LMFDB - Embedded newform 325.3.j.a.151.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(151,325)] 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("325.151"); 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([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,4,0,0,-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			151.2
Root			$1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	325.151
Dual form			325.3.j.a.226.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.58114 + 2.58114i) q^{2} -2.16228 q^{3} +9.32456i q^{4} +(-5.58114 - 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} +(-7.32456 + 7.32456i) q^{11} -20.1623i q^{12} +(-9.90569 + 8.41886i) q^{13} +7.32456 q^{14} -33.6491 q^{16} +15.9737i q^{17} +(-11.1623 - 11.1623i) q^{18} +(-3.16228 - 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -37.8114 q^{22} -27.4868i q^{23} +(29.7171 - 29.7171i) q^{24} +(-47.2982 - 3.83772i) q^{26} +28.8114 q^{27} +(13.2302 + 13.2302i) q^{28} +25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(15.8377 - 15.8377i) q^{33} +(-41.2302 + 41.2302i) q^{34} -40.3246i q^{36} +(4.23025 - 4.23025i) q^{37} -16.3246i q^{38} +(21.4189 - 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} -15.8377 q^{42} +11.5132i q^{43} +(-68.2982 - 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} +72.7587 q^{48} +44.9737i q^{49} -34.5395i q^{51} +(-78.5021 - 92.3662i) q^{52} +4.18861 q^{53} +(74.3662 + 74.3662i) q^{54} +39.0000i q^{56} +(6.83772 + 6.83772i) q^{57} +(66.6228 + 66.6228i) q^{58} +(-30.2719 + 30.2719i) q^{59} -67.6754 q^{61} +100.596i q^{62} +(-6.13594 + 6.13594i) q^{63} -29.9737i q^{64} +81.7587 q^{66} +(81.0833 + 81.0833i) q^{67} -148.947 q^{68} +59.4342i q^{69} +(50.4452 + 50.4452i) q^{71} +(59.4342 - 59.4342i) q^{72} +(31.6228 - 31.6228i) q^{73} +21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} +20.7851i q^{77} +(102.272 + 8.29822i) q^{78} +50.7851 q^{79} -23.3772 q^{81} +57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(-28.6075 - 28.6075i) q^{84} +(-29.7171 + 29.7171i) q^{86} -55.8114 q^{87} -201.329i q^{88} +(91.1096 - 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302 q^{92} +(-42.1359 - 42.1359i) q^{93} -182.570 q^{94} +(68.9320 + 68.9320i) q^{96} +(-87.3552 - 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +(31.6754 - 31.6754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} - 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9} - 4 q^{11} - 8 q^{13} + 4 q^{14} - 84 q^{16} - 32 q^{18} + 32 q^{21} - 88 q^{22} + 24 q^{24} - 88 q^{26} + 52 q^{27} - 4 q^{28} + 40 q^{29}+ \cdots + 152 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 - 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9 - 4 * q^11 - 8 * q^13 + 4 * q^14 - 84 * q^16 - 32 * q^18 + 32 * q^21 - 88 * q^22 + 24 * q^24 - 88 * q^26 + 52 * q^27 - 4 * q^28 + 40 * q^29 + 40 * q^31 - 20 * q^32 + 76 * q^33 - 108 * q^34 - 40 * q^37 + 92 * q^39 + 32 * q^41 - 76 * q^42 - 172 * q^44 + 132 * q^46 + 4 * q^47 + 76 * q^48 - 80 * q^52 + 80 * q^53 + 152 * q^54 + 40 * q^57 + 140 * q^58 + 56 * q^59 - 296 * q^61 + 64 * q^63 + 112 * q^66 + 84 * q^67 - 444 * q^68 + 284 * q^71 + 48 * q^72 + 100 * q^74 + 80 * q^76 + 232 * q^78 + 64 * q^79 - 220 * q^81 + 52 * q^83 - 184 * q^84 - 24 * q^86 - 160 * q^87 + 200 * q^89 + 156 * q^91 + 456 * q^92 - 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	0.934435	+	0.356135i	$0.115906\pi$
$2$	2.58114	+	2.58114i	1.29057	+	1.29057i	0.356135	+	0.934435i	$0.384094\pi$
$3$	−2.16228			−0.720759			−0.360380	−	0.932806i	$-0.617353\pi$
$3$	−2.16228			−0.720759			−0.360380	+	0.932806i	$0.617353\pi$
$4$			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	−0.598459	−	0.801153i	$-0.704220\pi$
$7$	1.41886	−	1.41886i	0.202694	−	0.202694i	0.801153	+	0.598459i	$0.204220\pi$
$8$	−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	$0.406049\pi$
$12$		−	20.1623i		−	1.68019i
$13$	−9.90569	+	8.41886i	−0.761976	+	0.647605i
$13$	−9.90569	+	8.41886i	−0.761976	+	0.647605i
$14$	7.32456			0.523183
$15$		0			0
$16$	−33.6491			−2.10307
$17$			15.9737i			0.939627i	0.882766	+	0.469814i	$0.155679\pi$
$17$			15.9737i			0.939627i	−0.882766	+	0.469814i	$0.844321\pi$
$18$	−11.1623	−	11.1623i	−0.620127	−	0.620127i
$19$	−3.16228	−	3.16228i	−0.166436	−	0.166436i	0.618975	−	0.785411i	$-0.287548\pi$
$19$	−3.16228	−	3.16228i	−0.166436	−	0.166436i	−0.785411	+	0.618975i	$0.787548\pi$
$20$		0			0
$21$	−3.06797	+	3.06797i	−0.146094	+	0.146094i
$22$	−37.8114			−1.71870
$23$		−	27.4868i		−	1.19508i	−0.801839	−	0.597540i	$-0.796145\pi$
$23$		−	27.4868i		−	1.19508i	0.801839	−	0.597540i	$-0.203855\pi$
$24$	29.7171	−	29.7171i	1.23821	−	1.23821i
$25$		0			0
$26$	−47.2982	−	3.83772i	−1.81916	−	0.147605i
$27$	28.8114			1.06709
$28$	13.2302	+	13.2302i	0.472509	+	0.472509i
$29$	25.8114			0.890048			0.445024	−	0.895519i	$-0.353195\pi$
$29$	25.8114			0.890048			0.445024	+	0.895519i	$0.353195\pi$
$30$		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	−0.647627	−	0.761958i	$-0.724238\pi$
$37$	4.23025	−	4.23025i	0.114331	−	0.114331i	0.761958	+	0.647627i	$0.224238\pi$
$38$		−	16.3246i		−	0.429594i
$39$	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	$0.688337\pi$
$42$	−15.8377			−0.377089
$43$			11.5132i			0.267748i	0.990998	+	0.133874i	$0.0427418\pi$
$43$			11.5132i			0.267748i	−0.990998	+	0.133874i	$0.957258\pi$
$44$	−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	−0.974940	−	0.222468i	$-0.928589\pi$
$47$	−35.3662	+	35.3662i	−0.752472	+	0.752472i	0.222468	+	0.974940i	$0.428589\pi$
$48$	72.7587			1.51581
$49$			44.9737i			0.917830i
$50$		0			0
$51$		−	34.5395i		−	0.677245i
$52$	−78.5021	−	92.3662i	−1.50966	−	1.77627i
$53$	4.18861			0.0790304			0.0395152	−	0.999219i	$-0.487419\pi$
$53$	4.18861			0.0790304			0.0395152	+	0.999219i	$0.487419\pi$
$54$	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	$-0.868181\pi$
$59$	−30.2719	+	30.2719i	−0.513083	+	0.513083i	0.402387	+	0.915470i	$0.368181\pi$
$60$		0			0
$61$	−67.6754			−1.10943			−0.554717	−	0.832039i	$-0.687173\pi$
$61$	−67.6754			−1.10943			−0.554717	+	0.832039i	$0.687173\pi$
$62$			100.596i			1.62252i
$63$	−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	$0.423103\pi$
$68$	−148.947			−2.19040
$69$			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	$-0.650905\pi$
$73$	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
$77$			20.7851i			0.269936i
$78$	102.272	+	8.29822i	1.31118	+	0.106387i
$79$	50.7851			0.642849			0.321424	−	0.946935i	$-0.395838\pi$
$79$	50.7851			0.642849			0.321424	+	0.946935i	$0.395838\pi$
$80$		0			0
$81$	−23.3772			−0.288608
$82$			57.6228i			0.702717i
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	0.585965	−	0.810336i	$-0.300715\pi$
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	−0.810336	+	0.585965i	$0.800715\pi$
$84$	−28.6075	−	28.6075i	−0.340565	−	0.340565i
$85$		0			0
$86$	−29.7171	+	29.7171i	−0.345547	+	0.345547i
$87$	−55.8114			−0.641510
$88$		−	201.329i		−	2.28783i
$89$	91.1096	−	91.1096i	1.02370	−	1.02370i	0.0239913	−	0.999712i	$-0.492363\pi$
$89$	91.1096	−	91.1096i	1.02370	−	1.02370i	0.999712	−	0.0239913i	$-0.00763740\pi$
$90$		0			0
$91$	−2.10961	+	26.0000i	−0.0231825	+	0.285714i
$92$	256.302			2.78590
$93$	−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	$-0.985938\pi$
$101$		−	8.92100i		−	0.0883267i	0.999024	−	0.0441634i	$-0.0140622\pi$
$102$	89.1512	−	89.1512i	0.874032	−	0.874032i
$103$		−	59.4342i		−	0.577031i	−0.957475	−	0.288515i	$-0.906838\pi$
$103$		−	59.4342i		−	0.577031i	0.957475	−	0.288515i	$-0.0931616\pi$
$104$	20.4342	−	251.842i	0.196482	−	2.42156i
$105$		0			0
$106$	10.8114	+	10.8114i	0.101994	+	0.101994i
$107$	143.570			1.34178			0.670888	−	0.741558i	$-0.265913\pi$
$107$	143.570			1.34178			0.670888	+	0.741558i	$0.265913\pi$
$108$			268.653i			2.48753i
$109$	−84.7740	−	84.7740i	−0.777743	−	0.777743i	0.201703	−	0.979447i	$-0.435352\pi$
$109$	−84.7740	−	84.7740i	−0.777743	−	0.777743i	−0.979447	+	0.201703i	$0.935352\pi$
$110$		0			0
$111$	−9.14697	+	9.14697i	−0.0824052	+	0.0824052i
$112$	−47.7434	+	47.7434i	−0.426281	+	0.426281i
$113$	108.544			0.960564			0.480282	−	0.877114i	$-0.340534\pi$
$113$	108.544			0.960564			0.480282	+	0.877114i	$0.340534\pi$
$114$			35.2982i			0.309634i
$115$		0			0
$116$			240.680i			2.07483i
$117$	42.8377	−	36.4078i	0.366134	−	0.311178i
$118$	−156.272			−1.32434
$119$	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
$127$			94.8377i			0.746754i	0.927680	+	0.373377i	$0.121800\pi$
$127$			94.8377i			0.746754i	−0.927680	+	0.373377i	$0.878200\pi$
$128$	−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
$133$	−8.97367			−0.0674712
$134$			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	−0.948832	−	0.315780i	$-0.897734\pi$
$137$	−86.7281	+	86.7281i	−0.633052	+	0.633052i	0.315780	+	0.948832i	$0.397734\pi$
$138$	−153.408	+	153.408i	−1.11165	+	1.11165i
$139$	78.5395			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$139$	78.5395			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$140$		0			0
$141$	76.4715	−	76.4715i	0.542351	−	0.542351i
$142$			260.412i			1.83389i
$143$	10.8904	−	134.219i	0.0761566	−	0.938596i
$144$	145.517			1.01054
$145$		0			0
$146$	163.246			1.11812
$147$		−	97.2456i		−	0.661534i
$148$	39.4452	+	39.4452i	0.266522	+	0.266522i
$149$	−128.219	−	128.219i	−0.860532	−	0.860532i	0.130868	−	0.991400i	$-0.458224\pi$
$149$	−128.219	−	128.219i	−0.860532	−	0.860532i	−0.991400	+	0.130868i	$0.958224\pi$
$150$		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	$0.206372\pi$
$152$	86.9210			0.571849
$153$		−	69.0790i		−	0.451497i
$154$	−53.6491	+	53.6491i	−0.348371	+	0.348371i
$155$		0			0
$156$	169.743	+	199.721i	1.08810	+	1.28027i
$157$	−232.544			−1.48117			−0.740585	−	0.671962i	$-0.765452\pi$
$157$	−232.544			−1.48117			−0.740585	+	0.671962i	$0.765452\pi$
$158$	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	$-0.410490\pi$
$167$	206.785	−	206.785i	1.23823	−	1.23823i	0.960722	−	0.277512i	$-0.0895097\pi$
$168$		−	84.3288i		−	0.501957i
$169$	27.2456	−	166.789i	0.161216	−	0.986919i
$170$		0			0
$171$	13.6754	+	13.6754i	0.0799734	+	0.0799734i
$172$	−107.355			−0.624158
$173$			91.3815i			0.528217i	0.964493	+	0.264108i	$0.0850777\pi$
$173$			91.3815i			0.528217i	−0.964493	+	0.264108i	$0.914922\pi$
$174$	−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
$178$	470.333			2.64232
$179$		−	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	$0.273484\pi$
$181$			274.144i			1.51461i	−0.653061	+	0.757305i	$0.726516\pi$
$182$	−72.5548	+	61.6644i	−0.398653	+	0.338815i
$183$	146.333			0.799634
$184$	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	$0.344097\pi$
$192$			64.8114i			0.337559i
$193$	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	$0.920115\pi$
$198$	163.517			0.825846
$199$		−	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
$207$			118.868i			0.574243i
$208$	333.318	−	283.287i	1.60249	−	1.36196i
$209$	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	$0.219505\pi$
$212$			39.0569i			0.184231i
$213$	−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
$217$	55.2982			0.254831
$218$		−	437.627i		−	2.00746i
$219$	−68.3772	+	68.3772i	−0.312225	+	0.312225i
$220$		0			0
$221$	−134.480	−	158.230i	−0.608507	−	0.715974i
$222$	−47.2192			−0.212699
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.995190	+	0.0979674i	$0.0312341\pi$
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.0979674	+	0.995190i	$0.468766\pi$
$224$	−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	−0.0509319	+	0.998702i	$0.516219\pi$
$229$	−240.366	+	240.366i	−1.04963	+	1.04963i	−0.998702	+	0.0509319i	$0.983781\pi$
$230$		0			0
$231$		−	44.9431i		−	0.194559i
$232$	−354.737	+	354.737i	−1.52904	+	1.52904i
$233$			10.7893i			0.0463061i	0.999732	+	0.0231531i	$0.00737051\pi$
$233$			10.7893i			0.0463061i	−0.999732	+	0.0231531i	$0.992629\pi$
$234$	204.544	+	16.5964i	0.874119	+	0.0709250i
$235$		0			0
$236$	−282.272	−	282.272i	−1.19607	−	1.19607i
$237$	−109.811			−0.463339
$238$			117.000i			0.491597i
$239$	−98.0153	−	98.0153i	−0.410106	−	0.410106i	0.471670	−	0.881775i	$-0.343652\pi$
$239$	−98.0153	−	98.0153i	−0.410106	−	0.410106i	−0.881775	+	0.471670i	$0.843652\pi$
$240$		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
$243$	−208.754			−0.859072
$244$		−	631.043i		−	2.58624i
$245$		0			0
$246$		−	124.596i		−	0.506490i
$247$	57.9473	+	4.70178i	0.234605	+	0.0190355i
$248$	−535.631			−2.15980
$249$	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
$257$		−	450.579i		−	1.75322i	−0.481198	−	0.876612i	$-0.659798\pi$
$257$		−	450.579i		−	1.75322i	0.481198	−	0.876612i	$-0.340202\pi$
$258$	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
$263$	−166.982			−0.634913			−0.317457	−	0.948273i	$-0.602829\pi$
$263$	−166.982			−0.634913			−0.317457	+	0.948273i	$0.602829\pi$
$264$			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	$-0.397627\pi$
$269$	170.061			0.632198			0.316099	+	0.948726i	$0.397627\pi$
$270$		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	$0.441663\pi$
$272$		−	537.500i		−	1.97610i
$273$	4.56156	−	56.2192i	0.0167090	−	0.205931i
$274$	−447.715			−1.63399
$275$		0			0
$276$	−554.197			−2.00796
$277$		−	187.947i		−	0.678510i	−0.940694	−	0.339255i	$-0.889825\pi$
$277$		−	187.947i		−	0.678510i	0.940694	−	0.339255i	$-0.110175\pi$
$278$	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	$-0.00669337\pi$
$282$	394.767			1.39988
$283$			399.201i			1.41061i	0.708906	+	0.705303i	$0.249189\pi$
$283$			399.201i			1.41061i	−0.708906	+	0.705303i	$0.750811\pi$
$284$	−470.379	+	470.379i	−1.65626	+	1.65626i
$285$		0			0
$286$	374.548	−	318.329i	1.30961	−	1.11304i
$287$	31.6754			0.110367
$288$	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
$298$		−	661.903i		−	2.22115i
$299$	231.408	+	272.276i	0.773939	+	0.910623i
$300$		0			0
$301$	16.3356	+	16.3356i	0.0542710	+	0.0542710i
$302$	150.623			0.498751
$303$			19.2897i			0.0636623i
$304$	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	−0.210001	−	0.977701i	$-0.567347\pi$
$307$	235.684	−	235.684i	0.767700	−	0.767700i	0.977701	+	0.210001i	$0.0673467\pi$
$308$	−193.811			−0.629258
$309$			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	$-0.0585069\pi$
$312$	−44.1843	+	544.552i	−0.141616	+	1.74536i
$313$	−223.483			−0.714002			−0.357001	−	0.934104i	$-0.616201\pi$
$313$	−223.483			−0.714002			−0.357001	+	0.934104i	$0.616201\pi$
$314$	−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
$322$		−	201.329i		−	0.625245i
$323$	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
$328$	−306.816			−0.935414
$329$			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
$337$		−	5.32456i		−	0.0157999i	−0.999969	−	0.00789993i	$-0.997485\pi$
$337$		−	5.32456i		−	0.0157999i	0.999969	−	0.00789993i	$-0.00251465\pi$
$338$	500.831	−	360.182i	1.48175	−	1.06563i
$339$	−234.702			−0.692336
$340$		0			0
$341$	−285.465			−0.837140
$342$			70.5964i			0.206422i
$343$	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
$347$	47.2413			0.136142			0.0680710	−	0.997680i	$-0.478316\pi$
$347$	47.2413			0.136142			0.0680710	+	0.997680i	$0.478316\pi$
$348$		−	520.416i		−	1.49545i
$349$	223.581	−	223.581i	0.640634	−	0.640634i	−0.310078	−	0.950711i	$-0.600355\pi$
$349$	223.581	−	223.581i	0.640634	−	0.640634i	0.950711	+	0.310078i	$0.100355\pi$
$350$		0			0
$351$	−285.397	+	242.559i	−0.813096	+	0.691052i
$352$	467.004			1.32672
$353$	−110.320	−	110.320i	−0.312522	−	0.312522i	0.533364	−	0.845886i	$-0.320928\pi$
$353$	−110.320	−	110.320i	−0.312522	−	0.312522i	−0.845886	+	0.533364i	$0.820928\pi$
$354$	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	$-0.710264\pi$
$359$	63.2149	−	63.2149i	0.176086	−	0.176086i	0.789647	+	0.613561i	$0.210264\pi$
$360$		0			0
$361$		−	341.000i		−	0.944598i
$362$	−707.605	+	707.605i	−1.95471	+	1.95471i
$363$		−	29.6271i		−	0.0816172i
$364$	−242.438	−	19.6712i	−0.666040	−	0.0540417i
$365$		0			0
$366$	377.706	+	377.706i	1.03198	+	1.03198i
$367$	318.416			0.867620			0.433810	−	0.901004i	$-0.357169\pi$
$367$	318.416			0.867620			0.433810	+	0.901004i	$0.357169\pi$
$368$			924.907i			2.51334i
$369$	−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
$373$	−8.87688			−0.0237986			−0.0118993	−	0.999929i	$-0.503788\pi$
$373$	−8.87688			−0.0237986			−0.0118993	+	0.999929i	$0.503788\pi$
$374$		−	603.986i		−	1.61494i
$375$		0			0
$376$		−	972.105i		−	2.58538i
$377$	−255.680	+	217.302i	−0.678196	+	0.576399i
$378$	211.031			0.558282
$379$	−144.698	−	144.698i	−0.381788	−	0.381788i	0.489958	−	0.871746i	$-0.337012\pi$
$379$	−144.698	−	144.698i	−0.381788	−	0.381788i	−0.871746	+	0.489958i	$0.837012\pi$
$380$		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	0.0650838	−	0.997880i	$-0.479269\pi$
$383$	−357.261	−	357.261i	−0.932796	−	0.932796i	−0.997880	+	0.0650838i	$0.979269\pi$
$384$	108.441	−	108.441i	0.282398	−	0.282398i
$385$		0			0
$386$	5.86406			0.0151919
$387$		−	49.7893i		−	0.128655i
$388$	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
$393$	242.754			0.617694
$394$		−	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	−0.948037	−	0.318160i	$-0.896935\pi$
$397$	−250.061	+	250.061i	−0.629877	+	0.629877i	0.318160	+	0.948037i	$0.396935\pi$
$398$	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	$0.197163\pi$
$402$		−	905.074i		−	2.25143i
$403$	−357.088	−	28.9737i	−0.886073	−	0.0718950i
$404$	83.1843			0.205902
$405$		0			0
$406$	189.057			0.465657
$407$			61.9694i			0.152259i
$408$	474.691	+	474.691i	1.16346	+	1.16346i
$409$	370.140	+	370.140i	0.904988	+	0.904988i	0.995862	−	0.0908741i	$-0.0289661\pi$
$409$	370.140	+	370.140i	0.904988	+	0.904988i	−0.0908741	+	0.995862i	$0.528966\pi$
$410$		0			0
$411$	187.530	−	187.530i	0.456278	−	0.456278i
$412$	554.197			1.34514
$413$			85.9032i			0.207998i
$414$	−306.816	+	306.816i	−0.741101	+	0.741101i
$415$		0			0
$416$	584.175	+	47.3993i	1.40427	+	0.113941i
$417$	−169.824			−0.407252
$418$	119.570	+	119.570i	0.286053	+	0.286053i
$419$	−658.767			−1.57224			−0.786118	−	0.618076i	$-0.787912\pi$
$419$	−658.767			−1.57224			−0.786118	+	0.618076i	$0.787912\pi$
$420$		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
$428$			1338.73i			3.12787i
$429$	−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	$0.588570\pi$
$432$	−969.478			−2.24416
$433$		−	156.140i		−	0.360601i	−0.983612	−	0.180300i	$-0.942293\pi$
$433$		−	156.140i		−	0.360601i	0.983612	−	0.180300i	$-0.0577070\pi$
$434$	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
$438$	−352.982			−0.805895
$439$			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
$442$	61.3025	−	755.526i	0.138693	−	1.70933i
$443$	577.372			1.30332			0.651662	−	0.758510i	$-0.274072\pi$
$443$	577.372			1.30332			0.651662	+	0.758510i	$0.274072\pi$
$444$	−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	$-0.803960\pi$
$449$	−107.127	+	107.127i	−0.238591	+	0.238591i	0.577675	+	0.816267i	$0.303960\pi$
$450$		0			0
$451$	−163.517			−0.362566
$452$			1012.12i			2.23921i
$453$	−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	$0.564256\pi$
$458$	−1240.84			−2.70925
$459$			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	$-0.921722\pi$
$463$	−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
$467$			308.263i			0.660093i	0.943965	+	0.330046i	$0.107064\pi$
$467$			308.263i			0.660093i	−0.943965	+	0.330046i	$0.892936\pi$
$468$	339.487	+	399.443i	0.725399	+	0.853510i
$469$	230.092			0.490601
$470$		0			0
$471$	502.824			1.06757
$472$		−	832.078i		−	1.76288i
$473$	−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
$477$	−18.1139			−0.0379746
$478$		−	505.982i		−	1.05854i
$479$	76.6424	−	76.6424i	0.160005	−	0.160005i	−0.622564	−	0.782569i	$-0.713909\pi$
$479$	76.6424	−	76.6424i	0.160005	−	0.160005i	0.782569	+	0.622564i	$0.213909\pi$
$480$		0			0
$481$	−6.28967	+	77.5174i	−0.0130762	+	0.161159i
$482$	−1012.82			−2.10130
$483$	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	$-0.754134\pi$
$491$		−	685.302i		−	1.39573i	0.716230	−	0.697864i	$-0.245866\pi$
$492$	225.057	−	225.057i	0.457433	−	0.457433i
$493$			412.302i			0.836313i
$494$	137.434	+	161.706i	0.278207	+	0.327340i
$495$		0			0
$496$	−655.715	−	655.715i	−1.32201	−	1.32201i
$497$	143.149			0.288027
$498$			207.873i			0.417415i
$499$	349.329	+	349.329i	0.700058	+	0.700058i	0.964423	−	0.264365i	$-0.0851623\pi$
$499$	349.329	+	349.329i	0.700058	+	0.700058i	−0.264365	+	0.964423i	$0.585162\pi$
$500$		0			0
$501$	−447.127	+	447.127i	−0.892468	+	0.892468i
$502$	247.381	−	247.381i	0.492792	−	0.492792i
$503$	−42.2719			−0.0840395			−0.0420198	−	0.999117i	$-0.513379\pi$
$503$	−42.2719			−0.0840395			−0.0420198	+	0.999117i	$0.513379\pi$
$504$		−	168.658i		−	0.334638i
$505$		0			0
$506$			1039.32i			2.05398i
$507$	−58.9125	+	360.645i	−0.116198	+	0.711331i
$508$	−884.320			−1.74079
$509$	184.280	+	184.280i	0.362044	+	0.362044i	0.864565	−	0.502521i	$-0.167594\pi$
$509$	184.280	+	184.280i	0.362044	+	0.362044i	−0.502521	+	0.864565i	$0.667594\pi$
$510$		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
$517$		−	518.083i		−	1.00210i
$518$	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
$523$	221.851			0.424188			0.212094	−	0.977249i	$-0.431972\pi$
$523$	221.851			0.424188			0.212094	+	0.977249i	$0.431972\pi$
$524$		−	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
$532$		−	83.6754i		−	0.157285i
$533$	−204.544	−	16.5964i	−0.383759	−	0.0311378i
$534$	−1016.99			−1.90448
$535$		0			0
$536$	−2228.72			−4.15806
$537$			154.973i			0.288590i
$538$	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	$0.353047\pi$
$542$	−1120.59			−2.06750
$543$		−	592.777i		−	1.09167i
$544$	509.230	−	509.230i	0.936085	−	0.936085i
$545$		0			0
$546$	156.884	−	133.336i	0.287333	−	0.244204i
$547$	317.777			0.580944			0.290472	−	0.956883i	$-0.406188\pi$
$547$	317.777			0.580944			0.290472	+	0.956883i	$0.406188\pi$
$548$	−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	−0.130698	−	0.991422i	$-0.541722\pi$
$557$	479.423	−	479.423i	0.860724	−	0.860724i	0.991422	+	0.130698i	$0.0417220\pi$
$558$		−	435.035i		−	0.779632i
$559$	−96.9278	−	114.046i	−0.173395	−	0.204018i
$560$		0			0
$561$	252.986	+	252.986i	0.450956	+	0.450956i
$562$	1480.78			2.63484
$563$			461.671i			0.820020i	0.912081	+	0.410010i	$0.134475\pi$
$563$			461.671i			0.820020i	−0.912081	+	0.410010i	$0.865525\pi$
$564$	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
$568$	−1386.58			−2.44116
$569$			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	$0.0323088\pi$
$571$			115.715i			0.202654i	−0.994853	+	0.101327i	$0.967691\pi$
$572$	1251.53	+	101.548i	2.18800	+	0.177532i
$573$	−388.574			−0.678140
$574$	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
$582$			975.083i			1.67540i
$583$	−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	$0.612600\pi$
$588$	906.772			1.54213
$589$		−	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
$597$			561.670i			0.940822i
$598$	−105.487	+	1300.08i	−0.176399	+	2.17404i
$599$	1044.77			1.74419			0.872096	−	0.489334i	$-0.162760\pi$
$599$	1044.77			1.74419			0.872096	+	0.489334i	$0.162760\pi$
$600$		0			0
$601$	933.298			1.55291			0.776454	−	0.630174i	$-0.217016\pi$
$601$	933.298			1.55291			0.776454	+	0.630174i	$0.217016\pi$
$602$			84.3288i			0.140081i
$603$	−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
$607$	−579.912			−0.955374			−0.477687	−	0.878530i	$-0.658525\pi$
$607$	−579.912			−0.955374			−0.477687	+	0.878530i	$0.658525\pi$
$608$			201.623i			0.331616i
$609$	−79.1886	+	79.1886i	−0.130031	+	0.130031i
$610$		0			0
$611$	52.5836	−	648.070i	0.0860616	−	1.06067i
$612$	644.131			1.05250
$613$	288.460	+	288.460i	0.470572	+	0.470572i	0.902100	−	0.431528i	$-0.142025\pi$
$613$	288.460	+	288.460i	0.470572	+	0.470572i	−0.431528	+	0.902100i	$0.642025\pi$
$614$	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	$-0.963890\pi$
$619$	−544.952	+	544.952i	−0.880374	+	0.880374i	0.113198	+	0.993572i	$0.463890\pi$
$620$		0			0
$621$		−	791.934i		−	1.27526i
$622$	293.434	−	293.434i	0.471759	−	0.471759i
$623$		−	258.544i		−	0.414998i
$624$	−720.726	+	612.546i	−1.15501	+	0.981644i
$625$		0			0
$626$	−576.840	−	576.840i	−0.921469	−	0.921469i
$627$	−100.167			−0.159755
$628$		−	2168.37i		−	3.45281i
$629$	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
$633$	−703.982			−1.11214
$634$			646.009i			1.01894i
$635$		0			0
$636$		−	84.4520i		−	0.132786i
$637$	−378.627	−	445.495i	−0.594391	−	0.699365i
$638$	−975.964			−1.52972
$639$	−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	0.959764	+	0.280809i	$0.0906028\pi$
$643$	797.688	+	797.688i	1.24057	+	1.24057i	0.280809	+	0.959764i	$0.409397\pi$
$644$	363.658	−	363.658i	0.564686	−	0.564686i
$645$		0			0
$646$	260.763			0.403658
$647$		−	989.526i		−	1.52941i	−0.644383	−	0.764703i	$-0.722886\pi$
$647$		−	989.526i		−	1.52941i	0.644383	−	0.764703i	$-0.277114\pi$
$648$	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
$653$	86.3075			0.132171			0.0660853	−	0.997814i	$-0.478949\pi$
$653$	86.3075			0.132171			0.0660853	+	0.997814i	$0.478949\pi$
$654$			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	$-0.855765\pi$
$659$	−1184.99			−1.79817			−0.899083	+	0.437779i	$0.855765\pi$
$660$		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	$0.316685\pi$
$662$			1600.21i			2.41724i
$663$	290.783	+	342.138i	0.438587	+	0.516045i
$664$	511.881			0.770905
$665$		0			0
$666$	−94.4384			−0.141799
$667$		−	709.473i		−	1.06368i
$668$	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
$672$	195.610			0.291086
$673$			615.500i			0.914561i	0.889322	+	0.457281i	$0.151176\pi$
$673$			615.500i			0.914561i	−0.889322	+	0.457281i	$0.848824\pi$
$674$	13.7434	−	13.7434i	0.0203908	−	0.0203908i
$675$		0			0
$676$	1555.24	+	254.053i	2.30065	+	0.375818i
$677$	412.031			0.608612			0.304306	−	0.952574i	$-0.401575\pi$
$677$	412.031			0.608612			0.304306	+	0.952574i	$0.401575\pi$
$678$	−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
$688$		−	387.408i		−	0.563093i
$689$	−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	$0.482901\pi$
$692$	−852.092			−1.23135
$693$		−	89.8861i		−	0.129706i
$694$	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
$698$	1154.19			1.65356
$699$		−	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	$0.850143\pi$
$702$	−1362.73	−	110.570i	−1.94121	−	0.157507i
$703$	−26.7544			−0.0380575
$704$	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	$-0.506086\pi$
$709$	695.315	−	695.315i	0.980699	−	0.980699i	0.999817	+	0.0191186i	$0.00608601\pi$
$710$		0			0
$711$	−219.623			−0.308893
$712$			2504.31i			3.51730i
$713$	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
$718$	326.333			0.454503
$719$		−	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
$727$		−	437.337i		−	0.601564i	−0.953693	−	0.300782i	$-0.902752\pi$
$727$		−	437.337i		−	0.601564i	0.953693	−	0.300782i	$-0.0972477\pi$
$728$	−328.336	−	386.322i	−0.451010	−	0.530662i
$729$	661.780			0.907792
$730$		0			0
$731$	−183.907			−0.251583
$732$			1364.49i			1.86406i
$733$	−39.5591	−	39.5591i	−0.0539687	−	0.0539687i	0.679607	−	0.733576i	$-0.262150\pi$
$733$	−39.5591	−	39.5591i	−0.0539687	−	0.0539687i	−0.733576	+	0.679607i	$0.762150\pi$
$734$	821.877	+	821.877i	1.11972	+	1.11972i
$735$		0			0
$736$	−876.263	+	876.263i	−1.19057	+	1.19057i
$737$	−1187.80			−1.61167
$738$		−	249.193i		−	0.337660i
$739$	919.732	−	919.732i	1.24456	−	1.24456i	0.286475	−	0.958088i	$-0.407517\pi$
$739$	919.732	−	919.732i	1.24456	−	1.24456i	0.958088	−	0.286475i	$-0.0924834\pi$
$740$		0			0
$741$	−125.298	−	10.1666i	−0.169093	−	0.0137200i
$742$	30.6797			0.0413473
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	0.0164960	−	0.999864i	$-0.494749\pi$
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	−0.999864	+	0.0164960i	$0.994749\pi$
$744$	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
$753$			207.237i			0.275215i
$754$	−1220.83	−	99.0569i	−1.61914	−	0.131375i
$755$		0			0
$756$	381.182	+	381.182i	0.504209	+	0.504209i
$757$	−124.549			−0.164529			−0.0822647	−	0.996611i	$-0.526215\pi$
$757$	−124.549			−0.164529			−0.0822647	+	0.996611i	$0.526215\pi$
$758$		−	746.969i		−	0.985447i
$759$	−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
$763$	−240.565			−0.315289
$764$			1675.68i			2.19330i
$765$		0			0
$766$		−	1844.28i		−	2.40768i
$767$	45.0092	−	554.719i	0.0586822	−	0.723232i
$768$	819.048			1.06647
$769$	137.947	+	137.947i	0.179385	+	0.179385i	0.791088	−	0.611703i	$-0.209515\pi$
$769$	137.947	+	137.947i	0.179385	+	0.179385i	−0.611703	+	0.791088i	$0.709515\pi$
$770$		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	0.254506	−	0.967071i	$-0.418087\pi$
$773$	−550.813	−	550.813i	−0.712566	−	0.712566i	−0.967071	+	0.254506i	$0.918087\pi$
$774$	128.513	−	128.513i	0.166038	−	0.166038i
$775$		0			0
$776$	2401.12			3.09422
$777$			25.9566i			0.0334061i
$778$	−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
$783$	743.662			0.949760
$784$		−	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	−0.997501	−	0.0706473i	$-0.977494\pi$
$787$	−729.434	+	729.434i	−0.926854	+	0.926854i	0.0706473	+	0.997501i	$0.477494\pi$
$788$	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
$792$			870.658i			1.09932i
$793$	670.372	−	569.750i	0.845362	−	0.718474i
$794$	−1290.89			−1.62580
$795$		0			0
$796$	2422.13			3.04288
$797$		−	444.974i		−	0.558311i	−0.960246	−	0.279155i	$-0.909946\pi$
$797$		−	444.974i		−	0.558311i	0.960246	−	0.279155i	$-0.0900545\pi$
$798$	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
$802$	483.715			0.603135
$803$			463.246i			0.576894i
$804$	1634.82	−	1634.82i	2.03336	−	2.03336i
$805$		0			0
$806$	−846.907	−	996.478i	−1.05075	−	1.23632i
$807$	−367.720			−0.455662
$808$	122.605	+	122.605i	0.151739	+	0.151739i
$809$	−1090.36			−1.34779			−0.673893	−	0.738829i	$-0.735379\pi$
$809$	−1090.36			−1.34779			−0.673893	+	0.738829i	$0.735379\pi$
$810$		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
$818$			1910.77i			2.33590i
$819$	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	$0.816887\pi$
$822$	968.083			1.17772
$823$		−	99.5787i		−	0.120995i	−0.998168	−	0.0604974i	$-0.980731\pi$
$823$		−	99.5787i		−	0.120995i	0.998168	−	0.0604974i	$-0.0192687\pi$
$824$	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	$-0.470686\pi$
$827$	899.548	−	899.548i	1.08772	−	1.08772i	0.995763	−	0.0919618i	$-0.0293138\pi$
$828$	−1108.39			−1.33864
$829$		−	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
$832$	252.344	+	296.910i	0.303298	+	0.356863i
$833$	−718.394			−0.862418
$834$	−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	$-0.638038\pi$
$839$	408.794	−	408.794i	0.487239	−	0.487239i	0.907434	+	0.420195i	$0.138038\pi$
$840$		0			0
$841$	−174.772			−0.207815
$842$		−	414.601i		−	0.492400i
$843$	−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
$848$	−140.943			−0.166206
$849$		−	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
$857$		−	1586.76i		−	1.85153i	−0.378097	−	0.925766i	$-0.623421\pi$
$857$		−	1586.76i		−	1.85153i	0.378097	−	0.925766i	$-0.376579\pi$
$858$	−809.877	+	688.315i	−0.943912	+	0.802232i
$859$	145.062			0.168873			0.0844365	−	0.996429i	$-0.473091\pi$
$859$	145.062			0.168873			0.0844365	+	0.996429i	$0.473091\pi$
$860$		0			0
$861$	−68.4911			−0.0795483
$862$			1528.23i			1.77289i
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.983258	+	0.182216i	$0.0583271\pi$
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.182216	+	0.983258i	$0.441673\pi$
$864$	−918.489	−	918.489i	−1.06307	−	1.06307i
$865$		0			0
$866$	403.020	−	403.020i	0.465381	−	0.465381i
$867$	−73.1758			−0.0844011
$868$			515.631i			0.594045i
$869$	−371.978	+	371.978i	−0.428053	+	0.428053i
$870$		0			0
$871$	−1485.81	−	120.557i	−1.70587	−	0.138413i
$872$	2330.17			2.67221
$873$	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	$-0.634374\pi$
$881$		−	1607.31i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$882$	502.009	−	502.009i	0.569171	−	0.569171i
$883$			153.969i			0.174370i	0.996192	+	0.0871850i	$0.0277871\pi$
$883$			153.969i			0.174370i	−0.996192	+	0.0871850i	$0.972213\pi$
$884$	1475.43	−	1253.97i	1.66903	−	1.41851i
$885$		0			0
$886$	1490.28	+	1490.28i	1.68203	+	1.68203i
$887$	−125.273			−0.141232			−0.0706159	−	0.997504i	$-0.522496\pi$
$887$	−125.273			−0.141232			−0.0706159	+	0.997504i	$0.522496\pi$
$888$		−	251.421i		−	0.283132i
$889$	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
$893$	223.675			0.250476
$894$			1431.22i			1.60092i
$895$		0			0
$896$			142.315i			0.158834i
$897$	−500.368	−	588.737i	−0.557824	−	0.656340i
$898$	−553.021			−0.615837
$899$	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
$907$			354.574i			0.390930i	0.980711	+	0.195465i	$0.0626216\pi$
$907$			354.574i			0.390930i	−0.980711	+	0.195465i	$0.937378\pi$
$908$	−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
$913$	272.807			0.298803
$914$			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	$-0.572709\pi$
$919$	−416.201			−0.452884			−0.226442	+	0.974025i	$0.572709\pi$
$920$		0			0
$921$	−509.614	+	509.614i	−0.553327	+	0.553327i
$922$			174.215i			0.188953i
$923$	−924.386	−	75.0036i	−1.00150	−	0.0812606i
$924$	419.074			0.453543
$925$		0			0
$926$	−1736.36			−1.87512
$927$			257.026i			0.277267i
$928$	−822.851	−	822.851i	−0.886692	−	0.886692i
$929$	−428.403	−	428.403i	−0.461144	−	0.461144i	0.437886	−	0.899030i	$-0.355727\pi$
$929$	−428.403	−	428.403i	−0.461144	−	0.461144i	−0.899030	+	0.437886i	$0.855727\pi$
$930$		0			0
$931$	142.219	−	142.219i	0.152760	−	0.152760i
$932$	−100.606			−0.107946
$933$			245.816i			0.263469i
$934$	−795.670	+	795.670i	−0.851896	+	0.851896i
$935$		0			0
$936$	−88.3687	+	1089.10i	−0.0944110	+	1.16357i
$937$	990.702			1.05731			0.528656	−	0.848836i	$-0.322696\pi$
$937$	990.702			1.05731			0.528656	+	0.848836i	$0.322696\pi$
$938$	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	−0.998704	−	0.0509007i	$-0.983791\pi$
$947$	−897.569	+	897.569i	−0.947803	+	0.947803i	0.0509007	+	0.998704i	$0.483791\pi$
$948$		−	1023.94i		−	1.08011i
$949$	−47.0178	+	579.473i	−0.0495446	+	0.610615i
$950$		0			0
$951$	−270.588	−	270.588i	−0.284530	−	0.284530i
$952$	−622.973			−0.654383
$953$		−	1111.71i		−	1.16654i	−0.812279	−	0.583269i	$-0.801773\pi$
$953$		−	1111.71i		−	1.16654i	0.812279	−	0.583269i	$-0.198227\pi$
$954$	−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
$958$	395.649			0.412995
$959$			246.110i			0.256632i
$960$		0			0
$961$		−	201.527i		−	0.209705i
$962$	−216.318	+	183.849i	−0.224863	+	0.191111i
$963$	−620.877			−0.644732
$964$	−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	$0.592445\pi$
$972$		−	1946.54i		−	2.00262i
$973$	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	$0.455518\pi$
$978$	127.925			0.130803
$979$			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
$987$		−	217.005i		−	0.219863i
$988$	−43.8420	+	540.333i	−0.0443745	+	0.546896i
$989$	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	$0.373806\pi$
$992$		−	1242.46i		−	1.25248i
$993$	−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
$997$	−1075.40			−1.07863			−0.539317	−	0.842103i	$-0.681318\pi$
$997$	−1075.40			−1.07863			−0.539317	+	0.842103i	$0.681318\pi$
$998$			1803.33i			1.80695i
$999$	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.j.a.151.2		4
5.2	odd	4		325.3.g.a.99.1		4
5.3	odd	4		325.3.g.b.99.2		4
5.4	even	2		13.3.d.a.8.1	yes	4
13.5	odd	4	inner	325.3.j.a.226.2		4
15.14	odd	2		117.3.j.a.73.2		4
20.19	odd	2		208.3.t.c.177.1		4
65.4	even	6		169.3.f.d.89.2		8
65.9	even	6		169.3.f.f.89.1		8
65.18	even	4		325.3.g.a.174.1		4
65.19	odd	12		169.3.f.f.80.2		8
65.24	odd	12		169.3.f.d.19.2		8
65.29	even	6		169.3.f.f.150.2		8
65.34	odd	4		169.3.d.d.70.2		4
65.44	odd	4		13.3.d.a.5.1	✓	4
65.49	even	6		169.3.f.d.150.1		8
65.54	odd	12		169.3.f.f.19.1		8
65.57	even	4		325.3.g.b.174.2		4
65.59	odd	12		169.3.f.d.80.1		8
65.64	even	2		169.3.d.d.99.2		4
195.44	even	4		117.3.j.a.109.2		4
260.239	even	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	65.44	odd	4
13.3.d.a.8.1	yes	4	5.4	even	2
117.3.j.a.73.2		4	15.14	odd	2
117.3.j.a.109.2		4	195.44	even	4
169.3.d.d.70.2		4	65.34	odd	4
169.3.d.d.99.2		4	65.64	even	2
169.3.f.d.19.2		8	65.24	odd	12
169.3.f.d.80.1		8	65.59	odd	12
169.3.f.d.89.2		8	65.4	even	6
169.3.f.d.150.1		8	65.49	even	6
169.3.f.f.19.1		8	65.54	odd	12
169.3.f.f.80.2		8	65.19	odd	12
169.3.f.f.89.1		8	65.9	even	6
169.3.f.f.150.2		8	65.29	even	6
208.3.t.c.161.1		4	260.239	even	4
208.3.t.c.177.1		4	20.19	odd	2
325.3.g.a.99.1		4	5.2	odd	4
325.3.g.a.174.1		4	65.18	even	4
325.3.g.b.99.2		4	5.3	odd	4
325.3.g.b.174.2		4	65.57	even	4
325.3.j.a.151.2		4	1.1	even	1	trivial
325.3.j.a.226.2		4	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58114 + 2.58114i) q^{2} -2.16228 q^{3} +9.32456i q^{4} +(-5.58114 - 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} +(-7.32456 + 7.32456i) q^{11} -20.1623i q^{12} +(-9.90569 + 8.41886i) q^{13} +7.32456 q^{14} -33.6491 q^{16} +15.9737i q^{17} +(-11.1623 - 11.1623i) q^{18} +(-3.16228 - 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -37.8114 q^{22} -27.4868i q^{23} +(29.7171 - 29.7171i) q^{24} +(-47.2982 - 3.83772i) q^{26} +28.8114 q^{27} +(13.2302 + 13.2302i) q^{28} +25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(15.8377 - 15.8377i) q^{33} +(-41.2302 + 41.2302i) q^{34} -40.3246i q^{36} +(4.23025 - 4.23025i) q^{37} -16.3246i q^{38} +(21.4189 - 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} -15.8377 q^{42} +11.5132i q^{43} +(-68.2982 - 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} +72.7587 q^{48} +44.9737i q^{49} -34.5395i q^{51} +(-78.5021 - 92.3662i) q^{52} +4.18861 q^{53} +(74.3662 + 74.3662i) q^{54} +39.0000i q^{56} +(6.83772 + 6.83772i) q^{57} +(66.6228 + 66.6228i) q^{58} +(-30.2719 + 30.2719i) q^{59} -67.6754 q^{61} +100.596i q^{62} +(-6.13594 + 6.13594i) q^{63} -29.9737i q^{64} +81.7587 q^{66} +(81.0833 + 81.0833i) q^{67} -148.947 q^{68} +59.4342i q^{69} +(50.4452 + 50.4452i) q^{71} +(59.4342 - 59.4342i) q^{72} +(31.6228 - 31.6228i) q^{73} +21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} +20.7851i q^{77} +(102.272 + 8.29822i) q^{78} +50.7851 q^{79} -23.3772 q^{81} +57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(-28.6075 - 28.6075i) q^{84} +(-29.7171 + 29.7171i) q^{86} -55.8114 q^{87} -201.329i q^{88} +(91.1096 - 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302 q^{92} +(-42.1359 - 42.1359i) q^{93} -182.570 q^{94} +(68.9320 + 68.9320i) q^{96} +(-87.3552 - 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +(31.6754 - 31.6754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} - 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9} - 4 q^{11} - 8 q^{13} + 4 q^{14} - 84 q^{16} - 32 q^{18} + 32 q^{21} - 88 q^{22} + 24 q^{24} - 88 q^{26} + 52 q^{27} - 4 q^{28} + 40 q^{29}+ \cdots + 152 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 - 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9 - 4 * q^11 - 8 * q^13 + 4 * q^14 - 84 * q^16 - 32 * q^18 + 32 * q^21 - 88 * q^22 + 24 * q^24 - 88 * q^26 + 52 * q^27 - 4 * q^28 + 40 * q^29 + 40 * q^31 - 20 * q^32 + 76 * q^33 - 108 * q^34 - 40 * q^37 + 92 * q^39 + 32 * q^41 - 76 * q^42 - 172 * q^44 + 132 * q^46 + 4 * q^47 + 76 * q^48 - 80 * q^52 + 80 * q^53 + 152 * q^54 + 40 * q^57 + 140 * q^58 + 56 * q^59 - 296 * q^61 + 64 * q^63 + 112 * q^66 + 84 * q^67 - 444 * q^68 + 284 * q^71 + 48 * q^72 + 100 * q^74 + 80 * q^76 + 232 * q^78 + 64 * q^79 - 220 * q^81 + 52 * q^83 - 184 * q^84 - 24 * q^86 - 160 * q^87 + 200 * q^89 + 156 * q^91 + 456 * q^92 - 80 * q^93 - 452 * q^94 + 320 * q^96 + 68 * q^97 - 224 * q^98 + 152 * q^99

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