LMFDB - Embedded newform 572.2.i.c.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} + 6x^{7} + 59x^{6} + 2x^{5} + 47x^{4} - 26x^{3} + 38x^{2} - 12x + 4 $ x^10 - x^9 + 9x^8 + 6x^7 + 59x^6 + 2x^5 + 47x^4 - 26x^3 + 38x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.2
Root			$-0.542661 - 0.939916i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.c.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.542661 - 0.939916i) q^{3} -1.28140 q^{5} +(-1.24710 + 2.16005i) q^{7} +(0.911039 - 1.57797i) q^{9} +O(q^{10})$	\(q+(-0.542661 - 0.939916i) q^{3} -1.28140 q^{5} +(-1.24710 + 2.16005i) q^{7} +(0.911039 - 1.57797i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-2.63419 + 2.46191i) q^{13} +(0.695365 + 1.20441i) q^{15} +(-3.07045 + 5.31818i) q^{17} +(0.187000 - 0.323894i) q^{19} +2.70702 q^{21} +(0.919404 + 1.59245i) q^{23} -3.35801 q^{25} -5.23350 q^{27} +(4.13056 + 7.15433i) q^{29} -6.44774 q^{31} +(-0.542661 + 0.939916i) q^{33} +(1.59804 - 2.76789i) q^{35} +(1.17428 + 2.03392i) q^{37} +(3.74346 + 1.13994i) q^{39} +(1.98513 + 3.43835i) q^{41} +(-2.14070 + 3.70780i) q^{43} +(-1.16741 + 2.02201i) q^{45} -9.03014 q^{47} +(0.389462 + 0.674568i) q^{49} +6.66485 q^{51} +12.6446 q^{53} +(0.640700 + 1.10972i) q^{55} -0.405911 q^{57} +(4.07882 - 7.06472i) q^{59} +(3.18336 - 5.51374i) q^{61} +(2.27232 + 3.93578i) q^{63} +(3.37546 - 3.15470i) q^{65} +(-5.93502 - 10.2798i) q^{67} +(0.997848 - 1.72832i) q^{69} +(-3.27291 + 5.66885i) q^{71} -14.8984 q^{73} +(1.82226 + 3.15625i) q^{75} +2.49421 q^{77} -3.17910 q^{79} +(0.106898 + 0.185154i) q^{81} -17.3167 q^{83} +(3.93448 - 6.81471i) q^{85} +(4.48298 - 7.76475i) q^{87} +(-0.905248 - 1.56793i) q^{89} +(-2.03274 - 8.76025i) q^{91} +(3.49893 + 6.06033i) q^{93} +(-0.239622 + 0.415038i) q^{95} +(3.68319 - 6.37947i) q^{97} -1.82208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	$ 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.542661	−	0.939916i	−0.313305	−	0.542661i	0.665771	−	0.746157i	$-0.268103\pi$
$3$	−0.542661	−	0.939916i	−0.313305	−	0.542661i	−0.979076	+	0.203496i	$0.934770\pi$
$4$		0			0
$5$	−1.28140			−0.573060			−0.286530	−	0.958071i	$-0.592502\pi$
$5$	−1.28140			−0.573060			−0.286530	+	0.958071i	$0.592502\pi$
$6$		0			0
$7$	−1.24710	+	2.16005i	−0.471361	+	0.816421i	−0.999463	−	0.0327594i	$-0.989570\pi$
$7$	−1.24710	+	2.16005i	−0.471361	+	0.816421i	0.528102	+	0.849181i	$0.322904\pi$
$8$		0			0
$9$	0.911039	−	1.57797i	0.303680	−	0.525989i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−2.63419	+	2.46191i	−0.730594	+	0.682812i
$13$	−2.63419	+	2.46191i	−0.730594	+	0.682812i
$14$		0			0
$15$	0.695365	+	1.20441i	0.179543	+	0.310977i
$16$		0			0
$17$	−3.07045	+	5.31818i	−0.744694	+	1.28985i	0.205644	+	0.978627i	$0.434071\pi$
$17$	−3.07045	+	5.31818i	−0.744694	+	1.28985i	−0.950338	+	0.311221i	$0.899262\pi$
$18$		0			0
$19$	0.187000	−	0.323894i	0.0429008	−	0.0743064i	−0.843778	−	0.536693i	$-0.819673\pi$
$19$	0.187000	−	0.323894i	0.0429008	−	0.0743064i	0.886679	+	0.462386i	$0.153007\pi$
$20$		0			0
$21$	2.70702			0.590720
$22$		0			0
$23$	0.919404	+	1.59245i	0.191709	+	0.332050i	0.945817	−	0.324701i	$-0.105264\pi$
$23$	0.919404	+	1.59245i	0.191709	+	0.332050i	−0.754108	+	0.656751i	$0.771930\pi$
$24$		0			0
$25$	−3.35801			−0.671603
$26$		0			0
$27$	−5.23350			−1.00719
$28$		0			0
$29$	4.13056	+	7.15433i	0.767025	+	1.32853i	0.939169	+	0.343454i	$0.111597\pi$
$29$	4.13056	+	7.15433i	0.767025	+	1.32853i	−0.172145	+	0.985072i	$0.555070\pi$
$30$		0			0
$31$	−6.44774			−1.15805			−0.579024	−	0.815310i	$-0.696566\pi$
$31$	−6.44774			−1.15805			−0.579024	+	0.815310i	$0.696566\pi$
$32$		0			0
$33$	−0.542661	+	0.939916i	−0.0944651	+	0.163618i
$34$		0			0
$35$	1.59804	−	2.76789i	0.270118	−	0.467858i
$36$		0			0
$37$	1.17428	+	2.03392i	0.193051	+	0.334374i	0.946260	−	0.323408i	$-0.104828\pi$
$37$	1.17428	+	2.03392i	0.193051	+	0.334374i	−0.753209	+	0.657781i	$0.771495\pi$
$38$		0			0
$39$	3.74346	+	1.13994i	0.599434	+	0.182536i
$40$		0			0
$41$	1.98513	+	3.43835i	0.310025	+	0.536979i	0.978368	−	0.206874i	$-0.0663292\pi$
$41$	1.98513	+	3.43835i	0.310025	+	0.536979i	−0.668342	+	0.743854i	$0.732996\pi$
$42$		0			0
$43$	−2.14070	+	3.70780i	−0.326454	+	0.565434i	−0.981805	−	0.189889i	$-0.939187\pi$
$43$	−2.14070	+	3.70780i	−0.326454	+	0.565434i	0.655352	+	0.755324i	$0.272520\pi$
$44$		0			0
$45$	−1.16741	+	2.02201i	−0.174027	+	0.301423i
$46$		0			0
$47$	−9.03014			−1.31718			−0.658591	−	0.752501i	$-0.728847\pi$
$47$	−9.03014			−1.31718			−0.658591	+	0.752501i	$0.728847\pi$
$48$		0			0
$49$	0.389462	+	0.674568i	0.0556374	+	0.0963668i
$50$		0			0
$51$	6.66485			0.933266
$52$		0			0
$53$	12.6446			1.73686			0.868432	−	0.495808i	$-0.165128\pi$
$53$	12.6446			1.73686			0.868432	+	0.495808i	$0.165128\pi$
$54$		0			0
$55$	0.640700	+	1.10972i	0.0863920	+	0.149635i
$56$		0			0
$57$	−0.405911			−0.0537642
$58$		0			0
$59$	4.07882	−	7.06472i	0.531017	−	0.919748i	−0.468328	−	0.883555i	$-0.655144\pi$
$59$	4.07882	−	7.06472i	0.531017	−	0.919748i	0.999345	−	0.0361932i	$-0.0115232\pi$
$60$		0			0
$61$	3.18336	−	5.51374i	0.407588	−	0.705962i	−0.587031	−	0.809564i	$-0.699703\pi$
$61$	3.18336	−	5.51374i	0.407588	−	0.705962i	0.994619	+	0.103602i	$0.0330368\pi$
$62$		0			0
$63$	2.27232	+	3.93578i	0.286286	+	0.495861i
$64$		0			0
$65$	3.37546	−	3.15470i	0.418674	−	0.391292i
$66$		0			0
$67$	−5.93502	−	10.2798i	−0.725078	−	1.25587i	−0.958942	−	0.283603i	$-0.908470\pi$
$67$	−5.93502	−	10.2798i	−0.725078	−	1.25587i	0.233864	−	0.972269i	$-0.424863\pi$
$68$		0			0
$69$	0.997848	−	1.72832i	0.120127	−	0.208066i
$70$		0			0
$71$	−3.27291	+	5.66885i	−0.388423	+	0.672769i	−0.992238	−	0.124356i	$-0.960313\pi$
$71$	−3.27291	+	5.66885i	−0.388423	+	0.672769i	0.603814	+	0.797125i	$0.293647\pi$
$72$		0			0
$73$	−14.8984			−1.74372			−0.871860	−	0.489755i	$-0.837086\pi$
$73$	−14.8984			−1.74372			−0.871860	+	0.489755i	$0.837086\pi$
$74$		0			0
$75$	1.82226	+	3.15625i	0.210417	+	0.364452i
$76$		0			0
$77$	2.49421			0.284241
$78$		0			0
$79$	−3.17910			−0.357677			−0.178839	−	0.983878i	$-0.557234\pi$
$79$	−3.17910			−0.357677			−0.178839	+	0.983878i	$0.557234\pi$
$80$		0			0
$81$	0.106898	+	0.185154i	0.0118776	+	0.0205726i
$82$		0			0
$83$	−17.3167			−1.90075			−0.950377	−	0.311101i	$-0.899302\pi$
$83$	−17.3167			−1.90075			−0.950377	+	0.311101i	$0.899302\pi$
$84$		0			0
$85$	3.93448	−	6.81471i	0.426754	−	0.739159i
$86$		0			0
$87$	4.48298	−	7.76475i	0.480626	−	0.832468i
$88$		0			0
$89$	−0.905248	−	1.56793i	−0.0959561	−	0.166201i	0.814051	−	0.580793i	$-0.197257\pi$
$89$	−0.905248	−	1.56793i	−0.0959561	−	0.166201i	−0.910007	+	0.414592i	$0.863924\pi$
$90$		0			0
$91$	−2.03274	−	8.76025i	−0.213089	−	0.918324i
$92$		0			0
$93$	3.49893	+	6.06033i	0.362823	+	0.628427i
$94$		0			0
$95$	−0.239622	+	0.415038i	−0.0245847	+	0.0425820i
$96$		0			0
$97$	3.68319	−	6.37947i	0.373971	−	0.647738i	−0.616201	−	0.787589i	$-0.711329\pi$
$97$	3.68319	−	6.37947i	0.373971	−	0.647738i	0.990173	+	0.139851i	$0.0446625\pi$
$98$		0			0
$99$	−1.82208			−0.183126
$100$		0			0
$101$	−0.649779	−	1.12545i	−0.0646554	−	0.111986i	0.831886	−	0.554947i	$-0.187261\pi$
$101$	−0.649779	−	1.12545i	−0.0646554	−	0.111986i	−0.896541	+	0.442961i	$0.853928\pi$
$102$		0			0
$103$	15.6572			1.54275			0.771376	−	0.636379i	$-0.219569\pi$
$103$	15.6572			1.54275			0.771376	+	0.636379i	$0.219569\pi$
$104$		0			0
$105$	−3.46877			−0.338517
$106$		0			0
$107$	−0.898540	−	1.55632i	−0.0868652	−	0.150455i	0.819319	−	0.573337i	$-0.194352\pi$
$107$	−0.898540	−	1.55632i	−0.0868652	−	0.150455i	−0.906184	+	0.422883i	$0.861018\pi$
$108$		0			0
$109$	10.1064			0.968019			0.484010	−	0.875063i	$-0.339180\pi$
$109$	10.1064			0.968019			0.484010	+	0.875063i	$0.339180\pi$
$110$		0			0
$111$	1.27447	−	2.20745i	0.120968	−	0.209522i
$112$		0			0
$113$	−2.47499	+	4.28680i	−0.232827	+	0.403268i	−0.958639	−	0.284625i	$-0.908131\pi$
$113$	−2.47499	+	4.28680i	−0.232827	+	0.403268i	0.725812	+	0.687893i	$0.241464\pi$
$114$		0			0
$115$	−1.17812	−	2.04057i	−0.109861	−	0.190284i
$116$		0			0
$117$	1.48496	+	6.39957i	0.137285	+	0.591640i
$118$		0			0
$119$	−7.65835	−	13.2646i	−0.702039	−	1.21597i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	2.15450	−	3.73171i	0.194265	−	0.336477i
$124$		0			0
$125$	10.7100			0.957928
$126$		0			0
$127$	−9.25186	−	16.0247i	−0.820970	−	1.42196i	−0.904961	−	0.425495i	$-0.860100\pi$
$127$	−9.25186	−	16.0247i	−0.820970	−	1.42196i	0.0839906	−	0.996467i	$-0.473233\pi$
$128$		0			0
$129$	4.64669			0.409119
$130$		0			0
$131$	10.9833			0.959619			0.479809	−	0.877373i	$-0.340706\pi$
$131$	10.9833			0.959619			0.479809	+	0.877373i	$0.340706\pi$
$132$		0			0
$133$	0.466418	+	0.807860i	0.0404436	+	0.0700503i
$134$		0			0
$135$	6.70621			0.577179
$136$		0			0
$137$	−4.72644	+	8.18644i	−0.403807	+	0.699415i	−0.994182	−	0.107715i	$-0.965647\pi$
$137$	−4.72644	+	8.18644i	−0.403807	+	0.699415i	0.590375	+	0.807129i	$0.298980\pi$
$138$		0			0
$139$	8.11547	−	14.0564i	0.688345	−	1.19225i	−0.284028	−	0.958816i	$-0.591671\pi$
$139$	8.11547	−	14.0564i	0.688345	−	1.19225i	0.972373	−	0.233432i	$-0.0749957\pi$
$140$		0			0
$141$	4.90030	+	8.48757i	0.412680	+	0.714783i
$142$		0			0
$143$	3.44918	+	1.05032i	0.288435	+	0.0878324i
$144$		0			0
$145$	−5.29289	−	9.16756i	−0.439551	−	0.761324i
$146$		0			0
$147$	0.422691	−	0.732122i	0.0348630	−	0.0603844i
$148$		0			0
$149$	−2.44897	+	4.24175i	−0.200628	+	0.347498i	−0.948731	−	0.316085i	$-0.897632\pi$
$149$	−2.44897	+	4.24175i	−0.200628	+	0.347498i	0.748103	+	0.663583i	$0.230965\pi$
$150$		0			0
$151$	−1.97273			−0.160539			−0.0802693	−	0.996773i	$-0.525578\pi$
$151$	−1.97273			−0.160539			−0.0802693	+	0.996773i	$0.525578\pi$
$152$		0			0
$153$	5.59460	+	9.69013i	0.452297	+	0.783401i
$154$		0			0
$155$	8.26213			0.663630
$156$		0			0
$157$	−9.84504			−0.785720			−0.392860	−	0.919598i	$-0.628514\pi$
$157$	−9.84504			−0.785720			−0.392860	+	0.919598i	$0.628514\pi$
$158$		0			0
$159$	−6.86170	−	11.8848i	−0.544169	−	0.942528i
$160$		0			0
$161$	−4.58637			−0.361457
$162$		0			0
$163$	5.61383	−	9.72343i	0.439709	−	0.761598i	−0.557958	−	0.829869i	$-0.688415\pi$
$163$	5.61383	−	9.72343i	0.439709	−	0.761598i	0.997667	+	0.0682713i	$0.0217483\pi$
$164$		0			0
$165$	0.695365	−	1.20441i	0.0541341	−	0.0937630i
$166$		0			0
$167$	7.55216	+	13.0807i	0.584404	+	1.01222i	0.994949	+	0.100377i	$0.0320049\pi$
$167$	7.55216	+	13.0807i	0.584404	+	1.01222i	−0.410546	+	0.911840i	$0.634662\pi$
$168$		0			0
$169$	0.877966	−	12.9703i	0.0675358	−	0.997717i
$170$		0			0
$171$	−0.340729	−	0.590161i	−0.0260562	−	0.0451307i
$172$		0			0
$173$	3.40040	−	5.88967i	0.258528	−	0.447783i	−0.707320	−	0.706893i	$-0.750096\pi$
$173$	3.40040	−	5.88967i	0.258528	−	0.447783i	0.965848	+	0.259110i	$0.0834294\pi$
$174$		0			0
$175$	4.18779	−	7.25347i	0.316567	−	0.548311i
$176$		0			0
$177$	−8.85365			−0.665481
$178$		0			0
$179$	7.06209	+	12.2319i	0.527845	+	0.914255i	0.999473	+	0.0324570i	$0.0103332\pi$
$179$	7.06209	+	12.2319i	0.527845	+	0.914255i	−0.471628	+	0.881798i	$0.656333\pi$
$180$		0			0
$181$	−22.6671			−1.68483			−0.842416	−	0.538828i	$-0.818867\pi$
$181$	−22.6671			−1.68483			−0.842416	+	0.538828i	$0.818867\pi$
$182$		0			0
$183$	−6.90994			−0.510797
$184$		0			0
$185$	−1.50472	−	2.60626i	−0.110630	−	0.191616i
$186$		0			0
$187$	6.14090			0.449067
$188$		0			0
$189$	6.52672	−	11.3046i	0.474749	−	0.822290i
$190$		0			0
$191$	−1.20912	+	2.09426i	−0.0874890	+	0.151535i	−0.906449	−	0.422315i	$-0.861218\pi$
$191$	−1.20912	+	2.09426i	−0.0874890	+	0.151535i	0.818960	+	0.573850i	$0.194551\pi$
$192$		0			0
$193$	11.2279	+	19.4473i	0.808203	+	1.39985i	0.914107	+	0.405473i	$0.132893\pi$
$193$	11.2279	+	19.4473i	0.808203	+	1.39985i	−0.105904	+	0.994376i	$0.533774\pi$
$194$		0			0
$195$	−4.79688	−	1.46072i	−0.343511	−	0.104604i
$196$		0			0
$197$	12.0633	+	20.8943i	0.859476	+	1.48866i	0.872429	+	0.488741i	$0.162544\pi$
$197$	12.0633	+	20.8943i	0.859476	+	1.48866i	−0.0129525	+	0.999916i	$0.504123\pi$
$198$		0			0
$199$	−11.8229	+	20.4778i	−0.838101	+	1.45163i	0.0533792	+	0.998574i	$0.483001\pi$
$199$	−11.8229	+	20.4778i	−0.838101	+	1.45163i	−0.891480	+	0.453059i	$0.850333\pi$
$200$		0			0
$201$	−6.44140	+	11.1568i	−0.454342	+	0.786943i
$202$		0			0
$203$	−20.6049			−1.44618
$204$		0			0
$205$	−2.54375	−	4.40590i	−0.177663	−	0.307721i
$206$		0			0
$207$	3.35045			0.232872
$208$		0			0
$209$	−0.374001			−0.0258702
$210$		0			0
$211$	−2.57916	−	4.46723i	−0.177557	−	0.307537i	0.763486	−	0.645824i	$-0.223486\pi$
$211$	−2.57916	−	4.46723i	−0.177557	−	0.307537i	−0.941043	+	0.338287i	$0.890153\pi$
$212$		0			0
$213$	7.10432			0.486780
$214$		0			0
$215$	2.74309	−	4.75118i	0.187077	−	0.324028i
$216$		0			0
$217$	8.04100	−	13.9274i	0.545859	−	0.945455i
$218$		0			0
$219$	8.08475	+	14.0032i	0.546317	+	0.946248i
$220$		0			0
$221$	−5.00472	−	21.5683i	−0.336654	−	1.45084i
$222$		0			0
$223$	7.58012	+	13.1292i	0.507602	+	0.879193i	0.999961	+	0.00880089i	$0.00280145\pi$
$223$	7.58012	+	13.1292i	0.507602	+	0.879193i	−0.492359	+	0.870392i	$0.663865\pi$
$224$		0			0
$225$	−3.05928	+	5.29883i	−0.203952	+	0.353255i
$226$		0			0
$227$	7.15433	−	12.3917i	0.474850	−	0.822464i	−0.524735	−	0.851265i	$-0.675836\pi$
$227$	7.15433	−	12.3917i	0.474850	−	0.822464i	0.999585	+	0.0288014i	$0.00916903\pi$
$228$		0			0
$229$	−20.2644			−1.33911			−0.669555	−	0.742762i	$-0.733515\pi$
$229$	−20.2644			−1.33911			−0.669555	+	0.742762i	$0.733515\pi$
$230$		0			0
$231$	−1.35351	−	2.34435i	−0.0890543	−	0.154247i
$232$		0			0
$233$	6.72266			0.440416			0.220208	−	0.975453i	$-0.429326\pi$
$233$	6.72266			0.440416			0.220208	+	0.975453i	$0.429326\pi$
$234$		0			0
$235$	11.5712			0.754824
$236$		0			0
$237$	1.72517	+	2.98809i	0.112062	+	0.194097i
$238$		0			0
$239$	1.53746			0.0994503			0.0497251	−	0.998763i	$-0.484165\pi$
$239$	1.53746			0.0994503			0.0497251	+	0.998763i	$0.484165\pi$
$240$		0			0
$241$	2.82985	−	4.90145i	0.182287	−	0.315730i	−0.760372	−	0.649488i	$-0.774983\pi$
$241$	2.82985	−	4.90145i	0.182287	−	0.315730i	0.942659	+	0.333758i	$0.108317\pi$
$242$		0			0
$243$	−7.73424	+	13.3961i	−0.496151	+	0.859360i
$244$		0			0
$245$	−0.499056	−	0.864391i	−0.0318835	−	0.0552239i
$246$		0			0
$247$	0.304804	+	1.31358i	0.0193942	+	0.0835810i
$248$		0			0
$249$	9.39709	+	16.2762i	0.595516	+	1.03146i
$250$		0			0
$251$	−8.21899	+	14.2357i	−0.518778	+	0.898550i	0.480984	+	0.876730i	$0.340280\pi$
$251$	−8.21899	+	14.2357i	−0.518778	+	0.898550i	−0.999762	+	0.0218208i	$0.993054\pi$
$252$		0			0
$253$	0.919404	−	1.59245i	0.0578024	−	0.100117i
$254$		0			0
$255$	−8.54034			−0.534817
$256$		0			0
$257$	4.42122	+	7.65777i	0.275788	+	0.477679i	0.970334	−	0.241770i	$-0.0777279\pi$
$257$	4.42122	+	7.65777i	0.275788	+	0.477679i	−0.694546	+	0.719449i	$0.744395\pi$
$258$		0			0
$259$	−5.85781			−0.363987
$260$		0			0
$261$	15.0524			0.931719
$262$		0			0
$263$	−0.796659	−	1.37985i	−0.0491241	−	0.0850854i	0.840418	−	0.541939i	$-0.182310\pi$
$263$	−0.796659	−	1.37985i	−0.0491241	−	0.0850854i	−0.889542	+	0.456854i	$0.848976\pi$
$264$		0			0
$265$	−16.2027			−0.995326
$266$		0			0
$267$	−0.982484	+	1.70171i	−0.0601271	+	0.104143i
$268$		0			0
$269$	12.4317	−	21.5324i	0.757976	−	1.31285i	−0.185905	−	0.982568i	$-0.559522\pi$
$269$	12.4317	−	21.5324i	0.757976	−	1.31285i	0.943881	−	0.330286i	$-0.107145\pi$
$270$		0			0
$271$	−0.984233	−	1.70474i	−0.0597879	−	0.103556i	0.834582	−	0.550883i	$-0.185709\pi$
$271$	−0.984233	−	1.70474i	−0.0597879	−	0.103556i	−0.894370	+	0.447328i	$0.852376\pi$
$272$		0			0
$273$	−7.13081	+	6.66444i	−0.431576	+	0.403350i
$274$		0			0
$275$	1.67901	+	2.90813i	0.101248	+	0.175367i
$276$		0			0
$277$	−7.63162	+	13.2184i	−0.458540	+	0.794214i	−0.998884	−	0.0472299i	$-0.984961\pi$
$277$	−7.63162	+	13.2184i	−0.458540	+	0.794214i	0.540344	+	0.841444i	$0.318294\pi$
$278$		0			0
$279$	−5.87414	+	10.1743i	−0.351676	+	0.609120i
$280$		0			0
$281$	−31.1697			−1.85943			−0.929713	−	0.368284i	$-0.879945\pi$
$281$	−31.1697			−1.85943			−0.929713	+	0.368284i	$0.879945\pi$
$282$		0			0
$283$	14.9768	+	25.9406i	0.890277	+	1.54201i	0.839543	+	0.543294i	$0.182823\pi$
$283$	14.9768	+	25.9406i	0.890277	+	1.54201i	0.0507346	+	0.998712i	$0.483844\pi$
$284$		0			0
$285$	0.520134			0.0308101
$286$		0			0
$287$	−9.90266			−0.584535
$288$		0			0
$289$	−10.3553	−	17.9360i	−0.609138	−	1.05506i
$290$		0			0
$291$	−7.99489			−0.468669
$292$		0			0
$293$	−6.57623	+	11.3904i	−0.384187	+	0.665432i	−0.991656	−	0.128912i	$-0.958852\pi$
$293$	−6.57623	+	11.3904i	−0.384187	+	0.665432i	0.607469	+	0.794343i	$0.292185\pi$
$294$		0			0
$295$	−5.22659	+	9.05273i	−0.304304	+	0.527070i
$296$		0			0
$297$	2.61675	+	4.53235i	0.151839	+	0.262993i
$298$		0			0
$299$	−6.34237	−	1.93134i	−0.366789	−	0.111692i
$300$		0			0
$301$	−5.33935	−	9.24803i	−0.307755	−	0.533048i
$302$		0			0
$303$	−0.705218	+	1.22147i	−0.0405137	+	0.0701718i
$304$		0			0
$305$	−4.07916	+	7.06531i	−0.233572	+	0.404558i
$306$		0			0
$307$	5.28323			0.301530			0.150765	−	0.988570i	$-0.451826\pi$
$307$	5.28323			0.301530			0.150765	+	0.988570i	$0.451826\pi$
$308$		0			0
$309$	−8.49656	−	14.7165i	−0.483353	−	0.837191i
$310$		0			0
$311$	0.149737			0.00849080			0.00424540	−	0.999991i	$-0.498649\pi$
$311$	0.149737			0.00849080			0.00424540	+	0.999991i	$0.498649\pi$
$312$		0			0
$313$	−28.9562			−1.63670			−0.818350	−	0.574720i	$-0.805111\pi$
$313$	−28.9562			−1.63670			−0.818350	+	0.574720i	$0.805111\pi$
$314$		0			0
$315$	−2.91175	−	5.04330i	−0.164059	−	0.284158i
$316$		0			0
$317$	17.1837			0.965134			0.482567	−	0.875859i	$-0.339705\pi$
$317$	17.1837			0.965134			0.482567	+	0.875859i	$0.339705\pi$
$318$		0			0
$319$	4.13056	−	7.15433i	0.231267	−	0.400566i
$320$		0			0
$321$	−0.975205	+	1.68910i	−0.0544306	+	0.0942766i
$322$		0			0
$323$	1.14835	+	1.98900i	0.0638960	+	0.110671i
$324$		0			0
$325$	8.84566	−	8.26714i	0.490669	−	0.458578i
$326$		0			0
$327$	−5.48436	−	9.49918i	−0.303286	−	0.525306i
$328$		0			0
$329$	11.2615	−	19.5055i	0.620868	−	1.07538i
$330$		0			0
$331$	−8.06900	+	13.9759i	−0.443512	+	0.768186i	−0.997947	−	0.0640414i	$-0.979601\pi$
$331$	−8.06900	+	13.9759i	−0.443512	+	0.768186i	0.554435	+	0.832227i	$0.312934\pi$
$332$		0			0
$333$	4.27927			0.234502
$334$		0			0
$335$	7.60514	+	13.1725i	0.415513	+	0.719690i
$336$		0			0
$337$	3.46802			0.188915			0.0944576	−	0.995529i	$-0.469888\pi$
$337$	3.46802			0.188915			0.0944576	+	0.995529i	$0.469888\pi$
$338$		0			0
$339$	5.37231			0.291784
$340$		0			0
$341$	3.22387	+	5.58391i	0.174582	+	0.302385i
$342$		0			0
$343$	−19.4023			−1.04762
$344$		0			0
$345$	−1.27864	+	2.21467i	−0.0688398	+	0.119234i
$346$		0			0
$347$	−4.90904	+	8.50271i	−0.263531	+	0.456450i	−0.967178	−	0.254101i	$-0.918221\pi$
$347$	−4.90904	+	8.50271i	−0.263531	+	0.456450i	0.703647	+	0.710550i	$0.251554\pi$
$348$		0			0
$349$	3.30899	+	5.73134i	0.177126	+	0.306791i	0.940895	−	0.338698i	$-0.109987\pi$
$349$	3.30899	+	5.73134i	0.177126	+	0.306791i	−0.763769	+	0.645490i	$0.776653\pi$
$350$		0			0
$351$	13.7861	−	12.8844i	0.735846	−	0.687720i
$352$		0			0
$353$	11.4955	+	19.9108i	0.611844	+	1.05975i	0.990929	+	0.134384i	$0.0429055\pi$
$353$	11.4955	+	19.9108i	0.611844	+	1.05975i	−0.379085	+	0.925362i	$0.623761\pi$
$354$		0			0
$355$	4.19391	−	7.26407i	0.222590	−	0.385537i
$356$		0			0
$357$	−8.31176	+	14.3964i	−0.439905	+	0.761938i
$358$		0			0
$359$	2.32235			0.122569			0.0612845	−	0.998120i	$-0.480480\pi$
$359$	2.32235			0.122569			0.0612845	+	0.998120i	$0.480480\pi$
$360$		0			0
$361$	9.43006	+	16.3333i	0.496319	+	0.859650i
$362$		0			0
$363$	1.08532			0.0569646
$364$		0			0
$365$	19.0908			0.999256
$366$		0			0
$367$	2.25524	+	3.90619i	0.117723	+	0.203901i	0.918865	−	0.394573i	$-0.129107\pi$
$367$	2.25524	+	3.90619i	0.117723	+	0.203901i	−0.801142	+	0.598474i	$0.795774\pi$
$368$		0			0
$369$	7.23412			0.376593
$370$		0			0
$371$	−15.7691	+	27.3129i	−0.818690	+	1.41801i
$372$		0			0
$373$	11.7495	−	20.3507i	0.608366	−	1.05372i	−0.383144	−	0.923689i	$-0.625159\pi$
$373$	11.7495	−	20.3507i	0.608366	−	1.05372i	0.991510	−	0.130032i	$-0.0415079\pi$
$374$		0			0
$375$	−5.81187	−	10.0665i	−0.300124	−	0.519830i
$376$		0			0
$377$	−28.4940	−	8.67683i	−1.46752	−	0.446880i
$378$		0			0
$379$	−11.1362	−	19.2885i	−0.572028	−	0.990782i	−0.996358	−	0.0852737i	$-0.972824\pi$
$379$	−11.1362	−	19.2885i	−0.572028	−	0.990782i	0.424330	−	0.905508i	$-0.360510\pi$
$380$		0			0
$381$	−10.0412	+	17.3919i	−0.514428	+	0.891016i
$382$		0			0
$383$	−1.79725	+	3.11292i	−0.0918350	+	0.159063i	−0.908283	−	0.418356i	$-0.862607\pi$
$383$	−1.79725	+	3.11292i	−0.0918350	+	0.159063i	0.816448	+	0.577419i	$0.195940\pi$
$384$		0			0
$385$	−3.19608			−0.162887
$386$		0			0
$387$	3.90052	+	6.75590i	0.198275	+	0.343422i
$388$		0			0
$389$	36.5723			1.85429			0.927144	−	0.374706i	$-0.122256\pi$
$389$	36.5723			1.85429			0.927144	+	0.374706i	$0.122256\pi$
$390$		0			0
$391$	−11.2919			−0.571058
$392$		0			0
$393$	−5.96022	−	10.3234i	−0.300654	−	0.520747i
$394$		0			0
$395$	4.07370			0.204970
$396$		0			0
$397$	−1.21753	+	2.10883i	−0.0611063	+	0.105839i	−0.894960	−	0.446146i	$-0.852796\pi$
$397$	−1.21753	+	2.10883i	−0.0611063	+	0.105839i	0.833854	+	0.551985i	$0.186130\pi$
$398$		0			0
$399$	0.506213	−	0.876787i	0.0253424	−	0.0438943i
$400$		0			0
$401$	−4.54048	−	7.86434i	−0.226741	−	0.392727i	0.730099	−	0.683341i	$-0.239474\pi$
$401$	−4.54048	−	7.86434i	−0.226741	−	0.392727i	−0.956840	+	0.290614i	$0.906140\pi$
$402$		0			0
$403$	16.9846	−	15.8738i	0.846063	−	0.790729i
$404$		0			0
$405$	−0.136980	−	0.237256i	−0.00680657	−	0.0117893i
$406$		0			0
$407$	1.17428	−	2.03392i	0.0582070	−	0.100817i
$408$		0			0
$409$	0.203111	−	0.351799i	0.0100432	−	0.0173953i	−0.860960	−	0.508672i	$-0.830136\pi$
$409$	0.203111	−	0.351799i	0.0100432	−	0.0173953i	0.871003	+	0.491277i	$0.163470\pi$
$410$		0			0
$411$	10.2594			0.506060
$412$		0			0
$413$	10.1734	+	17.6209i	0.500601	+	0.867067i
$414$		0			0
$415$	22.1896			1.08925
$416$		0			0
$417$	−17.6158			−0.862648
$418$		0			0
$419$	−4.27288	−	7.40084i	−0.208744	−	0.361555i	0.742575	−	0.669763i	$-0.233604\pi$
$419$	−4.27288	−	7.40084i	−0.208744	−	0.361555i	−0.951319	+	0.308208i	$0.900271\pi$
$420$		0			0
$421$	−7.68530			−0.374559			−0.187279	−	0.982307i	$-0.559967\pi$
$421$	−7.68530			−0.374559			−0.187279	+	0.982307i	$0.559967\pi$
$422$		0			0
$423$	−8.22681	+	14.2493i	−0.400001	+	0.692823i
$424$		0			0
$425$	10.3106	−	17.8585i	0.500138	−	0.866265i
$426$		0			0
$427$	7.93997	+	13.7524i	0.384242	+	0.665526i
$428$		0			0
$429$	−0.884517	−	3.81190i	−0.0427049	−	0.184040i
$430$		0			0
$431$	14.6713	+	25.4114i	0.706690	+	1.22402i	0.966078	+	0.258249i	$0.0831456\pi$
$431$	14.6713	+	25.4114i	0.706690	+	1.22402i	−0.259389	+	0.965773i	$0.583521\pi$
$432$		0			0
$433$	−4.27709	+	7.40814i	−0.205544	+	0.356013i	−0.950306	−	0.311318i	$-0.899230\pi$
$433$	−4.27709	+	7.40814i	−0.205544	+	0.356013i	0.744762	+	0.667330i	$0.232563\pi$
$434$		0			0
$435$	−5.74449	+	9.94975i	−0.275427	+	0.477054i
$436$		0			0
$437$	0.687716			0.0328979
$438$		0			0
$439$	2.89662	+	5.01709i	0.138248	+	0.239453i	0.926834	−	0.375473i	$-0.122520\pi$
$439$	2.89662	+	5.01709i	0.138248	+	0.239453i	−0.788586	+	0.614925i	$0.789186\pi$
$440$		0			0
$441$	1.41926			0.0675838
$442$		0			0
$443$	−21.3714			−1.01539			−0.507693	−	0.861538i	$-0.669501\pi$
$443$	−21.3714			−1.01539			−0.507693	+	0.861538i	$0.669501\pi$
$444$		0			0
$445$	1.15998	+	2.00915i	0.0549885	+	0.0952429i
$446$		0			0
$447$	5.31585			0.251431
$448$		0			0
$449$	10.2570	−	17.7657i	0.484058	−	0.838413i	−0.515774	−	0.856725i	$-0.672496\pi$
$449$	10.2570	−	17.7657i	0.484058	−	0.838413i	0.999832	+	0.0183112i	$0.00582896\pi$
$450$		0			0
$451$	1.98513	−	3.43835i	0.0934761	−	0.161905i
$452$		0			0
$453$	1.07052	+	1.85420i	0.0502976	+	0.0871180i
$454$		0			0
$455$	2.60475	+	11.2254i	0.122112	+	0.526254i
$456$		0			0
$457$	−15.3951	−	26.6651i	−0.720154	−	1.24734i	−0.960938	−	0.276764i	$-0.910738\pi$
$457$	−15.3951	−	26.6651i	−0.720154	−	1.24734i	0.240784	−	0.970579i	$-0.422595\pi$
$458$		0			0
$459$	16.0692	−	27.8327i	0.750047	−	1.29912i
$460$		0			0
$461$	−11.8077	+	20.4516i	−0.549942	+	0.952527i	0.448336	+	0.893865i	$0.352017\pi$
$461$	−11.8077	+	20.4516i	−0.549942	+	0.952527i	−0.998278	+	0.0586619i	$0.981317\pi$
$462$		0			0
$463$	−4.25379			−0.197691			−0.0988453	−	0.995103i	$-0.531515\pi$
$463$	−4.25379			−0.197691			−0.0988453	+	0.995103i	$0.531515\pi$
$464$		0			0
$465$	−4.48353	−	7.76571i	−0.207919	−	0.360126i
$466$		0			0
$467$	40.9716			1.89594			0.947970	−	0.318361i	$-0.103132\pi$
$467$	40.9716			1.89594			0.947970	+	0.318361i	$0.103132\pi$
$468$		0			0
$469$	29.6064			1.36709
$470$		0			0
$471$	5.34252	+	9.25351i	0.246170	+	0.426379i
$472$		0			0
$473$	4.28140			0.196859
$474$		0			0
$475$	−0.627950	+	1.08764i	−0.0288123	+	0.0499044i
$476$		0			0
$477$	11.5197	−	19.9527i	0.527450	−	0.913571i
$478$		0			0
$479$	−9.47023	−	16.4029i	−0.432706	−	0.749469i	0.564399	−	0.825502i	$-0.309108\pi$
$479$	−9.47023	−	16.4029i	−0.432706	−	0.749469i	−0.997105	+	0.0760332i	$0.975775\pi$
$480$		0			0
$481$	−8.10061	−	2.46675i	−0.369356	−	0.112474i
$482$		0			0
$483$	2.48884	+	4.31080i	0.113246	+	0.196148i
$484$		0			0
$485$	−4.71964	+	8.17466i	−0.214308	+	0.371192i
$486$		0			0
$487$	4.10920	−	7.11734i	0.186206	−	0.322517i	−0.757777	−	0.652514i	$-0.773714\pi$
$487$	4.10920	−	7.11734i	0.186206	−	0.322517i	0.943982	+	0.329997i	$0.107048\pi$
$488$		0			0
$489$	−12.1856			−0.551052
$490$		0			0
$491$	−6.75967	−	11.7081i	−0.305060	−	0.528379i	0.672215	−	0.740356i	$-0.265343\pi$
$491$	−6.75967	−	11.7081i	−0.305060	−	0.528379i	−0.977275	+	0.211977i	$0.932010\pi$
$492$		0			0
$493$	−50.7307			−2.28479
$494$		0			0
$495$	2.33481			0.104942
$496$		0			0
$497$	−8.16333	−	14.1393i	−0.366175	−	0.634234i
$498$		0			0
$499$	−6.63251			−0.296912			−0.148456	−	0.988919i	$-0.547430\pi$
$499$	−6.63251			−0.296912			−0.148456	+	0.988919i	$0.547430\pi$
$500$		0			0
$501$	8.19652	−	14.1968i	0.366193	−	0.634266i
$502$		0			0
$503$	−0.634098	+	1.09829i	−0.0282730	+	0.0489703i	−0.879816	−	0.475315i	$-0.842334\pi$
$503$	−0.634098	+	1.09829i	−0.0282730	+	0.0489703i	0.851543	+	0.524285i	$0.175667\pi$
$504$		0			0
$505$	0.832626	+	1.44215i	0.0370514	+	0.0641749i
$506$		0			0
$507$	−12.6674	+	6.21327i	−0.562581	+	0.275941i
$508$		0			0
$509$	0.0229687	+	0.0397830i	0.00101807	+	0.00176335i	0.866534	−	0.499118i	$-0.166343\pi$
$509$	0.0229687	+	0.0397830i	0.00101807	+	0.00176335i	−0.865516	+	0.500881i	$0.833009\pi$
$510$		0			0
$511$	18.5798	−	32.1812i	0.821922	−	1.42361i
$512$		0			0
$513$	−0.978667	+	1.69510i	−0.0432092	+	0.0748405i
$514$		0			0
$515$	−20.0632			−0.884089
$516$		0			0
$517$	4.51507	+	7.82033i	0.198573	+	0.343938i
$518$		0			0
$519$	−7.38105			−0.323992
$520$		0			0
$521$	−6.07130			−0.265989			−0.132994	−	0.991117i	$-0.542459\pi$
$521$	−6.07130			−0.265989			−0.132994	+	0.991117i	$0.542459\pi$
$522$		0			0
$523$	9.51895	+	16.4873i	0.416235	+	0.720940i	0.995557	−	0.0941587i	$-0.0300161\pi$
$523$	9.51895	+	16.4873i	0.416235	+	0.720940i	−0.579322	+	0.815099i	$0.696683\pi$
$524$		0			0
$525$	−9.09020			−0.396729
$526$		0			0
$527$	19.7975	−	34.2902i	0.862391	−	1.49371i
$528$		0			0
$529$	9.80939	−	16.9904i	0.426495	−	0.738712i
$530$		0			0
$531$	−7.43192	−	12.8725i	−0.322518	−	0.558617i
$532$		0			0
$533$	−13.6941	−	4.17006i	−0.593159	−	0.180625i
$534$		0			0
$535$	1.15139	+	1.99427i	0.0497789	+	0.0862196i
$536$		0			0
$537$	7.66463	−	13.2755i	0.330753	−	0.572881i
$538$		0			0
$539$	0.389462	−	0.674568i	0.0167753	−	0.0290557i
$540$		0			0
$541$	31.7778			1.36623			0.683116	−	0.730310i	$-0.260624\pi$
$541$	31.7778			1.36623			0.683116	+	0.730310i	$0.260624\pi$
$542$		0			0
$543$	12.3005	+	21.3051i	0.527866	+	0.914291i
$544$		0			0
$545$	−12.9504			−0.554733
$546$		0			0
$547$	−2.38974			−0.102178			−0.0510890	−	0.998694i	$-0.516269\pi$
$547$	−2.38974			−0.102178			−0.0510890	+	0.998694i	$0.516269\pi$
$548$		0			0
$549$	−5.80033	−	10.0465i	−0.247552	−	0.428773i
$550$		0			0
$551$	3.08966			0.131624
$552$		0			0
$553$	3.96467	−	6.86702i	0.168595	−	0.292015i
$554$		0			0
$555$	−1.63311	+	2.82863i	−0.0693216	+	0.120069i
$556$		0			0
$557$	−0.0775645	−	0.134346i	−0.00328651	−	0.00569241i	0.864377	−	0.502844i	$-0.167713\pi$
$557$	−0.0775645	−	0.134346i	−0.00328651	−	0.00569241i	−0.867664	+	0.497151i	$0.834379\pi$
$558$		0			0
$559$	−3.48926	−	15.0373i	−0.147580	−	0.636010i
$560$		0			0
$561$	−3.33243	−	5.77193i	−0.140695	−	0.243691i
$562$		0			0
$563$	−21.6644	+	37.5238i	−0.913044	+	1.58144i	−0.103304	+	0.994650i	$0.532941\pi$
$563$	−21.6644	+	37.5238i	−0.913044	+	1.58144i	−0.809740	+	0.586789i	$0.800392\pi$
$564$		0			0
$565$	3.17145	−	5.49311i	0.133424	−	0.231097i
$566$		0			0
$567$	−0.533254			−0.0223946
$568$		0			0
$569$	−7.53399	−	13.0492i	−0.315841	−	0.547053i	0.663775	−	0.747933i	$-0.268953\pi$
$569$	−7.53399	−	13.0492i	−0.315841	−	0.547053i	−0.979616	+	0.200880i	$0.935620\pi$
$570$		0			0
$571$	26.5521			1.11117			0.555586	−	0.831459i	$-0.312494\pi$
$571$	26.5521			1.11117			0.555586	+	0.831459i	$0.312494\pi$
$572$		0			0
$573$	2.62457			0.109643
$574$		0			0
$575$	−3.08737	−	5.34748i	−0.128752	−	0.223005i
$576$		0			0
$577$	−2.43141			−0.101221			−0.0506105	−	0.998718i	$-0.516117\pi$
$577$	−2.43141			−0.101221			−0.0506105	+	0.998718i	$0.516117\pi$
$578$		0			0
$579$	12.1859	−	21.1066i	0.506429	−	0.877160i
$580$		0			0
$581$	21.5957	−	37.4049i	0.895941	−	1.55182i
$582$		0			0
$583$	−6.32228	−	10.9505i	−0.261842	−	0.453524i
$584$		0			0
$585$	−1.90283	−	8.20041i	−0.0786723	−	0.339045i
$586$		0			0
$587$	−5.50352	−	9.53237i	−0.227154	−	0.393443i	0.729809	−	0.683651i	$-0.239609\pi$
$587$	−5.50352	−	9.53237i	−0.227154	−	0.393443i	−0.956964	+	0.290208i	$0.906276\pi$
$588$		0			0
$589$	−1.20573	+	2.08839i	−0.0496812	+	0.0860504i
$590$		0			0
$591$	13.0926	−	22.6770i	0.538557	−	0.932808i
$592$		0			0
$593$	43.1297			1.77113			0.885563	−	0.464520i	$-0.153773\pi$
$593$	43.1297			1.77113			0.885563	+	0.464520i	$0.153773\pi$
$594$		0			0
$595$	9.81340	+	16.9973i	0.402310	+	0.696822i
$596$		0			0
$597$	25.6632			1.05033
$598$		0			0
$599$	15.1586			0.619363			0.309682	−	0.950840i	$-0.399778\pi$
$599$	15.1586			0.619363			0.309682	+	0.950840i	$0.399778\pi$
$600$		0			0
$601$	−4.09213	−	7.08778i	−0.166922	−	0.289117i	0.770414	−	0.637543i	$-0.220049\pi$
$601$	−4.09213	−	7.08778i	−0.166922	−	0.289117i	−0.937336	+	0.348427i	$0.886716\pi$
$602$		0			0
$603$	−21.6281			−0.880766
$604$		0			0
$605$	0.640700	−	1.10972i	0.0260482	−	0.0451167i
$606$		0			0
$607$	12.1054	−	20.9671i	0.491341	−	0.851028i	−0.508609	−	0.860998i	$-0.669840\pi$
$607$	12.1054	−	20.9671i	0.491341	−	0.851028i	0.999950	+	0.00996936i	$0.00317340\pi$
$608$		0			0
$609$	11.1815	+	19.3669i	0.453097	+	0.784786i
$610$		0			0
$611$	23.7872	−	22.2314i	0.962326	−	0.899388i
$612$		0			0
$613$	−2.03140	−	3.51848i	−0.0820474	−	0.142110i	0.822082	−	0.569369i	$-0.192813\pi$
$613$	−2.03140	−	3.51848i	−0.0820474	−	0.142110i	−0.904129	+	0.427259i	$0.859479\pi$
$614$		0			0
$615$	−2.76078	+	4.78181i	−0.111325	+	0.192821i
$616$		0			0
$617$	11.8534	−	20.5307i	0.477200	−	0.826534i	−0.522459	−	0.852664i	$-0.674985\pi$
$617$	11.8534	−	20.5307i	0.477200	−	0.826534i	0.999659	+	0.0261305i	$0.00831855\pi$
$618$		0			0
$619$	−3.94190			−0.158438			−0.0792192	−	0.996857i	$-0.525243\pi$
$619$	−3.94190			−0.158438			−0.0792192	+	0.996857i	$0.525243\pi$
$620$		0			0
$621$	−4.81170	−	8.33411i	−0.193087	−	0.334436i
$622$		0			0
$623$	4.51575			0.180920
$624$		0			0
$625$	3.06633			0.122653
$626$		0			0
$627$	0.202955	+	0.351529i	0.00810526	+	0.0140387i
$628$		0			0
$629$	−14.4223			−0.575055
$630$		0			0
$631$	−22.2159	+	38.4790i	−0.884400	+	1.53183i	−0.0379993	+	0.999278i	$0.512098\pi$
$631$	−22.2159	+	38.4790i	−0.884400	+	1.53183i	−0.846400	+	0.532547i	$0.821235\pi$
$632$		0			0
$633$	−2.79921	+	4.84838i	−0.111259	+	0.192706i
$634$		0			0
$635$	11.8553	+	20.5340i	0.470465	+	0.814869i
$636$		0			0
$637$	−2.68664	−	0.818121i	−0.106449	−	0.0324151i
$638$		0			0
$639$	5.96350	+	10.3291i	0.235913	+	0.408612i
$640$		0			0
$641$	−6.28566	+	10.8871i	−0.248269	+	0.430014i	−0.963046	−	0.269338i	$-0.913195\pi$
$641$	−6.28566	+	10.8871i	−0.248269	+	0.430014i	0.714777	+	0.699353i	$0.246528\pi$
$642$		0			0
$643$	9.03031	−	15.6410i	0.356121	−	0.616819i	−0.631188	−	0.775630i	$-0.717432\pi$
$643$	9.03031	−	15.6410i	0.356121	−	0.616819i	0.987309	+	0.158810i	$0.0507658\pi$
$644$		0			0
$645$	−5.95427			−0.234449
$646$		0			0
$647$	12.4321	+	21.5330i	0.488755	+	0.846549i	0.999916	−	0.0129361i	$-0.00411780\pi$
$647$	12.4321	+	21.5330i	0.488755	+	0.846549i	−0.511161	+	0.859485i	$0.670784\pi$
$648$		0			0
$649$	−8.15763			−0.320215
$650$		0			0
$651$	−17.4541			−0.684082
$652$		0			0
$653$	−15.3196	−	26.5343i	−0.599502	−	1.03837i	−0.992895	−	0.118998i	$-0.962032\pi$
$653$	−15.3196	−	26.5343i	−0.599502	−	1.03837i	0.393392	−	0.919371i	$-0.371301\pi$
$654$		0			0
$655$	−14.0740			−0.549919
$656$		0			0
$657$	−13.5730	+	23.5091i	−0.529532	+	0.917177i
$658$		0			0
$659$	−8.14839	+	14.1134i	−0.317416	+	0.549781i	−0.979948	−	0.199253i	$-0.936149\pi$
$659$	−8.14839	+	14.1134i	−0.317416	+	0.549781i	0.662532	+	0.749034i	$0.269482\pi$
$660$		0			0
$661$	4.22990	+	7.32640i	0.164524	+	0.284964i	0.936486	−	0.350705i	$-0.114058\pi$
$661$	4.22990	+	7.32640i	0.164524	+	0.284964i	−0.771962	+	0.635669i	$0.780725\pi$
$662$		0			0
$663$	−17.5565	+	16.4083i	−0.681839	+	0.637245i
$664$		0			0
$665$	−0.597668	−	1.03519i	−0.0231766	−	0.0401430i
$666$		0			0
$667$	−7.59530	+	13.1554i	−0.294091	+	0.509381i
$668$		0			0
$669$	8.22686	−	14.2493i	0.318069	−	0.550912i
$670$		0			0
$671$	−6.36672			−0.245785
$672$		0			0
$673$	−19.1282	−	33.1310i	−0.737337	−	1.27711i	−0.953690	−	0.300790i	$-0.902750\pi$
$673$	−19.1282	−	33.1310i	−0.737337	−	1.27711i	0.216353	−	0.976315i	$-0.430584\pi$
$674$		0			0
$675$	17.5742			0.676430
$676$		0			0
$677$	1.74820			0.0671886			0.0335943	−	0.999436i	$-0.489305\pi$
$677$	1.74820			0.0671886			0.0335943	+	0.999436i	$0.489305\pi$
$678$		0			0
$679$	9.18665	+	15.9117i	0.352551	+	0.610637i
$680$		0			0
$681$	−15.5295			−0.595092
$682$		0			0
$683$	5.62994	−	9.75134i	0.215424	−	0.373125i	−0.737980	−	0.674823i	$-0.764220\pi$
$683$	5.62994	−	9.75134i	0.215424	−	0.373125i	0.953404	+	0.301698i	$0.0975534\pi$
$684$		0			0
$685$	6.05646	−	10.4901i	0.231406	−	0.400806i
$686$		0			0
$687$	10.9967	+	19.0468i	0.419550	+	0.726683i
$688$		0			0
$689$	−33.3082	+	31.1298i	−1.26894	+	1.18595i
$690$		0			0
$691$	15.5134	+	26.8699i	0.590156	+	1.02218i	0.994211	+	0.107445i	$0.0342671\pi$
$691$	15.5134	+	26.8699i	0.590156	+	1.02218i	−0.404055	+	0.914735i	$0.632400\pi$
$692$		0			0
$693$	2.27232	−	3.93578i	0.0863184	−	0.149508i
$694$		0			0
$695$	−10.3992	+	18.0119i	−0.394463	+	0.683229i
$696$		0			0
$697$	−24.3810			−0.923495
$698$		0			0
$699$	−3.64812	−	6.31873i	−0.137985	−	0.238996i
$700$		0			0
$701$	13.2113			0.498984			0.249492	−	0.968377i	$-0.419736\pi$
$701$	13.2113			0.498984			0.249492	+	0.968377i	$0.419736\pi$
$702$		0			0
$703$	0.878365			0.0331282
$704$		0			0
$705$	−6.27925	−	10.8760i	−0.236490	−	0.409613i
$706$		0			0
$707$	3.24137			0.121904
$708$		0			0
$709$	−12.8890	+	22.3245i	−0.484058	+	0.838413i	−0.999832	−	0.0183111i	$-0.994171\pi$
$709$	−12.8890	+	22.3245i	−0.484058	+	0.838413i	0.515774	+	0.856725i	$0.327504\pi$
$710$		0			0
$711$	−2.89629	+	5.01652i	−0.108619	+	0.188134i
$712$		0			0
$713$	−5.92808	−	10.2677i	−0.222008	−	0.384529i
$714$		0			0
$715$	−4.41978	−	1.34588i	−0.165290	−	0.0503332i
$716$		0			0
$717$	−0.834321	−	1.44509i	−0.0311583	−	0.0539677i
$718$		0			0
$719$	19.7004	−	34.1220i	0.734700	−	1.27254i	−0.220156	−	0.975465i	$-0.570656\pi$
$719$	19.7004	−	34.1220i	0.734700	−	1.27254i	0.954855	−	0.297072i	$-0.0960102\pi$
$720$		0			0
$721$	−19.5262	+	33.8204i	−0.727194	+	1.25954i
$722$		0			0
$723$	−6.14260			−0.228446
$724$		0			0
$725$	−13.8705	−	24.0243i	−0.515136	−	0.892242i
$726$		0			0
$727$	6.86872			0.254747			0.127373	−	0.991855i	$-0.459345\pi$
$727$	6.86872			0.254747			0.127373	+	0.991855i	$0.459345\pi$
$728$		0			0
$729$	17.4296			0.645543
$730$		0			0
$731$	−13.1458	−	22.7692i	−0.486216	−	0.842151i
$732$		0			0
$733$	−10.7310			−0.396359			−0.198180	−	0.980166i	$-0.563503\pi$
$733$	−10.7310			−0.396359			−0.198180	+	0.980166i	$0.563503\pi$
$734$		0			0
$735$	−0.541636	+	0.938142i	−0.0199786	+	0.0346039i
$736$		0			0
$737$	−5.93502	+	10.2798i	−0.218619	+	0.378660i
$738$		0			0
$739$	0.506275	+	0.876894i	0.0186236	+	0.0322571i	0.875187	−	0.483785i	$-0.160738\pi$
$739$	0.506275	+	0.876894i	0.0186236	+	0.0322571i	−0.856563	+	0.516042i	$0.827405\pi$
$740$		0			0
$741$	1.06925	−	0.999318i	0.0392798	−	0.0367108i
$742$		0			0
$743$	2.31579	+	4.01106i	0.0849580	+	0.147152i	0.905373	−	0.424616i	$-0.139591\pi$
$743$	2.31579	+	4.01106i	0.0849580	+	0.147152i	−0.820415	+	0.571768i	$0.806258\pi$
$744$		0			0
$745$	3.13812	−	5.43538i	0.114972	−	0.199137i
$746$		0			0
$747$	−15.7762	+	27.3251i	−0.577220	+	0.999775i
$748$		0			0
$749$	4.48229			0.163779
$750$		0			0
$751$	21.3718	+	37.0171i	0.779869	+	1.35077i	0.932017	+	0.362415i	$0.118048\pi$
$751$	21.3718	+	37.0171i	0.779869	+	1.35077i	−0.152147	+	0.988358i	$0.548619\pi$
$752$		0			0
$753$	17.8405			0.650144
$754$		0			0
$755$	2.52786			0.0919982
$756$		0			0
$757$	21.8352	+	37.8198i	0.793616	+	1.37458i	0.923715	+	0.383081i	$0.125137\pi$
$757$	21.8352	+	37.8198i	0.793616	+	1.37458i	−0.130099	+	0.991501i	$0.541530\pi$
$758$		0			0
$759$	−1.99570			−0.0724392
$760$		0			0
$761$	−14.3833	+	24.9126i	−0.521395	+	0.903082i	0.478296	+	0.878199i	$0.341255\pi$
$761$	−14.3833	+	24.9126i	−0.521395	+	0.903082i	−0.999690	+	0.0248833i	$0.992079\pi$
$762$		0			0
$763$	−12.6038	+	21.8304i	−0.456287	+	0.790312i
$764$		0			0
$765$	−7.16892	−	12.4169i	−0.259193	−	0.448935i
$766$		0			0
$767$	6.64832	+	28.6515i	0.240057	+	1.03455i
$768$		0			0
$769$	16.1419	+	27.9585i	0.582091	+	1.00821i	0.995231	+	0.0975432i	$0.0310984\pi$
$769$	16.1419	+	27.9585i	0.582091	+	1.00821i	−0.413141	+	0.910667i	$0.635568\pi$
$770$		0			0
$771$	4.79844	−	8.31114i	0.172812	−	0.299318i
$772$		0			0
$773$	−11.3216	+	19.6096i	−0.407210	+	0.705308i	−0.994576	−	0.104013i	$-0.966831\pi$
$773$	−11.3216	+	19.6096i	−0.407210	+	0.705308i	0.587366	+	0.809321i	$0.300165\pi$
$774$		0			0
$775$	21.6516			0.777748
$776$		0			0
$777$	3.17880	+	5.50585i	0.114039	+	0.197521i
$778$		0			0
$779$	1.48488			0.0532014
$780$		0			0
$781$	6.54582			0.234228
$782$		0			0
$783$	−21.6173	−	37.4422i	−0.772538	−	1.33808i
$784$		0			0
$785$	12.6154			0.450264
$786$		0			0
$787$	23.0984	−	40.0075i	0.823368	−	1.42611i	−0.0797930	−	0.996811i	$-0.525426\pi$
$787$	23.0984	−	40.0075i	0.823368	−	1.42611i	0.903161	−	0.429303i	$-0.141241\pi$
$788$		0			0
$789$	−0.864630	+	1.49758i	−0.0307817	+	0.0533154i
$790$		0			0
$791$	−6.17313	−	10.6922i	−0.219491	−	0.380170i
$792$		0			0
$793$	5.18876	+	22.3614i	0.184258	+	0.794078i
$794$		0			0
$795$	8.79259	+	15.2292i	0.311841	+	0.540124i
$796$		0			0
$797$	−8.95967	+	15.5186i	−0.317368	+	0.549697i	−0.979938	−	0.199303i	$-0.936132\pi$
$797$	−8.95967	+	15.5186i	−0.317368	+	0.549697i	0.662570	+	0.749000i	$0.269466\pi$
$798$		0			0
$799$	27.7266	−	48.0239i	0.980897	−	1.69896i
$800$		0			0
$801$	−3.29886			−0.116560
$802$		0			0
$803$	7.44918	+	12.9024i	0.262876	+	0.455314i
$804$		0			0
$805$	5.87697			0.207136
$806$		0			0
$807$	−26.9848			−0.949912
$808$		0			0
$809$	17.2511	+	29.8797i	0.606515	+	1.05052i	0.991810	+	0.127722i	$0.0407665\pi$
$809$	17.2511	+	29.8797i	0.606515	+	1.05052i	−0.385295	+	0.922794i	$0.625900\pi$
$810$		0			0
$811$	−7.99615			−0.280783			−0.140391	−	0.990096i	$-0.544836\pi$
$811$	−7.99615			−0.280783			−0.140391	+	0.990096i	$0.544836\pi$
$812$		0			0
$813$	−1.06821	+	1.85019i	−0.0374637	+	0.0648891i
$814$		0			0
$815$	−7.19356	+	12.4596i	−0.251979	+	0.436441i
$816$		0			0
$817$	0.800623	+	1.38672i	0.0280103	+	0.0485152i
$818$		0			0
$819$	−15.6753	−	4.77334i	−0.547739	−	0.166794i
$820$		0			0
$821$	−11.9602	−	20.7156i	−0.417413	−	0.722980i	0.578266	−	0.815849i	$-0.303730\pi$
$821$	−11.9602	−	20.7156i	−0.417413	−	0.722980i	−0.995678	+	0.0928684i	$0.970396\pi$
$822$		0			0
$823$	5.28214	−	9.14894i	0.184124	−	0.318912i	−0.759157	−	0.650907i	$-0.774389\pi$
$823$	5.28214	−	9.14894i	0.184124	−	0.318912i	0.943281	+	0.331996i	$0.107722\pi$
$824$		0			0
$825$	1.82226	−	3.15625i	0.0634430	−	0.109887i
$826$		0			0
$827$	−13.4854			−0.468934			−0.234467	−	0.972124i	$-0.575334\pi$
$827$	−13.4854			−0.468934			−0.234467	+	0.972124i	$0.575334\pi$
$828$		0			0
$829$	−27.6692	−	47.9244i	−0.960990	−	1.66448i	−0.720024	−	0.693949i	$-0.755869\pi$
$829$	−27.6692	−	47.9244i	−0.960990	−	1.66448i	−0.240966	−	0.970534i	$-0.577464\pi$
$830$		0			0
$831$	16.5655			0.574652
$832$		0			0
$833$	−4.78329			−0.165731
$834$		0			0
$835$	−9.67734	−	16.7616i	−0.334898	−	0.580061i
$836$		0			0
$837$	33.7443			1.16637
$838$		0			0
$839$	−20.6189	+	35.7129i	−0.711843	+	1.23295i	0.252322	+	0.967643i	$0.418806\pi$
$839$	−20.6189	+	35.7129i	−0.711843	+	1.23295i	−0.964165	+	0.265304i	$0.914528\pi$
$840$		0			0
$841$	−19.6230	+	33.9880i	−0.676654	+	1.17200i
$842$		0			0
$843$	16.9145	+	29.2969i	0.582568	+	1.00904i
$844$		0			0
$845$	−1.12503	+	16.6202i	−0.0387020	+	0.571751i
$846$		0			0
$847$	−1.24710	−	2.16005i	−0.0428510	−	0.0742201i
$848$		0			0
$849$	16.2546	−	28.1538i	0.557857	−	0.966237i
$850$		0			0
$851$	−2.15928	+	3.73998i	−0.0740191	+	0.128205i
$852$		0			0
$853$	−5.00722			−0.171444			−0.0857220	−	0.996319i	$-0.527320\pi$
$853$	−5.00722			−0.171444			−0.0857220	+	0.996319i	$0.527320\pi$
$854$		0			0
$855$	0.436611	+	0.756232i	0.0149318	+	0.0258626i
$856$		0			0
$857$	−42.2505			−1.44325			−0.721626	−	0.692284i	$-0.756605\pi$
$857$	−42.2505			−1.44325			−0.721626	+	0.692284i	$0.756605\pi$
$858$		0			0
$859$	−20.2658			−0.691461			−0.345731	−	0.938334i	$-0.612369\pi$
$859$	−20.2658			−0.691461			−0.345731	+	0.938334i	$0.612369\pi$
$860$		0			0
$861$	5.37378	+	9.30766i	0.183138	+	0.317204i
$862$		0			0
$863$	9.74439			0.331703			0.165851	−	0.986151i	$-0.446963\pi$
$863$	9.74439			0.331703			0.165851	+	0.986151i	$0.446963\pi$
$864$		0			0
$865$	−4.35727	+	7.54702i	−0.148152	+	0.256606i
$866$		0			0
$867$	−11.2389	+	19.4663i	−0.381692	+	0.661110i
$868$		0			0
$869$	1.58955	+	2.75318i	0.0539219	+	0.0933954i
$870$		0			0
$871$	40.9419	+	12.4674i	1.38726	+	0.422441i
$872$		0			0
$873$	−6.71106	−	11.6239i	−0.227135	−	0.393409i
$874$		0			0
$875$	−13.3564	+	23.1340i	−0.451530	+	0.782073i
$876$		0			0
$877$	−3.22766	+	5.59047i	−0.108990	+	0.188777i	−0.915362	−	0.402633i	$-0.868095\pi$
$877$	−3.22766	+	5.59047i	−0.108990	+	0.188777i	0.806371	+	0.591410i	$0.201428\pi$
$878$		0			0
$879$	14.2746			0.481471
$880$		0			0
$881$	−11.1154	−	19.2524i	−0.374487	−	0.648631i	0.615763	−	0.787931i	$-0.288848\pi$
$881$	−11.1154	−	19.2524i	−0.374487	−	0.648631i	−0.990250	+	0.139301i	$0.955515\pi$
$882$		0			0
$883$	−43.5781			−1.46652			−0.733260	−	0.679949i	$-0.762002\pi$
$883$	−43.5781			−1.46652			−0.733260	+	0.679949i	$0.762002\pi$
$884$		0			0
$885$	11.3451			0.381360
$886$		0			0
$887$	−8.53851	−	14.7891i	−0.286695	−	0.496570i	0.686324	−	0.727296i	$-0.259223\pi$
$887$	−8.53851	−	14.7891i	−0.286695	−	0.496570i	−0.973019	+	0.230726i	$0.925890\pi$
$888$		0			0
$889$	46.1521			1.54789
$890$		0			0
$891$	0.106898	−	0.185154i	0.00358123	−	0.00620288i
$892$		0			0
$893$	−1.68864	+	2.92481i	−0.0565082	+	0.0978751i
$894$		0			0
$895$	−9.04936	−	15.6739i	−0.302487	−	0.523922i
$896$		0			0
$897$	1.62646	+	7.00936i	0.0543058	+	0.234036i
$898$		0			0
$899$	−26.6327	−	46.1293i	−0.888252	−	1.53850i
$900$		0			0
$901$	−38.8245	+	67.2460i	−1.29343	+	2.24029i
$902$		0			0
$903$	−5.79491	+	10.0371i	−0.192843	+	0.334013i
$904$		0			0
$905$	29.0456			0.965509
$906$		0			0
$907$	8.83633	+	15.3050i	0.293405	+	0.508193i	0.974613	−	0.223897i	$-0.0718781\pi$
$907$	8.83633	+	15.3050i	0.293405	+	0.508193i	−0.681207	+	0.732091i	$0.738545\pi$
$908$		0			0
$909$	−2.36789			−0.0785381
$910$		0			0
$911$	−24.7970			−0.821560			−0.410780	−	0.911734i	$-0.634744\pi$
$911$	−24.7970			−0.821560			−0.410780	+	0.911734i	$0.634744\pi$
$912$		0			0
$913$	8.65835	+	14.9967i	0.286549	+	0.496318i
$914$		0			0
$915$	8.85439			0.292717
$916$		0			0
$917$	−13.6974	+	23.7245i	−0.452327	+	0.783453i
$918$		0			0
$919$	2.58343	−	4.47464i	0.0852196	−	0.147605i	−0.820265	−	0.571983i	$-0.806174\pi$
$919$	2.58343	−	4.47464i	0.0852196	−	0.147605i	0.905485	+	0.424379i	$0.139507\pi$
$920$		0			0
$921$	−2.86700	−	4.96579i	−0.0944709	−	0.163628i
$922$		0			0
$923$	−5.33473	−	22.9905i	−0.175595	−	0.756741i
$924$		0			0
$925$	−3.94326	−	6.82992i	−0.129653	−	0.224566i
$926$		0			0
$927$	14.2644	−	24.7066i	0.468503	−	0.811471i
$928$		0			0
$929$	3.98518	−	6.90254i	0.130750	−	0.226465i	−0.793216	−	0.608940i	$-0.791595\pi$
$929$	3.98518	−	6.90254i	0.130750	−	0.226465i	0.923966	+	0.382475i	$0.124928\pi$
$930$		0			0
$931$	0.291318			0.00954756
$932$		0			0
$933$	−0.0812563	−	0.140740i	−0.00266021	−	0.00460762i
$934$		0			0
$935$	−7.86895			−0.257342
$936$		0			0
$937$	−1.34395			−0.0439049			−0.0219525	−	0.999759i	$-0.506988\pi$
$937$	−1.34395			−0.0439049			−0.0219525	+	0.999759i	$0.506988\pi$
$938$		0			0
$939$	15.7134	+	27.2164i	0.512787	+	0.888172i
$940$		0			0
$941$	15.2405			0.496827			0.248414	−	0.968654i	$-0.420091\pi$
$941$	15.2405			0.496827			0.248414	+	0.968654i	$0.420091\pi$
$942$		0			0
$943$	−3.65027	+	6.32246i	−0.118869	+	0.205888i
$944$		0			0
$945$	−8.36334	+	14.4857i	−0.272060	+	0.471221i
$946$		0			0
$947$	−9.62129	−	16.6646i	−0.312650	−	0.541526i	0.666285	−	0.745697i	$-0.267883\pi$
$947$	−9.62129	−	16.6646i	−0.312650	−	0.541526i	−0.978935	+	0.204171i	$0.934550\pi$
$948$		0			0
$949$	39.2452	−	36.6785i	1.27395	−	1.19063i
$950$		0			0
$951$	−9.32493	−	16.1512i	−0.302381	−	0.523740i
$952$		0			0
$953$	−10.6391	+	18.4275i	−0.344634	+	0.596924i	−0.985287	−	0.170907i	$-0.945330\pi$
$953$	−10.6391	+	18.4275i	−0.344634	+	0.596924i	0.640653	+	0.767830i	$0.278664\pi$
$954$		0			0
$955$	1.54937	−	2.68359i	0.0501364	−	0.0868388i
$956$		0			0
$957$	−8.96596			−0.289828
$958$		0			0
$959$	−11.7887	−	20.4187i	−0.380678	−	0.659354i
$960$		0			0
$961$	10.5733			0.341075
$962$		0			0
$963$	−3.27442			−0.105517
$964$		0			0
$965$	−14.3875	−	24.9198i	−0.463148	−	0.802197i
$966$		0			0
$967$	−19.6914			−0.633232			−0.316616	−	0.948554i	$-0.602547\pi$
$967$	−19.6914			−0.633232			−0.316616	+	0.948554i	$0.602547\pi$
$968$		0			0
$969$	1.24633	−	2.15871i	0.0400379	−	0.0693476i
$970$		0			0
$971$	2.39292	−	4.14465i	0.0767923	−	0.133008i	−0.825072	−	0.565028i	$-0.808865\pi$
$971$	2.39292	−	4.14465i	0.0767923	−	0.133008i	0.901864	+	0.432019i	$0.142199\pi$
$972$		0			0
$973$	20.2417	+	35.0596i	0.648918	+	1.12396i
$974$		0			0
$975$	−12.5706	−	3.82793i	−0.402582	−	0.122592i
$976$		0			0
$977$	−17.0951	−	29.6096i	−0.546920	−	0.947294i	−0.998483	−	0.0550545i	$-0.982467\pi$
$977$	−17.0951	−	29.6096i	−0.546920	−	0.947294i	0.451563	−	0.892239i	$-0.350867\pi$
$978$		0			0
$979$	−0.905248	+	1.56793i	−0.0289318	+	0.0501114i
$980$		0			0
$981$	9.20734	−	15.9476i	0.293968	−	0.509167i
$982$		0			0
$983$	−39.2798			−1.25283			−0.626416	−	0.779489i	$-0.715479\pi$
$983$	−39.2798			−1.25283			−0.626416	+	0.779489i	$0.715479\pi$
$984$		0			0
$985$	−15.4579	−	26.7740i	−0.492531	−	0.853089i
$986$		0			0
$987$	−24.4448			−0.778085
$988$		0			0
$989$	−7.87267			−0.250336
$990$		0			0
$991$	28.3037	+	49.0235i	0.899098	+	1.55728i	0.828649	+	0.559768i	$0.189110\pi$
$991$	28.3037	+	49.0235i	0.899098	+	1.55728i	0.0704485	+	0.997515i	$0.477557\pi$
$992$		0			0
$993$	17.5149			0.555819
$994$		0			0
$995$	15.1498	−	26.2403i	0.480282	−	0.831873i
$996$		0			0
$997$	−26.1683	+	45.3248i	−0.828758	+	1.43545i	0.0702553	+	0.997529i	$0.477619\pi$
$997$	−26.1683	+	45.3248i	−0.828758	+	1.43545i	−0.899013	+	0.437922i	$0.855715\pi$
$998$		0			0
$999$	−6.14561	−	10.6445i	−0.194438	−	0.336777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.c.133.2	✓	10
13.3	even	3		7436.2.a.r.1.4		5
13.9	even	3	inner	572.2.i.c.529.2	yes	10
13.10	even	6		7436.2.a.q.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.c.133.2	✓	10	1.1	even	1	trivial
572.2.i.c.529.2	yes	10	13.9	even	3	inner
7436.2.a.q.1.4		5	13.10	even	6
7436.2.a.r.1.4		5	13.3	even	3

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.542661 - 0.939916i) q^{3} -1.28140 q^{5} +(-1.24710 + 2.16005i) q^{7} +(0.911039 - 1.57797i) q^{9} +O(q^{10})\)	\(q+(-0.542661 - 0.939916i) q^{3} -1.28140 q^{5} +(-1.24710 + 2.16005i) q^{7} +(0.911039 - 1.57797i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-2.63419 + 2.46191i) q^{13} +(0.695365 + 1.20441i) q^{15} +(-3.07045 + 5.31818i) q^{17} +(0.187000 - 0.323894i) q^{19} +2.70702 q^{21} +(0.919404 + 1.59245i) q^{23} -3.35801 q^{25} -5.23350 q^{27} +(4.13056 + 7.15433i) q^{29} -6.44774 q^{31} +(-0.542661 + 0.939916i) q^{33} +(1.59804 - 2.76789i) q^{35} +(1.17428 + 2.03392i) q^{37} +(3.74346 + 1.13994i) q^{39} +(1.98513 + 3.43835i) q^{41} +(-2.14070 + 3.70780i) q^{43} +(-1.16741 + 2.02201i) q^{45} -9.03014 q^{47} +(0.389462 + 0.674568i) q^{49} +6.66485 q^{51} +12.6446 q^{53} +(0.640700 + 1.10972i) q^{55} -0.405911 q^{57} +(4.07882 - 7.06472i) q^{59} +(3.18336 - 5.51374i) q^{61} +(2.27232 + 3.93578i) q^{63} +(3.37546 - 3.15470i) q^{65} +(-5.93502 - 10.2798i) q^{67} +(0.997848 - 1.72832i) q^{69} +(-3.27291 + 5.66885i) q^{71} -14.8984 q^{73} +(1.82226 + 3.15625i) q^{75} +2.49421 q^{77} -3.17910 q^{79} +(0.106898 + 0.185154i) q^{81} -17.3167 q^{83} +(3.93448 - 6.81471i) q^{85} +(4.48298 - 7.76475i) q^{87} +(-0.905248 - 1.56793i) q^{89} +(-2.03274 - 8.76025i) q^{91} +(3.49893 + 6.06033i) q^{93} +(-0.239622 + 0.415038i) q^{95} +(3.68319 - 6.37947i) q^{97} -1.82208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9	\( 10 q + q^{3} + 2 q^{5} + q^{7} - 2 q^{9} - 5 q^{11} + q^{13} + 12 q^{15} - 3 q^{17} + 12 q^{19} - 12 q^{21} - 7 q^{23} + 28 q^{25} - 32 q^{27} - 10 q^{29} - 18 q^{31} + q^{33} + 15 q^{35} + 10 q^{37} + 5 q^{41} - 14 q^{43} - 36 q^{45} - 24 q^{47} + 6 q^{49} + 14 q^{51} - 14 q^{53} - q^{55} + 52 q^{57} + 8 q^{59} + 18 q^{61} + 20 q^{63} - 45 q^{65} - q^{67} + 7 q^{69} + 3 q^{71} - 76 q^{73} + 57 q^{75} - 2 q^{77} + 12 q^{79} - 25 q^{81} - 28 q^{83} - 10 q^{85} + 27 q^{87} + 29 q^{89} + 17 q^{91} - 21 q^{93} + 11 q^{95} + 21 q^{97} + 4 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^5 + q^7 - 2 * q^9 - 5 * q^11 + q^13 + 12 * q^15 - 3 * q^17 + 12 * q^19 - 12 * q^21 - 7 * q^23 + 28 * q^25 - 32 * q^27 - 10 * q^29 - 18 * q^31 + q^33 + 15 * q^35 + 10 * q^37 + 5 * q^41 - 14 * q^43 - 36 * q^45 - 24 * q^47 + 6 * q^49 + 14 * q^51 - 14 * q^53 - q^55 + 52 * q^57 + 8 * q^59 + 18 * q^61 + 20 * q^63 - 45 * q^65 - q^67 + 7 * q^69 + 3 * q^71 - 76 * q^73 + 57 * q^75 - 2 * q^77 + 12 * q^79 - 25 * q^81 - 28 * q^83 - 10 * q^85 + 27 * q^87 + 29 * q^89 + 17 * q^91 - 21 * q^93 + 11 * q^95 + 21 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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