LMFDB - Embedded newform 75.3.k.a.28.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,3,Mod(13,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.13"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 19])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			28.2
Character	$\chi$	$=$	75.28
Dual form			75.3.k.a.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13229 - 2.22224i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.30514 + 1.79637i) q^{4} +(-4.95217 - 0.689916i) q^{5} +(-3.49485 + 2.53916i) q^{6} +(3.10232 - 3.10232i) q^{7} +(-4.38372 - 0.694313i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(4.07413 + 11.7861i) q^{10} +(-2.50856 + 7.72057i) q^{11} +(3.42674 + 1.74601i) q^{12} +(1.49656 - 2.93716i) q^{13} +(-10.4068 - 3.38139i) q^{14} +(0.161546 + 8.65875i) q^{15} +(6.16532 + 18.9749i) q^{16} +(4.41196 - 27.8560i) q^{17} +(5.29075 + 5.29075i) q^{18} +(-15.2294 - 20.9615i) q^{19} +(7.70264 - 7.99552i) q^{20} +(-6.14781 - 4.46664i) q^{21} +(19.9974 - 3.16728i) q^{22} +(17.4339 - 8.88304i) q^{23} +7.68747i q^{24} +(24.0480 + 6.83317i) q^{25} -8.22163 q^{26} +(2.35900 + 4.62981i) q^{27} +(1.52396 + 9.62191i) q^{28} +(20.3892 - 28.0633i) q^{29} +(19.0589 - 10.1632i) q^{30} +(8.77688 - 6.37677i) q^{31} +(22.6323 - 22.6323i) q^{32} +(13.8875 + 2.19956i) q^{33} +(-66.8985 + 21.7366i) q^{34} +(-17.5036 + 13.2229i) q^{35} +(2.05846 - 6.33529i) q^{36} +(-21.6628 - 11.0377i) q^{37} +(-29.3374 + 57.5779i) q^{38} +(-5.43018 - 1.76437i) q^{39} +(21.2299 + 6.46276i) q^{40} +(13.9284 + 42.8673i) q^{41} +(-2.96487 + 18.7195i) q^{42} +(-8.53203 - 8.53203i) q^{43} +(-10.5950 - 14.5828i) q^{44} +(14.7690 - 2.62247i) q^{45} +(-39.4805 - 28.6843i) q^{46} +(-39.8112 + 6.30548i) q^{47} +(30.7904 - 15.6885i) q^{48} +29.7512i q^{49} +(-12.0444 - 61.1777i) q^{50} -48.8495 q^{51} +(3.32302 + 6.52180i) q^{52} +(14.2819 + 90.1725i) q^{53} +(7.61748 - 10.4846i) q^{54} +(17.7494 - 36.5029i) q^{55} +(-15.7537 + 11.4457i) q^{56} +(-31.7329 + 31.7329i) q^{57} +(-85.4499 - 13.5339i) q^{58} +(101.152 - 32.8662i) q^{59} +(-15.7652 - 11.0107i) q^{60} +(-4.73879 + 14.5845i) q^{61} +(-24.1087 - 12.2840i) q^{62} +(-5.97544 + 11.7275i) q^{63} +(-0.0212563 - 0.00690660i) q^{64} +(-9.43761 + 13.5128i) q^{65} +(-10.8367 - 33.3519i) q^{66} +(4.18666 - 26.4335i) q^{67} +(44.2816 + 44.2816i) q^{68} +(-19.9202 - 27.4178i) q^{69} +(49.2036 + 23.9251i) q^{70} +(-41.3332 - 30.0303i) q^{71} +(13.1512 - 2.08294i) q^{72} +(101.623 - 51.7793i) q^{73} +60.6378i q^{74} +(5.17381 - 42.9911i) q^{75} +57.5312 q^{76} +(16.1693 + 31.7341i) q^{77} +(2.22767 + 14.0650i) q^{78} +(21.7607 - 29.9510i) q^{79} +(-17.4406 - 98.2206i) q^{80} +(7.28115 - 5.29007i) q^{81} +(79.4905 - 79.4905i) q^{82} +(-102.284 - 16.2002i) q^{83} +(16.0475 - 5.21416i) q^{84} +(-41.0671 + 134.904i) q^{85} +(-9.29951 + 28.6210i) q^{86} +(-53.5331 - 27.2765i) q^{87} +(16.3573 - 32.1031i) q^{88} +(108.616 + 35.2914i) q^{89} +(-22.5505 - 29.8509i) q^{90} +(-4.46922 - 13.7548i) q^{91} +(-6.79652 + 42.9115i) q^{92} +(-13.2870 - 13.2870i) q^{93} +(59.0902 + 81.3306i) q^{94} +(60.9570 + 114.312i) q^{95} +(-44.8500 - 32.5855i) q^{96} +(-58.1488 + 9.20986i) q^{97} +(66.1143 - 33.6869i) q^{98} -24.3537i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26}+ \cdots - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−1.13229	−	2.22224i	−0.566145	−	1.11112i	−0.979668	−	0.200628i	$-0.935702\pi$
$2$	−1.13229	−	2.22224i	−0.566145	−	1.11112i	0.413523	−	0.910494i	$-0.364298\pi$
$3$	−0.270952	−	1.71073i	−0.0903175	−	0.570242i
$3$	−0.270952	−	1.71073i	−0.0903175	−	0.570242i
$4$	−1.30514	+	1.79637i	−0.326286	+	0.449094i
$5$	−4.95217	−	0.689916i	−0.990435	−	0.137983i
$5$	−4.95217	−	0.689916i	−0.990435	−	0.137983i
$6$	−3.49485	+	2.53916i	−0.582475	+	0.423193i
$7$	3.10232	−	3.10232i	0.443189	−	0.443189i	−0.449893	−	0.893082i	$-0.648538\pi$
$7$	3.10232	−	3.10232i	0.443189	−	0.443189i	0.893082	+	0.449893i	$0.148538\pi$
$8$	−4.38372	−	0.694313i	−0.547965	−	0.0867892i
$9$	−2.85317	+	0.927051i	−0.317019	+	0.103006i
$10$	4.07413	+	11.7861i	0.407413	+	1.17861i
$11$	−2.50856	+	7.72057i	−0.228051	+	0.701870i	0.769916	+	0.638145i	$0.220298\pi$
$11$	−2.50856	+	7.72057i	−0.228051	+	0.701870i	−0.997968	+	0.0637248i	$0.979702\pi$
$12$	3.42674	+	1.74601i	0.285561	+	0.145501i
$13$	1.49656	−	2.93716i	0.115120	−	0.225936i	−0.826256	−	0.563295i	$-0.809534\pi$
$13$	1.49656	−	2.93716i	0.115120	−	0.225936i	0.941376	+	0.337359i	$0.109534\pi$
$14$	−10.4068	−	3.38139i	−0.743346	−	0.241528i
$15$	0.161546	+	8.65875i	0.0107697	+	0.577250i
$16$	6.16532	+	18.9749i	0.385333	+	1.18593i
$17$	4.41196	−	27.8560i	0.259527	−	1.63859i	−0.421856	−	0.906663i	$-0.638621\pi$
$17$	4.41196	−	27.8560i	0.259527	−	1.63859i	0.681383	−	0.731927i	$-0.261379\pi$
$18$	5.29075	+	5.29075i	0.293930	+	0.293930i
$19$	−15.2294	−	20.9615i	−0.801547	−	1.10324i	−0.992573	−	0.121650i	$-0.961181\pi$
$19$	−15.2294	−	20.9615i	−0.801547	−	1.10324i	0.191026	−	0.981585i	$-0.438819\pi$
$20$	7.70264	−	7.99552i	0.385132	−	0.399776i
$21$	−6.14781	−	4.46664i	−0.292753	−	0.212697i
$22$	19.9974	−	3.16728i	0.908972	−	0.143967i
$23$	17.4339	−	8.88304i	0.757997	−	0.386219i	−0.0318737	−	0.999492i	$-0.510147\pi$
$23$	17.4339	−	8.88304i	0.757997	−	0.386219i	0.789871	+	0.613273i	$0.210147\pi$
$24$			7.68747i			0.320311i
$25$	24.0480	+	6.83317i	0.961921	+	0.273327i
$26$	−8.22163			−0.316216
$27$	2.35900	+	4.62981i	0.0873705	+	0.171474i
$28$	1.52396	+	9.62191i	0.0544272	+	0.343640i
$29$	20.3892	−	28.0633i	0.703075	−	0.967699i	−0.296844	−	0.954926i	$-0.595934\pi$
$29$	20.3892	−	28.0633i	0.703075	−	0.967699i	0.999918	−	0.0127733i	$-0.00406596\pi$
$30$	19.0589	−	10.1632i	0.635297	−	0.338773i
$31$	8.77688	−	6.37677i	0.283125	−	0.205702i	−0.437154	−	0.899387i	$-0.644014\pi$
$31$	8.77688	−	6.37677i	0.283125	−	0.205702i	0.720279	+	0.693684i	$0.244014\pi$
$32$	22.6323	−	22.6323i	0.707261	−	0.707261i
$33$	13.8875	+	2.19956i	0.420833	+	0.0666534i
$34$	−66.8985	+	21.7366i	−1.96760	+	0.639313i
$35$	−17.5036	+	13.2229i	−0.500102	+	0.377797i
$36$	2.05846	−	6.33529i	0.0571795	−	0.175980i
$37$	−21.6628	−	11.0377i	−0.585480	−	0.298317i	0.136048	−	0.990702i	$-0.456560\pi$
$37$	−21.6628	−	11.0377i	−0.585480	−	0.298317i	−0.721528	+	0.692385i	$0.756560\pi$
$38$	−29.3374	+	57.5779i	−0.772037	+	1.51521i
$39$	−5.43018	−	1.76437i	−0.139235	−	0.0452403i
$40$	21.2299	+	6.46276i	0.530748	+	0.161569i
$41$	13.9284	+	42.8673i	0.339718	+	1.04554i	0.964351	+	0.264626i	$0.0852484\pi$
$41$	13.9284	+	42.8673i	0.339718	+	1.04554i	−0.624634	+	0.780918i	$0.714752\pi$
$42$	−2.96487	+	18.7195i	−0.0705921	+	0.445701i
$43$	−8.53203	−	8.53203i	−0.198419	−	0.198419i	0.600903	−	0.799322i	$-0.294808\pi$
$43$	−8.53203	−	8.53203i	−0.198419	−	0.198419i	−0.799322	+	0.600903i	$0.794808\pi$
$44$	−10.5950	−	14.5828i	−0.240795	−	0.331426i
$45$	14.7690	−	2.62247i	0.328199	−	0.0582771i
$46$	−39.4805	−	28.6843i	−0.858272	−	0.623571i
$47$	−39.8112	+	6.30548i	−0.847048	+	0.134159i	−0.564846	−	0.825196i	$-0.691065\pi$
$47$	−39.8112	+	6.30548i	−0.847048	+	0.134159i	−0.282201	+	0.959355i	$0.591065\pi$
$48$	30.7904	−	15.6885i	0.641466	−	0.326843i
$49$			29.7512i			0.607167i
$50$	−12.0444	−	61.1777i	−0.240887	−	1.22355i
$51$	−48.8495			−0.957833
$52$	3.32302	+	6.52180i	0.0639042	+	0.125419i
$53$	14.2819	+	90.1725i	0.269470	+	1.70137i	0.636597	+	0.771197i	$0.280341\pi$
$53$	14.2819	+	90.1725i	0.269470	+	1.70137i	−0.367127	+	0.930171i	$0.619659\pi$
$54$	7.61748	−	10.4846i	0.141064	−	0.194158i
$55$	17.7494	−	36.5029i	0.322716	−	0.663689i
$56$	−15.7537	+	11.4457i	−0.281316	+	0.204388i
$57$	−31.7329	+	31.7329i	−0.556718	+	0.556718i
$58$	−85.4499	−	13.5339i	−1.47327	−	0.233344i
$59$	101.152	−	32.8662i	1.71444	−	0.557055i	0.723377	−	0.690454i	$-0.242589\pi$
$59$	101.152	−	32.8662i	1.71444	−	0.557055i	0.991062	+	0.133399i	$0.0425890\pi$
$60$	−15.7652	−	11.0107i	−0.262753	−	0.183512i
$61$	−4.73879	+	14.5845i	−0.0776851	+	0.239090i	−0.982356	−	0.187021i	$-0.940117\pi$
$61$	−4.73879	+	14.5845i	−0.0776851	+	0.239090i	0.904671	+	0.426111i	$0.140117\pi$
$62$	−24.1087	−	12.2840i	−0.388850	−	0.198129i
$63$	−5.97544	+	11.7275i	−0.0948483	+	0.186150i
$64$	−0.0212563	−	0.00690660i	−0.000332130	−	0.000107916i
$65$	−9.43761	+	13.5128i	−0.145194	+	0.207890i
$66$	−10.8367	−	33.3519i	−0.164192	−	0.505332i
$67$	4.18666	−	26.4335i	0.0624874	−	0.394530i	−0.936545	−	0.350548i	$-0.885995\pi$
$67$	4.18666	−	26.4335i	0.0624874	−	0.394530i	0.999032	−	0.0439823i	$-0.0140045\pi$
$68$	44.2816	+	44.2816i	0.651200	+	0.651200i
$69$	−19.9202	−	27.4178i	−0.288699	−	0.397360i
$70$	49.2036	+	23.9251i	0.702909	+	0.341787i
$71$	−41.3332	−	30.0303i	−0.582158	−	0.422963i	0.257343	−	0.966320i	$-0.417153\pi$
$71$	−41.3332	−	30.0303i	−0.582158	−	0.422963i	−0.839501	+	0.543357i	$0.817153\pi$
$72$	13.1512	−	2.08294i	0.182655	−	0.0289297i
$73$	101.623	−	51.7793i	1.39209	−	0.709306i	0.412622	−	0.910902i	$-0.364613\pi$
$73$	101.623	−	51.7793i	1.39209	−	0.709306i	0.979469	+	0.201596i	$0.0646130\pi$
$74$			60.6378i			0.819430i
$75$	5.17381	−	42.9911i	0.0689841	−	0.573214i
$76$	57.5312			0.756989
$77$	16.1693	+	31.7341i	0.209991	+	0.412131i
$78$	2.22767	+	14.0650i	0.0285599	+	0.180320i
$79$	21.7607	−	29.9510i	0.275452	−	0.379127i	−0.648769	−	0.760985i	$-0.724716\pi$
$79$	21.7607	−	29.9510i	0.275452	−	0.379127i	0.924221	+	0.381859i	$0.124716\pi$
$80$	−17.4406	−	98.2206i	−0.218008	−	1.22776i
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	79.4905	−	79.4905i	0.969396	−	0.969396i
$83$	−102.284	−	16.2002i	−1.23234	−	0.195183i	−0.493907	−	0.869514i	$-0.664432\pi$
$83$	−102.284	−	16.2002i	−1.23234	−	0.195183i	−0.738429	+	0.674332i	$0.764432\pi$
$84$	16.0475	−	5.21416i	0.191042	−	0.0620733i
$85$	−41.0671	+	134.904i	−0.483142	+	1.58711i
$86$	−9.29951	+	28.6210i	−0.108134	+	0.332802i
$87$	−53.5331	−	27.2765i	−0.615323	−	0.313523i
$88$	16.3573	−	32.1031i	0.185879	−	0.364808i
$89$	108.616	+	35.2914i	1.22040	+	0.396533i	0.847229	−	0.531228i	$-0.178269\pi$
$89$	108.616	+	35.2914i	1.22040	+	0.396533i	0.373175	+	0.927761i	$0.378269\pi$
$90$	−22.5505	−	29.8509i	−0.250561	−	0.331676i
$91$	−4.46922	−	13.7548i	−0.0491123	−	0.151152i
$92$	−6.79652	+	42.9115i	−0.0738752	+	0.466429i
$93$	−13.2870	−	13.2870i	−0.142871	−	0.142871i
$94$	59.0902	+	81.3306i	0.628619	+	0.865219i
$95$	60.9570	+	114.312i	0.641652	+	1.20328i
$96$	−44.8500	−	32.5855i	−0.467188	−	0.339432i
$97$	−58.1488	+	9.20986i	−0.599472	+	0.0949470i	−0.448793	−	0.893636i	$-0.648146\pi$
$97$	−58.1488	+	9.20986i	−0.599472	+	0.0949470i	−0.150679	+	0.988583i	$0.548146\pi$
$98$	66.1143	−	33.6869i	0.674636	−	0.343744i
$99$		−	24.3537i		−	0.245997i
$100$	−43.6610	+	34.2810i	−0.436610	+	0.342810i
$101$	76.1042			0.753507			0.376754	−	0.926313i	$-0.377040\pi$
$101$	76.1042			0.753507			0.376754	+	0.926313i	$0.377040\pi$
$102$	55.3117	+	108.555i	0.542272	+	1.06427i
$103$	−0.501856	−	3.16859i	−0.00487239	−	0.0307631i	0.985132	−	0.171797i	$-0.0549573\pi$
$103$	−0.501856	−	3.16859i	−0.00487239	−	0.0307631i	−0.990005	+	0.141034i	$0.954957\pi$
$104$	−8.59981	+	11.8366i	−0.0826905	+	0.113814i
$105$	27.3634	+	26.3611i	0.260604	+	0.251058i
$106$	184.214	−	133.839i	1.73787	−	1.26263i
$107$	−93.9432	+	93.9432i	−0.877974	+	0.877974i	−0.993325	−	0.115351i	$-0.963201\pi$
$107$	−93.9432	+	93.9432i	−0.877974	+	0.877974i	0.115351	+	0.993325i	$0.463201\pi$
$108$	−11.3957	−	1.80490i	−0.105516	−	0.0167121i
$109$	−203.328	+	66.0652i	−1.86539	+	0.606103i	−0.872269	+	0.489026i	$0.837352\pi$
$109$	−203.328	+	66.0652i	−1.86539	+	0.606103i	−0.993123	+	0.117076i	$0.962648\pi$
$110$	−101.216	+	1.88838i	−0.920143	+	0.0171671i
$111$	−13.0130	+	40.0498i	−0.117234	+	0.360809i
$112$	77.9931	+	39.7395i	0.696367	+	0.354817i
$113$	64.1541	−	125.909i	0.567735	−	1.11424i	−0.411480	−	0.911419i	$-0.634988\pi$
$113$	64.1541	−	125.909i	0.567735	−	1.11424i	0.979215	−	0.202824i	$-0.0650119\pi$
$114$	106.449	+	34.5874i	0.933763	+	0.303398i
$115$	−92.4644	+	31.9624i	−0.804039	+	0.277934i
$116$	23.8014	+	73.2532i	0.205184	+	0.631493i
$117$	−1.54704	+	9.76761i	−0.0132225	+	0.0834838i
$118$	−187.570	−	187.570i	−1.58958	−	1.58958i
$119$	−72.7311	−	100.106i	−0.611185	−	0.841224i
$120$	5.30371	−	38.0697i	0.0441976	−	0.317247i
$121$	44.5768	+	32.3869i	0.368403	+	0.267661i
$122$	37.7760	−	5.98312i	0.309639	−	0.0490420i
$123$	69.5603	−	35.4427i	0.565531	−	0.288152i
$124$			24.0892i			0.194267i
$125$	−114.376	−	50.4301i	−0.915006	−	0.403441i
$126$	32.8272			0.260533
$127$	−84.6861	−	166.206i	−0.666820	−	1.30871i	−0.938152	−	0.346222i	$-0.887464\pi$
$127$	−84.6861	−	166.206i	−0.666820	−	1.30871i	0.271332	−	0.962486i	$-0.412536\pi$
$128$	−20.0193	−	126.397i	−0.156400	−	0.987473i
$129$	−12.2842	+	16.9077i	−0.0952263	+	0.131068i
$130$	40.7149	+	5.67223i	0.313192	+	0.0436325i
$131$	132.639	−	96.3682i	1.01251	−	0.735635i	0.0477795	−	0.998858i	$-0.484786\pi$
$131$	132.639	−	96.3682i	1.01251	−	0.735635i	0.964735	+	0.263223i	$0.0847855\pi$
$132$	−22.0764	+	22.0764i	−0.167245	+	0.167245i
$133$	−112.276	−	17.7827i	−0.844179	−	0.133705i
$134$	−63.4822	+	20.6266i	−0.473748	+	0.153930i
$135$	−8.48802	−	24.5551i	−0.0628742	−	0.181890i
$136$	−38.6816	+	119.050i	−0.284424	+	0.875366i
$137$	113.672	+	57.9190i	0.829726	+	0.422766i	0.816640	−	0.577148i	$-0.195834\pi$
$137$	113.672	+	57.9190i	0.829726	+	0.422766i	0.0130861	+	0.999914i	$0.495834\pi$
$138$	−38.3736	+	75.3124i	−0.278070	+	0.545742i
$139$	−17.6523	−	5.73557i	−0.126995	−	0.0412631i	0.244830	−	0.969566i	$-0.421268\pi$
$139$	−17.6523	−	5.73557i	−0.126995	−	0.0412631i	−0.371825	+	0.928303i	$0.621268\pi$
$140$	−0.908607	−	48.7008i	−0.00649005	−	0.347863i
$141$	21.5739	+	66.3977i	0.153006	+	0.470905i
$142$	−19.9335	+	125.855i	−0.140377	+	0.886306i
$143$	18.9223	+	18.9223i	0.132324	+	0.132324i
$144$	−35.1814	−	48.4231i	−0.244315	−	0.336271i
$145$	−120.332	+	124.907i	−0.829876	+	0.861430i
$146$	−230.132	−	167.201i	−1.57625	−	1.14521i
$147$	50.8961	−	8.06116i	0.346232	−	0.0548378i
$148$	48.1009	−	24.5086i	0.325006	−	0.165599i
$149$		−	10.5645i		−	0.0709024i	−0.999371	−	0.0354512i	$-0.988713\pi$
$149$		−	10.5645i		−	0.0709024i	0.999371	−	0.0354512i	$-0.0112868\pi$
$150$	−101.395	+	37.1809i	−0.675965	+	0.247872i
$151$	119.808			0.793433			0.396716	−	0.917941i	$-0.370150\pi$
$151$	119.808			0.793433			0.396716	+	0.917941i	$0.370150\pi$
$152$	52.2076	+	102.463i	0.343471	+	0.674100i
$153$	13.2359	+	83.5681i	0.0865090	+	0.546197i
$154$	52.2125	−	71.8643i	0.339042	−	0.466651i
$155$	−47.8640	+	25.5236i	−0.308800	+	0.164668i
$156$	10.2566	−	7.45188i	0.0657476	−	0.0477684i
$157$	61.8710	−	61.8710i	0.394083	−	0.394083i	−0.482057	−	0.876140i	$-0.660110\pi$
$157$	61.8710	−	61.8710i	0.394083	−	0.394083i	0.876140	+	0.482057i	$0.160110\pi$
$158$	−91.1978	−	14.4443i	−0.577202	−	0.0914197i
$159$	150.391	−	48.8649i	0.945854	−	0.307326i
$160$	−127.694	+	96.4649i	−0.798086	+	0.602905i
$161$	26.5277	−	81.6438i	0.164768	−	0.507104i
$162$	−20.0002	−	10.1906i	−0.123458	−	0.0629050i
$163$	−133.685	+	262.372i	−0.820153	+	1.60964i	−0.0277732	+	0.999614i	$0.508842\pi$
$163$	−133.685	+	262.372i	−0.820153	+	1.60964i	−0.792380	+	0.610028i	$0.791158\pi$
$164$	−95.1843	−	30.9272i	−0.580392	−	0.188581i
$165$	−67.2557	−	20.4738i	−0.407610	−	0.124084i
$166$	79.8142	+	245.643i	0.480809	+	1.47978i
$167$	4.43427	−	27.9969i	0.0265525	−	0.167646i	−0.970849	−	0.239693i	$-0.922953\pi$
$167$	4.43427	−	27.9969i	0.0265525	−	0.167646i	0.997401	+	0.0720471i	$0.0229532\pi$
$168$	23.8490	+	23.8490i	0.141958	+	0.141958i
$169$	92.9485	+	127.933i	0.549991	+	0.756998i
$170$	346.289	−	61.4892i	2.03700	−	0.361701i
$171$	62.8844	+	45.6882i	0.367745	+	0.267182i
$172$	26.4622	−	4.19120i	0.153850	−	0.0243675i
$173$	41.8042	−	21.3003i	0.241643	−	0.123123i	−0.328976	−	0.944338i	$-0.606703\pi$
$173$	41.8042	−	21.3003i	0.241643	−	0.123123i	0.570619	+	0.821215i	$0.306703\pi$
$174$			149.848i			0.861198i
$175$	95.8035	−	53.4061i	0.547448	−	0.305178i
$176$	−161.963			−0.920246
$177$	−83.6325	−	164.138i	−0.472500	−	0.927334i
$178$	−44.5585	−	281.331i	−0.250328	−	1.58051i
$179$	−65.0062	+	89.4733i	−0.363163	+	0.499851i	−0.951027	−	0.309109i	$-0.899969\pi$
$179$	−65.0062	+	89.4733i	−0.363163	+	0.499851i	0.587864	+	0.808960i	$0.299969\pi$
$180$	−14.5647	+	29.9533i	−0.0809149	+	0.166407i
$181$	152.214	−	110.590i	0.840962	−	0.610995i	−0.0816769	−	0.996659i	$-0.526028\pi$
$181$	152.214	−	110.590i	0.840962	−	0.610995i	0.922639	+	0.385664i	$0.126028\pi$
$182$	−25.5061	+	25.5061i	−0.140144	+	0.140144i
$183$	26.2341	+	4.15507i	0.143356	+	0.0227053i
$184$	−82.5931	+	26.8361i	−0.448876	+	0.145849i
$185$	99.6627	+	69.6062i	0.538717	+	0.376250i
$186$	−14.4822	+	44.5718i	−0.0778615	+	0.239633i
$187$	203.997	+	103.941i	1.09089	+	0.555837i
$188$	40.6323	−	79.7455i	0.216129	−	0.424178i
$189$	21.6815	+	7.04476i	0.114717	+	0.0372739i
$190$	185.008	−	264.895i	0.973725	−	1.39419i
$191$	−47.3319	−	145.673i	−0.247811	−	0.762683i	−0.995161	−	0.0982534i	$-0.968674\pi$
$191$	−47.3319	−	145.673i	−0.247811	−	0.762683i	0.747351	−	0.664430i	$-0.231326\pi$
$192$	−0.00605585	+	0.0382351i	−3.15409e−5	+	0.000199141i
$193$	243.828	+	243.828i	1.26336	+	1.26336i	0.949456	+	0.313901i	$0.101636\pi$
$193$	243.828	+	243.828i	1.26336	+	1.26336i	0.313901	+	0.949456i	$0.398364\pi$
$194$	86.3078	+	118.792i	0.444885	+	0.612332i
$195$	25.6739	+	12.4838i	0.131661	+	0.0640197i
$196$	−53.4443	−	38.8295i	−0.272675	−	0.198110i
$197$	−212.135	+	33.5989i	−1.07683	+	0.170553i	−0.669562	−	0.742757i	$-0.733518\pi$
$197$	−212.135	+	33.5989i	−1.07683	+	0.170553i	−0.407266	+	0.913309i	$0.633518\pi$
$198$	−54.1197	+	27.5754i	−0.273332	+	0.139270i
$199$		−	261.788i		−	1.31552i	−0.753228	−	0.657760i	$-0.771504\pi$
$199$		−	261.788i		−	1.31552i	0.753228	−	0.657760i	$-0.228496\pi$
$200$	−100.676	−	46.6516i	−0.503378	−	0.233258i
$201$	−46.3549			−0.230621
$202$	−86.1720	−	169.122i	−0.426594	−	0.837238i
$203$	−23.8076	−	150.315i	−0.117279	−	0.740469i
$204$	63.7555	−	87.7519i	0.312527	−	0.430157i
$205$	−39.4011	−	221.896i	−0.192201	−	1.08242i
$206$	−6.47314	+	4.70301i	−0.0314230	+	0.0228302i
$207$	−41.5070	+	41.5070i	−0.200517	+	0.200517i
$208$	64.9592	+	10.2885i	0.312304	+	0.0494641i
$209$	200.038	−	64.9964i	0.957121	−	0.310988i
$210$	27.5974	−	90.6565i	0.131416	−	0.431697i
$211$	−5.06063	+	15.5750i	−0.0239840	+	0.0738152i	−0.962332	−	0.271877i	$-0.912356\pi$
$211$	−5.06063	+	15.5750i	−0.0239840	+	0.0738152i	0.938348	+	0.345692i	$0.112356\pi$
$212$	−180.623	−	92.0323i	−0.851997	−	0.434114i
$213$	−40.1744	+	78.8466i	−0.188612	+	0.370172i
$214$	315.135	+	102.394i	1.47260	+	0.478475i
$215$	36.3657	+	48.1384i	0.169143	+	0.223900i
$216$	−7.12668	−	21.9337i	−0.0329939	−	0.101545i
$217$	7.44589	−	47.0115i	0.0343129	−	0.216643i
$218$	377.039	+	377.039i	1.72954	+	1.72954i
$219$	−116.115	−	159.819i	−0.530206	−	0.729766i
$220$	42.4074	+	79.5260i	0.192761	+	0.361482i
$221$	−75.2149	−	54.6468i	−0.340339	−	0.247271i
$222$	103.735	−	16.4300i	0.467274	−	0.0740089i
$223$	−38.6309	+	19.6834i	−0.173233	+	0.0882664i	−0.538457	−	0.842653i	$-0.680992\pi$
$223$	−38.6309	+	19.6834i	−0.173233	+	0.0882664i	0.365224	+	0.930920i	$0.380992\pi$
$224$		−	140.426i		−	0.626900i
$225$	−74.9478	+	2.79757i	−0.333101	+	0.0124336i
$226$	−352.442			−1.55948
$227$	74.0305	+	145.293i	0.326126	+	0.640058i	0.994612	−	0.103667i	$-0.0330575\pi$
$227$	74.0305	+	145.293i	0.326126	+	0.640058i	−0.668486	+	0.743724i	$0.733058\pi$
$228$	−15.5882	−	98.4201i	−0.0683694	−	0.431667i
$229$	−5.52850	+	7.60933i	−0.0241419	+	0.0332285i	−0.820917	−	0.571047i	$-0.806537\pi$
$229$	−5.52850	+	7.60933i	−0.0241419	+	0.0332285i	0.796775	+	0.604276i	$0.206537\pi$
$230$	175.725	+	169.288i	0.764020	+	0.736034i
$231$	49.9072	−	36.2597i	0.216048	−	0.156968i
$232$	−108.865	+	108.865i	−0.469246	+	0.469246i
$233$	26.5415	+	4.20377i	0.113912	+	0.0180419i	0.213130	−	0.977024i	$-0.431634\pi$
$233$	26.5415	+	4.20377i	0.113912	+	0.0180419i	−0.0992181	+	0.995066i	$0.531634\pi$
$234$	23.4577	−	7.62187i	0.100247	−	0.0325721i
$235$	201.502	−	3.75942i	0.857457	−	0.0159975i
$236$	−72.9776	+	224.602i	−0.309227	+	0.951703i
$237$	−57.1341	−	29.1113i	−0.241072	−	0.122832i
$238$	−140.107	+	274.975i	−0.588683	+	1.15536i
$239$	−325.106	−	105.633i	−1.36028	−	0.441981i	−0.464141	−	0.885761i	$-0.653637\pi$
$239$	−325.106	−	105.633i	−1.36028	−	0.441981i	−0.896135	+	0.443781i	$0.853637\pi$
$240$	−163.303	+	56.4493i	−0.680429	+	0.235205i
$241$	−27.6920	−	85.2271i	−0.114904	−	0.353639i	0.877023	−	0.480449i	$-0.159526\pi$
$241$	−27.6920	−	85.2271i	−0.114904	−	0.353639i	−0.991927	+	0.126810i	$0.959526\pi$
$242$	21.4978	−	135.732i	0.0888339	−	0.560875i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	−20.0144	−	27.5475i	−0.0820263	−	0.112900i
$245$	20.5258	−	147.333i	0.0837788	−	0.601359i
$246$	−157.525	−	114.448i	−0.640344	−	0.465237i
$247$	−84.3589	+	13.3611i	−0.341534	+	0.0540937i
$248$	−42.9029	+	21.8601i	−0.172995	+	0.0881456i
$249$			179.369i			0.720358i
$250$	17.4383	+	311.272i	0.0697534	+	1.24509i
$251$	−259.732			−1.03479			−0.517394	−	0.855747i	$-0.673098\pi$
$251$	−259.732			−1.03479			−0.517394	+	0.855747i	$0.673098\pi$
$252$	−13.2681	−	26.0401i	−0.0526513	−	0.103334i
$253$	24.8479	+	156.884i	0.0982131	+	0.620093i
$254$	−273.461	+	376.386i	−1.07662	+	1.48184i
$255$	241.911	+	33.7020i	0.948671	+	0.132165i
$256$	−258.289	+	187.658i	−1.00894	+	0.733038i
$257$	−124.723	+	124.723i	−0.485305	+	0.485305i	−0.906821	−	0.421516i	$-0.861498\pi$
$257$	−124.723	+	124.723i	−0.485305	+	0.485305i	0.421516	+	0.906821i	$0.361498\pi$
$258$	51.4823	+	8.15400i	0.199544	+	0.0316047i
$259$	−101.448	+	32.9623i	−0.391689	+	0.127268i
$260$	−11.9567	−	34.5897i	−0.0459872	−	0.133037i
$261$	−32.1577	+	98.9711i	−0.123209	+	0.379200i
$262$	−364.340	−	185.640i	−1.39061	−	0.708551i
$263$	−40.7100	+	79.8979i	−0.154791	+	0.303794i	−0.955359	−	0.295448i	$-0.904531\pi$
$263$	−40.7100	+	79.8979i	−0.154791	+	0.303794i	0.800568	+	0.599242i	$0.204531\pi$
$264$	−59.3517	−	19.2845i	−0.224817	−	0.0730474i
$265$	−8.51509	−	456.403i	−0.0321324	−	1.72228i
$266$	87.6111	+	269.639i	0.329365	+	1.01368i
$267$	30.9443	−	195.374i	0.115896	−	0.731739i
$268$	42.0203	+	42.0203i	0.156792	+	0.156792i
$269$	29.3157	+	40.3496i	0.108980	+	0.149999i	0.860023	−	0.510255i	$-0.170449\pi$
$269$	29.3157	+	40.3496i	0.108980	+	0.149999i	−0.751043	+	0.660253i	$0.770449\pi$
$270$	−44.9565	+	46.6659i	−0.166506	+	0.172837i
$271$	−176.269	−	128.067i	−0.650439	−	0.472571i	0.212982	−	0.977056i	$-0.431682\pi$
$271$	−176.269	−	128.067i	−0.650439	−	0.472571i	−0.863421	+	0.504485i	$0.831682\pi$
$272$	555.767	−	88.0248i	2.04326	−	0.323621i
$273$	−22.3198	+	11.3725i	−0.0817576	+	0.0416576i
$274$		−	318.189i		−	1.16127i
$275$	−113.082	+	168.523i	−0.411207	+	0.612811i
$276$	75.2514			0.272650
$277$	−16.1472	−	31.6907i	−0.0582933	−	0.114407i	0.860022	−	0.510257i	$-0.170450\pi$
$277$	−16.1472	−	31.6907i	−0.0582933	−	0.114407i	−0.918315	+	0.395850i	$0.870450\pi$
$278$	7.24165	+	45.7220i	0.0260491	+	0.164467i
$279$	−19.1303	+	26.3306i	−0.0685675	+	0.0943750i
$280$	85.9117	−	45.8125i	0.306827	−	0.163616i
$281$	300.785	−	218.533i	1.07041	−	0.777697i	0.0944226	−	0.995532i	$-0.469900\pi$
$281$	300.785	−	218.533i	1.07041	−	0.777697i	0.975986	+	0.217835i	$0.0698995\pi$
$282$	123.124	−	123.124i	0.436609	−	0.436609i
$283$	246.901	+	39.1052i	0.872441	+	0.138181i	0.576571	−	0.817047i	$-0.304391\pi$
$283$	246.901	+	39.1052i	0.872441	+	0.138181i	0.295870	+	0.955228i	$0.404391\pi$
$284$	107.891	−	35.0561i	0.379900	−	0.123437i
$285$	179.040	−	135.254i	0.628210	−	0.474575i
$286$	20.6245	−	63.4756i	0.0721136	−	0.221943i
$287$	176.199	+	89.7777i	0.613933	+	0.312814i
$288$	−43.5926	+	85.5552i	−0.151363	+	0.297067i
$289$	−481.637	−	156.493i	−1.66657	−	0.541500i
$290$	413.825	+	125.976i	1.42698	+	0.434399i
$291$	31.5111	+	96.9812i	0.108286	+	0.333269i
$292$	−39.6170	+	250.132i	−0.135675	+	0.856615i
$293$	−28.4897	−	28.4897i	−0.0972346	−	0.0972346i	0.656816	−	0.754051i	$-0.271903\pi$
$293$	−28.4897	−	28.4897i	−0.0972346	−	0.0972346i	−0.754051	+	0.656816i	$0.771903\pi$
$294$	−75.5430	−	103.976i	−0.256949	−	0.353660i
$295$	−523.597	+	92.9730i	−1.77490	+	0.315163i
$296$	87.2999	+	63.4271i	0.294932	+	0.214281i
$297$	−41.6624	+	6.59868i	−0.140278	+	0.0222178i
$298$	−23.4768	+	11.9620i	−0.0787812	+	0.0401410i
$299$		−	64.5003i		−	0.215720i
$300$	70.4755	+	65.4036i	0.234918	+	0.218012i
$301$	−52.9382			−0.175874
$302$	−135.658	−	266.243i	−0.449198	−	0.881600i
$303$	−20.6206	−	130.194i	−0.0680549	−	0.429682i
$304$	303.848	−	418.211i	0.999500	−	1.37569i
$305$	33.5294	−	68.9556i	0.109932	−	0.226084i
$306$	170.722	−	124.037i	0.557914	−	0.405348i
$307$	395.674	−	395.674i	1.28884	−	1.28884i	0.353351	−	0.935491i	$-0.385042\pi$
$307$	395.674	−	395.674i	1.28884	−	1.28884i	0.935491	−	0.353351i	$-0.114958\pi$
$308$	−78.1095	−	12.3713i	−0.253602	−	0.0401667i
$309$	−5.28462	+	1.71708i	−0.0171023	+	0.00555688i
$310$	110.916	+	77.4655i	0.357792	+	0.249889i
$311$	−149.055	+	458.744i	−0.479276	+	1.47506i	0.360826	+	0.932633i	$0.382495\pi$
$311$	−149.055	+	458.744i	−0.479276	+	1.47506i	−0.840102	+	0.542428i	$0.817505\pi$
$312$	22.5794	+	11.5048i	0.0723697	+	0.0368742i
$313$	99.5948	−	195.466i	0.318194	−	0.624492i	−0.675406	−	0.737446i	$-0.736032\pi$
$313$	99.5948	−	195.466i	0.318194	−	0.624492i	0.993600	+	0.112955i	$0.0360315\pi$
$314$	−207.548	−	67.4365i	−0.660982	−	0.214766i
$315$	37.6824	−	53.9539i	0.119627	−	0.171282i
$316$	25.4025	+	78.1807i	0.0803875	+	0.247407i
$317$	41.2111	−	260.197i	0.130003	−	0.820809i	−0.833384	−	0.552695i	$-0.813599\pi$
$317$	41.2111	−	260.197i	0.130003	−	0.820809i	0.963387	−	0.268114i	$-0.0864005\pi$
$318$	−278.875	−	278.875i	−0.876967	−	0.876967i
$319$	165.517	+	227.814i	0.518862	+	0.714152i
$320$	0.100500	+	0.0488678i	0.000314063	+	0.000152712i
$321$	186.165	+	135.257i	0.579954	+	0.421361i
$322$	−211.469	+	33.4934i	−0.656737	+	0.104017i
$323$	−651.095	+	331.749i	−2.01577	+	1.02709i
$324$			19.9840i			0.0616789i
$325$	56.0594	−	60.4067i	0.172491	−	0.185867i
$326$	734.423			2.25283
$327$	168.112	+	329.938i	0.514103	+	1.00898i
$328$	−31.2950	−	197.589i	−0.0954116	−	0.602405i
$329$	−103.946	+	143.069i	−0.315944	+	0.434860i
$330$	30.6551	+	172.641i	0.0928944	+	0.523154i
$331$	42.7419	−	31.0538i	0.129130	−	0.0938181i	−0.521346	−	0.853346i	$-0.674570\pi$
$331$	42.7419	−	31.0538i	0.129130	−	0.0938181i	0.650475	+	0.759527i	$0.274570\pi$
$332$	162.597	−	162.597i	0.489749	−	0.489749i
$333$	72.0401	+	11.4100i	0.216337	+	0.0342644i
$334$	−67.2367	+	21.8465i	−0.201307	+	0.0654088i
$335$	−38.9699	+	128.015i	−0.116328	+	0.382134i
$336$	46.8510	−	144.192i	0.139437	−	0.429144i
$337$	556.543	+	283.573i	1.65146	+	0.841463i	0.996297	+	0.0859789i	$0.0274018\pi$
$337$	556.543	+	283.573i	1.65146	+	0.841463i	0.655167	+	0.755484i	$0.272598\pi$
$338$	179.053	−	351.411i	0.529742	−	1.03968i
$339$	−232.779	−	75.6346i	−0.686664	−	0.223111i
$340$	−188.740	−	249.841i	−0.555116	−	0.734826i
$341$	27.2150	+	83.7590i	0.0798092	+	0.245628i
$342$	30.3269	−	191.477i	0.0886752	−	0.559873i
$343$	244.312	+	244.312i	0.712279	+	0.712279i
$344$	31.4781	+	43.3259i	0.0915062	+	0.125947i
$345$	79.7323	+	149.521i	0.231108	+	0.433394i
$346$	−94.6688	−	68.7809i	−0.273609	−	0.198789i
$347$	89.7958	−	14.2223i	0.258777	−	0.0409863i	−0.0256976	−	0.999670i	$-0.508181\pi$
$347$	89.7958	−	14.2223i	0.258777	−	0.0409863i	0.284475	+	0.958683i	$0.408181\pi$
$348$	118.867	−	60.5658i	0.341572	−	0.174040i
$349$			481.591i			1.37992i	0.723849	+	0.689958i	$0.242371\pi$
$349$			481.591i			1.37992i	−0.723849	+	0.689958i	$0.757629\pi$
$350$	−227.158	−	152.427i	−0.649024	−	0.435507i
$351$	17.1289			0.0488002
$352$	117.960	+	231.509i	0.335113	+	0.657697i
$353$	−51.1852	−	323.170i	−0.145000	−	0.915497i	−0.947711	−	0.319129i	$-0.896610\pi$
$353$	−51.1852	−	323.170i	−0.145000	−	0.915497i	0.802711	−	0.596368i	$-0.203390\pi$
$354$	−270.058	+	371.703i	−0.762877	+	1.05001i
$355$	183.971	+	177.232i	0.518228	+	0.499245i
$356$	−205.156	+	149.054i	−0.576281	+	0.418692i
$357$	−151.547	+	151.547i	−0.424501	+	0.424501i
$358$	272.437	+	43.1498i	0.760998	+	0.120530i
$359$	661.981	−	215.091i	1.84396	−	0.599138i	0.846152	−	0.532942i	$-0.178914\pi$
$359$	661.981	−	215.091i	1.84396	−	0.599138i	0.997807	−	0.0661963i	$-0.0210863\pi$
$360$	−66.5639	+	1.24188i	−0.184900	+	0.00344966i
$361$	−95.8935	+	295.130i	−0.265633	+	0.817534i
$362$	−418.109	−	213.037i	−1.15500	−	0.588500i
$363$	43.3270	−	85.0340i	0.119358	−	0.234253i
$364$	30.5418	+	9.92363i	0.0839061	+	0.0272627i
$365$	−538.976	+	186.309i	−1.47665	+	0.510436i
$366$	−20.4710	−	63.0032i	−0.0559316	−	0.172140i
$367$	−69.4532	+	438.510i	−0.189246	+	1.19485i	0.691896	+	0.721997i	$0.256776\pi$
$367$	−69.4532	+	438.510i	−0.189246	+	1.19485i	−0.881141	+	0.472853i	$0.843224\pi$
$368$	276.041	+	276.041i	0.750111	+	0.750111i
$369$	−79.4803	−	109.395i	−0.215394	−	0.296464i
$370$	41.8350	−	300.289i	0.113068	−	0.811592i
$371$	324.051	+	235.437i	0.873454	+	0.634601i
$372$	41.2100	−	6.52702i	0.110779	−	0.0175457i
$373$	208.656	−	106.315i	0.559399	−	0.285028i	−0.151342	−	0.988481i	$-0.548360\pi$
$373$	208.656	−	106.315i	0.559399	−	0.285028i	0.710741	+	0.703453i	$0.248360\pi$
$374$		−	571.022i		−	1.52680i
$375$	−55.2818	+	209.330i	−0.147418	+	0.558213i
$376$	178.899			0.475796
$377$	−51.9128	−	101.885i	−0.137700	−	0.270251i
$378$	−8.89461	−	56.1584i	−0.0235307	−	0.148567i
$379$	45.5534	−	62.6989i	0.120194	−	0.165432i	−0.744680	−	0.667421i	$-0.767398\pi$
$379$	45.5534	−	62.6989i	0.120194	−	0.165432i	0.864874	+	0.501989i	$0.167398\pi$
$380$	−284.904	−	39.6917i	−0.749748	−	0.104452i
$381$	−261.387	+	189.909i	−0.686055	+	0.498448i
$382$	−270.126	+	270.126i	−0.707137	+	0.707137i
$383$	−484.436	−	76.7271i	−1.26485	−	0.200332i	−0.512262	−	0.858829i	$-0.671192\pi$
$383$	−484.436	−	76.7271i	−1.26485	−	0.200332i	−0.752583	+	0.658497i	$0.771192\pi$
$384$	−210.806	+	68.4949i	−0.548973	+	0.178372i
$385$	−58.1794	−	168.308i	−0.151115	−	0.437164i
$386$	265.761	−	817.928i	0.688500	−	2.11898i
$387$	32.2529	+	16.4337i	0.0833409	+	0.0424643i
$388$	59.3481	−	116.477i	0.152959	−	0.300199i
$389$	−229.887	−	74.6949i	−0.590970	−	0.192018i	−0.00176103	−	0.999998i	$-0.500561\pi$
$389$	−229.887	−	74.6949i	−0.590970	−	0.192018i	−0.589209	+	0.807981i	$0.700561\pi$
$390$	−1.32817	−	71.1890i	−0.00340556	−	0.182536i
$391$	−170.528	−	524.832i	−0.436134	−	1.34228i
$392$	20.6566	−	130.421i	0.0526955	−	0.332706i
$393$	−200.799	−	200.799i	−0.510938	−	0.510938i
$394$	314.863	+	433.372i	0.799145	+	1.09993i
$395$	−128.426	+	133.310i	−0.325130	+	0.337493i
$396$	43.7483	+	31.7850i	0.110475	+	0.0802651i
$397$	−357.414	+	56.6087i	−0.900286	+	0.142591i	−0.589386	−	0.807851i	$-0.700630\pi$
$397$	−357.414	+	56.6087i	−0.900286	+	0.142591i	−0.310900	+	0.950443i	$0.600630\pi$
$398$	−581.757	+	296.420i	−1.46170	+	0.744774i
$399$			196.891i			0.493462i
$400$	18.6051	+	498.438i	0.0465128	+	1.24610i
$401$	−41.2205			−0.102794			−0.0513972	−	0.998678i	$-0.516367\pi$
$401$	−41.2205			−0.102794			−0.0513972	+	0.998678i	$0.516367\pi$
$402$	52.4871	+	103.012i	0.130565	+	0.256248i
$403$	−5.59451	−	35.3223i	−0.0138822	−	0.0876485i
$404$	−99.3269	+	136.712i	−0.245859	+	0.338395i
$405$	−39.7072	+	21.1739i	−0.0980425	+	0.0522813i
$406$	−307.080	+	223.106i	−0.756354	+	0.549523i
$407$	139.560	−	139.560i	0.342899	−	0.342899i
$408$	214.142	+	33.9168i	0.524859	+	0.0831295i
$409$	−11.1021	+	3.60730i	−0.0271446	+	0.00881980i	−0.322558	−	0.946550i	$-0.604543\pi$
$409$	−11.1021	+	3.60730i	−0.0271446	+	0.00881980i	0.295413	+	0.955370i	$0.404543\pi$
$410$	−448.492	+	338.809i	−1.09388	+	0.826363i
$411$	68.2837	−	210.156i	0.166140	−	0.511328i
$412$	6.34698	+	3.23395i	0.0154053	+	0.00784938i
$413$	211.844	−	415.768i	0.512940	−	1.00670i
$414$	139.236	+	45.2407i	0.336320	+	0.109277i
$415$	495.351	+	150.793i	1.19362	+	0.363358i
$416$	−32.6042	−	100.346i	−0.0783756	−	0.241215i
$417$	−5.02907	+	31.7523i	−0.0120601	+	0.0761445i
$418$	−370.939	−	370.939i	−0.887414	−	0.887414i
$419$	172.247	+	237.078i	0.411091	+	0.565818i	0.963484	−	0.267766i	$-0.0862853\pi$
$419$	172.247	+	237.078i	0.411091	+	0.565818i	−0.552393	+	0.833584i	$0.686285\pi$
$420$	−83.0675	+	14.7500i	−0.197780	+	0.0351190i
$421$	−180.537	−	131.168i	−0.428830	−	0.311563i	0.352351	−	0.935868i	$-0.385382\pi$
$421$	−180.537	−	131.168i	−0.428830	−	0.311563i	−0.781181	+	0.624305i	$0.785382\pi$
$422$	40.3415	−	6.38947i	0.0955960	−	0.0151409i
$423$	107.743	−	54.8977i	0.254711	−	0.129782i
$424$		−	405.207i		−	0.955677i
$425$	296.444	−	639.735i	0.697515	−	1.50526i
$426$	220.705			0.518088
$427$	30.5446	+	59.9471i	0.0715329	+	0.140391i
$428$	−46.1479	−	291.366i	−0.107822	−	0.680763i
$429$	27.2439	−	37.4980i	0.0635056	−	0.0874080i
$430$	65.7988	−	135.320i	0.153021	−	0.314698i
$431$	−251.983	+	183.076i	−0.584647	+	0.424771i	−0.840396	−	0.541972i	$-0.817678\pi$
$431$	−251.983	+	183.076i	−0.584647	+	0.424771i	0.255750	+	0.966743i	$0.417678\pi$
$432$	−73.3061	+	73.3061i	−0.169690	+	0.169690i
$433$	384.955	+	60.9708i	0.889041	+	0.140810i	0.584216	−	0.811598i	$-0.301402\pi$
$433$	384.955	+	60.9708i	0.889041	+	0.140810i	0.304825	+	0.952408i	$0.401402\pi$
$434$	−112.902	+	36.6841i	−0.260143	+	0.0845255i
$435$	246.287	+	172.011i	0.566176	+	0.395428i
$436$	146.694	−	451.477i	0.336454	−	1.03550i
$437$	−451.710	−	230.158i	−1.03366	−	0.526677i
$438$	−223.680	+	438.997i	−0.510685	+	1.00228i
$439$	648.013	+	210.552i	1.47611	+	0.479617i	0.932948	−	0.360010i	$-0.117227\pi$
$439$	648.013	+	210.552i	1.47611	+	0.479617i	0.543162	+	0.839628i	$0.317227\pi$
$440$	−103.153	+	147.695i	−0.234438	+	0.335670i
$441$	−27.5809	−	84.8852i	−0.0625416	−	0.192483i
$442$	−36.2735	+	229.022i	−0.0820667	+	0.518149i
$443$	109.896	+	109.896i	0.248072	+	0.248072i	0.820179	−	0.572107i	$-0.193874\pi$
$443$	109.896	+	109.896i	0.248072	+	0.248072i	−0.572107	+	0.820179i	$0.693874\pi$
$444$	−54.9606	−	75.6468i	−0.123785	−	0.170376i
$445$	−513.537	−	249.705i	−1.15401	−	0.561135i
$446$	87.4826	+	63.5598i	0.196149	+	0.142511i
$447$	−18.0729	+	2.86246i	−0.0404315	+	0.00640372i
$448$	−0.0873705	+	0.0445175i	−0.000195023	+	9.93694e-5i
$449$			352.558i			0.785208i	0.919708	+	0.392604i	$0.128426\pi$
$449$			352.558i			0.785208i	−0.919708	+	0.392604i	$0.871574\pi$
$450$	91.0795	+	163.385i	0.202399	+	0.363077i
$451$	−365.900			−0.811308
$452$	142.450	+	279.574i	0.315156	+	0.618527i
$453$	−32.4624	−	204.959i	−0.0716609	−	0.452449i
$454$	239.053	−	329.028i	0.526547	−	0.724730i
$455$	12.6427	+	71.1997i	0.0277861	+	0.156483i
$456$	161.141	−	117.076i	0.353379	−	0.256745i
$457$	−453.981	+	453.981i	−0.993395	+	0.993395i	−0.999978	−	0.00658340i	$-0.997904\pi$
$457$	−453.981	+	453.981i	−0.993395	+	0.993395i	0.00658340	+	0.999978i	$0.497904\pi$
$458$	23.1696	+	3.66971i	0.0505887	+	0.00801247i
$459$	139.376	−	45.2859i	0.303651	−	0.0986622i
$460$	63.2629	−	207.816i	0.137528	−	0.451774i
$461$	20.3868	−	62.7440i	0.0442229	−	0.136104i	−0.926507	−	0.376277i	$-0.877204\pi$
$461$	20.3868	−	62.7440i	0.0442229	−	0.136104i	0.970730	+	0.240173i	$0.0772041\pi$
$462$	−137.087	−	69.8494i	−0.296726	−	0.151189i
$463$	−186.633	+	366.287i	−0.403094	+	0.791117i	−0.999937	−	0.0112413i	$-0.996422\pi$
$463$	−186.633	+	366.287i	−0.403094	+	0.791117i	0.596843	+	0.802358i	$0.296422\pi$
$464$	658.204	+	213.863i	1.41854	+	0.460913i
$465$	56.6327	+	74.9666i	0.121791	+	0.161219i
$466$	−20.7109	−	63.7416i	−0.0444440	−	0.136785i
$467$	−35.3093	+	222.934i	−0.0756088	+	0.477375i	0.920609	+	0.390485i	$0.127693\pi$
$467$	−35.3093	+	222.934i	−0.0756088	+	0.477375i	−0.996218	+	0.0868898i	$0.972307\pi$
$468$	−15.5272	−	15.5272i	−0.0331777	−	0.0331777i
$469$	−69.0169	−	94.9936i	−0.147158	−	0.202545i
$470$	−236.513	−	443.531i	−0.503220	−	0.943682i
$471$	−122.608	−	89.0803i	−0.260315	−	0.189130i
$472$	−466.241	+	73.8454i	−0.987799	+	0.156452i
$473$	87.2752	−	44.4689i	0.184514	−	0.0940147i
$474$			159.928i			0.337401i
$475$	−223.004	−	608.147i	−0.469482	−	1.28031i
$476$	274.752			0.577210
$477$	−124.343	−	244.037i	−0.260678	−	0.511609i
$478$	133.371	+	842.072i	0.279019	+	1.76166i
$479$	107.714	−	148.256i	0.224874	−	0.309512i	−0.681641	−	0.731687i	$-0.738733\pi$
$479$	107.714	−	148.256i	0.224874	−	0.309512i	0.906514	+	0.422175i	$0.138733\pi$
$480$	199.624	+	192.312i	0.415883	+	0.400649i
$481$	−64.8392	+	47.1084i	−0.134801	+	0.0979386i
$482$	−158.040	+	158.040i	−0.327884	+	0.327884i
$483$	−146.858	−	23.2600i	−0.304054	−	0.0481574i
$484$	−116.358	+	37.8070i	−0.240409	+	0.0781137i
$485$	294.317	−	5.49105i	0.606839	−	0.0113218i
$486$	−12.0142	+	36.9760i	−0.0247206	+	0.0760823i
$487$	389.069	+	198.241i	0.798910	+	0.407065i	0.805265	−	0.592915i	$-0.202023\pi$
$487$	389.069	+	198.241i	0.798910	+	0.407065i	−0.00635532	+	0.999980i	$0.502023\pi$
$488$	30.8997	−	60.6441i	0.0633191	−	0.124271i
$489$	485.068	+	157.608i	0.991960	+	0.322307i
$490$	−350.651	+	121.210i	−0.715614	+	0.247368i
$491$	−58.5836	−	180.302i	−0.119315	−	0.367213i	0.873508	−	0.486810i	$-0.161840\pi$
$491$	−58.5836	−	180.302i	−0.119315	−	0.367213i	−0.992823	+	0.119597i	$0.961840\pi$
$492$	−27.1176	+	171.214i	−0.0551172	+	0.347996i
$493$	−691.775	−	691.775i	−1.40320	−	1.40320i
$494$	125.210	+	172.337i	0.253462	+	0.348861i
$495$	−16.8020	+	120.604i	−0.0339434	+	0.243643i
$496$	175.111	+	127.226i	0.353046	+	0.256503i
$497$	−221.393	+	35.0652i	−0.445458	+	0.0705537i
$498$	398.602	−	203.098i	0.800406	−	0.407827i
$499$			326.118i			0.653543i	0.945103	+	0.326772i	$0.105961\pi$
$499$			326.118i			0.653543i	−0.945103	+	0.326772i	$0.894039\pi$
$500$	239.868	−	139.643i	0.479736	−	0.279286i
$501$	−49.0964			−0.0979969
$502$	294.091	+	577.187i	0.585839	+	1.14977i
$503$	40.6961	+	256.945i	0.0809069	+	0.510826i	0.994546	+	0.104299i	$0.0332600\pi$
$503$	40.6961	+	256.945i	0.0809069	+	0.510826i	−0.913639	+	0.406526i	$0.866740\pi$
$504$	34.3372	−	47.2611i	0.0681294	−	0.0937720i
$505$	−376.881	−	52.5055i	−0.746300	−	0.103971i
$506$	320.498	−	232.856i	0.633396	−	0.460189i
$507$	193.673	−	193.673i	0.381998	−	0.381998i
$508$	409.096	+	64.7944i	0.805306	+	0.127548i
$509$	592.785	−	192.608i	1.16461	−	0.378404i	0.337980	−	0.941153i	$-0.390256\pi$
$509$	592.785	−	192.608i	1.16461	−	0.378404i	0.826627	+	0.562750i	$0.190256\pi$
$510$	−199.019	−	575.745i	−0.390234	−	1.12891i
$511$	154.630	−	475.902i	0.302603	−	0.931316i
$512$	253.382	+	129.105i	0.494887	+	0.252158i
$513$	61.1213	−	119.957i	0.119145	−	0.233835i
$514$	418.388	+	135.943i	0.813985	+	0.264480i
$515$	0.299214	+	16.0377i	0.000580998	+	0.0311411i
$516$	−14.3400	−	44.1340i	−0.0277907	−	0.0855310i
$517$	51.1872	−	323.183i	0.0990081	−	0.625112i
$518$	188.118	+	188.118i	0.363162	+	0.363162i
$519$	−47.7659	−	65.7441i	−0.0920345	−	0.126675i
$520$	50.7540	−	52.6838i	0.0976039	−	0.101315i
$521$	632.041	+	459.205i	1.21313	+	0.881391i	0.995511	−	0.0946427i	$-0.0301709\pi$
$521$	632.041	+	459.205i	1.21313	+	0.881391i	0.217619	+	0.976034i	$0.430171\pi$
$522$	256.350	−	40.6018i	0.491091	−	0.0777812i
$523$	−63.5674	+	32.3892i	−0.121544	+	0.0619296i	−0.513705	−	0.857967i	$-0.671727\pi$
$523$	−63.5674	+	32.3892i	−0.121544	+	0.0619296i	0.392161	+	0.919896i	$0.371727\pi$
$524$			364.044i			0.694741i
$525$	−117.321	−	149.423i	−0.223469	−	0.284615i
$526$	223.648			0.425186
$527$	−138.908	−	272.623i	−0.263583	−	0.517311i
$528$	43.8843	+	277.075i	0.0831143	+	0.524763i
$529$	−85.9045	+	118.237i	−0.162390	+	0.223511i
$530$	−1004.60	+	535.703i	−1.89547	+	1.01076i
$531$	−258.135	+	187.546i	−0.486130	+	0.353194i
$532$	178.480	−	178.480i	0.335489	−	0.335489i
$533$	146.753	+	23.2434i	0.275334	+	0.0436086i
$534$	−469.207	+	152.455i	−0.878665	+	0.285496i
$535$	530.036	−	400.410i	0.990721	−	0.748430i
$536$	−36.7063	+	112.970i	−0.0684818	+	0.210765i
$537$	170.678	+	86.9648i	0.317836	+	0.161946i
$538$	56.4728	−	110.834i	0.104968	−	0.206011i
$539$	−229.696	−	74.6328i	−0.426152	−	0.138465i
$540$	55.1882	+	16.8003i	0.102200	+	0.0311116i
$541$	146.082	+	449.594i	0.270022	+	0.831042i	0.990494	+	0.137558i	$0.0439252\pi$
$541$	146.082	+	449.594i	0.270022	+	0.831042i	−0.720472	+	0.693484i	$0.756075\pi$
$542$	−85.0083	+	536.721i	−0.156842	+	0.990260i
$543$	−230.432	−	230.432i	−0.424369	−	0.424369i
$544$	−530.594	−	730.300i	−0.975357	−	1.34246i
$545$	1052.49	−	186.887i	1.93118	−	0.342912i
$546$	50.5450	+	36.7231i	0.0925732	+	0.0672584i
$547$	−24.1496	+	3.82493i	−0.0441492	+	0.00699255i	−0.178470	−	0.983945i	$-0.557115\pi$
$547$	−24.1496	+	3.82493i	−0.0441492	+	0.00699255i	0.134321	+	0.990938i	$0.457115\pi$
$548$	−252.403	+	128.606i	−0.460589	+	0.234682i
$549$		−	46.0051i		−	0.0837981i
$550$	502.540	+	60.4788i	0.913710	+	0.109961i
$551$	−898.762			−1.63115
$552$	68.2881	+	134.023i	0.123710	+	0.242795i
$553$	−25.4091	−	160.426i	−0.0459477	−	0.290102i
$554$	−52.1412	+	71.7662i	−0.0941176	+	0.129542i
$555$	92.0734	−	189.356i	0.165898	−	0.341181i
$556$	33.3420	−	24.2244i	0.0599676	−	0.0435690i
$557$	361.027	−	361.027i	0.648163	−	0.648163i	−0.304385	−	0.952549i	$-0.598451\pi$
$557$	361.027	−	361.027i	0.648163	−	0.648163i	0.952549	+	0.304385i	$0.0984511\pi$
$558$	80.1741	+	12.6983i	0.143681	+	0.0227569i
$559$	−37.8286	+	12.2913i	−0.0676720	+	0.0219880i
$560$	−358.819	−	250.606i	−0.640747	−	0.447510i
$561$	122.542	−	377.146i	0.218435	−	0.672274i
$562$	−826.208	−	420.974i	−1.47012	−	0.749064i
$563$	412.123	−	808.836i	0.732012	−	1.43665i	−0.161155	−	0.986929i	$-0.551522\pi$
$563$	412.123	−	808.836i	0.732012	−	1.43665i	0.893167	−	0.449725i	$-0.148478\pi$
$564$	−147.432	−	47.9036i	−0.261404	−	0.0849354i
$565$	−404.569	+	579.264i	−0.716051	+	1.02525i
$566$	−192.662	−	592.952i	−0.340392	−	1.04762i
$567$	6.17699	−	39.0000i	0.0108942	−	0.0687830i
$568$	160.343	+	160.343i	0.282294	+	0.282294i
$569$	−100.389	−	138.174i	−0.176430	−	0.242836i	0.711639	−	0.702546i	$-0.247953\pi$
$569$	−100.389	−	138.174i	−0.176430	−	0.242836i	−0.888069	+	0.459710i	$0.847953\pi$
$570$	−503.292	−	244.724i	−0.882968	−	0.429340i
$571$	−18.3779	−	13.3524i	−0.0321855	−	0.0233842i	0.571576	−	0.820549i	$-0.306332\pi$
$571$	−18.3779	−	13.3524i	−0.0321855	−	0.0233842i	−0.603762	+	0.797165i	$0.706332\pi$
$572$	−58.6880	+	9.29526i	−0.102601	+	0.0162505i
$573$	−236.381	+	120.442i	−0.412533	+	0.210196i
$574$		−	493.210i		−	0.859252i
$575$	479.951	−	94.4905i	0.834698	−	0.164331i
$576$	0.0670507			0.000116407
$577$	−208.067	−	408.355i	−0.360602	−	0.707721i	0.637425	−	0.770512i	$-0.280000\pi$
$577$	−208.067	−	408.355i	−0.360602	−	0.707721i	−0.998027	+	0.0627918i	$0.980000\pi$
$578$	197.586	+	1247.51i	0.341845	+	2.15832i
$579$	351.057	−	483.188i	0.606316	−	0.834522i
$580$	−67.3301	−	379.183i	−0.116086	−	0.653764i
$581$	−367.576	+	267.059i	−0.632661	+	0.459655i
$582$	179.836	−	179.836i	0.308997	−	0.308997i
$583$	−732.010	−	115.939i	−1.25559	−	0.198866i
$584$	−481.436	+	156.428i	−0.824377	+	0.267856i
$585$	14.4000	−	47.3036i	0.0246154	−	0.0808608i
$586$	−31.0525	+	95.5697i	−0.0529906	+	0.163088i
$587$	804.250	+	409.786i	1.37010	+	0.698102i	0.975346	−	0.220683i	$-0.0708286\pi$
$587$	804.250	+	409.786i	1.37010	+	0.698102i	0.394757	+	0.918785i	$0.370829\pi$
$588$	−51.9459	+	101.949i	−0.0883433	+	0.173383i
$589$	−267.333	−	86.8618i	−0.453876	−	0.147473i
$590$	799.471	+	1058.29i	1.35504	+	1.79371i
$591$	114.957	+	353.801i	0.194513	+	0.598649i
$592$	75.8820	−	479.100i	0.128179	−	0.809291i
$593$	−244.551	−	244.551i	−0.412397	−	0.412397i	0.470176	−	0.882573i	$-0.344190\pi$
$593$	−244.551	−	244.551i	−0.412397	−	0.412397i	−0.882573	+	0.470176i	$0.844190\pi$
$594$	61.8378	+	85.1124i	0.104104	+	0.143287i
$595$	291.112	+	545.919i	0.489264	+	0.917511i
$596$	18.9777	+	13.7881i	0.0318418	+	0.0231344i
$597$	−447.848	+	70.9322i	−0.750164	+	0.118814i
$598$	−143.335	+	73.0330i	−0.239691	+	0.122129i
$599$			40.7095i			0.0679624i	0.999422	+	0.0339812i	$0.0108186\pi$
$599$			40.7095i			0.0679624i	−0.999422	+	0.0339812i	$0.989181\pi$
$600$	−52.5298	+	184.869i	−0.0875496	+	0.308114i
$601$	713.924			1.18789			0.593947	−	0.804504i	$-0.297569\pi$
$601$	713.924			1.18789			0.593947	+	0.804504i	$0.297569\pi$
$602$	59.9414	+	117.642i	0.0995704	+	0.195418i
$603$	12.5600	+	79.3005i	0.0208291	+	0.131510i
$604$	−156.367	+	215.221i	−0.258886	+	0.356326i
$605$	−198.408	−	191.140i	−0.327947	−	0.315934i
$606$	−265.973	+	193.241i	−0.438900	+	0.318879i
$607$	374.723	−	374.723i	0.617337	−	0.617337i	−0.327511	−	0.944847i	$-0.606210\pi$
$607$	374.723	−	374.723i	0.617337	−	0.617337i	0.944847	+	0.327511i	$0.106210\pi$
$608$	−819.084	−	129.730i	−1.34718	−	0.213372i
$609$	−250.697	+	81.4565i	−0.411654	+	0.133755i
$610$	−191.201	+	3.56723i	−0.313444	+	0.00584791i
$611$	−41.0597	+	126.369i	−0.0672007	+	0.206823i
$612$	−167.394	−	85.2916i	−0.273520	−	0.139365i
$613$	−117.286	+	230.186i	−0.191331	+	0.375508i	−0.966665	−	0.256043i	$-0.917581\pi$
$613$	−117.286	+	230.186i	−0.191331	+	0.375508i	0.775335	+	0.631551i	$0.217581\pi$
$614$	−1327.30	−	431.267i	−2.16173	−	0.702389i
$615$	−368.927	+	127.528i	−0.599881	+	0.207362i
$616$	−48.8484	−	150.340i	−0.0792993	−	0.244058i
$617$	−63.8697	+	403.258i	−0.103517	+	0.653578i	0.880302	+	0.474413i	$0.157340\pi$
$617$	−63.8697	+	403.258i	−0.103517	+	0.653578i	−0.983819	+	0.179165i	$0.942660\pi$
$618$	9.79948	+	9.79948i	0.0158568	+	0.0158568i
$619$	−400.379	−	551.074i	−0.646816	−	0.890265i	0.352140	−	0.935947i	$-0.385454\pi$
$619$	−400.379	−	551.074i	−0.646816	−	0.890265i	−0.998956	+	0.0456817i	$0.985454\pi$
$620$	16.6195	−	119.294i	0.0268056	−	0.192409i
$621$	82.2535	+	59.7606i	0.132453	+	0.0962329i
$622$	1188.21	−	188.195i	1.91031	−	0.302564i
$623$	446.447	−	227.476i	0.716608	−	0.365130i
$624$		−	113.915i		−	0.182556i
$625$	531.616	+	328.648i	0.850585	+	0.525837i
$626$	−547.143			−0.874030
$627$	−165.392	−	324.600i	−0.263783	−	0.517703i
$628$	30.3930	+	191.894i	0.0483965	+	0.305564i
$629$	−403.043	+	554.741i	−0.640767	+	0.881940i
$630$	−162.566	−	22.6480i	−0.258041	−	0.0359492i
$631$	−395.032	+	287.008i	−0.626042	+	0.454846i	−0.855027	−	0.518584i	$-0.826459\pi$
$631$	−395.032	+	287.008i	−0.626042	+	0.454846i	0.228985	+	0.973430i	$0.426459\pi$
$632$	−116.188	+	116.188i	−0.183842	+	0.183842i
$633$	28.0158	+	4.43726i	0.0442587	+	0.00700989i
$634$	−624.883	+	203.037i	−0.985620	+	0.320247i
$635$	304.712	+	881.507i	0.479862	+	1.38820i
$636$	−108.502	+	333.934i	−0.170600	+	0.525053i
$637$	87.3841	+	44.5244i	0.137181	+	0.0698970i
$638$	318.846	−	625.771i	0.499759	−	0.980832i
$639$	145.770	+	47.3637i	0.228123	+	0.0741215i
$640$	11.9358	+	639.749i	0.0186496	+	0.999608i
$641$	17.7948	+	54.7668i	0.0277610	+	0.0854396i	0.963977	−	0.265985i	$-0.0856973\pi$
$641$	17.7948	+	54.7668i	0.0277610	+	0.0854396i	−0.936216	+	0.351425i	$0.885697\pi$
$642$	89.7809	−	566.854i	0.139846	−	0.882951i
$643$	−178.471	−	178.471i	−0.277560	−	0.277560i	0.554575	−	0.832134i	$-0.312881\pi$
$643$	−178.471	−	178.471i	−0.277560	−	0.277560i	−0.832134	+	0.554575i	$0.812881\pi$
$644$	112.040	+	154.210i	0.173976	+	0.239457i
$645$	72.4983	−	75.2550i	0.112401	−	0.116674i
$646$	1474.46	+	1071.25i	2.28244	+	1.65829i
$647$	−323.144	+	51.1811i	−0.499450	+	0.0791052i	−0.401077	−	0.916044i	$-0.631364\pi$
$647$	−323.144	+	51.1811i	−0.499450	+	0.0791052i	−0.0983735	+	0.995150i	$0.531364\pi$
$648$	−35.5915	+	18.1348i	−0.0549252	+	0.0279858i
$649$			863.397i			1.33035i
$650$	−197.714	−	56.1797i	−0.304175	−	0.0864304i
$651$	−82.4413			−0.126638
$652$	−296.840	−	582.581i	−0.455276	−	0.893529i
$653$	51.9339	+	327.898i	0.0795313	+	0.502141i	0.995010	+	0.0997745i	$0.0318121\pi$
$653$	51.9339	+	327.898i	0.0795313	+	0.502141i	−0.915479	+	0.402366i	$0.868188\pi$
$654$	542.850	−	747.170i	0.830047	−	1.14246i
$655$	−723.339	+	385.722i	−1.10433	+	0.588888i
$656$	−727.530	+	528.581i	−1.10904	+	0.805764i
$657$	−241.945	+	241.945i	−0.368257	+	0.368257i
$658$	435.631	+	68.9971i	0.662053	+	0.104859i
$659$	−1028.88	+	334.304i	−1.56128	+	0.507290i	−0.957149	−	0.289597i	$-0.906479\pi$
$659$	−1028.88	+	334.304i	−1.56128	+	0.507290i	−0.604129	+	0.796887i	$0.706479\pi$
$660$	124.557	−	94.0952i	0.188723	−	0.142568i
$661$	−277.189	+	853.099i	−0.419348	+	1.29062i	0.488956	+	0.872308i	$0.337378\pi$
$661$	−277.189	+	853.099i	−0.419348	+	1.29062i	−0.908304	+	0.418311i	$0.862622\pi$
$662$	−117.405	−	59.8209i	−0.177349	−	0.0903640i
$663$	−73.1061	+	143.479i	−0.110266	+	0.216408i
$664$	437.136	+	142.034i	0.658337	+	0.213907i
$665$	543.740	+	165.524i	0.817655	+	0.248908i
$666$	−56.2144	−	173.010i	−0.0844059	−	0.259775i
$667$	106.176	−	670.371i	0.159185	−	1.00505i
$668$	44.5055	+	44.5055i	0.0666250	+	0.0666250i
$669$	44.1400	+	60.7536i	0.0659791	+	0.0908125i
$670$	328.605	−	58.3492i	0.490456	−	0.0870883i
$671$	−100.713	−	73.1723i	−0.150094	−	0.109050i
$672$	−240.230	+	38.0487i	−0.357485	+	0.0566201i
$673$	1010.22	−	514.734i	1.50107	−	0.764834i	0.505864	−	0.862613i	$-0.331174\pi$
$673$	1010.22	−	514.734i	1.50107	−	0.764834i	0.995208	+	0.0977789i	$0.0311738\pi$
$674$		−	1557.86i		−	2.31137i
$675$	25.0932	+	127.457i	0.0371751	+	0.188825i
$676$	−351.126			−0.519417
$677$	−3.48729	−	6.84418i	−0.00515109	−	0.0101096i	0.888417	−	0.459038i	$-0.151806\pi$
$677$	−3.48729	−	6.84418i	−0.00515109	−	0.0101096i	−0.893568	+	0.448928i	$0.851806\pi$
$678$	95.4951	+	602.932i	0.140848	+	0.889281i
$679$	−151.824	+	208.968i	−0.223600	+	0.307759i
$680$	273.692	−	562.868i	0.402489	−	0.827747i
$681$	228.498	−	166.013i	0.335533	−	0.243779i
$682$	155.318	−	155.318i	0.227738	−	0.227738i
$683$	406.342	+	64.3583i	0.594938	+	0.0942289i	0.446640	−	0.894714i	$-0.352621\pi$
$683$	406.342	+	64.3583i	0.594938	+	0.0942289i	0.148298	+	0.988943i	$0.452621\pi$
$684$	−164.146	+	53.3343i	−0.239980	+	0.0779742i
$685$	−522.966	−	365.249i	−0.763454	−	0.533211i
$686$	266.288	−	819.551i	0.388175	−	1.19468i
$687$	14.5154	+	7.39599i	0.0211287	+	0.0107656i
$688$	109.292	−	214.497i	0.158854	−	0.311769i
$689$	286.225	+	93.0001i	0.415421	+	0.134978i
$690$	241.992	−	346.486i	0.350713	−	0.502153i
$691$	−336.357	−	1035.20i	−0.486769	−	1.49812i	−0.829402	−	0.558652i	$-0.811319\pi$
$691$	−336.357	−	1035.20i	−0.486769	−	1.49812i	0.342633	−	0.939469i	$-0.388681\pi$
$692$	−16.2971	+	102.896i	−0.0235507	+	0.148693i
$693$	−75.5529	−	75.5529i	−0.109023	−	0.109023i
$694$	−133.280	−	183.444i	−0.192046	−	0.264329i
$695$	83.4600	+	40.5821i	0.120086	+	0.0583915i
$696$	215.736	+	156.741i	0.309965	+	0.225203i
$697$	1255.56	−	198.862i	1.80138	−	0.285311i
$698$	1070.21	−	545.300i	1.53325	−	0.781232i
$699$		−	46.5443i		−	0.0665870i
$700$	−29.0999	+	241.801i	−0.0415712	+	0.345431i
$701$	356.852			0.509061			0.254530	−	0.967065i	$-0.418079\pi$
$701$	356.852			0.509061			0.254530	+	0.967065i	$0.418079\pi$
$702$	−19.3948	−	38.0645i	−0.0276280	−	0.0542230i
$703$	98.5439	+	622.181i	0.140176	+	0.885038i
$704$	0.106646	−	0.146785i	0.000151485	−	0.000208502i
$705$	−61.0289	−	343.697i	−0.0865658	−	0.487513i
$706$	−660.207	+	479.668i	−0.935137	+	0.679417i
$707$	236.100	−	236.100i	0.333946	−	0.333946i
$708$	404.006	+	63.9882i	0.570630	+	0.0903788i
$709$	449.573	−	146.075i	0.634095	−	0.206030i	0.0257068	−	0.999670i	$-0.491816\pi$
$709$	449.573	−	146.075i	0.634095	−	0.206030i	0.608388	+	0.793640i	$0.291816\pi$
$710$	185.544	−	609.506i	0.261330	−	0.858458i
$711$	−34.3208	+	105.629i	−0.0482712	+	0.148563i
$712$	−451.639	−	230.121i	−0.634324	−	0.323204i
$713$	96.3704	−	189.138i	0.135162	−	0.265270i
$714$	508.369	+	165.179i	0.712001	+	0.231343i
$715$	−80.6519	−	106.762i	−0.112800	−	0.149317i
$716$	−75.8853	−	233.551i	−0.105985	−	0.326188i
$717$	−92.6215	+	584.789i	−0.129179	+	0.815606i
$718$	−1227.54	−	1227.54i	−1.70966	−	1.70966i
$719$	−396.460	−	545.680i	−0.551404	−	0.758943i	0.438798	−	0.898586i	$-0.355404\pi$
$719$	−396.460	−	545.680i	−0.551404	−	0.758943i	−0.990202	+	0.139643i	$0.955404\pi$
$720$	140.817	+	264.072i	0.195579	+	0.366766i
$721$	−11.3869	−	8.27308i	−0.0157932	−	0.0114745i
$722$	764.429	−	121.074i	1.05877	−	0.167692i
$723$	−138.297	+	70.4658i	−0.191282	+	0.0974631i
$724$			417.770i			0.577030i
$725$	682.080	−	535.544i	0.940801	−	0.738682i
$726$	−238.025			−0.327858
$727$	1.56077	+	3.06318i	0.00214686	+	0.00421345i	0.892077	−	0.451883i	$-0.149247\pi$
$727$	1.56077	+	3.06318i	0.00214686	+	0.00421345i	−0.889931	+	0.456096i	$0.849247\pi$
$728$	10.0416	+	63.4004i	0.0137935	+	0.0870885i
$729$	−15.8702	+	21.8435i	−0.0217698	+	0.0299636i
$730$	1024.30	+	986.780i	1.40315	+	1.35175i
$731$	−275.311	+	200.025i	−0.376623	+	0.273633i
$732$	−41.7032	+	41.7032i	−0.0569716	+	0.0569716i
$733$	−218.116	−	34.5462i	−0.297566	−	0.0471299i	0.00586626	−	0.999983i	$-0.498133\pi$
$733$	−218.116	−	34.5462i	−0.297566	−	0.0471299i	−0.303433	+	0.952853i	$0.598133\pi$
$734$	1053.12	−	342.178i	1.43476	−	0.466183i
$735$	−257.608	+	4.80618i	−0.350487	+	0.00653902i
$736$	193.527	−	595.615i	0.262944	−	0.809259i
$737$	193.579	+	98.6335i	0.262658	+	0.133831i
$738$	−153.108	+	300.492i	−0.207464	+	0.407170i
$739$	−218.413	−	70.9668i	−0.295553	−	0.0960308i	0.157488	−	0.987521i	$-0.449661\pi$
$739$	−218.413	−	70.9668i	−0.295553	−	0.0960308i	−0.453040	+	0.891490i	$0.649661\pi$
$740$	−255.113	+	88.1854i	−0.344747	+	0.119169i
$741$	45.7145	+	140.695i	0.0616930	+	0.189872i
$742$	156.278	−	986.703i	0.210618	−	1.32979i
$743$	308.291	+	308.291i	0.414927	+	0.414927i	0.883451	−	0.468524i	$-0.155214\pi$
$743$	308.291	+	308.291i	0.414927	+	0.414927i	−0.468524	+	0.883451i	$0.655214\pi$
$744$	49.0213	+	67.4720i	0.0658888	+	0.0906882i
$745$	−7.28859	+	52.3170i	−0.00978334	+	0.0702242i
$746$	−472.518	−	343.304i	−0.633401	−	0.460193i
$747$	306.852	−	48.6005i	0.410779	−	0.0650610i
$748$	−452.962	+	230.796i	−0.605565	+	0.308551i
$749$			582.884i			0.778217i
$750$	527.776	−	114.172i	0.703702	−	0.152230i
$751$	158.526			0.211087			0.105544	−	0.994415i	$-0.466342\pi$
$751$	158.526			0.211087			0.105544	+	0.994415i	$0.466342\pi$
$752$	−365.095	−	716.540i	−0.485499	−	0.952845i
$753$	70.3749	+	444.330i	0.0934594	+	0.590079i
$754$	−167.632	+	230.726i	−0.222324	+	0.306002i
$755$	−593.312	−	82.6577i	−0.785843	−	0.109480i
$756$	−40.9525	+	29.7538i	−0.0541700	+	0.0393568i
$757$	−211.358	+	211.358i	−0.279205	+	0.279205i	−0.832792	−	0.553587i	$-0.813259\pi$
$757$	−211.358	+	211.358i	−0.279205	+	0.279205i	0.553587	+	0.832792i	$0.313259\pi$
$758$	−190.912	−	30.2375i	−0.251863	−	0.0398911i
$759$	261.652	−	85.0160i	0.344733	−	0.112011i
$760$	−187.850	−	543.434i	−0.247171	−	0.715045i
$761$	−124.883	+	384.349i	−0.164103	+	0.505058i	−0.998969	−	0.0453953i	$-0.985545\pi$
$761$	−124.883	+	384.349i	−0.164103	+	0.505058i	0.834866	+	0.550454i	$0.185545\pi$
$762$	717.989	+	365.834i	0.942243	+	0.480097i
$763$	−425.833	+	835.744i	−0.558103	+	1.09534i
$764$	323.457	+	105.098i	0.423373	+	0.137562i
$765$	−7.89142	−	422.975i	−0.0103156	−	0.552909i
$766$	378.015	+	1163.41i	0.493493	+	1.51881i
$767$	54.8463	−	346.286i	0.0715076	−	0.451481i
$768$	391.015	+	391.015i	0.509134	+	0.509134i
$769$	−278.600	−	383.460i	−0.362289	−	0.498647i	0.588496	−	0.808500i	$-0.299720\pi$
$769$	−278.600	−	383.460i	−0.362289	−	0.498647i	−0.950785	+	0.309853i	$0.899720\pi$
$770$	−308.145	+	319.862i	−0.400189	+	0.415405i
$771$	247.162	+	179.573i	0.320573	+	0.232910i
$772$	−756.236	+	119.776i	−0.979580	+	0.155150i
$773$	−715.546	+	364.589i	−0.925674	+	0.471655i	−0.850771	−	0.525536i	$-0.823865\pi$
$773$	−715.546	+	364.589i	−0.925674	+	0.471655i	−0.0749030	+	0.997191i	$0.523865\pi$
$774$		−	90.2816i		−	0.116643i
$775$	254.640	−	93.3750i	0.328568	−	0.120484i
$776$	261.303			0.336730
$777$	83.8769	+	164.618i	0.107950	+	0.211863i
$778$	94.3087	+	595.442i	0.121219	+	0.765349i
$779$	686.440	−	944.803i	0.881181	−	1.21284i
$780$	−55.9338	+	29.8268i	−0.0717100	+	0.0382394i
$781$	335.538	−	243.783i	0.429626	−	0.312142i
$782$	−973.216	+	973.216i	−1.24452	+	1.24452i
$783$	178.026	+	28.1965i	0.227364	+	0.0360108i
$784$	−564.526	+	183.426i	−0.720059	+	0.233961i
$785$	−349.082	+	263.710i	−0.444690	+	0.335936i
$786$	−218.861	+	673.585i	−0.278449	+	0.856978i
$787$	−436.463	−	222.389i	−0.554591	−	0.282578i	0.154150	−	0.988048i	$-0.450736\pi$
$787$	−436.463	−	222.389i	−0.554591	−	0.282578i	−0.708740	+	0.705469i	$0.750736\pi$
$788$	216.510	−	424.925i	0.274759	−	0.539246i
$789$	147.714	+	47.9951i	0.187217	+	0.0608303i
$790$	441.662	+	134.450i	0.559066	+	0.170189i
$791$	−191.585	−	589.638i	−0.242206	−	0.745434i
$792$	−16.9091	+	106.760i	−0.0213498	+	0.134798i
$793$	35.7451	+	35.7451i	0.0450758	+	0.0450758i
$794$	530.494	+	730.162i	0.668128	+	0.919600i
$795$	−778.473	+	138.230i	−0.979212	+	0.173875i
$796$	470.270	+	341.671i	0.590791	+	0.429235i
$797$	−1507.22	+	238.720i	−1.89111	+	0.299523i	−0.990759	−	0.135633i	$-0.956693\pi$
$797$	−1507.22	+	238.720i	−1.89111	+	0.299523i	−0.900355	+	0.435156i	$0.856693\pi$
$798$	437.540	−	222.938i	0.548296	−	0.279371i
$799$			1136.80i			1.42278i
$800$	698.914	−	389.613i	0.873642	−	0.487016i
$801$	−342.617			−0.427736
$802$	46.6736	+	91.6020i	0.0581964	+	0.114217i
$803$	144.839	+	914.476i	0.180372	+	1.13882i
$804$	60.4997	−	83.2707i	0.0752484	−	0.103571i
$805$	−187.697	+	386.012i	−0.233164	+	0.479518i
$806$	−72.1602	+	52.4274i	−0.0895288	+	0.0650465i
$807$	61.0840	−	61.0840i	0.0756927	−	0.0756927i
$808$	−333.620	−	52.8402i	−0.412896	−	0.0653963i
$809$	−687.263	+	223.305i	−0.849522	+	0.276026i	−0.701246	−	0.712920i	$-0.747372\pi$
$809$	−687.263	+	223.305i	−0.849522	+	0.276026i	−0.148276	+	0.988946i	$0.547372\pi$
$810$	92.0137	+	64.2641i	0.113597	+	0.0793384i
$811$	268.108	−	825.153i	0.330590	−	1.01745i	−0.638264	−	0.769818i	$-0.720347\pi$
$811$	268.108	−	825.153i	0.330590	−	1.01745i	0.968854	−	0.247634i	$-0.0796529\pi$
$812$	301.095	+	153.415i	0.370806	+	0.188935i
$813$	−171.327	+	336.248i	−0.210734	+	0.413589i
$814$	−468.158	−	152.114i	−0.575133	−	0.186872i
$815$	843.046	−	1207.08i	1.03441	−	1.48108i
$816$	−301.173	−	926.914i	−0.369084	−	1.13592i
$817$	−48.9062	+	308.781i	−0.0598607	+	0.377945i
$818$	20.5871	+	20.5871i	0.0251676	+	0.0251676i
$819$	25.5029	+	35.1017i	0.0311390	+	0.0428592i
$820$	450.032	+	218.826i	0.548819	+	0.266861i
$821$	−114.066	−	82.8741i	−0.138936	−	0.100943i	0.516146	−	0.856500i	$-0.327366\pi$
$821$	−114.066	−	82.8741i	−0.138936	−	0.100943i	−0.655082	+	0.755558i	$0.727366\pi$
$822$	−544.334	+	86.2140i	−0.662207	+	0.104883i
$823$	−794.555	+	404.846i	−0.965437	+	0.491915i	−0.864311	−	0.502959i	$-0.832245\pi$
$823$	−794.555	+	404.846i	−0.965437	+	0.491915i	−0.101127	+	0.994874i	$0.532245\pi$
$824$			14.2387i			0.0172800i
$825$	318.937	+	147.791i	0.386590	+	0.179140i
$826$	−1163.81			−1.40897
$827$	131.943	+	258.953i	0.159545	+	0.313124i	0.956916	−	0.290365i	$-0.0937768\pi$
$827$	131.943	+	258.953i	0.159545	+	0.313124i	−0.797371	+	0.603489i	$0.793777\pi$
$828$	−20.3895	−	128.735i	−0.0246251	−	0.155476i
$829$	320.933	−	441.726i	0.387133	−	0.532842i	−0.570324	−	0.821420i	$-0.693182\pi$
$829$	320.933	−	441.726i	0.387133	−	0.532842i	0.957457	+	0.288578i	$0.0931823\pi$
$830$	−225.781	−	1271.53i	−0.272025	−	1.53197i
$831$	−49.8391	+	36.2102i	−0.0599748	+	0.0435742i
$832$	−0.0520972	+	0.0520972i	−6.26168e−5	+	6.26168e-5i
$833$	828.750	+	131.261i	0.994898	+	0.157576i
$834$	76.2556	−	24.7770i	0.0914336	−	0.0297086i
$835$	−41.2747	+	135.586i	−0.0494308	+	0.162378i
$836$	−144.321	+	444.173i	−0.172632	+	0.531308i
$837$	50.2279	+	25.5924i	0.0600095	+	0.0305763i
$838$	331.811	−	651.215i	0.395956	−	0.777107i
$839$	−400.077	−	129.993i	−0.476849	−	0.154938i	0.0607243	−	0.998155i	$-0.480659\pi$
$839$	−400.077	−	129.993i	−0.476849	−	0.154938i	−0.537574	+	0.843217i	$0.680659\pi$
$840$	−101.651	−	134.558i	−0.121013	−	0.160188i
$841$	−111.946	−	344.535i	−0.133111	−	0.409673i
$842$	−87.0668	+	549.718i	−0.103405	+	0.652872i
$843$	−455.348	−	455.348i	−0.540152	−	0.540152i
$844$	−21.3737	−	29.4184i	−0.0253243	−	0.0348559i
$845$	−372.034	−	697.671i	−0.440277	−	0.825646i
$846$	−243.992	−	177.270i	−0.288406	−	0.209540i
$847$	238.766	−	37.8169i	0.281897	−	0.0446480i
$848$	−1622.96	+	826.941i	−1.91387	+	0.975166i
$849$		−	432.975i		−	0.509983i
$850$	−1757.31	+	65.5948i	−2.06742	+	0.0771703i
$851$	−475.716			−0.559008
$852$	−89.2048	−	175.074i	−0.104700	−	0.205486i
$853$	−33.2422	−	209.883i	−0.0389709	−	0.246053i	0.960511	−	0.278242i	$-0.0897519\pi$
$853$	−33.2422	−	209.883i	−0.0389709	−	0.246053i	−0.999482	+	0.0321898i	$0.989752\pi$
$854$	98.6316	−	135.755i	0.115494	−	0.158963i
$855$	−279.893	−	269.641i	−0.327361	−	0.315369i
$856$	477.047	−	346.595i	0.557298	−	0.404900i
$857$	−549.525	+	549.525i	−0.641220	+	0.641220i	−0.950855	−	0.309636i	$-0.899793\pi$
$857$	−549.525	+	549.525i	−0.641220	+	0.641220i	0.309636	+	0.950855i	$0.399793\pi$
$858$	−114.178	−	18.0840i	−0.133074	−	0.0210769i
$859$	1586.71	−	515.554i	1.84716	−	0.600179i	0.849839	−	0.527043i	$-0.176699\pi$
$859$	1586.71	−	515.554i	1.84716	−	0.600179i	0.997322	−	0.0731359i	$-0.0233007\pi$
$860$	−133.937	+	2.49886i	−0.155741	+	0.00290565i
$861$	105.844	−	325.753i	0.122931	−	0.378343i
$862$	692.157	+	352.671i	0.802966	+	0.409132i
$863$	−31.5416	+	61.9038i	−0.0365488	+	0.0717310i	−0.908559	−	0.417757i	$-0.862816\pi$
$863$	−31.5416	+	61.9038i	−0.0365488	+	0.0717310i	0.872010	+	0.489488i	$0.162816\pi$
$864$	158.173	+	51.3936i	0.183071	+	0.0594833i
$865$	−221.717	+	76.6414i	−0.256320	+	0.0886027i
$866$	−300.388	−	924.499i	−0.346868	−	1.06755i
$867$	−137.217	+	866.352i	−0.158266	+	0.999253i
$868$	74.7323	+	74.7323i	0.0860972	+	0.0860972i
$869$	176.651	+	243.139i	0.203281	+	0.279792i
$870$	103.383	−	742.075i	0.118831	−	0.852960i
$871$	−71.3739	−	51.8562i	−0.0819448	−	0.0595364i
$872$	937.202	−	148.438i	1.07477	−	0.170227i
$873$	157.370	−	80.1842i	0.180264	−	0.0918490i
$874$			1264.41i			1.44670i
$875$	−511.281	+	198.380i	−0.584321	+	0.226720i
$876$	438.641			0.500732
$877$	154.577	+	303.375i	0.176257	+	0.345923i	0.962186	−	0.272393i	$-0.0878151\pi$
$877$	154.577	+	303.375i	0.176257	+	0.345923i	−0.785929	+	0.618316i	$0.787815\pi$
$878$	−265.840	−	1678.45i	−0.302779	−	1.91167i
$879$	−41.0188	+	56.4575i	−0.0466653	+	0.0642292i
$880$	802.070	+	111.741i	0.911443	+	0.126978i
$881$	−130.707	+	94.9645i	−0.148362	+	0.107792i	−0.659490	−	0.751713i	$-0.729228\pi$
$881$	−130.707	+	94.9645i	−0.148362	+	0.107792i	0.511128	+	0.859505i	$0.329228\pi$
$882$	−157.406	+	157.406i	−0.178465	+	0.178465i
$883$	81.8594	+	12.9653i	0.0927060	+	0.0146832i	0.202615	−	0.979258i	$-0.435056\pi$
$883$	81.8594	+	12.9653i	0.0927060	+	0.0146832i	−0.109909	+	0.993942i	$0.535056\pi$
$884$	196.332	−	63.7922i	0.222095	−	0.0721632i
$885$	300.921	+	870.539i	0.340024	+	0.983660i
$886$	119.782	−	368.650i	0.135194	−	0.416083i
$887$	−650.234	−	331.311i	−0.733071	−	0.373518i	0.0472620	−	0.998883i	$-0.484950\pi$
$887$	−650.234	−	331.311i	−0.733071	−	0.373518i	−0.780333	+	0.625364i	$0.784950\pi$
$888$	84.8523	−	166.532i	0.0955543	−	0.187536i
$889$	−778.348	−	252.901i	−0.875532	−	0.284478i
$890$	26.5664	+	1423.94i	0.0298499	+	1.59993i
$891$	22.5771	+	69.4851i	0.0253390	+	0.0779855i
$892$	15.0600	−	95.0851i	0.0168834	−	0.106598i
$893$	738.474	+	738.474i	0.826958	+	0.826958i
$894$	26.8248	+	36.9212i	0.0300054	+	0.0412989i
$895$	383.651	−	398.239i	0.428660	−	0.444959i
$896$	−454.229	−	330.017i	−0.506952	−	0.368322i
$897$	−110.342	+	17.4765i	−0.123013	+	0.0194833i
$898$	783.470	−	399.198i	0.872461	−	0.444541i
$899$		−	376.325i		−	0.418604i
$900$	92.7921	−	138.286i	0.103102	−	0.153651i
$901$	2574.86			2.85778
$902$	414.305	+	813.119i	0.459318	+	0.901462i
$903$	14.3437	+	90.5628i	0.0158845	+	0.100291i
$904$	−368.654	+	507.409i	−0.407803	+	0.561293i
$905$	−830.089	+	442.646i	−0.917225	+	0.489112i
$906$	−418.713	+	304.212i	−0.462155	+	0.335775i
$907$	−592.187	+	592.187i	−0.652907	+	0.652907i	−0.953692	−	0.300785i	$-0.902751\pi$
$907$	−592.187	+	592.187i	−0.652907	+	0.652907i	0.300785	+	0.953692i	$0.402751\pi$
$908$	−357.621	−	56.6416i	−0.393856	−	0.0623806i
$909$	−217.138	+	70.5525i	−0.238876	+	0.0776155i
$910$	143.908	−	108.714i	0.158141	−	0.119466i
$911$	470.455	−	1447.91i	0.516416	−	1.58936i	−0.264276	−	0.964447i	$-0.585133\pi$
$911$	470.455	−	1447.91i	0.516416	−	1.58936i	0.780691	−	0.624917i	$-0.214867\pi$
$912$	−797.773	−	406.485i	−0.874751	−	0.445708i
$913$	381.660	−	749.050i	0.418029	−	0.820428i
$914$	1522.90	+	494.819i	1.66619	+	0.541377i
$915$	−127.049	−	38.6759i	−0.138851	−	0.0422688i
$916$	−6.45372	−	19.8625i	−0.00704555	−	0.0216840i
$917$	112.525	−	710.455i	0.122710	−	0.774761i
$918$	−258.450	−	258.450i	−0.281536	−	0.281536i
$919$	−808.788	−	1113.20i	−0.880074	−	1.21132i	−0.976400	−	0.215968i	$-0.930709\pi$
$919$	−808.788	−	1113.20i	−0.880074	−	1.21132i	0.0963268	−	0.995350i	$-0.469291\pi$
$920$	427.530	−	75.9149i	0.464707	−	0.0825162i
$921$	−784.099	−	569.682i	−0.851357	−	0.618547i
$922$	−162.516	+	25.7400i	−0.176265	+	0.0279176i
$923$	−150.062	+	76.4602i	−0.162580	+	0.0828388i
$924$			136.976i			0.148243i
$925$	−445.524	−	413.461i	−0.481648	−	0.446985i
$926$	1025.30			1.10724
$927$	4.36933	+	8.57529i	0.00471341	+	0.00925058i
$928$	−173.683	−	1096.59i	−0.187159	−	1.18167i
$929$	−18.7994	+	25.8751i	−0.0202361	+	0.0278526i	−0.819015	−	0.573772i	$-0.805480\pi$
$929$	−18.7994	+	25.8751i	−0.0202361	+	0.0278526i	0.798779	+	0.601624i	$0.205480\pi$
$930$	102.469	−	210.736i	0.110182	−	0.226597i
$931$	623.629	−	453.093i	0.669848	−	0.486673i
$932$	−42.1920	+	42.1920i	−0.0452704	+	0.0452704i
$933$	825.172	+	130.694i	0.884429	+	0.140080i
$934$	535.394	−	173.960i	0.573227	−	0.186253i
$935$	−938.516	−	655.477i	−1.00376	−	0.701045i
$936$	13.5636	−	41.7443i	0.0144910	−	0.0445987i
$937$	−206.965	−	105.454i	−0.220880	−	0.112544i	0.340049	−	0.940408i	$-0.389556\pi$
$937$	−206.965	−	105.454i	−0.220880	−	0.112544i	−0.560930	+	0.827863i	$0.689556\pi$
$938$	−132.952	+	260.933i	−0.141740	+	0.278180i
$939$	−361.374	−	117.418i	−0.384850	−	0.125045i
$940$	−256.236	+	366.880i	−0.272592	+	0.390298i
$941$	503.761	+	1550.42i	0.535347	+	1.64763i	0.742899	+	0.669404i	$0.233450\pi$
$941$	503.761	+	1550.42i	0.535347	+	1.64763i	−0.207552	+	0.978224i	$0.566550\pi$
$942$	−59.1297	+	373.330i	−0.0627704	+	0.396317i
$943$	623.619	+	623.619i	0.661314	+	0.661314i
$944$	1247.27	+	1716.72i	1.32126	+	1.81856i
$945$	−102.510	−	49.8453i	−0.108477	−	0.0527464i
$946$	−197.642	−	143.595i	−0.208923	−	0.151792i
$947$	178.761	−	28.3129i	0.188765	−	0.0298975i	−0.0613359	−	0.998117i	$-0.519536\pi$
$947$	178.761	−	28.3129i	0.188765	−	0.0298975i	0.250101	+	0.968220i	$0.419536\pi$
$948$	126.863	−	64.6399i	0.133822	−	0.0681855i
$949$		−	375.973i		−	0.396178i
$950$	−1098.95	+	1184.17i	−1.15678	+	1.24649i
$951$	−456.291			−0.479802
$952$	249.328	+	489.334i	0.261899	+	0.514006i
$953$	33.8363	+	213.634i	0.0355050	+	0.224170i	0.999060	−	0.0433390i	$-0.0137996\pi$
$953$	33.8363	+	213.634i	0.0355050	+	0.224170i	−0.963555	+	0.267509i	$0.913800\pi$
$954$	−401.518	+	552.642i	−0.420878	+	0.579289i
$955$	133.894	+	754.051i	0.140203	+	0.789582i
$956$	614.067	−	446.146i	0.642329	−	0.466680i
$957$	344.881	−	344.881i	0.360377	−	0.360377i
$958$	−451.425	−	71.4988i	−0.471216	−	0.0746334i
$959$	532.332	−	172.965i	0.555091	−	0.180360i
$960$	0.0563686	−	0.185169i	5.87173e−5	−	0.000192884i
$961$	−260.595	+	802.029i	−0.271171	+	0.834578i
$962$	178.103	+	90.7481i	0.185138	+	0.0943327i
$963$	180.946	−	355.126i	0.187898	−	0.368770i
$964$	189.242	+	61.4883i	0.196309	+	0.0637846i
$965$	−1039.26	−	1375.70i	−1.07695	−	1.42559i
$966$	114.596	+	352.691i	0.118630	+	0.365104i
$967$	−229.353	+	1448.08i	−0.237180	+	1.49749i	0.525543	+	0.850767i	$0.323862\pi$
$967$	−229.353	+	1448.08i	−0.237180	+	1.49749i	−0.762723	+	0.646726i	$0.776138\pi$
$968$	−172.926	−	172.926i	−0.178642	−	0.178642i
$969$	743.948	+	1023.96i	0.767748	+	1.05671i
$970$	−345.454	−	647.826i	−0.356138	−	0.667862i
$971$	1546.53	+	1123.62i	1.59272	+	1.15718i	0.899925	+	0.436044i	$0.143621\pi$
$971$	1546.53	+	1123.62i	1.59272	+	1.15718i	0.692795	+	0.721135i	$0.256379\pi$
$972$	34.1871	−	5.41471i	0.0351719	−	0.00557068i
$973$	−72.5567	+	36.9695i	−0.0745700	+	0.0379953i
$974$		−	1089.07i		−	1.11814i
$975$	−118.529	−	79.5350i	−0.121568	−	0.0815743i
$976$	−305.956			−0.313479
$977$	46.2797	+	90.8290i	0.0473692	+	0.0929673i	0.913478	−	0.406889i	$-0.133386\pi$
$977$	46.2797	+	90.8290i	0.0473692	+	0.0929673i	−0.866109	+	0.499856i	$0.833386\pi$
$978$	−198.994	−	1256.40i	−0.203470	−	1.28466i
$979$	−544.940	+	750.046i	−0.556629	+	0.766134i
$980$	237.876	+	229.163i	0.242731	+	0.233839i
$981$	518.883	−	376.990i	0.528932	−	0.384292i
$982$	−334.341	+	334.341i	−0.340469	+	0.340469i
$983$	−195.928	−	31.0320i	−0.199317	−	0.0315687i	0.0559777	−	0.998432i	$-0.482172\pi$
$983$	−195.928	−	31.0320i	−0.199317	−	0.0315687i	−0.255295	+	0.966863i	$0.582172\pi$
$984$	−329.541	+	107.074i	−0.334900	+	0.108815i
$985$	1073.71	−	20.0322i	1.09006	−	0.0203372i
$986$	−754.003	+	2320.58i	−0.764709	+	2.35353i
$987$	272.916	+	139.058i	0.276511	+	0.140889i
$988$	86.0988	−	168.978i	0.0871446	−	0.171031i
$989$	−224.537	−	72.9565i	−0.227034	−	0.0737680i
$990$	287.035	−	99.2200i	0.289934	−	0.100222i
$991$	−126.479	−	389.263i	−0.127628	−	0.392798i	0.866743	−	0.498755i	$-0.166209\pi$
$991$	−126.479	−	389.263i	−0.127628	−	0.392798i	−0.994371	+	0.105957i	$0.966209\pi$
$992$	54.3199	−	342.963i	0.0547580	−	0.345728i
$993$	−64.7056	−	64.7056i	−0.0651617	−	0.0651617i
$994$	328.604	+	452.285i	0.330588	+	0.455015i
$995$	−180.612	+	1296.42i	−0.181520	+	1.30294i
$996$	−322.214	−	234.102i	−0.323508	−	0.235043i
$997$	928.943	−	147.130i	0.931738	−	0.147573i	0.327929	−	0.944702i	$-0.393649\pi$
$997$	928.943	−	147.130i	0.931738	−	0.147573i	0.603808	+	0.797129i	$0.293649\pi$
$998$	724.714	−	369.260i	0.726166	−	0.370000i
$999$		−	126.332i		−	0.126459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.28.2	✓	80
3.2	odd	2		225.3.r.b.28.9		80
5.2	odd	4		375.3.k.c.7.9		80
5.3	odd	4		375.3.k.b.7.2		80
5.4	even	2		375.3.k.a.118.9		80
25.6	even	5		375.3.k.c.268.9		80
25.8	odd	20		375.3.k.a.232.9		80
25.17	odd	20	inner	75.3.k.a.67.2	yes	80
25.19	even	10		375.3.k.b.268.2		80
75.17	even	20		225.3.r.b.217.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.28.2	✓	80	1.1	even	1	trivial
75.3.k.a.67.2	yes	80	25.17	odd	20	inner
225.3.r.b.28.9		80	3.2	odd	2
225.3.r.b.217.9		80	75.17	even	20
375.3.k.a.118.9		80	5.4	even	2
375.3.k.a.232.9		80	25.8	odd	20
375.3.k.b.7.2		80	5.3	odd	4
375.3.k.b.268.2		80	25.19	even	10
375.3.k.c.7.9		80	5.2	odd	4
375.3.k.c.268.9		80	25.6	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13229 - 2.22224i) q^{2} +(-0.270952 - 1.71073i) q^{3} +(-1.30514 + 1.79637i) q^{4} +(-4.95217 - 0.689916i) q^{5} +(-3.49485 + 2.53916i) q^{6} +(3.10232 - 3.10232i) q^{7} +(-4.38372 - 0.694313i) q^{8} +(-2.85317 + 0.927051i) q^{9} +(4.07413 + 11.7861i) q^{10} +(-2.50856 + 7.72057i) q^{11} +(3.42674 + 1.74601i) q^{12} +(1.49656 - 2.93716i) q^{13} +(-10.4068 - 3.38139i) q^{14} +(0.161546 + 8.65875i) q^{15} +(6.16532 + 18.9749i) q^{16} +(4.41196 - 27.8560i) q^{17} +(5.29075 + 5.29075i) q^{18} +(-15.2294 - 20.9615i) q^{19} +(7.70264 - 7.99552i) q^{20} +(-6.14781 - 4.46664i) q^{21} +(19.9974 - 3.16728i) q^{22} +(17.4339 - 8.88304i) q^{23} +7.68747i q^{24} +(24.0480 + 6.83317i) q^{25} -8.22163 q^{26} +(2.35900 + 4.62981i) q^{27} +(1.52396 + 9.62191i) q^{28} +(20.3892 - 28.0633i) q^{29} +(19.0589 - 10.1632i) q^{30} +(8.77688 - 6.37677i) q^{31} +(22.6323 - 22.6323i) q^{32} +(13.8875 + 2.19956i) q^{33} +(-66.8985 + 21.7366i) q^{34} +(-17.5036 + 13.2229i) q^{35} +(2.05846 - 6.33529i) q^{36} +(-21.6628 - 11.0377i) q^{37} +(-29.3374 + 57.5779i) q^{38} +(-5.43018 - 1.76437i) q^{39} +(21.2299 + 6.46276i) q^{40} +(13.9284 + 42.8673i) q^{41} +(-2.96487 + 18.7195i) q^{42} +(-8.53203 - 8.53203i) q^{43} +(-10.5950 - 14.5828i) q^{44} +(14.7690 - 2.62247i) q^{45} +(-39.4805 - 28.6843i) q^{46} +(-39.8112 + 6.30548i) q^{47} +(30.7904 - 15.6885i) q^{48} +29.7512i q^{49} +(-12.0444 - 61.1777i) q^{50} -48.8495 q^{51} +(3.32302 + 6.52180i) q^{52} +(14.2819 + 90.1725i) q^{53} +(7.61748 - 10.4846i) q^{54} +(17.7494 - 36.5029i) q^{55} +(-15.7537 + 11.4457i) q^{56} +(-31.7329 + 31.7329i) q^{57} +(-85.4499 - 13.5339i) q^{58} +(101.152 - 32.8662i) q^{59} +(-15.7652 - 11.0107i) q^{60} +(-4.73879 + 14.5845i) q^{61} +(-24.1087 - 12.2840i) q^{62} +(-5.97544 + 11.7275i) q^{63} +(-0.0212563 - 0.00690660i) q^{64} +(-9.43761 + 13.5128i) q^{65} +(-10.8367 - 33.3519i) q^{66} +(4.18666 - 26.4335i) q^{67} +(44.2816 + 44.2816i) q^{68} +(-19.9202 - 27.4178i) q^{69} +(49.2036 + 23.9251i) q^{70} +(-41.3332 - 30.0303i) q^{71} +(13.1512 - 2.08294i) q^{72} +(101.623 - 51.7793i) q^{73} +60.6378i q^{74} +(5.17381 - 42.9911i) q^{75} +57.5312 q^{76} +(16.1693 + 31.7341i) q^{77} +(2.22767 + 14.0650i) q^{78} +(21.7607 - 29.9510i) q^{79} +(-17.4406 - 98.2206i) q^{80} +(7.28115 - 5.29007i) q^{81} +(79.4905 - 79.4905i) q^{82} +(-102.284 - 16.2002i) q^{83} +(16.0475 - 5.21416i) q^{84} +(-41.0671 + 134.904i) q^{85} +(-9.29951 + 28.6210i) q^{86} +(-53.5331 - 27.2765i) q^{87} +(16.3573 - 32.1031i) q^{88} +(108.616 + 35.2914i) q^{89} +(-22.5505 - 29.8509i) q^{90} +(-4.46922 - 13.7548i) q^{91} +(-6.79652 + 42.9115i) q^{92} +(-13.2870 - 13.2870i) q^{93} +(59.0902 + 81.3306i) q^{94} +(60.9570 + 114.312i) q^{95} +(-44.8500 - 32.5855i) q^{96} +(-58.1488 + 9.20986i) q^{97} +(66.1143 - 33.6869i) q^{98} -24.3537i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26}+ \cdots - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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