LMFDB - Embedded newform 29.3.c.a.17.2

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			17.2
Root			$3.22189i$ of defining polynomial
Character	$\chi$	$=$	29.17
Dual form			29.3.c.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +O(q^{10})$	\(q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +(-0.527467 - 0.527467i) q^{10} +(11.3195 - 11.3195i) q^{11} +(-3.57807 - 3.57807i) q^{12} +10.0463i q^{13} +(-8.73320 + 8.73320i) q^{14} +(-1.04704 - 1.04704i) q^{15} +6.53103 q^{16} +(-9.69799 + 9.69799i) q^{17} +(0.195342 + 0.195342i) q^{18} +(8.58453 - 8.58453i) q^{19} -0.816116 q^{20} +(-17.3357 + 17.3357i) q^{21} +24.4355i q^{22} -14.4215 q^{23} +26.2244 q^{24} +24.7612 q^{25} +(-10.8434 - 10.8434i) q^{26} +(-18.8951 - 18.8951i) q^{27} +13.5123i q^{28} +(-11.8706 - 26.4592i) q^{29} +2.26024 q^{30} +(31.2221 - 31.2221i) q^{31} +(17.4304 - 17.4304i) q^{32} +48.5052i q^{33} -20.9350i q^{34} +3.95407i q^{35} +0.302241 q^{36} +(-31.2631 - 31.2631i) q^{37} +18.5314i q^{38} +(-21.5246 - 21.5246i) q^{39} +(2.99074 - 2.99074i) q^{40} +(19.6337 + 19.6337i) q^{41} -37.4225i q^{42} +(-50.2394 + 50.2394i) q^{43} +(18.9037 + 18.9037i) q^{44} +0.0884438 q^{45} +(15.5658 - 15.5658i) q^{46} +(42.2268 + 42.2268i) q^{47} +(-13.9930 + 13.9930i) q^{48} +16.4671 q^{49} +(-26.7260 + 26.7260i) q^{50} -41.5567i q^{51} -16.7774 q^{52} +16.5613 q^{53} +40.7889 q^{54} +(5.53173 + 5.53173i) q^{55} +(-49.5173 - 49.5173i) q^{56} +36.7855i q^{57} +(41.3713 + 15.7461i) q^{58} -14.5041 q^{59} +(1.74856 - 1.74856i) q^{60} +(-45.3849 + 45.3849i) q^{61} +67.3992i q^{62} -1.46435i q^{63} +63.7512i q^{64} -4.90950 q^{65} +(-52.3540 - 52.3540i) q^{66} -133.589i q^{67} +(-16.1957 - 16.1957i) q^{68} +(30.8987 - 30.8987i) q^{69} +(-4.26782 - 4.26782i) q^{70} -33.9204i q^{71} +(-1.10759 + 1.10759i) q^{72} +(-22.1752 - 22.1752i) q^{73} +67.4877 q^{74} +(-53.0519 + 53.0519i) q^{75} +(14.3363 + 14.3363i) q^{76} +(91.5883 - 91.5883i) q^{77} +46.4651 q^{78} +(9.72981 - 9.72981i) q^{79} +3.19164i q^{80} +82.5961 q^{81} -42.3833 q^{82} +64.2570 q^{83} +(-28.9508 - 28.9508i) q^{84} +(-4.73930 - 4.73930i) q^{85} -108.452i q^{86} +(82.1233 + 31.2565i) q^{87} -138.549 q^{88} +(-119.740 + 119.740i) q^{89} +(-0.0954618 + 0.0954618i) q^{90} +81.2861i q^{91} -24.0840i q^{92} +133.790i q^{93} -91.1550 q^{94} +(4.19517 + 4.19517i) q^{95} +74.6909i q^{96} +(-33.5755 - 33.5755i) q^{97} +(-17.7737 + 17.7737i) q^{98} +(-2.04863 - 2.04863i) 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.07935	+	1.07935i	−0.539675	+	0.539675i	−0.923433	−	0.383759i	$-0.874629\pi$
$2$	−1.07935	+	1.07935i	−0.539675	+	0.539675i	0.383759	+	0.923433i	$0.374629\pi$
$3$	−2.14254	+	2.14254i	−0.714181	+	0.714181i	−0.967407	−	0.253226i	$-0.918508\pi$
$3$	−2.14254	+	2.14254i	−0.714181	+	0.714181i	0.253226	+	0.967407i	$0.418508\pi$
$4$			1.67001i			0.417502i
$5$			0.488689i			0.0977379i	0.998805	+	0.0488689i	$0.0155617\pi$
$5$			0.488689i			0.0977379i	−0.998805	+	0.0488689i	$0.984438\pi$
$6$		−	4.62511i		−	0.770851i
$7$	8.09117			1.15588			0.577941	−	0.816079i	$-0.303856\pi$
$7$	8.09117			1.15588			0.577941	+	0.816079i	$0.303856\pi$
$8$	−6.11992	−	6.11992i	−0.764990	−	0.764990i
$9$		−	0.180982i		−	0.0201091i
$10$	−0.527467	−	0.527467i	−0.0527467	−	0.0527467i
$11$	11.3195	−	11.3195i	1.02905	−	1.02905i	0.0294830	−	0.999565i	$-0.490614\pi$
$11$	11.3195	−	11.3195i	1.02905	−	1.02905i	0.999565	−	0.0294830i	$-0.00938610\pi$
$12$	−3.57807	−	3.57807i	−0.298172	−	0.298172i
$13$			10.0463i			0.772790i	0.922333	+	0.386395i	$0.126280\pi$
$13$			10.0463i			0.772790i	−0.922333	+	0.386395i	$0.873720\pi$
$14$	−8.73320	+	8.73320i	−0.623800	+	0.623800i
$15$	−1.04704	−	1.04704i	−0.0698025	−	0.0698025i
$16$	6.53103			0.408189
$17$	−9.69799	+	9.69799i	−0.570470	+	0.570470i	−0.932260	−	0.361790i	$-0.882166\pi$
$17$	−9.69799	+	9.69799i	−0.570470	+	0.570470i	0.361790	+	0.932260i	$0.382166\pi$
$18$	0.195342	+	0.195342i	0.0108524	+	0.0108524i
$19$	8.58453	−	8.58453i	0.451818	−	0.451818i	−0.444140	−	0.895957i	$-0.646491\pi$
$19$	8.58453	−	8.58453i	0.451818	−	0.451818i	0.895957	+	0.444140i	$0.146491\pi$
$20$	−0.816116			−0.0408058
$21$	−17.3357	+	17.3357i	−0.825509	+	0.825509i
$22$			24.4355i			1.11070i
$23$	−14.4215			−0.627022			−0.313511	−	0.949585i	$-0.601505\pi$
$23$	−14.4215			−0.627022			−0.313511	+	0.949585i	$0.601505\pi$
$24$	26.2244			1.09268
$25$	24.7612			0.990447
$26$	−10.8434	−	10.8434i	−0.417055	−	0.417055i
$27$	−18.8951	−	18.8951i	−0.699820	−	0.699820i
$28$			13.5123i			0.482583i
$29$	−11.8706	−	26.4592i	−0.409333	−	0.912385i
$29$	−11.8706	−	26.4592i	−0.409333	−	0.912385i
$30$	2.26024			0.0753413
$31$	31.2221	−	31.2221i	1.00717	−	1.00717i	0.00719198	−	0.999974i	$-0.497711\pi$
$31$	31.2221	−	31.2221i	1.00717	−	1.00717i	0.999974	−	0.00719198i	$-0.00228930\pi$
$32$	17.4304	−	17.4304i	0.544701	−	0.544701i
$33$			48.5052i			1.46985i
$34$		−	20.9350i		−	0.615736i
$35$			3.95407i			0.112973i
$36$	0.302241			0.00839559
$37$	−31.2631	−	31.2631i	−0.844950	−	0.844950i	0.144548	−	0.989498i	$-0.453827\pi$
$37$	−31.2631	−	31.2631i	−0.844950	−	0.844950i	−0.989498	+	0.144548i	$0.953827\pi$
$38$			18.5314i			0.487669i
$39$	−21.5246	−	21.5246i	−0.551912	−	0.551912i
$40$	2.99074	−	2.99074i	0.0747685	−	0.0747685i
$41$	19.6337	+	19.6337i	0.478871	+	0.478871i	0.904770	−	0.425900i	$-0.140042\pi$
$41$	19.6337	+	19.6337i	0.478871	+	0.478871i	−0.425900	+	0.904770i	$0.640042\pi$
$42$		−	37.4225i		−	0.891013i
$43$	−50.2394	+	50.2394i	−1.16836	+	1.16836i	−0.185764	+	0.982594i	$0.559476\pi$
$43$	−50.2394	+	50.2394i	−1.16836	+	1.16836i	−0.982594	+	0.185764i	$0.940524\pi$
$44$	18.9037	+	18.9037i	0.429630	+	0.429630i
$45$	0.0884438			0.00196542
$46$	15.5658	−	15.5658i	0.338388	−	0.338388i
$47$	42.2268	+	42.2268i	0.898443	+	0.898443i	0.995298	−	0.0968555i	$-0.0308785\pi$
$47$	42.2268	+	42.2268i	0.898443	+	0.898443i	−0.0968555	+	0.995298i	$0.530878\pi$
$48$	−13.9930	+	13.9930i	−0.291521	+	0.291521i
$49$	16.4671			0.336063
$50$	−26.7260	+	26.7260i	−0.534519	+	0.534519i
$51$		−	41.5567i		−	0.814838i
$52$	−16.7774			−0.322642
$53$	16.5613			0.312477			0.156239	−	0.987719i	$-0.450063\pi$
$53$	16.5613			0.312477			0.156239	+	0.987719i	$0.450063\pi$
$54$	40.7889			0.755350
$55$	5.53173	+	5.53173i	0.100577	+	0.100577i
$56$	−49.5173	−	49.5173i	−0.884238	−	0.884238i
$57$			36.7855i			0.645359i
$58$	41.3713	+	15.7461i	0.713298	+	0.271485i
$59$	−14.5041			−0.245833			−0.122916	−	0.992417i	$-0.539225\pi$
$59$	−14.5041			−0.245833			−0.122916	+	0.992417i	$0.539225\pi$
$60$	1.74856	−	1.74856i	0.0291427	−	0.0291427i
$61$	−45.3849	+	45.3849i	−0.744014	+	0.744014i	−0.973348	−	0.229334i	$-0.926345\pi$
$61$	−45.3849	+	45.3849i	−0.744014	+	0.744014i	0.229334	+	0.973348i	$0.426345\pi$
$62$			67.3992i			1.08708i
$63$		−	1.46435i		−	0.0232437i
$64$			63.7512i			0.996112i
$65$	−4.90950			−0.0755308
$66$	−52.3540	−	52.3540i	−0.793243	−	0.793243i
$67$		−	133.589i		−	1.99386i	−0.0782703	−	0.996932i	$-0.524940\pi$
$67$		−	133.589i		−	1.99386i	0.0782703	−	0.996932i	$-0.475060\pi$
$68$	−16.1957	−	16.1957i	−0.238173	−	0.238173i
$69$	30.8987	−	30.8987i	0.447807	−	0.447807i
$70$	−4.26782	−	4.26782i	−0.0609689	−	0.0609689i
$71$		−	33.9204i		−	0.477752i	−0.971050	−	0.238876i	$-0.923221\pi$
$71$		−	33.9204i		−	0.477752i	0.971050	−	0.238876i	$-0.0767790\pi$
$72$	−1.10759	+	1.10759i	−0.0153832	+	0.0153832i
$73$	−22.1752	−	22.1752i	−0.303770	−	0.303770i	0.538717	−	0.842487i	$-0.318909\pi$
$73$	−22.1752	−	22.1752i	−0.303770	−	0.303770i	−0.842487	+	0.538717i	$0.818909\pi$
$74$	67.4877			0.911996
$75$	−53.0519	+	53.0519i	−0.707359	+	0.707359i
$76$	14.3363	+	14.3363i	0.188635	+	0.188635i
$77$	91.5883	−	91.5883i	1.18946	−	1.18946i
$78$	46.4651			0.595706
$79$	9.72981	−	9.72981i	0.123162	−	0.123162i	−0.642839	−	0.766001i	$-0.722244\pi$
$79$	9.72981	−	9.72981i	0.123162	−	0.123162i	0.766001	+	0.642839i	$0.222244\pi$
$80$			3.19164i			0.0398956i
$81$	82.5961			1.01970
$82$	−42.3833			−0.516869
$83$	64.2570			0.774181			0.387091	−	0.922042i	$-0.373480\pi$
$83$	64.2570			0.774181			0.387091	+	0.922042i	$0.373480\pi$
$84$	−28.9508	−	28.9508i	−0.344652	−	0.344652i
$85$	−4.73930	−	4.73930i	−0.0557565	−	0.0557565i
$86$		−	108.452i		−	1.26107i
$87$	82.1233	+	31.2565i	0.943946	+	0.359271i
$88$	−138.549			−1.57442
$89$	−119.740	+	119.740i	−1.34540	+	1.34540i	−0.454808	+	0.890590i	$0.650292\pi$
$89$	−119.740	+	119.740i	−1.34540	+	1.34540i	−0.890590	+	0.454808i	$0.849708\pi$
$90$	−0.0954618	+	0.0954618i	−0.00106069	+	0.00106069i
$91$			81.2861i			0.893254i
$92$		−	24.0840i		−	0.261783i
$93$			133.790i			1.43860i
$94$	−91.1550			−0.969734
$95$	4.19517	+	4.19517i	0.0441597	+	0.0441597i
$96$			74.6909i			0.778030i
$97$	−33.5755	−	33.5755i	−0.346139	−	0.346139i	0.512530	−	0.858669i	$-0.328708\pi$
$97$	−33.5755	−	33.5755i	−0.346139	−	0.346139i	−0.858669	+	0.512530i	$0.828708\pi$
$98$	−17.7737	+	17.7737i	−0.181365	+	0.181365i
$99$	−2.04863	−	2.04863i	−0.0206932	−	0.0206932i
$100$			41.3514i			0.413514i
$101$	−38.2463	+	38.2463i	−0.378676	+	0.378676i	−0.870624	−	0.491948i	$-0.836285\pi$
$101$	−38.2463	+	38.2463i	−0.378676	+	0.378676i	0.491948	+	0.870624i	$0.336285\pi$
$102$	44.8542	+	44.8542i	0.439747	+	0.439747i
$103$	61.6568			0.598609			0.299305	−	0.954158i	$-0.403245\pi$
$103$	61.6568			0.598609			0.299305	+	0.954158i	$0.403245\pi$
$104$	61.4824	−	61.4824i	0.591177	−	0.591177i
$105$	−8.47176	−	8.47176i	−0.0806835	−	0.0806835i
$106$	−17.8754	+	17.8754i	−0.168636	+	0.168636i
$107$	−48.5836			−0.454052			−0.227026	−	0.973889i	$-0.572900\pi$
$107$	−48.5836			−0.454052			−0.227026	+	0.973889i	$0.572900\pi$
$108$	31.5550	−	31.5550i	0.292176	−	0.292176i
$109$		−	82.0131i		−	0.752414i	−0.926536	−	0.376207i	$-0.877228\pi$
$109$		−	82.0131i		−	0.752414i	0.926536	−	0.376207i	$-0.122772\pi$
$110$	−11.9413			−0.108558
$111$	133.965			1.20689
$112$	52.8437			0.471819
$113$	0.444855	+	0.444855i	0.00393677	+	0.00393677i	0.709072	−	0.705136i	$-0.249114\pi$
$113$	0.444855	+	0.444855i	0.00393677	+	0.00393677i	−0.705136	+	0.709072i	$0.749114\pi$
$114$	−39.7044	−	39.7044i	−0.348284	−	0.348284i
$115$		−	7.04763i		−	0.0612838i
$116$	44.1871	−	19.8241i	0.380923	−	0.170897i
$117$	1.81819			0.0155401
$118$	15.6550	−	15.6550i	0.132670	−	0.132670i
$119$	−78.4681	+	78.4681i	−0.659396	+	0.659396i
$120$			12.8156i			0.106796i
$121$		−	135.264i		−	1.11788i
$122$		−	97.9722i		−	0.803051i
$123$	−84.1321			−0.684001
$124$	52.1413	+	52.1413i	0.420494	+	0.420494i
$125$			24.3178i			0.194542i
$126$	1.58055	+	1.58055i	0.0125440	+	0.0125440i
$127$	−21.4010	+	21.4010i	−0.168512	+	0.168512i	−0.786325	−	0.617813i	$-0.788019\pi$
$127$	−21.4010	+	21.4010i	−0.168512	+	0.168512i	0.617813	+	0.786325i	$0.288019\pi$
$128$	0.911922	+	0.911922i	0.00712439	+	0.00712439i
$129$		−	215.280i		−	1.66884i
$130$	5.29907	−	5.29907i	0.0407621	−	0.0407621i
$131$	−46.6907	−	46.6907i	−0.356417	−	0.356417i	0.506073	−	0.862491i	$-0.331097\pi$
$131$	−46.6907	−	46.6907i	−0.356417	−	0.356417i	−0.862491	+	0.506073i	$0.831097\pi$
$132$	−81.0041			−0.613667
$133$	69.4589	−	69.4589i	0.522248	−	0.522248i
$134$	144.189	+	144.189i	1.07604	+	1.07604i
$135$	9.23385	−	9.23385i	0.0683989	−	0.0683989i
$136$	118.702			0.872808
$137$	5.76576	−	5.76576i	0.0420858	−	0.0420858i	−0.685751	−	0.727837i	$-0.740526\pi$
$137$	5.76576	−	5.76576i	0.0420858	−	0.0420858i	0.727837	+	0.685751i	$0.240526\pi$
$138$			66.7010i			0.483340i
$139$	−223.985			−1.61140			−0.805701	−	0.592322i	$-0.798211\pi$
$139$	−223.985			−1.61140			−0.805701	+	0.592322i	$0.798211\pi$
$140$	−6.60333			−0.0471667
$141$	−180.946			−1.28330
$142$	36.6120	+	36.6120i	0.257831	+	0.257831i
$143$	113.719	+	113.719i	0.795238	+	0.795238i
$144$		−	1.18200i		−	0.00820831i
$145$	12.9303	−	5.80106i	0.0891746	−	0.0400073i
$146$	47.8696			0.327874
$147$	−35.2814	+	35.2814i	−0.240010	+	0.240010i
$148$	52.2097	−	52.2097i	0.352769	−	0.352769i
$149$		−	129.230i		−	0.867316i	−0.901078	−	0.433658i	$-0.857223\pi$
$149$		−	129.230i		−	0.867316i	0.901078	−	0.433658i	$-0.142777\pi$
$150$		−	114.523i		−	0.763487i
$151$			59.3971i			0.393359i	0.980468	+	0.196679i	$0.0630158\pi$
$151$			59.3971i			0.393359i	−0.980468	+	0.196679i	$0.936984\pi$
$152$	−105.073			−0.691272
$153$	1.75516	+	1.75516i	0.0114716	+	0.0114716i
$154$			197.712i			1.28384i
$155$	15.2579	+	15.2579i	0.0984383	+	0.0984383i
$156$	35.9462	−	35.9462i	0.230425	−	0.230425i
$157$	210.885	+	210.885i	1.34321	+	1.34321i	0.892840	+	0.450374i	$0.148709\pi$
$157$	210.885	+	210.885i	1.34321	+	1.34321i	0.450374	+	0.892840i	$0.351291\pi$
$158$			21.0037i			0.132935i
$159$	−35.4833	+	35.4833i	−0.223165	+	0.223165i
$160$	8.51806	+	8.51806i	0.0532379	+	0.0532379i
$161$	−116.687			−0.724763
$162$	−89.1500	+	89.1500i	−0.550309	+	0.550309i
$163$	−151.656	−	151.656i	−0.930405	−	0.930405i	0.0673260	−	0.997731i	$-0.478553\pi$
$163$	−151.656	−	151.656i	−0.930405	−	0.930405i	−0.997731	+	0.0673260i	$0.978553\pi$
$164$	−32.7885	+	32.7885i	−0.199930	+	0.199930i
$165$	−23.7040			−0.143660
$166$	−69.3558	+	69.3558i	−0.417806	+	0.417806i
$167$			117.024i			0.700743i	0.936611	+	0.350371i	$0.113945\pi$
$167$			117.024i			0.700743i	−0.936611	+	0.350371i	$0.886055\pi$
$168$	212.186			1.26301
$169$	68.0725			0.402796
$170$	10.2307			0.0601808
$171$	−1.55364	−	1.55364i	−0.00908563	−	0.00908563i
$172$	−83.9003	−	83.9003i	−0.487792	−	0.487792i
$173$		−	51.3836i		−	0.297015i	−0.988911	−	0.148508i	$-0.952553\pi$
$173$		−	51.3836i		−	0.297015i	0.988911	−	0.148508i	$-0.0474469\pi$
$174$	−122.376	+	54.9030i	−0.703313	+	0.315534i
$175$	200.347			1.14484
$176$	73.9282	−	73.9282i	0.420047	−	0.420047i
$177$	31.0757	−	31.0757i	0.175569	−	0.175569i
$178$		−	258.483i		−	1.45215i
$179$			292.744i			1.63544i	0.575615	+	0.817721i	$0.304763\pi$
$179$			292.744i			1.63544i	−0.575615	+	0.817721i	$0.695237\pi$
$180$			0.147702i			0.000820567i
$181$	175.159			0.967728			0.483864	−	0.875143i	$-0.339233\pi$
$181$	175.159			0.967728			0.483864	+	0.875143i	$0.339233\pi$
$182$	−87.7361	−	87.7361i	−0.482067	−	0.482067i
$183$		−	194.478i		−	1.06272i
$184$	88.2585	+	88.2585i	0.479666	+	0.479666i
$185$	15.2780	−	15.2780i	0.0825836	−	0.0825836i
$186$	−144.406	−	144.406i	−0.776375	−	0.776375i
$187$			219.553i			1.17408i
$188$	−70.5192	+	70.5192i	−0.375102	+	0.375102i
$189$	−152.884	−	152.884i	−0.808909	−	0.808909i
$190$	−9.05611			−0.0476637
$191$	46.8745	−	46.8745i	0.245416	−	0.245416i	−0.573670	−	0.819086i	$-0.694481\pi$
$191$	46.8745	−	46.8745i	0.245416	−	0.245416i	0.819086	+	0.573670i	$0.194481\pi$
$192$	−136.590	−	136.590i	−0.711404	−	0.711404i
$193$	49.8678	−	49.8678i	0.258382	−	0.258382i	−0.566014	−	0.824396i	$-0.691515\pi$
$193$	49.8678	−	49.8678i	0.258382	−	0.258382i	0.824396	+	0.566014i	$0.191515\pi$
$194$	72.4794			0.373605
$195$	10.5188	−	10.5188i	0.0539427	−	0.0539427i
$196$			27.5002i			0.140307i
$197$	−59.7514			−0.303307			−0.151653	−	0.988434i	$-0.548460\pi$
$197$	−59.7514			−0.303307			−0.151653	+	0.988434i	$0.548460\pi$
$198$	4.42237			0.0223352
$199$	−10.7830			−0.0541859			−0.0270929	−	0.999633i	$-0.508625\pi$
$199$	−10.7830			−0.0541859			−0.0270929	+	0.999633i	$0.508625\pi$
$200$	−151.536	−	151.536i	−0.757682	−	0.757682i
$201$	286.220	+	286.220i	1.42398	+	1.42398i
$202$		−	82.5622i		−	0.408724i
$203$	−96.0474	−	214.086i	−0.473140	−	1.05461i
$204$	69.4001			0.340197
$205$	−9.59478	+	9.59478i	−0.0468038	+	0.0468038i
$206$	−66.5492	+	66.5492i	−0.323054	+	0.323054i
$207$			2.61003i			0.0126088i
$208$			65.6125i			0.315445i
$209$		−	194.346i		−	0.929884i
$210$	18.2880			0.0870857
$211$	71.2119	+	71.2119i	0.337497	+	0.337497i	0.855424	−	0.517928i	$-0.173296\pi$
$211$	71.2119	+	71.2119i	0.337497	+	0.337497i	−0.517928	+	0.855424i	$0.673296\pi$
$212$			27.6575i			0.130460i
$213$	72.6759	+	72.6759i	0.341201	+	0.341201i
$214$	52.4387	−	52.4387i	0.245041	−	0.245041i
$215$	−24.5515	−	24.5515i	−0.114193	−	0.114193i
$216$			231.273i			1.07071i
$217$	252.624	−	252.624i	1.16417	−	1.16417i
$218$	88.5208	+	88.5208i	0.406059	+	0.406059i
$219$	95.0227			0.433894
$220$	−9.23805	+	9.23805i	−0.0419911	+	0.0419911i
$221$	−97.4286	−	97.4286i	−0.440853	−	0.440853i
$222$	−144.595	+	144.595i	−0.651330	+	0.651330i
$223$	−166.943			−0.748625			−0.374312	−	0.927303i	$-0.622121\pi$
$223$	−166.943			−0.748625			−0.374312	+	0.927303i	$0.622121\pi$
$224$	141.033	−	141.033i	0.629610	−	0.629610i
$225$		−	4.48132i		−	0.0199170i
$226$	−0.960307			−0.00424915
$227$	−120.332			−0.530095			−0.265048	−	0.964235i	$-0.585388\pi$
$227$	−120.332			−0.530095			−0.265048	+	0.964235i	$0.585388\pi$
$228$	−61.4321			−0.269439
$229$	9.30072	+	9.30072i	0.0406145	+	0.0406145i	0.727122	−	0.686508i	$-0.240857\pi$
$229$	9.30072	+	9.30072i	0.0406145	+	0.0406145i	−0.686508	+	0.727122i	$0.740857\pi$
$230$	7.60686	+	7.60686i	0.0330733	+	0.0330733i
$231$			392.464i			1.69898i
$232$	−89.2806	+	234.575i	−0.384830	+	1.01110i
$233$	−235.895			−1.01243			−0.506213	−	0.862408i	$-0.668955\pi$
$233$	−235.895			−1.01243			−0.506213	+	0.862408i	$0.668955\pi$
$234$	−1.96246	+	1.96246i	−0.00838660	+	0.00838660i
$235$	−20.6358	+	20.6358i	−0.0878119	+	0.0878119i
$236$		−	24.2220i		−	0.102636i
$237$			41.6931i			0.175920i
$238$		−	169.389i		−	0.711719i
$239$	389.332			1.62900			0.814501	−	0.580162i	$-0.197011\pi$
$239$	389.332			1.62900			0.814501	+	0.580162i	$0.197011\pi$
$240$	−6.83824	−	6.83824i	−0.0284926	−	0.0284926i
$241$			163.689i			0.679206i	0.940569	+	0.339603i	$0.110293\pi$
$241$			163.689i			0.679206i	−0.940569	+	0.339603i	$0.889707\pi$
$242$	145.997	+	145.997i	0.603292	+	0.603292i
$243$	−6.90952	+	6.90952i	−0.0284342	+	0.0284342i
$244$	−75.7931	−	75.7931i	−0.310628	−	0.310628i
$245$			8.04729i			0.0328461i
$246$	90.8080	−	90.8080i	0.369138	−	0.369138i
$247$	86.2425	+	86.2425i	0.349160	+	0.349160i
$248$	−382.154			−1.54094
$249$	−137.673	+	137.673i	−0.552905	+	0.552905i
$250$	−26.2474	−	26.2474i	−0.104989	−	0.104989i
$251$	−132.018	+	132.018i	−0.525968	+	0.525968i	−0.919368	−	0.393399i	$-0.871299\pi$
$251$	−132.018	+	132.018i	−0.525968	+	0.525968i	0.393399	+	0.919368i	$0.371299\pi$
$252$	2.44549			0.00970431
$253$	−163.245	+	163.245i	−0.645236	+	0.645236i
$254$		−	46.1983i		−	0.181883i
$255$	20.3083			0.0796405
$256$	−256.973			−1.00380
$257$	−113.634			−0.442155			−0.221078	−	0.975256i	$-0.570957\pi$
$257$	−113.634			−0.442155			−0.221078	+	0.975256i	$0.570957\pi$
$258$	232.363	+	232.363i	0.900630	+	0.900630i
$259$	−252.955	−	252.955i	−0.976662	−	0.976662i
$260$		−	8.19892i		−	0.0315343i
$261$	−4.78863	+	2.14837i	−0.0183472	+	0.00823130i
$262$	100.791			0.384699
$263$	279.851	−	279.851i	1.06407	−	1.06407i	0.0662687	−	0.997802i	$-0.478891\pi$
$263$	279.851	−	279.851i	1.06407	−	1.06407i	0.997802	−	0.0662687i	$-0.0211095\pi$
$264$	296.848	−	296.848i	1.12442	−	1.12442i
$265$			8.09332i			0.0305408i
$266$			149.941i			0.563688i
$267$		−	513.098i		−	1.92171i
$268$	223.095			0.832443
$269$	302.867	+	302.867i	1.12590	+	1.12590i	0.990837	+	0.135061i	$0.0431231\pi$
$269$	302.867	+	302.867i	1.12590	+	1.12590i	0.135061	+	0.990837i	$0.456877\pi$
$270$			19.9331i			0.0738263i
$271$	−222.952	−	222.952i	−0.822702	−	0.822702i	0.163793	−	0.986495i	$-0.447627\pi$
$271$	−222.952	−	222.952i	−0.822702	−	0.822702i	−0.986495	+	0.163793i	$0.947627\pi$
$272$	−63.3379	+	63.3379i	−0.232860	+	0.232860i
$273$	−174.159	−	174.159i	−0.637945	−	0.637945i
$274$			12.4465i			0.0454253i
$275$	280.285	−	280.285i	1.01922	−	1.01922i
$276$	51.6011	+	51.6011i	0.186961	+	0.186961i
$277$	290.196			1.04764			0.523820	−	0.851829i	$-0.324507\pi$
$277$	290.196			1.04764			0.523820	+	0.851829i	$0.324507\pi$
$278$	241.758	−	241.758i	0.869633	−	0.869633i
$279$	−5.65064	−	5.65064i	−0.0202532	−	0.0202532i
$280$	24.1986	−	24.1986i	0.0864236	−	0.0864236i
$281$	−486.000			−1.72954			−0.864768	−	0.502171i	$-0.832535\pi$
$281$	−486.000			−1.72954			−0.864768	+	0.502171i	$0.832535\pi$
$282$	195.303	−	195.303i	0.692566	−	0.692566i
$283$		−	95.1009i		−	0.336046i	−0.985783	−	0.168023i	$-0.946262\pi$
$283$		−	95.1009i		−	0.336046i	0.985783	−	0.168023i	$-0.0537382\pi$
$284$	56.6474			0.199463
$285$	−17.9767			−0.0630760
$286$	−245.485			−0.858340
$287$	158.860	+	158.860i	0.553518	+	0.553518i
$288$	−3.15459	−	3.15459i	−0.0109534	−	0.0109534i
$289$			100.898i			0.349128i
$290$	−7.69496	+	20.2177i	−0.0265343	+	0.0697162i
$291$	143.874			0.494412
$292$	37.0328	−	37.0328i	0.126825	−	0.126825i
$293$	21.2589	−	21.2589i	0.0725559	−	0.0725559i	−0.669898	−	0.742454i	$-0.733662\pi$
$293$	21.2589	−	21.2589i	0.0725559	−	0.0725559i	0.742454	+	0.669898i	$0.233662\pi$
$294$		−	76.1620i		−	0.259054i
$295$		−	7.08801i		−	0.0240272i
$296$			382.656i			1.29276i
$297$	−427.768			−1.44030
$298$	139.484	+	139.484i	0.468068	+	0.468068i
$299$		−	144.882i		−	0.484556i
$300$	−88.5972	−	88.5972i	−0.295324	−	0.295324i
$301$	−406.496	+	406.496i	−1.35048	+	1.35048i
$302$	−64.1103	−	64.1103i	−0.212286	−	0.212286i
$303$		−	163.889i		−	0.540887i
$304$	56.0658	−	56.0658i	0.184427	−	0.184427i
$305$	−22.1791	−	22.1791i	−0.0727183	−	0.0727183i
$306$	−3.78886			−0.0123819
$307$	−193.144	+	193.144i	−0.629135	+	0.629135i	−0.947850	−	0.318715i	$-0.896749\pi$
$307$	−193.144	+	193.144i	−0.629135	+	0.629135i	0.318715	+	0.947850i	$0.396749\pi$
$308$	152.953	+	152.953i	0.496602	+	0.496602i
$309$	−132.102	+	132.102i	−0.427516	+	0.427516i
$310$	−32.9373			−0.106249
$311$	112.842	−	112.842i	0.362835	−	0.362835i	−0.502021	−	0.864856i	$-0.667410\pi$
$311$	112.842	−	112.842i	0.362835	−	0.362835i	0.864856	+	0.502021i	$0.167410\pi$
$312$			263.457i			0.844414i
$313$	119.788			0.382710			0.191355	−	0.981521i	$-0.438712\pi$
$313$	119.788			0.382710			0.191355	+	0.981521i	$0.438712\pi$
$314$	−455.236			−1.44980
$315$	0.715614			0.00227179
$316$	16.2489	+	16.2489i	0.0514205	+	0.0514205i
$317$	270.382	+	270.382i	0.852942	+	0.852942i	0.990494	−	0.137553i	$-0.0439237\pi$
$317$	270.382	+	270.382i	0.852942	+	0.852942i	−0.137553	+	0.990494i	$0.543924\pi$
$318$		−	76.5977i		−	0.240873i
$319$	−433.876	−	165.135i	−1.36011	−	0.517665i
$320$	−31.1545			−0.0973578
$321$	104.092	−	104.092i	0.324276	−	0.324276i
$322$	125.946	−	125.946i	0.391136	−	0.391136i
$323$			166.505i			0.515497i
$324$			137.936i			0.425729i
$325$			248.758i			0.765408i
$326$	327.380			1.00423
$327$	175.717	+	175.717i	0.537360	+	0.537360i
$328$		−	240.313i		−	0.732663i
$329$	341.665	+	341.665i	1.03849	+	1.03849i
$330$	25.5849	−	25.5849i	0.0775299	−	0.0775299i
$331$	−64.5326	−	64.5326i	−0.194962	−	0.194962i	0.602874	−	0.797836i	$-0.294022\pi$
$331$	−64.5326	−	64.5326i	−0.194962	−	0.194962i	−0.797836	+	0.602874i	$0.794022\pi$
$332$			107.310i			0.323222i
$333$	−5.65806	+	5.65806i	−0.0169912	+	0.0169912i
$334$	−126.310	−	126.310i	−0.378173	−	0.378173i
$335$	65.2835			0.194876
$336$	−113.220	+	113.220i	−0.336964	+	0.336964i
$337$	−49.1921	−	49.1921i	−0.145971	−	0.145971i	0.630345	−	0.776315i	$-0.282914\pi$
$337$	−49.1921	−	49.1921i	−0.145971	−	0.145971i	−0.776315	+	0.630345i	$0.782914\pi$
$338$	−73.4740	+	73.4740i	−0.217379	+	0.217379i
$339$	−1.90624			−0.00562313
$340$	7.91468	−	7.91468i	0.0232785	−	0.0232785i
$341$		−	706.840i		−	2.07285i
$342$	3.35385			0.00980657
$343$	−263.229			−0.767433
$344$	614.923			1.78757
$345$	15.0999	+	15.0999i	0.0437677	+	0.0437677i
$346$	55.4609	+	55.4609i	0.160292	+	0.160292i
$347$			75.0323i			0.216231i	0.994138	+	0.108116i	$0.0344817\pi$
$347$			75.0323i			0.216231i	−0.994138	+	0.108116i	$0.965518\pi$
$348$	−52.1987	+	137.147i	−0.149996	+	0.394100i
$349$	284.109			0.814067			0.407033	−	0.913413i	$-0.366563\pi$
$349$	284.109			0.814067			0.407033	+	0.913413i	$0.366563\pi$
$350$	−216.244	+	216.244i	−0.617841	+	0.617841i
$351$	189.826	−	189.826i	0.540813	−	0.540813i
$352$		−	394.608i		−	1.12105i
$353$			157.587i			0.446422i	0.974770	+	0.223211i	$0.0716538\pi$
$353$			157.587i			0.446422i	−0.974770	+	0.223211i	$0.928346\pi$
$354$			67.0831i			0.189500i
$355$	16.5765			0.0466945
$356$	−199.968	−	199.968i	−0.561707	−	0.561707i
$357$		−	336.243i		−	0.941856i
$358$	−315.973	−	315.973i	−0.882606	−	0.882606i
$359$	−327.012	+	327.012i	−0.910896	+	0.910896i	−0.996343	−	0.0854467i	$-0.972768\pi$
$359$	−327.012	+	327.012i	−0.910896	+	0.910896i	0.0854467	+	0.996343i	$0.472768\pi$
$360$	−0.541269	−	0.541269i	−0.00150353	−	0.00150353i
$361$			213.612i			0.591722i
$362$	−189.058	+	189.058i	−0.522259	+	0.522259i
$363$	289.808	+	289.808i	0.798369	+	0.798369i
$364$	−135.749			−0.372936
$365$	10.8368	−	10.8368i	0.0296898	−	0.0296898i
$366$	209.910	+	209.910i	0.573524	+	0.573524i
$367$	243.021	−	243.021i	0.662182	−	0.662182i	−0.293712	−	0.955894i	$-0.594891\pi$
$367$	243.021	−	243.021i	0.662182	−	0.662182i	0.955894	+	0.293712i	$0.0948906\pi$
$368$	−94.1873			−0.255944
$369$	3.55334	−	3.55334i	0.00962965	−	0.00962965i
$370$			32.9805i			0.0891365i
$371$	134.000			0.361187
$372$	−223.430			−0.600618
$373$	−503.790			−1.35064			−0.675322	−	0.737523i	$-0.735995\pi$
$373$	−503.790			−1.35064			−0.675322	+	0.737523i	$0.735995\pi$
$374$	−236.975	−	236.975i	−0.633623	−	0.633623i
$375$	−52.1018	−	52.1018i	−0.138938	−	0.138938i
$376$		−	516.850i		−	1.37460i
$377$	265.816	−	119.256i	0.705082	−	0.316328i
$378$	330.030			0.873095
$379$	−74.1929	+	74.1929i	−0.195760	+	0.195760i	−0.798179	−	0.602420i	$-0.794203\pi$
$379$	−74.1929	+	74.1929i	−0.195760	+	0.195760i	0.602420	+	0.798179i	$0.294203\pi$
$380$	−7.00597	+	7.00597i	−0.0184368	+	0.0184368i
$381$		−	91.7051i		−	0.240696i
$382$			101.188i			0.264890i
$383$		−	561.592i		−	1.46630i	−0.680068	−	0.733149i	$-0.738050\pi$
$383$		−	561.592i		−	1.46630i	0.680068	−	0.733149i	$-0.261950\pi$
$384$	−3.90766			−0.0101762
$385$	44.7582	+	44.7582i	0.116255	+	0.116255i
$386$			107.649i			0.278885i
$387$	9.09241	+	9.09241i	0.0234946	+	0.0234946i
$388$	56.0714	−	56.0714i	0.144514	−	0.144514i
$389$	−111.236	−	111.236i	−0.285953	−	0.285953i	0.549525	−	0.835478i	$-0.314809\pi$
$389$	−111.236	−	111.236i	−0.285953	−	0.285953i	−0.835478	+	0.549525i	$0.814809\pi$
$390$			22.7070i			0.0582230i
$391$	139.860	−	139.860i	0.357697	−	0.357697i
$392$	−100.777	−	100.777i	−0.257085	−	0.257085i
$393$	200.074			0.509093
$394$	64.4927	−	64.4927i	0.163687	−	0.163687i
$395$	4.75485	+	4.75485i	0.0120376	+	0.0120376i
$396$	3.42123	−	3.42123i	0.00863947	−	0.00863947i
$397$	695.905			1.75291			0.876455	−	0.481484i	$-0.159902\pi$
$397$	695.905			1.75291			0.876455	+	0.481484i	$0.159902\pi$
$398$	11.6386	−	11.6386i	0.0292428	−	0.0292428i
$399$			297.638i			0.745959i
$400$	161.716			0.404290
$401$	450.193			1.12268			0.561338	−	0.827587i	$-0.310287\pi$
$401$	450.193			1.12268			0.561338	+	0.827587i	$0.310287\pi$
$402$	−617.863			−1.53697
$403$	313.666	+	313.666i	0.778328	+	0.778328i
$404$	−63.8717	−	63.8717i	−0.158098	−	0.158098i
$405$			40.3638i			0.0996638i
$406$	334.742	+	127.405i	0.824488	+	0.313804i
$407$	−707.768			−1.73899
$408$	−254.324	+	254.324i	−0.623343	+	0.623343i
$409$	−449.447	+	449.447i	−1.09889	+	1.09889i	−0.104353	+	0.994540i	$0.533277\pi$
$409$	−449.447	+	449.447i	−1.09889	+	1.09889i	−0.994540	+	0.104353i	$0.966723\pi$
$410$		−	20.7122i		−	0.0505177i
$411$			24.7068i			0.0601138i
$412$			102.967i			0.249921i
$413$	−117.355			−0.284154
$414$	−2.81713	−	2.81713i	−0.00680467	−	0.00680467i
$415$			31.4017i			0.0756668i
$416$	175.111	+	175.111i	0.420939	+	0.420939i
$417$	479.898	−	479.898i	1.15083	−	1.15083i
$418$	209.767	+	209.767i	0.501835	+	0.501835i
$419$		−	585.961i		−	1.39848i	−0.714889	−	0.699238i	$-0.753523\pi$
$419$		−	585.961i		−	1.39848i	0.714889	−	0.699238i	$-0.246477\pi$
$420$	14.1479	−	14.1479i	0.0336855	−	0.0336855i
$421$	−37.5863	−	37.5863i	−0.0892786	−	0.0892786i	0.661057	−	0.750336i	$-0.270108\pi$
$421$	−37.5863	−	37.5863i	−0.0892786	−	0.0892786i	−0.750336	+	0.661057i	$0.770108\pi$
$422$	−153.725			−0.364277
$423$	7.64228	−	7.64228i	0.0180669	−	0.0180669i
$424$	−101.354	−	101.354i	−0.239042	−	0.239042i
$425$	−240.134	+	240.134i	−0.565020	+	0.565020i
$426$	−156.885			−0.368276
$427$	−367.217	+	367.217i	−0.859992	+	0.859992i
$428$		−	81.1351i		−	0.189568i
$429$	−487.296			−1.13589
$430$	52.9992			0.123254
$431$	270.174			0.626853			0.313427	−	0.949612i	$-0.398523\pi$
$431$	270.174			0.626853			0.313427	+	0.949612i	$0.398523\pi$
$432$	−123.405	−	123.405i	−0.285659	−	0.285659i
$433$	214.672	+	214.672i	0.495779	+	0.495779i	0.910121	−	0.414342i	$-0.135988\pi$
$433$	214.672	+	214.672i	0.495779	+	0.495779i	−0.414342	+	0.910121i	$0.635988\pi$
$434$			545.339i			1.25654i
$435$	−15.2747	+	40.1328i	−0.0351143	+	0.0922592i
$436$	136.963			0.314135
$437$	−123.802	+	123.802i	−0.283299	+	0.283299i
$438$	−102.563	+	102.563i	−0.234161	+	0.234161i
$439$			380.066i			0.865753i	0.901453	+	0.432877i	$0.142501\pi$
$439$			380.066i			0.865753i	−0.901453	+	0.432877i	$0.857499\pi$
$440$		−	67.7076i		−	0.153881i
$441$		−	2.98024i		−	0.00675792i
$442$	210.319			0.475835
$443$	−248.852	−	248.852i	−0.561743	−	0.561743i	0.368059	−	0.929802i	$-0.380022\pi$
$443$	−248.852	−	248.852i	−0.561743	−	0.561743i	−0.929802	+	0.368059i	$0.880022\pi$
$444$			223.723i			0.503881i
$445$	−58.5158	−	58.5158i	−0.131496	−	0.131496i
$446$	180.190	−	180.190i	0.404014	−	0.404014i
$447$	276.881	+	276.881i	0.619420	+	0.619420i
$448$			515.822i			1.15139i
$449$	133.874	−	133.874i	0.298159	−	0.298159i	−0.542133	−	0.840293i	$-0.682383\pi$
$449$	133.874	−	133.874i	0.298159	−	0.298159i	0.840293	+	0.542133i	$0.182383\pi$
$450$	4.83691	+	4.83691i	0.0107487	+	0.0107487i
$451$	444.489			0.985562
$452$	−0.742911	+	0.742911i	−0.00164361	+	0.00164361i
$453$	−127.261	−	127.261i	−0.280929	−	0.280929i
$454$	129.880	−	129.880i	0.286079	−	0.286079i
$455$	−39.7236			−0.0873047
$456$	225.124	−	225.124i	0.493693	−	0.493693i
$457$			476.374i			1.04239i	0.853436	+	0.521197i	$0.174514\pi$
$457$			476.374i			1.04239i	−0.853436	+	0.521197i	$0.825486\pi$
$458$	−20.0775			−0.0438372
$459$	366.489			0.798452
$460$	11.7696			0.0255861
$461$	−478.069	−	478.069i	−1.03703	−	1.03703i	−0.999288	−	0.0377379i	$-0.987985\pi$
$461$	−478.069	−	478.069i	−1.03703	−	1.03703i	−0.0377379	−	0.999288i	$-0.512015\pi$
$462$	−423.605	−	423.605i	−0.916895	−	0.916895i
$463$		−	144.158i		−	0.311357i	−0.987808	−	0.155678i	$-0.950244\pi$
$463$		−	144.158i		−	0.311357i	0.987808	−	0.155678i	$-0.0497564\pi$
$464$	−77.5275	−	172.806i	−0.167085	−	0.372426i
$465$	−65.3815			−0.140605
$466$	254.613	−	254.613i	0.546381	−	0.546381i
$467$	−63.5129	+	63.5129i	−0.136002	+	0.136002i	−0.771830	−	0.635828i	$-0.780659\pi$
$467$	−63.5129	+	63.5129i	−0.136002	+	0.136002i	0.635828	+	0.771830i	$0.280659\pi$
$468$			3.03640i			0.00648803i
$469$		−	1080.89i		−	2.30467i
$470$		−	44.5465i		−	0.0947797i
$471$	−903.659			−1.91860
$472$	88.7641	+	88.7641i	0.188060	+	0.188060i
$473$			1137.37i			2.40459i
$474$	−45.0014	−	45.0014i	−0.0949396	−	0.0949396i
$475$	212.563	−	212.563i	0.447501	−	0.447501i
$476$	−131.042	−	131.042i	−0.275299	−	0.275299i
$477$		−	2.99729i		−	0.00628363i
$478$	−420.225	+	420.225i	−0.879132	+	0.879132i
$479$	−25.8901	−	25.8901i	−0.0540503	−	0.0540503i	0.679565	−	0.733615i	$-0.262169\pi$
$479$	−25.8901	−	25.8901i	−0.0540503	−	0.0540503i	−0.733615	+	0.679565i	$0.762169\pi$
$480$	−36.5006			−0.0760430
$481$	314.078	−	314.078i	0.652969	−	0.652969i
$482$	−176.677	−	176.677i	−0.366551	−	0.366551i
$483$	250.007	−	250.007i	0.517612	−	0.517612i
$484$	225.891			0.466718
$485$	16.4080	−	16.4080i	0.0338309	−	0.0338309i
$486$		−	14.9156i		−	0.0306905i
$487$	−383.625			−0.787730			−0.393865	−	0.919168i	$-0.628862\pi$
$487$	−383.625			−0.787730			−0.393865	+	0.919168i	$0.628862\pi$
$488$	555.504			1.13833
$489$	649.859			1.32896
$490$	−8.68584	−	8.68584i	−0.0177262	−	0.0177262i
$491$	196.364	+	196.364i	0.399927	+	0.399927i	0.878207	−	0.478280i	$-0.158740\pi$
$491$	196.364	+	196.364i	0.399927	+	0.399927i	−0.478280	+	0.878207i	$0.658740\pi$
$492$		−	140.501i		−	0.285572i
$493$	371.722	+	141.479i	0.754000	+	0.286976i
$494$	−186.172			−0.376866
$495$	1.00114	−	1.00114i	0.00202251	−	0.00202251i
$496$	203.913	−	203.913i	0.411114	−	0.411114i
$497$		−	274.456i		−	0.552225i
$498$		−	297.196i		−	0.596778i
$499$			513.725i			1.02951i	0.857337	+	0.514755i	$0.172117\pi$
$499$			513.725i			1.02951i	−0.857337	+	0.514755i	$0.827883\pi$
$500$	−40.6109			−0.0812218
$501$	−250.729	−	250.729i	−0.500457	−	0.500457i
$502$		−	284.987i		−	0.567703i
$503$	195.929	+	195.929i	0.389522	+	0.389522i	0.874517	−	0.484995i	$-0.161179\pi$
$503$	195.929	+	195.929i	0.389522	+	0.389522i	−0.484995	+	0.874517i	$0.661179\pi$
$504$	−8.96173	+	8.96173i	−0.0177812	+	0.0177812i
$505$	−18.6905	−	18.6905i	−0.0370110	−	0.0370110i
$506$		−	352.396i		−	0.696435i
$507$	−145.848	+	145.848i	−0.287669	+	0.287669i
$508$	−35.7399	−	35.7399i	−0.0703541	−	0.0703541i
$509$	−802.720			−1.57705			−0.788526	−	0.615001i	$-0.789155\pi$
$509$	−802.720			−1.57705			−0.788526	+	0.615001i	$0.789155\pi$
$510$	−21.9198	+	21.9198i	−0.0429800	+	0.0429800i
$511$	−179.424	−	179.424i	−0.351122	−	0.351122i
$512$	273.716	−	273.716i	0.534602	−	0.534602i
$513$	−324.412			−0.632381
$514$	122.651	−	122.651i	0.238620	−	0.238620i
$515$			30.1310i			0.0585068i
$516$	359.520			0.696744
$517$	955.976			1.84908
$518$	546.055			1.05416
$519$	110.092	+	110.092i	0.212123	+	0.212123i
$520$	30.0458	+	30.0458i	0.0577803	+	0.0577803i
$521$		−	913.769i		−	1.75388i	−0.480604	−	0.876938i	$-0.659583\pi$
$521$		−	913.769i		−	1.75388i	0.480604	−	0.876938i	$-0.340417\pi$
$522$	2.84976	−	7.48744i	0.00545931	−	0.0143438i
$523$	−280.930			−0.537151			−0.268575	−	0.963259i	$-0.586553\pi$
$523$	−280.930			−0.537151			−0.268575	+	0.963259i	$0.586553\pi$
$524$	77.9739	−	77.9739i	0.148805	−	0.148805i
$525$	−429.252	+	429.252i	−0.817623	+	0.817623i
$526$			604.113i			1.14850i
$527$			605.584i			1.14912i
$528$			316.789i			0.599979i
$529$	−321.020			−0.606844
$530$	−8.73553	−	8.73553i	−0.0164821	−	0.0164821i
$531$			2.62498i			0.00494347i
$532$	115.997	+	115.997i	0.218040	+	0.218040i
$533$	−197.245	+	197.245i	−0.370067	+	0.370067i
$534$	553.812	+	553.812i	1.03710	+	1.03710i
$535$		−	23.7423i		−	0.0443781i
$536$	−817.554	+	817.554i	−1.52529	+	1.52529i
$537$	−627.217	−	627.217i	−1.16800	−	1.16800i
$538$	−653.798			−1.21524
$539$	186.400	−	186.400i	0.345825	−	0.345825i
$540$	15.4206	+	15.4206i	0.0285567	+	0.0285567i
$541$	−17.1635	+	17.1635i	−0.0317255	+	0.0317255i	−0.722792	−	0.691066i	$-0.757141\pi$
$541$	−17.1635	+	17.1635i	−0.0317255	+	0.0317255i	0.691066	+	0.722792i	$0.257141\pi$
$542$	481.287			0.887983
$543$	−375.285	+	375.285i	−0.691133	+	0.691133i
$544$			338.080i			0.621471i
$545$	40.0789			0.0735393
$546$	375.957			0.688566
$547$	116.845			0.213610			0.106805	−	0.994280i	$-0.465938\pi$
$547$	116.845			0.213610			0.106805	+	0.994280i	$0.465938\pi$
$548$	9.62887	+	9.62887i	0.0175709	+	0.0175709i
$549$	8.21383	+	8.21383i	0.0149614	+	0.0149614i
$550$			605.051i			1.10009i
$551$	−329.044	−	125.236i	−0.597175	−	0.227288i
$552$	−378.195			−0.685136
$553$	78.7255	−	78.7255i	0.142361	−	0.142361i
$554$	−313.223	+	313.223i	−0.565385	+	0.565385i
$555$			65.4674i			0.117959i
$556$		−	374.057i		−	0.672765i
$557$			575.508i			1.03323i	0.856218	+	0.516614i	$0.172808\pi$
$557$			575.508i			1.03323i	−0.856218	+	0.516614i	$0.827192\pi$
$558$	12.1980			0.0218603
$559$	−504.719	−	504.719i	−0.902896	−	0.902896i
$560$			25.8241i			0.0461145i
$561$	−470.403	−	470.403i	−0.838507	−	0.838507i
$562$	524.564	−	524.564i	0.933387	−	0.933387i
$563$	465.411	+	465.411i	0.826662	+	0.826662i	0.987054	−	0.160391i	$-0.0512756\pi$
$563$	465.411	+	465.411i	0.826662	+	0.826662i	−0.160391	+	0.987054i	$0.551276\pi$
$564$		−	302.181i		−	0.535782i
$565$	−0.217396	+	0.217396i	−0.000384771	+	0.000384771i
$566$	102.647	+	102.647i	0.181355	+	0.181355i
$567$	668.299			1.17866
$568$	−207.590	+	207.590i	−0.365476	+	0.365476i
$569$	417.363	+	417.363i	0.733503	+	0.733503i	0.971312	−	0.237809i	$-0.0764292\pi$
$569$	417.363	+	417.363i	0.733503	+	0.733503i	−0.237809	+	0.971312i	$0.576429\pi$
$570$	19.4031	−	19.4031i	0.0340405	−	0.0340405i
$571$	24.6693			0.0432037			0.0216019	−	0.999767i	$-0.493123\pi$
$571$	24.6693			0.0432037			0.0216019	+	0.999767i	$0.493123\pi$
$572$	−189.912	+	189.912i	−0.332014	+	0.332014i
$573$			200.861i			0.350543i
$574$	−342.930			−0.597439
$575$	−357.093			−0.621032
$576$	11.5378			0.0200309
$577$	−152.708	−	152.708i	−0.264659	−	0.264659i	0.562285	−	0.826944i	$-0.309922\pi$
$577$	−152.708	−	152.708i	−0.264659	−	0.264659i	−0.826944	+	0.562285i	$0.809922\pi$
$578$	−108.904	−	108.904i	−0.188416	−	0.188416i
$579$			213.688i			0.369063i
$580$	9.68782	+	21.5937i	0.0167031	+	0.0372306i
$581$	519.915			0.894862
$582$	−155.290	+	155.290i	−0.266822	+	0.266822i
$583$	187.466	−	187.466i	0.321554	−	0.321554i
$584$			271.421i			0.464762i
$585$			0.888530i			0.00151886i
$586$			45.8915i			0.0783132i
$587$	891.866			1.51936			0.759681	−	0.650295i	$-0.225355\pi$
$587$	891.866			1.51936			0.759681	+	0.650295i	$0.225355\pi$
$588$	−58.9203	−	58.9203i	−0.100205	−	0.100205i
$589$		−	536.055i		−	0.910111i
$590$	7.65044	+	7.65044i	0.0129669	+	0.0129669i
$591$	128.020	−	128.020i	0.216616	−	0.216616i
$592$	−204.181	−	204.181i	−0.344900	−	0.344900i
$593$		−	1124.61i		−	1.89647i	−0.317563	−	0.948237i	$-0.602864\pi$
$593$		−	1124.61i		−	1.89647i	0.317563	−	0.948237i	$-0.397136\pi$
$594$	461.711	−	461.711i	0.777291	−	0.777291i
$595$	−38.3465	−	38.3465i	−0.0644479	−	0.0644479i
$596$	215.815			0.362106
$597$	23.1030	−	23.1030i	0.0386985	−	0.0386985i
$598$	156.379	+	156.379i	0.261503	+	0.261503i
$599$	222.555	−	222.555i	0.371544	−	0.371544i	−0.496495	−	0.868040i	$-0.665380\pi$
$599$	222.555	−	222.555i	0.371544	−	0.371544i	0.868040	+	0.496495i	$0.165380\pi$
$600$	649.347			1.08224
$601$	−196.657	+	196.657i	−0.327216	+	0.327216i	−0.851527	−	0.524311i	$-0.824323\pi$
$601$	−196.657	+	196.657i	−0.327216	+	0.327216i	0.524311	+	0.851527i	$0.324323\pi$
$602$		−	877.502i		−	1.45764i
$603$	−24.1771			−0.0400948
$604$	−99.1938			−0.164228
$605$	66.1019			0.109259
$606$	176.893	+	176.893i	0.291903	+	0.291903i
$607$	−660.823	−	660.823i	−1.08867	−	1.08867i	−0.995666	−	0.0930047i	$-0.970353\pi$
$607$	−660.823	−	660.823i	−1.08867	−	1.08867i	−0.0930047	−	0.995666i	$-0.529647\pi$
$608$		−	299.264i		−	0.492211i
$609$	664.474	+	252.902i	1.09109	+	0.415274i
$610$	47.8780			0.0784885
$611$	−424.222	+	424.222i	−0.694308	+	0.694308i
$612$	−2.93113	+	2.93113i	−0.00478943	+	0.00478943i
$613$		−	299.378i		−	0.488382i	−0.969727	−	0.244191i	$-0.921478\pi$
$613$		−	299.378i		−	0.488382i	0.969727	−	0.244191i	$-0.0785224\pi$
$614$		−	416.941i		−	0.679057i
$615$		−	41.1145i		−	0.0668528i
$616$	−1121.03			−1.81985
$617$	−419.542	−	419.542i	−0.679972	−	0.679972i	0.280022	−	0.959994i	$-0.409658\pi$
$617$	−419.542	−	419.542i	−0.679972	−	0.679972i	−0.959994	+	0.280022i	$0.909658\pi$
$618$		−	285.169i		−	0.461439i
$619$	243.311	+	243.311i	0.393072	+	0.393072i	0.875781	−	0.482709i	$-0.160347\pi$
$619$	243.311	+	243.311i	0.393072	+	0.393072i	−0.482709	+	0.875781i	$0.660347\pi$
$620$	−25.4809	+	25.4809i	−0.0410982	+	0.0410982i
$621$	272.496	+	272.496i	0.438802	+	0.438802i
$622$			243.591i			0.391626i
$623$	−968.840	+	968.840i	−1.55512	+	1.55512i
$624$	−140.578	−	140.578i	−0.225285	−	0.225285i
$625$	607.146			0.971433
$626$	−129.294	+	129.294i	−0.206539	+	0.206539i
$627$	416.394	+	416.394i	0.664106	+	0.664106i
$628$	−352.179	+	352.179i	−0.560795	+	0.560795i
$629$	606.379			0.964037
$630$	−0.772398	+	0.772398i	−0.00122603	+	0.00122603i
$631$		−	96.3199i		−	0.152647i	−0.997083	−	0.0763233i	$-0.975682\pi$
$631$		−	96.3199i		−	0.152647i	0.997083	−	0.0763233i	$-0.0243181\pi$
$632$	−119.091			−0.188436
$633$	−305.149			−0.482068
$634$	−583.674			−0.920622
$635$	−10.4584	−	10.4584i	−0.0164700	−	0.0164700i
$636$	−59.2574	−	59.2574i	−0.0931720	−	0.0931720i
$637$			165.433i			0.259706i
$638$	646.542	−	290.065i	1.01339	−	0.454647i
$639$	−6.13897			−0.00960715
$640$	−0.445646	+	0.445646i	−0.000696322	+	0.000696322i
$641$	−378.246	+	378.246i	−0.590088	+	0.590088i	−0.937655	−	0.347567i	$-0.887008\pi$
$641$	−378.246	+	378.246i	−0.590088	+	0.590088i	0.347567	+	0.937655i	$0.387008\pi$
$642$			224.704i			0.350007i
$643$		−	258.453i		−	0.401949i	−0.979597	−	0.200974i	$-0.935589\pi$
$643$		−	258.453i		−	0.401949i	0.979597	−	0.200974i	$-0.0644108\pi$
$644$		−	194.868i		−	0.302590i
$645$	105.205			0.163109
$646$	−179.718	−	179.718i	−0.278201	−	0.278201i
$647$		−	568.930i		−	0.879336i	−0.898160	−	0.439668i	$-0.855096\pi$
$647$		−	568.930i		−	0.879336i	0.898160	−	0.439668i	$-0.144904\pi$
$648$	−505.482	−	505.482i	−0.780064	−	0.780064i
$649$	−164.180	+	164.180i	−0.252974	+	0.252974i
$650$	−268.496	−	268.496i	−0.413071	−	0.413071i
$651$			1082.51i			1.66285i
$652$	253.267	−	253.267i	0.388446	−	0.388446i
$653$	810.018	+	810.018i	1.24046	+	1.24046i	0.959812	+	0.280645i	$0.0905485\pi$
$653$	810.018	+	810.018i	1.24046	+	1.24046i	0.280645	+	0.959812i	$0.409452\pi$
$654$	−379.319			−0.579999
$655$	22.8172	−	22.8172i	0.0348355	−	0.0348355i
$656$	128.228	+	128.228i	0.195470	+	0.195470i
$657$	−4.01331	+	4.01331i	−0.00610854	+	0.00610854i
$658$	−737.551			−1.12090
$659$	573.095	−	573.095i	0.869644	−	0.869644i	−0.122789	−	0.992433i	$-0.539184\pi$
$659$	573.095	−	573.095i	0.869644	−	0.869644i	0.992433	+	0.122789i	$0.0391839\pi$
$660$		−	39.5858i		−	0.0599785i
$661$	654.922			0.990804			0.495402	−	0.868664i	$-0.335021\pi$
$661$	654.922			0.990804			0.495402	+	0.868664i	$0.335021\pi$
$662$	139.306			0.210433
$663$	417.490			0.629698
$664$	−393.248	−	393.248i	−0.592241	−	0.592241i
$665$	33.9438	+	33.9438i	0.0510434	+	0.0510434i
$666$		−	12.2140i		−	0.0183394i
$667$	171.193	+	381.581i	0.256660	+	0.572085i
$668$	−195.431			−0.292562
$669$	357.683	−	357.683i	0.534653	−	0.534653i
$670$	−70.4637	+	70.4637i	−0.105170	+	0.105170i
$671$			1027.47i			1.53125i
$672$			604.337i			0.899311i
$673$			395.630i			0.587861i	0.955827	+	0.293930i	$0.0949633\pi$
$673$			395.630i			0.587861i	−0.955827	+	0.293930i	$0.905037\pi$
$674$	106.191			0.157553
$675$	−467.866	−	467.866i	−0.693134	−	0.693134i
$676$			113.682i			0.168168i
$677$	−161.375	−	161.375i	−0.238368	−	0.238368i	0.577806	−	0.816174i	$-0.303909\pi$
$677$	−161.375	−	161.375i	−0.238368	−	0.238368i	−0.816174	+	0.577806i	$0.803909\pi$
$678$	2.05750	−	2.05750i	0.00303466	−	0.00303466i
$679$	−271.665	−	271.665i	−0.400096	−	0.400096i
$680$			58.0083i			0.0853064i
$681$	257.816	−	257.816i	0.378584	−	0.378584i
$682$	762.928	+	762.928i	1.11866	+	1.11866i
$683$	635.971			0.931143			0.465572	−	0.885010i	$-0.345849\pi$
$683$	635.971			0.931143			0.465572	+	0.885010i	$0.345849\pi$
$684$	2.59460	−	2.59460i	0.00379327	−	0.00379327i
$685$	2.81766	+	2.81766i	0.00411338	+	0.00411338i
$686$	284.117	−	284.117i	0.414164	−	0.414164i
$687$	−39.8544			−0.0580122
$688$	−328.115	+	328.115i	−0.476911	+	0.476911i
$689$			166.379i			0.241479i
$690$	−32.5960			−0.0472406
$691$	−440.160			−0.636990			−0.318495	−	0.947925i	$-0.603177\pi$
$691$	−440.160			−0.636990			−0.318495	+	0.947925i	$0.603177\pi$
$692$	85.8112			0.124005
$693$	−16.5758	−	16.5758i	−0.0239189	−	0.0239189i
$694$	−80.9861	−	80.9861i	−0.116695	−	0.116695i
$695$		−	109.459i		−	0.157495i
$696$	−311.300	−	693.876i	−0.447271	−	0.996948i
$697$	−380.815			−0.546363
$698$	−306.653	+	306.653i	−0.439331	+	0.439331i
$699$	505.416	−	505.416i	0.723056	−	0.723056i
$700$			334.581i			0.477973i
$701$			330.622i			0.471643i	0.971796	+	0.235822i	$0.0757781\pi$
$701$			330.622i			0.471643i	−0.971796	+	0.235822i	$0.924222\pi$
$702$			409.776i			0.583727i
$703$	−536.759			−0.763526
$704$	721.633	+	721.633i	1.02505	+	1.02505i
$705$		−	88.4262i		−	0.125427i
$706$	−170.091	−	170.091i	−0.240922	−	0.240922i
$707$	−309.457	+	309.457i	−0.437705	+	0.437705i
$708$	51.8968	+	51.8968i	0.0733005	+	0.0733005i
$709$		−	740.213i		−	1.04402i	−0.852938	−	0.522012i	$-0.825182\pi$
$709$		−	740.213i		−	1.04402i	0.852938	−	0.522012i	$-0.174818\pi$
$710$	−17.8919	+	17.8919i	−0.0251998	+	0.0251998i
$711$	−1.76092	−	1.76092i	−0.00247668	−	0.00247668i
$712$	1465.60			2.05843
$713$	−450.270	+	450.270i	−0.631515	+	0.631515i
$714$	362.923	+	362.923i	0.508296	+	0.508296i
$715$	−55.5733	+	55.5733i	−0.0777249	+	0.0777249i
$716$	−488.885			−0.682801
$717$	−834.160	+	834.160i	−1.16340	+	1.16340i
$718$		−	705.920i		−	0.983175i
$719$	−177.916			−0.247449			−0.123725	−	0.992317i	$-0.539484\pi$
$719$	−177.916			−0.247449			−0.123725	+	0.992317i	$0.539484\pi$
$720$	0.577629			0.000802263
$721$	498.876			0.691922
$722$	−230.562	−	230.562i	−0.319337	−	0.319337i
$723$	−350.710	−	350.710i	−0.485076	−	0.485076i
$724$			292.517i			0.404029i
$725$	−293.931	−	655.160i	−0.405422	−	0.903670i
$726$	−625.608			−0.861719
$727$	−322.555	+	322.555i	−0.443680	+	0.443680i	−0.893247	−	0.449567i	$-0.851578\pi$
$727$	−322.555	+	322.555i	−0.443680	+	0.443680i	0.449567	+	0.893247i	$0.351578\pi$
$728$	497.465	−	497.465i	0.683330	−	0.683330i
$729$			713.757i			0.979090i
$730$			23.3934i			0.0320457i
$731$		−	974.443i		−	1.33303i
$732$	324.780			0.443689
$733$	691.012	+	691.012i	0.942718	+	0.942718i	0.998446	−	0.0557278i	$-0.0177479\pi$
$733$	691.012	+	691.012i	0.942718	+	0.942718i	−0.0557278	+	0.998446i	$0.517748\pi$
$734$			524.609i			0.714726i
$735$	−17.2417	−	17.2417i	−0.0234580	−	0.0234580i
$736$	−251.373	+	251.373i	−0.341539	+	0.341539i
$737$	−1512.16	−	1512.16i	−2.05178	−	2.05178i
$738$			7.67059i			0.0103938i
$739$	−80.9996	+	80.9996i	−0.109607	+	0.109607i	−0.759783	−	0.650176i	$-0.774695\pi$
$739$	−80.9996	+	80.9996i	−0.109607	+	0.109607i	0.650176	+	0.759783i	$0.274695\pi$
$740$	25.5143	+	25.5143i	0.0344788	+	0.0344788i
$741$	−369.557			−0.498727
$742$	−144.633	+	144.633i	−0.194923	+	0.194923i
$743$	−27.4691	−	27.4691i	−0.0369705	−	0.0369705i	0.688380	−	0.725350i	$-0.258322\pi$
$743$	−27.4691	−	27.4691i	−0.0369705	−	0.0369705i	−0.725350	+	0.688380i	$0.758322\pi$
$744$	818.782	−	818.782i	1.10051	−	1.10051i
$745$	63.1533			0.0847696
$746$	543.766	−	543.766i	0.728909	−	0.728909i
$747$		−	11.6293i		−	0.0155681i
$748$	−366.656			−0.490182
$749$	−393.098			−0.524831
$750$	112.472			0.149963
$751$	370.129	+	370.129i	0.492849	+	0.492849i	0.909203	−	0.416354i	$-0.136692\pi$
$751$	370.129	+	370.129i	0.492849	+	0.492849i	−0.416354	+	0.909203i	$0.636692\pi$
$752$	275.785	+	275.785i	0.366735	+	0.366735i
$753$		−	565.709i		−	0.751273i
$754$	−158.190	+	415.627i	−0.209801	+	0.551229i
$755$	−29.0267			−0.0384460
$756$	255.317	−	255.317i	0.337721	−	0.337721i
$757$	361.762	−	361.762i	0.477889	−	0.477889i	−0.426567	−	0.904456i	$-0.640277\pi$
$757$	361.762	−	361.762i	0.477889	−	0.477889i	0.904456	+	0.426567i	$0.140277\pi$
$758$		−	160.160i		−	0.211293i
$759$		−	699.517i		−	0.921630i
$760$		−	51.3482i		−	0.0675634i
$761$	955.440			1.25551			0.627753	−	0.778413i	$-0.283975\pi$
$761$	955.440			1.25551			0.627753	+	0.778413i	$0.283975\pi$
$762$	98.9819	+	98.9819i	0.129897	+	0.129897i
$763$		−	663.582i		−	0.869702i
$764$	78.2809	+	78.2809i	0.102462	+	0.102462i
$765$	−0.857727	+	0.857727i	−0.00112121	+	0.00112121i
$766$	606.154	+	606.154i	0.791324	+	0.791324i
$767$		−	145.712i		−	0.189977i
$768$	550.576	−	550.576i	0.716896	−	0.716896i
$769$	−881.047	−	881.047i	−1.14570	−	1.14570i	−0.987388	−	0.158316i	$-0.949393\pi$
$769$	−881.047	−	881.047i	−1.14570	−	1.14570i	−0.158316	−	0.987388i	$-0.550607\pi$
$770$	−96.6195			−0.125480
$771$	243.466	−	243.466i	0.315779	−	0.315779i
$772$	83.2796	+	83.2796i	0.107875	+	0.107875i
$773$	−46.5963	+	46.5963i	−0.0602799	+	0.0602799i	−0.736604	−	0.676324i	$-0.763572\pi$
$773$	−46.5963	+	46.5963i	−0.0602799	+	0.0602799i	0.676324	+	0.736604i	$0.263572\pi$
$774$	−19.6278			−0.0253589
$775$	773.097	−	773.097i	0.997545	−	0.997545i
$776$			410.959i			0.529586i
$777$	1083.94			1.39503
$778$	240.124			0.308643
$779$	337.092			0.432724
$780$	17.5665	+	17.5665i	0.0225212	+	0.0225212i
$781$	−383.963	−	383.963i	−0.491630	−	0.491630i
$782$			301.915i			0.386080i
$783$	−275.652	+	724.247i	−0.352046	+	0.924964i
$784$	107.547			0.137177
$785$	−103.057	+	103.057i	−0.131283	+	0.131283i
$786$	−215.949	+	215.949i	−0.274745	+	0.274745i
$787$		−	201.018i		−	0.255424i	−0.991811	−	0.127712i	$-0.959237\pi$
$787$		−	201.018i		−	0.255424i	0.991811	−	0.127712i	$-0.0407633\pi$
$788$		−	99.7854i		−	0.126631i
$789$			1199.18i			1.51988i
$790$	−10.2643			−0.0129928
$791$	3.59940	+	3.59940i	0.00455044	+	0.00455044i
$792$			25.0749i			0.0316602i
$793$	−455.948	−	455.948i	−0.574967	−	0.574967i
$794$	−751.125	+	751.125i	−0.946001	+	0.946001i
$795$	−17.3403	−	17.3403i	−0.0218117	−	0.0218117i
$796$		−	18.0077i		−	0.0226227i
$797$	−463.705	+	463.705i	−0.581813	+	0.581813i	−0.935401	−	0.353588i	$-0.884962\pi$
$797$	−463.705	+	463.705i	−0.581813	+	0.581813i	0.353588	+	0.935401i	$0.384962\pi$
$798$	−321.255	−	321.255i	−0.402575	−	0.402575i
$799$	−819.030			−1.02507
$800$	431.598	−	431.598i	0.539497	−	0.539497i
$801$	21.6708	+	21.6708i	0.0270547	+	0.0270547i
$802$	−485.916	+	485.916i	−0.605880	+	0.605880i
$803$	−502.026			−0.625188
$804$	−477.990	+	477.990i	−0.594515	+	0.594515i
$805$		−	57.0236i		−	0.0708368i
$806$	−677.111			−0.840088
$807$	−1297.81			−1.60819
$808$	468.128			0.579367
$809$	775.202	+	775.202i	0.958222	+	0.958222i	0.999162	−	0.0409393i	$-0.0130350\pi$
$809$	775.202	+	775.202i	0.958222	+	0.958222i	−0.0409393	+	0.999162i	$0.513035\pi$
$810$	−43.5667	−	43.5667i	−0.0537860	−	0.0537860i
$811$			612.179i			0.754845i	0.926041	+	0.377423i	$0.123190\pi$
$811$			612.179i			0.754845i	−0.926041	+	0.377423i	$0.876810\pi$
$812$	357.525	−	160.400i	0.440302	−	0.197537i
$813$	955.370			1.17512
$814$	763.929	−	763.929i	0.938488	−	0.938488i
$815$	74.1127	−	74.1127i	0.0909358	−	0.0909358i
$816$		−	271.408i		−	0.332608i
$817$			862.564i			1.05577i
$818$		−	970.221i		−	1.18609i
$819$	14.7113			0.0179625
$820$	−16.0234	−	16.0234i	−0.0195407	−	0.0195407i
$821$			436.309i			0.531436i	0.964051	+	0.265718i	$0.0856091\pi$
$821$			436.309i			0.531436i	−0.964051	+	0.265718i	$0.914391\pi$
$822$	−26.6672	−	26.6672i	−0.0324419	−	0.0324419i
$823$	1065.70	−	1065.70i	1.29489	−	1.29489i	0.363168	−	0.931724i	$-0.381695\pi$
$823$	1065.70	−	1065.70i	1.29489	−	1.29489i	0.931724	−	0.363168i	$-0.118305\pi$
$824$	−377.335	−	377.335i	−0.457930	−	0.457930i
$825$			1201.05i			1.45581i
$826$	126.668	−	126.668i	0.153351	−	0.153351i
$827$	348.391	+	348.391i	0.421271	+	0.421271i	0.885641	−	0.464370i	$-0.153719\pi$
$827$	348.391	+	348.391i	0.421271	+	0.421271i	−0.464370	+	0.885641i	$0.653719\pi$
$828$	−4.35877			−0.00526422
$829$	−973.035	+	973.035i	−1.17375	+	1.17375i	−0.192436	+	0.981310i	$0.561639\pi$
$829$	−973.035	+	973.035i	−1.17375	+	1.17375i	−0.981310	+	0.192436i	$0.938361\pi$
$830$	−33.8934	−	33.8934i	−0.0408355	−	0.0408355i
$831$	−621.758	+	621.758i	−0.748204	+	0.748204i
$832$	−640.461			−0.769785
$833$	−159.698	+	159.698i	−0.191714	+	0.191714i
$834$			1035.95i			1.24215i
$835$	−57.1884			−0.0684891
$836$	324.559			0.388229
$837$	−1179.89			−1.40967
$838$	632.457	+	632.457i	0.754722	+	0.754722i
$839$	356.180	+	356.180i	0.424530	+	0.424530i	0.886760	−	0.462230i	$-0.152951\pi$
$839$	356.180	+	356.180i	0.424530	+	0.424530i	−0.462230	+	0.886760i	$0.652951\pi$
$840$			103.693i			0.123444i
$841$	−559.176	+	628.175i	−0.664894	+	0.746938i
$842$	81.1375			0.0963628
$843$	1041.28	−	1041.28i	1.23520	−	1.23520i
$844$	−118.924	+	118.924i	−0.140906	+	0.140906i
$845$			33.2663i			0.0393684i
$846$			16.4974i			0.0195005i
$847$		−	1094.44i		−	1.29214i
$848$	108.162			0.127550
$849$	203.758	+	203.758i	0.239997	+	0.239997i
$850$		−	518.376i		−	0.609854i
$851$	450.861	+	450.861i	0.529802	+	0.529802i
$852$	−121.369	+	121.369i	−0.142452	+	0.142452i
$853$	386.118	+	386.118i	0.452658	+	0.452658i	0.896236	−	0.443578i	$-0.146291\pi$
$853$	386.118	+	386.118i	0.452658	+	0.452658i	−0.443578	+	0.896236i	$0.646291\pi$
$854$		−	792.710i		−	0.928232i
$855$	0.759249	−	0.759249i	0.000888010	−	0.000888010i
$856$	297.328	+	297.328i	0.347346	+	0.347346i
$857$	−1215.88			−1.41876			−0.709379	−	0.704827i	$-0.751025\pi$
$857$	−1215.88			−1.41876			−0.709379	+	0.704827i	$0.751025\pi$
$858$	525.963	−	525.963i	0.613010	−	0.613010i
$859$	255.287	+	255.287i	0.297191	+	0.297191i	0.839913	−	0.542721i	$-0.182606\pi$
$859$	255.287	+	255.287i	0.297191	+	0.297191i	−0.542721	+	0.839913i	$0.682606\pi$
$860$	41.0012	−	41.0012i	0.0476758	−	0.0476758i
$861$	−680.728			−0.790624
$862$	−291.612	+	291.612i	−0.338297	+	0.338297i
$863$		−	785.434i		−	0.910120i	−0.890461	−	0.455060i	$-0.849618\pi$
$863$		−	785.434i		−	0.910120i	0.890461	−	0.455060i	$-0.150382\pi$
$864$	−658.700			−0.762384
$865$	25.1106			0.0290296
$866$	−463.413			−0.535118
$867$	−216.178	−	216.178i	−0.249341	−	0.249341i
$868$	421.884	+	421.884i	0.486042	+	0.486042i
$869$		−	220.274i		−	0.253479i
$870$	−26.8305	−	59.8041i	−0.0308397	−	0.0687403i
$871$	1342.07			1.54084
$872$	−501.914	+	501.914i	−0.575589	+	0.575589i
$873$	−6.07655	+	6.07655i	−0.00696054	+	0.00696054i
$874$		−	267.251i		−	0.305779i
$875$			196.759i			0.224868i
$876$			158.689i			0.181152i
$877$	928.813			1.05908			0.529540	−	0.848285i	$-0.322365\pi$
$877$	928.813			1.05908			0.529540	+	0.848285i	$0.322365\pi$
$878$	−410.224	−	410.224i	−0.467225	−	0.467225i
$879$			91.0962i			0.103636i
$880$	36.1279	+	36.1279i	0.0410545	+	0.0410545i
$881$	254.765	−	254.765i	0.289177	−	0.289177i	−0.547578	−	0.836755i	$-0.684450\pi$
$881$	254.765	−	254.765i	0.289177	−	0.289177i	0.836755	+	0.547578i	$0.184450\pi$
$882$	3.21672	+	3.21672i	0.00364708	+	0.00364708i
$883$			3.93324i			0.00445441i	0.999998	+	0.00222720i	$0.000708941\pi$
$883$			3.93324i			0.00445441i	−0.999998	+	0.00222720i	$0.999291\pi$
$884$	162.707	−	162.707i	0.184057	−	0.184057i
$885$	15.1864	+	15.1864i	0.0171597	+	0.0171597i
$886$	537.197			0.606317
$887$	59.1814	−	59.1814i	0.0667208	−	0.0667208i	−0.672959	−	0.739680i	$-0.734977\pi$
$887$	59.1814	−	59.1814i	0.0667208	−	0.0667208i	0.739680	+	0.672959i	$0.234977\pi$
$888$	−819.857	−	819.857i	−0.923262	−	0.923262i
$889$	−173.159	+	173.159i	−0.194780	+	0.194780i
$890$	126.318			0.141930
$891$	934.949	−	934.949i	1.04933	−	1.04933i
$892$		−	278.797i		−	0.312553i
$893$	724.995			0.811865
$894$	−597.702			−0.668571
$895$	−143.061			−0.159845
$896$	7.37852	+	7.37852i	0.00823495	+	0.00823495i
$897$	310.417	+	310.417i	0.346061	+	0.346061i
$898$			288.993i			0.321818i
$899$	−1196.74	−	455.485i	−1.33119	−	0.506658i
$900$	7.48385			0.00831539
$901$	−160.611	+	160.611i	−0.178259	+	0.178259i
$902$	−479.759	+	479.759i	−0.531883	+	0.531883i
$903$		−	1741.87i		−	1.92898i
$904$		−	5.44495i		−	0.00602317i
$905$			85.5982i			0.0945837i
$906$	274.718			0.303221
$907$	−106.097	−	106.097i	−0.116976	−	0.116976i	0.646196	−	0.763172i	$-0.276359\pi$
$907$	−106.097	−	106.097i	−0.116976	−	0.116976i	−0.763172	+	0.646196i	$0.776359\pi$
$908$		−	200.955i		−	0.221316i
$909$	6.92188	+	6.92188i	0.00761483	+	0.00761483i
$910$	42.8757	−	42.8757i	0.0471161	−	0.0471161i
$911$	844.949	+	844.949i	0.927496	+	0.927496i	0.997544	−	0.0700474i	$-0.0223151\pi$
$911$	844.949	+	844.949i	0.927496	+	0.927496i	−0.0700474	+	0.997544i	$0.522315\pi$
$912$			240.247i			0.263429i
$913$	727.359	−	727.359i	0.796670	−	0.796670i
$914$	−514.174	−	514.174i	−0.562554	−	0.562554i
$915$	95.0393			0.103868
$916$	−15.5323	+	15.5323i	−0.0169567	+	0.0169567i
$917$	−377.782	−	377.782i	−0.411977	−	0.411977i
$918$	−395.570	+	395.570i	−0.430904	+	0.430904i
$919$	1137.34			1.23759			0.618793	−	0.785554i	$-0.287622\pi$
$919$	1137.34			1.23759			0.618793	+	0.785554i	$0.287622\pi$
$920$	−43.1310	+	43.1310i	−0.0468815	+	0.0468815i
$921$		−	827.641i		−	0.898633i
$922$	1032.01			1.11931
$923$	340.773			0.369202
$924$	−655.418			−0.709327
$925$	−774.112	−	774.112i	−0.836878	−	0.836878i
$926$	155.597	+	155.597i	0.168031	+	0.168031i
$927$		−	11.1587i		−	0.0120375i
$928$	−668.105	−	254.284i	−0.719941	−	0.274013i
$929$	−50.8383			−0.0547237			−0.0273619	−	0.999626i	$-0.508711\pi$
$929$	−50.8383			−0.0547237			−0.0273619	+	0.999626i	$0.508711\pi$
$930$	70.5695	−	70.5695i	0.0758812	−	0.0758812i
$931$	141.362	−	141.362i	0.151839	−	0.151839i
$932$		−	393.947i		−	0.422690i
$933$			483.536i			0.518259i
$934$		−	137.105i		−	0.146794i
$935$	−107.293			−0.114752
$936$	−11.1272	−	11.1272i	−0.0118880	−	0.0118880i
$937$			1022.04i			1.09076i	0.838189	+	0.545380i	$0.183615\pi$
$937$			1022.04i			1.09076i	−0.838189	+	0.545380i	$0.816385\pi$
$938$	1166.66	+	1166.66i	1.24377	+	1.24377i
$939$	−256.652	+	256.652i	−0.273325	+	0.273325i
$940$	−34.4620	−	34.4620i	−0.0366617	−	0.0366617i
$941$			1171.17i			1.24460i	0.782779	+	0.622300i	$0.213802\pi$
$941$			1171.17i			1.24460i	−0.782779	+	0.622300i	$0.786198\pi$
$942$	975.364	−	975.364i	1.03542	−	1.03542i
$943$	−283.148	−	283.148i	−0.300262	−	0.300262i
$944$	−94.7269			−0.100346
$945$	74.7126	−	74.7126i	0.0790610	−	0.0790610i
$946$	−1227.62	−	1227.62i	−1.29770	−	1.29770i
$947$	32.8294	−	32.8294i	0.0346668	−	0.0346668i	−0.689561	−	0.724228i	$-0.742196\pi$
$947$	32.8294	−	32.8294i	0.0346668	−	0.0346668i	0.724228	+	0.689561i	$0.242196\pi$
$948$	−69.6278			−0.0734470
$949$	222.778	−	222.778i	0.234751	−	0.234751i
$950$			458.860i			0.483010i
$951$	−1158.61			−1.21831
$952$	960.437			1.00886
$953$	−532.758			−0.559032			−0.279516	−	0.960141i	$-0.590174\pi$
$953$	−532.758			−0.559032			−0.279516	+	0.960141i	$0.590174\pi$
$954$	3.23512	+	3.23512i	0.00339111	+	0.00339111i
$955$	22.9071	+	22.9071i	0.0239865	+	0.0239865i
$956$			650.188i			0.680113i
$957$	1283.41	−	575.788i	1.34107	−	0.601659i
$958$	55.8889			0.0583392
$959$	46.6517	−	46.6517i	0.0486462	−	0.0486462i
$960$	66.7499	−	66.7499i	0.0695311	−	0.0695311i
$961$		−	988.645i		−	1.02877i
$962$			678.000i			0.704781i
$963$			8.79274i			0.00913058i
$964$	−273.362			−0.283570
$965$	24.3698	+	24.3698i	0.0252537	+	0.0252537i
$966$			539.689i			0.558684i
$967$	1050.69	+	1050.69i	1.08655	+	1.08655i	0.995881	+	0.0906692i	$0.0289006\pi$
$967$	1050.69	+	1050.69i	1.08655	+	1.08655i	0.0906692	+	0.995881i	$0.471099\pi$
$968$	−827.803	+	827.803i	−0.855168	+	0.855168i
$969$	−356.745	−	356.745i	−0.368158	−	0.368158i
$970$			35.4199i			0.0365154i
$971$	−645.432	+	645.432i	−0.664709	+	0.664709i	−0.956486	−	0.291777i	$-0.905753\pi$
$971$	−645.432	+	645.432i	−0.664709	+	0.664709i	0.291777	+	0.956486i	$0.405753\pi$
$972$	−11.5390	−	11.5390i	−0.0118714	−	0.0118714i
$973$	−1812.30			−1.86259
$974$	414.065	−	414.065i	0.425118	−	0.425118i
$975$	−532.974	−	532.974i	−0.546640	−	0.546640i
$976$	−296.410	+	296.410i	−0.303699	+	0.303699i
$977$	1341.58			1.37317			0.686583	−	0.727052i	$-0.259110\pi$
$977$	1341.58			1.37317			0.686583	+	0.727052i	$0.259110\pi$
$978$	−701.425	+	701.425i	−0.717204	+	0.717204i
$979$			2710.81i			2.76896i
$980$	−13.4390			−0.0137133
$981$	−14.8429			−0.0151303
$982$	−423.891			−0.431661
$983$	−717.569	−	717.569i	−0.729979	−	0.729979i	0.240636	−	0.970615i	$-0.422644\pi$
$983$	−717.569	−	717.569i	−0.729979	−	0.729979i	−0.970615	+	0.240636i	$0.922644\pi$
$984$	514.882	+	514.882i	0.523254	+	0.523254i
$985$		−	29.1999i		−	0.0296445i
$986$	−553.924	+	248.512i	−0.561789	+	0.252041i
$987$	−1464.06			−1.48335
$988$	−144.026	+	144.026i	−0.145775	+	0.145775i
$989$	724.528	−	724.528i	0.732586	−	0.732586i
$990$			2.16117i			0.00218300i
$991$			1257.05i			1.26846i	0.773142	+	0.634232i	$0.218684\pi$
$991$			1257.05i			1.26846i	−0.773142	+	0.634232i	$0.781316\pi$
$992$		−	1088.43i		−	1.09721i
$993$	276.528			0.278477
$994$	296.234	+	296.234i	0.298022	+	0.298022i
$995$		−	5.26953i		−	0.00529601i
$996$	−229.916	−	229.916i	−0.230839	−	0.230839i
$997$	19.5297	−	19.5297i	0.0195885	−	0.0195885i	−0.697245	−	0.716833i	$-0.745591\pi$
$997$	19.5297	−	19.5297i	0.0195885	−	0.0195885i	0.716833	+	0.697245i	$0.245591\pi$
$998$	−554.489	−	554.489i	−0.555600	−	0.555600i
$999$			1181.44i			1.18262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.3.c.a.17.2	yes	8
3.2	odd	2		261.3.f.a.46.3		8
4.3	odd	2		464.3.l.c.17.3		8
29.12	odd	4	inner	29.3.c.a.12.2	✓	8
87.41	even	4		261.3.f.a.244.3		8
116.99	even	4		464.3.l.c.273.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.2	✓	8	29.12	odd	4	inner
29.3.c.a.17.2	yes	8	1.1	even	1	trivial
261.3.f.a.46.3		8	3.2	odd	2
261.3.f.a.244.3		8	87.41	even	4
464.3.l.c.17.3		8	4.3	odd	2
464.3.l.c.273.3		8	116.99	even	4

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)

\(f(q)\)	\(=\)	\(q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +O(q^{10})\)	\(q+(-1.07935 + 1.07935i) q^{2} +(-2.14254 + 2.14254i) q^{3} +1.67001i q^{4} +0.488689i q^{5} -4.62511i q^{6} +8.09117 q^{7} +(-6.11992 - 6.11992i) q^{8} -0.180982i q^{9} +(-0.527467 - 0.527467i) q^{10} +(11.3195 - 11.3195i) q^{11} +(-3.57807 - 3.57807i) q^{12} +10.0463i q^{13} +(-8.73320 + 8.73320i) q^{14} +(-1.04704 - 1.04704i) q^{15} +6.53103 q^{16} +(-9.69799 + 9.69799i) q^{17} +(0.195342 + 0.195342i) q^{18} +(8.58453 - 8.58453i) q^{19} -0.816116 q^{20} +(-17.3357 + 17.3357i) q^{21} +24.4355i q^{22} -14.4215 q^{23} +26.2244 q^{24} +24.7612 q^{25} +(-10.8434 - 10.8434i) q^{26} +(-18.8951 - 18.8951i) q^{27} +13.5123i q^{28} +(-11.8706 - 26.4592i) q^{29} +2.26024 q^{30} +(31.2221 - 31.2221i) q^{31} +(17.4304 - 17.4304i) q^{32} +48.5052i q^{33} -20.9350i q^{34} +3.95407i q^{35} +0.302241 q^{36} +(-31.2631 - 31.2631i) q^{37} +18.5314i q^{38} +(-21.5246 - 21.5246i) q^{39} +(2.99074 - 2.99074i) q^{40} +(19.6337 + 19.6337i) q^{41} -37.4225i q^{42} +(-50.2394 + 50.2394i) q^{43} +(18.9037 + 18.9037i) q^{44} +0.0884438 q^{45} +(15.5658 - 15.5658i) q^{46} +(42.2268 + 42.2268i) q^{47} +(-13.9930 + 13.9930i) q^{48} +16.4671 q^{49} +(-26.7260 + 26.7260i) q^{50} -41.5567i q^{51} -16.7774 q^{52} +16.5613 q^{53} +40.7889 q^{54} +(5.53173 + 5.53173i) q^{55} +(-49.5173 - 49.5173i) q^{56} +36.7855i q^{57} +(41.3713 + 15.7461i) q^{58} -14.5041 q^{59} +(1.74856 - 1.74856i) q^{60} +(-45.3849 + 45.3849i) q^{61} +67.3992i q^{62} -1.46435i q^{63} +63.7512i q^{64} -4.90950 q^{65} +(-52.3540 - 52.3540i) q^{66} -133.589i q^{67} +(-16.1957 - 16.1957i) q^{68} +(30.8987 - 30.8987i) q^{69} +(-4.26782 - 4.26782i) q^{70} -33.9204i q^{71} +(-1.10759 + 1.10759i) q^{72} +(-22.1752 - 22.1752i) q^{73} +67.4877 q^{74} +(-53.0519 + 53.0519i) q^{75} +(14.3363 + 14.3363i) q^{76} +(91.5883 - 91.5883i) q^{77} +46.4651 q^{78} +(9.72981 - 9.72981i) q^{79} +3.19164i q^{80} +82.5961 q^{81} -42.3833 q^{82} +64.2570 q^{83} +(-28.9508 - 28.9508i) q^{84} +(-4.73930 - 4.73930i) q^{85} -108.452i q^{86} +(82.1233 + 31.2565i) q^{87} -138.549 q^{88} +(-119.740 + 119.740i) q^{89} +(-0.0954618 + 0.0954618i) q^{90} +81.2861i q^{91} -24.0840i q^{92} +133.790i q^{93} -91.1550 q^{94} +(4.19517 + 4.19517i) q^{95} +74.6909i q^{96} +(-33.5755 - 33.5755i) q^{97} +(-17.7737 + 17.7737i) q^{98} +(-2.04863 - 2.04863i) 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

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