LMFDB - Embedded newform 891.2.f.e.730.5

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			730.5
Character	$\chi$	$=$	891.730
Dual form			891.2.f.e.487.5

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

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

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	$-0.355480\pi$
$2$	−0.396818	−	0.288305i	−0.280593	−	0.203863i	−0.719176	+	0.694828i	$0.755480\pi$
$3$		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	$-0.575249\pi$
$5$	1.38194	−	1.00404i	0.618024	−	0.449021i	0.852231	+	0.523166i	$0.175249\pi$
$6$		0			0
$7$	1.05391	+	3.24360i	0.398340	+	1.22597i	0.926329	+	0.376714i	$0.122946\pi$
$7$	1.05391	+	3.24360i	0.398340	+	1.22597i	−0.527989	+	0.849251i	$0.677054\pi$
$8$	−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	0.937709	−	0.347423i	$-0.112943\pi$
$13$	3.23439	+	2.34992i	0.897058	+	0.651751i	−0.0406508	+	0.999173i	$0.512943\pi$
$14$	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	$-0.831246\pi$
$17$	−2.67346	+	1.94238i	−0.648409	+	0.471097i	0.214320	+	0.976763i	$0.431246\pi$
$18$		0			0
$19$	−1.36513	+	4.20144i	−0.313182	+	0.963875i	0.663314	+	0.748341i	$0.269149\pi$
$19$	−1.36513	+	4.20144i	−0.313182	+	0.963875i	−0.976496	+	0.215534i	$0.930851\pi$
$20$	−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	0.890732	−	0.454530i	$-0.150193\pi$
$29$	−0.522637	−	1.60851i	−0.0970512	−	0.298693i	−0.987783	+	0.155837i	$0.950193\pi$
$30$		0			0
$31$	3.15397	+	2.29149i	0.566469	+	0.411564i	0.833821	−	0.552035i	$-0.186149\pi$
$31$	3.15397	+	2.29149i	0.566469	+	0.411564i	−0.267352	+	0.963599i	$0.586149\pi$
$32$	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	0.998235	−	0.0593935i	$-0.0189167\pi$
$37$	0.947300	+	2.91549i	0.155735	+	0.479304i	−0.842499	+	0.538697i	$0.818917\pi$
$38$	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	$-0.909717\pi$
$41$	−0.120787	+	0.371744i	−0.0188637	+	0.0580566i	0.941182	+	0.337901i	$0.109717\pi$
$42$		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	$-0.874896\pi$
$47$	0.333818	−	1.02739i	0.0486924	−	0.149860i	0.972446	+	0.233127i	$0.0748956\pi$
$48$		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	−0.995156	−	0.0983117i	$-0.968656\pi$
$53$	−10.1643	−	7.38480i	−1.39618	−	1.01438i	−0.401020	−	0.916069i	$-0.631344\pi$
$54$		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	$-0.0235014\pi$
$59$	1.12993	+	3.47758i	0.147105	+	0.452742i	−0.850171	+	0.526507i	$0.823501\pi$
$60$		0			0
$61$	3.11728	−	2.26484i	0.399127	−	0.289983i	−0.370058	−	0.929009i	$-0.620662\pi$
$61$	3.11728	−	2.26484i	0.399127	−	0.289983i	0.769185	+	0.639026i	$0.220662\pi$
$62$	−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	$-0.563295\pi$
$71$	5.67699	−	4.12458i	0.673735	−	0.489497i	0.871273	+	0.490798i	$0.163295\pi$
$72$		0			0
$73$	−4.64842	−	14.3064i	−0.544057	−	1.67443i	−0.723222	−	0.690615i	$-0.757340\pi$
$73$	−4.64842	−	14.3064i	−0.544057	−	1.67443i	0.179165	−	0.983819i	$-0.442660\pi$
$74$	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	0.754721	−	0.656045i	$-0.227772\pi$
$79$	3.23536	+	2.35063i	0.364007	+	0.264467i	−0.390714	+	0.920512i	$0.627772\pi$
$80$	−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	$-0.702183\pi$
$83$	−0.101100	+	0.0734531i	−0.0110971	+	0.00806252i	0.582223	+	0.813029i	$0.302183\pi$
$84$		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	0.573602	−	0.819134i	$-0.305546\pi$
$97$	−0.277622	−	0.201704i	−0.0281882	−	0.0204800i	−0.601790	+	0.798654i	$0.705546\pi$
$98$	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	$-0.184817\pi$
$101$	5.75663	+	4.18244i	0.572806	+	0.416168i	−0.263318	+	0.964709i	$0.584817\pi$
$102$		0			0
$103$	−0.511203	−	1.57332i	−0.0503703	−	0.155024i	0.922707	−	0.385501i	$-0.125971\pi$
$103$	−0.511203	−	1.57332i	−0.0503703	−	0.155024i	−0.973078	+	0.230477i	$0.925971\pi$
$104$	−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	$-0.951098\pi$
$107$	−1.02187	+	3.14498i	−0.0987876	+	0.304037i	0.889435	+	0.457062i	$0.151098\pi$
$108$		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	−0.366208	−	0.930533i	$-0.619344\pi$
$113$	5.07073	−	15.6061i	0.477014	−	1.46810i	0.843222	−	0.537565i	$-0.180656\pi$
$114$		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	−0.903460	−	0.428673i	$-0.858981\pi$
$127$	−8.73327	+	6.34509i	−0.774952	+	0.563036i	0.128508	+	0.991709i	$0.458981\pi$
$128$	−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	−0.471657	−	0.881782i	$-0.656344\pi$
$137$	2.58928	−	1.88122i	0.221217	−	0.160724i	0.692874	+	0.721058i	$0.256344\pi$
$138$		0			0
$139$	−4.63329	−	14.2598i	−0.392991	−	1.20950i	−0.930515	−	0.366253i	$-0.880640\pi$
$139$	−4.63329	−	14.2598i	−0.392991	−	1.20950i	0.537525	−	0.843248i	$-0.319360\pi$
$140$	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	$-0.646934\pi$
$149$	3.27743	−	2.38119i	0.268497	−	0.195075i	0.713885	+	0.700263i	$0.246934\pi$
$150$		0			0
$151$	−2.40847	+	7.41252i	−0.195999	+	0.603222i	0.803965	+	0.594677i	$0.202720\pi$
$151$	−2.40847	+	7.41252i	−0.195999	+	0.603222i	−0.999963	+	0.00854528i	$0.997280\pi$
$152$	−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	−0.947172	−	0.320726i	$-0.896073\pi$
$157$	0.0955332	−	0.294021i	0.00762438	−	0.0234654i	0.954796	+	0.297261i	$0.0960731\pi$
$158$	−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	0.182179	−	0.983265i	$-0.441685\pi$
$163$	−8.89442	−	6.46217i	−0.696665	−	0.506157i	−0.878844	+	0.477109i	$0.841685\pi$
$164$	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	$-0.538000\pi$
$167$	−14.2176	−	10.3297i	−1.10019	−	0.799333i	−0.981090	+	0.193550i	$0.938000\pi$
$168$		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	0.694167	+	0.719814i	$0.255773\pi$
$173$	−3.82122	+	11.7605i	−0.290522	+	0.894135i	−0.984689	+	0.174321i	$0.944227\pi$
$174$		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	0.294655	+	0.955604i	$0.404795\pi$
$179$	−6.76200	+	20.8113i	−0.505416	+	1.55551i	−0.800071	+	0.599906i	$0.795205\pi$
$180$		0			0
$181$	3.54364	−	2.57460i	0.263396	−	0.191369i	−0.448247	−	0.893910i	$-0.647951\pi$
$181$	3.54364	−	2.57460i	0.263396	−	0.191369i	0.711643	+	0.702541i	$0.247951\pi$
$182$	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	−0.987902	−	0.155079i	$-0.950437\pi$
$191$	−3.86727	−	11.9022i	−0.279826	−	0.861214i	0.708077	−	0.706136i	$-0.249563\pi$
$192$		0			0
$193$	10.1659	−	7.38594i	0.731756	−	0.531652i	−0.158363	−	0.987381i	$-0.550622\pi$
$193$	10.1659	−	7.38594i	0.731756	−	0.531652i	0.890118	+	0.455729i	$0.150622\pi$
$194$	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	0.771849	−	0.635805i	$-0.219332\pi$
$211$	5.89280	+	4.28137i	0.405677	+	0.294742i	−0.366172	+	0.930547i	$0.619332\pi$
$212$	−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	−0.343294	−	0.939228i	$-0.611543\pi$
$223$	7.26501	−	22.3594i	0.486501	−	1.49730i	0.829795	−	0.558068i	$-0.188457\pi$
$224$	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	0.995714	+	0.0924858i	$0.0294813\pi$
$227$	3.68416	+	11.3387i	0.244526	+	0.752574i	−0.751188	+	0.660089i	$0.770519\pi$
$228$		0			0
$229$	−2.47363	−	1.79719i	−0.163462	−	0.118762i	0.503047	−	0.864259i	$-0.332212\pi$
$229$	−2.47363	−	1.79719i	−0.163462	−	0.118762i	−0.666509	+	0.745497i	$0.732212\pi$
$230$	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	$-0.597059\pi$
$233$	−19.8463	−	14.4192i	−1.30017	−	0.944632i	−0.999957	+	0.00923938i	$0.997059\pi$
$234$		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	$-0.827827\pi$
$239$	2.14786	−	6.61044i	0.138934	−	0.427594i	0.996181	+	0.0873108i	$0.0278273\pi$
$240$		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	$-0.296713\pi$
$251$	0.264684	+	0.192304i	0.0167067	+	0.0121381i	−0.579401	+	0.815043i	$0.696713\pi$
$252$		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	0.991775	+	0.127990i	$0.0408525\pi$
$257$	4.24255	+	13.0572i	0.264643	+	0.814487i	−0.727133	+	0.686497i	$0.759148\pi$
$258$		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	−0.238428	−	0.971160i	$-0.576632\pi$
$269$	10.0297	−	7.28700i	0.611522	−	0.444296i	0.849950	+	0.526864i	$0.176632\pi$
$270$		0			0
$271$	5.95460	+	18.3264i	0.361716	+	1.11325i	0.952012	+	0.306061i	$0.0990112\pi$
$271$	5.95460	+	18.3264i	0.361716	+	1.11325i	−0.590296	+	0.807187i	$0.700989\pi$
$272$	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	0.307065	−	0.951689i	$-0.400653\pi$
$277$	−8.37420	−	6.08421i	−0.503157	−	0.365565i	−0.810222	+	0.586124i	$0.800653\pi$
$278$	−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	$-0.863090\pi$
$281$	−13.2968	+	9.66072i	−0.793223	+	0.576310i	0.115695	+	0.993285i	$0.463090\pi$
$282$		0			0
$283$	−0.390892	+	1.20304i	−0.0232361	+	0.0715135i	−0.962002	−	0.273042i	$-0.911970\pi$
$283$	−0.390892	+	1.20304i	−0.0232361	+	0.0715135i	0.938766	+	0.344555i	$0.111970\pi$
$284$	−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	0.893241	+	0.449578i	$0.148426\pi$
$293$	7.44342	+	22.9085i	0.434849	+	1.33833i	−0.458392	+	0.888750i	$0.651574\pi$
$294$		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	0.569344	+	0.822100i	$0.307197\pi$
$311$	−6.60408	+	20.3253i	−0.374483	+	1.15254i	−0.943827	+	0.330441i	$0.892803\pi$
$312$		0			0
$313$	−2.52100	+	1.83161i	−0.142495	+	0.103529i	−0.656749	−	0.754109i	$-0.728069\pi$
$313$	−2.52100	+	1.83161i	−0.142495	+	0.103529i	0.514254	+	0.857638i	$0.328069\pi$
$314$	−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	$-0.471439\pi$
$317$	−14.7766	−	10.7358i	−0.829935	−	0.602983i	−0.919541	+	0.392994i	$0.871439\pi$
$318$		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	0.988631	−	0.150364i	$-0.0480445\pi$
$337$	1.84365	+	5.67417i	0.100430	+	0.309092i	−0.888201	+	0.459456i	$0.848045\pi$
$338$	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	$-0.473270\pi$
$347$	19.6990	−	14.3122i	1.05750	−	0.768318i	0.973624	+	0.228158i	$0.0732704\pi$
$348$		0			0
$349$	5.17349	−	15.9224i	0.276931	−	0.852305i	−0.711771	−	0.702411i	$-0.752107\pi$
$349$	5.17349	−	15.9224i	0.276931	−	0.852305i	0.988702	−	0.149894i	$-0.0478932\pi$
$350$	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	0.852433	+	0.522836i	$0.175126\pi$
$359$	8.90742	+	27.4142i	0.470116	+	1.44687i	−0.382317	+	0.924031i	$0.624874\pi$
$360$		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	0.952805	+	0.303583i	$0.0981831\pi$
$367$	6.90449	+	21.2498i	0.360411	+	1.10923i	−0.592394	+	0.805649i	$0.701817\pi$
$368$	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	0.0471638	−	0.998887i	$-0.484982\pi$
$379$	19.6964	−	14.3103i	1.01174	−	0.735070i	0.964573	+	0.263818i	$0.0849817\pi$
$380$	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	$-0.448800\pi$
$383$	−14.2694	−	10.3673i	−0.729130	−	0.529744i	−0.889288	+	0.457348i	$0.848800\pi$
$384$		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	0.987800	+	0.155727i	$0.0497719\pi$
$389$	5.52615	+	17.0077i	0.280187	+	0.862326i	−0.707613	+	0.706600i	$0.750228\pi$
$390$		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	$-0.656890\pi$
$401$	4.37481	−	3.17848i	0.218467	−	0.158726i	0.691636	+	0.722246i	$0.256890\pi$
$402$		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	0.00470736	−	0.999989i	$-0.498502\pi$
$409$	−19.1091	−	13.8836i	−0.944884	−	0.686498i	−0.949591	+	0.313491i	$0.898502\pi$
$410$	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	0.807035	+	0.590503i	$0.201071\pi$
$421$	−3.95919	+	12.1851i	−0.192959	+	0.593867i	−0.999994	+	0.00336355i	$0.998929\pi$
$422$	−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	$-0.350651\pi$
$431$	−5.32265	−	3.86713i	−0.256383	−	0.186273i	−0.708551	+	0.705660i	$0.750651\pi$
$432$		0			0
$433$	4.32555	+	13.3127i	0.207873	+	0.639767i	0.999583	+	0.0288700i	$0.00919089\pi$
$433$	4.32555	+	13.3127i	0.207873	+	0.639767i	−0.791710	+	0.610897i	$0.790809\pi$
$434$	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	0.536086	+	0.844163i	$0.319902\pi$
$443$	−8.28860	+	25.5097i	−0.393803	+	1.21200i	−0.929890	+	0.367839i	$0.880098\pi$
$444$		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	$-0.191433\pi$
$449$	11.4685	+	8.33234i	0.541231	+	0.393228i	−0.283311	+	0.959028i	$0.591433\pi$
$450$		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	−0.946611	−	0.322378i	$-0.895518\pi$
$457$	−19.9352	+	14.4838i	−0.932530	+	0.677523i	0.0140807	+	0.999901i	$0.495518\pi$
$458$	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	−0.969727	−	0.244190i	$-0.921478\pi$
$467$	−22.4130	+	16.2840i	−1.03715	+	0.753534i	−0.0674235	+	0.997724i	$0.521478\pi$
$468$		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	$-0.816166\pi$
$479$	−12.6386	+	9.18250i	−0.577474	+	0.419559i	0.260339	+	0.965517i	$0.416166\pi$
$480$		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	−0.565025	−	0.825074i	$-0.691133\pi$
$487$	8.32090	−	25.6091i	0.377056	−	1.16046i	0.942081	−	0.335386i	$-0.108867\pi$
$488$	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	−0.723637	−	0.690181i	$-0.757531\pi$
$491$	−12.0516	−	37.0910i	−0.543880	−	1.67389i	0.179757	−	0.983711i	$-0.442469\pi$
$492$		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	−0.967945	−	0.251161i	$-0.919188\pi$
$499$	−7.42726	−	22.8588i	−0.332490	−	1.02330i	0.635455	−	0.772138i	$-0.280812\pi$
$500$	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	−0.638404	−	0.769701i	$-0.720405\pi$
$503$	7.41223	−	22.8125i	0.330495	−	1.01716i	0.968899	−	0.247457i	$-0.0795949\pi$
$504$		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	$-0.926123\pi$
$509$	−1.14301	+	3.51783i	−0.0506631	+	0.155925i	0.922524	+	0.385939i	$0.126123\pi$
$510$		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	$-0.0551344\pi$
$521$	1.98178	+	6.09929i	0.0868234	+	0.267215i	−0.898213	+	0.439560i	$0.855134\pi$
$522$		0			0
$523$	2.21554	−	1.60969i	0.0968790	−	0.0703867i	−0.538291	−	0.842759i	$-0.680930\pi$
$523$	2.21554	−	1.60969i	0.0968790	−	0.0703867i	0.635170	+	0.772372i	$0.280930\pi$
$524$	−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	0.161559	−	0.986863i	$-0.448348\pi$
$541$	−16.9114	−	12.2869i	−0.727079	−	0.528254i	−0.888638	+	0.458609i	$0.848348\pi$
$542$	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	0.147105	+	0.989121i	$0.453004\pi$
$547$	−12.9405	+	39.8268i	−0.553296	+	1.70287i	−0.700401	+	0.713749i	$0.746996\pi$
$548$	−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	$-0.0145166\pi$
$557$	3.87025	+	11.9114i	0.163988	+	0.504702i	−0.834973	+	0.550291i	$0.814517\pi$
$558$		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	$-0.398902\pi$
$563$	−11.7378	−	8.52802i	−0.494690	−	0.359413i	−0.806985	+	0.590572i	$0.798902\pi$
$564$		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	−0.589236	−	0.807961i	$-0.700571\pi$
$569$	8.64395	−	26.6034i	0.362373	−	1.11527i	0.951610	−	0.307310i	$-0.0994287\pi$
$570$		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	−0.999835	−	0.0181683i	$-0.994217\pi$
$577$	−31.0234	+	22.5398i	−1.29152	+	0.938346i	−0.291687	+	0.956514i	$0.594217\pi$
$578$	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	$-0.0952529\pi$
$587$	0.223301	+	0.687250i	0.00921662	+	0.0283658i	−0.946342	+	0.323166i	$0.895253\pi$
$588$		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	−0.871217	−	0.490898i	$-0.836669\pi$
$599$	−16.4852	+	11.9772i	−0.673566	+	0.489374i	0.197651	+	0.980272i	$0.436669\pi$
$600$		0			0
$601$	−14.9477	−	46.0042i	−0.609729	−	1.87655i	−0.460257	−	0.887786i	$-0.652243\pi$
$601$	−14.9477	−	46.0042i	−0.609729	−	1.87655i	−0.149472	−	0.988766i	$-0.547757\pi$
$602$	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	0.862236	−	0.506508i	$-0.169064\pi$
$607$	15.9395	+	11.5807i	0.646964	+	0.470047i	−0.215272	+	0.976554i	$0.569064\pi$
$608$	−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	−0.909013	−	0.416768i	$-0.863163\pi$
$613$	1.76690	−	5.43796i	0.0713644	−	0.219637i	0.980377	+	0.197131i	$0.0631626\pi$
$614$	−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	−0.961501	−	0.274803i	$-0.911387\pi$
$619$	−0.549968	+	1.69263i	−0.0221051	+	0.0680324i	0.939395	+	0.342835i	$0.111387\pi$
$620$	−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	−0.704705	−	0.709501i	$-0.748921\pi$
$631$	−13.8566	−	42.6461i	−0.551621	−	1.69771i	0.153084	−	0.988213i	$-0.451079\pi$
$632$	−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	−0.639628	−	0.768685i	$-0.720912\pi$
$641$	8.34641	−	25.6876i	0.329663	−	1.01460i	0.969291	−	0.245915i	$-0.0790885\pi$
$642$		0			0
$643$	26.3395	−	19.1368i	1.03873	−	0.754680i	0.0686909	−	0.997638i	$-0.478118\pi$
$643$	26.3395	−	19.1368i	1.03873	−	0.754680i	0.970037	+	0.242958i	$0.0781178\pi$
$644$	−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	$-0.512408\pi$
$647$	−25.4705	−	18.5054i	−1.00135	−	0.727523i	−0.962377	+	0.271717i	$0.912408\pi$
$648$		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	$-0.0709376\pi$
$653$	1.43995	+	4.43171i	0.0563495	+	0.173426i	−0.918920	+	0.394443i	$0.870938\pi$
$654$		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	0.991907	−	0.126970i	$-0.0405251\pi$
$673$	30.5513	+	22.1968i	1.17767	+	0.855625i	0.185761	+	0.982595i	$0.440525\pi$
$674$	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	$-0.581682\pi$
$677$	15.2910	−	11.1095i	0.587679	−	0.426974i	0.841484	+	0.540281i	$0.181682\pi$
$678$		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	0.190958	−	0.981598i	$-0.438841\pi$
$691$	−17.9694	−	13.0555i	−0.683588	−	0.496656i	−0.874546	+	0.484942i	$0.838841\pi$
$692$	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	−0.609616	−	0.792697i	$-0.708677\pi$
$701$	9.25374	−	28.4801i	0.349509	−	1.07568i	0.959125	−	0.282981i	$-0.0913235\pi$
$702$		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	−0.817645	−	0.575723i	$-0.804721\pi$
$709$	−13.9197	+	10.1133i	−0.522766	+	0.379812i	0.294879	+	0.955535i	$0.404721\pi$
$710$	−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	$-0.128082\pi$
$719$	−1.46013	−	4.49382i	−0.0544537	−	0.167591i	−0.974585	+	0.224020i	$0.928082\pi$
$720$		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	−0.682367	−	0.731010i	$-0.739049\pi$
$733$	−15.1614	−	46.6618i	−0.559997	−	1.72349i	0.122369	−	0.992485i	$-0.460951\pi$
$734$	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	0.795132	−	0.606437i	$-0.207402\pi$
$739$	12.6160	+	9.16603i	0.464086	+	0.337178i	−0.331046	+	0.943615i	$0.607402\pi$
$740$	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	$-0.634527\pi$
$743$	9.00796	−	6.54466i	0.330470	−	0.240100i	0.740630	+	0.671913i	$0.234527\pi$
$744$		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	−0.986237	−	0.165340i	$-0.947128\pi$
$751$	−2.49846	+	7.68948i	−0.0911703	+	0.280593i	0.895066	+	0.445933i	$0.147128\pi$
$752$	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	0.0546803	−	0.998504i	$-0.482586\pi$
$757$	−24.1585	−	17.5522i	−0.878056	−	0.637945i	−0.932737	+	0.360559i	$0.882586\pi$
$758$	−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	$-0.0820586\pi$
$761$	28.2287	+	20.5093i	1.02329	+	0.743463i	0.0563348	+	0.998412i	$0.482059\pi$
$762$		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	$-0.837547\pi$
$773$	3.34979	−	10.3096i	0.120483	−	0.370810i	0.993051	+	0.117683i	$0.0375467\pi$
$774$		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	−0.551504	−	0.834172i	$-0.685946\pi$
$787$	2.00347	−	1.45561i	0.0714162	−	0.0518869i	0.622921	+	0.782285i	$0.285946\pi$
$788$	−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	$-0.754841\pi$
$797$	−7.83103	+	5.68958i	−0.277389	+	0.201535i	0.440389	+	0.897807i	$0.354841\pi$
$798$		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	$-0.744153\pi$
$809$	−6.36318	+	4.62312i	−0.223717	+	0.162540i	0.470281	+	0.882517i	$0.344153\pi$
$810$		0			0
$811$	12.2076	−	37.5712i	0.428668	−	1.31930i	−0.470770	−	0.882256i	$-0.656024\pi$
$811$	12.2076	−	37.5712i	0.428668	−	1.31930i	0.899438	−	0.437048i	$-0.143976\pi$
$812$	−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	$-0.0813615\pi$
$821$	1.03633	+	3.18948i	0.0361680	+	0.111314i	−0.931343	+	0.364144i	$0.881362\pi$
$822$		0			0
$823$	−13.0266	−	9.46441i	−0.454080	−	0.329909i	0.337124	−	0.941460i	$-0.390546\pi$
$823$	−13.0266	−	9.46441i	−0.454080	−	0.329909i	−0.791205	+	0.611552i	$0.790546\pi$
$824$	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	$-0.214347\pi$
$827$	12.3703	+	8.98751i	0.430156	+	0.312526i	−0.351555	+	0.936167i	$0.614347\pi$
$828$		0			0
$829$	−13.0239	−	40.0835i	−0.452340	−	1.39216i	−0.874230	−	0.485512i	$-0.838633\pi$
$829$	−13.0239	−	40.0835i	−0.452340	−	1.39216i	0.421890	−	0.906647i	$-0.361367\pi$
$830$	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	$-0.914552\pi$
$839$	−0.818089	+	2.51782i	−0.0282436	+	0.0869247i	0.935941	+	0.352157i	$0.114552\pi$
$840$		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	−0.708731	−	0.705479i	$-0.750732\pi$
$853$	−7.49989	+	5.44899i	−0.256791	+	0.186570i	0.451940	+	0.892048i	$0.350732\pi$
$854$	−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	−0.526761	−	0.850014i	$-0.676594\pi$
$863$	3.49209	−	2.53715i	0.118872	−	0.0863656i	0.645633	+	0.763648i	$0.276594\pi$
$864$		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	−0.646893	−	0.762581i	$-0.723932\pi$
$877$	9.61537	−	29.5931i	0.324688	−	0.999287i	0.971581	−	0.236707i	$-0.0760680\pi$
$878$	−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	−0.976962	−	0.213413i	$-0.931542\pi$
$883$	−1.81685	+	5.59170i	−0.0611420	+	0.188176i	0.915820	+	0.401589i	$0.131542\pi$
$884$	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	$-0.0587629\pi$
$887$	2.37792	+	7.31848i	0.0798427	+	0.245730i	−0.903165	+	0.429293i	$0.858763\pi$
$888$		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	−0.302735	−	0.953075i	$-0.597900\pi$
$907$	15.3637	−	11.1624i	0.510143	−	0.370640i	0.812878	+	0.582434i	$0.197900\pi$
$908$	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	0.999401	+	0.0346024i	$0.0110165\pi$
$911$	40.4794	+	29.4100i	1.34114	+	0.974397i	0.341741	+	0.939794i	$0.388983\pi$
$912$		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	−0.628050	−	0.778173i	$-0.716147\pi$
$919$	−2.48708	+	1.80697i	−0.0820411	+	0.0596063i	0.546009	+	0.837780i	$0.316147\pi$
$920$	−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	$-0.704729\pi$
$929$	−0.732625	+	0.532283i	−0.0240366	+	0.0174636i	0.575702	+	0.817660i	$0.304729\pi$
$930$		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	0.839762	−	0.542955i	$-0.182695\pi$
$937$	17.8423	+	12.9632i	0.582881	+	0.423488i	−0.256881	+	0.966443i	$0.582695\pi$
$938$	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	$-0.671630\pi$
$941$	4.41798	−	3.20985i	0.144022	−	0.104638i	0.657463	+	0.753487i	$0.271630\pi$
$942$		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	0.735677	+	0.677333i	$0.236864\pi$
$953$	16.6278	+	51.1752i	0.538628	+	1.65773i	−0.197049	+	0.980394i	$0.563136\pi$
$954$		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	$-0.927585\pi$
$971$	−1.66685	+	5.13005i	−0.0534919	+	0.164631i	0.920742	+	0.390173i	$0.127585\pi$
$972$		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	$-0.316874\pi$
$977$	−2.67975	−	1.94695i	−0.0857329	−	0.0622886i	−0.629826	+	0.776736i	$0.716874\pi$
$978$		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	−0.967287	−	0.253685i	$-0.918357\pi$
$983$	−10.4671	−	32.2143i	−0.333847	−	1.02748i	0.633440	−	0.773792i	$-0.281643\pi$
$984$		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	−0.982817	−	0.184585i	$-0.940906\pi$
$997$	−9.35253	−	28.7841i	−0.296197	−	0.911602i	0.686619	−	0.727017i	$-0.259094\pi$
$998$	−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.730.5		36
3.2	odd	2		891.2.f.f.730.5		36
9.2	odd	6		99.2.m.b.4.5	✓	72
9.4	even	3		297.2.n.b.235.5		72
9.5	odd	6		99.2.m.b.70.5	yes	72
9.7	even	3		297.2.n.b.37.5		72
11.3	even	5	inner	891.2.f.e.487.5		36
11.5	even	5		9801.2.a.cp.1.10		18
11.6	odd	10		9801.2.a.cn.1.9		18
33.5	odd	10		9801.2.a.cm.1.9		18
33.14	odd	10		891.2.f.f.487.5		36
33.17	even	10		9801.2.a.co.1.10		18
99.5	odd	30		1089.2.e.p.727.10		36
99.14	odd	30		99.2.m.b.25.5	yes	72
99.25	even	15		297.2.n.b.91.5		72
99.38	odd	30		1089.2.e.p.364.10		36
99.47	odd	30		99.2.m.b.58.5	yes	72
99.50	even	30		1089.2.e.o.727.9		36
99.58	even	15		297.2.n.b.289.5		72
99.83	even	30		1089.2.e.o.364.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.5	✓	72	9.2	odd	6
99.2.m.b.25.5	yes	72	99.14	odd	30
99.2.m.b.58.5	yes	72	99.47	odd	30
99.2.m.b.70.5	yes	72	9.5	odd	6
297.2.n.b.37.5		72	9.7	even	3
297.2.n.b.91.5		72	99.25	even	15
297.2.n.b.235.5		72	9.4	even	3
297.2.n.b.289.5		72	99.58	even	15
891.2.f.e.487.5		36	11.3	even	5	inner
891.2.f.e.730.5		36	1.1	even	1	trivial
891.2.f.f.487.5		36	33.14	odd	10
891.2.f.f.730.5		36	3.2	odd	2
1089.2.e.o.364.9		36	99.83	even	30
1089.2.e.o.727.9		36	99.50	even	30
1089.2.e.p.364.10		36	99.38	odd	30
1089.2.e.p.727.10		36	99.5	odd	30
9801.2.a.cm.1.9		18	33.5	odd	10
9801.2.a.cn.1.9		18	11.6	odd	10
9801.2.a.co.1.10		18	33.17	even	10
9801.2.a.cp.1.10		18	11.5	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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