LMFDB - Embedded newform 414.2.i.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			289.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	414.289
Dual form			414.2.i.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(-0.154861 + 0.339098i) q^{5} +(-1.97611 - 0.580239i) q^{7} +(0.841254 - 0.540641i) q^{8} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(-0.154861 + 0.339098i) q^{5} +(-1.97611 - 0.580239i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.357685 - 0.105026i) q^{10} +(1.61435 - 1.86306i) q^{11} +(3.58149 - 1.05162i) q^{13} +(0.855563 + 1.87342i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(-0.897877 - 6.24487i) q^{17} +(0.468056 - 3.25540i) q^{19} +(-0.313607 - 0.201543i) q^{20} -2.46519 q^{22} +(1.76381 - 4.45971i) q^{23} +(3.18330 + 3.67372i) q^{25} +(-3.14014 - 2.01804i) q^{26} +(0.855563 - 1.87342i) q^{28} +(1.01510 + 7.06018i) q^{29} +(4.91722 - 3.16011i) q^{31} +(0.415415 + 0.909632i) q^{32} +(-4.13158 + 4.76809i) q^{34} +(0.502780 - 0.580239i) q^{35} +(-1.94398 - 4.25672i) q^{37} +(-2.76678 + 1.77810i) q^{38} +(0.0530529 + 0.368991i) q^{40} +(1.98603 - 4.34881i) q^{41} +(-9.36979 - 6.02160i) q^{43} +(1.61435 + 1.86306i) q^{44} +(-4.52547 + 1.58749i) q^{46} -2.44502 q^{47} +(-2.32043 - 1.49125i) q^{49} +(0.691797 - 4.81155i) q^{50} +(0.531217 + 3.69470i) q^{52} +(5.80255 + 1.70378i) q^{53} +(0.381761 + 0.835939i) q^{55} +(-1.97611 + 0.580239i) q^{56} +(4.67098 - 5.39060i) q^{58} +(-11.3316 + 3.32727i) q^{59} +(1.41899 - 0.911927i) q^{61} +(-5.60835 - 1.64676i) q^{62} +(0.415415 - 0.909632i) q^{64} +(-0.198030 + 1.37733i) q^{65} +(9.23004 + 10.6520i) q^{67} +6.30909 q^{68} -0.767766 q^{70} +(2.64478 + 3.05224i) q^{71} +(-1.23672 + 8.60157i) q^{73} +(-1.94398 + 4.25672i) q^{74} +(3.15565 + 0.926583i) q^{76} +(-4.27116 + 2.74491i) q^{77} +(2.28741 - 0.671644i) q^{79} +(0.244123 - 0.281733i) q^{80} +(-4.58718 + 1.34692i) q^{82} +(-1.76013 - 3.85415i) q^{83} +(2.25667 + 0.662618i) q^{85} +(1.58509 + 11.0245i) q^{86} +(0.350833 - 2.44009i) q^{88} +(7.59749 + 4.88261i) q^{89} -7.68762 q^{91} +(4.16330 + 2.38054i) q^{92} +(1.60115 + 1.84783i) q^{94} +(1.03141 + 0.662850i) q^{95} +(-4.69697 + 10.2849i) q^{97} +(0.392548 + 2.73023i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$		0			0
$3$		0			0
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	−0.154861	+	0.339098i	−0.0692558	+	0.151649i	−0.941094	−	0.338145i	$-0.890201\pi$
$5$	−0.154861	+	0.339098i	−0.0692558	+	0.151649i	0.871838	+	0.489794i	$0.162928\pi$
$6$		0			0
$7$	−1.97611	−	0.580239i	−0.746900	−	0.219310i	−0.113933	−	0.993488i	$-0.536345\pi$
$7$	−1.97611	−	0.580239i	−0.746900	−	0.219310i	−0.632967	+	0.774179i	$0.718163\pi$
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$		0			0
$10$	0.357685	−	0.105026i	0.113110	−	0.0332121i
$11$	1.61435	−	1.86306i	0.486746	−	0.561735i	−0.458247	−	0.888825i	$-0.651523\pi$
$11$	1.61435	−	1.86306i	0.486746	−	0.561735i	0.944993	+	0.327090i	$0.106068\pi$
$12$		0			0
$13$	3.58149	−	1.05162i	0.993327	−	0.291667i	0.255612	−	0.966779i	$-0.417723\pi$
$13$	3.58149	−	1.05162i	0.993327	−	0.291667i	0.737715	+	0.675112i	$0.235905\pi$
$14$	0.855563	+	1.87342i	0.228659	+	0.500693i
$15$		0			0
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.897877	−	6.24487i	−0.217767	−	1.51460i	−0.746253	−	0.665662i	$-0.768149\pi$
$17$	−0.897877	−	6.24487i	−0.217767	−	1.51460i	0.528486	−	0.848942i	$-0.322760\pi$
$18$		0			0
$19$	0.468056	−	3.25540i	0.107379	−	0.746840i	−0.862991	−	0.505219i	$-0.831412\pi$
$19$	0.468056	−	3.25540i	0.107379	−	0.746840i	0.970371	−	0.241621i	$-0.0776791\pi$
$20$	−0.313607	−	0.201543i	−0.0701247	−	0.0450664i
$21$		0			0
$22$	−2.46519			−0.525579
$23$	1.76381	−	4.45971i	0.367780	−	0.929913i
$23$	1.76381	−	4.45971i	0.367780	−	0.929913i
$24$		0			0
$25$	3.18330	+	3.67372i	0.636660	+	0.734744i
$26$	−3.14014	−	2.01804i	−0.615832	−	0.395771i
$27$		0			0
$28$	0.855563	−	1.87342i	0.161686	−	0.354043i
$29$	1.01510	+	7.06018i	0.188499	+	1.31104i	0.835896	+	0.548889i	$0.184949\pi$
$29$	1.01510	+	7.06018i	0.188499	+	1.31104i	−0.647396	+	0.762154i	$0.724142\pi$
$30$		0			0
$31$	4.91722	−	3.16011i	0.883159	−	0.567572i	−0.0185921	−	0.999827i	$-0.505918\pi$
$31$	4.91722	−	3.16011i	0.883159	−	0.567572i	0.901751	+	0.432255i	$0.142282\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$		0			0
$34$	−4.13158	+	4.76809i	−0.708560	+	0.817721i
$35$	0.502780	−	0.580239i	0.0849853	−	0.0980782i
$36$		0			0
$37$	−1.94398	−	4.25672i	−0.319588	−	0.699801i	0.679849	−	0.733352i	$-0.262045\pi$
$37$	−1.94398	−	4.25672i	−0.319588	−	0.699801i	−0.999437	+	0.0335515i	$0.989318\pi$
$38$	−2.76678	+	1.77810i	−0.448831	+	0.288446i
$39$		0			0
$40$	0.0530529	+	0.368991i	0.00838840	+	0.0583426i
$41$	1.98603	−	4.34881i	0.310166	−	0.679169i	−0.688784	−	0.724966i	$-0.741855\pi$
$41$	1.98603	−	4.34881i	0.310166	−	0.679169i	0.998951	+	0.0457967i	$0.0145826\pi$
$42$		0			0
$43$	−9.36979	−	6.02160i	−1.42888	−	0.918285i	−0.999888	−	0.0149765i	$-0.995233\pi$
$43$	−9.36979	−	6.02160i	−1.42888	−	0.918285i	−0.428992	−	0.903309i	$-0.641131\pi$
$44$	1.61435	+	1.86306i	0.243373	+	0.280867i
$45$		0			0
$46$	−4.52547	+	1.58749i	−0.667244	+	0.234062i
$47$	−2.44502			−0.356643			−0.178322	−	0.983972i	$-0.557067\pi$
$47$	−2.44502			−0.356643			−0.178322	+	0.983972i	$0.557067\pi$
$48$		0			0
$49$	−2.32043	−	1.49125i	−0.331491	−	0.213036i
$50$	0.691797	−	4.81155i	0.0978348	−	0.680456i
$51$		0			0
$52$	0.531217	+	3.69470i	0.0736666	+	0.512362i
$53$	5.80255	+	1.70378i	0.797042	+	0.234033i	0.654803	−	0.755800i	$-0.272752\pi$
$53$	5.80255	+	1.70378i	0.797042	+	0.234033i	0.142239	+	0.989832i	$0.454570\pi$
$54$		0			0
$55$	0.381761	+	0.835939i	0.0514766	+	0.112718i
$56$	−1.97611	+	0.580239i	−0.264069	+	0.0775377i
$57$		0			0
$58$	4.67098	−	5.39060i	0.613329	−	0.707820i
$59$	−11.3316	+	3.32727i	−1.47526	+	0.433174i	−0.917803	−	0.397035i	$-0.870039\pi$
$59$	−11.3316	+	3.32727i	−1.47526	+	0.433174i	−0.557452	+	0.830209i	$0.688221\pi$
$60$		0			0
$61$	1.41899	−	0.911927i	0.181683	−	0.116760i	−0.446638	−	0.894715i	$-0.647379\pi$
$61$	1.41899	−	0.911927i	0.181683	−	0.116760i	0.628321	+	0.777954i	$0.283743\pi$
$62$	−5.60835	−	1.64676i	−0.712261	−	0.209139i
$63$		0			0
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.198030	+	1.37733i	−0.0245626	+	0.170837i
$66$		0			0
$67$	9.23004	+	10.6520i	1.12763	+	1.30135i	0.948232	+	0.317577i	$0.102869\pi$
$67$	9.23004	+	10.6520i	1.12763	+	1.30135i	0.179397	+	0.983777i	$0.442585\pi$
$68$	6.30909			0.765090
$69$		0			0
$70$	−0.767766			−0.0917656
$71$	2.64478	+	3.05224i	0.313878	+	0.362234i	0.890665	−	0.454660i	$-0.150239\pi$
$71$	2.64478	+	3.05224i	0.313878	+	0.362234i	−0.576787	+	0.816894i	$0.695694\pi$
$72$		0			0
$73$	−1.23672	+	8.60157i	−0.144747	+	1.00674i	0.779898	+	0.625907i	$0.215271\pi$
$73$	−1.23672	+	8.60157i	−0.144747	+	1.00674i	−0.924645	+	0.380831i	$0.875638\pi$
$74$	−1.94398	+	4.25672i	−0.225983	+	0.494834i
$75$		0			0
$76$	3.15565	+	0.926583i	0.361978	+	0.106286i
$77$	−4.27116	+	2.74491i	−0.486744	+	0.312812i
$78$		0			0
$79$	2.28741	−	0.671644i	0.257354	−	0.0755659i	−0.150511	−	0.988608i	$-0.548092\pi$
$79$	2.28741	−	0.671644i	0.257354	−	0.0755659i	0.407864	+	0.913043i	$0.366274\pi$
$80$	0.244123	−	0.281733i	0.0272937	−	0.0314987i
$81$		0			0
$82$	−4.58718	+	1.34692i	−0.506570	+	0.148742i
$83$	−1.76013	−	3.85415i	−0.193200	−	0.423048i	0.788097	−	0.615552i	$-0.211067\pi$
$83$	−1.76013	−	3.85415i	−0.193200	−	0.423048i	−0.981296	+	0.192503i	$0.938339\pi$
$84$		0			0
$85$	2.25667	+	0.662618i	0.244770	+	0.0718710i
$86$	1.58509	+	11.0245i	0.170924	+	1.18880i
$87$		0			0
$88$	0.350833	−	2.44009i	0.0373989	−	0.260115i
$89$	7.59749	+	4.88261i	0.805332	+	0.517556i	0.877352	−	0.479848i	$-0.159308\pi$
$89$	7.59749	+	4.88261i	0.805332	+	0.517556i	−0.0720196	+	0.997403i	$0.522944\pi$
$90$		0			0
$91$	−7.68762			−0.805881
$92$	4.16330	+	2.38054i	0.434054	+	0.248188i
$93$		0			0
$94$	1.60115	+	1.84783i	0.165146	+	0.190589i
$95$	1.03141	+	0.662850i	0.105821	+	0.0680070i
$96$		0			0
$97$	−4.69697	+	10.2849i	−0.476905	+	1.04428i	0.506398	+	0.862300i	$0.330977\pi$
$97$	−4.69697	+	10.2849i	−0.476905	+	1.04428i	−0.983303	+	0.181976i	$0.941751\pi$
$98$	0.392548	+	2.73023i	0.0396533	+	0.275795i
$99$		0			0
$100$	−4.08936	+	2.62807i	−0.408936	+	0.262807i
$101$	3.34482	+	7.32414i	0.332822	+	0.728780i	0.999868	−	0.0162372i	$-0.00516870\pi$
$101$	3.34482	+	7.32414i	0.332822	+	0.728780i	−0.667046	+	0.745017i	$0.732441\pi$
$102$		0			0
$103$	9.66041	−	11.1487i	0.951868	−	1.09851i	−0.0431747	−	0.999068i	$-0.513747\pi$
$103$	9.66041	−	11.1487i	0.951868	−	1.09851i	0.995043	−	0.0994469i	$-0.0317073\pi$
$104$	2.44439	−	2.82098i	0.239692	−	0.276620i
$105$		0			0
$106$	−2.51223	−	5.50102i	−0.244009	−	0.534306i
$107$	5.62090	−	3.61233i	0.543393	−	0.349217i	−0.239972	−	0.970780i	$-0.577138\pi$
$107$	5.62090	−	3.61233i	0.543393	−	0.349217i	0.783365	+	0.621562i	$0.213502\pi$
$108$		0			0
$109$	0.580602	+	4.03817i	0.0556116	+	0.386787i	0.998551	+	0.0538214i	$0.0171402\pi$
$109$	0.580602	+	4.03817i	0.0556116	+	0.386787i	−0.942939	+	0.332965i	$0.891951\pi$
$110$	0.381761	−	0.835939i	0.0363994	−	0.0797037i
$111$		0			0
$112$	1.73259	+	1.11347i	0.163715	+	0.105213i
$113$	3.65755	+	4.22104i	0.344073	+	0.397082i	0.901241	−	0.433318i	$-0.142657\pi$
$113$	3.65755	+	4.22104i	0.344073	+	0.397082i	−0.557168	+	0.830400i	$0.688112\pi$
$114$		0			0
$115$	1.23913	+	1.28874i	0.115550	+	0.120175i
$116$	−7.13278			−0.662262
$117$		0			0
$118$	9.93524	+	6.38499i	0.914613	+	0.587786i
$119$	−1.84921	+	12.8616i	−0.169517	+	1.17902i
$120$		0			0
$121$	0.700596	+	4.87275i	0.0636905	+	0.442977i
$122$	−1.61843	−	0.475213i	−0.146525	−	0.0430238i
$123$		0			0
$124$	2.42815	+	5.31690i	0.218054	+	0.477472i
$125$	−3.52714	+	1.03566i	−0.315477	+	0.0926325i
$126$		0			0
$127$	4.94344	−	5.70503i	0.438659	−	0.506240i	−0.492771	−	0.870159i	$-0.664016\pi$
$127$	4.94344	−	5.70503i	0.438659	−	0.506240i	0.931431	+	0.363919i	$0.118562\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$		0			0
$130$	1.17060	−	0.752298i	0.102668	−	0.0659809i
$131$	−3.13818	−	0.921454i	−0.274184	−	0.0805078i	0.141750	−	0.989903i	$-0.454727\pi$
$131$	−3.13818	−	0.921454i	−0.274184	−	0.0805078i	−0.415934	+	0.909395i	$0.636545\pi$
$132$		0			0
$133$	−2.81384	+	6.16145i	−0.243991	+	0.534265i
$134$	2.00588	−	13.9512i	0.173282	−	1.20520i
$135$		0			0
$136$	−4.13158	−	4.76809i	−0.354280	−	0.408861i
$137$	−15.9297			−1.36096			−0.680482	−	0.732765i	$-0.738229\pi$
$137$	−15.9297			−1.36096			−0.680482	+	0.732765i	$0.738229\pi$
$138$		0			0
$139$	−2.85447			−0.242113			−0.121056	−	0.992646i	$-0.538628\pi$
$139$	−2.85447			−0.242113			−0.121056	+	0.992646i	$0.538628\pi$
$140$	0.502780	+	0.580239i	0.0424926	+	0.0490391i
$141$		0			0
$142$	0.574766	−	3.99758i	0.0482333	−	0.335470i
$143$	3.82256	−	8.37023i	0.319658	−	0.699954i
$144$		0			0
$145$	−2.55129	−	0.749126i	−0.211873	−	0.0622115i
$146$	7.31051	−	4.69818i	0.605022	−	0.388824i
$147$		0			0
$148$	4.49005	−	1.31840i	0.369080	−	0.108372i
$149$	−1.91136	+	2.20583i	−0.156585	+	0.180709i	−0.828621	−	0.559809i	$-0.810874\pi$
$149$	−1.91136	+	2.20583i	−0.156585	+	0.180709i	0.672037	+	0.740518i	$0.265420\pi$
$150$		0			0
$151$	−23.5672	+	6.91997i	−1.91788	+	0.563139i	−0.949353	+	0.314212i	$0.898260\pi$
$151$	−23.5672	+	6.91997i	−1.91788	+	0.563139i	−0.968522	+	0.248927i	$0.919922\pi$
$152$	−1.36625	−	2.99167i	−0.110817	−	0.242656i
$153$		0			0
$154$	4.87148	+	1.43040i	0.392555	+	0.115265i
$155$	0.310100	+	2.15680i	0.0249079	+	0.173238i
$156$		0			0
$157$	1.86497	−	12.9711i	0.148840	−	1.03521i	−0.769282	−	0.638910i	$-0.779386\pi$
$157$	1.86497	−	12.9711i	0.148840	−	1.03521i	0.918122	−	0.396298i	$-0.129705\pi$
$158$	−2.00553	−	1.28888i	−0.159551	−	0.102537i
$159$		0			0
$160$	−0.372786			−0.0294713
$161$	−6.07318	+	7.78945i	−0.478634	+	0.613894i
$162$		0			0
$163$	−3.02485	−	3.49086i	−0.236924	−	0.273425i	0.624819	−	0.780770i	$-0.285173\pi$
$163$	−3.02485	−	3.49086i	−0.236924	−	0.273425i	−0.861743	+	0.507344i	$0.830627\pi$
$164$	4.02190	+	2.58472i	0.314058	+	0.201833i
$165$		0			0
$166$	−1.76013	+	3.85415i	−0.136613	+	0.299140i
$167$	−0.560648	−	3.89939i	−0.0433843	−	0.301744i	−0.999948	−	0.0102201i	$-0.996747\pi$
$167$	−0.560648	−	3.89939i	−0.0433843	−	0.301744i	0.956564	−	0.291524i	$-0.0941623\pi$
$168$		0			0
$169$	0.784872	−	0.504407i	0.0603748	−	0.0388005i
$170$	−0.977031	−	2.13940i	−0.0749348	−	0.164084i
$171$		0			0
$172$	7.29377	−	8.41745i	0.556144	−	0.641825i
$173$	12.4428	−	14.3598i	0.946009	−	1.09175i	−0.0496580	−	0.998766i	$-0.515813\pi$
$173$	12.4428	−	14.3598i	0.946009	−	1.09175i	0.995667	−	0.0929867i	$-0.0296414\pi$
$174$		0			0
$175$	−4.15892	−	9.10676i	−0.314385	−	0.688406i
$176$	−2.07385	+	1.33278i	−0.156322	+	0.100462i
$177$		0			0
$178$	−1.28527	−	8.93923i	−0.0963348	−	0.670024i
$179$	−0.996758	+	2.18260i	−0.0745012	+	0.163135i	−0.943218	−	0.332174i	$-0.892218\pi$
$179$	−0.996758	+	2.18260i	−0.0745012	+	0.163135i	0.868717	+	0.495309i	$0.164945\pi$
$180$		0			0
$181$	21.8779	+	14.0601i	1.62617	+	1.04508i	0.951815	+	0.306673i	$0.0992158\pi$
$181$	21.8779	+	14.0601i	1.62617	+	1.04508i	0.674358	+	0.738405i	$0.264421\pi$
$182$	5.03432	+	5.80991i	0.373168	+	0.430659i
$183$		0			0
$184$	−0.927287	−	4.70533i	−0.0683605	−	0.346882i
$185$	1.74449			0.128258
$186$		0			0
$187$	−13.0841	−	8.40863i	−0.956803	−	0.614900i
$188$	0.347963	−	2.42014i	0.0253778	−	0.176507i
$189$		0			0
$190$	−0.174484	−	1.21357i	−0.0126584	−	0.0880413i
$191$	−10.0451	−	2.94950i	−0.726836	−	0.213418i	−0.102676	−	0.994715i	$-0.532740\pi$
$191$	−10.0451	−	2.94950i	−0.726836	−	0.213418i	−0.624160	+	0.781297i	$0.714559\pi$
$192$		0			0
$193$	0.320385	+	0.701546i	0.0230618	+	0.0504984i	0.920812	−	0.390006i	$-0.127527\pi$
$193$	0.320385	+	0.701546i	0.0230618	+	0.0504984i	−0.897751	+	0.440504i	$0.854800\pi$
$194$	10.8487	−	3.18546i	0.778890	−	0.228703i
$195$		0			0
$196$	1.80631	−	2.08459i	0.129022	−	0.148899i
$197$	4.99637	−	1.46707i	0.355977	−	0.104524i	−0.0988543	−	0.995102i	$-0.531518\pi$
$197$	4.99637	−	1.46707i	0.355977	−	0.104524i	0.454831	+	0.890578i	$0.349700\pi$
$198$		0			0
$199$	−19.6372	+	12.6200i	−1.39204	+	0.894610i	−0.999682	−	0.0252020i	$-0.991977\pi$
$199$	−19.6372	+	12.6200i	−1.39204	+	0.894610i	−0.392358	+	0.919812i	$0.628341\pi$
$200$	4.66412	+	1.36951i	0.329803	+	0.0968390i
$201$		0			0
$202$	3.34482	−	7.32414i	0.235341	−	0.515325i
$203$	2.09064	−	14.5407i	0.146734	−	1.02056i
$204$		0			0
$205$	1.16711	+	1.34692i	0.0815146	+	0.0940729i
$206$	−14.7518			−1.02781
$207$		0			0
$208$	−3.73269			−0.258816
$209$	−5.30941	−	6.12738i	−0.367259	−	0.423840i
$210$		0			0
$211$	1.23757	−	8.60752i	0.0851981	−	0.592566i	−0.901839	−	0.432073i	$-0.857782\pi$
$211$	1.23757	−	8.60752i	0.0851981	−	0.592566i	0.987037	−	0.160493i	$-0.0513085\pi$
$212$	−2.51223	+	5.50102i	−0.172541	+	0.377812i
$213$		0			0
$214$	−6.41093	−	1.88242i	−0.438242	−	0.128679i
$215$	3.49292	−	2.24476i	0.238215	−	0.153092i
$216$		0			0
$217$	−11.5506	+	3.39156i	−0.784106	+	0.230234i
$218$	2.67163	−	3.08323i	0.180946	−	0.208823i
$219$		0			0
$220$	−0.881761	+	0.258908i	−0.0594483	+	0.0174556i
$221$	−9.78298	−	21.4217i	−0.658074	−	1.44098i
$222$		0			0
$223$	3.68556	+	1.08218i	0.246803	+	0.0724680i	0.402794	−	0.915290i	$-0.368039\pi$
$223$	3.68556	+	1.08218i	0.246803	+	0.0724680i	−0.155991	+	0.987758i	$0.549857\pi$
$224$	−0.293103	−	2.03857i	−0.0195838	−	0.136208i
$225$		0			0
$226$	0.794861	−	5.52838i	0.0528734	−	0.367743i
$227$	−1.71113	−	1.09968i	−0.113572	−	0.0729883i	0.482622	−	0.875829i	$-0.339685\pi$
$227$	−1.71113	−	1.09968i	−0.113572	−	0.0729883i	−0.596194	+	0.802841i	$0.703321\pi$
$228$		0			0
$229$	27.4406			1.81333			0.906664	−	0.421853i	$-0.138620\pi$
$229$	27.4406			1.81333			0.906664	+	0.421853i	$0.138620\pi$
$230$	0.162505	−	1.78042i	0.0107152	−	0.117397i
$231$		0			0
$232$	4.67098	+	5.39060i	0.306665	+	0.353910i
$233$	−5.92647	−	3.80871i	−0.388256	−	0.249517i	0.331921	−	0.943307i	$-0.392303\pi$
$233$	−5.92647	−	3.80871i	−0.388256	−	0.249517i	−0.720177	+	0.693790i	$0.755939\pi$
$234$		0			0
$235$	0.378638	−	0.829102i	0.0246996	−	0.0540847i
$236$	−1.68074	−	11.6898i	−0.109407	−	0.760943i
$237$		0			0
$238$	10.9311	−	7.02498i	0.708557	−	0.455362i
$239$	−10.8343	−	23.7238i	−0.700814	−	1.53457i	−0.838982	−	0.544159i	$-0.816849\pi$
$239$	−10.8343	−	23.7238i	−0.700814	−	1.53457i	0.138168	−	0.990409i	$-0.455879\pi$
$240$		0			0
$241$	−0.910396	+	1.05065i	−0.0586437	+	0.0676785i	−0.784313	−	0.620365i	$-0.786985\pi$
$241$	−0.910396	+	1.05065i	−0.0586437	+	0.0676785i	0.725670	+	0.688043i	$0.241530\pi$
$242$	3.22379	−	3.72045i	0.207233	−	0.239159i
$243$		0			0
$244$	0.700702	+	1.53432i	0.0448579	+	0.0982250i
$245$	0.865024	−	0.555917i	0.0552644	−	0.0355163i
$246$		0			0
$247$	−1.74711	−	12.1514i	−0.111166	−	0.773175i
$248$	2.42815	−	5.31690i	0.154188	−	0.337624i
$249$		0			0
$250$	3.09249	+	1.98742i	0.195586	+	0.125696i
$251$	17.0861	+	19.7184i	1.07847	+	1.24462i	0.968057	+	0.250729i	$0.0806703\pi$
$251$	17.0861	+	19.7184i	1.07847	+	1.24462i	0.110408	+	0.993886i	$0.464784\pi$
$252$		0			0
$253$	−5.46130	−	10.4856i	−0.343349	−	0.659226i
$254$	−7.54884			−0.473656
$255$		0			0
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−3.98415	+	27.7104i	−0.248524	+	1.72852i	0.358229	+	0.933634i	$0.383381\pi$
$257$	−3.98415	+	27.7104i	−0.248524	+	1.72852i	−0.606753	+	0.794890i	$0.707528\pi$
$258$		0			0
$259$	1.37161	+	9.53973i	0.0852275	+	0.592770i
$260$	−1.33513	−	0.392029i	−0.0828011	−	0.0243126i
$261$		0			0
$262$	1.35869	+	2.97511i	0.0839398	+	0.183803i
$263$	9.05134	−	2.65771i	0.558129	−	0.163882i	0.00951145	−	0.999955i	$-0.496972\pi$
$263$	9.05134	−	2.65771i	0.558129	−	0.163882i	0.548618	+	0.836073i	$0.315154\pi$
$264$		0			0
$265$	−1.47634	+	1.70378i	−0.0906907	+	0.104663i
$266$	6.49918	−	1.90833i	0.398490	−	0.117007i
$267$		0			0
$268$	−11.8572	+	7.62015i	−0.724293	+	0.465475i
$269$	16.6675	+	4.89401i	1.01623	+	0.298393i	0.747101	−	0.664710i	$-0.231445\pi$
$269$	16.6675	+	4.89401i	1.01623	+	0.298393i	0.269132	+	0.963103i	$0.413263\pi$
$270$		0			0
$271$	7.43784	−	16.2866i	0.451816	−	0.989340i	−0.537461	−	0.843289i	$-0.680616\pi$
$271$	7.43784	−	16.2866i	0.451816	−	0.989340i	0.989277	−	0.146051i	$-0.0466564\pi$
$272$	−0.897877	+	6.24487i	−0.0544418	+	0.378651i
$273$		0			0
$274$	10.4317	+	12.0388i	0.630203	+	0.727293i
$275$	11.9833			0.722623
$276$		0			0
$277$	−15.2821			−0.918212			−0.459106	−	0.888382i	$-0.651830\pi$
$277$	−15.2821			−0.918212			−0.459106	+	0.888382i	$0.651830\pi$
$278$	1.86928	+	2.15726i	0.112112	+	0.129384i
$279$		0			0
$280$	0.109264	−	0.759951i	0.00652980	−	0.0454158i
$281$	−2.46220	+	5.39146i	−0.146882	+	0.321627i	−0.968745	−	0.248058i	$-0.920208\pi$
$281$	−2.46220	+	5.39146i	−0.146882	+	0.321627i	0.821863	+	0.569685i	$0.192935\pi$
$282$		0			0
$283$	−1.50023	−	0.440506i	−0.0891791	−	0.0261854i	0.236839	−	0.971549i	$-0.423889\pi$
$283$	−1.50023	−	0.440506i	−0.0891791	−	0.0261854i	−0.326018	+	0.945364i	$0.605707\pi$
$284$	−3.39756	+	2.18348i	−0.201608	+	0.129566i
$285$		0			0
$286$	−8.82904	+	2.59244i	−0.522072	+	0.153294i
$287$	−6.44797	+	7.44135i	−0.380612	+	0.439249i
$288$		0			0
$289$	−21.8809	+	6.42481i	−1.28711	+	0.377930i
$290$	1.10459	+	2.41871i	0.0648636	+	0.142032i
$291$		0			0
$292$	−8.33802	−	2.44826i	−0.487945	−	0.143274i
$293$	0.292908	+	2.03722i	0.0171119	+	0.119016i	0.996587	−	0.0825496i	$-0.0263063\pi$
$293$	0.292908	+	2.03722i	0.0171119	+	0.119016i	−0.979475	+	0.201565i	$0.935397\pi$
$294$		0			0
$295$	0.626557	−	4.35780i	0.0364796	−	0.253721i
$296$	−3.93674	−	2.52999i	−0.228818	−	0.147053i
$297$		0			0
$298$	2.91873			0.169078
$299$	1.62715	−	17.8273i	0.0941007	−	1.03098i
$300$		0			0
$301$	15.0218	+	17.3361i	0.865841	+	0.999234i
$302$	20.6630	+	13.2793i	1.18902	+	0.764139i
$303$		0			0
$304$	−1.36625	+	2.99167i	−0.0783597	+	0.171584i
$305$	0.0894871	+	0.622397i	0.00512402	+	0.0356383i
$306$		0			0
$307$	9.11420	−	5.85734i	0.520175	−	0.334296i	−0.254066	−	0.967187i	$-0.581768\pi$
$307$	9.11420	−	5.85734i	0.520175	−	0.334296i	0.774241	+	0.632891i	$0.218132\pi$
$308$	−2.10912	−	4.61833i	−0.120178	−	0.263154i
$309$		0			0
$310$	1.42692	−	1.64676i	0.0810439	−	0.0935296i
$311$	−14.9945	+	17.3046i	−0.850260	+	0.981252i	−0.999972	−	0.00747762i	$-0.997620\pi$
$311$	−14.9945	+	17.3046i	−0.850260	+	0.981252i	0.149712	+	0.988730i	$0.452165\pi$
$312$		0			0
$313$	−9.69914	−	21.2382i	−0.548228	−	1.20045i	−0.957604	−	0.288086i	$-0.906981\pi$
$313$	−9.69914	−	21.2382i	−0.548228	−	1.20045i	0.409376	−	0.912366i	$-0.365746\pi$
$314$	−11.0242	+	7.08483i	−0.622132	+	0.399820i
$315$		0			0
$316$	0.339275	+	2.35971i	0.0190857	+	0.132744i
$317$	−0.209132	+	0.457936i	−0.0117460	+	0.0257202i	−0.915414	−	0.402513i	$-0.868137\pi$
$317$	−0.209132	+	0.457936i	−0.0117460	+	0.0257202i	0.903668	+	0.428234i	$0.140864\pi$
$318$		0			0
$319$	14.7923	+	9.50643i	0.828209	+	0.532258i
$320$	0.244123	+	0.281733i	0.0136469	+	0.0157493i
$321$		0			0
$322$	9.86396	−	0.511198i	0.549697	−	0.0284880i
$323$	−20.7498			−1.15455
$324$		0			0
$325$	15.2643	+	9.80978i	0.846712	+	0.544149i
$326$	−0.657362	+	4.57205i	−0.0364079	+	0.253223i
$327$		0			0
$328$	−0.680385	−	4.73218i	−0.0375680	−	0.261291i
$329$	4.83164	+	1.41870i	0.266377	+	0.0782153i
$330$		0			0
$331$	8.39272	+	18.3775i	0.461306	+	1.01012i	0.987188	+	0.159561i	$0.0510080\pi$
$331$	8.39272	+	18.3775i	0.461306	+	1.01012i	−0.525882	+	0.850557i	$0.676265\pi$
$332$	4.06542	−	1.19371i	0.223119	−	0.0655136i
$333$		0			0
$334$	−2.57982	+	2.97727i	−0.141161	+	0.162909i
$335$	−5.04145	+	1.48030i	−0.275444	+	0.0808777i
$336$		0			0
$337$	3.45398	−	2.21974i	0.188150	−	0.120917i	−0.443175	−	0.896435i	$-0.646148\pi$
$337$	3.45398	−	2.21974i	0.188150	−	0.120917i	0.631325	+	0.775518i	$0.282511\pi$
$338$	−0.895187	−	0.262851i	−0.0486918	−	0.0142972i
$339$		0			0
$340$	−0.977031	+	2.13940i	−0.0529869	+	0.116025i
$341$	2.05066	−	14.2626i	0.111049	−	0.772365i
$342$		0			0
$343$	13.1611	+	15.1887i	0.710634	+	0.820115i
$344$	−11.1379			−0.600515
$345$		0			0
$346$	−19.0007			−1.02148
$347$	15.9888	+	18.4520i	0.858322	+	0.990557i	1.00000		0.000643827i	$0.000204936\pi$
$347$	15.9888	+	18.4520i	0.858322	+	0.990557i	−0.141678	+	0.989913i	$0.545250\pi$
$348$		0			0
$349$	−2.46135	+	17.1191i	−0.131753	+	0.916362i	0.811516	+	0.584331i	$0.198643\pi$
$349$	−2.46135	+	17.1191i	−0.131753	+	0.916362i	−0.943268	+	0.332031i	$0.892266\pi$
$350$	−4.15892	+	9.10676i	−0.222303	+	0.486777i
$351$		0			0
$352$	2.36533	+	0.694523i	0.126072	+	0.0370182i
$353$	8.05818	−	5.17868i	0.428894	−	0.275633i	−0.308333	−	0.951278i	$-0.599771\pi$
$353$	8.05818	−	5.17868i	0.428894	−	0.275633i	0.737227	+	0.675645i	$0.236135\pi$
$354$		0			0
$355$	−1.44458	+	0.424167i	−0.0766703	+	0.0225124i
$356$	−5.91415	+	6.82529i	−0.313449	+	0.361740i
$357$		0			0
$358$	2.30223	−	0.675997i	0.121677	−	0.0357275i
$359$	−0.0520416	−	0.113955i	−0.00274665	−	0.00601433i	0.908254	−	0.418420i	$-0.137416\pi$
$359$	−0.0520416	−	0.113955i	−0.00274665	−	0.00601433i	−0.911000	+	0.412406i	$0.864689\pi$
$360$		0			0
$361$	7.85182	+	2.30550i	0.413254	+	0.121342i
$362$	−3.70109	−	25.7416i	−0.194525	−	1.35295i
$363$		0			0
$364$	1.09406	−	7.60937i	0.0573444	−	0.398839i
$365$	−2.72525	−	1.75141i	−0.142646	−	0.0916732i
$366$		0			0
$367$	−4.23470			−0.221050			−0.110525	−	0.993873i	$-0.535253\pi$
$367$	−4.23470			−0.221050			−0.110525	+	0.993873i	$0.535253\pi$
$368$	−2.94881	+	3.78213i	−0.153717	+	0.197157i
$369$		0			0
$370$	−1.14240	−	1.31840i	−0.0593905	−	0.0685403i
$371$	−10.4779	−	6.73373i	−0.543985	−	0.349598i
$372$		0			0
$373$	−0.260238	+	0.569842i	−0.0134746	+	0.0295053i	−0.916250	−	0.400608i	$-0.868799\pi$
$373$	−0.260238	+	0.569842i	−0.0134746	+	0.0295053i	0.902775	+	0.430113i	$0.141526\pi$
$374$	2.21344	+	15.3948i	0.114454	+	0.796045i
$375$		0			0
$376$	−2.05689	+	1.32188i	−0.106076	+	0.0681708i
$377$	11.0602	+	24.2185i	0.569629	+	1.24731i
$378$		0			0
$379$	6.88978	−	7.95124i	0.353904	−	0.408428i	−0.550684	−	0.834714i	$-0.685633\pi$
$379$	6.88978	−	7.95124i	0.353904	−	0.408428i	0.904588	+	0.426286i	$0.140178\pi$
$380$	−0.802889	+	0.926583i	−0.0411873	+	0.0475327i
$381$		0			0
$382$	4.34904	+	9.52307i	0.222516	+	0.487243i
$383$	12.9300	−	8.30958i	0.660690	−	0.424600i	−0.166868	−	0.985979i	$-0.553365\pi$
$383$	12.9300	−	8.30958i	0.660690	−	0.424600i	0.827559	+	0.561379i	$0.189729\pi$
$384$		0			0
$385$	−0.269357	−	1.87342i	−0.0137277	−	0.0954784i
$386$	0.320385	−	0.701546i	0.0163072	−	0.0357078i
$387$		0			0
$388$	−9.51179	−	6.11286i	−0.482888	−	0.310333i
$389$	14.2332	+	16.4260i	0.721653	+	0.832832i	0.991505	−	0.130069i	$-0.0415200\pi$
$389$	14.2332	+	16.4260i	0.721653	+	0.832832i	−0.269851	+	0.962902i	$0.586975\pi$
$390$		0			0
$391$	−29.4340	−	7.01051i	−1.48854	−	0.354537i
$392$	−2.75831			−0.139315
$393$		0			0
$394$	−4.38067	−	2.81528i	−0.220695	−	0.141832i
$395$	−0.126477	+	0.879667i	−0.00636375	+	0.0442608i
$396$		0			0
$397$	−1.44578	−	10.0556i	−0.0725615	−	0.504676i	−0.993397	−	0.114726i	$-0.963401\pi$
$397$	−1.44578	−	10.0556i	−0.0725615	−	0.504676i	0.920836	−	0.389951i	$-0.127508\pi$
$398$	22.3972	+	6.57641i	1.12267	+	0.329645i
$399$		0			0
$400$	−2.01935	−	4.42175i	−0.100967	−	0.221087i
$401$	−30.6059	+	8.98672i	−1.52839	+	0.448775i	−0.934557	−	0.355814i	$-0.884204\pi$
$401$	−30.6059	+	8.98672i	−1.52839	+	0.448775i	−0.593831	+	0.804590i	$0.702385\pi$
$402$		0			0
$403$	14.2878	−	16.4889i	0.711724	−	0.821373i
$404$	−7.72561	+	2.26844i	−0.384364	+	0.112859i
$405$		0			0
$406$	−12.3582	+	7.94214i	−0.613327	+	0.394162i
$407$	−11.0688	−	3.25010i	−0.548661	−	0.161101i
$408$		0			0
$409$	−5.48958	+	12.0205i	−0.271442	+	0.594375i	−0.995436	−	0.0954310i	$-0.969577\pi$
$409$	−5.48958	+	12.0205i	−0.271442	+	0.594375i	0.723994	+	0.689806i	$0.242304\pi$
$410$	0.253638	−	1.76409i	0.0125263	−	0.0871221i
$411$		0			0
$412$	9.66041	+	11.1487i	0.475934	+	0.549257i
$413$	24.3232			1.19687
$414$		0			0
$415$	1.57951			0.0775351
$416$	2.44439	+	2.82098i	0.119846	+	0.138310i
$417$		0			0
$418$	−1.15384	+	8.02516i	−0.0564364	+	0.392524i
$419$	−1.74597	+	3.82315i	−0.0852964	+	0.186773i	−0.947474	−	0.319834i	$-0.896373\pi$
$419$	−1.74597	+	3.82315i	−0.0852964	+	0.186773i	0.862177	+	0.506606i	$0.169100\pi$
$420$		0			0
$421$	−6.75035	−	1.98208i	−0.328992	−	0.0966007i	0.113066	−	0.993588i	$-0.463933\pi$
$421$	−6.75035	−	1.98208i	−0.328992	−	0.0966007i	−0.442057	+	0.896987i	$0.645751\pi$
$422$	−7.31557	+	4.70143i	−0.356116	+	0.228862i
$423$		0			0
$424$	5.80255	−	1.70378i	0.281797	−	0.0827430i
$425$	20.0837	−	23.1778i	0.974204	−	1.12429i
$426$		0			0
$427$	−3.33321	+	0.978719i	−0.161305	+	0.0473635i
$428$	2.77563	+	6.07778i	0.134165	+	0.293780i
$429$		0			0
$430$	−3.98386	−	1.16977i	−0.192119	−	0.0564111i
$431$	5.23996	+	36.4447i	0.252400	+	1.75548i	0.583714	+	0.811959i	$0.301599\pi$
$431$	5.23996	+	36.4447i	0.252400	+	1.75548i	−0.331315	+	0.943520i	$0.607492\pi$
$432$		0			0
$433$	3.87488	−	26.9504i	0.186215	−	1.29515i	−0.655486	−	0.755207i	$-0.727536\pi$
$433$	3.87488	−	26.9504i	0.186215	−	1.29515i	0.841701	−	0.539944i	$-0.181555\pi$
$434$	10.1272	+	6.50836i	0.486121	+	0.312411i
$435$		0			0
$436$	−4.07970			−0.195382
$437$	−13.6926	−	7.82930i	−0.655004	−	0.374526i
$438$		0			0
$439$	15.8395	+	18.2798i	0.755980	+	0.872448i	0.995134	−	0.0985339i	$-0.0314153\pi$
$439$	15.8395	+	18.2798i	0.755980	+	0.872448i	−0.239153	+	0.970982i	$0.576870\pi$
$440$	0.773100	+	0.496841i	0.0368561	+	0.0236860i
$441$		0			0
$442$	−9.78298	+	21.4217i	−0.465329	+	1.01893i
$443$	2.19556	+	15.2705i	0.104314	+	0.725522i	0.973108	+	0.230348i	$0.0739864\pi$
$443$	2.19556	+	15.2705i	0.104314	+	0.725522i	−0.868794	+	0.495174i	$0.835104\pi$
$444$		0			0
$445$	−2.83223	+	1.82017i	−0.134261	+	0.0862842i
$446$	−1.59567	−	3.49404i	−0.0755573	−	0.165447i
$447$		0			0
$448$	−1.34871	+	1.55649i	−0.0637206	+	0.0735375i
$449$	11.3449	−	13.0927i	0.535397	−	0.617881i	−0.422021	−	0.906586i	$-0.638679\pi$
$449$	11.3449	−	13.0927i	0.535397	−	0.617881i	0.957418	+	0.288705i	$0.0932247\pi$
$450$		0			0
$451$	−4.89594	−	10.7206i	−0.230541	−	0.504814i
$452$	−4.69860	+	3.01960i	−0.221003	+	0.142030i
$453$		0			0
$454$	0.289473	+	2.01333i	0.0135856	+	0.0944901i
$455$	1.19051	−	2.60685i	0.0558120	−	0.122211i
$456$		0			0
$457$	−5.77854	−	3.71364i	−0.270309	−	0.173717i	0.398464	−	0.917184i	$-0.369544\pi$
$457$	−5.77854	−	3.71364i	−0.270309	−	0.173717i	−0.668772	+	0.743467i	$0.733180\pi$
$458$	−17.9698	−	20.7383i	−0.839674	−	0.969035i
$459$		0			0
$460$	−1.45197	+	1.04311i	−0.0676983	+	0.0486353i
$461$	0.341091			0.0158862			0.00794309	−	0.999968i	$-0.497472\pi$
$461$	0.341091			0.0158862			0.00794309	+	0.999968i	$0.497472\pi$
$462$		0			0
$463$	13.7279	+	8.82237i	0.637988	+	0.410010i	0.819259	−	0.573423i	$-0.194385\pi$
$463$	13.7279	+	8.82237i	0.637988	+	0.410010i	−0.181271	+	0.983433i	$0.558021\pi$
$464$	1.01510	−	7.06018i	0.0471249	−	0.327761i
$465$		0			0
$466$	1.00258	+	6.97310i	0.0464436	+	0.323022i
$467$	−34.7667	−	10.2084i	−1.60881	−	0.472389i	−0.650830	−	0.759223i	$-0.725579\pi$
$467$	−34.7667	−	10.2084i	−1.60881	−	0.472389i	−0.957980	+	0.286834i	$0.907397\pi$
$468$		0			0
$469$	−12.0589	−	26.4052i	−0.556827	−	1.21928i
$470$	−0.874549	+	0.256791i	−0.0403399	+	0.0118449i
$471$		0			0
$472$	−7.73393	+	8.92543i	−0.355983	+	0.410826i
$473$	−26.3448	+	7.73552i	−1.21133	+	0.355680i
$474$		0			0
$475$	13.4494	−	8.64340i	0.617100	−	0.396586i
$476$	−12.4675	−	3.66078i	−0.571446	−	0.167792i
$477$		0			0
$478$	−10.8343	+	23.7238i	−0.495550	+	1.08510i
$479$	−1.81532	+	12.6259i	−0.0829443	+	0.576890i	0.905389	+	0.424583i	$0.139579\pi$
$479$	−1.81532	+	12.6259i	−0.0829443	+	0.576890i	−0.988333	+	0.152307i	$0.951330\pi$
$480$		0			0
$481$	−11.4388	−	13.2011i	−0.521565	−	0.601918i
$482$	1.39021			0.0633224
$483$		0			0
$484$	−4.92286			−0.223766
$485$	−2.76022	−	3.18546i	−0.125335	−	0.144644i
$486$		0			0
$487$	−4.77328	+	33.1989i	−0.216298	+	1.50438i	0.535243	+	0.844698i	$0.320220\pi$
$487$	−4.77328	+	33.1989i	−0.216298	+	1.50438i	−0.751541	+	0.659686i	$0.770689\pi$
$488$	0.700702	−	1.53432i	0.0317193	−	0.0694556i
$489$		0			0
$490$	−0.986605	−	0.289693i	−0.0445703	−	0.0130870i
$491$	31.0235	−	19.9376i	1.40007	−	0.899770i	0.400207	−	0.916425i	$-0.368938\pi$
$491$	31.0235	−	19.9376i	1.40007	−	0.899770i	0.999861	+	0.0166550i	$0.00530169\pi$
$492$		0			0
$493$	43.1785	−	12.6783i	1.94466	−	0.571004i
$494$	−8.03930	+	9.27785i	−0.361705	+	0.417430i
$495$		0			0
$496$	−5.60835	+	1.64676i	−0.251822	+	0.0739417i
$497$	−3.45535	−	7.56617i	−0.154994	−	0.339389i
$498$		0			0
$499$	−1.74302	−	0.511796i	−0.0780281	−	0.0229111i	0.242485	−	0.970155i	$-0.422037\pi$
$499$	−1.74302	−	0.511796i	−0.0780281	−	0.0229111i	−0.320514	+	0.947244i	$0.603856\pi$
$500$	−0.523157	−	3.63863i	−0.0233963	−	0.162725i
$501$		0			0
$502$	3.71317	−	25.8256i	0.165727	−	1.15265i
$503$	36.3640	+	23.3697i	1.62139	+	1.04200i	0.955087	+	0.296324i	$0.0957608\pi$
$503$	36.3640	+	23.3697i	1.62139	+	1.04200i	0.666304	+	0.745681i	$0.267876\pi$
$504$		0			0
$505$	−3.00158			−0.133569
$506$	−4.34812	+	10.9940i	−0.193298	+	0.488743i
$507$		0			0
$508$	4.94344	+	5.70503i	0.219330	+	0.253120i
$509$	−19.8613	−	12.7641i	−0.880335	−	0.565757i	0.0205626	−	0.999789i	$-0.493454\pi$
$509$	−19.8613	−	12.7641i	−0.880335	−	0.565757i	−0.900898	+	0.434032i	$0.857091\pi$
$510$		0			0
$511$	7.43486	−	16.2801i	0.328899	−	0.720188i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$		0			0
$514$	23.5511	−	15.1354i	1.03880	−	0.667594i
$515$	2.28448	+	5.00232i	0.100666	+	0.220428i
$516$		0			0
$517$	−3.94713	+	4.55524i	−0.173595	+	0.200339i
$518$	6.31144	−	7.28379i	0.277309	−	0.320031i
$519$		0			0
$520$	0.578047	+	1.26575i	0.0253490	+	0.0555067i
$521$	−11.1492	+	7.16515i	−0.488455	+	0.313911i	−0.761584	−	0.648067i	$-0.775578\pi$
$521$	−11.1492	+	7.16515i	−0.488455	+	0.313911i	0.273129	+	0.961977i	$0.411941\pi$
$522$		0			0
$523$	2.34845	+	16.3338i	0.102690	+	0.714227i	0.974501	+	0.224384i	$0.0720369\pi$
$523$	2.34845	+	16.3338i	0.102690	+	0.714227i	−0.871810	+	0.489843i	$0.837054\pi$
$524$	1.35869	−	2.97511i	0.0593544	−	0.129968i
$525$		0			0
$526$	−7.93593	−	5.10011i	−0.346023	−	0.222375i
$527$	−24.1495	−	27.8700i	−1.05197	−	1.21404i
$528$		0			0
$529$	−16.7779	−	15.7321i	−0.729476	−	0.684007i
$530$	2.25443			0.0979261
$531$		0			0
$532$	−5.69828	−	3.66206i	−0.247052	−	0.158771i
$533$	2.53967	−	17.6638i	0.110005	−	0.765102i
$534$		0			0
$535$	0.354477	+	2.46544i	0.0153254	+	0.106590i
$536$	13.5237	+	3.97093i	0.584136	+	0.171518i
$537$		0			0
$538$	−7.21622	−	15.8013i	−0.311113	−	0.681243i
$539$	−6.52430	+	1.91571i	−0.281021	+	0.0825154i
$540$		0			0
$541$	11.5093	−	13.2824i	0.494823	−	0.571056i	−0.452325	−	0.891853i	$-0.649405\pi$
$541$	11.5093	−	13.2824i	0.494823	−	0.571056i	0.947148	+	0.320797i	$0.103951\pi$
$542$	−17.1793	+	5.04431i	−0.737915	+	0.216672i
$543$		0			0
$544$	5.30755	−	3.41095i	0.227559	−	0.146243i
$545$	−1.45925	−	0.428474i	−0.0625073	−	0.0183538i
$546$		0			0
$547$	−6.97178	+	15.2661i	−0.298092	+	0.652730i	−0.998114	−	0.0613912i	$-0.980446\pi$
$547$	−6.97178	+	15.2661i	−0.298092	+	0.652730i	0.700022	+	0.714121i	$0.253174\pi$
$548$	2.26703	−	15.7675i	0.0968426	−	0.673555i
$549$		0			0
$550$	−7.84742	−	9.05641i	−0.334615	−	0.386167i
$551$	23.4588			0.999379
$552$		0			0
$553$	−4.90989			−0.208790
$554$	10.0076	+	11.5494i	0.425184	+	0.490688i
$555$		0			0
$556$	0.406233	−	2.82541i	0.0172281	−	0.119824i
$557$	2.94060	−	6.43902i	0.124597	−	0.272830i	−0.837046	−	0.547132i	$-0.815720\pi$
$557$	2.94060	−	6.43902i	0.124597	−	0.272830i	0.961644	+	0.274302i	$0.0884468\pi$
$558$		0			0
$559$	−39.8902	−	11.7128i	−1.68718	−	0.495400i
$560$	−0.645886	+	0.415086i	−0.0272937	+	0.0175406i
$561$		0			0
$562$	5.68699	−	1.66985i	0.239891	−	0.0704384i
$563$	13.8766	−	16.0145i	0.584830	−	0.674930i	−0.383806	−	0.923414i	$-0.625387\pi$
$563$	13.8766	−	16.0145i	0.584830	−	0.674930i	0.968636	+	0.248484i	$0.0799322\pi$
$564$		0			0
$565$	−1.99775	+	0.586594i	−0.0840462	+	0.0246782i
$566$	0.649526	+	1.42226i	0.0273016	+	0.0597822i
$567$		0			0
$568$	3.87510	+	1.13783i	0.162595	+	0.0477423i
$569$	−1.88114	−	13.0836i	−0.0788615	−	0.548494i	−0.990501	−	0.137504i	$-0.956092\pi$
$569$	−1.88114	−	13.0836i	−0.0788615	−	0.548494i	0.911640	−	0.410990i	$-0.134817\pi$
$570$		0			0
$571$	−3.20729	+	22.3072i	−0.134221	+	0.933527i	0.805746	+	0.592261i	$0.201765\pi$
$571$	−3.20729	+	22.3072i	−0.134221	+	0.933527i	−0.939967	+	0.341266i	$0.889144\pi$
$572$	7.74103	+	4.97486i	0.323669	+	0.208009i
$573$		0			0
$574$	9.84632			0.410978
$575$	21.9985	−	7.71682i	0.917399	−	0.321814i
$576$		0			0
$577$	9.68345	+	11.1753i	0.403127	+	0.465233i	0.920623	−	0.390452i	$-0.127681\pi$
$577$	9.68345	+	11.1753i	0.403127	+	0.465233i	−0.517496	+	0.855686i	$0.673136\pi$
$578$	19.1845	+	12.3291i	0.797969	+	0.512824i
$579$		0			0
$580$	1.10459	−	2.41871i	0.0458655	−	0.100431i
$581$	1.24189	+	8.63754i	0.0515223	+	0.358345i
$582$		0			0
$583$	12.5416	−	8.06002i	0.519421	−	0.333812i
$584$	3.60997	+	7.90472i	0.149381	+	0.327100i
$585$		0			0
$586$	1.34781	−	1.55546i	0.0556776	−	0.0642554i
$587$	9.99065	−	11.5298i	0.412358	−	0.475887i	−0.511136	−	0.859500i	$-0.670775\pi$
$587$	9.99065	−	11.5298i	0.412358	−	0.475887i	0.923494	+	0.383613i	$0.125320\pi$
$588$		0			0
$589$	−7.98587	−	17.4866i	−0.329052	−	0.720524i
$590$	−3.70371	+	2.38023i	−0.152479	+	0.0979926i
$591$		0			0
$592$	0.665978	+	4.63198i	0.0273715	+	0.190373i
$593$	1.54253	−	3.37768i	0.0633443	−	0.138705i	−0.875312	−	0.483558i	$-0.839344\pi$
$593$	1.54253	−	3.37768i	0.0633443	−	0.138705i	0.938657	+	0.344854i	$0.112071\pi$
$594$		0			0
$595$	−4.07495	−	2.61881i	−0.167057	−	0.107361i
$596$	−1.91136	−	2.20583i	−0.0782924	−	0.0903543i
$597$		0			0
$598$	−14.5385	+	10.4446i	−0.594523	+	0.427113i
$599$	8.17752			0.334124			0.167062	−	0.985946i	$-0.446572\pi$
$599$	8.17752			0.334124			0.167062	+	0.985946i	$0.446572\pi$
$600$		0			0
$601$	28.9896	+	18.6305i	1.18251	+	0.759952i	0.975846	−	0.218460i	$-0.0701033\pi$
$601$	28.9896	+	18.6305i	1.18251	+	0.759952i	0.206663	+	0.978412i	$0.433740\pi$
$602$	3.26455	−	22.7054i	0.133053	−	0.925404i
$603$		0			0
$604$	−3.49556	−	24.3122i	−0.142232	−	0.989248i
$605$	−1.76083	−	0.517027i	−0.0715880	−	0.0210201i
$606$		0			0
$607$	7.92178	+	17.3463i	0.321535	+	0.704063i	0.999519	−	0.0310132i	$-0.00987340\pi$
$607$	7.92178	+	17.3463i	0.321535	+	0.704063i	−0.677984	+	0.735077i	$0.737146\pi$
$608$	3.15565	−	0.926583i	0.127979	−	0.0375779i
$609$		0			0
$610$	0.411774	−	0.475213i	0.0166723	−	0.0192408i
$611$	−8.75683	+	2.57124i	−0.354263	+	0.104021i
$612$		0			0
$613$	9.99590	−	6.42398i	0.403731	−	0.259462i	−0.322980	−	0.946406i	$-0.604685\pi$
$613$	9.99590	−	6.42398i	0.403731	−	0.259462i	0.726710	+	0.686944i	$0.241048\pi$
$614$	−10.3952	−	3.05231i	−0.419517	−	0.123181i
$615$		0			0
$616$	−2.10912	+	4.61833i	−0.0849789	+	0.186078i
$617$	−1.52507	+	10.6071i	−0.0613972	+	0.427027i	0.935820	+	0.352478i	$0.114661\pi$
$617$	−1.52507	+	10.6071i	−0.0613972	+	0.427027i	−0.997217	+	0.0745490i	$0.976248\pi$
$618$		0			0
$619$	3.76265	+	4.34233i	0.151234	+	0.174533i	0.826311	−	0.563214i	$-0.190435\pi$
$619$	3.76265	+	4.34233i	0.151234	+	0.174533i	−0.675077	+	0.737747i	$0.735890\pi$
$620$	−2.17897			−0.0875097
$621$		0			0
$622$	22.8972			0.918095
$623$	−12.1804	−	14.0569i	−0.487998	−	0.563179i
$624$		0			0
$625$	−3.26396	+	22.7013i	−0.130558	+	0.908053i
$626$	−9.69914	+	21.2382i	−0.387656	+	0.848848i
$627$		0			0
$628$	12.5737	+	3.69197i	0.501744	+	0.147325i
$629$	−24.8372	+	15.9619i	−0.990326	+	0.636444i
$630$		0			0
$631$	13.1735	−	3.86808i	0.524428	−	0.153986i	−0.00879404	−	0.999961i	$-0.502799\pi$
$631$	13.1735	−	3.86808i	0.524428	−	0.153986i	0.533222	+	0.845975i	$0.320981\pi$
$632$	1.56117	−	1.80169i	0.0621001	−	0.0716674i
$633$		0			0
$634$	0.483037	−	0.141833i	0.0191839	−	0.00563289i
$635$	1.16902	+	2.55980i	0.0463911	+	0.101582i
$636$		0			0
$637$	−9.87884	−	2.90069i	−0.391414	−	0.114930i
$638$	−2.50241	−	17.4047i	−0.0990714	−	0.689057i
$639$		0			0
$640$	0.0530529	−	0.368991i	0.00209710	−	0.0145857i
$641$	−30.5273	−	19.6187i	−1.20576	−	0.774892i	−0.225813	−	0.974171i	$-0.572504\pi$
$641$	−30.5273	−	19.6187i	−1.20576	−	0.774892i	−0.979943	+	0.199279i	$0.936140\pi$
$642$		0			0
$643$	−14.8477			−0.585535			−0.292768	−	0.956184i	$-0.594576\pi$
$643$	−14.8477			−0.585535			−0.292768	+	0.956184i	$0.594576\pi$
$644$	−6.84586	−	7.11992i	−0.269765	−	0.280564i
$645$		0			0
$646$	13.5882	+	15.6817i	0.534622	+	0.616987i
$647$	−1.61467	−	1.03768i	−0.0634792	−	0.0407956i	0.508516	−	0.861052i	$-0.330194\pi$
$647$	−1.61467	−	1.03768i	−0.0634792	−	0.0407956i	−0.571995	+	0.820257i	$0.693831\pi$
$648$		0			0
$649$	−12.0944	+	26.4830i	−0.474746	+	1.03955i
$650$	−2.58226	−	17.9600i	−0.101285	−	0.704451i
$651$		0			0
$652$	3.88581	−	2.49726i	0.152180	−	0.0978001i
$653$	9.92317	+	21.7287i	0.388324	+	0.850310i	0.998322	+	0.0579075i	$0.0184428\pi$
$653$	9.92317	+	21.7287i	0.388324	+	0.850310i	−0.609998	+	0.792403i	$0.708830\pi$
$654$		0			0
$655$	0.798444	−	0.921454i	0.0311978	−	0.0360042i
$656$	−3.13079	+	3.61312i	−0.122237	+	0.141069i
$657$		0			0
$658$	−2.09187	−	4.58056i	−0.0815497	−	0.178569i
$659$	1.46729	−	0.942968i	0.0571574	−	0.0367328i	−0.511750	−	0.859134i	$-0.671003\pi$
$659$	1.46729	−	0.942968i	0.0571574	−	0.0367328i	0.568907	+	0.822402i	$0.307366\pi$
$660$		0			0
$661$	−4.36964	−	30.3915i	−0.169959	−	1.18209i	−0.878964	−	0.476888i	$-0.841765\pi$
$661$	−4.36964	−	30.3915i	−0.169959	−	1.18209i	0.709005	−	0.705204i	$-0.249144\pi$
$662$	8.39272	−	18.3775i	0.326192	−	0.714262i
$663$		0			0
$664$	−3.56443	−	2.29072i	−0.138327	−	0.0888972i
$665$	−1.65358	−	1.90833i	−0.0641231	−	0.0740020i
$666$		0			0
$667$	33.2768	+	7.92577i	1.28848	+	0.306887i
$668$	3.93949			0.152424
$669$		0			0
$670$	4.42019	+	2.84068i	0.170767	+	0.109745i
$671$	0.591768	−	4.11583i	0.0228449	−	0.158890i
$672$		0			0
$673$	−1.67682	−	11.6625i	−0.0646367	−	0.449558i	−0.996279	−	0.0861824i	$-0.972533\pi$
$673$	−1.67682	−	11.6625i	−0.0646367	−	0.449558i	0.931643	−	0.363376i	$-0.118376\pi$
$674$	−3.93944	−	1.15672i	−0.151742	−	0.0445554i
$675$		0			0
$676$	0.387574	+	0.848668i	0.0149067	+	0.0326411i
$677$	27.3889	−	8.04212i	1.05264	−	0.309084i	0.290758	−	0.956797i	$-0.406092\pi$
$677$	27.3889	−	8.04212i	1.05264	−	0.309084i	0.761885	+	0.647713i	$0.224274\pi$
$678$		0			0
$679$	15.2494	−	17.5988i	0.585220	−	0.675380i
$680$	2.25667	−	0.662618i	0.0865393	−	0.0254102i
$681$		0			0
$682$	−12.1219	+	7.79025i	−0.464170	+	0.298304i
$683$	14.4113	+	4.23154i	0.551433	+	0.161915i	0.545566	−	0.838068i	$-0.316315\pi$
$683$	14.4113	+	4.23154i	0.551433	+	0.161915i	0.00586616	+	0.999983i	$0.498133\pi$
$684$		0			0
$685$	2.46688	−	5.40171i	0.0942546	−	0.206389i
$686$	2.86019	−	19.8930i	0.109202	−	0.759519i
$687$		0			0
$688$	7.29377	+	8.41745i	0.278072	+	0.320912i
$689$	22.5735			0.859983
$690$		0			0
$691$	20.7588			0.789701			0.394851	−	0.918745i	$-0.370796\pi$
$691$	20.7588			0.789701			0.394851	+	0.918745i	$0.370796\pi$
$692$	12.4428	+	14.3598i	0.473005	+	0.545877i
$693$		0			0
$694$	3.47469	−	24.1670i	0.131898	−	0.917367i
$695$	0.442045	−	0.967943i	0.0167677	−	0.0367162i
$696$		0			0
$697$	−28.9410	−	8.49783i	−1.09622	−	0.321878i
$698$	14.5496	−	9.35043i	0.550709	−	0.353919i
$699$		0			0
$700$	9.60594	−	2.82056i	0.363070	−	0.106607i
$701$	15.6028	−	18.0066i	0.589311	−	0.680101i	−0.380269	−	0.924876i	$-0.624169\pi$
$701$	15.6028	−	18.0066i	0.589311	−	0.680101i	0.969580	+	0.244775i	$0.0787141\pi$
$702$		0			0
$703$	−14.7672	+	4.33605i	−0.556956	+	0.163537i
$704$	−1.02408	−	2.24241i	−0.0385963	−	0.0845141i
$705$		0			0
$706$	−9.19077	−	2.69865i	−0.345899	−	0.101565i
$707$	−2.35999	−	16.4141i	−0.0887567	−	0.617317i
$708$		0			0
$709$	2.59095	−	18.0204i	0.0973050	−	0.676771i	−0.881531	−	0.472126i	$-0.843487\pi$
$709$	2.59095	−	18.0204i	0.0973050	−	0.676771i	0.978836	−	0.204645i	$-0.0656041\pi$
$710$	1.26656	+	0.813970i	0.0475332	+	0.0305478i
$711$		0			0
$712$	9.03115			0.338457
$713$	−5.42010	−	27.5032i	−0.202984	−	1.03000i
$714$		0			0
$715$	2.24636	+	2.59244i	0.0840092	+	0.0969518i
$716$	−2.01853	−	1.29723i	−0.0754359	−	0.0484797i
$717$		0			0
$718$	−0.0520416	+	0.113955i	−0.00194218	+	0.00425277i
$719$	−1.78226	−	12.3959i	−0.0664671	−	0.462289i	−0.995688	−	0.0927643i	$-0.970430\pi$
$719$	−1.78226	−	12.3959i	−0.0664671	−	0.462289i	0.929221	−	0.369524i	$-0.120479\pi$
$720$		0			0
$721$	−25.5590	+	16.4257i	−0.951865	+	0.611727i
$722$	−3.39947	−	7.44380i	−0.126515	−	0.277029i
$723$		0			0
$724$	−17.0305	+	19.6543i	−0.632934	+	0.730445i
$725$	−22.7058	+	26.2039i	−0.843271	+	0.973187i
$726$		0			0
$727$	−5.15039	−	11.2778i	−0.191017	−	0.418270i	0.789756	−	0.613422i	$-0.210207\pi$
$727$	−5.15039	−	11.2778i	−0.191017	−	0.418270i	−0.980773	+	0.195152i	$0.937480\pi$
$728$	−6.46723	+	4.15624i	−0.239692	+	0.154040i
$729$		0			0
$730$	0.461031	+	3.20654i	0.0170635	+	0.118679i
$731$	−29.1912	+	63.9198i	−1.07968	+	2.36416i
$732$		0			0
$733$	−13.8021	−	8.87008i	−0.509793	−	0.327624i	0.260330	−	0.965520i	$-0.416169\pi$
$733$	−13.8021	−	8.87008i	−0.509793	−	0.327624i	−0.770123	+	0.637896i	$0.779805\pi$
$734$	2.77314	+	3.20037i	0.102358	+	0.118128i
$735$		0			0
$736$	4.78940	−	0.248210i	0.176540	−	0.00914915i
$737$	34.7460			1.27988
$738$		0			0
$739$	−35.5232	−	22.8294i	−1.30674	−	0.839792i	−0.312813	−	0.949815i	$-0.601271\pi$
$739$	−35.5232	−	22.8294i	−1.30674	−	0.839792i	−0.993929	+	0.110023i	$0.964908\pi$
$740$	−0.248267	+	1.72673i	−0.00912648	+	0.0634760i
$741$		0			0
$742$	1.77255	+	12.3283i	0.0650722	+	0.452587i
$743$	−13.8891	−	4.07820i	−0.509541	−	0.149615i	0.0168491	−	0.999858i	$-0.494637\pi$
$743$	−13.8891	−	4.07820i	−0.509541	−	0.149615i	−0.526390	+	0.850243i	$0.676455\pi$
$744$		0			0
$745$	−0.451997	−	0.989735i	−0.0165599	−	0.0362611i
$746$	0.601077	−	0.176492i	0.0220070	−	0.00646184i
$747$		0			0
$748$	10.1851	−	11.7542i	0.372404	−	0.429778i
$749$	−13.2035	+	3.87691i	−0.482447	+	0.141659i
$750$		0			0
$751$	−24.5633	+	15.7859i	−0.896327	+	0.576034i	−0.905699	−	0.423922i	$-0.860653\pi$
$751$	−24.5633	+	15.7859i	−0.896327	+	0.576034i	0.00937174	+	0.999956i	$0.497017\pi$
$752$	2.34598	+	0.688843i	0.0855492	+	0.0251195i
$753$		0			0
$754$	11.0602	−	24.2185i	0.402789	−	0.881984i
$755$	1.30310	−	9.06323i	0.0474245	−	0.329845i
$756$		0			0
$757$	10.7066	+	12.3561i	0.389140	+	0.449091i	0.916191	−	0.400743i	$-0.131248\pi$
$757$	10.7066	+	12.3561i	0.389140	+	0.449091i	−0.527051	+	0.849834i	$0.676702\pi$
$758$	−10.5210			−0.382140
$759$		0			0
$760$	1.22605			0.0444733
$761$	−3.34567	−	3.86111i	−0.121281	−	0.139965i	0.691862	−	0.722030i	$-0.256791\pi$
$761$	−3.34567	−	3.86111i	−0.121281	−	0.139965i	−0.813143	+	0.582064i	$0.802245\pi$
$762$		0			0
$763$	1.19577	−	8.31677i	0.0432898	−	0.301087i
$764$	4.34904	−	9.52307i	0.157343	−	0.344532i
$765$		0			0
$766$	−14.7473	−	4.33020i	−0.532841	−	0.156456i
$767$	−37.0852	+	23.8332i	−1.33907	+	0.860567i
$768$		0			0
$769$	−27.4772	+	8.06804i	−0.990854	+	0.290941i	−0.736698	−	0.676222i	$-0.763616\pi$
$769$	−27.4772	+	8.06804i	−0.990854	+	0.290941i	−0.254156	+	0.967163i	$0.581798\pi$
$770$	−1.23945	+	1.43040i	−0.0446665	+	0.0515479i
$771$		0			0
$772$	−0.740001	+	0.217284i	−0.0266332	+	0.00782022i
$773$	−10.3555	−	22.6753i	−0.372460	−	0.815575i	−0.999335	−	0.0364547i	$-0.988394\pi$
$773$	−10.3555	−	22.6753i	−0.372460	−	0.815575i	0.626875	−	0.779120i	$-0.284334\pi$
$774$		0			0
$775$	27.2623	+	8.00495i	0.979292	+	0.287546i
$776$	1.60911	+	11.1916i	0.0577636	+	0.401755i
$777$		0			0
$778$	3.09318	−	21.5135i	0.110896	−	0.771297i
$779$	−13.2275	−	8.50081i	−0.473925	−	0.304573i
$780$		0			0
$781$	9.95612			0.356258
$782$	13.9770	+	26.8356i	0.499816	+	0.959640i
$783$		0			0
$784$	1.80631	+	2.08459i	0.0645109	+	0.0744496i
$785$	4.10967	+	2.64112i	0.146680	+	0.0942657i
$786$		0			0
$787$	−2.13186	+	4.66813i	−0.0759927	+	0.166401i	−0.943815	−	0.330473i	$-0.892792\pi$
$787$	−2.13186	+	4.66813i	−0.0759927	+	0.166401i	0.867823	+	0.496874i	$0.165519\pi$
$788$	0.741077	+	5.15430i	0.0263998	+	0.183614i
$789$		0			0
$790$	0.747632	−	0.480474i	0.0265996	−	0.0170945i
$791$	−4.77852	−	10.4635i	−0.169904	−	0.372039i
$792$		0			0
$793$	4.12308	−	4.75829i	0.146415	−	0.168972i
$794$	−6.65273	+	7.67767i	−0.236097	+	0.272470i
$795$		0			0
$796$	−9.69692	−	21.2333i	−0.343698	−	0.752594i
$797$	8.01241	−	5.14926i	0.283814	−	0.182396i	−0.390986	−	0.920396i	$-0.627866\pi$
$797$	8.01241	−	5.14926i	0.283814	−	0.182396i	0.674800	+	0.738000i	$0.264230\pi$
$798$		0			0
$799$	2.19533	+	15.2689i	0.0776653	+	0.540174i
$800$	−2.01935	+	4.42175i	−0.0713946	+	0.156332i
$801$		0			0
$802$	26.8343	+	17.2454i	0.947553	+	0.608956i
$803$	14.0288	+	16.1901i	0.495065	+	0.571335i
$804$		0			0
$805$	−1.70089	−	3.26568i	−0.0599483	−	0.115100i
$806$	−21.8180			−0.768506
$807$		0			0
$808$	6.77358	+	4.35311i	0.238294	+	0.153142i
$809$	−1.51002	+	10.5024i	−0.0530894	+	0.369245i	0.945906	+	0.324440i	$0.105176\pi$
$809$	−1.51002	+	10.5024i	−0.0530894	+	0.369245i	−0.998996	+	0.0448052i	$0.985733\pi$
$810$		0			0
$811$	4.38612	+	30.5061i	0.154018	+	1.07122i	0.909397	+	0.415928i	$0.136543\pi$
$811$	4.38612	+	30.5061i	0.154018	+	1.07122i	−0.755380	+	0.655287i	$0.772548\pi$
$812$	14.0952	+	4.13872i	0.494643	+	0.145240i
$813$		0			0
$814$	4.79227	+	10.4936i	0.167969	+	0.367801i
$815$	1.65217	−	0.485122i	0.0578731	−	0.0169931i
$816$		0			0
$817$	−23.9883	+	27.6840i	−0.839244	+	0.968539i
$818$	12.6794	−	3.72301i	0.443325	−	0.130172i
$819$		0			0
$820$	−1.49931	+	0.963546i	−0.0523580	+	0.0336485i
$821$	40.3116	+	11.8365i	1.40688	+	0.413098i	0.895042	−	0.445982i	$-0.147145\pi$
$821$	40.3116	+	11.8365i	1.40688	+	0.413098i	0.511842	+	0.859080i	$0.328963\pi$
$822$		0			0
$823$	−11.6572	+	25.5257i	−0.406344	+	0.889770i	0.590243	+	0.807226i	$0.299032\pi$
$823$	−11.6572	+	25.5257i	−0.406344	+	0.889770i	−0.996587	+	0.0825444i	$0.973695\pi$
$824$	2.09941	−	14.6017i	0.0731363	−	0.508674i
$825$		0			0
$826$	−15.9283	−	18.3823i	−0.554217	−	0.639601i
$827$	−36.3429			−1.26377			−0.631883	−	0.775064i	$-0.717718\pi$
$827$	−36.3429			−1.26377			−0.631883	+	0.775064i	$0.717718\pi$
$828$		0			0
$829$	30.0375			1.04325			0.521623	−	0.853176i	$-0.325327\pi$
$829$	30.0375			1.04325			0.521623	+	0.853176i	$0.325327\pi$
$830$	−1.03436	−	1.19371i	−0.0359031	−	0.0414344i
$831$		0			0
$832$	0.531217	−	3.69470i	0.0184166	−	0.128091i
$833$	−7.22922	+	15.8298i	−0.250478	+	0.548469i
$834$		0			0
$835$	1.40910	+	0.413748i	0.0487638	+	0.0143184i
$836$	6.82062	−	4.38335i	0.235896	−	0.151601i
$837$		0			0
$838$	4.03271	−	1.18411i	0.139308	−	0.0409044i
$839$	−21.8884	+	25.2606i	−0.755671	+	0.872091i	−0.995105	−	0.0988214i	$-0.968493\pi$
$839$	−21.8884	+	25.2606i	−0.755671	+	0.872091i	0.239434	+	0.970913i	$0.423038\pi$
$840$		0			0
$841$	−20.9904	+	6.16334i	−0.723807	+	0.212529i
$842$	2.92258	+	6.39956i	0.100719	+	0.220543i
$843$		0			0
$844$	8.34378	+	2.44995i	0.287205	+	0.0843309i
$845$	0.0494973	+	0.344261i	0.00170276	+	0.0118429i
$846$		0			0
$847$	1.44290	−	10.0356i	0.0495787	−	0.344828i
$848$	−5.08750	−	3.26954i	−0.174705	−	0.112276i
$849$		0			0
$850$	−30.6687			−1.05193
$851$	−22.4125	+	1.16153i	−0.768292	+	0.0398166i
$852$		0			0
$853$	−3.84662	−	4.43924i	−0.131706	−	0.151997i	0.686066	−	0.727540i	$-0.259336\pi$
$853$	−3.84662	−	4.43924i	−0.131706	−	0.151997i	−0.817772	+	0.575543i	$0.804791\pi$
$854$	2.92245	+	1.87815i	0.100004	+	0.0642689i
$855$		0			0
$856$	2.77563	−	6.07778i	0.0948690	−	0.207734i
$857$	2.11934	+	14.7404i	0.0723954	+	0.503521i	0.993466	+	0.114126i	$0.0364067\pi$
$857$	2.11934	+	14.7404i	0.0723954	+	0.503521i	−0.921071	+	0.389395i	$0.872684\pi$
$858$		0			0
$859$	−6.65486	+	4.27682i	−0.227061	+	0.145923i	−0.649225	−	0.760596i	$-0.724907\pi$
$859$	−6.65486	+	4.27682i	−0.227061	+	0.145923i	0.422165	+	0.906519i	$0.361270\pi$
$860$	1.72482	+	3.77683i	0.0588159	+	0.128789i
$861$		0			0
$862$	24.1116	−	27.8263i	0.821245	−	0.947767i
$863$	−2.64187	+	3.04888i	−0.0899302	+	0.103785i	−0.798931	−	0.601423i	$-0.794601\pi$
$863$	−2.64187	+	3.04888i	−0.0899302	+	0.103785i	0.709001	+	0.705208i	$0.249146\pi$
$864$		0			0
$865$	2.94246	+	6.44309i	0.100047	+	0.219072i
$866$	−22.9052	+	14.7203i	−0.778351	+	0.500216i
$867$		0			0
$868$	−1.71322	−	11.9157i	−0.0581504	−	0.404445i
$869$	2.44137	−	5.34586i	0.0828179	−	0.181346i
$870$		0			0
$871$	44.2592	+	28.4437i	1.49967	+	0.963777i
$872$	2.67163	+	3.08323i	0.0904730	+	0.104411i
$873$		0			0
$874$	3.04973	+	15.4752i	0.103159	+	0.523458i
$875$	7.57096			0.255945
$876$		0			0
$877$	−43.6317	−	28.0404i	−1.47334	−	0.946857i	−0.997740	−	0.0671940i	$-0.978595\pi$
$877$	−43.6317	−	28.0404i	−1.47334	−	0.946857i	−0.475598	−	0.879663i	$-0.657768\pi$
$878$	3.44226	−	23.9415i	0.116171	−	0.807985i
$879$		0			0
$880$	−0.130785	−	0.909632i	−0.00440877	−	0.0306637i
$881$	−31.1274	−	9.13983i	−1.04871	−	0.307929i	−0.288413	−	0.957506i	$-0.593128\pi$
$881$	−31.1274	−	9.13983i	−1.04871	−	0.307929i	−0.760295	+	0.649578i	$0.774946\pi$
$882$		0			0
$883$	−2.76535	−	6.05528i	−0.0930615	−	0.203776i	0.857377	−	0.514689i	$-0.172093\pi$
$883$	−2.76535	−	6.05528i	−0.0930615	−	0.203776i	−0.950438	+	0.310913i	$0.899365\pi$
$884$	22.5960	−	6.63477i	0.759984	−	0.223151i
$885$		0			0
$886$	10.1029	−	11.6593i	0.339412	−	0.391703i
$887$	40.8783	−	12.0029i	1.37256	−	0.403019i	0.489385	−	0.872068i	$-0.337221\pi$
$887$	40.8783	−	12.0029i	1.37256	−	0.403019i	0.883172	+	0.469048i	$0.155403\pi$
$888$		0			0
$889$	−13.0791	+	8.40541i	−0.438658	+	0.281908i
$890$	3.23031	+	0.948504i	0.108280	+	0.0317939i
$891$		0			0
$892$	−1.59567	+	3.49404i	−0.0534271	+	0.116989i
$893$	−1.14441	+	7.95953i	−0.0382961	+	0.266355i
$894$		0			0
$895$	−0.585754	−	0.675997i	−0.0195796	−	0.0225961i
$896$	2.05954			0.0688043
$897$		0			0
$898$	−17.3241			−0.578112
$899$	27.3024	+	31.5086i	0.910586	+	1.05087i
$900$		0			0
$901$	5.42993	−	37.7660i	0.180897	−	1.25817i
$902$	−4.89594	+	10.7206i	−0.163017	+	0.356958i
$903$		0			0
$904$	5.35899	+	1.57354i	0.178237	+	0.0523352i
$905$	−8.15577	+	5.24140i	−0.271107	+	0.174230i
$906$		0			0
$907$	−32.8643	+	9.64984i	−1.09124	+	0.320418i	−0.777367	−	0.629047i	$-0.783445\pi$
$907$	−32.8643	+	9.64984i	−1.09124	+	0.320418i	−0.313875	+	0.949464i	$0.601627\pi$
$908$	1.33201	−	1.53722i	0.0442042	−	0.0510143i
$909$		0			0
$910$	−2.74975	+	0.807398i	−0.0911532	+	0.0267650i
$911$	14.6448	+	32.0677i	0.485205	+	1.06245i	0.980999	+	0.194011i	$0.0621499\pi$
$911$	14.6448	+	32.0677i	0.485205	+	1.06245i	−0.495794	+	0.868440i	$0.665123\pi$
$912$		0			0
$913$	−10.0220	−	2.94273i	−0.331680	−	0.0973901i
$914$	0.977556	+	6.79905i	0.0323347	+	0.224893i
$915$		0			0
$916$	−3.90521	+	27.1613i	−0.129032	+	0.897436i
$917$	5.66674	+	3.64179i	0.187132	+	0.120263i
$918$		0			0
$919$	34.5723			1.14043			0.570217	−	0.821494i	$-0.306859\pi$
$919$	34.5723			1.14043			0.570217	+	0.821494i	$0.306859\pi$
$920$	1.73917	+	0.414230i	0.0573386	+	0.0136568i
$921$		0			0
$922$	−0.223367	−	0.257779i	−0.00735620	−	0.00848951i
$923$	12.6821	+	8.15026i	0.417435	+	0.268269i
$924$		0			0
$925$	9.44975	−	20.6921i	0.310706	−	0.680351i
$926$	−2.32234	−	16.1523i	−0.0763169	−	0.530796i
$927$		0			0
$928$	−6.00048	+	3.85627i	−0.196975	+	0.126588i
$929$	−12.8087	−	28.0472i	−0.420241	−	0.920200i	−0.994811	−	0.101744i	$-0.967558\pi$
$929$	−12.8087	−	28.0472i	−0.420241	−	0.920200i	0.574569	−	0.818456i	$-0.305170\pi$
$930$		0			0
$931$	−5.94071	+	6.85595i	−0.194699	+	0.224695i
$932$	4.61337	−	5.32411i	0.151116	−	0.174397i
$933$		0			0
$934$	15.0523	+	32.9600i	0.492527	+	1.07848i
$935$	4.87756	−	3.13462i	0.159513	−	0.102513i
$936$		0			0
$937$	0.649995	+	4.52082i	0.0212344	+	0.147689i	0.997680	−	0.0680739i	$-0.0216854\pi$
$937$	0.649995	+	4.52082i	0.0212344	+	0.147689i	−0.976446	+	0.215763i	$0.930776\pi$
$938$	−12.0589	+	26.4052i	−0.393736	+	0.862162i
$939$		0			0
$940$	0.766777	+	0.492778i	0.0250095	+	0.0160726i
$941$	7.54865	+	8.71161i	0.246079	+	0.283990i	0.865330	−	0.501203i	$-0.167109\pi$
$941$	7.54865	+	8.71161i	0.246079	+	0.283990i	−0.619251	+	0.785193i	$0.712564\pi$
$942$		0			0
$943$	−15.8914	−	16.5276i	−0.517495	−	0.538212i
$944$	11.8100			0.384384
$945$		0			0
$946$	23.0983	+	14.8444i	0.750990	+	0.482632i
$947$	−8.54365	+	59.4224i	−0.277631	+	1.93097i	0.0793268	+	0.996849i	$0.474723\pi$
$947$	−8.54365	+	59.4224i	−0.277631	+	1.93097i	−0.356958	+	0.934120i	$0.616186\pi$
$948$		0			0
$949$	4.61629	+	32.1070i	0.149851	+	1.04224i
$950$	−15.3397	−	4.50415i	−0.497686	−	0.146134i
$951$		0			0
$952$	5.39782	+	11.8196i	0.174944	+	0.383075i
$953$	−9.06804	+	2.66262i	−0.293743	+	0.0862506i	−0.425284	−	0.905060i	$-0.639826\pi$
$953$	−9.06804	+	2.66262i	−0.293743	+	0.0862506i	0.131541	+	0.991311i	$0.458007\pi$
$954$		0			0
$955$	2.55575	−	2.94950i	0.0827023	−	0.0954435i
$956$	25.0243	−	7.34778i	0.809342	−	0.237644i
$957$		0			0
$958$	10.7308	−	6.89625i	0.346696	−	0.222808i
$959$	31.4788	+	9.24301i	1.01650	+	0.298472i
$960$		0			0
$961$	1.31494	−	2.87931i	0.0424173	−	0.0928809i
$962$	−2.48589	+	17.2897i	−0.0801483	+	0.557444i
$963$		0			0
$964$	−0.910396	−	1.05065i	−0.0293219	−	0.0338392i
$965$	−0.287508			−0.00925520
$966$		0			0
$967$	−39.0760			−1.25660			−0.628300	−	0.777971i	$-0.716249\pi$
$967$	−39.0760			−1.25660			−0.628300	+	0.777971i	$0.716249\pi$
$968$	3.22379	+	3.72045i	0.103616	+	0.119580i
$969$		0			0
$970$	−0.599853	+	4.17207i	−0.0192601	+	0.133957i
$971$	17.2322	−	37.7334i	0.553009	−	1.21092i	−0.402353	−	0.915484i	$-0.631808\pi$
$971$	17.2322	−	37.7334i	0.553009	−	1.21092i	0.955362	−	0.295437i	$-0.0954651\pi$
$972$		0			0
$973$	5.64075	+	1.65627i	0.180834	+	0.0530977i
$974$	28.2159	−	18.1332i	0.904094	−	0.581026i
$975$		0			0
$976$	−1.61843	+	0.475213i	−0.0518046	+	0.0152112i
$977$	−13.5638	+	15.6535i	−0.433944	+	0.500798i	−0.930034	−	0.367473i	$-0.880223\pi$
$977$	−13.5638	+	15.6535i	−0.433944	+	0.500798i	0.496090	+	0.868271i	$0.334769\pi$
$978$		0			0
$979$	21.3616	−	6.27235i	0.682721	−	0.200465i
$980$	0.427153	+	0.935335i	0.0136449	+	0.0298782i
$981$		0			0
$982$	−35.3838	−	10.3896i	−1.12914	−	0.331547i
$983$	−3.53975	−	24.6195i	−0.112901	−	0.785240i	−0.965073	−	0.261980i	$-0.915625\pi$
$983$	−3.53975	−	24.6195i	−0.112901	−	0.785240i	0.852173	−	0.523260i	$-0.175285\pi$
$984$		0			0
$985$	−0.276263	+	1.92145i	−0.00880247	+	0.0612225i
$986$	−37.8576	−	24.3296i	−1.20563	−	0.774811i
$987$		0			0
$988$	12.2764			0.390563
$989$	−43.3811	+	31.1655i	−1.37944	+	0.991007i
$990$		0			0
$991$	6.02871	+	6.95750i	0.191508	+	0.221012i	0.843381	−	0.537316i	$-0.180562\pi$
$991$	6.02871	+	6.95750i	0.191508	+	0.221012i	−0.651873	+	0.758328i	$0.726016\pi$
$992$	4.91722	+	3.16011i	0.156122	+	0.100334i
$993$		0			0
$994$	−3.45535	+	7.56617i	−0.109597	+	0.239984i
$995$	−1.23840	−	8.61326i	−0.0392599	−	0.273059i
$996$		0			0
$997$	35.9389	−	23.0965i	1.13820	−	0.731474i	0.170940	−	0.985281i	$-0.445319\pi$
$997$	35.9389	−	23.0965i	1.13820	−	0.731474i	0.967255	+	0.253808i	$0.0816831\pi$
$998$	0.754644	+	1.65244i	0.0238878	+	0.0523070i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.c.289.1		10
3.2	odd	2		46.2.c.b.13.1	✓	10
12.11	even	2		368.2.m.a.289.1		10
23.4	even	11		9522.2.a.bz.1.3		5
23.16	even	11	inner	414.2.i.c.361.1		10
23.19	odd	22		9522.2.a.bw.1.3		5
69.50	odd	22		1058.2.a.j.1.3		5
69.62	odd	22		46.2.c.b.39.1	yes	10
69.65	even	22		1058.2.a.k.1.3		5
276.119	even	22		8464.2.a.bu.1.3		5
276.131	even	22		368.2.m.a.177.1		10
276.203	odd	22		8464.2.a.bv.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.13.1	✓	10	3.2	odd	2
46.2.c.b.39.1	yes	10	69.62	odd	22
368.2.m.a.177.1		10	276.131	even	22
368.2.m.a.289.1		10	12.11	even	2
414.2.i.c.289.1		10	1.1	even	1	trivial
414.2.i.c.361.1		10	23.16	even	11	inner
1058.2.a.j.1.3		5	69.50	odd	22
1058.2.a.k.1.3		5	69.65	even	22
8464.2.a.bu.1.3		5	276.119	even	22
8464.2.a.bv.1.3		5	276.203	odd	22
9522.2.a.bw.1.3		5	23.19	odd	22
9522.2.a.bz.1.3		5	23.4	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(-0.154861 + 0.339098i) q^{5} +(-1.97611 - 0.580239i) q^{7} +(0.841254 - 0.540641i) q^{8} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.142315 + 0.989821i) q^{4} +(-0.154861 + 0.339098i) q^{5} +(-1.97611 - 0.580239i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.357685 - 0.105026i) q^{10} +(1.61435 - 1.86306i) q^{11} +(3.58149 - 1.05162i) q^{13} +(0.855563 + 1.87342i) q^{14} +(-0.959493 - 0.281733i) q^{16} +(-0.897877 - 6.24487i) q^{17} +(0.468056 - 3.25540i) q^{19} +(-0.313607 - 0.201543i) q^{20} -2.46519 q^{22} +(1.76381 - 4.45971i) q^{23} +(3.18330 + 3.67372i) q^{25} +(-3.14014 - 2.01804i) q^{26} +(0.855563 - 1.87342i) q^{28} +(1.01510 + 7.06018i) q^{29} +(4.91722 - 3.16011i) q^{31} +(0.415415 + 0.909632i) q^{32} +(-4.13158 + 4.76809i) q^{34} +(0.502780 - 0.580239i) q^{35} +(-1.94398 - 4.25672i) q^{37} +(-2.76678 + 1.77810i) q^{38} +(0.0530529 + 0.368991i) q^{40} +(1.98603 - 4.34881i) q^{41} +(-9.36979 - 6.02160i) q^{43} +(1.61435 + 1.86306i) q^{44} +(-4.52547 + 1.58749i) q^{46} -2.44502 q^{47} +(-2.32043 - 1.49125i) q^{49} +(0.691797 - 4.81155i) q^{50} +(0.531217 + 3.69470i) q^{52} +(5.80255 + 1.70378i) q^{53} +(0.381761 + 0.835939i) q^{55} +(-1.97611 + 0.580239i) q^{56} +(4.67098 - 5.39060i) q^{58} +(-11.3316 + 3.32727i) q^{59} +(1.41899 - 0.911927i) q^{61} +(-5.60835 - 1.64676i) q^{62} +(0.415415 - 0.909632i) q^{64} +(-0.198030 + 1.37733i) q^{65} +(9.23004 + 10.6520i) q^{67} +6.30909 q^{68} -0.767766 q^{70} +(2.64478 + 3.05224i) q^{71} +(-1.23672 + 8.60157i) q^{73} +(-1.94398 + 4.25672i) q^{74} +(3.15565 + 0.926583i) q^{76} +(-4.27116 + 2.74491i) q^{77} +(2.28741 - 0.671644i) q^{79} +(0.244123 - 0.281733i) q^{80} +(-4.58718 + 1.34692i) q^{82} +(-1.76013 - 3.85415i) q^{83} +(2.25667 + 0.662618i) q^{85} +(1.58509 + 11.0245i) q^{86} +(0.350833 - 2.44009i) q^{88} +(7.59749 + 4.88261i) q^{89} -7.68762 q^{91} +(4.16330 + 2.38054i) q^{92} +(1.60115 + 1.84783i) q^{94} +(1.03141 + 0.662850i) q^{95} +(-4.69697 + 10.2849i) q^{97} +(0.392548 + 2.73023i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Introduction

L-functions

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