LMFDB - Embedded newform 60.5.l.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	60.23
Dual form			60.5.l.a.47.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95843 + 3.48777i) q^{2} +(5.95729 + 6.74616i) q^{3} +(-8.32911 - 13.6611i) q^{4} +(24.5931 + 4.49233i) q^{5} +(-35.1960 + 7.56581i) q^{6} +(44.1332 + 44.1332i) q^{7} +(63.9588 - 2.29574i) q^{8} +(-10.0213 + 80.3777i) q^{9} +O(q^{10})$	\(q+(-1.95843 + 3.48777i) q^{2} +(5.95729 + 6.74616i) q^{3} +(-8.32911 - 13.6611i) q^{4} +(24.5931 + 4.49233i) q^{5} +(-35.1960 + 7.56581i) q^{6} +(44.1332 + 44.1332i) q^{7} +(63.9588 - 2.29574i) q^{8} +(-10.0213 + 80.3777i) q^{9} +(-63.8320 + 76.9771i) q^{10} -27.5699 q^{11} +(42.5410 - 137.573i) q^{12} +(-177.104 - 177.104i) q^{13} +(-240.358 + 67.4949i) q^{14} +(116.202 + 192.671i) q^{15} +(-117.252 + 227.570i) q^{16} +(241.784 + 241.784i) q^{17} +(-260.713 - 192.366i) q^{18} -409.432 q^{19} +(-143.468 - 373.386i) q^{20} +(-34.8151 + 560.644i) q^{21} +(53.9937 - 96.1576i) q^{22} +(-95.2117 - 95.2117i) q^{23} +(396.509 + 417.800i) q^{24} +(584.638 + 220.960i) q^{25} +(964.543 - 270.853i) q^{26} +(-601.940 + 411.228i) q^{27} +(235.318 - 970.500i) q^{28} +1195.81 q^{29} +(-899.566 + 27.9545i) q^{30} -664.535i q^{31} +(-564.083 - 854.627i) q^{32} +(-164.242 - 185.991i) q^{33} +(-1316.80 + 369.770i) q^{34} +(887.111 + 1283.63i) q^{35} +(1181.52 - 532.573i) q^{36} +(440.813 - 440.813i) q^{37} +(801.843 - 1428.01i) q^{38} +(139.711 - 2249.83i) q^{39} +(1583.26 + 230.865i) q^{40} +31.0745i q^{41} +(-1887.22 - 1219.41i) q^{42} +(1997.60 - 1997.60i) q^{43} +(229.633 + 376.636i) q^{44} +(-607.538 + 1931.72i) q^{45} +(518.542 - 145.611i) q^{46} +(-1221.96 + 1221.96i) q^{47} +(-2233.73 + 564.701i) q^{48} +1494.49i q^{49} +(-1915.63 + 1606.35i) q^{50} +(-190.734 + 3071.49i) q^{51} +(-944.317 + 3894.55i) q^{52} +(578.852 - 578.852i) q^{53} +(-255.413 - 2904.79i) q^{54} +(-678.029 - 123.853i) q^{55} +(2924.03 + 2721.39i) q^{56} +(-2439.11 - 2762.09i) q^{57} +(-2341.91 + 4170.72i) q^{58} -2432.13i q^{59} +(1664.24 - 3192.23i) q^{60} -915.302 q^{61} +(2317.75 + 1301.44i) q^{62} +(-3989.60 + 3105.06i) q^{63} +(4085.46 - 293.666i) q^{64} +(-3559.92 - 5151.14i) q^{65} +(970.351 - 208.589i) q^{66} +(-1105.20 - 1105.20i) q^{67} +(1289.19 - 5316.87i) q^{68} +(75.1091 - 1209.52i) q^{69} +(-6214.36 + 580.136i) q^{70} +7175.87 q^{71} +(-456.424 + 5163.87i) q^{72} +(-2655.36 - 2655.36i) q^{73} +(674.155 + 2400.76i) q^{74} +(1992.23 + 5260.39i) q^{75} +(3410.20 + 5593.29i) q^{76} +(-1216.75 - 1216.75i) q^{77} +(7573.28 + 4893.41i) q^{78} -426.851 q^{79} +(-3905.90 + 5069.91i) q^{80} +(-6360.15 - 1610.98i) q^{81} +(-108.381 - 60.8571i) q^{82} +(-4152.37 - 4152.37i) q^{83} +(7949.00 - 4194.06i) q^{84} +(4860.03 + 7032.37i) q^{85} +(3055.01 + 10879.3i) q^{86} +(7123.80 + 8067.13i) q^{87} +(-1763.34 + 63.2934i) q^{88} -4519.29 q^{89} +(-5547.56 - 5902.08i) q^{90} -15632.3i q^{91} +(-507.668 + 2093.73i) q^{92} +(4483.06 - 3958.83i) q^{93} +(-1868.79 - 6655.03i) q^{94} +(-10069.2 - 1839.30i) q^{95} +(2405.04 - 8896.65i) q^{96} +(12818.4 - 12818.4i) q^{97} +(-5212.42 - 2926.84i) q^{98} +(276.286 - 2216.01i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^6	$ 88 q - 4 q^{6} + 148 q^{10} - 164 q^{12} - 8 q^{13} - 484 q^{16} + 456 q^{18} + 600 q^{21} - 348 q^{22} - 8 q^{25} - 148 q^{28} + 68 q^{30} - 328 q^{33} - 1556 q^{36} + 2232 q^{37} + 2024 q^{40} - 2116 q^{42} - 2504 q^{45} - 4432 q^{46} + 1540 q^{48} + 80 q^{52} + 3192 q^{57} - 1948 q^{58} + 2836 q^{60} - 7568 q^{61} + 3384 q^{66} + 8348 q^{70} + 5256 q^{72} + 5592 q^{73} - 256 q^{76} + 13176 q^{78} - 12648 q^{81} + 20400 q^{82} + 5816 q^{85} + 7932 q^{88} - 13152 q^{90} + 3680 q^{93} - 18028 q^{96} - 15208 q^{97}+O(q^{100}) $ 88 * q - 4 * q^6 + 148 * q^10 - 164 * q^12 - 8 * q^13 - 484 * q^16 + 456 * q^18 + 600 * q^21 - 348 * q^22 - 8 * q^25 - 148 * q^28 + 68 * q^30 - 328 * q^33 - 1556 * q^36 + 2232 * q^37 + 2024 * q^40 - 2116 * q^42 - 2504 * q^45 - 4432 * q^46 + 1540 * q^48 + 80 * q^52 + 3192 * q^57 - 1948 * q^58 + 2836 * q^60 - 7568 * q^61 + 3384 * q^66 + 8348 * q^70 + 5256 * q^72 + 5592 * q^73 - 256 * q^76 + 13176 * q^78 - 12648 * q^81 + 20400 * q^82 + 5816 * q^85 + 7932 * q^88 - 13152 * q^90 + 3680 * q^93 - 18028 * q^96 - 15208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.95843	+	3.48777i	−0.489607	+	0.871943i
$2$	−1.95843	+	3.48777i	−0.489607	+	0.871943i
$3$	5.95729	+	6.74616i	0.661922	+	0.749573i
$3$	5.95729	+	6.74616i	0.661922	+	0.749573i
$4$	−8.32911	−	13.6611i	−0.520570	−	0.853819i
$5$	24.5931	+	4.49233i	0.983723	+	0.179693i
$5$	24.5931	+	4.49233i	0.983723	+	0.179693i
$6$	−35.1960	+	7.56581i	−0.977667	+	0.210161i
$7$	44.1332	+	44.1332i	0.900678	+	0.900678i	0.995495	−	0.0948165i	$-0.0302264\pi$
$7$	44.1332	+	44.1332i	0.900678	+	0.900678i	−0.0948165	+	0.995495i	$0.530226\pi$
$8$	63.9588	−	2.29574i	0.999356	−	0.0358710i
$9$	−10.0213	+	80.3777i	−0.123720	+	0.992317i
$10$	−63.8320	+	76.9771i	−0.638320	+	0.769771i
$11$	−27.5699			−0.227851			−0.113925	−	0.993489i	$-0.536342\pi$
$11$	−27.5699			−0.227851			−0.113925	+	0.993489i	$0.536342\pi$
$12$	42.5410	−	137.573i	0.295424	−	0.955366i
$13$	−177.104	−	177.104i	−1.04795	−	1.04795i	−0.998791	−	0.0491611i	$-0.984345\pi$
$13$	−177.104	−	177.104i	−1.04795	−	1.04795i	−0.0491611	−	0.998791i	$-0.515655\pi$
$14$	−240.358	+	67.4949i	−1.22632	+	0.344362i
$15$	116.202	+	192.671i	0.516454	+	0.856315i
$16$	−117.252	+	227.570i	−0.458015	+	0.888945i
$17$	241.784	+	241.784i	0.836621	+	0.836621i	0.988413	−	0.151791i	$-0.0485041\pi$
$17$	241.784	+	241.784i	0.836621	+	0.836621i	−0.151791	+	0.988413i	$0.548504\pi$
$18$	−260.713	−	192.366i	−0.804670	−	0.593722i
$19$	−409.432			−1.13416			−0.567080	−	0.823663i	$-0.691927\pi$
$19$	−409.432			−1.13416			−0.567080	+	0.823663i	$0.691927\pi$
$20$	−143.468	−	373.386i	−0.358671	−	0.933464i
$21$	−34.8151	+	560.644i	−0.0789459	+	1.27130i
$22$	53.9937	−	96.1576i	0.111557	−	0.198673i
$23$	−95.2117	−	95.2117i	−0.179984	−	0.179984i	0.611365	−	0.791349i	$-0.290621\pi$
$23$	−95.2117	−	95.2117i	−0.179984	−	0.179984i	−0.791349	+	0.611365i	$0.790621\pi$
$24$	396.509	+	417.800i	0.688383	+	0.725347i
$25$	584.638	+	220.960i	0.935421	+	0.353537i
$26$	964.543	−	270.853i	1.42684	−	0.400670i
$27$	−601.940	+	411.228i	−0.825707	+	0.564099i
$28$	235.318	−	970.500i	0.300151	−	1.23788i
$29$	1195.81			1.42189			0.710946	−	0.703247i	$-0.248267\pi$
$29$	1195.81			1.42189			0.710946	+	0.703247i	$0.248267\pi$
$30$	−899.566	+	27.9545i	−0.999518	+	0.0310605i
$31$		−	664.535i		−	0.691504i	−0.938326	−	0.345752i	$-0.887624\pi$
$31$		−	664.535i		−	0.691504i	0.938326	−	0.345752i	$-0.112376\pi$
$32$	−564.083	−	854.627i	−0.550862	−	0.834596i
$33$	−164.242	−	185.991i	−0.150819	−	0.170791i
$34$	−1316.80	+	369.770i	−1.13910	+	0.319870i
$35$	887.111	+	1283.63i	0.724172	+	1.04786i
$36$	1181.52	−	532.573i	0.911664	−	0.410936i
$37$	440.813	−	440.813i	0.321997	−	0.321997i	−0.527536	−	0.849533i	$-0.676884\pi$
$37$	440.813	−	440.813i	0.321997	−	0.321997i	0.849533	+	0.527536i	$0.176884\pi$
$38$	801.843	−	1428.01i	0.555293	−	0.988923i
$39$	139.711	−	2249.83i	0.0918547	−	1.47918i
$40$	1583.26	+	230.865i	0.989535	+	0.144291i
$41$			31.0745i			0.0184857i	0.999957	+	0.00924285i	$0.00294213\pi$
$41$			31.0745i			0.0184857i	−0.999957	+	0.00924285i	$0.997058\pi$
$42$	−1887.22	−	1219.41i	−1.06985	−	0.691275i
$43$	1997.60	−	1997.60i	1.08037	−	1.08037i	0.0838912	−	0.996475i	$-0.473265\pi$
$43$	1997.60	−	1997.60i	1.08037	−	1.08037i	0.996475	−	0.0838912i	$-0.0267348\pi$
$44$	229.633	+	376.636i	0.118612	+	0.194543i
$45$	−607.538	+	1931.72i	−0.300019	+	0.953933i
$46$	518.542	−	145.611i	0.245058	−	0.0688144i
$47$	−1221.96	+	1221.96i	−0.553173	+	0.553173i	−0.927355	−	0.374182i	$-0.877923\pi$
$47$	−1221.96	+	1221.96i	−0.553173	+	0.553173i	0.374182	+	0.927355i	$0.377923\pi$
$48$	−2233.73	+	564.701i	−0.969499	+	0.245096i
$49$			1494.49i			0.622443i
$50$	−1915.63	+	1606.35i	−0.766253	+	0.642540i
$51$	−190.734	+	3071.49i	−0.0733312	+	1.18089i
$52$	−944.317	+	3894.55i	−0.349230	+	1.44029i
$53$	578.852	−	578.852i	0.206071	−	0.206071i	−0.596524	−	0.802595i	$-0.703452\pi$
$53$	578.852	−	578.852i	0.206071	−	0.206071i	0.802595	+	0.596524i	$0.203452\pi$
$54$	−255.413	−	2904.79i	−0.0875902	−	0.996157i
$55$	−678.029	−	123.853i	−0.224142	−	0.0409432i
$56$	2924.03	+	2721.39i	0.932407	+	0.867790i
$57$	−2439.11	−	2762.09i	−0.750725	−	0.850136i
$58$	−2341.91	+	4170.72i	−0.696168	+	1.23981i
$59$		−	2432.13i		−	0.698686i	−0.936995	−	0.349343i	$-0.886405\pi$
$59$		−	2432.13i		−	0.698686i	0.936995	−	0.349343i	$-0.113595\pi$
$60$	1664.24	−	3192.23i	0.462288	−	0.886730i
$61$	−915.302			−0.245983			−0.122991	−	0.992408i	$-0.539249\pi$
$61$	−915.302			−0.245983			−0.122991	+	0.992408i	$0.539249\pi$
$62$	2317.75	+	1301.44i	0.602952	+	0.338565i
$63$	−3989.60	+	3105.06i	−1.00519	+	0.782327i
$64$	4085.46	−	293.666i	0.997427	−	0.0716957i
$65$	−3559.92	−	5151.14i	−0.842584	−	1.21920i
$66$	970.351	−	208.589i	0.222762	−	0.0478854i
$67$	−1105.20	−	1105.20i	−0.246203	−	0.246203i	0.573207	−	0.819410i	$-0.305699\pi$
$67$	−1105.20	−	1105.20i	−0.246203	−	0.246203i	−0.819410	+	0.573207i	$0.805699\pi$
$68$	1289.19	−	5316.87i	0.278804	−	1.14984i
$69$	75.1091	−	1209.52i	0.0157759	−	0.254047i
$70$	−6214.36	+	580.136i	−1.26824	+	0.118395i
$71$	7175.87			1.42350			0.711751	−	0.702432i	$-0.247903\pi$
$71$	7175.87			1.42350			0.711751	+	0.702432i	$0.247903\pi$
$72$	−456.424	+	5163.87i	−0.0880448	+	0.996117i
$73$	−2655.36	−	2655.36i	−0.498285	−	0.498285i	0.412618	−	0.910904i	$-0.364614\pi$
$73$	−2655.36	−	2655.36i	−0.498285	−	0.498285i	−0.910904	+	0.412618i	$0.864614\pi$
$74$	674.155	+	2400.76i	0.123111	+	0.438415i
$75$	1992.23	+	5260.39i	0.354174	+	0.935180i
$76$	3410.20	+	5593.29i	0.590409	+	0.968368i
$77$	−1216.75	−	1216.75i	−0.205220	−	0.205220i
$78$	7573.28	+	4893.41i	1.24479	+	0.804309i
$79$	−426.851			−0.0683946			−0.0341973	−	0.999415i	$-0.510887\pi$
$79$	−426.851			−0.0683946			−0.0341973	+	0.999415i	$0.510887\pi$
$80$	−3905.90	+	5069.91i	−0.610297	+	0.792173i
$81$	−6360.15	−	1610.98i	−0.969387	−	0.245539i
$82$	−108.381	−	60.8571i	−0.0161185	−	0.00905073i
$83$	−4152.37	−	4152.37i	−0.602754	−	0.602754i	0.338288	−	0.941043i	$-0.390152\pi$
$83$	−4152.37	−	4152.37i	−0.602754	−	0.602754i	−0.941043	+	0.338288i	$0.890152\pi$
$84$	7949.00	−	4194.06i	1.12656	−	0.594396i
$85$	4860.03	+	7032.37i	0.672668	+	0.973339i
$86$	3055.01	+	10879.3i	0.413063	+	1.47097i
$87$	7123.80	+	8067.13i	0.941180	+	1.06581i
$88$	−1763.34	+	63.2934i	−0.227704	+	0.00817322i
$89$	−4519.29			−0.570545			−0.285273	−	0.958446i	$-0.592084\pi$
$89$	−4519.29			−0.570545			−0.285273	+	0.958446i	$0.592084\pi$
$90$	−5547.56	−	5902.08i	−0.684884	−	0.728652i
$91$		−	15632.3i		−	1.88774i
$92$	−507.668	+	2093.73i	−0.0599797	+	0.247368i
$93$	4483.06	−	3958.83i	0.518332	−	0.457721i
$94$	−1868.79	−	6655.03i	−0.211498	−	0.753173i
$95$	−10069.2	−	1839.30i	−1.11570	−	0.203801i
$96$	2405.04	−	8896.65i	0.260964	−	0.965349i
$97$	12818.4	−	12818.4i	1.36236	−	1.36236i	0.491452	−	0.870905i	$-0.336466\pi$
$97$	12818.4	−	12818.4i	1.36236	−	1.36236i	0.870905	−	0.491452i	$-0.163534\pi$
$98$	−5212.42	−	2926.84i	−0.542735	−	0.304752i
$99$	276.286	−	2216.01i	0.0281896	−	0.226100i
$100$	−1850.95	−	9827.21i	−0.185095	−	0.982721i
$101$			10544.1i			1.03364i	0.856095	+	0.516819i	$0.172884\pi$
$101$			10544.1i			1.03364i	−0.856095	+	0.516819i	$0.827116\pi$
$102$	−10339.1	−	6680.53i	−0.993762	−	0.642111i
$103$	2230.56	−	2230.56i	0.210252	−	0.210252i	−0.594122	−	0.804375i	$-0.702501\pi$
$103$	2230.56	−	2230.56i	0.210252	−	0.210252i	0.804375	+	0.594122i	$0.202501\pi$
$104$	−11733.9	−	10920.8i	−1.08487	−	1.00969i
$105$	−3374.81	+	13631.6i	−0.306105	+	1.23642i
$106$	885.264	+	3152.54i	0.0787882	+	0.280575i
$107$	6222.73	−	6222.73i	0.543517	−	0.543517i	−0.381041	−	0.924558i	$-0.624434\pi$
$107$	6222.73	−	6222.73i	0.543517	−	0.543517i	0.924558	+	0.381041i	$0.124434\pi$
$108$	10631.5	+	4798.01i	0.911477	+	0.411352i
$109$			9928.44i			0.835657i	0.908526	+	0.417828i	$0.137209\pi$
$109$			9928.44i			0.835657i	−0.908526	+	0.417828i	$0.862791\pi$
$110$	1759.84	−	2122.25i	0.145442	−	0.175393i
$111$	5599.85	+	347.742i	0.454496	+	0.0282235i
$112$	−15218.1	+	4868.69i	−1.21318	+	0.388129i
$113$	−3224.03	+	3224.03i	−0.252488	+	0.252488i	−0.821990	−	0.569502i	$-0.807136\pi$
$113$	−3224.03	+	3224.03i	−0.252488	+	0.252488i	0.569502	+	0.821990i	$0.307136\pi$
$114$	14410.4	−	3097.69i	1.10883	−	0.238357i
$115$	−1913.82	−	2769.27i	−0.144713	−	0.209397i
$116$	−9960.04	−	16336.1i	−0.740193	−	1.21404i
$117$	16010.0	−	12460.4i	1.16955	−	0.910248i
$118$	8482.70	+	4763.15i	0.609214	+	0.342082i
$119$			21341.4i			1.50705i
$120$	7874.47	+	12056.2i	0.546838	+	0.837238i
$121$	−13880.9			−0.948084
$122$	1792.55	−	3192.37i	0.120435	−	0.214483i
$123$	−209.633	+	185.120i	−0.0138564	+	0.0122361i
$124$	−9078.28	+	5534.99i	−0.590419	+	0.359976i
$125$	13385.4	+	8060.48i	0.856666	+	0.515871i
$126$	−3016.38	−	19995.8i	−0.189996	−	1.25950i
$127$	−614.330	−	614.330i	−0.0380885	−	0.0380885i	0.687806	−	0.725895i	$-0.258574\pi$
$127$	−614.330	−	614.330i	−0.0380885	−	0.0380885i	−0.725895	+	0.687806i	$0.758574\pi$
$128$	−6976.84	+	14824.3i	−0.425833	+	0.904802i
$129$	25376.4	+	1575.83i	1.52493	+	0.0946958i
$130$	24937.8	−	2328.05i	1.47561	−	0.137754i
$131$	−13571.2			−0.790819			−0.395410	−	0.918505i	$-0.629397\pi$
$131$	−13571.2			−0.790819			−0.395410	+	0.918505i	$0.629397\pi$
$132$	−1172.85	+	3792.87i	−0.0673125	+	0.217681i
$133$	−18069.6	−	18069.6i	−1.02151	−	1.02151i
$134$	6019.16	−	1690.24i	0.335217	−	0.0941322i
$135$	−16650.9	+	7409.25i	−0.913632	+	0.406543i
$136$	16019.3	+	14909.1i	0.866093	+	0.806073i
$137$	14257.7	+	14257.7i	0.759643	+	0.759643i	0.976257	−	0.216615i	$-0.0695015\pi$
$137$	14257.7	+	14257.7i	0.759643	+	0.759643i	−0.216615	+	0.976257i	$0.569501\pi$
$138$	4071.42	+	2630.72i	0.213790	+	0.138139i
$139$	−6329.99			−0.327622			−0.163811	−	0.986492i	$-0.552379\pi$
$139$	−6329.99			−0.327622			−0.163811	+	0.986492i	$0.552379\pi$
$140$	10147.0	−	22810.4i	0.517704	−	1.16380i
$141$	−15523.1	−	963.960i	−0.780801	−	0.0484865i
$142$	−14053.4	+	25027.8i	−0.696957	+	1.24121i
$143$	4882.74	+	4882.74i	0.238776	+	0.238776i
$144$	−17116.5	−	11705.0i	−0.825450	−	0.564476i
$145$	29408.7	+	5371.98i	1.39875	+	0.255504i
$146$	14461.6	−	4060.96i	0.678441	−	0.190512i
$147$	−10082.0	+	8903.09i	−0.466566	+	0.412008i
$148$	−9693.58	−	2350.41i	−0.442549	−	0.107305i
$149$	−19043.5			−0.857776			−0.428888	−	0.903358i	$-0.641094\pi$
$149$	−19043.5			−0.857776			−0.428888	+	0.903358i	$0.641094\pi$
$150$	−22248.7	−	3353.66i	−0.988829	−	0.149052i
$151$			42139.7i			1.84815i	0.382210	+	0.924076i	$0.375163\pi$
$151$			42139.7i			1.84815i	−0.382210	+	0.924076i	$0.624837\pi$
$152$	−26186.8	+	939.950i	−1.13343	+	0.0406834i
$153$	−21857.0	+	17011.0i	−0.933700	+	0.726687i
$154$	6626.66	−	1860.83i	0.279417	−	0.0784630i
$155$	2985.31	−	16343.0i	0.124259	−	0.680248i
$156$	−31898.8	+	16830.5i	−1.31077	+	0.691588i
$157$	−11086.4	+	11086.4i	−0.449770	+	0.449770i	−0.895278	−	0.445508i	$-0.853023\pi$
$157$	−11086.4	+	11086.4i	−0.449770	+	0.449770i	0.445508	+	0.895278i	$0.353023\pi$
$158$	835.957	−	1488.76i	0.0334865	−	0.0596362i
$159$	7353.42	+	456.636i	0.290867	+	0.0180624i
$160$	−10033.3	−	23551.9i	−0.391924	−	0.919998i
$161$		−	8404.00i		−	0.324216i
$162$	18074.6	−	19027.8i	0.688714	−	0.725033i
$163$	22700.3	−	22700.3i	0.854391	−	0.854391i	−0.136279	−	0.990670i	$-0.543515\pi$
$163$	22700.3	−	22700.3i	0.854391	−	0.854391i	0.990670	+	0.136279i	$0.0435145\pi$
$164$	424.512	−	258.823i	0.0157834	−	0.00962309i
$165$	−3203.68	−	5311.92i	−0.117674	−	0.195112i
$166$	22614.7	−	6350.41i	0.820680	−	0.230455i
$167$	20334.0	−	20334.0i	0.729103	−	0.729103i	−0.241338	−	0.970441i	$-0.577586\pi$
$167$	20334.0	−	20334.0i	0.729103	−	0.729103i	0.970441	+	0.241338i	$0.0775863\pi$
$168$	−939.641	+	35938.1i	−0.0332923	+	1.27332i
$169$			34170.6i			1.19641i
$170$	−34045.3	+	3178.27i	−1.17804	+	0.109975i
$171$	4103.04	−	32909.2i	0.140318	−	1.12545i
$172$	−43927.6	−	10651.2i	−1.48484	−	0.360032i
$173$	19171.8	−	19171.8i	0.640575	−	0.640575i	−0.310121	−	0.950697i	$-0.600370\pi$
$173$	19171.8	−	19171.8i	0.640575	−	0.640575i	0.950697	+	0.310121i	$0.100370\pi$
$174$	−42087.8	+	9047.28i	−1.39014	+	0.298827i
$175$	16050.3	+	35553.7i	0.524090	+	1.16094i
$176$	3232.62	−	6274.08i	0.104359	−	0.202547i
$177$	16407.5	−	14488.9i	0.523716	−	0.462475i
$178$	8850.71	−	15762.3i	0.279343	−	0.497483i
$179$			9061.63i			0.282813i	0.989952	+	0.141407i	$0.0451625\pi$
$179$			9061.63i			0.282813i	−0.989952	+	0.141407i	$0.954837\pi$
$180$	31449.6	−	7789.83i	0.970667	−	0.240427i
$181$	12930.8			0.394700			0.197350	−	0.980333i	$-0.436766\pi$
$181$	12930.8			0.394700			0.197350	+	0.980333i	$0.436766\pi$
$182$	54522.0	+	30614.8i	1.64600	+	0.924249i
$183$	−5452.72	−	6174.77i	−0.162821	−	0.184382i
$184$	−6308.21	−	5871.04i	−0.186325	−	0.173412i
$185$	12821.2	−	8860.67i	0.374616	−	0.258895i
$186$	5027.75	+	23389.0i	0.145327	+	0.676060i
$187$	−6665.95	−	6665.95i	−0.190625	−	0.190625i
$188$	26871.1	+	6515.48i	0.760275	+	0.184345i
$189$	−44714.4	−	8416.75i	−1.25177	−	0.235625i
$190$	26134.9	−	31516.9i	0.723957	−	0.873044i
$191$	−54949.6			−1.50625			−0.753126	−	0.657876i	$-0.771455\pi$
$191$	−54949.6			−1.50625			−0.753126	+	0.657876i	$0.771455\pi$
$192$	26319.4	+	25811.7i	0.713959	+	0.700187i
$193$	−35439.0	−	35439.0i	−0.951409	−	0.951409i	0.0474641	−	0.998873i	$-0.484886\pi$
$193$	−35439.0	−	35439.0i	−0.951409	−	0.951409i	−0.998873	+	0.0474641i	$0.984886\pi$
$194$	19603.8	+	69811.7i	0.520878	+	1.85492i
$195$	13542.9	−	54702.6i	0.356158	−	1.43860i
$196$	20416.3	−	12447.7i	0.531454	−	0.324025i
$197$	−35501.5	−	35501.5i	−0.914776	−	0.914776i	0.0818676	−	0.996643i	$-0.473912\pi$
$197$	−35501.5	−	35501.5i	−0.914776	−	0.914776i	−0.996643	+	0.0818676i	$0.973912\pi$
$198$	7187.84	+	5303.51i	0.183345	+	0.135280i
$199$	−32902.7			−0.830855			−0.415428	−	0.909626i	$-0.636368\pi$
$199$	−32902.7			−0.830855			−0.415428	+	0.909626i	$0.636368\pi$
$200$	37900.0	+	12790.2i	0.947500	+	0.319755i
$201$	871.856	−	14039.9i	0.0215801	−	0.347514i
$202$	−36775.6	−	20650.0i	−0.901274	−	0.506077i
$203$	52775.0	+	52775.0i	1.28067	+	1.28067i
$204$	43548.6	−	22977.1i	1.04644	−	0.552122i
$205$	−139.597	+	764.216i	−0.00332176	+	0.0181848i
$206$	3411.30	+	12148.1i	0.0803869	+	0.286269i
$207$	8607.04	−	6698.75i	0.200869	−	0.156334i
$208$	61069.2	−	19537.8i	1.41155	−	0.451594i
$209$	11288.0			0.258419
$210$	−40934.5	−	38467.0i	−0.928219	−	0.872268i
$211$		−	29946.1i		−	0.672629i	−0.941750	−	0.336314i	$-0.890819\pi$
$211$		−	29946.1i		−	0.672629i	0.941750	−	0.336314i	$-0.109181\pi$
$212$	−12729.1	−	3086.44i	−0.283221	−	0.0686729i
$213$	42748.8	+	48409.6i	0.942246	+	1.06702i
$214$	9516.69	+	33890.2i	0.207806	+	0.740026i
$215$	58100.9	−	40153.2i	1.25692	−	0.868646i
$216$	−37555.3	+	27683.6i	−0.804941	+	0.593355i
$217$	29328.1	−	29328.1i	0.622822	−	0.622822i
$218$	−34628.1	−	19444.1i	−0.728645	−	0.409144i
$219$	2094.72	−	33732.3i	0.0436755	−	0.703327i
$220$	3955.41	+	10294.2i	0.0817233	+	0.212690i
$221$		−	85641.6i		−	1.75348i
$222$	−12179.8	+	18850.0i	−0.247134	+	0.382477i
$223$	−45263.8	+	45263.8i	−0.910209	+	0.910209i	−0.996288	−	0.0860789i	$-0.972566\pi$
$223$	−45263.8	+	45263.8i	−0.910209	+	0.910209i	0.0860789	+	0.996288i	$0.472566\pi$
$224$	12822.7	−	62612.2i	0.255554	−	1.24785i
$225$	−23619.1	+	44777.5i	−0.466551	+	0.884495i
$226$	−4930.64	−	17558.7i	−0.0965354	−	0.343776i
$227$	−36492.9	+	36492.9i	−0.708202	+	0.708202i	−0.966157	−	0.257955i	$-0.916951\pi$
$227$	−36492.9	+	36492.9i	−0.708202	+	0.708202i	0.257955	+	0.966157i	$0.416951\pi$
$228$	−17417.7	+	56326.7i	−0.335058	+	1.08354i
$229$		−	8526.73i		−	0.162597i	−0.996690	−	0.0812984i	$-0.974093\pi$
$229$		−	8526.73i		−	0.162597i	0.996690	−	0.0812984i	$-0.0259067\pi$
$230$	13406.7	−	1251.57i	0.253434	−	0.0236591i
$231$	959.850	−	15456.9i	0.0179879	−	0.289667i
$232$	76482.6	−	2745.27i	1.42098	−	0.0510046i
$233$	−50982.8	+	50982.8i	−0.939101	+	0.939101i	−0.998249	−	0.0591485i	$-0.981161\pi$
$233$	−50982.8	+	50982.8i	−0.939101	+	0.939101i	0.0591485	+	0.998249i	$0.481161\pi$
$234$	12104.5	+	80242.1i	0.221063	+	1.46545i
$235$	−35541.2	+	24562.3i	−0.643570	+	0.444767i
$236$	−33225.5	+	20257.5i	−0.596552	+	0.363715i
$237$	−2542.88	−	2879.60i	−0.0452719	−	0.0512668i
$238$	−74433.9	−	41795.6i	−1.31406	−	0.737864i
$239$		−	33467.5i		−	0.585906i	−0.956127	−	0.292953i	$-0.905362\pi$
$239$		−	33467.5i		−	0.585906i	0.956127	−	0.292953i	$-0.0946380\pi$
$240$	−57471.0	+	3853.11i	−0.997760	+	0.0668942i
$241$	−61598.3			−1.06056			−0.530279	−	0.847823i	$-0.677913\pi$
$241$	−61598.3			−1.06056			−0.530279	+	0.847823i	$0.677913\pi$
$242$	27184.8	−	48413.4i	0.464189	−	0.826675i
$243$	−27021.4	−	52503.6i	−0.457609	−	0.889154i
$244$	7623.65	+	12504.0i	0.128051	+	0.210025i
$245$	−6713.72	+	36754.0i	−0.111849	+	0.612311i
$246$	−235.104	−	1093.70i	−0.00388498	−	0.0180729i
$247$	72512.0	+	72512.0i	1.18855	+	1.18855i
$248$	−1525.60	−	42502.9i	−0.0248049	−	0.691058i
$249$	3275.66	−	52749.5i	0.0528324	−	0.850784i
$250$	−54327.5	+	30899.4i	−0.869240	+	0.494390i
$251$	−25803.6			−0.409575			−0.204787	−	0.978806i	$-0.565650\pi$
$251$	−25803.6			−0.409575			−0.204787	+	0.978806i	$0.565650\pi$
$252$	75648.3	+	28640.0i	1.19124	+	0.450995i
$253$	2624.98	+	2624.98i	0.0410095	+	0.0410095i
$254$	3345.76	−	939.521i	0.0518594	−	0.0145626i
$255$	−18488.9	+	74680.4i	−0.284335	+	1.14849i
$256$	−38040.0	−	53365.9i	−0.580445	−	0.814299i
$257$	12479.2	+	12479.2i	0.188938	+	0.188938i	0.795237	−	0.606299i	$-0.207346\pi$
$257$	12479.2	+	12479.2i	0.188938	+	0.188938i	−0.606299	+	0.795237i	$0.707346\pi$
$258$	−55194.0	+	85420.9i	−0.829187	+	1.28329i
$259$	38909.0			0.580031
$260$	−40719.3	+	91536.8i	−0.602356	+	1.35410i
$261$	−11983.6	+	96116.5i	−0.175916	+	1.41097i
$262$	26578.3	−	47333.4i	0.387191	−	0.689549i
$263$	12040.2	+	12040.2i	0.174069	+	0.174069i	0.788764	−	0.614696i	$-0.210721\pi$
$263$	12040.2	+	12040.2i	0.174069	+	0.174069i	−0.614696	+	0.788764i	$0.710721\pi$
$264$	−10931.7	−	11518.7i	−0.156849	−	0.165271i
$265$	16836.1	−	11635.4i	0.239746	−	0.165687i
$266$	98410.4	−	27634.6i	1.39084	−	0.390561i
$267$	−26922.7	−	30487.8i	−0.377656	−	0.427666i
$268$	−5892.94	+	24303.7i	−0.0820470	+	0.338378i
$269$	91931.4			1.27045			0.635227	−	0.772325i	$-0.280906\pi$
$269$	91931.4			1.27045			0.635227	+	0.772325i	$0.280906\pi$
$270$	6767.90	−	72585.2i	0.0928382	−	0.995681i
$271$			94150.3i			1.28199i	0.767547	+	0.640993i	$0.221477\pi$
$271$			94150.3i			1.28199i	−0.767547	+	0.640993i	$0.778523\pi$
$272$	−83372.2	+	26673.1i	−1.12689	+	0.360525i
$273$	105458.	−	93126.4i	1.41500	−	1.24953i
$274$	−77650.5	+	21805.0i	−1.03429	+	0.290439i
$275$	−16118.4	−	6091.86i	−0.213136	−	0.0805535i
$276$	−17148.9	+	9048.13i	−0.225123	+	0.118779i
$277$	−80546.1	+	80546.1i	−1.04975	+	1.04975i	−0.0510521	+	0.998696i	$0.516257\pi$
$277$	−80546.1	+	80546.1i	−1.04975	+	1.04975i	−0.998696	+	0.0510521i	$0.983743\pi$
$278$	12396.8	−	22077.6i	0.160406	−	0.285668i
$279$	53413.8	+	6659.50i	0.686191	+	0.0855527i
$280$	59685.4	+	80063.0i	0.761294	+	1.02121i
$281$			83062.4i			1.05194i	0.850502	+	0.525971i	$0.176298\pi$
$281$			83062.4i			1.05194i	−0.850502	+	0.525971i	$0.823702\pi$
$282$	33763.0	−	52253.2i	0.424563	−	0.657074i
$283$	38555.6	−	38555.6i	0.481410	−	0.481410i	−0.424172	−	0.905582i	$-0.639435\pi$
$283$	38555.6	−	38555.6i	0.481410	−	0.481410i	0.905582	+	0.424172i	$0.139435\pi$
$284$	−59768.6	−	98030.3i	−0.741032	−	1.21541i
$285$	−47576.9	−	78885.6i	−0.585742	−	0.971198i
$286$	−26592.4	+	7467.39i	−0.325106	+	0.0912928i
$287$	−1371.42	+	1371.42i	−0.0166497	+	0.0166497i
$288$	74345.8	−	36775.2i	0.896337	−	0.443374i
$289$			33397.6i			0.399871i
$290$	−76331.0	+	92050.0i	−0.907622	+	1.09453i
$291$	162838.	+	10112.0i	1.92296	+	0.119413i
$292$	−14158.4	+	58392.0i	−0.166053	+	0.684838i
$293$	−27279.7	+	27279.7i	−0.317764	+	0.317764i	−0.847908	−	0.530144i	$-0.822138\pi$
$293$	−27279.7	+	27279.7i	−0.317764	+	0.317764i	0.530144	+	0.847908i	$0.322138\pi$
$294$	−11307.0	−	52599.9i	−0.130814	−	0.608542i
$295$	10925.9	−	59813.4i	0.125549	−	0.687313i
$296$	27181.9	−	29205.9i	0.310239	−	0.333340i
$297$	16595.4	−	11337.5i	0.188138	−	0.128530i
$298$	37295.3	−	66419.3i	0.419973	−	0.747932i
$299$			33724.7i			0.377230i
$300$	55269.2	−	71030.4i	0.614103	−	0.789226i
$301$	176321.			1.94612
$302$	−146974.	−	82527.6i	−1.61148	−	0.904868i
$303$	−71132.5	+	62814.6i	−0.774787	+	0.684187i
$304$	48006.6	−	93174.3i	0.519462	−	1.00821i
$305$	−22510.1	−	4111.84i	−0.241979	−	0.0442015i
$306$	−16525.2	−	109547.i	−0.176483	−	1.16992i
$307$	−104172.	−	104172.i	−1.10528	−	1.10528i	−0.993762	−	0.111521i	$-0.964428\pi$
$307$	−104172.	−	104172.i	−1.10528	−	1.10528i	−0.111521	−	0.993762i	$-0.535572\pi$
$308$	−6487.70	+	26756.6i	−0.0683895	+	0.282052i
$309$	28335.9	+	1759.61i	0.296770	+	0.0184289i
$310$	51154.0	+	42418.6i	0.532299	+	0.441401i
$311$	−56861.9			−0.587896			−0.293948	−	0.955821i	$-0.594969\pi$
$311$	−56861.9			−0.587896			−0.293948	+	0.955821i	$0.594969\pi$
$312$	3770.72	−	144217.i	0.0387360	−	1.48152i
$313$	52709.9	+	52709.9i	0.538026	+	0.538026i	0.922949	−	0.384923i	$-0.125772\pi$
$313$	52709.9	+	52709.9i	0.538026	+	0.538026i	−0.384923	+	0.922949i	$0.625772\pi$
$314$	−16954.9	−	60378.6i	−0.171963	−	0.612384i
$315$	−112065.	+	58440.2i	−1.12941	+	0.588967i
$316$	3555.29	+	5831.26i	0.0356042	+	0.0583967i
$317$	118214.	+	118214.i	1.17639	+	1.17639i	0.980658	+	0.195731i	$0.0627079\pi$
$317$	118214.	+	118214.i	1.17639	+	1.17639i	0.195731	+	0.980658i	$0.437292\pi$
$318$	−15993.8	+	24752.8i	−0.158160	+	0.244776i
$319$	−32968.4			−0.323979
$320$	101793.	+	11131.1i	0.994074	+	0.108702i
$321$	79050.2	+	4908.89i	0.767172	+	0.0476402i
$322$	29311.2	+	16458.6i	0.282698	+	0.158738i
$323$	−98993.9	−	98993.9i	−0.948863	−	0.948863i
$324$	30966.6	+	100305.i	0.294988	+	0.955501i
$325$	−64408.7	−	142675.i	−0.609787	−	1.35077i
$326$	34716.6	+	123630.i	0.326664	+	1.16330i
$327$	−66978.8	+	59146.6i	−0.626386	+	0.553139i
$328$	71.3389	+	1987.49i	0.000663100	+	0.0184738i
$329$	−107858.			−0.996462
$330$	24801.0	−	770.703i	0.227741	−	0.00707716i
$331$		−	85478.0i		−	0.780187i	−0.920775	−	0.390093i	$-0.872443\pi$
$331$		−	85478.0i		−	0.780187i	0.920775	−	0.390093i	$-0.127557\pi$
$332$	−22140.4	+	91311.6i	−0.200868	+	0.828419i
$333$	31014.0	+	39849.1i	0.279685	+	0.359360i
$334$	31097.6	+	110743.i	0.278762	+	0.992710i
$335$	−22215.4	−	32145.3i	−0.197954	−	0.286436i
$336$	−123504.	−	73659.4i	−1.09396	−	0.652454i
$337$	−84582.0	+	84582.0i	−0.744763	+	0.744763i	−0.973491	−	0.228727i	$-0.926544\pi$
$337$	−84582.0	+	84582.0i	−0.744763	+	0.744763i	0.228727	+	0.973491i	$0.426544\pi$
$338$	−119179.	−	66920.6i	−1.04320	−	0.585769i
$339$	−40956.3	−	2543.32i	−0.356386	−	0.0221310i
$340$	55590.3	−	124967.i	0.480885	−	1.08103i
$341$			18321.2i			0.157559i
$342$	106744.	+	78760.8i	0.912625	+	0.673376i
$343$	40007.4	−	40007.4i	0.340058	−	0.340058i
$344$	123178.	−	132350.i	1.04092	−	1.11842i
$345$	7280.71	−	29408.3i	0.0611696	−	0.247077i
$346$	29320.2	+	104413.i	0.244915	+	0.872176i
$347$	112446.	−	112446.i	0.933865	−	0.933865i	−0.0640802	−	0.997945i	$-0.520411\pi$
$347$	112446.	−	112446.i	0.933865	−	0.933865i	0.997945	+	0.0640802i	$0.0204114\pi$
$348$	50871.0	−	164511.i	0.420061	−	1.35843i
$349$		−	181396.i		−	1.48928i	−0.667467	−	0.744640i	$-0.732621\pi$
$349$		−	181396.i		−	1.48928i	0.667467	−	0.744640i	$-0.267379\pi$
$350$	−155436.	−	13649.6i	−1.26887	−	0.111426i
$351$	179436.	+	33775.9i	1.45645	+	0.274153i
$352$	15551.7	+	23562.0i	0.125514	+	0.190163i
$353$	25988.0	−	25988.0i	0.208556	−	0.208556i	−0.595097	−	0.803654i	$-0.702886\pi$
$353$	25988.0	−	25988.0i	0.208556	−	0.208556i	0.803654	+	0.595097i	$0.202886\pi$
$354$	18401.0	+	85601.1i	0.146837	+	0.683082i
$355$	176477.	+	32236.4i	1.40033	+	0.255794i
$356$	37641.7	+	61738.5i	0.297009	+	0.487143i
$357$	−143972.	+	127137.i	−1.12965	+	0.997551i
$358$	−31604.9	−	17746.6i	−0.246597	−	0.138468i
$359$			120682.i			0.936382i	0.883627	+	0.468191i	$0.155094\pi$
$359$			120682.i			0.936382i	−0.883627	+	0.468191i	$0.844906\pi$
$360$	−34422.7	+	124945.i	−0.265607	+	0.964081i
$361$	37313.5			0.286320
$362$	−25324.0	+	45099.6i	−0.193248	+	0.344156i
$363$	−82692.6	−	93642.7i	−0.627557	−	0.710658i
$364$	−213555.	+	130203.i	−1.61178	+	0.982697i
$365$	−53374.8	−	77232.3i	−0.400636	−	0.579713i
$366$	32215.0	−	6925.01i	0.240489	−	0.0516961i
$367$	−87500.4	−	87500.4i	−0.649647	−	0.649647i	0.303260	−	0.952908i	$-0.401925\pi$
$367$	−87500.4	−	87500.4i	−0.649647	−	0.649647i	−0.952908	+	0.303260i	$0.901925\pi$
$368$	32831.0	−	10503.6i	0.242431	−	0.0775606i
$369$	−2497.69	−	311.407i	−0.0183437	−	0.00228705i
$370$	5794.54	+	62070.5i	0.0423268	+	0.453401i
$371$	51093.2			0.371206
$372$	−91421.9	−	28270.0i	−0.660639	−	0.204287i
$373$	79394.6	+	79394.6i	0.570655	+	0.570655i	0.932311	−	0.361657i	$-0.117789\pi$
$373$	79394.6	+	79394.6i	0.570655	+	0.570655i	−0.361657	+	0.932311i	$0.617789\pi$
$374$	36304.1	−	10194.5i	0.259545	−	0.0728826i
$375$	25363.6	+	138319.i	0.180363	+	0.983600i
$376$	−75349.7	+	80960.3i	−0.532974	+	0.572660i
$377$	−211783.	−	211783.i	−1.49007	−	1.49007i
$378$	116926.	−	139470.i	0.818326	−	0.976107i
$379$	2513.77			0.0175004			0.00875019	−	0.999962i	$-0.497215\pi$
$379$	2513.77			0.0175004			0.00875019	+	0.999962i	$0.497215\pi$
$380$	58740.5	+	152876.i	0.406790	+	1.05870i
$381$	484.623	−	7804.11i	0.00333852	−	0.0537617i
$382$	107615.	−	191652.i	0.737472	−	1.31337i
$383$	136150.	+	136150.i	0.928151	+	0.928151i	0.997586	−	0.0694352i	$-0.0221197\pi$
$383$	136150.	+	136150.i	0.928151	+	0.928151i	−0.0694352	+	0.997586i	$0.522120\pi$
$384$	−141570.	+	41245.7i	−0.960083	+	0.279715i
$385$	−24457.6	−	35389.6i	−0.165003	−	0.238756i
$386$	193008.	−	54198.4i	1.29539	−	0.363758i
$387$	140544.	+	180581.i	0.938403	+	1.20573i
$388$	−281880.	−	68347.7i	−1.87241	−	0.454005i
$389$	22219.4			0.146836			0.0734182	−	0.997301i	$-0.476609\pi$
$389$	22219.4			0.146836			0.0734182	+	0.997301i	$0.476609\pi$
$390$	164267.	+	154366.i	1.08000	+	1.01490i
$391$		−	46041.2i		−	0.301157i
$392$	3430.95	+	95585.5i	0.0223276	+	0.622042i
$393$	−80847.9	−	91553.8i	−0.523460	−	0.592777i
$394$	193348.	−	54294.0i	1.24551	−	0.349752i
$395$	−10497.6	−	1917.56i	−0.0672814	−	0.0122901i
$396$	−32574.3	+	14683.0i	−0.207723	+	0.0936319i
$397$	−80205.4	+	80205.4i	−0.508888	+	0.508888i	−0.914185	−	0.405297i	$-0.867168\pi$
$397$	−80205.4	+	80205.4i	−0.508888	+	0.508888i	0.405297	+	0.914185i	$0.367168\pi$
$398$	64437.6	−	114757.i	0.406793	−	0.724459i
$399$	14254.4	−	229546.i	0.0895373	−	1.44186i
$400$	−118834.	+	107138.i	−0.742711	+	0.669612i
$401$		−	129720.i		−	0.806708i	−0.915044	−	0.403354i	$-0.867844\pi$
$401$		−	129720.i		−	0.806708i	0.915044	−	0.403354i	$-0.132156\pi$
$402$	47260.5	+	30537.0i	0.292447	+	0.188962i
$403$	−117692.	+	117692.i	−0.724662	+	0.724662i
$404$	144045.	−	87823.4i	0.882540	−	0.538081i
$405$	−149178.	−	68190.8i	−0.909486	−	0.415734i
$406$	−287423.	+	80711.1i	−1.74369	+	0.489645i
$407$	−12153.2	+	12153.2i	−0.0733671	+	0.0733671i
$408$	−5147.81	+	196886.i	−0.0309245	+	1.18276i
$409$			85778.9i			0.512783i	0.966573	+	0.256392i	$0.0825337\pi$
$409$			85778.9i			0.512783i	−0.966573	+	0.256392i	$0.917466\pi$
$410$	−2392.02	−	1983.55i	−0.0142298	−	0.0117998i
$411$	−11247.4	+	181122.i	−0.0665839	+	1.07223i
$412$	−49050.6	−	11893.4i	−0.288968	−	0.0700665i
$413$	107338.	−	107338.i	0.629291	−	0.629291i
$414$	6507.44	+	43138.4i	0.0379673	+	0.251689i
$415$	−83465.8	−	120773.i	−0.484632	−	0.701254i
$416$	−51456.5	+	251259.i	−0.297340	+	1.45189i
$417$	−37709.6	−	42703.1i	−0.216860	−	0.245577i
$418$	−22106.7	+	39370.0i	−0.126524	+	0.225327i
$419$			17428.4i			0.0992725i	0.998767	+	0.0496363i	$0.0158062\pi$
$419$			17428.4i			0.0992725i	−0.998767	+	0.0496363i	$0.984194\pi$
$420$	214331.	−	67435.2i	1.21503	−	0.382286i
$421$	150269.			0.847822			0.423911	−	0.905704i	$-0.360657\pi$
$421$	150269.			0.847822			0.423911	+	0.905704i	$0.360657\pi$
$422$	104445.	+	58647.3i	0.586494	+	0.329324i
$423$	−85972.6	−	110464.i	−0.480485	−	0.617361i
$424$	35693.8	−	38351.6i	0.198546	−	0.213330i
$425$	87931.3	+	194780.i	0.486817	+	1.07837i
$426$	−252562.	+	54291.3i	−1.39171	+	0.299165i
$427$	−40395.2	−	40395.2i	−0.221551	−	0.221551i
$428$	−136839.	−	33179.6i	−0.747004	−	0.181127i
$429$	−3851.82	+	62027.6i	−0.0209291	+	0.337032i
$430$	26258.6	+	281280.i	0.142015	+	1.52125i
$431$	−187722.			−1.01056			−0.505278	−	0.862957i	$-0.668610\pi$
$431$	−187722.			−1.01056			−0.505278	+	0.862957i	$0.668610\pi$
$432$	−23004.6	−	185201.i	−0.123267	−	0.992374i
$433$	−30192.1	−	30192.1i	−0.161034	−	0.161034i	0.621991	−	0.783025i	$-0.286324\pi$
$433$	−30192.1	−	30192.1i	−0.161034	−	0.161034i	−0.783025	+	0.621991i	$0.786324\pi$
$434$	44852.7	+	159727.i	0.238127	+	0.848004i
$435$	138956.	+	230398.i	0.734341	+	1.21759i
$436$	135633.	−	82695.1i	0.713500	−	0.435018i
$437$	38982.7	+	38982.7i	0.204131	+	0.204131i
$438$	113548.	+	73368.2i	0.591877	+	0.382437i
$439$	65424.3			0.339477			0.169738	−	0.985489i	$-0.445708\pi$
$439$	65424.3			0.339477			0.169738	+	0.985489i	$0.445708\pi$
$440$	−43650.3	−	6364.92i	−0.225466	−	0.0328767i
$441$	−120123.	−	14976.7i	−0.617661	−	0.0770085i
$442$	298698.	+	167723.i	1.52893	+	0.858516i
$443$	140982.	+	140982.i	0.718383	+	0.718383i	0.968274	−	0.249891i	$-0.0803947\pi$
$443$	140982.	+	140982.i	0.718383	+	0.718383i	−0.249891	+	0.968274i	$0.580395\pi$
$444$	−41891.3	−	79396.6i	−0.212499	−	0.402750i
$445$	−111143.	−	20302.1i	−0.561258	−	0.102523i
$446$	−69223.9	−	246516.i	−0.348006	−	1.23930i
$447$	−113448.	−	128470.i	−0.567780	−	0.642966i
$448$	193265.	+	167344.i	0.962935	+	0.833786i
$449$	−150659.			−0.747313			−0.373657	−	0.927567i	$-0.621896\pi$
$449$	−150659.			−0.747313			−0.373657	+	0.927567i	$0.621896\pi$
$450$	−109917.	−	170072.i	−0.542802	−	0.839860i
$451$		−	856.720i		−	0.00421198i
$452$	70897.0	+	17190.5i	0.347017	+	0.0841417i
$453$	−284281.	+	251039.i	−1.38532	+	1.22333i
$454$	−55810.2	−	198748.i	−0.270771	−	0.964252i
$455$	70225.6	−	384447.i	0.339213	−	1.85701i
$456$	−162343.	−	171061.i	−0.780737	−	0.822660i
$457$	156233.	−	156233.i	0.748069	−	0.748069i	−0.226047	−	0.974116i	$-0.572580\pi$
$457$	156233.	−	156233.i	0.748069	−	0.748069i	0.974116	+	0.226047i	$0.0725804\pi$
$458$	29739.3	+	16699.0i	0.141775	+	0.0796085i
$459$	−244968.	−	46111.1i	−1.16274	−	0.218867i
$460$	−21890.8	+	49210.5i	−0.103454	+	0.232564i
$461$		−	163653.i		−	0.770055i	−0.922905	−	0.385027i	$-0.874192\pi$
$461$		−	163653.i		−	0.770055i	0.922905	−	0.385027i	$-0.125808\pi$
$462$	52030.4	+	33619.0i	0.243766	+	0.157507i
$463$	204261.	−	204261.i	0.952847	−	0.952847i	−0.0460899	−	0.998937i	$-0.514676\pi$
$463$	204261.	−	204261.i	0.952847	−	0.952847i	0.998937	+	0.0460899i	$0.0146761\pi$
$464$	−140211.	+	272130.i	−0.651247	+	1.26398i
$465$	128037.	−	77220.4i	0.592145	−	0.357130i
$466$	−77970.3	−	277663.i	−0.359052	−	1.27863i
$467$	6092.02	−	6092.02i	0.0279336	−	0.0279336i	−0.693002	−	0.720936i	$-0.743712\pi$
$467$	6092.02	−	6092.02i	0.0279336	−	0.0279336i	0.720936	+	0.693002i	$0.243712\pi$
$468$	−303572.	−	114931.i	−1.38602	−	0.524739i
$469$		−	97552.5i		−	0.443499i
$470$	−16062.8	−	172063.i	−0.0727152	−	0.778918i
$471$	−140835.	−	8745.65i	−0.634848	−	0.0394230i
$472$	−5583.53	−	155556.i	−0.0250625	−	0.698236i
$473$	−55073.6	+	55073.6i	−0.246162	+	0.246162i
$474$	15023.4	−	3229.47i	0.0668672	−	0.0143739i
$475$	−239369.	−	90468.2i	−1.06092	−	0.400967i
$476$	291547.	−	177755.i	1.28675	−	0.784526i
$477$	40725.9	+	52327.6i	0.178992	+	0.229982i
$478$	116727.	+	65543.8i	0.510877	+	0.286864i
$479$			188874.i			0.823192i	0.911366	+	0.411596i	$0.135029\pi$
$479$			188874.i			0.823192i	−0.911366	+	0.411596i	$0.864971\pi$
$480$	99114.1	−	207992.i	0.430183	−	0.902742i
$481$	−156140.			−0.674874
$482$	120636.	−	214841.i	0.519257	−	0.924746i
$483$	56694.7	−	50065.1i	0.243023	−	0.214605i
$484$	115616.	+	189628.i	0.493544	+	0.809492i
$485$	372829.	−	257660.i	1.58499	−	1.09537i
$486$	236040.	+	8580.30i	0.999340	+	0.0363270i
$487$	107163.	+	107163.i	0.451843	+	0.451843i	0.895966	−	0.444123i	$-0.146485\pi$
$487$	107163.	+	107163.i	0.451843	+	0.451843i	−0.444123	+	0.895966i	$0.646485\pi$
$488$	−58541.6	+	2101.30i	−0.245825	+	0.00882364i
$489$	288372.	+	17907.5i	1.20597	+	0.0748887i
$490$	−115041.	−	95396.0i	−0.479138	−	0.397318i
$491$	−276758.			−1.14799			−0.573995	−	0.818859i	$-0.694607\pi$
$491$	−276758.			−1.14799			−0.573995	+	0.818859i	$0.694607\pi$
$492$	4275.00	+	1321.94i	0.0176606	+	0.00546112i
$493$	289127.	+	289127.i	1.18958	+	1.18958i
$494$	−394915.	+	110896.i	−1.61826	+	0.454424i
$495$	16749.8	−	53257.2i	0.0683594	−	0.217354i
$496$	151228.	+	77917.9i	0.614708	+	0.316719i
$497$	316694.	+	316694.i	1.28212	+	1.28212i
$498$	177563.	+	114731.i	0.715968	+	0.462617i
$499$	457942.			1.83912			0.919559	−	0.392951i	$-0.128546\pi$
$499$	457942.			1.83912			0.919559	+	0.392951i	$0.128546\pi$
$500$	−1373.51	−	249996.i	−0.00549404	−	0.999985i
$501$	258311.	+	16040.7i	1.02912	+	0.0639070i
$502$	50534.6	−	89997.2i	0.200531	−	0.357126i
$503$	194867.	+	194867.i	0.770196	+	0.770196i	0.978141	−	0.207945i	$-0.0666774\pi$
$503$	194867.	+	194867.i	0.770196	+	0.770196i	−0.207945	+	0.978141i	$0.566677\pi$
$504$	−248042.	+	207755.i	−0.976481	+	0.817881i
$505$	−47367.8	+	259313.i	−0.185738	+	1.01681i
$506$	−14296.2	+	4014.49i	−0.0558365	+	0.0156794i
$507$	−230520.	+	203564.i	−0.896794	+	0.791927i
$508$	−3275.60	+	13509.2i	−0.0126930	+	0.0523484i
$509$	−104384.			−0.402901			−0.201451	−	0.979499i	$-0.564566\pi$
$509$	−104384.			−0.402901			−0.201451	+	0.979499i	$0.564566\pi$
$510$	−224259.	−	210741.i	−0.862204	−	0.810232i
$511$		−	234380.i		−	0.897590i
$512$	260627.	−	28161.7i	0.994213	−	0.107428i
$513$	246454.	−	168370.i	0.936484	−	0.639779i
$514$	−67964.0	+	19084.9i	−0.257248	+	0.0722377i
$515$	64876.9	−	44836.0i	0.244611	−	0.169049i
$516$	−189835.	−	359795.i	−0.712980	−	1.35131i
$517$	33689.3	−	33689.3i	0.126041	−	0.126041i
$518$	−76200.6	+	135706.i	−0.283987	+	0.505754i
$519$	243548.	+	15123.9i	0.904169	+	0.0561475i
$520$	−239514.	−	321288.i	−0.885776	−	1.18820i
$521$			404696.i			1.49092i	0.666552	+	0.745459i	$0.267770\pi$
$521$			404696.i			1.49092i	−0.666552	+	0.745459i	$0.732230\pi$
$522$	−311763.	−	230033.i	−1.14415	−	0.844209i
$523$	−381093.	+	381093.i	−1.39325	+	1.39325i	−0.575309	+	0.817936i	$0.695118\pi$
$523$	−381093.	+	381093.i	−1.39325	+	1.39325i	−0.817936	+	0.575309i	$0.804882\pi$
$524$	113036.	+	185398.i	0.411676	+	0.675217i
$525$	−144234.	+	320081.i	−0.523300	+	1.16129i
$526$	−65573.1	+	18413.5i	−0.237003	+	0.0665527i
$527$	160674.	−	160674.i	0.578527	−	0.578527i
$528$	61583.6	−	15568.8i	0.220901	−	0.0558453i
$529$		−	261710.i		−	0.935211i
$530$	7609.07	+	81507.6i	0.0270882	+	0.290166i
$531$	195489.	+	24373.1i	0.693318	+	0.0864413i
$532$	−96346.8	+	397353.i	−0.340419	+	1.40396i
$533$	5503.41	−	5503.41i	0.0193721	−	0.0193721i
$534$	159061.	−	34192.1i	0.557803	−	0.119907i
$535$	180991.	−	125081.i	0.632337	−	0.437004i
$536$	−73224.8	−	68150.3i	−0.254876	−	0.237213i
$537$	−61131.2	+	53982.8i	−0.211989	+	0.187200i
$538$	−180041.	+	320636.i	−0.622024	+	1.10776i
$539$		−	41202.8i		−	0.141824i
$540$	239906.	+	165758.i	0.822723	+	0.568442i
$541$	−441932.			−1.50994			−0.754972	−	0.655757i	$-0.772350\pi$
$541$	−441932.			−1.50994			−0.754972	+	0.655757i	$0.772350\pi$
$542$	−328375.	−	184387.i	−1.11782	−	0.627669i
$543$	77032.5	+	87233.1i	0.261261	+	0.295857i
$544$	70248.8	−	343021.i	0.237378	−	1.15910i
$545$	−44601.8	+	244171.i	−0.150162	+	0.822055i
$546$	118271.	+	550196.i	0.396729	+	1.84558i
$547$	321011.	+	321011.i	1.07287	+	1.07287i	0.997128	+	0.0757379i	$0.0241312\pi$
$547$	321011.	+	321011.i	1.07287	+	1.07287i	0.0757379	+	0.997128i	$0.475869\pi$
$548$	76022.2	−	313531.i	0.253151	−	1.04404i
$549$	9172.52	−	73569.9i	0.0304329	−	0.244093i
$550$	52813.8	−	44286.9i	0.174591	−	0.146403i
$551$	−489603.			−1.61265
$552$	2027.15	−	77531.7i	0.00665285	−	0.254449i
$553$	−18838.3	−	18838.3i	−0.0616016	−	0.0616016i
$554$	−123183.	−	438670.i	−0.401356	−	1.42928i
$555$	136155.	+	33708.4i	0.442027	+	0.109434i
$556$	52723.2	+	86474.7i	0.170550	+	0.279730i
$557$	−36402.7	−	36402.7i	−0.117334	−	0.117334i	0.646002	−	0.763336i	$-0.276440\pi$
$557$	−36402.7	−	36402.7i	−0.117334	−	0.117334i	−0.763336	+	0.646002i	$0.776440\pi$
$558$	−127834.	+	173253.i	−0.410561	+	0.556432i
$559$	−707564.			−2.26434
$560$	−396131.	+	51371.4i	−1.26317	+	0.163812i
$561$	5258.53	−	84680.6i	0.0167086	−	0.269066i
$562$	−289703.	−	162672.i	−0.917234	−	0.515038i
$563$	−56743.6	−	56743.6i	−0.179019	−	0.179019i	0.611909	−	0.790928i	$-0.290402\pi$
$563$	−56743.6	−	56743.6i	−0.179019	−	0.179019i	−0.790928	+	0.611909i	$0.790402\pi$
$564$	116125.	+	220092.i	0.365062	+	0.691903i
$565$	−93772.1	+	64805.3i	−0.293749	+	0.203008i
$566$	58964.8	+	209982.i	0.184060	+	0.655463i
$567$	−209596.	−	351792.i	−0.651954	−	1.09426i
$568$	458960.	−	16473.9i	1.42259	−	0.0510624i
$569$	−50610.4			−0.156320			−0.0781602	−	0.996941i	$-0.524905\pi$
$569$	−50610.4			−0.156320			−0.0781602	+	0.996941i	$0.524905\pi$
$570$	368311.	−	11445.5i	1.13361	−	0.0352276i
$571$			488181.i			1.49730i	0.662965	+	0.748650i	$0.269298\pi$
$571$			488181.i			1.49730i	−0.662965	+	0.748650i	$0.730702\pi$
$572$	26034.7	−	107373.i	0.0795722	−	0.328172i
$573$	−327351.	−	370699.i	−0.997021	−	1.12905i
$574$	−2097.37	−	7469.01i	−0.00636577	−	0.0226694i
$575$	−34626.3	−	76702.4i	−0.104730	−	0.231992i
$576$	−17337.4	+	331323.i	−0.0522565	+	0.998634i
$577$	266940.	−	266940.i	0.801792	−	0.801792i	−0.181583	−	0.983376i	$-0.558122\pi$
$577$	266940.	−	266940.i	0.801792	−	0.801792i	0.983376	+	0.181583i	$0.0581222\pi$
$578$	−116483.	−	65406.8i	−0.348665	−	0.195780i
$579$	27956.6	−	450198.i	0.0833925	−	1.34291i
$580$	−171561.	−	446499.i	−0.509991	−	1.32728i
$581$		−	366515.i		−	1.08578i
$582$	−354175.	+	548139.i	−1.04562	+	1.61825i
$583$	−15958.9	+	15958.9i	−0.0469533	+	0.0469533i
$584$	−175930.	−	163738.i	−0.515839	−	0.480091i
$585$	449712.	−	234517.i	1.31408	−	0.685271i
$586$	−41720.0	−	148571.i	−0.121492	−	0.432651i
$587$	−93565.0	+	93565.0i	−0.271542	+	0.271542i	−0.829721	−	0.558179i	$-0.811500\pi$
$587$	−93565.0	+	93565.0i	−0.271542	+	0.271542i	0.558179	+	0.829721i	$0.311500\pi$
$588$	205600.	+	63576.9i	0.594661	+	0.183884i
$589$			272082.i			0.784276i
$590$	187218.	+	155247.i	0.537828	+	0.445985i
$591$	28005.9	−	450992.i	0.0801815	−	1.29120i
$592$	48629.7	+	152002.i	0.138758	+	0.433716i
$593$	−433039.	+	433039.i	−1.23145	+	1.23145i	−0.268044	+	0.963407i	$0.586377\pi$
$593$	−433039.	+	433039.i	−1.23145	+	1.23145i	−0.963407	+	0.268044i	$0.913623\pi$
$594$	7041.71	+	80084.9i	0.0199575	+	0.226975i
$595$	−95872.6	+	524850.i	−0.270807	+	1.48252i
$596$	158615.	+	260155.i	0.446532	+	0.732386i
$597$	−196011.	−	221967.i	−0.549961	−	0.622787i
$598$	−117624.	−	66047.4i	−0.328923	−	0.184694i
$599$			581521.i			1.62074i	0.585922	+	0.810368i	$0.300733\pi$
$599$			581521.i			1.62074i	−0.585922	+	0.810368i	$0.699267\pi$
$600$	139497.	+	331874.i	0.387491	+	0.921873i
$601$	12808.0			0.0354595			0.0177298	−	0.999843i	$-0.494356\pi$
$601$	12808.0			0.0354595			0.0177298	+	0.999843i	$0.494356\pi$
$602$	−345312.	+	614967.i	−0.952837	+	1.69691i
$603$	99909.4	−	77758.2i	0.274771	−	0.213851i
$604$	575675.	−	350986.i	1.57799	−	0.962091i
$605$	−341374.	−	62357.6i	−0.932652	−	0.170364i
$606$	−79775.0	−	371112.i	−0.217231	−	1.01055i
$607$	98617.1	+	98617.1i	0.267655	+	0.267655i	0.828154	−	0.560500i	$-0.189391\pi$
$607$	98617.1	+	98617.1i	0.267655	+	0.267655i	−0.560500	+	0.828154i	$0.689391\pi$
$608$	230953.	+	349911.i	0.624766	+	0.946566i
$609$	−41632.3	+	670425.i	−0.112252	+	1.80765i
$610$	58425.6	−	70457.3i	0.157016	−	0.189350i
$611$	432827.			1.15940
$612$	414439.	+	156904.i	1.10652	+	0.418920i
$613$	−382161.	−	382161.i	−1.01701	−	1.01701i	−0.999853	−	0.0171573i	$-0.994538\pi$
$613$	−382161.	−	382161.i	−1.01701	−	1.01701i	−0.0171573	−	0.999853i	$-0.505462\pi$
$614$	567341.	−	159314.i	1.50490	−	0.422589i
$615$	−5987.14	+	3610.92i	−0.0158296	+	0.00954701i
$616$	−80615.2	−	75028.5i	−0.212449	−	0.197727i
$617$	−93393.5	−	93393.5i	−0.245328	−	0.245328i	0.573722	−	0.819050i	$-0.305499\pi$
$617$	−93393.5	−	93393.5i	−0.245328	−	0.245328i	−0.819050	+	0.573722i	$0.805499\pi$
$618$	−61630.9	+	95383.0i	−0.161370	+	0.249743i
$619$	−240580.			−0.627883			−0.313941	−	0.949442i	$-0.601650\pi$
$619$	−240580.			−0.627883			−0.313941	+	0.949442i	$0.601650\pi$
$620$	−248128.	+	95339.6i	−0.645494	+	0.248022i
$621$	96465.5	+	18158.0i	0.250143	+	0.0470853i
$622$	111360.	−	198321.i	0.287838	−	0.512612i
$623$	−199451.	−	199451.i	−0.513878	−	0.513878i
$624$	495612.	+	295591.i	1.27284	+	0.759139i
$625$	292978.	+	258364.i	0.750024	+	0.661411i
$626$	−287069.	+	80611.5i	−0.732549	+	0.205707i
$627$	67245.9	+	76150.6i	0.171053	+	0.193704i
$628$	243792.	+	59112.5i	0.618159	+	0.149886i
$629$	213163.			0.538778
$630$	15646.0	−	505310.i	0.0394205	−	1.27314i
$631$		−	206216.i		−	0.517921i	−0.965888	−	0.258960i	$-0.916620\pi$
$631$		−	206216.i		−	0.517921i	0.965888	−	0.258960i	$-0.0833799\pi$
$632$	−27300.9	+	979.939i	−0.0683506	+	0.00245338i
$633$	202021.	−	178398.i	0.504185	−	0.445228i
$634$	−643818.	+	180790.i	−1.60171	+	0.449776i
$635$	−12348.5	−	17868.0i	−0.0306243	−	0.0443128i
$636$	−55009.3	−	104259.i	−0.135995	−	0.257751i
$637$	264679.	−	264679.i	0.652290	−	0.652290i
$638$	64566.3	−	114986.i	0.158622	−	0.282491i
$639$	−71911.6	+	576780.i	−0.176115	+	1.41256i
$640$	−238177.	+	333232.i	−0.581488	+	0.813555i
$641$		−	221571.i		−	0.539258i	−0.962964	−	0.269629i	$-0.913099\pi$
$641$		−	221571.i		−	0.539258i	0.962964	−	0.269629i	$-0.0869011\pi$
$642$	−171935.	+	266095.i	−0.417152	+	0.645605i
$643$	289708.	−	289708.i	0.700711	−	0.700711i	−0.263852	−	0.964563i	$-0.584993\pi$
$643$	289708.	−	289708.i	0.700711	−	0.700711i	0.964563	+	0.263852i	$0.0849931\pi$
$644$	−114808.	+	69997.8i	−0.276822	+	0.168777i
$645$	617004.	+	152754.i	1.48309	+	0.367174i
$646$	539141.	−	151396.i	1.29192	−	0.362784i
$647$	481546.	−	481546.i	1.15035	−	1.15035i	0.163866	−	0.986483i	$-0.447604\pi$
$647$	481546.	−	481546.i	1.15035	−	1.15035i	0.986483	−	0.163866i	$-0.0523964\pi$
$648$	−410486.	−	88435.0i	−0.977571	−	0.210608i
$649$			67053.5i			0.159196i
$650$	623756.	+	54775.1i	1.47635	+	0.129645i
$651$	372568.	+	23135.9i	0.879110	+	0.0545914i
$652$	−499185.	−	121038.i	−1.17427	−	0.284726i
$653$	210083.	−	210083.i	0.492680	−	0.492680i	−0.416470	−	0.909150i	$-0.636733\pi$
$653$	210083.	−	210083.i	0.492680	−	0.492680i	0.909150	+	0.416470i	$0.136733\pi$
$654$	−75116.7	−	349441.i	−0.175623	−	0.816994i
$655$	−333759.	−	60966.5i	−0.777947	−	0.142105i
$656$	−7071.61	−	3643.54i	−0.0164328	−	0.00846672i
$657$	240042.	−	186822.i	0.556105	−	0.432809i
$658$	211232.	−	376184.i	0.487875	−	0.868858i
$659$		−	425598.i		−	0.980007i	−0.871721	−	0.490003i	$-0.836996\pi$
$659$		−	425598.i		−	0.980007i	0.871721	−	0.490003i	$-0.163004\pi$
$660$	−45882.9	+	88009.4i	−0.105333	+	0.202042i
$661$	−523713.			−1.19864			−0.599322	−	0.800508i	$-0.704563\pi$
$661$	−523713.			−1.19864			−0.599322	+	0.800508i	$0.704563\pi$
$662$	298128.	+	167403.i	0.680278	+	0.381985i
$663$	577752.	−	510192.i	1.31436	−	1.16066i
$664$	−275114.	−	256048.i	−0.623988	−	0.580745i
$665$	−363211.	−	525560.i	−0.821327	−	1.18845i
$666$	−199723.	+	30128.3i	−0.450278	+	0.0679245i
$667$	−113855.	−	113855.i	−0.255918	−	0.255918i
$668$	−447148.	−	108421.i	−1.00207	−	0.242973i
$669$	−575007.	−	35707.0i	−1.28476	−	0.0797813i
$670$	155623.	−	14528.0i	0.346676	−	0.0323636i
$671$	25234.8			0.0560473
$672$	498780.	−	286496.i	1.10451	−	0.634424i
$673$	−339325.	−	339325.i	−0.749178	−	0.749178i	0.225147	−	0.974325i	$-0.427714\pi$
$673$	−339325.	−	339325.i	−0.749178	−	0.749178i	−0.974325	+	0.225147i	$0.927714\pi$
$674$	−129355.	−	460651.i	−0.284750	−	1.01403i
$675$	−442782.	+	107415.i	−0.971813	+	0.235752i
$676$	466808.	−	284611.i	1.02152	−	0.622813i
$677$	−277446.	−	277446.i	−0.605342	−	0.605342i	0.336383	−	0.941725i	$-0.390796\pi$
$677$	−277446.	−	277446.i	−0.605342	−	0.605342i	−0.941725	+	0.336383i	$0.890796\pi$
$678$	89080.4	−	137865.i	0.193786	−	0.299913i
$679$	1.13144e6			2.45409
$680$	326986.	+	438625.i	0.707150	+	0.948583i
$681$	−463586.	−	28788.0i	−0.999623	−	0.0620750i
$682$	−63900.1	−	35880.7i	−0.137383	−	0.0771422i
$683$	−293838.	−	293838.i	−0.629892	−	0.629892i	0.318149	−	0.948041i	$-0.396939\pi$
$683$	−293838.	−	293838.i	−0.629892	−	0.629892i	−0.948041	+	0.318149i	$0.896939\pi$
$684$	−483751.	+	218052.i	−1.03397	+	0.466067i
$685$	286591.	+	414692.i	0.610775	+	0.883780i
$686$	61185.1	+	217889.i	0.130016	+	0.463006i
$687$	57522.7	−	50796.3i	0.121878	−	0.107626i
$688$	220371.	+	688815.i	0.465562	+	1.45521i
$689$	−205034.			−0.431904
$690$	88310.7	+	82987.6i	0.185488	+	0.174307i
$691$			55982.4i			0.117245i	0.998280	+	0.0586227i	$0.0186709\pi$
$691$			55982.4i			0.117245i	−0.998280	+	0.0586227i	$0.981329\pi$
$692$	−421592.	−	102224.i	−0.880400	−	0.213472i
$693$	109993.	−	85606.1i	0.229033	−	0.178254i
$694$	171968.	+	612402.i	0.357050	+	1.27150i
$695$	−155674.	−	28436.4i	−0.322290	−	0.0588715i
$696$	474150.	+	499610.i	0.978806	+	1.03136i
$697$	−7513.30	+	7513.30i	−0.0154655	+	0.0154655i
$698$	632667.	+	355251.i	1.29857	+	0.729162i
$699$	−647658.	−	40218.5i	−1.32554	−	0.0823137i
$700$	352018.	−	515395.i	0.718404	−	1.05183i
$701$			509042.i			1.03590i	0.855411	+	0.517949i	$0.173304\pi$
$701$			509042.i			1.03590i	−0.855411	+	0.517949i	$0.826696\pi$
$702$	−469215.	+	559685.i	−0.952134	+	1.13571i
$703$	−180483.	+	180483.i	−0.365196	+	0.365196i
$704$	−112636.	+	8096.34i	−0.227264	+	0.0163359i
$705$	−377430.	−	93441.6i	−0.759379	−	0.188002i
$706$	39744.6	+	141536.i	0.0797386	+	0.283960i
$707$	−465347.	+	465347.i	−0.930976	+	0.930976i
$708$	−334594.	−	103465.i	−0.667501	−	0.206408i
$709$			533306.i			1.06092i	0.847709	+	0.530462i	$0.177982\pi$
$709$			533306.i			1.06092i	−0.847709	+	0.530462i	$0.822018\pi$
$710$	−458050.	+	552378.i	−0.908649	+	1.09577i
$711$	4277.60	−	34309.3i	0.00846177	−	0.0678692i
$712$	−289048.	+	10375.1i	−0.570178	+	0.0204660i
$713$	−63271.5	+	63271.5i	−0.124460	+	0.124460i
$714$	−161465.	−	751131.i	−0.316725	−	1.47340i
$715$	98146.7	+	142016.i	0.191983	+	0.277796i
$716$	123792.	−	75475.3i	0.241472	−	0.147224i
$717$	225777.	−	199376.i	0.439180	−	0.387824i
$718$	−420911.	−	236347.i	−0.816472	−	0.458460i
$719$		−	291999.i		−	0.564838i	−0.959291	−	0.282419i	$-0.908863\pi$
$719$		−	291999.i		−	0.564838i	0.959291	−	0.282419i	$-0.0911368\pi$
$720$	−368365.	−	364754.i	−0.710581	−	0.703615i
$721$	196884.			0.378739
$722$	−73075.8	+	130141.i	−0.140184	+	0.249654i
$723$	−366959.	−	415552.i	−0.702006	−	0.794966i
$724$	−107702.	−	176649.i	−0.205469	−	0.337003i
$725$	699116.	+	264227.i	1.33007	+	0.502691i
$726$	488552.	−	105020.i	0.926910	−	0.199251i
$727$	−118411.	−	118411.i	−0.224038	−	0.224038i	0.586158	−	0.810196i	$-0.300640\pi$
$727$	−118411.	−	118411.i	−0.224038	−	0.224038i	−0.810196	+	0.586158i	$0.800640\pi$
$728$	−35887.8	−	999826.i	−0.0677149	−	1.88652i
$729$	193224.	−	495070.i	0.363584	−	0.931561i
$730$	373899.	−	34905.0i	0.701631	−	0.0655002i
$731$	965972.			1.80771
$732$	−38937.9	+	125921.i	−0.0726692	+	0.235004i
$733$	338196.	+	338196.i	0.629449	+	0.629449i	0.947929	−	0.318480i	$-0.103172\pi$
$733$	338196.	+	338196.i	0.629449	+	0.629449i	−0.318480	+	0.947929i	$0.603172\pi$
$734$	476545.	−	133818.i	0.884528	−	0.248384i
$735$	−287944.	+	173662.i	−0.533007	+	0.321463i
$736$	−27663.2	+	135078.i	−0.0510678	+	0.249361i
$737$	30470.4	+	30470.4i	0.0560974	+	0.0560974i
$738$	5977.67	−	8101.52i	0.0109754	−	0.0148749i
$739$	−324455.			−0.594109			−0.297055	−	0.954861i	$-0.596004\pi$
$739$	−324455.			−0.594109			−0.297055	+	0.954861i	$0.596004\pi$
$740$	−227836.	−	101351.i	−0.416063	−	0.185082i
$741$	−57202.1	+	921152.i	−0.104178	+	1.67763i
$742$	−100062.	+	178202.i	−0.181745	+	0.323671i
$743$	252389.	+	252389.i	0.457186	+	0.457186i	0.897731	−	0.440544i	$-0.145215\pi$
$743$	252389.	+	252389.i	0.457186	+	0.457186i	−0.440544	+	0.897731i	$0.645215\pi$
$744$	277643.	−	263494.i	0.501580	−	0.476020i
$745$	−468338.	−	85549.6i	−0.843814	−	0.154137i
$746$	−432399.	+	121422.i	−0.776975	+	0.218182i
$747$	375370.	−	292146.i	0.672696	−	0.523551i
$748$	−35542.8	+	146586.i	−0.0635256	+	0.261992i
$749$	549259.			0.979069
$750$	−532097.	−	182425.i	−0.945950	−	0.324311i
$751$			285311.i			0.505869i	0.967483	+	0.252934i	$0.0813957\pi$
$751$			285311.i			0.505869i	−0.967483	+	0.252934i	$0.918604\pi$
$752$	−134804.	−	421358.i	−0.238379	−	0.745101i
$753$	−153720.	−	174075.i	−0.271106	−	0.307006i
$754$	1.15341e6	−	323889.i	2.02881	−	0.569709i
$755$	−189305.	+	1.03634e6i	−0.332100	+	1.81807i
$756$	257449.	+	680953.i	0.450452	+	1.19144i
$757$	477930.	−	477930.i	0.834012	−	0.834012i	−0.154051	−	0.988063i	$-0.549232\pi$
$757$	477930.	−	477930.i	0.834012	−	0.834012i	0.988063	+	0.154051i	$0.0492321\pi$
$758$	−4923.04	+	8767.46i	−0.00856831	+	0.0152593i
$759$	−2070.75	+	33346.3i	−0.00359455	+	0.0578847i
$760$	−648236.	−	94523.4i	−1.12229	−	0.163649i
$761$			34125.1i			0.0589257i	0.999566	+	0.0294629i	$0.00937968\pi$
$761$			34125.1i			0.0589257i	−0.999566	+	0.0294629i	$0.990620\pi$
$762$	26269.8	+	16974.0i	0.0452426	+	0.0292331i
$763$	−438174.	+	438174.i	−0.752658	+	0.752658i
$764$	457681.	+	750672.i	0.784109	+	1.28607i
$765$	−613950.	+	320164.i	−1.04908	+	0.547079i
$766$	−741498.	+	208219.i	−1.26372	+	0.354866i
$767$	−430739.	+	430739.i	−0.732189	+	0.732189i
$768$	133399.	−	574541.i	0.226168	−	0.974088i
$769$		−	216104.i		−	0.365435i	−0.983165	−	0.182717i	$-0.941511\pi$
$769$		−	216104.i		−	0.365435i	0.983165	−	0.182717i	$-0.0584894\pi$
$770$	171329.	−	15994.3i	0.288969	−	0.0269764i
$771$	−9844.37	+	158528.i	−0.0165607	+	0.266685i
$772$	−188961.	+	779312.i	−0.317057	+	1.30761i
$773$	615645.	−	615645.i	1.03032	−	1.03032i	0.0307924	−	0.999526i	$-0.490197\pi$
$773$	615645.	−	615645.i	1.03032	−	1.03032i	0.999526	−	0.0307924i	$-0.00980306\pi$
$774$	−905069.	+	136530.i	−1.51078	+	0.227901i
$775$	146836.	−	388512.i	0.244472	−	0.646847i
$776$	790423.	−	849278.i	1.31261	−	1.41035i
$777$	231793.	+	262487.i	0.383935	+	0.434775i
$778$	−43515.2	+	77496.4i	−0.0718922	+	0.128033i
$779$		−	12722.9i		−	0.0209657i
$780$	−860099.	+	270613.i	−1.41371	+	0.444795i
$781$	−197838.			−0.324346
$782$	160581.	+	90168.5i	0.262592	+	0.147449i
$783$	−719807.	+	491751.i	−1.17407	+	0.802088i
$784$	−340100.	−	175231.i	−0.553317	−	0.285088i
$785$	−322452.	+	222844.i	−0.523269	+	0.361628i
$786$	477654.	−	102678.i	0.773157	−	0.166200i
$787$	426831.	+	426831.i	0.689139	+	0.689139i	0.962042	−	0.272903i	$-0.0879838\pi$
$787$	426831.	+	426831.i	0.689139	+	0.689139i	−0.272903	+	0.962042i	$0.587984\pi$
$788$	−189294.	+	780686.i	−0.304849	+	1.25726i
$789$	−9498.05	+	152952.i	−0.0152574	+	0.245697i
$790$	27246.8	−	32857.8i	0.0436577	−	0.0526482i
$791$	−284573.			−0.454822
$792$	12583.6	−	142367.i	0.0200611	−	0.226966i
$793$	162104.	+	162104.i	0.257778	+	0.257778i
$794$	−122662.	−	436815.i	−0.194566	−	0.692877i
$795$	178792.	+	44264.1i	0.282887	+	0.0700353i
$796$	274050.	+	449487.i	0.432518	+	0.709400i
$797$	447614.	+	447614.i	0.704672	+	0.704672i	0.965410	−	0.260738i	$-0.0839658\pi$
$797$	447614.	+	447614.i	0.704672	+	0.704672i	−0.260738	+	0.965410i	$0.583966\pi$
$798$	772687.	+	499265.i	1.21338	+	0.784017i
$799$	−590899.			−0.925592
$800$	−140945.	−	624287.i	−0.220227	−	0.975449i
$801$	45289.2	−	363250.i	0.0705877	−	0.566162i
$802$	452432.	+	254046.i	0.703404	+	0.394970i
$803$	73208.1	+	73208.1i	0.113535	+	0.113535i
$804$	−199063.	+	105029.i	−0.307948	+	0.162480i
$805$	37753.5	−	206680.i	0.0582594	−	0.318938i
$806$	−179991.	−	640973.i	−0.277064	−	0.986664i
$807$	547662.	+	620183.i	0.840941	+	0.952298i
$808$	24206.6	+	674391.i	0.0370776	+	1.03297i
$809$	770999.			1.17803			0.589015	−	0.808122i	$-0.299516\pi$
$809$	770999.			1.17803			0.589015	+	0.808122i	$0.299516\pi$
$810$	529989.	−	386754.i	0.807787	−	0.589474i
$811$		−	993738.i		−	1.51088i	−0.655218	−	0.755440i	$-0.727423\pi$
$811$		−	993738.i		−	1.51088i	0.655218	−	0.755440i	$-0.272577\pi$
$812$	281396.	−	1.16053e6i	0.426782	−	1.76013i
$813$	−635153.	+	560881.i	−0.960942	+	0.848574i
$814$	−18586.4	−	66188.7i	−0.0280509	−	0.0998930i
$815$	660248.	−	456293.i	0.994012	−	0.686956i
$816$	−676614.	−	403543.i	−1.01616	−	0.606051i
$817$	−817880.	+	817880.i	−1.22531	+	1.22531i
$818$	−299177.	−	167992.i	−0.447118	−	0.251062i
$819$	1.25649e6	+	156656.i	1.87323	+	0.233550i
$820$	11602.8	−	4458.20i	0.0172557	−	0.00663028i
$821$		−	159659.i		−	0.236868i	−0.992962	−	0.118434i	$-0.962213\pi$
$821$		−	159659.i		−	0.236868i	0.992962	−	0.118434i	$-0.0377874\pi$
$822$	−609687.	−	393944.i	−0.902325	−	0.583030i
$823$	384193.	−	384193.i	0.567217	−	0.567217i	−0.364131	−	0.931348i	$-0.618634\pi$
$823$	384193.	−	384193.i	0.567217	−	0.567217i	0.931348	+	0.364131i	$0.118634\pi$
$824$	137543.	−	147785.i	0.202575	−	0.217659i
$825$	−54925.5	−	145028.i	−0.0806986	−	0.213081i
$826$	164156.	+	584582.i	0.240601	+	0.856812i
$827$	−407356.	+	407356.i	−0.595611	+	0.595611i	−0.939142	−	0.343530i	$-0.888377\pi$
$827$	−407356.	+	407356.i	−0.595611	+	0.595611i	0.343530	+	0.939142i	$0.388377\pi$
$828$	−163201.	−	61787.1i	−0.238047	−	0.0901232i
$829$		−	659846.i		−	0.960138i	−0.877231	−	0.480069i	$-0.840612\pi$
$829$		−	659846.i		−	0.960138i	0.877231	−	0.480069i	$-0.159388\pi$
$830$	584692.	−	54583.4i	0.848733	−	0.0792327i
$831$	−1.02321e6	−	63540.0i	−1.48171	−	0.0920121i
$832$	−775560.	−	671541.i	−1.12039	−	0.970121i
$833$	−361342.	+	361342.i	−0.520749	+	0.520749i
$834$	222790.	−	47891.6i	0.320306	−	0.0688536i
$835$	591421.	−	408727.i	0.848250	−	0.586220i
$836$	−94019.0	−	154207.i	−0.134525	−	0.220643i
$837$	273276.	+	400010.i	0.390077	+	0.570979i
$838$	−60786.2	−	34132.2i	−0.0865600	−	0.0486045i
$839$		−	1.00912e6i		−	1.43358i	−0.697291	−	0.716789i	$-0.745611\pi$
$839$		−	1.00912e6i		−	1.43358i	0.697291	−	0.716789i	$-0.254389\pi$
$840$	−184554.	+	879606.i	−0.261557	+	1.24661i
$841$	722682.			1.02177
$842$	−294291.	+	524104.i	−0.415100	+	0.739253i
$843$	−560352.	+	494827.i	−0.788507	+	0.696303i
$844$	−409097.	+	249425.i	−0.574304	+	0.350150i
$845$	−153506.	+	840359.i	−0.214986	+	1.17693i
$846$	553644.	−	83517.3i	0.773553	−	0.116691i
$847$	−612609.	−	612609.i	−0.853919	−	0.853919i
$848$	63857.8	+	199601.i	0.0888020	+	0.277569i
$849$	489789.	+	30415.1i	0.679507	+	0.0421963i
$850$	−851557.	−	74779.4i	−1.17863	−	0.103501i
$851$	−83941.1			−0.115909
$852$	305269.	−	987204.i	0.420536	−	1.35997i
$853$	−254170.	−	254170.i	−0.349323	−	0.349323i	0.510534	−	0.859857i	$-0.329448\pi$
$853$	−254170.	−	254170.i	−0.349323	−	0.349323i	−0.859857	+	0.510534i	$0.829448\pi$
$854$	220001.	−	61778.2i	0.301653	−	0.0847070i
$855$	248745.	−	790906.i	0.340269	−	1.08191i
$856$	383713.	−	412284.i	0.523671	−	0.562664i
$857$	−685908.	−	685908.i	−0.933909	−	0.933909i	0.0640385	−	0.997947i	$-0.479602\pi$
$857$	−685908.	−	685908.i	−0.933909	−	0.933909i	−0.997947	+	0.0640385i	$0.979602\pi$
$858$	−208795.	−	134911.i	−0.283625	−	0.183262i
$859$	65552.9			0.0888394			0.0444197	−	0.999013i	$-0.485856\pi$
$859$	65552.9			0.0888394			0.0444197	+	0.999013i	$0.485856\pi$
$860$	−1.03247e6	−	459282.i	−1.39598	−	0.620988i
$861$	−17421.7	−	1081.86i	−0.0235009	−	0.00145937i
$862$	367640.	−	654731.i	0.494775	−	0.881147i
$863$	418699.	+	418699.i	0.562186	+	0.562186i	0.929928	−	0.367742i	$-0.119869\pi$
$863$	418699.	+	418699.i	0.562186	+	0.562186i	−0.367742	+	0.929928i	$0.619869\pi$
$864$	690991.	+	282468.i	0.925646	+	0.378392i
$865$	557619.	−	385367.i	0.745256	−	0.515042i
$866$	164432.	−	46174.1i	0.219256	−	0.0615690i
$867$	−225306.	+	198959.i	−0.299732	+	0.264683i
$868$	−644931.	−	156377.i	−0.856000	−	0.207555i
$869$	11768.2			0.0155838
$870$	−1.07571e6	+	33428.3i	−1.42121	+	0.0441647i
$871$			391472.i			0.516017i
$872$	22793.1	+	635011.i	0.0299758	+	0.835119i
$873$	901857.	+	1.15877e6i	1.18334	+	1.52044i
$874$	−212308.	+	59617.9i	−0.277935	+	0.0780466i
$875$	235006.	+	946477.i	0.306947	+	1.23621i
$876$	−478267.	+	252344.i	−0.623250	+	0.328840i
$877$	6387.86	−	6387.86i	0.00830532	−	0.00830532i	−0.702942	−	0.711247i	$-0.748131\pi$
$877$	6387.86	−	6387.86i	0.00830532	−	0.00830532i	0.711247	+	0.702942i	$0.248131\pi$
$878$	−128129.	+	228185.i	−0.166210	+	0.296005i
$879$	−346546.	−	21520.0i	−0.448522	−	0.0278525i
$880$	107685.	−	139777.i	0.139056	−	0.180497i
$881$			518204.i			0.667650i	0.942635	+	0.333825i	$0.108339\pi$
$881$			518204.i			0.667650i	−0.942635	+	0.333825i	$0.891661\pi$
$882$	287488.	−	389632.i	0.369558	−	0.500861i
$883$	890343.	−	890343.i	1.14192	−	1.14192i	0.153822	−	0.988099i	$-0.450842\pi$
$883$	890343.	−	890343.i	1.14192	−	1.14192i	0.988099	−	0.153822i	$-0.0491583\pi$
$884$	−1.16996e6	+	713319.i	−1.49715	+	0.912807i
$885$	468600.	−	282618.i	0.598295	−	0.360839i
$886$	−767816.	+	215610.i	−0.978115	+	0.274664i
$887$	23504.5	−	23504.5i	0.0298747	−	0.0298747i	−0.692012	−	0.721886i	$-0.743275\pi$
$887$	23504.5	−	23504.5i	0.0298747	−	0.0298747i	0.721886	+	0.692012i	$0.243275\pi$
$888$	358958.	+	9385.35i	0.455216	+	0.0119021i
$889$		−	54224.7i		−	0.0686110i
$890$	288475.	−	347882.i	0.364191	−	0.439189i
$891$	175349.	+	44414.5i	0.220875	+	0.0559461i
$892$	995361.	+	241346.i	1.25098	+	0.303327i
$893$	500309.	−	500309.i	0.627387	−	0.627387i
$894$	670254.	−	144079.i	0.838619	−	0.180271i
$895$	−40707.8	+	222853.i	−0.0508197	+	0.278210i
$896$	−962154.	+	346333.i	−1.19847	+	0.431397i
$897$	−227512.	+	200908.i	−0.282761	+	0.249696i
$898$	295055.	−	525465.i	0.365890	−	0.651614i
$899$		−	794658.i		−	0.983243i
$900$	808437.	−	50293.8i	0.998070	−	0.0620911i
$901$	279914.			0.344806
$902$	2988.05	+	1677.83i	0.00367260	+	0.00206221i
$903$	1.05040e6	+	1.18949e6i	1.28818	+	1.45876i
$904$	−198803.	+	213606.i	−0.243269	+	0.261383i
$905$	318008.	+	58089.3i	0.388276	+	0.0709250i
$906$	−318821.	−	1.48315e6i	−0.388410	−	1.80688i
$907$	−954549.	−	954549.i	−1.16034	−	1.16034i	−0.984402	−	0.175933i	$-0.943706\pi$
$907$	−954549.	−	954549.i	−1.16034	−	1.16034i	−0.175933	−	0.984402i	$-0.556294\pi$
$908$	802488.	+	194580.i	0.973345	+	0.236008i
$909$	−847514.	−	105666.i	−1.02570	−	0.127881i
$910$	1.20333e6	+	997843.i	1.45312	+	1.20498i
$911$	−703454.			−0.847615			−0.423808	−	0.905752i	$-0.639307\pi$
$911$	−703454.			−0.847615			−0.423808	+	0.905752i	$0.639307\pi$
$912$	914558.	−	231207.i	1.09957	−	0.277978i
$913$	114481.	+	114481.i	0.137338	+	0.137338i
$914$	238935.	+	850879.i	0.286014	+	1.01853i
$915$	−106360.	−	176352.i	−0.127039	−	0.210639i
$916$	−116485.	+	71020.1i	−0.138828	+	0.0846429i
$917$	−598943.	−	598943.i	−0.712274	−	0.712274i
$918$	640577.	−	764086.i	0.760126	−	0.906686i
$919$	−240595.			−0.284876			−0.142438	−	0.989804i	$-0.545494\pi$
$919$	−240595.			−0.284876			−0.142438	+	0.989804i	$0.545494\pi$
$920$	−128763.	−	172726.i	−0.152131	−	0.204071i
$921$	82177.4	−	1.32334e6i	0.0968798	−	1.56010i
$922$	570784.	+	320502.i	0.671444	+	0.377024i
$923$	−1.27087e6	−	1.27087e6i	−1.49176	−	1.49176i
$924$	−219153.	+	115630.i	−0.256687	+	0.135433i
$925$	355118.	−	160314.i	0.415040	−	0.187365i
$926$	312385.	+	1.11245e6i	0.364308	+	1.29735i
$927$	156934.	+	201641.i	0.182624	+	0.234649i
$928$	−674536.	−	1.02197e6i	−0.783266	−	1.18671i
$929$	−1.32878e6			−1.53964			−0.769822	−	0.638259i	$-0.779655\pi$
$929$	−1.32878e6			−1.53964			−0.769822	+	0.638259i	$0.779655\pi$
$930$	18576.7	+	597793.i	0.0214785	+	0.691170i
$931$		−	611890.i		−	0.705950i
$932$	1.12112e6	+	271840.i	1.29069	+	0.312955i
$933$	−338743.	−	383599.i	−0.389141	−	0.440671i
$934$	9316.79	+	33178.4i	0.0106800	+	0.0380331i
$935$	−133991.	−	193882.i	−0.153268	−	0.221776i
$936$	995376.	−	833707.i	1.13615	−	0.951616i
$937$	−138828.	+	138828.i	−0.158124	+	0.158124i	−0.781735	−	0.623611i	$-0.785665\pi$
$937$	−138828.	+	138828.i	−0.158124	+	0.158124i	0.623611	+	0.781735i	$0.285665\pi$
$938$	340241.	+	191050.i	0.386706	+	0.217140i
$939$	−41580.9	+	669597.i	−0.0471588	+	0.759421i
$940$	631574.	+	280950.i	0.714774	+	0.317960i
$941$		−	747204.i		−	0.843840i	−0.906633	−	0.421920i	$-0.861356\pi$
$941$		−	747204.i		−	0.843840i	0.906633	−	0.421920i	$-0.138644\pi$
$942$	306319.	−	474074.i	0.345201	−	0.534249i
$943$	2958.65	−	2958.65i	0.00332714	−	0.00332714i
$944$	553479.	+	285171.i	0.621093	+	0.320008i
$945$	−1.06185e6	−	407866.i	−1.18905	−	0.456724i
$946$	−84226.4	−	299942.i	−0.0941166	−	0.335162i
$947$	1.03422e6	−	1.03422e6i	1.15322	−	1.15322i	0.167321	−	0.985902i	$-0.446488\pi$
$947$	1.03422e6	−	1.03422e6i	1.15322	−	1.15322i	0.985902	−	0.167321i	$-0.0535118\pi$
$948$	−18158.7	+	58723.1i	−0.0202054	+	0.0653419i
$949$			940550.i			1.04436i
$950$	784321.	−	657690.i	0.869053	−	0.728743i
$951$	−93254.9	+	1.50173e6i	−0.103112	+	1.66047i
$952$	48994.3	+	1.36497e6i	0.0540594	+	1.50608i
$953$	−76744.9	+	76744.9i	−0.0845013	+	0.0845013i	−0.748094	−	0.663593i	$-0.769031\pi$
$953$	−76744.9	+	76744.9i	−0.0845013	+	0.0845013i	0.663593	+	0.748094i	$0.269031\pi$
$954$	−262266.	+	39562.9i	−0.288167	+	0.0434701i
$955$	−1.35138e6	−	246852.i	−1.48173	−	0.270663i
$956$	−457204.	+	278755.i	−0.500258	+	0.305005i
$957$	−196402.	−	222410.i	−0.214448	−	0.242846i
$958$	−658750.	−	369896.i	−0.717777	−	0.403041i
$959$			1.25848e6i			1.36839i
$960$	531320.	+	753024.i	0.576519	+	0.817084i
$961$	481914.			0.521823
$962$	305788.	−	544579.i	0.330423	−	0.588452i
$963$	437809.	+	562529.i	0.472098	+	0.606586i
$964$	513059.	+	841500.i	0.552094	+	0.905525i
$965$	−712351.	−	1.03076e6i	−0.764961	−	1.10688i
$966$	63583.1	+	295787.i	0.0681377	+	0.316975i
$967$	900246.	+	900246.i	0.962738	+	0.962738i	0.999330	−	0.0365923i	$-0.0116503\pi$
$967$	900246.	+	900246.i	0.962738	+	0.962738i	−0.0365923	+	0.999330i	$0.511650\pi$
$968$	−887806.	+	31867.0i	−0.947474	+	0.0340087i
$969$	78092.8	−	1.25756e6i	0.0831693	−	1.33931i
$970$	168499.	+	1.80495e6i	0.179083	+	1.91832i
$971$	1.26020e6			1.33660			0.668301	−	0.743891i	$-0.267022\pi$
$971$	1.26020e6			1.33660			0.668301	+	0.743891i	$0.267022\pi$
$972$	−492194.	+	806450.i	−0.520959	+	0.853582i
$973$	−279363.	−	279363.i	−0.295082	−	0.295082i
$974$	−583632.	+	163889.i	−0.615207	+	0.172756i
$975$	578804.	−	1.28447e6i	0.608867	−	1.35118i
$976$	107321.	−	208295.i	0.112664	−	0.218665i
$977$	812108.	+	812108.i	0.850794	+	0.850794i	0.990231	−	0.139437i	$-0.0445292\pi$
$977$	812108.	+	812108.i	0.850794	+	0.850794i	−0.139437	+	0.990231i	$0.544529\pi$
$978$	−627214.	+	970707.i	−0.655750	+	1.01487i
$979$	124596.			0.129999
$980$	558019.	−	214411.i	0.581028	−	0.223252i
$981$	−798025.	−	99495.9i	−0.829237	−	0.103387i
$982$	542012.	−	965271.i	0.562064	−	1.00098i
$983$	416114.	+	416114.i	0.430631	+	0.430631i	0.888843	−	0.458212i	$-0.151510\pi$
$983$	416114.	+	416114.i	0.430631	+	0.430631i	−0.458212	+	0.888843i	$0.651510\pi$
$984$	−12982.9	+	12321.3i	−0.0134085	+	0.0127253i
$985$	−713607.	−	1.03258e6i	−0.735507	−	1.06426i
$986$	−1.57465e6	+	442175.i	−1.61968	+	0.454821i
$987$	−642542.	−	727627.i	−0.659579	−	0.746921i
$988$	386634.	−	1.59455e6i	0.396082	−	1.63352i
$989$	−380389.			−0.388898
$990$	152946.	+	162720.i	0.156051	+	0.166024i
$991$			651143.i			0.663024i	0.943451	+	0.331512i	$0.107559\pi$
$991$			651143.i			0.663024i	−0.943451	+	0.331512i	$0.892441\pi$
$992$	−567929.	+	374853.i	−0.577126	+	0.380923i
$993$	576648.	−	509218.i	0.584807	−	0.516422i
$994$	−1.72478e6	+	484335.i	−1.74567	+	0.490199i
$995$	−809179.	−	147810.i	−0.817331	−	0.149299i
$996$	−747900.	+	394607.i	−0.753919	+	0.397783i
$997$	−582795.	+	582795.i	−0.586307	+	0.586307i	−0.936629	−	0.350322i	$-0.886072\pi$
$997$	−582795.	+	582795.i	−0.586307	+	0.586307i	0.350322	+	0.936629i	$0.386072\pi$
$998$	−896848.	+	1.59720e6i	−0.900446	+	1.60361i
$999$	−84068.5	+	446618.i	−0.0842369	+	0.447513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.l.a.23.16	yes	88
3.2	odd	2	inner	60.5.l.a.23.29	yes	88
4.3	odd	2	inner	60.5.l.a.23.38	yes	88
5.2	odd	4	inner	60.5.l.a.47.7	yes	88
12.11	even	2	inner	60.5.l.a.23.7	✓	88
15.2	even	4	inner	60.5.l.a.47.38	yes	88
20.7	even	4	inner	60.5.l.a.47.29	yes	88
60.47	odd	4	inner	60.5.l.a.47.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.l.a.23.7	✓	88	12.11	even	2	inner
60.5.l.a.23.16	yes	88	1.1	even	1	trivial
60.5.l.a.23.29	yes	88	3.2	odd	2	inner
60.5.l.a.23.38	yes	88	4.3	odd	2	inner
60.5.l.a.47.7	yes	88	5.2	odd	4	inner
60.5.l.a.47.16	yes	88	60.47	odd	4	inner
60.5.l.a.47.29	yes	88	20.7	even	4	inner
60.5.l.a.47.38	yes	88	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95843 + 3.48777i) q^{2} +(5.95729 + 6.74616i) q^{3} +(-8.32911 - 13.6611i) q^{4} +(24.5931 + 4.49233i) q^{5} +(-35.1960 + 7.56581i) q^{6} +(44.1332 + 44.1332i) q^{7} +(63.9588 - 2.29574i) q^{8} +(-10.0213 + 80.3777i) q^{9} +O(q^{10})\)	\(q+(-1.95843 + 3.48777i) q^{2} +(5.95729 + 6.74616i) q^{3} +(-8.32911 - 13.6611i) q^{4} +(24.5931 + 4.49233i) q^{5} +(-35.1960 + 7.56581i) q^{6} +(44.1332 + 44.1332i) q^{7} +(63.9588 - 2.29574i) q^{8} +(-10.0213 + 80.3777i) q^{9} +(-63.8320 + 76.9771i) q^{10} -27.5699 q^{11} +(42.5410 - 137.573i) q^{12} +(-177.104 - 177.104i) q^{13} +(-240.358 + 67.4949i) q^{14} +(116.202 + 192.671i) q^{15} +(-117.252 + 227.570i) q^{16} +(241.784 + 241.784i) q^{17} +(-260.713 - 192.366i) q^{18} -409.432 q^{19} +(-143.468 - 373.386i) q^{20} +(-34.8151 + 560.644i) q^{21} +(53.9937 - 96.1576i) q^{22} +(-95.2117 - 95.2117i) q^{23} +(396.509 + 417.800i) q^{24} +(584.638 + 220.960i) q^{25} +(964.543 - 270.853i) q^{26} +(-601.940 + 411.228i) q^{27} +(235.318 - 970.500i) q^{28} +1195.81 q^{29} +(-899.566 + 27.9545i) q^{30} -664.535i q^{31} +(-564.083 - 854.627i) q^{32} +(-164.242 - 185.991i) q^{33} +(-1316.80 + 369.770i) q^{34} +(887.111 + 1283.63i) q^{35} +(1181.52 - 532.573i) q^{36} +(440.813 - 440.813i) q^{37} +(801.843 - 1428.01i) q^{38} +(139.711 - 2249.83i) q^{39} +(1583.26 + 230.865i) q^{40} +31.0745i q^{41} +(-1887.22 - 1219.41i) q^{42} +(1997.60 - 1997.60i) q^{43} +(229.633 + 376.636i) q^{44} +(-607.538 + 1931.72i) q^{45} +(518.542 - 145.611i) q^{46} +(-1221.96 + 1221.96i) q^{47} +(-2233.73 + 564.701i) q^{48} +1494.49i q^{49} +(-1915.63 + 1606.35i) q^{50} +(-190.734 + 3071.49i) q^{51} +(-944.317 + 3894.55i) q^{52} +(578.852 - 578.852i) q^{53} +(-255.413 - 2904.79i) q^{54} +(-678.029 - 123.853i) q^{55} +(2924.03 + 2721.39i) q^{56} +(-2439.11 - 2762.09i) q^{57} +(-2341.91 + 4170.72i) q^{58} -2432.13i q^{59} +(1664.24 - 3192.23i) q^{60} -915.302 q^{61} +(2317.75 + 1301.44i) q^{62} +(-3989.60 + 3105.06i) q^{63} +(4085.46 - 293.666i) q^{64} +(-3559.92 - 5151.14i) q^{65} +(970.351 - 208.589i) q^{66} +(-1105.20 - 1105.20i) q^{67} +(1289.19 - 5316.87i) q^{68} +(75.1091 - 1209.52i) q^{69} +(-6214.36 + 580.136i) q^{70} +7175.87 q^{71} +(-456.424 + 5163.87i) q^{72} +(-2655.36 - 2655.36i) q^{73} +(674.155 + 2400.76i) q^{74} +(1992.23 + 5260.39i) q^{75} +(3410.20 + 5593.29i) q^{76} +(-1216.75 - 1216.75i) q^{77} +(7573.28 + 4893.41i) q^{78} -426.851 q^{79} +(-3905.90 + 5069.91i) q^{80} +(-6360.15 - 1610.98i) q^{81} +(-108.381 - 60.8571i) q^{82} +(-4152.37 - 4152.37i) q^{83} +(7949.00 - 4194.06i) q^{84} +(4860.03 + 7032.37i) q^{85} +(3055.01 + 10879.3i) q^{86} +(7123.80 + 8067.13i) q^{87} +(-1763.34 + 63.2934i) q^{88} -4519.29 q^{89} +(-5547.56 - 5902.08i) q^{90} -15632.3i q^{91} +(-507.668 + 2093.73i) q^{92} +(4483.06 - 3958.83i) q^{93} +(-1868.79 - 6655.03i) q^{94} +(-10069.2 - 1839.30i) q^{95} +(2405.04 - 8896.65i) q^{96} +(12818.4 - 12818.4i) q^{97} +(-5212.42 - 2926.84i) q^{98} +(276.286 - 2216.01i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^6	\( 88 q - 4 q^{6} + 148 q^{10} - 164 q^{12} - 8 q^{13} - 484 q^{16} + 456 q^{18} + 600 q^{21} - 348 q^{22} - 8 q^{25} - 148 q^{28} + 68 q^{30} - 328 q^{33} - 1556 q^{36} + 2232 q^{37} + 2024 q^{40} - 2116 q^{42} - 2504 q^{45} - 4432 q^{46} + 1540 q^{48} + 80 q^{52} + 3192 q^{57} - 1948 q^{58} + 2836 q^{60} - 7568 q^{61} + 3384 q^{66} + 8348 q^{70} + 5256 q^{72} + 5592 q^{73} - 256 q^{76} + 13176 q^{78} - 12648 q^{81} + 20400 q^{82} + 5816 q^{85} + 7932 q^{88} - 13152 q^{90} + 3680 q^{93} - 18028 q^{96} - 15208 q^{97}+O(q^{100}) \) 88 * q - 4 * q^6 + 148 * q^10 - 164 * q^12 - 8 * q^13 - 484 * q^16 + 456 * q^18 + 600 * q^21 - 348 * q^22 - 8 * q^25 - 148 * q^28 + 68 * q^30 - 328 * q^33 - 1556 * q^36 + 2232 * q^37 + 2024 * q^40 - 2116 * q^42 - 2504 * q^45 - 4432 * q^46 + 1540 * q^48 + 80 * q^52 + 3192 * q^57 - 1948 * q^58 + 2836 * q^60 - 7568 * q^61 + 3384 * q^66 + 8348 * q^70 + 5256 * q^72 + 5592 * q^73 - 256 * q^76 + 13176 * q^78 - 12648 * q^81 + 20400 * q^82 + 5816 * q^85 + 7932 * q^88 - 13152 * q^90 + 3680 * q^93 - 18028 * q^96 - 15208 * q^97

Introduction

L-functions

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