LMFDB - Embedded newform 891.2.n.b.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			433.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	891.433
Dual form			891.2.n.b.784.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0399263 + 0.379874i) q^{2} +(1.81359 + 0.385489i) q^{4} +(0.169131 + 1.60917i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} +O(q^{10})$	\(q+(-0.0399263 + 0.379874i) q^{2} +(1.81359 + 0.385489i) q^{4} +(0.169131 + 1.60917i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} -0.618034 q^{10} +(-3.25181 - 0.652498i) q^{11} +(-3.86984 + 1.72296i) q^{13} +(-0.255585 - 0.283856i) q^{14} +(2.87392 + 1.27955i) q^{16} +(-6.35410 + 4.61653i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(-0.313585 + 2.98357i) q^{20} +(0.377699 - 1.20922i) q^{22} +(-2.11803 + 3.66854i) q^{23} +(2.32991 - 0.495239i) q^{25} +(-0.500000 - 1.53884i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(4.01478 - 4.45887i) q^{29} +(4.65010 - 2.07036i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-1.30902 - 0.951057i) q^{35} +(-0.545085 - 1.67760i) q^{37} +(-0.298033 - 0.132693i) q^{38} +(-2.32991 - 0.495239i) q^{40} +(2.83448 + 3.14801i) q^{41} +(-3.35410 - 5.80948i) q^{43} +(-5.64590 - 2.43690i) q^{44} +(-1.30902 - 0.951057i) q^{46} +(1.06635 - 0.226659i) q^{47} +(0.627171 + 5.96713i) q^{49} +(0.0951031 + 0.904846i) q^{50} +(-7.68247 + 1.63296i) q^{52} +(-2.11803 - 1.53884i) q^{53} +(0.500000 - 5.34307i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.53351 + 1.70314i) q^{58} +(9.40786 + 1.99970i) q^{59} +(7.82206 + 3.48260i) q^{61} +(0.600813 + 1.84911i) q^{62} +(3.80902 + 2.76741i) q^{64} +(-3.42705 - 5.93583i) q^{65} +(2.42705 - 4.20378i) q^{67} +(-13.3033 + 5.92302i) q^{68} +(0.413545 - 0.459289i) q^{70} +(-4.30902 + 3.13068i) q^{71} +(2.38197 + 7.33094i) q^{73} +(0.659039 - 0.140083i) q^{74} +(-0.791796 + 1.37143i) q^{76} +(2.66078 - 1.97996i) q^{77} +(-1.14981 + 10.9397i) q^{79} +(-1.57295 + 4.84104i) q^{80} +(-1.30902 + 0.951057i) q^{82} +(6.82614 + 3.03919i) q^{83} +(-8.50345 - 9.44404i) q^{85} +(2.34078 - 1.04218i) q^{86} +(2.39285 - 4.25597i) q^{88} +3.76393 q^{89} +(1.30902 - 4.02874i) q^{91} +(-5.25542 + 5.83674i) q^{92} +(0.0435265 + 0.414127i) q^{94} +(-1.35177 - 0.287327i) q^{95} +(-0.119779 + 1.13962i) q^{97} -2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8}+O(q^{10}) $ 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8	$ 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8} + 4 q^{10} - 11 q^{11} - 7 q^{13} - 4 q^{14} - q^{16} - 24 q^{17} - 20 q^{19} + 3 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 12 q^{28} + 6 q^{29} + 12 q^{31} - 30 q^{32} - 12 q^{34} - 6 q^{35} + 18 q^{37} - 10 q^{38} + 6 q^{40} - 3 q^{41} - 72 q^{44} - 6 q^{46} + 17 q^{47} - 6 q^{49} + 6 q^{50} - 3 q^{52} - 8 q^{53} + 4 q^{55} + 12 q^{56} + 24 q^{58} - 6 q^{59} + 21 q^{61} + 54 q^{62} + 26 q^{64} - 14 q^{65} + 6 q^{67} - 27 q^{68} - 3 q^{70} - 30 q^{71} + 28 q^{73} - 26 q^{74} - 60 q^{76} + q^{77} + 11 q^{79} - 26 q^{80} - 6 q^{82} + 13 q^{83} + 9 q^{85} + 15 q^{86} + 37 q^{88} + 48 q^{89} + 6 q^{91} + 3 q^{92} - 17 q^{94} + 5 q^{95} - 3 q^{97} - 72 q^{98}+O(q^{100}) $ 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8 + 4 * q^10 - 11 * q^11 - 7 * q^13 - 4 * q^14 - q^16 - 24 * q^17 - 20 * q^19 + 3 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 6 * q^29 + 12 * q^31 - 30 * q^32 - 12 * q^34 - 6 * q^35 + 18 * q^37 - 10 * q^38 + 6 * q^40 - 3 * q^41 - 72 * q^44 - 6 * q^46 + 17 * q^47 - 6 * q^49 + 6 * q^50 - 3 * q^52 - 8 * q^53 + 4 * q^55 + 12 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 54 * q^62 + 26 * q^64 - 14 * q^65 + 6 * q^67 - 27 * q^68 - 3 * q^70 - 30 * q^71 + 28 * q^73 - 26 * q^74 - 60 * q^76 + q^77 + 11 * q^79 - 26 * q^80 - 6 * q^82 + 13 * q^83 + 9 * q^85 + 15 * q^86 + 37 * q^88 + 48 * q^89 + 6 * q^91 + 3 * q^92 - 17 * q^94 + 5 * q^95 - 3 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0399263	+	0.379874i	−0.0282322	+	0.268611i	0.971295	+	0.237877i	$0.0764514\pi$
$2$	−0.0399263	+	0.379874i	−0.0282322	+	0.268611i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$		0			0
$3$		0			0
$4$	1.81359	+	0.385489i	0.906793	+	0.192745i
$5$	0.169131	+	1.60917i	0.0756375	+	0.719643i	0.964966	+	0.262374i	$0.0845055\pi$
$5$	0.169131	+	1.60917i	0.0756375	+	0.719643i	−0.889329	+	0.457269i	$0.848828\pi$
$6$		0			0
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	0.603300	+	0.797514i	$0.293852\pi$
$8$	−0.454915	+	1.40008i	−0.160837	+	0.495005i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	−3.25181	−	0.652498i	−0.980457	−	0.196735i
$11$	−3.25181	−	0.652498i	−0.980457	−	0.196735i
$12$		0			0
$13$	−3.86984	+	1.72296i	−1.07330	+	0.477864i	−0.865810	−	0.500373i	$-0.833196\pi$
$13$	−3.86984	+	1.72296i	−1.07330	+	0.477864i	−0.207491	+	0.978237i	$0.566530\pi$
$14$	−0.255585	−	0.283856i	−0.0683080	−	0.0758637i
$15$		0			0
$16$	2.87392	+	1.27955i	0.718480	+	0.319888i
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.591452	+	0.806340i	$0.701445\pi$
$17$	−6.35410	+	4.61653i	−1.54110	+	1.11967i	−0.949644	+	0.313332i	$0.898555\pi$
$18$		0			0
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$	−0.313585	+	2.98357i	−0.0701198	+	0.667146i
$21$		0			0
$22$	0.377699	−	1.20922i	0.0805258	−	0.257807i
$23$	−2.11803	+	3.66854i	−0.441641	+	0.764944i	−0.997811	−	0.0661240i	$-0.978937\pi$
$23$	−2.11803	+	3.66854i	−0.441641	+	0.764944i	0.556171	+	0.831068i	$0.312270\pi$
$24$		0			0
$25$	2.32991	−	0.495239i	0.465983	−	0.0990477i
$26$	−0.500000	−	1.53884i	−0.0980581	−	0.301792i
$27$		0			0
$28$	−1.50000	+	1.08981i	−0.283473	+	0.205955i
$29$	4.01478	−	4.45887i	0.745527	−	0.827991i	−0.244385	−	0.969678i	$-0.578586\pi$
$29$	4.01478	−	4.45887i	0.745527	−	0.827991i	0.989911	+	0.141687i	$0.0452527\pi$
$30$		0			0
$31$	4.65010	−	2.07036i	0.835183	−	0.371847i	0.0558359	−	0.998440i	$-0.482218\pi$
$31$	4.65010	−	2.07036i	0.835183	−	0.371847i	0.779347	+	0.626593i	$0.215551\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−1.30902	−	0.951057i	−0.221264	−	0.160758i
$36$		0			0
$37$	−0.545085	−	1.67760i	−0.0896114	−	0.275796i	0.896201	−	0.443649i	$-0.146316\pi$
$37$	−0.545085	−	1.67760i	−0.0896114	−	0.275796i	−0.985812	+	0.167854i	$0.946316\pi$
$38$	−0.298033	−	0.132693i	−0.0483474	−	0.0215256i
$39$		0			0
$40$	−2.32991	−	0.495239i	−0.368392	−	0.0783041i
$41$	2.83448	+	3.14801i	0.442672	+	0.491637i	0.922647	−	0.385645i	$-0.126021\pi$
$41$	2.83448	+	3.14801i	0.442672	+	0.491637i	−0.479975	+	0.877282i	$0.659354\pi$
$42$		0			0
$43$	−3.35410	−	5.80948i	−0.511496	−	0.885937i	−0.999911	−	0.0133254i	$-0.995758\pi$
$43$	−3.35410	−	5.80948i	−0.511496	−	0.885937i	0.488415	−	0.872611i	$-0.337575\pi$
$44$	−5.64590	−	2.43690i	−0.851151	−	0.367376i
$45$		0			0
$46$	−1.30902	−	0.951057i	−0.193004	−	0.140226i
$47$	1.06635	−	0.226659i	0.155543	−	0.0330616i	−0.129482	−	0.991582i	$-0.541331\pi$
$47$	1.06635	−	0.226659i	0.155543	−	0.0330616i	0.285025	+	0.958520i	$0.407998\pi$
$48$		0			0
$49$	0.627171	+	5.96713i	0.0895958	+	0.852447i
$50$	0.0951031	+	0.904846i	0.0134496	+	0.127965i
$51$		0			0
$52$	−7.68247	+	1.63296i	−1.06537	+	0.226451i
$53$	−2.11803	−	1.53884i	−0.290934	−	0.211376i	0.432738	−	0.901520i	$-0.357547\pi$
$53$	−2.11803	−	1.53884i	−0.290934	−	0.211376i	−0.723673	+	0.690143i	$0.757547\pi$
$54$		0			0
$55$	0.500000	−	5.34307i	0.0674200	−	0.720459i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$		0			0
$58$	1.53351	+	1.70314i	0.201360	+	0.223633i
$59$	9.40786	+	1.99970i	1.22480	+	0.260339i	0.774520	−	0.632549i	$-0.217991\pi$
$59$	9.40786	+	1.99970i	1.22480	+	0.260339i	0.450278	+	0.892888i	$0.351325\pi$
$60$		0			0
$61$	7.82206	+	3.48260i	1.00151	+	0.445902i	0.840943	−	0.541123i	$-0.182001\pi$
$61$	7.82206	+	3.48260i	1.00151	+	0.445902i	0.160568	+	0.987025i	$0.448667\pi$
$62$	0.600813	+	1.84911i	0.0763033	+	0.234838i
$63$		0			0
$64$	3.80902	+	2.76741i	0.476127	+	0.345927i
$65$	−3.42705	−	5.93583i	−0.425073	−	0.736249i
$66$		0			0
$67$	2.42705	−	4.20378i	0.296511	−	0.513573i	−0.678824	−	0.734301i	$-0.737510\pi$
$67$	2.42705	−	4.20378i	0.296511	−	0.513573i	0.975335	+	0.220728i	$0.0708434\pi$
$68$	−13.3033	+	5.92302i	−1.61327	+	0.718272i
$69$		0			0
$70$	0.413545	−	0.459289i	0.0494281	−	0.0548955i
$71$	−4.30902	+	3.13068i	−0.511386	+	0.371544i	−0.813349	−	0.581776i	$-0.802358\pi$
$71$	−4.30902	+	3.13068i	−0.511386	+	0.371544i	0.301963	+	0.953320i	$0.402358\pi$
$72$		0			0
$73$	2.38197	+	7.33094i	0.278788	+	0.858021i	0.988192	+	0.153219i	$0.0489641\pi$
$73$	2.38197	+	7.33094i	0.278788	+	0.858021i	−0.709404	+	0.704802i	$0.751036\pi$
$74$	0.659039	−	0.140083i	0.0766117	−	0.0162843i
$75$		0			0
$76$	−0.791796	+	1.37143i	−0.0908252	+	0.157314i
$77$	2.66078	−	1.97996i	0.303224	−	0.225637i
$78$		0			0
$79$	−1.14981	+	10.9397i	−0.129364	+	1.23082i	0.716565	+	0.697521i	$0.245714\pi$
$79$	−1.14981	+	10.9397i	−0.129364	+	1.23082i	−0.845929	+	0.533296i	$0.820953\pi$
$80$	−1.57295	+	4.84104i	−0.175861	+	0.541245i
$81$		0			0
$82$	−1.30902	+	0.951057i	−0.144557	+	0.105027i
$83$	6.82614	+	3.03919i	0.749266	+	0.333595i	0.745596	−	0.666399i	$-0.232165\pi$
$83$	6.82614	+	3.03919i	0.749266	+	0.333595i	0.00367013	+	0.999993i	$0.498832\pi$
$84$		0			0
$85$	−8.50345	−	9.44404i	−0.922328	−	1.02435i
$86$	2.34078	−	1.04218i	0.252413	−	0.112382i
$87$		0			0
$88$	2.39285	−	4.25597i	0.255078	−	0.453688i
$89$	3.76393			0.398976			0.199488	−	0.979900i	$-0.436072\pi$
$89$	3.76393			0.398976			0.199488	+	0.979900i	$0.436072\pi$
$90$		0			0
$91$	1.30902	−	4.02874i	0.137222	−	0.422327i
$92$	−5.25542	+	5.83674i	−0.547915	+	0.608522i
$93$		0			0
$94$	0.0435265	+	0.414127i	0.00448941	+	0.0427139i
$95$	−1.35177	−	0.287327i	−0.138688	−	0.0294791i
$96$		0			0
$97$	−0.119779	+	1.13962i	−0.0121617	+	0.115711i	−0.998918	−	0.0464960i	$-0.985195\pi$
$97$	−0.119779	+	1.13962i	−0.0121617	+	0.115711i	0.986757	+	0.162207i	$0.0518612\pi$
$98$	−2.29180			−0.231506
$99$		0			0
$100$	4.41641			0.441641
$101$	−0.602495	+	5.73236i	−0.0599505	+	0.570391i	0.922777	+	0.385334i	$0.125914\pi$
$101$	−0.602495	+	5.73236i	−0.0599505	+	0.570391i	−0.982728	+	0.185057i	$0.940753\pi$
$102$		0			0
$103$	−6.79252	−	1.44380i	−0.669287	−	0.142261i	−0.139278	−	0.990253i	$-0.544478\pi$
$103$	−6.79252	−	1.44380i	−0.669287	−	0.142261i	−0.530009	+	0.847992i	$0.677812\pi$
$104$	−0.651847	−	6.20191i	−0.0639188	−	0.608147i
$105$		0			0
$106$	0.669131	−	0.743145i	0.0649917	−	0.0721806i
$107$	0.781153	−	2.40414i	0.0755169	−	0.232417i	−0.906172	−	0.422910i	$-0.861009\pi$
$107$	0.781153	−	2.40414i	0.0755169	−	0.232417i	0.981689	+	0.190493i	$0.0610086\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	2.00973	+	0.403266i	0.191620	+	0.0384499i
$111$		0			0
$112$	−2.87392	+	1.27955i	−0.271560	+	0.120906i
$113$	−3.02973	−	3.36486i	−0.285013	−	0.316539i	0.583589	−	0.812049i	$-0.301648\pi$
$113$	−3.02973	−	3.36486i	−0.285013	−	0.316539i	−0.868602	+	0.495510i	$0.834981\pi$
$114$		0			0
$115$	−6.26153	−	2.78781i	−0.583891	−	0.259965i
$116$	9.00000	−	6.53888i	0.835629	−	0.607120i
$117$		0			0
$118$	−1.13525	+	3.49396i	−0.104509	+	0.321645i
$119$	0.820977	−	7.81108i	0.0752589	−	0.716040i
$120$		0			0
$121$	10.1485	+	4.24359i	0.922590	+	0.385781i
$122$	−1.63525	+	2.83234i	−0.148049	+	0.256428i
$123$		0			0
$124$	9.23146	−	1.96221i	0.829009	−	0.176211i
$125$	3.69098	+	11.3597i	0.330132	+	1.01604i
$126$		0			0
$127$	4.61803	−	3.35520i	0.409784	−	0.297726i	−0.363730	−	0.931504i	$-0.618497\pi$
$127$	4.61803	−	3.35520i	0.409784	−	0.297726i	0.773514	+	0.633779i	$0.218497\pi$
$128$	−6.75164	+	7.49846i	−0.596766	+	0.662776i
$129$		0			0
$130$	2.39169	−	1.06485i	0.209765	−	0.0933936i
$131$	6.39919	−	11.0837i	0.559100	−	0.968389i	−0.438472	−	0.898745i	$-0.644480\pi$
$131$	6.39919	−	11.0837i	0.559100	−	0.968389i	0.997572	−	0.0696442i	$-0.0221864\pi$
$132$		0			0
$133$	−0.427051	−	0.739674i	−0.0370300	−	0.0641379i
$134$	1.50000	+	1.08981i	0.129580	+	0.0941456i
$135$		0			0
$136$	−3.57295	−	10.9964i	−0.306378	−	0.942934i
$137$	−13.0053	−	5.79033i	−1.11112	−	0.494701i	−0.232677	−	0.972554i	$-0.574749\pi$
$137$	−13.0053	−	5.79033i	−1.11112	−	0.494701i	−0.878440	+	0.477853i	$0.841415\pi$
$138$		0			0
$139$	5.44076	+	1.15647i	0.461479	+	0.0980904i	0.432784	−	0.901498i	$-0.357531\pi$
$139$	5.44076	+	1.15647i	0.461479	+	0.0980904i	0.0286953	+	0.999588i	$0.490865\pi$
$140$	−2.00739	−	2.22943i	−0.169656	−	0.188422i
$141$		0			0
$142$	−1.01722	−	1.76188i	−0.0853633	−	0.147854i
$143$	13.7082	−	3.07768i	1.14634	−	0.257369i
$144$		0			0
$145$	7.85410	+	5.70634i	0.652248	+	0.473886i
$146$	−2.87993	+	0.612149i	−0.238345	+	0.0506618i
$147$		0			0
$148$	−0.341861	−	3.25259i	−0.0281008	−	0.267362i
$149$	0.0246758	+	0.234775i	0.00202152	+	0.0192335i	0.995486	−	0.0949068i	$-0.0302553\pi$
$149$	0.0246758	+	0.234775i	0.00202152	+	0.0192335i	−0.993465	+	0.114140i	$0.963589\pi$
$150$		0			0
$151$	−18.5303	+	3.93874i	−1.50797	+	0.320530i	−0.886435	−	0.462853i	$-0.846826\pi$
$151$	−18.5303	+	3.93874i	−1.50797	+	0.320530i	−0.621539	+	0.783383i	$0.713492\pi$
$152$	−1.01722	−	0.739054i	−0.0825075	−	0.0599452i
$153$		0			0
$154$	0.645898	+	1.08981i	0.0520479	+	0.0878197i
$155$	4.11803	+	7.13264i	0.330768	+	0.572908i
$156$		0			0
$157$	1.53351	+	1.70314i	0.122387	+	0.135925i	0.801224	−	0.598364i	$-0.204182\pi$
$157$	1.53351	+	1.70314i	0.122387	+	0.135925i	−0.678837	+	0.734289i	$0.737516\pi$
$158$	−4.10981	−	0.873567i	−0.326959	−	0.0694973i
$159$		0			0
$160$	−6.12825	−	2.72847i	−0.484481	−	0.215705i
$161$	−1.30902	−	4.02874i	−0.103165	−	0.317509i
$162$		0			0
$163$	9.59017	+	6.96767i	0.751160	+	0.545750i	0.896186	−	0.443678i	$-0.146327\pi$
$163$	9.59017	+	6.96767i	0.751160	+	0.545750i	−0.145026	+	0.989428i	$0.546327\pi$
$164$	3.92705	+	6.80185i	0.306651	+	0.531135i
$165$		0			0
$166$	−1.42705	+	2.47172i	−0.110761	+	0.191843i
$167$	15.5617	−	6.92853i	1.20420	−	0.536146i	0.296207	−	0.955124i	$-0.404278\pi$
$167$	15.5617	−	6.92853i	1.20420	−	0.536146i	0.907996	+	0.418978i	$0.137612\pi$
$168$		0			0
$169$	3.30836	−	3.67431i	0.254490	−	0.282639i
$170$	3.92705	−	2.85317i	0.301191	−	0.218828i
$171$		0			0
$172$	−3.84346	−	11.8290i	−0.293061	−	0.901949i
$173$	10.7933	−	2.29419i	0.820600	−	0.174424i	0.221564	−	0.975146i	$-0.428884\pi$
$173$	10.7933	−	2.29419i	0.820600	−	0.174424i	0.599036	+	0.800722i	$0.295550\pi$
$174$		0			0
$175$	−1.19098	+	2.06284i	−0.0900299	+	0.155936i
$176$	−8.51053	−	6.03608i	−0.641505	−	0.454987i
$177$		0			0
$178$	−0.150280	+	1.42982i	−0.0112640	+	0.107169i
$179$	5.39919	−	16.6170i	0.403554	−	1.24201i	−0.518542	−	0.855052i	$-0.673525\pi$
$179$	5.39919	−	16.6170i	0.403554	−	1.24201i	0.922096	−	0.386960i	$-0.126475\pi$
$180$		0			0
$181$	−9.28115	+	6.74315i	−0.689863	+	0.501215i	−0.876615	−	0.481192i	$-0.840204\pi$
$181$	−9.28115	+	6.74315i	−0.689863	+	0.501215i	0.186752	+	0.982407i	$0.440204\pi$
$182$	1.47815	+	0.658114i	0.109568	+	0.0487826i
$183$		0			0
$184$	−4.17274	−	4.63430i	−0.307619	−	0.341645i
$185$	2.60735	−	1.16087i	0.191696	−	0.0853487i
$186$		0			0
$187$	23.6746	−	10.8660i	1.73126	−	0.794601i
$188$	2.02129			0.147417
$189$		0			0
$190$	0.163119	−	0.502029i	0.0118339	−	0.0364210i
$191$	15.5107	−	17.2263i	1.12231	−	1.24645i	0.156370	−	0.987698i	$-0.450021\pi$
$191$	15.5107	−	17.2263i	1.12231	−	1.24645i	0.965943	−	0.258756i	$-0.0833127\pi$
$192$		0			0
$193$	1.03003	+	9.80012i	0.0741435	+	0.705428i	0.966946	+	0.254980i	$0.0820690\pi$
$193$	1.03003	+	9.80012i	0.0741435	+	0.705428i	−0.892803	+	0.450448i	$0.851264\pi$
$194$	−0.428129	−	0.0910017i	−0.0307379	−	0.00653354i
$195$		0			0
$196$	−1.16284	+	11.0637i	−0.0830599	+	0.790262i
$197$	16.0344			1.14241			0.571203	−	0.820809i	$-0.306477\pi$
$197$	16.0344			1.14241			0.571203	+	0.820809i	$0.306477\pi$
$198$		0			0
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$	−0.366537	+	3.48737i	−0.0259181	+	0.246594i
$201$		0			0
$202$	−2.15352	−	0.457744i	−0.151521	−	0.0322067i
$203$	0.627171	+	5.96713i	0.0440188	+	0.418811i
$204$		0			0
$205$	−4.58629	+	5.09359i	−0.320320	+	0.355752i
$206$	0.819660	−	2.52265i	0.0571084	−	0.175762i
$207$		0			0
$208$	−13.3262			−0.924008
$209$	1.38828	−	2.46923i	0.0960293	−	0.170800i
$210$		0			0
$211$	1.26249	−	0.562096i	0.0869133	−	0.0386963i	−0.362820	−	0.931859i	$-0.618186\pi$
$211$	1.26249	−	0.562096i	0.0869133	−	0.0386963i	0.449733	+	0.893163i	$0.351519\pi$
$212$	−3.24803	−	3.60730i	−0.223075	−	0.247750i
$213$		0			0
$214$	0.882081	+	0.392728i	0.0602978	+	0.0268463i
$215$	8.78115	−	6.37988i	0.598870	−	0.435104i
$216$		0			0
$217$	−1.57295	+	4.84104i	−0.106779	+	0.328631i
$218$	0.479116	−	4.55848i	0.0324498	−	0.308739i
$219$		0			0
$220$	2.96649	−	9.49737i	0.200001	−	0.640312i
$221$	16.6353	−	28.8131i	1.11901	−	1.93818i
$222$		0			0
$223$	14.8486	−	3.15617i	0.994337	−	0.211353i	0.318116	−	0.948052i	$-0.396950\pi$
$223$	14.8486	−	3.15617i	0.994337	−	0.211353i	0.676221	+	0.736699i	$0.263617\pi$
$224$	−1.28115	−	3.94298i	−0.0856006	−	0.263452i
$225$		0			0
$226$	1.39919	−	1.01657i	0.0930725	−	0.0676212i
$227$	6.14285	−	6.82232i	0.407715	−	0.452813i	−0.503959	−	0.863728i	$-0.668124\pi$
$227$	6.14285	−	6.82232i	0.407715	−	0.452813i	0.911674	+	0.410914i	$0.134790\pi$
$228$		0			0
$229$	−7.73968	+	3.44593i	−0.511453	+	0.227713i	−0.646202	−	0.763166i	$-0.723644\pi$
$229$	−7.73968	+	3.44593i	−0.511453	+	0.227713i	0.134750	+	0.990880i	$0.456977\pi$
$230$	1.30902	−	2.26728i	0.0863140	−	0.149500i
$231$		0			0
$232$	4.41641	+	7.64944i	0.289951	+	0.502211i
$233$	−8.78115	−	6.37988i	−0.575272	−	0.417960i	0.261744	−	0.965137i	$-0.415702\pi$
$233$	−8.78115	−	6.37988i	−0.575272	−	0.417960i	−0.837017	+	0.547177i	$0.815702\pi$
$234$		0			0
$235$	0.545085	+	1.67760i	0.0355574	+	0.109434i
$236$	16.2911	+	7.25326i	1.06046	+	0.472147i
$237$		0			0
$238$	2.93444	+	0.623735i	0.190212	+	0.0404307i
$239$	−1.75181	−	1.94558i	−0.113315	−	0.125849i	0.683819	−	0.729652i	$-0.260318\pi$
$239$	−1.75181	−	1.94558i	−0.113315	−	0.125849i	−0.797133	+	0.603803i	$0.793651\pi$
$240$		0			0
$241$	−10.8541	−	18.7999i	−0.699174	−	1.21101i	−0.968753	−	0.248027i	$-0.920218\pi$
$241$	−10.8541	−	18.7999i	−0.699174	−	1.21101i	0.269579	−	0.962978i	$-0.413115\pi$
$242$	−2.01722	+	3.68571i	−0.129672	+	0.236927i
$243$		0			0
$244$	12.8435	+	9.33132i	0.822218	+	0.597376i
$245$	−9.49606	+	2.01845i	−0.606681	+	0.128954i
$246$		0			0
$247$	−0.378188	−	3.59821i	−0.0240635	−	0.228949i
$248$	0.783276	+	7.45237i	0.0497381	+	0.473226i
$249$		0			0
$250$	−4.46261	+	0.948557i	−0.282240	+	0.0599920i
$251$	20.2082	+	14.6821i	1.27553	+	0.926727i	0.999408	−	0.0343954i	$-0.0109505\pi$
$251$	20.2082	+	14.6821i	1.27553	+	0.926727i	0.276122	+	0.961123i	$0.410951\pi$
$252$		0			0
$253$	9.28115	−	10.5474i	0.583501	−	0.663108i
$254$	1.09017	+	1.88823i	0.0684033	+	0.118478i
$255$		0			0
$256$	3.72191	+	4.13360i	0.232619	+	0.258350i
$257$	−12.4642	−	2.64935i	−0.777495	−	0.165262i	−0.197961	−	0.980210i	$-0.563432\pi$
$257$	−12.4642	−	2.64935i	−0.777495	−	0.165262i	−0.579534	+	0.814948i	$0.696765\pi$
$258$		0			0
$259$	1.61143	+	0.717456i	0.100130	+	0.0445805i
$260$	−3.92705	−	12.0862i	−0.243545	−	0.749556i
$261$		0			0
$262$	3.95492	+	2.87341i	0.244335	+	0.177520i
$263$	9.13525	+	15.8227i	0.563304	+	0.975671i	0.997205	+	0.0747107i	$0.0238033\pi$
$263$	9.13525	+	15.8227i	0.563304	+	0.975671i	−0.433901	+	0.900960i	$0.642863\pi$
$264$		0			0
$265$	2.11803	−	3.66854i	0.130110	−	0.225357i
$266$	0.298033	−	0.132693i	0.0182736	−	0.00813592i
$267$		0			0
$268$	6.02218	−	6.68830i	0.367863	−	0.408553i
$269$	1.14590	−	0.832544i	0.0698666	−	0.0507611i	−0.552304	−	0.833643i	$-0.686251\pi$
$269$	1.14590	−	0.832544i	0.0698666	−	0.0507611i	0.622170	+	0.782882i	$0.286251\pi$
$270$		0			0
$271$	5.06231	+	15.5802i	0.307513	+	0.946428i	0.978727	+	0.205165i	$0.0657731\pi$
$271$	5.06231	+	15.5802i	0.307513	+	0.946428i	−0.671214	+	0.741263i	$0.734227\pi$
$272$	−24.1683	+	5.13712i	−1.46542	+	0.311484i
$273$		0			0
$274$	2.71885	−	4.70918i	0.164252	−	0.284492i
$275$	−7.89957	+	0.0901561i	−0.476362	+	0.00543662i
$276$		0			0
$277$	−2.32208	+	22.0931i	−0.139520	+	1.32744i	0.670879	+	0.741567i	$0.265917\pi$
$277$	−2.32208	+	22.0931i	−0.139520	+	1.32744i	−0.810399	+	0.585878i	$0.800750\pi$
$278$	−0.656541	+	2.02063i	−0.0393767	+	0.121189i
$279$		0			0
$280$	1.92705	−	1.40008i	0.115163	−	0.0836711i
$281$	−26.7085	−	11.8914i	−1.59329	−	0.709380i	−0.597575	−	0.801813i	$-0.703869\pi$
$281$	−26.7085	−	11.8914i	−1.59329	−	0.709380i	−0.995719	+	0.0924326i	$0.970536\pi$
$282$		0			0
$283$	5.15780	+	5.72831i	0.306599	+	0.340513i	0.876678	−	0.481077i	$-0.159754\pi$
$283$	5.15780	+	5.72831i	0.306599	+	0.340513i	−0.570079	+	0.821590i	$0.693088\pi$
$284$	−9.02162	+	4.01668i	−0.535334	+	0.238346i
$285$		0			0
$286$	0.621812	+	5.33026i	0.0367685	+	0.315185i
$287$	−4.23607			−0.250047
$288$		0			0
$289$	13.8090	−	42.4998i	0.812295	−	2.49999i
$290$	−2.48127	+	2.75573i	−0.145705	+	0.161822i
$291$		0			0
$292$	1.49390	+	14.2135i	0.0874239	+	0.831782i
$293$	9.44155	+	2.00686i	0.551581	+	0.117242i	0.475267	−	0.879842i	$-0.342351\pi$
$293$	9.44155	+	2.00686i	0.551581	+	0.117242i	0.0763141	+	0.997084i	$0.475685\pi$
$294$		0			0
$295$	−1.62670	+	15.4771i	−0.0947104	+	0.901109i
$296$	2.59675			0.150933
$297$		0			0
$298$	−0.0901699			−0.00522340
$299$	1.87569	−	17.8460i	0.108474	−	1.03206i
$300$		0			0
$301$	6.56161	+	1.39471i	0.378205	+	0.0803900i
$302$	−0.756375	−	7.19643i	−0.0435245	−	0.414108i
$303$		0			0
$304$	−1.79790	+	1.99677i	−0.103117	+	0.114523i
$305$	−4.28115	+	13.1760i	−0.245138	+	0.754458i
$306$		0			0
$307$	−18.9787			−1.08317			−0.541586	−	0.840645i	$-0.682176\pi$
$307$	−18.9787			−1.08317			−0.541586	+	0.840645i	$0.682176\pi$
$308$	5.58881	−	2.56512i	0.318452	−	0.146161i
$309$		0			0
$310$	−2.87392	+	1.27955i	−0.163228	+	0.0726737i
$311$	13.1501	+	14.6046i	0.745672	+	0.828153i	0.989930	−	0.141557i	$-0.0452110\pi$
$311$	13.1501	+	14.6046i	0.745672	+	0.828153i	−0.244258	+	0.969710i	$0.578544\pi$
$312$		0			0
$313$	−10.4803	−	4.66614i	−0.592383	−	0.263746i	0.0885739	−	0.996070i	$-0.471769\pi$
$313$	−10.4803	−	4.66614i	−0.592383	−	0.263746i	−0.680956	+	0.732324i	$0.738436\pi$
$314$	−0.708204	+	0.514540i	−0.0399663	+	0.0290372i
$315$		0			0
$316$	−6.30244	+	19.3969i	−0.354540	+	1.09116i
$317$	−3.05018	+	29.0205i	−0.171315	+	1.62995i	0.484331	+	0.874885i	$0.339063\pi$
$317$	−3.05018	+	29.0205i	−0.171315	+	1.62995i	−0.655646	+	0.755068i	$0.727604\pi$
$318$		0			0
$319$	−15.9647	+	11.8797i	−0.893852	+	0.665138i
$320$	−3.80902	+	6.59741i	−0.212931	+	0.368806i
$321$		0			0
$322$	1.58268	−	0.336408i	0.0881991	−	0.0187473i
$323$	−2.07295	−	6.37988i	−0.115342	−	0.354986i
$324$		0			0
$325$	−8.16312	+	5.93085i	−0.452808	+	0.328985i
$326$	−3.02973	+	3.36486i	−0.167801	+	0.186362i
$327$		0			0
$328$	−5.69693	+	2.53644i	−0.314560	+	0.140051i
$329$	−0.545085	+	0.944115i	−0.0300515	+	0.0520507i
$330$		0			0
$331$	−1.64590	−	2.85078i	−0.0904667	−	0.156693i	0.817241	−	0.576296i	$-0.195503\pi$
$331$	−1.64590	−	2.85078i	−0.0904667	−	0.156693i	−0.907708	+	0.419603i	$0.862169\pi$
$332$	11.2082	+	8.14324i	0.615130	+	0.446918i
$333$		0			0
$334$	2.01064	+	6.18812i	0.110017	+	0.338599i
$335$	7.17508	+	3.19455i	0.392016	+	0.174537i
$336$		0			0
$337$	−4.08899	−	0.869142i	−0.222741	−	0.0473452i	0.0951889	−	0.995459i	$-0.469654\pi$
$337$	−4.08899	−	0.869142i	−0.222741	−	0.0473452i	−0.317930	+	0.948114i	$0.602988\pi$
$338$	1.26368	+	1.40346i	0.0687353	+	0.0763382i
$339$		0			0
$340$	−11.7812	−	20.4056i	−0.638923	−	1.10665i
$341$	−16.4721	+	3.69822i	−0.892016	+	0.200270i
$342$		0			0
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	9.65959	−	2.05321i	0.520810	−	0.110702i
$345$		0			0
$346$	0.440565	+	4.19169i	0.0236849	+	0.225347i
$347$	−1.09464	−	10.4148i	−0.0587632	−	0.559094i	−0.983807	−	0.179233i	$-0.942638\pi$
$347$	−1.09464	−	10.4148i	−0.0587632	−	0.559094i	0.925044	−	0.379861i	$-0.124028\pi$
$348$		0			0
$349$	0.692728	−	0.147244i	0.0370809	−	0.00788178i	−0.189334	−	0.981913i	$-0.560633\pi$
$349$	0.692728	−	0.147244i	0.0370809	−	0.00788178i	0.226415	+	0.974031i	$0.427300\pi$
$350$	−0.736068	−	0.534785i	−0.0393445	−	0.0285854i
$351$		0			0
$352$	9.08359	−	10.3229i	0.484157	−	0.550211i
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$	−5.76659	−	6.40445i	−0.306059	−	0.339913i
$356$	6.82621	+	1.45096i	0.361789	+	0.0769005i
$357$		0			0
$358$	6.09679	+	2.71446i	0.322225	+	0.143464i
$359$	−1.14590	−	3.52671i	−0.0604782	−	0.186133i	0.916253	−	0.400600i	$-0.131198\pi$
$359$	−1.14590	−	3.52671i	−0.0604782	−	0.186133i	−0.976731	+	0.214468i	$0.931198\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	−2.19098	−	3.79489i	−0.115156	−	0.199455i
$363$		0			0
$364$	3.92705	−	6.80185i	0.205833	−	0.356514i
$365$	−11.3939	+	5.07287i	−0.596382	+	0.265526i
$366$		0			0
$367$	19.3072	−	21.4428i	1.00783	−	1.11930i	0.0149814	−	0.999888i	$-0.495231\pi$
$367$	19.3072	−	21.4428i	1.00783	−	1.11930i	0.992844	−	0.119416i	$-0.0381022\pi$
$368$	−10.7812	+	7.83297i	−0.562006	+	0.408322i
$369$		0			0
$370$	0.336881	+	1.03681i	0.0175136	+	0.0539014i
$371$	2.56082	−	0.544320i	0.132951	−	0.0282597i
$372$		0			0
$373$	17.4443	−	30.2144i	0.903230	−	1.56444i	0.0799547	−	0.996799i	$-0.474522\pi$
$373$	17.4443	−	30.2144i	0.903230	−	1.56444i	0.823275	−	0.567642i	$-0.192144\pi$
$374$	3.18247	+	9.42719i	0.164562	+	0.487468i
$375$		0			0
$376$	−0.167755	+	1.59609i	−0.00865133	+	0.0823119i
$377$	−7.85410	+	24.1724i	−0.404507	+	1.24494i
$378$		0			0
$379$	−8.80902	+	6.40013i	−0.452489	+	0.328752i	−0.790578	−	0.612362i	$-0.790220\pi$
$379$	−8.80902	+	6.40013i	−0.452489	+	0.328752i	0.338089	+	0.941114i	$0.390220\pi$
$380$	−2.34078	−	1.04218i	−0.120080	−	0.0534629i
$381$		0			0
$382$	5.92455	+	6.57988i	0.303126	+	0.336656i
$383$	−0.646976	+	0.288052i	−0.0330590	+	0.0147188i	−0.423200	−	0.906037i	$-0.639093\pi$
$383$	−0.646976	+	0.288052i	−0.0330590	+	0.0147188i	0.390141	+	0.920755i	$0.372426\pi$
$384$		0			0
$385$	3.63611	+	3.94678i	0.185313	+	0.201147i
$386$	−3.76393			−0.191579
$387$		0			0
$388$	−0.656541	+	2.02063i	−0.0333308	+	0.102582i
$389$	−3.84258	+	4.26762i	−0.194827	+	0.216377i	−0.832641	−	0.553813i	$-0.813172\pi$
$389$	−3.84258	+	4.26762i	−0.194827	+	0.216377i	0.637814	+	0.770190i	$0.279839\pi$
$390$		0			0
$391$	−3.47772	−	33.0883i	−0.175876	−	1.67334i
$392$	−8.63980	−	1.83645i	−0.436376	−	0.0927545i
$393$		0			0
$394$	−0.640196	+	6.09106i	−0.0322526	+	0.306863i
$395$	−17.7984			−0.895533
$396$		0			0
$397$	−5.29180			−0.265588			−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180			−0.265588			−0.132794	+	0.991144i	$0.542395\pi$
$398$	0.267834	−	2.54827i	0.0134253	−	0.127733i
$399$		0			0
$400$	7.32967	+	1.55797i	0.366484	+	0.0778985i
$401$	2.99860	+	28.5298i	0.149743	+	1.42471i	0.768864	+	0.639413i	$0.220822\pi$
$401$	2.99860	+	28.5298i	0.149743	+	1.42471i	−0.619121	+	0.785296i	$0.712511\pi$
$402$		0			0
$403$	−14.4280	+	16.0239i	−0.718710	+	0.798208i
$404$	−3.30244	+	10.1639i	−0.164302	+	0.505671i
$405$		0			0
$406$	−2.29180			−0.113740
$407$	0.677881	+	5.81089i	0.0336013	+	0.288035i
$408$		0			0
$409$	2.25841	−	1.00551i	0.111671	−	0.0497192i	−0.350141	−	0.936697i	$-0.613866\pi$
$409$	2.25841	−	1.00551i	0.111671	−	0.0497192i	0.461812	+	0.886978i	$0.347200\pi$
$410$	−1.75181	−	1.94558i	−0.0865156	−	0.0960853i
$411$		0			0
$412$	−11.7623	−	5.23689i	−0.579485	−	0.258003i
$413$	−7.78115	+	5.65334i	−0.382886	+	0.278183i
$414$		0			0
$415$	−3.73607	+	11.4984i	−0.183396	+	0.564436i
$416$	1.83576	−	17.4661i	0.0900056	−	0.856346i
$417$		0			0
$418$	0.882564	+	0.625958i	0.0431676	+	0.0306166i
$419$	−12.2254	+	21.1751i	−0.597251	+	1.03447i	0.395974	+	0.918262i	$0.370407\pi$
$419$	−12.2254	+	21.1751i	−0.597251	+	1.03447i	−0.993225	+	0.116207i	$0.962926\pi$
$420$		0			0
$421$	26.9055	−	5.71894i	1.31129	−	0.278724i	0.501356	−	0.865241i	$-0.332835\pi$
$421$	26.9055	−	5.71894i	1.31129	−	0.278724i	0.809937	+	0.586517i	$0.199501\pi$
$422$	0.163119	+	0.502029i	0.00794051	+	0.0244384i
$423$		0			0
$424$	3.11803	−	2.26538i	0.151425	−	0.110017i
$425$	−12.5182	+	13.9029i	−0.607223	+	0.674390i
$426$		0			0
$427$	−7.82206	+	3.48260i	−0.378536	+	0.168535i
$428$	2.34346	−	4.05899i	0.113275	−	0.196199i
$429$		0			0
$430$	2.07295	+	3.59045i	0.0999665	+	0.173147i
$431$	−13.8262	−	10.0453i	−0.665986	−	0.483867i	0.202693	−	0.979242i	$-0.435031\pi$
$431$	−13.8262	−	10.0453i	−0.665986	−	0.483867i	−0.868679	+	0.495375i	$0.835031\pi$
$432$		0			0
$433$	−8.43769	−	25.9686i	−0.405490	−	1.24797i	−0.920486	−	0.390776i	$-0.872207\pi$
$433$	−8.43769	−	25.9686i	−0.405490	−	1.24797i	0.514996	−	0.857193i	$-0.327793\pi$
$434$	−1.77618	−	0.790807i	−0.0852594	−	0.0379599i
$435$		0			0
$436$	−21.7630	−	4.62587i	−1.04226	−	0.221539i
$437$	−2.42094	−	2.68872i	−0.115809	−	0.128619i
$438$		0			0
$439$	−18.3541	−	31.7902i	−0.875993	−	1.51727i	−0.855701	−	0.517471i	$-0.826873\pi$
$439$	−18.3541	−	31.7902i	−0.875993	−	1.51727i	−0.0202928	−	0.999794i	$-0.506460\pi$
$440$	7.25329	+	3.13068i	0.345787	+	0.149250i
$441$		0			0
$442$	10.2812	+	7.46969i	0.489025	+	0.355297i
$443$	17.2122	−	3.65857i	0.817777	−	0.173824i	0.220014	−	0.975497i	$-0.429390\pi$
$443$	17.2122	−	3.65857i	0.817777	−	0.173824i	0.597763	+	0.801673i	$0.296056\pi$
$444$		0			0
$445$	0.636596	+	6.05681i	0.0301775	+	0.287120i
$446$	0.606095	+	5.76661i	0.0286994	+	0.273057i
$447$		0			0
$448$	−4.60532	+	0.978891i	−0.217581	+	0.0462482i
$449$	−21.7984	−	15.8374i	−1.02873	−	0.747415i	−0.0606750	−	0.998158i	$-0.519325\pi$
$449$	−21.7984	−	15.8374i	−1.02873	−	0.747415i	−0.968054	+	0.250742i	$0.919325\pi$
$450$		0			0
$451$	−7.16312	−	12.0862i	−0.337298	−	0.569118i
$452$	−4.19756	−	7.27039i	−0.197437	−	0.341970i
$453$		0			0
$454$	2.34636	+	2.60590i	0.110120	+	0.122301i
$455$	6.70432	+	1.42505i	0.314304	+	0.0668073i
$456$		0			0
$457$	−20.9921	−	9.34628i	−0.981969	−	0.437201i	−0.147985	−	0.988990i	$-0.547279\pi$
$457$	−20.9921	−	9.34628i	−0.981969	−	0.437201i	−0.833984	+	0.551789i	$0.813945\pi$
$458$	−1.00000	−	3.07768i	−0.0467269	−	0.143811i
$459$		0			0
$460$	−10.2812	−	7.46969i	−0.479361	−	0.348276i
$461$	−12.1353	−	21.0189i	−0.565195	−	0.978947i	−0.997031	−	0.0769948i	$-0.975468\pi$
$461$	−12.1353	−	21.0189i	−0.565195	−	0.978947i	0.431836	−	0.901952i	$-0.357866\pi$
$462$		0			0
$463$	−17.6353	+	30.5452i	−0.819580	+	1.41955i	0.0864124	+	0.996259i	$0.472460\pi$
$463$	−17.6353	+	30.5452i	−0.819580	+	1.41955i	−0.905992	+	0.423294i	$0.860874\pi$
$464$	17.2435	−	7.67731i	0.800511	−	0.356410i
$465$		0			0
$466$	2.77415	−	3.08100i	0.128510	−	0.142725i
$467$	−12.0451	+	8.75127i	−0.557380	+	0.404960i	−0.830499	−	0.557020i	$-0.811945\pi$
$467$	−12.0451	+	8.75127i	−0.557380	+	0.404960i	0.273119	+	0.961980i	$0.411945\pi$
$468$		0			0
$469$	1.50000	+	4.61653i	0.0692636	+	0.213171i
$470$	−0.659039	+	0.140083i	−0.0303992	+	0.00646155i
$471$		0			0
$472$	−7.07953	+	12.2621i	−0.325862	+	0.564409i
$473$	7.11622	+	21.0798i	0.327204	+	0.969252i
$474$		0			0
$475$	−0.212657	+	2.02330i	−0.00975738	+	0.0928352i
$476$	4.50000	−	13.8496i	0.206257	−	0.634794i
$477$		0			0
$478$	0.809017	−	0.587785i	0.0370036	−	0.0268847i
$479$	27.9710	+	12.4535i	1.27803	+	0.569014i	0.929686	−	0.368354i	$-0.120079\pi$
$479$	27.9710	+	12.4535i	1.27803	+	0.569014i	0.348341	+	0.937368i	$0.386745\pi$
$480$		0			0
$481$	4.99983	+	5.55288i	0.227973	+	0.253189i
$482$	7.57493	−	3.37258i	0.345029	−	0.153617i
$483$		0			0
$484$	16.7693	+	11.6083i	0.762241	+	0.527648i
$485$	−1.85410			−0.0841904
$486$		0			0
$487$	0.218847	−	0.673542i	0.00991691	−	0.0305211i	−0.945976	−	0.324238i	$-0.894892\pi$
$487$	0.218847	−	0.673542i	0.00991691	−	0.0305211i	0.955893	+	0.293717i	$0.0948922\pi$
$488$	−8.43431	+	9.36725i	−0.381803	+	0.424035i
$489$		0			0
$490$	−0.387613	−	3.68789i	−0.0175106	−	0.166602i
$491$	−28.4545	−	6.04819i	−1.28413	−	0.272951i	−0.485217	−	0.874394i	$-0.661259\pi$
$491$	−28.4545	−	6.04819i	−1.28413	−	0.272951i	−0.798916	+	0.601443i	$0.794593\pi$
$492$		0			0
$493$	−4.92586	+	46.8665i	−0.221850	+	2.11076i
$494$	1.38197			0.0621776
$495$		0			0
$496$	16.0132			0.719012
$497$	0.556743	−	5.29706i	0.0249734	−	0.237606i
$498$		0			0
$499$	24.3110	+	5.16746i	1.08831	+	0.231327i	0.716924	−	0.697152i	$-0.245550\pi$
$499$	24.3110	+	5.16746i	1.08831	+	0.231327i	0.371385	+	0.928479i	$0.378883\pi$
$500$	2.31488	+	22.0246i	0.103524	+	0.984969i
$501$		0			0
$502$	−6.38419	+	7.09036i	−0.284940	+	0.316458i
$503$	7.00000	−	21.5438i	0.312115	−	0.960590i	−0.664811	−	0.747011i	$-0.731488\pi$
$503$	7.00000	−	21.5438i	0.312115	−	0.960590i	0.976926	−	0.213579i	$-0.0685119\pi$
$504$		0			0
$505$	−9.32624			−0.415012
$506$	3.63611	+	3.94678i	0.161645	+	0.175456i
$507$		0			0
$508$	9.66859	−	4.30473i	0.428974	−	0.190992i
$509$	2.50432	+	2.78133i	0.111002	+	0.123280i	0.796085	−	0.605185i	$-0.206901\pi$
$509$	2.50432	+	2.78133i	0.111002	+	0.123280i	−0.685083	+	0.728465i	$0.740234\pi$
$510$		0			0
$511$	−7.04179	−	3.13521i	−0.311511	−	0.138693i
$512$	−18.0451	+	13.1105i	−0.797488	+	0.579409i
$513$		0			0
$514$	1.50407	−	4.62904i	0.0663415	−	0.204178i
$515$	1.17449	−	11.1745i	0.0517542	−	0.492408i
$516$		0			0
$517$	−3.61545	+	0.0412623i	−0.159007	+	0.00181472i
$518$	−0.336881	+	0.583495i	−0.0148017	+	0.0256373i
$519$		0			0
$520$	9.86968	−	2.09786i	0.432814	−	0.0919974i
$521$	2.76393	+	8.50651i	0.121090	+	0.372677i	0.993168	−	0.116689i	$-0.0372282\pi$
$521$	2.76393	+	8.50651i	0.121090	+	0.372677i	−0.872078	+	0.489366i	$0.837228\pi$
$522$		0			0
$523$	12.3541	−	8.97578i	0.540207	−	0.392483i	−0.283955	−	0.958838i	$-0.591647\pi$
$523$	12.3541	−	8.97578i	0.540207	−	0.392483i	0.824162	+	0.566354i	$0.191647\pi$
$524$	15.8781	−	17.6344i	0.693639	−	0.770364i
$525$		0			0
$526$	−6.37537	+	2.83850i	−0.277979	+	0.123764i
$527$	−19.9894	+	34.6226i	−0.870750	+	1.50818i
$528$		0			0
$529$	2.52786	+	4.37839i	0.109907	+	0.190365i
$530$	1.30902	+	0.951057i	0.0568601	+	0.0413113i
$531$		0			0
$532$	−0.489357	−	1.50609i	−0.0212163	−	0.0652971i
$533$	−16.3929	−	7.29859i	−0.710056	−	0.316137i
$534$		0			0
$535$	4.00079	+	0.850394i	0.172969	+	0.0367657i
$536$	4.78154	+	5.31044i	0.206531	+	0.229376i
$537$		0			0
$538$	0.270510	+	0.468537i	0.0116625	+	0.0202001i
$539$	1.85410	−	19.8132i	0.0798618	−	0.853414i
$540$		0			0
$541$	36.8156	+	26.7481i	1.58283	+	1.14999i	0.913364	+	0.407144i	$0.133475\pi$
$541$	36.8156	+	26.7481i	1.58283	+	1.14999i	0.669462	+	0.742846i	$0.266525\pi$
$542$	−6.12062	+	1.30098i	−0.262903	+	0.0558818i
$543$		0			0
$544$	−3.40369	−	32.3839i	−0.145932	−	1.38845i
$545$	−2.02957	−	19.3100i	−0.0869371	−	0.827151i
$546$		0			0
$547$	−11.4860	+	2.44143i	−0.491108	+	0.104388i	−0.446808	−	0.894630i	$-0.647439\pi$
$547$	−11.4860	+	2.44143i	−0.491108	+	0.104388i	−0.0443001	+	0.999018i	$0.514106\pi$
$548$	−21.3541	−	15.5147i	−0.912202	−	0.662754i
$549$		0			0
$550$	0.281153	−	3.00444i	0.0119884	−	0.128110i
$551$	2.56231	+	4.43804i	0.109158	+	0.189067i
$552$		0			0
$553$	−7.36044	−	8.17459i	−0.312998	−	0.347619i
$554$	−8.29987	−	1.76419i	−0.352628	−	0.0749533i
$555$		0			0
$556$	9.42147	+	4.19471i	0.399559	+	0.177895i
$557$	12.5557	+	38.6426i	0.532003	+	1.63734i	0.750037	+	0.661396i	$0.230036\pi$
$557$	12.5557	+	38.6426i	0.532003	+	1.63734i	−0.218033	+	0.975941i	$0.569964\pi$
$558$		0			0
$559$	22.9894	+	16.7027i	0.972346	+	0.706451i
$560$	−2.54508	−	4.40822i	−0.107549	−	0.186281i
$561$		0			0
$562$	5.58359	−	9.67107i	0.235530	−	0.407949i
$563$	7.85352	−	3.49661i	0.330986	−	0.147365i	−0.234514	−	0.972113i	$-0.575350\pi$
$563$	7.85352	−	3.49661i	0.330986	−	0.147365i	0.565500	+	0.824748i	$0.308683\pi$
$564$		0			0
$565$	4.90221	−	5.44446i	0.206238	−	0.229050i
$566$	−2.38197	+	1.73060i	−0.100121	+	0.0727425i
$567$		0			0
$568$	−2.42299	−	7.45718i	−0.101666	−	0.312896i
$569$	11.5614	−	2.45745i	0.484678	−	0.103021i	0.0409093	−	0.999163i	$-0.486975\pi$
$569$	11.5614	−	2.45745i	0.484678	−	0.103021i	0.443769	+	0.896141i	$0.353641\pi$
$570$		0			0
$571$	−1.04508	+	1.81014i	−0.0437354	+	0.0757520i	−0.887064	−	0.461646i	$-0.847259\pi$
$571$	−1.04508	+	1.81014i	−0.0437354	+	0.0757520i	0.843329	+	0.537398i	$0.180593\pi$
$572$	26.0474	−	0.297274i	1.08910	−	0.0124296i
$573$		0			0
$574$	0.169131	−	1.60917i	0.00705938	−	0.0671655i
$575$	−3.11803	+	9.59632i	−0.130031	+	0.400194i
$576$		0			0
$577$	−14.7984	+	10.7516i	−0.616064	+	0.447597i	−0.851545	−	0.524282i	$-0.824334\pi$
$577$	−14.7984	+	10.7516i	−0.616064	+	0.447597i	0.235480	+	0.971879i	$0.424334\pi$
$578$	15.5932	+	6.94254i	0.648592	+	0.288772i
$579$		0			0
$580$	12.0444	+	13.3766i	0.500114	+	0.555433i
$581$	−6.82614	+	3.03919i	−0.283196	+	0.126087i
$582$		0			0
$583$	5.88335	+	6.38603i	0.243663	+	0.264482i
$584$	−11.3475			−0.469564
$585$		0			0
$586$	−1.13932	+	3.50647i	−0.0470649	+	0.144851i
$587$	−25.5103	+	28.3321i	−1.05292	+	1.16939i	−0.0677737	+	0.997701i	$0.521590\pi$
$587$	−25.5103	+	28.3321i	−1.05292	+	1.16939i	−0.985151	+	0.171691i	$0.945077\pi$
$588$		0			0
$589$	0.454440	+	4.32371i	0.0187249	+	0.178155i
$590$	−5.81438	−	1.23588i	−0.239374	−	0.0508805i
$591$		0			0
$592$	0.580044	−	5.51875i	0.0238397	−	0.226819i
$593$	−15.0344			−0.617391			−0.308695	−	0.951161i	$-0.599892\pi$
$593$	−15.0344			−0.617391			−0.308695	+	0.951161i	$0.599892\pi$
$594$		0			0
$595$	12.7082			0.520986
$596$	−0.0457515	+	0.435296i	−0.00187405	+	0.0178304i
$597$		0			0
$598$	6.70432	+	1.42505i	0.274160	+	0.0582745i
$599$	−1.94971	−	18.5503i	−0.0796632	−	0.757945i	−0.959317	−	0.282330i	$-0.908893\pi$
$599$	−1.94971	−	18.5503i	−0.0796632	−	0.757945i	0.879654	−	0.475614i	$-0.157774\pi$
$600$		0			0
$601$	19.3302	−	21.4684i	0.788496	−	0.875713i	−0.206207	−	0.978508i	$-0.566112\pi$
$601$	19.3302	−	21.4684i	0.788496	−	0.875713i	0.994703	+	0.102795i	$0.0327787\pi$
$602$	−0.791796	+	2.43690i	−0.0322712	+	0.0993205i
$603$		0			0
$604$	−35.1246			−1.42920
$605$	−5.11224	+	17.0484i	−0.207842	+	0.693115i
$606$		0			0
$607$	3.25433	−	1.44892i	0.132089	−	0.0588099i	−0.339628	−	0.940560i	$-0.610301\pi$
$607$	3.25433	−	1.44892i	0.132089	−	0.0588099i	0.471717	+	0.881750i	$0.343634\pi$
$608$	−2.36940	−	2.63149i	−0.0960920	−	0.106721i
$609$		0			0
$610$	−4.83430	−	2.15237i	−0.195735	−	0.0871468i
$611$	−3.73607	+	2.71441i	−0.151145	+	0.109813i
$612$		0			0
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	0.615311	+	0.788285i	$0.289031\pi$
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	−0.961139	+	0.276065i	$0.910969\pi$
$614$	0.757750	−	7.20951i	0.0305803	−	0.290952i
$615$		0			0
$616$	1.56168	+	4.62603i	0.0629217	+	0.186388i
$617$	−5.59017	+	9.68246i	−0.225052	+	0.389801i	−0.956335	−	0.292273i	$-0.905588\pi$
$617$	−5.59017	+	9.68246i	−0.225052	+	0.389801i	0.731283	+	0.682074i	$0.238922\pi$
$618$		0			0
$619$	15.7723	−	3.35250i	0.633940	−	0.134748i	0.120277	−	0.992740i	$-0.461622\pi$
$619$	15.7723	−	3.35250i	0.633940	−	0.134748i	0.513663	+	0.857992i	$0.328288\pi$
$620$	4.71885	+	14.5231i	0.189513	+	0.583262i
$621$		0			0
$622$	−6.07295	+	4.41226i	−0.243503	+	0.176915i
$623$	−2.51856	+	2.79715i	−0.100904	+	0.112065i
$624$		0			0
$625$	−6.77523	+	3.01652i	−0.271009	+	0.120661i
$626$	2.19098	−	3.79489i	0.0875693	−	0.151674i
$627$		0			0
$628$	2.12461	+	3.67994i	0.0847812	+	0.146845i
$629$	11.2082	+	8.14324i	0.446900	+	0.324692i
$630$		0			0
$631$	−9.95492	−	30.6381i	−0.396299	−	1.21968i	−0.927945	−	0.372716i	$-0.878426\pi$
$631$	−9.95492	−	30.6381i	−0.396299	−	1.21968i	0.531646	−	0.846966i	$-0.321574\pi$
$632$	−14.7935	−	6.58649i	−0.588454	−	0.261996i
$633$		0			0
$634$	−10.9023	−	2.31736i	−0.432987	−	0.0920342i
$635$	6.18014	+	6.86374i	0.245251	+	0.272379i
$636$		0			0
$637$	−12.7082	−	22.0113i	−0.503517	−	0.872118i
$638$	−3.87539	−	6.53888i	−0.153428	−	0.258877i
$639$		0			0
$640$	−13.2082	−	9.59632i	−0.522100	−	0.379328i
$641$	−13.6059	+	2.89202i	−0.537399	+	0.114228i	−0.468613	−	0.883404i	$-0.655246\pi$
$641$	−13.6059	+	2.89202i	−0.537399	+	0.114228i	−0.0687865	+	0.997631i	$0.521913\pi$
$642$		0			0
$643$	−1.47865	−	14.0684i	−0.0583122	−	0.554804i	−0.984207	−	0.177022i	$-0.943354\pi$
$643$	−1.47865	−	14.0684i	−0.0583122	−	0.554804i	0.925895	−	0.377782i	$-0.123313\pi$
$644$	−0.820977	−	7.81108i	−0.0323510	−	0.307800i
$645$		0			0
$646$	2.50631	−	0.532733i	0.0986096	−	0.0209601i
$647$	12.9164	+	9.38432i	0.507796	+	0.368936i	0.811987	−	0.583676i	$-0.198386\pi$
$647$	12.9164	+	9.38432i	0.507796	+	0.368936i	−0.304191	+	0.952611i	$0.598386\pi$
$648$		0			0
$649$	−29.2877	−	12.6412i	−1.14964	−	0.496212i
$650$	−1.92705	−	3.33775i	−0.0755852	−	0.130917i
$651$		0			0
$652$	14.7066	+	16.3334i	0.575956	+	0.639664i
$653$	−3.30806	−	0.703150i	−0.129454	−	0.0275164i	0.142729	−	0.989762i	$-0.454412\pi$
$653$	−3.30806	−	0.703150i	−0.129454	−	0.0275164i	−0.272183	+	0.962245i	$0.587746\pi$
$654$		0			0
$655$	18.9179	+	8.42279i	0.739183	+	0.329105i
$656$	4.11803	+	12.6740i	0.160782	+	0.494837i
$657$		0			0
$658$	−0.336881	−	0.244758i	−0.0131330	−	0.00954168i
$659$	−0.437694	−	0.758108i	−0.0170501	−	0.0295317i	0.857374	−	0.514693i	$-0.172094\pi$
$659$	−0.437694	−	0.758108i	−0.0170501	−	0.0295317i	−0.874425	+	0.485161i	$0.838761\pi$
$660$		0			0
$661$	−8.21885	+	14.2355i	−0.319676	+	0.553695i	−0.980420	−	0.196916i	$-0.936907\pi$
$661$	−8.21885	+	14.2355i	−0.319676	+	0.553695i	0.660744	+	0.750611i	$0.270241\pi$
$662$	1.14865	−	0.511412i	0.0446436	−	0.0198766i
$663$		0			0
$664$	−7.36044	+	8.17459i	−0.285640	+	0.317236i
$665$	1.11803	−	0.812299i	0.0433555	−	0.0314996i
$666$		0			0
$667$	7.85410	+	24.1724i	0.304112	+	0.935961i
$668$	30.8934	−	6.56660i	1.19530	−	0.254069i
$669$		0			0
$670$	−1.50000	+	2.59808i	−0.0579501	+	0.100372i
$671$	−23.1634	−	16.4286i	−0.894214	−	0.634220i
$672$		0			0
$673$	1.86404	−	17.7351i	0.0718533	−	0.683639i	−0.898008	−	0.439980i	$-0.854986\pi$
$673$	1.86404	−	17.7351i	0.0718533	−	0.683639i	0.969861	−	0.243659i	$-0.0783478\pi$
$674$	0.493422	−	1.51860i	0.0190059	−	0.0584942i
$675$		0			0
$676$	7.41641	−	5.38834i	0.285246	−	0.207244i
$677$	−20.5293	−	9.14024i	−0.789006	−	0.351288i	−0.0276461	−	0.999618i	$-0.508801\pi$
$677$	−20.5293	−	9.14024i	−0.789006	−	0.351288i	−0.761360	+	0.648330i	$0.775468\pi$
$678$		0			0
$679$	−0.766755	−	0.851568i	−0.0294254	−	0.0326802i
$680$	17.0908	−	7.60931i	0.655402	−	0.291804i
$681$		0			0
$682$	−0.747186	−	6.40499i	−0.0286112	−	0.245260i
$683$	49.0689			1.87757			0.938784	−	0.344505i	$-0.111953\pi$
$683$	49.0689			1.87757			0.938784	+	0.344505i	$0.111953\pi$
$684$		0			0
$685$	7.11803	−	21.9071i	0.271966	−	0.837026i
$686$	3.32261	−	3.69013i	0.126858	−	0.140890i
$687$		0			0
$688$	−2.20590	−	20.9877i	−0.0840991	−	0.800149i
$689$	10.8478	+	2.30578i	0.413269	+	0.0878431i
$690$		0			0
$691$	−3.41311	+	32.4736i	−0.129841	+	1.23535i	0.714534	+	0.699601i	$0.246639\pi$
$691$	−3.41311	+	32.4736i	−0.129841	+	1.23535i	−0.844375	+	0.535753i	$0.820028\pi$
$692$	20.4590			0.777734
$693$		0			0
$694$	4.00000			0.151838
$695$	−0.940756	+	8.95070i	−0.0356849	+	0.339519i
$696$		0			0
$697$	−32.5435	−	6.91733i	−1.23267	−	0.262012i
$698$	0.0282760	+	0.269028i	0.00107026	+	0.0101829i
$699$		0			0
$700$	−2.95515	+	3.28203i	−0.111694	+	0.124049i
$701$	3.15248	−	9.70232i	0.119067	−	0.366452i	−0.873706	−	0.486454i	$-0.838290\pi$
$701$	3.15248	−	9.70232i	0.119067	−	0.366452i	0.992774	+	0.120002i	$0.0382902\pi$
$702$		0			0
$703$	1.50658			0.0568217
$704$	−10.5805	−	11.4845i	−0.398766	−	0.432837i
$705$		0			0
$706$	4.18732	−	1.86431i	0.157592	−	0.0701644i
$707$	−3.85682	−	4.28344i	−0.145051	−	0.161095i
$708$		0			0
$709$	−36.7380	−	16.3568i	−1.37973	−	0.614293i	−0.423225	−	0.906024i	$-0.639102\pi$
$709$	−36.7380	−	16.3568i	−1.37973	−	0.614293i	−0.956500	+	0.291731i	$0.905769\pi$
$710$	2.66312	−	1.93487i	0.0999451	−	0.0726143i
$711$		0			0
$712$	−1.71227	+	5.26982i	−0.0641700	+	0.197495i
$713$	−2.25387	+	21.4442i	−0.0844083	+	0.803091i
$714$		0			0
$715$	7.27099	+	21.5383i	0.271920	+	0.805487i
$716$	16.1976	−	28.0550i	0.605331	−	1.04846i
$717$		0			0
$718$	1.38546	−	0.294488i	0.0517048	−	0.0109902i
$719$	−14.3647	−	44.2101i	−0.535715	−	1.64876i	−0.742100	−	0.670289i	$-0.766170\pi$
$719$	−14.3647	−	44.2101i	−0.535715	−	1.64876i	0.206385	−	0.978471i	$-0.433830\pi$
$720$		0			0
$721$	5.61803	−	4.08174i	0.209227	−	0.152012i
$722$	−4.66967	+	5.18620i	−0.173787	+	0.193010i
$723$		0			0
$724$	−19.4316	+	8.65150i	−0.722169	+	0.321530i
$725$	7.14590	−	12.3771i	0.265392	−	0.459672i
$726$		0			0
$727$	7.92705	+	13.7301i	0.293998	+	0.509220i	0.974751	−	0.223293i	$-0.0716807\pi$
$727$	7.92705	+	13.7301i	0.293998	+	0.509220i	−0.680753	+	0.732513i	$0.738347\pi$
$728$	5.04508	+	3.66547i	0.186983	+	0.135851i
$729$		0			0
$730$	−1.47214	−	4.53077i	−0.0544862	−	0.167691i
$731$	48.1319	+	21.4297i	1.78022	+	0.792606i
$732$		0			0
$733$	48.5129	+	10.3117i	1.79187	+	0.380873i	0.979367	−	0.202089i	$-0.0647731\pi$
$733$	48.5129	+	10.3117i	1.79187	+	0.380873i	0.812499	+	0.582962i	$0.198106\pi$
$734$	7.37468	+	8.19041i	0.272204	+	0.302314i
$735$		0			0
$736$	−8.78115	−	15.2094i	−0.323678	−	0.560626i
$737$	−10.6353	+	12.0862i	−0.391755	+	0.445202i
$738$		0			0
$739$	−2.42705	−	1.76336i	−0.0892805	−	0.0648661i	0.542250	−	0.840218i	$-0.317573\pi$
$739$	−2.42705	−	1.76336i	−0.0892805	−	0.0648661i	−0.631530	+	0.775351i	$0.717573\pi$
$740$	5.17616	−	1.10023i	0.190279	−	0.0404451i
$741$		0			0
$742$	0.104528	+	0.994522i	0.00383736	+	0.0365100i
$743$	−0.743350	−	7.07250i	−0.0272709	−	0.259465i	−0.999659	−	0.0260971i	$-0.991692\pi$
$743$	−0.743350	−	7.07250i	−0.0272709	−	0.259465i	0.972389	−	0.233368i	$-0.0749746\pi$
$744$		0			0
$745$	−0.373619	+	0.0794152i	−0.0136883	+	0.00290955i
$746$	10.7812	+	7.83297i	0.394726	+	0.286785i
$747$		0			0
$748$	47.1246	−	10.5801i	1.72305	−	0.386848i
$749$	1.26393	+	2.18919i	0.0461831	+	0.0799914i
$750$		0			0
$751$	15.2924	+	16.9839i	0.558027	+	0.619752i	0.954470	−	0.298308i	$-0.0964222\pi$
$751$	15.2924	+	16.9839i	0.558027	+	0.619752i	−0.396443	+	0.918059i	$0.629756\pi$
$752$	3.35462	+	0.713046i	0.122330	+	0.0260021i
$753$		0			0
$754$	−8.86889	−	3.94868i	−0.322986	−	0.143803i
$755$	−9.47214	−	29.1522i	−0.344726	−	1.06096i
$756$		0			0
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	0.511843	−	0.859079i	$-0.328963\pi$
$757$	−4.04508	−	2.93893i	−0.147021	−	0.106817i	−0.658864	+	0.752262i	$0.728963\pi$
$758$	−2.07953	−	3.60185i	−0.0755318	−	0.130825i
$759$		0			0
$760$	1.01722	−	1.76188i	0.0368985	−	0.0639100i
$761$	−39.0159	+	17.3710i	−1.41432	+	0.629698i	−0.964660	−	0.263499i	$-0.915123\pi$
$761$	−39.0159	+	17.3710i	−1.41432	+	0.629698i	−0.449665	+	0.893197i	$0.648457\pi$
$762$		0			0
$763$	8.02957	−	8.91774i	0.290690	−	0.322844i
$764$	34.7705	−	25.2623i	1.25795	−	0.913956i
$765$		0			0
$766$	−0.0835921	−	0.257270i	−0.00302031	−	0.00929555i
$767$	−39.8523	+	8.47087i	−1.43898	+	0.305865i
$768$		0			0
$769$	−1.75329	+	3.03679i	−0.0632252	+	0.109509i	−0.895905	−	0.444245i	$-0.853472\pi$
$769$	−1.75329	+	3.03679i	−0.0632252	+	0.109509i	0.832680	+	0.553754i	$0.186805\pi$
$770$	−1.64445	+	1.22368i	−0.0592620	+	0.0440984i
$771$		0			0
$772$	−1.90979	+	18.1704i	−0.0687348	+	0.653968i
$773$	−1.48936	+	4.58377i	−0.0535684	+	0.164867i	−0.974262	−	0.225421i	$-0.927624\pi$
$773$	−1.48936	+	4.58377i	−0.0535684	+	0.164867i	0.920693	+	0.390287i	$0.127624\pi$
$774$		0			0
$775$	9.80902	−	7.12667i	0.352350	−	0.255997i
$776$	−1.54108	−	0.686131i	−0.0553214	−	0.0246307i
$777$		0			0
$778$	−1.46773	−	1.63008i	−0.0526208	−	0.0584414i
$779$	−3.30524	+	1.47159i	−0.118422	+	0.0527251i
$780$		0			0
$781$	16.0549	−	7.36876i	0.574488	−	0.263675i
$782$	12.7082			0.454444
$783$		0			0
$784$	−5.83282	+	17.9516i	−0.208315	+	0.641127i
$785$	−2.48127	+	2.75573i	−0.0885604	+	0.0983563i
$786$		0			0
$787$	−0.387613	−	3.68789i	−0.0138169	−	0.131459i	0.985439	−	0.170029i	$-0.0543863\pi$
$787$	−0.387613	−	3.68789i	−0.0138169	−	0.131459i	−0.999256	+	0.0385704i	$0.987720\pi$
$788$	29.0798	+	6.18111i	1.03593	+	0.220193i
$789$		0			0
$790$	0.710624	−	6.76113i	0.0252829	−	0.240550i
$791$	4.52786			0.160992
$792$		0			0
$793$	−36.2705			−1.28800
$794$	0.211282	−	2.01021i	0.00749812	−	0.0713398i
$795$		0			0
$796$	−12.1659	−	2.58594i	−0.431209	−	0.0916563i
$797$	−5.07392	−	48.2751i	−0.179727	−	1.70999i	−0.597855	−	0.801604i	$-0.703980\pi$
$797$	−5.07392	−	48.2751i	−0.179727	−	1.70999i	0.418128	−	0.908388i	$-0.362686\pi$
$798$		0			0
$799$	−5.72930	+	6.36303i	−0.202688	+	0.225108i
$800$	−3.05166	+	9.39205i	−0.107893	+	0.332059i
$801$		0			0
$802$	−10.9574			−0.386920
$803$	−2.96227	−	25.3930i	−0.104536	−	0.896100i
$804$		0			0
$805$	6.26153	−	2.78781i	0.220690	−	0.0982575i
$806$	−5.51101	−	6.12059i	−0.194117	−	0.215589i
$807$		0			0
$808$	−7.75170	−	3.45128i	−0.272704	−	0.121416i
$809$	12.8713	−	9.35156i	0.452532	−	0.328783i	−0.338063	−	0.941124i	$-0.609772\pi$
$809$	12.8713	−	9.35156i	0.452532	−	0.328783i	0.790594	+	0.612340i	$0.209772\pi$
$810$		0			0
$811$	5.07953	−	15.6332i	0.178366	−	0.548955i	−0.821405	−	0.570346i	$-0.806809\pi$
$811$	5.07953	−	15.6332i	0.178366	−	0.548955i	0.999771	+	0.0213905i	$0.00680931\pi$
$812$	−1.16284	+	11.0637i	−0.0408076	+	0.388259i
$813$		0			0
$814$	−2.23447	+	0.0255015i	−0.0783182	+	0.000893828i
$815$	−9.59017	+	16.6107i	−0.335929	+	0.581846i
$816$		0			0
$817$	5.60429	−	1.19123i	0.196069	−	0.0416758i
$818$	0.291796	+	0.898056i	0.0102024	+	0.0313998i
$819$		0			0
$820$	−10.2812	+	7.46969i	−0.359033	+	0.260853i
$821$	5.75235	−	6.38863i	0.200758	−	0.222965i	−0.634356	−	0.773041i	$-0.718735\pi$
$821$	5.75235	−	6.38863i	0.200758	−	0.222965i	0.835114	+	0.550076i	$0.185401\pi$
$822$		0			0
$823$	23.5995	−	10.5072i	0.822625	−	0.366256i	0.0481339	−	0.998841i	$-0.484673\pi$
$823$	23.5995	−	10.5072i	0.822625	−	0.366256i	0.774491	+	0.632585i	$0.218006\pi$
$824$	5.11146	−	8.85330i	0.178066	−	0.308419i
$825$		0			0
$826$	−1.83688	−	3.18157i	−0.0639133	−	0.110701i
$827$	16.7082	+	12.1392i	0.581001	+	0.422122i	0.839085	−	0.544000i	$-0.183091\pi$
$827$	16.7082	+	12.1392i	0.581001	+	0.422122i	−0.258084	+	0.966123i	$0.583091\pi$
$828$		0			0
$829$	13.1008	+	40.3202i	0.455010	+	1.40038i	0.871123	+	0.491064i	$0.163392\pi$
$829$	13.1008	+	40.3202i	0.455010	+	1.40038i	−0.416113	+	0.909313i	$0.636608\pi$
$830$	−4.21878	−	1.87832i	−0.146436	−	0.0651976i
$831$		0			0
$832$	−19.5084	−	4.14665i	−0.676334	−	0.143759i
$833$	−31.5325	−	35.0204i	−1.09254	−	1.21339i
$834$		0			0
$835$	13.7812	+	23.8697i	0.476916	+	0.826044i
$836$	3.46962	−	3.94298i	0.119999	−	0.136371i
$837$		0			0
$838$	−7.55573	−	5.48956i	−0.261008	−	0.189634i
$839$	35.0498	−	7.45006i	1.21005	−	0.257205i	0.441660	−	0.897183i	$-0.354390\pi$
$839$	35.0498	−	7.45006i	1.21005	−	0.257205i	0.768393	+	0.639978i	$0.221057\pi$
$840$		0			0
$841$	−0.731699	−	6.96165i	−0.0252310	−	0.240057i
$842$	1.09824	+	10.4490i	0.0378477	+	0.360097i
$843$		0			0
$844$	2.50631	−	0.532733i	0.0862709	−	0.0183374i
$845$	6.47214	+	4.70228i	0.222648	+	0.161763i
$846$		0			0
$847$	−9.94427	+	4.70228i	−0.341689	+	0.161572i
$848$	−4.11803	−	7.13264i	−0.141414	−	0.244936i
$849$		0			0
$850$	−4.78154	−	5.31044i	−0.164005	−	0.182146i
$851$	7.30885	+	1.55354i	0.250544	+	0.0532548i
$852$		0			0
$853$	−1.97982	−	0.881473i	−0.0677878	−	0.0301811i	0.372563	−	0.928007i	$-0.378479\pi$
$853$	−1.97982	−	0.881473i	−0.0677878	−	0.0301811i	−0.440351	+	0.897826i	$0.645146\pi$
$854$	−1.01064	−	3.11044i	−0.0345835	−	0.106437i
$855$		0			0
$856$	3.01064	+	2.18736i	0.102902	+	0.0747624i
$857$	16.1180	+	27.9173i	0.550582	+	0.953635i	0.998233	+	0.0594269i	$0.0189273\pi$
$857$	16.1180	+	27.9173i	0.550582	+	0.953635i	−0.447651	+	0.894208i	$0.647739\pi$
$858$		0			0
$859$	3.79180	−	6.56758i	0.129374	−	0.224083i	−0.794060	−	0.607839i	$-0.792036\pi$
$859$	3.79180	−	6.56758i	0.129374	−	0.224083i	0.923434	+	0.383756i	$0.125370\pi$
$860$	18.3847	−	8.18542i	0.626915	−	0.279120i
$861$		0			0
$862$	4.36799	−	4.85115i	0.148774	−	0.165231i
$863$	29.0344	−	21.0948i	0.988344	−	0.718074i	0.0287861	−	0.999586i	$-0.490836\pi$
$863$	29.0344	−	21.0948i	0.988344	−	0.718074i	0.959558	+	0.281512i	$0.0908358\pi$
$864$		0			0
$865$	5.51722	+	16.9803i	0.187591	+	0.577346i
$866$	10.2017	−	2.16843i	0.346666	−	0.0736862i
$867$		0			0
$868$	−4.71885	+	8.17328i	−0.160168	+	0.277419i
$869$	10.8771	−	34.8237i	0.368981	−	1.18131i
$870$		0			0
$871$	−2.14935	+	20.4497i	−0.0728278	+	0.692910i
$872$	5.45898	−	16.8010i	0.184864	−	0.568954i
$873$		0			0
$874$	1.11803	−	0.812299i	0.0378181	−	0.0274764i
$875$	−10.9116	−	4.85817i	−0.368881	−	0.164236i
$876$		0			0
$877$	−26.8025	−	29.7672i	−0.905057	−	1.00517i	−0.999953	−	0.00968002i	$-0.996919\pi$
$877$	−26.8025	−	29.7672i	−0.905057	−	1.00517i	0.0948966	−	0.995487i	$-0.469748\pi$
$878$	12.8091	−	5.70297i	0.432286	−	0.192466i
$879$		0			0
$880$	8.27369	−	14.7158i	0.278906	−	0.496069i
$881$	−30.7984			−1.03762			−0.518812	−	0.854888i	$-0.673625\pi$
$881$	−30.7984			−1.03762			−0.518812	+	0.854888i	$0.673625\pi$
$882$		0			0
$883$	5.85410	−	18.0171i	0.197006	−	0.606323i	−0.802941	−	0.596058i	$-0.796733\pi$
$883$	5.85410	−	18.0171i	0.197006	−	0.606323i	0.999947	−	0.0102644i	$-0.00326732\pi$
$884$	41.2766	−	45.8423i	1.38828	−	1.54184i
$885$		0			0
$886$	0.702573	+	6.68454i	0.0236034	+	0.224571i
$887$	29.8191	+	6.33825i	1.00123	+	0.212818i	0.679232	−	0.733924i	$-0.262313\pi$
$887$	29.8191	+	6.33825i	1.00123	+	0.212818i	0.321996	+	0.946741i	$0.395646\pi$
$888$		0			0
$889$	−0.596670	+	5.67693i	−0.0200117	+	0.190398i
$890$	−2.32624			−0.0779757
$891$		0			0
$892$	28.1459			0.942394
$893$	−0.0973282	+	0.926016i	−0.00325696	+	0.0309879i
$894$		0			0
$895$	27.6527	+	5.87777i	0.924329	+	0.196472i
$896$	−1.05471	−	10.0349i	−0.0352354	−	0.335242i
$897$		0			0
$898$	6.88656	−	7.64829i	0.229807	−	0.255227i
$899$	9.43769	−	29.0462i	0.314765	−	0.968746i
$900$		0			0
$901$	20.5623			0.685030
$902$	4.87723	−	2.23852i	0.162394	−	0.0745346i
$903$		0			0
$904$	6.08936	−	2.71116i	0.202529	−	0.0901717i
$905$	−12.4206	−	13.7945i	−0.412875	−	0.458544i
$906$		0			0
$907$	28.6809	+	12.7695i	0.952333	+	0.424006i	0.823282	−	0.567632i	$-0.192140\pi$
$907$	28.6809	+	12.7695i	0.952333	+	0.424006i	0.129050	+	0.991638i	$0.458807\pi$
$908$	13.7705	−	10.0049i	0.456990	−	0.332023i
$909$		0			0
$910$	−0.809017	+	2.48990i	−0.0268187	+	0.0825393i
$911$	−1.10766	+	10.5387i	−0.0366985	+	0.349163i	0.960729	+	0.277487i	$0.0895014\pi$
$911$	−1.10766	+	10.5387i	−0.0366985	+	0.349163i	−0.997428	+	0.0716760i	$0.977165\pi$
$912$		0			0
$913$	−20.2142	−	14.3369i	−0.668993	−	0.474482i
$914$	4.38854	−	7.60118i	0.145160	−	0.251425i
$915$		0			0
$916$	−15.3649	+	3.26592i	−0.507672	+	0.107909i
$917$	3.95492	+	12.1720i	0.130603	+	0.401954i
$918$		0			0
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	−0.509801	−	0.860292i	$-0.670281\pi$
$919$	4.57295	−	3.32244i	0.150848	−	0.109597i	0.660649	+	0.750695i	$0.270281\pi$
$920$	6.75164	−	7.49846i	0.222595	−	0.247217i
$921$		0			0
$922$	8.46903	−	3.77066i	0.278913	−	0.124180i
$923$	11.2812	−	19.5395i	0.371324	−	0.643151i
$924$		0			0
$925$	−2.10081	−	3.63871i	−0.0690743	−	0.119640i
$926$	−10.8992	−	7.91872i	−0.358170	−	0.260225i
$927$		0			0
$928$	7.68692	+	23.6579i	0.252335	+	0.776609i
$929$	−0.646976	−	0.288052i	−0.0212266	−	0.00945070i	0.396096	−	0.918209i	$-0.370365\pi$
$929$	−0.646976	−	0.288052i	−0.0212266	−	0.00945070i	−0.417322	+	0.908758i	$0.637031\pi$
$930$		0			0
$931$	−5.01263	−	1.06547i	−0.164282	−	0.0349193i
$932$	−13.4660	−	14.9555i	−0.441093	−	0.489884i
$933$		0			0
$934$	−2.84346	−	4.92502i	−0.0930408	−	0.161151i
$935$	21.4894	+	36.2587i	0.702777	+	1.18578i
$936$		0			0
$937$	−8.37132	−	6.08212i	−0.273479	−	0.198694i	0.442589	−	0.896725i	$-0.354060\pi$
$937$	−8.37132	−	6.08212i	−0.273479	−	0.198694i	−0.716068	+	0.698030i	$0.754060\pi$
$938$	−1.81359	+	0.385489i	−0.0592157	+	0.0125867i
$939$		0			0
$940$	0.341861	+	3.25259i	0.0111503	+	0.106088i
$941$	4.33279	+	41.2238i	0.141245	+	1.34386i	0.803825	+	0.594866i	$0.202795\pi$
$941$	4.33279	+	41.2238i	0.141245	+	1.34386i	−0.662580	+	0.748991i	$0.730539\pi$
$942$		0			0
$943$	−17.5521	+	3.73082i	−0.571577	+	0.121492i
$944$	24.4787	+	17.7848i	0.796714	+	0.578847i
$945$		0			0
$946$	−8.29180	+	1.86162i	−0.269590	+	0.0605266i
$947$	20.6976	+	35.8492i	0.672580	+	1.16494i	0.977170	+	0.212460i	$0.0681474\pi$
$947$	20.6976	+	35.8492i	0.672580	+	1.16494i	−0.304589	+	0.952484i	$0.598519\pi$
$948$		0			0
$949$	−21.8488	−	24.2655i	−0.709241	−	0.787692i
$950$	−0.760106	−	0.161566i	−0.0246611	−	0.00524188i
$951$		0			0
$952$	10.5627	+	4.70281i	0.342339	+	0.152419i
$953$	−13.1803	−	40.5649i	−0.426953	−	1.31403i	−0.901112	−	0.433587i	$-0.857248\pi$
$953$	−13.1803	−	40.5649i	−0.426953	−	1.31403i	0.474159	−	0.880439i	$-0.342752\pi$
$954$		0			0
$955$	30.3435	+	22.0458i	0.981891	+	0.713386i
$956$	−2.42705	−	4.20378i	−0.0784964	−	0.135960i
$957$		0			0
$958$	−5.84752	+	10.1282i	−0.188925	+	0.327228i
$959$	13.0053	−	5.79033i	0.419963	−	0.186980i
$960$		0			0
$961$	−3.40599	+	3.78273i	−0.109871	+	0.122024i
$962$	−2.30902	+	1.67760i	−0.0744457	+	0.0540880i
$963$		0			0
$964$	−12.4377	−	38.2793i	−0.400591	−	1.23289i
$965$	−15.5959	+	3.31500i	−0.502048	+	0.106714i
$966$		0			0
$967$	10.4615	−	18.1198i	0.336419	−	0.582695i	−0.647337	−	0.762204i	$-0.724118\pi$
$967$	10.4615	−	18.1198i	0.336419	−	0.582695i	0.983756	+	0.179509i	$0.0574509\pi$
$968$	−10.5581	+	12.2783i	−0.339350	+	0.394639i
$969$		0			0
$970$	0.0740275	−	0.704324i	0.00237688	−	0.0226145i
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	−0.494389	−	0.869240i	$-0.664608\pi$
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	0.910896	−	0.412635i	$-0.135392\pi$
$972$		0			0
$973$	−4.50000	+	3.26944i	−0.144263	+	0.104813i
$974$	0.247123	+	0.110026i	0.00791833	+	0.00352547i
$975$		0			0
$976$	18.0238	+	20.0175i	0.576928	+	0.640743i
$977$	−44.3953	+	19.7661i	−1.42033	+	0.632373i	−0.966020	−	0.258469i	$-0.916782\pi$
$977$	−44.3953	+	19.7661i	−1.42033	+	0.632373i	−0.454313	+	0.890842i	$0.650115\pi$
$978$		0			0
$979$	−12.2396	−	2.45596i	−0.391179	−	0.0784927i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	3.43363	−	10.5676i	0.109571	−	0.337226i
$983$	29.3672	−	32.6155i	0.936667	−	1.04027i	−0.0624409	−	0.998049i	$-0.519888\pi$
$983$	29.3672	−	32.6155i	0.936667	−	1.04027i	0.999108	−	0.0422256i	$-0.0134448\pi$
$984$		0			0
$985$	2.71191	+	25.8021i	0.0864088	+	0.822125i
$986$	−17.6067	−	3.74241i	−0.560710	−	0.119183i
$987$		0			0
$988$	0.701198	−	6.67146i	0.0223081	−	0.212247i
$989$	28.4164			0.903589
$990$		0			0
$991$	−38.7426			−1.23070			−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426			−1.23070			−0.615350	+	0.788254i	$0.710985\pi$
$992$	−2.20590	+	20.9877i	−0.0700373	+	0.666361i
$993$		0			0
$994$	1.98998	+	0.422984i	0.0631185	+	0.0134162i
$995$	−1.13456	−	10.7946i	−0.0359681	−	0.342213i
$996$		0			0
$997$	−30.6451	+	34.0348i	−0.970540	+	1.07789i	0.0263945	+	0.999652i	$0.491597\pi$
$997$	−30.6451	+	34.0348i	−0.970540	+	1.07789i	−0.996934	+	0.0782421i	$0.975069\pi$
$998$	−2.93363	+	9.02878i	−0.0928624	+	0.285801i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.b.433.1		8
3.2	odd	2		891.2.n.c.433.1		8
9.2	odd	6		891.2.n.c.136.1		8
9.4	even	3		99.2.f.a.37.1		4
9.5	odd	6		33.2.e.b.4.1	✓	4
9.7	even	3	inner	891.2.n.b.136.1		8
11.3	even	5	inner	891.2.n.b.190.1		8
33.14	odd	10		891.2.n.c.190.1		8
36.23	even	6		528.2.y.b.433.1		4
45.14	odd	6		825.2.n.c.301.1		4
45.23	even	12		825.2.bx.d.499.2		8
45.32	even	12		825.2.bx.d.499.1		8
99.5	odd	30		363.2.a.d.1.2		2
99.14	odd	30		33.2.e.b.25.1	yes	4
99.25	even	15	inner	891.2.n.b.784.1		8
99.32	even	6		363.2.e.f.202.1		4
99.41	even	30		363.2.e.f.124.1		4
99.47	odd	30		891.2.n.c.784.1		8
99.49	even	15		1089.2.a.t.1.1		2
99.50	even	30		363.2.a.i.1.1		2
99.58	even	15		99.2.f.a.91.1		4
99.59	odd	30		363.2.e.k.130.1		4
99.68	even	30		363.2.e.b.148.1		4
99.86	odd	30		363.2.e.k.148.1		4
99.94	odd	30		1089.2.a.l.1.2		2
99.95	even	30		363.2.e.b.130.1		4
396.203	even	30		5808.2.a.cj.1.2		2
396.311	even	30		528.2.y.b.289.1		4
396.347	odd	30		5808.2.a.ci.1.2		2
495.14	odd	30		825.2.n.c.751.1		4
495.104	odd	30		9075.2.a.cb.1.1		2
495.113	even	60		825.2.bx.d.124.1		8
495.149	even	30		9075.2.a.u.1.2		2
495.212	even	60		825.2.bx.d.124.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	9.5	odd	6
33.2.e.b.25.1	yes	4	99.14	odd	30
99.2.f.a.37.1		4	9.4	even	3
99.2.f.a.91.1		4	99.58	even	15
363.2.a.d.1.2		2	99.5	odd	30
363.2.a.i.1.1		2	99.50	even	30
363.2.e.b.130.1		4	99.95	even	30
363.2.e.b.148.1		4	99.68	even	30
363.2.e.f.124.1		4	99.41	even	30
363.2.e.f.202.1		4	99.32	even	6
363.2.e.k.130.1		4	99.59	odd	30
363.2.e.k.148.1		4	99.86	odd	30
528.2.y.b.289.1		4	396.311	even	30
528.2.y.b.433.1		4	36.23	even	6
825.2.n.c.301.1		4	45.14	odd	6
825.2.n.c.751.1		4	495.14	odd	30
825.2.bx.d.124.1		8	495.113	even	60
825.2.bx.d.124.2		8	495.212	even	60
825.2.bx.d.499.1		8	45.32	even	12
825.2.bx.d.499.2		8	45.23	even	12
891.2.n.b.136.1		8	9.7	even	3	inner
891.2.n.b.190.1		8	11.3	even	5	inner
891.2.n.b.433.1		8	1.1	even	1	trivial
891.2.n.b.784.1		8	99.25	even	15	inner
891.2.n.c.136.1		8	9.2	odd	6
891.2.n.c.190.1		8	33.14	odd	10
891.2.n.c.433.1		8	3.2	odd	2
891.2.n.c.784.1		8	99.47	odd	30
1089.2.a.l.1.2		2	99.94	odd	30
1089.2.a.t.1.1		2	99.49	even	15
5808.2.a.ci.1.2		2	396.347	odd	30
5808.2.a.cj.1.2		2	396.203	even	30
9075.2.a.u.1.2		2	495.149	even	30
9075.2.a.cb.1.1		2	495.104	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0399263 + 0.379874i) q^{2} +(1.81359 + 0.385489i) q^{4} +(0.169131 + 1.60917i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} +O(q^{10})\)	\(q+(-0.0399263 + 0.379874i) q^{2} +(1.81359 + 0.385489i) q^{4} +(0.169131 + 1.60917i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} -0.618034 q^{10} +(-3.25181 - 0.652498i) q^{11} +(-3.86984 + 1.72296i) q^{13} +(-0.255585 - 0.283856i) q^{14} +(2.87392 + 1.27955i) q^{16} +(-6.35410 + 4.61653i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(-0.313585 + 2.98357i) q^{20} +(0.377699 - 1.20922i) q^{22} +(-2.11803 + 3.66854i) q^{23} +(2.32991 - 0.495239i) q^{25} +(-0.500000 - 1.53884i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(4.01478 - 4.45887i) q^{29} +(4.65010 - 2.07036i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-1.30902 - 0.951057i) q^{35} +(-0.545085 - 1.67760i) q^{37} +(-0.298033 - 0.132693i) q^{38} +(-2.32991 - 0.495239i) q^{40} +(2.83448 + 3.14801i) q^{41} +(-3.35410 - 5.80948i) q^{43} +(-5.64590 - 2.43690i) q^{44} +(-1.30902 - 0.951057i) q^{46} +(1.06635 - 0.226659i) q^{47} +(0.627171 + 5.96713i) q^{49} +(0.0951031 + 0.904846i) q^{50} +(-7.68247 + 1.63296i) q^{52} +(-2.11803 - 1.53884i) q^{53} +(0.500000 - 5.34307i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.53351 + 1.70314i) q^{58} +(9.40786 + 1.99970i) q^{59} +(7.82206 + 3.48260i) q^{61} +(0.600813 + 1.84911i) q^{62} +(3.80902 + 2.76741i) q^{64} +(-3.42705 - 5.93583i) q^{65} +(2.42705 - 4.20378i) q^{67} +(-13.3033 + 5.92302i) q^{68} +(0.413545 - 0.459289i) q^{70} +(-4.30902 + 3.13068i) q^{71} +(2.38197 + 7.33094i) q^{73} +(0.659039 - 0.140083i) q^{74} +(-0.791796 + 1.37143i) q^{76} +(2.66078 - 1.97996i) q^{77} +(-1.14981 + 10.9397i) q^{79} +(-1.57295 + 4.84104i) q^{80} +(-1.30902 + 0.951057i) q^{82} +(6.82614 + 3.03919i) q^{83} +(-8.50345 - 9.44404i) q^{85} +(2.34078 - 1.04218i) q^{86} +(2.39285 - 4.25597i) q^{88} +3.76393 q^{89} +(1.30902 - 4.02874i) q^{91} +(-5.25542 + 5.83674i) q^{92} +(0.0435265 + 0.414127i) q^{94} +(-1.35177 - 0.287327i) q^{95} +(-0.119779 + 1.13962i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8}+O(q^{10}) \) 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8	\( 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8} + 4 q^{10} - 11 q^{11} - 7 q^{13} - 4 q^{14} - q^{16} - 24 q^{17} - 20 q^{19} + 3 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 12 q^{28} + 6 q^{29} + 12 q^{31} - 30 q^{32} - 12 q^{34} - 6 q^{35} + 18 q^{37} - 10 q^{38} + 6 q^{40} - 3 q^{41} - 72 q^{44} - 6 q^{46} + 17 q^{47} - 6 q^{49} + 6 q^{50} - 3 q^{52} - 8 q^{53} + 4 q^{55} + 12 q^{56} + 24 q^{58} - 6 q^{59} + 21 q^{61} + 54 q^{62} + 26 q^{64} - 14 q^{65} + 6 q^{67} - 27 q^{68} - 3 q^{70} - 30 q^{71} + 28 q^{73} - 26 q^{74} - 60 q^{76} + q^{77} + 11 q^{79} - 26 q^{80} - 6 q^{82} + 13 q^{83} + 9 q^{85} + 15 q^{86} + 37 q^{88} + 48 q^{89} + 6 q^{91} + 3 q^{92} - 17 q^{94} + 5 q^{95} - 3 q^{97} - 72 q^{98}+O(q^{100}) \) 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8 + 4 * q^10 - 11 * q^11 - 7 * q^13 - 4 * q^14 - q^16 - 24 * q^17 - 20 * q^19 + 3 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 6 * q^29 + 12 * q^31 - 30 * q^32 - 12 * q^34 - 6 * q^35 + 18 * q^37 - 10 * q^38 + 6 * q^40 - 3 * q^41 - 72 * q^44 - 6 * q^46 + 17 * q^47 - 6 * q^49 + 6 * q^50 - 3 * q^52 - 8 * q^53 + 4 * q^55 + 12 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 54 * q^62 + 26 * q^64 - 14 * q^65 + 6 * q^67 - 27 * q^68 - 3 * q^70 - 30 * q^71 + 28 * q^73 - 26 * q^74 - 60 * q^76 + q^77 + 11 * q^79 - 26 * q^80 - 6 * q^82 + 13 * q^83 + 9 * q^85 + 15 * q^86 + 37 * q^88 + 48 * q^89 + 6 * q^91 + 3 * q^92 - 17 * q^94 + 5 * q^95 - 3 * q^97 - 72 * q^98

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