LMFDB - Embedded newform 77.2.m.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(4,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("77.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.m (of order $15$, degree $8$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			53.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	77.53
Dual form			77.2.m.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58268 + 0.336408i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.564602 - 0.251377i) q^{4} +(1.49622 - 1.66172i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-1.51351 - 2.17009i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.95630 - 0.415823i) q^{9} +O(q^{10})$	\(q+(-1.58268 + 0.336408i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.564602 - 0.251377i) q^{4} +(1.49622 - 1.66172i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-1.51351 - 2.17009i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.95630 - 0.415823i) q^{9} +(-1.80902 + 3.13331i) q^{10} +(0.988830 - 3.16579i) q^{11} +(-0.309017 - 0.535233i) q^{12} +(-1.80902 + 5.56758i) q^{13} +(3.12543 + 2.92540i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(-3.24803 + 3.60730i) q^{16} +(-3.16535 - 0.672816i) q^{17} +(-2.95630 + 1.31623i) q^{18} +(1.04683 + 0.466079i) q^{19} +(0.427051 - 1.31433i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 + 5.34307i) q^{22} +(0.881966 + 1.52761i) q^{23} +(-1.49622 - 1.66172i) q^{24} +(0.990108 - 9.42025i) q^{26} +(-1.54508 - 4.75528i) q^{27} +(-1.40004 - 0.844778i) q^{28} +(6.35410 + 4.61653i) q^{29} +(3.30524 + 1.47159i) q^{30} +(2.93211 + 3.25644i) q^{31} +(1.69098 - 2.92887i) q^{32} +(-3.25181 - 0.652498i) q^{33} +5.23607 q^{34} +(-5.87063 - 0.731913i) q^{35} +(1.00000 - 0.726543i) q^{36} +(0.636596 - 6.05681i) q^{37} +(-1.81359 - 0.385489i) q^{38} +(5.72618 + 1.21714i) q^{39} +(0.522642 - 4.97261i) q^{40} +(1.92705 - 1.40008i) q^{41} +(2.58268 - 3.41409i) q^{42} +0.145898 q^{43} +(-0.237511 - 2.03598i) q^{44} +(2.23607 - 3.87298i) q^{45} +(-1.90977 - 2.12101i) q^{46} +(0.431318 + 0.192035i) q^{47} +(3.92705 + 2.85317i) q^{48} +(-2.41860 + 6.56889i) q^{49} +(-0.338261 + 3.21834i) q^{51} +(0.378188 + 3.59821i) q^{52} +(4.07512 + 4.52588i) q^{53} +(4.04508 + 7.00629i) q^{54} +(-3.78115 - 6.37988i) q^{55} +(-5.59017 - 1.93649i) q^{56} +(0.354102 - 1.08981i) q^{57} +(-11.6095 - 5.16889i) q^{58} +(-8.86889 + 3.94868i) q^{59} +(-1.35177 - 0.287327i) q^{60} +(-7.32315 + 8.13318i) q^{61} +(-5.73607 - 4.16750i) q^{62} +(-3.86324 - 3.61599i) q^{63} +(1.30902 - 4.02874i) q^{64} +(6.54508 + 11.3364i) q^{65} +(5.36606 - 0.0612417i) q^{66} +(-4.19098 + 7.25900i) q^{67} +(-1.95630 + 0.415823i) q^{68} +(1.42705 - 1.03681i) q^{69} +(9.53753 - 0.816547i) q^{70} +(0.236068 + 0.726543i) q^{71} +(2.99244 - 3.32344i) q^{72} +(9.91572 - 4.41476i) q^{73} +(1.03003 + 9.80012i) q^{74} +0.708204 q^{76} +(-8.36665 + 2.64559i) q^{77} -9.47214 q^{78} +(12.4305 - 2.64218i) q^{79} +(1.13456 + 10.7946i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-2.57890 + 2.86416i) q^{82} +(-2.78115 - 8.55951i) q^{83} +(-0.693806 + 1.48067i) q^{84} +(-5.85410 + 4.25325i) q^{85} +(-0.230909 + 0.0490813i) q^{86} +(3.92705 - 6.80185i) q^{87} +(-2.37207 - 7.02661i) q^{88} +(-0.763932 - 1.32317i) q^{89} +(-2.23607 + 6.88191i) q^{90} +(14.8201 - 4.50083i) q^{91} +(0.881966 + 0.640786i) q^{92} +(2.93211 - 3.25644i) q^{93} +(-0.747238 - 0.158830i) q^{94} +(2.34078 - 1.04218i) q^{95} +(-3.08958 - 1.37557i) q^{96} +(-1.19098 + 3.66547i) q^{97} +(1.61803 - 11.2101i) q^{98} +(0.618034 - 6.60440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.58268	+	0.336408i	−1.11912	+	0.237877i	−0.730092	−	0.683349i	$-0.760523\pi$
$2$	−1.58268	+	0.336408i	−1.11912	+	0.237877i	−0.389029	+	0.921225i	$0.627189\pi$
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i	−0.982357	−	0.187015i	$-0.940119\pi$
$3$	−0.104528	−	0.994522i	−0.0603495	−	0.574187i	0.922007	−	0.387172i	$-0.126548\pi$
$4$	0.564602	−	0.251377i	0.282301	−	0.125689i
$5$	1.49622	−	1.66172i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	1.49622	−	1.66172i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$6$	0.500000	+	1.53884i	0.204124	+	0.628230i
$7$	−1.51351	−	2.17009i	−0.572051	−	0.820218i
$7$	−1.51351	−	2.17009i	−0.572051	−	0.820218i
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	1.95630	−	0.415823i	0.652098	−	0.138608i
$10$	−1.80902	+	3.13331i	−0.572061	+	0.990839i
$11$	0.988830	−	3.16579i	0.298143	−	0.954521i
$11$	0.988830	−	3.16579i	0.298143	−	0.954521i
$12$	−0.309017	−	0.535233i	−0.0892055	−	0.154508i
$13$	−1.80902	+	5.56758i	−0.501731	+	1.54417i	0.304467	+	0.952523i	$0.401522\pi$
$13$	−1.80902	+	5.56758i	−0.501731	+	1.54417i	−0.806198	+	0.591646i	$0.798478\pi$
$14$	3.12543	+	2.92540i	0.835305	+	0.781845i
$15$	−1.80902	−	1.31433i	−0.467086	−	0.339358i
$16$	−3.24803	+	3.60730i	−0.812007	+	0.901825i
$17$	−3.16535	−	0.672816i	−0.767711	−	0.163182i	−0.192622	−	0.981273i	$-0.561699\pi$
$17$	−3.16535	−	0.672816i	−0.767711	−	0.163182i	−0.575089	+	0.818091i	$0.695032\pi$
$18$	−2.95630	+	1.31623i	−0.696805	+	0.310238i
$19$	1.04683	+	0.466079i	0.240159	+	0.106926i	0.523287	−	0.852156i	$-0.324705\pi$
$19$	1.04683	+	0.466079i	0.240159	+	0.106926i	−0.283128	+	0.959082i	$0.591372\pi$
$20$	0.427051	−	1.31433i	0.0954915	−	0.293893i
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−0.500000	+	5.34307i	−0.106600	+	1.13915i
$23$	0.881966	+	1.52761i	0.183903	+	0.318529i	0.943206	−	0.332208i	$-0.107794\pi$
$23$	0.881966	+	1.52761i	0.183903	+	0.318529i	−0.759304	+	0.650737i	$0.774460\pi$
$24$	−1.49622	−	1.66172i	−0.305415	−	0.339198i
$25$		0			0
$26$	0.990108	−	9.42025i	0.194176	−	1.84746i
$27$	−1.54508	−	4.75528i	−0.297352	−	0.915155i
$28$	−1.40004	−	0.844778i	−0.264583	−	0.159648i
$29$	6.35410	+	4.61653i	1.17993	+	0.857267i	0.992163	−	0.124947i	$-0.0398761\pi$
$29$	6.35410	+	4.61653i	1.17993	+	0.857267i	0.187764	+	0.982214i	$0.439876\pi$
$30$	3.30524	+	1.47159i	0.603451	+	0.268674i
$31$	2.93211	+	3.25644i	0.526622	+	0.584873i	0.946498	−	0.322708i	$-0.104593\pi$
$31$	2.93211	+	3.25644i	0.526622	+	0.584873i	−0.419876	+	0.907581i	$0.637927\pi$
$32$	1.69098	−	2.92887i	0.298926	−	0.517756i
$33$	−3.25181	−	0.652498i	−0.566067	−	0.113585i
$34$	5.23607			0.897978
$35$	−5.87063	−	0.731913i	−0.992318	−	0.123716i
$36$	1.00000	−	0.726543i	0.166667	−	0.121090i
$37$	0.636596	−	6.05681i	0.104656	−	0.995733i	−0.808603	−	0.588354i	$-0.799776\pi$
$37$	0.636596	−	6.05681i	0.104656	−	0.995733i	0.913259	−	0.407379i	$-0.133557\pi$
$38$	−1.81359	−	0.385489i	−0.294202	−	0.0625347i
$39$	5.72618	+	1.21714i	0.916922	+	0.194898i
$40$	0.522642	−	4.97261i	0.0826370	−	0.786239i
$41$	1.92705	−	1.40008i	0.300955	−	0.218656i	−0.427051	−	0.904228i	$-0.640447\pi$
$41$	1.92705	−	1.40008i	0.300955	−	0.218656i	0.728006	+	0.685571i	$0.240447\pi$
$42$	2.58268	−	3.41409i	0.398516	−	0.526806i
$43$	0.145898			0.0222492			0.0111246	−	0.999938i	$-0.496459\pi$
$43$	0.145898			0.0222492			0.0111246	+	0.999938i	$0.496459\pi$
$44$	−0.237511	−	2.03598i	−0.0358062	−	0.306936i
$45$	2.23607	−	3.87298i	0.333333	−	0.577350i
$46$	−1.90977	−	2.12101i	−0.281580	−	0.312726i
$47$	0.431318	+	0.192035i	0.0629141	+	0.0280112i	0.437953	−	0.898998i	$-0.355704\pi$
$47$	0.431318	+	0.192035i	0.0629141	+	0.0280112i	−0.375038	+	0.927009i	$0.622370\pi$
$48$	3.92705	+	2.85317i	0.566821	+	0.411820i
$49$	−2.41860	+	6.56889i	−0.345515	+	0.938413i
$50$		0			0
$51$	−0.338261	+	3.21834i	−0.0473660	+	0.450658i
$52$	0.378188	+	3.59821i	0.0524452	+	0.498983i
$53$	4.07512	+	4.52588i	0.559761	+	0.621677i	0.954894	−	0.296947i	$-0.0959683\pi$
$53$	4.07512	+	4.52588i	0.559761	+	0.621677i	−0.395133	+	0.918624i	$0.629302\pi$
$54$	4.04508	+	7.00629i	0.550466	+	0.953436i
$55$	−3.78115	−	6.37988i	−0.509851	−	0.860263i
$56$	−5.59017	−	1.93649i	−0.747018	−	0.258775i
$57$	0.354102	−	1.08981i	0.0469020	−	0.144349i
$58$	−11.6095	−	5.16889i	−1.52440	−	0.678709i
$59$	−8.86889	+	3.94868i	−1.15463	+	0.514075i	−0.892540	−	0.450969i	$-0.851079\pi$
$59$	−8.86889	+	3.94868i	−1.15463	+	0.514075i	−0.262091	+	0.965043i	$0.584412\pi$
$60$	−1.35177	−	0.287327i	−0.174512	−	0.0370937i
$61$	−7.32315	+	8.13318i	−0.937633	+	1.04135i	0.0614320	+	0.998111i	$0.480433\pi$
$61$	−7.32315	+	8.13318i	−0.937633	+	1.04135i	−0.999065	+	0.0432356i	$0.986233\pi$
$62$	−5.73607	−	4.16750i	−0.728481	−	0.529273i
$63$	−3.86324	−	3.61599i	−0.486722	−	0.455572i
$64$	1.30902	−	4.02874i	0.163627	−	0.503593i
$65$	6.54508	+	11.3364i	0.811818	+	1.40611i
$66$	5.36606	−	0.0612417i	0.660517	−	0.00753833i
$67$	−4.19098	+	7.25900i	−0.512010	+	0.886827i	0.487893	+	0.872903i	$0.337766\pi$
$67$	−4.19098	+	7.25900i	−0.512010	+	0.886827i	−0.999903	+	0.0139240i	$0.995568\pi$
$68$	−1.95630	+	0.415823i	−0.237236	+	0.0504260i
$69$	1.42705	−	1.03681i	0.171797	−	0.124818i
$70$	9.53753	−	0.816547i	1.13995	−	0.0975960i
$71$	0.236068	+	0.726543i	0.0280161	+	0.0862247i	0.964087	−	0.265587i	$-0.0855657\pi$
$71$	0.236068	+	0.726543i	0.0280161	+	0.0862247i	−0.936071	+	0.351812i	$0.885566\pi$
$72$	2.99244	−	3.32344i	0.352663	−	0.391672i
$73$	9.91572	−	4.41476i	1.16055	−	0.516709i	0.266127	−	0.963938i	$-0.414256\pi$
$73$	9.91572	−	4.41476i	1.16055	−	0.516709i	0.894419	+	0.447229i	$0.147589\pi$
$74$	1.03003	+	9.80012i	0.119739	+	1.13924i
$75$		0			0
$76$	0.708204			0.0812366
$77$	−8.36665	+	2.64559i	−0.953469	+	0.301493i
$78$	−9.47214			−1.07251
$79$	12.4305	−	2.64218i	1.39854	−	0.297269i	0.553891	−	0.832589i	$-0.313142\pi$
$79$	12.4305	−	2.64218i	1.39854	−	0.297269i	0.844649	+	0.535320i	$0.179809\pi$
$80$	1.13456	+	10.7946i	0.126848	+	1.20688i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−2.57890	+	2.86416i	−0.284792	+	0.316293i
$83$	−2.78115	−	8.55951i	−0.305271	−	0.939528i	−0.979576	−	0.201075i	$-0.935557\pi$
$83$	−2.78115	−	8.55951i	−0.305271	−	0.939528i	0.674305	−	0.738453i	$-0.264443\pi$
$84$	−0.693806	+	1.48067i	−0.0757005	+	0.161555i
$85$	−5.85410	+	4.25325i	−0.634967	+	0.461330i
$86$	−0.230909	+	0.0490813i	−0.0248996	+	0.00529257i
$87$	3.92705	−	6.80185i	0.421024	−	0.729235i
$88$	−2.37207	−	7.02661i	−0.252864	−	0.749039i
$89$	−0.763932	−	1.32317i	−0.0809766	−	0.140256i	0.822693	−	0.568486i	$-0.192471\pi$
$89$	−0.763932	−	1.32317i	−0.0809766	−	0.140256i	−0.903670	+	0.428230i	$0.859137\pi$
$90$	−2.23607	+	6.88191i	−0.235702	+	0.725417i
$91$	14.8201	−	4.50083i	1.55357	−	0.471815i
$92$	0.881966	+	0.640786i	0.0919513	+	0.0668065i
$93$	2.93211	−	3.25644i	0.304045	−	0.337677i
$94$	−0.747238	−	0.158830i	−0.0770717	−	0.0163821i
$95$	2.34078	−	1.04218i	0.240159	−	0.106926i
$96$	−3.08958	−	1.37557i	−0.315329	−	0.140393i
$97$	−1.19098	+	3.66547i	−0.120926	+	0.372172i	−0.993137	−	0.116958i	$-0.962686\pi$
$97$	−1.19098	+	3.66547i	−0.120926	+	0.372172i	0.872211	+	0.489130i	$0.162686\pi$
$98$	1.61803	−	11.2101i	0.163446	−	1.13239i
$99$	0.618034	−	6.60440i	0.0621148	−	0.663767i
$100$		0			0
$101$	−10.0973	−	11.2142i	−1.00472	−	1.11585i	−0.993259	−	0.115918i	$-0.963019\pi$
$101$	−10.0973	−	11.2142i	−1.00472	−	1.11585i	−0.0114596	−	0.999934i	$-0.503648\pi$
$102$	−0.547318	−	5.20738i	−0.0541926	−	0.515608i
$103$	−0.627171	+	5.96713i	−0.0617970	+	0.587959i	0.919180	+	0.393837i	$0.128852\pi$
$103$	−0.627171	+	5.96713i	−0.0617970	+	0.587959i	−0.980977	+	0.194122i	$0.937814\pi$
$104$	4.04508	+	12.4495i	0.396653	+	1.22077i
$105$	−0.114256	+	5.91498i	−0.0111502	+	0.577243i
$106$	−7.97214	−	5.79210i	−0.774322	−	0.562578i
$107$	−10.2137	−	4.54745i	−0.987400	−	0.439619i	−0.151474	−	0.988461i	$-0.548402\pi$
$107$	−10.2137	−	4.54745i	−0.987400	−	0.439619i	−0.835926	+	0.548842i	$0.815069\pi$
$108$	−2.06773	−	2.29644i	−0.198967	−	0.220975i
$109$	0.0729490	−	0.126351i	0.00698725	−	0.0121023i	−0.862511	−	0.506039i	$-0.831109\pi$
$109$	0.0729490	−	0.126351i	0.00698725	−	0.0121023i	0.869498	+	0.493937i	$0.164443\pi$
$110$	8.13058	+	8.82527i	0.775221	+	0.841457i
$111$	−6.09017			−0.578053
$112$	12.7441	+	1.58885i	1.20420	+	0.150132i
$113$	−1.69098	+	1.22857i	−0.159074	+	0.115574i	−0.664475	−	0.747311i	$-0.731345\pi$
$113$	−1.69098	+	1.22857i	−0.159074	+	0.115574i	0.505401	+	0.862885i	$0.331345\pi$
$114$	−0.193806	+	1.84395i	−0.0181516	+	0.172701i
$115$	3.85808	+	0.820060i	0.359768	+	0.0764710i
$116$	4.74803	+	1.00922i	0.440843	+	0.0937041i
$117$	−1.22384	+	11.6441i	−0.113144	+	1.07649i
$118$	12.7082	−	9.23305i	1.16988	−	0.849971i
$119$	3.33070	+	7.88742i	0.305325	+	0.723038i
$120$	−5.00000			−0.456435
$121$	−9.04443	−	6.26085i	−0.822221	−	0.569168i
$122$	8.85410	−	15.3358i	0.801613	−	1.38843i
$123$	−1.59385	−	1.77015i	−0.143712	−	0.159609i
$124$	2.47407	+	1.10153i	0.222178	+	0.0989199i
$125$	9.04508	+	6.57164i	0.809017	+	0.587785i
$126$	7.33070	+	4.42332i	0.653071	+	0.394060i
$127$	−0.0729490	−	0.224514i	−0.00647318	−	0.0199224i	0.947768	−	0.318961i	$-0.103334\pi$
$127$	−0.0729490	−	0.224514i	−0.00647318	−	0.0199224i	−0.954241	+	0.299039i	$0.903334\pi$
$128$	−1.42347	+	13.5434i	−0.125818	+	1.19708i
$129$	−0.0152505	−	0.145099i	−0.00134273	−	0.0127752i
$130$	−14.1724	−	15.7401i	−1.24300	−	1.38049i
$131$	−3.16312	−	5.47868i	−0.276363	−	0.478675i	0.694115	−	0.719864i	$-0.255796\pi$
$131$	−3.16312	−	5.47868i	−0.276363	−	0.478675i	−0.970478	+	0.241189i	$0.922463\pi$
$132$	−2.00000	+	0.449028i	−0.174078	+	0.0390829i
$133$	−0.572949	−	2.97713i	−0.0496810	−	0.258150i
$134$	4.19098	−	12.8985i	0.362046	−	1.11426i
$135$	−10.2137	−	4.54745i	−0.879060	−	0.391383i
$136$	−6.61048	+	2.94317i	−0.566844	+	0.252375i
$137$	−0.319109	−	0.0678287i	−0.0272633	−	0.00579500i	0.194260	−	0.980950i	$-0.437770\pi$
$137$	−0.319109	−	0.0678287i	−0.0272633	−	0.00579500i	−0.221523	+	0.975155i	$0.571103\pi$
$138$	−1.90977	+	2.12101i	−0.162570	+	0.180552i
$139$	−3.57295	−	2.59590i	−0.303054	−	0.220181i	0.425857	−	0.904791i	$-0.359973\pi$
$139$	−3.57295	−	2.59590i	−0.303054	−	0.220181i	−0.728910	+	0.684609i	$0.759973\pi$
$140$	−3.49856	+	1.06250i	−0.295682	+	0.0897978i
$141$	0.145898	−	0.449028i	0.0122868	−	0.0378150i
$142$	−0.618034	−	1.07047i	−0.0518643	−	0.0898315i
$143$	15.8370	+	11.2324i	1.32435	+	0.939297i
$144$	−4.85410	+	8.40755i	−0.404508	+	0.700629i
$145$	17.1785	−	3.65141i	1.42660	−	0.303233i
$146$	−14.2082	+	10.3229i	−1.17588	+	0.854326i
$147$	6.78572	+	1.71872i	0.559677	+	0.141757i
$148$	−1.16312	−	3.57971i	−0.0956078	−	0.294251i
$149$	13.7216	−	15.2394i	1.12412	−	1.24846i	0.158817	−	0.987308i	$-0.449232\pi$
$149$	13.7216	−	15.2394i	1.12412	−	1.24846i	0.965299	−	0.261149i	$-0.0841013\pi$
$150$		0			0
$151$	0.482716	+	4.59274i	0.0392829	+	0.373752i	0.996448	+	0.0842093i	$0.0268364\pi$
$151$	0.482716	+	4.59274i	0.0392829	+	0.373752i	−0.957165	+	0.289542i	$0.906497\pi$
$152$	2.50631	−	0.532733i	0.203289	−	0.0432104i
$153$	−6.47214			−0.523241
$154$	12.3517	−	7.00172i	0.995329	−	0.564214i
$155$	9.79837			0.787024
$156$	3.53897	−	0.752232i	0.283344	−	0.0602267i
$157$	1.22967	+	11.6995i	0.0981380	+	0.933721i	0.927201	+	0.374565i	$0.122208\pi$
$157$	1.22967	+	11.6995i	0.0981380	+	0.933721i	−0.829063	+	0.559156i	$0.811125\pi$
$158$	−18.7846	+	8.36344i	−1.49442	+	0.665360i
$159$	4.07512	−	4.52588i	0.323178	−	0.358925i
$160$	−2.33688	−	7.19218i	−0.184747	−	0.568592i
$161$	1.98019	−	4.22599i	0.156061	−	0.333055i
$162$	−1.30902	+	0.951057i	−0.102846	+	0.0747221i
$163$	−18.8157	+	3.99940i	−1.47376	+	0.313257i	−0.873609	−	0.486629i	$-0.838226\pi$
$163$	−18.8157	+	3.99940i	−1.47376	+	0.313257i	−0.600152	+	0.799886i	$0.704893\pi$
$164$	0.736068	−	1.27491i	0.0574773	−	0.0995535i
$165$	−5.94969	+	4.42732i	−0.463183	+	0.344666i
$166$	7.28115	+	12.6113i	0.565127	+	0.978829i
$167$	−4.61803	+	14.2128i	−0.357354	+	1.09982i	0.597278	+	0.802035i	$0.296249\pi$
$167$	−4.61803	+	14.2128i	−0.357354	+	1.09982i	−0.954632	+	0.297789i	$0.903751\pi$
$168$	−1.34155	+	5.76196i	−0.103503	+	0.444545i
$169$	−17.2082	−	12.5025i	−1.32371	−	0.961730i
$170$	7.83432	−	8.70089i	0.600865	−	0.667328i
$171$	2.24171	+	0.476491i	0.171428	+	0.0364382i
$172$	0.0823743	−	0.0366754i	0.00628098	−	0.00279647i
$173$	−9.61768	−	4.28207i	−0.731219	−	0.325560i	0.00713369	−	0.999975i	$-0.497729\pi$
$173$	−9.61768	−	4.28207i	−0.731219	−	0.325560i	−0.738353	+	0.674415i	$0.764396\pi$
$174$	−3.92705	+	12.0862i	−0.297709	+	0.916254i
$175$		0			0
$176$	8.20820	+	13.8496i	0.618717	+	1.04395i
$177$	4.85410	+	8.40755i	0.364857	+	0.631950i
$178$	1.65418	+	1.83716i	0.123986	+	0.137701i
$179$	−2.14352	−	20.3942i	−0.160214	−	1.52434i	−0.718991	−	0.695019i	$-0.755396\pi$
$179$	−2.14352	−	20.3942i	−0.160214	−	1.52434i	0.558777	−	0.829318i	$-0.311271\pi$
$180$	0.288910	−	2.74879i	0.0215340	−	0.204883i
$181$	−6.54508	−	20.1437i	−0.486492	−	1.49727i	−0.829808	−	0.558049i	$-0.811550\pi$
$181$	−6.54508	−	20.1437i	−0.486492	−	1.49727i	0.343315	−	0.939220i	$-0.388450\pi$
$182$	−21.9413	+	12.1090i	−1.62640	+	0.897577i
$183$	8.85410	+	6.43288i	0.654514	+	0.475532i
$184$	3.60327	+	1.60428i	0.265637	+	0.118269i
$185$	−9.11224	−	10.1202i	−0.669945	−	0.744050i
$186$	−3.54508	+	6.14027i	−0.259938	+	0.450226i
$187$	−5.25999	+	9.35553i	−0.384648	+	0.684144i
$188$	0.291796			0.0212814
$189$	−7.98091	+	10.5501i	−0.580526	+	0.767409i
$190$	−3.35410	+	2.43690i	−0.243332	+	0.176791i
$191$	−1.48807	+	14.1581i	−0.107673	+	1.02444i	0.798632	+	0.601819i	$0.205557\pi$
$191$	−1.48807	+	14.1581i	−0.107673	+	1.02444i	−0.906305	+	0.422623i	$0.861109\pi$
$192$	−4.14350	−	0.880728i	−0.299031	−	0.0635611i
$193$	17.7831	+	3.77991i	1.28005	+	0.272084i	0.797252	−	0.603647i	$-0.206286\pi$
$193$	17.7831	+	3.77991i	1.28005	+	0.272084i	0.482801	+	0.875730i	$0.339620\pi$
$194$	0.651847	−	6.20191i	0.0467999	−	0.445271i
$195$	10.5902	−	7.69421i	0.758378	−	0.550994i
$196$	0.285721	+	4.31679i	0.0204087	+	0.308342i
$197$	2.38197			0.169708			0.0848540	−	0.996393i	$-0.472958\pi$
$197$	2.38197			0.169708			0.0848540	+	0.996393i	$0.472958\pi$
$198$	1.24362	+	10.6605i	0.0883806	+	0.757611i
$199$	−10.7812	+	18.6735i	−0.764256	+	1.32373i	0.176384	+	0.984322i	$0.443560\pi$
$199$	−10.7812	+	18.6735i	−0.764256	+	1.32373i	−0.940639	+	0.339408i	$0.889773\pi$
$200$		0			0
$201$	7.65731	+	3.40925i	0.540105	+	0.240470i
$202$	19.7533	+	14.3516i	1.38984	+	1.00978i
$203$	0.401318	−	20.7761i	0.0281670	−	1.45820i
$204$	0.618034	+	1.90211i	0.0432710	+	0.133175i
$205$	0.556743	−	5.29706i	0.0388847	−	0.369963i
$206$	−1.01478	−	9.65502i	−0.0707033	−	0.672697i
$207$	2.36060	+	2.62171i	0.164073	+	0.182222i
$208$	−14.2082	−	24.6093i	−0.985162	−	1.70635i
$209$	2.51064	−	2.85317i	0.173665	−	0.197358i
$210$	−1.80902	−	9.39993i	−0.124834	−	0.648657i
$211$	−2.78115	+	8.55951i	−0.191462	+	0.589261i	0.808537	+	0.588445i	$0.200260\pi$
$211$	−2.78115	+	8.55951i	−0.191462	+	0.589261i	−1.00000		0.000815813i	$0.999740\pi$
$212$	3.43852	+	1.53093i	0.236159	+	0.105145i
$213$	0.697887	−	0.310719i	0.0478184	−	0.0212901i
$214$	17.6949	+	3.76116i	1.20960	+	0.257107i
$215$	0.218296	−	0.242442i	0.0148876	−	0.0165344i
$216$	−9.04508	−	6.57164i	−0.615440	−	0.447143i
$217$	2.62900	−	11.2916i	0.178468	−	0.766522i
$218$	−0.0729490	+	0.224514i	−0.00494073	+	0.0152060i
$219$	−5.42705	−	9.39993i	−0.366726	−	0.635188i
$220$	−3.73860	−	2.65160i	−0.252057	−	0.178771i
$221$	9.47214	−	16.4062i	0.637165	−	1.10360i
$222$	9.63877	−	2.04878i	0.646912	−	0.137505i
$223$	15.4894	−	11.2537i	1.03724	−	0.753602i	0.0674984	−	0.997719i	$-0.478498\pi$
$223$	15.4894	−	11.2537i	1.03724	−	0.753602i	0.969746	+	0.244117i	$0.0784982\pi$
$224$	−8.91523	+	0.763269i	−0.595674	+	0.0509981i
$225$		0			0
$226$	2.26298	−	2.51329i	0.150531	−	0.167182i
$227$	6.77523	−	3.01652i	0.449688	−	0.200214i	−0.169381	−	0.985551i	$-0.554177\pi$
$227$	6.77523	−	3.01652i	0.449688	−	0.200214i	0.619069	+	0.785337i	$0.287510\pi$
$228$	−0.0740275	−	0.704324i	−0.00490259	−	0.0466450i
$229$	−5.72618	+	1.21714i	−0.378396	+	0.0804306i	−0.393183	−	0.919460i	$-0.628626\pi$
$229$	−5.72618	+	1.21714i	−0.378396	+	0.0804306i	0.0147871	+	0.999891i	$0.495293\pi$
$230$	−6.38197			−0.420814
$231$	3.50565	+	8.04428i	0.230655	+	0.529275i
$232$	17.5623			1.15302
$233$	3.02264	−	0.642482i	0.198020	−	0.0420904i	−0.107834	−	0.994169i	$-0.534391\pi$
$233$	3.02264	−	0.642482i	0.198020	−	0.0420904i	0.305854	+	0.952079i	$0.401058\pi$
$234$	−1.98022	−	18.8405i	−0.129451	−	1.23164i
$235$	0.964456	−	0.429403i	0.0629141	−	0.0280112i
$236$	−4.01478	+	4.45887i	−0.261340	+	0.290248i
$237$	−3.92705	−	12.0862i	−0.255089	−	0.785084i
$238$	−7.92482	−	11.3628i	−0.513690	−	0.736538i
$239$	−10.2812	+	7.46969i	−0.665032	+	0.483174i	−0.868359	−	0.495937i	$-0.834825\pi$
$239$	−10.2812	+	7.46969i	−0.665032	+	0.483174i	0.203326	+	0.979111i	$0.434825\pi$
$240$	10.6169	−	2.25669i	0.685319	−	0.145669i
$241$	0.791796	−	1.37143i	0.0510041	−	0.0883416i	−0.839396	−	0.543520i	$-0.817091\pi$
$241$	0.791796	−	1.37143i	0.0510041	−	0.0883416i	0.890400	+	0.455178i	$0.150425\pi$
$242$	16.4206	+	6.86628i	1.05556	+	0.441381i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−2.09017	+	6.43288i	−0.133809	+	0.411823i
$245$	7.29691	+	13.8476i	0.466183	+	0.884688i
$246$	3.11803	+	2.26538i	0.198799	+	0.144436i
$247$	−4.48866	+	4.98517i	−0.285607	+	0.317199i
$248$	9.58426	+	2.03720i	0.608601	+	0.129362i
$249$	−8.22191	+	3.66063i	−0.521042	+	0.231983i
$250$	−16.5262	−	7.35793i	−1.04521	−	0.465357i
$251$	0.517221	−	1.59184i	0.0326467	−	0.100476i	−0.933405	−	0.358824i	$-0.883178\pi$
$251$	0.517221	−	1.59184i	0.0326467	−	0.100476i	0.966052	+	0.258347i	$0.0831779\pi$
$252$	−3.09017	−	1.07047i	−0.194662	−	0.0674330i
$253$	5.70820	−	1.28157i	0.358872	−	0.0805717i
$254$	0.190983	+	0.330792i	0.0119833	+	0.0207558i
$255$	4.84187	+	5.37745i	0.303210	+	0.336749i
$256$	−1.41765	−	13.4880i	−0.0886029	−	0.843001i
$257$	1.24852	−	11.8788i	0.0778803	−	0.740982i	−0.883996	−	0.467495i	$-0.845156\pi$
$257$	1.24852	−	11.8788i	0.0778803	−	0.740982i	0.961876	−	0.273486i	$-0.0881768\pi$
$258$	0.0729490	+	0.224514i	0.00454161	+	0.0139776i
$259$	−14.1073	+	7.78554i	−0.876586	+	0.483770i
$260$	6.54508	+	4.75528i	0.405909	+	0.294910i
$261$	14.3502	+	6.38910i	0.888253	+	0.395475i
$262$	6.84927	+	7.60688i	0.423149	+	0.469955i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	−6.74017	+	3.09356i	−0.414829	+	0.190395i
$265$	13.6180			0.836549
$266$	1.90832	+	4.51909i	0.117007	+	0.277083i
$267$	−1.23607	+	0.898056i	−0.0756461	+	0.0549601i
$268$	−0.541493	+	5.15196i	−0.0330769	+	0.314706i
$269$	−19.3112	−	4.10473i	−1.17743	−	0.250270i	−0.422675	−	0.906281i	$-0.638909\pi$
$269$	−19.3112	−	4.10473i	−1.17743	−	0.250270i	−0.754751	+	0.656012i	$0.772242\pi$
$270$	17.6949	+	3.76116i	1.07687	+	0.228897i
$271$	−1.58095	+	15.0418i	−0.0960360	+	0.913722i	0.835357	+	0.549707i	$0.185261\pi$
$271$	−1.58095	+	15.0418i	−0.0960360	+	0.913722i	−0.931393	+	0.364014i	$0.881406\pi$
$272$	12.7082	−	9.23305i	0.770548	−	0.559836i
$273$	−6.02530	−	14.2685i	−0.364668	−	0.863567i
$274$	0.527864			0.0318894
$275$		0			0
$276$	0.545085	−	0.944115i	0.0328103	−	0.0568290i
$277$	0.473881	+	0.526298i	0.0284727	+	0.0316222i	0.757213	−	0.653168i	$-0.226560\pi$
$277$	0.473881	+	0.526298i	0.0284727	+	0.0316222i	−0.728740	+	0.684790i	$0.759894\pi$
$278$	6.52810	+	2.90650i	0.391530	+	0.174320i
$279$	7.09017	+	5.15131i	0.424477	+	0.308401i
$280$	−11.5820	+	6.39189i	−0.692160	+	0.381988i
$281$	1.43769	+	4.42477i	0.0857656	+	0.263959i	0.984737	−	0.174047i	$-0.0556846\pi$
$281$	1.43769	+	4.42477i	0.0857656	+	0.263959i	−0.898972	+	0.438007i	$0.855685\pi$
$282$	−0.0798526	+	0.759747i	−0.00475516	+	0.0452423i
$283$	2.13410	+	20.3046i	0.126859	+	1.20698i	0.853918	+	0.520407i	$0.174220\pi$
$283$	2.13410	+	20.3046i	0.126859	+	1.20698i	−0.727060	+	0.686574i	$0.759114\pi$
$284$	0.315921	+	0.350865i	0.0187464	+	0.0208200i
$285$	−1.28115	−	2.21902i	−0.0758890	−	0.131444i
$286$	−28.8435	−	12.4495i	−1.70555	−	0.736154i
$287$	−5.95492	−	2.06284i	−0.351508	−	0.121766i
$288$	2.09017	−	6.43288i	0.123164	−	0.379061i
$289$	−5.96350	−	2.65512i	−0.350794	−	0.156184i
$290$	−25.9597	+	11.5580i	−1.52440	+	0.678709i
$291$	3.76988	+	0.801313i	0.220994	+	0.0469738i
$292$	4.48866	−	4.98517i	0.262679	−	0.291735i
$293$	10.0902	+	7.33094i	0.589474	+	0.428278i	0.842127	−	0.539279i	$-0.181303\pi$
$293$	10.0902	+	7.33094i	0.589474	+	0.428278i	−0.252653	+	0.967557i	$0.581303\pi$
$294$	−11.3178	−	0.437399i	−0.660067	−	0.0255096i
$295$	−6.70820	+	20.6457i	−0.390567	+	1.20204i
$296$	−6.80902	−	11.7936i	−0.395766	−	0.685487i
$297$	−16.5820	+	0.189247i	−0.962188	+	0.0109812i
$298$	−16.5902	+	28.7350i	−0.961043	+	1.66457i
$299$	−10.1006	+	2.14695i	−0.584132	+	0.124161i
$300$		0			0
$301$	−0.220817	−	0.316612i	−0.0127277	−	0.0182492i
$302$	−2.30902	−	7.10642i	−0.132869	−	0.408929i
$303$	−10.0973	+	11.2142i	−0.580074	+	0.644238i
$304$	−5.08142	+	2.26239i	−0.291439	+	0.129757i
$305$	2.55803	+	24.3381i	0.146473	+	1.39359i
$306$	10.2433	−	2.17728i	0.585570	−	0.124467i
$307$	13.5066			0.770861			0.385431	−	0.922737i	$-0.374053\pi$
$307$	13.5066			0.770861			0.385431	+	0.922737i	$0.374053\pi$
$308$	−4.05879	+	3.59689i	−0.231271	+	0.204952i
$309$	6.00000			0.341328
$310$	−15.5077	+	3.29625i	−0.880775	+	0.187215i
$311$	1.39657	+	13.2875i	0.0791923	+	0.753464i	0.960002	+	0.279994i	$0.0903324\pi$
$311$	1.39657	+	13.2875i	0.0791923	+	0.753464i	−0.880810	+	0.473471i	$0.843001\pi$
$312$	11.9585	−	5.32425i	0.677015	−	0.301426i
$313$	4.64662	−	5.16060i	0.262643	−	0.291694i	−0.597371	−	0.801965i	$-0.703788\pi$
$313$	4.64662	−	5.16060i	0.262643	−	0.291694i	0.860014	+	0.510271i	$0.170455\pi$
$314$	−5.88197	−	18.1028i	−0.331939	−	1.02160i
$315$	−11.7890	+	1.00931i	−0.664237	+	0.0568680i
$316$	6.35410	−	4.61653i	0.357446	−	0.259700i
$317$	0.373619	−	0.0794152i	0.0209845	−	0.00446040i	−0.197407	−	0.980322i	$-0.563252\pi$
$317$	0.373619	−	0.0794152i	0.0209845	−	0.00446040i	0.218392	+	0.975861i	$0.429919\pi$
$318$	−4.92705	+	8.53390i	−0.276295	+	0.478557i
$319$	20.8981	−	15.5508i	1.17007	−	0.870677i
$320$	−4.73607	−	8.20311i	−0.264754	−	0.458568i
$321$	−3.45492	+	10.6331i	−0.192835	+	0.593484i
$322$	−1.71235	+	7.35453i	−0.0954254	+	0.409852i
$323$	−3.00000	−	2.17963i	−0.166924	−	0.121278i
$324$	0.413545	−	0.459289i	0.0229747	−	0.0255160i
$325$		0			0
$326$	28.4337	−	12.6595i	1.57480	−	0.701146i
$327$	−0.133284	−	0.0593421i	−0.00737065	−	0.00328162i
$328$	1.64590	−	5.06555i	0.0908795	−	0.279698i
$329$	−0.236068	−	1.22665i	−0.0130148	−	0.0676271i
$330$	7.92705	−	9.00854i	0.436370	−	0.495904i
$331$	0.645898	+	1.11873i	0.0355018	+	0.0614909i	0.883230	−	0.468939i	$-0.155364\pi$
$331$	0.645898	+	1.11873i	0.0355018	+	0.0614909i	−0.847729	+	0.530430i	$0.822030\pi$
$332$	−3.72191	−	4.13360i	−0.204266	−	0.226861i
$333$	−1.27319	−	12.1136i	−0.0697705	−	0.663822i
$334$	2.52753	−	24.0479i	0.138300	−	1.31584i
$335$	5.79180	+	17.8253i	0.316440	+	0.973901i
$336$	0.248028	−	12.8404i	0.0135310	−	0.700499i
$337$	−11.8992	−	8.64527i	−0.648190	−	0.470938i	0.214464	−	0.976732i	$-0.431199\pi$
$337$	−11.8992	−	8.64527i	−0.648190	−	0.470938i	−0.862654	+	0.505794i	$0.831199\pi$
$338$	31.4410	+	13.9984i	1.71016	+	0.761413i
$339$	1.39860	+	1.55330i	0.0759613	+	0.0843636i
$340$	−2.23607	+	3.87298i	−0.121268	+	0.210042i
$341$	13.2085	−	6.06237i	0.715283	−	0.328296i
$342$	−3.70820			−0.200517
$343$	17.9157	−	4.69347i	0.967355	−	0.253423i
$344$	0.263932	−	0.191758i	0.0142303	−	0.0103389i
$345$	0.412289	−	3.92266i	0.0221969	−	0.211189i
$346$	16.6622	+	3.54166i	0.895765	+	0.190401i
$347$	−32.9716	−	7.00833i	−1.77001	−	0.376227i	−0.796457	−	0.604695i	$-0.793295\pi$
$347$	−32.9716	−	7.00833i	−1.77001	−	0.376227i	−0.973551	+	0.228469i	$0.926628\pi$
$348$	0.507392	−	4.82751i	0.0271991	−	0.258782i
$349$	−24.0623	+	17.4823i	−1.28803	+	0.935805i	−0.999764	−	0.0217461i	$-0.993077\pi$
$349$	−24.0623	+	17.4823i	−1.28803	+	0.935805i	−0.288262	+	0.957552i	$0.593077\pi$
$350$		0			0
$351$	29.2705			1.56234
$352$	−7.60008	−	8.24945i	−0.405086	−	0.439697i
$353$	−2.23607	+	3.87298i	−0.119014	+	0.206138i	−0.919377	−	0.393377i	$-0.871307\pi$
$353$	−2.23607	+	3.87298i	−0.119014	+	0.206138i	0.800363	+	0.599515i	$0.204640\pi$
$354$	−10.5108	−	11.6735i	−0.558645	−	0.620438i
$355$	1.56052	+	0.694789i	0.0828239	+	0.0368756i
$356$	−0.763932	−	0.555029i	−0.0404883	−	0.0294165i
$357$	7.49606	−	4.13692i	0.396733	−	0.218949i
$358$	10.2533	+	31.5564i	0.541903	+	1.66781i
$359$	0.974857	−	9.27515i	0.0514510	−	0.489524i	−0.938207	−	0.346075i	$-0.887514\pi$
$359$	0.974857	−	9.27515i	0.0514510	−	0.489524i	0.989658	−	0.143448i	$-0.0458191\pi$
$360$	−1.04528	−	9.94522i	−0.0550913	−	0.524159i
$361$	−11.8349	−	13.1439i	−0.622887	−	0.691786i
$362$	17.1353	+	29.6791i	0.900609	+	1.55990i
$363$	−5.28115	+	9.64932i	−0.277189	+	0.506458i
$364$	7.23607	−	6.26662i	0.379273	−	0.328460i
$365$	7.50000	−	23.0826i	0.392568	−	1.20820i
$366$	−16.1772	−	7.20258i	−0.845598	−	0.376485i
$367$	24.9129	−	11.0919i	1.30044	−	0.578993i	0.364517	−	0.931197i	$-0.381234\pi$
$367$	24.9129	−	11.0919i	1.30044	−	0.578993i	0.935923	+	0.352204i	$0.114568\pi$
$368$	−8.37520	−	1.78020i	−0.436587	−	0.0927995i
$369$	3.18769	−	3.54029i	0.165945	−	0.184300i
$370$	17.8262	+	12.9515i	0.926742	+	0.673317i
$371$	3.65386	−	15.6933i	0.189699	−	0.814757i
$372$	0.836881	−	2.57565i	0.0433903	−	0.133541i
$373$	11.7984	+	20.4354i	0.610897	+	1.05810i	0.991090	+	0.133197i	$0.0425242\pi$
$373$	11.7984	+	20.4354i	0.610897	+	1.05810i	−0.380193	+	0.924907i	$0.624142\pi$
$374$	5.17758	−	16.5763i	0.267726	−	0.857139i
$375$	5.59017	−	9.68246i	0.288675	−	0.500000i
$376$	1.03266	−	0.219498i	0.0532553	−	0.0113198i
$377$	−37.1976	+	27.0256i	−1.91577	+	1.39189i
$378$	9.08204	−	19.3823i	0.467130	−	0.996916i
$379$	6.70820	+	20.6457i	0.344577	+	1.06050i	0.961810	+	0.273719i	$0.0882538\pi$
$379$	6.70820	+	20.6457i	0.344577	+	1.06050i	−0.617232	+	0.786781i	$0.711746\pi$
$380$	1.05963	−	1.17684i	0.0543579	−	0.0603705i
$381$	−0.215659	+	0.0960175i	−0.0110485	+	0.00491913i
$382$	−2.40775	−	22.9083i	−0.123191	−	1.17209i
$383$	22.3002	−	4.74005i	1.13949	−	0.242205i	0.400742	−	0.916191i	$-0.368753\pi$
$383$	22.3002	−	4.74005i	1.13949	−	0.242205i	0.738744	+	0.673986i	$0.235419\pi$
$384$	13.6180			0.694942
$385$	−8.12214	+	17.8614i	−0.413942	+	0.910303i
$386$	−29.4164			−1.49726
$387$	0.285420	−	0.0606678i	0.0145087	−	0.00308392i
$388$	0.248983	+	2.36892i	0.0126402	+	0.120264i
$389$	−21.4938	+	9.56964i	−1.08978	+	0.485200i	−0.871355	−	0.490654i	$-0.836758\pi$
$389$	−21.4938	+	9.56964i	−1.08978	+	0.485200i	−0.218423	+	0.975854i	$0.570091\pi$
$390$	−14.1724	+	15.7401i	−0.717648	+	0.797029i
$391$	−1.76393	−	5.42882i	−0.0892059	−	0.274547i
$392$	4.25839	+	15.0621i	0.215081	+	0.760750i
$393$	−5.11803	+	3.71847i	−0.258171	+	0.187572i
$394$	−3.76988	+	0.801313i	−0.189924	+	0.0403696i
$395$	14.2082	−	24.6093i	0.714892	−	1.23823i
$396$	−1.31125	−	3.88422i	−0.0658928	−	0.195189i
$397$	−17.3435	−	30.0398i	−0.870443	−	1.50765i	−0.861539	−	0.507692i	$-0.830499\pi$
$397$	−17.3435	−	30.0398i	−0.870443	−	1.50765i	−0.00890435	−	0.999960i	$-0.502834\pi$
$398$	10.7812	−	33.1810i	0.540410	−	1.66321i
$399$	−2.90093	+	0.881005i	−0.145228	+	0.0441054i
$400$		0			0
$401$	−12.0071	+	13.3352i	−0.599604	+	0.665928i	−0.964181	−	0.265246i	$-0.914547\pi$
$401$	−12.0071	+	13.3352i	−0.599604	+	0.665928i	0.364577	+	0.931173i	$0.381214\pi$
$402$	−13.2659	−	2.81976i	−0.661645	−	0.140637i
$403$	−23.4347	+	10.4338i	−1.16737	+	0.519745i
$404$	−8.51994	−	3.79332i	−0.423883	−	0.188725i
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$	6.35410	+	33.0169i	0.315349	+	1.63860i
$407$	−18.5451	−	8.00448i	−0.919246	−	0.396767i
$408$	3.61803	+	6.26662i	0.179119	+	0.310244i
$409$	−16.8489	−	18.7126i	−0.833126	−	0.925280i	0.165011	−	0.986292i	$-0.447234\pi$
$409$	−16.8489	−	18.7126i	−0.833126	−	0.925280i	−0.998137	+	0.0610113i	$0.980567\pi$
$410$	0.900830	+	8.57082i	0.0444888	+	0.423283i
$411$	−0.0341011	+	0.324451i	−0.00168209	+	0.0160040i
$412$	1.14590	+	3.52671i	0.0564543	+	0.173749i
$413$	21.9921	+	13.2699i	1.08216	+	0.652971i
$414$	−4.61803	−	3.35520i	−0.226964	−	0.164899i
$415$	−18.3847	−	8.18542i	−0.902472	−	0.401806i
$416$	13.2477	+	14.7131i	0.649522	+	0.721367i
$417$	−2.20820	+	3.82472i	−0.108136	+	0.187297i
$418$	−3.01371	+	5.36024i	−0.147405	+	0.262178i
$419$	23.1803			1.13243			0.566217	−	0.824256i	$-0.308406\pi$
$419$	23.1803			1.13243			0.566217	+	0.824256i	$0.308406\pi$
$420$	1.42238	+	3.36833i	0.0694051	+	0.164358i
$421$	22.4164	−	16.2865i	1.09251	−	0.793754i	0.112688	−	0.993630i	$-0.464054\pi$
$421$	22.4164	−	16.2865i	1.09251	−	0.793754i	0.979821	+	0.199876i	$0.0640540\pi$
$422$	1.52218	−	14.4825i	0.0740983	−	0.704999i
$423$	0.923637	+	0.196325i	0.0449088	+	0.00954566i
$424$	13.3204	+	2.83135i	0.646898	+	0.137502i
$425$		0			0
$426$	−1.00000	+	0.726543i	−0.0484502	+	0.0352011i
$427$	28.7334	+	3.58229i	1.39051	+	0.173359i
$428$	−6.90983			−0.333999
$429$	9.51541	−	16.9243i	0.459408	−	0.817114i
$430$	−0.263932	+	0.457144i	−0.0127279	+	0.0220454i
$431$	−11.9698	−	13.2938i	−0.576564	−	0.640339i	0.382357	−	0.924015i	$-0.375113\pi$
$431$	−11.9698	−	13.2938i	−0.576564	−	0.640339i	−0.958920	+	0.283676i	$0.908446\pi$
$432$	22.1722	+	9.87171i	1.06676	+	0.474953i
$433$	11.6631	+	8.47375i	0.560494	+	0.407223i	0.831640	−	0.555316i	$-0.187403\pi$
$433$	11.6631	+	8.47375i	0.560494	+	0.407223i	−0.271146	+	0.962538i	$0.587403\pi$
$434$	−0.362284	+	18.7553i	−0.0173902	+	0.900285i
$435$	−5.42705	−	16.7027i	−0.260207	−	0.800835i
$436$	0.00942533	−	0.0896760i	0.000451391	−	0.00429470i
$437$	0.211282	+	2.01021i	0.0101070	+	0.0961615i
$438$	11.7515	+	13.0513i	0.561507	+	0.623617i
$439$	3.90983	+	6.77202i	0.186606	+	0.323211i	0.944117	−	0.329612i	$-0.106918\pi$
$439$	3.90983	+	6.77202i	0.186606	+	0.323211i	−0.757511	+	0.652823i	$0.773585\pi$
$440$	−15.2254	−	6.57164i	−0.725844	−	0.313291i
$441$	−2.00000	+	13.8564i	−0.0952381	+	0.659829i
$442$	−9.47214	+	29.1522i	−0.450544	+	1.38663i
$443$	13.0053	+	5.79033i	0.617900	+	0.275107i	0.691721	−	0.722165i	$-0.256853\pi$
$443$	13.0053	+	5.79033i	0.617900	+	0.275107i	−0.0738210	+	0.997272i	$0.523519\pi$
$444$	−3.43852	+	1.53093i	−0.163185	+	0.0726547i
$445$	−3.34175	−	0.710311i	−0.158414	−	0.0336720i
$446$	−20.7288	+	23.0217i	−0.981537	+	1.09011i
$447$	−16.5902	−	12.0535i	−0.784688	−	0.570109i
$448$	−10.7239	+	3.25683i	−0.506659	+	0.153871i
$449$	8.57953	−	26.4051i	0.404893	−	1.24613i	−0.516092	−	0.856533i	$-0.672614\pi$
$449$	8.57953	−	26.4051i	0.404893	−	1.24613i	0.920985	−	0.389599i	$-0.127386\pi$
$450$		0			0
$451$	−2.52685	−	7.48508i	−0.118985	−	0.352459i
$452$	−0.645898	+	1.11873i	−0.0303805	+	0.0526205i
$453$	4.51712	−	0.960143i	0.212233	−	0.0451115i
$454$	−9.70820	+	7.05342i	−0.455629	+	0.331034i
$455$	14.6951	−	31.3612i	0.688915	−	1.47023i
$456$	−0.791796	−	2.43690i	−0.0370792	−	0.114118i
$457$	4.78154	−	5.31044i	0.223671	−	0.248412i	−0.620856	−	0.783924i	$-0.713215\pi$
$457$	4.78154	−	5.31044i	0.223671	−	0.248412i	0.844527	+	0.535513i	$0.179882\pi$
$458$	8.65323	−	3.85266i	0.404339	−	0.180023i
$459$	1.69131	+	16.0917i	0.0789434	+	0.751096i
$460$	2.38442	−	0.506825i	0.111174	−	0.0236308i
$461$	−7.90983			−0.368398			−0.184199	−	0.982889i	$-0.558969\pi$
$461$	−7.90983			−0.368398			−0.184199	+	0.982889i	$0.558969\pi$
$462$	−8.25446	−	11.5522i	−0.384032	−	0.537455i
$463$	−38.5967			−1.79374			−0.896871	−	0.442291i	$-0.854166\pi$
$463$	−38.5967			−1.79374			−0.896871	+	0.442291i	$0.854166\pi$
$464$	−37.2915	+	7.92655i	−1.73121	+	0.367981i
$465$	−1.02421	−	9.74470i	−0.0474966	−	0.451900i
$466$	−4.56773	+	2.03368i	−0.211596	+	0.0942086i
$467$	−1.69147	+	1.87857i	−0.0782720	+	0.0869298i	−0.781009	−	0.624520i	$-0.785295\pi$
$467$	−1.69147	+	1.87857i	−0.0782720	+	0.0869298i	0.702737	+	0.711450i	$0.251961\pi$
$468$	2.23607	+	6.88191i	0.103362	+	0.318116i
$469$	22.0958	−	1.89171i	1.02029	−	0.0873510i
$470$	−1.38197	+	1.00406i	−0.0637453	+	0.0463137i
$471$	11.5069	−	2.44586i	0.530208	−	0.112699i
$472$	−10.8541	+	18.7999i	−0.499601	+	0.865334i
$473$	0.144268	−	0.461882i	0.00663346	−	0.0212374i
$474$	10.2812	+	17.8075i	0.472229	+	0.817925i
$475$		0			0
$476$	3.86324	+	3.61599i	0.177071	+	0.165739i
$477$	9.85410	+	7.15942i	0.451188	+	0.327808i
$478$	13.7589	−	15.2808i	0.629316	−	0.698926i
$479$	14.0677	+	2.99018i	0.642769	+	0.136625i	0.517753	−	0.855530i	$-0.326769\pi$
$479$	14.0677	+	2.99018i	0.642769	+	0.136625i	0.125016	+	0.992155i	$0.460102\pi$
$480$	−6.90851	+	3.07587i	−0.315329	+	0.140393i
$481$	32.5702	+	14.5012i	1.48507	+	0.661196i
$482$	−0.791796	+	2.43690i	−0.0360653	+	0.110998i
$483$	−4.40983	−	1.52761i	−0.200654	−	0.0695087i
$484$	−6.68034	−	1.26133i	−0.303652	−	0.0573331i
$485$	4.30902	+	7.46344i	0.195662	+	0.338897i
$486$	17.3228	+	19.2389i	0.785779	+	0.872696i
$487$	0.885579	+	8.42572i	0.0401294	+	0.381806i	0.996092	+	0.0883184i	$0.0281493\pi$
$487$	0.885579	+	8.42572i	0.0401294	+	0.381806i	−0.955963	+	0.293488i	$0.905184\pi$
$488$	−2.55803	+	24.3381i	−0.115797	+	1.10173i
$489$	5.94427	+	18.2946i	0.268809	+	0.827310i
$490$	−16.2071	−	19.4615i	−0.732161	−	0.879180i
$491$	−10.0623	−	7.31069i	−0.454106	−	0.329927i	0.337109	−	0.941466i	$-0.390551\pi$
$491$	−10.0623	−	7.31069i	−0.454106	−	0.329927i	−0.791215	+	0.611539i	$0.790551\pi$
$492$	−1.34486	−	0.598772i	−0.0606311	−	0.0269947i
$493$	−17.0069	−	18.8881i	−0.765952	−	0.850676i
$494$	5.42705	−	9.39993i	0.244175	−	0.422923i
$495$	−10.0500	−	10.9086i	−0.451712	−	0.490307i
$496$	−21.2705			−0.955074
$497$	1.21937	−	1.61192i	0.0546964	−	0.0723043i
$498$	11.7812	−	8.55951i	0.527926	−	0.383561i
$499$	0.374587	−	3.56396i	0.0167688	−	0.159545i	−0.982933	−	0.183964i	$-0.941107\pi$
$499$	0.374587	−	3.56396i	0.0167688	−	0.159545i	0.999702	+	0.0244193i	$0.00777366\pi$
$500$	6.75883	+	1.43663i	0.302264	+	0.0642482i
$501$	14.6177	+	3.10709i	0.653071	+	0.138814i
$502$	−0.283084	+	2.69337i	−0.0126347	+	0.120211i
$503$	22.6074	−	16.4252i	1.00801	−	0.732365i	0.0442222	−	0.999022i	$-0.485919\pi$
$503$	22.6074	−	16.4252i	1.00801	−	0.732365i	0.963792	+	0.266657i	$0.0859190\pi$
$504$	−11.7413	−	1.46383i	−0.522997	−	0.0652040i
$505$	−33.7426			−1.50153
$506$	−8.60311	+	3.94860i	−0.382455	+	0.175537i
$507$	−10.6353	+	18.4208i	−0.472328	+	0.818097i
$508$	−0.0976248	−	0.108423i	−0.00433140	−	0.00481051i
$509$	0.247123	+	0.110026i	0.0109535	+	0.00487683i	0.412206	−	0.911091i	$-0.364758\pi$
$509$	0.247123	+	0.110026i	0.0109535	+	0.00487683i	−0.401253	+	0.915967i	$0.631425\pi$
$510$	−9.47214	−	6.88191i	−0.419433	−	0.304736i
$511$	−24.5879	−	14.8363i	−1.08771	−	0.656317i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$	0.598895	−	5.69810i	0.0264419	−	0.251577i
$514$	2.02014	+	19.2204i	0.0891046	+	0.847774i
$515$	8.97733	+	9.97033i	0.395588	+	0.439345i
$516$	−0.0450850	−	0.0780895i	−0.00198476	−	0.00343770i
$517$	1.03444	−	1.17557i	0.0454947	−	0.0517015i
$518$	19.7082	−	17.0678i	0.865929	−	0.749916i
$519$	−3.25329	+	10.0126i	−0.142804	+	0.439504i
$520$	26.7399	+	11.9054i	1.17262	+	0.522086i
$521$	40.2275	−	17.9104i	1.76240	−	0.784670i	0.773923	−	0.633280i	$-0.218292\pi$
$521$	40.2275	−	17.9104i	1.76240	−	0.784670i	0.988474	−	0.151390i	$-0.0483750\pi$
$522$	−24.8610	−	5.28437i	−1.08814	−	0.231291i
$523$	−16.5561	+	18.3874i	−0.723946	+	0.804024i	−0.986994	−	0.160759i	$-0.948606\pi$
$523$	−16.5561	+	18.3874i	−0.723946	+	0.804024i	0.263048	+	0.964783i	$0.415272\pi$
$524$	−3.16312	−	2.29814i	−0.138181	−	0.100395i
$525$		0			0
$526$	6.00000	−	18.4661i	0.261612	−	0.805160i
$527$	−7.09017	−	12.2805i	−0.308853	−	0.534948i
$528$	12.9157	−	9.61091i	0.562084	−	0.418261i
$529$	9.94427	−	17.2240i	0.432360	−	0.748869i
$530$	−21.5529	+	4.58122i	−0.936200	+	0.198995i
$531$	−15.7082	+	11.4127i	−0.681678	+	0.495268i
$532$	−1.07187	−	1.53687i	−0.0464715	−	0.0666317i
$533$	4.30902	+	13.2618i	0.186644	+	0.574432i
$534$	1.65418	−	1.83716i	0.0715834	−	0.0795015i
$535$	−22.8386	+	10.1684i	−0.987400	+	0.439619i
$536$	1.95914	+	18.6400i	0.0846220	+	0.805124i
$537$	−20.0585	+	4.26356i	−0.865586	+	0.183986i
$538$	31.9443			1.37722
$539$	18.4041	+	14.1523i	0.792722	+	0.609583i
$540$	−6.90983			−0.297352
$541$	−19.1685	+	4.07439i	−0.824119	+	0.175172i	−0.600622	−	0.799533i	$-0.705080\pi$
$541$	−19.1685	+	4.07439i	−0.824119	+	0.175172i	−0.223496	+	0.974705i	$0.571747\pi$
$542$	−2.55803	−	24.3381i	−0.109877	−	1.04541i
$543$	−19.3492	+	8.61482i	−0.830354	+	0.369697i
$544$	−7.32315	+	8.13318i	−0.313977	+	0.348707i
$545$	−0.100813	−	0.310271i	−0.00431836	−	0.0132905i
$546$	14.3361	+	20.5554i	0.613530	+	0.879690i
$547$	28.4443	−	20.6660i	1.21619	−	0.883613i	0.220411	−	0.975407i	$-0.429260\pi$
$547$	28.4443	−	20.6660i	1.21619	−	0.883613i	0.995778	+	0.0917938i	$0.0292601\pi$
$548$	−0.197220	+	0.0419204i	−0.00842483	+	0.00179075i
$549$	−10.9443	+	18.9560i	−0.467090	+	0.809024i
$550$		0			0
$551$	4.50000	+	7.79423i	0.191706	+	0.332045i
$552$	1.21885	−	3.75123i	0.0518776	−	0.159663i
$553$	−24.5474	−	22.9764i	−1.04386	−	0.977055i
$554$	−0.927051	−	0.673542i	−0.0393866	−	0.0286161i
$555$	−9.11224	+	10.1202i	−0.386793	+	0.429577i
$556$	−2.66984	−	0.567493i	−0.113227	−	0.0240671i
$557$	12.6054	−	5.61230i	0.534110	−	0.237801i	−0.121915	−	0.992541i	$-0.538903\pi$
$557$	12.6054	−	5.61230i	0.534110	−	0.237801i	0.656024	+	0.754740i	$0.272237\pi$
$558$	−12.9544	−	5.76766i	−0.548403	−	0.244165i
$559$	−0.263932	+	0.812299i	−0.0111631	+	0.0343566i
$560$	21.7082	−	18.7999i	0.917339	−	0.794439i
$561$	9.85410	+	4.25325i	0.416041	+	0.179573i
$562$	−3.76393	−	6.51932i	−0.158772	−	0.275001i
$563$	2.36060	+	2.62171i	0.0994875	+	0.110492i	0.790832	−	0.612033i	$-0.209648\pi$
$563$	2.36060	+	2.62171i	0.0994875	+	0.110492i	−0.691345	+	0.722525i	$0.742981\pi$
$564$	−0.0305010	−	0.290198i	−0.00128432	−	0.0122195i
$565$	−0.488541	+	4.64816i	−0.0205531	+	0.195550i
$566$	−10.2082	−	31.4176i	−0.429083	−	1.32058i
$567$	−2.26531	−	1.36688i	−0.0951342	−	0.0574036i
$568$	1.38197	+	1.00406i	0.0579860	+	0.0421293i
$569$	−10.3979	−	4.62946i	−0.435904	−	0.194077i	0.177039	−	0.984204i	$-0.443348\pi$
$569$	−10.3979	−	4.62946i	−0.435904	−	0.194077i	−0.612944	+	0.790127i	$0.710015\pi$
$570$	2.77415	+	3.08100i	0.116196	+	0.129049i
$571$	3.78115	−	6.54915i	0.158236	−	0.274073i	−0.775996	−	0.630737i	$-0.782753\pi$
$571$	3.78115	−	6.54915i	0.158236	−	0.274073i	0.934233	+	0.356664i	$0.116086\pi$
$572$	11.7651	+	2.36076i	0.491926	+	0.0987083i
$573$	14.2361			0.594720
$574$	10.1187	+	1.26153i	0.422345	+	0.0526553i
$575$		0			0
$576$	0.885579	−	8.42572i	0.0368991	−	0.351072i
$577$	28.9163	+	6.14635i	1.20380	+	0.255876i	0.765788	−	0.643093i	$-0.222349\pi$
$577$	28.9163	+	6.14635i	1.20380	+	0.255876i	0.438013	+	0.898969i	$0.355682\pi$
$578$	10.3315	+	2.19603i	0.429734	+	0.0913427i
$579$	1.90036	−	18.0807i	0.0789764	−	0.751410i
$580$	8.78115	−	6.37988i	0.364618	−	0.264910i
$581$	−14.3656	+	18.9902i	−0.595987	+	0.787847i
$582$	−6.23607			−0.258493
$583$	18.3576	−	8.42564i	0.760293	−	0.348954i
$584$	12.1353	−	21.0189i	0.502160	−	0.869767i
$585$	17.5181	+	19.4558i	0.724283	+	0.804398i
$586$	−18.4357	−	8.20808i	−0.761570	−	0.339073i
$587$	−32.0795	−	23.3071i	−1.32406	−	0.961989i	−0.999872	−	0.0159972i	$-0.994908\pi$
$587$	−32.0795	−	23.3071i	−1.32406	−	0.961989i	−0.324192	−	0.945991i	$-0.605092\pi$
$588$	4.26328	−	0.735384i	0.175815	−	0.0303267i
$589$	1.55166	+	4.77553i	0.0639352	+	0.196772i
$590$	3.67152	−	34.9322i	0.151154	−	1.43814i
$591$	−0.248983	−	2.36892i	−0.0102418	−	0.0974442i
$592$	19.7810	+	21.9691i	0.812996	+	0.902923i
$593$	10.0344	+	17.3802i	0.412065	+	0.713718i	0.995115	−	0.0987183i	$-0.0314743\pi$
$593$	10.0344	+	17.3802i	0.412065	+	0.713718i	−0.583050	+	0.812436i	$0.698141\pi$
$594$	26.1803	−	5.87785i	1.07419	−	0.241171i
$595$	18.0902	+	6.26662i	0.741625	+	0.256906i
$596$	3.91641	−	12.0535i	0.160422	−	0.493729i
$597$	19.6981	+	8.77018i	0.806191	+	0.358940i
$598$	15.2637	−	6.79584i	0.624179	−	0.277903i
$599$	−8.30782	−	1.76588i	−0.339448	−	0.0721520i	0.0350337	−	0.999386i	$-0.488846\pi$
$599$	−8.30782	−	1.76588i	−0.339448	−	0.0721520i	−0.374482	+	0.927234i	$0.622179\pi$
$600$		0			0
$601$	15.4894	+	11.2537i	0.631824	+	0.459047i	0.857032	−	0.515264i	$-0.172306\pi$
$601$	15.4894	+	11.2537i	0.631824	+	0.459047i	−0.225208	+	0.974311i	$0.572306\pi$
$602$	0.455993	+	0.426810i	0.0185849	+	0.0173955i
$603$	−5.18034	+	15.9434i	−0.210960	+	0.649267i
$604$	1.42705	+	2.47172i	0.0580659	+	0.100573i
$605$	−23.9363	+	5.66171i	−0.973148	+	0.230181i
$606$	12.2082	−	21.1452i	0.495924	−	0.858966i
$607$	6.13348	−	1.30371i	0.248950	−	0.0529160i	−0.0817461	−	0.996653i	$-0.526050\pi$
$607$	6.13348	−	1.30371i	0.248950	−	0.0529160i	0.330697	+	0.943737i	$0.392716\pi$
$608$	3.13525	−	2.27790i	0.127151	−	0.0923809i
$609$	−20.7043	+	1.77258i	−0.838979	+	0.0718284i
$610$	−12.2361	−	37.6587i	−0.495424	−	1.52476i
$611$	−1.84943	+	2.05400i	−0.0748200	+	0.0830960i
$612$	−3.65418	+	1.62695i	−0.147712	+	0.0657654i
$613$	−0.682348	−	6.49210i	−0.0275598	−	0.262214i	−0.999622	−	0.0274906i	$-0.991248\pi$
$613$	−0.682348	−	6.49210i	−0.0275598	−	0.262214i	0.972062	−	0.234723i	$-0.0754183\pi$
$614$	−21.3765	+	4.54372i	−0.862687	+	0.183370i
$615$	−5.32624			−0.214775
$616$	−11.6582	+	15.7824i	−0.469724	+	0.635892i
$617$	16.5279			0.665387			0.332693	−	0.943035i	$-0.392043\pi$
$617$	16.5279			0.665387			0.332693	+	0.943035i	$0.392043\pi$
$618$	−9.49606	+	2.01845i	−0.381987	+	0.0811939i
$619$	−4.88011	−	46.4312i	−0.196148	−	1.86623i	−0.442129	−	0.896951i	$-0.645777\pi$
$619$	−4.88011	−	46.4312i	−0.196148	−	1.86623i	0.245981	−	0.969275i	$-0.420890\pi$
$620$	5.53218	−	2.46309i	0.222178	−	0.0989199i
$621$	5.90150	−	6.55428i	0.236819	−	0.263014i
$622$	−6.68034	−	20.5600i	−0.267857	−	0.824380i
$623$	−1.71518	+	3.66043i	−0.0687174	+	0.146652i
$624$	−22.9894	+	16.7027i	−0.920311	+	0.668645i
$625$	24.4537	−	5.19779i	0.978148	−	0.207912i
$626$	−5.61803	+	9.73072i	−0.224542	+	0.388918i
$627$	−3.09997	−	2.19865i	−0.123801	−	0.0878057i
$628$	3.63525	+	6.29645i	0.145062	+	0.251256i
$629$	−6.09017	+	18.7436i	−0.242831	+	0.747357i
$630$	18.3187	−	5.56333i	0.729834	−	0.221649i
$631$	0.545085	+	0.396027i	0.0216995	+	0.0157656i	0.598582	−	0.801061i	$-0.295731\pi$
$631$	0.545085	+	0.396027i	0.0216995	+	0.0157656i	−0.576883	+	0.816827i	$0.695731\pi$
$632$	19.0143	−	21.1175i	0.756348	−	0.840009i
$633$	8.80333	+	1.87121i	0.349901	+	0.0743737i
$634$	−0.564602	+	0.251377i	−0.0224232	+	0.00998346i
$635$	−0.482228	−	0.214702i	−0.0191366	−	0.00852018i
$636$	1.16312	−	3.57971i	0.0461207	−	0.141945i
$637$	−32.1976	−	25.3490i	−1.27571	−	1.00436i
$638$	−27.8435	+	31.6421i	−1.10233	+	1.25272i
$639$	0.763932	+	1.32317i	0.0302207	+	0.0523438i
$640$	20.3756	+	22.6294i	0.805416	+	0.894505i
$641$	3.16413	+	30.1047i	0.124976	+	1.18906i	0.859737	+	0.510738i	$0.170628\pi$
$641$	3.16413	+	30.1047i	0.124976	+	1.18906i	−0.734761	+	0.678326i	$0.762706\pi$
$642$	1.89094	−	17.9911i	0.0746294	−	0.710051i
$643$	−5.87132	−	18.0701i	−0.231542	−	0.712614i	−0.997561	−	0.0697961i	$-0.977765\pi$
$643$	−5.87132	−	18.0701i	−0.231542	−	0.712614i	0.766019	−	0.642818i	$-0.222235\pi$
$644$	0.0557040	−	2.88378i	0.00219504	−	0.113637i
$645$	−0.263932	−	0.191758i	−0.0103923	−	0.00755046i
$646$	5.48127	+	2.44042i	0.215658	+	0.0960170i
$647$	−4.52595	−	5.02658i	−0.177934	−	0.197615i	0.647580	−	0.761997i	$-0.275781\pi$
$647$	−4.52595	−	5.02658i	−0.177934	−	0.197615i	−0.825514	+	0.564382i	$0.809114\pi$
$648$	1.11803	−	1.93649i	0.0439205	−	0.0760726i
$649$	3.73087	+	31.9816i	0.146450	+	1.25539i
$650$		0			0
$651$	−11.5045	−	1.43431i	−0.450898	−	0.0562151i
$652$	−9.61803	+	6.98791i	−0.376671	+	0.273668i
$653$	−4.80608	+	45.7268i	−0.188077	+	1.78943i	0.340196	+	0.940355i	$0.389507\pi$
$653$	−4.80608	+	45.7268i	−0.188077	+	1.78943i	−0.528273	+	0.849075i	$0.677160\pi$
$654$	0.230909	+	0.0490813i	0.00902927	+	0.00191923i
$655$	−13.8368	−	2.94110i	−0.540648	−	0.114918i
$656$	−1.20859	+	11.4990i	−0.0471875	+	0.448959i
$657$	17.5623	−	12.7598i	0.685171	−	0.497806i
$658$	0.786273	+	1.86197i	0.0306521	+	0.0725870i
$659$	−14.5623			−0.567267			−0.283633	−	0.958933i	$-0.591540\pi$
$659$	−14.5623			−0.567267			−0.283633	+	0.958933i	$0.591540\pi$
$660$	−2.24628	+	3.99529i	−0.0874365	+	0.155516i
$661$	−4.28115	+	7.41517i	−0.166518	+	0.288417i	−0.937193	−	0.348811i	$-0.886586\pi$
$661$	−4.28115	+	7.41517i	−0.166518	+	0.288417i	0.770676	+	0.637228i	$0.219919\pi$
$662$	−1.39860	−	1.55330i	−0.0543580	−	0.0603707i
$663$	−17.3065	−	7.70533i	−0.672127	−	0.299250i
$664$	−16.2812	−	11.8290i	−0.631831	−	0.459052i
$665$	−5.80442	−	3.50236i	−0.225086	−	0.135816i
$666$	6.09017	+	18.7436i	0.235989	+	0.726300i
$667$	−1.44815	+	13.7782i	−0.0560725	+	0.533494i
$668$	0.965432	+	9.18547i	0.0373537	+	0.355397i
$669$	−12.8111	−	14.2282i	−0.495306	−	0.550093i
$670$	−15.1631	−	26.2633i	−0.585802	−	1.01464i
$671$	18.5066	+	31.2259i	0.714439	+	1.20546i
$672$	1.69098	+	8.78661i	0.0652311	+	0.338951i
$673$	2.34346	−	7.21242i	0.0903337	−	0.278019i	−0.895676	−	0.444708i	$-0.853308\pi$
$673$	2.34346	−	7.21242i	0.0903337	−	0.278019i	0.986010	+	0.166689i	$0.0533076\pi$
$674$	21.7409	+	9.67967i	0.837428	+	0.372847i
$675$		0			0
$676$	−12.8586	−	2.73319i	−0.494563	−	0.105123i
$677$	−20.5851	+	22.8621i	−0.791149	+	0.878660i	−0.994952	−	0.100352i	$-0.968003\pi$
$677$	−20.5851	+	22.8621i	−0.791149	+	0.878660i	0.203803	+	0.979012i	$0.434670\pi$
$678$	−2.73607	−	1.98787i	−0.105078	−	0.0763437i
$679$	9.75697	−	2.96316i	0.374438	−	0.113716i
$680$	−5.00000	+	15.3884i	−0.191741	+	0.590119i
$681$	−3.70820	−	6.42280i	−0.142099	−	0.246122i
$682$	−18.8654	+	14.0382i	−0.722394	+	0.537552i
$683$	−15.5902	+	27.0030i	−0.596541	+	1.03324i	0.396786	+	0.917911i	$0.370125\pi$
$683$	−15.5902	+	27.0030i	−0.596541	+	1.03324i	−0.993327	+	0.115329i	$0.963208\pi$
$684$	1.38546	−	0.294488i	0.0529742	−	0.0112600i
$685$	−0.590170	+	0.428784i	−0.0225492	+	0.0163830i
$686$	−26.7758	+	13.4552i	−1.02230	+	0.513723i
$687$	1.80902	+	5.56758i	0.0690183	+	0.212416i
$688$	−0.473881	+	0.526298i	−0.0180665	+	0.0200649i
$689$	−32.5702	+	14.5012i	−1.24082	+	0.552451i
$690$	0.667097	+	6.34700i	0.0253960	+	0.241626i
$691$	40.9187	−	8.69753i	1.55662	−	0.330870i	0.652379	−	0.757893i	$-0.273771\pi$
$691$	40.9187	−	8.69753i	1.55662	−	0.330870i	0.904241	+	0.427023i	$0.140438\pi$
$692$	−6.50658			−0.247343
$693$	−15.2675	+	8.65460i	−0.579966	+	0.328761i
$694$	54.5410			2.07035
$695$	−9.65959	+	2.05321i	−0.366409	+	0.0778826i
$696$	−1.83576	−	17.4661i	−0.0695843	−	0.662051i
$697$	−7.04179	+	3.13521i	−0.266727	+	0.118755i
$698$	32.2017	−	35.7636i	1.21885	−	1.35367i
$699$	−0.954915	−	2.93893i	−0.0361182	−	0.111160i
$700$		0			0
$701$	−20.5623	+	14.9394i	−0.776628	+	0.564253i	−0.903965	−	0.427606i	$-0.859357\pi$
$701$	−20.5623	+	14.9394i	−0.776628	+	0.564253i	0.127337	+	0.991859i	$0.459357\pi$
$702$	−46.3257	+	9.84684i	−1.74845	+	0.371645i
$703$	3.48936	−	6.04374i	0.131604	−	0.227944i
$704$	−11.4597	−	8.12781i	−0.431905	−	0.306328i
$705$	−0.527864	−	0.914287i	−0.0198805	−	0.0344341i
$706$	2.23607	−	6.88191i	0.0841555	−	0.259004i
$707$	−9.05350	+	38.8848i	−0.340492	+	1.46241i
$708$	4.85410	+	3.52671i	0.182428	+	0.132542i
$709$	0.924716	−	1.02700i	0.0347284	−	0.0385698i	−0.725530	−	0.688190i	$-0.758405\pi$
$709$	0.924716	−	1.02700i	0.0347284	−	0.0385698i	0.760259	+	0.649620i	$0.225072\pi$
$710$	−2.70353	−	0.574654i	−0.101462	−	0.0215664i
$711$	23.2190	−	10.3378i	0.870782	−	0.387697i
$712$	−3.12104	−	1.38958i	−0.116966	−	0.0520766i
$713$	−2.38854	+	7.35118i	−0.0894517	+	0.275304i
$714$	−10.4721	+	9.06914i	−0.391910	+	0.339404i
$715$	42.3607	−	9.51057i	1.58420	−	0.355675i
$716$	−6.33688	−	10.9758i	−0.236820	−	0.410185i
$717$	8.50345	+	9.44404i	0.317567	+	0.352694i
$718$	1.57735	+	15.0075i	0.0588663	+	0.560075i
$719$	−0.541493	+	5.15196i	−0.0201943	+	0.192136i	−0.999968	−	0.00797177i	$-0.997462\pi$
$719$	−0.541493	+	5.15196i	−0.0201943	+	0.192136i	0.979774	+	0.200108i	$0.0641291\pi$
$720$	6.70820	+	20.6457i	0.250000	+	0.769421i
$721$	13.8985	−	7.67027i	0.517605	−	0.285656i
$722$	23.1525	+	16.8213i	0.861646	+	0.626022i
$723$	−1.44668	−	0.644105i	−0.0538027	−	0.0239545i
$724$	−8.75903	−	9.72789i	−0.325527	−	0.361534i
$725$		0			0
$726$	5.11224	−	17.0484i	0.189733	−	0.632725i
$727$	−1.58359			−0.0587322			−0.0293661	−	0.999569i	$-0.509349\pi$
$727$	−1.58359			−0.0587322			−0.0293661	+	0.999569i	$0.509349\pi$
$728$	20.8943	−	27.6206i	0.774394	−	1.02369i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	−4.10489	+	39.0554i	−0.151929	+	1.44550i
$731$	−0.461819	−	0.0981626i	−0.0170810	−	0.00363067i
$732$	6.61612	+	1.40630i	0.244539	+	0.0519784i
$733$	3.46246	−	32.9432i	0.127889	−	1.21678i	−0.722779	−	0.691079i	$-0.757135\pi$
$733$	3.46246	−	32.9432i	0.127889	−	1.21678i	0.850668	−	0.525704i	$-0.176198\pi$
$734$	−35.6976	+	25.9358i	−1.31762	+	0.957308i
$735$	13.0090	−	8.70440i	0.479843	−	0.321067i
$736$	5.96556			0.219893
$737$	18.8363	+	20.4457i	0.693843	+	0.753126i
$738$	−3.85410	+	6.67550i	−0.141871	+	0.245729i
$739$	6.88656	+	7.64829i	0.253326	+	0.281347i	0.856372	−	0.516359i	$-0.172713\pi$
$739$	6.88656	+	7.64829i	0.253326	+	0.281347i	−0.603046	+	0.797706i	$0.706046\pi$
$740$	−7.68877	−	3.42326i	−0.282645	−	0.125842i
$741$	5.42705	+	3.94298i	0.199368	+	0.144849i
$742$	−0.503511	+	26.0666i	−0.0184845	+	0.956936i
$743$	−12.5066	−	38.4913i	−0.458822	−	1.41211i	−0.866589	−	0.499022i	$-0.833693\pi$
$743$	−12.5066	−	38.4913i	−0.458822	−	1.41211i	0.407767	−	0.913086i	$-0.366307\pi$
$744$	1.02421	−	9.74470i	0.0375493	−	0.357258i
$745$	−4.79306	−	45.6029i	−0.175604	−	1.67076i
$746$	−25.5476	−	28.3735i	−0.935365	−	1.03883i
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$	−0.618034	+	6.60440i	−0.0225976	+	0.241481i
$749$	5.59017	+	29.0474i	0.204260	+	1.06137i
$750$	−5.59017	+	17.2048i	−0.204124	+	0.628230i
$751$	−6.37537	−	2.83850i	−0.232641	−	0.103578i	0.287106	−	0.957899i	$-0.407307\pi$
$751$	−6.37537	−	2.83850i	−0.232641	−	0.103578i	−0.519746	+	0.854321i	$0.673974\pi$
$752$	−2.09366	+	0.932157i	−0.0763479	+	0.0339923i
$753$	−1.63719	−	0.347995i	−0.0596624	−	0.0126816i
$754$	49.7801	−	55.2863i	1.81288	−	2.01341i
$755$	8.35410	+	6.06961i	0.304037	+	0.220896i
$756$	−1.85398	+	7.96284i	−0.0674285	+	0.289606i
$757$	5.75329	−	17.7068i	0.209107	−	0.643565i	−0.790413	−	0.612575i	$-0.790134\pi$
$757$	5.75329	−	17.7068i	0.209107	−	0.643565i	0.999520	−	0.0309902i	$-0.00986606\pi$
$758$	−17.5623	−	30.4188i	−0.637892	−	1.10486i
$759$	−1.87122	−	5.54297i	−0.0679210	−	0.201197i
$760$	2.86475	−	4.96188i	0.103915	−	0.179986i
$761$	34.1598	−	7.26090i	1.23829	−	0.263207i	0.458188	−	0.888855i	$-0.348499\pi$
$761$	34.1598	−	7.26090i	1.23829	−	0.263207i	0.780105	+	0.625648i	$0.215165\pi$
$762$	0.309017	−	0.224514i	0.0111945	−	0.00813328i
$763$	−0.384603	+	0.0329274i	−0.0139236	+	0.00119205i
$764$	2.71885	+	8.36775i	0.0983644	+	0.302735i
$765$	−9.68375	+	10.7549i	−0.350117	+	0.388844i
$766$	−33.6994	+	15.0039i	−1.21761	+	0.542114i
$767$	−5.94065	−	56.5215i	−0.214504	−	2.04087i
$768$	−13.2659	+	2.81976i	−0.478693	+	0.101749i
$769$	−12.4721			−0.449757			−0.224878	−	0.974387i	$-0.572198\pi$
$769$	−12.4721			−0.449757			−0.224878	+	0.974387i	$0.572198\pi$
$770$	6.84598	−	31.0012i	0.246712	−	1.11721i
$771$	−11.9443			−0.430162
$772$	10.9905	−	2.33611i	0.395558	−	0.0840784i
$773$	2.34315	+	22.2936i	0.0842773	+	0.801845i	0.952268	+	0.305264i	$0.0987448\pi$
$773$	2.34315	+	22.2936i	0.0842773	+	0.801845i	−0.867990	+	0.496581i	$0.834589\pi$
$774$	−0.431318	+	0.192035i	−0.0155034	+	0.00690256i
$775$		0			0
$776$	2.66312	+	8.19624i	0.0956004	+	0.294228i
$777$	9.21751	+	13.2162i	0.330676	+	0.474130i
$778$	30.7984	−	22.3763i	1.10418	−	0.802230i
$779$	2.66984	−	0.567493i	0.0956571	−	0.0203325i
$780$	4.04508	−	7.00629i	0.144837	−	0.250866i
$781$	2.53351	−	0.0289144i	0.0906561	−	0.00103464i
$782$	4.61803	+	7.99867i	0.165141	+	0.286032i
$783$	12.1353	−	37.3485i	0.433679	−	1.33473i
$784$	−15.8403	−	30.0606i	−0.565725	−	1.07359i
$785$	21.2812	+	15.4617i	0.759557	+	0.551850i
$786$	6.84927	−	7.60688i	0.244305	−	0.271328i
$787$	30.3226	+	6.44526i	1.08088	+	0.229749i	0.713737	−	0.700414i	$-0.247001\pi$
$787$	30.3226	+	6.44526i	1.08088	+	0.229749i	0.367147	+	0.930163i	$0.380335\pi$
$788$	1.34486	−	0.598772i	0.0479088	−	0.0213304i
$789$	10.9625	+	4.88084i	0.390277	+	0.173762i
$790$	−14.2082	+	43.7284i	−0.505505	+	1.55579i
$791$	5.22542	+	1.81014i	0.185795	+	0.0643612i
$792$	−7.56231	−	12.7598i	−0.268715	−	0.453398i
$793$	−32.0344	−	55.4853i	−1.13758	−	1.97034i
$794$	37.5547	+	41.7087i	1.33277	+	1.48019i
$795$	−1.42347	−	13.5434i	−0.0504854	−	0.480336i
$796$	−1.39297	+	13.2532i	−0.0493726	+	0.469748i
$797$	−0.909830	−	2.80017i	−0.0322278	−	0.0991871i	0.933649	−	0.358190i	$-0.116606\pi$
$797$	−0.909830	−	2.80017i	−0.0322278	−	0.0991871i	−0.965877	+	0.259003i	$0.916606\pi$
$798$	4.29486	−	2.37024i	0.152036	−	0.0839057i
$799$	−1.23607	−	0.898056i	−0.0437289	−	0.0317709i
$800$		0			0
$801$	−2.04468	−	2.27085i	−0.0722453	−	0.0802365i
$802$	14.5172	−	25.1446i	0.512621	−	0.887885i
$803$	−4.17124	−	35.7565i	−0.147200	−	1.26182i
$804$	5.18034			0.182697
$805$	−4.05962	−	9.61356i	−0.143083	−	0.338833i
$806$	33.5795	−	24.3970i	1.18279	−	0.859346i
$807$	−2.06367	+	19.6345i	−0.0726446	+	0.691167i
$808$	−33.0053	−	7.01549i	−1.16112	−	0.246804i
$809$	12.8586	+	2.73319i	0.452085	+	0.0960937i	0.428327	−	0.903624i	$-0.359103\pi$
$809$	12.8586	+	2.73319i	0.452085	+	0.0960937i	0.0237588	+	0.999718i	$0.492437\pi$
$810$	−0.378188	+	3.59821i	−0.0132882	+	0.126428i
$811$	−31.5517	+	22.9236i	−1.10793	+	0.804957i	−0.982336	−	0.187125i	$-0.940083\pi$
$811$	−31.5517	+	22.9236i	−1.10793	+	0.804957i	−0.125593	+	0.992082i	$0.540083\pi$
$812$	−4.99606	−	11.8311i	−0.175327	−	0.415191i
$813$	15.1246			0.530443
$814$	32.0436	+	6.42978i	1.12313	+	0.225364i
$815$	−21.5066	+	37.2505i	−0.753343	+	1.30483i
$816$	−10.5108	−	11.6735i	−0.367953	−	0.408653i
$817$	0.152730	+	0.0680000i	0.00534336	+	0.00237902i
$818$	32.9615	+	23.9479i	1.15247	+	0.837320i
$819$	27.1210	−	14.9675i	0.947684	−	0.523007i
$820$	−1.01722	−	3.13068i	−0.0355229	−	0.109328i
$821$	4.12956	−	39.2902i	0.144123	−	1.37124i	−0.648356	−	0.761337i	$-0.724543\pi$
$821$	4.12956	−	39.2902i	0.144123	−	1.37124i	0.792479	−	0.609899i	$-0.208790\pi$
$822$	−0.0551768	−	0.524972i	−0.00192451	−	0.0183105i
$823$	−3.73615	−	4.14942i	−0.130234	−	0.144640i	0.674500	−	0.738274i	$-0.264359\pi$
$823$	−3.73615	−	4.14942i	−0.130234	−	0.144640i	−0.804735	+	0.593635i	$0.797692\pi$
$824$	6.70820	+	11.6190i	0.233691	+	0.404765i
$825$		0			0
$826$	−39.2705	−	13.6037i	−1.36640	−	0.473333i
$827$	−3.91641	+	12.0535i	−0.136187	+	0.419140i	−0.995773	−	0.0918513i	$-0.970722\pi$
$827$	−3.91641	+	12.0535i	−0.136187	+	0.419140i	0.859586	+	0.510991i	$0.170722\pi$
$828$	1.99184	+	0.886824i	0.0692212	+	0.0308193i
$829$	−9.26874	+	4.12671i	−0.321917	+	0.143327i	−0.561332	−	0.827591i	$-0.689711\pi$
$829$	−9.26874	+	4.12671i	−0.321917	+	0.143327i	0.239415	+	0.970917i	$0.423044\pi$
$830$	31.8507	+	6.77008i	1.10556	+	0.234993i
$831$	0.473881	−	0.526298i	0.0164387	−	0.0182571i
$832$	20.0623	+	14.5761i	0.695535	+	0.505336i
$833$	12.0754	−	19.1656i	0.418387	−	0.664048i
$834$	2.20820	−	6.79615i	0.0764638	−	0.235332i
$835$	16.7082	+	28.9395i	0.578211	+	1.00149i
$836$	0.700293	−	2.24202i	0.0242201	−	0.0775420i
$837$	10.9549	−	18.9745i	0.378657	−	0.655854i
$838$	−36.6870	+	7.79806i	−1.26733	+	0.269379i
$839$	31.0172	−	22.5353i	1.07083	−	0.778006i	0.0947715	−	0.995499i	$-0.469788\pi$
$839$	31.0172	−	22.5353i	1.07083	−	0.778006i	0.976062	+	0.217493i	$0.0697879\pi$
$840$	7.56753	+	10.8505i	0.261105	+	0.374377i
$841$	10.1008	+	31.0871i	0.348304	+	1.07197i
$842$	−29.9990	+	33.3173i	−1.03383	+	1.14819i
$843$	4.25025	−	1.89233i	0.146386	−	0.0651754i
$844$	0.581419	+	5.53184i	0.0200133	+	0.190414i
$845$	−46.5230	+	9.88876i	−1.60044	+	0.340184i
$846$	−1.52786			−0.0525290
$847$	0.102172	+	29.1031i	0.00351067	+	0.999994i
$848$	−29.5623			−1.01517
$849$	19.9703	−	4.24481i	0.685378	−	0.145681i
$850$		0			0
$851$	9.81390	−	4.36943i	0.336416	−	0.149782i
$852$	0.315921	−	0.350865i	0.0108233	−	0.0120205i
$853$	11.6738	+	35.9281i	0.399702	+	1.23016i	0.925239	+	0.379385i	$0.123865\pi$
$853$	11.6738	+	35.9281i	0.399702	+	1.23016i	−0.525537	+	0.850771i	$0.676135\pi$
$854$	−46.6807	+	3.99653i	−1.59738	+	0.136758i
$855$	4.14590	−	3.01217i	0.141787	−	0.103014i
$856$	−24.4537	+	5.19779i	−0.835810	+	0.177657i
$857$	5.73607	−	9.93516i	0.195940	−	0.339379i	−0.751268	−	0.659997i	$-0.770557\pi$
$857$	5.73607	−	9.93516i	0.195940	−	0.339379i	0.947208	+	0.320619i	$0.103891\pi$
$858$	−9.36633	+	29.9868i	−0.319761	+	1.02373i
$859$	−4.14590	−	7.18091i	−0.141456	−	0.245009i	0.786589	−	0.617477i	$-0.211845\pi$
$859$	−4.14590	−	7.18091i	−0.141456	−	0.245009i	−0.928045	+	0.372468i	$0.878512\pi$
$860$	0.0623059	−	0.191758i	0.00212461	−	0.00653889i
$861$	−1.42908	+	6.13792i	−0.0487031	+	0.209180i
$862$	23.4164	+	17.0130i	0.797566	+	0.579466i
$863$	−31.0213	+	34.4527i	−1.05598	+	1.17278i	−0.0714712	+	0.997443i	$0.522769\pi$
$863$	−31.0213	+	34.4527i	−1.05598	+	1.17278i	−0.984508	+	0.175341i	$0.943897\pi$
$864$	−16.5403	−	3.51575i	−0.562713	−	0.119608i
$865$	−21.5058	+	9.57500i	−0.731219	+	0.325560i
$866$	−21.3096	−	9.48764i	−0.724129	−	0.322403i
$867$	−2.01722	+	6.20837i	−0.0685084	+	0.210847i
$868$	−1.35410	−	7.03612i	−0.0459612	−	0.238821i
$869$	3.92705	−	41.9650i	0.133216	−	1.42357i
$870$	14.2082	+	24.6093i	0.481703	+	0.834334i
$871$	−32.8335	−	36.4653i	−1.11252	−	1.23558i
$872$	−0.0341011	−	0.324451i	−0.00115481	−	0.0109873i
$873$	−0.805727	+	7.66598i	−0.0272697	+	0.259454i
$874$	−1.01064	−	3.11044i	−0.0341855	−	0.105212i
$875$	0.571278	−	29.5749i	0.0193127	−	0.999813i
$876$	−5.42705	−	3.94298i	−0.183363	−	0.133221i
$877$	−5.01849	−	2.23438i	−0.169462	−	0.0754495i	0.320252	−	0.947332i	$-0.396232\pi$
$877$	−5.01849	−	2.23438i	−0.169462	−	0.0754495i	−0.489715	+	0.871883i	$0.662899\pi$
$878$	−8.46616	−	9.40262i	−0.285719	−	0.317323i
$879$	6.23607	−	10.8012i	0.210337	−	0.364315i
$880$	35.2954	+	7.08228i	1.18981	+	0.238744i
$881$	0.652476			0.0219825			0.0109912	−	0.999940i	$-0.496501\pi$
$881$	0.652476			0.0219825			0.0109912	+	0.999940i	$0.496501\pi$
$882$	−1.49606	−	22.6030i	−0.0503748	−	0.761083i
$883$	−26.1353	+	18.9884i	−0.879521	+	0.639010i	−0.933125	−	0.359553i	$-0.882929\pi$
$883$	−26.1353	+	18.9884i	−0.879521	+	0.639010i	0.0536035	+	0.998562i	$0.482929\pi$
$884$	1.22384	−	11.6441i	0.0411622	−	0.391632i
$885$	21.2338	+	4.51339i	0.713767	+	0.151716i
$886$	−22.5311	−	4.78913i	−0.756947	−	0.160894i
$887$	1.33779	−	12.7283i	0.0449187	−	0.427373i	−0.948835	−	0.315774i	$-0.897736\pi$
$887$	1.33779	−	12.7283i	0.0449187	−	0.427373i	0.993753	−	0.111600i	$-0.0355974\pi$
$888$	−11.0172	+	8.00448i	−0.369714	+	0.268613i
$889$	−0.376807	+	0.498109i	−0.0126377	+	0.0167060i
$890$	5.52786			0.185294
$891$	−0.384301	−	3.29428i	−0.0128746	−	0.110363i
$892$	5.91641	−	10.2475i	0.198096	−	0.343112i
$893$	0.362013	+	0.402056i	0.0121143	+	0.0134543i
$894$	30.3117	+	13.4957i	1.01378	+	0.451362i
$895$	−37.0967	−	26.9524i	−1.24001	−	0.900918i
$896$	31.5449	−	17.4090i	1.05384	−	0.581594i
$897$	3.19098	+	9.82084i	0.106544	+	0.327908i
$898$	−4.69573	+	44.6769i	−0.156699	+	1.49089i
$899$	3.59749	+	34.2279i	0.119983	+	1.14156i
$900$		0			0
$901$	−9.85410	−	17.0678i	−0.328288	−	0.568611i
$902$	6.51722	+	10.9964i	0.217000	+	0.366140i
$903$	−0.291796	+	0.252703i	−0.00971037	+	0.00840942i
$904$	−1.44427	+	4.44501i	−0.0480358	+	0.147839i
$905$	−43.2661	−	19.2633i	−1.43821	−	0.640335i
$906$	−6.82614	+	3.03919i	−0.226783	+	0.100970i
$907$	50.8429	+	10.8070i	1.68821	+	0.358840i	0.949156	−	0.314807i	$-0.101940\pi$
$907$	50.8429	+	10.8070i	1.68821	+	0.358840i	0.739053	+	0.673647i	$0.235273\pi$
$908$	3.06702	−	3.40627i	0.101783	−	0.113041i
$909$	−24.4164	−	17.7396i	−0.809841	−	0.588384i
$910$	−12.7074	+	54.5781i	−0.421245	+	1.80925i
$911$	−8.88197	+	27.3359i	−0.294273	+	0.905678i	0.689192	+	0.724579i	$0.257966\pi$
$911$	−8.88197	+	27.3359i	−0.294273	+	0.905678i	−0.983465	+	0.181099i	$0.942034\pi$
$912$	2.78115	+	4.81710i	0.0920932	+	0.159510i
$913$	−29.8477	+	0.340645i	−0.987814	+	0.0112737i
$914$	−5.78115	+	10.0133i	−0.191224	+	0.331209i
$915$	23.9374	−	5.08804i	0.791345	−	0.168206i
$916$	−2.92705	+	2.12663i	−0.0967125	+	0.0702657i
$917$	−7.10185	+	15.1563i	−0.234524	+	0.500504i
$918$	−8.09017	−	24.8990i	−0.267015	−	0.821789i
$919$	3.90292	−	4.33463i	0.128745	−	0.142986i	−0.675325	−	0.737520i	$-0.735997\pi$
$919$	3.90292	−	4.33463i	0.128745	−	0.142986i	0.804071	+	0.594534i	$0.202663\pi$
$920$	8.05716	−	3.58728i	0.265637	−	0.118269i
$921$	−1.41182	−	13.4326i	−0.0465211	−	0.442619i
$922$	12.5187	−	2.66093i	0.412281	−	0.0876331i
$923$	−4.47214			−0.147202
$924$	4.00144	+	3.66058i	0.131638	+	0.120424i
$925$		0			0
$926$	61.0861	−	12.9843i	2.00742	−	0.426689i
$927$	1.25434	+	11.9343i	0.0411980	+	0.391973i
$928$	24.2659	−	10.8039i	0.796566	−	0.354654i
$929$	7.21128	−	8.00894i	0.236594	−	0.262765i	−0.613142	−	0.789973i	$-0.710095\pi$
$929$	7.21128	−	8.00894i	0.236594	−	0.262765i	0.849736	+	0.527208i	$0.176761\pi$
$930$	4.89919	+	15.0781i	0.160651	+	0.494432i
$931$	−5.59349	+	5.74926i	−0.183319	+	0.188424i
$932$	1.54508	−	1.12257i	0.0506109	−	0.0367710i
$933$	13.0687	−	2.77784i	0.427851	−	0.0909424i
$934$	2.04508	−	3.54219i	0.0669172	−	0.115904i
$935$	7.67619	+	22.7386i	0.251038	+	0.743631i
$936$	13.0902	+	22.6728i	0.427866	+	0.741085i
$937$	3.26393	−	10.0453i	0.106628	−	0.328167i	−0.883481	−	0.468467i	$-0.844807\pi$
$937$	3.26393	−	10.0453i	0.106628	−	0.328167i	0.990109	+	0.140300i	$0.0448066\pi$
$938$	−34.3341	+	10.4272i	−1.12105	+	0.340459i
$939$	−5.61803	−	4.08174i	−0.183338	−	0.133203i
$940$	0.436592	−	0.484884i	0.0142400	−	0.0158152i
$941$	11.5406	+	2.45302i	0.376211	+	0.0799662i	0.392137	−	0.919907i	$-0.371736\pi$
$941$	11.5406	+	2.45302i	0.376211	+	0.0799662i	−0.0159253	+	0.999873i	$0.505069\pi$
$942$	−17.3888	+	7.74200i	−0.566559	+	0.252248i
$943$	3.83838	+	1.70896i	0.124995	+	0.0556512i
$944$	14.5623	−	44.8182i	0.473963	−	1.45871i
$945$	5.59017	+	29.0474i	0.181848	+	0.944911i
$946$	−0.0729490	+	0.779543i	−0.00237178	+	0.0253451i
$947$	−14.4443	−	25.0182i	−0.469376	−	0.812983i	0.530011	−	0.847991i	$-0.322188\pi$
$947$	−14.4443	−	25.0182i	−0.469376	−	0.812983i	−0.999387	+	0.0350079i	$0.988854\pi$
$948$	−5.25542	−	5.83674i	−0.170688	−	0.189568i
$949$	6.64185	+	63.1929i	0.215603	+	2.05133i
$950$		0			0
$951$	−0.118034	−	0.363271i	−0.00382751	−	0.0117799i
$952$	16.3920	+	9.89084i	0.531266	+	0.320564i
$953$	−1.10081	−	0.799788i	−0.0356588	−	0.0259077i	0.569813	−	0.821774i	$-0.307016\pi$
$953$	−1.10081	−	0.799788i	−0.0356588	−	0.0259077i	−0.605472	+	0.795867i	$0.707016\pi$
$954$	−18.0043	−	8.01605i	−0.582912	−	0.259529i
$955$	21.3003	+	23.6564i	0.689262	+	0.765503i
$956$	−3.92705	+	6.80185i	−0.127010	+	0.219988i
$957$	−17.6500	−	19.1581i	−0.570545	−	0.619293i
$958$	−23.2705			−0.751836
$959$	0.335778	+	0.795155i	0.0108429	+	0.0256769i
$960$	−7.66312	+	5.56758i	−0.247326	+	0.179693i
$961$	1.23327	−	11.7337i	0.0397828	−	0.378508i
$962$	−56.4263	−	11.9938i	−1.81926	−	0.386695i
$963$	−21.8720	−	4.64905i	−0.704817	−	0.149813i
$964$	0.102303	−	0.973352i	0.00329497	−	0.0313496i
$965$	32.8885	−	23.8949i	1.05872	−	0.769205i
$966$	7.49323	+	0.934209i	0.241091	+	0.0300577i
$967$	7.97871			0.256578			0.128289	−	0.991737i	$-0.459051\pi$
$967$	7.97871			0.256578			0.128289	+	0.991737i	$0.459051\pi$
$968$	−24.5903	+	0.561362i	−0.790363	+	0.0180428i
$969$	−1.85410	+	3.21140i	−0.0595623	+	0.103165i
$970$	−9.33054	−	10.3626i	−0.299586	−	0.332723i
$971$	−16.4438	−	7.32126i	−0.527707	−	0.234950i	0.125549	−	0.992087i	$-0.459931\pi$
$971$	−16.4438	−	7.32126i	−0.527707	−	0.234950i	−0.653256	+	0.757137i	$0.726597\pi$
$972$	−8.00000	−	5.81234i	−0.256600	−	0.186431i
$973$	−0.225664	+	11.6825i	−0.00723444	+	0.374525i
$974$	−4.23607	−	13.0373i	−0.135732	−	0.417741i
$975$		0			0
$976$	−5.55303	−	52.8336i	−0.177748	−	1.69116i
$977$	−2.66228	−	2.95676i	−0.0851739	−	0.0945952i	0.699051	−	0.715072i	$-0.253606\pi$
$977$	−2.66228	−	2.95676i	−0.0851739	−	0.0945952i	−0.784225	+	0.620476i	$0.786939\pi$
$978$	−15.5623	−	26.9547i	−0.497628	−	0.861916i
$979$	−4.94427	+	1.11006i	−0.158020	+	0.0354776i
$980$	7.60081	+	5.98409i	0.242799	+	0.191155i
$981$	0.0901699	−	0.277515i	0.00287890	−	0.00886036i
$982$	18.3847	+	8.18542i	0.586681	+	0.261207i
$983$	−10.4609	+	4.65748i	−0.333650	+	0.148551i	−0.566722	−	0.823909i	$-0.691789\pi$
$983$	−10.4609	+	4.65748i	−0.333650	+	0.148551i	0.233072	+	0.972459i	$0.425122\pi$
$984$	−5.20985	−	1.10739i	−0.166084	−	0.0353022i
$985$	3.56395	−	3.95817i	0.113557	−	0.126118i
$986$	33.2705	+	24.1724i	1.05955	+	0.769807i
$987$	−1.19525	+	0.362994i	−0.0380452	+	0.0115542i
$988$	−1.28115	+	3.94298i	−0.0407589	+	0.125443i
$989$	0.128677	+	0.222875i	0.00409169	+	0.00708702i
$990$	19.5756	+	13.8840i	0.622153	+	0.441261i
$991$	−3.01722	+	5.22598i	−0.0958452	+	0.166009i	−0.909961	−	0.414694i	$-0.863889\pi$
$991$	−3.01722	+	5.22598i	−0.0958452	+	0.166009i	0.814116	+	0.580702i	$0.197222\pi$
$992$	14.4958	−	3.08118i	0.460243	−	0.0978276i
$993$	1.04508	−	0.759299i	0.0331648	−	0.0240956i
$994$	−1.38761	+	2.96135i	−0.0440124	+	0.0939282i
$995$	14.8992	+	45.8550i	0.472336	+	1.45370i
$996$	−3.72191	+	4.13360i	−0.117933	+	0.130978i
$997$	46.4381	−	20.6756i	1.47071	−	0.654802i	0.494018	−	0.869452i	$-0.335528\pi$
$997$	46.4381	−	20.6756i	1.47071	−	0.654802i	0.976691	+	0.214650i	$0.0688610\pi$
$998$	0.606095	+	5.76661i	0.0191856	+	0.182539i
$999$	−29.7854	+	6.33109i	−0.942369	+	0.200307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.m.a.53.1	yes	8
3.2	odd	2		693.2.by.a.361.1		8
7.2	even	3	inner	77.2.m.a.9.1	✓	8
7.3	odd	6		539.2.f.b.295.1		4
7.4	even	3		539.2.f.a.295.1		4
7.5	odd	6		539.2.q.a.471.1		8
7.6	odd	2		539.2.q.a.361.1		8
11.2	odd	10		847.2.n.a.487.1		8
11.3	even	5		847.2.n.c.81.1		8
11.4	even	5		847.2.e.a.606.1		4
11.5	even	5	inner	77.2.m.a.60.1	yes	8
11.6	odd	10		847.2.n.b.753.1		8
11.7	odd	10		847.2.e.b.606.2		4
11.8	odd	10		847.2.n.a.81.1		8
11.9	even	5		847.2.n.c.487.1		8
11.10	odd	2		847.2.n.b.130.1		8
21.2	odd	6		693.2.by.a.163.1		8
33.5	odd	10		693.2.by.a.676.1		8
77.2	odd	30		847.2.n.a.366.1		8
77.4	even	15		5929.2.a.q.1.2		2
77.5	odd	30		539.2.q.a.324.1		8
77.9	even	15		847.2.n.c.366.1		8
77.16	even	15	inner	77.2.m.a.16.1	yes	8
77.18	odd	30		5929.2.a.l.1.1		2
77.27	odd	10		539.2.q.a.214.1		8
77.30	odd	30		847.2.n.a.807.1		8
77.37	even	15		847.2.e.a.485.1		4
77.38	odd	30		539.2.f.b.148.1		4
77.51	odd	30		847.2.e.b.485.2		4
77.58	even	15		847.2.n.c.807.1		8
77.59	odd	30		5929.2.a.o.1.2		2
77.60	even	15		539.2.f.a.148.1		4
77.65	odd	6		847.2.n.b.9.1		8
77.72	odd	30		847.2.n.b.632.1		8
77.73	even	30		5929.2.a.j.1.1		2
231.170	odd	30		693.2.by.a.478.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.a.9.1	✓	8	7.2	even	3	inner
77.2.m.a.16.1	yes	8	77.16	even	15	inner
77.2.m.a.53.1	yes	8	1.1	even	1	trivial
77.2.m.a.60.1	yes	8	11.5	even	5	inner
539.2.f.a.148.1		4	77.60	even	15
539.2.f.a.295.1		4	7.4	even	3
539.2.f.b.148.1		4	77.38	odd	30
539.2.f.b.295.1		4	7.3	odd	6
539.2.q.a.214.1		8	77.27	odd	10
539.2.q.a.324.1		8	77.5	odd	30
539.2.q.a.361.1		8	7.6	odd	2
539.2.q.a.471.1		8	7.5	odd	6
693.2.by.a.163.1		8	21.2	odd	6
693.2.by.a.361.1		8	3.2	odd	2
693.2.by.a.478.1		8	231.170	odd	30
693.2.by.a.676.1		8	33.5	odd	10
847.2.e.a.485.1		4	77.37	even	15
847.2.e.a.606.1		4	11.4	even	5
847.2.e.b.485.2		4	77.51	odd	30
847.2.e.b.606.2		4	11.7	odd	10
847.2.n.a.81.1		8	11.8	odd	10
847.2.n.a.366.1		8	77.2	odd	30
847.2.n.a.487.1		8	11.2	odd	10
847.2.n.a.807.1		8	77.30	odd	30
847.2.n.b.9.1		8	77.65	odd	6
847.2.n.b.130.1		8	11.10	odd	2
847.2.n.b.632.1		8	77.72	odd	30
847.2.n.b.753.1		8	11.6	odd	10
847.2.n.c.81.1		8	11.3	even	5
847.2.n.c.366.1		8	77.9	even	15
847.2.n.c.487.1		8	11.9	even	5
847.2.n.c.807.1		8	77.58	even	15
5929.2.a.j.1.1		2	77.73	even	30
5929.2.a.l.1.1		2	77.18	odd	30
5929.2.a.o.1.2		2	77.59	odd	30
5929.2.a.q.1.2		2	77.4	even	15

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58268 + 0.336408i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.564602 - 0.251377i) q^{4} +(1.49622 - 1.66172i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-1.51351 - 2.17009i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.95630 - 0.415823i) q^{9} +O(q^{10})\)	\(q+(-1.58268 + 0.336408i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(0.564602 - 0.251377i) q^{4} +(1.49622 - 1.66172i) q^{5} +(0.500000 + 1.53884i) q^{6} +(-1.51351 - 2.17009i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.95630 - 0.415823i) q^{9} +(-1.80902 + 3.13331i) q^{10} +(0.988830 - 3.16579i) q^{11} +(-0.309017 - 0.535233i) q^{12} +(-1.80902 + 5.56758i) q^{13} +(3.12543 + 2.92540i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(-3.24803 + 3.60730i) q^{16} +(-3.16535 - 0.672816i) q^{17} +(-2.95630 + 1.31623i) q^{18} +(1.04683 + 0.466079i) q^{19} +(0.427051 - 1.31433i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 + 5.34307i) q^{22} +(0.881966 + 1.52761i) q^{23} +(-1.49622 - 1.66172i) q^{24} +(0.990108 - 9.42025i) q^{26} +(-1.54508 - 4.75528i) q^{27} +(-1.40004 - 0.844778i) q^{28} +(6.35410 + 4.61653i) q^{29} +(3.30524 + 1.47159i) q^{30} +(2.93211 + 3.25644i) q^{31} +(1.69098 - 2.92887i) q^{32} +(-3.25181 - 0.652498i) q^{33} +5.23607 q^{34} +(-5.87063 - 0.731913i) q^{35} +(1.00000 - 0.726543i) q^{36} +(0.636596 - 6.05681i) q^{37} +(-1.81359 - 0.385489i) q^{38} +(5.72618 + 1.21714i) q^{39} +(0.522642 - 4.97261i) q^{40} +(1.92705 - 1.40008i) q^{41} +(2.58268 - 3.41409i) q^{42} +0.145898 q^{43} +(-0.237511 - 2.03598i) q^{44} +(2.23607 - 3.87298i) q^{45} +(-1.90977 - 2.12101i) q^{46} +(0.431318 + 0.192035i) q^{47} +(3.92705 + 2.85317i) q^{48} +(-2.41860 + 6.56889i) q^{49} +(-0.338261 + 3.21834i) q^{51} +(0.378188 + 3.59821i) q^{52} +(4.07512 + 4.52588i) q^{53} +(4.04508 + 7.00629i) q^{54} +(-3.78115 - 6.37988i) q^{55} +(-5.59017 - 1.93649i) q^{56} +(0.354102 - 1.08981i) q^{57} +(-11.6095 - 5.16889i) q^{58} +(-8.86889 + 3.94868i) q^{59} +(-1.35177 - 0.287327i) q^{60} +(-7.32315 + 8.13318i) q^{61} +(-5.73607 - 4.16750i) q^{62} +(-3.86324 - 3.61599i) q^{63} +(1.30902 - 4.02874i) q^{64} +(6.54508 + 11.3364i) q^{65} +(5.36606 - 0.0612417i) q^{66} +(-4.19098 + 7.25900i) q^{67} +(-1.95630 + 0.415823i) q^{68} +(1.42705 - 1.03681i) q^{69} +(9.53753 - 0.816547i) q^{70} +(0.236068 + 0.726543i) q^{71} +(2.99244 - 3.32344i) q^{72} +(9.91572 - 4.41476i) q^{73} +(1.03003 + 9.80012i) q^{74} +0.708204 q^{76} +(-8.36665 + 2.64559i) q^{77} -9.47214 q^{78} +(12.4305 - 2.64218i) q^{79} +(1.13456 + 10.7946i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-2.57890 + 2.86416i) q^{82} +(-2.78115 - 8.55951i) q^{83} +(-0.693806 + 1.48067i) q^{84} +(-5.85410 + 4.25325i) q^{85} +(-0.230909 + 0.0490813i) q^{86} +(3.92705 - 6.80185i) q^{87} +(-2.37207 - 7.02661i) q^{88} +(-0.763932 - 1.32317i) q^{89} +(-2.23607 + 6.88191i) q^{90} +(14.8201 - 4.50083i) q^{91} +(0.881966 + 0.640786i) q^{92} +(2.93211 - 3.25644i) q^{93} +(-0.747238 - 0.158830i) q^{94} +(2.34078 - 1.04218i) q^{95} +(-3.08958 - 1.37557i) q^{96} +(-1.19098 + 3.66547i) q^{97} +(1.61803 - 11.2101i) q^{98} +(0.618034 - 6.60440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

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