LMFDB - Embedded newform 13.3.d.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,3,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	13.d (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.354224343668$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$-1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.3.d.a.5.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.58114 - 2.58114i) q^{2} +2.16228 q^{3} +9.32456i q^{4} +(0.418861 + 0.418861i) q^{5} +(-5.58114 - 5.58114i) q^{6} +(-1.41886 + 1.41886i) q^{7} +(13.7434 - 13.7434i) q^{8} -4.32456 q^{9} -2.16228i q^{10} +(-7.32456 + 7.32456i) q^{11} +20.1623i q^{12} +(9.90569 - 8.41886i) q^{13} +7.32456 q^{14} +(0.905694 + 0.905694i) q^{15} -33.6491 q^{16} -15.9737i q^{17} +(11.1623 + 11.1623i) q^{18} +(-3.16228 - 3.16228i) q^{19} +(-3.90569 + 3.90569i) q^{20} +(-3.06797 + 3.06797i) q^{21} +37.8114 q^{22} +27.4868i q^{23} +(29.7171 - 29.7171i) q^{24} -24.6491i q^{25} +(-47.2982 - 3.83772i) q^{26} -28.8114 q^{27} +(-13.2302 - 13.2302i) q^{28} +25.8114 q^{29} -4.67544i q^{30} +(19.4868 + 19.4868i) q^{31} +(31.8794 + 31.8794i) q^{32} +(-15.8377 + 15.8377i) q^{33} +(-41.2302 + 41.2302i) q^{34} -1.18861 q^{35} -40.3246i q^{36} +(-4.23025 + 4.23025i) q^{37} +16.3246i q^{38} +(21.4189 - 18.2039i) q^{39} +11.5132 q^{40} +(11.1623 + 11.1623i) q^{41} +15.8377 q^{42} -11.5132i q^{43} +(-68.2982 - 68.2982i) q^{44} +(-1.81139 - 1.81139i) q^{45} +(70.9473 - 70.9473i) q^{46} +(35.3662 - 35.3662i) q^{47} -72.7587 q^{48} +44.9737i q^{49} +(-63.6228 + 63.6228i) q^{50} -34.5395i q^{51} +(78.5021 + 92.3662i) q^{52} -4.18861 q^{53} +(74.3662 + 74.3662i) q^{54} -6.13594 q^{55} +39.0000i q^{56} +(-6.83772 - 6.83772i) q^{57} +(-66.6228 - 66.6228i) q^{58} +(-30.2719 + 30.2719i) q^{59} +(-8.44520 + 8.44520i) q^{60} -67.6754 q^{61} -100.596i q^{62} +(6.13594 - 6.13594i) q^{63} -29.9737i q^{64} +(7.67544 + 0.622777i) q^{65} +81.7587 q^{66} +(-81.0833 - 81.0833i) q^{67} +148.947 q^{68} +59.4342i q^{69} +(3.06797 + 3.06797i) q^{70} +(50.4452 + 50.4452i) q^{71} +(-59.4342 + 59.4342i) q^{72} +(-31.6228 + 31.6228i) q^{73} +21.8377 q^{74} -53.2982i q^{75} +(29.4868 - 29.4868i) q^{76} -20.7851i q^{77} +(-102.272 - 8.29822i) q^{78} +50.7851 q^{79} +(-14.0943 - 14.0943i) q^{80} -23.3772 q^{81} -57.6228i q^{82} +(18.6228 + 18.6228i) q^{83} +(-28.6075 - 28.6075i) q^{84} +(6.69075 - 6.69075i) q^{85} +(-29.7171 + 29.7171i) q^{86} +55.8114 q^{87} +201.329i q^{88} +(91.1096 - 91.1096i) q^{89} +9.35089i q^{90} +(-2.10961 + 26.0000i) q^{91} -256.302 q^{92} +(42.1359 + 42.1359i) q^{93} -182.570 q^{94} -2.64911i q^{95} +(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})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 4 q^{2} - 4 q^{3} + 8 q^{5} - 16 q^{6} - 12 q^{7} + 36 q^{8} + 8 q^{9} - 4 q^{11} + 8 q^{13} + 4 q^{14} - 28 q^{15} - 84 q^{16} + 32 q^{18} + 16 q^{20} + 32 q^{21} + 88 q^{22} + 24 q^{24} - 88 q^{26}+ \cdots + 152 q^{99}+O(q^{100})$ 4 * q - 4 * q^2 - 4 * q^3 + 8 * q^5 - 16 * q^6 - 12 * q^7 + 36 * q^8 + 8 * q^9 - 4 * q^11 + 8 * q^13 + 4 * q^14 - 28 * q^15 - 84 * q^16 + 32 * q^18 + 16 * q^20 + 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 - 68 * q^35 + 40 * q^37 + 92 * q^39 + 84 * q^40 + 32 * q^41 + 76 * q^42 - 172 * q^44 + 56 * q^45 + 132 * q^46 - 4 * q^47 - 76 * q^48 - 128 * q^50 + 80 * q^52 - 80 * q^53 + 152 * q^54 + 64 * q^55 - 40 * q^57 - 140 * q^58 + 56 * q^59 - 116 * q^60 - 296 * q^61 - 64 * q^63 + 56 * q^65 + 112 * q^66 - 84 * q^67 + 444 * q^68 - 32 * q^70 + 284 * q^71 - 48 * q^72 + 100 * q^74 + 80 * q^76 - 232 * q^78 + 64 * q^79 - 88 * q^80 - 220 * q^81 - 52 * q^83 - 184 * q^84 - 144 * q^85 - 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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	$-0.884094\pi$
$2$	−2.58114	−	2.58114i	−1.29057	−	1.29057i	−0.356135	−	0.934435i	$-0.615906\pi$
$3$	2.16228			0.720759			0.360380	−	0.932806i	$-0.382647\pi$
$3$	2.16228			0.720759			0.360380	+	0.932806i	$0.382647\pi$
$4$			9.32456i			2.33114i
$5$	0.418861	+	0.418861i	0.0837722	+	0.0837722i	0.747751	−	0.663979i	$-0.231134\pi$
$5$	0.418861	+	0.418861i	0.0837722	+	0.0837722i	−0.663979	+	0.747751i	$0.731134\pi$
$6$	−5.58114	−	5.58114i	−0.930190	−	0.930190i
$7$	−1.41886	+	1.41886i	−0.202694	+	0.202694i	−0.801153	−	0.598459i	$-0.795780\pi$
$7$	−1.41886	+	1.41886i	−0.202694	+	0.202694i	0.598459	+	0.801153i	$0.295780\pi$
$8$	13.7434	−	13.7434i	1.71793	−	1.71793i
$9$	−4.32456			−0.480506
$10$		−	2.16228i		−	0.216228i
$11$	−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
$15$	0.905694	+	0.905694i	0.0603796	+	0.0603796i
$16$	−33.6491			−2.10307
$17$		−	15.9737i		−	0.939627i	−0.882766	−	0.469814i	$-0.844321\pi$
$17$		−	15.9737i		−	0.939627i	0.882766	−	0.469814i	$-0.155679\pi$
$18$	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	$0.787548\pi$
$20$	−3.90569	+	3.90569i	−0.195285	+	0.195285i
$21$	−3.06797	+	3.06797i	−0.146094	+	0.146094i
$22$	37.8114			1.71870
$23$			27.4868i			1.19508i	0.801839	+	0.597540i	$0.203855\pi$
$23$			27.4868i			1.19508i	−0.801839	+	0.597540i	$0.796145\pi$
$24$	29.7171	−	29.7171i	1.23821	−	1.23821i
$25$		−	24.6491i		−	0.985964i
$26$	−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	$0.353195\pi$
$30$		−	4.67544i		−	0.155848i
$31$	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
$35$	−1.18861			−0.0339603
$36$		−	40.3246i		−	1.12013i
$37$	−4.23025	+	4.23025i	−0.114331	+	0.114331i	−0.761958	−	0.647627i	$-0.775762\pi$
$37$	−4.23025	+	4.23025i	−0.114331	+	0.114331i	0.647627	+	0.761958i	$0.275762\pi$
$38$			16.3246i			0.429594i
$39$	21.4189	−	18.2039i	0.549202	−	0.466767i
$40$	11.5132			0.287829
$41$	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	$-0.957258\pi$
$43$		−	11.5132i		−	0.267748i	0.990998	−	0.133874i	$-0.0427418\pi$
$44$	−68.2982	−	68.2982i	−1.55223	−	1.55223i
$45$	−1.81139	−	1.81139i	−0.0402531	−	0.0402531i
$46$	70.9473	−	70.9473i	1.54233	−	1.54233i
$47$	35.3662	−	35.3662i	0.752472	−	0.752472i	−0.222468	−	0.974940i	$-0.571411\pi$
$47$	35.3662	−	35.3662i	0.752472	−	0.752472i	0.974940	+	0.222468i	$0.0714112\pi$
$48$	−72.7587			−1.51581
$49$			44.9737i			0.917830i
$50$	−63.6228	+	63.6228i	−1.27246	+	1.27246i
$51$		−	34.5395i		−	0.677245i
$52$	78.5021	+	92.3662i	1.50966	+	1.77627i
$53$	−4.18861			−0.0790304			−0.0395152	−	0.999219i	$-0.512581\pi$
$53$	−4.18861			−0.0790304			−0.0395152	+	0.999219i	$0.512581\pi$
$54$	74.3662	+	74.3662i	1.37715	+	1.37715i
$55$	−6.13594			−0.111563
$56$			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	$0.368181\pi$
$60$	−8.44520	+	8.44520i	−0.140753	+	0.140753i
$61$	−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
$65$	7.67544	+	0.622777i	0.118084	+	0.00958118i
$66$	81.7587			1.23877
$67$	−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
$69$			59.4342i			0.861365i
$70$	3.06797	+	3.06797i	0.0438282	+	0.0438282i
$71$	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	−0.889712	−	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
$75$		−	53.2982i		−	0.710643i
$76$	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	$0.395838\pi$
$80$	−14.0943	−	14.0943i	−0.176179	−	0.176179i
$81$	−23.3772			−0.288608
$82$		−	57.6228i		−	0.702717i
$83$	18.6228	+	18.6228i	0.224371	+	0.224371i	0.810336	−	0.585965i	$-0.199285\pi$
$83$	18.6228	+	18.6228i	0.224371	+	0.224371i	−0.585965	+	0.810336i	$0.699285\pi$
$84$	−28.6075	−	28.6075i	−0.340565	−	0.340565i
$85$	6.69075	−	6.69075i	0.0787147	−	0.0787147i
$86$	−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	$-0.00763740\pi$
$90$			9.35089i			0.103899i
$91$	−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
$95$		−	2.64911i		−	0.0278854i
$96$	68.9320	+	68.9320i	0.718042	+	0.718042i
$97$	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
$99$	31.6754	−	31.6754i	0.319954	−	0.319954i
$100$	229.842			2.29842
$101$		−	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	$0.0931616\pi$
$103$			59.4342i			0.577031i	−0.957475	+	0.288515i	$0.906838\pi$
$104$	20.4342	−	251.842i	0.196482	−	2.42156i
$105$	−2.57011			−0.0244772
$106$	10.8114	+	10.8114i	0.101994	+	0.101994i
$107$	−143.570			−1.34178			−0.670888	−	0.741558i	$-0.734087\pi$
$107$	−143.570			−1.34178			−0.670888	+	0.741558i	$0.734087\pi$
$108$		−	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	$0.935352\pi$
$110$	15.8377	+	15.8377i	0.143979	+	0.143979i
$111$	−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	$-0.659466\pi$
$113$	−108.544			−0.960564			−0.480282	+	0.877114i	$0.659466\pi$
$114$			35.2982i			0.309634i
$115$	−11.5132	+	11.5132i	−0.100114	+	0.100114i
$116$			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
$120$	24.8947			0.207456
$121$			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
$125$	20.7961	−	20.7961i	0.166369	−	0.166369i
$126$	−31.6754			−0.251392
$127$		−	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
$129$		−	24.8947i		−	0.192982i
$130$	−18.2039	−	21.4189i	−0.140030	−	0.164760i
$131$	−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
$135$	−12.0680	−	12.0680i	−0.0893924	−	0.0893924i
$136$	−219.533	−	219.533i	−1.61421	−	1.61421i
$137$	86.7281	−	86.7281i	0.633052	−	0.633052i	−0.315780	−	0.948832i	$-0.602266\pi$
$137$	86.7281	−	86.7281i	0.633052	−	0.633052i	0.948832	+	0.315780i	$0.102266\pi$
$138$	153.408	−	153.408i	1.11165	−	1.11165i
$139$	78.5395			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$139$	78.5395			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$140$		−	11.0833i		−	0.0791663i
$141$	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
$145$	10.8114	+	10.8114i	0.0745613	+	0.0745613i
$146$	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	$0.958224\pi$
$150$	−137.570	+	137.570i	−0.917134	+	0.917134i
$151$	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
$155$			16.3246i			0.105320i
$156$	169.743	+	199.721i	1.08810	+	1.28027i
$157$	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
$159$	−9.05694			−0.0569619
$160$			26.7061i			0.166913i
$161$	−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	−0.671077	−	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
$165$	−13.2676			−0.0804098
$166$		−	96.1359i		−	0.579132i
$167$	−206.785	+	206.785i	−1.23823	+	1.23823i	−0.277512	+	0.960722i	$0.589510\pi$
$167$	−206.785	+	206.785i	−1.23823	+	1.23823i	−0.960722	+	0.277512i	$0.910490\pi$
$168$			84.3288i			0.501957i
$169$	27.2456	−	166.789i	0.161216	−	0.986919i
$170$	−34.5395			−0.203174
$171$	13.6754	+	13.6754i	0.0799734	+	0.0799734i
$172$	107.355			0.624158
$173$		−	91.3815i		−	0.528217i	−0.964493	−	0.264108i	$-0.914922\pi$
$173$		−	91.3815i		−	0.528217i	0.964493	−	0.264108i	$-0.0850777\pi$
$174$	−144.057	−	144.057i	−0.827913	−	0.827913i
$175$	34.9737	+	34.9737i	0.199850	+	0.199850i
$176$	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	$-0.0641588\pi$
$180$	16.8904	−	16.8904i	0.0938355	−	0.0938355i
$181$			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
$185$	−3.54377			−0.0191555
$186$		−	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
$190$	−6.83772	+	6.83772i	−0.0359880	+	0.0359880i
$191$	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	−0.710044	−	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
$195$	16.5964	+	1.34662i	0.0851100	+	0.00690572i
$196$	−419.359			−2.13959
$197$	141.906	+	141.906i	0.720333	+	0.720333i	0.968673	−	0.248340i	$-0.0798849\pi$
$197$	141.906	+	141.906i	0.720333	+	0.720333i	−0.248340	+	0.968673i	$0.579885\pi$
$198$	−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	$-0.226347\pi$
$200$	−338.763	−	338.763i	−1.69381	−	1.69381i
$201$	−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
$205$			9.35089i			0.0456141i
$206$	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
$210$	6.63381	+	6.63381i	0.0315896	+	0.0315896i
$211$	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
$215$	4.82242	−	4.82242i	0.0224299	−	0.0224299i
$216$	−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
$220$		−	57.2149i		−	0.260068i
$221$	−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	$-0.968766\pi$
$223$	−243.774	−	243.774i	−1.09316	−	1.09316i	−0.0979674	−	0.995190i	$-0.531234\pi$
$224$	−90.4648			−0.403861
$225$			106.596i			0.473762i
$226$	280.167	+	280.167i	1.23968	+	1.23968i
$227$	−100.732	−	100.732i	−0.443755	−	0.443755i	0.449517	−	0.893272i	$-0.351596\pi$
$227$	−100.732	−	100.732i	−0.443755	−	0.443755i	−0.893272	+	0.449517i	$0.851596\pi$
$228$	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	$0.983781\pi$
$230$	59.4342			0.258409
$231$		−	44.9431i		−	0.194559i
$232$	354.737	−	354.737i	1.52904	−	1.52904i
$233$		−	10.7893i		−	0.0463061i	−0.999732	−	0.0231531i	$-0.992629\pi$
$233$		−	10.7893i		−	0.0463061i	0.999732	−	0.0231531i	$-0.00737051\pi$
$234$	204.544	+	16.5964i	0.874119	+	0.0709250i
$235$	29.6271			0.126073
$236$	−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	$0.843652\pi$
$240$	−30.4758	−	30.4758i	−0.126983	−	0.126983i
$241$	−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
$245$	−18.8377	+	18.8377i	−0.0768887	+	0.0768887i
$246$		−	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
$250$	−107.355			−0.429421
$251$		−	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
$255$	14.4673	−	14.4673i	0.0567343	−	0.0567343i
$256$	−378.789			−1.47965
$257$			450.579i			1.75322i	0.481198	+	0.876612i	$0.340202\pi$
$257$			450.579i			1.75322i	−0.481198	+	0.876612i	$0.659798\pi$
$258$	−64.2566	+	64.2566i	−0.249057	+	0.249057i
$259$		−	12.0043i		−	0.0463485i
$260$	−5.80711	+	71.5701i	−0.0223351	+	0.275270i
$261$	−111.623			−0.427673
$262$	289.778	+	289.778i	1.10602	+	1.10602i
$263$	166.982			0.634913			0.317457	−	0.948273i	$-0.397171\pi$
$263$	166.982			0.634913			0.317457	+	0.948273i	$0.397171\pi$
$264$			435.329i			1.64897i
$265$	−1.75445	−	1.75445i	−0.00662055	−	0.00662055i
$266$	−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	$0.397627\pi$
$270$			62.2982i			0.230734i
$271$	−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
$275$	180.544	+	180.544i	0.656523	+	0.656523i
$276$	−554.197			−2.00796
$277$			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
$279$	−84.2719	−	84.2719i	−0.302050	−	0.302050i
$280$	−16.3356	+	16.3356i	−0.0583414	+	0.0583414i
$281$	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	$-0.750811\pi$
$283$		−	399.201i		−	1.41061i	0.708906	−	0.705303i	$-0.249189\pi$
$284$	−470.379	+	470.379i	−1.65626	+	1.65626i
$285$		−	5.72811i		−	0.0200986i
$286$	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
$290$		−	55.8114i		−	0.192453i
$291$	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	−0.435496	−	0.900191i	$-0.643427\pi$
$293$	136.156	−	136.156i	0.464695	−	0.464695i	0.900191	+	0.435496i	$0.143427\pi$
$294$	251.004	−	251.004i	0.853756	−	0.853756i
$295$	−25.3594			−0.0859642
$296$			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
$300$	496.982			1.65661
$301$	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
$305$	−28.3466	−	28.3466i	−0.0929397	−	0.0929397i
$306$	178.302	−	178.302i	0.582688	−	0.582688i
$307$	−235.684	+	235.684i	−0.767700	+	0.767700i	−0.977701	−	0.210001i	$-0.932653\pi$
$307$	−235.684	+	235.684i	−0.767700	+	0.767700i	0.210001	+	0.977701i	$0.432653\pi$
$308$	193.811			0.629258
$309$			128.513i			0.415900i
$310$	42.1359	−	42.1359i	0.135922	−	0.135922i
$311$		−	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	$-0.383799\pi$
$313$	223.483			0.714002			0.357001	+	0.934104i	$0.383799\pi$
$314$	−600.228	−	600.228i	−1.91155	−	1.91155i
$315$	5.14022			0.0163181
$316$			473.548i			1.49857i
$317$	−125.140	−	125.140i	−0.394764	−	0.394764i	0.481617	−	0.876382i	$-0.340049\pi$
$317$	−125.140	−	125.140i	−0.394764	−	0.394764i	−0.876382	+	0.481617i	$0.840049\pi$
$318$	23.3772	+	23.3772i	0.0735133	+	0.0735133i
$319$	−189.057	+	189.057i	−0.592655	+	0.592655i
$320$	12.5548	−	12.5548i	0.0392338	−	0.0392338i
$321$	−310.438			−0.967098
$322$			201.329i			0.625245i
$323$	−50.5132	+	50.5132i	−0.156388	+	0.156388i
$324$		−	217.982i		−	0.672785i
$325$	−207.517	−	244.167i	−0.638515	−	0.751282i
$326$	−59.1623			−0.181479
$327$	−183.305	−	183.305i	−0.560566	−	0.560566i
$328$	306.816			0.935414
$329$			100.359i			0.305044i
$330$	34.2456	+	34.2456i	0.103774	+	0.103774i
$331$	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
$335$		−	67.9253i		−	0.202762i
$336$	103.235	−	103.235i	0.307246	−	0.307246i
$337$			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
$339$	−234.702			−0.692336
$340$	62.3883	+	62.3883i	0.183495	+	0.183495i
$341$	−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
$345$	−24.8947	+	24.8947i	−0.0721584	+	0.0721584i
$346$	−235.868	+	235.868i	−0.681700	+	0.681700i
$347$	−47.2413			−0.136142			−0.0680710	−	0.997680i	$-0.521684\pi$
$347$	−47.2413			−0.136142			−0.0680710	+	0.997680i	$0.521684\pi$
$348$			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	$0.100355\pi$
$350$		−	180.544i		−	0.515839i
$351$	−285.397	+	242.559i	−0.813096	+	0.691052i
$352$	−467.004			−1.32672
$353$	110.320	+	110.320i	0.312522	+	0.312522i	0.845886	−	0.533364i	$-0.179072\pi$
$353$	110.320	+	110.320i	0.312522	+	0.312522i	−0.533364	+	0.845886i	$0.679072\pi$
$354$	337.903			0.954529
$355$			42.2591i			0.119040i
$356$	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	$0.210264\pi$
$360$	−49.7893			−0.138304
$361$		−	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
$365$	−26.4911			−0.0725784
$366$	377.706	+	377.706i	1.03198	+	1.03198i
$367$	−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
$369$	−48.2719	−	48.2719i	−0.130818	−	0.130818i
$370$	9.14697	+	9.14697i	0.0247216	+	0.0247216i
$371$	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	$-0.496212\pi$
$373$	8.87688			0.0237986			0.0118993	+	0.999929i	$0.496212\pi$
$374$		−	603.986i		−	1.61494i
$375$	44.9669	−	44.9669i	0.119912	−	0.119912i
$376$		−	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	$0.837012\pi$
$380$	24.7018			0.0650047
$381$		−	205.065i		−	0.538230i
$382$	−463.846	−	463.846i	−1.21426	−	1.21426i
$383$	357.261	+	357.261i	0.932796	+	0.932796i	0.997880	−	0.0650838i	$-0.0207315\pi$
$383$	357.261	+	357.261i	0.932796	+	0.932796i	−0.0650838	+	0.997880i	$0.520731\pi$
$384$	108.441	−	108.441i	0.282398	−	0.282398i
$385$	8.70605	−	8.70605i	0.0226131	−	0.0226131i
$386$	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	$0.809485\pi$
$390$	−39.3619	−	46.3135i	−0.100928	−	0.118753i
$391$	439.065			1.12293
$392$	618.092	+	618.092i	1.57676	+	1.57676i
$393$	−242.754			−0.617694
$394$		−	732.557i		−	1.85928i
$395$	21.2719	+	21.2719i	0.0538529	+	0.0538529i
$396$	295.359	+	295.359i	0.745857	+	0.745857i
$397$	250.061	−	250.061i	0.629877	−	0.629877i	−0.318160	−	0.948037i	$-0.603065\pi$
$397$	250.061	−	250.061i	0.629877	−	0.629877i	0.948037	+	0.318160i	$0.103065\pi$
$398$	−670.473	+	670.473i	−1.68461	+	1.68461i
$399$	19.4036			0.0486305
$400$			829.421i			2.07355i
$401$	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
$405$	−9.79181	−	9.79181i	−0.0241773	−	0.0241773i
$406$	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	$0.528966\pi$
$410$	24.1359	−	24.1359i	0.0588682	−	0.0588682i
$411$	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
$415$			15.6007i			0.0375921i
$416$	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	$0.787912\pi$
$420$		−	23.9651i		−	0.0570598i
$421$	−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
$425$	−393.737			−0.926439
$426$		−	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
$430$	−24.8947			−0.0578946
$431$	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	$0.0577070\pi$
$433$			156.140i			0.360601i	−0.983612	+	0.180300i	$0.942293\pi$
$434$	142.732	+	142.732i	0.328876	+	0.328876i
$435$	23.3772	+	23.3772i	0.0537407	+	0.0537407i
$436$	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	$0.829253\pi$
$440$	−84.3288	+	84.3288i	−0.191656	+	0.191656i
$441$		−	194.491i		−	0.441023i
$442$	−61.3025	+	755.526i	−0.138693	+	1.70933i
$443$	−577.372			−1.30332			−0.651662	−	0.758510i	$-0.725928\pi$
$443$	−577.372			−1.30332			−0.651662	+	0.758510i	$0.725928\pi$
$444$	−85.2915	−	85.2915i	−0.192098	−	0.192098i
$445$	76.3246			0.171516
$446$			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	$0.303960\pi$
$450$	275.140	−	275.140i	0.611423	−	0.611423i
$451$	−163.517			−0.362566
$452$		−	1012.12i		−	2.23921i
$453$	63.0900	−	63.0900i	0.139272	−	0.139272i
$454$			520.009i			1.14539i
$455$	−11.7740	+	10.0068i	−0.0258770	+	0.0219929i
$456$	−187.947			−0.412165
$457$	−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
$459$			460.223i			1.00267i
$460$	−107.355	−	107.355i	−0.233381	−	0.233381i
$461$	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	−0.243446	−	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
$465$			35.2982i			0.0759102i
$466$	−27.8488	+	27.8488i	−0.0597613	+	0.0597613i
$467$		−	308.263i		−	0.660093i	−0.943965	−	0.330046i	$-0.892936\pi$
$467$		−	308.263i		−	0.660093i	0.943965	−	0.330046i	$-0.107064\pi$
$468$	−339.487	−	399.443i	−0.725399	−	0.853510i
$469$	230.092			0.490601
$470$	−76.4715	−	76.4715i	−0.162705	−	0.162705i
$471$	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
$475$	−77.9473	+	77.9473i	−0.164100	+	0.164100i
$476$	−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	$0.213909\pi$
$480$			57.7459i			0.120304i
$481$	−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
$485$			73.1794i			0.150885i
$486$	−538.824	−	538.824i	−1.10869	−	1.10869i
$487$	−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
$489$	24.7808	−	24.7808i	0.0506764	−	0.0506764i
$490$	97.2456			0.198460
$491$		−	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
$495$	26.5352			0.0536065
$496$	−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	$0.585162\pi$
$500$	193.914	+	193.914i	0.387828	+	0.387828i
$501$	−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	$-0.486621\pi$
$503$	42.2719			0.0840395			0.0420198	+	0.999117i	$0.486621\pi$
$504$		−	168.658i		−	0.334638i
$505$	3.73666	−	3.73666i	0.00739933	−	0.00739933i
$506$			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	$0.667594\pi$
$510$	−74.6840			−0.146439
$511$		−	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
$515$	−24.8947	+	24.8947i	−0.0483392	+	0.0483392i
$516$	232.132			0.449868
$517$			518.083i			1.00210i
$518$	−30.9847	+	30.9847i	−0.0598160	+	0.0598160i
$519$		−	197.592i		−	0.380717i
$520$	114.046	−	96.9278i	0.219319	−	0.186400i
$521$	−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	$-0.568028\pi$
$523$	−221.851			−0.424188			−0.212094	+	0.977249i	$0.568028\pi$
$524$		−	1046.85i		−	1.99780i
$525$	75.6228	+	75.6228i	0.144043	+	0.144043i
$526$	−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
$530$			9.05694i			0.0170886i
$531$	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
$535$	−60.1359	−	60.1359i	−0.112404	−	0.112404i
$536$	−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
$540$	112.528	−	112.528i	0.208386	−	0.208386i
$541$	−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
$545$		−	71.0171i		−	0.130307i
$546$	156.884	−	133.336i	0.287333	−	0.244204i
$547$	−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
$549$	292.666			0.533090
$550$		−	932.017i		−	1.69458i
$551$	−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
$555$	−7.66262			−0.0138065
$556$			732.346i			1.31717i
$557$	−479.423	+	479.423i	−0.860724	+	0.860724i	−0.991422	−	0.130698i	$-0.958278\pi$
$557$	−479.423	+	479.423i	−0.860724	+	0.860724i	0.130698	+	0.991422i	$0.458278\pi$
$558$			435.035i			0.779632i
$559$	−96.9278	−	114.046i	−0.173395	−	0.204018i
$560$	39.9957			0.0714209
$561$	252.986	+	252.986i	0.450956	+	0.450956i
$562$	−1480.78			−2.63484
$563$		−	461.671i		−	0.820020i	−0.912081	−	0.410010i	$-0.865525\pi$
$563$		−	461.671i		−	0.820020i	0.912081	−	0.410010i	$-0.134475\pi$
$564$	713.063	+	713.063i	1.26430	+	1.26430i
$565$	−45.4648	−	45.4648i	−0.0804686	−	0.0804686i
$566$	−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	$0.847876\pi$
$570$	−14.7851	+	14.7851i	−0.0259387	+	0.0259387i
$571$			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
$575$	677.526			1.17831
$576$			129.623i			0.225040i
$577$	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
$579$	−2.45623	+	2.45623i	−0.00424219	+	0.00424219i
$580$	−100.811	+	100.811i	−0.173813	+	0.173813i
$581$	−52.8463			−0.0909574
$582$		−	975.083i		−	1.67540i
$583$	30.6797	−	30.6797i	0.0526239	−	0.0526239i
$584$			869.210i			1.48837i
$585$	−33.1929	−	2.69323i	−0.0567400	−	0.00460382i
$586$	−702.873			−1.19944
$587$	−347.311	−	347.311i	−0.591671	−	0.591671i	0.346411	−	0.938083i	$-0.387400\pi$
$587$	−347.311	−	347.311i	−0.591671	−	0.591671i	−0.938083	+	0.346411i	$0.887400\pi$
$588$	−906.772			−1.54213
$589$		−	123.246i		−	0.209245i
$590$	65.4562	+	65.4562i	0.110943	+	0.110943i
$591$	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	−0.880062	−	0.474860i	$-0.842499\pi$
$593$	−240.285	+	240.285i	−0.405202	+	0.405202i	0.474860	+	0.880062i	$0.342499\pi$
$594$	−1089.40			−1.83400
$595$			18.9865i			0.0319101i
$596$	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	$0.162760\pi$
$600$	−732.500	−	732.500i	−1.22083	−	1.22083i
$601$	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
$605$	−5.73914	+	5.73914i	−0.00948619	+	0.00948619i
$606$	−49.7893	+	49.7893i	−0.0821606	+	0.0821606i
$607$	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
$609$	−79.1886	+	79.1886i	−0.130031	+	0.130031i
$610$			146.333i			0.239890i
$611$	52.5836	−	648.070i	0.0860616	−	1.06067i
$612$	−644.131			−1.05250
$613$	−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
$615$			20.2192i			0.0328768i
$616$	−285.658	−	285.658i	−0.463730	−	0.463730i
$617$	95.4121	+	95.4121i	0.154639	+	0.154639i	0.780186	−	0.625547i	$-0.215124\pi$
$617$	95.4121	+	95.4121i	0.154639	+	0.154639i	−0.625547	+	0.780186i	$0.715124\pi$
$618$	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	$0.463890\pi$
$620$	−152.219			−0.245515
$621$		−	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
$625$	−598.806			−0.958090
$626$	−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
$630$	−13.2676	−	13.2676i	−0.0210597	−	0.0210597i
$631$	−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
$635$	39.7238	−	39.7238i	0.0625572	−	0.0625572i
$636$		−	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
$640$	42.0128			0.0656450
$641$		−	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	$-0.909397\pi$
$643$	−797.688	−	797.688i	−1.24057	−	1.24057i	−0.280809	−	0.959764i	$-0.590603\pi$
$644$	363.658	−	363.658i	0.564686	−	0.564686i
$645$	10.4274	−	10.4274i	0.0161665	−	0.0161665i
$646$	260.763			0.403658
$647$			989.526i			1.52941i	0.644383	+	0.764703i	$0.277114\pi$
$647$			989.526i			1.52941i	−0.644383	+	0.764703i	$0.722886\pi$
$648$	−321.283	+	321.283i	−0.495807	+	0.495807i
$649$		−	443.456i		−	0.683292i
$650$	−94.5964	+	1165.86i	−0.145533	+	1.79363i
$651$	−119.570			−0.183671
$652$	106.864	+	106.864i	0.163902	+	0.163902i
$653$	−86.3075			−0.132171			−0.0660853	−	0.997814i	$-0.521051\pi$
$653$	−86.3075			−0.132171			−0.0660853	+	0.997814i	$0.521051\pi$
$654$			946.271i			1.44690i
$655$	−47.0245	−	47.0245i	−0.0717932	−	0.0717932i
$656$	−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	$0.855765\pi$
$660$		−	123.715i		−	0.187446i
$661$	−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
$665$	3.75872	+	3.75872i	0.00565221	+	0.00565221i
$666$	−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
$670$	−175.325	+	175.325i	−0.261678	+	0.261678i
$671$	495.693	−	495.693i	0.738737	−	0.738737i
$672$	−195.610			−0.291086
$673$		−	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
$675$			710.175i			1.05211i
$676$	1555.24	+	254.053i	2.30065	+	0.375818i
$677$	−412.031			−0.608612			−0.304306	−	0.952574i	$-0.598425\pi$
$677$	−412.031			−0.608612			−0.304306	+	0.952574i	$0.598425\pi$
$678$	605.798	+	605.798i	0.893507	+	0.893507i
$679$	−247.890			−0.365081
$680$		−	183.907i		−	0.270452i
$681$	−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	−0.606299	−	0.795237i	$-0.707347\pi$
$683$	129.044	−	129.044i	0.188937	−	0.188937i	0.795237	+	0.606299i	$0.207347\pi$
$684$	−127.517	+	127.517i	−0.186429	+	0.186429i
$685$	72.6541			0.106064
$686$			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
$690$	128.513			0.186251
$691$	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
$695$	32.8971	+	32.8971i	0.0473340	+	0.0473340i
$696$	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
$700$	−326.114	+	326.114i	−0.465877	+	0.465877i
$701$			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
$705$	64.0619			0.0908680
$706$		−	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	$0.00608601\pi$
$710$	109.077	−	109.077i	0.153629	−	0.153629i
$711$	−219.623			−0.308893
$712$		−	2504.31i		−	3.51730i
$713$	−535.631	+	535.631i	−0.751236	+	0.751236i
$714$		−	252.986i		−	0.354323i
$715$	−60.7808	+	51.6577i	−0.0850081	+	0.0722485i
$716$	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	$-0.203939\pi$
$720$	60.9516	+	60.9516i	0.0846550	+	0.0846550i
$721$	−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
$725$		−	636.228i		−	0.877556i
$726$	76.4715	−	76.4715i	0.105333	−	0.105333i
$727$			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
$729$	661.780			0.907792
$730$	68.3772	+	68.3772i	0.0936674	+	0.0936674i
$731$	−183.907			−0.251583
$732$		−	1364.49i		−	1.86406i
$733$	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
$735$	−40.7324	+	40.7324i	−0.0554182	+	0.0554182i
$736$	−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	$-0.0924834\pi$
$740$		−	33.0441i		−	0.0446542i
$741$	−125.298	−	10.1666i	−0.169093	−	0.0137200i
$742$	−30.6797			−0.0413473
$743$	730.642	+	730.642i	0.983368	+	0.983368i	0.999864	−	0.0164960i	$-0.00525109\pi$
$743$	730.642	+	730.642i	0.983368	+	0.983368i	−0.0164960	+	0.999864i	$0.505251\pi$
$744$	1158.18			1.55670
$745$		−	107.412i		−	0.144177i
$746$	−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
$750$	−232.132			−0.309509
$751$			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
$755$	24.4427			0.0323745
$756$	381.182	+	381.182i	0.504209	+	0.504209i
$757$	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
$759$	−435.329	−	435.329i	−0.573556	−	0.573556i
$760$	−36.4078	−	36.4078i	−0.0479050	−	0.0479050i
$761$	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
$765$	−28.9345	+	28.9345i	−0.0378229	+	0.0378229i
$766$		−	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	$0.709515\pi$
$770$	−44.9431			−0.0583676
$771$			974.276i			1.26365i
$772$	−10.5922	−	10.5922i	−0.0137204	−	0.0137204i
$773$	550.813	+	550.813i	0.712566	+	0.712566i	0.967071	−	0.254506i	$-0.0819128\pi$
$773$	550.813	+	550.813i	0.712566	+	0.712566i	−0.254506	+	0.967071i	$0.581913\pi$
$774$	128.513	−	128.513i	0.166038	−	0.166038i
$775$	480.333	−	480.333i	0.619785	−	0.619785i
$776$	2401.12			3.09422
$777$		−	25.9566i		−	0.0334061i
$778$	1131.42	−	1131.42i	1.45427	−	1.45427i
$779$		−	70.5964i		−	0.0906244i
$780$	−12.5566	+	154.754i	−0.0160982	+	0.198403i
$781$	−738.977			−0.946194
$782$	−1133.29	−	1133.29i	−1.44922	−	1.44922i
$783$	−743.662			−0.949760
$784$		−	1513.32i		−	1.93026i
$785$	97.4036	+	97.4036i	0.124081	+	0.124081i
$786$	626.581	+	626.581i	0.797177	+	0.797177i
$787$	729.434	−	729.434i	0.926854	−	0.926854i	−0.0706473	−	0.997501i	$-0.522506\pi$
$787$	729.434	−	729.434i	0.926854	−	0.926854i	0.997501	+	0.0706473i	$0.0225065\pi$
$788$	−1323.21	+	1323.21i	−1.67920	+	1.67920i
$789$	361.062			0.457620
$790$		−	109.811i		−	0.139002i
$791$	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
$795$	−3.79360	−	3.79360i	−0.00477183	−	0.00477183i
$796$	2422.13			3.04288
$797$			444.974i			0.558311i	0.960246	+	0.279155i	$0.0900545\pi$
$797$			444.974i			0.558311i	−0.960246	+	0.279155i	$0.909946\pi$
$798$	−50.0833	−	50.0833i	−0.0627610	−	0.0627610i
$799$	−564.928	−	564.928i	−0.707043	−	0.707043i
$800$	785.798	−	785.798i	0.982247	−	0.982247i
$801$	−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
$805$		−	32.6712i		−	0.0405853i
$806$	−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	$0.735379\pi$
$810$			50.5480i			0.0624050i
$811$	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
$815$	9.60072			0.0117800
$816$			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
$820$	−87.1929			−0.106333
$821$	−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	$0.0192687\pi$
$823$			99.5787i			0.120995i	−0.998168	+	0.0604974i	$0.980731\pi$
$824$	816.828	+	816.828i	0.991297	+	0.991297i
$825$	390.386	+	390.386i	0.473195	+	0.473195i
$826$	−221.728	+	221.728i	−0.268436	+	0.268436i
$827$	−899.548	+	899.548i	−1.08772	+	1.08772i	−0.0919618	+	0.995763i	$0.529314\pi$
$827$	−899.548	+	899.548i	−1.08772	+	1.08772i	−0.995763	+	0.0919618i	$0.970686\pi$
$828$	1108.39			1.33864
$829$		−	32.1103i		−	0.0387338i	−0.999812	−	0.0193669i	$-0.993835\pi$
$829$		−	32.1103i		−	0.0387338i	0.999812	−	0.0193669i	$-0.00616506\pi$
$830$	40.2676	−	40.2676i	0.0485152	−	0.0485152i
$831$			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
$835$	−173.228			−0.207459
$836$			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	$0.138038\pi$
$840$	−35.3221	+	35.3221i	−0.0420501	+	0.0420501i
$841$	−174.772			−0.207815
$842$			414.601i			0.492400i
$843$	620.241	−	620.241i	0.735755	−	0.735755i
$844$			3035.84i			3.59696i
$845$	81.2737	−	58.4495i	0.0961819	−	0.0691710i
$846$	789.535			0.933256
$847$	−19.4409	−	19.4409i	−0.0229527	−	0.0229527i
$848$	140.943			0.166206
$849$		−	863.184i		−	1.01671i
$850$	1016.29	+	1016.29i	1.19563	+	1.19563i
$851$	−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	−0.324933	−	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
$855$			11.4562i			0.0133991i
$856$	−1973.14	+	1973.14i	−2.30507	+	2.30507i
$857$			1586.76i			1.85153i	0.378097	+	0.925766i	$0.376579\pi$
$857$			1586.76i			1.85153i	−0.378097	+	0.925766i	$0.623421\pi$
$858$	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	$0.473091\pi$
$860$	44.9669	+	44.9669i	0.0522871	+	0.0522871i
$861$	−68.4911			−0.0795483
$862$		−	1528.23i		−	1.77289i
$863$	−1005.80	−	1005.80i	−1.16547	−	1.16547i	−0.983258	−	0.182216i	$-0.941673\pi$
$863$	−1005.80	−	1005.80i	−1.16547	−	1.16547i	−0.182216	−	0.983258i	$-0.558327\pi$
$864$	−918.489	−	918.489i	−1.06307	−	1.06307i
$865$	38.2762	−	38.2762i	0.0442499	−	0.0442499i
$866$	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
$870$		−	120.680i		−	0.138712i
$871$	−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
$875$			59.0135i			0.0674440i
$876$	−637.587	−	637.587i	−0.727839	−	0.727839i
$877$	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
$879$	294.406	−	294.406i	0.334933	−	0.334933i
$880$	206.469			0.234624
$881$		−	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	$-0.972213\pi$
$883$		−	153.969i		−	0.174370i	0.996192	−	0.0871850i	$-0.0277871\pi$
$884$	1475.43	−	1253.97i	1.66903	−	1.41851i
$885$	−54.8341			−0.0619595
$886$	1490.28	+	1490.28i	1.68203	+	1.68203i
$887$	125.273			0.141232			0.0706159	−	0.997504i	$-0.477504\pi$
$887$	125.273			0.141232			0.0706159	+	0.997504i	$0.477504\pi$
$888$			251.421i			0.283132i
$889$	134.562	+	134.562i	0.151363	+	0.151363i
$890$	−197.004	−	197.004i	−0.221353	−	0.221353i
$891$	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
$895$	30.0203	−	30.0203i	0.0335422	−	0.0335422i
$896$			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
$900$	−993.964			−1.10440
$901$			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
$905$	−114.828	+	114.828i	−0.126882	+	0.126882i
$906$	−325.688			−0.359479
$907$		−	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
$909$			38.5793i			0.0424415i
$910$	56.2192	+	4.56156i	0.0617794	+	0.00501271i
$911$	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
$915$	−61.2933	−	61.2933i	−0.0669872	−	0.0669872i
$916$	−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	$0.572709\pi$
$920$			316.460i			0.343979i
$921$	−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
$925$	104.272	+	104.272i	0.112726	+	0.112726i
$926$	−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	$0.855727\pi$
$930$	91.1096	−	91.1096i	0.0979673	−	0.0979673i
$931$	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
$935$			98.0135i			0.104827i
$936$	−88.3687	+	1089.10i	−0.0944110	+	1.16357i
$937$	−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
$939$	483.231			0.514623
$940$			276.259i			0.293893i
$941$	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
$945$	34.2456			0.0362387
$946$		−	435.329i		−	0.460178i
$947$	897.569	−	897.569i	0.947803	−	0.947803i	−0.0509007	−	0.998704i	$-0.516209\pi$
$947$	897.569	−	897.569i	0.947803	−	0.947803i	0.998704	+	0.0509007i	$0.0162092\pi$
$948$			1023.94i			1.08011i
$949$	−47.0178	+	579.473i	−0.0495446	+	0.610615i
$950$	402.386			0.423564
$951$	−270.588	−	270.588i	−0.284530	−	0.284530i
$952$	622.973			0.654383
$953$			1111.71i			1.16654i	0.812279	+	0.583269i	$0.198227\pi$
$953$			1111.71i			1.16654i	−0.812279	+	0.583269i	$0.801773\pi$
$954$	−46.7544	−	46.7544i	−0.0490089	−	0.0490089i
$955$	75.2719	+	75.2719i	0.0788187	+	0.0788187i
$956$	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
$960$	27.1470	−	27.1470i	0.0282781	−	0.0282781i
$961$		−	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
$965$	−0.951605			−0.000986120
$966$			435.329i			0.450651i
$967$	−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
$969$	−109.223	+	109.223i	−0.112718	+	0.112718i
$970$	188.886	−	188.886i	0.194728	−	0.194728i
$971$	−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
$975$	−448.710	−	527.956i	−0.460216	−	0.541493i
$976$	2277.22			2.33322
$977$	−1103.56	−	1103.56i	−1.12954	−	1.12954i	−0.990252	−	0.139288i	$-0.955518\pi$
$977$	−1103.56	−	1103.56i	−1.12954	−	1.12954i	−0.139288	−	0.990252i	$-0.544482\pi$
$978$	−127.925			−0.130803
$979$			1334.67i			1.36330i
$980$	−175.653	−	175.653i	−0.179238	−	0.179238i
$981$	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	−0.996815	−	0.0797497i	$-0.974588\pi$
$983$	−901.475	+	901.475i	−0.917065	+	0.917065i	0.0797497	+	0.996815i	$0.474588\pi$
$984$	663.421			0.674208
$985$			118.878i			0.120688i
$986$	−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
$990$	−68.4911	−	68.4911i	−0.0691829	−	0.0691829i
$991$	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
$995$	108.803	−	108.803i	0.109350	−	0.109350i
$996$	−375.478	+	375.478i	−0.376986	+	0.376986i
$997$	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
$999$	121.879	−	121.879i	0.122001	−	0.122001i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.3.d.a.8.1	yes	4
3.2	odd	2		117.3.j.a.73.2		4
4.3	odd	2		208.3.t.c.177.1		4
5.2	odd	4		325.3.g.b.99.2		4
5.3	odd	4		325.3.g.a.99.1		4
5.4	even	2		325.3.j.a.151.2		4
13.2	odd	12		169.3.f.f.19.1		8
13.3	even	3		169.3.f.f.150.2		8
13.4	even	6		169.3.f.d.89.2		8
13.5	odd	4	inner	13.3.d.a.5.1	✓	4
13.6	odd	12		169.3.f.f.80.2		8
13.7	odd	12		169.3.f.d.80.1		8
13.8	odd	4		169.3.d.d.70.2		4
13.9	even	3		169.3.f.f.89.1		8
13.10	even	6		169.3.f.d.150.1		8
13.11	odd	12		169.3.f.d.19.2		8
13.12	even	2		169.3.d.d.99.2		4
39.5	even	4		117.3.j.a.109.2		4
52.31	even	4		208.3.t.c.161.1		4
65.18	even	4		325.3.g.b.174.2		4
65.44	odd	4		325.3.j.a.226.2		4
65.57	even	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	13.5	odd	4	inner
13.3.d.a.8.1	yes	4	1.1	even	1	trivial
117.3.j.a.73.2		4	3.2	odd	2
117.3.j.a.109.2		4	39.5	even	4
169.3.d.d.70.2		4	13.8	odd	4
169.3.d.d.99.2		4	13.12	even	2
169.3.f.d.19.2		8	13.11	odd	12
169.3.f.d.80.1		8	13.7	odd	12
169.3.f.d.89.2		8	13.4	even	6
169.3.f.d.150.1		8	13.10	even	6
169.3.f.f.19.1		8	13.2	odd	12
169.3.f.f.80.2		8	13.6	odd	12
169.3.f.f.89.1		8	13.9	even	3
169.3.f.f.150.2		8	13.3	even	3
208.3.t.c.161.1		4	52.31	even	4
208.3.t.c.177.1		4	4.3	odd	2
325.3.g.a.99.1		4	5.3	odd	4
325.3.g.a.174.1		4	65.57	even	4
325.3.g.b.99.2		4	5.2	odd	4
325.3.g.b.174.2		4	65.18	even	4
325.3.j.a.151.2		4	5.4	even	2
325.3.j.a.226.2		4	65.44	odd	4

Overview	Random
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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	13.3.d.a.8.1

Level	$13$
Weight	$3$
Character	13.8
Analytic conductor	$0.354$
Analytic rank	$0$
Dimension	$4$
Inner twists	$2$