LMFDB - Embedded newform 891.2.n.l.433.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			433.6
Character	$\chi$	$=$	891.433
Dual form			891.2.n.l.784.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0658016 + 0.626061i) q^{2} +(1.56867 + 0.333432i) q^{4} +(-0.142868 - 1.35930i) q^{5} +(-0.393445 + 0.436965i) q^{7} +(-0.701028 + 2.15754i) q^{8} +0.860404 q^{10} +(0.927090 - 3.18442i) q^{11} +(3.47139 - 1.54556i) q^{13} +(-0.247677 - 0.275073i) q^{14} +(1.62551 + 0.723726i) q^{16} +(-0.156539 + 0.113732i) q^{17} +(-0.601281 + 1.85055i) q^{19} +(0.229120 - 2.17993i) q^{20} +(1.93263 + 0.789954i) q^{22} +(0.160616 - 0.278195i) q^{23} +(3.06346 - 0.651158i) q^{25} +(0.739193 + 2.27500i) q^{26} +(-0.762884 + 0.554268i) q^{28} +(2.79122 - 3.09996i) q^{29} +(5.14837 - 2.29220i) q^{31} +(-2.82863 + 4.89933i) q^{32} +(-0.0609029 - 0.105487i) q^{34} +(0.650176 + 0.472381i) q^{35} +(3.17822 + 9.78156i) q^{37} +(-1.11899 - 0.498208i) q^{38} +(3.03290 + 0.644662i) q^{40} +(-4.59078 - 5.09857i) q^{41} +(-3.40544 - 5.89840i) q^{43} +(2.51609 - 4.68619i) q^{44} +(0.163598 + 0.118861i) q^{46} +(4.97666 - 1.05782i) q^{47} +(0.695560 + 6.61781i) q^{49} +(0.206084 + 1.96076i) q^{50} +(5.96082 - 1.26701i) q^{52} +(6.36368 + 4.62348i) q^{53} +(-4.46102 - 0.805240i) q^{55} +(-0.666954 - 1.15520i) q^{56} +(1.75710 + 1.95146i) q^{58} +(-7.04719 - 1.49793i) q^{59} +(-7.89061 - 3.51312i) q^{61} +(1.09629 + 3.37402i) q^{62} +(-0.00210888 - 0.00153219i) q^{64} +(-2.59683 - 4.49784i) q^{65} +(4.54870 - 7.87858i) q^{67} +(-0.283481 + 0.126214i) q^{68} +(-0.338522 + 0.375966i) q^{70} +(-2.31775 + 1.68394i) q^{71} +(0.131206 + 0.403812i) q^{73} +(-6.33298 + 1.34612i) q^{74} +(-1.56025 + 2.70242i) q^{76} +(1.02672 + 1.65800i) q^{77} +(0.429138 - 4.08298i) q^{79} +(0.751525 - 2.31296i) q^{80} +(3.49410 - 2.53861i) q^{82} +(6.79686 + 3.02616i) q^{83} +(0.176961 + 0.196535i) q^{85} +(3.91684 - 1.74389i) q^{86} +(6.22060 + 4.23260i) q^{88} -3.38915 q^{89} +(-0.690444 + 2.12497i) q^{91} +(0.344713 - 0.382842i) q^{92} +(0.334788 + 3.18530i) q^{94} +(2.60135 + 0.552935i) q^{95} +(-0.675694 + 6.42880i) q^{97} -4.18892 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) $ 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0658016	+	0.626061i	−0.0465288	+	0.442692i	0.946313	+	0.323253i	$0.104776\pi$
$2$	−0.0658016	+	0.626061i	−0.0465288	+	0.442692i	−0.992842	+	0.119439i	$0.961890\pi$
$3$		0			0
$3$		0			0
$4$	1.56867	+	0.333432i	0.784336	+	0.166716i
$5$	−0.142868	−	1.35930i	−0.0638925	−	0.607896i	−0.978883	−	0.204421i	$-0.934469\pi$
$5$	−0.142868	−	1.35930i	−0.0638925	−	0.607896i	0.914991	−	0.403475i	$-0.132198\pi$
$6$		0			0
$7$	−0.393445	+	0.436965i	−0.148708	+	0.165157i	−0.812897	−	0.582408i	$-0.802111\pi$
$7$	−0.393445	+	0.436965i	−0.148708	+	0.165157i	0.664188	+	0.747565i	$0.268777\pi$
$8$	−0.701028	+	2.15754i	−0.247851	+	0.762806i
$9$		0			0
$10$	0.860404			0.272084
$11$	0.927090	−	3.18442i	0.279528	−	0.960138i
$11$	0.927090	−	3.18442i	0.279528	−	0.960138i
$12$		0			0
$13$	3.47139	−	1.54556i	0.962791	−	0.428662i	0.135712	−	0.990748i	$-0.456668\pi$
$13$	3.47139	−	1.54556i	0.962791	−	0.428662i	0.827079	+	0.562086i	$0.190001\pi$
$14$	−0.247677	−	0.275073i	−0.0661945	−	0.0735165i
$15$		0			0
$16$	1.62551	+	0.723726i	0.406379	+	0.180931i
$17$	−0.156539	+	0.113732i	−0.0379663	+	0.0275842i	−0.606607	−	0.795002i	$-0.707470\pi$
$17$	−0.156539	+	0.113732i	−0.0379663	+	0.0275842i	0.568640	+	0.822586i	$0.307470\pi$
$18$		0			0
$19$	−0.601281	+	1.85055i	−0.137943	+	0.424546i	−0.996036	−	0.0889487i	$-0.971649\pi$
$19$	−0.601281	+	1.85055i	−0.137943	+	0.424546i	0.858093	+	0.513494i	$0.171649\pi$
$20$	0.229120	−	2.17993i	0.0512328	−	0.487447i
$21$		0			0
$22$	1.93263	+	0.789954i	0.412039	+	0.168419i
$23$	0.160616	−	0.278195i	0.0334907	−	0.0580076i	−0.848794	−	0.528723i	$-0.822671\pi$
$23$	0.160616	−	0.278195i	0.0334907	−	0.0580076i	0.882285	+	0.470716i	$0.156004\pi$
$24$		0			0
$25$	3.06346	−	0.651158i	0.612692	−	0.130232i
$26$	0.739193	+	2.27500i	0.144968	+	0.446165i
$27$		0			0
$28$	−0.762884	+	0.554268i	−0.144172	+	0.104747i
$29$	2.79122	−	3.09996i	0.518316	−	0.575649i	−0.425985	−	0.904730i	$-0.640072\pi$
$29$	2.79122	−	3.09996i	0.518316	−	0.575649i	0.944301	+	0.329082i	$0.106739\pi$
$30$		0			0
$31$	5.14837	−	2.29220i	0.924674	−	0.411692i	0.111535	−	0.993761i	$-0.464423\pi$
$31$	5.14837	−	2.29220i	0.924674	−	0.411692i	0.813139	+	0.582069i	$0.197757\pi$
$32$	−2.82863	+	4.89933i	−0.500036	+	0.866088i
$33$		0			0
$34$	−0.0609029	−	0.105487i	−0.0104448	−	0.0180908i
$35$	0.650176	+	0.472381i	0.109900	+	0.0798469i
$36$		0			0
$37$	3.17822	+	9.78156i	0.522496	+	1.60808i	0.769214	+	0.638991i	$0.220648\pi$
$37$	3.17822	+	9.78156i	0.522496	+	1.60808i	−0.246718	+	0.969087i	$0.579352\pi$
$38$	−1.11899	−	0.498208i	−0.181525	−	0.0808199i
$39$		0			0
$40$	3.03290	+	0.644662i	0.479543	+	0.101930i
$41$	−4.59078	−	5.09857i	−0.716959	−	0.796263i	0.269020	−	0.963135i	$-0.413300\pi$
$41$	−4.59078	−	5.09857i	−0.716959	−	0.796263i	−0.985979	+	0.166871i	$0.946634\pi$
$42$		0			0
$43$	−3.40544	−	5.89840i	−0.519325	−	0.899497i	−0.999748	−	0.0224601i	$-0.992850\pi$
$43$	−3.40544	−	5.89840i	−0.519325	−	0.899497i	0.480423	−	0.877037i	$-0.340483\pi$
$44$	2.51609	−	4.68619i	0.379314	−	0.706469i
$45$		0			0
$46$	0.163598	+	0.118861i	0.0241212	+	0.0175251i
$47$	4.97666	−	1.05782i	0.725920	−	0.154299i	0.169892	−	0.985463i	$-0.445658\pi$
$47$	4.97666	−	1.05782i	0.725920	−	0.154299i	0.556028	+	0.831163i	$0.312325\pi$
$48$		0			0
$49$	0.695560	+	6.61781i	0.0993657	+	0.945401i
$50$	0.206084	+	1.96076i	0.0291447	+	0.277293i
$51$		0			0
$52$	5.96082	−	1.26701i	0.826616	−	0.175703i
$53$	6.36368	+	4.62348i	0.874119	+	0.635084i	0.931689	−	0.363257i	$-0.118335\pi$
$53$	6.36368	+	4.62348i	0.874119	+	0.635084i	−0.0575702	+	0.998341i	$0.518335\pi$
$54$		0			0
$55$	−4.46102	−	0.805240i	−0.601524	−	0.108579i
$56$	−0.666954	−	1.15520i	−0.0891255	−	0.154370i
$57$		0			0
$58$	1.75710	+	1.95146i	0.230718	+	0.256239i
$59$	−7.04719	−	1.49793i	−0.917465	−	0.195013i	−0.275103	−	0.961415i	$-0.588712\pi$
$59$	−7.04719	−	1.49793i	−0.917465	−	0.195013i	−0.642362	+	0.766401i	$0.722045\pi$
$60$		0			0
$61$	−7.89061	−	3.51312i	−1.01029	−	0.449809i	−0.166245	−	0.986084i	$-0.553164\pi$
$61$	−7.89061	−	3.51312i	−1.01029	−	0.449809i	−0.844043	+	0.536275i	$0.819831\pi$
$62$	1.09629	+	3.37402i	0.139229	+	0.428501i
$63$		0			0
$64$	−0.00210888	−	0.00153219i	−0.000263611	−	0.000191524i
$65$	−2.59683	−	4.49784i	−0.322097	−	0.557889i
$66$		0			0
$67$	4.54870	−	7.87858i	0.555712	−	0.962522i	−0.442135	−	0.896948i	$-0.645779\pi$
$67$	4.54870	−	7.87858i	0.555712	−	0.962522i	0.997848	−	0.0655738i	$-0.0208878\pi$
$68$	−0.283481	+	0.126214i	−0.0343771	+	0.0153057i
$69$		0			0
$70$	−0.338522	+	0.375966i	−0.0404611	+	0.0449366i
$71$	−2.31775	+	1.68394i	−0.275066	+	0.199847i	−0.716763	−	0.697317i	$-0.754377\pi$
$71$	−2.31775	+	1.68394i	−0.275066	+	0.199847i	0.441696	+	0.897165i	$0.354377\pi$
$72$		0			0
$73$	0.131206	+	0.403812i	0.0153565	+	0.0472626i	0.958441	−	0.285290i	$-0.0920900\pi$
$73$	0.131206	+	0.403812i	0.0153565	+	0.0472626i	−0.943085	+	0.332553i	$0.892090\pi$
$74$	−6.33298	+	1.34612i	−0.736194	+	0.156483i
$75$		0			0
$76$	−1.56025	+	2.70242i	−0.178972	+	0.309989i
$77$	1.02672	+	1.65800i	0.117005	+	0.188946i
$78$		0			0
$79$	0.429138	−	4.08298i	0.0482818	−	0.459371i	−0.943495	−	0.331388i	$-0.892483\pi$
$79$	0.429138	−	4.08298i	0.0482818	−	0.459371i	0.991776	−	0.127983i	$-0.0408502\pi$
$80$	0.751525	−	2.31296i	0.0840230	−	0.258596i
$81$		0			0
$82$	3.49410	−	2.53861i	0.385859	−	0.280343i
$83$	6.79686	+	3.02616i	0.746052	+	0.332164i	0.744310	−	0.667835i	$-0.232779\pi$
$83$	6.79686	+	3.02616i	0.746052	+	0.332164i	0.00174242	+	0.999998i	$0.499445\pi$
$84$		0			0
$85$	0.176961	+	0.196535i	0.0191941	+	0.0213172i
$86$	3.91684	−	1.74389i	0.422364	−	0.188048i
$87$		0			0
$88$	6.22060	+	4.23260i	0.663118	+	0.451197i
$89$	−3.38915			−0.359249			−0.179625	−	0.983735i	$-0.557488\pi$
$89$	−3.38915			−0.359249			−0.179625	+	0.983735i	$0.557488\pi$
$90$		0			0
$91$	−0.690444	+	2.12497i	−0.0723782	+	0.222757i
$92$	0.344713	−	0.382842i	0.0359388	−	0.0399141i
$93$		0			0
$94$	0.334788	+	3.18530i	0.0345308	+	0.328538i
$95$	2.60135	+	0.552935i	0.266893	+	0.0567299i
$96$		0			0
$97$	−0.675694	+	6.42880i	−0.0686063	+	0.652746i	0.905141	+	0.425112i	$0.139765\pi$
$97$	−0.675694	+	6.42880i	−0.0686063	+	0.652746i	−0.973747	+	0.227633i	$0.926901\pi$
$98$	−4.18892			−0.423145
$99$		0			0
$100$	5.02268			0.502268
$101$	−1.93351	+	18.3961i	−0.192391	+	1.83048i	0.292921	+	0.956137i	$0.405373\pi$
$101$	−1.93351	+	18.3961i	−0.192391	+	1.83048i	−0.485312	+	0.874341i	$0.661294\pi$
$102$		0			0
$103$	−3.16596	−	0.672945i	−0.311951	−	0.0663072i	0.0492758	−	0.998785i	$-0.484309\pi$
$103$	−3.16596	−	0.672945i	−0.311951	−	0.0663072i	−0.361227	+	0.932478i	$0.617642\pi$
$104$	0.901075	+	8.57316i	0.0883577	+	0.840667i
$105$		0			0
$106$	−3.31332	+	3.67982i	−0.321818	+	0.357416i
$107$	−5.21311	+	16.0443i	−0.503970	+	1.55106i	0.298524	+	0.954402i	$0.403506\pi$
$107$	−5.21311	+	16.0443i	−0.503970	+	1.55106i	−0.802495	+	0.596659i	$0.796494\pi$
$108$		0			0
$109$	8.90745			0.853179			0.426589	−	0.904445i	$-0.359715\pi$
$109$	8.90745			0.853179			0.426589	+	0.904445i	$0.359715\pi$
$110$	0.797672	−	2.73988i	0.0760550	−	0.261238i
$111$		0			0
$112$	−0.955793	+	0.425547i	−0.0903140	+	0.0402104i
$113$	−1.93074	−	2.14430i	−0.181629	−	0.201719i	0.645454	−	0.763799i	$-0.276668\pi$
$113$	−1.93074	−	2.14430i	−0.181629	−	0.201719i	−0.827083	+	0.562080i	$0.810001\pi$
$114$		0			0
$115$	−0.401097	−	0.178580i	−0.0374024	−	0.0166526i
$116$	5.41213	−	3.93215i	0.502504	−	0.365091i
$117$		0			0
$118$	1.40151	−	4.31340i	0.129019	−	0.397081i
$119$	0.0118925	−	0.113150i	0.00109018	−	0.0103724i
$120$		0			0
$121$	−9.28101	−	5.90448i	−0.843728	−	0.536771i
$122$	2.71864	−	4.70883i	0.246134	−	0.426317i
$123$		0			0
$124$	8.84040	−	1.87908i	0.793891	−	0.168747i
$125$	−3.43459	−	10.5706i	−0.307199	−	0.945461i
$126$		0			0
$127$	1.03914	−	0.754980i	0.0922088	−	0.0669936i	−0.540726	−	0.841199i	$-0.681850\pi$
$127$	1.03914	−	0.754980i	0.0922088	−	0.0669936i	0.632934	+	0.774205i	$0.281850\pi$
$128$	−7.56980	+	8.40711i	−0.669082	+	0.743091i
$129$		0			0
$130$	2.98680	−	1.32981i	0.261960	−	0.116632i
$131$	−3.16899	+	5.48885i	−0.276876	+	0.479563i	−0.970607	−	0.240671i	$-0.922632\pi$
$131$	−3.16899	+	5.48885i	−0.276876	+	0.479563i	0.693731	+	0.720234i	$0.255966\pi$
$132$		0			0
$133$	−0.572055	−	0.990829i	−0.0496035	−	0.0859157i
$134$	4.63316	+	3.36619i	0.400244	+	0.290794i
$135$		0			0
$136$	−0.135644	−	0.417470i	−0.0116314	−	0.0357977i
$137$	15.1320	+	6.73719i	1.29281	+	0.575597i	0.933820	−	0.357744i	$-0.116454\pi$
$137$	15.1320	+	6.73719i	1.29281	+	0.575597i	0.358992	+	0.933341i	$0.383121\pi$
$138$		0			0
$139$	−17.0679	−	3.62789i	−1.44768	−	0.307713i	−0.583998	−	0.811755i	$-0.698513\pi$
$139$	−17.0679	−	3.62789i	−1.44768	−	0.307713i	−0.863679	+	0.504041i	$0.831846\pi$
$140$	0.862407	+	0.957800i	0.0728867	+	0.0809489i
$141$		0			0
$142$	−0.901739	−	1.56186i	−0.0756723	−	0.131068i
$143$	−1.70342	−	12.4872i	−0.142447	−	1.04423i
$144$		0			0
$145$	−4.61255	−	3.35121i	−0.383051	−	0.278303i
$146$	−0.261444	+	0.0555717i	−0.0216373	+	0.00459915i
$147$		0			0
$148$	1.72411	+	16.4038i	0.141721	+	1.34838i
$149$	−0.659140	−	6.27130i	−0.0539989	−	0.513765i	−0.987773	−	0.155901i	$-0.950172\pi$
$149$	−0.659140	−	6.27130i	−0.0539989	−	0.513765i	0.933774	−	0.357864i	$-0.116495\pi$
$150$		0			0
$151$	−15.8769	+	3.37473i	−1.29204	+	0.274632i	−0.802135	−	0.597143i	$-0.796302\pi$
$151$	−15.8769	+	3.37473i	−1.29204	+	0.274632i	−0.489907	+	0.871775i	$0.662969\pi$
$152$	−3.57113	−	2.59458i	−0.289657	−	0.210448i
$153$		0			0
$154$	−1.10557	+	0.533690i	−0.0890892	+	0.0430059i
$155$	−3.85132	−	6.67068i	−0.309346	−	0.535802i
$156$		0			0
$157$	−11.4048	−	12.6663i	−0.910202	−	1.01088i	−0.999889	−	0.0149120i	$-0.995253\pi$
$157$	−11.4048	−	12.6663i	−0.910202	−	1.01088i	0.0896865	−	0.995970i	$-0.471413\pi$
$158$	2.52795	+	0.537333i	0.201113	+	0.0427479i
$159$		0			0
$160$	7.06378	+	3.14500i	0.558440	+	0.248634i
$161$	0.0583679	+	0.179638i	0.00460003	+	0.0141574i
$162$		0			0
$163$	−15.0263	−	10.9173i	−1.17695	−	0.855105i	−0.185127	−	0.982715i	$-0.559270\pi$
$163$	−15.0263	−	10.9173i	−1.17695	−	0.855105i	−0.991824	+	0.127609i	$0.959270\pi$
$164$	−5.50140	−	9.52870i	−0.429587	−	0.744067i
$165$		0			0
$166$	−2.34180	+	4.05612i	−0.181759	+	0.314816i
$167$	8.64837	−	3.85050i	0.669231	−	0.297961i	−0.0438545	−	0.999038i	$-0.513964\pi$
$167$	8.64837	−	3.85050i	0.669231	−	0.297961i	0.713085	+	0.701077i	$0.247297\pi$
$168$		0			0
$169$	0.963092	−	1.06962i	0.0740840	−	0.0822786i
$170$	−0.134687	+	0.0978558i	−0.0103300	+	0.00750520i
$171$		0			0
$172$	−3.37531	−	10.3881i	−0.257365	−	0.792088i
$173$	−17.5754	+	3.73576i	−1.33623	+	0.284025i	−0.819970	−	0.572406i	$-0.806010\pi$
$173$	−17.5754	+	3.73576i	−1.33623	+	0.284025i	−0.516261	+	0.856431i	$0.672677\pi$
$174$		0			0
$175$	−0.920769	+	1.59482i	−0.0696036	+	0.120557i
$176$	3.81164	−	4.50536i	0.287313	−	0.339604i
$177$		0			0
$178$	0.223012	−	2.12182i	0.0167154	−	0.159037i
$179$	8.17595	−	25.1630i	0.611099	−	1.88077i	0.163474	−	0.986548i	$-0.447730\pi$
$179$	8.17595	−	25.1630i	0.611099	−	1.88077i	0.447625	−	0.894221i	$-0.352270\pi$
$180$		0			0
$181$	0.711098	−	0.516643i	0.0528555	−	0.0384018i	−0.561044	−	0.827786i	$-0.689600\pi$
$181$	0.711098	−	0.516643i	0.0528555	−	0.0384018i	0.613899	+	0.789384i	$0.289600\pi$
$182$	−1.28493	−	0.572087i	−0.0952452	−	0.0424059i
$183$		0			0
$184$	0.487621	+	0.541558i	0.0359479	+	0.0399242i
$185$	12.8420	−	5.71762i	0.944161	−	0.420368i
$186$		0			0
$187$	0.217045	+	0.603926i	0.0158719	+	0.0441635i
$188$	8.15946			0.595090
$189$		0			0
$190$	−0.517344	+	1.59222i	−0.0375321	+	0.115512i
$191$	10.3859	−	11.5347i	0.751496	−	0.834621i	−0.239163	−	0.970979i	$-0.576873\pi$
$191$	10.3859	−	11.5347i	0.751496	−	0.834621i	0.990660	+	0.136358i	$0.0435398\pi$
$192$		0			0
$193$	−1.01127	−	9.62158i	−0.0727927	−	0.692577i	−0.968683	−	0.248301i	$-0.920128\pi$
$193$	−1.01127	−	9.62158i	−0.0727927	−	0.692577i	0.895890	−	0.444276i	$-0.146539\pi$
$194$	−3.98036	−	0.846051i	−0.285773	−	0.0607429i
$195$		0			0
$196$	−1.11548	+	10.6131i	−0.0796773	+	0.758079i
$197$	−26.0364			−1.85502			−0.927508	−	0.373803i	$-0.878053\pi$
$197$	−26.0364			−1.85502			−0.927508	+	0.373803i	$0.878053\pi$
$198$		0			0
$199$	−20.4538			−1.44993			−0.724967	−	0.688784i	$-0.758145\pi$
$199$	−20.4538			−1.44993			−0.724967	+	0.688784i	$0.758145\pi$
$200$	−0.742669	+	7.06602i	−0.0525146	+	0.499643i
$201$		0			0
$202$	−11.3898	−	2.42098i	−0.801386	−	0.170340i
$203$	0.256384	+	2.43933i	0.0179946	+	0.171207i
$204$		0			0
$205$	−6.27461	+	6.96866i	−0.438237	+	0.486712i
$206$	0.629630	−	1.93780i	0.0438684	−	0.135013i
$207$		0			0
$208$	6.76136			0.468816
$209$	5.33548	+	3.63035i	0.369063	+	0.251117i
$210$		0			0
$211$	−14.5408	+	6.47396i	−1.00103	+	0.445686i	−0.840772	−	0.541389i	$-0.817898\pi$
$211$	−14.5408	+	6.47396i	−1.00103	+	0.445686i	−0.160255	+	0.987076i	$0.551232\pi$
$212$	8.44092	+	9.37459i	0.579725	+	0.643849i
$213$		0			0
$214$	−9.70168	−	4.31947i	−0.663193	−	0.295273i
$215$	−7.53115	+	5.47170i	−0.513620	+	0.373167i
$216$		0			0
$217$	−1.02399	+	3.15151i	−0.0695128	+	0.213939i
$218$	−0.586125	+	5.57660i	−0.0396974	+	0.377695i
$219$		0			0
$220$	−6.72939	−	2.75060i	−0.453695	−	0.185446i
$221$	−0.367628	+	0.636751i	−0.0247294	+	0.0428325i
$222$		0			0
$223$	−2.44695	+	0.520115i	−0.163860	+	0.0348294i	−0.289111	−	0.957296i	$-0.593360\pi$
$223$	−2.44695	+	0.520115i	−0.163860	+	0.0348294i	0.125251	+	0.992125i	$0.460026\pi$
$224$	−1.02793	−	3.16363i	−0.0686812	−	0.211379i
$225$		0			0
$226$	1.46951	−	1.06766i	0.0977504	−	0.0710198i
$227$	−10.7822	+	11.9749i	−0.715641	+	0.794800i	−0.985783	−	0.168021i	$-0.946263\pi$
$227$	−10.7822	+	11.9749i	−0.715641	+	0.794800i	0.270143	+	0.962820i	$0.412929\pi$
$228$		0			0
$229$	3.01903	−	1.34416i	0.199503	−	0.0888245i	−0.304553	−	0.952495i	$-0.598507\pi$
$229$	3.01903	−	1.34416i	0.199503	−	0.0888245i	0.504056	+	0.863671i	$0.331840\pi$
$230$	0.138195	−	0.239360i	0.00911228	−	0.0157829i
$231$		0			0
$232$	4.73158	+	8.19533i	0.310643	+	0.538050i
$233$	3.48837	+	2.53445i	0.228531	+	0.166037i	0.696158	−	0.717888i	$-0.254891\pi$
$233$	3.48837	+	2.53445i	0.228531	+	0.166037i	−0.467627	+	0.883926i	$0.654891\pi$
$234$		0			0
$235$	−2.14890	−	6.61363i	−0.140179	−	0.431426i
$236$	−10.5553	−	4.69951i	−0.687090	−	0.305912i
$237$		0			0
$238$	0.0700560	+	0.0148909i	0.00454105	+	0.000965231i
$239$	10.0638	+	11.1770i	0.650974	+	0.722980i	0.974786	−	0.223141i	$-0.0716312\pi$
$239$	10.0638	+	11.1770i	0.650974	+	0.722980i	−0.323812	+	0.946121i	$0.604965\pi$
$240$		0			0
$241$	−6.88547	−	11.9260i	−0.443532	−	0.768220i	0.554417	−	0.832239i	$-0.312941\pi$
$241$	−6.88547	−	11.9260i	−0.443532	−	0.768220i	−0.997949	+	0.0640192i	$0.979608\pi$
$242$	4.30727	−	5.42195i	0.276882	−	0.348536i
$243$		0			0
$244$	−11.2064	−	8.14192i	−0.717416	−	0.521233i
$245$	8.89620	−	1.89095i	0.568357	−	0.120808i
$246$		0			0
$247$	0.772863	+	7.35330i	0.0491761	+	0.467880i
$248$	1.33637	+	12.7147i	0.0848596	+	0.807386i
$249$		0			0
$250$	6.84382	−	1.45470i	0.432841	−	0.0920033i
$251$	22.3625	+	16.2473i	1.41151	+	1.02552i	0.993101	+	0.117264i	$0.0374123\pi$
$251$	22.3625	+	16.2473i	1.41151	+	1.02552i	0.418409	+	0.908259i	$0.362588\pi$
$252$		0			0
$253$	−0.736983	−	0.769379i	−0.0463337	−	0.0483705i
$254$	0.404286	+	0.700244i	0.0253672	+	0.0439372i
$255$		0			0
$256$	−4.76875	−	5.29623i	−0.298047	−	0.331014i
$257$	−10.7426	−	2.28340i	−0.670103	−	0.142435i	−0.139718	−	0.990191i	$-0.544619\pi$
$257$	−10.7426	−	2.28340i	−0.670103	−	0.142435i	−0.530385	+	0.847757i	$0.677953\pi$
$258$		0			0
$259$	−5.52465	−	2.45973i	−0.343285	−	0.152840i
$260$	−2.57385	−	7.92151i	−0.159624	−	0.491271i
$261$		0			0
$262$	−3.22783	−	2.34516i	−0.199416	−	0.144884i
$263$	−8.97517	−	15.5455i	−0.553433	−	0.958574i	−0.998024	−	0.0628399i	$-0.979984\pi$
$263$	−8.97517	−	15.5455i	−0.553433	−	0.958574i	0.444591	−	0.895734i	$-0.353349\pi$
$264$		0			0
$265$	5.37553	−	9.31068i	0.330216	−	0.571951i
$266$	0.657961	−	0.292943i	0.0403422	−	0.0179615i
$267$		0			0
$268$	9.76239	−	10.8422i	0.596333	−	0.662295i
$269$	−19.5359	+	14.1937i	−1.19113	+	0.865404i	−0.993383	−	0.114850i	$-0.963361\pi$
$269$	−19.5359	+	14.1937i	−1.19113	+	0.865404i	−0.197743	+	0.980254i	$0.563361\pi$
$270$		0			0
$271$	−4.49596	−	13.8371i	−0.273110	−	0.840547i	−0.989713	−	0.143065i	$-0.954304\pi$
$271$	−4.49596	−	13.8371i	−0.273110	−	0.840547i	0.716603	−	0.697481i	$-0.245696\pi$
$272$	−0.336768	+	0.0715822i	−0.0204195	+	0.00434031i
$273$		0			0
$274$	−5.21360	+	9.03022i	−0.314965	+	0.545535i
$275$	0.766543	−	10.3590i	0.0462243	−	0.624672i
$276$		0			0
$277$	−2.52035	+	23.9795i	−0.151433	+	1.44079i	0.609925	+	0.792459i	$0.291200\pi$
$277$	−2.52035	+	23.9795i	−0.151433	+	1.44079i	−0.761358	+	0.648332i	$0.775467\pi$
$278$	3.39437	−	10.4468i	0.203581	−	0.626558i
$279$		0			0
$280$	−1.47497	+	1.07163i	−0.0881465	+	0.0640422i
$281$	1.08521	+	0.483167i	0.0647382	+	0.0288233i	0.438850	−	0.898560i	$-0.355386\pi$
$281$	1.08521	+	0.483167i	0.0647382	+	0.0288233i	−0.374112	+	0.927383i	$0.622052\pi$
$282$		0			0
$283$	10.2726	+	11.4089i	0.610645	+	0.678190i	0.966593	−	0.256316i	$-0.0825088\pi$
$283$	10.2726	+	11.4089i	0.610645	+	0.678190i	−0.355948	+	0.934506i	$0.615842\pi$
$284$	−4.19727	+	1.86875i	−0.249062	+	0.110890i
$285$		0			0
$286$	7.92985	−	0.244767i	0.468902	−	0.0144734i
$287$	4.03412			0.238126
$288$		0			0
$289$	−5.24172	+	16.1324i	−0.308336	+	0.948962i
$290$	2.40158	−	2.66722i	0.141025	−	0.156625i
$291$		0			0
$292$	0.0711762	+	0.677197i	0.00416527	+	0.0396299i
$293$	31.3963	+	6.67348i	1.83419	+	0.389869i	0.989398	−	0.145227i	$-0.0463912\pi$
$293$	31.3963	+	6.67348i	1.83419	+	0.389869i	0.844791	+	0.535096i	$0.179725\pi$
$294$		0			0
$295$	−1.02931	+	9.79323i	−0.0599287	+	0.570184i
$296$	−23.3321			−1.35615
$297$		0			0
$298$	3.96959			0.229952
$299$	0.127593	−	1.21396i	0.00737889	−	0.0702054i
$300$		0			0
$301$	3.91725	+	0.832636i	0.225786	+	0.0479924i
$302$	−1.06806	−	10.1619i	−0.0614602	−	0.584754i
$303$		0			0
$304$	−2.31668	+	2.57294i	−0.132871	+	0.147568i
$305$	−3.64807	+	11.2276i	−0.208888	+	0.642890i
$306$		0			0
$307$	33.1199			1.89025			0.945126	−	0.326707i	$-0.105939\pi$
$307$	33.1199			1.89025			0.945126	+	0.326707i	$0.105939\pi$
$308$	1.05776	+	2.94320i	0.0602713	+	0.167704i
$309$		0			0
$310$	4.42968	−	1.97222i	0.251589	−	0.112015i
$311$	−22.7387	−	25.2539i	−1.28939	−	1.43201i	−0.843687	−	0.536835i	$-0.819620\pi$
$311$	−22.7387	−	25.2539i	−1.28939	−	1.43201i	−0.445705	−	0.895180i	$-0.647047\pi$
$312$		0			0
$313$	4.30580	+	1.91706i	0.243378	+	0.108359i	0.524801	−	0.851225i	$-0.324140\pi$
$313$	4.30580	+	1.91706i	0.243378	+	0.108359i	−0.281423	+	0.959584i	$0.590806\pi$
$314$	8.68034	−	6.30664i	0.489860	−	0.355904i
$315$		0			0
$316$	2.03457	−	6.26176i	0.114454	−	0.352252i
$317$	−1.82058	+	17.3217i	−0.102254	+	0.972883i	0.816311	+	0.577613i	$0.196016\pi$
$317$	−1.82058	+	17.3217i	−0.102254	+	0.972883i	−0.918565	+	0.395270i	$0.870651\pi$
$318$		0			0
$319$	−7.28386	−	11.7623i	−0.407818	−	0.658565i
$320$	−0.00178142	+	0.00308550i	−9.95842e−5	+	0.000172485i
$321$		0			0
$322$	−0.116305	+	0.0247214i	−0.00648142	+	0.00137767i
$323$	−0.116344	−	0.358069i	−0.00647353	−	0.0199235i
$324$		0			0
$325$	9.62806	−	6.99519i	0.534068	−	0.388023i
$326$	7.82362	−	8.68901i	0.433310	−	0.481240i
$327$		0			0
$328$	14.2187	−	6.33055i	0.785094	−	0.349546i
$329$	−1.49581	+	2.59082i	−0.0824667	+	0.142837i
$330$		0			0
$331$	−6.48845	−	11.2383i	−0.356637	−	0.617714i	0.630759	−	0.775978i	$-0.282743\pi$
$331$	−6.48845	−	11.2383i	−0.356637	−	0.617714i	−0.987397	+	0.158264i	$0.949410\pi$
$332$	9.65303	+	7.01334i	0.529779	+	0.384907i
$333$		0			0
$334$	1.84157	+	5.66778i	0.100766	+	0.310127i
$335$	−11.3592	−	5.05744i	−0.620620	−	0.276318i
$336$		0			0
$337$	10.1176	+	2.15056i	0.551139	+	0.117148i	0.475060	−	0.879954i	$-0.342426\pi$
$337$	10.1176	+	2.15056i	0.551139	+	0.117148i	0.0760793	+	0.997102i	$0.475760\pi$
$338$	0.606275	+	0.673337i	0.0329770	+	0.0366247i
$339$		0			0
$340$	0.212062	+	0.367303i	0.0115007	+	0.0199198i
$341$	−2.52632	−	18.5196i	−0.136808	−	1.00289i
$342$		0			0
$343$	−6.49530	−	4.71911i	−0.350713	−	0.254808i
$344$	15.1134	−	3.21244i	0.814857	−	0.173203i
$345$		0			0
$346$	−1.18233	−	11.2491i	−0.0635622	−	0.604754i
$347$	−0.642191	−	6.11004i	−0.0344746	−	0.328004i	−0.998144	−	0.0609047i	$-0.980601\pi$
$347$	−0.642191	−	6.11004i	−0.0344746	−	0.328004i	0.963669	−	0.267099i	$-0.0860652\pi$
$348$		0			0
$349$	−19.9329	+	4.23686i	−1.06698	+	0.226794i	−0.707756	−	0.706457i	$-0.750292\pi$
$349$	−19.9329	+	4.23686i	−1.06698	+	0.226794i	−0.359225	+	0.933251i	$0.616959\pi$
$350$	−0.937866	−	0.681399i	−0.0501310	−	0.0364223i
$351$		0			0
$352$	12.9791	+	13.5497i	0.691790	+	0.722200i
$353$	5.99407	+	10.3820i	0.319032	+	0.552580i	0.980286	−	0.197582i	$-0.0633089\pi$
$353$	5.99407	+	10.3820i	0.319032	+	0.552580i	−0.661254	+	0.750162i	$0.729976\pi$
$354$		0			0
$355$	2.62011	+	2.90993i	0.139061	+	0.154443i
$356$	−5.31647	−	1.13005i	−0.281772	−	0.0598926i
$357$		0			0
$358$	15.2156	+	6.77441i	0.804167	+	0.358038i
$359$	5.52583	+	17.0067i	0.291642	+	0.897582i	0.984329	+	0.176343i	$0.0564269\pi$
$359$	5.52583	+	17.0067i	0.291642	+	0.897582i	−0.692687	+	0.721239i	$0.743573\pi$
$360$		0			0
$361$	12.3083	+	8.94252i	0.647806	+	0.470659i
$362$	0.276659	+	0.479187i	0.0145409	+	0.0251855i
$363$		0			0
$364$	−1.79161	+	3.10317i	−0.0939061	+	0.162650i
$365$	0.530155	−	0.236040i	0.0277496	−	0.0123549i
$366$		0			0
$367$	18.4810	−	20.5252i	0.964699	−	1.07141i	−0.0327103	−	0.999465i	$-0.510414\pi$
$367$	18.4810	−	20.5252i	0.964699	−	1.07141i	0.997409	−	0.0719415i	$-0.0229195\pi$
$368$	0.462420	−	0.335968i	0.0241053	−	0.0175135i
$369$		0			0
$370$	2.73455	+	8.41609i	0.142163	+	0.437532i
$371$	−4.52406	+	0.961618i	−0.234877	+	0.0499247i
$372$		0			0
$373$	−6.19435	+	10.7289i	−0.320731	+	0.555523i	−0.980639	−	0.195824i	$-0.937262\pi$
$373$	−6.19435	+	10.7289i	−0.320731	+	0.555523i	0.659908	+	0.751347i	$0.270595\pi$
$374$	−0.392376	+	0.0961443i	−0.0202893	+	0.00497150i
$375$		0			0
$376$	−1.20648	+	11.4789i	−0.0622196	+	0.591980i
$377$	4.89822	−	15.0752i	0.252271	−	0.776411i
$378$		0			0
$379$	−13.6170	+	9.89335i	−0.699459	+	0.508187i	−0.879756	−	0.475425i	$-0.842294\pi$
$379$	−13.6170	+	9.89335i	−0.699459	+	0.508187i	0.180297	+	0.983612i	$0.442294\pi$
$380$	3.89631	+	1.73475i	0.199876	+	0.0889907i
$381$		0			0
$382$	6.53801	+	7.26120i	0.334514	+	0.371515i
$383$	−11.3727	+	5.06346i	−0.581119	+	0.258731i	−0.676175	−	0.736741i	$-0.736364\pi$
$383$	−11.3727	+	5.06346i	−0.581119	+	0.258731i	0.0950561	+	0.995472i	$0.469697\pi$
$384$		0			0
$385$	2.10703	−	1.63249i	0.107384	−	0.0831995i
$386$	6.09024			0.309985
$387$		0			0
$388$	−3.20351	+	9.85939i	−0.162634	+	0.500534i
$389$	0.822220	−	0.913167i	0.0416882	−	0.0462994i	−0.721940	−	0.691956i	$-0.756749\pi$
$389$	0.822220	−	0.913167i	0.0416882	−	0.0462994i	0.763628	+	0.645656i	$0.223416\pi$
$390$		0			0
$391$	0.00649708	+	0.0618156i	0.000328572	+	0.00312615i
$392$	−14.7658	−	3.13857i	−0.745786	−	0.158522i
$393$		0			0
$394$	1.71324	−	16.3004i	0.0863117	−	0.821201i
$395$	−5.61129			−0.282335
$396$		0			0
$397$	20.5917			1.03347			0.516734	−	0.856146i	$-0.327148\pi$
$397$	20.5917			1.03347			0.516734	+	0.856146i	$0.327148\pi$
$398$	1.34590	−	12.8053i	0.0674637	−	0.641874i
$399$		0			0
$400$	5.45096	+	1.15864i	0.272548	+	0.0579318i
$401$	−0.704387	−	6.70180i	−0.0351754	−	0.334672i	−0.997931	−	0.0642977i	$-0.979519\pi$
$401$	−0.704387	−	6.70180i	−0.0351754	−	0.334672i	0.962755	−	0.270374i	$-0.0871474\pi$
$402$		0			0
$403$	14.3293	−	15.9143i	0.713791	−	0.792745i
$404$	−9.16687	+	28.2127i	−0.456069	+	1.40364i
$405$		0			0
$406$	−1.54404			−0.0766294
$407$	34.0950	−	1.05239i	1.69003	−	0.0521653i
$408$		0			0
$409$	26.6486	−	11.8647i	1.31769	−	0.586672i	0.377084	−	0.926179i	$-0.376927\pi$
$409$	26.6486	−	11.8647i	1.31769	−	0.586672i	0.940604	+	0.339507i	$0.110260\pi$
$410$	−3.94992	−	4.38683i	−0.195073	−	0.216650i
$411$		0			0
$412$	−4.74197	−	2.11126i	−0.233620	−	0.104014i
$413$	3.42722	−	2.49002i	0.168642	−	0.122526i
$414$		0			0
$415$	3.14239	−	9.67129i	0.154254	−	0.474745i
$416$	−2.24706	+	21.3793i	−0.110171	+	1.04821i
$417$		0			0
$418$	−2.62391	+	3.10145i	−0.128339	+	0.151697i
$419$	−18.9851	+	32.8832i	−0.927483	+	1.60645i	−0.139965	+	0.990156i	$0.544699\pi$
$419$	−18.9851	+	32.8832i	−0.927483	+	1.60645i	−0.787518	+	0.616292i	$0.788634\pi$
$420$		0			0
$421$	7.93108	−	1.68580i	0.386537	−	0.0821610i	−0.0105442	−	0.999944i	$-0.503356\pi$
$421$	7.93108	−	1.68580i	0.386537	−	0.0821610i	0.397081	+	0.917783i	$0.370023\pi$
$422$	−3.09629	−	9.52940i	−0.150725	−	0.463884i
$423$		0			0
$424$	−14.4365	+	10.4887i	−0.701098	+	0.509377i
$425$	−0.405494	+	0.450346i	−0.0196693	+	0.0218450i
$426$		0			0
$427$	4.63963	−	2.06570i	0.224527	−	0.0999661i
$428$	−13.5273	+	23.4301i	−0.653869	+	1.13253i
$429$		0			0
$430$	−2.93006	−	5.07500i	−0.141300	−	0.244738i
$431$	24.6339	+	17.8976i	1.18657	+	0.862095i	0.992898	−	0.118971i	$-0.0379595\pi$
$431$	24.6339	+	17.8976i	1.18657	+	0.862095i	0.193674	+	0.981066i	$0.437959\pi$
$432$		0			0
$433$	7.44285	+	22.9067i	0.357681	+	1.10083i	0.954439	+	0.298407i	$0.0964551\pi$
$433$	7.44285	+	22.9067i	0.357681	+	1.10083i	−0.596758	+	0.802421i	$0.703545\pi$
$434$	−1.90566	−	0.848454i	−0.0914745	−	0.0407271i
$435$		0			0
$436$	13.9729	+	2.97003i	0.669179	+	0.142238i
$437$	0.418239	+	0.464501i	0.0200071	+	0.0222201i
$438$		0			0
$439$	−17.1588	−	29.7199i	−0.818943	−	1.41845i	−0.906461	−	0.422289i	$-0.861227\pi$
$439$	−17.1588	−	29.7199i	−0.818943	−	1.41845i	0.0875179	−	0.996163i	$-0.472106\pi$
$440$	4.86464	−	9.06035i	0.231913	−	0.431935i
$441$		0			0
$442$	−0.374454	−	0.272057i	−0.0178110	−	0.0129404i
$443$	8.35358	−	1.77561i	0.396890	−	0.0843617i	−0.00514270	−	0.999987i	$-0.501637\pi$
$443$	8.35358	−	1.77561i	0.396890	−	0.0843617i	0.402033	+	0.915625i	$0.368304\pi$
$444$		0			0
$445$	0.484201	+	4.60687i	0.0229533	+	0.218386i
$446$	−0.164610	−	1.56616i	−0.00779452	−	0.0741599i
$447$		0			0
$448$	0.00149924		0.000318674i	7.08327e−5		1.50559e-5i
$449$	29.8272	+	21.6707i	1.40763	+	1.02271i	0.993661	+	0.112416i	$0.0358589\pi$
$449$	29.8272	+	21.6707i	1.40763	+	1.02271i	0.413972	+	0.910290i	$0.364141\pi$
$450$		0			0
$451$	−20.4920	+	9.89211i	−0.964933	+	0.465801i
$452$	−2.31372	−	4.00748i	−0.108828	−	0.188496i
$453$		0			0
$454$	−6.78751	−	7.53829i	−0.318554	−	0.353790i
$455$	2.98711	+	0.634930i	0.140038	+	0.0297660i
$456$		0			0
$457$	21.6365	+	9.63318i	1.01211	+	0.450621i	0.844685	−	0.535264i	$-0.179788\pi$
$457$	21.6365	+	9.63318i	1.01211	+	0.450621i	0.167426	+	0.985885i	$0.446454\pi$
$458$	0.642868	+	1.97854i	0.0300392	+	0.0924513i
$459$		0			0
$460$	−0.569645	−	0.413871i	−0.0265598	−	0.0192969i
$461$	−14.3431	−	24.8430i	−0.668024	−	1.15705i	−0.978456	−	0.206456i	$-0.933807\pi$
$461$	−14.3431	−	24.8430i	−0.668024	−	1.15705i	0.310432	−	0.950596i	$-0.399526\pi$
$462$		0			0
$463$	−5.43156	+	9.40774i	−0.252426	+	0.437215i	−0.964193	−	0.265201i	$-0.914562\pi$
$463$	−5.43156	+	9.40774i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$464$	6.78069	−	3.01896i	0.314786	−	0.140152i
$465$		0			0
$466$	−1.81626	+	2.01716i	−0.0841367	+	0.0934433i
$467$	−23.8560	+	17.3324i	−1.10392	+	0.802046i	−0.981696	−	0.190456i	$-0.939003\pi$
$467$	−23.8560	+	17.3324i	−1.10392	+	0.802046i	−0.122226	+	0.992502i	$0.539003\pi$
$468$		0			0
$469$	1.65300	+	5.08741i	0.0763285	+	0.234915i
$470$	4.28194	−	0.910154i	0.197511	−	0.0419823i
$471$		0			0
$472$	8.17211	−	14.1545i	0.376152	−	0.651514i
$473$	−21.9401	+	5.37600i	−1.00881	+	0.247189i
$474$		0			0
$475$	−0.636997	+	6.06062i	−0.0292274	+	0.278080i
$476$	0.0563831	−	0.173529i	0.00258431	−	0.00795370i
$477$		0			0
$478$	−7.65970	+	5.56510i	−0.350346	+	0.254542i
$479$	−19.5106	−	8.68669i	−0.891463	−	0.396905i	−0.0906944	−	0.995879i	$-0.528909\pi$
$479$	−19.5106	−	8.68669i	−0.891463	−	0.396905i	−0.800769	+	0.598974i	$0.795575\pi$
$480$		0			0
$481$	26.1509	+	29.0435i	1.19238	+	1.32427i
$482$	7.91947	−	3.52597i	0.360722	−	0.160604i
$483$		0			0
$484$	−12.5901	−	12.3568i	−0.572278	−	0.561672i
$485$	8.83519			0.401185
$486$		0			0
$487$	−0.703448	+	2.16499i	−0.0318763	+	0.0981051i	−0.965729	−	0.259553i	$-0.916425\pi$
$487$	−0.703448	+	2.16499i	−0.0318763	+	0.0981051i	0.933853	+	0.357658i	$0.116425\pi$
$488$	13.1112	−	14.5615i	0.593518	−	0.659169i
$489$		0			0
$490$	0.598463	+	5.69399i	0.0270358	+	0.257228i
$491$	−9.31751	−	1.98050i	−0.420493	−	0.0893786i	−0.00719464	−	0.999974i	$-0.502290\pi$
$491$	−9.31751	−	1.98050i	−0.420493	−	0.0893786i	−0.413299	+	0.910595i	$0.635623\pi$
$492$		0			0
$493$	−0.0843690	+	0.802718i	−0.00379979	+	0.0361526i
$494$	−4.65447			−0.209415
$495$		0			0
$496$	10.0277			0.450256
$497$	0.176083	−	1.67531i	0.00789838	−	0.0751481i
$498$		0			0
$499$	12.4452	+	2.64531i	0.557124	+	0.118420i	0.477864	−	0.878434i	$-0.341411\pi$
$499$	12.4452	+	2.64531i	0.557124	+	0.118420i	0.0792598	+	0.996854i	$0.474744\pi$
$500$	−1.86318	−	17.7270i	−0.0833239	−	0.792774i
$501$		0			0
$502$	−11.6433	+	12.9312i	−0.519666	+	0.577148i
$503$	1.78686	−	5.49939i	0.0796722	−	0.245206i	−0.903285	−	0.429041i	$-0.858851\pi$
$503$	1.78686	−	5.49939i	0.0796722	−	0.245206i	0.982957	+	0.183836i	$0.0588514\pi$
$504$		0			0
$505$	25.2820			1.12503
$506$	0.530173	−	0.410770i	0.0235691	−	0.0182609i
$507$		0			0
$508$	1.88181	−	0.837834i	0.0834916	−	0.0371729i
$509$	6.18794	+	6.87240i	0.274275	+	0.304614i	0.864508	−	0.502620i	$-0.167630\pi$
$509$	6.18794	+	6.87240i	0.274275	+	0.304614i	−0.590232	+	0.807234i	$0.700964\pi$
$510$		0			0
$511$	−0.228074	−	0.101545i	−0.0100894	−	0.00449209i
$512$	−14.6751	+	10.6621i	−0.648553	+	0.471201i
$513$		0			0
$514$	2.13643	−	6.57525i	0.0942338	−	0.290022i
$515$	−0.462419	+	4.39962i	−0.0203766	+	0.193870i
$516$		0			0
$517$	1.24527	−	16.8285i	0.0547667	−	0.740114i
$518$	1.90347	−	3.29691i	0.0836338	−	0.144858i
$519$		0			0
$520$	11.5247	−	2.44966i	0.505393	−	0.107425i
$521$	−7.83400	−	24.1106i	−0.343214	−	1.05630i	−0.962533	−	0.271164i	$-0.912591\pi$
$521$	−7.83400	−	24.1106i	−0.343214	−	1.05630i	0.619320	−	0.785139i	$-0.287409\pi$
$522$		0			0
$523$	−16.9781	+	12.3353i	−0.742398	+	0.539384i	−0.893461	−	0.449140i	$-0.851730\pi$
$523$	−16.9781	+	12.3353i	−0.742398	+	0.539384i	0.151063	+	0.988524i	$0.451730\pi$
$524$	−6.80127	+	7.55357i	−0.297115	+	0.329979i
$525$		0			0
$526$	10.3230	−	4.59609i	0.450103	−	0.200399i
$527$	−0.545224	+	0.944356i	−0.0237503	+	0.0411368i
$528$		0			0
$529$	11.4484	+	19.8292i	0.497757	+	0.862140i
$530$	5.47534	+	3.97806i	0.237833	+	0.172796i
$531$		0			0
$532$	−0.566994	−	1.74503i	−0.0245823	−	0.0756565i
$533$	−23.8165	−	10.6038i	−1.03161	−	0.459302i
$534$		0			0
$535$	22.5538	+	4.79395i	0.975085	+	0.207261i
$536$	13.8096	+	15.3371i	0.596484	+	0.662463i
$537$		0			0
$538$	−7.60061	−	13.1646i	−0.327686	−	0.567568i
$539$	21.7187	+	3.92035i	0.935491	+	0.168862i
$540$		0			0
$541$	9.02363	+	6.55605i	0.387956	+	0.281867i	0.764617	−	0.644484i	$-0.222928\pi$
$541$	9.02363	+	6.55605i	0.387956	+	0.281867i	−0.376661	+	0.926351i	$0.622928\pi$
$542$	8.95874	−	1.90424i	0.384811	−	0.0817940i
$543$		0			0
$544$	−0.114421	−	1.08865i	−0.00490577	−	0.0466753i
$545$	−1.27259	−	12.1079i	−0.0545117	−	0.518644i
$546$		0			0
$547$	−5.96315	+	1.26751i	−0.254966	+	0.0541947i	−0.333621	−	0.942707i	$-0.608271\pi$
$547$	−5.96315	+	1.26751i	−0.254966	+	0.0541947i	0.0786553	+	0.996902i	$0.474937\pi$
$548$	21.4907	+	15.6139i	0.918038	+	0.666994i
$549$		0			0
$550$	6.43493	+	1.16154i	0.274386	+	0.0495283i
$551$	4.05833	+	7.02924i	0.172891	+	0.299456i
$552$		0			0
$553$	1.61527	+	1.79394i	0.0686885	+	0.0762863i
$554$	−14.8468	−	3.15579i	−0.630780	−	0.134077i
$555$		0			0
$556$	−25.5643	−	11.3819i	−1.08417	−	0.482702i
$557$	3.05982	+	9.41715i	0.129649	+	0.399018i	0.994719	−	0.102632i	$-0.0327265\pi$
$557$	3.05982	+	9.41715i	0.129649	+	0.399018i	−0.865071	+	0.501650i	$0.832727\pi$
$558$		0			0
$559$	−20.9380	−	15.2123i	−0.885581	−	0.643412i
$560$	0.714997	+	1.23841i	0.0302141	+	0.0523324i
$561$		0			0
$562$	−0.373900	+	0.647614i	−0.0157720	+	0.0273180i
$563$	−0.503872	+	0.224338i	−0.0212357	+	0.00945473i	−0.417327	−	0.908756i	$-0.637033\pi$
$563$	−0.503872	+	0.224338i	−0.0212357	+	0.00945473i	0.396091	+	0.918211i	$0.370366\pi$
$564$		0			0
$565$	−2.63891	+	2.93080i	−0.111020	+	0.123300i
$566$	−7.81863	+	5.68057i	−0.328642	+	0.238772i
$567$		0			0
$568$	−2.00837	−	6.18113i	−0.0842694	−	0.259355i
$569$	18.8280	−	4.00202i	0.789313	−	0.167774i	0.204419	−	0.978884i	$-0.434470\pi$
$569$	18.8280	−	4.00202i	0.789313	−	0.167774i	0.584894	+	0.811110i	$0.301136\pi$
$570$		0			0
$571$	−13.7061	+	23.7396i	−0.573582	+	0.993473i	0.422612	+	0.906311i	$0.361113\pi$
$571$	−13.7061	+	23.7396i	−0.573582	+	0.993473i	−0.996194	+	0.0871624i	$0.972220\pi$
$572$	1.49152	−	20.1563i	0.0623637	−	0.842779i
$573$		0			0
$574$	−0.265451	+	2.52560i	−0.0110797	+	0.105417i
$575$	0.310891	−	0.956825i	0.0129651	−	0.0399024i
$576$		0			0
$577$	24.2732	−	17.6355i	1.01050	−	0.734175i	0.0461898	−	0.998933i	$-0.485292\pi$
$577$	24.2732	−	17.6355i	1.01050	−	0.734175i	0.964315	+	0.264758i	$0.0852921\pi$
$578$	−9.75492	−	4.34317i	−0.405751	−	0.180652i
$579$		0			0
$580$	−6.11818	−	6.79492i	−0.254043	−	0.282144i
$581$	−3.99651	+	1.77936i	−0.165803	+	0.0738204i
$582$		0			0
$583$	20.6228	−	15.9782i	0.854109	−	0.661750i
$584$	−0.963220			−0.0398583
$585$		0			0
$586$	−6.24393	+	19.2169i	−0.257935	+	0.793841i
$587$	3.90905	−	4.34143i	0.161344	−	0.179190i	−0.657052	−	0.753845i	$-0.728197\pi$
$587$	3.90905	−	4.34143i	0.161344	−	0.179190i	0.818396	+	0.574655i	$0.194864\pi$
$588$		0			0
$589$	1.14622	+	10.9056i	0.0472293	+	0.449357i
$590$	−6.06343	−	1.28882i	−0.249627	−	0.0530599i
$591$		0			0
$592$	−1.91292	+	18.2002i	−0.0786205	+	0.748025i
$593$	−35.2941			−1.44936			−0.724678	−	0.689088i	$-0.758011\pi$
$593$	−35.2941			−1.44936			−0.724678	+	0.689088i	$0.758011\pi$
$594$		0			0
$595$	−0.155503			−0.00637500
$596$	1.05707	−	10.0574i	0.0432995	−	0.411967i
$597$		0			0
$598$	0.751620	+	0.159762i	0.0307360	+	0.00653315i
$599$	2.38691	+	22.7099i	0.0975263	+	0.927901i	0.928436	+	0.371493i	$0.121154\pi$
$599$	2.38691	+	22.7099i	0.0975263	+	0.927901i	−0.830909	+	0.556408i	$0.812179\pi$
$600$		0			0
$601$	7.68359	−	8.53349i	0.313420	−	0.348088i	−0.565767	−	0.824565i	$-0.691420\pi$
$601$	7.68359	−	8.53349i	0.313420	−	0.348088i	0.879187	+	0.476477i	$0.158086\pi$
$602$	−0.779042	+	2.39765i	−0.0317514	+	0.0977207i
$603$		0			0
$604$	−26.0309			−1.05918
$605$	−6.69999	+	13.4592i	−0.272393	+	0.547195i
$606$		0			0
$607$	11.8036	−	5.25531i	0.479095	−	0.213307i	−0.152957	−	0.988233i	$-0.548880\pi$
$607$	11.8036	−	5.25531i	0.479095	−	0.213307i	0.632052	+	0.774926i	$0.282213\pi$
$608$	−7.36567	−	8.18040i	−0.298717	−	0.331759i
$609$		0			0
$610$	−6.78911	−	3.02271i	−0.274883	−	0.122386i
$611$	15.6410	−	11.3639i	0.632767	−	0.459732i
$612$		0			0
$613$	7.44676	−	22.9188i	0.300772	−	0.925680i	−0.680450	−	0.732795i	$-0.738216\pi$
$613$	7.44676	−	22.9188i	0.300772	−	0.925680i	0.981221	−	0.192885i	$-0.0617845\pi$
$614$	−2.17934	+	20.7351i	−0.0879511	+	0.836799i
$615$		0			0
$616$	−4.29696	+	1.05289i	−0.173129	+	0.0424220i
$617$	11.3955	−	19.7377i	0.458767	−	0.794608i	−0.540129	−	0.841582i	$-0.681625\pi$
$617$	11.3955	−	19.7377i	0.458767	−	0.794608i	0.998896	+	0.0469742i	$0.0149578\pi$
$618$		0			0
$619$	19.8734	−	4.22422i	0.798779	−	0.169786i	0.209599	−	0.977787i	$-0.432784\pi$
$619$	19.8734	−	4.22422i	0.798779	−	0.169786i	0.589180	+	0.808002i	$0.299451\pi$
$620$	−3.81725	−	11.7483i	−0.153304	−	0.471822i
$621$		0			0
$622$	17.3067	−	12.5740i	0.693935	−	0.504173i
$623$	1.33344	−	1.48094i	0.0534233	−	0.0593326i
$624$		0			0
$625$	0.427795	−	0.190466i	0.0171118	−	0.00761866i
$626$	−1.48353	+	2.56954i	−0.0592937	+	0.102700i
$627$		0			0
$628$	−13.6671	−	23.6720i	−0.545375	−	0.944617i
$629$	−1.61000	−	1.16973i	−0.0641947	−	0.0466402i
$630$		0			0
$631$	4.74547	+	14.6051i	0.188914	+	0.581418i	0.999994	−	0.00351764i	$-0.00111970\pi$
$631$	4.74547	+	14.6051i	0.188914	+	0.581418i	−0.811080	+	0.584936i	$0.801120\pi$
$632$	8.50836	+	3.78816i	0.338444	+	0.150685i
$633$		0			0
$634$	−10.7246	−	2.27959i	−0.425930	−	0.0905342i
$635$	−1.17470	−	1.30464i	−0.0466166	−	0.0517730i
$636$		0			0
$637$	12.6428	+	21.8980i	0.500926	+	0.867629i
$638$	7.84323	−	3.78616i	0.310517	−	0.149895i
$639$		0			0
$640$	12.5093	+	9.08850i	0.494472	+	0.359255i
$641$	13.2372	−	2.81365i	0.522837	−	0.111132i	0.0610695	−	0.998134i	$-0.480549\pi$
$641$	13.2372	−	2.81365i	0.522837	−	0.111132i	0.461767	+	0.887001i	$0.347216\pi$
$642$		0			0
$643$	−1.32215	−	12.5794i	−0.0521405	−	0.496083i	−0.989164	−	0.146816i	$-0.953097\pi$
$643$	−1.32215	−	12.5794i	−0.0521405	−	0.496083i	0.937023	−	0.349267i	$-0.113569\pi$
$644$	0.0316631	+	0.301255i	0.00124770	+	0.0118711i
$645$		0			0
$646$	0.231829	−	0.0492767i	0.00912117	−	0.00193877i
$647$	−1.31179	−	0.953069i	−0.0515717	−	0.0374690i	0.561701	−	0.827340i	$-0.310147\pi$
$647$	−1.31179	−	0.953069i	−0.0515717	−	0.0374690i	−0.613272	+	0.789871i	$0.710147\pi$
$648$		0			0
$649$	−11.3034	+	21.0525i	−0.443697	+	0.826381i
$650$	3.74587	+	6.48804i	0.146925	+	0.254482i
$651$		0			0
$652$	−19.9312	−	22.1358i	−0.780566	−	0.866907i
$653$	32.3315	+	6.87228i	1.26523	+	0.268933i	0.791190	−	0.611570i	$-0.209462\pi$
$653$	32.3315	+	6.87228i	1.26523	+	0.268933i	0.474040	+	0.880503i	$0.342795\pi$
$654$		0			0
$655$	7.91373	+	3.52342i	0.309215	+	0.137671i
$656$	−3.77240	−	11.6103i	−0.147288	−	0.453305i
$657$		0			0
$658$	−1.52358	−	1.10695i	−0.0593955	−	0.0431534i
$659$	−23.9506	−	41.4836i	−0.932983	−	1.61597i	−0.778192	−	0.628026i	$-0.783863\pi$
$659$	−23.9506	−	41.4836i	−0.932983	−	1.61597i	−0.154790	−	0.987947i	$-0.549470\pi$
$660$		0			0
$661$	9.25259	−	16.0260i	0.359884	−	0.623337i	−0.628057	−	0.778167i	$-0.716150\pi$
$661$	9.25259	−	16.0260i	0.359884	−	0.623337i	0.987941	+	0.154830i	$0.0494830\pi$
$662$	7.46282	−	3.32266i	0.290051	−	0.129139i
$663$		0			0
$664$	−11.2938	+	12.5431i	−0.438286	+	0.486766i
$665$	−1.26510	+	0.919151i	−0.0490586	+	0.0356431i
$666$		0			0
$667$	−0.414080	−	1.27441i	−0.0160332	−	0.0493452i
$668$	14.8503	−	3.15654i	0.574577	−	0.122130i
$669$		0			0
$670$	3.91372	−	6.77876i	0.151200	−	0.261887i
$671$	−18.5025	+	21.8700i	−0.714283	+	0.844282i
$672$		0			0
$673$	−4.09073	+	38.9207i	−0.157686	+	1.50028i	0.574121	+	0.818771i	$0.305344\pi$
$673$	−4.09073	+	38.9207i	−0.157686	+	1.50028i	−0.731807	+	0.681512i	$0.761323\pi$
$674$	−2.01213	+	6.19270i	−0.0775044	+	0.238534i
$675$		0			0
$676$	1.86742	−	1.35676i	0.0718239	−	0.0521831i
$677$	11.4043	+	5.07750i	0.438301	+	0.195144i	0.614010	−	0.789298i	$-0.289555\pi$
$677$	11.4043	+	5.07750i	0.438301	+	0.195144i	−0.175709	+	0.984442i	$0.556222\pi$
$678$		0			0
$679$	−2.54331	−	2.82463i	−0.0976033	−	0.108399i
$680$	−0.548086	+	0.244024i	−0.0210181	+	0.00935788i
$681$		0			0
$682$	11.7606	−	0.363010i	0.450338	−	0.0139004i
$683$	−17.3888			−0.665363			−0.332681	−	0.943039i	$-0.607953\pi$
$683$	−17.3888			−0.665363			−0.332681	+	0.943039i	$0.607953\pi$
$684$		0			0
$685$	6.99597	−	21.5314i	0.267302	−	0.822672i
$686$	3.38185	−	3.75593i	0.129120	−	0.143402i
$687$		0			0
$688$	−1.26677	−	12.0525i	−0.0482952	−	0.459499i
$689$	29.2367	+	6.21445i	1.11383	+	0.236752i
$690$		0			0
$691$	−0.382036	+	3.63483i	−0.0145333	+	0.138275i	−0.999382	−	0.0351379i	$-0.988813\pi$
$691$	−0.382036	+	3.63483i	−0.0145333	+	0.138275i	0.984849	+	0.173413i	$0.0554796\pi$
$692$	−28.8156			−1.09541
$693$		0			0
$694$	3.86751			0.146809
$695$	−2.49293	+	23.7186i	−0.0945621	+	0.899699i
$696$		0			0
$697$	1.29851	+	0.276007i	0.0491846	+	0.0104545i
$698$	−1.34092	−	12.7580i	−0.0507545	−	0.482896i
$699$		0			0
$700$	−1.97615	+	2.19474i	−0.0746914	+	0.0829532i
$701$	−1.72623	+	5.31280i	−0.0651989	+	0.200662i	−0.978349	−	0.206962i	$-0.933642\pi$
$701$	−1.72623	+	5.31280i	−0.0651989	+	0.200662i	0.913150	+	0.407624i	$0.133642\pi$
$702$		0			0
$703$	−20.0123			−0.754777
$704$	−0.00683427	+	0.00529508i	−0.000257576	+	0.000199566i
$705$		0			0
$706$	−6.89420	+	3.06950i	−0.259467	+	0.115522i
$707$	−7.27771	−	8.08272i	−0.273706	−	0.303982i
$708$		0			0
$709$	12.6591	+	5.63618i	0.475421	+	0.211671i	0.630436	−	0.776241i	$-0.282876\pi$
$709$	12.6591	+	5.63618i	0.475421	+	0.211671i	−0.155015	+	0.987912i	$0.549543\pi$
$710$	−1.99420	+	1.44887i	−0.0748410	+	0.0543752i
$711$		0			0
$712$	2.37589	−	7.31224i	0.0890403	−	0.274038i
$713$	0.189231	−	1.80041i	0.00708676	−	0.0674260i
$714$		0			0
$715$	−16.7305	+	4.09948i	−0.625685	+	0.153312i
$716$	21.2155	−	36.7464i	0.792861	−	1.37328i
$717$		0			0
$718$	−11.0109	+	2.34043i	−0.410922	+	0.0873442i
$719$	−8.24222	−	25.3669i	−0.307383	−	0.946027i	−0.978777	−	0.204927i	$-0.934304\pi$
$719$	−8.24222	−	25.3669i	−0.307383	−	0.946027i	0.671394	−	0.741100i	$-0.265696\pi$
$720$		0			0
$721$	1.53968	−	1.11865i	0.0573408	−	0.0416605i
$722$	−6.40847	+	7.11733i	−0.238499	+	0.264879i
$723$		0			0
$724$	1.28775	−	0.573342i	0.0478587	−	0.0213081i
$725$	6.53222	−	11.3141i	0.242600	−	0.420196i
$726$		0			0
$727$	11.3198	+	19.6065i	0.419830	+	0.727166i	0.995922	−	0.0902184i	$-0.0287565\pi$
$727$	11.3198	+	19.6065i	0.419830	+	0.727166i	−0.576092	+	0.817385i	$0.695423\pi$
$728$	−4.10069	−	2.97933i	−0.151982	−	0.110421i
$729$		0			0
$730$	0.112890	+	0.347441i	0.00417826	+	0.0128594i
$731$	1.20392	+	0.536021i	0.0445287	+	0.0198255i
$732$		0			0
$733$	−21.5549	−	4.58163i	−0.796148	−	0.169226i	−0.208159	−	0.978095i	$-0.566747\pi$
$733$	−21.5549	−	4.58163i	−0.796148	−	0.169226i	−0.587989	+	0.808869i	$0.700080\pi$
$734$	11.6339	+	12.9208i	0.429417	+	0.476915i
$735$		0			0
$736$	0.908646	+	1.57382i	0.0334932	+	0.0580118i
$737$	−20.8716	−	21.7891i	−0.768816	−	0.802612i
$738$		0			0
$739$	−39.3226	−	28.5696i	−1.44651	−	1.05095i	−0.986632	−	0.162965i	$-0.947894\pi$
$739$	−39.3226	−	28.5696i	−1.44651	−	1.05095i	−0.459875	−	0.887984i	$-0.652106\pi$
$740$	22.0513	−	4.68715i	0.810622	−	0.172303i
$741$		0			0
$742$	−0.304341	−	2.89561i	−0.0111727	−	0.106301i
$743$	0.575345	+	5.47405i	0.0211074	+	0.200823i	0.999994	−	0.00358270i	$-0.00114041\pi$
$743$	0.575345	+	5.47405i	0.0211074	+	0.200823i	−0.978886	+	0.204406i	$0.934474\pi$
$744$		0			0
$745$	−8.43039	+	1.79194i	−0.308866	+	0.0656514i
$746$	−6.30937	−	4.58402i	−0.231002	−	0.167833i
$747$		0			0
$748$	0.139105	+	1.01973i	0.00508618	+	0.0372851i
$749$	−4.95973	−	8.59050i	−0.181224	−	0.313890i
$750$		0			0
$751$	−2.48961	−	2.76499i	−0.0908470	−	0.100896i	0.696007	−	0.718035i	$-0.254958\pi$
$751$	−2.48961	−	2.76499i	−0.0908470	−	0.100896i	−0.786854	+	0.617139i	$0.788292\pi$
$752$	8.85521	+	1.88223i	0.322916	+	0.0686379i
$753$		0			0
$754$	9.11567	+	4.05856i	0.331973	+	0.147804i
$755$	6.85556	+	21.0993i	0.249499	+	0.767880i
$756$		0			0
$757$	24.6209	+	17.8881i	0.894862	+	0.650155i	0.937141	−	0.348951i	$-0.113462\pi$
$757$	24.6209	+	17.8881i	0.894862	+	0.650155i	−0.0422792	+	0.999106i	$0.513462\pi$
$758$	−5.29781	−	9.17608i	−0.192425	−	0.333290i
$759$		0			0
$760$	−3.01660	+	5.22491i	−0.109424	+	0.189527i
$761$	20.5182	−	9.13531i	0.743786	−	0.331155i	0.000383921	−	1.00000i	$-0.499878\pi$
$761$	20.5182	−	9.13531i	0.743786	−	0.331155i	0.743402	+	0.668845i	$0.233211\pi$
$762$		0			0
$763$	−3.50459	+	3.89224i	−0.126875	+	0.140909i
$764$	20.1381	−	14.6312i	0.728571	−	0.529338i
$765$		0			0
$766$	−2.42169	−	7.45320i	−0.0874992	−	0.269295i
$767$	−26.7787	+	5.69198i	−0.966922	+	0.205526i
$768$		0			0
$769$	−19.4798	+	33.7399i	−0.702458	+	1.21669i	0.265143	+	0.964209i	$0.414581\pi$
$769$	−19.4798	+	33.7399i	−0.702458	+	1.21669i	−0.967601	+	0.252484i	$0.918752\pi$
$770$	0.883393	+	1.42655i	0.0318353	+	0.0514092i
$771$		0			0
$772$	1.62179	−	15.4303i	0.0583695	−	0.555349i
$773$	16.4951	−	50.7667i	0.593287	−	1.82595i	0.0302135	−	0.999543i	$-0.490381\pi$
$773$	16.4951	−	50.7667i	0.593287	−	1.82595i	0.563074	−	0.826407i	$-0.309619\pi$
$774$		0			0
$775$	14.2792	−	10.3745i	0.512925	−	0.372662i
$776$	−13.3967	−	5.96461i	−0.480914	−	0.214117i
$777$		0			0
$778$	0.517595	+	0.574847i	0.0185567	+	0.0206093i
$779$	12.1955	−	5.42979i	0.436950	−	0.194543i
$780$		0			0
$781$	3.21361	+	8.94184i	0.114992	+	0.319964i
$782$	−0.0391279			−0.00139921
$783$		0			0
$784$	−3.65884	+	11.2607i	−0.130673	+	0.402169i
$785$	−15.5879	+	17.3121i	−0.556357	+	0.617897i
$786$		0			0
$787$	−3.01381	−	28.6745i	−0.107431	−	1.02213i	−0.906877	−	0.421396i	$-0.861540\pi$
$787$	−3.01381	−	28.6745i	−0.107431	−	1.02213i	0.799446	−	0.600738i	$-0.205126\pi$
$788$	−40.8426	−	8.68136i	−1.45496	−	0.309261i
$789$		0			0
$790$	0.369232	−	3.51301i	0.0131367	−	0.124987i
$791$	1.69662			0.0603250
$792$		0			0
$793$	−32.8211			−1.16551
$794$	−1.35497	+	12.8917i	−0.0480860	+	0.457508i
$795$		0			0
$796$	−32.0854	−	6.81996i	−1.13724	−	0.241727i
$797$	3.46749	+	32.9910i	0.122825	+	1.16860i	0.866190	+	0.499715i	$0.166562\pi$
$797$	3.46749	+	32.9910i	0.122825	+	1.16860i	−0.743365	+	0.668886i	$0.766772\pi$
$798$		0			0
$799$	−0.658734	+	0.731598i	−0.0233043	+	0.0258821i
$800$	−5.47516	+	16.8508i	−0.193576	+	0.595766i
$801$		0			0
$802$	4.24208			0.149793
$803$	1.40754	−	0.0434460i	0.0496711	−	0.00153317i
$804$		0			0
$805$	0.235842	−	0.105004i	0.00831235	−	0.00370090i
$806$	9.02040	+	10.0182i	0.317730	+	0.352875i
$807$		0			0
$808$	−38.3349	−	17.0678i	−1.34862	−	0.600443i
$809$	19.8771	−	14.4416i	0.698842	−	0.507739i	−0.180713	−	0.983536i	$-0.557840\pi$
$809$	19.8771	−	14.4416i	0.698842	−	0.507739i	0.879555	+	0.475797i	$0.157840\pi$
$810$		0			0
$811$	11.5446	−	35.5307i	0.405387	−	1.24765i	−0.515185	−	0.857079i	$-0.672277\pi$
$811$	11.5446	−	35.5307i	0.405387	−	1.24765i	0.920572	−	0.390573i	$-0.127723\pi$
$812$	−0.411167	+	3.91200i	−0.0144291	+	0.137284i
$813$		0			0
$814$	−1.58465	+	21.4148i	−0.0555418	+	0.750589i
$815$	−12.6930	+	21.9850i	−0.444617	+	0.770099i
$816$		0			0
$817$	12.9629	−	2.75535i	0.453515	−	0.0963976i
$818$	5.67451	+	17.4644i	0.198405	+	0.610627i
$819$		0			0
$820$	−12.1664	+	8.83939i	−0.424868	+	0.308685i
$821$	−8.16415	+	9.06720i	−0.284931	+	0.316448i	−0.868571	−	0.495565i	$-0.834961\pi$
$821$	−8.16415	+	9.06720i	−0.284931	+	0.316448i	0.583640	+	0.812012i	$0.301628\pi$
$822$		0			0
$823$	−45.2009	+	20.1248i	−1.57561	+	0.701505i	−0.993733	−	0.111776i	$-0.964346\pi$
$823$	−45.2009	+	20.1248i	−1.57561	+	0.701505i	−0.581872	+	0.813280i	$0.697680\pi$
$824$	3.67133	−	6.35893i	0.127897	−	0.221524i
$825$		0			0
$826$	1.33339	+	2.30950i	0.0463945	+	0.0803576i
$827$	2.45628	+	1.78459i	0.0854134	+	0.0620564i	0.629672	−	0.776861i	$-0.283189\pi$
$827$	2.45628	+	1.78459i	0.0854134	+	0.0620564i	−0.544259	+	0.838917i	$0.683189\pi$
$828$		0			0
$829$	−14.8814	−	45.8003i	−0.516853	−	1.59071i	−0.779885	−	0.625923i	$-0.784722\pi$
$829$	−14.8814	−	45.8003i	−0.516853	−	1.59071i	0.263032	−	0.964787i	$-0.415278\pi$
$830$	5.84804	+	2.60372i	0.202989	+	0.0903763i
$831$		0			0
$832$	−0.00968886	−	0.00205943i	−0.000335901	−	7.13979e-5i
$833$	−0.861542	−	0.956839i	−0.0298507	−	0.0331525i
$834$		0			0
$835$	−6.46955	−	11.2056i	−0.223888	−	0.387786i
$836$	7.15915	+	7.47386i	0.247605	+	0.258489i
$837$		0			0
$838$	−19.3376	−	14.0496i	−0.668007	−	0.485335i
$839$	−38.0873	+	8.09571i	−1.31492	+	0.279495i	−0.811401	−	0.584490i	$-0.801295\pi$
$839$	−38.0873	+	8.09571i	−1.31492	+	0.279495i	−0.503519	+	0.863984i	$0.667961\pi$
$840$		0			0
$841$	1.21246	+	11.5358i	0.0418090	+	0.397786i
$842$	0.533537	+	5.07627i	0.0183869	+	0.174940i
$843$		0			0
$844$	−24.9683	+	5.30718i	−0.859445	+	0.182681i
$845$	−1.59153	−	1.15631i	−0.0547503	−	0.0397784i
$846$		0			0
$847$	6.23162	−	1.73239i	0.214121	−	0.0595255i
$848$	6.99812	+	12.1211i	0.240316	+	0.416240i
$849$		0			0
$850$	−0.255262	−	0.283497i	−0.00875542	−	0.00972388i
$851$	3.23165	+	0.686909i	0.110780	+	0.0235469i
$852$		0			0
$853$	−33.8107	−	15.0535i	−1.15765	−	0.515421i	−0.264153	−	0.964481i	$-0.585092\pi$
$853$	−33.8107	−	15.0535i	−1.15765	−	0.515421i	−0.893502	+	0.449060i	$0.851759\pi$
$854$	0.987956	+	3.04062i	0.0338072	+	0.104048i
$855$		0			0
$856$	−30.9617	−	22.4950i	−1.05825	−	0.768864i
$857$	14.2713	+	24.7186i	0.487499	+	0.844372i	0.999897	−	0.0143758i	$-0.00457610\pi$
$857$	14.2713	+	24.7186i	0.487499	+	0.844372i	−0.512398	+	0.858748i	$0.671243\pi$
$858$		0			0
$859$	−19.1707	+	33.2046i	−0.654094	+	1.13292i	0.328025	+	0.944669i	$0.393617\pi$
$859$	−19.1707	+	33.2046i	−0.654094	+	1.13292i	−0.982120	+	0.188256i	$0.939717\pi$
$860$	−13.6383	+	6.07218i	−0.465064	+	0.207060i
$861$		0			0
$862$	−12.8259	+	14.2446i	−0.436852	+	0.485174i
$863$	22.6247	−	16.4378i	0.770153	−	0.559549i	−0.131855	−	0.991269i	$-0.542093\pi$
$863$	22.6247	−	16.4378i	0.770153	−	0.559549i	0.902008	+	0.431720i	$0.142093\pi$
$864$		0			0
$865$	7.58897	+	23.3565i	0.258033	+	0.794143i
$866$	−14.8308	+	3.15238i	−0.503970	+	0.107122i
$867$		0			0
$868$	−2.65712	+	4.60226i	−0.0901884	+	0.156211i
$869$	−12.6040	−	5.15184i	−0.427563	−	0.174764i
$870$		0			0
$871$	3.61348	−	34.3799i	0.122438	−	1.16492i
$872$	−6.24437	+	19.2182i	−0.211461	+	0.650810i
$873$		0			0
$874$	−0.318327	+	0.231278i	−0.0107676	+	0.00782309i
$875$	5.97029	+	2.65814i	0.201833	+	0.0898617i
$876$		0			0
$877$	−14.0783	−	15.6355i	−0.475390	−	0.527974i	0.456981	−	0.889476i	$-0.348931\pi$
$877$	−14.0783	−	15.6355i	−0.475390	−	0.527974i	−0.932371	+	0.361502i	$0.882264\pi$
$878$	19.7355	−	8.78682i	0.666041	−	0.296541i
$879$		0			0
$880$	−6.66868	−	4.53748i	−0.224801	−	0.152959i
$881$	−17.0076			−0.573000			−0.286500	−	0.958080i	$-0.592492\pi$
$881$	−17.0076			−0.573000			−0.286500	+	0.958080i	$0.592492\pi$
$882$		0			0
$883$	2.08724	−	6.42388i	0.0702414	−	0.216181i	−0.909773	−	0.415105i	$-0.863745\pi$
$883$	2.08724	−	6.42388i	0.0702414	−	0.216181i	0.980015	+	0.198924i	$0.0637448\pi$
$884$	−0.789001	+	0.876275i	−0.0265370	+	0.0294723i
$885$		0			0
$886$	0.561959	+	5.34669i	0.0188794	+	0.179625i
$887$	33.1095	+	7.03764i	1.11171	+	0.236301i	0.726932	−	0.686709i	$-0.240946\pi$
$887$	33.1095	+	7.03764i	1.11171	+	0.236301i	0.384775	+	0.923010i	$0.374279\pi$
$888$		0			0
$889$	−0.0789449	+	0.751111i	−0.00264773	+	0.0251915i
$890$	−2.91604			−0.0977459
$891$		0			0
$892$	−4.01188			−0.134328
$893$	−1.03482	+	9.84561i	−0.0346288	+	0.329471i
$894$		0			0
$895$	−35.3721	−	7.51856i	−1.18236	−	0.251318i
$896$	−0.695314	−	6.61547i	−0.0232288	−	0.221007i
$897$		0			0
$898$	−15.5299	+	17.2477i	−0.518239	+	0.575563i
$899$	7.26448	−	22.3578i	0.242284	−	0.745674i
$900$		0			0
$901$	−1.52201			−0.0507054
$902$	−4.84465	−	13.4802i	−0.161309	−	0.448841i
$903$		0			0
$904$	5.97993	−	2.66244i	0.198889	−	0.0885513i
$905$	−0.803865	−	0.892783i	−0.0267214	−	0.0296771i
$906$		0			0
$907$	25.7133	+	11.4483i	0.853795	+	0.380134i	0.786493	−	0.617599i	$-0.211894\pi$
$907$	25.7133	+	11.4483i	0.853795	+	0.380134i	0.0673015	+	0.997733i	$0.478561\pi$
$908$	−20.9066	+	15.1895i	−0.693809	+	0.504082i
$909$		0			0
$910$	−0.594061	+	1.82833i	−0.0196929	+	0.0606086i
$911$	0.855313	−	8.13776i	0.0283378	−	0.269616i	−0.971174	−	0.238372i	$-0.923386\pi$
$911$	0.855313	−	8.13776i	0.0283378	−	0.269616i	0.999512	−	0.0312443i	$-0.00994700\pi$
$912$		0			0
$913$	15.9378	−	18.8385i	0.527465	−	0.623463i
$914$	−7.45467	+	12.9119i	−0.246579	+	0.427087i
$915$		0			0
$916$	5.18405	−	1.10190i	0.171286	−	0.0364080i
$917$	−1.15161	−	3.54430i	−0.0380296	−	0.117043i
$918$		0			0
$919$	−9.43023	+	6.85146i	−0.311075	+	0.226009i	−0.732357	−	0.680920i	$-0.761580\pi$
$919$	−9.43023	+	6.85146i	−0.311075	+	0.226009i	0.421283	+	0.906929i	$0.361580\pi$
$920$	0.666473	−	0.740193i	0.0219730	−	0.0244035i
$921$		0			0
$922$	16.4970	−	7.34494i	0.543300	−	0.241893i
$923$	−5.44317	+	9.42785i	−0.179164	+	0.310322i
$924$		0			0
$925$	16.1057	+	27.8959i	0.529552	+	0.917211i
$926$	−5.53241	−	4.01953i	−0.181806	−	0.132090i
$927$		0			0
$928$	7.29242	+	22.4438i	0.239385	+	0.736753i
$929$	−29.0262	−	12.9233i	−0.952318	−	0.423999i	−0.129041	−	0.991639i	$-0.541190\pi$
$929$	−29.0262	−	12.9233i	−0.952318	−	0.423999i	−0.823277	+	0.567640i	$0.807857\pi$
$930$		0			0
$931$	−12.6648	−	2.69199i	−0.415073	−	0.0882265i
$932$	4.62705	+	5.13886i	0.151564	+	0.168329i
$933$		0			0
$934$	−9.28136	−	16.0758i	−0.303695	−	0.526016i
$935$	0.789907	−	0.381311i	0.0258327	−	0.0124702i
$936$		0			0
$937$	34.9908	+	25.4223i	1.14310	+	0.830510i	0.987548	−	0.157318i	$-0.0502847\pi$
$937$	34.9908	+	25.4223i	1.14310	+	0.830510i	0.155551	+	0.987828i	$0.450285\pi$
$938$	−3.29380	+	0.700119i	−0.107546	+	0.0228597i
$939$		0			0
$940$	−1.16573	−	11.0911i	−0.0380218	−	0.361753i
$941$	−1.27546	−	12.1352i	−0.0415790	−	0.395597i	−0.995443	−	0.0953585i	$-0.969600\pi$
$941$	−1.27546	−	12.1352i	−0.0415790	−	0.395597i	0.953864	−	0.300239i	$-0.0970664\pi$
$942$		0			0
$943$	−2.15575	+	0.458219i	−0.0702008	+	0.0149216i
$944$	−10.3712	−	7.53513i	−0.337554	−	0.245248i
$945$		0			0
$946$	−1.92201	−	14.0896i	−0.0624898	−	0.458092i
$947$	15.5930	+	27.0079i	0.506706	+	0.877640i	0.999970	+	0.00776032i	$0.00247021\pi$
$947$	15.5930	+	27.0079i	0.506706	+	0.877640i	−0.493264	+	0.869879i	$0.664196\pi$
$948$		0			0
$949$	1.07958	+	1.19900i	0.0350448	+	0.0389212i
$950$	−3.75240	−	0.797597i	−0.121744	−	0.0258775i
$951$		0			0
$952$	0.235788	+	0.104980i	0.00764193	+	0.00340241i
$953$	5.66371	+	17.4311i	0.183466	+	0.564649i	0.999919	−	0.0127629i	$-0.00406266\pi$
$953$	5.66371	+	17.4311i	0.183466	+	0.564649i	−0.816453	+	0.577412i	$0.804063\pi$
$954$		0			0
$955$	−17.1629	−	12.4696i	−0.555378	−	0.403506i
$956$	12.0601	+	20.8887i	0.390050	+	0.675587i
$957$		0			0
$958$	6.72223	−	11.6432i	0.217185	−	0.376176i
$959$	−8.89751	+	3.96143i	−0.287316	+	0.127921i
$960$		0			0
$961$	0.508465	−	0.564708i	0.0164021	−	0.0182164i
$962$	−19.9037	+	14.4609i	−0.641723	+	0.466239i
$963$		0			0
$964$	−6.82455	−	21.0038i	−0.219804	−	0.676487i
$965$	−12.9341	+	2.74923i	−0.416364	+	0.0885009i
$966$		0			0
$967$	−10.4254	+	18.0573i	−0.335258	+	0.580683i	−0.983534	−	0.180722i	$-0.942157\pi$
$967$	−10.4254	+	18.0573i	−0.335258	+	0.580683i	0.648277	+	0.761405i	$0.275490\pi$
$968$	19.2454	−	15.8850i	0.618571	−	0.510562i
$969$		0			0
$970$	−0.581370	+	5.53137i	−0.0186667	+	0.177601i
$971$	8.79427	−	27.0660i	0.282222	−	0.868589i	−0.704996	−	0.709211i	$-0.749051\pi$
$971$	8.79427	−	27.0660i	0.282222	−	0.868589i	0.987218	−	0.159378i	$-0.0509488\pi$
$972$		0			0
$973$	8.30053	−	6.03069i	0.266103	−	0.193335i
$974$	−1.30913	−	0.582861i	−0.0419472	−	0.0186761i
$975$		0			0
$976$	−10.2838	−	11.4213i	−0.329175	−	0.365586i
$977$	20.3347	−	9.05359i	0.650564	−	0.289650i	−0.0547974	−	0.998497i	$-0.517451\pi$
$977$	20.3347	−	9.05359i	0.650564	−	0.289650i	0.705362	+	0.708848i	$0.250785\pi$
$978$		0			0
$979$	−3.14205	+	10.7925i	−0.100420	+	0.344929i
$980$	14.5857			0.465924
$981$		0			0
$982$	1.85302	−	5.70301i	0.0591322	−	0.181990i
$983$	15.4525	−	17.1618i	0.492859	−	0.547375i	−0.444482	−	0.895788i	$-0.646612\pi$
$983$	15.4525	−	17.1618i	0.492859	−	0.547375i	0.937341	+	0.348412i	$0.113279\pi$
$984$		0			0
$985$	3.71977	+	35.3912i	0.118522	+	1.12766i
$986$	−0.496998	−	0.105640i	−0.0158277	−	0.00336427i
$987$		0			0
$988$	−1.23945	+	11.7926i	−0.0394323	+	0.375173i
$989$	−2.18787			−0.0695703
$990$		0			0
$991$	−6.16408			−0.195809			−0.0979043	−	0.995196i	$-0.531214\pi$
$991$	−6.16408			−0.195809			−0.0979043	+	0.995196i	$0.531214\pi$
$992$	−3.33258	+	31.7074i	−0.105810	+	1.00671i
$993$		0			0
$994$	1.03726	+	0.220477i	0.0329000	+	0.00699310i
$995$	2.92220	+	27.8028i	0.0926399	+	0.881409i
$996$		0			0
$997$	16.9821	−	18.8606i	0.537830	−	0.597320i	−0.411575	−	0.911376i	$-0.635021\pi$
$997$	16.9821	−	18.8606i	0.537830	−	0.597320i	0.949405	+	0.314056i	$0.101688\pi$
$998$	−2.47504	+	7.61739i	−0.0783461	+	0.241124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.l.433.6		96
3.2	odd	2	inner	891.2.n.l.433.7		96
9.2	odd	6	inner	891.2.n.l.136.6		96
9.4	even	3		891.2.f.g.730.6	yes	48
9.5	odd	6		891.2.f.g.730.7	yes	48
9.7	even	3	inner	891.2.n.l.136.7		96
11.3	even	5	inner	891.2.n.l.190.7		96
33.14	odd	10	inner	891.2.n.l.190.6		96
99.5	odd	30		9801.2.a.cr.1.10		24
99.14	odd	30		891.2.f.g.487.7	yes	48
99.25	even	15	inner	891.2.n.l.784.6		96
99.47	odd	30	inner	891.2.n.l.784.7		96
99.49	even	15		9801.2.a.cr.1.15		24
99.50	even	30		9801.2.a.cq.1.15		24
99.58	even	15		891.2.f.g.487.6	✓	48
99.94	odd	30		9801.2.a.cq.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.6	✓	48	99.58	even	15
891.2.f.g.487.7	yes	48	99.14	odd	30
891.2.f.g.730.6	yes	48	9.4	even	3
891.2.f.g.730.7	yes	48	9.5	odd	6
891.2.n.l.136.6		96	9.2	odd	6	inner
891.2.n.l.136.7		96	9.7	even	3	inner
891.2.n.l.190.6		96	33.14	odd	10	inner
891.2.n.l.190.7		96	11.3	even	5	inner
891.2.n.l.433.6		96	1.1	even	1	trivial
891.2.n.l.433.7		96	3.2	odd	2	inner
891.2.n.l.784.6		96	99.25	even	15	inner
891.2.n.l.784.7		96	99.47	odd	30	inner
9801.2.a.cq.1.10		24	99.94	odd	30
9801.2.a.cq.1.15		24	99.50	even	30
9801.2.a.cr.1.10		24	99.5	odd	30
9801.2.a.cr.1.15		24	99.49	even	15

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0658016 + 0.626061i) q^{2} +(1.56867 + 0.333432i) q^{4} +(-0.142868 - 1.35930i) q^{5} +(-0.393445 + 0.436965i) q^{7} +(-0.701028 + 2.15754i) q^{8} +0.860404 q^{10} +(0.927090 - 3.18442i) q^{11} +(3.47139 - 1.54556i) q^{13} +(-0.247677 - 0.275073i) q^{14} +(1.62551 + 0.723726i) q^{16} +(-0.156539 + 0.113732i) q^{17} +(-0.601281 + 1.85055i) q^{19} +(0.229120 - 2.17993i) q^{20} +(1.93263 + 0.789954i) q^{22} +(0.160616 - 0.278195i) q^{23} +(3.06346 - 0.651158i) q^{25} +(0.739193 + 2.27500i) q^{26} +(-0.762884 + 0.554268i) q^{28} +(2.79122 - 3.09996i) q^{29} +(5.14837 - 2.29220i) q^{31} +(-2.82863 + 4.89933i) q^{32} +(-0.0609029 - 0.105487i) q^{34} +(0.650176 + 0.472381i) q^{35} +(3.17822 + 9.78156i) q^{37} +(-1.11899 - 0.498208i) q^{38} +(3.03290 + 0.644662i) q^{40} +(-4.59078 - 5.09857i) q^{41} +(-3.40544 - 5.89840i) q^{43} +(2.51609 - 4.68619i) q^{44} +(0.163598 + 0.118861i) q^{46} +(4.97666 - 1.05782i) q^{47} +(0.695560 + 6.61781i) q^{49} +(0.206084 + 1.96076i) q^{50} +(5.96082 - 1.26701i) q^{52} +(6.36368 + 4.62348i) q^{53} +(-4.46102 - 0.805240i) q^{55} +(-0.666954 - 1.15520i) q^{56} +(1.75710 + 1.95146i) q^{58} +(-7.04719 - 1.49793i) q^{59} +(-7.89061 - 3.51312i) q^{61} +(1.09629 + 3.37402i) q^{62} +(-0.00210888 - 0.00153219i) q^{64} +(-2.59683 - 4.49784i) q^{65} +(4.54870 - 7.87858i) q^{67} +(-0.283481 + 0.126214i) q^{68} +(-0.338522 + 0.375966i) q^{70} +(-2.31775 + 1.68394i) q^{71} +(0.131206 + 0.403812i) q^{73} +(-6.33298 + 1.34612i) q^{74} +(-1.56025 + 2.70242i) q^{76} +(1.02672 + 1.65800i) q^{77} +(0.429138 - 4.08298i) q^{79} +(0.751525 - 2.31296i) q^{80} +(3.49410 - 2.53861i) q^{82} +(6.79686 + 3.02616i) q^{83} +(0.176961 + 0.196535i) q^{85} +(3.91684 - 1.74389i) q^{86} +(6.22060 + 4.23260i) q^{88} -3.38915 q^{89} +(-0.690444 + 2.12497i) q^{91} +(0.344713 - 0.382842i) q^{92} +(0.334788 + 3.18530i) q^{94} +(2.60135 + 0.552935i) q^{95} +(-0.675694 + 6.42880i) q^{97} -4.18892 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52}+ \cdots + 66 q^{97}+O(q^{100}) \) 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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