LMFDB - Embedded newform 1323.2.i.b.1097.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, degree $2$, not 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.3
Root			$-0.539982 - 0.935277i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.b.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.293869i q^{2} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +O(q^{10})$	\(q-0.293869i q^{2} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +(0.778834 - 0.449660i) q^{10} +(3.37445 + 1.94824i) q^{11} +(2.02935 + 1.17164i) q^{13} +3.48930 q^{16} +(-1.68263 - 2.91440i) q^{17} +(-2.20696 - 1.27419i) q^{19} +(2.92813 + 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(-2.58141 + 1.49038i) q^{23} +(-2.18263 + 3.78042i) q^{25} +(0.344311 - 0.596363i) q^{26} +(3.67241 - 2.12027i) q^{29} -0.472735i q^{31} -3.32560i q^{32} +(-0.856452 + 0.494473i) q^{34} +(-3.89395 + 6.74451i) q^{37} +(-0.374446 + 0.648559i) q^{38} +(3.04808 - 1.75981i) q^{40} +(3.12737 - 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} -4.05388 q^{47} +(1.11095 + 0.641408i) q^{50} +(3.88344 + 2.24211i) q^{52} +(-4.99439 + 2.88351i) q^{53} +11.9243i q^{55} +(-0.623082 - 1.07921i) q^{58} -4.68705 q^{59} +1.60018i q^{61} -0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +1.57566 q^{67} +(-3.21994 - 5.57711i) q^{68} -13.6132i q^{71} +(0.856452 - 0.494473i) q^{73} +(1.98201 + 1.14431i) q^{74} +(-4.22333 - 2.43834i) q^{76} -9.27815 q^{79} +(5.33910 + 9.24760i) q^{80} +(-1.59182 - 0.919038i) q^{82} +(5.49361 + 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(1.04950 - 0.605932i) q^{86} +(2.24067 - 3.88095i) q^{88} +(-2.15849 + 3.73861i) q^{89} +(-4.93989 + 2.85205i) q^{92} +1.19131i q^{94} -7.79874i q^{95} +(-4.98797 + 2.87980i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4}+O(q^{10}) $ 10 * q - 8 * q^4	$ 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) $ 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.293869i		−	0.207797i	−0.994588	−	0.103899i	$-0.966868\pi$
$2$		−	0.293869i		−	0.207797i	0.994588	−	0.103899i	$-0.0331317\pi$
$3$		0			0
$3$		0			0
$4$	1.91364			0.956820
$5$	1.53014	+	2.65027i	0.684297	+	1.18524i	0.973657	+	0.228017i	$0.0732243\pi$
$5$	1.53014	+	2.65027i	0.684297	+	1.18524i	−0.289360	+	0.957220i	$0.593442\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.15010i		−	0.406622i
$9$		0			0
$10$	0.778834	−	0.449660i	0.246289	−	0.142195i
$11$	3.37445	+	1.94824i	1.01743	+	0.587416i	0.913360	−	0.407154i	$-0.133479\pi$
$11$	3.37445	+	1.94824i	1.01743	+	0.587416i	0.104074	+	0.994570i	$0.466812\pi$
$12$		0			0
$13$	2.02935	+	1.17164i	0.562840	+	0.324956i	0.754285	−	0.656548i	$-0.227984\pi$
$13$	2.02935	+	1.17164i	0.562840	+	0.324956i	−0.191445	+	0.981503i	$0.561317\pi$
$14$		0			0
$15$		0			0
$16$	3.48930			0.872326
$17$	−1.68263	−	2.91440i	−0.408097	−	0.706845i	0.586579	−	0.809892i	$-0.300474\pi$
$17$	−1.68263	−	2.91440i	−0.408097	−	0.706845i	−0.994677	+	0.103047i	$0.967141\pi$
$18$		0			0
$19$	−2.20696	−	1.27419i	−0.506312	−	0.292319i	0.225004	−	0.974358i	$-0.427760\pi$
$19$	−2.20696	−	1.27419i	−0.506312	−	0.292319i	−0.731316	+	0.682038i	$0.761094\pi$
$20$	2.92813	+	5.07167i	0.654750	+	1.13406i
$21$		0			0
$22$	0.572527	−	0.991647i	0.122063	−	0.211420i
$23$	−2.58141	+	1.49038i	−0.538261	+	0.310765i	−0.744374	−	0.667763i	$-0.767252\pi$
$23$	−2.58141	+	1.49038i	−0.538261	+	0.310765i	0.206113	+	0.978528i	$0.433919\pi$
$24$		0			0
$25$	−2.18263	+	3.78042i	−0.436525	+	0.756084i
$26$	0.344311	−	0.596363i	0.0675249	−	0.116956i
$27$		0			0
$28$		0			0
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	−0.118640	−	0.992937i	$-0.537853\pi$
$29$	3.67241	−	2.12027i	0.681949	−	0.393724i	0.800589	+	0.599214i	$0.204520\pi$
$30$		0			0
$31$		−	0.472735i		−	0.0849057i	−0.999098	−	0.0424528i	$-0.986483\pi$
$31$		−	0.472735i		−	0.0849057i	0.999098	−	0.0424528i	$-0.0135172\pi$
$32$		−	3.32560i		−	0.587888i
$33$		0			0
$34$	−0.856452	+	0.494473i	−0.146880	+	0.0848014i
$35$		0			0
$36$		0			0
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	0.345236	+	0.938516i	$0.387799\pi$
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	−0.985397	+	0.170275i	$0.945534\pi$
$38$	−0.374446	+	0.648559i	−0.0607431	+	0.105210i
$39$		0			0
$40$	3.04808	−	1.75981i	0.481943	−	0.278250i
$41$	3.12737	−	5.41676i	0.488413	−	0.845956i	−0.511498	−	0.859284i	$-0.670909\pi$
$41$	3.12737	−	5.41676i	0.488413	−	0.845956i	0.999911	+	0.0133282i	$0.00424262\pi$
$42$		0			0
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	0.979318	−	0.202328i	$-0.0648506\pi$
$43$	2.06191	+	3.57133i	0.314438	+	0.544623i	−0.664880	+	0.746950i	$0.731517\pi$
$44$	6.45748	+	3.72823i	0.973501	+	0.562051i
$45$		0			0
$46$	0.437976	+	0.758597i	0.0645761	+	0.111849i
$47$	−4.05388			−0.591319			−0.295659	−	0.955293i	$-0.595539\pi$
$47$	−4.05388			−0.591319			−0.295659	+	0.955293i	$0.595539\pi$
$48$		0			0
$49$		0			0
$50$	1.11095	+	0.641408i	0.157112	+	0.0907087i
$51$		0			0
$52$	3.88344	+	2.24211i	0.538537	+	0.310924i
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	−0.802124	−	0.597157i	$-0.796297\pi$
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	0.116091	+	0.993239i	$0.462963\pi$
$54$		0			0
$55$			11.9243i			1.60787i
$56$		0			0
$57$		0			0
$58$	−0.623082	−	1.07921i	−0.0818146	−	0.141707i
$59$	−4.68705			−0.610201			−0.305101	−	0.952320i	$-0.598690\pi$
$59$	−4.68705			−0.610201			−0.305101	+	0.952320i	$0.598690\pi$
$60$		0			0
$61$			1.60018i			0.204883i	0.994739	+	0.102441i	$0.0326654\pi$
$61$			1.60018i			0.204883i	−0.994739	+	0.102441i	$0.967335\pi$
$62$	−0.138922			−0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$			7.17110i			0.889465i
$66$		0			0
$67$	1.57566			0.192498			0.0962489	−	0.995357i	$-0.469316\pi$
$67$	1.57566			0.192498			0.0962489	+	0.995357i	$0.469316\pi$
$68$	−3.21994	−	5.57711i	−0.390476	−	0.676324i
$69$		0			0
$70$		0			0
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$		0			0
$73$	0.856452	−	0.494473i	0.100240	−	0.0578737i	−0.449042	−	0.893511i	$-0.648235\pi$
$73$	0.856452	−	0.494473i	0.100240	−	0.0578737i	0.549282	+	0.835637i	$0.314901\pi$
$74$	1.98201	+	1.14431i	0.230404	+	0.133024i
$75$		0			0
$76$	−4.22333	−	2.43834i	−0.484450	−	0.279697i
$77$		0			0
$78$		0			0
$79$	−9.27815			−1.04387			−0.521937	−	0.852984i	$-0.674790\pi$
$79$	−9.27815			−1.04387			−0.521937	+	0.852984i	$0.674790\pi$
$80$	5.33910	+	9.24760i	0.596930	+	1.03391i
$81$		0			0
$82$	−1.59182	−	0.919038i	−0.175787	−	0.101491i
$83$	5.49361	+	9.51520i	0.603002	+	1.04443i	0.992364	+	0.123345i	$0.0393621\pi$
$83$	5.49361	+	9.51520i	0.603002	+	1.04443i	−0.389362	+	0.921085i	$0.627305\pi$
$84$		0			0
$85$	5.14930	−	8.91884i	0.558519	−	0.967384i
$86$	1.04950	−	0.605932i	0.113171	−	0.0653393i
$87$		0			0
$88$	2.24067	−	3.88095i	0.238856	−	0.413710i
$89$	−2.15849	+	3.73861i	−0.228799	+	0.396292i	−0.957452	−	0.288591i	$-0.906813\pi$
$89$	−2.15849	+	3.73861i	−0.228799	+	0.396292i	0.728653	+	0.684883i	$0.240147\pi$
$90$		0			0
$91$		0			0
$92$	−4.93989	+	2.85205i	−0.515019	+	0.297346i
$93$		0			0
$94$			1.19131i			0.122874i
$95$		−	7.79874i		−	0.800133i
$96$		0			0
$97$	−4.98797	+	2.87980i	−0.506451	+	0.292400i	−0.731374	−	0.681977i	$-0.761120\pi$
$97$	−4.98797	+	2.87980i	−0.506451	+	0.292400i	0.224923	+	0.974377i	$0.427787\pi$
$98$		0			0
$99$		0			0
$100$	−4.17676	+	7.23437i	−0.417676	+	0.723437i
$101$	8.57900	−	14.8593i	0.853642	−	1.47855i	−0.0242566	−	0.999706i	$-0.507722\pi$
$101$	8.57900	−	14.8593i	0.853642	−	1.47855i	0.877899	−	0.478846i	$-0.158945\pi$
$102$		0			0
$103$	−8.50422	+	4.90992i	−0.837946	+	0.483788i	−0.856566	−	0.516038i	$-0.827406\pi$
$103$	−8.50422	+	4.90992i	−0.837946	+	0.483788i	0.0186195	+	0.999827i	$0.494073\pi$
$104$	1.34751	−	2.33395i	0.132134	−	0.228863i
$105$		0			0
$106$	0.847377	+	1.46770i	0.0823045	+	0.142556i
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	0.638170	−	0.769896i	$-0.279692\pi$
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	−0.347664	+	0.937619i	$0.613025\pi$
$108$		0			0
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	0.893806	−	0.448455i	$-0.148025\pi$
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	−0.835276	+	0.549831i	$0.814692\pi$
$110$	3.50418			0.334110
$111$		0			0
$112$		0			0
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	0.585673	−	0.810547i	$-0.300830\pi$
$113$	1.87681	+	1.08358i	0.176555	+	0.101934i	−0.409118	+	0.912482i	$0.634164\pi$
$114$		0			0
$115$	−7.89981	−	4.56096i	−0.736661	−	0.425311i
$116$	7.02767	−	4.05743i	0.652503	−	0.376723i
$117$		0			0
$118$			1.37738i			0.126798i
$119$		0			0
$120$		0			0
$121$	2.09126	+	3.62216i	0.190114	+	0.329287i
$122$	0.470245			0.0425740
$123$		0			0
$124$		−	0.904645i		−	0.0812395i
$125$	1.94249			0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$		−	8.41480i		−	0.743770i
$129$		0			0
$130$	2.10737			0.184828
$131$	−3.73911	−	6.47632i	−0.326687	−	0.565839i	0.655165	−	0.755486i	$-0.272599\pi$
$131$	−3.73911	−	6.47632i	−0.326687	−	0.565839i	−0.981852	+	0.189647i	$0.939266\pi$
$132$		0			0
$133$		0			0
$134$		−	0.463039i		−	0.0400005i
$135$		0			0
$136$	−3.35185	+	1.93519i	−0.287418	+	0.165941i
$137$	10.5731	+	6.10439i	0.903321	+	0.521533i	0.878276	−	0.478153i	$-0.158694\pi$
$137$	10.5731	+	6.10439i	0.903321	+	0.521533i	0.0250451	+	0.999686i	$0.492027\pi$
$138$		0			0
$139$	11.5501	+	6.66842i	0.979663	+	0.565608i	0.902168	−	0.431384i	$-0.141975\pi$
$139$	11.5501	+	6.66842i	0.979663	+	0.565608i	0.0774943	+	0.996993i	$0.475308\pi$
$140$		0			0
$141$		0			0
$142$	−4.00051			−0.335715
$143$	4.56528	+	7.90730i	0.381768	+	0.661242i
$144$		0			0
$145$	11.2386	+	6.48859i	0.933312	+	0.538848i
$146$	−0.145310	−	0.251685i	−0.0120260	−	0.0208296i
$147$		0			0
$148$	−7.45161	+	12.9066i	−0.612519	+	1.06091i
$149$	7.33827	−	4.23675i	0.601174	−	0.347088i	−0.168329	−	0.985731i	$-0.553837\pi$
$149$	7.33827	−	4.23675i	0.601174	−	0.347088i	0.769503	+	0.638643i	$0.220504\pi$
$150$		0			0
$151$	1.67827	−	2.90685i	0.136576	−	0.236556i	−0.789623	−	0.613593i	$-0.789724\pi$
$151$	1.67827	−	2.90685i	0.136576	−	0.236556i	0.926198	+	0.377037i	$0.123057\pi$
$152$	−1.46545	+	2.53823i	−0.118863	+	0.205877i
$153$		0			0
$154$		0			0
$155$	1.25288	−	0.723348i	0.100633	−	0.0581007i
$156$		0			0
$157$		−	16.7085i		−	1.33349i	−0.745288	−	0.666743i	$-0.767688\pi$
$157$		−	16.7085i		−	1.33349i	0.745288	−	0.666743i	$-0.232312\pi$
$158$			2.72657i			0.216914i
$159$		0			0
$160$	8.81374	−	5.08862i	0.696787	−	0.402290i
$161$		0			0
$162$		0			0
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.387363	−	0.921927i	$-0.373386\pi$
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.604731	−	0.796430i	$-0.293281\pi$
$164$	5.98466	−	10.3657i	0.467324	−	0.809428i
$165$		0			0
$166$	2.79623	−	1.61440i	0.217029	−	0.125302i
$167$	0.875828	−	1.51698i	0.0677736	−	0.117387i	−0.830147	−	0.557544i	$-0.811744\pi$
$167$	0.875828	−	1.51698i	0.0677736	−	0.117387i	0.897921	+	0.440157i	$0.145077\pi$
$168$		0			0
$169$	−3.75450	−	6.50298i	−0.288808	−	0.500229i
$170$	−2.62097	−	1.51322i	−0.201020	−	0.116059i
$171$		0			0
$172$	3.94575	+	6.83424i	0.300861	+	0.521106i
$173$	23.9266			1.81910			0.909551	−	0.415592i	$-0.136426\pi$
$173$	23.9266			1.81910			0.909551	+	0.415592i	$0.136426\pi$
$174$		0			0
$175$		0			0
$176$	11.7745	+	6.79799i	0.887533	+	0.512418i
$177$		0			0
$178$	1.09866	+	0.634313i	0.0823482	+	0.0475438i
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.663639	+	0.748053i	$0.730989\pi$
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.979652	+	0.200702i	$0.935678\pi$
$180$		0			0
$181$		−	22.4032i		−	1.66522i	−0.553859	−	0.832610i	$-0.686845\pi$
$181$		−	22.4032i		−	1.66522i	0.553859	−	0.832610i	$-0.313155\pi$
$182$		0			0
$183$		0			0
$184$	1.71408	+	2.96888i	0.126364	+	0.218869i
$185$	−23.8331			−1.75224
$186$		0			0
$187$		−	13.1126i		−	0.958890i
$188$	−7.75766			−0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$		−	4.28895i		−	0.310337i	−0.987888	−	0.155169i	$-0.950408\pi$
$191$		−	4.28895i		−	0.310337i	0.987888	−	0.155169i	$-0.0495921\pi$
$192$		0			0
$193$	−23.3449			−1.68041			−0.840203	−	0.542272i	$-0.817564\pi$
$193$	−23.3449			−1.68041			−0.840203	+	0.542272i	$0.817564\pi$
$194$	0.846286	+	1.46581i	0.0607598	+	0.105239i
$195$		0			0
$196$		0			0
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$		0			0
$199$	3.92927	−	2.26856i	0.278539	−	0.160814i	−0.354223	−	0.935161i	$-0.615255\pi$
$199$	3.92927	−	2.26856i	0.278539	−	0.160814i	0.632762	+	0.774347i	$0.281921\pi$
$200$	4.34786	+	2.51024i	0.307440	+	0.177501i
$201$		0			0
$202$	−4.36668	−	2.52111i	−0.307239	−	0.177384i
$203$		0			0
$204$		0			0
$205$	19.1412			1.33688
$206$	1.44287	+	2.49913i	0.100530	+	0.174123i
$207$		0			0
$208$	7.08101	+	4.08822i	0.490980	+	0.283467i
$209$	−4.96485	−	8.59937i	−0.343426	−	0.594831i
$210$		0			0
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	−0.959829	−	0.280584i	$-0.909472\pi$
$211$	−3.44148	+	5.96082i	−0.236921	+	0.410360i	0.722908	+	0.690944i	$0.242805\pi$
$212$	−9.55747	+	5.51801i	−0.656410	+	0.378978i
$213$		0			0
$214$	0.509847	−	0.883081i	0.0348524	−	0.0603662i
$215$	−6.31000	+	10.9292i	−0.430338	+	0.745368i
$216$		0			0
$217$		0			0
$218$	0.311031	−	0.179574i	0.0210657	−	0.0121623i
$219$		0			0
$220$			22.8188i			1.53844i
$221$		−	7.88576i		−	0.530454i
$222$		0			0
$223$	−5.57176	+	3.21686i	−0.373113	+	0.215417i	−0.674818	−	0.737985i	$-0.735778\pi$
$223$	−5.57176	+	3.21686i	−0.373113	+	0.215417i	0.301705	+	0.953401i	$0.402444\pi$
$224$		0			0
$225$		0			0
$226$	0.318430	−	0.551537i	0.0211816	−	0.0366877i
$227$	−9.86983	+	17.0951i	−0.655084	+	1.13464i	0.326789	+	0.945097i	$0.394033\pi$
$227$	−9.86983	+	17.0951i	−0.655084	+	1.13464i	−0.981873	+	0.189541i	$0.939300\pi$
$228$		0			0
$229$	−9.44564	+	5.45344i	−0.624185	+	0.360373i	−0.778497	−	0.627649i	$-0.784017\pi$
$229$	−9.44564	+	5.45344i	−0.624185	+	0.360373i	0.154311	+	0.988022i	$0.450684\pi$
$230$	−1.34033	+	2.32151i	−0.0883785	+	0.153076i
$231$		0			0
$232$	−2.43852	−	4.22364i	−0.160097	−	0.277295i
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.223104	−	0.974795i	$-0.571619\pi$
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.955749	+	0.294184i	$0.904952\pi$
$234$		0			0
$235$	−6.20298	−	10.7439i	−0.404638	−	0.700853i
$236$	−8.96932			−0.583853
$237$		0			0
$238$		0			0
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.999300	−	0.0373991i	$-0.988093\pi$
$239$	−23.6739	−	13.6681i	−1.53134	−	0.884119i	−0.532039	−	0.846720i	$-0.678574\pi$
$240$		0			0
$241$	18.4688	+	10.6630i	1.18968	+	0.686861i	0.958234	−	0.285987i	$-0.0923213\pi$
$241$	18.4688	+	10.6630i	1.18968	+	0.686861i	0.231445	+	0.972848i	$0.425655\pi$
$242$	1.06444	−	0.614556i	0.0684250	−	0.0395052i
$243$		0			0
$244$			3.06218i			0.196036i
$245$		0			0
$246$		0			0
$247$	−2.98580	−	5.17155i	−0.189982	−	0.329058i
$248$	−0.543692			−0.0345245
$249$		0			0
$250$		−	0.570839i		−	0.0361030i
$251$	−26.7381			−1.68769			−0.843847	−	0.536584i	$-0.819714\pi$
$251$	−26.7381			−1.68769			−0.843847	+	0.536584i	$0.819714\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$		−	0.807815i		−	0.0506868i
$255$		0			0
$256$	9.52977			0.595611
$257$	−1.52640	−	2.64380i	−0.0952140	−	0.164916i	0.814484	−	0.580186i	$-0.197020\pi$
$257$	−1.52640	−	2.64380i	−0.0952140	−	0.164916i	−0.909698	+	0.415271i	$0.863687\pi$
$258$		0			0
$259$		0			0
$260$			13.7229i			0.851058i
$261$		0			0
$262$	−1.90319	+	1.09881i	−0.117580	+	0.0678847i
$263$	−14.0447	−	8.10868i	−0.866030	−	0.500003i	−3.24009e−6	−	1.00000i	$-0.500001\pi$
$263$	−14.0447	−	8.10868i	−0.866030	−	0.500003i	−0.866027	+	0.499997i	$0.833334\pi$
$264$		0			0
$265$	−15.2842	−	8.82433i	−0.938901	−	0.542074i
$266$		0			0
$267$		0			0
$268$	3.01525			0.184186
$269$	0.303255	+	0.525254i	0.0184898	+	0.0320253i	0.875122	−	0.483902i	$-0.160781\pi$
$269$	0.303255	+	0.525254i	0.0184898	+	0.0320253i	−0.856632	+	0.515927i	$0.827448\pi$
$270$		0			0
$271$	−19.8948	−	11.4863i	−1.20852	−	0.697742i	−0.246088	−	0.969248i	$-0.579145\pi$
$271$	−19.8948	−	11.4863i	−1.20852	−	0.697742i	−0.962437	+	0.271505i	$0.912479\pi$
$272$	−5.87120	−	10.1692i	−0.355994	−	0.616599i
$273$		0			0
$274$	1.79389	−	3.10711i	0.108373	−	0.187708i
$275$	−14.7303	+	8.50455i	−0.888271	+	0.512844i
$276$		0			0
$277$	−6.64173	+	11.5038i	−0.399063	+	0.691197i	−0.993611	−	0.112863i	$-0.963998\pi$
$277$	−6.64173	+	11.5038i	−0.399063	+	0.691197i	0.594548	+	0.804060i	$0.297331\pi$
$278$	1.95965	−	3.39421i	0.117532	−	0.203571i
$279$		0			0
$280$		0			0
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	−0.659859	−	0.751390i	$-0.729384\pi$
$281$	−5.68377	+	3.28153i	−0.339065	+	0.195759i	0.320793	+	0.947149i	$0.396050\pi$
$282$		0			0
$283$			2.97234i			0.176687i	0.996090	+	0.0883437i	$0.0281574\pi$
$283$			2.97234i			0.176687i	−0.996090	+	0.0883437i	$0.971843\pi$
$284$		−	26.0508i		−	1.54583i
$285$		0			0
$286$	2.32371	−	1.34160i	0.137404	−	0.0793303i
$287$		0			0
$288$		0			0
$289$	2.83753	−	4.91475i	0.166914	−	0.289103i
$290$	1.90680	−	3.30267i	0.111971	−	0.193940i
$291$		0			0
$292$	1.63894	−	0.946243i	0.0959118	−	0.0553747i
$293$	3.03087	−	5.24962i	0.177065	−	0.306686i	−0.763809	−	0.645443i	$-0.776673\pi$
$293$	3.03087	−	5.24962i	0.177065	−	0.306686i	0.940874	+	0.338756i	$0.110006\pi$
$294$		0			0
$295$	−7.17181	−	12.4219i	−0.417559	−	0.723234i
$296$	7.75686	+	4.47843i	0.450858	+	0.260303i
$297$		0			0
$298$	−1.24505	−	2.15649i	−0.0721239	−	0.124922i
$299$	−6.98477			−0.403940
$300$		0			0
$301$		0			0
$302$	−0.854235	−	0.493193i	−0.0491557	−	0.0283801i
$303$		0			0
$304$	−7.70076	−	4.44604i	−0.441669	−	0.254998i
$305$	−4.24092	+	2.44850i	−0.242834	+	0.140201i
$306$		0			0
$307$		−	21.6030i		−	1.23295i	−0.787375	−	0.616474i	$-0.788561\pi$
$307$		−	21.6030i		−	1.23295i	0.787375	−	0.616474i	$-0.211439\pi$
$308$		0			0
$309$		0			0
$310$	−0.212570	−	0.368182i	−0.0120732	−	0.0209113i
$311$	11.0234			0.625081			0.312540	−	0.949905i	$-0.398820\pi$
$311$	11.0234			0.625081			0.312540	+	0.949905i	$0.398820\pi$
$312$		0			0
$313$			13.5542i			0.766129i	0.923722	+	0.383064i	$0.125131\pi$
$313$			13.5542i			0.766129i	−0.923722	+	0.383064i	$0.874869\pi$
$314$	−4.91012			−0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$		−	11.1541i		−	0.626479i	−0.949674	−	0.313240i	$-0.898586\pi$
$317$		−	11.1541i		−	0.626479i	0.949674	−	0.313240i	$-0.101414\pi$
$318$		0			0
$319$	16.5231			0.925118
$320$	9.18282	+	15.9051i	0.513335	+	0.889123i
$321$		0			0
$322$		0			0
$323$			8.57595i			0.477179i
$324$		0			0
$325$	−8.85862	+	5.11453i	−0.491388	+	0.283703i
$326$	−6.44706	−	3.72221i	−0.357070	−	0.206154i
$327$		0			0
$328$	−6.22982	−	3.59679i	−0.343984	−	0.198599i
$329$		0			0
$330$		0			0
$331$	−19.0202			−1.04544			−0.522722	−	0.852503i	$-0.675083\pi$
$331$	−19.0202			−1.04544			−0.522722	+	0.852503i	$0.675083\pi$
$332$	10.5128	+	18.2087i	0.576964	+	0.999331i
$333$		0			0
$334$	−0.445794	−	0.257379i	−0.0243927	−	0.0140832i
$335$	2.41098	+	4.17593i	0.131726	+	0.228156i
$336$		0			0
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	−0.761091	−	0.648645i	$-0.775336\pi$
$337$	3.32635	−	5.76140i	0.181198	−	0.313843i	0.942289	+	0.334802i	$0.108669\pi$
$338$	−1.91103	+	1.10333i	−0.103946	+	0.0600134i
$339$		0			0
$340$	9.85390	−	17.0675i	0.534403	−	0.925613i
$341$	0.921000	−	1.59522i	0.0498749	−	0.0863859i
$342$		0			0
$343$		0			0
$344$	4.10738	−	2.37140i	0.221455	−	0.127857i
$345$		0			0
$346$		−	7.03128i		−	0.378004i
$347$			26.6501i			1.43065i	0.698792	+	0.715325i	$0.253721\pi$
$347$			26.6501i			1.43065i	−0.698792	+	0.715325i	$0.746279\pi$
$348$		0			0
$349$	20.5135	−	11.8435i	1.09806	−	0.633966i	0.162350	−	0.986733i	$-0.448093\pi$
$349$	20.5135	−	11.8435i	1.09806	−	0.633966i	0.935711	+	0.352768i	$0.114759\pi$
$350$		0			0
$351$		0			0
$352$	6.47905	−	11.2221i	0.345335	−	0.598137i
$353$	2.29422	−	3.97371i	0.122109	−	0.211499i	−0.798490	−	0.602008i	$-0.794368\pi$
$353$	2.29422	−	3.97371i	0.122109	−	0.211499i	0.920599	+	0.390509i	$0.127701\pi$
$354$		0			0
$355$	36.0788	−	20.8301i	1.91486	−	1.10555i
$356$	−4.13057	+	7.15435i	−0.218920	+	0.379180i
$357$		0			0
$358$	3.73022	+	6.46094i	0.197148	+	0.341471i
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	0.633523	−	0.773724i	$-0.281608\pi$
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	−0.353303	+	0.935509i	$0.614941\pi$
$360$		0			0
$361$	−6.25288	−	10.8303i	−0.329099	−	0.570016i
$362$	−6.58363			−0.346028
$363$		0			0
$364$		0			0
$365$	2.62097	+	1.51322i	0.137188	+	0.0792056i
$366$		0			0
$367$	−22.8860	−	13.2132i	−1.19464	−	0.689725i	−0.235283	−	0.971927i	$-0.575602\pi$
$367$	−22.8860	−	13.2132i	−1.19464	−	0.689725i	−0.959355	+	0.282202i	$0.908935\pi$
$368$	−9.00732	+	5.20038i	−0.469539	+	0.271088i
$369$		0			0
$370$			7.00381i			0.364111i
$371$		0			0
$372$		0			0
$373$	−10.0581	−	17.4211i	−0.520789	−	0.902033i	−0.999708	−	0.0241735i	$-0.992305\pi$
$373$	−10.0581	−	17.4211i	−0.520789	−	0.902033i	0.478919	−	0.877859i	$-0.341029\pi$
$374$	−3.85340			−0.199255
$375$		0			0
$376$			4.66236i			0.240443i
$377$	9.93679			0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$		−	14.9240i		−	0.765584i
$381$		0			0
$382$	−1.26039			−0.0644872
$383$	−14.0317	−	24.3036i	−0.716985	−	1.24185i	−0.962189	−	0.272383i	$-0.912188\pi$
$383$	−14.0317	−	24.3036i	−0.716985	−	1.24185i	0.245204	−	0.969471i	$-0.421145\pi$
$384$		0			0
$385$		0			0
$386$			6.86037i			0.349183i
$387$		0			0
$388$	−9.54517	+	5.51091i	−0.484583	+	0.279774i
$389$	29.6520	+	17.1196i	1.50342	+	0.867999i	0.999992	+	0.00396103i	$0.00126084\pi$
$389$	29.6520	+	17.1196i	1.50342	+	0.867999i	0.503426	+	0.864038i	$0.332072\pi$
$390$		0			0
$391$	8.68710	+	5.01550i	0.439325	+	0.253645i
$392$		0			0
$393$		0			0
$394$	5.51918			0.278052
$395$	−14.1968	−	24.5896i	−0.714320	−	1.23724i
$396$		0			0
$397$	11.2926	+	6.51981i	0.566762	+	0.327220i	0.755855	−	0.654739i	$-0.227222\pi$
$397$	11.2926	+	6.51981i	0.566762	+	0.327220i	−0.189093	+	0.981959i	$0.560555\pi$
$398$	−0.666662	−	1.15469i	−0.0334167	−	0.0578795i
$399$		0			0
$400$	−7.61585	+	13.1910i	−0.380792	+	0.659552i
$401$	15.8943	−	9.17659i	0.793725	−	0.458257i	−0.0475475	−	0.998869i	$-0.515141\pi$
$401$	15.8943	−	9.17659i	0.793725	−	0.458257i	0.841272	+	0.540612i	$0.181807\pi$
$402$		0			0
$403$	0.553877	−	0.959344i	0.0275906	−	0.0477883i
$404$	16.4171	−	28.4353i	0.816782	−	1.41471i
$405$		0			0
$406$		0			0
$407$	−26.2798	+	15.1727i	−1.30264	+	0.752081i
$408$		0			0
$409$		−	6.46786i		−	0.319815i	−0.987132	−	0.159907i	$-0.948880\pi$
$409$		−	6.46786i		−	0.319815i	0.987132	−	0.159907i	$-0.0511196\pi$
$410$		−	5.62501i		−	0.277800i
$411$		0			0
$412$	−16.2740	+	9.39581i	−0.801764	+	0.462899i
$413$		0			0
$414$		0			0
$415$	−16.8119	+	29.1191i	−0.825265	+	1.42940i
$416$	3.89642	−	6.74880i	0.191038	−	0.330887i
$417$		0			0
$418$	−2.52709	+	1.45902i	−0.123604	+	0.0713629i
$419$	7.11542	−	12.3243i	0.347611	−	0.602080i	−0.638214	−	0.769859i	$-0.720326\pi$
$419$	7.11542	−	12.3243i	0.347611	−	0.602080i	0.985825	+	0.167779i	$0.0536596\pi$
$420$		0			0
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	0.952753	+	0.303747i	$0.0982378\pi$
$421$	15.1718	+	26.2784i	0.739429	+	1.28073i	−0.213324	+	0.976982i	$0.568429\pi$
$422$	1.75170	+	1.01135i	0.0852716	+	0.0492316i
$423$		0			0
$424$	3.31633	+	5.74405i	0.161055	+	0.278956i
$425$	14.6902			0.712579
$426$		0			0
$427$		0			0
$428$	5.75051	+	3.32006i	0.277962	+	0.160481i
$429$		0			0
$430$	3.21177	+	1.85432i	0.154885	+	0.0894230i
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	−0.447907	−	0.894080i	$-0.647830\pi$
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	0.550343	+	0.834939i	$0.314497\pi$
$432$		0			0
$433$			12.4545i			0.598525i	0.954171	+	0.299262i	$0.0967406\pi$
$433$			12.4545i			0.598525i	−0.954171	+	0.299262i	$0.903259\pi$
$434$		0			0
$435$		0			0
$436$	1.16936	+	2.02539i	0.0560022	+	0.0969987i
$437$	7.59610			0.363371
$438$		0			0
$439$			17.5300i			0.836663i	0.908294	+	0.418331i	$0.137385\pi$
$439$			17.5300i			0.836663i	−0.908294	+	0.418331i	$0.862615\pi$
$440$	13.7141			0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$			9.00464i			0.427824i	0.976853	+	0.213912i	$0.0686205\pi$
$443$			9.00464i			0.427824i	−0.976853	+	0.213912i	$0.931379\pi$
$444$		0			0
$445$	−13.2111			−0.626266
$446$	0.945337	+	1.63737i	0.0447630	+	0.0775318i
$447$		0			0
$448$		0			0
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$		0			0
$451$	21.1063	−	12.1857i	0.993856	−	0.573803i
$452$	3.59154	+	2.07357i	0.168932	+	0.0975327i
$453$		0			0
$454$	5.02371	+	2.90044i	0.235775	+	0.136125i
$455$		0			0
$456$		0			0
$457$	13.8286			0.646874			0.323437	−	0.946250i	$-0.395162\pi$
$457$	13.8286			0.646874			0.323437	+	0.946250i	$0.395162\pi$
$458$	1.60260	+	2.77578i	0.0748846	+	0.129704i
$459$		0			0
$460$	−15.1174	−	8.72803i	−0.704852	−	0.406947i
$461$	6.16989	+	10.6866i	0.287360	+	0.497723i	0.973179	−	0.230050i	$-0.0738889\pi$
$461$	6.16989	+	10.6866i	0.287360	+	0.497723i	−0.685818	+	0.727773i	$0.740556\pi$
$462$		0			0
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	−0.678900	−	0.734230i	$-0.737543\pi$
$463$	6.37802	−	11.0471i	0.296412	−	0.513401i	0.975312	+	0.220830i	$0.0708765\pi$
$464$	12.8141	−	7.39825i	0.594882	−	0.343455i
$465$		0			0
$466$	−3.05303	+	5.28801i	−0.141429	+	0.244962i
$467$	−5.48999	+	9.50894i	−0.254046	+	0.440021i	−0.964636	−	0.263585i	$-0.915095\pi$
$467$	−5.48999	+	9.50894i	−0.254046	+	0.440021i	0.710590	+	0.703607i	$0.248428\pi$
$468$		0			0
$469$		0			0
$470$	−3.15730	+	1.82287i	−0.145635	+	0.0840825i
$471$		0			0
$472$			5.39057i			0.248121i
$473$			16.0683i			0.738823i
$474$		0			0
$475$	9.63396	−	5.56217i	0.442036	−	0.255210i
$476$		0			0
$477$		0			0
$478$	−4.01665	+	6.95704i	−0.183717	+	0.318208i
$479$	−5.59729	+	9.69478i	−0.255747	+	0.442966i	−0.965098	−	0.261889i	$-0.915655\pi$
$479$	−5.59729	+	9.69478i	−0.255747	+	0.442966i	0.709351	+	0.704855i	$0.248988\pi$
$480$		0			0
$481$	−15.8043	+	9.12464i	−0.720616	+	0.416048i
$482$	3.13352	−	5.42741i	0.142728	−	0.247212i
$483$		0			0
$484$	4.00191	+	6.93152i	0.181905	+	0.315069i
$485$	−15.2645	−	8.81298i	−0.693126	−	0.400177i
$486$		0			0
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	0.830459	−	0.557080i	$-0.188078\pi$
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	−0.897675	+	0.440659i	$0.854745\pi$
$488$	1.84037			0.0833097
$489$		0			0
$490$		0			0
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.880653	−	0.473762i	$-0.157104\pi$
$491$	20.1795	+	11.6507i	0.910690	+	0.525787i	0.0300367	+	0.999549i	$0.490438\pi$
$492$		0			0
$493$	−12.3586	−	7.13524i	−0.556603	−	0.321355i
$494$	−1.51976	+	0.877435i	−0.0683773	+	0.0394776i
$495$		0			0
$496$		−	1.64952i		−	0.0740654i
$497$		0			0
$498$		0			0
$499$	2.29296	+	3.97152i	0.102647	+	0.177790i	0.912774	−	0.408464i	$-0.133935\pi$
$499$	2.29296	+	3.97152i	0.102647	+	0.177790i	−0.810127	+	0.586254i	$0.800602\pi$
$500$	3.71723			0.166240
$501$		0			0
$502$			7.85751i			0.350698i
$503$	−23.1383			−1.03169			−0.515844	−	0.856683i	$-0.672521\pi$
$503$	−23.1383			−1.03169			−0.515844	+	0.856683i	$0.672521\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$			3.41313i			0.151732i
$507$		0			0
$508$	5.26039			0.233392
$509$	4.82853	+	8.36326i	0.214021	+	0.370695i	0.952969	−	0.303067i	$-0.0980106\pi$
$509$	4.82853	+	8.36326i	0.214021	+	0.370695i	−0.738948	+	0.673762i	$0.764677\pi$
$510$		0			0
$511$		0			0
$512$		−	19.6301i		−	0.867536i
$513$		0			0
$514$	−0.776931	+	0.448561i	−0.0342690	+	0.0197852i
$515$	−26.0252	−	15.0257i	−1.14681	−	0.662110i
$516$		0			0
$517$	−13.6796	−	7.89791i	−0.601627	−	0.347350i
$518$		0			0
$519$		0			0
$520$	8.24748			0.361676
$521$	5.00035	+	8.66086i	0.219069	+	0.379439i	0.954524	−	0.298135i	$-0.0963646\pi$
$521$	5.00035	+	8.66086i	0.219069	+	0.379439i	−0.735454	+	0.677574i	$0.763031\pi$
$522$		0			0
$523$	10.7796	+	6.22361i	0.471359	+	0.272139i	0.716809	−	0.697270i	$-0.245602\pi$
$523$	10.7796	+	6.22361i	0.471359	+	0.272139i	−0.245449	+	0.969409i	$0.578935\pi$
$524$	−7.15531	−	12.3934i	−0.312581	−	0.541406i
$525$		0			0
$526$	−2.38289	+	4.12729i	−0.103899	+	0.179959i
$527$	−1.37774	+	0.795437i	−0.0600152	+	0.0346498i
$528$		0			0
$529$	−7.05755	+	12.2240i	−0.306850	+	0.531480i
$530$	−2.59320	+	4.49156i	−0.112641	+	0.195101i
$531$		0			0
$532$		0			0
$533$	12.6930	−	7.32833i	0.549797	−	0.317425i
$534$		0			0
$535$			10.6188i			0.459091i
$536$		−	1.81217i		−	0.0782737i
$537$		0			0
$538$	0.154356	−	0.0891175i	0.00665476	−	0.00384213i
$539$		0			0
$540$		0			0
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	−0.676557	−	0.736391i	$-0.736529\pi$
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	0.976011	+	0.217720i	$0.0698619\pi$
$542$	−3.37547	+	5.84648i	−0.144989	+	0.251128i
$543$		0			0
$544$	−9.69211	+	5.59574i	−0.415546	+	0.239916i
$545$	−1.87003	+	3.23898i	−0.0801032	+	0.138743i
$546$		0			0
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.788584	−	0.614926i	$-0.789186\pi$
$547$	−21.6768	−	37.5454i	−0.926834	−	1.60532i	−0.138250	−	0.990397i	$-0.544148\pi$
$548$	20.2331	+	11.6816i	0.864316	+	0.499013i
$549$		0			0
$550$	2.49923	+	4.32879i	0.106567	+	0.184580i
$551$	−10.8065			−0.460372
$552$		0			0
$553$		0			0
$554$	3.38062	+	1.95180i	0.143629	+	0.0829241i
$555$		0			0
$556$	22.1026	+	12.7610i	0.937361	+	0.541186i
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.335588	−	0.942009i	$-0.391065\pi$
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.983598	+	0.180377i	$0.0577317\pi$
$558$		0			0
$559$			9.66329i			0.408714i
$560$		0			0
$561$		0			0
$562$	0.964340	+	1.67029i	0.0406782	+	0.0704568i
$563$	6.11108			0.257551			0.128776	−	0.991674i	$-0.458895\pi$
$563$	6.11108			0.257551			0.128776	+	0.991674i	$0.458895\pi$
$564$		0			0
$565$			6.63207i			0.279013i
$566$	0.873481			0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$			19.3045i			0.809285i	0.914475	+	0.404642i	$0.132604\pi$
$569$			19.3045i			0.809285i	−0.914475	+	0.404642i	$0.867396\pi$
$570$		0			0
$571$	12.7224			0.532415			0.266207	−	0.963916i	$-0.414229\pi$
$571$	12.7224			0.532415			0.266207	+	0.963916i	$0.414229\pi$
$572$	8.73631	+	15.1317i	0.365284	+	0.632690i
$573$		0			0
$574$		0			0
$575$		−	13.0118i		−	0.542628i
$576$		0			0
$577$	−7.05520	+	4.07332i	−0.293712	+	0.169575i	−0.639615	−	0.768696i	$-0.720906\pi$
$577$	−7.05520	+	4.07332i	−0.293712	+	0.169575i	0.345903	+	0.938270i	$0.387573\pi$
$578$	−1.44429	−	0.833863i	−0.0600747	−	0.0346841i
$579$		0			0
$580$	21.5066	+	12.4168i	0.893012	+	0.515581i
$581$		0			0
$582$		0			0
$583$	−22.4711			−0.930657
$584$	−0.568693	−	0.985005i	−0.0235327	−	0.0407598i
$585$		0			0
$586$	−1.54270	−	0.890680i	−0.0637285	−	0.0367937i
$587$	12.3041	+	21.3113i	0.507843	+	0.879610i	0.999959	+	0.00908019i	$0.00289036\pi$
$587$	12.3041	+	21.3113i	0.507843	+	0.879610i	−0.492116	+	0.870530i	$0.663776\pi$
$588$		0			0
$589$	−0.602354	+	1.04331i	−0.0248196	+	0.0429888i
$590$	−3.65043	+	2.10758i	−0.150286	+	0.0867676i
$591$		0			0
$592$	−13.5872	+	23.5336i	−0.558429	+	0.967227i
$593$	−18.9321	+	32.7913i	−0.777447	+	1.34658i	0.155962	+	0.987763i	$0.450152\pi$
$593$	−18.9321	+	32.7913i	−0.777447	+	1.34658i	−0.933409	+	0.358814i	$0.883181\pi$
$594$		0			0
$595$		0			0
$596$	14.0428	−	8.10762i	0.575216	−	0.332101i
$597$		0			0
$598$			2.05261i			0.0839375i
$599$		−	10.6529i		−	0.435268i	−0.976030	−	0.217634i	$-0.930166\pi$
$599$		−	10.6529i		−	0.435268i	0.976030	−	0.217634i	$-0.0698339\pi$
$600$		0			0
$601$	−39.8636	+	23.0153i	−1.62607	+	0.938812i	−0.640821	+	0.767691i	$0.721406\pi$
$601$	−39.8636	+	23.0153i	−1.62607	+	0.938812i	−0.985250	+	0.171122i	$0.945261\pi$
$602$		0			0
$603$		0			0
$604$	3.21161	−	5.56267i	0.130679	−	0.226342i
$605$	−6.39981	+	11.0848i	−0.260189	+	0.450661i
$606$		0			0
$607$	−3.74063	+	2.15965i	−0.151827	+	0.0876576i	−0.573989	−	0.818863i	$-0.694605\pi$
$607$	−3.74063	+	2.15965i	−0.151827	+	0.0876576i	0.422162	+	0.906521i	$0.361271\pi$
$608$	−4.23745	+	7.33947i	−0.171851	+	0.297655i
$609$		0			0
$610$	0.719539	+	1.24628i	0.0291333	+	0.0504603i
$611$	−8.22672	−	4.74970i	−0.332818	−	0.192152i
$612$		0			0
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	0.995366	+	0.0961549i	$0.0306544\pi$
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	−0.414411	+	0.910090i	$0.636012\pi$
$614$	−6.34846			−0.256203
$615$		0			0
$616$		0			0
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	0.481051	−	0.876693i	$-0.340255\pi$
$617$	−0.935498	−	0.540110i	−0.0376617	−	0.0217440i	−0.518713	+	0.854949i	$0.673589\pi$
$618$		0			0
$619$	6.57128	+	3.79393i	0.264122	+	0.152491i	0.626214	−	0.779652i	$-0.284604\pi$
$619$	6.57128	+	3.79393i	0.264122	+	0.152491i	−0.362091	+	0.932143i	$0.617937\pi$
$620$	2.39755	−	1.38423i	0.0962881	−	0.0555920i
$621$		0			0
$622$		−	3.23944i		−	0.129890i
$623$		0			0
$624$		0			0
$625$	13.8854	+	24.0502i	0.555416	+	0.962010i
$626$	3.98316			0.159199
$627$		0			0
$628$		−	31.9741i		−	1.27591i
$629$	26.2082			1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$			10.6708i			0.424462i
$633$		0			0
$634$	−3.27786			−0.130181
$635$	4.20618	+	7.28531i	0.166917	+	0.289109i
$636$		0			0
$637$		0			0
$638$		−	4.85564i		−	0.192237i
$639$		0			0
$640$	22.3015	−	12.8758i	0.881544	−	0.508960i
$641$	−26.9229	−	15.5439i	−1.06339	−	0.613949i	−0.137023	−	0.990568i	$-0.543753\pi$
$641$	−26.9229	−	15.5439i	−1.06339	−	0.613949i	−0.926368	+	0.376619i	$0.877087\pi$
$642$		0			0
$643$	−0.977928	−	0.564607i	−0.0385657	−	0.0222659i	0.480593	−	0.876944i	$-0.340421\pi$
$643$	−0.977928	−	0.564607i	−0.0385657	−	0.0222659i	−0.519159	+	0.854678i	$0.673755\pi$
$644$		0			0
$645$		0			0
$646$	2.52021			0.0991564
$647$	−13.5992	−	23.5545i	−0.534640	−	0.926023i	−0.999181	−	0.0404713i	$-0.987114\pi$
$647$	−13.5992	−	23.5545i	−0.534640	−	0.926023i	0.464541	−	0.885552i	$-0.346219\pi$
$648$		0			0
$649$	−15.8162	−	9.13148i	−0.620839	−	0.358442i
$650$	1.50300	+	2.60328i	0.0589526	+	0.102109i
$651$		0			0
$652$	24.2386	−	41.9824i	0.949256	−	1.64416i
$653$	19.3030	−	11.1446i	0.755384	−	0.436121i	−0.0722517	−	0.997386i	$-0.523019\pi$
$653$	19.3030	−	11.1446i	0.755384	−	0.436121i	0.827636	+	0.561265i	$0.189685\pi$
$654$		0			0
$655$	11.4427	−	19.8193i	0.447102	−	0.774404i
$656$	10.9123	−	18.9007i	0.426055	−	0.737949i
$657$		0			0
$658$		0			0
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	−0.342641	−	0.939467i	$-0.611321\pi$
$659$	7.69208	−	4.44103i	0.299641	−	0.172998i	0.642282	+	0.766469i	$0.277988\pi$
$660$		0			0
$661$			19.3670i			0.753291i	0.926358	+	0.376645i	$0.122922\pi$
$661$			19.3670i			0.753291i	−0.926358	+	0.376645i	$0.877078\pi$
$662$			5.58945i			0.217240i
$663$		0			0
$664$	10.9434	−	6.31819i	0.424687	−	0.245193i
$665$		0			0
$666$		0			0
$667$	−6.31999	+	10.9465i	−0.244711	+	0.423852i
$668$	1.67602	−	2.90295i	0.0648472	−	0.112319i
$669$		0			0
$670$	1.22718	−	0.708512i	0.0474101	−	0.0273722i
$671$	−3.11754	+	5.39973i	−0.120351	+	0.208454i
$672$		0			0
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	0.998154	−	0.0607292i	$-0.0193426\pi$
$673$	11.5828	+	20.0620i	0.446484	+	0.773333i	−0.551670	+	0.834062i	$0.686009\pi$
$674$	−1.69310	−	0.977511i	−0.0652157	−	0.0376523i
$675$		0			0
$676$	−7.18476	−	12.4444i	−0.276337	−	0.478630i
$677$	3.12693			0.120177			0.0600887	−	0.998193i	$-0.480862\pi$
$677$	3.12693			0.120177			0.0600887	+	0.998193i	$0.480862\pi$
$678$		0			0
$679$		0			0
$680$	−10.2576	−	5.92220i	−0.393359	−	0.227106i
$681$		0			0
$682$	−0.468786	−	0.270654i	−0.0179507	−	0.0103639i
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.120632	−	0.992697i	$-0.461508\pi$
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.920017	+	0.391878i	$0.128175\pi$
$684$		0			0
$685$			37.3621i			1.42753i
$686$		0			0
$687$		0			0
$688$	7.19462	+	12.4614i	0.274292	+	0.475088i
$689$	−13.5138			−0.514835
$690$		0			0
$691$		−	44.1739i		−	1.68045i	−0.542235	−	0.840227i	$-0.682422\pi$
$691$		−	44.1739i		−	1.68045i	0.542235	−	0.840227i	$-0.317578\pi$
$692$	45.7868			1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$			40.8144i			1.54818i
$696$		0			0
$697$	−21.0488			−0.797280
$698$	−3.48043	−	6.02828i	−0.131736	−	0.228174i
$699$		0			0
$700$		0			0
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$		0			0
$703$	17.1876	−	9.92326i	0.648242	−	0.374263i
$704$	20.2511	+	11.6920i	0.763242	+	0.440658i
$705$		0			0
$706$	−1.16775	−	0.674202i	−0.0439490	−	0.0253739i
$707$		0			0
$708$		0			0
$709$	−1.09786			−0.0412311			−0.0206156	−	0.999787i	$-0.506563\pi$
$709$	−1.09786			−0.0412311			−0.0206156	+	0.999787i	$0.506563\pi$
$710$	−6.12132	−	10.6024i	−0.229729	−	0.397903i
$711$		0			0
$712$	4.29977	+	2.48247i	0.161141	+	0.0930346i
$713$	0.704553	+	1.22032i	0.0263857	+	0.0457014i
$714$		0			0
$715$	−13.9710	+	24.1985i	−0.522486	+	0.904972i
$716$	−42.0728	+	24.2908i	−1.57233	+	0.907788i
$717$		0			0
$718$	0.900826	−	1.56028i	0.0336185	−	0.0582290i
$719$	11.3648	−	19.6844i	0.423835	−	0.734103i	−0.572476	−	0.819921i	$-0.694017\pi$
$719$	11.3648	−	19.6844i	0.423835	−	0.734103i	0.996311	+	0.0858183i	$0.0273505\pi$
$720$		0			0
$721$		0			0
$722$	−3.18269	+	1.83753i	−0.118448	+	0.0683858i
$723$		0			0
$724$		−	42.8718i		−	1.59332i
$725$			18.5110i			0.687482i
$726$		0			0
$727$	3.47919	−	2.00871i	0.129036	−	0.0744990i	−0.434093	−	0.900868i	$-0.642931\pi$
$727$	3.47919	−	2.00871i	0.129036	−	0.0744990i	0.563129	+	0.826369i	$0.309598\pi$
$728$		0			0
$729$		0			0
$730$	0.444689	−	0.770224i	0.0164587	−	0.0285073i
$731$	6.93885	−	12.0184i	0.256643	−	0.444518i
$732$		0			0
$733$	7.20188	−	4.15801i	0.266008	−	0.153580i	−0.361064	−	0.932541i	$-0.617587\pi$
$733$	7.20188	−	4.15801i	0.266008	−	0.153580i	0.627072	+	0.778961i	$0.284253\pi$
$734$	−3.88296	+	6.72549i	−0.143323	+	0.248242i
$735$		0			0
$736$	4.95640	+	8.58473i	0.182695	+	0.316437i
$737$	5.31698	+	3.06976i	0.195854	+	0.113076i
$738$		0			0
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	0.820932	−	0.571026i	$-0.193455\pi$
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	−0.904989	+	0.425434i	$0.860121\pi$
$740$	−45.6079			−1.67658
$741$		0			0
$742$		0			0
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	0.471998	−	0.881600i	$-0.343533\pi$
$743$	−1.51258	−	0.873286i	−0.0554910	−	0.0320378i	−0.527489	+	0.849562i	$0.676866\pi$
$744$		0			0
$745$	22.4571	+	12.9656i	0.822764	+	0.475023i
$746$	−5.11954	+	2.95577i	−0.187440	+	0.108218i
$747$		0			0
$748$		−	25.0929i		−	0.917486i
$749$		0			0
$750$		0			0
$751$	−2.91647	−	5.05147i	−0.106423	−	0.184331i	0.807895	−	0.589326i	$-0.200607\pi$
$751$	−2.91647	−	5.05147i	−0.106423	−	0.184331i	−0.914319	+	0.404995i	$0.867273\pi$
$752$	−14.1452			−0.515822
$753$		0			0
$754$		−	2.92012i		−	0.106345i
$755$	10.2719			0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$			5.12982i			0.186323i
$759$		0			0
$760$	−8.96932			−0.325352
$761$	0.293431	+	0.508238i	0.0106369	+	0.0184236i	0.871295	−	0.490760i	$-0.163281\pi$
$761$	0.293431	+	0.508238i	0.0106369	+	0.0184236i	−0.860658	+	0.509184i	$0.829947\pi$
$762$		0			0
$763$		0			0
$764$		−	8.20750i		−	0.296937i
$765$		0			0
$766$	−7.14208	+	4.12348i	−0.258054	+	0.148987i
$767$	−9.51165	−	5.49155i	−0.343446	−	0.198288i
$768$		0			0
$769$	45.1905	+	26.0907i	1.62961	+	0.940856i	0.984208	+	0.177014i	$0.0566437\pi$
$769$	45.1905	+	26.0907i	1.62961	+	0.940856i	0.645403	+	0.763843i	$0.276690\pi$
$770$		0			0
$771$		0			0
$772$	−44.6738			−1.60785
$773$	−16.3906	−	28.3894i	−0.589530	−	1.02110i	−0.994294	−	0.106674i	$-0.965980\pi$
$773$	−16.3906	−	28.3894i	−0.589530	−	1.02110i	0.404764	−	0.914421i	$-0.367354\pi$
$774$		0			0
$775$	1.78714	+	1.03180i	0.0641959	+	0.0370635i
$776$	3.31206	+	5.73666i	0.118896	+	0.205934i
$777$		0			0
$778$	5.03093	−	8.71383i	0.180368	−	0.312406i
$779$	−13.8040	+	7.96973i	−0.494579	+	0.285545i
$780$		0			0
$781$	26.5218	−	45.9371i	0.949024	−	1.64376i
$782$	1.47390	−	2.55287i	0.0527066	−	0.0912906i
$783$		0			0
$784$		0			0
$785$	44.2821	−	25.5663i	1.58050	−	0.912500i
$786$		0			0
$787$		−	40.9934i		−	1.46126i	−0.682775	−	0.730628i	$-0.739227\pi$
$787$		−	40.9934i		−	1.46126i	0.682775	−	0.730628i	$-0.260773\pi$
$788$			35.9402i			1.28032i
$789$		0			0
$790$	−7.22614	+	4.17201i	−0.257095	+	0.148434i
$791$		0			0
$792$		0			0
$793$	−1.87485	+	3.24733i	−0.0665778	+	0.115316i
$794$	1.91597	−	3.31856i	0.0679954	−	0.117771i
$795$		0			0
$796$	7.51921	−	4.34122i	0.266511	−	0.153870i
$797$	−17.0441	+	29.5213i	−0.603734	+	1.04570i	0.388516	+	0.921442i	$0.372988\pi$
$797$	−17.0441	+	29.5213i	−0.603734	+	1.04570i	−0.992250	+	0.124256i	$0.960346\pi$
$798$		0			0
$799$	6.82116	+	11.8146i	0.241315	+	0.417971i
$800$	12.5722	+	7.25854i	0.444493	+	0.256628i
$801$		0			0
$802$	−2.69672	−	4.67086i	−0.0952245	−	0.164934i
$803$	3.85340			0.135984
$804$		0			0
$805$		0			0
$806$	−0.281922	−	0.162768i	−0.00993027	−	0.00573324i
$807$		0			0
$808$	−17.0896	−	9.86670i	−0.601211	−	0.347109i
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	−0.390512	−	0.920598i	$-0.627702\pi$
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	0.602005	+	0.798492i	$0.294369\pi$
$810$		0			0
$811$			39.8573i			1.39958i	0.714350	+	0.699789i	$0.246723\pi$
$811$			39.8573i			1.39958i	−0.714350	+	0.699789i	$0.753277\pi$
$812$		0			0
$813$		0			0
$814$	4.45878	+	7.72284i	0.156280	+	0.270685i
$815$	77.5240			2.71555
$816$		0			0
$817$		−	10.5091i		−	0.367665i
$818$	−1.90071			−0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$		−	42.1017i		−	1.46936i	−0.678414	−	0.734680i	$-0.737332\pi$
$821$		−	42.1017i		−	1.46936i	0.678414	−	0.734680i	$-0.262668\pi$
$822$		0			0
$823$	32.6821			1.13923			0.569614	−	0.821913i	$-0.307093\pi$
$823$	32.6821			1.13923			0.569614	+	0.821913i	$0.307093\pi$
$824$	5.64689	+	9.78070i	0.196719	+	0.340727i
$825$		0			0
$826$		0			0
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$		0			0
$829$	−35.7122	+	20.6185i	−1.24034	+	0.716109i	−0.969163	−	0.246421i	$-0.920745\pi$
$829$	−35.7122	+	20.6185i	−1.24034	+	0.716109i	−0.271174	+	0.962530i	$0.587412\pi$
$830$	8.55721	+	4.94051i	0.297025	+	0.171488i
$831$		0			0
$832$	12.1788	+	7.03141i	0.422222	+	0.243770i
$833$		0			0
$834$		0			0
$835$	5.36054			0.185509
$836$	−9.50094	−	16.4561i	−0.328597	−	0.569147i
$837$		0			0
$838$	−3.62173	−	2.09100i	−0.125110	−	0.0722326i
$839$	−4.04385	−	7.00416i	−0.139609	−	0.241810i	0.787740	−	0.616009i	$-0.211251\pi$
$839$	−4.04385	−	7.00416i	−0.139609	−	0.241810i	−0.927349	+	0.374198i	$0.877918\pi$
$840$		0			0
$841$	−5.50894	+	9.54177i	−0.189963	+	0.329026i
$842$	7.72241	−	4.45853i	0.266132	−	0.153651i
$843$		0			0
$844$	−6.58576	+	11.4069i	−0.226691	+	0.392641i
$845$	11.4898	−	19.9009i	0.395260	−	0.684611i
$846$		0			0
$847$		0			0
$848$	−17.4269	+	10.0615i	−0.598444	+	0.345512i
$849$		0			0
$850$		−	4.31700i		−	0.148072i
$851$		−	23.2138i		−	0.795759i
$852$		0			0
$853$	24.5887	−	14.1963i	0.841900	−	0.486071i	−0.0160098	−	0.999872i	$-0.505096\pi$
$853$	24.5887	−	14.1963i	0.841900	−	0.486071i	0.857910	+	0.513801i	$0.171763\pi$
$854$		0			0
$855$		0			0
$856$	1.99536	−	3.45606i	0.0682000	−	0.118126i
$857$	−25.6587	+	44.4422i	−0.876485	+	1.51812i	−0.0213132	+	0.999773i	$0.506785\pi$
$857$	−25.6587	+	44.4422i	−0.876485	+	1.51812i	−0.855172	+	0.518344i	$0.826549\pi$
$858$		0			0
$859$	−14.5234	+	8.38509i	−0.495532	+	0.286096i	−0.726867	−	0.686779i	$-0.759024\pi$
$859$	−14.5234	+	8.38509i	−0.495532	+	0.286096i	0.231334	+	0.972874i	$0.425691\pi$
$860$	−12.0751	+	20.9146i	−0.411756	+	0.713183i
$861$		0			0
$862$	−0.360816	−	0.624951i	−0.0122894	−	0.0212859i
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	0.722360	−	0.691517i	$-0.243057\pi$
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	−0.237692	+	0.971341i	$0.576391\pi$
$864$		0			0
$865$	36.6109	+	63.4119i	1.24481	+	2.15607i
$866$	3.66000			0.124372
$867$		0			0
$868$		0			0
$869$	−31.3086	−	18.0760i	−1.06207	−	0.613188i
$870$		0			0
$871$	3.19757	+	1.84612i	0.108345	+	0.0625532i
$872$	1.21726	−	0.702787i	0.0412217	−	0.0237994i
$873$		0			0
$874$		−	2.23226i		−	0.0755074i
$875$		0			0
$876$		0			0
$877$	−3.06175	−	5.30311i	−0.103388	−	0.179073i	0.809690	−	0.586857i	$-0.199635\pi$
$877$	−3.06175	−	5.30311i	−0.103388	−	0.179073i	−0.913078	+	0.407784i	$0.866302\pi$
$878$	5.15154			0.173856
$879$		0			0
$880$			41.6074i			1.40258i
$881$	41.3283			1.39238			0.696192	−	0.717855i	$-0.254876\pi$
$881$	41.3283			1.39238			0.696192	+	0.717855i	$0.254876\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$		−	15.0905i		−	0.507549i
$885$		0			0
$886$	2.64619			0.0889005
$887$	3.35036	+	5.80299i	0.112494	+	0.194845i	0.916775	−	0.399404i	$-0.130783\pi$
$887$	3.35036	+	5.80299i	0.112494	+	0.194845i	−0.804281	+	0.594249i	$0.797449\pi$
$888$		0			0
$889$		0			0
$890$			3.88234i			0.130136i
$891$		0			0
$892$	−10.6624	+	6.15591i	−0.357002	+	0.206115i
$893$	8.94675	+	5.16541i	0.299392	+	0.172854i
$894$		0			0
$895$	−67.2823	−	38.8455i	−2.24900	−	1.29846i
$896$		0			0
$897$		0			0
$898$	−9.05470			−0.302159
$899$	−1.00232	−	1.73608i	−0.0334294	−	0.0579014i
$900$		0			0
$901$	16.8074	+	9.70376i	0.559936	+	0.323279i
$902$	−3.58101	−	6.20249i	−0.119235	−	0.206520i
$903$		0			0
$904$	1.24622	−	2.15852i	0.0414487	−	0.0717912i
$905$	59.3747	−	34.2800i	1.97368	−	1.13951i
$906$		0			0
$907$	−10.1494	+	17.5793i	−0.337005	+	0.583710i	−0.983868	−	0.178897i	$-0.942747\pi$
$907$	−10.1494	+	17.5793i	−0.337005	+	0.583710i	0.646863	+	0.762606i	$0.276081\pi$
$908$	−18.8873	+	32.7138i	−0.626798	+	1.08565i
$909$		0			0
$910$		0			0
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.0967861	−	0.995305i	$-0.469144\pi$
$911$	30.3982	−	17.5504i	1.00714	−	0.581472i	0.910353	+	0.413833i	$0.135810\pi$
$912$		0			0
$913$			42.8114i			1.41685i
$914$		−	4.06380i		−	0.134419i
$915$		0			0
$916$	−18.0756	+	10.4359i	−0.597233	+	0.344813i
$917$		0			0
$918$		0			0
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	0.439754	+	0.898118i	$0.355066\pi$
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	−0.997670	+	0.0682206i	$0.978268\pi$
$920$	−5.24555	+	9.08557i	−0.172941	+	0.299542i
$921$		0			0
$922$	3.14046	−	1.81314i	0.103425	−	0.0597127i
$923$	15.9499	−	27.6260i	0.524996	−	0.909320i
$924$		0			0
$925$	−16.9981	−	29.4415i	−0.558893	−	0.968031i
$926$	−3.24639	−	1.87431i	−0.106683	−	0.0615935i
$927$		0			0
$928$	−7.05115	−	12.2130i	−0.231465	−	0.400910i
$929$	32.1171			1.05373			0.526864	−	0.849950i	$-0.323368\pi$
$929$	32.1171			1.05373			0.526864	+	0.849950i	$0.323368\pi$
$930$		0			0
$931$		0			0
$932$	−34.4348	−	19.8810i	−1.12795	−	0.651222i
$933$		0			0
$934$	2.79439	+	1.61334i	0.0914351	+	0.0527901i
$935$	34.7520	−	20.0641i	1.13651	−	0.656166i
$936$		0			0
$937$		−	13.9224i		−	0.454824i	−0.973799	−	0.227412i	$-0.926974\pi$
$937$		−	13.9224i		−	0.454824i	0.973799	−	0.227412i	$-0.0730263\pi$
$938$		0			0
$939$		0			0
$940$	−11.8703	−	20.5599i	−0.387166	−	0.670590i
$941$	57.2094			1.86497			0.932487	−	0.361203i	$-0.117634\pi$
$941$	57.2094			1.86497			0.932487	+	0.361203i	$0.117634\pi$
$942$		0			0
$943$			18.6438i			0.607127i
$944$	−16.3545			−0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$			34.4861i			1.12065i	0.828274	+	0.560324i	$0.189323\pi$
$947$			34.4861i			1.12065i	−0.828274	+	0.560324i	$0.810677\pi$
$948$		0			0
$949$	2.31739			0.0752255
$950$	−1.63455	−	2.83113i	−0.0530318	−	0.0918538i
$951$		0			0
$952$		0			0
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$		0			0
$955$	11.3669	−	6.56267i	0.367824	−	0.212363i
$956$	−45.3034	−	26.1559i	−1.46522	−	0.845943i
$957$		0			0
$958$	2.84900	+	1.64487i	0.0920470	+	0.0531434i
$959$		0			0
$960$		0			0
$961$	30.7765			0.992791
$962$	2.68145	+	4.64441i	0.0864535	+	0.149742i
$963$		0			0
$964$	35.3426	+	20.4051i	1.13831	+	0.657203i
$965$	−35.7209	−	61.8704i	−1.14990	−	1.99168i
$966$		0			0
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	−0.817585	−	0.575808i	$-0.804688\pi$
$967$	2.79472	−	4.84059i	0.0898721	−	0.155663i	0.907457	+	0.420145i	$0.138021\pi$
$968$	4.16585	−	2.40515i	0.133895	−	0.0773045i
$969$		0			0
$970$	−2.58986	+	4.48578i	−0.0831555	+	0.144030i
$971$	8.01661	−	13.8852i	0.257265	−	0.445597i	−0.708243	−	0.705969i	$-0.750512\pi$
$971$	8.01661	−	13.8852i	0.257265	−	0.445597i	0.965508	+	0.260372i	$0.0838452\pi$
$972$		0			0
$973$		0			0
$974$	−0.755007	+	0.435904i	−0.0241920	+	0.0139673i
$975$		0			0
$976$			5.58353i			0.178724i
$977$			43.9026i			1.40457i	0.711896	+	0.702285i	$0.247837\pi$
$977$			43.9026i			1.40457i	−0.711896	+	0.702285i	$0.752163\pi$
$978$		0			0
$979$	−14.5674	+	8.41048i	−0.465576	+	0.268800i
$980$		0			0
$981$		0			0
$982$	3.42377	−	5.93015i	0.109257	−	0.189239i
$983$	−9.08808	+	15.7410i	−0.289865	+	0.502061i	−0.973777	−	0.227503i	$-0.926944\pi$
$983$	−9.08808	+	15.7410i	−0.289865	+	0.502061i	0.683912	+	0.729564i	$0.260277\pi$
$984$		0			0
$985$	−49.7749	+	28.7376i	−1.58596	+	0.915655i
$986$	−2.09683	+	3.63181i	−0.0667766	+	0.115660i
$987$		0			0
$988$	−5.71374	−	9.89649i	−0.181778	−	0.314849i
$989$	−10.6453	−	6.14604i	−0.338499	−	0.195433i
$990$		0			0
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	−0.944627	−	0.328145i	$-0.893576\pi$
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	0.188131	−	0.982144i	$-0.439757\pi$
$992$	−1.57213			−0.0499151
$993$		0			0
$994$		0			0
$995$	12.0246	+	6.94242i	0.381206	+	0.220090i
$996$		0			0
$997$	−28.4838	−	16.4451i	−0.902090	−	0.520822i	−0.0242120	−	0.999707i	$-0.507708\pi$
$997$	−28.4838	−	16.4451i	−0.902090	−	0.520822i	−0.877878	+	0.478885i	$0.841041\pi$
$998$	1.16711	−	0.673830i	0.0369442	−	0.0213297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.b.1097.3		10
3.2	odd	2		441.2.i.b.68.3		10
7.2	even	3		1323.2.o.d.881.3		10
7.3	odd	6		1323.2.s.b.962.3		10
7.4	even	3		189.2.s.b.17.3		10
7.5	odd	6		1323.2.o.c.881.3		10
7.6	odd	2		189.2.i.b.152.3		10
9.2	odd	6		1323.2.s.b.656.3		10
9.7	even	3		441.2.s.b.362.3		10
21.2	odd	6		441.2.o.c.293.3		10
21.5	even	6		441.2.o.d.293.3		10
21.11	odd	6		63.2.s.b.59.3	yes	10
21.17	even	6		441.2.s.b.374.3		10
21.20	even	2		63.2.i.b.5.3	✓	10
28.11	odd	6		3024.2.df.b.17.1		10
28.27	even	2		3024.2.ca.b.2609.1		10
63.2	odd	6		1323.2.o.c.440.3		10
63.4	even	3		567.2.p.d.80.3		10
63.11	odd	6		189.2.i.b.143.3		10
63.13	odd	6		567.2.p.c.404.3		10
63.16	even	3		441.2.o.d.146.3		10
63.20	even	6		189.2.s.b.89.3		10
63.25	even	3		63.2.i.b.38.3	yes	10
63.32	odd	6		567.2.p.c.80.3		10
63.34	odd	6		63.2.s.b.47.3	yes	10
63.38	even	6	inner	1323.2.i.b.521.3		10
63.41	even	6		567.2.p.d.404.3		10
63.47	even	6		1323.2.o.d.440.3		10
63.52	odd	6		441.2.i.b.227.3		10
63.61	odd	6		441.2.o.c.146.3		10
84.11	even	6		1008.2.df.b.689.5		10
84.83	odd	2		1008.2.ca.b.257.4		10
252.11	even	6		3024.2.ca.b.2033.1		10
252.83	odd	6		3024.2.df.b.1601.1		10
252.151	odd	6		1008.2.ca.b.353.4		10
252.223	even	6		1008.2.df.b.929.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	21.20	even	2
63.2.i.b.38.3	yes	10	63.25	even	3
63.2.s.b.47.3	yes	10	63.34	odd	6
63.2.s.b.59.3	yes	10	21.11	odd	6
189.2.i.b.143.3		10	63.11	odd	6
189.2.i.b.152.3		10	7.6	odd	2
189.2.s.b.17.3		10	7.4	even	3
189.2.s.b.89.3		10	63.20	even	6
441.2.i.b.68.3		10	3.2	odd	2
441.2.i.b.227.3		10	63.52	odd	6
441.2.o.c.146.3		10	63.61	odd	6
441.2.o.c.293.3		10	21.2	odd	6
441.2.o.d.146.3		10	63.16	even	3
441.2.o.d.293.3		10	21.5	even	6
441.2.s.b.362.3		10	9.7	even	3
441.2.s.b.374.3		10	21.17	even	6
567.2.p.c.80.3		10	63.32	odd	6
567.2.p.c.404.3		10	63.13	odd	6
567.2.p.d.80.3		10	63.4	even	3
567.2.p.d.404.3		10	63.41	even	6
1008.2.ca.b.257.4		10	84.83	odd	2
1008.2.ca.b.353.4		10	252.151	odd	6
1008.2.df.b.689.5		10	84.11	even	6
1008.2.df.b.929.5		10	252.223	even	6
1323.2.i.b.521.3		10	63.38	even	6	inner
1323.2.i.b.1097.3		10	1.1	even	1	trivial
1323.2.o.c.440.3		10	63.2	odd	6
1323.2.o.c.881.3		10	7.5	odd	6
1323.2.o.d.440.3		10	63.47	even	6
1323.2.o.d.881.3		10	7.2	even	3
1323.2.s.b.656.3		10	9.2	odd	6
1323.2.s.b.962.3		10	7.3	odd	6
3024.2.ca.b.2033.1		10	252.11	even	6
3024.2.ca.b.2609.1		10	28.27	even	2
3024.2.df.b.17.1		10	28.11	odd	6
3024.2.df.b.1601.1		10	252.83	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.293869i q^{2} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +O(q^{10})\)	\(q-0.293869i q^{2} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} -1.15010i q^{8} +(0.778834 - 0.449660i) q^{10} +(3.37445 + 1.94824i) q^{11} +(2.02935 + 1.17164i) q^{13} +3.48930 q^{16} +(-1.68263 - 2.91440i) q^{17} +(-2.20696 - 1.27419i) q^{19} +(2.92813 + 5.07167i) q^{20} +(0.572527 - 0.991647i) q^{22} +(-2.58141 + 1.49038i) q^{23} +(-2.18263 + 3.78042i) q^{25} +(0.344311 - 0.596363i) q^{26} +(3.67241 - 2.12027i) q^{29} -0.472735i q^{31} -3.32560i q^{32} +(-0.856452 + 0.494473i) q^{34} +(-3.89395 + 6.74451i) q^{37} +(-0.374446 + 0.648559i) q^{38} +(3.04808 - 1.75981i) q^{40} +(3.12737 - 5.41676i) q^{41} +(2.06191 + 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.437976 + 0.758597i) q^{46} -4.05388 q^{47} +(1.11095 + 0.641408i) q^{50} +(3.88344 + 2.24211i) q^{52} +(-4.99439 + 2.88351i) q^{53} +11.9243i q^{55} +(-0.623082 - 1.07921i) q^{58} -4.68705 q^{59} +1.60018i q^{61} -0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +1.57566 q^{67} +(-3.21994 - 5.57711i) q^{68} -13.6132i q^{71} +(0.856452 - 0.494473i) q^{73} +(1.98201 + 1.14431i) q^{74} +(-4.22333 - 2.43834i) q^{76} -9.27815 q^{79} +(5.33910 + 9.24760i) q^{80} +(-1.59182 - 0.919038i) q^{82} +(5.49361 + 9.51520i) q^{83} +(5.14930 - 8.91884i) q^{85} +(1.04950 - 0.605932i) q^{86} +(2.24067 - 3.88095i) q^{88} +(-2.15849 + 3.73861i) q^{89} +(-4.93989 + 2.85205i) q^{92} +1.19131i q^{94} -7.79874i q^{95} +(-4.98797 + 2.87980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4}+O(q^{10}) \) 10 * q - 8 * q^4	\( 10 q - 8 q^{4} + 15 q^{10} + 12 q^{11} + 6 q^{13} + 12 q^{16} + 12 q^{17} - 3 q^{19} + 3 q^{20} + 5 q^{22} + 15 q^{23} + 7 q^{25} - 3 q^{26} + 15 q^{29} + 3 q^{34} + 6 q^{37} + 18 q^{38} - 15 q^{40} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 13 q^{46} + 30 q^{47} - 3 q^{50} + 12 q^{52} - 9 q^{53} + 8 q^{58} - 36 q^{59} - 12 q^{62} + 6 q^{64} + 20 q^{67} - 27 q^{68} - 3 q^{73} + 30 q^{74} + 9 q^{76} - 40 q^{79} + 30 q^{80} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 54 q^{86} - 8 q^{88} - 24 q^{89} - 39 q^{92} + 6 q^{97}+O(q^{100}) \) 10 * q - 8 * q^4 + 15 * q^10 + 12 * q^11 + 6 * q^13 + 12 * q^16 + 12 * q^17 - 3 * q^19 + 3 * q^20 + 5 * q^22 + 15 * q^23 + 7 * q^25 - 3 * q^26 + 15 * q^29 + 3 * q^34 + 6 * q^37 + 18 * q^38 - 15 * q^40 + 9 * q^41 + 3 * q^43 + 24 * q^44 - 13 * q^46 + 30 * q^47 - 3 * q^50 + 12 * q^52 - 9 * q^53 + 8 * q^58 - 36 * q^59 - 12 * q^62 + 6 * q^64 + 20 * q^67 - 27 * q^68 - 3 * q^73 + 30 * q^74 + 9 * q^76 - 40 * q^79 + 30 * q^80 - 9 * q^82 + 15 * q^83 + 18 * q^85 - 54 * q^86 - 8 * q^88 - 24 * q^89 - 39 * q^92 + 6 * q^97

Introduction

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