LMFDB - Embedded newform 891.2.f.e.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.5
Character	$\chi$	$=$	891.487
Dual form			891.2.f.e.730.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.396818 + 0.288305i) q^{2} +(-0.543689 + 1.67330i) q^{4} +(1.38194 + 1.00404i) q^{5} +(1.05391 - 3.24360i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(1.07799 - 3.13655i) q^{11} +(3.23439 - 2.34992i) q^{13} +(0.516936 + 1.59097i) q^{14} +(-2.11507 - 1.53669i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(-2.43141 + 1.76653i) q^{20} +(0.476515 + 1.55543i) q^{22} -7.49201 q^{23} +(-0.643414 - 1.98022i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(-0.522637 + 1.60851i) q^{29} +(3.15397 - 2.29149i) q^{31} +4.97028 q^{32} +1.62087 q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(1.75300 + 1.27363i) q^{38} +(0.973351 - 2.99566i) q^{40} +(-0.120787 - 0.371744i) q^{41} +9.61268 q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(0.333818 + 1.02739i) q^{47} +(-3.74710 - 2.72242i) q^{49} +(0.826227 + 0.600289i) q^{50} +(2.17363 + 6.68974i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} -6.28890 q^{56} +(-0.256350 - 0.788965i) q^{58} +(1.12993 - 3.47758i) q^{59} +(3.11728 + 2.26484i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +6.82916 q^{65} +3.10120 q^{67} +(4.70372 - 3.41746i) q^{68} +(-0.883019 + 2.71765i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(0.464645 + 1.43003i) q^{74} +7.77248 q^{76} +(-9.03760 - 6.80222i) q^{77} +(3.23536 - 2.35063i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(-0.101100 - 0.0734531i) q^{83} +(-1.74434 - 5.36852i) q^{85} +(-3.81449 + 2.77139i) q^{86} +(-6.11489 - 0.103238i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(4.07333 - 12.5364i) q^{92} +(-0.428666 - 0.311444i) q^{94} +(2.33188 - 7.17680i) q^{95} +(-0.277622 + 0.201704i) q^{97} +2.27180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.396818	+	0.288305i	−0.280593	+	0.203863i	−0.719176	−	0.694828i	$-0.755480\pi$
$2$	−0.396818	+	0.288305i	−0.280593	+	0.203863i	0.438583	+	0.898691i	$0.355480\pi$
$3$		0			0
$3$		0			0
$4$	−0.543689	+	1.67330i	−0.271845	+	0.836652i
$5$	1.38194	+	1.00404i	0.618024	+	0.449021i	0.852231	−	0.523166i	$-0.175249\pi$
$5$	1.38194	+	1.00404i	0.618024	+	0.449021i	−0.234207	+	0.972187i	$0.575249\pi$
$6$		0			0
$7$	1.05391	−	3.24360i	0.398340	−	1.22597i	−0.527989	−	0.849251i	$-0.677054\pi$
$7$	1.05391	−	3.24360i	0.398340	−	1.22597i	0.926329	−	0.376714i	$-0.122946\pi$
$8$	−0.569818	−	1.75372i	−0.201461	−	0.620034i
$9$		0			0
$10$	−0.837851			−0.264952
$11$	1.07799	−	3.13655i	0.325027	−	0.945705i
$11$	1.07799	−	3.13655i	0.325027	−	0.945705i
$12$		0			0
$13$	3.23439	−	2.34992i	0.897058	−	0.651751i	−0.0406508	−	0.999173i	$-0.512943\pi$
$13$	3.23439	−	2.34992i	0.897058	−	0.651751i	0.937709	+	0.347423i	$0.112943\pi$
$14$	0.516936	+	1.59097i	0.138157	+	0.425204i
$15$		0			0
$16$	−2.11507	−	1.53669i	−0.528768	−	0.384173i
$17$	−2.67346	−	1.94238i	−0.648409	−	0.471097i	0.214320	−	0.976763i	$-0.431246\pi$
$17$	−2.67346	−	1.94238i	−0.648409	−	0.471097i	−0.862729	+	0.505667i	$0.831246\pi$
$18$		0			0
$19$	−1.36513	−	4.20144i	−0.313182	−	0.963875i	−0.976496	−	0.215534i	$-0.930851\pi$
$19$	−1.36513	−	4.20144i	−0.313182	−	0.963875i	0.663314	−	0.748341i	$-0.269149\pi$
$20$	−2.43141	+	1.76653i	−0.543681	+	0.395007i
$21$		0			0
$22$	0.476515	+	1.55543i	0.101593	+	0.331619i
$23$	−7.49201			−1.56219			−0.781096	−	0.624411i	$-0.785339\pi$
$23$	−7.49201			−1.56219			−0.781096	+	0.624411i	$0.785339\pi$
$24$		0			0
$25$	−0.643414	−	1.98022i	−0.128683	−	0.396045i
$26$	−0.605969	+	1.86498i	−0.118840	+	0.365753i
$27$		0			0
$28$	4.85453	+	3.52702i	0.917420	+	0.666544i
$29$	−0.522637	+	1.60851i	−0.0970512	+	0.298693i	−0.987783	−	0.155837i	$-0.950193\pi$
$29$	−0.522637	+	1.60851i	−0.0970512	+	0.298693i	0.890732	+	0.454530i	$0.150193\pi$
$30$		0			0
$31$	3.15397	−	2.29149i	0.566469	−	0.411564i	−0.267352	−	0.963599i	$-0.586149\pi$
$31$	3.15397	−	2.29149i	0.566469	−	0.411564i	0.833821	+	0.552035i	$0.186149\pi$
$32$	4.97028			0.878629
$33$		0			0
$34$	1.62087			0.277978
$35$	4.71315	−	3.42431i	0.796668	−	0.578813i
$36$		0			0
$37$	0.947300	−	2.91549i	0.155735	−	0.479304i	−0.842499	−	0.538697i	$-0.818917\pi$
$37$	0.947300	−	2.91549i	0.155735	−	0.479304i	0.998235	+	0.0593935i	$0.0189167\pi$
$38$	1.75300	+	1.27363i	0.284375	+	0.206610i
$39$		0			0
$40$	0.973351	−	2.99566i	0.153900	−	0.473656i
$41$	−0.120787	−	0.371744i	−0.0188637	−	0.0580566i	0.941182	−	0.337901i	$-0.109717\pi$
$41$	−0.120787	−	0.371744i	−0.0188637	−	0.0580566i	−0.960045	+	0.279845i	$0.909717\pi$
$42$		0			0
$43$	9.61268			1.46592			0.732960	−	0.680272i	$-0.238138\pi$
$43$	9.61268			1.46592			0.732960	+	0.680272i	$0.238138\pi$
$44$	4.66230	+	3.50912i	0.702869	+	0.529020i
$45$		0			0
$46$	2.97296	−	2.15999i	0.438340	−	0.318472i
$47$	0.333818	+	1.02739i	0.0486924	+	0.149860i	0.972446	−	0.233127i	$-0.0748956\pi$
$47$	0.333818	+	1.02739i	0.0486924	+	0.149860i	−0.923754	+	0.382986i	$0.874896\pi$
$48$		0			0
$49$	−3.74710	−	2.72242i	−0.535299	−	0.388918i
$50$	0.826227	+	0.600289i	0.116846	+	0.0848937i
$51$		0			0
$52$	2.17363	+	6.68974i	0.301428	+	0.927700i
$53$	−10.1643	+	7.38480i	−1.39618	+	1.01438i	−0.401020	+	0.916069i	$0.631344\pi$
$53$	−10.1643	+	7.38480i	−1.39618	+	1.01438i	−0.995156	+	0.0983117i	$0.968656\pi$
$54$		0			0
$55$	4.63895	−	3.25218i	0.625516	−	0.438524i
$56$	−6.28890			−0.840390
$57$		0			0
$58$	−0.256350	−	0.788965i	−0.0336604	−	0.103596i
$59$	1.12993	−	3.47758i	0.147105	−	0.452742i	−0.850171	−	0.526507i	$-0.823501\pi$
$59$	1.12993	−	3.47758i	0.147105	−	0.452742i	0.997276	+	0.0737648i	$0.0235014\pi$
$60$		0			0
$61$	3.11728	+	2.26484i	0.399127	+	0.289983i	0.769185	−	0.639026i	$-0.220662\pi$
$61$	3.11728	+	2.26484i	0.399127	+	0.289983i	−0.370058	+	0.929009i	$0.620662\pi$
$62$	−0.590902	+	1.81861i	−0.0750446	+	0.230964i
$63$		0			0
$64$	2.25785	−	1.64043i	0.282232	−	0.205053i
$65$	6.82916			0.847053
$66$		0			0
$67$	3.10120			0.378872			0.189436	−	0.981893i	$-0.439334\pi$
$67$	3.10120			0.378872			0.189436	+	0.981893i	$0.439334\pi$
$68$	4.70372	−	3.41746i	0.570410	−	0.414427i
$69$		0			0
$70$	−0.883019	+	2.71765i	−0.105541	+	0.324822i
$71$	5.67699	+	4.12458i	0.673735	+	0.489497i	0.871273	−	0.490798i	$-0.163295\pi$
$71$	5.67699	+	4.12458i	0.673735	+	0.489497i	−0.197538	+	0.980295i	$0.563295\pi$
$72$		0			0
$73$	−4.64842	+	14.3064i	−0.544057	+	1.67443i	0.179165	+	0.983819i	$0.442660\pi$
$73$	−4.64842	+	14.3064i	−0.544057	+	1.67443i	−0.723222	+	0.690615i	$0.757340\pi$
$74$	0.464645	+	1.43003i	0.0540139	+	0.166238i
$75$		0			0
$76$	7.77248			0.891565
$77$	−9.03760	−	6.80222i	−1.02993	−	0.775185i
$78$		0			0
$79$	3.23536	−	2.35063i	0.364007	−	0.264467i	−0.390714	−	0.920512i	$-0.627772\pi$
$79$	3.23536	−	2.35063i	0.364007	−	0.264467i	0.754721	+	0.656045i	$0.227772\pi$
$80$	−1.38001	−	4.24724i	−0.154290	−	0.474856i
$81$		0			0
$82$	0.155106	+	0.112691i	0.0171286	+	0.0124447i
$83$	−0.101100	−	0.0734531i	−0.0110971	−	0.00806252i	0.582223	−	0.813029i	$-0.302183\pi$
$83$	−0.101100	−	0.0734531i	−0.0110971	−	0.00806252i	−0.593320	+	0.804967i	$0.702183\pi$
$84$		0			0
$85$	−1.74434	−	5.36852i	−0.189200	−	0.582298i
$86$	−3.81449	+	2.77139i	−0.411327	+	0.298846i
$87$		0			0
$88$	−6.11489	−	0.103238i	−0.651849	−	0.0110052i
$89$	7.93327			0.840925			0.420462	−	0.907310i	$-0.361868\pi$
$89$	7.93327			0.840925			0.420462	+	0.907310i	$0.361868\pi$
$90$		0			0
$91$	−4.21345	−	12.9677i	−0.441690	−	1.35938i
$92$	4.07333	−	12.5364i	0.424674	−	1.30701i
$93$		0			0
$94$	−0.428666	−	0.311444i	−0.0442135	−	0.0321230i
$95$	2.33188	−	7.17680i	0.239246	−	0.736324i
$96$		0			0
$97$	−0.277622	+	0.201704i	−0.0281882	+	0.0204800i	−0.601790	−	0.798654i	$-0.705546\pi$
$97$	−0.277622	+	0.201704i	−0.0281882	+	0.0204800i	0.573602	+	0.819134i	$0.305546\pi$
$98$	2.27180			0.229487
$99$		0			0
$100$	3.66333			0.366333
$101$	5.75663	−	4.18244i	0.572806	−	0.416168i	−0.263318	−	0.964709i	$-0.584817\pi$
$101$	5.75663	−	4.18244i	0.572806	−	0.416168i	0.836123	+	0.548541i	$0.184817\pi$
$102$		0			0
$103$	−0.511203	+	1.57332i	−0.0503703	+	0.155024i	−0.973078	−	0.230477i	$-0.925971\pi$
$103$	−0.511203	+	1.57332i	−0.0503703	+	0.155024i	0.922707	+	0.385501i	$0.125971\pi$
$104$	−5.96412	−	4.33318i	−0.584830	−	0.424904i
$105$		0			0
$106$	1.90430	−	5.86085i	0.184962	−	0.569256i
$107$	−1.02187	−	3.14498i	−0.0987876	−	0.304037i	0.889435	−	0.457062i	$-0.151098\pi$
$107$	−1.02187	−	3.14498i	−0.0987876	−	0.304037i	−0.988222	+	0.153025i	$0.951098\pi$
$108$		0			0
$109$	−5.50709			−0.527484			−0.263742	−	0.964593i	$-0.584957\pi$
$109$	−5.50709			−0.527484			−0.263742	+	0.964593i	$0.584957\pi$
$110$	−0.903198	+	2.62796i	−0.0861165	+	0.250566i
$111$		0			0
$112$	−7.21351	+	5.24092i	−0.681612	+	0.495220i
$113$	5.07073	+	15.6061i	0.477014	+	1.46810i	0.843222	+	0.537565i	$0.180656\pi$
$113$	5.07073	+	15.6061i	0.477014	+	1.46810i	−0.366208	+	0.930533i	$0.619344\pi$
$114$		0			0
$115$	−10.3535	−	7.52229i	−0.965473	−	0.701457i
$116$	−2.40738	−	1.74906i	−0.223519	−	0.162396i
$117$		0			0
$118$	0.554226	+	1.70573i	0.0510206	+	0.157025i
$119$	−9.11789	+	6.62453i	−0.835835	+	0.607270i
$120$		0			0
$121$	−8.67586	−	6.76236i	−0.788714	−	0.614760i
$122$	−1.88996			−0.171109
$123$		0			0
$124$	2.11958	+	6.52340i	0.190344	+	0.585819i
$125$	3.73834	−	11.5054i	0.334368	−	1.02908i
$126$		0			0
$127$	−8.73327	−	6.34509i	−0.774952	−	0.563036i	0.128508	−	0.991709i	$-0.458981\pi$
$127$	−8.73327	−	6.34509i	−0.774952	−	0.563036i	−0.903460	+	0.428673i	$0.858981\pi$
$128$	−3.49481	+	10.7559i	−0.308901	+	0.950699i
$129$		0			0
$130$	−2.70993	+	1.96888i	−0.237677	+	0.172682i
$131$	21.1557			1.84838			0.924189	−	0.381935i	$-0.124742\pi$
$131$	21.1557			1.84838			0.924189	+	0.381935i	$0.124742\pi$
$132$		0			0
$133$	−15.0665			−1.30643
$134$	−1.23061	+	0.894092i	−0.106309	+	0.0772378i
$135$		0			0
$136$	−1.88301	+	5.79530i	−0.161467	+	0.496943i
$137$	2.58928	+	1.88122i	0.221217	+	0.160724i	0.692874	−	0.721058i	$-0.256344\pi$
$137$	2.58928	+	1.88122i	0.221217	+	0.160724i	−0.471657	+	0.881782i	$0.656344\pi$
$138$		0			0
$139$	−4.63329	+	14.2598i	−0.392991	+	1.20950i	0.537525	+	0.843248i	$0.319360\pi$
$139$	−4.63329	+	14.2598i	−0.392991	+	1.20950i	−0.930515	+	0.366253i	$0.880640\pi$
$140$	3.16741	+	9.74829i	0.267695	+	0.823881i
$141$		0			0
$142$	−3.44187			−0.288835
$143$	−3.88399	−	12.6780i	−0.324795	−	1.06019i
$144$		0			0
$145$	−2.33727	+	1.69812i	−0.194099	+	0.141021i
$146$	−2.28002	−	7.01719i	−0.188696	−	0.580747i
$147$		0			0
$148$	4.36346	+	3.17024i	0.358675	+	0.260592i
$149$	3.27743	+	2.38119i	0.268497	+	0.195075i	0.713885	−	0.700263i	$-0.246934\pi$
$149$	3.27743	+	2.38119i	0.268497	+	0.195075i	−0.445387	+	0.895338i	$0.646934\pi$
$150$		0			0
$151$	−2.40847	−	7.41252i	−0.195999	−	0.603222i	−0.999963	−	0.00854528i	$-0.997280\pi$
$151$	−2.40847	−	7.41252i	−0.195999	−	0.603222i	0.803965	−	0.594677i	$-0.202720\pi$
$152$	−6.59027	+	4.78811i	−0.534541	+	0.388367i
$153$		0			0
$154$	5.54740	+	0.0936570i	0.447022	+	0.00754709i
$155$	6.65936			0.534892
$156$		0			0
$157$	0.0955332	+	0.294021i	0.00762438	+	0.0234654i	0.954796	−	0.297261i	$-0.0960731\pi$
$157$	0.0955332	+	0.294021i	0.00762438	+	0.0234654i	−0.947172	+	0.320726i	$0.896073\pi$
$158$	−0.606152	+	1.86554i	−0.0482229	+	0.148415i
$159$		0			0
$160$	6.86865	+	4.99036i	0.543014	+	0.394523i
$161$	−7.89590	+	24.3011i	−0.622284	+	1.91519i
$162$		0			0
$163$	−8.89442	+	6.46217i	−0.696665	+	0.506157i	−0.878844	−	0.477109i	$-0.841685\pi$
$163$	−8.89442	+	6.46217i	−0.696665	+	0.506157i	0.182179	+	0.983265i	$0.441685\pi$
$164$	0.687711			0.0537012
$165$		0			0
$166$	0.0612950			0.00475741
$167$	−14.2176	+	10.3297i	−1.10019	+	0.799333i	−0.981090	−	0.193550i	$-0.938000\pi$
$167$	−14.2176	+	10.3297i	−1.10019	+	0.799333i	−0.119097	+	0.992883i	$0.538000\pi$
$168$		0			0
$169$	0.921919	−	2.83737i	0.0709168	−	0.218260i
$170$	2.23996	+	1.62742i	0.171797	+	0.124818i
$171$		0			0
$172$	−5.22631	+	16.0849i	−0.398503	+	1.22646i
$173$	−3.82122	−	11.7605i	−0.290522	−	0.894135i	−0.984689	−	0.174321i	$-0.944227\pi$
$173$	−3.82122	−	11.7605i	−0.290522	−	0.894135i	0.694167	−	0.719814i	$-0.255773\pi$
$174$		0			0
$175$	−7.10116			−0.536797
$176$	−7.09994	+	4.97748i	−0.535178	+	0.375192i
$177$		0			0
$178$	−3.14806	+	2.28720i	−0.235957	+	0.171433i
$179$	−6.76200	−	20.8113i	−0.505416	−	1.55551i	−0.800071	−	0.599906i	$-0.795205\pi$
$179$	−6.76200	−	20.8113i	−0.505416	−	1.55551i	0.294655	−	0.955604i	$-0.404795\pi$
$180$		0			0
$181$	3.54364	+	2.57460i	0.263396	+	0.191369i	0.711643	−	0.702541i	$-0.247951\pi$
$181$	3.54364	+	2.57460i	0.263396	+	0.191369i	−0.448247	+	0.893910i	$0.647951\pi$
$182$	5.41062	+	3.93104i	0.401062	+	0.291388i
$183$		0			0
$184$	4.26908	+	13.1389i	0.314721	+	0.968612i
$185$	4.23639	−	3.07792i	0.311466	−	0.226293i
$186$		0			0
$187$	−8.97434	+	6.29155i	−0.656269	+	0.460084i
$188$	−1.90062			−0.138617
$189$		0			0
$190$	1.14377	+	3.52018i	0.0829781	+	0.255380i
$191$	−3.86727	+	11.9022i	−0.279826	+	0.861214i	0.708077	+	0.706136i	$0.249563\pi$
$191$	−3.86727	+	11.9022i	−0.279826	+	0.861214i	−0.987902	+	0.155079i	$0.950437\pi$
$192$		0			0
$193$	10.1659	+	7.38594i	0.731756	+	0.531652i	0.890118	−	0.455729i	$-0.150622\pi$
$193$	10.1659	+	7.38594i	0.731756	+	0.531652i	−0.158363	+	0.987381i	$0.550622\pi$
$194$	0.0520130	−	0.160080i	0.00373432	−	0.0114930i
$195$		0			0
$196$	6.59270	−	4.78988i	0.470907	−	0.342134i
$197$	10.3453			0.737075			0.368538	−	0.929613i	$-0.379859\pi$
$197$	10.3453			0.737075			0.368538	+	0.929613i	$0.379859\pi$
$198$		0			0
$199$	26.4773			1.87693			0.938464	−	0.345376i	$-0.112249\pi$
$199$	26.4773			1.87693			0.938464	+	0.345376i	$0.112249\pi$
$200$	−3.10613	+	2.25674i	−0.219637	+	0.159575i
$201$		0			0
$202$	−1.07852	+	3.31933i	−0.0758841	+	0.233547i
$203$	4.66655	+	3.39045i	0.327528	+	0.237963i
$204$		0			0
$205$	0.206325	−	0.635004i	0.0144104	−	0.0443506i
$206$	−0.250742	−	0.771705i	−0.0174700	−	0.0537672i
$207$		0			0
$208$	−10.4521			−0.724721
$209$	−14.6496	−	0.247330i	−1.01333	−	0.0171082i
$210$		0			0
$211$	5.89280	−	4.28137i	0.405677	−	0.294742i	−0.366172	−	0.930547i	$-0.619332\pi$
$211$	5.89280	−	4.28137i	0.405677	−	0.294742i	0.771849	+	0.635805i	$0.219332\pi$
$212$	−6.83079	−	21.0230i	−0.469141	−	1.44387i
$213$		0			0
$214$	1.31221	+	0.953376i	0.0897008	+	0.0651715i
$215$	13.2842	+	9.65153i	0.905974	+	0.658229i
$216$		0			0
$217$	−4.10868	−	12.6452i	−0.278916	−	0.858414i
$218$	2.18531	−	1.58772i	0.148008	−	0.107534i
$219$		0			0
$220$	2.91974	+	9.53055i	0.196849	+	0.642550i
$221$	−13.2114			−0.888698
$222$		0			0
$223$	7.26501	+	22.3594i	0.486501	+	1.49730i	0.829795	+	0.558068i	$0.188457\pi$
$223$	7.26501	+	22.3594i	0.486501	+	1.49730i	−0.343294	+	0.939228i	$0.611543\pi$
$224$	5.23822	−	16.1216i	0.349993	−	1.07717i
$225$		0			0
$226$	−6.51148	−	4.73086i	−0.433137	−	0.314692i
$227$	3.68416	−	11.3387i	0.244526	−	0.752574i	−0.751188	−	0.660089i	$-0.770519\pi$
$227$	3.68416	−	11.3387i	0.244526	−	0.752574i	0.995714	−	0.0924858i	$-0.0294813\pi$
$228$		0			0
$229$	−2.47363	+	1.79719i	−0.163462	+	0.118762i	−0.666509	−	0.745497i	$-0.732212\pi$
$229$	−2.47363	+	1.79719i	−0.163462	+	0.118762i	0.503047	+	0.864259i	$0.332212\pi$
$230$	6.27719			0.413905
$231$		0			0
$232$	3.11869			0.204752
$233$	−19.8463	+	14.4192i	−1.30017	+	0.944632i	−0.999957	−	0.00923938i	$-0.997059\pi$
$233$	−19.8463	+	14.4192i	−1.30017	+	0.944632i	−0.300217	+	0.953871i	$0.597059\pi$
$234$		0			0
$235$	−0.570221	+	1.75496i	−0.0371971	+	0.114481i
$236$	5.20471	+	3.78145i	0.338798	+	0.246151i
$237$		0			0
$238$	1.70825	−	5.25747i	0.110730	−	0.340791i
$239$	2.14786	+	6.61044i	0.138934	+	0.427594i	0.996181	−	0.0873108i	$-0.0278273\pi$
$239$	2.14786	+	6.61044i	0.138934	+	0.427594i	−0.857247	+	0.514905i	$0.827827\pi$
$240$		0			0
$241$	−7.77059			−0.500547			−0.250274	−	0.968175i	$-0.580521\pi$
$241$	−7.77059			−0.500547			−0.250274	+	0.968175i	$0.580521\pi$
$242$	5.39236	+	0.182131i	0.346634	+	0.0117078i
$243$		0			0
$244$	−5.48460	+	3.98480i	−0.351116	+	0.255100i
$245$	−2.44485	−	7.52448i	−0.156196	−	0.480721i
$246$		0			0
$247$	−14.2884	−	10.3811i	−0.909149	−	0.660535i
$248$	−5.81582	−	4.22544i	−0.369305	−	0.268316i
$249$		0			0
$250$	1.83364	+	5.64335i	0.115969	+	0.356917i
$251$	0.264684	−	0.192304i	0.0167067	−	0.0121381i	−0.579401	−	0.815043i	$-0.696713\pi$
$251$	0.264684	−	0.192304i	0.0167067	−	0.0121381i	0.596107	+	0.802905i	$0.296713\pi$
$252$		0			0
$253$	−8.07634	+	23.4990i	−0.507755	+	1.47737i
$254$	5.29484			0.332228
$255$		0			0
$256$	0.0106606	+	0.0328101i	0.000666290	+	0.00205063i
$257$	4.24255	−	13.0572i	0.264643	−	0.814487i	−0.727133	−	0.686497i	$-0.759148\pi$
$257$	4.24255	−	13.0572i	0.264643	−	0.814487i	0.991775	−	0.127990i	$-0.0408525\pi$
$258$		0			0
$259$	−8.45832	−	6.14533i	−0.525574	−	0.381852i
$260$	−3.71294	+	11.4273i	−0.230267	+	0.708689i
$261$		0			0
$262$	−8.39495	+	6.09928i	−0.518641	+	0.376815i
$263$	16.8542			1.03927			0.519637	−	0.854387i	$-0.326067\pi$
$263$	16.8542			1.03927			0.519637	+	0.854387i	$0.326067\pi$
$264$		0			0
$265$	−21.4612			−1.31835
$266$	5.97866	−	4.34375i	0.366575	−	0.266332i
$267$		0			0
$268$	−1.68609	+	5.18925i	−0.102994	+	0.316984i
$269$	10.0297	+	7.28700i	0.611522	+	0.444296i	0.849950	−	0.526864i	$-0.176632\pi$
$269$	10.0297	+	7.28700i	0.611522	+	0.444296i	−0.238428	+	0.971160i	$0.576632\pi$
$270$		0			0
$271$	5.95460	−	18.3264i	0.361716	−	1.11325i	−0.590296	−	0.807187i	$-0.700989\pi$
$271$	5.95460	−	18.3264i	0.361716	−	1.11325i	0.952012	−	0.306061i	$-0.0990112\pi$
$272$	2.66972	+	8.21656i	0.161876	+	0.498202i
$273$		0			0
$274$	−1.56984			−0.0948374
$275$	−6.90466	−	0.116572i	−0.416367	−	0.00702954i
$276$		0			0
$277$	−8.37420	+	6.08421i	−0.503157	+	0.365565i	−0.810222	−	0.586124i	$-0.800653\pi$
$277$	−8.37420	+	6.08421i	−0.503157	+	0.365565i	0.307065	+	0.951689i	$0.400653\pi$
$278$	−2.27260	−	6.99435i	−0.136302	−	0.419493i
$279$		0			0
$280$	−8.69092	−	6.31432i	−0.519382	−	0.377353i
$281$	−13.2968	−	9.66072i	−0.793223	−	0.576310i	0.115695	−	0.993285i	$-0.463090\pi$
$281$	−13.2968	−	9.66072i	−0.793223	−	0.576310i	−0.908918	+	0.416974i	$0.863090\pi$
$282$		0			0
$283$	−0.390892	−	1.20304i	−0.0232361	−	0.0715135i	0.938766	−	0.344555i	$-0.111970\pi$
$283$	−0.390892	−	1.20304i	−0.0232361	−	0.0715135i	−0.962002	+	0.273042i	$0.911970\pi$
$284$	−9.98819	+	7.25685i	−0.592690	+	0.430615i
$285$		0			0
$286$	5.19637	+	3.91109i	0.307268	+	0.231268i
$287$	−1.33309			−0.0786896
$288$		0			0
$289$	−1.87876	−	5.78222i	−0.110515	−	0.340130i
$290$	0.437892	−	1.34769i	0.0257139	−	0.0791392i
$291$		0			0
$292$	−21.4116	−	15.5564i	−1.25302	−	0.910372i
$293$	7.44342	−	22.9085i	0.434849	−	1.33833i	−0.458392	−	0.888750i	$-0.651574\pi$
$293$	7.44342	−	22.9085i	0.434849	−	1.33833i	0.893241	−	0.449578i	$-0.148426\pi$
$294$		0			0
$295$	5.05314	−	3.67132i	0.294205	−	0.213753i
$296$	−5.65274			−0.328559
$297$		0			0
$298$	−1.98705			−0.115107
$299$	−24.2321	+	17.6056i	−1.40138	+	1.01816i
$300$		0			0
$301$	10.1309	−	31.1797i	0.583935	−	1.79717i
$302$	3.09279	+	2.24705i	0.177970	+	0.129303i
$303$		0			0
$304$	−3.56896	+	10.9841i	−0.204694	+	0.629983i
$305$	2.03392	+	6.25977i	0.116462	+	0.358433i
$306$		0			0
$307$	16.2949			0.930001			0.465001	−	0.885310i	$-0.346054\pi$
$307$	16.2949			0.930001			0.465001	+	0.885310i	$0.346054\pi$
$308$	16.2958	−	11.4244i	0.928541	−	0.650963i
$309$		0			0
$310$	−2.64255	+	1.91993i	−0.150087	+	0.109044i
$311$	−6.60408	−	20.3253i	−0.374483	−	1.15254i	−0.943827	−	0.330441i	$-0.892803\pi$
$311$	−6.60408	−	20.3253i	−0.374483	−	1.15254i	0.569344	−	0.822100i	$-0.307197\pi$
$312$		0			0
$313$	−2.52100	−	1.83161i	−0.142495	−	0.103529i	0.514254	−	0.857638i	$-0.328069\pi$
$313$	−2.52100	−	1.83161i	−0.142495	−	0.103529i	−0.656749	+	0.754109i	$0.728069\pi$
$314$	−0.122677	−	0.0891301i	−0.00692307	−	0.00502990i
$315$		0			0
$316$	2.17428	+	6.69176i	0.122313	+	0.376441i
$317$	−14.7766	+	10.7358i	−0.829935	+	0.602983i	−0.919541	−	0.392994i	$-0.871439\pi$
$317$	−14.7766	+	10.7358i	−0.829935	+	0.602983i	0.0896059	+	0.995977i	$0.471439\pi$
$318$		0			0
$319$	4.48177	+	3.37324i	0.250931	+	0.188865i
$320$	4.76728			0.266499
$321$		0			0
$322$	−3.87289	−	11.9195i	−0.215828	−	0.664250i
$323$	−4.51117	+	13.8840i	−0.251008	+	0.772524i
$324$		0			0
$325$	−6.73442	−	4.89284i	−0.373558	−	0.271406i
$326$	1.66639	−	5.12861i	0.0922927	−	0.284048i
$327$		0			0
$328$	−0.583108	+	0.423653i	−0.0321968	+	0.0233923i
$329$	3.68425			0.203119
$330$		0			0
$331$	3.76616			0.207007			0.103503	−	0.994629i	$-0.466995\pi$
$331$	3.76616			0.207007			0.103503	+	0.994629i	$0.466995\pi$
$332$	0.177876	−	0.129235i	0.00976222	−	0.00709267i
$333$		0			0
$334$	2.66369	−	8.19799i	0.145751	−	0.448574i
$335$	4.28569	+	3.11373i	0.234152	+	0.170121i
$336$		0			0
$337$	1.84365	−	5.67417i	0.100430	−	0.309092i	−0.888201	−	0.459456i	$-0.848045\pi$
$337$	1.84365	−	5.67417i	0.100430	−	0.309092i	0.988631	+	0.150364i	$0.0480445\pi$
$338$	0.452196	+	1.39171i	0.0245962	+	0.0756993i
$339$		0			0
$340$	9.93155			0.538614
$341$	−3.78741	−	12.3628i	−0.205100	−	0.669482i
$342$		0			0
$343$	6.53464	−	4.74769i	0.352837	−	0.256351i
$344$	−5.47748	−	16.8580i	−0.295326	−	0.908920i
$345$		0			0
$346$	4.90695	+	3.56511i	0.263799	+	0.191661i
$347$	19.6990	+	14.3122i	1.05750	+	0.768318i	0.973624	−	0.228158i	$-0.0732704\pi$
$347$	19.6990	+	14.3122i	1.05750	+	0.768318i	0.0838748	+	0.996476i	$0.473270\pi$
$348$		0			0
$349$	5.17349	+	15.9224i	0.276931	+	0.852305i	0.988702	+	0.149894i	$0.0478932\pi$
$349$	5.17349	+	15.9224i	0.276931	+	0.852305i	−0.711771	+	0.702411i	$0.752107\pi$
$350$	2.81787	−	2.04730i	0.150621	−	0.109433i
$351$		0			0
$352$	5.35793	−	15.5895i	0.285579	−	0.830924i
$353$	8.03132			0.427464			0.213732	−	0.976892i	$-0.431438\pi$
$353$	8.03132			0.427464			0.213732	+	0.976892i	$0.431438\pi$
$354$		0			0
$355$	3.70404	+	11.3999i	0.196590	+	0.605042i
$356$	−4.31323	+	13.2748i	−0.228601	+	0.703561i
$357$		0			0
$358$	8.68329	+	6.30878i	0.458926	+	0.333429i
$359$	8.90742	−	27.4142i	0.470116	−	1.44687i	−0.382317	−	0.924031i	$-0.624874\pi$
$359$	8.90742	−	27.4142i	0.470116	−	1.44687i	0.852433	−	0.522836i	$-0.175126\pi$
$360$		0			0
$361$	−0.417162	+	0.303086i	−0.0219559	+	0.0159519i
$362$	−2.14845			−0.112920
$363$		0			0
$364$	23.9896			1.25740
$365$	−20.7881	+	15.1034i	−1.08810	+	0.790548i
$366$		0			0
$367$	6.90449	−	21.2498i	0.360411	−	1.10923i	−0.592394	−	0.805649i	$-0.701817\pi$
$367$	6.90449	−	21.2498i	0.360411	−	1.10923i	0.952805	−	0.303583i	$-0.0981831\pi$
$368$	15.8462	+	11.5129i	0.826038	+	0.600152i
$369$		0			0
$370$	−0.793696	+	2.44275i	−0.0412623	+	0.126992i
$371$	13.2411	+	40.7519i	0.687443	+	2.11573i
$372$		0			0
$373$	7.07872			0.366522			0.183261	−	0.983064i	$-0.441335\pi$
$373$	7.07872			0.366522			0.183261	+	0.983064i	$0.441335\pi$
$374$	1.74729	−	5.08395i	0.0903504	−	0.262885i
$375$		0			0
$376$	1.61153	−	1.17085i	0.0831085	−	0.0603819i
$377$	2.08946	+	6.43070i	0.107613	+	0.331198i
$378$		0			0
$379$	19.6964	+	14.3103i	1.01174	+	0.735070i	0.964573	−	0.263818i	$-0.0849817\pi$
$379$	19.6964	+	14.3103i	1.01174	+	0.735070i	0.0471638	+	0.998887i	$0.484982\pi$
$380$	10.7411	+	7.80390i	0.551009	+	0.400331i
$381$		0			0
$382$	−1.89687	−	5.83797i	−0.0970523	−	0.298696i
$383$	−14.2694	+	10.3673i	−0.729130	+	0.529744i	−0.889288	−	0.457348i	$-0.848800\pi$
$383$	−14.2694	+	10.3673i	−0.729130	+	0.529744i	0.160158	+	0.987091i	$0.448800\pi$
$384$		0			0
$385$	−5.65975	−	18.4744i	−0.288447	−	0.941543i
$386$	−6.16341			−0.313709
$387$		0			0
$388$	−0.186572	−	0.574210i	−0.00947177	−	0.0291511i
$389$	5.52615	−	17.0077i	0.280187	−	0.862326i	−0.707613	−	0.706600i	$-0.750228\pi$
$389$	5.52615	−	17.0077i	0.280187	−	0.862326i	0.987800	−	0.155727i	$-0.0497719\pi$
$390$		0			0
$391$	20.0296	+	14.5523i	1.01294	+	0.735943i
$392$	−2.63921	+	8.12265i	−0.133300	+	0.410256i
$393$		0			0
$394$	−4.10522	+	2.98262i	−0.206818	+	0.150262i
$395$	6.83122			0.343716
$396$		0			0
$397$	−21.9395			−1.10111			−0.550556	−	0.834798i	$-0.685584\pi$
$397$	−21.9395			−1.10111			−0.550556	+	0.834798i	$0.685584\pi$
$398$	−10.5067	+	7.63355i	−0.526652	+	0.382635i
$399$		0			0
$400$	−1.68213	+	5.17705i	−0.0841063	+	0.258852i
$401$	4.37481	+	3.17848i	0.218467	+	0.158726i	0.691636	−	0.722246i	$-0.256890\pi$
$401$	4.37481	+	3.17848i	0.218467	+	0.158726i	−0.473169	+	0.880972i	$0.656890\pi$
$402$		0			0
$403$	4.81633	−	14.8231i	0.239918	−	0.738393i
$404$	3.86867	+	11.9065i	0.192473	+	0.592372i
$405$		0			0
$406$	−2.82926			−0.140414
$407$	−8.12339	−	6.11413i	−0.402662	−	0.303066i
$408$		0			0
$409$	−19.1091	+	13.8836i	−0.944884	+	0.686498i	−0.949591	−	0.313491i	$-0.898502\pi$
$409$	−19.1091	+	13.8836i	−0.944884	+	0.686498i	0.00470736	+	0.999989i	$0.498502\pi$
$410$	0.101201	+	0.311466i	0.00499798	+	0.0153822i
$411$		0			0
$412$	−2.35471	−	1.71080i	−0.116008	−	0.0842849i
$413$	−10.0890	−	7.33011i	−0.496449	−	0.360691i
$414$		0			0
$415$	−0.0659639	−	0.203016i	−0.00323804	−	0.00996567i
$416$	16.0758	−	11.6798i	0.788181	−	0.572647i
$417$		0			0
$418$	5.88453	−	4.12541i	0.287822	−	0.201780i
$419$	18.1313			0.885773			0.442886	−	0.896578i	$-0.353955\pi$
$419$	18.1313			0.885773			0.442886	+	0.896578i	$0.353955\pi$
$420$		0			0
$421$	−3.95919	−	12.1851i	−0.192959	−	0.593867i	−0.999994	−	0.00336355i	$-0.998929\pi$
$421$	−3.95919	−	12.1851i	−0.192959	−	0.593867i	0.807035	−	0.590503i	$-0.201071\pi$
$422$	−1.10403	+	3.39785i	−0.0537432	+	0.165405i
$423$		0			0
$424$	18.7427	+	13.6174i	0.910226	+	0.661318i
$425$	−2.12621	+	6.54380i	−0.103136	+	0.317421i
$426$		0			0
$427$	10.6316	−	7.72429i	0.514498	−	0.373805i
$428$	5.81809			0.281228
$429$		0			0
$430$	−8.05399			−0.388398
$431$	−5.32265	+	3.86713i	−0.256383	+	0.186273i	−0.708551	−	0.705660i	$-0.750651\pi$
$431$	−5.32265	+	3.86713i	−0.256383	+	0.186273i	0.452168	+	0.891933i	$0.350651\pi$
$432$		0			0
$433$	4.32555	−	13.3127i	0.207873	−	0.639767i	−0.791710	−	0.610897i	$-0.790809\pi$
$433$	4.32555	−	13.3127i	0.207873	−	0.639767i	0.999583	−	0.0288700i	$-0.00919089\pi$
$434$	5.27608	+	3.83330i	0.253260	+	0.184004i
$435$		0			0
$436$	2.99415	−	9.21504i	0.143394	−	0.441320i
$437$	10.2276	+	31.4772i	0.489251	+	1.50576i
$438$		0			0
$439$	25.1782			1.20169			0.600846	−	0.799365i	$-0.294831\pi$
$439$	25.1782			1.20169			0.600846	+	0.799365i	$0.294831\pi$
$440$	−8.34678	−	6.28227i	−0.397917	−	0.299495i
$441$		0			0
$442$	5.24254	−	3.80893i	0.249362	−	0.181172i
$443$	−8.28860	−	25.5097i	−0.393803	−	1.21200i	−0.929890	−	0.367839i	$-0.880098\pi$
$443$	−8.28860	−	25.5097i	−0.393803	−	1.21200i	0.536086	−	0.844163i	$-0.319902\pi$
$444$		0			0
$445$	10.9633	+	7.96533i	0.519712	+	0.377593i
$446$	−9.32921	−	6.77807i	−0.441751	−	0.320951i
$447$		0			0
$448$	−2.94131	−	9.05243i	−0.138964	−	0.427687i
$449$	11.4685	−	8.33234i	0.541231	−	0.393228i	−0.283311	−	0.959028i	$-0.591433\pi$
$449$	11.4685	−	8.33234i	0.541231	−	0.393228i	0.824542	+	0.565801i	$0.191433\pi$
$450$		0			0
$451$	−1.29620	−	0.0218838i	−0.0610357	−	0.00103047i
$452$	−28.8706			−1.35796
$453$		0			0
$454$	1.80706	+	5.56155i	0.0848094	+	0.261017i
$455$	7.19732	−	22.1511i	0.337415	−	1.03846i
$456$		0			0
$457$	−19.9352	−	14.4838i	−0.932530	−	0.677523i	0.0140807	−	0.999901i	$-0.495518\pi$
$457$	−19.9352	−	14.4838i	−0.932530	−	0.677523i	−0.946611	+	0.322378i	$0.895518\pi$
$458$	0.463439	−	1.42632i	0.0216551	−	0.0666475i
$459$		0			0
$460$	18.2162	−	13.2348i	0.849334	−	0.617077i
$461$	26.2454			1.22237			0.611185	−	0.791488i	$-0.290693\pi$
$461$	26.2454			1.22237			0.611185	+	0.791488i	$0.290693\pi$
$462$		0			0
$463$	12.6922			0.589855			0.294928	−	0.955520i	$-0.404704\pi$
$463$	12.6922			0.589855			0.294928	+	0.955520i	$0.404704\pi$
$464$	3.57720	−	2.59899i	0.166067	−	0.120655i
$465$		0			0
$466$	3.71824	−	11.4436i	0.172244	−	0.530113i
$467$	−22.4130	−	16.2840i	−1.03715	−	0.753534i	−0.0674235	−	0.997724i	$-0.521478\pi$
$467$	−22.4130	−	16.2840i	−1.03715	−	0.753534i	−0.969727	+	0.244190i	$0.921478\pi$
$468$		0			0
$469$	3.26838	−	10.0591i	0.150920	−	0.464484i
$470$	−0.279690	−	0.860797i	−0.0129011	−	0.0397056i
$471$		0			0
$472$	−6.74256			−0.310351
$473$	10.3624	−	30.1506i	0.476464	−	1.38633i
$474$		0			0
$475$	−7.44144	+	5.40652i	−0.341437	+	0.248068i
$476$	−6.12756	−	18.8587i	−0.280856	−	0.864386i
$477$		0			0
$478$	−2.75813	−	2.00390i	−0.126154	−	0.0916563i
$479$	−12.6386	−	9.18250i	−0.577474	−	0.419559i	0.260339	−	0.965517i	$-0.416166\pi$
$479$	−12.6386	−	9.18250i	−0.577474	−	0.419559i	−0.837812	+	0.545958i	$0.816166\pi$
$480$		0			0
$481$	−3.78723	−	11.6559i	−0.172683	−	0.531464i
$482$	3.08351	−	2.24030i	0.140450	−	0.102043i
$483$		0			0
$484$	16.0325	−	10.8407i	0.728748	−	0.492760i
$485$	−0.586177			−0.0266169
$486$		0			0
$487$	8.32090	+	25.6091i	0.377056	+	1.16046i	0.942081	+	0.335386i	$0.108867\pi$
$487$	8.32090	+	25.6091i	0.377056	+	1.16046i	−0.565025	+	0.825074i	$0.691133\pi$
$488$	2.19561	−	6.75739i	0.0993906	−	0.305893i
$489$		0			0
$490$	3.13951	+	2.28098i	0.141828	+	0.103044i
$491$	−12.0516	+	37.0910i	−0.543880	+	1.67389i	0.179757	+	0.983711i	$0.442469\pi$
$491$	−12.0516	+	37.0910i	−0.543880	+	1.67389i	−0.723637	+	0.690181i	$0.757531\pi$
$492$		0			0
$493$	4.52159	−	3.28513i	0.203642	−	0.147955i
$494$	8.66283			0.389759
$495$		0			0
$496$	−10.1922			−0.457642
$497$	19.3615	−	14.0670i	0.868483	−	0.630990i
$498$		0			0
$499$	−7.42726	+	22.8588i	−0.332490	+	1.02330i	0.635455	+	0.772138i	$0.280812\pi$
$499$	−7.42726	+	22.8588i	−0.332490	+	1.02330i	−0.967945	+	0.251161i	$0.919188\pi$
$500$	17.2196	+	12.5108i	0.770084	+	0.559499i
$501$		0			0
$502$	−0.0495891	+	0.152620i	−0.00221327	+	0.00681174i
$503$	7.41223	+	22.8125i	0.330495	+	1.01716i	0.968899	+	0.247457i	$0.0795949\pi$
$503$	7.41223	+	22.8125i	0.330495	+	1.01716i	−0.638404	+	0.769701i	$0.720405\pi$
$504$		0			0
$505$	12.1547			0.540876
$506$	−3.57006	−	11.6533i	−0.158708	−	0.518052i
$507$		0			0
$508$	15.3655	−	11.1637i	0.681732	−	0.495307i
$509$	−1.14301	−	3.51783i	−0.0506631	−	0.155925i	0.922524	−	0.385939i	$-0.126123\pi$
$509$	−1.14301	−	3.51783i	−0.0506631	−	0.155925i	−0.973187	+	0.230014i	$0.926123\pi$
$510$		0			0
$511$	41.5051	+	30.1552i	1.83608	+	1.33399i
$512$	−18.3128	−	13.3050i	−0.809318	−	0.588004i
$513$		0			0
$514$	2.08094	+	6.40449i	0.0917865	+	0.282490i
$515$	−2.28613	+	1.66097i	−0.100739	+	0.0731912i
$516$		0			0
$517$	3.58230	+	0.0604802i	0.157549	+	0.00265992i
$518$	5.12814			0.225318
$519$		0			0
$520$	−3.89138	−	11.9764i	−0.170648	−	0.525202i
$521$	1.98178	−	6.09929i	0.0868234	−	0.267215i	−0.898213	−	0.439560i	$-0.855134\pi$
$521$	1.98178	−	6.09929i	0.0868234	−	0.267215i	0.985037	+	0.172345i	$0.0551344\pi$
$522$		0			0
$523$	2.21554	+	1.60969i	0.0968790	+	0.0703867i	0.635170	−	0.772372i	$-0.280930\pi$
$523$	2.21554	+	1.60969i	0.0968790	+	0.0703867i	−0.538291	+	0.842759i	$0.680930\pi$
$524$	−11.5021	+	35.3998i	−0.502472	+	1.54645i
$525$		0			0
$526$	−6.68804	+	4.85915i	−0.291613	+	0.211869i
$527$	−12.8829			−0.561190
$528$		0			0
$529$	33.1302			1.44044
$530$	8.51617	−	6.18736i	0.369919	−	0.268762i
$531$		0			0
$532$	8.19149	−	25.2108i	0.355146	−	1.09303i
$533$	−1.26424	−	0.918524i	−0.0547603	−	0.0397857i
$534$		0			0
$535$	1.74553	−	5.37219i	0.0754658	−	0.232260i
$536$	−1.76712	−	5.43864i	−0.0763280	−	0.234913i
$537$		0			0
$538$	−6.08085			−0.262164
$539$	−12.5784	+	8.81819i	−0.541788	+	0.379826i
$540$		0			0
$541$	−16.9114	+	12.2869i	−0.727079	+	0.528254i	−0.888638	−	0.458609i	$-0.848348\pi$
$541$	−16.9114	+	12.2869i	−0.727079	+	0.528254i	0.161559	+	0.986863i	$0.448348\pi$
$542$	2.92070	+	8.98898i	0.125455	+	0.386110i
$543$		0			0
$544$	−13.2878	−	9.65417i	−0.569711	−	0.413919i
$545$	−7.61050	−	5.52935i	−0.325998	−	0.236851i
$546$		0			0
$547$	−12.9405	−	39.8268i	−0.553296	−	1.70287i	−0.700401	−	0.713749i	$-0.746996\pi$
$547$	−12.9405	−	39.8268i	−0.553296	−	1.70287i	0.147105	−	0.989121i	$-0.453004\pi$
$548$	−4.55562	+	3.30985i	−0.194606	+	0.141390i
$549$		0			0
$550$	2.77350	−	1.94439i	0.118263	−	0.0829092i
$551$	7.47152			0.318298
$552$		0			0
$553$	−4.21472	−	12.9716i	−0.179228	−	0.551608i
$554$	1.56892	−	4.82865i	0.0666572	−	0.205150i
$555$		0			0
$556$	−21.3419	−	15.5058i	−0.905099	−	0.657593i
$557$	3.87025	−	11.9114i	0.163988	−	0.504702i	−0.834973	−	0.550291i	$-0.814517\pi$
$557$	3.87025	−	11.9114i	0.163988	−	0.504702i	0.998960	+	0.0455895i	$0.0145166\pi$
$558$		0			0
$559$	31.0911	−	22.5890i	1.31502	−	0.955415i
$560$	−15.2308			−0.643617
$561$		0			0
$562$	8.06166			0.340061
$563$	−11.7378	+	8.52802i	−0.494690	+	0.359413i	−0.806985	−	0.590572i	$-0.798902\pi$
$563$	−11.7378	+	8.52802i	−0.494690	+	0.359413i	0.312295	+	0.949985i	$0.398902\pi$
$564$		0			0
$565$	−8.66170	+	26.6580i	−0.364401	+	1.12151i
$566$	0.501956	+	0.364693i	0.0210988	+	0.0153292i
$567$		0			0
$568$	3.99850	−	12.3061i	0.167773	−	0.516353i
$569$	8.64395	+	26.6034i	0.362373	+	1.11527i	0.951610	+	0.307310i	$0.0994287\pi$
$569$	8.64395	+	26.6034i	0.362373	+	1.11527i	−0.589236	+	0.807961i	$0.700571\pi$
$570$		0			0
$571$	9.04886			0.378683			0.189341	−	0.981911i	$-0.439365\pi$
$571$	9.04886			0.378683			0.189341	+	0.981911i	$0.439365\pi$
$572$	23.3258	+	0.393811i	0.975303	+	0.0164661i
$573$		0			0
$574$	0.528993	−	0.384336i	0.0220797	−	0.0160419i
$575$	4.82046	+	14.8359i	0.201027	+	0.618698i
$576$		0			0
$577$	−31.0234	−	22.5398i	−1.29152	−	0.938346i	−0.291687	−	0.956514i	$-0.594217\pi$
$577$	−31.0234	−	22.5398i	−1.29152	−	0.938346i	−0.999835	+	0.0181683i	$0.994217\pi$
$578$	2.41257	+	1.75283i	0.100350	+	0.0729082i
$579$		0			0
$580$	−1.57073	−	4.83421i	−0.0652210	−	0.200730i
$581$	−0.344802	+	0.250513i	−0.0143048	+	0.0103930i
$582$		0			0
$583$	12.2057	+	39.8416i	0.505509	+	1.65007i
$584$	27.7381			1.14781
$585$		0			0
$586$	3.65095	+	11.2365i	0.150819	+	0.464175i
$587$	0.223301	−	0.687250i	0.00921662	−	0.0283658i	−0.946342	−	0.323166i	$-0.895253\pi$
$587$	0.223301	−	0.687250i	0.00921662	−	0.0283658i	0.955559	+	0.294800i	$0.0952529\pi$
$588$		0			0
$589$	−13.9331	−	10.1230i	−0.574104	−	0.417111i
$590$	−0.946716	+	2.91369i	−0.0389757	+	0.119955i
$591$		0			0
$592$	−6.48382	+	4.71077i	−0.266483	+	0.193611i
$593$	39.6596			1.62863			0.814313	−	0.580426i	$-0.197114\pi$
$593$	39.6596			1.62863			0.814313	+	0.580426i	$0.197114\pi$
$594$		0			0
$595$	−19.2517			−0.789244
$596$	−5.76636	+	4.18950i	−0.236199	+	0.171609i
$597$		0			0
$598$	4.53993	−	13.9725i	0.185651	−	0.571376i
$599$	−16.4852	−	11.9772i	−0.673566	−	0.489374i	0.197651	−	0.980272i	$-0.436669\pi$
$599$	−16.4852	−	11.9772i	−0.673566	−	0.489374i	−0.871217	+	0.490898i	$0.836669\pi$
$600$		0			0
$601$	−14.9477	+	46.0042i	−0.609729	+	1.87655i	−0.149472	+	0.988766i	$0.547757\pi$
$601$	−14.9477	+	46.0042i	−0.609729	+	1.87655i	−0.460257	+	0.887786i	$0.652243\pi$
$602$	4.96914	+	15.2935i	0.202527	+	0.623315i
$603$		0			0
$604$	13.7129			0.557968
$605$	−5.19987	−	18.0561i	−0.211405	−	0.734086i
$606$		0			0
$607$	15.9395	−	11.5807i	0.646964	−	0.470047i	−0.215272	−	0.976554i	$-0.569064\pi$
$607$	15.9395	−	11.5807i	0.646964	−	0.470047i	0.862236	+	0.506508i	$0.169064\pi$
$608$	−6.78507	−	20.8823i	−0.275171	−	0.846889i
$609$		0			0
$610$	−2.61182	−	1.89760i	−0.105749	−	0.0768315i
$611$	3.49397	+	2.53852i	0.141351	+	0.102698i
$612$		0			0
$613$	1.76690	+	5.43796i	0.0713644	+	0.219637i	0.980377	−	0.197131i	$-0.0631626\pi$
$613$	1.76690	+	5.43796i	0.0713644	+	0.219637i	−0.909013	+	0.416768i	$0.863163\pi$
$614$	−6.46613	+	4.69791i	−0.260952	+	0.189592i
$615$		0			0
$616$	−6.77940	+	19.7254i	−0.273150	+	0.794761i
$617$	−6.10692			−0.245855			−0.122928	−	0.992416i	$-0.539228\pi$
$617$	−6.10692			−0.245855			−0.122928	+	0.992416i	$0.539228\pi$
$618$		0			0
$619$	−0.549968	−	1.69263i	−0.0221051	−	0.0680324i	0.939395	−	0.342835i	$-0.111387\pi$
$619$	−0.549968	−	1.69263i	−0.0221051	−	0.0680324i	−0.961501	+	0.274803i	$0.911387\pi$
$620$	−3.62062	+	11.1431i	−0.145408	+	0.447519i
$621$		0			0
$622$	8.48050	+	6.16144i	0.340037	+	0.247051i
$623$	8.36094	−	25.7323i	0.334974	−	1.03094i
$624$		0			0
$625$	8.29572	−	6.02719i	0.331829	−	0.241088i
$626$	1.52844			0.0610888
$627$		0			0
$628$	−0.543927			−0.0217050
$629$	−8.19556	+	5.95442i	−0.326778	+	0.237418i
$630$		0			0
$631$	−13.8566	+	42.6461i	−0.551621	+	1.69771i	0.153084	+	0.988213i	$0.451079\pi$
$631$	−13.8566	+	42.6461i	−0.551621	+	1.69771i	−0.704705	+	0.709501i	$0.748921\pi$
$632$	−5.96592	−	4.33449i	−0.237311	−	0.172417i
$633$		0			0
$634$	2.76842	−	8.52032i	0.109948	−	0.338385i
$635$	−5.69816	−	17.5371i	−0.226124	−	0.695940i
$636$		0			0
$637$	−18.5170			−0.733672
$638$	−2.75097	−	0.0464448i	−0.108912	−	0.00183877i
$639$		0			0
$640$	−15.6290	+	11.3552i	−0.617792	+	0.448852i
$641$	8.34641	+	25.6876i	0.329663	+	1.01460i	0.969291	+	0.245915i	$0.0790885\pi$
$641$	8.34641	+	25.6876i	0.329663	+	1.01460i	−0.639628	+	0.768685i	$0.720912\pi$
$642$		0			0
$643$	26.3395	+	19.1368i	1.03873	+	0.754680i	0.970037	−	0.242958i	$-0.0781178\pi$
$643$	26.3395	+	19.1368i	1.03873	+	0.754680i	0.0686909	+	0.997638i	$0.478118\pi$
$644$	−36.3702	−	26.4245i	−1.43319	−	1.04127i
$645$		0			0
$646$	−2.21270	−	6.81000i	−0.0870576	−	0.267936i
$647$	−25.4705	+	18.5054i	−1.00135	+	0.727523i	−0.962377	−	0.271717i	$-0.912408\pi$
$647$	−25.4705	+	18.5054i	−1.00135	+	0.727523i	−0.0389724	+	0.999240i	$0.512408\pi$
$648$		0			0
$649$	−9.68953	−	7.29290i	−0.380347	−	0.286271i
$650$	4.08297			0.160147
$651$		0			0
$652$	−5.97738	−	18.3965i	−0.234092	−	0.720462i
$653$	1.43995	−	4.43171i	0.0563495	−	0.173426i	−0.918920	−	0.394443i	$-0.870938\pi$
$653$	1.43995	−	4.43171i	0.0563495	−	0.173426i	0.975270	+	0.221017i	$0.0709376\pi$
$654$		0			0
$655$	29.2359	+	21.2412i	1.14234	+	0.829961i
$656$	−0.315782	+	0.971878i	−0.0123292	+	0.0379455i
$657$		0			0
$658$	−1.46197	+	1.06219i	−0.0569937	+	0.0414084i
$659$	32.0418			1.24817			0.624086	−	0.781355i	$-0.285471\pi$
$659$	32.0418			1.24817			0.624086	+	0.781355i	$0.285471\pi$
$660$		0			0
$661$	−40.7054			−1.58325			−0.791627	−	0.611004i	$-0.790766\pi$
$661$	−40.7054			−1.58325			−0.791627	+	0.611004i	$0.790766\pi$
$662$	−1.49448	+	1.08580i	−0.0580846	+	0.0422009i
$663$		0			0
$664$	−0.0712078	+	0.219155i	−0.00276340	+	0.00850487i
$665$	−20.8211	−	15.1274i	−0.807406	−	0.586615i
$666$		0			0
$667$	3.91560	−	12.0510i	0.151613	−	0.466616i
$668$	−9.55472	−	29.4064i	−0.369683	−	1.13777i
$669$		0			0
$670$	−2.59834			−0.100383
$671$	10.4642	−	7.33603i	0.403966	−	0.283204i
$672$		0			0
$673$	30.5513	−	22.1968i	1.17767	−	0.855625i	0.185761	−	0.982595i	$-0.440525\pi$
$673$	30.5513	−	22.1968i	1.17767	−	0.855625i	0.991907	+	0.126970i	$0.0405251\pi$
$674$	0.904299	+	2.78315i	0.0348323	+	0.107203i
$675$		0			0
$676$	4.24655	+	3.08530i	0.163329	+	0.118665i
$677$	15.2910	+	11.1095i	0.587679	+	0.426974i	0.841484	−	0.540281i	$-0.181682\pi$
$677$	15.2910	+	11.1095i	0.587679	+	0.426974i	−0.253805	+	0.967255i	$0.581682\pi$
$678$		0			0
$679$	0.361659	+	1.11307i	0.0138792	+	0.0427158i
$680$	−8.42093	+	6.11817i	−0.322928	+	0.234621i
$681$		0			0
$682$	5.06716	+	3.81384i	0.194032	+	0.146040i
$683$	−31.1053			−1.19021			−0.595105	−	0.803648i	$-0.702890\pi$
$683$	−31.1053			−1.19021			−0.595105	+	0.803648i	$0.702890\pi$
$684$		0			0
$685$	1.68941	+	5.19948i	0.0645492	+	0.198662i
$686$	−1.22428	+	3.76794i	−0.0467432	+	0.143861i
$687$		0			0
$688$	−20.3315	−	14.7717i	−0.775132	−	0.563167i
$689$	−15.5216	+	47.7706i	−0.591327	+	1.81992i
$690$		0			0
$691$	−17.9694	+	13.0555i	−0.683588	+	0.496656i	−0.874546	−	0.484942i	$-0.838841\pi$
$691$	−17.9694	+	13.0555i	−0.683588	+	0.496656i	0.190958	+	0.981598i	$0.438841\pi$
$692$	21.7565			0.827057
$693$		0			0
$694$	−11.9432			−0.453358
$695$	−20.7204	+	15.0542i	−0.785969	+	0.571040i
$696$		0			0
$697$	−0.399149	+	1.22846i	−0.0151189	+	0.0465311i
$698$	−6.64344	−	4.82674i	−0.251458	−	0.182695i
$699$		0			0
$700$	3.86082	−	11.8824i	0.145925	−	0.449112i
$701$	9.25374	+	28.4801i	0.349509	+	1.07568i	0.959125	+	0.282981i	$0.0913235\pi$
$701$	9.25374	+	28.4801i	0.349509	+	1.07568i	−0.609616	+	0.792697i	$0.708677\pi$
$702$		0			0
$703$	−13.5424			−0.510763
$704$	−2.71132	−	8.85023i	−0.102187	−	0.333556i
$705$		0			0
$706$	−3.18697	+	2.31547i	−0.119943	+	0.0871439i
$707$	−7.49918	−	23.0801i	−0.282036	−	0.868017i
$708$		0			0
$709$	−13.9197	−	10.1133i	−0.522766	−	0.379812i	0.294879	−	0.955535i	$-0.404721\pi$
$709$	−13.9197	−	10.1133i	−0.522766	−	0.379812i	−0.817645	+	0.575723i	$0.804721\pi$
$710$	−4.75647	−	3.45578i	−0.178507	−	0.129693i
$711$		0			0
$712$	−4.52052	−	13.9127i	−0.169414	−	0.521402i
$713$	−23.6295	+	17.1679i	−0.884933	+	0.642942i
$714$		0			0
$715$	7.36179	−	21.4200i	0.275315	−	0.801062i
$716$	38.5001			1.43881
$717$		0			0
$718$	4.36904	+	13.4465i	0.163051	+	0.501819i
$719$	−1.46013	+	4.49382i	−0.0544537	+	0.167591i	−0.974585	−	0.224020i	$-0.928082\pi$
$719$	−1.46013	+	4.49382i	−0.0544537	+	0.167591i	0.920131	+	0.391611i	$0.128082\pi$
$720$		0			0
$721$	4.56446	+	3.31628i	0.169989	+	0.123505i
$722$	0.0781561	−	0.240540i	0.00290867	−	0.00895196i
$723$		0			0
$724$	−6.23473	+	4.52980i	−0.231712	+	0.168349i
$725$	3.52148			0.130785
$726$		0			0
$727$	5.20088			0.192890			0.0964450	−	0.995338i	$-0.469253\pi$
$727$	5.20088			0.192890			0.0964450	+	0.995338i	$0.469253\pi$
$728$	−20.3408	+	14.7784i	−0.753879	+	0.547725i
$729$		0			0
$730$	3.89468	−	11.9866i	0.144149	−	0.443644i
$731$	−25.6991	−	18.6715i	−0.950516	−	0.690590i
$732$		0			0
$733$	−15.1614	+	46.6618i	−0.559997	+	1.72349i	0.122369	+	0.992485i	$0.460951\pi$
$733$	−15.1614	+	46.6618i	−0.559997	+	1.72349i	−0.682367	+	0.731010i	$0.739049\pi$
$734$	3.38661	+	10.4229i	0.125002	+	0.384717i
$735$		0			0
$736$	−37.2374			−1.37259
$737$	3.34308	−	9.72706i	0.123144	−	0.358301i
$738$		0			0
$739$	12.6160	−	9.16603i	0.464086	−	0.337178i	−0.331046	−	0.943615i	$-0.607402\pi$
$739$	12.6160	−	9.16603i	0.464086	−	0.337178i	0.795132	+	0.606437i	$0.207402\pi$
$740$	2.84701	+	8.76220i	0.104658	+	0.322105i
$741$		0			0
$742$	−17.0033	−	12.3536i	−0.624210	−	0.453515i
$743$	9.00796	+	6.54466i	0.330470	+	0.240100i	0.740630	−	0.671913i	$-0.234527\pi$
$743$	9.00796	+	6.54466i	0.330470	+	0.240100i	−0.410160	+	0.912014i	$0.634527\pi$
$744$		0			0
$745$	2.13841	+	6.58134i	0.0783452	+	0.241122i
$746$	−2.80897	+	2.04083i	−0.102844	+	0.0747202i
$747$		0			0
$748$	−5.64842	−	18.4374i	−0.206527	−	0.674140i
$749$	−11.2780			−0.412090
$750$		0			0
$751$	−2.49846	−	7.68948i	−0.0911703	−	0.280593i	0.895066	−	0.445933i	$-0.147128\pi$
$751$	−2.49846	−	7.68948i	−0.0911703	−	0.280593i	−0.986237	+	0.165340i	$0.947128\pi$
$752$	0.872726	−	2.68597i	0.0318250	−	0.0979474i
$753$		0			0
$754$	−2.68314	−	1.94942i	−0.0977142	−	0.0709935i
$755$	4.11410	−	12.6619i	0.149727	−	0.460814i
$756$		0			0
$757$	−24.1585	+	17.5522i	−0.878056	+	0.637945i	−0.932737	−	0.360559i	$-0.882586\pi$
$757$	−24.1585	+	17.5522i	−0.878056	+	0.637945i	0.0546803	+	0.998504i	$0.482586\pi$
$758$	−11.9416			−0.433739
$759$		0			0
$760$	−13.9148			−0.504744
$761$	28.2287	−	20.5093i	1.02329	−	0.743463i	0.0563348	−	0.998412i	$-0.482059\pi$
$761$	28.2287	−	20.5093i	1.02329	−	0.743463i	0.966955	+	0.254949i	$0.0820586\pi$
$762$		0			0
$763$	−5.80398	+	17.8628i	−0.210118	+	0.646677i
$764$	−17.8134	−	12.9422i	−0.644468	−	0.468233i
$765$		0			0
$766$	2.67339	−	8.22786i	0.0965936	−	0.297284i
$767$	−4.51739	−	13.9031i	−0.163113	−	0.502012i
$768$		0			0
$769$	−5.60723			−0.202202			−0.101101	−	0.994876i	$-0.532237\pi$
$769$	−5.60723			−0.202202			−0.101101	+	0.994876i	$0.532237\pi$
$770$	7.57216	+	5.69924i	0.272882	+	0.205386i
$771$		0			0
$772$	−17.8860	+	12.9949i	−0.643731	+	0.467698i
$773$	3.34979	+	10.3096i	0.120483	+	0.370810i	0.993051	−	0.117683i	$-0.0375467\pi$
$773$	3.34979	+	10.3096i	0.120483	+	0.370810i	−0.872568	+	0.488493i	$0.837547\pi$
$774$		0			0
$775$	−6.56697	−	4.77118i	−0.235893	−	0.171386i
$776$	0.511927	+	0.371937i	0.0183771	+	0.0133517i
$777$		0			0
$778$	2.71054	+	8.34219i	0.0971776	+	0.299082i
$779$	−1.39697	+	1.01496i	−0.0500516	+	0.0363646i
$780$		0			0
$781$	19.0567	−	13.3599i	0.681902	−	0.478054i
$782$	−12.1436			−0.434255
$783$		0			0
$784$	3.74186	+	11.5163i	0.133638	+	0.411295i
$785$	−0.163188	+	0.502240i	−0.00582442	+	0.0179257i
$786$		0			0
$787$	2.00347	+	1.45561i	0.0714162	+	0.0518869i	0.622921	−	0.782285i	$-0.285946\pi$
$787$	2.00347	+	1.45561i	0.0714162	+	0.0518869i	−0.551504	+	0.834172i	$0.685946\pi$
$788$	−5.62465	+	17.3109i	−0.200370	+	0.616676i
$789$		0			0
$790$	−2.71075	+	1.96948i	−0.0964442	+	0.0700708i
$791$	55.9640			1.98985
$792$		0			0
$793$	15.4047			0.547037
$794$	8.70599	−	6.32527i	0.308964	−	0.224475i
$795$		0			0
$796$	−14.3954	+	44.3046i	−0.510233	+	1.57034i
$797$	−7.83103	−	5.68958i	−0.277389	−	0.201535i	0.440389	−	0.897807i	$-0.354841\pi$
$797$	−7.83103	−	5.68958i	−0.277389	−	0.201535i	−0.717778	+	0.696272i	$0.754841\pi$
$798$		0			0
$799$	1.10313	−	3.39508i	0.0390258	−	0.120109i
$800$	−3.19795	−	9.84226i	−0.113064	−	0.347977i
$801$		0			0
$802$	−2.65237			−0.0936586
$803$	39.8616	+	30.0022i	1.40669	+	1.05875i
$804$		0			0
$805$	−35.3110	+	25.6549i	−1.24455	+	0.904218i
$806$	2.36238	+	7.27066i	0.0832113	+	0.256098i
$807$		0			0
$808$	−10.6151	−	7.71229i	−0.373436	−	0.271317i
$809$	−6.36318	−	4.62312i	−0.223717	−	0.162540i	0.470281	−	0.882517i	$-0.344153\pi$
$809$	−6.36318	−	4.62312i	−0.223717	−	0.162540i	−0.693998	+	0.719976i	$0.744153\pi$
$810$		0			0
$811$	12.2076	+	37.5712i	0.428668	+	1.31930i	0.899438	+	0.437048i	$0.143976\pi$
$811$	12.2076	+	37.5712i	0.428668	+	1.31930i	−0.470770	+	0.882256i	$0.656024\pi$
$812$	−8.21041	+	5.96521i	−0.288129	+	0.209338i
$813$		0			0
$814$	4.98624	+	0.0841830i	0.174768	+	0.00295061i
$815$	−18.7799			−0.657831
$816$		0			0
$817$	−13.1226	−	40.3871i	−0.459100	−	1.41296i
$818$	3.58013	−	11.0185i	0.125176	−	0.385253i
$819$		0			0
$820$	0.950378	+	0.690490i	0.0331886	+	0.0241130i
$821$	1.03633	−	3.18948i	0.0361680	−	0.111314i	−0.931343	−	0.364144i	$-0.881362\pi$
$821$	1.03633	−	3.18948i	0.0361680	−	0.111314i	0.967511	+	0.252831i	$0.0813615\pi$
$822$		0			0
$823$	−13.0266	+	9.46441i	−0.454080	+	0.329909i	−0.791205	−	0.611552i	$-0.790546\pi$
$823$	−13.0266	+	9.46441i	−0.454080	+	0.329909i	0.337124	+	0.941460i	$0.390546\pi$
$824$	3.05046			0.106268
$825$		0			0
$826$	6.11681			0.212831
$827$	12.3703	−	8.98751i	0.430156	−	0.312526i	−0.351555	−	0.936167i	$-0.614347\pi$
$827$	12.3703	−	8.98751i	0.430156	−	0.312526i	0.781711	+	0.623641i	$0.214347\pi$
$828$		0			0
$829$	−13.0239	+	40.0835i	−0.452340	+	1.39216i	0.421890	+	0.906647i	$0.361367\pi$
$829$	−13.0239	+	40.0835i	−0.452340	+	1.39216i	−0.874230	+	0.485512i	$0.838633\pi$
$830$	0.0847063	+	0.0615427i	0.00294020	+	0.00213618i
$831$		0			0
$832$	3.44790	−	10.6115i	0.119534	−	0.367889i
$833$	4.72972	+	14.5566i	0.163875	+	0.504355i
$834$		0			0
$835$	−30.0193			−1.03886
$836$	8.37869	−	24.3788i	0.289783	−	0.843157i
$837$		0			0
$838$	−7.19483	+	5.22735i	−0.248541	+	0.180576i
$839$	−0.818089	−	2.51782i	−0.0282436	−	0.0869247i	0.935941	−	0.352157i	$-0.114552\pi$
$839$	−0.818089	−	2.51782i	−0.0282436	−	0.0869247i	−0.964185	+	0.265232i	$0.914552\pi$
$840$		0			0
$841$	21.1473	+	15.3644i	0.729218	+	0.529808i
$842$	5.08411	+	3.69382i	0.175210	+	0.127298i
$843$		0			0
$844$	3.96018	+	12.1882i	0.136315	+	0.419534i
$845$	4.12288	−	2.99545i	0.141831	−	0.103047i
$846$		0			0
$847$	−31.0780	+	21.0141i	−1.06785	+	0.722053i
$848$	32.8464			1.12795
$849$		0			0
$850$	−1.04289	−	3.20970i	−0.0357709	−	0.110092i
$851$	−7.09718	+	21.8429i	−0.243288	+	0.748765i
$852$		0			0
$853$	−7.49989	−	5.44899i	−0.256791	−	0.186570i	0.451940	−	0.892048i	$-0.350732\pi$
$853$	−7.49989	−	5.44899i	−0.256791	−	0.186570i	−0.708731	+	0.705479i	$0.750732\pi$
$854$	−1.99185	+	6.13027i	−0.0681596	+	0.209774i
$855$		0			0
$856$	−4.93314	+	3.58414i	−0.168611	+	0.122503i
$857$	20.5356			0.701483			0.350742	−	0.936472i	$-0.385930\pi$
$857$	20.5356			0.701483			0.350742	+	0.936472i	$0.385930\pi$
$858$		0			0
$859$	36.0278			1.22925			0.614626	−	0.788819i	$-0.289307\pi$
$859$	36.0278			1.22925			0.614626	+	0.788819i	$0.289307\pi$
$860$	−23.3724	+	16.9811i	−0.796993	+	0.579049i
$861$		0			0
$862$	0.997209	−	3.06909i	0.0339651	−	0.104534i
$863$	3.49209	+	2.53715i	0.118872	+	0.0863656i	0.645633	−	0.763648i	$-0.276594\pi$
$863$	3.49209	+	2.53715i	0.118872	+	0.0863656i	−0.526761	+	0.850014i	$0.676594\pi$
$864$		0			0
$865$	6.52733	−	20.0890i	0.221936	−	0.683048i
$866$	2.12166	+	6.52979i	0.0720969	+	0.221891i
$867$		0			0
$868$	23.3932			0.794015
$869$	−3.88516	−	12.6818i	−0.131795	−	0.430202i
$870$		0			0
$871$	10.0305	−	7.28757i	0.339870	−	0.246930i
$872$	3.13804	+	9.65790i	0.106268	+	0.327058i
$873$		0			0
$874$	−13.1335	−	9.54206i	−0.444248	−	0.322765i
$875$	−33.3792	−	24.2514i	−1.12842	−	0.819846i
$876$		0			0
$877$	9.61537	+	29.5931i	0.324688	+	0.999287i	0.971581	+	0.236707i	$0.0760680\pi$
$877$	9.61537	+	29.5931i	0.324688	+	0.999287i	−0.646893	+	0.762581i	$0.723932\pi$
$878$	−9.99117	+	7.25901i	−0.337186	+	0.244980i
$879$		0			0
$880$	−14.8093	−	0.250027i	−0.499222	−	0.00842839i
$881$	−43.9267			−1.47993			−0.739964	−	0.672647i	$-0.765157\pi$
$881$	−43.9267			−1.47993			−0.739964	+	0.672647i	$0.765157\pi$
$882$		0			0
$883$	−1.81685	−	5.59170i	−0.0611420	−	0.188176i	0.915820	−	0.401589i	$-0.131542\pi$
$883$	−1.81685	−	5.59170i	−0.0611420	−	0.188176i	−0.976962	+	0.213413i	$0.931542\pi$
$884$	7.18292	−	22.1068i	0.241588	−	0.743530i
$885$		0			0
$886$	10.6436	+	7.73306i	0.357580	+	0.259797i
$887$	2.37792	−	7.31848i	0.0798427	−	0.245730i	−0.903165	−	0.429293i	$-0.858763\pi$
$887$	2.37792	−	7.31848i	0.0798427	−	0.245730i	0.983008	+	0.183562i	$0.0587629\pi$
$888$		0			0
$889$	−29.7850	+	21.6401i	−0.998957	+	0.725785i
$890$	−6.64689			−0.222804
$891$		0			0
$892$	−41.3640			−1.38497
$893$	3.86079	−	2.80503i	0.129197	−	0.0938668i
$894$		0			0
$895$	11.5507	−	35.5494i	0.386097	−	1.18829i
$896$	31.2047	+	22.6716i	1.04248	+	0.757403i
$897$		0			0
$898$	−2.14864	+	6.61285i	−0.0717012	+	0.220674i
$899$	2.03751	+	6.27081i	0.0679547	+	0.209143i
$900$		0			0
$901$	41.5180			1.38316
$902$	0.520665	−	0.365017i	0.0173362	−	0.0121537i
$903$		0			0
$904$	24.4793	−	17.7853i	0.814171	−	0.591530i
$905$	2.31210	+	7.11591i	0.0768568	+	0.236541i
$906$		0			0
$907$	15.3637	+	11.1624i	0.510143	+	0.370640i	0.812878	−	0.582434i	$-0.197900\pi$
$907$	15.3637	+	11.1624i	0.510143	+	0.370640i	−0.302735	+	0.953075i	$0.597900\pi$
$908$	16.9700	+	12.3294i	0.563170	+	0.409167i
$909$		0			0
$910$	3.53024	+	10.8650i	0.117026	+	0.360170i
$911$	40.4794	−	29.4100i	1.34114	−	0.974397i	0.341741	−	0.939794i	$-0.388983\pi$
$911$	40.4794	−	29.4100i	1.34114	−	0.974397i	0.999401	−	0.0346024i	$-0.0110165\pi$
$912$		0			0
$913$	−0.339374	+	0.237921i	−0.0112316	+	0.00787405i
$914$	12.0864			0.399783
$915$		0			0
$916$	−1.66237	−	5.11624i	−0.0549262	−	0.169045i
$917$	22.2961	−	68.6205i	0.736284	−	2.26605i
$918$		0			0
$919$	−2.48708	−	1.80697i	−0.0820411	−	0.0596063i	0.546009	−	0.837780i	$-0.316147\pi$
$919$	−2.48708	−	1.80697i	−0.0820411	−	0.0596063i	−0.628050	+	0.778173i	$0.716147\pi$
$920$	−7.29235	+	22.4436i	−0.240422	+	0.739942i
$921$		0			0
$922$	−10.4146	+	7.56668i	−0.342988	+	0.249195i
$923$	28.0540			0.923410
$924$		0			0
$925$	−6.38283			−0.209866
$926$	−5.03648	+	3.65922i	−0.165509	+	0.120249i
$927$		0			0
$928$	−2.59765	+	7.99474i	−0.0852720	+	0.262440i
$929$	−0.732625	−	0.532283i	−0.0240366	−	0.0174636i	0.575702	−	0.817660i	$-0.304729\pi$
$929$	−0.732625	−	0.532283i	−0.0240366	−	0.0174636i	−0.599739	+	0.800196i	$0.704729\pi$
$930$		0			0
$931$	−6.32282	+	19.4596i	−0.207222	+	0.637764i
$932$	−13.3374	−	41.0484i	−0.436882	−	1.34459i
$933$		0			0
$934$	13.5887			0.444634
$935$	−18.7190	−	0.316034i	−0.612177	−	0.0103354i
$936$		0			0
$937$	17.8423	−	12.9632i	0.582881	−	0.423488i	−0.256881	−	0.966443i	$-0.582695\pi$
$937$	17.8423	−	12.9632i	0.582881	−	0.423488i	0.839762	+	0.542955i	$0.182695\pi$
$938$	1.60312	+	4.93390i	0.0523438	+	0.161098i
$939$		0			0
$940$	−2.62656	−	1.90830i	−0.0856688	−	0.0622420i
$941$	4.41798	+	3.20985i	0.144022	+	0.104638i	0.657463	−	0.753487i	$-0.271630\pi$
$941$	4.41798	+	3.20985i	0.144022	+	0.104638i	−0.513441	+	0.858125i	$0.671630\pi$
$942$		0			0
$943$	0.904937	+	2.78511i	0.0294688	+	0.0906956i
$944$	−7.73386	+	5.61898i	−0.251716	+	0.182882i
$945$		0			0
$946$	4.58059	+	14.9519i	0.148928	+	0.486127i
$947$	−32.4406			−1.05418			−0.527089	−	0.849810i	$-0.676717\pi$
$947$	−32.4406			−1.05418			−0.527089	+	0.849810i	$0.676717\pi$
$948$		0			0
$949$	18.5840	+	57.1958i	0.603263	+	1.85665i
$950$	1.39417	−	4.29081i	0.0452328	−	0.139212i
$951$		0			0
$952$	16.8131	+	12.2154i	0.544916	+	0.395905i
$953$	16.6278	−	51.1752i	0.538628	−	1.65773i	−0.197049	−	0.980394i	$-0.563136\pi$
$953$	16.6278	−	51.1752i	0.538628	−	1.65773i	0.735677	−	0.677333i	$-0.236864\pi$
$954$		0			0
$955$	−17.2947	+	12.5653i	−0.559642	+	0.406604i
$956$	−12.2290			−0.395516
$957$		0			0
$958$	7.66260			0.247567
$959$	8.83079	−	6.41595i	0.285161	−	0.207182i
$960$		0			0
$961$	−4.88295	+	15.0282i	−0.157515	+	0.484780i
$962$	4.86330	+	3.53339i	0.156799	+	0.113921i
$963$		0			0
$964$	4.22478	−	13.0025i	0.136071	−	0.418784i
$965$	6.63288	+	20.4139i	0.213520	+	0.657147i
$966$		0			0
$967$	−28.8151			−0.926630			−0.463315	−	0.886194i	$-0.653340\pi$
$967$	−28.8151			−0.926630			−0.463315	+	0.886194i	$0.653340\pi$
$968$	−6.91562	+	19.0683i	−0.222277	+	0.612880i
$969$		0			0
$970$	0.232606	−	0.168998i	0.00746852	−	0.00542620i
$971$	−1.66685	−	5.13005i	−0.0534919	−	0.164631i	0.920742	−	0.390173i	$-0.127585\pi$
$971$	−1.66685	−	5.13005i	−0.0534919	−	0.164631i	−0.974233	+	0.225542i	$0.927585\pi$
$972$		0			0
$973$	41.3700	+	30.0571i	1.32626	+	0.963586i
$974$	−10.6851	−	7.76320i	−0.342373	−	0.248749i
$975$		0			0
$976$	−3.11293	−	9.58061i	−0.0996424	−	0.306668i
$977$	−2.67975	+	1.94695i	−0.0857329	+	0.0622886i	−0.629826	−	0.776736i	$-0.716874\pi$
$977$	−2.67975	+	1.94695i	−0.0857329	+	0.0622886i	0.544093	+	0.839025i	$0.316874\pi$
$978$		0			0
$979$	8.55201	−	24.8831i	0.273324	−	0.795266i
$980$	13.9200			0.444657
$981$		0			0
$982$	−5.91123	−	18.1929i	−0.188635	−	0.580559i
$983$	−10.4671	+	32.2143i	−0.333847	+	1.02748i	0.633440	+	0.773792i	$0.281643\pi$
$983$	−10.4671	+	32.2143i	−0.333847	+	1.02748i	−0.967287	+	0.253685i	$0.918357\pi$
$984$		0			0
$985$	14.2967	+	10.3872i	0.455530	+	0.330962i
$986$	−0.847129	+	2.60719i	−0.0269781	+	0.0830300i
$987$		0			0
$988$	25.1392	−	18.2647i	0.799785	−	0.581078i
$989$	−72.0183			−2.29005
$990$		0			0
$991$	8.66640			0.275297			0.137649	−	0.990481i	$-0.456046\pi$
$991$	8.66640			0.275297			0.137649	+	0.990481i	$0.456046\pi$
$992$	15.6761	−	11.3893i	0.497716	−	0.361612i
$993$		0			0
$994$	−3.62742	+	11.1640i	−0.115055	+	0.354102i
$995$	36.5902	+	26.5843i	1.15999	+	0.842780i
$996$		0			0
$997$	−9.35253	+	28.7841i	−0.296197	+	0.911602i	0.686619	+	0.727017i	$0.259094\pi$
$997$	−9.35253	+	28.7841i	−0.296197	+	0.911602i	−0.982817	+	0.184585i	$0.940906\pi$
$998$	−3.64303	−	11.2121i	−0.115318	−	0.354912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.487.5		36
3.2	odd	2		891.2.f.f.487.5		36
9.2	odd	6		99.2.m.b.58.5	yes	72
9.4	even	3		297.2.n.b.289.5		72
9.5	odd	6		99.2.m.b.25.5	yes	72
9.7	even	3		297.2.n.b.91.5		72
11.2	odd	10		9801.2.a.cn.1.9		18
11.4	even	5	inner	891.2.f.e.730.5		36
11.9	even	5		9801.2.a.cp.1.10		18
33.2	even	10		9801.2.a.co.1.10		18
33.20	odd	10		9801.2.a.cm.1.9		18
33.26	odd	10		891.2.f.f.730.5		36
99.2	even	30		1089.2.e.o.364.9		36
99.4	even	15		297.2.n.b.235.5		72
99.20	odd	30		1089.2.e.p.364.10		36
99.59	odd	30		99.2.m.b.70.5	yes	72
99.68	even	30		1089.2.e.o.727.9		36
99.70	even	15		297.2.n.b.37.5		72
99.86	odd	30		1089.2.e.p.727.10		36
99.92	odd	30		99.2.m.b.4.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	99.92	odd	30
99.2.m.b.25.5	yes	72	9.5	odd	6
99.2.m.b.58.5	yes	72	9.2	odd	6
99.2.m.b.70.5	yes	72	99.59	odd	30
297.2.n.b.37.5		72	99.70	even	15
297.2.n.b.91.5		72	9.7	even	3
297.2.n.b.235.5		72	99.4	even	15
297.2.n.b.289.5		72	9.4	even	3
891.2.f.e.487.5		36	1.1	even	1	trivial
891.2.f.e.730.5		36	11.4	even	5	inner
891.2.f.f.487.5		36	3.2	odd	2
891.2.f.f.730.5		36	33.26	odd	10
1089.2.e.o.364.9		36	99.2	even	30
1089.2.e.o.727.9		36	99.68	even	30
1089.2.e.p.364.10		36	99.20	odd	30
1089.2.e.p.727.10		36	99.86	odd	30
9801.2.a.cm.1.9		18	33.20	odd	10
9801.2.a.cn.1.9		18	11.2	odd	10
9801.2.a.co.1.10		18	33.2	even	10
9801.2.a.cp.1.10		18	11.9	even	5

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.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396818 + 0.288305i) q^{2} +(-0.543689 + 1.67330i) q^{4} +(1.38194 + 1.00404i) q^{5} +(1.05391 - 3.24360i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(1.07799 - 3.13655i) q^{11} +(3.23439 - 2.34992i) q^{13} +(0.516936 + 1.59097i) q^{14} +(-2.11507 - 1.53669i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(-2.43141 + 1.76653i) q^{20} +(0.476515 + 1.55543i) q^{22} -7.49201 q^{23} +(-0.643414 - 1.98022i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(-0.522637 + 1.60851i) q^{29} +(3.15397 - 2.29149i) q^{31} +4.97028 q^{32} +1.62087 q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(1.75300 + 1.27363i) q^{38} +(0.973351 - 2.99566i) q^{40} +(-0.120787 - 0.371744i) q^{41} +9.61268 q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(0.333818 + 1.02739i) q^{47} +(-3.74710 - 2.72242i) q^{49} +(0.826227 + 0.600289i) q^{50} +(2.17363 + 6.68974i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} -6.28890 q^{56} +(-0.256350 - 0.788965i) q^{58} +(1.12993 - 3.47758i) q^{59} +(3.11728 + 2.26484i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +6.82916 q^{65} +3.10120 q^{67} +(4.70372 - 3.41746i) q^{68} +(-0.883019 + 2.71765i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(0.464645 + 1.43003i) q^{74} +7.77248 q^{76} +(-9.03760 - 6.80222i) q^{77} +(3.23536 - 2.35063i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(-0.101100 - 0.0734531i) q^{83} +(-1.74434 - 5.36852i) q^{85} +(-3.81449 + 2.77139i) q^{86} +(-6.11489 - 0.103238i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(4.07333 - 12.5364i) q^{92} +(-0.428666 - 0.311444i) q^{94} +(2.33188 - 7.17680i) q^{95} +(-0.277622 + 0.201704i) q^{97} +2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

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