LMFDB - Embedded newform 243.2.e.a.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			190.1
Root			$0.500000 - 1.00210i$ of defining polynomial
Character	$\chi$	$=$	243.190
Dual form			243.2.e.a.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25679 - 0.821403i) q^{2} +(2.88629 + 2.42189i) q^{4} +(-0.0161638 + 0.0916693i) q^{5} +(-0.444200 + 0.372728i) q^{7} +(-2.12277 - 3.67675i) q^{8} +O(q^{10})$	\(q+(-2.25679 - 0.821403i) q^{2} +(2.88629 + 2.42189i) q^{4} +(-0.0161638 + 0.0916693i) q^{5} +(-0.444200 + 0.372728i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(0.537108 + 3.04609i) q^{11} +(-3.94834 + 1.43708i) q^{13} +(1.30862 - 0.476300i) q^{14} +(0.462014 + 2.62021i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(-0.268666 + 0.225437i) q^{20} +(1.28993 - 7.31556i) q^{22} +(3.41105 + 2.86221i) q^{23} +(4.69032 + 1.70714i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(6.01357 + 2.18876i) q^{29} +(1.26972 + 1.06542i) q^{31} +(-0.364882 + 2.06935i) q^{32} +(3.66291 - 3.07355i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-1.60368 - 9.09494i) q^{38} +(0.371357 - 0.135163i) q^{40} +(-1.03005 + 0.374907i) q^{41} +(-1.19837 - 6.79628i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-2.75255 + 2.30966i) q^{47} +(-1.15715 + 6.56252i) q^{49} +(-9.18280 - 7.70529i) q^{50} +(-14.8765 - 5.41460i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(2.31336 + 0.841995i) q^{56} +(-11.7735 - 9.87913i) q^{58} +(1.78591 - 10.1284i) q^{59} +(-10.1090 + 8.48243i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(-0.0679158 - 0.385170i) q^{65} +(8.30434 - 3.02253i) q^{67} +(-7.04920 + 2.56570i) q^{68} +(0.0225098 + 0.127659i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(7.41436 - 6.22139i) q^{74} +(-2.51594 + 14.2686i) q^{76} +(-1.37395 - 1.15288i) q^{77} +(6.77330 + 2.46528i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-14.0018 - 5.09625i) q^{83} +(-0.141969 - 0.119126i) q^{85} +(-2.87802 + 16.3221i) q^{86} +(10.0596 - 8.44098i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(2.91334 + 16.5224i) q^{92} +(8.10907 - 2.95146i) q^{94} +(-0.336358 + 0.122424i) q^{95} +(0.919560 + 5.21508i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−2.25679	−	0.821403i	−1.59579	−	0.580820i	−0.617229	−	0.786784i	$-0.711745\pi$
$2$	−2.25679	−	0.821403i	−1.59579	−	0.580820i	−0.978560	+	0.205964i	$0.933967\pi$
$3$		0			0
$3$		0			0
$4$	2.88629	+	2.42189i	1.44315	+	1.21094i
$5$	−0.0161638	+	0.0916693i	−0.00722866	+	0.0409957i	−0.988209	−	0.153113i	$-0.951070\pi$
$5$	−0.0161638	+	0.0916693i	−0.00722866	+	0.0409957i	0.980980	+	0.194108i	$0.0621814\pi$
$6$		0			0
$7$	−0.444200	+	0.372728i	−0.167892	+	0.140878i	−0.722862	−	0.690992i	$-0.757174\pi$
$7$	−0.444200	+	0.372728i	−0.167892	+	0.140878i	0.554971	+	0.831870i	$0.312729\pi$
$8$	−2.12277	−	3.67675i	−0.750514	−	1.29993i
$9$		0			0
$10$	0.111776	−	0.193601i	0.0353465	−	0.0612220i
$11$	0.537108	+	3.04609i	0.161944	+	0.918431i	0.952159	+	0.305602i	$0.0988577\pi$
$11$	0.537108	+	3.04609i	0.161944	+	0.918431i	−0.790215	+	0.612830i	$0.790031\pi$
$12$		0			0
$13$	−3.94834	+	1.43708i	−1.09507	+	0.398574i	−0.825497	−	0.564406i	$-0.809105\pi$
$13$	−3.94834	+	1.43708i	−1.09507	+	0.398574i	−0.269574	+	0.962980i	$0.586883\pi$
$14$	1.30862	−	0.476300i	0.349744	−	0.127296i
$15$		0			0
$16$	0.462014	+	2.62021i	0.115503	+	0.655052i
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	−0.961125	−	0.276112i	$-0.910954\pi$
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	0.719683	+	0.694303i	$0.244287\pi$
$18$		0			0
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	0.997771	−	0.0667249i	$-0.0212550\pi$
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	−0.556671	+	0.830733i	$0.687922\pi$
$20$	−0.268666	+	0.225437i	−0.0600755	+	0.0504093i
$21$		0			0
$22$	1.28993	−	7.31556i	0.275014	−	1.55968i
$23$	3.41105	+	2.86221i	0.711254	+	0.596813i	0.924951	−	0.380087i	$-0.124106\pi$
$23$	3.41105	+	2.86221i	0.711254	+	0.596813i	−0.213697	+	0.976900i	$0.568550\pi$
$24$		0			0
$25$	4.69032	+	1.70714i	0.938064	+	0.341427i
$26$	10.0910			1.97900
$27$		0			0
$28$	−2.18479			−0.412887
$29$	6.01357	+	2.18876i	1.11669	+	0.406443i	0.833444	−	0.552604i	$-0.186366\pi$
$29$	6.01357	+	2.18876i	1.11669	+	0.406443i	0.283248	+	0.959047i	$0.408588\pi$
$30$		0			0
$31$	1.26972	+	1.06542i	0.228048	+	0.191355i	0.749651	−	0.661833i	$-0.230221\pi$
$31$	1.26972	+	1.06542i	0.228048	+	0.191355i	−0.521603	+	0.853188i	$0.674666\pi$
$32$	−0.364882	+	2.06935i	−0.0645026	+	0.365812i
$33$		0			0
$34$	3.66291	−	3.07355i	0.628185	−	0.527109i
$35$	−0.0269877	−	0.0467441i	−0.00456176	−	0.00790120i
$36$		0			0
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	−0.982761	−	0.184878i	$-0.940811\pi$
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	0.651490	+	0.758657i	$0.274144\pi$
$38$	−1.60368	−	9.09494i	−0.260152	−	1.47539i
$39$		0			0
$40$	0.371357	−	0.135163i	0.0587167	−	0.0213711i
$41$	−1.03005	+	0.374907i	−0.160867	+	0.0585507i	−0.421198	−	0.906969i	$-0.638390\pi$
$41$	−1.03005	+	0.374907i	−0.160867	+	0.0585507i	0.260332	+	0.965519i	$0.416168\pi$
$42$		0			0
$43$	−1.19837	−	6.79628i	−0.182749	−	1.03642i	−0.928813	−	0.370548i	$-0.879170\pi$
$43$	−1.19837	−	6.79628i	−0.182749	−	1.03642i	0.746064	−	0.665874i	$-0.231941\pi$
$44$	−5.82704	+	10.0927i	−0.878459	+	1.52154i
$45$		0			0
$46$	−5.34699	−	9.26126i	−0.788370	−	1.36550i
$47$	−2.75255	+	2.30966i	−0.401500	+	0.336899i	−0.821073	−	0.570823i	$-0.806624\pi$
$47$	−2.75255	+	2.30966i	−0.401500	+	0.336899i	0.419573	+	0.907722i	$0.362180\pi$
$48$		0			0
$49$	−1.15715	+	6.56252i	−0.165307	+	0.937503i
$50$	−9.18280	−	7.70529i	−1.29864	−	1.08969i
$51$		0			0
$52$	−14.8765	−	5.41460i	−2.06300	−	0.750870i
$53$	−5.40034			−0.741793			−0.370897	−	0.928674i	$-0.620950\pi$
$53$	−5.40034			−0.741793			−0.370897	+	0.928674i	$0.620950\pi$
$54$		0			0
$55$	−0.287915			−0.0388224
$56$	2.31336	+	0.841995i	0.309136	+	0.112516i
$57$		0			0
$58$	−11.7735	−	9.87913i	−1.54593	−	1.29719i
$59$	1.78591	−	10.1284i	0.232506	−	1.31861i	−0.615297	−	0.788295i	$-0.710964\pi$
$59$	1.78591	−	10.1284i	0.232506	−	1.31861i	0.847803	−	0.530311i	$-0.177925\pi$
$60$		0			0
$61$	−10.1090	+	8.48243i	−1.29432	+	1.08606i	−0.303224	+	0.952919i	$0.598063\pi$
$61$	−10.1090	+	8.48243i	−1.29432	+	1.08606i	−0.991097	+	0.133145i	$0.957492\pi$
$62$	−1.99034	−	3.44738i	−0.252774	−	0.437817i
$63$		0			0
$64$	5.18386	−	8.97871i	0.647982	−	1.12234i
$65$	−0.0679158	−	0.385170i	−0.00842392	−	0.0477744i
$66$		0			0
$67$	8.30434	−	3.02253i	1.01454	−	0.369261i	0.219363	−	0.975643i	$-0.429602\pi$
$67$	8.30434	−	3.02253i	1.01454	−	0.369261i	0.795173	+	0.606382i	$0.207380\pi$
$68$	−7.04920	+	2.56570i	−0.854842	+	0.311137i
$69$		0			0
$70$	0.0225098	+	0.127659i	0.00269043	+	0.0152582i
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	−0.830054	−	0.557683i	$-0.811691\pi$
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	0.897994	+	0.440007i	$0.145024\pi$
$72$		0			0
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	0.860249	−	0.509874i	$-0.170308\pi$
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	−0.871688	+	0.490061i	$0.836975\pi$
$74$	7.41436	−	6.22139i	0.861902	−	0.723221i
$75$		0			0
$76$	−2.51594	+	14.2686i	−0.288598	+	1.63672i
$77$	−1.37395	−	1.15288i	−0.156576	−	0.131383i
$78$		0			0
$79$	6.77330	+	2.46528i	0.762056	+	0.277366i	0.693670	−	0.720293i	$-0.255993\pi$
$79$	6.77330	+	2.46528i	0.762056	+	0.277366i	0.0683861	+	0.997659i	$0.478215\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	−14.0018	−	5.09625i	−1.53690	−	0.559386i	−0.571602	−	0.820531i	$-0.693678\pi$
$83$	−14.0018	−	5.09625i	−1.53690	−	0.559386i	−0.965300	+	0.261145i	$0.915900\pi$
$84$		0			0
$85$	−0.141969	−	0.119126i	−0.0153987	−	0.0129211i
$86$	−2.87802	+	16.3221i	−0.310345	+	1.76006i
$87$		0			0
$88$	10.0596	−	8.44098i	1.07235	−	0.899812i
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	0.821929	−	0.569590i	$-0.192898\pi$
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	−0.904244	+	0.427016i	$0.859565\pi$
$90$		0			0
$91$	1.21821	−	2.11000i	0.127703	−	0.221189i
$92$	2.91334	+	16.5224i	0.303737	+	1.72258i
$93$		0			0
$94$	8.10907	−	2.95146i	0.836387	−	0.304420i
$95$	−0.336358	+	0.122424i	−0.0345096	+	0.0125605i
$96$		0			0
$97$	0.919560	+	5.21508i	0.0933672	+	0.529511i	0.995235	+	0.0975004i	$0.0310847\pi$
$97$	0.919560	+	5.21508i	0.0933672	+	0.529511i	−0.901868	+	0.432011i	$0.857804\pi$
$98$	8.00191	−	13.8597i	0.808315	−	1.40004i
$99$		0			0
$100$	9.40314	+	16.2867i	0.940314	+	1.62867i
$101$	5.56836	−	4.67241i	0.554073	−	0.464922i	−0.322245	−	0.946656i	$-0.604437\pi$
$101$	5.56836	−	4.67241i	0.554073	−	0.464922i	0.876317	+	0.481734i	$0.159993\pi$
$102$		0			0
$103$	1.11159	−	6.30412i	0.109528	−	0.621164i	−0.879787	−	0.475368i	$-0.842315\pi$
$103$	1.11159	−	6.30412i	0.109528	−	0.621164i	0.989315	−	0.145795i	$-0.0465741\pi$
$104$	13.6652	+	11.4665i	1.33998	+	1.12438i
$105$		0			0
$106$	12.1874	+	4.43585i	1.18374	+	0.430848i
$107$	5.54365			0.535925			0.267963	−	0.963429i	$-0.413650\pi$
$107$	5.54365			0.535925			0.267963	+	0.963429i	$0.413650\pi$
$108$		0			0
$109$	−6.23137			−0.596857			−0.298428	−	0.954432i	$-0.596462\pi$
$109$	−6.23137			−0.596857			−0.298428	+	0.954432i	$0.596462\pi$
$110$	0.649762	+	0.236494i	0.0619524	+	0.0225488i
$111$		0			0
$112$	−1.18185	−	0.991691i	−0.111674	−	0.0937060i
$113$	2.05669	−	11.6640i	0.193477	−	1.09726i	−0.721095	−	0.692836i	$-0.756361\pi$
$113$	2.05669	−	11.6640i	0.193477	−	1.09726i	0.914571	−	0.404424i	$-0.132528\pi$
$114$		0			0
$115$	−0.317513	+	0.266425i	−0.0296082	+	0.0248442i
$116$	12.0560	+	20.8816i	1.11937	+	1.93881i
$117$		0			0
$118$	−12.3499	+	21.3907i	−1.13690	+	1.96917i
$119$	−0.200476	−	1.13696i	−0.0183776	−	0.104225i
$120$		0			0
$121$	1.34642	−	0.490058i	0.122402	−	0.0445508i
$122$	29.7813	−	10.8395i	2.69627	−	0.981362i
$123$		0			0
$124$	1.08445	+	6.15022i	0.0973865	+	0.552306i
$125$	−0.465014	+	0.805428i	−0.0415921	+	0.0720396i
$126$		0			0
$127$	−5.76469	−	9.98473i	−0.511533	−	0.886002i	−0.999911	−	0.0133693i	$-0.995744\pi$
$127$	−5.76469	−	9.98473i	−0.511533	−	0.886002i	0.488377	−	0.872633i	$-0.337589\pi$
$128$	−15.8547	+	13.3036i	−1.40137	+	1.17589i
$129$		0			0
$130$	−0.163108	+	0.925032i	−0.0143055	+	0.0811307i
$131$	6.90342	+	5.79266i	0.603155	+	0.506107i	0.892458	−	0.451131i	$-0.148979\pi$
$131$	6.90342	+	5.79266i	0.603155	+	0.506107i	−0.289303	+	0.957237i	$0.593424\pi$
$132$		0			0
$133$	−2.09534	−	0.762641i	−0.181689	−	0.0661293i
$134$	−21.2238			−1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	10.8255	+	3.94015i	0.924883	+	0.336630i	0.760179	−	0.649713i	$-0.225111\pi$
$137$	10.8255	+	3.94015i	0.924883	+	0.336630i	0.164703	+	0.986343i	$0.447333\pi$
$138$		0			0
$139$	1.30521	+	1.09520i	0.110707	+	0.0928940i	0.696461	−	0.717595i	$-0.254757\pi$
$139$	1.30521	+	1.09520i	0.110707	+	0.0928940i	−0.585754	+	0.810489i	$0.699202\pi$
$140$	0.0353145	−	0.200278i	0.00298462	−	0.0169266i
$141$		0			0
$142$	−2.10641	+	1.76749i	−0.176766	+	0.148325i
$143$	−6.49816	−	11.2551i	−0.543403	−	0.941202i
$144$		0			0
$145$	−0.297844	+	0.515881i	−0.0247346	+	0.0428416i
$146$	0.0815191	+	0.462318i	0.00674657	+	0.0382617i
$147$		0			0
$148$	−14.2688	+	5.19341i	−1.17289	+	0.426896i
$149$	−20.3469	+	7.40568i	−1.66689	+	0.606697i	−0.991423	−	0.130696i	$-0.958279\pi$
$149$	−20.3469	+	7.40568i	−1.66689	+	0.606697i	−0.675464	+	0.737393i	$0.736057\pi$
$150$		0			0
$151$	−0.823357	−	4.66949i	−0.0670038	−	0.379998i	−0.999808	−	0.0196130i	$-0.993757\pi$
$151$	−0.823357	−	4.66949i	−0.0670038	−	0.379998i	0.932804	−	0.360385i	$-0.117355\pi$
$152$	8.16296	−	14.1387i	0.662104	−	1.14680i
$153$		0			0
$154$	2.15373	+	3.73036i	0.173552	+	0.300601i
$155$	−0.118190	+	0.0991730i	−0.00949323	+	0.00796576i
$156$		0			0
$157$	−0.0363282	+	0.206027i	−0.00289931	+	0.0164428i	−0.986223	−	0.165421i	$-0.947102\pi$
$157$	−0.0363282	+	0.206027i	−0.00289931	+	0.0164428i	0.983324	+	0.181864i	$0.0582129\pi$
$158$	−13.2609	−	11.1272i	−1.05498	−	0.885234i
$159$		0			0
$160$	−0.183798	−	0.0668969i	−0.0145305	−	0.00528866i
$161$	−2.58202			−0.203491
$162$		0			0
$163$	5.62384			0.440493			0.220247	−	0.975444i	$-0.429314\pi$
$163$	5.62384			0.440493			0.220247	+	0.975444i	$0.429314\pi$
$164$	−3.88100	−	1.41257i	−0.303056	−	0.110303i
$165$		0			0
$166$	27.4131	+	23.0023i	2.12767	+	1.78532i
$167$	−2.89654	+	16.4271i	−0.224141	+	1.27117i	0.640180	+	0.768225i	$0.278860\pi$
$167$	−2.89654	+	16.4271i	−0.224141	+	1.27117i	−0.864321	+	0.502941i	$0.832251\pi$
$168$		0			0
$169$	3.56560	−	2.99189i	0.274277	−	0.230146i
$170$	0.222544	+	0.385457i	0.0170683	+	0.0295632i
$171$		0			0
$172$	13.0010	−	22.5183i	0.991315	−	1.71701i
$173$	−3.29969	−	18.7135i	−0.250871	−	1.42276i	−0.806454	−	0.591297i	$-0.798616\pi$
$173$	−3.29969	−	18.7135i	−0.250871	−	1.42276i	0.555583	−	0.831461i	$-0.312495\pi$
$174$		0			0
$175$	−2.71974	+	0.989903i	−0.205593	+	0.0748296i
$176$	−7.73325	+	2.81467i	−0.582916	+	0.212164i
$177$		0			0
$178$	0.647711	+	3.67335i	0.0485480	+	0.275329i
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	−0.385035	−	0.922902i	$-0.625811\pi$
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	0.991774	−	0.128001i	$-0.0408560\pi$
$180$		0			0
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$182$	−4.48241	+	3.76118i	−0.332258	+	0.278798i
$183$		0			0
$184$	3.28276	−	18.6174i	0.242008	−	1.37250i
$185$	−0.287370	−	0.241132i	−0.0211279	−	0.0177284i
$186$		0			0
$187$	−5.78690	−	2.10626i	−0.423180	−	0.154025i
$188$	−13.5384			−0.987388
$189$		0			0
$190$	0.859649			0.0623655
$191$	−2.11790	−	0.770851i	−0.153246	−	0.0557768i	0.264258	−	0.964452i	$-0.414873\pi$
$191$	−2.11790	−	0.770851i	−0.153246	−	0.0557768i	−0.417504	+	0.908675i	$0.637095\pi$
$192$		0			0
$193$	−0.674328	−	0.565829i	−0.0485392	−	0.0407292i	0.618195	−	0.786025i	$-0.287864\pi$
$193$	−0.674328	−	0.565829i	−0.0485392	−	0.0407292i	−0.666735	+	0.745295i	$0.732309\pi$
$194$	2.20843	−	12.5247i	0.158556	−	0.899218i
$195$		0			0
$196$	−19.2335	+	16.1389i	−1.37382	+	1.15278i
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	0.960067	+	0.279771i	$0.0902586\pi$
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	−0.237744	+	0.971328i	$0.576408\pi$
$198$		0			0
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	−0.303054	−	0.952973i	$-0.598006\pi$
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	0.976826	−	0.214034i	$-0.0686603\pi$
$200$	−3.67977	−	20.8690i	−0.260199	−	1.47566i
$201$		0			0
$202$	−16.4045	+	5.97076i	−1.15422	+	0.420101i
$203$	−3.48704	+	1.26918i	−0.244742	+	0.0890788i
$204$		0			0
$205$	−0.0177180	−	0.100484i	−0.00123748	−	0.00701809i
$206$	−7.68684	+	13.3140i	−0.535567	+	0.927630i
$207$		0			0
$208$	−5.58963	−	9.68152i	−0.387571	−	0.671293i
$209$	−9.11150	+	7.64545i	−0.630255	+	0.528847i
$210$		0			0
$211$	2.81033	−	15.9382i	0.193471	−	1.09723i	−0.721108	−	0.692823i	$-0.756367\pi$
$211$	2.81033	−	15.9382i	0.193471	−	1.09723i	0.914579	−	0.404408i	$-0.132522\pi$
$212$	−15.5869	−	13.0790i	−1.07052	−	0.898269i
$213$		0			0
$214$	−12.5108	−	4.55357i	−0.855223	−	0.311276i
$215$	0.642380			0.0438100
$216$		0			0
$217$	−0.961120			−0.0652451
$218$	14.0629	+	5.11846i	0.952458	+	0.346666i
$219$		0			0
$220$	−0.831006	−	0.697297i	−0.0560264	−	0.0470117i
$221$	1.45267	−	8.23850i	0.0977171	−	0.554181i
$222$		0			0
$223$	16.4372	−	13.7925i	1.10072	−	0.923613i	0.103246	−	0.994656i	$-0.467077\pi$
$223$	16.4372	−	13.7925i	1.10072	−	0.923613i	0.997473	+	0.0710428i	$0.0226327\pi$
$224$	−0.609223	−	1.05520i	−0.0407054	−	0.0705038i
$225$		0			0
$226$	−14.2224	+	24.6339i	−0.946058	+	1.63862i
$227$	3.31915	+	18.8239i	0.220300	+	1.24938i	0.871469	+	0.490451i	$0.163168\pi$
$227$	3.31915	+	18.8239i	0.220300	+	1.24938i	−0.651169	+	0.758933i	$0.725721\pi$
$228$		0			0
$229$	−21.1150	+	7.68525i	−1.39532	+	0.507855i	−0.926786	−	0.375589i	$-0.877440\pi$
$229$	−21.1150	+	7.68525i	−1.39532	+	0.507855i	−0.468535	+	0.883445i	$0.655218\pi$
$230$	0.935400	−	0.340458i	0.0616784	−	0.0224491i
$231$		0			0
$232$	−4.71792	−	26.7567i	−0.309747	−	1.75666i
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	0.416398	+	0.909182i	$0.363292\pi$
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	−0.995574	+	0.0939796i	$0.970041\pi$
$234$		0			0
$235$	−0.167233	−	0.289657i	−0.0109091	−	0.0188951i
$236$	29.6845	−	24.9083i	1.93230	−	1.62139i
$237$		0			0
$238$	−0.481468	+	2.73054i	−0.0312089	+	0.176995i
$239$	11.8126	+	9.91199i	0.764097	+	0.641153i	0.939190	−	0.343399i	$-0.111578\pi$
$239$	11.8126	+	9.91199i	0.764097	+	0.641153i	−0.175093	+	0.984552i	$0.556023\pi$
$240$		0			0
$241$	−12.3583	−	4.49806i	−0.796069	−	0.289746i	−0.0882127	−	0.996102i	$-0.528116\pi$
$241$	−12.3583	−	4.49806i	−0.796069	−	0.289746i	−0.707857	+	0.706356i	$0.750338\pi$
$242$	−3.44113			−0.221204
$243$		0			0
$244$	−49.7209			−3.18305
$245$	−0.582878	−	0.212150i	−0.0372387	−	0.0135538i
$246$		0			0
$247$	−12.3773	−	10.3858i	−0.787550	−	0.660833i
$248$	1.22196	−	6.93009i	0.0775946	−	0.440061i
$249$		0			0
$250$	1.71102	−	1.43571i	0.108214	−	0.0908025i
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	0.998297	+	0.0583292i	$0.0185773\pi$
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	−0.448634	+	0.893716i	$0.648089\pi$
$252$		0			0
$253$	−6.88646	+	11.9277i	−0.432948	+	0.749889i
$254$	4.80818	+	27.2685i	0.301692	+	1.71098i
$255$		0			0
$256$	27.2233	−	9.90846i	1.70145	−	0.619279i
$257$	10.5129	−	3.82638i	0.655776	−	0.238683i	0.00736433	−	0.999973i	$-0.497656\pi$
$257$	10.5129	−	3.82638i	0.655776	−	0.238683i	0.648412	+	0.761290i	$0.275434\pi$
$258$		0			0
$259$	−0.405798	−	2.30139i	−0.0252150	−	0.143002i
$260$	0.736812	−	1.27620i	0.0456952	−	0.0791463i
$261$		0			0
$262$	−10.8214	−	18.7433i	−0.668550	−	1.15796i
$263$	15.8655	−	13.3127i	0.978306	−	0.820896i	−0.00552693	−	0.999985i	$-0.501759\pi$
$263$	15.8655	−	13.3127i	0.978306	−	0.820896i	0.983833	+	0.179088i	$0.0573148\pi$
$264$		0			0
$265$	0.0872898	−	0.495045i	0.00536217	−	0.0304104i
$266$	4.10229	+	3.44223i	0.251528	+	0.211057i
$267$		0			0
$268$	31.2890	+	11.3883i	1.91128	+	0.695648i
$269$	28.2449			1.72212			0.861060	−	0.508504i	$-0.169801\pi$
$269$	28.2449			1.72212			0.861060	+	0.508504i	$0.169801\pi$
$270$		0			0
$271$	17.2626			1.04863			0.524316	−	0.851524i	$-0.324321\pi$
$271$	17.2626			1.04863			0.524316	+	0.851524i	$0.324321\pi$
$272$	−4.97781	−	1.81178i	−0.301824	−	0.109855i
$273$		0			0
$274$	−21.1943	−	17.7842i	−1.28040	−	1.07438i
$275$	−2.68089	+	15.2041i	−0.161664	+	0.916840i
$276$		0			0
$277$	3.95967	−	3.32256i	0.237913	−	0.199633i	−0.516034	−	0.856568i	$-0.672592\pi$
$277$	3.95967	−	3.32256i	0.237913	−	0.199633i	0.753947	+	0.656935i	$0.228148\pi$
$278$	−2.04598	−	3.54375i	−0.122710	−	0.212540i
$279$		0			0
$280$	−0.114578	+	0.198454i	−0.00684733	+	0.0118599i
$281$	0.572421	+	3.24636i	0.0341478	+	0.193662i	0.997110	−	0.0759760i	$-0.0242072\pi$
$281$	0.572421	+	3.24636i	0.0341478	+	0.193662i	−0.962962	+	0.269638i	$0.913096\pi$
$282$		0			0
$283$	8.58007	−	3.12289i	0.510032	−	0.185637i	−0.0741686	−	0.997246i	$-0.523630\pi$
$283$	8.58007	−	3.12289i	0.510032	−	0.185637i	0.584201	+	0.811609i	$0.301408\pi$
$284$	4.05375	−	1.47544i	0.240546	−	0.0875516i
$285$		0			0
$286$	5.41994	+	30.7380i	0.320488	+	1.81758i
$287$	0.317809	−	0.550462i	0.0187597	−	0.0324927i
$288$		0			0
$289$	6.51799	+	11.2895i	0.383411	+	0.664087i
$290$	1.09592	−	0.919583i	0.0643544	−	0.0539998i
$291$		0			0
$292$	0.127891	−	0.725308i	0.00748427	−	0.0424454i
$293$	2.16517	+	1.81680i	0.126491	+	0.106138i	0.703839	−	0.710360i	$-0.251468\pi$
$293$	2.16517	+	1.81680i	0.126491	+	0.106138i	−0.577348	+	0.816498i	$0.695912\pi$
$294$		0			0
$295$	0.899597	+	0.327426i	0.0523766	+	0.0190635i
$296$	17.1100			0.994496
$297$		0			0
$298$	52.0017			3.01238
$299$	−17.5812	−	6.39904i	−1.01675	−	0.370066i
$300$		0			0
$301$	3.06548	+	2.57224i	0.176691	+	0.148261i
$302$	−1.97739	+	11.2143i	−0.113786	+	0.645313i
$303$		0			0
$304$	−7.83759	+	6.57652i	−0.449517	+	0.377189i
$305$	−0.614179	−	1.06379i	−0.0351678	−	0.0609124i
$306$		0			0
$307$	−3.14723	+	5.45116i	−0.179622	+	0.311114i	−0.941751	−	0.336311i	$-0.890821\pi$
$307$	−3.14723	+	5.45116i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$308$	−1.17347	−	6.65508i	−0.0668647	−	0.379208i
$309$		0			0
$310$	0.348190	−	0.126731i	0.0197759	−	0.00719782i
$311$	−6.92825	+	2.52168i	−0.392865	+	0.142991i	−0.530896	−	0.847437i	$-0.678145\pi$
$311$	−6.92825	+	2.52168i	−0.392865	+	0.142991i	0.138031	+	0.990428i	$0.455922\pi$
$312$		0			0
$313$	−0.741608	−	4.20587i	−0.0419182	−	0.237730i	0.956649	−	0.291244i	$-0.0940690\pi$
$313$	−0.741608	−	4.20587i	−0.0419182	−	0.237730i	−0.998567	+	0.0535138i	$0.982958\pi$
$314$	0.251217	−	0.435120i	0.0141770	−	0.0245552i
$315$		0			0
$316$	13.5791	+	23.5197i	0.763883	+	1.32308i
$317$	−12.3698	+	10.3795i	−0.694755	+	0.582968i	−0.920276	−	0.391270i	$-0.872036\pi$
$317$	−12.3698	+	10.3795i	−0.694755	+	0.582968i	0.225521	+	0.974238i	$0.427591\pi$
$318$		0			0
$319$	−3.43723	+	19.4935i	−0.192448	+	1.09143i
$320$	0.739281	+	0.620330i	0.0413271	+	0.0346775i
$321$		0			0
$322$	5.82706	+	2.12087i	0.324729	+	0.118192i
$323$	−7.65618			−0.426001
$324$		0			0
$325$	−20.9723			−1.16333
$326$	−12.6918	−	4.61944i	−0.702934	−	0.255847i
$327$		0			0
$328$	3.56500	+	2.99139i	0.196844	+	0.165172i
$329$	0.361805	−	2.05190i	0.0199470	−	0.113125i
$330$		0			0
$331$	14.7297	−	12.3597i	0.809616	−	0.679349i	−0.140900	−	0.990024i	$-0.545000\pi$
$331$	14.7297	−	12.3597i	0.809616	−	0.679349i	0.950516	+	0.310675i	$0.100555\pi$
$332$	−28.0708	−	48.6201i	−1.54059	−	2.66838i
$333$		0			0
$334$	20.0301	−	34.6932i	1.09600	−	1.89833i
$335$	0.142844	+	0.810108i	0.00780440	+	0.0442609i
$336$		0			0
$337$	27.6859	−	10.0769i	1.50815	−	0.548921i	0.549993	−	0.835169i	$-0.314630\pi$
$337$	27.6859	−	10.0769i	1.50815	−	0.548921i	0.958156	+	0.286248i	$0.0924080\pi$
$338$	−10.5043	+	3.82327i	−0.571361	+	0.207958i
$339$		0			0
$340$	−0.121254	−	0.687667i	−0.00657593	−	0.0372940i
$341$	−2.56339	+	4.43993i	−0.138815	+	0.240435i
$342$		0			0
$343$	−3.96154	−	6.86159i	−0.213903	−	0.370491i
$344$	−22.4444	+	18.8331i	−1.21012	+	1.01541i
$345$		0			0
$346$	−7.92460	+	44.9426i	−0.426029	+	2.41613i
$347$	−8.73063	−	7.32587i	−0.468685	−	0.393273i	0.377630	−	0.925957i	$-0.376739\pi$
$347$	−8.73063	−	7.32587i	−0.468685	−	0.393273i	−0.846315	+	0.532683i	$0.821184\pi$
$348$		0			0
$349$	−26.4633	−	9.63184i	−1.41655	−	0.515581i	−0.483502	−	0.875343i	$-0.660635\pi$
$349$	−26.4633	−	9.63184i	−1.41655	−	0.515581i	−0.933044	+	0.359763i	$0.882858\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	26.9260	+	9.80028i	1.43313	+	0.521616i	0.937826	−	0.347104i	$-0.112835\pi$
$353$	26.9260	+	9.80028i	1.43313	+	0.521616i	0.495302	+	0.868721i	$0.335057\pi$
$354$		0			0
$355$	0.0816416	+	0.0685054i	0.00433309	+	0.00363589i
$356$	1.01616	−	5.76294i	0.0538565	−	0.305435i
$357$		0			0
$358$	−29.8687	+	25.0628i	−1.57861	+	1.32461i
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	−0.906486	−	0.422235i	$-0.861246\pi$
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	0.0875770	−	0.996158i	$-0.472088\pi$
$360$		0			0
$361$	2.10636	−	3.64833i	0.110861	−	0.192017i
$362$	−1.24760	−	7.07549i	−0.0655724	−	0.371880i
$363$		0			0
$364$	8.62630	−	3.13972i	0.452141	−	0.164566i
$365$	0.0170979	−	0.00622313i	0.000894945	−	0.000325733i
$366$		0			0
$367$	4.18913	+	23.7577i	0.218671	+	1.24014i	0.874422	+	0.485166i	$0.161241\pi$
$367$	4.18913	+	23.7577i	0.218671	+	1.24014i	−0.655751	+	0.754977i	$0.727648\pi$
$368$	−5.92365	+	10.2601i	−0.308791	+	0.534843i
$369$		0			0
$370$	0.450466	+	0.780230i	0.0234186	+	0.0405622i
$371$	2.39883	−	2.01285i	0.124541	−	0.104502i
$372$		0			0
$373$	−2.18547	+	12.3944i	−0.113159	+	0.641758i	0.874486	+	0.485051i	$0.161199\pi$
$373$	−2.18547	+	12.3944i	−0.113159	+	0.641758i	−0.987645	+	0.156707i	$0.949912\pi$
$374$	11.3297	+	9.50675i	0.585845	+	0.491582i
$375$		0			0
$376$	14.3351	+	5.21754i	0.739276	+	0.269074i
$377$	−26.8890			−1.38486
$378$		0			0
$379$	−7.70522			−0.395790			−0.197895	−	0.980223i	$-0.563411\pi$
$379$	−7.70522			−0.395790			−0.197895	+	0.980223i	$0.563411\pi$
$380$	−1.26733	−	0.461269i	−0.0650124	−	0.0236626i
$381$		0			0
$382$	4.14646	+	3.47929i	0.212151	+	0.178016i
$383$	3.10164	−	17.5903i	0.158486	−	0.898821i	−0.797042	−	0.603923i	$-0.793603\pi$
$383$	3.10164	−	17.5903i	0.158486	−	0.898821i	0.955529	−	0.294898i	$-0.0952856\pi$
$384$		0			0
$385$	0.127892	−	0.107314i	0.00651796	−	0.00546922i
$386$	1.05704	+	1.83085i	0.0538020	+	0.0931878i
$387$		0			0
$388$	−9.97622	+	17.2793i	−0.506466	+	0.877224i
$389$	−4.75596	−	26.9724i	−0.241137	−	1.36755i	−0.829297	−	0.558809i	$-0.811259\pi$
$389$	−4.75596	−	26.9724i	−0.241137	−	1.36755i	0.588160	−	0.808744i	$-0.299852\pi$
$390$		0			0
$391$	−8.33084	+	3.03218i	−0.421309	+	0.153344i
$392$	26.5851	−	9.67620i	1.34275	−	0.488722i
$393$		0			0
$394$	−8.45608	−	47.9568i	−0.426011	−	2.41603i
$395$	−0.335472	+	0.581055i	−0.0168794	+	0.0292361i
$396$		0			0
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	0.808266	−	0.588817i	$-0.200406\pi$
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	−0.914064	+	0.405571i	$0.867073\pi$
$398$	−34.9726	+	29.3455i	−1.75302	+	1.47096i
$399$		0			0
$400$	−2.30606	+	13.0783i	−0.115303	+	0.653917i
$401$	−11.6228	−	9.75269i	−0.580415	−	0.487026i	0.304668	−	0.952459i	$-0.401454\pi$
$401$	−11.6228	−	9.75269i	−0.580415	−	0.487026i	−0.885084	+	0.465432i	$0.845899\pi$
$402$		0			0
$403$	−6.54437	−	2.38196i	−0.325998	−	0.118654i
$404$	27.3880			1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	−11.7137	−	4.26342i	−0.580625	−	0.211330i
$408$		0			0
$409$	3.60777	+	3.02728i	0.178393	+	0.149689i	0.727612	−	0.685989i	$-0.240630\pi$
$409$	3.60777	+	3.02728i	0.178393	+	0.149689i	−0.549219	+	0.835679i	$0.685075\pi$
$410$	−0.0425519	+	0.241324i	−0.00210149	+	0.0119181i
$411$		0			0
$412$	18.4762	−	15.5034i	0.910258	−	0.763797i
$413$	2.98184	+	5.16469i	0.146727	+	0.254138i
$414$		0			0
$415$	0.693492	−	1.20116i	0.0340422	−	0.0589628i
$416$	−1.53314	−	8.69485i	−0.0751682	−	0.426300i
$417$		0			0
$418$	26.8427	−	9.76994i	1.31292	−	0.477863i
$419$	18.5976	−	6.76897i	0.908551	−	0.330686i	0.154877	−	0.987934i	$-0.450502\pi$
$419$	18.5976	−	6.76897i	0.908551	−	0.330686i	0.753674	+	0.657248i	$0.228280\pi$
$420$		0			0
$421$	4.89440	+	27.7575i	0.238538	+	1.35282i	0.835032	+	0.550201i	$0.185449\pi$
$421$	4.89440	+	27.7575i	0.238538	+	1.35282i	−0.596494	+	0.802617i	$0.703440\pi$
$422$	−19.4340	+	33.6607i	−0.946032	+	1.63858i
$423$		0			0
$424$	11.4637	+	19.8557i	0.556726	+	0.964278i
$425$	−7.61270	+	6.38782i	−0.369270	+	0.309855i
$426$		0			0
$427$	1.32876	−	7.53578i	0.0643033	−	0.364682i
$428$	16.0006	+	13.4261i	0.773418	+	0.648975i
$429$		0			0
$430$	−1.44971	−	0.527653i	−0.0699114	−	0.0254457i
$431$	5.19681			0.250321			0.125161	−	0.992136i	$-0.460055\pi$
$431$	5.19681			0.250321			0.125161	+	0.992136i	$0.460055\pi$
$432$		0			0
$433$	25.3285			1.21721			0.608605	−	0.793473i	$-0.291730\pi$
$433$	25.3285			1.21721			0.608605	+	0.793473i	$0.291730\pi$
$434$	2.16904	+	0.789467i	0.104117	+	0.0378956i
$435$		0			0
$436$	−17.9855	−	15.0917i	−0.861351	−	0.722760i
$437$	−2.97337	+	16.8628i	−0.142236	+	0.806658i
$438$		0			0
$439$	−11.9972	+	10.0668i	−0.572595	+	0.480464i	−0.882506	−	0.470301i	$-0.844145\pi$
$439$	−11.9972	+	10.0668i	−0.572595	+	0.480464i	0.309911	+	0.950766i	$0.399701\pi$
$440$	0.611178	+	1.05859i	0.0291368	+	0.0504664i
$441$		0			0
$442$	−10.0455	+	17.3993i	−0.477815	+	0.827600i
$443$	3.16975	+	17.9765i	0.150599	+	0.854091i	0.962700	+	0.270573i	$0.0872131\pi$
$443$	3.16975	+	17.9765i	0.150599	+	0.854091i	−0.812100	+	0.583518i	$0.801676\pi$
$444$		0			0
$445$	0.135852	−	0.0494459i	0.00643998	−	0.00234396i
$446$	−48.4245	+	17.6251i	−2.29297	+	0.834572i
$447$		0			0
$448$	1.04394	+	5.92050i	0.0493218	+	0.279718i
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	−0.297934	−	0.954586i	$-0.596298\pi$
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	0.975663	−	0.219274i	$-0.0703690\pi$
$450$		0			0
$451$	−1.69525	−	2.93626i	−0.0798262	−	0.138263i
$452$	34.1852	−	28.6848i	1.60793	−	1.34922i
$453$		0			0
$454$	7.97135	−	45.2078i	0.374114	−	2.12171i
$455$	0.173732	+	0.145778i	0.00814466	+	0.00683419i
$456$		0			0
$457$	33.2538	+	12.1034i	1.55555	+	0.566172i	0.969710	−	0.244258i	$-0.0785444\pi$
$457$	33.2538	+	12.1034i	1.55555	+	0.566172i	0.585835	+	0.810430i	$0.300767\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	2.13943	+	0.778687i	0.0996430	+	0.0362671i	0.391361	−	0.920237i	$-0.372005\pi$
$461$	2.13943	+	0.778687i	0.0996430	+	0.0362671i	−0.291718	+	0.956504i	$0.594227\pi$
$462$		0			0
$463$	14.0757	+	11.8109i	0.654154	+	0.548900i	0.908328	−	0.418258i	$-0.137359\pi$
$463$	14.0757	+	11.8109i	0.654154	+	0.548900i	−0.254175	+	0.967158i	$0.581804\pi$
$464$	−2.95666	+	16.7681i	−0.137260	+	0.778437i
$465$		0			0
$466$	32.5295	−	27.2955i	1.50690	−	1.26444i
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	0.914874	−	0.403738i	$-0.132289\pi$
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	−0.807085	+	0.590435i	$0.798956\pi$
$468$		0			0
$469$	−2.56220	+	4.43786i	−0.118312	+	0.204922i
$470$	0.139485	+	0.791059i	0.00643397	+	0.0364888i
$471$		0			0
$472$	−41.0307	+	14.9340i	−1.88859	+	0.687392i
$473$	20.0584	−	7.30068i	0.922288	−	0.335685i
$474$		0			0
$475$	3.33297	+	18.9022i	0.152927	+	0.867292i
$476$	2.17495	−	3.76712i	0.0996885	−	0.172666i
$477$		0			0
$478$	−18.5169	−	32.0722i	−0.846942	−	1.46695i
$479$	10.8594	−	9.11209i	0.496177	−	0.416342i	−0.360057	−	0.932930i	$-0.617243\pi$
$479$	10.8594	−	9.11209i	0.496177	−	0.416342i	0.856234	+	0.516588i	$0.172798\pi$
$480$		0			0
$481$	2.94045	−	16.6761i	0.134073	−	0.760366i
$482$	24.1954	+	20.3023i	1.10207	+	0.924745i
$483$		0			0
$484$	5.07304	+	1.84643i	0.230593	+	0.0839288i
$485$	−0.492926			−0.0223826
$486$		0			0
$487$	−21.4338			−0.971258			−0.485629	−	0.874165i	$-0.661409\pi$
$487$	−21.4338			−0.971258			−0.485629	+	0.874165i	$0.661409\pi$
$488$	52.6469	+	19.1619i	2.38321	+	0.867418i
$489$		0			0
$490$	1.14117	+	0.957555i	0.0515528	+	0.0432579i
$491$	2.44633	−	13.8738i	0.110401	−	0.626117i	−0.878523	−	0.477699i	$-0.841471\pi$
$491$	2.44633	−	13.8738i	0.110401	−	0.626117i	0.988925	−	0.148418i	$-0.0474180\pi$
$492$		0			0
$493$	−9.76043	+	8.18997i	−0.439588	+	0.368858i
$494$	19.4020	+	33.6053i	0.872938	+	1.51197i
$495$		0			0
$496$	−2.20500	+	3.81917i	−0.0990073	+	0.171486i
$497$	0.115287	+	0.653824i	0.00517132	+	0.0293280i
$498$		0			0
$499$	−14.0102	+	5.09929i	−0.627182	+	0.228276i	−0.636004	−	0.771685i	$-0.719414\pi$
$499$	−14.0102	+	5.09929i	−0.627182	+	0.228276i	0.00882219	+	0.999961i	$0.497192\pi$
$500$	−3.29282	+	1.19849i	−0.147259	+	0.0535980i
$501$		0			0
$502$	−7.26337	−	41.1926i	−0.324180	−	1.83852i
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	−0.986886	−	0.161420i	$-0.948393\pi$
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	0.633236	+	0.773958i	$0.281726\pi$
$504$		0			0
$505$	0.338311	+	0.585972i	0.0150546	+	0.0260754i
$506$	25.3387	−	21.2617i	1.12644	−	0.945199i
$507$		0			0
$508$	7.54331	−	42.7803i	0.334680	−	1.89807i
$509$	−25.9894	−	21.8077i	−1.15196	−	0.966608i	−0.152194	−	0.988351i	$-0.548634\pi$
$509$	−25.9894	−	21.8077i	−1.15196	−	0.966608i	−0.999764	+	0.0217430i	$0.993078\pi$
$510$		0			0
$511$	0.106511	+	0.0387669i	0.00471177	+	0.00171495i
$512$	−28.1824			−1.24550
$513$		0			0
$514$	−26.8683			−1.18511
$515$	0.559927	+	0.203797i	0.0246733	+	0.00898036i
$516$		0			0
$517$	−8.51386	−	7.14397i	−0.374439	−	0.314192i
$518$	−0.974572	+	5.52707i	−0.0428203	+	0.242846i
$519$		0			0
$520$	−1.27200	+	1.06734i	−0.0557811	+	0.0468059i
$521$	−21.3899	−	37.0484i	−0.937108	−	1.62312i	−0.770831	−	0.637040i	$-0.780159\pi$
$521$	−21.3899	−	37.0484i	−0.937108	−	1.62312i	−0.166277	−	0.986079i	$-0.553175\pi$
$522$		0			0
$523$	1.38893	−	2.40569i	0.0607335	−	0.105193i	−0.834060	−	0.551674i	$-0.813989\pi$
$523$	1.38893	−	2.40569i	0.0607335	−	0.105193i	0.894793	+	0.446480i	$0.147323\pi$
$524$	5.89612	+	33.4386i	0.257573	+	1.46077i
$525$		0			0
$526$	−46.7400	+	17.0120i	−2.03796	+	0.741758i
$527$	−3.10104	+	1.12869i	−0.135083	+	0.0491664i
$528$		0			0
$529$	−0.550887	−	3.12424i	−0.0239516	−	0.135836i
$530$	−0.603626	+	1.04551i	−0.0262198	+	0.0454141i
$531$		0			0
$532$	−4.20073	−	7.27587i	−0.182125	−	0.315449i
$533$	3.52821	−	2.96052i	0.152824	−	0.128234i
$534$		0			0
$535$	−0.0896063	+	0.508183i	−0.00387402	+	0.0219707i
$536$	−28.7413	−	24.1168i	−1.24144	−	1.04169i
$537$		0			0
$538$	−63.7426	−	23.2004i	−2.74814	−	1.00024i
$539$	−20.6116			−0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$	−38.9581	−	14.1796i	−1.67339	−	0.609065i
$543$		0			0
$544$	−3.20482	−	2.68917i	−0.137406	−	0.115297i
$545$	0.100722	−	0.571225i	0.00431447	−	0.0244686i
$546$		0			0
$547$	−30.3245	+	25.4453i	−1.29658	+	1.08796i	−0.305858	+	0.952077i	$0.598943\pi$
$547$	−30.3245	+	25.4453i	−1.29658	+	1.08796i	−0.990725	+	0.135884i	$0.956612\pi$
$548$	21.7029	+	37.5905i	0.927101	+	1.60579i
$549$		0			0
$550$	18.5389	−	32.1102i	0.790499	−	1.36919i
$551$	4.27328	+	24.2350i	0.182048	+	1.03244i
$552$		0			0
$553$	−3.92757	+	1.42952i	−0.167017	+	0.0607894i
$554$	−11.6653	+	4.24581i	−0.495610	+	0.180387i
$555$		0			0
$556$	1.11477	+	6.32215i	0.0472766	+	0.268119i
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	−0.961355	−	0.275312i	$-0.911219\pi$
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	0.719105	+	0.694902i	$0.244552\pi$
$558$		0			0
$559$	14.4983	+	25.1119i	0.613214	+	1.06212i
$560$	0.110011	−	0.0923099i	0.00464880	−	0.00390081i
$561$		0			0
$562$	1.37474	−	7.79653i	0.0579898	−	0.328877i
$563$	−11.1159	−	9.32736i	−0.468480	−	0.393101i	0.377760	−	0.925904i	$-0.376694\pi$
$563$	−11.1159	−	9.32736i	−0.468480	−	0.393101i	−0.846240	+	0.532802i	$0.821139\pi$
$564$		0			0
$565$	1.03599	+	0.377070i	0.0435844	+	0.0158634i
$566$	−21.9285			−0.921725
$567$		0			0
$568$	−4.86093			−0.203960
$569$	−1.22083	−	0.444347i	−0.0511800	−	0.0186280i	0.316303	−	0.948658i	$-0.397558\pi$
$569$	−1.22083	−	0.444347i	−0.0511800	−	0.0186280i	−0.367483	+	0.930030i	$0.619780\pi$
$570$		0			0
$571$	12.3006	+	10.3214i	0.514765	+	0.431939i	0.862802	−	0.505542i	$-0.168707\pi$
$571$	12.3006	+	10.3214i	0.514765	+	0.431939i	−0.348037	+	0.937481i	$0.613152\pi$
$572$	8.50308	−	48.2234i	0.355532	−	2.01632i
$573$		0			0
$574$	−1.16938	+	0.981225i	−0.0488089	+	0.0409555i
$575$	11.1127	+	19.2478i	0.463434	+	0.802691i
$576$		0			0
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	−0.764439	−	0.644696i	$-0.776984\pi$
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	0.940543	+	0.339675i	$0.110317\pi$
$578$	−5.43649	−	30.8318i	−0.226128	−	1.28244i
$579$		0			0
$580$	−2.10907	+	0.767638i	−0.0875743	+	0.0318745i
$581$	8.11913	−	2.95512i	0.336838	−	0.122599i
$582$		0			0
$583$	−2.90057	−	16.4499i	−0.120129	−	0.681286i
$584$	−0.414943	+	0.718703i	−0.0171705	+	0.0297401i
$585$		0			0
$586$	−3.39401	−	5.87860i	−0.140205	−	0.242843i
$587$	14.0839	−	11.8178i	0.581304	−	0.487772i	−0.304071	−	0.952649i	$-0.598346\pi$
$587$	14.0839	−	11.8178i	0.581304	−	0.487772i	0.885375	+	0.464877i	$0.153902\pi$
$588$		0			0
$589$	−1.10680	+	6.27696i	−0.0456048	+	0.258637i
$590$	−1.76125	−	1.47786i	−0.0725094	−	0.0608426i
$591$		0			0
$592$	−10.0759	−	3.66734i	−0.414119	−	0.150727i
$593$	−13.5128			−0.554905			−0.277452	−	0.960739i	$-0.589490\pi$
$593$	−13.5128			−0.554905			−0.277452	+	0.960739i	$0.589490\pi$
$594$		0			0
$595$	0.107464			0.00440561
$596$	−76.6629	−	27.9030i	−3.14023	−	1.14295i
$597$		0			0
$598$	34.4209	+	28.8825i	1.40757	+	1.18109i
$599$	−1.91494	+	10.8602i	−0.0782425	+	0.443735i	0.920369	+	0.391051i	$0.127889\pi$
$599$	−1.91494	+	10.8602i	−0.0782425	+	0.443735i	−0.998611	+	0.0526835i	$0.983223\pi$
$600$		0			0
$601$	19.7624	−	16.5826i	0.806123	−	0.676418i	−0.143556	−	0.989642i	$-0.545854\pi$
$601$	19.7624	−	16.5826i	0.806123	−	0.676418i	0.949679	+	0.313225i	$0.101409\pi$
$602$	−4.80528	−	8.32298i	−0.195848	−	0.339219i
$603$		0			0
$604$	8.93252	−	15.4716i	0.363459	−	0.629529i
$605$	0.0231600	+	0.131347i	0.000941588	+	0.00534001i
$606$		0			0
$607$	13.8979	−	5.05843i	0.564100	−	0.205316i	−0.0442003	−	0.999023i	$-0.514074\pi$
$607$	13.8979	−	5.05843i	0.564100	−	0.205316i	0.608300	+	0.793707i	$0.291852\pi$
$608$	−7.59297	+	2.76362i	−0.307936	+	0.112079i
$609$		0			0
$610$	0.512271	+	2.90523i	0.0207413	+	0.117629i
$611$	7.54882	−	13.0749i	0.305393	−	0.528956i
$612$		0			0
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	−0.955792	−	0.294043i	$-0.904999\pi$
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	0.223248	−	0.974762i	$-0.428334\pi$
$614$	11.5802	−	9.71696i	0.467340	−	0.392145i
$615$		0			0
$616$	−1.32227	+	7.49896i	−0.0532757	+	0.302142i
$617$	30.9279	+	25.9516i	1.24511	+	1.04477i	0.997107	+	0.0760138i	$0.0242193\pi$
$617$	30.9279	+	25.9516i	1.24511	+	1.04477i	0.248005	+	0.968759i	$0.420225\pi$
$618$		0			0
$619$	6.47759	+	2.35765i	0.260356	+	0.0947619i	0.468900	−	0.883251i	$-0.344650\pi$
$619$	6.47759	+	2.35765i	0.260356	+	0.0947619i	−0.208544	+	0.978013i	$0.566873\pi$
$620$	−0.581315			−0.0233462
$621$		0			0
$622$	17.7069			0.709981
$623$	0.846285	+	0.308023i	0.0339057	+	0.0123407i
$624$		0			0
$625$	19.0516	+	15.9862i	0.762064	+	0.639448i
$626$	−1.78106	+	10.1009i	−0.0711856	+	0.403713i
$627$		0			0
$628$	−0.603829	+	0.506672i	−0.0240954	+	0.0202184i
$629$	−4.01193	−	6.94887i	−0.159966	−	0.277070i
$630$		0			0
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	0.400212	+	0.916423i	$0.368936\pi$
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	−0.993751	+	0.111617i	$0.964397\pi$
$632$	−5.31396	−	30.1370i	−0.211378	−	1.19878i
$633$		0			0
$634$	36.4416	−	13.2637i	1.44728	−	0.526767i
$635$	1.00847	−	0.367054i	0.0400200	−	0.0145661i
$636$		0			0
$637$	−4.86204	−	27.5740i	−0.192641	−	1.09252i
$638$	23.7691	−	41.1693i	0.941028	−	1.62991i
$639$		0			0
$640$	−0.963264	−	1.66842i	−0.0380763	−	0.0659502i
$641$	−32.8485	+	27.5632i	−1.29744	+	1.08868i	−0.306858	+	0.951755i	$0.599278\pi$
$641$	−32.8485	+	27.5632i	−1.29744	+	1.08868i	−0.990581	+	0.136926i	$0.956278\pi$
$642$		0			0
$643$	−4.76026	+	26.9968i	−0.187726	+	1.06465i	0.734676	+	0.678419i	$0.237334\pi$
$643$	−4.76026	+	26.9968i	−0.187726	+	1.06465i	−0.922402	+	0.386231i	$0.873777\pi$
$644$	−7.45245	−	6.25335i	−0.293668	−	0.246416i
$645$		0			0
$646$	17.2784	+	6.28881i	0.679808	+	0.247430i
$647$	16.1623			0.635407			0.317703	−	0.948190i	$-0.397088\pi$
$647$	16.1623			0.635407			0.317703	+	0.948190i	$0.397088\pi$
$648$		0			0
$649$	31.8113			1.24870
$650$	47.3299	+	17.2267i	1.85643	+	0.675686i
$651$		0			0
$652$	16.2320	+	13.6203i	0.635696	+	0.533412i
$653$	−5.59951	+	31.7564i	−0.219126	+	1.24272i	0.654476	+	0.756083i	$0.272889\pi$
$653$	−5.59951	+	31.7564i	−0.219126	+	1.24272i	−0.873602	+	0.486641i	$0.838222\pi$
$654$		0			0
$655$	−0.642594	+	0.539200i	−0.0251082	+	0.0210683i
$656$	−1.45823	−	2.52573i	−0.0569344	−	0.0986133i
$657$		0			0
$658$	−2.50195	+	4.33351i	−0.0975363	+	0.168938i
$659$	−4.83065	−	27.3960i	−0.188175	−	1.06719i	−0.921807	−	0.387648i	$-0.873288\pi$
$659$	−4.83065	−	27.3960i	−0.188175	−	1.06719i	0.733632	−	0.679547i	$-0.237824\pi$
$660$		0			0
$661$	−28.9318	+	10.5303i	−1.12532	+	0.409582i	−0.836590	−	0.547829i	$-0.815454\pi$
$661$	−28.9318	+	10.5303i	−1.12532	+	0.409582i	−0.288728	+	0.957411i	$0.593232\pi$
$662$	−43.3940	+	15.7941i	−1.68656	+	0.613856i
$663$		0			0
$664$	10.9851	+	62.2995i	0.426304	+	2.41769i
$665$	0.103779	−	0.179751i	0.00402439	−	0.00697044i
$666$		0			0
$667$	14.2479	+	24.6781i	0.551682	+	0.955540i
$668$	−48.1448	+	40.3982i	−1.86278	+	1.56306i
$669$		0			0
$670$	0.343057	−	1.94557i	0.0132534	−	0.0751640i
$671$	−31.2679	−	26.2369i	−1.20708	−	1.01286i
$672$		0			0
$673$	24.5547	+	8.93720i	0.946516	+	0.344504i	0.768736	−	0.639567i	$-0.220886\pi$
$673$	24.5547	+	8.93720i	0.946516	+	0.344504i	0.177780	+	0.984070i	$0.443108\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	17.0972	+	6.22288i	0.657100	+	0.239165i	0.648984	−	0.760802i	$-0.275194\pi$
$677$	17.0972	+	6.22288i	0.657100	+	0.239165i	0.00811624	+	0.999967i	$0.497416\pi$
$678$		0			0
$679$	−2.35227	−	1.97379i	−0.0902720	−	0.0757472i
$680$	−0.136630	+	0.774865i	−0.00523950	+	0.0297147i
$681$		0			0
$682$	9.43200	−	7.91438i	0.361170	−	0.303057i
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	0.998356	−	0.0573104i	$-0.0182525\pi$
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	−0.548811	+	0.835947i	$0.684919\pi$
$684$		0			0
$685$	−0.536171	+	0.928676i	−0.0204860	+	0.0354829i
$686$	3.30422	+	18.7392i	0.126156	+	0.715465i
$687$		0			0
$688$	17.2540	−	6.27995i	0.657803	−	0.239421i
$689$	21.3223	−	7.76070i	0.812317	−	0.295659i
$690$		0			0
$691$	−7.73393	−	43.8613i	−0.294213	−	1.66856i	−0.670386	−	0.742013i	$-0.733871\pi$
$691$	−7.73393	−	43.8613i	−0.294213	−	1.66856i	0.376173	−	0.926549i	$-0.377240\pi$
$692$	35.7980	−	62.0039i	1.36084	−	2.35704i
$693$		0			0
$694$	13.6857	+	23.7043i	0.519501	+	0.899802i
$695$	−0.121494	+	0.101945i	−0.00460852	+	0.00386701i
$696$		0			0
$697$	0.378975	−	2.14928i	0.0143547	−	0.0814096i
$698$	51.8103	+	43.4740i	1.96105	+	1.64552i
$699$		0			0
$700$	−10.2474	−	3.72974i	−0.387315	−	0.140971i
$701$	25.2567			0.953934			0.476967	−	0.878921i	$-0.341736\pi$
$701$	25.2567			0.953934			0.476967	+	0.878921i	$0.341736\pi$
$702$		0			0
$703$	−15.4974			−0.584496
$704$	30.1343	+	10.9680i	1.13573	+	0.413371i
$705$		0			0
$706$	−52.7163	−	44.2343i	−1.98401	−	1.66478i
$707$	−0.731927	+	4.15097i	−0.0275270	+	0.156113i
$708$		0			0
$709$	−12.0147	+	10.0815i	−0.451220	+	0.378618i	−0.839888	−	0.542759i	$-0.817380\pi$
$709$	−12.0147	+	10.0815i	−0.451220	+	0.378618i	0.388668	+	0.921378i	$0.372935\pi$
$710$	−0.127977	−	0.221663i	−0.00480289	−	0.00831886i
$711$		0			0
$712$	−3.29694	+	5.71046i	−0.123558	+	0.214009i
$713$	1.28162	+	7.26841i	0.0479970	+	0.272204i
$714$		0			0
$715$	1.13678	−	0.413756i	0.0425133	−	0.0154736i
$716$	57.4818	−	20.9217i	2.14820	−	0.781879i
$717$		0			0
$718$	12.9416	+	73.3954i	0.482976	+	2.73909i
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.381523	+	0.924359i	$0.624600\pi$
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.609757	+	0.792588i	$0.708733\pi$
$720$		0			0
$721$	1.85595	+	3.21461i	0.0691194	+	0.119718i
$722$	−7.75035	+	6.50332i	−0.288438	+	0.242028i
$723$		0			0
$724$	−1.95730	+	11.1004i	−0.0727424	+	0.412543i
$725$	24.4691	+	20.5320i	0.908758	+	0.762539i
$726$		0			0
$727$	−0.440878	−	0.160466i	−0.0163512	−	0.00595137i	0.333832	−	0.942633i	$-0.391658\pi$
$727$	−0.440878	−	0.160466i	−0.0163512	−	0.00595137i	−0.350183	+	0.936681i	$0.613881\pi$
$728$	−10.3440			−0.383372
$729$		0			0
$730$	−0.0436980			−0.00161734
$731$	12.9114	+	4.69937i	0.477546	+	0.173812i
$732$		0			0
$733$	−35.5493	−	29.8294i	−1.31304	−	1.10177i	−0.987731	−	0.156166i	$-0.950086\pi$
$733$	−35.5493	−	29.8294i	−1.31304	−	1.10177i	−0.325312	−	0.945607i	$-0.605469\pi$
$734$	10.0607	−	57.0570i	0.371347	−	2.10601i
$735$		0			0
$736$	−7.16755	+	6.01429i	−0.264199	+	0.221690i
$737$	13.6672	+	23.6724i	0.503439	+	0.871983i
$738$		0			0
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	−0.999580	−	0.0289653i	$-0.990779\pi$
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	0.524875	+	0.851179i	$0.324112\pi$
$740$	−0.245439	−	1.39195i	−0.00902252	−	0.0511693i
$741$		0			0
$742$	−7.06700	+	2.57218i	−0.259438	+	0.0944276i
$743$	32.6164	−	11.8714i	1.19658	−	0.435519i	0.334550	−	0.942378i	$-0.391416\pi$
$743$	32.6164	−	11.8714i	1.19658	−	0.435519i	0.862029	+	0.506859i	$0.169193\pi$
$744$		0			0
$745$	−0.349990	−	1.98489i	−0.0128226	−	0.0727209i
$746$	15.1129	−	26.1764i	0.553324	−	0.958385i
$747$		0			0
$748$	−11.6015	−	20.0945i	−0.424195	−	0.734727i
$749$	−2.46249	+	2.06627i	−0.0899774	+	0.0755000i
$750$		0			0
$751$	4.16510	−	23.6214i	0.151987	−	0.861959i	−0.809503	−	0.587116i	$-0.800263\pi$
$751$	4.16510	−	23.6214i	0.151987	−	0.861959i	0.961489	−	0.274843i	$-0.0886257\pi$
$752$	−7.32351	−	6.14515i	−0.267061	−	0.224091i
$753$		0			0
$754$	60.6828	+	22.0867i	2.20994	+	0.804351i
$755$	0.441357			0.0160626
$756$		0			0
$757$	−8.78780			−0.319398			−0.159699	−	0.987166i	$-0.551052\pi$
$757$	−8.78780			−0.319398			−0.159699	+	0.987166i	$0.551052\pi$
$758$	17.3890	+	6.32909i	0.631598	+	0.229883i
$759$		0			0
$760$	1.16414	+	0.976827i	0.0422277	+	0.0354332i
$761$	−2.38833	+	13.5449i	−0.0865771	+	0.491003i	0.910428	+	0.413667i	$0.135752\pi$
$761$	−2.38833	+	13.5449i	−0.0865771	+	0.491003i	−0.997005	+	0.0773355i	$0.975359\pi$
$762$		0			0
$763$	2.76797	−	2.32260i	0.100207	−	0.0840839i
$764$	−4.24595	−	7.35420i	−0.153613	−	0.266066i
$765$		0			0
$766$	−21.4484	+	37.1498i	−0.774963	+	1.34228i
$767$	7.50392	+	42.5569i	0.270951	+	1.53664i
$768$		0			0
$769$	29.4668	−	10.7250i	1.06260	−	0.386755i	0.249196	−	0.968453i	$-0.419834\pi$
$769$	29.4668	−	10.7250i	1.06260	−	0.386755i	0.813405	+	0.581698i	$0.197611\pi$
$770$	−0.376772	+	0.137134i	−0.0135779	+	0.00494196i
$771$		0			0
$772$	−0.575935	−	3.26629i	−0.0207284	−	0.117556i
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	−0.494249	−	0.869320i	$-0.664557\pi$
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	0.999978	−	0.00662776i	$-0.00210970\pi$
$774$		0			0
$775$	4.13657	+	7.16475i	0.148590	+	0.257365i
$776$	17.2226	−	14.4514i	0.618254	−	0.518776i
$777$		0			0
$778$	−11.4220	+	64.7774i	−0.409499	+	2.32238i
$779$	−3.22902	−	2.70947i	−0.115692	−	0.0970767i
$780$		0			0
$781$	3.32784	+	1.21124i	0.119080	+	0.0433414i
$782$	21.2916			0.761385
$783$		0			0
$784$	−17.7298			−0.633207
$785$	−0.0182992	−	0.00666036i	−0.000653126	−	0.000237718i
$786$		0			0
$787$	−27.7309	−	23.2690i	−0.988501	−	0.829451i	−0.00315089	−	0.999995i	$-0.501003\pi$
$787$	−27.7309	−	23.2690i	−0.988501	−	0.829451i	−0.985350	+	0.170544i	$0.945447\pi$
$788$	−13.2663	+	75.2370i	−0.472593	+	2.68021i
$789$		0			0
$790$	1.23437	−	1.03576i	0.0439169	−	0.0368507i
$791$	3.43393	+	5.94775i	0.122097	+	0.211478i
$792$		0			0
$793$	27.7237	−	48.0189i	0.984498	−	1.70520i
$794$	1.75822	+	9.97138i	0.0623970	+	0.353871i
$795$		0			0
$796$	67.3041	−	24.4967i	2.38553	−	0.868262i
$797$	−27.8150	+	10.1238i	−0.985258	+	0.358604i	−0.783882	−	0.620910i	$-0.786763\pi$
$797$	−27.8150	+	10.1238i	−0.985258	+	0.358604i	−0.201376	+	0.979514i	$0.564541\pi$
$798$		0			0
$799$	−1.24228	−	7.04531i	−0.0439487	−	0.249245i
$800$	−5.24407	+	9.08300i	−0.185406	+	0.321133i
$801$		0			0
$802$	18.2193	+	31.5568i	0.643346	+	1.11431i
$803$	0.463159	−	0.388637i	0.0163445	−	0.0137147i
$804$		0			0
$805$	0.0417351	−	0.236691i	0.00147097	−	0.00834228i
$806$	12.8127	+	10.7511i	0.451308	+	0.378692i
$807$		0			0
$808$	−28.9997	−	10.5550i	−1.02021	−	0.371324i
$809$	5.75943			0.202491			0.101245	−	0.994861i	$-0.467717\pi$
$809$	5.75943			0.202491			0.101245	+	0.994861i	$0.467717\pi$
$810$		0			0
$811$	12.4896			0.438569			0.219284	−	0.975661i	$-0.429628\pi$
$811$	12.4896			0.438569			0.219284	+	0.975661i	$0.429628\pi$
$812$	−13.1384	−	4.78199i	−0.461068	−	0.167815i
$813$		0			0
$814$	22.9332	+	19.2433i	0.803809	+	0.674476i
$815$	−0.0909025	+	0.515534i	−0.00318418	+	0.0180584i
$816$		0			0
$817$	20.3291	−	17.0581i	0.711225	−	0.596788i
$818$	−5.65535	−	9.79536i	−0.197735	−	0.342487i
$819$		0			0
$820$	0.192221	−	0.332936i	0.00671265	−	0.0116266i
$821$	−7.47846	−	42.4125i	−0.261000	−	1.48021i	−0.780188	−	0.625545i	$-0.784877\pi$
$821$	−7.47846	−	42.4125i	−0.261000	−	1.48021i	0.519188	−	0.854660i	$-0.326235\pi$
$822$		0			0
$823$	−9.66389	+	3.51737i	−0.336862	+	0.122608i	−0.504912	−	0.863171i	$-0.668475\pi$
$823$	−9.66389	+	3.51737i	−0.336862	+	0.122608i	0.168050	+	0.985778i	$0.446253\pi$
$824$	−25.5383	+	9.29520i	−0.889670	+	0.323814i
$825$		0			0
$826$	−2.48707	−	14.1049i	−0.0865364	−	0.490772i
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	−0.808167	−	0.588954i	$-0.799540\pi$
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	0.914132	+	0.405416i	$0.132873\pi$
$828$		0			0
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	0.994852	+	0.101339i	$0.0323126\pi$
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	−0.409664	+	0.912236i	$0.634354\pi$
$830$	−2.55170	+	2.14113i	−0.0885709	+	0.0743198i
$831$		0			0
$832$	−7.56453	+	42.9006i	−0.262253	+	1.48731i
$833$	−10.1635	−	8.52816i	−0.352143	−	0.295483i
$834$		0			0
$835$	−1.45904	−	0.531047i	−0.0504922	−	0.0183776i
$836$	−44.8148			−1.54995
$837$		0			0
$838$	−47.5308			−1.64192
$839$	−39.6797	−	14.4422i	−1.36989	−	0.498601i	−0.450795	−	0.892628i	$-0.648859\pi$
$839$	−39.6797	−	14.4422i	−1.36989	−	0.498601i	−0.919099	+	0.394027i	$0.871082\pi$
$840$		0			0
$841$	9.15708	+	7.68370i	0.315761	+	0.264955i
$842$	11.7545	−	66.6630i	0.405086	−	2.29736i
$843$		0			0
$844$	46.7119	−	39.1960i	1.60789	−	1.34918i
$845$	0.216631	+	0.375216i	0.00745234	+	0.0129078i
$846$		0			0
$847$	−0.415423	+	0.719533i	−0.0142741	+	0.0247235i
$848$	−2.49503	−	14.1500i	−0.0856796	−	0.485913i
$849$		0			0
$850$	22.4272	−	8.16284i	0.769247	−	0.279983i
$851$	−16.8630	+	6.13764i	−0.578057	+	0.210396i
$852$		0			0
$853$	−6.20438	−	35.1868i	−0.212434	−	1.20477i	−0.885304	−	0.465012i	$-0.846050\pi$
$853$	−6.20438	−	35.1868i	−0.212434	−	1.20477i	0.672870	−	0.739760i	$-0.265061\pi$
$854$	−9.18865	+	15.9152i	−0.314429	+	0.544607i
$855$		0			0
$856$	−11.7679	−	20.3826i	−0.402219	−	0.696664i
$857$	−6.05838	+	5.08358i	−0.206950	+	0.173652i	−0.740372	−	0.672198i	$-0.765350\pi$
$857$	−6.05838	+	5.08358i	−0.206950	+	0.173652i	0.533421	+	0.845850i	$0.320906\pi$
$858$		0			0
$859$	−7.76540	+	44.0398i	−0.264952	+	1.50262i	0.504220	+	0.863575i	$0.331780\pi$
$859$	−7.76540	+	44.0398i	−0.264952	+	1.50262i	−0.769172	+	0.639042i	$0.779331\pi$
$860$	1.85410	+	1.55577i	0.0632241	+	0.0530513i
$861$		0			0
$862$	−11.7281	−	4.26867i	−0.399460	−	0.145391i
$863$	22.9170			0.780103			0.390052	−	0.920793i	$-0.372457\pi$
$863$	22.9170			0.780103			0.390052	+	0.920793i	$0.372457\pi$
$864$		0			0
$865$	1.76878			0.0601405
$866$	−57.1610	−	20.8049i	−1.94241	−	0.706979i
$867$		0			0
$868$	−2.77407	−	2.32772i	−0.0941581	−	0.0790080i
$869$	−3.87147	+	21.9562i	−0.131331	+	0.744814i
$870$		0			0
$871$	−28.4447	+	23.8680i	−0.963813	+	0.808735i
$872$	13.2278	+	22.9112i	0.447950	+	0.775871i
$873$		0			0
$874$	20.5614	−	35.6134i	0.695501	−	1.20464i
$875$	−0.0936462	−	0.531094i	−0.00316582	−	0.0179543i
$876$		0			0
$877$	20.8026	−	7.57152i	0.702453	−	0.255672i	0.0339951	−	0.999422i	$-0.489177\pi$
$877$	20.8026	−	7.57152i	0.702453	−	0.255672i	0.668458	+	0.743750i	$0.266955\pi$
$878$	35.3441	−	12.8642i	1.19280	−	0.434145i
$879$		0			0
$880$	−0.133021	−	0.754397i	−0.00448412	−	0.0254307i
$881$	4.93202	−	8.54251i	0.166164	−	0.287804i	−0.770904	−	0.636951i	$-0.780195\pi$
$881$	4.93202	−	8.54251i	0.166164	−	0.287804i	0.937068	+	0.349147i	$0.113529\pi$
$882$		0			0
$883$	−23.7865	−	41.1995i	−0.800481	−	1.38647i	−0.919300	−	0.393558i	$-0.871244\pi$
$883$	−23.7865	−	41.1995i	−0.800481	−	1.38647i	0.118819	−	0.992916i	$-0.462089\pi$
$884$	24.1455	−	20.2605i	0.812102	−	0.681434i
$885$		0			0
$886$	7.61253	−	43.1728i	0.255748	−	1.45042i
$887$	−10.2323	−	8.58590i	−0.343566	−	0.288286i	0.454634	−	0.890678i	$-0.349770\pi$
$887$	−10.2323	−	8.58590i	−0.343566	−	0.288286i	−0.798200	+	0.602392i	$0.794214\pi$
$888$		0			0
$889$	6.28226	+	2.28656i	0.210700	+	0.0766886i
$890$	−0.347203			−0.0116383
$891$		0			0
$892$	80.8465			2.70694
$893$	−12.9841	−	4.72581i	−0.434495	−	0.158143i
$894$		0			0
$895$	1.15767	+	0.971400i	0.0386966	+	0.0324703i
$896$	2.08400	−	11.8189i	0.0696215	−	0.394843i
$897$		0			0
$898$	−52.8406	+	44.3385i	−1.76331	+	1.47960i
$899$	5.30359	+	9.18609i	0.176885	+	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$	1.41397	+	8.01899i	0.0470799	+	0.267003i
$903$		0			0
$904$	−47.2517	+	17.1982i	−1.57157	+	0.572004i
$905$	−0.261673	+	0.0952412i	−0.00869830	+	0.00316592i
$906$		0			0
$907$	6.41815	+	36.3991i	0.213111	+	1.20861i	0.884154	+	0.467195i	$0.154735\pi$
$907$	6.41815	+	36.3991i	0.213111	+	1.20861i	−0.671043	+	0.741418i	$0.734154\pi$
$908$	−36.0092	+	62.3697i	−1.19501	+	2.06981i
$909$		0			0
$910$	−0.272332	−	0.471694i	−0.00902773	−	0.0156365i
$911$	37.0851	−	31.1181i	1.22868	−	1.03099i	0.230359	−	0.973106i	$-0.426010\pi$
$911$	37.0851	−	31.1181i	1.22868	−	1.03099i	0.998323	−	0.0578814i	$-0.0184345\pi$
$912$		0			0
$913$	8.00315	−	45.3881i	0.264866	−	1.50213i
$914$	−65.1049	−	54.6295i	−2.15348	−	1.80698i
$915$		0			0
$916$	−79.5569	−	28.9564i	−2.62863	−	0.956745i
$917$	−5.22558			−0.172564
$918$		0			0
$919$	8.93459			0.294725			0.147363	−	0.989083i	$-0.452922\pi$
$919$	8.93459			0.294725			0.147363	+	0.989083i	$0.452922\pi$
$920$	1.65359	+	0.601856i	0.0545171	+	0.0198426i
$921$		0			0
$922$	−4.18861	−	3.51466i	−0.137945	−	0.115749i
$923$	−0.835380	+	4.73767i	−0.0274969	+	0.155942i
$924$		0			0
$925$	−15.4094	+	12.9300i	−0.506658	+	0.425137i
$926$	−22.0643	−	38.2165i	−0.725079	−	1.25587i
$927$		0			0
$928$	−6.72355	+	11.6455i	−0.220711	+	0.382283i
$929$	1.08429	+	6.14929i	0.0355742	+	0.201752i	0.997415	−	0.0718590i	$-0.0228932\pi$
$929$	1.08429	+	6.14929i	0.0355742	+	0.201752i	−0.961841	+	0.273611i	$0.911782\pi$
$930$		0			0
$931$	−24.0796	+	8.76426i	−0.789177	+	0.287237i
$932$	−62.6023	+	22.7854i	−2.05061	+	0.746360i
$933$		0			0
$934$	−1.94285	−	11.0185i	−0.0635720	−	0.360535i
$935$	0.286617	−	0.496435i	0.00937338	−	0.0162352i
$936$		0			0
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	−0.948397	−	0.317085i	$-0.897296\pi$
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	0.199595	−	0.979878i	$-0.436037\pi$
$938$	9.42762	−	7.91071i	0.307823	−	0.258294i
$939$		0			0
$940$	0.218831	−	1.24105i	0.00713749	−	0.0404787i
$941$	3.33431	+	2.79782i	0.108695	+	0.0912063i	0.695516	−	0.718511i	$-0.255176\pi$
$941$	3.33431	+	2.79782i	0.108695	+	0.0912063i	−0.586820	+	0.809717i	$0.699620\pi$
$942$		0			0
$943$	−4.58662	−	1.66939i	−0.149361	−	0.0543629i
$944$	27.3637			0.890612
$945$		0			0
$946$	−51.2644			−1.66675
$947$	1.89511	+	0.689764i	0.0615828	+	0.0224143i	0.372628	−	0.927981i	$-0.378457\pi$
$947$	1.89511	+	0.689764i	0.0615828	+	0.0224143i	−0.311045	+	0.950395i	$0.600679\pi$
$948$		0			0
$949$	0.629169	+	0.527935i	0.0204237	+	0.0171375i
$950$	8.00453	−	45.3959i	0.259701	−	1.47284i
$951$		0			0
$952$	−3.75474	+	3.15060i	−0.121692	+	0.102112i
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	−0.995631	−	0.0933786i	$-0.970233\pi$
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	0.416947	−	0.908931i	$-0.363100\pi$
$954$		0			0
$955$	0.104896	−	0.181686i	0.00339437	−	0.00587922i
$956$	10.0890	+	57.2178i	0.326303	+	1.85055i
$957$		0			0
$958$	−31.9920	+	11.6441i	−1.03361	+	0.376205i
$959$	−6.27727	+	2.28474i	−0.202704	+	0.0737781i
$960$		0			0
$961$	−4.90603	−	27.8235i	−0.158259	−	0.897531i
$962$	−20.3338	+	35.2191i	−0.655587	+	1.13551i
$963$		0			0
$964$	−24.7759	−	42.9131i	−0.797978	−	1.38214i
$965$	0.0627688	−	0.0526693i	0.00202060	−	0.00169548i
$966$		0			0
$967$	−0.120393	+	0.682784i	−0.00387159	+	0.0219569i	−0.986682	−	0.162659i	$-0.947993\pi$
$967$	−0.120393	+	0.682784i	−0.00387159	+	0.0219569i	0.982811	+	0.184616i	$0.0591041\pi$
$968$	−4.65998	−	3.91019i	−0.149777	−	0.125678i
$969$		0			0
$970$	1.11243	+	0.404891i	0.0357180	+	0.0130003i
$971$	−47.4942			−1.52416			−0.762081	−	0.647482i	$-0.775822\pi$
$971$	−47.4942			−1.52416			−0.762081	+	0.647482i	$0.775822\pi$
$972$		0			0
$973$	−0.987988			−0.0316734
$974$	48.3715	+	17.6058i	1.54992	+	0.564126i
$975$		0			0
$976$	−26.8962	−	22.5686i	−0.860927	−	0.722404i
$977$	2.18854	−	12.4118i	0.0700177	−	0.397090i	−0.929577	−	0.368628i	$-0.879828\pi$
$977$	2.18854	−	12.4118i	0.0700177	−	0.397090i	0.999595	−	0.0284625i	$-0.00906113\pi$
$978$		0			0
$979$	3.68004	−	3.08792i	0.117615	−	0.0986903i
$980$	−1.16855	−	2.02399i	−0.0373280	−	0.0646540i
$981$		0			0
$982$	−16.9168	+	29.3008i	−0.539838	+	0.935027i
$983$	−2.00477	−	11.3696i	−0.0639423	−	0.362635i	−0.999943	−	0.0106378i	$-0.996614\pi$
$983$	−2.00477	−	11.3696i	−0.0639423	−	0.362635i	0.936001	−	0.351997i	$-0.114497\pi$
$984$		0			0
$985$	−1.77359	+	0.645533i	−0.0565111	+	0.0205684i
$986$	28.7545	−	10.4658i	0.915729	−	0.333298i
$987$		0			0
$988$	−10.5713	−	59.9529i	−0.336318	−	1.90736i
$989$	15.3647	−	26.6125i	0.488569	−	0.846227i
$990$		0			0
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	0.678518	−	0.734584i	$-0.262623\pi$
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	−0.975427	+	0.220322i	$0.929289\pi$
$992$	−2.66802	+	2.23874i	−0.0847098	+	0.0710800i
$993$		0			0
$994$	0.276875	−	1.57024i	0.00878195	−	0.0498049i
$995$	1.35549	+	1.13739i	0.0429719	+	0.0360577i
$996$		0			0
$997$	−3.15624	−	1.14878i	−0.0999593	−	0.0363822i	0.291556	−	0.956554i	$-0.405827\pi$
$997$	−3.15624	−	1.14878i	−0.0999593	−	0.0363822i	−0.391516	+	0.920171i	$0.628049\pi$
$998$	35.8066			1.13344
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.a.190.1		12
3.2	odd	2		243.2.e.d.190.2		12
9.2	odd	6		27.2.e.a.13.1	✓	12
9.4	even	3		243.2.e.b.109.2		12
9.5	odd	6		243.2.e.c.109.1		12
9.7	even	3		81.2.e.a.10.2		12
27.2	odd	18		243.2.e.c.136.1		12
27.4	even	9		729.2.c.b.244.1		12
27.5	odd	18		729.2.c.e.487.6		12
27.7	even	9	inner	243.2.e.a.55.1		12
27.11	odd	18		27.2.e.a.25.1	yes	12
27.13	even	9		729.2.a.d.1.6		6
27.14	odd	18		729.2.a.a.1.1		6
27.16	even	9		81.2.e.a.73.2		12
27.20	odd	18		243.2.e.d.55.2		12
27.22	even	9		729.2.c.b.487.1		12
27.23	odd	18		729.2.c.e.244.6		12
27.25	even	9		243.2.e.b.136.2		12
36.11	even	6		432.2.u.c.337.1		12
45.2	even	12		675.2.u.b.499.4		24
45.29	odd	6		675.2.l.c.526.2		12
45.38	even	12		675.2.u.b.499.1		24
108.11	even	18		432.2.u.c.241.1		12
135.38	even	36		675.2.u.b.349.4		24
135.92	even	36		675.2.u.b.349.1		24
135.119	odd	18		675.2.l.c.376.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	9.2	odd	6
27.2.e.a.25.1	yes	12	27.11	odd	18
81.2.e.a.10.2		12	9.7	even	3
81.2.e.a.73.2		12	27.16	even	9
243.2.e.a.55.1		12	27.7	even	9	inner
243.2.e.a.190.1		12	1.1	even	1	trivial
243.2.e.b.109.2		12	9.4	even	3
243.2.e.b.136.2		12	27.25	even	9
243.2.e.c.109.1		12	9.5	odd	6
243.2.e.c.136.1		12	27.2	odd	18
243.2.e.d.55.2		12	27.20	odd	18
243.2.e.d.190.2		12	3.2	odd	2
432.2.u.c.241.1		12	108.11	even	18
432.2.u.c.337.1		12	36.11	even	6
675.2.l.c.376.2		12	135.119	odd	18
675.2.l.c.526.2		12	45.29	odd	6
675.2.u.b.349.1		24	135.92	even	36
675.2.u.b.349.4		24	135.38	even	36
675.2.u.b.499.1		24	45.38	even	12
675.2.u.b.499.4		24	45.2	even	12
729.2.a.a.1.1		6	27.14	odd	18
729.2.a.d.1.6		6	27.13	even	9
729.2.c.b.244.1		12	27.4	even	9
729.2.c.b.487.1		12	27.22	even	9
729.2.c.e.244.6		12	27.23	odd	18
729.2.c.e.487.6		12	27.5	odd	18

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.25679 - 0.821403i) q^{2} +(2.88629 + 2.42189i) q^{4} +(-0.0161638 + 0.0916693i) q^{5} +(-0.444200 + 0.372728i) q^{7} +(-2.12277 - 3.67675i) q^{8} +O(q^{10})\)	\(q+(-2.25679 - 0.821403i) q^{2} +(2.88629 + 2.42189i) q^{4} +(-0.0161638 + 0.0916693i) q^{5} +(-0.444200 + 0.372728i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(0.537108 + 3.04609i) q^{11} +(-3.94834 + 1.43708i) q^{13} +(1.30862 - 0.476300i) q^{14} +(0.462014 + 2.62021i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(-0.268666 + 0.225437i) q^{20} +(1.28993 - 7.31556i) q^{22} +(3.41105 + 2.86221i) q^{23} +(4.69032 + 1.70714i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(6.01357 + 2.18876i) q^{29} +(1.26972 + 1.06542i) q^{31} +(-0.364882 + 2.06935i) q^{32} +(3.66291 - 3.07355i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-1.60368 - 9.09494i) q^{38} +(0.371357 - 0.135163i) q^{40} +(-1.03005 + 0.374907i) q^{41} +(-1.19837 - 6.79628i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-2.75255 + 2.30966i) q^{47} +(-1.15715 + 6.56252i) q^{49} +(-9.18280 - 7.70529i) q^{50} +(-14.8765 - 5.41460i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(2.31336 + 0.841995i) q^{56} +(-11.7735 - 9.87913i) q^{58} +(1.78591 - 10.1284i) q^{59} +(-10.1090 + 8.48243i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(-0.0679158 - 0.385170i) q^{65} +(8.30434 - 3.02253i) q^{67} +(-7.04920 + 2.56570i) q^{68} +(0.0225098 + 0.127659i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(7.41436 - 6.22139i) q^{74} +(-2.51594 + 14.2686i) q^{76} +(-1.37395 - 1.15288i) q^{77} +(6.77330 + 2.46528i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-14.0018 - 5.09625i) q^{83} +(-0.141969 - 0.119126i) q^{85} +(-2.87802 + 16.3221i) q^{86} +(10.0596 - 8.44098i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(2.91334 + 16.5224i) q^{92} +(8.10907 - 2.95146i) q^{94} +(-0.336358 + 0.122424i) q^{95} +(0.919560 + 5.21508i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 + 6 * q^11 + 3 * q^13 + 21 * q^14 + 9 * q^16 - 9 * q^17 - 3 * q^19 - 24 * q^20 + 12 * q^22 + 12 * q^23 + 12 * q^25 + 30 * q^26 - 12 * q^28 + 24 * q^29 + 12 * q^31 - 27 * q^32 - 12 * q^35 - 3 * q^37 + 30 * q^38 - 15 * q^40 - 6 * q^41 - 15 * q^43 - 3 * q^44 - 3 * q^46 - 12 * q^47 - 33 * q^49 - 21 * q^50 - 45 * q^52 + 18 * q^53 - 12 * q^55 - 30 * q^56 - 51 * q^58 + 3 * q^59 - 33 * q^61 + 12 * q^62 + 12 * q^64 - 21 * q^65 - 6 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 + 21 * q^74 + 6 * q^76 + 12 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 6 * q^83 + 36 * q^85 + 21 * q^86 + 42 * q^88 - 9 * q^89 + 6 * q^91 + 3 * q^92 + 48 * q^94 - 3 * q^95 + 39 * q^97 + 45 * q^98

Introduction

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Database

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