LMFDB - Embedded newform 432.2.be.b.191.2

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			191.2
Character	$\chi$	$=$	432.191
Dual form			432.2.be.b.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +O(q^{10})$	\(q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +(-4.24267 - 3.56003i) q^{11} +(-0.0238977 - 0.135530i) q^{13} +(-0.837815 - 0.0535726i) q^{15} +(3.57989 - 2.06685i) q^{17} +(4.52888 + 2.61475i) q^{19} +(4.44500 + 1.94740i) q^{21} +(-2.38028 - 0.866350i) q^{23} +(0.827445 - 4.69267i) q^{25} +(3.92301 + 3.40735i) q^{27} +(-2.79825 - 0.493407i) q^{29} +(2.14487 - 5.89298i) q^{31} +(9.53413 - 1.05953i) q^{33} +(0.679019 - 1.17610i) q^{35} +(-4.89845 - 8.48436i) q^{37} +(0.198406 + 0.132114i) q^{39} +(-4.97642 + 0.877478i) q^{41} +(0.705455 - 0.840729i) q^{43} +(1.06894 - 0.985788i) q^{45} +(-1.84430 + 0.671271i) q^{47} +(-0.651243 + 0.546458i) q^{49} +(-1.69069 + 6.95730i) q^{51} +10.9889i q^{53} -2.68447i q^{55} +(-8.69184 + 2.54848i) q^{57} +(-3.92231 + 3.29121i) q^{59} +(5.00653 - 1.82223i) q^{61} +(-7.75531 + 3.24135i) q^{63} +(0.0428772 - 0.0510990i) q^{65} +(11.6299 - 2.05066i) q^{67} +(3.93180 - 1.94674i) q^{69} +(-7.77969 - 13.4748i) q^{71} +(-6.66989 + 11.5526i) q^{73} +(4.89088 + 6.64807i) q^{75} +(-5.30733 + 14.5818i) q^{77} +(2.12271 + 0.374291i) q^{79} +(-8.96057 + 0.841533i) q^{81} +(-1.26197 + 7.15699i) q^{83} +(1.88278 + 0.685274i) q^{85} +(3.96426 - 2.91644i) q^{87} +(2.58936 + 1.49497i) q^{89} +(-0.333929 + 0.192794i) q^{91} +(4.81966 + 9.73416i) q^{93} +(0.440153 + 2.49623i) q^{95} +(-4.42409 - 3.71225i) q^{97} +(-10.0727 + 13.2139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

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
$3$	−1.19574	+	1.25308i	−0.690361	+	0.723465i
$3$	−1.19574	+	1.25308i	−0.690361	+	0.723465i
$4$		0			0
$5$	0.311559	+	0.371302i	0.139334	+	0.166051i	0.831199	−	0.555975i	$-0.187655\pi$
$5$	0.311559	+	0.371302i	0.139334	+	0.166051i	−0.691865	+	0.722027i	$0.743211\pi$
$6$		0			0
$7$	−0.958275	−	2.63284i	−0.362194	−	0.995120i	−0.978252	−	0.207419i	$-0.933494\pi$
$7$	−0.958275	−	2.63284i	−0.362194	−	0.995120i	0.616058	−	0.787701i	$-0.288729\pi$
$8$		0			0
$9$	−0.140409	−	2.99671i	−0.0468031	−	0.998904i
$10$		0			0
$11$	−4.24267	−	3.56003i	−1.27921	−	1.07339i	−0.993352	−	0.115118i	$-0.963275\pi$
$11$	−4.24267	−	3.56003i	−1.27921	−	1.07339i	−0.285863	−	0.958271i	$-0.592280\pi$
$12$		0			0
$13$	−0.0238977	−	0.135530i	−0.00662802	−	0.0375894i	0.981314	−	0.192411i	$-0.0616307\pi$
$13$	−0.0238977	−	0.135530i	−0.00662802	−	0.0375894i	−0.987942	+	0.154822i	$0.950520\pi$
$14$		0			0
$15$	−0.837815	−	0.0535726i	−0.216323	−	0.0138324i
$16$		0			0
$17$	3.57989	−	2.06685i	0.868251	−	0.501285i	0.00148444	−	0.999999i	$-0.499527\pi$
$17$	3.57989	−	2.06685i	0.868251	−	0.501285i	0.866767	+	0.498714i	$0.166194\pi$
$18$		0			0
$19$	4.52888	+	2.61475i	1.03900	+	0.599864i	0.919549	−	0.392976i	$-0.128555\pi$
$19$	4.52888	+	2.61475i	1.03900	+	0.599864i	0.119447	+	0.992841i	$0.461888\pi$
$20$		0			0
$21$	4.44500	+	1.94740i	0.969979	+	0.424957i
$22$		0			0
$23$	−2.38028	−	0.866350i	−0.496322	−	0.180646i	0.0817170	−	0.996656i	$-0.473960\pi$
$23$	−2.38028	−	0.866350i	−0.496322	−	0.180646i	−0.578039	+	0.816009i	$0.696182\pi$
$24$		0			0
$25$	0.827445	−	4.69267i	0.165489	−	0.938535i
$26$		0			0
$27$	3.92301	+	3.40735i	0.754983	+	0.655744i
$28$		0			0
$29$	−2.79825	−	0.493407i	−0.519622	−	0.0916234i	−0.0923147	−	0.995730i	$-0.529427\pi$
$29$	−2.79825	−	0.493407i	−0.519622	−	0.0916234i	−0.427307	+	0.904107i	$0.640538\pi$
$30$		0			0
$31$	2.14487	−	5.89298i	0.385230	−	1.05841i	−0.583893	−	0.811831i	$-0.698471\pi$
$31$	2.14487	−	5.89298i	0.385230	−	1.05841i	0.969123	−	0.246580i	$-0.0793067\pi$
$32$		0			0
$33$	9.53413	−	1.05953i	1.65968	−	0.184441i
$34$		0			0
$35$	0.679019	−	1.17610i	0.114775	−	0.198796i
$36$		0			0
$37$	−4.89845	−	8.48436i	−0.805300	−	1.39482i	−0.916088	−	0.400977i	$-0.868671\pi$
$37$	−4.89845	−	8.48436i	−0.805300	−	1.39482i	0.110788	−	0.993844i	$-0.464663\pi$
$38$		0			0
$39$	0.198406	+	0.132114i	0.0317703	+	0.0211551i
$40$		0			0
$41$	−4.97642	+	0.877478i	−0.777187	+	0.137039i	−0.548152	−	0.836379i	$-0.684668\pi$
$41$	−4.97642	+	0.877478i	−0.777187	+	0.137039i	−0.229035	+	0.973418i	$0.573557\pi$
$42$		0			0
$43$	0.705455	−	0.840729i	0.107581	−	0.128210i	−0.709567	−	0.704638i	$-0.751109\pi$
$43$	0.705455	−	0.840729i	0.107581	−	0.128210i	0.817148	+	0.576428i	$0.195554\pi$
$44$		0			0
$45$	1.06894	−	0.985788i	0.159348	−	0.146953i
$46$		0			0
$47$	−1.84430	+	0.671271i	−0.269019	+	0.0979149i	−0.473008	−	0.881058i	$-0.656832\pi$
$47$	−1.84430	+	0.671271i	−0.269019	+	0.0979149i	0.203989	+	0.978973i	$0.434609\pi$
$48$		0			0
$49$	−0.651243	+	0.546458i	−0.0930347	+	0.0780654i
$50$		0			0
$51$	−1.69069	+	6.95730i	−0.236745	+	0.974217i
$52$		0			0
$53$			10.9889i			1.50944i	0.656048	+	0.754719i	$0.272227\pi$
$53$			10.9889i			1.50944i	−0.656048	+	0.754719i	$0.727773\pi$
$54$		0			0
$55$		−	2.68447i		−	0.361974i
$56$		0			0
$57$	−8.69184	+	2.54848i	−1.15126	+	0.337554i
$58$		0			0
$59$	−3.92231	+	3.29121i	−0.510642	+	0.428479i	−0.861355	−	0.508004i	$-0.830384\pi$
$59$	−3.92231	+	3.29121i	−0.510642	+	0.428479i	0.350713	+	0.936483i	$0.385939\pi$
$60$		0			0
$61$	5.00653	−	1.82223i	0.641020	−	0.233312i	−0.00100063	−	0.999999i	$-0.500319\pi$
$61$	5.00653	−	1.82223i	0.641020	−	0.233312i	0.642021	+	0.766687i	$0.278096\pi$
$62$		0			0
$63$	−7.75531	+	3.24135i	−0.977078	+	0.408372i
$64$		0			0
$65$	0.0428772	−	0.0510990i	0.00531826	−	0.00633805i
$66$		0			0
$67$	11.6299	−	2.05066i	1.42082	−	0.250528i	0.590148	−	0.807295i	$-0.299069\pi$
$67$	11.6299	−	2.05066i	1.42082	−	0.250528i	0.830669	+	0.556767i	$0.187958\pi$
$68$		0			0
$69$	3.93180	−	1.94674i	0.473333	−	0.234360i
$70$		0			0
$71$	−7.77969	−	13.4748i	−0.923279	−	1.59917i	−0.794306	−	0.607518i	$-0.792165\pi$
$71$	−7.77969	−	13.4748i	−0.923279	−	1.59917i	−0.128973	−	0.991648i	$-0.541168\pi$
$72$		0			0
$73$	−6.66989	+	11.5526i	−0.780651	+	1.35213i	0.150912	+	0.988547i	$0.451779\pi$
$73$	−6.66989	+	11.5526i	−0.780651	+	1.35213i	−0.931563	+	0.363580i	$0.881554\pi$
$74$		0			0
$75$	4.89088	+	6.64807i	0.564750	+	0.767653i
$76$		0			0
$77$	−5.30733	+	14.5818i	−0.604826	+	1.66175i
$78$		0			0
$79$	2.12271	+	0.374291i	0.238824	+	0.0421111i	0.291779	−	0.956486i	$-0.405753\pi$
$79$	2.12271	+	0.374291i	0.238824	+	0.0421111i	−0.0529551	+	0.998597i	$0.516864\pi$
$80$		0			0
$81$	−8.96057	+	0.841533i	−0.995619	+	0.0935036i
$82$		0			0
$83$	−1.26197	+	7.15699i	−0.138519	+	0.785582i	0.833825	+	0.552029i	$0.186146\pi$
$83$	−1.26197	+	7.15699i	−0.138519	+	0.785582i	−0.972344	+	0.233553i	$0.924965\pi$
$84$		0			0
$85$	1.88278	+	0.685274i	0.204216	+	0.0743284i
$86$		0			0
$87$	3.96426	−	2.91644i	0.425013	−	0.312675i
$88$		0			0
$89$	2.58936	+	1.49497i	0.274471	+	0.158466i	0.630918	−	0.775850i	$-0.282679\pi$
$89$	2.58936	+	1.49497i	0.274471	+	0.158466i	−0.356447	+	0.934316i	$0.616012\pi$
$90$		0			0
$91$	−0.333929	+	0.192794i	−0.0350053	+	0.0202103i
$92$		0			0
$93$	4.81966	+	9.73416i	0.499775	+	1.00939i
$94$		0			0
$95$	0.440153	+	2.49623i	0.0451587	+	0.256108i
$96$		0			0
$97$	−4.42409	−	3.71225i	−0.449198	−	0.376922i	0.389940	−	0.920840i	$-0.372496\pi$
$97$	−4.42409	−	3.71225i	−0.449198	−	0.376922i	−0.839138	+	0.543918i	$0.816940\pi$
$98$		0			0
$99$	−10.0727	+	13.2139i	−1.01234	+	1.32805i
$100$		0			0
$101$	−6.13983	−	16.8690i	−0.610936	−	1.67853i	−0.728143	−	0.685425i	$-0.759616\pi$
$101$	−6.13983	−	16.8690i	−0.610936	−	1.67853i	0.117208	−	0.993107i	$-0.462606\pi$
$102$		0			0
$103$	6.00094	+	7.15164i	0.591290	+	0.704672i	0.975853	−	0.218427i	$-0.0700925\pi$
$103$	6.00094	+	7.15164i	0.591290	+	0.704672i	−0.384564	+	0.923098i	$0.625648\pi$
$104$		0			0
$105$	0.661809	+	2.25717i	0.0645860	+	0.220277i
$106$		0			0
$107$	3.52898			0.341159			0.170580	−	0.985344i	$-0.445436\pi$
$107$	3.52898			0.341159			0.170580	+	0.985344i	$0.445436\pi$
$108$		0			0
$109$	−16.2622			−1.55763			−0.778817	−	0.627251i	$-0.784180\pi$
$109$	−16.2622			−1.55763			−0.778817	+	0.627251i	$0.784180\pi$
$110$		0			0
$111$	16.4888	+	4.00696i	1.56505	+	0.380324i
$112$		0			0
$113$	−1.05734	−	1.26008i	−0.0994658	−	0.118539i	0.714015	−	0.700130i	$-0.246875\pi$
$113$	−1.05734	−	1.26008i	−0.0994658	−	0.118539i	−0.813481	+	0.581591i	$0.802430\pi$
$114$		0			0
$115$	−0.419920	−	1.15372i	−0.0391578	−	0.107585i
$116$		0			0
$117$	−0.402790	+	0.0906441i	−0.0372380	+	0.00838005i
$118$		0			0
$119$	−8.87221	−	7.44467i	−0.813314	−	0.682452i
$120$		0			0
$121$	3.41637	+	19.3752i	0.310579	+	1.76138i
$122$		0			0
$123$	4.85096	−	7.28508i	0.437397	−	0.656874i
$124$		0			0
$125$	4.09901	−	2.36657i	0.366627	−	0.211672i
$126$		0			0
$127$	−1.57358	−	0.908504i	−0.139632	−	0.0806167i	0.428556	−	0.903515i	$-0.359022\pi$
$127$	−1.57358	−	0.908504i	−0.139632	−	0.0806167i	−0.568189	+	0.822898i	$0.692356\pi$
$128$		0			0
$129$	0.209957	+	1.88928i	0.0184857	+	0.166342i
$130$		0			0
$131$	9.98407	+	3.63390i	0.872312	+	0.317496i	0.739103	−	0.673592i	$-0.235250\pi$
$131$	9.98407	+	3.63390i	0.872312	+	0.317496i	0.133209	+	0.991088i	$0.457472\pi$
$132$		0			0
$133$	2.54430	−	14.4295i	0.220619	−	1.25119i
$134$		0			0
$135$	−0.0429048	+	2.51821i	−0.00369266	+	0.216733i
$136$		0			0
$137$	13.0939	+	2.30880i	1.11869	+	0.197254i	0.702264	−	0.711917i	$-0.252173\pi$
$137$	13.0939	+	2.30880i	1.11869	+	0.197254i	0.416422	+	0.909172i	$0.363284\pi$
$138$		0			0
$139$	0.765089	−	2.10206i	0.0648940	−	0.178295i	−0.903007	−	0.429625i	$-0.858646\pi$
$139$	0.765089	−	2.10206i	0.0648940	−	0.178295i	0.967901	+	0.251330i	$0.0808680\pi$
$140$		0			0
$141$	1.36415	−	3.11372i	0.114882	−	0.262222i
$142$		0			0
$143$	−0.381102	+	0.660087i	−0.0318693	+	0.0551993i
$144$		0			0
$145$	−0.688618	−	1.19272i	−0.0571866	−	0.0990501i
$146$		0			0
$147$	0.0939634	−	1.46948i	0.00774997	−	0.121201i
$148$		0			0
$149$	−19.1606	+	3.37854i	−1.56970	+	0.276781i	−0.889740	−	0.456467i	$-0.849115\pi$
$149$	−19.1606	+	3.37854i	−1.56970	+	0.276781i	−0.679961	+	0.733248i	$0.738003\pi$
$150$		0			0
$151$	6.86697	−	8.18374i	0.558826	−	0.665983i	−0.410471	−	0.911874i	$-0.634636\pi$
$151$	6.86697	−	8.18374i	0.558826	−	0.665983i	0.969298	+	0.245890i	$0.0790802\pi$
$152$		0			0
$153$	−6.69641	−	10.4377i	−0.541373	−	0.843838i
$154$		0			0
$155$	2.85633	−	1.03962i	0.229426	−	0.0835042i
$156$		0			0
$157$	0.0645257	−	0.0541435i	0.00514971	−	0.00432112i	−0.640209	−	0.768201i	$-0.721152\pi$
$157$	0.0645257	−	0.0541435i	0.00514971	−	0.00432112i	0.645359	+	0.763880i	$0.276708\pi$
$158$		0			0
$159$	−13.7699	−	13.1398i	−1.09203	−	1.04206i
$160$		0			0
$161$			7.09709i			0.559329i
$162$		0			0
$163$			16.6345i			1.30291i	0.758685	+	0.651457i	$0.225842\pi$
$163$			16.6345i			1.30291i	−0.758685	+	0.651457i	$0.774158\pi$
$164$		0			0
$165$	3.36386	+	3.20993i	0.261876	+	0.249893i
$166$		0			0
$167$	13.5617	−	11.3796i	1.04944	−	0.880582i	0.0564029	−	0.998408i	$-0.482037\pi$
$167$	13.5617	−	11.3796i	1.04944	−	0.880582i	0.993034	+	0.117826i	$0.0375924\pi$
$168$		0			0
$169$	12.1982	−	4.43978i	0.938324	−	0.341522i
$170$		0			0
$171$	7.19975	−	13.9389i	0.550579	−	1.06593i
$172$		0			0
$173$	−2.34385	+	2.79329i	−0.178199	+	0.212370i	−0.847749	−	0.530397i	$-0.822043\pi$
$173$	−2.34385	+	2.79329i	−0.178199	+	0.212370i	0.669550	+	0.742767i	$0.266487\pi$
$174$		0			0
$175$	−13.1480	+	2.31834i	−0.993894	+	0.175250i
$176$		0			0
$177$	0.565924	−	8.85040i	0.0425375	−	0.665237i
$178$		0			0
$179$	4.74075	+	8.21121i	0.354340	+	0.613735i	0.987005	−	0.160691i	$-0.0513722\pi$
$179$	4.74075	+	8.21121i	0.354340	+	0.613735i	−0.632665	+	0.774426i	$0.718039\pi$
$180$		0			0
$181$	8.69038	−	15.0522i	0.645951	−	1.11882i	−0.338130	−	0.941099i	$-0.609794\pi$
$181$	8.69038	−	15.0522i	0.645951	−	1.11882i	0.984081	−	0.177720i	$-0.0568722\pi$
$182$		0			0
$183$	−3.70311	+	8.45248i	−0.273742	+	0.624825i
$184$		0			0
$185$	1.62410	−	4.46219i	0.119407	−	0.328067i
$186$		0			0
$187$	−22.5464	−	3.97553i	−1.64875	−	0.290720i
$188$		0			0
$189$	5.21168	−	13.5938i	0.379094	−	0.988805i
$190$		0			0
$191$	−4.13148	+	23.4308i	−0.298944	+	1.69539i	0.351783	+	0.936082i	$0.385575\pi$
$191$	−4.13148	+	23.4308i	−0.298944	+	1.69539i	−0.650727	+	0.759312i	$0.725536\pi$
$192$		0			0
$193$	21.7760	+	7.92582i	1.56747	+	0.570513i	0.972433	−	0.233184i	$-0.0749146\pi$
$193$	21.7760	+	7.92582i	1.56747	+	0.570513i	0.595038	+	0.803697i	$0.297137\pi$
$194$		0			0
$195$	0.0127611	+	0.114830i	0.000913841	+	0.00822312i
$196$		0			0
$197$	18.8331	+	10.8733i	1.34181	+	0.774692i	0.987072	−	0.160275i	$-0.0512383\pi$
$197$	18.8331	+	10.8733i	1.34181	+	0.774692i	0.354734	+	0.934967i	$0.384572\pi$
$198$		0			0
$199$	−5.64708	+	3.26035i	−0.400311	+	0.231120i	−0.686618	−	0.727018i	$-0.740906\pi$
$199$	−5.64708	+	3.26035i	−0.400311	+	0.231120i	0.286307	+	0.958138i	$0.407572\pi$
$200$		0			0
$201$	−11.3367	+	17.0252i	−0.799628	+	1.20087i
$202$		0			0
$203$	1.38243	+	7.84016i	0.0970277	+	0.550272i
$204$		0			0
$205$	−1.87626	−	1.57437i	−0.131044	−	0.109959i
$206$		0			0
$207$	−2.26199	+	7.25465i	−0.157219	+	0.504233i
$208$		0			0
$209$	−9.90598	−	27.2164i	−0.685211	−	1.88260i
$210$		0			0
$211$	−9.18391	−	10.9450i	−0.632246	−	0.753482i	0.350878	−	0.936421i	$-0.385883\pi$
$211$	−9.18391	−	10.9450i	−0.632246	−	0.753482i	−0.983124	+	0.182940i	$0.941439\pi$
$212$		0			0
$213$	26.1875	+	6.36382i	1.79434	+	0.436042i
$214$		0			0
$215$	0.531956			0.0362791
$216$		0			0
$217$	−17.5706			−1.19277
$218$		0			0
$219$	−6.50083	−	22.1718i	−0.439286	−	1.49823i
$220$		0			0
$221$	−0.365672	−	0.435791i	−0.0245978	−	0.0293145i
$222$		0			0
$223$	−1.60102	−	4.39878i	−0.107212	−	0.294564i	0.874473	−	0.485075i	$-0.161208\pi$
$223$	−1.60102	−	4.39878i	−0.107212	−	0.294564i	−0.981685	+	0.190511i	$0.938985\pi$
$224$		0			0
$225$	−14.1788	−	1.82072i	−0.945252	−	0.121381i
$226$		0			0
$227$	−19.4156	−	16.2916i	−1.28866	−	1.08131i	−0.991988	−	0.126330i	$-0.959680\pi$
$227$	−19.4156	−	16.2916i	−1.28866	−	1.08131i	−0.296668	−	0.954981i	$-0.595875\pi$
$228$		0			0
$229$	1.18634	+	6.72808i	0.0783956	+	0.444604i	0.998587	+	0.0531356i	$0.0169216\pi$
$229$	1.18634	+	6.72808i	0.0783956	+	0.444604i	−0.920192	+	0.391468i	$0.871967\pi$
$230$		0			0
$231$	−11.9259	−	24.0865i	−0.784667	−	1.58478i
$232$		0			0
$233$	21.9589	−	12.6780i	1.43858	−	0.830563i	0.440827	−	0.897592i	$-0.354685\pi$
$233$	21.9589	−	12.6780i	1.43858	−	0.830563i	0.997751	+	0.0670288i	$0.0213519\pi$
$234$		0			0
$235$	−0.823854	−	0.475652i	−0.0537423	−	0.0310281i
$236$		0			0
$237$	−3.00723	+	2.21237i	−0.195340	+	0.143709i
$238$		0			0
$239$	8.57291	+	3.12029i	0.554536	+	0.201834i	0.604061	−	0.796938i	$-0.293548\pi$
$239$	8.57291	+	3.12029i	0.554536	+	0.201834i	−0.0495249	+	0.998773i	$0.515771\pi$
$240$		0			0
$241$	−1.09202	+	6.19316i	−0.0703432	+	0.398936i	0.929224	+	0.369517i	$0.120477\pi$
$241$	−1.09202	+	6.19316i	−0.0703432	+	0.398936i	−0.999567	+	0.0294192i	$0.990634\pi$
$242$		0			0
$243$	9.66001	−	12.2345i	0.619690	−	0.784847i
$244$		0			0
$245$	−0.405802	−	0.0715538i	−0.0259257	−	0.00457141i
$246$		0			0
$247$	0.246148	−	0.676287i	0.0156620	−	0.0430311i
$248$		0			0
$249$	−7.45928	−	10.1393i	−0.472713	−	0.642549i
$250$		0			0
$251$	11.4386	−	19.8122i	0.721997	−	1.25053i	−0.238202	−	0.971216i	$-0.576558\pi$
$251$	11.4386	−	19.8122i	0.721997	−	1.25053i	0.960198	−	0.279319i	$-0.0901087\pi$
$252$		0			0
$253$	7.01451	+	12.1495i	0.440999	+	0.763832i
$254$		0			0
$255$	−3.11001	+	1.53985i	−0.194757	+	0.0964294i
$256$		0			0
$257$	12.9323	−	2.28031i	0.806695	−	0.142242i	0.244932	−	0.969540i	$-0.421234\pi$
$257$	12.9323	−	2.28031i	0.806695	−	0.142242i	0.561763	+	0.827298i	$0.310123\pi$
$258$		0			0
$259$	−17.6439	+	21.0272i	−1.09634	+	1.30657i
$260$		0			0
$261$	−1.08570	+	8.45483i	−0.0672030	+	0.523341i
$262$		0			0
$263$	21.3619	−	7.77508i	1.31723	−	0.479432i	0.414660	−	0.909977i	$-0.363901\pi$
$263$	21.3619	−	7.77508i	1.31723	−	0.479432i	0.902569	+	0.430544i	$0.141678\pi$
$264$		0			0
$265$	−4.08019	+	3.42369i	−0.250644	+	0.210315i
$266$		0			0
$267$	−4.96950	+	1.45707i	−0.304129	+	0.0891715i
$268$		0			0
$269$		−	26.0160i		−	1.58622i	−0.609076	−	0.793112i	$-0.708460\pi$
$269$		−	26.0160i		−	1.58622i	0.609076	−	0.793112i	$-0.291540\pi$
$270$		0			0
$271$			16.0014i			0.972014i	0.873955	+	0.486007i	$0.161547\pi$
$271$			16.0014i			0.972014i	−0.873955	+	0.486007i	$0.838453\pi$
$272$		0			0
$273$	0.157707	−	0.648971i	0.00954484	−	0.0392775i
$274$		0			0
$275$	−20.2166	+	16.9638i	−1.21911	+	1.02295i
$276$		0			0
$277$	6.66285	−	2.42508i	0.400332	−	0.145709i	−0.134005	−	0.990981i	$-0.542784\pi$
$277$	6.66285	−	2.42508i	0.400332	−	0.145709i	0.534336	+	0.845272i	$0.320562\pi$
$278$		0			0
$279$	−17.9607	−	5.60013i	−1.07528	−	0.335271i
$280$		0			0
$281$	15.0752	−	17.9660i	0.899313	−	1.07176i	−0.0977532	−	0.995211i	$-0.531166\pi$
$281$	15.0752	−	17.9660i	0.899313	−	1.07176i	0.997066	−	0.0765484i	$-0.0243900\pi$
$282$		0			0
$283$	17.6229	−	3.10739i	1.04757	−	0.184715i	0.376736	−	0.926321i	$-0.377046\pi$
$283$	17.6229	−	3.10739i	1.04757	−	0.184715i	0.670836	+	0.741605i	$0.265935\pi$
$284$		0			0
$285$	−3.65428	−	2.43330i	−0.216461	−	0.144136i
$286$		0			0
$287$	7.07904	+	12.2613i	0.417863	+	0.723759i
$288$		0			0
$289$	0.0437466	−	0.0757713i	0.00257333	−	0.00445714i
$290$		0			0
$291$	9.94180	−	1.10484i	0.582799	−	0.0647668i
$292$		0			0
$293$	−2.24365	+	6.16437i	−0.131075	+	0.360126i	−0.987817	−	0.155619i	$-0.950263\pi$
$293$	−2.24365	+	6.16437i	−0.131075	+	0.360126i	0.856742	+	0.515745i	$0.172485\pi$
$294$		0			0
$295$	−2.44407	−	0.430955i	−0.142299	−	0.0250912i
$296$		0			0
$297$	−4.51380	−	28.4223i	−0.261917	−	1.64923i
$298$		0			0
$299$	−0.0605337	+	0.343304i	−0.00350075	+	0.0198538i
$300$		0			0
$301$	−2.88952	−	1.05170i	−0.166549	−	0.0606190i
$302$		0			0
$303$	28.4799	+	12.4773i	1.63613	+	0.716803i
$304$		0			0
$305$	2.23643	+	1.29120i	0.128057	+	0.0739340i
$306$		0			0
$307$	−5.82349	+	3.36219i	−0.332364	+	0.191891i	−0.656890	−	0.753986i	$-0.728129\pi$
$307$	−5.82349	+	3.36219i	−0.332364	+	0.191891i	0.324526	+	0.945877i	$0.394795\pi$
$308$		0			0
$309$	−16.1371	−	1.03186i	−0.918009	−	0.0587005i
$310$		0			0
$311$	3.81319	+	21.6257i	0.216226	+	1.22628i	0.878766	+	0.477253i	$0.158367\pi$
$311$	3.81319	+	21.6257i	0.216226	+	1.22628i	−0.662540	+	0.749027i	$0.730521\pi$
$312$		0			0
$313$	20.0381	+	16.8140i	1.13262	+	0.950384i	0.999173	−	0.0406719i	$-0.0129498\pi$
$313$	20.0381	+	16.8140i	1.13262	+	0.950384i	0.133450	+	0.991055i	$0.457394\pi$
$314$		0			0
$315$	−3.61976	−	1.86969i	−0.203950	−	0.105345i
$316$		0			0
$317$	1.25403	+	3.44541i	0.0704333	+	0.193514i	0.969915	−	0.243445i	$-0.0782777\pi$
$317$	1.25403	+	3.44541i	0.0704333	+	0.193514i	−0.899481	+	0.436959i	$0.856055\pi$
$318$		0			0
$319$	10.1155	+	12.0552i	0.566360	+	0.674962i
$320$		0			0
$321$	−4.21974	+	4.42208i	−0.235523	+	0.246817i
$322$		0			0
$323$	21.6172			1.20281
$324$		0			0
$325$	−0.655774			−0.0363758
$326$		0			0
$327$	19.4453	−	20.3778i	1.07533	−	1.12689i
$328$		0			0
$329$	3.53470	+	4.21249i	0.194874	+	0.232242i
$330$		0			0
$331$	−4.55568	−	12.5166i	−0.250403	−	0.687976i	−0.999670	−	0.0257074i	$-0.991816\pi$
$331$	−4.55568	−	12.5166i	−0.250403	−	0.687976i	0.749267	−	0.662268i	$-0.230406\pi$
$332$		0			0
$333$	−24.7374	+	15.8705i	−1.35560	+	0.869700i
$334$		0			0
$335$	4.38482	+	3.67930i	0.239568	+	0.201022i
$336$		0			0
$337$	−0.0452535	−	0.256645i	−0.00246512	−	0.0139804i	0.983550	−	0.180634i	$-0.0578149\pi$
$337$	−0.0452535	−	0.256645i	−0.00246512	−	0.0139804i	−0.986016	+	0.166654i	$0.946704\pi$
$338$		0			0
$339$	2.84328	+	0.181809i	0.154426	+	0.00987450i
$340$		0			0
$341$	−30.0791	+	17.3662i	−1.62888	+	0.940433i
$342$		0			0
$343$	−14.9223	−	8.61537i	−0.805726	−	0.465186i
$344$		0			0
$345$	1.94782	+	0.853359i	0.104867	+	0.0459433i
$346$		0			0
$347$	6.22431	+	2.26546i	0.334138	+	0.121616i	0.503640	−	0.863913i	$-0.331994\pi$
$347$	6.22431	+	2.26546i	0.334138	+	0.121616i	−0.169502	+	0.985530i	$0.554216\pi$
$348$		0			0
$349$	3.25911	−	18.4833i	0.174456	−	0.989390i	−0.764313	−	0.644845i	$-0.776922\pi$
$349$	3.25911	−	18.4833i	0.174456	−	0.989390i	0.938770	−	0.344545i	$-0.111967\pi$
$350$		0			0
$351$	0.368048	−	0.613114i	0.0196450	−	0.0327256i
$352$		0			0
$353$	−3.70879	−	0.653960i	−0.197399	−	0.0348068i	0.0740743	−	0.997253i	$-0.476400\pi$
$353$	−3.70879	−	0.653960i	−0.197399	−	0.0348068i	−0.271473	+	0.962446i	$0.587511\pi$
$354$		0			0
$355$	2.57939	−	7.08682i	0.136900	−	0.376129i
$356$		0			0
$357$	19.9376	−	2.21568i	1.05521	−	0.117266i
$358$		0			0
$359$	4.20804	−	7.28853i	0.222092	−	0.384674i	−0.733351	−	0.679850i	$-0.762045\pi$
$359$	4.20804	−	7.28853i	0.222092	−	0.384674i	0.955443	+	0.295176i	$0.0953782\pi$
$360$		0			0
$361$	4.17382	+	7.22926i	0.219674	+	0.380487i
$362$		0			0
$363$	−28.3637	−	18.8867i	−1.48871	−	0.991295i
$364$		0			0
$365$	−6.36756	+	1.12277i	−0.333294	+	0.0587686i
$366$		0			0
$367$	−12.4833	+	14.8770i	−0.651624	+	0.776575i	−0.986158	−	0.165809i	$-0.946977\pi$
$367$	−12.4833	+	14.8770i	−0.651624	+	0.776575i	0.334534	+	0.942384i	$0.391421\pi$
$368$		0			0
$369$	3.32829	+	14.7897i	0.173264	+	0.769921i
$370$		0			0
$371$	28.9319	−	10.5304i	1.50207	−	0.546709i
$372$		0			0
$373$	−4.94112	+	4.14610i	−0.255842	+	0.214677i	−0.761683	−	0.647950i	$-0.775627\pi$
$373$	−4.94112	+	4.14610i	−0.255842	+	0.214677i	0.505841	+	0.862627i	$0.331182\pi$
$374$		0			0
$375$	−1.93586	+	7.96618i	−0.0999676	+	0.411372i
$376$		0			0
$377$			0.391039i			0.0201395i
$378$		0			0
$379$			4.73511i			0.243226i	0.992578	+	0.121613i	$0.0388067\pi$
$379$			4.73511i			0.243226i	−0.992578	+	0.121613i	$0.961193\pi$
$380$		0			0
$381$	3.02001	−	0.885478i	0.154720	−	0.0453644i
$382$		0			0
$383$	10.5499	−	8.85244i	0.539076	−	0.452339i	−0.332146	−	0.943228i	$-0.607773\pi$
$383$	10.5499	−	8.85244i	0.539076	−	0.452339i	0.871222	+	0.490889i	$0.163328\pi$
$384$		0			0
$385$	−7.06779	+	2.57247i	−0.360208	+	0.131105i
$386$		0			0
$387$	−2.61847	−	1.99600i	−0.133105	−	0.101462i
$388$		0			0
$389$	−17.4011	+	20.7378i	−0.882269	+	1.05145i	0.116036	+	0.993245i	$0.462981\pi$
$389$	−17.4011	+	20.7378i	−0.882269	+	1.05145i	−0.998305	+	0.0582022i	$0.981463\pi$
$390$		0			0
$391$	−10.3117	+	1.81824i	−0.521488	+	0.0919523i
$392$		0			0
$393$	−16.4919	+	8.16561i	−0.831907	+	0.411901i
$394$		0			0
$395$	0.522376	+	0.904781i	0.0262836	+	0.0455245i
$396$		0			0
$397$	−15.3615	+	26.6068i	−0.770969	+	1.33536i	0.166063	+	0.986115i	$0.446894\pi$
$397$	−15.3615	+	26.6068i	−0.770969	+	1.33536i	−0.937032	+	0.349243i	$0.886439\pi$
$398$		0			0
$399$	15.0389	+	20.4421i	0.752887	+	1.02338i
$400$		0			0
$401$	−5.08217	+	13.9631i	−0.253791	+	0.697286i	0.745727	+	0.666252i	$0.232102\pi$
$401$	−5.08217	+	13.9631i	−0.253791	+	0.697286i	−0.999518	+	0.0310345i	$0.990120\pi$
$402$		0			0
$403$	−0.849935	−	0.149867i	−0.0423383	−	0.00746538i
$404$		0			0
$405$	−3.10421	−	3.06489i	−0.154250	−	0.152296i
$406$		0			0
$407$	−9.42203	+	53.4350i	−0.467033	+	2.64868i
$408$		0			0
$409$	−10.3068	−	3.75137i	−0.509639	−	0.185493i	0.0743856	−	0.997230i	$-0.476300\pi$
$409$	−10.3068	−	3.75137i	−0.509639	−	0.185493i	−0.584024	+	0.811736i	$0.698523\pi$
$410$		0			0
$411$	−18.5500	+	13.6469i	−0.915003	+	0.673153i
$412$		0			0
$413$	12.4239	+	7.17294i	0.611340	+	0.352957i
$414$		0			0
$415$	−3.05058	+	1.76126i	−0.149747	+	0.0864567i
$416$		0			0
$417$	1.71920	+	3.47224i	0.0841897	+	0.170036i
$418$		0			0
$419$	−2.14941	−	12.1899i	−0.105006	−	0.595517i	−0.991218	−	0.132237i	$-0.957784\pi$
$419$	−2.14941	−	12.1899i	−0.105006	−	0.595517i	0.886212	−	0.463279i	$-0.153327\pi$
$420$		0			0
$421$	−9.17447	−	7.69830i	−0.447137	−	0.375192i	0.391235	−	0.920291i	$-0.372048\pi$
$421$	−9.17447	−	7.69830i	−0.447137	−	0.375192i	−0.838372	+	0.545099i	$0.816492\pi$
$422$		0			0
$423$	2.27056	+	5.43259i	0.110399	+	0.264141i
$424$		0			0
$425$	−6.73689	−	18.5095i	−0.326787	−	0.897841i
$426$		0			0
$427$	−9.59526	−	11.4352i	−0.464347	−	0.553388i
$428$		0			0
$429$	−0.371442	−	1.26684i	−0.0179334	−	0.0611638i
$430$		0			0
$431$	−28.5275			−1.37412			−0.687061	−	0.726600i	$-0.741099\pi$
$431$	−28.5275			−1.37412			−0.687061	+	0.726600i	$0.741099\pi$
$432$		0			0
$433$	7.35698			0.353554			0.176777	−	0.984251i	$-0.443433\pi$
$433$	7.35698			0.353554			0.176777	+	0.984251i	$0.443433\pi$
$434$		0			0
$435$	2.31798	+	0.563293i	0.111139	+	0.0270078i
$436$		0			0
$437$	−8.51469	−	10.1474i	−0.407313	−	0.485417i
$438$		0			0
$439$	7.65771	+	21.0394i	0.365483	+	1.00415i	0.977059	+	0.212970i	$0.0683135\pi$
$439$	7.65771	+	21.0394i	0.365483	+	1.00415i	−0.611576	+	0.791185i	$0.709464\pi$
$440$		0			0
$441$	1.72902	+	1.87486i	0.0823341	+	0.0892790i
$442$		0			0
$443$	−25.0942	−	21.0565i	−1.19226	−	1.00043i	−0.999817	−	0.0191179i	$-0.993914\pi$
$443$	−25.0942	−	21.0565i	−1.19226	−	1.00043i	−0.192444	−	0.981308i	$-0.561641\pi$
$444$		0			0
$445$	0.251655	+	1.42720i	0.0119296	+	0.0676559i
$446$		0			0
$447$	18.6776	−	28.0496i	0.883420	−	1.32670i
$448$		0			0
$449$	−2.44069	+	1.40914i	−0.115184	+	0.0665012i	−0.556485	−	0.830858i	$-0.687850\pi$
$449$	−2.44069	+	1.40914i	−0.115184	+	0.0665012i	0.441301	+	0.897359i	$0.354517\pi$
$450$		0			0
$451$	24.2372	+	13.9933i	1.14128	+	0.658921i
$452$		0			0
$453$	2.04375	+	18.3905i	0.0960236	+	0.864060i
$454$		0			0
$455$	−0.175624	−	0.0639218i	−0.00823336	−	0.00299670i
$456$		0			0
$457$	−4.71792	+	26.7566i	−0.220695	+	1.25162i	0.650051	+	0.759890i	$0.274747\pi$
$457$	−4.71792	+	26.7566i	−0.220695	+	1.25162i	−0.870746	+	0.491733i	$0.836364\pi$
$458$		0			0
$459$	21.0864	+	4.08966i	0.984230	+	0.190889i
$460$		0			0
$461$	29.8003	+	5.25460i	1.38794	+	0.244731i	0.817178	−	0.576386i	$-0.195537\pi$
$461$	29.8003	+	5.25460i	1.38794	+	0.244731i	0.570761	+	0.821117i	$0.306648\pi$
$462$		0			0
$463$	−12.8689	+	35.3571i	−0.598070	+	1.64318i	0.157044	+	0.987592i	$0.449804\pi$
$463$	−12.8689	+	35.3571i	−0.598070	+	1.64318i	−0.755114	+	0.655593i	$0.772419\pi$
$464$		0			0
$465$	−2.11271	+	4.82232i	−0.0979744	+	0.223630i
$466$		0			0
$467$	−10.9543	+	18.9734i	−0.506905	+	0.877985i	0.493063	+	0.869994i	$0.335877\pi$
$467$	−10.9543	+	18.9734i	−0.506905	+	0.877985i	−0.999968	+	0.00799160i	$0.997456\pi$
$468$		0			0
$469$	−16.5437	−	28.6545i	−0.763917	−	1.32314i
$470$		0			0
$471$	−0.00930997	+	0.145597i	−0.000428981	+	0.00670877i
$472$		0			0
$473$	−5.98603	+	1.05550i	−0.275238	+	0.0485319i
$474$		0			0
$475$	16.0176	−	19.0890i	0.734936	−	0.875862i
$476$		0			0
$477$	32.9305	−	1.54294i	1.50778	−	0.0706464i
$478$		0			0
$479$	20.0677	−	7.30403i	0.916915	−	0.333730i	0.159904	−	0.987133i	$-0.448881\pi$
$479$	20.0677	−	7.30403i	0.916915	−	0.333730i	0.757010	+	0.653403i	$0.226659\pi$
$480$		0			0
$481$	−1.03283	+	0.866645i	−0.0470929	+	0.0395156i
$482$		0			0
$483$	−8.89321	−	8.48628i	−0.404655	−	0.386139i
$484$		0			0
$485$		−	2.79926i		−	0.127108i
$486$		0			0
$487$		−	37.8646i		−	1.71581i	−0.513809	−	0.857905i	$-0.671766\pi$
$487$		−	37.8646i		−	1.71581i	0.513809	−	0.857905i	$-0.328234\pi$
$488$		0			0
$489$	−20.8443	−	19.8905i	−0.942613	−	0.899482i
$490$		0			0
$491$	3.06806	−	2.57441i	0.138460	−	0.116181i	−0.570927	−	0.821001i	$-0.693416\pi$
$491$	3.06806	−	2.57441i	0.138460	−	0.116181i	0.709387	+	0.704819i	$0.248972\pi$
$492$		0			0
$493$	−11.0372	+	4.01722i	−0.497092	+	0.180927i
$494$		0			0
$495$	−8.04460	+	0.376925i	−0.361578	+	0.0169415i
$496$		0			0
$497$	−28.0219	+	33.3952i	−1.25696	+	1.49798i
$498$		0			0
$499$	−11.0174	+	1.94266i	−0.493205	+	0.0869653i	−0.414718	−	0.909950i	$-0.636120\pi$
$499$	−11.0174	+	1.94266i	−0.493205	+	0.0869653i	−0.0784866	+	0.996915i	$0.525009\pi$
$500$		0			0
$501$	−1.95673	+	30.6010i	−0.0874201	+	1.36715i
$502$		0			0
$503$	−4.23206	−	7.33014i	−0.188698	−	0.326835i	0.756118	−	0.654435i	$-0.227093\pi$
$503$	−4.23206	−	7.33014i	−0.188698	−	0.326835i	−0.944816	+	0.327600i	$0.893760\pi$
$504$		0			0
$505$	4.35059	−	7.53544i	0.193599	−	0.335323i
$506$		0			0
$507$	−9.02249	+	20.5941i	−0.400703	+	0.914618i
$508$		0			0
$509$	12.3898	−	34.0407i	0.549169	−	1.50883i	−0.285666	−	0.958329i	$-0.592215\pi$
$509$	12.3898	−	34.0407i	0.549169	−	1.50883i	0.834835	−	0.550500i	$-0.185563\pi$
$510$		0			0
$511$	36.8077	+	6.49019i	1.62828	+	0.287109i
$512$		0			0
$513$	8.85746	+	25.6891i	0.391067	+	1.13420i
$514$		0			0
$515$	−0.785769	+	4.45632i	−0.0346251	+	0.196369i
$516$		0			0
$517$	10.2145	+	3.71778i	0.449234	+	0.163508i
$518$		0			0
$519$	−0.697576	−	6.27707i	−0.0306202	−	0.275533i
$520$		0			0
$521$	4.12954	+	2.38419i	0.180918	+	0.104453i	0.587724	−	0.809061i	$-0.300024\pi$
$521$	4.12954	+	2.38419i	0.180918	+	0.104453i	−0.406806	+	0.913515i	$0.633357\pi$
$522$		0			0
$523$	10.1966	−	5.88699i	0.445865	−	0.257420i	−0.260218	−	0.965550i	$-0.583794\pi$
$523$	10.1966	−	5.88699i	0.445865	−	0.257420i	0.706082	+	0.708130i	$0.250461\pi$
$524$		0			0
$525$	12.8165	−	19.2476i	0.559358	−	0.840033i
$526$		0			0
$527$	−4.50151	−	25.5294i	−0.196089	−	1.11208i
$528$		0			0
$529$	−12.7039	−	10.6598i	−0.552342	−	0.463470i
$530$		0			0
$531$	10.4135	+	11.2919i	0.451910	+	0.490028i
$532$		0			0
$533$	0.237850	+	0.653487i	0.0103024	+	0.0283057i
$534$		0			0
$535$	1.09949	+	1.31032i	0.0475349	+	0.0566499i
$536$		0			0
$537$	−15.9580	−	3.87795i	−0.688638	−	0.167346i
$538$		0			0
$539$	4.70842			0.202806
$540$		0			0
$541$	34.5931			1.48727			0.743637	−	0.668583i	$-0.233099\pi$
$541$	34.5931			1.48727			0.743637	+	0.668583i	$0.233099\pi$
$542$		0			0
$543$	8.47012	+	28.8882i	0.363487	+	1.23971i
$544$		0			0
$545$	−5.06663	−	6.03818i	−0.217031	−	0.258647i
$546$		0			0
$547$	−4.30930	−	11.8397i	−0.184252	−	0.506229i	0.812835	−	0.582494i	$-0.197923\pi$
$547$	−4.30930	−	11.8397i	−0.184252	−	0.506229i	−0.997088	+	0.0762643i	$0.975701\pi$
$548$		0			0
$549$	−6.16365	−	14.7473i	−0.263058	−	0.629398i
$550$		0			0
$551$	−11.3828	−	9.55130i	−0.484923	−	0.406899i
$552$		0			0
$553$	−1.04869	−	5.94743i	−0.0445950	−	0.252911i
$554$		0			0
$555$	3.64946	+	7.37075i	0.154911	+	0.312871i
$556$		0			0
$557$	−8.87365	+	5.12320i	−0.375988	+	0.217077i	−0.676071	−	0.736836i	$-0.736319\pi$
$557$	−8.87365	+	5.12320i	−0.375988	+	0.217077i	0.300083	+	0.953913i	$0.402986\pi$
$558$		0			0
$559$	−0.130803	−	0.0755191i	−0.00553238	−	0.00319412i
$560$		0			0
$561$	31.9412	−	23.4986i	1.34856	−	0.992113i
$562$		0			0
$563$	−19.7212	−	7.17792i	−0.831148	−	0.302513i	−0.108818	−	0.994062i	$-0.534707\pi$
$563$	−19.7212	−	7.17792i	−0.831148	−	0.302513i	−0.722330	+	0.691548i	$0.756929\pi$
$564$		0			0
$565$	0.138449	−	0.785182i	0.00582458	−	0.0330329i
$566$		0			0
$567$	10.8023	+	22.7853i	0.453655	+	0.956894i
$568$		0			0
$569$	26.7748	+	4.72111i	1.12246	+	0.197919i	0.703919	−	0.710280i	$-0.251432\pi$
$569$	26.7748	+	4.72111i	1.12246	+	0.197919i	0.418537	+	0.908200i	$0.362543\pi$
$570$		0			0
$571$	6.09147	−	16.7362i	0.254920	−	0.700387i	−0.744541	−	0.667576i	$-0.767332\pi$
$571$	6.09147	−	16.7362i	0.254920	−	0.700387i	0.999462	−	0.0328110i	$-0.0104460\pi$
$572$		0			0
$573$	−24.4204	−	33.1942i	−1.02018	−	1.38671i
$574$		0			0
$575$	−6.03505	+	10.4530i	−0.251679	+	0.435920i
$576$		0			0
$577$	−1.62886	−	2.82127i	−0.0678103	−	0.117451i	0.830127	−	0.557575i	$-0.188268\pi$
$577$	−1.62886	−	2.82127i	−0.0678103	−	0.117451i	−0.897937	+	0.440124i	$0.854935\pi$
$578$		0			0
$579$	−35.9701	+	17.8098i	−1.49487	+	0.740150i
$580$		0			0
$581$	20.0525	−	3.53580i	0.831919	−	0.146690i
$582$		0			0
$583$	39.1207	−	46.6222i	1.62021	−	1.93089i
$584$		0			0
$585$	−0.159149	−	0.121316i	−0.00658002	−	0.00501579i
$586$		0			0
$587$	−5.88738	+	2.14283i	−0.242998	+	0.0884441i	−0.460648	−	0.887583i	$-0.652383\pi$
$587$	−5.88738	+	2.14283i	−0.242998	+	0.0884441i	0.217650	+	0.976027i	$0.430161\pi$
$588$		0			0
$589$	25.1225	−	21.0803i	1.03515	−	0.868598i
$590$		0			0
$591$	−36.1447	+	10.5977i	−1.48679	+	0.435932i
$592$		0			0
$593$			3.99725i			0.164147i	0.996626	+	0.0820737i	$0.0261543\pi$
$593$			3.99725i			0.164147i	−0.996626	+	0.0820737i	$0.973846\pi$
$594$		0			0
$595$		−	5.61373i		−	0.230140i
$596$		0			0
$597$	2.66698	−	10.9748i	0.109152	−	0.449167i
$598$		0			0
$599$	21.1491	−	17.7462i	0.864130	−	0.725091i	−0.0987241	−	0.995115i	$-0.531476\pi$
$599$	21.1491	−	17.7462i	0.864130	−	0.725091i	0.962854	+	0.270024i	$0.0870317\pi$
$600$		0			0
$601$	−2.17185	+	0.790488i	−0.0885915	+	0.0322447i	−0.385936	−	0.922526i	$-0.626121\pi$
$601$	−2.17185	+	0.790488i	−0.0885915	+	0.0322447i	0.297344	+	0.954770i	$0.403899\pi$
$602$		0			0
$603$	−7.77819	−	34.5635i	−0.316752	−	1.40753i
$604$		0			0
$605$	−6.12964	+	7.30503i	−0.249205	+	0.296992i
$606$		0			0
$607$	18.9616	−	3.34344i	0.769627	−	0.135706i	0.224971	−	0.974366i	$-0.427771\pi$
$607$	18.9616	−	3.34344i	0.769627	−	0.135706i	0.544656	+	0.838660i	$0.316660\pi$
$608$		0			0
$609$	−11.4774	−	7.64250i	−0.465086	−	0.309690i
$610$		0			0
$611$	0.135052	+	0.233917i	0.00546362	+	0.00946327i
$612$		0			0
$613$	−2.24284	+	3.88470i	−0.0905873	+	0.156902i	−0.907758	−	0.419493i	$-0.862208\pi$
$613$	−2.24284	+	3.88470i	−0.0905873	+	0.156902i	0.817171	+	0.576395i	$0.195541\pi$
$614$		0			0
$615$	4.21633	−	0.468564i	0.170019	−	0.0188943i
$616$		0			0
$617$	3.96204	−	10.8856i	0.159506	−	0.438238i	−0.834036	−	0.551711i	$-0.813975\pi$
$617$	3.96204	−	10.8856i	0.159506	−	0.438238i	0.993541	+	0.113473i	$0.0361975\pi$
$618$		0			0
$619$	−10.1776	−	1.79458i	−0.409072	−	0.0721304i	−0.0346742	−	0.999399i	$-0.511039\pi$
$619$	−10.1776	−	1.79458i	−0.409072	−	0.0721304i	−0.374398	+	0.927268i	$0.622150\pi$
$620$		0			0
$621$	−6.38589	−	11.5091i	−0.256257	−	0.461845i
$622$		0			0
$623$	1.45469	−	8.24995i	0.0582808	−	0.330527i
$624$		0			0
$625$	−20.2327	−	7.36410i	−0.809307	−	0.294564i
$626$		0			0
$627$	45.9493	+	20.1308i	1.83504	+	0.803948i
$628$		0			0
$629$	−35.0718	−	20.2487i	−1.39841	−	0.807370i
$630$		0			0
$631$	−3.26065	+	1.88254i	−0.129805	+	0.0749427i	−0.563496	−	0.826119i	$-0.690544\pi$
$631$	−3.26065	+	1.88254i	−0.129805	+	0.0749427i	0.433692	+	0.901061i	$0.357211\pi$
$632$		0			0
$633$	24.6964	+	1.57917i	0.981596	+	0.0627665i
$634$		0			0
$635$	−0.152933	−	0.867325i	−0.00606895	−	0.0344187i
$636$		0			0
$637$	0.0896248	+	0.0752041i	0.00355106	+	0.00297970i
$638$		0			0
$639$	−39.2878	+	25.2055i	−1.55420	+	0.997113i
$640$		0			0
$641$	6.94756	+	19.0883i	0.274412	+	0.753942i	0.997970	+	0.0636782i	$0.0202831\pi$
$641$	6.94756	+	19.0883i	0.274412	+	0.753942i	−0.723558	+	0.690263i	$0.757495\pi$
$642$		0			0
$643$	1.85353	+	2.20895i	0.0730961	+	0.0871125i	0.801353	−	0.598191i	$-0.204114\pi$
$643$	1.85353	+	2.20895i	0.0730961	+	0.0871125i	−0.728257	+	0.685304i	$0.759669\pi$
$644$		0			0
$645$	−0.636081	+	0.666582i	−0.0250457	+	0.0262466i
$646$		0			0
$647$	−39.5336			−1.55423			−0.777113	−	0.629361i	$-0.783317\pi$
$647$	−39.5336			−1.55423			−0.777113	+	0.629361i	$0.783317\pi$
$648$		0			0
$649$	28.3579			1.11315
$650$		0			0
$651$	21.0099	−	22.0174i	0.823444	−	0.862930i
$652$		0			0
$653$	22.1617	+	26.4113i	0.867255	+	1.03355i	0.999106	+	0.0422848i	$0.0134637\pi$
$653$	22.1617	+	26.4113i	0.867255	+	1.03355i	−0.131850	+	0.991270i	$0.542092\pi$
$654$		0			0
$655$	1.76136	+	4.83928i	0.0688218	+	0.189086i
$656$		0			0
$657$	35.5563	+	18.3656i	1.38718	+	0.716512i
$658$		0			0
$659$	−19.8289	−	16.6384i	−0.772424	−	0.648141i	0.168904	−	0.985632i	$-0.445977\pi$
$659$	−19.8289	−	16.6384i	−0.772424	−	0.648141i	−0.941329	+	0.337491i	$0.890422\pi$
$660$		0			0
$661$	−8.72527	−	49.4835i	−0.339374	−	1.92468i	−0.378837	−	0.925463i	$-0.623676\pi$
$661$	−8.72527	−	49.4835i	−0.339374	−	1.92468i	0.0394636	−	0.999221i	$-0.487435\pi$
$662$		0			0
$663$	0.983329	+	0.0628773i	0.0381893	+	0.00244195i
$664$		0			0
$665$	6.15039	−	3.55093i	0.238502	−	0.137699i
$666$		0			0
$667$	6.23315	+	3.59871i	0.241348	+	0.139343i
$668$		0			0
$669$	7.42642	+	3.25359i	0.287122	+	0.125791i
$670$		0			0
$671$	−27.7282	−	10.0923i	−1.07044	−	0.389607i
$672$		0			0
$673$	4.48612	−	25.4421i	0.172927	−	0.980720i	−0.767582	−	0.640951i	$-0.778540\pi$
$673$	4.48612	−	25.4421i	0.172927	−	0.980720i	0.940509	−	0.339769i	$-0.110349\pi$
$674$		0			0
$675$	19.2356	−	15.5900i	0.740380	−	0.600059i
$676$		0			0
$677$	10.5198	+	1.85492i	0.404307	+	0.0712903i	0.372104	−	0.928191i	$-0.378636\pi$
$677$	10.5198	+	1.85492i	0.404307	+	0.0712903i	0.0322033	+	0.999481i	$0.489748\pi$
$678$		0			0
$679$	−5.53427	+	15.2053i	−0.212386	+	0.583525i
$680$		0			0
$681$	43.6306	−	4.84870i	1.67193	−	0.185803i
$682$		0			0
$683$	−0.463561	+	0.802911i	−0.0177377	+	0.0307225i	−0.874758	−	0.484560i	$-0.838980\pi$
$683$	−0.463561	+	0.802911i	−0.0177377	+	0.0307225i	0.857020	+	0.515283i	$0.172313\pi$
$684$		0			0
$685$	3.22226	+	5.58111i	0.123116	+	0.213243i
$686$		0			0
$687$	−9.84936	−	6.55845i	−0.375777	−	0.250221i
$688$		0			0
$689$	1.48933	−	0.262608i	0.0567388	−	0.0100046i
$690$		0			0
$691$	−24.1572	+	28.7894i	−0.918982	+	1.09520i	0.0761939	+	0.997093i	$0.475723\pi$
$691$	−24.1572	+	28.7894i	−0.918982	+	1.09520i	−0.995176	+	0.0981070i	$0.968721\pi$
$692$		0			0
$693$	44.4426	+	13.8571i	1.68823	+	0.526389i
$694$		0			0
$695$	1.01887	−	0.370839i	0.0386480	−	0.0140667i
$696$		0			0
$697$	−16.0014	+	13.4268i	−0.606098	+	0.508576i
$698$		0			0
$699$	−10.3707	+	42.6759i	−0.392255	+	1.61415i
$700$		0			0
$701$			2.31861i			0.0875726i	0.999041	+	0.0437863i	$0.0139421\pi$
$701$			2.31861i			0.0875726i	−0.999041	+	0.0437863i	$0.986058\pi$
$702$		0			0
$703$		−	51.2329i		−	1.93228i
$704$		0			0
$705$	1.58114	−	0.463597i	0.0595494	−	0.0174601i
$706$		0			0
$707$	−38.5298	+	32.3304i	−1.44906	+	1.21591i
$708$		0			0
$709$	−15.2477	+	5.54971i	−0.572639	+	0.208424i	−0.612077	−	0.790798i	$-0.709666\pi$
$709$	−15.2477	+	5.54971i	−0.572639	+	0.208424i	0.0394375	+	0.999222i	$0.487443\pi$
$710$		0			0
$711$	0.823595	−	6.41371i	0.0308872	−	0.240533i
$712$		0			0
$713$	−10.2108	+	12.1687i	−0.382396	+	0.455722i
$714$		0			0
$715$	−0.363828	+	0.0641526i	−0.0136064	+	0.00239917i
$716$		0			0
$717$	−14.1609	+	7.01148i	−0.528850	+	0.261848i
$718$		0			0
$719$	−8.16209	−	14.1372i	−0.304395	−	0.527227i	0.672732	−	0.739886i	$-0.265121\pi$
$719$	−8.16209	−	14.1372i	−0.304395	−	0.527227i	−0.977126	+	0.212660i	$0.931787\pi$
$720$		0			0
$721$	13.0786	−	22.6527i	0.487071	−	0.843632i
$722$		0			0
$723$	−6.45474	−	8.77380i	−0.240054	−	0.326301i
$724$		0			0
$725$	−4.63079	+	12.7230i	−0.171983	+	0.472521i
$726$		0			0
$727$	11.7743	+	2.07612i	0.436684	+	0.0769992i	0.387669	−	0.921799i	$-0.373281\pi$
$727$	11.7743	+	2.07612i	0.436684	+	0.0769992i	0.0490155	+	0.998798i	$0.484392\pi$
$728$		0			0
$729$	3.77998	+	26.7341i	0.139999	+	0.990152i
$730$		0			0
$731$	0.787792	−	4.46779i	0.0291375	−	0.165247i
$732$		0			0
$733$	−21.5306	−	7.83651i	−0.795252	−	0.289448i	−0.0877347	−	0.996144i	$-0.527963\pi$
$733$	−21.5306	−	7.83651i	−0.795252	−	0.289448i	−0.707518	+	0.706696i	$0.750185\pi$
$734$		0			0
$735$	0.574896	−	0.422942i	0.0212054	−	0.0156004i
$736$		0			0
$737$	−56.6422	−	32.7024i	−2.08644	−	1.20461i
$738$		0			0
$739$	10.9086	−	6.29807i	0.401279	−	0.231678i	−0.285757	−	0.958302i	$-0.592245\pi$
$739$	10.9086	−	6.29807i	0.401279	−	0.231678i	0.687036	+	0.726624i	$0.258912\pi$
$740$		0			0
$741$	0.553111	+	1.11711i	0.0203190	+	0.0410379i
$742$		0			0
$743$	−5.72734	−	32.4813i	−0.210116	−	1.19162i	−0.889184	−	0.457550i	$-0.848727\pi$
$743$	−5.72734	−	32.4813i	−0.210116	−	1.19162i	0.679068	−	0.734075i	$-0.262384\pi$
$744$		0			0
$745$	−7.22414	−	6.06177i	−0.264672	−	0.222086i
$746$		0			0
$747$	21.6246	+	2.77685i	0.791204	+	0.101600i
$748$		0			0
$749$	−3.38173	−	9.29123i	−0.123566	−	0.339494i
$750$		0			0
$751$	−15.5734	−	18.5597i	−0.568282	−	0.677252i	0.402996	−	0.915202i	$-0.367969\pi$
$751$	−15.5734	−	18.5597i	−0.568282	−	0.677252i	−0.971277	+	0.237950i	$0.923524\pi$
$752$		0			0
$753$	11.1487	+	38.0237i	0.406280	+	1.38566i
$754$		0			0
$755$	5.17811			0.188451
$756$		0			0
$757$	2.53542			0.0921512			0.0460756	−	0.998938i	$-0.485328\pi$
$757$	2.53542			0.0921512			0.0460756	+	0.998938i	$0.485328\pi$
$758$		0			0
$759$	−23.6118	−	5.73791i	−0.857054	−	0.208273i
$760$		0			0
$761$	−1.16069	−	1.38325i	−0.0420749	−	0.0501429i	0.744597	−	0.667515i	$-0.232642\pi$
$761$	−1.16069	−	1.38325i	−0.0420749	−	0.0501429i	−0.786671	+	0.617372i	$0.788197\pi$
$762$		0			0
$763$	15.5836	+	42.8157i	0.564166	+	1.55003i
$764$		0			0
$765$	1.78921	−	5.73835i	0.0646890	−	0.207471i
$766$		0			0
$767$	0.539793	+	0.452940i	0.0194908	+	0.0163547i
$768$		0			0
$769$	−7.71366	−	43.7463i	−0.278162	−	1.57753i	−0.728736	−	0.684795i	$-0.759892\pi$
$769$	−7.71366	−	43.7463i	−0.278162	−	1.57753i	0.450575	−	0.892739i	$-0.351219\pi$
$770$		0			0
$771$	−12.6063	+	18.9319i	−0.454004	+	0.681814i
$772$		0			0
$773$	−15.4056	+	8.89445i	−0.554102	+	0.319911i	−0.750775	−	0.660558i	$-0.770320\pi$
$773$	−15.4056	+	8.89445i	−0.554102	+	0.319911i	0.196673	+	0.980469i	$0.436986\pi$
$774$		0			0
$775$	−25.8791	−	14.9413i	−0.929604	−	0.536707i
$776$		0			0
$777$	−5.25118	−	47.2523i	−0.188385	−	1.69517i
$778$		0			0
$779$	−24.8320	−	9.03811i	−0.889699	−	0.323824i
$780$		0			0
$781$	−14.9640	+	84.8651i	−0.535454	+	3.03671i
$782$		0			0
$783$	−9.29635	−	11.4702i	−0.332224	−	0.409913i
$784$		0			0
$785$	0.0402072	+	0.00708961i	0.00143506	+	0.000253039i
$786$		0			0
$787$	15.9081	−	43.7073i	0.567064	−	1.55800i	−0.242001	−	0.970276i	$-0.577804\pi$
$787$	15.9081	−	43.7073i	0.567064	−	1.55800i	0.809065	−	0.587719i	$-0.199974\pi$
$788$		0			0
$789$	−15.8005	+	36.0651i	−0.562511	+	1.28395i
$790$		0			0
$791$	−2.30438	+	3.99130i	−0.0819343	+	0.141914i
$792$		0			0
$793$	−0.366611	−	0.634989i	−0.0130188	−	0.0225491i
$794$		0			0
$795$	0.588703	−	9.20664i	0.0208791	−	0.326526i
$796$		0			0
$797$	44.5297	−	7.85179i	1.57732	−	0.278125i	0.684665	−	0.728858i	$-0.259949\pi$
$797$	44.5297	−	7.85179i	1.57732	−	0.278125i	0.892659	+	0.450733i	$0.148837\pi$
$798$		0			0
$799$	−5.21498	+	6.21497i	−0.184493	+	0.219870i
$800$		0			0
$801$	4.11641	−	7.96946i	0.145446	−	0.281587i
$802$		0			0
$803$	69.4257	−	25.2689i	2.44998	−	0.891719i
$804$		0			0
$805$	−2.63516	+	2.21117i	−0.0928773	+	0.0779333i
$806$		0			0
$807$	32.6001	+	31.1084i	1.14758	+	1.09507i
$808$		0			0
$809$			29.6804i			1.04351i	0.853096	+	0.521754i	$0.174722\pi$
$809$			29.6804i			1.04351i	−0.853096	+	0.521754i	$0.825278\pi$
$810$		0			0
$811$			18.7731i			0.659212i	0.944118	+	0.329606i	$0.106916\pi$
$811$			18.7731i			0.659212i	−0.944118	+	0.329606i	$0.893084\pi$
$812$		0			0
$813$	−20.0510	−	19.1335i	−0.703218	−	0.671041i
$814$		0			0
$815$	−6.17643	+	5.18264i	−0.216351	+	0.181540i
$816$		0			0
$817$	5.39321	−	1.96297i	0.188685	−	0.0686756i
$818$		0			0
$819$	0.624635	+	0.973620i	0.0218265	+	0.0340210i
$820$		0			0
$821$	−10.4915	+	12.5033i	−0.366157	+	0.436369i	−0.917394	−	0.397980i	$-0.869711\pi$
$821$	−10.4915	+	12.5033i	−0.366157	+	0.436369i	0.551237	+	0.834349i	$0.314156\pi$
$822$		0			0
$823$	−3.89068	+	0.686032i	−0.135621	+	0.0239136i	−0.241046	−	0.970514i	$-0.577491\pi$
$823$	−3.89068	+	0.686032i	−0.135621	+	0.0239136i	0.105426	+	0.994427i	$0.466379\pi$
$824$		0			0
$825$	2.91692	−	45.6173i	0.101554	−	1.58819i
$826$		0			0
$827$	3.09424	+	5.35938i	0.107597	+	0.186364i	0.914796	−	0.403915i	$-0.132351\pi$
$827$	3.09424	+	5.35938i	0.107597	+	0.186364i	−0.807199	+	0.590279i	$0.799018\pi$
$828$		0			0
$829$	13.3127	−	23.0583i	0.462369	−	0.800847i	−0.536709	−	0.843767i	$-0.680333\pi$
$829$	13.3127	−	23.0583i	0.462369	−	0.800847i	0.999079	+	0.0429202i	$0.0136661\pi$
$830$		0			0
$831$	−4.92822	+	11.2488i	−0.170958	+	0.390218i
$832$		0			0
$833$	−1.20193	+	3.30228i	−0.0416445	+	0.114417i
$834$		0			0
$835$	8.45056	+	1.49006i	0.292444	+	0.0515657i
$836$		0			0
$837$	28.4938	−	15.8099i	0.984889	−	0.546470i
$838$		0			0
$839$	−4.51239	+	25.5910i	−0.155785	+	0.883500i	0.802280	+	0.596948i	$0.203620\pi$
$839$	−4.51239	+	25.5910i	−0.155785	+	0.883500i	−0.958065	+	0.286552i	$0.907491\pi$
$840$		0			0
$841$	−19.6643	−	7.15723i	−0.678081	−	0.246801i
$842$		0			0
$843$	4.48669	+	40.3731i	0.154530	+	1.39052i
$844$		0			0
$845$	5.44897	+	3.14596i	0.187450	+	0.108224i
$846$		0			0
$847$	47.7379	−	27.5615i	1.64029	−	0.947024i
$848$		0			0
$849$	−17.1786	+	25.7985i	−0.589568	+	0.885402i
$850$		0			0
$851$	4.30924	+	24.4389i	0.147719	+	0.837755i
$852$		0			0
$853$	20.9654	+	17.5921i	0.717841	+	0.602340i	0.926787	−	0.375587i	$-0.122559\pi$
$853$	20.9654	+	17.5921i	0.717841	+	0.602340i	−0.208946	+	0.977927i	$0.567003\pi$
$854$		0			0
$855$	7.41868	−	1.66951i	0.253714	−	0.0570959i
$856$		0			0
$857$	13.4861	+	37.0527i	0.460675	+	1.26570i	0.924979	+	0.380019i	$0.124083\pi$
$857$	13.4861	+	37.0527i	0.460675	+	1.26570i	−0.464303	+	0.885676i	$0.653695\pi$
$858$		0			0
$859$	20.0194	+	23.8581i	0.683052	+	0.814029i	0.990497	−	0.137537i	$-0.0439185\pi$
$859$	20.0194	+	23.8581i	0.683052	+	0.814029i	−0.307445	+	0.951566i	$0.599474\pi$
$860$		0			0
$861$	−23.8290	−	5.79069i	−0.812091	−	0.197346i
$862$		0			0
$863$	15.3664			0.523080			0.261540	−	0.965193i	$-0.415770\pi$
$863$	15.3664			0.523080			0.261540	+	0.965193i	$0.415770\pi$
$864$		0			0
$865$	−1.76740			−0.0600935
$866$		0			0
$867$	0.0426378	+	0.145421i	0.00144806	+	0.00493875i
$868$		0			0
$869$	−7.67349	−	9.14491i	−0.260305	−	0.310220i
$870$		0			0
$871$	−0.555854	−	1.52720i	−0.0188344	−	0.0517471i
$872$		0			0
$873$	−10.5034	+	13.7790i	−0.355485	+	0.466347i
$874$		0			0
$875$	−10.1588	−	8.52422i	−0.343429	−	0.288171i
$876$		0			0
$877$	2.58618	+	14.6670i	0.0873292	+	0.495268i	0.996830	+	0.0795655i	$0.0253533\pi$
$877$	2.58618	+	14.6670i	0.0873292	+	0.495268i	−0.909500	+	0.415703i	$0.863536\pi$
$878$		0			0
$879$	−5.04162	−	10.1824i	−0.170049	−	0.343445i
$880$		0			0
$881$	5.64798	−	3.26086i	0.190285	−	0.109861i	−0.401831	−	0.915714i	$-0.631626\pi$
$881$	5.64798	−	3.26086i	0.190285	−	0.109861i	0.592116	+	0.805853i	$0.298293\pi$
$882$		0			0
$883$	7.48288	+	4.32025i	0.251819	+	0.145388i	0.620597	−	0.784130i	$-0.286890\pi$
$883$	7.48288	+	4.32025i	0.251819	+	0.145388i	−0.368778	+	0.929518i	$0.620224\pi$
$884$		0			0
$885$	3.46249	−	2.54730i	0.116390	−	0.0856265i
$886$		0			0
$887$	18.2775	+	6.65248i	0.613699	+	0.223368i	0.630121	−	0.776497i	$-0.283005\pi$
$887$	18.2775	+	6.65248i	0.613699	+	0.223368i	−0.0164218	+	0.999865i	$0.505227\pi$
$888$		0			0
$889$	−0.884027	+	5.01357i	−0.0296493	+	0.168150i
$890$		0			0
$891$	41.0127	+	28.3295i	1.37398	+	0.949075i
$892$		0			0
$893$	−10.1078	−	1.78228i	−0.338245	−	0.0596418i
$894$		0			0
$895$	−1.57182	+	4.31853i	−0.0525400	+	0.144353i
$896$		0			0
$897$	−0.357804	−	0.486355i	−0.0119467	−	0.0162389i
$898$		0			0
$899$	−8.90952	+	15.4317i	−0.297149	+	0.514677i
$900$		0			0
$901$	22.7124	+	39.3390i	0.756658	+	1.31057i
$902$		0			0
$903$	4.77298	−	2.36324i	0.158835	−	0.0786436i
$904$		0			0
$905$	8.29647	−	1.46289i	0.275784	−	0.0486282i
$906$		0			0
$907$	7.59722	−	9.05401i	0.252262	−	0.300634i	−0.625021	−	0.780608i	$-0.714910\pi$
$907$	7.59722	−	9.05401i	0.252262	−	0.300634i	0.877283	+	0.479974i	$0.159354\pi$
$908$		0			0
$909$	−49.6896	+	20.7679i	−1.64810	+	0.688827i
$910$		0			0
$911$	21.4631	−	7.81193i	0.711104	−	0.258821i	0.0389597	−	0.999241i	$-0.487596\pi$
$911$	21.4631	−	7.81193i	0.711104	−	0.258821i	0.672144	+	0.740420i	$0.265373\pi$
$912$		0			0
$913$	30.8332	−	25.8721i	1.02043	−	0.856243i
$914$		0			0
$915$	−4.29216	+	1.25848i	−0.141895	+	0.0416039i
$916$		0			0
$917$		−	29.7687i		−	0.983050i
$918$		0			0
$919$			37.8484i			1.24850i	0.781223	+	0.624252i	$0.214596\pi$
$919$			37.8484i			1.24850i	−0.781223	+	0.624252i	$0.785404\pi$
$920$		0			0
$921$	2.75029	−	11.3176i	0.0906252	−	0.372928i
$922$		0			0
$923$	−1.64033	+	1.37640i	−0.0539921	+	0.0453048i
$924$		0			0
$925$	−43.8676	+	15.9665i	−1.44236	+	0.524975i
$926$		0			0
$927$	20.5888	−	18.9872i	0.676225	−	0.623623i
$928$		0			0
$929$	−29.4994	+	35.1560i	−0.967842	+	1.15343i	0.0202851	+	0.999794i	$0.493543\pi$
$929$	−29.4994	+	35.1560i	−0.967842	+	1.15343i	−0.988128	+	0.153635i	$0.950902\pi$
$930$		0			0
$931$	−4.37825	+	0.772003i	−0.143491	+	0.0253014i
$932$		0			0
$933$	−31.6582	−	21.0805i	−1.03644	−	0.690144i
$934$		0			0
$935$	−5.54841	−	9.61012i	−0.181452	−	0.314285i
$936$		0			0
$937$	3.52727	−	6.10942i	0.115231	−	0.199586i	−0.802641	−	0.596462i	$-0.796572\pi$
$937$	3.52727	−	6.10942i	0.115231	−	0.199586i	0.917872	+	0.396876i	$0.129906\pi$
$938$		0			0
$939$	−45.0297	+	5.00418i	−1.46949	+	0.163305i
$940$		0			0
$941$	8.53894	−	23.4606i	0.278362	−	0.764792i	−0.719187	−	0.694816i	$-0.755486\pi$
$941$	8.53894	−	23.4606i	0.278362	−	0.764792i	0.997549	−	0.0699758i	$-0.0222922\pi$
$942$		0			0
$943$	12.6055	+	2.22268i	0.410491	+	0.0723806i
$944$		0			0
$945$	6.67116	−	2.30018i	0.217013	−	0.0748248i
$946$		0			0
$947$	−4.09418	+	23.2192i	−0.133043	+	0.754523i	0.843160	+	0.537663i	$0.180693\pi$
$947$	−4.09418	+	23.2192i	−0.133043	+	0.754523i	−0.976203	+	0.216860i	$0.930418\pi$
$948$		0			0
$949$	1.72512	+	0.627892i	0.0559998	+	0.0203823i
$950$		0			0
$951$	−5.81687	−	2.54843i	−0.188625	−	0.0826384i
$952$		0			0
$953$	−45.6991	−	26.3844i	−1.48034	−	0.854675i	−0.480588	−	0.876946i	$-0.659577\pi$
$953$	−45.6991	−	26.3844i	−1.48034	−	0.854675i	−0.999752	+	0.0222716i	$0.992910\pi$
$954$		0			0
$955$	−9.98711	+	5.76606i	−0.323175	+	0.186585i
$956$		0			0
$957$	−27.2017	−	1.73936i	−0.879305	−	0.0562256i
$958$		0			0
$959$	−6.46883	−	36.6865i	−0.208889	−	1.18467i
$960$		0			0
$961$	−6.37938	−	5.35293i	−0.205786	−	0.172675i
$962$		0			0
$963$	−0.495501	−	10.5753i	−0.0159673	−	0.340785i
$964$		0			0
$965$	3.84165	+	10.5548i	0.123667	+	0.339772i
$966$		0			0
$967$	−4.29031	−	5.11300i	−0.137967	−	0.164423i	0.692637	−	0.721287i	$-0.256449\pi$
$967$	−4.29031	−	5.11300i	−0.137967	−	0.164423i	−0.830604	+	0.556864i	$0.812005\pi$
$968$		0			0
$969$	−25.8485	+	27.0880i	−0.830375	+	0.870192i
$970$		0			0
$971$	47.2223			1.51544			0.757718	−	0.652583i	$-0.226314\pi$
$971$	47.2223			1.51544			0.757718	+	0.652583i	$0.226314\pi$
$972$		0			0
$973$	−6.26757			−0.200929
$974$		0			0
$975$	0.784135	−	0.821736i	0.0251124	−	0.0263166i
$976$		0			0
$977$	3.66923	+	4.37281i	0.117389	+	0.139899i	0.821539	−	0.570153i	$-0.193116\pi$
$977$	3.66923	+	4.37281i	0.117389	+	0.139899i	−0.704150	+	0.710052i	$0.748672\pi$
$978$		0			0
$979$	−5.66368	−	15.5608i	−0.181012	−	0.497326i
$980$		0			0
$981$	2.28336	+	48.7331i	0.0729021	+	1.55593i
$982$		0			0
$983$	−15.5327	−	13.0335i	−0.495417	−	0.415704i	0.360546	−	0.932741i	$-0.382590\pi$
$983$	−15.5327	−	13.0335i	−0.495417	−	0.415704i	−0.855963	+	0.517037i	$0.827035\pi$
$984$		0			0
$985$	1.83036	+	10.3805i	0.0583200	+	0.330749i
$986$		0			0
$987$	−9.50516	−	0.607791i	−0.302552	−	0.0193462i
$988$		0			0
$989$	−2.40754	+	1.39000i	−0.0765554	+	0.0441993i
$990$		0			0
$991$	−6.54540	−	3.77899i	−0.207922	−	0.120044i	0.392424	−	0.919785i	$-0.371637\pi$
$991$	−6.54540	−	3.77899i	−0.207922	−	0.120044i	−0.600345	+	0.799741i	$0.704970\pi$
$992$		0			0
$993$	21.1317	+	9.25801i	0.670594	+	0.293794i
$994$		0			0
$995$	−2.96998	−	1.08098i	−0.0941546	−	0.0342695i
$996$		0			0
$997$	0.942202	−	5.34349i	0.0298398	−	0.169230i	−0.966246	−	0.257621i	$-0.917061\pi$
$997$	0.942202	−	5.34349i	0.0298398	−	0.169230i	0.996086	+	0.0883910i	$0.0281725\pi$
$998$		0			0
$999$	9.69251	−	49.9749i	0.306658	−	1.58114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.b.191.2	yes	36
4.3	odd	2		432.2.be.c.191.5	yes	36
27.14	odd	18		432.2.be.c.95.5	yes	36
108.95	even	18	inner	432.2.be.b.95.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.95.2	✓	36	108.95	even	18	inner
432.2.be.b.191.2	yes	36	1.1	even	1	trivial
432.2.be.c.95.5	yes	36	27.14	odd	18
432.2.be.c.191.5	yes	36	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +O(q^{10})\)	\(q+(-1.19574 + 1.25308i) q^{3} +(0.311559 + 0.371302i) q^{5} +(-0.958275 - 2.63284i) q^{7} +(-0.140409 - 2.99671i) q^{9} +(-4.24267 - 3.56003i) q^{11} +(-0.0238977 - 0.135530i) q^{13} +(-0.837815 - 0.0535726i) q^{15} +(3.57989 - 2.06685i) q^{17} +(4.52888 + 2.61475i) q^{19} +(4.44500 + 1.94740i) q^{21} +(-2.38028 - 0.866350i) q^{23} +(0.827445 - 4.69267i) q^{25} +(3.92301 + 3.40735i) q^{27} +(-2.79825 - 0.493407i) q^{29} +(2.14487 - 5.89298i) q^{31} +(9.53413 - 1.05953i) q^{33} +(0.679019 - 1.17610i) q^{35} +(-4.89845 - 8.48436i) q^{37} +(0.198406 + 0.132114i) q^{39} +(-4.97642 + 0.877478i) q^{41} +(0.705455 - 0.840729i) q^{43} +(1.06894 - 0.985788i) q^{45} +(-1.84430 + 0.671271i) q^{47} +(-0.651243 + 0.546458i) q^{49} +(-1.69069 + 6.95730i) q^{51} +10.9889i q^{53} -2.68447i q^{55} +(-8.69184 + 2.54848i) q^{57} +(-3.92231 + 3.29121i) q^{59} +(5.00653 - 1.82223i) q^{61} +(-7.75531 + 3.24135i) q^{63} +(0.0428772 - 0.0510990i) q^{65} +(11.6299 - 2.05066i) q^{67} +(3.93180 - 1.94674i) q^{69} +(-7.77969 - 13.4748i) q^{71} +(-6.66989 + 11.5526i) q^{73} +(4.89088 + 6.64807i) q^{75} +(-5.30733 + 14.5818i) q^{77} +(2.12271 + 0.374291i) q^{79} +(-8.96057 + 0.841533i) q^{81} +(-1.26197 + 7.15699i) q^{83} +(1.88278 + 0.685274i) q^{85} +(3.96426 - 2.91644i) q^{87} +(2.58936 + 1.49497i) q^{89} +(-0.333929 + 0.192794i) q^{91} +(4.81966 + 9.73416i) q^{93} +(0.440153 + 2.49623i) q^{95} +(-4.42409 - 3.71225i) q^{97} +(-10.0727 + 13.2139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more