LMFDB - Embedded newform 31.5.h.a.11.6

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			11.6
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0742929 + 0.228650i) q^{2} +(-5.53397 + 4.98281i) q^{3} +(12.8975 - 9.37059i) q^{4} +(11.1159 + 19.2533i) q^{5} +(-1.55045 - 0.895155i) q^{6} +(8.89648 + 84.6444i) q^{7} +(6.21280 + 4.51386i) q^{8} +(-2.67036 + 25.4068i) q^{9} +(-3.57644 + 3.97204i) q^{10} +(69.7392 - 156.637i) q^{11} +(-24.6826 + 116.122i) q^{12} +(-30.5747 - 143.843i) q^{13} +(-18.6930 + 8.32266i) q^{14} +(-157.451 - 51.1588i) q^{15} +(78.2520 - 240.835i) q^{16} +(148.681 + 333.943i) q^{17} +(-6.00766 + 1.27697i) q^{18} +(-482.767 - 102.615i) q^{19} +(323.782 + 144.157i) q^{20} +(-471.000 - 424.090i) q^{21} +(40.9961 + 4.30887i) q^{22} +(169.249 - 232.951i) q^{23} +(-56.8732 + 5.97761i) q^{24} +(65.3733 - 113.230i) q^{25} +(30.6181 - 17.6774i) q^{26} +(-466.361 - 641.891i) q^{27} +(907.910 + 1008.34i) q^{28} +(701.572 - 227.955i) q^{29} -39.8018i q^{30} +(-546.031 + 790.804i) q^{31} +183.752 q^{32} +(394.557 + 1214.32i) q^{33} +(-65.3101 + 58.8055i) q^{34} +(-1530.79 + 1112.19i) q^{35} +(203.636 + 352.708i) q^{36} +(123.525 + 71.3174i) q^{37} +(-12.4032 - 118.008i) q^{38} +(885.940 + 643.673i) q^{39} +(-17.8459 + 169.793i) q^{40} +(2157.44 - 2396.08i) q^{41} +(61.9763 - 139.201i) q^{42} +(207.978 - 978.462i) q^{43} +(-568.317 - 2673.72i) q^{44} +(-518.849 + 231.006i) q^{45} +(65.8382 + 21.3921i) q^{46} +(-130.696 + 402.240i) q^{47} +(766.991 + 1722.69i) q^{48} +(-4736.99 + 1006.88i) q^{49} +(30.7468 + 6.53543i) q^{50} +(-2486.77 - 1107.18i) q^{51} +(-1742.23 - 1568.71i) q^{52} +(1444.08 + 151.779i) q^{53} +(112.121 - 154.321i) q^{54} +(3790.99 - 398.449i) q^{55} +(-326.801 + 566.036i) q^{56} +(3182.93 - 1837.67i) q^{57} +(104.244 + 143.479i) q^{58} +(-1072.92 - 1191.60i) q^{59} +(-2510.11 + 815.584i) q^{60} +2672.61i q^{61} +(-221.384 - 66.0987i) q^{62} -2174.30 q^{63} +(-1238.38 - 3811.35i) q^{64} +(2429.58 - 2187.60i) q^{65} +(-248.342 + 180.431i) q^{66} +(-872.117 - 1510.55i) q^{67} +(5046.86 + 2913.80i) q^{68} +(224.133 + 2132.48i) q^{69} +(-368.028 - 267.388i) q^{70} +(-467.086 + 4444.03i) q^{71} +(-131.273 + 145.794i) q^{72} +(-222.722 + 500.242i) q^{73} +(-7.12966 + 33.5424i) q^{74} +(202.429 + 952.354i) q^{75} +(-7188.06 + 3200.33i) q^{76} +(13878.9 + 4509.51i) q^{77} +(-81.3568 + 250.390i) q^{78} +(402.219 + 903.398i) q^{79} +(5506.71 - 1170.49i) q^{80} +(3755.18 + 798.189i) q^{81} +(708.148 + 315.288i) q^{82} +(-4456.06 - 4012.26i) q^{83} +(-10048.7 - 1056.16i) q^{84} +(-4776.78 + 6574.68i) q^{85} +(239.177 - 25.1385i) q^{86} +(-2746.62 + 4757.29i) q^{87} +(1140.31 - 658.360i) q^{88} +(-1631.84 - 2246.03i) q^{89} +(-91.3664 - 101.473i) q^{90} +(11903.5 - 3867.67i) q^{91} -4590.45i q^{92} +(-918.711 - 7097.06i) q^{93} -101.682 q^{94} +(-3390.71 - 10435.5i) q^{95} +(-1016.88 + 915.599i) q^{96} +(-2465.51 + 1791.30i) q^{97} +(-582.147 - 1008.31i) q^{98} +(3793.41 + 2190.13i) 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 $

$2$	0.0742929	+	0.228650i	0.0185732	+	0.0571625i	0.959914	−	0.280296i	$-0.0904327\pi$
$2$	0.0742929	+	0.228650i	0.0185732	+	0.0571625i	−0.941340	+	0.337459i	$0.890433\pi$
$3$	−5.53397	+	4.98281i	−0.614886	+	0.553646i	−0.916627	−	0.399744i	$-0.869099\pi$
$3$	−5.53397	+	4.98281i	−0.614886	+	0.553646i	0.301741	+	0.953390i	$0.402432\pi$
$4$	12.8975	−	9.37059i	0.806094	−	0.585662i
$5$	11.1159	+	19.2533i	0.444636	+	0.770132i	0.998027	−	0.0627894i	$-0.0199996\pi$
$5$	11.1159	+	19.2533i	0.444636	+	0.770132i	−0.553391	+	0.832922i	$0.686666\pi$
$6$	−1.55045	−	0.895155i	−0.0430682	−	0.0248654i
$7$	8.89648	+	84.6444i	0.181561	+	1.72744i	0.583797	+	0.811900i	$0.301567\pi$
$7$	8.89648	+	84.6444i	0.181561	+	1.72744i	−0.402236	+	0.915536i	$0.631767\pi$
$8$	6.21280	+	4.51386i	0.0970750	+	0.0705291i
$9$	−2.67036	+	25.4068i	−0.0329675	+	0.313664i
$10$	−3.57644	+	3.97204i	−0.0357644	+	0.0397204i
$11$	69.7392	−	156.637i	0.576357	−	1.29452i	−0.356508	−	0.934292i	$-0.616033\pi$
$11$	69.7392	−	156.637i	0.576357	−	1.29452i	0.932865	−	0.360227i	$-0.117301\pi$
$12$	−24.6826	+	116.122i	−0.171407	+	0.806406i
$13$	−30.5747	−	143.843i	−0.180915	−	0.851139i	−0.971175	−	0.238367i	$-0.923388\pi$
$13$	−30.5747	−	143.843i	−0.180915	−	0.851139i	0.790260	−	0.612772i	$-0.209946\pi$
$14$	−18.6930	+	8.32266i	−0.0953724	+	0.0424625i
$15$	−157.451	−	51.1588i	−0.699781	−	0.227373i
$16$	78.2520	−	240.835i	0.305672	−	0.940762i
$17$	148.681	+	333.943i	0.514467	+	1.15551i	0.964880	+	0.262691i	$0.0846101\pi$
$17$	148.681	+	333.943i	0.514467	+	1.15551i	−0.450413	+	0.892820i	$0.648723\pi$
$18$	−6.00766	+	1.27697i	−0.0185422	+	0.00394126i
$19$	−482.767	−	102.615i	−1.33730	−	0.284253i	−0.516905	−	0.856043i	$-0.672916\pi$
$19$	−482.767	−	102.615i	−1.33730	−	0.284253i	−0.820400	+	0.571790i	$0.806249\pi$
$20$	323.782	+	144.157i	0.809456	+	0.360393i
$21$	−471.000	−	424.090i	−1.06803	−	0.961655i
$22$	40.9961	+	4.30887i	0.0847028	+	0.00890262i
$23$	169.249	−	232.951i	0.319941	−	0.440361i	−0.618508	−	0.785778i	$-0.712263\pi$
$23$	169.249	−	232.951i	0.319941	−	0.440361i	0.938449	+	0.345417i	$0.112263\pi$
$24$	−56.8732	+	5.97761i	−0.0987382	+	0.0103778i
$25$	65.3733	−	113.230i	0.104597	−	0.181168i
$26$	30.6181	−	17.6774i	0.0452931	−	0.0261500i
$27$	−466.361	−	641.891i	−0.639727	−	0.880509i
$28$	907.910	+	1008.34i	1.15805	+	1.28614i
$29$	701.572	−	227.955i	0.834212	−	0.271052i	0.139393	−	0.990237i	$-0.455485\pi$
$29$	701.572	−	227.955i	0.834212	−	0.271052i	0.694818	+	0.719185i	$0.255485\pi$
$30$		−	39.8018i		−	0.0442243i
$31$	−546.031	+	790.804i	−0.568190	+	0.822897i
$31$	−546.031	+	790.804i	−0.568190	+	0.822897i
$32$	183.752			0.179445
$33$	394.557	+	1214.32i	0.362311	+	1.11508i
$34$	−65.3101	+	58.8055i	−0.0564966	+	0.0508698i
$35$	−1530.79	+	1112.19i	−1.24963	+	0.907906i
$36$	203.636	+	352.708i	0.157126	+	0.272151i
$37$	123.525	+	71.3174i	0.0902303	+	0.0520945i	0.544436	−	0.838802i	$-0.316744\pi$
$37$	123.525	+	71.3174i	0.0902303	+	0.0520945i	−0.454206	+	0.890897i	$0.650077\pi$
$38$	−12.4032	−	118.008i	−0.00858945	−	0.0817232i
$39$	885.940	+	643.673i	0.582472	+	0.423191i
$40$	−17.8459	+	169.793i	−0.0111537	+	0.106120i
$41$	2157.44	−	2396.08i	1.28343	−	1.42539i	0.431172	−	0.902270i	$-0.358100\pi$
$41$	2157.44	−	2396.08i	1.28343	−	1.42539i	0.852257	−	0.523123i	$-0.175233\pi$
$42$	61.9763	−	139.201i	0.0351339	−	0.0789121i
$43$	207.978	−	978.462i	0.112482	−	0.529184i	−0.885441	−	0.464753i	$-0.846143\pi$
$43$	207.978	−	978.462i	0.112482	−	0.529184i	0.997922	−	0.0644316i	$-0.0205234\pi$
$44$	−568.317	−	2673.72i	−0.293552	−	1.38106i
$45$	−518.849	+	231.006i	−0.256222	+	0.114077i
$46$	65.8382	+	21.3921i	0.0311145	+	0.0101097i
$47$	−130.696	+	402.240i	−0.0591651	+	0.182092i	−0.976271	−	0.216552i	$-0.930519\pi$
$47$	−130.696	+	402.240i	−0.0591651	+	0.182092i	0.917106	+	0.398644i	$0.130519\pi$
$48$	766.991	+	1722.69i	0.332895	+	0.747695i
$49$	−4736.99	+	1006.88i	−1.97292	+	0.419358i
$50$	30.7468	+	6.53543i	0.0122987	+	0.00261417i
$51$	−2486.77	−	1107.18i	−0.956082	−	0.425675i
$52$	−1742.23	−	1568.71i	−0.644315	−	0.580144i
$53$	1444.08	+	151.779i	0.514091	+	0.0540332i	0.358022	−	0.933713i	$-0.383451\pi$
$53$	1444.08	+	151.779i	0.514091	+	0.0540332i	0.156069	+	0.987746i	$0.450118\pi$
$54$	112.121	−	154.321i	0.0384503	−	0.0529223i
$55$	3790.99	−	398.449i	1.25322	−	0.131719i
$56$	−326.801	+	566.036i	−0.104210	+	0.180496i
$57$	3182.93	−	1837.67i	0.979665	−	0.565610i
$58$	104.244	+	143.479i	0.0309880	+	0.0426513i
$59$	−1072.92	−	1191.60i	−0.308222	−	0.342315i	0.569055	−	0.822299i	$-0.307309\pi$
$59$	−1072.92	−	1191.60i	−0.308222	−	0.342315i	−0.877277	+	0.479984i	$0.840642\pi$
$60$	−2510.11	+	815.584i	−0.697253	+	0.226551i
$61$			2672.61i			0.718249i	0.933290	+	0.359125i	$0.116925\pi$
$61$			2672.61i			0.718249i	−0.933290	+	0.359125i	$0.883075\pi$
$62$	−221.384	−	66.0987i	−0.0575920	−	0.0171953i
$63$	−2174.30			−0.547821
$64$	−1238.38	−	3811.35i	−0.302339	−	0.930504i
$65$	2429.58	−	2187.60i	0.575049	−	0.517776i
$66$	−248.342	+	180.431i	−0.0570114	+	0.0414212i
$67$	−872.117	−	1510.55i	−0.194279	−	0.336501i	0.752385	−	0.658724i	$-0.228903\pi$
$67$	−872.117	−	1510.55i	−0.194279	−	0.336501i	−0.946664	+	0.322223i	$0.895570\pi$
$68$	5046.86	+	2913.80i	1.09145	+	0.630148i
$69$	224.133	+	2132.48i	0.0470768	+	0.447906i
$70$	−368.028	−	267.388i	−0.0751078	−	0.0545690i
$71$	−467.086	+	4444.03i	−0.0926574	+	0.881577i	0.845175	+	0.534489i	$0.179496\pi$
$71$	−467.086	+	4444.03i	−0.0926574	+	0.881577i	−0.937833	+	0.347087i	$0.887171\pi$
$72$	−131.273	+	145.794i	−0.0253228	+	0.0281238i
$73$	−222.722	+	500.242i	−0.0417944	+	0.0938717i	−0.933236	−	0.359264i	$-0.883028\pi$
$73$	−222.722	+	500.242i	−0.0417944	+	0.0938717i	0.891442	+	0.453135i	$0.149695\pi$
$74$	−7.12966	+	33.5424i	−0.00130198	+	0.00612535i
$75$	202.429	+	952.354i	0.0359874	+	0.169307i
$76$	−7188.06	+	3200.33i	−1.24447	+	0.554074i
$77$	13878.9	+	4509.51i	2.34084	+	0.760586i
$78$	−81.3568	+	250.390i	−0.0133723	+	0.0411556i
$79$	402.219	+	903.398i	0.0644478	+	0.144752i	0.942898	−	0.333082i	$-0.108089\pi$
$79$	402.219	+	903.398i	0.0644478	+	0.144752i	−0.878450	+	0.477834i	$0.841422\pi$
$80$	5506.71	−	1170.49i	0.860424	−	0.182889i
$81$	3755.18	+	798.189i	0.572349	+	0.121657i
$82$	708.148	+	315.288i	0.105316	+	0.0468899i
$83$	−4456.06	−	4012.26i	−0.646837	−	0.582415i	0.279021	−	0.960285i	$-0.409990\pi$
$83$	−4456.06	−	4012.26i	−0.646837	−	0.582415i	−0.925859	+	0.377870i	$0.876657\pi$
$84$	−10048.7	−	1056.16i	−1.42414	−	0.149683i
$85$	−4776.78	+	6574.68i	−0.661146	+	0.909990i
$86$	239.177	−	25.1385i	0.0323386	−	0.00339893i
$87$	−2746.62	+	4757.29i	−0.362878	+	0.628523i
$88$	1140.31	−	658.360i	0.147251	−	0.0850155i
$89$	−1631.84	−	2246.03i	−0.206014	−	0.283554i	0.693490	−	0.720466i	$-0.256072\pi$
$89$	−1631.84	−	2246.03i	−0.206014	−	0.283554i	−0.899504	+	0.436912i	$0.856072\pi$
$90$	−91.3664	−	101.473i	−0.0112798	−	0.0125275i
$91$	11903.5	−	3867.67i	1.43744	−	0.467053i
$92$		−	4590.45i		−	0.542350i
$93$	−918.711	−	7097.06i	−0.106222	−	0.820564i
$94$	−101.682			−0.0115077
$95$	−3390.71	−	10435.5i	−0.375702	−	1.15629i
$96$	−1016.88	+	915.599i	−0.110338	+	0.0993489i
$97$	−2465.51	+	1791.30i	−0.262037	+	0.190381i	−0.711045	−	0.703147i	$-0.751778\pi$
$97$	−2465.51	+	1791.30i	−0.262037	+	0.190381i	0.449007	+	0.893528i	$0.351778\pi$
$98$	−582.147	−	1008.31i	−0.0606151	−	0.104988i
$99$	3793.41	+	2190.13i	0.387044	+	0.223460i
$100$	−217.878	−	2072.97i	−0.0217878	−	0.207297i
$101$	447.354	+	325.022i	0.0438539	+	0.0318618i	0.609496	−	0.792789i	$-0.291372\pi$
$101$	447.354	+	325.022i	0.0438539	+	0.0318618i	−0.565642	+	0.824651i	$0.691372\pi$
$102$	68.4077	−	650.856i	0.00657513	−	0.0625582i
$103$	−11868.5	+	13181.3i	−1.11872	+	1.24246i	−0.151514	+	0.988455i	$0.548415\pi$
$103$	−11868.5	+	13181.3i	−1.11872	+	1.24246i	−0.967203	+	0.254005i	$0.918252\pi$
$104$	459.331	−	1031.68i	0.0424678	−	0.0953842i
$105$	2929.55	−	13782.4i	0.265719	−	1.25011i
$106$	72.5807	+	341.465i	0.00645966	+	0.0303903i
$107$	−4156.83	+	1850.74i	−0.363073	+	0.161651i	−0.580162	−	0.814501i	$-0.697011\pi$
$107$	−4156.83	+	1850.74i	−0.363073	+	0.161651i	0.217088	+	0.976152i	$0.430344\pi$
$108$	−12029.8	−	3908.72i	−1.03136	−	0.335110i
$109$	2940.88	−	9051.10i	0.247528	−	0.761813i	−0.747682	−	0.664057i	$-0.768833\pi$
$109$	2940.88	−	9051.10i	0.247528	−	0.761813i	0.995210	−	0.0977565i	$-0.0311666\pi$
$110$	372.749	+	837.209i	0.0308057	+	0.0691908i
$111$	−1038.95	+	220.835i	−0.0843232	+	0.0179235i
$112$	21081.5	+	4481.01i	1.68060	+	0.357223i
$113$	−6093.12	−	2712.83i	−0.477181	−	0.212454i	0.154030	−	0.988066i	$-0.450775\pi$
$113$	−6093.12	−	2712.83i	−0.477181	−	0.212454i	−0.631210	+	0.775612i	$0.717442\pi$
$114$	656.652	+	591.252i	0.0505272	+	0.0454949i
$115$	6366.43	+	669.139i	0.481394	+	0.0505965i
$116$	6912.46	−	9514.19i	0.513709	−	0.707059i
$117$	3736.23	−	392.693i	0.272936	−	0.0286868i
$118$	192.749	−	333.850i	0.0138429	−	0.0239766i
$119$	−26943.6	+	15555.9i	−1.90267	+	1.09850i
$120$	−747.286	−	1028.55i	−0.0518948	−	0.0714271i
$121$	−9874.80	−	10967.1i	−0.674462	−	0.749066i
$122$	−611.091	+	198.556i	−0.0410569	+	0.0133402i
$123$			24010.0i			1.58702i
$124$	367.870	+	15316.0i	0.0239249	+	0.996100i
$125$	16801.6			1.07530
$126$	−161.535	−	497.154i	−0.0101748	−	0.0313148i
$127$	−904.909	+	814.784i	−0.0561045	+	0.0505167i	−0.696706	−	0.717357i	$-0.745352\pi$
$127$	−904.909	+	814.784i	−0.0561045	+	0.0505167i	0.640601	+	0.767874i	$0.278685\pi$
$128$	3157.99	−	2294.42i	0.192749	−	0.140040i
$129$	3724.54	+	6451.10i	0.223817	+	0.387663i
$130$	680.696	+	393.000i	0.0402779	+	0.0232544i
$131$	2004.27	+	19069.4i	0.116792	+	1.11120i	0.883248	+	0.468907i	$0.155352\pi$
$131$	2004.27	+	19069.4i	0.116792	+	1.11120i	−0.766455	+	0.642298i	$0.777981\pi$
$132$	16467.7	+	11964.5i	0.945116	+	0.686667i
$133$	4390.88	−	41776.4i	0.248227	−	2.36172i
$134$	280.596	−	311.633i	0.0156268	−	0.0173554i
$135$	7174.50	−	16114.2i	0.393663	−	0.884181i
$136$	−583.647	+	2745.85i	−0.0315553	+	0.148456i
$137$	2538.88	+	11944.5i	0.135270	+	0.636394i	0.992580	+	0.121594i	$0.0388005\pi$
$137$	2538.88	+	11944.5i	0.135270	+	0.636394i	−0.857310	+	0.514800i	$0.827866\pi$
$138$	−470.940	+	209.676i	−0.0247290	+	0.0110101i
$139$	3856.77	+	1253.14i	0.199616	+	0.0648590i	0.407118	−	0.913375i	$-0.366534\pi$
$139$	3856.77	+	1253.14i	0.199616	+	0.0648590i	−0.207503	+	0.978234i	$0.566534\pi$
$140$	−9321.57	+	28688.8i	−0.475590	+	1.46372i
$141$	−1281.02	−	2877.22i	−0.0644344	−	0.144722i
$142$	−1050.83	+	223.360i	−0.0521141	+	0.0110772i
$143$	−24663.3	−	5242.35i	−1.20609	−	0.256362i
$144$	5909.89	+	2631.25i	0.285006	+	0.126893i
$145$	12187.5	+	10973.7i	0.579666	+	0.521934i
$146$	−130.927	−	13.7610i	−0.00614220	−	0.000645571i
$147$	21197.3	−	29175.6i	0.980947	−	1.35016i
$148$	2261.45	−	237.688i	0.103244	−	0.0108514i
$149$	−11376.9	+	19705.4i	−0.512450	+	0.887590i	0.487445	+	0.873153i	$0.337929\pi$
$149$	−11376.9	+	19705.4i	−0.512450	+	0.887590i	−0.999896	+	0.0144365i	$0.995405\pi$
$150$	−202.717	+	117.039i	−0.00900963	+	0.00520171i
$151$	−24720.0	−	34024.2i	−1.08416	−	1.49222i	−0.854853	−	0.518870i	$-0.826353\pi$
$151$	−24720.0	−	34024.2i	−1.08416	−	1.49222i	−0.229311	−	0.973353i	$-0.573647\pi$
$152$	−2536.14	−	2816.67i	−0.109771	−	0.121913i
$153$	−8881.46	+	2885.76i	−0.379403	+	0.123276i
$154$			3508.43i			0.147935i
$155$	−21295.2	−	1722.39i	−0.886378	−	0.0716915i
$156$	17458.0			0.717374
$157$	8532.76	+	26261.1i	0.346171	+	1.06540i	0.960954	+	0.276708i	$0.0892434\pi$
$157$	8532.76	+	26261.1i	0.346171	+	1.06540i	−0.614784	+	0.788696i	$0.710757\pi$
$158$	−176.680	+	159.083i	−0.00707739	+	0.00637251i
$159$	−8747.79	+	6355.64i	−0.346022	+	0.251400i
$160$	2042.57	+	3537.83i	0.0797877	+	0.138196i
$161$	21223.7	+	12253.5i	0.818784	+	0.472725i
$162$	96.4775	+	917.922i	0.00367617	+	0.0349765i
$163$	−6794.35	−	4936.39i	−0.255725	−	0.185795i	0.452535	−	0.891746i	$-0.350520\pi$
$163$	−6794.35	−	4936.39i	−0.255725	−	0.185795i	−0.708260	+	0.705952i	$0.750520\pi$
$164$	5372.93	−	51120.1i	0.199767	−	1.90066i
$165$	−18993.8	+	21094.8i	−0.697662	+	0.774832i
$166$	586.349	−	1316.96i	0.0212784	−	0.0477922i
$167$	8249.20	−	38809.4i	0.295787	−	1.39157i	−0.539607	−	0.841917i	$-0.681427\pi$
$167$	8249.20	−	38809.4i	0.295787	−	1.39157i	0.835394	−	0.549651i	$-0.185239\pi$
$168$	−1011.94	−	4760.81i	−0.0358540	−	0.168680i
$169$	6335.90	−	2820.92i	0.221837	−	0.0987684i
$170$	−1858.18	−	603.760i	−0.0642969	−	0.0208913i
$171$	3896.29	−	11991.6i	0.133248	−	0.410094i
$172$	−6486.36	−	14568.6i	−0.219252	−	0.492449i
$173$	5413.64	−	1150.70i	0.180883	−	0.0384478i	−0.116580	−	0.993181i	$-0.537193\pi$
$173$	5413.64	−	1150.70i	0.180883	−	0.0384478i	0.297462	+	0.954734i	$0.403860\pi$
$174$	−1291.81	−	274.583i	−0.0426678	−	0.00906932i
$175$	10165.9	+	4526.14i	0.331947	+	0.147792i
$176$	−32266.4	−	29052.8i	−1.04166	−	0.937913i
$177$	11875.0	+	1248.11i	0.379042	+	0.0398389i
$178$	392.321	−	539.984i	0.0123823	−	0.0170428i
$179$	−62242.0	+	6541.89i	−1.94257	+	0.204173i	−0.993749	−	0.111636i	$-0.964391\pi$
$179$	−62242.0	+	6541.89i	−1.94257	+	0.204173i	−0.948823	+	0.315808i	$0.897724\pi$
$180$	−4527.19	+	7841.33i	−0.139728	+	0.242016i
$181$	−28208.8	+	16286.4i	−0.861048	+	0.497126i	−0.864363	−	0.502868i	$-0.832278\pi$
$181$	−28208.8	+	16286.4i	−0.861048	+	0.497126i	0.00331510	+	0.999995i	$0.498945\pi$
$182$	1768.68	+	2434.39i	0.0533959	+	0.0734931i
$183$	−13317.1	−	14790.1i	−0.397655	−	0.441641i
$184$	2103.02	−	683.312i	0.0621165	−	0.0201829i
$185$			3171.03i			0.0926524i
$186$	1554.49	−	737.324i	0.0449326	−	0.0213124i
$187$	62676.6			1.79235
$188$	2083.58	+	6412.60i	0.0589514	+	0.181434i
$189$	50183.5	−	45185.4i	1.40487	−	1.26495i
$190$	2134.18	−	1550.57i	0.0591185	−	0.0429521i
$191$	26247.1	+	45461.3i	0.719473	+	1.24616i	0.961209	+	0.275822i	$0.0889499\pi$
$191$	26247.1	+	45461.3i	0.719473	+	1.24616i	−0.241736	+	0.970342i	$0.577717\pi$
$192$	25844.4	+	14921.3i	0.701074	+	0.404765i
$193$	401.416	+	3819.22i	0.0107766	+	0.102532i	0.998588	−	0.0531234i	$-0.0169177\pi$
$193$	401.416	+	3819.22i	0.0107766	+	0.102532i	−0.987811	+	0.155656i	$0.950251\pi$
$194$	−592.750	−	430.658i	−0.0157495	−	0.0114427i
$195$	−2544.81	+	24212.3i	−0.0669247	+	0.636746i
$196$	−51660.3	+	57374.6i	−1.34476	+	1.49351i
$197$	1505.25	−	3380.84i	0.0387860	−	0.0871148i	−0.893113	−	0.449831i	$-0.851484\pi$
$197$	1505.25	−	3380.84i	0.0387860	−	0.0871148i	0.931899	+	0.362717i	$0.118151\pi$
$198$	−218.949	+	1030.08i	−0.00558487	+	0.0262747i
$199$	−5758.95	−	27093.7i	−0.145424	−	0.684168i	−0.989092	−	0.147302i	$-0.952941\pi$
$199$	−5758.95	−	27093.7i	−0.145424	−	0.684168i	0.843667	−	0.536867i	$-0.180392\pi$
$200$	917.256	−	408.389i	0.0229314	−	0.0102097i
$201$	12353.1	+	4013.75i	0.305761	+	0.0993479i
$202$	−41.0810	+	126.434i	−0.00100679	+	0.00309858i
$203$	25536.6	+	57356.1i	0.619685	+	1.39183i
$204$	−42448.1	+	9022.62i	−1.01999	+	0.216806i
$205$	70114.5	+	14903.3i	1.66840	+	0.354629i
$206$	−3895.64	−	1734.45i	−0.0918003	−	0.0408721i
$207$	5466.59	+	4922.14i	0.127578	+	0.114872i
$208$	−37034.9	−	3892.52i	−0.856020	−	0.0899713i
$209$	−49741.1	+	68462.8i	−1.13874	+	1.56734i
$210$	3369.00	−	354.096i	0.0763946	−	0.00802940i
$211$	10118.0	−	17524.9i	0.227264	−	0.393633i	−0.729732	−	0.683733i	$-0.760355\pi$
$211$	10118.0	−	17524.9i	0.227264	−	0.393633i	0.956996	+	0.290100i	$0.0936886\pi$
$212$	20047.3	−	11574.3i	0.446051	−	0.257528i
$213$	−19558.9	−	26920.5i	−0.431107	−	0.593368i
$214$	−731.994	−	812.962i	−0.0159838	−	0.0177518i
$215$	21150.5	−	6872.21i	0.457555	−	0.148669i
$216$		−	6093.03i		−	0.130595i
$217$	−71794.9	−	39183.0i	−1.52466	−	0.832106i
$218$	2288.02			0.0481445
$219$	−1260.07	−	3878.11i	−0.0262729	−	0.0808596i
$220$	45160.7	−	40662.8i	0.933071	−	0.840141i
$221$	43489.3	−	31596.8i	0.890426	−	0.646933i
$222$	−127.680	−	221.149i	−0.00259070	−	0.00448723i
$223$	70256.6	+	40562.7i	1.41279	+	0.815674i	0.995650	−	0.0931685i	$-0.0296995\pi$
$223$	70256.6	+	40562.7i	1.41279	+	0.815674i	0.417139	+	0.908843i	$0.363033\pi$
$224$	1634.74	+	15553.5i	0.0325802	+	0.309980i
$225$	2702.24	+	1963.29i	0.0533776	+	0.0387811i
$226$	167.613	−	1594.74i	0.00328165	−	0.0312228i
$227$	29133.6	−	32356.1i	0.565382	−	0.627920i	−0.390877	−	0.920443i	$-0.627828\pi$
$227$	29133.6	−	32356.1i	0.565382	−	0.627920i	0.956258	+	0.292523i	$0.0944948\pi$
$228$	23831.9	−	53527.3i	0.458446	−	1.02969i
$229$	6784.78	−	31919.9i	0.129379	−	0.608682i	−0.864907	−	0.501933i	$-0.832623\pi$
$229$	6784.78	−	31919.9i	0.129379	−	0.608682i	0.994286	−	0.106749i	$-0.0340441\pi$
$230$	319.982	+	1505.40i	0.00604881	+	0.0284574i
$231$	−99275.3	+	44200.2i	−1.86045	+	0.828324i
$232$	5387.68	+	1750.56i	0.100098	+	0.0325239i
$233$	−24953.3	+	76798.5i	−0.459639	+	1.41462i	0.405962	+	0.913890i	$0.366936\pi$
$233$	−24953.3	+	76798.5i	−0.459639	+	1.41462i	−0.865601	+	0.500734i	$0.833064\pi$
$234$	367.364	+	825.114i	0.00670912	+	0.0150689i
$235$	−9197.26	+	1954.94i	−0.166542	+	0.0353995i
$236$	−25004.0	−	5314.76i	−0.448936	−	0.0954244i
$237$	−6727.32	−	2995.20i	−0.119769	−	0.0533248i
$238$	−5558.58	−	5004.97i	−0.0981319	−	0.0883583i
$239$	−76837.7	−	8075.97i	−1.34518	−	0.141384i	−0.595588	−	0.803290i	$-0.703081\pi$
$239$	−76837.7	−	8075.97i	−1.34518	−	0.141384i	−0.749587	+	0.661906i	$0.769748\pi$
$240$	−24641.7	+	33916.4i	−0.427807	+	0.588826i
$241$	21439.5	−	2253.38i	0.369131	−	0.0387972i	0.0818529	−	0.996644i	$-0.473916\pi$
$241$	21439.5	−	2253.38i	0.369131	−	0.0387972i	0.287278	+	0.957847i	$0.407250\pi$
$242$	1774.00	−	3072.65i	0.0302916	−	0.0524665i
$243$	30898.7	−	17839.3i	0.523271	−	0.302111i
$244$	25043.9	+	34470.0i	0.420651	+	0.578977i
$245$	−72041.7	−	80010.4i	−1.20019	−	1.33295i
$246$	−5489.89	+	1783.77i	−0.0907179	+	0.0294760i
$247$			72579.9i			1.18966i
$248$	−6961.96	+	2448.40i	−0.113195	+	0.0398088i
$249$	44652.0			0.720182
$250$	1248.24	+	3841.69i	0.0199718	+	0.0614670i
$251$	51801.8	−	46642.6i	0.822238	−	0.740347i	−0.146292	−	0.989241i	$-0.546734\pi$
$251$	51801.8	−	46642.6i	0.822238	−	0.740347i	0.968531	+	0.248895i	$0.0800673\pi$
$252$	−28043.1	+	20374.5i	−0.441595	+	0.320838i
$253$	−24685.4	−	42756.4i	−0.385656	−	0.667975i
$254$	−253.529	−	146.375i	−0.00392970	−	0.00226881i
$255$	−6325.79	−	60185.9i	−0.0972824	−	0.925581i
$256$	−51114.8	−	37137.0i	−0.779949	−	0.566666i
$257$	6683.14	−	63585.9i	0.101185	−	0.962708i	−0.819679	−	0.572823i	$-0.805848\pi$
$257$	6683.14	−	63585.9i	0.101185	−	0.962708i	0.920864	−	0.389885i	$-0.127485\pi$
$258$	−1198.34	+	1330.89i	−0.0180028	+	0.0199941i
$259$	−4937.67	+	11090.2i	−0.0736076	+	0.165325i
$260$	10836.4	−	50981.2i	0.160302	−	0.754160i
$261$	3918.15	+	18433.4i	0.0575174	+	0.270598i
$262$	−4211.31	+	1875.00i	−0.0613500	+	0.0273148i
$263$	83741.3	+	27209.2i	1.21068	+	0.393373i	0.843679	−	0.536849i	$-0.180385\pi$
$263$	83741.3	+	27209.2i	1.21068	+	0.393373i	0.366999	+	0.930221i	$0.380385\pi$
$264$	−3029.98	+	9325.31i	−0.0434742	+	0.133800i
$265$	13130.0	+	29490.5i	0.186971	+	0.419943i
$266$	9878.39	−	2099.72i	0.139612	−	0.0296755i
$267$	20222.1	+	4298.34i	0.283664	+	0.0602946i
$268$	−25402.9	−	11310.1i	−0.353683	−	0.157470i
$269$	−72837.9	−	65583.6i	−1.00659	−	0.906338i	−0.0109810	−	0.999940i	$-0.503495\pi$
$269$	−72837.9	−	65583.6i	−1.00659	−	0.906338i	−0.995610	+	0.0936013i	$0.970162\pi$
$270$	4217.53	+	443.280i	0.0578536	+	0.00608066i
$271$	54229.5	−	74640.5i	0.738409	−	1.01633i	−0.260299	−	0.965528i	$-0.583821\pi$
$271$	54229.5	−	74640.5i	0.738409	−	1.01633i	0.998709	−	0.0508051i	$-0.0161787\pi$
$272$	92059.7	−	9675.87i	1.24432	−	0.130783i
$273$	−46601.5	+	80716.2i	−0.625281	+	1.08302i
$274$	−2542.48	+	1467.90i	−0.0338655	+	0.0195522i
$275$	−13176.9	−	18136.4i	−0.174240	−	0.239821i
$276$	22873.3	+	25403.4i	0.300270	+	0.333483i
$277$	−101396.	+	32945.4i	−1.32148	+	0.429374i	−0.883002	−	0.469369i	$-0.844481\pi$
$277$	−101396.	+	32945.4i	−1.32148	+	0.429374i	−0.438475	+	0.898743i	$0.644481\pi$
$278$			974.950i			0.0126152i
$279$	−18633.7	−	15984.6i	−0.239382	−	0.205350i
$280$	−14530.8			−0.185341
$281$	−176.164	−	542.177i	−0.00223102	−	0.00686639i	0.949935	−	0.312448i	$-0.101149\pi$
$281$	−176.164	−	542.177i	−0.00223102	−	0.00686639i	−0.952166	+	0.305582i	$0.901149\pi$
$282$	562.705	−	506.662i	0.00707592	−	0.00637119i
$283$	−70598.8	+	51293.0i	−0.881504	+	0.640450i	−0.933649	−	0.358189i	$-0.883394\pi$
$283$	−70598.8	+	51293.0i	−0.881504	+	0.640450i	0.0521447	+	0.998640i	$0.483394\pi$
$284$	35618.9	+	61693.8i	0.441615	+	0.764900i
$285$	70762.3	+	40854.7i	0.871189	+	0.502981i
$286$	−633.645	−	6028.73i	−0.00774665	−	0.0737045i
$287$	222009.	+	161299.i	2.69529	+	1.95825i
$288$	−490.684	+	4668.54i	−0.00591584	+	0.0562855i
$289$	−33525.3	+	37233.7i	−0.401400	+	0.445800i
$290$	−1603.68	+	3601.93i	−0.0190688	+	0.0428292i
$291$	4718.36	−	22198.1i	0.0557192	−	0.262138i
$292$	1815.00	+	8538.92i	0.0212869	+	0.100147i
$293$	−29970.4	+	13343.7i	−0.349106	+	0.155432i	−0.573796	−	0.818998i	$-0.694530\pi$
$293$	−29970.4	+	13343.7i	−0.349106	+	0.155432i	0.224690	+	0.974430i	$0.427863\pi$
$294$	8245.80	+	2679.22i	0.0953977	+	0.0309966i
$295$	11015.7	−	33902.9i	0.126581	−	0.389577i
$296$	445.521	+	1000.66i	0.00508493	+	0.0114209i
$297$	−133067.	+	28284.4i	−1.50855	+	0.320652i
$298$	−5350.86	−	1137.36i	−0.0602547	−	0.0128075i
$299$	−38683.0	−	17222.8i	−0.432691	−	0.192646i
$300$	11535.0	+	10386.1i	0.128166	+	0.115401i
$301$	84671.6	+	8899.34i	0.934554	+	0.0982256i
$302$	5943.11	−	8179.99i	0.0651628	−	0.0896889i
$303$	−4095.17	+	430.419i	−0.0446053	+	0.00468820i
$304$	−62490.9	+	108237.i	−0.676191	+	1.17120i
$305$	−51456.5	+	29708.4i	−0.553147	+	0.319360i
$306$	−1319.66	−	1816.35i	−0.0140935	−	0.0193980i
$307$	34160.3	+	37938.8i	0.362447	+	0.402538i	0.896594	−	0.442853i	$-0.146034\pi$
$307$	34160.3	+	37938.8i	0.362447	+	0.402538i	−0.534147	+	0.845392i	$0.679367\pi$
$308$	221260.	−	71891.6i	2.33239	−	0.757838i
$309$		−	132083.i		−	1.38334i
$310$	−1188.26	−	4997.12i	−0.0123648	−	0.0519991i
$311$	−8034.49			−0.0830687			−0.0415344	−	0.999137i	$-0.513225\pi$
$311$	−8034.49			−0.0830687			−0.0415344	+	0.999137i	$0.513225\pi$
$312$	2598.71	+	7998.02i	0.0266962	+	0.0821624i
$313$	−104778.	+	94342.5i	−1.06950	+	0.962984i	−0.999403	−	0.0345564i	$-0.988998\pi$
$313$	−104778.	+	94342.5i	−1.06950	+	0.962984i	−0.0700989	+	0.997540i	$0.522331\pi$
$314$	−5370.68	+	3902.03i	−0.0544716	+	0.0395760i
$315$	−24169.3	−	41862.5i	−0.243581	−	0.421895i
$316$	13653.0	+	7882.56i	0.136727	+	0.0789392i
$317$	8292.24	+	78895.3i	0.0825188	+	0.785114i	0.955028	+	0.296516i	$0.0958249\pi$
$317$	8292.24	+	78895.3i	0.0825188	+	0.785114i	−0.872509	+	0.488598i	$0.837508\pi$
$318$	−2103.12	−	1528.00i	−0.0207974	−	0.0151102i
$319$	13221.0	−	125789.i	0.129922	−	1.23613i
$320$	59615.3	−	66209.5i	0.582181	−	0.646577i
$321$	13781.9	−	30954.6i	0.133751	−	0.300411i
$322$	−1225.00	+	5763.15i	−0.0118147	+	0.0555838i
$323$	−37510.6	−	176474.i	−0.359542	−	1.69151i
$324$	55912.0	−	24893.6i	0.532617	−	0.237136i
$325$	−18286.1	−	5941.50i	−0.173122	−	0.0562509i
$326$	623.933	−	1920.27i	0.00587087	−	0.0180687i
$327$	28825.2	+	64742.4i	0.269573	+	0.605471i
$328$	24219.4	−	5147.99i	0.225121	−	0.0478509i
$329$	−35210.1	−	7484.14i	−0.325294	−	0.0691433i
$330$	−6234.43	−	2775.75i	−0.0572492	−	0.0254890i
$331$	37760.8	+	34000.0i	0.344655	+	0.310329i	0.823219	−	0.567724i	$-0.192176\pi$
$331$	37760.8	+	34000.0i	0.344655	+	0.310329i	−0.478564	+	0.878053i	$0.658842\pi$
$332$	−95069.3	−	9992.19i	−0.862510	−	0.0906535i
$333$	−2141.80	+	2947.94i	−0.0193148	+	0.0265846i
$334$	9486.64	−	997.086i	0.0850392	−	0.00893798i
$335$	19388.7	−	33582.3i	0.172767	−	0.299241i
$336$	−138992.	+	80247.3i	−1.23115	+	0.710807i
$337$	−117291.	−	161437.i	−1.03277	−	1.42149i	−0.902843	−	0.429969i	$-0.858524\pi$
$337$	−117291.	−	161437.i	−1.03277	−	1.42149i	−0.129931	−	0.991523i	$-0.541476\pi$
$338$	1115.72	+	1239.13i	0.00976609	+	0.0108463i
$339$	47236.7	−	15348.1i	0.411036	−	0.133554i
$340$			129558.i			1.12075i
$341$	85789.4	+	140679.i	0.737776	+	1.20982i
$342$	3031.34			0.0259168
$343$	−64221.3	−	197653.i	−0.545872	−	1.68002i
$344$	5708.77	−	5140.20i	0.0482421	−	0.0434373i
$345$	−38565.8	+	28019.7i	−0.324015	+	0.235410i
$346$	665.303	+	1152.34i	0.00555735	+	0.00962561i
$347$	−108830.	−	62833.3i	−0.903840	−	0.521832i	−0.0253960	−	0.999677i	$-0.508085\pi$
$347$	−108830.	−	62833.3i	−0.903840	−	0.521832i	−0.878444	+	0.477845i	$0.841418\pi$
$348$	9154.03	+	87094.7i	0.0755881	+	0.719173i
$349$	−33401.0	−	24267.2i	−0.274226	−	0.199237i	0.442169	−	0.896932i	$-0.354209\pi$
$349$	−33401.0	−	24267.2i	−0.274226	−	0.199237i	−0.716395	+	0.697695i	$0.754209\pi$
$350$	−279.649	+	2660.69i	−0.00228285	+	0.0217199i
$351$	−78072.4	+	86708.2i	−0.633700	+	0.703795i
$352$	12814.7	−	28782.3i	0.103424	−	0.232295i
$353$	−11201.2	+	52697.4i	−0.0898906	+	0.422902i	0.910074	+	0.414447i	$0.136025\pi$
$353$	−11201.2	+	52697.4i	−0.0898906	+	0.422902i	−0.999964	+	0.00845546i	$0.997309\pi$
$354$	596.848	+	2807.95i	0.00476274	+	0.0224069i
$355$	−90754.3	+	40406.4i	−0.720130	+	0.320622i
$356$	−42093.3	−	13676.9i	−0.332134	−	0.107917i
$357$	71593.2	−	220341.i	0.561740	−	1.72886i
$358$	−6119.94	−	13745.6i	−0.0477508	−	0.107250i
$359$	164669.	−	35001.4i	1.27768	−	0.271579i	0.481397	−	0.876503i	$-0.340130\pi$
$359$	164669.	−	35001.4i	1.27768	−	0.271579i	0.796284	+	0.604923i	$0.206796\pi$
$360$	−4266.24	−	906.816i	−0.0329185	−	0.00699704i
$361$	103480.	+	46072.3i	0.794039	+	0.353529i
$362$	−5819.59	−	5239.98i	−0.0444094	−	0.0399864i
$363$	109294.	+	11487.2i	0.829434	+	0.0871771i
$364$	117283.	−	161426.i	0.885179	−	1.21834i
$365$	−12107.1	+	1272.51i	−0.0908769	+	0.00955155i
$366$	2392.40	−	4143.75i	0.0178596	−	0.0309337i
$367$	22188.2	−	12810.4i	0.164737	−	0.0951109i	−0.415365	−	0.909655i	$-0.636346\pi$
$367$	22188.2	−	12810.4i	0.164737	−	0.0951109i	0.580102	+	0.814544i	$0.303013\pi$
$368$	−42858.7	−	58989.9i	−0.316478	−	0.435594i
$369$	55115.7	+	61212.2i	0.404783	+	0.449558i
$370$	−725.056	+	235.585i	−0.00529624	+	0.00172085i
$371$			123584.i			0.897870i
$372$	−78352.7	−	82925.5i	−0.566198	−	0.599242i
$373$	−16182.5			−0.116313			−0.0581564	−	0.998307i	$-0.518522\pi$
$373$	−16182.5			−0.116313			−0.0581564	+	0.998307i	$0.518522\pi$
$374$	4656.43	+	14331.0i	0.0332897	+	0.102455i
$375$	−92979.7	+	83719.3i	−0.661189	+	0.595337i
$376$	−2627.64	+	1909.10i	−0.0185862	+	0.0135037i
$377$	−54239.9	−	93946.3i	−0.381624	−	0.660993i
$378$	14059.9	+	8117.50i	0.0984010	+	0.0568118i
$379$	3548.31	+	33759.9i	0.0247026	+	0.235030i	0.999906	+	0.0137187i	$0.00436693\pi$
$379$	3548.31	+	33759.9i	0.0247026	+	0.235030i	−0.975203	+	0.221311i	$0.928966\pi$
$380$	−141519.	−	102819.i	−0.980047	−	0.712046i
$381$	947.828	−	9017.98i	0.00652949	−	0.0621240i
$382$	−8444.75	+	9378.85i	−0.0578709	+	0.0642722i
$383$	−17089.4	+	38383.3i	−0.116501	+	0.261665i	−0.962379	−	0.271712i	$-0.912410\pi$
$383$	−17089.4	+	38383.3i	−0.116501	+	0.261665i	0.845878	+	0.533376i	$0.179077\pi$
$384$	−6043.60	+	28432.9i	−0.0409858	+	0.192823i
$385$	67453.0	+	317341.i	0.455072	+	2.14094i
$386$	−843.442	+	375.525i	−0.00566084	+	0.00252037i
$387$	24304.2	+	7896.92i	0.162278	+	0.0527273i
$388$	−15013.4	+	46206.5i	−0.0997277	+	0.306930i
$389$	51793.4	+	116330.i	0.342275	+	0.768762i	0.999881	+	0.0154006i	$0.00490235\pi$
$389$	51793.4	+	116330.i	0.342275	+	0.768762i	−0.657606	+	0.753362i	$0.728431\pi$
$390$	−5725.20	+	1216.93i	−0.0376410	+	0.00800085i
$391$	102956.	+	21884.1i	0.673441	+	0.143144i
$392$	−33974.9	−	15126.6i	−0.221098	−	0.0984394i
$393$	−106111.	−	95542.5i	−0.687027	−	0.618602i
$394$	884.858	+	93.0023i	0.00570008	+	0.000599103i
$395$	−12922.4	+	17786.1i	−0.0828225	+	0.113995i
$396$	69448.4	−	7299.32i	0.442865	−	0.0465470i
$397$	87662.3	−	151836.i	0.556201	−	0.963369i	−0.441608	−	0.897208i	$-0.645592\pi$
$397$	87662.3	−	151836.i	0.556201	−	0.963369i	0.997809	−	0.0661607i	$-0.0210750\pi$
$398$	5767.14	−	3329.66i	0.0364078	−	0.0210200i
$399$	183865.	+	253068.i	1.15492	+	1.58962i
$400$	−22154.1	−	24604.7i	−0.138463	−	0.153779i
$401$	32275.4	−	10486.9i	0.200716	−	0.0652166i	−0.206934	−	0.978355i	$-0.566348\pi$
$401$	32275.4	−	10486.9i	0.200716	−	0.0652166i	0.407650	+	0.913138i	$0.366348\pi$
$402$			3122.72i			0.0193233i
$403$	130446.	+	54363.8i	0.803195	+	0.334734i
$404$	8815.40			0.0540106
$405$	26374.5	+	81172.3i	0.160795	+	0.494878i
$406$	−11217.3	+	10100.1i	−0.0680512	+	0.0612736i
$407$	19785.5	−	14375.0i	0.119442	−	0.0867798i
$408$	−10452.1	−	18103.6i	−0.0627892	−	0.108754i
$409$	27988.0	+	16158.9i	0.167311	+	0.0965973i	0.581318	−	0.813677i	$-0.302537\pi$
$409$	27988.0	+	16158.9i	0.167311	+	0.0965973i	−0.414006	+	0.910274i	$0.635871\pi$
$410$	1801.37	+	17138.9i	0.0107161	+	0.101957i
$411$	−73567.1	−	53449.7i	−0.435512	−	0.316418i
$412$	−29557.4	+	281220.i	−0.174129	+	1.65673i
$413$	91316.8	−	101418.i	0.535366	−	0.594584i
$414$	−719.318	+	1615.61i	−0.00419682	+	0.00942621i
$415$	27716.1	−	130394.i	0.160929	−	0.757113i
$416$	−5618.15	−	26431.3i	−0.0324643	−	0.152733i
$417$	−27587.4	+	12282.7i	−0.158650	+	0.0706354i
$418$	−19349.4	−	6287.01i	−0.110743	−	0.0359825i
$419$	−82971.1	+	255359.i	−0.472605	+	1.45453i	0.376555	+	0.926394i	$0.377109\pi$
$419$	−82971.1	+	255359.i	−0.472605	+	1.45453i	−0.849160	+	0.528136i	$0.822891\pi$
$420$	−91365.8	−	205211.i	−0.517947	−	1.16333i
$421$	167470.	−	35596.8i	0.944870	−	0.200838i	0.290382	−	0.956911i	$-0.406218\pi$
$421$	167470.	−	35596.8i	0.944870	−	0.200838i	0.654488	+	0.756073i	$0.272884\pi$
$422$	4758.77	+	1011.51i	0.0267221	+	0.00567995i
$423$	−9870.64	−	4394.69i	−0.0551651	−	0.0245611i
$424$	8286.68	+	7461.36i	0.0460945	+	0.0415037i
$425$	47532.1	+	4995.82i	0.263153	+	0.0276585i
$426$	4702.29	−	6472.15i	0.0259114	−	0.0356639i
$427$	−226221.	+	23776.8i	−1.24073	+	0.130406i
$428$	−36270.2	+	62821.8i	−0.197999	+	0.342944i
$429$	162608.	−	93881.5i	0.883540	−	0.510112i
$430$	3142.66	+	4325.51i	0.0169966	+	0.0233938i
$431$	−145019.	−	161060.i	−0.780677	−	0.867030i	0.213258	−	0.976996i	$-0.431592\pi$
$431$	−145019.	−	161060.i	−0.780677	−	0.867030i	−0.993935	+	0.109966i	$0.964926\pi$
$432$	−191084.	+	62086.8i	−1.02390	+	0.332684i
$433$		−	40710.4i		−	0.217135i	−0.994089	−	0.108568i	$-0.965374\pi$
$433$		−	40710.4i		−	0.217135i	0.994089	−	0.108568i	$-0.0346264\pi$
$434$	3625.35	−	19326.9i	0.0192473	−	0.102608i
$435$	−122125.			−0.645395
$436$	−46884.1	−	144294.i	−0.246634	−	0.759061i
$437$	−105612.	+	95093.5i	−0.553033	+	0.497953i
$438$	793.115	−	576.232i	0.00413417	−	0.00300365i
$439$	67079.8	+	116186.i	0.348067	+	0.602869i	0.985906	−	0.167300i	$-0.0535049\pi$
$439$	67079.8	+	116186.i	0.348067	+	0.602869i	−0.637839	+	0.770170i	$0.720172\pi$
$440$	25351.2	+	14636.5i	0.130946	+	0.0756019i
$441$	−12932.1	−	123041.i	−0.0664953	−	0.632661i
$442$	10455.6	+	7596.41i	0.0535184	+	0.0388834i
$443$	−18255.1	+	173685.i	−0.0930199	+	0.885025i	0.844139	+	0.536124i	$0.180112\pi$
$443$	−18255.1	+	173685.i	−0.0930199	+	0.885025i	−0.937159	+	0.348902i	$0.886555\pi$
$444$	−11330.5	+	12583.8i	−0.0574754	+	0.0638329i
$445$	25104.2	−	56385.0i	0.126773	−	0.284737i
$446$	−4055.09	+	19077.7i	−0.0203859	+	0.0959083i
$447$	−35228.7	−	165738.i	−0.176312	−	0.829482i
$448$	311592.	−	138730.i	1.55249	−	0.691215i
$449$	7302.01	+	2372.57i	0.0362201	+	0.0117686i	0.327071	−	0.945000i	$-0.393938\pi$
$449$	7302.01	+	2372.57i	0.0362201	+	0.0117686i	−0.290851	+	0.956768i	$0.593938\pi$
$450$	−248.150	+	763.726i	−0.00122543	+	0.00377149i
$451$	−224857.	−	505036.i	−1.10548	−	2.48296i
$452$	−104007.	+	22107.3i	−0.509079	+	0.108208i
$453$	306336.	+	65113.7i	1.49280	+	0.317304i
$454$	9562.64	+	4257.56i	0.0463944	+	0.0206561i
$455$	206783.	+	186188.i	0.998831	+	0.899352i
$456$	28069.9	+	2950.26i	0.134993	+	0.0141883i
$457$	−235350.	+	323932.i	−1.12689	+	1.55103i	−0.333052	+	0.942909i	$0.608078\pi$
$457$	−235350.	+	323932.i	−1.12689	+	1.55103i	−0.793841	+	0.608126i	$0.791922\pi$
$458$	7802.54	−	820.080i	0.0371967	−	0.00390954i
$459$	145016.	−	251175.i	0.688320	−	1.19220i
$460$	88381.3	−	51027.0i	0.417681	−	0.241148i
$461$	−163066.	−	224441.i	−0.767294	−	1.05609i	−0.996572	−	0.0827286i	$-0.973637\pi$
$461$	−163066.	−	224441.i	−0.767294	−	1.05609i	0.229278	−	0.973361i	$-0.426363\pi$
$462$	−17481.8	−	19415.5i	−0.0819036	−	0.0909631i
$463$	−265624.	+	86306.4i	−1.23910	+	0.402607i	−0.854002	−	0.520270i	$-0.825831\pi$
$463$	−265624.	+	86306.4i	−1.23910	+	0.402607i	−0.385095	+	0.922877i	$0.625831\pi$
$464$		−	186801.i		−	0.867647i
$465$	126430.	−	96578.4i	0.584713	−	0.446657i
$466$	−19413.8			−0.0894004
$467$	46633.0	+	143522.i	0.213826	+	0.658087i	0.999235	+	0.0391106i	$0.0124525\pi$
$467$	46633.0	+	143522.i	0.213826	+	0.658087i	−0.785409	+	0.618977i	$0.787548\pi$
$468$	44508.3	−	40075.4i	0.203212	−	0.182973i
$469$	120101.	−	87258.4i	0.546010	−	0.396700i
$470$	−1130.29	−	1957.72i	−0.00511674	−	0.00886245i
$471$	−178074.	−	102811.i	−0.802711	−	0.463446i
$472$	−1287.12	−	12246.2i	−0.00577745	−	0.0549688i
$473$	−138759.	−	100814.i	−0.620210	−	0.450609i
$474$	185.060	−	1760.72i	0.000823673	−	0.00783673i
$475$	−43179.2	+	47955.4i	−0.191376	+	0.212545i
$476$	−201738.	+	453110.i	−0.890376	+	1.99982i
$477$	−7712.45	+	36284.2i	−0.0338965	+	0.159471i
$478$	−3861.93	−	18168.9i	−0.0169024	−	0.0795195i
$479$	121514.	−	54101.4i	0.529608	−	0.235797i	−0.124470	−	0.992223i	$-0.539723\pi$
$479$	121514.	−	54101.4i	0.529608	−	0.235797i	0.654079	+	0.756427i	$0.273057\pi$
$480$	−28931.8	−	9400.52i	−0.125572	−	0.0408009i
$481$	6481.73	−	19948.7i	0.0280156	−	0.0862233i
$482$	2108.04	+	4734.73i	0.00907370	+	0.0203799i
$483$	−178508.	+	37943.1i	−0.765181	+	0.162644i
$484$	−230128.	−	48915.3i	−0.982380	−	0.208811i
$485$	−61894.7	−	27557.3i	−0.263130	−	0.117153i
$486$	6374.52	+	5739.64i	0.0269882	+	0.0243003i
$487$	−20847.5	−	2191.16i	−0.0879015	−	0.00923882i	0.0604756	−	0.998170i	$-0.480738\pi$
$487$	−20847.5	−	2191.16i	−0.0879015	−	0.00923882i	−0.148377	+	0.988931i	$0.547405\pi$
$488$	−12063.8	+	16604.4i	−0.0506575	+	0.0697240i
$489$	62196.8	−	6537.15i	0.260106	−	0.0273383i
$490$	12942.2	−	22416.5i	0.0539033	−	0.0933633i
$491$	248550.	−	143500.i	1.03098	−	0.595237i	0.113716	−	0.993513i	$-0.463725\pi$
$491$	248550.	−	143500.i	1.03098	−	0.595237i	0.917266	+	0.398276i	$0.130391\pi$
$492$	224988.	+	309669.i	0.929456	+	1.27929i
$493$	180434.	+	200392.i	0.742378	+	0.824494i
$494$	−16595.4	+	5392.17i	−0.0680039	+	0.0220958i
$495$			97381.0i			0.397433i
$496$	147725.	+	193385.i	0.600471	+	0.786068i
$497$	−380317.			−1.53969
$498$	3317.33	+	10209.7i	0.0133761	+	0.0411674i
$499$	219902.	−	198001.i	0.883138	−	0.795181i	−0.0966294	−	0.995320i	$-0.530806\pi$
$499$	219902.	−	198001.i	0.883138	−	0.795181i	0.979767	+	0.200139i	$0.0641395\pi$
$500$	216699.	−	157441.i	0.866796	−	0.629764i
$501$	147729.	+	255875.i	0.588560	+	1.01942i
$502$	14513.3	+	8379.28i	0.0575917	+	0.0332506i
$503$	−26777.6	−	254772.i	−0.105837	−	1.00697i	−0.910577	−	0.413341i	$-0.864362\pi$
$503$	−26777.6	−	254772.i	−0.105837	−	1.00697i	0.804740	−	0.593628i	$-0.202305\pi$
$504$	−13508.5	−	9814.50i	−0.0531797	−	0.0386373i
$505$	−1285.00	+	12226.0i	−0.00503872	+	0.0479402i
$506$	7942.30	−	8820.82i	0.0310203	−	0.0344515i
$507$	−21006.6	+	47181.5i	−0.0817220	+	0.183551i
$508$	−4036.07	+	18988.2i	−0.0156398	+	0.0735795i
$509$	39461.5	+	185652.i	0.152313	+	0.716578i	0.986322	+	0.164827i	$0.0527066\pi$
$509$	39461.5	+	185652.i	0.152313	+	0.716578i	−0.834009	+	0.551751i	$0.813960\pi$
$510$	13291.5	−	5917.77i	0.0511017	−	0.0227519i
$511$	−44324.1	−	14401.8i	−0.169746	−	0.0551537i
$512$	23993.9	−	73845.5i	0.0915293	−	0.281698i
$513$	159276.	+	357740.i	0.605223	+	1.35935i
$514$	15035.4	−	3195.88i	0.0569101	−	0.0120966i
$515$	−385712.	−	81985.5i	−1.45428	−	0.309117i
$516$	108488.	+	48301.9i	0.407457	+	0.181412i
$517$	53891.0	+	48523.7i	0.201621	+	0.181540i
$518$	−2902.61	−	305.076i	−0.0108175	−	0.00113697i
$519$	−24225.2	+	33343.1i	−0.0899357	+	0.123786i
$520$	24969.0	−	2624.35i	0.0923411	−	0.00970544i
$521$	12648.3	−	21907.5i	0.0465968	−	0.0807080i	−0.841786	−	0.539811i	$-0.818496\pi$
$521$	12648.3	−	21907.5i	0.0465968	−	0.0807080i	0.888383	+	0.459103i	$0.151829\pi$
$522$	−3923.71	+	2265.36i	−0.0143998	+	0.00831372i
$523$	228651.	+	314712.i	0.835931	+	1.15056i	0.986790	+	0.162005i	$0.0517962\pi$
$523$	228651.	+	314712.i	0.835931	+	1.15056i	−0.150859	+	0.988555i	$0.548204\pi$
$524$	204541.	+	227166.i	0.744936	+	0.827335i
$525$	−78810.5	+	25607.1i	−0.285934	+	0.0929055i
$526$			21168.9i			0.0765115i
$527$	−345268.	−	64765.4i	−1.24318	−	0.233197i
$528$	323326.			1.15977
$529$	60854.6	+	187291.i	0.217461	+	0.669277i
$530$	−5767.54	+	5193.12i	−0.0205324	+	0.0184874i
$531$	33139.8	−	24077.5i	0.117533	−	0.0853929i
$532$	−334838.	−	579957.i	−1.18307	−	2.04914i
$533$	−410622.	−	237073.i	−1.44540	−	0.834502i
$534$	519.543	+	4943.12i	0.00182196	+	0.0173348i
$535$	−81839.7	−	59460.1i	−0.285928	−	0.207739i
$536$	1400.13	−	13321.4i	0.00487349	−	0.0463681i
$537$	311848.	−	346343.i	1.08142	−	1.20104i
$538$	9584.34	−	21526.8i	0.0331129	−	0.0743729i
$539$	−172640.	+	812206.i	−0.594242	+	2.79569i
$540$	−58466.3	−	275062.i	−0.200502	−	0.943287i
$541$	298033.	−	132693.i	1.01829	−	0.453370i	0.171432	−	0.985196i	$-0.445160\pi$
$541$	298033.	−	132693.i	1.01829	−	0.453370i	0.846854	+	0.531826i	$0.178494\pi$
$542$	21095.4	+	6854.32i	0.0718108	+	0.0233327i
$543$	74954.8	−	230687.i	0.254214	−	0.782391i
$544$	27320.4	+	61362.5i	0.0923185	+	0.207351i
$545$	206954.	−	43989.5i	0.696757	−	0.148100i
$546$	−21917.9	−	4658.80i	−0.0735215	−	0.0156275i
$547$	227544.	+	101309.i	0.760484	+	0.338589i	0.750072	−	0.661357i	$-0.230019\pi$
$547$	227544.	+	101309.i	0.760484	+	0.338589i	0.0104122	+	0.999946i	$0.496686\pi$
$548$	144672.	+	130263.i	0.481752	+	0.433771i
$549$	−67902.4	−	7136.83i	−0.225289	−	0.0236788i
$550$	3167.95	−	4360.31i	0.0104726	−	0.0144142i
$551$	−362087.	+	38056.9i	−1.19264	+	0.125352i
$552$	−8233.23	+	14260.4i	−0.0270204	+	0.0468007i
$553$	−72889.2	+	42082.6i	−0.238349	+	0.137611i
$554$	−15065.9	−	20736.5i	−0.0490882	−	0.0675641i
$555$	−15800.6	−	17548.4i	−0.0512966	−	0.0569706i
$556$	61485.4	−	19977.8i	0.198894	−	0.0646247i
$557$		−	573758.i		−	1.84935i	−0.380759	−	0.924674i	$-0.624337\pi$
$557$		−	573758.i		−	1.84935i	0.380759	−	0.924674i	$-0.375663\pi$
$558$	2270.53	−	5448.15i	0.00729221	−	0.0174977i
$559$	−147103.			−0.470759
$560$	148066.	+	455699.i	0.472148	+	1.45312i
$561$	−346851.	+	312306.i	−1.10209	+	0.992326i
$562$	110.881	−	80.5598i	0.000351063	−	0.000255062i
$563$	130852.	+	226642.i	0.412823	+	0.715030i	0.995197	−	0.0978905i	$-0.0312095\pi$
$563$	130852.	+	226642.i	0.412823	+	0.715030i	−0.582374	+	0.812921i	$0.697876\pi$
$564$	−43483.2	−	25105.0i	−0.136698	−	0.0789229i
$565$	−15499.5	−	147468.i	−0.0485537	−	0.461957i
$566$	−16973.1	−	12331.7i	−0.0529821	−	0.0384938i
$567$	−34154.3	+	324956.i	−0.106238	+	1.01078i
$568$	−22961.6	+	25501.5i	−0.0711715	+	0.0790440i
$569$	222937.	−	500726.i	0.688587	−	1.54659i	−0.142101	−	0.989852i	$-0.545386\pi$
$569$	222937.	−	500726.i	0.688587	−	1.54659i	0.830688	−	0.556739i	$-0.187948\pi$
$570$	−4084.28	+	19215.0i	−0.0125709	+	0.0591413i
$571$	55867.2	+	262834.i	0.171350	+	0.806139i	0.976914	+	0.213631i	$0.0685290\pi$
$571$	55867.2	+	262834.i	0.171350	+	0.806139i	−0.805564	+	0.592508i	$0.798138\pi$
$572$	−367219.	+	163496.i	−1.12236	+	0.499708i
$573$	−371776.	−	120797.i	−1.13233	−	0.367915i
$574$	−20387.3	+	62745.7i	−0.0618779	+	0.190441i
$575$	−15312.7	−	34392.8i	−0.0463143	−	0.104024i
$576$	100141.	−	21285.6i	0.301833	−	0.0641567i
$577$	−597398.	−	126981.i	−1.79437	−	0.381405i	−0.814361	−	0.580358i	$-0.802913\pi$
$577$	−597398.	−	126981.i	−1.79437	−	0.381405i	−0.980009	+	0.198953i	$0.936246\pi$
$578$	−11004.2	−	4899.37i	−0.0329383	−	0.0146651i
$579$	−21251.9	−	19135.3i	−0.0633928	−	0.0570791i
$580$	260018.	+	27329.0i	0.772943	+	0.0812395i
$581$	299972.	−	412875.i	0.888644	−	1.22311i
$582$	5426.15	−	570.311i	0.0160194	−	0.00168370i
$583$	124483.	−	215611.i	0.366247	−	0.634359i
$584$	−3641.75	+	2102.57i	−0.0106779	+	0.00616487i
$585$	49092.2	+	67569.6i	0.143450	+	0.197442i
$586$	−5277.62	−	5861.39i	−0.0153689	−	0.0170689i
$587$	244473.	−	79434.1i	0.709504	−	0.230532i	0.0680374	−	0.997683i	$-0.478326\pi$
$587$	244473.	−	79434.1i	0.709504	−	0.230532i	0.641467	+	0.767151i	$0.278326\pi$
$588$		−	574923.i		−	1.66286i
$589$	344754.	−	325743.i	0.993754	−	0.938955i
$590$	8570.30			0.0246202
$591$	8516.09	+	26209.8i	0.0243818	+	0.0750393i
$592$	26841.8	−	24168.5i	0.0765894	−	0.0689614i
$593$	−263105.	+	191157.i	−0.748203	+	0.543601i	−0.895269	−	0.445525i	$-0.853017\pi$
$593$	−263105.	+	191157.i	−0.748203	+	0.543601i	0.147066	+	0.989127i	$0.453017\pi$
$594$	−16353.2	−	28324.5i	−0.0463478	−	0.0802768i
$595$	−599006.	−	345836.i	−1.69199	−	0.976869i
$596$	37917.3	+	360759.i	0.106744	+	1.01560i
$597$	166873.	+	121240.i	0.468206	+	0.340172i
$598$	1064.12	−	10124.4i	0.00297569	−	0.0283118i
$599$	392175.	−	435554.i	1.09302	−	1.21392i	0.117712	−	0.993048i	$-0.462444\pi$
$599$	392175.	−	435554.i	1.09302	−	1.21392i	0.975304	−	0.220869i	$-0.0708892\pi$
$600$	−3041.14	+	6830.52i	−0.00844762	+	0.0189737i
$601$	−30198.9	+	142075.i	−0.0836070	+	0.393340i	−0.999976	−	0.00699575i	$-0.997773\pi$
$601$	−30198.9	+	142075.i	−0.0836070	+	0.393340i	0.916369	+	0.400336i	$0.131106\pi$
$602$	4255.66	+	20021.3i	0.0117429	+	0.0552458i
$603$	40707.2	−	18124.0i	0.111953	−	0.0498448i
$604$	−637653.	−	207186.i	−1.74788	−	0.567920i
$605$	101385.	−	312032.i	0.276990	−	0.852487i
$606$	−402.657	−	904.383i	−0.00109645	−	0.00246267i
$607$	192299.	−	40874.4i	0.521915	−	0.110936i	0.0605815	−	0.998163i	$-0.480704\pi$
$607$	192299.	−	40874.4i	0.521915	−	0.110936i	0.461334	+	0.887227i	$0.347371\pi$
$608$	−88709.2	−	18855.7i	−0.239973	−	0.0510077i
$609$	−427113.	−	190163.i	−1.15162	−	0.512734i
$610$	−10615.7	−	9558.40i	−0.0285291	−	0.0256877i
$611$	61855.3	+	6501.25i	0.165689	+	0.0174146i
$612$	−87507.4	+	120444.i	−0.233637	+	0.321574i
$613$	343607.	−	36114.5i	0.914410	−	0.0961084i	0.364377	−	0.931251i	$-0.381282\pi$
$613$	343607.	−	36114.5i	0.914410	−	0.0961084i	0.550033	+	0.835143i	$0.314615\pi$
$614$	−6136.85	+	10629.3i	−0.0162783	+	0.0281948i
$615$	−462272.	+	266893.i	−1.22221	+	0.705646i
$616$	65871.2	+	90664.0i	0.173594	+	0.238932i
$617$	414149.	+	459959.i	1.08789	+	1.20823i	0.976741	+	0.214424i	$0.0687874\pi$
$617$	414149.	+	459959.i	1.08789	+	1.20823i	0.111152	+	0.993803i	$0.464546\pi$
$618$	30200.8	−	9812.83i	0.0790754	−	0.0256931i
$619$			48244.9i			0.125913i	0.998016	+	0.0629565i	$0.0200529\pi$
$619$			48244.9i			0.125913i	−0.998016	+	0.0629565i	$0.979947\pi$
$620$	−290795.	+	177334.i	−0.756491	+	0.461328i
$621$	−228460.			−0.592417
$622$	−596.905	−	1837.09i	−0.00154285	−	0.00474842i
$623$	175596.	−	158108.i	0.452418	−	0.407359i
$624$	224346.	−	162997.i	0.576167	−	0.418610i
$625$	145907.	+	252718.i	0.373521	+	0.646958i
$626$	−29355.7	−	16948.5i	−0.0749106	−	0.0432497i
$627$	−65871.1	−	626722.i	−0.167556	−	1.59419i
$628$	356134.	+	258746.i	0.903012	+	0.656077i
$629$	−5450.07	+	51853.9i	−0.0137753	+	0.131063i
$630$	7776.25	−	8636.40i	0.0195925	−	0.0217596i
$631$	−214893.	+	482658.i	−0.539715	+	1.21222i	0.413660	+	0.910431i	$0.364250\pi$
$631$	−214893.	+	482658.i	−0.539715	+	1.21222i	−0.953375	+	0.301788i	$0.902417\pi$
$632$	−1578.91	+	7428.19i	−0.00395297	+	0.0185973i
$633$	31330.5	+	147399.i	0.0781917	+	0.367863i
$634$	−17423.4	+	7757.38i	−0.0433465	+	0.0192991i
$635$	−25746.2	−	8365.43i	−0.0638506	−	0.0207463i
$636$	−53268.6	+	163944.i	−0.131691	+	0.405304i
$637$	289664.	+	650596.i	0.713864	+	1.60336i
$638$	29744.0	−	6322.28i	0.0730731	−	0.0155322i
$639$	−111661.	−	23734.3i	−0.273464	−	0.0581267i
$640$	79279.0	+	35297.3i	0.193552	+	0.0861750i
$641$	514368.	+	463139.i	1.25187	+	1.12718i	0.986626	+	0.163003i	$0.0521179\pi$
$641$	514368.	+	463139.i	1.25187	+	1.12718i	0.265240	+	0.964182i	$0.414549\pi$
$642$	8101.67	+	851.520i	0.0196564	+	0.00206597i
$643$	−218308.	+	300476.i	−0.528018	+	0.726754i	−0.986827	−	0.161781i	$-0.948276\pi$
$643$	−218308.	+	300476.i	−0.528018	+	0.726754i	0.458809	+	0.888535i	$0.348276\pi$
$644$	388556.	−	40838.8i	0.936875	−	0.0984695i
$645$	−82803.3	+	143420.i	−0.199034	+	0.344738i
$646$	37563.9	−	21687.5i	0.0900131	−	0.0519691i
$647$	52511.8	+	72276.2i	0.125443	+	0.172658i	0.867120	−	0.498100i	$-0.165969\pi$
$647$	52511.8	+	72276.2i	0.125443	+	0.172658i	−0.741676	+	0.670758i	$0.765969\pi$
$648$	19727.3	+	21909.4i	0.0469805	+	0.0521771i
$649$	−261473.	+	84957.6i	−0.620779	+	0.201703i
$650$		−	4622.52i		−	0.0109409i
$651$	592552.	−	140903.i	1.39819	−	0.332473i
$652$	−133887.			−0.314951
$653$	−56600.8	−	174199.i	−0.132738	−	0.408526i	0.862493	−	0.506069i	$-0.168902\pi$
$653$	−56600.8	−	174199.i	−0.132738	−	0.408526i	−0.995231	+	0.0975424i	$0.968902\pi$
$654$	−12661.8	+	11400.8i	−0.0296034	+	0.0266550i
$655$	−344869.	+	250562.i	−0.803845	+	0.584027i
$656$	−408237.	−	707087.i	−0.948646	−	1.64310i
$657$	−12114.8	−	6994.49i	−0.0280663	−	0.0162041i
$658$	−904.612	−	8606.81i	−0.00208935	−	0.0198788i
$659$	332131.	+	241307.i	0.764784	+	0.555648i	0.900374	−	0.435117i	$-0.143293\pi$
$659$	332131.	+	241307.i	0.764784	+	0.555648i	−0.135590	+	0.990765i	$0.543293\pi$
$660$	−47302.6	+	450054.i	−0.108592	+	1.03318i
$661$	−13709.0	+	15225.4i	−0.0313764	+	0.0348471i	−0.758629	−	0.651523i	$-0.774130\pi$
$661$	−13709.0	+	15225.4i	−0.0313764	+	0.0348471i	0.727252	+	0.686370i	$0.240797\pi$
$662$	−4968.74	+	11160.0i	−0.0113378	+	0.0254652i
$663$	−83227.6	+	391555.i	−0.189339	+	0.890770i
$664$	−9573.84	−	45041.4i	−0.0217145	−	0.102159i
$665$	853143.	−	379844.i	1.92921	−	0.858938i
$666$	−833.168	−	270.713i	−0.00187838	−	0.000610323i
$667$	65638.0	−	202013.i	0.147538	−	0.454075i
$668$	−257273.	−	577845.i	−0.576556	−	1.29497i
$669$	−590914.	+	125603.i	−1.32030	+	0.280638i
$670$	9119.04	+	1938.31i	0.0203142	+	0.00431791i
$671$	418628.	+	186385.i	0.929787	+	0.413968i
$672$	−86546.9	−	77927.2i	−0.191652	−	0.172564i
$673$	−128045.	−	13458.1i	−0.282704	−	0.0297134i	−0.0378847	−	0.999282i	$-0.512062\pi$
$673$	−128045.	−	13458.1i	−0.282704	−	0.0297134i	−0.244819	+	0.969569i	$0.578729\pi$
$674$	28198.8	−	38812.3i	0.0620741	−	0.0854377i
$675$	−103169.	+	10843.5i	−0.226434	+	0.0237991i
$676$	55283.6	−	95754.0i	0.120977	−	0.209538i
$677$	497860.	−	287440.i	1.08625	−	0.627147i	0.153675	−	0.988122i	$-0.450889\pi$
$677$	497860.	−	287440.i	1.08625	−	0.627147i	0.932576	+	0.360975i	$0.117556\pi$
$678$	7018.70	+	9660.41i	0.0152685	+	0.0210153i
$679$	−173557.	−	192755.i	−0.376447	−	0.418087i
$680$	−59354.4	+	19285.4i	−0.128362	+	0.0417072i
$681$			324225.i			0.699120i
$682$	−25792.6	+	30067.2i	−0.0554532	+	0.0646433i
$683$	−489774.			−1.04991			−0.524957	−	0.851129i	$-0.675919\pi$
$683$	−489774.			−1.04991			−0.524957	+	0.851129i	$0.675919\pi$
$684$	−62115.5	−	191172.i	−0.132766	−	0.408612i
$685$	−201749.	+	181655.i	−0.429962	+	0.387139i
$686$	40422.1	−	29368.4i	0.0858956	−	0.0624068i
$687$	121504.	+	210451.i	0.257440	+	0.445900i
$688$	−219373.	−	126655.i	−0.463454	−	0.267575i
$689$	−22320.0	−	212361.i	−0.0470172	−	0.447339i
$690$	−9271.88	−	6736.41i	−0.0194746	−	0.0141492i
$691$	65119.5	−	619570.i	0.136381	−	1.29758i	−0.685563	−	0.728013i	$-0.740444\pi$
$691$	65119.5	−	619570.i	0.136381	−	1.29758i	0.821944	−	0.569568i	$-0.192889\pi$
$692$	59039.7	−	65570.2i	0.123291	−	0.136929i
$693$	−151634.	+	340576.i	−0.315740	+	0.709165i
$694$	6281.51	−	29552.2i	0.0130420	−	0.0613579i
$695$	18744.4	+	88185.4i	0.0388063	+	0.182569i
$696$	−38538.0	+	17158.2i	−0.0795556	+	0.0354204i
$697$	1.12093e6	+	364211.i	2.30734	+	0.749700i
$698$	3067.25	−	9440.02i	0.00629561	−	0.0193759i
$699$	−244581.	−	549339.i	−0.500575	−	1.12431i
$700$	173527.	−	36884.3i	0.354137	−	0.0752741i
$701$	802022.	+	170475.i	1.63211	+	0.346917i	0.930685	−	0.365823i	$-0.119212\pi$
$701$	802022.	+	170475.i	1.63211	+	0.346917i	0.701429	+	0.712739i	$0.252546\pi$
$702$	−25626.1	−	11409.5i	−0.0520005	−	0.0231521i
$703$	−52315.7	−	47105.3i	−0.105857	−	0.0953144i
$704$	−683361.	−	71824.1i	−1.37881	−	0.144919i
$705$	41156.3	−	56646.8i	0.0828053	−	0.113972i
$706$	−12881.4	+	1353.89i	−0.0258437	+	0.00271628i
$707$	−23531.4	+	40757.5i	−0.0470770	+	0.0815397i
$708$	164854.	−	95178.3i	0.328876	−	0.189877i
$709$	96539.6	+	132875.i	0.192049	+	0.264333i	0.894173	−	0.447722i	$-0.147765\pi$
$709$	96539.6	+	132875.i	0.192049	+	0.264333i	−0.702123	+	0.712055i	$0.747765\pi$
$710$	−15981.3	−	17749.1i	−0.0317027	−	0.0352094i
$711$	−24026.5	+	7806.69i	−0.0475282	+	0.0154429i
$712$		−	21320.0i		−	0.0420560i
$713$	91803.7	+	261041.i	0.180585	+	0.513487i
$714$	55699.8			0.109259
$715$	−173222.	−	533124.i	−0.338838	−	1.04284i
$716$	−741465.	+	667618.i	−1.44632	+	1.30227i
$717$	465459.	−	338176.i	0.905405	−	0.657815i
$718$	20236.8	+	35051.2i	0.0392548	+	0.0679913i
$719$	45241.7	+	26120.3i	0.0875147	+	0.0505266i	0.543119	−	0.839656i	$-0.317243\pi$
$719$	45241.7	+	26120.3i	0.0875147	+	0.0505266i	−0.455604	+	0.890183i	$0.650577\pi$
$720$	15033.4	+	143034.i	0.0289997	+	0.275914i
$721$	−1.22131e6	−	887332.i	−2.34939	−	1.70693i
$722$	−2846.59	+	27083.5i	−0.00546074	+	0.0519554i
$723$	−107417.	+	119299.i	−0.205494	+	0.228224i
$724$	−211210.	+	474386.i	−0.402938	+	0.905014i
$725$	20052.8	−	94341.1i	0.0381504	−	0.179484i
$726$	5493.19	+	25843.4i	0.0104220	+	0.0490317i
$727$	−631206.	+	281031.i	−1.19427	+	0.531723i	−0.904953	−	0.425511i	$-0.860094\pi$
$727$	−631206.	+	281031.i	−1.19427	+	0.531723i	−0.289316	+	0.957234i	$0.593428\pi$
$728$	91411.9	+	29701.5i	0.172481	+	0.0560423i
$729$	−178196.	+	548430.i	−0.335307	+	1.03197i
$730$	−1190.43	−	2673.75i	−0.00223387	−	0.00501735i
$731$	357673.	−	76025.7i	0.669347	−	0.142274i
$732$	−310349.	−	65966.8i	−0.579200	−	0.123113i
$733$	−871827.	−	388163.i	−1.62264	−	0.722446i	−0.624365	−	0.781133i	$-0.714642\pi$
$733$	−871827.	−	388163.i	−1.62264	−	0.722446i	−0.998276	+	0.0586865i	$0.981309\pi$
$734$	4577.52	+	4121.62i	0.00849647	+	0.00765026i
$735$	797353.	+	83805.2i	1.47596	+	0.155130i
$736$	31099.7	−	42805.1i	0.0574118	−	0.0790205i
$737$	−297429.	+	31261.0i	−0.547581	+	0.0575530i
$738$	−9901.47	+	17149.8i	−0.0181797	+	0.0314882i
$739$	386851.	−	223348.i	0.708361	−	0.408972i	−0.102093	−	0.994775i	$-0.532554\pi$
$739$	386851.	−	223348.i	0.708361	−	0.408972i	0.810454	+	0.585802i	$0.199221\pi$
$740$	29714.4	+	40898.4i	0.0542630	+	0.0746866i
$741$	−361652.	−	401655.i	−0.658649	−	0.731504i
$742$	−28257.4	+	9181.39i	−0.0513245	+	0.0166763i
$743$		−	1184.54i		−	0.00214572i	−0.999999	−	0.00107286i	$-0.999658\pi$
$743$		−	1184.54i		−	0.00214572i	0.999999	−	0.00107286i	$-0.000341503\pi$
$744$	26327.4	−	48239.5i	0.0475622	−	0.0871479i
$745$	−505859.			−0.911416
$746$	−1202.24	−	3700.13i	−0.00216030	−	0.00664873i
$747$	113838.	−	102500.i	0.204007	−	0.183689i
$748$	808373.	−	587317.i	1.44480	−	1.04971i
$749$	−193636.	−	335387.i	−0.345161	−	0.597837i
$750$	−26050.1	−	15040.1i	−0.0463114	−	0.0267379i
$751$	37497.2	+	356762.i	0.0664842	+	0.632555i	0.976133	+	0.217176i	$0.0696845\pi$
$751$	37497.2	+	356762.i	0.0664842	+	0.632555i	−0.909648	+	0.415379i	$0.863649\pi$
$752$	86646.3	+	62952.3i	0.153220	+	0.111321i
$753$	−54258.7	+	516237.i	−0.0956929	+	0.910457i
$754$	17451.2	−	19381.5i	0.0306960	−	0.0340914i
$755$	380293.	−	854152.i	0.667151	−	1.49845i
$756$	223828.	−	1.05303e6i	0.391626	−	1.84245i
$757$	−102162.	−	480636.i	−0.178279	−	0.838735i	−0.972827	−	0.231534i	$-0.925626\pi$
$757$	−102162.	−	480636.i	−0.178279	−	0.838735i	0.794548	−	0.607201i	$-0.207708\pi$
$758$	−7455.59	+	3319.44i	−0.0129761	+	0.00577732i
$759$	349656.	+	113610.i	0.606956	+	0.197212i
$760$	26038.7	−	80139.0i	0.0450809	−	0.138745i
$761$	−178723.	−	401418.i	−0.308610	−	0.693150i	0.690947	−	0.722906i	$-0.257194\pi$
$761$	−178723.	−	401418.i	−0.308610	−	0.693150i	−0.999557	+	0.0297552i	$0.990527\pi$
$762$	2132.38	−	453.251i	0.00367244	−	0.000780600i
$763$	792288.	+	168406.i	1.36092	+	0.289273i
$764$	764521.	+	340387.i	1.30979	+	0.583158i
$765$	−154286.	−	138920.i	−0.263635	−	0.237378i
$766$	−10046.0	−	1055.87i	−0.0171212	−	0.00179951i
$767$	−138598.	+	190764.i	−0.235596	+	0.324270i
$768$	467914.	−	49179.8i	0.793312	−	0.0833804i
$769$	48612.8	−	84199.9i	0.0822050	−	0.142383i	−0.821992	−	0.569499i	$-0.807137\pi$
$769$	48612.8	−	84199.9i	0.0822050	−	0.142383i	0.904197	+	0.427116i	$0.140470\pi$
$770$	−67548.8	+	38999.3i	−0.113930	+	0.0657773i
$771$	279852.	+	385183.i	0.470782	+	0.647976i
$772$	40965.6	+	45496.9i	0.0687361	+	0.0763391i
$773$	−319733.	+	103888.i	−0.535092	+	0.173862i	−0.564084	−	0.825718i	$-0.690770\pi$
$773$	−319733.	+	103888.i	−0.535092	+	0.173862i	0.0289914	+	0.999580i	$0.490770\pi$
$774$			6143.84i			0.0102555i
$775$	53846.9	+	113525.i	0.0896514	+	0.189011i
$776$	−23403.4			−0.0388647
$777$	−27935.4	−	85976.3i	−0.0462714	−	0.142409i
$778$	−22750.9	+	20485.0i	−0.0375872	+	0.0338437i
$779$	−1.28742e6	+	935364.i	−2.12151	+	1.54137i
$780$	194062.	+	336124.i	0.318970	+	0.552473i
$781$	663524.	+	383086.i	1.08781	+	0.628050i
$782$	2645.14	+	25166.8i	0.00432548	+	0.0411542i
$783$	−473508.	−	344024.i	−0.772331	−	0.561132i
$784$	−128188.	+	1.21962e6i	−0.208552	+	1.98424i
$785$	−410764.	+	456200.i	−0.666582	+	0.740314i
$786$	13962.5	−	31360.3i	0.0226005	−	0.0507616i
$787$	−111997.	+	526903.i	−0.180824	+	0.850709i	0.790409	+	0.612579i	$0.209868\pi$
$787$	−111997.	+	526903.i	−0.180824	+	0.850709i	−0.971233	+	0.238130i	$0.923466\pi$
$788$	−12266.5	−	57709.4i	−0.0197546	−	0.0929382i
$789$	−599001.	+	266692.i	−0.962217	+	0.428407i
$790$	−5026.84	−	1633.32i	−0.00805454	−	0.00261708i
$791$	175419.	−	539883.i	0.280364	−	0.862872i
$792$	13681.8	+	30729.8i	0.0218118	+	0.0489902i
$793$	384434.	−	81714.0i	0.611330	−	0.129942i
$794$	41229.9	+	8763.69i	0.0653990	+	0.0139010i
$795$	−219607.	−	97775.3i	−0.347465	−	0.154702i
$796$	−328161.	−	295477.i	−0.517917	−	0.466335i
$797$	540852.	+	56845.8i	0.851455	+	0.0894915i	0.520194	−	0.854048i	$-0.325860\pi$
$797$	540852.	+	56845.8i	0.851455	+	0.0894915i	0.331260	+	0.943539i	$0.392526\pi$
$798$	−44204.2	+	60841.9i	−0.0694158	+	0.0955426i
$799$	−153757.	+	16160.5i	−0.240847	+	0.0253141i
$800$	12012.5	−	20806.2i	0.0187695	−	0.0325097i
$801$	61422.1	−	35462.1i	0.0957326	−	0.0552712i
$802$	4795.66	+	6600.66i	0.00745589	+	0.0102622i
$803$	62823.9	+	69773.0i	0.0974302	+	0.108207i
$804$	196935.	−	63988.1i	0.304657	−	0.0989890i
$805$			544835.i			0.840763i
$806$	−2739.08	+	33865.3i	−0.00421633	+	0.0521297i
$807$	729873.			1.12073
$808$	1312.22	+	4038.59i	0.00200994	+	0.00618596i
$809$	225656.	−	203181.i	0.344786	−	0.310446i	−0.478485	−	0.878096i	$-0.658814\pi$
$809$	225656.	−	203181.i	0.344786	−	0.310446i	0.823270	+	0.567649i	$0.192147\pi$
$810$	−16600.6	+	12061.0i	−0.0253019	+	0.0183829i
$811$	−49491.0	−	85720.9i	−0.0752462	−	0.130330i	0.825947	−	0.563748i	$-0.190641\pi$
$811$	−49491.0	−	85720.9i	−0.0752462	−	0.130330i	−0.901193	+	0.433417i	$0.857308\pi$
$812$	866819.	+	500458.i	1.31467	+	0.759024i
$813$	71815.0	+	683274.i	0.108651	+	1.03375i
$814$	4756.76	+	3455.99i	0.00717898	+	0.00521583i
$815$	19516.4	−	185686.i	0.0293822	−	0.279553i
$816$	−461243.	+	512262.i	−0.692707	+	0.769329i
$817$	−200810.	+	451027.i	−0.300844	+	0.675708i
$818$	−1615.42	+	7599.95i	−0.00241423	+	0.0113581i
$819$	66478.5	+	312757.i	0.0991091	+	0.466272i
$820$	1.04396e6	−	464799.i	1.55258	−	0.691254i
$821$	−1.00461e6	−	326418.i	−1.49043	−	0.484270i	−0.553220	−	0.833035i	$-0.686601\pi$
$821$	−1.00461e6	−	326418.i	−1.49043	−	0.484270i	−0.937210	+	0.348765i	$0.886601\pi$
$822$	6755.75	−	20792.1i	0.00999838	−	0.0307719i
$823$	198062.	+	444855.i	0.292416	+	0.656778i	0.998690	−	0.0511607i	$-0.0162921\pi$
$823$	198062.	+	444855.i	0.292416	+	0.656778i	−0.706274	+	0.707938i	$0.749625\pi$
$824$	−133235.	+	28319.9i	−0.196229	+	0.0417098i
$825$	163291.	+	34708.6i	0.239913	+	0.0509951i
$826$	29973.3	+	13345.0i	0.0439314	+	0.0195595i
$827$	−423731.	−	381529.i	−0.619554	−	0.557849i	0.298448	−	0.954426i	$-0.403531\pi$
$827$	−423731.	−	381529.i	−0.619554	−	0.557849i	−0.918001	+	0.396577i	$0.870198\pi$
$828$	116629.	+	12258.2i	0.170116	+	0.0178799i
$829$	−24501.7	+	33723.7i	−0.0356522	+	0.0490711i	−0.826471	−	0.562979i	$-0.809655\pi$
$829$	−24501.7	+	33723.7i	−0.0356522	+	0.0490711i	0.790819	+	0.612050i	$0.209655\pi$
$830$	31873.6	−	3350.06i	0.0462675	−	0.00486291i
$831$	396960.	−	687554.i	0.574836	−	0.995646i
$832$	−510371.	+	294663.i	−0.737291	+	0.425675i
$833$	−1.04054e6	−	1.43218e6i	−1.49958	−	2.06399i
$834$	−4857.99	−	5395.35i	−0.00698433	−	0.00775688i
$835$	838908.	−	272578.i	1.20321	−	0.390946i
$836$			1.34910e6i			1.93034i
$837$	762258.	−	18308.4i	1.08806	−	0.0261336i
$838$	−64551.9			−0.0919224
$839$	−200374.	−	616689.i	−0.284655	−	0.876077i	−0.986502	−	0.163749i	$-0.947641\pi$
$839$	−200374.	−	616689.i	−0.284655	−	0.876077i	0.701847	−	0.712327i	$-0.252359\pi$
$840$	80412.8	−	72404.0i	0.113964	−	0.102613i
$841$	−131963.	+	95876.4i	−0.186577	+	0.135556i
$842$	20581.0	+	35647.3i	0.0290297	+	0.0502809i
$843$	3676.45	+	2122.60i	0.00517337	+	0.00298685i
$844$	−33721.6	−	320840.i	−0.0473395	−	0.450405i
$845$	124741.	+	90629.9i	0.174702	+	0.126928i
$846$	271.528	−	2583.42i	0.000379380	−	0.00360956i
$847$	840450.	−	933415.i	1.17151	−	1.30109i
$848$	149556.	−	335908.i	0.207976	−	0.467121i
$849$	135108.	−	635635.i	0.187442	−	0.881845i
$850$	2389.00	+	11239.4i	0.00330658	+	0.0155562i
$851$	37520.0	−	16705.0i	0.0518088	−	0.0230667i
$852$	−504522.	−	163929.i	−0.695026	−	0.225828i
$853$	−385849.	+	1.18752e6i	−0.530297	+	1.63209i	0.223299	+	0.974750i	$0.428317\pi$
$853$	−385849.	+	1.18752e6i	−0.530297	+	1.63209i	−0.753596	+	0.657337i	$0.771683\pi$
$854$	−22243.2	−	49959.0i	−0.0304987	−	0.0685011i
$855$	274188.	−	58280.4i	0.375073	−	0.0797243i
$856$	−34179.5	−	7265.08i	−0.0466464	−	0.00991500i
$857$	296216.	+	131884.i	0.403318	+	0.179569i	0.598362	−	0.801226i	$-0.295818\pi$
$857$	296216.	+	131884.i	0.403318	+	0.179569i	−0.195044	+	0.980794i	$0.562485\pi$
$858$	33546.6	+	30205.5i	0.0455695	+	0.0410309i
$859$	−525873.	−	55271.4i	−0.712680	−	0.0749056i	−0.258751	−	0.965944i	$-0.583311\pi$
$859$	−525873.	−	55271.4i	−0.712680	−	0.0749056i	−0.453928	+	0.891038i	$0.649978\pi$
$860$	208392.	−	286827.i	0.281763	−	0.387814i
$861$	−2.03231e6	+	213605.i	−2.74147	+	0.288140i
$862$	26052.5	−	45124.3i	0.0350619	−	0.0607290i
$863$	−118302.	+	68301.5i	−0.158844	+	0.0917083i	−0.577315	−	0.816522i	$-0.695899\pi$
$863$	−118302.	+	68301.5i	−0.158844	+	0.0917083i	0.418471	+	0.908230i	$0.362566\pi$
$864$	−85694.6	−	117949.i	−0.114796	−	0.158003i
$865$	82332.3	+	91439.3i	0.110037	+	0.122208i
$866$	9308.44	−	3024.50i	0.0124120	−	0.00403290i
$867$		−	373100.i		−	0.496349i
$868$	−1.29314e6	+	167397.i	−1.71636	+	0.222182i
$869$	169556.			0.224529
$870$	−9073.01	−	27923.9i	−0.0119871	−	0.0368924i
$871$	−190617.	+	171632.i	−0.251261	+	0.226236i
$872$	59126.5	−	42957.9i	0.0777588	−	0.0564951i
$873$	−38927.3	−	67424.1i	−0.0510771	−	0.0884681i
$874$	−29589.4	−	17083.4i	−0.0387358	−	0.0223641i
$875$	149475.	+	1.42216e6i	0.195233	+	1.85752i
$876$	−52592.0	−	38210.3i	−0.0685348	−	0.0497935i
$877$	115460.	−	1.09853e6i	0.150118	−	1.42828i	−0.617098	−	0.786886i	$-0.711692\pi$
$877$	115460.	−	1.09853e6i	0.150118	−	1.42828i	0.767216	−	0.641389i	$-0.221642\pi$
$878$	−21582.3	+	23969.6i	−0.0279968	+	0.0310936i
$879$	99366.4	−	223180.i	0.128606	−	0.288854i
$880$	200692.	−	944183.i	0.259158	−	1.21924i
$881$	137459.	+	646692.i	0.177101	+	0.833193i	0.973548	+	0.228484i	$0.0733770\pi$
$881$	137459.	+	646692.i	0.177101	+	0.833193i	−0.796447	+	0.604708i	$0.793290\pi$
$882$	27172.5	−	12098.0i	0.0349294	−	0.0155516i
$883$	185744.	+	60351.7i	0.238228	+	0.0774049i	0.425698	−	0.904865i	$-0.360029\pi$
$883$	185744.	+	60351.7i	0.238228	+	0.0774049i	−0.187470	+	0.982270i	$0.560029\pi$
$884$	264823.	−	815041.i	0.338884	−	1.04298i
$885$	107971.	+	242507.i	0.137855	+	0.309627i
$886$	−41069.4	+	8729.56i	−0.0523179	+	0.0111205i
$887$	−331407.	−	70442.7i	−0.421225	−	0.0895342i	−0.00757765	−	0.999971i	$-0.502412\pi$
$887$	−331407.	−	70442.7i	−0.421225	−	0.0895342i	−0.413647	+	0.910437i	$0.635745\pi$
$888$	−7451.58	−	3317.66i	−0.00944980	−	0.00420732i
$889$	−77017.3	−	69346.7i	−0.0974507	−	0.0877450i
$890$	14757.5	+	1551.07i	0.0186308	+	0.00195818i
$891$	386909.	−	532535.i	0.487364	−	0.670799i
$892$	1.28623e6	−	135188.i	1.61655	−	0.169906i
$893$	104372.	−	180777.i	0.130882	−	0.226694i
$894$	35278.8	−	20368.2i	0.0441406	−	0.0254846i
$895$	−817829.	−	1.12564e6i	−1.02098	−	1.40526i
$896$	222304.	+	246894.i	0.276906	+	0.307535i
$897$	299888.	−	97439.6i	0.372713	−	0.121102i
$898$			1845.87i			0.00228901i
$899$	−202812.	+	679276.i	−0.250943	+	0.840479i
$900$	53249.4			0.0657400
$901$	164022.	+	504807.i	0.202047	+	0.621836i
$902$	98771.3	−	88934.1i	0.121400	−	0.109309i
$903$	−512914.	+	372654.i	−0.629026	+	0.457014i
$904$	−25610.0	−	44357.8i	−0.0313381	−	0.0542791i
$905$	−627133.	−	362075.i	−0.765706	−	0.442081i
$906$	7870.33	+	74881.2i	0.00958819	+	0.0912255i
$907$	707973.	+	514373.i	0.860602	+	0.625264i	0.928049	−	0.372459i	$-0.121485\pi$
$907$	707973.	+	514373.i	0.860602	+	0.625264i	−0.0674470	+	0.997723i	$0.521485\pi$
$908$	72554.7	−	690312.i	0.0880022	−	0.837285i
$909$	−9452.36	+	10497.9i	−0.0114396	+	0.0127050i
$910$	−27209.4	+	61113.4i	−0.0328577	+	0.0737996i
$911$	−176270.	+	829284.i	−0.212393	+	0.999232i	0.734729	+	0.678360i	$0.237309\pi$
$911$	−176270.	+	829284.i	−0.212393	+	0.999232i	−0.947123	+	0.320872i	$0.896024\pi$
$912$	−193504.	−	910363.i	−0.232648	−	1.09452i
$913$	−939229.	+	418172.i	−1.12676	+	0.501664i
$914$	−91551.9	−	29747.0i	−0.109591	−	0.0356083i
$915$	136727.	−	420804.i	0.163310	−	0.502617i
$916$	−211601.	−	475264.i	−0.252190	−	0.566427i
$917$	−1.59628e6	+	339301.i	−1.89833	+	0.403502i
$918$	68204.8	+	14497.4i	0.0809337	+	0.0172030i
$919$	170448.	+	75888.4i	0.201819	+	0.0898554i	0.505157	−	0.863027i	$-0.331435\pi$
$919$	170448.	+	75888.4i	0.201819	+	0.0898554i	−0.303338	+	0.952883i	$0.598101\pi$
$920$	36533.0	+	32894.4i	0.0431628	+	0.0388639i
$921$	−378084.	−	39738.2i	−0.445727	−	0.0468478i
$922$	39203.8	−	53959.4i	0.0461176	−	0.0634754i
$923$	653521.	−	68687.9i	0.767108	−	0.0806263i
$924$	−866222.	+	1.50034e6i	−1.01458	+	1.75730i
$925$	16150.5	−	9324.51i	0.0188757	−	0.0108979i
$926$	−39467.9	−	54322.9i	−0.0460280	−	0.0633521i
$927$	−303201.	−	336739.i	−0.352834	−	0.391862i
$928$	128915.	−	41887.0i	0.149695	−	0.0486389i
$929$		−	585643.i		−	0.678580i	−0.940682	−	0.339290i	$-0.889813\pi$
$929$		−	585643.i		−	0.678580i	0.940682	−	0.339290i	$-0.110187\pi$
$930$	31475.5	+	21733.0i	0.0363920	+	0.0251278i
$931$	2.39018e6			2.75760
$932$	397811.	+	1.22434e6i	0.457979	+	1.40951i
$933$	44462.6	−	40034.3i	0.0510778	−	0.0459906i
$934$	−29351.7	+	21325.3i	−0.0336465	+	0.0244456i
$935$	696708.	+	1.20673e6i	0.796943	+	1.38035i
$936$	24985.0	+	14425.1i	0.0285186	+	0.0164652i
$937$	−159084.	−	1.51358e6i	−0.181196	−	1.72396i	−0.586646	−	0.809843i	$-0.699552\pi$
$937$	−159084.	−	1.51358e6i	−0.181196	−	1.72396i	0.405450	−	0.914117i	$-0.367115\pi$
$938$	28874.3	+	20978.4i	0.0328175	+	0.0238433i
$939$	109748.	−	1.04418e6i	0.124470	−	1.18425i
$940$	−100303.	+	111398.i	−0.113516	+	0.126072i
$941$	114221.	−	256545.i	0.128994	−	0.289724i	−0.837490	−	0.546453i	$-0.815978\pi$
$941$	114221.	−	256545.i	0.128994	−	0.289724i	0.966484	+	0.256728i	$0.0826446\pi$
$942$	10278.1	−	48354.8i	0.0115828	−	0.0544927i
$943$	−193025.	−	908113.i	−0.217066	−	1.02121i
$944$	−370937.	+	165152.i	−0.416251	+	0.185327i
$945$	1.42780e6	+	463922.i	1.59884	+	0.519495i
$946$	12742.4	−	39217.0i	0.0142386	−	0.0438220i
$947$	566595.	+	1.27259e6i	0.631790	+	1.41902i	0.891359	+	0.453299i	$0.149753\pi$
$947$	566595.	+	1.27259e6i	0.631790	+	1.41902i	−0.259569	+	0.965725i	$0.583580\pi$
$948$	−114833.	+	24408.4i	−0.127776	+	0.0271596i
$949$	78765.8	+	16742.2i	0.0874591	+	0.0185900i
$950$	−14172.9	−	6310.18i	−0.0157041	−	0.00699189i
$951$	−439010.	−	395286.i	−0.485415	−	0.437069i
$952$	−237613.	−	24974.1i	−0.262178	−	0.0275560i
$953$	719642.	−	990502.i	0.792374	−	1.09061i	−0.201434	−	0.979502i	$-0.564560\pi$
$953$	719642.	−	990502.i	0.792374	−	1.09061i	0.993808	−	0.111108i	$-0.0354398\pi$
$954$	−8869.37	+	932.208i	−0.00974531	+	0.00102427i
$955$	−583520.	+	1.01069e6i	−0.639807	+	1.10818i
$956$	−1.06669e6	+	615855.i	−1.16714	+	0.673849i
$957$	553620.	+	761993.i	0.604488	+	0.832007i
$958$	21397.9	+	23764.8i	0.0233153	+	0.0258942i
$959$	−988446.	+	321165.i	−1.07477	+	0.349214i
$960$			663453.i			0.719893i
$961$	−327222.	−	863607.i	−0.354320	−	0.935124i
$962$	5042.82			0.00544908
$963$	−35921.1	−	110554.i	−0.0387345	−	0.119212i
$964$	255401.	−	229964.i	0.274832	−	0.247460i
$965$	−69070.5	+	50182.6i	−0.0741716	+	0.0538889i
$966$	−21937.6	−	37997.0i	−0.0235090	−	0.0407188i
$967$	741845.	+	428304.i	0.793341	+	0.458036i	0.841137	−	0.540821i	$-0.181887\pi$
$967$	741845.	+	428304.i	0.793341	+	0.458036i	−0.0477963	+	0.998857i	$0.515220\pi$
$968$	−11846.3	−	112710.i	−0.0126424	−	0.120285i
$969$	1.08692e6	+	789691.i	1.15757	+	0.841027i
$970$	1702.64	−	16199.5i	0.00180959	−	0.0172171i
$971$	−794053.	+	881886.i	−0.842192	+	0.935349i	−0.998629	−	0.0523386i	$-0.983332\pi$
$971$	−794053.	+	881886.i	−0.842192	+	0.935349i	0.156437	+	0.987688i	$0.449999\pi$
$972$	231350.	−	519622.i	0.244871	−	0.549990i
$973$	−71759.6	+	337603.i	−0.0757974	+	0.356599i
$974$	−1047.81	−	4929.57i	−0.00110450	−	0.00519626i
$975$	130800.	−	58235.8i	0.137594	−	0.0612606i
$976$	643657.	+	209137.i	0.675701	+	0.219549i
$977$	−387603.	+	1.19292e6i	−0.406067	+	1.24975i	0.513933	+	0.857830i	$0.328188\pi$
$977$	−387603.	+	1.19292e6i	−0.406067	+	1.24975i	−0.920001	+	0.391917i	$0.871812\pi$
$978$	6115.50	+	13735.6i	0.00639373	+	0.0143606i
$979$	−465615.	+	98969.4i	−0.485804	+	0.103261i
$980$	−1.67890e6	−	356862.i	−1.74813	−	0.371576i
$981$	222106.	+	98888.1i	0.230793	+	0.102756i
$982$	51276.9	+	46169.9i	0.0531739	+	0.0478780i
$983$	1.39025e6	+	146121.i	1.43875	+	0.151219i	0.791553	−	0.611101i	$-0.209273\pi$
$983$	1.39025e6	+	146121.i	1.43875	+	0.151219i	0.647201	+	0.762320i	$0.275940\pi$
$984$	−108378.	+	149169.i	−0.111931	+	0.154060i
$985$	81824.5	−	8600.10i	0.0843356	−	0.00886403i
$986$	−32414.8	+	56144.0i	−0.0333418	+	0.0577497i
$987$	232144.	−	134028.i	0.238299	−	0.137582i
$988$	680116.	+	936100.i	0.696738	+	0.958977i
$989$	−192734.	−	214052.i	−0.197045	−	0.218840i
$990$	−22266.2	+	7234.72i	−0.0227183	+	0.00738161i
$991$		−	325575.i		−	0.331515i	−0.986167	−	0.165758i	$-0.946993\pi$
$991$		−	325575.i		−	0.331515i	0.986167	−	0.165758i	$-0.0530069\pi$
$992$	−100334.	+	145312.i	−0.101959	+	0.147665i
$993$	−378383.			−0.383736
$994$	−28254.9	−	86959.6i	−0.0285970	−	0.0880125i
$995$	457628.	−	412050.i	0.462239	−	0.416202i
$996$	575900.	−	418416.i	0.580535	−	0.421783i
$997$	237636.	+	411598.i	0.239068	+	0.414079i	0.960447	−	0.278462i	$-0.0898246\pi$
$997$	237636.	+	411598.i	0.239068	+	0.414079i	−0.721379	+	0.692541i	$0.756491\pi$
$998$	61610.1	+	35570.6i	0.0618573	+	0.0357133i
$999$	−11829.4	−	112549.i	−0.0118531	−	0.112775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.11.6	✓	80
31.17	odd	30	inner	31.5.h.a.17.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.6	✓	80	1.1	even	1	trivial
31.5.h.a.17.6	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+(0.0742929 + 0.228650i) q^{2} +(-5.53397 + 4.98281i) q^{3} +(12.8975 - 9.37059i) q^{4} +(11.1159 + 19.2533i) q^{5} +(-1.55045 - 0.895155i) q^{6} +(8.89648 + 84.6444i) q^{7} +(6.21280 + 4.51386i) q^{8} +(-2.67036 + 25.4068i) q^{9} +(-3.57644 + 3.97204i) q^{10} +(69.7392 - 156.637i) q^{11} +(-24.6826 + 116.122i) q^{12} +(-30.5747 - 143.843i) q^{13} +(-18.6930 + 8.32266i) q^{14} +(-157.451 - 51.1588i) q^{15} +(78.2520 - 240.835i) q^{16} +(148.681 + 333.943i) q^{17} +(-6.00766 + 1.27697i) q^{18} +(-482.767 - 102.615i) q^{19} +(323.782 + 144.157i) q^{20} +(-471.000 - 424.090i) q^{21} +(40.9961 + 4.30887i) q^{22} +(169.249 - 232.951i) q^{23} +(-56.8732 + 5.97761i) q^{24} +(65.3733 - 113.230i) q^{25} +(30.6181 - 17.6774i) q^{26} +(-466.361 - 641.891i) q^{27} +(907.910 + 1008.34i) q^{28} +(701.572 - 227.955i) q^{29} -39.8018i q^{30} +(-546.031 + 790.804i) q^{31} +183.752 q^{32} +(394.557 + 1214.32i) q^{33} +(-65.3101 + 58.8055i) q^{34} +(-1530.79 + 1112.19i) q^{35} +(203.636 + 352.708i) q^{36} +(123.525 + 71.3174i) q^{37} +(-12.4032 - 118.008i) q^{38} +(885.940 + 643.673i) q^{39} +(-17.8459 + 169.793i) q^{40} +(2157.44 - 2396.08i) q^{41} +(61.9763 - 139.201i) q^{42} +(207.978 - 978.462i) q^{43} +(-568.317 - 2673.72i) q^{44} +(-518.849 + 231.006i) q^{45} +(65.8382 + 21.3921i) q^{46} +(-130.696 + 402.240i) q^{47} +(766.991 + 1722.69i) q^{48} +(-4736.99 + 1006.88i) q^{49} +(30.7468 + 6.53543i) q^{50} +(-2486.77 - 1107.18i) q^{51} +(-1742.23 - 1568.71i) q^{52} +(1444.08 + 151.779i) q^{53} +(112.121 - 154.321i) q^{54} +(3790.99 - 398.449i) q^{55} +(-326.801 + 566.036i) q^{56} +(3182.93 - 1837.67i) q^{57} +(104.244 + 143.479i) q^{58} +(-1072.92 - 1191.60i) q^{59} +(-2510.11 + 815.584i) q^{60} +2672.61i q^{61} +(-221.384 - 66.0987i) q^{62} -2174.30 q^{63} +(-1238.38 - 3811.35i) q^{64} +(2429.58 - 2187.60i) q^{65} +(-248.342 + 180.431i) q^{66} +(-872.117 - 1510.55i) q^{67} +(5046.86 + 2913.80i) q^{68} +(224.133 + 2132.48i) q^{69} +(-368.028 - 267.388i) q^{70} +(-467.086 + 4444.03i) q^{71} +(-131.273 + 145.794i) q^{72} +(-222.722 + 500.242i) q^{73} +(-7.12966 + 33.5424i) q^{74} +(202.429 + 952.354i) q^{75} +(-7188.06 + 3200.33i) q^{76} +(13878.9 + 4509.51i) q^{77} +(-81.3568 + 250.390i) q^{78} +(402.219 + 903.398i) q^{79} +(5506.71 - 1170.49i) q^{80} +(3755.18 + 798.189i) q^{81} +(708.148 + 315.288i) q^{82} +(-4456.06 - 4012.26i) q^{83} +(-10048.7 - 1056.16i) q^{84} +(-4776.78 + 6574.68i) q^{85} +(239.177 - 25.1385i) q^{86} +(-2746.62 + 4757.29i) q^{87} +(1140.31 - 658.360i) q^{88} +(-1631.84 - 2246.03i) q^{89} +(-91.3664 - 101.473i) q^{90} +(11903.5 - 3867.67i) q^{91} -4590.45i q^{92} +(-918.711 - 7097.06i) q^{93} -101.682 q^{94} +(-3390.71 - 10435.5i) q^{95} +(-1016.88 + 915.599i) q^{96} +(-2465.51 + 1791.30i) q^{97} +(-582.147 - 1008.31i) q^{98} +(3793.41 + 2190.13i) 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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