LMFDB - Embedded newform 552.2.q.b.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 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("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	552.169
Dual form			552.2.q.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{3} +(-1.20489 - 1.39052i) q^{5} +(-0.921355 - 0.592119i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{3} +(-1.20489 - 1.39052i) q^{5} +(-0.921355 - 0.592119i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.117067 - 0.814220i) q^{11} +(4.25780 - 2.73632i) q^{13} +(0.764332 - 1.67365i) q^{15} +(6.77653 - 1.98977i) q^{17} +(6.40403 + 1.88039i) q^{19} +(0.155866 - 1.08407i) q^{21} +(0.349293 - 4.78309i) q^{23} +(0.229793 - 1.59824i) q^{25} +(-0.959493 - 0.281733i) q^{27} +(-7.90735 + 2.32181i) q^{29} +(-3.03433 + 6.64425i) q^{31} +(0.692009 - 0.444727i) q^{33} +(0.286781 + 1.99460i) q^{35} +(6.75089 - 7.79094i) q^{37} +(4.25780 + 2.73632i) q^{39} +(-1.36620 - 1.57668i) q^{41} +(2.23098 + 4.88516i) q^{43} +1.83992 q^{45} +0.433464 q^{47} +(-2.40962 - 5.27632i) q^{49} +(4.62503 + 5.33757i) q^{51} +(-5.96781 - 3.83528i) q^{53} +(-0.991138 + 1.14383i) q^{55} +(0.949865 + 6.60646i) q^{57} +(4.38406 - 2.81747i) q^{59} +(-4.75509 + 10.4122i) q^{61} +(1.05085 - 0.308558i) q^{63} +(-8.93512 - 2.62359i) q^{65} +(-1.32957 + 9.24739i) q^{67} +(4.49596 - 1.66924i) q^{69} +(0.797551 - 5.54709i) q^{71} +(3.51022 + 1.03069i) q^{73} +(1.54927 - 0.454907i) q^{75} +(-0.374255 + 0.819503i) q^{77} +(6.05315 - 3.89012i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-6.97641 + 8.05121i) q^{83} +(-10.9318 - 7.02545i) q^{85} +(-5.39682 - 6.22826i) q^{87} +(-3.91100 - 8.56389i) q^{89} -5.54318 q^{91} -7.30433 q^{93} +(-5.10145 - 11.1706i) q^{95} +(4.70359 + 5.42823i) q^{97} +(0.692009 + 0.444727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$		0			0
$5$	−1.20489	−	1.39052i	−0.538845	−	0.621860i	0.419402	−	0.907800i	$-0.362240\pi$
$5$	−1.20489	−	1.39052i	−0.538845	−	0.621860i	−0.958248	+	0.285940i	$0.907694\pi$
$6$		0			0
$7$	−0.921355	−	0.592119i	−0.348239	−	0.223800i	0.354814	−	0.934937i	$-0.384544\pi$
$7$	−0.921355	−	0.592119i	−0.348239	−	0.223800i	−0.703053	+	0.711137i	$0.748181\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.117067	−	0.814220i	−0.0352971	−	0.245497i	0.964532	−	0.263965i	$-0.0850302\pi$
$11$	−0.117067	−	0.814220i	−0.0352971	−	0.245497i	−0.999829	+	0.0184680i	$0.994121\pi$
$12$		0			0
$13$	4.25780	−	2.73632i	1.18090	−	0.758920i	0.205350	−	0.978689i	$-0.434167\pi$
$13$	4.25780	−	2.73632i	1.18090	−	0.758920i	0.975552	+	0.219769i	$0.0705302\pi$
$14$		0			0
$15$	0.764332	−	1.67365i	0.197350	−	0.432136i
$16$		0			0
$17$	6.77653	−	1.98977i	1.64355	−	0.482589i	0.676344	−	0.736586i	$-0.263563\pi$
$17$	6.77653	−	1.98977i	1.64355	−	0.482589i	0.967205	+	0.253997i	$0.0817452\pi$
$18$		0			0
$19$	6.40403	+	1.88039i	1.46919	+	0.431392i	0.915834	−	0.401556i	$-0.131531\pi$
$19$	6.40403	+	1.88039i	1.46919	+	0.431392i	0.553351	+	0.832948i	$0.313349\pi$
$20$		0			0
$21$	0.155866	−	1.08407i	0.0340127	−	0.236563i
$22$		0			0
$23$	0.349293	−	4.78309i	0.0728326	−	0.997344i
$23$	0.349293	−	4.78309i	0.0728326	−	0.997344i
$24$		0			0
$25$	0.229793	−	1.59824i	0.0459585	−	0.319648i
$26$		0			0
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$		0			0
$29$	−7.90735	+	2.32181i	−1.46836	+	0.431149i	−0.915565	−	0.402170i	$-0.868256\pi$
$29$	−7.90735	+	2.32181i	−1.46836	+	0.431149i	−0.552792	+	0.833319i	$0.686438\pi$
$30$		0			0
$31$	−3.03433	+	6.64425i	−0.544981	+	1.19334i	0.414105	+	0.910229i	$0.364095\pi$
$31$	−3.03433	+	6.64425i	−0.544981	+	1.19334i	−0.959086	+	0.283113i	$0.908633\pi$
$32$		0			0
$33$	0.692009	−	0.444727i	0.120463	−	0.0774171i
$34$		0			0
$35$	0.286781	+	1.99460i	0.0484748	+	0.337150i
$36$		0			0
$37$	6.75089	−	7.79094i	1.10984	−	1.28082i	0.153633	−	0.988128i	$-0.450903\pi$
$37$	6.75089	−	7.79094i	1.10984	−	1.28082i	0.956206	−	0.292695i	$-0.0945520\pi$
$38$		0			0
$39$	4.25780	+	2.73632i	0.681794	+	0.438163i
$40$		0			0
$41$	−1.36620	−	1.57668i	−0.213365	−	0.246237i	0.638971	−	0.769231i	$-0.279360\pi$
$41$	−1.36620	−	1.57668i	−0.213365	−	0.246237i	−0.852336	+	0.522994i	$0.824815\pi$
$42$		0			0
$43$	2.23098	+	4.88516i	0.340221	+	0.744979i	0.999979	−	0.00649859i	$-0.00206858\pi$
$43$	2.23098	+	4.88516i	0.340221	+	0.744979i	−0.659758	+	0.751478i	$0.729341\pi$
$44$		0			0
$45$	1.83992			0.274280
$46$		0			0
$47$	0.433464			0.0632272			0.0316136	−	0.999500i	$-0.489935\pi$
$47$	0.433464			0.0632272			0.0316136	+	0.999500i	$0.489935\pi$
$48$		0			0
$49$	−2.40962	−	5.27632i	−0.344231	−	0.753760i
$50$		0			0
$51$	4.62503	+	5.33757i	0.647633	+	0.747409i
$52$		0			0
$53$	−5.96781	−	3.83528i	−0.819742	−	0.526816i	0.0622608	−	0.998060i	$-0.480169\pi$
$53$	−5.96781	−	3.83528i	−0.819742	−	0.526816i	−0.882003	+	0.471243i	$0.843805\pi$
$54$		0			0
$55$	−0.991138	+	1.14383i	−0.133645	+	0.154235i
$56$		0			0
$57$	0.949865	+	6.60646i	0.125813	+	0.875046i
$58$		0			0
$59$	4.38406	−	2.81747i	0.570756	−	0.366803i	−0.223204	−	0.974772i	$-0.571652\pi$
$59$	4.38406	−	2.81747i	0.570756	−	0.366803i	0.793961	+	0.607969i	$0.208015\pi$
$60$		0			0
$61$	−4.75509	+	10.4122i	−0.608826	+	1.33314i	0.314547	+	0.949242i	$0.398147\pi$
$61$	−4.75509	+	10.4122i	−0.608826	+	1.33314i	−0.923374	+	0.383902i	$0.874580\pi$
$62$		0			0
$63$	1.05085	−	0.308558i	0.132395	−	0.0388747i
$64$		0			0
$65$	−8.93512	−	2.62359i	−1.10827	−	0.325416i
$66$		0			0
$67$	−1.32957	+	9.24739i	−0.162433	+	1.12975i	0.731596	+	0.681739i	$0.238776\pi$
$67$	−1.32957	+	9.24739i	−0.162433	+	1.12975i	−0.894029	+	0.448009i	$0.852133\pi$
$68$		0			0
$69$	4.49596	−	1.66924i	0.541250	−	0.200953i
$70$		0			0
$71$	0.797551	−	5.54709i	0.0946519	−	0.658318i	−0.886163	−	0.463375i	$-0.846638\pi$
$71$	0.797551	−	5.54709i	0.0946519	−	0.658318i	0.980814	−	0.194944i	$-0.0624525\pi$
$72$		0			0
$73$	3.51022	+	1.03069i	0.410841	+	0.120634i	0.480620	−	0.876929i	$-0.340411\pi$
$73$	3.51022	+	1.03069i	0.410841	+	0.120634i	−0.0697798	+	0.997562i	$0.522230\pi$
$74$		0			0
$75$	1.54927	−	0.454907i	0.178894	−	0.0525282i
$76$		0			0
$77$	−0.374255	+	0.819503i	−0.0426503	+	0.0933911i
$78$		0			0
$79$	6.05315	−	3.89012i	0.681032	−	0.437673i	−0.153855	−	0.988093i	$-0.549169\pi$
$79$	6.05315	−	3.89012i	0.681032	−	0.437673i	0.834888	+	0.550421i	$0.185533\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−6.97641	+	8.05121i	−0.765761	+	0.883735i	−0.995996	−	0.0894001i	$-0.971505\pi$
$83$	−6.97641	+	8.05121i	−0.765761	+	0.883735i	0.230235	+	0.973135i	$0.426050\pi$
$84$		0			0
$85$	−10.9318	−	7.02545i	−1.18572	−	0.762017i
$86$		0			0
$87$	−5.39682	−	6.22826i	−0.578600	−	0.667740i
$88$		0			0
$89$	−3.91100	−	8.56389i	−0.414565	−	0.907771i	−0.995583	−	0.0938802i	$-0.970073\pi$
$89$	−3.91100	−	8.56389i	−0.414565	−	0.907771i	0.581019	−	0.813890i	$-0.302654\pi$
$90$		0			0
$91$	−5.54318			−0.581083
$92$		0			0
$93$	−7.30433			−0.757423
$94$		0			0
$95$	−5.10145	−	11.1706i	−0.523398	−	1.14608i
$96$		0			0
$97$	4.70359	+	5.42823i	0.477577	+	0.551153i	0.942504	−	0.334196i	$-0.108465\pi$
$97$	4.70359	+	5.42823i	0.477577	+	0.551153i	−0.464927	+	0.885349i	$0.653919\pi$
$98$		0			0
$99$	0.692009	+	0.444727i	0.0695496	+	0.0446968i
$100$		0			0
$101$	8.77788	−	10.1302i	0.873432	−	1.00799i	−0.126440	−	0.991974i	$-0.540355\pi$
$101$	8.77788	−	10.1302i	0.873432	−	1.00799i	0.999872	−	0.0160197i	$-0.00509946\pi$
$102$		0			0
$103$	0.0623729	+	0.433813i	0.00614579	+	0.0427449i	0.992664	−	0.120909i	$-0.0385810\pi$
$103$	0.0623729	+	0.433813i	0.00614579	+	0.0427449i	−0.986518	+	0.163654i	$0.947672\pi$
$104$		0			0
$105$	−1.69522	+	1.08945i	−0.165437	+	0.106320i
$106$		0			0
$107$	−7.12391	+	15.5992i	−0.688695	+	1.50803i	0.164466	+	0.986383i	$0.447410\pi$
$107$	−7.12391	+	15.5992i	−0.688695	+	1.50803i	−0.853161	+	0.521648i	$0.825317\pi$
$108$		0			0
$109$	−1.96230	+	0.576182i	−0.187954	+	0.0551882i	−0.374355	−	0.927286i	$-0.622136\pi$
$109$	−1.96230	+	0.576182i	−0.187954	+	0.0551882i	0.186401	+	0.982474i	$0.440318\pi$
$110$		0			0
$111$	9.89131	+	2.90435i	0.938841	+	0.275669i
$112$		0			0
$113$	−0.790908	+	5.50088i	−0.0744023	+	0.517480i	0.918205	+	0.396106i	$0.129639\pi$
$113$	−0.790908	+	5.50088i	−0.0744023	+	0.517480i	−0.992607	+	0.121373i	$0.961270\pi$
$114$		0			0
$115$	−7.07186	+	5.27742i	−0.659454	+	0.492122i
$116$		0			0
$117$	−0.720293	+	5.00975i	−0.0665911	+	0.463151i
$118$		0			0
$119$	−7.42176	−	2.17923i	−0.680352	−	0.199769i
$120$		0			0
$121$	9.90517	−	2.90842i	0.900470	−	0.264402i
$122$		0			0
$123$	0.866660	−	1.89772i	0.0781441	−	0.171112i
$124$		0			0
$125$	−10.2385	+	6.57987i	−0.915758	+	0.588522i
$126$		0			0
$127$	−1.00628	−	6.99886i	−0.0892933	−	0.621049i	−0.984498	−	0.175394i	$-0.943880\pi$
$127$	−1.00628	−	6.99886i	−0.0892933	−	0.621049i	0.895205	−	0.445655i	$-0.147029\pi$
$128$		0			0
$129$	−3.51691	+	4.05873i	−0.309647	+	0.357352i
$130$		0			0
$131$	4.29528	+	2.76041i	0.375280	+	0.241178i	0.714661	−	0.699471i	$-0.246581\pi$
$131$	4.29528	+	2.76041i	0.375280	+	0.241178i	−0.339380	+	0.940649i	$0.610217\pi$
$132$		0			0
$133$	−4.78697	−	5.52446i	−0.415083	−	0.479031i
$134$		0			0
$135$	0.764332	+	1.67365i	0.0657832	+	0.144045i
$136$		0			0
$137$	−7.71702			−0.659310			−0.329655	−	0.944102i	$-0.606932\pi$
$137$	−7.71702			−0.659310			−0.329655	+	0.944102i	$0.606932\pi$
$138$		0			0
$139$	−16.0282			−1.35949			−0.679746	−	0.733448i	$-0.737910\pi$
$139$	−16.0282			−1.35949			−0.679746	+	0.733448i	$0.737910\pi$
$140$		0			0
$141$	0.180067	+	0.394292i	0.0151644	+	0.0332054i
$142$		0			0
$143$	−2.72642	−	3.14646i	−0.227995	−	0.263120i
$144$		0			0
$145$	12.7560	+	8.19781i	1.05933	+	0.680791i
$146$		0			0
$147$	3.79852	−	4.38373i	0.313297	−	0.361564i
$148$		0			0
$149$	0.778192	+	5.41245i	0.0637520	+	0.443405i	0.996549	+	0.0830033i	$0.0264512\pi$
$149$	0.778192	+	5.41245i	0.0637520	+	0.443405i	−0.932797	+	0.360401i	$0.882640\pi$
$150$		0			0
$151$	−12.6569	+	8.13409i	−1.03000	+	0.661943i	−0.942495	−	0.334221i	$-0.891527\pi$
$151$	−12.6569	+	8.13409i	−1.03000	+	0.661943i	−0.0875081	+	0.996164i	$0.527890\pi$
$152$		0			0
$153$	−2.93391	+	6.42438i	−0.237193	+	0.519380i
$154$		0			0
$155$	12.8950	−	3.78632i	1.03575	−	0.304124i
$156$		0			0
$157$	8.80001	+	2.58392i	0.702317	+	0.206219i	0.613345	−	0.789815i	$-0.289824\pi$
$157$	8.80001	+	2.58392i	0.702317	+	0.206219i	0.0889722	+	0.996034i	$0.471642\pi$
$158$		0			0
$159$	1.00958	−	7.02175i	0.0800645	−	0.556861i
$160$		0			0
$161$	−3.15398	+	4.20010i	−0.248569	+	0.331015i
$162$		0			0
$163$	−1.63311	+	11.3585i	−0.127915	+	0.889669i	0.820276	+	0.571968i	$0.193820\pi$
$163$	−1.63311	+	11.3585i	−0.127915	+	0.889669i	−0.948191	+	0.317701i	$0.897089\pi$
$164$		0			0
$165$	−1.45220	−	0.426405i	−0.113054	−	0.0331956i
$166$		0			0
$167$	0.0201413	−	0.00591402i	0.00155858	−	0.000457641i	−0.280953	−	0.959721i	$-0.590651\pi$
$167$	0.0201413	−	0.00591402i	0.00155858	−	0.000457641i	0.282512	+	0.959264i	$0.408832\pi$
$168$		0			0
$169$	5.24103	−	11.4763i	0.403156	−	0.882789i
$170$		0			0
$171$	−5.61485	+	3.60845i	−0.429379	+	0.275945i
$172$		0			0
$173$	3.21842	+	22.3846i	0.244692	+	1.70187i	0.627969	+	0.778238i	$0.283886\pi$
$173$	3.21842	+	22.3846i	0.244692	+	1.70187i	−0.383277	+	0.923633i	$0.625205\pi$
$174$		0			0
$175$	−1.15807	+	1.33648i	−0.0875419	+	0.101029i
$176$		0			0
$177$	4.38406	+	2.81747i	0.329526	+	0.211774i
$178$		0			0
$179$	−15.3526	−	17.7178i	−1.14751	−	1.32429i	−0.938060	−	0.346473i	$-0.887379\pi$
$179$	−15.3526	−	17.7178i	−1.14751	−	1.32429i	−0.209446	−	0.977820i	$-0.567166\pi$
$180$		0			0
$181$	6.12031	+	13.4016i	0.454919	+	0.996133i	0.988616	+	0.150458i	$0.0480748\pi$
$181$	6.12031	+	13.4016i	0.454919	+	0.996133i	−0.533698	+	0.845675i	$0.679198\pi$
$182$		0			0
$183$	−11.4466			−0.846156
$184$		0			0
$185$	−18.9676			−1.39452
$186$		0			0
$187$	−2.41342	−	5.28465i	−0.176487	−	0.386452i
$188$		0			0
$189$	0.717214	+	0.827709i	0.0521697	+	0.0602070i
$190$		0			0
$191$	12.9880	+	8.34690i	0.939780	+	0.603960i	0.918333	−	0.395810i	$-0.129536\pi$
$191$	12.9880	+	8.34690i	0.939780	+	0.603960i	0.0214479	+	0.999770i	$0.493172\pi$
$192$		0			0
$193$	−2.26928	+	2.61889i	−0.163347	+	0.188512i	−0.831522	−	0.555492i	$-0.812530\pi$
$193$	−2.26928	+	2.61889i	−0.163347	+	0.188512i	0.668175	+	0.744004i	$0.267076\pi$
$194$		0			0
$195$	−1.32528	−	9.21755i	−0.0949056	−	0.660083i
$196$		0			0
$197$	0.764454	−	0.491284i	0.0544651	−	0.0350026i	−0.513125	−	0.858314i	$-0.671512\pi$
$197$	0.764454	−	0.491284i	0.0544651	−	0.0350026i	0.567590	+	0.823311i	$0.307876\pi$
$198$		0			0
$199$	4.11616	−	9.01313i	0.291787	−	0.638924i	−0.705796	−	0.708415i	$-0.749410\pi$
$199$	4.11616	−	9.01313i	0.291787	−	0.638924i	0.997583	+	0.0694916i	$0.0221377\pi$
$200$		0			0
$201$	−8.96405	+	2.63208i	−0.632275	+	0.185653i
$202$		0			0
$203$	8.66026	+	2.54288i	0.607831	+	0.178475i
$204$		0			0
$205$	−0.546282	+	3.79947i	−0.0381540	+	0.265367i
$206$		0			0
$207$	3.38608	+	3.39624i	0.235349	+	0.236055i
$208$		0			0
$209$	0.781352	−	5.43442i	0.0540473	−	0.375907i
$210$		0			0
$211$	23.3953	+	6.86949i	1.61060	+	0.472915i	0.958471	−	0.285191i	$-0.0920571\pi$
$211$	23.3953	+	6.86949i	1.61060	+	0.472915i	0.652131	+	0.758106i	$0.273875\pi$
$212$		0			0
$213$	5.37712	−	1.57887i	0.368435	−	0.108182i
$214$		0			0
$215$	4.10483	−	8.98832i	0.279947	−	0.612998i
$216$		0			0
$217$	6.72988	−	4.32503i	0.456854	−	0.293602i
$218$		0			0
$219$	0.520647	+	3.62118i	0.0351821	+	0.244697i
$220$		0			0
$221$	23.4085	−	27.0148i	1.57462	−	1.81721i
$222$		0			0
$223$	−13.0878	−	8.41104i	−0.876426	−	0.563245i	0.0232860	−	0.999729i	$-0.492587\pi$
$223$	−13.0878	−	8.41104i	−0.876426	−	0.563245i	−0.899712	+	0.436484i	$0.856224\pi$
$224$		0			0
$225$	1.05739	+	1.22029i	0.0704926	+	0.0813528i
$226$		0			0
$227$	−3.66259	−	8.01996i	−0.243095	−	0.532303i	0.748277	−	0.663387i	$-0.230882\pi$
$227$	−3.66259	−	8.01996i	−0.243095	−	0.532303i	−0.991371	+	0.131084i	$0.958154\pi$
$228$		0			0
$229$	3.57750			0.236408			0.118204	−	0.992989i	$-0.462286\pi$
$229$	3.57750			0.236408			0.118204	+	0.992989i	$0.462286\pi$
$230$		0			0
$231$	−0.900918			−0.0592760
$232$		0			0
$233$	5.46748	+	11.9721i	0.358186	+	0.784318i	0.999850	+	0.0173322i	$0.00551730\pi$
$233$	5.46748	+	11.9721i	0.358186	+	0.784318i	−0.641664	+	0.766986i	$0.721755\pi$
$234$		0			0
$235$	−0.522278	−	0.602741i	−0.0340697	−	0.0393185i
$236$		0			0
$237$	6.05315	+	3.89012i	0.393194	+	0.252691i
$238$		0			0
$239$	0.490074	−	0.565576i	0.0317003	−	0.0365840i	−0.739678	−	0.672961i	$-0.765022\pi$
$239$	0.490074	−	0.565576i	0.0317003	−	0.0365840i	0.771378	+	0.636377i	$0.219568\pi$
$240$		0			0
$241$	−3.15651	−	21.9540i	−0.203329	−	1.41418i	−0.794317	−	0.607504i	$-0.792171\pi$
$241$	−3.15651	−	21.9540i	−0.203329	−	1.41418i	0.590988	−	0.806680i	$-0.298738\pi$
$242$		0			0
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$		0			0
$245$	−4.43351	+	9.70803i	−0.283247	+	0.620223i
$246$		0			0
$247$	32.4125	−	9.51716i	2.06236	−	0.605562i
$248$		0			0
$249$	−10.2217	−	3.00137i	−0.647777	−	0.190204i
$250$		0			0
$251$	−1.87828	+	13.0638i	−0.118556	+	0.824577i	0.840591	+	0.541670i	$0.182208\pi$
$251$	−1.87828	+	13.0638i	−0.118556	+	0.824577i	−0.959147	+	0.282907i	$0.908701\pi$
$252$		0			0
$253$	−3.93538	+	0.275542i	−0.247415	+	0.0173232i
$254$		0			0
$255$	1.84933	−	12.8624i	0.115810	−	0.805475i
$256$		0			0
$257$	−0.774150	−	0.227311i	−0.0482901	−	0.0141793i	0.257498	−	0.966279i	$-0.417102\pi$
$257$	−0.774150	−	0.227311i	−0.0482901	−	0.0141793i	−0.305788	+	0.952099i	$0.598920\pi$
$258$		0			0
$259$	−10.8331	+	3.18089i	−0.673138	+	0.197651i
$260$		0			0
$261$	3.42351	−	7.49643i	0.211910	−	0.464018i
$262$		0			0
$263$	6.49025	−	4.17103i	0.400206	−	0.257197i	−0.325021	−	0.945707i	$-0.605371\pi$
$263$	6.49025	−	4.17103i	0.400206	−	0.257197i	0.725227	+	0.688510i	$0.241735\pi$
$264$		0			0
$265$	1.85754	+	12.9195i	0.114108	+	0.793638i
$266$		0			0
$267$	6.16530	−	7.11514i	0.377310	−	0.435439i
$268$		0			0
$269$	19.7278	+	12.6783i	1.20283	+	0.773010i	0.979443	−	0.201721i	$-0.0646535\pi$
$269$	19.7278	+	12.6783i	1.20283	+	0.773010i	0.223383	+	0.974731i	$0.428290\pi$
$270$		0			0
$271$	−16.8683	−	19.4671i	−1.02468	−	1.18254i	−0.983037	−	0.183408i	$-0.941287\pi$
$271$	−16.8683	−	19.4671i	−1.02468	−	1.18254i	−0.0416406	−	0.999133i	$-0.513258\pi$
$272$		0			0
$273$	−2.30272	−	5.04225i	−0.139367	−	0.305171i
$274$		0			0
$275$	−1.32822			−0.0800948
$276$		0			0
$277$	−30.2429			−1.81712			−0.908559	−	0.417756i	$-0.862817\pi$
$277$	−30.2429			−1.81712			−0.908559	+	0.417756i	$0.862817\pi$
$278$		0			0
$279$	−3.03433	−	6.64425i	−0.181660	−	0.397781i
$280$		0			0
$281$	17.4208	+	20.1046i	1.03924	+	1.19934i	0.979566	+	0.201124i	$0.0644593\pi$
$281$	17.4208	+	20.1046i	1.03924	+	1.19934i	0.0596697	+	0.998218i	$0.480995\pi$
$282$		0			0
$283$	−3.39715	−	2.18321i	−0.201939	−	0.129779i	0.435763	−	0.900061i	$-0.356479\pi$
$283$	−3.39715	−	2.18321i	−0.201939	−	0.129779i	−0.637702	+	0.770283i	$0.720115\pi$
$284$		0			0
$285$	8.04194	−	9.28089i	0.476363	−	0.549752i
$286$		0			0
$287$	0.325175	+	2.26164i	0.0191945	+	0.133500i
$288$		0			0
$289$	27.6608	−	17.7765i	1.62711	−	1.04568i
$290$		0			0
$291$	−2.98375	+	6.53350i	−0.174911	+	0.383001i
$292$		0			0
$293$	5.33624	−	1.56686i	0.311747	−	0.0915371i	−0.122117	−	0.992516i	$-0.538968\pi$
$293$	5.33624	−	1.56686i	0.311747	−	0.0915371i	0.433863	+	0.900979i	$0.357150\pi$
$294$		0			0
$295$	−9.20008	−	2.70139i	−0.535650	−	0.157281i
$296$		0			0
$297$	−0.117067	+	0.814220i	−0.00679293	+	0.0472458i
$298$		0			0
$299$	−11.6009	−	21.3213i	−0.670896	−	1.23304i
$300$		0			0
$301$	0.837072	−	5.82197i	0.0482480	−	0.335572i
$302$		0			0
$303$	12.8612	+	3.77640i	0.738858	+	0.216948i
$304$		0			0
$305$	20.2078	−	5.93353i	1.15709	−	0.339753i
$306$		0			0
$307$	7.32182	−	16.0325i	0.417878	−	0.915026i	−0.577262	−	0.816559i	$-0.695879\pi$
$307$	7.32182	−	16.0325i	0.417878	−	0.915026i	0.995140	−	0.0984669i	$-0.0313939\pi$
$308$		0			0
$309$	−0.368700	+	0.236949i	−0.0209746	+	0.0134796i
$310$		0			0
$311$	−0.127878	−	0.889408i	−0.00725127	−	0.0504337i	0.985875	−	0.167485i	$-0.0535647\pi$
$311$	−0.127878	−	0.889408i	−0.00725127	−	0.0504337i	−0.993126	+	0.117052i	$0.962656\pi$
$312$		0			0
$313$	−3.21572	+	3.71114i	−0.181763	+	0.209766i	−0.839318	−	0.543641i	$-0.817045\pi$
$313$	−3.21572	+	3.71114i	−0.181763	+	0.209766i	0.657555	+	0.753407i	$0.271591\pi$
$314$		0			0
$315$	−1.69522	−	1.08945i	−0.0955150	−	0.0613838i
$316$		0			0
$317$	12.1794	+	14.0558i	0.684064	+	0.789452i	0.986508	−	0.163716i	$-0.0523479\pi$
$317$	12.1794	+	14.0558i	0.684064	+	0.789452i	−0.302444	+	0.953167i	$0.597802\pi$
$318$		0			0
$319$	2.81615	+	6.16651i	0.157674	+	0.345258i
$320$		0			0
$321$	−17.1489			−0.957159
$322$		0			0
$323$	47.1386			2.62286
$324$		0			0
$325$	−3.39490	−	7.43379i	−0.188315	−	0.412353i
$326$		0			0
$327$	−1.33928	−	1.54561i	−0.0740624	−	0.0854726i
$328$		0			0
$329$	−0.399374	−	0.256662i	−0.0220182	−	0.0141502i
$330$		0			0
$331$	−4.59982	+	5.30847i	−0.252829	+	0.291780i	−0.867949	−	0.496653i	$-0.834562\pi$
$331$	−4.59982	+	5.30847i	−0.252829	+	0.291780i	0.615120	+	0.788433i	$0.289107\pi$
$332$		0			0
$333$	1.46711	+	10.2040i	0.0803970	+	0.559174i
$334$		0			0
$335$	14.4607	−	9.29333i	0.790072	−	0.507749i
$336$		0			0
$337$	−5.53142	+	12.1121i	−0.301316	+	0.659790i	−0.998361	−	0.0572380i	$-0.981771\pi$
$337$	−5.53142	+	12.1121i	−0.301316	+	0.659790i	0.697045	+	0.717028i	$0.254498\pi$
$338$		0			0
$339$	−5.33233	+	1.56571i	−0.289613	+	0.0850379i
$340$		0			0
$341$	5.76510	+	1.69279i	0.312198	+	0.0916695i
$342$		0			0
$343$	−1.99516	+	13.8766i	−0.107728	+	0.749267i
$344$		0			0
$345$	−7.73827	−	4.24047i	−0.416614	−	0.228299i
$346$		0			0
$347$	−3.68354	+	25.6196i	−0.197743	+	1.37533i	0.613072	+	0.790027i	$0.289933\pi$
$347$	−3.68354	+	25.6196i	−0.197743	+	1.37533i	−0.810815	+	0.585303i	$0.800976\pi$
$348$		0			0
$349$	−20.4349	−	6.00023i	−1.09386	−	0.321185i	−0.315447	−	0.948943i	$-0.602155\pi$
$349$	−20.4349	−	6.00023i	−1.09386	−	0.321185i	−0.778408	+	0.627758i	$0.783973\pi$
$350$		0			0
$351$	−4.85624	+	1.42592i	−0.259207	+	0.0761101i
$352$		0			0
$353$	0.0735392	−	0.161028i	0.00391410	−	0.00857068i	−0.907665	−	0.419696i	$-0.862137\pi$
$353$	0.0735392	−	0.161028i	0.00391410	−	0.00857068i	0.911579	+	0.411125i	$0.134864\pi$
$354$		0			0
$355$	−8.67432	+	5.57464i	−0.460385	+	0.295871i
$356$		0			0
$357$	−1.10082	−	7.65636i	−0.0582615	−	0.405217i
$358$		0			0
$359$	18.5896	−	21.4536i	0.981124	−	1.13228i	−0.0100821	−	0.999949i	$-0.503209\pi$
$359$	18.5896	−	21.4536i	0.981124	−	1.13228i	0.991206	−	0.132328i	$-0.0422452\pi$
$360$		0			0
$361$	21.4919	+	13.8120i	1.13115	+	0.726948i
$362$		0			0
$363$	6.76035	+	7.80186i	0.354826	+	0.409491i
$364$		0			0
$365$	−2.79625	−	6.12292i	−0.146362	−	0.320488i
$366$		0			0
$367$	−19.2279			−1.00369			−0.501845	−	0.864958i	$-0.667345\pi$
$367$	−19.2279			−1.00369			−0.501845	+	0.864958i	$0.667345\pi$
$368$		0			0
$369$	2.08625			0.108606
$370$		0			0
$371$	3.22753	+	7.06731i	0.167565	+	0.366916i
$372$		0			0
$373$	2.53858	+	2.92968i	0.131443	+	0.151693i	0.817655	−	0.575708i	$-0.195274\pi$
$373$	2.53858	+	2.92968i	0.131443	+	0.151693i	−0.686213	+	0.727401i	$0.740728\pi$
$374$		0			0
$375$	−10.2385	−	6.57987i	−0.528713	−	0.339783i
$376$		0			0
$377$	−27.3147	+	31.5229i	−1.40678	+	1.62351i
$378$		0			0
$379$	−0.00769544	−	0.0535230i	−0.000395288	−	0.00274929i	0.989623	−	0.143689i	$-0.0458966\pi$
$379$	−0.00769544	−	0.0535230i	−0.000395288	−	0.00274929i	−0.990018	+	0.140940i	$0.954988\pi$
$380$		0			0
$381$	5.94837	−	3.82278i	0.304744	−	0.195847i
$382$		0			0
$383$	−1.34135	+	2.93715i	−0.0685398	+	0.150081i	−0.940801	−	0.338958i	$-0.889925\pi$
$383$	−1.34135	+	2.93715i	−0.0685398	+	0.150081i	0.872262	+	0.489040i	$0.162653\pi$
$384$		0			0
$385$	1.59048	−	0.467006i	0.0810581	−	0.0238008i
$386$		0			0
$387$	−5.15293	−	1.51304i	−0.261938	−	0.0769120i
$388$		0			0
$389$	−1.94937	+	13.5582i	−0.0988369	+	0.687426i	0.878810	+	0.477172i	$0.158338\pi$
$389$	−1.94937	+	13.5582i	−0.0988369	+	0.687426i	−0.977647	+	0.210254i	$0.932571\pi$
$390$		0			0
$391$	−7.15025	−	33.1078i	−0.361604	−	1.67433i
$392$		0			0
$393$	−0.726633	+	5.05384i	−0.0366538	+	0.254933i
$394$		0			0
$395$	−12.7027	−	3.72985i	−0.639142	−	0.187669i
$396$		0			0
$397$	12.2973	−	3.61080i	0.617182	−	0.181221i	0.0418270	−	0.999125i	$-0.486682\pi$
$397$	12.2973	−	3.61080i	0.617182	−	0.181221i	0.575355	+	0.817904i	$0.304864\pi$
$398$		0			0
$399$	3.03664	−	6.64932i	0.152022	−	0.332882i
$400$		0			0
$401$	1.91168	−	1.22856i	0.0954646	−	0.0613514i	−0.492038	−	0.870574i	$-0.663748\pi$
$401$	1.91168	−	1.22856i	0.0954646	−	0.0613514i	0.587502	+	0.809223i	$0.300111\pi$
$402$		0			0
$403$	5.26125	+	36.5928i	0.262082	+	1.82282i
$404$		0			0
$405$	−1.20489	+	1.39052i	−0.0598717	+	0.0690956i
$406$		0			0
$407$	−7.13385	−	4.58465i	−0.353612	−	0.227252i
$408$		0			0
$409$	−12.9944	−	14.9963i	−0.642530	−	0.741519i	0.337290	−	0.941401i	$-0.390490\pi$
$409$	−12.9944	−	14.9963i	−0.642530	−	0.741519i	−0.979820	+	0.199882i	$0.935944\pi$
$410$		0			0
$411$	−3.20577	−	7.01965i	−0.158129	−	0.346254i
$412$		0			0
$413$	−5.70755			−0.280850
$414$		0			0
$415$	19.6012			0.962186
$416$		0			0
$417$	−6.65834	−	14.5797i	−0.326060	−	0.713973i
$418$		0			0
$419$	19.9060	+	22.9727i	0.972470	+	1.12229i	0.992470	+	0.122490i	$0.0390879\pi$
$419$	19.9060	+	22.9727i	0.972470	+	1.12229i	−0.0200001	+	0.999800i	$0.506367\pi$
$420$		0			0
$421$	12.8189	+	8.23823i	0.624757	+	0.401507i	0.814365	−	0.580353i	$-0.197085\pi$
$421$	12.8189	+	8.23823i	0.624757	+	0.401507i	−0.189608	+	0.981860i	$0.560722\pi$
$422$		0			0
$423$	−0.283858	+	0.327590i	−0.0138017	+	0.0159280i
$424$		0			0
$425$	−1.62294	−	11.2878i	−0.0787239	−	0.547537i
$426$		0			0
$427$	10.5464	−	6.77774i	0.510375	−	0.327998i
$428$		0			0
$429$	1.72952	−	3.78712i	0.0835021	−	0.182844i
$430$		0			0
$431$	−21.8247	+	6.40831i	−1.05126	+	0.308678i	−0.761326	−	0.648369i	$-0.775451\pi$
$431$	−21.8247	+	6.40831i	−1.05126	+	0.308678i	−0.289933	+	0.957047i	$0.593633\pi$
$432$		0			0
$433$	−15.1834	−	4.45824i	−0.729666	−	0.214249i	−0.104262	−	0.994550i	$-0.533248\pi$
$433$	−15.1834	−	4.45824i	−0.729666	−	0.214249i	−0.625405	+	0.780300i	$0.715066\pi$
$434$		0			0
$435$	−2.15794	+	15.0088i	−0.103465	+	0.719617i
$436$		0			0
$437$	11.2310	−	29.9743i	0.537251	−	1.43386i
$438$		0			0
$439$	−2.62157	+	18.2334i	−0.125121	+	0.870235i	0.826495	+	0.562944i	$0.190331\pi$
$439$	−2.62157	+	18.2334i	−0.125121	+	0.870235i	−0.951616	+	0.307291i	$0.900578\pi$
$440$		0			0
$441$	5.56554	+	1.63419i	0.265026	+	0.0778186i
$442$		0			0
$443$	−6.33470	+	1.86003i	−0.300970	+	0.0883729i	−0.428731	−	0.903432i	$-0.641039\pi$
$443$	−6.33470	+	1.86003i	−0.300970	+	0.0883729i	0.127761	+	0.991805i	$0.459221\pi$
$444$		0			0
$445$	−7.19594	+	15.7569i	−0.341120	+	0.746949i
$446$		0			0
$447$	−4.60006	+	2.95628i	−0.217575	+	0.139827i
$448$		0			0
$449$	−0.276018	−	1.91975i	−0.0130261	−	0.0905985i	0.982271	−	0.187465i	$-0.0600271\pi$
$449$	−0.276018	−	1.91975i	−0.0130261	−	0.0905985i	−0.995297	+	0.0968665i	$0.969118\pi$
$450$		0			0
$451$	−1.12383	+	1.29697i	−0.0529191	+	0.0610719i
$452$		0			0
$453$	−12.6569	−	8.13409i	−0.594672	−	0.382173i
$454$		0			0
$455$	6.67894	+	7.70791i	0.313114	+	0.361352i
$456$		0			0
$457$	−1.73606	−	3.80144i	−0.0812094	−	0.177824i	0.864672	−	0.502338i	$-0.167527\pi$
$457$	−1.73606	−	3.80144i	−0.0812094	−	0.177824i	−0.945881	+	0.324514i	$0.894799\pi$
$458$		0			0
$459$	−7.06261			−0.329654
$460$		0			0
$461$	−18.6041			−0.866478			−0.433239	−	0.901279i	$-0.642629\pi$
$461$	−18.6041			−0.866478			−0.433239	+	0.901279i	$0.642629\pi$
$462$		0			0
$463$	1.48372	+	3.24889i	0.0689543	+	0.150989i	0.940971	−	0.338487i	$-0.109915\pi$
$463$	1.48372	+	3.24889i	0.0689543	+	0.150989i	−0.872017	+	0.489476i	$0.837188\pi$
$464$		0			0
$465$	8.80094	+	10.1568i	0.408134	+	0.471012i
$466$		0			0
$467$	6.37001	+	4.09376i	0.294769	+	0.189437i	0.679664	−	0.733524i	$-0.262126\pi$
$467$	6.37001	+	4.09376i	0.294769	+	0.189437i	−0.384894	+	0.922961i	$0.625762\pi$
$468$		0			0
$469$	6.70056	−	7.73286i	0.309403	−	0.357070i
$470$		0			0
$471$	1.30524	+	9.07817i	0.0601424	+	0.418300i
$472$		0			0
$473$	3.71642	−	2.38840i	0.170881	−	0.109819i
$474$		0			0
$475$	4.47692	−	9.80309i	0.205415	−	0.449797i
$476$		0			0
$477$	6.80660	−	1.99860i	0.311653	−	0.0915095i
$478$		0			0
$479$	14.1281	+	4.14839i	0.645530	+	0.189545i	0.588079	−	0.808804i	$-0.299885\pi$
$479$	14.1281	+	4.14839i	0.645530	+	0.189545i	0.0574510	+	0.998348i	$0.481703\pi$
$480$		0			0
$481$	7.42542	−	51.6449i	0.338570	−	2.35481i
$482$		0			0
$483$	−5.13076	−	1.12418i	−0.233458	−	0.0511518i
$484$		0			0
$485$	1.88075	−	13.0809i	0.0854003	−	0.593972i
$486$		0			0
$487$	−4.95385	−	1.45458i	−0.224480	−	0.0659133i	0.167558	−	0.985862i	$-0.446412\pi$
$487$	−4.95385	−	1.45458i	−0.224480	−	0.0659133i	−0.392038	+	0.919949i	$0.628230\pi$
$488$		0			0
$489$	−11.0105	+	3.23297i	−0.497912	+	0.146200i
$490$		0			0
$491$	−14.6574	+	32.0952i	−0.661478	+	1.44843i	0.219661	+	0.975576i	$0.429505\pi$
$491$	−14.6574	+	32.0952i	−0.661478	+	1.44843i	−0.881139	+	0.472858i	$0.843222\pi$
$492$		0			0
$493$	−48.9645	+	31.4676i	−2.20525	+	1.41723i
$494$		0			0
$495$	−0.215395	−	1.49810i	−0.00968128	−	0.0673348i
$496$		0			0
$497$	−4.01936	+	4.63859i	−0.180293	+	0.208069i
$498$		0			0
$499$	−35.7318	−	22.9635i	−1.59958	−	1.02799i	−0.967431	−	0.253137i	$-0.918538\pi$
$499$	−35.7318	−	22.9635i	−1.59958	−	1.02799i	−0.632146	−	0.774849i	$-0.717826\pi$
$500$		0			0
$501$	0.0137466	+	0.0158644i	0.000614152	+	0.000708769i
$502$		0			0
$503$	5.07781	+	11.1189i	0.226408	+	0.495765i	0.988410	−	0.151810i	$-0.0485103\pi$
$503$	5.07781	+	11.1189i	0.226408	+	0.495765i	−0.762001	+	0.647576i	$0.775783\pi$
$504$		0			0
$505$	−24.6627			−1.09748
$506$		0			0
$507$	12.6164			0.560313
$508$		0			0
$509$	−6.00390	−	13.1467i	−0.266118	−	0.582718i	0.728649	−	0.684888i	$-0.240149\pi$
$509$	−6.00390	−	13.1467i	−0.266118	−	0.582718i	−0.994767	+	0.102170i	$0.967421\pi$
$510$		0			0
$511$	−2.62387	−	3.02811i	−0.116073	−	0.133956i
$512$		0			0
$513$	−5.61485	−	3.60845i	−0.247902	−	0.159317i
$514$		0			0
$515$	0.528074	−	0.609430i	0.0232697	−	0.0268547i
$516$		0			0
$517$	−0.0507444	−	0.352935i	−0.00223174	−	0.0155221i
$518$		0			0
$519$	−19.0248	+	12.2265i	−0.835096	+	0.536683i
$520$		0			0
$521$	−10.4757	+	22.9385i	−0.458947	+	1.00495i	0.528779	+	0.848759i	$0.322650\pi$
$521$	−10.4757	+	22.9385i	−0.458947	+	1.00495i	−0.987726	+	0.156194i	$0.950077\pi$
$522$		0			0
$523$	36.9999	−	10.8642i	1.61789	−	0.475056i	0.657442	−	0.753505i	$-0.271638\pi$
$523$	36.9999	−	10.8642i	1.61789	−	0.475056i	0.960451	+	0.278448i	$0.0898201\pi$
$524$		0			0
$525$	−1.69679	−	0.498222i	−0.0740539	−	0.0217442i
$526$		0			0
$527$	−7.34168	+	51.0625i	−0.319809	+	2.22432i
$528$		0			0
$529$	−22.7560	−	3.34140i	−0.989391	−	0.145278i
$530$		0			0
$531$	−0.741652	+	5.15830i	−0.0321850	+	0.223851i
$532$		0			0
$533$	−10.1313	−	2.97483i	−0.438837	−	0.128854i
$534$		0			0
$535$	30.2746	−	8.88942i	1.30888	−	0.384323i
$536$		0			0
$537$	9.73901	−	21.3255i	0.420269	−	0.920262i
$538$		0			0
$539$	−4.01400	+	2.57964i	−0.172895	+	0.111113i
$540$		0			0
$541$	5.32966	+	37.0686i	0.229140	+	1.59370i	0.701745	+	0.712428i	$0.252405\pi$
$541$	5.32966	+	37.0686i	0.229140	+	1.59370i	−0.472605	+	0.881274i	$0.656686\pi$
$542$		0			0
$543$	−9.64806	+	11.1345i	−0.414038	+	0.477825i
$544$		0			0
$545$	3.16555	+	2.03438i	0.135597	+	0.0871432i
$546$		0			0
$547$	−19.3538	−	22.3355i	−0.827509	−	0.954996i	0.172038	−	0.985090i	$-0.444965\pi$
$547$	−19.3538	−	22.3355i	−0.827509	−	0.954996i	−0.999547	+	0.0300942i	$0.990419\pi$
$548$		0			0
$549$	−4.75509	−	10.4122i	−0.202942	−	0.444381i
$550$		0			0
$551$	−55.0048			−2.34328
$552$		0			0
$553$	−7.88051			−0.335113
$554$		0			0
$555$	−7.87942	−	17.2535i	−0.334463	−	0.732371i
$556$		0			0
$557$	16.0987	+	18.5789i	0.682124	+	0.787213i	0.986222	−	0.165428i	$-0.0529005\pi$
$557$	16.0987	+	18.5789i	0.682124	+	0.787213i	−0.304098	+	0.952641i	$0.598355\pi$
$558$		0			0
$559$	22.8664	+	14.6954i	0.967147	+	0.621548i
$560$		0			0
$561$	3.80451	−	4.39064i	0.160627	−	0.185373i
$562$		0			0
$563$	−0.375642	−	2.61265i	−0.0158314	−	0.110110i	0.980373	−	0.197149i	$-0.0631684\pi$
$563$	−0.375642	−	2.61265i	−0.0158314	−	0.110110i	−0.996205	+	0.0870396i	$0.972259\pi$
$564$		0			0
$565$	8.60206	−	5.52821i	0.361891	−	0.232573i
$566$		0			0
$567$	−0.454969	+	0.996244i	−0.0191069	+	0.0418383i
$568$		0			0
$569$	36.2837	−	10.6539i	1.52109	−	0.446633i	0.588783	−	0.808291i	$-0.299607\pi$
$569$	36.2837	−	10.6539i	1.52109	−	0.446633i	0.932311	+	0.361658i	$0.117789\pi$
$570$		0			0
$571$	40.2460	+	11.8173i	1.68424	+	0.494539i	0.977145	−	0.212576i	$-0.0681852\pi$
$571$	40.2460	+	11.8173i	1.68424	+	0.494539i	0.707099	+	0.707114i	$0.250003\pi$
$572$		0			0
$573$	−2.19718	+	15.2817i	−0.0917887	+	0.638404i
$574$		0			0
$575$	−7.56428	−	1.65737i	−0.315452	−	0.0691173i
$576$		0			0
$577$	0.823276	−	5.72601i	0.0342734	−	0.238377i	−0.965483	−	0.260468i	$-0.916123\pi$
$577$	0.823276	−	5.72601i	0.0342734	−	0.238377i	0.999756	+	0.0220908i	$0.00703229\pi$
$578$		0			0
$579$	−3.32492	−	0.976286i	−0.138179	−	0.0405730i
$580$		0			0
$581$	11.1950	−	3.28715i	0.464448	−	0.136374i
$582$		0			0
$583$	−2.42413	+	5.30810i	−0.100397	+	0.219839i
$584$		0			0
$585$	7.83404	−	5.03463i	0.323898	−	0.208156i
$586$		0			0
$587$	−4.97780	−	34.6214i	−0.205456	−	1.42898i	−0.787748	−	0.615998i	$-0.788753\pi$
$587$	−4.97780	−	34.6214i	−0.205456	−	1.42898i	0.582292	−	0.812980i	$-0.302156\pi$
$588$		0			0
$589$	−31.9257	+	36.8442i	−1.31548	+	1.51814i
$590$		0			0
$591$	0.764454	+	0.491284i	0.0314454	+	0.0202087i
$592$		0			0
$593$	−19.9399	−	23.0119i	−0.818835	−	0.944986i	0.180419	−	0.983590i	$-0.442255\pi$
$593$	−19.9399	−	23.0119i	−0.818835	−	0.944986i	−0.999255	+	0.0386035i	$0.987709\pi$
$594$		0			0
$595$	5.91218	+	12.9459i	0.242376	+	0.530729i
$596$		0			0
$597$	9.90854			0.405530
$598$		0			0
$599$	−22.8232			−0.932532			−0.466266	−	0.884645i	$-0.654401\pi$
$599$	−22.8232			−0.932532			−0.466266	+	0.884645i	$0.654401\pi$
$600$		0			0
$601$	18.3676	+	40.2194i	0.749230	+	1.64058i	0.767745	+	0.640755i	$0.221379\pi$
$601$	18.3676	+	40.2194i	0.749230	+	1.64058i	−0.0185154	+	0.999829i	$0.505894\pi$
$602$		0			0
$603$	−6.11802	−	7.06058i	−0.249145	−	0.287529i
$604$		0			0
$605$	−15.9789	−	10.2690i	−0.649635	−	0.417495i
$606$		0			0
$607$	−24.3291	+	28.0773i	−0.987487	+	1.13962i	0.00271699	+	0.999996i	$0.499135\pi$
$607$	−24.3291	+	28.0773i	−0.987487	+	1.13962i	−0.990204	+	0.139625i	$0.955410\pi$
$608$		0			0
$609$	1.28451	+	8.93400i	0.0520512	+	0.362024i
$610$		0			0
$611$	1.84560	−	1.18610i	0.0746651	−	0.0479844i
$612$		0			0
$613$	13.9769	−	30.6051i	0.564521	−	1.23613i	−0.385143	−	0.922857i	$-0.625848\pi$
$613$	13.9769	−	30.6051i	0.564521	−	1.23613i	0.949664	−	0.313271i	$-0.101425\pi$
$614$		0			0
$615$	−3.68306	+	1.08144i	−0.148515	+	0.0436080i
$616$		0			0
$617$	−14.1961	−	4.16836i	−0.571514	−	0.167812i	−0.0168092	−	0.999859i	$-0.505351\pi$
$617$	−14.1961	−	4.16836i	−0.571514	−	0.167812i	−0.554705	+	0.832047i	$0.687169\pi$
$618$		0			0
$619$	1.99988	−	13.9095i	0.0803820	−	0.559069i	−0.909339	−	0.416056i	$-0.863412\pi$
$619$	1.99988	−	13.9095i	0.0803820	−	0.559069i	0.989721	−	0.143013i	$-0.0456790\pi$
$620$		0			0
$621$	−1.68270	+	4.49094i	−0.0675243	+	0.180215i
$622$		0			0
$623$	−1.46742	+	10.2062i	−0.0587911	+	0.408901i
$624$		0			0
$625$	13.7394	+	4.03425i	0.549576	+	0.161370i
$626$		0			0
$627$	5.26791	−	1.54680i	0.210380	−	0.0617732i
$628$		0			0
$629$	30.2454	−	66.2282i	1.20596	−	2.64069i
$630$		0			0
$631$	−26.2476	+	16.8683i	−1.04490	+	0.671517i	−0.946194	−	0.323600i	$-0.895107\pi$
$631$	−26.2476	+	16.8683i	−1.04490	+	0.671517i	−0.0987066	+	0.995117i	$0.531471\pi$
$632$		0			0
$633$	3.47007	+	24.1348i	0.137923	+	0.959274i
$634$		0			0
$635$	−8.51961	+	9.83215i	−0.338090	+	0.390177i
$636$		0			0
$637$	−24.6974	−	15.8721i	−0.978546	−	0.628874i
$638$		0			0
$639$	3.66993	+	4.23532i	0.145180	+	0.167547i
$640$		0			0
$641$	−7.47455	−	16.3670i	−0.295227	−	0.646457i	0.702653	−	0.711532i	$-0.251998\pi$
$641$	−7.47455	−	16.3670i	−0.295227	−	0.646457i	−0.997880	+	0.0650754i	$0.979271\pi$
$642$		0			0
$643$	−14.7221			−0.580582			−0.290291	−	0.956938i	$-0.593752\pi$
$643$	−14.7221			−0.580582			−0.290291	+	0.956938i	$0.593752\pi$
$644$		0			0
$645$	9.88127			0.389075
$646$		0			0
$647$	−0.658358	−	1.44160i	−0.0258827	−	0.0566753i	0.896249	−	0.443551i	$-0.146282\pi$
$647$	−0.658358	−	1.44160i	−0.0258827	−	0.0566753i	−0.922132	+	0.386876i	$0.873554\pi$
$648$		0			0
$649$	−2.80727	−	3.23976i	−0.110195	−	0.127172i
$650$		0			0
$651$	6.72988	+	4.32503i	0.263765	+	0.169511i
$652$		0			0
$653$	4.97282	−	5.73895i	0.194602	−	0.224582i	−0.650060	−	0.759883i	$-0.725256\pi$
$653$	4.97282	−	5.73895i	0.194602	−	0.224582i	0.844662	+	0.535301i	$0.179802\pi$
$654$		0			0
$655$	−1.33695	−	9.29868i	−0.0522389	−	0.363330i
$656$		0			0
$657$	−3.07766	+	1.97789i	−0.120071	+	0.0771648i
$658$		0			0
$659$	11.3879	−	24.9360i	0.443609	−	0.971368i	−0.547313	−	0.836928i	$-0.684349\pi$
$659$	11.3879	−	24.9360i	0.443609	−	0.971368i	0.990922	−	0.134440i	$-0.0429235\pi$
$660$		0			0
$661$	−6.28205	+	1.84458i	−0.244343	+	0.0717457i	−0.401611	−	0.915810i	$-0.631550\pi$
$661$	−6.28205	+	1.84458i	−0.244343	+	0.0717457i	0.157268	+	0.987556i	$0.449731\pi$
$662$		0			0
$663$	34.2978	+	10.0707i	1.33201	+	0.391115i
$664$		0			0
$665$	−1.91409	+	13.3128i	−0.0742251	+	0.516247i
$666$		0			0
$667$	8.34344	+	38.6326i	0.323059	+	1.49586i
$668$		0			0
$669$	2.21407	−	15.3992i	0.0856008	−	0.595367i
$670$		0			0
$671$	9.03448	+	2.65276i	0.348772	+	0.102409i
$672$		0			0
$673$	38.7760	−	11.3857i	1.49470	−	0.438885i	0.570665	−	0.821183i	$-0.306685\pi$
$673$	38.7760	−	11.3857i	1.49470	−	0.438885i	0.924039	+	0.382298i	$0.124867\pi$
$674$		0			0
$675$	−0.670761	+	1.46876i	−0.0258176	+	0.0565327i
$676$		0			0
$677$	−4.51725	+	2.90306i	−0.173612	+	0.111574i	−0.624561	−	0.780976i	$-0.714722\pi$
$677$	−4.51725	+	2.90306i	−0.173612	+	0.111574i	0.450949	+	0.892550i	$0.351086\pi$
$678$		0			0
$679$	−1.11952	−	7.78641i	−0.0429631	−	0.298815i
$680$		0			0
$681$	5.77371	−	6.66322i	0.221249	−	0.255335i
$682$		0			0
$683$	−26.6961	−	17.1566i	−1.02150	−	0.656478i	−0.0811550	−	0.996701i	$-0.525861\pi$
$683$	−26.6961	−	17.1566i	−1.02150	−	0.656478i	−0.940345	+	0.340224i	$0.889497\pi$
$684$		0			0
$685$	9.29820	+	10.7307i	0.355266	+	0.409999i
$686$		0			0
$687$	1.48615	+	3.25421i	0.0567001	+	0.124156i
$688$		0			0
$689$	−35.9044			−1.36785
$690$		0			0
$691$	−25.0555			−0.953156			−0.476578	−	0.879132i	$-0.658123\pi$
$691$	−25.0555			−0.953156			−0.476578	+	0.879132i	$0.658123\pi$
$692$		0			0
$693$	−0.374255	−	0.819503i	−0.0142168	−	0.0311304i
$694$		0			0
$695$	19.3122	+	22.2875i	0.732555	+	0.845414i
$696$		0			0
$697$	−12.3953	−	7.96601i	−0.469507	−	0.301734i
$698$		0			0
$699$	−8.61894	+	9.94678i	−0.325998	+	0.376222i
$700$		0			0
$701$	−2.73797	−	19.0430i	−0.103412	−	0.719245i	−0.973887	−	0.227033i	$-0.927098\pi$
$701$	−2.73797	−	19.0430i	−0.103412	−	0.719245i	0.870475	−	0.492212i	$-0.163812\pi$
$702$		0			0
$703$	57.8829	−	37.1991i	2.18310	−	1.40299i
$704$		0			0
$705$	0.331310	−	0.725468i	0.0124779	−	0.0273227i
$706$		0			0
$707$	−14.0858	+	4.13597i	−0.529752	+	0.155549i
$708$		0			0
$709$	−34.3507	−	10.0863i	−1.29007	−	0.378798i	−0.436465	−	0.899721i	$-0.643770\pi$
$709$	−34.3507	−	10.0863i	−1.29007	−	0.378798i	−0.853604	+	0.520923i	$0.825588\pi$
$710$		0			0
$711$	−1.02401	+	7.12215i	−0.0384034	+	0.267102i
$712$		0			0
$713$	30.7202	+	16.8343i	1.15048	+	0.630448i
$714$		0			0
$715$	−1.09017	+	7.58230i	−0.0407700	+	0.283562i
$716$		0			0
$717$	0.718050	+	0.210838i	0.0268161	+	0.00787391i
$718$		0			0
$719$	9.15557	−	2.68832i	0.341445	−	0.100257i	−0.106514	−	0.994311i	$-0.533969\pi$
$719$	9.15557	−	2.68832i	0.341445	−	0.100257i	0.447960	+	0.894054i	$0.352151\pi$
$720$		0			0
$721$	0.199401	−	0.436628i	0.00742610	−	0.0162609i
$722$		0			0
$723$	18.6588	−	11.9913i	0.693929	−	0.445961i
$724$		0			0
$725$	1.89376	+	13.1714i	0.0703325	+	0.489173i
$726$		0			0
$727$	21.0142	−	24.2516i	0.779372	−	0.899444i	−0.217691	−	0.976018i	$-0.569853\pi$
$727$	21.0142	−	24.2516i	0.779372	−	0.899444i	0.997064	+	0.0765739i	$0.0243981\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	24.8386	+	28.6653i	0.918688	+	1.06022i
$732$		0			0
$733$	0.858286	+	1.87938i	0.0317015	+	0.0694166i	0.924820	−	0.380404i	$-0.124215\pi$
$733$	0.858286	+	1.87938i	0.0317015	+	0.0694166i	−0.893119	+	0.449821i	$0.851488\pi$
$734$		0			0
$735$	−10.6725			−0.393660
$736$		0			0
$737$	7.68506			0.283083
$738$		0			0
$739$	−14.8276	−	32.4679i	−0.545442	−	1.19435i	−0.958878	−	0.283818i	$-0.908399\pi$
$739$	−14.8276	−	32.4679i	−0.545442	−	1.19435i	0.413437	−	0.910533i	$-0.364328\pi$
$740$		0			0
$741$	22.1217	+	25.5299i	0.812663	+	0.937863i
$742$		0			0
$743$	22.6212	+	14.5378i	0.829892	+	0.533339i	0.885244	−	0.465128i	$-0.153992\pi$
$743$	22.6212	+	14.5378i	0.829892	+	0.533339i	−0.0553514	+	0.998467i	$0.517628\pi$
$744$		0			0
$745$	6.58849	−	7.60352i	0.241383	−	0.278571i
$746$		0			0
$747$	−1.51612	−	10.5448i	−0.0554719	−	0.385816i
$748$		0			0
$749$	15.8002	−	10.1542i	0.577328	−	0.371026i
$750$		0			0
$751$	−5.91488	+	12.9518i	−0.215837	+	0.472617i	−0.986320	−	0.164844i	$-0.947288\pi$
$751$	−5.91488	+	12.9518i	−0.215837	+	0.472617i	0.770483	+	0.637461i	$0.220015\pi$
$752$		0			0
$753$	−12.6635	+	3.71833i	−0.461483	+	0.135504i
$754$		0			0
$755$	26.5608	+	7.79897i	0.966648	+	0.283833i
$756$		0			0
$757$	0.990211	−	6.88707i	0.0359898	−	0.250315i	−0.963882	−	0.266330i	$-0.914189\pi$
$757$	0.990211	−	6.88707i	0.0359898	−	0.250315i	0.999872	+	0.0160152i	$0.00509802\pi$
$758$		0			0
$759$	−1.88546	−	3.46529i	−0.0684378	−	0.125782i
$760$		0			0
$761$	−3.74734	+	26.0633i	−0.135841	+	0.944795i	0.801900	+	0.597459i	$0.203823\pi$
$761$	−3.74734	+	26.0633i	−0.135841	+	0.944795i	−0.937741	+	0.347336i	$0.887086\pi$
$762$		0			0
$763$	2.14914	+	0.631044i	0.0778041	+	0.0228453i
$764$		0			0
$765$	12.4683	−	3.66102i	0.450792	−	0.132365i
$766$		0			0
$767$	10.9570	−	23.9924i	0.395634	−	0.866317i
$768$		0			0
$769$	21.7777	−	13.9957i	0.785325	−	0.504697i	−0.0854723	−	0.996341i	$-0.527240\pi$
$769$	21.7777	−	13.9957i	0.785325	−	0.504697i	0.870797	+	0.491643i	$0.163604\pi$
$770$		0			0
$771$	−0.114824	−	0.798620i	−0.00413529	−	0.0287616i
$772$		0			0
$773$	−6.69983	+	7.73201i	−0.240976	+	0.278101i	−0.863335	−	0.504630i	$-0.831629\pi$
$773$	−6.69983	+	7.73201i	−0.240976	+	0.278101i	0.622359	+	0.782732i	$0.286174\pi$
$774$		0			0
$775$	9.92185	+	6.37639i	0.356404	+	0.229047i
$776$		0			0
$777$	−7.39368	−	8.53277i	−0.265247	−	0.306111i
$778$		0			0
$779$	−5.78443	−	12.6661i	−0.207249	−	0.453811i
$780$		0			0
$781$	−4.60992			−0.164956
$782$		0			0
$783$	8.24117			0.294515
$784$		0			0
$785$	−7.01009	−	15.3500i	−0.250201	−	0.547863i
$786$		0			0
$787$	8.75316	+	10.1017i	0.312016	+	0.360086i	0.889999	−	0.455963i	$-0.150705\pi$
$787$	8.75316	+	10.1017i	0.312016	+	0.360086i	−0.577982	+	0.816049i	$0.696160\pi$
$788$		0			0
$789$	6.49025	+	4.17103i	0.231059	+	0.148493i
$790$		0			0
$791$	3.98588	−	4.59995i	0.141722	−	0.163556i
$792$		0			0
$793$	8.24490	+	57.3445i	0.292785	+	2.03636i
$794$		0			0
$795$	−10.9803	+	7.05663i	−0.389432	+	0.250273i
$796$		0			0
$797$	2.24308	−	4.91166i	0.0794540	−	0.173980i	−0.865736	−	0.500501i	$-0.833149\pi$
$797$	2.24308	−	4.91166i	0.0794540	−	0.173980i	0.945190	+	0.326521i	$0.105876\pi$
$798$		0			0
$799$	2.93738	−	0.862492i	0.103917	−	0.0305128i
$800$		0			0
$801$	9.03331	+	2.65242i	0.319176	+	0.0937187i
$802$		0			0
$803$	0.428281	−	2.97876i	0.0151137	−	0.105118i
$804$		0			0
$805$	9.64055	−	0.674999i	0.339785	−	0.0237906i
$806$		0			0
$807$	−3.33735	+	23.2118i	−0.117480	+	0.817094i
$808$		0			0
$809$	−23.1533	−	6.79843i	−0.814027	−	0.239020i	−0.151885	−	0.988398i	$-0.548534\pi$
$809$	−23.1533	−	6.79843i	−0.814027	−	0.239020i	−0.662142	+	0.749378i	$0.730353\pi$
$810$		0			0
$811$	16.5191	−	4.85045i	0.580065	−	0.170322i	0.0214794	−	0.999769i	$-0.493162\pi$
$811$	16.5191	−	4.85045i	0.580065	−	0.170322i	0.558586	+	0.829447i	$0.311344\pi$
$812$		0			0
$813$	10.7005	−	23.4309i	0.375284	−	0.821757i
$814$		0			0
$815$	17.7620	−	11.4150i	0.622176	−	0.399848i
$816$		0			0
$817$	5.10123	+	35.4798i	0.178469	+	1.24128i
$818$		0			0
$819$	3.63001	−	4.18925i	0.126843	−	0.146384i
$820$		0			0
$821$	9.34706	+	6.00699i	0.326215	+	0.209645i	0.693489	−	0.720467i	$-0.256073\pi$
$821$	9.34706	+	6.00699i	0.326215	+	0.209645i	−0.367274	+	0.930113i	$0.619709\pi$
$822$		0			0
$823$	7.65374	+	8.83289i	0.266793	+	0.307895i	0.873300	−	0.487183i	$-0.161975\pi$
$823$	7.65374	+	8.83289i	0.266793	+	0.307895i	−0.606507	+	0.795078i	$0.707430\pi$
$824$		0			0
$825$	−0.551764	−	1.20819i	−0.0192099	−	0.0420639i
$826$		0			0
$827$	−23.7592			−0.826187			−0.413094	−	0.910689i	$-0.635552\pi$
$827$	−23.7592			−0.826187			−0.413094	+	0.910689i	$0.635552\pi$
$828$		0			0
$829$	−50.8917			−1.76754			−0.883771	−	0.467919i	$-0.845004\pi$
$829$	−50.8917			−1.76754			−0.883771	+	0.467919i	$0.845004\pi$
$830$		0			0
$831$	−12.5633	−	27.5099i	−0.435818	−	0.954308i
$832$		0			0
$833$	−26.8275	−	30.9605i	−0.929517	−	1.07272i
$834$		0			0
$835$	−0.0324917	−	0.0208812i	−0.00112442	−	0.000722622i
$836$		0			0
$837$	4.78332	−	5.52024i	0.165336	−	0.190807i
$838$		0			0
$839$	−7.64085	−	53.1432i	−0.263791	−	1.83471i	−0.503658	−	0.863903i	$-0.668013\pi$
$839$	−7.64085	−	53.1432i	−0.263791	−	1.83471i	0.239867	−	0.970806i	$-0.422896\pi$
$840$		0			0
$841$	32.7390	−	21.0401i	1.12893	−	0.725519i
$842$		0			0
$843$	−11.0510	+	24.1982i	−0.380616	+	0.833432i
$844$		0			0
$845$	−22.2729	+	6.53991i	−0.766210	+	0.224980i
$846$		0			0
$847$	−10.8483	−	3.18535i	−0.372752	−	0.109450i
$848$		0			0
$849$	0.574695	−	3.99709i	0.0197235	−	0.137180i
$850$		0			0
$851$	−34.9068	−	35.0115i	−1.19659	−	1.20018i
$852$		0			0
$853$	−5.80957	+	40.4064i	−0.198916	+	1.38349i	0.608522	+	0.793537i	$0.291763\pi$
$853$	−5.80957	+	40.4064i	−0.198916	+	1.38349i	−0.807437	+	0.589953i	$0.799146\pi$
$854$		0			0
$855$	11.7829	+	3.45978i	0.402968	+	0.118322i
$856$		0			0
$857$	−7.47845	+	2.19587i	−0.255459	+	0.0750096i	−0.406955	−	0.913448i	$-0.633409\pi$
$857$	−7.47845	+	2.19587i	−0.255459	+	0.0750096i	0.151496	+	0.988458i	$0.451591\pi$
$858$		0			0
$859$	16.8673	−	36.9342i	0.575504	−	1.26018i	−0.368311	−	0.929703i	$-0.620064\pi$
$859$	16.8673	−	36.9342i	0.575504	−	1.26018i	0.943815	−	0.330475i	$-0.107209\pi$
$860$		0			0
$861$	−1.92218	+	1.23531i	−0.0655076	+	0.0420992i
$862$		0			0
$863$	6.65467	+	46.2843i	0.226528	+	1.57553i	0.712571	+	0.701600i	$0.247531\pi$
$863$	6.65467	+	46.2843i	0.226528	+	1.57553i	−0.486044	+	0.873935i	$0.661560\pi$
$864$		0			0
$865$	27.2485	−	31.4464i	0.926475	−	1.06921i
$866$		0			0
$867$	27.6608	+	17.7765i	0.939410	+	0.603722i
$868$		0			0
$869$	−3.87604	−	4.47319i	−0.131486	−	0.151743i
$870$		0			0
$871$	19.6428	+	43.0117i	0.665571	+	1.45740i
$872$		0			0
$873$	−7.18258			−0.243093
$874$		0			0
$875$	13.3293			0.450614
$876$		0			0
$877$	15.2360	+	33.3621i	0.514482	+	1.12656i	0.971487	+	0.237094i	$0.0761950\pi$
$877$	15.2360	+	33.3621i	0.514482	+	1.12656i	−0.457005	+	0.889464i	$0.651078\pi$
$878$		0			0
$879$	3.64202	+	4.20312i	0.122842	+	0.141768i
$880$		0			0
$881$	11.5699	+	7.43550i	0.389799	+	0.250508i	0.720831	−	0.693111i	$-0.243760\pi$
$881$	11.5699	+	7.43550i	0.389799	+	0.250508i	−0.331032	+	0.943619i	$0.607397\pi$
$882$		0			0
$883$	26.6634	−	30.7712i	0.897295	−	1.03553i	−0.101874	−	0.994797i	$-0.532484\pi$
$883$	26.6634	−	30.7712i	0.897295	−	1.03553i	0.999170	−	0.0407369i	$-0.0129705\pi$
$884$		0			0
$885$	−1.36458	−	9.49089i	−0.0458700	−	0.319033i
$886$		0			0
$887$	−42.1170	+	27.0670i	−1.41415	+	0.908819i	−0.999999	−	0.00138846i	$-0.999558\pi$
$887$	−42.1170	+	27.0670i	−1.41415	+	0.908819i	−0.414152	+	0.910208i	$0.635922\pi$
$888$		0			0
$889$	−3.21701	+	7.04428i	−0.107895	+	0.236257i
$890$		0			0
$891$	−0.789272	+	0.231751i	−0.0264416	+	0.00776396i
$892$		0			0
$893$	2.77592	+	0.815082i	0.0928925	+	0.0272757i
$894$		0			0
$895$	−6.13879	+	42.6962i	−0.205197	+	1.42718i
$896$		0			0
$897$	14.5753	−	19.4097i	0.486656	−	0.648071i
$898$		0			0
$899$	8.56681	−	59.5835i	0.285719	−	1.98722i
$900$		0			0
$901$	−48.0724	−	14.1153i	−1.60152	−	0.470250i
$902$		0			0
$903$	5.64358	−	1.65710i	0.187807	−	0.0551450i
$904$		0			0
$905$	11.2609	−	24.6579i	0.374325	−	0.819657i
$906$		0			0
$907$	30.9785	−	19.9087i	1.02862	−	0.661056i	0.0864757	−	0.996254i	$-0.472440\pi$
$907$	30.9785	−	19.9087i	1.02862	−	0.661056i	0.942148	+	0.335198i	$0.108803\pi$
$908$		0			0
$909$	1.90762	+	13.2678i	0.0632716	+	0.440064i
$910$		0			0
$911$	−3.44904	+	3.98040i	−0.114272	+	0.131877i	−0.810003	−	0.586425i	$-0.800535\pi$
$911$	−3.44904	+	3.98040i	−0.114272	+	0.131877i	0.695732	+	0.718302i	$0.255080\pi$
$912$		0			0
$913$	7.37217	+	4.73780i	0.243983	+	0.156798i
$914$		0			0
$915$	13.7919	+	15.9167i	0.455947	+	0.526191i
$916$		0			0
$917$	−2.32299	−	5.08663i	−0.0767118	−	0.167975i
$918$		0			0
$919$	47.8591			1.57873			0.789363	−	0.613927i	$-0.210411\pi$
$919$	47.8591			1.57873			0.789363	+	0.613927i	$0.210411\pi$
$920$		0			0
$921$	17.6253			0.580774
$922$		0			0
$923$	−11.7828	−	25.8008i	−0.387836	−	0.849243i
$924$		0			0
$925$	−10.9005	−	12.5799i	−0.358406	−	0.413623i
$926$		0			0
$927$	−0.368700	−	0.236949i	−0.0121097	−	0.00778243i
$928$		0			0
$929$	35.0672	−	40.4697i	1.15052	−	1.32777i	0.214127	−	0.976806i	$-0.431309\pi$
$929$	35.0672	−	40.4697i	1.15052	−	1.32777i	0.936390	−	0.350962i	$-0.114145\pi$
$930$		0			0
$931$	−5.50969	−	38.3207i	−0.180573	−	1.25591i
$932$		0			0
$933$	0.755912	−	0.485795i	0.0247474	−	0.0159042i
$934$		0			0
$935$	−4.44051	+	9.72335i	−0.145220	+	0.317988i
$936$		0			0
$937$	41.1221	−	12.0746i	1.34340	−	0.394458i	0.470520	−	0.882389i	$-0.344066\pi$
$937$	41.1221	−	12.0746i	1.34340	−	0.394458i	0.872882	+	0.487931i	$0.162248\pi$
$938$		0			0
$939$	−4.71162	−	1.38346i	−0.153758	−	0.0451474i
$940$		0			0
$941$	5.64928	−	39.2916i	0.184161	−	1.28087i	−0.662632	−	0.748946i	$-0.730560\pi$
$941$	5.64928	−	39.2916i	0.184161	−	1.28087i	0.846793	−	0.531923i	$-0.178530\pi$
$942$		0			0
$943$	−8.01863	+	5.98396i	−0.261123	+	0.194864i
$944$		0			0
$945$	0.286781	−	1.99460i	0.00932898	−	0.0648845i
$946$		0			0
$947$	−14.3929	−	4.22613i	−0.467706	−	0.137331i	0.0393838	−	0.999224i	$-0.487460\pi$
$947$	−14.3929	−	4.22613i	−0.467706	−	0.137331i	−0.507090	+	0.861893i	$0.669279\pi$
$948$		0			0
$949$	17.7662	−	5.21662i	0.576714	−	0.169339i
$950$		0			0
$951$	−7.72608	+	16.9178i	−0.250535	+	0.548596i
$952$		0			0
$953$	−35.9866	+	23.1272i	−1.16572	+	0.749164i	−0.972708	−	0.232032i	$-0.925462\pi$
$953$	−35.9866	+	23.1272i	−1.16572	+	0.749164i	−0.193014	+	0.981196i	$0.561826\pi$
$954$		0			0
$955$	−4.04265	−	28.1173i	−0.130817	−	0.909853i
$956$		0			0
$957$	−4.43939	+	5.12332i	−0.143505	+	0.165614i
$958$		0			0
$959$	7.11011	+	4.56939i	0.229598	+	0.147553i
$960$		0			0
$961$	−14.6382	−	16.8934i	−0.472201	−	0.544949i
$962$		0			0
$963$	−7.12391	−	15.5992i	−0.229565	−	0.502677i
$964$		0			0
$965$	6.37588			0.205247
$966$		0			0
$967$	16.8941			0.543279			0.271640	−	0.962399i	$-0.412434\pi$
$967$	16.8941			0.543279			0.271640	+	0.962399i	$0.412434\pi$
$968$		0			0
$969$	19.5821	+	42.8788i	0.629067	+	1.37747i
$970$		0			0
$971$	−29.5345	−	34.0847i	−0.947808	−	1.09383i	−0.995481	−	0.0949662i	$-0.969726\pi$
$971$	−29.5345	−	34.0847i	−0.947808	−	1.09383i	0.0476721	−	0.998863i	$-0.484820\pi$
$972$		0			0
$973$	14.7676	+	9.49058i	0.473428	+	0.304254i
$974$		0			0
$975$	5.35172	−	6.17622i	0.171392	−	0.197797i
$976$		0			0
$977$	3.95333	+	27.4960i	0.126478	+	0.879676i	0.949968	+	0.312346i	$0.101115\pi$
$977$	3.95333	+	27.4960i	0.126478	+	0.879676i	−0.823490	+	0.567331i	$0.807976\pi$
$978$		0			0
$979$	−6.51504	+	4.18696i	−0.208222	+	0.133816i
$980$		0			0
$981$	0.849581	−	1.86032i	0.0271250	−	0.0593956i
$982$		0			0
$983$	−21.9919	+	6.45741i	−0.701433	+	0.205959i	−0.612954	−	0.790119i	$-0.710019\pi$
$983$	−21.9919	+	6.45741i	−0.701433	+	0.205959i	−0.0884792	+	0.996078i	$0.528201\pi$
$984$		0			0
$985$	−1.60423	−	0.471044i	−0.0511149	−	0.0150087i
$986$		0			0
$987$	0.0675621	−	0.469904i	0.00215052	−	0.0149572i
$988$		0			0
$989$	24.1454	−	8.96462i	0.767780	−	0.285058i
$990$		0			0
$991$	−2.61270	+	18.1717i	−0.0829950	+	0.577243i	0.905310	+	0.424752i	$0.139639\pi$
$991$	−2.61270	+	18.1717i	−0.0829950	+	0.577243i	−0.988305	+	0.152491i	$0.951270\pi$
$992$		0			0
$993$	−6.73959	−	1.97892i	−0.213874	−	0.0627992i
$994$		0			0
$995$	−17.4925	+	5.13626i	−0.554549	+	0.162830i
$996$		0			0
$997$	−3.14128	+	6.87844i	−0.0994853	+	0.217842i	−0.952830	−	0.303505i	$-0.901843\pi$
$997$	−3.14128	+	6.87844i	−0.0994853	+	0.217842i	0.853345	+	0.521347i	$0.174570\pi$
$998$		0			0
$999$	−8.67239	+	5.57341i	−0.274382	+	0.176335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.169.1	yes	30
23.3	even	11	inner	552.2.q.b.49.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.49.1	✓	30	23.3	even	11	inner
552.2.q.b.169.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{3} +(-1.20489 - 1.39052i) q^{5} +(-0.921355 - 0.592119i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{3} +(-1.20489 - 1.39052i) q^{5} +(-0.921355 - 0.592119i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.117067 - 0.814220i) q^{11} +(4.25780 - 2.73632i) q^{13} +(0.764332 - 1.67365i) q^{15} +(6.77653 - 1.98977i) q^{17} +(6.40403 + 1.88039i) q^{19} +(0.155866 - 1.08407i) q^{21} +(0.349293 - 4.78309i) q^{23} +(0.229793 - 1.59824i) q^{25} +(-0.959493 - 0.281733i) q^{27} +(-7.90735 + 2.32181i) q^{29} +(-3.03433 + 6.64425i) q^{31} +(0.692009 - 0.444727i) q^{33} +(0.286781 + 1.99460i) q^{35} +(6.75089 - 7.79094i) q^{37} +(4.25780 + 2.73632i) q^{39} +(-1.36620 - 1.57668i) q^{41} +(2.23098 + 4.88516i) q^{43} +1.83992 q^{45} +0.433464 q^{47} +(-2.40962 - 5.27632i) q^{49} +(4.62503 + 5.33757i) q^{51} +(-5.96781 - 3.83528i) q^{53} +(-0.991138 + 1.14383i) q^{55} +(0.949865 + 6.60646i) q^{57} +(4.38406 - 2.81747i) q^{59} +(-4.75509 + 10.4122i) q^{61} +(1.05085 - 0.308558i) q^{63} +(-8.93512 - 2.62359i) q^{65} +(-1.32957 + 9.24739i) q^{67} +(4.49596 - 1.66924i) q^{69} +(0.797551 - 5.54709i) q^{71} +(3.51022 + 1.03069i) q^{73} +(1.54927 - 0.454907i) q^{75} +(-0.374255 + 0.819503i) q^{77} +(6.05315 - 3.89012i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-6.97641 + 8.05121i) q^{83} +(-10.9318 - 7.02545i) q^{85} +(-5.39682 - 6.22826i) q^{87} +(-3.91100 - 8.56389i) q^{89} -5.54318 q^{91} -7.30433 q^{93} +(-5.10145 - 11.1706i) q^{95} +(4.70359 + 5.42823i) q^{97} +(0.692009 + 0.444727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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