LMFDB - Embedded newform 888.2.bo.c.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			673.2
Character	$\chi$	$=$	888.673
Dual form			888.2.bo.c.793.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(-0.482804 - 2.73812i) q^{5} +(0.268451 + 1.52246i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(-0.482804 - 2.73812i) q^{5} +(0.268451 + 1.52246i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.47480 + 4.28647i) q^{11} +(-2.48230 + 2.08289i) q^{13} +(-0.482804 + 2.73812i) q^{15} +(-1.92986 - 1.61934i) q^{17} +(6.30349 + 2.29428i) q^{19} +(0.268451 - 1.52246i) q^{21} +(0.772973 + 1.33883i) q^{23} +(-2.56572 + 0.933846i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.83100 + 4.90344i) q^{29} +5.79163 q^{31} +(3.79161 - 3.18154i) q^{33} +(4.03906 - 1.47010i) q^{35} +(3.05948 + 5.25734i) q^{37} +(3.04499 - 1.10829i) q^{39} +(4.71802 - 3.95889i) q^{41} -1.60150 q^{43} +(1.39018 - 2.40786i) q^{45} +(-0.689152 - 1.19365i) q^{47} +(4.33203 - 1.57673i) q^{49} +(1.25963 + 2.18173i) q^{51} +(-0.934856 + 5.30183i) q^{53} +(12.9317 + 4.70675i) q^{55} +(-5.13865 - 4.31184i) q^{57} +(0.121572 - 0.689471i) q^{59} +(-9.43805 + 7.91947i) q^{61} +(-0.772973 + 1.33883i) q^{63} +(6.90167 + 5.79119i) q^{65} +(2.54524 + 14.4348i) q^{67} +(-0.268451 - 1.52246i) q^{69} +(3.59330 + 1.30785i) q^{71} -1.58345 q^{73} +2.73038 q^{75} +(-7.19034 - 2.61707i) q^{77} +(1.65944 + 9.41117i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-2.52763 - 2.12093i) q^{83} +(-3.50221 + 6.06600i) q^{85} +(4.33734 - 3.63946i) q^{87} +(-1.76482 + 10.0088i) q^{89} +(-3.83750 - 3.22004i) q^{91} +(-5.44235 - 1.98085i) q^{93} +(3.23866 - 18.3674i) q^{95} +(-7.88989 - 13.6657i) q^{97} +(-4.65109 + 1.69286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	−0.482804	−	2.73812i	−0.215916	−	1.22452i	−0.879309	−	0.476252i	$-0.841995\pi$
$5$	−0.482804	−	2.73812i	−0.215916	−	1.22452i	0.663393	−	0.748271i	$-0.269116\pi$
$6$		0			0
$7$	0.268451	+	1.52246i	0.101465	+	0.575435i	0.992574	+	0.121646i	$0.0388172\pi$
$7$	0.268451	+	1.52246i	0.101465	+	0.575435i	−0.891109	+	0.453790i	$0.850072\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	−2.47480	+	4.28647i	−0.746179	+	1.29242i	0.203463	+	0.979083i	$0.434780\pi$
$11$	−2.47480	+	4.28647i	−0.746179	+	1.29242i	−0.949642	+	0.313337i	$0.898553\pi$
$12$		0			0
$13$	−2.48230	+	2.08289i	−0.688465	+	0.577691i	−0.918466	−	0.395499i	$-0.870572\pi$
$13$	−2.48230	+	2.08289i	−0.688465	+	0.577691i	0.230001	+	0.973190i	$0.426127\pi$
$14$		0			0
$15$	−0.482804	+	2.73812i	−0.124659	+	0.706979i
$16$		0			0
$17$	−1.92986	−	1.61934i	−0.468059	−	0.392748i	0.378027	−	0.925795i	$-0.376603\pi$
$17$	−1.92986	−	1.61934i	−0.468059	−	0.392748i	−0.846086	+	0.533046i	$0.821047\pi$
$18$		0			0
$19$	6.30349	+	2.29428i	1.44612	+	0.526345i	0.941505	−	0.337000i	$-0.109412\pi$
$19$	6.30349	+	2.29428i	1.44612	+	0.526345i	0.504615	+	0.863344i	$0.331634\pi$
$20$		0			0
$21$	0.268451	−	1.52246i	0.0585807	−	0.332228i
$22$		0			0
$23$	0.772973	+	1.33883i	0.161176	+	0.279165i	0.935291	−	0.353880i	$-0.115138\pi$
$23$	0.772973	+	1.33883i	0.161176	+	0.279165i	−0.774115	+	0.633045i	$0.781805\pi$
$24$		0			0
$25$	−2.56572	+	0.933846i	−0.513144	+	0.186769i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−2.83100	+	4.90344i	−0.525703	+	0.910545i	0.473848	+	0.880607i	$0.342865\pi$
$29$	−2.83100	+	4.90344i	−0.525703	+	0.910545i	−0.999552	+	0.0299386i	$0.990469\pi$
$30$		0			0
$31$	5.79163			1.04021			0.520103	−	0.854103i	$-0.325893\pi$
$31$	5.79163			1.04021			0.520103	+	0.854103i	$0.325893\pi$
$32$		0			0
$33$	3.79161	−	3.18154i	0.660034	−	0.553834i
$34$		0			0
$35$	4.03906	−	1.47010i	0.682726	−	0.248492i
$36$		0			0
$37$	3.05948	+	5.25734i	0.502976	+	0.864301i
$37$	3.05948	+	5.25734i	0.502976	+	0.864301i
$38$		0			0
$39$	3.04499	−	1.10829i	0.487588	−	0.177468i
$40$		0			0
$41$	4.71802	−	3.95889i	0.736831	−	0.618274i	−0.195154	−	0.980773i	$-0.562521\pi$
$41$	4.71802	−	3.95889i	0.736831	−	0.618274i	0.931984	+	0.362498i	$0.118076\pi$
$42$		0			0
$43$	−1.60150			−0.244227			−0.122113	−	0.992516i	$-0.538967\pi$
$43$	−1.60150			−0.244227			−0.122113	+	0.992516i	$0.538967\pi$
$44$		0			0
$45$	1.39018	−	2.40786i	0.207236	−	0.358943i
$46$		0			0
$47$	−0.689152	−	1.19365i	−0.100523	−	0.174111i	0.811377	−	0.584523i	$-0.198718\pi$
$47$	−0.689152	−	1.19365i	−0.100523	−	0.174111i	−0.911900	+	0.410412i	$0.865385\pi$
$48$		0			0
$49$	4.33203	−	1.57673i	0.618862	−	0.225247i
$50$		0			0
$51$	1.25963	+	2.18173i	0.176383	+	0.305504i
$52$		0			0
$53$	−0.934856	+	5.30183i	−0.128412	+	0.728263i	0.850810	+	0.525473i	$0.176112\pi$
$53$	−0.934856	+	5.30183i	−0.128412	+	0.728263i	−0.979222	+	0.202789i	$0.934999\pi$
$54$		0			0
$55$	12.9317	+	4.70675i	1.74371	+	0.634659i
$56$		0			0
$57$	−5.13865	−	4.31184i	−0.680631	−	0.571117i
$58$		0			0
$59$	0.121572	−	0.689471i	0.0158274	−	0.0897615i	−0.975871	−	0.218349i	$-0.929933\pi$
$59$	0.121572	−	0.689471i	0.0158274	−	0.0897615i	0.991698	+	0.128587i	$0.0410442\pi$
$60$		0			0
$61$	−9.43805	+	7.91947i	−1.20842	+	1.01398i	−0.209070	+	0.977901i	$0.567044\pi$
$61$	−9.43805	+	7.91947i	−1.20842	+	1.01398i	−0.999349	+	0.0360834i	$0.988512\pi$
$62$		0			0
$63$	−0.772973	+	1.33883i	−0.0973854	+	0.168676i
$64$		0			0
$65$	6.90167	+	5.79119i	0.856047	+	0.718309i
$66$		0			0
$67$	2.54524	+	14.4348i	0.310951	+	1.76349i	0.594077	+	0.804408i	$0.297517\pi$
$67$	2.54524	+	14.4348i	0.310951	+	1.76349i	−0.283126	+	0.959083i	$0.591371\pi$
$68$		0			0
$69$	−0.268451	−	1.52246i	−0.0323177	−	0.183283i
$70$		0			0
$71$	3.59330	+	1.30785i	0.426446	+	0.155214i	0.546322	−	0.837575i	$-0.316027\pi$
$71$	3.59330	+	1.30785i	0.426446	+	0.155214i	−0.119876	+	0.992789i	$0.538250\pi$
$72$		0			0
$73$	−1.58345			−0.185328			−0.0926642	−	0.995697i	$-0.529538\pi$
$73$	−1.58345			−0.185328			−0.0926642	+	0.995697i	$0.529538\pi$
$74$		0			0
$75$	2.73038			0.315278
$76$		0			0
$77$	−7.19034	−	2.61707i	−0.819415	−	0.298243i
$78$		0			0
$79$	1.65944	+	9.41117i	0.186702	+	1.05884i	0.923749	+	0.382998i	$0.125108\pi$
$79$	1.65944	+	9.41117i	0.186702	+	1.05884i	−0.737047	+	0.675841i	$0.763780\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	−2.52763	−	2.12093i	−0.277443	−	0.232802i	0.493439	−	0.869781i	$-0.335740\pi$
$83$	−2.52763	−	2.12093i	−0.277443	−	0.232802i	−0.770882	+	0.636978i	$0.780184\pi$
$84$		0			0
$85$	−3.50221	+	6.06600i	−0.379868	+	0.657950i
$86$		0			0
$87$	4.33734	−	3.63946i	0.465012	−	0.390191i
$88$		0			0
$89$	−1.76482	+	10.0088i	−0.187071	+	1.06093i	0.736196	+	0.676769i	$0.236620\pi$
$89$	−1.76482	+	10.0088i	−0.187071	+	1.06093i	−0.923266	+	0.384161i	$0.874491\pi$
$90$		0			0
$91$	−3.83750	−	3.22004i	−0.402279	−	0.337552i
$92$		0			0
$93$	−5.44235	−	1.98085i	−0.564345	−	0.205405i
$94$		0			0
$95$	3.23866	−	18.3674i	0.332280	−	1.88445i
$96$		0			0
$97$	−7.88989	−	13.6657i	−0.801097	−	1.38754i	−0.918895	−	0.394502i	$-0.870917\pi$
$97$	−7.88989	−	13.6657i	−0.801097	−	1.38754i	0.117798	−	0.993038i	$-0.462416\pi$
$98$		0			0
$99$	−4.65109	+	1.69286i	−0.467453	+	0.170139i
$100$		0			0
$101$	−4.34942	−	7.53342i	−0.432784	−	0.749603i	0.564328	−	0.825550i	$-0.309135\pi$
$101$	−4.34942	−	7.53342i	−0.432784	−	0.749603i	−0.997112	+	0.0759474i	$0.975802\pi$
$102$		0			0
$103$	−3.54751	+	6.14447i	−0.349546	+	0.605432i	−0.986169	−	0.165743i	$-0.946998\pi$
$103$	−3.54751	+	6.14447i	−0.349546	+	0.605432i	0.636622	+	0.771176i	$0.280331\pi$
$104$		0			0
$105$	−4.29828			−0.419469
$106$		0			0
$107$	−4.03341	+	3.38443i	−0.389925	+	0.327186i	−0.816584	−	0.577227i	$-0.804135\pi$
$107$	−4.03341	+	3.38443i	−0.389925	+	0.327186i	0.426659	+	0.904412i	$0.359690\pi$
$108$		0			0
$109$	3.55173	−	1.29272i	0.340194	−	0.123820i	−0.166273	−	0.986080i	$-0.553173\pi$
$109$	3.55173	−	1.29272i	0.340194	−	0.123820i	0.506467	+	0.862259i	$0.330951\pi$
$110$		0			0
$111$	−1.07686	−	5.98668i	−0.102211	−	0.568231i
$112$		0			0
$113$	9.55625	−	3.47819i	0.898976	−	0.327201i	0.149134	−	0.988817i	$-0.452351\pi$
$113$	9.55625	−	3.47819i	0.898976	−	0.327201i	0.749843	+	0.661616i	$0.230129\pi$
$114$		0			0
$115$	3.29267	−	2.76288i	0.307043	−	0.257640i
$116$		0			0
$117$	−3.24041			−0.299576
$118$		0			0
$119$	1.94731	−	3.37284i	0.178510	−	0.309188i
$120$		0			0
$121$	−6.74923	−	11.6900i	−0.613566	−	1.06273i
$122$		0			0
$123$	−5.78751	+	2.10648i	−0.521842	+	0.189935i
$124$		0			0
$125$	−3.15517	−	5.46492i	−0.282207	−	0.488797i
$126$		0			0
$127$	−3.04549	+	17.2718i	−0.270243	+	1.53263i	0.483434	+	0.875381i	$0.339389\pi$
$127$	−3.04549	+	17.2718i	−0.270243	+	1.53263i	−0.753677	+	0.657245i	$0.771722\pi$
$128$		0			0
$129$	1.50492	+	0.547746i	0.132501	+	0.0482263i
$130$		0			0
$131$	15.9444	+	13.3789i	1.39307	+	1.16892i	0.964081	+	0.265608i	$0.0855728\pi$
$131$	15.9444	+	13.3789i	1.39307	+	1.16892i	0.428984	+	0.903312i	$0.358872\pi$
$132$		0			0
$133$	−1.80078	+	10.2127i	−0.156147	+	0.885554i
$134$		0			0
$135$	−2.12988	+	1.78718i	−0.183311	+	0.153816i
$136$		0			0
$137$	4.84352	−	8.38922i	0.413810	−	0.716739i	−0.581493	−	0.813551i	$-0.697531\pi$
$137$	4.84352	−	8.38922i	0.413810	−	0.716739i	0.995303	+	0.0968120i	$0.0308646\pi$
$138$		0			0
$139$	−11.7859	−	9.88953i	−0.999665	−	0.838819i	−0.0127272	−	0.999919i	$-0.504051\pi$
$139$	−11.7859	−	9.88953i	−0.999665	−	0.838819i	−0.986938	+	0.161100i	$0.948496\pi$
$140$		0			0
$141$	0.239340	+	1.35736i	0.0201561	+	0.114311i
$142$		0			0
$143$	−2.78509	−	15.7950i	−0.232901	−	1.32085i
$144$		0			0
$145$	14.7930	+	5.38421i	1.22849	+	0.447134i
$146$		0			0
$147$	−4.61005			−0.380231
$148$		0			0
$149$	10.5299			0.862642			0.431321	−	0.902198i	$-0.358048\pi$
$149$	10.5299			0.862642			0.431321	+	0.902198i	$0.358048\pi$
$150$		0			0
$151$	−10.2717	−	3.73858i	−0.835897	−	0.304242i	−0.111620	−	0.993751i	$-0.535604\pi$
$151$	−10.2717	−	3.73858i	−0.835897	−	0.304242i	−0.724277	+	0.689509i	$0.757826\pi$
$152$		0			0
$153$	−0.437463	−	2.48098i	−0.0353668	−	0.200575i
$154$		0			0
$155$	−2.79622	−	15.8581i	−0.224598	−	1.27376i
$156$		0			0
$157$	−6.71146	−	5.63158i	−0.535632	−	0.449449i	0.334409	−	0.942428i	$-0.391463\pi$
$157$	−6.71146	−	5.63158i	−0.535632	−	0.449449i	−0.870041	+	0.492979i	$0.835908\pi$
$158$		0			0
$159$	2.69181	−	4.66235i	0.213474	−	0.369749i
$160$		0			0
$161$	−1.83081	+	1.53623i	−0.144288	+	0.121072i
$162$		0			0
$163$	−1.59294	+	9.03402i	−0.124769	+	0.707599i	0.856676	+	0.515855i	$0.172526\pi$
$163$	−1.59294	+	9.03402i	−0.124769	+	0.707599i	−0.981445	+	0.191744i	$0.938586\pi$
$164$		0			0
$165$	−10.5420	−	8.84581i	−0.820695	−	0.688645i
$166$		0			0
$167$	−13.8923	−	5.05639i	−1.07502	−	0.391275i	−0.256968	−	0.966420i	$-0.582724\pi$
$167$	−13.8923	−	5.05639i	−1.07502	−	0.391275i	−0.818052	+	0.575145i	$0.804946\pi$
$168$		0			0
$169$	−0.434077	+	2.46178i	−0.0333906	+	0.189367i
$170$		0			0
$171$	3.35402	+	5.80933i	0.256488	+	0.444250i
$172$		0			0
$173$	7.84163	−	2.85412i	0.596188	−	0.216995i	−0.0262610	−	0.999655i	$-0.508360\pi$
$173$	7.84163	−	2.85412i	0.596188	−	0.216995i	0.622449	+	0.782660i	$0.286138\pi$
$174$		0			0
$175$	−2.11051	−	3.65551i	−0.159540	−	0.276331i
$176$		0			0
$177$	−0.350054	+	0.606311i	−0.0263117	+	0.0455731i
$178$		0			0
$179$	0.738674			0.0552111			0.0276055	−	0.999619i	$-0.491212\pi$
$179$	0.738674			0.0552111			0.0276055	+	0.999619i	$0.491212\pi$
$180$		0			0
$181$	10.9604	−	9.19685i	0.814679	−	0.683597i	−0.137041	−	0.990565i	$-0.543759\pi$
$181$	10.9604	−	9.19685i	0.814679	−	0.683597i	0.951720	+	0.306969i	$0.0993148\pi$
$182$		0			0
$183$	11.5775	−	4.21386i	0.855833	−	0.311498i
$184$		0			0
$185$	12.9181	−	10.9155i	0.949755	−	0.802522i
$186$		0			0
$187$	11.7173	−	4.26474i	0.856852	−	0.311869i
$188$		0			0
$189$	1.18426	−	0.993715i	0.0861425	−	0.0722821i
$190$		0			0
$191$	−23.8094			−1.72279			−0.861395	−	0.507936i	$-0.830409\pi$
$191$	−23.8094			−1.72279			−0.861395	+	0.507936i	$0.830409\pi$
$192$		0			0
$193$	2.15032	−	3.72447i	0.154784	−	0.268093i	−0.778197	−	0.628021i	$-0.783865\pi$
$193$	2.15032	−	3.72447i	0.154784	−	0.268093i	0.932980	+	0.359928i	$0.117199\pi$
$194$		0			0
$195$	−4.50475	−	7.80245i	−0.322592	−	0.558745i
$196$		0			0
$197$	−11.7718	+	4.28459i	−0.838708	+	0.305265i	−0.725428	−	0.688298i	$-0.758358\pi$
$197$	−11.7718	+	4.28459i	−0.838708	+	0.305265i	−0.113280	+	0.993563i	$0.536136\pi$
$198$		0			0
$199$	6.01986	+	10.4267i	0.426736	+	0.739129i	0.996581	−	0.0826236i	$-0.0263299\pi$
$199$	6.01986	+	10.4267i	0.426736	+	0.739129i	−0.569845	+	0.821753i	$0.692997\pi$
$200$		0			0
$201$	2.54524	−	14.4348i	0.179528	−	1.01815i
$202$		0			0
$203$	−8.22526	−	2.99375i	−0.577300	−	0.210120i
$204$		0			0
$205$	−13.1178	−	11.0071i	−0.916185	−	0.768771i
$206$		0			0
$207$	−0.268451	+	1.52246i	−0.0186586	+	0.105818i
$208$		0			0
$209$	−25.4342	+	21.3419i	−1.75932	+	1.47625i
$210$		0			0
$211$	7.52049	−	13.0259i	0.517732	−	0.896738i	−0.482056	−	0.876140i	$-0.660110\pi$
$211$	7.52049	−	13.0259i	0.517732	−	0.896738i	0.999788	−	0.0205976i	$-0.00655690\pi$
$212$		0			0
$213$	−2.92929	−	2.45796i	−0.200711	−	0.168417i
$214$		0			0
$215$	0.773211	+	4.38510i	0.0527325	+	0.299061i
$216$		0			0
$217$	1.55477	+	8.81751i	0.105544	+	0.598572i
$218$		0			0
$219$	1.48795	+	0.541571i	0.100547	+	0.0365959i
$220$		0			0
$221$	8.16340			0.549130
$222$		0			0
$223$	18.6446			1.24854			0.624269	−	0.781210i	$-0.285397\pi$
$223$	18.6446			1.24854			0.624269	+	0.781210i	$0.285397\pi$
$224$		0			0
$225$	−2.56572	−	0.933846i	−0.171048	−	0.0622564i
$226$		0			0
$227$	−0.924465	−	5.24290i	−0.0613589	−	0.347984i	−0.999995	−	0.00307535i	$-0.999021\pi$
$227$	−0.924465	−	5.24290i	−0.0613589	−	0.347984i	0.938636	−	0.344908i	$-0.112090\pi$
$228$		0			0
$229$	1.50469	+	8.53353i	0.0994328	+	0.563912i	0.993299	+	0.115577i	$0.0368717\pi$
$229$	1.50469	+	8.53353i	0.0994328	+	0.563912i	−0.893866	+	0.448335i	$0.852017\pi$
$230$		0			0
$231$	5.86162	+	4.91848i	0.385666	+	0.323612i
$232$		0			0
$233$	11.4714	−	19.8691i	0.751519	−	1.30167i	−0.195567	−	0.980690i	$-0.562655\pi$
$233$	11.4714	−	19.8691i	0.751519	−	1.30167i	0.947086	−	0.320979i	$-0.104012\pi$
$234$		0			0
$235$	−2.93562	+	2.46328i	−0.191499	+	0.160686i
$236$		0			0
$237$	1.65944	−	9.41117i	0.107792	−	0.611321i
$238$		0			0
$239$	−21.0576	−	17.6694i	−1.36210	−	1.14294i	−0.975327	−	0.220767i	$-0.929144\pi$
$239$	−21.0576	−	17.6694i	−1.36210	−	1.14294i	−0.386776	−	0.922174i	$-0.626411\pi$
$240$		0			0
$241$	25.2323	+	9.18379i	1.62535	+	0.591580i	0.984391	−	0.175994i	$-0.0563139\pi$
$241$	25.2323	+	9.18379i	1.62535	+	0.591580i	0.640961	+	0.767574i	$0.278536\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	−6.40879	−	11.1004i	−0.409443	−	0.709176i
$246$		0			0
$247$	−20.4259	+	7.43441i	−1.29967	+	0.473040i
$248$		0			0
$249$	1.64979	+	2.85752i	0.104551	+	0.181088i
$250$		0			0
$251$	−8.27532	+	14.3333i	−0.522334	+	0.904708i	0.477329	+	0.878725i	$0.341605\pi$
$251$	−8.27532	+	14.3333i	−0.522334	+	0.904708i	−0.999662	+	0.0259835i	$0.991728\pi$
$252$		0			0
$253$	−7.65180			−0.481065
$254$		0			0
$255$	5.36569	−	4.50235i	0.336013	−	0.281948i
$256$		0			0
$257$	−24.9198	+	9.07005i	−1.55445	+	0.565774i	−0.969457	−	0.245262i	$-0.921126\pi$
$257$	−24.9198	+	9.07005i	−1.55445	+	0.565774i	−0.584996	+	0.811036i	$0.698904\pi$
$258$		0			0
$259$	−7.18276	+	6.06927i	−0.446315	+	0.377126i
$260$		0			0
$261$	−5.32054	+	1.93652i	−0.329333	+	0.119867i
$262$		0			0
$263$	1.72258	−	1.44542i	0.106219	−	0.0891283i	−0.588131	−	0.808765i	$-0.700136\pi$
$263$	1.72258	−	1.44542i	0.106219	−	0.0891283i	0.694350	+	0.719637i	$0.255692\pi$
$264$		0			0
$265$	14.9684			0.919501
$266$		0			0
$267$	5.08160	−	8.80158i	0.310989	−	0.538648i
$268$		0			0
$269$	−2.59982	−	4.50302i	−0.158514	−	0.274554i	0.775819	−	0.630955i	$-0.217337\pi$
$269$	−2.59982	−	4.50302i	−0.158514	−	0.274554i	−0.934333	+	0.356401i	$0.884004\pi$
$270$		0			0
$271$	−5.02861	+	1.83026i	−0.305466	+	0.111181i	−0.490205	−	0.871607i	$-0.663078\pi$
$271$	−5.02861	+	1.83026i	−0.305466	+	0.111181i	0.184739	+	0.982788i	$0.440856\pi$
$272$		0			0
$273$	2.50475	+	4.33835i	0.151594	+	0.262569i
$274$		0			0
$275$	2.34673	−	13.3090i	0.141513	−	0.802561i
$276$		0			0
$277$	−27.1321	−	9.87528i	−1.63021	−	0.593348i	−0.644923	−	0.764248i	$-0.723110\pi$
$277$	−27.1321	−	9.87528i	−1.63021	−	0.593348i	−0.985288	+	0.170900i	$0.945333\pi$
$278$		0			0
$279$	4.43664	+	3.72279i	0.265615	+	0.222877i
$280$		0			0
$281$	−5.26959	+	29.8853i	−0.314357	+	1.78281i	0.261442	+	0.965219i	$0.415802\pi$
$281$	−5.26959	+	29.8853i	−0.314357	+	1.78281i	−0.575800	+	0.817591i	$0.695309\pi$
$282$		0			0
$283$	−3.20121	+	2.68613i	−0.190292	+	0.159674i	−0.732956	−	0.680276i	$-0.761860\pi$
$283$	−3.20121	+	2.68613i	−0.190292	+	0.159674i	0.542664	+	0.839950i	$0.317416\pi$
$284$		0			0
$285$	−9.32536	+	16.1520i	−0.552387	+	0.956762i
$286$		0			0
$287$	7.29380	+	6.12022i	0.430539	+	0.361265i
$288$		0			0
$289$	−1.84994	−	10.4915i	−0.108820	−	0.617149i
$290$		0			0
$291$	2.74013	+	15.5400i	0.160629	+	0.910973i
$292$		0			0
$293$	0.433010	+	0.157603i	0.0252967	+	0.00920726i	0.354638	−	0.935004i	$-0.384604\pi$
$293$	0.433010	+	0.157603i	0.0252967	+	0.00920726i	−0.329341	+	0.944211i	$0.606826\pi$
$294$		0			0
$295$	−1.94655			−0.113332
$296$		0			0
$297$	4.94959			0.287204
$298$		0			0
$299$	−4.70739	−	1.71335i	−0.272235	−	0.0990855i
$300$		0			0
$301$	−0.429924	−	2.43822i	−0.0247804	−	0.140537i
$302$		0			0
$303$	1.51054	+	8.56669i	0.0867781	+	0.492143i
$304$		0			0
$305$	26.2412	+	22.0189i	1.50256	+	1.26080i
$306$		0			0
$307$	13.8473	−	23.9842i	0.790306	−	1.36885i	−0.135471	−	0.990781i	$-0.543255\pi$
$307$	13.8473	−	23.9842i	0.790306	−	1.36885i	0.925777	−	0.378069i	$-0.123412\pi$
$308$		0			0
$309$	5.43510	−	4.56059i	0.309192	−	0.259443i
$310$		0			0
$311$	−4.68033	+	26.5435i	−0.265397	+	1.50514i	0.502504	+	0.864575i	$0.332412\pi$
$311$	−4.68033	+	26.5435i	−0.265397	+	1.50514i	−0.767902	+	0.640568i	$0.778699\pi$
$312$		0			0
$313$	11.8240	+	9.92155i	0.668335	+	0.560799i	0.912572	−	0.408916i	$-0.134093\pi$
$313$	11.8240	+	9.92155i	0.668335	+	0.560799i	−0.244237	+	0.969715i	$0.578538\pi$
$314$		0			0
$315$	4.03906	+	1.47010i	0.227575	+	0.0828307i
$316$		0			0
$317$	−1.04289	+	5.91455i	−0.0585748	+	0.332194i	−0.999987	−	0.00506354i	$-0.998388\pi$
$317$	−1.04289	+	5.91455i	−0.0585748	+	0.332194i	0.941412	+	0.337258i	$0.109499\pi$
$318$		0			0
$319$	−14.0123	−	24.2700i	−0.784538	−	1.35886i
$320$		0			0
$321$	4.94771	−	1.80082i	0.276154	−	0.100512i
$322$		0			0
$323$	−8.44961	−	14.6352i	−0.470149	−	0.814322i
$324$		0			0
$325$	4.42378	−	7.66221i	0.245387	−	0.425023i
$326$		0			0
$327$	−3.77967			−0.209016
$328$		0			0
$329$	1.63227	−	1.36964i	0.0899902	−	0.0755107i
$330$		0			0
$331$	−2.19734	+	0.799765i	−0.120777	+	0.0439591i	−0.401701	−	0.915771i	$-0.631581\pi$
$331$	−2.19734	+	0.799765i	−0.120777	+	0.0439591i	0.280925	+	0.959730i	$0.409359\pi$
$332$		0			0
$333$	−1.03565	+	5.99395i	−0.0567533	+	0.328466i
$334$		0			0
$335$	38.2953	−	13.9383i	2.09230	−	0.761533i
$336$		0			0
$337$	−9.86869	+	8.28082i	−0.537582	+	0.451085i	−0.870710	−	0.491797i	$-0.836340\pi$
$337$	−9.86869	+	8.28082i	−0.537582	+	0.451085i	0.333128	+	0.942882i	$0.391896\pi$
$338$		0			0
$339$	−10.1695			−0.552334
$340$		0			0
$341$	−14.3331	+	24.8256i	−0.776180	+	1.34438i
$342$		0			0
$343$	8.97425	+	15.5439i	0.484564	+	0.839290i
$344$		0			0
$345$	−4.03906	+	1.47010i	−0.217456	+	0.0791474i
$346$		0			0
$347$	−4.37602	−	7.57949i	−0.234917	−	0.406888i	0.724332	−	0.689452i	$-0.242148\pi$
$347$	−4.37602	−	7.57949i	−0.234917	−	0.406888i	−0.959249	+	0.282564i	$0.908815\pi$
$348$		0			0
$349$	2.92302	−	16.5773i	0.156466	−	0.887362i	−0.800967	−	0.598708i	$-0.795681\pi$
$349$	2.92302	−	16.5773i	0.156466	−	0.887362i	0.957433	−	0.288654i	$-0.0932079\pi$
$350$		0			0
$351$	3.04499	+	1.10829i	0.162529	+	0.0591559i
$352$		0			0
$353$	18.2945	+	15.3509i	0.973718	+	0.817046i	0.983130	−	0.182909i	$-0.0585515\pi$
$353$	18.2945	+	15.3509i	0.973718	+	0.817046i	−0.00941197	+	0.999956i	$0.502996\pi$
$354$		0			0
$355$	1.84620	−	10.4703i	0.0979861	−	0.555707i
$356$		0			0
$357$	−2.98345	+	2.50342i	−0.157901	+	0.132495i
$358$		0			0
$359$	11.5469	−	19.9997i	0.609420	−	1.05555i	−0.381917	−	0.924197i	$-0.624736\pi$
$359$	11.5469	−	19.9997i	0.609420	−	1.05555i	0.991336	−	0.131349i	$-0.0419308\pi$
$360$		0			0
$361$	19.9154	+	16.7110i	1.04818	+	0.879527i
$362$		0			0
$363$	2.34398	+	13.2934i	0.123027	+	0.697722i
$364$		0			0
$365$	0.764494	+	4.33566i	0.0400154	+	0.226939i
$366$		0			0
$367$	21.8416	+	7.94968i	1.14012	+	0.414970i	0.841957	−	0.539545i	$-0.181404\pi$
$367$	21.8416	+	7.94968i	1.14012	+	0.414970i	0.298163	+	0.954515i	$0.403626\pi$
$368$		0			0
$369$	6.15894			0.320621
$370$		0			0
$371$	−8.32278			−0.432097
$372$		0			0
$373$	−15.9197	−	5.79431i	−0.824293	−	0.300018i	−0.104779	−	0.994496i	$-0.533413\pi$
$373$	−15.9197	−	5.79431i	−0.824293	−	0.300018i	−0.719514	+	0.694477i	$0.755636\pi$
$374$		0			0
$375$	1.09578	+	6.21448i	0.0565858	+	0.320914i
$376$		0			0
$377$	−3.18596	−	18.0685i	−0.164085	−	0.930573i
$378$		0			0
$379$	−4.96653	−	4.16742i	−0.255114	−	0.214066i	0.506257	−	0.862383i	$-0.331029\pi$
$379$	−4.96653	−	4.16742i	−0.255114	−	0.214066i	−0.761371	+	0.648317i	$0.775473\pi$
$380$		0			0
$381$	8.76913	−	15.1886i	0.449256	−	0.778134i
$382$		0			0
$383$	−0.990563	+	0.831181i	−0.0506154	+	0.0424714i	−0.667744	−	0.744391i	$-0.732740\pi$
$383$	−0.990563	+	0.831181i	−0.0506154	+	0.0424714i	0.617129	+	0.786862i	$0.288296\pi$
$384$		0			0
$385$	−3.69432	+	20.9515i	−0.188280	+	1.06779i
$386$		0			0
$387$	−1.22682	−	1.02942i	−0.0623628	−	0.0523286i
$388$		0			0
$389$	14.0576	+	5.11655i	0.712749	+	0.259420i	0.672845	−	0.739784i	$-0.265072\pi$
$389$	14.0576	+	5.11655i	0.712749	+	0.259420i	0.0399049	+	0.999203i	$0.487295\pi$
$390$		0			0
$391$	0.676294	−	3.83546i	0.0342017	−	0.193967i
$392$		0			0
$393$	−10.4069	−	18.0254i	−0.524961	−	0.909259i
$394$		0			0
$395$	24.9677	−	9.08750i	1.25626	−	0.457242i
$396$		0			0
$397$	−4.87577	−	8.44507i	−0.244708	−	0.423846i	0.717342	−	0.696721i	$-0.245359\pi$
$397$	−4.87577	−	8.44507i	−0.244708	−	0.423846i	−0.962049	+	0.272875i	$0.912025\pi$
$398$		0			0
$399$	5.18513	−	8.98090i	0.259581	−	0.449608i
$400$		0			0
$401$	34.8243			1.73904			0.869521	−	0.493897i	$-0.164428\pi$
$401$	34.8243			1.73904			0.869521	+	0.493897i	$0.164428\pi$
$402$		0			0
$403$	−14.3765	+	12.0633i	−0.716146	+	0.600918i
$404$		0			0
$405$	2.61268	−	0.950938i	0.129825	−	0.0472525i
$406$		0			0
$407$	−30.1070	+	0.103550i	−1.49235	+	0.00513276i
$408$		0			0
$409$	0.773041	−	0.281364i	0.0382244	−	0.0139126i	−0.322837	−	0.946455i	$-0.604637\pi$
$409$	0.773041	−	0.281364i	0.0382244	−	0.0139126i	0.361062	+	0.932542i	$0.382414\pi$
$410$		0			0
$411$	−7.42070	+	6.22671i	−0.366036	+	0.307141i
$412$		0			0
$413$	1.08233			0.0532579
$414$		0			0
$415$	−4.58701	+	7.94493i	−0.225167	+	0.390001i
$416$		0			0
$417$	7.69269	+	13.3241i	0.376712	+	0.652485i
$418$		0			0
$419$	20.5564	−	7.48192i	1.00425	−	0.365516i	0.213025	−	0.977047i	$-0.431668\pi$
$419$	20.5564	−	7.48192i	1.00425	−	0.365516i	0.791220	+	0.611531i	$0.209446\pi$
$420$		0			0
$421$	5.33199	+	9.23528i	0.259865	+	0.450100i	0.966206	−	0.257772i	$-0.0829885\pi$
$421$	5.33199	+	9.23528i	0.259865	+	0.450100i	−0.706340	+	0.707872i	$0.749655\pi$
$422$		0			0
$423$	0.239340	−	1.35736i	0.0116371	−	0.0659973i
$424$		0			0
$425$	6.46369	+	2.35259i	0.313535	+	0.114117i
$426$		0			0
$427$	−14.5907	−	12.2431i	−0.706094	−	0.592484i
$428$		0			0
$429$	−2.78509	+	15.7950i	−0.134465	+	0.762592i
$430$		0			0
$431$	9.20902	−	7.72729i	0.443583	−	0.372210i	−0.393465	−	0.919340i	$-0.628724\pi$
$431$	9.20902	−	7.72729i	0.443583	−	0.372210i	0.837048	+	0.547129i	$0.184279\pi$
$432$		0			0
$433$	3.86977	−	6.70263i	0.185969	−	0.322108i	−0.757934	−	0.652332i	$-0.773791\pi$
$433$	3.86977	−	6.70263i	0.185969	−	0.322108i	0.943903	+	0.330224i	$0.107124\pi$
$434$		0			0
$435$	−12.0594	−	10.1190i	−0.578202	−	0.485169i
$436$		0			0
$437$	1.80078	+	10.2127i	0.0861428	+	0.488540i
$438$		0			0
$439$	−2.44427	−	13.8621i	−0.116659	−	0.661604i	−0.985916	−	0.167244i	$-0.946513\pi$
$439$	−2.44427	−	13.8621i	−0.116659	−	0.661604i	0.869257	−	0.494361i	$-0.164598\pi$
$440$		0			0
$441$	4.33203	+	1.57673i	0.206287	+	0.0750824i
$442$		0			0
$443$	−8.79116			−0.417681			−0.208840	−	0.977950i	$-0.566969\pi$
$443$	−8.79116			−0.417681			−0.208840	+	0.977950i	$0.566969\pi$
$444$		0			0
$445$	28.2573			1.33952
$446$		0			0
$447$	−9.89486	−	3.60144i	−0.468011	−	0.170342i
$448$		0			0
$449$	−3.36686	−	19.0944i	−0.158892	−	0.901121i	−0.955141	−	0.296152i	$-0.904296\pi$
$449$	−3.36686	−	19.0944i	−0.158892	−	0.901121i	0.796249	−	0.604969i	$-0.206815\pi$
$450$		0			0
$451$	5.29353	+	30.0211i	0.249263	+	1.41364i
$452$		0			0
$453$	8.37354	+	7.02624i	0.393423	+	0.330121i
$454$		0			0
$455$	−6.96409	+	12.0622i	−0.326482	+	0.565483i
$456$		0			0
$457$	17.4228	−	14.6194i	0.815002	−	0.683868i	−0.136794	−	0.990600i	$-0.543680\pi$
$457$	17.4228	−	14.6194i	0.815002	−	0.683868i	0.951796	+	0.306732i	$0.0992354\pi$
$458$		0			0
$459$	−0.437463	+	2.48098i	−0.0204190	+	0.115802i
$460$		0			0
$461$	22.8299	+	19.1566i	1.06329	+	0.892210i	0.994428	−	0.105416i	$-0.0336175\pi$
$461$	22.8299	+	19.1566i	1.06329	+	0.892210i	0.0688660	+	0.997626i	$0.478062\pi$
$462$		0			0
$463$	10.1627	+	3.69891i	0.472299	+	0.171903i	0.567194	−	0.823585i	$-0.308029\pi$
$463$	10.1627	+	3.69891i	0.472299	+	0.171903i	−0.0948945	+	0.995487i	$0.530251\pi$
$464$		0			0
$465$	−2.79622	+	15.8581i	−0.129672	+	0.735404i
$466$		0			0
$467$	11.4961	+	19.9119i	0.531977	+	0.921411i	0.999303	+	0.0373262i	$0.0118841\pi$
$467$	11.4961	+	19.9119i	0.531977	+	0.921411i	−0.467326	+	0.884085i	$0.654783\pi$
$468$		0			0
$469$	−21.2931	+	7.75006i	−0.983225	+	0.357864i
$470$		0			0
$471$	4.38059	+	7.58741i	0.201847	+	0.349609i
$472$		0			0
$473$	3.96339	−	6.86479i	0.182237	−	0.315643i
$474$		0			0
$475$	−18.3155			−0.840373
$476$		0			0
$477$	−4.12409	+	3.46052i	−0.188829	+	0.158447i
$478$		0			0
$479$	−35.9760	+	13.0942i	−1.64378	+	0.598289i	−0.987695	−	0.156394i	$-0.950013\pi$
$479$	−35.9760	+	13.0942i	−1.64378	+	0.598289i	−0.656090	+	0.754683i	$0.727791\pi$
$480$		0			0
$481$	−18.5450	−	6.67769i	−0.845580	−	0.304477i
$482$		0			0
$483$	2.24582	−	0.817410i	0.102188	−	0.0371935i
$484$		0			0
$485$	−33.6090	+	28.2013i	−1.52610	+	1.28055i
$486$		0			0
$487$	−41.6687			−1.88819			−0.944095	−	0.329673i	$-0.893061\pi$
$487$	−41.6687			−1.88819			−0.944095	+	0.329673i	$0.893061\pi$
$488$		0			0
$489$	4.58669	−	7.94439i	0.207417	−	0.359258i
$490$		0			0
$491$	1.94079	+	3.36155i	0.0875868	+	0.151705i	0.906491	−	0.422226i	$-0.138751\pi$
$491$	1.94079	+	3.36155i	0.0875868	+	0.151705i	−0.818904	+	0.573931i	$0.805418\pi$
$492$		0			0
$493$	13.4038	−	4.87857i	0.603675	−	0.219720i
$494$		0			0
$495$	6.88082	+	11.9179i	0.309270	+	0.535671i
$496$		0			0
$497$	−1.02653	+	5.82175i	−0.0460462	+	0.261141i
$498$		0			0
$499$	22.8183	+	8.30517i	1.02149	+	0.371791i	0.797833	−	0.602878i	$-0.205980\pi$
$499$	22.8183	+	8.30517i	1.02149	+	0.371791i	0.223653	+	0.974669i	$0.428202\pi$
$500$		0			0
$501$	11.3251	+	9.50290i	0.505969	+	0.424558i
$502$		0			0
$503$	−3.02567	+	17.1594i	−0.134908	+	0.765100i	0.840016	+	0.542561i	$0.182545\pi$
$503$	−3.02567	+	17.1594i	−0.134908	+	0.765100i	−0.974924	+	0.222539i	$0.928566\pi$
$504$		0			0
$505$	−18.5275	+	15.5464i	−0.824461	+	0.691805i
$506$		0			0
$507$	1.24988	−	2.16485i	0.0555089	−	0.0961443i
$508$		0			0
$509$	2.94020	+	2.46712i	0.130322	+	0.109353i	0.705619	−	0.708591i	$-0.250669\pi$
$509$	2.94020	+	2.46712i	0.130322	+	0.109353i	−0.575297	+	0.817945i	$0.695113\pi$
$510$		0			0
$511$	−0.425077	−	2.41073i	−0.0188043	−	0.106645i
$512$		0			0
$513$	−1.16484	−	6.60612i	−0.0514288	−	0.291668i
$514$		0			0
$515$	18.5370	+	6.74692i	0.816838	+	0.297305i
$516$		0			0
$517$	6.82204			0.300033
$518$		0			0
$519$	−8.34489			−0.366300
$520$		0			0
$521$	34.0767	+	12.4029i	1.49293	+	0.543381i	0.954218	−	0.299111i	$-0.0966900\pi$
$521$	34.0767	+	12.4029i	1.49293	+	0.543381i	0.538709	+	0.842492i	$0.318912\pi$
$522$		0			0
$523$	−3.18975	−	18.0900i	−0.139478	−	0.791019i	−0.971636	−	0.236481i	$-0.924006\pi$
$523$	−3.18975	−	18.0900i	−0.139478	−	0.791019i	0.832158	−	0.554538i	$-0.187105\pi$
$524$		0			0
$525$	0.732973	+	4.15690i	0.0319896	+	0.181422i
$526$		0			0
$527$	−11.1770	−	9.37863i	−0.486878	−	0.408539i
$528$		0			0
$529$	10.3050	−	17.8488i	0.448045	−	0.776036i
$530$		0			0
$531$	0.536314	−	0.450020i	0.0232740	−	0.0195292i
$532$		0			0
$533$	−3.46558	+	19.6543i	−0.150111	+	0.851321i
$534$		0			0
$535$	11.2143	+	9.40993i	0.484837	+	0.406827i
$536$		0			0
$537$	−0.694127	−	0.252641i	−0.0299538	−	0.0109023i
$538$		0			0
$539$	−3.96228	+	22.4712i	−0.170668	+	0.967904i
$540$		0			0
$541$	−18.5783	−	32.1786i	−0.798745	−	1.38347i	−0.920434	−	0.390899i	$-0.872164\pi$
$541$	−18.5783	−	32.1786i	−0.798745	−	1.38347i	0.121689	−	0.992568i	$-0.461169\pi$
$542$		0			0
$543$	−13.4449	+	4.89354i	−0.576976	+	0.210002i
$544$		0			0
$545$	−5.25442	−	9.10092i	−0.225074	−	0.389840i
$546$		0			0
$547$	9.38017	−	16.2469i	0.401067	−	0.694668i	−0.592788	−	0.805359i	$-0.701973\pi$
$547$	9.38017	−	16.2469i	0.401067	−	0.694668i	0.993855	+	0.110690i	$0.0353061\pi$
$548$		0			0
$549$	−12.3205			−0.525826
$550$		0			0
$551$	−29.0950	+	24.4136i	−1.23949	+	1.04006i
$552$		0			0
$553$	−13.8826	+	5.05287i	−0.590350	+	0.214870i
$554$		0			0
$555$	−15.8723	+	5.83896i	−0.673743	+	0.247850i
$556$		0			0
$557$	15.7762	−	5.74206i	0.668459	−	0.243299i	0.0145745	−	0.999894i	$-0.495361\pi$
$557$	15.7762	−	5.74206i	0.668459	−	0.243299i	0.653884	+	0.756595i	$0.273138\pi$
$558$		0			0
$559$	3.97540	−	3.33576i	0.168142	−	0.141087i
$560$		0			0
$561$	−12.4693			−0.526453
$562$		0			0
$563$	13.8284	−	23.9515i	0.582798	−	1.00944i	−0.412347	−	0.911027i	$-0.635291\pi$
$563$	13.8284	−	23.9515i	0.582798	−	1.00944i	0.995146	−	0.0984099i	$-0.0313756\pi$
$564$		0			0
$565$	−14.1375	−	24.4868i	−0.594769	−	1.03017i
$566$		0			0
$567$	−1.45271	+	0.528745i	−0.0610082	+	0.0222052i
$568$		0			0
$569$	8.65282	+	14.9871i	0.362745	+	0.628293i	0.988412	−	0.151798i	$-0.0485063\pi$
$569$	8.65282	+	14.9871i	0.362745	+	0.628293i	−0.625667	+	0.780091i	$0.715173\pi$
$570$		0			0
$571$	−0.479490	+	2.71932i	−0.0200660	+	0.113800i	−0.993196	−	0.116458i	$-0.962846\pi$
$571$	−0.479490	+	2.71932i	−0.0200660	+	0.113800i	0.973130	+	0.230258i	$0.0739571\pi$
$572$		0			0
$573$	22.3735	+	8.14330i	0.934668	+	0.340191i
$574$		0			0
$575$	−3.23349	−	2.71322i	−0.134846	−	0.113149i
$576$		0			0
$577$	7.65437	−	43.4101i	0.318655	−	1.80718i	−0.232293	−	0.972646i	$-0.574623\pi$
$577$	7.65437	−	43.4101i	0.318655	−	1.80718i	0.550949	−	0.834539i	$-0.314266\pi$
$578$		0			0
$579$	−3.29448	+	2.76440i	−0.136914	+	0.114885i
$580$		0			0
$581$	2.55049	−	4.41757i	0.105812	−	0.183272i
$582$		0			0
$583$	−20.4126	−	17.1282i	−0.845402	−	0.709377i
$584$		0			0
$585$	1.56448	+	8.87262i	0.0646834	+	0.366838i
$586$		0			0
$587$	7.00630	+	39.7347i	0.289181	+	1.64003i	0.689957	+	0.723850i	$0.257629\pi$
$587$	7.00630	+	39.7347i	0.289181	+	1.64003i	−0.400776	+	0.916176i	$0.631260\pi$
$588$		0			0
$589$	36.5075	+	13.2876i	1.50426	+	0.547507i
$590$		0			0
$591$	12.5273			0.515305
$592$		0			0
$593$	−16.9490			−0.696012			−0.348006	−	0.937492i	$-0.613141\pi$
$593$	−16.9490			−0.696012			−0.348006	+	0.937492i	$0.613141\pi$
$594$		0			0
$595$	−10.1754	−	3.70355i	−0.417151	−	0.151831i
$596$		0			0
$597$	−2.09067	−	11.8568i	−0.0855656	−	0.485267i
$598$		0			0
$599$	−0.819233	−	4.64610i	−0.0334730	−	0.189835i	0.963486	−	0.267757i	$-0.0862825\pi$
$599$	−0.819233	−	4.64610i	−0.0334730	−	0.189835i	−0.996959	+	0.0779225i	$0.975171\pi$
$600$		0			0
$601$	11.1215	+	9.33207i	0.453656	+	0.380663i	0.840791	−	0.541360i	$-0.182091\pi$
$601$	11.1215	+	9.33207i	0.453656	+	0.380663i	−0.387134	+	0.922023i	$0.626535\pi$
$602$		0			0
$603$	−7.32874	+	12.6937i	−0.298449	+	0.516929i
$604$		0			0
$605$	−28.7501	+	24.1242i	−1.16886	+	0.980787i
$606$		0			0
$607$	5.44106	−	30.8578i	0.220846	−	1.25248i	−0.649624	−	0.760256i	$-0.725074\pi$
$607$	5.44106	−	30.8578i	0.220846	−	1.25248i	0.870469	−	0.492223i	$-0.163815\pi$
$608$		0			0
$609$	6.70530	+	5.62641i	0.271712	+	0.227994i
$610$		0			0
$611$	4.19692	+	1.52755i	0.169789	+	0.0617982i
$612$		0			0
$613$	−0.896248	+	5.08288i	−0.0361991	+	0.205295i	−0.997543	−	0.0700546i	$-0.977683\pi$
$613$	−0.896248	+	5.08288i	−0.0361991	+	0.205295i	0.961344	+	0.275350i	$0.0887938\pi$
$614$		0			0
$615$	8.56202	+	14.8299i	0.345254	+	0.597997i
$616$		0			0
$617$	18.4413	−	6.71208i	0.742418	−	0.270218i	0.0570062	−	0.998374i	$-0.481845\pi$
$617$	18.4413	−	6.71208i	0.742418	−	0.270218i	0.685412	+	0.728156i	$0.259622\pi$
$618$		0			0
$619$	14.9881	+	25.9602i	0.602423	+	1.04343i	0.992453	+	0.122625i	$0.0391311\pi$
$619$	14.9881	+	25.9602i	0.602423	+	1.04343i	−0.390031	+	0.920802i	$0.627536\pi$
$620$		0			0
$621$	0.772973	−	1.33883i	0.0310183	−	0.0537253i
$622$		0			0
$623$	−15.7117			−0.629478
$624$		0			0
$625$	−23.8982	+	20.0530i	−0.955929	+	0.802120i
$626$		0			0
$627$	31.1997	−	11.3558i	1.24600	−	0.453506i
$628$		0			0
$629$	2.60906	−	15.1003i	0.104030	−	0.602087i
$630$		0			0
$631$	40.6995	−	14.8134i	1.62022	−	0.589713i	0.636798	−	0.771031i	$-0.280259\pi$
$631$	40.6995	−	14.8134i	1.62022	−	0.589713i	0.983424	+	0.181318i	$0.0580364\pi$
$632$		0			0
$633$	−11.5221	+	9.66816i	−0.457961	+	0.384275i
$634$		0			0
$635$	48.7626			1.93509
$636$		0			0
$637$	−7.46923	+	12.9371i	−0.295942	+	0.512586i
$638$		0			0
$639$	1.91196	+	3.31160i	0.0756358	+	0.131005i
$640$		0			0
$641$	35.6830	−	12.9875i	1.40939	−	0.512977i	0.478441	−	0.878120i	$-0.341202\pi$
$641$	35.6830	−	12.9875i	1.40939	−	0.512977i	0.930951	+	0.365143i	$0.118980\pi$
$642$		0			0
$643$	−18.8789	−	32.6993i	−0.744512	−	1.28953i	−0.950422	−	0.310962i	$-0.899349\pi$
$643$	−18.8789	−	32.6993i	−0.744512	−	1.28953i	0.205910	−	0.978571i	$-0.433984\pi$
$644$		0			0
$645$	0.773211	−	4.38510i	0.0304451	−	0.172663i
$646$		0			0
$647$	−2.97944	−	1.08443i	−0.117134	−	0.0426333i	0.282788	−	0.959182i	$-0.408741\pi$
$647$	−2.97944	−	1.08443i	−0.117134	−	0.0426333i	−0.399922	+	0.916549i	$0.630963\pi$
$648$		0			0
$649$	2.65453	+	2.22742i	0.104200	+	0.0874338i
$650$		0			0
$651$	1.55477	−	8.81751i	0.0609361	−	0.345586i
$652$		0			0
$653$	11.3883	−	9.55595i	0.445660	−	0.373953i	−0.392162	−	0.919896i	$-0.628273\pi$
$653$	11.3883	−	9.55595i	0.445660	−	0.373953i	0.837823	+	0.545943i	$0.183828\pi$
$654$		0			0
$655$	28.9350	−	50.1169i	1.13058	−	1.95823i
$656$		0			0
$657$	−1.21299	−	1.01782i	−0.0473233	−	0.0397089i
$658$		0			0
$659$	6.09157	+	34.5470i	0.237294	+	1.34576i	0.837729	+	0.546086i	$0.183883\pi$
$659$	6.09157	+	34.5470i	0.237294	+	1.34576i	−0.600435	+	0.799673i	$0.705006\pi$
$660$		0			0
$661$	7.84310	+	44.4804i	0.305061	+	1.73009i	0.623216	+	0.782049i	$0.285826\pi$
$661$	7.84310	+	44.4804i	0.305061	+	1.73009i	−0.318155	+	0.948039i	$0.603063\pi$
$662$		0			0
$663$	−7.67109	−	2.79205i	−0.297920	−	0.108434i
$664$		0			0
$665$	28.8330			1.11810
$666$		0			0
$667$	−8.75314			−0.338923
$668$		0			0
$669$	−17.5202	−	6.37684i	−0.677371	−	0.246543i
$670$		0			0
$671$	−10.5893	−	60.0550i	−0.408796	−	2.31840i
$672$		0			0
$673$	4.33031	+	24.5584i	0.166921	+	0.946657i	0.947062	+	0.321052i	$0.104036\pi$
$673$	4.33031	+	24.5584i	0.166921	+	0.946657i	−0.780140	+	0.625604i	$0.784852\pi$
$674$		0			0
$675$	2.09159	+	1.75506i	0.0805055	+	0.0675522i
$676$		0			0
$677$	18.9510	−	32.8241i	0.728347	−	1.26153i	−0.229235	−	0.973371i	$-0.573622\pi$
$677$	18.9510	−	32.8241i	0.728347	−	1.26153i	0.957581	−	0.288163i	$-0.0930444\pi$
$678$		0			0
$679$	18.6874	−	15.6806i	0.717157	−	0.601766i
$680$		0			0
$681$	−0.924465	+	5.24290i	−0.0354256	+	0.200909i
$682$		0			0
$683$	−14.3106	−	12.0080i	−0.547581	−	0.459475i	0.326540	−	0.945183i	$-0.394117\pi$
$683$	−14.3106	−	12.0080i	−0.547581	−	0.459475i	−0.874121	+	0.485708i	$0.838562\pi$
$684$		0			0
$685$	−25.3091	−	9.21177i	−0.967012	−	0.351964i
$686$		0			0
$687$	1.50469	−	8.53353i	0.0574076	−	0.325575i
$688$		0			0
$689$	−8.72257	−	15.1079i	−0.332303	−	0.575566i
$690$		0			0
$691$	43.6586	−	15.8904i	1.66085	−	0.604501i	0.670355	−	0.742040i	$-0.266142\pi$
$691$	43.6586	−	15.8904i	1.66085	−	0.604501i	0.990496	+	0.137540i	$0.0439195\pi$
$692$		0			0
$693$	−3.82590	−	6.62665i	−0.145334	−	0.251726i
$694$		0			0
$695$	−21.3884	+	37.0458i	−0.811309	+	1.40523i
$696$		0			0
$697$	−15.5159			−0.587707
$698$		0			0
$699$	−17.5753	+	14.7474i	−0.664758	+	0.557798i
$700$		0			0
$701$	−19.9896	+	7.27563i	−0.754998	+	0.274797i	−0.690707	−	0.723135i	$-0.742701\pi$
$701$	−19.9896	+	7.27563i	−0.754998	+	0.274797i	−0.0642905	+	0.997931i	$0.520478\pi$
$702$		0			0
$703$	7.22360	+	40.1589i	0.272443	+	1.51462i
$704$		0			0
$705$	3.60107	−	1.31068i	0.135624	−	0.0493631i
$706$		0			0
$707$	10.3017	−	8.64417i	0.387436	−	0.325097i
$708$		0			0
$709$	7.50197			0.281743			0.140871	−	0.990028i	$-0.455010\pi$
$709$	7.50197			0.281743			0.140871	+	0.990028i	$0.455010\pi$
$710$		0			0
$711$	−4.77818	+	8.27605i	−0.179196	+	0.310376i
$712$		0			0
$713$	4.47677	+	7.75399i	0.167656	+	0.290389i
$714$		0			0
$715$	−41.9040	+	15.2518i	−1.56712	+	0.570385i
$716$		0			0
$717$	13.7444	+	23.8060i	0.513293	+	0.889050i
$718$		0			0
$719$	0.764384	−	4.33504i	0.0285067	−	0.161670i	−0.967231	−	0.253897i	$-0.918288\pi$
$719$	0.764384	−	4.33504i	0.0285067	−	0.161670i	0.995738	+	0.0922275i	$0.0293987\pi$
$720$		0			0
$721$	−10.3070	−	3.75145i	−0.383854	−	0.139711i
$722$		0			0
$723$	−20.5695	−	17.2599i	−0.764989	−	0.641902i
$724$		0			0
$725$	2.68450	−	15.2246i	0.0996999	−	0.565426i
$726$		0			0
$727$	3.36957	−	2.82741i	0.124971	−	0.104863i	−0.578160	−	0.815923i	$-0.696229\pi$
$727$	3.36957	−	2.82741i	0.124971	−	0.104863i	0.703131	+	0.711060i	$0.251785\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	3.09067	+	2.59338i	0.114312	+	0.0959196i
$732$		0			0
$733$	3.11342	+	17.6571i	0.114997	+	0.652178i	0.986752	+	0.162237i	$0.0518708\pi$
$733$	3.11342	+	17.6571i	0.114997	+	0.652178i	−0.871755	+	0.489942i	$0.837018\pi$
$734$		0			0
$735$	2.22575	+	12.6229i	0.0820981	+	0.465601i
$736$		0			0
$737$	−68.1733	−	24.8131i	−2.51120	−	0.914001i
$738$		0			0
$739$	−6.28055			−0.231034			−0.115517	−	0.993306i	$-0.536852\pi$
$739$	−6.28055			−0.231034			−0.115517	+	0.993306i	$0.536852\pi$
$740$		0			0
$741$	21.7368			0.798520
$742$		0			0
$743$	−23.8162	−	8.66840i	−0.873733	−	0.318013i	−0.134055	−	0.990974i	$-0.542800\pi$
$743$	−23.8162	−	8.66840i	−0.873733	−	0.318013i	−0.739678	+	0.672961i	$0.765022\pi$
$744$		0			0
$745$	−5.08387	−	28.8321i	−0.186259	−	1.05633i
$746$		0			0
$747$	−0.572967	−	3.24946i	−0.0209638	−	0.118891i
$748$		0			0
$749$	−6.23543	−	5.23215i	−0.227838	−	0.191179i
$750$		0			0
$751$	5.13263	−	8.88998i	0.187292	−	0.324400i	−0.757054	−	0.653352i	$-0.773362\pi$
$751$	5.13263	−	8.88998i	0.187292	−	0.324400i	0.944347	+	0.328952i	$0.106695\pi$
$752$		0			0
$753$	12.6785	−	10.6385i	0.462031	−	0.387690i
$754$		0			0
$755$	−5.27747	+	29.9300i	−0.192067	+	1.08927i
$756$		0			0
$757$	−32.0848	−	26.9223i	−1.16614	−	0.978509i	−0.166171	−	0.986097i	$-0.553140\pi$
$757$	−32.0848	−	26.9223i	−1.16614	−	0.978509i	−0.999971	+	0.00758789i	$0.997585\pi$
$758$		0			0
$759$	7.19034	+	2.61707i	0.260993	+	0.0949936i
$760$		0			0
$761$	4.13326	−	23.4409i	0.149831	−	0.849731i	−0.813530	−	0.581523i	$-0.802457\pi$
$761$	4.13326	−	23.4409i	0.149831	−	0.849731i	0.963361	−	0.268209i	$-0.0864317\pi$
$762$		0			0
$763$	2.92158	+	5.06033i	0.105768	+	0.183196i
$764$		0			0
$765$	−6.58200	+	2.39565i	−0.237973	+	0.0866149i
$766$		0			0
$767$	1.13432	+	1.96470i	0.0409578	+	0.0709410i
$768$		0			0
$769$	11.8051	−	20.4470i	0.425702	−	0.737337i	−0.570784	−	0.821100i	$-0.693361\pi$
$769$	11.8051	−	20.4470i	0.425702	−	0.737337i	0.996486	+	0.0837634i	$0.0266940\pi$
$770$		0			0
$771$	26.5191			0.955061
$772$		0			0
$773$	−27.7703	+	23.3021i	−0.998829	+	0.838117i	−0.986822	−	0.161811i	$-0.948267\pi$
$773$	−27.7703	+	23.3021i	−0.998829	+	0.838117i	−0.0120075	+	0.999928i	$0.503822\pi$
$774$		0			0
$775$	−14.8597	+	5.40849i	−0.533776	+	0.194279i
$776$		0			0
$777$	8.82540	−	3.24660i	0.316609	−	0.116471i
$778$		0			0
$779$	38.8228	−	14.1303i	1.39097	−	0.506272i
$780$		0			0
$781$	−14.4988	+	12.1659i	−0.518807	+	0.435331i
$782$		0			0
$783$	5.66200			0.202343
$784$		0			0
$785$	−12.1796	+	21.0957i	−0.434709	+	0.752938i
$786$		0			0
$787$	−25.8414	−	44.7587i	−0.921148	−	1.59547i	−0.797642	−	0.603131i	$-0.793920\pi$
$787$	−25.8414	−	44.7587i	−0.921148	−	1.59547i	−0.123505	−	0.992344i	$-0.539414\pi$
$788$		0			0
$789$	−2.11306	+	0.769091i	−0.0752270	+	0.0273804i
$790$		0			0
$791$	7.86078	+	13.6153i	0.279497	+	0.484104i
$792$		0			0
$793$	6.93264	−	39.3169i	0.246185	−	1.39619i
$794$		0			0
$795$	−14.0657	−	5.11949i	−0.498858	−	0.181570i
$796$		0			0
$797$	−33.2954	−	27.9382i	−1.17938	−	0.989621i	−0.999983	−	0.00584453i	$-0.998140\pi$
$797$	−33.2954	−	27.9382i	−1.17938	−	0.989621i	−0.179401	−	0.983776i	$-0.557416\pi$
$798$		0			0
$799$	−0.602957	+	3.41954i	−0.0213311	+	0.120975i
$800$		0			0
$801$	−7.78546	+	6.53277i	−0.275086	+	0.230824i
$802$		0			0
$803$	3.91871	−	6.78740i	0.138288	−	0.239522i
$804$		0			0
$805$	5.09029	+	4.27126i	0.179409	+	0.150542i
$806$		0			0
$807$	0.902908	+	5.12065i	0.0317839	+	0.180255i
$808$		0			0
$809$	−2.44363	−	13.8585i	−0.0859134	−	0.487239i	−0.997156	−	0.0753685i	$-0.975987\pi$
$809$	−2.44363	−	13.8585i	−0.0859134	−	0.487239i	0.911242	−	0.411871i	$-0.135124\pi$
$810$		0			0
$811$	−16.1066	−	5.86231i	−0.565578	−	0.205854i	0.0433764	−	0.999059i	$-0.486189\pi$
$811$	−16.1066	−	5.86231i	−0.565578	−	0.205854i	−0.608954	+	0.793205i	$0.708411\pi$
$812$		0			0
$813$	5.35133			0.187679
$814$		0			0
$815$	25.5053			0.893411
$816$		0			0
$817$	−10.0950	−	3.67430i	−0.353181	−	0.128547i
$818$		0			0
$819$	−0.869890	−	4.93339i	−0.0303964	−	0.172387i
$820$		0			0
$821$	−2.90727	−	16.4880i	−0.101464	−	0.575433i	−0.992574	−	0.121645i	$-0.961183\pi$
$821$	−2.90727	−	16.4880i	−0.101464	−	0.575433i	0.891109	−	0.453789i	$-0.149928\pi$
$822$		0			0
$823$	25.9980	+	21.8149i	0.906233	+	0.760420i	0.971399	−	0.237454i	$-0.0763130\pi$
$823$	25.9980	+	21.8149i	0.906233	+	0.760420i	−0.0651653	+	0.997874i	$0.520757\pi$
$824$		0			0
$825$	−6.75714	+	11.7037i	−0.235253	+	0.407471i
$826$		0			0
$827$	−4.28826	+	3.59828i	−0.149117	+	0.125124i	−0.714294	−	0.699845i	$-0.753252\pi$
$827$	−4.28826	+	3.59828i	−0.149117	+	0.125124i	0.565177	+	0.824970i	$0.308808\pi$
$828$		0			0
$829$	5.97913	−	33.9093i	0.207664	−	1.17772i	−0.685529	−	0.728045i	$-0.740429\pi$
$829$	5.97913	−	33.9093i	0.207664	−	1.17772i	0.893193	−	0.449674i	$-0.148460\pi$
$830$		0			0
$831$	22.1183	+	18.5595i	0.767276	+	0.643821i
$832$		0			0
$833$	−10.9135	−	3.97218i	−0.378129	−	0.137628i
$834$		0			0
$835$	−7.13772	+	40.4800i	−0.247011	+	1.40087i
$836$		0			0
$837$	−2.89581	−	5.01569i	−0.100094	−	0.173368i
$838$		0			0
$839$	−20.6383	+	7.51172i	−0.712512	+	0.259333i	−0.672744	−	0.739876i	$-0.734884\pi$
$839$	−20.6383	+	7.51172i	−0.712512	+	0.259333i	−0.0397686	+	0.999209i	$0.512662\pi$
$840$		0			0
$841$	−1.52912	−	2.64852i	−0.0527283	−	0.0913281i
$842$		0			0
$843$	15.1732	−	26.2807i	0.522592	−	0.905156i
$844$		0			0
$845$	6.95020			0.239094
$846$		0			0
$847$	15.9857	−	13.4136i	0.549276	−	0.460897i
$848$		0			0
$849$	3.92687	−	1.42926i	0.134770	−	0.0490521i
$850$		0			0
$851$	−4.67377	+	8.15990i	−0.160215	+	0.279718i
$852$		0			0
$853$	−6.10815	+	2.22319i	−0.209139	+	0.0761205i	−0.444465	−	0.895796i	$-0.646606\pi$
$853$	−6.10815	+	2.22319i	−0.209139	+	0.0761205i	0.235326	+	0.971916i	$0.424384\pi$
$854$		0			0
$855$	14.2873	−	11.9885i	0.488615	−	0.409997i
$856$		0			0
$857$	−27.5253			−0.940247			−0.470124	−	0.882601i	$-0.655791\pi$
$857$	−27.5253			−0.940247			−0.470124	+	0.882601i	$0.655791\pi$
$858$		0			0
$859$	−5.99408	+	10.3821i	−0.204515	+	0.354231i	−0.949978	−	0.312316i	$-0.898895\pi$
$859$	−5.99408	+	10.3821i	−0.204515	+	0.354231i	0.745463	+	0.666547i	$0.232228\pi$
$860$		0			0
$861$	−4.76069	−	8.24576i	−0.162244	−	0.281015i
$862$		0			0
$863$	4.19411	−	1.52653i	0.142769	−	0.0519638i	−0.269647	−	0.962959i	$-0.586907\pi$
$863$	4.19411	−	1.52653i	0.142769	−	0.0519638i	0.412417	+	0.910995i	$0.364685\pi$
$864$		0			0
$865$	−11.6009	−	20.0933i	−0.394442	−	0.683193i
$866$		0			0
$867$	−1.84994	+	10.4915i	−0.0628273	+	0.356311i
$868$		0			0
$869$	−44.4475	−	16.1776i	−1.50778	−	0.548786i
$870$		0			0
$871$	−36.3842	−	30.5300i	−1.23283	−	1.03447i
$872$		0			0
$873$	2.74013	−	15.5400i	0.0927393	−	0.525951i
$874$		0			0
$875$	7.47311	−	6.27068i	0.252637	−	0.211988i
$876$		0			0
$877$	−14.9127	+	25.8295i	−0.503565	+	0.872201i	0.496426	+	0.868079i	$0.334645\pi$
$877$	−14.9127	+	25.8295i	−0.503565	+	0.872201i	−0.999992	+	0.00412172i	$0.998688\pi$
$878$		0			0
$879$	−0.352993	−	0.296197i	−0.0119062	−	0.00999046i
$880$		0			0
$881$	−3.28822	−	18.6484i	−0.110783	−	0.628281i	−0.988752	−	0.149564i	$-0.952213\pi$
$881$	−3.28822	−	18.6484i	−0.110783	−	0.628281i	0.877969	−	0.478717i	$-0.158898\pi$
$882$		0			0
$883$	−3.61927	−	20.5259i	−0.121798	−	0.690751i	−0.983158	−	0.182756i	$-0.941498\pi$
$883$	−3.61927	−	20.5259i	−0.121798	−	0.690751i	0.861360	−	0.507995i	$-0.169613\pi$
$884$		0			0
$885$	1.82916	+	0.665759i	0.0614865	+	0.0223792i
$886$		0			0
$887$	21.7818			0.731361			0.365681	−	0.930740i	$-0.380836\pi$
$887$	21.7818			0.731361			0.365681	+	0.930740i	$0.380836\pi$
$888$		0			0
$889$	−27.1132			−0.909347
$890$		0			0
$891$	−4.65109	−	1.69286i	−0.155818	−	0.0567129i
$892$		0			0
$893$	−1.60550	−	9.10525i	−0.0537260	−	0.304695i
$894$		0			0
$895$	−0.356635	−	2.02258i	−0.0119210	−	0.0676072i
$896$		0			0
$897$	3.83750	+	3.22004i	0.128130	+	0.107514i
$898$		0			0
$899$	−16.3961	+	28.3989i	−0.546840	+	0.947155i
$900$		0			0
$901$	10.3896	−	8.71793i	0.346128	−	0.290436i
$902$		0			0
$903$	−0.429924	+	2.43822i	−0.0143070	+	0.0811389i
$904$		0			0
$905$	−30.4738	−	25.5705i	−1.01298	−	0.849993i
$906$		0			0
$907$	−24.5304	−	8.92835i	−0.814520	−	0.296461i	−0.0990302	−	0.995084i	$-0.531574\pi$
$907$	−24.5304	−	8.92835i	−0.814520	−	0.296461i	−0.715489	+	0.698624i	$0.753796\pi$
$908$		0			0
$909$	1.51054	−	8.56669i	0.0501014	−	0.284139i
$910$		0			0
$911$	27.2467	+	47.1927i	0.902724	+	1.56356i	0.823943	+	0.566672i	$0.191769\pi$
$911$	27.2467	+	47.1927i	0.902724	+	1.56356i	0.0787808	+	0.996892i	$0.474897\pi$
$912$		0			0
$913$	15.3467	−	5.58573i	0.507901	−	0.184861i
$914$		0			0
$915$	−17.1277	−	29.6660i	−0.566224	−	0.980729i
$916$		0			0
$917$	−16.0886	+	27.8662i	−0.531291	+	0.920223i
$918$		0			0
$919$	−6.97809			−0.230186			−0.115093	−	0.993355i	$-0.536717\pi$
$919$	−6.97809			−0.230186			−0.115093	+	0.993355i	$0.536717\pi$
$920$		0			0
$921$	−21.2153	+	17.8017i	−0.699067	+	0.586587i
$922$		0			0
$923$	−11.6438	+	4.23798i	−0.383259	+	0.139495i
$924$		0			0
$925$	−12.7593	−	10.6318i	−0.419524	−	0.349570i
$926$		0			0
$927$	−6.66714	+	2.42664i	−0.218977	+	0.0797013i
$928$		0			0
$929$	−18.3473	+	15.3952i	−0.601957	+	0.505102i	−0.892074	−	0.451890i	$-0.850750\pi$
$929$	−18.3473	+	15.3952i	−0.601957	+	0.505102i	0.290117	+	0.956991i	$0.406306\pi$
$930$		0			0
$931$	30.9244			1.01351
$932$		0			0
$933$	13.4765	−	23.3419i	0.441200	−	0.764181i
$934$		0			0
$935$	−17.3345	−	30.0242i	−0.566899	−	0.981897i
$936$		0			0
$937$	−32.7223	+	11.9100i	−1.06899	+	0.389081i	−0.815800	−	0.578335i	$-0.803703\pi$
$937$	−32.7223	+	11.9100i	−1.06899	+	0.389081i	−0.253192	+	0.967416i	$0.581481\pi$
$938$		0			0
$939$	−7.71760	−	13.3673i	−0.251854	−	0.436224i
$940$		0			0
$941$	−0.866931	+	4.91661i	−0.0282612	+	0.160277i	−0.995672	−	0.0929338i	$-0.970376\pi$
$941$	−0.866931	+	4.91661i	−0.0282612	+	0.160277i	0.967411	+	0.253211i	$0.0814866\pi$
$942$		0			0
$943$	8.94717	+	3.25650i	0.291360	+	0.106046i
$944$		0			0
$945$	−3.29267	−	2.76288i	−0.107111	−	0.0898765i
$946$		0			0
$947$	7.81678	−	44.3312i	0.254011	−	1.44057i	−0.544587	−	0.838704i	$-0.683314\pi$
$947$	7.81678	−	44.3312i	0.254011	−	1.44057i	0.798598	−	0.601865i	$-0.205575\pi$
$948$		0			0
$949$	3.93058	−	3.29815i	0.127592	−	0.107063i
$950$		0			0
$951$	3.00289	−	5.20117i	0.0973755	−	0.168659i
$952$		0			0
$953$	−33.2341	−	27.8867i	−1.07656	−	0.903340i	−0.0809282	−	0.996720i	$-0.525788\pi$
$953$	−33.2341	−	27.8867i	−1.07656	−	0.903340i	−0.995631	+	0.0933799i	$0.970233\pi$
$954$		0			0
$955$	11.4953	+	65.1930i	0.371979	+	2.10960i
$956$		0			0
$957$	4.86642	+	27.5988i	0.157309	+	0.892144i
$958$		0			0
$959$	14.0725	+	5.12197i	0.454424	+	0.165397i
$960$		0			0
$961$	2.54293			0.0820298
$962$		0			0
$963$	−5.26524			−0.169670
$964$		0			0
$965$	−11.2362	−	4.08964i	−0.361706	−	0.131650i
$966$		0			0
$967$	−1.20529	−	6.83557i	−0.0387597	−	0.219817i	0.959276	−	0.282472i	$-0.0911544\pi$
$967$	−1.20529	−	6.83557i	−0.0387597	−	0.219817i	−0.998035	+	0.0626549i	$0.980043\pi$
$968$		0			0
$969$	2.93452	+	16.6425i	0.0942703	+	0.534633i
$970$		0			0
$971$	21.5661	+	18.0961i	0.692089	+	0.580731i	0.919511	−	0.393065i	$-0.128585\pi$
$971$	21.5661	+	18.0961i	0.692089	+	0.580731i	−0.227422	+	0.973796i	$0.573030\pi$
$972$		0			0
$973$	11.8925	−	20.5984i	0.381255	−	0.660353i
$974$		0			0
$975$	−6.77762	+	5.68710i	−0.217058	+	0.182133i
$976$		0			0
$977$	−0.440793	+	2.49986i	−0.0141022	+	0.0799777i	−0.991047	−	0.133516i	$-0.957373\pi$
$977$	−0.440793	+	2.49986i	−0.0141022	+	0.0799777i	0.976944	+	0.213494i	$0.0684843\pi$
$978$		0			0
$979$	−38.5348	−	32.3346i	−1.23158	−	1.03342i
$980$		0			0
$981$	3.55173	+	1.29272i	0.113398	+	0.0412735i
$982$		0			0
$983$	3.01201	−	17.0819i	0.0960681	−	0.544829i	−0.898347	−	0.439287i	$-0.855231\pi$
$983$	3.01201	−	17.0819i	0.0960681	−	0.544829i	0.994415	−	0.105542i	$-0.0336578\pi$
$984$		0			0
$985$	17.4152	+	30.1640i	0.554894	+	0.961105i
$986$		0			0
$987$	−2.00228	+	0.728771i	−0.0637333	+	0.0231970i
$988$		0			0
$989$	−1.23792	−	2.14413i	−0.0393635	−	0.0681795i
$990$		0			0
$991$	−6.67355	+	11.5589i	−0.211992	+	0.367181i	−0.952338	−	0.305045i	$-0.901328\pi$
$991$	−6.67355	+	11.5589i	−0.211992	+	0.367181i	0.740346	+	0.672226i	$0.234662\pi$
$992$		0			0
$993$	2.33836			0.0742055
$994$		0			0
$995$	25.6431	−	21.5171i	0.812941	−	0.682139i
$996$		0			0
$997$	33.6380	−	12.2432i	1.06533	−	0.387747i	0.250899	−	0.968013i	$-0.419274\pi$
$997$	33.6380	−	12.2432i	1.06533	−	0.387747i	0.814427	+	0.580266i	$0.197052\pi$
$998$		0			0
$999$	3.02325	−	5.27826i	0.0956512	−	0.166997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.673.2	✓	24
37.16	even	9	inner	888.2.bo.c.793.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.673.2	✓	24	1.1	even	1	trivial
888.2.bo.c.793.2	yes	24	37.16	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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(-0.482804 - 2.73812i) q^{5} +(0.268451 + 1.52246i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(-0.482804 - 2.73812i) q^{5} +(0.268451 + 1.52246i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.47480 + 4.28647i) q^{11} +(-2.48230 + 2.08289i) q^{13} +(-0.482804 + 2.73812i) q^{15} +(-1.92986 - 1.61934i) q^{17} +(6.30349 + 2.29428i) q^{19} +(0.268451 - 1.52246i) q^{21} +(0.772973 + 1.33883i) q^{23} +(-2.56572 + 0.933846i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-2.83100 + 4.90344i) q^{29} +5.79163 q^{31} +(3.79161 - 3.18154i) q^{33} +(4.03906 - 1.47010i) q^{35} +(3.05948 + 5.25734i) q^{37} +(3.04499 - 1.10829i) q^{39} +(4.71802 - 3.95889i) q^{41} -1.60150 q^{43} +(1.39018 - 2.40786i) q^{45} +(-0.689152 - 1.19365i) q^{47} +(4.33203 - 1.57673i) q^{49} +(1.25963 + 2.18173i) q^{51} +(-0.934856 + 5.30183i) q^{53} +(12.9317 + 4.70675i) q^{55} +(-5.13865 - 4.31184i) q^{57} +(0.121572 - 0.689471i) q^{59} +(-9.43805 + 7.91947i) q^{61} +(-0.772973 + 1.33883i) q^{63} +(6.90167 + 5.79119i) q^{65} +(2.54524 + 14.4348i) q^{67} +(-0.268451 - 1.52246i) q^{69} +(3.59330 + 1.30785i) q^{71} -1.58345 q^{73} +2.73038 q^{75} +(-7.19034 - 2.61707i) q^{77} +(1.65944 + 9.41117i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-2.52763 - 2.12093i) q^{83} +(-3.50221 + 6.06600i) q^{85} +(4.33734 - 3.63946i) q^{87} +(-1.76482 + 10.0088i) q^{89} +(-3.83750 - 3.22004i) q^{91} +(-5.44235 - 1.98085i) q^{93} +(3.23866 - 18.3674i) q^{95} +(-7.88989 - 13.6657i) q^{97} +(-4.65109 + 1.69286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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