LMFDB - Embedded newform 169.5.d.c.99.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,5,Mod(70,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("169.70");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	169.d (of order $4$, 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:	$17.4695237612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.7
Root			$3.98977i$ of defining polynomial
Character	$\chi$	$=$	169.99
Dual form			169.5.d.c.70.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.03282 + 4.03282i) q^{2} +8.56159 q^{3} +16.5272i q^{4} +(29.3294 + 29.3294i) q^{5} +(34.5273 + 34.5273i) q^{6} +(33.5543 - 33.5543i) q^{7} +(-2.12627 + 2.12627i) q^{8} -7.69920 q^{9} +O(q^{10})$	\(q+(4.03282 + 4.03282i) q^{2} +8.56159 q^{3} +16.5272i q^{4} +(29.3294 + 29.3294i) q^{5} +(34.5273 + 34.5273i) q^{6} +(33.5543 - 33.5543i) q^{7} +(-2.12627 + 2.12627i) q^{8} -7.69920 q^{9} +236.560i q^{10} +(-31.3041 + 31.3041i) q^{11} +141.499i q^{12} +270.637 q^{14} +(251.106 + 251.106i) q^{15} +247.286 q^{16} -237.462i q^{17} +(-31.0495 - 31.0495i) q^{18} +(-348.888 - 348.888i) q^{19} +(-484.734 + 484.734i) q^{20} +(287.279 - 287.279i) q^{21} -252.488 q^{22} +298.164i q^{23} +(-18.2042 + 18.2042i) q^{24} +1095.43i q^{25} -759.406 q^{27} +(554.561 + 554.561i) q^{28} -371.384 q^{29} +2025.33i q^{30} +(-625.946 - 625.946i) q^{31} +(1031.28 + 1031.28i) q^{32} +(-268.013 + 268.013i) q^{33} +(957.641 - 957.641i) q^{34} +1968.26 q^{35} -127.247i q^{36} +(-540.096 + 540.096i) q^{37} -2814.01i q^{38} -124.724 q^{40} +(-491.434 - 491.434i) q^{41} +2317.08 q^{42} +1126.26i q^{43} +(-517.371 - 517.371i) q^{44} +(-225.813 - 225.813i) q^{45} +(-1202.44 + 1202.44i) q^{46} +(-609.937 + 609.937i) q^{47} +2117.16 q^{48} +149.212i q^{49} +(-4417.66 + 4417.66i) q^{50} -2033.05i q^{51} +897.855 q^{53} +(-3062.55 - 3062.55i) q^{54} -1836.26 q^{55} +142.691i q^{56} +(-2987.04 - 2987.04i) q^{57} +(-1497.72 - 1497.72i) q^{58} +(351.769 - 351.769i) q^{59} +(-4150.10 + 4150.10i) q^{60} +248.429 q^{61} -5048.65i q^{62} +(-258.342 + 258.342i) q^{63} +4361.35i q^{64} -2161.69 q^{66} +(1319.92 + 1319.92i) q^{67} +3924.59 q^{68} +2552.76i q^{69} +(7937.63 + 7937.63i) q^{70} +(-2121.75 - 2121.75i) q^{71} +(16.3705 - 16.3705i) q^{72} +(6818.40 - 6818.40i) q^{73} -4356.22 q^{74} +9378.61i q^{75} +(5766.16 - 5766.16i) q^{76} +2100.78i q^{77} +2503.91 q^{79} +(7252.76 + 7252.76i) q^{80} -5878.09 q^{81} -3963.73i q^{82} +(-7971.73 - 7971.73i) q^{83} +(4747.92 + 4747.92i) q^{84} +(6964.62 - 6964.62i) q^{85} +(-4541.98 + 4541.98i) q^{86} -3179.64 q^{87} -133.122i q^{88} +(10252.7 - 10252.7i) q^{89} -1821.33i q^{90} -4927.83 q^{92} +(-5359.09 - 5359.09i) q^{93} -4919.53 q^{94} -20465.4i q^{95} +(8829.40 + 8829.40i) q^{96} +(5238.81 + 5238.81i) q^{97} +(-601.744 + 601.744i) q^{98} +(241.017 - 241.017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9	$ 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9} - 500 q^{11} + 808 q^{14} - 844 q^{15} - 460 q^{16} - 2434 q^{18} - 1712 q^{19} - 838 q^{20} + 1076 q^{21} + 3048 q^{22} - 5772 q^{24} + 3352 q^{27} - 2980 q^{28} - 1628 q^{29} - 4060 q^{31} - 3662 q^{32} + 860 q^{33} + 2502 q^{34} + 9784 q^{35} - 10468 q^{37} + 18816 q^{40} - 3440 q^{41} + 2408 q^{42} - 10736 q^{44} + 1004 q^{45} - 11436 q^{46} - 1484 q^{47} + 6004 q^{48} - 21616 q^{50} + 7204 q^{53} - 6760 q^{54} - 13872 q^{55} - 12736 q^{57} - 7974 q^{58} + 4840 q^{59} + 6472 q^{60} + 324 q^{61} + 13988 q^{63} - 23872 q^{66} - 2216 q^{67} + 12888 q^{68} + 34524 q^{70} + 1240 q^{71} + 6606 q^{72} + 15448 q^{73} + 5764 q^{74} + 39688 q^{76} - 17064 q^{79} + 37630 q^{80} - 4256 q^{81} - 12788 q^{83} + 7736 q^{84} + 22884 q^{85} - 67260 q^{86} - 58684 q^{87} + 37624 q^{89} - 49884 q^{92} + 2492 q^{93} + 61212 q^{94} + 94664 q^{96} + 57056 q^{97} - 27950 q^{98} + 21632 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9 - 500 * q^11 + 808 * q^14 - 844 * q^15 - 460 * q^16 - 2434 * q^18 - 1712 * q^19 - 838 * q^20 + 1076 * q^21 + 3048 * q^22 - 5772 * q^24 + 3352 * q^27 - 2980 * q^28 - 1628 * q^29 - 4060 * q^31 - 3662 * q^32 + 860 * q^33 + 2502 * q^34 + 9784 * q^35 - 10468 * q^37 + 18816 * q^40 - 3440 * q^41 + 2408 * q^42 - 10736 * q^44 + 1004 * q^45 - 11436 * q^46 - 1484 * q^47 + 6004 * q^48 - 21616 * q^50 + 7204 * q^53 - 6760 * q^54 - 13872 * q^55 - 12736 * q^57 - 7974 * q^58 + 4840 * q^59 + 6472 * q^60 + 324 * q^61 + 13988 * q^63 - 23872 * q^66 - 2216 * q^67 + 12888 * q^68 + 34524 * q^70 + 1240 * q^71 + 6606 * q^72 + 15448 * q^73 + 5764 * q^74 + 39688 * q^76 - 17064 * q^79 + 37630 * q^80 - 4256 * q^81 - 12788 * q^83 + 7736 * q^84 + 22884 * q^85 - 67260 * q^86 - 58684 * q^87 + 37624 * q^89 - 49884 * q^92 + 2492 * q^93 + 61212 * q^94 + 94664 * q^96 + 57056 * q^97 - 27950 * q^98 + 21632 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.03282	+	4.03282i	1.00820	+	1.00820i	0.999966	+	0.00823842i	$0.00262240\pi$
$2$	4.03282	+	4.03282i	1.00820	+	1.00820i	0.00823842	+	0.999966i	$0.497378\pi$
$3$	8.56159			0.951288			0.475644	−	0.879638i	$-0.342215\pi$
$3$	8.56159			0.951288			0.475644	+	0.879638i	$0.342215\pi$
$4$			16.5272i			1.03295i
$5$	29.3294	+	29.3294i	1.17318	+	1.17318i	0.981448	+	0.191728i	$0.0614093\pi$
$5$	29.3294	+	29.3294i	1.17318	+	1.17318i	0.191728	+	0.981448i	$0.438591\pi$
$6$	34.5273	+	34.5273i	0.959092	+	0.959092i
$7$	33.5543	−	33.5543i	0.684783	−	0.684783i	−0.276291	−	0.961074i	$-0.589105\pi$
$7$	33.5543	−	33.5543i	0.684783	−	0.684783i	0.961074	+	0.276291i	$0.0891055\pi$
$8$	−2.12627	+	2.12627i	−0.0332229	+	0.0332229i
$9$	−7.69920			−0.0950518
$10$			236.560i			2.36560i
$11$	−31.3041	+	31.3041i	−0.258712	+	0.258712i	−0.824530	−	0.565818i	$-0.808560\pi$
$11$	−31.3041	+	31.3041i	−0.258712	+	0.258712i	0.565818	+	0.824530i	$0.308560\pi$
$12$			141.499i			0.982635i
$13$		0			0
$13$		0			0
$14$	270.637			1.38080
$15$	251.106	+	251.106i	1.11603	+	1.11603i
$16$	247.286			0.965962
$17$		−	237.462i		−	0.821668i	−0.911710	−	0.410834i	$-0.865238\pi$
$17$		−	237.462i		−	0.821668i	0.911710	−	0.410834i	$-0.134762\pi$
$18$	−31.0495	−	31.0495i	−0.0958317	−	0.0958317i
$19$	−348.888	−	348.888i	−0.966449	−	0.966449i	0.0330058	−	0.999455i	$-0.489492\pi$
$19$	−348.888	−	348.888i	−0.966449	−	0.966449i	−0.999455	+	0.0330058i	$0.989492\pi$
$20$	−484.734	+	484.734i	−1.21184	+	1.21184i
$21$	287.279	−	287.279i	0.651425	−	0.651425i
$22$	−252.488			−0.521669
$23$			298.164i			0.563638i	0.959468	+	0.281819i	$0.0909377\pi$
$23$			298.164i			0.563638i	−0.959468	+	0.281819i	$0.909062\pi$
$24$	−18.2042	+	18.2042i	−0.0316045	+	0.0316045i
$25$			1095.43i			1.75269i
$26$		0			0
$27$	−759.406			−1.04171
$28$	554.561	+	554.561i	0.707348	+	0.707348i
$29$	−371.384			−0.441598			−0.220799	−	0.975319i	$-0.570866\pi$
$29$	−371.384			−0.441598			−0.220799	+	0.975319i	$0.570866\pi$
$30$			2025.33i			2.25037i
$31$	−625.946	−	625.946i	−0.651348	−	0.651348i	0.301969	−	0.953318i	$-0.402356\pi$
$31$	−625.946	−	625.946i	−0.651348	−	0.651348i	−0.953318	+	0.301969i	$0.902356\pi$
$32$	1031.28	+	1031.28i	1.00711	+	1.00711i
$33$	−268.013	+	268.013i	−0.246109	+	0.246109i
$34$	957.641	−	957.641i	0.828409	−	0.828409i
$35$	1968.26			1.60674
$36$		−	127.247i		−	0.0981840i
$37$	−540.096	+	540.096i	−0.394518	+	0.394518i	−0.876294	−	0.481776i	$-0.839992\pi$
$37$	−540.096	+	540.096i	−0.394518	+	0.394518i	0.481776	+	0.876294i	$0.339992\pi$
$38$		−	2814.01i		−	1.94876i
$39$		0			0
$40$	−124.724			−0.0779527
$41$	−491.434	−	491.434i	−0.292346	−	0.292346i	0.545660	−	0.838006i	$-0.316279\pi$
$41$	−491.434	−	491.434i	−0.292346	−	0.292346i	−0.838006	+	0.545660i	$0.816279\pi$
$42$	2317.08			1.31354
$43$			1126.26i			0.609116i	0.952494	+	0.304558i	$0.0985087\pi$
$43$			1126.26i			0.609116i	−0.952494	+	0.304558i	$0.901491\pi$
$44$	−517.371	−	517.371i	−0.267237	−	0.267237i
$45$	−225.813	−	225.813i	−0.111513	−	0.111513i
$46$	−1202.44	+	1202.44i	−0.568262	+	0.568262i
$47$	−609.937	+	609.937i	−0.276114	+	0.276114i	−0.831556	−	0.555441i	$-0.812549\pi$
$47$	−609.937	+	609.937i	−0.276114	+	0.276114i	0.555441	+	0.831556i	$0.312549\pi$
$48$	2117.16			0.918907
$49$			149.212i			0.0621457i
$50$	−4417.66	+	4417.66i	−1.76707	+	1.76707i
$51$		−	2033.05i		−	0.781642i
$52$		0			0
$53$	897.855			0.319635			0.159818	−	0.987147i	$-0.448909\pi$
$53$	897.855			0.319635			0.159818	+	0.987147i	$0.448909\pi$
$54$	−3062.55	−	3062.55i	−1.05026	−	1.05026i
$55$	−1836.26			−0.607029
$56$			142.691i			0.0455009i
$57$	−2987.04	−	2987.04i	−0.919371	−	0.919371i
$58$	−1497.72	−	1497.72i	−0.445221	−	0.445221i
$59$	351.769	−	351.769i	0.101054	−	0.101054i	−0.654772	−	0.755826i	$-0.727235\pi$
$59$	351.769	−	351.769i	0.101054	−	0.101054i	0.755826	+	0.654772i	$0.227235\pi$
$60$	−4150.10	+	4150.10i	−1.15280	+	1.15280i
$61$	248.429			0.0667640			0.0333820	−	0.999443i	$-0.489372\pi$
$61$	248.429			0.0667640			0.0333820	+	0.999443i	$0.489372\pi$
$62$		−	5048.65i		−	1.31338i
$63$	−258.342	+	258.342i	−0.0650898	+	0.0650898i
$64$			4361.35i			1.06478i
$65$		0			0
$66$	−2161.69			−0.496257
$67$	1319.92	+	1319.92i	0.294034	+	0.294034i	0.838672	−	0.544638i	$-0.183333\pi$
$67$	1319.92	+	1319.92i	0.294034	+	0.294034i	−0.544638	+	0.838672i	$0.683333\pi$
$68$	3924.59			0.848744
$69$			2552.76i			0.536182i
$70$	7937.63	+	7937.63i	1.61992	+	1.61992i
$71$	−2121.75	−	2121.75i	−0.420898	−	0.420898i	0.464615	−	0.885513i	$-0.346193\pi$
$71$	−2121.75	−	2121.75i	−0.420898	−	0.420898i	−0.885513	+	0.464615i	$0.846193\pi$
$72$	16.3705	−	16.3705i	0.00315790	−	0.00315790i
$73$	6818.40	−	6818.40i	1.27949	−	1.27949i	0.338536	−	0.940953i	$-0.390068\pi$
$73$	6818.40	−	6818.40i	1.27949	−	1.27949i	0.940953	−	0.338536i	$-0.109932\pi$
$74$	−4356.22			−0.795510
$75$			9378.61i			1.66731i
$76$	5766.16	−	5766.16i	0.998296	−	0.998296i
$77$			2100.78i			0.354323i
$78$		0			0
$79$	2503.91			0.401204			0.200602	−	0.979673i	$-0.435710\pi$
$79$	2503.91			0.401204			0.200602	+	0.979673i	$0.435710\pi$
$80$	7252.76	+	7252.76i	1.13324	+	1.13324i
$81$	−5878.09			−0.895913
$82$		−	3963.73i		−	0.589489i
$83$	−7971.73	−	7971.73i	−1.15717	−	1.15717i	−0.985082	−	0.172086i	$-0.944949\pi$
$83$	−7971.73	−	7971.73i	−1.15717	−	1.15717i	−0.172086	−	0.985082i	$-0.555051\pi$
$84$	4747.92	+	4747.92i	0.672891	+	0.672891i
$85$	6964.62	−	6964.62i	0.963961	−	0.963961i
$86$	−4541.98	+	4541.98i	−0.614113	+	0.614113i
$87$	−3179.64			−0.420087
$88$		−	133.122i		−	0.0171903i
$89$	10252.7	−	10252.7i	1.29437	−	1.29437i	0.362314	−	0.932056i	$-0.381987\pi$
$89$	10252.7	−	10252.7i	1.29437	−	1.29437i	0.932056	−	0.362314i	$-0.118013\pi$
$90$		−	1821.33i		−	0.224855i
$91$		0			0
$92$	−4927.83			−0.582211
$93$	−5359.09	−	5359.09i	−0.619619	−	0.619619i
$94$	−4919.53			−0.556760
$95$		−	20465.4i		−	2.26763i
$96$	8829.40	+	8829.40i	0.958051	+	0.958051i
$97$	5238.81	+	5238.81i	0.556787	+	0.556787i	0.928391	−	0.371605i	$-0.121192\pi$
$97$	5238.81	+	5238.81i	0.556787	+	0.556787i	−0.371605	+	0.928391i	$0.621192\pi$
$98$	−601.744	+	601.744i	−0.0626555	+	0.0626555i
$99$	241.017	−	241.017i	0.0245910	−	0.0245910i
$100$	−18104.4			−1.81044
$101$		−	246.646i		−	0.0241786i	−0.999927	−	0.0120893i	$-0.996152\pi$
$101$		−	246.646i		−	0.0241786i	0.999927	−	0.0120893i	$-0.00384824\pi$
$102$	8198.93	−	8198.93i	0.788055	−	0.788055i
$103$			6944.63i			0.654598i	0.944921	+	0.327299i	$0.106138\pi$
$103$			6944.63i			0.654598i	−0.944921	+	0.327299i	$0.893862\pi$
$104$		0			0
$105$	16851.4			1.52847
$106$	3620.89	+	3620.89i	0.322258	+	0.322258i
$107$	−1489.08			−0.130062			−0.0650311	−	0.997883i	$-0.520715\pi$
$107$	−1489.08			−0.130062			−0.0650311	+	0.997883i	$0.520715\pi$
$108$		−	12550.9i		−	1.07604i
$109$	12063.2	+	12063.2i	1.01534	+	1.01534i	0.999881	+	0.0154553i	$0.00491977\pi$
$109$	12063.2	+	12063.2i	1.01534	+	1.01534i	0.0154553	+	0.999881i	$0.495080\pi$
$110$	−7405.31	−	7405.31i	−0.612009	−	0.612009i
$111$	−4624.08	+	4624.08i	−0.375300	+	0.375300i
$112$	8297.53	−	8297.53i	0.661474	−	0.661474i
$113$	9077.08			0.710869			0.355434	−	0.934701i	$-0.384333\pi$
$113$	9077.08			0.710869			0.355434	+	0.934701i	$0.384333\pi$
$114$		−	24092.4i		−	1.85383i
$115$	−8744.99	+	8744.99i	−0.661247	+	0.661247i
$116$		−	6137.95i		−	0.456150i
$117$		0			0
$118$	2837.24			0.203766
$119$	−7967.88	−	7967.88i	−0.562664	−	0.562664i
$120$	−1067.84			−0.0741554
$121$			12681.1i			0.866137i
$122$	1001.87	+	1001.87i	0.0673118	+	0.0673118i
$123$	−4207.45	−	4207.45i	−0.278105	−	0.278105i
$124$	10345.2	−	10345.2i	0.672812	−	0.672812i
$125$	−13797.4	+	13797.4i	−0.883033	+	0.883033i
$126$	−2083.69			−0.131248
$127$			258.250i			0.0160115i	0.999968	+	0.00800577i	$0.00254834\pi$
$127$			258.250i			0.0160115i	−0.999968	+	0.00800577i	$0.997452\pi$
$128$	−1088.06	+	1088.06i	−0.0664097	+	0.0664097i
$129$			9642.53i			0.579444i
$130$		0			0
$131$	−19031.9			−1.10902			−0.554511	−	0.832177i	$-0.687095\pi$
$131$	−19031.9			−1.10902			−0.554511	+	0.832177i	$0.687095\pi$
$132$	−4429.51	−	4429.51i	−0.254219	−	0.254219i
$133$	−23413.4			−1.32362
$134$			10646.0i			0.592893i
$135$	−22272.9	−	22272.9i	−1.22211	−	1.22211i
$136$	504.907	+	504.907i	0.0272982	+	0.0272982i
$137$	23164.2	−	23164.2i	1.23418	−	1.23418i	0.271830	−	0.962345i	$-0.412371\pi$
$137$	23164.2	−	23164.2i	1.23418	−	1.23418i	0.962345	−	0.271830i	$-0.0876288\pi$
$138$	−10294.8	+	10294.8i	−0.540581	+	0.540581i
$139$	18205.8			0.942283			0.471141	−	0.882058i	$-0.343842\pi$
$139$	18205.8			0.942283			0.471141	+	0.882058i	$0.343842\pi$
$140$			32529.9i			1.65969i
$141$	−5222.03	+	5222.03i	−0.262664	+	0.262664i
$142$		−	17113.2i		−	0.848702i
$143$		0			0
$144$	−1903.91			−0.0918164
$145$	−10892.5	−	10892.5i	−0.518072	−	0.518072i
$146$	54994.7			2.57997
$147$			1277.49i			0.0591184i
$148$	−8926.29	−	8926.29i	−0.407519	−	0.407519i
$149$	7548.87	+	7548.87i	0.340024	+	0.340024i	0.856376	−	0.516352i	$-0.172711\pi$
$149$	7548.87	+	7548.87i	0.340024	+	0.340024i	−0.516352	+	0.856376i	$0.672711\pi$
$150$	−37822.2	+	37822.2i	−1.68099	+	1.68099i
$151$	−6497.73	+	6497.73i	−0.284976	+	0.284976i	−0.835090	−	0.550114i	$-0.814584\pi$
$151$	−6497.73	+	6497.73i	−0.284976	+	0.284976i	0.550114	+	0.835090i	$0.314584\pi$
$152$	1483.66			0.0642165
$153$			1828.27i			0.0781010i
$154$	−8472.06	+	8472.06i	−0.357230	+	0.357230i
$155$		−	36717.2i		−	1.52829i
$156$		0			0
$157$	−41173.9			−1.67041			−0.835203	−	0.549941i	$-0.814650\pi$
$157$	−41173.9			−1.67041			−0.835203	+	0.549941i	$0.814650\pi$
$158$	10097.8	+	10097.8i	0.404496	+	0.404496i
$159$	7687.06			0.304065
$160$			60493.7i			2.36303i
$161$	10004.7	+	10004.7i	0.385969	+	0.385969i
$162$	−23705.3	−	23705.3i	−0.903264	−	0.903264i
$163$	184.071	−	184.071i	0.00692805	−	0.00692805i	−0.703634	−	0.710562i	$-0.748441\pi$
$163$	184.071	−	184.071i	0.00692805	−	0.00692805i	0.710562	+	0.703634i	$0.248441\pi$
$164$	8122.04	−	8122.04i	0.301980	−	0.301980i
$165$	−15721.3			−0.577459
$166$		−	64297.1i		−	2.33332i
$167$	−30782.0	+	30782.0i	−1.10373	+	1.10373i	−0.109777	+	0.993956i	$0.535014\pi$
$167$	−30782.0	+	30782.0i	−1.10373	+	1.10373i	−0.993956	+	0.109777i	$0.964986\pi$
$168$			1221.66i			0.0432845i
$169$		0			0
$170$	56174.1			1.94374
$171$	2686.16	+	2686.16i	0.0918628	+	0.0918628i
$172$	−18613.9			−0.629188
$173$		−	26014.5i		−	0.869206i	−0.900622	−	0.434603i	$-0.856889\pi$
$173$		−	26014.5i		−	0.869206i	0.900622	−	0.434603i	$-0.143111\pi$
$174$	−12822.9	−	12822.9i	−0.423533	−	0.423533i
$175$	36756.4	+	36756.4i	1.20021	+	1.20021i
$176$	−7741.07	+	7741.07i	−0.249906	+	0.249906i
$177$	3011.70	−	3011.70i	0.0961315	−	0.0961315i
$178$	82694.6			2.60998
$179$			34894.6i			1.08906i	0.838742	+	0.544530i	$0.183292\pi$
$179$			34894.6i			1.08906i	−0.838742	+	0.544530i	$0.816708\pi$
$180$	3732.07	−	3732.07i	0.115187	−	0.115187i
$181$			38784.9i			1.18387i	0.805984	+	0.591937i	$0.201637\pi$
$181$			38784.9i			1.18387i	−0.805984	+	0.591937i	$0.798363\pi$
$182$		0			0
$183$	2126.95			0.0635118
$184$	−633.977	−	633.977i	−0.0187257	−	0.0187257i
$185$	−31681.4			−0.925679
$186$		−	43224.5i		−	1.24941i
$187$	7433.54	+	7433.54i	0.212575	+	0.212575i
$188$	−10080.6	−	10080.6i	−0.285213	−	0.285213i
$189$	−25481.4	+	25481.4i	−0.713344	+	0.713344i
$190$	82533.1	−	82533.1i	2.28624	−	2.28624i
$191$	−47264.1			−1.29558			−0.647791	−	0.761818i	$-0.724307\pi$
$191$	−47264.1			−1.29558			−0.647791	+	0.761818i	$0.724307\pi$
$192$			37340.1i			1.01292i
$193$	15720.9	−	15720.9i	0.422049	−	0.422049i	−0.463859	−	0.885909i	$-0.653536\pi$
$193$	15720.9	−	15720.9i	0.422049	−	0.422049i	0.885909	+	0.463859i	$0.153536\pi$
$194$			42254.3i			1.12271i
$195$		0			0
$196$	−2466.06			−0.0641935
$197$	3331.72	+	3331.72i	0.0858492	+	0.0858492i	0.748727	−	0.662878i	$-0.230665\pi$
$197$	3331.72	+	3331.72i	0.0858492	+	0.0858492i	−0.662878	+	0.748727i	$0.730665\pi$
$198$	1943.95			0.0495856
$199$			67470.8i			1.70377i	0.523732	+	0.851883i	$0.324539\pi$
$199$			67470.8i			1.70377i	−0.523732	+	0.851883i	$0.675461\pi$
$200$	−2329.17	−	2329.17i	−0.0582293	−	0.0582293i
$201$	11300.6	+	11300.6i	0.279711	+	0.279711i
$202$	994.679	−	994.679i	0.0243770	−	0.0243770i
$203$	−12461.5	+	12461.5i	−0.302399	+	0.302399i
$204$	33600.7			0.807399
$205$		−	28826.9i		−	0.685947i
$206$	−28006.4	+	28006.4i	−0.659969	+	0.659969i
$207$		−	2295.63i		−	0.0535748i
$208$		0			0
$209$	21843.3			0.500063
$210$	67958.7	+	67958.7i	1.54101	+	1.54101i
$211$	34787.0			0.781363			0.390681	−	0.920526i	$-0.372239\pi$
$211$	34787.0			0.781363			0.390681	+	0.920526i	$0.372239\pi$
$212$			14839.1i			0.330168i
$213$	−18165.5	−	18165.5i	−0.400395	−	0.400395i
$214$	−6005.20	−	6005.20i	−0.131129	−	0.131129i
$215$	−33032.4	+	33032.4i	−0.714600	+	0.714600i
$216$	1614.70	−	1614.70i	0.0346086	−	0.0346086i
$217$	−42006.4			−0.892064
$218$			97297.4i			2.04733i
$219$	58376.3	−	58376.3i	1.21716	−	1.21716i
$220$		−	30348.4i		−	0.627032i
$221$		0			0
$222$	−37296.1			−0.756759
$223$	22684.9	+	22684.9i	0.456171	+	0.456171i	0.897396	−	0.441225i	$-0.145456\pi$
$223$	22684.9	+	22684.9i	0.456171	+	0.456171i	−0.441225	+	0.897396i	$0.645456\pi$
$224$	69207.9			1.37930
$225$		−	8433.92i		−	0.166596i
$226$	36606.2	+	36606.2i	0.716701	+	0.716701i
$227$	−45810.4	−	45810.4i	−0.889021	−	0.889021i	0.105408	−	0.994429i	$-0.466385\pi$
$227$	−45810.4	−	45810.4i	−0.889021	−	0.889021i	−0.994429	+	0.105408i	$0.966385\pi$
$228$	49367.5	−	49367.5i	0.949667	−	0.949667i
$229$	−54161.9	+	54161.9i	−1.03282	+	1.03282i	−0.0333737	+	0.999443i	$0.510625\pi$
$229$	−54161.9	+	54161.9i	−1.03282	+	1.03282i	−0.999443	+	0.0333737i	$0.989375\pi$
$230$	−70533.9			−1.33334
$231$			17986.0i			0.337063i
$232$	789.661	−	789.661i	0.0146712	−	0.0146712i
$233$			61901.5i			1.14022i	0.821568	+	0.570111i	$0.193100\pi$
$233$			61901.5i			1.14022i	−0.821568	+	0.570111i	$0.806900\pi$
$234$		0			0
$235$	−35778.2			−0.647862
$236$	5813.77	+	5813.77i	0.104384	+	0.104384i
$237$	21437.5			0.381660
$238$		−	64266.0i		−	1.13456i
$239$	−34967.7	−	34967.7i	−0.612169	−	0.612169i	0.331342	−	0.943511i	$-0.392499\pi$
$239$	−34967.7	−	34967.7i	−0.612169	−	0.612169i	−0.943511	+	0.331342i	$0.892499\pi$
$240$	62095.1	+	62095.1i	1.07804	+	1.07804i
$241$	−1194.63	+	1194.63i	−0.0205684	+	0.0205684i	−0.717316	−	0.696748i	$-0.754630\pi$
$241$	−1194.63	+	1194.63i	−0.0205684	+	0.0205684i	0.696748	+	0.717316i	$0.254630\pi$
$242$	−51140.6	+	51140.6i	−0.873243	+	0.873243i
$243$	11186.1			0.189438
$244$			4105.84i			0.0689640i
$245$	−4376.29	+	4376.29i	−0.0729078	+	0.0729078i
$246$		−	33935.8i		−	0.560774i
$247$		0			0
$248$	2661.85			0.0432794
$249$	−68250.7	−	68250.7i	−1.10080	−	1.10080i
$250$	−111285.			−1.78056
$251$			45604.5i			0.723870i	0.932203	+	0.361935i	$0.117884\pi$
$251$			45604.5i			0.723870i	−0.932203	+	0.361935i	$0.882116\pi$
$252$	−4269.67	−	4269.67i	−0.0672347	−	0.0672347i
$253$	−9333.77	−	9333.77i	−0.145820	−	0.145820i
$254$	−1041.48	+	1041.48i	−0.0161429	+	0.0161429i
$255$	59628.2	−	59628.2i	0.917004	−	0.917004i
$256$	61005.8			0.930874
$257$		−	13013.4i		−	0.197027i	−0.995136	−	0.0985134i	$-0.968591\pi$
$257$		−	13013.4i		−	0.197027i	0.995136	−	0.0985134i	$-0.0314087\pi$
$258$	−38886.6	+	38886.6i	−0.584198	+	0.584198i
$259$			36245.1i			0.540319i
$260$		0			0
$261$	2859.36			0.0419747
$262$	−76752.2	−	76752.2i	−1.11812	−	1.11812i
$263$	−19388.3			−0.280304			−0.140152	−	0.990130i	$-0.544759\pi$
$263$	−19388.3			−0.280304			−0.140152	+	0.990130i	$0.544759\pi$
$264$		−	1139.73i		−	0.0163529i
$265$	26333.6	+	26333.6i	0.374988	+	0.374988i
$266$	−94422.1	−	94422.1i	−1.33447	−	1.33447i
$267$	87779.4	−	87779.4i	1.23132	−	1.23132i
$268$	−21814.6	+	21814.6i	−0.303723	+	0.303723i
$269$	21911.2			0.302804			0.151402	−	0.988472i	$-0.451621\pi$
$269$	21911.2			0.302804			0.151402	+	0.988472i	$0.451621\pi$
$270$		−	179645.i		−	2.46427i
$271$	−30254.4	+	30254.4i	−0.411956	+	0.411956i	−0.882419	−	0.470464i	$-0.844087\pi$
$271$	−30254.4	+	30254.4i	−0.411956	+	0.411956i	0.470464	+	0.882419i	$0.344087\pi$
$272$		−	58721.0i		−	0.793699i
$273$		0			0
$274$	186834.			2.48860
$275$	−34291.4	−	34291.4i	−0.453440	−	0.453440i
$276$	−42190.1			−0.553850
$277$		−	96564.2i		−	1.25851i	−0.777199	−	0.629255i	$-0.783360\pi$
$277$		−	96564.2i		−	1.25851i	0.777199	−	0.629255i	$-0.216640\pi$
$278$	73420.8	+	73420.8i	0.950013	+	0.950013i
$279$	4819.28	+	4819.28i	0.0619118	+	0.0619118i
$280$	−4185.04	+	4185.04i	−0.0533806	+	0.0533806i
$281$	−50030.4	+	50030.4i	−0.633609	+	0.633609i	−0.948971	−	0.315362i	$-0.897874\pi$
$281$	−50030.4	+	50030.4i	−0.633609	+	0.633609i	0.315362	+	0.948971i	$0.397874\pi$
$282$	−42119.0			−0.529639
$283$		−	147680.i		−	1.84394i	−0.387256	−	0.921972i	$-0.626577\pi$
$283$		−	147680.i		−	1.84394i	0.387256	−	0.921972i	$-0.373423\pi$
$284$	35066.6	−	35066.6i	0.434768	−	0.434768i
$285$		−	175216.i		−	2.15717i
$286$		0			0
$287$	−32979.5			−0.400387
$288$	−7940.03	−	7940.03i	−0.0957276	−	0.0957276i
$289$	27132.8			0.324862
$290$		−	87854.7i		−	1.04465i
$291$	44852.5	+	44852.5i	0.529664	+	0.529664i
$292$	112689.	+	112689.i	1.32165	+	1.32165i
$293$	−7052.35	+	7052.35i	−0.0821483	+	0.0821483i	−0.746987	−	0.664839i	$-0.768500\pi$
$293$	−7052.35	+	7052.35i	−0.0821483	+	0.0821483i	0.664839	+	0.746987i	$0.268500\pi$
$294$	−5151.88	+	5151.88i	−0.0596034	+	0.0596034i
$295$	20634.4			0.237108
$296$		−	2296.77i		−	0.0262141i
$297$	23772.5	−	23772.5i	0.269502	−	0.269502i
$298$			60886.4i			0.685627i
$299$		0			0
$300$	−155003.			−1.72225
$301$	37790.8	+	37790.8i	0.417112	+	0.417112i
$302$	−52408.3			−0.574628
$303$		−	2111.68i		−	0.0230008i
$304$	−86275.2	−	86275.2i	−0.933553	−	0.933553i
$305$	7286.27	+	7286.27i	0.0783259	+	0.0783259i
$306$	−7373.07	+	7373.07i	−0.0787418	+	0.0787418i
$307$	58686.7	−	58686.7i	0.622677	−	0.622677i	−0.323538	−	0.946215i	$-0.604872\pi$
$307$	58686.7	−	58686.7i	0.622677	−	0.622677i	0.946215	+	0.323538i	$0.104872\pi$
$308$	−34720.1			−0.365998
$309$			59457.1i			0.622711i
$310$	148074.	−	148074.i	1.54083	−	1.54083i
$311$		−	38813.8i		−	0.401296i	−0.979663	−	0.200648i	$-0.935695\pi$
$311$		−	38813.8i		−	0.401296i	0.979663	−	0.200648i	$-0.0643048\pi$
$312$		0			0
$313$	−98727.3			−1.00774			−0.503870	−	0.863779i	$-0.668091\pi$
$313$	−98727.3			−1.00774			−0.503870	+	0.863779i	$0.668091\pi$
$314$	−166047.	−	166047.i	−1.68411	−	1.68411i
$315$	−15154.0			−0.152724
$316$			41382.8i			0.414425i
$317$	−49531.4	−	49531.4i	−0.492904	−	0.492904i	0.416316	−	0.909220i	$-0.363321\pi$
$317$	−49531.4	−	49531.4i	−0.492904	−	0.492904i	−0.909220	+	0.416316i	$0.863321\pi$
$318$	31000.5	+	31000.5i	0.306560	+	0.306560i
$319$	11625.8	−	11625.8i	0.114247	−	0.114247i
$320$	−127916.	+	127916.i	−1.24918	+	1.24918i
$321$	−12748.9			−0.123727
$322$			80694.4i			0.778272i
$323$	−82847.7	+	82847.7i	−0.794100	+	0.794100i
$324$		−	97148.6i		−	0.925436i
$325$		0			0
$326$	1484.65			0.0139698
$327$	103280.	+	103280.i	0.965876	+	0.965876i
$328$	2089.84			0.0194252
$329$			40932.1i			0.378157i
$330$	−63401.2	−	63401.2i	−0.582197	−	0.582197i
$331$	−47550.4	−	47550.4i	−0.434009	−	0.434009i	0.455981	−	0.889990i	$-0.349289\pi$
$331$	−47550.4	−	47550.4i	−0.434009	−	0.434009i	−0.889990	+	0.455981i	$0.849289\pi$
$332$	131751.	−	131751.i	1.19530	−	1.19530i
$333$	4158.30	−	4158.30i	0.0374997	−	0.0374997i
$334$	−248277.			−2.22558
$335$			77424.9i			0.689907i
$336$	71040.0	−	71040.0i	0.629252	−	0.629252i
$337$			104833.i			0.923075i	0.887121	+	0.461538i	$0.152702\pi$
$337$			104833.i			0.923075i	−0.887121	+	0.461538i	$0.847298\pi$
$338$		0			0
$339$	77714.3			0.676241
$340$	115106.	+	115106.i	0.995726	+	0.995726i
$341$	39189.3			0.337023
$342$			21665.6i			0.185233i
$343$	85570.7	+	85570.7i	0.727339	+	0.727339i
$344$	−2394.72	−	2394.72i	−0.0202366	−	0.0202366i
$345$	−74871.0	+	74871.0i	−0.629036	+	0.629036i
$346$	104912.	−	104912.i	0.876338	−	0.876338i
$347$	152401.			1.26569			0.632846	−	0.774277i	$-0.281887\pi$
$347$	152401.			1.26569			0.632846	+	0.774277i	$0.281887\pi$
$348$		−	52550.6i		−	0.433930i
$349$	150748.	−	150748.i	1.23766	−	1.23766i	0.276699	−	0.960956i	$-0.410759\pi$
$349$	150748.	−	150748.i	1.23766	−	1.23766i	0.960956	−	0.276699i	$-0.0892407\pi$
$350$			296464.i			2.42011i
$351$		0			0
$352$	−64566.6			−0.521102
$353$	146322.	+	146322.i	1.17425	+	1.17425i	0.981186	+	0.193066i	$0.0618431\pi$
$353$	146322.	+	146322.i	1.17425	+	1.17425i	0.193066	+	0.981186i	$0.438157\pi$
$354$	24291.3			0.193840
$355$		−	124459.i		−	0.987575i
$356$	169449.	+	169449.i	1.33702	+	1.33702i
$357$	−68217.7	−	68217.7i	−0.535255	−	0.535255i
$358$	−140723.	+	140723.i	−1.09799	+	1.09799i
$359$	100758.	−	100758.i	0.781795	−	0.781795i	−0.198339	−	0.980134i	$-0.563555\pi$
$359$	100758.	−	100758.i	0.781795	−	0.781795i	0.980134	+	0.198339i	$0.0635546\pi$
$360$	960.277			0.00740954
$361$			113125.i			0.868049i
$362$	−156412.	+	156412.i	−1.19359	+	1.19359i
$363$			108570.i			0.823945i
$364$		0			0
$365$	399959.			3.00213
$366$	8577.58	+	8577.58i	0.0640328	+	0.0640328i
$367$	−100859.			−0.748832			−0.374416	−	0.927261i	$-0.622157\pi$
$367$	−100859.			−0.748832			−0.374416	+	0.927261i	$0.622157\pi$
$368$			73731.9i			0.544452i
$369$	3783.65	+	3783.65i	0.0277880	+	0.0277880i
$370$	−127765.	−	127765.i	−0.933274	−	0.933274i
$371$	30126.9	−	30126.9i	0.218881	−	0.218881i
$372$	88571.0	−	88571.0i	0.640038	−	0.640038i
$373$	82341.2			0.591834			0.295917	−	0.955214i	$-0.404375\pi$
$373$	82341.2			0.591834			0.295917	+	0.955214i	$0.404375\pi$
$374$			59956.2i			0.428638i
$375$	−118128.	+	118128.i	−0.840018	+	0.840018i
$376$		−	2593.78i		−	0.0183467i
$377$		0			0
$378$	−205523.			−1.43839
$379$	−25664.7	−	25664.7i	−0.178673	−	0.178673i	0.612104	−	0.790777i	$-0.290323\pi$
$379$	−25664.7	−	25664.7i	−0.178673	−	0.178673i	−0.790777	+	0.612104i	$0.790323\pi$
$380$	338236.			2.34236
$381$			2211.03i			0.0152316i
$382$	−190608.	−	190608.i	−1.30621	−	1.30621i
$383$	108692.	+	108692.i	0.740972	+	0.740972i	0.972765	−	0.231793i	$-0.0744592\pi$
$383$	108692.	+	108692.i	0.740972	+	0.740972i	−0.231793	+	0.972765i	$0.574459\pi$
$384$	−9315.50	+	9315.50i	−0.0631748	+	0.0631748i
$385$	−61614.6	+	61614.6i	−0.415683	+	0.415683i
$386$	126799.			0.851024
$387$		−	8671.26i		−	0.0578976i
$388$	−86583.0	+	86583.0i	−0.575134	+	0.575134i
$389$			15749.1i			0.104077i	0.998645	+	0.0520387i	$0.0165719\pi$
$389$			15749.1i			0.104077i	−0.998645	+	0.0520387i	$0.983428\pi$
$390$		0			0
$391$	70802.7			0.463123
$392$	−317.264	−	317.264i	−0.00206466	−	0.00206466i
$393$	−162943.			−1.05500
$394$			26872.4i			0.173107i
$395$	73438.3	+	73438.3i	0.470683	+	0.470683i
$396$	3983.34	+	3983.34i	0.0254014	+	0.0254014i
$397$	−144465.	+	144465.i	−0.916605	+	0.916605i	−0.996781	−	0.0801760i	$-0.974452\pi$
$397$	−144465.	+	144465.i	−0.916605	+	0.916605i	0.0801760	+	0.996781i	$0.474452\pi$
$398$	−272098.	+	272098.i	−1.71774	+	1.71774i
$399$	−200456.			−1.25914
$400$			270884.i			1.69303i
$401$	−83242.2	+	83242.2i	−0.517672	+	0.517672i	−0.916866	−	0.399194i	$-0.869290\pi$
$401$	−83242.2	+	83242.2i	−0.517672	+	0.517672i	0.399194	+	0.916866i	$0.369290\pi$
$402$			91146.5i			0.564011i
$403$		0			0
$404$	4076.38			0.0249754
$405$	−172401.	−	172401.i	−1.05106	−	1.05106i
$406$	−100510.			−0.609759
$407$		−	33814.4i		−	0.204133i
$408$	4322.81	+	4322.81i	0.0259684	+	0.0259684i
$409$	42949.5	+	42949.5i	0.256751	+	0.256751i	0.823731	−	0.566980i	$-0.191888\pi$
$409$	42949.5	+	42949.5i	0.256751	+	0.256751i	−0.566980	+	0.823731i	$0.691888\pi$
$410$	116254.	−	116254.i	0.691575	−	0.691575i
$411$	198323.	−	198323.i	1.17406	−	1.17406i
$412$	−114776.			−0.676169
$413$		−	23606.8i		−	0.138400i
$414$	9257.85	−	9257.85i	0.0540144	−	0.0540144i
$415$		−	467612.i		−	2.71512i
$416$		0			0
$417$	155871.			0.896382
$418$	88089.9	+	88089.9i	0.504166	+	0.504166i
$419$	325761.			1.85554			0.927770	−	0.373152i	$-0.121723\pi$
$419$	325761.			1.85554			0.927770	+	0.373152i	$0.121723\pi$
$420$			278507.i			1.57884i
$421$	−84760.5	−	84760.5i	−0.478222	−	0.478222i	0.426341	−	0.904563i	$-0.359802\pi$
$421$	−84760.5	−	84760.5i	−0.478222	−	0.478222i	−0.904563	+	0.426341i	$0.859802\pi$
$422$	140290.	+	140290.i	0.787773	+	0.787773i
$423$	4696.03	−	4696.03i	0.0262452	−	0.0262452i
$424$	−1909.08	+	1909.08i	−0.0106192	+	0.0106192i
$425$	260123.			1.44013
$426$		−	146516.i		−	0.807360i
$427$	8335.87	−	8335.87i	0.0457188	−	0.0457188i
$428$		−	24610.4i		−	0.134348i
$429$		0			0
$430$	−266427.			−1.44093
$431$	220269.	+	220269.i	1.18576	+	1.18576i	0.978227	+	0.207537i	$0.0665447\pi$
$431$	220269.	+	220269.i	1.18576	+	1.18576i	0.207537	+	0.978227i	$0.433455\pi$
$432$	−187791.			−1.00625
$433$			65965.0i			0.351834i	0.984405	+	0.175917i	$0.0562890\pi$
$433$			65965.0i			0.351834i	−0.984405	+	0.175917i	$0.943711\pi$
$434$	−169404.	−	169404.i	−0.899383	−	0.899383i
$435$	−93256.9	−	93256.9i	−0.492836	−	0.492836i
$436$	−199371.	+	199371.i	−1.04879	+	1.04879i
$437$	104026.	−	104026.i	0.544727	−	0.544727i
$438$	470842.			2.45430
$439$		−	159531.i		−	0.827784i	−0.910326	−	0.413892i	$-0.864169\pi$
$439$		−	159531.i		−	0.827784i	0.910326	−	0.413892i	$-0.135831\pi$
$440$	3904.38	−	3904.38i	0.0201673	−	0.0201673i
$441$		−	1148.81i		−	0.00590706i
$442$		0			0
$443$	−372577.			−1.89849			−0.949246	−	0.314535i	$-0.898151\pi$
$443$	−372577.			−1.89849			−0.949246	+	0.314535i	$0.898151\pi$
$444$	−76423.2	−	76423.2i	−0.387668	−	0.387668i
$445$	601411.			3.03705
$446$			182968.i			0.919828i
$447$	64630.3	+	64630.3i	0.323460	+	0.323460i
$448$	146342.	+	146342.i	0.729145	+	0.729145i
$449$	−51939.7	+	51939.7i	−0.257636	+	0.257636i	−0.824092	−	0.566456i	$-0.808314\pi$
$449$	−51939.7	+	51939.7i	−0.257636	+	0.257636i	0.566456	+	0.824092i	$0.308314\pi$
$450$	34012.5	−	34012.5i	0.167963	−	0.167963i
$451$	30767.8			0.151267
$452$			150019.i			0.734294i
$453$	−55630.9	+	55630.9i	−0.271094	+	0.271094i
$454$		−	369490.i		−	1.79263i
$455$		0			0
$456$	12702.5			0.0610884
$457$	−227956.	−	227956.i	−1.09149	−	1.09149i	−0.995370	−	0.0961183i	$-0.969357\pi$
$457$	−227956.	−	227956.i	−1.09149	−	1.09149i	−0.0961183	−	0.995370i	$-0.530643\pi$
$458$	−436850.			−2.08258
$459$			180330.i			0.855939i
$460$	−144530.	−	144530.i	−0.683036	−	0.683036i
$461$	−122668.	−	122668.i	−0.577202	−	0.577202i	0.356929	−	0.934131i	$-0.383824\pi$
$461$	−122668.	−	122668.i	−0.577202	−	0.577202i	−0.934131	+	0.356929i	$0.883824\pi$
$462$	−72534.3	+	72534.3i	−0.339828	+	0.339828i
$463$	−88275.9	+	88275.9i	−0.411794	+	0.411794i	−0.882363	−	0.470569i	$-0.844049\pi$
$463$	−88275.9	+	88275.9i	−0.411794	+	0.411794i	0.470569	+	0.882363i	$0.344049\pi$
$464$	−91838.1			−0.426567
$465$		−	314358.i		−	1.45385i
$466$	−249637.	+	249637.i	−1.14958	+	1.14958i
$467$			2610.83i			0.0119714i	0.999982	+	0.00598570i	$0.00190532\pi$
$467$			2610.83i			0.0119714i	−0.999982	+	0.00598570i	$0.998095\pi$
$468$		0			0
$469$	88578.0			0.402699
$470$	−144287.	−	144287.i	−0.653177	−	0.653177i
$471$	−352514.			−1.58904
$472$			1495.91i			0.00671462i
$473$	−35256.4	−	35256.4i	−0.157585	−	0.157585i
$474$	86453.5	+	86453.5i	0.384792	+	0.384792i
$475$	382182.	−	382182.i	1.69388	−	1.69388i
$476$	131687.	−	131687.i	0.581205	−	0.581205i
$477$	−6912.76			−0.0303819
$478$		−	282037.i		−	1.23438i
$479$	244175.	−	244175.i	1.06422	−	1.06422i	0.0664278	−	0.997791i	$-0.478840\pi$
$479$	244175.	−	244175.i	1.06422	−	1.06422i	0.997791	−	0.0664278i	$-0.0211602\pi$
$480$			517922.i			2.24793i
$481$		0			0
$482$	−9635.48			−0.0414743
$483$	85656.2	+	85656.2i	0.367168	+	0.367168i
$484$	−209584.			−0.894678
$485$			307302.i			1.30642i
$486$	45111.6	+	45111.6i	0.190992	+	0.190992i
$487$	−219809.	−	219809.i	−0.926805	−	0.926805i	0.0706935	−	0.997498i	$-0.477479\pi$
$487$	−219809.	−	219809.i	−0.926805	−	0.926805i	−0.997498	+	0.0706935i	$0.977479\pi$
$488$	−528.226	+	528.226i	−0.00221809	+	0.00221809i
$489$	1575.94	−	1575.94i	0.00659057	−	0.00659057i
$490$	−35297.6			−0.147012
$491$			16431.7i			0.0681583i	0.999419	+	0.0340791i	$0.0108498\pi$
$491$			16431.7i			0.0681583i	−0.999419	+	0.0340791i	$0.989150\pi$
$492$	69537.6	−	69537.6i	0.287269	−	0.287269i
$493$			88189.5i			0.362847i
$494$		0			0
$495$	14137.7			0.0576992
$496$	−154788.	−	154788.i	−0.629177	−	0.629177i
$497$	−142388.			−0.576447
$498$		−	550485.i		−	2.21966i
$499$	−165805.	−	165805.i	−0.665883	−	0.665883i	0.290877	−	0.956760i	$-0.406053\pi$
$499$	−165805.	−	165805.i	−0.665883	−	0.665883i	−0.956760	+	0.290877i	$0.906053\pi$
$500$	−228033.	−	228033.i	−0.912131	−	0.912131i
$501$	−263543.	+	263543.i	−1.04997	+	1.04997i
$502$	−183915.	+	183915.i	−0.729809	+	0.729809i
$503$	−305660.			−1.20810			−0.604050	−	0.796946i	$-0.706447\pi$
$503$	−305660.			−1.20810			−0.604050	+	0.796946i	$0.706447\pi$
$504$		−	1098.61i		−	0.00432495i
$505$	7233.99	−	7233.99i	0.0283658	−	0.0283658i
$506$		−	75282.8i		−	0.294032i
$507$		0			0
$508$	−4268.16			−0.0165392
$509$	98134.2	+	98134.2i	0.378778	+	0.378778i	0.870661	−	0.491883i	$-0.163691\pi$
$509$	98134.2	+	98134.2i	0.378778	+	0.378778i	−0.491883	+	0.870661i	$0.663691\pi$
$510$	480939.			1.84906
$511$		−	457574.i		−	1.75234i
$512$	263434.	+	263434.i	1.00492	+	1.00492i
$513$	264948.	+	264948.i	1.00676	+	1.00676i
$514$	52480.8	−	52480.8i	0.198643	−	0.198643i
$515$	−203682.	+	203682.i	−0.767959	+	0.767959i
$516$	−159364.			−0.598538
$517$		−	38187.1i		−	0.142868i
$518$	−146170.	+	146170.i	−0.544752	+	0.544752i
$519$		−	222725.i		−	0.826865i
$520$		0			0
$521$	−82330.3			−0.303308			−0.151654	−	0.988434i	$-0.548460\pi$
$521$	−82330.3			−0.303308			−0.151654	+	0.988434i	$0.548460\pi$
$522$	11531.3	+	11531.3i	0.0423191	+	0.0423191i
$523$	352506.			1.28873			0.644367	−	0.764717i	$-0.277121\pi$
$523$	352506.			1.28873			0.644367	+	0.764717i	$0.277121\pi$
$524$		−	314545.i		−	1.14557i
$525$	314693.	+	314693.i	1.14174	+	1.14174i
$526$	−78189.6	−	78189.6i	−0.282603	−	0.282603i
$527$	−148638.	+	148638.i	−0.535192	+	0.535192i
$528$	−66275.9	+	66275.9i	−0.237732	+	0.237732i
$529$	190939.			0.682312
$530$			212397.i			0.756130i
$531$	−2708.34	+	2708.34i	−0.00960537	+	0.00960537i
$532$		−	386959.i		−	1.36723i
$533$		0			0
$534$	707997.			2.48284
$535$	−43673.9	−	43673.9i	−0.152586	−	0.152586i
$536$	−5613.00			−0.0195373
$537$			298753.i			1.03601i
$538$	88363.7	+	88363.7i	0.305288	+	0.305288i
$539$	−4670.94	−	4670.94i	−0.0160778	−	0.0160778i
$540$	368110.	−	368110.i	1.26238	−	1.26238i
$541$	−148284.	+	148284.i	−0.506642	+	0.506642i	−0.913494	−	0.406852i	$-0.866626\pi$
$541$	−148284.	+	148284.i	−0.506642	+	0.506642i	0.406852	+	0.913494i	$0.366626\pi$
$542$	−244021.			−0.830671
$543$			332060.i			1.12620i
$544$	244890.	−	244890.i	0.827509	−	0.827509i
$545$			707613.i			2.38234i
$546$		0			0
$547$	−103249.			−0.345075			−0.172537	−	0.985003i	$-0.555197\pi$
$547$	−103249.			−0.345075			−0.172537	+	0.985003i	$0.555197\pi$
$548$	382841.	+	382841.i	1.27484	+	1.27484i
$549$	−1912.70			−0.00634604
$550$		−	276582.i		−	0.914321i
$551$	129571.	+	129571.i	0.426782	+	0.426782i
$552$	−5427.85	−	5427.85i	−0.0178135	−	0.0178135i
$553$	84017.2	−	84017.2i	0.274737	−	0.274737i
$554$	389426.	−	389426.i	1.26883	−	1.26883i
$555$	−271243.			−0.880587
$556$			300892.i			0.973333i
$557$	107744.	−	107744.i	0.347281	−	0.347281i	−0.511815	−	0.859096i	$-0.671027\pi$
$557$	107744.	−	107744.i	0.347281	−	0.347281i	0.859096	+	0.511815i	$0.171027\pi$
$558$			38870.6i			0.124840i
$559$		0			0
$560$	486723.			1.55205
$561$	63642.9	+	63642.9i	0.202220	+	0.202220i
$562$	−403527.			−1.27762
$563$		−	522914.i		−	1.64973i	−0.565328	−	0.824866i	$-0.691250\pi$
$563$		−	522914.i		−	1.64973i	0.565328	−	0.824866i	$-0.308750\pi$
$564$	−86305.7	−	86305.7i	−0.271320	−	0.271320i
$565$	266226.	+	266226.i	0.833974	+	0.833974i
$566$	595565.	−	595565.i	1.85907	−	1.85907i
$567$	−197235.	+	197235.i	−0.613506	+	0.613506i
$568$	9022.80			0.0279669
$569$			315341.i			0.973994i	0.873404	+	0.486997i	$0.161908\pi$
$569$			315341.i			0.973994i	−0.873404	+	0.486997i	$0.838092\pi$
$570$	706615.	−	706615.i	2.17487	−	2.17487i
$571$			6380.52i			0.0195697i	0.999952	+	0.00978484i	$0.00311466\pi$
$571$			6380.52i			0.0195697i	−0.999952	+	0.00978484i	$0.996885\pi$
$572$		0			0
$573$	−404656.			−1.23247
$574$	−133000.	−	133000.i	−0.403672	−	0.403672i
$575$	−326618.			−0.987880
$576$		−	33578.9i		−	0.101210i
$577$	78575.8	+	78575.8i	0.236014	+	0.236014i	0.815197	−	0.579184i	$-0.196629\pi$
$577$	78575.8	+	78575.8i	0.236014	+	0.236014i	−0.579184	+	0.815197i	$0.696629\pi$
$578$	109422.	+	109422.i	0.327528	+	0.327528i
$579$	134596.	−	134596.i	0.401490	−	0.401490i
$580$	180022.	−	180022.i	0.535144	−	0.535144i
$581$	−534972.			−1.58482
$582$			361764.i			1.06802i
$583$	−28106.6	+	28106.6i	−0.0826933	+	0.0826933i
$584$			28995.5i			0.0850167i
$585$		0			0
$586$	−56881.7			−0.165645
$587$	−84677.0	−	84677.0i	−0.245748	−	0.245748i	0.573475	−	0.819223i	$-0.305595\pi$
$587$	−84677.0	−	84677.0i	−0.245748	−	0.245748i	−0.819223	+	0.573475i	$0.805595\pi$
$588$	−21113.4			−0.0610665
$589$			436770.i			1.25899i
$590$	83214.6	+	83214.6i	0.239054	+	0.239054i
$591$	28524.8	+	28524.8i	0.0816672	+	0.0816672i
$592$	−133558.	+	133558.i	−0.381090	+	0.381090i
$593$	−86441.2	+	86441.2i	−0.245817	+	0.245817i	−0.819251	−	0.573435i	$-0.805611\pi$
$593$	−86441.2	+	86441.2i	−0.245817	+	0.245817i	0.573435	+	0.819251i	$0.305611\pi$
$594$	191741.			0.543427
$595$		−	467386.i		−	1.32021i
$596$	−124762.	+	124762.i	−0.351228	+	0.351228i
$597$			577657.i			1.62077i
$598$		0			0
$599$	−256983.			−0.716228			−0.358114	−	0.933678i	$-0.616580\pi$
$599$	−256983.			−0.716228			−0.358114	+	0.933678i	$0.616580\pi$
$600$	−19941.4	−	19941.4i	−0.0553928	−	0.0553928i
$601$	−344146.			−0.952781			−0.476391	−	0.879234i	$-0.658055\pi$
$601$	−344146.			−0.952781			−0.476391	+	0.879234i	$0.658055\pi$
$602$			304806.i			0.841068i
$603$	−10162.3	−	10162.3i	−0.0279485	−	0.0279485i
$604$	−107390.	−	107390.i	−0.294366	−	0.294366i
$605$	−371929.	+	371929.i	−1.01613	+	1.01613i
$606$	8516.03	−	8516.03i	0.0231895	−	0.0231895i
$607$	−158686.			−0.430688			−0.215344	−	0.976538i	$-0.569087\pi$
$607$	−158686.			−0.430688			−0.215344	+	0.976538i	$0.569087\pi$
$608$		−	719603.i		−	1.94664i
$609$	−106691.	+	106691.i	−0.287668	+	0.287668i
$610$			58768.4i			0.157937i
$611$		0			0
$612$	−30216.2			−0.0806746
$613$	464914.	+	464914.i	1.23723	+	1.23723i	0.961127	+	0.276105i	$0.0890438\pi$
$613$	464914.	+	464914.i	1.23723	+	1.23723i	0.276105	+	0.961127i	$0.410956\pi$
$614$	473345.			1.25557
$615$		−	246804.i		−	0.652533i
$616$	−4466.81	−	4466.81i	−0.0117716	−	0.0117716i
$617$	−82086.7	−	82086.7i	−0.215627	−	0.215627i	0.591026	−	0.806653i	$-0.298723\pi$
$617$	−82086.7	−	82086.7i	−0.215627	−	0.215627i	−0.806653	+	0.591026i	$0.798723\pi$
$618$	−239779.	+	239779.i	−0.627820	+	0.627820i
$619$	349306.	−	349306.i	0.911644	−	0.911644i	−0.0847577	−	0.996402i	$-0.527012\pi$
$619$	349306.	−	349306.i	0.911644	−	0.911644i	0.996402	+	0.0847577i	$0.0270116\pi$
$620$	606834.			1.57865
$621$		−	226428.i		−	0.587147i
$622$	156529.	−	156529.i	0.404589	−	0.404589i
$623$		−	688046.i		−	1.77272i
$624$		0			0
$625$	−124696.			−0.319221
$626$	−398149.	−	398149.i	−1.01601	−	1.01601i
$627$	187013.			0.475704
$628$		−	680490.i		−	1.72545i
$629$	128252.	+	128252.i	0.324163	+	0.324163i
$630$	−61113.4	−	61113.4i	−0.153977	−	0.153977i
$631$	−29344.9	+	29344.9i	−0.0737011	+	0.0737011i	−0.742996	−	0.669295i	$-0.766596\pi$
$631$	−29344.9	+	29344.9i	−0.0737011	+	0.0737011i	0.669295	+	0.742996i	$0.266596\pi$
$632$	−5323.99	+	5323.99i	−0.0133292	+	0.0133292i
$633$	297832.			0.743301
$634$		−	399502.i		−	0.993896i
$635$	−7574.33	+	7574.33i	−0.0187844	+	0.0187844i
$636$			127046.i			0.314085i
$637$		0			0
$638$	93769.8			0.230368
$639$	16335.7	+	16335.7i	0.0400071	+	0.0400071i
$640$	−63824.2			−0.155821
$641$			74714.1i			0.181839i	0.995858	+	0.0909194i	$0.0289806\pi$
$641$			74714.1i			0.181839i	−0.995858	+	0.0909194i	$0.971019\pi$
$642$	−51414.1	−	51414.1i	−0.124742	−	0.124742i
$643$	−464484.	−	464484.i	−1.12344	−	1.12344i	−0.991221	−	0.132216i	$-0.957791\pi$
$643$	−464484.	−	464484.i	−1.12344	−	1.12344i	−0.132216	−	0.991221i	$-0.542209\pi$
$644$	−165350.	+	165350.i	−0.398688	+	0.398688i
$645$	−282810.	+	282810.i	−0.679790	+	0.679790i
$646$	−668219.			−1.60123
$647$		−	431810.i		−	1.03153i	−0.856729	−	0.515767i	$-0.827507\pi$
$647$		−	431810.i		−	1.03153i	0.856729	−	0.515767i	$-0.172493\pi$
$648$	12498.4	−	12498.4i	0.0297648	−	0.0297648i
$649$			22023.6i			0.0522877i
$650$		0			0
$651$	−359641.			−0.848609
$652$	3042.19	+	3042.19i	0.00715635	+	0.00715635i
$653$	−562003.			−1.31799			−0.658995	−	0.752147i	$-0.729018\pi$
$653$	−562003.			−1.31799			−0.658995	+	0.752147i	$0.729018\pi$
$654$			833020.i			1.94760i
$655$	−558195.	−	558195.i	−1.30108	−	1.30108i
$656$	−121525.	−	121525.i	−0.282395	−	0.282395i
$657$	−52496.2	+	52496.2i	−0.121618	+	0.121618i
$658$	−165072.	+	165072.i	−0.381259	+	0.381259i
$659$	−765929.			−1.76367			−0.881835	−	0.471557i	$-0.843692\pi$
$659$	−765929.			−1.76367			−0.881835	+	0.471557i	$0.843692\pi$
$660$		−	259830.i		−	0.596488i
$661$	−158559.	+	158559.i	−0.362900	+	0.362900i	−0.864880	−	0.501979i	$-0.832605\pi$
$661$	−158559.	+	158559.i	−0.362900	+	0.362900i	0.501979	+	0.864880i	$0.332605\pi$
$662$		−	383524.i		−	0.875139i
$663$		0			0
$664$	33900.0			0.0768889
$665$	−686702.	−	686702.i	−1.55283	−	1.55283i
$666$	33539.4			0.0756147
$667$		−	110733.i		−	0.248901i
$668$	−508742.	−	508742.i	−1.14010	−	1.14010i
$669$	194219.	+	194219.i	0.433950	+	0.433950i
$670$	−312240.	+	312240.i	−0.695568	+	0.695568i
$671$	−7776.84	+	7776.84i	−0.0172726	+	0.0172726i
$672$	592529.			1.31211
$673$			532008.i			1.17459i	0.809372	+	0.587297i	$0.199808\pi$
$673$			532008.i			1.17459i	−0.809372	+	0.587297i	$0.800192\pi$
$674$	−422771.	+	422771.i	−0.930649	+	0.930649i
$675$		−	831875.i		−	1.82579i
$676$		0			0
$677$	538896.			1.17578			0.587892	−	0.808940i	$-0.299958\pi$
$677$	538896.			1.17578			0.587892	+	0.808940i	$0.299958\pi$
$678$	313407.	+	313407.i	0.681789	+	0.681789i
$679$	351569.			0.762556
$680$			29617.3i			0.0640512i
$681$	−392209.	−	392209.i	−0.845715	−	0.845715i
$682$	158043.	+	158043.i	0.339788	+	0.339788i
$683$	548460.	−	548460.i	1.17572	−	1.17572i	0.194895	−	0.980824i	$-0.437564\pi$
$683$	548460.	−	548460.i	1.17572	−	1.17572i	0.980824	−	0.194895i	$-0.0624365\pi$
$684$	−44394.8	+	44394.8i	−0.0948899	+	0.0948899i
$685$	1.35879e6			2.89581
$686$			690182.i			1.46661i
$687$	−463712.	+	463712.i	−0.982506	+	0.982506i
$688$			278507.i			0.588382i
$689$		0			0
$690$	−603882.			−1.26839
$691$	−468251.	−	468251.i	−0.980670	−	0.980670i	0.0191471	−	0.999817i	$-0.493905\pi$
$691$	−468251.	−	468251.i	−0.980670	−	0.980670i	−0.999817	+	0.0191471i	$0.993905\pi$
$692$	429947.			0.897849
$693$		−	16174.3i		−	0.0336790i
$694$	614605.	+	614605.i	1.27608	+	1.27608i
$695$	533967.	+	533967.i	1.10546	+	1.10546i
$696$	6760.75	−	6760.75i	0.0139565	−	0.0139565i
$697$	−116697.	+	116697.i	−0.240211	+	0.240211i
$698$	1.21588e6			2.49562
$699$			529975.i			1.08468i
$700$	−607482.	+	607482.i	−1.23976	+	1.23976i
$701$		−	263737.i		−	0.536705i	−0.963321	−	0.268352i	$-0.913521\pi$
$701$		−	263737.i		−	0.536705i	0.963321	−	0.268352i	$-0.0864791\pi$
$702$		0			0
$703$	376866.			0.762564
$704$	−136528.	−	136528.i	−0.275472	−	0.275472i
$705$	−306318.			−0.616303
$706$			1.18018e6i			2.36777i
$707$	−8276.05	−	8276.05i	−0.0165571	−	0.0165571i
$708$	49775.1	+	49775.1i	0.0992992	+	0.0992992i
$709$	342335.	−	342335.i	0.681018	−	0.681018i	−0.279212	−	0.960230i	$-0.590073\pi$
$709$	342335.	−	342335.i	0.681018	−	0.681018i	0.960230	+	0.279212i	$0.0900732\pi$
$710$	501921.	−	501921.i	0.995678	−	0.995678i
$711$	−19278.1			−0.0381352
$712$			43600.0i			0.0860055i
$713$	186635.	−	186635.i	0.367124	−	0.367124i
$714$		−	550219.i		−	1.07929i
$715$		0			0
$716$	−576711.			−1.12495
$717$	−299379.	−	299379.i	−0.582348	−	0.582348i
$718$	812681.			1.57642
$719$			477053.i			0.922802i	0.887192	+	0.461401i	$0.152653\pi$
$719$			477053.i			0.922802i	−0.887192	+	0.461401i	$0.847347\pi$
$720$	−55840.4	−	55840.4i	−0.107717	−	0.107717i
$721$	233022.	+	233022.i	0.448257	+	0.448257i
$722$	−456212.	+	456212.i	−0.875171	+	0.875171i
$723$	−10228.0	+	10228.0i	−0.0195665	+	0.0195665i
$724$	−641007.			−1.22289
$725$		−	406825.i		−	0.773982i
$726$	−437845.	+	437845.i	−0.830705	+	0.830705i
$727$			1.00958e6i			1.91017i	0.296330	+	0.955086i	$0.404237\pi$
$727$			1.00958e6i			1.91017i	−0.296330	+	0.955086i	$0.595763\pi$
$728$		0			0
$729$	571896.			1.07612
$730$	1.61296e6	+	1.61296e6i	3.02676	+	3.02676i
$731$	267443.			0.500491
$732$			35152.5i			0.0656046i
$733$	438348.	+	438348.i	0.815851	+	0.815851i	0.985504	−	0.169653i	$-0.0542647\pi$
$733$	438348.	+	438348.i	0.815851	+	0.815851i	−0.169653	+	0.985504i	$0.554265\pi$
$734$	−406748.	−	406748.i	−0.754975	−	0.754975i
$735$	−37468.0	+	37468.0i	−0.0693563	+	0.0693563i
$736$	−307491.	+	307491.i	−0.567645	+	0.567645i
$737$	−82637.8			−0.152140
$738$			30517.5i			0.0560320i
$739$	396206.	−	396206.i	0.725491	−	0.725491i	−0.244227	−	0.969718i	$-0.578534\pi$
$739$	396206.	−	396206.i	0.725491	−	0.725491i	0.969718	+	0.244227i	$0.0785342\pi$
$740$		−	523606.i		−	0.956183i
$741$		0			0
$742$	242993.			0.441353
$743$	323825.	+	323825.i	0.586587	+	0.586587i	0.936706	−	0.350118i	$-0.113859\pi$
$743$	323825.	+	323825.i	0.586587	+	0.586587i	−0.350118	+	0.936706i	$0.613859\pi$
$744$	22789.7			0.0411711
$745$			442808.i			0.797816i
$746$	332067.	+	332067.i	0.596689	+	0.596689i
$747$	61375.9	+	61375.9i	0.109991	+	0.109991i
$748$	−122856.	+	122856.i	−0.219580	+	0.219580i
$749$	−49965.2	+	49965.2i	−0.0890644	+	0.0890644i
$750$	−952774.			−1.69382
$751$			833642.i			1.47809i	0.673658	+	0.739043i	$0.264722\pi$
$751$			833642.i			1.47809i	−0.673658	+	0.739043i	$0.735278\pi$
$752$	−150829.	+	150829.i	−0.266716	+	0.266716i
$753$			390447.i			0.688608i
$754$		0			0
$755$	−381149.			−0.668653
$756$	−421137.	−	421137.i	−0.736851	−	0.736851i
$757$	299160.			0.522050			0.261025	−	0.965332i	$-0.415940\pi$
$757$	299160.			0.522050			0.261025	+	0.965332i	$0.415940\pi$
$758$		−	207002.i		−	0.360277i
$759$	−79911.9	−	79911.9i	−0.138716	−	0.138716i
$760$	43514.8	+	43514.8i	0.0753373	+	0.0753373i
$761$	−332199.	+	332199.i	−0.573627	+	0.573627i	−0.933140	−	0.359513i	$-0.882943\pi$
$761$	−332199.	+	332199.i	−0.573627	+	0.573627i	0.359513	+	0.933140i	$0.382943\pi$
$762$	−8916.69	+	8916.69i	−0.0153566	+	0.0153566i
$763$	809546.			1.39057
$764$		−	781146.i		−	1.33827i
$765$	−53622.0	+	53622.0i	−0.0916263	+	0.0916263i
$766$			876674.i			1.49410i
$767$		0			0
$768$	522306.			0.885529
$769$	−501329.	−	501329.i	−0.847754	−	0.847754i	0.142098	−	0.989853i	$-0.454615\pi$
$769$	−501329.	−	501329.i	−0.847754	−	0.847754i	−0.989853	+	0.142098i	$0.954615\pi$
$770$	−496961.			−0.838187
$771$		−	111416.i		−	0.187429i
$772$	259823.	+	259823.i	0.435957	+	0.435957i
$773$	−266737.	−	266737.i	−0.446400	−	0.446400i	0.447756	−	0.894156i	$-0.352223\pi$
$773$	−266737.	−	266737.i	−0.446400	−	0.446400i	−0.894156	+	0.447756i	$0.852223\pi$
$774$	34969.6	−	34969.6i	0.0583726	−	0.0583726i
$775$	685679.	−	685679.i	1.14161	−	1.14161i
$776$	−22278.2			−0.0369961
$777$			310316.i			0.513998i
$778$	−63513.2	+	63513.2i	−0.104931	+	0.104931i
$779$			342911.i			0.565075i
$780$		0			0
$781$	132839.			0.217782
$782$	285534.	+	285534.i	0.466923	+	0.466923i
$783$	282031.			0.460017
$784$			36898.0i			0.0600303i
$785$	−1.20761e6	−	1.20761e6i	−1.95968	−	1.95968i
$786$	−657121.	−	657121.i	−1.06365	−	1.06365i
$787$	282531.	−	282531.i	0.456159	−	0.456159i	−0.441234	−	0.897392i	$-0.645459\pi$
$787$	282531.	−	282531.i	0.456159	−	0.456159i	0.897392	+	0.441234i	$0.145459\pi$
$788$	−55064.1	+	55064.1i	−0.0886781	+	0.0886781i
$789$	−165995.			−0.266649
$790$			592327.i			0.949090i
$791$	304576.	−	304576.i	0.486791	−	0.486791i
$792$			1024.93i			0.00163397i
$793$		0			0
$794$	−1.16520e6			−1.84825
$795$	225457.	+	225457.i	0.356722	+	0.356722i
$796$	−1.11511e6			−1.75991
$797$		−	577074.i		−	0.908479i	−0.890880	−	0.454240i	$-0.849911\pi$
$797$		−	577074.i		−	0.908479i	0.890880	−	0.454240i	$-0.150089\pi$
$798$	−808403.	−	808403.i	−1.26947	−	1.26947i
$799$	144837.	+	144837.i	0.226874	+	0.226874i
$800$	−1.12969e6	+	1.12969e6i	−1.76515	+	1.76515i
$801$	−78937.6	+	78937.6i	−0.123032	+	0.123032i
$802$	−671401.			−1.04384
$803$			426888.i			0.662038i
$804$	−186768.	+	186768.i	−0.288928	+	0.288928i
$805$			586865.i			0.905620i
$806$		0			0
$807$	187594.			0.288053
$808$	524.435	+	524.435i	0.000803284	+	0.000803284i
$809$	−88438.0			−0.135127			−0.0675635	−	0.997715i	$-0.521523\pi$
$809$	−88438.0			−0.135127			−0.0675635	+	0.997715i	$0.521523\pi$
$810$		−	1.39052e6i		−	2.11938i
$811$	342385.	+	342385.i	0.520562	+	0.520562i	0.917741	−	0.397179i	$-0.130011\pi$
$811$	342385.	+	342385.i	0.520562	+	0.520562i	−0.397179	+	0.917741i	$0.630011\pi$
$812$	−205955.	−	205955.i	−0.312363	−	0.312363i
$813$	−259026.	+	259026.i	−0.391889	+	0.391889i
$814$	136367.	−	136367.i	0.205808	−	0.205808i
$815$	10797.4			0.0162556
$816$		−	502745.i		−	0.755036i
$817$	392937.	−	392937.i	0.588680	−	0.588680i
$818$			346415.i			0.517715i
$819$		0			0
$820$	476430.			0.708551
$821$	391227.	+	391227.i	0.580421	+	0.580421i	0.935019	−	0.354598i	$-0.115382\pi$
$821$	391227.	+	391227.i	0.580421	+	0.580421i	−0.354598	+	0.935019i	$0.615382\pi$
$822$	1.59960e6			2.36738
$823$		−	328220.i		−	0.484579i	−0.970204	−	0.242290i	$-0.922102\pi$
$823$		−	328220.i		−	0.484579i	0.970204	−	0.242290i	$-0.0778984\pi$
$824$	−14766.1	−	14766.1i	−0.0217476	−	0.0217476i
$825$	−293589.	−	293589.i	−0.431352	−	0.431352i
$826$	95201.8	−	95201.8i	0.139536	−	0.139536i
$827$	440313.	−	440313.i	0.643800	−	0.643800i	−0.307688	−	0.951487i	$-0.599555\pi$
$827$	440313.	−	440313.i	0.643800	−	0.643800i	0.951487	+	0.307688i	$0.0995552\pi$
$828$	37940.4			0.0553402
$829$			44855.4i			0.0652687i	0.999467	+	0.0326344i	$0.0103897\pi$
$829$			44855.4i			0.0652687i	−0.999467	+	0.0326344i	$0.989610\pi$
$830$	1.88579e6	−	1.88579e6i	2.73740	−	2.73740i
$831$		−	826743.i		−	1.19720i
$832$		0			0
$833$	35432.1			0.0510631
$834$	628599.	+	628599.i	0.903736	+	0.903736i
$835$	−1.80564e6			−2.58975
$836$			361009.i			0.516542i
$837$	475347.	+	475347.i	0.678515	+	0.678515i
$838$	1.31373e6	+	1.31373e6i	1.87076	+	1.87076i
$839$	449717.	−	449717.i	0.638874	−	0.638874i	−0.311404	−	0.950278i	$-0.600799\pi$
$839$	449717.	−	449717.i	0.638874	−	0.638874i	0.950278	+	0.311404i	$0.100799\pi$
$840$	−35830.6	+	35830.6i	−0.0507803	+	0.0507803i
$841$	−569355.			−0.804991
$842$		−	683647.i		−	0.964291i
$843$	−428340.	+	428340.i	−0.602745	+	0.602745i
$844$			574934.i			0.807110i
$845$		0			0
$846$	37876.4			0.0529210
$847$	425506.	+	425506.i	0.593115	+	0.593115i
$848$	222027.			0.308755
$849$		−	1.26437e6i		−	1.75412i
$850$	1.04903e6	+	1.04903e6i	1.45194	+	1.45194i
$851$	−161037.	−	161037.i	−0.222365	−	0.222365i
$852$	300226.	−	300226.i	0.413589	−	0.413589i
$853$	467145.	−	467145.i	0.642027	−	0.642027i	−0.309026	−	0.951053i	$-0.600003\pi$
$853$	467145.	−	467145.i	0.642027	−	0.642027i	0.951053	+	0.309026i	$0.100003\pi$
$854$	67234.1			0.0921878
$855$			157567.i			0.215543i
$856$	3166.19	−	3166.19i	0.00432105	−	0.00432105i
$857$		−	481160.i		−	0.655131i	−0.944829	−	0.327565i	$-0.893772\pi$
$857$		−	481160.i		−	0.655131i	0.944829	−	0.327565i	$-0.106228\pi$
$858$		0			0
$859$	480348.			0.650983			0.325491	−	0.945545i	$-0.394470\pi$
$859$	480348.			0.650983			0.325491	+	0.945545i	$0.394470\pi$
$860$	−545934.	−	545934.i	−0.738148	−	0.738148i
$861$	−282357.			−0.380883
$862$			1.77661e6i			2.39099i
$863$	−415207.	−	415207.i	−0.557497	−	0.557497i	0.371097	−	0.928594i	$-0.378982\pi$
$863$	−415207.	−	415207.i	−0.557497	−	0.557497i	−0.928594	+	0.371097i	$0.878982\pi$
$864$	−783161.	−	783161.i	−1.04912	−	1.04912i
$865$	762989.	−	762989.i	1.01973	−	1.01973i
$866$	−266025.	+	266025.i	−0.354721	+	0.354721i
$867$	232300.			0.309038
$868$		−	694250.i		−	0.921460i
$869$	−78382.8	+	78382.8i	−0.103796	+	0.103796i
$870$		−	752176.i		−	0.993759i
$871$		0			0
$872$	−51299.2			−0.0674648
$873$	−40334.6	−	40334.6i	−0.0529236	−	0.0529236i
$874$	839036.			1.09839
$875$			925925.i			1.20937i
$876$	964800.	+	964800.i	1.25727	+	1.25727i
$877$	−39229.5	−	39229.5i	−0.0510051	−	0.0510051i	0.681144	−	0.732149i	$-0.261483\pi$
$877$	−39229.5	−	39229.5i	−0.0510051	−	0.0510051i	−0.732149	+	0.681144i	$0.761483\pi$
$878$	643361.	−	643361.i	0.834576	−	0.834576i
$879$	−60379.3	+	60379.3i	−0.0781467	+	0.0781467i
$880$	−454082.			−0.586367
$881$			466304.i			0.600783i	0.953816	+	0.300391i	$0.0971173\pi$
$881$			466304.i			0.600783i	−0.953816	+	0.300391i	$0.902883\pi$
$882$	4632.95	−	4632.95i	0.00595552	−	0.00595552i
$883$		−	280955.i		−	0.360343i	−0.983635	−	0.180171i	$-0.942335\pi$
$883$		−	280955.i		−	0.360343i	0.983635	−	0.180171i	$-0.0576652\pi$
$884$		0			0
$885$	176663.			0.225558
$886$	−1.50254e6	−	1.50254e6i	−1.91407	−	1.91407i
$887$	−881569.			−1.12049			−0.560246	−	0.828326i	$-0.689293\pi$
$887$	−881569.			−1.12049			−0.560246	+	0.828326i	$0.689293\pi$
$888$		−	19664.0i		−	0.0249371i
$889$	8665.42	+	8665.42i	0.0109644	+	0.0109644i
$890$	2.42538e6	+	2.42538e6i	3.06197	+	3.06197i
$891$	184008.	−	184008.i	0.231783	−	0.231783i
$892$	−374919.	+	374919.i	−0.471203	+	0.471203i
$893$	425600.			0.533701
$894$			521284.i			0.652228i
$895$	−1.02344e6	+	1.02344e6i	−1.27766	+	1.27766i
$896$			73018.1i			0.0909525i
$897$		0			0
$898$	−418927.			−0.519500
$899$	232466.	+	232466.i	0.287634	+	0.287634i
$900$	139389.			0.172086
$901$		−	213206.i		−	0.262634i
$902$	124081.	+	124081.i	0.152508	+	0.152508i
$903$	323549.	+	323549.i	0.396793	+	0.396793i
$904$	−19300.3	+	19300.3i	−0.0236171	+	0.0236171i
$905$	−1.13754e6	+	1.13754e6i	−1.38889	+	1.38889i
$906$	−448699.			−0.546636
$907$		−	692963.i		−	0.842356i	−0.906978	−	0.421178i	$-0.861617\pi$
$907$		−	692963.i		−	0.842356i	0.906978	−	0.421178i	$-0.138383\pi$
$908$	757119.	−	757119.i	0.918316	−	0.918316i
$909$			1898.98i			0.00229822i
$910$		0			0
$911$	−1.13827e6			−1.37154			−0.685769	−	0.727819i	$-0.740534\pi$
$911$	−1.13827e6			−1.37154			−0.685769	+	0.727819i	$0.740534\pi$
$912$	−738653.	−	738653.i	−0.888077	−	0.888077i
$913$	499096.			0.598746
$914$		−	1.83861e6i		−	2.20089i
$915$	62382.1	+	62382.1i	0.0745105	+	0.0745105i
$916$	−895147.	−	895147.i	−1.06685	−	1.06685i
$917$	−638603.	+	638603.i	−0.759438	+	0.759438i
$918$	−727238.	+	727238.i	−0.862961	+	0.862961i
$919$	1.25828e6			1.48986			0.744930	−	0.667143i	$-0.232483\pi$
$919$	1.25828e6			1.48986			0.744930	+	0.667143i	$0.232483\pi$
$920$		−	37188.3i		−	0.0439371i
$921$	502451.	−	502451.i	0.592345	−	0.592345i
$922$		−	989392.i		−	1.16388i
$923$		0			0
$924$	−297259.			−0.348170
$925$	−591636.	−	591636.i	−0.691467	−	0.691467i
$926$	−712002.			−0.830346
$927$		−	53468.1i		−	0.0622207i
$928$	−383001.	−	383001.i	−0.444738	−	0.444738i
$929$	271956.	+	271956.i	0.315114	+	0.315114i	0.846887	−	0.531773i	$-0.178474\pi$
$929$	271956.	+	271956.i	0.315114	+	0.315114i	−0.531773	+	0.846887i	$0.678474\pi$
$930$	1.26775e6	−	1.26775e6i	1.46577	−	1.46577i
$931$	52058.2	−	52058.2i	0.0600606	−	0.0600606i
$932$	−1.02306e6			−1.17779
$933$		−	332308.i		−	0.381748i
$934$	−10529.0	+	10529.0i	−0.0120696	+	0.0120696i
$935$			436042.i			0.498776i
$936$		0			0
$937$	−310991.			−0.354216			−0.177108	−	0.984191i	$-0.556674\pi$
$937$	−310991.			−0.354216			−0.177108	+	0.984191i	$0.556674\pi$
$938$	357219.	+	357219.i	0.406003	+	0.406003i
$939$	−845263.			−0.958651
$940$		−	591315.i		−	0.669211i
$941$	−685037.	−	685037.i	−0.773633	−	0.773633i	0.205107	−	0.978740i	$-0.434246\pi$
$941$	−685037.	−	685037.i	−0.773633	−	0.773633i	−0.978740	+	0.205107i	$0.934246\pi$
$942$	−1.42162e6	−	1.42162e6i	−1.60207	−	1.60207i
$943$	146528.	−	146528.i	0.164777	−	0.164777i
$944$	86987.6	−	86987.6i	0.0976143	−	0.0976143i
$945$	−1.49471e6			−1.67376
$946$		−	284365.i		−	0.317757i
$947$	−700532.	+	700532.i	−0.781139	+	0.781139i	−0.980023	−	0.198884i	$-0.936268\pi$
$947$	−700532.	+	700532.i	−0.781139	+	0.781139i	0.198884	+	0.980023i	$0.436268\pi$
$948$			354302.i			0.394237i
$949$		0			0
$950$	3.08254e6			3.41556
$951$	−424068.	−	424068.i	−0.468893	−	0.468893i
$952$	33883.7			0.0373866
$953$		−	981938.i		−	1.08118i	−0.841286	−	0.540590i	$-0.818201\pi$
$953$		−	981938.i		−	1.08118i	0.841286	−	0.540590i	$-0.181799\pi$
$954$	−27877.9	−	27877.9i	−0.0306312	−	0.0306312i
$955$	−1.38623e6	−	1.38623e6i	−1.51995	−	1.51995i
$956$	577919.	−	577919.i	0.632341	−	0.632341i
$957$	99535.7	−	99535.7i	0.108681	−	0.108681i
$958$	1.96943e6			2.14590
$959$		−	1.55452e6i		−	1.69028i
$960$	−1.09516e6	+	1.09516e6i	−1.18833	+	1.18833i
$961$		−	139905.i		−	0.151491i
$962$		0			0
$963$	11464.7			0.0123627
$964$	−19744.0	−	19744.0i	−0.0212462	−	0.0212462i
$965$	922171.			0.990277
$966$			690872.i			0.740361i
$967$	751098.	+	751098.i	0.803237	+	0.803237i	0.983600	−	0.180363i	$-0.0577273\pi$
$967$	751098.	+	751098.i	0.803237	+	0.803237i	−0.180363	+	0.983600i	$0.557727\pi$
$968$	−26963.4	−	26963.4i	−0.0287756	−	0.0287756i
$969$	−709308.	+	709308.i	−0.755418	+	0.755418i
$970$	−1.23929e6	+	1.23929e6i	−1.31714	+	1.31714i
$971$	−373637.			−0.396288			−0.198144	−	0.980173i	$-0.563491\pi$
$971$	−373637.			−0.396288			−0.198144	+	0.980173i	$0.563491\pi$
$972$			184876.i			0.195680i
$973$	610885.	−	610885.i	0.645259	−	0.645259i
$974$		−	1.77290e6i		−	1.86882i
$975$		0			0
$976$	61433.0			0.0644915
$977$	−22942.7	−	22942.7i	−0.0240356	−	0.0240356i	0.694987	−	0.719022i	$-0.255410\pi$
$977$	−22942.7	−	22942.7i	−0.0240356	−	0.0240356i	−0.719022	+	0.694987i	$0.755410\pi$
$978$	12711.0			0.0132893
$979$			641904.i			0.669737i
$980$	−72328.0	−	72328.0i	−0.0753103	−	0.0753103i
$981$	−92877.0	−	92877.0i	−0.0965095	−	0.0965095i
$982$	−66265.9	+	66265.9i	−0.0687175	+	0.0687175i
$983$	−7991.46	+	7991.46i	−0.00827026	+	0.00827026i	−0.711230	−	0.702960i	$-0.751861\pi$
$983$	−7991.46	+	7991.46i	−0.00827026	+	0.00827026i	0.702960	+	0.711230i	$0.251861\pi$
$984$	17892.3			0.0184789
$985$			195435.i			0.201432i
$986$	−355652.	+	355652.i	−0.365824	+	0.365824i
$987$			350444.i			0.359736i
$988$		0			0
$989$	−335809.			−0.343321
$990$	57015.0	+	57015.0i	0.0581726	+	0.0581726i
$991$	1.30914e6			1.33303			0.666515	−	0.745491i	$-0.267785\pi$
$991$	1.30914e6			1.33303			0.666515	+	0.745491i	$0.267785\pi$
$992$		−	1.29105e6i		−	1.31196i
$993$	−407107.	−	407107.i	−0.412867	−	0.412867i
$994$	−574223.	−	574223.i	−0.581177	−	0.581177i
$995$	−1.97888e6	+	1.97888e6i	−1.99882	+	1.99882i
$996$	1.12799e6	−	1.12799e6i	1.13707	−	1.13707i
$997$	−624154.			−0.627916			−0.313958	−	0.949437i	$-0.601655\pi$
$997$	−624154.			−0.627916			−0.313958	+	0.949437i	$0.601655\pi$
$998$		−	1.33733e6i		−	1.34269i
$999$	410152.	−	410152.i	0.410973	−	0.410973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.5.d.c.99.7		16
13.5	odd	4	inner	169.5.d.c.70.7		16
13.7	odd	12		13.5.f.a.2.4	✓	16
13.8	odd	4		169.5.d.d.70.2		16
13.10	even	6		13.5.f.a.7.4	yes	16
13.12	even	2		169.5.d.d.99.2		16
39.20	even	12		117.5.bd.c.28.1		16
39.23	odd	6		117.5.bd.c.46.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.2.4	✓	16	13.7	odd	12
13.5.f.a.7.4	yes	16	13.10	even	6
117.5.bd.c.28.1		16	39.20	even	12
117.5.bd.c.46.1		16	39.23	odd	6
169.5.d.c.70.7		16	13.5	odd	4	inner
169.5.d.c.99.7		16	1.1	even	1	trivial
169.5.d.d.70.2		16	13.8	odd	4
169.5.d.d.99.2		16	13.12	even	2

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	169.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.03282 + 4.03282i) q^{2} +8.56159 q^{3} +16.5272i q^{4} +(29.3294 + 29.3294i) q^{5} +(34.5273 + 34.5273i) q^{6} +(33.5543 - 33.5543i) q^{7} +(-2.12627 + 2.12627i) q^{8} -7.69920 q^{9} +O(q^{10})\)	\(q+(4.03282 + 4.03282i) q^{2} +8.56159 q^{3} +16.5272i q^{4} +(29.3294 + 29.3294i) q^{5} +(34.5273 + 34.5273i) q^{6} +(33.5543 - 33.5543i) q^{7} +(-2.12627 + 2.12627i) q^{8} -7.69920 q^{9} +236.560i q^{10} +(-31.3041 + 31.3041i) q^{11} +141.499i q^{12} +270.637 q^{14} +(251.106 + 251.106i) q^{15} +247.286 q^{16} -237.462i q^{17} +(-31.0495 - 31.0495i) q^{18} +(-348.888 - 348.888i) q^{19} +(-484.734 + 484.734i) q^{20} +(287.279 - 287.279i) q^{21} -252.488 q^{22} +298.164i q^{23} +(-18.2042 + 18.2042i) q^{24} +1095.43i q^{25} -759.406 q^{27} +(554.561 + 554.561i) q^{28} -371.384 q^{29} +2025.33i q^{30} +(-625.946 - 625.946i) q^{31} +(1031.28 + 1031.28i) q^{32} +(-268.013 + 268.013i) q^{33} +(957.641 - 957.641i) q^{34} +1968.26 q^{35} -127.247i q^{36} +(-540.096 + 540.096i) q^{37} -2814.01i q^{38} -124.724 q^{40} +(-491.434 - 491.434i) q^{41} +2317.08 q^{42} +1126.26i q^{43} +(-517.371 - 517.371i) q^{44} +(-225.813 - 225.813i) q^{45} +(-1202.44 + 1202.44i) q^{46} +(-609.937 + 609.937i) q^{47} +2117.16 q^{48} +149.212i q^{49} +(-4417.66 + 4417.66i) q^{50} -2033.05i q^{51} +897.855 q^{53} +(-3062.55 - 3062.55i) q^{54} -1836.26 q^{55} +142.691i q^{56} +(-2987.04 - 2987.04i) q^{57} +(-1497.72 - 1497.72i) q^{58} +(351.769 - 351.769i) q^{59} +(-4150.10 + 4150.10i) q^{60} +248.429 q^{61} -5048.65i q^{62} +(-258.342 + 258.342i) q^{63} +4361.35i q^{64} -2161.69 q^{66} +(1319.92 + 1319.92i) q^{67} +3924.59 q^{68} +2552.76i q^{69} +(7937.63 + 7937.63i) q^{70} +(-2121.75 - 2121.75i) q^{71} +(16.3705 - 16.3705i) q^{72} +(6818.40 - 6818.40i) q^{73} -4356.22 q^{74} +9378.61i q^{75} +(5766.16 - 5766.16i) q^{76} +2100.78i q^{77} +2503.91 q^{79} +(7252.76 + 7252.76i) q^{80} -5878.09 q^{81} -3963.73i q^{82} +(-7971.73 - 7971.73i) q^{83} +(4747.92 + 4747.92i) q^{84} +(6964.62 - 6964.62i) q^{85} +(-4541.98 + 4541.98i) q^{86} -3179.64 q^{87} -133.122i q^{88} +(10252.7 - 10252.7i) q^{89} -1821.33i q^{90} -4927.83 q^{92} +(-5359.09 - 5359.09i) q^{93} -4919.53 q^{94} -20465.4i q^{95} +(8829.40 + 8829.40i) q^{96} +(5238.81 + 5238.81i) q^{97} +(-601.744 + 601.744i) q^{98} +(241.017 - 241.017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9	\( 16 q - 2 q^{2} + 4 q^{3} - 8 q^{5} + 128 q^{6} - 56 q^{7} - 90 q^{8} + 328 q^{9} - 500 q^{11} + 808 q^{14} - 844 q^{15} - 460 q^{16} - 2434 q^{18} - 1712 q^{19} - 838 q^{20} + 1076 q^{21} + 3048 q^{22} - 5772 q^{24} + 3352 q^{27} - 2980 q^{28} - 1628 q^{29} - 4060 q^{31} - 3662 q^{32} + 860 q^{33} + 2502 q^{34} + 9784 q^{35} - 10468 q^{37} + 18816 q^{40} - 3440 q^{41} + 2408 q^{42} - 10736 q^{44} + 1004 q^{45} - 11436 q^{46} - 1484 q^{47} + 6004 q^{48} - 21616 q^{50} + 7204 q^{53} - 6760 q^{54} - 13872 q^{55} - 12736 q^{57} - 7974 q^{58} + 4840 q^{59} + 6472 q^{60} + 324 q^{61} + 13988 q^{63} - 23872 q^{66} - 2216 q^{67} + 12888 q^{68} + 34524 q^{70} + 1240 q^{71} + 6606 q^{72} + 15448 q^{73} + 5764 q^{74} + 39688 q^{76} - 17064 q^{79} + 37630 q^{80} - 4256 q^{81} - 12788 q^{83} + 7736 q^{84} + 22884 q^{85} - 67260 q^{86} - 58684 q^{87} + 37624 q^{89} - 49884 q^{92} + 2492 q^{93} + 61212 q^{94} + 94664 q^{96} + 57056 q^{97} - 27950 q^{98} + 21632 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^3 - 8 * q^5 + 128 * q^6 - 56 * q^7 - 90 * q^8 + 328 * q^9 - 500 * q^11 + 808 * q^14 - 844 * q^15 - 460 * q^16 - 2434 * q^18 - 1712 * q^19 - 838 * q^20 + 1076 * q^21 + 3048 * q^22 - 5772 * q^24 + 3352 * q^27 - 2980 * q^28 - 1628 * q^29 - 4060 * q^31 - 3662 * q^32 + 860 * q^33 + 2502 * q^34 + 9784 * q^35 - 10468 * q^37 + 18816 * q^40 - 3440 * q^41 + 2408 * q^42 - 10736 * q^44 + 1004 * q^45 - 11436 * q^46 - 1484 * q^47 + 6004 * q^48 - 21616 * q^50 + 7204 * q^53 - 6760 * q^54 - 13872 * q^55 - 12736 * q^57 - 7974 * q^58 + 4840 * q^59 + 6472 * q^60 + 324 * q^61 + 13988 * q^63 - 23872 * q^66 - 2216 * q^67 + 12888 * q^68 + 34524 * q^70 + 1240 * q^71 + 6606 * q^72 + 15448 * q^73 + 5764 * q^74 + 39688 * q^76 - 17064 * q^79 + 37630 * q^80 - 4256 * q^81 - 12788 * q^83 + 7736 * q^84 + 22884 * q^85 - 67260 * q^86 - 58684 * q^87 + 37624 * q^89 - 49884 * q^92 + 2492 * q^93 + 61212 * q^94 + 94664 * q^96 + 57056 * q^97 - 27950 * q^98 + 21632 * q^99

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