LMFDB - Embedded newform 864.2.y.c.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.8
Character	$\chi$	$=$	864.193
Dual form			864.2.y.c.385.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67597 - 0.437160i) q^{3} +(-0.158606 + 0.899497i) q^{5} +(1.25116 - 1.04985i) q^{7} +(2.61778 - 1.46534i) q^{9} +O(q^{10})$	\(q+(1.67597 - 0.437160i) q^{3} +(-0.158606 + 0.899497i) q^{5} +(1.25116 - 1.04985i) q^{7} +(2.61778 - 1.46534i) q^{9} +(0.887648 + 5.03410i) q^{11} +(1.45896 - 0.531018i) q^{13} +(0.127405 + 1.57687i) q^{15} +(-0.661128 + 1.14511i) q^{17} +(1.16059 + 2.01020i) q^{19} +(1.63796 - 2.30648i) q^{21} +(-2.86651 - 2.40528i) q^{23} +(3.91452 + 1.42477i) q^{25} +(3.74675 - 3.60026i) q^{27} +(0.0747537 + 0.0272081i) q^{29} +(-4.09516 - 3.43625i) q^{31} +(3.68838 + 8.04898i) q^{33} +(0.745894 + 1.29193i) q^{35} +(2.08453 - 3.61052i) q^{37} +(2.21304 - 1.52777i) q^{39} +(7.69988 - 2.80253i) q^{41} +(-1.29485 - 7.34345i) q^{43} +(0.902872 + 2.58710i) q^{45} +(-4.78889 + 4.01836i) q^{47} +(-0.752316 + 4.26660i) q^{49} +(-0.607438 + 2.20819i) q^{51} +10.3219 q^{53} -4.66894 q^{55} +(2.82390 + 2.86169i) q^{57} +(-1.03999 + 5.89807i) q^{59} +(-1.68954 + 1.41769i) q^{61} +(1.73688 - 4.58165i) q^{63} +(0.246250 + 1.39655i) q^{65} +(0.0698559 - 0.0254255i) q^{67} +(-5.85568 - 2.77807i) q^{69} +(-3.73567 + 6.47037i) q^{71} +(-3.83421 - 6.64105i) q^{73} +(7.18350 + 0.676606i) q^{75} +(6.39564 + 5.36658i) q^{77} +(-14.7441 - 5.36643i) q^{79} +(4.70557 - 7.67187i) q^{81} +(1.07899 + 0.392719i) q^{83} +(-0.925161 - 0.776302i) q^{85} +(0.137180 + 0.0129208i) q^{87} +(-9.09078 - 15.7457i) q^{89} +(1.26790 - 2.19608i) q^{91} +(-8.36557 - 3.96882i) q^{93} +(-1.99225 + 0.725119i) q^{95} +(1.75201 + 9.93616i) q^{97} +(9.70033 + 11.8775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.67597	−	0.437160i	0.967624	−	0.252394i
$3$	1.67597	−	0.437160i	0.967624	−	0.252394i
$4$		0			0
$5$	−0.158606	+	0.899497i	−0.0709306	+	0.402267i	0.928584	+	0.371122i	$0.121027\pi$
$5$	−0.158606	+	0.899497i	−0.0709306	+	0.402267i	−0.999515	+	0.0311456i	$0.990084\pi$
$6$		0			0
$7$	1.25116	−	1.04985i	0.472894	−	0.396805i	−0.374955	−	0.927043i	$-0.622342\pi$
$7$	1.25116	−	1.04985i	0.472894	−	0.396805i	0.847849	+	0.530238i	$0.177897\pi$
$8$		0			0
$9$	2.61778	−	1.46534i	0.872594	−	0.488446i
$10$		0			0
$11$	0.887648	+	5.03410i	0.267636	+	1.51784i	0.761423	+	0.648256i	$0.224501\pi$
$11$	0.887648	+	5.03410i	0.267636	+	1.51784i	−0.493787	+	0.869583i	$0.664388\pi$
$12$		0			0
$13$	1.45896	−	0.531018i	0.404643	−	0.147278i	−0.131677	−	0.991293i	$-0.542036\pi$
$13$	1.45896	−	0.531018i	0.404643	−	0.147278i	0.536320	+	0.844015i	$0.319814\pi$
$14$		0			0
$15$	0.127405	+	1.57687i	0.0328958	+	0.407146i
$16$		0			0
$17$	−0.661128	+	1.14511i	−0.160347	+	0.277729i	−0.934993	−	0.354666i	$-0.884595\pi$
$17$	−0.661128	+	1.14511i	−0.160347	+	0.277729i	0.774646	+	0.632395i	$0.217928\pi$
$18$		0			0
$19$	1.16059	+	2.01020i	0.266258	+	0.461173i	0.967892	−	0.251365i	$-0.0808793\pi$
$19$	1.16059	+	2.01020i	0.266258	+	0.461173i	−0.701634	+	0.712537i	$0.747546\pi$
$20$		0			0
$21$	1.63796	−	2.30648i	0.357433	−	0.503315i
$22$		0			0
$23$	−2.86651	−	2.40528i	−0.597708	−	0.501536i	0.293000	−	0.956112i	$-0.405346\pi$
$23$	−2.86651	−	2.40528i	−0.597708	−	0.501536i	−0.890708	+	0.454576i	$0.849791\pi$
$24$		0			0
$25$	3.91452	+	1.42477i	0.782905	+	0.284954i
$26$		0			0
$27$	3.74675	−	3.60026i	0.721062	−	0.692870i
$28$		0			0
$29$	0.0747537	+	0.0272081i	0.0138814	+	0.00505242i	0.348952	−	0.937141i	$-0.386538\pi$
$29$	0.0747537	+	0.0272081i	0.0138814	+	0.00505242i	−0.335070	+	0.942193i	$0.608760\pi$
$30$		0			0
$31$	−4.09516	−	3.43625i	−0.735512	−	0.617168i	0.196116	−	0.980581i	$-0.437167\pi$
$31$	−4.09516	−	3.43625i	−0.735512	−	0.617168i	−0.931628	+	0.363413i	$0.881612\pi$
$32$		0			0
$33$	3.68838	+	8.04898i	0.642065	+	1.40115i
$34$		0			0
$35$	0.745894	+	1.29193i	0.126079	+	0.218376i
$36$		0			0
$37$	2.08453	−	3.61052i	0.342695	−	0.593566i	−0.642237	−	0.766506i	$-0.721993\pi$
$37$	2.08453	−	3.61052i	0.342695	−	0.593566i	0.984932	+	0.172940i	$0.0553268\pi$
$38$		0			0
$39$	2.21304	−	1.52777i	0.354370	−	0.244639i
$40$		0			0
$41$	7.69988	−	2.80253i	1.20252	−	0.437681i	0.338417	−	0.940996i	$-0.390109\pi$
$41$	7.69988	−	2.80253i	1.20252	−	0.437681i	0.864103	+	0.503315i	$0.167887\pi$
$42$		0			0
$43$	−1.29485	−	7.34345i	−0.197463	−	1.11987i	−0.908868	−	0.417084i	$-0.863052\pi$
$43$	−1.29485	−	7.34345i	−0.197463	−	1.11987i	0.711405	−	0.702782i	$-0.248059\pi$
$44$		0			0
$45$	0.902872	+	2.58710i	0.134592	+	0.385662i
$46$		0			0
$47$	−4.78889	+	4.01836i	−0.698531	+	0.586137i	−0.921355	−	0.388721i	$-0.872917\pi$
$47$	−4.78889	+	4.01836i	−0.698531	+	0.586137i	0.222824	+	0.974859i	$0.428472\pi$
$48$		0			0
$49$	−0.752316	+	4.26660i	−0.107474	+	0.609514i
$50$		0			0
$51$	−0.607438	+	2.20819i	−0.0850584	+	0.309208i
$52$		0			0
$53$	10.3219			1.41782			0.708911	−	0.705298i	$-0.249187\pi$
$53$	10.3219			1.41782			0.708911	+	0.705298i	$0.249187\pi$
$54$		0			0
$55$	−4.66894			−0.629560
$56$		0			0
$57$	2.82390	+	2.86169i	0.374035	+	0.379040i
$58$		0			0
$59$	−1.03999	+	5.89807i	−0.135395	+	0.767864i	0.839189	+	0.543840i	$0.183030\pi$
$59$	−1.03999	+	5.89807i	−0.135395	+	0.767864i	−0.974584	+	0.224023i	$0.928081\pi$
$60$		0			0
$61$	−1.68954	+	1.41769i	−0.216324	+	0.181517i	−0.744510	−	0.667612i	$-0.767317\pi$
$61$	−1.68954	+	1.41769i	−0.216324	+	0.181517i	0.528186	+	0.849129i	$0.322872\pi$
$62$		0			0
$63$	1.73688	−	4.58165i	0.218827	−	0.577233i
$64$		0			0
$65$	0.246250	+	1.39655i	0.0305435	+	0.173221i
$66$		0			0
$67$	0.0698559	−	0.0254255i	0.00853425	−	0.00310621i	−0.337749	−	0.941236i	$-0.609666\pi$
$67$	0.0698559	−	0.0254255i	0.00853425	−	0.00310621i	0.346284	+	0.938130i	$0.387443\pi$
$68$		0			0
$69$	−5.85568	−	2.77807i	−0.704942	−	0.334441i
$70$		0			0
$71$	−3.73567	+	6.47037i	−0.443343	+	0.767892i	−0.997935	−	0.0642300i	$-0.979541\pi$
$71$	−3.73567	+	6.47037i	−0.443343	+	0.767892i	0.554592	+	0.832122i	$0.312874\pi$
$72$		0			0
$73$	−3.83421	−	6.64105i	−0.448760	−	0.777276i	0.549545	−	0.835464i	$-0.314801\pi$
$73$	−3.83421	−	6.64105i	−0.448760	−	0.777276i	−0.998306	+	0.0581881i	$0.981468\pi$
$74$		0			0
$75$	7.18350	+	0.676606i	0.829479	+	0.0781277i
$76$		0			0
$77$	6.39564	+	5.36658i	0.728850	+	0.611578i
$78$		0			0
$79$	−14.7441	−	5.36643i	−1.65884	−	0.603770i	−0.668664	−	0.743565i	$-0.733133\pi$
$79$	−14.7441	−	5.36643i	−1.65884	−	0.603770i	−0.990180	+	0.139795i	$0.955356\pi$
$80$		0			0
$81$	4.70557	−	7.67187i	0.522841	−	0.852430i
$82$		0			0
$83$	1.07899	+	0.392719i	0.118434	+	0.0431066i	0.400558	−	0.916272i	$-0.368816\pi$
$83$	1.07899	+	0.392719i	0.118434	+	0.0431066i	−0.282123	+	0.959378i	$0.591039\pi$
$84$		0			0
$85$	−0.925161	−	0.776302i	−0.100348	−	0.0842018i
$86$		0			0
$87$	0.137180	+	0.0129208i	0.0147072	+	0.00138526i
$88$		0			0
$89$	−9.09078	−	15.7457i	−0.963621	−	1.66904i	−0.713276	−	0.700883i	$-0.752789\pi$
$89$	−9.09078	−	15.7457i	−0.963621	−	1.66904i	−0.250344	−	0.968157i	$-0.580544\pi$
$90$		0			0
$91$	1.26790	−	2.19608i	0.132913	−	0.230211i
$92$		0			0
$93$	−8.36557	−	3.96882i	−0.867470	−	0.411548i
$94$		0			0
$95$	−1.99225	+	0.725119i	−0.204400	+	0.0743957i
$96$		0			0
$97$	1.75201	+	9.93616i	0.177890	+	1.00886i	0.934755	+	0.355293i	$0.115619\pi$
$97$	1.75201	+	9.93616i	0.177890	+	1.00886i	−0.756865	+	0.653571i	$0.773270\pi$
$98$		0			0
$99$	9.70033	+	11.8775i	0.974920	+	1.19373i
$100$		0			0
$101$	−9.92348	+	8.32679i	−0.987424	+	0.828547i	−0.985193	−	0.171451i	$-0.945155\pi$
$101$	−9.92348	+	8.32679i	−0.987424	+	0.828547i	−0.00223089	+	0.999998i	$0.500710\pi$
$102$		0			0
$103$	1.35040	−	7.65849i	0.133059	−	0.754613i	−0.843133	−	0.537705i	$-0.819292\pi$
$103$	1.35040	−	7.65849i	0.133059	−	0.754613i	0.976192	−	0.216909i	$-0.0695974\pi$
$104$		0			0
$105$	1.81488	+	1.83916i	0.177114	+	0.179484i
$106$		0			0
$107$	−8.66656			−0.837828			−0.418914	−	0.908026i	$-0.637589\pi$
$107$	−8.66656			−0.837828			−0.418914	+	0.908026i	$0.637589\pi$
$108$		0			0
$109$	17.3261			1.65954			0.829768	−	0.558109i	$-0.188473\pi$
$109$	17.3261			1.65954			0.829768	+	0.558109i	$0.188473\pi$
$110$		0			0
$111$	1.91525	−	6.96241i	0.181788	−	0.660843i
$112$		0			0
$113$	0.381238	−	2.16211i	0.0358639	−	0.203394i	−0.961611	−	0.274417i	$-0.911515\pi$
$113$	0.381238	−	2.16211i	0.0358639	−	0.203394i	0.997475	+	0.0710227i	$0.0226263\pi$
$114$		0			0
$115$	2.61819	−	2.19692i	0.244147	−	0.204864i
$116$		0			0
$117$	3.04112	−	3.52796i	0.281151	−	0.326160i
$118$		0			0
$119$	0.375012	+	2.12680i	0.0343773	+	0.194963i
$120$		0			0
$121$	−14.2176	+	5.17480i	−1.29251	+	0.470436i
$122$		0			0
$123$	11.6797	−	8.06304i	1.05312	−	0.727020i
$124$		0			0
$125$	−4.18587	+	7.25015i	−0.374396	+	0.648473i
$126$		0			0
$127$	−10.0273	−	17.3678i	−0.889777	−	1.54114i	−0.840139	−	0.542372i	$-0.817527\pi$
$127$	−10.0273	−	17.3678i	−0.889777	−	1.54114i	−0.0496382	−	0.998767i	$-0.515807\pi$
$128$		0			0
$129$	−5.38040	−	11.7414i	−0.473718	−	1.03377i
$130$		0			0
$131$	9.91431	+	8.31909i	0.866217	+	0.726843i	0.963298	−	0.268434i	$-0.0865061\pi$
$131$	9.91431	+	8.31909i	0.866217	+	0.726843i	−0.0970808	+	0.995277i	$0.530951\pi$
$132$		0			0
$133$	3.56250	+	1.29664i	0.308908	+	0.112433i
$134$		0			0
$135$	2.64417	+	3.94121i	0.227574	+	0.339205i
$136$		0			0
$137$	−12.8377	−	4.67256i	−1.09680	−	0.399204i	−0.270666	−	0.962673i	$-0.587244\pi$
$137$	−12.8377	−	4.67256i	−1.09680	−	0.399204i	−0.826137	+	0.563470i	$0.809466\pi$
$138$		0			0
$139$	−4.92501	−	4.13257i	−0.417734	−	0.350520i	0.409566	−	0.912280i	$-0.365680\pi$
$139$	−4.92501	−	4.13257i	−0.417734	−	0.350520i	−0.827300	+	0.561760i	$0.810124\pi$
$140$		0			0
$141$	−6.26939	+	8.82817i	−0.527978	+	0.743466i
$142$		0			0
$143$	3.96824	+	6.87320i	0.331841	+	0.574765i
$144$		0			0
$145$	−0.0363300	+	0.0629254i	−0.00301704	+	0.00522567i
$146$		0			0
$147$	0.604322	+	7.47959i	0.0498436	+	0.616906i
$148$		0			0
$149$	2.52311	−	0.918335i	0.206701	−	0.0752329i	−0.236595	−	0.971608i	$-0.576031\pi$
$149$	2.52311	−	0.918335i	0.206701	−	0.0752329i	0.443296	+	0.896375i	$0.353809\pi$
$150$		0			0
$151$	3.61660	+	20.5107i	0.294314	+	1.66914i	0.669975	+	0.742383i	$0.266305\pi$
$151$	3.61660	+	20.5107i	0.294314	+	1.66914i	−0.375661	+	0.926757i	$0.622584\pi$
$152$		0			0
$153$	−0.0527201	+	3.96641i	−0.00426217	+	0.320666i
$154$		0			0
$155$	3.74041	−	3.13858i	0.300437	−	0.252096i
$156$		0			0
$157$	1.34143	−	7.60761i	0.107058	−	0.607154i	−0.883321	−	0.468769i	$-0.844698\pi$
$157$	1.34143	−	7.60761i	0.107058	−	0.607154i	0.990379	−	0.138385i	$-0.0441911\pi$
$158$		0			0
$159$	17.2992	−	4.51232i	1.37192	−	0.357850i
$160$		0			0
$161$	−6.11164			−0.481665
$162$		0			0
$163$	−4.18421			−0.327733			−0.163866	−	0.986483i	$-0.552397\pi$
$163$	−4.18421			−0.327733			−0.163866	+	0.986483i	$0.552397\pi$
$164$		0			0
$165$	−7.82503	+	2.04108i	−0.609178	+	0.158898i
$166$		0			0
$167$	−1.87330	+	10.6240i	−0.144960	+	0.822111i	0.822439	+	0.568854i	$0.192613\pi$
$167$	−1.87330	+	10.6240i	−0.144960	+	0.822111i	−0.967399	+	0.253257i	$0.918498\pi$
$168$		0			0
$169$	−8.11199	+	6.80677i	−0.624000	+	0.523598i
$170$		0			0
$171$	5.98381	+	3.56162i	0.457593	+	0.272364i
$172$		0			0
$173$	2.50365	+	14.1989i	0.190349	+	1.07952i	0.918888	+	0.394519i	$0.129089\pi$
$173$	2.50365	+	14.1989i	0.190349	+	1.07952i	−0.728538	+	0.685005i	$0.759800\pi$
$174$		0			0
$175$	6.39349	−	2.32704i	0.483303	−	0.175908i
$176$		0			0
$177$	0.835405	+	10.3397i	0.0627929	+	0.777177i
$178$		0			0
$179$	−5.33967	+	9.24858i	−0.399106	+	0.691271i	−0.993616	−	0.112817i	$-0.964013\pi$
$179$	−5.33967	+	9.24858i	−0.399106	+	0.691271i	0.594510	+	0.804088i	$0.297346\pi$
$180$		0			0
$181$	−11.4877	−	19.8973i	−0.853876	−	1.47896i	−0.877684	−	0.479239i	$-0.840913\pi$
$181$	−11.4877	−	19.8973i	−0.853876	−	1.47896i	0.0238086	−	0.999717i	$-0.492421\pi$
$182$		0			0
$183$	−2.21187	+	3.11462i	−0.163506	+	0.230239i
$184$		0			0
$185$	2.91703	+	2.44768i	0.214464	+	0.179957i
$186$		0			0
$187$	−6.35143	−	2.31173i	−0.464463	−	0.169051i
$188$		0			0
$189$	0.908060	−	8.43802i	0.0660517	−	0.613776i
$190$		0			0
$191$	−4.56758	−	1.66246i	−0.330498	−	0.120292i	0.171441	−	0.985194i	$-0.445158\pi$
$191$	−4.56758	−	1.66246i	−0.330498	−	0.120292i	−0.501939	+	0.864903i	$0.667380\pi$
$192$		0			0
$193$	−15.0728	−	12.6476i	−1.08496	−	0.910392i	−0.0886394	−	0.996064i	$-0.528252\pi$
$193$	−15.0728	−	12.6476i	−1.08496	−	0.910392i	−0.996323	+	0.0856719i	$0.972696\pi$
$194$		0			0
$195$	1.02322	+	2.23294i	0.0732747	+	0.159904i
$196$		0			0
$197$	−8.86378	−	15.3525i	−0.631518	−	1.09382i	−0.987242	−	0.159230i	$-0.949099\pi$
$197$	−8.86378	−	15.3525i	−0.631518	−	1.09382i	0.355724	−	0.934591i	$-0.384234\pi$
$198$		0			0
$199$	2.78507	−	4.82388i	0.197428	−	0.341956i	−0.750266	−	0.661137i	$-0.770074\pi$
$199$	2.78507	−	4.82388i	0.197428	−	0.341956i	0.947694	+	0.319181i	$0.103408\pi$
$200$		0			0
$201$	0.105962	−	0.0731506i	0.00747396	−	0.00515965i
$202$		0			0
$203$	0.122093	−	0.0444383i	0.00856927	−	0.00311896i
$204$		0			0
$205$	1.29962	+	7.37051i	0.0907694	+	0.514779i
$206$		0			0
$207$	−11.0284	−	2.09611i	−0.766530	−	0.145690i
$208$		0			0
$209$	−9.08938	+	7.62689i	−0.628725	+	0.527563i
$210$		0			0
$211$	−0.818207	+	4.64028i	−0.0563277	+	0.319450i	−0.999932	−	0.0116239i	$-0.996300\pi$
$211$	−0.818207	+	4.64028i	−0.0563277	+	0.319450i	0.943605	+	0.331074i	$0.107411\pi$
$212$		0			0
$213$	−3.43230	+	12.4773i	−0.235178	+	0.854928i
$214$		0			0
$215$	6.81078			0.464491
$216$		0			0
$217$	−8.73124			−0.592715
$218$		0			0
$219$	−9.32924	−	9.45407i	−0.630412	−	0.638847i
$220$		0			0
$221$	−0.356486	+	2.02173i	−0.0239799	+	0.135997i
$222$		0			0
$223$	9.44885	−	7.92852i	0.632742	−	0.530933i	−0.269038	−	0.963130i	$-0.586706\pi$
$223$	9.44885	−	7.92852i	0.632742	−	0.530933i	0.901780	+	0.432196i	$0.142261\pi$
$224$		0			0
$225$	12.3351	−	2.00636i	0.822343	−	0.133757i
$226$		0			0
$227$	−0.621004	−	3.52189i	−0.0412175	−	0.233756i	0.957239	−	0.289299i	$-0.0934222\pi$
$227$	−0.621004	−	3.52189i	−0.0412175	−	0.233756i	−0.998456	+	0.0555429i	$0.982311\pi$
$228$		0			0
$229$	−19.6799	+	7.16289i	−1.30048	+	0.473337i	−0.897154	−	0.441718i	$-0.854369\pi$
$229$	−19.6799	+	7.16289i	−1.30048	+	0.473337i	−0.403329	+	0.915055i	$0.632147\pi$
$230$		0			0
$231$	13.0650	+	6.19833i	0.859612	+	0.407820i
$232$		0			0
$233$	12.4263	−	21.5230i	0.814074	−	1.41002i	−0.0959174	−	0.995389i	$-0.530578\pi$
$233$	12.4263	−	21.5230i	0.814074	−	1.41002i	0.909991	−	0.414628i	$-0.136088\pi$
$234$		0			0
$235$	−2.85495	−	4.94492i	−0.186237	−	0.322571i
$236$		0			0
$237$	−27.0568	−	2.54845i	−1.75753	−	0.165540i
$238$		0			0
$239$	−11.3987	−	9.56464i	−0.737320	−	0.618685i	0.194796	−	0.980844i	$-0.437595\pi$
$239$	−11.3987	−	9.56464i	−0.737320	−	0.618685i	−0.932117	+	0.362158i	$0.882040\pi$
$240$		0			0
$241$	3.15858	+	1.14963i	0.203462	+	0.0740542i	0.441741	−	0.897143i	$-0.354361\pi$
$241$	3.15858	+	1.14963i	0.203462	+	0.0740542i	−0.238279	+	0.971197i	$0.576583\pi$
$242$		0			0
$243$	4.53258	−	14.9149i	0.290765	−	0.956794i
$244$		0			0
$245$	−3.71847	−	1.35341i	−0.237564	−	0.0864663i
$246$		0			0
$247$	2.76071	+	2.31651i	0.175660	+	0.147396i
$248$		0			0
$249$	1.98004	+	0.186498i	0.125480	+	0.0118188i
$250$		0			0
$251$	−4.93370	−	8.54542i	−0.311412	−	0.539382i	0.667256	−	0.744828i	$-0.267469\pi$
$251$	−4.93370	−	8.54542i	−0.311412	−	0.539382i	−0.978668	+	0.205446i	$0.934135\pi$
$252$		0			0
$253$	9.56400	−	16.5653i	0.601283	−	1.04145i
$254$		0			0
$255$	−1.88991	−	0.896620i	−0.118351	−	0.0561485i
$256$		0			0
$257$	3.22778	−	1.17482i	0.201344	−	0.0732831i	−0.239380	−	0.970926i	$-0.576944\pi$
$257$	3.22778	−	1.17482i	0.201344	−	0.0732831i	0.440724	+	0.897643i	$0.354722\pi$
$258$		0			0
$259$	−1.18241	−	6.70579i	−0.0734714	−	0.416677i
$260$		0			0
$261$	0.235558	−	0.0383145i	0.0145807	−	0.00237161i
$262$		0			0
$263$	−12.4722	+	10.4654i	−0.769066	+	0.645323i	−0.940470	−	0.339878i	$-0.889614\pi$
$263$	−12.4722	+	10.4654i	−0.769066	+	0.645323i	0.171403	+	0.985201i	$0.445170\pi$
$264$		0			0
$265$	−1.63711	+	9.28452i	−0.100567	+	0.570343i
$266$		0			0
$267$	−22.1193	−	22.4153i	−1.35368	−	1.37179i
$268$		0			0
$269$	−16.8944			−1.03007			−0.515035	−	0.857169i	$-0.672221\pi$
$269$	−16.8944			−1.03007			−0.515035	+	0.857169i	$0.672221\pi$
$270$		0			0
$271$	2.50352			0.152078			0.0760389	−	0.997105i	$-0.475773\pi$
$271$	2.50352			0.152078			0.0760389	+	0.997105i	$0.475773\pi$
$272$		0			0
$273$	1.16494	−	4.23484i	0.0705054	−	0.256304i
$274$		0			0
$275$	−3.69772	+	20.9708i	−0.222981	+	1.26459i
$276$		0			0
$277$	16.6397	−	13.9624i	0.999785	−	0.838919i	0.0128303	−	0.999918i	$-0.495916\pi$
$277$	16.6397	−	13.9624i	0.999785	−	0.838919i	0.986955	+	0.160998i	$0.0514714\pi$
$278$		0			0
$279$	−15.7555	−	2.99455i	−0.943257	−	0.179279i
$280$		0			0
$281$	−1.76595	−	10.0152i	−0.105348	−	0.597456i	−0.991081	−	0.133261i	$-0.957455\pi$
$281$	−1.76595	−	10.0152i	−0.105348	−	0.597456i	0.885733	−	0.464194i	$-0.153656\pi$
$282$		0			0
$283$	−21.3886	+	7.78482i	−1.27142	+	0.462760i	−0.887586	−	0.460642i	$-0.847619\pi$
$283$	−21.3886	+	7.78482i	−1.27142	+	0.462760i	−0.383836	+	0.923401i	$0.625397\pi$
$284$		0			0
$285$	−3.02197	+	2.08621i	−0.179006	+	0.123577i
$286$		0			0
$287$	6.69156	−	11.5901i	0.394990	−	0.684143i
$288$		0			0
$289$	7.62582	+	13.2083i	0.448578	+	0.776959i
$290$		0			0
$291$	7.28002	+	15.8868i	0.426762	+	0.931303i
$292$		0			0
$293$	25.9472	+	21.7723i	1.51585	+	1.27195i	0.851265	+	0.524737i	$0.175836\pi$
$293$	25.9472	+	21.7723i	1.51585	+	1.27195i	0.664585	+	0.747213i	$0.268608\pi$
$294$		0			0
$295$	−5.14035	−	1.87093i	−0.299283	−	0.108930i
$296$		0			0
$297$	21.4499	+	15.6658i	1.24465	+	0.909020i
$298$		0			0
$299$	−5.45936	−	1.98705i	−0.315723	−	0.114914i
$300$		0			0
$301$	−9.32958	−	7.82844i	−0.537748	−	0.451224i
$302$		0			0
$303$	−12.9914	+	18.2936i	−0.746335	+	1.05094i
$304$		0			0
$305$	−1.00724	−	1.74459i	−0.0576744	−	0.0998950i
$306$		0			0
$307$	−3.49176	+	6.04791i	−0.199285	+	0.345173i	−0.948297	−	0.317384i	$-0.897195\pi$
$307$	−3.49176	+	6.04791i	−0.199285	+	0.345173i	0.749011	+	0.662557i	$0.230529\pi$
$308$		0			0
$309$	−1.08475	−	13.4258i	−0.0617093	−	0.763766i
$310$		0			0
$311$	8.44915	−	3.07524i	0.479107	−	0.174381i	−0.0911662	−	0.995836i	$-0.529059\pi$
$311$	8.44915	−	3.07524i	0.479107	−	0.174381i	0.570273	+	0.821455i	$0.306837\pi$
$312$		0			0
$313$	4.11285	+	23.3251i	0.232472	+	1.31841i	0.847873	+	0.530199i	$0.177883\pi$
$313$	4.11285	+	23.3251i	0.232472	+	1.31841i	−0.615401	+	0.788214i	$0.711006\pi$
$314$		0			0
$315$	3.84570	+	2.28900i	0.216681	+	0.128970i
$316$		0			0
$317$	−13.0106	+	10.9172i	−0.730749	+	0.613171i	−0.930336	−	0.366709i	$-0.880484\pi$
$317$	−13.0106	+	10.9172i	−0.730749	+	0.613171i	0.199587	+	0.979880i	$0.436040\pi$
$318$		0			0
$319$	−0.0706135	+	0.400469i	−0.00395360	+	0.0224220i
$320$		0			0
$321$	−14.5249	+	3.78867i	−0.810703	+	0.211463i
$322$		0			0
$323$	−3.06920			−0.170775
$324$		0			0
$325$	6.46771			0.358764
$326$		0			0
$327$	29.0380	−	7.57426i	1.60581	−	0.418858i
$328$		0			0
$329$	−1.77301	+	10.0552i	−0.0977490	+	0.554362i
$330$		0			0
$331$	15.7632	−	13.2269i	0.866423	−	0.727015i	−0.0969185	−	0.995292i	$-0.530899\pi$
$331$	15.7632	−	13.2269i	0.866423	−	0.727015i	0.963342	+	0.268277i	$0.0864542\pi$
$332$		0			0
$333$	0.166226	−	12.5061i	0.00910915	−	0.685330i
$334$		0			0
$335$	0.0117906	+	0.0668678i	0.000644189	+	0.00365338i
$336$		0			0
$337$	−9.92735	+	3.61326i	−0.540777	+	0.196827i	−0.597944	−	0.801538i	$-0.704016\pi$
$337$	−9.92735	+	3.61326i	−0.540777	+	0.196827i	0.0571669	+	0.998365i	$0.481793\pi$
$338$		0			0
$339$	−0.306242	−	3.79030i	−0.0166328	−	0.205861i
$340$		0			0
$341$	13.6634	−	23.6656i	0.739912	−	1.28157i
$342$		0			0
$343$	9.25447	+	16.0292i	0.499694	+	0.865496i
$344$		0			0
$345$	3.42761	−	4.82655i	0.184536	−	0.259853i
$346$		0			0
$347$	−13.9395	−	11.6966i	−0.748312	−	0.627908i	0.186744	−	0.982409i	$-0.440207\pi$
$347$	−13.9395	−	11.6966i	−0.748312	−	0.627908i	−0.935056	+	0.354500i	$0.884651\pi$
$348$		0			0
$349$	32.8524	+	11.9573i	1.75855	+	0.640060i	0.999934	−	0.0114776i	$-0.00365353\pi$
$349$	32.8524	+	11.9573i	1.75855	+	0.640060i	0.758616	+	0.651538i	$0.225876\pi$
$350$		0			0
$351$	3.55456	−	7.24222i	0.189728	−	0.386561i
$352$		0			0
$353$	3.45455	+	1.25735i	0.183867	+	0.0669222i	0.432313	−	0.901724i	$-0.357698\pi$
$353$	3.45455	+	1.25735i	0.183867	+	0.0669222i	−0.248446	+	0.968646i	$0.579920\pi$
$354$		0			0
$355$	−5.22758	−	4.38646i	−0.277451	−	0.232809i
$356$		0			0
$357$	1.55826	+	3.40052i	0.0824719	+	0.179974i
$358$		0			0
$359$	10.2575	+	17.7665i	0.541370	+	0.937680i	0.998826	+	0.0484479i	$0.0154275\pi$
$359$	10.2575	+	17.7665i	0.541370	+	0.937680i	−0.457456	+	0.889232i	$0.651239\pi$
$360$		0			0
$361$	6.80605	−	11.7884i	0.358213	−	0.620444i
$362$		0			0
$363$	−21.5662	+	14.8882i	−1.13193	+	0.781429i
$364$		0			0
$365$	6.58173	−	2.39555i	0.344503	−	0.125389i
$366$		0			0
$367$	5.80904	+	32.9447i	0.303229	+	1.71970i	0.631725	+	0.775193i	$0.282347\pi$
$367$	5.80904	+	32.9447i	0.303229	+	1.71970i	−0.328496	+	0.944505i	$0.606542\pi$
$368$		0			0
$369$	16.0500	−	18.6193i	0.835528	−	0.969284i
$370$		0			0
$371$	12.9144	−	10.8364i	0.670480	−	0.562600i
$372$		0			0
$373$	−2.34279	+	13.2866i	−0.121305	+	0.687954i	0.862129	+	0.506688i	$0.169130\pi$
$373$	−2.34279	+	13.2866i	−0.121305	+	0.687954i	−0.983434	+	0.181266i	$0.941981\pi$
$374$		0			0
$375$	−3.84595	+	13.9810i	−0.198604	+	0.721974i
$376$		0			0
$377$	0.123511			0.00636112
$378$		0			0
$379$	30.7527			1.57966			0.789830	−	0.613325i	$-0.210169\pi$
$379$	30.7527			1.57966			0.789830	+	0.613325i	$0.210169\pi$
$380$		0			0
$381$	−24.3979	−	24.7244i	−1.24994	−	1.26667i
$382$		0			0
$383$	5.78899	−	32.8310i	0.295804	−	1.67759i	−0.368115	−	0.929780i	$-0.619997\pi$
$383$	5.78899	−	32.8310i	0.295804	−	1.67759i	0.663918	−	0.747805i	$-0.268892\pi$
$384$		0			0
$385$	−5.84160	+	4.90168i	−0.297716	+	0.249813i
$386$		0			0
$387$	−14.1503	−	17.3262i	−0.719299	−	0.880739i
$388$		0			0
$389$	4.57033	+	25.9196i	0.231725	+	1.31418i	0.849402	+	0.527746i	$0.176963\pi$
$389$	4.57033	+	25.9196i	0.231725	+	1.31418i	−0.617677	+	0.786432i	$0.711926\pi$
$390$		0			0
$391$	4.64943	−	1.69225i	0.235132	−	0.0855810i
$392$		0			0
$393$	20.2529	+	9.60845i	1.02162	+	0.484682i
$394$		0			0
$395$	7.16558	−	12.4112i	0.360540	−	0.624473i
$396$		0			0
$397$	−5.56953	−	9.64672i	−0.279527	−	0.484155i	0.691740	−	0.722146i	$-0.256844\pi$
$397$	−5.56953	−	9.64672i	−0.279527	−	0.484155i	−0.971267	+	0.237992i	$0.923511\pi$
$398$		0			0
$399$	6.53750	+	0.615760i	0.327284	+	0.0308266i
$400$		0			0
$401$	−5.96288	−	5.00345i	−0.297772	−	0.249860i	0.481644	−	0.876367i	$-0.340040\pi$
$401$	−5.96288	−	5.00345i	−0.297772	−	0.249860i	−0.779416	+	0.626506i	$0.784484\pi$
$402$		0			0
$403$	−7.79938	−	2.83874i	−0.388515	−	0.141408i
$404$		0			0
$405$	6.15449	+	5.44945i	0.305819	+	0.270785i
$406$		0			0
$407$	20.0261	+	7.28889i	0.992655	+	0.361297i
$408$		0			0
$409$	1.53837	+	1.29084i	0.0760674	+	0.0638281i	0.680029	−	0.733186i	$-0.261967\pi$
$409$	1.53837	+	1.29084i	0.0760674	+	0.0638281i	−0.603961	+	0.797014i	$0.706412\pi$
$410$		0			0
$411$	−23.5584	−	2.21894i	−1.16205	−	0.109452i
$412$		0			0
$413$	4.89089	+	8.47127i	0.240665	+	0.416844i
$414$		0			0
$415$	−0.524383	+	0.908259i	−0.0257410	+	0.0445847i
$416$		0			0
$417$	−10.0608	−	4.77307i	−0.492679	−	0.233738i
$418$		0			0
$419$	−1.54093	+	0.560851i	−0.0752792	+	0.0273994i	−0.379385	−	0.925239i	$-0.623864\pi$
$419$	−1.54093	+	0.560851i	−0.0752792	+	0.0273994i	0.304106	+	0.952638i	$0.401642\pi$
$420$		0			0
$421$	2.80867	+	15.9288i	0.136886	+	0.776321i	0.973528	+	0.228570i	$0.0734049\pi$
$421$	2.80867	+	15.9288i	0.136886	+	0.776321i	−0.836641	+	0.547751i	$0.815484\pi$
$422$		0			0
$423$	−6.64802	+	17.5365i	−0.323238	+	0.852655i
$424$		0			0
$425$	−4.21951	+	3.54059i	−0.204676	+	0.171744i
$426$		0			0
$427$	−0.625524	+	3.54752i	−0.0302712	+	0.171677i
$428$		0			0
$429$	9.65536	+	9.78455i	0.466165	+	0.472402i
$430$		0			0
$431$	34.7870			1.67563			0.837816	−	0.545952i	$-0.183832\pi$
$431$	34.7870			1.67563			0.837816	+	0.545952i	$0.183832\pi$
$432$		0			0
$433$	28.2579			1.35799			0.678994	−	0.734144i	$-0.262416\pi$
$433$	28.2579			1.35799			0.678994	+	0.734144i	$0.262416\pi$
$434$		0			0
$435$	−0.0333797	+	0.121343i	−0.00160043	+	0.00581797i
$436$		0			0
$437$	1.50827	−	8.55382i	0.0721503	−	0.409185i
$438$		0			0
$439$	11.0220	−	9.24858i	0.526053	−	0.441411i	−0.340683	−	0.940178i	$-0.610658\pi$
$439$	11.0220	−	9.24858i	0.526053	−	0.441411i	0.866736	+	0.498768i	$0.166214\pi$
$440$		0			0
$441$	4.28260	+	12.2714i	0.203934	+	0.584353i
$442$		0			0
$443$	−1.80438	−	10.2331i	−0.0857285	−	0.486191i	−0.997197	−	0.0748208i	$-0.976162\pi$
$443$	−1.80438	−	10.2331i	−0.0857285	−	0.486191i	0.911468	−	0.411370i	$-0.134950\pi$
$444$		0			0
$445$	15.6050	−	5.67977i	0.739750	−	0.269247i
$446$		0			0
$447$	3.82720	−	2.64211i	0.181020	−	0.124967i
$448$		0			0
$449$	11.5067	−	19.9301i	0.543033	−	0.940560i	−0.455695	−	0.890136i	$-0.650609\pi$
$449$	11.5067	−	19.9301i	0.543033	−	0.940560i	0.998728	−	0.0504241i	$-0.0160573\pi$
$450$		0			0
$451$	20.9430	+	36.2743i	0.986167	+	1.70809i
$452$		0			0
$453$	15.0278	+	32.7945i	0.706068	+	1.54082i
$454$		0			0
$455$	1.77427	+	1.48879i	0.0831789	+	0.0697954i
$456$		0			0
$457$	−1.42490	−	0.518622i	−0.0666541	−	0.0242601i	0.308478	−	0.951231i	$-0.400180\pi$
$457$	−1.42490	−	0.518622i	−0.0666541	−	0.0242601i	−0.375132	+	0.926971i	$0.622403\pi$
$458$		0			0
$459$	1.64560	+	6.67066i	0.0768100	+	0.311360i
$460$		0			0
$461$	7.20103	+	2.62096i	0.335385	+	0.122070i	0.504223	−	0.863574i	$-0.331779\pi$
$461$	7.20103	+	2.62096i	0.335385	+	0.122070i	−0.168837	+	0.985644i	$0.554001\pi$
$462$		0			0
$463$	25.2827	+	21.2147i	1.17499	+	0.985931i	0.999999	+	0.00136057i	$0.000433082\pi$
$463$	25.2827	+	21.2147i	1.17499	+	0.985931i	0.174988	+	0.984571i	$0.444011\pi$
$464$		0			0
$465$	4.89677	−	6.89533i	0.227082	−	0.319763i
$466$		0			0
$467$	−15.9624	−	27.6477i	−0.738653	−	1.27938i	−0.953102	−	0.302649i	$-0.902129\pi$
$467$	−15.9624	−	27.6477i	−0.738653	−	1.27938i	0.214449	−	0.976735i	$-0.431204\pi$
$468$		0			0
$469$	0.0607081	−	0.105149i	0.00280324	−	0.00485535i
$470$		0			0
$471$	−1.07754	−	13.3366i	−0.0496507	−	0.614517i
$472$		0			0
$473$	35.8183	−	13.0368i	1.64693	−	0.599433i
$474$		0			0
$475$	1.67909	+	9.52257i	0.0770418	+	0.436926i
$476$		0			0
$477$	27.0205	−	15.1251i	1.23718	−	0.692530i
$478$		0			0
$479$	−8.68278	+	7.28571i	−0.396726	+	0.332893i	−0.819227	−	0.573470i	$-0.805597\pi$
$479$	−8.68278	+	7.28571i	−0.396726	+	0.332893i	0.422500	+	0.906363i	$0.361152\pi$
$480$		0			0
$481$	1.12400	−	6.37453i	0.0512500	−	0.290653i
$482$		0			0
$483$	−10.2430	+	2.67177i	−0.466071	+	0.121570i
$484$		0			0
$485$	−9.21542			−0.418451
$486$		0			0
$487$	−31.9729			−1.44883			−0.724415	−	0.689365i	$-0.757890\pi$
$487$	−31.9729			−1.44883			−0.724415	+	0.689365i	$0.757890\pi$
$488$		0			0
$489$	−7.01263	+	1.82917i	−0.317122	+	0.0827179i
$490$		0			0
$491$	2.40328	−	13.6297i	0.108458	−	0.615098i	−0.881324	−	0.472512i	$-0.843347\pi$
$491$	2.40328	−	13.6297i	0.108458	−	0.615098i	0.989782	−	0.142586i	$-0.0455416\pi$
$492$		0			0
$493$	−0.0805779	+	0.0676129i	−0.00362905	+	0.00304513i
$494$		0			0
$495$	−12.2223	+	6.84158i	−0.549351	+	0.307506i
$496$		0			0
$497$	2.11899	+	12.0174i	0.0950495	+	0.539053i
$498$		0			0
$499$	−7.12831	+	2.59449i	−0.319107	+	0.116145i	−0.496607	−	0.867975i	$-0.665421\pi$
$499$	−7.12831	+	2.59449i	−0.319107	+	0.116145i	0.177500	+	0.984121i	$0.443199\pi$
$500$		0			0
$501$	1.50479	+	18.6245i	0.0672290	+	0.832082i
$502$		0			0
$503$	8.50373	−	14.7289i	0.379162	−	0.656728i	−0.611778	−	0.791029i	$-0.709546\pi$
$503$	8.50373	−	14.7289i	0.379162	−	0.656728i	0.990941	+	0.134301i	$0.0428789\pi$
$504$		0			0
$505$	−5.91600	−	10.2468i	−0.263259	−	0.455977i
$506$		0			0
$507$	−10.6198	+	14.9542i	−0.471644	+	0.664140i
$508$		0			0
$509$	18.9563	+	15.9063i	0.840225	+	0.705033i	0.957614	−	0.288053i	$-0.0930080\pi$
$509$	18.9563	+	15.9063i	0.840225	+	0.705033i	−0.117389	+	0.993086i	$0.537452\pi$
$510$		0			0
$511$	−11.7693	−	4.28368i	−0.520644	−	0.189499i
$512$		0			0
$513$	11.5857	+	3.35330i	0.511521	+	0.148052i
$514$		0			0
$515$	6.67461	+	2.42936i	0.294118	+	0.107050i
$516$		0			0
$517$	−24.4797	−	20.5409i	−1.07661	−	0.903387i
$518$		0			0
$519$	10.4033	+	22.7025i	0.456652	+	0.996531i
$520$		0			0
$521$	−4.92213	−	8.52538i	−0.215643	−	0.373504i	0.737829	−	0.674988i	$-0.235851\pi$
$521$	−4.92213	−	8.52538i	−0.215643	−	0.373504i	−0.953471	+	0.301484i	$0.902518\pi$
$522$		0			0
$523$	−5.49604	+	9.51943i	−0.240325	+	0.416256i	−0.960807	−	0.277218i	$-0.910587\pi$
$523$	−5.49604	+	9.51943i	−0.240325	+	0.416256i	0.720482	+	0.693474i	$0.243921\pi$
$524$		0			0
$525$	9.69804	−	6.69504i	0.423257	−	0.292196i
$526$		0			0
$527$	6.64229	−	2.41760i	0.289343	−	0.105312i
$528$		0			0
$529$	−1.56244	−	8.86106i	−0.0679323	−	0.385263i
$530$		0			0
$531$	5.92021	+	16.9638i	0.256915	+	0.736167i
$532$		0			0
$533$	9.74562	−	8.17755i	0.422130	−	0.354209i
$534$		0			0
$535$	1.37456	−	7.79554i	0.0594276	−	0.337031i
$536$		0			0
$537$	−4.90604	+	17.8347i	−0.211711	+	0.769623i
$538$		0			0
$539$	−22.1463			−0.953907
$540$		0			0
$541$	6.17773			0.265601			0.132801	−	0.991143i	$-0.457603\pi$
$541$	6.17773			0.265601			0.132801	+	0.991143i	$0.457603\pi$
$542$		0			0
$543$	−27.9514	−	28.3254i	−1.19951	−	1.21556i
$544$		0			0
$545$	−2.74801	+	15.5847i	−0.117712	+	0.667577i
$546$		0			0
$547$	26.0849	−	21.8878i	1.11531	−	0.935857i	0.116952	−	0.993138i	$-0.462687\pi$
$547$	26.0849	−	21.8878i	1.11531	−	0.935857i	0.998358	+	0.0572808i	$0.0182430\pi$
$548$		0			0
$549$	−2.34545	+	6.18696i	−0.100101	+	0.264053i
$550$		0			0
$551$	0.0320647	+	0.181848i	0.00136600	+	0.00774698i
$552$		0			0
$553$	−24.0812	+	8.76484i	−1.02404	+	0.372719i
$554$		0			0
$555$	5.95890	+	2.82704i	0.252941	+	0.120001i
$556$		0			0
$557$	6.11418	−	10.5901i	0.259066	−	0.448716i	−0.706926	−	0.707288i	$-0.749919\pi$
$557$	6.11418	−	10.5901i	0.259066	−	0.448716i	0.965992	+	0.258572i	$0.0832519\pi$
$558$		0			0
$559$	−5.78864	−	10.0262i	−0.244833	−	0.424064i
$560$		0			0
$561$	−11.6554	−	1.09781i	−0.492093	−	0.0463497i
$562$		0			0
$563$	18.5963	+	15.6042i	0.783742	+	0.657637i	0.944188	−	0.329407i	$-0.106849\pi$
$563$	18.5963	+	15.6042i	0.783742	+	0.657637i	−0.160446	+	0.987045i	$0.551293\pi$
$564$		0			0
$565$	1.88434	+	0.685845i	0.0792750	+	0.0288537i
$566$		0			0
$567$	−2.16688	−	14.5389i	−0.0910004	−	0.610576i
$568$		0			0
$569$	−11.5281	−	4.19590i	−0.483284	−	0.175901i	0.0888763	−	0.996043i	$-0.471672\pi$
$569$	−11.5281	−	4.19590i	−0.483284	−	0.175901i	−0.572161	+	0.820142i	$0.693895\pi$
$570$		0			0
$571$	8.91500	+	7.48058i	0.373081	+	0.313052i	0.809979	−	0.586459i	$-0.199478\pi$
$571$	8.91500	+	7.48058i	0.373081	+	0.313052i	−0.436898	+	0.899511i	$0.643923\pi$
$572$		0			0
$573$	−8.38191	−	0.789483i	−0.350159	−	0.0329811i
$574$		0			0
$575$	−7.79403	−	13.4997i	−0.325033	−	0.562974i
$576$		0			0
$577$	18.3725	−	31.8220i	0.764856	−	1.32477i	−0.175467	−	0.984485i	$-0.556144\pi$
$577$	18.3725	−	31.8220i	0.764856	−	1.32477i	0.940323	−	0.340283i	$-0.110523\pi$
$578$		0			0
$579$	−30.7906	−	14.6078i	−1.27961	−	0.607079i
$580$		0			0
$581$	1.76228	−	0.641419i	0.0731118	−	0.0266105i
$582$		0			0
$583$	9.16222	+	51.9615i	0.379460	+	2.15203i
$584$		0			0
$585$	2.69105	+	3.29503i	0.111261	+	0.136233i
$586$		0			0
$587$	31.8718	−	26.7436i	1.31549	−	1.10383i	0.328249	−	0.944591i	$-0.393542\pi$
$587$	31.8718	−	26.7436i	1.31549	−	1.10383i	0.987241	−	0.159236i	$-0.0509029\pi$
$588$		0			0
$589$	2.15475	−	12.2202i	0.0887849	−	0.503524i
$590$		0			0
$591$	−21.5670	−	21.8555i	−0.887146	−	0.899016i
$592$		0			0
$593$	−18.6260			−0.764877			−0.382438	−	0.923981i	$-0.624916\pi$
$593$	−18.6260			−0.764877			−0.382438	+	0.923981i	$0.624916\pi$
$594$		0			0
$595$	−1.97253			−0.0808656
$596$		0			0
$597$	2.55890	−	9.30223i	0.104729	−	0.380715i
$598$		0			0
$599$	6.05175	−	34.3212i	0.247268	−	1.40232i	−0.567899	−	0.823098i	$-0.692244\pi$
$599$	6.05175	−	34.3212i	0.247268	−	1.40232i	0.815167	−	0.579227i	$-0.196645\pi$
$600$		0			0
$601$	4.05833	−	3.40534i	0.165543	−	0.138907i	−0.556253	−	0.831013i	$-0.687761\pi$
$601$	4.05833	−	3.40534i	0.165543	−	0.138907i	0.721796	+	0.692106i	$0.243317\pi$
$602$		0			0
$603$	0.145611	−	0.168921i	0.00592972	−	0.00687899i
$604$		0			0
$605$	−2.39972	−	13.6095i	−0.0975624	−	0.553304i
$606$		0			0
$607$	42.8968	−	15.6132i	1.74113	−	0.633719i	0.741809	−	0.670611i	$-0.233968\pi$
$607$	42.8968	−	15.6132i	1.74113	−	0.633719i	0.999319	+	0.0368918i	$0.0117457\pi$
$608$		0			0
$609$	0.185199	−	0.127852i	0.00750463	−	0.00518082i
$610$		0			0
$611$	−4.85298	+	8.40561i	−0.196330	+	0.340054i
$612$		0			0
$613$	14.3555	+	24.8644i	0.579812	+	1.00426i	0.995500	+	0.0947573i	$0.0302075\pi$
$613$	14.3555	+	24.8644i	0.579812	+	1.00426i	−0.415688	+	0.909507i	$0.636459\pi$
$614$		0			0
$615$	5.40023	+	11.7847i	0.217758	+	0.475203i
$616$		0			0
$617$	−8.30054	−	6.96498i	−0.334167	−	0.280399i	0.460228	−	0.887801i	$-0.347768\pi$
$617$	−8.30054	−	6.96498i	−0.334167	−	0.280399i	−0.794395	+	0.607401i	$0.792212\pi$
$618$		0			0
$619$	−45.1107	−	16.4189i	−1.81315	−	0.659933i	−0.996575	−	0.0826968i	$-0.973647\pi$
$619$	−45.1107	−	16.4189i	−1.81315	−	0.659933i	−0.816577	−	0.577236i	$-0.804131\pi$
$620$		0			0
$621$	−19.3997	+	1.30816i	−0.778484	+	0.0524948i
$622$		0			0
$623$	−27.9046	−	10.1564i	−1.11797	−	0.406910i
$624$		0			0
$625$	10.0982	+	8.47337i	0.403927	+	0.338935i
$626$		0			0
$627$	−11.8994	+	16.7560i	−0.475216	+	0.669170i
$628$		0			0
$629$	2.75629	+	4.77403i	0.109900	+	0.190353i
$630$		0			0
$631$	1.97244	−	3.41636i	0.0785214	−	0.136003i	−0.824091	−	0.566458i	$-0.808313\pi$
$631$	1.97244	−	3.41636i	0.0785214	−	0.136003i	0.902612	+	0.430455i	$0.141647\pi$
$632$		0			0
$633$	0.657251	+	8.13468i	0.0261234	+	0.323325i
$634$		0			0
$635$	17.2126	−	6.26488i	0.683062	−	0.248614i
$636$		0			0
$637$	1.16804	+	6.62428i	0.0462794	+	0.262464i
$638$		0			0
$639$	−0.297893	+	22.4121i	−0.0117844	+	0.886607i
$640$		0			0
$641$	−30.9739	+	25.9902i	−1.22339	+	1.02655i	−0.224754	+	0.974416i	$0.572158\pi$
$641$	−30.9739	+	25.9902i	−1.22339	+	1.02655i	−0.998640	+	0.0521339i	$0.983398\pi$
$642$		0			0
$643$	−3.48821	+	19.7826i	−0.137561	+	0.780150i	0.835480	+	0.549520i	$0.185190\pi$
$643$	−3.48821	+	19.7826i	−0.137561	+	0.780150i	−0.973042	+	0.230629i	$0.925922\pi$
$644$		0			0
$645$	11.4147	−	2.97740i	0.449453	−	0.117235i
$646$		0			0
$647$	−24.0065			−0.943794			−0.471897	−	0.881654i	$-0.656431\pi$
$647$	−24.0065			−0.943794			−0.471897	+	0.881654i	$0.656431\pi$
$648$		0			0
$649$	−30.6147			−1.20173
$650$		0			0
$651$	−14.6333	+	3.81695i	−0.573526	+	0.149598i
$652$		0			0
$653$	−1.65099	+	9.36326i	−0.0646084	+	0.366412i	0.935312	+	0.353823i	$0.115119\pi$
$653$	−1.65099	+	9.36326i	−0.0646084	+	0.366412i	−0.999921	+	0.0125893i	$0.995993\pi$
$654$		0			0
$655$	−9.05546	+	7.59844i	−0.353826	+	0.296895i
$656$		0			0
$657$	−19.7685	−	11.7664i	−0.771243	−	0.459051i
$658$		0			0
$659$	−4.02748	−	22.8410i	−0.156888	−	0.889758i	−0.957039	−	0.289959i	$-0.906358\pi$
$659$	−4.02748	−	22.8410i	−0.156888	−	0.889758i	0.800151	−	0.599799i	$-0.204753\pi$
$660$		0			0
$661$	−18.4498	+	6.71518i	−0.717614	+	0.261190i	−0.674912	−	0.737898i	$-0.735819\pi$
$661$	−18.4498	+	6.71518i	−0.717614	+	0.261190i	−0.0427014	+	0.999088i	$0.513596\pi$
$662$		0			0
$663$	0.286359	+	3.54422i	0.0111213	+	0.137646i
$664$		0			0
$665$	−1.73136	+	2.99880i	−0.0671392	+	0.116289i
$666$		0			0
$667$	−0.148839	−	0.257796i	−0.00576306	−	0.00998190i
$668$		0			0
$669$	12.3700	−	17.4187i	0.478252	−	0.673444i
$670$		0			0
$671$	−8.63653	−	7.24691i	−0.333410	−	0.279764i
$672$		0			0
$673$	37.7532	+	13.7410i	1.45528	+	0.529678i	0.944060	−	0.329773i	$-0.106972\pi$
$673$	37.7532	+	13.7410i	1.45528	+	0.529678i	0.511218	+	0.859451i	$0.329194\pi$
$674$		0			0
$675$	19.7963	−	8.75504i	0.761959	−	0.336982i
$676$		0			0
$677$	−22.7982	−	8.29787i	−0.876206	−	0.318913i	−0.135529	−	0.990773i	$-0.543273\pi$
$677$	−22.7982	−	8.29787i	−0.876206	−	0.318913i	−0.740678	+	0.671860i	$0.765495\pi$
$678$		0			0
$679$	12.6235	+	10.5924i	0.484446	+	0.406498i
$680$		0			0
$681$	−2.58042	−	5.63112i	−0.0988818	−	0.215785i
$682$		0			0
$683$	5.13229	+	8.88938i	0.196382	+	0.340143i	0.947353	−	0.320192i	$-0.103748\pi$
$683$	5.13229	+	8.88938i	0.196382	+	0.340143i	−0.750971	+	0.660335i	$0.770414\pi$
$684$		0			0
$685$	6.23909	−	10.8064i	0.238383	−	0.412892i
$686$		0			0
$687$	−29.8517	+	20.6081i	−1.13891	+	0.786247i
$688$		0			0
$689$	15.0592	−	5.48112i	0.573711	−	0.208814i
$690$		0			0
$691$	8.11802	+	46.0396i	0.308824	+	1.75143i	0.604936	+	0.796274i	$0.293199\pi$
$691$	8.11802	+	46.0396i	0.308824	+	1.75143i	−0.296112	+	0.955153i	$0.595690\pi$
$692$		0			0
$693$	24.6062	+	4.67676i	0.934713	+	0.177655i
$694$		0			0
$695$	4.49837	−	3.77458i	0.170633	−	0.143178i
$696$		0			0
$697$	−1.88141	+	10.6700i	−0.0712635	+	0.404156i
$698$		0			0
$699$	11.4172	−	41.5042i	0.431837	−	1.56983i
$700$		0			0
$701$	−10.7090			−0.404475			−0.202237	−	0.979337i	$-0.564821\pi$
$701$	−10.7090			−0.404475			−0.202237	+	0.979337i	$0.564821\pi$
$702$		0			0
$703$	9.67718			0.364982
$704$		0			0
$705$	−6.94655	−	7.03950i	−0.261622	−	0.265123i
$706$		0			0
$707$	−3.67400	+	20.8363i	−0.138175	+	0.783630i
$708$		0			0
$709$	−39.4897	+	33.1358i	−1.48307	+	1.24444i	−0.580230	+	0.814453i	$0.697037\pi$
$709$	−39.4897	+	33.1358i	−1.48307	+	1.24444i	−0.902835	+	0.429987i	$0.858518\pi$
$710$		0			0
$711$	−46.4606	+	7.55700i	−1.74241	+	0.283410i
$712$		0			0
$713$	3.47365	+	19.7000i	0.130089	+	0.737772i
$714$		0			0
$715$	−6.81180	+	2.47929i	−0.254747	+	0.0927203i
$716$		0			0
$717$	−23.2852	−	11.0470i	−0.869602	−	0.412560i
$718$		0			0
$719$	−7.78782	+	13.4889i	−0.290437	+	0.503051i	−0.973913	−	0.226922i	$-0.927134\pi$
$719$	−7.78782	+	13.4889i	−0.290437	+	0.503051i	0.683476	+	0.729973i	$0.260467\pi$
$720$		0			0
$721$	−6.35069	−	10.9997i	−0.236512	−	0.409651i
$722$		0			0
$723$	5.79628	+	0.545945i	0.215566	+	0.0203039i
$724$		0			0
$725$	0.253860	+	0.213014i	0.00942812	+	0.00791113i
$726$		0			0
$727$	9.61987	+	3.50135i	0.356781	+	0.129858i	0.514191	−	0.857676i	$-0.328092\pi$
$727$	9.61987	+	3.50135i	0.356781	+	0.129858i	−0.157410	+	0.987533i	$0.550314\pi$
$728$		0			0
$729$	1.07627	−	26.9785i	0.0398620	−	0.999205i
$730$		0			0
$731$	9.26510	+	3.37222i	0.342682	+	0.124726i
$732$		0			0
$733$	28.4760	+	23.8942i	1.05179	+	0.882553i	0.993280	−	0.115734i	$-0.0369221\pi$
$733$	28.4760	+	23.8942i	1.05179	+	0.882553i	0.0585052	+	0.998287i	$0.481367\pi$
$734$		0			0
$735$	−6.82371	−	0.642718i	−0.251697	−	0.0237070i
$736$		0			0
$737$	0.190002	+	0.329093i	0.00699881	+	0.0121223i
$738$		0			0
$739$	4.39183	−	7.60687i	0.161556	−	0.279823i	−0.773871	−	0.633343i	$-0.781682\pi$
$739$	4.39183	−	7.60687i	0.161556	−	0.279823i	0.935427	+	0.353520i	$0.115015\pi$
$740$		0			0
$741$	5.63957	+	2.67554i	0.207175	+	0.0982885i
$742$		0			0
$743$	11.7938	−	4.29260i	0.432673	−	0.157480i	−0.116496	−	0.993191i	$-0.537166\pi$
$743$	11.7938	−	4.29260i	0.432673	−	0.157480i	0.549170	+	0.835711i	$0.314944\pi$
$744$		0			0
$745$	0.425861	+	2.41518i	0.0156023	+	0.0884853i
$746$		0			0
$747$	3.40002	−	0.553028i	0.124400	−	0.0202342i
$748$		0			0
$749$	−10.8433	+	9.09858i	−0.396204	+	0.332455i
$750$		0			0
$751$	−0.723810	+	4.10493i	−0.0264122	+	0.149791i	−0.995162	−	0.0982497i	$-0.968676\pi$
$751$	−0.723810	+	4.10493i	−0.0264122	+	0.149791i	0.968750	+	0.248041i	$0.0797867\pi$
$752$		0			0
$753$	−12.0045	−	12.1651i	−0.437467	−	0.443321i
$754$		0			0
$755$	−19.0230			−0.692316
$756$		0			0
$757$	−22.7574			−0.827131			−0.413566	−	0.910474i	$-0.635717\pi$
$757$	−22.7574			−0.827131			−0.413566	+	0.910474i	$0.635717\pi$
$758$		0			0
$759$	8.78732	−	31.9441i	0.318959	−	1.15950i
$760$		0			0
$761$	−0.391625	+	2.22102i	−0.0141964	+	0.0805118i	−0.991083	−	0.133247i	$-0.957460\pi$
$761$	−0.391625	+	2.22102i	−0.0141964	+	0.0805118i	0.976886	+	0.213759i	$0.0685707\pi$
$762$		0			0
$763$	21.6777	−	18.1897i	0.784785	−	0.658513i
$764$		0			0
$765$	−3.55942	−	0.676517i	−0.128691	−	0.0244595i
$766$		0			0
$767$	1.61468	+	9.15731i	0.0583027	+	0.330651i
$768$		0			0
$769$	18.2524	−	6.64334i	0.658200	−	0.239565i	0.00874088	−	0.999962i	$-0.497218\pi$
$769$	18.2524	−	6.64334i	0.658200	−	0.239565i	0.649459	+	0.760397i	$0.274995\pi$
$770$		0			0
$771$	4.89610	−	3.38002i	0.176329	−	0.121729i
$772$		0			0
$773$	0.866208	−	1.50032i	0.0311553	−	0.0539626i	−0.850027	−	0.526739i	$-0.823415\pi$
$773$	0.866208	−	1.50032i	0.0311553	−	0.0539626i	0.881183	+	0.472776i	$0.156748\pi$
$774$		0			0
$775$	−11.1347	−	19.2859i	−0.399972	−	0.692771i
$776$		0			0
$777$	−4.91319	−	10.7218i	−0.176260	−	0.384643i
$778$		0			0
$779$	14.5701	+	12.2257i	0.522027	+	0.438033i
$780$		0			0
$781$	−35.8885	−	13.0623i	−1.28419	−	0.467407i
$782$		0			0
$783$	0.378040	−	0.167191i	0.0135100	−	0.00597491i
$784$		0			0
$785$	6.63027	+	2.41322i	0.236644	+	0.0861315i
$786$		0			0
$787$	−7.34653	−	6.16447i	−0.261875	−	0.219740i	0.502390	−	0.864641i	$-0.332454\pi$
$787$	−7.34653	−	6.16447i	−0.261875	−	0.219740i	−0.764266	+	0.644901i	$0.776898\pi$
$788$		0			0
$789$	−16.3280	+	22.9920i	−0.581291	+	0.818539i
$790$		0			0
$791$	−1.79290	−	3.10539i	−0.0637481	−	0.110415i
$792$		0			0
$793$	−1.71215	+	2.96553i	−0.0608003	+	0.105309i
$794$		0			0
$795$	1.31506	+	16.2763i	0.0466405	+	0.577261i
$796$		0			0
$797$	−49.4162	+	17.9860i	−1.75041	+	0.637097i	−0.999722	−	0.0235589i	$-0.992500\pi$
$797$	−49.4162	+	17.9860i	−1.75041	+	0.637097i	−0.750688	+	0.660656i	$0.770278\pi$
$798$		0			0
$799$	−1.43538	−	8.14043i	−0.0507800	−	0.287988i
$800$		0			0
$801$	−46.8704	−	27.8977i	−1.65609	−	0.985718i
$802$		0			0
$803$	30.0283	−	25.1967i	1.05968	−	0.889173i
$804$		0			0
$805$	0.969341	−	5.49740i	0.0341648	−	0.193758i
$806$		0			0
$807$	−28.3146	+	7.38556i	−0.996721	+	0.259984i
$808$		0			0
$809$	10.1781			0.357842			0.178921	−	0.983863i	$-0.442739\pi$
$809$	10.1781			0.357842			0.178921	+	0.983863i	$0.442739\pi$
$810$		0			0
$811$	49.5069			1.73842			0.869211	−	0.494441i	$-0.164627\pi$
$811$	49.5069			1.73842			0.869211	+	0.494441i	$0.164627\pi$
$812$		0			0
$813$	4.19583	−	1.09444i	0.147154	−	0.0383836i
$814$		0			0
$815$	0.663639	−	3.76368i	0.0232463	−	0.131836i
$816$		0			0
$817$	13.2591	−	11.1257i	0.463875	−	0.389238i
$818$		0			0
$819$	0.101106	−	7.60676i	0.00353293	−	0.265802i
$820$		0			0
$821$	−8.44421	−	47.8895i	−0.294705	−	1.67136i	−0.668399	−	0.743803i	$-0.733020\pi$
$821$	−8.44421	−	47.8895i	−0.294705	−	1.67136i	0.373694	−	0.927552i	$-0.378091\pi$
$822$		0			0
$823$	20.9283	−	7.61729i	0.729516	−	0.265522i	0.0495559	−	0.998771i	$-0.484219\pi$
$823$	20.9283	−	7.61729i	0.729516	−	0.265522i	0.679960	+	0.733249i	$0.261997\pi$
$824$		0			0
$825$	2.97031	+	36.7630i	0.103413	+	1.27992i
$826$		0			0
$827$	6.93673	−	12.0148i	0.241214	−	0.417795i	−0.719847	−	0.694133i	$-0.755788\pi$
$827$	6.93673	−	12.0148i	0.241214	−	0.417795i	0.961060	+	0.276339i	$0.0891212\pi$
$828$		0			0
$829$	0.222661	+	0.385659i	0.00773332	+	0.0133945i	0.869866	−	0.493288i	$-0.164205\pi$
$829$	0.222661	+	0.385659i	0.00773332	+	0.0133945i	−0.862133	+	0.506682i	$0.830872\pi$
$830$		0			0
$831$	21.7840	−	30.6749i	0.755678	−	1.06410i
$832$		0			0
$833$	−4.38833	−	3.68225i	−0.152047	−	0.127582i
$834$		0			0
$835$	−9.25915	−	3.37005i	−0.320426	−	0.116626i
$836$		0			0
$837$	−27.7149	+	1.86888i	−0.957968	+	0.0645978i
$838$		0			0
$839$	−14.3991	−	5.24083i	−0.497111	−	0.180934i	0.0812832	−	0.996691i	$-0.474098\pi$
$839$	−14.3991	−	5.24083i	−0.497111	−	0.180934i	−0.578394	+	0.815757i	$0.696320\pi$
$840$		0			0
$841$	−22.2104	−	18.6368i	−0.765877	−	0.642647i
$842$		0			0
$843$	−7.33792	−	16.0132i	−0.252731	−	0.551523i
$844$		0			0
$845$	−4.83606	−	8.37630i	−0.166366	−	0.288154i
$846$		0			0
$847$	−12.3558	+	21.4009i	−0.424551	+	0.735343i
$848$		0			0
$849$	−32.4436	+	22.3974i	−1.11346	+	0.768677i
$850$		0			0
$851$	−14.6597	+	5.33568i	−0.502526	+	0.182905i
$852$		0			0
$853$	−3.21377	−	18.2262i	−0.110037	−	0.624052i	−0.989088	−	0.147324i	$-0.952934\pi$
$853$	−3.21377	−	18.2262i	−0.110037	−	0.624052i	0.879051	−	0.476728i	$-0.158177\pi$
$854$		0			0
$855$	−4.15273	+	4.81752i	−0.142020	+	0.164756i
$856$		0			0
$857$	28.1960	−	23.6592i	0.963156	−	0.808184i	−0.0183076	−	0.999832i	$-0.505828\pi$
$857$	28.1960	−	23.6592i	0.963156	−	0.808184i	0.981464	+	0.191648i	$0.0613834\pi$
$858$		0			0
$859$	−3.38976	+	19.2243i	−0.115657	+	0.655924i	0.870766	+	0.491698i	$0.163624\pi$
$859$	−3.38976	+	19.2243i	−0.115657	+	0.655924i	−0.986423	+	0.164226i	$0.947487\pi$
$860$		0			0
$861$	6.14815	−	22.3500i	0.209528	−	0.761687i
$862$		0			0
$863$	44.0808			1.50053			0.750263	−	0.661139i	$-0.229927\pi$
$863$	44.0808			1.50053			0.750263	+	0.661139i	$0.229927\pi$
$864$		0			0
$865$	−13.1690			−0.447759
$866$		0			0
$867$	18.5548	+	18.8031i	0.630155	+	0.638586i
$868$		0			0
$869$	13.9275	−	78.9870i	0.472459	−	2.67945i
$870$		0			0
$871$	0.0884155	−	0.0741894i	0.00299585	−	0.00251381i
$872$		0			0
$873$	19.1462	+	23.4434i	0.648001	+	0.793439i
$874$		0			0
$875$	2.37435	+	13.4656i	0.0802678	+	0.455221i
$876$		0			0
$877$	−23.5133	+	8.55813i	−0.793987	+	0.288987i	−0.706992	−	0.707221i	$-0.749948\pi$
$877$	−23.5133	+	8.55813i	−0.793987	+	0.288987i	−0.0869944	+	0.996209i	$0.527726\pi$
$878$		0			0
$879$	53.0048	+	25.1467i	1.78781	+	0.848177i
$880$		0			0
$881$	−22.3706	+	38.7470i	−0.753684	+	1.30542i	0.192343	+	0.981328i	$0.438392\pi$
$881$	−22.3706	+	38.7470i	−0.753684	+	1.30542i	−0.946026	+	0.324090i	$0.894942\pi$
$882$		0			0
$883$	19.1927	+	33.2427i	0.645885	+	1.11871i	0.984096	+	0.177636i	$0.0568449\pi$
$883$	19.1927	+	33.2427i	0.645885	+	1.11871i	−0.338211	+	0.941070i	$0.609822\pi$
$884$		0			0
$885$	−9.43300	−	0.888484i	−0.317087	−	0.0298661i
$886$		0			0
$887$	−6.35934	−	5.33612i	−0.213526	−	0.179169i	0.529751	−	0.848153i	$-0.322285\pi$
$887$	−6.35934	−	5.33612i	−0.213526	−	0.179169i	−0.743277	+	0.668984i	$0.766730\pi$
$888$		0			0
$889$	−30.7792	−	11.2027i	−1.03230	−	0.375727i
$890$		0			0
$891$	42.7979	+	16.8784i	1.43378	+	0.565448i
$892$		0			0
$893$	−13.6357	−	4.96298i	−0.456300	−	0.166080i
$894$		0			0
$895$	−7.47217	−	6.26989i	−0.249767	−	0.209579i
$896$		0			0
$897$	−10.0184	−	0.943624i	−0.334505	−	0.0315067i
$898$		0			0
$899$	−0.212635	−	0.368294i	−0.00709176	−	0.0122833i
$900$		0			0
$901$	−6.82409	+	11.8197i	−0.227344	+	0.393771i
$902$		0			0
$903$	−19.0584	−	9.04176i	−0.634224	−	0.300891i
$904$		0			0
$905$	19.7196	−	7.17734i	0.655501	−	0.238583i
$906$		0			0
$907$	5.55783	+	31.5200i	0.184545	+	1.04661i	0.926539	+	0.376199i	$0.122769\pi$
$907$	5.55783	+	31.5200i	0.184545	+	1.04661i	−0.741994	+	0.670407i	$0.766120\pi$
$908$		0			0
$909$	−13.7760	+	36.3390i	−0.456920	+	1.20529i
$910$		0			0
$911$	−38.8843	+	32.6278i	−1.28829	+	1.08101i	−0.296250	+	0.955111i	$0.595736\pi$
$911$	−38.8843	+	32.6278i	−1.28829	+	1.08101i	−0.992043	+	0.125896i	$0.959819\pi$
$912$		0			0
$913$	−1.01923	+	5.78033i	−0.0337315	+	0.191301i
$914$		0			0
$915$	−2.45077	−	2.48357i	−0.0810201	−	0.0821041i
$916$		0			0
$917$	21.1382			0.698044
$918$		0			0
$919$	−22.2511			−0.733995			−0.366998	−	0.930222i	$-0.619614\pi$
$919$	−22.2511			−0.733995			−0.366998	+	0.930222i	$0.619614\pi$
$920$		0			0
$921$	−3.20820	+	11.6626i	−0.105714	+	0.384296i
$922$		0			0
$923$	−2.01431	+	11.4237i	−0.0663018	+	0.376016i
$924$		0			0
$925$	13.3041	−	11.1635i	0.437437	−	0.367053i
$926$		0			0
$927$	−7.68723	−	22.0270i	−0.252482	−	0.723463i
$928$		0			0
$929$	3.10163	+	17.5902i	0.101761	+	0.577116i	0.992465	+	0.122532i	$0.0391013\pi$
$929$	3.10163	+	17.5902i	0.101761	+	0.577116i	−0.890703	+	0.454585i	$0.849788\pi$
$930$		0			0
$931$	−9.44986	+	3.43947i	−0.309707	+	0.112724i
$932$		0			0
$933$	12.8162	−	8.84765i	0.419583	−	0.289659i
$934$		0			0
$935$	3.08677	−	5.34644i	0.100948	−	0.174847i
$936$		0			0
$937$	6.68749	+	11.5831i	0.218471	+	0.378402i	0.954341	−	0.298721i	$-0.0965598\pi$
$937$	6.68749	+	11.5831i	0.218471	+	0.378402i	−0.735870	+	0.677123i	$0.763227\pi$
$938$		0			0
$939$	17.0898	+	37.2943i	0.557706	+	1.21705i
$940$		0			0
$941$	6.69590	+	5.61853i	0.218280	+	0.183159i	0.745371	−	0.666650i	$-0.232273\pi$
$941$	6.69590	+	5.61853i	0.218280	+	0.183159i	−0.527090	+	0.849809i	$0.676717\pi$
$942$		0			0
$943$	−28.8126	−	10.4869i	−0.938268	−	0.341502i
$944$		0			0
$945$	7.44595	+	2.15511i	0.242217	+	0.0701059i
$946$		0			0
$947$	19.9691	+	7.26815i	0.648908	+	0.236183i	0.645440	−	0.763811i	$-0.276674\pi$
$947$	19.9691	+	7.26815i	0.648908	+	0.236183i	0.00346769	+	0.999994i	$0.498896\pi$
$948$		0			0
$949$	−9.12047	−	7.65299i	−0.296063	−	0.248426i
$950$		0			0
$951$	−17.0329	+	23.9847i	−0.552329	+	0.777756i
$952$		0			0
$953$	3.80567	+	6.59162i	0.123278	+	0.213523i	0.921058	−	0.389424i	$-0.127326\pi$
$953$	3.80567	+	6.59162i	0.123278	+	0.213523i	−0.797781	+	0.602948i	$0.793993\pi$
$954$		0			0
$955$	2.21982	−	3.84485i	0.0718318	−	0.124416i
$956$		0			0
$957$	0.0567226	+	0.702045i	0.00183358	+	0.0226939i
$958$		0			0
$959$	−20.9676	+	7.63157i	−0.677078	+	0.246436i
$960$		0			0
$961$	−0.420554	−	2.38508i	−0.0135663	−	0.0769381i
$962$		0			0
$963$	−22.6872	+	12.6994i	−0.731084	+	0.409234i
$964$		0			0
$965$	13.7671	−	11.5519i	0.443178	−	0.371870i
$966$		0			0
$967$	2.95220	−	16.7428i	0.0949364	−	0.538411i	−0.899830	−	0.436240i	$-0.856310\pi$
$967$	2.95220	−	16.7428i	0.0949364	−	0.538411i	0.994767	−	0.102171i	$-0.0325789\pi$
$968$		0			0
$969$	−5.14390	+	1.34173i	−0.165246	+	0.0431026i
$970$		0			0
$971$	33.0729			1.06136			0.530679	−	0.847573i	$-0.321937\pi$
$971$	33.0729			1.06136			0.530679	+	0.847573i	$0.321937\pi$
$972$		0			0
$973$	−10.5006			−0.336632
$974$		0			0
$975$	10.8397	−	2.82742i	0.347149	−	0.0905500i
$976$		0			0
$977$	−8.76021	+	49.6816i	−0.280264	+	1.58946i	0.441464	+	0.897279i	$0.354459\pi$
$977$	−8.76021	+	49.6816i	−0.280264	+	1.58946i	−0.721728	+	0.692177i	$0.756652\pi$
$978$		0			0
$979$	71.1960	−	59.7405i	2.27543	−	1.90932i
$980$		0			0
$981$	45.3559	−	25.3885i	1.44810	−	0.810594i
$982$		0			0
$983$	−2.02177	−	11.4660i	−0.0644843	−	0.365709i	−0.999925	−	0.0122258i	$-0.996108\pi$
$983$	−2.02177	−	11.4660i	−0.0644843	−	0.365709i	0.935441	−	0.353483i	$-0.115003\pi$
$984$		0			0
$985$	15.2154	−	5.53794i	0.484802	−	0.176454i
$986$		0			0
$987$	1.42422	+	17.6274i	0.0453336	+	0.561086i
$988$		0			0
$989$	−13.9514	+	24.1645i	−0.443629	+	0.768387i
$990$		0			0
$991$	−16.9339	−	29.3304i	−0.537923	−	0.931710i	−0.999016	−	0.0443581i	$-0.985876\pi$
$991$	−16.9339	−	29.3304i	−0.537923	−	0.931710i	0.461093	−	0.887352i	$-0.347458\pi$
$992$		0			0
$993$	20.6364	−	29.0590i	0.654878	−	0.922158i
$994$		0			0
$995$	3.89734	+	3.27026i	0.123554	+	0.103674i
$996$		0			0
$997$	−20.9654	−	7.63077i	−0.663980	−	0.241669i	−0.0120262	−	0.999928i	$-0.503828\pi$
$997$	−20.9654	−	7.63077i	−0.663980	−	0.241669i	−0.651954	+	0.758259i	$0.726050\pi$
$998$		0			0
$999$	−5.18858	−	21.0326i	−0.164159	−	0.665441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.193.8	yes	54
4.3	odd	2		864.2.y.b.193.2	✓	54
27.7	even	9	inner	864.2.y.c.385.8	yes	54
108.7	odd	18		864.2.y.b.385.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.2	✓	54	4.3	odd	2
864.2.y.b.385.2	yes	54	108.7	odd	18
864.2.y.c.193.8	yes	54	1.1	even	1	trivial
864.2.y.c.385.8	yes	54	27.7	even	9	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67597 - 0.437160i) q^{3} +(-0.158606 + 0.899497i) q^{5} +(1.25116 - 1.04985i) q^{7} +(2.61778 - 1.46534i) q^{9} +O(q^{10})\)	\(q+(1.67597 - 0.437160i) q^{3} +(-0.158606 + 0.899497i) q^{5} +(1.25116 - 1.04985i) q^{7} +(2.61778 - 1.46534i) q^{9} +(0.887648 + 5.03410i) q^{11} +(1.45896 - 0.531018i) q^{13} +(0.127405 + 1.57687i) q^{15} +(-0.661128 + 1.14511i) q^{17} +(1.16059 + 2.01020i) q^{19} +(1.63796 - 2.30648i) q^{21} +(-2.86651 - 2.40528i) q^{23} +(3.91452 + 1.42477i) q^{25} +(3.74675 - 3.60026i) q^{27} +(0.0747537 + 0.0272081i) q^{29} +(-4.09516 - 3.43625i) q^{31} +(3.68838 + 8.04898i) q^{33} +(0.745894 + 1.29193i) q^{35} +(2.08453 - 3.61052i) q^{37} +(2.21304 - 1.52777i) q^{39} +(7.69988 - 2.80253i) q^{41} +(-1.29485 - 7.34345i) q^{43} +(0.902872 + 2.58710i) q^{45} +(-4.78889 + 4.01836i) q^{47} +(-0.752316 + 4.26660i) q^{49} +(-0.607438 + 2.20819i) q^{51} +10.3219 q^{53} -4.66894 q^{55} +(2.82390 + 2.86169i) q^{57} +(-1.03999 + 5.89807i) q^{59} +(-1.68954 + 1.41769i) q^{61} +(1.73688 - 4.58165i) q^{63} +(0.246250 + 1.39655i) q^{65} +(0.0698559 - 0.0254255i) q^{67} +(-5.85568 - 2.77807i) q^{69} +(-3.73567 + 6.47037i) q^{71} +(-3.83421 - 6.64105i) q^{73} +(7.18350 + 0.676606i) q^{75} +(6.39564 + 5.36658i) q^{77} +(-14.7441 - 5.36643i) q^{79} +(4.70557 - 7.67187i) q^{81} +(1.07899 + 0.392719i) q^{83} +(-0.925161 - 0.776302i) q^{85} +(0.137180 + 0.0129208i) q^{87} +(-9.09078 - 15.7457i) q^{89} +(1.26790 - 2.19608i) q^{91} +(-8.36557 - 3.96882i) q^{93} +(-1.99225 + 0.725119i) q^{95} +(1.75201 + 9.93616i) q^{97} +(9.70033 + 11.8775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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