$19$	0.233611	−	0.404626i	0.0535940	−	0.0928275i	0.891578	+	0.452868i	$0.149599\pi$
$20$		0			0
$21$	4.47365	+	0.993210i	0.976230	+	0.216736i
$22$		0			0
$23$	−5.49899			−1.14662			−0.573309	−	0.819339i	$-0.694341\pi$
$23$	−5.49899			−1.14662			−0.573309	+	0.819339i	$0.694341\pi$
$24$		0			0
$25$	6.61011			1.32202
$26$		0			0
$27$	4.68276	−	2.25205i	0.901198	−	0.433407i
$28$		0			0
$29$	0.400332	−	0.693396i	0.0743399	−	0.128760i	−0.826459	−	0.562997i	$-0.809648\pi$
$29$	0.400332	−	0.693396i	0.0743399	−	0.128760i	0.900799	+	0.434236i	$0.142982\pi$
$30$		0			0
$31$	4.95366	−	8.57999i	0.889703	−	1.54101i	0.0494772	−	0.998775i	$-0.484244\pi$
$31$	4.95366	−	8.57999i	0.889703	−	1.54101i	0.840226	−	0.542236i	$-0.182422\pi$
$32$		0			0
$33$	−5.82635	−	7.30865i	−1.01424	−	1.27227i
$34$		0			0
$35$	−7.01378	+	5.66371i	−1.18555	+	0.957342i
$36$		0			0
$37$	4.34210	−	7.52074i	0.713837	−	1.23640i	−0.249569	−	0.968357i	$-0.580289\pi$
$37$	4.34210	−	7.52074i	0.713837	−	1.23640i	0.963406	−	0.268045i	$-0.0863777\pi$
$38$		0			0
$39$	2.40059	−	6.11343i	0.384402	−	0.978933i
$40$		0			0
$41$	1.84467	+	3.19507i	0.288090	+	0.498986i	0.973354	−	0.229309i	$-0.0736465\pi$
$41$	1.84467	+	3.19507i	0.288090	+	0.498986i	−0.685264	+	0.728295i	$0.740313\pi$
$42$		0			0
$43$	−4.36356	+	7.55790i	−0.665436	+	1.15257i	0.313731	+	0.949512i	$0.398421\pi$
$43$	−4.36356	+	7.55790i	−0.665436	+	1.15257i	−0.979167	+	0.203057i	$0.934912\pi$
$44$		0			0
$45$	−2.27814	+	9.96499i	−0.339605	+	1.48549i
$46$		0			0
$47$	5.24957	+	9.09252i	0.765728	+	1.32628i	0.939861	+	0.341558i	$0.110955\pi$
$47$	5.24957	+	9.09252i	0.765728	+	1.32628i	−0.174133	+	0.984722i	$0.555712\pi$
$48$		0			0
$49$	1.47420	−	6.84301i	0.210599	−	0.977572i
$50$		0			0
$51$	0.521623	−	1.32838i	0.0730418	−	0.186011i
$52$		0			0
$53$	−4.71820	−	8.17217i	−0.648095	−	1.12253i	−0.983577	−	0.180487i	$-0.942233\pi$
$53$	−4.71820	−	8.17217i	−0.648095	−	1.12253i	0.335483	−	0.942046i	$-0.391101\pi$
$54$		0			0
$55$	18.3874			2.47936
$56$		0			0
$57$	−0.800234	+	0.120472i	−0.105994	+	0.0159569i
$58$		0			0
$59$	0.830344	−	1.43820i	0.108102	−	0.187238i	−0.806900	−	0.590689i	$-0.798856\pi$
$59$	0.830344	−	1.43820i	0.108102	−	0.187238i	0.915001	+	0.403451i	$0.132189\pi$
$60$		0			0
$61$	−0.474405	−	0.821694i	−0.0607414	−	0.105207i	0.834056	−	0.551680i	$-0.186013\pi$
$61$	−0.474405	−	0.821694i	−0.0607414	−	0.105207i	−0.894797	+	0.446473i	$0.852680\pi$
$62$		0			0
$63$	−3.48493	−	7.13129i	−0.439060	−	0.898458i
$64$		0			0
$65$	6.46029	+	11.1896i	0.801301	+	1.38789i
$66$		0			0
$67$	−0.269592	+	0.466947i	−0.0329359	+	0.0570467i	−0.882024	−	0.471205i	$-0.843819\pi$
$67$	−0.269592	+	0.466947i	−0.0329359	+	0.0570467i	0.849088	+	0.528252i	$0.177152\pi$
$68$		0			0
$69$	5.93714	+	7.44762i	0.714747	+	0.896589i
$70$		0			0
$71$	−3.86901			−0.459167			−0.229583	−	0.973289i	$-0.573736\pi$
$71$	−3.86901			−0.459167			−0.229583	+	0.973289i	$0.573736\pi$
$72$		0			0
$73$	2.58943	+	4.48502i	0.303070	+	0.524932i	0.976830	−	0.214018i	$-0.0686551\pi$
$73$	2.58943	+	4.48502i	0.303070	+	0.524932i	−0.673760	+	0.738950i	$0.735322\pi$
$74$		0			0
$75$	−7.13679	−	8.95248i	−0.824085	−	1.03374i
$76$		0			0
$77$	−11.1080	+	8.96985i	−1.26588	+	1.02221i
$78$		0			0
$79$	−3.91449	−	6.78010i	−0.440415	−	0.762821i	0.557305	−	0.830308i	$-0.311835\pi$
$79$	−3.91449	−	6.78010i	−0.440415	−	0.762821i	−0.997720	+	0.0674866i	$0.978502\pi$
$80$		0			0
$81$	−8.10597	−	3.91067i	−0.900663	−	0.434519i
$82$		0			0
$83$	−3.79623	+	6.57527i	−0.416691	+	0.721729i	−0.995604	−	0.0936595i	$-0.970143\pi$
$83$	−3.79623	+	6.57527i	−0.416691	+	0.721729i	0.578914	+	0.815389i	$0.303477\pi$
$84$		0			0
$85$	1.40375	+	2.43137i	0.152258	+	0.263719i
$86$		0			0
$87$	−1.37134	+	0.206449i	−0.147023	+	0.0221337i
$88$		0			0
$89$	−3.73498	+	6.46917i	−0.395907	+	0.685730i	−0.993216	−	0.116280i	$-0.962903\pi$
$89$	−3.73498	+	6.46917i	−0.395907	+	0.685730i	0.597310	+	0.802011i	$0.296236\pi$
$90$		0			0
$91$	−9.36128	−	3.60823i	−0.981328	−	0.378245i
$92$		0			0
$93$	−16.9688	+	2.55457i	−1.75958	+	0.264897i
$94$		0			0
$95$	0.795996	−	1.37871i	0.0816675	−	0.141452i
$96$		0			0
$97$	−3.22500	+	5.58587i	−0.327450	+	0.567159i	−0.982005	−	0.188855i	$-0.939522\pi$
$97$	−3.22500	+	5.58587i	−0.327450	+	0.567159i	0.654555	+	0.756014i	$0.272856\pi$
$98$		0			0
$99$	−3.60798	+	15.7820i	−0.362616	+	1.58615i
$100$		0			0
$101$	−16.1995			−1.61191			−0.805953	−	0.591979i	$-0.798347\pi$
$101$	−16.1995			−1.61191			−0.805953	+	0.591979i	$0.798347\pi$
$102$		0			0
$103$	−15.6986			−1.54683			−0.773414	−	0.633901i	$-0.781453\pi$
$103$	−15.6986			−1.54683			−0.773414	+	0.633901i	$0.781453\pi$
$104$		0			0
$105$	15.2433	+	3.38423i	1.48760	+	0.330267i
$106$		0			0
$107$	2.85024	−	4.93675i	0.275543	−	0.477254i	−0.694729	−	0.719271i	$-0.744476\pi$
$107$	2.85024	−	4.93675i	0.275543	−	0.477254i	0.970272	+	0.242017i	$0.0778091\pi$
$108$		0			0
$109$	−2.19196	−	3.79659i	−0.209952	−	0.363648i	0.741747	−	0.670680i	$-0.233997\pi$
$109$	−2.19196	−	3.79659i	−0.209952	−	0.363648i	−0.951699	+	0.307032i	$0.900664\pi$
$110$		0			0
$111$	−14.8739	+	2.23920i	−1.41177	+	0.212535i
$112$		0			0
$113$	−4.96607	−	8.60149i	−0.467169	−	0.809160i	0.532128	−	0.846664i	$-0.321393\pi$
$113$	−4.96607	−	8.60149i	−0.467169	−	0.809160i	−0.999296	+	0.0375041i	$0.988059\pi$
$114$		0			0
$115$	−18.7370			−1.74724
$116$		0			0
$117$	−10.8717	+	3.34927i	−1.00509	+	0.309640i
$118$		0			0
$119$	−2.03411	−	0.784029i	−0.186466	−	0.0718718i
$120$		0			0
$121$	18.1209			1.64735
$122$		0			0
$123$	2.33563	−	5.94800i	0.210597	−	0.536313i
$124$		0			0
$125$	5.48623			0.490703
$126$		0			0
$127$	16.1122			1.42973			0.714864	−	0.699263i	$-0.246488\pi$
$127$	16.1122			1.42973			0.714864	+	0.699263i	$0.246488\pi$
$128$		0			0
$129$	14.9474	−	2.25026i	1.31604	−	0.198124i
$130$		0			0
$131$	13.9408			1.21801			0.609006	−	0.793166i	$-0.291569\pi$
$131$	13.9408			1.21801			0.609006	+	0.793166i	$0.291569\pi$
$132$		0			0
$133$	0.191699	+	1.22120i	0.0166224	+	0.105891i
$134$		0			0
$135$	15.9559	−	7.67355i	1.37326	−	0.660434i
$136$		0			0
$137$	−11.1520			−0.952776			−0.476388	−	0.879235i	$-0.658054\pi$
$137$	−11.1520			−0.952776			−0.476388	+	0.879235i	$0.658054\pi$
$138$		0			0
$139$	3.17737	+	5.50337i	0.269501	+	0.466790i	0.968733	−	0.248105i	$-0.0798078\pi$
$139$	3.17737	+	5.50337i	0.269501	+	0.466790i	−0.699232	+	0.714895i	$0.746474\pi$
$140$		0			0
$141$	6.64672	−	16.9268i	0.559755	−	1.42549i
$142$		0			0
$143$	10.2314	+	17.7214i	0.855595	+	1.48193i
$144$		0			0
$145$	1.36408	−	2.36265i	0.113280	−	0.196207i
$146$		0			0
$147$	−10.8596	+	5.39165i	−0.895682	+	0.444695i
$148$		0			0
$149$	−11.5304			−0.944609			−0.472304	−	0.881435i	$-0.656578\pi$
$149$	−11.5304			−0.944609			−0.472304	+	0.881435i	$0.656578\pi$
$150$		0			0
$151$	−0.694634			−0.0565285			−0.0282643	−	0.999600i	$-0.508998\pi$
$151$	−0.694634			−0.0565285			−0.0282643	+	0.999600i	$0.508998\pi$
$152$		0			0
$153$	−2.36230	+	0.727761i	−0.190980	+	0.0588360i
$154$		0			0
$155$	16.8789	−	29.2351i	1.35575	−	2.34822i
$156$		0			0
$157$	2.02423	−	3.50606i	0.161551	−	0.279814i	−0.773874	−	0.633339i	$-0.781684\pi$
$157$	2.02423	−	3.50606i	0.161551	−	0.279814i	0.935425	+	0.353525i	$0.115017\pi$
$158$		0			0
$159$	−5.97394	+	15.2135i	−0.473764	+	1.20651i
$160$		0			0
$161$	11.3192	−	9.14041i	0.892081	−	0.720365i
$162$		0			0
$163$	−5.05968	+	8.76363i	−0.396305	+	0.686420i	−0.993267	−	0.115849i	$-0.963041\pi$
$163$	−5.05968	+	8.76363i	−0.396305	+	0.686420i	0.596962	+	0.802270i	$0.296374\pi$
$164$		0			0
$165$	−19.8525	−	24.9032i	−1.54551	−	1.93871i
$166$		0			0
$167$	8.76377	+	15.1793i	0.678161	+	1.17461i	0.975534	+	0.219847i	$0.0705560\pi$
$167$	8.76377	+	15.1793i	0.678161	+	1.17461i	−0.297374	+	0.954761i	$0.596111\pi$
$168$		0			0
$169$	−0.689486	+	1.19422i	−0.0530374	+	0.0918634i
$170$		0			0
$171$	1.02716	+	0.953736i	0.0785486	+	0.0729340i
$172$		0			0
$173$	3.91758	+	6.78544i	0.297848	+	0.515887i	0.975643	−	0.219363i	$-0.0703979\pi$
$173$	3.91758	+	6.78544i	0.297848	+	0.515887i	−0.677796	+	0.735250i	$0.737065\pi$
$174$		0			0
$175$	−13.6064	+	10.9873i	−1.02855	+	0.830563i
$176$		0			0
$177$	−2.84435	+	0.428204i	−0.213794	+	0.0321858i
$178$		0			0
$179$	4.61920	+	8.00069i	0.345255	+	0.597999i	0.985400	−	0.170255i	$-0.0544591\pi$
$179$	4.61920	+	8.00069i	0.345255	+	0.597999i	−0.640145	+	0.768254i	$0.721126\pi$
$180$		0			0
$181$	9.45977			0.703139			0.351569	−	0.936162i	$-0.385648\pi$
$181$	9.45977			0.703139			0.351569	+	0.936162i	$0.385648\pi$
$182$		0			0
$183$	−0.600667	+	1.52968i	−0.0444026	+	0.113077i
$184$		0			0
$185$	14.7951	−	25.6259i	1.08776	−	1.88405i
$186$		0			0
$187$	2.22318	+	3.85066i	0.162575	+	0.281588i
$188$		0			0
$189$	−5.89574	+	12.4193i	−0.428852	+	0.903375i
$190$		0			0
$191$	−0.0226484	−	0.0392281i	−0.00163878	−	0.00283845i	0.865205	−	0.501419i	$-0.167188\pi$
$191$	−0.0226484	−	0.0392281i	−0.00163878	−	0.00283845i	−0.866844	+	0.498580i	$0.833855\pi$
$192$		0			0
$193$	9.40991	−	16.2984i	0.677340	−	1.17319i	−0.298438	−	0.954429i	$-0.596466\pi$
$193$	9.40991	−	16.2984i	0.677340	−	1.17319i	0.975779	−	0.218759i	$-0.0702009\pi$
$194$		0			0
$195$	8.17968	−	20.8307i	0.585759	−	1.49172i
$196$		0			0
$197$	−22.3886			−1.59512			−0.797561	−	0.603239i	$-0.793877\pi$
$197$	−22.3886			−1.59512			−0.797561	+	0.603239i	$0.793877\pi$
$198$		0			0
$199$	−11.3709	−	19.6949i	−0.806060	−	1.39614i	−0.915573	−	0.402152i	$-0.868262\pi$
$199$	−11.3709	−	19.6949i	−0.806060	−	1.39614i	0.109513	−	0.993985i	$-0.465071\pi$
$200$		0			0
$201$	0.923488	−	0.139027i	0.0651378	−	0.00980620i
$202$		0			0
$203$	0.328509	+	2.09273i	0.0230568	+	0.146881i
$204$		0			0
$205$	6.28547	+	10.8868i	0.438997	+	0.760364i
$206$		0			0
$207$	3.67659	−	16.0821i	0.255541	−	1.11778i
$208$		0			0
$209$	1.26065	−	2.18351i	0.0872011	−	0.151037i
$210$		0			0
$211$	−2.95868	−	5.12458i	−0.203684	−	0.352791i	0.746029	−	0.665914i	$-0.231958\pi$
$211$	−2.95868	−	5.12458i	−0.203684	−	0.352791i	−0.949713	+	0.313123i	$0.898625\pi$
$212$		0			0
$213$	4.17728	+	5.24004i	0.286223	+	0.359042i
$214$		0			0
$215$	−14.8682	+	25.7525i	−1.01400	+	1.75631i
$216$		0			0
$217$	4.06492	+	25.8952i	0.275945	+	1.75788i
$218$		0			0
$219$	3.27860	−	8.34940i	0.221547	−	0.564200i
$220$		0			0
$221$	−1.56220	+	2.70581i	−0.105085	+	0.182012i
$222$		0			0
$223$	−1.20124	+	2.08062i	−0.0804412	+	0.139328i	−0.903440	−	0.428716i	$-0.858966\pi$
$223$	−1.20124	+	2.08062i	−0.0804412	+	0.139328i	0.822998	+	0.568044i	$0.192300\pi$
$224$		0			0
$225$	−4.41948	+	19.3316i	−0.294632	+	1.28877i
$226$		0			0
$227$	−6.97702			−0.463081			−0.231540	−	0.972825i	$-0.574377\pi$
$227$	−6.97702			−0.463081			−0.231540	+	0.972825i	$0.574377\pi$
$228$		0			0
$229$	−19.2156			−1.26981			−0.634903	−	0.772592i	$-0.718960\pi$
$229$	−19.2156			−1.26981			−0.634903	+	0.772592i	$0.718960\pi$
$230$		0			0
$231$	24.1415	+	5.35974i	1.58839	+	0.352645i
$232$		0			0
$233$	12.9002	−	22.3439i	0.845122	−	1.46379i	−0.0403930	−	0.999184i	$-0.512861\pi$
$233$	12.9002	−	22.3439i	0.845122	−	1.46379i	0.885515	−	0.464611i	$-0.153806\pi$
$234$		0			0
$235$	17.8872	+	30.9815i	1.16683	+	2.02101i
$236$		0			0
$237$	−4.95632	+	12.6220i	−0.321948	+	0.819885i
$238$		0			0
$239$	−6.65732	−	11.5308i	−0.430626	−	0.745866i	0.566301	−	0.824198i	$-0.308374\pi$
$239$	−6.65732	−	11.5308i	−0.430626	−	0.745866i	−0.996927	+	0.0783322i	$0.975041\pi$
$240$		0			0
$241$	1.85648			0.119586			0.0597931	−	0.998211i	$-0.480956\pi$
$241$	1.85648			0.119586			0.0597931	+	0.998211i	$0.480956\pi$
$242$		0			0
$243$	3.45537	+	15.2007i	0.221662	+	0.975124i
$244$		0			0
$245$	5.02312	−	23.3166i	0.320915	−	1.48964i
$246$		0			0
$247$	1.77169			0.112730
$248$		0			0
$249$	13.0040	−	1.95769i	0.824095	−	0.124064i
$250$		0			0
$251$	11.6947			0.738165			0.369083	−	0.929397i	$-0.379672\pi$
$251$	11.6947			0.738165			0.369083	+	0.929397i	$0.379672\pi$
$252$		0			0
$253$	−29.6746			−1.86563
$254$		0			0
$255$	1.77736	−	4.52628i	0.111302	−	0.283447i
$256$		0			0
$257$	2.93188			0.182886			0.0914429	−	0.995810i	$-0.470852\pi$
$257$	2.93188			0.182886			0.0914429	+	0.995810i	$0.470852\pi$
$258$		0			0
$259$	3.56309	+	22.6983i	0.221399	+	1.41040i
$260$		0			0
$261$	1.76021	+	1.63439i	0.108954	+	0.101166i
$262$		0			0
$263$	−28.2840			−1.74406			−0.872032	−	0.489449i	$-0.837198\pi$
$263$	−28.2840			−1.74406			−0.872032	+	0.489449i	$0.837198\pi$
$264$		0			0
$265$	−16.0766	−	27.8455i	−0.987579	−	1.71054i
$266$		0			0
$267$	12.7942	−	1.92610i	0.782990	−	0.117876i
$268$		0			0
$269$	4.79128	+	8.29874i	0.292129	+	0.505983i	0.974313	−	0.225198i	$-0.0723028\pi$
$269$	4.79128	+	8.29874i	0.292129	+	0.505983i	−0.682184	+	0.731181i	$0.738970\pi$
$270$		0			0
$271$	9.14220	−	15.8348i	0.555349	−	0.961893i	−0.442527	−	0.896755i	$-0.645918\pi$
$271$	9.14220	−	15.8348i	0.555349	−	0.961893i	0.997876	−	0.0651381i	$-0.0207488\pi$
$272$		0			0
$273$	5.22031	+	16.5743i	0.315948	+	1.00312i
$274$		0			0
$275$	35.6707			2.15102
$276$		0			0
$277$	4.65553			0.279723			0.139862	−	0.990171i	$-0.455334\pi$
$277$	4.65553			0.279723			0.139862	+	0.990171i	$0.455334\pi$
$278$		0			0
$279$	21.7806	+	20.2237i	1.30397	+	1.21076i
$280$		0			0
$281$	−9.06669	+	15.7040i	−0.540873	+	0.936820i	0.457981	+	0.888962i	$0.348573\pi$
$281$	−9.06669	+	15.7040i	−0.540873	+	0.936820i	−0.998854	+	0.0478580i	$0.984760\pi$
$282$		0			0
$283$	8.30969	−	14.3928i	0.493960	−	0.855564i	−0.506016	−	0.862524i	$-0.668882\pi$
$283$	8.30969	−	14.3928i	0.493960	−	0.855564i	0.999976	+	0.00696045i	$0.00221560\pi$
$284$		0			0
$285$	−2.72669	+	0.410490i	−0.161515	+	0.0243153i
$286$		0			0
$287$	−9.10796	−	3.51059i	−0.537626	−	0.207223i
$288$		0			0
$289$	8.16055	−	14.1345i	0.480032	−	0.831441i
$290$		0			0
$291$	11.0473	−	1.66311i	0.647602	−	0.0974935i
$292$		0			0
$293$	1.94284	+	3.36510i	0.113502	+	0.196591i	0.917180	−	0.398473i	$-0.130460\pi$
$293$	1.94284	+	3.36510i	0.113502	+	0.196591i	−0.803678	+	0.595064i	$0.797127\pi$
$294$		0			0
$295$	2.82928	−	4.90046i	0.164727	−	0.285316i
$296$		0			0
$297$	25.2700	−	12.1529i	1.46631	−	0.705184i
$298$		0			0
$299$	−10.4260	−	18.0583i	−0.602950	−	1.04434i
$300$		0			0
$301$	−3.58069	−	22.8104i	−0.206388	−	1.31477i
$302$		0			0
$303$	17.4902	+	21.9399i	1.00479	+	1.26042i
$304$		0			0
$305$	−1.61647	−	2.79981i	−0.0925588	−	0.160317i
$306$		0			0
$307$	−3.48452			−0.198872			−0.0994361	−	0.995044i	$-0.531704\pi$
$307$	−3.48452			−0.198872			−0.0994361	+	0.995044i	$0.531704\pi$
$308$		0			0
$309$	16.9494	+	21.2616i	0.964219	+	1.20953i
$310$		0			0
$311$	6.49273	−	11.2457i	0.368169	−	0.637687i	−0.621110	−	0.783723i	$-0.713318\pi$
$311$	6.49273	−	11.2457i	0.368169	−	0.637687i	0.989279	+	0.146036i	$0.0466515\pi$
$312$		0			0
$313$	−7.52193	−	13.0284i	−0.425164	−	0.736406i	0.571271	−	0.820761i	$-0.306450\pi$
$313$	−7.52193	−	13.0284i	−0.425164	−	0.736406i	−0.996436	+	0.0843548i	$0.973117\pi$
$314$		0			0
$315$	−11.8744	−	24.2989i	−0.669048	−	1.36909i
$316$		0			0
$317$	4.22919	+	7.32518i	0.237535	+	0.411423i	0.960006	−	0.279978i	$-0.0903272\pi$
$317$	4.22919	+	7.32518i	0.237535	+	0.411423i	−0.722471	+	0.691401i	$0.756994\pi$
$318$		0			0
$319$	2.16035	−	3.74183i	0.120956	−	0.209502i
$320$		0			0
$321$	−9.76349	+	1.46985i	−0.544945	+	0.0820390i
$322$		0			0
$323$	0.384968			0.0214202
$324$		0			0
$325$	12.5326	+	21.7072i	0.695186	+	1.20410i
$326$		0			0
$327$	−2.77535	+	7.06781i	−0.153477	+	0.390851i
$328$		0			0
$329$	−25.9194	−	9.99041i	−1.42898	−	0.550789i
$330$		0			0
$331$	−5.01224	−	8.68146i	−0.275498	−	0.477176i	0.694763	−	0.719239i	$-0.255509\pi$
$331$	−5.01224	−	8.68146i	−0.275498	−	0.477176i	−0.970261	+	0.242063i	$0.922176\pi$
$332$		0			0
$333$	19.0917	+	17.7270i	1.04622	+	0.971434i
$334$		0			0
$335$	−0.918597	+	1.59106i	−0.0501883	+	0.0869287i
$336$		0			0
$337$	−9.33242	−	16.1642i	−0.508369	−	0.880522i	−0.999953	−	0.00969119i	$-0.996915\pi$
$337$	−9.33242	−	16.1642i	−0.508369	−	0.880522i	0.491584	−	0.870830i	$-0.336418\pi$
$338$		0			0
$339$	−6.28778	+	16.0127i	−0.341505	+	0.869690i
$340$		0			0
$341$	26.7318	−	46.3009i	1.44761	−	2.50733i
$342$		0			0
$343$	8.33992	+	16.5362i	0.450313	+	0.892871i
$344$		0			0
$345$	20.2300	+	25.3767i	1.08914	+	1.36624i
$346$		0			0
$347$	−7.90240	+	13.6874i	−0.424223	+	0.734776i	−0.996348	−	0.0853910i	$-0.972786\pi$
$347$	−7.90240	+	13.6874i	−0.424223	+	0.734776i	0.572125	+	0.820167i	$0.306119\pi$
$348$		0			0
$349$	4.51578	−	7.82156i	0.241724	−	0.418678i	−0.719481	−	0.694512i	$-0.755620\pi$
$349$	4.51578	−	7.82156i	0.241724	−	0.418678i	0.961205	+	0.275833i	$0.0889538\pi$
$350$		0			0
$351$	16.2740	+	11.1080i	0.868643	+	0.592904i
$352$		0			0
$353$	14.4788			0.770627			0.385314	−	0.922786i	$-0.374093\pi$
$353$	14.4788			0.770627			0.385314	+	0.922786i	$0.374093\pi$
$354$		0			0
$355$	−13.1831			−0.699687
$356$		0			0
$357$	1.13432	+	3.60141i	0.0600345	+	0.190607i
$358$		0			0
$359$	7.85517	−	13.6056i	0.414580	−	0.718074i	−0.580804	−	0.814043i	$-0.697262\pi$
$359$	7.85517	−	13.6056i	0.414580	−	0.718074i	0.995384	+	0.0959695i	$0.0305951\pi$
$360$		0			0
$361$	9.39085	+	16.2654i	0.494255	+	0.856075i
$362$		0			0
$363$	−19.5647	−	24.5423i	−1.02688	−	1.28813i
$364$		0			0
$365$	8.82312	+	15.2821i	0.461823	+	0.799902i
$366$		0			0
$367$	−18.8589			−0.984428			−0.492214	−	0.870474i	$-0.663812\pi$
$367$	−18.8589			−0.984428			−0.492214	+	0.870474i	$0.663812\pi$
$368$		0			0
$369$	−10.5775	+	3.25864i	−0.550641	+	0.169638i
$370$		0			0
$371$	23.2958	+	8.97917i	1.20946	+	0.466175i
$372$		0			0
$373$	−33.7137			−1.74563			−0.872814	−	0.488052i	$-0.837708\pi$
$373$	−33.7137			−1.74563			−0.872814	+	0.488052i	$0.837708\pi$
$374$		0			0
$375$	−5.92336	−	7.43034i	−0.305881	−	0.383701i
$376$		0			0
$377$	3.03609			0.156367
$378$		0			0
$379$	−33.7263			−1.73241			−0.866203	−	0.499693i	$-0.833446\pi$
$379$	−33.7263			−1.73241			−0.866203	+	0.499693i	$0.833446\pi$
$380$		0			0
$381$	−17.3960	−	21.8218i	−0.891224	−	1.11796i
$382$		0			0
$383$	−18.3240			−0.936314			−0.468157	−	0.883645i	$-0.655082\pi$
$383$	−18.3240			−0.936314			−0.468157	+	0.883645i	$0.655082\pi$
$384$		0			0
$385$	−37.8490	+	30.5635i	−1.92897	+	1.55766i
$386$		0			0
$387$	−19.1860	−	17.8146i	−0.975280	−	0.905567i
$388$		0			0
$389$	4.27488			0.216745			0.108373	−	0.994110i	$-0.465436\pi$
$389$	4.27488			0.216745			0.108373	+	0.994110i	$0.465436\pi$
$390$		0			0
$391$	−2.26545	−	3.92388i	−0.114569	−	0.198439i
$392$		0			0
$393$	−15.0516	−	18.8809i	−0.759250	−	0.952414i
$394$		0			0
$395$	−13.3381	−	23.1023i	−0.671112	−	1.16240i
$396$		0			0
$397$	17.9312	−	31.0577i	0.899939	−	1.55874i	0.0723687	−	0.997378i	$-0.476944\pi$
$397$	17.9312	−	31.0577i	0.899939	−	1.55874i	0.827570	−	0.561362i	$-0.189723\pi$
$398$		0			0
$399$	1.44697	−	1.57813i	0.0724391	−	0.0790052i
$400$		0			0
$401$	−23.4015			−1.16861			−0.584307	−	0.811533i	$-0.698634\pi$
$401$	−23.4015			−1.16861			−0.584307	+	0.811533i	$0.698634\pi$
$402$		0			0
$403$	37.5682			1.87140
$404$		0			0
$405$	−27.6200	−	13.3251i	−1.37245	−	0.662128i
$406$		0			0
$407$	23.4316	−	40.5848i	1.16146	−	2.01171i
$408$		0			0
$409$	−17.4016	+	30.1404i	−0.860453	+	1.49035i	0.0110389	+	0.999939i	$0.496486\pi$
$409$	−17.4016	+	30.1404i	−0.860453	+	1.49035i	−0.871492	+	0.490410i	$0.836847\pi$
$410$		0			0
$411$	12.0405	+	15.1038i	0.593915	+	0.745015i
$412$		0			0
$413$	0.681372	+	4.34062i	0.0335281	+	0.213588i
$414$		0			0
$415$	−12.9351	+	22.4043i	−0.634961	+	1.09978i
$416$		0			0
$417$	4.02302	−	10.2452i	0.197008	−	0.501709i
$418$		0			0
$419$	−2.90894	−	5.03843i	−0.142111	−	0.246143i	0.786180	−	0.617997i	$-0.212056\pi$
$419$	−2.90894	−	5.03843i	−0.142111	−	0.246143i	−0.928291	+	0.371854i	$0.878722\pi$
$420$		0			0
$421$	−17.7765	+	30.7898i	−0.866375	+	1.50061i	−0.000699237		1.00000i	$0.500223\pi$
$421$	−17.7765	+	30.7898i	−0.866375	+	1.50061i	−0.865676	+	0.500605i	$0.833111\pi$
$422$		0			0
$423$	−30.1013	+	9.27341i	−1.46358	+	0.450889i
$424$		0			0
$425$	2.72321	+	4.71674i	0.132095	+	0.228795i
$426$		0			0
$427$	2.34234	+	0.902837i	0.113354	+	0.0436913i
$428$		0			0
$429$	12.9545	−	32.9904i	0.625449	−	1.59279i
$430$		0			0
$431$	2.48374	+	4.30196i	0.119637	+	0.207218i	0.919624	−	0.392800i	$-0.128493\pi$
$431$	2.48374	+	4.30196i	0.119637	+	0.207218i	−0.799987	+	0.600018i	$0.795160\pi$
$432$		0			0
$433$	22.9062			1.10080			0.550401	−	0.834900i	$-0.314475\pi$
$433$	22.9062			1.10080			0.550401	+	0.834900i	$0.314475\pi$
$434$		0			0
$435$	−4.67265	+	0.703446i	−0.224036	+	0.0337277i
$436$		0			0
$437$	−1.28462	+	2.22503i	−0.0614519	+	0.106438i
$438$		0			0
$439$	4.02947	+	6.97925i	0.192316	+	0.333101i	0.946017	−	0.324116i	$-0.105067\pi$
$439$	4.02947	+	6.97925i	0.192316	+	0.333101i	−0.753701	+	0.657217i	$0.771733\pi$
$440$		0			0
$441$	19.0271	+	8.88655i	0.906051	+	0.423169i
$442$		0			0
$443$	−1.88883	−	3.27155i	−0.0897410	−	0.155436i	0.817661	−	0.575701i	$-0.195271\pi$
$443$	−1.88883	−	3.27155i	−0.0897410	−	0.155436i	−0.907402	+	0.420265i	$0.861937\pi$
$444$		0			0
$445$	−12.7264	+	22.0428i	−0.603290	+	1.04493i
$446$		0			0
$447$	12.4491	+	15.6164i	0.588824	+	0.738629i
$448$		0			0
$449$	33.5069			1.58129			0.790644	−	0.612276i	$-0.209746\pi$
$449$	33.5069			1.58129			0.790644	+	0.612276i	$0.209746\pi$
$450$		0			0
$451$	9.95457	+	17.2418i	0.468742	+	0.811885i
$452$		0			0
$453$	0.749980	+	0.940786i	0.0352372	+	0.0442020i
$454$		0			0
$455$	−31.8973	−	12.2945i	−1.49537	−	0.576376i
$456$		0			0
$457$	−0.369753	−	0.640431i	−0.0172963	−	0.0299581i	0.857248	−	0.514904i	$-0.172173\pi$
$457$	−0.369753	−	0.640431i	−0.0172963	−	0.0299581i	−0.874544	+	0.484946i	$0.838839\pi$
$458$		0			0
$459$	3.53617	+	2.41366i	0.165054	+	0.112660i
$460$		0			0
$461$	−3.30465	+	5.72383i	−0.153913	+	0.266585i	−0.932663	−	0.360750i	$-0.882521\pi$
$461$	−3.30465	+	5.72383i	−0.153913	+	0.266585i	0.778750	+	0.627335i	$0.215854\pi$
$462$		0			0
$463$	5.96606	+	10.3335i	0.277266	+	0.480239i	0.970704	−	0.240277i	$-0.0772383\pi$
$463$	5.96606	+	10.3335i	0.277266	+	0.480239i	−0.693438	+	0.720516i	$0.743905\pi$
$464$		0			0
$465$	−57.8187	+	8.70435i	−2.68128	+	0.403654i
$466$		0			0
$467$	5.11184	−	8.85396i	0.236548	−	0.409713i	−0.723174	−	0.690666i	$-0.757317\pi$
$467$	5.11184	−	8.85396i	0.236548	−	0.409713i	0.959721	+	0.280954i	$0.0906507\pi$
$468$		0			0
$469$	−0.221225	−	1.40929i	−0.0102152	−	0.0650749i
$470$		0			0
$471$	−6.93399	+	1.04388i	−0.319501	+	0.0480995i
$472$		0			0
$473$	−23.5474	+	40.7853i	−1.08271	+	1.87531i
$474$		0			0
$475$	1.54419	−	2.67462i	0.0708524	−	0.122720i
$476$		0			0
$477$	27.0545	−	8.33475i	1.23874	−	0.381622i
$478$		0			0
$479$	2.03791			0.0931145			0.0465573	−	0.998916i	$-0.485175\pi$
$479$	2.03791			0.0931145			0.0465573	+	0.998916i	$0.485175\pi$
$480$		0			0
$481$	32.9302			1.50149
$482$		0			0
$483$	−24.6006	−	5.46165i	−1.11936	−	0.248514i
$484$		0			0
$485$	−10.9888	+	19.0331i	−0.498974	+	0.864248i
$486$		0			0
$487$	−17.5958	−	30.4767i	−0.797340	−	1.38103i	−0.921343	−	0.388751i	$-0.872907\pi$
$487$	−17.5958	−	30.4767i	−0.797340	−	1.38103i	0.124003	−	0.992282i	$-0.460427\pi$
$488$		0			0
$489$	17.3319	−	2.60925i	0.783778	−	0.117994i
$490$		0			0
$491$	17.5708	+	30.4335i	0.792958	+	1.37344i	0.924128	+	0.382083i	$0.124793\pi$
$491$	17.5708	+	30.4335i	0.792958	+	1.37344i	−0.131170	+	0.991360i	$0.541873\pi$
$492$		0			0
$493$	0.659710			0.0297118
$494$		0			0
$495$	−12.2937	+	53.7749i	−0.552561	+	2.41700i
$496$		0			0
$497$	7.96405	−	6.43106i	0.357236	−	0.288472i
$498$		0			0
$499$	−4.65266			−0.208282			−0.104141	−	0.994563i	$-0.533209\pi$
$499$	−4.65266			−0.208282			−0.104141	+	0.994563i	$0.533209\pi$
$500$		0			0
$501$	11.0962	−	28.2580i	0.495742	−	1.26248i
$502$		0			0
$503$	−12.0660			−0.537997			−0.268999	−	0.963141i	$-0.586693\pi$
$503$	−12.0660			−0.537997			−0.268999	+	0.963141i	$0.586693\pi$
$504$		0			0
$505$	−55.1974			−2.45625
$506$		0			0
$507$	2.36183	−	0.355564i	0.104893	−	0.0157911i
$508$		0			0
$509$	22.3477			0.990546			0.495273	−	0.868737i	$-0.335068\pi$
$509$	22.3477			0.990546			0.495273	+	0.868737i	$0.335068\pi$
$510$		0			0
$511$	−12.7851	−	4.92792i	−0.565581	−	0.217998i
$512$		0			0
$513$	0.182706	−	2.42087i	0.00806667	−	0.106884i
$514$		0			0
$515$	−53.4908			−2.35709
$516$		0			0
$517$	28.3287	+	49.0667i	1.24589	+	2.15795i
$518$		0			0
$519$	4.96022	−	12.6319i	0.217730	−	0.554479i
$520$		0			0
$521$	0.854260	+	1.47962i	0.0374258	+	0.0648234i	0.884132	−	0.467238i	$-0.154751\pi$
$521$	0.854260	+	1.47962i	0.0374258	+	0.0648234i	−0.846706	+	0.532061i	$0.821418\pi$
$522$		0			0
$523$	10.6036	−	18.3659i	0.463662	−	0.803087i	−0.535478	−	0.844549i	$-0.679868\pi$
$523$	10.6036	−	18.3659i	0.463662	−	0.803087i	0.999140	+	0.0414627i	$0.0132018\pi$
$524$		0			0
$525$	29.5713	+	6.56523i	1.29060	+	0.286530i
$526$		0			0
$527$	8.16316			0.355593
$528$		0			0
$529$	7.23889			0.314735
$530$		0			0
$531$	3.65092	+	3.38995i	0.158436	+	0.147111i
$532$		0			0
$533$	−6.99494	+	12.1156i	−0.302984	+	0.524784i
$534$		0			0
$535$	9.71179	−	16.8213i	0.419877	−	0.727248i
$536$		0			0
$537$	5.84858	−	14.8942i	0.252385	−	0.642733i
$538$		0			0
$539$	7.95532	−	36.9275i	0.342660	−	1.59058i
$540$		0			0
$541$	4.79443	−	8.30419i	0.206129	−	0.357025i	−0.744363	−	0.667775i	$-0.767247\pi$
$541$	4.79443	−	8.30419i	0.206129	−	0.357025i	0.950492	+	0.310750i	$0.100580\pi$
$542$		0			0
$543$	−10.2135	−	12.8119i	−0.438303	−	0.549813i
$544$		0			0
$545$	−7.46882	−	12.9364i	−0.319929	−	0.554133i
$546$		0			0
$547$	5.65927	−	9.80214i	0.241973	−	0.419109i	−0.719303	−	0.694696i	$-0.755539\pi$
$547$	5.65927	−	9.80214i	0.241973	−	0.419109i	0.961276	+	0.275587i	$0.0888722\pi$
$548$		0			0
$549$	2.72027	−	0.838042i	0.116098	−	0.0357668i
$550$		0			0
$551$	−0.187044	−	0.323969i	−0.00796834	−	0.0138016i
$552$		0			0
$553$	19.3275	+	7.44964i	0.821891	+	0.316791i
$554$		0			0
$555$	−50.6807	+	7.62975i	−2.15127	+	0.323865i
$556$		0			0
$557$	1.68102	+	2.91162i	0.0712272	+	0.123369i	0.899439	−	0.437045i	$-0.143975\pi$
$557$	1.68102	+	2.91162i	0.0712272	+	0.123369i	−0.828212	+	0.560415i	$0.810642\pi$
$558$		0			0
$559$	−33.0929			−1.39968
$560$		0			0
$561$	2.81487	−	7.16846i	0.118844	−	0.302653i
$562$		0			0
$563$	−9.54570	+	16.5336i	−0.402303	+	0.696810i	−0.994003	−	0.109348i	$-0.965124\pi$
$563$	−9.54570	+	16.5336i	−0.402303	+	0.696810i	0.591700	+	0.806158i	$0.298457\pi$
$564$		0			0
$565$	−16.9212	−	29.3084i	−0.711880	−	1.23301i
$566$		0			0
$567$	23.1858	−	5.42392i	0.973712	−	0.227783i
$568$		0			0
$569$	−1.31363	−	2.27527i	−0.0550702	−	0.0953844i	0.837176	−	0.546933i	$-0.184205\pi$
$569$	−1.31363	−	2.27527i	−0.0550702	−	0.0953844i	−0.892246	+	0.451549i	$0.850872\pi$
$570$		0			0
$571$	−4.99113	+	8.64489i	−0.208872	+	0.361777i	−0.951360	−	0.308083i	$-0.900313\pi$
$571$	−4.99113	+	8.64489i	−0.208872	+	0.361777i	0.742487	+	0.669860i	$0.233646\pi$
$572$		0			0
$573$	−0.0286761	+	0.0730278i	−0.00119796	+	0.00305078i
$574$		0			0
$575$	−36.3489			−1.51586
$576$		0			0
$577$	6.05761	+	10.4921i	0.252182	+	0.436791i	0.964126	−	0.265444i	$-0.0855187\pi$
$577$	6.05761	+	10.4921i	0.252182	+	0.436791i	−0.711945	+	0.702236i	$0.752185\pi$
$578$		0			0
$579$	−32.2337	+	4.85264i	−1.33959	+	0.201669i
$580$		0			0
$581$	−3.11515	−	19.8448i	−0.129238	−	0.823299i
$582$		0			0
$583$	−25.4612	−	44.1001i	−1.05450	−	1.82644i
$584$		0			0
$585$	−37.0437	+	11.4122i	−1.53157	+	0.471835i
$586$		0			0
$587$	−15.1857	+	26.3025i	−0.626782	+	1.08562i	0.361411	+	0.932407i	$0.382295\pi$
$587$	−15.1857	+	26.3025i	−0.626782	+	1.08562i	−0.988193	+	0.153212i	$0.951038\pi$
$588$		0			0
$589$	−2.31446	−	4.00875i	−0.0953655	−	0.165178i
$590$		0			0
$591$	24.1725	+	30.3223i	0.994322	+	1.24729i
$592$		0			0
$593$	−20.5788	+	35.6434i	−0.845068	+	1.46370i	0.0404940	+	0.999180i	$0.487107\pi$
$593$	−20.5788	+	35.6434i	−0.845068	+	1.46370i	−0.885562	+	0.464521i	$0.846226\pi$
$594$		0			0
$595$	−6.93093	−	2.67147i	−0.284141	−	0.109520i
$596$		0			0
$597$	−14.3972	+	36.6645i	−0.589238	+	1.50058i
$598$		0			0
$599$	4.05521	−	7.02382i	0.165691	−	0.286986i	−0.771209	−	0.636582i	$-0.780348\pi$
$599$	4.05521	−	7.02382i	0.165691	−	0.286986i	0.936901	+	0.349596i	$0.113681\pi$
$600$		0			0
$601$	15.8320	−	27.4218i	0.645801	−	1.11856i	−0.338315	−	0.941033i	$-0.609857\pi$
$601$	15.8320	−	27.4218i	0.645801	−	1.11856i	0.984116	−	0.177527i	$-0.0568098\pi$
$602$		0			0
$603$	−1.18536	−	1.10063i	−0.0482717	−	0.0448212i
$604$		0			0
$605$	61.7445			2.51027
$606$		0			0
$607$	23.0261			0.934601			0.467300	−	0.884099i	$-0.345227\pi$
$607$	23.0261			0.934601			0.467300	+	0.884099i	$0.345227\pi$
$608$		0			0
$609$	2.47963	−	2.70440i	0.100480	−	0.109588i
$610$		0			0
$611$	−19.9062	+	34.4785i	−0.805317	+	1.39485i
$612$		0			0
$613$	11.4750	+	19.8752i	0.463470	+	0.802753i	0.999131	−	0.0416796i	$-0.0132709\pi$
$613$	11.4750	+	19.8752i	0.463470	+	0.802753i	−0.535661	+	0.844433i	$0.679938\pi$
$614$		0			0
$615$	7.95833	−	20.2670i	0.320911	−	0.817244i
$616$		0			0
$617$	11.1183	+	19.2574i	0.447605	+	0.775274i	0.998230	−	0.0594788i	$-0.0189439\pi$
$617$	11.1183	+	19.2574i	0.447605	+	0.775274i	−0.550625	+	0.834753i	$0.685611\pi$
$618$		0			0
$619$	5.50603			0.221306			0.110653	−	0.993859i	$-0.464706\pi$
$619$	5.50603			0.221306			0.110653	+	0.993859i	$0.464706\pi$
$620$		0			0
$621$	−25.7505	+	12.3840i	−1.03333	+	0.496953i
$622$		0			0
$623$	−3.06488	−	19.5245i	−0.122792	−	0.782234i
$624$		0			0
$625$	−14.3570			−0.574280
$626$		0			0
$627$	−4.31836	+	0.650110i	−0.172459	+	0.0259629i
$628$		0			0
$629$	7.15538			0.285303
$630$		0			0
$631$	32.9276			1.31083			0.655413	−	0.755271i	$-0.272495\pi$
$631$	32.9276			1.31083			0.655413	+	0.755271i	$0.272495\pi$
$632$		0			0
$633$	−3.74612	+	9.54002i	−0.148895	+	0.379182i
$634$		0			0
$635$	54.9002			2.17865
$636$		0			0
$637$	25.2670	−	8.13305i	1.00112	−	0.322243i
$638$		0			0
$639$	2.58679	−	11.3151i	0.102332	−	0.447619i
$640$		0			0
$641$	−1.89176			−0.0747201			−0.0373600	−	0.999302i	$-0.511895\pi$
$641$	−1.89176			−0.0747201			−0.0373600	+	0.999302i	$0.511895\pi$
$642$		0			0
$643$	−22.8742	−	39.6193i	−0.902070	−	1.56243i	−0.824803	−	0.565421i	$-0.808714\pi$
$643$	−22.8742	−	39.6193i	−0.902070	−	1.56243i	−0.0772675	−	0.997010i	$-0.524620\pi$
$644$		0			0
$645$	50.9311	−	7.66745i	2.00541	−	0.301906i
$646$		0			0
$647$	−8.98067	−	15.5550i	−0.353066	−	0.611529i	0.633719	−	0.773564i	$-0.281528\pi$
$647$	−8.98067	−	15.5550i	−0.353066	−	0.611529i	−0.986785	+	0.162035i	$0.948194\pi$
$648$		0			0
$649$	4.48085	−	7.76106i	0.175889	−	0.304648i
$650$		0			0
$651$	30.6827	−	33.4638i	1.20255	−	1.31155i
$652$		0			0
$653$	−22.1482			−0.866726			−0.433363	−	0.901219i	$-0.642673\pi$
$653$	−22.1482			−0.866726			−0.433363	+	0.901219i	$0.642673\pi$
$654$		0			0
$655$	47.5013			1.85603
$656$		0			0
$657$	−14.8479	+	4.57425i	−0.579274	+	0.178459i
$658$		0			0
$659$	5.39543	−	9.34515i	0.210176	−	0.364035i	−0.741594	−	0.670850i	$-0.765930\pi$
$659$	5.39543	−	9.34515i	0.210176	−	0.364035i	0.951769	+	0.306814i	$0.0992630\pi$
$660$		0			0
$661$	2.56954	−	4.45057i	0.0999434	−	0.173107i	−0.811718	−	0.584050i	$-0.801467\pi$
$661$	2.56954	−	4.45057i	0.0999434	−	0.173107i	0.911661	+	0.410943i	$0.134800\pi$
$662$		0			0
$663$	5.35131	−	0.805616i	0.207828	−	0.0312875i
$664$		0			0
$665$	0.653187	+	4.16106i	0.0253295	+	0.161359i
$666$		0			0
$667$	−2.20142	+	3.81298i	−0.0852395	+	0.147639i
$668$		0			0
$669$	4.11486	−	0.619474i	0.159090	−	0.0239503i
$670$		0			0
$671$	−2.56007	−	4.43417i	−0.0988304	−	0.171179i
$672$		0			0
$673$	10.9290	−	18.9295i	0.421281	−	0.729680i	−0.574784	−	0.818305i	$-0.694914\pi$
$673$	10.9290	−	18.9295i	0.421281	−	0.729680i	0.996065	+	0.0886254i	$0.0282474\pi$
$674$		0			0
$675$	30.9536	−	14.8863i	1.19140	−	0.572974i
$676$		0			0
$677$	5.86482	+	10.1582i	0.225403	+	0.390410i	0.956440	−	0.291928i	$-0.0942967\pi$
$677$	5.86482	+	10.1582i	0.225403	+	0.390410i	−0.731037	+	0.682338i	$0.760963\pi$
$678$		0			0
$679$	−2.64641	−	16.8587i	−0.101560	−	0.646976i
$680$		0			0
$681$	7.53293	+	9.44941i	0.288662	+	0.362102i
$682$		0			0
$683$	0.260358	+	0.450954i	0.00996234	+	0.0172553i	0.870964	−	0.491348i	$-0.163496\pi$
$683$	0.260358	+	0.450954i	0.00996234	+	0.0172553i	−0.861001	+	0.508603i	$0.830162\pi$
$684$		0			0
$685$	−37.9987			−1.45186
$686$		0			0
$687$	20.7467	+	26.0249i	0.791536	+	0.992913i
$688$		0			0
$689$	17.8912	−	30.9885i	0.681602	−	1.18057i
$690$		0			0
$691$	23.0956	+	40.0028i	0.878599	+	1.52178i	0.852879	+	0.522108i	$0.174854\pi$
$691$	23.0956	+	40.0028i	0.878599	+	1.52178i	0.0257196	+	0.999669i	$0.491812\pi$
$692$		0			0
$693$	−18.8060	−	38.4831i	−0.714381	−	1.46185i
$694$		0			0
$695$	10.8265	+	18.7520i	0.410671	+	0.711303i
$696$		0			0
$697$	−1.51993	+	2.63259i	−0.0575713	+	0.0997164i
$698$		0			0
$699$	−44.1898	+	6.65257i	−1.67141	+	0.251623i
$700$		0			0
$701$	−32.7166			−1.23569			−0.617844	−	0.786301i	$-0.711994\pi$
$701$	−32.7166			−1.23569			−0.617844	+	0.786301i	$0.711994\pi$
$702$		0			0
$703$	−2.02872	−	3.51385i	−0.0765148	−	0.132527i
$704$		0			0
$705$	22.6478	−	57.6757i	0.852965	−	2.17219i
$706$		0			0
$707$	33.3453	−	26.9267i	1.25408	−	1.01268i
$708$		0			0
$709$	16.7275	+	28.9730i	0.628216	+	1.08810i	0.987910	+	0.155032i	$0.0495480\pi$
$709$	16.7275	+	28.9730i	0.628216	+	1.08810i	−0.359693	+	0.933071i	$0.617119\pi$
$710$		0			0
$711$	22.4459	−	6.91499i	0.841789	−	0.259332i
$712$		0			0
$713$	−27.2401	+	47.1813i	−1.02015	+	1.76695i
$714$		0			0
$715$	34.8622	+	60.3831i	1.30377	+	2.25820i
$716$		0			0
$717$	−8.42914	+	21.4660i	−0.314792	+	0.801661i
$718$		0			0
$719$	−9.42685	+	16.3278i	−0.351562	+	0.608924i	−0.986523	−	0.163621i	$-0.947683\pi$
$719$	−9.42685	+	16.3278i	−0.351562	+	0.608924i	0.634961	+	0.772544i	$0.281016\pi$
$720$		0			0
$721$	32.3143	−	26.0942i	1.20345	−	0.971798i
$722$		0			0
$723$	−2.00440	−	2.51434i	−0.0745443	−	0.0935094i
$724$		0			0
$725$	2.64624	−	4.58342i	0.0982789	−	0.170224i
$726$		0			0
$727$	19.3107	−	33.4471i	0.716194	−	1.24048i	−0.246303	−	0.969193i	$-0.579216\pi$
$727$	19.3107	−	33.4471i	0.716194	−	1.24048i	0.962497	−	0.271291i	$-0.0874507\pi$
$728$		0			0
$729$	16.8565	−	21.0916i	0.624316	−	0.781172i
$730$		0			0
$731$	−7.19073			−0.265959
$732$		0			0
$733$	−18.7118			−0.691137			−0.345569	−	0.938394i	$-0.612314\pi$
$733$	−18.7118			−0.691137			−0.345569	+	0.938394i	$0.612314\pi$
$734$		0			0
$735$	−37.0025	+	18.3713i	−1.36486	+	0.677635i
$736$		0			0
$737$	−1.45482	+	2.51982i	−0.0535890	+	0.0928189i
$738$		0			0
$739$	−7.15949	−	12.4006i	−0.263366	−	0.456163i	0.703768	−	0.710430i	$-0.251499\pi$
$739$	−7.15949	−	12.4006i	−0.263366	−	0.456163i	−0.967134	+	0.254266i	$0.918166\pi$
$740$		0			0
$741$	−1.91285	−	2.39950i	−0.0702703	−	0.0881480i
$742$		0			0
$743$	−14.2068	−	24.6069i	−0.521197	−	0.902740i	−0.999696	−	0.0246519i	$-0.992152\pi$
$743$	−14.2068	−	24.6069i	−0.521197	−	0.902740i	0.478499	−	0.878088i	$-0.341181\pi$
$744$		0			0
$745$	−39.2883			−1.43941
$746$		0			0
$747$	−16.6915	−	15.4984i	−0.610712	−	0.567058i
$748$		0			0
$749$	2.33888	+	14.8996i	0.0854607	+	0.544419i
$750$		0			0
$751$	31.4418			1.14733			0.573663	−	0.819091i	$-0.305522\pi$
$751$	31.4418			1.14733			0.573663	+	0.819091i	$0.305522\pi$
$752$		0			0
$753$	−12.6265	−	15.8389i	−0.460137	−	0.577202i
$754$		0			0
$755$	−2.36687			−0.0861392
$756$		0			0
$757$	0.405916			0.0147533			0.00737663	−	0.999973i	$-0.497652\pi$
$757$	0.405916			0.0147533			0.00737663	+	0.999973i	$0.497652\pi$
$758$		0			0
$759$	32.0390	+	40.1902i	1.16294	+	1.45881i
$760$		0			0
$761$	5.31375			0.192623			0.0963117	−	0.995351i	$-0.469295\pi$
$761$	5.31375			0.192623			0.0963117	+	0.995351i	$0.469295\pi$
$762$		0			0
$763$	10.8227	+	4.17151i	0.391807	+	0.151019i
$764$		0			0
$765$	−8.04920	+	2.47974i	−0.291019	+	0.0896553i
$766$		0			0
$767$	6.29727			0.227381
$768$		0			0
$769$	11.9430	+	20.6858i	0.430674	+	0.745949i	0.996931	−	0.0782793i	$-0.0249426\pi$
$769$	11.9430	+	20.6858i	0.430674	+	0.745949i	−0.566258	+	0.824228i	$0.691609\pi$
$770$		0			0
$771$	−3.16549	−	3.97083i	−0.114002	−	0.143006i
$772$		0			0
$773$	12.8525	+	22.2613i	0.462274	+	0.800682i	0.999074	−	0.0430274i	$-0.0137003\pi$
$773$	12.8525	+	22.2613i	0.462274	+	0.800682i	−0.536800	+	0.843710i	$0.680367\pi$
$774$		0			0
$775$	32.7442	−	56.7147i	1.17621	−	2.03725i
$776$		0			0
$777$	26.8947	−	29.3325i	0.964843	−	1.05230i
$778$		0			0
$779$	1.72374			0.0617595
$780$		0			0
$781$	−20.8786			−0.747096
$782$		0			0
$783$	0.313099	−	4.14858i	0.0111892	−	0.148258i
$784$		0			0
$785$	6.89727	−	11.9464i	0.246174	−	0.426386i
$786$		0			0
$787$	8.05546	−	13.9525i	0.287146	−	0.497352i	−0.685981	−	0.727619i	$-0.740627\pi$
$787$	8.05546	−	13.9525i	0.287146	−	0.497352i	0.973127	+	0.230268i	$0.0739602\pi$
$788$		0			0
$789$	30.5376	+	38.3067i	1.08717	+	1.36376i
$790$		0			0
$791$	24.5196	+	9.45089i	0.871818	+	0.336035i
$792$		0			0
$793$	1.79893	−	3.11583i	0.0638818	−	0.110646i
$794$		0			0
$795$	−20.3554	+	51.8377i	−0.721930	+	1.83850i
$796$		0			0
$797$	0.556852	+	0.964495i	0.0197247	+	0.0341642i	0.875719	−	0.482821i	$-0.160388\pi$
$797$	0.556852	+	0.964495i	0.0197247	+	0.0341642i	−0.855995	+	0.516985i	$0.827054\pi$
$798$		0			0
$799$	−4.32540	+	7.49181i	−0.153022	+	0.265041i
$800$		0			0
$801$	−16.4222	−	15.2484i	−0.580250	−	0.538774i
$802$		0			0
$803$	13.9735	+	24.2029i	0.493116	+	0.854101i
$804$		0			0
$805$	38.5687	−	31.1447i	1.35937	−	1.09771i
$806$		0			0
$807$	6.06646	−	15.4491i	0.213550	−	0.543834i
$808$		0			0
$809$	10.1461	+	17.5736i	0.356718	+	0.617853i	0.987410	−	0.158179i	$-0.0505624\pi$
$809$	10.1461	+	17.5736i	0.356718	+	0.617853i	−0.630693	+	0.776033i	$0.717229\pi$
$810$		0			0
$811$	9.72686			0.341556			0.170778	−	0.985310i	$-0.445372\pi$
$811$	9.72686			0.341556			0.170778	+	0.985310i	$0.445372\pi$
$812$		0			0
$813$	−31.3166	+	4.71458i	−1.09832	+	0.165348i
$814$		0			0
$815$	−17.2402	+	29.8608i	−0.603897	+	1.04598i
$816$		0			0
$817$	2.03875	+	3.53121i	0.0713267	+	0.123542i
$818$		0			0
$819$	16.8113	−	24.9651i	0.587435	−	0.872350i
$820$		0			0
$821$	2.03552	+	3.52562i	0.0710401	+	0.123045i	0.899357	−	0.437214i	$-0.144035\pi$
$821$	2.03552	+	3.52562i	0.0710401	+	0.123045i	−0.828317	+	0.560259i	$0.810701\pi$
$822$		0			0
$823$	1.30600	−	2.26206i	0.0455242	−	0.0788503i	−0.842365	−	0.538907i	$-0.818838\pi$
$823$	1.30600	−	2.26206i	0.0455242	−	0.0788503i	0.887890	+	0.460056i	$0.152171\pi$
$824$		0			0
$825$	−38.5128	−	48.3110i	−1.34084	−	1.68197i
$826$		0			0
$827$	30.0054			1.04339			0.521695	−	0.853132i	$-0.325300\pi$
$827$	30.0054			1.04339			0.521695	+	0.853132i	$0.325300\pi$
$828$		0			0
$829$	−14.0676	−	24.3658i	−0.488588	−	0.846260i	0.511325	−	0.859387i	$-0.329155\pi$
$829$	−14.0676	−	24.3658i	−0.488588	−	0.846260i	−0.999914	+	0.0131272i	$0.995821\pi$
$830$		0			0
$831$	−5.02647	−	6.30527i	−0.174366	−	0.218727i
$832$		0			0
$833$	5.49026	−	1.76722i	0.190226	−	0.0612307i
$834$		0			0
$835$	29.8613	+	51.7213i	1.03339	+	1.78989i
$836$		0			0
$837$	3.87424	−	51.3339i	0.133913	−	1.77436i
$838$		0			0
$839$	3.61277	−	6.25750i	0.124727	−	0.216033i	−0.796899	−	0.604112i	$-0.793528\pi$
$839$	3.61277	−	6.25750i	0.124727	−	0.216033i	0.921626	+	0.388079i	$0.126861\pi$
$840$		0			0
$841$	14.1795	+	24.5596i	0.488947	+	0.846881i
$842$		0			0
$843$	31.0580	−	4.67564i	1.06969	−	0.161037i
$844$		0			0
$845$	−2.34933	+	4.06915i	−0.0808193	+	0.139983i
$846$		0			0
$847$	−37.3005	+	30.1205i	−1.28166	+	1.03495i
$848$		0			0
$849$	−28.4649	+	4.28526i	−0.976912	+	0.147070i
$850$		0			0
$851$	−23.8772	+	41.3565i	−0.818499	+	1.41768i
$852$		0			0
$853$	16.0767	−	27.8457i	0.550457	−	0.953419i	−0.447785	−	0.894141i	$-0.647787\pi$
$853$	16.0767	−	27.8457i	0.550457	−	0.953419i	0.998242	−	0.0592779i	$-0.0188798\pi$
$854$		0			0
$855$	3.49989	+	3.24972i	0.119694	+	0.111138i
$856$		0			0
$857$	−6.97170			−0.238149			−0.119074	−	0.992885i	$-0.537993\pi$
$857$	−6.97170			−0.238149			−0.119074	+	0.992885i	$0.537993\pi$
$858$		0			0
$859$	34.7047			1.18411			0.592054	−	0.805898i	$-0.298317\pi$
$859$	34.7047			1.18411			0.592054	+	0.805898i	$0.298317\pi$
$860$		0			0
$861$	5.07905	+	16.1258i	0.173094	+	0.549565i
$862$		0			0
$863$	−25.9863	+	45.0095i	−0.884583	+	1.53214i	−0.0383914	+	0.999263i	$0.512223\pi$
$863$	−25.9863	+	45.0095i	−0.884583	+	1.53214i	−0.846191	+	0.532879i	$0.821110\pi$
$864$		0			0
$865$	13.3486	+	23.1204i	0.453866	+	0.786119i
$866$		0			0
$867$	−27.9540	+	4.20835i	−0.949367	+	0.142923i
$868$		0			0
$869$	−21.1241	−	36.5880i	−0.716586	−	1.24116i
$870$		0			0
$871$	−2.04456			−0.0692774
$872$		0			0
$873$	−14.1799	−	13.1664i	−0.479918	−	0.445614i
$874$		0			0
$875$	−11.2930	+	9.11920i	−0.381772	+	0.308285i
$876$		0			0
$877$	40.7643			1.37651			0.688257	−	0.725467i	$-0.258376\pi$
$877$	40.7643			1.37651			0.688257	+	0.725467i	$0.258376\pi$
$878$		0			0
$879$	2.45992	−	6.26453i	0.0829710	−	0.211297i
$880$		0			0
$881$	−6.07339			−0.204618			−0.102309	−	0.994753i	$-0.532623\pi$
$881$	−6.07339			−0.204618			−0.102309	+	0.994753i	$0.532623\pi$
$882$		0			0
$883$	10.0958			0.339751			0.169875	−	0.985466i	$-0.445664\pi$
$883$	10.0958			0.339751			0.169875	+	0.985466i	$0.445664\pi$
$884$		0			0
$885$	−9.69171	+	1.45904i	−0.325783	+	0.0490452i
$886$		0			0
$887$	−13.1043			−0.440000			−0.220000	−	0.975500i	$-0.570606\pi$
$887$	−13.1043			−0.440000			−0.220000	+	0.975500i	$0.570606\pi$
$888$		0			0
$889$	−33.1657	+	26.7817i	−1.11234	+	0.898230i
$890$		0			0
$891$	−43.7429	−	21.1034i	−1.46544	−	0.706992i
$892$		0			0
$893$	4.90542			0.164154
$894$		0			0
$895$	15.7393	+	27.2612i	0.526106	+	0.911242i
$896$		0			0
$897$	−13.2008	+	33.6177i	−0.440763	+	1.12246i
$898$		0			0
$899$	−3.96622	−	6.86969i	−0.132281	−	0.229117i
$900$		0			0
$901$	3.88758	−	6.73348i	0.129514	−	0.224325i
$902$		0			0
$903$	−27.0276	+	29.4775i	−0.899423	+	0.980949i
$904$		0			0
$905$	32.2328			1.07146
$906$		0			0
$907$	−12.8340			−0.426144			−0.213072	−	0.977036i	$-0.568347\pi$
$907$	−12.8340			−0.426144			−0.213072	+	0.977036i	$0.568347\pi$
$908$		0			0
$909$	10.8309	−	47.3761i	0.359237	−	1.57137i
$910$		0			0
$911$	−17.5089	+	30.3262i	−0.580094	+	1.00475i	0.415373	+	0.909651i	$0.363651\pi$
$911$	−17.5089	+	30.3262i	−0.580094	+	1.00475i	−0.995468	+	0.0951015i	$0.969682\pi$
$912$		0			0
$913$	−20.4859	+	35.4826i	−0.677985	+	1.17430i
$914$		0			0
$915$	−2.04669	+	5.21218i	−0.0676614	+	0.172309i
$916$		0			0
$917$	−28.6960	+	23.1723i	−0.947626	+	0.765218i
$918$		0			0
$919$	4.12422	−	7.14336i	0.136046	−	0.235638i	−0.789951	−	0.613170i	$-0.789894\pi$
$919$	4.12422	−	7.14336i	0.136046	−	0.235638i	0.925996	+	0.377532i	$0.123227\pi$
$920$		0			0
$921$	3.76216	+	4.71931i	0.123967	+	0.155506i
$922$		0			0
$923$	−7.33557	−	12.7056i	−0.241453	−	0.418209i
$924$		0			0
$925$	28.7018	−	49.7129i	0.943709	−	1.63455i
$926$		0			0
$927$	10.4960	−	45.9113i	0.344733	−	1.50792i
$928$		0			0
$929$	28.4256	+	49.2346i	0.932614	+	1.61533i	0.778835	+	0.627229i	$0.215811\pi$
$929$	28.4256	+	49.2346i	0.932614	+	1.61533i	0.153779	+	0.988105i	$0.450856\pi$
$930$		0			0
$931$	−2.42447	−	2.19510i	−0.0794587	−	0.0719414i
$932$		0			0
$933$	−22.2409	+	3.34826i	−0.728133	+	0.109617i
$934$		0			0
$935$	7.57518	+	13.1206i	0.247735	+	0.429089i
$936$		0			0
$937$	−46.6213			−1.52305			−0.761526	−	0.648134i	$-0.775550\pi$
$937$	−46.6213			−1.52305			−0.761526	+	0.648134i	$0.775550\pi$
$938$		0			0
$939$	−9.52386	+	24.2538i	−0.310800	+	0.791494i
$940$		0			0
$941$	−12.6701	+	21.9453i	−0.413033	+	0.715395i	−0.995220	−	0.0976604i	$-0.968864\pi$
$941$	−12.6701	+	21.9453i	−0.413033	+	0.715395i	0.582186	+	0.813055i	$0.302197\pi$
$942$		0			0
$943$	−10.1438	−	17.5697i	−0.330329	−	0.572147i
$944$		0			0
$945$	−20.0889	+	42.3172i	−0.653493	+	1.37658i
$946$		0			0
$947$	−14.9786	−	25.9437i	−0.486739	−	0.843056i	0.513145	−	0.858302i	$-0.328480\pi$
$947$	−14.9786	−	25.9437i	−0.486739	−	0.843056i	−0.999884	+	0.0152455i	$0.995147\pi$
$948$		0			0
$949$	−9.81902	+	17.0070i	−0.318739	+	0.552072i
$950$		0			0
$951$	5.35478	−	13.6367i	0.173641	−	0.442200i
$952$		0			0
$953$	38.6721			1.25271			0.626356	−	0.779537i	$-0.284546\pi$
$953$	38.6721			1.25271			0.626356	+	0.779537i	$0.284546\pi$
$954$		0			0
$955$	−0.0771711	−	0.133664i	−0.00249720	−	0.00432528i
$956$		0			0
$957$	−7.40027	+	1.11408i	−0.239217	+	0.0360130i
$958$		0			0
$959$	22.9554	−	18.5368i	0.741269	−	0.598583i
$960$		0			0
$961$	−33.5775	−	58.1579i	−1.08314	−	1.87606i
$962$		0			0
$963$	12.5321	+	11.6363i	0.403842	+	0.374976i
$964$		0			0
$965$	32.0630	−	55.5347i	1.03214	−	1.78773i
$966$		0			0
$967$	16.2161	+	28.0870i	0.521473	+	0.903218i	0.999688	+	0.0249755i	$0.00795076\pi$
$967$	16.2161	+	28.0870i	0.521473	+	0.903218i	−0.478215	+	0.878243i	$0.658716\pi$
$968$		0			0
$969$	−0.415642	−	0.521387i	−0.0133523	−	0.0167494i
$970$		0			0
$971$	8.53128	−	14.7766i	0.273782	−	0.474204i	−0.696045	−	0.717998i	$-0.745059\pi$
$971$	8.53128	−	14.7766i	0.273782	−	0.474204i	0.969827	+	0.243794i	$0.0783921\pi$
$972$		0			0
$973$	−15.6881	−	6.04683i	−0.502936	−	0.193853i
$974$		0			0
$975$	15.8682	−	40.4105i	0.508188	−	1.29417i
$976$		0			0
$977$	7.27566	−	12.6018i	0.232769	−	0.403168i	−0.725853	−	0.687850i	$-0.758555\pi$
$977$	7.27566	−	12.6018i	0.232769	−	0.403168i	0.958622	+	0.284682i	$0.0918881\pi$
$978$		0			0
$979$	−20.1553	+	34.9101i	−0.644168	+	1.11573i
$980$		0			0
$981$	12.5689	−	3.87213i	0.401293	−	0.123628i
$982$		0			0
$983$	−32.3851			−1.03293			−0.516463	−	0.856310i	$-0.672751\pi$
$983$	−32.3851			−1.03293			−0.516463	+	0.856310i	$0.672751\pi$
$984$		0			0
$985$	−76.2860			−2.43068
$986$		0			0
$987$	14.4539	+	45.8907i	0.460074	+	1.46072i
$988$		0			0
$989$	23.9952	−	41.5608i	0.763002	−	1.32156i
$990$		0			0
$991$	12.7165	+	22.0256i	0.403952	+	0.699665i	0.994199	−	0.107558i	$-0.0343030\pi$
$991$	12.7165	+	22.0256i	0.403952	+	0.699665i	−0.590247	+	0.807223i	$0.700970\pi$
$992$		0			0
$993$	−6.34624	+	16.1616i	−0.201392	+	0.512872i
$994$		0			0
$995$	−38.7447	−	67.1078i	−1.22829	−	2.12746i
$996$		0			0
$997$	−1.39333			−0.0441272			−0.0220636	−	0.999757i	$-0.507024\pi$
$997$	−1.39333			−0.0441272			−0.0220636	+	0.999757i	$0.507024\pi$
$998$		0			0
$999$	3.39594	−	44.9965i	0.107443	−	1.42363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.3	yes	22
3.2	odd	2		1512.2.t.c.289.1		22
4.3	odd	2		1008.2.t.l.961.9		22
7.4	even	3		504.2.q.c.25.6	✓	22
9.4	even	3		504.2.q.c.121.6	yes	22
9.5	odd	6		1512.2.q.d.793.11		22
12.11	even	2		3024.2.t.k.289.1		22
21.11	odd	6		1512.2.q.d.1369.11		22
28.11	odd	6		1008.2.q.l.529.6		22
36.23	even	6		3024.2.q.l.2305.11		22
36.31	odd	6		1008.2.q.l.625.6		22
63.4	even	3	inner	504.2.t.c.193.3	yes	22
63.32	odd	6		1512.2.t.c.361.1		22
84.11	even	6		3024.2.q.l.2881.11		22
252.67	odd	6		1008.2.t.l.193.9		22
252.95	even	6		3024.2.t.k.1873.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.6	✓	22	7.4	even	3
504.2.q.c.121.6	yes	22	9.4	even	3
504.2.t.c.193.3	yes	22	63.4	even	3	inner
504.2.t.c.457.3	yes	22	1.1	even	1	trivial
1008.2.q.l.529.6		22	28.11	odd	6
1008.2.q.l.625.6		22	36.31	odd	6
1008.2.t.l.193.9		22	252.67	odd	6
1008.2.t.l.961.9		22	4.3	odd	2
1512.2.q.d.793.11		22	9.5	odd	6
1512.2.q.d.1369.11		22	21.11	odd	6
1512.2.t.c.289.1		22	3.2	odd	2
1512.2.t.c.361.1		22	63.32	odd	6
3024.2.q.l.2305.11		22	36.23	even	6
3024.2.q.l.2881.11		22	84.11	even	6
3024.2.t.k.289.1		22	12.11	even	2
3024.2.t.k.1873.1		22	252.95	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07968 - 1.35436i) q^{3} +3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +(-0.668594 + 2.92455i) q^{9} +O(q^{10})\)	\(q+(-1.07968 - 1.35436i) q^{3} +3.40736 q^{5} +(-2.05842 + 1.66220i) q^{7} +(-0.668594 + 2.92455i) q^{9} +5.39638 q^{11} +(1.89598 + 3.28393i) q^{13} +(-3.67885 - 4.61480i) q^{15} +(0.411976 + 0.713564i) q^{17} +(0.233611 - 0.404626i) q^{19} +(4.47365 + 0.993210i) q^{21} -5.49899 q^{23} +6.61011 q^{25} +(4.68276 - 2.25205i) q^{27} +(0.400332 - 0.693396i) q^{29} +(4.95366 - 8.57999i) q^{31} +(-5.82635 - 7.30865i) q^{33} +(-7.01378 + 5.66371i) q^{35} +(4.34210 - 7.52074i) q^{37} +(2.40059 - 6.11343i) q^{39} +(1.84467 + 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(-2.27814 + 9.96499i) q^{45} +(5.24957 + 9.09252i) q^{47} +(1.47420 - 6.84301i) q^{49} +(0.521623 - 1.32838i) q^{51} +(-4.71820 - 8.17217i) q^{53} +18.3874 q^{55} +(-0.800234 + 0.120472i) q^{57} +(0.830344 - 1.43820i) q^{59} +(-0.474405 - 0.821694i) q^{61} +(-3.48493 - 7.13129i) q^{63} +(6.46029 + 11.1896i) q^{65} +(-0.269592 + 0.466947i) q^{67} +(5.93714 + 7.44762i) q^{69} -3.86901 q^{71} +(2.58943 + 4.48502i) q^{73} +(-7.13679 - 8.95248i) q^{75} +(-11.1080 + 8.96985i) q^{77} +(-3.91449 - 6.78010i) q^{79} +(-8.10597 - 3.91067i) q^{81} +(-3.79623 + 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(-1.37134 + 0.206449i) q^{87} +(-3.73498 + 6.46917i) q^{89} +(-9.36128 - 3.60823i) q^{91} +(-16.9688 + 2.55457i) q^{93} +(0.795996 - 1.37871i) q^{95} +(-3.22500 + 5.58587i) q^{97} +(-3.60798 + 15.7820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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