LMFDB - Embedded newform 324.3.f.r.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.119023932416481.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 $ x^12 - 2x^11 - 3x^10 + 11x^9 - 5x^8 - 14x^7 + 29x^6 - 28x^5 - 20x^4 + 88x^3 - 48x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Root			$-1.36237 + 0.379393i$ of defining polynomial
Character	$\chi$	$=$	324.271
Dual form			324.3.f.r.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91597 - 0.573621i) q^{2} +(3.34192 + 2.19809i) q^{4} +(-2.18740 + 3.78869i) q^{5} +(1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +O(q^{10})$	\(q+(-1.91597 - 0.573621i) q^{2} +(3.34192 + 2.19809i) q^{4} +(-2.18740 + 3.78869i) q^{5} +(1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +(6.36427 - 6.00429i) q^{10} +(-10.9277 + 6.30914i) q^{11} +(-4.63163 + 8.02222i) q^{13} +(-4.15539 + 0.984811i) q^{14} +(6.33682 + 14.6917i) q^{16} +14.6381 q^{17} -34.5778i q^{19} +(-15.6380 + 7.85338i) q^{20} +(24.5563 - 5.81976i) q^{22} +(-35.3255 - 20.3952i) q^{23} +(2.93057 + 5.07589i) q^{25} +(13.4758 - 12.7136i) q^{26} +(8.52653 + 0.496747i) q^{28} +(-9.52010 - 16.4893i) q^{29} +(-0.860391 - 0.496747i) q^{31} +(-3.71373 - 31.7838i) q^{32} +(-28.0462 - 8.39671i) q^{34} +9.34128i q^{35} -66.4263 q^{37} +(-19.8346 + 66.2502i) q^{38} +(34.4668 - 6.07660i) q^{40} +(-12.9434 + 22.4187i) q^{41} +(-36.4816 + 21.0627i) q^{43} +(-50.3877 - 2.93554i) q^{44} +(55.9836 + 59.3401i) q^{46} +(30.1126 - 17.3855i) q^{47} +(-22.2204 + 38.4868i) q^{49} +(-2.70325 - 11.4063i) q^{50} +(-33.1121 + 16.6289i) q^{52} -12.2231 q^{53} -55.2024i q^{55} +(-16.0517 - 5.84275i) q^{56} +(8.78165 + 37.0540i) q^{58} +(-49.1301 - 28.3653i) q^{59} +(-36.8804 - 63.8788i) q^{61} +(1.36354 + 1.44529i) q^{62} +(-11.1164 + 63.0272i) q^{64} +(-20.2625 - 35.0956i) q^{65} +(-82.4391 - 47.5962i) q^{67} +(48.9192 + 32.1758i) q^{68} +(5.35836 - 17.8976i) q^{70} +75.5614i q^{71} -56.7185 q^{73} +(127.271 + 38.1035i) q^{74} +(76.0051 - 115.556i) q^{76} +(-13.4716 + 23.3334i) q^{77} +(64.5777 - 37.2839i) q^{79} +(-69.5232 - 8.12830i) q^{80} +(37.6591 - 35.5290i) q^{82} +(56.7179 - 32.7461i) q^{83} +(-32.0193 + 55.4590i) q^{85} +(81.9798 - 19.4289i) q^{86} +(94.8576 + 34.5279i) q^{88} +150.050 q^{89} +19.7794i q^{91} +(-73.2244 - 145.808i) q^{92} +(-67.6677 + 16.0370i) q^{94} +(131.005 + 75.6355i) q^{95} +(56.4426 + 97.7615i) q^{97} +(64.6505 - 60.9936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.91597	−	0.573621i	−0.957987	−	0.286811i
$2$	−1.91597	−	0.573621i	−0.957987	−	0.286811i
$3$		0			0
$3$		0			0
$4$	3.34192	+	2.19809i	0.835479	+	0.549522i
$5$	−2.18740	+	3.78869i	−0.437480	+	0.757737i	−0.997494	−	0.0707454i	$-0.977462\pi$
$5$	−2.18740	+	3.78869i	−0.437480	+	0.757737i	0.560014	+	0.828483i	$0.310796\pi$
$6$		0			0
$7$	1.84918	−	1.06762i	0.264168	−	0.152518i	−0.362066	−	0.932152i	$-0.617929\pi$
$7$	1.84918	−	1.06762i	0.264168	−	0.152518i	0.626235	+	0.779635i	$0.284595\pi$
$8$	−5.14216	−	6.12848i	−0.642770	−	0.766059i
$9$		0			0
$10$	6.36427	−	6.00429i	0.636427	−	0.600429i
$11$	−10.9277	+	6.30914i	−0.993432	+	0.573558i	−0.906298	−	0.422639i	$-0.861104\pi$
$11$	−10.9277	+	6.30914i	−0.993432	+	0.573558i	−0.0871333	+	0.996197i	$0.527771\pi$
$12$		0			0
$13$	−4.63163	+	8.02222i	−0.356279	+	0.617094i	−0.987336	−	0.158643i	$-0.949288\pi$
$13$	−4.63163	+	8.02222i	−0.356279	+	0.617094i	0.631057	+	0.775737i	$0.282622\pi$
$14$	−4.15539	+	0.984811i	−0.296814	+	0.0703437i
$15$		0			0
$16$	6.33682	+	14.6917i	0.396051	+	0.918228i
$17$	14.6381			0.861063			0.430531	−	0.902576i	$-0.358326\pi$
$17$	14.6381			0.861063			0.430531	+	0.902576i	$0.358326\pi$
$18$		0			0
$19$		−	34.5778i		−	1.81989i	−0.414734	−	0.909943i	$-0.636125\pi$
$19$		−	34.5778i		−	1.81989i	0.414734	−	0.909943i	$-0.363875\pi$
$20$	−15.6380	+	7.85338i	−0.781899	+	0.392669i
$21$		0			0
$22$	24.5563	−	5.81976i	1.11620	−	0.264534i
$23$	−35.3255	−	20.3952i	−1.53589	−	0.886747i	−0.999073	−	0.0430488i	$-0.986293\pi$
$23$	−35.3255	−	20.3952i	−1.53589	−	0.886747i	−0.536818	−	0.843698i	$-0.680374\pi$
$24$		0			0
$25$	2.93057	+	5.07589i	0.117223	+	0.203036i
$26$	13.4758	−	12.7136i	0.518300	−	0.488983i
$27$		0			0
$28$	8.52653	+	0.496747i	0.304519	+	0.0177410i
$29$	−9.52010	−	16.4893i	−0.328279	−	0.568596i	0.653891	−	0.756589i	$-0.273135\pi$
$29$	−9.52010	−	16.4893i	−0.328279	−	0.568596i	−0.982171	+	0.187992i	$0.939802\pi$
$30$		0			0
$31$	−0.860391	−	0.496747i	−0.0277546	−	0.0160241i	0.486059	−	0.873926i	$-0.338434\pi$
$31$	−0.860391	−	0.496747i	−0.0277546	−	0.0160241i	−0.513813	+	0.857902i	$0.671768\pi$
$32$	−3.71373	−	31.7838i	−0.116054	−	0.993243i
$33$		0			0
$34$	−28.0462	−	8.39671i	−0.824887	−	0.246962i
$35$			9.34128i			0.266894i
$36$		0			0
$37$	−66.4263			−1.79530			−0.897652	−	0.440705i	$-0.854729\pi$
$37$	−66.4263			−1.79530			−0.897652	+	0.440705i	$0.854729\pi$
$38$	−19.8346	+	66.2502i	−0.521963	+	1.74343i
$39$		0			0
$40$	34.4668	−	6.07660i	0.861671	−	0.151915i
$41$	−12.9434	+	22.4187i	−0.315693	+	0.546797i	−0.979585	−	0.201032i	$-0.935570\pi$
$41$	−12.9434	+	22.4187i	−0.315693	+	0.546797i	0.663891	+	0.747829i	$0.268904\pi$
$42$		0			0
$43$	−36.4816	+	21.0627i	−0.848409	+	0.489829i	−0.860114	−	0.510102i	$-0.829608\pi$
$43$	−36.4816	+	21.0627i	−0.848409	+	0.489829i	0.0117046	+	0.999931i	$0.496274\pi$
$44$	−50.3877	−	2.93554i	−1.14517	−	0.0667167i
$45$		0			0
$46$	55.9836	+	59.3401i	1.21704	+	1.29000i
$47$	30.1126	−	17.3855i	0.640694	−	0.369905i	−0.144188	−	0.989550i	$-0.546057\pi$
$47$	30.1126	−	17.3855i	0.640694	−	0.369905i	0.784882	+	0.619646i	$0.212724\pi$
$48$		0			0
$49$	−22.2204	+	38.4868i	−0.453477	+	0.785445i
$50$	−2.70325	−	11.4063i	−0.0540650	−	0.228126i
$51$		0			0
$52$	−33.1121	+	16.6289i	−0.636771	+	0.319786i
$53$	−12.2231			−0.230624			−0.115312	−	0.993329i	$-0.536787\pi$
$53$	−12.2231			−0.230624			−0.115312	+	0.993329i	$0.536787\pi$
$54$		0			0
$55$		−	55.2024i		−	1.00368i
$56$	−16.0517	−	5.84275i	−0.286637	−	0.104335i
$57$		0			0
$58$	8.78165	+	37.0540i	0.151408	+	0.638862i
$59$	−49.1301	−	28.3653i	−0.832714	−	0.480768i	0.0220670	−	0.999756i	$-0.492975\pi$
$59$	−49.1301	−	28.3653i	−0.832714	−	0.480768i	−0.854781	+	0.518989i	$0.826309\pi$
$60$		0			0
$61$	−36.8804	−	63.8788i	−0.604597	−	1.04719i	−0.992115	−	0.125331i	$-0.960001\pi$
$61$	−36.8804	−	63.8788i	−0.604597	−	1.04719i	0.387518	−	0.921862i	$-0.373333\pi$
$62$	1.36354	+	1.44529i	0.0219926	+	0.0233112i
$63$		0			0
$64$	−11.1164	+	63.0272i	−0.173694	+	0.984800i
$65$	−20.2625	−	35.0956i	−0.311730	−	0.539932i
$66$		0			0
$67$	−82.4391	−	47.5962i	−1.23043	−	0.710392i	−0.263314	−	0.964710i	$-0.584816\pi$
$67$	−82.4391	−	47.5962i	−1.23043	−	0.710392i	−0.967121	+	0.254318i	$0.918149\pi$
$68$	48.9192	+	32.1758i	0.719400	+	0.473173i
$69$		0			0
$70$	5.35836	−	17.8976i	0.0765479	−	0.255681i
$71$			75.5614i			1.06424i	0.846667	+	0.532122i	$0.178605\pi$
$71$			75.5614i			1.06424i	−0.846667	+	0.532122i	$0.821395\pi$
$72$		0			0
$73$	−56.7185			−0.776965			−0.388483	−	0.921456i	$-0.627001\pi$
$73$	−56.7185			−0.776965			−0.388483	+	0.921456i	$0.627001\pi$
$74$	127.271	+	38.1035i	1.71988	+	0.514912i
$75$		0			0
$76$	76.0051	−	115.556i	1.00007	−	1.52048i
$77$	−13.4716	+	23.3334i	−0.174955	+	0.303032i
$78$		0			0
$79$	64.5777	−	37.2839i	0.817439	−	0.471949i	−0.0320934	−	0.999485i	$-0.510217\pi$
$79$	64.5777	−	37.2839i	0.817439	−	0.471949i	0.849533	+	0.527536i	$0.176884\pi$
$80$	−69.5232	−	8.12830i	−0.869040	−	0.101604i
$81$		0			0
$82$	37.6591	−	35.5290i	0.459257	−	0.433280i
$83$	56.7179	−	32.7461i	0.683349	−	0.394532i	−0.117767	−	0.993041i	$-0.537574\pi$
$83$	56.7179	−	32.7461i	0.683349	−	0.394532i	0.801116	+	0.598510i	$0.204240\pi$
$84$		0			0
$85$	−32.0193	+	55.4590i	−0.376698	+	0.652459i
$86$	81.9798	−	19.4289i	0.953254	−	0.225917i
$87$		0			0
$88$	94.8576	+	34.5279i	1.07793	+	0.392362i
$89$	150.050			1.68595			0.842977	−	0.537950i	$-0.180801\pi$
$89$	150.050			1.68595			0.842977	+	0.537950i	$0.180801\pi$
$90$		0			0
$91$			19.7794i			0.217356i
$92$	−73.2244	−	145.808i	−0.795918	−	1.58486i
$93$		0			0
$94$	−67.6677	+	16.0370i	−0.719869	+	0.170606i
$95$	131.005	+	75.6355i	1.37900	+	0.796163i
$96$		0			0
$97$	56.4426	+	97.7615i	0.581883	+	1.00785i	0.995256	+	0.0972889i	$0.0310171\pi$
$97$	56.4426	+	97.7615i	0.581883	+	1.00785i	−0.413373	+	0.910562i	$0.635650\pi$
$98$	64.6505	−	60.9936i	0.659699	−	0.622384i
$99$		0			0
$100$	−1.36354	+	23.4048i	−0.0136354	+	0.234048i
$101$	21.9708	+	38.0545i	0.217532	+	0.376777i	0.954053	−	0.299638i	$-0.0968659\pi$
$101$	21.9708	+	38.0545i	0.217532	+	0.376777i	−0.736521	+	0.676415i	$0.763533\pi$
$102$		0			0
$103$	−66.4269	−	38.3516i	−0.644921	−	0.372345i	0.141587	−	0.989926i	$-0.454780\pi$
$103$	−66.4269	−	38.3516i	−0.644921	−	0.372345i	−0.786508	+	0.617581i	$0.788113\pi$
$104$	72.9806	−	12.8667i	0.701736	−	0.123718i
$105$		0			0
$106$	23.4191	+	7.01141i	0.220935	+	0.0661454i
$107$		−	9.53448i		−	0.0891073i	−0.999007	−	0.0445537i	$-0.985813\pi$
$107$		−	9.53448i		−	0.0891073i	0.999007	−	0.0445537i	$-0.0141866\pi$
$108$		0			0
$109$	51.4021			0.471579			0.235790	−	0.971804i	$-0.424232\pi$
$109$	51.4021			0.471579			0.235790	+	0.971804i	$0.424232\pi$
$110$	−31.6653	+	105.766i	−0.287866	+	0.961513i
$111$		0			0
$112$	27.4031	+	20.4022i	0.244670	+	0.182162i
$113$	−0.914995	+	1.58482i	−0.00809730	+	0.0140249i	−0.870046	−	0.492971i	$-0.835911\pi$
$113$	−0.914995	+	1.58482i	−0.00809730	+	0.0140249i	0.861948	+	0.506996i	$0.169244\pi$
$114$		0			0
$115$	154.542	−	89.2248i	1.34384	−	0.775868i
$116$	4.42954	−	76.0319i	0.0381857	−	0.655447i
$117$		0			0
$118$	77.8611	+	82.5293i	0.659840	+	0.699401i
$119$	27.0684	−	15.6279i	0.227465	−	0.131327i
$120$		0			0
$121$	19.1104	−	33.1002i	0.157937	−	0.273556i
$122$	34.0197	+	143.546i	0.278850	+	1.17660i
$123$		0			0
$124$	−1.78346	−	3.55130i	−0.0143828	−	0.0286395i
$125$	−135.011			−1.08009
$126$		0			0
$127$			46.6614i			0.367413i	0.982981	+	0.183706i	$0.0588096\pi$
$127$			46.6614i			0.367413i	−0.982981	+	0.183706i	$0.941190\pi$
$128$	57.4525	−	114.382i	0.448848	−	0.893608i
$129$		0			0
$130$	18.6908	+	78.8653i	0.143775	+	0.606656i
$131$	100.596	+	58.0793i	0.767910	+	0.443353i	0.832129	−	0.554583i	$-0.187122\pi$
$131$	100.596	+	58.0793i	0.767910	+	0.443353i	−0.0642183	+	0.997936i	$0.520455\pi$
$132$		0			0
$133$	−36.9161	−	63.9406i	−0.277565	−	0.480756i
$134$	130.649	+	138.482i	0.974993	+	1.03345i
$135$		0			0
$136$	−75.2712	−	89.7090i	−0.553465	−	0.659625i
$137$	−53.9555	−	93.4536i	−0.393836	−	0.682143i	0.599116	−	0.800662i	$-0.295519\pi$
$137$	−53.9555	−	93.4536i	−0.393836	−	0.682143i	−0.992952	+	0.118519i	$0.962185\pi$
$138$		0			0
$139$	130.016	+	75.0646i	0.935365	+	0.540033i	0.888504	−	0.458868i	$-0.151745\pi$
$139$	130.016	+	75.0646i	0.935365	+	0.540033i	0.0468609	+	0.998901i	$0.485078\pi$
$140$	−20.5329	+	31.2178i	−0.146664	+	0.222984i
$141$		0			0
$142$	43.3436	−	144.774i	0.305237	−	1.01953i
$143$		−	116.886i		−	0.817388i
$144$		0			0
$145$	83.2970			0.574462
$146$	108.671	+	32.5349i	0.744323	+	0.222842i
$147$		0			0
$148$	−221.991	−	146.011i	−1.49994	−	0.986559i
$149$	−3.81611	+	6.60970i	−0.0256115	+	0.0443604i	−0.878547	−	0.477656i	$-0.841487\pi$
$149$	−3.81611	+	6.60970i	−0.0256115	+	0.0443604i	0.852936	+	0.522016i	$0.174820\pi$
$150$		0			0
$151$	−183.627	+	106.017i	−1.21607	+	0.702099i	−0.964075	−	0.265629i	$-0.914420\pi$
$151$	−183.627	+	106.017i	−1.21607	+	0.702099i	−0.251996	+	0.967728i	$0.581087\pi$
$152$	−211.909	+	177.805i	−1.39414	+	1.16977i
$153$		0			0
$154$	39.1957	−	36.9787i	0.254518	−	0.240121i
$155$	3.76404	−	2.17317i	0.0242841	−	0.0140204i
$156$		0			0
$157$	30.6558	−	53.0973i	0.195260	−	0.338199i	−0.751726	−	0.659476i	$-0.770778\pi$
$157$	30.6558	−	53.0973i	0.195260	−	0.338199i	0.946986	+	0.321276i	$0.104112\pi$
$158$	−145.116	+	34.3920i	−0.918456	+	0.217671i
$159$		0			0
$160$	128.542	+	55.4536i	0.803389	+	0.346585i
$161$	−87.0975			−0.540978
$162$		0			0
$163$			25.3264i			0.155377i	0.996978	+	0.0776885i	$0.0247540\pi$
$163$			25.3264i			0.155377i	−0.996978	+	0.0776885i	$0.975246\pi$
$164$	−92.5341	+	46.4706i	−0.564232	+	0.283357i
$165$		0			0
$166$	−127.454	+	30.2061i	−0.767795	+	0.181964i
$167$	−120.244	−	69.4230i	−0.720025	−	0.415707i	0.0947370	−	0.995502i	$-0.469799\pi$
$167$	−120.244	−	69.4230i	−0.720025	−	0.415707i	−0.814762	+	0.579796i	$0.803132\pi$
$168$		0			0
$169$	41.5960	+	72.0463i	0.246130	+	0.426310i
$170$	93.1606	−	87.8912i	0.548004	−	0.517007i
$171$		0			0
$172$	−168.216	−	9.80010i	−0.978000	−	0.0569773i
$173$	45.1000	+	78.1155i	0.260694	+	0.451534i	0.966426	−	0.256944i	$-0.0827155\pi$
$173$	45.1000	+	78.1155i	0.260694	+	0.451534i	−0.705733	+	0.708478i	$0.749382\pi$
$174$		0			0
$175$	10.8383	+	6.25748i	0.0619330	+	0.0357570i
$176$	−161.939	−	120.567i	−0.920107	−	0.685039i
$177$		0			0
$178$	−287.492	−	86.0718i	−1.61512	−	0.483549i
$179$			41.7114i			0.233025i	0.993189	+	0.116512i	$0.0371715\pi$
$179$			41.7114i			0.233025i	−0.993189	+	0.116512i	$0.962829\pi$
$180$		0			0
$181$	84.6616			0.467744			0.233872	−	0.972267i	$-0.424860\pi$
$181$	84.6616			0.467744			0.233872	+	0.972267i	$0.424860\pi$
$182$	11.3459	−	37.8967i	0.0623399	−	0.208224i
$183$		0			0
$184$	56.6579	+	321.367i	0.307923	+	1.74656i
$185$	145.301	−	251.668i	0.785409	−	1.36037i
$186$		0			0
$187$	−159.961	+	92.3536i	−0.855407	+	0.493869i
$188$	138.849	+	8.08919i	0.738557	+	0.0430276i
$189$		0			0
$190$	−207.615	−	220.063i	−1.09271	−	1.15823i
$191$	−152.525	+	88.0606i	−0.798562	+	0.461050i	−0.842968	−	0.537963i	$-0.819194\pi$
$191$	−152.525	+	88.0606i	−0.798562	+	0.461050i	0.0444058	+	0.999014i	$0.485861\pi$
$192$		0			0
$193$	166.424	−	288.255i	0.862300	−	1.49355i	−0.00740395	−	0.999973i	$-0.502357\pi$
$193$	166.424	−	288.255i	0.862300	−	1.49355i	0.869704	−	0.493574i	$-0.164310\pi$
$194$	−52.0645	−	219.685i	−0.268374	−	1.13240i
$195$		0			0
$196$	−158.856	+	79.7774i	−0.810490	+	0.407027i
$197$	−137.238			−0.696637			−0.348319	−	0.937376i	$-0.613247\pi$
$197$	−137.238			−0.696637			−0.348319	+	0.937376i	$0.613247\pi$
$198$		0			0
$199$			286.157i			1.43798i	0.695023	+	0.718988i	$0.255394\pi$
$199$			286.157i			1.43798i	−0.695023	+	0.718988i	$0.744606\pi$
$200$	16.0380	−	44.0609i	0.0801902	−	0.220305i
$201$		0			0
$202$	−20.2666	−	85.5143i	−0.100330	−	0.423338i
$203$	−35.2087	−	20.3278i	−0.173442	−	0.100137i
$204$		0			0
$205$	−56.6249	−	98.0772i	−0.276219	−	0.478425i
$206$	105.273	+	111.585i	0.511034	+	0.541672i
$207$		0			0
$208$	−147.210	−	17.2110i	−0.707738	−	0.0827451i
$209$	218.156	+	377.858i	1.04381	+	1.80793i
$210$		0			0
$211$	273.062	+	157.653i	1.29413	+	0.747169i	0.979384	−	0.202006i	$-0.0647460\pi$
$211$	273.062	+	157.653i	1.29413	+	0.747169i	0.314750	+	0.949175i	$0.398079\pi$
$212$	−40.8485	−	26.8674i	−0.192682	−	0.126733i
$213$		0			0
$214$	−5.46918	+	18.2678i	−0.0255569	+	0.0853637i
$215$		−	184.290i		−	0.857162i
$216$		0			0
$217$	−2.12136			−0.00977583
$218$	−98.4852	−	29.4854i	−0.451767	−	0.135254i
$219$		0			0
$220$	121.340	−	184.482i	0.551544	−	0.838554i
$221$	−67.7981	+	117.430i	−0.306779	+	0.531357i
$222$		0			0
$223$	25.8734	−	14.9380i	0.116024	−	0.0669865i	−0.440865	−	0.897573i	$-0.645328\pi$
$223$	25.8734	−	14.9380i	0.116024	−	0.0669865i	0.556889	+	0.830587i	$0.311995\pi$
$224$	−40.8005	−	54.8090i	−0.182145	−	0.244683i
$225$		0			0
$226$	2.66219	−	2.51161i	0.0117796	−	0.0111133i
$227$	−307.799	+	177.708i	−1.35594	+	0.782855i	−0.989074	−	0.147418i	$-0.952904\pi$
$227$	−307.799	+	177.708i	−1.35594	+	0.782855i	−0.366870	+	0.930272i	$0.619571\pi$
$228$		0			0
$229$	−44.0925	+	76.3705i	−0.192544	+	0.333496i	−0.946093	−	0.323896i	$-0.895007\pi$
$229$	−44.0925	+	76.3705i	−0.192544	+	0.333496i	0.753549	+	0.657392i	$0.228340\pi$
$230$	−347.280	+	82.3039i	−1.50991	+	0.357843i
$231$		0			0
$232$	−52.1004	+	143.134i	−0.224571	+	0.616958i
$233$	251.720			1.08034			0.540172	−	0.841555i	$-0.318359\pi$
$233$	251.720			1.08034			0.540172	+	0.841555i	$0.318359\pi$
$234$		0			0
$235$			152.116i			0.647303i
$236$	−101.839	−	202.787i	−0.431523	−	0.859266i
$237$		0			0
$238$	−60.8269	+	14.4157i	−0.255575	+	0.0605703i
$239$	−123.211	−	71.1356i	−0.515525	−	0.297639i	0.219577	−	0.975595i	$-0.429532\pi$
$239$	−123.211	−	71.1356i	−0.515525	−	0.297639i	−0.735102	+	0.677957i	$0.762866\pi$
$240$		0			0
$241$	28.5164	+	49.3918i	0.118325	+	0.204945i	0.919104	−	0.394015i	$-0.128914\pi$
$241$	28.5164	+	49.3918i	0.118325	+	0.204945i	−0.800779	+	0.598960i	$0.795581\pi$
$242$	−55.6021	+	52.4571i	−0.229761	+	0.216765i
$243$		0			0
$244$	17.1598	−	294.544i	0.0703272	−	1.20715i
$245$	−97.2096	−	168.372i	−0.396774	−	0.687233i
$246$		0			0
$247$	277.391	+	160.152i	1.12304	+	0.648388i
$248$	1.37996	+	7.82724i	0.00556437	+	0.0315615i
$249$		0			0
$250$	258.678	+	77.4453i	1.03471	+	0.309781i
$251$		−	0.579617i		−	0.00230923i	−0.999999	−	0.00115462i	$-0.999632\pi$
$251$		−	0.579617i		−	0.00230923i	0.999999	−	0.00115462i	$-0.000367526\pi$
$252$		0			0
$253$	514.704			2.03440
$254$	26.7660	−	89.4021i	0.105378	−	0.351977i
$255$		0			0
$256$	−175.689	+	186.197i	−0.686287	+	0.727331i
$257$	159.160	−	275.674i	0.619301	−	1.07266i	−0.370313	−	0.928907i	$-0.620750\pi$
$257$	159.160	−	275.674i	0.619301	−	1.07266i	0.989614	−	0.143753i	$-0.0459171\pi$
$258$		0			0
$259$	−122.834	+	70.9182i	−0.474262	+	0.273816i
$260$	9.42778	−	161.825i	0.0362607	−	0.622405i
$261$		0			0
$262$	−159.424	−	168.983i	−0.608490	−	0.644972i
$263$	−270.344	+	156.083i	−1.02792	+	0.593472i	−0.916389	−	0.400288i	$-0.868910\pi$
$263$	−270.344	+	156.083i	−1.02792	+	0.593472i	−0.111535	+	0.993761i	$0.535577\pi$
$264$		0			0
$265$	26.7367	−	46.3094i	0.100893	−	0.174752i
$266$	34.0526	+	143.684i	0.128017	+	0.540167i
$267$		0			0
$268$	−170.884	−	340.271i	−0.637627	−	1.26967i
$269$	−480.302			−1.78551			−0.892755	−	0.450542i	$-0.851231\pi$
$269$	−480.302			−1.78551			−0.892755	+	0.450542i	$0.851231\pi$
$270$		0			0
$271$		−	457.090i		−	1.68668i	−0.537381	−	0.843340i	$-0.680586\pi$
$271$		−	457.090i		−	1.68668i	0.537381	−	0.843340i	$-0.319414\pi$
$272$	92.7587	+	215.057i	0.341025	+	0.790652i
$273$		0			0
$274$	49.7703	+	210.005i	0.181644	+	0.766441i
$275$	−64.0490	−	36.9787i	−0.232905	−	0.134468i
$276$		0			0
$277$	85.6037	+	148.270i	0.309039	+	0.535271i	0.978152	−	0.207889i	$-0.0666594\pi$
$277$	85.6037	+	148.270i	0.309039	+	0.535271i	−0.669114	+	0.743160i	$0.733326\pi$
$278$	−206.048	−	218.402i	−0.741181	−	0.785618i
$279$		0			0
$280$	57.2478	−	48.0343i	0.204456	−	0.171551i
$281$	19.9973	+	34.6363i	0.0711647	+	0.123261i	0.899412	−	0.437102i	$-0.143995\pi$
$281$	19.9973	+	34.6363i	0.0711647	+	0.123261i	−0.828247	+	0.560363i	$0.810662\pi$
$282$		0			0
$283$	−338.527	−	195.449i	−1.19621	−	0.690632i	−0.236501	−	0.971631i	$-0.576001\pi$
$283$	−338.527	−	195.449i	−1.19621	−	0.690632i	−0.959708	+	0.281000i	$0.909334\pi$
$284$	−166.091	+	252.520i	−0.584826	+	0.889155i
$285$		0			0
$286$	−67.0486	+	223.951i	−0.234436	+	0.783047i
$287$			55.2748i			0.192595i
$288$		0			0
$289$	−74.7271			−0.258571
$290$	−159.595	−	47.7810i	−0.550328	−	0.164762i
$291$		0			0
$292$	−189.548	−	124.672i	−0.649138	−	0.426959i
$293$	−251.725	+	436.001i	−0.859131	+	1.48806i	0.0136273	+	0.999907i	$0.495662\pi$
$293$	−251.725	+	436.001i	−0.859131	+	1.48806i	−0.872759	+	0.488152i	$0.837671\pi$
$294$		0			0
$295$	214.934	−	124.092i	0.728591	−	0.420652i
$296$	341.574	+	407.092i	1.15397	+	1.37531i
$297$		0			0
$298$	11.1030	−	10.4750i	0.0372585	−	0.0351511i
$299$	327.229	−	188.926i	1.09441	−	0.631859i
$300$		0			0
$301$	−44.9740	+	77.8972i	−0.149415	+	0.258795i
$302$	412.638	−	97.7936i	1.36635	−	0.323820i
$303$		0			0
$304$	508.006	−	219.113i	1.67107	−	0.720768i
$305$	322.689			1.05800
$306$		0			0
$307$			103.154i			0.336006i	0.985786	+	0.168003i	$0.0537318\pi$
$307$			103.154i			0.336006i	−0.985786	+	0.168003i	$0.946268\pi$
$308$	−96.3098	+	48.3667i	−0.312694	+	0.157035i
$309$		0			0
$310$	−8.45838	+	2.00460i	−0.0272851	+	0.00646646i
$311$	396.709	+	229.040i	1.27559	+	0.736463i	0.976035	−	0.217615i	$-0.0698277\pi$
$311$	396.709	+	229.040i	1.27559	+	0.736463i	0.299557	+	0.954078i	$0.403161\pi$
$312$		0			0
$313$	−9.31582	−	16.1355i	−0.0297630	−	0.0515510i	0.850760	−	0.525554i	$-0.176142\pi$
$313$	−9.31582	−	16.1355i	−0.0297630	−	0.0515510i	−0.880523	+	0.474003i	$0.842809\pi$
$314$	−89.1934	+	84.1483i	−0.284055	+	0.267988i
$315$		0			0
$316$	297.767	+	17.3476i	0.942300	+	0.0548974i
$317$	−107.895	−	186.880i	−0.340363	−	0.589527i	0.644137	−	0.764910i	$-0.277217\pi$
$317$	−107.895	−	186.880i	−0.340363	−	0.589527i	−0.984500	+	0.175384i	$0.943883\pi$
$318$		0			0
$319$	208.066	+	120.127i	0.652246	+	0.376574i
$320$	−214.474	−	179.982i	−0.670232	−	0.562445i
$321$		0			0
$322$	166.877	+	49.9610i	0.518250	+	0.155158i
$323$		−	506.152i		−	1.56704i
$324$		0			0
$325$	−54.2932			−0.167056
$326$	14.5278	−	48.5248i	0.0445638	−	0.148849i
$327$		0			0
$328$	203.949	−	35.9569i	0.621797	−	0.109625i
$329$	37.1224	−	64.2978i	0.112834	−	0.195434i
$330$		0			0
$331$	215.753	−	124.565i	0.651822	−	0.376329i	−0.137332	−	0.990525i	$-0.543853\pi$
$331$	215.753	−	124.565i	0.651822	−	0.376329i	0.789154	+	0.614196i	$0.210519\pi$
$332$	261.526	+	15.2362i	0.787727	+	0.0458922i
$333$		0			0
$334$	190.562	+	201.987i	0.570546	+	0.604752i
$335$	360.655	−	208.224i	1.07658	−	0.621564i
$336$		0			0
$337$	135.945	−	235.464i	0.403398	−	0.698705i	−0.590736	−	0.806865i	$-0.701162\pi$
$337$	135.945	−	235.464i	0.403398	−	0.698705i	0.994134	+	0.108160i	$0.0344958\pi$
$338$	−38.3695	−	161.899i	−0.113519	−	0.478992i
$339$		0			0
$340$	−228.910	+	114.958i	−0.673264	+	0.338113i
$341$	12.5362			0.0367630
$342$		0			0
$343$			199.519i			0.581688i
$344$	316.676	+	115.269i	0.920570	+	0.335084i
$345$		0			0
$346$	−41.6017	−	175.538i	−0.120236	−	0.507334i
$347$	280.781	+	162.109i	0.809169	+	0.467174i	0.846667	−	0.532123i	$-0.178606\pi$
$347$	280.781	+	162.109i	0.809169	+	0.467174i	−0.0374985	+	0.999297i	$0.511939\pi$
$348$		0			0
$349$	50.5198	+	87.5029i	0.144756	+	0.250725i	0.929282	−	0.369371i	$-0.120427\pi$
$349$	50.5198	+	87.5029i	0.144756	+	0.250725i	−0.784526	+	0.620096i	$0.787094\pi$
$350$	−17.1764	−	18.2062i	−0.0490755	−	0.0520178i
$351$		0			0
$352$	241.111	+	323.895i	0.684974	+	0.920155i
$353$	−75.9329	−	131.520i	−0.215107	−	0.372577i	0.738198	−	0.674584i	$-0.235677\pi$
$353$	−75.9329	−	131.520i	−0.215107	−	0.372577i	−0.953306	+	0.302007i	$0.902343\pi$
$354$		0			0
$355$	−286.278	−	165.283i	−0.806418	−	0.465586i
$356$	501.454	+	329.823i	1.40858	+	0.926468i
$357$		0			0
$358$	23.9266	−	79.9181i	0.0668340	−	0.223235i
$359$			594.808i			1.65685i	0.560102	+	0.828424i	$0.310762\pi$
$359$			594.808i			1.65685i	−0.560102	+	0.828424i	$0.689238\pi$
$360$		0			0
$361$	−834.626			−2.31198
$362$	−162.209	−	48.5637i	−0.448092	−	0.134154i
$363$		0			0
$364$	−43.4768	+	66.1010i	−0.119442	+	0.181596i
$365$	124.066	−	214.888i	0.339907	−	0.588736i
$366$		0			0
$367$	−151.089	+	87.2311i	−0.411686	+	0.237687i	−0.691514	−	0.722363i	$-0.743056\pi$
$367$	−151.089	+	87.2311i	−0.411686	+	0.237687i	0.279828	+	0.960050i	$0.409723\pi$
$368$	75.7878	−	648.230i	0.205945	−	1.76150i
$369$		0			0
$370$	−422.755	+	398.842i	−1.14258	+	1.07795i
$371$	−22.6026	+	13.0496i	−0.0609235	+	0.0351742i
$372$		0			0
$373$	−144.383	+	250.078i	−0.387085	+	0.670452i	−0.992056	−	0.125796i	$-0.959851\pi$
$373$	−144.383	+	250.078i	−0.387085	+	0.670452i	0.604971	+	0.796248i	$0.293185\pi$
$374$	359.457	−	85.1900i	0.961116	−	0.227781i
$375$		0			0
$376$	−261.390	−	95.1453i	−0.695187	−	0.253046i
$377$	176.374			0.467837
$378$		0			0
$379$		−	260.534i		−	0.687425i	−0.939075	−	0.343713i	$-0.888315\pi$
$379$		−	260.534i		−	0.687425i	0.939075	−	0.343713i	$-0.111685\pi$
$380$	271.553	+	540.727i	0.714613	+	1.42297i
$381$		0			0
$382$	342.748	−	81.2300i	0.897247	−	0.212644i
$383$	−303.817	−	175.409i	−0.793257	−	0.457987i	0.0478509	−	0.998854i	$-0.484763\pi$
$383$	−303.817	−	175.409i	−0.793257	−	0.457987i	−0.841108	+	0.540867i	$0.818096\pi$
$384$		0			0
$385$	−58.9354	−	102.079i	−0.153079	−	0.265141i
$386$	−484.213	+	456.824i	−1.25444	+	1.18348i
$387$		0			0
$388$	−26.2618	+	450.777i	−0.0676851	+	1.16180i
$389$	16.5571	+	28.6777i	0.0425632	+	0.0737216i	0.886522	−	0.462686i	$-0.153114\pi$
$389$	16.5571	+	28.6777i	0.0425632	+	0.0737216i	−0.843959	+	0.536408i	$0.819781\pi$
$390$		0			0
$391$	−517.097	−	298.546i	−1.32250	−	0.763545i
$392$	350.126	−	61.7282i	0.893179	−	0.157470i
$393$		0			0
$394$	262.944	+	78.7224i	0.667370	+	0.199803i
$395$			326.220i			0.825872i
$396$		0			0
$397$	357.151			0.899625			0.449813	−	0.893123i	$-0.351491\pi$
$397$	357.151			0.899625			0.449813	+	0.893123i	$0.351491\pi$
$398$	164.146	−	548.270i	0.412427	−	1.37756i
$399$		0			0
$400$	−56.0028	+	75.2199i	−0.140007	+	0.188050i
$401$	159.123	−	275.608i	0.396814	−	0.687303i	−0.596517	−	0.802601i	$-0.703449\pi$
$401$	159.123	−	275.608i	0.396814	−	0.687303i	0.993331	+	0.115298i	$0.0367823\pi$
$402$		0			0
$403$	7.97003	−	4.60150i	0.0197768	−	0.0114181i
$404$	−10.2226	+	175.469i	−0.0253035	+	0.434328i
$405$		0			0
$406$	55.7986	+	59.1439i	0.137435	+	0.145675i
$407$	725.889	−	419.092i	1.78351	−	1.02971i
$408$		0			0
$409$	−256.803	+	444.796i	−0.627880	+	1.08752i	0.360097	+	0.932915i	$0.382744\pi$
$409$	−256.803	+	444.796i	−0.627880	+	1.08752i	−0.987976	+	0.154605i	$0.950590\pi$
$410$	52.2327	+	220.395i	0.127397	+	0.537548i
$411$		0			0
$412$	−137.693	−	274.180i	−0.334206	−	0.665485i
$413$	−121.134			−0.293302
$414$		0			0
$415$			286.515i			0.690399i
$416$	272.177	+	117.418i	0.654272	+	0.282256i
$417$		0			0
$418$	−201.235	−	849.105i	−0.481422	−	2.03135i
$419$	−62.7466	−	36.2268i	−0.149753	−	0.0864601i	0.423251	−	0.906012i	$-0.360889\pi$
$419$	−62.7466	−	36.2268i	−0.149753	−	0.0864601i	−0.573004	+	0.819552i	$0.694222\pi$
$420$		0			0
$421$	−315.617	−	546.665i	−0.749685	−	1.29849i	−0.947974	−	0.318349i	$-0.896872\pi$
$421$	−315.617	−	546.665i	−0.749685	−	1.29849i	0.198289	−	0.980144i	$-0.436462\pi$
$422$	−432.748	−	458.693i	−1.02547	−	1.08695i
$423$		0			0
$424$	62.8529	+	74.9088i	0.148238	+	0.176672i
$425$	42.8978	+	74.3012i	0.100936	+	0.174826i
$426$		0			0
$427$	−136.397	−	78.7488i	−0.319431	−	0.184423i
$428$	20.9576	−	31.8634i	0.0489664	−	0.0744473i
$429$		0			0
$430$	−105.713	+	353.095i	−0.245843	+	0.821150i
$431$			73.3222i			0.170121i	0.996376	+	0.0850606i	$0.0271084\pi$
$431$			73.3222i			0.170121i	−0.996376	+	0.0850606i	$0.972892\pi$
$432$		0			0
$433$	−575.286			−1.32860			−0.664302	−	0.747464i	$-0.731271\pi$
$433$	−575.286			−1.32860			−0.664302	+	0.747464i	$0.731271\pi$
$434$	4.06446	+	1.21686i	0.00936512	+	0.00280381i
$435$		0			0
$436$	171.782	+	112.986i	0.393995	+	0.259143i
$437$	−705.221	+	1221.48i	−1.61378	+	2.79515i
$438$		0			0
$439$	206.677	−	119.325i	0.470791	−	0.271811i	−0.245780	−	0.969326i	$-0.579044\pi$
$439$	206.677	−	119.325i	0.470791	−	0.271811i	0.716571	+	0.697514i	$0.245711\pi$
$440$	−338.307	+	283.860i	−0.768879	+	0.645135i
$441$		0			0
$442$	197.260	−	186.102i	0.446289	−	0.421045i
$443$	45.3661	−	26.1921i	0.102407	−	0.0591244i	−0.447922	−	0.894073i	$-0.647836\pi$
$443$	45.3661	−	26.1921i	0.102407	−	0.0591244i	0.550329	+	0.834948i	$0.314502\pi$
$444$		0			0
$445$	−328.219	+	568.492i	−0.737571	+	1.27751i
$446$	−58.1414	+	13.7793i	−0.130362	+	0.0308953i
$447$		0			0
$448$	46.7330	+	128.417i	0.104315	+	0.286644i
$449$	566.091			1.26078			0.630391	−	0.776277i	$-0.282894\pi$
$449$	566.091			1.26078			0.630391	+	0.776277i	$0.282894\pi$
$450$		0			0
$451$		−	326.648i		−	0.724274i
$452$	−6.54141	+	3.28509i	−0.0144721	+	0.00726790i
$453$		0			0
$454$	691.673	−	163.924i	1.52351	−	0.361066i
$455$	−74.9378	−	43.2654i	−0.164698	−	0.0950887i
$456$		0			0
$457$	17.1799	+	29.7564i	0.0375927	+	0.0651125i	0.884210	−	0.467090i	$-0.154698\pi$
$457$	17.1799	+	29.7564i	0.0375927	+	0.0651125i	−0.846617	+	0.532203i	$0.821364\pi$
$458$	128.288	−	121.032i	0.280105	−	0.264261i
$459$		0			0
$460$	712.590	+	41.5148i	1.54911	+	0.0902496i
$461$	−136.272	−	236.031i	−0.295602	−	0.511997i	0.679523	−	0.733654i	$-0.262187\pi$
$461$	−136.272	−	236.031i	−0.295602	−	0.511997i	−0.975125	+	0.221657i	$0.928853\pi$
$462$		0			0
$463$	−489.759	−	282.763i	−1.05780	−	0.610719i	−0.132974	−	0.991120i	$-0.542453\pi$
$463$	−489.759	−	282.763i	−1.05780	−	0.610719i	−0.924822	+	0.380401i	$0.875786\pi$
$464$	181.928	−	244.356i	0.392086	−	0.526629i
$465$		0			0
$466$	−482.289	−	144.392i	−1.03496	−	0.309854i
$467$			893.925i			1.91419i	0.289780	+	0.957093i	$0.406418\pi$
$467$			893.925i			1.91419i	−0.289780	+	0.957093i	$0.593582\pi$
$468$		0			0
$469$	−203.259			−0.433389
$470$	87.2572	−	291.451i	0.185654	−	0.620108i
$471$		0			0
$472$	78.7988	+	446.952i	0.166947	+	0.946931i
$473$	265.774	−	460.335i	0.561891	−	0.973224i
$474$		0			0
$475$	175.513	−	101.333i	0.369502	−	0.213332i
$476$	124.812	+	7.27142i	0.262210	+	0.0152761i
$477$		0			0
$478$	195.263	+	206.970i	0.408501	+	0.432992i
$479$	−467.745	+	270.053i	−0.976504	+	0.563785i	−0.901213	−	0.433377i	$-0.857322\pi$
$479$	−467.745	+	270.053i	−0.976504	+	0.563785i	−0.0752909	+	0.997162i	$0.523989\pi$
$480$		0			0
$481$	307.662	−	532.886i	0.639630	−	1.10787i
$482$	−26.3044	−	110.991i	−0.0545735	−	0.230272i
$483$		0			0
$484$	136.623	−	68.6118i	0.282278	−	0.141760i
$485$	−493.850			−1.01825
$486$		0			0
$487$		−	518.681i		−	1.06505i	−0.846413	−	0.532526i	$-0.821243\pi$
$487$		−	518.681i		−	1.06505i	0.846413	−	0.532526i	$-0.178757\pi$
$488$	−201.835	+	554.496i	−0.413595	+	1.13626i
$489$		0			0
$490$	89.6694	+	378.358i	0.182999	+	0.772159i
$491$	−130.195	−	75.1683i	−0.265163	−	0.153092i	0.361524	−	0.932363i	$-0.382256\pi$
$491$	−130.195	−	75.1683i	−0.265163	−	0.153092i	−0.626688	+	0.779271i	$0.715590\pi$
$492$		0			0
$493$	−139.356	−	241.371i	−0.282669	−	0.489597i
$494$	−439.608	−	465.964i	−0.889894	−	0.943247i
$495$		0			0
$496$	1.84589	−	15.7884i	0.00372156	−	0.0318314i
$497$	80.6711	+	139.726i	0.162316	+	0.281140i
$498$		0			0
$499$	265.749	+	153.430i	0.532564	+	0.307476i	0.742060	−	0.670334i	$-0.233849\pi$
$499$	265.749	+	153.430i	0.532564	+	0.307476i	−0.209496	+	0.977810i	$0.567182\pi$
$500$	−451.196	−	296.767i	−0.902393	−	0.593533i
$501$		0			0
$502$	−0.332481	+	1.11053i	−0.000662312	+	0.00221221i
$503$		−	731.474i		−	1.45422i	−0.686520	−	0.727111i	$-0.740863\pi$
$503$		−	731.474i		−	1.45422i	0.686520	−	0.727111i	$-0.259137\pi$
$504$		0			0
$505$	−192.235			−0.380664
$506$	−986.160	−	295.245i	−1.94893	−	0.583489i
$507$		0			0
$508$	−102.566	+	155.939i	−0.201901	+	0.306966i
$509$	−29.6107	+	51.2873i	−0.0581743	+	0.100761i	−0.893646	−	0.448773i	$-0.851861\pi$
$509$	−29.6107	+	51.2873i	−0.0581743	+	0.100761i	0.835472	+	0.549534i	$0.185195\pi$
$510$		0			0
$511$	−104.883	+	60.5540i	−0.205250	+	0.118501i
$512$	443.423	−	255.969i	0.866060	−	0.499939i
$513$		0			0
$514$	−463.079	+	436.886i	−0.900933	+	0.849973i
$515$	290.604	−	167.780i	0.564280	−	0.325787i
$516$		0			0
$517$	−219.375	+	379.969i	−0.424323	+	0.734950i
$518$	276.027	−	65.4173i	0.532871	−	0.126288i
$519$		0			0
$520$	−110.890	+	304.645i	−0.213250	+	0.585856i
$521$	689.100			1.32265			0.661324	−	0.750100i	$-0.269995\pi$
$521$	689.100			1.32265			0.661324	+	0.750100i	$0.269995\pi$
$522$		0			0
$523$		−	431.237i		−	0.824544i	−0.911061	−	0.412272i	$-0.864735\pi$
$523$		−	431.237i		−	0.824544i	0.911061	−	0.412272i	$-0.135265\pi$
$524$	208.521	+	415.216i	0.397941	+	0.792396i
$525$		0			0
$526$	607.505	−	143.976i	1.15495	−	0.273719i
$527$	−12.5945	−	7.27142i	−0.0238984	−	0.0137978i
$528$		0			0
$529$	567.427	+	982.812i	1.07264	+	1.85787i
$530$	−77.7910	+	73.3908i	−0.146775	+	0.138473i
$531$		0			0
$532$	17.1764	−	294.829i	0.0322865	−	0.554190i
$533$	−119.898	−	207.670i	−0.224950	−	0.389625i
$534$		0			0
$535$	36.1232	+	20.8557i	0.0675199	+	0.0389827i
$536$	132.222	+	749.974i	0.246684	+	1.39920i
$537$		0			0
$538$	920.247	+	275.512i	1.71050	+	0.512103i
$539$		−	560.765i		−	1.04038i
$540$		0			0
$541$	99.8398			0.184547			0.0922734	−	0.995734i	$-0.470587\pi$
$541$	99.8398			0.184547			0.0922734	+	0.995734i	$0.470587\pi$
$542$	−262.197	+	875.773i	−0.483758	+	1.61582i
$543$		0			0
$544$	−54.3619	−	465.253i	−0.0999299	−	0.855244i
$545$	−112.437	+	194.747i	−0.206306	+	0.357333i
$546$		0			0
$547$	−413.671	+	238.833i	−0.756254	+	0.436624i	−0.827949	−	0.560803i	$-0.810493\pi$
$547$	−413.671	+	238.833i	−0.756254	+	0.436624i	0.0716949	+	0.997427i	$0.477159\pi$
$548$	25.1046	−	430.913i	0.0458113	−	0.786338i
$549$		0			0
$550$	101.504	+	107.590i	0.184554	+	0.195618i
$551$	−570.164	+	329.184i	−1.03478	+	0.597431i
$552$		0			0
$553$	79.6104	−	137.889i	0.143961	−	0.249348i
$554$	−78.9637	−	333.186i	−0.142534	−	0.601418i
$555$		0			0
$556$	269.503	+	536.646i	0.484718	+	0.965191i
$557$	227.316			0.408108			0.204054	−	0.978960i	$-0.434588\pi$
$557$	227.316			0.408108			0.204054	+	0.978960i	$0.434588\pi$
$558$		0			0
$559$		−	390.218i		−	0.698064i
$560$	−137.239	+	59.1940i	−0.245069	+	0.105704i
$561$		0			0
$562$	−18.4462	−	77.8332i	−0.0328224	−	0.138493i
$563$	−671.826	−	387.879i	−1.19330	−	0.688950i	−0.234244	−	0.972178i	$-0.575262\pi$
$563$	−671.826	−	387.879i	−1.19330	−	0.688950i	−0.959053	+	0.283227i	$0.908595\pi$
$564$		0			0
$565$	−4.00292	−	6.93326i	−0.00708481	−	0.0122713i
$566$	536.496	+	568.661i	0.947872	+	1.00470i
$567$		0			0
$568$	463.076	−	388.549i	0.815275	−	0.684064i
$569$	−477.933	−	827.803i	−0.839952	−	1.45484i	−0.889934	−	0.456089i	$-0.849250\pi$
$569$	−477.933	−	827.803i	−0.839952	−	1.45484i	0.0499825	−	0.998750i	$-0.484083\pi$
$570$		0			0
$571$	754.720	+	435.738i	1.32175	+	0.763113i	0.984008	−	0.178125i	$-0.0570032\pi$
$571$	754.720	+	435.738i	1.32175	+	0.763113i	0.337743	+	0.941238i	$0.390337\pi$
$572$	256.927	−	390.625i	0.449172	−	0.682910i
$573$		0			0
$574$	31.7068	−	105.905i	0.0552384	−	0.184504i
$575$		−	239.078i		−	0.415787i
$576$		0			0
$577$	241.573			0.418671			0.209335	−	0.977844i	$-0.432870\pi$
$577$	241.573			0.418671			0.209335	+	0.977844i	$0.432870\pi$
$578$	143.175	+	42.8651i	0.247708	+	0.0741610i
$579$		0			0
$580$	278.372	+	183.094i	0.479951	+	0.315680i
$581$	69.9210	−	121.107i	0.120346	−	0.208445i
$582$		0			0
$583$	133.571	−	77.1170i	0.229109	−	0.132276i
$584$	291.655	+	347.598i	0.499410	+	0.595202i
$585$		0			0
$586$	732.399	−	690.972i	1.24983	−	1.17913i
$587$	−577.552	+	333.450i	−0.983905	+	0.568058i	−0.903447	−	0.428700i	$-0.858972\pi$
$587$	−577.552	+	333.450i	−0.983905	+	0.568058i	−0.0804579	+	0.996758i	$0.525638\pi$
$588$		0			0
$589$	−17.1764	+	29.7505i	−0.0291620	+	0.0505101i
$590$	−482.991	+	114.467i	−0.818629	+	0.194012i
$591$		0			0
$592$	−420.931	−	975.912i	−0.711032	−	1.64850i
$593$	−207.914			−0.350613			−0.175307	−	0.984514i	$-0.556092\pi$
$593$	−207.914			−0.350613			−0.175307	+	0.984514i	$0.556092\pi$
$594$		0			0
$595$			136.738i			0.229812i
$596$	−27.2818	+	13.7009i	−0.0457749	+	0.0229881i
$597$		0			0
$598$	−735.335	+	174.272i	−1.22966	+	0.291424i
$599$	−283.333	−	163.582i	−0.473010	−	0.273092i	0.244489	−	0.969652i	$-0.421380\pi$
$599$	−283.333	−	163.582i	−0.473010	−	0.273092i	−0.717499	+	0.696560i	$0.754713\pi$
$600$		0			0
$601$	−25.0218	−	43.3391i	−0.0416337	−	0.0721116i	0.844458	−	0.535622i	$-0.179923\pi$
$601$	−25.0218	−	43.3391i	−0.0416337	−	0.0721116i	−0.886091	+	0.463511i	$0.846590\pi$
$602$	130.853	−	123.451i	0.217363	−	0.205068i
$603$		0			0
$604$	−846.700	−	49.3279i	−1.40182	−	0.0816687i
$605$	83.6043	+	144.807i	0.138189	+	0.239350i
$606$		0			0
$607$	359.185	+	207.375i	0.591737	+	0.341640i	0.765784	−	0.643098i	$-0.222351\pi$
$607$	359.185	+	207.375i	0.591737	+	0.341640i	−0.174047	+	0.984737i	$0.555684\pi$
$608$	−1099.01	+	128.413i	−1.80759	+	0.211205i
$609$		0			0
$610$	−618.264	−	185.101i	−1.01355	−	0.303445i
$611$			322.093i			0.527158i
$612$		0			0
$613$	−287.998			−0.469817			−0.234909	−	0.972017i	$-0.575479\pi$
$613$	−287.998			−0.469817			−0.234909	+	0.972017i	$0.575479\pi$
$614$	59.1713	−	197.640i	0.0963701	−	0.321890i
$615$		0			0
$616$	212.271	−	37.4240i	0.344596	−	0.0607533i
$617$	127.843	−	221.430i	0.207201	−	0.358882i	−0.743631	−	0.668590i	$-0.766898\pi$
$617$	127.843	−	221.430i	0.207201	−	0.358882i	0.950832	+	0.309708i	$0.100231\pi$
$618$		0			0
$619$	−8.60391	+	4.96747i	−0.0138997	+	0.00802499i	−0.506934	−	0.861985i	$-0.669221\pi$
$619$	−8.60391	+	4.96747i	−0.0138997	+	0.00802499i	0.493034	+	0.870010i	$0.335888\pi$
$620$	17.3559	+	1.01114i	0.0279934	+	0.00163087i
$621$		0			0
$622$	−628.702	−	666.396i	−1.01078	−	1.07138i
$623$	277.469	−	160.197i	0.445375	−	0.257138i
$624$		0			0
$625$	222.059	−	384.618i	0.355295	−	0.615389i
$626$	8.59322	+	36.2589i	0.0137272	+	0.0579216i
$627$		0			0
$628$	219.162	−	110.063i	0.348983	−	0.175259i
$629$	−972.352			−1.54587
$630$		0			0
$631$		−	784.610i		−	1.24344i	−0.783240	−	0.621719i	$-0.786434\pi$
$631$		−	784.610i		−	1.24344i	0.783240	−	0.621719i	$-0.213566\pi$
$632$	−560.562	−	204.043i	−0.886966	−	0.322853i
$633$		0			0
$634$	99.5261	+	419.948i	0.156981	+	0.662379i
$635$	−176.786	−	102.067i	−0.278402	−	0.160736i
$636$		0			0
$637$	−205.833	−	356.513i	−0.323129	−	0.559676i
$638$	−329.742	−	349.512i	−0.516838	−	0.547825i
$639$		0			0
$640$	307.685	+	467.868i	0.480758	+	0.731045i
$641$	585.512	+	1014.14i	0.913436	+	1.58212i	0.809175	+	0.587567i	$0.199914\pi$
$641$	585.512	+	1014.14i	0.913436	+	1.58212i	0.104261	+	0.994550i	$0.466752\pi$
$642$		0			0
$643$	−466.249	−	269.189i	−0.725115	−	0.418645i	0.0915175	−	0.995803i	$-0.470828\pi$
$643$	−466.249	−	269.189i	−0.725115	−	0.418645i	−0.816632	+	0.577158i	$0.804162\pi$
$644$	−291.073	−	191.448i	−0.451976	−	0.297279i
$645$		0			0
$646$	−290.340	+	969.775i	−0.449443	+	1.50120i
$647$			170.070i			0.262860i	0.991325	+	0.131430i	$0.0419568\pi$
$647$			170.070i			0.262860i	−0.991325	+	0.131430i	$0.958043\pi$
$648$		0			0
$649$	715.842			1.10299
$650$	104.024	+	31.1438i	0.160038	+	0.0479135i
$651$		0			0
$652$	−55.6698	+	84.6389i	−0.0853831	+	0.129814i
$653$	−79.1035	+	137.011i	−0.121139	+	0.209818i	−0.920217	−	0.391409i	$-0.871988\pi$
$653$	−79.1035	+	137.011i	−0.121139	+	0.209818i	0.799078	+	0.601227i	$0.205321\pi$
$654$		0			0
$655$	−440.088	+	254.085i	−0.671891	+	0.387916i
$656$	−411.388	−	48.0973i	−0.627115	−	0.0733191i
$657$		0			0
$658$	−108.008	+	101.899i	−0.164146	+	0.154861i
$659$	227.314	−	131.240i	0.344938	−	0.199150i	−0.317516	−	0.948253i	$-0.602849\pi$
$659$	227.314	−	131.240i	0.344938	−	0.199150i	0.662453	+	0.749103i	$0.269515\pi$
$660$		0			0
$661$	133.649	−	231.487i	0.202192	−	0.350207i	−0.747042	−	0.664776i	$-0.768527\pi$
$661$	133.649	−	231.487i	0.202192	−	0.350207i	0.949234	+	0.314569i	$0.101860\pi$
$662$	−484.830	+	114.903i	−0.732372	+	0.173569i
$663$		0			0
$664$	−492.336	−	179.209i	−0.741471	−	0.269893i
$665$	323.001			0.485716
$666$		0			0
$667$			776.656i			1.16440i
$668$	−249.248	−	496.313i	−0.373126	−	0.742984i
$669$		0			0
$670$	−810.447	+	192.073i	−1.20962	+	0.286676i
$671$	806.040	+	465.367i	1.20125	+	0.693543i
$672$		0			0
$673$	47.8491	+	82.8770i	0.0710982	+	0.123146i	0.899383	−	0.437162i	$-0.144016\pi$
$673$	47.8491	+	82.8770i	0.0710982	+	0.123146i	−0.828285	+	0.560307i	$0.810683\pi$
$674$	−395.534	+	373.161i	−0.586846	+	0.553652i
$675$		0			0
$676$	−19.3539	+	332.204i	−0.0286300	+	0.491427i
$677$	266.057	+	460.825i	0.392995	+	0.680687i	0.992843	−	0.119427i	$-0.0381057\pi$
$677$	266.057	+	460.825i	0.392995	+	0.680687i	−0.599848	+	0.800114i	$0.704772\pi$
$678$		0			0
$679$	208.745	+	120.519i	0.307430	+	0.177495i
$680$	504.528	−	88.9497i	0.741952	−	0.130808i
$681$		0			0
$682$	−24.0190	−	7.19102i	−0.0352185	−	0.0105440i
$683$		−	622.200i		−	0.910981i	−0.890241	−	0.455491i	$-0.849464\pi$
$683$		−	622.200i		−	0.910981i	0.890241	−	0.455491i	$-0.150536\pi$
$684$		0			0
$685$	472.089			0.689181
$686$	114.448	−	382.273i	0.166834	−	0.557250i
$687$		0			0
$688$	−540.623	−	402.505i	−0.785789	−	0.585036i
$689$	56.6128	−	98.0562i	0.0821666	−	0.142317i
$690$		0			0
$691$	225.074	−	129.946i	0.325722	−	0.188056i	−0.328218	−	0.944602i	$-0.606448\pi$
$691$	225.074	−	129.946i	0.325722	−	0.188056i	0.653940	+	0.756546i	$0.273115\pi$
$692$	−20.9843	+	360.189i	−0.0303241	+	0.520505i
$693$		0			0
$694$	−444.981	−	471.660i	−0.641183	−	0.679625i
$695$	−568.793	+	328.393i	−0.818407	+	0.472508i
$696$		0			0
$697$	−189.467	+	328.166i	−0.271832	+	0.470826i
$698$	−46.6011	−	196.633i	−0.0667638	−	0.281708i
$699$		0			0
$700$	22.4661	+	44.7355i	0.0320945	+	0.0639078i
$701$	−1233.75			−1.75998			−0.879992	−	0.474988i	$-0.842452\pi$
$701$	−1233.75			−1.75998			−0.879992	+	0.474988i	$0.842452\pi$
$702$		0			0
$703$			2296.88i			3.26725i
$704$	−276.170	−	758.880i	−0.392286	−	1.07795i
$705$		0			0
$706$	70.0430	+	295.545i	0.0992111	+	0.418619i
$707$	81.2557	+	46.9130i	0.114930	+	0.0663550i
$708$		0			0
$709$	−124.002	−	214.778i	−0.174897	−	0.302930i	0.765229	−	0.643759i	$-0.222626\pi$
$709$	−124.002	−	214.778i	−0.174897	−	0.302930i	−0.940126	+	0.340828i	$0.889293\pi$
$710$	453.692	+	480.893i	0.639003	+	0.677315i
$711$		0			0
$712$	−771.580	−	919.577i	−1.08368	−	1.29154i
$713$	20.2625	+	35.0957i	0.0284186	+	0.0492225i
$714$		0			0
$715$	442.846	+	255.677i	0.619365	+	0.357591i
$716$	−91.6854	+	139.396i	−0.128052	+	0.194687i
$717$		0			0
$718$	341.195	−	1139.64i	0.475202	−	1.58724i
$719$			925.022i			1.28654i	0.765639	+	0.643270i	$0.222423\pi$
$719$			925.022i			1.28654i	−0.765639	+	0.643270i	$0.777577\pi$
$720$		0			0
$721$	−163.780			−0.227157
$722$	1599.12	+	478.759i	2.21485	+	0.663102i
$723$		0			0
$724$	282.932	+	186.094i	0.390790	+	0.257035i
$725$	55.7986	−	96.6459i	0.0769635	−	0.133305i
$726$		0			0
$727$	−611.539	+	353.072i	−0.841182	+	0.485657i	−0.857666	−	0.514207i	$-0.828086\pi$
$727$	−611.539	+	353.072i	−0.841182	+	0.485657i	0.0164837	+	0.999864i	$0.494753\pi$
$728$	121.217	−	101.709i	0.166507	−	0.139710i
$729$		0			0
$730$	−360.972	+	340.554i	−0.494482	+	0.466512i
$731$	−534.020	+	308.317i	−0.730533	+	0.421774i
$732$		0			0
$733$	392.416	−	679.684i	0.535356	−	0.927264i	−0.463790	−	0.885945i	$-0.653511\pi$
$733$	392.416	−	679.684i	0.535356	−	0.927264i	0.999146	−	0.0413185i	$-0.0131558\pi$
$734$	339.520	−	80.4649i	0.462561	−	0.109625i
$735$		0			0
$736$	−517.046	+	1198.52i	−0.702509	+	1.62842i
$737$	1201.17			1.62980
$738$		0			0
$739$			758.298i			1.02611i	0.858355	+	0.513057i	$0.171487\pi$
$739$			758.298i			1.02611i	−0.858355	+	0.513057i	$0.828513\pi$
$740$	1038.77	−	521.671i	1.40375	−	0.704960i
$741$		0			0
$742$	50.7916	−	12.0374i	0.0684523	−	0.0162229i
$743$	103.996	+	60.0421i	0.139968	+	0.0808103i	0.568349	−	0.822788i	$-0.307583\pi$
$743$	103.996	+	60.0421i	0.139968	+	0.0808103i	−0.428381	+	0.903598i	$0.640916\pi$
$744$		0			0
$745$	−16.6947	−	28.9161i	−0.0224090	−	0.0388136i
$746$	420.084	−	396.323i	0.563116	−	0.531264i
$747$		0			0
$748$	−737.578	−	42.9706i	−0.986067	−	0.0574473i
$749$	−10.1792	−	17.6310i	−0.0135904	−	0.0235393i
$750$		0			0
$751$	175.822	+	101.511i	0.234117	+	0.135167i	0.612470	−	0.790494i	$-0.290176\pi$
$751$	175.822	+	101.511i	0.234117	+	0.135167i	−0.378353	+	0.925661i	$0.623509\pi$
$752$	446.240	+	332.235i	0.593404	+	0.441802i
$753$		0			0
$754$	−337.929	−	101.172i	−0.448181	−	0.134181i
$755$		−	927.606i		−	1.22862i
$756$		0			0
$757$	690.610			0.912298			0.456149	−	0.889903i	$-0.349228\pi$
$757$	690.610			0.912298			0.456149	+	0.889903i	$0.349228\pi$
$758$	−149.448	+	499.177i	−0.197161	+	0.658545i
$759$		0			0
$760$	−210.116	−	1191.79i	−0.276468	−	1.56814i
$761$	574.862	−	995.691i	0.755404	−	1.30840i	−0.189770	−	0.981829i	$-0.560774\pi$
$761$	574.862	−	995.691i	0.755404	−	1.30840i	0.945173	−	0.326569i	$-0.105893\pi$
$762$		0			0
$763$	95.0517	−	54.8781i	0.124576	−	0.0719241i
$764$	−703.292	−	40.9731i	−0.920540	−	0.0536297i
$765$		0			0
$766$	481.488	+	510.355i	0.628574	+	0.666260i
$767$	455.105	−	262.755i	0.593358	−	0.342575i
$768$		0			0
$769$	317.346	−	549.659i	0.412673	−	0.714771i	−0.582508	−	0.812825i	$-0.697929\pi$
$769$	317.346	−	549.659i	0.412673	−	0.714771i	0.995181	+	0.0980542i	$0.0312618\pi$
$770$	54.3640	+	229.388i	0.0706025	+	0.297906i
$771$		0			0
$772$	1189.78	−	597.509i	1.54117	−	0.773975i
$773$	−267.560			−0.346132			−0.173066	−	0.984910i	$-0.555367\pi$
$773$	−267.560			−0.346132			−0.173066	+	0.984910i	$0.555367\pi$
$774$		0			0
$775$		−	5.82300i		−	0.00751355i
$776$	308.892	−	848.612i	0.398057	−	1.09357i
$777$		0			0
$778$	−15.2728	−	64.4432i	−0.0196308	−	0.0828319i
$779$	775.189	+	447.556i	0.995108	+	0.574526i
$780$		0			0
$781$	−476.727	−	825.716i	−0.610406	−	1.05725i
$782$	819.492	+	868.624i	1.04794	+	1.11077i
$783$		0			0
$784$	−706.241	−	82.5701i	−0.900818	−	0.105319i
$785$	134.113	+	232.290i	0.170844	+	0.295911i
$786$		0			0
$787$	−563.164	−	325.143i	−0.715583	−	0.413142i	0.0975416	−	0.995231i	$-0.468902\pi$
$787$	−563.164	−	325.143i	−0.715583	−	0.413142i	−0.813125	+	0.582089i	$0.802235\pi$
$788$	−458.636	−	301.660i	−0.582026	−	0.382817i
$789$		0			0
$790$	187.127	−	625.028i	0.236869	−	0.791175i
$791$			3.90748i			0.00493993i
$792$		0			0
$793$	683.266			0.861622
$794$	−684.293	−	204.870i	−0.861830	−	0.258022i
$795$		0			0
$796$	−628.998	+	956.313i	−0.790199	+	1.20140i
$797$	503.422	−	871.953i	0.631646	−	1.09404i	−0.355569	−	0.934650i	$-0.615713\pi$
$797$	503.422	−	871.953i	0.631646	−	1.09404i	0.987215	−	0.159393i	$-0.0509538\pi$
$798$		0			0
$799$	440.790	−	254.490i	0.551677	−	0.318511i
$800$	150.448	−	111.995i	0.188059	−	0.139994i
$801$		0			0
$802$	−462.970	+	436.783i	−0.577269	+	0.544617i
$803$	619.805	−	357.845i	0.771862	−	0.445635i
$804$		0			0
$805$	190.517	−	329.985i	0.236667	−	0.409919i
$806$	−17.9099	+	4.24458i	−0.0222207	+	0.00526622i
$807$		0			0
$808$	120.239	−	330.329i	0.148810	−	0.408824i
$809$	135.483			0.167469			0.0837347	−	0.996488i	$-0.473315\pi$
$809$	135.483			0.167469			0.0837347	+	0.996488i	$0.473315\pi$
$810$		0			0
$811$		−	86.4723i		−	0.106624i	−0.998578	−	0.0533122i	$-0.983022\pi$
$811$		−	86.4723i		−	0.106624i	0.998578	−	0.0533122i	$-0.0169778\pi$
$812$	−72.9824	−	145.326i	−0.0898798	−	0.178972i
$813$		0			0
$814$	−1631.19	+	386.585i	−2.00391	+	0.474920i
$815$	−95.9540	−	55.3991i	−0.117735	−	0.0679743i
$816$		0			0
$817$	728.301	+	1261.45i	0.891433	+	1.54401i
$818$	747.172	−	704.909i	0.913413	−	0.861748i
$819$		0			0
$820$	26.3466	−	452.232i	0.0321300	−	0.551503i
$821$	334.340	+	579.094i	0.407235	+	0.705352i	0.994579	−	0.103986i	$-0.0331596\pi$
$821$	334.340	+	579.094i	0.407235	+	0.705352i	−0.587344	+	0.809338i	$0.699826\pi$
$822$		0			0
$823$	710.023	+	409.932i	0.862725	+	0.498095i	0.864924	−	0.501903i	$-0.167367\pi$
$823$	710.023	+	409.932i	0.862725	+	0.498095i	−0.00219864	+	0.999998i	$0.500700\pi$
$824$	106.541	+	604.305i	0.129297	+	0.733380i
$825$		0			0
$826$	232.089	+	69.4849i	0.280980	+	0.0841222i
$827$			357.121i			0.431827i	0.976413	+	0.215913i	$0.0692729\pi$
$827$			357.121i			0.431827i	−0.976413	+	0.215913i	$0.930727\pi$
$828$		0			0
$829$	257.314			0.310390			0.155195	−	0.987884i	$-0.450399\pi$
$829$	257.314			0.310390			0.155195	+	0.987884i	$0.450399\pi$
$830$	164.351	−	548.956i	0.198014	−	0.661393i
$831$		0			0
$832$	−454.131	−	381.097i	−0.545830	−	0.458050i
$833$	−325.263	+	563.372i	−0.390472	+	0.676317i
$834$		0			0
$835$	526.044	−	303.712i	0.629993	−	0.363726i
$836$	−101.504	+	1742.30i	−0.121417	+	2.08409i
$837$		0			0
$838$	99.4405	+	105.402i	0.118664	+	0.125779i
$839$	580.117	−	334.931i	0.691439	−	0.399203i	−0.112712	−	0.993628i	$-0.535954\pi$
$839$	580.117	−	334.931i	0.691439	−	0.399203i	0.804151	+	0.594425i	$0.202620\pi$
$840$		0			0
$841$	239.235	−	414.368i	0.284465	−	0.492709i
$842$	291.136	+	1228.44i	0.345767	+	1.45896i
$843$		0			0
$844$	566.017	+	1127.08i	0.670637	+	1.33540i
$845$	−363.948			−0.430708
$846$		0			0
$847$		−	81.6110i		−	0.0963530i
$848$	−77.4554	−	179.577i	−0.0913389	−	0.211765i
$849$		0			0
$850$	−39.5704	−	166.966i	−0.0465534	−	0.196431i
$851$	2346.54	+	1354.78i	2.75739	+	1.59198i
$852$		0			0
$853$	444.254	+	769.470i	0.520813	+	0.902075i	0.999707	+	0.0242024i	$0.00770462\pi$
$853$	444.254	+	769.470i	0.520813	+	0.902075i	−0.478894	+	0.877873i	$0.658962\pi$
$854$	216.161	+	229.121i	0.253116	+	0.268291i
$855$		0			0
$856$	−58.4318	+	49.0278i	−0.0682615	+	0.0572755i
$857$	−238.204	−	412.582i	−0.277951	−	0.481426i	0.692924	−	0.721011i	$-0.256322\pi$
$857$	−238.204	−	412.582i	−0.277951	−	0.481426i	−0.970876	+	0.239585i	$0.922989\pi$
$858$		0			0
$859$	−719.684	−	415.510i	−0.837816	−	0.483714i	0.0187050	−	0.999825i	$-0.494046\pi$
$859$	−719.684	−	415.510i	−0.837816	−	0.483714i	−0.856521	+	0.516112i	$0.827379\pi$
$860$	405.085	−	615.881i	0.471029	−	0.716141i
$861$		0			0
$862$	42.0592	−	140.483i	0.0487926	−	0.162974i
$863$		−	985.009i		−	1.14138i	−0.821166	−	0.570689i	$-0.806676\pi$
$863$		−	985.009i		−	1.14138i	0.821166	−	0.570689i	$-0.193324\pi$
$864$		0			0
$865$	−394.607			−0.456193
$866$	1102.23	+	329.996i	1.27279	+	0.381058i
$867$		0			0
$868$	−7.08939	−	4.66293i	−0.00816751	−	0.00537204i
$869$	−470.459	+	814.859i	−0.541380	+	0.937697i
$870$		0			0
$871$	763.655	−	440.897i	0.876757	−	0.506196i
$872$	−264.318	−	315.017i	−0.303117	−	0.361258i
$873$		0			0
$874$	2051.85	−	1935.79i	2.34766	−	2.21487i
$875$	−249.660	+	144.141i	−0.285326	+	0.164733i
$876$		0			0
$877$	−266.136	+	460.961i	−0.303462	+	0.525611i	−0.976918	−	0.213616i	$-0.931476\pi$
$877$	−266.136	+	460.961i	−0.303462	+	0.525611i	0.673456	+	0.739227i	$0.264809\pi$
$878$	−464.436	+	110.070i	−0.528970	+	0.125364i
$879$		0			0
$880$	811.015	−	349.808i	0.921608	−	0.397509i
$881$	−1579.81			−1.79320			−0.896599	−	0.442844i	$-0.853970\pi$
$881$	−1579.81			−1.79320			−0.896599	+	0.442844i	$0.853970\pi$
$882$		0			0
$883$		−	89.6114i		−	0.101485i	−0.998712	−	0.0507426i	$-0.983841\pi$
$883$		−	89.6114i		−	0.101485i	0.998712	−	0.0507426i	$-0.0161588\pi$
$884$	−484.697	+	243.414i	−0.548300	+	0.275356i
$885$		0			0
$886$	−101.945	+	24.1605i	−0.115062	+	0.0272692i
$887$	−79.9393	−	46.1530i	−0.0901232	−	0.0520327i	0.454261	−	0.890869i	$-0.349903\pi$
$887$	−79.9393	−	46.1530i	−0.0901232	−	0.0520327i	−0.544384	+	0.838836i	$0.683237\pi$
$888$		0			0
$889$	49.8168	+	86.2853i	0.0560369	+	0.0970588i
$890$	954.958	−	900.943i	1.07299	−	1.01230i
$891$		0			0
$892$	119.302	+	6.95039i	0.133746	+	0.00779192i
$893$	−601.153	−	1041.23i	−0.673184	−	1.16599i
$894$		0			0
$895$	−158.032	−	91.2396i	−0.176572	−	0.101944i
$896$	−15.8768	−	272.850i	−0.0177196	−	0.304520i
$897$		0			0
$898$	−1084.62	−	324.722i	−1.20781	−	0.361606i
$899$			18.9163i			0.0210415i
$900$		0			0
$901$	−178.922			−0.198582
$902$	−187.372	+	625.848i	−0.207729	+	0.693845i
$903$		0			0
$904$	14.4176	−	2.54186i	0.0159486	−	0.00281179i
$905$	−185.189	+	320.756i	−0.204628	+	0.354427i
$906$		0			0
$907$	−457.854	+	264.342i	−0.504801	+	0.291447i	−0.730694	−	0.682705i	$-0.760803\pi$
$907$	−457.854	+	264.342i	−0.504801	+	0.291447i	0.225893	+	0.974152i	$0.427470\pi$
$908$	−1419.26	−	82.6846i	−1.56306	−	0.0910623i
$909$		0			0
$910$	118.761	+	125.881i	0.130507	+	0.138331i
$911$	291.269	−	168.164i	0.319725	−	0.184593i	−0.331545	−	0.943439i	$-0.607570\pi$
$911$	291.269	−	168.164i	0.319725	−	0.184593i	0.651270	+	0.758846i	$0.274237\pi$
$912$		0			0
$913$	−413.200	+	715.683i	−0.452573	+	0.783880i
$914$	−15.8473	−	66.8672i	−0.0173384	−	0.0731589i
$915$		0			0
$916$	−315.223	+	158.305i	−0.344130	+	0.172822i
$917$	248.027			0.270477
$918$		0			0
$919$			1037.58i			1.12903i	0.825423	+	0.564515i	$0.190937\pi$
$919$			1037.58i			1.12903i	−0.825423	+	0.564515i	$0.809063\pi$
$920$	−1341.49	−	488.298i	−1.45814	−	0.530759i
$921$		0			0
$922$	125.702	+	530.397i	0.136336	+	0.575268i
$923$	−606.170	−	349.973i	−0.656739	−	0.379169i
$924$		0			0
$925$	−194.667	−	337.172i	−0.210450	−	0.364511i
$926$	776.168	+	822.703i	0.838194	+	0.888448i
$927$		0			0
$928$	−488.737	+	363.821i	−0.526656	+	0.392049i
$929$	−248.930	−	431.159i	−0.267954	−	0.464111i	0.700379	−	0.713771i	$-0.253014\pi$
$929$	−248.930	−	431.159i	−0.267954	−	0.464111i	−0.968333	+	0.249661i	$0.919681\pi$
$930$		0			0
$931$	1330.79	+	768.332i	1.42942	+	0.825276i
$932$	841.228	+	553.303i	0.902605	+	0.593673i
$933$		0			0
$934$	512.775	−	1712.74i	0.549009	−	1.83377i
$935$		−	808.057i		−	0.864232i
$936$		0			0
$937$	1236.91			1.32008			0.660039	−	0.751231i	$-0.270540\pi$
$937$	1236.91			1.32008			0.660039	+	0.751231i	$0.270540\pi$
$938$	389.440	+	116.594i	0.415181	+	0.124301i
$939$		0			0
$940$	−334.365	+	508.360i	−0.355707	+	0.540808i
$941$	337.684	−	584.887i	0.358857	−	0.621558i	−0.628913	−	0.777476i	$-0.716500\pi$
$941$	337.684	−	584.887i	0.358857	−	0.621558i	0.987770	+	0.155917i	$0.0498333\pi$
$942$		0			0
$943$	914.466	−	527.967i	0.969741	−	0.559880i
$944$	105.404	−	901.549i	0.111657	−	0.955030i
$945$		0			0
$946$	−773.275	+	729.536i	−0.817415	+	0.771180i
$947$	−160.432	+	92.6256i	−0.169411	+	0.0978095i	−0.582308	−	0.812968i	$-0.697850\pi$
$947$	−160.432	+	92.6256i	−0.169411	+	0.0978095i	0.412897	+	0.910778i	$0.364517\pi$
$948$		0			0
$949$	262.699	−	455.008i	0.276817	−	0.479461i
$950$	−394.405	+	93.4726i	−0.415164	+	0.0983922i
$951$		0			0
$952$	−234.965	−	85.5266i	−0.246812	−	0.0898389i
$953$	399.942			0.419667			0.209833	−	0.977737i	$-0.432708\pi$
$953$	399.942			0.419667			0.209833	+	0.977737i	$0.432708\pi$
$954$		0			0
$955$		−	770.495i		−	0.806801i
$956$	−255.397	−	508.557i	−0.267152	−	0.531963i
$957$		0			0
$958$	1051.10	−	249.106i	1.09718	−	0.260027i
$959$	−199.547	−	115.208i	−0.208078	−	0.120134i
$960$		0			0
$961$	−480.006	−	831.396i	−0.499486	−	0.865136i
$962$	−895.147	+	844.515i	−0.930507	+	0.877874i
$963$		0			0
$964$	−13.2682	+	227.745i	−0.0137637	+	0.236250i
$965$	728.071	+	1261.06i	0.754478	+	1.30679i
$966$		0			0
$967$	62.7437	+	36.2251i	0.0648849	+	0.0374613i	0.532091	−	0.846687i	$-0.321406\pi$
$967$	62.7437	+	36.2251i	0.0648849	+	0.0374613i	−0.467207	+	0.884148i	$0.654740\pi$
$968$	−301.123	+	53.0888i	−0.311077	+	0.0548438i
$969$		0			0
$970$	946.205	+	283.283i	0.975469	+	0.292044i
$971$			1165.69i			1.20051i	0.799810	+	0.600253i	$0.204933\pi$
$971$			1165.69i			1.20051i	−0.799810	+	0.600253i	$0.795067\pi$
$972$		0			0
$973$	320.563			0.329458
$974$	−297.526	+	993.779i	−0.305469	+	1.02031i
$975$		0			0
$976$	704.780	−	946.623i	0.722111	−	0.969900i
$977$	−182.949	+	316.877i	−0.187256	+	0.324337i	−0.944334	−	0.328987i	$-0.893293\pi$
$977$	−182.949	+	316.877i	−0.187256	+	0.324337i	0.757078	+	0.653324i	$0.226626\pi$
$978$		0			0
$979$	−1639.71	+	946.685i	−1.67488	+	0.966992i
$980$	45.2300	−	776.360i	0.0461531	−	0.792205i
$981$		0			0
$982$	206.333	+	218.703i	0.210115	+	0.222712i
$983$	−892.550	+	515.314i	−0.907986	+	0.524226i	−0.879782	−	0.475376i	$-0.842312\pi$
$983$	−892.550	+	515.314i	−0.907986	+	0.524226i	−0.0282031	+	0.999602i	$0.508979\pi$
$984$		0			0
$985$	300.193	−	519.950i	0.304765	−	0.527868i
$986$	128.546	+	542.399i	0.130372	+	0.550100i
$987$		0			0
$988$	574.990	+	1144.94i	0.581974	+	1.15885i
$989$	1718.31			1.73742
$990$		0			0
$991$		−	1893.70i		−	1.91090i	−0.295148	−	0.955451i	$-0.595369\pi$
$991$		−	1893.70i		−	1.91090i	0.295148	−	0.955451i	$-0.404631\pi$
$992$	−12.5932	+	29.1913i	−0.0126948	+	0.0294267i
$993$		0			0
$994$	−74.4137	−	313.987i	−0.0748629	−	0.315882i
$995$	−1084.16	−	625.940i	−1.08961	−	0.629085i
$996$		0			0
$997$	644.593	+	1116.47i	0.646533	+	1.11983i	0.983945	+	0.178471i	$0.0571150\pi$
$997$	644.593	+	1116.47i	0.646533	+	1.11983i	−0.337412	+	0.941357i	$0.609552\pi$
$998$	−421.158	−	446.408i	−0.422002	−	0.447303i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.r.271.1		12
3.2	odd	2		324.3.f.q.271.6		12
4.3	odd	2	inner	324.3.f.r.271.4		12
9.2	odd	6		324.3.f.q.55.3		12
9.4	even	3		324.3.d.e.163.5	✓	6
9.5	odd	6		324.3.d.f.163.2	yes	6
9.7	even	3	inner	324.3.f.r.55.4		12
12.11	even	2		324.3.f.q.271.3		12
36.7	odd	6	inner	324.3.f.r.55.1		12
36.11	even	6		324.3.f.q.55.6		12
36.23	even	6		324.3.d.f.163.1	yes	6
36.31	odd	6		324.3.d.e.163.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.5	✓	6	9.4	even	3
324.3.d.e.163.6	yes	6	36.31	odd	6
324.3.d.f.163.1	yes	6	36.23	even	6
324.3.d.f.163.2	yes	6	9.5	odd	6
324.3.f.q.55.3		12	9.2	odd	6
324.3.f.q.55.6		12	36.11	even	6
324.3.f.q.271.3		12	12.11	even	2
324.3.f.q.271.6		12	3.2	odd	2
324.3.f.r.55.1		12	36.7	odd	6	inner
324.3.f.r.55.4		12	9.7	even	3	inner
324.3.f.r.271.1		12	1.1	even	1	trivial
324.3.f.r.271.4		12	4.3	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91597 - 0.573621i) q^{2} +(3.34192 + 2.19809i) q^{4} +(-2.18740 + 3.78869i) q^{5} +(1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +O(q^{10})\)	\(q+(-1.91597 - 0.573621i) q^{2} +(3.34192 + 2.19809i) q^{4} +(-2.18740 + 3.78869i) q^{5} +(1.84918 - 1.06762i) q^{7} +(-5.14216 - 6.12848i) q^{8} +(6.36427 - 6.00429i) q^{10} +(-10.9277 + 6.30914i) q^{11} +(-4.63163 + 8.02222i) q^{13} +(-4.15539 + 0.984811i) q^{14} +(6.33682 + 14.6917i) q^{16} +14.6381 q^{17} -34.5778i q^{19} +(-15.6380 + 7.85338i) q^{20} +(24.5563 - 5.81976i) q^{22} +(-35.3255 - 20.3952i) q^{23} +(2.93057 + 5.07589i) q^{25} +(13.4758 - 12.7136i) q^{26} +(8.52653 + 0.496747i) q^{28} +(-9.52010 - 16.4893i) q^{29} +(-0.860391 - 0.496747i) q^{31} +(-3.71373 - 31.7838i) q^{32} +(-28.0462 - 8.39671i) q^{34} +9.34128i q^{35} -66.4263 q^{37} +(-19.8346 + 66.2502i) q^{38} +(34.4668 - 6.07660i) q^{40} +(-12.9434 + 22.4187i) q^{41} +(-36.4816 + 21.0627i) q^{43} +(-50.3877 - 2.93554i) q^{44} +(55.9836 + 59.3401i) q^{46} +(30.1126 - 17.3855i) q^{47} +(-22.2204 + 38.4868i) q^{49} +(-2.70325 - 11.4063i) q^{50} +(-33.1121 + 16.6289i) q^{52} -12.2231 q^{53} -55.2024i q^{55} +(-16.0517 - 5.84275i) q^{56} +(8.78165 + 37.0540i) q^{58} +(-49.1301 - 28.3653i) q^{59} +(-36.8804 - 63.8788i) q^{61} +(1.36354 + 1.44529i) q^{62} +(-11.1164 + 63.0272i) q^{64} +(-20.2625 - 35.0956i) q^{65} +(-82.4391 - 47.5962i) q^{67} +(48.9192 + 32.1758i) q^{68} +(5.35836 - 17.8976i) q^{70} +75.5614i q^{71} -56.7185 q^{73} +(127.271 + 38.1035i) q^{74} +(76.0051 - 115.556i) q^{76} +(-13.4716 + 23.3334i) q^{77} +(64.5777 - 37.2839i) q^{79} +(-69.5232 - 8.12830i) q^{80} +(37.6591 - 35.5290i) q^{82} +(56.7179 - 32.7461i) q^{83} +(-32.0193 + 55.4590i) q^{85} +(81.9798 - 19.4289i) q^{86} +(94.8576 + 34.5279i) q^{88} +150.050 q^{89} +19.7794i q^{91} +(-73.2244 - 145.808i) q^{92} +(-67.6677 + 16.0370i) q^{94} +(131.005 + 75.6355i) q^{95} +(56.4426 + 97.7615i) q^{97} +(64.6505 - 60.9936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

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