LMFDB - Embedded newform 31.5.h.a.11.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.774721 + 2.38435i) q^{2} +(7.54548 - 6.79398i) q^{3} +(7.85936 - 5.71016i) q^{4} +(-19.1726 - 33.2079i) q^{5} +(22.0448 + 12.7276i) q^{6} +(3.49477 + 33.2505i) q^{7} +(52.1557 + 37.8934i) q^{8} +(2.30929 - 21.9714i) q^{9} +(64.3257 - 71.4409i) q^{10} +(2.10738 - 4.73326i) q^{11} +(20.5079 - 96.4822i) q^{12} +(59.4243 + 279.569i) q^{13} +(-76.5733 + 34.0926i) q^{14} +(-370.280 - 120.311i) q^{15} +(-1.91265 + 5.88652i) q^{16} +(-17.5751 - 39.4743i) q^{17} +(54.1765 - 11.5156i) q^{18} +(-363.175 - 77.1953i) q^{19} +(-340.306 - 151.514i) q^{20} +(252.273 + 227.148i) q^{21} +(12.9184 + 1.35778i) q^{22} +(175.605 - 241.699i) q^{23} +(650.987 - 68.4215i) q^{24} +(-422.675 + 732.095i) q^{25} +(-620.553 + 358.276i) q^{26} +(351.563 + 483.885i) q^{27} +(217.332 + 241.372i) q^{28} +(867.623 - 281.908i) q^{29} -976.083i q^{30} +(-865.848 - 416.927i) q^{31} +1015.97 q^{32} +(-16.2565 - 50.0323i) q^{33} +(80.5046 - 72.4867i) q^{34} +(1037.18 - 753.552i) q^{35} +(-107.311 - 185.867i) q^{36} +(-1288.56 - 743.952i) q^{37} +(-97.2993 - 925.741i) q^{38} +(2347.77 + 1705.76i) q^{39} +(258.398 - 2458.49i) q^{40} +(-1395.44 + 1549.79i) q^{41} +(-346.158 + 777.483i) q^{42} +(-612.461 + 2881.40i) q^{43} +(-10.4650 - 49.2339i) q^{44} +(-773.899 + 344.562i) q^{45} +(712.340 + 231.453i) q^{46} +(840.189 - 2585.83i) q^{47} +(25.5611 + 57.4111i) q^{48} +(1255.15 - 266.790i) q^{49} +(-2073.02 - 440.635i) q^{50} +(-400.800 - 178.448i) q^{51} +(2063.42 + 1857.91i) q^{52} +(-3972.00 - 417.474i) q^{53} +(-881.386 + 1213.12i) q^{54} +(-197.586 + 20.7671i) q^{55} +(-1077.70 + 1866.63i) q^{56} +(-3264.80 + 1884.93i) q^{57} +(1344.33 + 1850.31i) q^{58} +(-1740.08 - 1932.55i) q^{59} +(-3597.16 + 1168.79i) q^{60} -2551.53i q^{61} +(323.308 - 2387.48i) q^{62} +738.631 q^{63} +(817.697 + 2516.61i) q^{64} +(8144.58 - 7333.41i) q^{65} +(106.700 - 77.5221i) q^{66} +(2731.32 + 4730.78i) q^{67} +(-363.533 - 209.886i) q^{68} +(-317.078 - 3016.80i) q^{69} +(2600.25 + 1889.19i) q^{70} +(233.787 - 2224.34i) q^{71} +(953.013 - 1058.43i) q^{72} +(3486.48 - 7830.75i) q^{73} +(775.562 - 3648.73i) q^{74} +(1784.55 + 8395.65i) q^{75} +(-3295.12 + 1467.08i) q^{76} +(164.748 + 53.5300i) q^{77} +(-2248.25 + 6919.39i) q^{78} +(750.048 + 1684.64i) q^{79} +(232.149 - 49.3448i) q^{80} +(7690.60 + 1634.69i) q^{81} +(-4776.32 - 2126.55i) q^{82} +(-2033.37 - 1830.85i) q^{83} +(3279.75 + 344.716i) q^{84} +(-973.898 + 1340.46i) q^{85} +(-7344.75 + 771.964i) q^{86} +(4631.35 - 8021.74i) q^{87} +(289.272 - 167.011i) q^{88} +(-1420.59 - 1955.27i) q^{89} +(-1421.11 - 1578.30i) q^{90} +(-9088.15 + 2952.92i) q^{91} -2902.33i q^{92} +(-9365.83 + 2736.64i) q^{93} +6816.44 q^{94} +(4399.51 + 13540.3i) q^{95} +(7665.99 - 6902.49i) q^{96} +(6267.04 - 4553.27i) q^{97} +(1608.51 + 2786.02i) q^{98} +(-99.1299 - 57.2327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) $ 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.774721	+	2.38435i	0.193680	+	0.596087i	0.999989	+	0.00459232i	$0.00146179\pi$
$2$	0.774721	+	2.38435i	0.193680	+	0.596087i	−0.806309	+	0.591494i	$0.798538\pi$
$3$	7.54548	−	6.79398i	0.838387	−	0.754887i	−0.133321	−	0.991073i	$-0.542564\pi$
$3$	7.54548	−	6.79398i	0.838387	−	0.754887i	0.971708	+	0.236186i	$0.0758975\pi$
$4$	7.85936	−	5.71016i	0.491210	−	0.356885i
$5$	−19.1726	−	33.2079i	−0.766903	−	1.32831i	−0.939235	−	0.343276i	$-0.888463\pi$
$5$	−19.1726	−	33.2079i	−0.766903	−	1.32831i	0.172332	−	0.985039i	$-0.444870\pi$
$6$	22.0448	+	12.7276i	0.612357	+	0.353544i
$7$	3.49477	+	33.2505i	0.0713219	+	0.678582i	0.970517	+	0.241034i	$0.0774865\pi$
$7$	3.49477	+	33.2505i	0.0713219	+	0.678582i	−0.899195	+	0.437548i	$0.855847\pi$
$8$	52.1557	+	37.8934i	0.814933	+	0.592084i
$9$	2.30929	−	21.9714i	0.0285097	−	0.271252i
$10$	64.3257	−	71.4409i	0.643257	−	0.714409i
$11$	2.10738	−	4.73326i	0.0174164	−	0.0391179i	−0.904628	−	0.426202i	$-0.859851\pi$
$11$	2.10738	−	4.73326i	0.0174164	−	0.0391179i	0.922044	+	0.387084i	$0.126518\pi$
$12$	20.5079	−	96.4822i	0.142416	−	0.670015i
$13$	59.4243	+	279.569i	0.351623	+	1.65426i	0.697954	+	0.716143i	$0.254094\pi$
$13$	59.4243	+	279.569i	0.351623	+	1.65426i	−0.346331	+	0.938113i	$0.612572\pi$
$14$	−76.5733	+	34.0926i	−0.390680	+	0.173942i
$15$	−370.280	−	120.311i	−1.64569	−	0.534717i
$16$	−1.91265	+	5.88652i	−0.00747128	+	0.0229942i
$17$	−17.5751	−	39.4743i	−0.0608135	−	0.136589i	0.880582	−	0.473893i	$-0.157152\pi$
$17$	−17.5751	−	39.4743i	−0.0608135	−	0.136589i	−0.941396	+	0.337304i	$0.890485\pi$
$18$	54.1765	−	11.5156i	0.167211	−	0.0355419i
$19$	−363.175	−	77.1953i	−1.00603	−	0.213837i	−0.324699	−	0.945817i	$-0.605263\pi$
$19$	−363.175	−	77.1953i	−1.00603	−	0.213837i	−0.681326	+	0.731980i	$0.738596\pi$
$20$	−340.306	−	151.514i	−0.850766	−	0.378785i
$21$	252.273	+	227.148i	0.572048	+	0.515074i
$22$	12.9184	+	1.35778i	0.0266909	+	0.00280532i
$23$	175.605	−	241.699i	0.331956	−	0.456899i	−0.610114	−	0.792314i	$-0.708876\pi$
$23$	175.605	−	241.699i	0.331956	−	0.456899i	0.942071	+	0.335415i	$0.108876\pi$
$24$	650.987	−	68.4215i	1.13019	−	0.118787i
$25$	−422.675	+	732.095i	−0.676280	+	1.17135i
$26$	−620.553	+	358.276i	−0.917977	+	0.529994i
$27$	351.563	+	483.885i	0.482254	+	0.663765i
$28$	217.332	+	241.372i	0.277210	+	0.307873i
$29$	867.623	−	281.908i	1.03166	−	0.335205i	0.256211	−	0.966621i	$-0.417526\pi$
$29$	867.623	−	281.908i	1.03166	−	0.335205i	0.775445	+	0.631415i	$0.217526\pi$
$30$		−	976.083i		−	1.08454i
$31$	−865.848	−	416.927i	−0.900986	−	0.433847i
$31$	−865.848	−	416.927i	−0.900986	−	0.433847i
$32$	1015.97			0.992160
$33$	−16.2565	−	50.0323i	−0.0149279	−	0.0459433i
$34$	80.5046	−	72.4867i	0.0696407	−	0.0627047i
$35$	1037.18	−	753.552i	0.846674	−	0.615145i
$36$	−107.311	−	185.867i	−0.0828014	−	0.143416i
$37$	−1288.56	−	743.952i	−0.941244	−	0.543427i	−0.0508936	−	0.998704i	$-0.516207\pi$
$37$	−1288.56	−	743.952i	−0.941244	−	0.543427i	−0.890350	+	0.455277i	$0.849540\pi$
$38$	−97.2993	−	925.741i	−0.0673818	−	0.641095i
$39$	2347.77	+	1705.76i	1.54357	+	1.12147i
$40$	258.398	−	2458.49i	0.161499	−	1.53656i
$41$	−1395.44	+	1549.79i	−0.830124	+	0.921946i	−0.997958	−	0.0638690i	$-0.979656\pi$
$41$	−1395.44	+	1549.79i	−0.830124	+	0.921946i	0.167834	+	0.985815i	$0.446323\pi$
$42$	−346.158	+	777.483i	−0.196235	+	0.440750i
$43$	−612.461	+	2881.40i	−0.331239	+	1.55836i	0.425695	+	0.904867i	$0.360030\pi$
$43$	−612.461	+	2881.40i	−0.331239	+	1.55836i	−0.756934	+	0.653491i	$0.773304\pi$
$44$	−10.4650	−	49.2339i	−0.00540547	−	0.0254307i
$45$	−773.899	+	344.562i	−0.382172	+	0.170154i
$46$	712.340	+	231.453i	0.336645	+	0.109383i
$47$	840.189	−	2585.83i	0.380348	−	1.17059i	−0.559451	−	0.828863i	$-0.688988\pi$
$47$	840.189	−	2585.83i	0.380348	−	1.17059i	0.939799	−	0.341727i	$-0.111012\pi$
$48$	25.5611	+	57.4111i	0.0110942	+	0.0249180i
$49$	1255.15	−	266.790i	0.522761	−	0.111116i
$50$	−2073.02	−	440.635i	−0.829209	−	0.176254i
$51$	−400.800	−	178.448i	−0.154095	−	0.0686073i
$52$	2063.42	+	1857.91i	0.763099	+	0.687098i
$53$	−3972.00	−	417.474i	−1.41403	−	0.148620i	−0.633500	−	0.773742i	$-0.718383\pi$
$53$	−3972.00	−	417.474i	−1.41403	−	0.148620i	−0.780527	+	0.625122i	$0.785049\pi$
$54$	−881.386	+	1213.12i	−0.302259	+	0.416023i
$55$	−197.586	+	20.7671i	−0.0653176	+	0.00686515i
$56$	−1077.70	+	1866.63i	−0.343655	+	0.595228i
$57$	−3264.80	+	1884.93i	−1.00486	+	0.580157i
$58$	1344.33	+	1850.31i	0.399623	+	0.550034i
$59$	−1740.08	−	1932.55i	−0.499878	−	0.555171i	0.439416	−	0.898284i	$-0.355185\pi$
$59$	−1740.08	−	1932.55i	−0.499878	−	0.555171i	−0.939294	+	0.343113i	$0.888519\pi$
$60$	−3597.16	+	1168.79i	−0.999210	+	0.324663i
$61$		−	2551.53i		−	0.685712i	−0.939388	−	0.342856i	$-0.888606\pi$
$61$		−	2551.53i		−	0.685712i	0.939388	−	0.342856i	$-0.111394\pi$
$62$	323.308	−	2387.48i	0.0841072	−	0.621094i
$63$	738.631			0.186100
$64$	817.697	+	2516.61i	0.199633	+	0.614407i
$65$	8144.58	−	7333.41i	1.92771	−	1.73572i
$66$	106.700	−	77.5221i	0.0244950	−	0.0177966i
$67$	2731.32	+	4730.78i	0.608447	+	1.05386i	0.991497	+	0.130133i	$0.0415404\pi$
$67$	2731.32	+	4730.78i	0.608447	+	1.05386i	−0.383050	+	0.923728i	$0.625126\pi$
$68$	−363.533	−	209.886i	−0.0786188	−	0.0453906i
$69$	−317.078	−	3016.80i	−0.0665990	−	0.633647i
$70$	2600.25	+	1889.19i	0.530664	+	0.385550i
$71$	233.787	−	2224.34i	0.0463772	−	0.441249i	−0.946553	−	0.322549i	$-0.895460\pi$
$71$	233.787	−	2224.34i	0.0463772	−	0.441249i	0.992930	−	0.118701i	$-0.0378729\pi$
$72$	953.013	−	1058.43i	0.183837	−	0.204172i
$73$	3486.48	−	7830.75i	0.654246	−	1.46946i	−0.215774	−	0.976443i	$-0.569228\pi$
$73$	3486.48	−	7830.75i	0.654246	−	1.46946i	0.870020	−	0.493017i	$-0.164106\pi$
$74$	775.562	−	3648.73i	0.141629	−	0.666314i
$75$	1784.55	+	8395.65i	0.317254	+	1.49256i
$76$	−3295.12	+	1467.08i	−0.570485	+	0.253996i
$77$	164.748	+	53.5300i	0.0277869	+	0.00902850i
$78$	−2248.25	+	6919.39i	−0.369534	+	1.13731i
$79$	750.048	+	1684.64i	0.120181	+	0.269931i	0.963611	−	0.267308i	$-0.0861341\pi$
$79$	750.048	+	1684.64i	0.120181	+	0.269931i	−0.843430	+	0.537239i	$0.819467\pi$
$80$	232.149	−	49.3448i	0.0362733	−	0.00771013i
$81$	7690.60	+	1634.69i	1.17217	+	0.249152i
$82$	−4776.32	−	2126.55i	−0.710339	−	0.316263i
$83$	−2033.37	−	1830.85i	−0.295161	−	0.265764i	0.508223	−	0.861226i	$-0.330303\pi$
$83$	−2033.37	−	1830.85i	−0.295161	−	0.265764i	−0.803384	+	0.595461i	$0.796969\pi$
$84$	3279.75	+	344.716i	0.464818	+	0.0488543i
$85$	−973.898	+	1340.46i	−0.134796	+	0.185530i
$86$	−7344.75	+	771.964i	−0.993071	+	0.104376i
$87$	4631.35	−	8021.74i	0.611884	−	1.05982i
$88$	289.272	−	167.011i	0.0373543	−	0.0215665i
$89$	−1420.59	−	1955.27i	−0.179344	−	0.246846i	0.709875	−	0.704328i	$-0.248752\pi$
$89$	−1420.59	−	1955.27i	−0.179344	−	0.246846i	−0.889219	+	0.457482i	$0.848752\pi$
$90$	−1421.11	−	1578.30i	−0.175446	−	0.194852i
$91$	−9088.15	+	2952.92i	−1.09747	+	0.356590i
$92$		−	2902.33i		−	0.342903i
$93$	−9365.83	+	2736.64i	−1.08288	+	0.316411i
$94$	6816.44			0.771439
$95$	4399.51	+	13540.3i	0.487481	+	1.50031i
$96$	7665.99	−	6902.49i	0.831813	−	0.748968i
$97$	6267.04	−	4553.27i	0.666068	−	0.483927i	−0.202638	−	0.979254i	$-0.564952\pi$
$97$	6267.04	−	4553.27i	0.666068	−	0.483927i	0.868707	+	0.495327i	$0.164952\pi$
$98$	1608.51	+	2786.02i	0.167483	+	0.290090i
$99$	−99.1299	−	57.2327i	−0.0101143	−	0.00583947i
$100$	858.422	+	8167.34i	0.0858422	+	0.816734i
$101$	−10509.4	−	7635.53i	−1.03023	−	0.748508i	−0.0618776	−	0.998084i	$-0.519709\pi$
$101$	−10509.4	−	7635.53i	−1.03023	−	0.748508i	−0.968355	+	0.249576i	$0.919709\pi$
$102$	114.973	−	1093.89i	0.0110508	−	0.105142i
$103$	−9319.25	+	10350.1i	−0.878429	+	0.975594i	−0.999855	−	0.0170062i	$-0.994587\pi$
$103$	−9319.25	+	10350.1i	−0.878429	+	0.975594i	0.121426	+	0.992600i	$0.461253\pi$
$104$	−7494.50	+	16832.9i	−0.692909	+	1.55630i
$105$	2706.37	−	12732.5i	0.245476	−	1.15487i
$106$	−2081.79	−	9794.06i	−0.185279	−	0.871668i
$107$	−931.138	+	414.569i	−0.0813292	+	0.0362101i	−0.446998	−	0.894535i	$-0.647507\pi$
$107$	−931.138	+	414.569i	−0.0813292	+	0.0362101i	0.365669	+	0.930745i	$0.380840\pi$
$108$	5526.12	+	1795.54i	0.473776	+	0.153939i
$109$	−45.7610	+	140.838i	−0.00385161	+	0.0118540i	−0.952964	−	0.303084i	$-0.901984\pi$
$109$	−45.7610	+	140.838i	−0.00385161	+	0.0118540i	0.949112	+	0.314938i	$0.101984\pi$
$110$	−202.590	−	455.024i	−0.0167429	−	0.0376053i
$111$	−14777.2	+	3140.99i	−1.19935	+	0.254930i
$112$	−202.414	−	43.0245i	−0.0161363	−	0.00342988i
$113$	3922.76	+	1746.52i	0.307210	+	0.136779i	0.554551	−	0.832150i	$-0.312890\pi$
$113$	3922.76	+	1746.52i	0.307210	+	0.136779i	−0.247341	+	0.968928i	$0.579557\pi$
$114$	−7023.63	−	6324.11i	−0.540446	−	0.486620i
$115$	−11393.1	−	1197.47i	−0.861484	−	0.0905456i
$116$	5209.22	−	7169.87i	0.387130	−	0.532838i
$117$	6279.76	−	660.029i	0.458745	−	0.0482160i
$118$	3259.80	−	5646.13i	0.234113	−	0.405496i
$119$	1251.12	−	722.335i	0.0883497	−	0.0510087i
$120$	−14753.2	−	20306.1i	−1.02453	−	1.41014i
$121$	9778.78	+	10860.4i	0.667904	+	0.741782i
$122$	6083.74	−	1976.73i	0.408744	−	0.132809i
$123$			21174.5i			1.39960i
$124$	−9185.73	+	1667.35i	−0.597407	+	0.108438i
$125$	8449.37			0.540760
$126$	572.233	+	1761.15i	0.0360439	+	0.110932i
$127$	10960.6	−	9869.00i	0.679561	−	0.611879i	−0.255314	−	0.966858i	$-0.582179\pi$
$127$	10960.6	−	9869.00i	0.679561	−	0.611879i	0.934874	+	0.354979i	$0.115512\pi$
$128$	7784.02	−	5655.42i	0.475099	−	0.345180i
$129$	14954.9	+	25902.6i	0.898677	+	1.55655i
$130$	23795.2	+	13738.2i	1.40800	+	0.812909i
$131$	2646.91	+	25183.6i	0.154240	+	1.46749i	0.748454	+	0.663186i	$0.230796\pi$
$131$	2646.91	+	25183.6i	0.154240	+	1.46749i	−0.594215	+	0.804307i	$0.702537\pi$
$132$	−413.458	−	300.394i	−0.0237292	−	0.0172403i
$133$	1297.57	−	12345.6i	0.0733546	−	0.697922i
$134$	−9163.81	+	10177.4i	−0.510348	+	0.566799i
$135$	9328.42	−	20952.0i	0.511848	−	1.14963i
$136$	579.172	−	2724.79i	0.0313134	−	0.147318i
$137$	−3122.30	−	14689.3i	−0.166354	−	0.782635i	−0.979639	−	0.200769i	$-0.935656\pi$
$137$	−3122.30	−	14689.3i	−0.166354	−	0.782635i	0.813284	−	0.581866i	$-0.197677\pi$
$138$	6947.44	−	3093.20i	0.364810	−	0.162424i
$139$	8856.04	+	2877.50i	0.458363	+	0.148931i	0.529092	−	0.848564i	$-0.322533\pi$
$139$	8856.04	+	2877.50i	0.458363	+	0.148931i	−0.0707289	+	0.997496i	$0.522533\pi$
$140$	3848.63	−	11844.9i	0.196359	−	0.604330i
$141$	−11228.5	−	25219.6i	−0.564785	−	1.26853i
$142$	5484.71	−	1165.81i	0.272005	−	0.0578165i
$143$	1448.50	+	307.889i	0.0708350	+	0.0150564i
$144$	124.918	+	55.6172i	0.00602422	+	0.00268216i
$145$	−25996.1	−	23407.0i	−1.23644	−	1.11329i
$146$	21372.3	+	2246.32i	1.00264	+	0.105382i
$147$	7658.13	−	10540.5i	0.354395	−	0.487783i
$148$	−14375.4	+	1510.91i	−0.656289	+	0.0689787i
$149$	−17517.5	+	30341.2i	−0.789041	+	1.36666i	0.137514	+	0.990500i	$0.456089\pi$
$149$	−17517.5	+	30341.2i	−0.789041	+	1.36666i	−0.926555	+	0.376159i	$0.877245\pi$
$150$	−18635.6	+	10759.3i	−0.828250	+	0.478190i
$151$	−2307.46	−	3175.95i	−0.101200	−	0.139290i	0.755414	−	0.655248i	$-0.227436\pi$
$151$	−2307.46	−	3175.95i	−0.101200	−	0.139290i	−0.856614	+	0.515958i	$0.827436\pi$
$152$	−16016.5	−	17788.1i	−0.693234	−	0.769915i
$153$	−907.892	+	294.992i	−0.0387839	+	0.0126016i
$154$			434.288i			0.0183120i
$155$	2755.27	+	36746.5i	0.114683	+	1.52951i
$156$	28192.1			1.15845
$157$	−9545.48	−	29378.0i	−0.387256	−	1.19185i	−0.934830	−	0.355095i	$-0.884448\pi$
$157$	−9545.48	−	29378.0i	−0.387256	−	1.19185i	0.547574	−	0.836758i	$-0.315552\pi$
$158$	−3435.68	+	3093.50i	−0.137625	+	0.123918i
$159$	−32807.0	+	23835.7i	−1.29769	+	0.942829i
$160$	−19478.8	−	33738.3i	−0.760890	−	1.31790i
$161$	8650.33	+	4994.27i	0.333719	+	0.192673i
$162$	2060.41	+	19603.5i	0.0785097	+	0.746970i
$163$	27837.4	+	20225.1i	1.04774	+	0.761228i	0.971781	−	0.235883i	$-0.0757983\pi$
$163$	27837.4	+	20225.1i	1.04774	+	0.761228i	0.0759586	+	0.997111i	$0.475798\pi$
$164$	−2117.70	+	20148.5i	−0.0787365	+	0.749128i
$165$	−1349.79	+	1499.09i	−0.0495790	+	0.0550630i
$166$	2790.09	−	6266.65i	0.101252	−	0.227415i
$167$	8990.77	−	42298.3i	0.322377	−	1.51666i	−0.456634	−	0.889654i	$-0.650945\pi$
$167$	8990.77	−	42298.3i	0.322377	−	1.51666i	0.779011	−	0.627010i	$-0.215721\pi$
$168$	4550.10	+	21406.5i	0.161214	+	0.758452i
$169$	−48535.9	+	21609.6i	−1.69938	+	0.756612i
$170$	−3950.61	−	1283.63i	−0.136699	−	0.0444163i
$171$	−2534.77	+	7801.20i	−0.0866853	+	0.266790i
$172$	11639.7	+	26143.2i	0.393446	+	0.883695i
$173$	22743.3	−	4834.23i	0.759907	−	0.161523i	0.188368	−	0.982098i	$-0.439680\pi$
$173$	22743.3	−	4834.23i	0.759907	−	0.161523i	0.571538	+	0.820575i	$0.306347\pi$
$174$	22714.6	+	4828.14i	0.750252	+	0.159471i
$175$	−25819.7	−	11495.7i	−0.843092	−	0.375369i
$176$	23.8318	+	21.4582i	0.000769363	+	0.000692737i
$177$	−26259.4	−	2759.98i	−0.838182	−	0.0880965i
$178$	3561.48	−	4901.96i	0.112406	−	0.154714i
$179$	38793.4	−	4077.35i	1.21074	−	0.127254i	0.522439	−	0.852677i	$-0.325022\pi$
$179$	38793.4	−	4077.35i	1.21074	−	0.127254i	0.688304	+	0.725422i	$0.258356\pi$
$180$	−4114.84	+	7127.12i	−0.127001	+	0.219973i
$181$	−12385.4	+	7150.74i	−0.378054	+	0.218270i	−0.676971	−	0.736009i	$-0.736708\pi$
$181$	−12385.4	+	7150.74i	−0.378054	+	0.218270i	0.298917	+	0.954279i	$0.403375\pi$
$182$	−14081.6	−	19381.6i	−0.425117	−	0.585123i
$183$	−17335.1	−	19252.6i	−0.517635	−	0.574892i
$184$	18317.6	−	5951.75i	0.541045	−	0.175796i
$185$			57053.9i			1.66702i
$186$	−13781.0	−	20211.3i	−0.398341	−	0.584208i
$187$	−223.880			−0.00640223
$188$	−8162.18	−	25120.6i	−0.230935	−	0.710746i
$189$	−14860.8	+	13380.7i	−0.416024	+	0.374590i
$190$	−28876.4	+	20979.9i	−0.799900	+	0.581162i
$191$	19275.9	+	33386.9i	0.528383	+	0.915186i	0.999452	+	0.0330898i	$0.0105347\pi$
$191$	19275.9	+	33386.9i	0.528383	+	0.915186i	−0.471070	+	0.882096i	$0.656132\pi$
$192$	23267.7	+	13433.6i	0.631178	+	0.364411i
$193$	−4576.39	−	43541.5i	−0.122860	−	1.16893i	−0.866088	−	0.499892i	$-0.833373\pi$
$193$	−4576.39	−	43541.5i	−0.122860	−	1.16893i	0.743228	−	0.669038i	$-0.233294\pi$
$194$	15711.8	+	11415.3i	0.417467	+	0.303307i
$195$	11631.7	−	110668.i	0.305896	−	2.91041i
$196$	8341.24	−	9263.89i	0.217129	−	0.241147i
$197$	12355.2	−	27750.2i	0.318358	−	0.715045i	−0.681501	−	0.731817i	$-0.738672\pi$
$197$	12355.2	−	27750.2i	0.318358	−	0.715045i	0.999859	+	0.0167725i	$0.00533910\pi$
$198$	59.6645	−	280.699i	0.00152190	−	0.00715997i
$199$	2455.34	+	11551.5i	0.0620021	+	0.291697i	0.998214	−	0.0597391i	$-0.0190269\pi$
$199$	2455.34	+	11551.5i	0.0620021	+	0.291697i	−0.936212	+	0.351436i	$0.885694\pi$
$200$	−49786.5	+	22166.4i	−1.24466	+	0.554159i
$201$	52749.9	+	17139.5i	1.30566	+	0.424234i
$202$	10063.9	−	30973.5i	0.246640	−	0.759079i
$203$	12405.7	+	27863.7i	0.301044	+	0.676156i
$204$	−4168.99	+	886.147i	−0.100178	+	0.0212934i
$205$	78219.4	+	16626.1i	1.86126	+	0.395623i
$206$	−31898.0	−	14201.9i	−0.751673	−	0.334666i
$207$	−4904.95	−	4416.44i	−0.114471	−	0.103070i
$208$	−1759.35	−	184.915i	−0.0406654	−	0.00427411i
$209$	−1130.74	+	1556.32i	−0.0258862	+	0.0356293i
$210$	32455.3	−	3411.19i	0.735947	−	0.0773512i
$211$	−17571.3	+	30434.4i	−0.394674	+	0.683596i	−0.993060	−	0.117613i	$-0.962476\pi$
$211$	−17571.3	+	30434.4i	−0.394674	+	0.683596i	0.598385	+	0.801209i	$0.295809\pi$
$212$	−33601.2	+	19399.7i	−0.747624	+	0.431641i
$213$	−13348.1	−	18372.0i	−0.294211	−	0.404947i
$214$	−1709.85	−	1898.98i	−0.0373362	−	0.0414661i
$215$	107428.	−	34905.4i	2.32402	−	0.755119i
$216$			38559.3i			0.826459i
$217$	10837.1	−	30247.0i	0.230141	−	0.642336i
$218$	−371.258			−0.00781201
$219$	−26894.8	−	82773.8i	−0.560765	−	1.72586i
$220$	−1434.31	+	1291.46i	−0.0296346	+	0.0266831i
$221$	9991.41	−	7259.18i	0.204570	−	0.148629i
$222$	−18937.4	−	32800.6i	−0.384251	−	0.665543i
$223$	43392.2	+	25052.5i	0.872573	+	0.503780i	0.868203	−	0.496210i	$-0.165275\pi$
$223$	43392.2	+	25052.5i	0.872573	+	0.503780i	0.00437082	+	0.999990i	$0.498609\pi$
$224$	3550.59	+	33781.6i	0.0707627	+	0.673262i
$225$	15109.1	+	10977.4i	0.298451	+	0.216837i
$226$	−1125.28	+	10706.3i	−0.0220314	+	0.209615i
$227$	−51769.4	+	57495.8i	−1.00467	+	1.11579i	−0.0113999	+	0.999935i	$0.503629\pi$
$227$	−51769.4	+	57495.8i	−1.00467	+	1.11579i	−0.993266	+	0.115859i	$0.963038\pi$
$228$	−14895.9	+	33456.8i	−0.286549	+	0.643599i
$229$	−3009.34	+	14157.8i	−0.0573852	+	0.269976i	−0.997481	−	0.0709343i	$-0.977402\pi$
$229$	−3009.34	+	14157.8i	−0.0573852	+	0.269976i	0.940096	+	0.340910i	$0.110735\pi$
$230$	−5971.32	−	28092.9i	−0.112879	−	0.531056i
$231$	1606.79	−	715.388i	0.0301116	−	0.0134066i
$232$	55933.9	+	18174.0i	1.03920	+	0.337657i
$233$	−21332.0	+	65653.1i	−0.392934	+	1.20933i	0.537625	+	0.843184i	$0.319322\pi$
$233$	−21332.0	+	65653.1i	−0.392934	+	1.20933i	−0.930559	+	0.366142i	$0.880678\pi$
$234$	6438.80	+	14461.8i	0.117591	+	0.264113i
$235$	−101979.	+	21676.2i	−1.84660	+	0.392508i
$236$	−24711.0	−	5252.49i	−0.443677	−	0.0943065i
$237$	17104.9	+	7615.57i	0.304525	+	0.135583i
$238$	2691.57	+	2423.50i	0.0475172	+	0.0427847i
$239$	−53118.4	−	5582.97i	−0.929928	−	0.0977394i	−0.372563	−	0.928007i	$-0.621521\pi$
$239$	−53118.4	−	5582.97i	−0.929928	−	0.0977394i	−0.557365	+	0.830267i	$0.688188\pi$
$240$	1416.43	−	1949.55i	0.0245908	−	0.0338463i
$241$	1519.66	−	159.722i	0.0261645	−	0.00275000i	−0.0914372	−	0.995811i	$-0.529146\pi$
$241$	1519.66	−	159.722i	0.0261645	−	0.00275000i	0.117602	+	0.993061i	$0.462479\pi$
$242$	−18319.2	+	31729.8i	−0.312807	+	0.541797i
$243$	27178.7	−	15691.6i	0.460274	−	0.265739i
$244$	−14569.7	−	20053.4i	−0.244720	−	0.336828i
$245$	−32923.9	−	36565.8i	−0.548504	−	0.609175i
$246$	−50487.4	+	16404.3i	−0.834281	+	0.271074i
$247$		−	106120.i		−	1.73941i
$248$	−29360.2	−	54555.0i	−0.477370	−	0.887016i
$249$	−27781.5			−0.448081
$250$	6545.91	+	20146.2i	0.104734	+	0.322340i
$251$	4945.08	−	4452.57i	0.0784921	−	0.0706746i	−0.628951	−	0.777445i	$-0.716515\pi$
$251$	4945.08	−	4452.57i	0.0784921	−	0.0706746i	0.707443	+	0.706770i	$0.249849\pi$
$252$	5805.17	−	4217.70i	0.0914142	−	0.0664163i
$253$	−773.960	−	1340.54i	−0.0120914	−	0.0209430i
$254$	32022.5	+	18488.2i	0.496350	+	0.286568i
$255$	1758.50	+	16731.0i	0.0270435	+	0.257301i
$256$	53767.1	+	39064.1i	0.820420	+	0.596070i
$257$	2304.50	−	21925.8i	0.0348907	−	0.331963i	−0.963128	−	0.269044i	$-0.913292\pi$
$257$	2304.50	−	21925.8i	0.0348907	−	0.331963i	0.998019	−	0.0629190i	$-0.0200410\pi$
$258$	−50175.0	+	55724.9i	−0.753785	+	0.837163i
$259$	20233.6	−	45445.3i	0.301629	−	0.677469i
$260$	22136.2	−	104143.i	0.327459	−	1.54057i
$261$	−4190.32	−	19713.9i	−0.0615129	−	0.289395i
$262$	−57995.9	+	25821.4i	−0.844880	+	0.376165i
$263$	−28129.0	−	9139.67i	−0.406671	−	0.132135i	0.0985365	−	0.995133i	$-0.468584\pi$
$263$	−28129.0	−	9139.67i	−0.406671	−	0.132135i	−0.505207	+	0.862998i	$0.668584\pi$
$264$	1048.02	−	3225.48i	0.0150371	−	0.0462793i
$265$	62290.1	+	139906.i	0.887007	+	1.99225i
$266$	30441.3	−	6470.50i	0.430230	−	0.0914481i
$267$	−24003.1	−	5102.01i	−0.336701	−	0.0715680i
$268$	48479.9	+	21584.6i	0.674982	+	0.300521i
$269$	−66077.0	−	59496.0i	−0.913157	−	0.822210i	0.0713686	−	0.997450i	$-0.477263\pi$
$269$	−66077.0	−	59496.0i	−0.913157	−	0.822210i	−0.984526	+	0.175240i	$0.943930\pi$
$270$	57183.7	+	6010.25i	0.784413	+	0.0824451i
$271$	−17993.3	+	24765.6i	−0.245003	+	0.337218i	−0.913753	−	0.406269i	$-0.866830\pi$
$271$	−17993.3	+	24765.6i	−0.245003	+	0.337218i	0.668750	+	0.743487i	$0.266830\pi$
$272$	265.981	−	27.9558i	0.00359512	−	0.000377862i
$273$	−48512.4	+	84025.9i	−0.650919	+	1.12743i
$274$	32605.4	−	18824.7i	0.434299	−	0.250743i
$275$	2574.46	+	3543.44i	0.0340424	+	0.0468554i
$276$	−19718.4	−	21899.5i	−0.258853	−	0.287486i
$277$	−7825.38	+	2542.62i	−0.101987	+	0.0331377i	−0.359566	−	0.933120i	$-0.617075\pi$
$277$	−7825.38	+	2542.62i	−0.101987	+	0.0331377i	0.257579	+	0.966257i	$0.417075\pi$
$278$			23345.1i			0.302069i
$279$	−11160.0	+	18061.1i	−0.143369	+	0.232025i
$280$	82649.3			1.05420
$281$	12711.0	+	39120.4i	0.160978	+	0.495439i	0.998717	−	0.0506310i	$-0.0161232\pi$
$281$	12711.0	+	39120.4i	0.160978	+	0.495439i	−0.837740	+	0.546070i	$0.816123\pi$
$282$	51433.3	−	46310.7i	0.646764	−	0.582349i
$283$	−44154.1	+	32079.8i	−0.551313	+	0.400552i	−0.828269	−	0.560330i	$-0.810674\pi$
$283$	−44154.1	+	32079.8i	−0.551313	+	0.400552i	0.276956	+	0.960883i	$0.410674\pi$
$284$	−10863.9	−	18816.8i	−0.134694	−	0.233297i
$285$	125189.	+	72277.9i	1.54126	+	0.889848i
$286$	388.073	+	3692.27i	0.00474440	+	0.0451399i
$287$	−56408.1	−	40982.9i	−0.684822	−	0.497553i
$288$	2346.17	−	22322.3i	0.0282862	−	0.269125i
$289$	54637.1	−	60680.7i	0.654172	−	0.726532i
$290$	35670.7	−	80117.7i	0.424146	−	0.952647i
$291$	16353.0	−	76934.7i	0.193113	−	0.908524i
$292$	−17313.4	−	81453.0i	−0.203056	−	0.955303i
$293$	103857.	−	46240.0i	1.20976	−	0.538621i	0.300075	−	0.953916i	$-0.402988\pi$
$293$	103857.	−	46240.0i	1.20976	−	0.538621i	0.909687	+	0.415295i	$0.136322\pi$
$294$	31065.1	+	10093.7i	0.359401	+	0.116776i
$295$	−30814.1	+	94836.2i	−0.354084	+	1.08976i
$296$	−39015.1	−	87629.3i	−0.445296	−	1.00015i
$297$	3031.23	−	644.309i	0.0343642	−	0.00730434i
$298$	−85915.1	−	18261.8i	−0.967469	−	0.205642i
$299$	78006.9	+	34730.9i	0.872551	+	0.388485i
$300$	61965.9	+	55794.4i	0.688510	+	0.619937i
$301$	−97948.6	−	10294.8i	−1.08110	−	0.113628i
$302$	5784.93	−	7962.27i	0.0634285	−	0.0873018i
$303$	−131174.	+	13787.0i	−1.42877	+	0.150170i
$304$	1149.04	−	1990.19i	0.0124333	−	0.0215351i
$305$	−84731.0	+	48919.5i	−0.910842	+	0.525875i
$306$	−1406.73	−	1936.19i	−0.0150233	−	0.0206779i
$307$	31948.8	+	35482.7i	0.338982	+	0.376478i	0.888400	−	0.459070i	$-0.151817\pi$
$307$	31948.8	+	35482.7i	0.338982	+	0.376478i	−0.549418	+	0.835548i	$0.685150\pi$
$308$	1600.48	−	520.028i	0.0168713	−	0.00548182i
$309$			141411.i			1.48104i
$310$	−85481.9	+	35037.8i	−0.889510	+	0.364598i
$311$	138309.			1.42998			0.714991	−	0.699134i	$-0.246431\pi$
$311$	138309.			1.42998			0.714991	+	0.699134i	$0.246431\pi$
$312$	57813.0	+	177930.i	0.593904	+	1.82785i
$313$	141166.	−	127106.i	1.44093	−	1.29741i	0.556406	−	0.830910i	$-0.312180\pi$
$313$	141166.	−	127106.i	1.44093	−	1.29741i	0.884519	−	0.466504i	$-0.154487\pi$
$314$	62652.2	−	45519.5i	0.635444	−	0.461677i
$315$	−14161.5	−	24528.4i	−0.142721	−	0.247200i
$316$	15514.4	+	8957.26i	0.155368	+	0.0897018i
$317$	−4212.40	−	40078.3i	−0.0419190	−	0.398833i	−0.995283	−	0.0970108i	$-0.969072\pi$
$317$	−4212.40	−	40078.3i	−0.0419190	−	0.398833i	0.953364	−	0.301822i	$-0.0975948\pi$
$318$	−82248.8	−	59757.2i	−0.813346	−	0.590930i
$319$	494.071	−	4700.77i	0.00485521	−	0.0461943i
$320$	67894.0	−	75403.9i	0.663027	−	0.736366i
$321$	−4209.31	+	9454.25i	−0.0408508	+	0.0917524i
$322$	−5206.48	+	24494.6i	−0.0502149	+	0.236242i
$323$	3335.61	+	15692.8i	0.0319720	+	0.150417i
$324$	69777.5	−	31066.9i	0.664699	−	0.295943i
$325$	−229788.	−	74662.8i	−2.17551	−	0.706866i
$326$	−26657.3	+	82042.8i	−0.250831	+	0.771979i
$327$	611.561	+	1373.59i	0.00571931	+	0.0128458i
$328$	−131507.	+	27952.7i	−1.22237	+	0.259822i
$329$	88916.6	+	18899.8i	0.821469	+	0.174609i
$330$	−4620.06	−	2056.98i	−0.0424248	−	0.0188887i
$331$	−16862.9	−	15183.4i	−0.153913	−	0.138584i	0.588577	−	0.808441i	$-0.299689\pi$
$331$	−16862.9	−	15183.4i	−0.153913	−	0.138584i	−0.742490	+	0.669857i	$0.766355\pi$
$332$	−26435.4	−	2778.47i	−0.239833	−	0.0252075i
$333$	−19321.3	+	26593.5i	−0.174240	+	0.239821i
$334$	107819.	−	11332.2i	0.966501	−	0.101583i
$335$	104733.	−	181402.i	0.933239	−	1.61642i
$336$	−1819.62	+	1050.56i	−0.0161177	+	0.00930554i
$337$	−9071.28	−	12485.6i	−0.0798746	−	0.109938i	0.767210	−	0.641396i	$-0.221644\pi$
$337$	−9071.28	−	12485.6i	−0.0798746	−	0.109938i	−0.847085	+	0.531458i	$0.821644\pi$
$338$	−89126.5	−	98985.0i	−0.780142	−	0.866435i
$339$	41465.0	−	13472.8i	0.360813	−	0.117235i
$340$			16096.2i			0.139241i
$341$	−3798.10	+	3219.66i	−0.0326631	+	0.0276886i
$342$	−20564.5			−0.175819
$343$	38063.5	+	117147.i	0.323534	+	0.995736i
$344$	−141129.	+	127074.i	−1.19262	+	1.07384i
$345$	−94102.2	+	68369.2i	−0.790608	+	0.574411i
$346$	29146.2	+	50482.6i	0.243461	+	0.421686i
$347$	−38037.9	−	21961.2i	−0.315906	−	0.182388i	0.333661	−	0.942693i	$-0.391716\pi$
$347$	−38037.9	−	21961.2i	−0.315906	−	0.182388i	−0.649566	+	0.760305i	$0.725049\pi$
$348$	−9405.93	−	89491.5i	−0.0776682	−	0.738964i
$349$	591.600	+	429.823i	0.00485711	+	0.00352889i	0.590211	−	0.807249i	$-0.299044\pi$
$349$	591.600	+	429.823i	0.00485711	+	0.00352889i	−0.585354	+	0.810778i	$0.699044\pi$
$350$	7406.60	−	70469.0i	0.0604620	−	0.575258i
$351$	−114388.	+	127041.i	−0.928466	+	1.03117i
$352$	2141.04	−	4808.86i	0.0172799	−	0.0388112i
$353$	−34778.2	+	163619.i	−0.279099	+	1.31306i	0.585533	+	0.810649i	$0.300885\pi$
$353$	−34778.2	+	163619.i	−0.279099	+	1.31306i	−0.864631	+	0.502407i	$0.832448\pi$
$354$	−13763.0	−	64749.8i	−0.109826	−	0.516692i
$355$	−78347.8	+	34882.7i	−0.621685	+	0.276792i
$356$	−22329.8	−	7255.39i	−0.176191	−	0.0572481i
$357$	4532.78	−	13950.4i	0.0355654	−	0.109459i
$358$	39775.9	+	89338.1i	0.310352	+	0.697061i
$359$	−57191.7	+	12156.5i	−0.443756	+	0.0943232i	−0.424370	−	0.905489i	$-0.639504\pi$
$359$	−57191.7	+	12156.5i	−0.443756	+	0.0943232i	−0.0193858	+	0.999812i	$0.506171\pi$
$360$	−53419.9	−	11354.7i	−0.412190	−	0.0876138i
$361$	6883.02	+	3064.52i	0.0528159	+	0.0235152i
$362$	−26645.1	−	23991.4i	−0.203329	−	0.183079i
$363$	147571.	+	15510.4i	1.11992	+	0.117709i
$364$	−54565.4	+	75102.8i	−0.411827	+	0.566831i
$365$	−326887.	+	34357.2i	−2.45365	+	0.257889i
$366$	32474.9	−	56248.2i	0.242430	−	0.419900i
$367$	172027.	−	99319.6i	1.27721	−	0.737399i	0.300878	−	0.953663i	$-0.402720\pi$
$367$	172027.	−	99319.6i	1.27721	−	0.737399i	0.976335	+	0.216263i	$0.0693870\pi$
$368$	1086.90	+	1495.99i	0.00802590	+	0.0110467i
$369$	30828.6	+	34238.7i	0.226413	+	0.251457i
$370$	−136036.	+	44200.9i	−0.993691	+	0.322870i
$371$		−	133530.i		−	0.970134i
$372$	−57982.8	+	74988.6i	−0.418999	+	0.541888i
$373$	243163.			1.74775			0.873874	−	0.486152i	$-0.161600\pi$
$373$	243163.			1.74775			0.873874	+	0.486152i	$0.161600\pi$
$374$	−173.444	−	533.807i	−0.00123999	−	0.00381629i
$375$	63754.5	−	57404.9i	0.453366	−	0.408212i
$376$	141807.	−	103029.i	1.00305	−	0.728756i
$377$	130371.	+	225808.i	0.917269	+	1.58876i
$378$	−43417.3	−	25067.0i	−0.303864	−	0.175436i
$379$	−9207.45	−	87603.0i	−0.0641004	−	0.609875i	−0.978669	−	0.205444i	$-0.934136\pi$
$379$	−9207.45	−	87603.0i	−0.0641004	−	0.609875i	0.914569	−	0.404431i	$-0.132530\pi$
$380$	111895.	+	81296.2i	0.774894	+	0.562993i
$381$	15653.5	−	148933.i	0.107835	−	1.02598i
$382$	−64672.5	+	71826.0i	−0.443193	+	0.492215i
$383$	−19783.6	+	44434.8i	−0.134868	+	0.302918i	−0.968337	−	0.249649i	$-0.919685\pi$
$383$	−19783.6	+	44434.8i	−0.134868	+	0.302918i	0.833469	+	0.552567i	$0.186352\pi$
$384$	20311.3	−	95557.4i	0.137745	−	0.648040i
$385$	−1381.03	−	6497.25i	−0.00931714	−	0.0438337i
$386$	100273.	−	44644.2i	0.672988	−	0.299634i
$387$	61894.1	+	20110.6i	0.413264	+	0.134278i
$388$	23255.0	−	71571.5i	0.154473	−	0.475419i
$389$	−72445.1	−	162714.i	−0.478751	−	1.07529i	−0.977956	−	0.208809i	$-0.933041\pi$
$389$	−72445.1	−	162714.i	−0.478751	−	1.07529i	0.499205	−	0.866484i	$-0.333625\pi$
$390$	272883.	−	58003.0i	1.79410	−	0.381348i
$391$	−12627.2	−	2683.99i	−0.0825949	−	0.0175561i
$392$	75572.8	+	33647.2i	0.491805	+	0.218966i
$393$	191069.	+	172040.i	1.23710	+	1.11389i
$394$	75737.8	+	7960.37i	0.487888	+	0.0512791i
$395$	41562.8	−	57206.3i	0.266386	−	0.366648i
$396$	−1105.90	+	116.235i	−0.00705224	+	0.000741221i
$397$	−94419.4	+	163539.i	−0.599074	+	1.03763i	0.393884	+	0.919160i	$0.371131\pi$
$397$	−94419.4	+	163539.i	−0.599074	+	1.03763i	−0.992958	+	0.118466i	$0.962202\pi$
$398$	−25640.5	+	14803.6i	−0.161868	+	0.0934545i
$399$	−74084.6	−	101969.i	−0.465353	−	0.640503i
$400$	−3501.06	−	3888.33i	−0.0218817	−	0.0243020i
$401$	−19828.4	+	6442.64i	−0.123310	+	0.0400659i	−0.370022	−	0.929023i	$-0.620650\pi$
$401$	−19828.4	+	6442.64i	−0.123310	+	0.0400659i	0.246712	+	0.969089i	$0.420650\pi$
$402$			139052.i			0.860451i
$403$	65107.6	−	266840.i	0.400887	−	1.64301i
$404$	−126197.			−0.773192
$405$	−93164.1	−	286730.i	−0.567987	−	1.74808i
$406$	−56825.8	+	51166.1i	−0.344741	+	0.310406i
$407$	−6236.82	+	4531.31i	−0.0376508	+	0.0273549i
$408$	−14142.0	−	24494.7i	−0.0849556	−	0.147147i
$409$	−81271.6	−	46922.2i	−0.485839	−	0.280499i	0.237008	−	0.971508i	$-0.423833\pi$
$409$	−81271.6	−	46922.2i	−0.485839	−	0.280499i	−0.722847	+	0.691008i	$0.757167\pi$
$410$	20956.0	+	199383.i	0.124664	+	1.18610i
$411$	−123358.	−	89624.8i	−0.730270	−	0.530572i
$412$	−14142.8	+	134559.i	−0.0833182	+	0.792719i
$413$	58177.1	−	64612.3i	0.341077	−	0.378804i
$414$	6730.35	−	15116.6i	0.0392679	−	0.0881971i
$415$	−21813.8	+	102626.i	−0.126659	+	0.595883i
$416$	60373.4	+	284034.i	0.348866	+	1.64129i
$417$	86372.7	−	38455.6i	0.496712	−	0.221150i
$418$	−4586.82	−	1490.35i	−0.0262518	−	0.00852973i
$419$	18249.8	−	56167.2i	0.103951	−	0.319930i	−0.885531	−	0.464579i	$-0.846206\pi$
$419$	18249.8	−	56167.2i	0.103951	−	0.319930i	0.989483	+	0.144650i	$0.0462055\pi$
$420$	−51434.0	−	115523.i	−0.291576	−	0.654891i
$421$	53149.8	−	11297.3i	0.299873	−	0.0637399i	−0.0555182	−	0.998458i	$-0.517681\pi$
$421$	53149.8	−	11297.3i	0.299873	−	0.0637399i	0.355391	+	0.934718i	$0.384348\pi$
$422$	−86179.0	−	18317.9i	−0.483923	−	0.102861i
$423$	−54874.2	−	24431.6i	−0.306681	−	0.136543i
$424$	−191343.	−	172286.i	−1.06434	−	0.958338i
$425$	36327.5	+	3818.17i	0.201121	+	0.0211387i
$426$	33464.3	−	46059.6i	0.184401	−	0.253806i
$427$	84839.9	−	8917.03i	0.465312	−	0.0489063i
$428$	−4950.89	+	8575.19i	−0.0270269	+	0.0468119i
$429$	13021.5	−	7517.94i	0.0707530	−	0.0408493i
$430$	166453.	+	229103.i	0.900233	+	1.23906i
$431$	49967.6	+	55494.6i	0.268988	+	0.298742i	0.862473	−	0.506104i	$-0.168915\pi$
$431$	49967.6	+	55494.6i	0.268988	+	0.298742i	−0.593484	+	0.804846i	$0.702248\pi$
$432$	−3520.82	+	1143.98i	−0.0188658	+	0.00612988i
$433$		−	303174.i		−	1.61702i	−0.588482	−	0.808510i	$-0.700274\pi$
$433$		−	303174.i		−	1.61702i	0.588482	−	0.808510i	$-0.299726\pi$
$434$	80515.0	+	2406.45i	0.427462	+	0.0127761i
$435$	−355180.			−1.87702
$436$	444.554	+	1368.20i	0.00233858	+	0.00719740i
$437$	−82433.4	+	74223.4i	−0.431659	+	0.388667i
$438$	176525.	−	128253.i	0.920151	−	0.668529i
$439$	−5374.07	−	9308.16i	−0.0278852	−	0.0482986i	0.851746	−	0.523955i	$-0.175544\pi$
$439$	−5374.07	−	9308.16i	−0.0278852	−	0.0482986i	−0.879631	+	0.475656i	$0.842211\pi$
$440$	−11092.2	−	6404.06i	−0.0572942	−	0.0330788i
$441$	−2963.25	−	28193.5i	−0.0152367	−	0.144968i
$442$	25049.0	+	18199.1i	0.128217	+	0.0931550i
$443$	−503.399	+	4789.52i	−0.00256510	+	0.0244053i	−0.995730	−	0.0923179i	$-0.970572\pi$
$443$	−503.399	+	4789.52i	−0.00256510	+	0.0244053i	0.993164	+	0.116723i	$0.0372391\pi$
$444$	−98203.8	+	109066.i	−0.498153	+	0.553255i
$445$	−37694.1	+	84662.2i	−0.190350	+	0.427533i
$446$	−26117.0	+	122871.i	−0.131297	+	0.617702i
$447$	73959.6	+	347952.i	0.370151	+	1.74143i
$448$	−80821.0	+	35983.8i	−0.402688	+	0.179288i
$449$	232602.	+	75576.8i	1.15377	+	0.374883i	0.822563	−	0.568674i	$-0.192543\pi$
$449$	232602.	+	75576.8i	1.15377	+	0.374883i	0.331209	+	0.943557i	$0.392543\pi$
$450$	−14468.6	+	44529.7i	−0.0714497	+	0.219900i
$451$	4394.85	+	9870.99i	0.0216068	+	0.0485297i
$452$	40803.3	−	8673.01i	0.199719	−	0.0424515i
$453$	−38988.3	−	8287.21i	−0.189993	−	0.0403843i
$454$	−177197.	−	78893.0i	−0.859694	−	0.382760i
$455$	272303.	+	245183.i	1.31532	+	1.18432i
$456$	−241704.	−	25404.1i	−1.16240	−	0.122173i
$457$	−89084.0	+	122614.i	−0.426547	+	0.587092i	−0.967156	−	0.254182i	$-0.918194\pi$
$457$	−89084.0	+	122614.i	−0.426547	+	0.587092i	0.540609	+	0.841274i	$0.318194\pi$
$458$	−36088.5	+	3793.06i	−0.172044	+	0.0180825i
$459$	12922.3	−	22382.0i	0.0613357	−	0.106237i
$460$	−96380.3	+	55645.2i	−0.455484	+	0.262974i
$461$	9681.10	+	13324.9i	0.0455536	+	0.0626992i	0.831186	−	0.555994i	$-0.187662\pi$
$461$	9681.10	+	13324.9i	0.0455536	+	0.0626992i	−0.785633	+	0.618693i	$0.787662\pi$
$462$	2950.54	+	3276.91i	0.0138235	+	0.0153526i
$463$	−27360.8	+	8890.07i	−0.127634	+	0.0414709i	−0.372138	−	0.928178i	$-0.621375\pi$
$463$	−27360.8	+	8890.07i	−0.127634	+	0.0414709i	0.244503	+	0.969648i	$0.421375\pi$
$464$			5646.47i			0.0262265i
$465$	270445.	+	258551.i	1.25076	+	1.19575i
$466$	−173066.			−0.796967
$467$	−30373.0	−	93478.4i	−0.139269	−	0.428625i	0.856961	−	0.515381i	$-0.172350\pi$
$467$	−30373.0	−	93478.4i	−0.139269	−	0.428625i	−0.996230	+	0.0867566i	$0.972350\pi$
$468$	45586.0	−	41045.8i	0.208132	−	0.187403i
$469$	−147756.	+	107351.i	−0.671735	+	0.488044i
$470$	−130689.	−	226359.i	−0.591619	−	1.02471i
$471$	−271619.	−	156819.i	−1.22438	−	0.706899i
$472$	−17524.1	−	166731.i	−0.0786597	−	0.748397i
$473$	12347.8	+	8971.17i	0.0551907	+	0.0400984i
$474$	−4906.67	+	46683.9i	−0.0218389	+	0.207783i
$475$	210019.	−	233250.i	0.930834	−	1.03380i
$476$	5708.36	−	12821.2i	0.0251940	−	0.0565867i
$477$	−18345.0	+	86306.4i	−0.0806271	+	0.379321i
$478$	−27840.2	−	130978.i	−0.121848	−	0.573248i
$479$	−182041.	+	81049.9i	−0.793412	+	0.353250i	−0.763091	−	0.646291i	$-0.776319\pi$
$479$	−182041.	+	81049.9i	−0.793412	+	0.353250i	−0.0303202	+	0.999540i	$0.509653\pi$
$480$	−376194.	−	122233.i	−1.63279	−	0.530524i
$481$	131414.	−	404451.i	0.568005	−	1.74814i
$482$	1558.14	+	3499.65i	0.00670678	+	0.0150637i
$483$	99201.9	−	21086.0i	0.425232	−	0.0903858i
$484$	138870.	+	29517.7i	0.592812	+	0.126006i
$485$	−271360.	−	120817.i	−1.15362	−	0.513623i
$486$	58470.2	+	52646.8i	0.247549	+	0.222895i
$487$	60727.8	+	6382.75i	0.256053	+	0.0269122i	0.231685	−	0.972791i	$-0.425576\pi$
$487$	60727.8	+	6382.75i	0.256053	+	0.0269122i	0.0243677	+	0.999703i	$0.492243\pi$
$488$	96686.2	−	133077.i	0.405999	−	0.558810i
$489$	347455.	−	36519.0i	1.45305	−	0.152722i
$490$	61678.5	−	106830.i	0.256887	−	0.444941i
$491$	−295013.	+	170326.i	−1.22371	+	0.706508i	−0.965706	−	0.259637i	$-0.916397\pi$
$491$	−295013.	+	170326.i	−1.22371	+	0.706508i	−0.258001	+	0.966145i	$0.583064\pi$
$492$	120910.	+	166418.i	0.499495	+	0.687496i
$493$	−26376.7	−	29294.2i	−0.108524	−	0.120528i
$494$	253027.	−	82213.3i	1.03684	−	0.336890i
$495$			4389.19i			0.0179132i
$496$	4110.31	−	4299.40i	0.0167075	−	0.0174761i
$497$	74777.4			0.302732
$498$	−21522.9	−	66240.7i	−0.0867845	−	0.267095i
$499$	−62705.0	+	56459.8i	−0.251826	+	0.226745i	−0.785369	−	0.619028i	$-0.787527\pi$
$499$	−62705.0	+	56459.8i	−0.251826	+	0.226745i	0.533543	+	0.845773i	$0.320860\pi$
$500$	66406.6	−	48247.2i	0.265626	−	0.192989i
$501$	−219534.	−	380244.i	−0.874633	−	1.51491i
$502$	14447.5	+	8341.29i	0.0573306	+	0.0330998i
$503$	31041.0	+	295336.i	0.122687	+	1.16729i	0.866595	+	0.499011i	$0.166303\pi$
$503$	31041.0	+	295336.i	0.122687	+	1.16729i	−0.743908	+	0.668282i	$0.767030\pi$
$504$	38523.9	+	27989.2i	0.151659	+	0.110187i
$505$	−52067.4	+	495388.i	−0.204166	+	1.94251i
$506$	2596.70	−	2883.93i	0.0101420	−	0.0112638i
$507$	−219412.	+	492807.i	−0.853579	+	1.91717i
$508$	29790.0	−	140151.i	0.115436	−	0.543086i
$509$	−59852.5	−	281584.i	−0.231018	−	1.08686i	−0.928810	−	0.370555i	$-0.879167\pi$
$509$	−59852.5	−	281584.i	−0.231018	−	1.08686i	0.697792	−	0.716300i	$-0.254166\pi$
$510$	−38530.2	+	17154.8i	−0.148136	+	0.0659544i
$511$	272561.	+	88560.5i	1.04381	+	0.339155i
$512$	−3916.07	+	12052.4i	−0.0149386	+	0.0459763i
$513$	−90325.4	−	202874.i	−0.343222	−	0.770889i
$514$	54064.1	−	11491.7i	0.204636	−	0.0434968i
$515$	522378.	+	111035.i	1.96957	+	0.418644i
$516$	265444.	+	118183.i	0.996950	+	0.443871i
$517$	−10468.8	−	9426.18i	−0.0391667	−	0.0352659i
$518$	124033.	+	13036.4i	0.462250	+	0.0485844i
$519$	138765.	−	190994.i	0.515164	−	0.709062i
$520$	702674.	−	73854.1i	2.59865	−	0.273129i
$521$	54885.7	−	95064.8i	0.202201	−	0.350223i	−0.747036	−	0.664783i	$-0.768524\pi$
$521$	54885.7	−	95064.8i	0.202201	−	0.350223i	0.949237	+	0.314561i	$0.101857\pi$
$522$	43758.4	−	25263.9i	0.160591	−	0.0927172i
$523$	86331.3	+	118825.i	0.315620	+	0.434414i	0.937124	−	0.348997i	$-0.113478\pi$
$523$	86331.3	+	118825.i	0.315620	+	0.434414i	−0.621503	+	0.783411i	$0.713478\pi$
$524$	164606.	+	182813.i	0.599490	+	0.665801i
$525$	−272923.	+	88678.2i	−0.990198	+	0.321735i
$526$		−	74150.0i		−	0.268003i
$527$	−1240.55	+	41506.3i	−0.00446677	+	0.149449i
$528$	325.609			0.00116796
$529$	58894.1	+	181257.i	0.210456	+	0.647715i
$530$	−285327.	+	256909.i	−1.01576	+	0.914593i
$531$	−46479.2	+	33769.1i	−0.164843	+	0.119765i
$532$	−60297.0	−	104437.i	−0.213045	−	0.369005i
$533$	−516197.	−	298026.i	−1.81703	−	1.04906i
$534$	−6430.73	−	61184.3i	−0.0225516	−	0.214564i
$535$	31619.3	+	22972.7i	0.110470	+	0.0802611i
$536$	−36811.3	+	350236.i	−0.128130	+	1.21908i
$537$	265013.	−	294327.i	0.919008	−	1.02066i
$538$	90667.8	−	203643.i	0.313248	−	0.703567i
$539$	1382.29	−	6503.18i	0.00475798	−	0.0223845i
$540$	−46323.7	−	217936.i	−0.158860	−	0.747379i
$541$	321415.	−	143103.i	1.09817	−	0.488939i	0.224019	−	0.974585i	$-0.428082\pi$
$541$	321415.	−	143103.i	1.09817	−	0.488939i	0.874156	+	0.485646i	$0.161416\pi$
$542$	−72989.6	−	23715.8i	−0.248464	−	0.0807307i
$543$	−44872.1	+	138102.i	−0.152187	+	0.468383i
$544$	−17855.8	−	40104.8i	−0.0603367	−	0.135518i
$545$	5554.28	−	1180.60i	0.0186997	−	0.00397474i
$546$	−237930.	−	50573.7i	−0.798114	−	0.169644i
$547$	−199845.	−	88976.5i	−0.667910	−	0.297373i	0.0446309	−	0.999004i	$-0.485789\pi$
$547$	−199845.	−	88976.5i	−0.667910	−	0.297373i	−0.712540	+	0.701631i	$0.752456\pi$
$548$	−108417.	−	97619.4i	−0.361025	−	0.325069i
$549$	−56060.8	−	5892.23i	−0.186001	−	0.0195495i
$550$	−6454.30	+	8883.58i	−0.0213365	+	0.0293672i
$551$	−336861.	+	35405.5i	−1.10955	+	0.116619i
$552$	97779.1	−	169358.i	0.320899	−	0.555813i
$553$	−53393.8	+	30826.9i	−0.174599	+	0.100805i
$554$	−12125.0	−	16688.6i	−0.0395058	−	0.0543751i
$555$	387623.	+	430499.i	1.25841	+	1.39761i
$556$	86033.7	−	27954.1i	0.278304	−	0.0904264i
$557$		−	138224.i		−	0.445527i	−0.974873	−	0.222763i	$-0.928492\pi$
$557$		−	138224.i		−	0.445527i	0.974873	−	0.222763i	$-0.0715077\pi$
$558$	−51709.8	−	12616.9i	−0.166075	−	0.0405214i
$559$	−841947.			−2.69439
$560$	2452.05	+	7546.64i	0.00781904	+	0.0240645i
$561$	−1689.28	+	1521.03i	−0.00536755	+	0.00483296i
$562$	−83429.0	+	60614.8i	−0.264146	+	0.191914i
$563$	245710.	+	425582.i	0.775186	+	1.34266i	0.934690	+	0.355464i	$0.115677\pi$
$563$	245710.	+	425582.i	0.775186	+	1.34266i	−0.159504	+	0.987197i	$0.550989\pi$
$564$	−232256.	−	134093.i	−0.730146	−	0.421550i
$565$	−17211.0	−	163752.i	−0.0539150	−	0.512967i
$566$	−110697.	−	80425.8i	−0.345542	−	0.251051i
$567$	−27477.3	+	261429.i	−0.0854690	+	0.813183i
$568$	96481.0	−	107153.i	0.299051	−	0.332130i
$569$	70581.6	−	158529.i	0.218005	−	0.489648i	−0.771126	−	0.636682i	$-0.780306\pi$
$569$	70581.6	−	158529.i	0.218005	−	0.489648i	0.989131	+	0.147035i	$0.0469729\pi$
$570$	−75349.0	+	354489.i	−0.231915	+	1.09107i
$571$	46656.0	+	219499.i	0.143099	+	0.673226i	0.989952	+	0.141400i	$0.0451605\pi$
$571$	46656.0	+	219499.i	0.143099	+	0.673226i	−0.846854	+	0.531826i	$0.821506\pi$
$572$	13142.4	−	5851.38i	0.0401682	−	0.0178841i
$573$	372276.	+	120960.i	1.13385	+	0.368410i
$574$	54016.9	−	166247.i	0.163948	−	0.504580i
$575$	102723.	+	230720.i	0.310694	+	0.697830i
$576$	57181.8	−	12154.4i	0.172351	−	0.0366343i
$577$	−625954.	−	133051.i	−1.88014	−	0.399637i	−0.882627	−	0.470074i	$-0.844227\pi$
$577$	−625954.	−	133051.i	−1.88014	−	0.399637i	−0.997516	+	0.0704371i	$0.977561\pi$
$578$	187012.	+	83263.2i	0.559776	+	0.249228i
$579$	−330351.	−	297449.i	−0.985414	−	0.887270i
$580$	−337970.	−	35522.1i	−1.00467	−	0.105595i
$581$	53770.6	−	74008.9i	0.159292	−	0.219246i
$582$	196108.	−	20611.8i	0.578961	−	0.0608513i
$583$	−10346.6	+	17920.8i	−0.0304410	+	0.0527253i
$584$	478573.	−	276304.i	1.40321	−	0.810144i
$585$	−142317.	−	195883.i	−0.415859	−	0.572380i
$586$	190712.	+	211808.i	0.555372	+	0.616803i
$587$	−95572.3	+	31053.3i	−0.277368	+	0.0901222i	−0.444398	−	0.895830i	$-0.646582\pi$
$587$	−95572.3	+	31053.3i	−0.277368	+	0.0901222i	0.167030	+	0.985952i	$0.446582\pi$
$588$		−	126571.i		−	0.366082i
$589$	282270.	+	218257.i	0.813643	+	0.629126i
$590$	−249995.			−0.718169
$591$	−95308.4	−	293329.i	−0.272870	−	0.839809i
$592$	6843.85	−	6162.23i	0.0195280	−	0.0175831i
$593$	−286919.	+	208459.i	−0.815924	+	0.592804i	−0.915542	−	0.402222i	$-0.868238\pi$
$593$	−286919.	+	208459.i	−0.815924	+	0.592804i	0.0996178	+	0.995026i	$0.468238\pi$
$594$	3884.62	+	6728.35i	0.0110097	+	0.0190693i
$595$	−47974.4	−	27698.0i	−0.135511	−	0.0782375i
$596$	35576.7	+	338490.i	0.100155	+	0.952913i
$597$	97007.3	+	70479.9i	0.272180	+	0.197750i
$598$	−22376.9	+	212902.i	−0.0625746	+	0.595358i
$599$	194114.	−	215586.i	0.541008	−	0.600850i	−0.409208	−	0.912441i	$-0.634195\pi$
$599$	194114.	−	215586.i	0.541008	−	0.600850i	0.950216	+	0.311591i	$0.100862\pi$
$600$	−225065.	+	505504.i	−0.625181	+	1.40418i
$601$	−58754.6	+	276419.i	−0.162665	+	0.765277i	0.818868	+	0.573982i	$0.194602\pi$
$601$	−58754.6	+	276419.i	−0.162665	+	0.765277i	−0.981533	+	0.191295i	$0.938731\pi$
$602$	−51336.5	−	241519.i	−0.141655	−	0.666436i
$603$	110249.	−	49086.1i	0.303208	−	0.134997i
$604$	−36270.4	−	11785.0i	−0.0994210	−	0.0323038i
$605$	173168.	−	532955.i	0.473103	−	1.45606i
$606$	−134496.	−	302084.i	−0.366239	−	0.822587i
$607$	−546010.	+	116058.i	−1.48192	+	0.314991i	−0.876687	−	0.481061i	$-0.840252\pi$
$607$	−546010.	+	116058.i	−1.48192	+	0.314991i	−0.605228	+	0.796052i	$0.706918\pi$
$608$	−368976.	−	78428.2i	−0.998138	−	0.212161i
$609$	282913.	+	125961.i	0.762812	+	0.339626i
$610$	−182284.	−	164129.i	−0.489879	−	0.441089i
$611$	772847.	+	81229.5i	2.07020	+	0.217586i
$612$	−5450.99	+	7502.65i	−0.0145537	+	0.0200314i
$613$	−478993.	+	50344.2i	−1.27470	+	0.133976i	−0.717592	−	0.696463i	$-0.754756\pi$
$613$	−478993.	+	50344.2i	−1.27470	+	0.133976i	−0.557108	+	0.830440i	$0.688089\pi$
$614$	−59851.6	+	103666.i	−0.158759	+	0.274979i
$615$	703160.	−	405970.i	1.85911	−	1.07336i
$616$	6564.14	+	9034.77i	0.0172988	+	0.0238098i
$617$	−223548.	−	248275.i	−0.587220	−	0.652174i	0.374171	−	0.927360i	$-0.377927\pi$
$617$	−223548.	−	248275.i	−0.587220	−	0.652174i	−0.961391	+	0.275186i	$0.911261\pi$
$618$	−337173.	+	109554.i	−0.882828	+	0.286848i
$619$			151445.i			0.395251i	0.980278	+	0.197625i	$0.0633230\pi$
$619$			151445.i			0.395251i	−0.980278	+	0.197625i	$0.936677\pi$
$620$	231483.	+	273071.i	0.602193	+	0.710383i
$621$	178691.			0.463361
$622$	107151.	+	329777.i	0.276959	+	0.852393i
$623$	60049.1	−	54068.5i	0.154714	−	0.139305i
$624$	−14531.4	+	10557.7i	−0.0373198	+	0.0271144i
$625$	102176.	+	176974.i	0.261570	+	0.453053i
$626$	412430.	+	238117.i	1.05245	+	0.607633i
$627$	2041.69	+	19425.4i	0.00519344	+	0.0494123i
$628$	−242774.	−	176386.i	−0.615578	−	0.447244i
$629$	−6720.38	+	63940.1i	−0.0169860	+	0.161611i
$630$	47513.0	−	52768.5i	0.119710	−	0.132952i
$631$	87793.1	−	197186.i	0.220496	−	0.495243i	−0.769097	−	0.639131i	$-0.779294\pi$
$631$	87793.1	−	197186.i	0.220496	−	0.495243i	0.989594	+	0.143888i	$0.0459606\pi$
$632$	−24717.2	+	116285.i	−0.0618821	+	0.291133i
$633$	74186.7	+	349021.i	0.185148	+	0.871052i
$634$	92297.1	−	41093.3i	0.229620	−	0.102233i
$635$	−537872.	−	174765.i	−1.33393	−	0.433419i
$636$	−121736.	+	374666.i	−0.300958	+	0.926254i
$637$	149173.	+	335047.i	0.367629	+	0.825709i
$638$	11591.0	−	2463.75i	0.0284761	−	0.00605279i
$639$	−48331.9	−	10273.3i	−0.118367	−	0.0251598i
$640$	−337044.	−	150062.i	−0.822862	−	0.366362i
$641$	22463.9	+	20226.6i	0.0546726	+	0.0492275i	0.696014	−	0.718028i	$-0.254955\pi$
$641$	22463.9	+	20226.6i	0.0546726	+	0.0492275i	−0.641341	+	0.767256i	$0.721622\pi$
$642$	−25803.3	−	2712.03i	−0.0626043	−	0.00657998i
$643$	−237371.	+	326714.i	−0.574125	+	0.790216i	−0.993036	−	0.117812i	$-0.962412\pi$
$643$	−237371.	+	326714.i	−0.574125	+	0.790216i	0.418911	+	0.908027i	$0.362412\pi$
$644$	96504.1	−	10143.0i	0.232688	−	0.0244565i
$645$	573447.	−	993240.i	1.37840	−	2.38745i
$646$	−34832.9	+	20110.8i	−0.0834689	+	0.0481908i
$647$	−59371.3	−	81717.5i	−0.141830	−	0.195212i	0.732193	−	0.681098i	$-0.238497\pi$
$647$	−59371.3	−	81717.5i	−0.141830	−	0.195212i	−0.874022	+	0.485886i	$0.838497\pi$
$648$	339165.	+	376681.i	0.807721	+	0.897065i
$649$	−12814.3	+	4163.61i	−0.0304232	+	0.00988510i
$650$		−	605738.i		−	1.43370i
$651$	−123726.	−	301855.i	−0.291944	−	0.712256i
$652$	334272.			0.786331
$653$	52961.5	+	162999.i	0.124203	+	0.382259i	0.993755	−	0.111583i	$-0.0355921\pi$
$653$	52961.5	+	162999.i	0.124203	+	0.382259i	−0.869552	+	0.493842i	$0.835592\pi$
$654$	−2801.32	+	2522.32i	−0.00654949	+	0.00589718i
$655$	785547.	−	570733.i	1.83101	−	1.33030i
$656$	−6453.90	−	11178.5i	−0.0149974	−	0.0259762i
$657$	−164001.	−	94686.2i	−0.379941	−	0.219359i
$658$	23821.9	+	226650.i	0.0550205	+	0.523485i
$659$	−125117.	−	90902.6i	−0.288101	−	0.209317i	0.434342	−	0.900748i	$-0.356981\pi$
$659$	−125117.	−	90902.6i	−0.288101	−	0.209317i	−0.722443	+	0.691431i	$0.756981\pi$
$660$	−2048.42	+	19489.4i	−0.00470252	+	0.0447415i
$661$	299496.	−	332624.i	0.685470	−	0.761292i	−0.295523	−	0.955336i	$-0.595494\pi$
$661$	299496.	−	332624.i	0.685470	−	0.761292i	0.980993	+	0.194044i	$0.0621605\pi$
$662$	23138.5	−	51969.9i	0.0527982	−	0.118587i
$663$	26071.2	−	122655.i	0.0593109	−	0.279036i
$664$	−36674.6	−	172540.i	−0.0831820	−	0.391341i
$665$	−434847.	+	193606.i	−0.983317	+	0.437801i
$666$	−78376.8	−	25466.2i	−0.176701	−	0.0574137i
$667$	84221.9	−	259208.i	0.189310	−	0.582636i
$668$	−170868.	−	383776.i	−0.382920	−	0.860052i
$669$	497621.	−	105773.i	1.11185	−	0.236331i
$670$	513665.	+	109183.i	1.14427	+	0.243223i
$671$	−12077.1	−	5377.07i	−0.0268236	−	0.0119426i
$672$	256302.	+	230776.i	0.567563	+	0.511036i
$673$	541781.	+	56943.5i	1.19617	+	0.125723i	0.681601	−	0.731724i	$-0.261284\pi$
$673$	541781.	+	56943.5i	1.19617	+	0.125723i	0.514572	+	0.857447i	$0.327951\pi$
$674$	22742.2	−	31301.9i	0.0500624	−	0.0689050i
$675$	−502847.	+	52851.3i	−1.10364	+	0.115997i
$676$	−258067.	+	446985.i	−0.564728	+	0.978137i
$677$	402432.	−	232344.i	0.878043	−	0.506938i	0.00803014	−	0.999968i	$-0.497444\pi$
$677$	402432.	−	232344.i	0.878043	−	0.506938i	0.870013	+	0.493030i	$0.164111\pi$
$678$	64247.5	+	88429.2i	0.139765	+	0.192369i
$679$	173300.	+	192470.i	0.375889	+	0.417468i
$680$	−101589.	+	33008.2i	−0.219699	+	0.0713845i
$681$			785553.i			1.69388i
$682$	−10619.3	−	6561.65i	−0.0228310	−	0.0141073i
$683$	−659379.			−1.41349			−0.706747	−	0.707467i	$-0.749838\pi$
$683$	−659379.			−1.41349			−0.706747	+	0.707467i	$0.749838\pi$
$684$	24624.5	+	75786.4i	0.0526326	+	0.161986i
$685$	−427937.	+	385316.i	−0.912008	+	0.821176i
$686$	−249831.	+	181513.i	−0.530883	+	0.385709i
$687$	73481.0	+	127273.i	0.155690	+	0.269664i
$688$	−15790.0	−	9116.37i	−0.0333584	−	0.0192595i
$689$	−119320.	−	1.13526e6i	−0.251348	−	2.39142i
$690$	−235919.	−	171405.i	−0.495524	−	0.360019i
$691$	−550.336	+	5236.09i	−0.00115258	+	0.0109661i	−0.995083	−	0.0990438i	$-0.968422\pi$
$691$	−550.336	+	5236.09i	−0.00115258	+	0.0109661i	0.993930	+	0.110010i	$0.0350883\pi$
$692$	151143.	−	167861.i	0.315628	−	0.350541i
$693$	1556.58	−	3496.14i	0.00324119	−	0.00727984i
$694$	22894.3	−	107709.i	0.0475345	−	0.223632i
$695$	−74237.4	−	349259.i	−0.153693	−	0.723067i
$696$	545522.	−	242882.i	1.12614	−	0.501392i
$697$	85701.9	+	27846.2i	0.176411	+	0.0573193i
$698$	−566.521	+	1743.57i	−0.00116280	+	0.00357873i
$699$	285086.	+	640313.i	0.583474	+	1.31050i
$700$	−268568.	+	57085.9i	−0.548099	+	0.116502i
$701$	123587.	+	26269.3i	0.251500	+	0.0534580i	0.331936	−	0.943302i	$-0.392298\pi$
$701$	123587.	+	26269.3i	0.251500	+	0.0534580i	−0.0804364	+	0.996760i	$0.525631\pi$
$702$	−391528.	−	174319.i	−0.794490	−	0.353730i
$703$	410544.	+	369656.i	0.830710	+	0.747975i
$704$	13635.0	+	1433.10i	0.0275112	+	0.00289154i
$705$	−622210.	+	856398.i	−1.25187	+	1.72305i
$706$	−417067.	+	43835.5i	−0.836751	+	0.0879460i
$707$	217157.	−	376128.i	0.434446	−	0.752483i
$708$	−222142.	+	128254.i	−0.443164	+	0.255861i
$709$	373095.	+	513522.i	0.742211	+	1.02157i	0.998488	+	0.0549622i	$0.0175038\pi$
$709$	373095.	+	513522.i	0.742211	+	1.02157i	−0.256278	+	0.966603i	$0.582496\pi$
$710$	−143870.	−	159784.i	−0.285400	−	0.316969i
$711$	38745.9	−	12589.3i	0.0766455	−	0.0249036i
$712$		−	155809.i		−	0.307350i
$713$	−252818.	+	136061.i	−0.497313	+	0.267641i
$714$	36774.3			0.0721354
$715$	−17547.2	−	54004.8i	−0.0343239	−	0.105638i
$716$	281609.	−	253562.i	0.549314	−	0.494604i
$717$	−438735.	+	318759.i	−0.853422	+	0.620047i
$718$	−73292.9	−	126947.i	−0.142172	−	0.246248i
$719$	−495616.	−	286144.i	−0.958710	−	0.553511i	−0.0629341	−	0.998018i	$-0.520046\pi$
$719$	−495616.	−	286144.i	−0.958710	−	0.553511i	−0.895776	+	0.444506i	$0.853379\pi$
$720$	−548.076	−	5214.60i	−0.00105725	−	0.0100590i
$721$	−376714.	−	273699.i	−0.724672	−	0.526505i
$722$	−1974.45	+	18785.7i	−0.00378767	+	0.0360373i
$723$	10381.4	−	11529.7i	0.0198600	−	0.0220568i
$724$	−56509.8	+	126923.i	−0.107807	+	0.242138i
$725$	−160339.	+	754338.i	−0.305045	+	1.43512i
$726$	77344.4	+	363877.i	0.146742	+	0.690369i
$727$	337709.	−	150358.i	0.638960	−	0.284483i	−0.0615740	−	0.998103i	$-0.519612\pi$
$727$	337709.	−	150358.i	0.638960	−	0.284483i	0.700534	+	0.713619i	$0.252945\pi$
$728$	−585895.	−	190369.i	−1.10550	−	0.359197i
$729$	−98331.4	+	302633.i	−0.185028	+	0.569457i
$730$	−335166.	−	752795.i	−0.628947	−	1.41264i
$731$	124505.	−	26464.4i	0.232999	−	0.0495254i
$732$	−246178.	−	52326.7i	−0.459437	−	0.0976565i
$733$	49966.4	+	22246.5i	0.0929972	+	0.0414050i	0.452708	−	0.891659i	$-0.350458\pi$
$733$	49966.4	+	22246.5i	0.0929972	+	0.0414050i	−0.359711	+	0.933064i	$0.617125\pi$
$734$	370085.	+	333226.i	0.686925	+	0.618510i
$735$	−496854.	−	52221.5i	−0.919717	−	0.0966661i
$736$	178410.	−	245560.i	0.329354	−	0.453317i
$737$	28148.0	−	2958.47i	0.0518217	−	0.00544668i
$738$	−57753.2	+	100032.i	−0.106039	+	0.183664i
$739$	−537377.	+	310255.i	−0.983990	+	0.568107i	−0.903472	−	0.428646i	$-0.858991\pi$
$739$	−537377.	+	310255.i	−0.983990	+	0.568107i	−0.0805174	+	0.996753i	$0.525657\pi$
$740$	325787.	+	448407.i	0.594935	+	0.818858i
$741$	−720976.	−	800726.i	−1.31306	−	1.45830i
$742$	318382.	−	103449.i	0.578284	−	0.187896i
$743$		−	233292.i		−	0.422594i	−0.977422	−	0.211297i	$-0.932231\pi$
$743$		−	233292.i		−	0.422594i	0.977422	−	0.211297i	$-0.0677687\pi$
$744$	−592182.	−	212172.i	−1.06982	−	0.383302i
$745$	1.34342e6			2.42047
$746$	188383.	+	579784.i	0.338504	+	1.04181i
$747$	−44922.0	+	40447.9i	−0.0805041	+	0.0724862i
$748$	−1759.55	+	1278.39i	−0.00314484	+	0.00228486i
$749$	−17038.8	−	29512.0i	−0.0303721	−	0.0526060i
$750$	186265.	+	107540.i	0.331138	+	0.191183i
$751$	−37253.0	−	354439.i	−0.0660513	−	0.628436i	−0.976604	−	0.215044i	$-0.931010\pi$
$751$	−37253.0	−	354439.i	−0.0660513	−	0.628436i	0.910553	−	0.413392i	$-0.135656\pi$
$752$	13614.6	+	9891.58i	0.0240751	+	0.0174916i
$753$	7062.33	−	67193.6i	0.0124554	−	0.118505i
$754$	−437405.	+	485787.i	−0.769380	+	0.854483i
$755$	−61226.6	+	137517.i	−0.107410	+	0.241248i
$756$	−40390.3	+	190021.i	−0.0706697	+	0.332475i
$757$	125268.	+	589338.i	0.218598	+	1.02842i	0.941380	+	0.337348i	$0.109530\pi$
$757$	125268.	+	589338.i	0.218598	+	1.02842i	−0.722782	+	0.691076i	$0.757137\pi$
$758$	201743.	−	89821.6i	0.351123	−	0.156330i
$759$	−14947.5	−	4856.73i	−0.0259469	−	0.00843065i
$760$	−283628.	+	872917.i	−0.491046	+	1.51128i
$761$	−190373.	−	427584.i	−0.328727	−	0.738333i	0.671269	−	0.741214i	$-0.265750\pi$
$761$	−190373.	−	427584.i	−0.328727	−	0.738333i	−0.999996	+	0.00288069i	$0.999083\pi$
$762$	367234.	−	78058.0i	0.632460	−	0.134434i
$763$	−4842.85	−	1029.38i	−0.00831864	−	0.00176818i
$764$	342141.	+	152331.i	0.586163	+	0.260976i
$765$	27202.7	+	24493.4i	0.0464824	+	0.0418530i
$766$	−121275.	−	12746.5i	−0.206687	−	0.0217237i
$767$	436879.	−	601312.i	0.742626	−	1.02214i
$768$	671099.	−	70535.3i	1.13779	−	0.119587i
$769$	−179635.	+	311136.i	−0.303765	+	0.526136i	−0.976986	−	0.213306i	$-0.931577\pi$
$769$	−179635.	+	311136.i	−0.303765	+	0.526136i	0.673221	+	0.739441i	$0.264910\pi$
$770$	14421.8	−	8326.42i	0.0243241	−	0.0140435i
$771$	−131575.	−	181098.i	−0.221342	−	0.304652i
$772$	−284596.	−	316076.i	−0.477523	−	0.530343i
$773$	−11946.3	+	3881.58i	−0.0199928	+	0.00649606i	−0.318996	−	0.947756i	$-0.603346\pi$
$773$	−11946.3	+	3881.58i	−0.0199928	+	0.00649606i	0.299004	+	0.954252i	$0.403346\pi$
$774$			163157.i			0.272348i
$775$	671203.	−	457658.i	1.11751	−	0.761970i
$776$	499401.			0.829327
$777$	−156083.	−	480373.i	−0.258531	−	0.795677i
$778$	331843.	−	298792.i	0.548243	−	0.493640i
$779$	626425.	−	455125.i	1.03227	−	0.749990i
$780$	−540515.	−	936200.i	−0.888421	−	1.53879i
$781$	−10035.7	−	5794.11i	−0.0164530	−	0.00949915i
$782$	−3382.98	−	32186.9i	−0.00553205	−	0.0526340i
$783$	441435.	+	320721.i	0.720018	+	0.523123i
$784$	−830.190	+	7898.73i	−0.00135066	+	0.0128507i
$785$	−792569.	+	880237.i	−1.28617	+	1.42843i
$786$	−262177.	+	588858.i	−0.424374	+	0.953160i
$787$	169748.	−	798603.i	0.274066	−	1.28938i	−0.598594	−	0.801053i	$-0.704274\pi$
$787$	169748.	−	798603.i	0.274066	−	1.28938i	0.872660	−	0.488328i	$-0.162393\pi$
$788$	−61354.1	−	288648.i	−0.0988078	−	0.464854i
$789$	−274342.	+	122145.i	−0.440694	+	0.196210i
$790$	168599.	+	54781.2i	0.270148	+	0.0877764i
$791$	−44363.7	+	136538.i	−0.0709047	+	0.218222i
$792$	−3001.45	−	6741.38i	−0.00478499	−	0.0107473i
$793$	713330.	−	151623.i	1.13434	−	0.241112i
$794$	−463083.	−	98431.3i	−0.734544	−	0.156132i
$795$	1.42053e6	+	632459.i	2.24758	+	1.00069i
$796$	85258.2	+	76766.8i	0.134558	+	0.121157i
$797$	−714952.	−	75144.5i	−1.12554	−	0.118299i	−0.476586	−	0.879128i	$-0.658126\pi$
$797$	−714952.	−	75144.5i	−1.12554	−	0.118299i	−0.648952	+	0.760829i	$0.724792\pi$
$798$	185734.	−	255641.i	0.291666	−	0.401443i
$799$	−116840.	+	12280.4i	−0.183020	+	0.0192362i
$800$	−429426.	+	743788.i	−0.670978	+	1.16217i
$801$	−46240.6	+	26697.0i	−0.0720706	+	0.0416100i
$802$	−30723.0	−	42286.5i	−0.0477655	−	0.0657436i
$803$	−29717.7	−	33004.8i	−0.0460875	−	0.0511854i
$804$	512450.	−	166505.i	0.792755	−	0.257582i
$805$		−	383012.i		−	0.591046i
$806$	686679.	−	51487.5i	1.05702	−	0.0792559i
$807$	−902797.			−1.38625
$808$	−258790.	−	796473.i	−0.396392	−	1.21997i
$809$	−503502.	+	453355.i	−0.769314	+	0.692694i	−0.957178	−	0.289501i	$-0.906510\pi$
$809$	−503502.	+	453355.i	−0.769314	+	0.692694i	0.187863	+	0.982195i	$0.439844\pi$
$810$	611487.	−	444271.i	0.932002	−	0.677139i
$811$	110159.	+	190801.i	0.167486	+	0.290094i	0.937535	−	0.347890i	$-0.113102\pi$
$811$	110159.	+	190801.i	0.167486	+	0.290094i	−0.770049	+	0.637984i	$0.779768\pi$
$812$	256607.	+	148152.i	0.389186	+	0.224696i
$813$	32489.3	+	309115.i	0.0491540	+	0.467669i
$814$	−15636.0	−	11360.2i	−0.0235981	−	0.0171450i
$815$	137916.	−	1.31219e6i	0.207635	−	1.97552i
$816$	1817.03	−	2018.01i	0.00272886	−	0.00303070i
$817$	444862.	−	999175.i	0.666470	−	1.49692i
$818$	48915.9	−	230131.i	0.0731044	−	0.343929i
$819$	43892.6	+	206499.i	0.0654370	+	0.307857i
$820$	709692.	−	315975.i	1.05546	−	0.469921i
$821$	−301694.	−	98026.4i	−0.447590	−	0.145431i	0.0765445	−	0.997066i	$-0.475611\pi$
$821$	−301694.	−	98026.4i	−0.447590	−	0.145431i	−0.524135	+	0.851635i	$0.675611\pi$
$822$	118129.	−	363562.i	0.174828	−	0.538066i
$823$	77489.7	+	174045.i	0.114405	+	0.256958i	0.961668	−	0.274215i	$-0.0884181\pi$
$823$	77489.7	+	174045.i	0.114405	+	0.256958i	−0.847263	+	0.531173i	$0.821751\pi$
$824$	−878252.	+	186678.i	−1.29349	+	0.274941i
$825$	43499.6	+	9246.12i	0.0639112	+	0.0135848i
$826$	199129.	+	88658.0i	0.291860	+	0.129944i
$827$	449840.	+	405038.i	0.657730	+	0.592223i	0.928910	−	0.370306i	$-0.120747\pi$
$827$	449840.	+	405038.i	0.657730	+	0.592223i	−0.271180	+	0.962529i	$0.587414\pi$
$828$	−63768.4	−	6702.32i	−0.0930132	−	0.00977608i
$829$	−736274.	+	1.01339e6i	−1.07135	+	1.47458i	−0.202644	+	0.979253i	$0.564953\pi$
$829$	−736274.	+	1.01339e6i	−1.07135	+	1.47458i	−0.868704	+	0.495331i	$0.835047\pi$
$830$	−261595.	+	27494.8i	−0.379729	+	0.0399111i
$831$	−41771.7	+	72350.7i	−0.0604895	+	0.104771i
$832$	−654976.	+	378151.i	−0.946191	+	0.546284i
$833$	−32590.7	−	44857.2i	−0.0469682	−	0.0646461i
$834$	158606.	+	176150.i	0.228028	+	0.253251i
$835$	−1.57701e6	+	512402.i	−2.26184	+	0.734916i
$836$			18688.4i			0.0267399i
$837$	−102655.	−	565547.i	−0.146531	−	0.807268i
$838$	148061.			0.210839
$839$	390361.	+	1.20141e6i	0.554552	+	1.70674i	0.697123	+	0.716952i	$0.254463\pi$
$839$	390361.	+	1.20141e6i	0.554552	+	1.70674i	−0.142570	+	0.989785i	$0.545537\pi$
$840$	623629.	−	561518.i	0.883827	−	0.795802i
$841$	101095.	−	73449.7i	0.142934	−	0.103848i
$842$	68113.0	+	117975.i	0.0960740	+	0.166405i
$843$	361693.	+	208824.i	0.508962	+	0.293849i
$844$	35686.0	+	339529.i	0.0500971	+	0.476642i
$845$	1.64817e6	+	1.19746e6i	2.30828	+	1.67706i
$846$	15741.1	−	149767.i	0.0219935	−	0.209254i
$847$	−326941.	+	363104.i	−0.455724	+	0.506133i
$848$	10054.5	−	22582.8i	0.0139820	−	0.0314041i
$849$	−115214.	+	542040.i	−0.159842	+	0.751997i
$850$	19039.8	+	89575.3i	0.0263527	+	0.123980i
$851$	−406091.	+	180803.i	−0.560743	+	0.249659i
$852$	−209814.	−	68172.8i	−0.289039	−	0.0939144i
$853$	9549.50	−	29390.4i	0.0131245	−	0.0403931i	−0.944280	−	0.329144i	$-0.893240\pi$
$853$	9549.50	−	29390.4i	0.0131245	−	0.0403931i	0.957404	+	0.288751i	$0.0932399\pi$
$854$	86988.5	+	195379.i	0.119274	+	0.267894i
$855$	307659.	−	65395.0i	0.420860	−	0.0894566i
$856$	−64273.6	−	13661.8i	−0.0877173	−	0.0186449i
$857$	311909.	+	138871.i	0.424685	+	0.189082i	0.607939	−	0.793984i	$-0.291997\pi$
$857$	311909.	+	138871.i	0.424685	+	0.189082i	−0.183254	+	0.983066i	$0.558663\pi$
$858$	28013.4	+	25223.4i	0.0380532	+	0.0342632i
$859$	100764.	+	10590.7i	0.136559	+	0.0143529i	0.172561	−	0.984999i	$-0.444796\pi$
$859$	100764.	+	10590.7i	0.136559	+	0.0143529i	−0.0360024	+	0.999352i	$0.511462\pi$
$860$	644998.	−	887763.i	0.872090	−	1.20033i
$861$	−704063.	+	74000.0i	−0.949742	+	0.0998219i
$862$	−93607.4	+	162133.i	−0.125978	+	0.218201i
$863$	−513236.	+	296317.i	−0.689121	+	0.397864i	−0.803283	−	0.595598i	$-0.796915\pi$
$863$	−513236.	+	296317.i	−0.689121	+	0.397864i	0.114161	+	0.993462i	$0.463582\pi$
$864$	357178.	+	491613.i	0.478473	+	0.658561i
$865$	−596581.	−	662570.i	−0.797328	−	0.885523i
$866$	722871.	−	234875.i	0.963884	−	0.313185i
$867$		−	829068.i		−	1.10294i
$868$	−87542.2	−	299603.i	−0.116193	−	0.397656i
$869$	9554.47			0.0126522
$870$	−275165.	−	846872.i	−0.363543	−	1.11887i
$871$	−1.16027e6	+	1.04472e6i	−1.52941	+	1.37709i
$872$	−7723.51	+	5611.46i	−0.0101574	+	0.00737977i
$873$	−85569.3	−	148210.i	−0.112277	−	0.194469i
$874$	−240837.	−	139047.i	−0.315283	−	0.182029i
$875$	29528.6	+	280946.i	0.0385680	+	0.366950i
$876$	−684028.	−	496975.i	−0.891385	−	0.647629i
$877$	81603.7	−	776407.i	0.106099	−	1.00946i	−0.803875	−	0.594798i	$-0.797232\pi$
$877$	81603.7	−	776407.i	0.106099	−	1.00946i	0.909974	−	0.414665i	$-0.136101\pi$
$878$	18030.5	−	20024.9i	0.0233893	−	0.0259765i
$879$	469496.	−	1.05450e6i	0.607650	−	1.36481i
$880$	255.666	−	1202.81i	0.000330147	−	0.00155322i
$881$	−89296.3	−	420106.i	−0.115049	−	0.541261i	−0.997488	−	0.0708353i	$-0.977434\pi$
$881$	−89296.3	−	420106.i	−0.115049	−	0.541261i	0.882439	−	0.470426i	$-0.155900\pi$
$882$	64927.3	−	28907.5i	0.0834623	−	0.0371598i
$883$	313972.	+	102016.i	0.402689	+	0.130842i	0.503357	−	0.864078i	$-0.332098\pi$
$883$	313972.	+	102016.i	0.402689	+	0.130842i	−0.100668	+	0.994920i	$0.532098\pi$
$884$	37075.0	−	114105.i	0.0474435	−	0.146016i
$885$	411808.	+	924935.i	0.525785	+	1.18093i
$886$	−11809.9	+	2510.26i	−0.0150445	+	0.00319781i
$887$	−220649.	−	46900.3i	−0.280449	−	0.0596113i	0.0655397	−	0.997850i	$-0.479123\pi$
$887$	−220649.	−	46900.3i	−0.280449	−	0.0596113i	−0.345989	+	0.938239i	$0.612456\pi$
$888$	−889739.	−	396138.i	−1.12833	−	0.502366i
$889$	366454.	+	329957.i	0.463678	+	0.417497i
$890$	−231066.	−	24286.1i	−0.291714	−	0.0306604i
$891$	23944.5	−	32956.7i	0.0301613	−	0.0415134i
$892$	484088.	−	50879.7i	0.608408	−	0.0639463i
$893$	−504750.	+	874253.i	−0.632956	+	1.09631i
$894$	−772341.	+	445911.i	−0.966349	+	0.557922i
$895$	−879170.	−	1.21007e6i	−1.09756	−	1.51066i
$896$	215249.	+	239058.i	0.268118	+	0.297775i
$897$	824561.	−	267916.i	1.02480	−	0.332977i
$898$			613154.i			0.760356i
$899$	−868764.	−	117646.i	−1.07494	−	0.145566i
$900$	181430.			0.223988
$901$	53328.8	+	164129.i	0.0656920	+	0.202179i
$902$	−20131.1	+	18126.1i	−0.0247431	+	0.0222788i
$903$	−809012.	+	587782.i	−0.992155	+	0.720843i
$904$	138413.	+	239738.i	0.169371	+	0.293359i
$905$	474922.	+	274196.i	0.579862	+	0.334784i
$906$	−10445.5	−	99381.9i	−0.0127254	−	0.121074i
$907$	−697114.	−	506483.i	−0.847402	−	0.615674i	0.0770266	−	0.997029i	$-0.475457\pi$
$907$	−697114.	−	506483.i	−0.847402	−	0.615674i	−0.924428	+	0.381356i	$0.875457\pi$
$908$	−78564.5	+	747491.i	−0.0952916	+	0.906639i
$909$	−192033.	+	213274.i	−0.232406	+	0.258113i
$910$	−373642.	+	839214.i	−0.451204	+	1.01342i
$911$	277438.	−	1.30524e6i	0.334294	−	1.57273i	−0.414576	−	0.910015i	$-0.636070\pi$
$911$	277438.	−	1.30524e6i	0.334294	−	1.57273i	0.748871	−	0.662716i	$-0.230596\pi$
$912$	−4851.28	−	22823.5i	−0.00583266	−	0.0274405i
$913$	−12951.0	+	5766.15i	−0.0155368	+	0.00691742i
$914$	−361368.	−	117416.i	−0.432571	−	0.140551i
$915$	−306978.	+	944782.i	−0.366662	+	1.12847i
$916$	57191.9	+	128455.i	0.0681622	+	0.153095i
$917$	−828119.	+	176022.i	−0.984814	+	0.209329i
$918$	63377.7	+	13471.3i	0.0752057	+	0.0159855i
$919$	−1.29549e6	−	576791.i	−1.53393	−	0.682948i	−0.545988	−	0.837793i	$-0.683846\pi$
$919$	−1.29549e6	−	576791.i	−1.53393	−	0.682948i	−0.987939	+	0.154845i	$0.950512\pi$
$920$	−548841.	−	494179.i	−0.648442	−	0.583859i
$921$	482137.	+	50674.7i	0.568397	+	0.0597409i
$922$	−24271.0	+	33406.2i	−0.0285513	+	0.0392975i
$923$	635749.	−	66819.9i	0.746246	−	0.0784336i
$924$	8543.34	−	14797.5i	0.0100065	−	0.0173318i
$925$	1.08929e6	−	628900.i	1.27309	−	0.735018i
$926$	−42394.0	−	58350.4i	−0.0494405	−	0.0680490i
$927$	205885.	+	228658.i	0.239588	+	0.266089i
$928$	881480.	−	286410.i	1.02357	−	0.332577i
$929$			1.36340e6i			1.57976i	0.613259	+	0.789882i	$0.289858\pi$
$929$			1.36340e6i			1.57976i	−0.613259	+	0.789882i	$0.710142\pi$
$930$	−406956.	+	845140.i	−0.470523	+	0.977153i
$931$	−476434.			−0.549671
$932$	207234.	+	637800.i	0.238577	+	0.734265i
$933$	1.04361e6	−	939670.i	1.19888	−	1.07947i
$934$	199354.	−	144839.i	0.228524	−	0.166032i
$935$	4292.35	+	7434.57i	0.00490989	+	0.00850418i
$936$	352536.	+	203537.i	0.402394	+	0.232322i
$937$	−115199.	−	1.09605e6i	−0.131211	−	1.24839i	−0.839851	−	0.542817i	$-0.817358\pi$
$937$	−115199.	−	1.09605e6i	−0.131211	−	1.24839i	0.708640	−	0.705570i	$-0.249309\pi$
$938$	−370431.	−	269134.i	−0.421019	−	0.305888i
$939$	201607.	−	1.91816e6i	0.228651	−	2.17547i
$940$	−677712.	+	752675.i	−0.766989	+	0.851828i
$941$	297182.	−	667481.i	0.335616	−	0.753807i	−0.664363	−	0.747410i	$-0.731297\pi$
$941$	297182.	−	667481.i	0.335616	−	0.753807i	0.999980	−	0.00639676i	$-0.00203617\pi$
$942$	163482.	−	769124.i	0.184234	−	0.866752i
$943$	129538.	+	609428.i	0.145671	+	0.685329i
$944$	14704.1	−	6546.71i	0.0165005	−	0.00734648i
$945$	729265.	+	236953.i	0.816623	+	0.265337i
$946$	−11824.3	+	36391.5i	−0.0132128	+	0.0406647i
$947$	616948.	+	1.38569e6i	0.687936	+	1.54513i	0.831522	+	0.555493i	$0.187470\pi$
$947$	616948.	+	1.38569e6i	0.687936	+	1.54513i	−0.143585	+	0.989638i	$0.545863\pi$
$948$	177919.	−	37817.9i	0.197973	−	0.0420805i
$949$	2.39642e6	+	509374.i	2.66091	+	0.565594i
$950$	718856.	+	320055.i	0.796516	+	0.354632i
$951$	−304076.	−	273791.i	−0.336218	−	0.302732i
$952$	92624.8	+	9735.26i	0.102201	+	0.0107417i
$953$	305599.	−	420621.i	0.336486	−	0.463133i	−0.606925	−	0.794759i	$-0.707597\pi$
$953$	305599.	−	420621.i	0.336486	−	0.463133i	0.943411	+	0.331626i	$0.107597\pi$
$954$	−219997.	+	23122.6i	−0.241724	+	0.0254062i
$955$	739139.	−	1.28023e6i	0.810437	−	1.40372i
$956$	−449356.	+	259436.i	−0.491672	+	0.283867i
$957$	−28209.0	−	38826.3i	−0.0308009	−	0.0423938i
$958$	−334282.	−	371258.i	−0.364236	−	0.404525i
$959$	477514.	−	155154.i	0.519218	−	0.168704i
$960$		−	1.03023e6i		−	1.11787i
$961$	575864.	+	721991.i	0.623553	+	0.781781i
$962$	1.06616e6			1.15205
$963$	6958.40	+	21415.8i	0.00750338	+	0.0230930i
$964$	11031.5	−	9932.80i	0.0118708	−	0.0106885i
$965$	−1.35818e6	+	986775.i	−1.45849	+	1.05965i
$966$	127130.	+	220196.i	0.136237	+	0.235969i
$967$	970056.	+	560062.i	1.03739	+	0.598940i	0.919094	−	0.394038i	$-0.128922\pi$
$967$	970056.	+	560062.i	1.03739	+	0.598940i	0.118300	+	0.992978i	$0.462256\pi$
$968$	98481.1	+	936985.i	0.105100	+	0.999958i
$969$	131785.	+	95747.7i	0.140352	+	0.101972i
$970$	77841.8	−	740615.i	0.0827312	−	0.787135i
$971$	720378.	−	800061.i	0.764050	−	0.848564i	−0.228097	−	0.973638i	$-0.573250\pi$
$971$	720378.	−	800061.i	0.764050	−	0.848564i	0.992147	+	0.125075i	$0.0399171\pi$
$972$	124005.	−	278521.i	0.131253	−	0.294798i
$973$	−64728.6	+	304524.i	−0.0683708	+	0.321659i
$974$	31828.4	+	149741.i	0.0335504	+	0.157842i
$975$	−2.24112e6	+	997811.i	−2.35752	+	1.04964i
$976$	15019.7	+	4880.18i	0.0157674	+	0.00512314i
$977$	45563.7	−	140231.i	0.0477342	−	0.146911i	−0.924348	−	0.381549i	$-0.875391\pi$
$977$	45563.7	−	140231.i	0.0477342	−	0.146911i	0.972083	+	0.234638i	$0.0753906\pi$
$978$	356255.	+	800162.i	0.372463	+	0.836566i
$979$	−12248.5	+	2603.51i	−0.0127796	+	0.00271640i
$980$	−467557.	−	99382.4i	−0.486836	−	0.103480i
$981$	2988.73	+	1330.67i	0.00310562	+	0.00138271i
$982$	−634668.	−	571457.i	−0.658148	−	0.592599i
$983$	1.38188e6	+	145241.i	1.43009	+	0.150308i	0.787694	−	0.616067i	$-0.211275\pi$
$983$	1.38188e6	+	145241.i	1.43009	+	0.150308i	0.642393	+	0.766375i	$0.277942\pi$
$984$	−802373.	+	1.10437e6i	−0.828679	+	1.14058i
$985$	−1.15840e6	+	121753.i	−1.19395	+	0.125490i
$986$	49413.1	−	85586.0i	0.0508262	−	0.0880336i
$987$	799324.	−	461490.i	0.820518	−	0.473727i
$988$	−605961.	−	834034.i	−0.620770	−	0.854417i
$989$	588883.	+	654020.i	0.602055	+	0.668650i
$990$	−10465.4	+	3400.40i	−0.0106778	+	0.00346944i
$991$			1.01527e6i			1.03380i	0.856046	+	0.516899i	$0.172914\pi$
$991$			1.01527e6i			1.03380i	−0.856046	+	0.516899i	$0.827086\pi$
$992$	−879677.	−	423586.i	−0.893922	−	0.430446i
$993$	−230394.			−0.233654
$994$	57931.7	+	178295.i	0.0586331	+	0.180454i
$995$	336525.	−	303008.i	0.339916	−	0.306061i
$996$	−218345.	+	158637.i	−0.220102	+	0.159913i
$997$	152247.	+	263700.i	0.153165	+	0.265289i	0.932389	−	0.361456i	$-0.117720\pi$
$997$	152247.	+	263700.i	0.153165	+	0.265289i	−0.779225	+	0.626745i	$0.784387\pi$
$998$	−183199.	−	105770.i	−0.183934	−	0.106194i
$999$	−93023.8	−	885062.i	−0.0932101	−	0.886835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.11.7	✓	80
31.17	odd	30	inner	31.5.h.a.17.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.7	✓	80	1.1	even	1	trivial
31.5.h.a.17.7	yes	80	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.774721 + 2.38435i) q^{2} +(7.54548 - 6.79398i) q^{3} +(7.85936 - 5.71016i) q^{4} +(-19.1726 - 33.2079i) q^{5} +(22.0448 + 12.7276i) q^{6} +(3.49477 + 33.2505i) q^{7} +(52.1557 + 37.8934i) q^{8} +(2.30929 - 21.9714i) q^{9} +(64.3257 - 71.4409i) q^{10} +(2.10738 - 4.73326i) q^{11} +(20.5079 - 96.4822i) q^{12} +(59.4243 + 279.569i) q^{13} +(-76.5733 + 34.0926i) q^{14} +(-370.280 - 120.311i) q^{15} +(-1.91265 + 5.88652i) q^{16} +(-17.5751 - 39.4743i) q^{17} +(54.1765 - 11.5156i) q^{18} +(-363.175 - 77.1953i) q^{19} +(-340.306 - 151.514i) q^{20} +(252.273 + 227.148i) q^{21} +(12.9184 + 1.35778i) q^{22} +(175.605 - 241.699i) q^{23} +(650.987 - 68.4215i) q^{24} +(-422.675 + 732.095i) q^{25} +(-620.553 + 358.276i) q^{26} +(351.563 + 483.885i) q^{27} +(217.332 + 241.372i) q^{28} +(867.623 - 281.908i) q^{29} -976.083i q^{30} +(-865.848 - 416.927i) q^{31} +1015.97 q^{32} +(-16.2565 - 50.0323i) q^{33} +(80.5046 - 72.4867i) q^{34} +(1037.18 - 753.552i) q^{35} +(-107.311 - 185.867i) q^{36} +(-1288.56 - 743.952i) q^{37} +(-97.2993 - 925.741i) q^{38} +(2347.77 + 1705.76i) q^{39} +(258.398 - 2458.49i) q^{40} +(-1395.44 + 1549.79i) q^{41} +(-346.158 + 777.483i) q^{42} +(-612.461 + 2881.40i) q^{43} +(-10.4650 - 49.2339i) q^{44} +(-773.899 + 344.562i) q^{45} +(712.340 + 231.453i) q^{46} +(840.189 - 2585.83i) q^{47} +(25.5611 + 57.4111i) q^{48} +(1255.15 - 266.790i) q^{49} +(-2073.02 - 440.635i) q^{50} +(-400.800 - 178.448i) q^{51} +(2063.42 + 1857.91i) q^{52} +(-3972.00 - 417.474i) q^{53} +(-881.386 + 1213.12i) q^{54} +(-197.586 + 20.7671i) q^{55} +(-1077.70 + 1866.63i) q^{56} +(-3264.80 + 1884.93i) q^{57} +(1344.33 + 1850.31i) q^{58} +(-1740.08 - 1932.55i) q^{59} +(-3597.16 + 1168.79i) q^{60} -2551.53i q^{61} +(323.308 - 2387.48i) q^{62} +738.631 q^{63} +(817.697 + 2516.61i) q^{64} +(8144.58 - 7333.41i) q^{65} +(106.700 - 77.5221i) q^{66} +(2731.32 + 4730.78i) q^{67} +(-363.533 - 209.886i) q^{68} +(-317.078 - 3016.80i) q^{69} +(2600.25 + 1889.19i) q^{70} +(233.787 - 2224.34i) q^{71} +(953.013 - 1058.43i) q^{72} +(3486.48 - 7830.75i) q^{73} +(775.562 - 3648.73i) q^{74} +(1784.55 + 8395.65i) q^{75} +(-3295.12 + 1467.08i) q^{76} +(164.748 + 53.5300i) q^{77} +(-2248.25 + 6919.39i) q^{78} +(750.048 + 1684.64i) q^{79} +(232.149 - 49.3448i) q^{80} +(7690.60 + 1634.69i) q^{81} +(-4776.32 - 2126.55i) q^{82} +(-2033.37 - 1830.85i) q^{83} +(3279.75 + 344.716i) q^{84} +(-973.898 + 1340.46i) q^{85} +(-7344.75 + 771.964i) q^{86} +(4631.35 - 8021.74i) q^{87} +(289.272 - 167.011i) q^{88} +(-1420.59 - 1955.27i) q^{89} +(-1421.11 - 1578.30i) q^{90} +(-9088.15 + 2952.92i) q^{91} -2902.33i q^{92} +(-9365.83 + 2736.64i) q^{93} +6816.44 q^{94} +(4399.51 + 13540.3i) q^{95} +(7665.99 - 6902.49i) q^{96} +(6267.04 - 4553.27i) q^{97} +(1608.51 + 2786.02i) q^{98} +(-99.1299 - 57.2327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) \) 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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