LMFDB - Embedded newform 243.2.e.a.55.1

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			55.1
Root			$0.500000 + 1.00210i$ of defining polynomial
Character	$\chi$	$=$	243.55
Dual form			243.2.e.a.190.1

$q$-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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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	−0.978560	−	0.205964i	$-0.933967\pi$
$2$	−2.25679	+	0.821403i	−1.59579	+	0.580820i	−0.617229	+	0.786784i	$0.711745\pi$
$3$		0			0
$3$		0			0
$4$	2.88629	−	2.42189i	1.44315	−	1.21094i
$5$	−0.0161638	−	0.0916693i	−0.00722866	−	0.0409957i	0.980980	−	0.194108i	$-0.0621814\pi$
$5$	−0.0161638	−	0.0916693i	−0.00722866	−	0.0409957i	−0.988209	+	0.153113i	$0.951070\pi$
$6$		0			0
$7$	−0.444200	−	0.372728i	−0.167892	−	0.140878i	0.554971	−	0.831870i	$-0.312729\pi$
$7$	−0.444200	−	0.372728i	−0.167892	−	0.140878i	−0.722862	+	0.690992i	$0.757174\pi$
$8$	−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	−0.790215	−	0.612830i	$-0.790031\pi$
$11$	0.537108	−	3.04609i	0.161944	−	0.918431i	0.952159	−	0.305602i	$-0.0988577\pi$
$12$		0			0
$13$	−3.94834	−	1.43708i	−1.09507	−	0.398574i	−0.269574	−	0.962980i	$-0.586883\pi$
$13$	−3.94834	−	1.43708i	−1.09507	−	0.398574i	−0.825497	+	0.564406i	$0.809105\pi$
$14$	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	0.719683	−	0.694303i	$-0.244287\pi$
$17$	−0.995493	−	1.72424i	−0.241443	−	0.418191i	−0.961125	+	0.276112i	$0.910954\pi$
$18$		0			0
$19$	1.92271	−	3.33023i	0.441100	−	0.764008i	−0.556671	−	0.830733i	$-0.687922\pi$
$19$	1.92271	−	3.33023i	0.441100	−	0.764008i	0.997771	+	0.0667249i	$0.0212550\pi$
$20$	−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	−0.213697	−	0.976900i	$-0.568550\pi$
$23$	3.41105	−	2.86221i	0.711254	−	0.596813i	0.924951	+	0.380087i	$0.124106\pi$
$24$		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	0.283248	−	0.959047i	$-0.408588\pi$
$29$	6.01357	−	2.18876i	1.11669	−	0.406443i	0.833444	+	0.552604i	$0.186366\pi$
$30$		0			0
$31$	1.26972	−	1.06542i	0.228048	−	0.191355i	−0.521603	−	0.853188i	$-0.674666\pi$
$31$	1.26972	−	1.06542i	0.228048	−	0.191355i	0.749651	+	0.661833i	$0.230221\pi$
$32$	−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	0.651490	−	0.758657i	$-0.274144\pi$
$37$	−2.01505	−	3.49016i	−0.331272	−	0.573779i	−0.982761	+	0.184878i	$0.940811\pi$
$38$	−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	0.260332	−	0.965519i	$-0.416168\pi$
$41$	−1.03005	−	0.374907i	−0.160867	−	0.0585507i	−0.421198	+	0.906969i	$0.638390\pi$
$42$		0			0
$43$	−1.19837	+	6.79628i	−0.182749	+	1.03642i	0.746064	+	0.665874i	$0.231941\pi$
$43$	−1.19837	+	6.79628i	−0.182749	+	1.03642i	−0.928813	+	0.370548i	$0.879170\pi$
$44$	−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	0.419573	−	0.907722i	$-0.362180\pi$
$47$	−2.75255	−	2.30966i	−0.401500	−	0.336899i	−0.821073	+	0.570823i	$0.806624\pi$
$48$		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	0.847803	+	0.530311i	$0.177925\pi$
$59$	1.78591	+	10.1284i	0.232506	+	1.31861i	−0.615297	+	0.788295i	$0.710964\pi$
$60$		0			0
$61$	−10.1090	−	8.48243i	−1.29432	−	1.08606i	−0.991097	−	0.133145i	$-0.957492\pi$
$61$	−10.1090	−	8.48243i	−1.29432	−	1.08606i	−0.303224	−	0.952919i	$-0.598063\pi$
$62$	−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	0.795173	−	0.606382i	$-0.207380\pi$
$67$	8.30434	+	3.02253i	1.01454	+	0.369261i	0.219363	+	0.975643i	$0.429602\pi$
$68$	−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	0.897994	−	0.440007i	$-0.145024\pi$
$71$	0.572473	+	0.991553i	0.0679401	+	0.117676i	−0.830054	+	0.557683i	$0.811691\pi$
$72$		0			0
$73$	−0.0977361	+	0.169284i	−0.0114391	+	0.0198132i	−0.871688	−	0.490061i	$-0.836975\pi$
$73$	−0.0977361	+	0.169284i	−0.0114391	+	0.0198132i	0.860249	+	0.509874i	$0.170308\pi$
$74$	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	0.0683861	−	0.997659i	$-0.478215\pi$
$79$	6.77330	−	2.46528i	0.762056	−	0.277366i	0.693670	+	0.720293i	$0.255993\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	−14.0018	+	5.09625i	−1.53690	+	0.559386i	−0.965300	−	0.261145i	$-0.915900\pi$
$83$	−14.0018	+	5.09625i	−1.53690	+	0.559386i	−0.571602	+	0.820531i	$0.693678\pi$
$84$		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	−0.904244	−	0.427016i	$-0.859565\pi$
$89$	−0.776563	+	1.34505i	−0.0823155	+	0.142575i	0.821929	+	0.569590i	$0.192898\pi$
$90$		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	−0.901868	−	0.432011i	$-0.857804\pi$
$97$	0.919560	−	5.21508i	0.0933672	−	0.529511i	0.995235	−	0.0975004i	$-0.0310847\pi$
$98$	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	0.876317	−	0.481734i	$-0.159993\pi$
$101$	5.56836	+	4.67241i	0.554073	+	0.464922i	−0.322245	+	0.946656i	$0.604437\pi$
$102$		0			0
$103$	1.11159	+	6.30412i	0.109528	+	0.621164i	0.989315	+	0.145795i	$0.0465741\pi$
$103$	1.11159	+	6.30412i	0.109528	+	0.621164i	−0.879787	+	0.475368i	$0.842315\pi$
$104$	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	0.914571	+	0.404424i	$0.132528\pi$
$113$	2.05669	+	11.6640i	0.193477	+	1.09726i	−0.721095	+	0.692836i	$0.756361\pi$
$114$		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	0.488377	+	0.872633i	$0.337589\pi$
$127$	−5.76469	+	9.98473i	−0.511533	+	0.886002i	−0.999911	+	0.0133693i	$0.995744\pi$
$128$	−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	−0.289303	−	0.957237i	$-0.593424\pi$
$131$	6.90342	−	5.79266i	0.603155	−	0.506107i	0.892458	+	0.451131i	$0.148979\pi$
$132$		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	0.164703	−	0.986343i	$-0.447333\pi$
$137$	10.8255	−	3.94015i	0.924883	−	0.336630i	0.760179	+	0.649713i	$0.225111\pi$
$138$		0			0
$139$	1.30521	−	1.09520i	0.110707	−	0.0928940i	−0.585754	−	0.810489i	$-0.699202\pi$
$139$	1.30521	−	1.09520i	0.110707	−	0.0928940i	0.696461	+	0.717595i	$0.254757\pi$
$140$	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	−0.675464	−	0.737393i	$-0.736057\pi$
$149$	−20.3469	−	7.40568i	−1.66689	−	0.606697i	−0.991423	+	0.130696i	$0.958279\pi$
$150$		0			0
$151$	−0.823357	+	4.66949i	−0.0670038	+	0.379998i	0.932804	+	0.360385i	$0.117355\pi$
$151$	−0.823357	+	4.66949i	−0.0670038	+	0.379998i	−0.999808	+	0.0196130i	$0.993757\pi$
$152$	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	0.983324	−	0.181864i	$-0.0582129\pi$
$157$	−0.0363282	−	0.206027i	−0.00289931	−	0.0164428i	−0.986223	+	0.165421i	$0.947102\pi$
$158$	−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	−0.864321	−	0.502941i	$-0.832251\pi$
$167$	−2.89654	−	16.4271i	−0.224141	−	1.27117i	0.640180	−	0.768225i	$-0.278860\pi$
$168$		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	0.555583	+	0.831461i	$0.312495\pi$
$173$	−3.29969	+	18.7135i	−0.250871	+	1.42276i	−0.806454	+	0.591297i	$0.798616\pi$
$174$		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	0.991774	+	0.128001i	$0.0408560\pi$
$179$	8.11761	+	14.0601i	0.606739	+	1.05090i	−0.385035	+	0.922902i	$0.625811\pi$
$180$		0			0
$181$	1.49579	−	2.59078i	0.111181	−	0.192571i	−0.805066	−	0.593186i	$-0.797870\pi$
$181$	1.49579	−	2.59078i	0.111181	−	0.192571i	0.916247	+	0.400614i	$0.131203\pi$
$182$	−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	−0.417504	−	0.908675i	$-0.637095\pi$
$191$	−2.11790	+	0.770851i	−0.153246	+	0.0557768i	0.264258	+	0.964452i	$0.414873\pi$
$192$		0			0
$193$	−0.674328	+	0.565829i	−0.0485392	+	0.0407292i	−0.666735	−	0.745295i	$-0.732309\pi$
$193$	−0.674328	+	0.565829i	−0.0485392	+	0.0407292i	0.618195	+	0.786025i	$0.287864\pi$
$194$	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	−0.237744	−	0.971328i	$-0.576408\pi$
$197$	10.1383	−	17.5600i	0.722322	−	1.25110i	0.960067	−	0.279771i	$-0.0902586\pi$
$198$		0			0
$199$	9.50472	+	16.4627i	0.673772	+	1.16701i	0.976826	+	0.214034i	$0.0686603\pi$
$199$	9.50472	+	16.4627i	0.673772	+	1.16701i	−0.303054	+	0.952973i	$0.598006\pi$
$200$	−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	0.914579	+	0.404408i	$0.132522\pi$
$211$	2.81033	+	15.9382i	0.193471	+	1.09723i	−0.721108	+	0.692823i	$0.756367\pi$
$212$	−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	0.997473	−	0.0710428i	$-0.0226327\pi$
$223$	16.4372	+	13.7925i	1.10072	+	0.923613i	0.103246	+	0.994656i	$0.467077\pi$
$224$	−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	−0.651169	−	0.758933i	$-0.725721\pi$
$227$	3.31915	−	18.8239i	0.220300	−	1.24938i	0.871469	−	0.490451i	$-0.163168\pi$
$228$		0			0
$229$	−21.1150	−	7.68525i	−1.39532	−	0.507855i	−0.468535	−	0.883445i	$-0.655218\pi$
$229$	−21.1150	−	7.68525i	−1.39532	−	0.507855i	−0.926786	+	0.375589i	$0.877440\pi$
$230$	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	−0.995574	−	0.0939796i	$-0.970041\pi$
$233$	−8.84074	−	15.3126i	−0.579176	−	1.00316i	0.416398	−	0.909182i	$-0.363292\pi$
$234$		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	−0.175093	−	0.984552i	$-0.556023\pi$
$239$	11.8126	−	9.91199i	0.764097	−	0.641153i	0.939190	+	0.343399i	$0.111578\pi$
$240$		0			0
$241$	−12.3583	+	4.49806i	−0.796069	+	0.289746i	−0.707857	−	0.706356i	$-0.750338\pi$
$241$	−12.3583	+	4.49806i	−0.796069	+	0.289746i	−0.0882127	+	0.996102i	$0.528116\pi$
$242$	−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	−0.448634	−	0.893716i	$-0.648089\pi$
$251$	8.70830	−	15.0832i	0.549663	−	0.952045i	0.998297	−	0.0583292i	$-0.0185773\pi$
$252$		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	0.648412	−	0.761290i	$-0.275434\pi$
$257$	10.5129	+	3.82638i	0.655776	+	0.238683i	0.00736433	+	0.999973i	$0.497656\pi$
$258$		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	0.983833	−	0.179088i	$-0.0573148\pi$
$263$	15.8655	+	13.3127i	0.978306	+	0.820896i	−0.00552693	+	0.999985i	$0.501759\pi$
$264$		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	0.753947	−	0.656935i	$-0.228148\pi$
$277$	3.95967	+	3.32256i	0.237913	+	0.199633i	−0.516034	+	0.856568i	$0.672592\pi$
$278$	−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	−0.962962	−	0.269638i	$-0.913096\pi$
$281$	0.572421	−	3.24636i	0.0341478	−	0.193662i	0.997110	+	0.0759760i	$0.0242072\pi$
$282$		0			0
$283$	8.58007	+	3.12289i	0.510032	+	0.185637i	0.584201	−	0.811609i	$-0.301408\pi$
$283$	8.58007	+	3.12289i	0.510032	+	0.185637i	−0.0741686	+	0.997246i	$0.523630\pi$
$284$	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	−0.577348	−	0.816498i	$-0.695912\pi$
$293$	2.16517	−	1.81680i	0.126491	−	0.106138i	0.703839	+	0.710360i	$0.251468\pi$
$294$		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	0.762129	−	0.647425i	$-0.224154\pi$
$307$	−3.14723	−	5.45116i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$308$	−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	0.138031	−	0.990428i	$-0.455922\pi$
$311$	−6.92825	−	2.52168i	−0.392865	−	0.142991i	−0.530896	+	0.847437i	$0.678145\pi$
$312$		0			0
$313$	−0.741608	+	4.20587i	−0.0419182	+	0.237730i	−0.998567	−	0.0535138i	$-0.982958\pi$
$313$	−0.741608	+	4.20587i	−0.0419182	+	0.237730i	0.956649	+	0.291244i	$0.0940690\pi$
$314$	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	0.225521	−	0.974238i	$-0.427591\pi$
$317$	−12.3698	−	10.3795i	−0.694755	−	0.582968i	−0.920276	+	0.391270i	$0.872036\pi$
$318$		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	0.950516	−	0.310675i	$-0.100555\pi$
$331$	14.7297	+	12.3597i	0.809616	+	0.679349i	−0.140900	+	0.990024i	$0.545000\pi$
$332$	−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	0.958156	−	0.286248i	$-0.0924080\pi$
$337$	27.6859	+	10.0769i	1.50815	+	0.548921i	0.549993	+	0.835169i	$0.314630\pi$
$338$	−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	−0.846315	−	0.532683i	$-0.821184\pi$
$347$	−8.73063	+	7.32587i	−0.468685	+	0.393273i	0.377630	+	0.925957i	$0.376739\pi$
$348$		0			0
$349$	−26.4633	+	9.63184i	−1.41655	+	0.515581i	−0.933044	−	0.359763i	$-0.882858\pi$
$349$	−26.4633	+	9.63184i	−1.41655	+	0.515581i	−0.483502	+	0.875343i	$0.660635\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	26.9260	−	9.80028i	1.43313	−	0.521616i	0.495302	−	0.868721i	$-0.335057\pi$
$353$	26.9260	−	9.80028i	1.43313	−	0.521616i	0.937826	+	0.347104i	$0.112835\pi$
$354$		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	0.0875770	+	0.996158i	$0.472088\pi$
$359$	−15.5161	+	26.8747i	−0.818909	+	1.41839i	−0.906486	+	0.422235i	$0.861246\pi$
$360$		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	−0.655751	−	0.754977i	$-0.727648\pi$
$367$	4.18913	−	23.7577i	0.218671	−	1.24014i	0.874422	−	0.485166i	$-0.161241\pi$
$368$	−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	−0.987645	−	0.156707i	$-0.949912\pi$
$373$	−2.18547	−	12.3944i	−0.113159	−	0.641758i	0.874486	−	0.485051i	$-0.161199\pi$
$374$	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	0.955529	+	0.294898i	$0.0952856\pi$
$383$	3.10164	+	17.5903i	0.158486	+	0.898821i	−0.797042	+	0.603923i	$0.793603\pi$
$384$		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	0.588160	+	0.808744i	$0.299852\pi$
$389$	−4.75596	+	26.9724i	−0.241137	+	1.36755i	−0.829297	+	0.558809i	$0.811259\pi$
$390$		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	−0.914064	−	0.405571i	$-0.867073\pi$
$397$	−2.10799	+	3.65115i	−0.105797	+	0.183246i	0.808266	+	0.588817i	$0.200406\pi$
$398$	−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	−0.885084	−	0.465432i	$-0.845899\pi$
$401$	−11.6228	+	9.75269i	−0.580415	+	0.487026i	0.304668	+	0.952459i	$0.401454\pi$
$402$		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	−0.549219	−	0.835679i	$-0.685075\pi$
$409$	3.60777	−	3.02728i	0.178393	−	0.149689i	0.727612	+	0.685989i	$0.240630\pi$
$410$	−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	0.753674	−	0.657248i	$-0.228280\pi$
$419$	18.5976	+	6.76897i	0.908551	+	0.330686i	0.154877	+	0.987934i	$0.450502\pi$
$420$		0			0
$421$	4.89440	−	27.7575i	0.238538	−	1.35282i	−0.596494	−	0.802617i	$-0.703440\pi$
$421$	4.89440	−	27.7575i	0.238538	−	1.35282i	0.835032	−	0.550201i	$-0.185449\pi$
$422$	−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	0.309911	−	0.950766i	$-0.399701\pi$
$439$	−11.9972	−	10.0668i	−0.572595	−	0.480464i	−0.882506	+	0.470301i	$0.844145\pi$
$440$	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	−0.812100	−	0.583518i	$-0.801676\pi$
$443$	3.16975	−	17.9765i	0.150599	−	0.854091i	0.962700	−	0.270573i	$-0.0872131\pi$
$444$		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	0.975663	+	0.219274i	$0.0703690\pi$
$449$	14.3608	+	24.8737i	0.677729	+	1.17386i	−0.297934	+	0.954586i	$0.596298\pi$
$450$		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	0.585835	−	0.810430i	$-0.300767\pi$
$457$	33.2538	−	12.1034i	1.55555	−	0.566172i	0.969710	+	0.244258i	$0.0785444\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	2.13943	−	0.778687i	0.0996430	−	0.0362671i	−0.291718	−	0.956504i	$-0.594227\pi$
$461$	2.13943	−	0.778687i	0.0996430	−	0.0362671i	0.391361	+	0.920237i	$0.372005\pi$
$462$		0			0
$463$	14.0757	−	11.8109i	0.654154	−	0.548900i	−0.254175	−	0.967158i	$-0.581804\pi$
$463$	14.0757	−	11.8109i	0.654154	−	0.548900i	0.908328	+	0.418258i	$0.137359\pi$
$464$	−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	−0.807085	−	0.590435i	$-0.798956\pi$
$467$	2.32935	−	4.03455i	0.107789	−	0.186697i	0.914874	+	0.403738i	$0.132289\pi$
$468$		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	0.856234	−	0.516588i	$-0.172798\pi$
$479$	10.8594	+	9.11209i	0.496177	+	0.416342i	−0.360057	+	0.932930i	$0.617243\pi$
$480$		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	0.988925	+	0.148418i	$0.0474180\pi$
$491$	2.44633	+	13.8738i	0.110401	+	0.626117i	−0.878523	+	0.477699i	$0.841471\pi$
$492$		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	0.00882219	−	0.999961i	$-0.497192\pi$
$499$	−14.0102	−	5.09929i	−0.627182	−	0.228276i	−0.636004	+	0.771685i	$0.719414\pi$
$500$	−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	0.633236	−	0.773958i	$-0.281726\pi$
$503$	−7.93153	−	13.7378i	−0.353650	−	0.612539i	−0.986886	+	0.161420i	$0.948393\pi$
$504$		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	−0.999764	−	0.0217430i	$-0.993078\pi$
$509$	−25.9894	+	21.8077i	−1.15196	+	0.966608i	−0.152194	+	0.988351i	$0.548634\pi$
$510$		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	−0.166277	+	0.986079i	$0.553175\pi$
$521$	−21.3899	+	37.0484i	−0.937108	+	1.62312i	−0.770831	+	0.637040i	$0.780159\pi$
$522$		0			0
$523$	1.38893	+	2.40569i	0.0607335	+	0.105193i	0.894793	−	0.446480i	$-0.147323\pi$
$523$	1.38893	+	2.40569i	0.0607335	+	0.105193i	−0.834060	+	0.551674i	$0.813989\pi$
$524$	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	−0.990725	−	0.135884i	$-0.956612\pi$
$547$	−30.3245	−	25.4453i	−1.29658	−	1.08796i	−0.305858	−	0.952077i	$-0.598943\pi$
$548$	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	0.719105	−	0.694902i	$-0.244552\pi$
$557$	−5.71731	−	9.90267i	−0.242250	−	0.419590i	−0.961355	+	0.275312i	$0.911219\pi$
$558$		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	−0.846240	−	0.532802i	$-0.821139\pi$
$563$	−11.1159	+	9.32736i	−0.468480	+	0.393101i	0.377760	+	0.925904i	$0.376694\pi$
$564$		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	−0.367483	−	0.930030i	$-0.619780\pi$
$569$	−1.22083	+	0.444347i	−0.0511800	+	0.0186280i	0.316303	+	0.948658i	$0.397558\pi$
$570$		0			0
$571$	12.3006	−	10.3214i	0.514765	−	0.431939i	−0.348037	−	0.937481i	$-0.613152\pi$
$571$	12.3006	−	10.3214i	0.514765	−	0.431939i	0.862802	+	0.505542i	$0.168707\pi$
$572$	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	0.940543	−	0.339675i	$-0.110317\pi$
$577$	4.23017	+	7.32686i	0.176104	+	0.305021i	−0.764439	+	0.644696i	$0.776984\pi$
$578$	−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	0.885375	−	0.464877i	$-0.153902\pi$
$587$	14.0839	+	11.8178i	0.581304	+	0.487772i	−0.304071	+	0.952649i	$0.598346\pi$
$588$		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	−0.998611	−	0.0526835i	$-0.983223\pi$
$599$	−1.91494	−	10.8602i	−0.0782425	−	0.443735i	0.920369	−	0.391051i	$-0.127889\pi$
$600$		0			0
$601$	19.7624	+	16.5826i	0.806123	+	0.676418i	0.949679	−	0.313225i	$-0.101409\pi$
$601$	19.7624	+	16.5826i	0.806123	+	0.676418i	−0.143556	+	0.989642i	$0.545854\pi$
$602$	−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	0.608300	−	0.793707i	$-0.291852\pi$
$607$	13.8979	+	5.05843i	0.564100	+	0.205316i	−0.0442003	+	0.999023i	$0.514074\pi$
$608$	−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	0.223248	+	0.974762i	$0.428334\pi$
$613$	−18.1370	+	31.4141i	−0.732545	+	1.26880i	−0.955792	+	0.294043i	$0.904999\pi$
$614$	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	0.248005	−	0.968759i	$-0.420225\pi$
$617$	30.9279	−	25.9516i	1.24511	−	1.04477i	0.997107	−	0.0760138i	$-0.0242193\pi$
$618$		0			0
$619$	6.47759	−	2.35765i	0.260356	−	0.0947619i	−0.208544	−	0.978013i	$-0.566873\pi$
$619$	6.47759	−	2.35765i	0.260356	−	0.0947619i	0.468900	+	0.883251i	$0.344650\pi$
$620$	−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	−0.993751	−	0.111617i	$-0.964397\pi$
$631$	−14.9095	−	25.8241i	−0.593539	−	1.02804i	0.400212	−	0.916423i	$-0.368936\pi$
$632$	−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	−0.990581	−	0.136926i	$-0.956278\pi$
$641$	−32.8485	−	27.5632i	−1.29744	−	1.08868i	−0.306858	−	0.951755i	$-0.599278\pi$
$642$		0			0
$643$	−4.76026	−	26.9968i	−0.187726	−	1.06465i	−0.922402	−	0.386231i	$-0.873777\pi$
$643$	−4.76026	−	26.9968i	−0.187726	−	1.06465i	0.734676	−	0.678419i	$-0.237334\pi$
$644$	−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	−0.873602	−	0.486641i	$-0.838222\pi$
$653$	−5.59951	−	31.7564i	−0.219126	−	1.24272i	0.654476	−	0.756083i	$-0.272889\pi$
$654$		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	0.733632	+	0.679547i	$0.237824\pi$
$659$	−4.83065	+	27.3960i	−0.188175	+	1.06719i	−0.921807	+	0.387648i	$0.873288\pi$
$660$		0			0
$661$	−28.9318	−	10.5303i	−1.12532	−	0.409582i	−0.288728	−	0.957411i	$-0.593232\pi$
$661$	−28.9318	−	10.5303i	−1.12532	−	0.409582i	−0.836590	+	0.547829i	$0.815454\pi$
$662$	−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	0.177780	−	0.984070i	$-0.443108\pi$
$673$	24.5547	−	8.93720i	0.946516	−	0.344504i	0.768736	+	0.639567i	$0.220886\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	17.0972	−	6.22288i	0.657100	−	0.239165i	0.00811624	−	0.999967i	$-0.497416\pi$
$677$	17.0972	−	6.22288i	0.657100	−	0.239165i	0.648984	+	0.760802i	$0.275194\pi$
$678$		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	−0.548811	−	0.835947i	$-0.684919\pi$
$683$	11.7486	−	20.3491i	0.449546	−	0.778636i	0.998356	+	0.0573104i	$0.0182525\pi$
$684$		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	0.376173	+	0.926549i	$0.377240\pi$
$691$	−7.73393	+	43.8613i	−0.294213	+	1.66856i	−0.670386	+	0.742013i	$0.733871\pi$
$692$	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	0.388668	−	0.921378i	$-0.372935\pi$
$709$	−12.0147	−	10.0815i	−0.451220	−	0.378618i	−0.839888	+	0.542759i	$0.817380\pi$
$710$	−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	−0.609757	−	0.792588i	$-0.708733\pi$
$719$	−26.5804	−	46.0385i	−0.991280	−	1.71695i	−0.381523	−	0.924359i	$-0.624600\pi$
$720$		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	−0.350183	−	0.936681i	$-0.613881\pi$
$727$	−0.440878	+	0.160466i	−0.0163512	+	0.00595137i	0.333832	+	0.942633i	$0.391658\pi$
$728$	−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	−0.325312	+	0.945607i	$0.605469\pi$
$733$	−35.5493	+	29.8294i	−1.31304	+	1.10177i	−0.987731	+	0.156166i	$0.950086\pi$
$734$	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	0.524875	−	0.851179i	$-0.324112\pi$
$739$	−12.9047	−	22.3515i	−0.474706	−	0.822214i	−0.999580	+	0.0289653i	$0.990779\pi$
$740$	−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	0.862029	−	0.506859i	$-0.169193\pi$
$743$	32.6164	+	11.8714i	1.19658	+	0.435519i	0.334550	+	0.942378i	$0.391416\pi$
$744$		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	0.961489	+	0.274843i	$0.0886257\pi$
$751$	4.16510	+	23.6214i	0.151987	+	0.861959i	−0.809503	+	0.587116i	$0.800263\pi$
$752$	−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	−0.997005	−	0.0773355i	$-0.975359\pi$
$761$	−2.38833	−	13.5449i	−0.0865771	−	0.491003i	0.910428	−	0.413667i	$-0.135752\pi$
$762$		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	0.813405	−	0.581698i	$-0.197611\pi$
$769$	29.4668	+	10.7250i	1.06260	+	0.386755i	0.249196	+	0.968453i	$0.419834\pi$
$770$	−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	0.999978	+	0.00662776i	$0.00210970\pi$
$773$	14.0607	+	24.3539i	0.505729	+	0.875948i	−0.494249	+	0.869320i	$0.664557\pi$
$774$		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	+

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

L-functions

Modular forms

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Database

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