LMFDB - Embedded newform 396.2.w.a.71.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(71,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 4]))

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

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

chi := DirichletCharacter("396.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			71.15
Character	$\chi$	$=$	396.71
Dual form			396.2.w.a.251.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.399974 - 1.35647i) q^{2} +(-1.68004 - 1.08511i) q^{4} +(-1.73701 - 0.564387i) q^{5} +(-1.29028 - 1.77592i) q^{7} +(-2.14389 + 1.84492i) q^{8} +O(q^{10})$	\(q+(0.399974 - 1.35647i) q^{2} +(-1.68004 - 1.08511i) q^{4} +(-1.73701 - 0.564387i) q^{5} +(-1.29028 - 1.77592i) q^{7} +(-2.14389 + 1.84492i) q^{8} +(-1.46033 + 2.13046i) q^{10} +(-3.30416 - 0.287275i) q^{11} +(1.55349 + 4.78117i) q^{13} +(-2.92506 + 1.03991i) q^{14} +(1.64508 + 3.64605i) q^{16} +(-2.77612 - 0.902015i) q^{17} +(2.06053 - 2.83607i) q^{19} +(2.30582 + 2.83303i) q^{20} +(-1.71126 + 4.36710i) q^{22} -3.20825 q^{23} +(-1.34643 - 0.978237i) q^{25} +(7.10688 - 0.194933i) q^{26} +(0.240660 + 4.38370i) q^{28} +(-4.65295 - 6.40423i) q^{29} +(-8.07200 + 2.62275i) q^{31} +(5.60377 - 0.773179i) q^{32} +(-2.33393 + 3.40495i) q^{34} +(1.23892 + 3.81299i) q^{35} +(7.25549 - 5.27142i) q^{37} +(-3.02290 - 3.92941i) q^{38} +(4.76521 - 1.99464i) q^{40} +(1.91862 - 2.64075i) q^{41} +1.91735i q^{43} +(5.23940 + 4.06801i) q^{44} +(-1.28322 + 4.35191i) q^{46} +(-1.08154 - 0.785788i) q^{47} +(0.674061 - 2.07455i) q^{49} +(-1.86549 + 1.43512i) q^{50} +(2.57815 - 9.71827i) q^{52} +(3.71127 - 1.20587i) q^{53} +(5.57721 + 2.36383i) q^{55} +(6.04264 + 1.42692i) q^{56} +(-10.5482 + 3.75007i) q^{58} +(7.77178 - 5.64653i) q^{59} +(1.01790 - 3.13277i) q^{61} +(0.329103 + 11.9985i) q^{62} +(1.19256 - 7.91061i) q^{64} -9.18169i q^{65} -9.45286i q^{67} +(3.68521 + 4.52781i) q^{68} +(5.66776 - 0.155459i) q^{70} +(-3.78338 + 11.6440i) q^{71} +(-2.21680 + 1.61060i) q^{73} +(-4.24854 - 11.9503i) q^{74} +(-6.53922 + 2.52882i) q^{76} +(3.75311 + 6.23857i) q^{77} +(-3.68907 + 1.19865i) q^{79} +(-0.799725 - 7.26168i) q^{80} +(-2.81471 - 3.65879i) q^{82} +(0.0446672 - 0.137472i) q^{83} +(4.31305 + 3.13361i) q^{85} +(2.60084 + 0.766892i) q^{86} +(7.61377 - 5.48001i) q^{88} +11.8533i q^{89} +(6.48651 - 8.92791i) q^{91} +(5.38999 + 3.48130i) q^{92} +(-1.49849 + 1.15279i) q^{94} +(-5.17979 + 3.76334i) q^{95} +(-4.71365 - 14.5071i) q^{97} +(-2.54446 - 1.74411i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) $ 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$

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 $

$2$	0.399974	−	1.35647i	0.282824	−	0.959172i
$2$	0.399974	−	1.35647i	0.282824	−	0.959172i
$3$		0			0
$3$		0			0
$4$	−1.68004	−	1.08511i	−0.840021	−	0.542554i
$5$	−1.73701	−	0.564387i	−0.776813	−	0.252402i	−0.106334	−	0.994330i	$-0.533911\pi$
$5$	−1.73701	−	0.564387i	−0.776813	−	0.252402i	−0.670479	+	0.741929i	$0.733911\pi$
$6$		0			0
$7$	−1.29028	−	1.77592i	−0.487679	−	0.671233i	0.492279	−	0.870438i	$-0.336164\pi$
$7$	−1.29028	−	1.77592i	−0.487679	−	0.671233i	−0.979958	+	0.199205i	$0.936164\pi$
$8$	−2.14389	+	1.84492i	−0.757981	+	0.652277i
$9$		0			0
$10$	−1.46033	+	2.13046i	−0.461798	+	0.673711i
$11$	−3.30416	−	0.287275i	−0.996242	−	0.0866168i
$11$	−3.30416	−	0.287275i	−0.996242	−	0.0866168i
$12$		0			0
$13$	1.55349	+	4.78117i	0.430862	+	1.32606i	0.897268	+	0.441486i	$0.145549\pi$
$13$	1.55349	+	4.78117i	0.430862	+	1.32606i	−0.466406	+	0.884571i	$0.654451\pi$
$14$	−2.92506	+	1.03991i	−0.781755	+	0.277927i
$15$		0			0
$16$	1.64508	+	3.64605i	0.411270	+	0.911514i
$17$	−2.77612	−	0.902015i	−0.673307	−	0.218771i	−0.0476443	−	0.998864i	$-0.515171\pi$
$17$	−2.77612	−	0.902015i	−0.673307	−	0.218771i	−0.625663	+	0.780094i	$0.715171\pi$
$18$		0			0
$19$	2.06053	−	2.83607i	0.472718	−	0.650640i	−0.504368	−	0.863489i	$-0.668274\pi$
$19$	2.06053	−	2.83607i	0.472718	−	0.650640i	0.977085	+	0.212849i	$0.0682743\pi$
$20$	2.30582	+	2.83303i	0.515597	+	0.633486i
$21$		0			0
$22$	−1.71126	+	4.36710i	−0.364842	+	0.931070i
$23$	−3.20825			−0.668966			−0.334483	−	0.942402i	$-0.608562\pi$
$23$	−3.20825			−0.668966			−0.334483	+	0.942402i	$0.608562\pi$
$24$		0			0
$25$	−1.34643	−	0.978237i	−0.269286	−	0.195647i
$26$	7.10688	−	0.194933i	1.39377	−	0.0382295i
$27$		0			0
$28$	0.240660	+	4.38370i	0.0454804	+	0.828442i
$29$	−4.65295	−	6.40423i	−0.864031	−	1.18924i	−0.980593	−	0.196053i	$-0.937188\pi$
$29$	−4.65295	−	6.40423i	−0.864031	−	1.18924i	0.116563	−	0.993183i	$-0.462812\pi$
$30$		0			0
$31$	−8.07200	+	2.62275i	−1.44977	+	0.471060i	−0.924930	−	0.380139i	$-0.875876\pi$
$31$	−8.07200	+	2.62275i	−1.44977	+	0.471060i	−0.524844	+	0.851198i	$0.675876\pi$
$32$	5.60377	−	0.773179i	0.990615	−	0.136680i
$33$		0			0
$34$	−2.33393	+	3.40495i	−0.400266	+	0.583943i
$35$	1.23892	+	3.81299i	0.209415	+	0.644513i
$36$		0			0
$37$	7.25549	−	5.27142i	1.19280	−	0.866616i	0.199238	−	0.979951i	$-0.436153\pi$
$37$	7.25549	−	5.27142i	1.19280	−	0.866616i	0.993557	+	0.113335i	$0.0361532\pi$
$38$	−3.02290	−	3.92941i	−0.490379	−	0.637434i
$39$		0			0
$40$	4.76521	−	1.99464i	0.753445	−	0.315381i
$41$	1.91862	−	2.64075i	0.299638	−	0.412416i	−0.632477	−	0.774579i	$-0.717962\pi$
$41$	1.91862	−	2.64075i	0.299638	−	0.412416i	0.932115	+	0.362163i	$0.117962\pi$
$42$		0			0
$43$			1.91735i			0.292394i	0.989256	+	0.146197i	$0.0467033\pi$
$43$			1.91735i			0.292394i	−0.989256	+	0.146197i	$0.953297\pi$
$44$	5.23940	+	4.06801i	0.789869	+	0.613275i
$45$		0			0
$46$	−1.28322	+	4.35191i	−0.189200	+	0.641654i
$47$	−1.08154	−	0.785788i	−0.157759	−	0.114619i	0.506105	−	0.862472i	$-0.331085\pi$
$47$	−1.08154	−	0.785788i	−0.157759	−	0.114619i	−0.663864	+	0.747853i	$0.731085\pi$
$48$		0			0
$49$	0.674061	−	2.07455i	0.0962944	−	0.296364i
$50$	−1.86549	+	1.43512i	−0.263820	+	0.202957i
$51$		0			0
$52$	2.57815	−	9.71827i	0.357525	−	1.34768i
$53$	3.71127	−	1.20587i	0.509782	−	0.165638i	−0.0428209	−	0.999083i	$-0.513634\pi$
$53$	3.71127	−	1.20587i	0.509782	−	0.165638i	0.552603	+	0.833444i	$0.313634\pi$
$54$		0			0
$55$	5.57721	+	2.36383i	0.752031	+	0.318738i
$56$	6.04264	+	1.42692i	0.807481	+	0.190680i
$57$		0			0
$58$	−10.5482	+	3.75007i	−1.38505	+	0.492409i
$59$	7.77178	−	5.64653i	1.01180	−	0.735115i	0.0472134	−	0.998885i	$-0.484966\pi$
$59$	7.77178	−	5.64653i	1.01180	−	0.735115i	0.964586	+	0.263770i	$0.0849659\pi$
$60$		0			0
$61$	1.01790	−	3.13277i	0.130329	−	0.401110i	−0.864506	−	0.502623i	$-0.832368\pi$
$61$	1.01790	−	3.13277i	0.130329	−	0.401110i	0.994834	+	0.101513i	$0.0323684\pi$
$62$	0.329103	+	11.9985i	0.0417961	+	1.52381i
$63$		0			0
$64$	1.19256	−	7.91061i	0.149070	−	0.988827i
$65$		−	9.18169i		−	1.13885i
$66$		0			0
$67$		−	9.45286i		−	1.15485i	−0.816443	−	0.577425i	$-0.804057\pi$
$67$		−	9.45286i		−	1.15485i	0.816443	−	0.577425i	$-0.195943\pi$
$68$	3.68521	+	4.52781i	0.446897	+	0.549078i
$69$		0			0
$70$	5.66776	−	0.155459i	0.677427	−	0.0185810i
$71$	−3.78338	+	11.6440i	−0.449004	+	1.38189i	0.429028	+	0.903291i	$0.358856\pi$
$71$	−3.78338	+	11.6440i	−0.449004	+	1.38189i	−0.878032	+	0.478601i	$0.841144\pi$
$72$		0			0
$73$	−2.21680	+	1.61060i	−0.259457	+	0.188507i	−0.709908	−	0.704295i	$-0.751263\pi$
$73$	−2.21680	+	1.61060i	−0.259457	+	0.188507i	0.450450	+	0.892801i	$0.351263\pi$
$74$	−4.24854	−	11.9503i	−0.493882	−	1.38920i
$75$		0			0
$76$	−6.53922	+	2.52882i	−0.750100	+	0.290076i
$77$	3.75311	+	6.23857i	0.427706	+	0.710952i
$78$		0			0
$79$	−3.68907	+	1.19865i	−0.415053	+	0.134859i	−0.509097	−	0.860709i	$-0.670021\pi$
$79$	−3.68907	+	1.19865i	−0.415053	+	0.134859i	0.0940441	+	0.995568i	$0.470021\pi$
$80$	−0.799725	−	7.26168i	−0.0894120	−	0.811881i
$81$		0			0
$82$	−2.81471	−	3.65879i	−0.310833	−	0.404045i
$83$	0.0446672	−	0.137472i	0.00490286	−	0.0150895i	−0.948575	−	0.316552i	$-0.897475\pi$
$83$	0.0446672	−	0.137472i	0.00490286	−	0.0150895i	0.953478	+	0.301463i	$0.0974748\pi$
$84$		0			0
$85$	4.31305	+	3.13361i	0.467815	+	0.339888i
$86$	2.60084	+	0.766892i	0.280456	+	0.0826960i
$87$		0			0
$88$	7.61377	−	5.48001i	0.811630	−	0.584171i
$89$			11.8533i			1.25645i	0.778032	+	0.628224i	$0.216218\pi$
$89$			11.8533i			1.25645i	−0.778032	+	0.628224i	$0.783782\pi$
$90$		0			0
$91$	6.48651	−	8.92791i	0.679971	−	0.935899i
$92$	5.38999	+	3.48130i	0.561946	+	0.362951i
$93$		0			0
$94$	−1.49849	+	1.15279i	−0.154558	+	0.118901i
$95$	−5.17979	+	3.76334i	−0.531436	+	0.386111i
$96$		0			0
$97$	−4.71365	−	14.5071i	−0.478599	−	1.47298i	−0.841042	−	0.540970i	$-0.818057\pi$
$97$	−4.71365	−	14.5071i	−0.478599	−	1.47298i	0.362443	−	0.932006i	$-0.381943\pi$
$98$	−2.54446	−	1.74411i	−0.257029	−	0.176182i
$99$		0			0
$100$	1.20056	+	3.10450i	0.120056	+	0.310450i
$101$	−4.75932	+	1.54640i	−0.473570	+	0.153872i	−0.536071	−	0.844173i	$-0.680092\pi$
$101$	−4.75932	+	1.54640i	−0.473570	+	0.153872i	0.0625014	+	0.998045i	$0.480092\pi$
$102$		0			0
$103$	6.11716	+	8.41955i	0.602742	+	0.829603i	0.995956	−	0.0898442i	$-0.0286369\pi$
$103$	6.11716	+	8.41955i	0.602742	+	0.829603i	−0.393214	+	0.919447i	$0.628637\pi$
$104$	−12.1514	−	7.38424i	−1.19154	−	0.724085i
$105$		0			0
$106$	−0.151312	−	5.51656i	−0.0146967	−	0.535815i
$107$	−14.9592	−	10.8685i	−1.44616	−	1.05069i	−0.986710	−	0.162489i	$-0.948048\pi$
$107$	−14.9592	−	10.8685i	−1.44616	−	1.05069i	−0.459447	−	0.888205i	$-0.651952\pi$
$108$		0			0
$109$	−16.0257			−1.53499			−0.767493	−	0.641058i	$-0.778496\pi$
$109$	−16.0257			−1.53499			−0.767493	+	0.641058i	$0.778496\pi$
$110$	5.43721	−	6.61987i	0.518417	−	0.631180i
$111$		0			0
$112$	4.35248	−	7.62595i	0.411270	−	0.720584i
$113$	4.41964	−	6.08312i	0.415765	−	0.572251i	−0.548848	−	0.835922i	$-0.684933\pi$
$113$	4.41964	−	6.08312i	0.415765	−	0.572251i	0.964613	+	0.263671i	$0.0849333\pi$
$114$		0			0
$115$	5.57275	+	1.81070i	0.519662	+	0.168848i
$116$	0.867858	+	15.8083i	0.0805786	+	1.46777i
$117$		0			0
$118$	−4.55085	−	12.8007i	−0.418940	−	1.17840i
$119$	1.98006	+	6.09400i	0.181512	+	0.558636i
$120$		0			0
$121$	10.8349	+	1.89841i	0.984995	+	0.172582i
$122$	−3.84239	−	2.63378i	−0.347873	−	0.238451i
$123$		0			0
$124$	16.4073	+	4.35266i	1.47342	+	0.390881i
$125$	7.15429	+	9.84704i	0.639899	+	0.880746i
$126$		0			0
$127$	7.29034	+	2.36877i	0.646913	+	0.210195i	0.614052	−	0.789265i	$-0.289538\pi$
$127$	7.29034	+	2.36877i	0.646913	+	0.210195i	0.0328605	+	0.999460i	$0.489538\pi$
$128$	−10.2535	−	4.78172i	−0.906294	−	0.422648i
$129$		0			0
$130$	−12.4547	−	3.67244i	−1.09235	−	0.322094i
$131$	19.9420			1.74234			0.871171	−	0.490980i	$-0.163361\pi$
$131$	19.9420			1.74234			0.871171	+	0.490980i	$0.163361\pi$
$132$		0			0
$133$	−7.69528			−0.667266
$134$	−12.8226	−	3.78090i	−1.10770	−	0.326620i
$135$		0			0
$136$	7.61584	−	3.18788i	0.653053	−	0.273358i
$137$	7.53060	+	2.44684i	0.643382	+	0.209048i	0.612494	−	0.790475i	$-0.290166\pi$
$137$	7.53060	+	2.44684i	0.643382	+	0.209048i	0.0308883	+	0.999523i	$0.490166\pi$
$138$		0			0
$139$	−9.06957	−	12.4832i	−0.769271	−	1.05881i	−0.996386	−	0.0849425i	$-0.972929\pi$
$139$	−9.06957	−	12.4832i	−0.769271	−	1.05881i	0.227115	−	0.973868i	$-0.427071\pi$
$140$	2.05608	−	7.75035i	0.173770	−	0.655024i
$141$		0			0
$142$	14.2816	+	9.78936i	1.19848	+	0.821505i
$143$	−3.75948	−	16.2440i	−0.314384	−	1.35839i
$144$		0			0
$145$	4.46773	+	13.7503i	0.371025	+	1.14190i
$146$	1.29808	+	3.65124i	0.107430	+	0.302178i
$147$		0			0
$148$	−17.9096	+	0.983214i	−1.47216	+	0.0808197i
$149$	1.04502	+	0.339547i	0.0856114	+	0.0278168i	0.351510	−	0.936184i	$-0.385668\pi$
$149$	1.04502	+	0.339547i	0.0856114	+	0.0278168i	−0.265898	+	0.964001i	$0.585668\pi$
$150$		0			0
$151$	−13.8460	+	19.0574i	−1.12677	+	1.55087i	−0.332710	+	0.943029i	$0.607963\pi$
$151$	−13.8460	+	19.0574i	−1.12677	+	1.55087i	−0.794061	+	0.607838i	$0.792037\pi$
$152$	0.814766	+	9.88174i	0.0660863	+	0.801515i
$153$		0			0
$154$	9.96361	−	2.59573i	0.802890	−	0.209170i
$155$	15.5014			1.24510
$156$		0			0
$157$	−8.28412	−	6.01877i	−0.661145	−	0.480350i	0.205904	−	0.978572i	$-0.433986\pi$
$157$	−8.28412	−	6.01877i	−0.661145	−	0.480350i	−0.867049	+	0.498222i	$0.833986\pi$
$158$	0.150407	+	5.48356i	0.0119657	+	0.436248i
$159$		0			0
$160$	−10.1701	−	1.81968i	−0.804021	−	0.143858i
$161$	4.13954	+	5.69758i	0.326241	+	0.449032i
$162$		0			0
$163$	−10.4105	+	3.38258i	−0.815413	+	0.264944i	−0.686889	−	0.726762i	$-0.741024\pi$
$163$	−10.4105	+	3.38258i	−0.815413	+	0.264944i	−0.128524	+	0.991706i	$0.541024\pi$
$164$	−6.08886	+	2.35466i	−0.475460	+	0.183868i
$165$		0			0
$166$	−0.168611	−	0.115575i	−0.0130867	−	0.00897035i
$167$	−3.08331	−	9.48945i	−0.238594	−	0.734316i	−0.996624	−	0.0820968i	$-0.973838\pi$
$167$	−3.08331	−	9.48945i	−0.238594	−	0.734316i	0.758031	−	0.652219i	$-0.226162\pi$
$168$		0			0
$169$	−9.92898	+	7.21382i	−0.763767	+	0.554909i
$170$	5.97577	−	4.59717i	0.458320	−	0.352587i
$171$		0			0
$172$	2.08054	−	3.22123i	0.158639	−	0.245617i
$173$	0.926882	−	1.27574i	0.0704695	−	0.0969929i	−0.772327	−	0.635225i	$-0.780907\pi$
$173$	0.926882	−	1.27574i	0.0704695	−	0.0969929i	0.842797	+	0.538232i	$0.180907\pi$
$174$		0			0
$175$			3.65334i			0.276167i
$176$	−4.38818	−	12.5197i	−0.330772	−	0.943711i
$177$		0			0
$178$	16.0787	+	4.74102i	1.20515	+	0.355354i
$179$	16.5094	+	11.9948i	1.23397	+	0.896532i	0.997181	−	0.0750292i	$-0.0239050\pi$
$179$	16.5094	+	11.9948i	1.23397	+	0.896532i	0.236789	+	0.971561i	$0.423905\pi$
$180$		0			0
$181$	−0.0377346	+	0.116135i	−0.00280479	+	0.00863225i	−0.952449	−	0.304698i	$-0.901445\pi$
$181$	−0.0377346	+	0.116135i	−0.00280479	+	0.00863225i	0.949644	+	0.313330i	$0.101445\pi$
$182$	−9.51604	−	12.3697i	−0.705376	−	0.916904i
$183$		0			0
$184$	6.87815	−	5.91896i	0.507064	−	0.436351i
$185$	−15.5780	+	5.06158i	−1.14531	+	0.372135i
$186$		0			0
$187$	8.91361	+	3.77791i	0.651827	+	0.276268i
$188$	0.964374	+	2.49375i	0.0703342	+	0.181875i
$189$		0			0
$190$	3.03309	+	8.53149i	0.220043	+	0.618940i
$191$	11.1650	−	8.11186i	0.807873	−	0.586954i	−0.105340	−	0.994436i	$-0.533593\pi$
$191$	11.1650	−	8.11186i	0.807873	−	0.586954i	0.913213	+	0.407482i	$0.133593\pi$
$192$		0			0
$193$	−3.11152	+	9.57627i	−0.223972	+	0.689315i	0.774422	+	0.632669i	$0.218041\pi$
$193$	−3.11152	+	9.57627i	−0.223972	+	0.689315i	−0.998394	+	0.0566461i	$0.981959\pi$
$194$	−21.5639	+	0.591470i	−1.54820	+	0.0424650i
$195$		0			0
$196$	−3.38356	+	2.75389i	−0.241683	+	0.196707i
$197$			14.3320i			1.02111i	0.859845	+	0.510555i	$0.170560\pi$
$197$			14.3320i			1.02111i	−0.859845	+	0.510555i	$0.829440\pi$
$198$		0			0
$199$			18.3337i			1.29964i	0.760087	+	0.649822i	$0.225157\pi$
$199$			18.3337i			1.29964i	−0.760087	+	0.649822i	$0.774843\pi$
$200$	4.69137	−	0.386811i	0.331730	−	0.0273517i
$201$		0			0
$202$	0.194042	+	7.07441i	0.0136528	+	0.497754i
$203$	−5.36978	+	16.5265i	−0.376885	+	1.15993i
$204$		0			0
$205$	−4.82306	+	3.50416i	−0.336857	+	0.244741i
$206$	13.8676	−	4.93017i	0.966201	−	0.343501i
$207$		0			0
$208$	−14.8768	+	13.5295i	−1.03152	+	0.938104i
$209$	−7.62305	+	8.77890i	−0.527297	+	0.607249i
$210$		0			0
$211$	8.07977	−	2.62528i	0.556235	−	0.180732i	−0.0173917	−	0.999849i	$-0.505536\pi$
$211$	8.07977	−	2.62528i	0.556235	−	0.180732i	0.573626	+	0.819117i	$0.305536\pi$
$212$	−7.54359	−	2.00123i	−0.518096	−	0.137445i
$213$		0			0
$214$	−20.7261	+	15.9446i	−1.41680	+	1.08995i
$215$	1.08213	−	3.33045i	0.0738007	−	0.227135i
$216$		0			0
$217$	15.0729	+	10.9511i	1.02322	+	0.743410i
$218$	−6.40987	+	21.7385i	−0.434131	+	1.47231i
$219$		0			0
$220$	−6.80494	−	10.0232i	−0.458789	−	0.675764i
$221$		−	14.6743i		−	0.987103i
$222$		0			0
$223$	4.59271	−	6.32132i	0.307551	−	0.423307i	−0.627065	−	0.778967i	$-0.715744\pi$
$223$	4.59271	−	6.32132i	0.307551	−	0.423307i	0.934615	+	0.355660i	$0.115744\pi$
$224$	−8.60352	−	8.95420i	−0.574847	−	0.598278i
$225$		0			0
$226$	−6.48384	−	8.42822i	−0.431299	−	0.560637i
$227$	7.10996	−	5.16569i	0.471905	−	0.342859i	−0.326278	−	0.945274i	$-0.605795\pi$
$227$	7.10996	−	5.16569i	0.471905	−	0.342859i	0.798183	+	0.602415i	$0.205795\pi$
$228$		0			0
$229$	8.46024	+	26.0380i	0.559069	+	1.72064i	0.684949	+	0.728591i	$0.259825\pi$
$229$	8.46024	+	26.0380i	0.559069	+	1.72064i	−0.125880	+	0.992045i	$0.540175\pi$
$230$	4.68512	−	6.83506i	0.308928	−	0.450690i
$231$		0			0
$232$	21.7907	+	5.14570i	1.43063	+	0.337832i
$233$	−6.67059	+	2.16741i	−0.437005	+	0.141991i	−0.519253	−	0.854620i	$-0.673790\pi$
$233$	−6.67059	+	2.16741i	−0.437005	+	0.141991i	0.0822485	+	0.996612i	$0.473790\pi$
$234$		0			0
$235$	1.43516	+	1.97533i	0.0936195	+	0.128856i
$236$	−19.1840	+	1.05318i	−1.24877	+	0.0685560i
$237$		0			0
$238$	9.05832	−	0.248458i	0.587164	−	0.0161052i
$239$	−21.0594	−	15.3005i	−1.36222	−	0.989709i	−0.998300	−	0.0582781i	$-0.981439\pi$
$239$	−21.0594	−	15.3005i	−1.36222	−	0.989709i	−0.363918	−	0.931431i	$-0.618561\pi$
$240$		0			0
$241$	−10.6121			−0.683586			−0.341793	−	0.939775i	$-0.611034\pi$
$241$	−10.6121			−0.683586			−0.341793	+	0.939775i	$0.611034\pi$
$242$	6.90884	−	13.9380i	0.444117	−	0.895969i
$243$		0			0
$244$	−5.10951	+	4.15865i	−0.327103	+	0.266230i
$245$	−2.34169	+	3.22307i	−0.149605	+	0.205914i
$246$		0			0
$247$	16.7608	+	5.44590i	1.06646	+	0.346514i
$248$	12.4667	−	20.5151i	0.791639	−	1.30271i
$249$		0			0
$250$	16.2188	−	5.76605i	1.02577	−	0.364677i
$251$	2.49513	+	7.67922i	0.157491	+	0.484708i	0.998405	−	0.0564613i	$-0.0179817\pi$
$251$	2.49513	+	7.67922i	0.157491	+	0.484708i	−0.840914	+	0.541169i	$0.817982\pi$
$252$		0			0
$253$	10.6006	+	0.921651i	0.666452	+	0.0579437i
$254$	6.12913	−	8.94170i	0.384576	−	0.561052i
$255$		0			0
$256$	−10.5874	+	11.9961i	−0.661714	+	0.749756i
$257$	6.23033	+	8.57531i	0.388637	+	0.534913i	0.957847	−	0.287279i	$-0.0927507\pi$
$257$	6.23033	+	8.57531i	0.388637	+	0.534913i	−0.569210	+	0.822192i	$0.692751\pi$
$258$		0			0
$259$	−18.7232	−	6.08354i	−1.16340	−	0.378013i
$260$	−9.96313	+	15.4256i	−0.617887	+	0.956656i
$261$		0			0
$262$	7.97629	−	27.0508i	0.492777	−	1.67121i
$263$	−5.37487			−0.331429			−0.165714	−	0.986174i	$-0.552993\pi$
$263$	−5.37487			−0.331429			−0.165714	+	0.986174i	$0.552993\pi$
$264$		0			0
$265$	−7.12708			−0.437813
$266$	−3.07791	+	10.4384i	−0.188719	+	0.640022i
$267$		0			0
$268$	−10.2574	+	15.8812i	−0.626569	+	0.970099i
$269$	10.2310	+	3.32424i	0.623793	+	0.202682i	0.603823	−	0.797118i	$-0.293643\pi$
$269$	10.2310	+	3.32424i	0.623793	+	0.202682i	0.0199691	+	0.999801i	$0.493643\pi$
$270$		0			0
$271$	−17.1935	−	23.6648i	−1.04443	−	1.43753i	−0.893542	−	0.448980i	$-0.851787\pi$
$271$	−17.1935	−	23.6648i	−1.04443	−	1.43753i	−0.150886	−	0.988551i	$-0.548213\pi$
$272$	−1.27814	−	11.6058i	−0.0774984	−	0.703702i
$273$		0			0
$274$	6.33112	−	9.23638i	0.382477	−	0.557990i
$275$	4.16779	+	3.61905i	0.251327	+	0.218237i
$276$		0			0
$277$	−6.61972	−	20.3734i	−0.397740	−	1.22412i	−0.926807	−	0.375539i	$-0.877458\pi$
$277$	−6.61972	−	20.3734i	−0.397740	−	1.22412i	0.529066	−	0.848580i	$-0.322542\pi$
$278$	−20.5607	+	7.30968i	−1.23315	+	0.438405i
$279$		0			0
$280$	−9.69076	−	5.88896i	−0.579134	−	0.351932i
$281$	6.73867	+	2.18953i	0.401995	+	0.130616i	0.503035	−	0.864266i	$-0.332217\pi$
$281$	6.73867	+	2.18953i	0.401995	+	0.130616i	−0.101039	+	0.994882i	$0.532217\pi$
$282$		0			0
$283$	12.2201	−	16.8195i	0.726409	−	0.999816i	−0.272878	−	0.962049i	$-0.587975\pi$
$283$	12.2201	−	16.8195i	0.726409	−	0.999816i	0.999287	−	0.0377674i	$-0.0120246\pi$
$284$	18.9913	−	15.4571i	1.12692	−	0.917209i
$285$		0			0
$286$	−23.5383	−	1.39754i	−1.39185	−	0.0826385i
$287$	−7.16530			−0.422954
$288$		0			0
$289$	−6.86010	−	4.98415i	−0.403535	−	0.293185i
$290$	20.4388	−	0.560611i	1.20021	−	0.0329202i
$291$		0			0
$292$	5.47200	−	0.300406i	0.320225	−	0.0175799i
$293$	−16.8634	−	23.2105i	−0.985172	−	1.35597i	−0.933996	−	0.357283i	$-0.883703\pi$
$293$	−16.8634	−	23.2105i	−0.985172	−	1.35597i	−0.0511758	−	0.998690i	$-0.516297\pi$
$294$		0			0
$295$	−16.6865	+	5.42176i	−0.971523	+	0.315667i
$296$	−5.82967	+	24.6871i	−0.338842	+	1.43491i
$297$		0			0
$298$	0.878568	−	1.28173i	0.0508941	−	0.0742487i
$299$	−4.98400	−	15.3392i	−0.288232	−	0.887087i
$300$		0			0
$301$	3.40506	−	2.47392i	0.196264	−	0.142594i
$302$	20.3128	+	26.4042i	1.16887	+	1.51939i
$303$		0			0
$304$	13.7302	+	2.84723i	0.787482	+	0.163300i
$305$	−3.53619	+	4.86715i	−0.202482	+	0.278692i
$306$		0			0
$307$		−	24.8361i		−	1.41747i	−0.705476	−	0.708734i	$-0.749267\pi$
$307$		−	24.8361i		−	1.41747i	0.705476	−	0.708734i	$-0.250733\pi$
$308$	0.464151	−	14.5536i	0.0264475	−	0.829268i
$309$		0			0
$310$	6.20014	−	21.0272i	0.352144	−	1.19426i
$311$	−2.42196	−	1.75966i	−0.137337	−	0.0997810i	0.516996	−	0.855988i	$-0.327050\pi$
$311$	−2.42196	−	1.75966i	−0.137337	−	0.0997810i	−0.654332	+	0.756207i	$0.727050\pi$
$312$		0			0
$313$	9.23726	−	28.4293i	0.522121	−	1.60692i	−0.247820	−	0.968806i	$-0.579714\pi$
$313$	9.23726	−	28.4293i	0.522121	−	1.60692i	0.769941	−	0.638116i	$-0.220286\pi$
$314$	−11.4777	+	8.82984i	−0.647726	+	0.498297i
$315$		0			0
$316$	7.49846	+	1.98926i	0.421821	+	0.111904i
$317$	−5.75172	+	1.86885i	−0.323049	+	0.104965i	−0.466052	−	0.884757i	$-0.654324\pi$
$317$	−5.75172	+	1.86885i	−0.323049	+	0.104965i	0.143003	+	0.989722i	$0.454324\pi$
$318$		0			0
$319$	13.5343	+	22.4973i	0.757776	+	1.25961i
$320$	−6.53614	+	13.0677i	−0.365381	+	0.730507i
$321$		0			0
$322$	9.38433	−	3.33629i	0.522968	−	0.185924i
$323$	−8.27845	+	6.01464i	−0.460625	+	0.334664i
$324$		0			0
$325$	2.58545	−	7.95718i	0.143415	−	0.441385i
$326$	0.424446	+	15.4745i	0.0235079	+	0.857054i
$327$		0			0
$328$	0.758653	+	9.20118i	0.0418896	+	0.508050i
$329$			2.93462i			0.161791i
$330$		0			0
$331$			14.5648i			0.800555i	0.916394	+	0.400277i	$0.131086\pi$
$331$			14.5648i			0.800555i	−0.916394	+	0.400277i	$0.868914\pi$
$332$	−0.224214	+	0.182489i	−0.0123054	+	0.0100154i
$333$		0			0
$334$	−14.1054	+	0.386894i	−0.771815	+	0.0211699i
$335$	−5.33508	+	16.4197i	−0.291486	+	0.897103i
$336$		0			0
$337$	2.29427	−	1.66689i	0.124977	−	0.0908010i	−0.523541	−	0.852001i	$-0.675389\pi$
$337$	2.29427	−	1.66689i	0.124977	−	0.0908010i	0.648518	+	0.761200i	$0.275389\pi$
$338$	5.81403	+	16.3537i	0.316241	+	0.889526i
$339$		0			0
$340$	−3.84579	−	9.94472i	−0.208567	−	0.539328i
$341$	27.4246	−	6.34710i	1.48513	−	0.343715i
$342$		0			0
$343$	−19.1679	+	6.22804i	−1.03497	+	0.336283i
$344$	−3.53736	−	4.11060i	−0.190722	−	0.221629i
$345$		0			0
$346$	−1.35978	−	1.76755i	−0.0731024	−	0.0950243i
$347$	−7.92331	+	24.3854i	−0.425346	+	1.30908i	0.477317	+	0.878731i	$0.341609\pi$
$347$	−7.92331	+	24.3854i	−0.425346	+	1.30908i	−0.902663	+	0.430348i	$0.858391\pi$
$348$		0			0
$349$	−8.16928	−	5.93533i	−0.437291	−	0.317711i	0.347266	−	0.937767i	$-0.387110\pi$
$349$	−8.16928	−	5.93533i	−0.437291	−	0.317711i	−0.784558	+	0.620056i	$0.787110\pi$
$350$	4.95566	+	1.46124i	0.264891	+	0.0781066i
$351$		0			0
$352$	−18.7379	+	0.944884i	−0.998731	+	0.0503625i
$353$		−	27.0924i		−	1.44198i	−0.692944	−	0.720991i	$-0.743687\pi$
$353$		−	27.0924i		−	1.44198i	0.692944	−	0.720991i	$-0.256313\pi$
$354$		0			0
$355$	13.1435	−	18.0905i	0.697584	−	0.960142i
$356$	12.8621	−	19.9141i	0.681692	−	1.05544i
$357$		0			0
$358$	22.8739	−	17.5970i	1.20892	−	0.930028i
$359$	3.90897	−	2.84003i	0.206308	−	0.149891i	−0.479834	−	0.877359i	$-0.659303\pi$
$359$	3.90897	−	2.84003i	0.206308	−	0.149891i	0.686141	+	0.727468i	$0.259303\pi$
$360$		0			0
$361$	2.07379	+	6.38246i	0.109147	+	0.335919i
$362$	0.142441	+	0.0976369i	0.00748655	+	0.00513168i
$363$		0			0
$364$	−20.5853	+	7.96070i	−1.07897	+	0.417254i
$365$	4.75961	−	1.54649i	0.249129	−	0.0809470i
$366$		0			0
$367$	11.3087	+	15.5650i	0.590307	+	0.812488i	0.994778	−	0.102063i	$-0.0325444\pi$
$367$	11.3087	+	15.5650i	0.590307	+	0.812488i	−0.404471	+	0.914551i	$0.632544\pi$
$368$	−5.27783	−	11.6975i	−0.275126	−	0.609772i
$369$		0			0
$370$	0.635128	+	23.1556i	0.0330187	+	1.20380i
$371$	−6.93009	−	5.03500i	−0.359792	−	0.261404i
$372$		0			0
$373$	22.3835			1.15897			0.579487	−	0.814981i	$-0.303253\pi$
$373$	22.3835			1.15897			0.579487	+	0.814981i	$0.303253\pi$
$374$	8.68985	−	10.5800i	0.449341	−	0.547079i
$375$		0			0
$376$	3.76843	−	0.310713i	0.194342	−	0.0160238i
$377$	23.3914	−	32.1955i	1.20472	−	1.65815i
$378$		0			0
$379$	20.4579	+	6.64718i	1.05085	+	0.341443i	0.783003	−	0.622018i	$-0.213687\pi$
$379$	20.4579	+	6.64718i	1.05085	+	0.341443i	0.267850	+	0.963461i	$0.413687\pi$
$380$	12.7859	−	0.701930i	0.655903	−	0.0360083i
$381$		0			0
$382$	−6.53781	−	18.3896i	−0.334503	−	0.940893i
$383$	−3.38448	−	10.4164i	−0.172939	−	0.532251i	0.826594	−	0.562798i	$-0.190275\pi$
$383$	−3.38448	−	10.4164i	−0.172939	−	0.532251i	−0.999533	+	0.0305467i	$0.990275\pi$
$384$		0			0
$385$	−2.99820	−	12.9546i	−0.152802	−	0.660230i
$386$	11.7454	+	8.05096i	0.597827	+	0.409783i
$387$		0			0
$388$	−7.82268	+	29.4874i	−0.397136	+	1.49700i
$389$	−7.55507	−	10.3987i	−0.383057	−	0.527233i	0.573334	−	0.819322i	$-0.305650\pi$
$389$	−7.55507	−	10.3987i	−0.383057	−	0.527233i	−0.956391	+	0.292089i	$0.905650\pi$
$390$		0			0
$391$	8.90648	+	2.89389i	0.450420	+	0.146350i
$392$	2.38225	+	5.69119i	0.120322	+	0.287449i
$393$		0			0
$394$	19.4409	+	5.73242i	0.979421	+	0.288795i
$395$	7.08444			0.356457
$396$		0			0
$397$	24.8285			1.24611			0.623054	−	0.782178i	$-0.285891\pi$
$397$	24.8285			1.24611			0.623054	+	0.782178i	$0.285891\pi$
$398$	24.8692	+	7.33302i	1.24658	+	0.367571i
$399$		0			0
$400$	1.35173	−	6.51843i	0.0675863	−	0.325921i
$401$	−9.70297	−	3.15268i	−0.484543	−	0.157438i	0.0565510	−	0.998400i	$-0.481990\pi$
$401$	−9.70297	−	3.15268i	−0.484543	−	0.157438i	−0.541094	+	0.840962i	$0.681990\pi$
$402$		0			0
$403$	−25.0796	−	34.5191i	−1.24930	−	1.71952i
$404$	9.67386	+	2.56637i	0.481293	+	0.127682i
$405$		0			0
$406$	20.2700	+	13.8941i	1.00598	+	0.689554i
$407$	−25.4876	+	15.3333i	−1.26338	+	0.760043i
$408$		0			0
$409$	−4.48582	−	13.8059i	−0.221810	−	0.682660i	−0.998600	−	0.0529005i	$-0.983153\pi$
$409$	−4.48582	−	13.8059i	−0.221810	−	0.682660i	0.776790	−	0.629760i	$-0.216847\pi$
$410$	2.82420	+	7.94392i	0.139477	+	0.392322i
$411$		0			0
$412$	−1.14096	−	20.7830i	−0.0562110	−	1.02390i
$413$	−20.0555	−	6.51643i	−0.986867	−	0.320653i
$414$		0			0
$415$	−0.155174	+	0.213579i	−0.00761721	+	0.0104842i
$416$	12.4021	+	25.5914i	0.608064	+	1.25472i
$417$		0			0
$418$	8.85933	+	13.8518i	0.433324	+	0.677514i
$419$	34.9421			1.70703			0.853517	−	0.521064i	$-0.174465\pi$
$419$	34.9421			1.70703			0.853517	+	0.521064i	$0.174465\pi$
$420$		0			0
$421$	−10.1069	−	7.34307i	−0.492579	−	0.357879i	0.313596	−	0.949556i	$-0.398466\pi$
$421$	−10.1069	−	7.34307i	−0.492579	−	0.357879i	−0.806175	+	0.591677i	$0.798466\pi$
$422$	−0.329420	−	12.0100i	−0.0160359	−	0.584640i
$423$		0			0
$424$	−5.73185	+	9.43224i	−0.278363	+	0.458070i
$425$	2.85546	+	3.93020i	0.138510	+	0.190643i
$426$		0			0
$427$	−6.87691	+	2.23444i	−0.332797	+	0.108132i
$428$	13.3385	+	34.4918i	0.644743	+	1.66722i
$429$		0			0
$430$	−4.08485	−	2.79998i	−0.196989	−	0.135027i
$431$	1.60245	+	4.93185i	0.0771875	+	0.237559i	0.982204	−	0.187818i	$-0.0601416\pi$
$431$	1.60245	+	4.93185i	0.0771875	+	0.237559i	−0.905016	+	0.425377i	$0.860142\pi$
$432$		0			0
$433$	−8.22325	+	5.97454i	−0.395184	+	0.287118i	−0.767577	−	0.640957i	$-0.778538\pi$
$433$	−8.22325	+	5.97454i	−0.395184	+	0.287118i	0.372392	+	0.928075i	$0.378538\pi$
$434$	20.8837	−	16.0658i	1.00245	−	0.771185i
$435$		0			0
$436$	26.9239	+	17.3896i	1.28942	+	0.832813i
$437$	−6.61069	+	9.09883i	−0.316232	+	0.435256i
$438$		0			0
$439$			16.1358i			0.770120i	0.922891	+	0.385060i	$0.125819\pi$
$439$			16.1358i			0.770120i	−0.922891	+	0.385060i	$0.874181\pi$
$440$	−16.3180	+	5.22170i	−0.777931	+	0.248935i
$441$		0			0
$442$	−19.9054	−	5.86936i	−0.946802	−	0.279177i
$443$	8.23948	+	5.98633i	0.391469	+	0.284419i	0.766057	−	0.642772i	$-0.222216\pi$
$443$	8.23948	+	5.98633i	0.391469	+	0.284419i	−0.374588	+	0.927191i	$0.622216\pi$
$444$		0			0
$445$	6.68986	−	20.5893i	0.317130	−	0.976025i
$446$	−6.73774	−	8.75825i	−0.319041	−	0.414715i
$447$		0			0
$448$	−15.5873	+	8.08900i	−0.736432	+	0.382169i
$449$	−24.4706	+	7.95098i	−1.15484	+	0.375230i	−0.822964	−	0.568094i	$-0.807681\pi$
$449$	−24.4706	+	7.95098i	−1.15484	+	0.375230i	−0.331875	+	0.943324i	$0.607681\pi$
$450$		0			0
$451$	−7.09804	+	8.17429i	−0.334234	+	0.384912i
$452$	−14.0260	+	5.42410i	−0.659729	+	0.255128i
$453$		0			0
$454$	−4.16332	−	11.7106i	−0.195394	−	0.549606i
$455$	−16.3059	+	11.8469i	−0.764432	+	0.555393i
$456$		0			0
$457$	5.61789	−	17.2901i	0.262794	−	0.808797i	−0.729399	−	0.684088i	$-0.760200\pi$
$457$	5.61789	−	17.2901i	0.262794	−	0.808797i	0.992193	−	0.124709i	$-0.0397996\pi$
$458$	38.7037	−	1.06159i	1.80850	−	0.0496050i
$459$		0			0
$460$	−7.39765	−	9.08908i	−0.344917	−	0.423781i
$461$		−	13.5980i		−	0.633324i	−0.948539	−	0.316662i	$-0.897438\pi$
$461$		−	13.5980i		−	0.633324i	0.948539	−	0.316662i	$-0.102562\pi$
$462$		0			0
$463$		−	36.2439i		−	1.68440i	−0.539166	−	0.842200i	$-0.681260\pi$
$463$		−	36.2439i		−	1.68440i	0.539166	−	0.842200i	$-0.318740\pi$
$464$	15.6957	−	27.5004i	0.728655	−	1.27667i
$465$		0			0
$466$	0.271966	+	9.91538i	0.0125986	+	0.459321i
$467$	3.15546	−	9.71150i	0.146017	−	0.449395i	−0.851123	−	0.524966i	$-0.824078\pi$
$467$	3.15546	−	9.71150i	0.146017	−	0.449395i	0.997140	+	0.0755714i	$0.0240781\pi$
$468$		0			0
$469$	−16.7875	+	12.1968i	−0.775174	+	0.563197i
$470$	3.25351	−	1.15668i	0.150073	−	0.0533535i
$471$		0			0
$472$	−6.24449	+	26.4438i	−0.287426	+	1.21718i
$473$	0.550808	−	6.33524i	0.0253262	−	0.291295i
$474$		0			0
$475$	−5.54871	+	1.80288i	−0.254592	+	0.0827220i
$476$	3.28607	−	12.3868i	0.150617	−	0.567746i
$477$		0			0
$478$	−29.1780	+	22.4467i	−1.33457	+	1.02669i
$479$	−1.46586	+	4.51146i	−0.0669769	+	0.206134i	−0.978944	−	0.204130i	$-0.934563\pi$
$479$	−1.46586	+	4.51146i	−0.0669769	+	0.206134i	0.911967	+	0.410264i	$0.134563\pi$
$480$		0			0
$481$	36.4749	+	26.5006i	1.66311	+	1.20832i
$482$	−4.24457	+	14.3950i	−0.193335	+	0.655676i
$483$		0			0
$484$	−16.1432	−	14.9465i	−0.733781	−	0.679386i
$485$			27.8593i			1.26503i
$486$		0			0
$487$	3.46726	−	4.77228i	0.157117	−	0.216252i	−0.723201	−	0.690638i	$-0.757330\pi$
$487$	3.46726	−	4.77228i	0.157117	−	0.216252i	0.880317	+	0.474386i	$0.157330\pi$
$488$	3.59743	+	8.59426i	0.162848	+	0.389044i
$489$		0			0
$490$	3.43539	+	4.46559i	0.155195	+	0.201735i
$491$	−8.22409	+	5.97515i	−0.371148	+	0.269655i	−0.757687	−	0.652618i	$-0.773671\pi$
$491$	−8.22409	+	5.97515i	−0.371148	+	0.269655i	0.386539	+	0.922273i	$0.373671\pi$
$492$		0			0
$493$	7.14041	+	21.9759i	0.321588	+	0.989746i
$494$	14.0911	−	20.5573i	0.633988	−	0.924917i
$495$		0			0
$496$	−22.8418	−	25.1163i	−1.02563	−	1.12776i
$497$	25.5604	−	8.30509i	1.14654	−	0.372534i
$498$		0			0
$499$	−20.2604	−	27.8860i	−0.906980	−	1.24835i	−0.968187	−	0.250226i	$-0.919495\pi$
$499$	−20.2604	−	27.8860i	−0.906980	−	1.24835i	0.0612074	−	0.998125i	$-0.480505\pi$
$500$	−1.33440	−	24.3066i	−0.0596763	−	1.08703i
$501$		0			0
$502$	11.4146	−	0.313089i	0.509461	−	0.0139739i
$503$	−7.77493	−	5.64882i	−0.346667	−	0.251868i	0.400802	−	0.916164i	$-0.368731\pi$
$503$	−7.77493	−	5.64882i	−0.346667	−	0.251868i	−0.747469	+	0.664296i	$0.768731\pi$
$504$		0			0
$505$	9.13973			0.406713
$506$	5.49015	−	14.0108i	0.244067	−	0.622854i
$507$		0			0
$508$	−9.67769	−	11.8904i	−0.429378	−	0.527553i
$509$	−9.33894	+	12.8539i	−0.413941	+	0.569741i	−0.964174	−	0.265270i	$-0.914539\pi$
$509$	−9.33894	+	12.8539i	−0.413941	+	0.569741i	0.550233	+	0.835011i	$0.314539\pi$
$510$		0			0
$511$	5.72059	+	1.85873i	0.253064	+	0.0822255i
$512$	12.0377	+	19.1597i	0.531996	+	0.846747i
$513$		0			0
$514$	14.1242	−	5.02137i	0.622990	−	0.221483i
$515$	−5.87366	−	18.0773i	−0.258824	−	0.796579i
$516$		0			0
$517$	3.34786	+	2.90707i	0.147239	+	0.127853i
$518$	−15.7410	+	22.9643i	−0.691618	+	1.00899i
$519$		0			0
$520$	16.9394	+	19.6846i	0.742844	+	0.863225i
$521$	−24.4258	−	33.6192i	−1.07011	−	1.47288i	−0.869962	−	0.493118i	$-0.835857\pi$
$521$	−24.4258	−	33.6192i	−1.07011	−	1.47288i	−0.200150	−	0.979765i	$-0.564143\pi$
$522$		0			0
$523$	23.5022	+	7.63632i	1.02768	+	0.333913i	0.773872	−	0.633342i	$-0.218317\pi$
$523$	23.5022	+	7.63632i	1.02768	+	0.333913i	0.253807	+	0.967255i	$0.418317\pi$
$524$	−33.5034	−	21.6393i	−1.46360	−	0.945315i
$525$		0			0
$526$	−2.14981	+	7.29087i	−0.0937362	+	0.317897i
$527$	24.7746			1.07920
$528$		0			0
$529$	−12.7071			−0.552484
$530$	−2.85065	+	9.66769i	−0.123824	+	0.419938i
$531$		0			0
$532$	12.9284	+	8.35022i	0.560517	+	0.362028i
$533$	15.6064	+	5.07084i	0.675990	+	0.219642i
$534$		0			0
$535$	19.8501	+	27.3214i	0.858196	+	1.18121i
$536$	17.4397	+	20.2659i	0.753282	+	0.875355i
$537$		0			0
$538$	8.60136	−	12.5484i	0.370831	−	0.541001i
$539$	−2.82317	+	6.66099i	−0.121603	+	0.286909i
$540$		0			0
$541$	2.90492	+	8.94042i	0.124892	+	0.384379i	0.993881	−	0.110452i	$-0.0352299\pi$
$541$	2.90492	+	8.94042i	0.124892	+	0.384379i	−0.868989	+	0.494831i	$0.835230\pi$
$542$	−38.9776	+	13.8572i	−1.67423	+	0.595217i
$543$		0			0
$544$	−16.2541	−	2.90824i	−0.696890	−	0.124690i
$545$	27.8368	+	9.04472i	1.19240	+	0.387433i
$546$		0			0
$547$	−19.3067	+	26.5733i	−0.825493	+	1.13619i	0.163252	+	0.986584i	$0.447802\pi$
$547$	−19.3067	+	26.5733i	−0.825493	+	1.13619i	−0.988745	+	0.149609i	$0.952198\pi$
$548$	−9.99663	−	12.2823i	−0.427035	−	0.524674i
$549$		0			0
$550$	6.57615	−	4.20597i	0.280408	−	0.179343i
$551$	−27.7504			−1.18221
$552$		0			0
$553$	6.88863	+	5.00488i	0.292934	+	0.212829i
$554$	−30.2837	+	0.830643i	−1.28663	+	0.0352907i
$555$		0			0
$556$	1.69164	+	30.8137i	0.0717414	+	1.30679i
$557$	−12.4396	−	17.1217i	−0.527083	−	0.725468i	0.459599	−	0.888127i	$-0.347993\pi$
$557$	−12.4396	−	17.1217i	−0.527083	−	0.725468i	−0.986682	+	0.162659i	$0.947993\pi$
$558$		0			0
$559$	−9.16718	+	2.97860i	−0.387731	+	0.125981i
$560$	−11.8643	+	10.7898i	−0.501357	+	0.455954i
$561$		0			0
$562$	5.66532	−	8.26507i	0.238977	−	0.348641i
$563$	−5.31776	−	16.3664i	−0.224117	−	0.689761i	−0.998380	−	0.0568969i	$-0.981879\pi$
$563$	−5.31776	−	16.3664i	−0.224117	−	0.689761i	0.774263	−	0.632864i	$-0.218121\pi$
$564$		0			0
$565$	−11.1102	+	8.07202i	−0.467409	+	0.339592i
$566$	−17.9275	−	23.3036i	−0.753549	−	0.979523i
$567$		0			0
$568$	−13.3711	−	31.9436i	−0.561040	−	1.34032i
$569$	−24.1291	+	33.2109i	−1.01155	+	1.39227i	−0.0935803	+	0.995612i	$0.529831\pi$
$569$	−24.1291	+	33.2109i	−1.01155	+	1.39227i	−0.917965	+	0.396661i	$0.870169\pi$
$570$		0			0
$571$		−	19.4513i		−	0.814013i	−0.913425	−	0.407006i	$-0.866573\pi$
$571$		−	19.4513i		−	0.814013i	0.913425	−	0.407006i	$-0.133427\pi$
$572$	−11.3104	+	31.3701i	−0.472913	+	1.31165i
$573$		0			0
$574$	−2.86594	+	9.71954i	−0.119622	+	0.405686i
$575$	4.31968	+	3.13843i	0.180143	+	0.130882i
$576$		0			0
$577$	7.85896	−	24.1874i	0.327173	−	1.00693i	−0.643277	−	0.765633i	$-0.722426\pi$
$577$	7.85896	−	24.1874i	0.327173	−	1.00693i	0.970450	−	0.241301i	$-0.0775742\pi$
$578$	−9.50473	+	7.31201i	−0.395345	+	0.304140i
$579$		0			0
$580$	7.41455	−	27.9490i	0.307872	−	1.16052i
$581$	−0.301771	+	0.0980513i	−0.0125196	+	0.00406785i
$582$		0			0
$583$	−12.6091	+	2.91821i	−0.522214	+	0.120860i
$584$	1.78117	−	7.54278i	0.0737052	−	0.312122i
$585$		0			0
$586$	−38.2294	+	13.5912i	−1.57924	+	0.561447i
$587$	−0.288985	+	0.209960i	−0.0119277	+	0.00866597i	−0.593733	−	0.804662i	$-0.702347\pi$
$587$	−0.288985	+	0.209960i	−0.0119277	+	0.00866597i	0.581805	+	0.813328i	$0.302347\pi$
$588$		0			0
$589$	−9.19426	+	28.2970i	−0.378843	+	1.16596i
$590$	0.680323	+	24.8033i	0.0280084	+	1.02114i
$591$		0			0
$592$	31.1557	+	17.7820i	1.28049	+	0.730836i
$593$		−	17.6123i		−	0.723250i	−0.932324	−	0.361625i	$-0.882222\pi$
$593$		−	17.6123i		−	0.723250i	0.932324	−	0.361625i	$-0.117778\pi$
$594$		0			0
$595$		−	11.7028i		−	0.479769i
$596$	−1.38723	−	1.70441i	−0.0568232	−	0.0698155i
$597$		0			0
$598$	−22.8007	+	0.625393i	−0.932388	+	0.0255742i
$599$	1.01222	−	3.11530i	0.0413582	−	0.127288i	−0.928246	−	0.371968i	$-0.878683\pi$
$599$	1.01222	−	3.11530i	0.0413582	−	0.127288i	0.969604	+	0.244681i	$0.0786831\pi$
$600$		0			0
$601$	−24.6496	+	17.9090i	−1.00548	+	0.730523i	−0.963256	−	0.268585i	$-0.913444\pi$
$601$	−24.6496	+	17.9090i	−1.00548	+	0.730523i	−0.0422225	+	0.999108i	$0.513444\pi$
$602$	−1.99387	−	5.60837i	−0.0812641	−	0.228580i
$603$		0			0
$604$	43.9412	−	16.9928i	1.78794	−	0.691426i
$605$	−17.7489	−	9.41265i	−0.721597	−	0.382679i
$606$		0			0
$607$	−14.3104	+	4.64974i	−0.580842	+	0.188727i	−0.584678	−	0.811266i	$-0.698779\pi$
$607$	−14.3104	+	4.64974i	−0.580842	+	0.188727i	0.00383565	+	0.999993i	$0.498779\pi$
$608$	9.35392	−	17.4859i	0.379352	−	0.709145i
$609$		0			0
$610$	5.18778	+	6.74349i	0.210047	+	0.273036i
$611$	2.07681	−	6.39176i	0.0840187	−	0.258583i
$612$		0			0
$613$	−4.53106	−	3.29201i	−0.183008	−	0.132963i	0.492510	−	0.870307i	$-0.336080\pi$
$613$	−4.53106	−	3.29201i	−0.183008	−	0.132963i	−0.675517	+	0.737344i	$0.736080\pi$
$614$	−33.6895	−	9.93378i	−1.35960	−	0.400895i
$615$		0			0
$616$	−19.5559	−	6.45067i	−0.787930	−	0.259905i
$617$		−	5.84197i		−	0.235189i	−0.993062	−	0.117594i	$-0.962482\pi$
$617$		−	5.84197i		−	0.235189i	0.993062	−	0.117594i	$-0.0375183\pi$
$618$		0			0
$619$	8.56301	−	11.7860i	0.344177	−	0.473718i	−0.601479	−	0.798889i	$-0.705422\pi$
$619$	8.56301	−	11.7860i	0.344177	−	0.473718i	0.945655	+	0.325170i	$0.105422\pi$
$620$	−26.0429	−	16.8207i	−1.04591	−	0.675534i
$621$		0			0
$622$	−3.35565	+	2.58151i	−0.134549	+	0.103509i
$623$	21.0505	−	15.2941i	0.843370	−	0.612744i
$624$		0			0
$625$	−4.29806	−	13.2281i	−0.171922	−	0.529122i
$626$	−34.8690	−	23.9011i	−1.39365	−	0.955280i
$627$		0			0
$628$	7.38665	+	19.1009i	0.294760	+	0.762211i
$629$	−24.8970	+	8.08952i	−0.992708	+	0.322550i
$630$		0			0
$631$	1.76590	+	2.43055i	0.0702994	+	0.0967589i	0.842719	−	0.538354i	$-0.180954\pi$
$631$	1.76590	+	2.43055i	0.0702994	+	0.0967589i	−0.772419	+	0.635113i	$0.780954\pi$
$632$	5.69756	−	9.37581i	0.226637	−	0.372950i
$633$		0			0
$634$	0.234503	+	8.54955i	0.00931331	+	0.339546i
$635$	−11.3265	−	8.22915i	−0.449477	−	0.326564i
$636$		0			0
$637$	10.9659			0.434484
$638$	35.9304	−	9.36060i	1.42250	−	0.370590i
$639$		0			0
$640$	15.1117	+	14.0928i	0.597343	+	0.557069i
$641$	−21.1677	+	29.1348i	−0.836073	+	1.15076i	0.150689	+	0.988581i	$0.451851\pi$
$641$	−21.1677	+	29.1348i	−0.836073	+	1.15076i	−0.986762	+	0.162175i	$0.948149\pi$
$642$		0			0
$643$	21.1765	+	6.88066i	0.835119	+	0.271347i	0.695200	−	0.718816i	$-0.255316\pi$
$643$	21.1765	+	6.88066i	0.835119	+	0.271347i	0.139919	+	0.990163i	$0.455316\pi$
$644$	−0.772097	−	14.0640i	−0.0304249	−	0.554200i
$645$		0			0
$646$	4.84754	+	13.6352i	0.190724	+	0.536470i
$647$	−2.47173	−	7.60721i	−0.0971739	−	0.299070i	0.890640	−	0.454709i	$-0.150257\pi$
$647$	−2.47173	−	7.60721i	−0.0971739	−	0.299070i	−0.987814	+	0.155638i	$0.950257\pi$
$648$		0			0
$649$	−27.3013	+	16.4244i	−1.07167	+	0.644713i
$650$	−9.75960	−	6.68975i	−0.382803	−	0.262394i
$651$		0			0
$652$	21.1605	+	5.61365i	0.828711	+	0.219848i
$653$	14.8293	+	20.4108i	0.580317	+	0.798737i	0.993730	−	0.111806i	$-0.0356635\pi$
$653$	14.8293	+	20.4108i	0.580317	+	0.798737i	−0.413413	+	0.910543i	$0.635664\pi$
$654$		0			0
$655$	−34.6394	−	11.2550i	−1.35347	−	0.439770i
$656$	12.7846	+	2.65114i	0.499155	+	0.103510i
$657$		0			0
$658$	3.98073	+	1.17377i	0.155185	+	0.0457583i
$659$	0.154253			0.00600886			0.00300443	−	0.999995i	$-0.499044\pi$
$659$	0.154253			0.00600886			0.00300443	+	0.999995i	$0.499044\pi$
$660$		0			0
$661$	−24.6462			−0.958625			−0.479313	−	0.877644i	$-0.659114\pi$
$661$	−24.6462			−0.958625			−0.479313	+	0.877644i	$0.659114\pi$
$662$	19.7568	+	5.82555i	0.767869	+	0.226416i
$663$		0			0
$664$	0.157862	+	0.377132i	0.00612622	+	0.0146355i
$665$	13.3668	+	4.34312i	0.518340	+	0.168419i
$666$		0			0
$667$	14.9278	+	20.5464i	0.578008	+	0.795559i
$668$	−5.11699	+	19.2884i	−0.197982	+	0.746290i
$669$		0			0
$670$	20.1390	+	13.8043i	0.778036	+	0.533308i
$671$	−4.26327	+	10.0588i	−0.164582	+	0.388314i
$672$		0			0
$673$	13.2378	+	40.7418i	0.510280	+	1.57048i	0.791708	+	0.610899i	$0.209192\pi$
$673$	13.2378	+	40.7418i	0.510280	+	1.57048i	−0.281428	+	0.959582i	$0.590808\pi$
$674$	−1.34344	−	3.77883i	−0.0517473	−	0.145555i
$675$		0			0
$676$	24.5089	−	1.34551i	0.942649	−	0.0517503i
$677$	31.1553	+	10.1230i	1.19740	+	0.389058i	0.838803	−	0.544436i	$-0.183256\pi$
$677$	31.1553	+	10.1230i	1.19740	+	0.389058i	0.358594	+	0.933494i	$0.383256\pi$
$678$		0			0
$679$	−19.6815	+	27.0893i	−0.755307	+	1.03959i
$680$	−15.0280	+	1.23908i	−0.576296	+	0.0475166i
$681$		0			0
$682$	2.35946	−	39.7395i	0.0903484	−	1.52170i
$683$	−12.5974			−0.482024			−0.241012	−	0.970522i	$-0.577479\pi$
$683$	−12.5974			−0.482024			−0.241012	+	0.970522i	$0.577479\pi$
$684$		0			0
$685$	−11.6997	−	8.50035i	−0.447024	−	0.324782i
$686$	0.781496	+	28.4919i	0.0298376	+	1.08782i
$687$		0			0
$688$	−6.99078	+	3.15420i	−0.266521	+	0.120253i
$689$	11.5309	+	15.8709i	0.439292	+	0.604633i
$690$		0			0
$691$	31.5174	−	10.2406i	1.19898	−	0.389572i	0.359593	−	0.933109i	$-0.382915\pi$
$691$	31.5174	−	10.2406i	1.19898	−	0.389572i	0.839385	+	0.543537i	$0.182915\pi$
$692$	−2.94152	+	1.13753i	−0.111820	+	0.0432426i
$693$		0			0
$694$	29.9091	+	20.5013i	1.13533	+	0.778219i
$695$	8.70854	+	26.8021i	0.330334	+	1.01666i
$696$		0			0
$697$	−7.70830	+	5.60041i	−0.291973	+	0.212131i
$698$	−11.3186	+	8.70743i	−0.428416	+	0.329581i
$699$		0			0
$700$	3.96427	−	6.13776i	0.149835	−	0.231986i
$701$	4.53262	−	6.23862i	0.171195	−	0.235630i	−0.714795	−	0.699334i	$-0.753480\pi$
$701$	4.53262	−	6.23862i	0.171195	−	0.235630i	0.885990	+	0.463704i	$0.153480\pi$
$702$		0			0
$703$		−	31.4390i		−	1.18574i
$704$	−6.21294	+	25.7953i	−0.234159	+	0.972198i
$705$		0			0
$706$	−36.7501	−	10.8363i	−1.38311	−	0.407828i
$707$	8.88712	+	6.45687i	0.334234	+	0.242836i
$708$		0			0
$709$	0.232588	−	0.715833i	0.00873504	−	0.0268837i	−0.946594	−	0.322428i	$-0.895501\pi$
$709$	0.232588	−	0.715833i	0.00873504	−	0.0268837i	0.955329	+	0.295544i	$0.0955010\pi$
$710$	−19.2822	−	25.0645i	−0.723647	−	0.940655i
$711$		0			0
$712$	−21.8684	−	25.4122i	−0.819552	−	0.952364i
$713$	25.8970	−	8.41444i	0.969850	−	0.315123i
$714$		0			0
$715$	−2.63767	+	30.3378i	−0.0986433	+	1.13457i
$716$	−14.7208	−	38.0662i	−0.550143	−	1.42260i
$717$		0			0
$718$	−2.28894	−	6.43835i	−0.0854226	−	0.240277i
$719$	22.7193	−	16.5066i	0.847289	−	0.615591i	−0.0771084	−	0.997023i	$-0.524569\pi$
$719$	22.7193	−	16.5066i	0.847289	−	0.615591i	0.924397	+	0.381431i	$0.124569\pi$
$720$		0			0
$721$	7.05957	−	21.7271i	0.262912	−	0.809160i
$722$	9.48709	−	0.260219i	0.353073	−	0.00968434i
$723$		0			0
$724$	0.189415	−	0.154166i	0.00703954	−	0.00572952i
$725$			13.1745i			0.489290i
$726$		0			0
$727$		−	2.32738i		−	0.0863177i	−0.999068	−	0.0431589i	$-0.986258\pi$
$727$		−	2.32738i		−	0.0863177i	0.999068	−	0.0431589i	$-0.0137422\pi$
$728$	2.56487	+	31.1076i	0.0950604	+	1.15292i
$729$		0			0
$730$	−0.194054	−	7.07484i	−0.00718225	−	0.261851i
$731$	1.72948	−	5.32280i	0.0639672	−	0.196871i
$732$		0			0
$733$	5.18607	−	3.76790i	0.191552	−	0.139170i	−0.487876	−	0.872913i	$-0.662228\pi$
$733$	5.18607	−	3.76790i	0.191552	−	0.139170i	0.679428	+	0.733743i	$0.262228\pi$
$734$	25.6367	−	9.11428i	0.946268	−	0.336414i
$735$		0			0
$736$	−17.9783	+	2.48055i	−0.662688	+	0.0914344i
$737$	−2.71557	+	31.2338i	−0.100029	+	1.15051i
$738$		0			0
$739$	2.28216	−	0.741518i	0.0839505	−	0.0272772i	−0.266741	−	0.963768i	$-0.585947\pi$
$739$	2.28216	−	0.741518i	0.0839505	−	0.0272772i	0.350691	+	0.936491i	$0.385947\pi$
$740$	31.6640	+	8.40010i	1.16399	+	0.308794i
$741$		0			0
$742$	−9.60171	+	7.38661i	−0.352490	+	0.271171i
$743$	8.78297	−	27.0312i	0.322216	−	0.991678i	−0.650466	−	0.759536i	$-0.725426\pi$
$743$	8.78297	−	27.0312i	0.322216	−	0.991678i	0.972682	−	0.232143i	$-0.0745737\pi$
$744$		0			0
$745$	−1.62357	−	1.17959i	−0.0594830	−	0.0432169i
$746$	8.95282	−	30.3626i	0.327786	−	1.11166i
$747$		0			0
$748$	−10.8758	−	16.0193i	−0.397658	−	0.585723i
$749$			40.5896i			1.48311i
$750$		0			0
$751$	−1.43130	+	1.97001i	−0.0522288	+	0.0718868i	−0.834333	−	0.551261i	$-0.814147\pi$
$751$	−1.43130	+	1.97001i	−0.0522288	+	0.0718868i	0.782104	+	0.623148i	$0.214147\pi$
$752$	1.08580	−	5.23605i	0.0395951	−	0.190939i
$753$		0			0
$754$	−34.3164	−	44.6071i	−1.24973	−	1.62450i
$755$	34.8063	−	25.2883i	1.26673	−	0.920335i
$756$		0			0
$757$	3.98805	+	12.2739i	0.144948	+	0.446104i	0.997004	−	0.0773461i	$-0.0246447\pi$
$757$	3.98805	+	12.2739i	0.144948	+	0.446104i	−0.852056	+	0.523450i	$0.824645\pi$
$758$	17.1994	−	25.0919i	0.624709	−	0.911380i
$759$		0			0
$760$	4.16188	−	17.6245i	0.150967	−	0.639308i
$761$	6.48711	−	2.10779i	0.235157	−	0.0764073i	−0.189068	−	0.981964i	$-0.560547\pi$
$761$	6.48711	−	2.10779i	0.235157	−	0.0764073i	0.424225	+	0.905557i	$0.360547\pi$
$762$		0			0
$763$	20.6776	+	28.4603i	0.748581	+	1.03033i
$764$	−27.5600	+	1.51301i	−0.997084	+	0.0547387i
$765$		0			0
$766$	−15.4832	+	0.424685i	−0.559432	+	0.0153445i
$767$	39.0704	+	28.3863i	1.41075	+	1.02497i
$768$		0			0
$769$	−31.1660			−1.12387			−0.561937	−	0.827180i	$-0.689944\pi$
$769$	−31.1660			−1.12387			−0.561937	+	0.827180i	$0.689944\pi$
$770$	−18.7718	−	1.11454i	−0.676490	−	0.0401654i
$771$		0			0
$772$	15.6188	−	12.7122i	0.562132	−	0.457522i
$773$	23.2768	−	32.0378i	0.837210	−	1.15232i	−0.149328	−	0.988788i	$-0.547711\pi$
$773$	23.2768	−	32.0378i	0.837210	−	1.15232i	0.986538	−	0.163533i	$-0.0522890\pi$
$774$		0			0
$775$	13.4340	+	4.36498i	0.482565	+	0.156795i
$776$	36.8700	+	22.4054i	1.32356	+	0.804309i
$777$		0			0
$778$	−17.1273	+	6.08906i	−0.614045	+	0.218303i
$779$	−3.53600	−	10.8827i	−0.126690	−	0.389913i
$780$		0			0
$781$	15.8459	−	37.3869i	0.567012	−	1.33781i
$782$	7.48784	−	10.9239i	0.267765	−	0.390639i
$783$		0			0
$784$	8.67279	−	0.955129i	0.309742	−	0.0341118i
$785$	10.9927	+	15.1301i	0.392345	+	0.540016i
$786$		0			0
$787$	−2.50556	−	0.814105i	−0.0893135	−	0.0290197i	0.264019	−	0.964517i	$-0.414952\pi$
$787$	−2.50556	−	0.814105i	−0.0893135	−	0.0290197i	−0.353333	+	0.935498i	$0.614952\pi$
$788$	15.5517	−	24.0783i	0.554008	−	0.857754i
$789$		0			0
$790$	2.83359	−	9.60986i	0.100815	−	0.341903i
$791$	−16.5057			−0.586874
$792$		0			0
$793$	16.5596			0.588048
$794$	9.93077	−	33.6793i	0.352430	−	1.19523i
$795$		0			0
$796$	19.8941	−	30.8014i	0.705127	−	1.09173i
$797$	16.0148	+	5.20354i	0.567275	+	0.184319i	0.578592	−	0.815617i	$-0.303602\pi$
$797$	16.0148	+	5.20354i	0.567275	+	0.184319i	−0.0113171	+	0.999936i	$0.503602\pi$
$798$		0			0
$799$	2.29370	+	3.15701i	0.0811453	+	0.111687i
$800$	−8.30142	−	4.44078i	−0.293500	−	0.157005i
$801$		0			0
$802$	−8.15747	+	11.9008i	−0.288050	+	0.420233i
$803$	7.78736	−	4.68486i	0.274810	−	0.165325i
$804$		0			0
$805$	−3.97475	−	12.2330i	−0.140092	−	0.431158i
$806$	−56.8555	+	20.2131i	−2.00265	+	0.711975i
$807$		0			0
$808$	7.35050	−	12.0959i	0.258590	−	0.425531i
$809$	−42.8302	−	13.9164i	−1.50583	−	0.489274i	−0.564118	−	0.825694i	$-0.690784\pi$
$809$	−42.8302	−	13.9164i	−1.50583	−	0.489274i	−0.941712	+	0.336420i	$0.890784\pi$
$810$		0			0
$811$	−13.2392	+	18.2222i	−0.464892	+	0.639868i	−0.975514	−	0.219937i	$-0.929415\pi$
$811$	−13.2392	+	18.2222i	−0.464892	+	0.639868i	0.510623	+	0.859805i	$0.329415\pi$
$812$	26.9545	−	21.9384i	0.945917	−	0.769887i
$813$		0			0
$814$	10.6048	+	40.7062i	0.371699	+	1.42675i
$815$	19.9922			0.700296
$816$		0			0
$817$	5.43776	+	3.95076i	0.190243	+	0.138220i
$818$	−20.5216	+	0.562882i	−0.717521	+	0.0196807i
$819$		0			0
$820$	11.9053	−	0.653588i	0.415752	−	0.0228243i
$821$	−1.93977	−	2.66987i	−0.0676986	−	0.0931791i	0.773825	−	0.633399i	$-0.218341\pi$
$821$	−1.93977	−	2.66987i	−0.0676986	−	0.0931791i	−0.841524	+	0.540220i	$0.818341\pi$
$822$		0			0
$823$	6.91730	−	2.24757i	0.241122	−	0.0783452i	−0.185963	−	0.982557i	$-0.559541\pi$
$823$	6.91730	−	2.24757i	0.241122	−	0.0783452i	0.427085	+	0.904212i	$0.359541\pi$
$824$	−28.6479	−	6.76497i	−0.997997	−	0.235669i
$825$		0			0
$826$	−16.8610	+	24.5984i	−0.586671	+	0.855887i
$827$	9.10817	+	28.0321i	0.316722	+	0.974770i	0.975040	+	0.222030i	$0.0712683\pi$
$827$	9.10817	+	28.0321i	0.316722	+	0.974770i	−0.658318	+	0.752740i	$0.728732\pi$
$828$		0			0
$829$	10.1227	−	7.35456i	0.351575	−	0.255434i	−0.397954	−	0.917405i	$-0.630280\pi$
$829$	10.1227	−	7.35456i	0.351575	−	0.255434i	0.749530	+	0.661971i	$0.230280\pi$
$830$	0.227649	+	0.295916i	0.00790181	+	0.0102714i
$831$		0			0
$832$	39.6746	−	6.58725i	1.37547	−	0.228372i
$833$	−3.74254	+	5.15117i	−0.129671	+	0.178477i
$834$		0			0
$835$			18.2234i			0.630647i
$836$	22.3331	−	6.47709i	0.772406	−	0.224015i
$837$		0			0
$838$	13.9759	−	47.3981i	0.482791	−	1.63734i
$839$	27.7483	+	20.1603i	0.957978	+	0.696012i	0.952680	−	0.303974i	$-0.0983136\pi$
$839$	27.7483	+	20.1603i	0.957978	+	0.696012i	0.00529808	+	0.999986i	$0.498314\pi$
$840$		0			0
$841$	−10.4028	+	32.0165i	−0.358717	+	1.10402i
$842$	−14.0032	+	10.7727i	−0.482581	+	0.371251i
$843$		0			0
$844$	−16.4231	−	4.35686i	−0.565305	−	0.149969i
$845$	21.3181	−	6.92666i	0.733364	−	0.238285i
$846$		0			0
$847$	−10.6087	−	21.6914i	−0.364519	−	0.745326i
$848$	10.5020	+	11.5478i	0.360640	+	0.396552i
$849$		0			0
$850$	6.47332	−	2.30137i	0.222033	−	0.0789365i
$851$	−23.2774	+	16.9120i	−0.797940	+	0.579737i
$852$		0			0
$853$	1.01368	−	3.11978i	0.0347077	−	0.106819i	−0.932202	−	0.361939i	$-0.882115\pi$
$853$	1.01368	−	3.11978i	0.0347077	−	0.106819i	0.966909	+	0.255120i	$0.0821149\pi$
$854$	0.280378	+	10.2221i	0.00959434	+	0.349792i
$855$		0			0
$856$	52.1223	−	4.29757i	1.78150	−	0.146888i
$857$			17.7513i			0.606374i	0.952931	+	0.303187i	$0.0980506\pi$
$857$			17.7513i			0.606374i	−0.952931	+	0.303187i	$0.901949\pi$
$858$		0			0
$859$			19.1036i			0.651808i	0.945403	+	0.325904i	$0.105669\pi$
$859$			19.1036i			0.651808i	−0.945403	+	0.325904i	$0.894331\pi$
$860$	−5.43193	+	4.42107i	−0.185227	+	0.150757i
$861$		0			0
$862$	7.33086	−	0.201076i	0.249690	−	0.00684868i
$863$	−8.92185	+	27.4586i	−0.303703	+	0.934702i	0.676455	+	0.736484i	$0.263515\pi$
$863$	−8.92185	+	27.4586i	−0.303703	+	0.934702i	−0.980158	+	0.198218i	$0.936485\pi$
$864$		0			0
$865$	−2.33001	+	1.69285i	−0.0792228	+	0.0575587i
$866$	4.81522	+	13.5443i	0.163628	+	0.460254i
$867$		0			0
$868$	−13.4400	−	34.7541i	−0.456182	−	1.17963i
$869$	12.5336	−	2.90076i	0.425174	−	0.0984015i
$870$		0			0
$871$	45.1957	−	14.6850i	1.53140	−	0.497581i
$872$	34.3574	−	29.5661i	1.16349	−	1.00124i
$873$		0			0
$874$	9.69822	+	12.6065i	0.328047	+	0.426422i
$875$	8.25648	−	25.4108i	0.279120	−	0.859043i
$876$		0			0
$877$	−27.7862	−	20.1878i	−0.938272	−	0.681694i	0.00973235	−	0.999953i	$-0.496902\pi$
$877$	−27.7862	−	20.1878i	−0.938272	−	0.681694i	−0.948004	+	0.318258i	$0.896902\pi$
$878$	21.8878	+	6.45391i	0.738678	+	0.217809i
$879$		0			0
$880$	0.556317	+	24.2235i	0.0187534	+	0.816574i
$881$		−	29.8598i		−	1.00600i	−0.864286	−	0.503001i	$-0.832229\pi$
$881$		−	29.8598i		−	1.00600i	0.864286	−	0.503001i	$-0.167771\pi$
$882$		0			0
$883$	−2.02276	+	2.78408i	−0.0680711	+	0.0936919i	−0.841695	−	0.539953i	$-0.818442\pi$
$883$	−2.02276	+	2.78408i	−0.0680711	+	0.0936919i	0.773624	+	0.633645i	$0.218442\pi$
$884$	−15.9233	+	24.6535i	−0.535557	+	0.829187i
$885$		0			0
$886$	11.4159	−	8.78226i	0.383524	−	0.295046i
$887$	14.8724	−	10.8055i	0.499367	−	0.362812i	−0.309408	−	0.950929i	$-0.600131\pi$
$887$	14.8724	−	10.8055i	0.499367	−	0.362812i	0.808775	+	0.588118i	$0.200131\pi$
$888$		0			0
$889$	−5.19982	−	16.0034i	−0.174396	−	0.536737i
$890$	−25.2530	−	17.3098i	−0.846484	−	0.580226i
$891$		0			0
$892$	−14.5753	+	5.63650i	−0.488016	+	0.188724i
$893$	−4.45711	+	1.44820i	−0.149151	+	0.0484622i
$894$		0			0
$895$	−21.9072	−	30.1527i	−0.732278	−	1.00789i
$896$	4.73799	+	24.3792i	0.158285	+	0.814451i
$897$		0			0
$898$	0.997689	+	36.3739i	0.0332933	+	1.21381i
$899$	54.3553	+	39.4914i	1.81285	+	1.31711i
$900$		0			0
$901$	−11.3906			−0.379477
$902$	8.24918	+	12.8978i	0.274668	+	0.429450i
$903$		0			0
$904$	1.74760	+	21.1954i	0.0581243	+	0.704950i
$905$	0.131090	−	0.180430i	0.00435759	−	0.00599771i
$906$		0			0
$907$	9.91117	+	3.22033i	0.329095	+	0.106929i	0.468904	−	0.883249i	$-0.344649\pi$
$907$	9.91117	+	3.22033i	0.329095	+	0.106929i	−0.139809	+	0.990178i	$0.544649\pi$
$908$	−17.5504	+	0.963493i	−0.582429	+	0.0319746i
$909$		0			0
$910$	9.54811	+	26.8570i	0.316517	+	0.890301i
$911$	−9.98751	−	30.7384i	−0.330901	−	1.01841i	−0.968706	−	0.248211i	$-0.920157\pi$
$911$	−9.98751	−	30.7384i	−0.330901	−	1.01841i	0.637805	−	0.770198i	$-0.279843\pi$
$912$		0			0
$913$	−0.187080	+	0.441396i	−0.00619144	+	0.0146081i
$914$	−21.2066	−	14.5361i	−0.701451	−	0.480812i
$915$		0			0
$916$	14.0404	−	52.9251i	0.463909	−	1.74870i
$917$	−25.7307	−	35.4153i	−0.849704	−	1.16952i
$918$		0			0
$919$	47.3452	+	15.3834i	1.56177	+	0.507451i	0.957281	−	0.289159i	$-0.0933756\pi$
$919$	47.3452	+	15.3834i	1.56177	+	0.507451i	0.604493	+	0.796610i	$0.293376\pi$
$920$	−15.2880	+	6.39932i	−0.504030	+	0.210979i
$921$		0			0
$922$	−18.4454	−	5.43886i	−0.607466	−	0.179119i
$923$	−61.5495			−2.02593
$924$		0			0
$925$	−14.9257			−0.490754
$926$	−49.1640	−	14.4966i	−1.61563	−	0.476389i
$927$		0			0
$928$	−31.0257	−	32.2903i	−1.01847	−	1.05998i
$929$	28.8322	+	9.36815i	0.945954	+	0.307359i	0.741070	−	0.671427i	$-0.234318\pi$
$929$	28.8322	+	9.36815i	0.945954	+	0.307359i	0.204883	+	0.978786i	$0.434318\pi$
$930$		0			0
$931$	−4.49464	−	6.18634i	−0.147306	−	0.202749i
$932$	13.5587	+	3.59698i	0.444131	+	0.117823i
$933$		0			0
$934$	−11.9113	−	8.16464i	−0.389749	−	0.267155i
$935$	−13.3508	−	11.5930i	−0.436617	−	0.379131i
$936$		0			0
$937$	−5.49876	−	16.9234i	−0.179637	−	0.552864i	0.820178	−	0.572108i	$-0.193874\pi$
$937$	−5.49876	−	16.9234i	−0.179637	−	0.552864i	−0.999815	+	0.0192436i	$0.993874\pi$
$938$	9.83011	+	27.6502i	0.320964	+	0.902811i
$939$		0			0
$940$	−0.267683	−	4.87594i	−0.00873086	−	0.159036i
$941$	22.6781	+	7.36856i	0.739285	+	0.240208i	0.654364	−	0.756180i	$-0.272936\pi$
$941$	22.6781	+	7.36856i	0.739285	+	0.240208i	0.0849206	+	0.996388i	$0.472936\pi$
$942$		0			0
$943$	−6.15541	+	8.47219i	−0.200448	+	0.275893i
$944$	33.3727	+	19.0473i	1.08619	+	0.619938i
$945$		0			0
$946$	−8.37328	−	3.28109i	−0.272239	−	0.106677i
$947$	−52.7868			−1.71534			−0.857670	−	0.514200i	$-0.828089\pi$
$947$	−52.7868			−1.71534			−0.857670	+	0.514200i	$0.828089\pi$
$948$		0			0
$949$	−11.1444	−	8.09684i	−0.361761	−	0.262835i
$950$	0.226226	+	8.24778i	0.00733974	+	0.267593i
$951$		0			0
$952$	−15.4880	−	9.41184i	−0.501968	−	0.305040i
$953$	28.1059	+	38.6844i	0.910438	+	1.25311i	0.967017	+	0.254712i	$0.0819807\pi$
$953$	28.1059	+	38.6844i	0.910438	+	1.25311i	−0.0565789	+	0.998398i	$0.518019\pi$
$954$		0			0
$955$	−23.9719	+	7.78896i	−0.775714	+	0.252045i
$956$	18.7779	+	48.5572i	0.607320	+	1.57045i
$957$		0			0
$958$	5.53337	+	3.79287i	0.178775	+	0.122542i
$959$	−5.37118	−	16.5308i	−0.173445	−	0.533808i
$960$		0			0
$961$	33.1988	−	24.1203i	1.07093	−	0.778075i
$962$	50.5363	−	38.8777i	1.62936	−	1.25347i
$963$		0			0
$964$	17.8288	+	11.5153i	0.574226	+	0.370882i
$965$	10.8095	−	14.8779i	0.347969	−	0.478938i
$966$		0			0
$967$		−	1.65505i		−	0.0532227i	−0.999646	−	0.0266114i	$-0.991528\pi$
$967$		−	1.65505i		−	0.0532227i	0.999646	−	0.0266114i	$-0.00847166\pi$
$968$	−26.7314	+	15.9196i	−0.859179	+	0.511675i
$969$		0			0
$970$	37.7904	+	11.1430i	1.21338	+	0.357780i
$971$	−37.5620	−	27.2904i	−1.20542	−	0.875791i	−0.210616	−	0.977569i	$-0.567547\pi$
$971$	−37.5620	−	27.2904i	−1.20542	−	0.875791i	−0.994807	+	0.101778i	$0.967547\pi$
$972$		0			0
$973$	−10.4668	+	32.2136i	−0.335551	+	1.03272i
$974$	−5.08665	−	6.61203i	−0.162987	−	0.211863i
$975$		0			0
$976$	13.0968	−	1.44234i	0.419217	−	0.0461682i
$977$	7.30418	−	2.37327i	0.233681	−	0.0759277i	−0.189835	−	0.981816i	$-0.560795\pi$
$977$	7.30418	−	2.37327i	0.233681	−	0.0759277i	0.423517	+	0.905888i	$0.360795\pi$
$978$		0			0
$979$	3.40516	−	39.1652i	0.108830	−	1.25173i
$980$	7.43152	−	2.87389i	0.237391	−	0.0918031i
$981$		0			0
$982$	4.81572	+	13.5457i	0.153676	+	0.432260i
$983$	−45.4955	+	33.0544i	−1.45108	+	1.05427i	−0.465502	+	0.885047i	$0.654126\pi$
$983$	−45.4955	+	33.0544i	−1.45108	+	1.05427i	−0.985578	+	0.169224i	$0.945874\pi$
$984$		0			0
$985$	8.08879	−	24.8947i	0.257730	−	0.793212i
$986$	32.6657	−	0.895980i	1.04029	−	0.0285338i
$987$		0			0
$988$	−22.2494	−	27.3366i	−0.707847	−	0.869692i
$989$		−	6.15135i		−	0.195602i
$990$		0			0
$991$		−	2.70439i		−	0.0859077i	−0.999077	−	0.0429539i	$-0.986323\pi$
$991$		−	2.70439i		−	0.0859077i	0.999077	−	0.0429539i	$-0.0136768\pi$
$992$	−43.2057	+	20.9384i	−1.37178	+	0.664794i
$993$		0			0
$994$	−1.04212	−	37.9939i	−0.0330541	−	1.20509i
$995$	10.3473	−	31.8458i	0.328032	−	1.00958i
$996$		0			0
$997$	−0.0736127	+	0.0534827i	−0.00233134	+	0.00169381i	−0.588950	−	0.808169i	$-0.700459\pi$
$997$	−0.0736127	+	0.0534827i	−0.00233134	+	0.00169381i	0.586619	+	0.809863i	$0.300459\pi$
$998$	−45.9303	+	16.3290i	−1.45390	+	0.516886i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.w.a.71.15	yes	96
3.2	odd	2	inner	396.2.w.a.71.10	yes	96
4.3	odd	2	inner	396.2.w.a.71.20	yes	96
11.9	even	5	inner	396.2.w.a.251.5	yes	96
12.11	even	2	inner	396.2.w.a.71.5	✓	96
33.20	odd	10	inner	396.2.w.a.251.20	yes	96
44.31	odd	10	inner	396.2.w.a.251.10	yes	96
132.119	even	10	inner	396.2.w.a.251.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.w.a.71.5	✓	96	12.11	even	2	inner
396.2.w.a.71.10	yes	96	3.2	odd	2	inner
396.2.w.a.71.15	yes	96	1.1	even	1	trivial
396.2.w.a.71.20	yes	96	4.3	odd	2	inner
396.2.w.a.251.5	yes	96	11.9	even	5	inner
396.2.w.a.251.10	yes	96	44.31	odd	10	inner
396.2.w.a.251.15	yes	96	132.119	even	10	inner
396.2.w.a.251.20	yes	96	33.20	odd	10	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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.399974 - 1.35647i) q^{2} +(-1.68004 - 1.08511i) q^{4} +(-1.73701 - 0.564387i) q^{5} +(-1.29028 - 1.77592i) q^{7} +(-2.14389 + 1.84492i) q^{8} +O(q^{10})\)	\(q+(0.399974 - 1.35647i) q^{2} +(-1.68004 - 1.08511i) q^{4} +(-1.73701 - 0.564387i) q^{5} +(-1.29028 - 1.77592i) q^{7} +(-2.14389 + 1.84492i) q^{8} +(-1.46033 + 2.13046i) q^{10} +(-3.30416 - 0.287275i) q^{11} +(1.55349 + 4.78117i) q^{13} +(-2.92506 + 1.03991i) q^{14} +(1.64508 + 3.64605i) q^{16} +(-2.77612 - 0.902015i) q^{17} +(2.06053 - 2.83607i) q^{19} +(2.30582 + 2.83303i) q^{20} +(-1.71126 + 4.36710i) q^{22} -3.20825 q^{23} +(-1.34643 - 0.978237i) q^{25} +(7.10688 - 0.194933i) q^{26} +(0.240660 + 4.38370i) q^{28} +(-4.65295 - 6.40423i) q^{29} +(-8.07200 + 2.62275i) q^{31} +(5.60377 - 0.773179i) q^{32} +(-2.33393 + 3.40495i) q^{34} +(1.23892 + 3.81299i) q^{35} +(7.25549 - 5.27142i) q^{37} +(-3.02290 - 3.92941i) q^{38} +(4.76521 - 1.99464i) q^{40} +(1.91862 - 2.64075i) q^{41} +1.91735i q^{43} +(5.23940 + 4.06801i) q^{44} +(-1.28322 + 4.35191i) q^{46} +(-1.08154 - 0.785788i) q^{47} +(0.674061 - 2.07455i) q^{49} +(-1.86549 + 1.43512i) q^{50} +(2.57815 - 9.71827i) q^{52} +(3.71127 - 1.20587i) q^{53} +(5.57721 + 2.36383i) q^{55} +(6.04264 + 1.42692i) q^{56} +(-10.5482 + 3.75007i) q^{58} +(7.77178 - 5.64653i) q^{59} +(1.01790 - 3.13277i) q^{61} +(0.329103 + 11.9985i) q^{62} +(1.19256 - 7.91061i) q^{64} -9.18169i q^{65} -9.45286i q^{67} +(3.68521 + 4.52781i) q^{68} +(5.66776 - 0.155459i) q^{70} +(-3.78338 + 11.6440i) q^{71} +(-2.21680 + 1.61060i) q^{73} +(-4.24854 - 11.9503i) q^{74} +(-6.53922 + 2.52882i) q^{76} +(3.75311 + 6.23857i) q^{77} +(-3.68907 + 1.19865i) q^{79} +(-0.799725 - 7.26168i) q^{80} +(-2.81471 - 3.65879i) q^{82} +(0.0446672 - 0.137472i) q^{83} +(4.31305 + 3.13361i) q^{85} +(2.60084 + 0.766892i) q^{86} +(7.61377 - 5.48001i) q^{88} +11.8533i q^{89} +(6.48651 - 8.92791i) q^{91} +(5.38999 + 3.48130i) q^{92} +(-1.49849 + 1.15279i) q^{94} +(-5.17979 + 3.76334i) q^{95} +(-4.71365 - 14.5071i) q^{97} +(-2.54446 - 1.74411i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{10} + 32 q^{16} + 60 q^{22} + 8 q^{25} - 12 q^{28} + 24 q^{34} + 16 q^{40} - 40 q^{46} + 40 q^{49} - 32 q^{52} - 80 q^{58} - 72 q^{64} - 48 q^{70} - 24 q^{73} - 136 q^{76} - 132 q^{82} - 48 q^{85} - 64 q^{88} - 80 q^{94} - 80 q^{97}+O(q^{100}) \) 96 * q - 16 * q^10 + 32 * q^16 + 60 * q^22 + 8 * q^25 - 12 * q^28 + 24 * q^34 + 16 * q^40 - 40 * q^46 + 40 * q^49 - 32 * q^52 - 80 * q^58 - 72 * q^64 - 48 * q^70 - 24 * q^73 - 136 * q^76 - 132 * q^82 - 48 * q^85 - 64 * q^88 - 80 * q^94 - 80 * q^97

Introduction

L-functions

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