LMFDB - Embedded newform 891.2.f.f.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.f.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	−0.438583	−	0.898691i	$-0.644520\pi$
$2$	0.396818	−	0.288305i	0.280593	−	0.203863i	0.719176	+	0.694828i	$0.244520\pi$
$3$		0			0
$3$		0			0
$4$	−0.543689	+	1.67330i	−0.271845	+	0.836652i
$5$	−1.38194	−	1.00404i	−0.618024	−	0.449021i	0.234207	−	0.972187i	$-0.424751\pi$
$5$	−1.38194	−	1.00404i	−0.618024	−	0.449021i	−0.852231	+	0.523166i	$0.824751\pi$
$6$		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	0.862729	−	0.505667i	$-0.168754\pi$
$17$	2.67346	+	1.94238i	0.648409	+	0.471097i	−0.214320	+	0.976763i	$0.568754\pi$
$18$		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	$-0.214661\pi$
$23$	7.49201			1.56219			0.781096	+	0.624411i	$0.214661\pi$
$24$		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	−0.890732	−	0.454530i	$-0.849807\pi$
$29$	0.522637	−	1.60851i	0.0970512	−	0.298693i	0.987783	+	0.155837i	$0.0498074\pi$
$30$		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	0.960045	−	0.279845i	$-0.0902830\pi$
$41$	0.120787	+	0.371744i	0.0188637	+	0.0580566i	−0.941182	+	0.337901i	$0.890283\pi$
$42$		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	0.923754	−	0.382986i	$-0.125104\pi$
$47$	−0.333818	−	1.02739i	−0.0486924	−	0.149860i	−0.972446	+	0.233127i	$0.925104\pi$
$48$		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	$-0.368656\pi$
$53$	10.1643	−	7.38480i	1.39618	−	1.01438i	0.995156	−	0.0983117i	$-0.0313442\pi$
$54$		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	−0.997276	−	0.0737648i	$-0.976499\pi$
$59$	−1.12993	+	3.47758i	−0.147105	+	0.452742i	0.850171	+	0.526507i	$0.176499\pi$
$60$		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	0.197538	−	0.980295i	$-0.436705\pi$
$71$	−5.67699	−	4.12458i	−0.673735	−	0.489497i	−0.871273	+	0.490798i	$0.836705\pi$
$72$		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	0.593320	−	0.804967i	$-0.297817\pi$
$83$	0.101100	+	0.0734531i	0.0110971	+	0.00806252i	−0.582223	+	0.813029i	$0.697817\pi$
$84$		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	$-0.638132\pi$
$89$	−7.93327			−0.840925			−0.420462	+	0.907310i	$0.638132\pi$
$90$		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	−0.836123	−	0.548541i	$-0.815183\pi$
$101$	−5.75663	+	4.18244i	−0.572806	+	0.416168i	0.263318	+	0.964709i	$0.415183\pi$
$102$		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	0.988222	−	0.153025i	$-0.0489016\pi$
$107$	1.02187	+	3.14498i	0.0987876	+	0.304037i	−0.889435	+	0.457062i	$0.848902\pi$
$108$		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	$-0.819344\pi$
$113$	−5.07073	−	15.6061i	−0.477014	−	1.46810i	0.366208	−	0.930533i	$-0.380656\pi$
$114$		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	$-0.875258\pi$
$131$	−21.1557			−1.84838			−0.924189	+	0.381935i	$0.875258\pi$
$132$		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	0.471657	−	0.881782i	$-0.343656\pi$
$137$	−2.58928	−	1.88122i	−0.221217	−	0.160724i	−0.692874	+	0.721058i	$0.743656\pi$
$138$		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	0.445387	−	0.895338i	$-0.353066\pi$
$149$	−3.27743	−	2.38119i	−0.268497	−	0.195075i	−0.713885	+	0.700263i	$0.753066\pi$
$150$		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	0.119097	−	0.992883i	$-0.462000\pi$
$167$	14.2176	−	10.3297i	1.10019	−	0.799333i	0.981090	+	0.193550i	$0.0620001\pi$
$168$		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	$0.0557731\pi$
$173$	3.82122	+	11.7605i	0.290522	+	0.894135i	−0.694167	+	0.719814i	$0.744227\pi$
$174$		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	$0.204795\pi$
$179$	6.76200	+	20.8113i	0.505416	+	1.55551i	−0.294655	+	0.955604i	$0.595205\pi$
$180$		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	$-0.750437\pi$
$191$	3.86727	−	11.9022i	0.279826	−	0.861214i	0.987902	−	0.155079i	$-0.0495631\pi$
$192$		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	$-0.620141\pi$
$197$	−10.3453			−0.737075			−0.368538	+	0.929613i	$0.620141\pi$
$198$		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	$0.229481\pi$
$227$	−3.68416	+	11.3387i	−0.244526	+	0.752574i	−0.995714	+	0.0924858i	$0.970519\pi$
$228$		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	0.300217	−	0.953871i	$-0.402941\pi$
$233$	19.8463	−	14.4192i	1.30017	−	0.944632i	0.999957	+	0.00923938i	$0.00294103\pi$
$234$		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	0.857247	−	0.514905i	$-0.172173\pi$
$239$	−2.14786	−	6.61044i	−0.138934	−	0.427594i	−0.996181	+	0.0873108i	$0.972173\pi$
$240$		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	−0.596107	−	0.802905i	$-0.703287\pi$
$251$	−0.264684	+	0.192304i	−0.0167067	+	0.0121381i	0.579401	+	0.815043i	$0.303287\pi$
$252$		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	$0.240852\pi$
$257$	−4.24255	+	13.0572i	−0.264643	+	0.814487i	−0.991775	+	0.127990i	$0.959148\pi$
$258$		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	$-0.673933\pi$
$263$	−16.8542			−1.03927			−0.519637	+	0.854387i	$0.673933\pi$
$264$		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	0.238428	−	0.971160i	$-0.423368\pi$
$269$	−10.0297	−	7.28700i	−0.611522	−	0.444296i	−0.849950	+	0.526864i	$0.823368\pi$
$270$		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	0.908918	−	0.416974i	$-0.136910\pi$
$281$	13.2968	+	9.66072i	0.793223	+	0.576310i	−0.115695	+	0.993285i	$0.536910\pi$
$282$		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	$0.348426\pi$
$293$	−7.44342	+	22.9085i	−0.434849	+	1.33833i	−0.893241	+	0.449578i	$0.851574\pi$
$294$		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	$0.107197\pi$
$311$	6.60408	+	20.3253i	0.374483	+	1.15254i	−0.569344	+	0.822100i	$0.692803\pi$
$312$		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	−0.0896059	−	0.995977i	$-0.528561\pi$
$317$	14.7766	−	10.7358i	0.829935	−	0.602983i	0.919541	+	0.392994i	$0.128561\pi$
$318$		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	−0.0838748	−	0.996476i	$-0.526730\pi$
$347$	−19.6990	−	14.3122i	−1.05750	−	0.768318i	−0.973624	+	0.228158i	$0.926730\pi$
$348$		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	$-0.568562\pi$
$353$	−8.03132			−0.427464			−0.213732	+	0.976892i	$0.568562\pi$
$354$		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	$0.375126\pi$
$359$	−8.90742	+	27.4142i	−0.470116	+	1.44687i	−0.852433	+	0.522836i	$0.824874\pi$
$360$		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	−0.160158	−	0.987091i	$-0.551200\pi$
$383$	14.2694	−	10.3673i	0.729130	−	0.529744i	0.889288	+	0.457348i	$0.151200\pi$
$384$		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	$0.249772\pi$
$389$	−5.52615	+	17.0077i	−0.280187	+	0.862326i	−0.987800	+	0.155727i	$0.950228\pi$
$390$		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	0.473169	−	0.880972i	$-0.343110\pi$
$401$	−4.37481	−	3.17848i	−0.218467	−	0.158726i	−0.691636	+	0.722246i	$0.743110\pi$
$402$		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	$-0.646045\pi$
$419$	−18.1313			−0.885773			−0.442886	+	0.896578i	$0.646045\pi$
$420$		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	−0.452168	−	0.891933i	$-0.649349\pi$
$431$	5.32265	−	3.86713i	0.256383	−	0.186273i	0.708551	+	0.705660i	$0.249349\pi$
$432$		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	$0.119902\pi$
$443$	8.28860	+	25.5097i	0.393803	+	1.21200i	−0.536086	+	0.844163i	$0.680098\pi$
$444$		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	−0.824542	−	0.565801i	$-0.808567\pi$
$449$	−11.4685	+	8.33234i	−0.541231	+	0.393228i	0.283311	+	0.959028i	$0.408567\pi$
$450$		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	$-0.709307\pi$
$461$	−26.2454			−1.22237			−0.611185	+	0.791488i	$0.709307\pi$
$462$		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	0.969727	−	0.244190i	$-0.0785221\pi$
$467$	22.4130	+	16.2840i	1.03715	+	0.753534i	0.0674235	+	0.997724i	$0.478522\pi$
$468$		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	0.837812	−	0.545958i	$-0.183834\pi$
$479$	12.6386	+	9.18250i	0.577474	+	0.419559i	−0.260339	+	0.965517i	$0.583834\pi$
$480$		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	$-0.557531\pi$
$491$	12.0516	−	37.0910i	0.543880	−	1.67389i	0.723637	−	0.690181i	$-0.242469\pi$
$492$		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	$-0.920405\pi$
$503$	−7.41223	−	22.8125i	−0.330495	−	1.01716i	0.638404	−	0.769701i	$-0.279595\pi$
$504$		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	0.973187	−	0.230014i	$-0.0738774\pi$
$509$	1.14301	+	3.51783i	0.0506631	+	0.155925i	−0.922524	+	0.385939i	$0.873877\pi$
$510$		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	−0.985037	−	0.172345i	$-0.944866\pi$
$521$	−1.98178	+	6.09929i	−0.0868234	+	0.267215i	0.898213	+	0.439560i	$0.144866\pi$
$522$		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	−0.998960	−	0.0455895i	$-0.985483\pi$
$557$	−3.87025	+	11.9114i	−0.163988	+	0.504702i	0.834973	+	0.550291i	$0.185483\pi$
$558$		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	−0.312295	−	0.949985i	$-0.601098\pi$
$563$	11.7378	−	8.52802i	0.494690	−	0.359413i	0.806985	+	0.590572i	$0.201098\pi$
$564$		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	$-0.900571\pi$
$569$	−8.64395	−	26.6034i	−0.362373	−	1.11527i	0.589236	−	0.807961i	$-0.299429\pi$
$570$		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	−0.955559	−	0.294800i	$-0.904747\pi$
$587$	−0.223301	+	0.687250i	−0.00921662	+	0.0283658i	0.946342	+	0.323166i	$0.104747\pi$
$588$		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	$-0.802886\pi$
$593$	−39.6596			−1.62863			−0.814313	+	0.580426i	$0.802886\pi$
$594$		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	0.871217	−	0.490898i	$-0.163331\pi$
$599$	16.4852	+	11.9772i	0.673566	+	0.489374i	−0.197651	+	0.980272i	$0.563331\pi$
$600$		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	$-0.460772\pi$
$617$	6.10692			0.245855			0.122928	+	0.992416i	$0.460772\pi$
$618$		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	$-0.920912\pi$
$641$	−8.34641	−	25.6876i	−0.329663	−	1.01460i	0.639628	−	0.768685i	$-0.279088\pi$
$642$		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	0.0389724	−	0.999240i	$-0.487592\pi$
$647$	25.4705	−	18.5054i	1.00135	−	0.727523i	0.962377	+	0.271717i	$0.0875916\pi$
$648$		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	−0.975270	−	0.221017i	$-0.929062\pi$
$653$	−1.43995	+	4.43171i	−0.0563495	+	0.173426i	0.918920	+	0.394443i	$0.129062\pi$
$654$		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	$-0.714529\pi$
$659$	−32.0418			−1.24817			−0.624086	+	0.781355i	$0.714529\pi$
$660$		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	0.253805	−	0.967255i	$-0.418318\pi$
$677$	−15.2910	−	11.1095i	−0.587679	−	0.426974i	−0.841484	+	0.540281i	$0.818318\pi$
$678$		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	$-0.297110\pi$
$683$	31.1053			1.19021			0.595105	+	0.803648i	$0.297110\pi$
$684$		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	$-0.908677\pi$
$701$	−9.25374	−	28.4801i	−0.349509	−	1.07568i	0.609616	−	0.792697i	$-0.291323\pi$
$702$		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	−0.920131	−	0.391611i	$-0.871918\pi$
$719$	1.46013	−	4.49382i	0.0544537	−	0.167591i	0.974585	+	0.224020i	$0.0719180\pi$
$720$		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	0.410160	−	0.912014i	$-0.365473\pi$
$743$	−9.00796	−	6.54466i	−0.330470	−	0.240100i	−0.740630	+	0.671913i	$0.765473\pi$
$744$		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	−0.966955	−	0.254949i	$-0.917941\pi$
$761$	−28.2287	+	20.5093i	−1.02329	+	0.743463i	−0.0563348	+	0.998412i	$0.517941\pi$
$762$		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	0.872568	−	0.488493i	$-0.162453\pi$
$773$	−3.34979	−	10.3096i	−0.120483	−	0.370810i	−0.993051	+	0.117683i	$0.962453\pi$
$774$		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	0.717778	−	0.696272i	$-0.245159\pi$
$797$	7.83103	+	5.68958i	0.277389	+	0.201535i	−0.440389	+	0.897807i	$0.645159\pi$
$798$		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	0.693998	−	0.719976i	$-0.255847\pi$
$809$	6.36318	+	4.62312i	0.223717	+	0.162540i	−0.470281	+	0.882517i	$0.655847\pi$
$810$		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	−0.967511	−	0.252831i	$-0.918638\pi$
$821$	−1.03633	+	3.18948i	−0.0361680	+	0.111314i	0.931343	+	0.364144i	$0.118638\pi$
$822$		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	−0.781711	−	0.623641i	$-0.785653\pi$
$827$	−12.3703	+	8.98751i	−0.430156	+	0.312526i	0.351555	+	0.936167i	$0.385653\pi$
$828$		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	0.964185	−	0.265232i	$-0.0854485\pi$
$839$	0.818089	+	2.51782i	0.0282436	+	0.0869247i	−0.935941	+	0.352157i	$0.885448\pi$
$840$		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	$-0.614070\pi$
$857$	−20.5356			−0.701483			−0.350742	+	0.936472i	$0.614070\pi$
$858$		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	0.526761	−	0.850014i	$-0.323406\pi$
$863$	−3.49209	−	2.53715i	−0.118872	−	0.0863656i	−0.645633	+	0.763648i	$0.723406\pi$
$864$		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	$-0.234843\pi$
$881$	43.9267			1.47993			0.739964	+	0.672647i	$0.234843\pi$
$882$		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	−0.983008	−	0.183562i	$-0.941237\pi$
$887$	−2.37792	+	7.31848i	−0.0798427	+	0.245730i	0.903165	+	0.429293i	$0.141237\pi$
$888$		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	$0.611017\pi$
$911$	−40.4794	+	29.4100i	−1.34114	+	0.974397i	−0.999401	+	0.0346024i	$0.988983\pi$
$912$		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	0.599739	−	0.800196i	$-0.295271\pi$
$929$	0.732625	+	0.532283i	0.0240366	+	0.0174636i	−0.575702	+	0.817660i	$0.695271\pi$
$930$		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	0.513441	−	0.858125i	$-0.328370\pi$
$941$	−4.41798	−	3.20985i	−0.144022	−	0.104638i	−0.657463	+	0.753487i	$0.728370\pi$
$942$		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	$-0.323283\pi$
$947$	32.4406			1.05418			0.527089	+	0.849810i	$0.323283\pi$
$948$		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	$0.436864\pi$
$953$	−16.6278	+	51.1752i	−0.538628	+	1.65773i	−0.735677	+	0.677333i	$0.763136\pi$
$954$		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	0.974233	−	0.225542i	$-0.0724152\pi$
$971$	1.66685	+	5.13005i	0.0534919	+	0.164631i	−0.920742	+	0.390173i	$0.872415\pi$
$972$		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	−0.544093	−	0.839025i	$-0.683126\pi$
$977$	2.67975	−	1.94695i	0.0857329	−	0.0622886i	0.629826	+	0.776736i	$0.283126\pi$
$978$		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	$-0.718357\pi$
$983$	10.4671	−	32.2143i	0.333847	−	1.02748i	0.967287	−	0.253685i	$-0.0816425\pi$
$984$		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.f.487.5		36
3.2	odd	2		891.2.f.e.487.5		36
9.2	odd	6		297.2.n.b.91.5		72
9.4	even	3		99.2.m.b.25.5	yes	72
9.5	odd	6		297.2.n.b.289.5		72
9.7	even	3		99.2.m.b.58.5	yes	72
11.2	odd	10		9801.2.a.co.1.10		18
11.4	even	5	inner	891.2.f.f.730.5		36
11.9	even	5		9801.2.a.cm.1.9		18
33.2	even	10		9801.2.a.cn.1.9		18
33.20	odd	10		9801.2.a.cp.1.10		18
33.26	odd	10		891.2.f.e.730.5		36
99.4	even	15		99.2.m.b.70.5	yes	72
99.13	odd	30		1089.2.e.o.727.9		36
99.31	even	15		1089.2.e.p.727.10		36
99.59	odd	30		297.2.n.b.235.5		72
99.70	even	15		99.2.m.b.4.5	✓	72
99.79	odd	30		1089.2.e.o.364.9		36
99.92	odd	30		297.2.n.b.37.5		72
99.97	even	15		1089.2.e.p.364.10		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	99.70	even	15
99.2.m.b.25.5	yes	72	9.4	even	3
99.2.m.b.58.5	yes	72	9.7	even	3
99.2.m.b.70.5	yes	72	99.4	even	15
297.2.n.b.37.5		72	99.92	odd	30
297.2.n.b.91.5		72	9.2	odd	6
297.2.n.b.235.5		72	99.59	odd	30
297.2.n.b.289.5		72	9.5	odd	6
891.2.f.e.487.5		36	3.2	odd	2
891.2.f.e.730.5		36	33.26	odd	10
891.2.f.f.487.5		36	1.1	even	1	trivial
891.2.f.f.730.5		36	11.4	even	5	inner
1089.2.e.o.364.9		36	99.79	odd	30
1089.2.e.o.727.9		36	99.13	odd	30
1089.2.e.p.364.10		36	99.97	even	15
1089.2.e.p.727.10		36	99.31	even	15
9801.2.a.cm.1.9		18	11.9	even	5
9801.2.a.cn.1.9		18	33.2	even	10
9801.2.a.co.1.10		18	11.2	odd	10
9801.2.a.cp.1.10		18	33.20	odd	10

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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