LMFDB - Embedded newform 288.3.u.b.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	288.19
Dual form			288.3.u.b.91.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92437 + 0.544810i) q^{2} +(3.40636 + 2.09683i) q^{4} +(8.76568 - 3.63086i) q^{5} +(-4.20494 - 4.20494i) q^{7} +(5.41272 + 5.89088i) q^{8} +O(q^{10})$	\(q+(1.92437 + 0.544810i) q^{2} +(3.40636 + 2.09683i) q^{4} +(8.76568 - 3.63086i) q^{5} +(-4.20494 - 4.20494i) q^{7} +(5.41272 + 5.89088i) q^{8} +(18.8465 - 2.21148i) q^{10} +(5.56206 - 2.30388i) q^{11} +(-14.9974 - 6.21214i) q^{13} +(-5.80095 - 10.3827i) q^{14} +(7.20663 + 14.2851i) q^{16} -12.9832i q^{17} +(-10.3282 + 24.9345i) q^{19} +(37.4724 + 6.01208i) q^{20} +(11.9586 - 1.40324i) q^{22} +(-8.55583 + 8.55583i) q^{23} +(45.9763 - 45.9763i) q^{25} +(-25.4761 - 20.1252i) q^{26} +(-5.50653 - 23.1406i) q^{28} +(-9.46145 + 22.8420i) q^{29} +48.3450i q^{31} +(6.08552 + 31.4160i) q^{32} +(7.07337 - 24.9844i) q^{34} +(-52.1268 - 21.5916i) q^{35} +(11.1557 - 4.62085i) q^{37} +(-33.4598 + 42.3561i) q^{38} +(68.8351 + 31.9848i) q^{40} +(27.8116 + 27.8116i) q^{41} +(-12.7950 + 5.29987i) q^{43} +(23.7772 + 3.81482i) q^{44} +(-21.1258 + 11.8032i) q^{46} +11.5912 q^{47} -13.6369i q^{49} +(113.524 - 63.4269i) q^{50} +(-38.0610 - 52.6079i) q^{52} +(-14.2996 - 34.5222i) q^{53} +(40.3902 - 40.3902i) q^{55} +(2.01066 - 47.5310i) q^{56} +(-30.6518 + 38.8016i) q^{58} +(0.579648 + 1.39939i) q^{59} +(-26.5897 + 64.1932i) q^{61} +(-26.3388 + 93.0334i) q^{62} +(-5.40501 + 63.7714i) q^{64} -154.018 q^{65} +(-27.4843 - 11.3844i) q^{67} +(27.2235 - 44.2255i) q^{68} +(-88.5476 - 69.9494i) q^{70} +(-68.0841 - 68.0841i) q^{71} +(-44.4027 - 44.4027i) q^{73} +(23.9852 - 2.81446i) q^{74} +(-87.4648 + 63.2794i) q^{76} +(-33.0758 - 13.7005i) q^{77} -128.678 q^{79} +(115.038 + 99.0525i) q^{80} +(38.3677 + 68.6718i) q^{82} +(28.1951 - 68.0690i) q^{83} +(-47.1402 - 113.806i) q^{85} +(-27.5097 + 3.22803i) q^{86} +(43.6778 + 20.2952i) q^{88} +(-24.5112 + 24.5112i) q^{89} +(36.9417 + 89.1851i) q^{91} +(-47.0843 + 11.2042i) q^{92} +(22.3057 + 6.31499i) q^{94} +256.068i q^{95} +114.722 q^{97} +(7.42952 - 26.2424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) $ 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.92437	+	0.544810i	0.962183	+	0.272405i
$2$	1.92437	+	0.544810i	0.962183	+	0.272405i
$3$		0			0
$3$		0			0
$4$	3.40636	+	2.09683i	0.851591	+	0.524207i
$5$	8.76568	−	3.63086i	1.75314	−	0.726173i	0.755676	−	0.654945i	$-0.227308\pi$
$5$	8.76568	−	3.63086i	1.75314	−	0.726173i	0.997460	−	0.0712277i	$-0.0226917\pi$
$6$		0			0
$7$	−4.20494	−	4.20494i	−0.600706	−	0.600706i	0.339794	−	0.940500i	$-0.389643\pi$
$7$	−4.20494	−	4.20494i	−0.600706	−	0.600706i	−0.940500	+	0.339794i	$0.889643\pi$
$8$	5.41272	+	5.89088i	0.676590	+	0.736360i
$9$		0			0
$10$	18.8465	−	2.21148i	1.88465	−	0.221148i
$11$	5.56206	−	2.30388i	0.505642	−	0.209444i	−0.115255	−	0.993336i	$-0.536769\pi$
$11$	5.56206	−	2.30388i	0.505642	−	0.209444i	0.620897	+	0.783892i	$0.286769\pi$
$12$		0			0
$13$	−14.9974	−	6.21214i	−1.15365	−	0.477857i	−0.277894	−	0.960612i	$-0.589636\pi$
$13$	−14.9974	−	6.21214i	−1.15365	−	0.477857i	−0.875756	+	0.482755i	$0.839636\pi$
$14$	−5.80095	−	10.3827i	−0.414354	−	0.741624i
$15$		0			0
$16$	7.20663	+	14.2851i	0.450414	+	0.892820i
$17$		−	12.9832i		−	0.763717i	−0.924221	−	0.381858i	$-0.875284\pi$
$17$		−	12.9832i		−	0.763717i	0.924221	−	0.381858i	$-0.124716\pi$
$18$		0			0
$19$	−10.3282	+	24.9345i	−0.543589	+	1.31234i	0.378586	+	0.925566i	$0.376411\pi$
$19$	−10.3282	+	24.9345i	−0.543589	+	1.31234i	−0.922175	+	0.386774i	$0.873589\pi$
$20$	37.4724	+	6.01208i	1.87362	+	0.300604i
$21$		0			0
$22$	11.9586	−	1.40324i	0.543573	−	0.0637837i
$23$	−8.55583	+	8.55583i	−0.371992	+	0.371992i	−0.868203	−	0.496210i	$-0.834725\pi$
$23$	−8.55583	+	8.55583i	−0.371992	+	0.371992i	0.496210	+	0.868203i	$0.334725\pi$
$24$		0			0
$25$	45.9763	−	45.9763i	1.83905	−	1.83905i
$26$	−25.4761	−	20.1252i	−0.979851	−	0.774046i
$27$		0			0
$28$	−5.50653	−	23.1406i	−0.196662	−	0.826450i
$29$	−9.46145	+	22.8420i	−0.326257	+	0.787654i	0.672607	+	0.740000i	$0.265174\pi$
$29$	−9.46145	+	22.8420i	−0.326257	+	0.787654i	−0.998864	+	0.0476539i	$0.984826\pi$
$30$		0			0
$31$			48.3450i			1.55952i	0.626081	+	0.779758i	$0.284658\pi$
$31$			48.3450i			1.55952i	−0.626081	+	0.779758i	$0.715342\pi$
$32$	6.08552	+	31.4160i	0.190172	+	0.981751i
$33$		0			0
$34$	7.07337	−	24.9844i	0.208040	−	0.734835i
$35$	−52.1268	−	21.5916i	−1.48934	−	0.616903i
$36$		0			0
$37$	11.1557	−	4.62085i	0.301506	−	0.124888i	−0.226802	−	0.973941i	$-0.572827\pi$
$37$	11.1557	−	4.62085i	0.301506	−	0.124888i	0.528307	+	0.849053i	$0.322827\pi$
$38$	−33.4598	+	42.3561i	−0.880520	+	1.11463i
$39$		0			0
$40$	68.8351	+	31.9848i	1.72088	+	0.799619i
$41$	27.8116	+	27.8116i	0.678332	+	0.678332i	0.959623	−	0.281291i	$-0.0907625\pi$
$41$	27.8116	+	27.8116i	0.678332	+	0.678332i	−0.281291	+	0.959623i	$0.590762\pi$
$42$		0			0
$43$	−12.7950	+	5.29987i	−0.297558	+	0.123253i	−0.526468	−	0.850195i	$-0.676484\pi$
$43$	−12.7950	+	5.29987i	−0.297558	+	0.123253i	0.228910	+	0.973448i	$0.426484\pi$
$44$	23.7772	+	3.81482i	0.540392	+	0.0867005i
$45$		0			0
$46$	−21.1258	+	11.8032i	−0.459257	+	0.256592i
$47$	11.5912			0.246621			0.123310	−	0.992368i	$-0.460649\pi$
$47$	11.5912			0.246621			0.123310	+	0.992368i	$0.460649\pi$
$48$		0			0
$49$		−	13.6369i		−	0.278304i
$50$	113.524	−	63.4269i	2.27047	−	1.26854i
$51$		0			0
$52$	−38.0610	−	52.6079i	−0.731941	−	1.01169i
$53$	−14.2996	−	34.5222i	−0.269803	−	0.651362i	0.729671	−	0.683799i	$-0.239673\pi$
$53$	−14.2996	−	34.5222i	−0.269803	−	0.651362i	−0.999474	+	0.0324364i	$0.989673\pi$
$54$		0			0
$55$	40.3902	−	40.3902i	0.734367	−	0.734367i
$56$	2.01066	−	47.5310i	0.0359047	−	0.848768i
$57$		0			0
$58$	−30.6518	+	38.8016i	−0.528480	+	0.668993i
$59$	0.579648	+	1.39939i	0.00982454	+	0.0237185i	0.928716	−	0.370793i	$-0.120914\pi$
$59$	0.579648	+	1.39939i	0.00982454	+	0.0237185i	−0.918891	+	0.394511i	$0.870914\pi$
$60$		0			0
$61$	−26.5897	+	64.1932i	−0.435897	+	1.05235i	0.541455	+	0.840729i	$0.317873\pi$
$61$	−26.5897	+	64.1932i	−0.435897	+	1.05235i	−0.977352	+	0.211619i	$0.932127\pi$
$62$	−26.3388	+	93.0334i	−0.424820	+	1.50054i
$63$		0			0
$64$	−5.40501	+	63.7714i	−0.0844532	+	0.996427i
$65$	−154.018			−2.36951
$66$		0			0
$67$	−27.4843	−	11.3844i	−0.410214	−	0.169916i	0.168027	−	0.985782i	$-0.446261\pi$
$67$	−27.4843	−	11.3844i	−0.410214	−	0.169916i	−0.578241	+	0.815866i	$0.696261\pi$
$68$	27.2235	−	44.2255i	0.400346	−	0.650374i
$69$		0			0
$70$	−88.5476	−	69.9494i	−1.26497	−	0.999276i
$71$	−68.0841	−	68.0841i	−0.958931	−	0.958931i	0.0402582	−	0.999189i	$-0.487182\pi$
$71$	−68.0841	−	68.0841i	−0.958931	−	0.958931i	−0.999189	+	0.0402582i	$0.987182\pi$
$72$		0			0
$73$	−44.4027	−	44.4027i	−0.608256	−	0.608256i	0.334234	−	0.942490i	$-0.391522\pi$
$73$	−44.4027	−	44.4027i	−0.608256	−	0.608256i	−0.942490	+	0.334234i	$0.891522\pi$
$74$	23.9852	−	2.81446i	0.324124	−	0.0380332i
$75$		0			0
$76$	−87.4648	+	63.2794i	−1.15085	+	0.832624i
$77$	−33.0758	−	13.7005i	−0.429556	−	0.177928i
$78$		0			0
$79$	−128.678			−1.62884			−0.814418	−	0.580278i	$-0.802944\pi$
$79$	−128.678			−1.62884			−0.814418	+	0.580278i	$0.802944\pi$
$80$	115.038	+	99.0525i	1.43798	+	1.23816i
$81$		0			0
$82$	38.3677	+	68.6718i	0.467898	+	0.837460i
$83$	28.1951	−	68.0690i	0.339700	−	0.820109i	−0.658044	−	0.752979i	$-0.728616\pi$
$83$	28.1951	−	68.0690i	0.339700	−	0.820109i	0.997744	−	0.0671293i	$-0.0213840\pi$
$84$		0			0
$85$	−47.1402	−	113.806i	−0.554590	−	1.33890i
$86$	−27.5097	+	3.22803i	−0.319880	+	0.0375352i
$87$		0			0
$88$	43.6778	+	20.2952i	0.496338	+	0.230627i
$89$	−24.5112	+	24.5112i	−0.275406	+	0.275406i	−0.831272	−	0.555866i	$-0.812387\pi$
$89$	−24.5112	+	24.5112i	−0.275406	+	0.275406i	0.555866	+	0.831272i	$0.312387\pi$
$90$		0			0
$91$	36.9417	+	89.1851i	0.405953	+	0.980056i
$92$	−47.0843	+	11.2042i	−0.511786	+	0.121784i
$93$		0			0
$94$	22.3057	+	6.31499i	0.237294	+	0.0671807i
$95$			256.068i			2.69545i
$96$		0			0
$97$	114.722			1.18270			0.591351	−	0.806415i	$-0.298595\pi$
$97$	114.722			1.18270			0.591351	+	0.806415i	$0.298595\pi$
$98$	7.42952	−	26.2424i	0.0758115	−	0.267779i
$99$		0			0
$100$	253.017	−	60.2077i	2.53017	−	0.602077i
$101$	103.219	−	42.7548i	1.02197	−	0.423315i	0.192164	−	0.981363i	$-0.438449\pi$
$101$	103.219	−	42.7548i	1.02197	−	0.423315i	0.829809	+	0.558048i	$0.188449\pi$
$102$		0			0
$103$	−46.3769	−	46.3769i	−0.450261	−	0.450261i	0.445180	−	0.895441i	$-0.353140\pi$
$103$	−46.3769	−	46.3769i	−0.450261	−	0.450261i	−0.895441	+	0.445180i	$0.853140\pi$
$104$	−44.5819	−	121.973i	−0.428672	−	1.17281i
$105$		0			0
$106$	−8.70954	−	74.2239i	−0.0821655	−	0.700225i
$107$	59.8100	−	24.7741i	0.558972	−	0.231534i	−0.0852669	−	0.996358i	$-0.527174\pi$
$107$	59.8100	−	24.7741i	0.558972	−	0.231534i	0.644239	+	0.764824i	$0.277174\pi$
$108$		0			0
$109$	−38.9228	−	16.1224i	−0.357090	−	0.147912i	0.196924	−	0.980419i	$-0.436905\pi$
$109$	−38.9228	−	16.1224i	−0.357090	−	0.147912i	−0.554014	+	0.832507i	$0.686905\pi$
$110$	99.7305	−	55.7205i	0.906640	−	0.506550i
$111$		0			0
$112$	29.7646	−	90.3716i	0.265756	−	0.806889i
$113$		−	10.4054i		−	0.0920829i	−0.998940	−	0.0460414i	$-0.985339\pi$
$113$		−	10.4054i		−	0.0920829i	0.998940	−	0.0460414i	$-0.0146606\pi$
$114$		0			0
$115$	−43.9326	+	106.063i	−0.382023	+	0.922284i
$116$	−80.1248	+	57.9690i	−0.690731	+	0.499733i
$117$		0			0
$118$	0.353050	+	3.00874i	0.00299195	+	0.0254978i
$119$	−54.5936	+	54.5936i	−0.458769	+	0.458769i
$120$		0			0
$121$	−59.9313	+	59.9313i	−0.495300	+	0.495300i
$122$	−86.1414	+	109.045i	−0.706077	+	0.893811i
$123$		0			0
$124$	−101.371	+	164.681i	−0.817509	+	1.32807i
$125$	145.309	−	350.806i	1.16247	−	2.80645i
$126$		0			0
$127$		−	13.8578i		−	0.109117i	−0.998511	−	0.0545584i	$-0.982625\pi$
$127$		−	13.8578i		−	0.109117i	0.998511	−	0.0545584i	$-0.0173751\pi$
$128$	−45.1445	+	119.775i	−0.352691	+	0.935740i
$129$		0			0
$130$	−296.387	−	83.9107i	−2.27990	−	0.645467i
$131$	1.56083	+	0.646516i	0.0119147	+	0.00493524i	0.388633	−	0.921393i	$-0.372947\pi$
$131$	1.56083	+	0.646516i	0.0119147	+	0.00493524i	−0.376718	+	0.926328i	$0.622947\pi$
$132$		0			0
$133$	148.277	−	61.4185i	1.11487	−	0.461793i
$134$	−46.6876	−	36.8815i	−0.348415	−	0.275235i
$135$		0			0
$136$	76.4824	−	70.2743i	0.562371	−	0.516723i
$137$	188.033	+	188.033i	1.37251	+	1.37251i	0.856713	+	0.515793i	$0.172503\pi$
$137$	188.033	+	188.033i	1.37251	+	1.37251i	0.515793	+	0.856713i	$0.327497\pi$
$138$		0			0
$139$	127.171	−	52.6760i	0.914900	−	0.378964i	0.124970	−	0.992161i	$-0.460117\pi$
$139$	127.171	−	52.6760i	0.914900	−	0.378964i	0.789930	+	0.613197i	$0.210117\pi$
$140$	−132.289	−	182.850i	−0.944921	−	1.30607i
$141$		0			0
$142$	−93.9258	−	168.112i	−0.661449	−	1.18388i
$143$	−97.7287			−0.683418
$144$		0			0
$145$			234.579i			1.61778i
$146$	−61.2560	−	109.638i	−0.419562	−	0.750946i
$147$		0			0
$148$	47.6896	+	7.65132i	0.322227	+	0.0516981i
$149$	−47.9858	−	115.848i	−0.322052	−	0.777503i	−0.999135	−	0.0415956i	$-0.986756\pi$
$149$	−47.9858	−	115.848i	−0.322052	−	0.777503i	0.677082	−	0.735907i	$-0.263244\pi$
$150$		0			0
$151$	−42.3659	+	42.3659i	−0.280569	+	0.280569i	−0.833336	−	0.552767i	$-0.813572\pi$
$151$	−42.3659	+	42.3659i	−0.280569	+	0.280569i	0.552767	+	0.833336i	$0.313572\pi$
$152$	−202.790	+	74.1210i	−1.33414	+	0.487638i
$153$		0			0
$154$	−56.1859	−	44.3847i	−0.364843	−	0.288213i
$155$	175.534	+	423.777i	1.13248	+	2.73404i
$156$		0			0
$157$	66.6053	−	160.799i	0.424238	−	1.02420i	−0.556846	−	0.830616i	$-0.687989\pi$
$157$	66.6053	−	160.799i	0.424238	−	1.02420i	0.981084	−	0.193584i	$-0.0620114\pi$
$158$	−247.624	−	70.1051i	−1.56724	−	0.443703i
$159$		0			0
$160$	167.411	+	253.287i	1.04632	+	1.58304i
$161$	71.9535			0.446916
$162$		0			0
$163$	149.926	+	62.1012i	0.919789	+	0.380989i	0.791796	−	0.610786i	$-0.209146\pi$
$163$	149.926	+	62.1012i	0.919789	+	0.380989i	0.127993	+	0.991775i	$0.459146\pi$
$164$	36.4203	+	153.053i	0.222075	+	0.933248i
$165$		0			0
$166$	91.3424	−	115.629i	0.550255	−	0.696558i
$167$	−80.1804	−	80.1804i	−0.480122	−	0.480122i	0.425048	−	0.905171i	$-0.360257\pi$
$167$	−80.1804	−	80.1804i	−0.480122	−	0.480122i	−0.905171	+	0.425048i	$0.860257\pi$
$168$		0			0
$169$	66.8315	+	66.8315i	0.395453	+	0.395453i
$170$	−28.7120	−	244.688i	−0.168894	−	1.43934i
$171$		0			0
$172$	−54.6974	−	8.77565i	−0.318008	−	0.0510212i
$173$	206.185	+	85.4045i	1.19182	+	0.493668i	0.888347	−	0.459173i	$-0.151854\pi$
$173$	206.185	+	85.4045i	1.19182	+	0.493668i	0.303472	+	0.952840i	$0.401854\pi$
$174$		0			0
$175$	−386.656			−2.20946
$176$	72.9949	+	62.8515i	0.414744	+	0.357111i
$177$		0			0
$178$	−60.5224	+	33.8145i	−0.340013	+	0.189969i
$179$	5.58318	−	13.4790i	0.0311910	−	0.0753017i	−0.907517	−	0.420016i	$-0.862024\pi$
$179$	5.58318	−	13.4790i	0.0311910	−	0.0753017i	0.938708	+	0.344715i	$0.112024\pi$
$180$		0			0
$181$	−78.1182	−	188.594i	−0.431592	−	1.04196i	−0.978774	−	0.204942i	$-0.934299\pi$
$181$	−78.1182	−	188.594i	−0.431592	−	1.04196i	0.547182	−	0.837014i	$-0.315701\pi$
$182$	22.5003	+	191.751i	0.123628	+	1.05358i
$183$		0			0
$184$	−96.7116	−	4.09111i	−0.525607	−	0.0222343i
$185$	81.0098	−	81.0098i	0.437891	−	0.437891i
$186$		0			0
$187$	−29.9117	−	72.2133i	−0.159956	−	0.386167i
$188$	39.4838	+	24.3047i	0.210020	+	0.129280i
$189$		0			0
$190$	−139.508	+	492.768i	−0.734254	+	2.59352i
$191$		−	380.881i		−	1.99414i	−0.0764937	−	0.997070i	$-0.524373\pi$
$191$		−	380.881i		−	1.99414i	0.0764937	−	0.997070i	$-0.475627\pi$
$192$		0			0
$193$	−179.274			−0.928882			−0.464441	−	0.885604i	$-0.653745\pi$
$193$	−179.274			−0.928882			−0.464441	+	0.885604i	$0.653745\pi$
$194$	220.767	+	62.5017i	1.13797	+	0.322174i
$195$		0			0
$196$	28.5942	−	46.4523i	0.145889	−	0.237001i
$197$	−254.222	+	105.302i	−1.29047	+	0.534529i	−0.919125	−	0.393967i	$-0.871103\pi$
$197$	−254.222	+	105.302i	−1.29047	+	0.534529i	−0.371343	+	0.928496i	$0.621103\pi$
$198$		0			0
$199$	234.958	+	234.958i	1.18069	+	1.18069i	0.979565	+	0.201128i	$0.0644607\pi$
$199$	234.958	+	234.958i	1.18069	+	1.18069i	0.201128	+	0.979565i	$0.435539\pi$
$200$	519.698	+	21.9844i	2.59849	+	0.109922i
$201$		0			0
$202$	221.925	−	26.0410i	1.09864	−	0.128916i
$203$	135.834	−	56.2643i	0.669133	−	0.277164i
$204$		0			0
$205$	344.768	+	142.808i	1.68180	+	0.696622i
$206$	−63.9794	−	114.513i	−0.310580	−	0.555886i
$207$		0			0
$208$	−19.3399	−	259.009i	−0.0929801	−	1.24523i
$209$			162.482i			0.777425i
$210$		0			0
$211$	80.8495	−	195.188i	0.383173	−	0.925061i	−0.608175	−	0.793803i	$-0.708098\pi$
$211$	80.8495	−	195.188i	0.383173	−	0.925061i	0.991348	−	0.131259i	$-0.0419018\pi$
$212$	23.6776	−	147.579i	0.111687	−	0.696127i
$213$		0			0
$214$	128.593	−	15.0894i	0.600904	−	0.0705110i
$215$	−92.9139	+	92.9139i	−0.432158	+	0.432158i
$216$		0			0
$217$	203.288	−	203.288i	0.936811	−	0.936811i
$218$	−66.1181	−	52.2308i	−0.303294	−	0.239591i
$219$		0			0
$220$	222.275	−	52.8924i	1.01034	−	0.240420i
$221$	−80.6534	+	194.715i	−0.364948	+	0.881061i
$222$		0			0
$223$			160.581i			0.720094i	0.932934	+	0.360047i	$0.117239\pi$
$223$			160.581i			0.720094i	−0.932934	+	0.360047i	$0.882761\pi$
$224$	106.513	−	157.692i	0.475506	−	0.703981i
$225$		0			0
$226$	5.66895	−	20.0237i	0.0250838	−	0.0886006i
$227$	188.221	+	77.9638i	0.829169	+	0.343453i	0.756574	−	0.653909i	$-0.226872\pi$
$227$	188.221	+	77.9638i	0.829169	+	0.343453i	0.0725951	+	0.997361i	$0.476872\pi$
$228$		0			0
$229$	85.4831	−	35.4083i	0.373289	−	0.154621i	−0.188149	−	0.982141i	$-0.560249\pi$
$229$	85.4831	−	35.4083i	0.373289	−	0.154621i	0.561437	+	0.827519i	$0.310249\pi$
$230$	−142.326	+	180.168i	−0.618811	+	0.783341i
$231$		0			0
$232$	−185.771	+	67.9007i	−0.800739	+	0.292676i
$233$	−96.6127	−	96.6127i	−0.414647	−	0.414647i	0.468707	−	0.883354i	$-0.344720\pi$
$233$	−96.6127	−	96.6127i	−0.414647	−	0.414647i	−0.883354	+	0.468707i	$0.844720\pi$
$234$		0			0
$235$	101.605	−	42.0860i	0.432360	−	0.179089i
$236$	−0.959795	+	5.98227i	−0.00406693	+	0.0253486i
$237$		0			0
$238$	−134.801	+	75.3148i	−0.566391	+	0.316449i
$239$	−75.6472			−0.316515			−0.158258	−	0.987398i	$-0.550588\pi$
$239$	−75.6472			−0.316515			−0.158258	+	0.987398i	$0.550588\pi$
$240$		0			0
$241$			231.147i			0.959115i	0.877511	+	0.479557i	$0.159203\pi$
$241$			231.147i			0.959115i	−0.877511	+	0.479557i	$0.840797\pi$
$242$	−147.981	+	82.6785i	−0.611491	+	0.341647i
$243$		0			0
$244$	−225.176	+	162.912i	−0.922854	+	0.667670i
$245$	−49.5138	−	119.537i	−0.202097	−	0.487905i
$246$		0			0
$247$	309.793	−	309.793i	1.25422	−	1.25422i
$248$	−284.795	+	261.678i	−1.14837	+	1.05515i
$249$		0			0
$250$	470.749	−	595.913i	1.88300	−	2.38365i
$251$	5.36552	+	12.9535i	0.0213766	+	0.0516076i	0.934207	−	0.356730i	$-0.116109\pi$
$251$	5.36552	+	12.9535i	0.0213766	+	0.0516076i	−0.912831	+	0.408338i	$0.866109\pi$
$252$		0			0
$253$	−27.8764	+	67.2996i	−0.110184	+	0.266007i
$254$	7.54988	−	26.6675i	0.0297239	−	0.104990i
$255$		0			0
$256$	−152.129	+	205.895i	−0.594254	+	0.804278i
$257$	245.472			0.955146			0.477573	−	0.878592i	$-0.341517\pi$
$257$	245.472			0.955146			0.477573	+	0.878592i	$0.341517\pi$
$258$		0			0
$259$	−66.3396	−	27.4787i	−0.256137	−	0.106096i
$260$	−524.642	−	322.950i	−2.01785	−	1.24211i
$261$		0			0
$262$	2.65138	+	2.09449i	0.0101198	+	0.00799423i
$263$	57.2700	+	57.2700i	0.217757	+	0.217757i	0.807552	−	0.589796i	$-0.200792\pi$
$263$	57.2700	+	57.2700i	0.217757	+	0.217757i	−0.589796	+	0.807552i	$0.700792\pi$
$264$		0			0
$265$	−250.691	−	250.691i	−0.946003	−	0.946003i
$266$	318.801	−	37.4086i	1.19850	−	0.140634i
$267$		0			0
$268$	−69.7506	−	96.4093i	−0.260263	−	0.359736i
$269$	51.8299	+	21.4686i	0.192676	+	0.0798091i	0.476935	−	0.878938i	$-0.341748\pi$
$269$	51.8299	+	21.4686i	0.192676	+	0.0798091i	−0.284259	+	0.958747i	$0.591748\pi$
$270$		0			0
$271$	186.512			0.688238			0.344119	−	0.938926i	$-0.388178\pi$
$271$	186.512			0.688238			0.344119	+	0.938926i	$0.388178\pi$
$272$	185.466	−	93.5650i	0.681861	−	0.343989i
$273$		0			0
$274$	259.402	+	464.287i	0.946724	+	1.69448i
$275$	149.799	−	361.647i	0.544724	−	1.31508i
$276$		0			0
$277$	−20.1307	−	48.5999i	−0.0726741	−	0.175451i	0.883368	−	0.468680i	$-0.155270\pi$
$277$	−20.1307	−	48.5999i	−0.0726741	−	0.175451i	−0.956042	+	0.293229i	$0.905270\pi$
$278$	273.422	−	32.0838i	0.983533	−	0.115409i
$279$		0			0
$280$	−154.954	−	423.942i	−0.553406	−	1.51408i
$281$	−161.993	+	161.993i	−0.576488	+	0.576488i	−0.933934	−	0.357446i	$-0.883648\pi$
$281$	−161.993	+	161.993i	−0.576488	+	0.576488i	0.357446	+	0.933934i	$0.383648\pi$
$282$		0			0
$283$	104.116	+	251.358i	0.367901	+	0.888192i	0.994094	+	0.108523i	$0.0346123\pi$
$283$	104.116	+	251.358i	0.367901	+	0.888192i	−0.626193	+	0.779668i	$0.715388\pi$
$284$	−89.1586	−	374.680i	−0.313939	−	1.31930i
$285$		0			0
$286$	−188.066	−	53.2436i	−0.657573	−	0.186166i
$287$		−	233.893i		−	0.814957i
$288$		0			0
$289$	120.437			0.416737
$290$	−127.801	+	451.415i	−0.440692	+	1.55660i
$291$		0			0
$292$	−58.1470	−	244.357i	−0.199133	−	0.836838i
$293$	−432.623	+	179.198i	−1.47653	+	0.611599i	−0.968338	−	0.249645i	$-0.919686\pi$
$293$	−432.623	+	179.198i	−1.47653	+	0.611599i	−0.508193	+	0.861243i	$0.669686\pi$
$294$		0			0
$295$	10.1620	+	10.1620i	0.0344475	+	0.0344475i
$296$	87.6036	+	40.7057i	0.295958	+	0.137519i
$297$		0			0
$298$	−29.2271	−	249.077i	−0.0980774	−	0.835829i
$299$	181.466	−	75.1655i	0.606908	−	0.251390i
$300$		0			0
$301$	76.0879	+	31.5167i	0.252784	+	0.104707i
$302$	−104.609	+	58.4461i	−0.346387	+	0.193530i
$303$		0			0
$304$	−430.623	+	32.1541i	−1.41652	+	0.105770i
$305$			659.241i			2.16145i
$306$		0			0
$307$	54.2770	−	131.036i	0.176798	−	0.426828i	−0.810494	−	0.585747i	$-0.800801\pi$
$307$	54.2770	−	131.036i	0.176798	−	0.426828i	0.987292	+	0.158920i	$0.0508010\pi$
$308$	−83.9409	−	116.023i	−0.272535	−	0.376698i
$309$		0			0
$310$	106.914	+	911.134i	0.344883	+	2.93914i
$311$	165.421	−	165.421i	0.531900	−	0.531900i	−0.389238	−	0.921137i	$-0.627261\pi$
$311$	165.421	−	165.421i	0.531900	−	0.531900i	0.921137	+	0.389238i	$0.127261\pi$
$312$		0			0
$313$	−232.912	+	232.912i	−0.744127	+	0.744127i	−0.973369	−	0.229242i	$-0.926375\pi$
$313$	−232.912	+	232.912i	−0.744127	+	0.744127i	0.229242	+	0.973369i	$0.426375\pi$
$314$	215.778	−	273.150i	0.687191	−	0.869903i
$315$		0			0
$316$	−438.324	−	269.816i	−1.38710	−	0.853847i
$317$	128.526	−	310.289i	0.405444	−	0.978829i	−0.580877	−	0.813992i	$-0.697290\pi$
$317$	128.526	−	310.289i	0.405444	−	0.978829i	0.986321	−	0.164837i	$-0.0527099\pi$
$318$		0			0
$319$			148.846i			0.466603i
$320$	184.167	+	578.624i	0.575521	+	1.80820i
$321$		0			0
$322$	138.465	+	39.2010i	0.430015	+	0.121742i
$323$	323.729	+	134.093i	1.00226	+	0.415148i
$324$		0			0
$325$	−975.139	+	403.916i	−3.00043	+	1.24282i
$326$	254.678	+	201.186i	0.781221	+	0.617136i
$327$		0			0
$328$	−13.2986	+	314.371i	−0.0405445	+	0.958449i
$329$	−48.7402	−	48.7402i	−0.148147	−	0.148147i
$330$		0			0
$331$	−256.865	+	106.397i	−0.776027	+	0.321441i	−0.735311	−	0.677730i	$-0.762964\pi$
$331$	−256.865	+	106.397i	−0.776027	+	0.321441i	−0.0407160	+	0.999171i	$0.512964\pi$
$332$	238.772	−	172.748i	0.719192	−	0.520324i
$333$		0			0
$334$	−110.613	−	197.980i	−0.331178	−	0.592753i
$335$	−282.254			−0.842550
$336$		0			0
$337$			118.357i			0.351208i	0.984461	+	0.175604i	$0.0561878\pi$
$337$			118.357i			0.351208i	−0.984461	+	0.175604i	$0.943812\pi$
$338$	92.1977	+	165.019i	0.272774	+	0.488221i
$339$		0			0
$340$	78.0559	−	486.511i	0.229576	−	1.43091i
$341$	111.381	+	268.898i	0.326631	+	0.788557i
$342$		0			0
$343$	−263.385	+	263.385i	−0.767885	+	0.767885i
$344$	−100.477	−	46.6872i	−0.292083	−	0.135719i
$345$		0			0
$346$	350.245	+	276.681i	1.01227	+	0.799656i
$347$	−209.712	−	506.290i	−0.604357	−	1.45905i	−0.869055	−	0.494716i	$-0.835272\pi$
$347$	−209.712	−	506.290i	−0.604357	−	1.45905i	0.264697	−	0.964332i	$-0.414728\pi$
$348$		0			0
$349$	95.2106	−	229.859i	0.272810	−	0.658621i	−0.726791	−	0.686858i	$-0.758989\pi$
$349$	95.2106	−	229.859i	0.272810	−	0.658621i	0.999601	+	0.0282371i	$0.00898933\pi$
$350$	−744.067	−	210.654i	−2.12591	−	0.601868i
$351$		0			0
$352$	106.227	+	160.718i	0.301781	+	0.456584i
$353$	−77.3693			−0.219176			−0.109588	−	0.993977i	$-0.534953\pi$
$353$	−77.3693			−0.219176			−0.109588	+	0.993977i	$0.534953\pi$
$354$		0			0
$355$	−844.008	−	349.600i	−2.37749	−	0.984787i
$356$	−134.890	+	32.0983i	−0.378904	+	0.0901637i
$357$		0			0
$358$	18.0876	−	22.8967i	0.0505240	−	0.0639574i
$359$	−37.4966	−	37.4966i	−0.104447	−	0.104447i	0.652952	−	0.757399i	$-0.273530\pi$
$359$	−37.4966	−	37.4966i	−0.104447	−	0.104447i	−0.757399	+	0.652952i	$0.773530\pi$
$360$		0			0
$361$	−259.790	−	259.790i	−0.719640	−	0.719640i
$362$	−47.5800	−	405.483i	−0.131437	−	1.12012i
$363$		0			0
$364$	−61.1689	+	381.257i	−0.168047	+	1.04741i
$365$	−550.440	−	228.000i	−1.50806	−	0.624657i
$366$		0			0
$367$	−164.952			−0.449461			−0.224731	−	0.974421i	$-0.572150\pi$
$367$	−164.952			−0.449461			−0.224731	+	0.974421i	$0.572150\pi$
$368$	−183.880	−	60.5623i	−0.499673	−	0.164571i
$369$		0			0
$370$	200.027	−	111.757i	0.540615	−	0.302047i
$371$	−85.0351	+	205.293i	−0.229205	+	0.553350i
$372$		0			0
$373$	28.3621	+	68.4722i	0.0760379	+	0.183572i	0.957328	−	0.289004i	$-0.0933242\pi$
$373$	28.3621	+	68.4722i	0.0760379	+	0.183572i	−0.881290	+	0.472576i	$0.843324\pi$
$374$	−18.2186	−	155.261i	−0.0487127	−	0.415136i
$375$		0			0
$376$	62.7397	+	68.2822i	0.166861	+	0.181602i
$377$	283.795	−	283.795i	0.752772	−	0.752772i
$378$		0			0
$379$	−130.081	−	314.044i	−0.343222	−	0.828611i	−0.997386	−	0.0722585i	$-0.976979\pi$
$379$	−130.081	−	314.044i	−0.343222	−	0.828611i	0.654164	−	0.756353i	$-0.273021\pi$
$380$	−536.930	+	872.260i	−1.41297	+	2.29542i
$381$		0			0
$382$	207.508	−	732.954i	0.543214	−	1.91873i
$383$			199.739i			0.521512i	0.965405	+	0.260756i	$0.0839719\pi$
$383$			199.739i			0.521512i	−0.965405	+	0.260756i	$0.916028\pi$
$384$		0			0
$385$	−339.677			−0.882278
$386$	−344.989	−	97.6704i	−0.893754	−	0.253032i
$387$		0			0
$388$	390.785	+	240.552i	1.00718	+	0.619980i
$389$	58.8068	−	24.3586i	0.151174	−	0.0626184i	−0.305813	−	0.952091i	$-0.598928\pi$
$389$	58.8068	−	24.3586i	0.151174	−	0.0626184i	0.456988	+	0.889473i	$0.348928\pi$
$390$		0			0
$391$	111.082	+	111.082i	0.284097	+	0.284097i
$392$	80.3334	−	73.8127i	0.204932	−	0.188298i
$393$		0			0
$394$	−546.586	+	64.1372i	−1.38727	+	0.162785i
$395$	−1127.95	+	467.213i	−2.85557	+	1.18282i
$396$		0			0
$397$	282.925	+	117.191i	0.712656	+	0.295192i	0.709403	−	0.704803i	$-0.248965\pi$
$397$	282.925	+	117.191i	0.712656	+	0.295192i	0.00325310	+	0.999995i	$0.498965\pi$
$398$	324.137	+	580.152i	0.814416	+	1.45767i
$399$		0			0
$400$	988.112	+	325.443i	2.47028	+	0.813607i
$401$		−	203.523i		−	0.507538i	−0.967265	−	0.253769i	$-0.918330\pi$
$401$		−	203.523i		−	0.507538i	0.967265	−	0.253769i	$-0.0816703\pi$
$402$		0			0
$403$	300.326	−	725.051i	0.745226	−	1.79913i
$404$	441.252	+	70.7945i	1.09221	+	0.175234i
$405$		0			0
$406$	292.048	−	34.2693i	0.719329	−	0.0844072i
$407$	51.4029	−	51.4029i	0.126297	−	0.126297i
$408$		0			0
$409$	163.744	−	163.744i	0.400352	−	0.400352i	−0.478005	−	0.878357i	$-0.658640\pi$
$409$	163.744	−	163.744i	0.400352	−	0.400352i	0.878357	+	0.478005i	$0.158640\pi$
$410$	585.657	+	462.647i	1.42843	+	1.12841i
$411$		0			0
$412$	−60.7322	−	255.221i	−0.147408	−	0.619468i
$413$	3.44698	−	8.32176i	0.00834621	−	0.0201495i
$414$		0			0
$415$		−	699.044i		−	1.68444i
$416$	103.894	−	508.964i	0.249744	−	1.22347i
$417$		0			0
$418$	−88.5218	+	312.675i	−0.211775	+	0.748025i
$419$	−260.900	−	108.068i	−0.622673	−	0.257920i	0.0489634	−	0.998801i	$-0.484408\pi$
$419$	−260.900	−	108.068i	−0.622673	−	0.257920i	−0.671636	+	0.740881i	$0.734408\pi$
$420$		0			0
$421$	−256.659	+	106.312i	−0.609641	+	0.252522i	−0.666075	−	0.745885i	$-0.732027\pi$
$421$	−256.659	+	106.312i	−0.609641	+	0.252522i	0.0564337	+	0.998406i	$0.482027\pi$
$422$	261.924	−	331.565i	0.620674	−	0.785700i
$423$		0			0
$424$	125.967	−	271.096i	0.297091	−	0.639377i
$425$	−596.919	−	596.919i	−1.40452	−	1.40452i
$426$		0			0
$427$	381.737	−	158.121i	0.893998	−	0.370306i
$428$	255.682	+	41.0216i	0.597387	+	0.0958448i
$429$		0			0
$430$	−229.421	+	128.180i	−0.533537	+	0.298093i
$431$	−735.913			−1.70746			−0.853728	−	0.520720i	$-0.825664\pi$
$431$	−735.913			−1.70746			−0.853728	+	0.520720i	$0.825664\pi$
$432$		0			0
$433$			723.976i			1.67200i	0.548729	+	0.836000i	$0.315112\pi$
$433$			723.976i			1.67200i	−0.548729	+	0.836000i	$0.684888\pi$
$434$	501.953	−	280.447i	1.15657	−	0.646191i
$435$		0			0
$436$	−98.7795	−	136.533i	−0.226558	−	0.313149i
$437$	−124.969	−	301.701i	−0.285970	−	0.690392i
$438$		0			0
$439$	530.334	−	530.334i	1.20805	−	1.20805i	0.236392	−	0.971658i	$-0.424035\pi$
$439$	530.334	−	530.334i	1.20805	−	1.20805i	0.971658	−	0.236392i	$-0.0759650\pi$
$440$	456.554	+	19.3132i	1.03762	+	0.0438937i
$441$		0			0
$442$	−261.289	+	330.761i	−0.591152	+	0.748328i
$443$	106.327	+	256.697i	0.240017	+	0.579451i	0.997284	−	0.0736537i	$-0.0234660\pi$
$443$	106.327	+	256.697i	0.240017	+	0.579451i	−0.757267	+	0.653105i	$0.773466\pi$
$444$		0			0
$445$	−125.860	+	303.854i	−0.282832	+	0.682818i
$446$	−87.4861	+	309.017i	−0.196157	+	0.692862i
$447$		0			0
$448$	290.883	−	245.427i	0.649292	−	0.547829i
$449$	−168.746			−0.375825			−0.187913	−	0.982186i	$-0.560172\pi$
$449$	−168.746			−0.375825			−0.187913	+	0.982186i	$0.560172\pi$
$450$		0			0
$451$	218.765	+	90.6153i	0.485066	+	0.200921i
$452$	21.8183	−	35.4445i	0.0482705	−	0.0784170i
$453$		0			0
$454$	319.731	+	252.576i	0.704253	+	0.556334i
$455$	647.638	+	647.638i	1.42338	+	1.42338i
$456$		0			0
$457$	421.173	+	421.173i	0.921604	+	0.921604i	0.997143	−	0.0755390i	$-0.0240677\pi$
$457$	421.173	+	421.173i	0.921604	+	0.921604i	−0.0755390	+	0.997143i	$0.524068\pi$
$458$	183.791	−	21.5664i	0.401291	−	0.0470881i
$459$		0			0
$460$	−372.046	+	269.169i	−0.808795	+	0.585150i
$461$	640.120	+	265.146i	1.38855	+	0.575155i	0.946753	−	0.321962i	$-0.104342\pi$
$461$	640.120	+	265.146i	1.38855	+	0.575155i	0.441794	+	0.897117i	$0.354342\pi$
$462$		0			0
$463$	−165.894			−0.358303			−0.179152	−	0.983821i	$-0.557335\pi$
$463$	−165.894			−0.358303			−0.179152	+	0.983821i	$0.557335\pi$
$464$	−394.485	+	29.4557i	−0.850183	+	0.0634821i
$465$		0			0
$466$	−133.283	−	238.554i	−0.286014	−	0.511918i
$467$	61.9685	−	149.605i	0.132695	−	0.320354i	−0.843541	−	0.537065i	$-0.819533\pi$
$467$	61.9685	−	149.605i	0.132695	−	0.320354i	0.976236	+	0.216711i	$0.0695330\pi$
$468$		0			0
$469$	67.6994	+	163.441i	0.144348	+	0.348488i
$470$	218.453	−	25.6336i	0.464794	−	0.0545396i
$471$		0			0
$472$	−5.10620	+	10.9892i	−0.0108182	+	0.0232821i
$473$	−58.9564	+	58.9564i	−0.124644	+	0.124644i
$474$		0			0
$475$	671.543	+	1621.25i	1.41377	+	3.41315i
$476$	−300.439	+	71.4923i	−0.631174	+	0.150194i
$477$		0			0
$478$	−145.573	−	41.2133i	−0.304546	−	0.0862204i
$479$			174.653i			0.364621i	0.983241	+	0.182310i	$0.0583575\pi$
$479$			174.653i			0.364621i	−0.983241	+	0.182310i	$0.941642\pi$
$480$		0			0
$481$	−196.013			−0.407511
$482$	−125.931	+	444.811i	−0.261268	+	0.922843i
$483$		0			0
$484$	−329.813	+	78.4822i	−0.681432	+	0.162153i
$485$	1005.62	−	416.540i	2.07344	−	0.858846i
$486$		0			0
$487$	−664.259	−	664.259i	−1.36398	−	1.36398i	−0.868775	−	0.495208i	$-0.835092\pi$
$487$	−664.259	−	664.259i	−1.36398	−	1.36398i	−0.495208	−	0.868775i	$-0.664908\pi$
$488$	−522.077	+	190.823i	−1.06983	+	0.391031i
$489$		0			0
$490$	−30.1577	−	257.008i	−0.0615464	−	0.524506i
$491$	869.121	−	360.002i	1.77010	−	0.733201i	0.775276	−	0.631623i	$-0.217611\pi$
$491$	869.121	−	360.002i	1.77010	−	0.733201i	0.994828	−	0.101578i	$-0.0323891\pi$
$492$		0			0
$493$	296.561	+	122.840i	0.601544	+	0.249168i
$494$	764.933	−	427.376i	1.54845	−	0.865134i
$495$		0			0
$496$	−690.614	+	348.404i	−1.39237	+	0.702428i
$497$			572.580i			1.15207i
$498$		0			0
$499$	313.305	−	756.385i	0.627866	−	1.51580i	−0.214404	−	0.976745i	$-0.568781\pi$
$499$	313.305	−	756.385i	0.627866	−	1.51580i	0.842270	−	0.539056i	$-0.181219\pi$
$500$	1230.55	−	890.285i	2.46111	−	1.78057i
$501$		0			0
$502$	3.26802	+	27.8505i	0.00650999	+	0.0554790i
$503$	233.309	−	233.309i	0.463836	−	0.463836i	−0.436075	−	0.899910i	$-0.643632\pi$
$503$	233.309	−	233.309i	0.463836	−	0.463836i	0.899910	+	0.436075i	$0.143632\pi$
$504$		0			0
$505$	749.550	−	749.550i	1.48426	−	1.48426i
$506$	−90.3100	+	114.322i	−0.178478	+	0.225932i
$507$		0			0
$508$	29.0575	−	47.2048i	0.0571997	−	0.0929228i
$509$	−263.629	+	636.457i	−0.517936	+	1.25041i	0.421233	+	0.906952i	$0.361597\pi$
$509$	−263.629	+	636.457i	−0.517936	+	1.25041i	−0.939169	+	0.343455i	$0.888403\pi$
$510$		0			0
$511$			373.422i			0.730767i
$512$	−404.925	+	313.336i	−0.790870	+	0.611984i
$513$		0			0
$514$	472.379	+	133.736i	0.919025	+	0.260187i
$515$	−574.913	−	238.137i	−1.11634	−	0.462401i
$516$		0			0
$517$	64.4708	−	26.7047i	0.124702	−	0.0516532i
$518$	−112.691	−	89.0216i	−0.217550	−	0.171856i
$519$		0			0
$520$	−833.657	−	907.304i	−1.60319	−	1.74481i
$521$	−71.2450	−	71.2450i	−0.136747	−	0.136747i	0.635420	−	0.772167i	$-0.280827\pi$
$521$	−71.2450	−	71.2450i	−0.136747	−	0.136747i	−0.772167	+	0.635420i	$0.780827\pi$
$522$		0			0
$523$	−746.862	+	309.360i	−1.42803	+	0.591511i	−0.956865	−	0.290532i	$-0.906168\pi$
$523$	−746.862	+	309.360i	−1.42803	+	0.591511i	−0.471169	+	0.882043i	$0.656168\pi$
$524$	3.96112	+	5.47506i	0.00755938	+	0.0104486i
$525$		0			0
$526$	79.0071	+	141.410i	0.150204	+	0.268840i
$527$	627.672			1.19103
$528$		0			0
$529$			382.596i			0.723243i
$530$	−345.842	−	619.000i	−0.652532	−	1.16792i
$531$		0			0
$532$	633.871	+	101.698i	1.19149	+	0.191162i
$533$	−244.333	−	589.873i	−0.458412	−	1.10670i
$534$		0			0
$535$	434.324	−	434.324i	0.811821	−	0.811821i
$536$	−81.7008	−	223.527i	−0.152427	−	0.417029i
$537$		0			0
$538$	88.0433	+	69.5509i	0.163649	+	0.129277i
$539$	−31.4178	−	75.8493i	−0.0582891	−	0.140722i
$540$		0			0
$541$	212.526	−	513.083i	0.392839	−	0.948398i	−0.596479	−	0.802629i	$-0.703434\pi$
$541$	212.526	−	513.083i	0.392839	−	0.948398i	0.989319	−	0.145770i	$-0.0465658\pi$
$542$	358.918	+	101.614i	0.662210	+	0.187479i
$543$		0			0
$544$	407.880	−	79.0094i	0.749779	−	0.145238i
$545$	−399.723			−0.733437
$546$		0			0
$547$	854.342	+	353.880i	1.56187	+	0.646947i	0.985413	−	0.170181i	$-0.0544352\pi$
$547$	854.342	+	353.880i	1.56187	+	0.646947i	0.576456	+	0.817128i	$0.304435\pi$
$548$	246.237	+	1034.78i	0.449337	+	1.88829i
$549$		0			0
$550$	485.297	−	614.329i	0.882359	−	1.11696i
$551$	−471.832	−	471.832i	−0.856320	−	0.856320i
$552$		0			0
$553$	541.084	+	541.084i	0.978452	+	0.978452i
$554$	−12.2612	−	104.491i	−0.0221321	−	0.188612i
$555$		0			0
$556$	543.643	+	87.2222i	0.977776	+	0.156874i
$557$	400.791	+	166.013i	0.719553	+	0.298049i	0.712251	−	0.701925i	$-0.247676\pi$
$557$	400.791	+	166.013i	0.719553	+	0.298049i	0.00730213	+	0.999973i	$0.497676\pi$
$558$		0			0
$559$	224.816			0.402175
$560$	−67.2197	−	900.240i	−0.120035	−	1.60757i
$561$		0			0
$562$	−399.989	+	223.478i	−0.711725	+	0.397648i
$563$	−39.6368	+	95.6917i	−0.0704028	+	0.169967i	−0.955164	−	0.296077i	$-0.904321\pi$
$563$	−39.6368	+	95.6917i	−0.0704028	+	0.169967i	0.884761	+	0.466045i	$0.154321\pi$
$564$		0			0
$565$	−37.7805	−	91.2101i	−0.0668681	−	0.161434i
$566$	63.4147	+	540.429i	0.112040	+	0.954821i
$567$		0			0
$568$	32.5556	−	769.595i	0.0573161	−	1.35492i
$569$	−558.300	+	558.300i	−0.981196	+	0.981196i	−0.999826	−	0.0186309i	$-0.994069\pi$
$569$	−558.300	+	558.300i	−0.981196	+	0.981196i	0.0186309	+	0.999826i	$0.494069\pi$
$570$		0			0
$571$	50.9827	+	123.083i	0.0892867	+	0.215557i	0.962215	−	0.272292i	$-0.0877816\pi$
$571$	50.9827	+	123.083i	0.0892867	+	0.215557i	−0.872928	+	0.487849i	$0.837782\pi$
$572$	−332.900	−	204.920i	−0.581992	−	0.358252i
$573$		0			0
$574$	127.427	−	450.095i	0.221998	−	0.784137i
$575$			786.731i			1.36823i
$576$		0			0
$577$	−502.854			−0.871497			−0.435748	−	0.900069i	$-0.643516\pi$
$577$	−502.854			−0.871497			−0.435748	+	0.900069i	$0.643516\pi$
$578$	231.765	+	65.6153i	0.400977	+	0.113521i
$579$		0			0
$580$	−491.871	+	799.060i	−0.848053	+	1.37769i
$581$	−404.785	+	167.668i	−0.696704	+	0.288584i
$582$		0			0
$583$	−159.070	−	159.070i	−0.272848	−	0.272848i
$584$	21.2319	−	501.910i	0.0363560	−	0.859436i
$585$		0			0
$586$	−930.154	+	109.146i	−1.58729	+	0.186256i
$587$	863.332	−	357.604i	1.47075	−	0.609206i	0.503722	−	0.863866i	$-0.331964\pi$
$587$	863.332	−	357.604i	1.47075	−	0.609206i	0.967031	+	0.254660i	$0.0819637\pi$
$588$		0			0
$589$	−1205.46	−	499.316i	−2.04661	−	0.847735i
$590$	14.0191	+	25.0918i	0.0237611	+	0.0425285i
$591$		0			0
$592$	146.405	+	126.060i	0.247305	+	0.212939i
$593$		−	764.474i		−	1.28916i	−0.764536	−	0.644581i	$-0.777032\pi$
$593$		−	764.474i		−	1.28916i	0.764536	−	0.644581i	$-0.222968\pi$
$594$		0			0
$595$	−280.328	+	676.772i	−0.471139	+	1.13743i
$596$	79.4561	−	495.238i	0.133316	−	0.830937i
$597$		0			0
$598$	390.157	−	45.7816i	0.652436	−	0.0765579i
$599$	404.946	−	404.946i	0.676037	−	0.676037i	−0.283064	−	0.959101i	$-0.591351\pi$
$599$	404.946	−	404.946i	0.676037	−	0.676037i	0.959101	+	0.283064i	$0.0913510\pi$
$600$		0			0
$601$	−313.140	+	313.140i	−0.521032	+	0.521032i	−0.917883	−	0.396851i	$-0.870103\pi$
$601$	−313.140	+	313.140i	−0.521032	+	0.521032i	0.396851	+	0.917883i	$0.370103\pi$
$602$	129.250	+	102.103i	0.214702	+	0.169606i
$603$		0			0
$604$	−233.148	+	55.4797i	−0.386006	+	0.0918538i
$605$	−307.736	+	742.941i	−0.508655	+	1.22800i
$606$		0			0
$607$			621.334i			1.02361i	0.859100	+	0.511807i	$0.171024\pi$
$607$			621.334i			1.02361i	−0.859100	+	0.511807i	$0.828976\pi$
$608$	−846.194	−	172.732i	−1.39177	−	0.284098i
$609$		0			0
$610$	−359.161	+	1268.62i	−0.588789	+	2.07971i
$611$	−173.838	−	72.0060i	−0.284514	−	0.117849i
$612$		0			0
$613$	−427.709	+	177.163i	−0.697730	+	0.289009i	−0.703217	−	0.710976i	$-0.748254\pi$
$613$	−427.709	+	177.163i	−0.697730	+	0.289009i	0.00548640	+	0.999985i	$0.498254\pi$
$614$	175.839	−	222.591i	0.286382	−	0.362526i
$615$		0			0
$616$	−98.3223	−	269.003i	−0.159614	−	0.436693i
$617$	478.013	+	478.013i	0.774738	+	0.774738i	0.978931	−	0.204193i	$-0.0654570\pi$
$617$	478.013	+	478.013i	0.774738	+	0.774738i	−0.204193	+	0.978931i	$0.565457\pi$
$618$		0			0
$619$	1085.36	−	449.572i	1.75341	−	0.726287i	0.755986	−	0.654588i	$-0.227158\pi$
$619$	1085.36	−	449.572i	1.75341	−	0.726287i	0.997426	−	0.0716991i	$-0.0228421\pi$
$620$	−290.654	+	1811.60i	−0.468796	+	2.92194i
$621$		0			0
$622$	408.453	−	228.207i	0.656677	−	0.366893i
$623$	206.136			0.330877
$624$		0			0
$625$		−	1977.14i		−	3.16342i
$626$	−575.100	+	321.315i	−0.918691	+	0.513282i
$627$		0			0
$628$	564.051	−	408.082i	0.898170	−	0.649811i
$629$	−59.9933	−	144.837i	−0.0953789	−	0.230265i
$630$		0			0
$631$	−386.336	+	386.336i	−0.612260	+	0.612260i	−0.943534	−	0.331275i	$-0.892521\pi$
$631$	−386.336	+	386.336i	−0.612260	+	0.612260i	0.331275	+	0.943534i	$0.392521\pi$
$632$	−696.498	−	758.027i	−1.10205	−	1.19941i
$633$		0			0
$634$	416.379	−	527.087i	0.656749	−	0.831367i
$635$	−50.3159	−	121.473i	−0.0792376	−	0.191297i
$636$		0			0
$637$	−84.7144	+	204.519i	−0.132990	+	0.321065i
$638$	−81.0930	+	286.435i	−0.127105	+	0.448958i
$639$		0			0
$640$	39.1635	+	1213.82i	0.0611929	+	1.89659i
$641$	622.533			0.971190			0.485595	−	0.874184i	$-0.338603\pi$
$641$	622.533			0.971190			0.485595	+	0.874184i	$0.338603\pi$
$642$		0			0
$643$	−1070.08	−	443.243i	−1.66421	−	0.689336i	−0.665818	−	0.746114i	$-0.731917\pi$
$643$	−1070.08	−	443.243i	−1.66421	−	0.689336i	−0.998387	+	0.0567776i	$0.981917\pi$
$644$	245.100	+	150.874i	0.380590	+	0.234277i
$645$		0			0
$646$	549.917	+	434.414i	0.851265	+	0.672468i
$647$	160.140	+	160.140i	0.247511	+	0.247511i	0.819948	−	0.572437i	$-0.194002\pi$
$647$	160.140	+	160.140i	0.247511	+	0.247511i	−0.572437	+	0.819948i	$0.694002\pi$
$648$		0			0
$649$	6.44807	+	6.44807i	0.00993540	+	0.00993540i
$650$	−2096.58	+	246.016i	−3.22551	+	0.378486i
$651$		0			0
$652$	380.486	+	525.907i	0.583567	+	0.806606i
$653$	7.42145	+	3.07407i	0.0113652	+	0.00470760i	0.388359	−	0.921508i	$-0.373042\pi$
$653$	7.42145	+	3.07407i	0.0113652	+	0.00470760i	−0.376994	+	0.926216i	$0.623042\pi$
$654$		0			0
$655$	16.0291			0.0244720
$656$	−196.864	+	597.720i	−0.300098	+	0.911159i
$657$		0			0
$658$	−67.2398	−	120.348i	−0.102188	−	0.182900i
$659$	−246.471	+	595.034i	−0.374008	+	0.902935i	0.619055	+	0.785348i	$0.287516\pi$
$659$	−246.471	+	595.034i	−0.374008	+	0.902935i	−0.993063	+	0.117587i	$0.962484\pi$
$660$		0			0
$661$	−158.963	−	383.770i	−0.240488	−	0.580591i	0.756843	−	0.653597i	$-0.226741\pi$
$661$	−158.963	−	383.770i	−0.240488	−	0.580591i	−0.997331	+	0.0730061i	$0.976741\pi$
$662$	−552.268	+	64.8040i	−0.834242	+	0.0978912i
$663$		0			0
$664$	553.599	−	202.344i	0.833733	−	0.304735i
$665$	1076.75	−	1076.75i	1.61917	−	1.61917i
$666$		0			0
$667$	−114.481	−	276.382i	−0.171636	−	0.414366i
$668$	−104.999	−	441.248i	−0.157184	−	0.660551i
$669$		0			0
$670$	−543.160	−	153.775i	−0.810687	−	0.229515i
$671$			418.306i			0.623407i
$672$		0			0
$673$	−48.0214			−0.0713543			−0.0356772	−	0.999363i	$-0.511359\pi$
$673$	−48.0214			−0.0713543			−0.0356772	+	0.999363i	$0.511359\pi$
$674$	−64.4821	+	227.762i	−0.0956707	+	0.337926i
$675$		0			0
$676$	87.5183	+	367.786i	0.129465	+	0.544063i
$677$	197.994	−	82.0118i	0.292458	−	0.121140i	−0.231631	−	0.972804i	$-0.574406\pi$
$677$	197.994	−	82.0118i	0.292458	−	0.121140i	0.524089	+	0.851664i	$0.324406\pi$
$678$		0			0
$679$	−482.400	−	482.400i	−0.710456	−	0.710456i
$680$	415.264	−	893.699i	0.610683	−	1.31426i
$681$		0			0
$682$	67.8397	+	578.139i	0.0994717	+	0.847711i
$683$	189.585	−	78.5287i	0.277577	−	0.114976i	−0.239552	−	0.970883i	$-0.577001\pi$
$683$	189.585	−	78.5287i	0.277577	−	0.114976i	0.517129	+	0.855907i	$0.327001\pi$
$684$		0			0
$685$	2330.96	+	965.517i	3.40287	+	1.40951i
$686$	−650.343	+	363.354i	−0.948022	+	0.529670i
$687$		0			0
$688$	−167.918	−	144.584i	−0.244067	−	0.210151i
$689$			606.576i			0.880371i
$690$		0			0
$691$	−481.880	+	1163.36i	−0.697366	+	1.68359i	0.0320194	+	0.999487i	$0.489806\pi$
$691$	−481.880	+	1163.36i	−0.697366	+	1.68359i	−0.729385	+	0.684103i	$0.760194\pi$
$692$	523.262	+	723.252i	0.756158	+	1.04516i
$693$		0			0
$694$	−127.731	−	1088.54i	−0.184050	−	1.56850i
$695$	923.482	−	923.482i	1.32875	−	1.32875i
$696$		0			0
$697$	361.083	−	361.083i	0.518054	−	0.518054i
$698$	308.449	−	390.461i	0.441905	−	0.559399i
$699$		0			0
$700$	−1317.09	−	810.750i	−1.88156	−	1.15821i
$701$	−167.051	+	403.296i	−0.238303	+	0.575315i	−0.997108	−	0.0760038i	$-0.975784\pi$
$701$	−167.051	+	403.296i	−0.238303	+	0.575315i	0.758804	+	0.651319i	$0.225784\pi$
$702$		0			0
$703$			325.887i			0.463566i
$704$	116.859	+	367.153i	0.165992	+	0.521524i
$705$		0			0
$706$	−148.887	−	42.1516i	−0.210888	−	0.0597048i
$707$	−613.813	−	254.249i	−0.868193	−	0.359617i
$708$		0			0
$709$	381.101	−	157.857i	0.537519	−	0.222648i	−0.0973740	−	0.995248i	$-0.531044\pi$
$709$	381.101	−	157.857i	0.537519	−	0.222648i	0.634893	+	0.772600i	$0.281044\pi$
$710$	−1433.71	−	1132.58i	−2.01932	−	1.59518i
$711$		0			0
$712$	−277.064	−	11.7204i	−0.389135	−	0.0164613i
$713$	−413.631	−	413.631i	−0.580128	−	0.580128i
$714$		0			0
$715$	−856.659	+	354.840i	−1.19812	+	0.496279i
$716$	47.2815	−	34.2074i	0.0660356	−	0.0477757i
$717$		0			0
$718$	−51.7286	−	92.5856i	−0.0720454	−	0.128949i
$719$	−584.715			−0.813234			−0.406617	−	0.913599i	$-0.633292\pi$
$719$	−584.715			−0.813234			−0.406617	+	0.913599i	$0.633292\pi$
$720$		0			0
$721$			390.024i			0.540949i
$722$	−358.395	−	641.467i	−0.496392	−	0.888459i
$723$		0			0
$724$	129.350	−	806.220i	0.178660	−	1.11356i
$725$	615.187	+	1485.19i	0.848534	+	2.04854i
$726$		0			0
$727$	−262.637	+	262.637i	−0.361261	+	0.361261i	−0.864277	−	0.503016i	$-0.832224\pi$
$727$	−262.637	+	262.637i	−0.361261	+	0.361261i	0.503016	+	0.864277i	$0.332224\pi$
$728$	−325.424	+	700.353i	−0.447011	+	0.962023i
$729$		0			0
$730$	−935.031	−	738.640i	−1.28086	−	1.01184i
$731$	68.8092	+	166.120i	0.0941302	+	0.227250i
$732$		0			0
$733$	−229.848	+	554.903i	−0.313572	+	0.757030i	0.685995	+	0.727606i	$0.259367\pi$
$733$	−229.848	+	554.903i	−0.313572	+	0.757030i	−0.999567	+	0.0294238i	$0.990633\pi$
$734$	−317.428	−	89.8676i	−0.432464	−	0.122435i
$735$		0			0
$736$	−320.857	−	216.723i	−0.435947	−	0.294461i
$737$	−179.098			−0.243009
$738$		0			0
$739$	−1026.47	−	425.177i	−1.38900	−	0.575341i	−0.442125	−	0.896954i	$-0.645775\pi$
$739$	−1026.47	−	425.177i	−1.38900	−	0.575341i	−0.946871	+	0.321612i	$0.895775\pi$
$740$	445.812	−	106.085i	0.602449	−	0.143359i
$741$		0			0
$742$	−275.484	+	348.730i	−0.371272	+	0.469987i
$743$	−61.1606	−	61.1606i	−0.0823158	−	0.0823158i	0.664750	−	0.747066i	$-0.268538\pi$
$743$	−61.1606	−	61.1606i	−0.0823158	−	0.0823158i	−0.747066	+	0.664750i	$0.768538\pi$
$744$		0			0
$745$	−841.256	−	841.256i	−1.12920	−	1.12920i
$746$	17.2747	+	147.218i	0.0231565	+	0.197343i
$747$		0			0
$748$	49.5286	−	308.704i	0.0662147	−	0.412706i
$749$	−355.671	−	147.324i	−0.474862	−	0.196694i
$750$		0			0
$751$	−94.7017			−0.126101			−0.0630504	−	0.998010i	$-0.520083\pi$
$751$	−94.7017			−0.126101			−0.0630504	+	0.998010i	$0.520083\pi$
$752$	83.5333	+	165.581i	0.111082	+	0.220188i
$753$		0			0
$754$	700.740	−	391.511i	0.929363	−	0.519245i
$755$	−217.541	+	525.191i	−0.288134	+	0.695617i
$756$		0			0
$757$	−247.689	−	597.975i	−0.327199	−	0.789927i	−0.998798	−	0.0490129i	$-0.984392\pi$
$757$	−247.689	−	597.975i	−0.327199	−	0.789927i	0.671600	−	0.740914i	$-0.265608\pi$
$758$	−79.2295	−	675.204i	−0.104524	−	0.890771i
$759$		0			0
$760$	−1508.47	+	1386.02i	−1.98482	+	1.82371i
$761$	260.140	−	260.140i	0.341840	−	0.341840i	−0.515219	−	0.857059i	$-0.672289\pi$
$761$	260.140	−	260.140i	0.341840	−	0.341840i	0.857059	+	0.515219i	$0.172289\pi$
$762$		0			0
$763$	95.8746	+	231.462i	0.125655	+	0.303358i
$764$	798.641	−	1297.42i	1.04534	−	1.69819i
$765$		0			0
$766$	−108.820	+	384.371i	−0.142063	+	0.501790i
$767$		−	24.5882i		−	0.0320576i
$768$		0			0
$769$	157.402			0.204685			0.102342	−	0.994749i	$-0.467366\pi$
$769$	157.402			0.204685			0.102342	+	0.994749i	$0.467366\pi$
$770$	−653.662	−	185.059i	−0.848912	−	0.240337i
$771$		0			0
$772$	−610.673	−	375.907i	−0.791028	−	0.486926i
$773$	516.732	−	214.037i	0.668476	−	0.276892i	−0.0225244	−	0.999746i	$-0.507170\pi$
$773$	516.732	−	214.037i	0.668476	−	0.276892i	0.691000	+	0.722855i	$0.257170\pi$
$774$		0			0
$775$	2222.73	+	2222.73i	2.86803	+	2.86803i
$776$	620.958	+	675.814i	0.800203	+	0.870894i
$777$		0			0
$778$	126.436	−	14.8362i	0.162515	−	0.0190697i
$779$	−980.711	+	406.224i	−1.25894	+	0.521468i
$780$		0			0
$781$	−535.546	−	221.830i	−0.685718	−	0.284034i
$782$	153.244	+	274.281i	0.195964	+	0.350742i
$783$		0			0
$784$	194.805	−	98.2761i	0.248475	−	0.125352i
$785$		−	1651.35i		−	2.10363i
$786$		0			0
$787$	−55.4219	+	133.800i	−0.0704217	+	0.170013i	−0.955171	−	0.296054i	$-0.904329\pi$
$787$	−55.4219	+	133.800i	−0.0704217	+	0.170013i	0.884750	+	0.466067i	$0.154329\pi$
$788$	−1086.77	−	174.362i	−1.37915	−	0.221272i
$789$		0			0
$790$	−2425.13	+	284.569i	−3.06979	+	0.360214i
$791$	−43.7540	+	43.7540i	−0.0553148	+	0.0553148i
$792$		0			0
$793$	797.555	−	797.555i	1.00574	−	1.00574i
$794$	480.603	+	379.659i	0.605294	+	0.478160i
$795$		0			0
$796$	307.686	+	1293.02i	0.386540	+	1.62439i
$797$	171.786	−	414.729i	0.215541	−	0.520363i	−0.778716	−	0.627376i	$-0.784129\pi$
$797$	171.786	−	414.729i	0.215541	−	0.520363i	0.994258	+	0.107013i	$0.0341288\pi$
$798$		0			0
$799$		−	150.490i		−	0.188348i
$800$	1724.18	+	1164.60i	2.15523	+	1.45575i
$801$		0			0
$802$	110.881	−	391.652i	0.138256	−	0.488344i
$803$	−349.269	−	144.672i	−0.434955	−	0.180164i
$804$		0			0
$805$	630.722	−	261.254i	0.783505	−	0.324539i
$806$	972.952	−	1231.64i	1.20714	−	1.52809i
$807$		0			0
$808$	810.560	+	376.633i	1.00317	+	0.466130i
$809$	937.121	+	937.121i	1.15837	+	1.15837i	0.984826	+	0.173543i	$0.0555215\pi$
$809$	937.121	+	937.121i	1.15837	+	1.15837i	0.173543	+	0.984826i	$0.444478\pi$
$810$		0			0
$811$	−333.127	+	137.986i	−0.410761	+	0.170143i	−0.578488	−	0.815691i	$-0.696357\pi$
$811$	−333.127	+	137.986i	−0.410761	+	0.170143i	0.167727	+	0.985833i	$0.446357\pi$
$812$	580.677	+	93.1638i	0.715119	+	0.114734i
$813$		0			0
$814$	126.923	−	70.9131i	0.155925	−	0.0871169i
$815$	1539.68			1.88918
$816$		0			0
$817$		−	373.775i		−	0.457497i
$818$	404.313	−	225.894i	0.494270	−	0.276154i
$819$		0			0
$820$	874.962	+	1209.37i	1.06703	+	1.47485i
$821$	−5.28894	−	12.7686i	−0.00644207	−	0.0155525i	0.920626	−	0.390446i	$-0.127679\pi$
$821$	−5.28894	−	12.7686i	−0.00644207	−	0.0155525i	−0.927068	+	0.374894i	$0.877679\pi$
$822$		0			0
$823$	392.597	−	392.597i	0.477032	−	0.477032i	−0.427149	−	0.904181i	$-0.640482\pi$
$823$	392.597	−	392.597i	0.477032	−	0.477032i	0.904181	+	0.427149i	$0.140482\pi$
$824$	22.1759	−	524.225i	0.0269125	−	0.636196i
$825$		0			0
$826$	11.1670	−	14.1361i	0.0135194	−	0.0171140i
$827$	−201.697	−	486.939i	−0.243889	−	0.588801i	0.753773	−	0.657135i	$-0.228232\pi$
$827$	−201.697	−	486.939i	−0.243889	−	0.588801i	−0.997663	+	0.0683336i	$0.978232\pi$
$828$		0			0
$829$	−42.1058	+	101.652i	−0.0507911	+	0.122620i	−0.947238	−	0.320530i	$-0.896139\pi$
$829$	−42.1058	+	101.652i	−0.0507911	+	0.122620i	0.896447	+	0.443150i	$0.146139\pi$
$830$	380.846	−	1345.22i	0.458851	−	1.62074i
$831$		0			0
$832$	477.218	−	922.831i	0.573579	−	1.10917i
$833$	−177.050			−0.212546
$834$		0			0
$835$	−993.961	−	411.712i	−1.19037	−	0.493068i
$836$	−340.697	+	553.473i	−0.407532	+	0.662049i
$837$		0			0
$838$	−443.190	−	350.104i	−0.528866	−	0.417785i
$839$	1132.35	+	1132.35i	1.34964	+	1.34964i	0.886047	+	0.463595i	$0.153441\pi$
$839$	1132.35	+	1132.35i	1.34964	+	1.34964i	0.463595	+	0.886047i	$0.346559\pi$
$840$		0			0
$841$	162.441	+	162.441i	0.193152	+	0.193152i
$842$	−551.825	+	64.7520i	−0.655375	+	0.0769027i
$843$		0			0
$844$	684.678	−	495.354i	0.811230	−	0.586912i
$845$	828.480	+	343.167i	0.980449	+	0.406115i
$846$		0			0
$847$	504.015			0.595059
$848$	390.102	−	453.060i	0.460026	−	0.534269i
$849$		0			0
$850$	−823.483	−	1473.90i	−0.968804	−	1.73400i
$851$	−55.9112	+	134.982i	−0.0657006	+	0.158615i
$852$		0			0
$853$	87.6702	+	211.655i	0.102779	+	0.248130i	0.966901	−	0.255153i	$-0.0821257\pi$
$853$	87.6702	+	211.655i	0.102779	+	0.248130i	−0.864122	+	0.503282i	$0.832126\pi$
$854$	820.747	−	96.3078i	0.961063	−	0.112773i
$855$		0			0
$856$	469.676	+	218.238i	0.548687	+	0.254951i
$857$	827.920	−	827.920i	0.966067	−	0.966067i	−0.0333756	−	0.999443i	$-0.510626\pi$
$857$	827.920	−	827.920i	0.966067	−	0.966067i	0.999443	+	0.0333756i	$0.0106258\pi$
$858$		0			0
$859$	270.599	+	653.284i	0.315016	+	0.760516i	0.999504	+	0.0314921i	$0.0100259\pi$
$859$	270.599	+	653.284i	0.315016	+	0.760516i	−0.684488	+	0.729024i	$0.739974\pi$
$860$	−511.323	+	121.674i	−0.594562	+	0.141482i
$861$		0			0
$862$	−1416.17	−	400.933i	−1.64288	−	0.465119i
$863$			80.9076i			0.0937516i	0.998901	+	0.0468758i	$0.0149265\pi$
$863$			80.9076i			0.0937516i	−0.998901	+	0.0468758i	$0.985074\pi$
$864$		0			0
$865$	2117.44			2.44791
$866$	−394.429	+	1393.19i	−0.455461	+	1.60877i
$867$		0			0
$868$	1118.73	−	266.213i	1.28886	−	0.306697i
$869$	−715.715	+	296.459i	−0.823608	+	0.341150i
$870$		0			0
$871$	341.473	+	341.473i	0.392047	+	0.392047i
$872$	−115.703	−	316.555i	−0.132687	−	0.363022i
$873$		0			0
$874$	−76.1156	−	648.667i	−0.0870888	−	0.742182i
$875$	−2086.13	+	864.104i	−2.38415	+	0.987548i
$876$		0			0
$877$	124.664	+	51.6377i	0.142149	+	0.0588799i	0.452624	−	0.891702i	$-0.350488\pi$
$877$	124.664	+	51.6377i	0.142149	+	0.0588799i	−0.310475	+	0.950582i	$0.600488\pi$
$878$	1309.49	−	731.625i	1.49144	−	0.833286i
$879$		0			0
$880$	868.056	+	285.901i	0.986427	+	0.324888i
$881$		−	699.206i		−	0.793650i	−0.917894	−	0.396825i	$-0.870112\pi$
$881$		−	699.206i		−	0.793650i	0.917894	−	0.396825i	$-0.129888\pi$
$882$		0			0
$883$	389.667	−	940.740i	0.441299	−	1.06539i	−0.534194	−	0.845362i	$-0.679385\pi$
$883$	389.667	−	940.740i	0.441299	−	1.06539i	0.975493	−	0.220029i	$-0.0706151\pi$
$884$	−683.018	+	494.152i	−0.772644	+	0.558996i
$885$		0			0
$886$	64.7616	+	551.907i	0.0730944	+	0.622920i
$887$	−935.403	+	935.403i	−1.05457	+	1.05457i	−0.0561466	+	0.998423i	$0.517881\pi$
$887$	−935.403	+	935.403i	−1.05457	+	1.05457i	−0.998423	+	0.0561466i	$0.982119\pi$
$888$		0			0
$889$	−58.2714	+	58.2714i	−0.0655471	+	0.0655471i
$890$	−407.744	+	516.156i	−0.458139	+	0.579950i
$891$		0			0
$892$	−336.711	+	546.997i	−0.377478	+	0.613226i
$893$	−119.716	+	289.020i	−0.134060	+	0.323650i
$894$		0			0
$895$		−	138.424i		−	0.154664i
$896$	693.476	−	313.816i	0.773968	−	0.350241i
$897$		0			0
$898$	−324.728	−	91.9343i	−0.361613	−	0.102377i
$899$	−1104.29	−	457.414i	−1.22836	−	0.508803i
$900$		0			0
$901$	−448.208	+	185.654i	−0.497456	+	0.206053i
$902$	371.615	+	293.562i	0.411990	+	0.325457i
$903$		0			0
$904$	61.2968	−	56.3213i	0.0678062	−	0.0623023i
$905$	−1369.52	−	1369.52i	−1.51328	−	1.51328i
$906$		0			0
$907$	215.676	−	89.3360i	0.237791	−	0.0984961i	−0.260606	−	0.965445i	$-0.583922\pi$
$907$	215.676	−	89.3360i	0.237791	−	0.0984961i	0.498397	+	0.866949i	$0.333922\pi$
$908$	477.674	+	660.241i	0.526072	+	0.727137i
$909$		0			0
$910$	893.452	+	1599.13i	0.981816	+	1.75729i
$911$	−522.037			−0.573037			−0.286518	−	0.958075i	$-0.592498\pi$
$911$	−522.037			−0.573037			−0.286518	+	0.958075i	$0.592498\pi$
$912$		0			0
$913$		−	443.562i		−	0.485829i
$914$	581.031	+	1039.95i	0.635702	+	1.13780i
$915$		0			0
$916$	365.432	+	58.6299i	0.398943	+	0.0640064i
$917$	−3.84463	−	9.28176i	−0.00419262	−	0.0101219i
$918$		0			0
$919$	−784.078	+	784.078i	−0.853187	+	0.853187i	−0.990524	−	0.137338i	$-0.956145\pi$
$919$	−784.078	+	784.078i	−0.853187	+	0.853187i	0.137338	+	0.990524i	$0.456145\pi$
$920$	−862.598	+	315.285i	−0.937606	+	0.342702i
$921$		0			0
$922$	1087.37	+	858.982i	1.17936	+	0.931651i
$923$	598.139	+	1444.04i	0.648038	+	1.56450i
$924$		0			0
$925$	300.449	−	725.349i	0.324810	−	0.784161i
$926$	−319.241	−	90.3809i	−0.344753	−	0.0976035i
$927$		0			0
$928$	−775.181	−	158.236i	−0.835325	−	0.170513i
$929$	−856.222			−0.921660			−0.460830	−	0.887489i	$-0.652448\pi$
$929$	−856.222			−0.921660			−0.460830	+	0.887489i	$0.652448\pi$
$930$		0			0
$931$	340.029	+	140.845i	0.365230	+	0.151283i
$932$	−126.518	−	531.678i	−0.135749	−	0.570470i
$933$		0			0
$934$	200.756	−	254.134i	0.214943	−	0.272092i
$935$	−524.393	−	524.393i	−0.560848	−	0.560848i
$936$		0			0
$937$	−987.588	−	987.588i	−1.05399	−	1.05399i	−0.998457	−	0.0555320i	$-0.982315\pi$
$937$	−987.588	−	987.588i	−1.05399	−	1.05399i	−0.0555320	−	0.998457i	$-0.517685\pi$
$938$	41.2342	+	351.403i	0.0439597	+	0.374630i
$939$		0			0
$940$	434.349	+	69.6870i	0.462073	+	0.0741351i
$941$	−1401.14	−	580.369i	−1.48899	−	0.616758i	−0.517889	−	0.855448i	$-0.673282\pi$
$941$	−1401.14	−	580.369i	−1.48899	−	0.616758i	−0.971096	+	0.238690i	$0.923282\pi$
$942$		0			0
$943$	−475.903			−0.504669
$944$	−15.8132	+	18.3653i	−0.0167513	+	0.0194547i
$945$		0			0
$946$	−145.574	+	81.3336i	−0.153883	+	0.0859763i
$947$	553.827	−	1337.06i	0.584823	−	1.41189i	−0.303573	−	0.952808i	$-0.598180\pi$
$947$	553.827	−	1337.06i	0.584823	−	1.41189i	0.888396	−	0.459079i	$-0.151820\pi$
$948$		0			0
$949$	390.091	+	941.763i	0.411055	+	0.992374i
$950$	409.022	+	3485.74i	0.430549	+	3.66920i
$951$		0			0
$952$	−617.104	−	26.1048i	−0.648218	−	0.0274210i
$953$	−276.860	+	276.860i	−0.290514	+	0.290514i	−0.837283	−	0.546769i	$-0.815857\pi$
$953$	−276.860	+	276.860i	−0.290514	+	0.290514i	0.546769	+	0.837283i	$0.315857\pi$
$954$		0			0
$955$	−1382.93	−	3338.68i	−1.44809	−	3.49600i
$956$	−257.682	−	158.619i	−0.269542	−	0.165919i
$957$		0			0
$958$	−95.1528	+	336.097i	−0.0993245	+	0.350832i
$959$		−	1581.34i		−	1.64895i
$960$		0			0
$961$	−1376.24			−1.43209
$962$	−377.200	−	106.790i	−0.392100	−	0.111008i
$963$		0			0
$964$	−484.675	+	787.370i	−0.502774	+	0.816773i
$965$	−1571.46	+	650.920i	−1.62846	+	0.674529i
$966$		0			0
$967$	227.945	+	227.945i	0.235724	+	0.235724i	0.815077	−	0.579353i	$-0.196695\pi$
$967$	227.945	+	227.945i	0.235724	+	0.235724i	−0.579353	+	0.815077i	$0.696695\pi$
$968$	−677.439	−	28.6571i	−0.699834	−	0.0296045i
$969$		0			0
$970$	2162.11	−	253.705i	2.22898	−	0.261552i
$971$	161.530	−	66.9080i	0.166354	−	0.0689062i	−0.297952	−	0.954581i	$-0.596304\pi$
$971$	161.530	−	66.9080i	0.166354	−	0.0689062i	0.464307	+	0.885675i	$0.346304\pi$
$972$		0			0
$973$	−756.247	−	313.248i	−0.777232	−	0.321940i
$974$	−916.383	−	1640.17i	−0.940845	−	1.68396i
$975$		0			0
$976$	−1108.63	+	82.7800i	−1.13589	+	0.0848155i
$977$		−	746.755i		−	0.764335i	−0.924093	−	0.382167i	$-0.875178\pi$
$977$		−	746.755i		−	0.764335i	0.924093	−	0.382167i	$-0.124822\pi$
$978$		0			0
$979$	−79.8618	+	192.803i	−0.0815749	+	0.196939i
$980$	81.9861	−	511.008i	0.0836593	−	0.521436i
$981$		0			0
$982$	1868.64	−	219.269i	1.90289	−	0.223288i
$983$	−748.040	+	748.040i	−0.760977	+	0.760977i	−0.976499	−	0.215522i	$-0.930855\pi$
$983$	−748.040	+	748.040i	−0.760977	+	0.760977i	0.215522	+	0.976499i	$0.430855\pi$
$984$		0			0
$985$	−1846.09	+	1846.09i	−1.87421	+	1.87421i
$986$	503.768	+	397.958i	0.510921	+	0.403609i
$987$		0			0
$988$	1704.85	−	405.685i	1.72556	−	0.410612i
$989$	64.1272	−	154.817i	0.0648404	−	0.156539i
$990$		0			0
$991$			1167.71i			1.17832i	0.808017	+	0.589159i	$0.200541\pi$
$991$			1167.71i			1.17832i	−0.808017	+	0.589159i	$0.799459\pi$
$992$	−1518.81	+	294.204i	−1.53106	+	0.296577i
$993$		0			0
$994$	−311.947	+	1101.85i	−0.313830	+	1.10850i
$995$	2912.67	+	1206.47i	2.92730	+	1.21253i
$996$		0			0
$997$	519.078	−	215.009i	0.520640	−	0.215656i	−0.106858	−	0.994274i	$-0.534079\pi$
$997$	519.078	−	215.009i	0.520640	−	0.215656i	0.627498	+	0.778618i	$0.284079\pi$
$998$	1015.00	−	1284.87i	1.01703	−	1.28744i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.b.19.15		64
3.2	odd	2		96.3.m.a.19.2	✓	64
12.11	even	2		384.3.m.a.367.1		64
32.27	odd	8	inner	288.3.u.b.91.15		64
96.5	odd	8		384.3.m.a.271.1		64
96.59	even	8		96.3.m.a.91.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.2	✓	64	3.2	odd	2
96.3.m.a.91.2	yes	64	96.59	even	8
288.3.u.b.19.15		64	1.1	even	1	trivial
288.3.u.b.91.15		64	32.27	odd	8	inner
384.3.m.a.271.1		64	96.5	odd	8
384.3.m.a.367.1		64	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92437 + 0.544810i) q^{2} +(3.40636 + 2.09683i) q^{4} +(8.76568 - 3.63086i) q^{5} +(-4.20494 - 4.20494i) q^{7} +(5.41272 + 5.89088i) q^{8} +O(q^{10})\)	\(q+(1.92437 + 0.544810i) q^{2} +(3.40636 + 2.09683i) q^{4} +(8.76568 - 3.63086i) q^{5} +(-4.20494 - 4.20494i) q^{7} +(5.41272 + 5.89088i) q^{8} +(18.8465 - 2.21148i) q^{10} +(5.56206 - 2.30388i) q^{11} +(-14.9974 - 6.21214i) q^{13} +(-5.80095 - 10.3827i) q^{14} +(7.20663 + 14.2851i) q^{16} -12.9832i q^{17} +(-10.3282 + 24.9345i) q^{19} +(37.4724 + 6.01208i) q^{20} +(11.9586 - 1.40324i) q^{22} +(-8.55583 + 8.55583i) q^{23} +(45.9763 - 45.9763i) q^{25} +(-25.4761 - 20.1252i) q^{26} +(-5.50653 - 23.1406i) q^{28} +(-9.46145 + 22.8420i) q^{29} +48.3450i q^{31} +(6.08552 + 31.4160i) q^{32} +(7.07337 - 24.9844i) q^{34} +(-52.1268 - 21.5916i) q^{35} +(11.1557 - 4.62085i) q^{37} +(-33.4598 + 42.3561i) q^{38} +(68.8351 + 31.9848i) q^{40} +(27.8116 + 27.8116i) q^{41} +(-12.7950 + 5.29987i) q^{43} +(23.7772 + 3.81482i) q^{44} +(-21.1258 + 11.8032i) q^{46} +11.5912 q^{47} -13.6369i q^{49} +(113.524 - 63.4269i) q^{50} +(-38.0610 - 52.6079i) q^{52} +(-14.2996 - 34.5222i) q^{53} +(40.3902 - 40.3902i) q^{55} +(2.01066 - 47.5310i) q^{56} +(-30.6518 + 38.8016i) q^{58} +(0.579648 + 1.39939i) q^{59} +(-26.5897 + 64.1932i) q^{61} +(-26.3388 + 93.0334i) q^{62} +(-5.40501 + 63.7714i) q^{64} -154.018 q^{65} +(-27.4843 - 11.3844i) q^{67} +(27.2235 - 44.2255i) q^{68} +(-88.5476 - 69.9494i) q^{70} +(-68.0841 - 68.0841i) q^{71} +(-44.4027 - 44.4027i) q^{73} +(23.9852 - 2.81446i) q^{74} +(-87.4648 + 63.2794i) q^{76} +(-33.0758 - 13.7005i) q^{77} -128.678 q^{79} +(115.038 + 99.0525i) q^{80} +(38.3677 + 68.6718i) q^{82} +(28.1951 - 68.0690i) q^{83} +(-47.1402 - 113.806i) q^{85} +(-27.5097 + 3.22803i) q^{86} +(43.6778 + 20.2952i) q^{88} +(-24.5112 + 24.5112i) q^{89} +(36.9417 + 89.1851i) q^{91} +(-47.0843 + 11.2042i) q^{92} +(22.3057 + 6.31499i) q^{94} +256.068i q^{95} +114.722 q^{97} +(7.42952 - 26.2424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) \) 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

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