LMFDB - Embedded newform 552.2.q.c.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.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(-2.29838 - 2.65247i) q^{5} +(-2.05854 - 1.32294i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.29838 - 2.65247i) q^{5} +(-2.05854 - 1.32294i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(0.516583 + 3.59291i) q^{11} +(-1.06754 + 0.686067i) q^{13} +(-1.45799 + 3.19256i) q^{15} +(-3.04373 + 0.893720i) q^{17} +(5.42582 + 1.59316i) q^{19} +(-0.348244 + 2.42209i) q^{21} +(-2.27256 + 4.22321i) q^{23} +(-1.04148 + 7.24368i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-3.58685 + 1.05319i) q^{29} +(1.20314 - 2.63450i) q^{31} +(3.05363 - 1.96245i) q^{33} +(1.22224 + 8.50086i) q^{35} +(0.367275 - 0.423858i) q^{37} +(1.06754 + 0.686067i) q^{39} +(-6.77685 - 7.82090i) q^{41} +(1.22675 + 2.68620i) q^{43} +3.50972 q^{45} -11.8576 q^{47} +(-0.420491 - 0.920747i) q^{49} +(2.07737 + 2.39741i) q^{51} +(-9.81751 - 6.30933i) q^{53} +(8.34280 - 9.62810i) q^{55} +(-0.804773 - 5.59732i) q^{57} +(9.75532 - 6.26936i) q^{59} +(-2.34534 + 5.13557i) q^{61} +(2.34787 - 0.689398i) q^{63} +(4.27339 + 1.25478i) q^{65} +(-1.66547 + 11.5836i) q^{67} +(4.78562 + 0.312806i) q^{69} +(-0.110048 + 0.765404i) q^{71} +(-13.7538 - 4.03848i) q^{73} +(7.02173 - 2.06177i) q^{75} +(3.68982 - 8.07957i) q^{77} +(-5.98253 + 3.84474i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-2.61290 + 3.01545i) q^{83} +(9.36622 + 6.01931i) q^{85} +(2.44805 + 2.82520i) q^{87} +(3.55432 + 7.78287i) q^{89} +3.10521 q^{91} -2.89622 q^{93} +(-8.24477 - 18.0535i) q^{95} +(-5.63529 - 6.50347i) q^{97} +(-3.05363 - 1.96245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * 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
$5$	−2.29838	−	2.65247i	−1.02787	−	1.18622i	−0.982310	−	0.187260i	$-0.940039\pi$
$5$	−2.29838	−	2.65247i	−1.02787	−	1.18622i	−0.0455569	−	0.998962i	$-0.514506\pi$
$6$		0			0
$7$	−2.05854	−	1.32294i	−0.778056	−	0.500026i	0.0903320	−	0.995912i	$-0.471207\pi$
$7$	−2.05854	−	1.32294i	−0.778056	−	0.500026i	−0.868388	+	0.495886i	$0.834844\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	0.516583	+	3.59291i	0.155756	+	1.08330i	0.906346	+	0.422536i	$0.138860\pi$
$11$	0.516583	+	3.59291i	0.155756	+	1.08330i	−0.750590	+	0.660768i	$0.770231\pi$
$12$		0			0
$13$	−1.06754	+	0.686067i	−0.296083	+	0.190281i	−0.680245	−	0.732985i	$-0.738127\pi$
$13$	−1.06754	+	0.686067i	−0.296083	+	0.190281i	0.384162	+	0.923266i	$0.374490\pi$
$14$		0			0
$15$	−1.45799	+	3.19256i	−0.376452	+	0.824315i
$16$		0			0
$17$	−3.04373	+	0.893720i	−0.738213	+	0.216759i	−0.629159	−	0.777277i	$-0.716600\pi$
$17$	−3.04373	+	0.893720i	−0.738213	+	0.216759i	−0.109054	+	0.994036i	$0.534782\pi$
$18$		0			0
$19$	5.42582	+	1.59316i	1.24477	+	0.365497i	0.836805	−	0.547502i	$-0.184421\pi$
$19$	5.42582	+	1.59316i	1.24477	+	0.365497i	0.407963	+	0.912998i	$0.366239\pi$
$20$		0			0
$21$	−0.348244	+	2.42209i	−0.0759930	+	0.528543i
$22$		0			0
$23$	−2.27256	+	4.22321i	−0.473861	+	0.880600i
$23$	−2.27256	+	4.22321i	−0.473861	+	0.880600i
$24$		0			0
$25$	−1.04148	+	7.24368i	−0.208297	+	1.44874i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−3.58685	+	1.05319i	−0.666061	+	0.195573i	−0.597248	−	0.802057i	$-0.703739\pi$
$29$	−3.58685	+	1.05319i	−0.666061	+	0.195573i	−0.0688125	+	0.997630i	$0.521921\pi$
$30$		0			0
$31$	1.20314	−	2.63450i	0.216089	−	0.473170i	−0.770282	−	0.637703i	$-0.779885\pi$
$31$	1.20314	−	2.63450i	0.216089	−	0.473170i	0.986372	+	0.164533i	$0.0526118\pi$
$32$		0			0
$33$	3.05363	−	1.96245i	0.531569	−	0.341619i
$34$		0			0
$35$	1.22224	+	8.50086i	0.206596	+	1.43691i
$36$		0			0
$37$	0.367275	−	0.423858i	0.0603797	−	0.0696818i	−0.724756	−	0.689005i	$-0.758048\pi$
$37$	0.367275	−	0.423858i	0.0603797	−	0.0696818i	0.785136	+	0.619324i	$0.212593\pi$
$38$		0			0
$39$	1.06754	+	0.686067i	0.170943	+	0.109859i
$40$		0			0
$41$	−6.77685	−	7.82090i	−1.05837	−	1.22142i	−0.974369	−	0.224954i	$-0.927777\pi$
$41$	−6.77685	−	7.82090i	−1.05837	−	1.22142i	−0.0839966	−	0.996466i	$-0.526768\pi$
$42$		0			0
$43$	1.22675	+	2.68620i	0.187077	+	0.409642i	0.979811	−	0.199926i	$-0.0640703\pi$
$43$	1.22675	+	2.68620i	0.187077	+	0.409642i	−0.792734	+	0.609568i	$0.791343\pi$
$44$		0			0
$45$	3.50972			0.523199
$46$		0			0
$47$	−11.8576			−1.72961			−0.864804	−	0.502110i	$-0.832557\pi$
$47$	−11.8576			−1.72961			−0.864804	+	0.502110i	$0.832557\pi$
$48$		0			0
$49$	−0.420491	−	0.920747i	−0.0600702	−	0.131535i
$50$		0			0
$51$	2.07737	+	2.39741i	0.290890	+	0.335705i
$52$		0			0
$53$	−9.81751	−	6.30933i	−1.34854	−	0.866653i	−0.350973	−	0.936386i	$-0.614149\pi$
$53$	−9.81751	−	6.30933i	−1.34854	−	0.866653i	−0.997566	+	0.0697323i	$0.977785\pi$
$54$		0			0
$55$	8.34280	−	9.62810i	1.12494	−	1.29825i
$56$		0			0
$57$	−0.804773	−	5.59732i	−0.106595	−	0.741383i
$58$		0			0
$59$	9.75532	−	6.26936i	1.27003	−	0.816201i	0.280410	−	0.959880i	$-0.409530\pi$
$59$	9.75532	−	6.26936i	1.27003	−	0.816201i	0.989624	+	0.143679i	$0.0458932\pi$
$60$		0			0
$61$	−2.34534	+	5.13557i	−0.300289	+	0.657542i	−0.998284	−	0.0585611i	$-0.981349\pi$
$61$	−2.34534	+	5.13557i	−0.300289	+	0.657542i	0.697994	+	0.716103i	$0.254076\pi$
$62$		0			0
$63$	2.34787	−	0.689398i	0.295804	−	0.0868560i
$64$		0			0
$65$	4.27339	+	1.25478i	0.530049	+	0.155636i
$66$		0			0
$67$	−1.66547	+	11.5836i	−0.203469	+	1.41516i	0.590421	+	0.807096i	$0.298962\pi$
$67$	−1.66547	+	11.5836i	−0.203469	+	1.41516i	−0.793890	+	0.608062i	$0.791947\pi$
$68$		0			0
$69$	4.78562	+	0.312806i	0.576121	+	0.0376575i
$70$		0			0
$71$	−0.110048	+	0.765404i	−0.0130603	+	0.0908367i	−0.995309	−	0.0967466i	$-0.969156\pi$
$71$	−0.110048	+	0.765404i	−0.0130603	+	0.0908367i	0.982249	+	0.187583i	$0.0600654\pi$
$72$		0			0
$73$	−13.7538	−	4.03848i	−1.60976	−	0.472668i	−0.651519	−	0.758632i	$-0.725868\pi$
$73$	−13.7538	−	4.03848i	−1.60976	−	0.472668i	−0.958240	+	0.285964i	$0.907686\pi$
$74$		0			0
$75$	7.02173	−	2.06177i	0.810800	−	0.238072i
$76$		0			0
$77$	3.68982	−	8.07957i	0.420494	−	0.920753i
$78$		0			0
$79$	−5.98253	+	3.84474i	−0.673087	+	0.432567i	−0.832037	−	0.554720i	$-0.812825\pi$
$79$	−5.98253	+	3.84474i	−0.673087	+	0.432567i	0.158950	+	0.987287i	$0.449189\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−2.61290	+	3.01545i	−0.286804	+	0.330989i	−0.880809	−	0.473472i	$-0.843000\pi$
$83$	−2.61290	+	3.01545i	−0.286804	+	0.330989i	0.594005	+	0.804461i	$0.297546\pi$
$84$		0			0
$85$	9.36622	+	6.01931i	1.01591	+	0.652885i
$86$		0			0
$87$	2.44805	+	2.82520i	0.262458	+	0.302893i
$88$		0			0
$89$	3.55432	+	7.78287i	0.376757	+	0.824983i	0.999107	+	0.0422438i	$0.0134506\pi$
$89$	3.55432	+	7.78287i	0.376757	+	0.824983i	−0.622350	+	0.782739i	$0.713822\pi$
$90$		0			0
$91$	3.10521			0.325514
$92$		0			0
$93$	−2.89622			−0.300325
$94$		0			0
$95$	−8.24477	−	18.0535i	−0.845896	−	1.85225i
$96$		0			0
$97$	−5.63529	−	6.50347i	−0.572177	−	0.660328i	0.393727	−	0.919227i	$-0.371186\pi$
$97$	−5.63529	−	6.50347i	−0.572177	−	0.660328i	−0.965904	+	0.258900i	$0.916640\pi$
$98$		0			0
$99$	−3.05363	−	1.96245i	−0.306902	−	0.197234i
$100$		0			0
$101$	7.01701	−	8.09806i	0.698219	−	0.805787i	−0.290292	−	0.956938i	$-0.593752\pi$
$101$	7.01701	−	8.09806i	0.698219	−	0.805787i	0.988511	+	0.151151i	$0.0482979\pi$
$102$		0			0
$103$	−0.132448	−	0.921197i	−0.0130505	−	0.0907683i	0.982255	−	0.187549i	$-0.0600544\pi$
$103$	−0.132448	−	0.921197i	−0.0130505	−	0.0907683i	−0.995306	+	0.0967810i	$0.969145\pi$
$104$		0			0
$105$	7.22492	−	4.64317i	0.705080	−	0.453127i
$106$		0			0
$107$	−2.32137	+	5.08310i	−0.224415	+	0.491401i	−0.988028	−	0.154273i	$-0.950696\pi$
$107$	−2.32137	+	5.08310i	−0.224415	+	0.491401i	0.763613	+	0.645674i	$0.223424\pi$
$108$		0			0
$109$	15.2551	−	4.47929i	1.46117	−	0.429039i	0.547953	−	0.836509i	$-0.315407\pi$
$109$	15.2551	−	4.47929i	1.46117	−	0.429039i	0.913218	+	0.407470i	$0.133589\pi$
$110$		0			0
$111$	−0.538127	−	0.158008i	−0.0510767	−	0.0149975i
$112$		0			0
$113$	−0.809546	+	5.63052i	−0.0761557	+	0.529674i	0.915656	+	0.401963i	$0.131672\pi$
$113$	−0.809546	+	5.63052i	−0.0761557	+	0.529674i	−0.991811	+	0.127711i	$0.959237\pi$
$114$		0			0
$115$	16.4251	−	3.67865i	1.53165	−	0.343035i
$116$		0			0
$117$	0.180596	−	1.25607i	0.0166961	−	0.116124i
$118$		0			0
$119$	7.44799	+	2.18693i	0.682756	+	0.200475i
$120$		0			0
$121$	−2.08774	+	0.613016i	−0.189795	+	0.0557287i
$122$		0			0
$123$	−4.29894	+	9.41336i	−0.387622	+	0.848774i
$124$		0			0
$125$	6.84455	−	4.39873i	0.612195	−	0.393434i
$126$		0			0
$127$	−1.39870	−	9.72815i	−0.124114	−	0.863234i	−0.952817	−	0.303545i	$-0.901830\pi$
$127$	−1.39870	−	9.72815i	−0.124114	−	0.863234i	0.828703	−	0.559689i	$-0.189079\pi$
$128$		0			0
$129$	1.93384	−	2.23178i	0.170265	−	0.196497i
$130$		0			0
$131$	−14.7823	−	9.50001i	−1.29154	−	0.830019i	−0.299272	−	0.954168i	$-0.596744\pi$
$131$	−14.7823	−	9.50001i	−1.29154	−	0.830019i	−0.992264	+	0.124149i	$0.960380\pi$
$132$		0			0
$133$	−9.06161	−	10.4577i	−0.785741	−	0.906793i
$134$		0			0
$135$	−1.45799	−	3.19256i	−0.125484	−	0.274772i
$136$		0			0
$137$	−3.59670			−0.307287			−0.153643	−	0.988126i	$-0.549101\pi$
$137$	−3.59670			−0.307287			−0.153643	+	0.988126i	$0.549101\pi$
$138$		0			0
$139$	−4.59723			−0.389932			−0.194966	−	0.980810i	$-0.562460\pi$
$139$	−4.59723			−0.389932			−0.194966	+	0.980810i	$0.562460\pi$
$140$		0			0
$141$	4.92582	+	10.7860i	0.414829	+	0.908349i
$142$		0			0
$143$	−3.01645	−	3.48117i	−0.252248	−	0.291110i
$144$		0			0
$145$	11.0375	+	7.09337i	0.916615	+	0.589073i
$146$		0			0
$147$	−0.662863	+	0.764984i	−0.0546720	+	0.0630949i
$148$		0			0
$149$	−1.15315	−	8.02034i	−0.0944697	−	0.657051i	−0.980946	−	0.194278i	$-0.937764\pi$
$149$	−1.15315	−	8.02034i	−0.0944697	−	0.657051i	0.886477	−	0.462773i	$-0.153146\pi$
$150$		0			0
$151$	7.47081	−	4.80120i	0.607966	−	0.390716i	−0.200128	−	0.979770i	$-0.564136\pi$
$151$	7.47081	−	4.80120i	0.607966	−	0.390716i	0.808094	+	0.589054i	$0.200499\pi$
$152$		0			0
$153$	1.31779	−	2.88556i	0.106537	−	0.233284i
$154$		0			0
$155$	−9.75320	+	2.86380i	−0.783396	+	0.230026i
$156$		0			0
$157$	21.0092	+	6.16886i	1.67672	+	0.492329i	0.975386	−	0.220506i	$-0.0707708\pi$
$157$	21.0092	+	6.16886i	1.67672	+	0.492329i	0.701332	+	0.712835i	$0.252589\pi$
$158$		0			0
$159$	−1.66083	+	11.5513i	−0.131712	+	0.916079i
$160$		0			0
$161$	10.2652	−	5.68719i	0.809013	−	0.448213i
$162$		0			0
$163$	1.60254	−	11.1459i	0.125520	−	0.873014i	−0.825614	−	0.564236i	$-0.809171\pi$
$163$	1.60254	−	11.1459i	0.125520	−	0.873014i	0.951134	−	0.308778i	$-0.0999200\pi$
$164$		0			0
$165$	−12.2238	−	3.58922i	−0.951618	−	0.279420i
$166$		0			0
$167$	10.8435	−	3.18393i	0.839092	−	0.246380i	0.166174	−	0.986096i	$-0.446859\pi$
$167$	10.8435	−	3.18393i	0.839092	−	0.246380i	0.672918	+	0.739717i	$0.265041\pi$
$168$		0			0
$169$	−4.73144	+	10.3604i	−0.363957	+	0.796954i
$170$		0			0
$171$	−4.75719	+	3.05726i	−0.363791	+	0.233794i
$172$		0			0
$173$	3.01076	+	20.9403i	0.228904	+	1.59206i	0.702740	+	0.711447i	$0.251960\pi$
$173$	3.01076	+	20.9403i	0.228904	+	1.59206i	−0.473836	+	0.880613i	$0.657131\pi$
$174$		0			0
$175$	11.7269	−	13.5336i	0.886473	−	1.02304i
$176$		0			0
$177$	−9.75532	−	6.26936i	−0.733255	−	0.471234i
$178$		0			0
$179$	6.66146	+	7.68773i	0.497901	+	0.574608i	0.947960	−	0.318391i	$-0.103142\pi$
$179$	6.66146	+	7.68773i	0.497901	+	0.574608i	−0.450059	+	0.892999i	$0.648597\pi$
$180$		0			0
$181$	−4.42318	−	9.68542i	−0.328772	−	0.719911i	0.670995	−	0.741462i	$-0.265867\pi$
$181$	−4.42318	−	9.68542i	−0.328772	−	0.719911i	−0.999768	+	0.0215503i	$0.993140\pi$
$182$		0			0
$183$	5.64576			0.417347
$184$		0			0
$185$	−1.96841			−0.144720
$186$		0			0
$187$	−4.78340	−	10.4742i	−0.349797	−	0.765948i
$188$		0			0
$189$	−1.60244	−	1.84931i	−0.116560	−	0.134518i
$190$		0			0
$191$	−8.60852	−	5.53236i	−0.622890	−	0.400307i	0.190781	−	0.981633i	$-0.438898\pi$
$191$	−8.60852	−	5.53236i	−0.622890	−	0.400307i	−0.813671	+	0.581325i	$0.802534\pi$
$192$		0			0
$193$	6.64157	−	7.66478i	0.478071	−	0.551723i	−0.464568	−	0.885537i	$-0.653790\pi$
$193$	6.64157	−	7.66478i	0.478071	−	0.551723i	0.942639	+	0.333814i	$0.108336\pi$
$194$		0			0
$195$	−0.633842	−	4.40847i	−0.0453903	−	0.315697i
$196$		0			0
$197$	−17.7533	+	11.4093i	−1.26487	+	0.812881i	−0.988943	−	0.148298i	$-0.952620\pi$
$197$	−17.7533	+	11.4093i	−1.26487	+	0.812881i	−0.275925	+	0.961179i	$0.588984\pi$
$198$		0			0
$199$	2.47795	−	5.42595i	0.175657	−	0.384635i	−0.801241	−	0.598342i	$-0.795826\pi$
$199$	2.47795	−	5.42595i	0.175657	−	0.384635i	0.976898	+	0.213707i	$0.0685537\pi$
$200$		0			0
$201$	11.2286	−	3.29703i	0.792007	−	0.232554i
$202$		0			0
$203$	8.77699	+	2.57716i	0.616024	+	0.180881i
$204$		0			0
$205$	−5.16895	+	35.9508i	−0.361015	+	2.51091i
$206$		0			0
$207$	−1.70348	−	4.48310i	−0.118400	−	0.311597i
$208$		0			0
$209$	−2.92121	+	20.3175i	−0.202065	+	1.40539i
$210$		0			0
$211$	−18.4390	−	5.41417i	−1.26939	−	0.372727i	−0.423409	−	0.905939i	$-0.639167\pi$
$211$	−18.4390	−	5.41417i	−1.26939	−	0.372727i	−0.845982	+	0.533212i	$0.820985\pi$
$212$		0			0
$213$	0.741951	−	0.217857i	0.0508377	−	0.0149273i
$214$		0			0
$215$	4.30554	−	9.42782i	0.293635	−	0.642972i
$216$		0			0
$217$	−5.96200	+	3.83155i	−0.404727	+	0.260102i
$218$		0			0
$219$	2.04000	+	14.1885i	0.137851	+	0.958772i
$220$		0			0
$221$	2.63616	−	3.04229i	0.177327	−	0.204646i
$222$		0			0
$223$	0.265575	+	0.170675i	0.0177842	+	0.0114292i	0.549503	−	0.835492i	$-0.314817\pi$
$223$	0.265575	+	0.170675i	0.0177842	+	0.0114292i	−0.531718	+	0.846921i	$0.678454\pi$
$224$		0			0
$225$	−4.79238	−	5.53070i	−0.319492	−	0.368714i
$226$		0			0
$227$	11.1097	+	24.3269i	0.737377	+	1.61463i	0.787821	+	0.615904i	$0.211209\pi$
$227$	11.1097	+	24.3269i	0.737377	+	1.61463i	−0.0504439	+	0.998727i	$0.516064\pi$
$228$		0			0
$229$	−25.3339			−1.67411			−0.837057	−	0.547116i	$-0.815726\pi$
$229$	−25.3339			−1.67411			−0.837057	+	0.547116i	$0.815726\pi$
$230$		0			0
$231$	−8.88224			−0.584409
$232$		0			0
$233$	−9.93226	−	21.7486i	−0.650684	−	1.42480i	−0.890954	−	0.454093i	$-0.849963\pi$
$233$	−9.93226	−	21.7486i	−0.650684	−	1.42480i	0.240270	−	0.970706i	$-0.422764\pi$
$234$		0			0
$235$	27.2533	+	31.4519i	1.77781	+	2.05170i
$236$		0			0
$237$	5.98253	+	3.84474i	0.388607	+	0.249743i
$238$		0			0
$239$	−0.935153	+	1.07922i	−0.0604900	+	0.0698092i	−0.785188	−	0.619257i	$-0.787434\pi$
$239$	−0.935153	+	1.07922i	−0.0604900	+	0.0698092i	0.724698	+	0.689067i	$0.241979\pi$
$240$		0			0
$241$	−0.0338900	−	0.235710i	−0.00218305	−	0.0151834i	0.988701	−	0.149902i	$-0.0478959\pi$
$241$	−0.0338900	−	0.235710i	−0.00218305	−	0.0151834i	−0.990884	+	0.134719i	$0.956987\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−1.47581	+	3.23157i	−0.0942859	+	0.206457i
$246$		0			0
$247$	−6.88530	+	2.02171i	−0.438101	+	0.128638i
$248$		0			0
$249$	3.82839	+	1.12412i	0.242615	+	0.0712381i
$250$		0			0
$251$	2.88789	−	20.0857i	0.182282	−	1.26780i	−0.669068	−	0.743201i	$-0.733306\pi$
$251$	2.88789	−	20.0857i	0.182282	−	1.26780i	0.851350	−	0.524598i	$-0.175784\pi$
$252$		0			0
$253$	−16.3476	−	5.98346i	−1.02776	−	0.376177i
$254$		0			0
$255$	1.58448	−	11.0203i	0.0992242	−	0.690120i
$256$		0			0
$257$	15.9917	+	4.69557i	0.997532	+	0.292902i	0.739443	−	0.673219i	$-0.235089\pi$
$257$	15.9917	+	4.69557i	0.997532	+	0.292902i	0.258089	+	0.966121i	$0.416907\pi$
$258$		0			0
$259$	−1.31679	+	0.386645i	−0.0818215	+	0.0240250i
$260$		0			0
$261$	1.55293	−	3.40045i	0.0961242	−	0.210483i
$262$		0			0
$263$	−14.2732	+	9.17281i	−0.880122	+	0.565620i	−0.900833	−	0.434166i	$-0.857043\pi$
$263$	−14.2732	+	9.17281i	−0.880122	+	0.565620i	0.0207113	+	0.999785i	$0.493407\pi$
$264$		0			0
$265$	5.82905	+	40.5419i	0.358076	+	2.49047i
$266$		0			0
$267$	5.60303	−	6.46624i	0.342900	−	0.395728i
$268$		0			0
$269$	3.58110	+	2.30144i	0.218344	+	0.140321i	0.645241	−	0.763979i	$-0.276757\pi$
$269$	3.58110	+	2.30144i	0.218344	+	0.140321i	−0.426897	+	0.904300i	$0.640393\pi$
$270$		0			0
$271$	−3.90435	−	4.50586i	−0.237172	−	0.273712i	0.624669	−	0.780890i	$-0.285234\pi$
$271$	−3.90435	−	4.50586i	−0.237172	−	0.273712i	−0.861841	+	0.507178i	$0.830689\pi$
$272$		0			0
$273$	−1.28995	−	2.82460i	−0.0780713	−	0.170952i
$274$		0			0
$275$	−26.5639			−1.60186
$276$		0			0
$277$	19.8240			1.19111			0.595553	−	0.803316i	$-0.296933\pi$
$277$	19.8240			1.19111			0.595553	+	0.803316i	$0.296933\pi$
$278$		0			0
$279$	1.20314	+	2.63450i	0.0720298	+	0.157723i
$280$		0			0
$281$	7.56805	+	8.73400i	0.451472	+	0.521027i	0.935166	−	0.354211i	$-0.115251\pi$
$281$	7.56805	+	8.73400i	0.451472	+	0.521027i	−0.483693	+	0.875237i	$0.660705\pi$
$282$		0			0
$283$	−23.2358	−	14.9327i	−1.38122	−	0.887659i	−0.381893	−	0.924207i	$-0.624728\pi$
$283$	−23.2358	−	14.9327i	−1.38122	−	0.887659i	−0.999332	+	0.0365476i	$0.988364\pi$
$284$		0			0
$285$	−12.9971	+	14.9994i	−0.769880	+	0.888489i
$286$		0			0
$287$	3.60381	+	25.0651i	0.212726	+	1.47954i
$288$		0			0
$289$	−5.83575	+	3.75041i	−0.343279	+	0.220612i
$290$		0			0
$291$	−3.57478	+	7.82768i	−0.209557	+	0.458867i
$292$		0			0
$293$	17.6302	−	5.17670i	1.02997	−	0.302426i	0.277270	−	0.960792i	$-0.410570\pi$
$293$	17.6302	−	5.17670i	1.02997	−	0.302426i	0.752698	+	0.658366i	$0.228752\pi$
$294$		0			0
$295$	−39.0508	−	11.4663i	−2.27362	−	0.667596i
$296$		0			0
$297$	−0.516583	+	3.59291i	−0.0299752	+	0.208482i
$298$		0			0
$299$	−0.471356	−	6.06757i	−0.0272592	−	0.350897i
$300$		0			0
$301$	1.02838	−	7.15257i	0.0592751	−	0.412267i
$302$		0			0
$303$	−10.2812	−	3.01884i	−0.590641	−	0.173428i
$304$		0			0
$305$	19.0124	−	5.58255i	1.08865	−	0.319656i
$306$		0			0
$307$	4.63405	−	10.1472i	0.264479	−	0.579129i	−0.730073	−	0.683369i	$-0.760514\pi$
$307$	4.63405	−	10.1472i	0.264479	−	0.579129i	0.994552	+	0.104240i	$0.0332411\pi$
$308$		0			0
$309$	−0.782930	+	0.503158i	−0.0445393	+	0.0286237i
$310$		0			0
$311$	3.08650	+	21.4671i	0.175019	+	1.21729i	0.868086	+	0.496413i	$0.165350\pi$
$311$	3.08650	+	21.4671i	0.175019	+	1.21729i	−0.693067	+	0.720873i	$0.743741\pi$
$312$		0			0
$313$	−11.4658	+	13.2322i	−0.648083	+	0.747927i	−0.980782	−	0.195105i	$-0.937495\pi$
$313$	−11.4658	+	13.2322i	−0.648083	+	0.747927i	0.332699	+	0.943033i	$0.392041\pi$
$314$		0			0
$315$	−7.22492	−	4.64317i	−0.407078	−	0.261613i
$316$		0			0
$317$	−18.5905	−	21.4546i	−1.04415	−	1.20501i	−0.978303	−	0.207179i	$-0.933572\pi$
$317$	−18.5905	−	21.4546i	−1.04415	−	1.20501i	−0.0658429	−	0.997830i	$-0.520974\pi$
$318$		0			0
$319$	−5.63693	−	12.3432i	−0.315608	−	0.691085i
$320$		0			0
$321$	5.58808			0.311896
$322$		0			0
$323$	−17.9386			−0.998129
$324$		0			0
$325$	−3.85782	−	8.44745i	−0.213993	−	0.468580i
$326$		0			0
$327$	−10.4117	−	12.0157i	−0.575768	−	0.664472i
$328$		0			0
$329$	24.4094	+	15.6869i	1.34573	+	0.864849i
$330$		0			0
$331$	−17.9331	+	20.6959i	−0.985691	+	1.13755i	0.00480243	+	0.999988i	$0.498471\pi$
$331$	−17.9331	+	20.6959i	−0.985691	+	1.13755i	−0.990493	+	0.137560i	$0.956074\pi$
$332$		0			0
$333$	0.0798165	+	0.555136i	0.00437392	+	0.0304213i
$334$		0			0
$335$	34.5530	−	22.2058i	1.88783	−	1.21324i
$336$		0			0
$337$	4.56933	−	10.0054i	0.248907	−	0.545031i	−0.743397	−	0.668850i	$-0.766787\pi$
$337$	4.56933	−	10.0054i	0.248907	−	0.545031i	0.992305	+	0.123819i	$0.0395141\pi$
$338$		0			0
$339$	5.45800	−	1.60261i	0.296438	−	0.0870419i
$340$		0			0
$341$	10.0870	+	2.96182i	0.546244	+	0.160392i
$342$		0			0
$343$	−2.79020	+	19.4063i	−0.150657	+	1.04784i
$344$		0			0
$345$	−10.1695	−	13.4127i	−0.547506	−	0.722114i
$346$		0			0
$347$	0.678050	−	4.71594i	0.0363996	−	0.253165i	−0.963494	−	0.267729i	$-0.913727\pi$
$347$	0.678050	−	4.71594i	0.0363996	−	0.253165i	0.999894	+	0.0145639i	$0.00463598\pi$
$348$		0			0
$349$	−7.96416	−	2.33849i	−0.426312	−	0.125176i	0.0615367	−	0.998105i	$-0.480400\pi$
$349$	−7.96416	−	2.33849i	−0.426312	−	0.125176i	−0.487848	+	0.872928i	$0.662218\pi$
$350$		0			0
$351$	−1.21759	+	0.357515i	−0.0649899	+	0.0190828i
$352$		0			0
$353$	13.4551	−	29.4626i	0.716145	−	1.56814i	−0.103085	−	0.994673i	$-0.532871\pi$
$353$	13.4551	−	29.4626i	0.716145	−	1.56814i	0.819229	−	0.573466i	$-0.194402\pi$
$354$		0			0
$355$	2.28315	−	1.46729i	0.121177	−	0.0778756i
$356$		0			0
$357$	−1.10471	−	7.68341i	−0.0584674	−	0.406649i
$358$		0			0
$359$	−4.96350	+	5.72818i	−0.261963	+	0.302322i	−0.871460	−	0.490467i	$-0.836826\pi$
$359$	−4.96350	+	5.72818i	−0.261963	+	0.302322i	0.609496	+	0.792789i	$0.291372\pi$
$360$		0			0
$361$	10.9175	+	7.01625i	0.574605	+	0.369277i
$362$		0			0
$363$	1.42490	+	1.64442i	0.0747878	+	0.0863097i
$364$		0			0
$365$	20.8995	+	45.7635i	1.09393	+	2.39537i
$366$		0			0
$367$	−31.6972			−1.65458			−0.827291	−	0.561774i	$-0.810119\pi$
$367$	−31.6972			−1.65458			−0.827291	+	0.561774i	$0.810119\pi$
$368$		0			0
$369$	10.3485			0.538723
$370$		0			0
$371$	11.8629	+	25.9761i	0.615889	+	1.34861i
$372$		0			0
$373$	−9.46556	−	10.9238i	−0.490108	−	0.565615i	0.455786	−	0.890089i	$-0.349358\pi$
$373$	−9.46556	−	10.9238i	−0.490108	−	0.565615i	−0.945895	+	0.324474i	$0.894813\pi$
$374$		0			0
$375$	−6.84455	−	4.39873i	−0.353451	−	0.227149i
$376$		0			0
$377$	3.10654	−	3.58514i	0.159995	−	0.184644i
$378$		0			0
$379$	1.19331	+	8.29968i	0.0612964	+	0.426326i	0.997244	+	0.0741874i	$0.0236363\pi$
$379$	1.19331	+	8.29968i	0.0612964	+	0.426326i	−0.935948	+	0.352138i	$0.885455\pi$
$380$		0			0
$381$	−8.26800	+	5.31352i	−0.423582	+	0.272220i
$382$		0			0
$383$	8.09331	−	17.7219i	0.413549	−	0.905546i	−0.582166	−	0.813070i	$-0.697795\pi$
$383$	8.09331	−	17.7219i	0.413549	−	0.905546i	0.995715	−	0.0924757i	$-0.0294781\pi$
$384$		0			0
$385$	−29.9115	+	8.78280i	−1.52443	+	0.447613i
$386$		0			0
$387$	−2.83344	−	0.831974i	−0.144032	−	0.0422916i
$388$		0			0
$389$	3.08550	−	21.4601i	0.156441	−	1.08807i	−0.748684	−	0.662927i	$-0.769314\pi$
$389$	3.08550	−	21.4601i	0.156441	−	1.08807i	0.905125	−	0.425145i	$-0.139777\pi$
$390$		0			0
$391$	3.14269	−	14.8853i	0.158932	−	0.752784i
$392$		0			0
$393$	−2.50072	+	17.3929i	−0.126145	+	0.877355i
$394$		0			0
$395$	23.9482	+	7.03182i	1.20496	+	0.353809i
$396$		0			0
$397$	21.5975	−	6.34161i	1.08395	−	0.318276i	0.309492	−	0.950902i	$-0.399841\pi$
$397$	21.5975	−	6.34161i	1.08395	−	0.318276i	0.774457	+	0.632626i	$0.218023\pi$
$398$		0			0
$399$	−5.74829	+	12.5870i	−0.287774	+	0.630138i
$400$		0			0
$401$	−10.8294	+	6.95964i	−0.540795	+	0.347548i	−0.782350	−	0.622839i	$-0.785979\pi$
$401$	−10.8294	+	6.95964i	−0.540795	+	0.347548i	0.241555	+	0.970387i	$0.422343\pi$
$402$		0			0
$403$	0.523046	+	3.63787i	0.0260548	+	0.181215i
$404$		0			0
$405$	−2.29838	+	2.65247i	−0.114207	+	0.131802i
$406$		0			0
$407$	1.71261	+	1.10063i	0.0848911	+	0.0545562i
$408$		0			0
$409$	22.7662	+	26.2736i	1.12572	+	1.29915i	0.949138	+	0.314859i	$0.101957\pi$
$409$	22.7662	+	26.2736i	1.12572	+	1.29915i	0.176578	+	0.984287i	$0.443497\pi$
$410$		0			0
$411$	1.49412	+	3.27167i	0.0736997	+	0.161380i
$412$		0			0
$413$	−28.3758			−1.39628
$414$		0			0
$415$	14.0039			0.687422
$416$		0			0
$417$	1.90976	+	4.18179i	0.0935213	+	0.204783i
$418$		0			0
$419$	17.6919	+	20.4176i	0.864307	+	0.997463i	0.999977	+	0.00670920i	$0.00213562\pi$
$419$	17.6919	+	20.4176i	0.864307	+	0.997463i	−0.135671	+	0.990754i	$0.543319\pi$
$420$		0			0
$421$	12.9955	+	8.35171i	0.633363	+	0.407037i	0.817553	−	0.575853i	$-0.195330\pi$
$421$	12.9955	+	8.35171i	0.633363	+	0.407037i	−0.184191	+	0.982891i	$0.558966\pi$
$422$		0			0
$423$	7.76507	−	8.96137i	0.377551	−	0.435717i
$424$		0			0
$425$	−3.30383	−	22.9786i	−0.160259	−	1.11463i
$426$		0			0
$427$	11.6220	−	7.46904i	0.562430	−	0.361452i
$428$		0			0
$429$	−1.91350	+	4.18999i	−0.0923849	+	0.202295i
$430$		0			0
$431$	−3.11328	+	0.914140i	−0.149961	+	0.0440326i	−0.355852	−	0.934542i	$-0.615809\pi$
$431$	−3.11328	+	0.914140i	−0.149961	+	0.0440326i	0.205890	+	0.978575i	$0.433991\pi$
$432$		0			0
$433$	−13.4286	−	3.94300i	−0.645339	−	0.189489i	−0.0573457	−	0.998354i	$-0.518264\pi$
$433$	−13.4286	−	3.94300i	−0.645339	−	0.189489i	−0.587993	+	0.808866i	$0.700082\pi$
$434$		0			0
$435$	1.86721	−	12.9868i	0.0895261	−	0.622668i
$436$		0			0
$437$	−19.0587	+	19.2938i	−0.911703	+	0.922948i
$438$		0			0
$439$	−2.79383	+	19.4315i	−0.133342	+	0.927414i	0.807813	+	0.589439i	$0.200651\pi$
$439$	−2.79383	+	19.4315i	−0.133342	+	0.927414i	−0.941155	+	0.337975i	$0.890258\pi$
$440$		0			0
$441$	0.971218	+	0.285175i	0.0462485	+	0.0135798i
$442$		0			0
$443$	24.3705	−	7.15583i	1.15788	−	0.339984i	0.354271	−	0.935143i	$-0.384729\pi$
$443$	24.3705	−	7.15583i	1.15788	−	0.339984i	0.803608	+	0.595159i	$0.202911\pi$
$444$		0			0
$445$	12.4747	−	27.3157i	0.591356	−	1.29489i
$446$		0			0
$447$	−6.81652	+	4.38071i	−0.322410	+	0.207200i
$448$		0			0
$449$	−1.49936	−	10.4283i	−0.0707591	−	0.492140i	−0.994127	−	0.108223i	$-0.965484\pi$
$449$	−1.49936	−	10.4283i	−0.0707591	−	0.492140i	0.923368	−	0.383917i	$-0.125425\pi$
$450$		0			0
$451$	24.5990	−	28.3888i	1.15832	−	1.33678i
$452$		0			0
$453$	−7.47081	−	4.80120i	−0.351009	−	0.225580i
$454$		0			0
$455$	−7.13695	−	8.23648i	−0.334585	−	0.386132i
$456$		0			0
$457$	−12.5634	−	27.5100i	−0.587691	−	1.28686i	−0.936827	−	0.349792i	$-0.886252\pi$
$457$	−12.5634	−	27.5100i	−0.587691	−	1.28686i	0.349136	−	0.937072i	$-0.386475\pi$
$458$		0			0
$459$	−3.17223			−0.148067
$460$		0			0
$461$	−20.0214			−0.932491			−0.466245	−	0.884655i	$-0.654394\pi$
$461$	−20.0214			−0.932491			−0.466245	+	0.884655i	$0.654394\pi$
$462$		0			0
$463$	4.12893	+	9.04111i	0.191888	+	0.420176i	0.980983	−	0.194096i	$-0.0621772\pi$
$463$	4.12893	+	9.04111i	0.191888	+	0.420176i	−0.789095	+	0.614272i	$0.789450\pi$
$464$		0			0
$465$	6.65663	+	7.68216i	0.308694	+	0.356252i
$466$		0			0
$467$	27.4856	+	17.6639i	1.27188	+	0.817388i	0.989864	−	0.142021i	$-0.0453602\pi$
$467$	27.4856	+	17.6639i	1.27188	+	0.817388i	0.282017	+	0.959409i	$0.408997\pi$
$468$		0			0
$469$	18.7529	−	21.6419i	0.865926	−	0.999332i
$470$		0			0
$471$	−3.11615	−	21.6733i	−0.143585	−	0.998653i
$472$		0			0
$473$	−9.01756	+	5.79524i	−0.414628	+	0.266465i
$474$		0			0
$475$	−17.1913	+	37.6436i	−0.788790	+	1.72721i
$476$		0			0
$477$	11.1974	−	3.28785i	0.512693	−	0.150540i
$478$		0			0
$479$	9.09607	+	2.67085i	0.415610	+	0.122034i	0.482851	−	0.875703i	$-0.339601\pi$
$479$	9.09607	+	2.67085i	0.415610	+	0.122034i	−0.0672406	+	0.997737i	$0.521420\pi$
$480$		0			0
$481$	−0.101286	+	0.704461i	−0.00461825	+	0.0321207i
$482$		0			0
$483$	−9.43758	−	6.97504i	−0.429425	−	0.317375i
$484$		0			0
$485$	−4.29824	+	29.8949i	−0.195173	+	1.35746i
$486$		0			0
$487$	17.6216	+	5.17416i	0.798509	+	0.234463i	0.655438	−	0.755249i	$-0.272484\pi$
$487$	17.6216	+	5.17416i	0.798509	+	0.234463i	0.143071	+	0.989712i	$0.454302\pi$
$488$		0			0
$489$	−10.8044	+	3.17245i	−0.488591	+	0.143463i
$490$		0			0
$491$	9.39577	−	20.5739i	0.424025	−	0.928485i	−0.570234	−	0.821483i	$-0.693147\pi$
$491$	9.39577	−	20.5739i	0.424025	−	0.928485i	0.994259	−	0.107003i	$-0.0341254\pi$
$492$		0			0
$493$	9.97614	−	6.41127i	0.449303	−	0.288749i
$494$		0			0
$495$	1.81306	+	12.6101i	0.0814912	+	0.566783i
$496$		0			0
$497$	1.23913	−	1.43003i	0.0555824	−	0.0641455i
$498$		0			0
$499$	12.8226	+	8.24060i	0.574020	+	0.368900i	0.795213	−	0.606330i	$-0.207359\pi$
$499$	12.8226	+	8.24060i	0.574020	+	0.368900i	−0.221194	+	0.975230i	$0.570995\pi$
$500$		0			0
$501$	−7.40074	−	8.54091i	−0.330641	−	0.381580i
$502$		0			0
$503$	−11.3672	−	24.8908i	−0.506841	−	1.10983i	−0.974185	−	0.225751i	$-0.927516\pi$
$503$	−11.3672	−	24.8908i	−0.506841	−	1.10983i	0.467345	−	0.884075i	$-0.345211\pi$
$504$		0			0
$505$	−37.6077			−1.67352
$506$		0			0
$507$	11.3897			0.505833
$508$		0			0
$509$	5.96078	+	13.0523i	0.264207	+	0.578532i	0.994516	−	0.104584i	$-0.0333512\pi$
$509$	5.96078	+	13.0523i	0.264207	+	0.578532i	−0.730309	+	0.683117i	$0.760624\pi$
$510$		0			0
$511$	22.9701	+	26.5089i	1.01614	+	1.17268i
$512$		0			0
$513$	4.75719	+	3.05726i	0.210035	+	0.134981i
$514$		0			0
$515$	−2.13903	+	2.46858i	−0.0942571	+	0.108779i
$516$		0			0
$517$	−6.12543	−	42.6033i	−0.269396	−	1.87369i
$518$		0			0
$519$	17.7972	−	11.4376i	0.781212	−	0.502054i
$520$		0			0
$521$	16.1919	−	35.4554i	0.709381	−	1.55333i	−0.118832	−	0.992914i	$-0.537915\pi$
$521$	16.1919	−	35.4554i	0.709381	−	1.55333i	0.828213	−	0.560413i	$-0.189358\pi$
$522$		0			0
$523$	32.4675	−	9.53331i	1.41970	−	0.416863i	0.520301	−	0.853983i	$-0.325820\pi$
$523$	32.4675	−	9.53331i	1.41970	−	0.416863i	0.899403	+	0.437121i	$0.144002\pi$
$524$		0			0
$525$	−17.1821	−	5.04513i	−0.749890	−	0.220188i
$526$		0			0
$527$	−1.30752	+	9.09397i	−0.0569563	+	0.396140i
$528$		0			0
$529$	−12.6710	−	19.1950i	−0.550912	−	0.834563i
$530$		0			0
$531$	−1.65031	+	11.4781i	−0.0716172	+	0.498109i
$532$		0			0
$533$	12.6002	+	3.69976i	0.545776	+	0.160254i
$534$		0			0
$535$	18.8182	−	5.52551i	0.813580	−	0.238889i
$536$		0			0
$537$	4.22574	−	9.25308i	0.182354	−	0.399300i
$538$		0			0
$539$	3.09095	−	1.98643i	0.133136	−	0.0855616i
$540$		0			0
$541$	−4.94069	−	34.3632i	−0.212417	−	1.47739i	−0.765053	−	0.643968i	$-0.777287\pi$
$541$	−4.94069	−	34.3632i	−0.212417	−	1.47739i	0.552636	−	0.833423i	$-0.313622\pi$
$542$		0			0
$543$	−6.97271	+	8.04693i	−0.299228	+	0.345327i
$544$		0			0
$545$	−46.9432	−	30.1686i	−2.01083	−	1.29228i
$546$		0			0
$547$	−9.22896	−	10.6508i	−0.394602	−	0.455395i	0.523332	−	0.852129i	$-0.324689\pi$
$547$	−9.22896	−	10.6508i	−0.394602	−	0.455395i	−0.917933	+	0.396734i	$0.870143\pi$
$548$		0			0
$549$	−2.34534	−	5.13557i	−0.100096	−	0.219181i
$550$		0			0
$551$	−21.1395			−0.900572
$552$		0			0
$553$	17.4017			0.739994
$554$		0			0
$555$	0.817707	+	1.79053i	0.0347097	+	0.0760037i
$556$		0			0
$557$	11.2096	+	12.9366i	0.474968	+	0.548142i	0.941787	−	0.336211i	$-0.109146\pi$
$557$	11.2096	+	12.9366i	0.474968	+	0.548142i	−0.466819	+	0.884353i	$0.654600\pi$
$558$		0			0
$559$	−3.15251	−	2.02600i	−0.133337	−	0.0856906i
$560$		0			0
$561$	−7.54055	+	8.70226i	−0.318362	+	0.367410i
$562$		0			0
$563$	−5.10761	−	35.5242i	−0.215260	−	1.49717i	−0.755217	−	0.655475i	$-0.772469\pi$
$563$	−5.10761	−	35.5242i	−0.215260	−	1.49717i	0.539957	−	0.841693i	$-0.318441\pi$
$564$		0			0
$565$	16.7954	−	10.7938i	0.706589	−	0.454097i
$566$		0			0
$567$	−1.01652	+	2.22586i	−0.0426897	+	0.0934775i
$568$		0			0
$569$	9.76922	−	2.86850i	0.409547	−	0.120254i	−0.0704682	−	0.997514i	$-0.522449\pi$
$569$	9.76922	−	2.86850i	0.409547	−	0.120254i	0.480015	+	0.877260i	$0.340631\pi$
$570$		0			0
$571$	1.96770	+	0.577770i	0.0823458	+	0.0241789i	0.322646	−	0.946520i	$-0.395428\pi$
$571$	1.96770	+	0.577770i	0.0823458	+	0.0241789i	−0.240300	+	0.970699i	$0.577246\pi$
$572$		0			0
$573$	−1.45630	+	10.1288i	−0.0608379	+	0.423137i
$574$		0			0
$575$	−28.2247	−	20.8601i	−1.17705	−	0.869925i
$576$		0			0
$577$	1.29934	−	9.03714i	0.0540924	−	0.376221i	−0.944736	−	0.327832i	$-0.893682\pi$
$577$	1.29934	−	9.03714i	0.0540924	−	0.376221i	0.998829	−	0.0483893i	$-0.0154088\pi$
$578$		0			0
$579$	−9.73114	−	2.85732i	−0.404412	−	0.118746i
$580$		0			0
$581$	9.36805	−	2.75071i	0.388652	−	0.114119i
$582$		0			0
$583$	17.5973	−	38.5328i	0.728806	−	1.59586i
$584$		0			0
$585$	−3.74677	+	2.40791i	−0.154910	+	0.0995546i
$586$		0			0
$587$	0.370355	+	2.57588i	0.0152862	+	0.106318i	0.996036	−	0.0889505i	$-0.0283513\pi$
$587$	0.370355	+	2.57588i	0.0152862	+	0.106318i	−0.980750	+	0.195268i	$0.937442\pi$
$588$		0			0
$589$	10.7252	−	12.3775i	0.441923	−	0.510007i
$590$		0			0
$591$	17.7533	+	11.4093i	0.730271	+	0.469317i
$592$		0			0
$593$	−8.01595	−	9.25090i	−0.329176	−	0.379889i	0.566903	−	0.823785i	$-0.308141\pi$
$593$	−8.01595	−	9.25090i	−0.329176	−	0.379889i	−0.896078	+	0.443896i	$0.853596\pi$
$594$		0			0
$595$	−11.3176	−	24.7820i	−0.463975	−	1.01596i
$596$		0			0
$597$	−5.96499			−0.244131
$598$		0			0
$599$	12.1215			0.495270			0.247635	−	0.968853i	$-0.420347\pi$
$599$	12.1215			0.495270			0.247635	+	0.968853i	$0.420347\pi$
$600$		0			0
$601$	−13.8159	−	30.2527i	−0.563564	−	1.23403i	−0.950154	−	0.311781i	$-0.899074\pi$
$601$	−13.8159	−	30.2527i	−0.563564	−	1.23403i	0.386590	−	0.922252i	$-0.373653\pi$
$602$		0			0
$603$	−7.66363	−	8.84430i	−0.312087	−	0.360168i
$604$		0			0
$605$	6.42443	+	4.12873i	0.261190	+	0.167857i
$606$		0			0
$607$	−9.71185	+	11.2081i	−0.394192	+	0.454922i	−0.917803	−	0.397036i	$-0.870039\pi$
$607$	−9.71185	+	11.2081i	−0.394192	+	0.454922i	0.523611	+	0.851957i	$0.324584\pi$
$608$		0			0
$609$	−1.30183	−	9.05442i	−0.0527528	−	0.366904i
$610$		0			0
$611$	12.6585	−	8.13510i	0.512106	−	0.329111i
$612$		0			0
$613$	−13.2703	+	29.0578i	−0.535980	+	1.17363i	0.427047	+	0.904230i	$0.359554\pi$
$613$	−13.2703	+	29.0578i	−0.535980	+	1.17363i	−0.963027	+	0.269404i	$0.913173\pi$
$614$		0			0
$615$	34.8493	−	10.2327i	1.40526	−	0.412621i
$616$		0			0
$617$	44.9152	+	13.1883i	1.80822	+	0.530941i	0.998442	−	0.0557986i	$-0.0177705\pi$
$617$	44.9152	+	13.1883i	1.80822	+	0.530941i	0.809776	+	0.586739i	$0.199589\pi$
$618$		0			0
$619$	−2.13534	+	14.8516i	−0.0858266	+	0.596937i	0.900836	+	0.434159i	$0.142954\pi$
$619$	−2.13534	+	14.8516i	−0.0858266	+	0.596937i	−0.986663	+	0.162778i	$0.947955\pi$
$620$		0			0
$621$	−3.37032	+	3.41189i	−0.135246	+	0.136914i
$622$		0			0
$623$	2.97959	−	20.7235i	0.119375	−	0.830271i
$624$		0			0
$625$	7.70976	+	2.26379i	0.308391	+	0.0905516i
$626$		0			0
$627$	19.6950	−	5.78296i	0.786541	−	0.230949i
$628$		0			0
$629$	−0.739076	+	1.61835i	−0.0294689	+	0.0645279i
$630$		0			0
$631$	−32.9969	+	21.2058i	−1.31359	+	0.844190i	−0.994621	−	0.103577i	$-0.966971\pi$
$631$	−32.9969	+	21.2058i	−1.31359	+	0.844190i	−0.318964	+	0.947767i	$0.603335\pi$
$632$		0			0
$633$	2.73492	+	19.0218i	0.108703	+	0.756049i
$634$		0			0
$635$	−22.5889	+	26.0690i	−0.896414	+	1.03452i
$636$		0			0
$637$	1.08059	+	0.694450i	0.0428144	+	0.0275151i
$638$		0			0
$639$	−0.506387	−	0.584402i	−0.0200324	−	0.0231186i
$640$		0			0
$641$	−11.5294	−	25.2459i	−0.455384	−	0.997153i	−0.988515	−	0.151120i	$-0.951712\pi$
$641$	−11.5294	−	25.2459i	−0.455384	−	0.997153i	0.533131	−	0.846033i	$-0.321015\pi$
$642$		0			0
$643$	−1.26270			−0.0497958			−0.0248979	−	0.999690i	$-0.507926\pi$
$643$	−1.26270			−0.0497958			−0.0248979	+	0.999690i	$0.507926\pi$
$644$		0			0
$645$	−10.3644			−0.408099
$646$		0			0
$647$	5.24476	+	11.4844i	0.206193	+	0.451499i	0.984270	−	0.176669i	$-0.0565323\pi$
$647$	5.24476	+	11.4844i	0.206193	+	0.451499i	−0.778078	+	0.628168i	$0.783805\pi$
$648$		0			0
$649$	27.5647	+	31.8114i	1.08201	+	1.24871i
$650$		0			0
$651$	5.96200	+	3.83155i	0.233669	+	0.150170i
$652$		0			0
$653$	−28.6300	+	33.0408i	−1.12038	+	1.29299i	−0.168777	+	0.985654i	$0.553982\pi$
$653$	−28.6300	+	33.0408i	−1.12038	+	1.29299i	−0.951602	+	0.307333i	$0.900564\pi$
$654$		0			0
$655$	8.77684	+	61.0443i	0.342940	+	2.38520i
$656$		0			0
$657$	12.0589	−	7.74978i	0.470462	−	0.302348i
$658$		0			0
$659$	−3.31001	+	7.24790i	−0.128940	+	0.282338i	−0.963081	−	0.269213i	$-0.913237\pi$
$659$	−3.31001	+	7.24790i	−0.128940	+	0.282338i	0.834141	+	0.551551i	$0.185964\pi$
$660$		0			0
$661$	−12.6323	+	3.70918i	−0.491339	+	0.144270i	−0.518011	−	0.855374i	$-0.673327\pi$
$661$	−12.6323	+	3.70918i	−0.491339	+	0.144270i	0.0266715	+	0.999644i	$0.491509\pi$
$662$		0			0
$663$	−3.86246	−	1.13412i	−0.150005	−	0.0440456i
$664$		0			0
$665$	−6.91162	+	48.0713i	−0.268021	+	1.86413i
$666$		0			0
$667$	3.70346	−	17.5414i	0.143398	−	0.679207i
$668$		0			0
$669$	0.0449274	−	0.312477i	0.00173699	−	0.0120810i
$670$		0			0
$671$	−19.6632	−	5.77364i	−0.759090	−	0.222889i
$672$		0			0
$673$	−34.9936	+	10.2750i	−1.34890	+	0.396074i	−0.874838	−	0.484416i	$-0.839032\pi$
$673$	−34.9936	+	10.2750i	−1.34890	+	0.396074i	−0.474065	+	0.880490i	$0.657214\pi$
$674$		0			0
$675$	−3.04008	+	6.65684i	−0.117013	+	0.256222i
$676$		0			0
$677$	8.29781	−	5.33268i	0.318911	−	0.204951i	−0.371385	−	0.928479i	$-0.621117\pi$
$677$	8.29781	−	5.33268i	0.318911	−	0.204951i	0.690295	+	0.723528i	$0.257481\pi$
$678$		0			0
$679$	2.99675	+	20.8429i	0.115005	+	0.799876i
$680$		0			0
$681$	17.5134	−	20.2115i	0.671113	−	0.774506i
$682$		0			0
$683$	−2.38499	−	1.53274i	−0.0912591	−	0.0586487i	0.494215	−	0.869339i	$-0.335455\pi$
$683$	−2.38499	−	1.53274i	−0.0912591	−	0.0586487i	−0.585475	+	0.810691i	$0.699092\pi$
$684$		0			0
$685$	8.26659	+	9.54015i	0.315850	+	0.364510i
$686$		0			0
$687$	10.5241	+	23.0446i	0.401519	+	0.879205i
$688$		0			0
$689$	14.8092			0.564186
$690$		0			0
$691$	−35.4217			−1.34750			−0.673752	−	0.738957i	$-0.735318\pi$
$691$	−35.4217			−1.34750			−0.673752	+	0.738957i	$0.735318\pi$
$692$		0			0
$693$	3.68982	+	8.07957i	0.140165	+	0.306918i
$694$		0			0
$695$	10.5662	+	12.1940i	0.400799	+	0.462546i
$696$		0			0
$697$	27.6166	+	17.7481i	1.04605	+	0.672258i
$698$		0			0
$699$	−15.6572	+	18.0694i	−0.592211	+	0.683447i
$700$		0			0
$701$	2.56956	+	17.8717i	0.0970508	+	0.675003i	0.979030	+	0.203715i	$0.0653017\pi$
$701$	2.56956	+	17.8717i	0.0970508	+	0.675003i	−0.881979	+	0.471288i	$0.843789\pi$
$702$		0			0
$703$	2.66804	−	1.71465i	0.100627	−	0.0646691i
$704$		0			0
$705$	17.2883	−	37.8560i	0.651114	−	1.42574i
$706$		0			0
$707$	−25.1581	+	7.38709i	−0.946168	+	0.277820i
$708$		0			0
$709$	37.1662	+	10.9130i	1.39581	+	0.409845i	0.891242	−	0.453529i	$-0.149835\pi$
$709$	37.1662	+	10.9130i	1.39581	+	0.409845i	0.504564	+	0.863374i	$0.331653\pi$
$710$		0			0
$711$	1.01206	−	7.03906i	0.0379554	−	0.263985i
$712$		0			0
$713$	8.39184	+	11.0681i	0.314277	+	0.414505i
$714$		0			0
$715$	−2.30076	+	16.0021i	−0.0860434	+	0.598445i
$716$		0			0
$717$	1.37017	+	0.402319i	0.0511701	+	0.0150249i
$718$		0			0
$719$	49.1790	−	14.4402i	1.83407	−	0.538530i	0.834151	−	0.551536i	$-0.185958\pi$
$719$	49.1790	−	14.4402i	1.83407	−	0.538530i	0.999915	+	0.0130060i	$0.00414007\pi$
$720$		0			0
$721$	−0.946043	+	2.07155i	−0.0352325	+	0.0771484i
$722$		0			0
$723$	−0.200331	+	0.128745i	−0.00745040	+	0.00478808i
$724$		0			0
$725$	−3.89335	−	27.0789i	−0.144595	−	1.00568i
$726$		0			0
$727$	−32.4331	+	37.4298i	−1.20288	+	1.38819i	−0.302461	+	0.953162i	$0.597808\pi$
$727$	−32.4331	+	37.4298i	−1.20288	+	1.38819i	−0.900415	+	0.435031i	$0.856737\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−6.13460	−	7.07970i	−0.226896	−	0.261852i
$732$		0			0
$733$	−13.8110	−	30.2418i	−0.510120	−	1.11701i	−0.973046	−	0.230610i	$-0.925928\pi$
$733$	−13.8110	−	30.2418i	−0.510120	−	1.11701i	0.462926	−	0.886397i	$-0.346800\pi$
$734$		0			0
$735$	3.55261			0.131040
$736$		0			0
$737$	−42.4791			−1.56474
$738$		0			0
$739$	16.3928	+	35.8953i	0.603020	+	1.32043i	0.927247	+	0.374451i	$0.122169\pi$
$739$	16.3928	+	35.8953i	0.603020	+	1.32043i	−0.324227	+	0.945979i	$0.605104\pi$
$740$		0			0
$741$	4.69926	+	5.42324i	0.172632	+	0.199228i
$742$		0			0
$743$	28.4816	+	18.3040i	1.04489	+	0.671508i	0.946191	−	0.323609i	$-0.104896\pi$
$743$	28.4816	+	18.3040i	1.04489	+	0.671508i	0.0986965	+	0.995118i	$0.468533\pi$
$744$		0			0
$745$	−18.6233	+	21.4925i	−0.682307	+	0.787424i
$746$		0			0
$747$	−0.567839	−	3.94940i	−0.0207761	−	0.144501i
$748$		0			0
$749$	11.5033	−	7.39272i	0.420321	−	0.270124i
$750$		0			0
$751$	−11.8182	+	25.8781i	−0.431251	+	0.944307i	0.561872	+	0.827224i	$0.310081\pi$
$751$	−11.8182	+	25.8781i	−0.431251	+	0.944307i	−0.993122	+	0.117083i	$0.962646\pi$
$752$		0			0
$753$	−19.4703	+	5.71699i	−0.709537	+	0.208339i
$754$		0			0
$755$	−29.9058	−	8.78114i	−1.08838	−	0.319578i
$756$		0			0
$757$	3.15222	−	21.9241i	0.114569	−	0.796847i	−0.848809	−	0.528700i	$-0.822680\pi$
$757$	3.15222	−	21.9241i	0.114569	−	0.796847i	0.963378	−	0.268147i	$-0.0864112\pi$
$758$		0			0
$759$	1.34828	+	17.3559i	0.0489396	+	0.629979i
$760$		0			0
$761$	−4.00085	+	27.8265i	−0.145031	+	1.00871i	0.779172	+	0.626810i	$0.215640\pi$
$761$	−4.00085	+	27.8265i	−0.145031	+	1.00871i	−0.924203	+	0.381901i	$0.875269\pi$
$762$		0			0
$763$	−37.3291	−	10.9608i	−1.35140	−	0.396808i
$764$		0			0
$765$	−10.6827	+	3.13671i	−0.386232	+	0.113408i
$766$		0			0
$767$	−6.11300	+	13.3856i	−0.220728	+	0.483326i
$768$		0			0
$769$	−15.8579	+	10.1913i	−0.571852	+	0.367507i	−0.794382	−	0.607419i	$-0.792205\pi$
$769$	−15.8579	+	10.1913i	−0.571852	+	0.367507i	0.222530	+	0.974926i	$0.428569\pi$
$770$		0			0
$771$	−2.37193	−	16.4971i	−0.0854230	−	0.594130i
$772$		0			0
$773$	10.5832	−	12.2137i	0.380651	−	0.439295i	−0.532801	−	0.846240i	$-0.678861\pi$
$773$	10.5832	−	12.2137i	0.380651	−	0.439295i	0.913452	+	0.406946i	$0.133406\pi$
$774$		0			0
$775$	17.8304	+	11.4589i	0.640488	+	0.411616i
$776$		0			0
$777$	0.898720	+	1.03718i	0.0322414	+	0.0372086i
$778$		0			0
$779$	−24.3100	−	53.2314i	−0.870995	−	1.90721i
$780$		0			0
$781$	−2.80688			−0.100438
$782$		0			0
$783$	−3.73827			−0.133595
$784$		0			0
$785$	−31.9244	−	69.9048i	−1.13943	−	2.49501i
$786$		0			0
$787$	7.88438	+	9.09906i	0.281048	+	0.324346i	0.878668	−	0.477433i	$-0.158433\pi$
$787$	7.88438	+	9.09906i	0.281048	+	0.324346i	−0.597621	+	0.801779i	$0.703887\pi$
$788$		0			0
$789$	14.2732	+	9.17281i	0.508139	+	0.326561i
$790$		0			0
$791$	9.11535	−	10.5197i	0.324104	−	0.374037i
$792$		0			0
$793$	−1.01960	−	7.09148i	−0.0362071	−	0.251826i
$794$		0			0
$795$	34.4568	−	22.1440i	1.22206	−	0.785367i
$796$		0			0
$797$	−18.6721	+	40.8863i	−0.661401	+	1.44827i	0.219809	+	0.975543i	$0.429457\pi$
$797$	−18.6721	+	40.8863i	−0.661401	+	1.44827i	−0.881210	+	0.472724i	$0.843271\pi$
$798$		0			0
$799$	36.0913	−	10.5974i	1.27682	−	0.374908i
$800$		0			0
$801$	−8.20948	−	2.41052i	−0.290068	−	0.0851716i
$802$		0			0
$803$	7.40492	−	51.5024i	0.261314	−	1.81748i
$804$		0			0
$805$	−38.6785	−	14.1569i	−1.36324	−	0.498966i
$806$		0			0
$807$	0.605815	−	4.21354i	0.0213257	−	0.148324i
$808$		0			0
$809$	−19.0920	−	5.60591i	−0.671238	−	0.197093i	−0.0716836	−	0.997427i	$-0.522837\pi$
$809$	−19.0920	−	5.60591i	−0.671238	−	0.197093i	−0.599554	+	0.800334i	$0.704655\pi$
$810$		0			0
$811$	−31.3402	+	9.20230i	−1.10050	+	0.323137i	−0.781052	−	0.624466i	$-0.785316\pi$
$811$	−31.3402	+	9.20230i	−1.10050	+	0.323137i	−0.319450	+	0.947603i	$0.603498\pi$
$812$		0			0
$813$	−2.47675	+	5.42332i	−0.0868634	+	0.190204i
$814$		0			0
$815$	−33.2474	+	21.3668i	−1.16461	+	0.748447i
$816$		0			0
$817$	2.37655	+	16.5292i	0.0831448	+	0.578285i
$818$		0			0
$819$	−2.03348	+	2.34676i	−0.0710555	+	0.0820024i
$820$		0			0
$821$	−11.3204	−	7.27518i	−0.395085	−	0.253905i	0.327982	−	0.944684i	$-0.393632\pi$
$821$	−11.3204	−	7.27518i	−0.395085	−	0.253905i	−0.723066	+	0.690779i	$0.757268\pi$
$822$		0			0
$823$	12.2385	+	14.1239i	0.426606	+	0.492329i	0.927838	−	0.372984i	$-0.121665\pi$
$823$	12.2385	+	14.1239i	0.426606	+	0.492329i	−0.501232	+	0.865313i	$0.667120\pi$
$824$		0			0
$825$	11.0351	+	24.1634i	0.384191	+	0.841261i
$826$		0			0
$827$	−18.1631			−0.631594			−0.315797	−	0.948827i	$-0.602272\pi$
$827$	−18.1631			−0.631594			−0.315797	+	0.948827i	$0.602272\pi$
$828$		0			0
$829$	37.8172			1.31345			0.656723	−	0.754132i	$-0.271942\pi$
$829$	37.8172			1.31345			0.656723	+	0.754132i	$0.271942\pi$
$830$		0			0
$831$	−8.23517	−	18.0325i	−0.285675	−	0.625541i
$832$		0			0
$833$	2.10275	+	2.42671i	0.0728561	+	0.0840804i
$834$		0			0
$835$	−33.3677	−	21.4441i	−1.15474	−	0.742104i
$836$		0			0
$837$	1.89662	−	2.18882i	0.0655569	−	0.0756567i
$838$		0			0
$839$	4.59025	+	31.9259i	0.158473	+	1.10220i	0.901449	+	0.432885i	$0.142505\pi$
$839$	4.59025	+	31.9259i	0.158473	+	1.10220i	−0.742976	+	0.669318i	$0.766586\pi$
$840$		0			0
$841$	−12.6401	+	8.12330i	−0.435866	+	0.280114i
$842$		0			0
$843$	4.80084	−	10.5124i	0.165350	−	0.362065i
$844$		0			0
$845$	38.3554	−	11.2621i	1.31946	−	0.387430i
$846$		0			0
$847$	5.10869	+	1.50005i	0.175537	+	0.0515422i
$848$		0			0
$849$	−3.93080	+	27.3393i	−0.134905	+	0.938282i
$850$		0			0
$851$	0.955387	+	2.51432i	0.0327503	+	0.0861898i
$852$		0			0
$853$	−1.97706	+	13.7508i	−0.0676933	+	0.470817i	0.927574	+	0.373640i	$0.121890\pi$
$853$	−1.97706	+	13.7508i	−0.0676933	+	0.470817i	−0.995267	+	0.0971771i	$0.969019\pi$
$854$		0			0
$855$	19.0431	+	5.59157i	0.651261	+	0.191228i
$856$		0			0
$857$	−33.4741	+	9.82889i	−1.14345	+	0.335749i	−0.797983	−	0.602680i	$-0.794099\pi$
$857$	−33.4741	+	9.82889i	−1.14345	+	0.335749i	−0.345472	+	0.938429i	$0.612281\pi$
$858$		0			0
$859$	1.26281	−	2.76518i	0.0430866	−	0.0943466i	−0.886865	−	0.462029i	$-0.847121\pi$
$859$	1.26281	−	2.76518i	0.0430866	−	0.0943466i	0.929951	+	0.367683i	$0.119849\pi$
$860$		0			0
$861$	21.3029	−	13.6905i	0.726001	−	0.466572i
$862$		0			0
$863$	3.47453	+	24.1659i	0.118275	+	0.822617i	0.959455	+	0.281863i	$0.0909522\pi$
$863$	3.47453	+	24.1659i	0.118275	+	0.822617i	−0.841180	+	0.540755i	$0.818139\pi$
$864$		0			0
$865$	48.6236	−	56.1147i	1.65325	−	1.90796i
$866$		0			0
$867$	5.83575	+	3.75041i	0.198192	+	0.127371i
$868$		0			0
$869$	−16.9043	−	19.5086i	−0.573438	−	0.661783i
$870$		0			0
$871$	−6.16915	−	13.5085i	−0.209034	−	0.457720i
$872$		0			0
$873$	8.60533			0.291246
$874$		0			0
$875$	−19.9091			−0.673050
$876$		0			0
$877$	−7.75427	−	16.9795i	−0.261843	−	0.573356i	0.732355	−	0.680923i	$-0.238421\pi$
$877$	−7.75427	−	16.9795i	−0.261843	−	0.573356i	−0.994198	+	0.107567i	$0.965694\pi$
$878$		0			0
$879$	−12.0327	−	13.8865i	−0.405854	−	0.468381i
$880$		0			0
$881$	0.407658	+	0.261986i	0.0137343	+	0.00882652i	0.547490	−	0.836812i	$-0.315583\pi$
$881$	0.407658	+	0.261986i	0.0137343	+	0.00882652i	−0.533756	+	0.845639i	$0.679220\pi$
$882$		0			0
$883$	31.6473	−	36.5229i	1.06502	−	1.22909i	0.0926345	−	0.995700i	$-0.470471\pi$
$883$	31.6473	−	36.5229i	1.06502	−	1.22909i	0.972382	−	0.233395i	$-0.0749834\pi$
$884$		0			0
$885$	5.79212	+	40.2851i	0.194700	+	1.35417i
$886$		0			0
$887$	−9.98107	+	6.41445i	−0.335132	+	0.215376i	−0.697373	−	0.716708i	$-0.745648\pi$
$887$	−9.98107	+	6.41445i	−0.335132	+	0.215376i	0.362241	+	0.932084i	$0.382012\pi$
$888$		0			0
$889$	−9.99053	+	21.8762i	−0.335072	+	0.733705i
$890$		0			0
$891$	3.48282	−	1.02265i	0.116679	−	0.0342601i
$892$		0			0
$893$	−64.3371	−	18.8911i	−2.15296	−	0.632166i
$894$		0			0
$895$	5.08094	−	35.3387i	0.169837	−	1.18124i
$896$		0			0
$897$	−5.32345	+	2.94932i	−0.177745	+	0.0984750i
$898$		0			0
$899$	−1.54083	+	10.7167i	−0.0513894	+	0.357421i
$900$		0			0
$901$	35.5206	+	10.4298i	1.18336	+	0.347467i
$902$		0			0
$903$	−6.93342	+	2.03583i	−0.230730	+	0.0677483i
$904$		0			0
$905$	−15.5242	+	33.9931i	−0.516040	+	1.12997i
$906$		0			0
$907$	17.2104	−	11.0605i	0.571462	−	0.367256i	−0.222770	−	0.974871i	$-0.571510\pi$
$907$	17.2104	−	11.0605i	0.571462	−	0.367256i	0.794232	+	0.607615i	$0.207874\pi$
$908$		0			0
$909$	1.52494	+	10.6062i	0.0505791	+	0.351786i
$910$		0			0
$911$	−7.35328	+	8.48614i	−0.243625	+	0.281158i	−0.864372	−	0.502853i	$-0.832284\pi$
$911$	−7.35328	+	8.48614i	−0.243625	+	0.281158i	0.620747	+	0.784011i	$0.286829\pi$
$912$		0			0
$913$	−12.1840	−	7.83021i	−0.403233	−	0.259142i
$914$		0			0
$915$	−12.9761	−	14.9752i	−0.428977	−	0.495066i
$916$		0			0
$917$	17.8620	+	39.1123i	0.589855	+	1.29160i
$918$		0			0
$919$	−15.5940			−0.514399			−0.257200	−	0.966358i	$-0.582800\pi$
$919$	−15.5940			−0.514399			−0.257200	+	0.966358i	$0.582800\pi$
$920$		0			0
$921$	−11.1552			−0.367578
$922$		0			0
$923$	−0.407637	−	0.892600i	−0.0134175	−	0.0293803i
$924$		0			0
$925$	2.68778	+	3.10187i	0.0883737	+	0.101989i
$926$		0			0
$927$	0.782930	+	0.503158i	0.0257148	+	0.0165259i
$928$		0			0
$929$	−11.9711	+	13.8154i	−0.392758	+	0.453267i	−0.917347	−	0.398089i	$-0.869674\pi$
$929$	−11.9711	+	13.8154i	−0.392758	+	0.453267i	0.524589	+	0.851356i	$0.324219\pi$
$930$		0			0
$931$	−0.814607	−	5.66572i	−0.0266977	−	0.185686i
$932$		0			0
$933$	18.2450	−	11.7253i	0.597313	−	0.383870i
$934$		0			0
$935$	−16.7884	+	36.7615i	−0.549040	+	1.20223i
$936$		0			0
$937$	−32.1451	+	9.43864i	−1.05013	+	0.308347i	−0.760871	−	0.648903i	$-0.775228\pi$
$937$	−32.1451	+	9.43864i	−1.05013	+	0.308347i	−0.289262	+	0.957250i	$0.593410\pi$
$938$		0			0
$939$	16.7995	+	4.93277i	0.548230	+	0.160975i
$940$		0			0
$941$	−7.98942	+	55.5677i	−0.260448	+	1.81145i	0.269032	+	0.963131i	$0.413296\pi$
$941$	−7.98942	+	55.5677i	−0.260448	+	1.81145i	−0.529480	+	0.848323i	$0.677613\pi$
$942$		0			0
$943$	48.4301	−	10.8466i	1.57710	−	0.353214i
$944$		0			0
$945$	−1.22224	+	8.50086i	−0.0397594	+	0.276533i
$946$		0			0
$947$	−37.6807	−	11.0640i	−1.22446	−	0.359533i	−0.395302	−	0.918551i	$-0.629360\pi$
$947$	−37.6807	−	11.0640i	−1.22446	−	0.359533i	−0.829155	+	0.559018i	$0.811178\pi$
$948$		0			0
$949$	17.4534	−	5.12478i	0.566561	−	0.166357i
$950$		0			0
$951$	−11.7930	+	25.8231i	−0.382414	+	0.837370i
$952$		0			0
$953$	−17.1159	+	10.9997i	−0.554438	+	0.356316i	−0.787662	−	0.616107i	$-0.788709\pi$
$953$	−17.1159	+	10.9997i	−0.554438	+	0.356316i	0.233224	+	0.972423i	$0.425072\pi$
$954$		0			0
$955$	5.11122	+	35.5493i	0.165395	+	1.15035i
$956$		0			0
$957$	−8.88607	+	10.2551i	−0.287246	+	0.331499i
$958$		0			0
$959$	7.40396	+	4.75824i	0.239086	+	0.153651i
$960$		0			0
$961$	14.8076	+	17.0889i	0.477666	+	0.551255i
$962$		0			0
$963$	−2.32137	−	5.08310i	−0.0748052	−	0.163800i
$964$		0			0
$965$	−35.5955			−1.14586
$966$		0			0
$967$	5.66729			0.182248			0.0911239	−	0.995840i	$-0.470954\pi$
$967$	5.66729			0.182248			0.0911239	+	0.995840i	$0.470954\pi$
$968$		0			0
$969$	7.45195	+	16.3175i	0.239391	+	0.524194i
$970$		0			0
$971$	−9.50053	−	10.9642i	−0.304886	−	0.351858i	0.582544	−	0.812799i	$-0.302057\pi$
$971$	−9.50053	−	10.9642i	−0.304886	−	0.351858i	−0.887431	+	0.460941i	$0.847512\pi$
$972$		0			0
$973$	9.46360	+	6.08189i	0.303389	+	0.194976i
$974$		0			0
$975$	−6.08148	+	7.01840i	−0.194763	+	0.224769i
$976$		0			0
$977$	−3.20624	−	22.2999i	−0.102577	−	0.713436i	−0.974597	−	0.223966i	$-0.928099\pi$
$977$	−3.20624	−	22.2999i	−0.102577	−	0.713436i	0.872020	−	0.489470i	$-0.162810\pi$
$978$		0			0
$979$	−26.1271	+	16.7908i	−0.835025	+	0.536638i
$980$		0			0
$981$	−6.60473	+	14.4623i	−0.210873	+	0.461747i
$982$		0			0
$983$	43.6709	−	12.8229i	1.39288	−	0.408988i	0.502650	−	0.864490i	$-0.332359\pi$
$983$	43.6709	−	12.8229i	1.39288	−	0.408988i	0.890235	+	0.455502i	$0.150540\pi$
$984$		0			0
$985$	71.0667	+	20.8671i	2.26437	+	0.664880i
$986$		0			0
$987$	4.12933	−	28.7201i	0.131438	−	0.914171i
$988$		0			0
$989$	−14.1322	−	0.923736i	−0.449379	−	0.0293731i
$990$		0			0
$991$	0.355063	−	2.46952i	0.0112790	−	0.0784469i	−0.983405	−	0.181427i	$-0.941929\pi$
$991$	0.355063	−	2.46952i	0.0112790	−	0.0784469i	0.994683	+	0.102980i	$0.0328376\pi$
$992$		0			0
$993$	26.2753	+	7.71512i	0.833821	+	0.244832i
$994$		0			0
$995$	−20.0874	+	5.89821i	−0.636815	+	0.186986i
$996$		0			0
$997$	17.0870	−	37.4152i	0.541149	−	1.18495i	−0.419645	−	0.907689i	$-0.637845\pi$
$997$	17.0870	−	37.4152i	0.541149	−	1.18495i	0.960794	−	0.277263i	$-0.0894275\pi$
$998$		0			0
$999$	0.471813	−	0.303216i	0.0149275	−	0.00959331i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.49.1	✓	30	23.3	even	11	inner
552.2.q.c.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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.29838 - 2.65247i) q^{5} +(-2.05854 - 1.32294i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-2.29838 - 2.65247i) q^{5} +(-2.05854 - 1.32294i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(0.516583 + 3.59291i) q^{11} +(-1.06754 + 0.686067i) q^{13} +(-1.45799 + 3.19256i) q^{15} +(-3.04373 + 0.893720i) q^{17} +(5.42582 + 1.59316i) q^{19} +(-0.348244 + 2.42209i) q^{21} +(-2.27256 + 4.22321i) q^{23} +(-1.04148 + 7.24368i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-3.58685 + 1.05319i) q^{29} +(1.20314 - 2.63450i) q^{31} +(3.05363 - 1.96245i) q^{33} +(1.22224 + 8.50086i) q^{35} +(0.367275 - 0.423858i) q^{37} +(1.06754 + 0.686067i) q^{39} +(-6.77685 - 7.82090i) q^{41} +(1.22675 + 2.68620i) q^{43} +3.50972 q^{45} -11.8576 q^{47} +(-0.420491 - 0.920747i) q^{49} +(2.07737 + 2.39741i) q^{51} +(-9.81751 - 6.30933i) q^{53} +(8.34280 - 9.62810i) q^{55} +(-0.804773 - 5.59732i) q^{57} +(9.75532 - 6.26936i) q^{59} +(-2.34534 + 5.13557i) q^{61} +(2.34787 - 0.689398i) q^{63} +(4.27339 + 1.25478i) q^{65} +(-1.66547 + 11.5836i) q^{67} +(4.78562 + 0.312806i) q^{69} +(-0.110048 + 0.765404i) q^{71} +(-13.7538 - 4.03848i) q^{73} +(7.02173 - 2.06177i) q^{75} +(3.68982 - 8.07957i) q^{77} +(-5.98253 + 3.84474i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-2.61290 + 3.01545i) q^{83} +(9.36622 + 6.01931i) q^{85} +(2.44805 + 2.82520i) q^{87} +(3.55432 + 7.78287i) q^{89} +3.10521 q^{91} -2.89622 q^{93} +(-8.24477 - 18.0535i) q^{95} +(-5.63529 - 6.50347i) q^{97} +(-3.05363 - 1.96245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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