LMFDB - Embedded newform 552.2.q.d.193.1

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			193.1
Character	$\chi$	$=$	552.193
Dual form			552.2.q.d.409.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-0.280570 - 1.95141i) q^{5} +(1.41601 - 3.10064i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-0.280570 - 1.95141i) q^{5} +(1.41601 - 3.10064i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-5.15073 - 1.51239i) q^{11} +(-2.46573 - 5.39919i) q^{13} +(1.29104 - 1.48994i) q^{15} +(-0.305847 - 0.196556i) q^{17} +(-0.994958 + 0.639421i) q^{19} +(3.27060 - 0.960334i) q^{21} +(1.02979 + 4.68397i) q^{23} +(1.06818 - 0.313647i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(0.983903 + 0.632316i) q^{29} +(-0.519228 + 0.599221i) q^{31} +(-2.23002 - 4.88307i) q^{33} +(-6.44791 - 1.89328i) q^{35} +(1.18016 - 8.20819i) q^{37} +(2.46573 - 5.39919i) q^{39} +(0.106194 + 0.738593i) q^{41} +(4.42802 + 5.11020i) q^{43} +1.97148 q^{45} +12.3892 q^{47} +(-3.02484 - 3.49085i) q^{49} +(-0.0517400 - 0.359860i) q^{51} +(1.43442 - 3.14093i) q^{53} +(-1.50615 + 10.4755i) q^{55} +(-1.13480 - 0.333208i) q^{57} +(1.36210 + 2.98259i) q^{59} +(6.91855 - 7.98443i) q^{61} +(2.86756 + 1.84287i) q^{63} +(-9.84423 + 6.32650i) q^{65} +(10.9964 - 3.22884i) q^{67} +(-2.86554 + 3.84561i) q^{69} +(-9.31062 + 2.73385i) q^{71} +(0.510932 - 0.328356i) q^{73} +(0.936549 + 0.601884i) q^{75} +(-11.9829 + 13.8290i) q^{77} +(6.00460 + 13.1482i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.783317 - 5.44809i) q^{83} +(-0.297749 + 0.651980i) q^{85} +(0.166447 + 1.15766i) q^{87} +(-7.37709 - 8.51362i) q^{89} -20.2325 q^{91} -0.792882 q^{93} +(1.52693 + 1.76217i) q^{95} +(-1.24037 - 8.62699i) q^{97} +(2.23002 - 4.88307i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−0.280570	−	1.95141i	−0.125475	−	0.872697i	−0.951189	−	0.308609i	$-0.900137\pi$
$5$	−0.280570	−	1.95141i	−0.125475	−	0.872697i	0.825714	−	0.564089i	$-0.190772\pi$
$6$		0			0
$7$	1.41601	−	3.10064i	0.535203	−	1.17193i	−0.428153	−	0.903706i	$-0.640836\pi$
$7$	1.41601	−	3.10064i	0.535203	−	1.17193i	0.963356	−	0.268225i	$-0.0864371\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−5.15073	−	1.51239i	−1.55300	−	0.456003i	−0.611008	−	0.791625i	$-0.709236\pi$
$11$	−5.15073	−	1.51239i	−1.55300	−	0.456003i	−0.941997	+	0.335621i	$0.891054\pi$
$12$		0			0
$13$	−2.46573	−	5.39919i	−0.683870	−	1.49747i	−0.858490	−	0.512831i	$-0.828597\pi$
$13$	−2.46573	−	5.39919i	−0.683870	−	1.49747i	0.174619	−	0.984636i	$-0.444131\pi$
$14$		0			0
$15$	1.29104	−	1.48994i	0.333346	−	0.384702i
$16$		0			0
$17$	−0.305847	−	0.196556i	−0.0741787	−	0.0476717i	0.503026	−	0.864271i	$-0.332220\pi$
$17$	−0.305847	−	0.196556i	−0.0741787	−	0.0476717i	−0.577204	+	0.816600i	$0.695856\pi$
$18$		0			0
$19$	−0.994958	+	0.639421i	−0.228259	+	0.146693i	−0.649772	−	0.760129i	$-0.725136\pi$
$19$	−0.994958	+	0.639421i	−0.228259	+	0.146693i	0.421513	+	0.906822i	$0.361499\pi$
$20$		0			0
$21$	3.27060	−	0.960334i	0.713703	−	0.209562i
$22$		0			0
$23$	1.02979	+	4.68397i	0.214726	+	0.976674i
$23$	1.02979	+	4.68397i	0.214726	+	0.976674i
$24$		0			0
$25$	1.06818	−	0.313647i	0.213637	−	0.0627294i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	0.983903	+	0.632316i	0.182706	+	0.117418i	0.628797	−	0.777570i	$-0.283548\pi$
$29$	0.983903	+	0.632316i	0.182706	+	0.117418i	−0.446091	+	0.894988i	$0.647184\pi$
$30$		0			0
$31$	−0.519228	+	0.599221i	−0.0932560	+	0.107623i	−0.800459	−	0.599387i	$-0.795411\pi$
$31$	−0.519228	+	0.599221i	−0.0932560	+	0.107623i	0.707203	+	0.707010i	$0.249957\pi$
$32$		0			0
$33$	−2.23002	−	4.88307i	−0.388197	−	0.850034i
$34$		0			0
$35$	−6.44791	−	1.89328i	−1.08990	−	0.320022i
$36$		0			0
$37$	1.18016	−	8.20819i	0.194017	−	1.34942i	−0.627225	−	0.778838i	$-0.715809\pi$
$37$	1.18016	−	8.20819i	0.194017	−	1.34942i	0.821242	−	0.570580i	$-0.193282\pi$
$38$		0			0
$39$	2.46573	−	5.39919i	0.394833	−	0.864563i
$40$		0			0
$41$	0.106194	+	0.738593i	0.0165847	+	0.115349i	0.996432	−	0.0843986i	$-0.0268969\pi$
$41$	0.106194	+	0.738593i	0.0165847	+	0.115349i	−0.979847	+	0.199747i	$0.935988\pi$
$42$		0			0
$43$	4.42802	+	5.11020i	0.675266	+	0.779299i	0.985191	−	0.171462i	$-0.0548492\pi$
$43$	4.42802	+	5.11020i	0.675266	+	0.779299i	−0.309924	+	0.950761i	$0.600304\pi$
$44$		0			0
$45$	1.97148			0.293890
$46$		0			0
$47$	12.3892			1.80716			0.903578	−	0.428424i	$-0.140931\pi$
$47$	12.3892			1.80716			0.903578	+	0.428424i	$0.140931\pi$
$48$		0			0
$49$	−3.02484	−	3.49085i	−0.432120	−	0.498693i
$50$		0			0
$51$	−0.0517400	−	0.359860i	−0.00724506	−	0.0503905i
$52$		0			0
$53$	1.43442	−	3.14093i	0.197032	−	0.431440i	−0.785167	−	0.619285i	$-0.787423\pi$
$53$	1.43442	−	3.14093i	0.197032	−	0.431440i	0.982199	+	0.187844i	$0.0601500\pi$
$54$		0			0
$55$	−1.50615	+	10.4755i	−0.203090	+	1.41252i
$56$		0			0
$57$	−1.13480	−	0.333208i	−0.150308	−	0.0441344i
$58$		0			0
$59$	1.36210	+	2.98259i	0.177331	+	0.388300i	0.977336	−	0.211693i	$-0.0678975\pi$
$59$	1.36210	+	2.98259i	0.177331	+	0.388300i	−0.800006	+	0.599992i	$0.795170\pi$
$60$		0			0
$61$	6.91855	−	7.98443i	0.885829	−	1.02230i	−0.113756	−	0.993509i	$-0.536288\pi$
$61$	6.91855	−	7.98443i	0.885829	−	1.02230i	0.999585	−	0.0287930i	$-0.00916636\pi$
$62$		0			0
$63$	2.86756	+	1.84287i	0.361278	+	0.232180i
$64$		0			0
$65$	−9.84423	+	6.32650i	−1.22103	+	0.784706i
$66$		0			0
$67$	10.9964	−	3.22884i	1.34343	−	0.394466i	0.470536	−	0.882381i	$-0.344060\pi$
$67$	10.9964	−	3.22884i	1.34343	−	0.394466i	0.872891	+	0.487915i	$0.162242\pi$
$68$		0			0
$69$	−2.86554	+	3.84561i	−0.344970	+	0.462957i
$70$		0			0
$71$	−9.31062	+	2.73385i	−1.10497	+	0.324448i	−0.782824	−	0.622243i	$-0.786222\pi$
$71$	−9.31062	+	2.73385i	−1.10497	+	0.324448i	−0.322144	+	0.946691i	$0.604403\pi$
$72$		0			0
$73$	0.510932	−	0.328356i	0.0598001	−	0.0384312i	−0.510399	−	0.859938i	$-0.670502\pi$
$73$	0.510932	−	0.328356i	0.0598001	−	0.0384312i	0.570199	+	0.821506i	$0.306866\pi$
$74$		0			0
$75$	0.936549	+	0.601884i	0.108143	+	0.0694996i
$76$		0			0
$77$	−11.9829	+	13.8290i	−1.36558	+	1.57596i
$78$		0			0
$79$	6.00460	+	13.1482i	0.675570	+	1.47929i	0.867270	+	0.497838i	$0.165873\pi$
$79$	6.00460	+	13.1482i	0.675570	+	1.47929i	−0.191700	+	0.981454i	$0.561400\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	0.783317	−	5.44809i	0.0859802	−	0.598006i	−0.900590	−	0.434669i	$-0.856865\pi$
$83$	0.783317	−	5.44809i	0.0859802	−	0.598006i	0.986570	−	0.163336i	$-0.0522256\pi$
$84$		0			0
$85$	−0.297749	+	0.651980i	−0.0322954	+	0.0707171i
$86$		0			0
$87$	0.166447	+	1.15766i	0.0178450	+	0.124114i
$88$		0			0
$89$	−7.37709	−	8.51362i	−0.781970	−	0.902442i	0.215280	−	0.976552i	$-0.430934\pi$
$89$	−7.37709	−	8.51362i	−0.781970	−	0.902442i	−0.997250	+	0.0741104i	$0.976388\pi$
$90$		0			0
$91$	−20.2325			−2.12094
$92$		0			0
$93$	−0.792882			−0.0822181
$94$		0			0
$95$	1.52693	+	1.76217i	0.156659	+	0.180795i
$96$		0			0
$97$	−1.24037	−	8.62699i	−0.125941	−	0.875938i	−0.950625	−	0.310343i	$-0.899556\pi$
$97$	−1.24037	−	8.62699i	−0.125941	−	0.875938i	0.824684	−	0.565594i	$-0.191353\pi$
$98$		0			0
$99$	2.23002	−	4.88307i	0.224126	−	0.490767i
$100$		0			0
$101$	−1.83823	+	12.7851i	−0.182910	+	1.27217i	0.666926	+	0.745124i	$0.267610\pi$
$101$	−1.83823	+	12.7851i	−0.182910	+	1.27217i	−0.849837	+	0.527046i	$0.823299\pi$
$102$		0			0
$103$	−9.88370	−	2.90211i	−0.973869	−	0.285954i	−0.244178	−	0.969730i	$-0.578518\pi$
$103$	−9.88370	−	2.90211i	−0.973869	−	0.285954i	−0.729691	+	0.683777i	$0.760336\pi$
$104$		0			0
$105$	−2.79164	−	6.11284i	−0.272436	−	0.596552i
$106$		0			0
$107$	−3.15022	+	3.63555i	−0.304543	+	0.351462i	−0.887306	−	0.461180i	$-0.847426\pi$
$107$	−3.15022	+	3.63555i	−0.304543	+	0.351462i	0.582763	+	0.812642i	$0.301972\pi$
$108$		0			0
$109$	16.5761	+	10.6528i	1.58770	+	1.02035i	0.972770	+	0.231774i	$0.0744530\pi$
$109$	16.5761	+	10.6528i	1.58770	+	1.02035i	0.614932	+	0.788580i	$0.289183\pi$
$110$		0			0
$111$	6.97618	−	4.48332i	0.662150	−	0.425538i
$112$		0			0
$113$	−5.89736	+	1.73162i	−0.554777	+	0.162897i	−0.547091	−	0.837073i	$-0.684265\pi$
$113$	−5.89736	+	1.73162i	−0.554777	+	0.162897i	−0.00768613	+	0.999970i	$0.502447\pi$
$114$		0			0
$115$	8.85141	−	3.32372i	0.825398	−	0.309939i
$116$		0			0
$117$	5.69515	−	1.67225i	0.526517	−	0.154599i
$118$		0			0
$119$	−1.04253	+	0.669994i	−0.0955687	+	0.0614182i
$120$		0			0
$121$	14.9889	+	9.63281i	1.36263	+	0.875710i
$122$		0			0
$123$	−0.488649	+	0.563932i	−0.0440600	+	0.0508480i
$124$		0			0
$125$	−5.00666	−	10.9631i	−0.447809	−	0.980566i
$126$		0			0
$127$	−7.60578	−	2.23326i	−0.674904	−	0.198170i	−0.0737182	−	0.997279i	$-0.523487\pi$
$127$	−7.60578	−	2.23326i	−0.674904	−	0.198170i	−0.601186	+	0.799109i	$0.705305\pi$
$128$		0			0
$129$	−0.962300	+	6.69295i	−0.0847258	+	0.589281i
$130$		0			0
$131$	−3.16382	+	6.92779i	−0.276424	+	0.605284i	−0.996022	−	0.0891068i	$-0.971599\pi$
$131$	−3.16382	+	6.92779i	−0.276424	+	0.605284i	0.719598	+	0.694391i	$0.244326\pi$
$132$		0			0
$133$	0.573738	+	3.99043i	0.0497494	+	0.346014i
$134$		0			0
$135$	1.29104	+	1.48994i	0.111115	+	0.128234i
$136$		0			0
$137$	17.4299			1.48914			0.744569	−	0.667546i	$-0.232655\pi$
$137$	17.4299			1.48914			0.744569	+	0.667546i	$0.232655\pi$
$138$		0			0
$139$	−12.0155			−1.01914			−0.509569	−	0.860430i	$-0.670195\pi$
$139$	−12.0155			−1.01914			−0.509569	+	0.860430i	$0.670195\pi$
$140$		0			0
$141$	8.11322	+	9.36316i	0.683257	+	0.788520i
$142$		0			0
$143$	4.53462	+	31.5390i	0.379204	+	2.63742i
$144$		0			0
$145$	0.957854	−	2.09741i	0.0795454	−	0.174180i
$146$		0			0
$147$	0.657360	−	4.57204i	0.0542182	−	0.377096i
$148$		0			0
$149$	−12.6685	−	3.71981i	−1.03784	−	0.304739i	−0.281948	−	0.959430i	$-0.590981\pi$
$149$	−12.6685	−	3.71981i	−1.03784	−	0.304739i	−0.755897	+	0.654691i	$0.772799\pi$
$150$		0			0
$151$	5.05353	+	11.0657i	0.411251	+	0.900513i	0.996005	+	0.0893025i	$0.0284638\pi$
$151$	5.05353	+	11.0657i	0.411251	+	0.900513i	−0.584754	+	0.811211i	$0.698809\pi$
$152$		0			0
$153$	0.238081	−	0.274761i	0.0192477	−	0.0222131i
$154$		0			0
$155$	1.31500	+	0.845102i	0.105624	+	0.0678803i
$156$		0			0
$157$	8.47504	−	5.44658i	0.676382	−	0.434684i	−0.156839	−	0.987624i	$-0.550130\pi$
$157$	8.47504	−	5.44658i	0.676382	−	0.434684i	0.833221	+	0.552940i	$0.186494\pi$
$158$		0			0
$159$	3.31310	−	0.972815i	0.262746	−	0.0771492i
$160$		0			0
$161$	15.9815	+	3.43956i	1.25952	+	0.271075i
$162$		0			0
$163$	−15.3807	+	4.51619i	−1.20471	+	0.353735i	−0.821653	−	0.569988i	$-0.806948\pi$
$163$	−15.3807	+	4.51619i	−1.20471	+	0.353735i	−0.383060	+	0.923724i	$0.625130\pi$
$164$		0			0
$165$	−8.90320	+	5.72174i	−0.693113	+	0.445437i
$166$		0			0
$167$	2.41211	+	1.55017i	0.186654	+	0.119955i	0.630631	−	0.776083i	$-0.282796\pi$
$167$	2.41211	+	1.55017i	0.186654	+	0.119955i	−0.443976	+	0.896038i	$0.646433\pi$
$168$		0			0
$169$	−14.5583	+	16.8012i	−1.11987	+	1.29240i
$170$		0			0
$171$	−0.491315	−	1.07583i	−0.0375718	−	0.0822708i
$172$		0			0
$173$	−1.83830	−	0.539774i	−0.139763	−	0.0410382i	0.211103	−	0.977464i	$-0.432295\pi$
$173$	−1.83830	−	0.539774i	−0.139763	−	0.0410382i	−0.350866	+	0.936426i	$0.614113\pi$
$174$		0			0
$175$	0.540057	−	3.75618i	0.0408245	−	0.283940i
$176$		0			0
$177$	−1.36210	+	2.98259i	−0.102382	+	0.224185i
$178$		0			0
$179$	−3.17333	−	22.0710i	−0.237186	−	1.64967i	−0.665765	−	0.746161i	$-0.731895\pi$
$179$	−3.17333	−	22.0710i	−0.237186	−	1.64967i	0.428579	−	0.903504i	$-0.359014\pi$
$180$		0			0
$181$	−5.95267	−	6.86974i	−0.442458	−	0.510624i	0.490089	−	0.871673i	$-0.336964\pi$
$181$	−5.95267	−	6.86974i	−0.442458	−	0.510624i	−0.932547	+	0.361048i	$0.882419\pi$
$182$		0			0
$183$	10.5649			0.780981
$184$		0			0
$185$	−16.3487			−1.20198
$186$		0			0
$187$	1.27806	+	1.47497i	0.0934614	+	0.107860i
$188$		0			0
$189$	0.485105	+	3.37398i	0.0352862	+	0.245421i
$190$		0			0
$191$	6.87419	−	15.0524i	0.497399	−	1.08915i	−0.479907	−	0.877319i	$-0.659330\pi$
$191$	6.87419	−	15.0524i	0.497399	−	1.08915i	0.977306	−	0.211832i	$-0.0679430\pi$
$192$		0			0
$193$	1.46386	−	10.1814i	0.105371	−	0.732871i	−0.866810	−	0.498639i	$-0.833833\pi$
$193$	1.46386	−	10.1814i	0.105371	−	0.732871i	0.972181	−	0.234232i	$-0.0752575\pi$
$194$		0			0
$195$	−11.2279	−	3.29680i	−0.804043	−	0.236088i
$196$		0			0
$197$	9.85357	+	21.5763i	0.702037	+	1.53725i	0.837483	+	0.546463i	$0.184026\pi$
$197$	9.85357	+	21.5763i	0.702037	+	1.53725i	−0.135446	+	0.990785i	$0.543247\pi$
$198$		0			0
$199$	10.1538	−	11.7181i	0.719782	−	0.830673i	−0.271498	−	0.962439i	$-0.587519\pi$
$199$	10.1538	−	11.7181i	0.719782	−	0.830673i	0.991281	+	0.131766i	$0.0420647\pi$
$200$		0			0
$201$	9.64133	+	6.19610i	0.680047	+	0.437040i
$202$		0			0
$203$	3.35380	−	2.15536i	0.235391	−	0.151277i
$204$		0			0
$205$	1.41150	−	0.414455i	0.0985837	−	0.0289468i
$206$		0			0
$207$	−4.78284	+	0.352710i	−0.332431	+	0.0245151i
$208$		0			0
$209$	6.09182	−	1.78872i	0.421380	−	0.123728i
$210$		0			0
$211$	21.6165	−	13.8921i	1.48814	−	0.956372i	0.491820	−	0.870697i	$-0.336332\pi$
$211$	21.6165	−	13.8921i	1.48814	−	0.956372i	0.996323	−	0.0856750i	$-0.0273047\pi$
$212$		0			0
$213$	−8.16326	−	5.24621i	−0.559338	−	0.359464i
$214$		0			0
$215$	8.72974	−	10.0747i	0.595363	−	0.687086i
$216$		0			0
$217$	1.12273	+	2.45844i	0.0762161	+	0.166890i
$218$		0			0
$219$	0.582744	+	0.171109i	0.0393782	+	0.0115625i
$220$		0			0
$221$	−0.307107	+	2.13598i	−0.0206583	+	0.143681i
$222$		0			0
$223$	−8.35935	+	18.3044i	−0.559783	+	1.22575i	0.392278	+	0.919847i	$0.371687\pi$
$223$	−8.35935	+	18.3044i	−0.559783	+	1.22575i	−0.952061	+	0.305908i	$0.901040\pi$
$224$		0			0
$225$	0.158436	+	1.10195i	0.0105624	+	0.0734631i
$226$		0			0
$227$	−7.93174	−	9.15371i	−0.526448	−	0.607553i	0.428786	−	0.903406i	$-0.358942\pi$
$227$	−7.93174	−	9.15371i	−0.526448	−	0.607553i	−0.955233	+	0.295853i	$0.904396\pi$
$228$		0			0
$229$	−13.9307			−0.920566			−0.460283	−	0.887772i	$-0.652252\pi$
$229$	−13.9307			−0.920566			−0.460283	+	0.887772i	$0.652252\pi$
$230$		0			0
$231$	−18.2984			−1.20395
$232$		0			0
$233$	16.6960	+	19.2682i	1.09379	+	1.26230i	0.962595	+	0.270944i	$0.0873357\pi$
$233$	16.6960	+	19.2682i	1.09379	+	1.26230i	0.131194	+	0.991357i	$0.458119\pi$
$234$		0			0
$235$	−3.47605	−	24.1765i	−0.226753	−	1.57710i
$236$		0			0
$237$	−6.00460	+	13.1482i	−0.390041	+	0.854070i
$238$		0			0
$239$	3.42048	−	23.7899i	0.221252	−	1.53884i	−0.512060	−	0.858950i	$-0.671117\pi$
$239$	3.42048	−	23.7899i	0.221252	−	1.53884i	0.733312	−	0.679893i	$-0.237974\pi$
$240$		0			0
$241$	7.78547	+	2.28602i	0.501506	+	0.147256i	0.522695	−	0.852520i	$-0.324927\pi$
$241$	7.78547	+	2.28602i	0.501506	+	0.147256i	−0.0211884	+	0.999776i	$0.506745\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−5.96340	+	6.88213i	−0.380988	+	0.439683i
$246$		0			0
$247$	5.90565	+	3.79533i	0.375768	+	0.241491i
$248$		0			0
$249$	4.63036	−	2.97575i	0.293437	−	0.188580i
$250$		0			0
$251$	2.20616	−	0.647787i	0.139252	−	0.0408879i	−0.211364	−	0.977407i	$-0.567791\pi$
$251$	2.20616	−	0.647787i	0.139252	−	0.0408879i	0.350616	+	0.936519i	$0.385972\pi$
$252$		0			0
$253$	1.77982	−	25.6833i	0.111896	−	1.61470i
$254$		0			0
$255$	−0.687718	+	0.201932i	−0.0430665	+	0.0126455i
$256$		0			0
$257$	13.8900	−	8.92658i	0.866436	−	0.556825i	−0.0302247	−	0.999543i	$-0.509622\pi$
$257$	13.8900	−	8.92658i	0.866436	−	0.556825i	0.896661	+	0.442719i	$0.145986\pi$
$258$		0			0
$259$	−23.7795	−	15.2822i	−1.47759	−	0.949588i
$260$		0			0
$261$	−0.765904	+	0.883900i	−0.0474083	+	0.0547120i
$262$		0			0
$263$	−5.63672	−	12.3427i	−0.347575	−	0.761083i	−0.999995	−	0.00322547i	$-0.998973\pi$
$263$	−5.63672	−	12.3427i	−0.347575	−	0.761083i	0.652420	−	0.757858i	$-0.273754\pi$
$264$		0			0
$265$	−6.53171	−	1.91788i	−0.401239	−	0.117815i
$266$		0			0
$267$	1.60320	−	11.1505i	0.0981140	−	0.682398i
$268$		0			0
$269$	6.90560	−	15.1211i	0.421042	−	0.921953i	−0.573655	−	0.819097i	$-0.694475\pi$
$269$	6.90560	−	15.1211i	0.421042	−	0.921953i	0.994696	−	0.102855i	$-0.0327979\pi$
$270$		0			0
$271$	2.42323	+	16.8539i	0.147200	+	1.02380i	0.920774	+	0.390096i	$0.127558\pi$
$271$	2.42323	+	16.8539i	0.147200	+	1.02380i	−0.773574	+	0.633706i	$0.781533\pi$
$272$		0			0
$273$	−13.2494	−	15.2907i	−0.801893	−	0.925434i
$274$		0			0
$275$	−5.97628			−0.360383
$276$		0			0
$277$	−17.4222			−1.04680			−0.523398	−	0.852088i	$-0.675336\pi$
$277$	−17.4222			−1.04680			−0.523398	+	0.852088i	$0.675336\pi$
$278$		0			0
$279$	−0.519228	−	0.599221i	−0.0310853	−	0.0358744i
$280$		0			0
$281$	1.56461	+	10.8821i	0.0933368	+	0.649172i	0.981757	+	0.190140i	$0.0608943\pi$
$281$	1.56461	+	10.8821i	0.0933368	+	0.649172i	−0.888420	+	0.459031i	$0.848197\pi$
$282$		0			0
$283$	−5.95461	+	13.0388i	−0.353965	+	0.775074i	0.645967	+	0.763365i	$0.276454\pi$
$283$	−5.95461	+	13.0388i	−0.353965	+	0.775074i	−0.999931	+	0.0117089i	$0.996273\pi$
$284$		0			0
$285$	−0.331833	+	2.30795i	−0.0196561	+	0.136711i
$286$		0			0
$287$	2.44048	+	0.716590i	0.144057	+	0.0422990i
$288$		0			0
$289$	−7.00715	−	15.3435i	−0.412185	−	0.902560i
$290$		0			0
$291$	5.70757	−	6.58689i	0.334584	−	0.386130i
$292$		0			0
$293$	1.04799	+	0.673499i	0.0612240	+	0.0393462i	0.570895	−	0.821023i	$-0.306596\pi$
$293$	1.04799	+	0.673499i	0.0612240	+	0.0393462i	−0.509671	+	0.860370i	$0.670233\pi$
$294$		0			0
$295$	5.43809	−	3.49485i	0.316618	−	0.203478i
$296$		0			0
$297$	5.15073	−	1.51239i	0.298876	−	0.0877579i
$298$		0			0
$299$	22.7505	−	17.1094i	1.31569	−	0.989464i
$300$		0			0
$301$	22.1150	−	6.49356i	1.27469	−	0.374283i
$302$		0			0
$303$	−10.8662	+	6.98325i	−0.624244	+	0.401177i
$304$		0			0
$305$	−17.5220	−	11.2607i	−1.00331	−	0.644788i
$306$		0			0
$307$	−0.401621	+	0.463496i	−0.0229217	+	0.0264531i	−0.767095	−	0.641534i	$-0.778298\pi$
$307$	−0.401621	+	0.463496i	−0.0229217	+	0.0264531i	0.744173	+	0.667987i	$0.232844\pi$
$308$		0			0
$309$	−4.27917	−	9.37008i	−0.243434	−	0.533045i
$310$		0			0
$311$	−3.90663	−	1.14709i	−0.221525	−	0.0650455i	0.169087	−	0.985601i	$-0.445918\pi$
$311$	−3.90663	−	1.14709i	−0.221525	−	0.0650455i	−0.390611	+	0.920556i	$0.627736\pi$
$312$		0			0
$313$	−4.68400	+	32.5779i	−0.264755	+	1.84141i	0.231003	+	0.972953i	$0.425799\pi$
$313$	−4.68400	+	32.5779i	−0.264755	+	1.84141i	−0.495759	+	0.868460i	$0.665110\pi$
$314$		0			0
$315$	2.79164	−	6.11284i	0.157291	−	0.344419i
$316$		0			0
$317$	−0.261861	−	1.82129i	−0.0147076	−	0.102294i	0.981145	−	0.193272i	$-0.0619098\pi$
$317$	−0.261861	−	1.82129i	−0.0147076	−	0.102294i	−0.995853	+	0.0909779i	$0.971001\pi$
$318$		0			0
$319$	−4.11151	−	4.74494i	−0.230200	−	0.265666i
$320$		0			0
$321$	−4.81052			−0.268497
$322$		0			0
$323$	0.429986			0.0239251
$324$		0			0
$325$	−4.32729	−	4.99396i	−0.240035	−	0.277015i
$326$		0			0
$327$	2.80418	+	19.5035i	0.155071	+	1.07855i
$328$		0			0
$329$	17.5433	−	38.4145i	0.967195	−	2.11786i
$330$		0			0
$331$	−2.72253	+	18.9356i	−0.149644	+	1.04080i	0.767159	+	0.641457i	$0.221670\pi$
$331$	−2.72253	+	18.9356i	−0.149644	+	1.04080i	−0.916803	+	0.399340i	$0.869239\pi$
$332$		0			0
$333$	7.95669	+	2.33630i	0.436024	+	0.128028i
$334$		0			0
$335$	−9.38607	−	20.5526i	−0.512816	−	1.12291i
$336$		0			0
$337$	−10.4528	+	12.0631i	−0.569398	+	0.657120i	−0.965291	−	0.261176i	$-0.915890\pi$
$337$	−10.4528	+	12.0631i	−0.569398	+	0.657120i	0.395893	+	0.918297i	$0.370435\pi$
$338$		0			0
$339$	−5.17062	−	3.32296i	−0.280830	−	0.180478i
$340$		0			0
$341$	3.58066	−	2.30115i	0.193904	−	0.124614i
$342$		0			0
$343$	7.78711	−	2.28650i	0.420464	−	0.123459i
$344$		0			0
$345$	8.30834	+	4.51287i	0.447306	+	0.242965i
$346$		0			0
$347$	−5.98749	+	1.75809i	−0.321425	+	0.0943790i	−0.438465	−	0.898748i	$-0.644478\pi$
$347$	−5.98749	+	1.75809i	−0.321425	+	0.0943790i	0.117040	+	0.993127i	$0.462659\pi$
$348$		0			0
$349$	23.2736	−	14.9570i	1.24581	−	0.800631i	0.259530	−	0.965735i	$-0.416432\pi$
$349$	23.2736	−	14.9570i	1.24581	−	0.800631i	0.986276	+	0.165104i	$0.0527959\pi$
$350$		0			0
$351$	4.99333	+	3.20902i	0.266524	+	0.171285i
$352$		0			0
$353$	−3.27243	+	3.77659i	−0.174174	+	0.201007i	−0.836124	−	0.548541i	$-0.815184\pi$
$353$	−3.27243	+	3.77659i	−0.174174	+	0.201007i	0.661950	+	0.749548i	$0.269729\pi$
$354$		0			0
$355$	7.94714	+	17.4018i	0.421790	+	0.923592i
$356$		0			0
$357$	−1.18906	−	0.349140i	−0.0629317	−	0.0184784i
$358$		0			0
$359$	0.924782	−	6.43200i	0.0488081	−	0.339468i	−0.950756	−	0.309941i	$-0.899691\pi$
$359$	0.924782	−	6.43200i	0.0488081	−	0.339468i	0.999564	−	0.0295271i	$-0.00940015\pi$
$360$		0			0
$361$	−7.31180	+	16.0106i	−0.384832	+	0.842664i
$362$		0			0
$363$	2.53568	+	17.6360i	0.133089	+	0.925652i
$364$		0			0
$365$	−0.784110	−	0.904911i	−0.0410422	−	0.0473652i
$366$		0			0
$367$	15.3594			0.801754			0.400877	−	0.916132i	$-0.368705\pi$
$367$	15.3594			0.801754			0.400877	+	0.916132i	$0.368705\pi$
$368$		0			0
$369$	−0.746188			−0.0388450
$370$		0			0
$371$	−7.70775	−	8.89521i	−0.400166	−	0.461816i
$372$		0			0
$373$	4.15294	+	28.8843i	0.215031	+	1.49557i	0.756023	+	0.654545i	$0.227140\pi$
$373$	4.15294	+	28.8843i	0.215031	+	1.49557i	−0.540992	+	0.841028i	$0.681951\pi$
$374$		0			0
$375$	5.00666	−	10.9631i	0.258543	−	0.566130i
$376$		0			0
$377$	0.987959	−	6.87140i	0.0508825	−	0.353895i
$378$		0			0
$379$	−22.3081	−	6.55026i	−1.14589	−	0.336464i	−0.346956	−	0.937881i	$-0.612785\pi$
$379$	−22.3081	−	6.55026i	−1.14589	−	0.336464i	−0.798935	+	0.601417i	$0.794603\pi$
$380$		0			0
$381$	−3.29294	−	7.21054i	−0.168703	−	0.369407i
$382$		0			0
$383$	17.7155	−	20.4448i	0.905221	−	1.04468i	−0.0935742	−	0.995612i	$-0.529829\pi$
$383$	17.7155	−	20.4448i	0.905221	−	1.04468i	0.998795	−	0.0490687i	$-0.0156253\pi$
$384$		0			0
$385$	30.3481	+	19.5035i	1.54668	+	0.993992i
$386$		0			0
$387$	−5.68836	+	3.65569i	−0.289156	+	0.185829i
$388$		0			0
$389$	15.6424	−	4.59301i	0.793100	−	0.232875i	0.140004	−	0.990151i	$-0.455288\pi$
$389$	15.6424	−	4.59301i	0.793100	−	0.232875i	0.653095	+	0.757276i	$0.273470\pi$
$390$		0			0
$391$	0.605702	−	1.63499i	0.0306317	−	0.0826848i
$392$		0			0
$393$	−7.30753	+	2.14569i	−0.368616	+	0.108236i
$394$		0			0
$395$	23.9729	−	15.4064i	1.20621	−	0.775182i
$396$		0			0
$397$	−18.0194	−	11.5804i	−0.904370	−	0.581203i	0.00371317	−	0.999993i	$-0.498818\pi$
$397$	−18.0194	−	11.5804i	−0.904370	−	0.581203i	−0.908083	+	0.418790i	$0.862454\pi$
$398$		0			0
$399$	−2.64005	+	3.04678i	−0.132168	+	0.152530i
$400$		0			0
$401$	2.42072	+	5.30064i	0.120885	+	0.264701i	0.960395	−	0.278644i	$-0.0898849\pi$
$401$	2.42072	+	5.30064i	0.120885	+	0.264701i	−0.839510	+	0.543345i	$0.817158\pi$
$402$		0			0
$403$	4.51558	+	1.32589i	0.224937	+	0.0660475i
$404$		0			0
$405$	−0.280570	+	1.95141i	−0.0139417	+	0.0969664i
$406$		0			0
$407$	−18.4927	+	40.4934i	−0.916649	+	2.00718i
$408$		0			0
$409$	−2.45687	−	17.0879i	−0.121484	−	0.844942i	−0.955876	−	0.293770i	$-0.905090\pi$
$409$	−2.45687	−	17.0879i	−0.121484	−	0.844942i	0.834392	−	0.551172i	$-0.185819\pi$
$410$		0			0
$411$	11.4142	+	13.1726i	0.563019	+	0.649759i
$412$		0			0
$413$	11.1767			0.549969
$414$		0			0
$415$	−10.8512			−0.532666
$416$		0			0
$417$	−7.86845	−	9.08068i	−0.385320	−	0.444683i
$418$		0			0
$419$	3.04187	+	21.1567i	0.148605	+	1.03357i	0.918506	+	0.395407i	$0.129397\pi$
$419$	3.04187	+	21.1567i	0.148605	+	1.03357i	−0.769901	+	0.638163i	$0.779694\pi$
$420$		0			0
$421$	0.859294	−	1.88159i	0.0418794	−	0.0917031i	−0.887536	−	0.460738i	$-0.847585\pi$
$421$	0.859294	−	1.88159i	0.0418794	−	0.0917031i	0.929415	+	0.369035i	$0.120312\pi$
$422$		0			0
$423$	−1.76317	+	12.2631i	−0.0857283	+	0.596254i
$424$		0			0
$425$	−0.388349	−	0.114030i	−0.0188377	−	0.00553125i
$426$		0			0
$427$	−14.9601	−	32.7580i	−0.723969	−	1.58527i
$428$		0			0
$429$	−20.8660	+	24.0807i	−1.00742	+	1.16263i
$430$		0			0
$431$	10.1923	+	6.55021i	0.490947	+	0.315512i	0.762586	−	0.646887i	$-0.223929\pi$
$431$	10.1923	+	6.55021i	0.490947	+	0.315512i	−0.271639	+	0.962399i	$0.587566\pi$
$432$		0			0
$433$	−4.08019	+	2.62218i	−0.196082	+	0.126014i	−0.634998	−	0.772514i	$-0.718999\pi$
$433$	−4.08019	+	2.62218i	−0.196082	+	0.126014i	0.438916	+	0.898528i	$0.355363\pi$
$434$		0			0
$435$	2.21238	−	0.649612i	0.106075	−	0.0311465i
$436$		0			0
$437$	−4.01962	−	4.00188i	−0.192285	−	0.191436i
$438$		0			0
$439$	0.0381628	−	0.0112056i	0.00182141	−	0.000534815i	−0.280822	−	0.959760i	$-0.590607\pi$
$439$	0.0381628	−	0.0112056i	0.00182141	−	0.000534815i	0.282643	+	0.959225i	$0.408789\pi$
$440$		0			0
$441$	3.88580	−	2.49725i	0.185038	−	0.118917i
$442$		0			0
$443$	−8.55959	−	5.50091i	−0.406678	−	0.261356i	0.321271	−	0.946987i	$-0.395890\pi$
$443$	−8.55959	−	5.50091i	−0.406678	−	0.261356i	−0.727949	+	0.685631i	$0.759526\pi$
$444$		0			0
$445$	−14.5438	+	16.7844i	−0.689441	+	0.795657i
$446$		0			0
$447$	−5.48487	−	12.0102i	−0.259425	−	0.568062i
$448$		0			0
$449$	−16.3334	−	4.79591i	−0.770819	−	0.226333i	−0.127404	−	0.991851i	$-0.540665\pi$
$449$	−16.3334	−	4.79591i	−0.770819	−	0.226333i	−0.643414	+	0.765518i	$0.722483\pi$
$450$		0			0
$451$	0.570067	−	3.96490i	0.0268434	−	0.186700i
$452$		0			0
$453$	−5.05353	+	11.0657i	−0.237436	+	0.519912i
$454$		0			0
$455$	5.67663	+	39.4818i	0.266125	+	1.85094i
$456$		0			0
$457$	17.2455	+	19.9024i	0.806711	+	0.930994i	0.998729	−	0.0503975i	$-0.0160488\pi$
$457$	17.2455	+	19.9024i	0.806711	+	0.930994i	−0.192019	+	0.981391i	$0.561503\pi$
$458$		0			0
$459$	0.363560			0.0169695
$460$		0			0
$461$	24.1023			1.12256			0.561278	−	0.827627i	$-0.310310\pi$
$461$	24.1023			1.12256			0.561278	+	0.827627i	$0.310310\pi$
$462$		0			0
$463$	−1.32884	−	1.53357i	−0.0617566	−	0.0712709i	0.724031	−	0.689768i	$-0.242287\pi$
$463$	−1.32884	−	1.53357i	−0.0617566	−	0.0712709i	−0.785787	+	0.618497i	$0.787742\pi$
$464$		0			0
$465$	0.222459	+	1.54724i	0.0103163	+	0.0717515i
$466$		0			0
$467$	−9.67692	+	21.1895i	−0.447794	+	0.980533i	0.542307	+	0.840180i	$0.317551\pi$
$467$	−9.67692	+	21.1895i	−0.447794	+	0.980533i	−0.990102	+	0.140353i	$0.955176\pi$
$468$		0			0
$469$	5.55963	−	38.6680i	0.256720	−	1.78552i
$470$		0			0
$471$	9.66622	+	2.83826i	0.445396	+	0.130780i
$472$		0			0
$473$	−15.0789	−	33.0182i	−0.693329	−	1.51818i
$474$		0			0
$475$	−0.862245	+	0.995084i	−0.0395625	+	0.0456576i
$476$		0			0
$477$	2.90482	+	1.86682i	0.133003	+	0.0854757i
$478$		0			0
$479$	12.6148	−	8.10706i	0.576387	−	0.370421i	−0.219733	−	0.975560i	$-0.570519\pi$
$479$	12.6148	−	8.10706i	0.576387	−	0.370421i	0.796120	+	0.605139i	$0.206882\pi$
$480$		0			0
$481$	−47.2276	+	13.8673i	−2.15339	+	0.632293i
$482$		0			0
$483$	7.86620	+	14.3304i	0.357925	+	0.652057i
$484$		0			0
$485$	−16.4868	+	4.84095i	−0.748626	+	0.219816i
$486$		0			0
$487$	22.2335	−	14.2886i	1.00750	−	0.647479i	0.0707530	−	0.997494i	$-0.477460\pi$
$487$	22.2335	−	14.2886i	1.00750	−	0.647479i	0.936744	+	0.350015i	$0.113823\pi$
$488$		0			0
$489$	−13.4854	−	8.66651i	−0.609829	−	0.391913i
$490$		0			0
$491$	0.930801	−	1.07420i	0.0420065	−	0.0484780i	−0.734358	−	0.678763i	$-0.762516\pi$
$491$	0.930801	−	1.07420i	0.0420065	−	0.0484780i	0.776364	+	0.630285i	$0.217062\pi$
$492$		0			0
$493$	−0.176638	−	0.386783i	−0.00795537	−	0.0174198i
$494$		0			0
$495$	−10.1546	−	2.98165i	−0.456413	−	0.134015i
$496$		0			0
$497$	−4.70731	+	32.7400i	−0.211152	+	1.46859i
$498$		0			0
$499$	−13.1359	+	28.7636i	−0.588044	+	1.28764i	0.348573	+	0.937282i	$0.386666\pi$
$499$	−13.1359	+	28.7636i	−0.588044	+	1.28764i	−0.936617	+	0.350355i	$0.886061\pi$
$500$		0			0
$501$	0.408056	+	2.83809i	0.0182306	+	0.126797i
$502$		0			0
$503$	20.4289	+	23.5763i	0.910881	+	1.05121i	0.998483	+	0.0550575i	$0.0175342\pi$
$503$	20.4289	+	23.5763i	0.910881	+	1.05121i	−0.0876019	+	0.996156i	$0.527920\pi$
$504$		0			0
$505$	25.4648			1.13317
$506$		0			0
$507$	−22.2311			−0.987319
$508$		0			0
$509$	23.3068	+	26.8975i	1.03306	+	1.19221i	0.981088	+	0.193563i	$0.0620043\pi$
$509$	23.3068	+	26.8975i	1.03306	+	1.19221i	0.0519692	+	0.998649i	$0.483450\pi$
$510$		0			0
$511$	−0.294626	−	2.04917i	−0.0130335	−	0.0906500i
$512$		0			0
$513$	0.491315	−	1.07583i	0.0216921	−	0.0474990i
$514$		0			0
$515$	−2.89014	+	20.1014i	−0.127355	+	0.885773i
$516$		0			0
$517$	−63.8136	−	18.7374i	−2.80652	−	0.824069i
$518$		0			0
$519$	−0.795897	−	1.74277i	−0.0349360	−	0.0764992i
$520$		0			0
$521$	−7.39243	+	8.53132i	−0.323868	+	0.373764i	−0.894213	−	0.447641i	$-0.852264\pi$
$521$	−7.39243	+	8.53132i	−0.323868	+	0.373764i	0.570345	+	0.821405i	$0.306810\pi$
$522$		0			0
$523$	9.48391	+	6.09494i	0.414702	+	0.266513i	0.731312	−	0.682043i	$-0.238908\pi$
$523$	9.48391	+	6.09494i	0.414702	+	0.266513i	−0.316610	+	0.948556i	$0.602545\pi$
$524$		0			0
$525$	3.19239	−	2.05163i	0.139327	−	0.0895403i
$526$		0			0
$527$	0.276584	−	0.0812124i	0.0120482	−	0.00353767i
$528$		0			0
$529$	−20.8791	+	9.64700i	−0.907785	+	0.419435i
$530$		0			0
$531$	−3.14608	+	0.923771i	−0.136528	+	0.0400883i
$532$		0			0
$533$	3.72596	−	2.39453i	0.161389	−	0.103719i
$534$		0			0
$535$	7.97831	+	5.12735i	0.344932	+	0.221675i
$536$		0			0
$537$	14.6021	−	16.8517i	0.630126	−	0.727204i
$538$		0			0
$539$	10.3006	+	22.5552i	0.443679	+	0.971520i
$540$		0			0
$541$	−21.2804	−	6.24848i	−0.914915	−	0.268643i	−0.209807	−	0.977743i	$-0.567283\pi$
$541$	−21.2804	−	6.24848i	−0.914915	−	0.268643i	−0.705108	+	0.709100i	$0.749102\pi$
$542$		0			0
$543$	1.29364	−	8.99745i	0.0555153	−	0.386118i
$544$		0			0
$545$	16.1372	−	35.3356i	0.691243	−	1.51361i
$546$		0			0
$547$	5.51610	+	38.3653i	0.235851	+	1.64038i	0.672031	+	0.740523i	$0.265422\pi$
$547$	5.51610	+	38.3653i	0.235851	+	1.64038i	−0.436180	+	0.899860i	$0.643669\pi$
$548$		0			0
$549$	6.91855	+	7.98443i	0.295276	+	0.340767i
$550$		0			0
$551$	−1.38326			−0.0589288
$552$		0			0
$553$	49.2705			2.09520
$554$		0			0
$555$	−10.7061	−	12.3555i	−0.454449	−	0.524462i
$556$		0			0
$557$	4.26786	+	29.6836i	0.180835	+	1.25774i	0.854794	+	0.518967i	$0.173683\pi$
$557$	4.26786	+	29.6836i	0.180835	+	1.25774i	−0.673959	+	0.738769i	$0.735408\pi$
$558$		0			0
$559$	16.6727	−	36.5081i	0.705180	−	1.54413i
$560$		0			0
$561$	−0.277750	+	1.93179i	−0.0117266	+	0.0815604i
$562$		0			0
$563$	32.8360	+	9.64153i	1.38387	+	0.406342i	0.887116	−	0.461547i	$-0.152705\pi$
$563$	32.8360	+	9.64153i	1.38387	+	0.406342i	0.496758	+	0.867889i	$0.334524\pi$
$564$		0			0
$565$	5.03373	+	11.0223i	0.211771	+	0.463713i
$566$		0			0
$567$	−2.23221	+	2.57610i	−0.0937439	+	0.108186i
$568$		0			0
$569$	−7.29637	−	4.68909i	−0.305880	−	0.196577i	0.378692	−	0.925523i	$-0.376374\pi$
$569$	−7.29637	−	4.68909i	−0.305880	−	0.196577i	−0.684571	+	0.728946i	$0.740011\pi$
$570$		0			0
$571$	−21.3762	+	13.7376i	−0.894565	+	0.574902i	−0.905174	−	0.425042i	$-0.860259\pi$
$571$	−21.3762	+	13.7376i	−0.894565	+	0.574902i	0.0106086	+	0.999944i	$0.496623\pi$
$572$		0			0
$573$	15.8775	−	4.66204i	0.663290	−	0.194760i
$574$		0			0
$575$	2.56911	+	4.68034i	0.107139	+	0.195184i
$576$		0			0
$577$	20.0438	−	5.88540i	0.834435	−	0.245012i	0.163514	−	0.986541i	$-0.447717\pi$
$577$	20.0438	−	5.88540i	0.834435	−	0.245012i	0.670921	+	0.741529i	$0.265899\pi$
$578$		0			0
$579$	8.65319	−	5.56107i	0.359614	−	0.231110i
$580$		0			0
$581$	−15.7834	−	10.1434i	−0.654805	−	0.420817i
$582$		0			0
$583$	−12.1386	+	14.0087i	−0.502730	+	0.580182i
$584$		0			0
$585$	−4.86113	−	10.6444i	−0.200983	−	0.440091i
$586$		0			0
$587$	−3.59093	−	1.05439i	−0.148214	−	0.0435194i	0.206784	−	0.978387i	$-0.433700\pi$
$587$	−3.59093	−	1.05439i	−0.148214	−	0.0435194i	−0.354998	+	0.934867i	$0.615518\pi$
$588$		0			0
$589$	0.133456	−	0.928204i	0.00549894	−	0.0382460i
$590$		0			0
$591$	−9.85357	+	21.5763i	−0.405322	+	0.887530i
$592$		0			0
$593$	−2.74555	−	19.0957i	−0.112746	−	0.784167i	−0.965228	−	0.261410i	$-0.915813\pi$
$593$	−2.74555	−	19.0957i	−0.112746	−	0.784167i	0.852482	−	0.522757i	$-0.175097\pi$
$594$		0			0
$595$	1.59994	+	1.84643i	0.0655910	+	0.0756960i
$596$		0			0
$597$	15.5053			0.634588
$598$		0			0
$599$	12.3165			0.503238			0.251619	−	0.967826i	$-0.419037\pi$
$599$	12.3165			0.503238			0.251619	+	0.967826i	$0.419037\pi$
$600$		0			0
$601$	20.3087	+	23.4375i	0.828408	+	0.956034i	0.999573	−	0.0292086i	$-0.00929871\pi$
$601$	20.3087	+	23.4375i	0.828408	+	0.956034i	−0.171165	+	0.985242i	$0.554753\pi$
$602$		0			0
$603$	1.63102	+	11.3440i	0.0664204	+	0.461964i
$604$		0			0
$605$	14.5921	−	31.9523i	0.593254	−	1.29904i
$606$		0			0
$607$	−2.41638	+	16.8063i	−0.0980777	+	0.682145i	0.880163	+	0.474672i	$0.157433\pi$
$607$	−2.41638	+	16.8063i	−0.0980777	+	0.682145i	−0.978241	+	0.207474i	$0.933476\pi$
$608$		0			0
$609$	3.82519	+	1.12318i	0.155004	+	0.0455134i
$610$		0			0
$611$	−30.5485	−	66.8919i	−1.23586	−	2.70616i
$612$		0			0
$613$	−0.937626	+	1.08208i	−0.0378703	+	0.0437047i	−0.774369	−	0.632735i	$-0.781932\pi$
$613$	−0.937626	+	1.08208i	−0.0378703	+	0.0437047i	0.736498	+	0.676439i	$0.236478\pi$
$614$		0			0
$615$	1.23756	+	0.795333i	0.0499033	+	0.0320709i
$616$		0			0
$617$	26.0834	−	16.7628i	1.05008	−	0.674843i	0.102617	−	0.994721i	$-0.467278\pi$
$617$	26.0834	−	16.7628i	1.05008	−	0.674843i	0.947459	+	0.319878i	$0.103642\pi$
$618$		0			0
$619$	1.05844	−	0.310787i	0.0425425	−	0.0124916i	−0.260392	−	0.965503i	$-0.583852\pi$
$619$	1.05844	−	0.310787i	0.0425425	−	0.0124916i	0.302935	+	0.953011i	$0.402034\pi$
$620$		0			0
$621$	−3.39866	−	3.38366i	−0.136383	−	0.135781i
$622$		0			0
$623$	−36.8437	+	10.8183i	−1.47611	+	0.433426i
$624$		0			0
$625$	−15.3060	+	9.83654i	−0.612238	+	0.393461i
$626$		0			0
$627$	5.34112	+	3.43253i	0.213304	+	0.137082i
$628$		0			0
$629$	−1.97431	+	2.27848i	−0.0787211	+	0.0908490i
$630$		0			0
$631$	−12.8844	−	28.2128i	−0.512919	−	1.12313i	−0.972052	−	0.234767i	$-0.924567\pi$
$631$	−12.8844	−	28.2128i	−0.512919	−	1.12313i	0.459133	−	0.888368i	$-0.348160\pi$
$632$		0			0
$633$	24.6548	+	7.23929i	0.979939	+	0.287736i
$634$		0			0
$635$	−2.22405	+	15.4686i	−0.0882586	+	0.613852i
$636$		0			0
$637$	−11.3893	+	24.9392i	−0.451262	+	0.988126i
$638$		0			0
$639$	−1.38098	−	9.60492i	−0.0546307	−	0.379965i
$640$		0			0
$641$	−7.27619	−	8.39717i	−0.287392	−	0.331668i	0.593635	−	0.804735i	$-0.297692\pi$
$641$	−7.27619	−	8.39717i	−0.287392	−	0.331668i	−0.881027	+	0.473067i	$0.843147\pi$
$642$		0			0
$643$	7.84007			0.309182			0.154591	−	0.987979i	$-0.450594\pi$
$643$	7.84007			0.309182			0.154591	+	0.987979i	$0.450594\pi$
$644$		0			0
$645$	13.3307			0.524895
$646$		0			0
$647$	−30.5753	−	35.2858i	−1.20204	−	1.38723i	−0.901114	−	0.433581i	$-0.857250\pi$
$647$	−30.5753	−	35.2858i	−1.20204	−	1.38723i	−0.300926	−	0.953647i	$-0.597296\pi$
$648$		0			0
$649$	−2.50498	−	17.4225i	−0.0983292	−	0.683895i
$650$		0			0
$651$	−1.12273	+	2.45844i	−0.0440034	+	0.0963539i
$652$		0			0
$653$	−7.00737	+	48.7373i	−0.274219	+	1.90724i	0.128140	+	0.991756i	$0.459099\pi$
$653$	−7.00737	+	48.7373i	−0.274219	+	1.90724i	−0.402359	+	0.915482i	$0.631810\pi$
$654$		0			0
$655$	14.4066	+	4.23017i	0.562914	+	0.165286i
$656$		0			0
$657$	0.252301	+	0.552461i	0.00984318	+	0.0215536i
$658$		0			0
$659$	−19.1079	+	22.0517i	−0.744338	+	0.859012i	−0.994007	−	0.109319i	$-0.965133\pi$
$659$	−19.1079	+	22.0517i	−0.744338	+	0.859012i	0.249668	+	0.968331i	$0.419678\pi$
$660$		0			0
$661$	2.87726	+	1.84910i	0.111912	+	0.0719217i	0.595400	−	0.803430i	$-0.296994\pi$
$661$	2.87726	+	1.84910i	0.111912	+	0.0719217i	−0.483487	+	0.875351i	$0.660630\pi$
$662$		0			0
$663$	−1.81538	+	1.16667i	−0.0705034	+	0.0453098i
$664$		0			0
$665$	7.62600	−	2.23920i	0.295724	−	0.0868323i
$666$		0			0
$667$	−1.94853	+	5.25972i	−0.0754475	+	0.203657i
$668$		0			0
$669$	−19.3078	+	5.66927i	−0.746481	+	0.219187i
$670$		0			0
$671$	−47.7112	+	30.6621i	−1.84187	+	1.18370i
$672$		0			0
$673$	−0.792238	−	0.509140i	−0.0305385	−	0.0196259i	0.525282	−	0.850928i	$-0.323960\pi$
$673$	−0.792238	−	0.509140i	−0.0305385	−	0.0196259i	−0.555821	+	0.831302i	$0.687596\pi$
$674$		0			0
$675$	−0.729042	+	0.841360i	−0.0280609	+	0.0323840i
$676$		0			0
$677$	−8.97993	−	19.6633i	−0.345127	−	0.755722i	0.654873	−	0.755739i	$-0.272722\pi$
$677$	−8.97993	−	19.6633i	−0.345127	−	0.755722i	−1.00000		1.64493e-5i	$0.999995\pi$
$678$		0			0
$679$	−28.5056	−	8.36998i	−1.09394	−	0.321211i
$680$		0			0
$681$	1.72373	−	11.9888i	0.0660535	−	0.459412i
$682$		0			0
$683$	−4.33791	+	9.49871i	−0.165986	+	0.363458i	−0.974287	−	0.225311i	$-0.927660\pi$
$683$	−4.33791	+	9.49871i	−0.165986	+	0.363458i	0.808301	+	0.588769i	$0.200387\pi$
$684$		0			0
$685$	−4.89032	−	34.0129i	−0.186849	−	1.29957i
$686$		0			0
$687$	−9.12266	−	10.5281i	−0.348051	−	0.401673i
$688$		0			0
$689$	−20.4954			−0.780812
$690$		0			0
$691$	36.4374			1.38614			0.693072	−	0.720869i	$-0.256257\pi$
$691$	36.4374			1.38614			0.693072	+	0.720869i	$0.256257\pi$
$692$		0			0
$693$	−11.9829	−	13.8290i	−0.455192	−	0.525320i
$694$		0			0
$695$	3.37118	+	23.4471i	0.127876	+	0.889399i
$696$		0			0
$697$	0.112696	−	0.246769i	0.00426865	−	0.00934705i
$698$		0			0
$699$	−3.62838	+	25.2359i	−0.137238	+	0.954511i
$700$		0			0
$701$	−16.8547	−	4.94900i	−0.636594	−	0.186921i	−0.0525184	−	0.998620i	$-0.516725\pi$
$701$	−16.8547	−	4.94900i	−0.636594	−	0.186921i	−0.584076	+	0.811699i	$0.698543\pi$
$702$		0			0
$703$	4.07428	+	8.92143i	0.153664	+	0.336478i
$704$		0			0
$705$	15.9950	−	18.4593i	0.602408	−	0.695216i
$706$		0			0
$707$	37.0392	+	23.8036i	1.39300	+	0.895228i
$708$		0			0
$709$	31.2129	−	20.0593i	1.17223	−	0.753344i	0.198285	−	0.980144i	$-0.436463\pi$
$709$	31.2129	−	20.0593i	1.17223	−	0.753344i	0.973941	+	0.226800i	$0.0728265\pi$
$710$		0			0
$711$	−13.8689	+	4.07229i	−0.520126	+	0.152723i
$712$		0			0
$713$	−3.34142	−	1.81497i	−0.125137	−	0.0679713i
$714$		0			0
$715$	60.2732	−	17.6978i	2.25409	−	0.661860i
$716$		0			0
$717$	20.2192	−	12.9941i	0.755098	−	0.485272i
$718$		0			0
$719$	−14.0690	−	9.04160i	−0.524685	−	0.337195i	0.251338	−	0.967899i	$-0.419130\pi$
$719$	−14.0690	−	9.04160i	−0.524685	−	0.337195i	−0.776023	+	0.630705i	$0.782766\pi$
$720$		0			0
$721$	−22.9939	+	26.5363i	−0.856336	+	0.988265i
$722$		0			0
$723$	3.37074	+	7.38089i	0.125359	+	0.274498i
$724$		0			0
$725$	1.24931	+	0.366831i	0.0463983	+	0.0136238i
$726$		0			0
$727$	−2.33220	+	16.2208i	−0.0864966	+	0.601597i	0.899761	+	0.436383i	$0.143741\pi$
$727$	−2.33220	+	16.2208i	−0.0864966	+	0.601597i	−0.986258	+	0.165214i	$0.947168\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−0.349854	−	2.43329i	−0.0129398	−	0.0899985i
$732$		0			0
$733$	−0.898465	−	1.03688i	−0.0331856	−	0.0382982i	0.738914	−	0.673800i	$-0.235339\pi$
$733$	−0.898465	−	1.03688i	−0.0331856	−	0.0382982i	−0.772100	+	0.635501i	$0.780793\pi$
$734$		0			0
$735$	−9.10636			−0.335893
$736$		0			0
$737$	−61.5230			−2.26623
$738$		0			0
$739$	0.790041	+	0.911755i	0.0290621	+	0.0335395i	0.770095	−	0.637930i	$-0.220209\pi$
$739$	0.790041	+	0.911755i	0.0290621	+	0.0335395i	−0.741032	+	0.671469i	$0.765664\pi$
$740$		0			0
$741$	0.999059	+	6.94861i	0.0367014	+	0.255264i
$742$		0			0
$743$	5.41944	−	11.8669i	0.198820	−	0.435355i	−0.783793	−	0.621023i	$-0.786718\pi$
$743$	5.41944	−	11.8669i	0.198820	−	0.435355i	0.982613	+	0.185668i	$0.0594448\pi$
$744$		0			0
$745$	−3.70447	+	25.7651i	−0.135721	+	0.943961i
$746$		0			0
$747$	5.28116	+	1.55069i	0.193227	+	0.0567367i
$748$		0			0
$749$	6.81177	+	14.9157i	0.248897	+	0.545007i
$750$		0			0
$751$	24.0228	−	27.7238i	0.876604	−	1.01166i	−0.123210	−	0.992381i	$-0.539319\pi$
$751$	24.0228	−	27.7238i	0.876604	−	1.01166i	0.999814	−	0.0192746i	$-0.00613566\pi$
$752$		0			0
$753$	1.93429	+	1.24309i	0.0704895	+	0.0453009i
$754$		0			0
$755$	20.1758	−	12.9662i	0.734274	−	0.471889i
$756$		0			0
$757$	−13.9582	+	4.09848i	−0.507318	+	0.148962i	−0.525368	−	0.850875i	$-0.676072\pi$
$757$	−13.9582	+	4.09848i	−0.507318	+	0.148962i	0.0180502	+	0.999837i	$0.494254\pi$
$758$		0			0
$759$	20.5757	−	15.4739i	0.746850	−	0.561667i
$760$		0			0
$761$	−12.0606	+	3.54132i	−0.437197	+	0.128373i	−0.492922	−	0.870073i	$-0.664071\pi$
$761$	−12.0606	+	3.54132i	−0.437197	+	0.128373i	0.0557249	+	0.998446i	$0.482253\pi$
$762$		0			0
$763$	56.5025	−	36.3119i	2.04553	−	1.31458i
$764$		0			0
$765$	−0.602969	−	0.387505i	−0.0218004	−	0.0140103i
$766$		0			0
$767$	12.7450	−	14.7085i	0.460195	−	0.531093i
$768$		0			0
$769$	7.13046	+	15.6135i	0.257131	+	0.563039i	0.993538	−	0.113500i	$-0.0362063\pi$
$769$	7.13046	+	15.6135i	0.257131	+	0.563039i	−0.736407	+	0.676539i	$0.763479\pi$
$770$		0			0
$771$	15.8423	+	4.65172i	0.570546	+	0.167527i
$772$		0			0
$773$	3.41753	−	23.7694i	0.122920	−	0.854926i	−0.831301	−	0.555823i	$-0.812403\pi$
$773$	3.41753	−	23.7694i	0.122920	−	0.854926i	0.954221	−	0.299104i	$-0.0966876\pi$
$774$		0			0
$775$	−0.366686	+	0.802931i	−0.0131718	+	0.0288421i
$776$		0			0
$777$	−4.02278	−	27.9791i	−0.144316	−	1.00374i
$778$		0			0
$779$	−0.577930	−	0.666967i	−0.0207065	−	0.0238966i
$780$		0			0
$781$	52.0912			1.86397
$782$		0			0
$783$	−1.16957			−0.0417969
$784$		0			0
$785$	−13.0064	−	15.0101i	−0.464217	−	0.535735i
$786$		0			0
$787$	−3.09856	−	21.5510i	−0.110452	−	0.768209i	−0.967481	−	0.252942i	$-0.918602\pi$
$787$	−3.09856	−	21.5510i	−0.110452	−	0.768209i	0.857030	−	0.515267i	$-0.172307\pi$
$788$		0			0
$789$	5.63672	−	12.3427i	0.200673	−	0.439412i
$790$		0			0
$791$	−2.98161	+	20.7376i	−0.106014	+	0.737344i
$792$		0			0
$793$	−60.1688	−	17.6671i	−2.13666	−	0.627379i
$794$		0			0
$795$	−2.82792	−	6.19228i	−0.100296	−	0.219617i
$796$		0			0
$797$	3.98323	−	4.59689i	0.141093	−	0.162830i	−0.680805	−	0.732465i	$-0.738370\pi$
$797$	3.98323	−	4.59689i	0.141093	−	0.162830i	0.821898	+	0.569635i	$0.192915\pi$
$798$		0			0
$799$	−3.78920	−	2.43517i	−0.134052	−	0.0861502i
$800$		0			0
$801$	9.47683	−	6.09039i	0.334847	−	0.215193i
$802$		0			0
$803$	−3.12828	+	0.918545i	−0.110395	+	0.0324148i
$804$		0			0
$805$	2.22805	−	32.1515i	0.0785285	−	1.13319i
$806$		0			0
$807$	15.9500	−	4.68334i	0.561467	−	0.164862i
$808$		0			0
$809$	21.0082	−	13.5011i	0.738608	−	0.474674i	−0.116457	−	0.993196i	$-0.537154\pi$
$809$	21.0082	−	13.5011i	0.738608	−	0.474674i	0.855065	+	0.518521i	$0.173517\pi$
$810$		0			0
$811$	−4.29791	−	2.76210i	−0.150920	−	0.0969904i	0.463001	−	0.886358i	$-0.346772\pi$
$811$	−4.29791	−	2.76210i	−0.150920	−	0.0969904i	−0.613921	+	0.789367i	$0.710409\pi$
$812$		0			0
$813$	−11.1505	+	12.8683i	−0.391064	+	0.451311i
$814$		0			0
$815$	13.1283	+	28.7470i	0.459865	+	1.00696i
$816$		0			0
$817$	−7.67326	−	2.25307i	−0.268453	−	0.0788250i
$818$		0			0
$819$	2.87938	−	20.0265i	0.100614	−	0.699783i
$820$		0			0
$821$	−8.94522	+	19.5873i	−0.312190	+	0.683602i	−0.999068	−	0.0431718i	$-0.986254\pi$
$821$	−8.94522	+	19.5873i	−0.312190	+	0.683602i	0.686877	+	0.726773i	$0.258981\pi$
$822$		0			0
$823$	−2.85023	−	19.8238i	−0.0993529	−	0.691015i	−0.977238	−	0.212144i	$-0.931955\pi$
$823$	−2.85023	−	19.8238i	−0.0993529	−	0.691015i	0.877886	−	0.478871i	$-0.158954\pi$
$824$		0			0
$825$	−3.91363	−	4.51657i	−0.136255	−	0.157247i
$826$		0			0
$827$	−41.3451			−1.43771			−0.718855	−	0.695160i	$-0.755333\pi$
$827$	−41.3451			−1.43771			−0.718855	+	0.695160i	$0.755333\pi$
$828$		0			0
$829$	26.8970			0.934170			0.467085	−	0.884212i	$-0.345304\pi$
$829$	26.8970			0.934170			0.467085	+	0.884212i	$0.345304\pi$
$830$		0			0
$831$	−11.4091	−	13.1668i	−0.395777	−	0.456751i
$832$		0			0
$833$	0.238990	+	1.66221i	0.00828052	+	0.0575923i
$834$		0			0
$835$	2.34824	−	5.14194i	0.0812644	−	0.177944i
$836$		0			0
$837$	0.112839	−	0.784812i	0.00390028	−	0.0271271i
$838$		0			0
$839$	−17.9217	−	5.26229i	−0.618726	−	0.181674i	−0.0426763	−	0.999089i	$-0.513588\pi$
$839$	−17.9217	−	5.26229i	−0.618726	−	0.181674i	−0.576050	+	0.817415i	$0.695407\pi$
$840$		0			0
$841$	−11.4788	−	25.1351i	−0.395820	−	0.866726i
$842$		0			0
$843$	−7.19954	+	8.30872i	−0.247965	+	0.286167i
$844$		0			0
$845$	36.8706	+	23.6953i	1.26839	+	0.815143i
$846$		0			0
$847$	51.0924	−	32.8351i	1.75556	−	1.12823i
$848$		0			0
$849$	−13.7535	+	4.03839i	−0.472018	+	0.138597i
$850$		0			0
$851$	39.6622	−	2.92489i	1.35960	−	0.100264i
$852$		0			0
$853$	−16.6313	+	4.88339i	−0.569445	+	0.167204i	−0.553765	−	0.832673i	$-0.686809\pi$
$853$	−16.6313	+	4.88339i	−0.569445	+	0.167204i	−0.0156797	+	0.999877i	$0.504991\pi$
$854$		0			0
$855$	−1.96154	+	1.26060i	−0.0670831	+	0.0431117i
$856$		0			0
$857$	33.2564	+	21.3726i	1.13602	+	0.730074i	0.966807	−	0.255506i	$-0.0822420\pi$
$857$	33.2564	+	21.3726i	1.13602	+	0.730074i	0.169210	+	0.985580i	$0.445878\pi$
$858$		0			0
$859$	35.5819	−	41.0636i	1.21404	−	1.40107i	0.323460	−	0.946242i	$-0.395154\pi$
$859$	35.5819	−	41.0636i	1.21404	−	1.40107i	0.890577	−	0.454832i	$-0.150301\pi$
$860$		0			0
$861$	1.05661	+	2.31366i	0.0360093	+	0.0788493i
$862$		0			0
$863$	−2.46479	−	0.723728i	−0.0839025	−	0.0246360i	0.239512	−	0.970893i	$-0.423013\pi$
$863$	−2.46479	−	0.723728i	−0.0839025	−	0.0246360i	−0.323414	+	0.946257i	$0.604831\pi$
$864$		0			0
$865$	−0.537547	+	3.73872i	−0.0182771	+	0.127120i
$866$		0			0
$867$	7.00715	−	15.3435i	0.237975	−	0.521093i
$868$		0			0
$869$	−11.0428	−	76.8044i	−0.374601	−	2.60541i
$870$		0			0
$871$	−44.5474	−	51.4104i	−1.50943	−	1.74198i
$872$		0			0
$873$	8.71570			0.294982
$874$		0			0
$875$	−41.0820			−1.38882
$876$		0			0
$877$	20.7063	+	23.8963i	0.699201	+	0.806921i	0.988644	−	0.150274i	$-0.0480157\pi$
$877$	20.7063	+	23.8963i	0.699201	+	0.806921i	−0.289443	+	0.957195i	$0.593470\pi$
$878$		0			0
$879$	0.177288	+	1.23306i	0.00597976	+	0.0415902i
$880$		0			0
$881$	−13.0660	+	28.6105i	−0.440203	+	0.963911i	0.551358	+	0.834269i	$0.314110\pi$
$881$	−13.0660	+	28.6105i	−0.440203	+	0.963911i	−0.991561	+	0.129642i	$0.958617\pi$
$882$		0			0
$883$	−2.95936	+	20.5828i	−0.0995903	+	0.692666i	0.877459	+	0.479652i	$0.159237\pi$
$883$	−2.95936	+	20.5828i	−0.0995903	+	0.692666i	−0.977049	+	0.213014i	$0.931672\pi$
$884$		0			0
$885$	6.20242	+	1.82119i	0.208492	+	0.0612188i
$886$		0			0
$887$	−19.2914	−	42.2423i	−0.647741	−	1.41836i	−0.893517	−	0.449029i	$-0.851770\pi$
$887$	−19.2914	−	42.2423i	−0.647741	−	1.41836i	0.245776	−	0.969327i	$-0.420957\pi$
$888$		0			0
$889$	−17.6944	+	20.4204i	−0.593452	+	0.684880i
$890$		0			0
$891$	4.51600	+	2.90226i	0.151292	+	0.0972293i
$892$		0			0
$893$	−12.3268	+	7.92193i	−0.412499	+	0.265097i
$894$		0			0
$895$	−42.1793	+	12.3850i	−1.40990	+	0.413983i
$896$		0			0
$897$	27.8288	+	5.98936i	0.929177	+	0.199979i
$898$		0			0
$899$	−0.889766	+	0.261259i	−0.0296754	+	0.00871347i
$900$		0			0
$901$	−1.05608	+	0.678701i	−0.0351831	+	0.0226108i
$902$		0			0
$903$	19.3898	+	12.4611i	0.645251	+	0.414678i
$904$		0			0
$905$	−11.7355	+	13.5435i	−0.390103	+	0.450203i
$906$		0			0
$907$	−0.661817	−	1.44918i	−0.0219753	−	0.0481191i	0.898326	−	0.439329i	$-0.144784\pi$
$907$	−0.661817	−	1.44918i	−0.0219753	−	0.0481191i	−0.920301	+	0.391210i	$0.872057\pi$
$908$		0			0
$909$	−12.3934	−	3.63903i	−0.411063	−	0.120699i
$910$		0			0
$911$	−1.72952	+	12.0291i	−0.0573017	+	0.398542i	0.940905	+	0.338672i	$0.109978\pi$
$911$	−1.72952	+	12.0291i	−0.0573017	+	0.398542i	−0.998206	+	0.0598699i	$0.980931\pi$
$912$		0			0
$913$	−12.2743	+	26.8770i	−0.406220	+	0.889498i
$914$		0			0
$915$	−2.96420	−	20.6165i	−0.0979935	−	0.681560i
$916$		0			0
$917$	17.0006	+	19.6197i	0.561408	+	0.647900i
$918$		0			0
$919$	−48.1383			−1.58793			−0.793967	−	0.607960i	$-0.791988\pi$
$919$	−48.1383			−1.58793			−0.793967	+	0.607960i	$0.791988\pi$
$920$		0			0
$921$	−0.613293			−0.0202087
$922$		0			0
$923$	37.7180	+	43.5289i	1.24150	+	1.43277i
$924$		0			0
$925$	−1.31385	−	9.13801i	−0.0431990	−	0.300456i
$926$		0			0
$927$	4.27917	−	9.37008i	0.140546	−	0.307754i
$928$		0			0
$929$	−0.209637	+	1.45806i	−0.00687796	+	0.0478373i	−0.992971	−	0.118355i	$-0.962238\pi$
$929$	−0.209637	+	1.45806i	−0.00687796	+	0.0478373i	0.986093	+	0.166192i	$0.0531471\pi$
$930$		0			0
$931$	5.24171	+	1.53910i	0.171790	+	0.0504421i
$932$		0			0
$933$	−1.69138	−	3.70362i	−0.0553735	−	0.121251i
$934$		0			0
$935$	2.51968	−	2.90786i	0.0824022	−	0.0950972i
$936$		0			0
$937$	−7.90966	−	5.08323i	−0.258397	−	0.166062i	0.405028	−	0.914304i	$-0.367262\pi$
$937$	−7.90966	−	5.08323i	−0.258397	−	0.166062i	−0.663426	+	0.748242i	$0.730898\pi$
$938$		0			0
$939$	−27.6881	+	17.7941i	−0.903568	+	0.580688i
$940$		0			0
$941$	28.2082	−	8.28268i	0.919561	−	0.270008i	0.212501	−	0.977161i	$-0.431839\pi$
$941$	28.2082	−	8.28268i	0.919561	−	0.270008i	0.707060	+	0.707153i	$0.250021\pi$
$942$		0			0
$943$	−3.35019	+	1.25800i	−0.109097	+	0.0409662i
$944$		0			0
$945$	6.44791	−	1.89328i	0.209751	−	0.0615883i
$946$		0			0
$947$	−42.5757	+	27.3618i	−1.38353	+	0.889138i	−0.999417	−	0.0341504i	$-0.989127\pi$
$947$	−42.5757	+	27.3618i	−1.38353	+	0.889138i	−0.384108	+	0.923288i	$0.625491\pi$
$948$		0			0
$949$	−3.03268	−	1.94898i	−0.0984449	−	0.0632667i
$950$		0			0
$951$	1.20495	−	1.39059i	0.0390733	−	0.0450930i
$952$		0			0
$953$	−15.2536	−	33.4007i	−0.494112	−	1.08195i	−0.978339	−	0.207011i	$-0.933626\pi$
$953$	−15.2536	−	33.4007i	−0.494112	−	1.08195i	0.484227	−	0.874942i	$-0.339101\pi$
$954$		0			0
$955$	−31.3020	−	9.19111i	−1.01291	−	0.297417i
$956$		0			0
$957$	0.893517	−	6.21455i	0.0288833	−	0.200888i
$958$		0			0
$959$	24.6810	−	54.0439i	0.796991	−	1.74517i
$960$		0			0
$961$	4.32229	+	30.0622i	0.139429	+	0.969748i
$962$		0			0
$963$	−3.15022	−	3.63555i	−0.101514	−	0.117154i
$964$		0			0
$965$	−20.2787			−0.652796
$966$		0			0
$967$	−31.1749			−1.00252			−0.501259	−	0.865297i	$-0.667130\pi$
$967$	−31.1749			−1.00252			−0.501259	+	0.865297i	$0.667130\pi$
$968$		0			0
$969$	0.281581	+	0.324962i	0.00904569	+	0.0104393i
$970$		0			0
$971$	−3.81867	−	26.5595i	−0.122547	−	0.852333i	−0.954654	−	0.297718i	$-0.903774\pi$
$971$	−3.81867	−	26.5595i	−0.122547	−	0.852333i	0.832107	−	0.554615i	$-0.187135\pi$
$972$		0			0
$973$	−17.0141	+	37.2556i	−0.545446	+	1.19436i
$974$		0			0
$975$	0.940410	−	6.54070i	0.0301172	−	0.209470i
$976$		0			0
$977$	−30.5829	−	8.97996i	−0.978435	−	0.287294i	−0.246857	−	0.969052i	$-0.579398\pi$
$977$	−30.5829	−	8.97996i	−0.978435	−	0.287294i	−0.731578	+	0.681758i	$0.761216\pi$
$978$		0			0
$979$	25.1215	+	55.0085i	0.802887	+	1.75808i
$980$		0			0
$981$	−12.9034	+	14.8913i	−0.411974	+	0.475443i
$982$		0			0
$983$	−8.96246	−	5.75982i	−0.285858	−	0.183710i	0.389852	−	0.920878i	$-0.372526\pi$
$983$	−8.96246	−	5.75982i	−0.285858	−	0.183710i	−0.675710	+	0.737168i	$0.736163\pi$
$984$		0			0
$985$	39.3396	−	25.2820i	1.25346	−	0.805552i
$986$		0			0
$987$	40.5202	−	11.8978i	1.28977	−	0.378711i
$988$		0			0
$989$	−19.3761	+	26.0031i	−0.616124	+	0.826851i
$990$		0			0
$991$	7.53823	−	2.21342i	0.239460	−	0.0703117i	−0.159801	−	0.987149i	$-0.551085\pi$
$991$	7.53823	−	2.21342i	0.239460	−	0.0703117i	0.399260	+	0.916838i	$0.369267\pi$
$992$		0			0
$993$	−16.0935	+	10.3427i	−0.510711	+	0.328214i
$994$		0			0
$995$	−25.7156	−	16.5264i	−0.815241	−	0.523923i
$996$		0			0
$997$	28.6178	−	33.0268i	0.906336	−	1.04597i	−0.0924006	−	0.995722i	$-0.529454\pi$
$997$	28.6178	−	33.0268i	0.906336	−	1.04597i	0.998737	−	0.0502460i	$-0.0160005\pi$
$998$		0			0
$999$	3.44487	+	7.54321i	0.108991	+	0.238657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.193.1	✓	30
23.18	even	11	inner	552.2.q.d.409.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.193.1	✓	30	1.1	even	1	trivial
552.2.q.d.409.1	yes	30	23.18	even	11	inner

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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.280570 - 1.95141i) q^{5} +(1.41601 - 3.10064i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.280570 - 1.95141i) q^{5} +(1.41601 - 3.10064i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-5.15073 - 1.51239i) q^{11} +(-2.46573 - 5.39919i) q^{13} +(1.29104 - 1.48994i) q^{15} +(-0.305847 - 0.196556i) q^{17} +(-0.994958 + 0.639421i) q^{19} +(3.27060 - 0.960334i) q^{21} +(1.02979 + 4.68397i) q^{23} +(1.06818 - 0.313647i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(0.983903 + 0.632316i) q^{29} +(-0.519228 + 0.599221i) q^{31} +(-2.23002 - 4.88307i) q^{33} +(-6.44791 - 1.89328i) q^{35} +(1.18016 - 8.20819i) q^{37} +(2.46573 - 5.39919i) q^{39} +(0.106194 + 0.738593i) q^{41} +(4.42802 + 5.11020i) q^{43} +1.97148 q^{45} +12.3892 q^{47} +(-3.02484 - 3.49085i) q^{49} +(-0.0517400 - 0.359860i) q^{51} +(1.43442 - 3.14093i) q^{53} +(-1.50615 + 10.4755i) q^{55} +(-1.13480 - 0.333208i) q^{57} +(1.36210 + 2.98259i) q^{59} +(6.91855 - 7.98443i) q^{61} +(2.86756 + 1.84287i) q^{63} +(-9.84423 + 6.32650i) q^{65} +(10.9964 - 3.22884i) q^{67} +(-2.86554 + 3.84561i) q^{69} +(-9.31062 + 2.73385i) q^{71} +(0.510932 - 0.328356i) q^{73} +(0.936549 + 0.601884i) q^{75} +(-11.9829 + 13.8290i) q^{77} +(6.00460 + 13.1482i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.783317 - 5.44809i) q^{83} +(-0.297749 + 0.651980i) q^{85} +(0.166447 + 1.15766i) q^{87} +(-7.37709 - 8.51362i) q^{89} -20.2325 q^{91} -0.792882 q^{93} +(1.52693 + 1.76217i) q^{95} +(-1.24037 - 8.62699i) q^{97} +(2.23002 - 4.88307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more