LMFDB - Embedded newform 325.3.g.b.174.2

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			174.2
Root			$1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	325.174
Dual form			325.3.g.b.99.2

$q$-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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	0.934435	+	0.356135i	$0.115906\pi$
$2$	2.58114	+	2.58114i	1.29057	+	1.29057i	0.356135	+	0.934435i	$0.384094\pi$
$3$			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	$-0.795780\pi$
$7$	−1.41886	+	1.41886i	−0.202694	+	0.202694i	0.598459	+	0.801153i	$0.295780\pi$
$8$	−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	0.290888	−	0.956757i	$-0.406049\pi$
$11$	−7.32456	−	7.32456i	−0.665869	−	0.665869i	−0.956757	+	0.290888i	$0.906049\pi$
$12$	−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	$-0.344321\pi$
$17$	15.9737			0.939627			0.469814	+	0.882766i	$0.344321\pi$
$18$	11.1623	+	11.1623i	0.620127	+	0.620127i
$19$	3.16228	−	3.16228i	0.166436	−	0.166436i	−0.618975	−	0.785411i	$-0.712452\pi$
$19$	3.16228	−	3.16228i	0.166436	−	0.166436i	0.785411	+	0.618975i	$0.212452\pi$
$20$		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	$-0.296145\pi$
$23$	27.4868			1.19508			0.597540	+	0.801839i	$0.296145\pi$
$24$	−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	−0.319110	−	0.947718i	$-0.603384\pi$
$31$	19.4868	−	19.4868i	0.628608	−	0.628608i	0.947718	+	0.319110i	$0.103384\pi$
$32$	−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	$-0.775762\pi$
$37$	−4.23025	+	4.23025i	−0.114331	+	0.114331i	0.647627	+	0.761958i	$0.275762\pi$
$38$	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	−0.557755	−	0.830006i	$-0.688337\pi$
$41$	11.1623	−	11.1623i	0.272251	−	0.272251i	0.830006	+	0.557755i	$0.188337\pi$
$42$		−	15.8377i		−	0.377089i
$43$	−11.5132			−0.267748			−0.133874	−	0.990998i	$-0.542742\pi$
$43$	−11.5132			−0.267748			−0.133874	+	0.990998i	$0.542742\pi$
$44$	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	$-0.571411\pi$
$47$	35.3662	−	35.3662i	0.752472	−	0.752472i	0.974940	+	0.222468i	$0.0714112\pi$
$48$		−	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	0.915470	−	0.402387i	$-0.131819\pi$
$59$	30.2719	+	30.2719i	0.513083	+	0.513083i	−0.402387	+	0.915470i	$0.631819\pi$
$60$		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	0.970961	+	0.239237i	$0.0768973\pi$
$67$	81.0833	+	81.0833i	1.21020	+	1.21020i	0.239237	+	0.970961i	$0.423103\pi$
$68$			148.947i			2.19040i
$69$			59.4342i			0.861365i
$70$		0			0
$71$	50.4452	−	50.4452i	0.710496	−	0.710496i	−0.256143	−	0.966639i	$-0.582452\pi$
$71$	50.4452	−	50.4452i	0.710496	−	0.710496i	0.966639	+	0.256143i	$0.0824518\pi$
$72$	−59.4342	+	59.4342i	−0.825475	+	0.825475i
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	−0.456523	−	0.889712i	$-0.650905\pi$
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	0.889712	+	0.456523i	$0.150905\pi$
$74$	−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	$-0.199285\pi$
$83$	18.6228	+	18.6228i	0.224371	+	0.224371i	−0.585965	+	0.810336i	$0.699285\pi$
$84$	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	−0.999712	−	0.0239913i	$-0.992363\pi$
$89$	−91.1096	−	91.1096i	−1.02370	−	1.02370i	−0.0239913	−	0.999712i	$-0.507637\pi$
$90$		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	$-0.469742\pi$
$97$	−87.3552	−	87.3552i	−0.900569	−	0.900569i	−0.995485	+	0.0949165i	$0.969742\pi$
$98$	−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	$0.0140622\pi$
$101$			8.92100i			0.0883267i	−0.999024	+	0.0441634i	$0.985938\pi$
$102$	−89.1512	+	89.1512i	−0.874032	+	0.874032i
$103$	59.4342			0.577031			0.288515	−	0.957475i	$-0.406838\pi$
$103$	59.4342			0.577031			0.288515	+	0.957475i	$0.406838\pi$
$104$	−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	−0.201703	−	0.979447i	$-0.564648\pi$
$109$	84.7740	−	84.7740i	0.777743	−	0.777743i	0.979447	+	0.201703i	$0.0646477\pi$
$110$		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	$-0.378200\pi$
$127$	94.8377			0.746754			0.373377	+	0.927680i	$0.378200\pi$
$128$	−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	$-0.602266\pi$
$137$	86.7281	−	86.7281i	0.633052	−	0.633052i	0.948832	+	0.315780i	$0.102266\pi$
$138$	−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	−0.130868	−	0.991400i	$-0.541776\pi$
$149$	128.219	−	128.219i	0.860532	−	0.860532i	0.991400	+	0.130868i	$0.0417764\pi$
$150$		0			0
$151$	29.1776	+	29.1776i	0.193229	+	0.193229i	0.797090	−	0.603861i	$-0.206372\pi$
$151$	29.1776	+	29.1776i	0.193229	+	0.193229i	−0.603861	+	0.797090i	$0.706372\pi$
$152$			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	$-0.765832\pi$
$163$	−11.4605	+	11.4605i	−0.0703098	+	0.0703098i	0.671077	+	0.741387i	$0.265832\pi$
$164$	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	−0.277512	+	0.960722i	$0.589510\pi$
$167$	−206.785	+	206.785i	−1.23823	+	1.23823i	−0.960722	+	0.277512i	$0.910490\pi$
$168$	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	$-0.585078\pi$
$173$	−91.3815			−0.528217			−0.264108	+	0.964493i	$0.585078\pi$
$174$	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	$-0.935841\pi$
$179$		−	71.6712i		−	0.400398i	0.979755	−	0.200199i	$-0.0641588\pi$
$180$		0			0
$181$		−	274.144i		−	1.51461i	−0.653061	−	0.757305i	$-0.726516\pi$
$181$		−	274.144i		−	1.51461i	0.653061	−	0.757305i	$-0.273484\pi$
$182$	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	$-0.748675\pi$
$193$	1.13594	−	1.13594i	0.00588572	−	0.00588572i	0.710044	+	0.704158i	$0.248675\pi$
$194$		−	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	$-0.420115\pi$
$197$	−141.906	−	141.906i	−0.720333	−	0.720333i	−0.968673	+	0.248340i	$0.920115\pi$
$198$		−	163.517i		−	0.825846i
$199$		−	259.759i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$199$		−	259.759i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$200$		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	−0.995190	−	0.0979674i	$-0.968766\pi$
$223$	−243.774	−	243.774i	−1.09316	−	1.09316i	−0.0979674	−	0.995190i	$-0.531234\pi$
$224$	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	$-0.148404\pi$
$227$	100.732	+	100.732i	0.443755	+	0.443755i	−0.449517	+	0.893272i	$0.648404\pi$
$228$	−63.7587	+	63.7587i	−0.279644	+	0.279644i
$229$	240.366	+	240.366i	1.04963	+	1.04963i	0.998702	+	0.0509319i	$0.0162191\pi$
$229$	240.366	+	240.366i	1.04963	+	1.04963i	0.0509319	+	0.998702i	$0.483781\pi$
$230$		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	$-0.507371\pi$
$233$	−10.7893			−0.0463061			−0.0231531	+	0.999732i	$0.507371\pi$
$234$	−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	−0.471670	−	0.881775i	$-0.656348\pi$
$239$	98.0153	−	98.0153i	0.410106	−	0.410106i	0.881775	+	0.471670i	$0.156348\pi$
$240$		0			0
$241$	−196.197	−	196.197i	−0.814096	−	0.814096i	0.171149	−	0.985245i	$-0.445252\pi$
$241$	−196.197	−	196.197i	−0.814096	−	0.814096i	−0.985245	+	0.171149i	$0.945252\pi$
$242$	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	$0.0611472\pi$
$251$			95.8420i			0.381841i	−0.981606	+	0.190920i	$0.938853\pi$
$252$	−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	$-0.840202\pi$
$257$	−450.579			−1.75322			−0.876612	+	0.481198i	$0.840202\pi$
$258$	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	0.182248	−	0.983253i	$-0.441663\pi$
$271$	−217.072	−	217.072i	−0.801005	−	0.801005i	−0.983253	+	0.182248i	$0.941663\pi$
$272$	−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	$-0.610175\pi$
$277$	−187.947			−0.678510			−0.339255	+	0.940694i	$0.610175\pi$
$278$	−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	0.999779	+	0.0210263i	$0.00669337\pi$
$281$	286.846	+	286.846i	1.02081	+	1.02081i	0.0210263	+	0.999779i	$0.493307\pi$
$282$			394.767i			1.39988i
$283$	−399.201			−1.41061			−0.705303	−	0.708906i	$-0.749189\pi$
$283$	−399.201			−1.41061			−0.705303	+	0.708906i	$0.749189\pi$
$284$	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	$-0.856573\pi$
$293$	−136.156	+	136.156i	−0.464695	+	0.464695i	0.435496	+	0.900191i	$0.356573\pi$
$294$	−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	$-0.932653\pi$
$307$	−235.684	+	235.684i	−0.767700	+	0.767700i	0.210001	+	0.977701i	$0.432653\pi$
$308$			193.811i			0.629258i
$309$			128.513i			0.415900i
$310$		0			0
$311$			113.684i			0.365543i	0.983155	+	0.182772i	$0.0585069\pi$
$311$			113.684i			0.365543i	−0.983155	+	0.182772i	$0.941493\pi$
$312$	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	$-0.159951\pi$
$317$	125.140	+	125.140i	0.394764	+	0.394764i	−0.481617	+	0.876382i	$0.659951\pi$
$318$	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	−0.0615988	−	0.998101i	$-0.519620\pi$
$331$	309.982	−	309.982i	0.936502	−	0.936502i	0.998101	+	0.0615988i	$0.0196199\pi$
$332$	−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	$-0.502515\pi$
$337$	−5.32456			−0.0157999			−0.00789993	+	0.999969i	$0.502515\pi$
$338$	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	0.310078	−	0.950711i	$-0.399645\pi$
$349$	−223.581	−	223.581i	−0.640634	−	0.640634i	−0.950711	+	0.310078i	$0.899645\pi$
$350$		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	$-0.179072\pi$
$353$	110.320	+	110.320i	0.312522	+	0.312522i	−0.533364	+	0.845886i	$0.679072\pi$
$354$	−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	0.613561	−	0.789647i	$-0.289736\pi$
$359$	−63.2149	−	63.2149i	−0.176086	−	0.176086i	−0.789647	+	0.613561i	$0.789736\pi$
$360$		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	−0.489958	−	0.871746i	$-0.662988\pi$
$379$	144.698	−	144.698i	0.381788	−	0.381788i	0.871746	+	0.489958i	$0.162988\pi$
$380$		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	$-0.0207315\pi$
$383$	357.261	+	357.261i	0.932796	+	0.932796i	−0.0650838	+	0.997880i	$0.520731\pi$
$384$	−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	$0.190515\pi$
$389$			438.342i			1.12684i	−0.826170	+	0.563421i	$0.809485\pi$
$390$		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	$-0.603065\pi$
$397$	250.061	−	250.061i	0.629877	−	0.629877i	0.948037	+	0.318160i	$0.103065\pi$
$398$	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	0.814223	−	0.580553i	$-0.197163\pi$
$401$	93.7018	+	93.7018i	0.233670	+	0.233670i	−0.580553	+	0.814223i	$0.697163\pi$
$402$	−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	−0.995862	−	0.0908741i	$-0.971034\pi$
$409$	−370.140	+	370.140i	−0.904988	+	0.904988i	0.0908741	+	0.995862i	$0.471034\pi$
$410$		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	−0.796028	−	0.605260i	$-0.793069\pi$
$421$	−80.3135	+	80.3135i	−0.190768	+	0.190768i	0.605260	+	0.796028i	$0.293069\pi$
$422$	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	−0.274675	−	0.961537i	$-0.588570\pi$
$431$	296.037	−	296.037i	0.686862	−	0.686862i	0.961537	+	0.274675i	$0.0885704\pi$
$432$		−	969.478i		−	2.24416i
$433$	156.140			0.360601			0.180300	−	0.983612i	$-0.442293\pi$
$433$	156.140			0.360601			0.180300	+	0.983612i	$0.442293\pi$
$434$	−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	$0.170747\pi$
$439$			448.710i			1.02212i	−0.859545	+	0.511060i	$0.829253\pi$
$440$		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	0.816267	−	0.577675i	$-0.196040\pi$
$449$	107.127	+	107.127i	0.238591	+	0.238591i	−0.577675	+	0.816267i	$0.696040\pi$
$450$		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	$-0.0642565\pi$
$457$	356.092	+	356.092i	0.779194	+	0.779194i	−0.200499	+	0.979694i	$0.564256\pi$
$458$			1240.84i			2.70925i
$459$			460.223i			1.00267i
$460$		0			0
$461$	33.7477	−	33.7477i	0.0732054	−	0.0732054i	−0.669556	−	0.742761i	$-0.733516\pi$
$461$	33.7477	−	33.7477i	0.0732054	−	0.0732054i	0.742761	+	0.669556i	$0.233516\pi$
$462$	−116.004	+	116.004i	−0.251092	+	0.251092i
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	−0.969915	−	0.243446i	$-0.921722\pi$
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	0.243446	+	0.969915i	$0.421722\pi$
$464$	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	$-0.392936\pi$
$467$	308.263			0.660093			0.330046	+	0.943965i	$0.392936\pi$
$468$	−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	0.622564	−	0.782569i	$-0.286091\pi$
$479$	−76.6424	−	76.6424i	−0.160005	−	0.160005i	−0.782569	+	0.622564i	$0.786091\pi$
$480$		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	$-0.218026\pi$
$487$	69.0655	+	69.0655i	0.141818	+	0.141818i	−0.632633	+	0.774452i	$0.718026\pi$
$488$	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	$0.245866\pi$
$491$			685.302i			1.39573i	−0.716230	+	0.697864i	$0.754134\pi$
$492$	−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	−0.964423	−	0.264365i	$-0.914838\pi$
$499$	−349.329	+	349.329i	−0.700058	+	0.700058i	0.264365	+	0.964423i	$0.414838\pi$
$500$		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	−0.864565	−	0.502521i	$-0.832406\pi$
$509$	−184.280	+	184.280i	−0.362044	+	0.362044i	0.502521	+	0.864565i	$0.332406\pi$
$510$		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	0.445442	−	0.895311i	$-0.353047\pi$
$541$	−243.379	−	243.379i	−0.449869	−	0.449869i	−0.895311	+	0.445442i	$0.853047\pi$
$542$		−	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	$-0.958278\pi$
$557$	−479.423	+	479.423i	−0.860724	+	0.860724i	0.130698	+	0.991422i	$0.458278\pi$
$558$	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	$-0.634475\pi$
$563$	−461.671			−0.820020			−0.410010	+	0.912081i	$0.634475\pi$
$564$	−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	$0.152124\pi$
$569$			523.394i			0.919849i	−0.887958	+	0.459925i	$0.847876\pi$
$570$		0			0
$571$		−	115.715i		−	0.202654i	−0.994853	−	0.101327i	$-0.967691\pi$
$571$		−	115.715i		−	0.202654i	0.994853	−	0.101327i	$-0.0323088\pi$
$572$	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	$-0.300990\pi$
$577$	−130.158	−	130.158i	−0.225577	−	0.225577i	−0.810842	+	0.585265i	$0.800990\pi$
$578$	−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	$-0.112600\pi$
$587$	347.311	+	347.311i	0.591671	+	0.591671i	−0.346411	+	0.938083i	$0.612600\pi$
$588$		−	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	$-0.657501\pi$
$593$	240.285	−	240.285i	0.405202	−	0.405202i	0.880062	+	0.474860i	$0.157501\pi$
$594$	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	$-0.357975\pi$
$613$	−288.460	−	288.460i	−0.470572	−	0.470572i	−0.902100	+	0.431528i	$0.857975\pi$
$614$	−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	$-0.284876\pi$
$617$	−95.4121	−	95.4121i	−0.154639	−	0.154639i	−0.780186	+	0.625547i	$0.784876\pi$
$618$	−331.710	+	331.710i	−0.536748	+	0.536748i
$619$	544.952	+	544.952i	0.880374	+	0.880374i	0.993572	−	0.113198i	$-0.0361095\pi$
$619$	544.952	+	544.952i	0.880374	+	0.880374i	−0.113198	+	0.993572i	$0.536110\pi$
$620$		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	−0.999830	−	0.0184540i	$-0.994126\pi$
$631$	−642.537	−	642.537i	−1.01828	−	1.01828i	−0.0184540	−	0.999830i	$-0.505874\pi$
$632$	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	$0.124111\pi$
$641$			487.290i			0.760202i	−0.924945	+	0.380101i	$0.875889\pi$
$642$	−801.285	−	801.285i	−1.24811	−	1.24811i
$643$	−797.688	−	797.688i	−1.24057	−	1.24057i	−0.959764	−	0.280809i	$-0.909397\pi$
$643$	−797.688	−	797.688i	−1.24057	−	1.24057i	−0.280809	−	0.959764i	$-0.590603\pi$
$644$	−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	$-0.777114\pi$
$647$	−989.526			−1.52941			−0.764703	+	0.644383i	$0.777114\pi$
$648$	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	0.544590	−	0.838702i	$-0.316685\pi$
$661$	−194.408	−	194.408i	−0.294112	−	0.294112i	−0.838702	+	0.544590i	$0.816685\pi$
$662$	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	$-0.651176\pi$
$673$	−615.500			−0.914561			−0.457281	+	0.889322i	$0.651176\pi$
$674$	−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	$-0.792653\pi$
$683$	−129.044	+	129.044i	−0.188937	+	0.188937i	0.606299	+	0.795237i	$0.292653\pi$
$684$	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	0.0536923	−	0.998558i	$-0.482901\pi$
$691$	727.105	−	727.105i	1.05225	−	1.05225i	0.998558	−	0.0536923i	$-0.0170990\pi$
$692$		−	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	$-0.850143\pi$
$701$		−	635.934i		−	0.907181i	0.891210	−	0.453590i	$-0.149857\pi$
$702$	−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	0.0191186	−	0.999817i	$-0.493914\pi$
$709$	−695.315	−	695.315i	−0.980699	−	0.980699i	−0.999817	+	0.0191186i	$0.993914\pi$
$710$		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	$-0.796061\pi$
$719$		−	859.565i		−	1.19550i	0.801682	−	0.597750i	$-0.203939\pi$
$720$		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	$-0.597248\pi$
$727$	−437.337			−0.601564			−0.300782	+	0.953693i	$0.597248\pi$
$728$	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	$-0.237850\pi$
$733$	39.5591	+	39.5591i	0.0539687	+	0.0539687i	−0.679607	+	0.733576i	$0.737850\pi$
$734$	−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	−0.958088	−	0.286475i	$-0.907517\pi$
$739$	−919.732	−	919.732i	−1.24456	−	1.24456i	−0.286475	−	0.958088i	$-0.592483\pi$
$740$		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	$-0.00525109\pi$
$743$	730.642	+	730.642i	0.983368	+	0.983368i	−0.0164960	+	0.999864i	$0.505251\pi$
$744$	−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	$-0.957539\pi$
$751$		−	199.764i		−	0.265997i	0.991116	−	0.132998i	$-0.0424605\pi$
$752$	−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	0.805161	−	0.593056i	$-0.202079\pi$
$761$	161.412	+	161.412i	0.212105	+	0.212105i	−0.593056	+	0.805161i	$0.702079\pi$
$762$	−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	−0.791088	−	0.611703i	$-0.790485\pi$
$769$	−137.947	+	137.947i	−0.179385	+	0.179385i	0.611703	+	0.791088i	$0.290485\pi$
$770$		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	$-0.0819128\pi$
$773$	550.813	+	550.813i	0.712566	+	0.712566i	−0.254506	+	0.967071i	$0.581913\pi$
$774$	−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	$-0.522506\pi$
$787$	729.434	−	729.434i	0.926854	−	0.926854i	0.997501	+	0.0706473i	$0.0225065\pi$
$788$	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	$-0.590054\pi$
$797$	−444.974			−0.558311			−0.279155	+	0.960246i	$0.590054\pi$
$798$	−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	−0.376823	−	0.926285i	$-0.622983\pi$
$811$	445.614	−	445.614i	0.549463	−	0.549463i	0.926285	+	0.376823i	$0.122983\pi$
$812$	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	−0.839047	−	0.544058i	$-0.816887\pi$
$821$	−242.186	+	242.186i	−0.294989	+	0.294989i	0.544058	+	0.839047i	$0.316887\pi$
$822$			968.083i			1.17772i
$823$	99.5787			0.120995			0.0604974	−	0.998168i	$-0.480731\pi$
$823$	99.5787			0.120995			0.0604974	+	0.998168i	$0.480731\pi$
$824$	−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	−0.0919618	+	0.995763i	$0.529314\pi$
$827$	−899.548	+	899.548i	−1.08772	+	1.08772i	−0.995763	+	0.0919618i	$0.970686\pi$
$828$			1108.39i			1.33864i
$829$		−	32.1103i		−	0.0387338i	−0.999812	−	0.0193669i	$-0.993835\pi$
$829$		−	32.1103i		−	0.0387338i	0.999812	−	0.0193669i	$-0.00616506\pi$
$830$		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	0.420195	−	0.907434i	$-0.361962\pi$
$839$	−408.794	−	408.794i	−0.487239	−	0.487239i	−0.907434	+	0.420195i	$0.861962\pi$
$840$		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	$-0.894658\pi$
$853$	−529.546	+	529.546i	−0.620804	+	0.620804i	0.324933	+	0.945737i	$0.394658\pi$
$854$	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	$-0.876579\pi$
$857$	−1586.76			−1.85153			−0.925766	+	0.378097i	$0.876579\pi$
$858$	−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	−0.983258	−	0.182216i	$-0.941673\pi$
$863$	−1005.80	−	1005.80i	−1.16547	−	1.16547i	−0.182216	−	0.983258i	$-0.558327\pi$
$864$	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	$-0.437647\pi$
$877$	−689.532	−	689.532i	−0.786240	−	0.786240i	−0.980876	+	0.194636i	$0.937647\pi$
$878$	−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	$0.365626\pi$
$881$			1607.31i			1.82442i	−0.409722	+	0.912210i	$0.634374\pi$
$882$	−502.009	+	502.009i	−0.569171	+	0.569171i
$883$	−153.969			−0.174370			−0.0871850	−	0.996192i	$-0.527787\pi$
$883$	−153.969			−0.174370			−0.0871850	+	0.996192i	$0.527787\pi$
$884$	−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	$-0.437378\pi$
$907$	354.574			0.390930			0.195465	+	0.980711i	$0.437378\pi$
$908$	−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	−0.437886	−	0.899030i	$-0.644273\pi$
$929$	428.403	−	428.403i	0.461144	−	0.461144i	0.899030	+	0.437886i	$0.144273\pi$
$930$		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	0.0361387	−	0.999347i	$-0.488494\pi$
$941$	974.392	−	974.392i	1.03549	−	1.03549i	0.999347	−	0.0361387i	$-0.0115058\pi$
$942$	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	$-0.516209\pi$
$947$	897.569	−	897.569i	0.947803	−	0.947803i	0.998704	+	0.0509007i	$0.0162092\pi$
$948$	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	$-0.301773\pi$
$953$	1111.71			1.16654			0.583269	+	0.812279i	$0.301773\pi$
$954$	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	0.845561	+	0.533879i	$0.179266\pi$
$967$	1333.92	+	1333.92i	1.37944	+	1.37944i	0.533879	+	0.845561i	$0.320734\pi$
$968$	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	0.990252	+	0.139288i	$0.0444815\pi$
$977$	1103.56	+	1103.56i	1.12954	+	1.12954i	0.139288	+	0.990252i	$0.455518\pi$
$978$		−	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	$-0.525412\pi$
$983$	901.475	−	901.475i	0.917065	−	0.917065i	0.996815	+	0.0797497i	$0.0254121\pi$
$984$	−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.b.174.2		4
5.2	odd	4		13.3.d.a.5.1	✓	4
5.3	odd	4		325.3.j.a.226.2		4
5.4	even	2		325.3.g.a.174.1		4
13.8	odd	4		325.3.g.a.99.1		4
15.2	even	4		117.3.j.a.109.2		4
20.7	even	4		208.3.t.c.161.1		4
65.2	even	12		169.3.f.d.150.1		8
65.7	even	12		169.3.f.f.89.1		8
65.8	even	4		325.3.j.a.151.2		4
65.12	odd	4		169.3.d.d.70.2		4
65.17	odd	12		169.3.f.d.80.1		8
65.22	odd	12		169.3.f.f.80.2		8
65.32	even	12		169.3.f.d.89.2		8
65.34	odd	4	inner	325.3.g.b.99.2		4
65.37	even	12		169.3.f.f.150.2		8
65.42	odd	12		169.3.f.f.19.1		8
65.47	even	4		13.3.d.a.8.1	yes	4
65.57	even	4		169.3.d.d.99.2		4
65.62	odd	12		169.3.f.d.19.2		8
195.47	odd	4		117.3.j.a.73.2		4
260.47	odd	4		208.3.t.c.177.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	5.2	odd	4
13.3.d.a.8.1	yes	4	65.47	even	4
117.3.j.a.73.2		4	195.47	odd	4
117.3.j.a.109.2		4	15.2	even	4
169.3.d.d.70.2		4	65.12	odd	4
169.3.d.d.99.2		4	65.57	even	4
169.3.f.d.19.2		8	65.62	odd	12
169.3.f.d.80.1		8	65.17	odd	12
169.3.f.d.89.2		8	65.32	even	12
169.3.f.d.150.1		8	65.2	even	12
169.3.f.f.19.1		8	65.42	odd	12
169.3.f.f.80.2		8	65.22	odd	12
169.3.f.f.89.1		8	65.7	even	12
169.3.f.f.150.2		8	65.37	even	12
208.3.t.c.161.1		4	20.7	even	4
208.3.t.c.177.1		4	260.47	odd	4
325.3.g.a.99.1		4	13.8	odd	4
325.3.g.a.174.1		4	5.4	even	2
325.3.g.b.99.2		4	65.34	odd	4	inner
325.3.g.b.174.2		4	1.1	even	1	trivial
325.3.j.a.151.2		4	65.8	even	4
325.3.j.a.226.2		4	5.3	odd	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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