LMFDB - Embedded newform 29.3.c.a.12.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,3,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	29.c (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:	$0.790192766645$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.3
Root			$1.35225i$ of defining polynomial
Character	$\chi$	$=$	29.12
Dual form			29.3.c.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +O(q^{10})$	\(q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +(-3.78796 + 3.78796i) q^{10} +(-0.334930 - 0.334930i) q^{11} +(1.03817 - 1.03817i) q^{12} +12.2282i q^{13} +(-8.81223 - 8.81223i) q^{14} +(-1.84345 + 1.84345i) q^{15} +1.11839 q^{16} +(6.80978 + 6.80978i) q^{17} +(7.82983 - 7.82983i) q^{18} +(14.6673 + 14.6673i) q^{19} +9.76693 q^{20} +(-4.28855 - 4.28855i) q^{21} -0.609296i q^{22} -10.0844 q^{23} +5.10972 q^{24} +7.65715 q^{25} +(-11.1226 + 11.1226i) q^{26} +(7.79440 - 7.79440i) q^{27} +22.7216i q^{28} +(28.1041 - 7.15263i) q^{29} -3.35355 q^{30} +(-37.3099 - 37.3099i) q^{31} +(-22.0692 - 22.0692i) q^{32} -0.296520i q^{33} +12.3882i q^{34} -40.3460i q^{35} -20.1886 q^{36} +(-45.0215 + 45.0215i) q^{37} +26.6824i q^{38} +(-5.41292 + 5.41292i) q^{39} +(24.0357 + 24.0357i) q^{40} +(22.8142 - 22.8142i) q^{41} -7.80164i q^{42} +(-17.5030 - 17.5030i) q^{43} +(-0.785510 + 0.785510i) q^{44} +35.8482 q^{45} +(-9.17268 - 9.17268i) q^{46} +(2.20999 - 2.20999i) q^{47} +(0.495064 + 0.495064i) q^{48} +44.8602 q^{49} +(6.96485 + 6.96485i) q^{50} +6.02883i q^{51} +28.6787 q^{52} +90.1375 q^{53} +14.1794 q^{54} +(1.39481 - 1.39481i) q^{55} +(-55.9162 + 55.9162i) q^{56} +12.9852i q^{57} +(32.0691 + 19.0572i) q^{58} -90.4223 q^{59} +(4.32343 + 4.32343i) q^{60} +(-29.4354 - 29.4354i) q^{61} -67.8734i q^{62} +83.3966i q^{63} -44.6213i q^{64} -50.9239 q^{65} +(0.269711 - 0.269711i) q^{66} -31.5543i q^{67} +(15.9710 - 15.9710i) q^{68} +(-4.46397 - 4.46397i) q^{69} +(36.6983 - 36.6983i) q^{70} +99.8673i q^{71} +(-49.6826 - 49.6826i) q^{72} +(-3.96285 + 3.96285i) q^{73} -81.9020 q^{74} +(3.38951 + 3.38951i) q^{75} +(34.3992 - 34.3992i) q^{76} +(3.24485 + 3.24485i) q^{77} -9.84706 q^{78} +(-40.3117 - 40.3117i) q^{79} +4.65749i q^{80} -70.5724 q^{81} +41.5030 q^{82} +137.714 q^{83} +(-10.0579 + 10.0579i) q^{84} +(-28.3592 + 28.3592i) q^{85} -31.8411i q^{86} +(15.6067 + 9.27437i) q^{87} -3.86616 q^{88} +(83.1506 + 83.1506i) q^{89} +(32.6071 + 32.6071i) q^{90} -118.468i q^{91} +23.6510i q^{92} -33.0312i q^{93} +4.02036 q^{94} +(-61.0816 + 61.0816i) q^{95} -19.5383i q^{96} +(-79.9850 + 79.9850i) q^{97} +(40.8043 + 40.8043i) q^{98} +(-2.88311 + 2.88311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.909588	+	0.909588i	0.454794	+	0.454794i	0.896942	−	0.442148i	$-0.145783\pi$
$2$	0.909588	+	0.909588i	0.454794	+	0.454794i	−0.442148	+	0.896942i	$0.645783\pi$
$3$	0.442660	+	0.442660i	0.147553	+	0.147553i	0.777024	−	0.629471i	$-0.216728\pi$
$3$	0.442660	+	0.442660i	0.147553	+	0.147553i	−0.629471	+	0.777024i	$0.716728\pi$
$4$		−	2.34530i		−	0.586324i
$5$			4.16447i			0.832895i	0.909160	+	0.416447i	$0.136725\pi$
$5$			4.16447i			0.832895i	−0.909160	+	0.416447i	$0.863275\pi$
$6$			0.805276i			0.134213i
$7$	−9.68815			−1.38402			−0.692011	−	0.721887i	$-0.743275\pi$
$7$	−9.68815			−1.38402			−0.692011	+	0.721887i	$0.743275\pi$
$8$	5.77161	−	5.77161i	0.721451	−	0.721451i
$9$		−	8.60810i		−	0.956456i
$10$	−3.78796	+	3.78796i	−0.378796	+	0.378796i
$11$	−0.334930	−	0.334930i	−0.0304481	−	0.0304481i	0.691719	−	0.722167i	$-0.256854\pi$
$11$	−0.334930	−	0.334930i	−0.0304481	−	0.0304481i	−0.722167	+	0.691719i	$0.756854\pi$
$12$	1.03817	−	1.03817i	0.0865141	−	0.0865141i
$13$			12.2282i			0.940628i	0.882499	+	0.470314i	$0.155859\pi$
$13$			12.2282i			0.940628i	−0.882499	+	0.470314i	$0.844141\pi$
$14$	−8.81223	−	8.81223i	−0.629445	−	0.629445i
$15$	−1.84345	+	1.84345i	−0.122896	+	0.122896i
$16$	1.11839			0.0698991
$17$	6.80978	+	6.80978i	0.400575	+	0.400575i	0.878436	−	0.477861i	$-0.158588\pi$
$17$	6.80978	+	6.80978i	0.400575	+	0.400575i	−0.477861	+	0.878436i	$0.658588\pi$
$18$	7.82983	−	7.82983i	0.434991	−	0.434991i
$19$	14.6673	+	14.6673i	0.771963	+	0.771963i	0.978449	−	0.206486i	$-0.0662029\pi$
$19$	14.6673	+	14.6673i	0.771963	+	0.771963i	−0.206486	+	0.978449i	$0.566203\pi$
$20$	9.76693			0.488347
$21$	−4.28855	−	4.28855i	−0.204217	−	0.204217i
$22$		−	0.609296i		−	0.0276953i
$23$	−10.0844			−0.438454			−0.219227	−	0.975674i	$-0.570353\pi$
$23$	−10.0844			−0.438454			−0.219227	+	0.975674i	$0.570353\pi$
$24$	5.10972			0.212905
$25$	7.65715			0.306286
$26$	−11.1226	+	11.1226i	−0.427792	+	0.427792i
$27$	7.79440	−	7.79440i	0.288681	−	0.288681i
$28$			22.7216i			0.811485i
$29$	28.1041	−	7.15263i	0.969107	−	0.246642i
$29$	28.1041	−	7.15263i	0.969107	−	0.246642i
$30$	−3.35355			−0.111785
$31$	−37.3099	−	37.3099i	−1.20355	−	1.20355i	−0.973080	−	0.230466i	$-0.925975\pi$
$31$	−37.3099	−	37.3099i	−1.20355	−	1.20355i	−0.230466	−	0.973080i	$-0.574025\pi$
$32$	−22.0692	−	22.0692i	−0.689661	−	0.689661i
$33$		−	0.296520i		−	0.00898545i
$34$			12.3882i			0.364359i
$35$		−	40.3460i		−	1.15274i
$36$	−20.1886			−0.560794
$37$	−45.0215	+	45.0215i	−1.21680	+	1.21680i	−0.248050	+	0.968747i	$0.579790\pi$
$37$	−45.0215	+	45.0215i	−1.21680	+	1.21680i	−0.968747	+	0.248050i	$0.920210\pi$
$38$			26.6824i			0.702169i
$39$	−5.41292	+	5.41292i	−0.138793	+	0.138793i
$40$	24.0357	+	24.0357i	0.600893	+	0.600893i
$41$	22.8142	−	22.8142i	0.556443	−	0.556443i	−0.371850	−	0.928293i	$-0.621276\pi$
$41$	22.8142	−	22.8142i	0.556443	−	0.556443i	0.928293	+	0.371850i	$0.121276\pi$
$42$		−	7.80164i		−	0.185753i
$43$	−17.5030	−	17.5030i	−0.407048	−	0.407048i	0.473660	−	0.880708i	$-0.342933\pi$
$43$	−17.5030	−	17.5030i	−0.407048	−	0.407048i	−0.880708	+	0.473660i	$0.842933\pi$
$44$	−0.785510	+	0.785510i	−0.0178525	+	0.0178525i
$45$	35.8482			0.796627
$46$	−9.17268	−	9.17268i	−0.199406	−	0.199406i
$47$	2.20999	−	2.20999i	0.0470210	−	0.0470210i	−0.683205	−	0.730226i	$-0.739415\pi$
$47$	2.20999	−	2.20999i	0.0470210	−	0.0470210i	0.730226	+	0.683205i	$0.239415\pi$
$48$	0.495064	+	0.495064i	0.0103138	+	0.0103138i
$49$	44.8602			0.915514
$50$	6.96485	+	6.96485i	0.139297	+	0.139297i
$51$			6.02883i			0.118212i
$52$	28.6787			0.551513
$53$	90.1375			1.70071			0.850354	−	0.526212i	$-0.176388\pi$
$53$	90.1375			1.70071			0.850354	+	0.526212i	$0.176388\pi$
$54$	14.1794			0.262581
$55$	1.39481	−	1.39481i	0.0253601	−	0.0253601i
$56$	−55.9162	+	55.9162i	−0.998504	+	0.998504i
$57$			12.9852i			0.227811i
$58$	32.0691	+	19.0572i	0.552916	+	0.328573i
$59$	−90.4223			−1.53258			−0.766291	−	0.642494i	$-0.777900\pi$
$59$	−90.4223			−1.53258			−0.766291	+	0.642494i	$0.777900\pi$
$60$	4.32343	+	4.32343i	0.0720572	+	0.0720572i
$61$	−29.4354	−	29.4354i	−0.482548	−	0.482548i	0.423397	−	0.905944i	$-0.360838\pi$
$61$	−29.4354	−	29.4354i	−0.482548	−	0.482548i	−0.905944	+	0.423397i	$0.860838\pi$
$62$		−	67.8734i		−	1.09473i
$63$			83.3966i			1.32376i
$64$		−	44.6213i		−	0.697207i
$65$	−50.9239			−0.783445
$66$	0.269711	−	0.269711i	0.00408653	−	0.00408653i
$67$		−	31.5543i		−	0.470960i	−0.971879	−	0.235480i	$-0.924334\pi$
$67$		−	31.5543i		−	0.470960i	0.971879	−	0.235480i	$-0.0756662\pi$
$68$	15.9710	−	15.9710i	0.234867	−	0.234867i
$69$	−4.46397	−	4.46397i	−0.0646953	−	0.0646953i
$70$	36.6983	−	36.6983i	0.524261	−	0.524261i
$71$			99.8673i			1.40658i	0.710902	+	0.703291i	$0.248287\pi$
$71$			99.8673i			1.40658i	−0.710902	+	0.703291i	$0.751713\pi$
$72$	−49.6826	−	49.6826i	−0.690036	−	0.690036i
$73$	−3.96285	+	3.96285i	−0.0542856	+	0.0542856i	−0.733728	−	0.679443i	$-0.762222\pi$
$73$	−3.96285	+	3.96285i	−0.0542856	+	0.0542856i	0.679443	+	0.733728i	$0.262222\pi$
$74$	−81.9020			−1.10678
$75$	3.38951	+	3.38951i	0.0451935	+	0.0451935i
$76$	34.3992	−	34.3992i	0.452621	−	0.452621i
$77$	3.24485	+	3.24485i	0.0421409	+	0.0421409i
$78$	−9.84706			−0.126244
$79$	−40.3117	−	40.3117i	−0.510275	−	0.510275i	0.404335	−	0.914611i	$-0.367503\pi$
$79$	−40.3117	−	40.3117i	−0.510275	−	0.510275i	−0.914611	+	0.404335i	$0.867503\pi$
$80$			4.65749i			0.0582186i
$81$	−70.5724			−0.871264
$82$	41.5030			0.506134
$83$	137.714			1.65921			0.829604	−	0.558352i	$-0.188566\pi$
$83$	137.714			1.65921			0.829604	+	0.558352i	$0.188566\pi$
$84$	−10.0579	+	10.0579i	−0.119737	+	0.119737i
$85$	−28.3592	+	28.3592i	−0.333637	+	0.333637i
$86$		−	31.8411i		−	0.370246i
$87$	15.6067	+	9.27437i	0.179388	+	0.106602i
$88$	−3.86616			−0.0439337
$89$	83.1506	+	83.1506i	0.934276	+	0.934276i	0.997969	−	0.0636936i	$-0.0202880\pi$
$89$	83.1506	+	83.1506i	0.934276	+	0.934276i	−0.0636936	+	0.997969i	$0.520288\pi$
$90$	32.6071	+	32.6071i	0.362302	+	0.362302i
$91$		−	118.468i		−	1.30185i
$92$			23.6510i			0.257076i
$93$		−	33.0312i		−	0.355174i
$94$	4.02036			0.0427698
$95$	−61.0816	+	61.0816i	−0.642964	+	0.642964i
$96$		−	19.5383i		−	0.203524i
$97$	−79.9850	+	79.9850i	−0.824588	+	0.824588i	−0.986762	−	0.162174i	$-0.948149\pi$
$97$	−79.9850	+	79.9850i	−0.824588	+	0.824588i	0.162174	+	0.986762i	$0.448149\pi$
$98$	40.8043	+	40.8043i	0.416371	+	0.416371i
$99$	−2.88311	+	2.88311i	−0.0291223	+	0.0291223i
$100$		−	17.9583i		−	0.179583i
$101$	−52.1216	−	52.1216i	−0.516055	−	0.516055i	0.400320	−	0.916375i	$-0.368899\pi$
$101$	−52.1216	−	52.1216i	−0.516055	−	0.516055i	−0.916375	+	0.400320i	$0.868899\pi$
$102$	−5.48375	+	5.48375i	−0.0537623	+	0.0537623i
$103$	139.377			1.35318			0.676588	−	0.736361i	$-0.263458\pi$
$103$	139.377			1.35318			0.676588	+	0.736361i	$0.263458\pi$
$104$	70.5762	+	70.5762i	0.678617	+	0.678617i
$105$	17.8596	−	17.8596i	0.170091	−	0.170091i
$106$	81.9880	+	81.9880i	0.773472	+	0.773472i
$107$	−14.9646			−0.139856			−0.0699282	−	0.997552i	$-0.522277\pi$
$107$	−14.9646			−0.139856			−0.0699282	+	0.997552i	$0.522277\pi$
$108$	−18.2802	−	18.2802i	−0.169261	−	0.169261i
$109$		−	38.6223i		−	0.354333i	−0.984181	−	0.177167i	$-0.943307\pi$
$109$		−	38.6223i		−	0.354333i	0.984181	−	0.177167i	$-0.0566931\pi$
$110$	2.53740			0.0230673
$111$	−39.8584			−0.359085
$112$	−10.8351			−0.0967418
$113$	−20.2695	+	20.2695i	−0.179376	+	0.179376i	−0.791084	−	0.611708i	$-0.790483\pi$
$113$	−20.2695	+	20.2695i	−0.179376	+	0.179376i	0.611708	+	0.791084i	$0.290483\pi$
$114$	−11.8112	+	11.8112i	−0.103607	+	0.103607i
$115$		−	41.9964i		−	0.365186i
$116$	−16.7750	−	65.9125i	−0.144612	−	0.568211i
$117$	105.261			0.899670
$118$	−82.2471	−	82.2471i	−0.697009	−	0.697009i
$119$	−65.9741	−	65.9741i	−0.554405	−	0.554405i
$120$			21.2793i			0.177327i
$121$		−	120.776i		−	0.998146i
$122$		−	53.5482i		−	0.438920i
$123$	20.1978			0.164210
$124$	−87.5029	+	87.5029i	−0.705669	+	0.705669i
$125$			136.000i			1.08800i
$126$	−75.8566	+	75.8566i	−0.602036	+	0.602036i
$127$	52.2215	+	52.2215i	0.411193	+	0.411193i	0.882154	−	0.470961i	$-0.156093\pi$
$127$	52.2215	+	52.2215i	0.411193	+	0.411193i	−0.470961	+	0.882154i	$0.656093\pi$
$128$	−47.6897	+	47.6897i	−0.372576	+	0.372576i
$129$		−	15.4958i		−	0.120122i
$130$	−46.3198	−	46.3198i	−0.356306	−	0.356306i
$131$	25.3821	−	25.3821i	0.193756	−	0.193756i	−0.603561	−	0.797317i	$-0.706252\pi$
$131$	25.3821	−	25.3821i	0.193756	−	0.193756i	0.797317	+	0.603561i	$0.206252\pi$
$132$	−0.695427			−0.00526839
$133$	−142.099	−	142.099i	−1.06841	−	1.06841i
$134$	28.7014	−	28.7014i	0.214190	−	0.214190i
$135$	32.4596	+	32.4596i	0.240441	+	0.240441i
$136$	78.6068			0.577991
$137$	−117.179	−	117.179i	−0.855320	−	0.855320i	0.135462	−	0.990782i	$-0.456748\pi$
$137$	−117.179	−	117.179i	−0.855320	−	0.855320i	−0.990782	+	0.135462i	$0.956748\pi$
$138$		−	8.12075i		−	0.0588460i
$139$	62.2884			0.448118			0.224059	−	0.974576i	$-0.428069\pi$
$139$	62.2884			0.448118			0.224059	+	0.974576i	$0.428069\pi$
$140$	−94.6235			−0.675882
$141$	1.95655			0.0138762
$142$	−90.8381	+	90.8381i	−0.639705	+	0.639705i
$143$	4.09558	−	4.09558i	0.0286404	−	0.0286404i
$144$		−	9.62718i		−	0.0668554i
$145$	29.7869	+	117.039i	0.205427	+	0.807164i
$146$	−7.20912			−0.0493776
$147$	19.8578	+	19.8578i	0.135087	+	0.135087i
$148$	105.589	+	105.589i	0.713438	+	0.713438i
$149$		−	140.996i		−	0.946284i	−0.880986	−	0.473142i	$-0.843120\pi$
$149$		−	140.996i		−	0.946284i	0.880986	−	0.473142i	$-0.156880\pi$
$150$			6.16612i			0.0411075i
$151$			269.100i			1.78212i	0.453889	+	0.891058i	$0.350036\pi$
$151$			269.100i			1.78212i	−0.453889	+	0.891058i	$0.649964\pi$
$152$	169.308			1.11387
$153$	58.6193	−	58.6193i	0.383133	−	0.383133i
$154$			5.90295i			0.0383308i
$155$	155.376	−	155.376i	1.00243	−	1.00243i
$156$	12.6949	+	12.6949i	0.0813776	+	0.0813776i
$157$	−82.6681	+	82.6681i	−0.526549	+	0.526549i	−0.919541	−	0.392993i	$-0.871440\pi$
$157$	−82.6681	+	82.6681i	−0.526549	+	0.526549i	0.392993	+	0.919541i	$0.371440\pi$
$158$		−	73.3342i		−	0.464140i
$159$	39.9002	+	39.9002i	0.250945	+	0.250945i
$160$	91.9065	−	91.9065i	0.574416	−	0.574416i
$161$	97.6995			0.606829
$162$	−64.1918	−	64.1918i	−0.396246	−	0.396246i
$163$	16.1649	−	16.1649i	0.0991711	−	0.0991711i	−0.655780	−	0.754952i	$-0.727660\pi$
$163$	16.1649	−	16.1649i	0.0991711	−	0.0991711i	0.754952	+	0.655780i	$0.227660\pi$
$164$	−53.5060	−	53.5060i	−0.326256	−	0.326256i
$165$	1.23485			0.00748393
$166$	125.263	+	125.263i	0.754598	+	0.754598i
$167$			134.528i			0.805558i	0.915297	+	0.402779i	$0.131956\pi$
$167$			134.528i			0.805558i	−0.915297	+	0.402779i	$0.868044\pi$
$168$	−49.5037			−0.294665
$169$	19.4719			0.115218
$170$	−51.5903			−0.303472
$171$	126.258	−	126.258i	0.738349	−	0.738349i
$172$	−41.0499	+	41.0499i	−0.238662	+	0.238662i
$173$			94.1756i			0.544368i	0.962245	+	0.272184i	$0.0877459\pi$
$173$			94.1756i			0.544368i	−0.962245	+	0.272184i	$0.912254\pi$
$174$	5.75984	+	22.6316i	0.0331025	+	0.130066i
$175$	−74.1836			−0.423906
$176$	−0.374580	−	0.374580i	−0.00212830	−	0.00212830i
$177$	−40.0263	−	40.0263i	−0.226137	−	0.226137i
$178$			151.266i			0.849806i
$179$			55.6892i			0.311113i	0.987827	+	0.155557i	$0.0497171\pi$
$179$			55.6892i			0.311113i	−0.987827	+	0.155557i	$0.950283\pi$
$180$		−	84.0748i		−	0.467082i
$181$	−131.878			−0.728610			−0.364305	−	0.931280i	$-0.618693\pi$
$181$	−131.878			−0.728610			−0.364305	+	0.931280i	$0.618693\pi$
$182$	107.757	−	107.757i	0.592074	−	0.592074i
$183$		−	26.0598i		−	0.142403i
$184$	−58.2034	+	58.2034i	−0.316323	+	0.316323i
$185$	−187.491	−	187.491i	−1.01346	−	1.01346i
$186$	30.0448	−	30.0448i	0.161531	−	0.161531i
$187$		−	4.56159i		−	0.0243935i
$188$	−5.18308	−	5.18308i	−0.0275696	−	0.0275696i
$189$	−75.5133	+	75.5133i	−0.399541	+	0.399541i
$190$	−111.118			−0.584833
$191$	122.543	+	122.543i	0.641588	+	0.641588i	0.950946	−	0.309358i	$-0.100114\pi$
$191$	122.543	+	122.543i	0.641588	+	0.641588i	−0.309358	+	0.950946i	$0.600114\pi$
$192$	19.7520	−	19.7520i	0.102875	−	0.102875i
$193$	−175.959	−	175.959i	−0.911702	−	0.911702i	0.0847039	−	0.996406i	$-0.473006\pi$
$193$	−175.959	−	175.959i	−0.911702	−	0.911702i	−0.996406	+	0.0847039i	$0.973006\pi$
$194$	−145.507			−0.750036
$195$	−22.5420	−	22.5420i	−0.115600	−	0.115600i
$196$		−	105.211i		−	0.536789i
$197$	42.7699			0.217106			0.108553	−	0.994091i	$-0.465378\pi$
$197$	42.7699			0.217106			0.108553	+	0.994091i	$0.465378\pi$
$198$	−5.24488			−0.0264893
$199$	−101.732			−0.511216			−0.255608	−	0.966781i	$-0.582276\pi$
$199$	−101.732			−0.511216			−0.255608	+	0.966781i	$0.582276\pi$
$200$	44.1941	−	44.1941i	0.220970	−	0.220970i
$201$	13.9678	−	13.9678i	0.0694916	−	0.0694916i
$202$		−	94.8184i		−	0.469398i
$203$	−272.277	+	69.2957i	−1.34126	+	0.341358i
$204$	14.1394			0.0693108
$205$	95.0090	+	95.0090i	0.463459	+	0.463459i
$206$	126.776	+	126.776i	0.615417	+	0.615417i
$207$			86.8078i			0.419362i
$208$			13.6758i			0.0657491i
$209$		−	9.82502i		−	0.0470097i
$210$	32.4897			0.154713
$211$	84.0454	−	84.0454i	0.398319	−	0.398319i	−0.479321	−	0.877640i	$-0.659117\pi$
$211$	84.0454	−	84.0454i	0.398319	−	0.398319i	0.877640	+	0.479321i	$0.159117\pi$
$212$		−	211.399i		−	0.997166i
$213$	−44.2072	+	44.2072i	−0.207546	+	0.207546i
$214$	−13.6117	−	13.6117i	−0.0636058	−	0.0636058i
$215$	72.8910	−	72.8910i	0.339028	−	0.339028i
$216$		−	89.9725i		−	0.416539i
$217$	361.464	+	361.464i	1.66573	+	1.66573i
$218$	35.1304	−	35.1304i	0.161149	−	0.161149i
$219$	−3.50839			−0.0160200
$220$	−3.27123	−	3.27123i	−0.0148692	−	0.0148692i
$221$	−83.2711	+	83.2711i	−0.376792	+	0.376792i
$222$	−36.2547	−	36.2547i	−0.163310	−	0.163310i
$223$	−306.140			−1.37283			−0.686413	−	0.727212i	$-0.740816\pi$
$223$	−306.140			−1.37283			−0.686413	+	0.727212i	$0.740816\pi$
$224$	213.809	+	213.809i	0.954506	+	0.954506i
$225$		−	65.9135i		−	0.292949i
$226$	−36.8739			−0.163159
$227$	19.8257			0.0873379			0.0436689	−	0.999046i	$-0.486095\pi$
$227$	19.8257			0.0873379			0.0436689	+	0.999046i	$0.486095\pi$
$228$	30.4543			0.133571
$229$	150.087	−	150.087i	0.655402	−	0.655402i	−0.298887	−	0.954289i	$-0.596615\pi$
$229$	150.087	−	150.087i	0.655402	−	0.655402i	0.954289	+	0.298887i	$0.0966153\pi$
$230$	38.1994	−	38.1994i	0.166084	−	0.166084i
$231$			2.87273i			0.0124360i
$232$	120.924	−	203.488i	0.521223	−	0.877103i
$233$	132.431			0.568375			0.284187	−	0.958769i	$-0.408276\pi$
$233$	132.431			0.568375			0.284187	+	0.958769i	$0.408276\pi$
$234$	95.7445	+	95.7445i	0.409165	+	0.409165i
$235$	9.20344	+	9.20344i	0.0391636	+	0.0391636i
$236$			212.067i			0.898590i
$237$		−	35.6888i		−	0.150586i
$238$		−	120.019i		−	0.504280i
$239$	176.690			0.739288			0.369644	−	0.929173i	$-0.379480\pi$
$239$	176.690			0.739288			0.369644	+	0.929173i	$0.379480\pi$
$240$	−2.06168	+	2.06168i	−0.00859034	+	0.00859034i
$241$			161.010i			0.668093i	0.942557	+	0.334046i	$0.108414\pi$
$241$			161.010i			0.668093i	−0.942557	+	0.334046i	$0.891586\pi$
$242$	109.856	−	109.856i	0.453951	−	0.453951i
$243$	−101.389	−	101.389i	−0.417239	−	0.417239i
$244$	−69.0348	+	69.0348i	−0.282930	+	0.282930i
$245$			186.819i			0.762527i
$246$	18.3717	+	18.3717i	0.0746817	+	0.0746817i
$247$	−179.354	+	179.354i	−0.726130	+	0.726130i
$248$	−430.677			−1.73660
$249$	60.9606	+	60.9606i	0.244822	+	0.244822i
$250$	−123.704	+	123.704i	−0.494816	+	0.494816i
$251$	136.621	+	136.621i	0.544306	+	0.544306i	0.924788	−	0.380482i	$-0.124242\pi$
$251$	136.621	+	136.621i	0.544306	+	0.544306i	−0.380482	+	0.924788i	$0.624242\pi$
$252$	195.590			0.776150
$253$	3.37757	+	3.37757i	0.0133501	+	0.0133501i
$254$			95.0001i			0.374016i
$255$	−25.1069			−0.0984585
$256$	−265.241			−1.03610
$257$	−275.616			−1.07244			−0.536218	−	0.844079i	$-0.680148\pi$
$257$	−275.616			−1.07244			−0.536218	+	0.844079i	$0.680148\pi$
$258$	14.0948	−	14.0948i	0.0546310	−	0.0546310i
$259$	436.175	−	436.175i	1.68407	−	1.68407i
$260$			119.432i			0.459353i
$261$	−61.5706	−	241.923i	−0.235903	−	0.926908i
$262$	46.1744			0.176238
$263$	−242.820	−	242.820i	−0.923269	−	0.923269i	0.0739900	−	0.997259i	$-0.476427\pi$
$263$	−242.820	−	242.820i	−0.923269	−	0.923269i	−0.997259	+	0.0739900i	$0.976427\pi$
$264$	−1.71140	−	1.71140i	−0.00648256	−	0.00648256i
$265$			375.375i			1.41651i
$266$		−	258.503i		−	0.971816i
$267$			73.6148i			0.275711i
$268$	−74.0042			−0.276135
$269$	167.754	−	167.754i	0.623620	−	0.623620i	−0.322836	−	0.946455i	$-0.604636\pi$
$269$	167.754	−	167.754i	0.623620	−	0.623620i	0.946455	+	0.322836i	$0.104636\pi$
$270$			59.0497i			0.218703i
$271$	282.361	−	282.361i	1.04192	−	1.04192i	0.0428420	−	0.999082i	$-0.486359\pi$
$271$	282.361	−	282.361i	1.04192	−	1.04192i	0.999082	−	0.0428420i	$-0.0136412\pi$
$272$	7.61596	+	7.61596i	0.0279998	+	0.0279998i
$273$	52.4412	−	52.4412i	0.192092	−	0.192092i
$274$		−	213.169i		−	0.777989i
$275$	−2.56461	−	2.56461i	−0.00932584	−	0.00932584i
$276$	−10.4693	+	10.4693i	−0.0379324	+	0.0379324i
$277$	30.5322			0.110224			0.0551122	−	0.998480i	$-0.482448\pi$
$277$	30.5322			0.110224			0.0551122	+	0.998480i	$0.482448\pi$
$278$	56.6568	+	56.6568i	0.203802	+	0.203802i
$279$	−321.168	+	321.168i	−1.15114	+	1.15114i
$280$	−232.862	−	232.862i	−0.831649	−	0.831649i
$281$	−2.92201			−0.0103986			−0.00519931	−	0.999986i	$-0.501655\pi$
$281$	−2.92201			−0.0103986			−0.00519931	+	0.999986i	$0.501655\pi$
$282$	1.77965	+	1.77965i	0.00631082	+	0.00631082i
$283$			26.9414i			0.0951993i	0.998866	+	0.0475997i	$0.0151572\pi$
$283$			26.9414i			0.0951993i	−0.998866	+	0.0475997i	$0.984843\pi$
$284$	234.219			0.824713
$285$	−54.0767			−0.189743
$286$	7.45058			0.0260510
$287$	−221.027	+	221.027i	−0.770129	+	0.770129i
$288$	−189.974	+	189.974i	−0.659631	+	0.659631i
$289$		−	196.254i		−	0.679079i
$290$	−79.3633	+	133.551i	−0.273666	+	0.460521i
$291$	−70.8123			−0.243341
$292$	9.29406	+	9.29406i	0.0318290	+	0.0318290i
$293$	−255.770	−	255.770i	−0.872934	−	0.872934i	0.119857	−	0.992791i	$-0.461756\pi$
$293$	−255.770	−	255.770i	−0.872934	−	0.872934i	−0.992791	+	0.119857i	$0.961756\pi$
$294$			36.1249i			0.122874i
$295$		−	376.561i		−	1.27648i
$296$			519.693i			1.75572i
$297$	−5.22115			−0.0175796
$298$	128.249	−	128.249i	0.430364	−	0.430364i
$299$		−	123.314i		−	0.412422i
$300$	7.94942	−	7.94942i	0.0264981	−	0.0264981i
$301$	169.572	+	169.572i	0.563362	+	0.563362i
$302$	−244.770	+	244.770i	−0.810496	+	0.810496i
$303$		−	46.1443i		−	0.152291i
$304$	16.4037	+	16.4037i	0.0539595	+	0.0539595i
$305$	122.583	−	122.583i	0.401912	−	0.401912i
$306$	106.639			0.348493
$307$	−9.20371	−	9.20371i	−0.0299795	−	0.0299795i	0.691958	−	0.721938i	$-0.256748\pi$
$307$	−9.20371	−	9.20371i	−0.0299795	−	0.0299795i	−0.721938	+	0.691958i	$0.756748\pi$
$308$	7.61013	−	7.61013i	0.0247082	−	0.0247082i
$309$	61.6967	+	61.6967i	0.199666	+	0.199666i
$310$	282.657			0.911796
$311$	94.0902	+	94.0902i	0.302541	+	0.302541i	0.842007	−	0.539466i	$-0.181374\pi$
$311$	94.0902	+	94.0902i	0.302541	+	0.302541i	−0.539466	+	0.842007i	$0.681374\pi$
$312$			62.4825i			0.200264i
$313$	133.762			0.427356			0.213678	−	0.976904i	$-0.431456\pi$
$313$	133.762			0.427356			0.213678	+	0.976904i	$0.431456\pi$
$314$	−150.388			−0.478942
$315$	−347.303			−1.10255
$316$	−94.5431	+	94.5431i	−0.299187	+	0.299187i
$317$	405.329	−	405.329i	1.27864	−	1.27864i	0.337213	−	0.941428i	$-0.390516\pi$
$317$	405.329	−	405.329i	1.27864	−	1.27864i	0.941428	−	0.337213i	$-0.109484\pi$
$318$			72.5856i			0.228257i
$319$	−11.8085	−	7.01726i	−0.0370173	−	0.0219977i
$320$	185.824			0.580700
$321$	−6.62424	−	6.62424i	−0.0206363	−	0.0206363i
$322$	88.8663	+	88.8663i	0.275982	+	0.275982i
$323$			199.762i			0.618458i
$324$			165.513i			0.510844i
$325$			93.6329i			0.288101i
$326$	29.4068			0.0902049
$327$	17.0965	−	17.0965i	0.0522830	−	0.0522830i
$328$		−	263.349i		−	0.802893i
$329$	−21.4107	+	21.4107i	−0.0650781	+	0.0650781i
$330$	1.12320	+	1.12320i	0.00340365	+	0.00340365i
$331$	185.108	−	185.108i	0.559238	−	0.559238i	−0.369853	−	0.929090i	$-0.620592\pi$
$331$	185.108	−	185.108i	0.559238	−	0.559238i	0.929090	+	0.369853i	$0.120592\pi$
$332$		−	322.981i		−	0.972834i
$333$	387.550	+	387.550i	1.16381	+	1.16381i
$334$	−122.365	+	122.365i	−0.366363	+	0.366363i
$335$	131.407			0.392260
$336$	−4.79626	−	4.79626i	−0.0142746	−	0.0142746i
$337$	−71.8022	+	71.8022i	−0.213063	+	0.213063i	−0.805567	−	0.592504i	$-0.798139\pi$
$337$	−71.8022	+	71.8022i	−0.213063	+	0.213063i	0.592504	+	0.805567i	$0.298139\pi$
$338$	17.7114	+	17.7114i	0.0524006	+	0.0524006i
$339$	−17.9450			−0.0529351
$340$	66.5107	+	66.5107i	0.195620	+	0.195620i
$341$			24.9924i			0.0732915i
$342$	229.685			0.671593
$343$	40.1069			0.116930
$344$	−202.041			−0.587330
$345$	18.5901	−	18.5901i	0.0538843	−	0.0538843i
$346$	−85.6610	+	85.6610i	−0.247575	+	0.247575i
$347$			181.565i			0.523241i	0.965171	+	0.261621i	$0.0842569\pi$
$347$			181.565i			0.523241i	−0.965171	+	0.261621i	$0.915743\pi$
$348$	21.7512	−	36.6024i	0.0625033	−	0.105179i
$349$	205.399			0.588536			0.294268	−	0.955723i	$-0.404924\pi$
$349$	205.399			0.588536			0.294268	+	0.955723i	$0.404924\pi$
$350$	−67.4765	−	67.4765i	−0.192790	−	0.192790i
$351$	95.3112	+	95.3112i	0.271542	+	0.271542i
$352$			14.7832i			0.0419978i
$353$			150.904i			0.427489i	0.976890	+	0.213745i	$0.0685660\pi$
$353$			150.904i			0.427489i	−0.976890	+	0.213745i	$0.931434\pi$
$354$		−	72.8149i		−	0.205692i
$355$	−415.895			−1.17153
$356$	195.013	−	195.013i	0.547789	−	0.547789i
$357$		−	58.4082i		−	0.163608i
$358$	−50.6543	+	50.6543i	−0.141492	+	0.141492i
$359$	−366.501	−	366.501i	−1.02089	−	1.02089i	−0.999777	−	0.0211170i	$-0.993278\pi$
$359$	−366.501	−	366.501i	−1.02089	−	1.02089i	−0.0211170	−	0.999777i	$-0.506722\pi$
$360$	206.902	−	206.902i	0.574728	−	0.574728i
$361$			69.2592i			0.191854i
$362$	−119.955	−	119.955i	−0.331368	−	0.331368i
$363$	53.4625	−	53.4625i	0.147280	−	0.147280i
$364$	−277.843			−0.763306
$365$	−16.5032	−	16.5032i	−0.0452142	−	0.0452142i
$366$	23.7037	−	23.7037i	0.0647641	−	0.0647641i
$367$	−84.3213	−	84.3213i	−0.229758	−	0.229758i	0.582833	−	0.812592i	$-0.301944\pi$
$367$	−84.3213	−	84.3213i	−0.229758	−	0.229758i	−0.812592	+	0.582833i	$0.801944\pi$
$368$	−11.2783			−0.0306475
$369$	−196.387	−	196.387i	−0.532213	−	0.532213i
$370$		−	341.079i		−	0.921835i
$371$	−873.265			−2.35381
$372$	−77.4680			−0.208247
$373$	91.4080			0.245062			0.122531	−	0.992465i	$-0.460899\pi$
$373$	91.4080			0.245062			0.122531	+	0.992465i	$0.460899\pi$
$374$	4.14917	−	4.14917i	0.0110940	−	0.0110940i
$375$	−60.2017	+	60.2017i	−0.160538	+	0.160538i
$376$		−	25.5104i		−	0.0678468i
$377$	87.4635	+	343.662i	0.231999	+	0.911569i
$378$	−137.372			−0.363418
$379$	178.021	+	178.021i	0.469713	+	0.469713i	0.901822	−	0.432108i	$-0.142230\pi$
$379$	178.021	+	178.021i	0.469713	+	0.469713i	−0.432108	+	0.901822i	$0.642230\pi$
$380$	143.255	+	143.255i	0.376986	+	0.376986i
$381$			46.2327i			0.121346i
$382$			222.928i			0.583581i
$383$			142.083i			0.370973i	0.982647	+	0.185486i	$0.0593860\pi$
$383$			142.083i			0.370973i	−0.982647	+	0.185486i	$0.940614\pi$
$384$	−42.2206			−0.109950
$385$	−13.5131	+	13.5131i	−0.0350989	+	0.0350989i
$386$		−	320.100i		−	0.829274i
$387$	−150.668	+	150.668i	−0.389323	+	0.389323i
$388$	187.589	+	187.589i	0.483476	+	0.483476i
$389$	−339.694	+	339.694i	−0.873250	+	0.873250i	−0.992825	−	0.119575i	$-0.961847\pi$
$389$	−339.694	+	339.694i	−0.873250	+	0.873250i	0.119575	+	0.992825i	$0.461847\pi$
$390$		−	41.0078i		−	0.105148i
$391$	−68.6727	−	68.6727i	−0.175634	−	0.175634i
$392$	258.916	−	258.916i	0.660499	−	0.660499i
$393$	22.4712			0.0571787
$394$	38.9030	+	38.9030i	0.0987386	+	0.0987386i
$395$	167.877	−	167.877i	0.425006	−	0.425006i
$396$	6.76175	+	6.76175i	0.0170751	+	0.0170751i
$397$	−657.787			−1.65689			−0.828447	−	0.560068i	$-0.810775\pi$
$397$	−657.787			−1.65689			−0.828447	+	0.560068i	$0.810775\pi$
$398$	−92.5342	−	92.5342i	−0.232498	−	0.232498i
$399$		−	125.803i		−	0.315296i
$400$	8.56364			0.0214091
$401$	343.872			0.857537			0.428768	−	0.903414i	$-0.358948\pi$
$401$	343.872			0.857537			0.428768	+	0.903414i	$0.358948\pi$
$402$	25.4099			0.0632088
$403$	456.232	−	456.232i	1.13209	−	1.13209i
$404$	−122.241	+	122.241i	−0.302576	+	0.302576i
$405$		−	293.897i		−	0.725672i
$406$	−310.690	−	184.629i	−0.765247	−	0.454751i
$407$	30.1581			0.0740984
$408$	34.7961	+	34.7961i	0.0852844	+	0.0852844i
$409$	219.662	+	219.662i	0.537072	+	0.537072i	0.922668	−	0.385596i	$-0.126004\pi$
$409$	219.662	+	219.662i	0.537072	+	0.537072i	−0.385596	+	0.922668i	$0.626004\pi$
$410$			172.838i			0.421557i
$411$		−	103.741i		−	0.252411i
$412$		−	326.881i		−	0.793401i
$413$	876.024			2.12112
$414$	−78.9594	+	78.9594i	−0.190723	+	0.190723i
$415$			573.508i			1.38195i
$416$	269.866	−	269.866i	0.648715	−	0.648715i
$417$	27.5726	+	27.5726i	0.0661213	+	0.0661213i
$418$	8.93673	−	8.93673i	0.0213797	−	0.0213797i
$419$			512.017i			1.22200i	0.791631	+	0.610999i	$0.209232\pi$
$419$			512.017i			1.22200i	−0.791631	+	0.610999i	$0.790768\pi$
$420$	−41.8860	−	41.8860i	−0.0997286	−	0.0997286i
$421$	−426.710	+	426.710i	−1.01356	+	1.01356i	−0.0136572	+	0.999907i	$0.504347\pi$
$421$	−426.710	+	426.710i	−1.01356	+	1.01356i	−0.999907	+	0.0136572i	$0.995653\pi$
$422$	152.893			0.362307
$423$	−19.0238	−	19.0238i	−0.0449735	−	0.0449735i
$424$	520.238	−	520.238i	1.22698	−	1.22698i
$425$	52.1435	+	52.1435i	0.122691	+	0.122691i
$426$	−80.4208			−0.188781
$427$	285.175	+	285.175i	0.667857	+	0.667857i
$428$			35.0965i			0.0820012i
$429$	3.62589			0.00845197
$430$	132.602			0.308376
$431$	596.638			1.38431			0.692156	−	0.721748i	$-0.256661\pi$
$431$	596.638			1.38431			0.692156	+	0.721748i	$0.256661\pi$
$432$	8.71714	−	8.71714i	0.0201786	−	0.0201786i
$433$	−41.8737	+	41.8737i	−0.0967059	+	0.0967059i	−0.753805	−	0.657099i	$-0.771783\pi$
$433$	−41.8737	+	41.8737i	−0.0967059	+	0.0967059i	0.657099	+	0.753805i	$0.271783\pi$
$434$			657.567i			1.51513i
$435$	−38.6229	+	64.9938i	−0.0887882	+	0.149411i
$436$	−90.5808			−0.207754
$437$	−147.911	−	147.911i	−0.338470	−	0.338470i
$438$	−3.19119	−	3.19119i	−0.00728582	−	0.00728582i
$439$		−	344.567i		−	0.784891i	−0.919775	−	0.392445i	$-0.871629\pi$
$439$		−	344.567i		−	0.784891i	0.919775	−	0.392445i	$-0.128371\pi$
$440$		−	16.1005i		−	0.0365922i
$441$		−	386.161i		−	0.875649i
$442$	−151.485			−0.342726
$443$	−124.564	+	124.564i	−0.281184	+	0.281184i	−0.833581	−	0.552397i	$-0.813713\pi$
$443$	−124.564	+	124.564i	−0.281184	+	0.281184i	0.552397	+	0.833581i	$0.313713\pi$
$444$			93.4798i			0.210540i
$445$	−346.278	+	346.278i	−0.778154	+	0.778154i
$446$	−278.462	−	278.462i	−0.624353	−	0.624353i
$447$	62.4134	−	62.4134i	0.139627	−	0.139627i
$448$			432.297i			0.964949i
$449$	−562.904	−	562.904i	−1.25368	−	1.25368i	−0.954056	−	0.299628i	$-0.903137\pi$
$449$	−562.904	−	562.904i	−1.25368	−	1.25368i	−0.299628	−	0.954056i	$-0.596863\pi$
$450$	59.9542	−	59.9542i	0.133232	−	0.133232i
$451$	−15.2823			−0.0338853
$452$	47.5381	+	47.5381i	0.105173	+	0.105173i
$453$	−119.120	+	119.120i	−0.262957	+	0.262957i
$454$	18.0332	+	18.0332i	0.0397208	+	0.0397208i
$455$	493.358			1.08430
$456$	74.9458	+	74.9458i	0.164355	+	0.164355i
$457$			377.138i			0.825247i	0.910902	+	0.412623i	$0.135387\pi$
$457$			377.138i			0.825247i	−0.910902	+	0.412623i	$0.864613\pi$
$458$	273.035			0.596146
$459$	106.156			0.231277
$460$	−98.4940			−0.214117
$461$	−40.0863	+	40.0863i	−0.0869552	+	0.0869552i	−0.749246	−	0.662291i	$-0.769584\pi$
$461$	−40.0863	+	40.0863i	−0.0869552	+	0.0869552i	0.662291	+	0.749246i	$0.269584\pi$
$462$	−2.61300	+	2.61300i	−0.00565584	+	0.00565584i
$463$		−	410.934i		−	0.887546i	−0.896139	−	0.443773i	$-0.853640\pi$
$463$		−	410.934i		−	0.887546i	0.896139	−	0.443773i	$-0.146360\pi$
$464$	31.4312	−	7.99939i	0.0677397	−	0.0172401i
$465$	137.558			0.295823
$466$	120.458	+	120.458i	0.258494	+	0.258494i
$467$	−427.051	−	427.051i	−0.914455	−	0.914455i	0.0821634	−	0.996619i	$-0.473817\pi$
$467$	−427.051	−	427.051i	−0.914455	−	0.914455i	−0.996619	+	0.0821634i	$0.973817\pi$
$468$		−	246.869i		−	0.527498i
$469$			305.703i			0.651818i
$470$			16.7427i			0.0356227i
$471$	−73.1877			−0.155388
$472$	−521.882	+	521.882i	−1.10568	+	1.10568i
$473$			11.7246i			0.0247877i
$474$	32.4621	−	32.4621i	0.0684854	−	0.0684854i
$475$	112.310	+	112.310i	0.236441	+	0.236441i
$476$	−154.729	+	154.729i	−0.325061	+	0.325061i
$477$		−	775.913i		−	1.62665i
$478$	160.715	+	160.715i	0.336224	+	0.336224i
$479$	223.602	−	223.602i	0.466811	−	0.466811i	−0.434069	−	0.900880i	$-0.642923\pi$
$479$	223.602	−	223.602i	0.466811	−	0.466811i	0.900880	+	0.434069i	$0.142923\pi$
$480$	81.3666			0.169514
$481$	−550.530	−	550.530i	−1.14455	−	1.14455i
$482$	−146.453	+	146.453i	−0.303845	+	0.303845i
$483$	43.2476	+	43.2476i	0.0895396	+	0.0895396i
$484$	−283.255			−0.585237
$485$	−333.096	−	333.096i	−0.686795	−	0.686795i
$486$		−	184.445i		−	0.379516i
$487$	397.009			0.815214			0.407607	−	0.913157i	$-0.366363\pi$
$487$	397.009			0.815214			0.407607	+	0.913157i	$0.366363\pi$
$488$	−339.780			−0.696270
$489$	14.3111			0.0292661
$490$	−169.929	+	169.929i	−0.346793	+	0.346793i
$491$	−441.208	+	441.208i	−0.898591	+	0.898591i	−0.995312	−	0.0967208i	$-0.969165\pi$
$491$	−441.208	+	441.208i	−0.898591	+	0.898591i	0.0967208	+	0.995312i	$0.469165\pi$
$492$		−	47.3699i		−	0.0962803i
$493$	240.090	+	142.675i	0.486999	+	0.289401i
$494$	−326.277			−0.660480
$495$	−12.0066	−	12.0066i	−0.0242558	−	0.0242558i
$496$	−41.7269	−	41.7269i	−0.0841268	−	0.0841268i
$497$		−	967.529i		−	1.94674i
$498$			110.898i			0.222687i
$499$			94.9470i			0.190275i	0.995464	+	0.0951373i	$0.0303290\pi$
$499$			94.9470i			0.190275i	−0.995464	+	0.0951373i	$0.969671\pi$
$500$	318.960			0.637920
$501$	−59.5502	+	59.5502i	−0.118863	+	0.118863i
$502$			248.537i			0.495094i
$503$	−35.4061	+	35.4061i	−0.0703899	+	0.0703899i	−0.741425	−	0.671035i	$-0.765850\pi$
$503$	−35.4061	+	35.4061i	−0.0703899	+	0.0703899i	0.671035	+	0.741425i	$0.265850\pi$
$504$	481.333	+	481.333i	0.955025	+	0.955025i
$505$	217.059	−	217.059i	0.429820	−	0.429820i
$506$			6.14440i			0.0121431i
$507$	8.61942	+	8.61942i	0.0170008	+	0.0170008i
$508$	122.475	−	122.475i	0.241092	−	0.241092i
$509$	215.741			0.423852			0.211926	−	0.977286i	$-0.432026\pi$
$509$	215.741			0.423852			0.211926	+	0.977286i	$0.432026\pi$
$510$	−22.8370	−	22.8370i	−0.0447783	−	0.0447783i
$511$	38.3927	−	38.3927i	0.0751324	−	0.0751324i
$512$	−50.5014	−	50.5014i	−0.0986355	−	0.0986355i
$513$	228.646			0.445703
$514$	−250.697	−	250.697i	−0.487738	−	0.487738i
$515$			580.433i			1.12705i
$516$	−36.3422			−0.0704307
$517$	−1.48038			−0.00286341
$518$	793.479			1.53181
$519$	−41.6878	+	41.6878i	−0.0803232	+	0.0803232i
$520$	−293.913	+	293.913i	−0.565217	+	0.565217i
$521$		−	279.099i		−	0.535700i	−0.963461	−	0.267850i	$-0.913687\pi$
$521$		−	279.099i		−	0.535700i	0.963461	−	0.267850i	$-0.0863131\pi$
$522$	164.046	−	276.054i	0.314265	−	0.528839i
$523$	−135.622			−0.259316			−0.129658	−	0.991559i	$-0.541388\pi$
$523$	−135.622			−0.259316			−0.129658	+	0.991559i	$0.541388\pi$
$524$	−59.5285	−	59.5285i	−0.113604	−	0.113604i
$525$	−32.8381	−	32.8381i	−0.0625488	−	0.0625488i
$526$		−	441.732i		−	0.839795i
$527$		−	508.145i		−	0.964221i
$528$		−	0.331623i		−	0.000628074i
$529$	−427.304			−0.807758
$530$	−341.437	+	341.437i	−0.644221	+	0.644221i
$531$			778.365i			1.46585i
$532$	−333.264	+	333.264i	−0.626437	+	0.626437i
$533$	278.975	+	278.975i	0.523406	+	0.523406i
$534$	−66.9592	+	66.9592i	−0.125392	+	0.125392i
$535$		−	62.3198i		−	0.116486i
$536$	−182.119	−	182.119i	−0.339774	−	0.339774i
$537$	−24.6514	+	24.6514i	−0.0459057	+	0.0459057i
$538$	305.174			0.567237
$539$	−15.0250	−	15.0250i	−0.0278757	−	0.0278757i
$540$	76.1274	−	76.1274i	0.140977	−	0.140977i
$541$	381.445	+	381.445i	0.705074	+	0.705074i	0.965495	−	0.260421i	$-0.0838614\pi$
$541$	381.445	+	381.445i	0.705074	+	0.705074i	−0.260421	+	0.965495i	$0.583861\pi$
$542$	513.665			0.947722
$543$	−58.3773	−	58.3773i	−0.107509	−	0.107509i
$544$		−	300.572i		−	0.552523i
$545$	160.842			0.295122
$546$	95.3997			0.174725
$547$	104.335			0.190739			0.0953697	−	0.995442i	$-0.469597\pi$
$547$	104.335			0.190739			0.0953697	+	0.995442i	$0.469597\pi$
$548$	−274.819	+	274.819i	−0.501495	+	0.501495i
$549$	−253.383	+	253.383i	−0.461536	+	0.461536i
$550$		−	4.66547i		−	0.00848268i
$551$	517.121	+	307.301i	0.938513	+	0.557716i
$552$	−51.5286			−0.0933489
$553$	390.546	+	390.546i	0.706232	+	0.706232i
$554$	27.7717	+	27.7717i	0.0501295	+	0.0501295i
$555$		−	165.989i		−	0.299080i
$556$		−	146.085i		−	0.262743i
$557$		−	132.616i		−	0.238090i	−0.992889	−	0.119045i	$-0.962017\pi$
$557$		−	132.616i		−	0.238090i	0.992889	−	0.119045i	$-0.0379833\pi$
$558$	−584.261			−1.04706
$559$	214.030	−	214.030i	0.382880	−	0.382880i
$560$		−	45.1224i		−	0.0805758i
$561$	2.01923	−	2.01923i	0.00359935	−	0.00359935i
$562$	−2.65783	−	2.65783i	−0.00472923	−	0.00472923i
$563$	253.583	−	253.583i	0.450413	−	0.450413i	−0.445078	−	0.895492i	$-0.646824\pi$
$563$	253.583	−	253.583i	0.450413	−	0.450413i	0.895492	+	0.445078i	$0.146824\pi$
$564$		−	4.58868i		−	0.00813596i
$565$	−84.4120	−	84.4120i	−0.149402	−	0.149402i
$566$	−24.5056	+	24.5056i	−0.0432961	+	0.0432961i
$567$	683.716			1.20585
$568$	576.395	+	576.395i	1.01478	+	1.01478i
$569$	216.864	−	216.864i	0.381133	−	0.381133i	−0.490377	−	0.871510i	$-0.663141\pi$
$569$	216.864	−	216.864i	0.381133	−	0.381133i	0.871510	+	0.490377i	$0.163141\pi$
$570$	−49.1876	−	49.1876i	−0.0862940	−	0.0862940i
$571$	398.256			0.697472			0.348736	−	0.937221i	$-0.386611\pi$
$571$	398.256			0.697472			0.348736	+	0.937221i	$0.386611\pi$
$572$	−9.60534	−	9.60534i	−0.0167926	−	0.0167926i
$573$			108.490i			0.189337i
$574$	−402.087			−0.700500
$575$	−77.2180			−0.134292
$576$	−384.104			−0.666848
$577$	−504.599	+	504.599i	−0.874521	+	0.874521i	−0.992961	−	0.118440i	$-0.962211\pi$
$577$	−504.599	+	504.599i	−0.874521	+	0.874521i	0.118440	+	0.992961i	$0.462211\pi$
$578$	178.510	−	178.510i	0.308841	−	0.308841i
$579$		−	155.780i		−	0.269049i
$580$	274.491	−	69.8592i	0.473260	−	0.120447i
$581$	−1334.20			−2.29638
$582$	−64.4101	−	64.4101i	−0.110670	−	0.110670i
$583$	−30.1897	−	30.1897i	−0.0517834	−	0.0517834i
$584$			45.7440i			0.0783288i
$585$			438.358i			0.749330i
$586$		−	465.290i		−	0.794011i
$587$	110.932			0.188982			0.0944911	−	0.995526i	$-0.469878\pi$
$587$	110.932			0.188982			0.0944911	+	0.995526i	$0.469878\pi$
$588$	46.5725	−	46.5725i	0.0792049	−	0.0792049i
$589$		−	1094.47i		−	1.85819i
$590$	342.516	−	342.516i	0.580535	−	0.580535i
$591$	18.9325	+	18.9325i	0.0320347	+	0.0320347i
$592$	−50.3514	+	50.3514i	−0.0850530	+	0.0850530i
$593$			988.969i			1.66774i	0.551962	+	0.833870i	$0.313879\pi$
$593$			988.969i			1.66774i	−0.551962	+	0.833870i	$0.686121\pi$
$594$	−4.74910	−	4.74910i	−0.00799511	−	0.00799511i
$595$	274.748	−	274.748i	0.461761	−	0.461761i
$596$	−330.678			−0.554829
$597$	−45.0326	−	45.0326i	−0.0754315	−	0.0754315i
$598$	112.165	−	112.165i	0.187567	−	0.187567i
$599$	262.125	+	262.125i	0.437604	+	0.437604i	0.891205	−	0.453601i	$-0.149861\pi$
$599$	262.125	+	262.125i	0.437604	+	0.437604i	−0.453601	+	0.891205i	$0.649861\pi$
$600$	39.1259			0.0652098
$601$	−496.848	−	496.848i	−0.826702	−	0.826702i	0.160357	−	0.987059i	$-0.448735\pi$
$601$	−496.848	−	496.848i	−0.826702	−	0.826702i	−0.987059	+	0.160357i	$0.948735\pi$
$602$			308.482i			0.512428i
$603$	−271.623			−0.450452
$604$	631.119			1.04490
$605$	502.967			0.831351
$606$	41.9723	−	41.9723i	0.0692612	−	0.0692612i
$607$	−466.144	+	466.144i	−0.767947	+	0.767947i	−0.977745	−	0.209798i	$-0.932719\pi$
$607$	−466.144	+	466.144i	−0.767947	+	0.767947i	0.209798	+	0.977745i	$0.432719\pi$
$608$		−	647.390i		−	1.06479i
$609$	−151.200	−	89.8515i	−0.248276	−	0.147539i
$610$	223.000			0.365574
$611$	27.0241	+	27.0241i	0.0442293	+	0.0442293i
$612$	−137.480	−	137.480i	−0.224640	−	0.224640i
$613$		−	581.681i		−	0.948908i	−0.880280	−	0.474454i	$-0.842645\pi$
$613$		−	581.681i		−	0.948908i	0.880280	−	0.474454i	$-0.157355\pi$
$614$		−	16.7432i		−	0.0272690i
$615$			84.1133i			0.136770i
$616$	37.4560			0.0608052
$617$	−546.898	+	546.898i	−0.886383	+	0.886383i	−0.994174	−	0.107791i	$-0.965622\pi$
$617$	−546.898	+	546.898i	−0.886383	+	0.886383i	0.107791	+	0.994174i	$0.465622\pi$
$618$			112.237i			0.181614i
$619$	−650.477	+	650.477i	−1.05085	+	1.05085i	−0.0522157	+	0.998636i	$0.516628\pi$
$619$	−650.477	+	650.477i	−1.05085	+	1.05085i	−0.998636	+	0.0522157i	$0.983372\pi$
$620$	−364.404	−	364.404i	−0.587748	−	0.587748i
$621$	−78.6021	+	78.6021i	−0.126573	+	0.126573i
$622$			171.167i			0.275188i
$623$	−805.575	−	805.575i	−1.29306	−	1.29306i
$624$	−6.05373	+	6.05373i	−0.00970149	+	0.00970149i
$625$	−374.939			−0.599903
$626$	121.669	+	121.669i	0.194359	+	0.194359i
$627$	4.34914	−	4.34914i	0.00693643	−	0.00693643i
$628$	193.881	+	193.881i	0.308728	+	0.308728i
$629$	−613.173			−0.974837
$630$	−315.903	−	315.903i	−0.501433	−	0.501433i
$631$		−	1020.55i		−	1.61735i	−0.588253	−	0.808677i	$-0.700184\pi$
$631$		−	1020.55i		−	1.61735i	0.588253	−	0.808677i	$-0.299816\pi$
$632$	−465.327			−0.736277
$633$	74.4070			0.117547
$634$	737.366			1.16304
$635$	−217.475	+	217.475i	−0.342480	+	0.342480i
$636$	93.5780	−	93.5780i	0.147135	−	0.147135i
$637$			548.558i			0.861159i
$638$	−4.35807	−	17.1237i	−0.00683083	−	0.0268397i
$639$	859.668			1.34533
$640$	−198.603	−	198.603i	−0.310316	−	0.310316i
$641$	65.0163	+	65.0163i	0.101430	+	0.101430i	0.756001	−	0.654571i	$-0.227151\pi$
$641$	65.0163	+	65.0163i	0.101430	+	0.101430i	−0.654571	+	0.756001i	$0.727151\pi$
$642$		−	12.0507i		−	0.0187705i
$643$			590.198i			0.917882i	0.888467	+	0.458941i	$0.151771\pi$
$643$			590.198i			0.917882i	−0.888467	+	0.458941i	$0.848229\pi$
$644$		−	229.134i		−	0.355799i
$645$	64.5318			0.100049
$646$	−181.701	+	181.701i	−0.281271	+	0.281271i
$647$			96.4448i			0.149065i	0.997219	+	0.0745323i	$0.0237464\pi$
$647$			96.4448i			0.149065i	−0.997219	+	0.0745323i	$0.976254\pi$
$648$	−407.316	+	407.316i	−0.628575	+	0.628575i
$649$	30.2851	+	30.2851i	0.0466642	+	0.0466642i
$650$	−85.1674	+	85.1674i	−0.131027	+	0.131027i
$651$			320.011i			0.491569i
$652$	−37.9115	−	37.9115i	−0.0581465	−	0.0581465i
$653$	−185.978	+	185.978i	−0.284806	+	0.284806i	−0.835022	−	0.550216i	$-0.814545\pi$
$653$	−185.978	+	185.978i	−0.284806	+	0.284806i	0.550216	+	0.835022i	$0.314545\pi$
$654$	31.1016			0.0475560
$655$	105.703	+	105.703i	0.161379	+	0.161379i
$656$	25.5150	−	25.5150i	0.0388949	−	0.0388949i
$657$	34.1126	+	34.1126i	0.0519218	+	0.0519218i
$658$	−38.9498			−0.0591943
$659$	811.110	+	811.110i	1.23082	+	1.23082i	0.963649	+	0.267170i	$0.0860886\pi$
$659$	811.110	+	811.110i	1.23082	+	1.23082i	0.267170	+	0.963649i	$0.413911\pi$
$660$		−	2.89609i		−	0.00438801i
$661$	442.227			0.669027			0.334513	−	0.942391i	$-0.391428\pi$
$661$	442.227			0.669027			0.334513	+	0.942391i	$0.391428\pi$
$662$	336.744			0.508676
$663$	−73.7216			−0.111194
$664$	794.833	−	794.833i	1.19704	−	1.19704i
$665$	591.767	−	591.767i	0.889876	−	0.889876i
$666$			705.021i			1.05859i
$667$	−283.414	+	72.1302i	−0.424908	+	0.108141i
$668$	315.509			0.472318
$669$	−135.516	−	135.516i	−0.202565	−	0.202565i
$670$	119.526	+	119.526i	0.178398	+	0.178398i
$671$			19.7176i			0.0293854i
$672$			189.290i			0.281681i
$673$		−	725.102i		−	1.07742i	−0.842492	−	0.538708i	$-0.818912\pi$
$673$		−	725.102i		−	1.07742i	0.842492	−	0.538708i	$-0.181088\pi$
$674$	−130.621			−0.193799
$675$	59.6829	−	59.6829i	0.0884191	−	0.0884191i
$676$		−	45.6673i		−	0.0675552i
$677$	650.790	−	650.790i	0.961285	−	0.961285i	−0.0379933	−	0.999278i	$-0.512097\pi$
$677$	650.790	−	650.790i	0.961285	−	0.961285i	0.999278	+	0.0379933i	$0.0120965\pi$
$678$	−16.3226	−	16.3226i	−0.0240746	−	0.0240746i
$679$	774.907	−	774.907i	1.14125	−	1.14125i
$680$			327.356i			0.481406i
$681$	8.77604	+	8.77604i	0.0128870	+	0.0128870i
$682$	−22.7328	+	22.7328i	−0.0333325	+	0.0333325i
$683$	−791.357			−1.15865			−0.579324	−	0.815097i	$-0.696683\pi$
$683$	−791.357			−1.15865			−0.579324	+	0.815097i	$0.696683\pi$
$684$	−296.112	−	296.112i	−0.432912	−	0.432912i
$685$	487.988	−	487.988i	0.712392	−	0.712392i
$686$	36.4808	+	36.4808i	0.0531790	+	0.0531790i
$687$	132.875			0.193413
$688$	−19.5751	−	19.5751i	−0.0284522	−	0.0284522i
$689$			1102.22i			1.59973i
$690$	33.8187			0.0490126
$691$	646.166			0.935118			0.467559	−	0.883962i	$-0.345134\pi$
$691$	646.166			0.935118			0.467559	+	0.883962i	$0.345134\pi$
$692$	220.870			0.319176
$693$	27.9320	−	27.9320i	0.0403059	−	0.0403059i
$694$	−165.149	+	165.149i	−0.237967	+	0.237967i
$695$			259.399i			0.373235i
$696$	143.604	−	36.5479i	0.206328	−	0.0525114i
$697$	310.719			0.445795
$698$	186.829	+	186.829i	0.267663	+	0.267663i
$699$	58.6220	+	58.6220i	0.0838656	+	0.0838656i
$700$			173.983i			0.248547i
$701$			738.399i			1.05335i	0.850066	+	0.526676i	$0.176562\pi$
$701$			738.399i			1.05335i	−0.850066	+	0.526676i	$0.823438\pi$
$702$			173.388i			0.246991i
$703$	−1320.69			−1.87864
$704$	−14.9450	+	14.9450i	−0.0212287	+	0.0212287i
$705$			8.14799i			0.0115574i
$706$	−137.260	+	137.260i	−0.194420	+	0.194420i
$707$	504.962	+	504.962i	0.714231	+	0.714231i
$708$	−93.8736	+	93.8736i	−0.132590	+	0.132590i
$709$		−	211.506i		−	0.298316i	−0.988813	−	0.149158i	$-0.952344\pi$
$709$		−	211.506i		−	0.298316i	0.988813	−	0.149158i	$-0.0476564\pi$
$710$	−378.293	−	378.293i	−0.532807	−	0.532807i
$711$	−347.008	+	347.008i	−0.488056	+	0.488056i
$712$	959.825			1.34807
$713$	376.249	+	376.249i	0.527699	+	0.527699i
$714$	53.1274	−	53.1274i	0.0744081	−	0.0744081i
$715$	17.0559	+	17.0559i	0.0238544	+	0.0238544i
$716$	130.608			0.182413
$717$	78.2135	+	78.2135i	0.109084	+	0.109084i
$718$		−	666.730i		−	0.928593i
$719$	−479.844			−0.667376			−0.333688	−	0.942684i	$-0.608293\pi$
$719$	−479.844			−0.667376			−0.333688	+	0.942684i	$0.608293\pi$
$720$	40.0921			0.0556835
$721$	−1350.31			−1.87283
$722$	−62.9974	+	62.9974i	−0.0872540	+	0.0872540i
$723$	−71.2728	+	71.2728i	−0.0985792	+	0.0985792i
$724$			309.294i			0.427202i
$725$	215.197	−	54.7687i	0.296824	−	0.0755431i
$726$	97.2578			0.133964
$727$	−943.499	−	943.499i	−1.29780	−	1.29780i	−0.929844	−	0.367953i	$-0.880059\pi$
$727$	−943.499	−	943.499i	−1.29780	−	1.29780i	−0.367953	−	0.929844i	$-0.619941\pi$
$728$	−683.753	−	683.753i	−0.939221	−	0.939221i
$729$			545.390i			0.748134i
$730$		−	30.0222i		−	0.0411263i
$731$		−	238.384i		−	0.326106i
$732$	−61.1179			−0.0834944
$733$	256.074	−	256.074i	0.349350	−	0.349350i	−0.510517	−	0.859868i	$-0.670546\pi$
$733$	256.074	−	256.074i	0.349350	−	0.349350i	0.859868	+	0.510517i	$0.170546\pi$
$734$		−	153.395i		−	0.208986i
$735$	−82.6973	+	82.6973i	−0.112513	+	0.112513i
$736$	222.555	+	222.555i	0.302385	+	0.302385i
$737$	−10.5685	+	10.5685i	−0.0143398	+	0.0143398i
$738$		−	357.262i		−	0.484095i
$739$	9.12101	+	9.12101i	0.0123424	+	0.0123424i	0.713251	−	0.700909i	$-0.247222\pi$
$739$	9.12101	+	9.12101i	0.0123424	+	0.0123424i	−0.700909	+	0.713251i	$0.747222\pi$
$740$	−439.722	+	439.722i	−0.594219	+	0.594219i
$741$	−158.786			−0.214286
$742$	−794.312	−	794.312i	−1.07050	−	1.07050i
$743$	−343.894	+	343.894i	−0.462845	+	0.462845i	−0.899587	−	0.436742i	$-0.856132\pi$
$743$	−343.894	+	343.894i	−0.462845	+	0.462845i	0.436742	+	0.899587i	$0.356132\pi$
$744$	−190.643	−	190.643i	−0.256241	−	0.256241i
$745$	587.175			0.788155
$746$	83.1437	+	83.1437i	0.111453	+	0.111453i
$747$		−	1185.46i		−	1.58696i
$748$	−10.6983			−0.0143025
$749$	144.980			0.193564
$750$	−109.517			−0.146023
$751$	485.159	−	485.159i	0.646017	−	0.646017i	−0.306011	−	0.952028i	$-0.598994\pi$
$751$	485.159	−	485.159i	0.646017	−	0.646017i	0.952028	+	0.306011i	$0.0989945\pi$
$752$	2.47162	−	2.47162i	0.00328673	−	0.00328673i
$753$			120.953i			0.160628i
$754$	−233.035	+	392.146i	−0.309065	+	0.520088i
$755$	−1120.66			−1.48432
$756$	177.101	+	177.101i	0.234261	+	0.234261i
$757$	−158.090	−	158.090i	−0.208838	−	0.208838i	0.594936	−	0.803773i	$-0.297178\pi$
$757$	−158.090	−	158.090i	−0.208838	−	0.208838i	−0.803773	+	0.594936i	$0.797178\pi$
$758$			323.852i			0.427246i
$759$			2.99023i			0.00393970i
$760$			705.078i			0.927734i
$761$	1412.54			1.85617			0.928084	−	0.372371i	$-0.121455\pi$
$761$	1412.54			1.85617			0.928084	+	0.372371i	$0.121455\pi$
$762$	−42.0527	+	42.0527i	−0.0551873	+	0.0551873i
$763$			374.179i			0.490405i
$764$	287.400	−	287.400i	0.376179	−	0.376179i
$765$	244.119	+	244.119i	0.319109	+	0.319109i
$766$	−129.237	+	129.237i	−0.168716	+	0.168716i
$767$		−	1105.70i		−	1.44159i
$768$	−117.412	−	117.412i	−0.152880	−	0.152880i
$769$	−137.717	+	137.717i	−0.179086	+	0.179086i	−0.790957	−	0.611871i	$-0.790417\pi$
$769$	−137.717	+	137.717i	−0.179086	+	0.179086i	0.611871	+	0.790957i	$0.290417\pi$
$770$	−24.5827			−0.0319256
$771$	−122.004	−	122.004i	−0.158242	−	0.158242i
$772$	−412.675	+	412.675i	−0.534553	+	0.534553i
$773$	−349.001	−	349.001i	−0.451489	−	0.451489i	0.444360	−	0.895848i	$-0.353431\pi$
$773$	−349.001	−	349.001i	−0.451489	−	0.451489i	−0.895848	+	0.444360i	$0.853431\pi$
$774$	−274.092			−0.354124
$775$	−285.688	−	285.688i	−0.368629	−	0.368629i
$776$			923.285i			1.18980i
$777$	386.154			0.496981
$778$	−617.964			−0.794298
$779$	669.244			0.859107
$780$	−52.8676	+	52.8676i	−0.0677790	+	0.0677790i
$781$	33.4485	−	33.4485i	0.0428278	−	0.0428278i
$782$		−	124.928i		−	0.159754i
$783$	163.304	−	274.805i	0.208562	−	0.350964i
$784$	50.1710			0.0639936
$785$	−344.269	−	344.269i	−0.438560	−	0.438560i
$786$	20.4396	+	20.4396i	0.0260045	+	0.0260045i
$787$			880.918i			1.11934i	0.828717	+	0.559668i	$0.189071\pi$
$787$			880.918i			1.11934i	−0.828717	+	0.559668i	$0.810929\pi$
$788$		−	100.308i		−	0.127295i
$789$		−	214.973i		−	0.272463i
$790$	305.398			0.386580
$791$	196.374	−	196.374i	0.248261	−	0.248261i
$792$			33.2804i			0.0420206i
$793$	359.941	−	359.941i	0.453898	−	0.453898i
$794$	−598.315	−	598.315i	−0.753545	−	0.753545i
$795$	−166.164	+	166.164i	−0.209011	+	0.209011i
$796$			238.592i			0.299738i
$797$	634.695	+	634.695i	0.796356	+	0.796356i	0.982519	−	0.186163i	$-0.0596053\pi$
$797$	634.695	+	634.695i	0.796356	+	0.796356i	−0.186163	+	0.982519i	$0.559605\pi$
$798$	114.429	−	114.429i	0.143395	−	0.143395i
$799$	30.0991			0.0376709
$800$	−168.987	−	168.987i	−0.211234	−	0.211234i
$801$	715.769	−	715.769i	0.893594	−	0.893594i
$802$	312.782	+	312.782i	0.390003	+	0.390003i
$803$	2.65455			0.00330579
$804$	−32.7587	−	32.7587i	−0.0407446	−	0.0407446i
$805$			406.867i			0.505425i
$806$	829.967			1.02974
$807$	148.516			0.184034
$808$	−601.651			−0.744617
$809$	−768.799	+	768.799i	−0.950308	+	0.950308i	−0.998822	−	0.0485143i	$-0.984551\pi$
$809$	−768.799	+	768.799i	−0.950308	+	0.950308i	0.0485143	+	0.998822i	$0.484551\pi$
$810$	267.325	−	267.325i	0.330031	−	0.330031i
$811$			615.818i			0.759332i	0.925124	+	0.379666i	$0.123961\pi$
$811$			615.818i			0.759332i	−0.925124	+	0.379666i	$0.876039\pi$
$812$	162.519	+	638.570i	0.200147	+	0.786416i
$813$	249.980			0.307479
$814$	27.4314	+	27.4314i	0.0336995	+	0.0336995i
$815$	67.3183	+	67.3183i	0.0825991	+	0.0825991i
$816$			6.74256i			0.00826294i
$817$		−	513.445i		−	0.628451i
$818$			399.605i			0.488514i
$819$	−1019.79			−1.24516
$820$	222.824	−	222.824i	0.271737	−	0.271737i
$821$		−	998.934i		−	1.21673i	−0.793658	−	0.608364i	$-0.791826\pi$
$821$		−	998.934i		−	1.21673i	0.793658	−	0.608364i	$-0.208174\pi$
$822$	94.3614	−	94.3614i	0.114795	−	0.114795i
$823$	−117.268	−	117.268i	−0.142489	−	0.142489i	0.632264	−	0.774753i	$-0.282126\pi$
$823$	−117.268	−	117.268i	−0.142489	−	0.142489i	−0.774753	+	0.632264i	$0.782126\pi$
$824$	804.431	−	804.431i	0.976251	−	0.976251i
$825$		−	2.27050i		−	0.00275212i
$826$	796.822	+	796.822i	0.964675	+	0.964675i
$827$	1079.32	−	1079.32i	1.30510	−	1.30510i	0.380195	−	0.924906i	$-0.375857\pi$
$827$	1079.32	−	1079.32i	1.30510	−	1.30510i	0.924906	−	0.380195i	$-0.124143\pi$
$828$	203.590			0.245882
$829$	671.650	+	671.650i	0.810192	+	0.810192i	0.984662	−	0.174470i	$-0.0558212\pi$
$829$	671.650	+	671.650i	0.810192	+	0.810192i	−0.174470	+	0.984662i	$0.555821\pi$
$830$	−521.656	+	521.656i	−0.628501	+	0.628501i
$831$	13.5154	+	13.5154i	0.0162640	+	0.0162640i
$832$	545.636			0.655813
$833$	305.488	+	305.488i	0.366732	+	0.366732i
$834$			50.1594i			0.0601432i
$835$	−560.239			−0.670945
$836$	−23.0426			−0.0275629
$837$	−581.617			−0.694883
$838$	−465.725	+	465.725i	−0.555758	+	0.555758i
$839$	−100.846	+	100.846i	−0.120197	+	0.120197i	−0.764647	−	0.644449i	$-0.777087\pi$
$839$	−100.846	+	100.846i	−0.120197	+	0.120197i	0.644449	+	0.764647i	$0.277087\pi$
$840$		−	206.157i		−	0.245425i
$841$	738.680	−	402.036i	0.878335	−	0.478045i
$842$	−776.262			−0.921926
$843$	−1.29346	−	1.29346i	−0.00153435	−	0.00153435i
$844$	−197.111	−	197.111i	−0.233544	−	0.233544i
$845$			81.0901i			0.0959646i
$846$		−	34.6077i		−	0.0409074i
$847$			1170.09i			1.38145i
$848$	100.808			0.118878
$849$	−11.9259	+	11.9259i	−0.0140470	+	0.0140470i
$850$			94.8582i			0.111598i
$851$	454.016	−	454.016i	0.533509	−	0.533509i
$852$	103.679	+	103.679i	0.121689	+	0.121689i
$853$	−922.579	+	922.579i	−1.08157	+	1.08157i	−0.0852066	+	0.996363i	$0.527155\pi$
$853$	−922.579	+	922.579i	−1.08157	+	1.08157i	−0.996363	+	0.0852066i	$0.972845\pi$
$854$			518.783i			0.607475i
$855$	525.797	+	525.797i	0.614967	+	0.614967i
$856$	−86.3700	+	86.3700i	−0.100900	+	0.100900i
$857$	−633.774			−0.739527			−0.369763	−	0.929126i	$-0.620561\pi$
$857$	−633.774			−0.739527			−0.369763	+	0.929126i	$0.620561\pi$
$858$	3.29807	+	3.29807i	0.00384390	+	0.00384390i
$859$	−834.541	+	834.541i	−0.971526	+	0.971526i	−0.999606	−	0.0280796i	$-0.991061\pi$
$859$	−834.541	+	834.541i	−0.971526	+	0.971526i	0.0280796	+	0.999606i	$0.491061\pi$
$860$	−170.951	−	170.951i	−0.198780	−	0.198780i
$861$	−195.680			−0.227270
$862$	542.695	+	542.695i	0.629577	+	0.629577i
$863$		−	805.408i		−	0.933265i	−0.884451	−	0.466632i	$-0.845467\pi$
$863$		−	805.408i		−	0.933265i	0.884451	−	0.466632i	$-0.154533\pi$
$864$	−344.032			−0.398185
$865$	−392.192			−0.453401
$866$	−76.1756			−0.0879626
$867$	86.8737	−	86.8737i	0.100200	−	0.100200i
$868$	847.741	−	847.741i	0.976660	−	0.976660i
$869$			27.0032i			0.0310739i
$870$	−94.2486	+	23.9867i	−0.108332	+	0.0275709i
$871$	385.851			0.442998
$872$	−222.913	−	222.913i	−0.255634	−	0.255634i
$873$	688.520	+	688.520i	0.788682	+	0.788682i
$874$		−	269.077i		−	0.307868i
$875$		−	1317.59i		−	1.50581i
$876$			8.22822i			0.00939294i
$877$	427.725			0.487714			0.243857	−	0.969811i	$-0.421587\pi$
$877$	427.725			0.487714			0.243857	+	0.969811i	$0.421587\pi$
$878$	313.414	−	313.414i	0.356964	−	0.356964i
$879$		−	226.438i		−	0.257609i
$880$	1.55993	−	1.55993i	0.00177265	−	0.00177265i
$881$	−977.952	−	977.952i	−1.11005	−	1.11005i	−0.993143	−	0.116905i	$-0.962703\pi$
$881$	−977.952	−	977.952i	−1.11005	−	1.11005i	−0.116905	−	0.993143i	$-0.537297\pi$
$882$	351.248	−	351.248i	0.398240	−	0.398240i
$883$		−	1215.83i		−	1.37693i	−0.725270	−	0.688464i	$-0.758285\pi$
$883$		−	1215.83i		−	1.37693i	0.725270	−	0.688464i	$-0.241715\pi$
$884$	195.296	+	195.296i	0.220923	+	0.220923i
$885$	166.689	−	166.689i	0.188349	−	0.188349i
$886$	−226.604			−0.255761
$887$	1221.32	+	1221.32i	1.37691	+	1.37691i	0.849790	+	0.527122i	$0.176729\pi$
$887$	1221.32	+	1221.32i	1.37691	+	1.37691i	0.527122	+	0.849790i	$0.323271\pi$
$888$	−230.047	+	230.047i	−0.259062	+	0.259062i
$889$	−505.929	−	505.929i	−0.569099	−	0.569099i
$890$	−629.942			−0.707800
$891$	23.6368	+	23.6368i	0.0265284	+	0.0265284i
$892$			717.990i			0.804922i
$893$	64.8291			0.0725970
$894$	113.541			0.127003
$895$	−231.916			−0.259124
$896$	462.025	−	462.025i	0.515653	−	0.515653i
$897$	54.5862	−	54.5862i	0.0608542	−	0.0608542i
$898$		−	1024.02i		−	1.14034i
$899$	−1315.43	−	781.698i	−1.46321	−	0.869519i
$900$	−154.587			−0.171763
$901$	613.816	+	613.816i	0.681261	+	0.681261i
$902$	−13.9006	−	13.9006i	−0.0154108	−	0.0154108i
$903$			150.125i			0.166252i
$904$			233.976i			0.258823i
$905$		−	549.204i		−	0.606856i
$906$	−216.700			−0.239183
$907$	−236.820	+	236.820i	−0.261103	+	0.261103i	−0.825502	−	0.564399i	$-0.809108\pi$
$907$	−236.820	+	236.820i	−0.261103	+	0.261103i	0.564399	+	0.825502i	$0.309108\pi$
$908$		−	46.4972i		−	0.0512083i
$909$	−448.668	+	448.668i	−0.493584	+	0.493584i
$910$	448.753	+	448.753i	0.493135	+	0.493135i
$911$	−807.445	+	807.445i	−0.886328	+	0.886328i	−0.994168	−	0.107840i	$-0.965606\pi$
$911$	−807.445	+	807.445i	−0.886328	+	0.886328i	0.107840	+	0.994168i	$0.465606\pi$
$912$			14.5225i			0.0159238i
$913$	−46.1246	−	46.1246i	−0.0505198	−	0.0505198i
$914$	−343.040	+	343.040i	−0.375317	+	0.375317i
$915$	108.525			0.118607
$916$	−351.999	−	351.999i	−0.384278	−	0.384278i
$917$	−245.905	+	245.905i	−0.268163	+	0.268163i
$918$	96.5585	+	96.5585i	0.105184	+	0.105184i
$919$	−791.267			−0.861009			−0.430504	−	0.902589i	$-0.641664\pi$
$919$	−791.267			−0.861009			−0.430504	+	0.902589i	$0.641664\pi$
$920$	−242.387	−	242.387i	−0.263464	−	0.263464i
$921$		−	8.14823i		−	0.00884715i
$922$	−72.9241			−0.0790934
$923$	−1221.19			−1.32307
$924$	6.73740			0.00729156
$925$	−344.736	+	344.736i	−0.372688	+	0.372688i
$926$	373.781	−	373.781i	0.403651	−	0.403651i
$927$		−	1199.77i		−	1.29425i
$928$	−778.086	−	462.381i	−0.838455	−	0.498256i
$929$	1491.46			1.60545			0.802724	−	0.596351i	$-0.203383\pi$
$929$	1491.46			1.60545			0.802724	+	0.596351i	$0.203383\pi$
$930$	125.121	+	125.121i	0.134539	+	0.134539i
$931$	657.978	+	657.978i	0.706743	+	0.706743i
$932$		−	310.591i		−	0.333252i
$933$			83.2999i			0.0892818i
$934$		−	776.881i		−	0.831778i
$935$	18.9966			0.0203173
$936$	607.527	−	607.527i	0.649068	−	0.649068i
$937$			910.587i			0.971811i	0.874011	+	0.485905i	$0.161510\pi$
$937$			910.587i			0.971811i	−0.874011	+	0.485905i	$0.838490\pi$
$938$	−278.064	+	278.064i	−0.296443	+	0.296443i
$939$	59.2113	+	59.2113i	0.0630578	+	0.0630578i
$940$	21.5848	−	21.5848i	0.0229626	−	0.0229626i
$941$			1302.28i			1.38393i	0.721929	+	0.691967i	$0.243256\pi$
$941$			1302.28i			1.38393i	−0.721929	+	0.691967i	$0.756744\pi$
$942$	−66.5707	−	66.5707i	−0.0706695	−	0.0706695i
$943$	−230.068	+	230.068i	−0.243974	+	0.243974i
$944$	−101.127			−0.107126
$945$	−314.473	−	314.473i	−0.332776	−	0.332776i
$946$	−10.6645	+	10.6645i	−0.0112733	+	0.0112733i
$947$	−455.078	−	455.078i	−0.480547	−	0.480547i	0.424759	−	0.905306i	$-0.360359\pi$
$947$	−455.078	−	455.078i	−0.480547	−	0.480547i	−0.905306	+	0.424759i	$0.860359\pi$
$948$	−83.7008			−0.0882920
$949$	−48.4584	−	48.4584i	−0.0510626	−	0.0510626i
$950$			204.311i			0.215064i
$951$	358.846			0.377335
$952$	−761.554			−0.799952
$953$	299.880			0.314670			0.157335	−	0.987545i	$-0.449710\pi$
$953$	299.880			0.314670			0.157335	+	0.987545i	$0.449710\pi$
$954$	705.761	−	705.761i	0.739792	−	0.739792i
$955$	−510.328	+	510.328i	−0.534375	+	0.534375i
$956$		−	414.391i		−	0.433463i
$957$	−2.12090	−	8.33342i	−0.00221619	−	0.00870785i
$958$	406.772			0.424606
$959$	1135.25	+	1135.25i	1.18378	+	1.18378i
$960$	82.2569	+	82.2569i	0.0856842	+	0.0856842i
$961$			1823.06i			1.89705i
$962$		−	1001.51i		−	1.04107i
$963$			128.817i			0.133766i
$964$	377.617			0.391719
$965$	732.775	−	732.775i	0.759352	−	0.759352i
$966$			78.6751i			0.0814442i
$967$	136.707	−	136.707i	0.141372	−	0.141372i	−0.632879	−	0.774251i	$-0.718127\pi$
$967$	136.707	−	136.707i	0.141372	−	0.141372i	0.774251	+	0.632879i	$0.218127\pi$
$968$	−697.070	−	697.070i	−0.720113	−	0.720113i
$969$	−88.4266	+	88.4266i	−0.0912556	+	0.0912556i
$970$		−	605.960i		−	0.624701i
$971$	225.421	+	225.421i	0.232153	+	0.232153i	0.813591	−	0.581438i	$-0.197510\pi$
$971$	225.421	+	225.421i	0.232153	+	0.232153i	−0.581438	+	0.813591i	$0.697510\pi$
$972$	−237.788	+	237.788i	−0.244638	+	0.244638i
$973$	−603.459			−0.620205
$974$	361.115	+	361.115i	0.370755	+	0.370755i
$975$	−41.4475	+	41.4475i	−0.0425103	+	0.0425103i
$976$	−32.9201	−	32.9201i	−0.0337297	−	0.0337297i
$977$	119.816			0.122637			0.0613186	−	0.998118i	$-0.480469\pi$
$977$	119.816			0.122637			0.0613186	+	0.998118i	$0.480469\pi$
$978$	13.0172	+	13.0172i	0.0133100	+	0.0133100i
$979$		−	55.6992i		−	0.0568939i
$980$	438.147			0.447088
$981$	−332.465			−0.338904
$982$	−802.635			−0.817348
$983$	727.465	−	727.465i	0.740046	−	0.740046i	−0.232540	−	0.972587i	$-0.574704\pi$
$983$	727.465	−	727.465i	0.740046	−	0.740046i	0.972587	+	0.232540i	$0.0747038\pi$
$984$	116.574	−	116.574i	0.118469	−	0.118469i
$985$			178.114i			0.180827i
$986$	88.6081	+	348.159i	0.0898662	+	0.353102i
$987$	−18.9553			−0.0192050
$988$	420.639	+	420.639i	0.425748	+	0.425748i
$989$	176.508	+	176.508i	0.178471	+	0.178471i
$990$		−	21.8422i		−	0.0220628i
$991$			76.7646i			0.0774617i	0.999250	+	0.0387309i	$0.0123315\pi$
$991$			76.7646i			0.0774617i	−0.999250	+	0.0387309i	$0.987669\pi$
$992$			1646.80i			1.66008i
$993$	163.879			0.165035
$994$	880.053	−	880.053i	0.885365	−	0.885365i
$995$		−	423.660i		−	0.425789i
$996$	142.971	−	142.971i	0.143545	−	0.143545i
$997$	−352.075	−	352.075i	−0.353135	−	0.353135i	0.508140	−	0.861275i	$-0.330333\pi$
$997$	−352.075	−	352.075i	−0.353135	−	0.353135i	−0.861275	+	0.508140i	$0.830333\pi$
$998$	−86.3627	+	86.3627i	−0.0865358	+	0.0865358i
$999$			701.831i			0.702533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.3.c.a.12.3	✓	8
3.2	odd	2		261.3.f.a.244.2		8
4.3	odd	2		464.3.l.c.273.2		8
29.17	odd	4	inner	29.3.c.a.17.3	yes	8
87.17	even	4		261.3.f.a.46.2		8
116.75	even	4		464.3.l.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.3	✓	8	1.1	even	1	trivial
29.3.c.a.17.3	yes	8	29.17	odd	4	inner
261.3.f.a.46.2		8	87.17	even	4
261.3.f.a.244.2		8	3.2	odd	2
464.3.l.c.17.2		8	116.75	even	4
464.3.l.c.273.2		8	4.3	odd	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +O(q^{10})\)	\(q+(0.909588 + 0.909588i) q^{2} +(0.442660 + 0.442660i) q^{3} -2.34530i q^{4} +4.16447i q^{5} +0.805276i q^{6} -9.68815 q^{7} +(5.77161 - 5.77161i) q^{8} -8.60810i q^{9} +(-3.78796 + 3.78796i) q^{10} +(-0.334930 - 0.334930i) q^{11} +(1.03817 - 1.03817i) q^{12} +12.2282i q^{13} +(-8.81223 - 8.81223i) q^{14} +(-1.84345 + 1.84345i) q^{15} +1.11839 q^{16} +(6.80978 + 6.80978i) q^{17} +(7.82983 - 7.82983i) q^{18} +(14.6673 + 14.6673i) q^{19} +9.76693 q^{20} +(-4.28855 - 4.28855i) q^{21} -0.609296i q^{22} -10.0844 q^{23} +5.10972 q^{24} +7.65715 q^{25} +(-11.1226 + 11.1226i) q^{26} +(7.79440 - 7.79440i) q^{27} +22.7216i q^{28} +(28.1041 - 7.15263i) q^{29} -3.35355 q^{30} +(-37.3099 - 37.3099i) q^{31} +(-22.0692 - 22.0692i) q^{32} -0.296520i q^{33} +12.3882i q^{34} -40.3460i q^{35} -20.1886 q^{36} +(-45.0215 + 45.0215i) q^{37} +26.6824i q^{38} +(-5.41292 + 5.41292i) q^{39} +(24.0357 + 24.0357i) q^{40} +(22.8142 - 22.8142i) q^{41} -7.80164i q^{42} +(-17.5030 - 17.5030i) q^{43} +(-0.785510 + 0.785510i) q^{44} +35.8482 q^{45} +(-9.17268 - 9.17268i) q^{46} +(2.20999 - 2.20999i) q^{47} +(0.495064 + 0.495064i) q^{48} +44.8602 q^{49} +(6.96485 + 6.96485i) q^{50} +6.02883i q^{51} +28.6787 q^{52} +90.1375 q^{53} +14.1794 q^{54} +(1.39481 - 1.39481i) q^{55} +(-55.9162 + 55.9162i) q^{56} +12.9852i q^{57} +(32.0691 + 19.0572i) q^{58} -90.4223 q^{59} +(4.32343 + 4.32343i) q^{60} +(-29.4354 - 29.4354i) q^{61} -67.8734i q^{62} +83.3966i q^{63} -44.6213i q^{64} -50.9239 q^{65} +(0.269711 - 0.269711i) q^{66} -31.5543i q^{67} +(15.9710 - 15.9710i) q^{68} +(-4.46397 - 4.46397i) q^{69} +(36.6983 - 36.6983i) q^{70} +99.8673i q^{71} +(-49.6826 - 49.6826i) q^{72} +(-3.96285 + 3.96285i) q^{73} -81.9020 q^{74} +(3.38951 + 3.38951i) q^{75} +(34.3992 - 34.3992i) q^{76} +(3.24485 + 3.24485i) q^{77} -9.84706 q^{78} +(-40.3117 - 40.3117i) q^{79} +4.65749i q^{80} -70.5724 q^{81} +41.5030 q^{82} +137.714 q^{83} +(-10.0579 + 10.0579i) q^{84} +(-28.3592 + 28.3592i) q^{85} -31.8411i q^{86} +(15.6067 + 9.27437i) q^{87} -3.86616 q^{88} +(83.1506 + 83.1506i) q^{89} +(32.6071 + 32.6071i) q^{90} -118.468i q^{91} +23.6510i q^{92} -33.0312i q^{93} +4.02036 q^{94} +(-61.0816 + 61.0816i) q^{95} -19.5383i q^{96} +(-79.9850 + 79.9850i) q^{97} +(40.8043 + 40.8043i) q^{98} +(-2.88311 + 2.88311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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