LMFDB - Embedded newform 29.4.d.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [29,4,Mod(7,29)] 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("29.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, 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:	$1.71105539017$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	29.7
Dual form			29.4.d.a.25.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.764111 - 3.34779i) q^{2} +(8.23892 + 3.96766i) q^{3} +(-3.41608 + 1.64510i) q^{4} +(1.31115 + 5.74451i) q^{5} +(6.98743 - 30.6139i) q^{6} +(-25.5210 - 12.2903i) q^{7} +(-9.01023 - 11.2985i) q^{8} +(35.3034 + 44.2690i) q^{9} +(18.2296 - 8.77890i) q^{10} +(-12.2720 + 15.3887i) q^{11} -34.6720 q^{12} +(6.21305 - 7.79091i) q^{13} +(-21.6443 + 94.8301i) q^{14} +(-11.9898 + 52.5308i) q^{15} +(-49.8521 + 62.5126i) q^{16} -55.5715 q^{17} +(121.228 - 152.015i) q^{18} +(123.926 - 59.6797i) q^{19} +(-13.9293 - 17.4668i) q^{20} +(-161.502 - 202.517i) q^{21} +(60.8952 + 29.3256i) q^{22} +(-25.7533 + 112.832i) q^{23} +(-29.4061 - 128.837i) q^{24} +(81.3408 - 39.1717i) q^{25} +(-30.8298 - 14.8469i) q^{26} +(60.2766 + 264.089i) q^{27} +107.401 q^{28} +(-89.4863 + 127.989i) q^{29} +185.024 q^{30} +(-39.1945 - 171.722i) q^{31} +(143.210 + 68.9664i) q^{32} +(-162.165 + 78.0947i) q^{33} +(42.4628 + 186.042i) q^{34} +(37.1398 - 162.720i) q^{35} +(-193.426 - 93.1491i) q^{36} +(-7.21365 - 9.04563i) q^{37} +(-294.488 - 369.277i) q^{38} +(82.1005 - 39.5375i) q^{39} +(53.0905 - 66.5733i) q^{40} +326.005 q^{41} +(-554.579 + 695.421i) q^{42} +(29.5107 - 129.295i) q^{43} +(16.6065 - 72.7576i) q^{44} +(-208.016 + 260.844i) q^{45} +397.418 q^{46} +(91.9205 - 115.265i) q^{47} +(-658.756 + 317.240i) q^{48} +(286.414 + 359.152i) q^{49} +(-193.292 - 242.380i) q^{50} +(-457.849 - 220.488i) q^{51} +(-8.40746 + 36.8355i) q^{52} +(-45.9269 - 201.219i) q^{53} +(838.057 - 403.587i) q^{54} +(-104.491 - 50.3201i) q^{55} +(91.0888 + 399.086i) q^{56} +1257.81 q^{57} +(496.858 + 201.784i) q^{58} +58.8115 q^{59} +(-45.4602 - 199.174i) q^{60} +(-320.413 - 154.303i) q^{61} +(-544.941 + 262.430i) q^{62} +(-356.899 - 1563.68i) q^{63} +(-20.8795 + 91.4792i) q^{64} +(52.9012 + 25.4759i) q^{65} +(385.357 + 483.222i) q^{66} +(-263.197 - 330.039i) q^{67} +(189.837 - 91.4205i) q^{68} +(-659.860 + 827.438i) q^{69} -573.132 q^{70} +(192.611 - 241.526i) q^{71} +(182.081 - 797.748i) q^{72} +(-231.351 + 1013.61i) q^{73} +(-24.7709 + 31.0617i) q^{74} +825.580 q^{75} +(-325.163 + 407.741i) q^{76} +(502.325 - 241.907i) q^{77} +(-195.097 - 244.644i) q^{78} +(232.256 + 291.240i) q^{79} +(-424.468 - 204.413i) q^{80} +(-211.011 + 924.498i) q^{81} +(-249.104 - 1091.40i) q^{82} +(-533.782 + 257.056i) q^{83} +(884.865 + 426.129i) q^{84} +(-72.8624 - 319.231i) q^{85} -455.402 q^{86} +(-1245.09 + 699.441i) q^{87} +284.442 q^{88} +(164.980 + 722.823i) q^{89} +(1032.20 + 497.080i) q^{90} +(-254.316 + 122.472i) q^{91} +(-97.6452 - 427.812i) q^{92} +(358.415 - 1570.32i) q^{93} +(-456.119 - 219.656i) q^{94} +(505.316 + 633.647i) q^{95} +(906.263 + 1136.42i) q^{96} +(-766.073 + 368.921i) q^{97} +(983.512 - 1233.29i) q^{98} -1114.48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) $ 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.764111	−	3.34779i	−0.270154	−	1.18362i	−0.909831	−	0.414979i	$-0.863789\pi$
$2$	−0.764111	−	3.34779i	−0.270154	−	1.18362i	0.639677	−	0.768644i	$-0.279068\pi$
$3$	8.23892	+	3.96766i	1.58558	+	0.763576i	0.998929	−	0.0462628i	$-0.0147312\pi$
$3$	8.23892	+	3.96766i	1.58558	+	0.763576i	0.586653	+	0.809839i	$0.300445\pi$
$4$	−3.41608	+	1.64510i	−0.427010	+	0.205637i
$5$	1.31115	+	5.74451i	0.117273	+	0.513805i	0.999107	+	0.0422461i	$0.0134514\pi$
$5$	1.31115	+	5.74451i	0.117273	+	0.513805i	−0.881835	+	0.471559i	$0.843691\pi$
$6$	6.98743	−	30.6139i	0.475434	−	2.08301i
$7$	−25.5210	−	12.2903i	−1.37800	−	0.663612i	−0.409431	−	0.912341i	$-0.634273\pi$
$7$	−25.5210	−	12.2903i	−1.37800	−	0.663612i	−0.968573	+	0.248729i	$0.919987\pi$
$8$	−9.01023	−	11.2985i	−0.398199	−	0.499326i
$9$	35.3034	+	44.2690i	1.30753	+	1.63959i
$10$	18.2296	−	8.77890i	0.576469	−	0.277613i
$11$	−12.2720	+	15.3887i	−0.336378	+	0.421805i	−0.921037	−	0.389474i	$-0.872657\pi$
$11$	−12.2720	+	15.3887i	−0.336378	+	0.421805i	0.584659	+	0.811279i	$0.301228\pi$
$12$	−34.6720			−0.834079
$13$	6.21305	−	7.79091i	0.132553	−	0.166216i	−0.711125	−	0.703065i	$-0.751814\pi$
$13$	6.21305	−	7.79091i	0.132553	−	0.166216i	0.843678	+	0.536849i	$0.180386\pi$
$14$	−21.6443	+	94.8301i	−0.413193	+	1.81031i
$15$	−11.9898	+	52.5308i	−0.206384	+	0.904226i
$16$	−49.8521	+	62.5126i	−0.778939	+	0.976759i
$17$	−55.5715			−0.792827			−0.396413	−	0.918072i	$-0.629745\pi$
$17$	−55.5715			−0.792827			−0.396413	+	0.918072i	$0.629745\pi$
$18$	121.228	−	152.015i	1.58742	−	1.99057i
$19$	123.926	−	59.6797i	1.49635	−	0.720603i	0.506434	−	0.862278i	$-0.330963\pi$
$19$	123.926	−	59.6797i	1.49635	−	0.720603i	0.989913	+	0.141675i	$0.0452489\pi$
$20$	−13.9293	−	17.4668i	−0.155734	−	0.195284i
$21$	−161.502	−	202.517i	−1.67822	−	2.10442i
$22$	60.8952	+	29.3256i	0.590132	+	0.284192i
$23$	−25.7533	+	112.832i	−0.233475	+	1.02292i	0.713258	+	0.700902i	$0.247219\pi$
$23$	−25.7533	+	112.832i	−0.233475	+	1.02292i	−0.946733	+	0.322020i	$0.895638\pi$
$24$	−29.4061	−	128.837i	−0.250104	−	1.09578i
$25$	81.3408	−	39.1717i	0.650726	−	0.313373i
$26$	−30.8298	−	14.8469i	−0.232547	−	0.111989i
$27$	60.2766	+	264.089i	0.429638	+	1.88237i
$28$	107.401			0.724886
$29$	−89.4863	+	127.989i	−0.573007	+	0.819551i
$29$	−89.4863	+	127.989i	−0.573007	+	0.819551i
$30$	185.024			1.12602
$31$	−39.1945	−	171.722i	−0.227082	−	0.994911i	−0.952005	−	0.306081i	$-0.900982\pi$
$31$	−39.1945	−	171.722i	−0.227082	−	0.994911i	0.724923	−	0.688829i	$-0.241875\pi$
$32$	143.210	+	68.9664i	0.791132	+	0.380989i
$33$	−162.165	+	78.0947i	−0.855435	+	0.411956i
$34$	42.4628	+	186.042i	0.214185	+	0.938408i
$35$	37.1398	−	162.720i	0.179365	−	0.785849i
$36$	−193.426	−	93.1491i	−0.895491	−	0.431246i
$37$	−7.21365	−	9.04563i	−0.0320518	−	0.0401917i	0.765547	−	0.643380i	$-0.222468\pi$
$37$	−7.21365	−	9.04563i	−0.0320518	−	0.0401917i	−0.797599	+	0.603188i	$0.793897\pi$
$38$	−294.488	−	369.277i	−1.25717	−	1.57644i
$39$	82.1005	−	39.5375i	0.337092	−	0.162335i
$40$	53.0905	−	66.5733i	0.209858	−	0.263154i
$41$	326.005			1.24179			0.620895	−	0.783893i	$-0.286769\pi$
$41$	326.005			1.24179			0.620895	+	0.783893i	$0.286769\pi$
$42$	−554.579	+	695.421i	−2.03746	+	2.55490i
$43$	29.5107	−	129.295i	0.104659	−	0.458542i	−0.895256	−	0.445551i	$-0.853008\pi$
$43$	29.5107	−	129.295i	0.104659	−	0.458542i	0.999916	−	0.0129905i	$-0.00413513\pi$
$44$	16.6065	−	72.7576i	0.0568981	−	0.249287i
$45$	−208.016	+	260.844i	−0.689093	+	0.864096i
$46$	397.418			1.27383
$47$	91.9205	−	115.265i	0.285276	−	0.357725i	−0.618459	−	0.785817i	$-0.712243\pi$
$47$	91.9205	−	115.265i	0.285276	−	0.357725i	0.903735	+	0.428092i	$0.140814\pi$
$48$	−658.756	+	317.240i	−1.98090	+	0.953952i
$49$	286.414	+	359.152i	0.835026	+	1.04709i
$50$	−193.292	−	242.380i	−0.546712	−	0.685555i
$51$	−457.849	−	220.488i	−1.25709	−	0.605384i
$52$	−8.40746	+	36.8355i	−0.0224212	+	0.0982339i
$53$	−45.9269	−	201.219i	−0.119029	−	0.521501i	−0.998926	−	0.0463361i	$-0.985245\pi$
$53$	−45.9269	−	201.219i	−0.119029	−	0.521501i	0.879897	−	0.475165i	$-0.157612\pi$
$54$	838.057	−	403.587i	2.11195	−	1.01706i
$55$	−104.491	−	50.3201i	−0.256173	−	0.123367i
$56$	91.0888	+	399.086i	0.217362	+	0.952324i
$57$	1257.81			2.92282
$58$	496.858	+	201.784i	1.12484	+	0.456819i
$59$	58.8115			0.129773			0.0648865	−	0.997893i	$-0.479331\pi$
$59$	58.8115			0.129773			0.0648865	+	0.997893i	$0.479331\pi$
$60$	−45.4602	−	199.174i	−0.0978147	−	0.428554i
$61$	−320.413	−	154.303i	−0.672536	−	0.323876i	0.0662628	−	0.997802i	$-0.478892\pi$
$61$	−320.413	−	154.303i	−0.672536	−	0.323876i	−0.738799	+	0.673926i	$0.764607\pi$
$62$	−544.941	+	262.430i	−1.11625	+	0.537559i
$63$	−356.899	−	1563.68i	−0.713731	−	3.12706i
$64$	−20.8795	+	91.4792i	−0.0407803	+	0.178670i
$65$	52.9012	+	25.4759i	0.100948	+	0.0486138i
$66$	385.357	+	483.222i	0.718700	+	0.901221i
$67$	−263.197	−	330.039i	−0.479920	−	0.601801i	0.481649	−	0.876364i	$-0.340038\pi$
$67$	−263.197	−	330.039i	−0.479920	−	0.601801i	−0.961569	+	0.274563i	$0.911467\pi$
$68$	189.837	−	91.4205i	0.338545	−	0.163035i
$69$	−659.860	+	827.438i	−1.15127	+	1.44365i
$70$	−573.132			−0.978605
$71$	192.611	−	241.526i	0.321954	−	0.403717i	−0.594347	−	0.804209i	$-0.702589\pi$
$71$	192.611	−	241.526i	0.321954	−	0.403717i	0.916300	+	0.400492i	$0.131161\pi$
$72$	182.081	−	797.748i	0.298034	−	1.30577i
$73$	−231.351	+	1013.61i	−0.370925	+	1.62513i	0.353261	+	0.935525i	$0.385073\pi$
$73$	−231.351	+	1013.61i	−0.370925	+	1.62513i	−0.724186	+	0.689605i	$0.757784\pi$
$74$	−24.7709	+	31.0617i	−0.0389129	+	0.0487952i
$75$	825.580			1.27106
$76$	−325.163	+	407.741i	−0.490773	+	0.615410i
$77$	502.325	−	241.907i	0.743445	−	0.358024i
$78$	−195.097	−	244.644i	−0.283210	−	0.355135i
$79$	232.256	+	291.240i	0.330770	+	0.414773i	0.919210	−	0.393769i	$-0.128829\pi$
$79$	232.256	+	291.240i	0.330770	+	0.414773i	−0.588439	+	0.808541i	$0.700257\pi$
$80$	−424.468	−	204.413i	−0.593212	−	0.285676i
$81$	−211.011	+	924.498i	−0.289452	+	1.26817i
$82$	−249.104	−	1091.40i	−0.335475	−	1.46981i
$83$	−533.782	+	257.056i	−0.705906	+	0.339946i	−0.752157	−	0.658983i	$-0.770987\pi$
$83$	−533.782	+	257.056i	−0.705906	+	0.339946i	0.0462515	+	0.998930i	$0.485272\pi$
$84$	884.865	+	426.129i	1.14937	+	0.553505i
$85$	−72.8624	−	319.231i	−0.0929769	−	0.407358i
$86$	−455.402			−0.571014
$87$	−1245.09	+	699.441i	−1.53434	+	0.861930i
$88$	284.442			0.344564
$89$	164.980	+	722.823i	0.196492	+	0.860888i	0.973004	+	0.230786i	$0.0741298\pi$
$89$	164.980	+	722.823i	0.196492	+	0.860888i	−0.776512	+	0.630102i	$0.783013\pi$
$90$	1032.20	+	497.080i	1.20892	+	0.582187i
$91$	−254.316	+	122.472i	−0.292962	+	0.141083i
$92$	−97.6452	−	427.812i	−0.110655	−	0.484809i
$93$	358.415	−	1570.32i	0.399633	−	1.75091i
$94$	−456.119	−	219.656i	−0.500480	−	0.241019i
$95$	505.316	+	633.647i	0.545730	+	0.684324i
$96$	906.263	+	1136.42i	0.963491	+	1.20818i
$97$	−766.073	+	368.921i	−0.801885	+	0.386168i	−0.789496	−	0.613756i	$-0.789658\pi$
$97$	−766.073	+	368.921i	−0.801885	+	0.386168i	−0.0123893	+	0.999923i	$0.503944\pi$
$98$	983.512	−	1233.29i	1.01377	−	1.27123i
$99$	−1114.48			−1.13141
$100$	−213.426	+	267.627i	−0.213426	+	0.267627i
$101$	−270.349	+	1184.48i	−0.266344	+	1.16693i	0.647886	+	0.761737i	$0.275653\pi$
$101$	−270.349	+	1184.48i	−0.266344	+	1.16693i	−0.914231	+	0.405194i	$0.867204\pi$
$102$	−388.302	+	1701.26i	−0.376937	+	1.65147i
$103$	1201.75	−	1506.94i	1.14963	−	1.44159i	0.271964	−	0.962307i	$-0.412327\pi$
$103$	1201.75	−	1506.94i	1.14963	−	1.44159i	0.877663	−	0.479279i	$-0.159102\pi$
$104$	−144.006			−0.135779
$105$	951.610	−	1193.28i	0.884453	−	1.10907i
$106$	−638.546	+	307.508i	−0.585104	+	0.281771i
$107$	−635.220	−	796.540i	−0.573916	−	0.719668i	0.407146	−	0.913363i	$-0.366524\pi$
$107$	−635.220	−	796.540i	−0.573916	−	0.719668i	−0.981062	+	0.193695i	$0.937953\pi$
$108$	−640.362	−	802.989i	−0.570545	−	0.715441i
$109$	−409.677	−	197.290i	−0.359999	−	0.173366i	0.245137	−	0.969488i	$-0.421167\pi$
$109$	−409.677	−	197.290i	−0.359999	−	0.173366i	−0.605136	+	0.796122i	$0.706881\pi$
$110$	−88.6186	+	388.263i	−0.0768132	+	0.336541i
$111$	−23.5428	−	103.148i	−0.0201314	−	0.0882012i
$112$	2040.57	−	982.687i	1.72157	−	0.829065i
$113$	208.569	+	100.442i	0.173633	+	0.0836172i	0.518681	−	0.854968i	$-0.326423\pi$
$113$	208.569	+	100.442i	0.173633	+	0.0836172i	−0.345048	+	0.938585i	$0.612137\pi$
$114$	−961.104	−	4210.87i	−0.789611	−	3.45951i
$115$	−681.934			−0.552962
$116$	95.1381	−	584.435i	0.0761496	−	0.467788i
$117$	564.237			0.445844
$118$	−44.9385	−	196.889i	−0.0350587	−	0.153602i
$119$	1418.24	+	682.988i	1.09252	+	0.526129i
$120$	701.548	−	337.848i	0.533686	−	0.257010i
$121$	209.968	+	919.929i	0.157752	+	0.691156i
$122$	−271.742	+	1190.58i	−0.201659	+	0.883526i
$123$	2685.93	+	1293.48i	1.96896	+	0.948202i
$124$	416.392	+	522.139i	0.301557	+	0.378141i
$125$	790.891	+	991.746i	0.565916	+	0.709636i
$126$	−4962.15	+	2389.65i	−3.50844	+	1.68958i
$127$	15.8463	−	19.8707i	0.0110719	−	0.0138838i	−0.776265	−	0.630407i	$-0.782888\pi$
$127$	15.8463	−	19.8707i	0.0110719	−	0.0138838i	0.787337	+	0.616523i	$0.211459\pi$
$128$	1593.82			1.10059
$129$	756.135	−	948.163i	0.516077	−	0.647140i
$130$	44.8655	−	196.569i	0.0302690	−	0.132617i
$131$	−139.123	+	609.539i	−0.0927882	+	0.406532i	−0.999897	−	0.0143649i	$-0.995427\pi$
$131$	−139.123	+	609.539i	−0.0927882	+	0.406532i	0.907109	+	0.420897i	$0.138285\pi$
$132$	425.497	−	533.556i	0.280566	−	0.351819i
$133$	−3896.20			−2.54017
$134$	−903.789	+	1133.32i	−0.582653	+	0.730624i
$135$	−1438.03	+	692.520i	−0.916786	+	0.441501i
$136$	500.711	+	627.872i	0.315703	+	0.395879i
$137$	−924.552	−	1159.35i	−0.576568	−	0.722993i	0.404955	−	0.914336i	$-0.367287\pi$
$137$	−924.552	−	1159.35i	−0.576568	−	0.722993i	−0.981523	+	0.191343i	$0.938716\pi$
$138$	3274.30	+	1576.82i	2.01976	+	0.972664i
$139$	274.985	−	1204.79i	0.167798	−	0.735171i	−0.819077	−	0.573684i	$-0.805514\pi$
$139$	274.985	−	1204.79i	0.167798	−	0.735171i	0.986875	−	0.161487i	$-0.0516291\pi$
$140$	140.818	+	616.964i	0.0850092	+	0.372450i
$141$	1214.66	−	584.948i	0.725479	−	0.349372i
$142$	−955.756	−	460.268i	−0.564826	−	0.272006i
$143$	43.6449	+	191.221i	0.0255229	+	0.111823i
$144$	−4527.31			−2.61997
$145$	−852.565	−	346.243i	−0.488287	−	0.198303i
$146$	3570.14			2.02375
$147$	934.752	+	4095.42i	0.524470	+	2.29785i
$148$	39.5234	+	19.0335i	0.0219514	+	0.0105712i
$149$	−869.154	+	418.563i	−0.477879	+	0.230134i	−0.657287	−	0.753641i	$-0.728296\pi$
$149$	−869.154	+	418.563i	−0.477879	+	0.230134i	0.179408	+	0.983775i	$0.442582\pi$
$150$	−630.835	−	2763.87i	−0.343383	−	1.50446i
$151$	−20.9863	+	91.9471i	−0.0113102	+	0.0495533i	−0.980268	−	0.197672i	$-0.936662\pi$
$151$	−20.9863	+	91.9471i	−0.0113102	+	0.0495533i	0.968958	+	0.247226i	$0.0795189\pi$
$152$	−1790.89	−	862.448i	−0.955661	−	0.460222i
$153$	−1961.86	−	2460.09i	−1.03665	−	1.29991i
$154$	−1193.69	−	1496.84i	−0.624611	−	0.783237i
$155$	935.071	−	450.307i	0.484560	−	0.233352i
$156$	−215.419	+	270.127i	−0.110560	+	0.138638i
$157$	1304.76			0.663255			0.331627	−	0.943410i	$-0.392402\pi$
$157$	1304.76			0.663255			0.331627	+	0.943410i	$0.392402\pi$
$158$	797.540	−	1000.08i	0.401575	−	0.503560i
$159$	419.980	−	1840.05i	0.209475	−	0.917771i
$160$	−208.409	+	913.098i	−0.102976	+	0.451167i
$161$	2043.99	−	2563.08i	1.00055	−	1.25465i
$162$	3256.26			1.57923
$163$	−568.706	+	713.134i	−0.273279	+	0.342681i	−0.899465	−	0.436993i	$-0.856044\pi$
$163$	−568.706	+	713.134i	−0.273279	+	0.342681i	0.626186	+	0.779674i	$0.284615\pi$
$164$	−1113.66	+	536.310i	−0.530257	+	0.255358i
$165$	−661.239	−	829.167i	−0.311984	−	0.391216i
$166$	1268.44	+	1590.57i	0.593072	+	0.743688i
$167$	−3403.55	−	1639.06i	−1.57709	−	0.759488i	−0.578666	−	0.815565i	$-0.696426\pi$
$167$	−3403.55	−	1639.06i	−1.57709	−	0.759488i	−0.998426	+	0.0560770i	$0.982141\pi$
$168$	−832.963	+	3649.45i	−0.382527	+	1.67596i
$169$	466.782	+	2045.11i	0.212463	+	0.930863i
$170$	−1013.04	+	487.856i	−0.457041	+	0.220099i
$171$	7016.97	+	3379.19i	3.13802	+	1.51119i
$172$	111.892	+	490.230i	0.0496028	+	0.217324i
$173$	−1148.42			−0.504696			−0.252348	−	0.967637i	$-0.581203\pi$
$173$	−1148.42			−0.504696			−0.252348	+	0.967637i	$0.581203\pi$
$174$	3292.97	+	3633.84i	1.43471	+	1.58322i
$175$	−2557.33			−1.10466
$176$	−350.197	−	1534.31i	−0.149983	−	0.657121i
$177$	484.544	+	233.344i	0.205766	+	0.0990915i
$178$	2293.80	−	1104.63i	0.965884	−	0.465145i
$179$	−411.824	−	1804.32i	−0.171962	−	0.753414i	−0.985190	−	0.171468i	$-0.945149\pi$
$179$	−411.824	−	1804.32i	−0.171962	−	0.753414i	0.813228	−	0.581946i	$-0.197708\pi$
$180$	281.486	−	1233.27i	0.116560	−	0.510681i
$181$	232.061	+	111.755i	0.0952982	+	0.0458932i	0.480926	−	0.876761i	$-0.340301\pi$
$181$	232.061	+	111.755i	0.0952982	+	0.0458932i	−0.385627	+	0.922655i	$0.626015\pi$
$182$	604.336	+	757.813i	0.246134	+	0.308642i
$183$	−2027.64	−	2542.58i	−0.819057	−	1.02707i
$184$	1506.88	−	725.674i	0.603741	−	0.290747i
$185$	42.5046	−	53.2991i	0.0168919	−	0.0211818i
$186$	−5530.96			−2.18038
$187$	681.975	−	855.170i	0.266690	−	0.334418i
$188$	−124.386	+	544.972i	−0.0482543	+	0.211416i
$189$	1707.41	−	7480.63i	0.657119	−	2.87903i
$190$	1735.20	−	2175.87i	0.662550	−	0.830811i
$191$	−291.002			−0.110242			−0.0551208	−	0.998480i	$-0.517554\pi$
$191$	−291.002			−0.110242			−0.0551208	+	0.998480i	$0.517554\pi$
$192$	−534.983	+	670.848i	−0.201089	+	0.252158i
$193$	−906.201	+	436.403i	−0.337978	+	0.162762i	−0.595172	−	0.803598i	$-0.702916\pi$
$193$	−906.201	+	436.403i	−0.337978	+	0.162762i	0.257194	+	0.966360i	$0.417202\pi$
$194$	1820.44	+	2282.75i	0.673709	+	0.844805i
$195$	334.770	+	419.788i	0.122940	+	0.154162i
$196$	−1569.25	−	755.713i	−0.571885	−	0.275405i
$197$	−315.729	+	1383.30i	−0.114186	+	0.500284i	0.885198	+	0.465214i	$0.154023\pi$
$197$	−315.729	+	1383.30i	−0.114186	+	0.500284i	−0.999385	+	0.0350699i	$0.988835\pi$
$198$	851.590	+	3731.06i	0.305656	+	1.33917i
$199$	−2261.94	+	1089.29i	−0.805752	+	0.388030i	−0.790965	−	0.611861i	$-0.790421\pi$
$199$	−2261.94	+	1089.29i	−0.805752	+	0.388030i	−0.0147866	+	0.999891i	$0.504707\pi$
$200$	−1175.48	−	566.081i	−0.415594	−	0.200140i
$201$	−858.981	−	3763.44i	−0.301432	−	1.32066i
$202$	4171.96			1.45316
$203$	3856.80	−	2166.60i	1.33347	−	0.749090i
$204$	1926.78			0.661281
$205$	427.441	+	1872.74i	0.145628	+	0.638038i
$206$	−5963.19	−	2871.72i	−2.01687	−	0.971274i
$207$	−5904.16	+	2843.29i	−1.98245	+	0.954698i
$208$	177.297	+	776.787i	0.0591024	+	0.258945i
$209$	−602.437	+	2639.45i	−0.199385	+	0.873562i
$210$	−4721.99	−	2273.99i	−1.55166	−	0.747239i
$211$	1477.11	+	1852.24i	0.481937	+	0.604330i	0.962049	−	0.272877i	$-0.0879754\pi$
$211$	1477.11	+	1852.24i	0.481937	+	0.604330i	−0.480112	+	0.877207i	$0.659404\pi$
$212$	487.915	+	611.827i	0.158067	+	0.198210i
$213$	2545.20	−	1225.70i	0.818753	−	0.394290i
$214$	−2181.27	+	2735.23i	−0.696769	+	0.873721i
$215$	781.430			0.247875
$216$	2440.70	−	3060.53i	0.768835	−	0.964088i
$217$	−1110.23	+	4864.24i	−0.347315	+	1.52169i
$218$	−347.447	+	1522.26i	−0.107945	+	0.472939i
$219$	−5927.75	+	7433.16i	−1.82904	+	2.29355i
$220$	439.731			0.134757
$221$	−345.268	+	432.952i	−0.105092	+	0.131781i
$222$	−327.327	+	157.632i	−0.0989584	+	0.0476559i
$223$	302.878	+	379.797i	0.0909516	+	0.114050i	0.825225	−	0.564804i	$-0.191048\pi$
$223$	302.878	+	379.797i	0.0909516	+	0.114050i	−0.734273	+	0.678854i	$0.762477\pi$
$224$	−2807.25	−	3520.18i	−0.837355	−	1.05001i
$225$	4605.69	+	2217.98i	1.36465	+	0.657181i
$226$	176.887	−	774.994i	0.0520636	−	0.228105i
$227$	−1005.93	−	4407.27i	−0.294123	−	1.28864i	−0.878729	−	0.477320i	$-0.841608\pi$
$227$	−1005.93	−	4407.27i	−0.294123	−	1.28864i	0.584606	−	0.811317i	$-0.301249\pi$
$228$	−4296.77	+	2069.22i	−1.24807	+	0.601040i
$229$	4338.97	+	2089.54i	1.25208	+	0.602971i	0.938069	−	0.346447i	$-0.112612\pi$
$229$	4338.97	+	2089.54i	1.25208	+	0.602971i	0.314013	+	0.949419i	$0.398326\pi$
$230$	521.073	+	2282.97i	0.149385	+	0.654499i
$231$	5098.43			1.45217
$232$	2252.37	−	142.152i	0.637394	−	0.0402272i
$233$	4969.07			1.39714			0.698571	−	0.715540i	$-0.253819\pi$
$233$	4969.07			1.39714			0.698571	+	0.715540i	$0.253819\pi$
$234$	−431.140	−	1888.95i	−0.120447	−	0.527711i
$235$	782.661	+	376.910i	0.217256	+	0.104625i
$236$	−200.905	+	96.7507i	−0.0554144	+	0.0266862i
$237$	758.000	+	3321.02i	0.207753	+	0.910224i
$238$	1202.81	−	5269.85i	0.327590	−	1.43527i
$239$	1386.90	+	667.896i	0.375360	+	0.180764i	0.612046	−	0.790822i	$-0.290347\pi$
$239$	1386.90	+	667.896i	0.375360	+	0.180764i	−0.236685	+	0.971586i	$0.576061\pi$
$240$	−2686.12	−	3368.28i	−0.722451	−	0.905924i
$241$	−3123.72	−	3917.02i	−0.834924	−	1.04696i	−0.998176	−	0.0603771i	$-0.980770\pi$
$241$	−3123.72	−	3917.02i	−0.834924	−	1.04696i	0.163252	−	0.986584i	$-0.447802\pi$
$242$	2919.29	−	1405.86i	0.775451	−	0.373437i
$243$	−846.526	+	1061.51i	−0.223476	+	0.280230i
$244$	1348.40			0.353781
$245$	−1687.62	+	2116.21i	−0.440074	+	0.551835i
$246$	2277.94	−	9980.29i	0.590390	−	2.58667i
$247$	305.000	−	1336.29i	0.0785695	−	0.344235i
$248$	−1587.05	+	1990.09i	−0.406361	+	0.509561i
$249$	−5417.70			−1.37885
$250$	2715.83	−	3405.54i	0.687057	−	0.861542i
$251$	−1515.32	+	729.738i	−0.381060	+	0.183509i	−0.614601	−	0.788838i	$-0.710683\pi$
$251$	−1515.32	+	729.738i	−0.381060	+	0.183509i	0.233541	+	0.972347i	$0.424969\pi$
$252$	3791.60	+	4754.52i	0.947811	+	1.18852i
$253$	−1420.29	−	1780.99i	−0.352937	−	0.442569i
$254$	−78.6312	−	37.8668i	−0.0194243	−	0.00935423i
$255$	666.291	−	2919.21i	0.163627	−	0.716895i
$256$	−1050.82	−	4603.94i	−0.256547	−	1.12401i
$257$	1129.36	−	543.872i	0.274116	−	0.132007i	−0.291776	−	0.956487i	$-0.594246\pi$
$257$	1129.36	−	543.872i	0.274116	−	0.132007i	0.565892	+	0.824480i	$0.308532\pi$
$258$	−3752.02	−	1806.88i	−0.905390	−	0.436013i
$259$	72.9264	+	319.511i	0.0174958	+	0.0766543i
$260$	−222.625			−0.0531025
$261$	−8825.12	+	556.971i	−2.09295	+	0.132090i
$262$	2146.91			0.506247
$263$	12.9474	+	56.7261i	0.00303562	+	0.0132999i	0.976423	−	0.215866i	$-0.0692574\pi$
$263$	12.9474	+	56.7261i	0.00303562	+	0.0132999i	−0.973387	+	0.229166i	$0.926400\pi$
$264$	2343.50	+	1128.57i	0.546334	+	0.263101i
$265$	1095.69	−	527.656i	0.253991	−	0.122316i
$266$	2977.13	+	13043.7i	0.686239	+	3.00661i
$267$	−1508.66	+	6609.86i	−0.345799	+	1.51505i
$268$	1442.05	+	694.455i	0.328684	+	0.158286i
$269$	−1220.27	−	1530.17i	−0.276584	−	0.346825i	0.624065	−	0.781372i	$-0.285480\pi$
$269$	−1220.27	−	1530.17i	−0.276584	−	0.346825i	−0.900649	+	0.434547i	$0.856909\pi$
$270$	3417.23	+	4285.07i	0.770244	+	0.965855i
$271$	5571.62	−	2683.15i	1.24890	−	0.601438i	0.311682	−	0.950186i	$-0.399107\pi$
$271$	5571.62	−	2683.15i	1.24890	−	0.601438i	0.937216	+	0.348748i	$0.113393\pi$
$272$	2770.35	−	3473.91i	0.617564	−	0.774401i
$273$	−2581.21			−0.572242
$274$	−3174.80	+	3981.08i	−0.699989	+	0.877758i
$275$	−395.418	+	1732.44i	−0.0867077	+	0.379891i
$276$	892.918	−	3912.13i	0.194737	−	0.853198i
$277$	4697.62	−	5890.63i	1.01896	−	1.27774i	0.0588093	−	0.998269i	$-0.481270\pi$
$277$	4697.62	−	5890.63i	1.01896	−	1.27774i	0.960154	−	0.279471i	$-0.0901590\pi$
$278$	−4243.50			−0.915496
$279$	6218.28	−	7797.47i	1.33433	−	1.67320i
$280$	−2173.13	+	1046.52i	−0.463818	+	0.223363i
$281$	−4240.26	−	5317.12i	−0.900188	−	1.12880i	−0.991124	−	0.132943i	$-0.957557\pi$
$281$	−4240.26	−	5317.12i	−0.900188	−	1.12880i	0.0909362	−	0.995857i	$-0.471014\pi$
$282$	−2886.42	−	3619.45i	−0.609516	−	0.764309i
$283$	3935.46	+	1895.22i	0.826640	+	0.398089i	0.798854	−	0.601525i	$-0.205440\pi$
$283$	3935.46	+	1895.22i	0.826640	+	0.398089i	0.0277859	+	0.999614i	$0.491154\pi$
$284$	−260.640	+	1141.94i	−0.0544582	+	0.238597i
$285$	1649.17	+	7225.49i	0.342766	+	1.50176i
$286$	606.818	−	292.228i	0.125461	−	0.0604189i
$287$	−8319.97	−	4006.69i	−1.71119	−	0.824067i
$288$	2002.73	+	8774.52i	0.409763	+	1.79529i
$289$	−1824.81			−0.371425
$290$	−507.695	+	3118.78i	−0.102803	+	0.631520i
$291$	−7775.37			−1.56632
$292$	−877.181	−	3843.18i	−0.175798	−	0.770223i
$293$	5142.04	+	2476.28i	1.02526	+	0.493739i	0.869436	−	0.494045i	$-0.164482\pi$
$293$	5142.04	+	2476.28i	1.02526	+	0.493739i	0.155824	+	0.987785i	$0.450197\pi$
$294$	12996.3	−	6258.71i	2.57810	−	1.24155i
$295$	77.1106	+	337.844i	0.0152188	+	0.0666780i
$296$	−37.2051	+	163.006i	−0.00730576	+	0.0320086i
$297$	−4803.69	−	2313.34i	−0.938513	−	0.451964i
$298$	2065.39	+	2589.92i	0.401493	+	0.503456i
$299$	719.062	+	901.675i	0.139078	+	0.174399i
$300$	−2820.25	+	1358.16i	−0.542757	+	0.261378i
$301$	−2342.21	+	2937.04i	−0.448515	+	0.562420i
$302$	323.856			0.0617079
$303$	−6926.99	+	8686.18i	−1.31335	+	1.64689i
$304$	−2447.25	+	10722.1i	−0.461708	+	2.02288i
$305$	466.286	−	2042.93i	0.0875392	−	0.383534i
$306$	−6736.80	+	8447.68i	−1.25855	+	1.57817i
$307$	−1288.73			−0.239582			−0.119791	−	0.992799i	$-0.538222\pi$
$307$	−1288.73			−0.239582			−0.119791	+	0.992799i	$0.538222\pi$
$308$	−1318.02	+	1652.75i	−0.243836	+	0.305760i
$309$	15880.1	−	7647.46i	2.92359	−	1.40793i
$310$	−2222.03	−	2786.34i	−0.407106	−	0.510495i
$311$	5573.85	+	6989.39i	1.01628	+	1.27438i	0.961187	+	0.275898i	$0.0889753\pi$
$311$	5573.85	+	6989.39i	1.01628	+	1.27438i	0.0550966	+	0.998481i	$0.482453\pi$
$312$	−1186.46	−	571.368i	−0.215288	−	0.103677i
$313$	−867.093	+	3798.98i	−0.156585	+	0.686043i	0.834298	+	0.551314i	$0.185873\pi$
$313$	−867.093	+	3798.98i	−0.156585	+	0.686043i	−0.990883	+	0.134729i	$0.956984\pi$
$314$	−996.980	−	4368.06i	−0.179181	−	0.785043i
$315$	8514.62	−	4100.42i	1.52300	−	0.733437i
$316$	−1272.52	−	612.815i	−0.226535	−	0.109094i
$317$	−287.223	−	1258.41i	−0.0508898	−	0.222963i	0.943088	−	0.332543i	$-0.107907\pi$
$317$	−287.223	−	1258.41i	−0.0508898	−	0.222963i	−0.993978	+	0.109580i	$0.965049\pi$
$318$	−6481.02			−1.14288
$319$	−871.399	−	2947.76i	−0.152943	−	0.517376i
$320$	−552.880			−0.0965841
$321$	−2073.13	−	9082.97i	−0.360470	−	1.57932i
$322$	−10142.5	−	4884.37i	−1.75534	−	0.845327i
$323$	−6886.76	+	3316.49i	−1.18634	+	0.571313i
$324$	−800.060	−	3505.29i	−0.137185	−	0.601045i
$325$	200.191	−	877.094i	0.0341680	−	0.149700i
$326$	2821.98	+	1358.99i	0.479432	+	0.230882i
$327$	−2592.52	−	3250.91i	−0.438430	−	0.549773i
$328$	−2937.38	−	3683.36i	−0.494480	−	0.620059i
$329$	−3762.54	+	1811.94i	−0.630503	+	0.303634i
$330$	−2270.62	+	2847.27i	−0.378768	+	0.474960i
$331$	5596.52			0.929343			0.464671	−	0.885483i	$-0.346172\pi$
$331$	5596.52			0.929343			0.464671	+	0.885483i	$0.346172\pi$
$332$	1400.56	−	1756.25i	0.231523	−	0.290321i
$333$	145.775	−	638.682i	0.0239893	−	0.105104i
$334$	−2886.55	+	12646.8i	−0.472889	+	2.07186i
$335$	1550.82	−	1944.67i	0.252927	−	0.317160i
$336$	20711.1			3.36274
$337$	−4253.33	+	5333.51i	−0.687518	+	0.862120i	−0.996022	−	0.0891025i	$-0.971600\pi$
$337$	−4253.33	+	5333.51i	−0.687518	+	0.862120i	0.308504	+	0.951223i	$0.400172\pi$
$338$	6489.91	−	3125.38i	1.04439	−	0.502953i
$339$	1319.87	+	1655.06i	0.211461	+	0.265164i
$340$	774.070	+	970.654i	0.123470	+	0.154827i
$341$	3123.57	+	1504.23i	0.496044	+	0.238882i
$342$	5951.09	−	26073.4i	0.940930	−	4.12248i
$343$	−733.513	−	3213.73i	−0.115469	−	0.505904i
$344$	−1726.73	+	831.551i	−0.270637	+	0.130332i
$345$	−5618.40	−	2705.68i	−0.876767	−	0.422229i
$346$	877.517	+	3844.65i	0.136346	+	0.597369i
$347$	11277.8			1.74473			0.872366	−	0.488854i	$-0.162585\pi$
$347$	11277.8			1.74473			0.872366	+	0.488854i	$0.162585\pi$
$348$	3102.67	−	4437.64i	0.477933	−	0.683570i
$349$	−8979.20			−1.37721			−0.688604	−	0.725138i	$-0.741776\pi$
$349$	−8979.20			−1.37721			−0.688604	+	0.725138i	$0.741776\pi$
$350$	1954.08	+	8561.40i	0.298429	+	1.30750i
$351$	2432.00	+	1171.19i	0.369830	+	0.178101i
$352$	−2818.78	+	1357.45i	−0.426823	+	0.205547i
$353$	−2416.24	−	10586.3i	−0.364316	−	1.59617i	−0.742106	−	0.670282i	$-0.766173\pi$
$353$	−2416.24	−	10586.3i	−0.364316	−	1.59617i	0.377790	−	0.925891i	$-0.376684\pi$
$354$	410.941	−	1800.45i	0.0616985	−	0.270319i
$355$	1639.99	+	789.779i	0.245188	+	0.118076i
$356$	−1752.70	−	2197.81i	−0.260935	−	0.327202i
$357$	8974.90	+	11254.2i	1.33054	+	1.66844i
$358$	−5725.80	+	2757.40i	−0.845302	+	0.407076i
$359$	5644.77	−	7078.31i	0.829859	−	1.04061i	−0.168631	−	0.985679i	$-0.553935\pi$
$359$	5644.77	−	7078.31i	0.829859	−	1.04061i	0.998490	−	0.0549310i	$-0.0174939\pi$
$360$	4821.41			0.705862
$361$	7519.51	−	9429.16i	1.09630	−	1.37471i
$362$	196.811	−	862.286i	0.0285750	−	0.125195i
$363$	−1920.05	+	8412.30i	−0.277622	+	1.21634i
$364$	667.285	−	836.748i	0.0960858	−	0.120488i
$365$	−6126.05			−0.878499
$366$	−6962.68	+	8730.93i	−0.994386	+	1.24692i
$367$	−3579.16	+	1723.63i	−0.509076	+	0.245158i	−0.670746	−	0.741687i	$-0.734026\pi$
$367$	−3579.16	+	1723.63i	−0.509076	+	0.245158i	0.161671	+	0.986845i	$0.448312\pi$
$368$	−5769.59	−	7234.84i	−0.817284	−	1.02484i
$369$	11509.1	+	14431.9i	1.62368	+	2.03603i
$370$	−210.912	−	101.570i	−0.0296346	−	0.0142713i
$371$	−1300.93	+	5699.77i	−0.182052	+	0.797620i
$372$	1358.95	+	5953.96i	0.189404	+	0.829835i
$373$	−3527.81	+	1698.91i	−0.489714	+	0.235834i	−0.662410	−	0.749141i	$-0.730466\pi$
$373$	−3527.81	+	1698.91i	−0.489714	+	0.235834i	0.172696	+	0.984975i	$0.444752\pi$
$374$	−3384.03	−	1629.67i	−0.467872	−	0.225315i
$375$	2581.18	+	11308.9i	0.355445	+	1.55731i
$376$	−2130.54			−0.292218
$377$	441.169	+	1492.38i	0.0602688	+	0.203877i
$378$	−26348.2			−3.58520
$379$	−3006.13	−	13170.7i	−0.407427	−	1.78505i	−0.595990	−	0.802992i	$-0.703240\pi$
$379$	−3006.13	−	13170.7i	−0.407427	−	1.78505i	0.188563	−	0.982061i	$-0.439617\pi$
$380$	−2768.61	−	1333.29i	−0.373755	−	0.179991i
$381$	209.397	−	100.840i	0.0281568	−	0.0135596i
$382$	222.358	+	974.213i	0.0297822	+	0.130484i
$383$	2646.55	−	11595.3i	0.353088	−	1.54698i	−0.416920	−	0.908943i	$-0.636890\pi$
$383$	2646.55	−	11595.3i	0.353088	−	1.54698i	0.770007	−	0.638035i	$-0.220253\pi$
$384$	13131.3	+	6323.72i	1.74507	+	0.840381i
$385$	2048.26	+	2568.44i	0.271141	+	0.340000i
$386$	2153.43	+	2700.31i	0.283955	+	0.356068i
$387$	6765.59	−	3258.13i	0.888667	−	0.427959i
$388$	2010.06	−	2520.53i	0.263003	−	0.329795i
$389$	4540.73			0.591836			0.295918	−	0.955213i	$-0.404375\pi$
$389$	4540.73			0.591836			0.295918	+	0.955213i	$0.404375\pi$
$390$	1149.56	−	1441.50i	0.149257	−	0.187162i
$391$	1431.15	−	6270.26i	0.185105	−	0.811000i
$392$	1477.21	−	6472.08i	0.190332	−	0.833901i
$393$	−3564.67	+	4469.95i	−0.457541	+	0.573739i
$394$	4872.24			0.622995
$395$	−1368.51	+	1716.06i	−0.174322	+	0.218593i
$396$	3807.17	−	1833.44i	0.483125	−	0.232661i
$397$	4764.95	+	5975.06i	0.602383	+	0.755364i	0.985747	−	0.168233i	$-0.0538061\pi$
$397$	4764.95	+	5975.06i	0.602383	+	0.755364i	−0.383364	+	0.923597i	$0.625235\pi$
$398$	5375.10	+	6740.16i	0.676958	+	0.848878i
$399$	−32100.5	−	15458.8i	−4.02765	−	1.93962i
$400$	−1606.29	+	7037.61i	−0.200786	+	0.879701i
$401$	1075.68	+	4712.88i	0.133958	+	0.586907i	0.996694	+	0.0812524i	$0.0258920\pi$
$401$	1075.68	+	4712.88i	0.133958	+	0.586907i	−0.862736	+	0.505655i	$0.831251\pi$
$402$	−11942.9	+	5751.38i	−1.48173	+	0.713564i
$403$	−1581.39	−	761.558i	−0.195471	−	0.0941337i
$404$	−1025.05	−	4491.03i	−0.126233	−	0.553062i
$405$	−5587.46			−0.685538
$406$	−10200.3	−	11256.2i	−1.24688	−	1.37595i
$407$	227.726			0.0277346
$408$	1634.14	+	7159.64i	0.198289	+	0.868763i
$409$	−9469.91	−	4560.47i	−1.14488	−	0.551346i	−0.237390	−	0.971414i	$-0.576292\pi$
$409$	−9469.91	−	4560.47i	−1.14488	−	0.551346i	−0.907493	+	0.420068i	$0.862006\pi$
$410$	5942.93	−	2861.96i	0.715854	−	0.344737i
$411$	−3017.40	−	13220.1i	−0.362135	−	1.58662i
$412$	−1626.20	+	7124.83i	−0.194458	+	0.851978i
$413$	−1500.93	−	722.809i	−0.178828	−	0.0861189i
$414$	14030.2	+	17593.3i	1.66557	+	2.08856i
$415$	−2176.53	−	2729.28i	−0.257450	−	0.322832i
$416$	1427.08	−	687.247i	0.168194	−	0.0809977i
$417$	7045.77	−	8835.11i	0.827416	−	1.03755i
$418$	9296.65			1.08783
$419$	−6818.15	+	8549.69i	−0.794960	+	0.996849i	0.204877	+	0.978788i	$0.434321\pi$
$419$	−6818.15	+	8549.69i	−0.794960	+	0.996849i	−0.999837	+	0.0180610i	$0.994251\pi$
$420$	−1287.71	+	5641.84i	−0.149605	+	0.655461i
$421$	306.984	−	1344.99i	0.0355380	−	0.155702i	−0.954046	−	0.299661i	$-0.903126\pi$
$421$	306.984	−	1344.99i	0.0355380	−	0.155702i	0.989584	+	0.143959i	$0.0459834\pi$
$422$	5072.24	−	6360.39i	0.585101	−	0.733694i
$423$	8347.76			0.959531
$424$	−1859.65	+	2331.93i	−0.213002	+	0.267096i
$425$	−4520.23	+	2176.83i	−0.515913	+	0.248451i
$426$	−6048.22	−	7584.22i	−0.687880	−	0.862575i
$427$	6280.84	+	7875.93i	0.711830	+	0.892606i
$428$	3480.35	+	1676.05i	0.393059	+	0.189287i
$429$	−399.112	+	1748.62i	−0.0449168	+	0.196793i
$430$	−597.099	−	2616.06i	−0.0669644	−	0.293390i
$431$	−1677.24	+	807.715i	−0.187447	+	0.0902698i	−0.525253	−	0.850946i	$-0.676029\pi$
$431$	−1677.24	+	807.715i	−0.187447	+	0.0902698i	0.337806	+	0.941216i	$0.390315\pi$
$432$	−19513.8	−	9397.35i	−2.17328	−	1.04660i
$433$	1770.05	+	7755.08i	0.196450	+	0.860705i	0.973029	+	0.230684i	$0.0740964\pi$
$433$	1770.05	+	7755.08i	0.196450	+	0.860705i	−0.776578	+	0.630021i	$0.783046\pi$
$434$	17132.8			1.89493
$435$	−5650.44	−	6235.35i	−0.622800	−	0.687270i
$436$	1724.05			0.189374
$437$	3542.30	+	15519.8i	0.387760	+	1.69889i
$438$	29414.1	+	14165.1i	3.20882	+	1.54528i
$439$	9265.52	−	4462.04i	1.00733	−	0.485106i	0.143912	−	0.989590i	$-0.454032\pi$
$439$	9265.52	−	4462.04i	1.00733	−	0.485106i	0.863421	+	0.504485i	$0.168317\pi$
$440$	372.946	+	1633.98i	0.0404079	+	0.177039i
$441$	−5787.92	+	25358.5i	−0.624977	+	2.73821i
$442$	1713.26	+	825.061i	0.184370	+	0.0887877i
$443$	2930.78	+	3675.09i	0.314324	+	0.394150i	0.913748	−	0.406282i	$-0.133175\pi$
$443$	2930.78	+	3675.09i	0.314324	+	0.394150i	−0.599423	+	0.800432i	$0.704603\pi$
$444$	250.112	+	313.630i	0.0267338	+	0.0335231i
$445$	−3935.95	+	1895.45i	−0.419286	+	0.201917i
$446$	1040.05	−	1304.18i	0.110421	−	0.138463i
$447$	−8821.61			−0.933440
$448$	1657.17	−	2078.03i	0.174763	−	0.219146i
$449$	2634.48	−	11542.4i	0.276902	−	1.21319i	−0.624785	−	0.780797i	$-0.714813\pi$
$449$	2634.48	−	11542.4i	0.276902	−	1.21319i	0.901687	−	0.432390i	$-0.142329\pi$
$450$	3906.09	−	17113.7i	0.409188	−	1.79277i
$451$	−4000.75	+	5016.78i	−0.417711	+	0.523793i
$452$	−877.725			−0.0913379
$453$	−537.719	+	674.279i	−0.0557710	+	0.0699346i
$454$	−13986.0	+	6735.29i	−1.44580	+	0.696261i
$455$	−1036.99	−	1300.34i	−0.106846	−	0.133980i
$456$	−11333.1	−	14211.3i	−1.16386	−	1.45944i
$457$	16699.1	+	8041.88i	1.70931	+	0.823158i	0.991976	+	0.126424i	$0.0403501\pi$
$457$	16699.1	+	8041.88i	1.70931	+	0.823158i	0.717330	+	0.696734i	$0.245364\pi$
$458$	3679.88	−	16122.6i	0.375435	−	1.64489i
$459$	−3349.66	−	14675.8i	−0.340629	−	1.49239i
$460$	2329.54	−	1121.85i	0.236121	−	0.113710i
$461$	5235.10	+	2521.09i	0.528900	+	0.254705i	0.679223	−	0.733932i	$-0.262317\pi$
$461$	5235.10	+	2521.09i	0.528900	+	0.254705i	−0.150323	+	0.988637i	$0.548031\pi$
$462$	−3895.77	−	17068.5i	−0.392310	−	1.71882i
$463$	−16949.4			−1.70131			−0.850655	−	0.525725i	$-0.823794\pi$
$463$	−16949.4			−1.70131			−0.850655	+	0.525725i	$0.823794\pi$
$464$	−3539.84	−	11974.5i	−0.354166	−	1.19807i
$465$	9490.65			0.946491
$466$	−3796.92	−	16635.4i	−0.377444	−	1.65369i
$467$	−11018.4	−	5306.17i	−1.09180	−	0.525783i	−0.200728	−	0.979647i	$-0.564331\pi$
$467$	−11018.4	−	5306.17i	−1.09180	−	0.525783i	−0.891071	+	0.453865i	$0.850045\pi$
$468$	−1927.48	+	928.226i	−0.190380	+	0.0916822i
$469$	2660.79	+	11657.7i	0.261970	+	1.14777i
$470$	663.774	−	2908.19i	0.0651439	−	0.285414i
$471$	10749.8	+	5176.83i	1.05164	+	0.506445i
$472$	−529.905	−	664.480i	−0.0516755	−	0.0647991i
$473$	1627.52	+	2040.84i	0.158210	+	0.198389i
$474$	10538.9	−	5075.25i	1.02124	−	0.491802i
$475$	7742.50	−	9708.78i	0.747895	−	0.937831i
$476$	−5968.40			−0.574709
$477$	7286.39	−	9136.85i	0.699415	−	0.877039i
$478$	1176.23	−	5153.40i	0.112551	−	0.493119i
$479$	−4219.12	+	18485.2i	−0.402456	+	1.76328i	0.214944	+	0.976626i	$0.431043\pi$
$479$	−4219.12	+	18485.2i	−0.402456	+	1.76328i	−0.617400	+	0.786649i	$0.711814\pi$
$480$	−5339.93	+	6696.05i	−0.507777	+	0.636733i
$481$	−115.293			−0.0109291
$482$	−10726.5	+	13450.6i	−1.01365	+	1.27108i
$483$	27009.7	−	13007.2i	2.54448	−	1.22536i
$484$	−2230.64	−	2797.13i	−0.209489	−	0.262691i
$485$	−3123.71	−	3917.00i	−0.292454	−	0.366726i
$486$	4200.55	+	2022.88i	0.392059	+	0.188806i
$487$	−228.251	+	1000.03i	−0.0212383	+	0.0930509i	−0.984436	−	0.175742i	$-0.943768\pi$
$487$	−228.251	+	1000.03i	−0.0212383	+	0.0930509i	0.963198	+	0.268793i	$0.0866247\pi$
$488$	1143.61	+	5010.48i	0.106084	+	0.464783i
$489$	−7514.99	+	3619.03i	−0.694969	+	0.334679i
$490$	8374.16	+	4032.78i	0.772053	+	0.371801i
$491$	2547.63	+	11161.9i	0.234161	+	1.02593i	0.946148	+	0.323733i	$0.104938\pi$
$491$	2547.63	+	11161.9i	0.234161	+	1.02593i	−0.711988	+	0.702192i	$0.752205\pi$
$492$	−11303.3			−1.03575
$493$	4972.89	−	7112.54i	0.454295	−	0.649762i
$494$	−4706.67			−0.428671
$495$	−1461.25	−	6402.17i	−0.132684	−	0.581326i
$496$	12688.7	+	6110.57i	1.14867	+	0.553171i
$497$	−7884.05	+	3796.76i	−0.711565	+	0.342672i
$498$	4139.73	+	18137.3i	0.372501	+	1.63203i
$499$	−929.808	+	4073.76i	−0.0834147	+	0.365464i	−0.999357	−	0.0358455i	$-0.988588\pi$
$499$	−929.808	+	4073.76i	−0.0834147	+	0.365464i	0.915943	+	0.401309i	$0.131445\pi$
$500$	−4333.27	−	2086.79i	−0.387579	−	0.186648i
$501$	−21538.3	−	27008.2i	−1.92068	−	2.40846i
$502$	3600.88	+	4515.36i	0.320150	+	0.401455i
$503$	−14231.0	+	6853.28i	−1.26149	+	0.607500i	−0.940568	−	0.339607i	$-0.889706\pi$
$503$	−14231.0	+	6853.28i	−1.26149	+	0.607500i	−0.320919	+	0.947107i	$0.603992\pi$
$504$	−14451.4	+	18121.5i	−1.27722	+	1.60158i
$505$	−7158.72			−0.630810
$506$	−4877.13	+	6115.72i	−0.428488	+	0.537307i
$507$	−4268.50	+	18701.5i	−0.373906	+	1.63819i
$508$	−21.4432	+	93.9486i	−0.00187281	+	0.00820531i
$509$	−1208.85	+	1515.85i	−0.105268	+	0.132002i	−0.831675	−	0.555263i	$-0.812617\pi$
$509$	−1208.85	+	1515.85i	−0.105268	+	0.132002i	0.726407	+	0.687265i	$0.241189\pi$
$510$	−10282.0			−0.892738
$511$	18361.9	−	23025.1i	1.58959	−	1.99329i
$512$	−3122.22	+	1503.58i	−0.269500	+	0.129784i
$513$	23230.6	+	29130.2i	1.99933	+	2.50708i
$514$	−2683.73	−	3365.29i	−0.230300	−	0.288787i
$515$	10232.3	+	4927.62i	0.875514	+	0.421625i
$516$	−1023.20	+	4482.92i	−0.0872941	+	0.382460i
$517$	645.716	+	2829.07i	0.0549295	+	0.240662i
$518$	1013.93	−	488.284i	0.0860032	−	0.0414170i
$519$	−9461.71	−	4556.52i	−0.800237	−	0.385374i
$520$	−188.814	−	827.246i	−0.0159231	−	0.0697638i
$521$	1479.09			0.124377			0.0621884	−	0.998064i	$-0.480192\pi$
$521$	1479.09			0.124377			0.0621884	+	0.998064i	$0.480192\pi$
$522$	8607.99	+	29119.0i	0.721765	+	2.44158i
$523$	2891.84			0.241781			0.120891	−	0.992666i	$-0.461425\pi$
$523$	2891.84			0.241781			0.120891	+	0.992666i	$0.461425\pi$
$524$	−527.495	−	2311.11i	−0.0439766	−	0.192674i
$525$	−21069.6	−	10146.6i	−1.75153	−	0.843493i
$526$	180.014	−	86.6901i	0.0149220	−	0.00718606i
$527$	2178.10	+	9542.86i	0.180037	+	0.788792i
$528$	3202.38	−	14030.6i	0.263950	−	1.15644i
$529$	−1105.84	−	532.547i	−0.0908889	−	0.0437698i
$530$	−2603.71	−	3264.95i	−0.213392	−	0.267585i
$531$	2076.24	+	2603.53i	0.169682	+	0.212775i
$532$	13309.7	−	6409.63i	1.08468	−	0.522355i
$533$	2025.48	−	2539.88i	0.164603	−	0.206406i
$534$	23281.2			1.88666
$535$	3742.87	−	4693.41i	0.302464	−	0.379278i
$536$	−1357.47	+	5947.45i	−0.109391	+	0.479274i
$537$	3765.93	−	16499.6i	0.302629	−	1.32591i
$538$	−4190.26	+	5254.42i	−0.335790	+	0.421067i
$539$	−9041.74			−0.722552
$540$	3773.17	−	4731.41i	0.300688	−	0.377051i
$541$	−16274.2	+	7837.24i	−1.29331	+	0.622827i	−0.948777	−	0.315946i	$-0.897678\pi$
$541$	−16274.2	+	7837.24i	−1.29331	+	0.622827i	−0.344537	+	0.938773i	$0.611964\pi$
$542$	−13240.0	−	16602.4i	−1.04927	−	1.31574i
$543$	1468.53	+	1841.48i	0.116060	+	0.145535i
$544$	−7958.40	−	3832.56i	−0.627231	−	0.302058i
$545$	596.188	−	2612.07i	0.0468585	−	0.205300i
$546$	1972.33	+	8641.36i	0.154594	+	0.677319i
$547$	21371.3	−	10291.9i	1.67051	−	0.804475i	0.672589	−	0.740016i	$-0.265182\pi$
$547$	21371.3	−	10291.9i	1.67051	−	0.804475i	0.997920	−	0.0644589i	$-0.0205321\pi$
$548$	5065.59	+	2439.46i	0.394875	+	0.190162i
$549$	−4480.83	−	19631.8i	−0.348337	−	1.52616i
$550$	6101.99			0.473072
$551$	−3451.35	+	21201.7i	−0.266847	+	1.63924i
$552$	15294.3			1.17929
$553$	−2347.99	−	10287.2i	−0.180555	−	0.791062i
$554$	−23310.1	−	11225.6i	−1.78764	−	0.860882i
$555$	561.665	−	270.484i	0.0429574	−	0.0206872i
$556$	1042.62	+	4568.03i	0.0795271	+	0.348431i
$557$	1347.45	−	5903.56i	0.102501	−	0.449088i	−0.897467	−	0.441083i	$-0.854595\pi$
$557$	1347.45	−	5903.56i	0.102501	−	0.449088i	0.999968	−	0.00800546i	$-0.00254825\pi$
$558$	−30855.8	−	14859.4i	−2.34091	−	1.12732i
$559$	−823.974	−	1033.23i	−0.0623442	−	0.0781771i
$560$	8320.55	+	10433.6i	0.627871	+	0.787325i
$561$	9011.76	−	4339.84i	0.678212	−	0.326610i
$562$	−14560.6	+	18258.4i	−1.09288	+	1.37043i
$563$	−16045.1			−1.20110			−0.600550	−	0.799587i	$-0.705052\pi$
$563$	−16045.1			−1.20110			−0.600550	+	0.799587i	$0.705052\pi$
$564$	−3187.07	+	3996.46i	−0.237943	+	0.298371i
$565$	−303.523	+	1329.82i	−0.0226006	+	0.0990195i
$566$	3337.66	−	14623.3i	0.247867	−	1.08597i
$567$	16747.5	−	21000.7i	1.24044	−	1.55546i
$568$	−4464.35			−0.329788
$569$	14085.6	−	17662.8i	1.03778	−	1.30134i	0.0854285	−	0.996344i	$-0.472774\pi$
$569$	14085.6	−	17662.8i	1.03778	−	1.30134i	0.952354	−	0.304994i	$-0.0986545\pi$
$570$	22929.3	−	11042.2i	1.68491	−	0.811412i
$571$	−1225.65	−	1536.91i	−0.0898280	−	0.112641i	0.734886	−	0.678190i	$-0.237236\pi$
$571$	−1225.65	−	1536.91i	−0.0898280	−	0.112641i	−0.824714	+	0.565550i	$0.808664\pi$
$572$	−463.672	−	581.426i	−0.0338935	−	0.0425011i
$573$	−2397.54	−	1154.59i	−0.174797	−	0.0841778i
$574$	−7056.17	+	30915.1i	−0.513099	+	2.24803i
$575$	2325.04	+	10186.7i	0.168628	+	0.738807i
$576$	−4786.81	+	2305.21i	−0.346268	+	0.166754i
$577$	15702.7	+	7562.04i	1.13295	+	0.545601i	0.903871	−	0.427806i	$-0.140713\pi$
$577$	15702.7	+	7562.04i	1.13295	+	0.545601i	0.229082	+	0.973407i	$0.426428\pi$
$578$	1394.36	+	6109.09i	0.100342	+	0.439628i
$579$	−9197.62			−0.660173
$580$	3482.03	−	219.758i	0.249282	−	0.0157327i
$581$	16781.9			1.19833
$582$	5941.25	+	26030.3i	0.423149	+	1.85394i
$583$	3660.11	+	1762.62i	0.260011	+	0.125215i
$584$	13536.8	−	6518.98i	0.959172	−	0.461913i
$585$	739.799	+	3241.27i	0.0522853	+	0.229077i
$586$	4360.96	−	19106.6i	0.307423	−	1.34691i
$587$	−12104.6	−	5829.29i	−0.851127	−	0.409881i	−0.0431315	−	0.999069i	$-0.513733\pi$
$587$	−12104.6	−	5829.29i	−0.851127	−	0.409881i	−0.807996	+	0.589188i	$0.799448\pi$
$588$	−9930.55	−	12452.5i	−0.696478	−	0.873356i
$589$	−15105.6	−	18941.8i	−1.05673	−	1.32510i
$590$	1072.11	−	516.300i	0.0748102	−	0.0360267i
$591$	−8089.71	+	10144.2i	−0.563057	+	0.706051i
$592$	925.081			0.0642240
$593$	−277.952	+	348.541i	−0.0192481	+	0.0241363i	−0.791362	−	0.611347i	$-0.790628\pi$
$593$	−277.952	+	348.541i	−0.0192481	+	0.0241363i	0.772114	+	0.635484i	$0.219199\pi$
$594$	−4074.01	+	17849.4i	−0.281412	+	1.23295i
$595$	−2063.91	+	9042.59i	−0.142205	+	0.623042i
$596$	2280.53	−	2859.69i	0.156735	−	0.196539i
$597$	−22957.9			−1.57388
$598$	2469.18	−	3096.25i	0.168850	−	0.211731i
$599$	1008.14	−	485.496i	0.0687673	−	0.0331166i	−0.399184	−	0.916871i	$-0.630707\pi$
$599$	1008.14	−	485.496i	0.0687673	−	0.0331166i	0.467951	+	0.883754i	$0.344992\pi$
$600$	−7438.66	−	9327.79i	−0.506137	−	0.634676i
$601$	3499.16	+	4387.80i	0.237493	+	0.297807i	0.886267	−	0.463174i	$-0.153289\pi$
$601$	3499.16	+	4387.80i	0.237493	+	0.297807i	−0.648774	+	0.760981i	$0.724718\pi$
$602$	11622.3	+	5597.01i	0.786861	+	0.378932i
$603$	5318.75	−	23303.0i	0.359198	−	1.57375i
$604$	−79.5710	−	348.624i	−0.00536043	−	0.0234856i
$605$	−5009.24	+	2412.32i	−0.336619	+	0.162107i
$606$	34372.5	+	16552.9i	2.30410	+	1.10960i
$607$	5693.98	+	24947.0i	0.380744	+	1.66815i	0.695154	+	0.718861i	$0.255336\pi$
$607$	5693.98	+	24947.0i	0.380744	+	1.66815i	−0.314410	+	0.949287i	$0.601807\pi$
$608$	21863.4			1.45835
$609$	40372.2	−	2547.97i	2.68631	−	0.169539i
$610$	−7195.60			−0.477609
$611$	−326.911	−	1432.29i	−0.0216455	−	0.0948351i
$612$	10749.0	+	5176.43i	0.709969	+	0.341903i
$613$	−5989.59	+	2884.43i	−0.394645	+	0.190051i	−0.620672	−	0.784070i	$-0.713140\pi$
$613$	−5989.59	+	2884.43i	−0.394645	+	0.190051i	0.226028	+	0.974121i	$0.427426\pi$
$614$	984.733	+	4314.40i	0.0647241	+	0.283575i
$615$	−3908.74	+	17125.3i	−0.256285	+	1.12286i
$616$	−7259.25	−	3495.87i	−0.474811	−	0.228657i
$617$	−5954.17	−	7466.29i	−0.388502	−	0.487166i	0.548667	−	0.836041i	$-0.315135\pi$
$617$	−5954.17	−	7466.29i	−0.388502	−	0.487166i	−0.937169	+	0.348875i	$0.886564\pi$
$618$	−37736.3	−	47319.8i	−2.45627	−	3.08007i
$619$	−5110.47	+	2461.07i	−0.331837	+	0.159804i	−0.592382	−	0.805658i	$-0.701812\pi$
$619$	−5110.47	+	2461.07i	−0.331837	+	0.159804i	0.260545	+	0.965462i	$0.416098\pi$
$620$	−2453.48	+	3076.57i	−0.158926	+	0.199287i
$621$	−31350.1			−2.02583
$622$	19140.0	−	24000.8i	1.23383	−	1.54717i
$623$	4673.24	−	20474.8i	0.300529	−	1.31670i
$624$	−1621.29	+	7103.34i	−0.104012	+	0.455707i
$625$	2376.07	−	2979.50i	0.152068	−	0.190688i
$626$	13380.8			0.854317
$627$	−15435.9	+	19356.0i	−0.983172	+	1.23286i
$628$	−4457.16	+	2146.46i	−0.283217	+	0.136390i
$629$	400.873	+	502.679i	0.0254115	+	0.0318651i
$630$	−20233.5	−	25372.0i	−1.27956	−	1.60451i
$631$	22529.6	+	10849.7i	1.42138	+	0.684499i	0.977373	−	0.211525i	$-0.0678430\pi$
$631$	22529.6	+	10849.7i	1.42138	+	0.684499i	0.444005	+	0.896024i	$0.353557\pi$
$632$	1197.88	−	5248.27i	0.0753944	−	0.330325i
$633$	4820.77	+	21121.2i	0.302699	+	1.32621i
$634$	−3993.41	+	1923.13i	−0.250156	+	0.120469i
$635$	134.924	+	64.9761i	0.00843198	+	0.00406063i
$636$	1592.38	+	6976.67i	0.0992799	+	0.434973i
$637$	4577.62			0.284728
$638$	−9202.64	+	5169.68i	−0.571060	+	0.320799i
$639$	17491.9			1.08290
$640$	2089.73	+	9155.71i	0.129069	+	0.565486i
$641$	−10707.1	−	5156.26i	−0.659757	−	0.317722i	0.0738766	−	0.997267i	$-0.476463\pi$
$641$	−10707.1	−	5156.26i	−0.659757	−	0.317722i	−0.733634	+	0.679545i	$0.762177\pi$
$642$	−28823.8	+	13880.8i	−1.77194	+	0.853320i
$643$	−666.259	−	2919.07i	−0.0408626	−	0.179031i	0.950378	−	0.311096i	$-0.100696\pi$
$643$	−666.259	−	2919.07i	−0.0408626	−	0.179031i	−0.991241	+	0.132065i	$0.957839\pi$
$644$	−2765.92	+	12118.3i	−0.169243	+	0.741501i
$645$	6438.14	+	3100.44i	0.393026	+	0.189271i
$646$	16365.1	+	20521.2i	0.996715	+	1.24984i
$647$	4764.24	+	5974.17i	0.289493	+	0.363012i	0.905217	−	0.424949i	$-0.139708\pi$
$647$	4764.24	+	5974.17i	0.289493	+	0.363012i	−0.615725	+	0.787961i	$0.711137\pi$
$648$	12346.7	−	5945.84i	0.748492	−	0.360455i
$649$	−721.737	+	905.030i	−0.0436528	+	0.0547389i
$650$	−3089.30			−0.186419
$651$	−28446.7	+	35671.1i	−1.71262	+	2.14756i
$652$	769.569	−	3371.70i	0.0462249	−	0.202525i
$653$	6858.74	−	30050.1i	0.411031	−	1.80084i	−0.168283	−	0.985739i	$-0.553822\pi$
$653$	6858.74	−	30050.1i	0.411031	−	1.80084i	0.579313	−	0.815105i	$-0.303321\pi$
$654$	−8902.40	+	11163.3i	−0.532281	+	0.667459i
$655$	−3683.92			−0.219760
$656$	−16252.0	+	20379.4i	−0.967279	+	1.21293i
$657$	−53039.1	+	25542.3i	−3.14955	+	1.51674i
$658$	8941.00	+	11211.7i	0.529721	+	0.664249i
$659$	−17161.5	−	21519.9i	−1.01444	−	1.27207i	−0.961885	−	0.273455i	$-0.911834\pi$
$659$	−17161.5	−	21519.9i	−1.01444	−	1.27207i	−0.0525593	−	0.998618i	$-0.516738\pi$
$660$	3622.91	+	1744.70i	0.213669	+	0.102898i
$661$	−1457.18	+	6384.34i	−0.0857457	+	0.375676i	−0.999534	−	0.0305135i	$-0.990286\pi$
$661$	−1457.18	+	6384.34i	−0.0857457	+	0.375676i	0.913789	+	0.406190i	$0.133143\pi$
$662$	−4276.36	−	18736.0i	−0.251066	−	1.09999i
$663$	−4562.44	+	2197.16i	−0.267256	+	0.128704i
$664$	7713.84	+	3714.79i	0.450836	+	0.217111i
$665$	−5108.49	−	22381.8i	−0.297893	−	1.30515i
$666$	−2249.56			−0.130884
$667$	−12136.8	−	13393.1i	−0.704553	−	0.777486i
$668$	14323.2			0.829614
$669$	988.485	+	4330.84i	0.0571256	+	0.250284i
$670$	−7695.35	−	3705.89i	−0.443727	−	0.213688i
$671$	6306.64	−	3037.12i	0.362839	−	0.174734i
$672$	−9161.86	−	40140.7i	−0.525932	−	2.30426i
$673$	3140.23	−	13758.2i	0.179862	−	0.788025i	−0.801831	−	0.597551i	$-0.796140\pi$
$673$	3140.23	−	13758.2i	0.179862	−	0.788025i	0.981692	−	0.190474i	$-0.0610024\pi$
$674$	21105.5	+	10163.9i	1.20616	+	0.580857i
$675$	15247.7	+	19120.1i	0.869461	+	1.09027i
$676$	−4958.97	−	6218.35i	−0.282144	−	0.353798i
$677$	8400.46	−	4045.45i	0.476892	−	0.229659i	−0.179967	−	0.983673i	$-0.557599\pi$
$677$	8400.46	−	4045.45i	0.476892	−	0.229659i	0.656859	+	0.754014i	$0.271885\pi$
$678$	4532.27	−	5683.29i	0.256727	−	0.321925i
$679$	24085.1			1.36127
$680$	−2950.31	+	3699.58i	−0.166381	+	0.208636i
$681$	9198.75	−	40302.3i	0.517616	−	2.26783i
$682$	2649.10	−	11606.5i	0.148738	−	0.651663i
$683$	−3032.44	+	3802.56i	−0.169887	+	0.213032i	−0.859485	−	0.511160i	$-0.829216\pi$
$683$	−3032.44	+	3802.56i	−0.169887	+	0.213032i	0.689598	+	0.724192i	$0.257787\pi$
$684$	−29529.6			−1.65072
$685$	5447.69	−	6831.18i	0.303862	−	0.381031i
$686$	−10198.4	+	4911.30i	−0.567605	+	0.273344i
$687$	27457.9	+	34431.1i	1.52487	+	1.91212i
$688$	6611.39	+	8290.42i	0.366361	+	0.459403i
$689$	−1853.03	−	892.371i	−0.102460	−	0.0493420i
$690$	−4764.97	+	20876.7i	−0.262897	+	1.15183i
$691$	−1837.28	−	8049.66i	−0.101148	−	0.443160i	−0.999988	−	0.00488244i	$-0.998446\pi$
$691$	−1837.28	−	8049.66i	−0.101148	−	0.443160i	0.898840	−	0.438277i	$-0.144411\pi$
$692$	3923.08	−	1889.26i	0.215510	−	0.103784i
$693$	28442.8	+	13697.3i	1.55909	+	0.750820i
$694$	−8617.46	−	37755.6i	−0.471346	−	2.06510i
$695$	7281.47			0.397413
$696$	19121.1	+	7765.46i	1.04136	+	0.422915i
$697$	−18116.6			−0.984525
$698$	6861.11	+	30060.5i	0.372058	+	1.63009i
$699$	40939.8	+	19715.5i	2.21528	+	1.06682i
$700$	8736.04	−	4207.06i	0.471702	−	0.227160i
$701$	−3941.03	−	17266.8i	−0.212341	−	0.930325i	−0.962971	−	0.269603i	$-0.913107\pi$
$701$	−3941.03	−	17266.8i	−0.212341	−	0.930325i	0.750631	−	0.660722i	$-0.229750\pi$
$702$	2062.57	−	9036.73i	0.110893	−	0.485854i
$703$	−1433.80	−	690.482i	−0.0769229	−	0.0370441i
$704$	−1151.51	−	1443.94i	−0.0616464	−	0.0773022i
$705$	4952.84	+	6210.66i	0.264588	+	0.331783i
$706$	−33594.3	+	16178.1i	−1.79085	+	0.862426i
$707$	21457.1	−	26906.4i	1.14141	−	1.43129i
$708$	−2039.11			−0.108241
$709$	−7112.41	+	8918.68i	−0.376745	+	0.472423i	−0.933667	−	0.358141i	$-0.883411\pi$
$709$	−7112.41	+	8918.68i	−0.376745	+	0.472423i	0.556922	+	0.830564i	$0.311982\pi$
$710$	1390.88	−	6093.83i	0.0735193	−	0.322109i
$711$	−4693.48	+	20563.5i	−0.247566	+	1.08466i
$712$	6680.28	−	8376.81i	0.351621	−	0.440919i
$713$	20385.2			1.07073
$714$	30818.8	−	38645.5i	1.61536	−	2.02559i
$715$	−1041.25	+	501.438i	−0.0544621	+	0.0262276i
$716$	4375.11	+	5486.21i	0.228359	+	0.286354i
$717$	8776.59	+	11005.5i	0.457138	+	0.573232i
$718$	−28009.9	−	13488.9i	−1.45588	−	0.701115i
$719$	−5387.84	+	23605.7i	−0.279461	+	1.22440i	0.619016	+	0.785378i	$0.287532\pi$
$719$	−5387.84	+	23605.7i	−0.279461	+	1.22440i	−0.898477	+	0.439020i	$0.855326\pi$
$720$	−5935.98	−	26007.2i	−0.307251	−	1.34616i
$721$	−49190.5	+	23688.9i	−2.54084	+	1.22361i
$722$	−37312.6	−	17968.8i	−1.92331	−	0.926218i
$723$	−10194.7	−	44665.9i	−0.524406	−	2.29757i
$724$	−976.588			−0.0501307
$725$	−2265.35	+	13916.1i	−0.116045	+	0.712868i
$726$	29629.8			1.51469
$727$	−5909.68	−	25892.0i	−0.301483	−	1.32088i	−0.867890	−	0.496756i	$-0.834524\pi$
$727$	−5909.68	−	25892.0i	−0.301483	−	1.32088i	0.566407	−	0.824125i	$-0.308333\pi$
$728$	3675.19	+	1769.88i	0.187104	+	0.0901044i
$729$	11881.7	−	5721.91i	0.603651	−	0.290703i
$730$	4680.98	+	20508.7i	0.237330	+	1.03981i
$731$	−1639.95	+	7185.11i	−0.0829766	+	0.363544i
$732$	11109.4	+	5349.99i	0.560949	+	0.270139i
$733$	9739.96	+	12213.5i	0.490796	+	0.615439i	0.964126	−	0.265447i	$-0.0855194\pi$
$733$	9739.96	+	12213.5i	0.490796	+	0.615439i	−0.473329	+	0.880886i	$0.656948\pi$
$734$	8505.24	+	10665.2i	0.427703	+	0.536323i
$735$	−22300.6	+	10739.4i	−1.11914	+	0.538950i
$736$	−11469.8	+	14382.7i	−0.574432	+	0.720315i
$737$	8308.83			0.415277
$738$	39520.8	−	49557.5i	1.97125	−	2.47187i
$739$	−6844.23	+	29986.5i	−0.340689	+	1.49266i	0.456935	+	0.889500i	$0.348947\pi$
$739$	−6844.23	+	29986.5i	−0.340689	+	1.49266i	−0.797624	+	0.603156i	$0.793910\pi$
$740$	−57.5170	+	251.998i	−0.00285725	+	0.0125184i
$741$	7814.81	−	9799.46i	0.387428	−	0.485820i
$742$	20075.7			0.993263
$743$	−12183.0	+	15277.0i	−0.601549	+	0.754319i	−0.985619	−	0.168985i	$-0.945951\pi$
$743$	−12183.0	+	15277.0i	−0.601549	+	0.754319i	0.384069	+	0.923304i	$0.374522\pi$
$744$	−20971.6	+	10099.4i	−1.03341	+	0.497663i
$745$	−3544.03	−	4444.07i	−0.174286	−	0.218548i
$746$	8383.22	+	10512.2i	0.411436	+	0.515925i
$747$	−30223.9	−	14555.1i	−1.48037	−	0.712908i
$748$	−922.845	+	4043.25i	−0.0451104	+	0.197641i
$749$	6421.75	+	28135.5i	0.313279	+	1.37256i
$750$	35887.5	−	17282.5i	1.74724	−	0.841425i
$751$	−11664.5	−	5617.34i	−0.566770	−	0.272942i	0.128477	−	0.991712i	$-0.458991\pi$
$751$	−11664.5	−	5617.34i	−0.566770	−	0.272942i	−0.695248	+	0.718770i	$0.744705\pi$
$752$	2623.06	+	11492.4i	0.127198	+	0.557292i
$753$	−15379.9			−0.744324
$754$	4659.08	−	2617.29i	0.225031	−	0.126414i
$755$	−555.708			−0.0267871
$756$	6473.74	+	28363.3i	0.311439	+	1.36450i
$757$	13612.2	+	6555.27i	0.653556	+	0.314736i	0.731118	−	0.682252i	$-0.238999\pi$
$757$	13612.2	+	6555.27i	0.653556	+	0.314736i	−0.0775614	+	0.996988i	$0.524713\pi$
$758$	−41795.8	+	20127.8i	−2.00276	+	0.964479i
$759$	−4635.33	−	20308.7i	−0.221676	−	0.971225i
$760$	2606.22	−	11418.6i	0.124392	−	0.544995i
$761$	−13523.4	−	6512.53i	−0.644183	−	0.310222i	0.0831189	−	0.996540i	$-0.473512\pi$
$761$	−13523.4	−	6512.53i	−0.644183	−	0.310222i	−0.727302	+	0.686317i	$0.759226\pi$
$762$	−497.594	−	623.963i	−0.0236561	−	0.0296638i
$763$	8030.61	+	10070.1i	0.381032	+	0.477799i
$764$	994.086	−	478.726i	0.0470743	−	0.0226698i
$765$	11559.8	−	14495.5i	0.546332	−	0.685078i
$766$	−40840.9			−1.92643
$767$	365.399	−	458.195i	0.0172018	−	0.0215704i
$768$	9609.23	−	42100.8i	0.451488	−	1.97810i
$769$	4403.16	−	19291.5i	0.206479	−	0.904642i	−0.760410	−	0.649443i	$-0.775002\pi$
$769$	4403.16	−	19291.5i	0.206479	−	0.904642i	0.966889	−	0.255199i	$-0.0821409\pi$
$770$	7033.50	−	8819.73i	0.329181	−	0.412780i
$771$	11462.6			0.535430
$772$	2377.73	−	2981.58i	0.110850	−	0.139002i
$773$	1886.53	−	908.504i	0.0877797	−	0.0422725i	−0.389479	−	0.921035i	$-0.627345\pi$
$773$	1886.53	−	908.504i	0.0877797	−	0.0422725i	0.477258	+	0.878763i	$0.341631\pi$
$774$	−16077.2	−	20160.2i	−0.746619	−	0.936231i
$775$	−9914.76	−	12432.7i	−0.459547	−	0.576253i
$776$	11070.7	+	5331.38i	0.512134	+	0.246631i
$777$	−666.876	+	2921.78i	−0.0307903	+	0.134901i
$778$	−3469.62	−	15201.4i	−0.159887	−	0.700510i
$779$	40400.5	−	19455.9i	1.85815	−	0.894838i
$780$	−1834.19	−	883.301i	−0.0841983	−	0.0405478i
$781$	1353.04	+	5928.05i	0.0619917	+	0.271603i
$782$	−22085.1			−1.00992
$783$	−39194.4	−	15917.6i	−1.78888	−	0.726500i
$784$	−36729.8			−1.67319
$785$	1710.73	+	7495.20i	0.0777816	+	0.340784i
$786$	17688.3	+	8518.22i	0.802697	+	0.386558i
$787$	−23598.7	+	11364.6i	−1.06887	+	0.514743i	−0.883744	−	0.467971i	$-0.844985\pi$
$787$	−23598.7	+	11364.6i	−1.06887	+	0.514743i	−0.185130	+	0.982714i	$0.559271\pi$
$788$	−1197.11	−	5244.86i	−0.0541182	−	0.237107i
$789$	−118.397	+	518.733i	−0.00534228	+	0.0234061i
$790$	6790.69	+	3270.22i	0.305825	+	0.147278i
$791$	−4088.44	−	5126.74i	−0.183778	−	0.230450i
$792$	10041.8	+	12592.0i	0.450528	+	0.564945i
$793$	−3192.90	+	1537.62i	−0.142980	+	0.0688556i
$794$	16362.3	−	20517.7i	0.731330	−	0.917059i
$795$	11120.9			0.496121
$796$	5934.98	−	7442.23i	0.264271	−	0.331385i
$797$	−9675.38	+	42390.6i	−0.430012	+	1.88400i	0.0362233	+	0.999344i	$0.488467\pi$
$797$	−9675.38	+	42390.6i	−0.430012	+	1.88400i	−0.466235	+	0.884661i	$0.654390\pi$
$798$	−27224.4	+	119278.i	−1.20769	+	5.29122i
$799$	−5108.16	+	6405.43i	−0.226175	+	0.283614i
$800$	14350.4			0.634202
$801$	−26174.3	+	32821.5i	−1.15459	+	1.44781i
$802$	14955.8	−	7202.33i	0.658488	−	0.317111i
$803$	−12759.0	−	15999.3i	−0.560716	−	0.703116i
$804$	9125.59	+	11443.1i	0.400292	+	0.501950i
$805$	17403.6	+	8381.15i	0.761985	+	0.366953i
$806$	−1341.18	+	5876.08i	−0.0586116	+	0.256794i
$807$	−3982.52	−	17448.5i	−0.173719	−	0.761113i
$808$	15818.7	−	7617.88i	0.688738	−	0.331679i
$809$	30611.1	+	14741.5i	1.33032	+	0.640648i	0.957816	−	0.287383i	$-0.0927852\pi$
$809$	30611.1	+	14741.5i	1.33032	+	0.640648i	0.372504	+	0.928031i	$0.378499\pi$
$810$	4269.44	+	18705.6i	0.185201	+	0.811418i
$811$	−3732.02			−0.161589			−0.0807947	−	0.996731i	$-0.525746\pi$
$811$	−3732.02			−0.161589			−0.0807947	+	0.996731i	$0.525746\pi$
$812$	−9610.88	+	13746.1i	−0.415364	+	0.594080i
$813$	56549.9			2.43948
$814$	−174.008	−	762.380i	−0.00749261	−	0.0328273i
$815$	−4842.27	−	2331.91i	−0.208119	−	0.100225i
$816$	36608.0	−	17629.5i	1.57051	−	0.756319i
$817$	−4059.13	−	17784.2i	−0.173820	−	0.761556i
$818$	−8031.43	+	35188.0i	−0.343291	+	1.50406i
$819$	−14399.9	−	6934.63i	−0.614375	−	0.295868i
$820$	−4541.01	−	5694.25i	−0.193389	−	0.242502i
$821$	5717.38	+	7169.36i	0.243042	+	0.304766i	0.888359	−	0.459150i	$-0.151846\pi$
$821$	5717.38	+	7169.36i	0.243042	+	0.304766i	−0.645316	+	0.763915i	$0.723274\pi$
$822$	−41952.5	+	20203.3i	−1.78012	+	0.857263i
$823$	−22381.8	+	28065.9i	−0.947971	+	1.18872i	0.0339493	+	0.999424i	$0.489192\pi$
$823$	−22381.8	+	28065.9i	−0.947971	+	1.18872i	−0.981920	+	0.189295i	$0.939380\pi$
$824$	−27854.1			−1.17760
$825$	−10131.6	+	12704.6i	−0.427558	+	0.536141i
$826$	−1272.94	+	5577.10i	−0.0536212	+	0.234930i
$827$	−7229.10	+	31672.8i	−0.303967	+	1.33177i	0.560116	+	0.828414i	$0.310757\pi$
$827$	−7229.10	+	31672.8i	−0.303967	+	1.33177i	−0.864082	+	0.503351i	$0.832100\pi$
$828$	15491.6	−	19425.8i	0.650205	−	0.815332i
$829$	−1759.23			−0.0737040			−0.0368520	−	0.999321i	$-0.511733\pi$
$829$	−1759.23			−0.0737040			−0.0368520	+	0.999321i	$0.511733\pi$
$830$	−7473.95	+	9372.04i	−0.312560	+	0.391937i
$831$	62075.4	−	29893.9i	2.59130	−	1.24791i
$832$	582.981	+	731.035i	0.0242924	+	0.0304616i
$833$	−15916.4	−	19958.6i	−0.662031	−	0.830161i
$834$	−34961.9	−	16836.7i	−1.45159	−	0.699051i
$835$	4953.06	−	21700.8i	0.205279	−	0.899385i
$836$	−2284.18	−	10007.6i	−0.0944976	−	0.414021i
$837$	42987.5	−	20701.7i	1.77523	−	0.854904i
$838$	33832.4	+	16292.8i	1.39465	+	0.671630i
$839$	−2700.95	−	11833.6i	−0.111141	−	0.486939i	−0.999608	−	0.0279993i	$-0.991086\pi$
$839$	−2700.95	−	11833.6i	−0.111141	−	0.486939i	0.888467	−	0.458940i	$-0.151771\pi$
$840$	−22056.5			−0.905976
$841$	−8373.39	−	22906.5i	−0.343326	−	0.939216i
$842$	−4737.30			−0.193893
$843$	−13838.7	−	60631.2i	−0.565397	−	2.47717i
$844$	−8093.06	−	3897.41i	−0.330065	−	0.158951i
$845$	−11136.1	+	5362.87i	−0.453366	+	0.218330i
$846$	−6378.61	−	27946.5i	−0.259221	−	1.13572i
$847$	5947.58	−	26058.1i	0.241277	−	1.05710i
$848$	14868.3	+	7160.18i	0.602097	+	0.289955i
$849$	24904.4	+	31229.1i	1.00673	+	1.26240i
$850$	10741.5	+	13469.4i	0.433448	+	0.543527i
$851$	1206.42	−	580.979i	0.0485963	−	0.0234027i
$852$	−6678.21	+	8374.21i	−0.268535	+	0.336732i
$853$	−79.0685			−0.00317380			−0.00158690	−	0.999999i	$-0.500505\pi$
$853$	−79.0685			−0.00317380			−0.00158690	+	0.999999i	$0.500505\pi$
$854$	21567.7	−	27045.0i	0.864205	−	1.08368i
$855$	−10211.5	+	44739.7i	−0.408453	+	1.78955i
$856$	−3276.21	+	14354.0i	−0.130816	+	0.573143i
$857$	13275.3	−	16646.7i	0.529144	−	0.663526i	−0.443378	−	0.896335i	$-0.646220\pi$
$857$	13275.3	−	16646.7i	0.529144	−	0.663526i	0.972523	+	0.232809i	$0.0747915\pi$
$858$	6158.99			0.245063
$859$	9940.33	−	12464.8i	0.394831	−	0.495102i	−0.544190	−	0.838962i	$-0.683163\pi$
$859$	9940.33	−	12464.8i	0.394831	−	0.495102i	0.939021	+	0.343860i	$0.111734\pi$
$860$	−2669.43	+	1285.53i	−0.105845	+	0.0509723i
$861$	−52650.5	−	66021.6i	−2.08400	−	2.61325i
$862$	3985.66	+	4997.86i	0.157485	+	0.197480i
$863$	−3117.02	−	1501.08i	−0.122948	−	0.0592088i	0.371398	−	0.928474i	$-0.378878\pi$
$863$	−3117.02	−	1501.08i	−0.122948	−	0.0592088i	−0.494347	+	0.869265i	$0.664593\pi$
$864$	−9581.05	+	41977.3i	−0.377261	+	1.65289i
$865$	−1505.74	−	6597.09i	−0.0591870	−	0.259315i
$866$	24609.9	−	11851.5i	0.965678	−	0.465046i
$867$	−15034.5	−	7240.23i	−0.588925	−	0.283612i
$868$	−4209.51	−	18443.1i	−0.164608	−	0.721196i
$869$	−7332.05			−0.286217
$870$	−16557.1	+	23681.0i	−0.645216	+	0.922829i
$871$	−4206.56			−0.163644
$872$	1462.21	+	6406.34i	0.0567850	+	0.248791i
$873$	−43376.7	−	20889.1i	−1.68165	−	0.809839i
$874$	49250.4	−	23717.8i	1.90609	−	0.917924i
$875$	−7995.51	−	35030.6i	−0.308912	−	1.35343i
$876$	8021.40	−	35144.0i	0.309381	−	1.35549i
$877$	25157.8	+	12115.4i	0.968665	+	0.466485i	0.850192	−	0.526473i	$-0.176486\pi$
$877$	25157.8	+	12115.4i	0.968665	+	0.466485i	0.118473	+	0.992957i	$0.462200\pi$
$878$	−22017.9	−	27609.5i	−0.846317	−	1.06125i
$879$	32539.9	+	40803.7i	1.24863	+	1.56573i
$880$	8354.73	−	4023.42i	0.320043	−	0.154125i
$881$	13067.1	−	16385.6i	0.499707	−	0.626613i	−0.466456	−	0.884544i	$-0.654469\pi$
$881$	13067.1	−	16385.6i	0.499707	−	0.626613i	0.966163	+	0.257931i	$0.0830408\pi$
$882$	89317.6			3.40984
$883$	−20701.9	+	25959.4i	−0.788988	+	0.989359i	0.210942	+	0.977499i	$0.432347\pi$
$883$	−20701.9	+	25959.4i	−0.788988	+	0.989359i	−0.999930	+	0.0118606i	$0.996225\pi$
$884$	467.215	−	2047.00i	0.0177762	−	0.0778825i
$885$	−705.139	+	3089.42i	−0.0267830	+	0.117344i
$886$	10064.0	−	12619.8i	0.381609	−	0.478523i
$887$	8053.49			0.304859			0.152429	−	0.988314i	$-0.451290\pi$
$887$	8053.49			0.304859			0.152429	+	0.988314i	$0.451290\pi$
$888$	−953.284	+	1195.38i	−0.0360249	+	0.0451738i
$889$	−648.630	+	312.364i	−0.0244706	+	0.0117844i
$890$	9353.09	+	11728.4i	0.352266	+	0.441727i
$891$	−11637.2	−	14592.6i	−0.437556	−	0.548678i
$892$	−1659.46	−	799.154i	−0.0622902	−	0.0299974i
$893$	4512.39	−	19770.1i	0.169095	−	0.740852i
$894$	6740.69	+	29532.9i	0.252173	+	1.10484i
$895$	9824.97	−	4731.46i	0.366941	−	0.176710i
$896$	−40675.8	−	19588.5i	−1.51661	−	0.730362i
$897$	2346.76	+	10281.8i	0.0873534	+	0.382720i
$898$	−40654.7			−1.51076
$899$	25485.9	+	10350.3i	0.945499	+	0.383986i
$900$	−19382.2			−0.717860
$901$	2552.23	+	11182.0i	0.0943696	+	0.413460i
$902$	19852.1	+	9560.28i	0.732820	+	0.352908i
$903$	−30950.5	+	14905.0i	−1.14061	+	0.549287i
$904$	−744.419	−	3261.51i	−0.0273883	−	0.119996i
$905$	−337.711	+	1479.61i	−0.0124043	+	0.0543467i
$906$	2668.22	+	1284.95i	0.0978430	+	0.0471187i
$907$	3924.88	+	4921.64i	0.143686	+	0.180177i	0.848467	−	0.529248i	$-0.177526\pi$
$907$	3924.88	+	4921.64i	0.143686	+	0.180177i	−0.704781	+	0.709425i	$0.748955\pi$
$908$	10686.7	+	13400.7i	0.390586	+	0.489779i
$909$	−61979.9	+	29848.0i	−2.26155	+	1.08910i
$910$	−3560.89	+	4465.22i	−0.129717	+	0.162660i
$911$	36317.6			1.32081			0.660404	−	0.750910i	$-0.270385\pi$
$911$	36317.6			1.32081			0.660404	+	0.750910i	$0.270385\pi$
$912$	−62704.3	+	78628.7i	−2.27670	+	2.85489i
$913$	2594.85	−	11368.8i	0.0940603	−	0.412105i
$914$	14162.5	−	62050.1i	0.512533	−	2.24555i
$915$	11947.4	−	14981.5i	0.431658	−	0.541282i
$916$	−18259.8			−0.658646
$917$	11042.0	−	13846.2i	0.397642	−	0.498627i
$918$	−46572.0	+	22427.9i	−1.67441	+	0.806352i
$919$	26299.8	+	32978.9i	0.944016	+	1.18376i	0.982830	+	0.184513i	$0.0590706\pi$
$919$	26299.8	+	32978.9i	0.944016	+	1.18376i	−0.0388138	+	0.999246i	$0.512358\pi$
$920$	6144.38	+	7704.81i	0.220189	+	0.276109i
$921$	−10617.7	−	5113.24i	−0.379877	−	0.182939i
$922$	4439.89	−	19452.4i	0.158590	−	0.694828i
$923$	−685.011	−	3001.23i	−0.0244284	−	0.107028i
$924$	−17416.6	+	8387.41i	−0.620093	+	0.298621i
$925$	−941.096	−	453.208i	−0.0334520	−	0.0161096i
$926$	12951.2	+	56743.1i	0.459616	+	2.01371i
$927$	109136.			3.86679
$928$	−21642.3	+	12157.8i	−0.765564	+	0.430063i
$929$	−48418.9			−1.70998			−0.854991	−	0.518643i	$-0.826437\pi$
$929$	−48418.9			−1.70998			−0.854991	+	0.518643i	$0.826437\pi$
$930$	−7251.91	−	31772.7i	−0.255698	−	1.12029i
$931$	56928.2	+	27415.2i	2.00402	+	0.965087i
$932$	−16974.7	+	8174.60i	−0.596594	+	0.287305i
$933$	18191.0	+	79700.2i	0.638315	+	2.79664i
$934$	−9344.69	+	40941.7i	−0.327374	+	1.43432i
$935$	5806.71	+	2796.36i	0.203101	+	0.0978084i
$936$	−5083.91	−	6375.02i	−0.177535	−	0.222622i
$937$	−20578.9	−	25805.2i	−0.717486	−	0.899699i	0.280707	−	0.959794i	$-0.409431\pi$
$937$	−20578.9	−	25805.2i	−0.717486	−	0.899699i	−0.998193	+	0.0600947i	$0.980860\pi$
$938$	36994.4	−	17815.5i	1.28775	−	0.620147i
$939$	−22217.0	+	27859.2i	−0.772123	+	0.968212i
$940$	−3293.69			−0.114285
$941$	19431.4	−	24366.2i	0.673162	−	0.844119i	−0.321542	−	0.946895i	$-0.604201\pi$
$941$	19431.4	−	24366.2i	0.673162	−	0.844119i	0.994704	+	0.102776i	$0.0327726\pi$
$942$	9116.90	−	39943.8i	0.315334	−	1.38157i
$943$	−8395.69	+	36783.9i	−0.289927	+	1.27025i
$944$	−2931.88	+	3676.46i	−0.101085	+	0.126757i
$945$	45211.3			1.55632
$946$	5588.71	−	7008.02i	0.192077	−	0.240857i
$947$	−37470.1	+	18044.6i	−1.28576	+	0.619189i	−0.946864	−	0.321635i	$-0.895768\pi$
$947$	−37470.1	+	18044.6i	−1.28576	+	0.619189i	−0.338896	+	0.940824i	$0.610053\pi$
$948$	−8052.79	−	10097.9i	−0.275889	−	0.345953i
$949$	6459.58	+	8100.06i	0.220956	+	0.277070i
$950$	−38419.1	−	18501.7i	−1.31208	−	0.631866i
$951$	2626.52	−	11507.5i	0.0895591	−	0.392384i
$952$	−5061.94	−	22177.8i	−0.172330	−	0.755028i
$953$	−32379.4	+	15593.1i	−1.10060	+	0.530020i	−0.893846	−	0.448373i	$-0.852004\pi$
$953$	−32379.4	+	15593.1i	−1.10060	+	0.530020i	−0.206752	+	0.978393i	$0.566289\pi$
$954$	−36155.9	−	17411.7i	−1.22703	−	0.590908i
$955$	−381.546	−	1671.66i	−0.0129283	−	0.0566427i
$956$	−5836.52			−0.197455
$957$	4516.32	−	27743.8i	0.152552	−	0.937126i
$958$	65108.3			2.19578
$959$	9346.75	+	40950.8i	0.314726	+	1.37891i
$960$	−4555.14	−	2193.64i	−0.153142	−	0.0737493i
$961$	−1111.57	+	535.306i	−0.0373124	+	0.0179687i
$962$	88.0963	+	385.975i	0.00295254	+	0.0129359i
$963$	12836.7	−	56241.1i	0.429549	−	1.88198i
$964$	17114.8	+	8242.05i	0.571815	+	0.275372i
$965$	−3695.09	−	4633.50i	−0.123263	−	0.154567i
$966$	−64183.8	−	80483.9i	−2.13776	−	2.68067i
$967$	2433.57	−	1171.94i	0.0809290	−	0.0389733i	−0.392981	−	0.919546i	$-0.628556\pi$
$967$	2433.57	−	1171.94i	0.0809290	−	0.0389733i	0.473910	+	0.880573i	$0.342842\pi$
$968$	8501.93	−	10661.1i	0.282296	−	0.353988i
$969$	−69898.1			−2.31729
$970$	−10726.4	+	13450.5i	−0.355057	+	0.445228i
$971$	−4187.51	+	18346.7i	−0.138397	+	0.606358i	0.857390	+	0.514667i	$0.172084\pi$
$971$	−4187.51	+	18346.7i	−0.138397	+	0.606358i	−0.995787	+	0.0916911i	$0.970773\pi$
$972$	1145.51	−	5018.82i	0.0378008	−	0.165616i
$973$	−21825.1	+	27367.8i	−0.719095	+	0.901716i
$974$	3522.31			0.115875
$975$	5129.37	−	6432.02i	0.168483	−	0.211271i
$976$	25619.1	−	12337.5i	0.840214	−	0.404626i
$977$	22468.7	+	28174.8i	0.735759	+	0.922612i	0.999114	−	0.0420867i	$-0.0134006\pi$
$977$	22468.7	+	28174.8i	0.735759	+	0.922612i	−0.263355	+	0.964699i	$0.584829\pi$
$978$	17858.0	+	22393.3i	0.583883	+	0.732166i
$979$	−13147.9	−	6331.70i	−0.429223	−	0.206703i
$980$	2283.68	−	10005.4i	0.0744382	−	0.326135i
$981$	−5729.13	−	25101.0i	−0.186460	−	0.816934i
$982$	35421.0	−	17057.9i	1.15105	−	0.554316i
$983$	−39864.8	−	19197.9i	−1.29348	−	0.622906i	−0.344660	−	0.938728i	$-0.612006\pi$
$983$	−39864.8	−	19197.9i	−1.29348	−	0.622906i	−0.948819	+	0.315821i	$0.897720\pi$
$984$	−9586.55	−	42001.4i	−0.310577	−	1.36073i
$985$	−8360.34			−0.270439
$986$	−27611.1	−	11213.4i	−0.891802	−	0.362178i
$987$	−38188.4			−1.23156
$988$	1156.43	+	5066.63i	0.0372377	+	0.163149i
$989$	13828.7	+	6659.54i	0.444617	+	0.214116i
$990$	−20316.6	+	9783.95i	−0.652225	+	0.314095i
$991$	−10706.6	−	46908.5i	−0.343194	−	1.50363i	−0.792289	−	0.610146i	$-0.791111\pi$
$991$	−10706.6	−	46908.5i	−0.343194	−	1.50363i	0.449095	−	0.893484i	$-0.351746\pi$
$992$	6230.02	−	27295.5i	0.199398	−	0.873622i
$993$	46109.3	+	22205.1i	1.47355	+	0.709624i
$994$	18735.0	+	23493.0i	0.597826	+	0.749650i
$995$	−9223.19	−	11565.5i	−0.293864	−	0.368494i
$996$	18507.3	−	8912.65i	0.588782	−	0.283542i
$997$	−24480.2	+	30697.2i	−0.777628	+	0.975115i	0.222372	+	0.974962i	$0.428620\pi$
$997$	−24480.2	+	30697.2i	−0.777628	+	0.975115i	−1.00000		0.000152711i	$0.999951\pi$
$998$	14348.6			0.455106
$999$	1954.04	−	2450.29i	0.0618849	−	0.0776012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.4.d.a.7.2	✓	42
29.5	even	14		841.4.a.i.1.5		21
29.24	even	7		841.4.a.h.1.17		21
29.25	even	7	inner	29.4.d.a.25.2	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.7.2	✓	42	1.1	even	1	trivial
29.4.d.a.25.2	yes	42	29.25	even	7	inner
841.4.a.h.1.17		21	29.24	even	7
841.4.a.i.1.5		21	29.5	even	14

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764111 - 3.34779i) q^{2} +(8.23892 + 3.96766i) q^{3} +(-3.41608 + 1.64510i) q^{4} +(1.31115 + 5.74451i) q^{5} +(6.98743 - 30.6139i) q^{6} +(-25.5210 - 12.2903i) q^{7} +(-9.01023 - 11.2985i) q^{8} +(35.3034 + 44.2690i) q^{9} +(18.2296 - 8.77890i) q^{10} +(-12.2720 + 15.3887i) q^{11} -34.6720 q^{12} +(6.21305 - 7.79091i) q^{13} +(-21.6443 + 94.8301i) q^{14} +(-11.9898 + 52.5308i) q^{15} +(-49.8521 + 62.5126i) q^{16} -55.5715 q^{17} +(121.228 - 152.015i) q^{18} +(123.926 - 59.6797i) q^{19} +(-13.9293 - 17.4668i) q^{20} +(-161.502 - 202.517i) q^{21} +(60.8952 + 29.3256i) q^{22} +(-25.7533 + 112.832i) q^{23} +(-29.4061 - 128.837i) q^{24} +(81.3408 - 39.1717i) q^{25} +(-30.8298 - 14.8469i) q^{26} +(60.2766 + 264.089i) q^{27} +107.401 q^{28} +(-89.4863 + 127.989i) q^{29} +185.024 q^{30} +(-39.1945 - 171.722i) q^{31} +(143.210 + 68.9664i) q^{32} +(-162.165 + 78.0947i) q^{33} +(42.4628 + 186.042i) q^{34} +(37.1398 - 162.720i) q^{35} +(-193.426 - 93.1491i) q^{36} +(-7.21365 - 9.04563i) q^{37} +(-294.488 - 369.277i) q^{38} +(82.1005 - 39.5375i) q^{39} +(53.0905 - 66.5733i) q^{40} +326.005 q^{41} +(-554.579 + 695.421i) q^{42} +(29.5107 - 129.295i) q^{43} +(16.6065 - 72.7576i) q^{44} +(-208.016 + 260.844i) q^{45} +397.418 q^{46} +(91.9205 - 115.265i) q^{47} +(-658.756 + 317.240i) q^{48} +(286.414 + 359.152i) q^{49} +(-193.292 - 242.380i) q^{50} +(-457.849 - 220.488i) q^{51} +(-8.40746 + 36.8355i) q^{52} +(-45.9269 - 201.219i) q^{53} +(838.057 - 403.587i) q^{54} +(-104.491 - 50.3201i) q^{55} +(91.0888 + 399.086i) q^{56} +1257.81 q^{57} +(496.858 + 201.784i) q^{58} +58.8115 q^{59} +(-45.4602 - 199.174i) q^{60} +(-320.413 - 154.303i) q^{61} +(-544.941 + 262.430i) q^{62} +(-356.899 - 1563.68i) q^{63} +(-20.8795 + 91.4792i) q^{64} +(52.9012 + 25.4759i) q^{65} +(385.357 + 483.222i) q^{66} +(-263.197 - 330.039i) q^{67} +(189.837 - 91.4205i) q^{68} +(-659.860 + 827.438i) q^{69} -573.132 q^{70} +(192.611 - 241.526i) q^{71} +(182.081 - 797.748i) q^{72} +(-231.351 + 1013.61i) q^{73} +(-24.7709 + 31.0617i) q^{74} +825.580 q^{75} +(-325.163 + 407.741i) q^{76} +(502.325 - 241.907i) q^{77} +(-195.097 - 244.644i) q^{78} +(232.256 + 291.240i) q^{79} +(-424.468 - 204.413i) q^{80} +(-211.011 + 924.498i) q^{81} +(-249.104 - 1091.40i) q^{82} +(-533.782 + 257.056i) q^{83} +(884.865 + 426.129i) q^{84} +(-72.8624 - 319.231i) q^{85} -455.402 q^{86} +(-1245.09 + 699.441i) q^{87} +284.442 q^{88} +(164.980 + 722.823i) q^{89} +(1032.20 + 497.080i) q^{90} +(-254.316 + 122.472i) q^{91} +(-97.6452 - 427.812i) q^{92} +(358.415 - 1570.32i) q^{93} +(-456.119 - 219.656i) q^{94} +(505.316 + 633.647i) q^{95} +(906.263 + 1136.42i) q^{96} +(-766.073 + 368.921i) q^{97} +(983.512 - 1233.29i) q^{98} -1114.48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) \) 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

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