LMFDB - Embedded newform 432.2.be.c.95.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.3
Character	$\chi$	$=$	432.95
Dual form			432.2.be.c.191.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.536320 + 1.64692i) q^{3} +(-1.32159 + 1.57501i) q^{5} +(-1.34711 + 3.70114i) q^{7} +(-2.42472 - 1.76656i) q^{9} +O(q^{10})$	\(q+(-0.536320 + 1.64692i) q^{3} +(-1.32159 + 1.57501i) q^{5} +(-1.34711 + 3.70114i) q^{7} +(-2.42472 - 1.76656i) q^{9} +(1.12995 - 0.948137i) q^{11} +(0.716807 - 4.06522i) q^{13} +(-1.88513 - 3.02127i) q^{15} +(-4.21362 - 2.43274i) q^{17} +(0.0640532 - 0.0369811i) q^{19} +(-5.37302 - 4.20358i) q^{21} +(-7.06058 + 2.56984i) q^{23} +(0.134184 + 0.760995i) q^{25} +(4.20981 - 3.04590i) q^{27} +(4.84957 - 0.855110i) q^{29} +(2.86544 + 7.87273i) q^{31} +(0.955499 + 2.36944i) q^{33} +(-4.04902 - 7.01310i) q^{35} +(-2.58271 + 4.47338i) q^{37} +(6.31067 + 3.36078i) q^{39} +(-8.47540 - 1.49444i) q^{41} +(0.636160 + 0.758146i) q^{43} +(5.98684 - 1.48430i) q^{45} +(-6.18694 - 2.25186i) q^{47} +(-6.52144 - 5.47214i) q^{49} +(6.26638 - 5.63480i) q^{51} +7.92783i q^{53} +3.03273i q^{55} +(0.0265522 + 0.125325i) q^{57} +(0.418512 + 0.351174i) q^{59} +(11.8089 + 4.29808i) q^{61} +(9.80463 - 6.59450i) q^{63} +(5.45544 + 6.50153i) q^{65} +(-11.0229 - 1.94363i) q^{67} +(-0.445607 - 13.0065i) q^{69} +(-3.59983 + 6.23508i) q^{71} +(4.52432 + 7.83635i) q^{73} +(-1.32527 - 0.187146i) q^{75} +(1.98703 + 5.45933i) q^{77} +(2.35092 - 0.414531i) q^{79} +(2.75856 + 8.56682i) q^{81} +(-0.677795 - 3.84397i) q^{83} +(9.40028 - 3.42142i) q^{85} +(-1.19262 + 8.44549i) q^{87} +(14.2677 - 8.23747i) q^{89} +(14.0803 + 8.12928i) q^{91} +(-14.5026 + 0.496864i) q^{93} +(-0.0264065 + 0.149759i) q^{95} +(10.1301 - 8.50015i) q^{97} +(-4.41474 + 0.302857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.536320	+	1.64692i	−0.309644	+	0.950852i
$3$	−0.536320	+	1.64692i	−0.309644	+	0.950852i
$4$		0			0
$5$	−1.32159	+	1.57501i	−0.591034	+	0.704367i	−0.975804	−	0.218646i	$-0.929836\pi$
$5$	−1.32159	+	1.57501i	−0.591034	+	0.704367i	0.384771	+	0.923012i	$0.374281\pi$
$6$		0			0
$7$	−1.34711	+	3.70114i	−0.509158	+	1.39890i	0.372950	+	0.927852i	$0.378346\pi$
$7$	−1.34711	+	3.70114i	−0.509158	+	1.39890i	−0.882107	+	0.471048i	$0.843876\pi$
$8$		0			0
$9$	−2.42472	−	1.76656i	−0.808241	−	0.588852i
$10$		0			0
$11$	1.12995	−	0.948137i	0.340692	−	0.285874i	−0.456348	−	0.889801i	$-0.650843\pi$
$11$	1.12995	−	0.948137i	0.340692	−	0.285874i	0.797039	+	0.603927i	$0.206398\pi$
$12$		0			0
$13$	0.716807	−	4.06522i	0.198807	−	1.12749i	−0.708086	−	0.706126i	$-0.750441\pi$
$13$	0.716807	−	4.06522i	0.198807	−	1.12749i	0.906893	−	0.421362i	$-0.138448\pi$
$14$		0			0
$15$	−1.88513	−	3.02127i	−0.486738	−	0.780089i
$16$		0			0
$17$	−4.21362	−	2.43274i	−1.02195	−	0.590025i	−0.107284	−	0.994228i	$-0.534216\pi$
$17$	−4.21362	−	2.43274i	−1.02195	−	0.590025i	−0.914669	+	0.404203i	$0.867549\pi$
$18$		0			0
$19$	0.0640532	−	0.0369811i	0.0146948	−	0.00848406i	−0.492635	−	0.870236i	$-0.663966\pi$
$19$	0.0640532	−	0.0369811i	0.0146948	−	0.00848406i	0.507329	+	0.861752i	$0.330633\pi$
$20$		0			0
$21$	−5.37302	−	4.20358i	−1.17249	−	0.917295i
$22$		0			0
$23$	−7.06058	+	2.56984i	−1.47223	+	0.535849i	−0.948706	−	0.316160i	$-0.897606\pi$
$23$	−7.06058	+	2.56984i	−1.47223	+	0.535849i	−0.523527	+	0.852009i	$0.675384\pi$
$24$		0			0
$25$	0.134184	+	0.760995i	0.0268368	+	0.152199i
$26$		0			0
$27$	4.20981	−	3.04590i	0.810179	−	0.586183i
$28$		0			0
$29$	4.84957	−	0.855110i	0.900543	−	0.158790i	0.295837	−	0.955239i	$-0.404402\pi$
$29$	4.84957	−	0.855110i	0.900543	−	0.158790i	0.604706	+	0.796449i	$0.293291\pi$
$30$		0			0
$31$	2.86544	+	7.87273i	0.514648	+	1.41398i	0.876343	+	0.481688i	$0.159976\pi$
$31$	2.86544	+	7.87273i	0.514648	+	1.41398i	−0.361695	+	0.932297i	$0.617802\pi$
$32$		0			0
$33$	0.955499	+	2.36944i	0.166331	+	0.412467i
$34$		0			0
$35$	−4.04902	−	7.01310i	−0.684409	−	1.18543i
$36$		0			0
$37$	−2.58271	+	4.47338i	−0.424594	+	0.735419i	−0.996382	−	0.0849823i	$-0.972917\pi$
$37$	−2.58271	+	4.47338i	−0.424594	+	0.735419i	0.571788	+	0.820401i	$0.306250\pi$
$38$		0			0
$39$	6.31067	+	3.36078i	1.01052	+	0.538156i
$40$		0			0
$41$	−8.47540	−	1.49444i	−1.32363	−	0.233392i	−0.533226	−	0.845973i	$-0.679021\pi$
$41$	−8.47540	−	1.49444i	−1.32363	−	0.233392i	−0.790408	+	0.612580i	$0.790132\pi$
$42$		0			0
$43$	0.636160	+	0.758146i	0.0970136	+	0.115616i	0.812367	−	0.583147i	$-0.198179\pi$
$43$	0.636160	+	0.758146i	0.0970136	+	0.115616i	−0.715353	+	0.698763i	$0.753734\pi$
$44$		0			0
$45$	5.98684	−	1.48430i	0.892465	−	0.221266i
$46$		0			0
$47$	−6.18694	−	2.25186i	−0.902459	−	0.328468i	−0.151221	−	0.988500i	$-0.548321\pi$
$47$	−6.18694	−	2.25186i	−0.902459	−	0.328468i	−0.751238	+	0.660032i	$0.770543\pi$
$48$		0			0
$49$	−6.52144	−	5.47214i	−0.931635	−	0.781734i
$50$		0			0
$51$	6.26638	−	5.63480i	0.877469	−	0.789029i
$52$		0			0
$53$			7.92783i			1.08897i	0.838770	+	0.544486i	$0.183275\pi$
$53$			7.92783i			1.08897i	−0.838770	+	0.544486i	$0.816725\pi$
$54$		0			0
$55$			3.03273i			0.408933i
$56$		0			0
$57$	0.0265522	+	0.125325i	0.00351692	+	0.0165996i
$58$		0			0
$59$	0.418512	+	0.351174i	0.0544857	+	0.0457189i	0.669624	−	0.742700i	$-0.266455\pi$
$59$	0.418512	+	0.351174i	0.0544857	+	0.0457189i	−0.615138	+	0.788419i	$0.710900\pi$
$60$		0			0
$61$	11.8089	+	4.29808i	1.51197	+	0.550313i	0.959128	−	0.282972i	$-0.0913205\pi$
$61$	11.8089	+	4.29808i	1.51197	+	0.550313i	0.552844	+	0.833285i	$0.313543\pi$
$62$		0			0
$63$	9.80463	−	6.59450i	1.23527	−	0.830829i
$64$		0			0
$65$	5.45544	+	6.50153i	0.676663	+	0.806416i
$66$		0			0
$67$	−11.0229	−	1.94363i	−1.34666	−	0.237452i	−0.546610	−	0.837387i	$-0.684082\pi$
$67$	−11.0229	−	1.94363i	−1.34666	−	0.237452i	−0.800049	+	0.599935i	$0.795193\pi$
$68$		0			0
$69$	−0.445607	−	13.0065i	−0.0536448	−	1.56580i
$70$		0			0
$71$	−3.59983	+	6.23508i	−0.427221	+	0.739968i	−0.996625	−	0.0820894i	$-0.973841\pi$
$71$	−3.59983	+	6.23508i	−0.427221	+	0.739968i	0.569404	+	0.822058i	$0.307174\pi$
$72$		0			0
$73$	4.52432	+	7.83635i	0.529531	+	0.917175i	0.999407	+	0.0344425i	$0.0109655\pi$
$73$	4.52432	+	7.83635i	0.529531	+	0.917175i	−0.469875	+	0.882733i	$0.655701\pi$
$74$		0			0
$75$	−1.32527	−	0.187146i	−0.153029	−	0.0216097i
$76$		0			0
$77$	1.98703	+	5.45933i	0.226444	+	0.622149i
$78$		0			0
$79$	2.35092	−	0.414531i	0.264499	−	0.0466384i	−0.0398256	−	0.999207i	$-0.512680\pi$
$79$	2.35092	−	0.414531i	0.264499	−	0.0466384i	0.304325	+	0.952568i	$0.401569\pi$
$80$		0			0
$81$	2.75856	+	8.56682i	0.306507	+	0.951869i
$82$		0			0
$83$	−0.677795	−	3.84397i	−0.0743977	−	0.421930i	−0.999145	−	0.0413481i	$-0.986835\pi$
$83$	−0.677795	−	3.84397i	−0.0743977	−	0.421930i	0.924747	−	0.380582i	$-0.124276\pi$
$84$		0			0
$85$	9.40028	−	3.42142i	1.01960	−	0.371105i
$86$		0			0
$87$	−1.19262	+	8.44549i	−0.127862	+	0.905452i
$88$		0			0
$89$	14.2677	−	8.23747i	1.51238	−	0.873170i	0.512480	−	0.858699i	$-0.328727\pi$
$89$	14.2677	−	8.23747i	1.51238	−	0.873170i	0.999895	−	0.0144711i	$-0.00460646\pi$
$90$		0			0
$91$	14.0803	+	8.12928i	1.47602	+	0.852180i
$92$		0			0
$93$	−14.5026	+	0.496864i	−1.50385	+	0.0515224i
$94$		0			0
$95$	−0.0264065	+	0.149759i	−0.00270925	+	0.0153649i
$96$		0			0
$97$	10.1301	−	8.50015i	1.02855	−	0.863059i	0.0378760	−	0.999282i	$-0.487941\pi$
$97$	10.1301	−	8.50015i	1.02855	−	0.863059i	0.990678	+	0.136223i	$0.0434964\pi$
$98$		0			0
$99$	−4.41474	+	0.302857i	−0.443698	+	0.0304383i
$100$		0			0
$101$	−5.76614	+	15.8423i	−0.573752	+	1.57637i	0.224773	+	0.974411i	$0.427836\pi$
$101$	−5.76614	+	15.8423i	−0.573752	+	1.57637i	−0.798526	+	0.601961i	$0.794386\pi$
$102$		0			0
$103$	−4.32854	+	5.15856i	−0.426504	+	0.508288i	−0.935910	−	0.352238i	$-0.885421\pi$
$103$	−4.32854	+	5.15856i	−0.426504	+	0.508288i	0.509406	+	0.860526i	$0.329865\pi$
$104$		0			0
$105$	13.7216	−	2.90716i	1.33909	−	0.283710i
$106$		0			0
$107$	−8.78059			−0.848851			−0.424426	−	0.905463i	$-0.639524\pi$
$107$	−8.78059			−0.848851			−0.424426	+	0.905463i	$0.639524\pi$
$108$		0			0
$109$	1.91765			0.183677			0.0918386	−	0.995774i	$-0.470726\pi$
$109$	1.91765			0.183677			0.0918386	+	0.995774i	$0.470726\pi$
$110$		0			0
$111$	−5.98216	−	6.65269i	−0.567802	−	0.631445i
$112$		0			0
$113$	−7.65159	+	9.11880i	−0.719801	+	0.857825i	−0.994611	−	0.103673i	$-0.966940\pi$
$113$	−7.65159	+	9.11880i	−0.719801	+	0.857825i	0.274811	+	0.961498i	$0.411385\pi$
$114$		0			0
$115$	5.28367	−	14.5168i	0.492705	−	1.35370i
$116$		0			0
$117$	−8.91949	+	8.59074i	−0.824607	+	0.794214i
$118$		0			0
$119$	14.6801	−	12.3181i	1.34572	−	1.12919i
$120$		0			0
$121$	−1.53232	+	8.69020i	−0.139301	+	0.790018i
$122$		0			0
$123$	7.00675	−	13.1568i	0.631778	−	1.18631i
$124$		0			0
$125$	−10.2788	−	5.93446i	−0.919363	−	0.530794i
$126$		0			0
$127$	0.433667	−	0.250378i	0.0384818	−	0.0222175i	−0.480636	−	0.876920i	$-0.659594\pi$
$127$	0.433667	−	0.250378i	0.0384818	−	0.0222175i	0.519117	+	0.854703i	$0.326261\pi$
$128$		0			0
$129$	−1.58980	+	0.641100i	−0.139974	+	0.0564457i
$130$		0			0
$131$	19.9609	−	7.26518i	1.74399	−	0.634762i	0.744533	−	0.667586i	$-0.232672\pi$
$131$	19.9609	−	7.26518i	1.74399	−	0.634762i	0.999461	+	0.0328244i	$0.0104502\pi$
$132$		0			0
$133$	0.0505860	+	0.286887i	0.00438636	+	0.0248763i
$134$		0			0
$135$	−0.766328	+	10.6559i	−0.0659550	+	0.917117i
$136$		0			0
$137$	10.4088	−	1.83535i	0.889280	−	0.156804i	0.289699	−	0.957118i	$-0.406445\pi$
$137$	10.4088	−	1.83535i	0.889280	−	0.156804i	0.599581	+	0.800314i	$0.295334\pi$
$138$		0			0
$139$	1.15117	+	3.16282i	0.0976411	+	0.268267i	0.978891	−	0.204385i	$-0.0655193\pi$
$139$	1.15117	+	3.16282i	0.0976411	+	0.268267i	−0.881250	+	0.472651i	$0.843297\pi$
$140$		0			0
$141$	7.02683	−	8.98171i	0.591766	−	0.756397i
$142$		0			0
$143$	−3.04443	−	5.27311i	−0.254588	−	0.440959i
$144$		0			0
$145$	−5.06234	+	8.76824i	−0.420405	+	0.728163i
$146$		0			0
$147$	12.5098	−	7.80551i	1.03179	−	0.643788i
$148$		0			0
$149$	−2.15275	−	0.379587i	−0.176360	−	0.0310970i	0.0847707	−	0.996400i	$-0.472984\pi$
$149$	−2.15275	−	0.379587i	−0.176360	−	0.0310970i	−0.261131	+	0.965303i	$0.584095\pi$
$150$		0			0
$151$	−4.22950	−	5.04052i	−0.344192	−	0.410192i	0.565983	−	0.824417i	$-0.308497\pi$
$151$	−4.22950	−	5.04052i	−0.344192	−	0.410192i	−0.910174	+	0.414225i	$0.864052\pi$
$152$		0			0
$153$	5.91930	+	13.3423i	0.478547	+	1.07866i
$154$		0			0
$155$	−16.1866	−	5.89144i	−1.30014	−	0.473211i
$156$		0			0
$157$	−9.24982	−	7.76152i	−0.738216	−	0.619437i	0.194142	−	0.980973i	$-0.437808\pi$
$157$	−9.24982	−	7.76152i	−0.738216	−	0.619437i	−0.932358	+	0.361537i	$0.882252\pi$
$158$		0			0
$159$	−13.0565	−	4.25185i	−1.03545	−	0.337194i
$160$		0			0
$161$		−	29.5940i		−	2.33234i
$162$		0			0
$163$			16.5220i			1.29410i	0.762447	+	0.647050i	$0.223998\pi$
$163$			16.5220i			1.29410i	−0.762447	+	0.647050i	$0.776002\pi$
$164$		0			0
$165$	−4.99468	−	1.62651i	−0.388835	−	0.126624i
$166$		0			0
$167$	8.17419	+	6.85896i	0.632538	+	0.530763i	0.901717	−	0.432328i	$-0.142308\pi$
$167$	8.17419	+	6.85896i	0.632538	+	0.530763i	−0.269178	+	0.963090i	$0.586752\pi$
$168$		0			0
$169$	−3.79616	−	1.38169i	−0.292013	−	0.106284i
$170$		0			0
$171$	−0.220641	−	0.0234846i	−0.0168728	−	0.00179591i
$172$		0			0
$173$	−1.52491	−	1.81732i	−0.115937	−	0.138168i	0.704955	−	0.709252i	$-0.250967\pi$
$173$	−1.52491	−	1.81732i	−0.115937	−	0.138168i	−0.820891	+	0.571084i	$0.806523\pi$
$174$		0			0
$175$	−2.99731	−	0.528507i	−0.226575	−	0.0399513i
$176$		0			0
$177$	−0.802813	+	0.500917i	−0.0603431	+	0.0376512i
$178$		0			0
$179$	−6.04118	+	10.4636i	−0.451539	+	0.782089i	−0.998482	−	0.0550812i	$-0.982458\pi$
$179$	−6.04118	+	10.4636i	−0.451539	+	0.782089i	0.546943	+	0.837170i	$0.315792\pi$
$180$		0			0
$181$	−1.86315	−	3.22706i	−0.138487	−	0.239866i	0.788437	−	0.615115i	$-0.210890\pi$
$181$	−1.86315	−	3.22706i	−0.138487	−	0.239866i	−0.926924	+	0.375249i	$0.877557\pi$
$182$		0			0
$183$	−13.4119	+	17.1432i	−0.991440	+	1.26726i
$184$		0			0
$185$	−3.63234	−	9.97977i	−0.267055	−	0.733728i
$186$		0			0
$187$	−7.06774	+	1.24623i	−0.516844	+	0.0911335i
$188$		0			0
$189$	5.60224	+	19.6842i	0.407503	+	1.43182i
$190$		0			0
$191$	3.49623	+	19.8281i	0.252978	+	1.43471i	0.801210	+	0.598383i	$0.204190\pi$
$191$	3.49623	+	19.8281i	0.252978	+	1.43471i	−0.548232	+	0.836326i	$0.684699\pi$
$192$		0			0
$193$	−18.9102	+	6.88274i	−1.36118	+	0.495431i	−0.916420	−	0.400217i	$-0.868935\pi$
$193$	−18.9102	+	6.88274i	−1.36118	+	0.495431i	−0.444764	+	0.895648i	$0.646712\pi$
$194$		0			0
$195$	−13.6334	+	5.49779i	−0.976308	+	0.393705i
$196$		0			0
$197$	8.04132	−	4.64266i	0.572920	−	0.330776i	−0.185395	−	0.982664i	$-0.559356\pi$
$197$	8.04132	−	4.64266i	0.572920	−	0.330776i	0.758315	+	0.651888i	$0.226023\pi$
$198$		0			0
$199$	−8.66567	−	5.00313i	−0.614293	−	0.354662i	0.160351	−	0.987060i	$-0.448737\pi$
$199$	−8.66567	−	5.00313i	−0.614293	−	0.354662i	−0.774644	+	0.632398i	$0.782071\pi$
$200$		0			0
$201$	9.11280	−	17.1114i	0.642767	−	1.20695i
$202$		0			0
$203$	−3.36800	+	19.1009i	−0.236387	+	1.34062i
$204$		0			0
$205$	13.5548	−	11.3738i	0.946706	−	0.794381i
$206$		0			0
$207$	21.6597	+	6.24176i	1.50545	+	0.433832i
$208$		0			0
$209$	0.0373135	−	0.102518i	0.00258103	−	0.00709131i
$210$		0			0
$211$	6.63507	−	7.90737i	0.456777	−	0.544366i	−0.487671	−	0.873028i	$-0.662153\pi$
$211$	6.63507	−	7.90737i	0.456777	−	0.544366i	0.944448	+	0.328662i	$0.106598\pi$
$212$		0			0
$213$	−8.33806	−	9.27264i	−0.571314	−	0.635351i
$214$		0			0
$215$	−2.03483			−0.138774
$216$		0			0
$217$	−32.9981			−2.24006
$218$		0			0
$219$	−15.3324	+	3.24842i	−1.03606	+	0.219508i
$220$		0			0
$221$	−12.9100	+	15.3855i	−0.868418	+	1.03494i
$222$		0			0
$223$	3.56137	−	9.78478i	0.238487	−	0.655237i	−0.761488	−	0.648179i	$-0.775531\pi$
$223$	3.56137	−	9.78478i	0.238487	−	0.655237i	0.999975	−	0.00705855i	$-0.00224682\pi$
$224$		0			0
$225$	1.01898	−	2.08224i	0.0679321	−	0.138816i
$226$		0			0
$227$	15.2498	−	12.7961i	1.01216	−	0.849305i	0.0235395	−	0.999723i	$-0.492506\pi$
$227$	15.2498	−	12.7961i	1.01216	−	0.849305i	0.988622	+	0.150418i	$0.0480620\pi$
$228$		0			0
$229$	3.18933	−	18.0876i	0.210757	−	1.19526i	−0.677363	−	0.735649i	$-0.736877\pi$
$229$	3.18933	−	18.0876i	0.210757	−	1.19526i	0.888120	−	0.459612i	$-0.152012\pi$
$230$		0			0
$231$	−10.0568	+	0.344549i	−0.661688	+	0.0226697i
$232$		0			0
$233$	2.78293	+	1.60673i	0.182316	+	0.105260i	0.588380	−	0.808584i	$-0.299766\pi$
$233$	2.78293	+	1.60673i	0.182316	+	0.105260i	−0.406064	+	0.913844i	$0.633099\pi$
$234$		0			0
$235$	11.7233	−	6.76846i	0.764745	−	0.441526i
$236$		0			0
$237$	−0.578144	+	4.09411i	−0.0375545	+	0.265941i
$238$		0			0
$239$	−18.0336	+	6.56371i	−1.16650	+	0.424571i	−0.851415	−	0.524493i	$-0.824255\pi$
$239$	−18.0336	+	6.56371i	−1.16650	+	0.424571i	−0.315084	+	0.949064i	$0.602033\pi$
$240$		0			0
$241$	0.861143	+	4.88379i	0.0554711	+	0.314592i	0.999900	−	0.0141227i	$-0.00449553\pi$
$241$	0.861143	+	4.88379i	0.0554711	+	0.314592i	−0.944429	+	0.328715i	$0.893384\pi$
$242$		0			0
$243$	−15.5884	−	0.0514129i	−0.999995	−	0.00329814i
$244$		0			0
$245$	17.2374	−	3.03941i	1.10125	−	0.194181i
$246$		0			0
$247$	−0.104423	−	0.286898i	−0.00664425	−	0.0182549i
$248$		0			0
$249$	6.69424	+	0.945318i	0.424230	+	0.0599071i
$250$		0			0
$251$	8.07253	+	13.9820i	0.509534	+	0.882538i	0.999939	+	0.0110438i	$0.00351543\pi$
$251$	8.07253	+	13.9820i	0.509534	+	0.882538i	−0.490405	+	0.871495i	$0.663151\pi$
$252$		0			0
$253$	−5.54151	+	9.59818i	−0.348392	+	0.603432i
$254$		0			0
$255$	0.593270	+	17.3165i	0.0371520	+	1.08440i
$256$		0			0
$257$	0.187499	+	0.0330612i	0.0116959	+	0.00206230i	0.179493	−	0.983759i	$-0.442554\pi$
$257$	0.187499	+	0.0330612i	0.0116959	+	0.00206230i	−0.167797	+	0.985822i	$0.553665\pi$
$258$		0			0
$259$	−13.0774	−	15.5851i	−0.812592	−	0.968410i
$260$		0			0
$261$	−13.2695	−	6.49364i	−0.821359	−	0.401946i
$262$		0			0
$263$	19.2898	+	7.02091i	1.18946	+	0.432928i	0.859534	−	0.511079i	$-0.170754\pi$
$263$	19.2898	+	7.02091i	1.18946	+	0.432928i	0.329926	+	0.944007i	$0.392976\pi$
$264$		0			0
$265$	−12.4864	−	10.4774i	−0.767035	−	0.643619i
$266$		0			0
$267$	5.91444	+	27.9158i	0.361958	+	1.70842i
$268$		0			0
$269$		−	14.6740i		−	0.894688i	−0.894362	−	0.447344i	$-0.852370\pi$
$269$		−	14.6740i		−	0.894688i	0.894362	−	0.447344i	$-0.147630\pi$
$270$		0			0
$271$		−	30.7796i		−	1.86973i	−0.355007	−	0.934864i	$-0.615521\pi$
$271$		−	30.7796i		−	1.86973i	0.355007	−	0.934864i	$-0.384479\pi$
$272$		0			0
$273$	−20.9399	+	18.8293i	−1.26734	+	1.13960i
$274$		0			0
$275$	0.873148	+	0.732658i	0.0526528	+	0.0441810i
$276$		0			0
$277$	24.4226	+	8.88910i	1.46741	+	0.534094i	0.947397	−	0.320062i	$-0.103704\pi$
$277$	24.4226	+	8.88910i	1.46741	+	0.534094i	0.520016	+	0.854157i	$0.325926\pi$
$278$		0			0
$279$	6.95973	−	24.1512i	0.416668	−	1.44589i
$280$		0			0
$281$	−5.67475	−	6.76290i	−0.338527	−	0.403441i	0.569745	−	0.821822i	$-0.307042\pi$
$281$	−5.67475	−	6.76290i	−0.338527	−	0.403441i	−0.908272	+	0.418381i	$0.862598\pi$
$282$		0			0
$283$	−13.7083	−	2.41714i	−0.814874	−	0.143684i	−0.249347	−	0.968414i	$-0.580216\pi$
$283$	−13.7083	−	2.41714i	−0.814874	−	0.143684i	−0.565527	+	0.824730i	$0.691327\pi$
$284$		0			0
$285$	−0.232479	−	0.123808i	−0.0137708	−	0.00733375i
$286$		0			0
$287$	16.9484	−	29.3555i	1.00043	−	1.73280i
$288$		0			0
$289$	3.33641	+	5.77884i	0.196260	+	0.339932i
$290$		0			0
$291$	8.56614	+	21.2423i	0.502156	+	1.24524i
$292$		0			0
$293$	1.63952	+	4.50455i	0.0957819	+	0.263159i	0.978326	−	0.207071i	$-0.0663932\pi$
$293$	1.63952	+	4.50455i	0.0957819	+	0.263159i	−0.882544	+	0.470230i	$0.844171\pi$
$294$		0			0
$295$	−1.10620	+	0.195054i	−0.0644057	+	0.0113565i
$296$		0			0
$297$	1.86893	−	7.43318i	0.108446	−	0.431317i
$298$		0			0
$299$	5.38588	+	30.5449i	0.311474	+	1.76645i
$300$		0			0
$301$	−3.66298	+	1.33322i	−0.211131	+	0.0768453i
$302$		0			0
$303$	−22.9986	−	17.9930i	−1.32124	−	1.03367i
$304$		0			0
$305$	−22.3760	+	12.9188i	−1.28125	+	0.739729i
$306$		0			0
$307$	−4.81893	−	2.78221i	−0.275031	−	0.158789i	0.356141	−	0.934432i	$-0.384092\pi$
$307$	−4.81893	−	2.78221i	−0.275031	−	0.158789i	−0.631172	+	0.775643i	$0.717426\pi$
$308$		0			0
$309$	−6.17427	−	9.89542i	−0.351242	−	0.562931i
$310$		0			0
$311$	−0.869874	+	4.93330i	−0.0493260	+	0.279742i	−0.999487	−	0.0320170i	$-0.989807\pi$
$311$	−0.869874	+	4.93330i	−0.0493260	+	0.279742i	0.950161	+	0.311759i	$0.100918\pi$
$312$		0			0
$313$	−16.5639	+	13.8987i	−0.936245	+	0.785603i	−0.976928	−	0.213569i	$-0.931491\pi$
$313$	−16.5639	+	13.8987i	−0.936245	+	0.785603i	0.0406830	+	0.999172i	$0.487047\pi$
$314$		0			0
$315$	−2.57130	+	24.1576i	−0.144876	+	1.36113i
$316$		0			0
$317$	−2.93605	+	8.06674i	−0.164905	+	0.453073i	−0.994430	−	0.105396i	$-0.966389\pi$
$317$	−2.93605	+	8.06674i	−0.164905	+	0.453073i	0.829525	+	0.558469i	$0.188611\pi$
$318$		0			0
$319$	4.66899	−	5.56429i	0.261413	−	0.311540i
$320$		0			0
$321$	4.70920	−	14.4610i	0.262842	−	0.807132i
$322$		0			0
$323$	−0.359861			−0.0200232
$324$		0			0
$325$	3.18979			0.176938
$326$		0			0
$327$	−1.02847	+	3.15822i	−0.0568746	+	0.174650i
$328$		0			0
$329$	16.6689	−	19.8653i	0.918988	−	1.09521i
$330$		0			0
$331$	−2.92776	+	8.04395i	−0.160924	+	0.442135i	−0.993781	−	0.111353i	$-0.964482\pi$
$331$	−2.92776	+	8.04395i	−0.160924	+	0.442135i	0.832857	+	0.553489i	$0.186704\pi$
$332$		0			0
$333$	14.1648	−	6.28421i	0.776228	−	0.344372i
$334$		0			0
$335$	17.6290	−	14.7925i	0.963174	−	0.808199i
$336$		0			0
$337$	4.93833	−	28.0067i	0.269008	−	1.52562i	−0.488365	−	0.872639i	$-0.662407\pi$
$337$	4.93833	−	28.0067i	0.269008	−	1.52562i	0.757373	−	0.652982i	$-0.226482\pi$
$338$		0			0
$339$	−10.9143	−	17.4922i	−0.592783	−	0.950045i
$340$		0			0
$341$	10.7022	+	6.17893i	0.579558	+	0.334608i
$342$		0			0
$343$	5.16130	−	2.97988i	0.278684	−	0.160898i
$344$		0			0
$345$	21.0743	+	16.4874i	1.13460	+	0.887654i
$346$		0			0
$347$	27.8204	−	10.1258i	1.49348	−	0.543581i	0.539115	−	0.842232i	$-0.318759\pi$
$347$	27.8204	−	10.1258i	1.49348	−	0.543581i	0.954362	+	0.298651i	$0.0965367\pi$
$348$		0			0
$349$	−3.33838	−	18.9329i	−0.178700	−	1.01346i	−0.933786	−	0.357831i	$-0.883516\pi$
$349$	−3.33838	−	18.9329i	−0.178700	−	1.01346i	0.755087	−	0.655625i	$-0.227595\pi$
$350$		0			0
$351$	−9.36461	−	19.2971i	−0.499846	−	1.03000i
$352$		0			0
$353$	25.8338	−	4.55520i	1.37500	−	0.242449i	0.563167	−	0.826343i	$-0.309583\pi$
$353$	25.8338	−	4.55520i	1.37500	−	0.242449i	0.811830	+	0.583894i	$0.198472\pi$
$354$		0			0
$355$	−5.06283	−	13.9100i	−0.268707	−	0.738266i
$356$		0			0
$357$	12.4137	+	30.7834i	0.657003	+	1.62923i
$358$		0			0
$359$	−2.38742	−	4.13514i	−0.126003	−	0.218244i	0.796121	−	0.605137i	$-0.206882\pi$
$359$	−2.38742	−	4.13514i	−0.126003	−	0.218244i	−0.922125	+	0.386893i	$0.873548\pi$
$360$		0			0
$361$	−9.49726	+	16.4497i	−0.499856	+	0.865776i
$362$		0			0
$363$	−13.4903	−	7.18433i	−0.708057	−	0.377080i
$364$		0			0
$365$	−18.3216	−	3.23060i	−0.958998	−	0.169097i
$366$		0			0
$367$	5.30033	+	6.31669i	0.276675	+	0.329728i	0.886431	−	0.462861i	$-0.153177\pi$
$367$	5.30033	+	6.31669i	0.276675	+	0.329728i	−0.609756	+	0.792589i	$0.708733\pi$
$368$		0			0
$369$	17.9105	+	18.5959i	0.932382	+	0.968062i
$370$		0			0
$371$	−29.3420	−	10.6796i	−1.52336	−	0.554458i
$372$		0			0
$373$	6.16301	+	5.17138i	0.319109	+	0.267764i	0.788245	−	0.615362i	$-0.210990\pi$
$373$	6.16301	+	5.17138i	0.319109	+	0.267764i	−0.469136	+	0.883126i	$0.655435\pi$
$374$		0			0
$375$	15.2863	−	13.7456i	0.789383	−	0.709821i
$376$		0			0
$377$		−	20.3275i		−	1.04692i
$378$		0			0
$379$		−	4.86129i		−	0.249708i	−0.992175	−	0.124854i	$-0.960154\pi$
$379$		−	4.86129i		−	0.249708i	0.992175	−	0.124854i	$-0.0398462\pi$
$380$		0			0
$381$	0.179769	+	0.848500i	0.00920987	+	0.0434700i
$382$		0			0
$383$	5.48805	+	4.60502i	0.280426	+	0.235306i	0.772142	−	0.635450i	$-0.219186\pi$
$383$	5.48805	+	4.60502i	0.280426	+	0.235306i	−0.491715	+	0.870756i	$0.663630\pi$
$384$		0			0
$385$	−11.2246	−	4.08540i	−0.572056	−	0.208211i
$386$		0			0
$387$	−0.203204	−	2.96211i	−0.0103295	−	0.150572i
$388$		0			0
$389$	2.93311	+	3.49554i	0.148715	+	0.177231i	0.835259	−	0.549857i	$-0.185318\pi$
$389$	2.93311	+	3.49554i	0.148715	+	0.177231i	−0.686544	+	0.727088i	$0.740873\pi$
$390$		0			0
$391$	36.0024	+	6.34819i	1.82072	+	0.321042i
$392$		0			0
$393$	1.25977	+	36.7706i	0.0635472	+	1.85483i
$394$		0			0
$395$	−2.45407	+	4.25057i	−0.123477	+	0.213869i
$396$		0			0
$397$	11.2617	+	19.5059i	0.565211	+	0.978974i	0.997030	+	0.0770139i	$0.0245386\pi$
$397$	11.2617	+	19.5059i	0.565211	+	0.978974i	−0.431819	+	0.901960i	$0.642128\pi$
$398$		0			0
$399$	−0.499612	−	0.0705520i	−0.0250119	−	0.00353202i
$400$		0			0
$401$	1.09876	+	3.01882i	0.0548694	+	0.150752i	0.964099	−	0.265542i	$-0.0855508\pi$
$401$	1.09876	+	3.01882i	0.0548694	+	0.150752i	−0.909230	+	0.416294i	$0.863329\pi$
$402$		0			0
$403$	34.0583	−	6.00540i	1.69657	−	0.299150i
$404$		0			0
$405$	−17.1385	−	6.97707i	−0.851620	−	0.346693i
$406$		0			0
$407$	1.32306	+	7.50344i	0.0655816	+	0.371932i
$408$		0			0
$409$	7.52505	−	2.73890i	0.372090	−	0.135430i	−0.149205	−	0.988806i	$-0.547671\pi$
$409$	7.52505	−	2.73890i	0.372090	−	0.135430i	0.521295	+	0.853377i	$0.325449\pi$
$410$		0			0
$411$	−2.55975	+	18.1268i	−0.126263	+	0.894128i
$412$		0			0
$413$	−1.86352	+	1.07591i	−0.0916980	+	0.0529418i
$414$		0			0
$415$	6.95006	+	4.01262i	0.341165	+	0.196972i
$416$		0			0
$417$	−5.82632	+	0.199612i	−0.285316	+	0.00977503i
$418$		0			0
$419$	1.10342	−	6.25781i	0.0539057	−	0.305714i	−0.945920	−	0.324401i	$-0.894837\pi$
$419$	1.10342	−	6.25781i	0.0539057	−	0.305714i	0.999825	+	0.0186866i	$0.00594848\pi$
$420$		0			0
$421$	−13.8085	+	11.5867i	−0.672985	+	0.564702i	−0.913947	−	0.405833i	$-0.866982\pi$
$421$	−13.8085	+	11.5867i	−0.672985	+	0.564702i	0.240962	+	0.970535i	$0.422537\pi$
$422$		0			0
$423$	11.0236	+	16.3897i	0.535985	+	0.796896i
$424$		0			0
$425$	1.28590	−	3.53298i	0.0623753	−	0.171375i
$426$		0			0
$427$	−31.8156	+	37.9164i	−1.53966	+	1.83490i
$428$		0			0
$429$	10.3172	−	2.18588i	0.498119	−	0.105535i
$430$		0			0
$431$	2.84773			0.137170			0.0685852	−	0.997645i	$-0.478151\pi$
$431$	2.84773			0.137170			0.0685852	+	0.997645i	$0.478151\pi$
$432$		0			0
$433$	30.7388			1.47721			0.738607	−	0.674136i	$-0.235484\pi$
$433$	30.7388			1.47721			0.738607	+	0.674136i	$0.235484\pi$
$434$		0			0
$435$	−11.7256	−	13.0399i	−0.562199	−	0.625214i
$436$		0			0
$437$	−0.357217	+	0.425715i	−0.0170880	+	0.0203647i
$438$		0			0
$439$	−4.11871	+	11.3161i	−0.196575	+	0.540087i	−0.998343	−	0.0575499i	$-0.981671\pi$
$439$	−4.11871	+	11.3161i	−0.196575	+	0.540087i	0.801767	+	0.597636i	$0.203893\pi$
$440$		0			0
$441$	6.14585	+	24.7889i	0.292659	+	1.18042i
$442$		0			0
$443$	24.2195	−	20.3225i	1.15070	−	0.965553i	0.150965	−	0.988539i	$-0.451762\pi$
$443$	24.2195	−	20.3225i	1.15070	−	0.965553i	0.999736	+	0.0229864i	$0.00731743\pi$
$444$		0			0
$445$	−5.88199	+	33.3584i	−0.278833	+	1.58134i
$446$		0			0
$447$	1.77971	−	3.34183i	0.0841775	−	0.158063i
$448$		0			0
$449$	26.3821	+	15.2317i	1.24505	+	0.718830i	0.970118	−	0.242634i	$-0.0780113\pi$
$449$	26.3821	+	15.2317i	1.24505	+	0.718830i	0.274932	+	0.961464i	$0.411345\pi$
$450$		0			0
$451$	−10.9937	+	6.34720i	−0.517672	+	0.298878i
$452$		0			0
$453$	10.5697	−	4.26234i	0.496609	−	0.200262i
$454$		0			0
$455$	−31.4121	+	11.4331i	−1.47262	+	0.535991i
$456$		0			0
$457$	6.14414	+	34.8452i	0.287411	+	1.62999i	0.696545	+	0.717514i	$0.254720\pi$
$457$	6.14414	+	34.8452i	0.287411	+	1.62999i	−0.409134	+	0.912474i	$0.634169\pi$
$458$		0			0
$459$	−25.1484	+	2.59290i	−1.17383	+	0.121026i
$460$		0			0
$461$	21.3801	−	3.76990i	0.995773	−	0.175582i	0.348065	−	0.937470i	$-0.386839\pi$
$461$	21.3801	−	3.76990i	0.995773	−	0.175582i	0.647708	+	0.761889i	$0.275728\pi$
$462$		0			0
$463$	−9.72265	−	26.7128i	−0.451850	−	1.24145i	−0.931421	−	0.363944i	$-0.881430\pi$
$463$	−9.72265	−	26.7128i	−0.451850	−	1.24145i	0.479571	−	0.877503i	$-0.340792\pi$
$464$		0			0
$465$	18.3839	−	23.4984i	0.852535	−	1.08971i
$466$		0			0
$467$	16.9497	+	29.3577i	0.784337	+	1.35851i	0.929394	+	0.369088i	$0.120330\pi$
$467$	16.9497	+	29.3577i	0.784337	+	1.35851i	−0.145058	+	0.989423i	$0.546337\pi$
$468$		0			0
$469$	22.0426	−	38.1789i	1.01783	−	1.76294i
$470$		0			0
$471$	17.7435	−	11.0711i	0.817577	−	0.510129i
$472$		0			0
$473$	1.43765	+	0.253497i	0.0661034	+	0.0116558i
$474$		0			0
$475$	0.0367374	+	0.0437819i	0.00168563	+	0.00200885i
$476$		0			0
$477$	14.0050	−	19.2228i	0.641243	−	0.880151i
$478$		0			0
$479$	−35.9606	−	13.0886i	−1.64308	−	0.598033i	−0.655507	−	0.755189i	$-0.727545\pi$
$479$	−35.9606	−	13.0886i	−1.64308	−	0.598033i	−0.987574	+	0.157156i	$0.949767\pi$
$480$		0			0
$481$	16.3340	+	13.7058i	0.744764	+	0.624931i
$482$		0			0
$483$	48.7392	+	15.8719i	2.21771	+	0.722195i
$484$		0			0
$485$			27.1887i			1.23458i
$486$		0			0
$487$			6.27805i			0.284486i	0.989832	+	0.142243i	$0.0454314\pi$
$487$			6.27805i			0.284486i	−0.989832	+	0.142243i	$0.954569\pi$
$488$		0			0
$489$	−27.2104	−	8.86106i	−1.23050	−	0.400711i
$490$		0			0
$491$	13.7871	+	11.5688i	0.622205	+	0.522092i	0.898496	−	0.438982i	$-0.144661\pi$
$491$	13.7871	+	11.5688i	0.622205	+	0.522092i	−0.276291	+	0.961074i	$0.589105\pi$
$492$		0			0
$493$	−22.5145	−	8.19462i	−1.01400	−	0.369067i
$494$		0			0
$495$	5.35749	−	7.35353i	0.240801	−	0.330516i
$496$		0			0
$497$	−18.2276	−	21.7228i	−0.817619	−	0.974400i
$498$		0			0
$499$	−5.25720	−	0.926986i	−0.235345	−	0.0414976i	0.0547318	−	0.998501i	$-0.482570\pi$
$499$	−5.25720	−	0.926986i	−0.235345	−	0.0414976i	−0.290076	+	0.957003i	$0.593681\pi$
$500$		0			0
$501$	−15.6802	+	9.78369i	−0.700539	+	0.437103i
$502$		0			0
$503$	0.145531	−	0.252067i	0.00648889	−	0.0112391i	−0.862763	−	0.505609i	$-0.831268\pi$
$503$	0.145531	−	0.252067i	0.00648889	−	0.0112391i	0.869252	+	0.494370i	$0.164601\pi$
$504$		0			0
$505$	−17.3314	−	30.0188i	−0.771237	−	1.33582i
$506$		0			0
$507$	4.31150	−	5.51097i	0.191480	−	0.244751i
$508$		0			0
$509$	−1.90334	−	5.22938i	−0.0843640	−	0.231788i	0.890337	−	0.455303i	$-0.150469\pi$
$509$	−1.90334	−	5.22938i	−0.0843640	−	0.231788i	−0.974701	+	0.223515i	$0.928247\pi$
$510$		0			0
$511$	−35.0982	+	6.18875i	−1.55265	+	0.273774i
$512$		0			0
$513$	0.157011	−	0.350783i	0.00693221	−	0.0154875i
$514$		0			0
$515$	−2.40422	−	13.6350i	−0.105943	−	0.600831i
$516$		0			0
$517$	−9.12599	+	3.32159i	−0.401361	+	0.146083i
$518$		0			0
$519$	3.81082	−	1.53675i	0.167277	−	0.0674558i
$520$		0			0
$521$	−22.0203	+	12.7134i	−0.964727	+	0.556985i	−0.897625	−	0.440761i	$-0.854709\pi$
$521$	−22.0203	+	12.7134i	−0.964727	+	0.556985i	−0.0671023	+	0.997746i	$0.521375\pi$
$522$		0			0
$523$	13.8218	+	7.98001i	0.604384	+	0.348941i	0.770764	−	0.637120i	$-0.219875\pi$
$523$	13.8218	+	7.98001i	0.604384	+	0.348941i	−0.166380	+	0.986062i	$0.553208\pi$
$524$		0			0
$525$	2.47793	−	4.65289i	0.108146	−	0.203069i
$526$		0			0
$527$	7.07840	−	40.1436i	0.308340	−	1.74868i
$528$		0			0
$529$	25.6287	−	21.5050i	1.11429	−	0.935000i
$530$		0			0
$531$	−0.394409	−	1.59082i	−0.0171159	−	0.0690359i
$532$		0			0
$533$	−12.1505	+	33.3831i	−0.526294	+	1.44598i
$534$		0			0
$535$	11.6043	−	13.8295i	0.501700	−	0.597903i
$536$		0			0
$537$	−13.9928	−	15.5612i	−0.603835	−	0.671517i
$538$		0			0
$539$	−12.5572			−0.540878
$540$		0			0
$541$	10.3738			0.446006			0.223003	−	0.974818i	$-0.428414\pi$
$541$	10.3738			0.446006			0.223003	+	0.974818i	$0.428414\pi$
$542$		0			0
$543$	6.31397	−	1.33772i	0.270959	−	0.0574072i
$544$		0			0
$545$	−2.53434	+	3.02031i	−0.108559	+	0.129376i
$546$		0			0
$547$	10.2018	−	28.0292i	0.436197	−	1.19844i	−0.505750	−	0.862680i	$-0.668784\pi$
$547$	10.2018	−	28.0292i	0.436197	−	1.19844i	0.941947	−	0.335762i	$-0.108994\pi$
$548$		0			0
$549$	−21.0405	−	31.2827i	−0.897985	−	1.33511i
$550$		0			0
$551$	0.279008	−	0.234115i	0.0118861	−	0.00997365i
$552$		0			0
$553$	−1.63270	+	9.25951i	−0.0694295	+	0.393754i
$554$		0			0
$555$	18.3840	−	0.629843i	0.780359	−	0.0267354i
$556$		0			0
$557$	−6.15446	−	3.55328i	−0.260773	−	0.150557i	0.363914	−	0.931432i	$-0.381440\pi$
$557$	−6.15446	−	3.55328i	−0.260773	−	0.150557i	−0.624687	+	0.780875i	$0.714773\pi$
$558$		0			0
$559$	3.53803	−	2.04268i	0.149643	−	0.0863964i
$560$		0			0
$561$	1.73811	−	12.3084i	0.0733832	−	0.519661i
$562$		0			0
$563$	−11.6874	+	4.25388i	−0.492567	+	0.179280i	−0.576348	−	0.817204i	$-0.695523\pi$
$563$	−11.6874	+	4.25388i	−0.492567	+	0.179280i	0.0837808	+	0.996484i	$0.473300\pi$
$564$		0			0
$565$	−4.24995	−	24.1027i	−0.178797	−	1.01401i
$566$		0			0
$567$	−35.4231	−	1.33059i	−1.48763	−	0.0558794i
$568$		0			0
$569$	−32.9270	+	5.80592i	−1.38037	+	0.243397i	−0.814054	−	0.580790i	$-0.802744\pi$
$569$	−32.9270	+	5.80592i	−1.38037	+	0.243397i	−0.566319	+	0.824186i	$0.691633\pi$
$570$		0			0
$571$	−3.44978	−	9.47820i	−0.144369	−	0.396650i	0.846341	−	0.532641i	$-0.178800\pi$
$571$	−3.44978	−	9.47820i	−0.144369	−	0.396650i	−0.990710	+	0.135991i	$0.956578\pi$
$572$		0			0
$573$	−34.5305	−	4.87617i	−1.44253	−	0.203705i
$574$		0			0
$575$	−2.90305	−	5.02823i	−0.121066	−	0.209692i
$576$		0			0
$577$	3.85501	−	6.67707i	0.160486	−	0.277970i	−0.774557	−	0.632504i	$-0.782027\pi$
$577$	3.85501	−	6.67707i	0.160486	−	0.277970i	0.935043	+	0.354534i	$0.115360\pi$
$578$		0			0
$579$	−1.19346	−	34.8350i	−0.0495985	−	1.44769i
$580$		0			0
$581$	15.1401	+	2.66961i	0.628118	+	0.110754i
$582$		0			0
$583$	7.51667	+	8.95802i	0.311309	+	0.371003i
$584$		0			0
$585$	−1.74259	−	25.4018i	−0.0720473	−	1.05023i
$586$		0			0
$587$	−43.5402	−	15.8474i	−1.79710	−	0.654090i	−0.998645	−	0.0520323i	$-0.983430\pi$
$587$	−43.5402	−	15.8474i	−1.79710	−	0.654090i	−0.798453	−	0.602058i	$-0.794348\pi$
$588$		0			0
$589$	0.474683	+	0.398307i	0.0195590	+	0.0164119i
$590$		0			0
$591$	3.33339	+	15.7334i	0.137117	+	0.647186i
$592$		0			0
$593$			30.9200i			1.26973i	0.772623	+	0.634865i	$0.218944\pi$
$593$			30.9200i			1.26973i	−0.772623	+	0.634865i	$0.781056\pi$
$594$		0			0
$595$			39.4008i			1.61527i
$596$		0			0
$597$	12.8873	−	11.5884i	0.527444	−	0.474283i
$598$		0			0
$599$	−11.2593	−	9.44769i	−0.460043	−	0.386022i	0.383104	−	0.923705i	$-0.374855\pi$
$599$	−11.2593	−	9.44769i	−0.460043	−	0.386022i	−0.843147	+	0.537683i	$0.819300\pi$
$600$		0			0
$601$	−9.62834	−	3.50443i	−0.392748	−	0.142949i	0.138094	−	0.990419i	$-0.455902\pi$
$601$	−9.62834	−	3.50443i	−0.392748	−	0.142949i	−0.530843	+	0.847470i	$0.678124\pi$
$602$		0			0
$603$	23.2939	+	24.1853i	0.948600	+	0.984901i
$604$		0			0
$605$	−11.6621	−	13.8983i	−0.474130	−	0.565047i
$606$		0			0
$607$	6.97797	+	1.23040i	0.283227	+	0.0499406i	0.313457	−	0.949602i	$-0.398513\pi$
$607$	6.97797	+	1.23040i	0.283227	+	0.0499406i	−0.0302300	+	0.999543i	$0.509624\pi$
$608$		0			0
$609$	−29.6514	−	15.7910i	−1.20153	−	0.639884i
$610$		0			0
$611$	−13.5892	+	23.5371i	−0.549758	+	0.952210i
$612$		0			0
$613$	0.308457	+	0.534263i	0.0124585	+	0.0215787i	0.872187	−	0.489172i	$-0.162701\pi$
$613$	0.308457	+	0.534263i	0.0124585	+	0.0215787i	−0.859729	+	0.510751i	$0.829368\pi$
$614$		0			0
$615$	11.4621	+	28.4237i	0.462197	+	1.14615i
$616$		0			0
$617$	−2.09283	−	5.75001i	−0.0842542	−	0.231487i	0.890410	−	0.455159i	$-0.150418\pi$
$617$	−2.09283	−	5.75001i	−0.0842542	−	0.231487i	−0.974664	+	0.223672i	$0.928195\pi$
$618$		0			0
$619$	25.9300	−	4.57216i	1.04221	−	0.183770i	0.373761	−	0.927525i	$-0.378068\pi$
$619$	25.9300	−	4.57216i	1.04221	−	0.183770i	0.668453	+	0.743754i	$0.266957\pi$
$620$		0			0
$621$	−21.8962	+	32.3243i	−0.878666	+	1.29713i
$622$		0			0
$623$	11.2679	+	63.9036i	0.451440	+	2.56024i
$624$		0			0
$625$	19.3005	−	7.02482i	0.772022	−	0.280993i
$626$		0			0
$627$	0.148827	+	0.116435i	0.00594359	+	0.00464996i
$628$		0			0
$629$	21.7651	−	12.5661i	0.867832	−	0.501043i
$630$		0			0
$631$	−26.5740	−	15.3425i	−1.05790	−	0.610776i	−0.133046	−	0.991110i	$-0.542476\pi$
$631$	−26.5740	−	15.3425i	−1.05790	−	0.610776i	−0.924849	+	0.380334i	$0.875809\pi$
$632$		0			0
$633$	9.46432	+	15.1683i	0.376173	+	0.602887i
$634$		0			0
$635$	−0.178783	+	1.01393i	−0.00709479	+	0.0402365i
$636$		0			0
$637$	−26.9200	+	22.5886i	−1.06661	+	0.894993i
$638$		0			0
$639$	19.7432	−	8.75905i	0.781029	−	0.346503i
$640$		0			0
$641$	−8.83774	+	24.2815i	−0.349070	+	0.959061i	0.633594	+	0.773665i	$0.281579\pi$
$641$	−8.83774	+	24.2815i	−0.349070	+	0.959061i	−0.982664	+	0.185395i	$0.940643\pi$
$642$		0			0
$643$	−13.8364	+	16.4896i	−0.545654	+	0.650285i	−0.966445	−	0.256872i	$-0.917308\pi$
$643$	−13.8364	+	16.4896i	−0.545654	+	0.650285i	0.420791	+	0.907157i	$0.361752\pi$
$644$		0			0
$645$	1.09132	−	3.35122i	0.0429707	−	0.131954i
$646$		0			0
$647$	0.928743			0.0365127			0.0182563	−	0.999833i	$-0.494189\pi$
$647$	0.928743			0.0365127			0.0182563	+	0.999833i	$0.494189\pi$
$648$		0			0
$649$	0.805857			0.0316327
$650$		0			0
$651$	17.6976	−	54.3455i	0.693622	−	2.12997i
$652$		0			0
$653$	16.9109	−	20.1536i	0.661774	−	0.788672i	−0.325865	−	0.945416i	$-0.605655\pi$
$653$	16.9109	−	20.1536i	0.661774	−	0.788672i	0.987639	+	0.156744i	$0.0500999\pi$
$654$		0			0
$655$	−14.9374	+	41.0403i	−0.583654	+	1.60358i
$656$		0			0
$657$	2.87313	−	26.9934i	0.112092	−	1.05311i
$658$		0			0
$659$	−22.9954	+	19.2954i	−0.895774	+	0.751644i	−0.969360	−	0.245645i	$-0.921000\pi$
$659$	−22.9954	+	19.2954i	−0.895774	+	0.751644i	0.0735854	+	0.997289i	$0.476556\pi$
$660$		0			0
$661$	3.79072	−	21.4982i	0.147442	−	0.836184i	−0.817932	−	0.575315i	$-0.804880\pi$
$661$	3.79072	−	21.4982i	0.147442	−	0.836184i	0.965374	−	0.260870i	$-0.0840092\pi$
$662$		0			0
$663$	−18.4149	−	29.5133i	−0.715174	−	1.14620i
$664$		0			0
$665$	−0.518705	−	0.299475i	−0.0201145	−	0.0116131i
$666$		0			0
$667$	−32.0433	+	18.5002i	−1.24072	+	0.716331i
$668$		0			0
$669$	14.2048	+	11.1131i	0.549188	+	0.429656i
$670$		0			0
$671$	17.4186	−	6.33984i	0.672436	−	0.244747i
$672$		0			0
$673$	−1.87849	−	10.6534i	−0.0724103	−	0.410659i	−0.999370	−	0.0354977i	$-0.988698\pi$
$673$	−1.87849	−	10.6534i	−0.0724103	−	0.410659i	0.926959	−	0.375162i	$-0.122413\pi$
$674$		0			0
$675$	2.88280	+	2.79493i	0.110959	+	0.107577i
$676$		0			0
$677$	−40.8652	+	7.20563i	−1.57058	+	0.276935i	−0.890076	−	0.455813i	$-0.849349\pi$
$677$	−40.8652	+	7.20563i	−1.57058	+	0.276935i	−0.680501	+	0.732748i	$0.738238\pi$
$678$		0			0
$679$	17.8140	+	48.9435i	0.683637	+	1.87828i
$680$		0			0
$681$	12.8954	+	31.9780i	0.494153	+	1.22540i
$682$		0			0
$683$	−18.1240	−	31.3917i	−0.693496	−	1.20117i	−0.970685	−	0.240355i	$-0.922736\pi$
$683$	−18.1240	−	31.3917i	−0.693496	−	1.20117i	0.277189	−	0.960815i	$-0.410597\pi$
$684$		0			0
$685$	−10.8654	+	18.8195i	−0.415147	+	0.719056i
$686$		0			0
$687$	28.0784	+	14.9533i	1.07126	+	0.570504i
$688$		0			0
$689$	32.2283	+	5.68273i	1.22780	+	0.216495i
$690$		0			0
$691$	25.2629	+	30.1072i	0.961047	+	1.14533i	0.989324	+	0.145732i	$0.0465536\pi$
$691$	25.2629	+	30.1072i	0.961047	+	1.14533i	−0.0282768	+	0.999600i	$0.509002\pi$
$692$		0			0
$693$	4.82621	−	16.7476i	0.183333	−	0.636188i
$694$		0			0
$695$	−6.50285	−	2.36684i	−0.246667	−	0.0897795i
$696$		0			0
$697$	32.0765	+	26.9154i	1.21499	+	1.01949i
$698$		0			0
$699$	−4.13870	+	3.72156i	−0.156540	+	0.140762i
$700$		0			0
$701$			7.41875i			0.280202i	0.990137	+	0.140101i	$0.0447428\pi$
$701$			7.41875i			0.280202i	−0.990137	+	0.140101i	$0.955257\pi$
$702$		0			0
$703$			0.382046i			0.0144091i
$704$		0			0
$705$	4.85970	+	22.9375i	0.183027	+	0.863876i
$706$		0			0
$707$	−50.8671	−	42.6826i	−1.91306	−	1.60524i
$708$		0			0
$709$	1.68692	+	0.613990i	0.0633538	+	0.0230589i	0.373503	−	0.927629i	$-0.378157\pi$
$709$	1.68692	+	0.613990i	0.0633538	+	0.0230589i	−0.310149	+	0.950688i	$0.600379\pi$
$710$		0			0
$711$	−6.43262	−	3.14791i	−0.241242	−	0.118056i
$712$		0			0
$713$	−40.4633	−	48.2223i	−1.51536	−	1.80594i
$714$		0			0
$715$	12.3287	+	2.17388i	0.461067	+	0.0812986i
$716$		0			0
$717$	−1.13814	−	33.2203i	−0.0425046	−	1.24063i
$718$		0			0
$719$	11.8709	−	20.5610i	0.442710	−	0.766797i	−0.555179	−	0.831731i	$-0.687350\pi$
$719$	11.8709	−	20.5610i	0.442710	−	0.766797i	0.997890	+	0.0649341i	$0.0206837\pi$
$720$		0			0
$721$	−13.2615	−	22.9697i	−0.493886	−	0.855435i
$722$		0			0
$723$	−8.50508	−	1.20103i	−0.316307	−	0.0446669i
$724$		0			0
$725$	1.30147	+	3.57576i	0.0483354	+	0.132800i
$726$		0			0
$727$	−49.1597	+	8.66818i	−1.82323	+	0.321485i	−0.977309	−	0.211819i	$-0.932061\pi$
$727$	−49.1597	+	8.66818i	−1.82323	+	0.321485i	−0.845924	+	0.533304i	$0.820950\pi$
$728$		0			0
$729$	8.44502	−	25.6453i	0.312779	−	0.949826i
$730$		0			0
$731$	−0.836170	−	4.74215i	−0.0309269	−	0.175395i
$732$		0			0
$733$	−14.6838	+	5.34446i	−0.542358	+	0.197402i	−0.598648	−	0.801012i	$-0.704295\pi$
$733$	−14.6838	+	5.34446i	−0.542358	+	0.197402i	0.0562901	+	0.998414i	$0.482073\pi$
$734$		0			0
$735$	−4.23905	+	30.0187i	−0.156360	+	1.10726i
$736$		0			0
$737$	−14.2981	+	8.25500i	−0.526677	+	0.304077i
$738$		0			0
$739$	19.0474	+	10.9970i	0.700671	+	0.404532i	0.807597	−	0.589735i	$-0.200768\pi$
$739$	19.0474	+	10.9970i	0.700671	+	0.404532i	−0.106927	+	0.994267i	$0.534101\pi$
$740$		0			0
$741$	0.528504	−	0.0181067i	0.0194151	−	0.000665168i
$742$		0			0
$743$	−4.13356	+	23.4426i	−0.151646	+	0.860025i	0.810143	+	0.586232i	$0.199389\pi$
$743$	−4.13356	+	23.4426i	−0.151646	+	0.860025i	−0.961789	+	0.273793i	$0.911722\pi$
$744$		0			0
$745$	3.44291	−	2.88894i	0.126138	−	0.105843i
$746$		0			0
$747$	−5.14712	+	10.5179i	−0.188323	+	0.384831i
$748$		0			0
$749$	11.8284	−	32.4982i	0.432199	−	1.18746i
$750$		0			0
$751$	6.07013	−	7.23410i	0.221502	−	0.263976i	−0.643837	−	0.765163i	$-0.722659\pi$
$751$	6.07013	−	7.23410i	0.221502	−	0.263976i	0.865339	+	0.501187i	$0.167103\pi$
$752$		0			0
$753$	−27.3568	+	5.79601i	−0.996938	+	0.211218i
$754$		0			0
$755$	13.5285			0.492354
$756$		0			0
$757$	−4.10163			−0.149076			−0.0745381	−	0.997218i	$-0.523748\pi$
$757$	−4.10163			−0.149076			−0.0745381	+	0.997218i	$0.523748\pi$
$758$		0			0
$759$	−12.8355	−	14.2741i	−0.465898	−	0.518119i
$760$		0			0
$761$	2.38630	−	2.84388i	0.0865031	−	0.103090i	−0.721057	−	0.692876i	$-0.756343\pi$
$761$	2.38630	−	2.84388i	0.0865031	−	0.103090i	0.807560	+	0.589786i	$0.200788\pi$
$762$		0			0
$763$	−2.58327	+	7.09748i	−0.0935207	+	0.256946i
$764$		0			0
$765$	−28.8372	−	8.31012i	−1.04261	−	0.300453i
$766$		0			0
$767$	1.72759	−	1.44962i	0.0623796	−	0.0523427i
$768$		0			0
$769$	−3.33857	+	18.9340i	−0.120392	+	0.682777i	0.863547	+	0.504269i	$0.168238\pi$
$769$	−3.33857	+	18.9340i	−0.120392	+	0.682777i	−0.983939	+	0.178508i	$0.942873\pi$
$770$		0			0
$771$	−0.155009	+	0.291066i	−0.00558250	+	0.0104825i
$772$		0			0
$773$	−46.8648	−	27.0574i	−1.68561	−	0.973187i	−0.957812	−	0.287394i	$-0.907211\pi$
$773$	−46.8648	−	27.0574i	−1.68561	−	0.973187i	−0.727797	−	0.685793i	$-0.759456\pi$
$774$		0			0
$775$	−5.60661	+	3.23698i	−0.201396	+	0.116276i
$776$		0			0
$777$	32.6811	−	13.1790i	1.17243	−	0.472793i
$778$		0			0
$779$	−0.598143	+	0.217706i	−0.0214307	+	0.00780013i
$780$		0			0
$781$	1.84411	+	10.4584i	0.0659873	+	0.374232i
$782$		0			0
$783$	17.8112	−	18.3711i	0.636521	−	0.656531i
$784$		0			0
$785$	24.4490	−	4.31101i	0.872621	−	0.153867i
$786$		0			0
$787$	3.10446	+	8.52944i	0.110662	+	0.304042i	0.982645	−	0.185494i	$-0.0593885\pi$
$787$	3.10446	+	8.52944i	0.110662	+	0.304042i	−0.871983	+	0.489536i	$0.837166\pi$
$788$		0			0
$789$	−21.9084	+	28.0034i	−0.779960	+	0.996947i
$790$		0			0
$791$	−23.4425	−	40.6036i	−0.833519	−	1.44370i
$792$		0			0
$793$	25.9373	−	44.9247i	0.921061	−	1.59532i
$794$		0			0
$795$	23.9521	−	14.9450i	0.849494	−	0.530044i
$796$		0			0
$797$	14.0596	+	2.47908i	0.498015	+	0.0878135i	0.417013	−	0.908900i	$-0.363077\pi$
$797$	14.0596	+	2.47908i	0.498015	+	0.0878135i	0.0810020	+	0.996714i	$0.474188\pi$
$798$		0			0
$799$	20.5913	+	24.5397i	0.728466	+	0.868153i
$800$		0			0
$801$	−49.1472	−	5.23114i	−1.73653	−	0.184833i
$802$		0			0
$803$	12.5422	+	4.56498i	0.442604	+	0.161095i
$804$		0			0
$805$	46.6110	+	39.1112i	1.64282	+	1.37849i
$806$		0			0
$807$	24.1669	+	7.86994i	0.850716	+	0.277035i
$808$		0			0
$809$			25.4973i			0.896439i	0.893924	+	0.448219i	$0.147942\pi$
$809$			25.4973i			0.896439i	−0.893924	+	0.448219i	$0.852058\pi$
$810$		0			0
$811$		−	20.0469i		−	0.703942i	−0.936011	−	0.351971i	$-0.885511\pi$
$811$		−	20.0469i		−	0.703942i	0.936011	−	0.351971i	$-0.114489\pi$
$812$		0			0
$813$	50.6917	+	16.5077i	1.77783	+	0.578950i
$814$		0			0
$815$	−26.0223	−	21.8353i	−0.911521	−	0.764857i
$816$		0			0
$817$	0.0687852	+	0.0250358i	0.00240649	+	0.000875891i
$818$		0			0
$819$	−19.7801	−	44.5849i	−0.691171	−	1.55792i
$820$		0			0
$821$	−0.418628	−	0.498901i	−0.0146102	−	0.0174118i	0.758690	−	0.651452i	$-0.225840\pi$
$821$	−0.418628	−	0.498901i	−0.0146102	−	0.0174118i	−0.773300	+	0.634040i	$0.781395\pi$
$822$		0			0
$823$	47.6805	+	8.40737i	1.66204	+	0.293062i	0.924199	−	0.381912i	$-0.124734\pi$
$823$	47.6805	+	8.40737i	1.66204	+	0.293062i	0.737841	+	0.674975i	$0.235845\pi$
$824$		0			0
$825$	−1.67492	+	1.04507i	−0.0583132	+	0.0363847i
$826$		0			0
$827$	−4.39612	+	7.61431i	−0.152868	+	0.264775i	−0.932281	−	0.361736i	$-0.882184\pi$
$827$	−4.39612	+	7.61431i	−0.152868	+	0.264775i	0.779413	+	0.626511i	$0.215518\pi$
$828$		0			0
$829$	−13.9643	−	24.1869i	−0.485000	−	0.840045i	0.514851	−	0.857279i	$-0.327847\pi$
$829$	−13.9643	−	24.1869i	−0.485000	−	0.840045i	−0.999851	+	0.0172346i	$0.994514\pi$
$830$		0			0
$831$	−27.7380	+	35.4548i	−0.962221	+	1.22991i
$832$		0			0
$833$	14.1666	+	38.9225i	0.490845	+	1.34858i
$834$		0			0
$835$	−21.6059	+	3.80970i	−0.747703	+	0.131840i
$836$		0			0
$837$	36.0425	+	24.4149i	1.24581	+	0.843902i
$838$		0			0
$839$	8.99089	+	50.9899i	0.310400	+	1.76037i	0.596928	+	0.802295i	$0.296388\pi$
$839$	8.99089	+	50.9899i	0.310400	+	1.76037i	−0.286528	+	0.958072i	$0.592501\pi$
$840$		0			0
$841$	−4.46395	+	1.62475i	−0.153929	+	0.0560257i
$842$		0			0
$843$	14.1815	−	5.71880i	0.488436	−	0.196966i
$844$		0			0
$845$	7.19316	−	4.15297i	0.247452	−	0.142867i
$846$		0			0
$847$	−30.0995	−	17.3779i	−1.03423	−	0.597113i
$848$		0			0
$849$	11.3329	−	21.2802i	0.388943	−	0.730334i
$850$		0			0
$851$	6.73953	−	38.2218i	0.231028	−	1.31023i
$852$		0			0
$853$	15.1451	−	12.7082i	0.518557	−	0.435121i	−0.345572	−	0.938392i	$-0.612315\pi$
$853$	15.1451	−	12.7082i	0.518557	−	0.435121i	0.864128	+	0.503272i	$0.167870\pi$
$854$		0			0
$855$	0.328585	−	0.316474i	0.0112374	−	0.0108232i
$856$		0			0
$857$	−12.8271	+	35.2420i	−0.438164	+	1.20385i	0.502521	+	0.864565i	$0.332406\pi$
$857$	−12.8271	+	35.2420i	−0.438164	+	1.20385i	−0.940685	+	0.339281i	$0.889816\pi$
$858$		0			0
$859$	35.8059	−	42.6718i	1.22168	−	1.45594i	0.372342	−	0.928096i	$-0.378555\pi$
$859$	35.8059	−	42.6718i	1.22168	−	1.45594i	0.849339	−	0.527848i	$-0.177001\pi$
$860$		0			0
$861$	39.2565	+	43.6566i	1.33786	+	1.48781i
$862$		0			0
$863$	31.9231			1.08668			0.543338	−	0.839514i	$-0.317160\pi$
$863$	31.9231			1.08668			0.543338	+	0.839514i	$0.317160\pi$
$864$		0			0
$865$	4.87760			0.165843
$866$		0			0
$867$	−11.3067	+	2.39552i	−0.383996	+	0.0813561i
$868$		0			0
$869$	2.26338	−	2.69739i	0.0767800	−	0.0915028i
$870$		0			0
$871$	−15.8026	+	43.4172i	−0.535449	+	1.47113i
$872$		0			0
$873$	−39.5786	+	2.71514i	−1.33953	+	0.0918937i
$874$		0			0
$875$	35.8109	−	30.0489i	1.21063	−	1.01584i
$876$		0			0
$877$	−4.45707	+	25.2773i	−0.150504	+	0.853553i	0.812277	+	0.583272i	$0.198228\pi$
$877$	−4.45707	+	25.2773i	−0.150504	+	0.853553i	−0.962781	+	0.270281i	$0.912883\pi$
$878$		0			0
$879$	−8.29796	+	0.284291i	−0.279883	+	0.00958890i
$880$		0			0
$881$	16.5326	+	9.54510i	0.556997	+	0.321582i	0.751939	−	0.659232i	$-0.229119\pi$
$881$	16.5326	+	9.54510i	0.556997	+	0.321582i	−0.194942	+	0.980815i	$0.562452\pi$
$882$		0			0
$883$	7.99341	−	4.61500i	0.269000	−	0.155307i	−0.359433	−	0.933171i	$-0.617030\pi$
$883$	7.99341	−	4.61500i	0.269000	−	0.155307i	0.628433	+	0.777864i	$0.283697\pi$
$884$		0			0
$885$	0.272040	−	1.92645i	0.00914454	−	0.0647568i
$886$		0			0
$887$	−4.31271	+	1.56970i	−0.144807	+	0.0527053i	−0.413407	−	0.910546i	$-0.635661\pi$
$887$	−4.31271	+	1.56970i	−0.144807	+	0.0527053i	0.268600	+	0.963252i	$0.413439\pi$
$888$		0			0
$889$	0.342489	+	1.94235i	0.0114867	+	0.0651443i
$890$		0			0
$891$	11.2395	+	7.06455i	0.376539	+	0.236671i
$892$		0			0
$893$	−0.479570	+	0.0845612i	−0.0160482	+	0.00282973i
$894$		0			0
$895$	−8.49637	−	23.3436i	−0.284002	−	0.780290i
$896$		0			0
$897$	−53.1936	−	7.51166i	−1.77608	−	0.250807i
$898$		0			0
$899$	20.6282	+	35.7291i	0.687989	+	1.19163i
$900$		0			0
$901$	19.2863	−	33.4049i	0.642521	−	1.11288i
$902$		0			0
$903$	−0.231178	−	6.74769i	−0.00769313	−	0.224549i
$904$		0			0
$905$	7.54498	+	1.33038i	0.250804	+	0.0442234i
$906$		0			0
$907$	−17.1965	−	20.4940i	−0.571001	−	0.680493i	0.400835	−	0.916150i	$-0.368720\pi$
$907$	−17.1965	−	20.4940i	−0.571001	−	0.680493i	−0.971836	+	0.235657i	$0.924276\pi$
$908$		0			0
$909$	41.9677	−	28.2271i	1.39198	−	0.936233i
$910$		0			0
$911$	−12.4757	−	4.54078i	−0.413338	−	0.150443i	0.126977	−	0.991906i	$-0.459473\pi$
$911$	−12.4757	−	4.54078i	−0.413338	−	0.150443i	−0.540315	+	0.841463i	$0.681695\pi$
$912$		0			0
$913$	−4.41048	−	3.70083i	−0.145966	−	0.122480i
$914$		0			0
$915$	−9.27560	−	43.7803i	−0.306642	−	1.44733i
$916$		0			0
$917$			83.6651i			2.76287i
$918$		0			0
$919$		−	39.8408i		−	1.31423i	−0.753792	−	0.657113i	$-0.771778\pi$
$919$		−	39.8408i		−	1.31423i	0.753792	−	0.657113i	$-0.228222\pi$
$920$		0			0
$921$	7.16658	−	6.44427i	0.236147	−	0.212346i
$922$		0			0
$923$	22.7666	+	19.1034i	0.749371	+	0.628797i
$924$		0			0
$925$	−3.75078	−	1.36517i	−0.123325	−	0.0448866i
$926$		0			0
$927$	19.6084	−	4.86146i	0.644024	−	0.159671i
$928$		0			0
$929$	10.7123	+	12.7665i	0.351460	+	0.418854i	0.912591	−	0.408873i	$-0.134078\pi$
$929$	10.7123	+	12.7665i	0.351460	+	0.418854i	−0.561131	+	0.827727i	$0.689634\pi$
$930$		0			0
$931$	−0.620085	−	0.109338i	−0.0203225	−	0.00358340i
$932$		0			0
$933$	−7.65824	−	4.07844i	−0.250720	−	0.133522i
$934$		0			0
$935$	7.37783	−	12.7788i	0.241281	−	0.417911i
$936$		0			0
$937$	22.4638	+	38.9084i	0.733860	+	1.27108i	0.955222	+	0.295892i	$0.0956167\pi$
$937$	22.4638	+	38.9084i	0.733860	+	1.27108i	−0.221361	+	0.975192i	$0.571050\pi$
$938$		0			0
$939$	−14.0066	−	34.7336i	−0.457089	−	1.13349i
$940$		0			0
$941$	−2.19719	−	6.03672i	−0.0716262	−	0.196791i	0.898714	−	0.438536i	$-0.144503\pi$
$941$	−2.19719	−	6.03672i	−0.0716262	−	0.196791i	−0.970340	+	0.241744i	$0.922281\pi$
$942$		0			0
$943$	63.6817	−	11.2288i	2.07376	−	0.365660i
$944$		0			0
$945$	−38.4068	−	17.1910i	−1.24937	−	0.559222i
$946$		0			0
$947$	−1.65412	−	9.38098i	−0.0537517	−	0.304841i	0.946065	−	0.323976i	$-0.105020\pi$
$947$	−1.65412	−	9.38098i	−0.0537517	−	0.304841i	−0.999817	+	0.0191352i	$0.993909\pi$
$948$		0			0
$949$	35.0995	−	12.7752i	1.13938	−	0.414700i
$950$		0			0
$951$	−11.7106	−	9.16181i	−0.379744	−	0.297092i
$952$		0			0
$953$	7.00032	−	4.04163i	0.226762	−	0.130921i	−0.382315	−	0.924032i	$-0.624873\pi$
$953$	7.00032	−	4.04163i	0.226762	−	0.130921i	0.609078	+	0.793111i	$0.291540\pi$
$954$		0			0
$955$	−35.8500	−	20.6980i	−1.16008	−	0.669773i
$956$		0			0
$957$	6.65989	+	10.6737i	0.215284	+	0.345032i
$958$		0			0
$959$	−7.22882	+	40.9967i	−0.233431	+	1.32385i
$960$		0			0
$961$	−30.0218	+	25.1913i	−0.968445	+	0.812622i
$962$		0			0
$963$	21.2905	+	15.5114i	0.686076	+	0.499848i
$964$		0			0
$965$	14.1511	−	38.8799i	0.455541	−	1.25159i
$966$		0			0
$967$	16.3234	−	19.4534i	0.524924	−	0.625580i	−0.436814	−	0.899552i	$-0.643893\pi$
$967$	16.3234	−	19.4534i	0.524924	−	0.625580i	0.961738	+	0.273972i	$0.0883376\pi$
$968$		0			0
$969$	0.193001	−	0.592665i	0.00620008	−	0.0190391i
$970$		0			0
$971$	36.3786			1.16745			0.583723	−	0.811953i	$-0.301595\pi$
$971$	36.3786			1.16745			0.583723	+	0.811953i	$0.301595\pi$
$972$		0			0
$973$	−13.2568			−0.424993
$974$		0			0
$975$	−1.71075	+	5.25335i	−0.0547878	+	0.168242i
$976$		0			0
$977$	−11.2491	+	13.4061i	−0.359889	+	0.428900i	−0.915360	−	0.402637i	$-0.868094\pi$
$977$	−11.2491	+	13.4061i	−0.359889	+	0.428900i	0.555470	+	0.831536i	$0.312538\pi$
$978$		0			0
$979$	8.31150	−	22.8357i	0.265637	−	0.729831i
$980$		0			0
$981$	−4.64976	−	3.38763i	−0.148455	−	0.108159i
$982$		0			0
$983$	−11.7563	+	9.86475i	−0.374969	+	0.314637i	−0.810724	−	0.585429i	$-0.800926\pi$
$983$	−11.7563	+	9.86475i	−0.374969	+	0.314637i	0.435754	+	0.900066i	$0.356482\pi$
$984$		0			0
$985$	−3.31510	+	18.8009i	−0.105628	+	0.599046i
$986$		0			0
$987$	23.7767	+	38.1066i	0.756821	+	1.21295i
$988$		0			0
$989$	−6.43998	−	3.71812i	−0.204779	−	0.118229i
$990$		0			0
$991$	−19.7778	+	11.4187i	−0.628262	+	0.362727i	−0.780079	−	0.625682i	$-0.784821\pi$
$991$	−19.7778	+	11.4187i	−0.628262	+	0.362727i	0.151817	+	0.988409i	$0.451488\pi$
$992$		0			0
$993$	−11.6776	−	9.13592i	−0.370576	−	0.289920i
$994$		0			0
$995$	19.3325	−	7.03644i	0.612880	−	0.223070i
$996$		0			0
$997$	3.26590	+	18.5218i	0.103432	+	0.586592i	0.991835	+	0.127528i	$0.0407041\pi$
$997$	3.26590	+	18.5218i	0.103432	+	0.586592i	−0.888403	+	0.459064i	$0.848185\pi$
$998$		0			0
$999$	2.75274	+	26.6987i	0.0870930	+	0.844711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.95.3	yes	36
4.3	odd	2		432.2.be.b.95.4	✓	36
27.2	odd	18		432.2.be.b.191.4	yes	36
108.83	even	18	inner	432.2.be.c.191.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.95.4	✓	36	4.3	odd	2
432.2.be.b.191.4	yes	36	27.2	odd	18
432.2.be.c.95.3	yes	36	1.1	even	1	trivial
432.2.be.c.191.3	yes	36	108.83	even	18	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.536320 + 1.64692i) q^{3} +(-1.32159 + 1.57501i) q^{5} +(-1.34711 + 3.70114i) q^{7} +(-2.42472 - 1.76656i) q^{9} +O(q^{10})\)	\(q+(-0.536320 + 1.64692i) q^{3} +(-1.32159 + 1.57501i) q^{5} +(-1.34711 + 3.70114i) q^{7} +(-2.42472 - 1.76656i) q^{9} +(1.12995 - 0.948137i) q^{11} +(0.716807 - 4.06522i) q^{13} +(-1.88513 - 3.02127i) q^{15} +(-4.21362 - 2.43274i) q^{17} +(0.0640532 - 0.0369811i) q^{19} +(-5.37302 - 4.20358i) q^{21} +(-7.06058 + 2.56984i) q^{23} +(0.134184 + 0.760995i) q^{25} +(4.20981 - 3.04590i) q^{27} +(4.84957 - 0.855110i) q^{29} +(2.86544 + 7.87273i) q^{31} +(0.955499 + 2.36944i) q^{33} +(-4.04902 - 7.01310i) q^{35} +(-2.58271 + 4.47338i) q^{37} +(6.31067 + 3.36078i) q^{39} +(-8.47540 - 1.49444i) q^{41} +(0.636160 + 0.758146i) q^{43} +(5.98684 - 1.48430i) q^{45} +(-6.18694 - 2.25186i) q^{47} +(-6.52144 - 5.47214i) q^{49} +(6.26638 - 5.63480i) q^{51} +7.92783i q^{53} +3.03273i q^{55} +(0.0265522 + 0.125325i) q^{57} +(0.418512 + 0.351174i) q^{59} +(11.8089 + 4.29808i) q^{61} +(9.80463 - 6.59450i) q^{63} +(5.45544 + 6.50153i) q^{65} +(-11.0229 - 1.94363i) q^{67} +(-0.445607 - 13.0065i) q^{69} +(-3.59983 + 6.23508i) q^{71} +(4.52432 + 7.83635i) q^{73} +(-1.32527 - 0.187146i) q^{75} +(1.98703 + 5.45933i) q^{77} +(2.35092 - 0.414531i) q^{79} +(2.75856 + 8.56682i) q^{81} +(-0.677795 - 3.84397i) q^{83} +(9.40028 - 3.42142i) q^{85} +(-1.19262 + 8.44549i) q^{87} +(14.2677 - 8.23747i) q^{89} +(14.0803 + 8.12928i) q^{91} +(-14.5026 + 0.496864i) q^{93} +(-0.0264065 + 0.149759i) q^{95} +(10.1301 - 8.50015i) q^{97} +(-4.41474 + 0.302857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59} + 63 q^{63} - 57 q^{65} - 63 q^{69} - 36 q^{71} + 9 q^{73} + 45 q^{75} - 81 q^{77} - 54 q^{81} + 27 q^{83} - 36 q^{85} - 45 q^{87} - 63 q^{89} - 27 q^{91} - 63 q^{93} + 72 q^{95} - 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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