LMFDB - Embedded newform 243.2.e.b.136.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(28,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,-3,0,3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			136.2
Root			$0.500000 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	243.136
Dual form			243.2.e.b.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

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

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	0.989989	+	0.141144i	$0.0450781\pi$
$2$	1.83975	+	1.54373i	1.30090	+	1.09158i	0.310910	+	0.950439i	$0.399366\pi$
$3$		0			0
$3$		0			0
$4$	0.654269	+	3.71054i	0.327134	+	1.85527i
$5$	0.0874698	+	0.0318364i	0.0391177	+	0.0142377i	0.361505	−	0.932370i	$-0.382263\pi$
$5$	0.0874698	+	0.0318364i	0.0391177	+	0.0142377i	−0.322387	+	0.946608i	$0.604485\pi$
$6$		0			0
$7$	−0.100692	+	0.571052i	−0.0380579	+	0.215837i	−0.997906	−	0.0646837i	$-0.979396\pi$
$7$	−0.100692	+	0.571052i	−0.0380579	+	0.215837i	0.959848	+	0.280521i	$0.0905073\pi$
$8$	−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	−0.740739	−	0.671793i	$-0.765524\pi$
$11$	−2.90655	+	1.05790i	−0.876357	+	0.318968i	−0.135618	+	0.990761i	$0.543302\pi$
$12$		0			0
$13$	3.21871	−	2.70082i	0.892711	−	0.749073i	−0.0760413	−	0.997105i	$-0.524228\pi$
$13$	3.21871	−	2.70082i	0.892711	−	0.749073i	0.968752	+	0.248031i	$0.0797836\pi$
$14$	−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	0.719683	−	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	$0.0212550\pi$
$20$	−0.0609016	+	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	0.952869	+	0.303383i	$0.0981163\pi$
$23$	0.773223	+	4.38517i	0.161228	+	0.914371i	−0.791640	+	0.610987i	$0.790773\pi$
$24$		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	0.0618470	−	0.998086i	$-0.480301\pi$
$29$	−4.90231	−	4.11353i	−0.910336	−	0.763862i	−0.972183	+	0.234223i	$0.924745\pi$
$30$		0			0
$31$	0.287822	+	1.63232i	0.0516943	+	0.293173i	0.999684	−	0.0251272i	$-0.00799908\pi$
$31$	0.287822	+	1.63232i	0.0516943	+	0.293173i	−0.947990	+	0.318300i	$0.896888\pi$
$32$	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	0.651490	−	0.758657i	$-0.274144\pi$
$37$	−2.01505	−	3.49016i	−0.331272	−	0.573779i	−0.982761	+	0.184878i	$0.940811\pi$
$38$	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	−0.574859	−	0.818253i	$-0.694943\pi$
$41$	0.839704	−	0.704595i	0.131140	−	0.110039i	0.705998	+	0.708213i	$0.250499\pi$
$42$		0			0
$43$	6.48493	−	2.36032i	0.988943	−	0.359946i	0.203632	−	0.979047i	$-0.434725\pi$
$43$	6.48493	−	2.36032i	0.988943	−	0.359946i	0.785311	+	0.619102i	$0.212503\pi$
$44$	−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	0.904884	+	0.425659i	$0.139958\pi$
$47$	−0.623952	+	3.53861i	−0.0910127	+	0.516159i	−0.995896	+	0.0904999i	$0.971154\pi$
$48$		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	−0.375035	−	0.927011i	$-0.622369\pi$
$59$	−9.66442	−	3.51756i	−1.25820	−	0.457947i	−0.883165	+	0.469063i	$0.844592\pi$
$60$		0			0
$61$	−2.29152	+	12.9958i	−0.293399	+	1.66395i	0.380242	+	0.924887i	$0.375841\pi$
$61$	−2.29152	+	12.9958i	−0.293399	+	1.66395i	−0.673640	+	0.739059i	$0.735270\pi$
$62$	−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	−0.954613	−	0.297848i	$-0.903731\pi$
$67$	−6.76976	+	5.68050i	−0.827058	+	0.693984i	0.127556	+	0.991831i	$0.459287\pi$
$68$	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	0.897994	−	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	$0.170308\pi$
$74$	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	0.276958	−	0.960882i	$-0.410674\pi$
$79$	−5.52164	−	4.63321i	−0.621233	−	0.521277i	−0.898191	+	0.439605i	$0.855118\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	11.4144	+	9.57782i	1.25289	+	1.05130i	0.996402	+	0.0847562i	$0.0270111\pi$
$83$	11.4144	+	9.57782i	1.25289	+	1.05130i	0.256492	+	0.966546i	$0.417433\pi$
$84$		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	−0.904244	−	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
$92$	−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	−0.582056	−	0.813149i	$-0.697751\pi$
$97$	−4.97617	+	1.81118i	−0.505254	+	0.183897i	0.0768016	+	0.997046i	$0.475529\pi$
$98$	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	−0.855353	−	0.518046i	$-0.826660\pi$
$101$	1.26225	−	7.15855i	0.125598	−	0.712302i	0.980951	−	0.194256i	$-0.0622293\pi$
$102$		0			0
$103$	−6.01532	−	2.18940i	−0.592707	−	0.215728i	0.0282124	−	0.999602i	$-0.491019\pi$
$103$	−6.01532	−	2.18940i	−0.592707	−	0.215728i	−0.620920	+	0.783874i	$0.713241\pi$
$104$	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	−0.239467	−	0.970905i	$-0.576973\pi$
$113$	−11.1297	−	4.05088i	−1.04699	−	0.381075i	−0.807528	+	0.589830i	$0.799195\pi$
$114$		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	0.488377	+	0.872633i	$0.337589\pi$
$127$	−5.76469	+	9.98473i	−0.511533	+	0.886002i	−0.999911	+	0.0133693i	$0.995744\pi$
$128$	−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	0.973644	+	0.228075i	$0.0732431\pi$
$131$	1.56488	+	8.87487i	0.136724	+	0.775401i	−0.836920	+	0.547326i	$0.815646\pi$
$132$		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	0.182579	−	0.983191i	$-0.441556\pi$
$137$	−8.82501	−	7.40506i	−0.753971	−	0.632657i	−0.936550	+	0.350534i	$0.886000\pi$
$138$		0			0
$139$	0.295868	+	1.67795i	0.0250952	+	0.142322i	0.994781	−	0.102033i	$-0.0325348\pi$
$139$	0.295868	+	1.67795i	0.0250952	+	0.142322i	−0.969686	+	0.244355i	$0.921424\pi$
$140$	−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	0.382525	−	0.923945i	$-0.375054\pi$
$149$	16.5870	−	13.9181i	1.35886	−	1.14022i	0.976333	−	0.216273i	$-0.0693900\pi$
$150$		0			0
$151$	4.45557	−	1.62170i	0.362589	−	0.131972i	−0.154300	−	0.988024i	$-0.549312\pi$
$151$	4.45557	−	1.62170i	0.362589	−	0.131972i	0.516889	+	0.856052i	$0.327090\pi$
$152$	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	0.349853	−	0.936805i	$-0.386232\pi$
$157$	0.196589	+	0.0715526i	0.0156895	+	0.00571052i	−0.334163	+	0.942515i	$0.608454\pi$
$158$	−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	0.867720	−	0.497053i	$-0.165585\pi$
$167$	15.6745	+	5.70507i	1.21293	+	0.441471i	0.345212	+	0.938525i	$0.387807\pi$
$168$		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	0.442275	−	0.896880i	$-0.354172\pi$
$173$	17.8562	−	6.49912i	1.35758	−	0.494119i	0.915305	+	0.402761i	$0.131949\pi$
$174$		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	0.991774	+	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	$0.131203\pi$
$182$	−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	0.703111	−	0.711081i	$-0.251794\pi$
$191$	1.72652	+	1.44873i	0.124927	+	0.104826i	−0.578184	+	0.815907i	$0.696238\pi$
$192$		0			0
$193$	−0.152858	−	0.866900i	−0.0110029	−	0.0624008i	0.978812	−	0.204761i	$-0.0656418\pi$
$193$	−0.152858	−	0.866900i	−0.0110029	−	0.0624008i	−0.989815	+	0.142361i	$0.954531\pi$
$194$	−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	−0.237744	−	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	$0.598006\pi$
$200$	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	−0.239449	−	0.970909i	$-0.576967\pi$
$211$	−15.2080	−	5.53528i	−1.04697	−	0.381064i	−0.807517	+	0.589845i	$0.799189\pi$
$212$	−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	−0.560261	−	0.828316i	$-0.689299\pi$
$223$	3.72602	−	21.1313i	0.249513	−	1.41506i	0.809774	−	0.586742i	$-0.199590\pi$
$224$	−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	−0.860477	−	0.509489i	$-0.829834\pi$
$227$	−17.9615	+	6.53746i	−1.19215	+	0.433906i	−0.331671	+	0.943395i	$0.607612\pi$
$228$		0			0
$229$	17.2131	−	14.4435i	1.13748	−	0.954456i	0.138123	−	0.990415i	$-0.455893\pi$
$229$	17.2131	−	14.4435i	1.13748	−	0.954456i	0.999353	+	0.0359590i	$0.0114486\pi$
$230$	−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	−0.995574	−	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
$236$	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	0.940193	+	0.340641i	$0.110644\pi$
$239$	2.67771	+	15.1860i	0.173207	+	0.982304i	−0.766987	+	0.641663i	$0.778245\pi$
$240$		0			0
$241$	10.0746	+	8.45359i	0.648962	+	0.544544i	0.906756	−	0.421656i	$-0.138551\pi$
$241$	10.0746	+	8.45359i	0.648962	+	0.544544i	−0.257794	+	0.966200i	$0.582996\pi$
$242$	−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	−0.448634	−	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
$254$	−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	−0.869684	−	0.493609i	$-0.835677\pi$
$257$	−8.57018	+	7.19124i	−0.534593	+	0.448577i	0.335091	+	0.942186i	$0.391233\pi$
$258$		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	−0.647012	−	0.762480i	$-0.723982\pi$
$263$	3.59641	−	20.3962i	0.221764	−	1.25769i	0.868776	−	0.495206i	$-0.164907\pi$
$264$		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	−0.945896	−	0.324469i	$-0.894814\pi$
$277$	0.897584	−	5.09045i	0.0539306	−	0.305855i	0.999827	+	0.0186140i	$0.00592536\pi$
$278$	−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	−0.432758	−	0.901510i	$-0.642459\pi$
$281$	−3.09764	+	1.12745i	−0.184790	+	0.0672580i	0.247968	+	0.968768i	$0.420237\pi$
$282$		0			0
$283$	−6.99454	+	5.86911i	−0.415782	+	0.348883i	−0.826556	−	0.562855i	$-0.809703\pi$
$283$	−6.99454	+	5.86911i	−0.415782	+	0.348883i	0.410774	+	0.911737i	$0.365259\pi$
$284$	−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	0.995782	−	0.0917487i	$-0.0292456\pi$
$293$	0.490805	+	2.78349i	0.0286731	+	0.162613i	−0.967109	+	0.254362i	$0.918135\pi$
$294$		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	0.762129	−	0.647425i	$-0.224154\pi$
$307$	−3.14723	−	5.45116i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$308$	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	−0.468453	−	0.883488i	$-0.655189\pi$
$311$	5.64796	−	4.73920i	0.320266	−	0.268735i	0.788720	+	0.614753i	$0.210744\pi$
$312$		0			0
$313$	4.01319	−	1.46068i	0.226839	−	0.0825627i	−0.226100	−	0.974104i	$-0.572598\pi$
$313$	4.01319	−	1.46068i	0.226839	−	0.0825627i	0.452939	+	0.891541i	$0.350375\pi$
$314$	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	0.798988	+	0.601348i	$0.205369\pi$
$317$	−2.80400	+	15.9023i	−0.157488	+	0.893160i	−0.956476	+	0.291812i	$0.905742\pi$
$318$		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	−0.744311	−	0.667834i	$-0.767222\pi$
$331$	3.33895	−	18.9361i	0.183525	−	1.04082i	0.927836	−	0.372989i	$-0.121667\pi$
$332$	−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	−0.231180	+	0.972911i	$0.574259\pi$
$337$	−22.5698	+	18.9383i	−1.22945	+	1.03163i	−0.998274	+	0.0587237i	$0.981297\pi$
$338$	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	−0.990717	−	0.135941i	$-0.956594\pi$
$347$	−1.97907	−	11.2239i	−0.106242	−	0.602530i	0.884475	−	0.466588i	$-0.154517\pi$
$348$		0			0
$349$	21.5731	+	18.1019i	1.15478	+	0.968975i	0.999821	−	0.0189464i	$-0.00603120\pi$
$349$	21.5731	+	18.1019i	1.15478	+	0.968975i	0.154958	+	0.987921i	$0.450476\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	−21.9503	−	18.4185i	−1.16830	−	0.980318i	−0.168312	−	0.985734i	$-0.553832\pi$
$353$	−21.9503	−	18.4185i	−1.16830	−	0.980318i	−0.999985	+	0.00541596i	$0.998276\pi$
$354$		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	0.0875770	+	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
$362$	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	−0.857377	−	0.514689i	$-0.827907\pi$
$367$	−22.6694	+	8.25097i	−1.18333	+	0.430697i	−0.325953	+	0.945386i	$0.605685\pi$
$368$	−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	0.629535	−	0.776972i	$-0.283245\pi$
$373$	11.8266	+	4.30453i	0.612359	+	0.222880i	−0.0171764	+	0.999852i	$0.505468\pi$
$374$	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	−0.124492	−	0.992221i	$-0.539730\pi$
$383$	−16.7844	−	6.10904i	−0.857645	−	0.312157i	−0.733153	+	0.680063i	$0.761952\pi$
$384$		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	0.406313	−	0.913734i	$-0.366814\pi$
$389$	25.7367	−	9.36740i	1.30490	−	0.474946i	0.898591	+	0.438788i	$0.144592\pi$
$390$		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	−0.914064	−	0.405571i	$-0.867073\pi$
$397$	−2.10799	+	3.65115i	−0.105797	+	0.183246i	0.808266	+	0.588817i	$0.200406\pi$
$398$	−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	−0.977187	−	0.212379i	$-0.931879\pi$
$401$	−2.63468	−	14.9420i	−0.131569	−	0.746168i	0.845618	−	0.533789i	$-0.179232\pi$
$402$		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	0.998328	−	0.0577983i	$-0.0184080\pi$
$409$	0.817816	+	4.63806i	0.0404384	+	0.229337i	−0.957890	+	0.287136i	$0.907297\pi$
$410$	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	−0.933014	−	0.359839i	$-0.882831\pi$
$419$	−15.1609	+	12.7215i	−0.740658	+	0.621486i	0.192356	+	0.981325i	$0.438387\pi$
$420$		0			0
$421$	−26.4859	+	9.64008i	−1.29084	+	0.469829i	−0.894004	−	0.448059i	$-0.852115\pi$
$421$	−26.4859	+	9.64008i	−1.29084	+	0.469829i	−0.396840	+	0.917888i	$0.629893\pi$
$422$	−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	0.848546	+	0.529122i	$0.177479\pi$
$439$	−2.71955	+	15.4233i	−0.129797	+	0.736114i	−0.978343	+	0.206992i	$0.933633\pi$
$440$	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	−0.715673	−	0.698436i	$-0.753880\pi$
$443$	−17.1530	+	6.24318i	−0.814964	+	0.296623i	−0.0992911	+	0.995058i	$0.531658\pi$
$444$		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	0.975663	+	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
$452$	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	−0.994771	−	0.102133i	$-0.967433\pi$
$457$	−27.1087	−	22.7469i	−1.26809	−	1.06406i	−0.273321	−	0.961923i	$-0.588122\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	−1.74408	−	1.46345i	−0.0812297	−	0.0681598i	0.601269	−	0.799047i	$-0.294662\pi$
$461$	−1.74408	−	1.46345i	−0.0812297	−	0.0681598i	−0.682498	+	0.730887i	$0.739107\pi$
$462$		0			0
$463$	3.19070	+	18.0954i	0.148285	+	0.840964i	0.964671	+	0.263458i	$0.0848629\pi$
$463$	3.19070	+	18.0954i	0.148285	+	0.840964i	−0.816386	+	0.577506i	$0.804026\pi$
$464$	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	−0.807085	−	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
$470$	−0.754820	+	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	−0.875496	−	0.483226i	$-0.839465\pi$
$479$	2.46162	−	13.9605i	0.112474	−	0.637873i	0.987970	−	0.154647i	$-0.0494240\pi$
$480$		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	0.0255621	−	0.999673i	$-0.491862\pi$
$491$	−13.2382	−	4.81833i	−0.597434	−	0.217448i	−0.622996	+	0.782225i	$0.714085\pi$
$492$		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	−0.350297	−	0.936639i	$-0.613919\pi$
$499$	11.4212	−	9.58353i	0.511284	−	0.429018i	0.861581	+	0.507621i	$0.169475\pi$
$500$	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	0.633236	−	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
$506$	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	−0.779839	−	0.625980i	$-0.784699\pi$
$509$	−5.89131	−	33.4113i	−0.261128	−	1.48093i	0.518712	−	0.854949i	$-0.326412\pi$
$510$		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	−0.166277	+	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	$0.813989\pi$
$524$	−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	0.377683	+	0.925935i	$0.376721\pi$
$547$	−6.87401	+	38.9844i	−0.293911	+	1.66685i	−0.671594	+	0.740919i	$0.734390\pi$
$548$	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	0.719105	−	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
$560$	0.0249374	−	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	−0.990736	−	0.135802i	$-0.956639\pi$
$563$	−2.51977	−	14.2903i	−0.106196	−	0.602266i	0.884540	−	0.466464i	$-0.154472\pi$
$564$		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	0.663410	−	0.748256i	$-0.269108\pi$
$569$	0.995232	+	0.835099i	0.0417223	+	0.0350092i	−0.621688	+	0.783265i	$0.713553\pi$
$570$		0			0
$571$	2.78833	+	15.8134i	0.116688	+	0.661769i	0.985901	+	0.167331i	$0.0535150\pi$
$571$	2.78833	+	15.8134i	0.116688	+	0.661769i	−0.869213	+	0.494438i	$0.835374\pi$
$572$	−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	0.940543	−	0.339675i	$-0.110317\pi$
$577$	4.23017	+	7.32686i	0.176104	+	0.305021i	−0.764439	+	0.644696i	$0.776984\pi$
$578$	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	−0.845283	−	0.534319i	$-0.820568\pi$
$587$	3.19256	−	18.1059i	0.131771	−	0.747310i	0.977054	−	0.212991i	$-0.0683206\pi$
$588$		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	0.544931	−	0.838481i	$-0.316556\pi$
$599$	10.3627	+	3.77170i	0.423407	+	0.154108i	−0.121524	+	0.992589i	$0.538778\pi$
$600$		0			0
$601$	4.47976	−	25.4060i	0.182733	−	1.03633i	−0.746100	−	0.665834i	$-0.768076\pi$
$601$	4.47976	−	25.4060i	0.182733	−	1.03633i	0.928833	−	0.370498i	$-0.120813\pi$
$602$	−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	−0.843079	−	0.537790i	$-0.819259\pi$
$607$	−11.3297	+	9.50675i	−0.459858	+	0.385867i	0.383221	+	0.923657i	$0.374815\pi$
$608$	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	0.223248	+	0.974762i	$0.428334\pi$
$613$	−18.1370	+	31.4141i	−0.732545	+	1.26880i	−0.955792	+	0.294043i	$0.904999\pi$
$614$	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	0.714967	+	0.699158i	$0.246442\pi$
$617$	7.01079	+	39.7602i	0.282244	+	1.60068i	−0.432724	+	0.901527i	$0.642447\pi$
$618$		0			0
$619$	−5.28058	−	4.43093i	−0.212244	−	0.178094i	0.530468	−	0.847705i	$-0.322016\pi$
$619$	−5.28058	−	4.43093i	−0.212244	−	0.178094i	−0.742712	+	0.669611i	$0.766461\pi$
$620$	−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	−0.993751	−	0.111617i	$-0.964397\pi$
$631$	−14.9095	−	25.8241i	−0.593539	−	1.02804i	0.400212	−	0.916423i	$-0.368936\pi$
$632$	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	0.376709	+	0.926331i	$0.377056\pi$
$641$	−7.44616	+	42.2293i	−0.294106	+	1.66796i	−0.670815	+	0.741625i	$0.734056\pi$
$642$		0			0
$643$	25.7600	+	9.37589i	1.01588	+	0.369749i	0.795687	−	0.605708i	$-0.207110\pi$
$643$	25.7600	+	9.37589i	1.01588	+	0.369749i	0.220190	+	0.975457i	$0.429332\pi$
$644$	−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	0.858245	−	0.513241i	$-0.171555\pi$
$653$	30.3016	+	11.0289i	1.18579	+	0.431593i	0.327549	+	0.944834i	$0.393777\pi$
$654$		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	0.221689	−	0.975117i	$-0.428843\pi$
$659$	26.1409	−	9.51452i	1.01831	−	0.370633i	0.796617	+	0.604485i	$0.206621\pi$
$660$		0			0
$661$	23.5854	−	19.7905i	0.917367	−	0.769763i	−0.0561388	−	0.998423i	$-0.517879\pi$
$661$	23.5854	−	19.7905i	0.917367	−	0.769763i	0.973506	+	0.228660i	$0.0734345\pi$
$662$	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	0.169513	−	0.985528i	$-0.445780\pi$
$673$	−20.0172	−	16.7964i	−0.771607	−	0.647455i	−0.941120	+	0.338073i	$0.890225\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	−13.9378	−	11.6952i	−0.535673	−	0.449483i	0.334382	−	0.942438i	$-0.391472\pi$
$677$	−13.9378	−	11.6952i	−0.535673	−	0.449483i	−0.870055	+	0.492955i	$0.835917\pi$
$678$		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	−0.548811	−	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
$686$	−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	0.614329	−	0.789050i	$-0.289427\pi$
$691$	41.8520	−	15.2329i	1.59212	−	0.579486i	0.977795	+	0.209565i	$0.0672046\pi$
$692$	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	0.889987	+	0.455985i	$0.150713\pi$
$709$	−2.72350	+	15.4457i	−0.102283	+	0.580077i	−0.992271	+	0.124092i	$0.960398\pi$
$710$	−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	−0.609757	−	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
$722$	−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	0.649428	−	0.760423i	$-0.275008\pi$
$727$	0.359407	+	0.301578i	0.0133297	+	0.0111849i	−0.636098	+	0.771608i	$0.719453\pi$
$728$	−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	−0.656264	−	0.754532i	$-0.727864\pi$
$733$	−8.05837	−	45.7013i	−0.297643	−	1.68801i	0.358621	−	0.933483i	$-0.383247\pi$
$734$	−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	0.524875	−	0.851179i	$-0.324112\pi$
$739$	−12.9047	−	22.3515i	−0.474706	−	0.822214i	−0.999580	+	0.0289653i	$0.990779\pi$
$740$	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	−0.983398	−	0.181460i	$-0.941918\pi$
$743$	−26.5891	+	22.3109i	−0.975460	+	0.818508i	0.00793799	+	0.999968i	$0.497473\pi$
$744$		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	−0.103706	−	0.994608i	$-0.533070\pi$
$751$	−22.5393	−	8.20364i	−0.822472	−	0.299355i	−0.718765	+	0.695253i	$0.755292\pi$
$752$	−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	0.565477	−	0.824764i	$-0.308692\pi$
$761$	12.9244	+	4.70410i	0.468510	+	0.170524i	−0.0969675	+	0.995288i	$0.530914\pi$
$762$		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	−0.963303	−	0.268417i	$-0.913500\pi$
$769$	−24.0216	+	20.1565i	−0.866240	+	0.726862i	0.0970630	+	0.995278i	$0.469055\pi$
$770$	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	0.999978	+	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
$776$	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	−0.864446	−	0.502726i	$-0.832330\pi$
$787$	−6.28609	−	35.6502i	−0.224075	−	1.27079i	0.640371	−	0.768066i	$-0.278781\pi$
$788$	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	−0.145782	−	0.989317i	$-0.546570\pi$
$797$	22.6750	−	19.0266i	0.803189	−	0.673956i	0.948972	+	0.315361i	$0.102126\pi$
$798$		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	0.480564	−	0.876960i	$-0.340432\pi$
$821$	40.4695	−	14.7297i	1.41240	−	0.514070i	0.931832	+	0.362890i	$0.118210\pi$
$822$		0			0
$823$	7.87807	−	6.61049i	0.274612	−	0.230427i	−0.495072	−	0.868852i	$-0.664858\pi$
$823$	7.87807	−	6.61049i	0.274612	−	0.230427i	0.769684	+	0.638425i	$0.220414\pi$
$824$	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	0.914132	−	0.405416i	$-0.132873\pi$
$827$	3.04731	+	5.27810i	0.105965	+	0.183538i	−0.808167	+	0.588954i	$0.799540\pi$
$828$		0			0
$829$	16.8489	−	29.1832i	0.585188	−	1.01358i	−0.409664	−	0.912236i	$-0.634354\pi$
$829$	16.8489	−	29.1832i	0.585188	−	1.01358i	0.994852	−	0.101339i	$-0.0323126\pi$
$830$	−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	0.998436	−	0.0559139i	$-0.0178072\pi$
$839$	32.3472	+	27.1425i	1.11675	+	0.937063i	0.118312	+	0.992976i	$0.462252\pi$
$840$		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	0.304216	−	0.952603i	$-0.401606\pi$
$853$	33.5748	−	12.2202i	1.14958	−	0.418413i	0.845364	+	0.534190i	$0.179383\pi$
$854$	−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	−0.999238	−	0.0390316i	$-0.987573\pi$
$857$	−1.37332	+	7.78850i	−0.0469118	+	0.266050i	0.952326	+	0.305082i	$0.0986838\pi$
$858$		0			0
$859$	42.0223	+	15.2948i	1.43378	+	0.521853i	0.938013	−	0.346601i	$-0.112664\pi$
$859$	42.0223	+	15.2948i	1.43378	+	0.521853i	0.495768	+	0.868455i	$0.334887\pi$
$860$	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	−0.882522	−	0.470270i	$-0.844156\pi$
$877$	−16.9584	+	14.2298i	−0.572645	+	0.480506i	0.309877	+	0.950776i	$0.399712\pi$
$878$	−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	0.937068	−	0.349147i	$-0.113529\pi$
$881$	4.93202	+	8.54251i	0.166164	+	0.287804i	−0.770904	+	0.636951i	$0.780195\pi$
$882$		0			0
$883$	−23.7865	+	41.1995i	−0.800481	+	1.38647i	0.118819	+	0.992916i	$0.462089\pi$
$883$	−23.7865	+	41.1995i	−0.800481	+	1.38647i	−0.919300	+	0.393558i	$0.871244\pi$
$884$	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	−0.998667	−	0.0516143i	$-0.983563\pi$
$887$	−2.31947	−	13.1544i	−0.0778801	−	0.441680i	0.920787	−	0.390066i	$-0.127548\pi$
$888$		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	−0.846680	−	0.532103i	$-0.821402\pi$
$907$	−34.7316	+	12.6413i	−1.15325	+	0.419747i	−0.306565	+	0.951850i	$0.599180\pi$
$908$	−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	−0.449035	−	0.893514i	$-0.648232\pi$
$911$	8.40650	−	47.6756i	0.278520	−	1.57956i	0.727555	−	0.686050i	$-0.240657\pi$
$912$		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	−0.436476	−	0.899716i	$-0.643774\pi$
$929$	−5.86758	+	2.13562i	−0.192509	+	0.0700676i	0.243967	+	0.969784i	$0.421551\pi$
$930$		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	0.199595	+	0.979878i	$0.436037\pi$
$937$	−22.9212	+	39.7006i	−0.748802	+	1.29696i	−0.948397	+	0.317085i	$0.897296\pi$
$938$	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	0.994646	−	0.103343i	$-0.0329538\pi$
$941$	0.755827	+	4.28651i	0.0246392	+	0.139736i	−0.970007	+	0.243079i	$0.921843\pi$
$942$		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	0.617341	−	0.786696i	$-0.288210\pi$
$947$	−1.54491	−	1.29633i	−0.0502028	−	0.0421251i	−0.667544	+	0.744571i	$0.732654\pi$
$948$		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	0.416947	+	0.908931i	$0.363100\pi$
$953$	−17.8644	+	30.9420i	−0.578684	+	1.00231i	−0.995631	+	0.0933786i	$0.970233\pi$
$954$		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	0.352474	−	0.935821i	$-0.385340\pi$
$967$	0.651505	+	0.237128i	0.0209510	+	0.00762553i	−0.331523	+	0.943447i	$0.607563\pi$
$968$	−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	0.145548	−	0.989351i	$-0.453506\pi$
$977$	−11.8432	−	4.31059i	−0.378899	−	0.137908i	−0.524447	+	0.851443i	$0.675728\pi$
$978$		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	−0.163162	−	0.986599i	$-0.552169\pi$
$983$	10.8488	−	3.94863i	0.346022	−	0.125942i	0.509184	+	0.860657i	$0.329947\pi$
$984$		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	−0.975427	−	0.220322i	$-0.929289\pi$
$991$	−9.34676	+	16.1891i	−0.296910	+	0.514263i	0.678518	+	0.734584i	$0.262623\pi$
$992$	−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	0.682622	−	0.730772i	$-0.260840\pi$
$997$	2.57299	+	2.15900i	0.0814875	+	0.0683762i	−0.601134	+	0.799148i	$0.705284\pi$
$998$	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.136.2		12
3.2	odd	2		243.2.e.c.136.1		12
9.2	odd	6		27.2.e.a.25.1	yes	12
9.4	even	3		243.2.e.a.55.1		12
9.5	odd	6		243.2.e.d.55.2		12
9.7	even	3		81.2.e.a.73.2		12
27.2	odd	18		729.2.c.e.244.6		12
27.4	even	9		81.2.e.a.10.2		12
27.5	odd	18		243.2.e.c.109.1		12
27.7	even	9		729.2.a.d.1.6		6
27.11	odd	18		729.2.c.e.487.6		12
27.13	even	9		243.2.e.a.190.1		12
27.14	odd	18		243.2.e.d.190.2		12
27.16	even	9		729.2.c.b.487.1		12
27.20	odd	18		729.2.a.a.1.1		6
27.22	even	9	inner	243.2.e.b.109.2		12
27.23	odd	18		27.2.e.a.13.1	✓	12
27.25	even	9		729.2.c.b.244.1		12
36.11	even	6		432.2.u.c.241.1		12
45.2	even	12		675.2.u.b.349.1		24
45.29	odd	6		675.2.l.c.376.2		12
45.38	even	12		675.2.u.b.349.4		24
108.23	even	18		432.2.u.c.337.1		12
135.23	even	36		675.2.u.b.499.1		24
135.77	even	36		675.2.u.b.499.4		24
135.104	odd	18		675.2.l.c.526.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	27.23	odd	18
27.2.e.a.25.1	yes	12	9.2	odd	6
81.2.e.a.10.2		12	27.4	even	9
81.2.e.a.73.2		12	9.7	even	3
243.2.e.a.55.1		12	9.4	even	3
243.2.e.a.190.1		12	27.13	even	9
243.2.e.b.109.2		12	27.22	even	9	inner
243.2.e.b.136.2		12	1.1	even	1	trivial
243.2.e.c.109.1		12	27.5	odd	18
243.2.e.c.136.1		12	3.2	odd	2
243.2.e.d.55.2		12	9.5	odd	6
243.2.e.d.190.2		12	27.14	odd	18
432.2.u.c.241.1		12	36.11	even	6
432.2.u.c.337.1		12	108.23	even	18
675.2.l.c.376.2		12	45.29	odd	6
675.2.l.c.526.2		12	135.104	odd	18
675.2.u.b.349.1		24	45.2	even	12
675.2.u.b.349.4		24	45.38	even	12
675.2.u.b.499.1		24	135.23	even	36
675.2.u.b.499.4		24	135.77	even	36
729.2.a.a.1.1		6	27.20	odd	18
729.2.a.d.1.6		6	27.7	even	9
729.2.c.b.244.1		12	27.25	even	9
729.2.c.b.487.1		12	27.16	even	9
729.2.c.e.244.6		12	27.2	odd	18
729.2.c.e.487.6		12	27.11	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 $\F_{q}$
Belyi maps

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more