LMFDB - Embedded newform 325.3.g.a.99.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(99,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.99"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.g (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,0,0,0,-16,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.1
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	325.99
Dual form			325.3.g.a.174.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.58114 + 2.58114i) q^{2} +2.16228i q^{3} -9.32456i q^{4} +(-5.58114 - 5.58114i) q^{6} +(1.41886 + 1.41886i) q^{7} +(13.7434 + 13.7434i) q^{8} +4.32456 q^{9} +(-7.32456 + 7.32456i) q^{11} +20.1623 q^{12} +(8.41886 + 9.90569i) q^{13} -7.32456 q^{14} -33.6491 q^{16} -15.9737 q^{17} +(-11.1623 + 11.1623i) q^{18} +(3.16228 + 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -37.8114i q^{22} -27.4868 q^{23} +(-29.7171 + 29.7171i) q^{24} +(-47.2982 - 3.83772i) q^{26} +28.8114i q^{27} +(13.2302 - 13.2302i) q^{28} -25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(31.8794 - 31.8794i) q^{32} +(-15.8377 - 15.8377i) q^{33} +(41.2302 - 41.2302i) q^{34} -40.3246i q^{36} +(4.23025 + 4.23025i) q^{37} -16.3246 q^{38} +(-21.4189 + 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} -15.8377i q^{42} +11.5132 q^{43} +(68.2982 + 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 - 35.3662i) q^{47} -72.7587i q^{48} -44.9737i q^{49} -34.5395i q^{51} +(92.3662 - 78.5021i) q^{52} -4.18861i q^{53} +(-74.3662 - 74.3662i) q^{54} +39.0000i q^{56} +(-6.83772 + 6.83772i) q^{57} +(66.6228 - 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} -100.596 q^{62} +(6.13594 + 6.13594i) q^{63} +29.9737i q^{64} +81.7587 q^{66} +(-81.0833 + 81.0833i) q^{67} +148.947i q^{68} -59.4342i q^{69} +(50.4452 + 50.4452i) q^{71} +(59.4342 + 59.4342i) q^{72} +(-31.6228 - 31.6228i) q^{73} -21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} -20.7851 q^{77} +(8.29822 - 102.272i) q^{78} -50.7851 q^{79} -23.3772 q^{81} -57.6228 q^{82} +(-18.6228 + 18.6228i) q^{83} +(28.6075 + 28.6075i) q^{84} +(-29.7171 + 29.7171i) q^{86} -55.8114i q^{87} -201.329 q^{88} +(-91.1096 + 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302i q^{92} +(-42.1359 + 42.1359i) q^{93} +182.570 q^{94} +(68.9320 + 68.9320i) q^{96} +(87.3552 - 87.3552i) q^{97} +(116.083 + 116.083i) q^{98} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 16 q^{6} + 12 q^{7} + 36 q^{8} - 8 q^{9} - 4 q^{11} + 68 q^{12} + 40 q^{13} - 4 q^{14} - 84 q^{16} + 12 q^{17} - 32 q^{18} + 32 q^{21} - 72 q^{23} - 24 q^{24} - 88 q^{26} - 4 q^{28} - 40 q^{29}+ \cdots - 152 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 16 * q^6 + 12 * q^7 + 36 * q^8 - 8 * q^9 - 4 * q^11 + 68 * q^12 + 40 * q^13 - 4 * q^14 - 84 * q^16 + 12 * q^17 - 32 * q^18 + 32 * q^21 - 72 * q^23 - 24 * q^24 - 88 * q^26 - 4 * q^28 - 40 * q^29 + 40 * q^31 + 20 * q^32 - 76 * q^33 + 108 * q^34 - 40 * q^37 - 40 * q^38 - 92 * q^39 + 32 * q^41 + 84 * q^43 + 172 * q^44 + 132 * q^46 + 4 * q^47 + 224 * q^52 - 152 * q^54 - 40 * q^57 + 140 * q^58 - 56 * q^59 - 296 * q^61 - 200 * q^62 - 64 * q^63 + 112 * q^66 - 84 * q^67 + 284 * q^71 + 48 * q^72 - 100 * q^74 + 80 * q^76 + 56 * q^77 - 68 * q^78 - 64 * q^79 - 220 * q^81 - 104 * q^82 + 52 * q^83 + 184 * q^84 - 24 * q^86 - 312 * q^88 - 200 * q^89 + 156 * q^91 - 80 * q^93 + 452 * q^94 + 320 * q^96 - 68 * q^97 + 224 * q^98 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.58114	+	2.58114i	−1.29057	+	1.29057i	−0.356135	+	0.934435i	$0.615906\pi$
$2$	−2.58114	+	2.58114i	−1.29057	+	1.29057i	−0.934435	+	0.356135i	$0.884094\pi$
$3$			2.16228i			0.720759i	0.932806	+	0.360380i	$0.117353\pi$
$3$			2.16228i			0.720759i	−0.932806	+	0.360380i	$0.882647\pi$
$4$		−	9.32456i		−	2.33114i
$5$		0			0
$5$		0			0
$6$	−5.58114	−	5.58114i	−0.930190	−	0.930190i
$7$	1.41886	+	1.41886i	0.202694	+	0.202694i	0.801153	−	0.598459i	$-0.204220\pi$
$7$	1.41886	+	1.41886i	0.202694	+	0.202694i	−0.598459	+	0.801153i	$0.704220\pi$
$8$	13.7434	+	13.7434i	1.71793	+	1.71793i
$9$	4.32456			0.480506
$10$		0			0
$11$	−7.32456	+	7.32456i	−0.665869	+	0.665869i	−0.956757	−	0.290888i	$-0.906049\pi$
$11$	−7.32456	+	7.32456i	−0.665869	+	0.665869i	0.290888	+	0.956757i	$0.406049\pi$
$12$	20.1623			1.68019
$13$	8.41886	+	9.90569i	0.647605	+	0.761976i
$13$	8.41886	+	9.90569i	0.647605	+	0.761976i
$14$	−7.32456			−0.523183
$15$		0			0
$16$	−33.6491			−2.10307
$17$	−15.9737			−0.939627			−0.469814	−	0.882766i	$-0.655679\pi$
$17$	−15.9737			−0.939627			−0.469814	+	0.882766i	$0.655679\pi$
$18$	−11.1623	+	11.1623i	−0.620127	+	0.620127i
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	0.785411	−	0.618975i	$-0.212452\pi$
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	−0.618975	+	0.785411i	$0.712452\pi$
$20$		0			0
$21$	−3.06797	+	3.06797i	−0.146094	+	0.146094i
$22$		−	37.8114i		−	1.71870i
$23$	−27.4868			−1.19508			−0.597540	−	0.801839i	$-0.703855\pi$
$23$	−27.4868			−1.19508			−0.597540	+	0.801839i	$0.703855\pi$
$24$	−29.7171	+	29.7171i	−1.23821	+	1.23821i
$25$		0			0
$26$	−47.2982	−	3.83772i	−1.81916	−	0.147605i
$27$			28.8114i			1.06709i
$28$	13.2302	−	13.2302i	0.472509	−	0.472509i
$29$	−25.8114			−0.890048			−0.445024	−	0.895519i	$-0.646805\pi$
$29$	−25.8114			−0.890048			−0.445024	+	0.895519i	$0.646805\pi$
$30$		0			0
$31$	19.4868	+	19.4868i	0.628608	+	0.628608i	0.947718	−	0.319110i	$-0.103384\pi$
$31$	19.4868	+	19.4868i	0.628608	+	0.628608i	−0.319110	+	0.947718i	$0.603384\pi$
$32$	31.8794	−	31.8794i	0.996230	−	0.996230i
$33$	−15.8377	−	15.8377i	−0.479931	−	0.479931i
$34$	41.2302	−	41.2302i	1.21265	−	1.21265i
$35$		0			0
$36$		−	40.3246i		−	1.12013i
$37$	4.23025	+	4.23025i	0.114331	+	0.114331i	0.761958	−	0.647627i	$-0.224238\pi$
$37$	4.23025	+	4.23025i	0.114331	+	0.114331i	−0.647627	+	0.761958i	$0.724238\pi$
$38$	−16.3246			−0.429594
$39$	−21.4189	+	18.2039i	−0.549202	+	0.466767i
$40$		0			0
$41$	11.1623	+	11.1623i	0.272251	+	0.272251i	0.830006	−	0.557755i	$-0.188337\pi$
$41$	11.1623	+	11.1623i	0.272251	+	0.272251i	−0.557755	+	0.830006i	$0.688337\pi$
$42$		−	15.8377i		−	0.377089i
$43$	11.5132			0.267748			0.133874	−	0.990998i	$-0.457258\pi$
$43$	11.5132			0.267748			0.133874	+	0.990998i	$0.457258\pi$
$44$	68.2982	+	68.2982i	1.55223	+	1.55223i
$45$		0			0
$46$	70.9473	−	70.9473i	1.54233	−	1.54233i
$47$	−35.3662	−	35.3662i	−0.752472	−	0.752472i	0.222468	−	0.974940i	$-0.428589\pi$
$47$	−35.3662	−	35.3662i	−0.752472	−	0.752472i	−0.974940	+	0.222468i	$0.928589\pi$
$48$		−	72.7587i		−	1.51581i
$49$		−	44.9737i		−	0.917830i
$50$		0			0
$51$		−	34.5395i		−	0.677245i
$52$	92.3662	−	78.5021i	1.77627	−	1.50966i
$53$		−	4.18861i		−	0.0790304i	−0.999219	−	0.0395152i	$-0.987419\pi$
$53$		−	4.18861i		−	0.0790304i	0.999219	−	0.0395152i	$-0.0125814\pi$
$54$	−74.3662	−	74.3662i	−1.37715	−	1.37715i
$55$		0			0
$56$			39.0000i			0.696429i
$57$	−6.83772	+	6.83772i	−0.119960	+	0.119960i
$58$	66.6228	−	66.6228i	1.14867	−	1.14867i
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	−0.402387	−	0.915470i	$-0.631819\pi$
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	0.915470	+	0.402387i	$0.131819\pi$
$60$		0			0
$61$	−67.6754			−1.10943			−0.554717	−	0.832039i	$-0.687173\pi$
$61$	−67.6754			−1.10943			−0.554717	+	0.832039i	$0.687173\pi$
$62$	−100.596			−1.62252
$63$	6.13594	+	6.13594i	0.0973959	+	0.0973959i
$64$			29.9737i			0.468339i
$65$		0			0
$66$	81.7587			1.23877
$67$	−81.0833	+	81.0833i	−1.21020	+	1.21020i	−0.239237	+	0.970961i	$0.576897\pi$
$67$	−81.0833	+	81.0833i	−1.21020	+	1.21020i	−0.970961	+	0.239237i	$0.923103\pi$
$68$			148.947i			2.19040i
$69$		−	59.4342i		−	0.861365i
$70$		0			0
$71$	50.4452	+	50.4452i	0.710496	+	0.710496i	0.966639	−	0.256143i	$-0.0824518\pi$
$71$	50.4452	+	50.4452i	0.710496	+	0.710496i	−0.256143	+	0.966639i	$0.582452\pi$
$72$	59.4342	+	59.4342i	0.825475	+	0.825475i
$73$	−31.6228	−	31.6228i	−0.433189	−	0.433189i	0.456523	−	0.889712i	$-0.349095\pi$
$73$	−31.6228	−	31.6228i	−0.433189	−	0.433189i	−0.889712	+	0.456523i	$0.849095\pi$
$74$	−21.8377			−0.295104
$75$		0			0
$76$	29.4868	−	29.4868i	0.387985	−	0.387985i
$77$	−20.7851			−0.269936
$78$	8.29822	−	102.272i	0.106387	−	1.31118i
$79$	−50.7851			−0.642849			−0.321424	−	0.946935i	$-0.604162\pi$
$79$	−50.7851			−0.642849			−0.321424	+	0.946935i	$0.604162\pi$
$80$		0			0
$81$	−23.3772			−0.288608
$82$	−57.6228			−0.702717
$83$	−18.6228	+	18.6228i	−0.224371	+	0.224371i	−0.810336	−	0.585965i	$-0.800715\pi$
$83$	−18.6228	+	18.6228i	−0.224371	+	0.224371i	0.585965	+	0.810336i	$0.300715\pi$
$84$	28.6075	+	28.6075i	0.340565	+	0.340565i
$85$		0			0
$86$	−29.7171	+	29.7171i	−0.345547	+	0.345547i
$87$		−	55.8114i		−	0.641510i
$88$	−201.329			−2.28783
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.0239913	+	0.999712i	$0.507637\pi$
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.999712	+	0.0239913i	$0.992363\pi$
$90$		0			0
$91$	−2.10961	+	26.0000i	−0.0231825	+	0.285714i
$92$			256.302i			2.78590i
$93$	−42.1359	+	42.1359i	−0.453075	+	0.453075i
$94$	182.570			1.94224
$95$		0			0
$96$	68.9320	+	68.9320i	0.718042	+	0.718042i
$97$	87.3552	−	87.3552i	0.900569	−	0.900569i	−0.0949165	−	0.995485i	$-0.530258\pi$
$97$	87.3552	−	87.3552i	0.900569	−	0.900569i	0.995485	+	0.0949165i	$0.0302584\pi$
$98$	116.083	+	116.083i	1.18452	+	1.18452i
$99$	−31.6754	+	31.6754i	−0.319954	+	0.319954i
$100$		0			0
$101$		−	8.92100i		−	0.0883267i	−0.999024	−	0.0441634i	$-0.985938\pi$
$101$		−	8.92100i		−	0.0883267i	0.999024	−	0.0441634i	$-0.0140622\pi$
$102$	89.1512	+	89.1512i	0.874032	+	0.874032i
$103$	−59.4342			−0.577031			−0.288515	−	0.957475i	$-0.593162\pi$
$103$	−59.4342			−0.577031			−0.288515	+	0.957475i	$0.593162\pi$
$104$	−20.4342	+	251.842i	−0.196482	+	2.42156i
$105$		0			0
$106$	10.8114	+	10.8114i	0.101994	+	0.101994i
$107$			143.570i			1.34178i	0.741558	+	0.670888i	$0.234087\pi$
$107$			143.570i			1.34178i	−0.741558	+	0.670888i	$0.765913\pi$
$108$	268.653			2.48753
$109$	84.7740	+	84.7740i	0.777743	+	0.777743i	0.979447	−	0.201703i	$-0.0646477\pi$
$109$	84.7740	+	84.7740i	0.777743	+	0.777743i	−0.201703	+	0.979447i	$0.564648\pi$
$110$		0			0
$111$	−9.14697	+	9.14697i	−0.0824052	+	0.0824052i
$112$	−47.7434	−	47.7434i	−0.426281	−	0.426281i
$113$		−	108.544i		−	0.960564i	−0.877114	−	0.480282i	$-0.840534\pi$
$113$		−	108.544i		−	0.960564i	0.877114	−	0.480282i	$-0.159466\pi$
$114$		−	35.2982i		−	0.309634i
$115$		0			0
$116$			240.680i			2.07483i
$117$	36.4078	+	42.8377i	0.311178	+	0.366134i
$118$			156.272i			1.32434i
$119$	−22.6644	−	22.6644i	−0.190457	−	0.190457i
$120$		0			0
$121$			13.7018i			0.113238i
$122$	174.680	−	174.680i	1.43180	−	1.43180i
$123$	−24.1359	+	24.1359i	−0.196227	+	0.196227i
$124$	181.706	−	181.706i	1.46537	−	1.46537i
$125$		0			0
$126$	−31.6754			−0.251392
$127$	−94.8377			−0.746754			−0.373377	−	0.927680i	$-0.621800\pi$
$127$	−94.8377			−0.746754			−0.373377	+	0.927680i	$0.621800\pi$
$128$	50.1512	+	50.1512i	0.391807	+	0.391807i
$129$			24.8947i			0.192982i
$130$		0			0
$131$	−112.268			−0.857005			−0.428502	−	0.903541i	$-0.640959\pi$
$131$	−112.268			−0.857005			−0.428502	+	0.903541i	$0.640959\pi$
$132$	−147.680	+	147.680i	−1.11879	+	1.11879i
$133$			8.97367i			0.0674712i
$134$		−	418.574i		−	3.12369i
$135$		0			0
$136$	−219.533	−	219.533i	−1.61421	−	1.61421i
$137$	−86.7281	−	86.7281i	−0.633052	−	0.633052i	0.315780	−	0.948832i	$-0.397734\pi$
$137$	−86.7281	−	86.7281i	−0.633052	−	0.633052i	−0.948832	+	0.315780i	$0.897734\pi$
$138$	153.408	+	153.408i	1.11165	+	1.11165i
$139$	−78.5395			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$139$	−78.5395			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$140$		0			0
$141$	76.4715	−	76.4715i	0.542351	−	0.542351i
$142$	−260.412			−1.83389
$143$	−134.219	−	10.8904i	−0.938596	−	0.0761566i
$144$	−145.517			−1.01054
$145$		0			0
$146$	163.246			1.11812
$147$	97.2456			0.661534
$148$	39.4452	−	39.4452i	0.266522	−	0.266522i
$149$	128.219	+	128.219i	0.860532	+	0.860532i	0.991400	−	0.130868i	$-0.0417764\pi$
$149$	128.219	+	128.219i	0.860532	+	0.860532i	−0.130868	+	0.991400i	$0.541776\pi$
$150$		0			0
$151$	29.1776	−	29.1776i	0.193229	−	0.193229i	−0.603861	−	0.797090i	$-0.706372\pi$
$151$	29.1776	−	29.1776i	0.193229	−	0.193229i	0.797090	+	0.603861i	$0.206372\pi$
$152$			86.9210i			0.571849i
$153$	−69.0790			−0.451497
$154$	53.6491	−	53.6491i	0.348371	−	0.348371i
$155$		0			0
$156$	169.743	+	199.721i	1.08810	+	1.28027i
$157$		−	232.544i		−	1.48117i	−0.671962	−	0.740585i	$-0.734548\pi$
$157$		−	232.544i		−	1.48117i	0.671962	−	0.740585i	$-0.265452\pi$
$158$	131.083	−	131.083i	0.829641	−	0.829641i
$159$	9.05694			0.0569619
$160$		0			0
$161$	−39.0000	−	39.0000i	−0.242236	−	0.242236i
$162$	60.3399	−	60.3399i	0.372468	−	0.372468i
$163$	11.4605	+	11.4605i	0.0703098	+	0.0703098i	0.741387	−	0.671077i	$-0.234168\pi$
$163$	11.4605	+	11.4605i	0.0703098	+	0.0703098i	−0.671077	+	0.741387i	$0.734168\pi$
$164$	104.083	−	104.083i	0.634654	−	0.634654i
$165$		0			0
$166$		−	96.1359i		−	0.579132i
$167$	206.785	+	206.785i	1.23823	+	1.23823i	0.960722	+	0.277512i	$0.0895097\pi$
$167$	206.785	+	206.785i	1.23823	+	1.23823i	0.277512	+	0.960722i	$0.410490\pi$
$168$	−84.3288			−0.501957
$169$	−27.2456	+	166.789i	−0.161216	+	0.986919i
$170$		0			0
$171$	13.6754	+	13.6754i	0.0799734	+	0.0799734i
$172$		−	107.355i		−	0.624158i
$173$	91.3815			0.528217			0.264108	−	0.964493i	$-0.414922\pi$
$173$	91.3815			0.528217			0.264108	+	0.964493i	$0.414922\pi$
$174$	144.057	+	144.057i	0.827913	+	0.827913i
$175$		0			0
$176$	246.465	−	246.465i	1.40037	−	1.40037i
$177$	65.4562	+	65.4562i	0.369809	+	0.369809i
$178$		−	470.333i		−	2.64232i
$179$			71.6712i			0.400398i	0.979755	+	0.200199i	$0.0641588\pi$
$179$			71.6712i			0.400398i	−0.979755	+	0.200199i	$0.935841\pi$
$180$		0			0
$181$			274.144i			1.51461i	0.653061	+	0.757305i	$0.273484\pi$
$181$			274.144i			1.51461i	−0.653061	+	0.757305i	$0.726516\pi$
$182$	−61.6644	−	72.5548i	−0.338815	−	0.398653i
$183$		−	146.333i		−	0.799634i
$184$	−377.763	−	377.763i	−2.05306	−	2.05306i
$185$		0			0
$186$		−	217.517i		−	1.16945i
$187$	117.000	−	117.000i	0.625668	−	0.625668i
$188$	−329.774	+	329.774i	−1.75412	+	1.75412i
$189$	−40.8794	+	40.8794i	−0.216293	+	0.216293i
$190$		0			0
$191$	179.706			0.940869			0.470435	−	0.882435i	$-0.344097\pi$
$191$	179.706			0.940869			0.470435	+	0.882435i	$0.344097\pi$
$192$	−64.8114			−0.337559
$193$	−1.13594	−	1.13594i	−0.00588572	−	0.00588572i	0.704158	−	0.710044i	$-0.251325\pi$
$193$	−1.13594	−	1.13594i	−0.00588572	−	0.00588572i	−0.710044	+	0.704158i	$0.751325\pi$
$194$			450.952i			2.32449i
$195$		0			0
$196$	−419.359			−2.13959
$197$	141.906	−	141.906i	0.720333	−	0.720333i	−0.248340	−	0.968673i	$-0.579885\pi$
$197$	141.906	−	141.906i	0.720333	−	0.720333i	0.968673	+	0.248340i	$0.0798849\pi$
$198$		−	163.517i		−	0.825846i
$199$			259.759i			1.30532i	0.757651	+	0.652660i	$0.226347\pi$
$199$			259.759i			1.30532i	−0.757651	+	0.652660i	$0.773653\pi$
$200$		0			0
$201$	−175.325	−	175.325i	−0.872261	−	0.872261i
$202$	23.0263	+	23.0263i	0.113992	+	0.113992i
$203$	−36.6228	−	36.6228i	−0.180408	−	0.180408i
$204$	−322.065			−1.57875
$205$		0			0
$206$	153.408	−	153.408i	0.744698	−	0.744698i
$207$	−118.868			−0.574243
$208$	−283.287	−	333.318i	−1.36196	−	1.60249i
$209$	−46.3246			−0.221649
$210$		0			0
$211$	325.574			1.54301			0.771503	−	0.636225i	$-0.219505\pi$
$211$	325.574			1.54301			0.771503	+	0.636225i	$0.219505\pi$
$212$	−39.0569			−0.184231
$213$	−109.077	+	109.077i	−0.512096	+	0.512096i
$214$	−370.574	−	370.574i	−1.73166	−	1.73166i
$215$		0			0
$216$	−395.967	+	395.967i	−1.83318	+	1.83318i
$217$			55.2982i			0.254831i
$218$	−437.627			−2.00746
$219$	68.3772	−	68.3772i	0.312225	−	0.312225i
$220$		0			0
$221$	−134.480	−	158.230i	−0.608507	−	0.715974i
$222$		−	47.2192i		−	0.212699i
$223$	243.774	−	243.774i	1.09316	−	1.09316i	0.0979674	−	0.995190i	$-0.468766\pi$
$223$	243.774	−	243.774i	1.09316	−	1.09316i	0.995190	−	0.0979674i	$-0.0312341\pi$
$224$	90.4648			0.403861
$225$		0			0
$226$	280.167	+	280.167i	1.23968	+	1.23968i
$227$	−100.732	+	100.732i	−0.443755	+	0.443755i	−0.893272	−	0.449517i	$-0.851596\pi$
$227$	−100.732	+	100.732i	−0.443755	+	0.443755i	0.449517	+	0.893272i	$0.351596\pi$
$228$	63.7587	+	63.7587i	0.279644	+	0.279644i
$229$	240.366	−	240.366i	1.04963	−	1.04963i	0.0509319	−	0.998702i	$-0.483781\pi$
$229$	240.366	−	240.366i	1.04963	−	1.04963i	0.998702	−	0.0509319i	$-0.0162191\pi$
$230$		0			0
$231$		−	44.9431i		−	0.194559i
$232$	−354.737	−	354.737i	−1.52904	−	1.52904i
$233$	10.7893			0.0463061			0.0231531	−	0.999732i	$-0.492629\pi$
$233$	10.7893			0.0463061			0.0231531	+	0.999732i	$0.492629\pi$
$234$	−204.544	−	16.5964i	−0.874119	−	0.0709250i
$235$		0			0
$236$	−282.272	−	282.272i	−1.19607	−	1.19607i
$237$		−	109.811i		−	0.463339i
$238$	117.000			0.491597
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	0.881775	−	0.471670i	$-0.156348\pi$
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	−0.471670	+	0.881775i	$0.656348\pi$
$240$		0			0
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	−0.985245	−	0.171149i	$-0.945252\pi$
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	0.171149	+	0.985245i	$0.445252\pi$
$242$	−35.3662	−	35.3662i	−0.146141	−	0.146141i
$243$			208.754i			0.859072i
$244$			631.043i			2.58624i
$245$		0			0
$246$		−	124.596i		−	0.506490i
$247$	−4.70178	+	57.9473i	−0.0190355	+	0.234605i
$248$			535.631i			2.15980i
$249$	−40.2676	−	40.2676i	−0.161717	−	0.161717i
$250$		0			0
$251$		−	95.8420i		−	0.381841i	−0.981606	−	0.190920i	$-0.938853\pi$
$251$		−	95.8420i		−	0.381841i	0.981606	−	0.190920i	$-0.0611472\pi$
$252$	57.2149	−	57.2149i	0.227043	−	0.227043i
$253$	201.329	−	201.329i	0.795766	−	0.795766i
$254$	244.789	−	244.789i	0.963738	−	0.963738i
$255$		0			0
$256$	−378.789			−1.47965
$257$	450.579			1.75322			0.876612	−	0.481198i	$-0.159798\pi$
$257$	450.579			1.75322			0.876612	+	0.481198i	$0.159798\pi$
$258$	−64.2566	−	64.2566i	−0.249057	−	0.249057i
$259$			12.0043i			0.0463485i
$260$		0			0
$261$	−111.623			−0.427673
$262$	289.778	−	289.778i	1.10602	−	1.10602i
$263$			166.982i			0.634913i	0.948273	+	0.317457i	$0.102829\pi$
$263$			166.982i			0.634913i	−0.948273	+	0.317457i	$0.897171\pi$
$264$		−	435.329i		−	1.64897i
$265$		0			0
$266$	−23.1623	−	23.1623i	−0.0870762	−	0.0870762i
$267$	−197.004	−	197.004i	−0.737844	−	0.737844i
$268$	756.065	+	756.065i	2.82114	+	2.82114i
$269$	−170.061			−0.632198			−0.316099	−	0.948726i	$-0.602373\pi$
$269$	−170.061			−0.632198			−0.316099	+	0.948726i	$0.602373\pi$
$270$		0			0
$271$	−217.072	+	217.072i	−0.801005	+	0.801005i	−0.983253	−	0.182248i	$-0.941663\pi$
$271$	−217.072	+	217.072i	−0.801005	+	0.801005i	0.182248	+	0.983253i	$0.441663\pi$
$272$	537.500			1.97610
$273$	−56.2192	−	4.56156i	−0.205931	−	0.0167090i
$274$	447.715			1.63399
$275$		0			0
$276$	−554.197			−2.00796
$277$	187.947			0.678510			0.339255	−	0.940694i	$-0.389825\pi$
$277$	187.947			0.678510			0.339255	+	0.940694i	$0.389825\pi$
$278$	202.721	−	202.721i	0.729214	−	0.729214i
$279$	84.2719	+	84.2719i	0.302050	+	0.302050i
$280$		0			0
$281$	286.846	−	286.846i	1.02081	−	1.02081i	0.0210263	−	0.999779i	$-0.493307\pi$
$281$	286.846	−	286.846i	1.02081	−	1.02081i	0.999779	−	0.0210263i	$-0.00669337\pi$
$282$			394.767i			1.39988i
$283$	399.201			1.41061			0.705303	−	0.708906i	$-0.250811\pi$
$283$	399.201			1.41061			0.705303	+	0.708906i	$0.250811\pi$
$284$	470.379	−	470.379i	1.65626	−	1.65626i
$285$		0			0
$286$	374.548	−	318.329i	1.30961	−	1.11304i
$287$			31.6754i			0.110367i
$288$	137.864	−	137.864i	0.478695	−	0.478695i
$289$	−33.8420			−0.117100
$290$		0			0
$291$	188.886	+	188.886i	0.649093	+	0.649093i
$292$	−294.868	+	294.868i	−1.00982	+	1.00982i
$293$	136.156	+	136.156i	0.464695	+	0.464695i	0.900191	−	0.435496i	$-0.143427\pi$
$293$	136.156	+	136.156i	0.464695	+	0.464695i	−0.435496	+	0.900191i	$0.643427\pi$
$294$	−251.004	+	251.004i	−0.853756	+	0.853756i
$295$		0			0
$296$			116.276i			0.392825i
$297$	−211.031	−	211.031i	−0.710541	−	0.710541i
$298$	−661.903			−2.22115
$299$	−231.408	−	272.276i	−0.773939	−	0.910623i
$300$		0			0
$301$	16.3356	+	16.3356i	0.0542710	+	0.0542710i
$302$			150.623i			0.498751i
$303$	19.2897			0.0636623
$304$	−106.408	−	106.408i	−0.350026	−	0.350026i
$305$		0			0
$306$	178.302	−	178.302i	0.582688	−	0.582688i
$307$	235.684	+	235.684i	0.767700	+	0.767700i	0.977701	−	0.210001i	$-0.0673467\pi$
$307$	235.684	+	235.684i	0.767700	+	0.767700i	−0.210001	+	0.977701i	$0.567347\pi$
$308$			193.811i			0.629258i
$309$		−	128.513i		−	0.415900i
$310$		0			0
$311$		−	113.684i		−	0.365543i	−0.983155	−	0.182772i	$-0.941493\pi$
$311$		−	113.684i		−	0.365543i	0.983155	−	0.182772i	$-0.0585069\pi$
$312$	−544.552	−	44.1843i	−1.74536	−	0.141616i
$313$			223.483i			0.714002i	0.934104	+	0.357001i	$0.116201\pi$
$313$			223.483i			0.714002i	−0.934104	+	0.357001i	$0.883799\pi$
$314$	600.228	+	600.228i	1.91155	+	1.91155i
$315$		0			0
$316$			473.548i			1.49857i
$317$	−125.140	+	125.140i	−0.394764	+	0.394764i	−0.876382	−	0.481617i	$-0.840049\pi$
$317$	−125.140	+	125.140i	−0.394764	+	0.394764i	0.481617	+	0.876382i	$0.340049\pi$
$318$	−23.3772	+	23.3772i	−0.0735133	+	0.0735133i
$319$	189.057	−	189.057i	0.592655	−	0.592655i
$320$		0			0
$321$	−310.438			−0.967098
$322$	201.329			0.625245
$323$	−50.5132	−	50.5132i	−0.156388	−	0.156388i
$324$			217.982i			0.672785i
$325$		0			0
$326$	−59.1623			−0.181479
$327$	−183.305	+	183.305i	−0.560566	+	0.560566i
$328$			306.816i			0.935414i
$329$		−	100.359i		−	0.305044i
$330$		0			0
$331$	309.982	+	309.982i	0.936502	+	0.936502i	0.998101	−	0.0615988i	$-0.0196199\pi$
$331$	309.982	+	309.982i	0.936502	+	0.936502i	−0.0615988	+	0.998101i	$0.519620\pi$
$332$	173.649	+	173.649i	0.523039	+	0.523039i
$333$	18.2939	+	18.2939i	0.0549368	+	0.0549368i
$334$	−1067.48			−3.19605
$335$		0			0
$336$	103.235	−	103.235i	0.307246	−	0.307246i
$337$	5.32456			0.0157999			0.00789993	−	0.999969i	$-0.497485\pi$
$337$	5.32456			0.0157999			0.00789993	+	0.999969i	$0.497485\pi$
$338$	−360.182	−	500.831i	−1.06563	−	1.48175i
$339$	234.702			0.692336
$340$		0			0
$341$	−285.465			−0.837140
$342$	−70.5964			−0.206422
$343$	133.336	−	133.336i	0.388733	−	0.388733i
$344$	158.230	+	158.230i	0.459972	+	0.459972i
$345$		0			0
$346$	−235.868	+	235.868i	−0.681700	+	0.681700i
$347$			47.2413i			0.136142i	0.997680	+	0.0680710i	$0.0216844\pi$
$347$			47.2413i			0.136142i	−0.997680	+	0.0680710i	$0.978316\pi$
$348$	−520.416			−1.49545
$349$	−223.581	+	223.581i	−0.640634	+	0.640634i	−0.950711	−	0.310078i	$-0.899645\pi$
$349$	−223.581	+	223.581i	−0.640634	+	0.640634i	0.310078	+	0.950711i	$0.399645\pi$
$350$		0			0
$351$	−285.397	+	242.559i	−0.813096	+	0.691052i
$352$			467.004i			1.32672i
$353$	−110.320	+	110.320i	−0.312522	+	0.312522i	−0.845886	−	0.533364i	$-0.820928\pi$
$353$	−110.320	+	110.320i	−0.312522	+	0.312522i	0.533364	+	0.845886i	$0.320928\pi$
$354$	−337.903			−0.954529
$355$		0			0
$356$	849.557	+	849.557i	2.38639	+	2.38639i
$357$	49.0068	−	49.0068i	0.137274	−	0.137274i
$358$	−184.993	−	184.993i	−0.516741	−	0.516741i
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	−0.789647	−	0.613561i	$-0.789736\pi$
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	0.613561	+	0.789647i	$0.289736\pi$
$360$		0			0
$361$		−	341.000i		−	0.944598i
$362$	−707.605	−	707.605i	−1.95471	−	1.95471i
$363$	−29.6271			−0.0816172
$364$	242.438	+	19.6712i	0.666040	+	0.0540417i
$365$		0			0
$366$	377.706	+	377.706i	1.03198	+	1.03198i
$367$			318.416i			0.867620i	0.901004	+	0.433810i	$0.142831\pi$
$367$			318.416i			0.867620i	−0.901004	+	0.433810i	$0.857169\pi$
$368$	924.907			2.51334
$369$	48.2719	+	48.2719i	0.130818	+	0.130818i
$370$		0			0
$371$	5.94306	−	5.94306i	0.0160190	−	0.0160190i
$372$	392.899	+	392.899i	1.05618	+	1.05618i
$373$			8.87688i			0.0237986i	0.999929	+	0.0118993i	$0.00378775\pi$
$373$			8.87688i			0.0237986i	−0.999929	+	0.0118993i	$0.996212\pi$
$374$			603.986i			1.61494i
$375$		0			0
$376$		−	972.105i		−	2.58538i
$377$	−217.302	−	255.680i	−0.576399	−	0.678196i
$378$		−	211.031i		−	0.558282i
$379$	144.698	+	144.698i	0.381788	+	0.381788i	0.871746	−	0.489958i	$-0.162988\pi$
$379$	144.698	+	144.698i	0.381788	+	0.381788i	−0.489958	+	0.871746i	$0.662988\pi$
$380$		0			0
$381$		−	205.065i		−	0.538230i
$382$	−463.846	+	463.846i	−1.21426	+	1.21426i
$383$	−357.261	+	357.261i	−0.932796	+	0.932796i	−0.997880	−	0.0650838i	$-0.979269\pi$
$383$	−357.261	+	357.261i	−0.932796	+	0.932796i	0.0650838	+	0.997880i	$0.479269\pi$
$384$	−108.441	+	108.441i	−0.282398	+	0.282398i
$385$		0			0
$386$	5.86406			0.0151919
$387$	49.7893			0.128655
$388$	−814.548	−	814.548i	−2.09935	−	2.09935i
$389$		−	438.342i		−	1.12684i	−0.826170	−	0.563421i	$-0.809485\pi$
$389$		−	438.342i		−	1.12684i	0.826170	−	0.563421i	$-0.190515\pi$
$390$		0			0
$391$	439.065			1.12293
$392$	618.092	−	618.092i	1.57676	−	1.57676i
$393$		−	242.754i		−	0.617694i
$394$			732.557i			1.85928i
$395$		0			0
$396$	295.359	+	295.359i	0.745857	+	0.745857i
$397$	−250.061	−	250.061i	−0.629877	−	0.629877i	0.318160	−	0.948037i	$-0.396935\pi$
$397$	−250.061	−	250.061i	−0.629877	−	0.629877i	−0.948037	+	0.318160i	$0.896935\pi$
$398$	−670.473	−	670.473i	−1.68461	−	1.68461i
$399$	−19.4036			−0.0486305
$400$		0			0
$401$	93.7018	−	93.7018i	0.233670	−	0.233670i	−0.580553	−	0.814223i	$-0.697163\pi$
$401$	93.7018	−	93.7018i	0.233670	−	0.233670i	0.814223	+	0.580553i	$0.197163\pi$
$402$	905.074			2.25143
$403$	−28.9737	+	357.088i	−0.0718950	+	0.886073i
$404$	−83.1843			−0.205902
$405$		0			0
$406$	189.057			0.465657
$407$	−61.9694			−0.152259
$408$	474.691	−	474.691i	1.16346	−	1.16346i
$409$	−370.140	−	370.140i	−0.904988	−	0.904988i	0.0908741	−	0.995862i	$-0.471034\pi$
$409$	−370.140	−	370.140i	−0.904988	−	0.904988i	−0.995862	+	0.0908741i	$0.971034\pi$
$410$		0			0
$411$	187.530	−	187.530i	0.456278	−	0.456278i
$412$			554.197i			1.34514i
$413$	85.9032			0.207998
$414$	306.816	−	306.816i	0.741101	−	0.741101i
$415$		0			0
$416$	584.175	+	47.3993i	1.40427	+	0.113941i
$417$		−	169.824i		−	0.407252i
$418$	119.570	−	119.570i	0.286053	−	0.286053i
$419$	658.767			1.57224			0.786118	−	0.618076i	$-0.212088\pi$
$419$	658.767			1.57224			0.786118	+	0.618076i	$0.212088\pi$
$420$		0			0
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	0.605260	−	0.796028i	$-0.293069\pi$
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	−0.796028	+	0.605260i	$0.793069\pi$
$422$	−840.353	+	840.353i	−1.99136	+	1.99136i
$423$	−152.943	−	152.943i	−0.361568	−	0.361568i
$424$	57.5658	−	57.5658i	0.135768	−	0.135768i
$425$		0			0
$426$		−	563.083i		−	1.32179i
$427$	−96.0221	−	96.0221i	−0.224876	−	0.224876i
$428$	1338.73			3.12787
$429$	23.5480	−	290.219i	0.0548906	−	0.676502i
$430$		0			0
$431$	296.037	+	296.037i	0.686862	+	0.686862i	0.961537	−	0.274675i	$-0.0885704\pi$
$431$	296.037	+	296.037i	0.686862	+	0.686862i	−0.274675	+	0.961537i	$0.588570\pi$
$432$		−	969.478i		−	2.24416i
$433$	−156.140			−0.360601			−0.180300	−	0.983612i	$-0.557707\pi$
$433$	−156.140			−0.360601			−0.180300	+	0.983612i	$0.557707\pi$
$434$	−142.732	−	142.732i	−0.328876	−	0.328876i
$435$		0			0
$436$	790.480	−	790.480i	1.81303	−	1.81303i
$437$	−86.9210	−	86.9210i	−0.198904	−	0.198904i
$438$			352.982i			0.805895i
$439$		−	448.710i		−	1.02212i	−0.859545	−	0.511060i	$-0.829253\pi$
$439$		−	448.710i		−	1.02212i	0.859545	−	0.511060i	$-0.170747\pi$
$440$		0			0
$441$		−	194.491i		−	0.441023i
$442$	755.526	+	61.3025i	1.70933	+	0.138693i
$443$		−	577.372i		−	1.30332i	−0.758510	−	0.651662i	$-0.774072\pi$
$443$		−	577.372i		−	1.30332i	0.758510	−	0.651662i	$-0.225928\pi$
$444$	85.2915	+	85.2915i	0.192098	+	0.192098i
$445$		0			0
$446$			1258.43i			2.82159i
$447$	−277.246	+	277.246i	−0.620236	+	0.620236i
$448$	−42.5285	+	42.5285i	−0.0949296	+	0.0949296i
$449$	107.127	−	107.127i	0.238591	−	0.238591i	−0.577675	−	0.816267i	$-0.696040\pi$
$449$	107.127	−	107.127i	0.238591	−	0.238591i	0.816267	+	0.577675i	$0.196040\pi$
$450$		0			0
$451$	−163.517			−0.362566
$452$	−1012.12			−2.23921
$453$	63.0900	+	63.0900i	0.139272	+	0.139272i
$454$		−	520.009i		−	1.14539i
$455$		0			0
$456$	−187.947			−0.412165
$457$	−356.092	+	356.092i	−0.779194	+	0.779194i	−0.979694	−	0.200499i	$-0.935744\pi$
$457$	−356.092	+	356.092i	−0.779194	+	0.779194i	0.200499	+	0.979694i	$0.435744\pi$
$458$			1240.84i			2.70925i
$459$		−	460.223i		−	1.00267i
$460$		0			0
$461$	33.7477	+	33.7477i	0.0732054	+	0.0732054i	0.742761	−	0.669556i	$-0.233516\pi$
$461$	33.7477	+	33.7477i	0.0732054	+	0.0732054i	−0.669556	+	0.742761i	$0.733516\pi$
$462$	116.004	+	116.004i	0.251092	+	0.251092i
$463$	336.355	+	336.355i	0.726469	+	0.726469i	0.969915	−	0.243446i	$-0.0782777\pi$
$463$	336.355	+	336.355i	0.726469	+	0.726469i	−0.243446	+	0.969915i	$0.578278\pi$
$464$	868.530			1.87183
$465$		0			0
$466$	−27.8488	+	27.8488i	−0.0597613	+	0.0597613i
$467$	−308.263			−0.660093			−0.330046	−	0.943965i	$-0.607064\pi$
$467$	−308.263			−0.660093			−0.330046	+	0.943965i	$0.607064\pi$
$468$	399.443	−	339.487i	0.853510	−	0.725399i
$469$	−230.092			−0.490601
$470$		0			0
$471$	502.824			1.06757
$472$	832.078			1.76288
$473$	−84.3288	+	84.3288i	−0.178285	+	0.178285i
$474$	283.438	+	283.438i	0.597971	+	0.597971i
$475$		0			0
$476$	−211.336	+	211.336i	−0.443982	+	0.443982i
$477$		−	18.1139i		−	0.0379746i
$478$	−505.982			−1.05854
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	−0.782569	−	0.622564i	$-0.786091\pi$
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	0.622564	+	0.782569i	$0.286091\pi$
$480$		0			0
$481$	−6.28967	+	77.5174i	−0.0130762	+	0.161159i
$482$		−	1012.82i		−	2.10130i
$483$	84.3288	−	84.3288i	0.174594	−	0.174594i
$484$	127.763			0.263973
$485$		0			0
$486$	−538.824	−	538.824i	−1.10869	−	1.10869i
$487$	−69.0655	+	69.0655i	−0.141818	+	0.141818i	−0.774452	−	0.632633i	$-0.781974\pi$
$487$	−69.0655	+	69.0655i	−0.141818	+	0.141818i	0.632633	+	0.774452i	$0.281974\pi$
$488$	−930.092	−	930.092i	−1.90593	−	1.90593i
$489$	−24.7808	+	24.7808i	−0.0506764	+	0.0506764i
$490$		0			0
$491$		−	685.302i		−	1.39573i	−0.716230	−	0.697864i	$-0.754134\pi$
$491$		−	685.302i		−	1.39573i	0.716230	−	0.697864i	$-0.245866\pi$
$492$	225.057	+	225.057i	0.457433	+	0.457433i
$493$	412.302			0.836313
$494$	−137.434	−	161.706i	−0.278207	−	0.327340i
$495$		0			0
$496$	−655.715	−	655.715i	−1.32201	−	1.32201i
$497$			143.149i			0.288027i
$498$	207.873			0.417415
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	0.264365	−	0.964423i	$-0.414838\pi$
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	−0.964423	+	0.264365i	$0.914838\pi$
$500$		0			0
$501$	−447.127	+	447.127i	−0.892468	+	0.892468i
$502$	247.381	+	247.381i	0.492792	+	0.492792i
$503$			42.2719i			0.0840395i	0.999117	+	0.0420198i	$0.0133792\pi$
$503$			42.2719i			0.0840395i	−0.999117	+	0.0420198i	$0.986621\pi$
$504$			168.658i			0.334638i
$505$		0			0
$506$			1039.32i			2.05398i
$507$	−360.645	−	58.9125i	−0.711331	−	0.116198i
$508$			884.320i			1.74079i
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	0.502521	−	0.864565i	$-0.332406\pi$
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	−0.864565	+	0.502521i	$0.832406\pi$
$510$		0			0
$511$		−	89.7367i		−	0.175610i
$512$	777.103	−	777.103i	1.51778	−	1.51778i
$513$	−91.1096	+	91.1096i	−0.177602	+	0.177602i
$514$	−1163.01	+	1163.01i	−2.26266	+	2.26266i
$515$		0			0
$516$	232.132			0.449868
$517$	518.083			1.00210
$518$	−30.9847	−	30.9847i	−0.0598160	−	0.0598160i
$519$			197.592i			0.380717i
$520$		0			0
$521$	−757.122			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$521$	−757.122			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$522$	288.114	−	288.114i	0.551942	−	0.551942i
$523$		−	221.851i		−	0.424188i	−0.977249	−	0.212094i	$-0.931972\pi$
$523$		−	221.851i		−	0.424188i	0.977249	−	0.212094i	$-0.0680284\pi$
$524$			1046.85i			1.99780i
$525$		0			0
$526$	−431.004	−	431.004i	−0.819400	−	0.819400i
$527$	−311.276	−	311.276i	−0.590657	−	0.590657i
$528$	532.925	+	532.925i	1.00933	+	1.00933i
$529$	226.526			0.428215
$530$		0			0
$531$	130.912	−	130.912i	0.246539	−	0.246539i
$532$	83.6754			0.157285
$533$	−16.5964	+	204.544i	−0.0311378	+	0.383759i
$534$	1016.99			1.90448
$535$		0			0
$536$	−2228.72			−4.15806
$537$	−154.973			−0.288590
$538$	438.952	−	438.952i	0.815895	−	0.815895i
$539$	329.412	+	329.412i	0.611154	+	0.611154i
$540$		0			0
$541$	−243.379	+	243.379i	−0.449869	+	0.449869i	−0.895311	−	0.445442i	$-0.853047\pi$
$541$	−243.379	+	243.379i	−0.449869	+	0.449869i	0.445442	+	0.895311i	$0.353047\pi$
$542$		−	1120.59i		−	2.06750i
$543$	−592.777			−1.09167
$544$	−509.230	+	509.230i	−0.936085	+	0.936085i
$545$		0			0
$546$	156.884	−	133.336i	0.287333	−	0.244204i
$547$			317.777i			0.580944i	0.956883	+	0.290472i	$0.0938124\pi$
$547$			317.777i			0.580944i	−0.956883	+	0.290472i	$0.906188\pi$
$548$	−808.701	+	808.701i	−1.47573	+	1.47573i
$549$	−292.666			−0.533090
$550$		0			0
$551$	−81.6228	−	81.6228i	−0.148136	−	0.148136i
$552$	816.828	−	816.828i	1.47976	−	1.47976i
$553$	−72.0569	−	72.0569i	−0.130302	−	0.130302i
$554$	−485.118	+	485.118i	−0.875665	+	0.875665i
$555$		0			0
$556$			732.346i			1.31717i
$557$	479.423	+	479.423i	0.860724	+	0.860724i	0.991422	−	0.130698i	$-0.0417220\pi$
$557$	479.423	+	479.423i	0.860724	+	0.860724i	−0.130698	+	0.991422i	$0.541722\pi$
$558$	−435.035			−0.779632
$559$	96.9278	+	114.046i	0.173395	+	0.204018i
$560$		0			0
$561$	252.986	+	252.986i	0.450956	+	0.450956i
$562$			1480.78i			2.63484i
$563$	461.671			0.820020			0.410010	−	0.912081i	$-0.365525\pi$
$563$	461.671			0.820020			0.410010	+	0.912081i	$0.365525\pi$
$564$	−713.063	−	713.063i	−1.26430	−	1.26430i
$565$		0			0
$566$	−1030.39	+	1030.39i	−1.82048	+	1.82048i
$567$	−33.1690	−	33.1690i	−0.0584992	−	0.0584992i
$568$			1386.58i			2.44116i
$569$		−	523.394i		−	0.919849i	−0.887958	−	0.459925i	$-0.847876\pi$
$569$		−	523.394i		−	0.919849i	0.887958	−	0.459925i	$-0.152124\pi$
$570$		0			0
$571$			115.715i			0.202654i	0.994853	+	0.101327i	$0.0323088\pi$
$571$			115.715i			0.202654i	−0.994853	+	0.101327i	$0.967691\pi$
$572$	−101.548	+	1251.53i	−0.177532	+	2.18800i
$573$			388.574i			0.678140i
$574$	−81.7587	−	81.7587i	−0.142437	−	0.142437i
$575$		0			0
$576$			129.623i			0.225040i
$577$	130.158	−	130.158i	0.225577	−	0.225577i	−0.585265	−	0.810842i	$-0.699010\pi$
$577$	130.158	−	130.158i	0.225577	−	0.225577i	0.810842	+	0.585265i	$0.199010\pi$
$578$	87.3509	−	87.3509i	0.151126	−	0.151126i
$579$	2.45623	−	2.45623i	0.00424219	−	0.00424219i
$580$		0			0
$581$	−52.8463			−0.0909574
$582$	−975.083			−1.67540
$583$	30.6797	+	30.6797i	0.0526239	+	0.0526239i
$584$		−	869.210i		−	1.48837i
$585$		0			0
$586$	−702.873			−1.19944
$587$	−347.311	+	347.311i	−0.591671	+	0.591671i	−0.938083	−	0.346411i	$-0.887400\pi$
$587$	−347.311	+	347.311i	−0.591671	+	0.591671i	0.346411	+	0.938083i	$0.387400\pi$
$588$		−	906.772i		−	1.54213i
$589$			123.246i			0.209245i
$590$		0			0
$591$	306.840	+	306.840i	0.519187	+	0.519187i
$592$	−142.344	−	142.344i	−0.240446	−	0.240446i
$593$	−240.285	−	240.285i	−0.405202	−	0.405202i	0.474860	−	0.880062i	$-0.342499\pi$
$593$	−240.285	−	240.285i	−0.405202	−	0.405202i	−0.880062	+	0.474860i	$0.842499\pi$
$594$	1089.40			1.83400
$595$		0			0
$596$	1195.59	−	1195.59i	2.00602	−	2.00602i
$597$	−561.670			−0.940822
$598$	1300.08	+	105.487i	2.17404	+	0.176399i
$599$	−1044.77			−1.74419			−0.872096	−	0.489334i	$-0.837240\pi$
$599$	−1044.77			−1.74419			−0.872096	+	0.489334i	$0.837240\pi$
$600$		0			0
$601$	933.298			1.55291			0.776454	−	0.630174i	$-0.217016\pi$
$601$	933.298			1.55291			0.776454	+	0.630174i	$0.217016\pi$
$602$	−84.3288			−0.140081
$603$	−350.649	+	350.649i	−0.581508	+	0.581508i
$604$	−272.068	−	272.068i	−0.450444	−	0.450444i
$605$		0			0
$606$	−49.7893	+	49.7893i	−0.0821606	+	0.0821606i
$607$		−	579.912i		−	0.955374i	−0.878530	−	0.477687i	$-0.841475\pi$
$607$		−	579.912i		−	0.955374i	0.878530	−	0.477687i	$-0.158525\pi$
$608$	201.623			0.331616
$609$	79.1886	−	79.1886i	0.130031	−	0.130031i
$610$		0			0
$611$	52.5836	−	648.070i	0.0860616	−	1.06067i
$612$			644.131i			1.05250i
$613$	288.460	−	288.460i	0.470572	−	0.470572i	−0.431528	−	0.902100i	$-0.642025\pi$
$613$	288.460	−	288.460i	0.470572	−	0.470572i	0.902100	+	0.431528i	$0.142025\pi$
$614$	−1216.67			−1.98154
$615$		0			0
$616$	−285.658	−	285.658i	−0.463730	−	0.463730i
$617$	95.4121	−	95.4121i	0.154639	−	0.154639i	−0.625547	−	0.780186i	$-0.715124\pi$
$617$	95.4121	−	95.4121i	0.154639	−	0.154639i	0.780186	+	0.625547i	$0.215124\pi$
$618$	331.710	+	331.710i	0.536748	+	0.536748i
$619$	544.952	−	544.952i	0.880374	−	0.880374i	−0.113198	−	0.993572i	$-0.536110\pi$
$619$	544.952	−	544.952i	0.880374	−	0.880374i	0.993572	+	0.113198i	$0.0361095\pi$
$620$		0			0
$621$		−	791.934i		−	1.27526i
$622$	293.434	+	293.434i	0.471759	+	0.471759i
$623$	−258.544			−0.414998
$624$	720.726	−	612.546i	1.15501	−	0.981644i
$625$		0			0
$626$	−576.840	−	576.840i	−0.921469	−	0.921469i
$627$		−	100.167i		−	0.159755i
$628$	−2168.37			−3.45281
$629$	−67.5726	−	67.5726i	−0.107429	−	0.107429i
$630$		0			0
$631$	−642.537	+	642.537i	−1.01828	+	1.01828i	−0.0184540	+	0.999830i	$0.505874\pi$
$631$	−642.537	+	642.537i	−1.01828	+	1.01828i	−0.999830	+	0.0184540i	$0.994126\pi$
$632$	−697.960	−	697.960i	−1.10437	−	1.10437i
$633$			703.982i			1.11214i
$634$		−	646.009i		−	1.01894i
$635$		0			0
$636$		−	84.4520i		−	0.132786i
$637$	445.495	−	378.627i	0.699365	−	0.594391i
$638$			975.964i			1.52972i
$639$	218.153	+	218.153i	0.341398	+	0.341398i
$640$		0			0
$641$		−	487.290i		−	0.760202i	−0.924945	−	0.380101i	$-0.875889\pi$
$641$		−	487.290i		−	0.760202i	0.924945	−	0.380101i	$-0.124111\pi$
$642$	801.285	−	801.285i	1.24811	−	1.24811i
$643$	797.688	−	797.688i	1.24057	−	1.24057i	0.280809	−	0.959764i	$-0.409397\pi$
$643$	797.688	−	797.688i	1.24057	−	1.24057i	0.959764	−	0.280809i	$-0.0906028\pi$
$644$	−363.658	+	363.658i	−0.564686	+	0.564686i
$645$		0			0
$646$	260.763			0.403658
$647$	989.526			1.52941			0.764703	−	0.644383i	$-0.222886\pi$
$647$	989.526			1.52941			0.764703	+	0.644383i	$0.222886\pi$
$648$	−321.283	−	321.283i	−0.495807	−	0.495807i
$649$			443.456i			0.683292i
$650$		0			0
$651$	−119.570			−0.183671
$652$	106.864	−	106.864i	0.163902	−	0.163902i
$653$		−	86.3075i		−	0.132171i	−0.997814	−	0.0660853i	$-0.978949\pi$
$653$		−	86.3075i		−	0.132171i	0.997814	−	0.0660853i	$-0.0210510\pi$
$654$		−	946.271i		−	1.44690i
$655$		0			0
$656$	−375.601	−	375.601i	−0.572562	−	0.572562i
$657$	−136.754	−	136.754i	−0.208150	−	0.208150i
$658$	259.042	+	259.042i	0.393680	+	0.393680i
$659$	1184.99			1.79817			0.899083	−	0.437779i	$-0.144235\pi$
$659$	1184.99			1.79817			0.899083	+	0.437779i	$0.144235\pi$
$660$		0			0
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	−0.838702	−	0.544590i	$-0.816685\pi$
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	0.544590	+	0.838702i	$0.316685\pi$
$662$	−1600.21			−2.41724
$663$	342.138	−	290.783i	0.516045	−	0.438587i
$664$	−511.881			−0.770905
$665$		0			0
$666$	−94.4384			−0.141799
$667$	709.473			1.06368
$668$	1928.18	−	1928.18i	2.88650	−	2.88650i
$669$	527.107	+	527.107i	0.787903	+	0.787903i
$670$		0			0
$671$	495.693	−	495.693i	0.738737	−	0.738737i
$672$			195.610i			0.291086i
$673$	615.500			0.914561			0.457281	−	0.889322i	$-0.348824\pi$
$673$	615.500			0.914561			0.457281	+	0.889322i	$0.348824\pi$
$674$	−13.7434	+	13.7434i	−0.0203908	+	0.0203908i
$675$		0			0
$676$	1555.24	+	254.053i	2.30065	+	0.375818i
$677$			412.031i			0.608612i	0.952574	+	0.304306i	$0.0984246\pi$
$677$			412.031i			0.608612i	−0.952574	+	0.304306i	$0.901575\pi$
$678$	−605.798	+	605.798i	−0.893507	+	0.893507i
$679$	247.890			0.365081
$680$		0			0
$681$	−217.811	−	217.811i	−0.319841	−	0.319841i
$682$	736.824	−	736.824i	1.08039	−	1.08039i
$683$	129.044	+	129.044i	0.188937	+	0.188937i	0.795237	−	0.606299i	$-0.207347\pi$
$683$	129.044	+	129.044i	0.188937	+	0.188937i	−0.606299	+	0.795237i	$0.707347\pi$
$684$	127.517	−	127.517i	0.186429	−	0.186429i
$685$		0			0
$686$			688.315i			1.00338i
$687$	519.738	+	519.738i	0.756533	+	0.756533i
$688$	−387.408			−0.563093
$689$	41.4911	−	35.2633i	0.0602193	−	0.0511805i
$690$		0			0
$691$	727.105	+	727.105i	1.05225	+	1.05225i	0.998558	+	0.0536923i	$0.0170990\pi$
$691$	727.105	+	727.105i	1.05225	+	1.05225i	0.0536923	+	0.998558i	$0.482901\pi$
$692$		−	852.092i		−	1.23135i
$693$	−89.8861			−0.129706
$694$	−121.936	−	121.936i	−0.175701	−	0.175701i
$695$		0			0
$696$	767.039	−	767.039i	1.10207	−	1.10207i
$697$	−178.302	−	178.302i	−0.255814	−	0.255814i
$698$		−	1154.19i		−	1.65356i
$699$			23.3295i			0.0333756i
$700$		0			0
$701$			635.934i			0.907181i	0.891210	+	0.453590i	$0.149857\pi$
$701$			635.934i			0.907181i	−0.891210	+	0.453590i	$0.850143\pi$
$702$	110.570	−	1362.73i	0.157507	−	1.94121i
$703$			26.7544i			0.0380575i
$704$	−219.544	−	219.544i	−0.311852	−	0.311852i
$705$		0			0
$706$		−	569.504i		−	0.806663i
$707$	12.6577	−	12.6577i	0.0179033	−	0.0179033i
$708$	610.350	−	610.350i	0.862077	−	0.862077i
$709$	−695.315	+	695.315i	−0.980699	+	0.980699i	−0.999817	−	0.0191186i	$-0.993914\pi$
$709$	−695.315	+	695.315i	−0.980699	+	0.980699i	0.0191186	+	0.999817i	$0.493914\pi$
$710$		0			0
$711$	−219.623			−0.308893
$712$	−2504.31			−3.51730
$713$	−535.631	−	535.631i	−0.751236	−	0.751236i
$714$			252.986i			0.354323i
$715$		0			0
$716$	668.302			0.933382
$717$	−211.936	+	211.936i	−0.295588	+	0.295588i
$718$		−	326.333i		−	0.454503i
$719$			859.565i			1.19550i	0.801682	+	0.597750i	$0.203939\pi$
$719$			859.565i			1.19550i	−0.801682	+	0.597750i	$0.796061\pi$
$720$		0			0
$721$	−84.3288	−	84.3288i	−0.116961	−	0.116961i
$722$	880.168	+	880.168i	1.21907	+	1.21907i
$723$	−424.233	−	424.233i	−0.586767	−	0.586767i
$724$	2556.28			3.53077
$725$		0			0
$726$	76.4715	−	76.4715i	0.105333	−	0.105333i
$727$	437.337			0.601564			0.300782	−	0.953693i	$-0.402752\pi$
$727$	437.337			0.601564			0.300782	+	0.953693i	$0.402752\pi$
$728$	−386.322	+	328.336i	−0.530662	+	0.451010i
$729$	−661.780			−0.907792
$730$		0			0
$731$	−183.907			−0.251583
$732$	−1364.49			−1.86406
$733$	−39.5591	+	39.5591i	−0.0539687	+	0.0539687i	−0.733576	−	0.679607i	$-0.762150\pi$
$733$	−39.5591	+	39.5591i	−0.0539687	+	0.0539687i	0.679607	+	0.733576i	$0.262150\pi$
$734$	−821.877	−	821.877i	−1.11972	−	1.11972i
$735$		0			0
$736$	−876.263	+	876.263i	−1.19057	+	1.19057i
$737$		−	1187.80i		−	1.61167i
$738$	−249.193			−0.337660
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.286475	+	0.958088i	$0.592483\pi$
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.958088	+	0.286475i	$0.907517\pi$
$740$		0			0
$741$	−125.298	−	10.1666i	−0.169093	−	0.0137200i
$742$			30.6797i			0.0413473i
$743$	−730.642	+	730.642i	−0.983368	+	0.983368i	−0.999864	−	0.0164960i	$-0.994749\pi$
$743$	−730.642	+	730.642i	−0.983368	+	0.983368i	0.0164960	+	0.999864i	$0.494749\pi$
$744$	−1158.18			−1.55670
$745$		0			0
$746$	−22.9125	−	22.9125i	−0.0307137	−	0.0307137i
$747$	−80.5352	+	80.5352i	−0.107812	+	0.107812i
$748$	−1090.97	−	1090.97i	−1.45852	−	1.45852i
$749$	−203.706	+	203.706i	−0.271971	+	0.271971i
$750$		0			0
$751$			199.764i			0.265997i	0.991116	+	0.132998i	$0.0424605\pi$
$751$			199.764i			0.265997i	−0.991116	+	0.132998i	$0.957539\pi$
$752$	1190.04	+	1190.04i	1.58250	+	1.58250i
$753$	207.237			0.275215
$754$	1220.83	+	99.0569i	1.61914	+	0.131375i
$755$		0			0
$756$	381.182	+	381.182i	0.504209	+	0.504209i
$757$		−	124.549i		−	0.164529i	−0.996611	−	0.0822647i	$-0.973785\pi$
$757$		−	124.549i		−	0.164529i	0.996611	−	0.0822647i	$-0.0262153\pi$
$758$	−746.969			−0.985447
$759$	435.329	+	435.329i	0.573556	+	0.573556i
$760$		0			0
$761$	161.412	−	161.412i	0.212105	−	0.212105i	−0.593056	−	0.805161i	$-0.702079\pi$
$761$	161.412	−	161.412i	0.212105	−	0.212105i	0.805161	+	0.593056i	$0.202079\pi$
$762$	529.302	+	529.302i	0.694623	+	0.694623i
$763$			240.565i			0.315289i
$764$		−	1675.68i		−	2.19330i
$765$		0			0
$766$		−	1844.28i		−	2.40768i
$767$	554.719	+	45.0092i	0.723232	+	0.0586822i
$768$		−	819.048i		−	1.06647i
$769$	−137.947	−	137.947i	−0.179385	−	0.179385i	0.611703	−	0.791088i	$-0.290485\pi$
$769$	−137.947	−	137.947i	−0.179385	−	0.179385i	−0.791088	+	0.611703i	$0.790485\pi$
$770$		0			0
$771$			974.276i			1.26365i
$772$	−10.5922	+	10.5922i	−0.0137204	+	0.0137204i
$773$	−550.813	+	550.813i	−0.712566	+	0.712566i	−0.967071	−	0.254506i	$-0.918087\pi$
$773$	−550.813	+	550.813i	−0.712566	+	0.712566i	0.254506	+	0.967071i	$0.418087\pi$
$774$	−128.513	+	128.513i	−0.166038	+	0.166038i
$775$		0			0
$776$	2401.12			3.09422
$777$	−25.9566			−0.0334061
$778$	1131.42	+	1131.42i	1.45427	+	1.45427i
$779$			70.5964i			0.0906244i
$780$		0			0
$781$	−738.977			−0.946194
$782$	−1133.29	+	1133.29i	−1.44922	+	1.44922i
$783$		−	743.662i		−	0.949760i
$784$			1513.32i			1.93026i
$785$		0			0
$786$	626.581	+	626.581i	0.797177	+	0.797177i
$787$	−729.434	−	729.434i	−0.926854	−	0.926854i	0.0706473	−	0.997501i	$-0.477494\pi$
$787$	−729.434	−	729.434i	−0.926854	−	0.926854i	−0.997501	+	0.0706473i	$0.977494\pi$
$788$	−1323.21	−	1323.21i	−1.67920	−	1.67920i
$789$	−361.062			−0.457620
$790$		0			0
$791$	154.009	−	154.009i	0.194701	−	0.194701i
$792$	−870.658			−1.09932
$793$	−569.750	−	670.372i	−0.718474	−	0.845362i
$794$	1290.89			1.62580
$795$		0			0
$796$	2422.13			3.04288
$797$	444.974			0.558311			0.279155	−	0.960246i	$-0.409946\pi$
$797$	444.974			0.558311			0.279155	+	0.960246i	$0.409946\pi$
$798$	50.0833	−	50.0833i	0.0627610	−	0.0627610i
$799$	564.928	+	564.928i	0.707043	+	0.707043i
$800$		0			0
$801$	−394.009	+	394.009i	−0.491896	+	0.491896i
$802$			483.715i			0.603135i
$803$	463.246			0.576894
$804$	−1634.82	+	1634.82i	−2.03336	+	2.03336i
$805$		0			0
$806$	−846.907	−	996.478i	−1.05075	−	1.23632i
$807$		−	367.720i		−	0.455662i
$808$	122.605	−	122.605i	0.151739	−	0.151739i
$809$	1090.36			1.34779			0.673893	−	0.738829i	$-0.264621\pi$
$809$	1090.36			1.34779			0.673893	+	0.738829i	$0.264621\pi$
$810$		0			0
$811$	445.614	+	445.614i	0.549463	+	0.549463i	0.926285	−	0.376823i	$-0.122983\pi$
$811$	445.614	+	445.614i	0.549463	+	0.549463i	−0.376823	+	0.926285i	$0.622983\pi$
$812$	−341.491	+	341.491i	−0.420556	+	0.420556i
$813$	−469.370	−	469.370i	−0.577331	−	0.577331i
$814$	159.952	−	159.952i	0.196501	−	0.196501i
$815$		0			0
$816$			1162.22i			1.42429i
$817$	36.4078	+	36.4078i	0.0445628	+	0.0445628i
$818$	1910.77			2.33590
$819$	−9.12312	+	112.438i	−0.0111393	+	0.137287i
$820$		0			0
$821$	−242.186	−	242.186i	−0.294989	−	0.294989i	0.544058	−	0.839047i	$-0.316887\pi$
$821$	−242.186	−	242.186i	−0.294989	−	0.294989i	−0.839047	+	0.544058i	$0.816887\pi$
$822$			968.083i			1.17772i
$823$	−99.5787			−0.120995			−0.0604974	−	0.998168i	$-0.519269\pi$
$823$	−99.5787			−0.120995			−0.0604974	+	0.998168i	$0.519269\pi$
$824$	−816.828	−	816.828i	−0.991297	−	0.991297i
$825$		0			0
$826$	−221.728	+	221.728i	−0.268436	+	0.268436i
$827$	899.548	+	899.548i	1.08772	+	1.08772i	0.995763	+	0.0919618i	$0.0293138\pi$
$827$	899.548	+	899.548i	1.08772	+	1.08772i	0.0919618	+	0.995763i	$0.470686\pi$
$828$			1108.39i			1.33864i
$829$			32.1103i			0.0387338i	0.999812	+	0.0193669i	$0.00616506\pi$
$829$			32.1103i			0.0387338i	−0.999812	+	0.0193669i	$0.993835\pi$
$830$		0			0
$831$			406.394i			0.489042i
$832$	−296.910	+	252.344i	−0.356863	+	0.303298i
$833$			718.394i			0.862418i
$834$	438.340	+	438.340i	0.525587	+	0.525587i
$835$		0			0
$836$			431.956i			0.516694i
$837$	−561.443	+	561.443i	−0.670780	+	0.670780i
$838$	−1700.37	+	1700.37i	−2.02908	+	2.02908i
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	−0.907434	−	0.420195i	$-0.861962\pi$
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	0.420195	+	0.907434i	$0.361962\pi$
$840$		0			0
$841$	−174.772			−0.207815
$842$	414.601			0.492400
$843$	620.241	+	620.241i	0.735755	+	0.735755i
$844$		−	3035.84i		−	3.59696i
$845$		0			0
$846$	789.535			0.933256
$847$	−19.4409	+	19.4409i	−0.0229527	+	0.0229527i
$848$			140.943i			0.166206i
$849$			863.184i			1.01671i
$850$		0			0
$851$	−116.276	−	116.276i	−0.136635	−	0.136635i
$852$	1017.09	+	1017.09i	1.19377	+	1.19377i
$853$	529.546	+	529.546i	0.620804	+	0.620804i	0.945737	−	0.324933i	$-0.105342\pi$
$853$	529.546	+	529.546i	0.620804	+	0.620804i	−0.324933	+	0.945737i	$0.605342\pi$
$854$	495.693			0.580436
$855$		0			0
$856$	−1973.14	+	1973.14i	−2.30507	+	2.30507i
$857$	1586.76			1.85153			0.925766	−	0.378097i	$-0.123421\pi$
$857$	1586.76			1.85153			0.925766	+	0.378097i	$0.123421\pi$
$858$	688.315	+	809.877i	0.802232	+	0.943912i
$859$	−145.062			−0.168873			−0.0844365	−	0.996429i	$-0.526909\pi$
$859$	−145.062			−0.168873			−0.0844365	+	0.996429i	$0.526909\pi$
$860$		0			0
$861$	−68.4911			−0.0795483
$862$	−1528.23			−1.77289
$863$	1005.80	−	1005.80i	1.16547	−	1.16547i	0.182216	−	0.983258i	$-0.441673\pi$
$863$	1005.80	−	1005.80i	1.16547	−	1.16547i	0.983258	−	0.182216i	$-0.0583271\pi$
$864$	918.489	+	918.489i	1.06307	+	1.06307i
$865$		0			0
$866$	403.020	−	403.020i	0.465381	−	0.465381i
$867$		−	73.1758i		−	0.0844011i
$868$	515.631			0.594045
$869$	371.978	−	371.978i	0.428053	−	0.428053i
$870$		0			0
$871$	−1485.81	−	120.557i	−1.70587	−	0.138413i
$872$			2330.17i			2.67221i
$873$	377.772	−	377.772i	0.432729	−	0.432729i
$874$	448.710			0.513399
$875$		0			0
$876$	−637.587	−	637.587i	−0.727839	−	0.727839i
$877$	689.532	−	689.532i	0.786240	−	0.786240i	−0.194636	−	0.980876i	$-0.562353\pi$
$877$	689.532	−	689.532i	0.786240	−	0.786240i	0.980876	+	0.194636i	$0.0623526\pi$
$878$	1158.18	+	1158.18i	1.31912	+	1.31912i
$879$	−294.406	+	294.406i	−0.334933	+	0.334933i
$880$		0			0
$881$		−	1607.31i		−	1.82442i	−0.409722	−	0.912210i	$-0.634374\pi$
$881$		−	1607.31i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$882$	502.009	+	502.009i	0.569171	+	0.569171i
$883$	153.969			0.174370			0.0871850	−	0.996192i	$-0.472213\pi$
$883$	153.969			0.174370			0.0871850	+	0.996192i	$0.472213\pi$
$884$	−1475.43	+	1253.97i	−1.66903	+	1.41851i
$885$		0			0
$886$	1490.28	+	1490.28i	1.68203	+	1.68203i
$887$		−	125.273i		−	0.141232i	−0.997504	−	0.0706159i	$-0.977504\pi$
$887$		−	125.273i		−	0.141232i	0.997504	−	0.0706159i	$-0.0224965\pi$
$888$	−251.421			−0.283132
$889$	−134.562	−	134.562i	−0.151363	−	0.151363i
$890$		0			0
$891$	171.228	−	171.228i	0.192175	−	0.192175i
$892$	−2273.08	−	2273.08i	−2.54830	−	2.54830i
$893$		−	223.675i		−	0.250476i
$894$		−	1431.22i		−	1.60092i
$895$		0			0
$896$			142.315i			0.158834i
$897$	588.737	−	500.368i	0.656340	−	0.557824i
$898$			553.021i			0.615837i
$899$	−502.982	−	502.982i	−0.559491	−	0.559491i
$900$		0			0
$901$			66.9075i			0.0742591i
$902$	422.061	−	422.061i	0.467917	−	0.467917i
$903$	−35.3221	+	35.3221i	−0.0391164	+	0.0391164i
$904$	1491.76	−	1491.76i	1.65018	−	1.65018i
$905$		0			0
$906$	−325.688			−0.359479
$907$	−354.574			−0.390930			−0.195465	−	0.980711i	$-0.562622\pi$
$907$	−354.574			−0.390930			−0.195465	+	0.980711i	$0.562622\pi$
$908$	939.285	+	939.285i	1.03445	+	1.03445i
$909$		−	38.5793i		−	0.0424415i
$910$		0			0
$911$	1040.31			1.14194			0.570972	−	0.820970i	$-0.306566\pi$
$911$	1040.31			1.14194			0.570972	+	0.820970i	$0.306566\pi$
$912$	230.083	−	230.083i	0.252284	−	0.252284i
$913$		−	272.807i		−	0.298803i
$914$		−	1838.24i		−	2.01121i
$915$		0			0
$916$	−2241.31	−	2241.31i	−2.44684	−	2.44684i
$917$	−159.292	−	159.292i	−0.173710	−	0.173710i
$918$	1187.90	+	1187.90i	1.29401	+	1.29401i
$919$	416.201			0.452884			0.226442	−	0.974025i	$-0.427291\pi$
$919$	416.201			0.452884			0.226442	+	0.974025i	$0.427291\pi$
$920$		0			0
$921$	−509.614	+	509.614i	−0.553327	+	0.553327i
$922$	−174.215			−0.188953
$923$	−75.0036	+	924.386i	−0.0812606	+	1.00150i
$924$	−419.074			−0.453543
$925$		0			0
$926$	−1736.36			−1.87512
$927$	−257.026			−0.277267
$928$	−822.851	+	822.851i	−0.886692	+	0.886692i
$929$	428.403	+	428.403i	0.461144	+	0.461144i	0.899030	−	0.437886i	$-0.144273\pi$
$929$	428.403	+	428.403i	0.461144	+	0.461144i	−0.437886	+	0.899030i	$0.644273\pi$
$930$		0			0
$931$	142.219	−	142.219i	0.152760	−	0.152760i
$932$		−	100.606i		−	0.107946i
$933$	245.816			0.263469
$934$	795.670	−	795.670i	0.851896	−	0.851896i
$935$		0			0
$936$	−88.3687	+	1089.10i	−0.0944110	+	1.16357i
$937$			990.702i			1.05731i	0.848836	+	0.528656i	$0.177304\pi$
$937$			990.702i			1.05731i	−0.848836	+	0.528656i	$0.822696\pi$
$938$	593.899	−	593.899i	0.633155	−	0.633155i
$939$	−483.231			−0.514623
$940$		0			0
$941$	974.392	+	974.392i	1.03549	+	1.03549i	0.999347	+	0.0361387i	$0.0115058\pi$
$941$	974.392	+	974.392i	1.03549	+	1.03549i	0.0361387	+	0.999347i	$0.488494\pi$
$942$	−1297.86	+	1297.86i	−1.37777	+	1.37777i
$943$	−306.816	−	306.816i	−0.325361	−	0.325361i
$944$	−1018.62	+	1018.62i	−1.07905	+	1.07905i
$945$		0			0
$946$		−	435.329i		−	0.460178i
$947$	−897.569	−	897.569i	−0.947803	−	0.947803i	0.0509007	−	0.998704i	$-0.483791\pi$
$947$	−897.569	−	897.569i	−0.947803	−	0.947803i	−0.998704	+	0.0509007i	$0.983791\pi$
$948$	−1023.94			−1.08011
$949$	47.0178	−	579.473i	0.0495446	−	0.610615i
$950$		0			0
$951$	−270.588	−	270.588i	−0.284530	−	0.284530i
$952$		−	622.973i		−	0.654383i
$953$	−1111.71			−1.16654			−0.583269	−	0.812279i	$-0.698227\pi$
$953$	−1111.71			−1.16654			−0.583269	+	0.812279i	$0.698227\pi$
$954$	46.7544	+	46.7544i	0.0490089	+	0.0490089i
$955$		0			0
$956$	913.949	−	913.949i	0.956014	−	0.956014i
$957$	408.794	+	408.794i	0.427162	+	0.427162i
$958$		−	395.649i		−	0.412995i
$959$		−	246.110i		−	0.256632i
$960$		0			0
$961$		−	201.527i		−	0.209705i
$962$	−183.849	−	216.318i	−0.191111	−	0.224863i
$963$			620.877i			0.644732i
$964$	1829.45	+	1829.45i	1.89777	+	1.89777i
$965$		0			0
$966$			435.329i			0.450651i
$967$	−1333.92	+	1333.92i	−1.37944	+	1.37944i	−0.533879	+	0.845561i	$0.679266\pi$
$967$	−1333.92	+	1333.92i	−1.37944	+	1.37944i	−0.845561	+	0.533879i	$0.820734\pi$
$968$	−188.309	+	188.309i	−0.194534	+	0.194534i
$969$	109.223	−	109.223i	0.112718	−	0.112718i
$970$		0			0
$971$	−556.110			−0.572718			−0.286359	−	0.958122i	$-0.592445\pi$
$971$	−556.110			−0.572718			−0.286359	+	0.958122i	$0.592445\pi$
$972$	1946.54			2.00262
$973$	−111.437	−	111.437i	−0.114529	−	0.114529i
$974$		−	356.535i		−	0.366053i
$975$		0			0
$976$	2277.22			2.33322
$977$	−1103.56	+	1103.56i	−1.12954	+	1.12954i	−0.139288	+	0.990252i	$0.544482\pi$
$977$	−1103.56	+	1103.56i	−1.12954	+	1.12954i	−0.990252	+	0.139288i	$0.955518\pi$
$978$		−	127.925i		−	0.130803i
$979$		−	1334.67i		−	1.36330i
$980$		0			0
$981$	366.610	+	366.610i	0.373710	+	0.373710i
$982$	1768.86	+	1768.86i	1.80128	+	1.80128i
$983$	−901.475	−	901.475i	−0.917065	−	0.917065i	0.0797497	−	0.996815i	$-0.474588\pi$
$983$	−901.475	−	901.475i	−0.917065	−	0.917065i	−0.996815	+	0.0797497i	$0.974588\pi$
$984$	−663.421			−0.674208
$985$		0			0
$986$	−1064.21	+	1064.21i	−1.07932	+	1.07932i
$987$	217.005			0.219863
$988$	540.333	+	43.8420i	0.546896	+	0.0443745i
$989$	−316.460			−0.319980
$990$		0			0
$991$	765.341			0.772292			0.386146	−	0.922438i	$-0.373806\pi$
$991$	765.341			0.772292			0.386146	+	0.922438i	$0.373806\pi$
$992$	1242.46			1.25248
$993$	−670.268	+	670.268i	−0.674993	+	0.674993i
$994$	−369.489	−	369.489i	−0.371719	−	0.371719i
$995$		0			0
$996$	−375.478	+	375.478i	−0.376986	+	0.376986i
$997$		−	1075.40i		−	1.07863i	−0.842103	−	0.539317i	$-0.818682\pi$
$997$		−	1075.40i		−	1.07863i	0.842103	−	0.539317i	$-0.181318\pi$
$998$	1803.33			1.80695
$999$	−121.879	+	121.879i	−0.122001	+	0.122001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.g.a.99.1		4
5.2	odd	4		13.3.d.a.8.1	yes	4
5.3	odd	4		325.3.j.a.151.2		4
5.4	even	2		325.3.g.b.99.2		4
13.5	odd	4		325.3.g.b.174.2		4
15.2	even	4		117.3.j.a.73.2		4
20.7	even	4		208.3.t.c.177.1		4
65.2	even	12		169.3.f.f.19.1		8
65.7	even	12		169.3.f.d.80.1		8
65.12	odd	4		169.3.d.d.99.2		4
65.17	odd	12		169.3.f.d.89.2		8
65.18	even	4		325.3.j.a.226.2		4
65.22	odd	12		169.3.f.f.89.1		8
65.32	even	12		169.3.f.f.80.2		8
65.37	even	12		169.3.f.d.19.2		8
65.42	odd	12		169.3.f.f.150.2		8
65.44	odd	4	inner	325.3.g.a.174.1		4
65.47	even	4		169.3.d.d.70.2		4
65.57	even	4		13.3.d.a.5.1	✓	4
65.62	odd	12		169.3.f.d.150.1		8
195.122	odd	4		117.3.j.a.109.2		4
260.187	odd	4		208.3.t.c.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	65.57	even	4
13.3.d.a.8.1	yes	4	5.2	odd	4
117.3.j.a.73.2		4	15.2	even	4
117.3.j.a.109.2		4	195.122	odd	4
169.3.d.d.70.2		4	65.47	even	4
169.3.d.d.99.2		4	65.12	odd	4
169.3.f.d.19.2		8	65.37	even	12
169.3.f.d.80.1		8	65.7	even	12
169.3.f.d.89.2		8	65.17	odd	12
169.3.f.d.150.1		8	65.62	odd	12
169.3.f.f.19.1		8	65.2	even	12
169.3.f.f.80.2		8	65.32	even	12
169.3.f.f.89.1		8	65.22	odd	12
169.3.f.f.150.2		8	65.42	odd	12
208.3.t.c.161.1		4	260.187	odd	4
208.3.t.c.177.1		4	20.7	even	4
325.3.g.a.99.1		4	1.1	even	1	trivial
325.3.g.a.174.1		4	65.44	odd	4	inner
325.3.g.b.99.2		4	5.4	even	2
325.3.g.b.174.2		4	13.5	odd	4
325.3.j.a.151.2		4	5.3	odd	4
325.3.j.a.226.2		4	65.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.58114 + 2.58114i) q^{2} +2.16228i q^{3} -9.32456i q^{4} +(-5.58114 - 5.58114i) q^{6} +(1.41886 + 1.41886i) q^{7} +(13.7434 + 13.7434i) q^{8} +4.32456 q^{9} +(-7.32456 + 7.32456i) q^{11} +20.1623 q^{12} +(8.41886 + 9.90569i) q^{13} -7.32456 q^{14} -33.6491 q^{16} -15.9737 q^{17} +(-11.1623 + 11.1623i) q^{18} +(3.16228 + 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -37.8114i q^{22} -27.4868 q^{23} +(-29.7171 + 29.7171i) q^{24} +(-47.2982 - 3.83772i) q^{26} +28.8114i q^{27} +(13.2302 - 13.2302i) q^{28} -25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(31.8794 - 31.8794i) q^{32} +(-15.8377 - 15.8377i) q^{33} +(41.2302 - 41.2302i) q^{34} -40.3246i q^{36} +(4.23025 + 4.23025i) q^{37} -16.3246 q^{38} +(-21.4189 + 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} -15.8377i q^{42} +11.5132 q^{43} +(68.2982 + 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 - 35.3662i) q^{47} -72.7587i q^{48} -44.9737i q^{49} -34.5395i q^{51} +(92.3662 - 78.5021i) q^{52} -4.18861i q^{53} +(-74.3662 - 74.3662i) q^{54} +39.0000i q^{56} +(-6.83772 + 6.83772i) q^{57} +(66.6228 - 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} -100.596 q^{62} +(6.13594 + 6.13594i) q^{63} +29.9737i q^{64} +81.7587 q^{66} +(-81.0833 + 81.0833i) q^{67} +148.947i q^{68} -59.4342i q^{69} +(50.4452 + 50.4452i) q^{71} +(59.4342 + 59.4342i) q^{72} +(-31.6228 - 31.6228i) q^{73} -21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} -20.7851 q^{77} +(8.29822 - 102.272i) q^{78} -50.7851 q^{79} -23.3772 q^{81} -57.6228 q^{82} +(-18.6228 + 18.6228i) q^{83} +(28.6075 + 28.6075i) q^{84} +(-29.7171 + 29.7171i) q^{86} -55.8114i q^{87} -201.329 q^{88} +(-91.1096 + 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302i q^{92} +(-42.1359 + 42.1359i) q^{93} +182.570 q^{94} +(68.9320 + 68.9320i) q^{96} +(87.3552 - 87.3552i) q^{97} +(116.083 + 116.083i) q^{98} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 16 q^{6} + 12 q^{7} + 36 q^{8} - 8 q^{9} - 4 q^{11} + 68 q^{12} + 40 q^{13} - 4 q^{14} - 84 q^{16} + 12 q^{17} - 32 q^{18} + 32 q^{21} - 72 q^{23} - 24 q^{24} - 88 q^{26} - 4 q^{28} - 40 q^{29}+ \cdots - 152 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 16 * q^6 + 12 * q^7 + 36 * q^8 - 8 * q^9 - 4 * q^11 + 68 * q^12 + 40 * q^13 - 4 * q^14 - 84 * q^16 + 12 * q^17 - 32 * q^18 + 32 * q^21 - 72 * q^23 - 24 * q^24 - 88 * q^26 - 4 * q^28 - 40 * q^29 + 40 * q^31 + 20 * q^32 - 76 * q^33 + 108 * q^34 - 40 * q^37 - 40 * q^38 - 92 * q^39 + 32 * q^41 + 84 * q^43 + 172 * q^44 + 132 * q^46 + 4 * q^47 + 224 * q^52 - 152 * q^54 - 40 * q^57 + 140 * q^58 - 56 * q^59 - 296 * q^61 - 200 * q^62 - 64 * q^63 + 112 * q^66 - 84 * q^67 + 284 * q^71 + 48 * q^72 - 100 * q^74 + 80 * q^76 + 56 * q^77 - 68 * q^78 - 64 * q^79 - 220 * q^81 - 104 * q^82 + 52 * q^83 + 184 * q^84 - 24 * q^86 - 312 * q^88 - 200 * q^89 + 156 * q^91 - 80 * q^93 + 452 * q^94 + 320 * q^96 - 68 * q^97 + 224 * q^98 - 152 * q^99

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