LMFDB - Embedded newform 504.2.q.c.25.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (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			25.6
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.633073 + 1.61221i) q^{3} +(-1.70368 + 2.95086i) q^{5} +(-0.410295 + 2.61374i) q^{7} +(-2.19844 - 2.04129i) q^{9} +O(q^{10})$	\(q+(-0.633073 + 1.61221i) q^{3} +(-1.70368 + 2.95086i) q^{5} +(-0.410295 + 2.61374i) q^{7} +(-2.19844 - 2.04129i) q^{9} +(-2.69819 - 4.67340i) q^{11} +(1.89598 + 3.28393i) q^{13} +(-3.67885 - 4.61480i) q^{15} +(0.411976 - 0.713564i) q^{17} +(0.233611 + 0.404626i) q^{19} +(-3.95416 - 2.31617i) q^{21} +(2.74950 - 4.76227i) q^{23} +(-3.30506 - 5.72452i) q^{25} +(4.68276 - 2.25205i) q^{27} +(0.400332 - 0.693396i) q^{29} -9.90732 q^{31} +(9.24265 - 1.39144i) q^{33} +(-7.01378 - 5.66371i) q^{35} +(4.34210 + 7.52074i) q^{37} +(-6.49468 + 0.977746i) q^{39} +(1.84467 + 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(9.76901 - 3.00957i) q^{45} -10.4991 q^{47} +(-6.66332 - 2.14481i) q^{49} +(0.889603 + 1.11593i) q^{51} +(-4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +(-0.800234 + 0.120472i) q^{57} -1.66069 q^{59} +0.948811 q^{61} +(6.23743 - 4.90862i) q^{63} -12.9206 q^{65} +0.539184 q^{67} +(5.93714 + 7.44762i) q^{69} -3.86901 q^{71} +(2.58943 - 4.48502i) q^{73} +(11.3215 - 1.70440i) q^{75} +(13.3221 - 5.13490i) q^{77} +7.82899 q^{79} +(0.666244 + 8.97531i) q^{81} +(-3.79623 + 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(0.864460 + 1.08439i) q^{87} +(-3.73498 - 6.46917i) q^{89} +(-9.36128 + 3.60823i) q^{91} +(6.27206 - 15.9727i) q^{93} -1.59199 q^{95} +(-3.22500 + 5.58587i) q^{97} +(-3.60798 + 15.7820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.633073	+	1.61221i	−0.365505	+	0.930809i
$3$	−0.633073	+	1.61221i	−0.365505	+	0.930809i
$4$		0			0
$5$	−1.70368	+	2.95086i	−0.761909	+	1.31967i	0.179956	+	0.983675i	$0.442404\pi$
$5$	−1.70368	+	2.95086i	−0.761909	+	1.31967i	−0.941865	+	0.335991i	$0.890929\pi$
$6$		0			0
$7$	−0.410295	+	2.61374i	−0.155077	+	0.987902i
$7$	−0.410295	+	2.61374i	−0.155077	+	0.987902i
$8$		0			0
$9$	−2.19844	−	2.04129i	−0.732812	−	0.680431i
$10$		0			0
$11$	−2.69819	−	4.67340i	−0.813535	−	1.40908i	−0.910375	−	0.413784i	$-0.864207\pi$
$11$	−2.69819	−	4.67340i	−0.813535	−	1.40908i	0.0968406	−	0.995300i	$-0.469126\pi$
$12$		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	−0.811732	−	0.584030i	$-0.801475\pi$
$17$	0.411976	−	0.713564i	0.0999190	−	0.173065i	0.911651	+	0.410965i	$0.134808\pi$
$18$		0			0
$19$	0.233611	+	0.404626i	0.0535940	+	0.0928275i	0.891578	−	0.452868i	$-0.149599\pi$
$19$	0.233611	+	0.404626i	0.0535940	+	0.0928275i	−0.837984	+	0.545695i	$0.816266\pi$
$20$		0			0
$21$	−3.95416	−	2.31617i	−0.862867	−	0.505430i
$22$		0			0
$23$	2.74950	−	4.76227i	0.573309	−	0.993001i	−0.422914	−	0.906170i	$-0.638993\pi$
$23$	2.74950	−	4.76227i	0.573309	−	0.993001i	0.996223	−	0.0868310i	$-0.0276740\pi$
$24$		0			0
$25$	−3.30506	−	5.72452i	−0.661011	−	1.14490i
$26$		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
$31$	−9.90732			−1.77941			−0.889703	−	0.456539i	$-0.849089\pi$
$31$	−9.90732			−1.77941			−0.889703	+	0.456539i	$0.849089\pi$
$32$		0			0
$33$	9.24265	−	1.39144i	1.60894	−	0.242219i
$34$		0			0
$35$	−7.01378	−	5.66371i	−1.18555	−	0.957342i
$36$		0			0
$37$	4.34210	+	7.52074i	0.713837	+	1.23640i	0.963406	+	0.268045i	$0.0863777\pi$
$37$	4.34210	+	7.52074i	0.713837	+	1.23640i	−0.249569	+	0.968357i	$0.580289\pi$
$38$		0			0
$39$	−6.49468	+	0.977746i	−1.03998	+	0.156565i
$40$		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
$45$	9.76901	−	3.00957i	1.45628	−	0.448640i
$46$		0			0
$47$	−10.4991			−1.53146			−0.765728	−	0.643164i	$-0.777621\pi$
$47$	−10.4991			−1.53146			−0.765728	+	0.643164i	$0.777621\pi$
$48$		0			0
$49$	−6.66332	−	2.14481i	−0.951902	−	0.306402i
$50$		0			0
$51$	0.889603	+	1.11593i	0.124569	+	0.156262i
$52$		0			0
$53$	−4.71820	+	8.17217i	−0.648095	+	1.12253i	0.335483	+	0.942046i	$0.391101\pi$
$53$	−4.71820	+	8.17217i	−0.648095	+	1.12253i	−0.983577	+	0.180487i	$0.942233\pi$
$54$		0			0
$55$	18.3874			2.47936
$56$		0			0
$57$	−0.800234	+	0.120472i	−0.105994	+	0.0159569i
$58$		0			0
$59$	−1.66069			−0.216203			−0.108102	−	0.994140i	$-0.534477\pi$
$59$	−1.66069			−0.216203			−0.108102	+	0.994140i	$0.534477\pi$
$60$		0			0
$61$	0.948811			0.121483			0.0607414	−	0.998154i	$-0.480654\pi$
$61$	0.948811			0.121483			0.0607414	+	0.998154i	$0.480654\pi$
$62$		0			0
$63$	6.23743	−	4.90862i	0.785842	−	0.618428i
$64$		0			0
$65$	−12.9206			−1.60260
$66$		0			0
$67$	0.539184			0.0658718			0.0329359	−	0.999457i	$-0.489514\pi$
$67$	0.539184			0.0658718			0.0329359	+	0.999457i	$0.489514\pi$
$68$		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	−0.673760	−	0.738950i	$-0.735322\pi$
$73$	2.58943	−	4.48502i	0.303070	−	0.524932i	0.976830	+	0.214018i	$0.0686551\pi$
$74$		0			0
$75$	11.3215	−	1.70440i	1.30729	−	0.196807i
$76$		0			0
$77$	13.3221	−	5.13490i	1.51820	−	0.585176i
$78$		0			0
$79$	7.82899			0.880830			0.440415	−	0.897794i	$-0.354831\pi$
$79$	7.82899			0.880830			0.440415	+	0.897794i	$0.354831\pi$
$80$		0			0
$81$	0.666244	+	8.97531i	0.0740272	+	0.997256i
$82$		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
$87$	0.864460	+	1.08439i	0.0926798	+	0.116259i
$88$		0			0
$89$	−3.73498	−	6.46917i	−0.395907	−	0.685730i	0.597310	−	0.802011i	$-0.296236\pi$
$89$	−3.73498	−	6.46917i	−0.395907	−	0.685730i	−0.993216	+	0.116280i	$0.962903\pi$
$90$		0			0
$91$	−9.36128	+	3.60823i	−0.981328	+	0.378245i
$92$		0			0
$93$	6.27206	−	15.9727i	0.650382	−	1.65629i
$94$		0			0
$95$	−1.59199			−0.163335
$96$		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
$101$	8.09973	+	14.0291i	0.805953	+	1.39595i	0.915646	+	0.401987i	$0.131680\pi$
$101$	8.09973	+	14.0291i	0.805953	+	1.39595i	−0.109692	+	0.993966i	$0.534986\pi$
$102$		0			0
$103$	7.84930	−	13.5954i	0.773414	−	1.33959i	−0.162267	−	0.986747i	$-0.551881\pi$
$103$	7.84930	−	13.5954i	0.773414	−	1.33959i	0.935681	−	0.352846i	$-0.114786\pi$
$104$		0			0
$105$	13.5713	−	7.72214i	1.32443	−	0.753604i
$106$		0			0
$107$	2.85024	+	4.93675i	0.275543	+	0.477254i	0.970272	−	0.242017i	$-0.0778091\pi$
$107$	2.85024	+	4.93675i	0.275543	+	0.477254i	−0.694729	+	0.719271i	$0.744476\pi$
$108$		0			0
$109$	−2.19196	+	3.79659i	−0.209952	+	0.363648i	−0.951699	−	0.307032i	$-0.900664\pi$
$109$	−2.19196	+	3.79659i	−0.209952	+	0.363648i	0.741747	+	0.670680i	$0.233997\pi$
$110$		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
$115$	9.36852	+	16.2268i	0.873619	+	1.51315i
$116$		0			0
$117$	2.53528	−	11.0898i	0.234387	−	1.02525i
$118$		0			0
$119$	1.69604	+	1.36957i	0.155476	+	0.125549i
$120$		0			0
$121$	−9.06045	+	15.6932i	−0.823677	+	1.42665i
$122$		0			0
$123$	−6.31894	+	0.951288i	−0.569759	+	0.0857747i
$124$		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
$129$	−9.42247	−	11.8197i	−0.829602	−	1.04066i
$130$		0			0
$131$	−6.97039	+	12.0731i	−0.609006	+	1.05483i	0.382399	+	0.923997i	$0.375098\pi$
$131$	−6.97039	+	12.0731i	−0.609006	+	1.05483i	−0.991405	+	0.130832i	$0.958235\pi$
$132$		0			0
$133$	−1.15344	+	0.444583i	−0.100016	+	0.0385502i
$134$		0			0
$135$	−1.33244	+	17.6550i	−0.114678	+	1.51950i
$136$		0			0
$137$	5.57598	+	9.65787i	0.476388	+	0.825128i	0.999634	−	0.0270537i	$-0.00861250\pi$
$137$	5.57598	+	9.65787i	0.476388	+	0.825128i	−0.523246	+	0.852182i	$0.675279\pi$
$138$		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
$147$	7.67625	−	9.38483i	0.633127	−	0.774048i
$148$		0			0
$149$	5.76521	−	9.98564i	0.472304	−	0.818055i	−0.527193	−	0.849745i	$-0.676756\pi$
$149$	5.76521	−	9.98564i	0.472304	−	0.818055i	0.999498	+	0.0316900i	$0.0100889\pi$
$150$		0			0
$151$	0.347317	+	0.601571i	0.0282643	+	0.0489551i	0.879812	−	0.475323i	$-0.157669\pi$
$151$	0.347317	+	0.601571i	0.0282643	+	0.0489551i	−0.851547	+	0.524278i	$0.824335\pi$
$152$		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
$157$	−4.04845			−0.323102			−0.161551	−	0.986864i	$-0.551650\pi$
$157$	−4.04845			−0.323102			−0.161551	+	0.986864i	$0.551650\pi$
$158$		0			0
$159$	−10.1883	−	12.7803i	−0.807982	−	1.01354i
$160$		0			0
$161$	11.3192	+	9.14041i	0.892081	+	0.720365i
$162$		0			0
$163$	−5.05968	−	8.76363i	−0.396305	−	0.686420i	0.596962	−	0.802270i	$-0.296374\pi$
$163$	−5.05968	−	8.76363i	−0.396305	−	0.686420i	−0.993267	+	0.115849i	$0.963041\pi$
$164$		0			0
$165$	−11.6406	+	29.6444i	−0.906218	+	2.30781i
$166$		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
$171$	0.312381	−	1.36641i	0.0238884	−	0.104492i
$172$		0			0
$173$	−7.83515			−0.595695			−0.297848	−	0.954613i	$-0.596269\pi$
$173$	−7.83515			−0.595695			−0.297848	+	0.954613i	$0.596269\pi$
$174$		0			0
$175$	16.3185	−	6.28982i	1.23356	−	0.475466i
$176$		0			0
$177$	1.05134	−	2.67738i	0.0790234	−	0.201244i
$178$		0			0
$179$	4.61920	−	8.00069i	0.345255	−	0.597999i	−0.640145	−	0.768254i	$-0.721126\pi$
$179$	4.61920	−	8.00069i	0.345255	−	0.597999i	0.985400	+	0.170255i	$0.0544591\pi$
$180$		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
$185$	−29.5902			−2.17552
$186$		0			0
$187$	−4.44636			−0.325150
$188$		0			0
$189$	3.96497	+	13.1635i	0.288409	+	0.957507i
$190$		0			0
$191$	0.0452967			0.00327756			0.00163878	−	0.999999i	$-0.499478\pi$
$191$	0.0452967			0.00327756			0.00163878	+	0.999999i	$0.499478\pi$
$192$		0			0
$193$	−18.8198			−1.35468			−0.677340	−	0.735670i	$-0.736868\pi$
$193$	−18.8198			−1.35468			−0.677340	+	0.735670i	$0.736868\pi$
$194$		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	0.109513	+	0.993985i	$0.465071\pi$
$199$	−11.3709	+	19.6949i	−0.806060	+	1.39614i	−0.915573	+	0.402152i	$0.868262\pi$
$200$		0			0
$201$	−0.341343	+	0.869277i	−0.0240765	+	0.0613141i
$202$		0			0
$203$	1.64811	+	1.33086i	0.115674	+	0.0934083i
$204$		0			0
$205$	−12.5709			−0.877993
$206$		0			0
$207$	−15.7658	+	4.85701i	−1.09580	+	0.337586i
$208$		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
$213$	2.44937	−	6.23765i	0.167828	−	0.427397i
$214$		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
$219$	5.59150	+	7.01405i	0.377838	+	0.473966i
$220$		0			0
$221$	3.12440			0.210170
$222$		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
$227$	3.48851	+	6.04227i	0.231540	+	0.401040i	0.958262	−	0.285893i	$-0.0922901\pi$
$227$	3.48851	+	6.04227i	0.231540	+	0.401040i	−0.726721	+	0.686933i	$0.758957\pi$
$228$		0			0
$229$	9.60782	−	16.6412i	0.634903	−	1.09968i	−0.351633	−	0.936138i	$-0.614374\pi$
$229$	9.60782	−	16.6412i	0.634903	−	1.09968i	0.986536	−	0.163546i	$-0.0522931\pi$
$230$		0			0
$231$	−0.155347	+	24.7288i	−0.0102211	+	1.62704i
$232$		0			0
$233$	12.9002	+	22.3439i	0.845122	+	1.46379i	0.885515	+	0.464611i	$0.153806\pi$
$233$	12.9002	+	22.3439i	0.845122	+	1.46379i	−0.0403930	+	0.999184i	$0.512861\pi$
$234$		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
$241$	−0.928238	−	1.60776i	−0.0597931	−	0.103565i	0.834579	−	0.550888i	$-0.185711\pi$
$241$	−0.928238	−	1.60776i	−0.0597931	−	0.103565i	−0.894372	+	0.447323i	$0.852377\pi$
$242$		0			0
$243$	−14.8919	−	4.60790i	−0.955313	−	0.295597i
$244$		0			0
$245$	17.6812	−	16.0084i	1.12961	−	1.02274i
$246$		0			0
$247$	−0.885843	+	1.53432i	−0.0563648	+	0.0976267i
$248$		0			0
$249$	−8.19741	−	10.2829i	−0.519490	−	0.651655i
$250$		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
$255$	−4.80856	+	0.723907i	−0.301123	+	0.0453328i
$256$		0			0
$257$	−1.46594	+	2.53908i	−0.0914429	+	0.158384i	−0.908118	−	0.418713i	$-0.862481\pi$
$257$	−1.46594	+	2.53908i	−0.0914429	+	0.158384i	0.816676	+	0.577097i	$0.195815\pi$
$258$		0			0
$259$	−21.4388	+	8.26342i	−1.33214	+	0.513464i
$260$		0			0
$261$	−2.29553	+	0.707191i	−0.142090	+	0.0437740i
$262$		0			0
$263$	14.1420	+	24.4946i	0.872032	+	1.51040i	0.859891	+	0.510477i	$0.170531\pi$
$263$	14.1420	+	24.4946i	0.872032	+	1.51040i	0.0121407	+	0.999926i	$0.496135\pi$
$264$		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	−0.682184	−	0.731181i	$-0.738970\pi$
$269$	4.79128	−	8.29874i	0.292129	−	0.505983i	0.974313	+	0.225198i	$0.0723028\pi$
$270$		0			0
$271$	9.14220	+	15.8348i	0.555349	+	0.961893i	0.997876	+	0.0651381i	$0.0207488\pi$
$271$	9.14220	+	15.8348i	0.555349	+	0.961893i	−0.442527	+	0.896755i	$0.645918\pi$
$272$		0			0
$273$	0.109160	−	17.3766i	0.00660668	−	1.05168i
$274$		0			0
$275$	−17.8353	+	30.8917i	−1.07551	+	1.86284i
$276$		0			0
$277$	−2.32776	−	4.03180i	−0.139862	−	0.242248i	0.787582	−	0.616209i	$-0.211332\pi$
$277$	−2.32776	−	4.03180i	−0.139862	−	0.242248i	−0.927444	+	0.373962i	$0.877999\pi$
$278$		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
$283$	−16.6194			−0.987920			−0.493960	−	0.869485i	$-0.664451\pi$
$283$	−16.6194			−0.987920			−0.493960	+	0.869485i	$0.664451\pi$
$284$		0			0
$285$	1.00785	−	2.56662i	0.0596997	−	0.152034i
$286$		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
$291$	−6.96393	−	8.73565i	−0.408233	−	0.512093i
$292$		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
$297$	−23.1597	−	15.8080i	−1.34386	−	0.917271i
$298$		0			0
$299$	20.8520			1.20590
$300$		0			0
$301$	−17.9641	−	14.5062i	−1.03543	−	0.836123i
$302$		0			0
$303$	−27.7456	+	4.17698i	−1.59395	+	0.239961i
$304$		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
$311$	−12.9855			−0.736338			−0.368169	−	0.929759i	$-0.620015\pi$
$311$	−12.9855			−0.736338			−0.368169	+	0.929759i	$0.620015\pi$
$312$		0			0
$313$	15.0439			0.850329			0.425164	−	0.905116i	$-0.360216\pi$
$313$	15.0439			0.850329			0.425164	+	0.905116i	$0.360216\pi$
$314$		0			0
$315$	3.85807	+	26.7685i	0.217378	+	1.50823i
$316$		0			0
$317$	−8.45839			−0.475070			−0.237535	−	0.971379i	$-0.576340\pi$
$317$	−8.45839			−0.475070			−0.237535	+	0.971379i	$0.576340\pi$
$318$		0			0
$319$	−4.32069			−0.241912
$320$		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
$327$	−4.73323	−	5.93743i	−0.261748	−	0.328341i
$328$		0			0
$329$	4.30774	−	27.4421i	0.237494	−	1.51293i
$330$		0			0
$331$	10.0245			0.550996			0.275498	−	0.961302i	$-0.411157\pi$
$331$	10.0245			0.550996			0.275498	+	0.961302i	$0.411157\pi$
$332$		0			0
$333$	5.80620	−	25.3974i	0.318178	−	1.39177i
$334$		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
$339$	17.0113	−	2.56097i	0.923926	−	0.139093i
$340$		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
$345$	−32.0919	+	4.83129i	−1.72777	+	0.260108i
$346$		0			0
$347$	15.8048			0.848446			0.424223	−	0.905558i	$-0.360547\pi$
$347$	15.8048			0.848446			0.424223	+	0.905558i	$0.360547\pi$
$348$		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
$353$	−7.23939	−	12.5390i	−0.385314	−	0.667383i	0.606499	−	0.795084i	$-0.292573\pi$
$353$	−7.23939	−	12.5390i	−0.385314	−	0.667383i	−0.991813	+	0.127701i	$0.959240\pi$
$354$		0			0
$355$	6.59155	−	11.4169i	0.349843	−	0.605947i
$356$		0			0
$357$	−3.28176	+	1.86733i	−0.173689	+	0.0988298i
$358$		0			0
$359$	7.85517	+	13.6056i	0.414580	+	0.718074i	0.995384	−	0.0959695i	$-0.0305951\pi$
$359$	7.85517	+	13.6056i	0.414580	+	0.718074i	−0.580804	+	0.814043i	$0.697262\pi$
$360$		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
$367$	9.42947	+	16.3323i	0.492214	+	0.852540i	0.999960	−	0.00896710i	$-0.00285436\pi$
$367$	9.42947	+	16.3323i	0.492214	+	0.852540i	−0.507746	+	0.861507i	$0.669521\pi$
$368$		0			0
$369$	2.46668	−	10.7897i	0.128410	−	0.561688i
$370$		0			0
$371$	−19.4241	−	15.6852i	−1.00845	−	0.814334i
$372$		0			0
$373$	16.8568	−	29.1969i	0.872814	−	1.51176i	0.0137417	−	0.999906i	$-0.495626\pi$
$373$	16.8568	−	29.1969i	0.872814	−	1.51176i	0.859073	−	0.511853i	$-0.171041\pi$
$374$		0			0
$375$	−3.47318	+	8.84495i	−0.179354	+	0.456751i
$376$		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
$381$	−10.2002	+	25.9763i	−0.522573	+	1.33080i
$382$		0			0
$383$	9.16201	−	15.8691i	0.468157	−	0.810871i	−0.531181	−	0.847258i	$-0.678252\pi$
$383$	9.16201	−	15.8691i	0.468157	−	0.810871i	0.999338	+	0.0363870i	$0.0115849\pi$
$384$		0			0
$385$	−7.54427	+	48.0600i	−0.384491	+	2.44936i
$386$		0			0
$387$	25.0209	−	7.70827i	1.27188	−	0.391833i
$388$		0			0
$389$	−2.13744	−	3.70216i	−0.108373	−	0.187707i	0.806739	−	0.590909i	$-0.201231\pi$
$389$	−2.13744	−	3.70216i	−0.108373	−	0.187707i	−0.915111	+	0.403202i	$0.867897\pi$
$390$		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	0.827570	+	0.561362i	$0.189723\pi$
$397$	17.9312	+	31.0577i	0.899939	+	1.55874i	0.0723687	+	0.997378i	$0.476944\pi$
$398$		0			0
$399$	0.0134500	−	2.14104i	0.000673344	−	0.107186i
$400$		0			0
$401$	11.7007	−	20.2663i	0.584307	−	1.01205i	−0.410654	−	0.911791i	$-0.634700\pi$
$401$	11.7007	−	20.2663i	0.584307	−	1.01205i	0.994961	−	0.100259i	$-0.0319670\pi$
$402$		0			0
$403$	−18.7841	−	32.5350i	−0.935702	−	1.62068i
$404$		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
$409$	34.8032			1.72091			0.860453	−	0.509530i	$-0.170181\pi$
$409$	34.8032			1.72091			0.860453	+	0.509530i	$0.170181\pi$
$410$		0			0
$411$	−19.1005	+	2.87550i	−0.942159	+	0.141838i
$412$		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
$417$	−10.8841	+	1.63855i	−0.532997	+	0.0802403i
$418$		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
$423$	23.0817	+	21.4318i	1.12227	+	1.04205i
$424$		0			0
$425$	−5.44642			−0.264190
$426$		0			0
$427$	−0.389292	+	2.47995i	−0.0188392	+	0.120013i
$428$		0			0
$429$	22.0933	+	27.7141i	1.06667	+	1.33805i
$430$		0			0
$431$	2.48374	−	4.30196i	0.119637	−	0.207218i	−0.799987	−	0.600018i	$-0.795160\pi$
$431$	2.48374	−	4.30196i	0.119637	−	0.207218i	0.919624	+	0.392800i	$0.128493\pi$
$432$		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
$437$	2.56925			0.122904
$438$		0			0
$439$	−8.05894			−0.384632			−0.192316	−	0.981333i	$-0.561600\pi$
$439$	−8.05894			−0.384632			−0.192316	+	0.981333i	$0.561600\pi$
$440$		0			0
$441$	10.2707	+	18.3170i	0.489080	+	0.872239i
$442$		0			0
$443$	3.77766			0.179482			0.0897410	−	0.995965i	$-0.471396\pi$
$443$	3.77766			0.179482			0.0897410	+	0.995965i	$0.471396\pi$
$444$		0			0
$445$	25.4528			1.20658
$446$		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
$453$	−1.18973	+	0.179109i	−0.0558986	+	0.00841529i
$454$		0			0
$455$	5.30125	−	33.7711i	0.248527	−	1.58321i
$456$		0			0
$457$	0.739506			0.0345926			0.0172963	−	0.999850i	$-0.494494\pi$
$457$	0.739506			0.0345926			0.0172963	+	0.999850i	$0.494494\pi$
$458$		0			0
$459$	0.322205	−	4.26924i	0.0150393	−	0.199271i
$460$		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
$465$	36.4475	+	45.7203i	1.69021	+	2.12023i
$466$		0			0
$467$	5.11184	+	8.85396i	0.236548	+	0.409713i	0.959721	−	0.280954i	$-0.0906507\pi$
$467$	5.11184	+	8.85396i	0.236548	+	0.409713i	−0.723174	+	0.690666i	$0.757317\pi$
$468$		0			0
$469$	−0.221225	+	1.40929i	−0.0102152	+	0.0650749i
$470$		0			0
$471$	2.56297	−	6.52695i	0.118095	−	0.300746i
$472$		0			0
$473$	47.0948			2.16542
$474$		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
$479$	−1.01896	−	1.76488i	−0.0465573	−	0.0806395i	0.841808	−	0.539778i	$-0.181492\pi$
$479$	−1.01896	−	1.76488i	−0.0465573	−	0.0806395i	−0.888365	+	0.459138i	$0.848158\pi$
$480$		0			0
$481$	−16.4651	+	28.5184i	−0.750743	+	1.30033i
$482$		0			0
$483$	−21.9022	+	12.4624i	−0.996583	+	0.567060i
$484$		0			0
$485$	−10.9888	−	19.0331i	−0.498974	−	0.864248i
$486$		0			0
$487$	−17.5958	+	30.4767i	−0.797340	+	1.38103i	0.124003	+	0.992282i	$0.460427\pi$
$487$	−17.5958	+	30.4767i	−0.797340	+	1.38103i	−0.921343	+	0.388751i	$0.872907\pi$
$488$		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
$493$	−0.329855	−	0.571326i	−0.0148559	−	0.0257312i
$494$		0			0
$495$	−40.4236	−	37.5341i	−1.81690	−	1.68703i
$496$		0			0
$497$	1.58744	−	10.1126i	0.0712062	−	0.453612i
$498$		0			0
$499$	2.32633	−	4.02932i	0.104141	−	0.180377i	−0.809246	−	0.587470i	$-0.800124\pi$
$499$	2.32633	−	4.02932i	0.104141	−	0.180377i	0.913387	+	0.407093i	$0.133457\pi$
$500$		0			0
$501$	−30.0203	+	4.51942i	−1.34121	+	0.201913i
$502$		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
$507$	−1.48884	−	1.86763i	−0.0661219	−	0.0829442i
$508$		0			0
$509$	−11.1739	+	19.3537i	−0.495273	+	0.857838i	−0.999985	−	0.00544958i	$-0.998265\pi$
$509$	−11.1739	+	19.3537i	−0.495273	+	0.857838i	0.504712	+	0.863288i	$0.331599\pi$
$510$		0			0
$511$	10.6603	+	8.60829i	0.471583	+	0.380808i
$512$		0			0
$513$	2.00518	+	1.36866i	0.0885309	+	0.0604279i
$514$		0			0
$515$	26.7454	+	46.3244i	1.17854	+	2.04130i
$516$		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	−0.846706	−	0.532061i	$-0.821418\pi$
$521$	0.854260	−	1.47962i	0.0374258	−	0.0648234i	0.884132	+	0.467238i	$0.154751\pi$
$522$		0			0
$523$	10.6036	+	18.3659i	0.463662	+	0.803087i	0.999140	−	0.0414627i	$-0.0132018\pi$
$523$	10.6036	+	18.3659i	0.463662	+	0.803087i	−0.535478	+	0.844549i	$0.679868\pi$
$524$		0			0
$525$	−0.190287	+	30.2907i	−0.00830481	+	1.32200i
$526$		0			0
$527$	−4.08158	+	7.06951i	−0.177796	+	0.307952i
$528$		0			0
$529$	−3.61945	−	6.26907i	−0.157367	−	0.272568i
$530$		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
$535$	−19.4236			−0.839754
$536$		0			0
$537$	9.97449	+	12.5121i	0.430431	+	0.539939i
$538$		0			0
$539$	7.95532	+	36.9275i	0.342660	+	1.59058i
$540$		0			0
$541$	4.79443	+	8.30419i	0.206129	+	0.357025i	0.950492	−	0.310750i	$-0.100580\pi$
$541$	4.79443	+	8.30419i	0.206129	+	0.357025i	−0.744363	+	0.667775i	$0.767247\pi$
$542$		0			0
$543$	−5.98873	+	15.2511i	−0.257001	+	0.654488i
$544$		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
$549$	−2.08590	−	1.93680i	−0.0890240	−	0.0826606i
$550$		0			0
$551$	0.374088			0.0159367
$552$		0			0
$553$	−3.21220	+	20.4630i	−0.136596	+	0.870174i
$554$		0			0
$555$	18.7328	−	47.7056i	0.795162	−	2.02499i
$556$		0			0
$557$	1.68102	−	2.91162i	0.0712272	−	0.123369i	−0.828212	−	0.560415i	$-0.810642\pi$
$557$	1.68102	−	2.91162i	0.0712272	−	0.123369i	0.899439	+	0.437045i	$0.143975\pi$
$558$		0			0
$559$	−33.0929			−1.39968
$560$		0			0
$561$	2.81487	−	7.16846i	0.118844	−	0.302653i
$562$		0			0
$563$	19.0914			0.804606			0.402303	−	0.915506i	$-0.368210\pi$
$563$	19.0914			0.804606			0.402303	+	0.915506i	$0.368210\pi$
$564$		0			0
$565$	33.8424			1.42376
$566$		0			0
$567$	−23.7325	−	1.94113i	−0.996672	−	0.0815199i
$568$		0			0
$569$	2.62726			0.110140			0.0550702	−	0.998482i	$-0.482462\pi$
$569$	2.62726			0.110140			0.0550702	+	0.998482i	$0.482462\pi$
$570$		0			0
$571$	9.98226			0.417745			0.208872	−	0.977943i	$-0.433021\pi$
$571$	9.98226			0.417745			0.208872	+	0.977943i	$0.433021\pi$
$572$		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	−0.711945	−	0.702236i	$-0.752185\pi$
$577$	6.05761	−	10.4921i	0.252182	−	0.436791i	0.964126	+	0.265444i	$0.0855187\pi$
$578$		0			0
$579$	11.9143	−	30.3415i	0.495143	−	1.26095i
$580$		0			0
$581$	−15.6285	−	12.6202i	−0.648379	−	0.523573i
$582$		0			0
$583$	50.9224			2.10899
$584$		0			0
$585$	28.4051	+	26.3747i	1.17441	+	1.09046i
$586$		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
$591$	14.1736	−	36.0951i	0.583025	−	1.48475i
$592$		0			0
$593$	−20.5788	−	35.6434i	−0.845068	−	1.46370i	−0.885562	−	0.464521i	$-0.846226\pi$
$593$	−20.5788	−	35.6434i	−0.845068	−	1.46370i	0.0404940	−	0.999180i	$-0.487107\pi$
$594$		0			0
$595$	−6.93093	+	2.67147i	−0.284141	+	0.109520i
$596$		0			0
$597$	−24.5538	−	30.8006i	−1.00492	−	1.26058i
$598$		0			0
$599$	−8.11041			−0.331382			−0.165691	−	0.986178i	$-0.552986\pi$
$599$	−8.11041			−0.331382			−0.165691	+	0.986178i	$0.552986\pi$
$600$		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
$605$	−30.8722	−	53.4723i	−1.25513	−	2.17396i
$606$		0			0
$607$	−11.5131	+	19.9412i	−0.467300	+	0.809388i	−0.999302	−	0.0373552i	$-0.988107\pi$
$607$	−11.5131	+	19.9412i	−0.467300	+	0.809388i	0.532002	+	0.846743i	$0.321440\pi$
$608$		0			0
$609$	−3.18900	+	1.81456i	−0.129225	+	0.0735295i
$610$		0			0
$611$	−19.9062	−	34.4785i	−0.805317	−	1.39485i
$612$		0			0
$613$	11.4750	−	19.8752i	0.463470	−	0.802753i	−0.535661	−	0.844433i	$-0.679938\pi$
$613$	11.4750	−	19.8752i	0.463470	−	0.802753i	0.999131	+	0.0416796i	$0.0132709\pi$
$614$		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
$619$	−2.75302	−	4.76836i	−0.110653	−	0.191657i	0.805381	−	0.592758i	$-0.201961\pi$
$619$	−2.75302	−	4.76836i	−0.110653	−	0.191657i	−0.916034	+	0.401101i	$0.868628\pi$
$620$		0			0
$621$	2.15037	−	28.4926i	0.0862914	−	1.14337i
$622$		0			0
$623$	18.4412	−	7.10800i	0.738831	−	0.284776i
$624$		0			0
$625$	7.17850	−	12.4335i	0.287140	−	0.497341i
$626$		0			0
$627$	2.72219	+	3.41476i	0.108714	+	0.136372i
$628$		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
$633$	10.1350	−	1.52577i	0.402829	−	0.0606440i
$634$		0			0
$635$	−27.4501	+	47.5449i	−1.08932	+	1.88676i
$636$		0			0
$637$	−5.59009	−	25.9484i	−0.221488	−	1.02811i
$638$		0			0
$639$	8.50577	+	7.89778i	0.336483	+	0.312431i
$640$		0			0
$641$	0.945880	+	1.63831i	0.0373600	+	0.0647095i	0.884101	−	0.467296i	$-0.154772\pi$
$641$	0.945880	+	1.63831i	0.0373600	+	0.0647095i	−0.846741	+	0.532006i	$0.821438\pi$
$642$		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	−0.986785	−	0.162035i	$-0.948194\pi$
$647$	−8.98067	+	15.5550i	−0.353066	+	0.611529i	0.633719	+	0.773564i	$0.281528\pi$
$648$		0			0
$649$	4.48085	+	7.76106i	0.175889	+	0.304648i
$650$		0			0
$651$	39.1751	+	22.9471i	1.53539	+	0.899366i
$652$		0			0
$653$	11.0741	−	19.1809i	0.433363	−	0.750607i	−0.563797	−	0.825913i	$-0.690660\pi$
$653$	11.0741	−	19.1809i	0.433363	−	0.750607i	0.997160	+	0.0753063i	$0.0239935\pi$
$654$		0			0
$655$	−23.7506	−	41.1373i	−0.928015	−	1.60737i
$656$		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
$661$	−5.13907			−0.199887			−0.0999434	−	0.994993i	$-0.531866\pi$
$661$	−5.13907			−0.199887			−0.0999434	+	0.994993i	$0.531866\pi$
$662$		0			0
$663$	−1.97797	+	5.03718i	−0.0768181	+	0.195628i
$664$		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
$669$	−2.59391	−	3.25384i	−0.100286	−	0.125801i
$670$		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
$675$	−28.3687	−	19.3634i	−1.09191	−	0.745299i
$676$		0			0
$677$	−11.7296			−0.450807			−0.225403	−	0.974266i	$-0.572370\pi$
$677$	−11.7296			−0.450807			−0.225403	+	0.974266i	$0.572370\pi$
$678$		0			0
$679$	−13.2768	−	10.7212i	−0.509518	−	0.411442i
$680$		0			0
$681$	−11.9499	+	1.79900i	−0.457921	+	0.0689379i
$682$		0			0
$683$	0.260358	−	0.450954i	0.00996234	−	0.0172553i	−0.861001	−	0.508603i	$-0.830162\pi$
$683$	0.260358	−	0.450954i	0.00996234	−	0.0172553i	0.870964	+	0.491348i	$0.163496\pi$
$684$		0			0
$685$	−37.9987			−1.45186
$686$		0			0
$687$	20.7467	+	26.0249i	0.791536	+	0.992913i
$688$		0			0
$689$	−35.7825			−1.36320
$690$		0			0
$691$	−46.1912			−1.75720			−0.878599	−	0.477561i	$-0.841521\pi$
$691$	−46.1912			−1.75720			−0.878599	+	0.477561i	$0.841521\pi$
$692$		0			0
$693$	−39.7697	−	15.9056i	−1.51073	−	0.604204i
$694$		0			0
$695$	−21.6529			−0.821342
$696$		0			0
$697$	3.03985			0.115143
$698$		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
$705$	38.6248	+	48.4514i	1.45469	+	1.82479i
$706$		0			0
$707$	−39.9919	+	15.4145i	−1.50405	+	0.579723i
$708$		0			0
$709$	−33.4551			−1.25643			−0.628216	−	0.778039i	$-0.716215\pi$
$709$	−33.4551			−1.25643			−0.628216	+	0.778039i	$0.716215\pi$
$710$		0			0
$711$	−17.2115	−	15.9813i	−0.645483	−	0.599344i
$712$		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
$717$	22.8046	−	3.43314i	0.851655	−	0.128213i
$718$		0			0
$719$	−9.42685	−	16.3278i	−0.351562	−	0.608924i	0.634961	−	0.772544i	$-0.281016\pi$
$719$	−9.42685	−	16.3278i	−0.351562	−	0.608924i	−0.986523	+	0.163621i	$0.947683\pi$
$720$		0			0
$721$	32.3143	+	26.0942i	1.20345	+	0.971798i
$722$		0			0
$723$	3.17968	−	0.478687i	0.118254	−	0.0178026i
$724$		0			0
$725$	−5.29248			−0.196558
$726$		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
$731$	3.59537	+	6.22736i	0.132979	+	0.230327i
$732$		0			0
$733$	9.35591	−	16.2049i	0.345569	−	0.598542i	−0.639888	−	0.768468i	$-0.721019\pi$
$733$	9.35591	−	16.2049i	0.345569	−	0.598542i	0.985457	+	0.169926i	$0.0543527\pi$
$734$		0			0
$735$	14.6155	+	38.6403i	0.539099	+	1.42527i
$736$		0			0
$737$	−1.45482	−	2.51982i	−0.0535890	−	0.0928189i
$738$		0			0
$739$	−7.15949	+	12.4006i	−0.263366	+	0.456163i	−0.967134	−	0.254266i	$-0.918166\pi$
$739$	−7.15949	+	12.4006i	−0.263366	+	0.456163i	0.703768	+	0.710430i	$0.251499\pi$
$740$		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
$745$	19.6442	+	34.0247i	0.719706	+	1.24657i
$746$		0			0
$747$	21.7678	−	6.70608i	0.796443	−	0.245363i
$748$		0			0
$749$	−14.0729	+	5.42426i	−0.514211	+	0.198198i
$750$		0			0
$751$	−15.7209	+	27.2294i	−0.573663	+	0.993614i	0.422522	+	0.906353i	$0.361145\pi$
$751$	−15.7209	+	27.2294i	−0.573663	+	0.993614i	−0.996185	+	0.0872612i	$0.972189\pi$
$752$		0			0
$753$	−7.40362	+	18.8544i	−0.269803	+	0.687091i
$754$		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
$759$	18.7862	−	47.8417i	0.681897	−	1.73654i
$760$		0			0
$761$	−2.65688	+	4.60184i	−0.0963117	+	0.166817i	−0.910155	−	0.414267i	$-0.864038\pi$
$761$	−2.65688	+	4.60184i	−0.0963117	+	0.166817i	0.813844	+	0.581084i	$0.197371\pi$
$762$		0			0
$763$	−9.02397	−	7.28696i	−0.326690	−	0.263806i
$764$		0			0
$765$	1.87708	−	8.21068i	0.0678660	−	0.296858i
$766$		0			0
$767$	−3.14863	−	5.45359i	−0.113691	−	0.196918i
$768$		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	−0.536800	−	0.843710i	$-0.680367\pi$
$773$	12.8525	−	22.2613i	0.462274	−	0.800682i	0.999074	+	0.0430274i	$0.0137003\pi$
$774$		0			0
$775$	32.7442	+	56.7147i	1.17621	+	2.03725i
$776$		0			0
$777$	0.249995	−	39.7952i	0.00896851	−	1.42765i
$778$		0			0
$779$	−0.861872	+	1.49281i	−0.0308798	+	0.0534853i
$780$		0			0
$781$	10.4393	+	18.0814i	0.373548	+	0.647004i
$782$		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
$787$	−16.1109			−0.574292			−0.287146	−	0.957887i	$-0.592707\pi$
$787$	−16.1109			−0.574292			−0.287146	+	0.957887i	$0.592707\pi$
$788$		0			0
$789$	−48.4434	+	7.29293i	−1.72463	+	0.259635i
$790$		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
$795$	55.0705	−	8.29061i	1.95315	−	0.294038i
$796$		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
$801$	−4.99436	+	21.8462i	−0.176467	+	0.771899i
$802$		0			0
$803$	−27.9471			−0.986231
$804$		0			0
$805$	−46.2565	+	17.8292i	−1.63033	+	0.628395i
$806$		0			0
$807$	10.3461	+	12.9783i	0.364199	+	0.456856i
$808$		0			0
$809$	10.1461	−	17.5736i	0.356718	−	0.617853i	−0.630693	−	0.776033i	$-0.717229\pi$
$809$	10.1461	−	17.5736i	0.356718	−	0.617853i	0.987410	+	0.158179i	$0.0505624\pi$
$810$		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
$815$	34.4803			1.20779
$816$		0			0
$817$	−4.07749			−0.142653
$818$		0			0
$819$	27.9456	+	11.1767i	0.976499	+	0.390544i
$820$		0			0
$821$	−4.07104			−0.142080			−0.0710401	−	0.997473i	$-0.522632\pi$
$821$	−4.07104			−0.142080			−0.0710401	+	0.997473i	$0.522632\pi$
$822$		0			0
$823$	−2.61200			−0.0910485			−0.0455242	−	0.998963i	$-0.514496\pi$
$823$	−2.61200			−0.0910485			−0.0455242	+	0.998963i	$0.514496\pi$
$824$		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	−0.999914	−	0.0131272i	$-0.995821\pi$
$829$	−14.0676	+	24.3658i	−0.488588	+	0.846260i	0.511325	+	0.859387i	$0.329155\pi$
$830$		0			0
$831$	7.97375	−	1.20041i	0.276606	−	0.0416419i
$832$		0			0
$833$	−4.27559	+	3.87109i	−0.148140	+	0.134125i
$834$		0			0
$835$	−59.7226			−2.06679
$836$		0			0
$837$	−46.3936	+	22.3118i	−1.60360	+	0.771208i
$838$		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
$843$	−19.5782	−	24.5592i	−0.674309	−	0.845862i
$844$		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
$849$	10.5213	−	26.7939i	0.361090	−	0.919565i
$850$		0			0
$851$	47.7544			1.63700
$852$		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
$857$	3.48585	+	6.03767i	0.119074	+	0.206243i	0.919401	−	0.393321i	$-0.128674\pi$
$857$	3.48585	+	6.03767i	0.119074	+	0.206243i	−0.800327	+	0.599564i	$0.795341\pi$
$858$		0			0
$859$	−17.3523	+	30.0551i	−0.592054	+	1.02547i	0.401901	+	0.915683i	$0.368350\pi$
$859$	−17.3523	+	30.0551i	−0.592054	+	1.02547i	−0.993955	+	0.109785i	$0.964984\pi$
$860$		0			0
$861$	0.106206	−	16.9064i	0.00361950	−	0.576168i
$862$		0			0
$863$	−25.9863	−	45.0095i	−0.884583	−	1.53214i	−0.846191	−	0.532879i	$-0.821110\pi$
$863$	−25.9863	−	45.0095i	−0.884583	−	1.53214i	−0.0383914	−	0.999263i	$-0.512223\pi$
$864$		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
$871$	1.02228	+	1.77064i	0.0346387	+	0.0599960i
$872$		0			0
$873$	18.4924	−	5.69700i	0.625872	−	0.192814i
$874$		0			0
$875$	−2.25097	+	14.3396i	−0.0760968	+	0.484767i
$876$		0			0
$877$	−20.3822	+	35.3029i	−0.688257	+	1.19210i	0.284145	+	0.958781i	$0.408290\pi$
$877$	−20.3822	+	35.3029i	−0.688257	+	1.19210i	−0.972401	+	0.233314i	$0.925043\pi$
$878$		0			0
$879$	−6.65520	+	1.00191i	−0.224474	+	0.0337936i
$880$		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
$885$	6.10943	+	7.66375i	0.205366	+	0.257614i
$886$		0			0
$887$	6.55215	−	11.3487i	0.220000	−	0.381051i	−0.734808	−	0.678275i	$-0.762728\pi$
$887$	6.55215	−	11.3487i	0.220000	−	0.381051i	0.954808	+	0.297225i	$0.0960610\pi$
$888$		0			0
$889$	−6.61077	+	42.1132i	−0.221718	+	1.41243i
$890$		0			0
$891$	40.1476	−	27.3307i	1.34499	−	0.915613i
$892$		0			0
$893$	−2.45271	−	4.24822i	−0.0820768	−	0.142161i
$894$		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
$903$	34.7596	−	19.7784i	1.15673	−	0.658183i
$904$		0			0
$905$	−16.1164	+	27.9145i	−0.535728	+	0.927908i
$906$		0			0
$907$	6.41698	+	11.1145i	0.213072	+	0.369052i	0.952674	−	0.303992i	$-0.0983197\pi$
$907$	6.41698	+	11.1145i	0.213072	+	0.369052i	−0.739602	+	0.673044i	$0.764986\pi$
$908$		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
$913$	40.9718			1.35597
$914$		0			0
$915$	−3.49053	−	4.37857i	−0.115393	−	0.144751i
$916$		0			0
$917$	−28.6960	−	23.1723i	−0.947626	−	0.765218i
$918$		0			0
$919$	4.12422	+	7.14336i	0.136046	+	0.235638i	0.925996	−	0.377532i	$-0.123227\pi$
$919$	4.12422	+	7.14336i	0.136046	+	0.235638i	−0.789951	+	0.613170i	$0.789894\pi$
$920$		0			0
$921$	2.20596	−	5.61778i	0.0726888	−	0.185112i
$922$		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
$927$	−45.0083	+	13.8659i	−1.47827	+	0.455415i
$928$		0			0
$929$	−56.8512			−1.86523			−0.932614	−	0.360876i	$-0.882478\pi$
$929$	−56.8512			−1.86523			−0.932614	+	0.360876i	$0.882478\pi$
$930$		0			0
$931$	−0.688776	−	3.19720i	−0.0225737	−	0.104784i
$932$		0			0
$933$	8.22075	−	20.9353i	0.269135	−	0.685390i
$934$		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
$941$	25.3402			0.826067			0.413033	−	0.910716i	$-0.364469\pi$
$941$	25.3402			0.826067			0.413033	+	0.910716i	$0.364469\pi$
$942$		0			0
$943$	20.2877			0.660658
$944$		0			0
$945$	−45.5988	−	10.7264i	−1.48333	−	0.348930i
$946$		0			0
$947$	29.9572			0.973478			0.486739	−	0.873548i	$-0.338186\pi$
$947$	29.9572			0.973478			0.486739	+	0.873548i	$0.338186\pi$
$948$		0			0
$949$	19.6380			0.637478
$950$		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
$957$	2.73531	−	6.96586i	0.0884201	−	0.225174i
$958$		0			0
$959$	−27.5310	+	10.6116i	−0.889023	+	0.342666i
$960$		0			0
$961$	67.1549			2.16629
$962$		0			0
$963$	3.81130	−	16.6713i	0.122817	−	0.537225i
$964$		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
$969$	−0.243713	+	0.620650i	−0.00782920	+	0.0199381i
$970$		0			0
$971$	8.53128	+	14.7766i	0.273782	+	0.474204i	0.969827	−	0.243794i	$-0.0783921\pi$
$971$	8.53128	+	14.7766i	0.273782	+	0.474204i	−0.696045	+	0.717998i	$0.745059\pi$
$972$		0			0
$973$	−15.6881	+	6.04683i	−0.502936	+	0.193853i
$974$		0			0
$975$	27.0624	+	33.9475i	0.866691	+	1.08719i
$976$		0			0
$977$	−14.5513			−0.465538			−0.232769	−	0.972532i	$-0.574779\pi$
$977$	−14.5513			−0.465538			−0.232769	+	0.972532i	$0.574779\pi$
$978$		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
$983$	16.1926	+	28.0463i	0.516463	+	0.894540i	0.999817	+	0.0191149i	$0.00608483\pi$
$983$	16.1926	+	28.0463i	0.516463	+	0.894540i	−0.483355	+	0.875425i	$0.660582\pi$
$984$		0			0
$985$	38.1430	−	66.0657i	1.21534	−	2.10503i
$986$		0			0
$987$	41.5152	+	24.3178i	1.32144	+	0.774045i
$988$		0			0
$989$	23.9952	+	41.5608i	0.763002	+	1.32156i
$990$		0			0
$991$	12.7165	−	22.0256i	0.403952	−	0.699665i	−0.590247	−	0.807223i	$-0.700970\pi$
$991$	12.7165	−	22.0256i	0.403952	−	0.699665i	0.994199	+	0.107558i	$0.0343030\pi$
$992$		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
$997$	0.696665	+	1.20666i	0.0220636	+	0.0382153i	0.876846	−	0.480771i	$-0.159643\pi$
$997$	0.696665	+	1.20666i	0.0220636	+	0.0382153i	−0.854783	+	0.518986i	$0.826310\pi$
$998$		0			0
$999$	37.2701	+	25.4392i	1.17917	+	0.804861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.25.6	✓	22
3.2	odd	2		1512.2.q.d.1369.11		22
4.3	odd	2		1008.2.q.l.529.6		22
7.2	even	3		504.2.t.c.457.3	yes	22
9.4	even	3		504.2.t.c.193.3	yes	22
9.5	odd	6		1512.2.t.c.361.1		22
12.11	even	2		3024.2.q.l.2881.11		22
21.2	odd	6		1512.2.t.c.289.1		22
28.23	odd	6		1008.2.t.l.961.9		22
36.23	even	6		3024.2.t.k.1873.1		22
36.31	odd	6		1008.2.t.l.193.9		22
63.23	odd	6		1512.2.q.d.793.11		22
63.58	even	3	inner	504.2.q.c.121.6	yes	22
84.23	even	6		3024.2.t.k.289.1		22
252.23	even	6		3024.2.q.l.2305.11		22
252.247	odd	6		1008.2.q.l.625.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.6	✓	22	1.1	even	1	trivial
504.2.q.c.121.6	yes	22	63.58	even	3	inner
504.2.t.c.193.3	yes	22	9.4	even	3
504.2.t.c.457.3	yes	22	7.2	even	3
1008.2.q.l.529.6		22	4.3	odd	2
1008.2.q.l.625.6		22	252.247	odd	6
1008.2.t.l.193.9		22	36.31	odd	6
1008.2.t.l.961.9		22	28.23	odd	6
1512.2.q.d.793.11		22	63.23	odd	6
1512.2.q.d.1369.11		22	3.2	odd	2
1512.2.t.c.289.1		22	21.2	odd	6
1512.2.t.c.361.1		22	9.5	odd	6
3024.2.q.l.2305.11		22	252.23	even	6
3024.2.q.l.2881.11		22	12.11	even	2
3024.2.t.k.289.1		22	84.23	even	6
3024.2.t.k.1873.1		22	36.23	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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.633073 + 1.61221i) q^{3} +(-1.70368 + 2.95086i) q^{5} +(-0.410295 + 2.61374i) q^{7} +(-2.19844 - 2.04129i) q^{9} +O(q^{10})\)	\(q+(-0.633073 + 1.61221i) q^{3} +(-1.70368 + 2.95086i) q^{5} +(-0.410295 + 2.61374i) q^{7} +(-2.19844 - 2.04129i) q^{9} +(-2.69819 - 4.67340i) q^{11} +(1.89598 + 3.28393i) q^{13} +(-3.67885 - 4.61480i) q^{15} +(0.411976 - 0.713564i) q^{17} +(0.233611 + 0.404626i) q^{19} +(-3.95416 - 2.31617i) q^{21} +(2.74950 - 4.76227i) q^{23} +(-3.30506 - 5.72452i) q^{25} +(4.68276 - 2.25205i) q^{27} +(0.400332 - 0.693396i) q^{29} -9.90732 q^{31} +(9.24265 - 1.39144i) q^{33} +(-7.01378 - 5.66371i) q^{35} +(4.34210 + 7.52074i) q^{37} +(-6.49468 + 0.977746i) q^{39} +(1.84467 + 3.19507i) q^{41} +(-4.36356 + 7.55790i) q^{43} +(9.76901 - 3.00957i) q^{45} -10.4991 q^{47} +(-6.66332 - 2.14481i) q^{49} +(0.889603 + 1.11593i) q^{51} +(-4.71820 + 8.17217i) q^{53} +18.3874 q^{55} +(-0.800234 + 0.120472i) q^{57} -1.66069 q^{59} +0.948811 q^{61} +(6.23743 - 4.90862i) q^{63} -12.9206 q^{65} +0.539184 q^{67} +(5.93714 + 7.44762i) q^{69} -3.86901 q^{71} +(2.58943 - 4.48502i) q^{73} +(11.3215 - 1.70440i) q^{75} +(13.3221 - 5.13490i) q^{77} +7.82899 q^{79} +(0.666244 + 8.97531i) q^{81} +(-3.79623 + 6.57527i) q^{83} +(1.40375 + 2.43137i) q^{85} +(0.864460 + 1.08439i) q^{87} +(-3.73498 - 6.46917i) q^{89} +(-9.36128 + 3.60823i) q^{91} +(6.27206 - 15.9727i) q^{93} -1.59199 q^{95} +(-3.22500 + 5.58587i) q^{97} +(-3.60798 + 15.7820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more