LMFDB - Embedded newform 261.3.s.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	261.37
Dual form			261.3.s.a.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +O(q^{10})$	\(q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +(-1.59042 - 14.1154i) q^{10} +(-3.16517 + 5.03734i) q^{11} +(14.6839 - 3.35151i) q^{13} +(-3.98966 - 11.4018i) q^{14} +(-4.38044 - 19.1919i) q^{16} +(-22.0898 - 22.0898i) q^{17} +(-0.835449 + 0.0941325i) q^{19} +(1.95054 - 8.54589i) q^{20} +(-10.8478 + 8.65079i) q^{22} +(21.1449 + 10.1828i) q^{23} +(-7.54184 + 9.45717i) q^{25} +(34.9058 + 3.93294i) q^{26} -7.45431i q^{28} +(18.7362 + 22.1350i) q^{29} +(21.3525 + 7.47156i) q^{31} +(2.46561 - 21.8829i) q^{32} +(-31.6117 - 65.6424i) q^{34} +(-13.6875 + 28.4225i) q^{35} +(4.25720 + 6.77529i) q^{37} +(-1.91161 - 0.436313i) q^{38} +(-19.3529 + 30.8000i) q^{40} +(8.24028 - 8.24028i) q^{41} +(-3.09691 - 8.85047i) q^{43} +(-8.08161 + 2.82788i) q^{44} +(38.7033 + 38.7033i) q^{46} +(22.1022 + 13.8877i) q^{47} +(4.93392 - 21.6169i) q^{49} +(-23.8868 + 15.0091i) q^{50} +(19.5299 + 9.40509i) q^{52} +(-47.7265 + 22.9839i) q^{53} +(36.0068 + 4.05699i) q^{55} +(-10.2167 + 29.1977i) q^{56} +(24.1944 + 63.1585i) q^{58} -17.4148 q^{59} +(6.87260 - 60.9960i) q^{61} +(41.2488 + 32.8948i) q^{62} +(-11.8813 + 24.6717i) q^{64} +(-57.1957 - 71.7211i) q^{65} +(-26.2055 - 5.98124i) q^{67} +(-5.03393 - 44.6774i) q^{68} +(-52.0241 + 52.0241i) q^{70} +(4.93086 - 1.12544i) q^{71} +(-53.0793 + 18.5732i) q^{73} +(4.15264 + 18.1939i) q^{74} +(-1.02452 - 0.643750i) q^{76} +(30.6201 - 3.45006i) q^{77} +(74.2026 - 46.6246i) q^{79} +(-93.7398 + 74.7550i) q^{80} +(24.4869 - 11.7923i) q^{82} +(48.3929 - 60.6827i) q^{83} +(-62.8424 + 179.593i) q^{85} -21.8683i q^{86} +35.5306 q^{88} +(138.036 + 48.3009i) q^{89} +(-60.9916 - 48.6392i) q^{91} +(14.6551 + 30.4317i) q^{92} +(37.9568 + 47.5963i) q^{94} +(2.72434 + 4.33577i) q^{95} +(0.115126 + 1.02177i) q^{97} +(27.5123 - 43.7855i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.20133	+	0.770280i	1.10067	+	0.385140i	0.818663	−	0.574274i	$-0.194715\pi$
$2$	2.20133	+	0.770280i	1.10067	+	0.385140i	0.282003	+	0.959414i	$0.409001\pi$
$3$		0			0
$3$		0			0
$4$	1.12521	+	0.897324i	0.281302	+	0.224331i
$5$	−2.64264	−	5.48750i	−0.528528	−	1.09750i	−0.978840	−	0.204628i	$-0.934401\pi$
$5$	−2.64264	−	5.48750i	−0.528528	−	1.09750i	0.450312	−	0.892871i	$-0.351313\pi$
$6$		0			0
$7$	−3.22936	−	4.04949i	−0.461337	−	0.578499i	0.495689	−	0.868500i	$-0.334916\pi$
$7$	−3.22936	−	4.04949i	−0.461337	−	0.578499i	−0.957026	+	0.290001i	$0.906344\pi$
$8$	−3.17747	−	5.05691i	−0.397184	−	0.632114i
$9$		0			0
$10$	−1.59042	−	14.1154i	−0.159042	−	1.41154i
$11$	−3.16517	+	5.03734i	−0.287743	+	0.457940i	−0.959049	−	0.283240i	$-0.908591\pi$
$11$	−3.16517	+	5.03734i	−0.287743	+	0.457940i	0.671306	+	0.741180i	$0.265734\pi$
$12$		0			0
$13$	14.6839	−	3.35151i	1.12953	−	0.257808i	0.383385	−	0.923589i	$-0.374758\pi$
$13$	14.6839	−	3.35151i	1.12953	−	0.257808i	0.746148	+	0.665780i	$0.231901\pi$
$14$	−3.98966	−	11.4018i	−0.284976	−	0.814414i
$15$		0			0
$16$	−4.38044	−	19.1919i	−0.273777	−	1.19950i
$17$	−22.0898	−	22.0898i	−1.29940	−	1.29940i	−0.928787	−	0.370615i	$-0.879147\pi$
$17$	−22.0898	−	22.0898i	−1.29940	−	1.29940i	−0.370615	−	0.928787i	$-0.620853\pi$
$18$		0			0
$19$	−0.835449	+	0.0941325i	−0.0439710	+	0.00495434i	−0.133923	−	0.990992i	$-0.542757\pi$
$19$	−0.835449	+	0.0941325i	−0.0439710	+	0.00495434i	0.0899516	+	0.995946i	$0.471329\pi$
$20$	1.95054	−	8.54589i	0.0975272	−	0.427294i
$21$		0			0
$22$	−10.8478	+	8.65079i	−0.493080	+	0.393218i
$23$	21.1449	+	10.1828i	0.919344	+	0.442733i	0.832837	−	0.553519i	$-0.186715\pi$
$23$	21.1449	+	10.1828i	0.919344	+	0.442733i	0.0865068	+	0.996251i	$0.472430\pi$
$24$		0			0
$25$	−7.54184	+	9.45717i	−0.301674	+	0.378287i
$26$	34.9058	+	3.93294i	1.34253	+	0.151267i
$27$		0			0
$28$		−	7.45431i		−	0.266225i
$29$	18.7362	+	22.1350i	0.646074	+	0.763274i
$29$	18.7362	+	22.1350i	0.646074	+	0.763274i
$30$		0			0
$31$	21.3525	+	7.47156i	0.688790	+	0.241018i	0.651904	−	0.758301i	$-0.273970\pi$
$31$	21.3525	+	7.47156i	0.688790	+	0.241018i	0.0368860	+	0.999319i	$0.488256\pi$
$32$	2.46561	−	21.8829i	0.0770504	−	0.683841i
$33$		0			0
$34$	−31.6117	−	65.6424i	−0.929756	−	1.93066i
$35$	−13.6875	+	28.4225i	−0.391073	+	0.812070i
$36$		0			0
$37$	4.25720	+	6.77529i	0.115059	+	0.183116i	0.899289	−	0.437355i	$-0.144085\pi$
$37$	4.25720	+	6.77529i	0.115059	+	0.183116i	−0.784230	+	0.620470i	$0.786942\pi$
$38$	−1.91161	−	0.436313i	−0.0503055	−	0.0114819i
$39$		0			0
$40$	−19.3529	+	30.8000i	−0.483822	+	0.769999i
$41$	8.24028	−	8.24028i	0.200982	−	0.200982i	−0.599438	−	0.800421i	$-0.704609\pi$
$41$	8.24028	−	8.24028i	0.200982	−	0.200982i	0.800421	+	0.599438i	$0.204609\pi$
$42$		0			0
$43$	−3.09691	−	8.85047i	−0.0720212	−	0.205825i	0.902246	−	0.431222i	$-0.141918\pi$
$43$	−3.09691	−	8.85047i	−0.0720212	−	0.205825i	−0.974267	+	0.225398i	$0.927632\pi$
$44$	−8.08161	+	2.82788i	−0.183673	+	0.0642699i
$45$		0			0
$46$	38.7033	+	38.7033i	0.841377	+	0.841377i
$47$	22.1022	+	13.8877i	0.470259	+	0.295483i	0.746237	−	0.665681i	$-0.231859\pi$
$47$	22.1022	+	13.8877i	0.470259	+	0.295483i	−0.275978	+	0.961164i	$0.589002\pi$
$48$		0			0
$49$	4.93392	−	21.6169i	0.100692	−	0.441162i
$50$	−23.8868	+	15.0091i	−0.477735	+	0.300181i
$51$		0			0
$52$	19.5299	+	9.40509i	0.375574	+	0.180867i
$53$	−47.7265	+	22.9839i	−0.900501	+	0.433658i	−0.826070	−	0.563568i	$-0.809428\pi$
$53$	−47.7265	+	22.9839i	−0.900501	+	0.433658i	−0.0744311	+	0.997226i	$0.523714\pi$
$54$		0			0
$55$	36.0068	+	4.05699i	0.654669	+	0.0737635i
$56$	−10.2167	+	29.1977i	−0.182442	+	0.521388i
$57$		0			0
$58$	24.1944	+	63.1585i	0.417145	+	1.08894i
$59$	−17.4148			−0.295166			−0.147583	−	0.989050i	$-0.547149\pi$
$59$	−17.4148			−0.295166			−0.147583	+	0.989050i	$0.547149\pi$
$60$		0			0
$61$	6.87260	−	60.9960i	0.112666	−	0.999935i	−0.802443	−	0.596728i	$-0.796467\pi$
$61$	6.87260	−	60.9960i	0.112666	−	0.999935i	0.915109	−	0.403207i	$-0.132104\pi$
$62$	41.2488	+	32.8948i	0.665303	+	0.530561i
$63$		0			0
$64$	−11.8813	+	24.6717i	−0.185645	+	0.385496i
$65$	−57.1957	−	71.7211i	−0.879934	−	1.10340i
$66$		0			0
$67$	−26.2055	−	5.98124i	−0.391127	−	0.0892722i	0.0224346	−	0.999748i	$-0.492858\pi$
$67$	−26.2055	−	5.98124i	−0.391127	−	0.0892722i	−0.413562	+	0.910476i	$0.635715\pi$
$68$	−5.03393	−	44.6774i	−0.0740285	−	0.657021i
$69$		0			0
$70$	−52.0241	+	52.0241i	−0.743201	+	0.743201i
$71$	4.93086	−	1.12544i	0.0694487	−	0.0158512i	−0.187655	−	0.982235i	$-0.560089\pi$
$71$	4.93086	−	1.12544i	0.0694487	−	0.0158512i	0.257104	+	0.966384i	$0.417232\pi$
$72$		0			0
$73$	−53.0793	+	18.5732i	−0.727113	+	0.254428i	−0.668353	−	0.743844i	$-0.733000\pi$
$73$	−53.0793	+	18.5732i	−0.727113	+	0.254428i	−0.0587602	+	0.998272i	$0.518715\pi$
$74$	4.15264	+	18.1939i	0.0561167	+	0.245863i
$75$		0			0
$76$	−1.02452	−	0.643750i	−0.0134806	−	0.00847040i
$77$	30.6201	−	3.45006i	0.397664	−	0.0448060i
$78$		0			0
$79$	74.2026	−	46.6246i	0.939274	−	0.590185i	0.0269421	−	0.999637i	$-0.491423\pi$
$79$	74.2026	−	46.6246i	0.939274	−	0.590185i	0.912332	+	0.409452i	$0.134280\pi$
$80$	−93.7398	+	74.7550i	−1.17175	+	0.934438i
$81$		0			0
$82$	24.4869	−	11.7923i	0.298621	−	0.143808i
$83$	48.3929	−	60.6827i	0.583047	−	0.731117i	−0.399583	−	0.916697i	$-0.630845\pi$
$83$	48.3929	−	60.6827i	0.583047	−	0.731117i	0.982629	+	0.185580i	$0.0594164\pi$
$84$		0			0
$85$	−62.8424	+	179.593i	−0.739322	+	2.11286i
$86$		−	21.8683i		−	0.254283i
$87$		0			0
$88$	35.5306			0.403757
$89$	138.036	+	48.3009i	1.55097	+	0.542707i	0.963769	−	0.266737i	$-0.0859455\pi$
$89$	138.036	+	48.3009i	1.55097	+	0.542707i	0.587197	+	0.809444i	$0.300231\pi$
$90$		0			0
$91$	−60.9916	−	48.6392i	−0.670237	−	0.534497i
$92$	14.6551	+	30.4317i	0.159295	+	0.330779i
$93$		0			0
$94$	37.9568	+	47.5963i	0.403796	+	0.506344i
$95$	2.72434	+	4.33577i	0.0286773	+	0.0456397i
$96$		0			0
$97$	0.115126	+	1.02177i	0.00118686	+	0.0105337i	0.994292	−	0.106696i	$-0.0340272\pi$
$97$	0.115126	+	1.02177i	0.00118686	+	0.0105337i	−0.993105	+	0.117230i	$0.962599\pi$
$98$	27.5123	−	43.7855i	0.280737	−	0.446791i
$99$		0			0
$100$	−16.9723	+	3.87382i	−0.169723	+	0.0387382i
$101$	−43.9053	−	125.474i	−0.434706	−	1.24232i	−0.928040	−	0.372479i	$-0.878508\pi$
$101$	−43.9053	−	125.474i	−0.434706	−	1.24232i	0.493334	−	0.869840i	$-0.335778\pi$
$102$		0			0
$103$	1.55354	+	6.80648i	0.0150829	+	0.0660824i	0.981909	−	0.189352i	$-0.0606387\pi$
$103$	1.55354	+	6.80648i	0.0150829	+	0.0660824i	−0.966826	+	0.255434i	$0.917782\pi$
$104$	−63.6060	−	63.6060i	−0.611596	−	0.611596i
$105$		0			0
$106$	−122.766	+	13.8324i	−1.15817	+	0.130494i
$107$	−14.9676	+	65.5774i	−0.139884	+	0.612873i	0.855574	+	0.517680i	$0.173204\pi$
$107$	−14.9676	+	65.5774i	−0.139884	+	0.612873i	−0.995459	+	0.0951935i	$0.969653\pi$
$108$		0			0
$109$	139.358	−	111.134i	1.27851	−	1.01958i	0.280291	−	0.959915i	$-0.409569\pi$
$109$	139.358	−	111.134i	1.27851	−	1.01958i	0.998219	−	0.0596621i	$-0.0190023\pi$
$110$	76.1379	+	36.6661i	0.692163	+	0.333328i
$111$		0			0
$112$	−63.5716	+	79.7163i	−0.567604	+	0.711752i
$113$	−14.1294	−	1.59200i	−0.125039	−	0.0140885i	0.0492231	−	0.998788i	$-0.484325\pi$
$113$	−14.1294	−	1.59200i	−0.125039	−	0.0140885i	−0.174262	+	0.984699i	$0.555754\pi$
$114$		0			0
$115$		−	142.942i		−	1.24298i
$116$	1.21986	+	41.7189i	0.0105161	+	0.359645i
$117$		0			0
$118$	−38.3357	−	13.4143i	−0.324879	−	0.113680i
$119$	−18.1165	+	160.789i	−0.152240	+	1.35116i
$120$		0			0
$121$	37.1435	+	77.1292i	0.306971	+	0.637431i
$122$	62.1129	−	128.979i	0.509122	−	1.05720i
$123$		0			0
$124$	17.3216	+	27.5672i	0.139690	+	0.222316i
$125$	−76.6224	−	17.4886i	−0.612979	−	0.139908i
$126$		0			0
$127$	−56.8872	+	90.5354i	−0.447931	+	0.712877i	−0.992010	−	0.126156i	$-0.959736\pi$
$127$	−56.8872	+	90.5354i	−0.447931	+	0.712877i	0.544080	+	0.839033i	$0.316879\pi$
$128$	−107.445	+	107.445i	−0.839411	+	0.839411i
$129$		0			0
$130$	−70.6614	−	201.939i	−0.543550	−	1.55338i
$131$	15.0564	−	5.26846i	0.114934	−	0.0402172i	−0.272199	−	0.962241i	$-0.587751\pi$
$131$	15.0564	−	5.26846i	0.114934	−	0.0402172i	0.387133	+	0.922024i	$0.373465\pi$
$132$		0			0
$133$	3.07916	+	3.07916i	0.0231516	+	0.0231516i
$134$	−53.0798	−	33.3523i	−0.396118	−	0.248897i
$135$		0			0
$136$	−41.5166	+	181.896i	−0.305269	+	1.33747i
$137$	120.235	−	75.5488i	0.877630	−	0.551451i	−0.0161943	−	0.999869i	$-0.505155\pi$
$137$	120.235	−	75.5488i	0.877630	−	0.551451i	0.893824	+	0.448417i	$0.148012\pi$
$138$		0			0
$139$	199.013	+	95.8394i	1.43174	+	0.689492i	0.979321	−	0.202311i	$-0.0648453\pi$
$139$	199.013	+	95.8394i	1.43174	+	0.689492i	0.452423	+	0.891803i	$0.350560\pi$
$140$	−40.9055	+	19.6991i	−0.292182	+	0.140708i
$141$		0			0
$142$	11.7214	+	1.32068i	0.0825448	+	0.00930057i
$143$	−29.5944	+	84.5760i	−0.206954	+	0.591440i
$144$		0			0
$145$	71.9526	−	161.309i	0.496225	−	1.11248i
$146$	−131.152			−0.898299
$147$		0			0
$148$	−1.28940	+	11.4437i	−0.00871213	+	0.0773223i
$149$	122.156	+	97.4158i	0.819836	+	0.653797i	0.940839	−	0.338855i	$-0.110040\pi$
$149$	122.156	+	97.4158i	0.819836	+	0.653797i	−0.121003	+	0.992652i	$0.538611\pi$
$150$		0			0
$151$	81.9702	−	170.213i	0.542849	−	1.12724i	−0.431483	−	0.902121i	$-0.642009\pi$
$151$	81.9702	−	170.213i	0.542849	−	1.12724i	0.974332	−	0.225117i	$-0.0722764\pi$
$152$	3.13064	+	3.92569i	0.0205963	+	0.0258269i
$153$		0			0
$154$	70.0626	+	15.9913i	0.454952	+	0.103840i
$155$	−15.4268	−	136.916i	−0.0995276	−	0.883332i
$156$		0			0
$157$	−108.735	+	108.735i	−0.692577	+	0.692577i	−0.962798	−	0.270221i	$-0.912903\pi$
$157$	−108.735	+	108.735i	−0.692577	+	0.692577i	0.270221	+	0.962798i	$0.412903\pi$
$158$	199.259	−	45.4795i	1.26113	−	0.287845i
$159$		0			0
$160$	−126.598	+	44.2986i	−0.791239	+	0.276866i
$161$	−27.0492	−	118.510i	−0.168007	−	0.736088i
$162$		0			0
$163$	−194.774	−	122.385i	−1.19493	−	0.750826i	−0.220474	−	0.975393i	$-0.570760\pi$
$163$	−194.774	−	122.385i	−1.19493	−	0.750826i	−0.974459	+	0.224567i	$0.927903\pi$
$164$	16.6662	−	1.87783i	0.101623	−	0.0114502i
$165$		0			0
$166$	153.271	−	96.3068i	0.923322	−	0.580162i
$167$	96.4643	−	76.9277i	0.577631	−	0.460645i	−0.290573	−	0.956853i	$-0.593846\pi$
$167$	96.4643	−	76.9277i	0.577631	−	0.460645i	0.868204	+	0.496208i	$0.165275\pi$
$168$		0			0
$169$	52.1212	−	25.1002i	0.308409	−	0.148522i
$170$	−276.674	+	346.938i	−1.62749	+	2.04081i
$171$		0			0
$172$	4.45707	−	12.7376i	0.0259132	−	0.0740556i
$173$		−	32.3262i		−	0.186857i	−0.995626	−	0.0934283i	$-0.970217\pi$
$173$		−	32.3262i		−	0.186857i	0.995626	−	0.0934283i	$-0.0297826\pi$
$174$		0			0
$175$	62.6521			0.358012
$176$	110.541	+	38.6800i	0.628075	+	0.219773i
$177$		0			0
$178$	266.658	+	212.653i	1.49808	+	1.19468i
$179$	116.664	+	242.255i	0.651754	+	1.35338i	0.920717	+	0.390231i	$0.127605\pi$
$179$	116.664	+	242.255i	0.651754	+	1.35338i	−0.268963	+	0.963151i	$0.586681\pi$
$180$		0			0
$181$	−66.4061	−	83.2706i	−0.366884	−	0.460058i	0.563784	−	0.825922i	$-0.309345\pi$
$181$	−66.4061	−	83.2706i	−0.366884	−	0.460058i	−0.930668	+	0.365864i	$0.880774\pi$
$182$	−96.7970	−	154.052i	−0.531852	−	0.846437i
$183$		0			0
$184$	−15.6935	−	139.284i	−0.0852908	−	0.756976i
$185$	25.9291	−	41.2660i	0.140158	−	0.223059i
$186$		0			0
$187$	181.192	−	41.3559i	0.968941	−	0.221154i
$188$	12.4078	+	35.4594i	0.0659988	+	0.188614i
$189$		0			0
$190$	2.65743	+	11.6430i	0.0139865	+	0.0612788i
$191$	−72.7058	−	72.7058i	−0.380659	−	0.380659i	0.490681	−	0.871339i	$-0.336748\pi$
$191$	−72.7058	−	72.7058i	−0.380659	−	0.380659i	−0.871339	+	0.490681i	$0.836748\pi$
$192$		0			0
$193$	−190.040	+	21.4124i	−0.984665	+	0.110945i	−0.589589	−	0.807703i	$-0.700710\pi$
$193$	−190.040	+	21.4124i	−0.984665	+	0.110945i	−0.395076	+	0.918649i	$0.629282\pi$
$194$	−0.533617	+	2.33793i	−0.00275061	+	0.0120512i
$195$		0			0
$196$	24.9491	−	19.8962i	0.127291	−	0.101511i
$197$	−46.6020	−	22.4423i	−0.236558	−	0.113920i	0.311849	−	0.950132i	$-0.399052\pi$
$197$	−46.6020	−	22.4423i	−0.236558	−	0.113920i	−0.548408	+	0.836211i	$0.684766\pi$
$198$		0			0
$199$	0.321680	−	0.403373i	0.00161648	−	0.00202700i	−0.781023	−	0.624503i	$-0.785302\pi$
$199$	0.321680	−	0.403373i	0.00161648	−	0.00202700i	0.782639	+	0.622476i	$0.213873\pi$
$200$	71.7881	+	8.08857i	0.358940	+	0.0404429i
$201$		0			0
$202$		−	310.030i		−	1.53480i
$203$	29.1295	−	147.354i	0.143495	−	0.725880i
$204$		0			0
$205$	−66.9946	−	23.4424i	−0.326803	−	0.114353i
$206$	−1.82305	+	16.1800i	−0.00884974	+	0.0785437i
$207$		0			0
$208$	−128.644	−	267.132i	−0.618480	−	1.28429i
$209$	2.17016	−	4.50639i	0.0103835	−	0.0215617i
$210$		0			0
$211$	81.6700	+	129.977i	0.387062	+	0.616005i	0.982249	−	0.187582i	$-0.0600650\pi$
$211$	81.6700	+	129.977i	0.387062	+	0.616005i	−0.595187	+	0.803587i	$0.702922\pi$
$212$	−74.3264	−	16.9645i	−0.350596	−	0.0800213i
$213$		0			0
$214$	−83.4617	+	132.829i	−0.390008	+	0.620694i
$215$	−40.3829	+	40.3829i	−0.187827	+	0.187827i
$216$		0			0
$217$	−38.6989	−	110.595i	−0.178336	−	0.509655i
$218$	392.376	−	137.298i	1.79989	−	0.629810i
$219$		0			0
$220$	36.8747	+	36.8747i	0.167612	+	0.167612i
$221$	−398.399	−	250.331i	−1.80271	−	1.13272i
$222$		0			0
$223$	−17.7211	+	77.6414i	−0.0794670	+	0.348168i	−0.998993	−	0.0448610i	$-0.985716\pi$
$223$	−17.7211	+	77.6414i	−0.0794670	+	0.348168i	0.919526	+	0.393029i	$0.128573\pi$
$224$	−96.5770	+	60.6834i	−0.431148	+	0.270908i
$225$		0			0
$226$	−29.8773	−	14.3881i	−0.132200	−	0.0636643i
$227$	379.261	−	182.642i	1.67075	−	0.804592i	0.672855	−	0.739774i	$-0.265068\pi$
$227$	379.261	−	182.642i	1.67075	−	0.804592i	0.997897	−	0.0648180i	$-0.0206467\pi$
$228$		0			0
$229$	−196.110	−	22.0963i	−0.856378	−	0.0964906i	−0.327152	−	0.944972i	$-0.606089\pi$
$229$	−196.110	−	22.0963i	−0.856378	−	0.0964906i	−0.529226	+	0.848481i	$0.677518\pi$
$230$	110.105	−	314.663i	0.478719	−	1.36810i
$231$		0			0
$232$	52.4010	−	165.080i	0.225866	−	0.711553i
$233$	−122.019			−0.523687			−0.261843	−	0.965110i	$-0.584330\pi$
$233$	−122.019			−0.523687			−0.261843	+	0.965110i	$0.584330\pi$
$234$		0			0
$235$	17.8007	−	157.986i	0.0757477	−	0.672280i
$236$	−19.5953	−	15.6267i	−0.0830308	−	0.0662149i
$237$		0			0
$238$	−163.733	+	339.994i	−0.687952	+	1.42855i
$239$	−191.297	−	239.879i	−0.800405	−	1.00368i	−0.999718	−	0.0237404i	$-0.992442\pi$
$239$	−191.297	−	239.879i	−0.800405	−	1.00368i	0.199313	−	0.979936i	$-0.436129\pi$
$240$		0			0
$241$	−133.954	−	30.5741i	−0.555826	−	0.126864i	−0.0646245	−	0.997910i	$-0.520585\pi$
$241$	−133.954	−	30.5741i	−0.555826	−	0.126864i	−0.491201	+	0.871046i	$0.663442\pi$
$242$	22.3541	+	198.398i	0.0923722	+	0.819826i
$243$		0			0
$244$	62.4663	−	62.4663i	0.256010	−	0.256010i
$245$	−131.661	+	30.0508i	−0.537393	+	0.122656i
$246$		0			0
$247$	−11.9522	+	4.18225i	−0.0483894	+	0.0169322i
$248$	−30.0639	−	131.718i	−0.121225	−	0.531123i
$249$		0			0
$250$	−155.200	−	97.5188i	−0.620801	−	0.390075i
$251$	330.590	−	37.2486i	1.31709	−	0.148401i	0.574699	−	0.818365i	$-0.305119\pi$
$251$	330.590	−	37.2486i	1.31709	−	0.148401i	0.742393	+	0.669964i	$0.233691\pi$
$252$		0			0
$253$	−118.222	+	74.2836i	−0.467279	+	0.293611i
$254$	−194.965	+	155.480i	−0.767580	+	0.612124i
$255$		0			0
$256$	−220.597	+	106.234i	−0.861707	+	0.414976i
$257$	−44.4882	+	55.7865i	−0.173106	+	0.217068i	−0.860814	−	0.508919i	$-0.830045\pi$
$257$	−44.4882	+	55.7865i	−0.173106	+	0.217068i	0.687709	+	0.725987i	$0.258617\pi$
$258$		0			0
$259$	13.6885	−	39.1193i	0.0528512	−	0.151040i
$260$		−	132.024i		−	0.507786i
$261$		0			0
$262$	37.2023			0.141993
$263$	−220.348	−	77.1032i	−0.837826	−	0.293168i	−0.122944	−	0.992414i	$-0.539234\pi$
$263$	−220.348	−	77.1032i	−0.837826	−	0.293168i	−0.714882	+	0.699246i	$0.753519\pi$
$264$		0			0
$265$	252.248	+	201.161i	0.951880	+	0.759099i
$266$	4.40644	+	9.15006i	0.0165656	+	0.0343987i
$267$		0			0
$268$	−24.1196	−	30.2450i	−0.0899984	−	0.112854i
$269$	176.731	+	281.266i	0.656993	+	1.04560i	0.994547	+	0.104293i	$0.0332578\pi$
$269$	176.731	+	281.266i	0.656993	+	1.04560i	−0.337553	+	0.941306i	$0.609599\pi$
$270$		0			0
$271$	14.5758	+	129.364i	0.0537851	+	0.477356i	0.991515	+	0.129991i	$0.0414949\pi$
$271$	14.5758	+	129.364i	0.0537851	+	0.477356i	−0.937730	+	0.347365i	$0.887077\pi$
$272$	−327.184	+	520.710i	−1.20288	+	1.91437i
$273$		0			0
$274$	322.872	−	73.6933i	1.17836	−	0.268954i
$275$	−23.7678	−	67.9244i	−0.0864282	−	0.246998i
$276$		0			0
$277$	10.5344	+	46.1541i	0.0380303	+	0.166621i	0.990377	−	0.138396i	$-0.0441948\pi$
$277$	10.5344	+	46.1541i	0.0380303	+	0.166621i	−0.952347	+	0.305018i	$0.901338\pi$
$278$	364.270	+	364.270i	1.31032	+	1.31032i
$279$		0			0
$280$	187.222	−	21.0948i	0.668649	−	0.0753386i
$281$	−15.5090	+	67.9492i	−0.0551921	+	0.241812i	−0.994998	−	0.0998970i	$-0.968149\pi$
$281$	−15.5090	+	67.9492i	−0.0551921	+	0.241812i	0.939806	+	0.341709i	$0.111006\pi$
$282$		0			0
$283$	430.103	−	342.995i	1.51980	−	1.21200i	0.613253	−	0.789887i	$-0.289861\pi$
$283$	430.103	−	342.995i	1.51980	−	1.21200i	0.906544	−	0.422111i	$-0.138711\pi$
$284$	6.55813	+	3.15823i	0.0230920	+	0.0111205i
$285$		0			0
$286$	−130.294	+	163.384i	−0.455574	+	0.571272i
$287$	−59.9798	−	6.75810i	−0.208989	−	0.0235474i
$288$		0			0
$289$			686.921i			2.37689i
$290$	282.645	−	299.672i	0.974638	−	1.03335i
$291$		0			0
$292$	−76.3915	−	26.7305i	−0.261615	−	0.0915430i
$293$	−35.7040	+	316.882i	−0.121857	+	1.08151i	0.772768	+	0.634689i	$0.218872\pi$
$293$	−35.7040	+	316.882i	−0.121857	+	1.08151i	−0.894624	+	0.446819i	$0.852557\pi$
$294$		0			0
$295$	46.0210	+	95.5636i	0.156003	+	0.323944i
$296$	20.7349	−	43.0566i	0.0700505	−	0.145461i
$297$		0			0
$298$	193.868	+	308.538i	0.650562	+	1.03536i
$299$	344.618	+	78.6568i	1.15257	+	0.263066i
$300$		0			0
$301$	−25.8389	+	41.1223i	−0.0858434	+	0.136619i
$302$	311.555	−	311.555i	1.03164	−	1.03164i
$303$		0			0
$304$	5.46622	+	15.6216i	0.0179810	+	0.0513867i
$305$	−352.877	+	123.477i	−1.15698	+	0.404843i
$306$		0			0
$307$	361.966	+	361.966i	1.17904	+	1.17904i	0.979989	+	0.199053i	$0.0637867\pi$
$307$	361.966	+	361.966i	1.17904	+	1.17904i	0.199053	+	0.979989i	$0.436213\pi$
$308$	37.5499	+	23.5942i	0.121915	+	0.0766044i
$309$		0			0
$310$	71.5045	−	313.282i	0.230660	−	1.01059i
$311$	−409.769	+	257.475i	−1.31758	+	0.827893i	−0.993017	−	0.117970i	$-0.962361\pi$
$311$	−409.769	+	257.475i	−1.31758	+	0.827893i	−0.324567	+	0.945863i	$0.605218\pi$
$312$		0			0
$313$	276.742	+	133.272i	0.884159	+	0.425789i	0.820142	−	0.572160i	$-0.193894\pi$
$313$	276.742	+	133.272i	0.884159	+	0.425789i	0.0640173	+	0.997949i	$0.479609\pi$
$314$	−323.117	+	155.605i	−1.02903	+	0.495557i
$315$		0			0
$316$	125.331	+	14.1214i	0.396617	+	0.0446880i
$317$	−184.663	+	527.737i	−0.582534	+	1.66479i	0.153747	+	0.988110i	$0.450866\pi$
$317$	−184.663	+	527.737i	−0.582534	+	1.66479i	−0.736281	+	0.676676i	$0.763420\pi$
$318$		0			0
$319$	−170.804	+	24.3195i	−0.535437	+	0.0762366i
$320$	166.784			0.521200
$321$		0			0
$322$	31.7418	−	281.716i	0.0985769	−	0.874894i
$323$	20.5343	+	16.3756i	0.0635737	+	0.0506983i
$324$		0			0
$325$	−79.0480	+	164.145i	−0.243225	+	0.505061i
$326$	−334.492	−	419.440i	−1.02605	−	1.28663i
$327$		0			0
$328$	−67.8536	−	15.4871i	−0.206871	−	0.0472169i
$329$	−15.1377	−	134.351i	−0.0460113	−	0.408362i
$330$		0			0
$331$	−418.557	+	418.557i	−1.26452	+	1.26452i	−0.315645	+	0.948877i	$0.602221\pi$
$331$	−418.557	+	418.557i	−1.26452	+	1.26452i	−0.948877	+	0.315645i	$0.897779\pi$
$332$	108.904	−	24.8567i	0.328025	−	0.0748695i
$333$		0			0
$334$	271.606	−	95.0390i	0.813191	−	0.284548i
$335$	36.4297	+	159.609i	0.108745	+	0.476445i
$336$		0			0
$337$	−535.661	−	336.578i	−1.58950	−	0.998748i	−0.978281	−	0.207285i	$-0.933537\pi$
$337$	−535.661	−	336.578i	−1.58950	−	0.998748i	−0.611218	−	0.791463i	$-0.709320\pi$
$338$	134.070	−	15.1061i	0.396657	−	0.0446926i
$339$		0			0
$340$	−231.864	+	145.690i	−0.681954	+	0.428500i
$341$	−105.221	+	83.9110i	−0.308566	+	0.246073i
$342$		0			0
$343$	−332.133	+	159.947i	−0.968316	+	0.466317i
$344$	−34.9157	+	43.7829i	−0.101499	+	0.127276i
$345$		0			0
$346$	24.9002	−	71.1607i	0.0719659	−	0.205667i
$347$			141.419i			0.407547i	0.979018	+	0.203774i	$0.0653207\pi$
$347$			141.419i			0.407547i	−0.979018	+	0.203774i	$0.934679\pi$
$348$		0			0
$349$	−571.537			−1.63764			−0.818821	−	0.574048i	$-0.805372\pi$
$349$	−571.537			−1.63764			−0.818821	+	0.574048i	$0.805372\pi$
$350$	137.918	+	48.2596i	0.394052	+	0.137885i
$351$		0			0
$352$	102.428	+	81.6833i	0.290987	+	0.232055i
$353$	−6.08107	−	12.6275i	−0.0172268	−	0.0357719i	0.892178	−	0.451684i	$-0.149177\pi$
$353$	−6.08107	−	12.6275i	−0.0172268	−	0.0357719i	−0.909405	+	0.415912i	$0.863462\pi$
$354$		0			0
$355$	−19.2063	−	24.0840i	−0.0541023	−	0.0678421i
$356$	111.978	+	178.212i	0.314545	+	0.500595i
$357$		0			0
$358$	70.2120	+	623.148i	0.196123	+	1.74064i
$359$	−8.23661	+	13.1085i	−0.0229432	+	0.0365139i	−0.857999	−	0.513651i	$-0.828292\pi$
$359$	−8.23661	+	13.1085i	−0.0229432	+	0.0365139i	0.835056	+	0.550165i	$0.185435\pi$
$360$		0			0
$361$	−351.260	+	80.1728i	−0.973019	+	0.222085i
$362$	−82.0402	−	234.457i	−0.226630	−	0.647672i
$363$		0			0
$364$	−24.9832	−	109.459i	−0.0686351	−	0.300710i
$365$	242.190	+	242.190i	0.663534	+	0.663534i
$366$		0			0
$367$	281.948	−	31.7679i	0.768249	−	0.0865609i	0.280864	−	0.959748i	$-0.409379\pi$
$367$	281.948	−	31.7679i	0.768249	−	0.0865609i	0.487386	+	0.873187i	$0.337951\pi$
$368$	102.805	−	450.417i	0.279361	−	1.22396i
$369$		0			0
$370$	88.8650	−	70.8675i	0.240176	−	0.191534i
$371$	247.199	+	119.045i	0.666306	+	0.320876i
$372$		0			0
$373$	146.301	−	183.455i	0.392227	−	0.491837i	−0.546035	−	0.837762i	$-0.683863\pi$
$373$	146.301	−	183.455i	0.392227	−	0.491837i	0.938262	+	0.345925i	$0.112435\pi$
$374$	430.719	+	48.5304i	1.15166	+	0.129760i
$375$		0			0
$376$		−	155.896i		−	0.414618i
$377$	349.306	+	262.234i	0.926541	+	0.695580i
$378$		0			0
$379$	549.482	+	192.272i	1.44982	+	0.507314i	0.936434	−	0.350844i	$-0.114105\pi$
$379$	549.482	+	192.272i	1.44982	+	0.507314i	0.513386	+	0.858158i	$0.328391\pi$
$380$	−0.825134	+	7.32327i	−0.00217140	+	0.0192718i
$381$		0			0
$382$	−104.046	−	216.054i	−0.272371	−	0.565585i
$383$	177.905	−	369.424i	0.464504	−	0.964553i	−0.528770	−	0.848765i	$-0.677346\pi$
$383$	177.905	−	369.424i	0.464504	−	0.964553i	0.993274	−	0.115788i	$-0.0369393\pi$
$384$		0			0
$385$	−99.8502	−	158.911i	−0.259351	−	0.412755i
$386$	−434.835	−	99.2484i	−1.12652	−	0.257120i
$387$		0			0
$388$	−0.787317	+	1.25301i	−0.00202917	+	0.00322940i
$389$	−57.4399	+	57.4399i	−0.147661	+	0.147661i	−0.777072	−	0.629412i	$-0.783296\pi$
$389$	−57.4399	+	57.4399i	−0.147661	+	0.147661i	0.629412	+	0.777072i	$0.283296\pi$
$390$		0			0
$391$	−242.150	−	692.024i	−0.619309	−	1.76988i
$392$	−124.992	+	43.7367i	−0.318858	+	0.111573i
$393$		0			0
$394$	−85.2996	−	85.2996i	−0.216496	−	0.216496i
$395$	−451.943	−	283.975i	−1.14416	−	0.718923i
$396$		0			0
$397$	22.5451	−	98.7767i	0.0567887	−	0.248808i	−0.938564	−	0.345106i	$-0.887843\pi$
$397$	22.5451	−	98.7767i	0.0567887	−	0.248808i	0.995353	+	0.0962980i	$0.0307002\pi$
$398$	1.01883	−	0.640176i	0.00255988	−	0.00160848i
$399$		0			0
$400$	214.538	+	103.316i	0.536345	+	0.258290i
$401$	−107.974	+	51.9976i	−0.269262	+	0.129670i	−0.563643	−	0.826018i	$-0.690601\pi$
$401$	−107.974	+	51.9976i	−0.269262	+	0.129670i	0.294381	+	0.955688i	$0.404887\pi$
$402$		0			0
$403$	338.579	+	38.1487i	0.840147	+	0.0946619i
$404$	63.1884	−	180.582i	0.156407	−	0.446985i
$405$		0			0
$406$	177.627	−	301.937i	0.437506	−	0.743687i
$407$	−47.6042			−0.116964
$408$		0			0
$409$	−42.0942	+	373.596i	−0.102920	+	0.913438i	0.831077	+	0.556157i	$0.187725\pi$
$409$	−42.0942	+	373.596i	−0.102920	+	0.913438i	−0.933997	+	0.357281i	$0.883704\pi$
$410$	−129.420	−	103.209i	−0.315659	−	0.251730i
$411$		0			0
$412$	−4.35957	+	9.05274i	−0.0105815	+	0.0219727i
$413$	56.2386	+	70.5210i	0.136171	+	0.170753i
$414$		0			0
$415$	−460.881	−	105.193i	−1.11056	−	0.253477i
$416$	−37.1359	−	329.590i	−0.0892691	−	0.792285i
$417$		0			0
$418$	8.24843	−	8.24843i	0.0197331	−	0.0197331i
$419$	231.325	−	52.7983i	0.552087	−	0.126010i	0.0626288	−	0.998037i	$-0.480052\pi$
$419$	231.325	−	52.7983i	0.552087	−	0.126010i	0.489459	+	0.872027i	$0.337194\pi$
$420$		0			0
$421$	120.085	−	42.0197i	0.285238	−	0.0998092i	−0.183868	−	0.982951i	$-0.558862\pi$
$421$	120.085	−	42.0197i	0.285238	−	0.0998092i	0.469106	+	0.883142i	$0.344576\pi$
$422$	79.6642	+	349.032i	0.188778	+	0.827089i
$423$		0			0
$424$	267.877	+	168.318i	0.631786	+	0.396977i
$425$	375.505	−	42.3093i	0.883542	−	0.0995512i
$426$		0			0
$427$	−269.197	+	169.148i	−0.630438	+	0.396131i
$428$	−75.6860	+	60.3575i	−0.176836	+	0.141022i
$429$		0			0
$430$	−120.002	+	57.7901i	−0.279075	+	0.134396i
$431$	−102.073	+	127.996i	−0.236828	+	0.296973i	−0.886016	−	0.463655i	$-0.846538\pi$
$431$	−102.073	+	127.996i	−0.236828	+	0.296973i	0.649187	+	0.760629i	$0.275109\pi$
$432$		0			0
$433$	−29.3711	+	83.9378i	−0.0678316	+	0.193852i	−0.972809	−	0.231607i	$-0.925602\pi$
$433$	−29.3711	+	83.9378i	−0.0678316	+	0.193852i	0.904978	+	0.425459i	$0.139887\pi$
$434$		−	273.266i		−	0.629644i
$435$		0			0
$436$	256.530			0.588371
$437$	−18.6240	−	6.51683i	−0.0426179	−	0.0149127i
$438$		0			0
$439$	377.689	+	301.197i	0.860340	+	0.686098i	0.950801	−	0.309802i	$-0.100263\pi$
$439$	377.689	+	301.197i	0.860340	+	0.686098i	−0.0904611	+	0.995900i	$0.528834\pi$
$440$	−93.8946	−	194.974i	−0.213397	−	0.443123i
$441$		0			0
$442$	−684.185	−	857.941i	−1.54793	−	1.94104i
$443$	33.5662	+	53.4203i	0.0757703	+	0.120588i	0.882460	−	0.470388i	$-0.155886\pi$
$443$	33.5662	+	53.4203i	0.0757703	+	0.120588i	−0.806690	+	0.590975i	$0.798743\pi$
$444$		0			0
$445$	−99.7284	−	885.114i	−0.224109	−	1.98902i
$446$	−98.8157	+	157.264i	−0.221560	+	0.352610i
$447$		0			0
$448$	138.277	−	31.5608i	0.308654	−	0.0704482i
$449$	−224.975	−	642.941i	−0.501058	−	1.43194i	−0.865592	−	0.500751i	$-0.833057\pi$
$449$	−224.975	−	642.941i	−0.501058	−	1.43194i	0.364534	−	0.931190i	$-0.381228\pi$
$450$		0			0
$451$	15.4272	+	67.5910i	0.0342066	+	0.149869i
$452$	−14.4700	−	14.4700i	−0.0320133	−	0.0320133i
$453$		0			0
$454$	975.565	−	109.920i	2.14882	−	0.242114i
$455$	−105.729	+	463.227i	−0.232370	+	1.01808i
$456$		0			0
$457$	−81.2493	+	64.7942i	−0.177788	+	0.141782i	−0.708341	−	0.705871i	$-0.750556\pi$
$457$	−81.2493	+	64.7942i	−0.177788	+	0.141782i	0.530552	+	0.847652i	$0.321985\pi$
$458$	−414.684	−	199.701i	−0.905424	−	0.436029i
$459$		0			0
$460$	128.266	−	160.840i	0.278838	−	0.349652i
$461$	−286.769	−	32.3111i	−0.622058	−	0.0700891i	−0.204690	−	0.978827i	$-0.565619\pi$
$461$	−286.769	−	32.3111i	−0.622058	−	0.0700891i	−0.417368	+	0.908738i	$0.637047\pi$
$462$		0			0
$463$			377.960i			0.816329i	0.912908	+	0.408164i	$0.133831\pi$
$463$			377.960i			0.816329i	−0.912908	+	0.408164i	$0.866169\pi$
$464$	342.740	−	456.544i	0.738664	−	0.983931i
$465$		0			0
$466$	−268.604	−	93.9888i	−0.576404	−	0.201693i
$467$	89.7450	−	796.509i	0.192173	−	1.70559i	−0.414019	−	0.910268i	$-0.635875\pi$
$467$	89.7450	−	796.509i	0.192173	−	1.70559i	0.606193	−	0.795318i	$-0.292696\pi$
$468$		0			0
$469$	60.4061	+	125.435i	0.128798	+	0.267451i
$470$	160.879	−	334.068i	0.342295	−	0.710782i
$471$		0			0
$472$	55.3349	+	88.0650i	0.117235	+	0.186578i
$473$	54.3851	+	12.4130i	0.114979	+	0.0262432i
$474$		0			0
$475$	5.41060	−	8.61092i	0.0113907	−	0.0181283i
$476$	−164.664	+	164.664i	−0.345934	+	0.345934i
$477$		0			0
$478$	−236.334	−	675.405i	−0.494423	−	1.41298i
$479$	392.771	−	137.436i	0.819981	−	0.286924i	0.112496	−	0.993652i	$-0.464115\pi$
$479$	392.771	−	137.436i	0.819981	−	0.286924i	0.707485	+	0.706729i	$0.249830\pi$
$480$		0			0
$481$	85.2198	+	85.2198i	0.177172	+	0.177172i
$482$	−271.327	−	170.486i	−0.562919	−	0.353705i
$483$		0			0
$484$	−27.4157	+	120.116i	−0.0566441	+	0.248174i
$485$	5.30271	−	3.33192i	0.0109334	−	0.00686993i
$486$		0			0
$487$	−642.025	−	309.183i	−1.31833	−	0.634873i	−0.363378	−	0.931642i	$-0.618377\pi$
$487$	−642.025	−	309.183i	−1.31833	−	0.634873i	−0.954949	+	0.296769i	$0.904091\pi$
$488$	−330.289	+	159.059i	−0.676822	+	0.325940i
$489$		0			0
$490$	−312.978	−	35.2641i	−0.638731	−	0.0719676i
$491$	16.0776	−	45.9471i	0.0327446	−	0.0935786i	−0.926351	−	0.376662i	$-0.877072\pi$
$491$	16.0776	−	45.9471i	0.0327446	−	0.0935786i	0.959095	+	0.283084i	$0.0913574\pi$
$492$		0			0
$493$	75.0788	−	902.836i	0.152290	−	1.83131i
$494$	−29.5322			−0.0597819
$495$		0			0
$496$	49.8605	−	442.525i	0.100525	−	0.892187i
$497$	−20.4810	−	16.3330i	−0.0412092	−	0.0328632i
$498$		0			0
$499$	336.600	−	698.958i	0.674550	−	1.40072i	−0.229508	−	0.973307i	$-0.573712\pi$
$499$	336.600	−	698.958i	0.674550	−	1.40072i	0.904058	−	0.427410i	$-0.140574\pi$
$500$	−70.5233	−	88.4334i	−0.141047	−	0.176867i
$501$		0			0
$502$	756.431	+	172.650i	1.50683	+	0.343925i
$503$	52.8932	+	469.440i	0.105156	+	0.933281i	0.929909	+	0.367789i	$0.119885\pi$
$503$	52.8932	+	469.440i	0.105156	+	0.933281i	−0.824754	+	0.565492i	$0.808686\pi$
$504$		0			0
$505$	−572.514	+	572.514i	−1.13369	+	1.13369i
$506$	−317.464	+	72.4592i	−0.627400	+	0.143200i
$507$		0			0
$508$	−145.250	+	50.8250i	−0.285924	+	0.100049i
$509$	171.270	+	750.383i	0.336483	+	1.47423i	0.806322	+	0.591477i	$0.201455\pi$
$509$	171.270	+	750.383i	0.336483	+	1.47423i	−0.469838	+	0.882753i	$0.655688\pi$
$510$		0			0
$511$	246.624	+	154.964i	0.482631	+	0.303257i
$512$	36.5399	−	4.11706i	0.0713670	−	0.00804114i
$513$		0			0
$514$	−140.905	+	88.5362i	−0.274133	+	0.172249i
$515$	33.2451	−	26.5121i	0.0645537	−	0.0514798i
$516$		0			0
$517$	−139.914	+	67.3791i	−0.270627	+	0.130327i
$518$	60.2657	−	75.5708i	0.116343	−	0.145890i
$519$		0			0
$520$	−180.950	+	517.126i	−0.347981	+	0.994472i
$521$		−	306.568i		−	0.588421i	−0.955741	−	0.294211i	$-0.904943\pi$
$521$		−	306.568i		−	0.588421i	0.955741	−	0.294211i	$-0.0950567\pi$
$522$		0			0
$523$	789.078			1.50875			0.754377	−	0.656442i	$-0.227939\pi$
$523$	789.078			1.50875			0.754377	+	0.656442i	$0.227939\pi$
$524$	21.6691	+	7.58234i	0.0413532	+	0.0144701i
$525$		0			0
$526$	−425.669	−	339.459i	−0.809256	−	0.645360i
$527$	−306.627	−	636.718i	−0.581836	−	1.20819i
$528$		0			0
$529$	13.5904	+	17.0418i	0.0256907	+	0.0322151i
$530$	400.332	+	637.124i	0.755343	+	1.20212i
$531$		0			0
$532$	0.701693	+	6.22770i	0.00131897	+	0.0117062i
$533$	93.3822	−	148.617i	0.175201	−	0.278831i
$534$		0			0
$535$	399.410	−	91.1628i	0.746561	−	0.170398i
$536$	53.0206	+	151.524i	0.0989191	+	0.282694i
$537$		0			0
$538$	172.391	+	755.293i	0.320429	+	1.40389i
$539$	93.2750	+	93.2750i	0.173052	+	0.173052i
$540$		0			0
$541$	231.201	−	26.0502i	0.427359	−	0.0481518i	0.104334	−	0.994542i	$-0.466729\pi$
$541$	231.201	−	26.0502i	0.427359	−	0.0481518i	0.323025	+	0.946390i	$0.395300\pi$
$542$	−67.5600	+	296.000i	−0.124649	+	0.546125i
$543$		0			0
$544$	−537.855	+	428.925i	−0.988703	+	0.788465i
$545$	−978.119	−	471.037i	−1.79471	−	0.864288i
$546$		0			0
$547$	5.46184	−	6.84892i	0.00998507	−	0.0125209i	−0.776814	−	0.629730i	$-0.783165\pi$
$547$	5.46184	−	6.84892i	0.00998507	−	0.0125209i	0.786799	+	0.617209i	$0.211737\pi$
$548$	203.082	+	22.8818i	0.370587	+	0.0417551i
$549$		0			0
$550$		−	167.832i		−	0.305149i
$551$	−17.7367	−	16.7290i	−0.0321901	−	0.0303611i
$552$		0			0
$553$	−428.433	−	149.915i	−0.774743	−	0.271094i
$554$	−12.3619	+	109.715i	−0.0223139	+	0.198042i
$555$		0			0
$556$	137.932	+	286.418i	0.248079	+	0.515141i
$557$	184.669	−	383.470i	0.331543	−	0.688456i	−0.666846	−	0.745195i	$-0.732356\pi$
$557$	184.669	−	383.470i	0.331543	−	0.688456i	0.998389	+	0.0567395i	$0.0180704\pi$
$558$		0			0
$559$	−75.1373	−	119.580i	−0.134414	−	0.213918i
$560$	605.440	+	138.188i	1.08114	+	0.246764i
$561$		0			0
$562$	−86.4803	+	137.633i	−0.153880	+	0.244898i
$563$	−493.000	+	493.000i	−0.875666	+	0.875666i	−0.993083	−	0.117416i	$-0.962539\pi$
$563$	−493.000	+	493.000i	−0.875666	+	0.875666i	0.117416	+	0.993083i	$0.462539\pi$
$564$		0			0
$565$	28.6029	+	81.7423i	0.0506245	+	0.144677i
$566$	1211.00	−	423.748i	2.13958	−	0.748671i
$567$		0			0
$568$	−21.3589	−	21.3589i	−0.0376037	−	0.0376037i
$569$	267.135	+	167.852i	0.469482	+	0.294995i	0.745919	−	0.666037i	$-0.232011\pi$
$569$	267.135	+	167.852i	0.469482	+	0.294995i	−0.276436	+	0.961032i	$0.589154\pi$
$570$		0			0
$571$	−136.850	+	599.581i	−0.239668	+	1.05005i	0.701647	+	0.712525i	$0.252448\pi$
$571$	−136.850	+	599.581i	−0.239668	+	1.05005i	−0.941315	+	0.337529i	$0.890409\pi$
$572$	−109.192	+	68.6099i	−0.190895	+	0.119947i
$573$		0			0
$574$	−126.830	−	61.0780i	−0.220958	−	0.106408i
$575$	−255.772	+	123.174i	−0.444822	+	0.214215i
$576$		0			0
$577$	−468.624	−	52.8013i	−0.812173	−	0.0915100i	−0.303898	−	0.952705i	$-0.598288\pi$
$577$	−468.624	−	52.8013i	−0.812173	−	0.0915100i	−0.508275	+	0.861195i	$0.669717\pi$
$578$	−529.121	+	1512.14i	−0.915434	+	2.61616i
$579$		0			0
$580$	225.709	−	116.942i	0.389153	−	0.201624i
$581$	−402.012			−0.691932
$582$		0			0
$583$	35.2850	−	313.163i	0.0605231	−	0.537157i
$584$	262.581	+	209.401i	0.449625	+	0.358564i
$585$		0			0
$586$	−322.684	+	670.061i	−0.550656	+	1.14345i
$587$	125.247	+	157.054i	0.213367	+	0.267554i	0.876985	−	0.480518i	$-0.159551\pi$
$587$	125.247	+	157.054i	0.213367	+	0.267554i	−0.663618	+	0.748072i	$0.730980\pi$
$588$		0			0
$589$	−18.5422	−	4.23215i	−0.0314809	−	0.00718531i
$590$	27.6968	+	245.816i	0.0469438	+	0.416638i
$591$		0			0
$592$	111.383	−	111.383i	0.188146	−	0.188146i
$593$	372.413	−	85.0008i	0.628015	−	0.143340i	0.103344	−	0.994646i	$-0.467046\pi$
$593$	372.413	−	85.0008i	0.628015	−	0.143340i	0.524671	+	0.851305i	$0.324188\pi$
$594$		0			0
$595$	930.202	−	325.492i	1.56337	−	0.547045i
$596$	50.0370	+	219.226i	0.0839546	+	0.367829i
$597$		0			0
$598$	698.031	+	438.602i	1.16728	+	0.733448i
$599$	289.961	−	32.6708i	0.484076	−	0.0545422i	0.133445	−	0.991056i	$-0.457396\pi$
$599$	289.961	−	32.6708i	0.484076	−	0.0545422i	0.350630	+	0.936514i	$0.385967\pi$
$600$		0			0
$601$	434.543	−	273.041i	0.723033	−	0.454312i	−0.119585	−	0.992824i	$-0.538156\pi$
$601$	434.543	−	273.041i	0.723033	−	0.454312i	0.842618	+	0.538512i	$0.181013\pi$
$602$	−88.5556	+	70.6207i	−0.147102	+	0.117310i
$603$		0			0
$604$	244.970	−	117.971i	0.405579	−	0.195317i
$605$	325.089	−	407.649i	0.537338	−	0.673800i
$606$		0			0
$607$	182.154	−	520.567i	0.300090	−	0.857607i	−0.690814	−	0.723033i	$-0.742748\pi$
$607$	182.154	−	520.567i	0.300090	−	0.857607i	0.990904	−	0.134574i	$-0.0429667\pi$
$608$			18.5142i			0.0304509i
$609$		0			0
$610$	−871.912			−1.42936
$611$	371.091	+	129.850i	0.607350	+	0.212521i
$612$		0			0
$613$	280.338	+	223.562i	0.457321	+	0.364701i	0.824888	−	0.565295i	$-0.191238\pi$
$613$	280.338	+	223.562i	0.457321	+	0.364701i	−0.367567	+	0.929997i	$0.619809\pi$
$614$	517.992	+	1075.62i	0.843636	+	1.75183i
$615$		0			0
$616$	−114.741	−	143.881i	−0.186268	−	0.233573i
$617$	279.227	+	444.387i	0.452555	+	0.720238i	0.992604	−	0.121396i	$-0.0387371\pi$
$617$	279.227	+	444.387i	0.452555	+	0.720238i	−0.540049	+	0.841634i	$0.681594\pi$
$618$		0			0
$619$	112.177	+	995.602i	0.181224	+	1.60840i	0.674327	+	0.738433i	$0.264434\pi$
$619$	112.177	+	995.602i	0.181224	+	1.60840i	−0.493103	+	0.869971i	$0.664137\pi$
$620$	105.500	−	167.902i	0.170161	−	0.270810i
$621$		0			0
$622$	−1100.36	+	251.151i	−1.76907	+	0.403780i
$623$	−250.174	−	714.957i	−0.401564	−	1.14760i
$624$		0			0
$625$	173.808	+	761.503i	0.278093	+	1.21841i
$626$	506.544	+	506.544i	0.809176	+	0.809176i
$627$		0			0
$628$	−219.919	+	24.7790i	−0.350190	+	0.0394569i
$629$	55.6242	−	243.706i	0.0884328	−	0.387449i
$630$		0			0
$631$	−434.398	+	346.421i	−0.688427	+	0.549002i	−0.904025	−	0.427480i	$-0.859401\pi$
$631$	−434.398	+	346.421i	−0.688427	+	0.549002i	0.215598	+	0.976482i	$0.430830\pi$
$632$	−471.553	−	227.088i	−0.746128	−	0.359317i
$633$		0			0
$634$	−813.011	+	1019.48i	−1.28235	+	1.60802i
$635$	647.145	+	72.9158i	1.01913	+	0.114828i
$636$		0			0
$637$		−	333.957i		−	0.524266i
$638$	−394.730	−	78.0319i	−0.618699	−	0.122307i
$639$		0			0
$640$	873.540	+	305.665i	1.36491	+	0.477601i
$641$	75.0000	−	665.643i	0.117005	−	1.03845i	−0.788771	−	0.614687i	$-0.789282\pi$
$641$	75.0000	−	665.643i	0.117005	−	1.03845i	0.905775	−	0.423758i	$-0.139289\pi$
$642$		0			0
$643$	38.4657	+	79.8749i	0.0598223	+	0.124222i	0.928737	−	0.370740i	$-0.120896\pi$
$643$	38.4657	+	79.8749i	0.0598223	+	0.124222i	−0.868914	+	0.494963i	$0.835182\pi$
$644$	75.9061	−	157.621i	0.117867	−	0.244753i
$645$		0			0
$646$	32.5891	+	51.8652i	0.0504475	+	0.0802867i
$647$	399.560	+	91.1970i	0.617558	+	0.140954i	0.519844	−	0.854261i	$-0.325990\pi$
$647$	399.560	+	91.1970i	0.617558	+	0.140954i	0.0977136	+	0.995215i	$0.468847\pi$
$648$		0			0
$649$	55.1207	−	87.7241i	0.0849318	−	0.135168i
$650$	−300.448	+	300.448i	−0.462228	+	0.462228i
$651$		0			0
$652$	−109.343	−	312.484i	−0.167704	−	0.479270i
$653$	28.0410	−	9.81196i	0.0429418	−	0.0150260i	−0.308723	−	0.951152i	$-0.599902\pi$
$653$	28.0410	−	9.81196i	0.0429418	−	0.0150260i	0.351664	+	0.936126i	$0.385616\pi$
$654$		0			0
$655$	−68.6992	−	68.6992i	−0.104884	−	0.104884i
$656$	−194.243	−	122.051i	−0.296102	−	0.186053i
$657$		0			0
$658$	70.1647	−	307.411i	0.106633	−	0.467191i
$659$	−839.507	+	527.497i	−1.27391	+	0.800451i	−0.987494	−	0.157655i	$-0.949607\pi$
$659$	−839.507	+	527.497i	−1.27391	+	0.800451i	−0.286416	+	0.958105i	$0.592464\pi$
$660$		0			0
$661$	34.7693	+	16.7440i	0.0526010	+	0.0253313i	0.459999	−	0.887919i	$-0.347850\pi$
$661$	34.7693	+	16.7440i	0.0526010	+	0.0253313i	−0.407398	+	0.913251i	$0.633564\pi$
$662$	−1243.79	+	598.977i	−1.87883	+	0.904799i
$663$		0			0
$664$	−460.634	−	51.9010i	−0.693726	−	0.0781642i
$665$	8.75977	−	25.0340i	0.0131726	−	0.0376451i
$666$		0			0
$667$	170.777	+	658.829i	0.256038	+	0.987750i
$668$	177.572			0.265826
$669$		0			0
$670$	−42.7496	+	379.413i	−0.0638054	+	0.566289i
$671$	285.505	+	227.682i	0.425491	+	0.339318i
$672$		0			0
$673$	340.019	−	706.057i	0.505229	−	1.04912i	−0.479903	−	0.877321i	$-0.659328\pi$
$673$	340.019	−	706.057i	0.505229	−	1.04912i	0.985132	−	0.171797i	$-0.0549575\pi$
$674$	−919.909	−	1153.53i	−1.36485	−	1.71147i
$675$		0			0
$676$	81.1703	+	18.5266i	0.120074	+	0.0274062i
$677$	−72.2705	−	641.418i	−0.106751	−	0.947442i	−0.926904	−	0.375298i	$-0.877540\pi$
$677$	−72.2705	−	641.418i	−0.106751	−	0.947442i	0.820153	−	0.572144i	$-0.193888\pi$
$678$		0			0
$679$	3.76586	−	3.76586i	0.00554618	−	0.00554618i
$680$	1107.87	−	252.864i	1.62922	−	0.371858i
$681$		0			0
$682$	−296.261	+	103.666i	−0.434401	+	0.152003i
$683$	−196.973	−	862.994i	−0.288393	−	1.26353i	−0.886729	−	0.462289i	$-0.847028\pi$
$683$	−196.973	−	862.994i	−0.288393	−	1.26353i	0.598336	−	0.801245i	$-0.295829\pi$
$684$		0			0
$685$	−732.313	−	460.143i	−1.06907	−	0.671741i
$686$	−854.338	+	96.2608i	−1.24539	+	0.140322i
$687$		0			0
$688$	−156.292	+	98.2047i	−0.227168	+	0.142739i
$689$	−623.782	+	497.450i	−0.905344	+	0.721988i
$690$		0			0
$691$	553.507	−	266.555i	0.801023	−	0.385752i	0.0118551	−	0.999930i	$-0.496226\pi$
$691$	553.507	−	266.555i	0.801023	−	0.385752i	0.789168	+	0.614177i	$0.210512\pi$
$692$	29.0071	−	36.3737i	0.0419177	−	0.0525632i
$693$		0			0
$694$	−108.932	+	311.310i	−0.156963	+	0.448574i
$695$		−	1345.35i		−	1.93575i
$696$		0			0
$697$	−364.053			−0.522314
$698$	−1258.14	−	440.244i	−1.80250	−	0.630721i
$699$		0			0
$700$	70.4967	+	56.2192i	0.100710	+	0.0803132i
$701$	−92.4303	−	191.933i	−0.131855	−	0.273800i	0.824580	−	0.565745i	$-0.191412\pi$
$701$	−92.4303	−	191.933i	−0.131855	−	0.273800i	−0.956435	+	0.291946i	$0.905697\pi$
$702$		0			0
$703$	−4.19445	−	5.25967i	−0.00596650	−	0.00748175i
$704$	−86.6736	−	137.940i	−0.123116	−	0.195938i
$705$		0			0
$706$	−3.65977	−	32.4814i	−0.00518381	−	0.0460076i
$707$	−366.321	+	582.996i	−0.518134	+	0.824606i
$708$		0			0
$709$	976.236	−	222.819i	1.37692	−	0.314273i	0.530904	−	0.847432i	$-0.321852\pi$
$709$	976.236	−	222.819i	1.37692	−	0.314273i	0.846015	+	0.533159i	$0.178995\pi$
$710$	−23.7281	−	67.8110i	−0.0334199	−	0.0955085i
$711$		0			0
$712$	−194.352	−	851.511i	−0.272966	−	1.19594i
$713$	375.415	+	375.415i	0.526528	+	0.526528i
$714$		0			0
$715$	542.318	−	61.1045i	0.758486	−	0.0854609i
$716$	−86.1102	+	377.273i	−0.120266	+	0.526918i
$717$		0			0
$718$	−28.2287	+	22.5116i	−0.0393158	+	0.0313533i
$719$	1085.74	+	522.866i	1.51007	+	0.727213i	0.991776	−	0.127987i	$-0.0408517\pi$
$719$	1085.74	+	522.866i	1.51007	+	0.727213i	0.518298	+	0.855200i	$0.326566\pi$
$720$		0			0
$721$	22.5459	−	28.2716i	0.0312703	−	0.0392117i
$722$	−834.995	−	94.0814i	−1.15650	−	0.130307i
$723$		0			0
$724$		−	153.285i		−	0.211719i
$725$	−350.639	+	10.2527i	−0.483640	+	0.0141417i
$726$		0			0
$727$	−984.289	−	344.418i	−1.35391	−	0.473752i	−0.446792	−	0.894638i	$-0.647433\pi$
$727$	−984.289	−	344.418i	−1.35391	−	0.473752i	−0.907113	+	0.420886i	$0.861719\pi$
$728$	−52.1652	+	462.979i	−0.0716555	+	0.635960i
$729$		0			0
$730$	346.587	+	719.695i	0.474776	+	0.985883i
$731$	−127.095	+	263.916i	−0.173865	+	0.361034i
$732$		0			0
$733$	365.036	+	580.951i	0.498002	+	0.792566i	0.997267	−	0.0738833i	$-0.0235392\pi$
$733$	365.036	+	580.951i	0.498002	+	0.792566i	−0.499264	+	0.866450i	$0.666396\pi$
$734$	645.131	+	147.247i	0.878924	+	0.200609i
$735$		0			0
$736$	274.966	−	437.605i	0.373594	−	0.594572i
$737$	113.074	−	113.074i	0.153425	−	0.153425i
$738$		0			0
$739$	282.220	+	806.539i	0.381895	+	1.09139i	0.961098	+	0.276209i	$0.0890782\pi$
$739$	282.220	+	806.539i	0.381895	+	1.09139i	−0.579203	+	0.815183i	$0.696636\pi$
$740$	66.2047	−	23.1660i	0.0894658	−	0.0313054i
$741$		0			0
$742$	452.470	+	452.470i	0.609798	+	0.609798i
$743$	277.918	+	174.627i	0.374048	+	0.235030i	0.705915	−	0.708296i	$-0.250536\pi$
$743$	277.918	+	174.627i	0.374048	+	0.235030i	−0.331868	+	0.943326i	$0.607679\pi$
$744$		0			0
$745$	211.756	−	927.763i	0.284236	−	1.24532i
$746$	463.369	−	291.154i	0.621138	−	0.390287i
$747$		0			0
$748$	240.988	+	116.054i	0.322177	+	0.155152i
$749$	313.891	−	151.162i	0.419080	−	0.201818i
$750$		0			0
$751$	971.174	+	109.425i	1.29318	+	0.145706i	0.731608	−	0.681725i	$-0.238770\pi$
$751$	971.174	+	109.425i	1.29318	+	0.145706i	0.561567	+	0.827431i	$0.310199\pi$
$752$	169.715	−	485.018i	0.225685	−	0.644970i
$753$		0			0
$754$	566.945	+	846.326i	0.751917	+	1.12245i
$755$	−1150.66			−1.52405
$756$		0			0
$757$	−0.974699	+	8.65069i	−0.00128758	+	0.0114276i	−0.994340	−	0.106249i	$-0.966116\pi$
$757$	−0.974699	+	8.65069i	−0.00128758	+	0.0114276i	0.993052	+	0.117676i	$0.0375446\pi$
$758$	1061.49	+	846.509i	1.40038	+	1.11677i
$759$		0			0
$760$	13.2691	−	27.5535i	0.0174593	−	0.0362547i
$761$	380.683	+	477.361i	0.500240	+	0.627282i	0.966284	−	0.257480i	$-0.0828923\pi$
$761$	380.683	+	477.361i	0.500240	+	0.627282i	−0.466043	+	0.884762i	$0.654321\pi$
$762$		0			0
$763$	−900.072	−	205.436i	−1.17965	−	0.269247i
$764$	−16.5686	−	147.050i	−0.0216866	−	0.192474i
$765$		0			0
$766$	676.188	−	676.188i	0.882752	−	0.882752i
$767$	−255.717	+	58.3658i	−0.333399	+	0.0760962i
$768$		0			0
$769$	61.7689	−	21.6139i	0.0803237	−	0.0281065i	−0.289818	−	0.957082i	$-0.593595\pi$
$769$	61.7689	−	21.6139i	0.0803237	−	0.0281065i	0.370142	+	0.928975i	$0.379309\pi$
$770$	−97.3979	−	426.728i	−0.126491	−	0.554192i
$771$		0			0
$772$	−233.049	−	146.434i	−0.301877	−	0.189682i
$773$	−199.336	+	22.4598i	−0.257873	+	0.0290554i	−0.239955	−	0.970784i	$-0.577133\pi$
$773$	−199.336	+	22.4598i	−0.257873	+	0.0290554i	−0.0179188	+	0.999839i	$0.505704\pi$
$774$		0			0
$775$	−231.697	+	145.585i	−0.298964	+	0.187851i
$776$	4.80119	−	3.82882i	0.00618709	−	0.00493404i
$777$		0			0
$778$	−170.689	+	82.1996i	−0.219395	+	0.105655i
$779$	−6.10866	+	7.66001i	−0.00784167	+	0.00983314i
$780$		0			0
$781$	−9.93780	+	28.4006i	−0.0127245	+	0.0363644i
$782$		−	1709.90i		−	2.18657i
$783$		0			0
$784$	−436.483			−0.556739
$785$	884.027	+	309.334i	1.12615	+	0.394057i
$786$		0			0
$787$	−350.315	−	279.367i	−0.445126	−	0.354977i	0.375130	−	0.926972i	$-0.377598\pi$
$787$	−350.315	−	279.367i	−0.445126	−	0.354977i	−0.820257	+	0.571996i	$0.806169\pi$
$788$	−32.2989	−	67.0694i	−0.0409885	−	0.0851135i
$789$		0			0
$790$	−776.137	−	973.245i	−0.982452	−	1.23196i
$791$	39.1822	+	62.3582i	0.0495351	+	0.0788346i
$792$		0			0
$793$	−103.512	−	918.694i	−0.130532	−	1.15850i
$794$	125.715	−	200.074i	0.158331	−	0.251983i
$795$		0			0
$796$	0.723914	−	0.165229i	0.000909439	−	0.000207574i
$797$	−217.496	−	621.567i	−0.272893	−	0.779883i	−0.996017	−	0.0891649i	$-0.971580\pi$
$797$	−217.496	−	621.567i	−0.272893	−	0.779883i	0.723124	−	0.690718i	$-0.242706\pi$
$798$		0			0
$799$	−181.456	−	795.010i	−0.227104	−	0.995006i
$800$	188.355	+	188.355i	0.235444	+	0.235444i
$801$		0			0
$802$	−277.740	+	31.2938i	−0.346309	+	0.0390197i
$803$	74.4452	−	326.166i	0.0927088	−	0.406184i
$804$		0			0
$805$	−578.843	+	461.612i	−0.719060	+	0.573431i
$806$	715.941	+	344.779i	0.888264	+	0.427765i
$807$		0			0
$808$	−495.005	+	620.716i	−0.612630	+	0.768213i
$809$	−181.264	−	20.4235i	−0.224059	−	0.0252454i	−0.000778885	−	1.00000i	$-0.500248\pi$
$809$	−181.264	−	20.4235i	−0.224059	−	0.0252454i	−0.223280	+	0.974754i	$0.571676\pi$
$810$		0			0
$811$		−	657.923i		−	0.811249i	−0.914040	−	0.405625i	$-0.867054\pi$
$811$		−	657.923i		−	0.811249i	0.914040	−	0.405625i	$-0.132946\pi$
$812$	165.001	−	139.665i	0.203203	−	0.172001i
$813$		0			0
$814$	−104.793	−	36.6685i	−0.128738	−	0.0450473i
$815$	−156.868	+	1392.24i	−0.192476	+	1.70827i
$816$		0			0
$817$	3.42043	+	7.10260i	0.00418657	+	0.00869351i
$818$	−380.437	+	789.985i	−0.465081	+	0.965752i
$819$		0			0
$820$	−54.3475	−	86.4935i	−0.0662774	−	0.105480i
$821$	805.317	+	183.808i	0.980897	+	0.223883i	0.682763	−	0.730640i	$-0.260778\pi$
$821$	805.317	+	183.808i	0.980897	+	0.223883i	0.298135	+	0.954524i	$0.403635\pi$
$822$		0			0
$823$	−477.203	+	759.464i	−0.579833	+	0.922799i	0.420050	+	0.907501i	$0.362013\pi$
$823$	−477.203	+	759.464i	−0.579833	+	0.922799i	−0.999883	+	0.0152980i	$0.995130\pi$
$824$	29.4835	−	29.4835i	0.0357809	−	0.0357809i
$825$		0			0
$826$	69.4790	+	198.560i	0.0841151	+	0.240387i
$827$	768.394	−	268.873i	0.929135	−	0.325118i	0.177063	−	0.984200i	$-0.443340\pi$
$827$	768.394	−	268.873i	0.929135	−	0.325118i	0.752072	+	0.659081i	$0.229055\pi$
$828$		0			0
$829$	242.583	+	242.583i	0.292621	+	0.292621i	0.838115	−	0.545494i	$-0.183658\pi$
$829$	242.583	+	242.583i	0.292621	+	0.292621i	−0.545494	+	0.838115i	$0.683658\pi$
$830$	−933.525	−	586.573i	−1.12473	−	0.706714i
$831$		0			0
$832$	−91.7762	+	402.098i	−0.110308	+	0.483291i
$833$	−586.503	+	368.524i	−0.704085	+	0.442406i
$834$		0			0
$835$	−677.061	−	326.055i	−0.810852	−	0.390486i
$836$	6.48558	−	3.12329i	0.00775787	−	0.00373599i
$837$		0			0
$838$	549.892	+	61.9579i	0.656196	+	0.0739355i
$839$	259.165	−	740.652i	0.308898	−	0.882779i	−0.679872	−	0.733331i	$-0.737965\pi$
$839$	259.165	−	740.652i	0.308898	−	0.882779i	0.988770	−	0.149448i	$-0.0477497\pi$
$840$		0			0
$841$	−138.913	+	829.448i	−0.165176	+	0.986264i
$842$	296.715			0.352393
$843$		0			0
$844$	−24.7358	+	219.536i	−0.0293078	+	0.260114i
$845$	−275.475	−	219.684i	−0.326006	−	0.259981i
$846$		0			0
$847$	192.384	−	399.490i	0.227136	−	0.471653i
$848$	650.169	+	815.286i	0.766708	+	0.961422i
$849$		0			0
$850$	859.202	+	196.107i	1.01083	+	0.230714i
$851$	21.0263	+	186.613i	0.0247077	+	0.219287i
$852$		0			0
$853$	398.813	−	398.813i	0.467542	−	0.467542i	−0.433575	−	0.901117i	$-0.642748\pi$
$853$	398.813	−	398.813i	0.467542	−	0.467542i	0.901117	+	0.433575i	$0.142748\pi$
$854$	−722.883	+	164.993i	−0.846468	+	0.193201i
$855$		0			0
$856$	379.179	−	132.680i	0.442966	−	0.155000i
$857$	−234.380	−	1026.89i	−0.273489	−	1.19824i	−0.905863	−	0.423572i	$-0.860776\pi$
$857$	−234.380	−	1026.89i	−0.273489	−	1.19824i	0.632373	−	0.774664i	$-0.282081\pi$
$858$		0			0
$859$	−1397.29	−	877.978i	−1.62665	−	1.02209i	−0.961277	−	0.275585i	$-0.911129\pi$
$859$	−1397.29	−	877.978i	−1.62665	−	1.02209i	−0.665376	−	0.746509i	$-0.731729\pi$
$860$	−81.6758	+	9.20265i	−0.0949718	+	0.0107008i
$861$		0			0
$862$	−323.289	+	203.136i	−0.375045	+	0.235657i
$863$	703.807	−	561.267i	0.815535	−	0.650367i	−0.124205	−	0.992257i	$-0.539638\pi$
$863$	703.807	−	561.267i	0.815535	−	0.650367i	0.939740	+	0.341889i	$0.111067\pi$
$864$		0			0
$865$	−177.390	+	85.4265i	−0.205075	+	0.0987589i
$866$	−129.311	+	162.151i	−0.149320	+	0.187241i
$867$		0			0
$868$	55.6953	−	159.168i	0.0641651	−	0.183373i
$869$			521.358i			0.599952i
$870$		0			0
$871$	−404.846			−0.464806
$872$	−1004.80	−	351.594i	−1.15229	−	0.403205i
$873$		0			0
$874$	−35.9779	−	28.6914i	−0.0411647	−	0.0328277i
$875$	176.622	+	366.759i	0.201853	+	0.419153i
$876$		0			0
$877$	944.016	+	1183.76i	1.07641	+	1.34978i	0.932901	+	0.360133i	$0.117269\pi$
$877$	944.016	+	1183.76i	1.07641	+	1.34978i	0.143514	+	0.989648i	$0.454160\pi$
$878$	599.414	+	953.962i	0.682704	+	1.08652i
$879$		0			0
$880$	−79.8639	−	708.812i	−0.0907544	−	0.805468i
$881$	199.252	−	317.108i	0.226166	−	0.359942i	−0.714294	−	0.699846i	$-0.753252\pi$
$881$	199.252	−	317.108i	0.226166	−	0.359942i	0.940460	+	0.339905i	$0.110395\pi$
$882$		0			0
$883$	89.8803	−	20.5146i	0.101790	−	0.0232328i	−0.171323	−	0.985215i	$-0.554804\pi$
$883$	89.8803	−	20.5146i	0.101790	−	0.0232328i	0.273112	+	0.961982i	$0.411947\pi$
$884$	−223.655	−	639.168i	−0.253003	−	0.723041i
$885$		0			0
$886$	32.7418	+	143.451i	0.0369547	+	0.161909i
$887$	511.932	+	511.932i	0.577150	+	0.577150i	0.934117	−	0.356967i	$-0.116189\pi$
$887$	511.932	+	511.932i	0.577150	+	0.577150i	−0.356967	+	0.934117i	$0.616189\pi$
$888$		0			0
$889$	550.332	−	62.0075i	0.619046	−	0.0697497i
$890$	462.250	−	2025.25i	0.519382	−	2.27556i
$891$		0			0
$892$	−89.6095	+	71.4612i	−0.100459	+	0.0801134i
$893$	−19.7725	−	9.52194i	−0.0221417	−	0.0106629i
$894$		0			0
$895$	1021.07	−	1280.39i	1.14087	−	1.43060i
$896$	782.074	+	88.1186i	0.872850	+	0.0983466i
$897$		0			0
$898$		−	1588.62i		−	1.76907i
$899$	234.681	+	612.625i	0.261047	+	0.681452i
$900$		0			0
$901$	1561.98	+	546.561i	1.73361	+	0.606616i
$902$	−18.1036	+	160.673i	−0.0200705	+	0.178130i
$903$		0			0
$904$	36.8452	+	76.5098i	0.0407580	+	0.0846348i
$905$	−281.460	+	584.457i	−0.311005	+	0.645809i
$906$		0			0
$907$	−351.881	−	560.016i	−0.387962	−	0.617437i	0.594457	−	0.804127i	$-0.297367\pi$
$907$	−351.881	−	560.016i	−0.387962	−	0.617437i	−0.982419	+	0.186690i	$0.940224\pi$
$908$	590.637	+	134.809i	0.650482	+	0.148468i
$909$		0			0
$910$	−589.558	+	938.276i	−0.647866	+	1.03107i
$911$	−969.484	+	969.484i	−1.06420	+	1.06420i	−0.0664049	+	0.997793i	$0.521153\pi$
$911$	−969.484	+	969.484i	−1.06420	+	1.06420i	−0.997793	+	0.0664049i	$0.978847\pi$
$912$		0			0
$913$	152.508	+	435.842i	0.167040	+	0.477374i
$914$	−228.766	+	80.0488i	−0.250292	+	0.0875808i
$915$		0			0
$916$	−200.838	−	200.838i	−0.219255	−	0.219255i
$917$	−69.9571	−	43.9569i	−0.0762891	−	0.0479356i
$918$		0			0
$919$	−107.866	+	472.593i	−0.117374	+	0.514247i	0.881724	+	0.471766i	$0.156383\pi$
$919$	−107.866	+	472.593i	−0.117374	+	0.514247i	−0.999097	+	0.0424811i	$0.986474\pi$
$920$	−722.846	+	454.195i	−0.785703	+	0.493690i
$921$		0			0
$922$	−606.385	−	292.019i	−0.657684	−	0.316724i
$923$	68.6324	−	33.0516i	0.0743580	−	0.0358089i
$924$		0			0
$925$	−96.1822	−	10.8371i	−0.103981	−	0.0117158i
$926$	−291.135	+	832.016i	−0.314401	+	0.898506i
$927$		0			0
$928$	530.573	−	355.426i	0.571739	−	0.383002i
$929$	500.880			0.539160			0.269580	−	0.962978i	$-0.413115\pi$
$929$	500.880			0.539160			0.269580	+	0.962978i	$0.413115\pi$
$930$		0			0
$931$	−2.08718	+	18.5243i	−0.00224187	+	0.0198972i
$932$	−137.297	−	109.491i	−0.147314	−	0.117479i
$933$		0			0
$934$	811.093	−	1684.25i	0.868408	−	1.80327i
$935$	−705.765	−	885.002i	−0.754829	−	0.946526i
$936$		0			0
$937$	−125.487	−	28.6417i	−0.133925	−	0.0305674i	0.155033	−	0.987909i	$-0.450452\pi$
$937$	−125.487	−	28.6417i	−0.133925	−	0.0305674i	−0.288958	+	0.957342i	$0.593309\pi$
$938$	36.3542	+	322.653i	0.0387572	+	0.343980i
$939$		0			0
$940$	161.794	−	161.794i	0.172121	−	0.172121i
$941$	−1671.51	+	381.511i	−1.77631	+	0.405431i	−0.979926	−	0.199360i	$-0.936114\pi$
$941$	−1671.51	+	381.511i	−1.77631	+	0.405431i	−0.796384	+	0.604791i	$0.793257\pi$
$942$		0			0
$943$	258.149	−	90.3304i	0.273753	−	0.0957904i
$944$	76.2843	+	334.223i	0.0808097	+	0.354050i
$945$		0			0
$946$	110.158	+	69.2169i	0.116446	+	0.0731680i
$947$	−178.516	+	20.1139i	−0.188506	+	0.0212396i	−0.205713	−	0.978612i	$-0.565951\pi$
$947$	−178.516	+	20.1139i	−0.188506	+	0.0212396i	0.0172065	+	0.999852i	$0.494523\pi$
$948$		0			0
$949$	−717.163	+	450.624i	−0.755704	+	0.474840i
$950$	18.5433	−	14.7878i	0.0195193	−	0.0155661i
$951$		0			0
$952$	870.659	−	419.287i	0.914558	−	0.440428i
$953$	540.058	−	677.211i	0.566692	−	0.710610i	−0.413087	−	0.910692i	$-0.635549\pi$
$953$	540.058	−	677.211i	0.566692	−	0.710610i	0.979779	+	0.200082i	$0.0641209\pi$
$954$		0			0
$955$	−206.838	+	591.108i	−0.216584	+	0.618962i
$956$		−	441.569i		−	0.461892i
$957$		0			0
$958$	970.484			1.01303
$959$	−694.218	−	242.917i	−0.723898	−	0.253303i
$960$		0			0
$961$	−351.235	−	280.101i	−0.365489	−	0.291468i
$962$	121.954	+	253.240i	0.126771	+	0.263243i
$963$		0			0
$964$	−123.291	−	154.603i	−0.127896	−	0.160376i
$965$	619.709	+	986.260i	0.642185	+	1.02203i
$966$		0			0
$967$	−32.1854	−	285.653i	−0.0332837	−	0.295401i	−0.999316	−	0.0369798i	$-0.988226\pi$
$967$	−32.1854	−	285.653i	−0.0332837	−	0.295401i	0.966032	−	0.258421i	$-0.0832023\pi$
$968$	272.013	−	432.907i	0.281006	−	0.447218i
$969$		0			0
$970$	14.2395	−	3.25008i	0.0146799	−	0.00335060i
$971$	314.882	+	899.881i	0.324286	+	0.926757i	0.984455	+	0.175639i	$0.0561992\pi$
$971$	314.882	+	899.881i	0.324286	+	0.926757i	−0.660168	+	0.751118i	$0.729515\pi$
$972$		0			0
$973$	−254.583	−	1115.40i	−0.261647	−	1.14635i
$974$	−1175.15	−	1175.15i	−1.20652	−	1.20652i
$975$		0			0
$976$	−1200.74	+	135.291i	−1.23026	+	0.138617i
$977$	−7.07897	+	31.0150i	−0.00724562	+	0.0317451i	−0.978422	−	0.206619i	$-0.933754\pi$
$977$	−7.07897	+	31.0150i	−0.00724562	+	0.0317451i	0.971176	+	0.238364i	$0.0766111\pi$
$978$		0			0
$979$	−680.215	+	542.454i	−0.694806	+	0.554090i
$980$	−175.112	−	84.3295i	−0.178686	−	0.0860505i
$981$		0			0
$982$	70.7842	−	88.7606i	0.0720817	−	0.0903875i
$983$	−336.563	−	37.9215i	−0.342383	−	0.0385773i	−0.0609010	−	0.998144i	$-0.519397\pi$
$983$	−336.563	−	37.9215i	−0.342383	−	0.0385773i	−0.281482	+	0.959567i	$0.590826\pi$
$984$		0			0
$985$			315.035i			0.319833i
$986$	860.709	−	1929.61i	0.872931	−	1.95701i
$987$		0			0
$988$	−17.2015	−	6.01908i	−0.0174105	−	0.00609219i
$989$	24.6391	−	218.678i	0.0249131	−	0.221110i
$990$		0			0
$991$	−325.849	−	676.633i	−0.328809	−	0.682778i	0.669381	−	0.742919i	$-0.266559\pi$
$991$	−325.849	−	676.633i	−0.328809	−	0.682778i	−0.998190	+	0.0601410i	$0.980845\pi$
$992$	216.147	−	448.833i	0.217890	−	0.452452i
$993$		0			0
$994$	−32.5044	−	51.7305i	−0.0327006	−	0.0520428i
$995$	−3.06359	−	0.699245i	−0.00307899	−	0.000702759i
$996$		0			0
$997$	41.4061	−	65.8975i	0.0415307	−	0.0660957i	−0.825314	−	0.564675i	$-0.809002\pi$
$997$	41.4061	−	65.8975i	0.0415307	−	0.0660957i	0.866844	+	0.498579i	$0.166145\pi$
$998$	1279.36	−	1279.36i	1.28193	−	1.28193i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.37.3		48
3.2	odd	2		29.3.f.a.8.2	✓	48
29.11	odd	28	inner	261.3.s.a.127.3		48
87.11	even	28		29.3.f.a.11.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.8.2	✓	48	3.2	odd	2
29.3.f.a.11.2	yes	48	87.11	even	28
261.3.s.a.37.3		48	1.1	even	1	trivial
261.3.s.a.127.3		48	29.11	odd	28	inner

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +O(q^{10})\)	\(q+(2.20133 + 0.770280i) q^{2} +(1.12521 + 0.897324i) q^{4} +(-2.64264 - 5.48750i) q^{5} +(-3.22936 - 4.04949i) q^{7} +(-3.17747 - 5.05691i) q^{8} +(-1.59042 - 14.1154i) q^{10} +(-3.16517 + 5.03734i) q^{11} +(14.6839 - 3.35151i) q^{13} +(-3.98966 - 11.4018i) q^{14} +(-4.38044 - 19.1919i) q^{16} +(-22.0898 - 22.0898i) q^{17} +(-0.835449 + 0.0941325i) q^{19} +(1.95054 - 8.54589i) q^{20} +(-10.8478 + 8.65079i) q^{22} +(21.1449 + 10.1828i) q^{23} +(-7.54184 + 9.45717i) q^{25} +(34.9058 + 3.93294i) q^{26} -7.45431i q^{28} +(18.7362 + 22.1350i) q^{29} +(21.3525 + 7.47156i) q^{31} +(2.46561 - 21.8829i) q^{32} +(-31.6117 - 65.6424i) q^{34} +(-13.6875 + 28.4225i) q^{35} +(4.25720 + 6.77529i) q^{37} +(-1.91161 - 0.436313i) q^{38} +(-19.3529 + 30.8000i) q^{40} +(8.24028 - 8.24028i) q^{41} +(-3.09691 - 8.85047i) q^{43} +(-8.08161 + 2.82788i) q^{44} +(38.7033 + 38.7033i) q^{46} +(22.1022 + 13.8877i) q^{47} +(4.93392 - 21.6169i) q^{49} +(-23.8868 + 15.0091i) q^{50} +(19.5299 + 9.40509i) q^{52} +(-47.7265 + 22.9839i) q^{53} +(36.0068 + 4.05699i) q^{55} +(-10.2167 + 29.1977i) q^{56} +(24.1944 + 63.1585i) q^{58} -17.4148 q^{59} +(6.87260 - 60.9960i) q^{61} +(41.2488 + 32.8948i) q^{62} +(-11.8813 + 24.6717i) q^{64} +(-57.1957 - 71.7211i) q^{65} +(-26.2055 - 5.98124i) q^{67} +(-5.03393 - 44.6774i) q^{68} +(-52.0241 + 52.0241i) q^{70} +(4.93086 - 1.12544i) q^{71} +(-53.0793 + 18.5732i) q^{73} +(4.15264 + 18.1939i) q^{74} +(-1.02452 - 0.643750i) q^{76} +(30.6201 - 3.45006i) q^{77} +(74.2026 - 46.6246i) q^{79} +(-93.7398 + 74.7550i) q^{80} +(24.4869 - 11.7923i) q^{82} +(48.3929 - 60.6827i) q^{83} +(-62.8424 + 179.593i) q^{85} -21.8683i q^{86} +35.5306 q^{88} +(138.036 + 48.3009i) q^{89} +(-60.9916 - 48.6392i) q^{91} +(14.6551 + 30.4317i) q^{92} +(37.9568 + 47.5963i) q^{94} +(2.72434 + 4.33577i) q^{95} +(0.115126 + 1.02177i) q^{97} +(27.5123 - 43.7855i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more