LMFDB - Embedded newform 1550.2.e.r.1451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1550,2,Mod(501,1550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1550, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1550.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1550 = 2 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1550.e (of order $3$, degree $2$, 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:	$12.3768123133$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 16 x^{14} - 20 x^{13} + 157 x^{12} - 204 x^{11} + 742 x^{10} - 850 x^{9} + 2386 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 16x^14 - 20x^13 + 157x^12 - 204x^11 + 742x^10 - 850x^9 + 2386x^8 - 2498x^7 + 3603x^6 - 1674x^5 + 1356x^4 - 514x^3 + 359x^2 - 90*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 310)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1451.1
Root			$-1.34467 - 2.32904i$ of defining polynomial
Character	$\chi$	$=$	1550.1451
Dual form			1550.2.e.r.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.34467 - 2.32904i) q^{3} +1.00000 q^{4} +(-1.34467 - 2.32904i) q^{6} +(1.66997 + 2.89246i) q^{7} +1.00000 q^{8} +(-2.11630 + 3.66553i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.34467 - 2.32904i) q^{3} +1.00000 q^{4} +(-1.34467 - 2.32904i) q^{6} +(1.66997 + 2.89246i) q^{7} +1.00000 q^{8} +(-2.11630 + 3.66553i) q^{9} +(-1.25570 + 2.17494i) q^{11} +(-1.34467 - 2.32904i) q^{12} +(0.534502 - 0.925785i) q^{13} +(1.66997 + 2.89246i) q^{14} +1.00000 q^{16} +(-0.565452 - 0.979392i) q^{17} +(-2.11630 + 3.66553i) q^{18} +(3.42647 + 5.93482i) q^{19} +(4.49112 - 7.77885i) q^{21} +(-1.25570 + 2.17494i) q^{22} +4.55942 q^{23} +(-1.34467 - 2.32904i) q^{24} +(0.534502 - 0.925785i) q^{26} +3.31488 q^{27} +(1.66997 + 2.89246i) q^{28} -2.14564 q^{29} +(0.527107 + 5.54276i) q^{31} +1.00000 q^{32} +6.75404 q^{33} +(-0.565452 - 0.979392i) q^{34} +(-2.11630 + 3.66553i) q^{36} +(5.75839 + 9.97382i) q^{37} +(3.42647 + 5.93482i) q^{38} -2.87493 q^{39} +(-3.61032 + 6.25326i) q^{41} +(4.49112 - 7.77885i) q^{42} +(-0.230984 - 0.400075i) q^{43} +(-1.25570 + 2.17494i) q^{44} +4.55942 q^{46} +6.54587 q^{47} +(-1.34467 - 2.32904i) q^{48} +(-2.07757 + 3.59845i) q^{49} +(-1.52070 + 2.63393i) q^{51} +(0.534502 - 0.925785i) q^{52} +(4.86625 - 8.42860i) q^{53} +3.31488 q^{54} +(1.66997 + 2.89246i) q^{56} +(9.21497 - 15.9608i) q^{57} -2.14564 q^{58} +(-4.93480 - 8.54733i) q^{59} -1.86761 q^{61} +(0.527107 + 5.54276i) q^{62} -14.1366 q^{63} +1.00000 q^{64} +6.75404 q^{66} +(7.98521 - 13.8308i) q^{67} +(-0.565452 - 0.979392i) q^{68} +(-6.13094 - 10.6191i) q^{69} +(1.50751 - 2.61109i) q^{71} +(-2.11630 + 3.66553i) q^{72} +(-2.09086 + 3.62147i) q^{73} +(5.75839 + 9.97382i) q^{74} +(3.42647 + 5.93482i) q^{76} -8.38791 q^{77} -2.87493 q^{78} +(-2.71853 - 4.70863i) q^{79} +(1.89146 + 3.27611i) q^{81} +(-3.61032 + 6.25326i) q^{82} +(6.79944 - 11.7770i) q^{83} +(4.49112 - 7.77885i) q^{84} +(-0.230984 - 0.400075i) q^{86} +(2.88519 + 4.99729i) q^{87} +(-1.25570 + 2.17494i) q^{88} +13.9990 q^{89} +3.57040 q^{91} +4.55942 q^{92} +(12.2005 - 8.68086i) q^{93} +6.54587 q^{94} +(-1.34467 - 2.32904i) q^{96} -10.0509 q^{97} +(-2.07757 + 3.59845i) q^{98} +(-5.31487 - 9.20563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 2 q^{3} + 16 q^{4} + 2 q^{6} + 16 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 + 2 * q^6 + 16 * q^8 - 4 * q^9	$ 16 q + 16 q^{2} + 2 q^{3} + 16 q^{4} + 2 q^{6} + 16 q^{8} - 4 q^{9} + 2 q^{11} + 2 q^{12} + 6 q^{13} + 16 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 8 q^{21} + 2 q^{22} - 4 q^{23} + 2 q^{24} + 6 q^{26} - 4 q^{27} + 4 q^{29} + 6 q^{31} + 16 q^{32} - 12 q^{33} + 6 q^{34} - 4 q^{36} + 14 q^{37} + 4 q^{38} + 32 q^{39} - 8 q^{41} + 8 q^{42} + 6 q^{43} + 2 q^{44} - 4 q^{46} - 8 q^{47} + 2 q^{48} - 10 q^{49} - 20 q^{51} + 6 q^{52} + 8 q^{53} - 4 q^{54} + 34 q^{57} + 4 q^{58} - 8 q^{59} - 20 q^{61} + 6 q^{62} - 36 q^{63} + 16 q^{64} - 12 q^{66} - 6 q^{67} + 6 q^{68} - 18 q^{69} + 24 q^{71} - 4 q^{72} + 22 q^{73} + 14 q^{74} + 4 q^{76} + 48 q^{77} + 32 q^{78} - 2 q^{79} - 16 q^{81} - 8 q^{82} + 10 q^{83} + 8 q^{84} + 6 q^{86} - 20 q^{87} + 2 q^{88} - 36 q^{89} + 12 q^{91} - 4 q^{92} + 36 q^{93} - 8 q^{94} + 2 q^{96} + 20 q^{97} - 10 q^{98} - 32 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 + 2 * q^6 + 16 * q^8 - 4 * q^9 + 2 * q^11 + 2 * q^12 + 6 * q^13 + 16 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 8 * q^21 + 2 * q^22 - 4 * q^23 + 2 * q^24 + 6 * q^26 - 4 * q^27 + 4 * q^29 + 6 * q^31 + 16 * q^32 - 12 * q^33 + 6 * q^34 - 4 * q^36 + 14 * q^37 + 4 * q^38 + 32 * q^39 - 8 * q^41 + 8 * q^42 + 6 * q^43 + 2 * q^44 - 4 * q^46 - 8 * q^47 + 2 * q^48 - 10 * q^49 - 20 * q^51 + 6 * q^52 + 8 * q^53 - 4 * q^54 + 34 * q^57 + 4 * q^58 - 8 * q^59 - 20 * q^61 + 6 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^66 - 6 * q^67 + 6 * q^68 - 18 * q^69 + 24 * q^71 - 4 * q^72 + 22 * q^73 + 14 * q^74 + 4 * q^76 + 48 * q^77 + 32 * q^78 - 2 * q^79 - 16 * q^81 - 8 * q^82 + 10 * q^83 + 8 * q^84 + 6 * q^86 - 20 * q^87 + 2 * q^88 - 36 * q^89 + 12 * q^91 - 4 * q^92 + 36 * q^93 - 8 * q^94 + 2 * q^96 + 20 * q^97 - 10 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1550\mathbb{Z}\right)^\times$.

$n$	$251$	$1427$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.34467	−	2.32904i	−0.776348	−	1.34467i	−0.934034	−	0.357185i	$-0.883737\pi$
$3$	−1.34467	−	2.32904i	−0.776348	−	1.34467i	0.157686	−	0.987489i	$-0.449597\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.34467	−	2.32904i	−0.548961	−	0.950828i
$7$	1.66997	+	2.89246i	0.631188	+	1.09325i	0.987309	+	0.158809i	$0.0507655\pi$
$7$	1.66997	+	2.89246i	0.631188	+	1.09325i	−0.356122	+	0.934440i	$0.615901\pi$
$8$	1.00000			0.353553
$9$	−2.11630	+	3.66553i	−0.705432	+	1.22184i
$10$		0			0
$11$	−1.25570	+	2.17494i	−0.378608	+	0.655769i	−0.990860	−	0.134894i	$-0.956931\pi$
$11$	−1.25570	+	2.17494i	−0.378608	+	0.655769i	0.612252	+	0.790663i	$0.290264\pi$
$12$	−1.34467	−	2.32904i	−0.388174	−	0.672337i
$13$	0.534502	−	0.925785i	0.148244	−	0.256767i	−0.782334	−	0.622859i	$-0.785971\pi$
$13$	0.534502	−	0.925785i	0.148244	−	0.256767i	0.930579	+	0.366092i	$0.119304\pi$
$14$	1.66997	+	2.89246i	0.446317	+	0.773044i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.565452	−	0.979392i	−0.137142	−	0.237537i	0.789271	−	0.614044i	$-0.210458\pi$
$17$	−0.565452	−	0.979392i	−0.137142	−	0.237537i	−0.926414	+	0.376507i	$0.877125\pi$
$18$	−2.11630	+	3.66553i	−0.498816	+	0.863975i
$19$	3.42647	+	5.93482i	0.786086	+	1.36154i	0.928348	+	0.371712i	$0.121229\pi$
$19$	3.42647	+	5.93482i	0.786086	+	1.36154i	−0.142262	+	0.989829i	$0.545438\pi$
$20$		0			0
$21$	4.49112	−	7.77885i	0.980042	−	1.69748i
$22$	−1.25570	+	2.17494i	−0.267716	+	0.463698i
$23$	4.55942			0.950705			0.475353	−	0.879795i	$-0.342321\pi$
$23$	4.55942			0.950705			0.475353	+	0.879795i	$0.342321\pi$
$24$	−1.34467	−	2.32904i	−0.274480	−	0.475414i
$25$		0			0
$26$	0.534502	−	0.925785i	0.104825	−	0.181561i
$27$	3.31488			0.637948
$28$	1.66997	+	2.89246i	0.315594	+	0.546624i
$29$	−2.14564			−0.398436			−0.199218	−	0.979955i	$-0.563840\pi$
$29$	−2.14564			−0.398436			−0.199218	+	0.979955i	$0.563840\pi$
$30$		0			0
$31$	0.527107	+	5.54276i	0.0946712	+	0.995509i
$31$	0.527107	+	5.54276i	0.0946712	+	0.995509i
$32$	1.00000			0.176777
$33$	6.75404			1.17573
$34$	−0.565452	−	0.979392i	−0.0969743	−	0.167964i
$35$		0			0
$36$	−2.11630	+	3.66553i	−0.352716	+	0.610922i
$37$	5.75839	+	9.97382i	0.946673	+	1.63969i	0.752367	+	0.658745i	$0.228912\pi$
$37$	5.75839	+	9.97382i	0.946673	+	1.63969i	0.194306	+	0.980941i	$0.437754\pi$
$38$	3.42647	+	5.93482i	0.555847	+	0.962755i
$39$	−2.87493			−0.460357
$40$		0			0
$41$	−3.61032	+	6.25326i	−0.563838	+	0.976595i	0.433319	+	0.901241i	$0.357342\pi$
$41$	−3.61032	+	6.25326i	−0.563838	+	0.976595i	−0.997157	+	0.0753549i	$0.975991\pi$
$42$	4.49112	−	7.77885i	0.692995	−	1.20030i
$43$	−0.230984	−	0.400075i	−0.0352247	−	0.0610109i	0.847876	−	0.530195i	$-0.177881\pi$
$43$	−0.230984	−	0.400075i	−0.0352247	−	0.0610109i	−0.883100	+	0.469184i	$0.844548\pi$
$44$	−1.25570	+	2.17494i	−0.189304	+	0.327884i
$45$		0			0
$46$	4.55942			0.672250
$47$	6.54587			0.954813			0.477406	−	0.878683i	$-0.341577\pi$
$47$	6.54587			0.954813			0.477406	+	0.878683i	$0.341577\pi$
$48$	−1.34467	−	2.32904i	−0.194087	−	0.336169i
$49$	−2.07757	+	3.59845i	−0.296796	+	0.514065i
$50$		0			0
$51$	−1.52070	+	2.63393i	−0.212940	+	0.368823i
$52$	0.534502	−	0.925785i	0.0741222	−	0.128383i
$53$	4.86625	−	8.42860i	0.668431	−	1.15776i	−0.309911	−	0.950765i	$-0.600299\pi$
$53$	4.86625	−	8.42860i	0.668431	−	1.15776i	0.978343	−	0.206992i	$-0.0663673\pi$
$54$	3.31488			0.451098
$55$		0			0
$56$	1.66997	+	2.89246i	0.223159	+	0.386522i
$57$	9.21497	−	15.9608i	1.22055	−	2.11406i
$58$	−2.14564			−0.281737
$59$	−4.93480	−	8.54733i	−0.642457	−	1.11277i	−0.984883	−	0.173223i	$-0.944582\pi$
$59$	−4.93480	−	8.54733i	−0.642457	−	1.11277i	0.342426	−	0.939545i	$-0.388751\pi$
$60$		0			0
$61$	−1.86761			−0.239123			−0.119562	−	0.992827i	$-0.538149\pi$
$61$	−1.86761			−0.239123			−0.119562	+	0.992827i	$0.538149\pi$
$62$	0.527107	+	5.54276i	0.0669426	+	0.703931i
$63$	−14.1366			−1.78104
$64$	1.00000			0.125000
$65$		0			0
$66$	6.75404			0.831364
$67$	7.98521	−	13.8308i	0.975549	−	1.68970i	0.297436	−	0.954742i	$-0.403869\pi$
$67$	7.98521	−	13.8308i	0.975549	−	1.68970i	0.678113	−	0.734958i	$-0.262798\pi$
$68$	−0.565452	−	0.979392i	−0.0685712	−	0.118769i
$69$	−6.13094	−	10.6191i	−0.738078	−	1.27839i
$70$		0			0
$71$	1.50751	−	2.61109i	0.178909	−	0.309879i	−0.762598	−	0.646872i	$-0.776077\pi$
$71$	1.50751	−	2.61109i	0.178909	−	0.309879i	0.941507	+	0.336993i	$0.109410\pi$
$72$	−2.11630	+	3.66553i	−0.249408	+	0.431987i
$73$	−2.09086	+	3.62147i	−0.244716	+	0.423861i	−0.962052	−	0.272867i	$-0.912028\pi$
$73$	−2.09086	+	3.62147i	−0.244716	+	0.423861i	0.717336	+	0.696728i	$0.245361\pi$
$74$	5.75839	+	9.97382i	0.669399	+	1.15943i
$75$		0			0
$76$	3.42647	+	5.93482i	0.393043	+	0.680770i
$77$	−8.38791			−0.955891
$78$	−2.87493			−0.325521
$79$	−2.71853	−	4.70863i	−0.305859	−	0.529763i	0.671594	−	0.740920i	$-0.265610\pi$
$79$	−2.71853	−	4.70863i	−0.305859	−	0.529763i	−0.977452	+	0.211157i	$0.932277\pi$
$80$		0			0
$81$	1.89146	+	3.27611i	0.210163	+	0.364012i
$82$	−3.61032	+	6.25326i	−0.398693	+	0.690557i
$83$	6.79944	−	11.7770i	0.746336	−	1.29269i	−0.203233	−	0.979130i	$-0.565145\pi$
$83$	6.79944	−	11.7770i	0.746336	−	1.29269i	0.949568	−	0.313561i	$-0.101522\pi$
$84$	4.49112	−	7.77885i	0.490021	−	0.848742i
$85$		0			0
$86$	−0.230984	−	0.400075i	−0.0249076	−	0.0431412i
$87$	2.88519	+	4.99729i	0.309325	+	0.535766i
$88$	−1.25570	+	2.17494i	−0.133858	+	0.231849i
$89$	13.9990			1.48389			0.741947	−	0.670459i	$-0.233903\pi$
$89$	13.9990			1.48389			0.741947	+	0.670459i	$0.233903\pi$
$90$		0			0
$91$	3.57040			0.374280
$92$	4.55942			0.475353
$93$	12.2005	−	8.68086i	1.26514	−	0.900163i
$94$	6.54587			0.675155
$95$		0			0
$96$	−1.34467	−	2.32904i	−0.137240	−	0.237707i
$97$	−10.0509			−1.02052			−0.510259	−	0.860021i	$-0.670450\pi$
$97$	−10.0509			−1.02052			−0.510259	+	0.860021i	$0.670450\pi$
$98$	−2.07757	+	3.59845i	−0.209866	+	0.363499i
$99$	−5.31487	−	9.20563i	−0.534165	−	0.925201i
$100$		0			0
$101$	−14.8784			−1.48045			−0.740227	−	0.672357i	$-0.765282\pi$
$101$	−14.8784			−1.48045			−0.740227	+	0.672357i	$0.765282\pi$
$102$	−1.52070	+	2.63393i	−0.150572	+	0.260798i
$103$	−2.13628	+	3.70015i	−0.210494	+	0.364587i	−0.951869	−	0.306504i	$-0.900841\pi$
$103$	−2.13628	+	3.70015i	−0.210494	+	0.364587i	0.741375	+	0.671091i	$0.234174\pi$
$104$	0.534502	−	0.925785i	0.0524123	−	0.0907807i
$105$		0			0
$106$	4.86625	−	8.42860i	0.472652	−	0.818658i
$107$	4.91637	+	8.51540i	0.475283	+	0.823215i	0.999599	−	0.0283088i	$-0.00901217\pi$
$107$	4.91637	+	8.51540i	0.475283	+	0.823215i	−0.524316	+	0.851524i	$0.675679\pi$
$108$	3.31488			0.318974
$109$	−12.2368			−1.17207			−0.586037	−	0.810284i	$-0.699313\pi$
$109$	−12.2368			−1.17207			−0.586037	+	0.810284i	$0.699313\pi$
$110$		0			0
$111$	15.4863	−	26.8231i	1.46990	−	2.54593i
$112$	1.66997	+	2.89246i	0.157797	+	0.273312i
$113$	−6.88486	+	11.9249i	−0.647673	+	1.12180i	0.336004	+	0.941860i	$0.390924\pi$
$113$	−6.88486	+	11.9249i	−0.647673	+	1.12180i	−0.983677	+	0.179942i	$0.942409\pi$
$114$	9.21497	−	15.9608i	0.863061	−	1.49487i
$115$		0			0
$116$	−2.14564			−0.199218
$117$	2.26233	+	3.91847i	0.209153	+	0.362263i
$118$	−4.93480	−	8.54733i	−0.454285	−	0.786845i
$119$	1.88857	−	3.27110i	0.173125	−	0.299861i
$120$		0			0
$121$	2.34643	+	4.06414i	0.213312	+	0.369467i
$122$	−1.86761			−0.169086
$123$	19.4188			1.75094
$124$	0.527107	+	5.54276i	0.0473356	+	0.497754i
$125$		0			0
$126$	−14.1366			−1.25939
$127$	−0.631179	−	1.09323i	−0.0560081	−	0.0970088i	0.836662	−	0.547720i	$-0.184504\pi$
$127$	−0.631179	−	1.09323i	−0.0560081	−	0.0970088i	−0.892670	+	0.450711i	$0.851171\pi$
$128$	1.00000			0.0883883
$129$	−0.621195	+	1.07594i	−0.0546932	+	0.0947314i
$130$		0			0
$131$	−2.00041	−	3.46482i	−0.174777	−	0.302723i	0.765307	−	0.643665i	$-0.222587\pi$
$131$	−2.00041	−	3.46482i	−0.174777	−	0.302723i	−0.940084	+	0.340943i	$0.889254\pi$
$132$	6.75404			0.587863
$133$	−11.4442	+	19.8219i	−0.992335	+	1.71878i
$134$	7.98521	−	13.8308i	0.689817	−	1.19480i
$135$		0			0
$136$	−0.565452	−	0.979392i	−0.0484871	−	0.0839822i
$137$	5.44408	−	9.42943i	0.465119	−	0.805611i	−0.534087	−	0.845429i	$-0.679345\pi$
$137$	5.44408	−	9.42943i	0.465119	−	0.805611i	0.999207	+	0.0398187i	$0.0126780\pi$
$138$	−6.13094	−	10.6191i	−0.521900	−	0.903957i
$139$	10.7590			0.912569			0.456285	−	0.889834i	$-0.349180\pi$
$139$	10.7590			0.912569			0.456285	+	0.889834i	$0.349180\pi$
$140$		0			0
$141$	−8.80206	−	15.2456i	−0.741267	−	1.28391i
$142$	1.50751	−	2.61109i	0.126508	−	0.219118i
$143$	1.34235	+	2.32502i	0.112253	+	0.194428i
$144$	−2.11630	+	3.66553i	−0.176358	+	0.305461i
$145$		0			0
$146$	−2.09086	+	3.62147i	−0.173040	+	0.299715i
$147$	11.1746			0.921666
$148$	5.75839	+	9.97382i	0.473336	+	0.819843i
$149$	5.86843	+	10.1644i	0.480761	+	0.832702i	0.999756	−	0.0220752i	$-0.00702731\pi$
$149$	5.86843	+	10.1644i	0.480761	+	0.832702i	−0.518996	+	0.854777i	$0.673694\pi$
$150$		0			0
$151$	5.08955			0.414182			0.207091	−	0.978322i	$-0.433600\pi$
$151$	5.08955			0.414182			0.207091	+	0.978322i	$0.433600\pi$
$152$	3.42647	+	5.93482i	0.277923	+	0.481377i
$153$	4.78666			0.386979
$154$	−8.38791			−0.675917
$155$		0			0
$156$	−2.87493			−0.230178
$157$	−5.04463			−0.402605			−0.201303	−	0.979529i	$-0.564517\pi$
$157$	−5.04463			−0.402605			−0.201303	+	0.979529i	$0.564517\pi$
$158$	−2.71853	−	4.70863i	−0.216275	−	0.374599i
$159$	−26.1741			−2.07574
$160$		0			0
$161$	7.61408	+	13.1880i	0.600073	+	1.03936i
$162$	1.89146	+	3.27611i	0.148607	+	0.257395i
$163$	−12.4987			−0.978972			−0.489486	−	0.872011i	$-0.662816\pi$
$163$	−12.4987			−0.978972			−0.489486	+	0.872011i	$0.662816\pi$
$164$	−3.61032	+	6.25326i	−0.281919	+	0.488298i
$165$		0			0
$166$	6.79944	−	11.7770i	0.527739	−	0.914071i
$167$	−8.91775	−	15.4460i	−0.690076	−	1.19525i	−0.971812	−	0.235755i	$-0.924244\pi$
$167$	−8.91775	−	15.4460i	−0.690076	−	1.19525i	0.281736	−	0.959492i	$-0.409090\pi$
$168$	4.49112	−	7.77885i	0.346497	−	0.600151i
$169$	5.92861	+	10.2687i	0.456047	+	0.789897i
$170$		0			0
$171$	−29.0057			−2.21812
$172$	−0.230984	−	0.400075i	−0.0176123	−	0.0305055i
$173$	−4.05190	+	7.01810i	−0.308060	+	0.533576i	−0.977938	−	0.208895i	$-0.933013\pi$
$173$	−4.05190	+	7.01810i	−0.308060	+	0.533576i	0.669878	+	0.742472i	$0.266347\pi$
$174$	2.88519	+	4.99729i	0.218726	+	0.378844i
$175$		0			0
$176$	−1.25570	+	2.17494i	−0.0946520	+	0.163942i
$177$	−13.2714	+	22.9867i	−0.997540	+	1.72779i
$178$	13.9990			1.04927
$179$	9.47460	+	16.4105i	0.708165	+	1.22658i	0.965537	+	0.260265i	$0.0838099\pi$
$179$	9.47460	+	16.4105i	0.708165	+	1.22658i	−0.257373	+	0.966312i	$0.582857\pi$
$180$		0			0
$181$	−6.25755	+	10.8384i	−0.465120	+	0.805612i	−0.999207	−	0.0398180i	$-0.987322\pi$
$181$	−6.25755	+	10.8384i	−0.465120	+	0.805612i	0.534087	+	0.845430i	$0.320656\pi$
$182$	3.57040			0.264656
$183$	2.51133	+	4.34975i	0.185643	+	0.321543i
$184$	4.55942			0.336125
$185$		0			0
$186$	12.2005	−	8.68086i	0.894587	−	0.636511i
$187$	2.84016			0.207693
$188$	6.54587			0.477406
$189$	5.53573	+	9.58817i	0.402665	+	0.697436i
$190$		0			0
$191$	−0.719583	+	1.24636i	−0.0520672	+	0.0901831i	−0.890884	−	0.454230i	$-0.849914\pi$
$191$	−0.719583	+	1.24636i	−0.0520672	+	0.0901831i	0.838817	+	0.544413i	$0.183248\pi$
$192$	−1.34467	−	2.32904i	−0.0970435	−	0.168084i
$193$	9.14408	+	15.8380i	0.658205	+	1.14005i	0.981080	+	0.193603i	$0.0620175\pi$
$193$	9.14408	+	15.8380i	0.658205	+	1.14005i	−0.322874	+	0.946442i	$0.604649\pi$
$194$	−10.0509			−0.721615
$195$		0			0
$196$	−2.07757	+	3.59845i	−0.148398	+	0.257032i
$197$	1.59430	−	2.76140i	0.113589	−	0.196742i	−0.803626	−	0.595135i	$-0.797099\pi$
$197$	1.59430	−	2.76140i	0.113589	−	0.196742i	0.917215	+	0.398393i	$0.130432\pi$
$198$	−5.31487	−	9.20563i	−0.377712	−	0.654216i
$199$	7.53070	−	13.0436i	0.533837	−	0.924633i	−0.465381	−	0.885110i	$-0.654083\pi$
$199$	7.53070	−	13.0436i	0.533837	−	0.924633i	0.999219	−	0.0395230i	$-0.0125838\pi$
$200$		0			0
$201$	−42.9500			−3.02946
$202$	−14.8784			−1.04684
$203$	−3.58315	−	6.20619i	−0.251488	−	0.435589i
$204$	−1.52070	+	2.63393i	−0.106470	+	0.184412i
$205$		0			0
$206$	−2.13628	+	3.70015i	−0.148842	+	0.257802i
$207$	−9.64909	+	16.7127i	−0.670658	+	1.16161i
$208$	0.534502	−	0.925785i	0.0370611	−	0.0641917i
$209$	−17.2105			−1.19047
$210$		0			0
$211$	9.05661	+	15.6865i	0.623483	+	1.07990i	0.988832	+	0.149033i	$0.0476161\pi$
$211$	9.05661	+	15.6865i	0.623483	+	1.07990i	−0.365350	+	0.930870i	$0.619051\pi$
$212$	4.86625	−	8.42860i	0.334216	−	0.578879i
$213$	−8.10845			−0.555582
$214$	4.91637	+	8.51540i	0.336076	+	0.582101i
$215$		0			0
$216$	3.31488			0.225549
$217$	−15.1520	+	10.7809i	−1.02858	+	0.731852i
$218$	−12.2368			−0.828782
$219$	11.2461			0.759940
$220$		0			0
$221$	−1.20894			−0.0813223
$222$	15.4863	−	26.8231i	1.03937	−	1.80025i
$223$	−3.17734	−	5.50332i	−0.212770	−	0.368529i	0.739810	−	0.672816i	$-0.234915\pi$
$223$	−3.17734	−	5.50332i	−0.212770	−	0.368529i	−0.952581	+	0.304286i	$0.901582\pi$
$224$	1.66997	+	2.89246i	0.111579	+	0.193261i
$225$		0			0
$226$	−6.88486	+	11.9249i	−0.457974	+	0.793234i
$227$	11.7745	−	20.3941i	0.781503	−	1.35360i	−0.149562	−	0.988752i	$-0.547786\pi$
$227$	11.7745	−	20.3941i	0.781503	−	1.35360i	0.931066	−	0.364851i	$-0.118880\pi$
$228$	9.21497	−	15.9608i	0.610276	−	1.05703i
$229$	−11.2948	−	19.5632i	−0.746384	−	1.29278i	−0.949545	−	0.313630i	$-0.898455\pi$
$229$	−11.2948	−	19.5632i	−0.746384	−	1.29278i	0.203161	−	0.979145i	$-0.434878\pi$
$230$		0			0
$231$	11.2790	+	19.5358i	0.742104	+	1.28536i
$232$	−2.14564			−0.140868
$233$	11.4137			0.747735			0.373867	−	0.927482i	$-0.378032\pi$
$233$	11.4137			0.747735			0.373867	+	0.927482i	$0.378032\pi$
$234$	2.26233	+	3.91847i	0.147893	+	0.256159i
$235$		0			0
$236$	−4.93480	−	8.54733i	−0.321228	−	0.556384i
$237$	−7.31108	+	12.6632i	−0.474905	+	0.822560i
$238$	1.88857	−	3.27110i	0.122418	−	0.212034i
$239$	−7.99093	+	13.8407i	−0.516890	+	0.895280i	0.482918	+	0.875666i	$0.339577\pi$
$239$	−7.99093	+	13.8407i	−0.516890	+	0.895280i	−0.999808	+	0.0196140i	$0.993756\pi$
$240$		0			0
$241$	−3.42853	−	5.93840i	−0.220851	−	0.382526i	0.734215	−	0.678917i	$-0.237550\pi$
$241$	−3.42853	−	5.93840i	−0.220851	−	0.382526i	−0.955067	+	0.296391i	$0.904217\pi$
$242$	2.34643	+	4.06414i	0.150834	+	0.261253i
$243$	10.0591	−	17.4229i	0.645293	−	1.11768i
$244$	−1.86761			−0.119562
$245$		0			0
$246$	19.4188			1.23810
$247$	7.32582			0.466131
$248$	0.527107	+	5.54276i	0.0334713	+	0.351965i
$249$	−36.5721			−2.31766
$250$		0			0
$251$	−0.519274	−	0.899409i	−0.0327763	−	0.0567702i	0.849172	−	0.528116i	$-0.177102\pi$
$251$	−0.519274	−	0.899409i	−0.0327763	−	0.0567702i	−0.881948	+	0.471346i	$0.843768\pi$
$252$	−14.1366			−0.890520
$253$	−5.72527	+	9.91646i	−0.359945	+	0.623443i
$254$	−0.631179	−	1.09323i	−0.0396037	−	0.0685956i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.77037	+	9.99457i	−0.359946	+	0.623444i	−0.987951	−	0.154765i	$-0.950538\pi$
$257$	−5.77037	+	9.99457i	−0.359946	+	0.623444i	0.628006	+	0.778209i	$0.283871\pi$
$258$	−0.621195	+	1.07594i	−0.0386739	+	0.0669852i
$259$	−19.2326	+	33.3119i	−1.19506	+	2.06990i
$260$		0			0
$261$	4.54082	−	7.86492i	0.281069	−	0.486827i
$262$	−2.00041	−	3.46482i	−0.123586	−	0.214057i
$263$	−27.8728			−1.71871			−0.859356	−	0.511377i	$-0.829136\pi$
$263$	−27.8728			−1.71871			−0.859356	+	0.511377i	$0.829136\pi$
$264$	6.75404			0.415682
$265$		0			0
$266$	−11.4442	+	19.8219i	−0.701687	+	1.21536i
$267$	−18.8241	−	32.6043i	−1.15202	−	1.99535i
$268$	7.98521	−	13.8308i	0.487774	−	0.844850i
$269$	3.72020	−	6.44358i	0.226825	−	0.392872i	−0.730040	−	0.683404i	$-0.760499\pi$
$269$	3.72020	−	6.44358i	0.226825	−	0.392872i	0.956865	+	0.290532i	$0.0938322\pi$
$270$		0			0
$271$	12.3624			0.750962			0.375481	−	0.926830i	$-0.377478\pi$
$271$	12.3624			0.750962			0.375481	+	0.926830i	$0.377478\pi$
$272$	−0.565452	−	0.979392i	−0.0342856	−	0.0593844i
$273$	−4.80103	−	8.31562i	−0.290571	−	0.503284i
$274$	5.44408	−	9.42943i	0.328889	−	0.569653i
$275$		0			0
$276$	−6.13094	−	10.6191i	−0.369039	−	0.639194i
$277$	11.1581			0.670423			0.335211	−	0.942143i	$-0.391192\pi$
$277$	11.1581			0.670423			0.335211	+	0.942143i	$0.391192\pi$
$278$	10.7590			0.645284
$279$	−21.4327	−	9.79800i	−1.28314	−	0.586591i
$280$		0			0
$281$	3.11884			0.186055			0.0930273	−	0.995664i	$-0.470346\pi$
$281$	3.11884			0.186055			0.0930273	+	0.995664i	$0.470346\pi$
$282$	−8.80206	−	15.2456i	−0.524155	−	0.907863i
$283$	−22.2481			−1.32251			−0.661255	−	0.750161i	$-0.729976\pi$
$283$	−22.2481			−1.32251			−0.661255	+	0.750161i	$0.729976\pi$
$284$	1.50751	−	2.61109i	0.0894544	−	0.154940i
$285$		0			0
$286$	1.34235	+	2.32502i	0.0793749	+	0.137481i
$287$	−24.1165			−1.42355
$288$	−2.11630	+	3.66553i	−0.124704	+	0.215994i
$289$	7.86053	−	13.6148i	0.462384	−	0.800873i
$290$		0			0
$291$	13.5152	+	23.4091i	0.792277	+	1.37226i
$292$	−2.09086	+	3.62147i	−0.122358	+	0.211930i
$293$	−15.3428	−	26.5745i	−0.896335	−	1.55250i	−0.832144	−	0.554559i	$-0.812887\pi$
$293$	−15.3428	−	26.5745i	−0.896335	−	1.55250i	−0.0641905	−	0.997938i	$-0.520447\pi$
$294$	11.1746			0.651717
$295$		0			0
$296$	5.75839	+	9.97382i	0.334699	+	0.579716i
$297$	−4.16249	+	7.20965i	−0.241532	+	0.418346i
$298$	5.86843	+	10.1644i	0.339949	+	0.588809i
$299$	2.43702	−	4.22105i	0.140937	−	0.244109i
$300$		0			0
$301$	0.771469	−	1.33622i	0.0444667	−	0.0770187i
$302$	5.08955			0.292871
$303$	20.0066	+	34.6524i	1.14935	+	1.99073i
$304$	3.42647	+	5.93482i	0.196521	+	0.340385i
$305$		0			0
$306$	4.78666			0.273635
$307$	6.79649	+	11.7719i	0.387896	+	0.671855i	0.992166	−	0.124924i	$-0.0398687\pi$
$307$	6.79649	+	11.7719i	0.387896	+	0.671855i	−0.604270	+	0.796779i	$0.706535\pi$
$308$	−8.38791			−0.477945
$309$	11.4904			0.653667
$310$		0			0
$311$	8.28787			0.469962			0.234981	−	0.972000i	$-0.424497\pi$
$311$	8.28787			0.469962			0.234981	+	0.972000i	$0.424497\pi$
$312$	−2.87493			−0.162761
$313$	4.97379	+	8.61486i	0.281135	+	0.486940i	0.971665	−	0.236364i	$-0.0759557\pi$
$313$	4.97379	+	8.61486i	0.281135	+	0.486940i	−0.690529	+	0.723304i	$0.742622\pi$
$314$	−5.04463			−0.284685
$315$		0			0
$316$	−2.71853	−	4.70863i	−0.152929	−	0.264881i
$317$	1.12141	+	1.94235i	0.0629849	+	0.109093i	0.895798	−	0.444461i	$-0.146605\pi$
$317$	1.12141	+	1.94235i	0.0629849	+	0.109093i	−0.832813	+	0.553554i	$0.813271\pi$
$318$	−26.1741			−1.46777
$319$	2.69428	−	4.66664i	0.150851	−	0.261282i
$320$		0			0
$321$	13.2218	−	22.9009i	0.737971	−	1.27820i
$322$	7.61408	+	13.1880i	0.424316	+	0.734937i
$323$	3.87501	−	6.71171i	0.215611	−	0.373450i
$324$	1.89146	+	3.27611i	0.105081	+	0.182006i
$325$		0			0
$326$	−12.4987			−0.692238
$327$	16.4545	+	28.5001i	0.909938	+	1.57606i
$328$	−3.61032	+	6.25326i	−0.199347	+	0.345279i
$329$	10.9314	+	18.9337i	0.602666	+	1.04385i
$330$		0			0
$331$	11.7477	−	20.3476i	0.645712	−	1.11841i	−0.338424	−	0.940994i	$-0.609894\pi$
$331$	11.7477	−	20.3476i	0.645712	−	1.11841i	0.984137	−	0.177413i	$-0.0567727\pi$
$332$	6.79944	−	11.7770i	0.373168	−	0.646346i
$333$	−48.7458			−2.67126
$334$	−8.91775	−	15.4460i	−0.487958	−	0.845167i
$335$		0			0
$336$	4.49112	−	7.77885i	0.245011	−	0.424371i
$337$	−5.10345			−0.278003			−0.139001	−	0.990292i	$-0.544389\pi$
$337$	−5.10345			−0.278003			−0.139001	+	0.990292i	$0.544389\pi$
$338$	5.92861	+	10.2687i	0.322474	+	0.558542i
$339$	37.0316			2.01128
$340$		0			0
$341$	−12.7170	−	5.81362i	−0.688666	−	0.314825i
$342$	−29.0057			−1.56845
$343$	9.50164			0.513041
$344$	−0.230984	−	0.400075i	−0.0124538	−	0.0215706i
$345$		0			0
$346$	−4.05190	+	7.01810i	−0.217832	+	0.377296i
$347$	−15.1378	−	26.2194i	−0.812639	−	1.40753i	−0.911011	−	0.412382i	$-0.864697\pi$
$347$	−15.1378	−	26.2194i	−0.812639	−	1.40753i	0.0983723	−	0.995150i	$-0.468636\pi$
$348$	2.88519	+	4.99729i	0.154662	+	0.267883i
$349$	−11.9756			−0.641038			−0.320519	−	0.947242i	$-0.603857\pi$
$349$	−11.9756			−0.641038			−0.320519	+	0.947242i	$0.603857\pi$
$350$		0			0
$351$	1.77181	−	3.06886i	0.0945722	−	0.163804i
$352$	−1.25570	+	2.17494i	−0.0669291	+	0.115925i
$353$	8.54181	+	14.7949i	0.454635	+	0.787450i	0.998667	−	0.0516138i	$-0.0164365\pi$
$353$	8.54181	+	14.7949i	0.454635	+	0.787450i	−0.544032	+	0.839064i	$0.683103\pi$
$354$	−13.2714	+	22.9867i	−0.705367	+	1.22173i
$355$		0			0
$356$	13.9990			0.741947
$357$	−10.1581			−0.537621
$358$	9.47460	+	16.4105i	0.500748	+	0.867321i
$359$	−14.7258	+	25.5058i	−0.777198	+	1.34615i	0.156352	+	0.987701i	$0.450026\pi$
$359$	−14.7258	+	25.5058i	−0.777198	+	1.34615i	−0.933551	+	0.358446i	$0.883307\pi$
$360$		0			0
$361$	−13.9814	+	24.2165i	−0.735862	+	1.27455i
$362$	−6.25755	+	10.8384i	−0.328890	+	0.569653i
$363$	6.31037	−	10.9299i	0.331208	−	0.573670i
$364$	3.57040			0.187140
$365$		0			0
$366$	2.51133	+	4.34975i	0.131269	+	0.227365i
$367$	−15.6459	+	27.0994i	−0.816707	+	1.41458i	0.0913882	+	0.995815i	$0.470870\pi$
$367$	−15.6459	+	27.0994i	−0.816707	+	1.41458i	−0.908096	+	0.418763i	$0.862464\pi$
$368$	4.55942			0.237676
$369$	−15.2810	−	26.4675i	−0.795499	−	1.37784i
$370$		0			0
$371$	32.5059			1.68762
$372$	12.2005	−	8.68086i	0.632568	−	0.450082i
$373$	19.9316			1.03202			0.516009	−	0.856583i	$-0.327417\pi$
$373$	19.9316			1.03202			0.516009	+	0.856583i	$0.327417\pi$
$374$	2.84016			0.146861
$375$		0			0
$376$	6.54587			0.337577
$377$	−1.14685	+	1.98640i	−0.0590658	+	0.102305i
$378$	5.53573	+	9.58817i	0.284727	+	0.493162i
$379$	−7.41755	−	12.8476i	−0.381014	−	0.659936i	0.610193	−	0.792252i	$-0.291092\pi$
$379$	−7.41755	−	12.8476i	−0.381014	−	0.659936i	−0.991207	+	0.132317i	$0.957758\pi$
$380$		0			0
$381$	−1.69746	+	2.94009i	−0.0869635	+	0.150625i
$382$	−0.719583	+	1.24636i	−0.0368171	+	0.0637691i
$383$	2.42574	−	4.20151i	0.123950	−	0.214687i	−0.797372	−	0.603488i	$-0.793777\pi$
$383$	2.42574	−	4.20151i	0.123950	−	0.214687i	0.921322	+	0.388801i	$0.127111\pi$
$384$	−1.34467	−	2.32904i	−0.0686201	−	0.118854i
$385$		0			0
$386$	9.14408	+	15.8380i	0.465422	+	0.806134i
$387$	1.95532			0.0993945
$388$	−10.0509			−0.510259
$389$	−1.13556	−	1.96685i	−0.0575752	−	0.0997232i	0.835801	−	0.549032i	$-0.185004\pi$
$389$	−1.13556	−	1.96685i	−0.0575752	−	0.0997232i	−0.893376	+	0.449309i	$0.851670\pi$
$390$		0			0
$391$	−2.57814	−	4.46546i	−0.130382	−	0.225828i
$392$	−2.07757	+	3.59845i	−0.104933	+	0.181749i
$393$	−5.37981	+	9.31811i	−0.271376	+	0.470036i
$394$	1.59430	−	2.76140i	0.0803194	−	0.139117i
$395$		0			0
$396$	−5.31487	−	9.20563i	−0.267082	−	0.462600i
$397$	−4.72369	−	8.18167i	−0.237075	−	0.410626i	0.722799	−	0.691059i	$-0.242855\pi$
$397$	−4.72369	−	8.18167i	−0.237075	−	0.410626i	−0.959874	+	0.280432i	$0.909522\pi$
$398$	7.53070	−	13.0436i	0.377480	−	0.653814i
$399$	61.5547			3.08159
$400$		0			0
$401$	20.3650			1.01698			0.508490	−	0.861068i	$-0.330204\pi$
$401$	20.3650			1.01698			0.508490	+	0.861068i	$0.330204\pi$
$402$	−42.9500			−2.14215
$403$	5.41314	+	2.47463i	0.269648	+	0.123270i
$404$	−14.8784			−0.740227
$405$		0			0
$406$	−3.58315	−	6.20619i	−0.177829	−	0.308008i
$407$	−28.9232			−1.43367
$408$	−1.52070	+	2.63393i	−0.0752858	+	0.130399i
$409$	−6.41855	−	11.1173i	−0.317377	−	0.549713i	0.662563	−	0.749006i	$-0.269469\pi$
$409$	−6.41855	−	11.1173i	−0.317377	−	0.549713i	−0.979940	+	0.199293i	$0.936135\pi$
$410$		0			0
$411$	−29.2821			−1.44438
$412$	−2.13628	+	3.70015i	−0.105247	+	0.182293i
$413$	16.4819	−	28.5475i	0.811021	−	1.40473i
$414$	−9.64909	+	16.7127i	−0.474227	+	0.821385i
$415$		0			0
$416$	0.534502	−	0.925785i	0.0262061	−	0.0453904i
$417$	−14.4674	−	25.0583i	−0.708471	−	1.22711i
$418$	−17.2105			−0.841792
$419$	16.9178			0.826488			0.413244	−	0.910620i	$-0.364396\pi$
$419$	16.9178			0.826488			0.413244	+	0.910620i	$0.364396\pi$
$420$		0			0
$421$	4.96613	−	8.60160i	0.242035	−	0.419216i	−0.719259	−	0.694742i	$-0.755519\pi$
$421$	4.96613	−	8.60160i	0.242035	−	0.419216i	0.961294	+	0.275526i	$0.0888519\pi$
$422$	9.05661	+	15.6865i	0.440869	+	0.763607i
$423$	−13.8530	+	23.9941i	−0.673556	+	1.16663i
$424$	4.86625	−	8.42860i	0.236326	−	0.409329i
$425$		0			0
$426$	−8.10845			−0.392856
$427$	−3.11885	−	5.40200i	−0.150931	−	0.261421i
$428$	4.91637	+	8.51540i	0.237642	+	0.411608i
$429$	3.61005	−	6.25279i	0.174295	−	0.301887i
$430$		0			0
$431$	0.257626	+	0.446222i	0.0124094	+	0.0214938i	0.872163	−	0.489215i	$-0.162717\pi$
$431$	0.257626	+	0.446222i	0.0124094	+	0.0214938i	−0.859754	+	0.510708i	$0.829383\pi$
$432$	3.31488			0.159487
$433$	−37.7395			−1.81365			−0.906823	−	0.421511i	$-0.861500\pi$
$433$	−37.7395			−1.81365			−0.906823	+	0.421511i	$0.861500\pi$
$434$	−15.1520	+	10.7809i	−0.727318	+	0.517497i
$435$		0			0
$436$	−12.2368			−0.586037
$437$	15.6227	+	27.0593i	0.747336	+	1.29442i
$438$	11.2461			0.537358
$439$	7.16777	−	12.4149i	0.342099	−	0.592533i	−0.642723	−	0.766098i	$-0.722196\pi$
$439$	7.16777	−	12.4149i	0.342099	−	0.592533i	0.984822	+	0.173566i	$0.0555289\pi$
$440$		0			0
$441$	−8.79351	−	15.2308i	−0.418738	−	0.725276i
$442$	−1.20894			−0.0575035
$443$	13.7112	−	23.7485i	0.651440	−	1.12833i	−0.331334	−	0.943514i	$-0.607499\pi$
$443$	13.7112	−	23.7485i	0.651440	−	1.12833i	0.982774	−	0.184813i	$-0.0591680\pi$
$444$	15.4863	−	26.8231i	0.734948	−	1.27297i
$445$		0			0
$446$	−3.17734	−	5.50332i	−0.150451	−	0.260590i
$447$	15.7823	−	27.3357i	0.746475	−	1.29293i
$448$	1.66997	+	2.89246i	0.0788984	+	0.136656i
$449$	−39.8495			−1.88062			−0.940308	−	0.340326i	$-0.889463\pi$
$449$	−39.8495			−1.88062			−0.940308	+	0.340326i	$0.889463\pi$
$450$		0			0
$451$	−9.06697	−	15.7045i	−0.426947	−	0.739494i
$452$	−6.88486	+	11.9249i	−0.323836	+	0.560901i
$453$	−6.84379	−	11.8538i	−0.321549	−	0.556940i
$454$	11.7745	−	20.3941i	0.552606	−	0.957142i
$455$		0			0
$456$	9.21497	−	15.9608i	0.431530	−	0.747433i
$457$	−17.5445			−0.820696			−0.410348	−	0.911929i	$-0.634593\pi$
$457$	−17.5445			−0.820696			−0.410348	+	0.911929i	$0.634593\pi$
$458$	−11.2948	−	19.5632i	−0.527773	−	0.914130i
$459$	−1.87440	−	3.24656i	−0.0874897	−	0.151537i
$460$		0			0
$461$	−9.00321			−0.419321			−0.209661	−	0.977774i	$-0.567236\pi$
$461$	−9.00321			−0.419321			−0.209661	+	0.977774i	$0.567236\pi$
$462$	11.2790	+	19.5358i	0.524747	+	0.908888i
$463$	−23.2104			−1.07868			−0.539340	−	0.842088i	$-0.681326\pi$
$463$	−23.2104			−1.07868			−0.539340	+	0.842088i	$0.681326\pi$
$464$	−2.14564			−0.0996089
$465$		0			0
$466$	11.4137			0.528728
$467$	−6.78086			−0.313781			−0.156890	−	0.987616i	$-0.550147\pi$
$467$	−6.78086			−0.313781			−0.156890	+	0.987616i	$0.550147\pi$
$468$	2.26233	+	3.91847i	0.104576	+	0.181132i
$469$	53.3401			2.46302
$470$		0			0
$471$	6.78338	+	11.7492i	0.312562	+	0.541373i
$472$	−4.93480	−	8.54733i	−0.227143	−	0.393423i
$473$	1.16019			0.0533454
$474$	−7.31108	+	12.6632i	−0.335809	+	0.581638i
$475$		0			0
$476$	1.88857	−	3.27110i	0.0865625	−	0.149931i
$477$	20.5969	+	35.6748i	0.943066	+	1.63344i
$478$	−7.99093	+	13.8407i	−0.365496	+	0.633058i
$479$	6.75903	+	11.7070i	0.308828	+	0.534906i	0.978106	−	0.208106i	$-0.0667299\pi$
$479$	6.75903	+	11.7070i	0.308828	+	0.534906i	−0.669278	+	0.743012i	$0.733397\pi$
$480$		0			0
$481$	12.3115			0.561355
$482$	−3.42853	−	5.93840i	−0.156165	−	0.270487i
$483$	20.4769	−	35.4670i	0.931731	−	1.61381i
$484$	2.34643	+	4.06414i	0.106656	+	0.184733i
$485$		0			0
$486$	10.0591	−	17.4229i	0.456291	−	0.790319i
$487$	7.61835	−	13.1954i	0.345220	−	0.597939i	−0.640173	−	0.768230i	$-0.721137\pi$
$487$	7.61835	−	13.1954i	0.345220	−	0.597939i	0.985394	+	0.170291i	$0.0544708\pi$
$488$	−1.86761			−0.0845428
$489$	16.8066	+	29.1100i	0.760023	+	1.31640i
$490$		0			0
$491$	13.4117	−	23.2298i	0.605262	−	1.04834i	−0.386748	−	0.922186i	$-0.626402\pi$
$491$	13.4117	−	23.2298i	0.605262	−	1.04834i	0.992010	−	0.126159i	$-0.0402651\pi$
$492$	19.4188			0.875468
$493$	1.21326	+	2.10142i	0.0546424	+	0.0946434i
$494$	7.32582			0.329604
$495$		0			0
$496$	0.527107	+	5.54276i	0.0236678	+	0.248877i
$497$	10.0700			0.451700
$498$	−36.5721			−1.63884
$499$	12.6708	+	21.9465i	0.567224	+	0.982461i	0.996839	+	0.0794487i	$0.0253160\pi$
$499$	12.6708	+	21.9465i	0.567224	+	0.982461i	−0.429615	+	0.903012i	$0.641351\pi$
$500$		0			0
$501$	−23.9829	+	41.5397i	−1.07148	+	1.85586i
$502$	−0.519274	−	0.899409i	−0.0231763	−	0.0401426i
$503$	−10.8862	−	18.8555i	−0.485392	−	0.840723i	0.514467	−	0.857510i	$-0.327990\pi$
$503$	−10.8862	−	18.8555i	−0.485392	−	0.840723i	−0.999859	+	0.0167866i	$0.994656\pi$
$504$	−14.1366			−0.629693
$505$		0			0
$506$	−5.72527	+	9.91646i	−0.254519	+	0.440840i
$507$	15.9441	−	27.6160i	0.708103	−	1.22647i
$508$	−0.631179	−	1.09323i	−0.0280040	−	0.0485044i
$509$	6.84283	−	11.8521i	0.303303	−	0.525337i	−0.673579	−	0.739115i	$-0.735244\pi$
$509$	6.84283	−	11.8521i	0.303303	−	0.525337i	0.976882	+	0.213779i	$0.0685772\pi$
$510$		0			0
$511$	−13.9666			−0.617847
$512$	1.00000			0.0441942
$513$	11.3583	+	19.6732i	0.501482	+	0.868593i
$514$	−5.77037	+	9.99457i	−0.254520	+	0.440842i
$515$		0			0
$516$	−0.621195	+	1.07594i	−0.0273466	+	0.0473657i
$517$	−8.21965	+	14.2369i	−0.361500	+	0.626136i
$518$	−19.2326	+	33.3119i	−0.845032	+	1.46364i
$519$	21.7940			0.956649
$520$		0			0
$521$	9.85190	+	17.0640i	0.431620	+	0.747587i	0.997013	−	0.0772342i	$-0.0246089\pi$
$521$	9.85190	+	17.0640i	0.431620	+	0.747587i	−0.565393	+	0.824821i	$0.691276\pi$
$522$	4.54082	−	7.86492i	0.198746	−	0.344238i
$523$	−2.63019			−0.115010			−0.0575050	−	0.998345i	$-0.518315\pi$
$523$	−2.63019			−0.115010			−0.0575050	+	0.998345i	$0.518315\pi$
$524$	−2.00041	−	3.46482i	−0.0873885	−	0.151361i
$525$		0			0
$526$	−27.8728			−1.21531
$527$	5.13048	−	3.65041i	0.223487	−	0.159014i
$528$	6.75404			0.293932
$529$	−2.21167			−0.0961597
$530$		0			0
$531$	41.7740			1.81284
$532$	−11.4442	+	19.8219i	−0.496168	+	0.859388i
$533$	3.85945	+	6.68477i	0.167171	+	0.289549i
$534$	−18.8241	−	32.6043i	−0.814600	−	1.41093i
$535$		0			0
$536$	7.98521	−	13.8308i	0.344909	−	0.597399i
$537$	25.4805	−	44.1335i	1.09956	−	1.90450i
$538$	3.72020	−	6.44358i	0.160389	−	0.277803i
$539$	−5.21761	−	9.03717i	−0.224738	−	0.389258i
$540$		0			0
$541$	−3.36443	−	5.82736i	−0.144648	−	0.250538i	0.784594	−	0.620010i	$-0.212872\pi$
$541$	−3.36443	−	5.82736i	−0.144648	−	0.250538i	−0.929242	+	0.369473i	$0.879538\pi$
$542$	12.3624			0.531010
$543$	33.6575			1.44438
$544$	−0.565452	−	0.979392i	−0.0242436	−	0.0419911i
$545$		0			0
$546$	−4.80103	−	8.31562i	−0.205465	−	0.355876i
$547$	4.37949	−	7.58550i	0.187254	−	0.324333i	−0.757080	−	0.653322i	$-0.773375\pi$
$547$	4.37949	−	7.58550i	0.187254	−	0.324333i	0.944334	+	0.328989i	$0.106708\pi$
$548$	5.44408	−	9.42943i	0.232560	−	0.402805i
$549$	3.95242	−	6.84579i	0.168685	−	0.292171i
$550$		0			0
$551$	−7.35198	−	12.7340i	−0.313205	−	0.542486i
$552$	−6.13094	−	10.6191i	−0.260950	−	0.451979i
$553$	9.07970	−	15.7265i	0.386108	−	0.668759i
$554$	11.1581			0.474060
$555$		0			0
$556$	10.7590			0.456285
$557$	26.2133			1.11069			0.555347	−	0.831619i	$-0.312586\pi$
$557$	26.2133			1.11069			0.555347	+	0.831619i	$0.312586\pi$
$558$	−21.4327	−	9.79800i	−0.907318	−	0.414782i
$559$	−0.493845			−0.0208874
$560$		0			0
$561$	−3.81908	−	6.61485i	−0.161242	−	0.279279i
$562$	3.11884			0.131560
$563$	16.2826	−	28.2023i	0.686230	−	1.18858i	−0.286819	−	0.957985i	$-0.592598\pi$
$563$	16.2826	−	28.2023i	0.686230	−	1.18858i	0.973049	−	0.230600i	$-0.0740688\pi$
$564$	−8.80206	−	15.2456i	−0.370634	−	0.641956i
$565$		0			0
$566$	−22.2481			−0.935156
$567$	−6.31735	+	10.9420i	−0.265304	+	0.459520i
$568$	1.50751	−	2.61109i	0.0632538	−	0.109559i
$569$	6.76602	−	11.7191i	0.283646	−	0.491290i	−0.688634	−	0.725109i	$-0.741789\pi$
$569$	6.76602	−	11.7191i	0.283646	−	0.491290i	0.972280	+	0.233820i	$0.0751225\pi$
$570$		0			0
$571$	5.51144	−	9.54610i	0.230647	−	0.399492i	−0.727352	−	0.686265i	$-0.759249\pi$
$571$	5.51144	−	9.54610i	0.230647	−	0.399492i	0.957999	+	0.286773i	$0.0925825\pi$
$572$	1.34235	+	2.32502i	0.0561265	+	0.0972139i
$573$	3.87042			0.161689
$574$	−24.1165			−1.00660
$575$		0			0
$576$	−2.11630	+	3.66553i	−0.0881791	+	0.152731i
$577$	−18.2827	−	31.6666i	−0.761119	−	1.31830i	−0.942274	−	0.334842i	$-0.891317\pi$
$577$	−18.2827	−	31.6666i	−0.761119	−	1.31830i	0.181155	−	0.983455i	$-0.442016\pi$
$578$	7.86053	−	13.6148i	0.326955	−	0.566302i
$579$	24.5916	−	42.5939i	1.02199	−	1.77014i
$580$		0			0
$581$	45.4193			1.88431
$582$	13.5152	+	23.4091i	0.560225	+	0.970337i
$583$	12.2211	+	21.1676i	0.506147	+	0.876672i
$584$	−2.09086	+	3.62147i	−0.0865202	+	0.149857i
$585$		0			0
$586$	−15.3428	−	26.5745i	−0.633804	−	1.09778i
$587$	4.97632			0.205395			0.102697	−	0.994713i	$-0.467253\pi$
$587$	4.97632			0.205395			0.102697	+	0.994713i	$0.467253\pi$
$588$	11.1746			0.460833
$589$	−31.0891	+	22.1204i	−1.28101	+	0.911454i
$590$		0			0
$591$	−8.57523			−0.352738
$592$	5.75839	+	9.97382i	0.236668	+	0.409921i
$593$	−4.23391			−0.173866			−0.0869330	−	0.996214i	$-0.527707\pi$
$593$	−4.23391			−0.173866			−0.0869330	+	0.996214i	$0.527707\pi$
$594$	−4.16249	+	7.20965i	−0.170789	+	0.295816i
$595$		0			0
$596$	5.86843	+	10.1644i	0.240380	+	0.416351i
$597$	−40.5054			−1.65777
$598$	2.43702	−	4.22105i	0.0996572	−	0.172611i
$599$	15.3524	−	26.5911i	0.627282	−	1.08648i	−0.360813	−	0.932638i	$-0.617501\pi$
$599$	15.3524	−	26.5911i	0.627282	−	1.08648i	0.988095	−	0.153845i	$-0.0491658\pi$
$600$		0			0
$601$	−9.18723	−	15.9128i	−0.374755	−	0.649095i	0.615535	−	0.788109i	$-0.288940\pi$
$601$	−9.18723	−	15.9128i	−0.374755	−	0.649095i	−0.990290	+	0.139015i	$0.955607\pi$
$602$	0.771469	−	1.33622i	0.0314427	−	0.0544604i
$603$	33.7982	+	58.5401i	1.37637	+	2.38394i
$604$	5.08955			0.207091
$605$		0			0
$606$	20.0066	+	34.6524i	0.812711	+	1.40766i
$607$	18.7835	−	32.5339i	0.762398	−	1.32051i	−0.179214	−	0.983810i	$-0.557355\pi$
$607$	18.7835	−	32.5339i	0.762398	−	1.32051i	0.941612	−	0.336701i	$-0.109311\pi$
$608$	3.42647	+	5.93482i	0.138962	+	0.240689i
$609$	−9.63633	+	16.6906i	−0.390484	+	0.676338i
$610$		0			0
$611$	3.49878	−	6.06007i	0.141546	−	0.245164i
$612$	4.78666			0.193489
$613$	−13.5751	−	23.5128i	−0.548295	−	0.949674i	−0.998392	−	0.0566946i	$-0.981944\pi$
$613$	−13.5751	−	23.5128i	−0.548295	−	0.949674i	0.450097	−	0.892980i	$-0.351389\pi$
$614$	6.79649	+	11.7719i	0.274284	+	0.475074i
$615$		0			0
$616$	−8.38791			−0.337958
$617$	2.93300	+	5.08011i	0.118078	+	0.204518i	0.919006	−	0.394243i	$-0.128993\pi$
$617$	2.93300	+	5.08011i	0.118078	+	0.204518i	−0.800928	+	0.598761i	$0.795660\pi$
$618$	11.4904			0.462213
$619$	−23.8518			−0.958683			−0.479342	−	0.877628i	$-0.659124\pi$
$619$	−23.8518			−0.958683			−0.479342	+	0.877628i	$0.659124\pi$
$620$		0			0
$621$	15.1139			0.606501
$622$	8.28787			0.332313
$623$	23.3779	+	40.4917i	0.936615	+	1.62227i
$624$	−2.87493			−0.115089
$625$		0			0
$626$	4.97379	+	8.61486i	0.198793	+	0.344319i
$627$	23.1425	+	40.0840i	0.924222	+	1.60080i
$628$	−5.04463			−0.201303
$629$	6.51219	−	11.2794i	0.259658	−	0.449741i
$630$		0			0
$631$	−21.9338	+	37.9904i	−0.873170	+	1.51238i	−0.0144711	+	0.999895i	$0.504606\pi$
$631$	−21.9338	+	37.9904i	−0.873170	+	1.51238i	−0.858699	+	0.512480i	$0.828727\pi$
$632$	−2.71853	−	4.70863i	−0.108137	−	0.187299i
$633$	24.3564	−	42.1865i	0.968079	−	1.67676i
$634$	1.12141	+	1.94235i	0.0445371	+	0.0771404i
$635$		0			0
$636$	−26.1741			−1.03787
$637$	2.22093	+	3.84677i	0.0879965	+	0.152414i
$638$	2.69428	−	4.66664i	0.106668	−	0.184754i
$639$	6.38069	+	11.0517i	0.252416	+	0.437198i
$640$		0			0
$641$	2.13146	−	3.69179i	0.0841874	−	0.145817i	−0.820857	−	0.571133i	$-0.806504\pi$
$641$	2.13146	−	3.69179i	0.0841874	−	0.145817i	0.905045	+	0.425317i	$0.139837\pi$
$642$	13.2218	−	22.9009i	0.521824	−	0.903826i
$643$	−22.7470			−0.897055			−0.448528	−	0.893769i	$-0.648051\pi$
$643$	−22.7470			−0.897055			−0.448528	+	0.893769i	$0.648051\pi$
$644$	7.61408	+	13.1880i	0.300037	+	0.519679i
$645$		0			0
$646$	3.87501	−	6.71171i	0.152460	−	0.264069i
$647$	−21.1723			−0.832368			−0.416184	−	0.909280i	$-0.636633\pi$
$647$	−21.1723			−0.832368			−0.416184	+	0.909280i	$0.636633\pi$
$648$	1.89146	+	3.27611i	0.0743037	+	0.128698i
$649$	24.7865			0.972957
$650$		0			0
$651$	45.4836	+	20.7929i	1.78264	+	0.814938i
$652$	−12.4987			−0.489486
$653$	7.50358			0.293638			0.146819	−	0.989163i	$-0.453097\pi$
$653$	7.50358			0.293638			0.146819	+	0.989163i	$0.453097\pi$
$654$	16.4545	+	28.5001i	0.643423	+	1.11444i
$655$		0			0
$656$	−3.61032	+	6.25326i	−0.140959	+	0.244149i
$657$	−8.84975	−	15.3282i	−0.345261	−	0.598010i
$658$	10.9314	+	18.9337i	0.426149	+	0.738112i
$659$	−41.7093			−1.62476			−0.812382	−	0.583126i	$-0.801829\pi$
$659$	−41.7093			−1.62476			−0.812382	+	0.583126i	$0.801829\pi$
$660$		0			0
$661$	−18.3974	+	31.8652i	−0.715576	+	1.23941i	0.247161	+	0.968974i	$0.420502\pi$
$661$	−18.3974	+	31.8652i	−0.715576	+	1.23941i	−0.962737	+	0.270439i	$0.912831\pi$
$662$	11.7477	−	20.3476i	0.456587	−	0.790833i
$663$	1.62563	+	2.81568i	0.0631344	+	0.109352i
$664$	6.79944	−	11.7770i	0.263869	−	0.457035i
$665$		0			0
$666$	−48.7458			−1.88886
$667$	−9.78289			−0.378795
$668$	−8.91775	−	15.4460i	−0.345038	−	0.597624i
$669$	−8.54498	+	14.8003i	−0.330368	+	0.572214i
$670$		0			0
$671$	2.34516	−	4.06194i	0.0905339	−	0.156809i
$672$	4.49112	−	7.77885i	0.173249	−	0.300075i
$673$	2.36200	−	4.09110i	0.0910483	−	0.157700i	−0.816904	−	0.576773i	$-0.804312\pi$
$673$	2.36200	−	4.09110i	0.0910483	−	0.157700i	0.907952	+	0.419073i	$0.137645\pi$
$674$	−5.10345			−0.196578
$675$		0			0
$676$	5.92861	+	10.2687i	0.228024	+	0.394949i
$677$	5.58240	−	9.66900i	0.214549	−	0.371610i	−0.738584	−	0.674162i	$-0.764505\pi$
$677$	5.58240	−	9.66900i	0.214549	−	0.371610i	0.953133	+	0.302552i	$0.0978385\pi$
$678$	37.0316			1.42219
$679$	−16.7847	−	29.0720i	−0.644138	−	1.11568i
$680$		0			0
$681$	−63.3317			−2.42687
$682$	−12.7170	−	5.81362i	−0.486961	−	0.222615i
$683$	27.2295			1.04191			0.520954	−	0.853585i	$-0.325576\pi$
$683$	27.2295			1.04191			0.520954	+	0.853585i	$0.325576\pi$
$684$	−29.0057			−1.10906
$685$		0			0
$686$	9.50164			0.362774
$687$	−30.3758	+	52.6124i	−1.15891	+	2.00729i
$688$	−0.230984	−	0.400075i	−0.00880617	−	0.0152527i
$689$	−5.20205	−	9.01021i	−0.198182	−	0.343262i
$690$		0			0
$691$	18.4515	−	31.9589i	0.701927	−	1.21577i	−0.265862	−	0.964011i	$-0.585657\pi$
$691$	18.4515	−	31.9589i	0.701927	−	1.21577i	0.967789	−	0.251762i	$-0.0810101\pi$
$692$	−4.05190	+	7.01810i	−0.154030	+	0.266788i
$693$	17.7513	−	30.7462i	0.674317	−	1.16795i
$694$	−15.1378	−	26.2194i	−0.574622	−	0.995275i
$695$		0			0
$696$	2.88519	+	4.99729i	0.109363	+	0.189422i
$697$	8.16586			0.309304
$698$	−11.9756			−0.453282
$699$	−15.3477	−	26.5829i	−0.580502	−	1.00546i
$700$		0			0
$701$	−15.2412	−	26.3985i	−0.575652	−	0.997058i	−0.995970	−	0.0896816i	$-0.971415\pi$
$701$	−15.2412	−	26.3985i	−0.575652	−	0.997058i	0.420319	−	0.907377i	$-0.361918\pi$
$702$	1.77181	−	3.06886i	0.0668727	−	0.115827i
$703$	−39.4619	+	68.3500i	−1.48833	+	2.57787i
$704$	−1.25570	+	2.17494i	−0.0473260	+	0.0819711i
$705$		0			0
$706$	8.54181	+	14.7949i	0.321475	+	0.556812i
$707$	−24.8464	−	43.0352i	−0.934444	−	1.61850i
$708$	−13.2714	+	22.9867i	−0.498770	+	0.863895i
$709$	30.1272			1.13145			0.565726	−	0.824593i	$-0.308596\pi$
$709$	30.1272			1.13145			0.565726	+	0.824593i	$0.308596\pi$
$710$		0			0
$711$	23.0129			0.863050
$712$	13.9990			0.524636
$713$	2.40330	+	25.2718i	0.0900044	+	0.946435i
$714$	−10.1581			−0.380156
$715$		0			0
$716$	9.47460	+	16.4105i	0.354082	+	0.613289i
$717$	42.9808			1.60515
$718$	−14.7258	+	25.5058i	−0.549562	+	0.951870i
$719$	14.7187	+	25.4936i	0.548917	+	0.950752i	0.998349	+	0.0574372i	$0.0182929\pi$
$719$	14.7187	+	25.4936i	0.548917	+	0.950752i	−0.449432	+	0.893314i	$0.648374\pi$
$720$		0			0
$721$	−14.2701			−0.531446
$722$	−13.9814	+	24.2165i	−0.520333	+	0.901244i
$723$	−9.22052	+	15.9704i	−0.342915	+	0.593946i
$724$	−6.25755	+	10.8384i	−0.232560	+	0.402806i
$725$		0			0
$726$	6.31037	−	10.9299i	0.234200	−	0.405646i
$727$	5.66696	+	9.81546i	0.210176	+	0.364035i	0.951769	−	0.306814i	$-0.0992630\pi$
$727$	5.66696	+	9.81546i	0.210176	+	0.364035i	−0.741594	+	0.670849i	$0.765930\pi$
$728$	3.57040			0.132328
$729$	−42.7562			−1.58356
$730$		0			0
$731$	−0.261220	+	0.452447i	−0.00966159	+	0.0167344i
$732$	2.51133	+	4.34975i	0.0928213	+	0.160771i
$733$	−3.01512	+	5.22234i	−0.111366	+	0.192891i	−0.916321	−	0.400444i	$-0.868856\pi$
$733$	−3.01512	+	5.22234i	−0.111366	+	0.192891i	0.804955	+	0.593335i	$0.202189\pi$
$734$	−15.6459	+	27.0994i	−0.577499	+	1.00026i
$735$		0			0
$736$	4.55942			0.168063
$737$	20.0541	+	34.7347i	0.738701	+	1.27947i
$738$	−15.2810	−	26.4675i	−0.562503	−	0.974283i
$739$	−4.45863	+	7.72257i	−0.164013	+	0.284079i	−0.936304	−	0.351189i	$-0.885777\pi$
$739$	−4.45863	+	7.72257i	−0.164013	+	0.284079i	0.772291	+	0.635269i	$0.219111\pi$
$740$		0			0
$741$	−9.85085	−	17.0622i	−0.361880	−	0.626794i
$742$	32.5059			1.19333
$743$	−33.6977			−1.23625			−0.618124	−	0.786081i	$-0.712107\pi$
$743$	−33.6977			−1.23625			−0.618124	+	0.786081i	$0.712107\pi$
$744$	12.2005	−	8.68086i	0.447293	−	0.318256i
$745$		0			0
$746$	19.9316			0.729747
$747$	28.7793	+	49.8472i	1.05298	+	1.82381i
$748$	2.84016			0.103846
$749$	−16.4203	+	28.4409i	−0.599986	+	1.03921i
$750$		0			0
$751$	15.1183	+	26.1857i	0.551675	+	0.955529i	0.998154	+	0.0607351i	$0.0193445\pi$
$751$	15.1183	+	26.1857i	0.551675	+	0.955529i	−0.446479	+	0.894794i	$0.647322\pi$
$752$	6.54587			0.238703
$753$	−1.39651	+	2.41882i	−0.0508916	+	0.0881468i
$754$	−1.14685	+	1.98640i	−0.0417658	+	0.0723406i
$755$		0			0
$756$	5.53573	+	9.58817i	0.201333	+	0.348718i
$757$	10.3803	−	17.9791i	0.377277	−	0.653463i	−0.613388	−	0.789782i	$-0.710194\pi$
$757$	10.3803	−	17.9791i	0.377277	−	0.653463i	0.990665	+	0.136319i	$0.0435272\pi$
$758$	−7.41755	−	12.8476i	−0.269418	−	0.466645i
$759$	30.7945			1.11777
$760$		0			0
$761$	−18.2860	−	31.6722i	−0.662866	−	1.14812i	−0.979859	−	0.199690i	$-0.936007\pi$
$761$	−18.2860	−	31.6722i	−0.662866	−	1.14812i	0.316993	−	0.948428i	$-0.397327\pi$
$762$	−1.69746	+	2.94009i	−0.0614925	+	0.106508i
$763$	−20.4351	−	35.3946i	−0.739799	−	1.28137i
$764$	−0.719583	+	1.24636i	−0.0260336	+	0.0450915i
$765$		0			0
$766$	2.42574	−	4.20151i	0.0876457	−	0.151807i
$767$	−10.5507			−0.380962
$768$	−1.34467	−	2.32904i	−0.0485218	−	0.0840421i
$769$	4.76428	+	8.25198i	0.171804	+	0.297574i	0.939051	−	0.343779i	$-0.111707\pi$
$769$	4.76428	+	8.25198i	0.171804	+	0.297574i	−0.767246	+	0.641353i	$0.778374\pi$
$770$		0			0
$771$	31.0371			1.11777
$772$	9.14408	+	15.8380i	0.329103	+	0.570023i
$773$	3.33060			0.119793			0.0598966	−	0.998205i	$-0.480923\pi$
$773$	3.33060			0.119793			0.0598966	+	0.998205i	$0.480923\pi$
$774$	1.95532			0.0702825
$775$		0			0
$776$	−10.0509			−0.360808
$777$	103.446			3.71112
$778$	−1.13556	−	1.96685i	−0.0407118	−	0.0705149i
$779$	−49.4826			−1.77290
$780$		0			0
$781$	3.78597	+	6.55749i	0.135473	+	0.234646i
$782$	−2.57814	−	4.46546i	−0.0921939	−	0.159685i
$783$	−7.11254			−0.254181
$784$	−2.07757	+	3.59845i	−0.0741989	+	0.128516i
$785$		0			0
$786$	−5.37981	+	9.31811i	−0.191892	+	0.332366i
$787$	13.4518	+	23.2991i	0.479503	+	0.830524i	0.999724	−	0.0235082i	$-0.00748357\pi$
$787$	13.4518	+	23.2991i	0.479503	+	0.830524i	−0.520220	+	0.854032i	$0.674150\pi$
$788$	1.59430	−	2.76140i	0.0567944	−	0.0983708i
$789$	37.4799	+	64.9171i	1.33432	+	2.31111i
$790$		0			0
$791$	−45.9899			−1.63521
$792$	−5.31487	−	9.20563i	−0.188856	−	0.327108i
$793$	−0.998242	+	1.72901i	−0.0354486	+	0.0613988i
$794$	−4.72369	−	8.18167i	−0.167637	−	0.290357i
$795$		0			0
$796$	7.53070	−	13.0436i	0.266919	−	0.462317i
$797$	9.83785	−	17.0397i	0.348474	−	0.603576i	−0.637504	−	0.770447i	$-0.720033\pi$
$797$	9.83785	−	17.0397i	0.348474	−	0.603576i	0.985979	+	0.166871i	$0.0533665\pi$
$798$	61.5547			2.17901
$799$	−3.70138	−	6.41097i	−0.130945	−	0.226804i
$800$		0			0
$801$	−29.6261	+	51.3139i	−1.04679	+	1.81309i
$802$	20.3650			0.719113
$803$	−5.25098	−	9.09496i	−0.185303	−	0.320954i
$804$	−42.9500			−1.51473
$805$		0			0
$806$	5.41314	+	2.47463i	0.190670	+	0.0871651i
$807$	−20.0099			−0.704380
$808$	−14.8784			−0.523419
$809$	−19.5953	−	33.9401i	−0.688936	−	1.19327i	−0.972183	−	0.234225i	$-0.924745\pi$
$809$	−19.5953	−	33.9401i	−0.688936	−	1.19327i	0.283247	−	0.959047i	$-0.408588\pi$
$810$		0			0
$811$	−6.00390	+	10.3991i	−0.210825	+	0.365160i	−0.951973	−	0.306182i	$-0.900948\pi$
$811$	−6.00390	+	10.3991i	−0.210825	+	0.365160i	0.741148	+	0.671342i	$0.234282\pi$
$812$	−3.58315	−	6.20619i	−0.125744	−	0.217795i
$813$	−16.6234	−	28.7926i	−0.583008	−	1.00980i
$814$	−28.9232			−1.01376
$815$		0			0
$816$	−1.52070	+	2.63393i	−0.0532351	+	0.0922059i
$817$	1.58292	−	2.74169i	0.0553792	−	0.0959197i
$818$	−6.41855	−	11.1173i	−0.224419	−	0.388706i
$819$	−7.55603	+	13.0874i	−0.264029	+	0.457312i
$820$		0			0
$821$	−45.3721			−1.58350			−0.791748	−	0.610848i	$-0.790829\pi$
$821$	−45.3721			−1.58350			−0.791748	+	0.610848i	$0.790829\pi$
$822$	−29.2821			−1.02133
$823$	−19.8966	−	34.4620i	−0.693553	−	1.20127i	−0.970666	−	0.240432i	$-0.922711\pi$
$823$	−19.8966	−	34.4620i	−0.693553	−	1.20127i	0.277112	−	0.960838i	$-0.410623\pi$
$824$	−2.13628	+	3.70015i	−0.0744210	+	0.128901i
$825$		0			0
$826$	16.4819	−	28.5475i	0.573479	−	0.993294i
$827$	−6.28245	+	10.8815i	−0.218462	+	0.378387i	−0.954338	−	0.298729i	$-0.903437\pi$
$827$	−6.28245	+	10.8815i	−0.218462	+	0.378387i	0.735876	+	0.677116i	$0.236771\pi$
$828$	−9.64909	+	16.7127i	−0.335329	+	0.580807i
$829$	48.2511			1.67583			0.837914	−	0.545802i	$-0.183775\pi$
$829$	48.2511			1.67583			0.837914	+	0.545802i	$0.183775\pi$
$830$		0			0
$831$	−15.0040	−	25.9876i	−0.520481	−	0.901500i
$832$	0.534502	−	0.925785i	0.0185305	−	0.0320958i
$833$	4.69906			0.162813
$834$	−14.4674	−	25.0583i	−0.500965	−	0.867696i
$835$		0			0
$836$	−17.2105			−0.595237
$837$	1.74729	+	18.3736i	0.0603953	+	0.635083i
$838$	16.9178			0.584415
$839$	32.2788			1.11439			0.557193	−	0.830383i	$-0.311878\pi$
$839$	32.2788			1.11439			0.557193	+	0.830383i	$0.311878\pi$
$840$		0			0
$841$	−24.3962			−0.841249
$842$	4.96613	−	8.60160i	0.171144	−	0.296431i
$843$	−4.19383	−	7.26392i	−0.144443	−	0.250183i
$844$	9.05661	+	15.6865i	0.311741	+	0.539952i
$845$		0			0
$846$	−13.8530	+	23.9941i	−0.476276	+	0.824934i
$847$	−7.83691	+	13.5739i	−0.269279	+	0.466406i
$848$	4.86625	−	8.42860i	0.167108	−	0.289439i
$849$	29.9164	+	51.8167i	1.02673	+	1.77834i
$850$		0			0
$851$	26.2549	+	45.4748i	0.900007	+	1.55886i
$852$	−8.10845			−0.277791
$853$	3.23296			0.110694			0.0553472	−	0.998467i	$-0.482373\pi$
$853$	3.23296			0.110694			0.0553472	+	0.998467i	$0.482373\pi$
$854$	−3.11885	−	5.40200i	−0.106725	−	0.184853i
$855$		0			0
$856$	4.91637	+	8.51540i	0.168038	+	0.291050i
$857$	−1.21696	+	2.10784i	−0.0415707	+	0.0720025i	−0.886062	−	0.463567i	$-0.846570\pi$
$857$	−1.21696	+	2.10784i	−0.0415707	+	0.0720025i	0.844491	+	0.535569i	$0.179903\pi$
$858$	3.61005	−	6.25279i	0.123245	−	0.213467i
$859$	−4.93095	+	8.54066i	−0.168242	+	0.291403i	−0.937802	−	0.347171i	$-0.887142\pi$
$859$	−4.93095	+	8.54066i	−0.168242	+	0.291403i	0.769560	+	0.638575i	$0.220476\pi$
$860$		0			0
$861$	32.4288	+	56.1683i	1.10517	+	1.91421i
$862$	0.257626	+	0.446222i	0.00877479	+	0.0151984i
$863$	−3.92974	+	6.80650i	−0.133770	+	0.231696i	−0.925127	−	0.379658i	$-0.876042\pi$
$863$	−3.92974	+	6.80650i	−0.133770	+	0.231696i	0.791357	+	0.611354i	$0.209375\pi$
$864$	3.31488			0.112774
$865$		0			0
$866$	−37.7395			−1.28244
$867$	−42.2794			−1.43588
$868$	−15.1520	+	10.7809i	−0.514292	+	0.365926i
$869$	13.6546			0.463202
$870$		0			0
$871$	−8.53623	−	14.7852i	−0.289239	−	0.500977i
$872$	−12.2368			−0.414391
$873$	21.2708	−	36.8421i	0.719907	−	1.24691i
$874$	15.6227	+	27.0593i	0.528446	+	0.915296i
$875$		0			0
$876$	11.2461			0.379970
$877$	26.8584	−	46.5201i	0.906943	−	1.57087i	0.0886546	−	0.996062i	$-0.471743\pi$
$877$	26.8584	−	46.5201i	0.906943	−	1.57087i	0.818288	−	0.574808i	$-0.194923\pi$
$878$	7.16777	−	12.4149i	0.241900	−	0.418984i
$879$	−41.2621	+	71.4680i	−1.39174	+	2.41056i
$880$		0			0
$881$	15.3470	−	26.5818i	0.517054	−	0.895564i	−0.482750	−	0.875758i	$-0.660362\pi$
$881$	15.3470	−	26.5818i	0.517054	−	0.895564i	0.999804	−	0.0198057i	$-0.00630477\pi$
$882$	−8.79351	−	15.2308i	−0.296093	−	0.512848i
$883$	47.7407			1.60660			0.803301	−	0.595573i	$-0.203075\pi$
$883$	47.7407			1.60660			0.803301	+	0.595573i	$0.203075\pi$
$884$	−1.20894			−0.0406611
$885$		0			0
$886$	13.7112	−	23.7485i	0.460637	−	0.797847i
$887$	10.6609	+	18.4652i	0.357958	+	0.620001i	0.987620	−	0.156868i	$-0.0501399\pi$
$887$	10.6609	+	18.4652i	0.357958	+	0.620001i	−0.629662	+	0.776869i	$0.716807\pi$
$888$	15.4863	−	26.8231i	0.519686	−	0.900123i
$889$	2.10809	−	3.65132i	0.0707032	−	0.122461i
$890$		0			0
$891$	−9.50045			−0.318277
$892$	−3.17734	−	5.50332i	−0.106385	−	0.184265i
$893$	22.4292	+	38.8485i	0.750565	+	1.30002i
$894$	15.7823	−	27.3357i	0.527837	−	0.914241i
$895$		0			0
$896$	1.66997	+	2.89246i	0.0557896	+	0.0966305i
$897$	−13.1080			−0.437663
$898$	−39.8495			−1.32980
$899$	−1.13098	−	11.8928i	−0.0377204	−	0.396646i
$900$		0			0
$901$	−11.0065			−0.366681
$902$	−9.06697	−	15.7045i	−0.301897	−	0.522901i
$903$	−4.14950			−0.138087
$904$	−6.88486	+	11.9249i	−0.228987	+	0.396617i
$905$		0			0
$906$	−6.84379	−	11.8538i	−0.227370	−	0.393816i
$907$	3.01352			0.100062			0.0500311	−	0.998748i	$-0.484068\pi$
$907$	3.01352			0.100062			0.0500311	+	0.998748i	$0.484068\pi$
$908$	11.7745	−	20.3941i	0.390752	−	0.676802i
$909$	31.4871	−	54.5372i	1.04436	−	1.80888i
$910$		0			0
$911$	9.27333	+	16.0619i	0.307239	+	0.532154i	0.977757	−	0.209739i	$-0.0672615\pi$
$911$	9.27333	+	16.0619i	0.307239	+	0.532154i	−0.670518	+	0.741893i	$0.733928\pi$
$912$	9.21497	−	15.9608i	0.305138	−	0.528515i
$913$	17.0761	+	29.5767i	0.565137	+	0.978847i
$914$	−17.5445			−0.580319
$915$		0			0
$916$	−11.2948	−	19.5632i	−0.373192	−	0.646388i
$917$	6.68125	−	11.5723i	0.220634	−	0.382150i
$918$	−1.87440	−	3.24656i	−0.0618646	−	0.107153i
$919$	−5.30786	+	9.19349i	−0.175090	+	0.303265i	−0.940192	−	0.340644i	$-0.889355\pi$
$919$	−5.30786	+	9.19349i	−0.175090	+	0.303265i	0.765102	+	0.643909i	$0.222688\pi$
$920$		0			0
$921$	18.2781	−	31.6586i	0.602285	−	1.04319i
$922$	−9.00321			−0.296505
$923$	−1.61154	−	2.79127i	−0.0530444	−	0.0918757i
$924$	11.2790	+	19.5358i	0.371052	+	0.642681i
$925$		0			0
$926$	−23.2104			−0.762742
$927$	−9.04202	−	15.6612i	−0.296979	−	0.514383i
$928$	−2.14564			−0.0704341
$929$	−28.8336			−0.945999			−0.473000	−	0.881063i	$-0.656829\pi$
$929$	−28.8336			−0.945999			−0.473000	+	0.881063i	$0.656829\pi$
$930$		0			0
$931$	−28.4749			−0.933227
$932$	11.4137			0.373867
$933$	−11.1445	−	19.3028i	−0.364854	−	0.631946i
$934$	−6.78086			−0.221877
$935$		0			0
$936$	2.26233	+	3.91847i	0.0739466	+	0.128079i
$937$	−11.0878	−	19.2047i	−0.362224	−	0.627390i	0.626103	−	0.779741i	$-0.284649\pi$
$937$	−11.0878	−	19.2047i	−0.362224	−	0.627390i	−0.988327	+	0.152350i	$0.951316\pi$
$938$	53.3401			1.74162
$939$	13.3763	−	23.1683i	0.436517	−	0.756070i
$940$		0			0
$941$	5.67462	−	9.82873i	0.184987	−	0.320407i	−0.758585	−	0.651574i	$-0.774109\pi$
$941$	5.67462	−	9.82873i	0.184987	−	0.320407i	0.943572	+	0.331167i	$0.107442\pi$
$942$	6.78338	+	11.7492i	0.221015	+	0.382808i
$943$	−16.4610	+	28.5113i	−0.536043	+	0.928454i
$944$	−4.93480	−	8.54733i	−0.160614	−	0.278192i
$945$		0			0
$946$	1.16019			0.0377209
$947$	0.817838	+	1.41654i	0.0265762	+	0.0460313i	0.879008	−	0.476808i	$-0.158206\pi$
$947$	0.817838	+	1.41654i	0.0265762	+	0.0460313i	−0.852431	+	0.522839i	$0.824873\pi$
$948$	−7.31108	+	12.6632i	−0.237453	+	0.411280i
$949$	2.23514	+	3.87137i	0.0725556	+	0.125670i
$950$		0			0
$951$	3.01587	−	5.22365i	0.0977964	−	0.169388i
$952$	1.88857	−	3.27110i	0.0612090	−	0.106017i
$953$	−2.67046			−0.0865047			−0.0432524	−	0.999064i	$-0.513772\pi$
$953$	−2.67046			−0.0865047			−0.0432524	+	0.999064i	$0.513772\pi$
$954$	20.5969	+	35.6748i	0.666849	+	1.15502i
$955$		0			0
$956$	−7.99093	+	13.8407i	−0.258445	+	0.447640i
$957$	−14.4917			−0.468451
$958$	6.75903	+	11.7070i	0.218374	+	0.378235i
$959$	36.3657			1.17431
$960$		0			0
$961$	−30.4443	+	5.84325i	−0.982075	+	0.188492i
$962$	12.3115			0.396938
$963$	−41.6180			−1.34112
$964$	−3.42853	−	5.93840i	−0.110426	−	0.191263i
$965$		0			0
$966$	20.4769	−	35.4670i	0.658834	−	1.14113i
$967$	30.3709	+	52.6039i	0.976662	+	1.69163i	0.674337	+	0.738424i	$0.264430\pi$
$967$	30.3709	+	52.6039i	0.976662	+	1.69163i	0.302326	+	0.953205i	$0.402237\pi$
$968$	2.34643	+	4.06414i	0.0754171	+	0.130626i
$969$	−20.8425			−0.669558
$970$		0			0
$971$	23.2342	−	40.2428i	0.745621	−	1.29145i	−0.204283	−	0.978912i	$-0.565486\pi$
$971$	23.2342	−	40.2428i	0.745621	−	1.29145i	0.949904	−	0.312542i	$-0.101180\pi$
$972$	10.0591	−	17.4229i	0.322646	−	0.558840i
$973$	17.9672	+	31.1201i	0.576002	+	0.997665i
$974$	7.61835	−	13.1954i	0.244108	−	0.422807i
$975$		0			0
$976$	−1.86761			−0.0597808
$977$	1.40935			0.0450891			0.0225445	−	0.999746i	$-0.492823\pi$
$977$	1.40935			0.0450891			0.0225445	+	0.999746i	$0.492823\pi$
$978$	16.8066	+	29.1100i	0.537417	+	0.930834i
$979$	−17.5786	+	30.4470i	−0.561814	+	0.973091i
$980$		0			0
$981$	25.8968	−	44.8545i	0.826820	−	1.43209i
$982$	13.4117	−	23.2298i	0.427985	−	0.741292i
$983$	9.83737	−	17.0388i	0.313763	−	0.543454i	−0.665410	−	0.746478i	$-0.731743\pi$
$983$	9.83737	−	17.0388i	0.313763	−	0.543454i	0.979174	+	0.203024i	$0.0650768\pi$
$984$	19.4188			0.619050
$985$		0			0
$986$	1.21326	+	2.10142i	0.0386380	+	0.0669230i
$987$	29.3983	−	50.9193i	0.935757	−	1.62078i
$988$	7.32582			0.233066
$989$	−1.05315	−	1.82411i	−0.0334883	−	0.0580034i
$990$		0			0
$991$	28.9565			0.919834			0.459917	−	0.887962i	$-0.347879\pi$
$991$	28.9565			0.919834			0.459917	+	0.887962i	$0.347879\pi$
$992$	0.527107	+	5.54276i	0.0167357	+	0.175983i
$993$	−63.1873			−2.00519
$994$	10.0700			0.319400
$995$		0			0
$996$	−36.5721			−1.15883
$997$	−15.1209	+	26.1902i	−0.478884	+	0.829451i	−0.999707	−	0.0242137i	$-0.992292\pi$
$997$	−15.1209	+	26.1902i	−0.478884	+	0.829451i	0.520823	+	0.853665i	$0.325625\pi$
$998$	12.6708	+	21.9465i	0.401088	+	0.694705i
$999$	19.0883	+	33.0620i	0.603928	+	1.04603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1550.2.e.r.1451.1		16
5.2	odd	4		310.2.k.a.149.9	yes	32
5.3	odd	4		310.2.k.a.149.8	yes	32
5.4	even	2		1550.2.e.q.1451.8		16
31.5	even	3	inner	1550.2.e.r.501.1		16
155.67	odd	12		310.2.k.a.129.16	yes	32
155.98	odd	12		310.2.k.a.129.1	✓	32
155.129	even	6		1550.2.e.q.501.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.k.a.129.1	✓	32	155.98	odd	12
310.2.k.a.129.16	yes	32	155.67	odd	12
310.2.k.a.149.8	yes	32	5.3	odd	4
310.2.k.a.149.9	yes	32	5.2	odd	4
1550.2.e.q.501.8		16	155.129	even	6
1550.2.e.q.1451.8		16	5.4	even	2
1550.2.e.r.501.1		16	31.5	even	3	inner
1550.2.e.r.1451.1		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1550.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.34467 - 2.32904i) q^{3} +1.00000 q^{4} +(-1.34467 - 2.32904i) q^{6} +(1.66997 + 2.89246i) q^{7} +1.00000 q^{8} +(-2.11630 + 3.66553i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.34467 - 2.32904i) q^{3} +1.00000 q^{4} +(-1.34467 - 2.32904i) q^{6} +(1.66997 + 2.89246i) q^{7} +1.00000 q^{8} +(-2.11630 + 3.66553i) q^{9} +(-1.25570 + 2.17494i) q^{11} +(-1.34467 - 2.32904i) q^{12} +(0.534502 - 0.925785i) q^{13} +(1.66997 + 2.89246i) q^{14} +1.00000 q^{16} +(-0.565452 - 0.979392i) q^{17} +(-2.11630 + 3.66553i) q^{18} +(3.42647 + 5.93482i) q^{19} +(4.49112 - 7.77885i) q^{21} +(-1.25570 + 2.17494i) q^{22} +4.55942 q^{23} +(-1.34467 - 2.32904i) q^{24} +(0.534502 - 0.925785i) q^{26} +3.31488 q^{27} +(1.66997 + 2.89246i) q^{28} -2.14564 q^{29} +(0.527107 + 5.54276i) q^{31} +1.00000 q^{32} +6.75404 q^{33} +(-0.565452 - 0.979392i) q^{34} +(-2.11630 + 3.66553i) q^{36} +(5.75839 + 9.97382i) q^{37} +(3.42647 + 5.93482i) q^{38} -2.87493 q^{39} +(-3.61032 + 6.25326i) q^{41} +(4.49112 - 7.77885i) q^{42} +(-0.230984 - 0.400075i) q^{43} +(-1.25570 + 2.17494i) q^{44} +4.55942 q^{46} +6.54587 q^{47} +(-1.34467 - 2.32904i) q^{48} +(-2.07757 + 3.59845i) q^{49} +(-1.52070 + 2.63393i) q^{51} +(0.534502 - 0.925785i) q^{52} +(4.86625 - 8.42860i) q^{53} +3.31488 q^{54} +(1.66997 + 2.89246i) q^{56} +(9.21497 - 15.9608i) q^{57} -2.14564 q^{58} +(-4.93480 - 8.54733i) q^{59} -1.86761 q^{61} +(0.527107 + 5.54276i) q^{62} -14.1366 q^{63} +1.00000 q^{64} +6.75404 q^{66} +(7.98521 - 13.8308i) q^{67} +(-0.565452 - 0.979392i) q^{68} +(-6.13094 - 10.6191i) q^{69} +(1.50751 - 2.61109i) q^{71} +(-2.11630 + 3.66553i) q^{72} +(-2.09086 + 3.62147i) q^{73} +(5.75839 + 9.97382i) q^{74} +(3.42647 + 5.93482i) q^{76} -8.38791 q^{77} -2.87493 q^{78} +(-2.71853 - 4.70863i) q^{79} +(1.89146 + 3.27611i) q^{81} +(-3.61032 + 6.25326i) q^{82} +(6.79944 - 11.7770i) q^{83} +(4.49112 - 7.77885i) q^{84} +(-0.230984 - 0.400075i) q^{86} +(2.88519 + 4.99729i) q^{87} +(-1.25570 + 2.17494i) q^{88} +13.9990 q^{89} +3.57040 q^{91} +4.55942 q^{92} +(12.2005 - 8.68086i) q^{93} +6.54587 q^{94} +(-1.34467 - 2.32904i) q^{96} -10.0509 q^{97} +(-2.07757 + 3.59845i) q^{98} +(-5.31487 - 9.20563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 2 q^{3} + 16 q^{4} + 2 q^{6} + 16 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 + 2 * q^6 + 16 * q^8 - 4 * q^9	\( 16 q + 16 q^{2} + 2 q^{3} + 16 q^{4} + 2 q^{6} + 16 q^{8} - 4 q^{9} + 2 q^{11} + 2 q^{12} + 6 q^{13} + 16 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 8 q^{21} + 2 q^{22} - 4 q^{23} + 2 q^{24} + 6 q^{26} - 4 q^{27} + 4 q^{29} + 6 q^{31} + 16 q^{32} - 12 q^{33} + 6 q^{34} - 4 q^{36} + 14 q^{37} + 4 q^{38} + 32 q^{39} - 8 q^{41} + 8 q^{42} + 6 q^{43} + 2 q^{44} - 4 q^{46} - 8 q^{47} + 2 q^{48} - 10 q^{49} - 20 q^{51} + 6 q^{52} + 8 q^{53} - 4 q^{54} + 34 q^{57} + 4 q^{58} - 8 q^{59} - 20 q^{61} + 6 q^{62} - 36 q^{63} + 16 q^{64} - 12 q^{66} - 6 q^{67} + 6 q^{68} - 18 q^{69} + 24 q^{71} - 4 q^{72} + 22 q^{73} + 14 q^{74} + 4 q^{76} + 48 q^{77} + 32 q^{78} - 2 q^{79} - 16 q^{81} - 8 q^{82} + 10 q^{83} + 8 q^{84} + 6 q^{86} - 20 q^{87} + 2 q^{88} - 36 q^{89} + 12 q^{91} - 4 q^{92} + 36 q^{93} - 8 q^{94} + 2 q^{96} + 20 q^{97} - 10 q^{98} - 32 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 + 2 * q^6 + 16 * q^8 - 4 * q^9 + 2 * q^11 + 2 * q^12 + 6 * q^13 + 16 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 8 * q^21 + 2 * q^22 - 4 * q^23 + 2 * q^24 + 6 * q^26 - 4 * q^27 + 4 * q^29 + 6 * q^31 + 16 * q^32 - 12 * q^33 + 6 * q^34 - 4 * q^36 + 14 * q^37 + 4 * q^38 + 32 * q^39 - 8 * q^41 + 8 * q^42 + 6 * q^43 + 2 * q^44 - 4 * q^46 - 8 * q^47 + 2 * q^48 - 10 * q^49 - 20 * q^51 + 6 * q^52 + 8 * q^53 - 4 * q^54 + 34 * q^57 + 4 * q^58 - 8 * q^59 - 20 * q^61 + 6 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^66 - 6 * q^67 + 6 * q^68 - 18 * q^69 + 24 * q^71 - 4 * q^72 + 22 * q^73 + 14 * q^74 + 4 * q^76 + 48 * q^77 + 32 * q^78 - 2 * q^79 - 16 * q^81 - 8 * q^82 + 10 * q^83 + 8 * q^84 + 6 * q^86 - 20 * q^87 + 2 * q^88 - 36 * q^89 + 12 * q^91 - 4 * q^92 + 36 * q^93 - 8 * q^94 + 2 * q^96 + 20 * q^97 - 10 * q^98 - 32 * q^99

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