LMFDB - Embedded newform 243.2.e.b.109.2

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			109.2
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	243.109
Dual form			243.2.e.b.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83975 - 1.54373i) q^{2} +(0.654269 - 3.71054i) q^{4} +(0.0874698 - 0.0318364i) q^{5} +(-0.100692 - 0.571052i) q^{7} +(-2.12277 - 3.67675i) q^{8} +O(q^{10})$	\(q+(1.83975 - 1.54373i) q^{2} +(0.654269 - 3.71054i) q^{4} +(0.0874698 - 0.0318364i) q^{5} +(-0.100692 - 0.571052i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(-2.90655 - 1.05790i) q^{11} +(3.21871 + 2.70082i) q^{13} +(-1.06680 - 0.895151i) q^{14} +(-2.50017 - 0.909989i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(-0.0609016 - 0.345390i) q^{20} +(-6.98043 + 2.54067i) q^{22} +(0.773223 - 4.38517i) q^{23} +(-3.82358 + 3.20837i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(-4.90231 + 4.11353i) q^{29} +(0.287822 - 1.63232i) q^{31} +(1.97455 - 0.718677i) q^{32} +(0.830315 + 4.70895i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(8.67830 + 3.15864i) q^{38} +(-0.302733 - 0.254023i) q^{40} +(0.839704 + 0.704595i) q^{41} +(6.48493 + 2.36032i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-0.623952 - 3.53861i) q^{47} +(6.26189 - 2.27914i) q^{49} +(-2.08157 + 11.8052i) q^{50} +(12.1274 - 10.1761i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(-1.88587 + 1.58243i) q^{56} +(-2.66883 + 15.1357i) q^{58} +(-9.66442 + 3.51756i) q^{59} +(-2.29152 - 12.9958i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(0.367525 + 0.133768i) q^{65} +(-6.76976 - 5.68050i) q^{67} +(5.74656 + 4.82194i) q^{68} +(-0.121811 - 0.0443356i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(1.68070 + 9.53172i) q^{74} +(13.6149 - 4.95544i) q^{76} +(-0.311448 + 1.76631i) q^{77} +(-5.52164 + 4.63321i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(11.4144 - 9.57782i) q^{83} +(-0.0321818 + 0.182512i) q^{85} +(15.5744 - 5.66860i) q^{86} +(2.28032 + 12.9323i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(-15.7655 - 5.73816i) q^{92} +(-6.61057 - 5.54693i) q^{94} +(0.274202 + 0.230083i) q^{95} +(-4.97617 - 1.81118i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.83975	−	1.54373i	1.30090	−	1.09158i	0.310910	−	0.950439i	$-0.399366\pi$
$2$	1.83975	−	1.54373i	1.30090	−	1.09158i	0.989989	−	0.141144i	$-0.0450781\pi$
$3$		0			0
$3$		0			0
$4$	0.654269	−	3.71054i	0.327134	−	1.85527i
$5$	0.0874698	−	0.0318364i	0.0391177	−	0.0142377i	−0.322387	−	0.946608i	$-0.604485\pi$
$5$	0.0874698	−	0.0318364i	0.0391177	−	0.0142377i	0.361505	+	0.932370i	$0.382263\pi$
$6$		0			0
$7$	−0.100692	−	0.571052i	−0.0380579	−	0.215837i	0.959848	−	0.280521i	$-0.0905073\pi$
$7$	−0.100692	−	0.571052i	−0.0380579	−	0.215837i	−0.997906	+	0.0646837i	$0.979396\pi$
$8$	−2.12277	−	3.67675i	−0.750514	−	1.29993i
$9$		0			0
$10$	0.111776	−	0.193601i	0.0353465	−	0.0612220i
$11$	−2.90655	−	1.05790i	−0.876357	−	0.318968i	−0.135618	−	0.990761i	$-0.543302\pi$
$11$	−2.90655	−	1.05790i	−0.876357	−	0.318968i	−0.740739	+	0.671793i	$0.765524\pi$
$12$		0			0
$13$	3.21871	+	2.70082i	0.892711	+	0.749073i	0.968752	−	0.248031i	$-0.0797836\pi$
$13$	3.21871	+	2.70082i	0.892711	+	0.749073i	−0.0760413	+	0.997105i	$0.524228\pi$
$14$	−1.06680	−	0.895151i	−0.285114	−	0.239239i
$15$		0			0
$16$	−2.50017	−	0.909989i	−0.625044	−	0.227497i
$17$	−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	$0.687922\pi$
$20$	−0.0609016	−	0.345390i	−0.0136180	−	0.0772316i
$21$		0			0
$22$	−6.98043	+	2.54067i	−1.48823	+	0.541672i
$23$	0.773223	−	4.38517i	0.161228	−	0.914371i	−0.791640	−	0.610987i	$-0.790773\pi$
$23$	0.773223	−	4.38517i	0.161228	−	0.914371i	0.952869	−	0.303383i	$-0.0981163\pi$
$24$		0			0
$25$	−3.82358	+	3.20837i	−0.764717	+	0.641674i
$26$	10.0910			1.97900
$27$		0			0
$28$	−2.18479			−0.412887
$29$	−4.90231	+	4.11353i	−0.910336	+	0.763862i	−0.972183	−	0.234223i	$-0.924745\pi$
$29$	−4.90231	+	4.11353i	−0.910336	+	0.763862i	0.0618470	+	0.998086i	$0.480301\pi$
$30$		0			0
$31$	0.287822	−	1.63232i	0.0516943	−	0.293173i	−0.947990	−	0.318300i	$-0.896888\pi$
$31$	0.287822	−	1.63232i	0.0516943	−	0.293173i	0.999684	+	0.0251272i	$0.00799908\pi$
$32$	1.97455	−	0.718677i	0.349054	−	0.127045i
$33$		0			0
$34$	0.830315	+	4.70895i	0.142398	+	0.807578i
$35$	−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	$0.274144\pi$
$38$	8.67830	+	3.15864i	1.40781	+	0.512399i
$39$		0			0
$40$	−0.302733	−	0.254023i	−0.0478663	−	0.0401646i
$41$	0.839704	+	0.704595i	0.131140	+	0.110039i	0.705998	−	0.708213i	$-0.250499\pi$
$41$	0.839704	+	0.704595i	0.131140	+	0.110039i	−0.574859	+	0.818253i	$0.694943\pi$
$42$		0			0
$43$	6.48493	+	2.36032i	0.988943	+	0.359946i	0.785311	−	0.619102i	$-0.212503\pi$
$43$	6.48493	+	2.36032i	0.988943	+	0.359946i	0.203632	+	0.979047i	$0.434725\pi$
$44$	−5.82704	+	10.0927i	−0.878459	+	1.52154i
$45$		0			0
$46$	−5.34699	−	9.26126i	−0.788370	−	1.36550i
$47$	−0.623952	−	3.53861i	−0.0910127	−	0.516159i	−0.995896	−	0.0904999i	$-0.971154\pi$
$47$	−0.623952	−	3.53861i	−0.0910127	−	0.516159i	0.904884	−	0.425659i	$-0.139958\pi$
$48$		0			0
$49$	6.26189	−	2.27914i	0.894555	−	0.325591i
$50$	−2.08157	+	11.8052i	−0.294379	+	1.66951i
$51$		0			0
$52$	12.1274	−	10.1761i	1.68177	−	1.41117i
$53$	−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
$56$	−1.88587	+	1.58243i	−0.252010	+	0.211462i
$57$		0			0
$58$	−2.66883	+	15.1357i	−0.350435	+	1.98742i
$59$	−9.66442	+	3.51756i	−1.25820	+	0.457947i	−0.883165	−	0.469063i	$-0.844592\pi$
$59$	−9.66442	+	3.51756i	−1.25820	+	0.457947i	−0.375035	+	0.927011i	$0.622369\pi$
$60$		0			0
$61$	−2.29152	−	12.9958i	−0.293399	−	1.66395i	−0.673640	−	0.739059i	$-0.735270\pi$
$61$	−2.29152	−	12.9958i	−0.293399	−	1.66395i	0.380242	−	0.924887i	$-0.375841\pi$
$62$	−1.99034	−	3.44738i	−0.252774	−	0.437817i
$63$		0			0
$64$	5.18386	−	8.97871i	0.647982	−	1.12234i
$65$	0.367525	+	0.133768i	0.0455858	+	0.0165919i
$66$		0			0
$67$	−6.76976	−	5.68050i	−0.827058	−	0.693984i	0.127556	−	0.991831i	$-0.459287\pi$
$67$	−6.76976	−	5.68050i	−0.827058	−	0.693984i	−0.954613	+	0.297848i	$0.903731\pi$
$68$	5.74656	+	4.82194i	0.696873	+	0.584746i
$69$		0			0
$70$	−0.121811	−	0.0443356i	−0.0145592	−	0.00529912i
$71$	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	$0.836975\pi$
$74$	1.68070	+	9.53172i	0.195377	+	1.10804i
$75$		0			0
$76$	13.6149	−	4.95544i	1.56174	−	0.568427i
$77$	−0.311448	+	1.76631i	−0.0354928	+	0.201290i
$78$		0			0
$79$	−5.52164	+	4.63321i	−0.621233	+	0.521277i	−0.898191	−	0.439605i	$-0.855118\pi$
$79$	−5.52164	+	4.63321i	−0.621233	+	0.521277i	0.276958	+	0.960882i	$0.410674\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	11.4144	−	9.57782i	1.25289	−	1.05130i	0.256492	−	0.966546i	$-0.417433\pi$
$83$	11.4144	−	9.57782i	1.25289	−	1.05130i	0.996402	−	0.0847562i	$-0.0270111\pi$
$84$		0			0
$85$	−0.0321818	+	0.182512i	−0.00349061	+	0.0197962i
$86$	15.5744	−	5.66860i	1.67943	−	0.611261i
$87$		0			0
$88$	2.28032	+	12.9323i	0.243083	+	1.37859i
$89$	−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
$92$	−15.7655	−	5.73816i	−1.64366	−	0.598244i
$93$		0			0
$94$	−6.61057	−	5.54693i	−0.681829	−	0.572122i
$95$	0.274202	+	0.230083i	0.0281325	+	0.0236060i
$96$		0			0
$97$	−4.97617	−	1.81118i	−0.505254	−	0.183897i	0.0768016	−	0.997046i	$-0.475529\pi$
$97$	−4.97617	−	1.81118i	−0.505254	−	0.183897i	−0.582056	+	0.813149i	$0.697751\pi$
$98$	8.00191	−	13.8597i	0.808315	−	1.40004i
$99$		0			0
$100$	9.40314	+	16.2867i	0.940314	+	1.62867i
$101$	1.26225	+	7.15855i	0.125598	+	0.712302i	0.980951	+	0.194256i	$0.0622293\pi$
$101$	1.26225	+	7.15855i	0.125598	+	0.712302i	−0.855353	+	0.518046i	$0.826660\pi$
$102$		0			0
$103$	−6.01532	+	2.18940i	−0.592707	+	0.215728i	−0.620920	−	0.783874i	$-0.713241\pi$
$103$	−6.01532	+	2.18940i	−0.592707	+	0.215728i	0.0282124	+	0.999602i	$0.491019\pi$
$104$	3.09765	−	17.5677i	0.303750	−	1.72265i
$105$		0			0
$106$	−9.93526	+	8.33667i	−0.964998	+	0.809729i
$107$	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	$0.596462\pi$
$110$	−0.529691	+	0.444463i	−0.0505040	+	0.0423779i
$111$		0			0
$112$	−0.267904	+	1.51936i	−0.0253145	+	0.143566i
$113$	−11.1297	+	4.05088i	−1.04699	+	0.381075i	−0.807528	−	0.589830i	$-0.799195\pi$
$113$	−11.1297	+	4.05088i	−1.04699	+	0.381075i	−0.239467	+	0.970905i	$0.576973\pi$
$114$		0			0
$115$	−0.0719743	−	0.408186i	−0.00671164	−	0.0380636i
$116$	12.0560	+	20.8816i	1.11937	+	1.93881i
$117$		0			0
$118$	−12.3499	+	21.3907i	−1.13690	+	1.96917i
$119$	1.08487	+	0.394861i	0.0994500	+	0.0361968i
$120$		0			0
$121$	−1.09762	−	0.921009i	−0.0997832	−	0.0837281i
$122$	−24.2779	−	20.3716i	−2.19802	−	1.84436i
$123$		0			0
$124$	−5.86848	−	2.13595i	−0.527005	−	0.191814i
$125$	−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	$-0.337589\pi$
$128$	−3.59396	−	20.3824i	−0.317664	−	1.80156i
$129$		0			0
$130$	0.882655	−	0.321260i	0.0774140	−	0.0281764i
$131$	1.56488	−	8.87487i	0.136724	−	0.775401i	−0.836920	−	0.547326i	$-0.815646\pi$
$131$	1.56488	−	8.87487i	0.136724	−	0.775401i	0.973644	−	0.228075i	$-0.0732431\pi$
$132$		0			0
$133$	1.70814	−	1.43330i	0.148114	−	0.124282i
$134$	−21.2238			−1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	−8.82501	+	7.40506i	−0.753971	+	0.632657i	−0.936550	−	0.350534i	$-0.886000\pi$
$137$	−8.82501	+	7.40506i	−0.753971	+	0.632657i	0.182579	+	0.983191i	$0.441556\pi$
$138$		0			0
$139$	0.295868	−	1.67795i	0.0250952	−	0.142322i	−0.969686	−	0.244355i	$-0.921424\pi$
$139$	0.295868	−	1.67795i	0.0250952	−	0.142322i	0.994781	+	0.102033i	$0.0325348\pi$
$140$	−0.191103	+	0.0695559i	−0.0161512	+	0.00587855i
$141$		0			0
$142$	−0.477485	−	2.70795i	−0.0400697	−	0.227246i
$143$	−6.49816	−	11.2551i	−0.543403	−	0.941202i
$144$		0			0
$145$	−0.297844	+	0.515881i	−0.0247346	+	0.0428416i
$146$	−0.441139	−	0.160561i	−0.0365089	−	0.0132882i
$147$		0			0
$148$	11.6320	+	9.76042i	0.956146	+	0.802302i
$149$	16.5870	+	13.9181i	1.35886	+	1.14022i	0.976333	+	0.216273i	$0.0693900\pi$
$149$	16.5870	+	13.9181i	1.35886	+	1.14022i	0.382525	+	0.923945i	$0.375054\pi$
$150$		0			0
$151$	4.45557	+	1.62170i	0.362589	+	0.131972i	0.516889	−	0.856052i	$-0.327090\pi$
$151$	4.45557	+	1.62170i	0.362589	+	0.131972i	−0.154300	+	0.988024i	$0.549312\pi$
$152$	8.16296	−	14.1387i	0.662104	−	1.14680i
$153$		0			0
$154$	2.15373	+	3.73036i	0.173552	+	0.300601i
$155$	−0.0267914	−	0.151942i	−0.00215194	−	0.0122043i
$156$		0			0
$157$	0.196589	−	0.0715526i	0.0156895	−	0.00571052i	−0.334163	−	0.942515i	$-0.608454\pi$
$157$	0.196589	−	0.0715526i	0.0156895	−	0.00571052i	0.349853	+	0.936805i	$0.386232\pi$
$158$	−3.00600	+	17.0479i	−0.239145	+	1.35626i
$159$		0			0
$160$	0.149833	−	0.125725i	0.0118454	−	0.00993944i
$161$	−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	$0.429314\pi$
$164$	3.16382	−	2.65476i	0.247053	−	0.207302i
$165$		0			0
$166$	6.21404	−	35.2416i	0.482303	−	2.73528i
$167$	15.6745	−	5.70507i	1.21293	−	0.441471i	0.345212	−	0.938525i	$-0.387807\pi$
$167$	15.6745	−	5.70507i	1.21293	−	0.441471i	0.867720	+	0.497053i	$0.165585\pi$
$168$		0			0
$169$	0.808256	+	4.58385i	0.0621735	+	0.352604i
$170$	0.222544	+	0.385457i	0.0170683	+	0.0295632i
$171$		0			0
$172$	13.0010	−	22.5183i	0.991315	−	1.71701i
$173$	17.8562	+	6.49912i	1.35758	+	0.494119i	0.915305	−	0.402761i	$-0.131949\pi$
$173$	17.8562	+	6.49912i	1.35758	+	0.494119i	0.442275	+	0.896880i	$0.354172\pi$
$174$		0			0
$175$	2.21715	+	1.86041i	0.167601	+	0.140634i
$176$	6.30420	+	5.28985i	0.475197	+	0.398738i
$177$		0			0
$178$	−3.50507	−	1.27574i	−0.262716	−	0.0956209i
$179$	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	$0.797870\pi$
$182$	−1.01608	−	5.76247i	−0.0753168	−	0.427143i
$183$		0			0
$184$	−17.7646	+	6.46577i	−1.30962	+	0.476663i
$185$	−0.0651415	+	0.369436i	−0.00478930	+	0.0271615i
$186$		0			0
$187$	4.71752	−	3.95847i	0.344979	−	0.289472i
$188$	−13.5384			−0.987388
$189$		0			0
$190$	0.859649			0.0623655
$191$	1.72652	−	1.44873i	0.124927	−	0.104826i	−0.578184	−	0.815907i	$-0.696238\pi$
$191$	1.72652	−	1.44873i	0.124927	−	0.104826i	0.703111	+	0.711081i	$0.251794\pi$
$192$		0			0
$193$	−0.152858	+	0.866900i	−0.0110029	+	0.0624008i	−0.989815	−	0.142361i	$-0.954531\pi$
$193$	−0.152858	+	0.866900i	−0.0110029	+	0.0624008i	0.978812	+	0.204761i	$0.0656418\pi$
$194$	−11.9509	+	4.34977i	−0.858024	+	0.312295i
$195$		0			0
$196$	−4.35989	−	24.7262i	−0.311421	−	1.76616i
$197$	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	$-0.0686603\pi$
$200$	19.9130	+	7.24773i	1.40806	+	0.512492i
$201$		0			0
$202$	13.3731	+	11.2214i	0.940928	+	0.789532i
$203$	2.84266	+	2.38527i	0.199516	+	0.167413i
$204$		0			0
$205$	0.0958805	+	0.0348977i	0.00669659	+	0.00243736i
$206$	−7.68684	+	13.3140i	−0.535567	+	0.927630i
$207$		0			0
$208$	−5.58963	−	9.68152i	−0.387571	−	0.671293i
$209$	−2.06541	−	11.7135i	−0.142867	−	0.810241i
$210$		0			0
$211$	−15.2080	+	5.53528i	−1.04697	+	0.381064i	−0.807517	−	0.589845i	$-0.799189\pi$
$211$	−15.2080	+	5.53528i	−1.04697	+	0.381064i	−0.239449	+	0.970909i	$0.576967\pi$
$212$	−3.53327	+	20.0382i	−0.242666	+	1.37623i
$213$		0			0
$214$	10.1989	−	8.55792i	0.697184	−	0.585007i
$215$	0.642380			0.0438100
$216$		0			0
$217$	−0.961120			−0.0652451
$218$	−11.4642	+	9.61957i	−0.776450	+	0.651519i
$219$		0			0
$220$	−0.188374	+	1.06832i	−0.0127002	+	0.0720261i
$221$	−7.86109	+	2.86120i	−0.528794	+	0.192465i
$222$		0			0
$223$	3.72602	+	21.1313i	0.249513	+	1.41506i	0.809774	+	0.586742i	$0.199590\pi$
$223$	3.72602	+	21.1313i	0.249513	+	1.41506i	−0.560261	+	0.828316i	$0.689299\pi$
$224$	−0.609223	−	1.05520i	−0.0407054	−	0.0705038i
$225$		0			0
$226$	−14.2224	+	24.6339i	−0.946058	+	1.63862i
$227$	−17.9615	−	6.53746i	−1.19215	−	0.433906i	−0.331671	−	0.943395i	$-0.607612\pi$
$227$	−17.9615	−	6.53746i	−1.19215	−	0.433906i	−0.860477	+	0.509489i	$0.829834\pi$
$228$		0			0
$229$	17.2131	+	14.4435i	1.13748	+	0.954456i	0.999353	−	0.0359590i	$-0.0114486\pi$
$229$	17.2131	+	14.4435i	1.13748	+	0.954456i	0.138123	+	0.990415i	$0.455893\pi$
$230$	−0.762545	−	0.639851i	−0.0502807	−	0.0421905i
$231$		0			0
$232$	25.5309	+	9.29249i	1.67619	+	0.610082i
$233$	−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
$236$	6.72893	+	38.1617i	0.438016	+	2.48411i
$237$		0			0
$238$	2.60545	−	0.948306i	0.168886	−	0.0614696i
$239$	2.67771	−	15.1860i	0.173207	−	0.982304i	−0.766987	−	0.641663i	$-0.778245\pi$
$239$	2.67771	−	15.1860i	0.173207	−	0.982304i	0.940193	−	0.340641i	$-0.110644\pi$
$240$		0			0
$241$	10.0746	−	8.45359i	0.648962	−	0.544544i	−0.257794	−	0.966200i	$-0.582996\pi$
$241$	10.0746	−	8.45359i	0.648962	−	0.544544i	0.906756	+	0.421656i	$0.138551\pi$
$242$	−3.44113			−0.221204
$243$		0			0
$244$	−49.7209			−3.18305
$245$	0.475166	−	0.398712i	0.0303573	−	0.0254728i
$246$		0			0
$247$	−2.80571	+	15.9120i	−0.178523	+	1.01245i
$248$	−6.61261	+	2.40679i	−0.419901	+	0.152832i
$249$		0			0
$250$	0.387856	+	2.19964i	0.0245302	+	0.139118i
$251$	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
$254$	−26.0193	−	9.47026i	−1.63260	−	0.594217i
$255$		0			0
$256$	−22.1926	−	18.6218i	−1.38704	−	1.16386i
$257$	−8.57018	−	7.19124i	−0.534593	−	0.448577i	0.335091	−	0.942186i	$-0.391233\pi$
$257$	−8.57018	−	7.19124i	−0.534593	−	0.448577i	−0.869684	+	0.493609i	$0.835677\pi$
$258$		0			0
$259$	2.19596	+	0.799265i	0.136451	+	0.0496639i
$260$	0.736812	−	1.27620i	0.0456952	−	0.0791463i
$261$		0			0
$262$	−10.8214	−	18.7433i	−0.668550	−	1.15796i
$263$	3.59641	+	20.3962i	0.221764	+	1.25769i	0.868776	+	0.495206i	$0.164907\pi$
$263$	3.59641	+	20.3962i	0.221764	+	1.25769i	−0.647012	+	0.762480i	$0.723982\pi$
$264$		0			0
$265$	−0.472366	+	0.171927i	−0.0290172	+	0.0105614i
$266$	0.929914	−	5.27381i	0.0570167	−	0.323358i
$267$		0			0
$268$	−25.5070	+	21.4029i	−1.55809	+	1.30739i
$269$	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	$0.324321\pi$
$272$	4.05795	−	3.40502i	0.246049	−	0.206460i
$273$		0			0
$274$	−4.80436	+	27.2469i	−0.290242	+	1.64605i
$275$	14.5076	−	5.28032i	0.874838	−	0.318415i
$276$		0			0
$277$	0.897584	+	5.09045i	0.0539306	+	0.305855i	0.999827	−	0.0186140i	$-0.00592536\pi$
$277$	0.897584	+	5.09045i	0.0539306	+	0.305855i	−0.945896	+	0.324469i	$0.894814\pi$
$278$	−2.04598	−	3.54375i	−0.122710	−	0.212540i
$279$		0			0
$280$	−0.114578	+	0.198454i	−0.00684733	+	0.0118599i
$281$	−3.09764	−	1.12745i	−0.184790	−	0.0672580i	0.247968	−	0.968768i	$-0.420237\pi$
$281$	−3.09764	−	1.12745i	−0.184790	−	0.0672580i	−0.432758	+	0.901510i	$0.642459\pi$
$282$		0			0
$283$	−6.99454	−	5.86911i	−0.415782	−	0.348883i	0.410774	−	0.911737i	$-0.365259\pi$
$283$	−6.99454	−	5.86911i	−0.415782	−	0.348883i	−0.826556	+	0.562855i	$0.809703\pi$
$284$	−3.30465	−	2.77293i	−0.196095	−	0.164543i
$285$		0			0
$286$	−29.3299	−	10.6752i	−1.73431	−	0.631238i
$287$	0.317809	−	0.550462i	0.0187597	−	0.0324927i
$288$		0			0
$289$	6.51799	+	11.2895i	0.383411	+	0.664087i
$290$	0.248424	+	1.40888i	0.0145880	+	0.0827325i
$291$		0			0
$292$	−0.692081	+	0.251897i	−0.0405010	+	0.0147411i
$293$	0.490805	−	2.78349i	0.0286731	−	0.162613i	−0.967109	−	0.254362i	$-0.918135\pi$
$293$	0.490805	−	2.78349i	0.0286731	−	0.162613i	0.995782	+	0.0917487i	$0.0292456\pi$
$294$		0			0
$295$	−0.733358	+	0.615360i	−0.0426978	+	0.0358277i
$296$	17.1100			0.994496
$297$		0			0
$298$	52.0017			3.01238
$299$	14.3323	−	12.0263i	0.828861	−	0.695497i
$300$		0			0
$301$	0.694887	−	3.94090i	0.0400526	−	0.227150i
$302$	10.7006	−	3.89470i	0.615750	−	0.224115i
$303$		0			0
$304$	−1.77664	−	10.0758i	−0.101897	−	0.577888i
$305$	−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	$0.224154\pi$
$308$	6.35020	+	2.31129i	0.361836	+	0.131698i
$309$		0			0
$310$	−0.283847	−	0.238176i	−0.0161214	−	0.0135275i
$311$	5.64796	+	4.73920i	0.320266	+	0.268735i	0.788720	−	0.614753i	$-0.210744\pi$
$311$	5.64796	+	4.73920i	0.320266	+	0.268735i	−0.468453	+	0.883488i	$0.655189\pi$
$312$		0			0
$313$	4.01319	+	1.46068i	0.226839	+	0.0825627i	0.452939	−	0.891541i	$-0.350375\pi$
$313$	4.01319	+	1.46068i	0.226839	+	0.0825627i	−0.226100	+	0.974104i	$0.572598\pi$
$314$	0.251217	−	0.435120i	0.0141770	−	0.0245552i
$315$		0			0
$316$	13.5791	+	23.5197i	0.763883	+	1.32308i
$317$	−2.80400	−	15.9023i	−0.157488	−	0.893160i	−0.956476	−	0.291812i	$-0.905742\pi$
$317$	−2.80400	−	15.9023i	−0.157488	−	0.893160i	0.798988	−	0.601348i	$-0.205369\pi$
$318$		0			0
$319$	18.6005	−	6.77002i	1.04143	−	0.379048i
$320$	0.167581	−	0.950401i	0.00936808	−	0.0531290i
$321$		0			0
$322$	−4.75026	+	3.98594i	−0.264722	+	0.222128i
$323$	−7.65618			−0.426001
$324$		0			0
$325$	−20.9723			−1.16333
$326$	10.3465	−	8.68171i	0.573037	−	0.480835i
$327$		0			0
$328$	0.808121	−	4.58308i	0.0446210	−	0.253058i
$329$	−1.95790	+	0.712618i	−0.107943	+	0.0392879i
$330$		0			0
$331$	3.33895	+	18.9361i	0.183525	+	1.04082i	0.927836	+	0.372989i	$0.121667\pi$
$331$	3.33895	+	18.9361i	0.183525	+	1.04082i	−0.744311	+	0.667834i	$0.767222\pi$
$332$	−28.0708	−	48.6201i	−1.54059	−	2.66838i
$333$		0			0
$334$	20.0301	−	34.6932i	1.09600	−	1.89833i
$335$	−0.772996	−	0.281348i	−0.0422333	−	0.0153717i
$336$		0			0
$337$	−22.5698	−	18.9383i	−1.22945	−	1.03163i	−0.998274	−	0.0587237i	$-0.981297\pi$
$337$	−22.5698	−	18.9383i	−1.22945	−	1.03163i	−0.231180	−	0.972911i	$-0.574259\pi$
$338$	8.56322	+	7.18540i	0.465778	+	0.390834i
$339$		0			0
$340$	0.656164	+	0.238824i	0.0355855	+	0.0129521i
$341$	−2.56339	+	4.43993i	−0.138815	+	0.240435i
$342$		0			0
$343$	−3.96154	−	6.86159i	−0.213903	−	0.370491i
$344$	−5.08773	−	28.8539i	−0.274312	−	1.55570i
$345$		0			0
$346$	42.8838	−	15.6084i	2.30545	−	0.839114i
$347$	−1.97907	+	11.2239i	−0.106242	+	0.602530i	0.884475	+	0.466588i	$0.154517\pi$
$347$	−1.97907	+	11.2239i	−0.106242	+	0.602530i	−0.990717	+	0.135941i	$0.956594\pi$
$348$		0			0
$349$	21.5731	−	18.1019i	1.15478	−	0.968975i	0.154958	−	0.987921i	$-0.450476\pi$
$349$	21.5731	−	18.1019i	1.15478	−	0.968975i	0.999821	+	0.0189464i	$0.00603120\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	−21.9503	+	18.4185i	−1.16830	+	0.980318i	−0.999985	−	0.00541596i	$-0.998276\pi$
$353$	−21.9503	+	18.4185i	−1.16830	+	0.980318i	−0.168312	+	0.985734i	$0.553832\pi$
$354$		0			0
$355$	0.0185067	−	0.104956i	0.000982231	−	0.00557051i
$356$	−5.49893	+	2.00145i	−0.291443	+	0.106077i
$357$		0			0
$358$	−6.77069	−	38.3985i	−0.357842	−	2.02942i
$359$	−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
$362$	6.75136	+	2.45729i	0.354843	+	0.129152i
$363$		0			0
$364$	−7.03222	−	5.90074i	−0.368589	−	0.309283i
$365$	−0.0139383	−	0.0116957i	−0.000729566	−	0.000612179i
$366$		0			0
$367$	−22.6694	−	8.25097i	−1.18333	−	0.430697i	−0.325953	−	0.945386i	$-0.605685\pi$
$367$	−22.6694	−	8.25097i	−1.18333	−	0.430697i	−0.857377	+	0.514689i	$0.827907\pi$
$368$	−5.92365	+	10.2601i	−0.308791	+	0.534843i
$369$		0			0
$370$	0.450466	+	0.780230i	0.0234186	+	0.0405622i
$371$	0.543770	+	3.08387i	0.0282311	+	0.160107i
$372$		0			0
$373$	11.8266	−	4.30453i	0.612359	−	0.222880i	−0.0171764	−	0.999852i	$-0.505468\pi$
$373$	11.8266	−	4.30453i	0.612359	−	0.222880i	0.629535	+	0.776972i	$0.283245\pi$
$374$	2.56823	−	14.5652i	0.132800	−	0.753147i
$375$		0			0
$376$	−11.6861	+	9.80578i	−0.602663	+	0.505694i
$377$	−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	$0.563411\pi$
$380$	1.03313	−	0.866902i	0.0529986	−	0.0444711i
$381$		0			0
$382$	0.939925	−	5.33058i	0.0480908	−	0.272736i
$383$	−16.7844	+	6.10904i	−0.857645	+	0.312157i	−0.733153	−	0.680063i	$-0.761952\pi$
$383$	−16.7844	+	6.10904i	−0.857645	+	0.312157i	−0.124492	+	0.992221i	$0.539730\pi$
$384$		0			0
$385$	0.0289907	+	0.164414i	0.00147750	+	0.00837933i
$386$	1.05704	+	1.83085i	0.0538020	+	0.0931878i
$387$		0			0
$388$	−9.97622	+	17.2793i	−0.506466	+	0.877224i
$389$	25.7367	+	9.36740i	1.30490	+	0.474946i	0.898591	−	0.438788i	$-0.144592\pi$
$389$	25.7367	+	9.36740i	1.30490	+	0.474946i	0.406313	+	0.913734i	$0.366814\pi$
$390$		0			0
$391$	6.79136	+	5.69863i	0.343454	+	0.288192i
$392$	−21.6724	−	18.1853i	−1.09462	−	0.918497i
$393$		0			0
$394$	45.7598	+	16.6552i	2.30535	+	0.839078i
$395$	−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	$0.867073\pi$
$398$	−7.92764	−	44.9599i	−0.397377	−	2.25364i
$399$		0			0
$400$	12.4792	−	4.54206i	0.623961	−	0.227103i
$401$	−2.63468	+	14.9420i	−0.131569	+	0.746168i	0.845618	+	0.533789i	$0.179232\pi$
$401$	−2.63468	+	14.9420i	−0.131569	+	0.746168i	−0.977187	+	0.212379i	$0.931879\pi$
$402$		0			0
$403$	5.33502	−	4.47661i	0.265756	−	0.222996i
$404$	27.3880			1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	9.54906	−	8.01262i	0.473330	−	0.397171i
$408$		0			0
$409$	0.817816	−	4.63806i	0.0404384	−	0.229337i	−0.957890	−	0.287136i	$-0.907297\pi$
$409$	0.817816	−	4.63806i	0.0404384	−	0.229337i	0.998328	+	0.0577983i	$0.0184080\pi$
$410$	0.230269	−	0.0838110i	0.0113722	−	0.00413913i
$411$		0			0
$412$	4.18822	+	23.7526i	0.206339	+	1.17021i
$413$	2.98184	+	5.16469i	0.146727	+	0.254138i
$414$		0			0
$415$	0.693492	−	1.20116i	0.0340422	−	0.0589628i
$416$	8.29653	+	3.01969i	0.406771	+	0.148052i
$417$		0			0
$418$	−21.8824	−	18.3615i	−1.07030	−	0.898089i
$419$	−15.1609	−	12.7215i	−0.740658	−	0.621486i	0.192356	−	0.981325i	$-0.438387\pi$
$419$	−15.1609	−	12.7215i	−0.740658	−	0.621486i	−0.933014	+	0.359839i	$0.882831\pi$
$420$		0			0
$421$	−26.4859	−	9.64008i	−1.29084	−	0.469829i	−0.396840	−	0.917888i	$-0.629893\pi$
$421$	−26.4859	−	9.64008i	−1.29084	−	0.469829i	−0.894004	+	0.448059i	$0.852115\pi$
$422$	−19.4340	+	33.6607i	−0.946032	+	1.63858i
$423$		0			0
$424$	11.4637	+	19.8557i	0.556726	+	0.964278i
$425$	−1.72566	−	9.78670i	−0.0837068	−	0.474725i
$426$		0			0
$427$	−7.19056	+	2.61715i	−0.347976	+	0.126653i
$428$	3.62704	−	20.5700i	0.175320	−	0.994287i
$429$		0			0
$430$	1.18182	−	0.991663i	0.0569923	−	0.0478222i
$431$	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	$0.291730\pi$
$434$	−1.76822	+	1.48371i	−0.0848772	+	0.0712205i
$435$		0			0
$436$	−4.07699	+	23.1218i	−0.195252	+	1.10733i
$437$	16.0903	−	5.85640i	0.769704	−	0.280149i
$438$		0			0
$439$	−2.71955	−	15.4233i	−0.129797	−	0.736114i	−0.978343	−	0.206992i	$-0.933633\pi$
$439$	−2.71955	−	15.4233i	−0.129797	−	0.736114i	0.848546	−	0.529122i	$-0.177479\pi$
$440$	0.611178	+	1.05859i	0.0291368	+	0.0504664i
$441$		0			0
$442$	−10.0455	+	17.3993i	−0.477815	+	0.827600i
$443$	−17.1530	−	6.24318i	−0.814964	−	0.296623i	−0.0992911	−	0.995058i	$-0.531658\pi$
$443$	−17.1530	−	6.24318i	−0.814964	−	0.296623i	−0.715673	+	0.698436i	$0.753880\pi$
$444$		0			0
$445$	−0.110747	−	0.0929280i	−0.00524992	−	0.00440521i
$446$	39.4760	+	33.1243i	1.86924	+	1.56848i
$447$		0			0
$448$	−5.64928	−	2.05617i	−0.266903	−	0.0971449i
$449$	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
$452$	7.74915	+	43.9476i	0.364489	+	2.06712i
$453$		0			0
$454$	−43.1368	+	15.7005i	−2.02451	+	0.736861i
$455$	0.0393818	−	0.223345i	0.00184625	−	0.0104706i
$456$		0			0
$457$	−27.1087	+	22.7469i	−1.26809	+	1.06406i	−0.273321	+	0.961923i	$0.588122\pi$
$457$	−27.1087	+	22.7469i	−1.26809	+	1.06406i	−0.994771	+	0.102133i	$0.967433\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	−1.74408	+	1.46345i	−0.0812297	+	0.0681598i	−0.682498	−	0.730887i	$-0.739107\pi$
$461$	−1.74408	+	1.46345i	−0.0812297	+	0.0681598i	0.601269	+	0.799047i	$0.294662\pi$
$462$		0			0
$463$	3.19070	−	18.0954i	0.148285	−	0.840964i	−0.816386	−	0.577506i	$-0.804026\pi$
$463$	3.19070	−	18.0954i	0.148285	−	0.840964i	0.964671	−	0.263458i	$-0.0848629\pi$
$464$	15.9999	−	5.82348i	0.742776	−	0.270348i
$465$		0			0
$466$	7.37383	+	41.8191i	0.341586	+	1.93723i
$467$	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
$470$	−0.754820	−	0.274732i	−0.0348172	−	0.0126724i
$471$		0			0
$472$	33.4486	+	28.0667i	1.53960	+	1.29187i
$473$	−16.3518	−	13.7208i	−0.751856	−	0.630882i
$474$		0			0
$475$	−18.0363	−	6.56466i	−0.827561	−	0.301207i
$476$	2.17495	−	3.76712i	0.0996885	−	0.172666i
$477$		0			0
$478$	−18.5169	−	32.0722i	−0.846942	−	1.46695i
$479$	2.46162	+	13.9605i	0.112474	+	0.637873i	0.987970	+	0.154647i	$0.0494240\pi$
$479$	2.46162	+	13.9605i	0.112474	+	0.637873i	−0.875496	+	0.483226i	$0.839465\pi$
$480$		0			0
$481$	−15.9122	+	5.79156i	−0.725533	+	0.264072i
$482$	5.48464	−	31.1050i	0.249819	−	1.41679i
$483$		0			0
$484$	−4.13558	+	3.47016i	−0.187981	+	0.157735i
$485$	−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	$0.661409\pi$
$488$	−42.9181	+	36.0126i	−1.94281	+	1.63021i
$489$		0			0
$490$	0.258682	−	1.46706i	0.0116861	−	0.0662750i
$491$	−13.2382	+	4.81833i	−0.597434	+	0.217448i	−0.622996	−	0.782225i	$-0.714085\pi$
$491$	−13.2382	+	4.81833i	−0.597434	+	0.217448i	0.0255621	+	0.999673i	$0.491862\pi$
$492$		0			0
$493$	−2.21251	−	12.5478i	−0.0996464	−	0.565123i
$494$	19.4020	+	33.6053i	0.872938	+	1.51197i
$495$		0			0
$496$	−2.20500	+	3.81917i	−0.0990073	+	0.171486i
$497$	−0.623872	−	0.227071i	−0.0279845	−	0.0101855i
$498$		0			0
$499$	11.4212	+	9.58353i	0.511284	+	0.429018i	0.861581	−	0.507621i	$-0.169475\pi$
$499$	11.4212	+	9.58353i	0.511284	+	0.429018i	−0.350297	+	0.936639i	$0.613919\pi$
$500$	2.68433	+	2.25242i	0.120047	+	0.100731i
$501$		0			0
$502$	39.3056	+	14.3061i	1.75429	+	0.638510i
$503$	−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
$506$	5.74382	+	32.5748i	0.255344	+	1.44813i
$507$		0			0
$508$	−40.8204	+	14.8574i	−1.81111	+	0.659192i
$509$	−5.89131	+	33.4113i	−0.261128	+	1.48093i	0.518712	+	0.854949i	$0.326412\pi$
$509$	−5.89131	+	33.4113i	−0.261128	+	1.48093i	−0.779839	+	0.625980i	$0.784699\pi$
$510$		0			0
$511$	−0.0868286	+	0.0728579i	−0.00384107	+	0.00322304i
$512$	−28.1824			−1.24550
$513$		0			0
$514$	−26.8683			−1.18511
$515$	−0.456457	+	0.383013i	−0.0201139	+	0.0168775i
$516$		0			0
$517$	−1.92993	+	10.9452i	−0.0848784	+	0.481369i
$518$	5.27387	−	1.91953i	0.231721	−	0.0843394i
$519$		0			0
$520$	−0.288340	−	1.63526i	−0.0126445	−	0.0717108i
$521$	−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	$0.147323\pi$
$524$	−31.9067	−	11.6131i	−1.39385	−	0.507321i
$525$		0			0
$526$	38.1028	+	31.9721i	1.66136	+	1.39405i
$527$	2.52799	+	2.12124i	0.110121	+	0.0924025i
$528$		0			0
$529$	2.98111	+	1.08504i	0.129614	+	0.0471755i
$530$	−0.603626	+	1.04551i	−0.0262198	+	0.0454141i
$531$		0			0
$532$	−4.20073	−	7.27587i	−0.182125	−	0.315449i
$533$	0.799781	+	4.53578i	0.0346424	+	0.196467i
$534$		0			0
$535$	0.484902	−	0.176490i	0.0209642	−	0.00763033i
$536$	−6.51513	+	36.9492i	−0.281411	+	1.59596i
$537$		0			0
$538$	51.9634	−	43.6025i	2.24030	−	1.87984i
$539$	−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	$0.524616\pi$
$542$	31.7589	−	26.6489i	1.36416	−	1.14467i
$543$		0			0
$544$	−0.726475	+	4.12004i	−0.0311473	+	0.176645i
$545$	−0.545057	+	0.198384i	−0.0233477	+	0.00849785i
$546$		0			0
$547$	−6.87401	−	38.9844i	−0.293911	−	1.66685i	−0.671594	−	0.740919i	$-0.734390\pi$
$547$	−6.87401	−	38.9844i	−0.293911	−	1.66685i	0.377683	−	0.925935i	$-0.376721\pi$
$548$	21.7029	+	37.5905i	0.927101	+	1.60579i
$549$		0			0
$550$	18.5389	−	32.1102i	0.790499	−	1.36919i
$551$	−23.1247	−	8.41671i	−0.985146	−	0.358564i
$552$		0			0
$553$	3.20179	+	2.68662i	0.136154	+	0.114247i
$554$	9.50962	+	7.97952i	0.404025	+	0.339017i
$555$		0			0
$556$	−6.03253	−	2.19566i	−0.255836	−	0.0931167i
$557$	−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
$560$	0.0249374	+	0.141427i	0.00105380	+	0.00597638i
$561$		0			0
$562$	−7.43936	+	2.70771i	−0.313810	+	0.114218i
$563$	−2.51977	+	14.2903i	−0.106196	+	0.602266i	0.884540	+	0.466464i	$0.154472\pi$
$563$	−2.51977	+	14.2903i	−0.106196	+	0.602266i	−0.990736	+	0.135802i	$0.956639\pi$
$564$		0			0
$565$	−0.844547	+	0.708659i	−0.0355304	+	0.0298135i
$566$	−21.9285			−0.921725
$567$		0			0
$568$	−4.86093			−0.203960
$569$	0.995232	−	0.835099i	0.0417223	−	0.0350092i	−0.621688	−	0.783265i	$-0.713553\pi$
$569$	0.995232	−	0.835099i	0.0417223	−	0.0350092i	0.663410	+	0.748256i	$0.269108\pi$
$570$		0			0
$571$	2.78833	−	15.8134i	0.116688	−	0.661769i	−0.869213	−	0.494438i	$-0.835374\pi$
$571$	2.78833	−	15.8134i	0.116688	−	0.661769i	0.985901	−	0.167331i	$-0.0535150\pi$
$572$	−46.0142	+	16.7478i	−1.92395	+	0.700261i
$573$		0			0
$574$	−0.265077	−	1.50332i	−0.0110641	−	0.0627475i
$575$	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	$0.110317\pi$
$578$	29.4194	+	10.7078i	1.22369	+	0.445385i
$579$		0			0
$580$	1.71933	+	1.44269i	0.0713912	+	0.0599044i
$581$	−6.61877	−	5.55381i	−0.274593	−	0.230411i
$582$		0			0
$583$	15.6963	+	5.71300i	0.650076	+	0.236608i
$584$	−0.414943	+	0.718703i	−0.0171705	+	0.0297401i
$585$		0			0
$586$	−3.39401	−	5.87860i	−0.140205	−	0.242843i
$587$	3.19256	+	18.1059i	0.131771	+	0.747310i	0.977054	+	0.212991i	$0.0683206\pi$
$587$	3.19256	+	18.1059i	0.131771	+	0.747310i	−0.845283	+	0.534319i	$0.820568\pi$
$588$		0			0
$589$	5.98940	−	2.17996i	0.246789	−	0.0898238i
$590$	−0.399243	+	2.26422i	−0.0164366	+	0.0932163i
$591$		0			0
$592$	8.21398	−	6.89235i	0.337593	−	0.283274i
$593$	−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
$596$	62.4962	−	52.4405i	2.55994	−	2.14805i
$597$		0			0
$598$	7.80257	−	44.2506i	0.319071	−	1.80954i
$599$	10.3627	−	3.77170i	0.423407	−	0.154108i	−0.121524	−	0.992589i	$-0.538778\pi$
$599$	10.3627	−	3.77170i	0.423407	−	0.154108i	0.544931	+	0.838481i	$0.316556\pi$
$600$		0			0
$601$	4.47976	+	25.4060i	0.182733	+	1.03633i	0.928833	+	0.370498i	$0.120813\pi$
$601$	4.47976	+	25.4060i	0.182733	+	1.03633i	−0.746100	+	0.665834i	$0.768076\pi$
$602$	−4.80528	−	8.32298i	−0.195848	−	0.339219i
$603$		0			0
$604$	8.93252	−	15.4716i	0.363459	−	0.629529i
$605$	−0.125330	−	0.0456163i	−0.00509538	−	0.00185457i
$606$		0			0
$607$	−11.3297	−	9.50675i	−0.459858	−	0.385867i	0.383221	−	0.923657i	$-0.374815\pi$
$607$	−11.3297	−	9.50675i	−0.459858	−	0.385867i	−0.843079	+	0.537790i	$0.819259\pi$
$608$	6.18985	+	5.19390i	0.251032	+	0.210640i
$609$		0			0
$610$	−2.77214	−	1.00898i	−0.112241	−	0.0408523i
$611$	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	$-0.428334\pi$
$614$	2.62502	+	14.8873i	0.105937	+	0.600801i
$615$		0			0
$616$	7.15542	−	2.60436i	0.288300	−	0.104933i
$617$	7.01079	−	39.7602i	0.282244	−	1.60068i	−0.432724	−	0.901527i	$-0.642447\pi$
$617$	7.01079	−	39.7602i	0.282244	−	1.60068i	0.714967	−	0.699158i	$-0.246442\pi$
$618$		0			0
$619$	−5.28058	+	4.43093i	−0.212244	+	0.178094i	−0.742712	−	0.669611i	$-0.766461\pi$
$619$	−5.28058	+	4.43093i	−0.212244	+	0.178094i	0.530468	+	0.847705i	$0.322016\pi$
$620$	−0.581315			−0.0233462
$621$		0			0
$622$	17.7069			0.709981
$623$	−0.689898	+	0.578893i	−0.0276402	+	0.0231929i
$624$		0			0
$625$	4.31865	−	24.4923i	0.172746	−	0.979691i
$626$	9.63817	−	3.50801i	0.385219	−	0.140208i
$627$		0			0
$628$	−0.136877	−	0.776267i	−0.00546198	−	0.0309764i
$629$	−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	$0.964397\pi$
$632$	28.7564	+	10.4665i	1.14387	+	0.416334i
$633$		0			0
$634$	−29.7075	−	24.9275i	−1.17983	−	0.989999i
$635$	−0.822114	−	0.689836i	−0.0326246	−	0.0273753i
$636$		0			0
$637$	26.3108	+	9.57634i	1.04247	+	0.379428i
$638$	23.7691	−	41.1693i	0.941028	−	1.62991i
$639$		0			0
$640$	−0.963264	−	1.66842i	−0.0380763	−	0.0659502i
$641$	−7.44616	−	42.2293i	−0.294106	−	1.66796i	−0.670815	−	0.741625i	$-0.734056\pi$
$641$	−7.44616	−	42.2293i	−0.294106	−	1.66796i	0.376709	−	0.926331i	$-0.377056\pi$
$642$		0			0
$643$	25.7600	−	9.37589i	1.01588	−	0.369749i	0.220190	−	0.975457i	$-0.429332\pi$
$643$	25.7600	−	9.37589i	1.01588	−	0.369749i	0.795687	+	0.605708i	$0.207110\pi$
$644$	−1.68933	+	9.58068i	−0.0665690	+	0.377532i
$645$		0			0
$646$	−14.0855	+	11.8191i	−0.554185	+	0.465016i
$647$	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
$650$	−38.5837	+	32.3756i	−1.51338	+	1.26987i
$651$		0			0
$652$	3.67951	−	20.8675i	0.144101	−	0.817235i
$653$	30.3016	−	11.0289i	1.18579	−	0.431593i	0.327549	−	0.944834i	$-0.393777\pi$
$653$	30.3016	−	11.0289i	1.18579	−	0.431593i	0.858245	+	0.513241i	$0.171555\pi$
$654$		0			0
$655$	−0.145664	−	0.826103i	−0.00569157	−	0.0322785i
$656$	−1.45823	−	2.52573i	−0.0569344	−	0.0986133i
$657$		0			0
$658$	−2.50195	+	4.33351i	−0.0975363	+	0.168938i
$659$	26.1409	+	9.51452i	1.01831	+	0.370633i	0.796617	−	0.604485i	$-0.206621\pi$
$659$	26.1409	+	9.51452i	1.01831	+	0.370633i	0.221689	+	0.975117i	$0.428843\pi$
$660$		0			0
$661$	23.5854	+	19.7905i	0.917367	+	0.769763i	0.973506	−	0.228660i	$-0.0734345\pi$
$661$	23.5854	+	19.7905i	0.917367	+	0.769763i	−0.0561388	+	0.998423i	$0.517879\pi$
$662$	35.3751	+	29.6832i	1.37489	+	1.15367i
$663$		0			0
$664$	−59.4455	−	21.6364i	−2.30693	−	0.839655i
$665$	0.103779	−	0.179751i	0.00402439	−	0.00697044i
$666$		0			0
$667$	14.2479	+	24.6781i	0.551682	+	0.955540i
$668$	−10.9135	−	61.8937i	−0.422257	−	2.39474i
$669$		0			0
$670$	−1.85644	+	0.675690i	−0.0717207	+	0.0261042i
$671$	−7.08785	+	40.1972i	−0.273624	+	1.55180i
$672$		0			0
$673$	−20.0172	+	16.7964i	−0.771607	+	0.647455i	−0.941120	−	0.338073i	$-0.890225\pi$
$673$	−20.0172	+	16.7964i	−0.771607	+	0.647455i	0.169513	+	0.985528i	$0.445780\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	−13.9378	+	11.6952i	−0.535673	+	0.449483i	−0.870055	−	0.492955i	$-0.835917\pi$
$677$	−13.9378	+	11.6952i	−0.535673	+	0.449483i	0.334382	+	0.942438i	$0.391472\pi$
$678$		0			0
$679$	−0.533217	+	3.02403i	−0.0204630	+	0.116051i
$680$	0.739367	−	0.269108i	0.0283534	−	0.0103198i
$681$		0			0
$682$	2.13806	+	12.1255i	0.0818705	+	0.464311i
$683$	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
$686$	−17.8807	−	6.50805i	−0.682689	−	0.248478i
$687$		0			0
$688$	−14.0656	−	11.8024i	−0.536246	−	0.449964i
$689$	−17.3821	−	14.5853i	−0.662207	−	0.555657i
$690$		0			0
$691$	41.8520	+	15.2329i	1.59212	+	0.579486i	0.977795	−	0.209565i	$-0.0672046\pi$
$691$	41.8520	+	15.2329i	1.59212	+	0.579486i	0.614329	+	0.789050i	$0.289427\pi$
$692$	35.7980	−	62.0039i	1.36084	−	2.35704i
$693$		0			0
$694$	13.6857	+	23.7043i	0.519501	+	0.899802i
$695$	−0.0275404	−	0.156189i	−0.00104467	−	0.00592460i
$696$		0			0
$697$	−2.05081	+	0.746435i	−0.0776801	+	0.0282733i
$698$	11.7444	−	66.6060i	0.444534	−	2.52108i
$699$		0			0
$700$	8.35374	−	7.00962i	0.315742	−	0.264939i
$701$	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
$704$	−24.5657	+	20.6130i	−0.925854	+	0.776884i
$705$		0			0
$706$	−11.9498	+	67.7708i	−0.449738	+	2.55059i
$707$	3.96081	−	1.44162i	0.148961	−	0.0542175i
$708$		0			0
$709$	−2.72350	−	15.4457i	−0.102283	−	0.580077i	−0.992271	−	0.124092i	$-0.960398\pi$
$709$	−2.72350	−	15.4457i	−0.102283	−	0.580077i	0.889987	−	0.455985i	$-0.150713\pi$
$710$	−0.127977	−	0.221663i	−0.00480289	−	0.00831886i
$711$		0			0
$712$	−3.29694	+	5.71046i	−0.123558	+	0.214009i
$713$	−6.93544	−	2.52429i	−0.259734	−	0.0945355i
$714$		0			0
$715$	−0.926715	−	0.777607i	−0.0346572	−	0.0290808i
$716$	−46.8596	−	39.3199i	−1.75122	−	1.46945i
$717$		0			0
$718$	−70.0331	−	25.4900i	−2.61361	−	0.951277i
$719$	−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
$722$	−1.75686	−	9.96366i	−0.0653836	−	0.370809i
$723$		0			0
$724$	10.5919	−	3.85512i	0.393644	−	0.143275i
$725$	5.54669	−	31.4568i	0.205999	−	1.16828i
$726$		0			0
$727$	0.359407	−	0.301578i	0.0133297	−	0.0111849i	−0.636098	−	0.771608i	$-0.719453\pi$
$727$	0.359407	−	0.301578i	0.0133297	−	0.0111849i	0.649428	+	0.760423i	$0.275008\pi$
$728$	−10.3440			−0.383372
$729$		0			0
$730$	−0.0436980			−0.00161734
$731$	−10.5255	+	8.83193i	−0.389299	+	0.326661i
$732$		0			0
$733$	−8.05837	+	45.7013i	−0.297643	+	1.68801i	0.358621	+	0.933483i	$0.383247\pi$
$733$	−8.05837	+	45.7013i	−0.297643	+	1.68801i	−0.656264	+	0.754532i	$0.727864\pi$
$734$	−54.4432	+	19.8157i	−2.00953	+	0.731411i
$735$		0			0
$736$	−1.62475	−	9.21442i	−0.0598891	−	0.339648i
$737$	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	$0.324112\pi$
$740$	1.32819	+	0.483421i	0.0488251	+	0.0177709i
$741$		0			0
$742$	5.76107	+	4.83411i	0.211496	+	0.177466i
$743$	−26.5891	−	22.3109i	−0.975460	−	0.818508i	0.00793799	−	0.999968i	$-0.497473\pi$
$743$	−26.5891	−	22.3109i	−0.975460	−	0.818508i	−0.983398	+	0.181460i	$0.941918\pi$
$744$		0			0
$745$	1.89396	+	0.689346i	0.0693894	+	0.0252557i
$746$	15.1129	−	26.1764i	0.553324	−	0.958385i
$747$		0			0
$748$	−11.6015	−	20.0945i	−0.424195	−	0.734727i
$749$	−0.558201	−	3.16571i	−0.0203962	−	0.115673i
$750$		0			0
$751$	−22.5393	+	8.20364i	−0.822472	+	0.299355i	−0.718765	−	0.695253i	$-0.755292\pi$
$751$	−22.5393	+	8.20364i	−0.822472	+	0.299355i	−0.103706	+	0.994608i	$0.533070\pi$
$752$	−1.66010	+	9.41492i	−0.0605378	+	0.343327i
$753$		0			0
$754$	−49.4691	+	41.5095i	−1.80156	+	1.51169i
$755$	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	$0.551052\pi$
$758$	−14.1757	+	11.8948i	−0.514883	+	0.432038i
$759$		0			0
$760$	0.263888	−	1.49659i	0.00957224	−	0.0542869i
$761$	12.9244	−	4.70410i	0.468510	−	0.170524i	−0.0969675	−	0.995288i	$-0.530914\pi$
$761$	12.9244	−	4.70410i	0.468510	−	0.170524i	0.565477	+	0.824764i	$0.308692\pi$
$762$		0			0
$763$	0.627448	+	3.55844i	0.0227152	+	0.128824i
$764$	−4.24595	−	7.35420i	−0.153613	−	0.266066i
$765$		0			0
$766$	−21.4484	+	37.1498i	−0.774963	+	1.34228i
$767$	−40.6073	−	14.7798i	−1.46624	−	0.533669i
$768$		0			0
$769$	−24.0216	−	20.1565i	−0.866240	−	0.726862i	0.0970630	−	0.995278i	$-0.469055\pi$
$769$	−24.0216	−	20.1565i	−0.866240	−	0.726862i	−0.963303	+	0.268417i	$0.913500\pi$
$770$	0.307147	+	0.257727i	0.0110688	+	0.00928784i
$771$		0			0
$772$	3.11666	+	1.13437i	0.112171	+	0.0408269i
$773$	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
$776$	3.90404	+	22.1409i	0.140147	+	0.794812i
$777$		0			0
$778$	61.8099	−	22.4970i	2.21599	−	0.806555i
$779$	−0.731959	+	4.15114i	−0.0262251	+	0.148730i
$780$		0			0
$781$	−2.71288	+	2.27638i	−0.0970745	+	0.0814552i
$782$	21.2916			0.761385
$783$		0			0
$784$	−17.7298			−0.633207
$785$	0.0149176	−	0.0125174i	0.000532433	−	0.000446764i
$786$		0			0
$787$	−6.28609	+	35.6502i	−0.224075	+	1.27079i	0.640371	+	0.768066i	$0.278781\pi$
$787$	−6.28609	+	35.6502i	−0.224075	+	1.27079i	−0.864446	+	0.502726i	$0.832330\pi$
$788$	71.7903	−	26.1295i	2.55742	−	0.930827i
$789$		0			0
$790$	0.279809	+	1.58687i	0.00995515	+	0.0564585i
$791$	3.43393	+	5.94775i	0.122097	+	0.211478i
$792$		0			0
$793$	27.7237	−	48.0189i	0.984498	−	1.70520i
$794$	−9.51458	−	3.46302i	−0.337660	−	0.122898i
$795$		0			0
$796$	−54.8668	−	46.0387i	−1.94470	−	1.63180i
$797$	22.6750	+	19.0266i	0.803189	+	0.673956i	0.948972	−	0.315361i	$-0.102126\pi$
$797$	22.6750	+	19.0266i	0.803189	+	0.673956i	−0.145782	+	0.989317i	$0.546570\pi$
$798$		0			0
$799$	6.72256	+	2.44681i	0.237827	+	0.0865620i
$800$	−5.24407	+	9.08300i	−0.185406	+	0.321133i
$801$		0			0
$802$	18.2193	+	31.5568i	0.643346	+	1.11431i
$803$	0.104990	+	0.595426i	0.00370501	+	0.0210121i
$804$		0			0
$805$	−0.225848	+	0.0822021i	−0.00796011	+	0.00289724i
$806$	2.90440	−	16.4717i	0.102303	−	0.580190i
$807$		0			0
$808$	23.6408	−	19.8370i	0.831679	−	0.697861i
$809$	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	$0.429628\pi$
$812$	10.7105	−	8.98720i	0.375866	−	0.315389i
$813$		0			0
$814$	5.19854	−	29.4824i	0.182209	−	1.03336i
$815$	0.491916	−	0.179043i	0.0172311	−	0.00627160i
$816$		0			0
$817$	4.60823	+	26.1346i	0.161222	+	0.914333i
$818$	−5.65535	−	9.79536i	−0.197735	−	0.342487i
$819$		0			0
$820$	0.192221	−	0.332936i	0.00671265	−	0.0116266i
$821$	40.4695	+	14.7297i	1.41240	+	0.514070i	0.931832	−	0.362890i	$-0.118210\pi$
$821$	40.4695	+	14.7297i	1.41240	+	0.514070i	0.480564	+	0.876960i	$0.340432\pi$
$822$		0			0
$823$	7.87807	+	6.61049i	0.274612	+	0.230427i	0.769684	−	0.638425i	$-0.220414\pi$
$823$	7.87807	+	6.61049i	0.274612	+	0.230427i	−0.495072	+	0.868852i	$0.664858\pi$
$824$	20.8190	+	17.4693i	0.725266	+	0.608570i
$825$		0			0
$826$	13.4587	+	4.89858i	0.468289	+	0.170443i
$827$	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	$0.634354\pi$
$830$	−0.578424	−	3.28041i	−0.0200774	−	0.113865i
$831$		0			0
$832$	40.9352	−	14.8992i	1.41917	−	0.516537i
$833$	−2.30387	+	13.0659i	−0.0798243	+	0.452706i
$834$		0			0
$835$	1.18942	−	0.998042i	0.0411616	−	0.0345387i
$836$	−44.8148			−1.54995
$837$		0			0
$838$	−47.5308			−1.64192
$839$	32.3472	−	27.1425i	1.11675	−	0.937063i	0.118312	−	0.992976i	$-0.462252\pi$
$839$	32.3472	−	27.1425i	1.11675	−	0.937063i	0.998436	+	0.0559139i	$0.0178072\pi$
$840$		0			0
$841$	2.07574	−	11.7721i	0.0715773	−	0.405935i
$842$	−63.6091	+	23.1518i	−2.19211	+	0.797865i
$843$		0			0
$844$	10.5887	+	60.0517i	0.364479	+	2.06706i
$845$	0.216631	+	0.375216i	0.00745234	+	0.0129078i
$846$		0			0
$847$	−0.415423	+	0.719533i	−0.0142741	+	0.0247235i
$848$	13.5018	+	4.91425i	0.463653	+	0.168756i
$849$		0			0
$850$	−18.2828	−	15.3411i	−0.627096	−	0.526196i
$851$	13.7469	+	11.5350i	0.471237	+	0.395415i
$852$		0			0
$853$	33.5748	+	12.2202i	1.14958	+	0.418413i	0.845364	−	0.534190i	$-0.179383\pi$
$853$	33.5748	+	12.2202i	1.14958	+	0.418413i	0.304216	+	0.952603i	$0.401606\pi$
$854$	−9.18865	+	15.9152i	−0.314429	+	0.544607i
$855$		0			0
$856$	−11.7679	−	20.3826i	−0.402219	−	0.696664i
$857$	−1.37332	−	7.78850i	−0.0469118	−	0.266050i	0.952326	−	0.305082i	$-0.0986838\pi$
$857$	−1.37332	−	7.78850i	−0.0469118	−	0.266050i	−0.999238	+	0.0390316i	$0.987573\pi$
$858$		0			0
$859$	42.0223	−	15.2948i	1.43378	−	0.521853i	0.495768	−	0.868455i	$-0.334887\pi$
$859$	42.0223	−	15.2948i	1.43378	−	0.521853i	0.938013	+	0.346601i	$0.112664\pi$
$860$	0.420289	−	2.38358i	0.0143317	−	0.0812794i
$861$		0			0
$862$	9.56081	−	8.02248i	0.325643	−	0.273247i
$863$	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
$866$	46.5981	−	39.1004i	1.58347	−	1.32869i
$867$		0			0
$868$	−0.628831	+	3.56628i	−0.0213439	+	0.121047i
$869$	20.9504	−	7.62531i	0.710693	−	0.258671i
$870$		0			0
$871$	−6.44790	−	36.5678i	−0.218479	−	1.23905i
$872$	13.2278	+	22.9112i	0.447950	+	0.775871i
$873$		0			0
$874$	20.5614	−	35.6134i	0.695501	−	1.20464i
$875$	0.506764	+	0.184447i	0.0171318	+	0.00623545i
$876$		0			0
$877$	−16.9584	−	14.2298i	−0.572645	−	0.480506i	0.309877	−	0.950776i	$-0.399712\pi$
$877$	−16.9584	−	14.2298i	−0.572645	−	0.480506i	−0.882522	+	0.470270i	$0.844156\pi$
$878$	−28.8127	−	24.1768i	−0.972383	−	0.815926i
$879$		0			0
$880$	0.719837	+	0.261999i	0.0242657	+	0.00883200i
$881$	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	$-0.462089\pi$
$884$	5.47335	+	31.0409i	0.184089	+	1.04402i
$885$		0			0
$886$	−41.1950	+	14.9938i	−1.38397	+	0.503725i
$887$	−2.31947	+	13.1544i	−0.0778801	+	0.441680i	0.920787	+	0.390066i	$0.127548\pi$
$887$	−2.31947	+	13.1544i	−0.0778801	+	0.441680i	−0.998667	+	0.0516143i	$0.983563\pi$
$888$		0			0
$889$	−5.12134	+	4.29732i	−0.171764	+	0.144127i
$890$	−0.347203			−0.0116383
$891$		0			0
$892$	80.8465			2.70694
$893$	10.5847	−	8.88162i	0.354204	−	0.297212i
$894$		0			0
$895$	0.262422	−	1.48827i	0.00877181	−	0.0497474i
$896$	−11.2775	+	4.10468i	−0.376755	+	0.137128i
$897$		0			0
$898$	−11.9780	−	67.9306i	−0.399711	−	2.26687i
$899$	5.30359	+	9.18609i	0.176885	+	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$	−7.65164	−	2.78497i	−0.254772	−	0.0927293i
$903$		0			0
$904$	38.5199	+	32.3221i	1.28115	+	1.07502i
$905$	0.213318	+	0.178995i	0.00709092	+	0.00594999i
$906$		0			0
$907$	−34.7316	−	12.6413i	−1.15325	−	0.419747i	−0.306565	−	0.951850i	$-0.599180\pi$
$907$	−34.7316	−	12.6413i	−1.15325	−	0.419747i	−0.846680	+	0.532103i	$0.821402\pi$
$908$	−36.0092	+	62.3697i	−1.19501	+	2.06981i
$909$		0			0
$910$	−0.272332	−	0.471694i	−0.00902773	−	0.0156365i
$911$	8.40650	+	47.6756i	0.278520	+	1.57956i	0.727555	+	0.686050i	$0.240657\pi$
$911$	8.40650	+	47.6756i	0.278520	+	1.57956i	−0.449035	+	0.893514i	$0.648232\pi$
$912$		0			0
$913$	−43.3089	+	15.7631i	−1.43331	+	0.521684i
$914$	−14.7581	+	83.6972i	−0.488154	+	2.76846i
$915$		0			0
$916$	64.8554	−	54.4201i	2.14288	−	1.79809i
$917$	−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	$0.452922\pi$
$920$	−1.34802	+	1.13112i	−0.0444427	+	0.0372919i
$921$		0			0
$922$	−0.949481	+	5.38477i	−0.0312695	+	0.177338i
$923$	4.52064	−	1.64538i	0.148799	−	0.0541582i
$924$		0			0
$925$	−3.49303	−	19.8100i	−0.114850	−	0.651347i
$926$	−22.0643	−	38.2165i	−0.725079	−	1.25587i
$927$		0			0
$928$	−6.72355	+	11.6455i	−0.220711	+	0.382283i
$929$	−5.86758	−	2.13562i	−0.192509	−	0.0700676i	0.243967	−	0.969784i	$-0.421551\pi$
$929$	−5.86758	−	2.13562i	−0.192509	−	0.0700676i	−0.436476	+	0.899716i	$0.643774\pi$
$930$		0			0
$931$	19.6299	+	16.4714i	0.643343	+	0.539829i
$932$	51.0339	+	42.8225i	1.67167	+	1.40270i
$933$		0			0
$934$	10.5137	+	3.82667i	0.344018	+	0.125212i
$935$	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	$-0.436037\pi$
$938$	2.13707	+	12.1199i	0.0697777	+	0.395729i
$939$		0			0
$940$	−1.18420	+	0.431013i	−0.0386243	+	0.0140581i
$941$	0.755827	−	4.28651i	0.0246392	−	0.139736i	−0.970007	−	0.243079i	$-0.921843\pi$
$941$	0.755827	−	4.28651i	0.0246392	−	0.139736i	0.994646	+	0.103343i	$0.0329538\pi$
$942$		0			0
$943$	3.73905	−	3.13743i	0.121760	−	0.102169i
$944$	27.3637			0.890612
$945$		0			0
$946$	−51.2644			−1.66675
$947$	−1.54491	+	1.29633i	−0.0502028	+	0.0421251i	−0.667544	−	0.744571i	$-0.732654\pi$
$947$	−1.54491	+	1.29633i	−0.0502028	+	0.0421251i	0.617341	+	0.786696i	$0.288210\pi$
$948$		0			0
$949$	0.142621	−	0.808844i	0.00462967	−	0.0262562i
$950$	−43.3163	+	15.7658i	−1.40537	+	0.511511i
$951$		0			0
$952$	−0.851131	−	4.82700i	−0.0275853	−	0.156444i
$953$	−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
$956$	−54.5965	−	19.8715i	−1.76578	−	0.642691i
$957$		0			0
$958$	26.0801	+	21.8838i	0.842609	+	0.707033i
$959$	5.11728	+	4.29391i	0.165246	+	0.138658i
$960$		0			0
$961$	26.5488	+	9.66299i	0.856414	+	0.311709i
$962$	−20.3338	+	35.2191i	−0.655587	+	1.13551i
$963$		0			0
$964$	−24.7759	−	42.9131i	−0.797978	−	1.38214i
$965$	0.0142285	+	0.0806940i	0.000458032	+	0.00259763i
$966$		0			0
$967$	0.651505	−	0.237128i	0.0209510	−	0.00762553i	−0.331523	−	0.943447i	$-0.607563\pi$
$967$	0.651505	−	0.237128i	0.0209510	−	0.00762553i	0.352474	+	0.935821i	$0.385340\pi$
$968$	−1.05633	+	5.99075i	−0.0339518	+	0.192550i
$969$		0			0
$970$	−0.906861	+	0.760946i	−0.0291175	+	0.0244325i
$971$	−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
$974$	−39.4328	+	33.0881i	−1.26351	+	1.06021i
$975$		0			0
$976$	−6.09688	+	34.5771i	−0.195156	+	1.10679i
$977$	−11.8432	+	4.31059i	−0.378899	+	0.137908i	−0.524447	−	0.851443i	$-0.675728\pi$
$977$	−11.8432	+	4.31059i	−0.378899	+	0.137908i	0.145548	+	0.989351i	$0.453506\pi$
$978$		0			0
$979$	0.834197	+	4.73096i	0.0266610	+	0.151202i
$980$	−1.16855	−	2.02399i	−0.0373280	−	0.0646540i
$981$		0			0
$982$	−16.9168	+	29.3008i	−0.539838	+	0.935027i
$983$	10.8488	+	3.94863i	0.346022	+	0.125942i	0.509184	−	0.860657i	$-0.329947\pi$
$983$	10.8488	+	3.94863i	0.346022	+	0.125942i	−0.163162	+	0.986599i	$0.552169\pi$
$984$		0			0
$985$	1.44584	+	1.21320i	0.0460683	+	0.0386559i
$986$	−23.4409	−	19.6692i	−0.746509	−	0.626395i
$987$		0			0
$988$	57.2064	+	20.8214i	1.81998	+	0.662418i
$989$	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	$0.929289\pi$
$992$	−0.604792	−	3.42994i	−0.0192022	−	0.108901i
$993$		0			0
$994$	−1.49830	+	0.545338i	−0.0475233	+	0.0172971i
$995$	0.307264	−	1.74258i	0.00974093	−	0.0552436i
$996$		0			0
$997$	2.57299	−	2.15900i	0.0814875	−	0.0683762i	−0.601134	−	0.799148i	$-0.705284\pi$
$997$	2.57299	−	2.15900i	0.0814875	−	0.0683762i	0.682622	+	0.730772i	$0.260840\pi$
$998$	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.b.109.2		12
3.2	odd	2		243.2.e.c.109.1		12
9.2	odd	6		243.2.e.d.190.2		12
9.4	even	3		81.2.e.a.10.2		12
9.5	odd	6		27.2.e.a.13.1	✓	12
9.7	even	3		243.2.e.a.190.1		12
27.2	odd	18		243.2.e.d.55.2		12
27.4	even	9		729.2.a.d.1.6		6
27.5	odd	18		729.2.c.e.244.6		12
27.7	even	9		81.2.e.a.73.2		12
27.11	odd	18		243.2.e.c.136.1		12
27.13	even	9		729.2.c.b.487.1		12
27.14	odd	18		729.2.c.e.487.6		12
27.16	even	9	inner	243.2.e.b.136.2		12
27.20	odd	18		27.2.e.a.25.1	yes	12
27.22	even	9		729.2.c.b.244.1		12
27.23	odd	18		729.2.a.a.1.1		6
27.25	even	9		243.2.e.a.55.1		12
36.23	even	6		432.2.u.c.337.1		12
45.14	odd	6		675.2.l.c.526.2		12
45.23	even	12		675.2.u.b.499.1		24
45.32	even	12		675.2.u.b.499.4		24
108.47	even	18		432.2.u.c.241.1		12
135.47	even	36		675.2.u.b.349.1		24
135.74	odd	18		675.2.l.c.376.2		12
135.128	even	36		675.2.u.b.349.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	9.5	odd	6
27.2.e.a.25.1	yes	12	27.20	odd	18
81.2.e.a.10.2		12	9.4	even	3
81.2.e.a.73.2		12	27.7	even	9
243.2.e.a.55.1		12	27.25	even	9
243.2.e.a.190.1		12	9.7	even	3
243.2.e.b.109.2		12	1.1	even	1	trivial
243.2.e.b.136.2		12	27.16	even	9	inner
243.2.e.c.109.1		12	3.2	odd	2
243.2.e.c.136.1		12	27.11	odd	18
243.2.e.d.55.2		12	27.2	odd	18
243.2.e.d.190.2		12	9.2	odd	6
432.2.u.c.241.1		12	108.47	even	18
432.2.u.c.337.1		12	36.23	even	6
675.2.l.c.376.2		12	135.74	odd	18
675.2.l.c.526.2		12	45.14	odd	6
675.2.u.b.349.1		24	135.47	even	36
675.2.u.b.349.4		24	135.128	even	36
675.2.u.b.499.1		24	45.23	even	12
675.2.u.b.499.4		24	45.32	even	12
729.2.a.a.1.1		6	27.23	odd	18
729.2.a.d.1.6		6	27.4	even	9
729.2.c.b.244.1		12	27.22	even	9
729.2.c.b.487.1		12	27.13	even	9
729.2.c.e.244.6		12	27.5	odd	18
729.2.c.e.487.6		12	27.14	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)

\(f(q)\)	\(=\)	\(q+(1.83975 - 1.54373i) q^{2} +(0.654269 - 3.71054i) q^{4} +(0.0874698 - 0.0318364i) q^{5} +(-0.100692 - 0.571052i) q^{7} +(-2.12277 - 3.67675i) q^{8} +O(q^{10})\)	\(q+(1.83975 - 1.54373i) q^{2} +(0.654269 - 3.71054i) q^{4} +(0.0874698 - 0.0318364i) q^{5} +(-0.100692 - 0.571052i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(-2.90655 - 1.05790i) q^{11} +(3.21871 + 2.70082i) q^{13} +(-1.06680 - 0.895151i) q^{14} +(-2.50017 - 0.909989i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(-0.0609016 - 0.345390i) q^{20} +(-6.98043 + 2.54067i) q^{22} +(0.773223 - 4.38517i) q^{23} +(-3.82358 + 3.20837i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(-4.90231 + 4.11353i) q^{29} +(0.287822 - 1.63232i) q^{31} +(1.97455 - 0.718677i) q^{32} +(0.830315 + 4.70895i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(8.67830 + 3.15864i) q^{38} +(-0.302733 - 0.254023i) q^{40} +(0.839704 + 0.704595i) q^{41} +(6.48493 + 2.36032i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(-0.623952 - 3.53861i) q^{47} +(6.26189 - 2.27914i) q^{49} +(-2.08157 + 11.8052i) q^{50} +(12.1274 - 10.1761i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(-1.88587 + 1.58243i) q^{56} +(-2.66883 + 15.1357i) q^{58} +(-9.66442 + 3.51756i) q^{59} +(-2.29152 - 12.9958i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(0.367525 + 0.133768i) q^{65} +(-6.76976 - 5.68050i) q^{67} +(5.74656 + 4.82194i) q^{68} +(-0.121811 - 0.0443356i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(1.68070 + 9.53172i) q^{74} +(13.6149 - 4.95544i) q^{76} +(-0.311448 + 1.76631i) q^{77} +(-5.52164 + 4.63321i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(11.4144 - 9.57782i) q^{83} +(-0.0321818 + 0.182512i) q^{85} +(15.5744 - 5.66860i) q^{86} +(2.28032 + 12.9323i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(-15.7655 - 5.73816i) q^{92} +(-6.61057 - 5.54693i) q^{94} +(0.274202 + 0.230083i) q^{95} +(-4.97617 - 1.81118i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Introduction

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