LMFDB - Embedded newform 117.3.j.a.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,3,Mod(73,117)] 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("117.73"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18801909302$
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			73.2
Root			$1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	117.73
Dual form			117.3.j.a.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.58114 + 2.58114i) q^{2} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(-1.41886 + 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -2.16228i q^{10} +(7.32456 - 7.32456i) q^{11} +(9.90569 - 8.41886i) q^{13} -7.32456 q^{14} -33.6491 q^{16} +15.9737i q^{17} +(-3.16228 - 3.16228i) q^{19} +(3.90569 - 3.90569i) q^{20} +37.8114 q^{22} -27.4868i q^{23} -24.6491i q^{25} +(47.2982 + 3.83772i) q^{26} +(-13.2302 - 13.2302i) q^{28} -25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(-41.2302 + 41.2302i) q^{34} +1.18861 q^{35} +(-4.23025 + 4.23025i) q^{37} -16.3246i q^{38} +11.5132 q^{40} +(-11.1623 - 11.1623i) q^{41} -11.5132i q^{43} +(68.2982 + 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} +44.9737i q^{49} +(63.6228 - 63.6228i) q^{50} +(78.5021 + 92.3662i) q^{52} +4.18861 q^{53} -6.13594 q^{55} -39.0000i q^{56} +(-66.6228 - 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} +100.596i q^{62} -29.9737i q^{64} +(-7.67544 - 0.622777i) q^{65} +(-81.0833 - 81.0833i) q^{67} -148.947 q^{68} +(3.06797 + 3.06797i) q^{70} +(-50.4452 - 50.4452i) q^{71} +(-31.6228 + 31.6228i) q^{73} -21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} +20.7851i q^{77} +50.7851 q^{79} +(14.0943 + 14.0943i) q^{80} -57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(6.69075 - 6.69075i) q^{85} +(29.7171 - 29.7171i) q^{86} +201.329i q^{88} +(-91.1096 + 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302 q^{92} -182.570 q^{94} +2.64911i q^{95} +(87.3552 + 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{5} - 12 q^{7} - 36 q^{8} + 4 q^{11} + 8 q^{13} - 4 q^{14} - 84 q^{16} - 16 q^{20} + 88 q^{22} + 88 q^{26} + 4 q^{28} - 40 q^{29} + 40 q^{31} - 20 q^{32} - 108 q^{34} + 68 q^{35} + 40 q^{37}+ \cdots - 224 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^5 - 12 * q^7 - 36 * q^8 + 4 * q^11 + 8 * q^13 - 4 * q^14 - 84 * q^16 - 16 * q^20 + 88 * q^22 + 88 * q^26 + 4 * q^28 - 40 * q^29 + 40 * q^31 - 20 * q^32 - 108 * q^34 + 68 * q^35 + 40 * q^37 + 84 * q^40 - 32 * q^41 + 172 * q^44 + 132 * q^46 + 4 * q^47 + 128 * q^50 + 80 * q^52 + 80 * q^53 + 64 * q^55 - 140 * q^58 - 56 * q^59 - 296 * q^61 - 56 * q^65 - 84 * q^67 - 444 * q^68 - 32 * q^70 - 284 * q^71 - 100 * q^74 + 80 * q^76 + 64 * q^79 + 88 * q^80 + 52 * q^83 - 144 * q^85 + 24 * q^86 - 200 * q^89 + 156 * q^91 + 456 * q^92 - 452 * q^94 - 68 * q^97 - 224 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	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	$0.384094\pi$
$3$		0			0
$3$		0			0
$4$			9.32456i			2.33114i
$5$	−0.418861	−	0.418861i	−0.0837722	−	0.0837722i	0.663979	−	0.747751i	$-0.268866\pi$
$5$	−0.418861	−	0.418861i	−0.0837722	−	0.0837722i	−0.747751	+	0.663979i	$0.768866\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$		−	2.16228i		−	0.216228i
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	−0.290888	−	0.956757i	$-0.593951\pi$
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	0.956757	+	0.290888i	$0.0939508\pi$
$12$		0			0
$13$	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	$0.844321\pi$
$18$		0			0
$19$	−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	$0.787548\pi$
$20$	3.90569	−	3.90569i	0.195285	−	0.195285i
$21$		0			0
$22$	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	$-0.203855\pi$
$24$		0			0
$25$		−	24.6491i		−	0.985964i
$26$	47.2982	+	3.83772i	1.81916	+	0.147605i
$27$		0			0
$28$	−13.2302	−	13.2302i	−0.472509	−	0.472509i
$29$	−25.8114			−0.890048			−0.445024	−	0.895519i	$-0.646805\pi$
$29$	−25.8114			−0.890048			−0.445024	+	0.895519i	$0.646805\pi$
$30$		0			0
$31$	19.4868	+	19.4868i	0.628608	+	0.628608i	0.947718	−	0.319110i	$-0.103384\pi$
$31$	19.4868	+	19.4868i	0.628608	+	0.628608i	−0.319110	+	0.947718i	$0.603384\pi$
$32$	−31.8794	−	31.8794i	−0.996230	−	0.996230i
$33$		0			0
$34$	−41.2302	+	41.2302i	−1.21265	+	1.21265i
$35$	1.18861			0.0339603
$36$		0			0
$37$	−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	$0.275762\pi$
$38$		−	16.3246i		−	0.429594i
$39$		0			0
$40$	11.5132			0.287829
$41$	−11.1623	−	11.1623i	−0.272251	−	0.272251i	0.557755	−	0.830006i	$-0.311663\pi$
$41$	−11.1623	−	11.1623i	−0.272251	−	0.272251i	−0.830006	+	0.557755i	$0.811663\pi$
$42$		0			0
$43$		−	11.5132i		−	0.267748i	−0.990998	−	0.133874i	$-0.957258\pi$
$43$		−	11.5132i		−	0.267748i	0.990998	−	0.133874i	$-0.0427418\pi$
$44$	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	$0.428589\pi$
$48$		0			0
$49$			44.9737i			0.917830i
$50$	63.6228	−	63.6228i	1.27246	−	1.27246i
$51$		0			0
$52$	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	$0.487419\pi$
$54$		0			0
$55$	−6.13594			−0.111563
$56$		−	39.0000i		−	0.696429i
$57$		0			0
$58$	−66.6228	−	66.6228i	−1.14867	−	1.14867i
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	−0.402387	−	0.915470i	$-0.631819\pi$
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	0.915470	+	0.402387i	$0.131819\pi$
$60$		0			0
$61$	−67.6754			−1.10943			−0.554717	−	0.832039i	$-0.687173\pi$
$61$	−67.6754			−1.10943			−0.554717	+	0.832039i	$0.687173\pi$
$62$			100.596i			1.62252i
$63$		0			0
$64$		−	29.9737i		−	0.468339i
$65$	−7.67544	−	0.622777i	−0.118084	−	0.00958118i
$66$		0			0
$67$	−81.0833	−	81.0833i	−1.21020	−	1.21020i	−0.970961	−	0.239237i	$-0.923103\pi$
$67$	−81.0833	−	81.0833i	−1.21020	−	1.21020i	−0.239237	−	0.970961i	$-0.576897\pi$
$68$	−148.947			−2.19040
$69$		0			0
$70$	3.06797	+	3.06797i	0.0438282	+	0.0438282i
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	0.256143	−	0.966639i	$-0.417548\pi$
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	−0.966639	+	0.256143i	$0.917548\pi$
$72$		0			0
$73$	−31.6228	+	31.6228i	−0.433189	+	0.433189i	−0.889712	−	0.456523i	$-0.849095\pi$
$73$	−31.6228	+	31.6228i	−0.433189	+	0.433189i	0.456523	+	0.889712i	$0.349095\pi$
$74$	−21.8377			−0.295104
$75$		0			0
$76$	29.4868	−	29.4868i	0.387985	−	0.387985i
$77$			20.7851i			0.269936i
$78$		0			0
$79$	50.7851			0.642849			0.321424	−	0.946935i	$-0.395838\pi$
$79$	50.7851			0.642849			0.321424	+	0.946935i	$0.395838\pi$
$80$	14.0943	+	14.0943i	0.176179	+	0.176179i
$81$		0			0
$82$		−	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	$0.800715\pi$
$84$		0			0
$85$	6.69075	−	6.69075i	0.0787147	−	0.0787147i
$86$	29.7171	−	29.7171i	0.345547	−	0.345547i
$87$		0			0
$88$			201.329i			2.28783i
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.0239913	+	0.999712i	$0.507637\pi$
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.999712	+	0.0239913i	$0.992363\pi$
$90$		0			0
$91$	−2.10961	+	26.0000i	−0.0231825	+	0.285714i
$92$	256.302			2.78590
$93$		0			0
$94$	−182.570			−1.94224
$95$			2.64911i			0.0278854i
$96$		0			0
$97$	87.3552	+	87.3552i	0.900569	+	0.900569i	0.995485	−	0.0949165i	$-0.0302584\pi$
$97$	87.3552	+	87.3552i	0.900569	+	0.900569i	−0.0949165	+	0.995485i	$0.530258\pi$
$98$	−116.083	+	116.083i	−1.18452	+	1.18452i
$99$		0			0
$100$	229.842			2.29842
$101$			8.92100i			0.0883267i	0.999024	+	0.0441634i	$0.0140622\pi$
$101$			8.92100i			0.0883267i	−0.999024	+	0.0441634i	$0.985938\pi$
$102$		0			0
$103$			59.4342i			0.577031i	0.957475	+	0.288515i	$0.0931616\pi$
$103$			59.4342i			0.577031i	−0.957475	+	0.288515i	$0.906838\pi$
$104$	−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	$0.265913\pi$
$108$		0			0
$109$	−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	$0.935352\pi$
$110$	−15.8377	−	15.8377i	−0.143979	−	0.143979i
$111$		0			0
$112$	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	$0.340534\pi$
$114$		0			0
$115$	−11.5132	+	11.5132i	−0.100114	+	0.100114i
$116$		−	240.680i		−	2.07483i
$117$		0			0
$118$	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
$123$		0			0
$124$	−181.706	+	181.706i	−1.46537	+	1.46537i
$125$	−20.7961	+	20.7961i	−0.166369	+	0.166369i
$126$		0			0
$127$		−	94.8377i		−	0.746754i	−0.927680	−	0.373377i	$-0.878200\pi$
$127$		−	94.8377i		−	0.746754i	0.927680	−	0.373377i	$-0.121800\pi$
$128$	−50.1512	+	50.1512i	−0.391807	+	0.391807i
$129$		0			0
$130$	−18.2039	−	21.4189i	−0.140030	−	0.164760i
$131$	112.268			0.857005			0.428502	−	0.903541i	$-0.359041\pi$
$131$	112.268			0.857005			0.428502	+	0.903541i	$0.359041\pi$
$132$		0			0
$133$	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	$0.397734\pi$
$138$		0			0
$139$	78.5395			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$139$	78.5395			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$140$			11.0833i			0.0791663i
$141$		0			0
$142$		−	260.412i		−	1.83389i
$143$	10.8904	−	134.219i	0.0761566	−	0.938596i
$144$		0			0
$145$	10.8114	+	10.8114i	0.0745613	+	0.0745613i
$146$	−163.246			−1.11812
$147$		0			0
$148$	−39.4452	−	39.4452i	−0.266522	−	0.266522i
$149$	128.219	+	128.219i	0.860532	+	0.860532i	0.991400	−	0.130868i	$-0.0417764\pi$
$149$	128.219	+	128.219i	0.860532	+	0.860532i	−0.130868	+	0.991400i	$0.541776\pi$
$150$		0			0
$151$	29.1776	−	29.1776i	0.193229	−	0.193229i	−0.603861	−	0.797090i	$-0.706372\pi$
$151$	29.1776	−	29.1776i	0.193229	−	0.193229i	0.797090	+	0.603861i	$0.206372\pi$
$152$	86.9210			0.571849
$153$		0			0
$154$	−53.6491	+	53.6491i	−0.348371	+	0.348371i
$155$		−	16.3246i		−	0.105320i
$156$		0			0
$157$	232.544			1.48117			0.740585	−	0.671962i	$-0.234548\pi$
$157$	232.544			1.48117			0.740585	+	0.671962i	$0.234548\pi$
$158$	131.083	+	131.083i	0.829641	+	0.829641i
$159$		0			0
$160$			26.7061i			0.166913i
$161$	39.0000	+	39.0000i	0.242236	+	0.242236i
$162$		0			0
$163$	11.4605	−	11.4605i	0.0703098	−	0.0703098i	−0.671077	−	0.741387i	$-0.734168\pi$
$163$	11.4605	−	11.4605i	0.0703098	−	0.0703098i	0.741387	+	0.671077i	$0.234168\pi$
$164$	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	$-0.0895097\pi$
$168$		0			0
$169$	27.2456	−	166.789i	0.161216	−	0.986919i
$170$	34.5395			0.203174
$171$		0			0
$172$	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	$0.914922\pi$
$174$		0			0
$175$	34.9737	+	34.9737i	0.199850	+	0.199850i
$176$	−246.465	+	246.465i	−1.40037	+	1.40037i
$177$		0			0
$178$	−470.333			−2.64232
$179$			71.6712i			0.400398i	0.979755	+	0.200199i	$0.0641588\pi$
$179$			71.6712i			0.400398i	−0.979755	+	0.200199i	$0.935841\pi$
$180$		0			0
$181$			274.144i			1.51461i	0.653061	+	0.757305i	$0.273484\pi$
$181$			274.144i			1.51461i	−0.653061	+	0.757305i	$0.726516\pi$
$182$	−72.5548	+	61.6644i	−0.398653	+	0.338815i
$183$		0			0
$184$	377.763	+	377.763i	2.05306	+	2.05306i
$185$	3.54377			0.0191555
$186$		0			0
$187$	117.000	+	117.000i	0.625668	+	0.625668i
$188$	−329.774	−	329.774i	−1.75412	−	1.75412i
$189$		0			0
$190$	−6.83772	+	6.83772i	−0.0359880	+	0.0359880i
$191$	−179.706			−0.940869			−0.470435	−	0.882435i	$-0.655903\pi$
$191$	−179.706			−0.940869			−0.470435	+	0.882435i	$0.655903\pi$
$192$		0			0
$193$	−1.13594	+	1.13594i	−0.00588572	+	0.00588572i	−0.710044	−	0.704158i	$-0.751325\pi$
$193$	−1.13594	+	1.13594i	−0.00588572	+	0.00588572i	0.704158	+	0.710044i	$0.251325\pi$
$194$			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	$0.920115\pi$
$198$		0			0
$199$		−	259.759i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$199$		−	259.759i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$200$	338.763	+	338.763i	1.69381	+	1.69381i
$201$		0			0
$202$	−23.0263	+	23.0263i	−0.113992	+	0.113992i
$203$	36.6228	−	36.6228i	0.180408	−	0.180408i
$204$		0			0
$205$			9.35089i			0.0456141i
$206$	−153.408	+	153.408i	−0.744698	+	0.744698i
$207$		0			0
$208$	−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
$213$		0			0
$214$	370.574	+	370.574i	1.73166	+	1.73166i
$215$	−4.82242	+	4.82242i	−0.0224299	+	0.0224299i
$216$		0			0
$217$	−55.2982			−0.254831
$218$		−	437.627i		−	2.00746i
$219$		0			0
$220$		−	57.2149i		−	0.260068i
$221$	134.480	+	158.230i	0.608507	+	0.715974i
$222$		0			0
$223$	−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	$0.648404\pi$
$228$		0			0
$229$	−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	$0.983781\pi$
$230$	−59.4342			−0.258409
$231$		0			0
$232$	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	$0.992629\pi$
$234$		0			0
$235$	29.6271			0.126073
$236$	282.272	+	282.272i	1.19607	+	1.19607i
$237$		0			0
$238$		−	117.000i		−	0.491597i
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	0.881775	−	0.471670i	$-0.156348\pi$
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	−0.471670	+	0.881775i	$0.656348\pi$
$240$		0			0
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	−0.985245	−	0.171149i	$-0.945252\pi$
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	0.171149	+	0.985245i	$0.445252\pi$
$242$	−35.3662	+	35.3662i	−0.146141	+	0.146141i
$243$		0			0
$244$		−	631.043i		−	2.58624i
$245$	18.8377	−	18.8377i	0.0768887	−	0.0768887i
$246$		0			0
$247$	−57.9473	−	4.70178i	−0.234605	−	0.0190355i
$248$	−535.631			−2.15980
$249$		0			0
$250$	−107.355			−0.429421
$251$			95.8420i			0.381841i	0.981606	+	0.190920i	$0.0611472\pi$
$251$			95.8420i			0.381841i	−0.981606	+	0.190920i	$0.938853\pi$
$252$		0			0
$253$	−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	$-0.340202\pi$
$258$		0			0
$259$		−	12.0043i		−	0.0463485i
$260$	5.80711	−	71.5701i	0.0223351	−	0.275270i
$261$		0			0
$262$	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	$0.602829\pi$
$264$		0			0
$265$	−1.75445	−	1.75445i	−0.00662055	−	0.00662055i
$266$	23.1623	+	23.1623i	0.0870762	+	0.0870762i
$267$		0			0
$268$	756.065	−	756.065i	2.82114	−	2.82114i
$269$	−170.061			−0.632198			−0.316099	−	0.948726i	$-0.602373\pi$
$269$	−170.061			−0.632198			−0.316099	+	0.948726i	$0.602373\pi$
$270$		0			0
$271$	−217.072	+	217.072i	−0.801005	+	0.801005i	−0.983253	−	0.182248i	$-0.941663\pi$
$271$	−217.072	+	217.072i	−0.801005	+	0.801005i	0.182248	+	0.983253i	$0.441663\pi$
$272$		−	537.500i		−	1.97610i
$273$		0			0
$274$	−447.715			−1.63399
$275$	−180.544	−	180.544i	−0.656523	−	0.656523i
$276$		0			0
$277$			187.947i			0.678510i	0.940694	+	0.339255i	$0.110175\pi$
$277$			187.947i			0.678510i	−0.940694	+	0.339255i	$0.889825\pi$
$278$	202.721	+	202.721i	0.729214	+	0.729214i
$279$		0			0
$280$	−16.3356	+	16.3356i	−0.0583414	+	0.0583414i
$281$	−286.846	+	286.846i	−1.02081	+	1.02081i	−0.0210263	+	0.999779i	$0.506693\pi$
$281$	−286.846	+	286.846i	−1.02081	+	1.02081i	−0.999779	+	0.0210263i	$0.993307\pi$
$282$		0			0
$283$		−	399.201i		−	1.41061i	−0.708906	−	0.705303i	$-0.750811\pi$
$283$		−	399.201i		−	1.41061i	0.708906	−	0.705303i	$-0.249189\pi$
$284$	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
$288$		0			0
$289$	33.8420			0.117100
$290$			55.8114i			0.192453i
$291$		0			0
$292$	−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	$0.356573\pi$
$294$		0			0
$295$	−25.3594			−0.0859642
$296$		−	116.276i		−	0.392825i
$297$		0			0
$298$			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
$303$		0			0
$304$	106.408	+	106.408i	0.350026	+	0.350026i
$305$	28.3466	+	28.3466i	0.0929397	+	0.0929397i
$306$		0			0
$307$	−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	$0.432653\pi$
$308$	−193.811			−0.629258
$309$		0			0
$310$	42.1359	−	42.1359i	0.135922	−	0.135922i
$311$			113.684i			0.365543i	0.983155	+	0.182772i	$0.0585069\pi$
$311$			113.684i			0.365543i	−0.983155	+	0.182772i	$0.941493\pi$
$312$		0			0
$313$	223.483			0.714002			0.357001	−	0.934104i	$-0.383799\pi$
$313$	223.483			0.714002			0.357001	+	0.934104i	$0.383799\pi$
$314$	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	$0.659951\pi$
$318$		0			0
$319$	−189.057	+	189.057i	−0.592655	+	0.592655i
$320$	−12.5548	+	12.5548i	−0.0392338	+	0.0392338i
$321$		0			0
$322$			201.329i			0.625245i
$323$	50.5132	−	50.5132i	0.156388	−	0.156388i
$324$		0			0
$325$	−207.517	−	244.167i	−0.638515	−	0.751282i
$326$	59.1623			0.181479
$327$		0			0
$328$	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
$333$		0			0
$334$	1067.48			3.19605
$335$			67.9253i			0.202762i
$336$		0			0
$337$			5.32456i			0.0157999i	0.999969	+	0.00789993i	$0.00251465\pi$
$337$			5.32456i			0.0157999i	−0.999969	+	0.00789993i	$0.997485\pi$
$338$	500.831	−	360.182i	1.48175	−	1.06563i
$339$		0			0
$340$	62.3883	+	62.3883i	0.183495	+	0.183495i
$341$	285.465			0.837140
$342$		0			0
$343$	−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	$0.478316\pi$
$348$		0			0
$349$	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	$0.100355\pi$
$350$			180.544i			0.515839i
$351$		0			0
$352$	−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	$0.820928\pi$
$354$		0			0
$355$			42.2591i			0.119040i
$356$	−849.557	−	849.557i	−2.38639	−	2.38639i
$357$		0			0
$358$	−184.993	+	184.993i	−0.516741	+	0.516741i
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	−0.789647	−	0.613561i	$-0.789736\pi$
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	0.613561	+	0.789647i	$0.289736\pi$
$360$		0			0
$361$		−	341.000i		−	0.944598i
$362$	−707.605	+	707.605i	−1.95471	+	1.95471i
$363$		0			0
$364$	−242.438	−	19.6712i	−0.666040	−	0.0540417i
$365$	26.4911			0.0725784
$366$		0			0
$367$	−318.416			−0.867620			−0.433810	−	0.901004i	$-0.642831\pi$
$367$	−318.416			−0.867620			−0.433810	+	0.901004i	$0.642831\pi$
$368$			924.907i			2.51334i
$369$		0			0
$370$	9.14697	+	9.14697i	0.0247216	+	0.0247216i
$371$	−5.94306	+	5.94306i	−0.0160190	+	0.0160190i
$372$		0			0
$373$	8.87688			0.0237986			0.0118993	−	0.999929i	$-0.496212\pi$
$373$	8.87688			0.0237986			0.0118993	+	0.999929i	$0.496212\pi$
$374$			603.986i			1.61494i
$375$		0			0
$376$		−	972.105i		−	2.58538i
$377$	−255.680	+	217.302i	−0.678196	+	0.576399i
$378$		0			0
$379$	−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	$0.837012\pi$
$380$	−24.7018			−0.0650047
$381$		0			0
$382$	−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	$0.979269\pi$
$384$		0			0
$385$	8.70605	−	8.70605i	0.0226131	−	0.0226131i
$386$	−5.86406			−0.0151919
$387$		0			0
$388$	−814.548	+	814.548i	−2.09935	+	2.09935i
$389$		−	438.342i		−	1.12684i	−0.826170	−	0.563421i	$-0.809485\pi$
$389$		−	438.342i		−	1.12684i	0.826170	−	0.563421i	$-0.190515\pi$
$390$		0			0
$391$	439.065			1.12293
$392$	−618.092	−	618.092i	−1.57676	−	1.57676i
$393$		0			0
$394$		−	732.557i		−	1.85928i
$395$	−21.2719	−	21.2719i	−0.0538529	−	0.0538529i
$396$		0			0
$397$	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
$399$		0			0
$400$			829.421i			2.07355i
$401$	−93.7018	+	93.7018i	−0.233670	+	0.233670i	−0.814223	−	0.580553i	$-0.802837\pi$
$401$	−93.7018	+	93.7018i	−0.233670	+	0.233670i	0.580553	+	0.814223i	$0.302837\pi$
$402$		0			0
$403$	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
$408$		0			0
$409$	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	$0.528966\pi$
$410$	−24.1359	+	24.1359i	−0.0588682	+	0.0588682i
$411$		0			0
$412$	−554.197			−1.34514
$413$			85.9032i			0.207998i
$414$		0			0
$415$			15.6007i			0.0375921i
$416$	−584.175	−	47.3993i	−1.40427	−	0.113941i
$417$		0			0
$418$	−119.570	−	119.570i	−0.286053	−	0.286053i
$419$	658.767			1.57224			0.786118	−	0.618076i	$-0.212088\pi$
$419$	658.767			1.57224			0.786118	+	0.618076i	$0.212088\pi$
$420$		0			0
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	0.605260	−	0.796028i	$-0.293069\pi$
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	−0.796028	+	0.605260i	$0.793069\pi$
$422$	840.353	+	840.353i	1.99136	+	1.99136i
$423$		0			0
$424$	−57.5658	+	57.5658i	−0.135768	+	0.135768i
$425$	393.737			0.926439
$426$		0			0
$427$	96.0221	−	96.0221i	0.224876	−	0.224876i
$428$			1338.73i			3.12787i
$429$		0			0
$430$	−24.8947			−0.0578946
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	0.274675	−	0.961537i	$-0.411430\pi$
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	−0.961537	+	0.274675i	$0.911430\pi$
$432$		0			0
$433$			156.140i			0.360601i	0.983612	+	0.180300i	$0.0577070\pi$
$433$			156.140i			0.360601i	−0.983612	+	0.180300i	$0.942293\pi$
$434$	−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
$438$		0			0
$439$			448.710i			1.02212i	0.859545	+	0.511060i	$0.170747\pi$
$439$			448.710i			1.02212i	−0.859545	+	0.511060i	$0.829253\pi$
$440$	84.3288	−	84.3288i	0.191656	−	0.191656i
$441$		0			0
$442$	−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	$0.274072\pi$
$444$		0			0
$445$	76.3246			0.171516
$446$		−	1258.43i		−	2.82159i
$447$		0			0
$448$	42.5285	+	42.5285i	0.0949296	+	0.0949296i
$449$	107.127	−	107.127i	0.238591	−	0.238591i	−0.577675	−	0.816267i	$-0.696040\pi$
$449$	107.127	−	107.127i	0.238591	−	0.238591i	0.816267	+	0.577675i	$0.196040\pi$
$450$		0			0
$451$	−163.517			−0.362566
$452$			1012.12i			2.23921i
$453$		0			0
$454$			520.009i			1.14539i
$455$	11.7740	−	10.0068i	0.0258770	−	0.0219929i
$456$		0			0
$457$	−356.092	−	356.092i	−0.779194	−	0.779194i	0.200499	−	0.979694i	$-0.435744\pi$
$457$	−356.092	−	356.092i	−0.779194	−	0.779194i	−0.979694	+	0.200499i	$0.935744\pi$
$458$	−1240.84			−2.70925
$459$		0			0
$460$	−107.355	−	107.355i	−0.233381	−	0.233381i
$461$	−33.7477	−	33.7477i	−0.0732054	−	0.0732054i	0.669556	−	0.742761i	$-0.266484\pi$
$461$	−33.7477	−	33.7477i	−0.0732054	−	0.0732054i	−0.742761	+	0.669556i	$0.766484\pi$
$462$		0			0
$463$	336.355	−	336.355i	0.726469	−	0.726469i	−0.243446	−	0.969915i	$-0.578278\pi$
$463$	336.355	−	336.355i	0.726469	−	0.726469i	0.969915	+	0.243446i	$0.0782777\pi$
$464$	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	$0.892936\pi$
$468$		0			0
$469$	230.092			0.490601
$470$	76.4715	+	76.4715i	0.162705	+	0.162705i
$471$		0			0
$472$			832.078i			1.76288i
$473$	−84.3288	−	84.3288i	−0.178285	−	0.178285i
$474$		0			0
$475$	−77.9473	+	77.9473i	−0.164100	+	0.164100i
$476$	211.336	−	211.336i	0.443982	−	0.443982i
$477$		0			0
$478$			505.982i			1.05854i
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	−0.782569	−	0.622564i	$-0.786091\pi$
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	0.622564	+	0.782569i	$0.286091\pi$
$480$		0			0
$481$	−6.28967	+	77.5174i	−0.0130762	+	0.161159i
$482$	−1012.82			−2.10130
$483$		0			0
$484$	−127.763			−0.263973
$485$		−	73.1794i		−	0.150885i
$486$		0			0
$487$	−69.0655	−	69.0655i	−0.141818	−	0.141818i	0.632633	−	0.774452i	$-0.281974\pi$
$487$	−69.0655	−	69.0655i	−0.141818	−	0.141818i	−0.774452	+	0.632633i	$0.781974\pi$
$488$	930.092	−	930.092i	1.90593	−	1.90593i
$489$		0			0
$490$	97.2456			0.198460
$491$			685.302i			1.39573i	0.716230	+	0.697864i	$0.245866\pi$
$491$			685.302i			1.39573i	−0.716230	+	0.697864i	$0.754134\pi$
$492$		0			0
$493$		−	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
$498$		0			0
$499$	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	$0.585162\pi$
$500$	−193.914	−	193.914i	−0.387828	−	0.387828i
$501$		0			0
$502$	−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	$0.513379\pi$
$504$		0			0
$505$	3.73666	−	3.73666i	0.00739933	−	0.00739933i
$506$		−	1039.32i		−	2.05398i
$507$		0			0
$508$	884.320			1.74079
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	0.502521	−	0.864565i	$-0.332406\pi$
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	−0.864565	+	0.502521i	$0.832406\pi$
$510$		0			0
$511$		−	89.7367i		−	0.175610i
$512$	−777.103	−	777.103i	−1.51778	−	1.51778i
$513$		0			0
$514$	1163.01	−	1163.01i	2.26266	−	2.26266i
$515$	24.8947	−	24.8947i	0.0483392	−	0.0483392i
$516$		0			0
$517$			518.083i			1.00210i
$518$	30.9847	−	30.9847i	0.0598160	−	0.0598160i
$519$		0			0
$520$	114.046	−	96.9278i	0.219319	−	0.186400i
$521$	757.122			1.45321			0.726605	−	0.687055i	$-0.241097\pi$
$521$	757.122			1.45321			0.726605	+	0.687055i	$0.241097\pi$
$522$		0			0
$523$	−221.851			−0.424188			−0.212094	−	0.977249i	$-0.568028\pi$
$523$	−221.851			−0.424188			−0.212094	+	0.977249i	$0.568028\pi$
$524$			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
$528$		0			0
$529$	−226.526			−0.428215
$530$		−	9.05694i		−	0.0170886i
$531$		0			0
$532$			83.6754i			0.157285i
$533$	−204.544	−	16.5964i	−0.383759	−	0.0311378i
$534$		0			0
$535$	−60.1359	−	60.1359i	−0.112404	−	0.112404i
$536$	2228.72			4.15806
$537$		0			0
$538$	−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
$543$		0			0
$544$	509.230	−	509.230i	0.936085	−	0.936085i
$545$			71.0171i			0.130307i
$546$		0			0
$547$	−317.777			−0.580944			−0.290472	−	0.956883i	$-0.593812\pi$
$547$	−317.777			−0.580944			−0.290472	+	0.956883i	$0.593812\pi$
$548$	−808.701	−	808.701i	−1.47573	−	1.47573i
$549$		0			0
$550$		−	932.017i		−	1.69458i
$551$	81.6228	+	81.6228i	0.148136	+	0.148136i
$552$		0			0
$553$	−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	$0.0417220\pi$
$558$		0			0
$559$	−96.9278	−	114.046i	−0.173395	−	0.204018i
$560$	−39.9957			−0.0714209
$561$		0			0
$562$	−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	$0.865525\pi$
$564$		0			0
$565$	−45.4648	−	45.4648i	−0.0804686	−	0.0804686i
$566$	1030.39	−	1030.39i	1.82048	−	1.82048i
$567$		0			0
$568$	1386.58			2.44116
$569$		−	523.394i		−	0.919849i	−0.887958	−	0.459925i	$-0.847876\pi$
$569$		−	523.394i		−	0.919849i	0.887958	−	0.459925i	$-0.152124\pi$
$570$		0			0
$571$			115.715i			0.202654i	0.994853	+	0.101327i	$0.0323088\pi$
$571$			115.715i			0.202654i	−0.994853	+	0.101327i	$0.967691\pi$
$572$	1251.53	+	101.548i	2.18800	+	0.177532i
$573$		0			0
$574$	81.7587	+	81.7587i	0.142437	+	0.142437i
$575$	−677.526			−1.17831
$576$		0			0
$577$	130.158	+	130.158i	0.225577	+	0.225577i	0.810842	−	0.585265i	$-0.199010\pi$
$577$	130.158	+	130.158i	0.225577	+	0.225577i	−0.585265	+	0.810842i	$0.699010\pi$
$578$	87.3509	+	87.3509i	0.151126	+	0.151126i
$579$		0			0
$580$	−100.811	+	100.811i	−0.173813	+	0.173813i
$581$	52.8463			0.0909574
$582$		0			0
$583$	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	$0.612600\pi$
$588$		0			0
$589$		−	123.246i		−	0.209245i
$590$	−65.4562	−	65.4562i	−0.110943	−	0.110943i
$591$		0			0
$592$	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	$0.157501\pi$
$594$		0			0
$595$			18.9865i			0.0319101i
$596$	−1195.59	+	1195.59i	−2.00602	+	2.00602i
$597$		0			0
$598$	105.487	−	1300.08i	0.176399	−	2.17404i
$599$	−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	$0.217016\pi$
$602$			84.3288i			0.140081i
$603$		0			0
$604$	272.068	+	272.068i	0.450444	+	0.450444i
$605$	5.73914	−	5.73914i	0.00948619	−	0.00948619i
$606$		0			0
$607$	579.912			0.955374			0.477687	−	0.878530i	$-0.341475\pi$
$607$	579.912			0.955374			0.477687	+	0.878530i	$0.341475\pi$
$608$			201.623i			0.331616i
$609$		0			0
$610$			146.333i			0.239890i
$611$	−52.5836	+	648.070i	−0.0860616	+	1.06067i
$612$		0			0
$613$	−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	$0.784876\pi$
$618$		0			0
$619$	−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	$0.463890\pi$
$620$	152.219			0.245515
$621$		0			0
$622$	−293.434	+	293.434i	−0.471759	+	0.471759i
$623$		−	258.544i		−	0.414998i
$624$		0			0
$625$	−598.806			−0.958090
$626$	576.840	+	576.840i	0.921469	+	0.921469i
$627$		0			0
$628$			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
$633$		0			0
$634$			646.009i			1.01894i
$635$	−39.7238	+	39.7238i	−0.0625572	+	0.0625572i
$636$		0			0
$637$	378.627	+	445.495i	0.594391	+	0.699365i
$638$	−975.964			−1.52972
$639$		0			0
$640$	42.0128			0.0656450
$641$			487.290i			0.760202i	0.924945	+	0.380101i	$0.124111\pi$
$641$			487.290i			0.760202i	−0.924945	+	0.380101i	$0.875889\pi$
$642$		0			0
$643$	−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
$647$		−	989.526i		−	1.52941i	−0.644383	−	0.764703i	$-0.722886\pi$
$647$		−	989.526i		−	1.52941i	0.644383	−	0.764703i	$-0.277114\pi$
$648$		0			0
$649$		−	443.456i		−	0.683292i
$650$	94.5964	−	1165.86i	0.145533	−	1.79363i
$651$		0			0
$652$	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	$0.478949\pi$
$654$		0			0
$655$	−47.0245	−	47.0245i	−0.0717932	−	0.0717932i
$656$	375.601	+	375.601i	0.572562	+	0.572562i
$657$		0			0
$658$	259.042	−	259.042i	0.393680	−	0.393680i
$659$	1184.99			1.79817			0.899083	−	0.437779i	$-0.144235\pi$
$659$	1184.99			1.79817			0.899083	+	0.437779i	$0.144235\pi$
$660$		0			0
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	−0.838702	−	0.544590i	$-0.816685\pi$
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	0.544590	+	0.838702i	$0.316685\pi$
$662$			1600.21i			2.41724i
$663$		0			0
$664$	511.881			0.770905
$665$	−3.75872	−	3.75872i	−0.00565221	−	0.00565221i
$666$		0			0
$667$			709.473i			1.06368i
$668$	1928.18	+	1928.18i	2.88650	+	2.88650i
$669$		0			0
$670$	−175.325	+	175.325i	−0.261678	+	0.261678i
$671$	−495.693	+	495.693i	−0.738737	+	0.738737i
$672$		0			0
$673$		−	615.500i		−	0.914561i	−0.889322	−	0.457281i	$-0.848824\pi$
$673$		−	615.500i		−	0.914561i	0.889322	−	0.457281i	$-0.151176\pi$
$674$	−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	$0.401575\pi$
$678$		0			0
$679$	−247.890			−0.365081
$680$			183.907i			0.270452i
$681$		0			0
$682$	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	$0.292653\pi$
$684$		0			0
$685$	72.6541			0.106064
$686$		−	688.315i		−	1.00338i
$687$		0			0
$688$			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
$693$		0			0
$694$	121.936	+	121.936i	0.175701	+	0.175701i
$695$	−32.8971	−	32.8971i	−0.0473340	−	0.0473340i
$696$		0			0
$697$	178.302	−	178.302i	0.255814	−	0.255814i
$698$	1154.19			1.65356
$699$		0			0
$700$	−326.114	+	326.114i	−0.465877	+	0.465877i
$701$		−	635.934i		−	0.907181i	−0.891210	−	0.453590i	$-0.850143\pi$
$701$		−	635.934i		−	0.907181i	0.891210	−	0.453590i	$-0.149857\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$	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	$0.00608601\pi$
$710$	−109.077	+	109.077i	−0.153629	+	0.153629i
$711$		0			0
$712$		−	2504.31i		−	3.51730i
$713$	535.631	−	535.631i	0.751236	−	0.751236i
$714$		0			0
$715$	−60.7808	+	51.6577i	−0.0850081	+	0.0722485i
$716$	−668.302			−0.933382
$717$		0			0
$718$	−326.333			−0.454503
$719$			859.565i			1.19550i	0.801682	+	0.597750i	$0.203939\pi$
$719$			859.565i			1.19550i	−0.801682	+	0.597750i	$0.796061\pi$
$720$		0			0
$721$	−84.3288	−	84.3288i	−0.116961	−	0.116961i
$722$	880.168	−	880.168i	1.21907	−	1.21907i
$723$		0			0
$724$	−2556.28			−3.53077
$725$			636.228i			0.877556i
$726$		0			0
$727$			437.337i			0.601564i	0.953693	+	0.300782i	$0.0972477\pi$
$727$			437.337i			0.601564i	−0.953693	+	0.300782i	$0.902752\pi$
$728$	−328.336	−	386.322i	−0.451010	−	0.530662i
$729$		0			0
$730$	68.3772	+	68.3772i	0.0936674	+	0.0936674i
$731$	183.907			0.251583
$732$		0			0
$733$	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
$737$	−1187.80			−1.61167
$738$		0			0
$739$	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	$-0.0924834\pi$
$740$			33.0441i			0.0446542i
$741$		0			0
$742$	−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	$0.994749\pi$
$744$		0			0
$745$		−	107.412i		−	0.144177i
$746$	22.9125	+	22.9125i	0.0307137	+	0.0307137i
$747$		0			0
$748$	−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
$753$		0			0
$754$	−1220.83	−	99.0569i	−1.61914	−	0.131375i
$755$	−24.4427			−0.0323745
$756$		0			0
$757$	124.549			0.164529			0.0822647	−	0.996611i	$-0.473785\pi$
$757$	124.549			0.164529			0.0822647	+	0.996611i	$0.473785\pi$
$758$		−	746.969i		−	0.985447i
$759$		0			0
$760$	−36.4078	−	36.4078i	−0.0479050	−	0.0479050i
$761$	−161.412	+	161.412i	−0.212105	+	0.212105i	−0.805161	−	0.593056i	$-0.797921\pi$
$761$	−161.412	+	161.412i	−0.212105	+	0.212105i	0.593056	+	0.805161i	$0.297921\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$	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	$0.709515\pi$
$770$	44.9431			0.0583676
$771$		0			0
$772$	−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	$0.918087\pi$
$774$		0			0
$775$	480.333	−	480.333i	0.619785	−	0.619785i
$776$	−2401.12			−3.09422
$777$		0			0
$778$	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
$783$		0			0
$784$		−	1513.32i		−	1.93026i
$785$	−97.4036	−	97.4036i	−0.124081	−	0.124081i
$786$		0			0
$787$	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
$789$		0			0
$790$		−	109.811i		−	0.139002i
$791$	−154.009	+	154.009i	−0.194701	+	0.194701i
$792$		0			0
$793$	−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	$-0.0900545\pi$
$798$		0			0
$799$	−564.928	−	564.928i	−0.707043	−	0.707043i
$800$	−785.798	+	785.798i	−0.982247	+	0.982247i
$801$		0			0
$802$	−483.715			−0.603135
$803$			463.246i			0.576894i
$804$		0			0
$805$		−	32.6712i		−	0.0405853i
$806$	846.907	+	996.478i	1.05075	+	1.23632i
$807$		0			0
$808$	−122.605	−	122.605i	−0.151739	−	0.151739i
$809$	1090.36			1.34779			0.673893	−	0.738829i	$-0.264621\pi$
$809$	1090.36			1.34779			0.673893	+	0.738829i	$0.264621\pi$
$810$		0			0
$811$	445.614	+	445.614i	0.549463	+	0.549463i	0.926285	−	0.376823i	$-0.122983\pi$
$811$	445.614	+	445.614i	0.549463	+	0.549463i	−0.376823	+	0.926285i	$0.622983\pi$
$812$	341.491	+	341.491i	0.420556	+	0.420556i
$813$		0			0
$814$	−159.952	+	159.952i	−0.196501	+	0.196501i
$815$	−9.60072			−0.0117800
$816$		0			0
$817$	−36.4078	+	36.4078i	−0.0445628	+	0.0445628i
$818$			1910.77i			2.33590i
$819$		0			0
$820$	−87.1929			−0.106333
$821$	242.186	+	242.186i	0.294989	+	0.294989i	0.839047	−	0.544058i	$-0.183113\pi$
$821$	242.186	+	242.186i	0.294989	+	0.294989i	−0.544058	+	0.839047i	$0.683113\pi$
$822$		0			0
$823$			99.5787i			0.120995i	0.998168	+	0.0604974i	$0.0192687\pi$
$823$			99.5787i			0.120995i	−0.998168	+	0.0604974i	$0.980731\pi$
$824$	−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	$-0.0293138\pi$
$828$		0			0
$829$		−	32.1103i		−	0.0387338i	−0.999812	−	0.0193669i	$-0.993835\pi$
$829$		−	32.1103i		−	0.0387338i	0.999812	−	0.0193669i	$-0.00616506\pi$
$830$	−40.2676	+	40.2676i	−0.0485152	+	0.0485152i
$831$		0			0
$832$	−252.344	−	296.910i	−0.303298	−	0.356863i
$833$	−718.394			−0.862418
$834$		0			0
$835$	−173.228			−0.207459
$836$		−	431.956i		−	0.516694i
$837$		0			0
$838$	1700.37	+	1700.37i	2.02908	+	2.02908i
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	−0.907434	−	0.420195i	$-0.861962\pi$
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	0.420195	+	0.907434i	$0.361962\pi$
$840$		0			0
$841$	−174.772			−0.207815
$842$		−	414.601i		−	0.492400i
$843$		0			0
$844$			3035.84i			3.59696i
$845$	−81.2737	+	58.4495i	−0.0961819	+	0.0691710i
$846$		0			0
$847$	−19.4409	−	19.4409i	−0.0229527	−	0.0229527i
$848$	−140.943			−0.166206
$849$		0			0
$850$	1016.29	+	1016.29i	1.19563	+	1.19563i
$851$	116.276	+	116.276i	0.136635	+	0.136635i
$852$		0			0
$853$	529.546	−	529.546i	0.620804	−	0.620804i	−0.324933	−	0.945737i	$-0.605342\pi$
$853$	529.546	−	529.546i	0.620804	−	0.620804i	0.945737	+	0.324933i	$0.105342\pi$
$854$	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	$-0.376579\pi$
$858$		0			0
$859$	145.062			0.168873			0.0844365	−	0.996429i	$-0.473091\pi$
$859$	145.062			0.168873			0.0844365	+	0.996429i	$0.473091\pi$
$860$	−44.9669	−	44.9669i	−0.0522871	−	0.0522871i
$861$		0			0
$862$		−	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	$0.441673\pi$
$864$		0			0
$865$	38.2762	−	38.2762i	0.0442499	−	0.0442499i
$866$	−403.020	+	403.020i	−0.465381	+	0.465381i
$867$		0			0
$868$		−	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
$873$		0			0
$874$	−448.710			−0.513399
$875$		−	59.0135i		−	0.0674440i
$876$		0			0
$877$	689.532	+	689.532i	0.786240	+	0.786240i	0.980876	−	0.194636i	$-0.0623526\pi$
$877$	689.532	+	689.532i	0.786240	+	0.786240i	−0.194636	+	0.980876i	$0.562353\pi$
$878$	−1158.18	+	1158.18i	−1.31912	+	1.31912i
$879$		0			0
$880$	206.469			0.234624
$881$			1607.31i			1.82442i	0.409722	+	0.912210i	$0.365626\pi$
$881$			1607.31i			1.82442i	−0.409722	+	0.912210i	$0.634374\pi$
$882$		0			0
$883$		−	153.969i		−	0.174370i	−0.996192	−	0.0871850i	$-0.972213\pi$
$883$		−	153.969i		−	0.174370i	0.996192	−	0.0871850i	$-0.0277871\pi$
$884$	−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	$0.522496\pi$
$888$		0			0
$889$	134.562	+	134.562i	0.151363	+	0.151363i
$890$	197.004	+	197.004i	0.221353	+	0.221353i
$891$		0			0
$892$	2273.08	−	2273.08i	2.54830	−	2.54830i
$893$	223.675			0.250476
$894$		0			0
$895$	30.0203	−	30.0203i	0.0335422	−	0.0335422i
$896$		−	142.315i		−	0.158834i
$897$		0			0
$898$	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
$903$		0			0
$904$	−1491.76	+	1491.76i	−1.65018	+	1.65018i
$905$	114.828	−	114.828i	0.126882	−	0.126882i
$906$		0			0
$907$		−	354.574i		−	0.390930i	−0.980711	−	0.195465i	$-0.937378\pi$
$907$		−	354.574i		−	0.390930i	0.980711	−	0.195465i	$-0.0626216\pi$
$908$	−939.285	+	939.285i	−1.03445	+	1.03445i
$909$		0			0
$910$	56.2192	+	4.56156i	0.0617794	+	0.00501271i
$911$	−1040.31			−1.14194			−0.570972	−	0.820970i	$-0.693434\pi$
$911$	−1040.31			−1.14194			−0.570972	+	0.820970i	$0.693434\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$	−416.201			−0.452884			−0.226442	−	0.974025i	$-0.572709\pi$
$919$	−416.201			−0.452884			−0.226442	+	0.974025i	$0.572709\pi$
$920$		−	316.460i		−	0.343979i
$921$		0			0
$922$		−	174.215i		−	0.188953i
$923$	−924.386	−	75.0036i	−1.00150	−	0.0812606i
$924$		0			0
$925$	104.272	+	104.272i	0.112726	+	0.112726i
$926$	1736.36			1.87512
$927$		0			0
$928$	822.851	+	822.851i	0.886692	+	0.886692i
$929$	428.403	+	428.403i	0.461144	+	0.461144i	0.899030	−	0.437886i	$-0.144273\pi$
$929$	428.403	+	428.403i	0.461144	+	0.461144i	−0.437886	+	0.899030i	$0.644273\pi$
$930$		0			0
$931$	142.219	−	142.219i	0.152760	−	0.152760i
$932$	−100.606			−0.107946
$933$		0			0
$934$	−795.670	+	795.670i	−0.851896	+	0.851896i
$935$		−	98.0135i		−	0.104827i
$936$		0			0
$937$	−990.702			−1.05731			−0.528656	−	0.848836i	$-0.677304\pi$
$937$	−990.702			−1.05731			−0.528656	+	0.848836i	$0.677304\pi$
$938$	593.899	+	593.899i	0.633155	+	0.633155i
$939$		0			0
$940$			276.259i			0.293893i
$941$	−974.392	−	974.392i	−1.03549	−	1.03549i	−0.999347	−	0.0361387i	$-0.988494\pi$
$941$	−974.392	−	974.392i	−1.03549	−	1.03549i	−0.0361387	−	0.999347i	$-0.511506\pi$
$942$		0			0
$943$	−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	$0.483791\pi$
$948$		0			0
$949$	−47.0178	+	579.473i	−0.0495446	+	0.610615i
$950$	−402.386			−0.423564
$951$		0			0
$952$	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	$-0.198227\pi$
$954$		0			0
$955$	75.2719	+	75.2719i	0.0788187	+	0.0788187i
$956$	−913.949	+	913.949i	−0.956014	+	0.956014i
$957$		0			0
$958$	−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
$963$		0			0
$964$	−1829.45	−	1829.45i	−1.89777	−	1.89777i
$965$	0.951605			0.000986120
$966$		0			0
$967$	−1333.92	−	1333.92i	−1.37944	−	1.37944i	−0.845561	−	0.533879i	$-0.820734\pi$
$967$	−1333.92	−	1333.92i	−1.37944	−	1.37944i	−0.533879	−	0.845561i	$-0.679266\pi$
$968$	−188.309	−	188.309i	−0.194534	−	0.194534i
$969$		0			0
$970$	188.886	−	188.886i	0.194728	−	0.194728i
$971$	556.110			0.572718			0.286359	−	0.958122i	$-0.407555\pi$
$971$	556.110			0.572718			0.286359	+	0.958122i	$0.407555\pi$
$972$		0			0
$973$	−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	$0.455518\pi$
$978$		0			0
$979$			1334.67i			1.36330i
$980$	175.653	+	175.653i	0.179238	+	0.179238i
$981$		0			0
$982$	−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	$0.0254121\pi$
$984$		0			0
$985$			118.878i			0.120688i
$986$	1064.21	−	1064.21i	1.07932	−	1.07932i
$987$		0			0
$988$	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
$993$		0			0
$994$	369.489	+	369.489i	0.371719	+	0.371719i
$995$	−108.803	+	108.803i	−0.109350	+	0.109350i
$996$		0			0
$997$	1075.40			1.07863			0.539317	−	0.842103i	$-0.318682\pi$
$997$	1075.40			1.07863			0.539317	+	0.842103i	$0.318682\pi$
$998$			1803.33i			1.80695i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.j.a.73.2		4
3.2	odd	2		13.3.d.a.8.1	yes	4
12.11	even	2		208.3.t.c.177.1		4
13.5	odd	4	inner	117.3.j.a.109.2		4
15.2	even	4		325.3.g.b.99.2		4
15.8	even	4		325.3.g.a.99.1		4
15.14	odd	2		325.3.j.a.151.2		4
39.2	even	12		169.3.f.f.19.1		8
39.5	even	4		13.3.d.a.5.1	✓	4
39.8	even	4		169.3.d.d.70.2		4
39.11	even	12		169.3.f.d.19.2		8
39.17	odd	6		169.3.f.d.89.2		8
39.20	even	12		169.3.f.d.80.1		8
39.23	odd	6		169.3.f.d.150.1		8
39.29	odd	6		169.3.f.f.150.2		8
39.32	even	12		169.3.f.f.80.2		8
39.35	odd	6		169.3.f.f.89.1		8
39.38	odd	2		169.3.d.d.99.2		4
156.83	odd	4		208.3.t.c.161.1		4
195.44	even	4		325.3.j.a.226.2		4
195.83	odd	4		325.3.g.b.174.2		4
195.122	odd	4		325.3.g.a.174.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	39.5	even	4
13.3.d.a.8.1	yes	4	3.2	odd	2
117.3.j.a.73.2		4	1.1	even	1	trivial
117.3.j.a.109.2		4	13.5	odd	4	inner
169.3.d.d.70.2		4	39.8	even	4
169.3.d.d.99.2		4	39.38	odd	2
169.3.f.d.19.2		8	39.11	even	12
169.3.f.d.80.1		8	39.20	even	12
169.3.f.d.89.2		8	39.17	odd	6
169.3.f.d.150.1		8	39.23	odd	6
169.3.f.f.19.1		8	39.2	even	12
169.3.f.f.80.2		8	39.32	even	12
169.3.f.f.89.1		8	39.35	odd	6
169.3.f.f.150.2		8	39.29	odd	6
208.3.t.c.161.1		4	156.83	odd	4
208.3.t.c.177.1		4	12.11	even	2
325.3.g.a.99.1		4	15.8	even	4
325.3.g.a.174.1		4	195.122	odd	4
325.3.g.b.99.2		4	15.2	even	4
325.3.g.b.174.2		4	195.83	odd	4
325.3.j.a.151.2		4	15.14	odd	2
325.3.j.a.226.2		4	195.44	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58114 + 2.58114i) q^{2} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(-1.41886 + 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -2.16228i q^{10} +(7.32456 - 7.32456i) q^{11} +(9.90569 - 8.41886i) q^{13} -7.32456 q^{14} -33.6491 q^{16} +15.9737i q^{17} +(-3.16228 - 3.16228i) q^{19} +(3.90569 - 3.90569i) q^{20} +37.8114 q^{22} -27.4868i q^{23} -24.6491i q^{25} +(47.2982 + 3.83772i) q^{26} +(-13.2302 - 13.2302i) q^{28} -25.8114 q^{29} +(19.4868 + 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(-41.2302 + 41.2302i) q^{34} +1.18861 q^{35} +(-4.23025 + 4.23025i) q^{37} -16.3246i q^{38} +11.5132 q^{40} +(-11.1623 - 11.1623i) q^{41} -11.5132i q^{43} +(68.2982 + 68.2982i) q^{44} +(70.9473 - 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} +44.9737i q^{49} +(63.6228 - 63.6228i) q^{50} +(78.5021 + 92.3662i) q^{52} +4.18861 q^{53} -6.13594 q^{55} -39.0000i q^{56} +(-66.6228 - 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} +100.596i q^{62} -29.9737i q^{64} +(-7.67544 - 0.622777i) q^{65} +(-81.0833 - 81.0833i) q^{67} -148.947 q^{68} +(3.06797 + 3.06797i) q^{70} +(-50.4452 - 50.4452i) q^{71} +(-31.6228 + 31.6228i) q^{73} -21.8377 q^{74} +(29.4868 - 29.4868i) q^{76} +20.7851i q^{77} +50.7851 q^{79} +(14.0943 + 14.0943i) q^{80} -57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(6.69075 - 6.69075i) q^{85} +(29.7171 - 29.7171i) q^{86} +201.329i q^{88} +(-91.1096 + 91.1096i) q^{89} +(-2.10961 + 26.0000i) q^{91} +256.302 q^{92} -182.570 q^{94} +2.64911i q^{95} +(87.3552 + 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{5} - 12 q^{7} - 36 q^{8} + 4 q^{11} + 8 q^{13} - 4 q^{14} - 84 q^{16} - 16 q^{20} + 88 q^{22} + 88 q^{26} + 4 q^{28} - 40 q^{29} + 40 q^{31} - 20 q^{32} - 108 q^{34} + 68 q^{35} + 40 q^{37}+ \cdots - 224 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^5 - 12 * q^7 - 36 * q^8 + 4 * q^11 + 8 * q^13 - 4 * q^14 - 84 * q^16 - 16 * q^20 + 88 * q^22 + 88 * q^26 + 4 * q^28 - 40 * q^29 + 40 * q^31 - 20 * q^32 - 108 * q^34 + 68 * q^35 + 40 * q^37 + 84 * q^40 - 32 * q^41 + 172 * q^44 + 132 * q^46 + 4 * q^47 + 128 * q^50 + 80 * q^52 + 80 * q^53 + 64 * q^55 - 140 * q^58 - 56 * q^59 - 296 * q^61 - 56 * q^65 - 84 * q^67 - 444 * q^68 - 32 * q^70 - 284 * q^71 - 100 * q^74 + 80 * q^76 + 64 * q^79 + 88 * q^80 + 52 * q^83 - 144 * q^85 + 24 * q^86 - 200 * q^89 + 156 * q^91 + 456 * q^92 - 452 * q^94 - 68 * q^97 - 224 * q^98

Introduction

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