LMFDB - Embedded newform 31.5.h.a.17.1

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			17.1
Character	$\chi$	$=$	31.17
Dual form			31.5.h.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.06958 + 6.36951i) q^{2} +(1.99917 + 1.80007i) q^{3} +(-23.3433 - 16.9599i) q^{4} +(-16.3958 + 28.3984i) q^{5} +(-15.6030 + 9.00839i) q^{6} +(2.86136 - 27.2240i) q^{7} +(69.6453 - 50.6002i) q^{8} +(-7.71034 - 73.3590i) q^{9} +(-146.952 - 163.206i) q^{10} +(43.7569 + 98.2796i) q^{11} +(-16.1384 - 75.9252i) q^{12} +(-53.5234 + 251.808i) q^{13} +(167.482 + 74.5677i) q^{14} +(-83.8972 + 27.2598i) q^{15} +(35.5011 + 109.261i) q^{16} +(-138.498 + 311.072i) q^{17} +(483.218 + 102.711i) q^{18} +(-49.9620 + 10.6197i) q^{19} +(864.366 - 384.841i) q^{20} +(54.7253 - 49.2749i) q^{21} +(-716.552 + 75.3126i) q^{22} +(276.766 + 380.935i) q^{23} +(230.317 + 24.2073i) q^{24} +(-225.147 - 389.966i) q^{25} +(-1493.12 - 862.055i) q^{26} +(244.717 - 336.823i) q^{27} +(-528.509 + 586.969i) q^{28} +(590.889 + 191.991i) q^{29} -590.801i q^{30} +(819.395 - 502.108i) q^{31} +607.968 q^{32} +(-89.4320 + 275.243i) q^{33} +(-1694.75 - 1525.96i) q^{34} +(726.204 + 527.618i) q^{35} +(-1064.17 + 1843.21i) q^{36} +(-329.720 + 190.364i) q^{37} +(35.7577 - 340.212i) q^{38} +(-560.273 + 407.062i) q^{39} +(295.075 + 2807.45i) q^{40} +(-1756.28 - 1950.54i) q^{41} +(200.599 + 450.552i) q^{42} +(536.106 + 2522.18i) q^{43} +(645.381 - 3036.28i) q^{44} +(2209.70 + 983.820i) q^{45} +(-2999.16 + 974.487i) q^{46} +(-1075.85 - 3311.12i) q^{47} +(-125.704 + 282.336i) q^{48} +(1615.57 + 343.401i) q^{49} +(2949.85 - 627.011i) q^{50} +(-836.833 + 372.582i) q^{51} +(5520.04 - 4970.27i) q^{52} +(5204.78 - 547.045i) q^{53} +(1638.94 + 2255.81i) q^{54} +(-3508.42 - 368.750i) q^{55} +(-1178.26 - 2040.81i) q^{56} +(-118.999 - 68.7041i) q^{57} +(-2445.78 + 3366.33i) q^{58} +(-2861.91 + 3178.47i) q^{59} +(2420.76 + 786.552i) q^{60} -1231.90i q^{61} +(1502.38 + 6258.30i) q^{62} -2019.19 q^{63} +(-1826.26 + 5620.64i) q^{64} +(-6273.39 - 5648.58i) q^{65} +(-1568.08 - 1139.28i) q^{66} +(1050.86 - 1820.14i) q^{67} +(8508.76 - 4912.53i) q^{68} +(-132.405 + 1259.75i) q^{69} +(-4863.61 + 3533.62i) q^{70} +(976.182 + 9287.76i) q^{71} +(-4248.97 - 4718.96i) q^{72} +(-718.637 - 1614.09i) q^{73} +(-530.143 - 2494.13i) q^{74} +(251.856 - 1184.89i) q^{75} +(1346.39 + 599.449i) q^{76} +(2800.77 - 910.024i) q^{77} +(-1433.26 - 4411.12i) q^{78} +(1114.06 - 2502.22i) q^{79} +(-3684.91 - 783.252i) q^{80} +(-4748.71 + 1009.37i) q^{81} +(16058.8 - 7149.83i) q^{82} +(-4168.92 + 3753.71i) q^{83} +(-2113.16 + 222.102i) q^{84} +(-6563.17 - 9033.43i) q^{85} +(-17174.6 - 1805.12i) q^{86} +(835.693 + 1447.46i) q^{87} +(8020.43 + 4630.60i) q^{88} +(2572.25 - 3540.40i) q^{89} +(-10839.6 + 12038.6i) q^{90} +(6702.06 + 2177.63i) q^{91} -13586.2i q^{92} +(2541.94 + 471.163i) q^{93} +23316.8 q^{94} +(517.584 - 1592.96i) q^{95} +(1215.43 + 1094.38i) q^{96} +(-2885.42 - 2096.38i) q^{97} +(-5530.86 + 9579.73i) q^{98} +(6872.31 - 3967.73i) 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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−2.06958	+	6.36951i	−0.517395	+	1.59238i	0.261486	+	0.965207i	$0.415787\pi$
$2$	−2.06958	+	6.36951i	−0.517395	+	1.59238i	−0.778881	+	0.627171i	$0.784213\pi$
$3$	1.99917	+	1.80007i	0.222131	+	0.200007i	0.772681	−	0.634795i	$-0.218915\pi$
$3$	1.99917	+	1.80007i	0.222131	+	0.200007i	−0.550550	+	0.834802i	$0.685582\pi$
$4$	−23.3433	−	16.9599i	−1.45895	−	1.05999i
$5$	−16.3958	+	28.3984i	−0.655833	+	1.13594i	0.325851	+	0.945421i	$0.394349\pi$
$5$	−16.3958	+	28.3984i	−0.655833	+	1.13594i	−0.981684	+	0.190516i	$0.938984\pi$
$6$	−15.6030	+	9.00839i	−0.433416	+	0.250233i
$7$	2.86136	−	27.2240i	0.0583950	−	0.555591i	−0.925739	−	0.378164i	$-0.876556\pi$
$7$	2.86136	−	27.2240i	0.0583950	−	0.555591i	0.984134	−	0.177428i	$-0.0567776\pi$
$8$	69.6453	−	50.6002i	1.08821	−	0.790629i
$9$	−7.71034	−	73.3590i	−0.0951894	−	0.905666i
$10$	−146.952	−	163.206i	−1.46952	−	1.63206i
$11$	43.7569	+	98.2796i	0.361627	+	0.812228i	0.999127	+	0.0417777i	$0.0133021\pi$
$11$	43.7569	+	98.2796i	0.361627	+	0.812228i	−0.637500	+	0.770451i	$0.720031\pi$
$12$	−16.1384	−	75.9252i	−0.112072	−	0.527258i
$13$	−53.5234	+	251.808i	−0.316707	+	1.48999i	0.475490	+	0.879721i	$0.342271\pi$
$13$	−53.5234	+	251.808i	−0.316707	+	1.48999i	−0.792196	+	0.610266i	$0.791062\pi$
$14$	167.482	+	74.5677i	0.854499	+	0.380447i
$15$	−83.8972	+	27.2598i	−0.372876	+	0.121155i
$16$	35.5011	+	109.261i	0.138676	+	0.426801i
$17$	−138.498	+	311.072i	−0.479233	+	1.07638i	0.498570	+	0.866849i	$0.333859\pi$
$17$	−138.498	+	311.072i	−0.479233	+	1.07638i	−0.977803	+	0.209526i	$0.932808\pi$
$18$	483.218	+	102.711i	1.49141	+	0.317010i
$19$	−49.9620	+	10.6197i	−0.138399	+	0.0294176i	−0.276590	−	0.960988i	$-0.589204\pi$
$19$	−49.9620	+	10.6197i	−0.138399	+	0.0294176i	0.138191	+	0.990406i	$0.455871\pi$
$20$	864.366	−	384.841i	2.16092	−	0.962102i
$21$	54.7253	−	49.2749i	0.124094	−	0.111734i
$22$	−716.552	+	75.3126i	−1.48048	+	0.155605i
$23$	276.766	+	380.935i	0.523187	+	0.720105i	0.986073	−	0.166313i	$-0.0531862\pi$
$23$	276.766	+	380.935i	0.523187	+	0.720105i	−0.462886	+	0.886418i	$0.653186\pi$
$24$	230.317	+	24.2073i	0.399855	+	0.0420265i
$25$	−225.147	−	389.966i	−0.360235	−	0.623945i
$26$	−1493.12	−	862.055i	−2.20876	−	1.27523i
$27$	244.717	−	336.823i	0.335688	−	0.462035i
$28$	−528.509	+	586.969i	−0.674118	+	0.748684i
$29$	590.889	+	191.991i	0.702603	+	0.228290i	0.638464	−	0.769651i	$-0.279570\pi$
$29$	590.889	+	191.991i	0.702603	+	0.228290i	0.0641386	+	0.997941i	$0.479570\pi$
$30$		−	590.801i		−	0.656445i
$31$	819.395	−	502.108i	0.852649	−	0.522485i
$31$	819.395	−	502.108i	0.852649	−	0.522485i
$32$	607.968			0.593719
$33$	−89.4320	+	275.243i	−0.0821231	+	0.252749i
$34$	−1694.75	−	1525.96i	−1.46604	−	1.32003i
$35$	726.204	+	527.618i	0.592819	+	0.430709i
$36$	−1064.17	+	1843.21i	−0.821123	+	1.42223i
$37$	−329.720	+	190.364i	−0.240847	+	0.139053i	−0.615566	−	0.788085i	$-0.711073\pi$
$37$	−329.720	+	190.364i	−0.240847	+	0.139053i	0.374719	+	0.927138i	$0.377739\pi$
$38$	35.7577	−	340.212i	0.0247630	−	0.235604i
$39$	−560.273	+	407.062i	−0.368358	+	0.267628i
$40$	295.075	+	2807.45i	0.184422	+	1.75466i
$41$	−1756.28	−	1950.54i	−1.04478	−	1.16035i	−0.986786	−	0.162031i	$-0.948195\pi$
$41$	−1756.28	−	1950.54i	−1.04478	−	1.16035i	−0.0579964	−	0.998317i	$-0.518471\pi$
$42$	200.599	+	450.552i	0.113718	+	0.255415i
$43$	536.106	+	2522.18i	0.289944	+	1.36408i	0.846110	+	0.533008i	$0.178938\pi$
$43$	536.106	+	2522.18i	0.289944	+	1.36408i	−0.556166	+	0.831071i	$0.687728\pi$
$44$	645.381	−	3036.28i	0.333358	−	1.56833i
$45$	2209.70	+	983.820i	1.09121	+	0.485837i
$46$	−2999.16	+	974.487i	−1.41737	+	0.460533i
$47$	−1075.85	−	3311.12i	−0.487029	−	1.49892i	−0.829020	−	0.559219i	$-0.811101\pi$
$47$	−1075.85	−	3311.12i	−0.487029	−	1.49892i	0.341991	−	0.939703i	$-0.388899\pi$
$48$	−125.704	+	282.336i	−0.0545591	+	0.122542i
$49$	1615.57	+	343.401i	0.672876	+	0.143024i
$50$	2949.85	−	627.011i	1.17994	−	0.250804i
$51$	−836.833	+	372.582i	−0.321735	+	0.143246i
$52$	5520.04	−	4970.27i	2.04144	−	1.83812i
$53$	5204.78	−	547.045i	1.85290	−	0.194747i	0.888440	−	0.458993i	$-0.151790\pi$
$53$	5204.78	−	547.045i	1.85290	−	0.194747i	0.964455	+	0.264245i	$0.0851229\pi$
$54$	1638.94	+	2255.81i	0.562051	+	0.773597i
$55$	−3508.42	−	368.750i	−1.15981	−	0.121901i
$56$	−1178.26	−	2040.81i	−0.375721	−	0.650767i
$57$	−118.999	−	68.7041i	−0.0366263	−	0.0211462i
$58$	−2445.78	+	3366.33i	−0.727047	+	1.00069i
$59$	−2861.91	+	3178.47i	−0.822151	+	0.913091i	−0.997446	−	0.0714248i	$-0.977245\pi$
$59$	−2861.91	+	3178.47i	−0.822151	+	0.913091i	0.175295	+	0.984516i	$0.443912\pi$
$60$	2420.76	+	786.552i	0.672433	+	0.218487i
$61$		−	1231.90i		−	0.331068i	−0.986204	−	0.165534i	$-0.947065\pi$
$61$		−	1231.90i		−	0.331068i	0.986204	−	0.165534i	$-0.0529347\pi$
$62$	1502.38	+	6258.30i	0.390838	+	1.62807i
$63$	−2019.19			−0.508739
$64$	−1826.26	+	5620.64i	−0.445863	+	1.37223i
$65$	−6273.39	−	5648.58i	−1.48482	−	1.33694i
$66$	−1568.08	−	1139.28i	−0.359982	−	0.261542i
$67$	1050.86	−	1820.14i	0.234096	−	0.405467i	−0.724913	−	0.688840i	$-0.758120\pi$
$67$	1050.86	−	1820.14i	0.234096	−	0.405467i	0.959010	+	0.283373i	$0.0914535\pi$
$68$	8508.76	−	4912.53i	1.84013	−	1.06240i
$69$	−132.405	+	1259.75i	−0.0278104	+	0.264598i
$70$	−4863.61	+	3533.62i	−0.992573	+	0.721146i
$71$	976.182	+	9287.76i	0.193649	+	1.84244i	0.471557	+	0.881836i	$0.343692\pi$
$71$	976.182	+	9287.76i	0.193649	+	1.84244i	−0.277908	+	0.960608i	$0.589641\pi$
$72$	−4248.97	−	4718.96i	−0.819632	−	0.910293i
$73$	−718.637	−	1614.09i	−0.134854	−	0.302887i	0.833478	−	0.552552i	$-0.186346\pi$
$73$	−718.637	−	1614.09i	−0.134854	−	0.302887i	−0.968332	+	0.249665i	$0.919679\pi$
$74$	−530.143	−	2494.13i	−0.0968121	−	0.455465i
$75$	251.856	−	1184.89i	0.0447744	−	0.210647i
$76$	1346.39	+	599.449i	0.233100	+	0.103783i
$77$	2800.77	−	910.024i	0.472384	−	0.153487i
$78$	−1433.26	−	4411.12i	−0.235578	−	0.725036i
$79$	1114.06	−	2502.22i	0.178507	−	0.400932i	−0.802026	−	0.597289i	$-0.796244\pi$
$79$	1114.06	−	2502.22i	0.178507	−	0.400932i	0.980533	+	0.196357i	$0.0629111\pi$
$80$	−3684.91	−	783.252i	−0.575768	−	0.122383i
$81$	−4748.71	+	1009.37i	−0.723778	+	0.153844i
$82$	16058.8	−	7149.83i	2.38828	−	1.06333i
$83$	−4168.92	+	3753.71i	−0.605156	+	0.544885i	−0.913733	−	0.406314i	$-0.866814\pi$
$83$	−4168.92	+	3753.71i	−0.605156	+	0.544885i	0.308577	+	0.951199i	$0.400147\pi$
$84$	−2113.16	+	222.102i	−0.299485	+	0.0314771i
$85$	−6563.17	−	9033.43i	−0.908397	−	1.25030i
$86$	−17174.6	−	1805.12i	−2.32215	−	0.244067i
$87$	835.693	+	1447.46i	0.110410	+	0.191236i
$88$	8020.43	+	4630.60i	1.03570	+	0.597960i
$89$	2572.25	−	3540.40i	0.324738	−	0.446963i	−0.615169	−	0.788396i	$-0.710912\pi$
$89$	2572.25	−	3540.40i	0.324738	−	0.446963i	0.939906	+	0.341432i	$0.110912\pi$
$90$	−10839.6	+	12038.6i	−1.33822	+	1.48625i
$91$	6702.06	+	2177.63i	0.809330	+	0.262967i
$92$		−	13586.2i		−	1.60517i
$93$	2541.94	+	471.163i	0.293900	+	0.0544760i
$94$	23316.8			2.63884
$95$	517.584	−	1592.96i	0.0573501	−	0.176505i
$96$	1215.43	+	1094.38i	0.131883	+	0.118748i
$97$	−2885.42	−	2096.38i	−0.306666	−	0.222806i	0.423798	−	0.905757i	$-0.360696\pi$
$97$	−2885.42	−	2096.38i	−0.306666	−	0.222806i	−0.730465	+	0.682950i	$0.760696\pi$
$98$	−5530.86	+	9579.73i	−0.575891	+	0.997473i
$99$	6872.31	−	3967.73i	0.701185	−	0.404829i
$100$	−1358.11	+	12921.5i	−0.135811	+	1.29215i
$101$	307.775	−	223.612i	0.0301711	−	0.0219206i	−0.572598	−	0.819837i	$-0.694064\pi$
$101$	307.775	−	223.612i	0.0301711	−	0.0219206i	0.602769	+	0.797916i	$0.294064\pi$
$102$	−641.273	−	6101.31i	−0.0616372	−	0.586439i
$103$	4985.52	+	5536.98i	0.469933	+	0.521914i	0.930787	−	0.365562i	$-0.119123\pi$
$103$	4985.52	+	5536.98i	0.469933	+	0.521914i	−0.460854	+	0.887476i	$0.652457\pi$
$104$	9013.89	+	20245.5i	0.833384	+	1.87181i
$105$	502.062	+	2362.01i	0.0455385	+	0.214242i
$106$	−7287.31	+	34284.1i	−0.648568	+	3.05127i
$107$	8392.72	+	3736.68i	0.733053	+	0.326376i	0.739091	−	0.673606i	$-0.235255\pi$
$107$	8392.72	+	3736.68i	0.733053	+	0.326376i	−0.00603816	+	0.999982i	$0.501922\pi$
$108$	−11425.0	+	3712.20i	−0.979507	+	0.318261i
$109$	−4991.49	−	15362.2i	−0.420124	−	1.29301i	−0.907587	−	0.419865i	$-0.862077\pi$
$109$	−4991.49	−	15362.2i	−0.420124	−	1.29301i	0.487462	−	0.873144i	$-0.337923\pi$
$110$	9609.71	−	21583.8i	0.794191	−	1.78378i
$111$	−1001.83	−	212.946i	−0.0813111	−	0.0172832i
$112$	3076.10	−	653.846i	0.245225	−	0.0521242i
$113$	6036.86	−	2687.78i	0.472775	−	0.210493i	−0.156497	−	0.987678i	$-0.550020\pi$
$113$	6036.86	−	2687.78i	0.472775	−	0.210493i	0.629271	+	0.777186i	$0.283353\pi$
$114$	683.890	−	615.777i	0.0526231	−	0.0473820i
$115$	−15355.8	+	1613.96i	−1.16112	+	0.122038i
$116$	−10537.1	−	14503.1i	−0.783080	−	1.07782i
$117$	18885.1	+	1984.90i	1.37958	+	0.145000i
$118$	−14322.4	−	24807.1i	−1.02861	−	1.78160i
$119$	8072.34	+	4660.57i	0.570040	+	0.329113i
$120$	−4463.68	+	6143.73i	−0.309978	+	0.426648i
$121$	2052.52	−	2279.56i	0.140190	−	0.155697i
$122$	7846.62	+	2549.52i	0.527185	+	0.171293i
$123$		−	7060.90i		−	0.466713i
$124$	−27643.1	−	2176.00i	−1.79781	−	0.141519i
$125$	−5728.91			−0.366650
$126$	4178.87	−	12861.2i	0.263219	−	0.810105i
$127$	−1036.47	−	933.243i	−0.0642614	−	0.0578612i	0.636374	−	0.771380i	$-0.280433\pi$
$127$	−1036.47	−	933.243i	−0.0642614	−	0.0578612i	−0.700636	+	0.713519i	$0.747100\pi$
$128$	−24151.4	−	17547.1i	−1.47409	−	1.07099i
$129$	−3468.32	+	6007.31i	−0.208420	+	0.360994i
$130$	48962.0	−	28268.2i	2.89716	−	1.67268i
$131$	−2208.57	+	21013.2i	−0.128697	+	1.22447i	0.719387	+	0.694610i	$0.244423\pi$
$131$	−2208.57	+	21013.2i	−0.128697	+	1.22447i	−0.848084	+	0.529862i	$0.822244\pi$
$132$	6755.73	−	4908.33i	0.387726	−	0.281699i
$133$	146.153	+	1390.55i	0.00826235	+	0.0786110i
$134$	9418.58	+	10460.4i	0.524537	+	0.582557i
$135$	5552.92	+	12472.1i	0.304687	+	0.684338i
$136$	6094.59	+	28672.8i	0.329508	+	1.55021i
$137$	−948.999	+	4464.69i	−0.0505620	+	0.237876i	−0.996171	−	0.0874311i	$-0.972134\pi$
$137$	−948.999	+	4464.69i	−0.0505620	+	0.237876i	0.945609	+	0.325307i	$0.105468\pi$
$138$	−7749.99	−	3450.52i	−0.406952	−	0.181187i
$139$	−22272.2	+	7236.69i	−1.15275	+	0.374550i	−0.822178	−	0.569231i	$-0.807241\pi$
$139$	−22272.2	+	7236.69i	−1.15275	+	0.374550i	−0.330570	+	0.943781i	$0.607241\pi$
$140$	−8003.64	−	24632.7i	−0.408349	−	1.25677i
$141$	3809.42	−	8556.10i	0.191611	−	0.430366i
$142$	−61178.8	−	13004.0i	−3.03406	−	0.644909i
$143$	−27089.6	+	5758.07i	−1.32474	+	0.281582i
$144$	7741.56	−	3446.76i	0.373339	−	0.166221i
$145$	−15140.4	+	13632.5i	−0.720113	+	0.648393i
$146$	11768.2	−	1236.89i	0.552084	−	0.0580263i
$147$	2611.67	+	3594.66i	0.120860	+	0.166350i
$148$	10925.3	+	1148.29i	0.498780	+	0.0524239i
$149$	3732.47	+	6464.82i	0.168122	+	0.291195i	0.937759	−	0.347286i	$-0.112897\pi$
$149$	3732.47	+	6464.82i	0.168122	+	0.291195i	−0.769638	+	0.638481i	$0.779563\pi$
$150$	7025.93	+	4056.42i	0.312264	+	0.180285i
$151$	3620.76	−	4983.55i	0.158798	−	0.218567i	−0.722203	−	0.691681i	$-0.756870\pi$
$151$	3620.76	−	4983.55i	0.158798	−	0.218567i	0.881001	+	0.473114i	$0.156870\pi$
$152$	−2942.25	+	3267.70i	−0.127348	+	0.141435i
$153$	23887.8	+	7761.63i	1.02046	+	0.331566i
$154$			19722.9i			0.831628i
$155$	824.404	+	31502.0i	0.0343144	+	1.31122i
$156$	19982.3			0.821102
$157$	7757.22	−	23874.3i	0.314707	−	0.968570i	−0.661167	−	0.750239i	$-0.729939\pi$
$157$	7757.22	−	23874.3i	0.314707	−	0.968570i	0.975875	−	0.218331i	$-0.0700614\pi$
$158$	13632.3	+	12274.6i	0.546078	+	0.491691i
$159$	11390.0	+	8275.31i	0.450536	+	0.327333i
$160$	−9968.14	+	17265.3i	−0.389381	+	0.674427i
$161$	11162.5	−	6444.67i	0.430636	−	0.248628i
$162$	3398.64	−	32335.9i	0.129502	−	1.23213i
$163$	22973.7	−	16691.4i	0.864680	−	0.628227i	−0.0644742	−	0.997919i	$-0.520537\pi$
$163$	22973.7	−	16691.4i	0.864680	−	0.628227i	0.929154	+	0.369693i	$0.120537\pi$
$164$	7916.28	+	75318.4i	0.294329	+	2.80036i
$165$	−6350.17	−	7052.58i	−0.233248	−	0.259048i
$166$	−15281.4	−	34322.6i	−0.554558	−	1.24556i
$167$	−726.994	−	3420.24i	−0.0260674	−	0.122638i	0.963190	−	0.268822i	$-0.0866342\pi$
$167$	−726.994	−	3420.24i	−0.0260674	−	0.122638i	−0.989257	+	0.146184i	$0.953301\pi$
$168$	1318.04	−	6200.87i	0.0466991	−	0.219702i
$169$	−34450.7	−	15338.4i	−1.20621	−	0.537041i
$170$	71121.6	−	23108.8i	2.46095	−	0.799612i
$171$	1164.28	+	3583.28i	0.0398166	+	0.122543i
$172$	30261.4	−	67968.3i	1.02290	−	2.29747i
$173$	−4394.43	−	934.064i	−0.146828	−	0.0312093i	0.133911	−	0.990993i	$-0.457246\pi$
$173$	−4394.43	−	934.064i	−0.146828	−	0.0312093i	−0.280739	+	0.959784i	$0.590580\pi$
$174$	−10949.2	+	2327.32i	−0.361645	+	0.0768701i
$175$	−11260.7	+	5013.56i	−0.367695	+	0.163708i
$176$	−9184.72	+	8269.96i	−0.296511	+	0.266980i
$177$	−11442.9	+	1202.70i	−0.365250	+	0.0383893i
$178$	17227.1	+	23711.1i	0.543717	+	0.748362i
$179$	−5067.96	−	532.664i	−0.158171	−	0.0166245i	0.0251119	−	0.999685i	$-0.492006\pi$
$179$	−5067.96	−	532.664i	−0.158171	−	0.0166245i	−0.183283	+	0.983060i	$0.558672\pi$
$180$	−34896.1	−	60441.8i	−1.07704	−	1.86549i
$181$	11617.9	+	6707.62i	0.354627	+	0.204744i	0.666721	−	0.745307i	$-0.267697\pi$
$181$	11617.9	+	6707.62i	0.354627	+	0.204744i	−0.312094	+	0.950051i	$0.601030\pi$
$182$	−27740.9	+	38182.1i	−0.837487	+	1.15270i
$183$	2217.50	−	2462.79i	0.0662159	−	0.0735402i
$184$	38550.8	+	12525.9i	1.13867	+	0.369977i
$185$		−	12484.7i		−	0.364783i
$186$	−8261.83	+	15215.8i	−0.238809	+	0.439814i
$187$	−36632.4			−1.04757
$188$	−31042.4	+	95538.6i	−0.878293	+	2.70311i
$189$	−8469.45	−	7625.93i	−0.237100	−	0.213486i
$190$	9075.20	+	6593.52i	0.251391	+	0.182646i
$191$	27862.6	−	48259.4i	0.763756	−	1.32286i	−0.177146	−	0.984185i	$-0.556687\pi$
$191$	27862.6	−	48259.4i	0.763756	−	1.32286i	0.940902	−	0.338679i	$-0.109980\pi$
$192$	−13768.5	+	7949.26i	−0.373495	+	0.215637i
$193$	882.049	−	8392.14i	0.0236798	−	0.225298i	−0.976282	−	0.216505i	$-0.930534\pi$
$193$	882.049	−	8392.14i	0.0236798	−	0.225298i	0.999961	−	0.00879339i	$-0.00279906\pi$
$194$	19324.6	−	14040.1i	0.513459	−	0.373050i
$195$	−2373.78	−	22585.0i	−0.0624268	−	0.593951i
$196$	−31888.8	−	35416.1i	−0.830091	−	0.921909i
$197$	29404.6	+	66043.9i	0.757676	+	1.70177i	0.711347	+	0.702841i	$0.248085\pi$
$197$	29404.6	+	66043.9i	0.757676	+	1.70177i	0.0463284	+	0.998926i	$0.485248\pi$
$198$	11049.7	+	51984.8i	0.281852	+	1.32601i
$199$	−5475.07	+	25758.2i	−0.138256	+	0.650443i	0.853371	+	0.521305i	$0.174554\pi$
$199$	−5475.07	+	25758.2i	−0.138256	+	0.650443i	−0.991627	+	0.129138i	$0.958779\pi$
$200$	−35412.8	−	15766.8i	−0.885320	−	0.394170i
$201$	5377.22	−	1747.17i	0.133096	−	0.0432456i
$202$	787.332	+	2423.16i	0.0192955	+	0.0593853i
$203$	6917.52	−	15537.0i	0.167864	−	0.377029i
$204$	25853.4	+	5495.30i	0.621236	+	0.132048i
$205$	84188.1	−	17894.7i	2.00329	−	0.425811i
$206$	−45585.8	+	20296.1i	−1.07423	+	0.478276i
$207$	25811.1	−	23240.4i	0.602373	−	0.542379i
$208$	−29412.9	+	3091.42i	−0.679848	+	0.0714549i
$209$	−3229.89	−	4445.56i	−0.0739426	−	0.101773i
$210$	−16083.9	−	1690.49i	−0.364715	−	0.0383331i
$211$	11071.2	+	19175.9i	0.248674	+	0.430716i	0.963158	−	0.268935i	$-0.0866718\pi$
$211$	11071.2	+	19175.9i	0.248674	+	0.430716i	−0.714484	+	0.699652i	$0.753339\pi$
$212$	−130774.	−	75502.7i	−2.90972	−	1.67993i
$213$	−14767.0	+	20325.0i	−0.325487	+	0.447994i
$214$	−41170.3	+	45724.2i	−0.898992	+	0.998432i
$215$	−80415.9	−	26128.7i	−1.73966	−	0.565251i
$216$		−	35840.9i		−	0.768194i
$217$	−11324.8	−	23743.9i	−0.240498	−	0.504235i
$218$	108180.			2.27633
$219$	1468.78	−	4520.43i	0.0306244	−	0.0942523i
$220$	75644.0	+	68110.2i	1.56289	+	1.40723i
$221$	−70917.6	−	51524.7i	−1.45201	−	1.05495i
$222$	3429.74	−	5940.49i	0.0695914	−	0.120536i
$223$	20135.7	−	11625.3i	0.404908	−	0.233774i	−0.283691	−	0.958916i	$-0.591559\pi$
$223$	20135.7	−	11625.3i	0.404908	−	0.233774i	0.688600	+	0.725142i	$0.258226\pi$
$224$	1739.61	−	16551.3i	0.0346702	−	0.329865i
$225$	−26871.5	+	19523.3i	−0.530796	+	0.385646i
$226$	4626.11	+	44014.5i	0.0905730	+	0.861744i
$227$	−50376.2	−	55948.5i	−0.977628	−	1.08577i	−0.996300	−	0.0859406i	$-0.972610\pi$
$227$	−50376.2	−	55948.5i	−0.977628	−	1.08577i	0.0186719	−	0.999826i	$-0.494056\pi$
$228$	1612.61	+	3621.99i	0.0310213	+	0.0696750i
$229$	−21352.1	−	100454.i	−0.407164	−	1.91556i	−0.402161	−	0.915569i	$-0.631741\pi$
$229$	−21352.1	−	100454.i	−0.407164	−	1.91556i	−0.00500362	−	0.999987i	$-0.501593\pi$
$230$	21499.9	−	101149.i	0.406425	−	1.91208i
$231$	7237.33	+	3222.27i	0.135630	+	0.0603861i
$232$	50867.4	−	16527.8i	0.945070	−	0.307072i
$233$	26641.9	+	81995.2i	0.490742	+	1.51035i	0.823490	+	0.567331i	$0.192024\pi$
$233$	26641.9	+	81995.2i	0.490742	+	1.51035i	−0.332748	+	0.943016i	$0.607976\pi$
$234$	−51727.0	+	116181.i	−0.944682	+	2.12179i
$235$	111670.	+	23736.2i	2.02209	+	0.429809i
$236$	120713.	−	25658.3i	2.16735	−	0.460685i
$237$	6731.36	−	2996.99i	0.119841	−	0.0533567i
$238$	−46391.9	+	41771.5i	−0.819008	+	0.737438i
$239$	9982.22	−	1049.17i	0.174756	−	0.0183676i	−0.0167464	−	0.999860i	$-0.505331\pi$
$239$	9982.22	−	1049.17i	0.174756	−	0.0183676i	0.191502	+	0.981492i	$0.438664\pi$
$240$	−5956.88	−	8198.94i	−0.103418	−	0.142343i
$241$	57500.5	+	6043.55i	0.990006	+	0.104054i	0.585664	−	0.810554i	$-0.300834\pi$
$241$	57500.5	+	6043.55i	0.990006	+	0.104054i	0.404342	+	0.914608i	$0.367501\pi$
$242$	10271.8	+	17791.3i	0.175395	+	0.303792i
$243$	−40515.6	−	23391.7i	−0.686136	−	0.396141i
$244$	−20892.9	+	28756.6i	−0.350929	+	0.483012i
$245$	−36240.7	+	40249.4i	−0.603761	+	0.670544i
$246$	44974.5	+	14613.1i	0.743183	+	0.241475i
$247$		−	13149.2i		−	0.215529i
$248$	31660.2	−	76431.0i	0.514767	−	1.24270i
$249$	−15091.3			−0.243405
$250$	11856.4	−	36490.4i	0.189703	−	0.583846i
$251$	−4300.85	−	3872.50i	−0.0682663	−	0.0614673i	0.634291	−	0.773094i	$-0.281292\pi$
$251$	−4300.85	−	3872.50i	−0.0682663	−	0.0614673i	−0.702558	+	0.711627i	$0.747959\pi$
$252$	47134.4	+	34245.1i	0.742227	+	0.539260i
$253$	−25327.8	+	43869.0i	−0.395691	+	0.685357i
$254$	8089.37	−	4670.40i	0.125385	−	0.0723913i
$255$	3139.84	−	29873.5i	0.0482866	−	0.459416i
$256$	85250.3	−	61938.0i	1.30082	−	0.945099i
$257$	5456.92	+	51919.1i	0.0826193	+	0.786070i	0.954873	+	0.297016i	$0.0959914\pi$
$257$	5456.92	+	51919.1i	0.0826193	+	0.786070i	−0.872253	+	0.489054i	$0.837342\pi$
$258$	−31085.7	−	34524.1i	−0.467004	−	0.518661i
$259$	4239.01	+	9520.98i	0.0631924	+	0.141933i
$260$	50642.1	+	238252.i	0.749143	+	3.52444i
$261$	9528.34	−	44827.3i	0.139874	−	0.658055i
$262$	−129273.	−	57555.9i	−1.88323	−	0.838470i
$263$	2666.09	−	866.264i	0.0385445	−	0.0125239i	−0.289681	−	0.957123i	$-0.593549\pi$
$263$	2666.09	−	866.264i	0.0385445	−	0.0125239i	0.328226	+	0.944599i	$0.393549\pi$
$264$	7698.87	+	23694.7i	0.110464	+	0.339972i
$265$	−69801.6	+	156777.i	−0.993970	+	2.23249i
$266$	−9159.61	−	1946.93i	−0.129453	−	0.0275162i
$267$	11515.3	−	2447.66i	0.161530	−	0.0343343i
$268$	−55399.9	+	24665.6i	−0.771328	+	0.343417i
$269$	−56831.8	+	51171.6i	−0.785393	+	0.707171i	−0.960775	−	0.277329i	$-0.910551\pi$
$269$	−56831.8	+	51171.6i	−0.785393	+	0.707171i	0.175382	+	0.984501i	$0.443884\pi$
$270$	−90933.2	+	9557.47i	−1.24737	+	0.131104i
$271$	85791.2	+	118081.i	1.16816	+	1.60784i	0.674751	+	0.738046i	$0.264251\pi$
$271$	85791.2	+	118081.i	1.16816	+	1.60784i	0.493414	+	0.869795i	$0.335749\pi$
$272$	−38905.0	−	4089.08i	−0.525856	−	0.0552697i
$273$	9478.72	+	16417.6i	0.127182	+	0.220285i
$274$	−26473.9	−	15284.7i	−0.352628	−	0.203590i
$275$	28474.0	−	39191.1i	0.376515	−	0.518229i
$276$	24456.0	−	27161.2i	0.321046	−	0.356558i
$277$	−83971.0	−	27283.8i	−1.09438	−	0.355587i	−0.294445	−	0.955668i	$-0.595135\pi$
$277$	−83971.0	−	27283.8i	−1.09438	−	0.355587i	−0.799939	+	0.600082i	$0.795135\pi$
$278$		−	156840.i		−	2.02940i
$279$	−43151.9	−	56238.6i	−0.554360	−	0.722480i
$280$	77274.2			0.985641
$281$	2294.23	−	7060.91i	0.0290552	−	0.0894228i	−0.935477	−	0.353387i	$-0.885030\pi$
$281$	2294.23	−	7060.91i	0.0290552	−	0.0894228i	0.964533	+	0.263964i	$0.0850300\pi$
$282$	46614.3	+	41971.7i	0.586167	+	0.527787i
$283$	79707.4	+	57910.8i	0.995235	+	0.723081i	0.961061	−	0.276335i	$-0.0891201\pi$
$283$	79707.4	+	57910.8i	0.995235	+	0.723081i	0.0341737	+	0.999416i	$0.489120\pi$
$284$	134732.	−	233363.i	1.67045	−	2.89331i
$285$	3902.18	−	2252.92i	0.0480416	−	0.0277368i
$286$	19388.0	−	184464.i	0.237029	−	2.25518i
$287$	−58126.9	+	42231.7i	−0.705689	+	0.512713i
$288$	−4687.64	−	44599.9i	−0.0565157	−	0.537711i
$289$	−21697.8	−	24097.9i	−0.259789	−	0.288525i
$290$	−55497.9	−	124650.i	−0.659904	−	1.48217i
$291$	−1994.84	−	9384.98i	−0.0235571	−	0.110828i
$292$	−10599.4	+	49866.0i	−0.124312	+	0.584843i
$293$	54364.1	+	24204.5i	0.633253	+	0.281942i	0.698152	−	0.715949i	$-0.254006\pi$
$293$	54364.1	+	24204.5i	0.633253	+	0.281942i	−0.0648992	+	0.997892i	$0.520673\pi$
$294$	−28301.3	+	9195.65i	−0.327425	+	0.106387i
$295$	−43340.2	−	133387.i	−0.498020	−	1.53275i
$296$	−13331.0	+	29941.8i	−0.152152	+	0.341739i
$297$	43810.9	+	9312.30i	0.496672	+	0.105571i
$298$	−48902.4	+	10394.5i	−0.550678	+	0.117050i
$299$	−110736.	+	49302.8i	−1.23864	+	0.551480i
$300$	−25974.7	+	23387.7i	−0.288608	+	0.259864i
$301$	70197.8	−	7378.09i	0.774802	−	0.0814350i
$302$	24249.3	+	33376.3i	0.265880	+	0.365952i
$303$	1017.81	+	106.976i	0.0110862	+	0.00116520i
$304$	−2934.03	−	5081.89i	−0.0317481	−	0.0549893i
$305$	34984.1	+	20198.1i	0.376072	+	0.217125i
$306$	−98875.6	+	136091.i	−1.05596	+	1.45340i
$307$	42066.3	−	46719.4i	0.446332	−	0.495702i	−0.477430	−	0.878670i	$-0.658431\pi$
$307$	42066.3	−	46719.4i	0.446332	−	0.495702i	0.923762	+	0.382968i	$0.125098\pi$
$308$	−80813.0	−	26257.7i	−0.851882	−	0.276793i
$309$			20043.7i			0.209923i
$310$	−202359.	−	59944.9i	−2.10571	−	0.623776i
$311$	14519.7			0.150120			0.0750598	−	0.997179i	$-0.476085\pi$
$311$	14519.7			0.150120			0.0750598	+	0.997179i	$0.476085\pi$
$312$	−18422.9	+	56699.9i	−0.189256	+	0.582470i
$313$	56499.3	+	50872.2i	0.576706	+	0.519268i	0.905059	−	0.425287i	$-0.139827\pi$
$313$	56499.3	+	50872.2i	0.576706	+	0.519268i	−0.328353	+	0.944555i	$0.606493\pi$
$314$	136013.	+	98819.5i	1.37950	+	1.00227i
$315$	33106.2	−	57341.7i	0.333648	−	0.577896i
$316$	−68443.1	+	39515.7i	−0.685418	+	0.395726i
$317$	6026.78	−	57341.0i	0.0599745	−	0.570620i	−0.922731	−	0.385445i	$-0.874048\pi$
$317$	6026.78	−	57341.0i	0.0599745	−	0.570620i	0.982706	−	0.185175i	$-0.0592852\pi$
$318$	−76282.2	+	55422.3i	−0.754343	+	0.548062i
$319$	6986.63	+	66473.3i	0.0686572	+	0.653230i
$320$	−129674.	−	144018.i	−1.26635	−	1.40642i
$321$	10052.2	+	22577.7i	0.0975558	+	0.219114i
$322$	17947.7	+	84437.5i	0.173100	+	0.814373i
$323$	3616.14	−	17012.6i	0.0346610	−	0.163067i
$324$	127969.	+	56975.6i	1.21903	+	0.542748i
$325$	110247.	−	35821.5i	1.04376	−	0.339138i
$326$	58769.9	+	180875.i	0.552994	+	1.70194i
$327$	17674.2	−	39696.8i	0.165289	−	0.371245i
$328$	−221015.	−	46978.1i	−2.05434	−	0.436664i
$329$	−93220.2	+	19814.6i	−0.861229	+	0.183060i
$330$	58063.7	−	25851.6i	0.533183	−	0.237388i
$331$	−21962.9	+	19775.5i	−0.200463	+	0.180498i	−0.763248	−	0.646106i	$-0.776397\pi$
$331$	−21962.9	+	19775.5i	−0.200463	+	0.180498i	0.562785	+	0.826603i	$0.309730\pi$
$332$	160979.	−	16919.5i	1.46047	−	0.153501i
$333$	16507.1	+	22720.1i	0.148862	+	0.204891i
$334$	23289.8	+	2447.86i	0.208773	+	0.0219429i
$335$	34459.4	+	59685.5i	0.307057	+	0.531838i
$336$	7326.63	+	4230.03i	0.0648972	+	0.0374684i
$337$	−5901.45	+	8122.65i	−0.0519636	+	0.0715217i	−0.834208	−	0.551450i	$-0.814075\pi$
$337$	−5901.45	+	8122.65i	−0.0519636	+	0.0715217i	0.782244	+	0.622972i	$0.214075\pi$
$338$	168997.	−	187690.i	1.47926	−	1.64289i
$339$	16906.9	+	5493.39i	0.147118	+	0.0478015i
$340$			322180.i			2.78703i
$341$	85201.2	+	58559.2i	0.732718	+	0.503601i
$342$	−25233.3			−0.215736
$343$	34281.6	−	105508.i	0.291388	−	0.896802i
$344$	164960.	+	148531.i	1.39400	+	1.25516i
$345$	−33604.1	−	24414.8i	−0.282328	−	0.205123i
$346$	15044.2	−	26057.2i	0.125665	−	0.217659i
$347$	24937.4	−	14397.6i	0.207105	−	0.119572i	−0.392860	−	0.919598i	$-0.628514\pi$
$347$	24937.4	−	14397.6i	0.207105	−	0.119572i	0.599965	+	0.800026i	$0.295181\pi$
$348$	5040.99	−	47961.8i	0.0416253	−	0.396038i
$349$	96818.9	−	70343.0i	0.794894	−	0.577524i	−0.114518	−	0.993421i	$-0.536532\pi$
$349$	96818.9	−	70343.0i	0.794894	−	0.577524i	0.909412	+	0.415897i	$0.136532\pi$
$350$	−8629.15	−	82100.8i	−0.0704420	−	0.670211i
$351$	71716.7	+	79649.5i	0.582112	+	0.646500i
$352$	26602.8	+	59750.9i	0.214705	+	0.482235i
$353$	−30635.4	−	144128.i	−0.245852	−	1.15664i	−0.911797	−	0.410641i	$-0.865305\pi$
$353$	−30635.4	−	144128.i	−0.245852	−	1.15664i	0.665945	−	0.746001i	$-0.268028\pi$
$354$	16021.4	−	75374.8i	0.127848	−	0.601478i
$355$	−279763.	−	124558.i	−2.21990	−	0.988363i
$356$	−120089.	+	39019.4i	−0.947555	+	0.307879i
$357$	7748.69	+	23848.0i	0.0607984	+	0.187118i
$358$	13881.4	−	31178.0i	0.108309	−	0.243267i
$359$	−18548.6	−	3942.62i	−0.143920	−	0.0305911i	0.135388	−	0.990793i	$-0.456772\pi$
$359$	−18548.6	−	3942.62i	−0.143920	−	0.0305911i	−0.279308	+	0.960201i	$0.590105\pi$
$360$	203676.	−	43292.8i	1.57158	−	0.334049i
$361$	−116671.	+	51945.2i	−0.895257	+	0.398594i
$362$	−66768.6	+	60118.7i	−0.509513	+	0.458767i
$363$	8206.70	−	862.559i	0.0622810	−	0.00654599i
$364$	−119516.	−	164499.i	−0.902033	−	1.24154i
$365$	57620.1	+	6056.12i	0.432503	+	0.0454578i
$366$	11097.5	+	19221.4i	0.0828441	+	0.143490i
$367$	86433.9	+	49902.6i	0.641730	+	0.370503i	0.785280	−	0.619140i	$-0.212519\pi$
$367$	86433.9	+	49902.6i	0.641730	+	0.370503i	−0.143551	+	0.989643i	$0.545852\pi$
$368$	−31795.9	+	43763.3i	−0.234788	+	0.323158i
$369$	−129548.	+	143878.i	−0.951436	+	1.05668i
$370$	79521.4	+	25838.1i	0.580872	+	0.188737i
$371$		−	143260.i		−	1.04083i
$372$	−51346.4	−	54109.5i	−0.371043	−	0.391010i
$373$	23739.0			0.170626			0.0853129	−	0.996354i	$-0.472811\pi$
$373$	23739.0			0.170626			0.0853129	+	0.996354i	$0.472811\pi$
$374$	75813.6	−	233330.i	0.542006	−	1.66812i
$375$	−11453.1	−	10312.4i	−0.0814442	−	0.0733327i
$376$	−242471.	−	176166.i	−1.71508	−	1.24608i
$377$	−79971.4	+	138514.i	−0.562668	+	0.974569i
$378$	66101.7	−	38163.8i	0.462625	−	0.267097i
$379$	−2400.00	+	22834.5i	−0.0167083	+	0.158969i	−0.999695	−	0.0247095i	$-0.992134\pi$
$379$	−2400.00	+	22834.5i	−0.0167083	+	0.158969i	0.982986	+	0.183679i	$0.0588006\pi$
$380$	−39098.5	+	28406.8i	−0.270765	+	0.196723i
$381$	−392.189	−	3731.43i	−0.00270175	−	0.0257055i
$382$	249725.	+	277348.i	1.71134	+	1.90063i
$383$	−41624.8	−	93490.9i	−0.283762	−	0.637341i	0.714282	−	0.699858i	$-0.246754\pi$
$383$	−41624.8	−	93490.9i	−0.283762	−	0.637341i	−0.998044	+	0.0625179i	$0.980087\pi$
$384$	−16697.1	−	78553.8i	−0.113235	−	0.532727i
$385$	−20077.7	+	94458.0i	−0.135454	+	0.637261i
$386$	51628.4	+	22986.4i	0.346508	+	0.154275i
$387$	180891.	−	58775.1i	1.20780	−	0.392438i
$388$	31800.8	+	97872.9i	0.211239	+	0.650128i
$389$	116957.	−	262690.i	0.772909	−	1.73598i	0.101573	−	0.994828i	$-0.467612\pi$
$389$	116957.	−	262690.i	0.772909	−	1.73598i	0.671335	−	0.741154i	$-0.265721\pi$
$390$	148768.	+	31621.7i	0.978095	+	0.207900i
$391$	−156830.	+	33335.3i	−1.02583	+	0.218047i
$392$	129893.	−	57832.2i	0.845307	−	0.376355i
$393$	−42240.4	+	38033.4i	−0.273491	+	0.246252i
$394$	−481523.	+	50610.1i	−3.10187	+	0.326020i
$395$	52793.1	+	72663.5i	0.338363	+	0.465717i
$396$	−227715.	−	23933.8i	−1.45211	−	0.152623i
$397$	56458.2	+	97788.5i	0.358217	+	0.620450i	0.987663	−	0.156594i	$-0.0500514\pi$
$397$	56458.2	+	97788.5i	0.358217	+	0.620450i	−0.629446	+	0.777044i	$0.716718\pi$
$398$	−152736.	−	88182.2i	−0.964218	−	0.556692i
$399$	−2210.90	+	3043.04i	−0.0138875	+	0.0191144i
$400$	34615.1	−	38444.0i	0.216345	−	0.240275i
$401$	−230575.	−	74918.4i	−1.43392	−	0.465907i	−0.513921	−	0.857838i	$-0.671807\pi$
$401$	−230575.	−	74918.4i	−1.43392	−	0.465907i	−0.919995	+	0.391930i	$0.871807\pi$
$402$			37866.2i			0.234315i
$403$	82577.9	+	233205.i	0.508457	+	1.43591i
$404$	−10976.9			−0.0672538
$405$	49194.6	−	151405.i	0.299921	−	0.923062i
$406$	84646.8	+	76216.3i	0.513521	+	0.462376i
$407$	−33136.4	−	24075.0i	−0.200040	−	0.145337i
$408$	−39428.7	+	68292.5i	−0.236860	+	0.410254i
$409$	−78307.0	+	45210.6i	−0.468117	+	0.270267i	−0.715451	−	0.698663i	$-0.753779\pi$
$409$	−78307.0	+	45210.6i	−0.468117	+	0.270267i	0.247334	+	0.968930i	$0.420445\pi$
$410$	−60253.3	+	573272.i	−0.358437	+	3.41030i
$411$	−9933.95	+	7217.44i	−0.0588082	+	0.0427267i
$412$	−22471.8	−	213805.i	−0.132387	−	1.25957i
$413$	78341.7	+	87007.3i	0.459296	+	0.510100i
$414$	94611.9	+	212502.i	0.552008	+	1.23983i
$415$	−38246.6	−	179936.i	−0.222073	−	1.04477i
$416$	−32540.5	+	153091.i	−0.188035	+	0.884633i
$417$	−57552.6	−	25624.1i	−0.330973	−	0.147359i
$418$	35000.6	−	11372.4i	0.200319	−	0.0650876i
$419$	−55843.2	−	171868.i	−0.318084	−	0.978963i	−0.974466	−	0.224534i	$-0.927914\pi$
$419$	−55843.2	−	171868.i	−0.318084	−	0.978963i	0.656382	−	0.754429i	$-0.272086\pi$
$420$	28339.7	−	63652.1i	0.160656	−	0.360839i
$421$	25390.9	+	5397.01i	0.143257	+	0.0304501i	0.278982	−	0.960296i	$-0.410003\pi$
$421$	25390.9	+	5397.01i	0.143257	+	0.0304501i	−0.135725	+	0.990747i	$0.543336\pi$
$422$	−145054.	+	30832.2i	−0.814526	+	0.173133i
$423$	−234605.	+	104453.i	−1.31116	+	0.583768i
$424$	334808.	−	301462.i	1.86236	−	1.67688i
$425$	152490.	−	16027.4i	0.844236	−	0.0887328i
$426$	−98899.1	−	136123.i	−0.544971	−	0.750088i
$427$	−33537.3	−	3524.91i	−0.183938	−	0.0193327i
$428$	−132540.	−	229566.i	−0.723534	−	1.25320i
$429$	−64521.8	−	37251.7i	−0.350584	−	0.202410i
$430$	332854.	−	458135.i	1.80019	−	2.47774i
$431$	−76502.5	+	84964.6i	−0.411833	+	0.457387i	−0.912997	−	0.407965i	$-0.866238\pi$
$431$	−76502.5	+	84964.6i	−0.411833	+	0.457387i	0.501165	+	0.865352i	$0.332905\pi$
$432$	45489.4	+	14780.4i	0.243749	+	0.0791988i
$433$			39335.7i			0.209803i	0.994483	+	0.104901i	$0.0334527\pi$
$433$			39335.7i			0.209803i	−0.994483	+	0.104901i	$0.966547\pi$
$434$	174675.	−	22993.5i	0.927365	−	0.122075i
$435$	−54807.6			−0.289642
$436$	−144024.	+	443260.i	−0.757638	+	2.33177i
$437$	−17873.2	−	16093.1i	−0.0935922	−	0.0842708i
$438$	25753.2	+	18710.8i	0.134240	+	0.0975313i
$439$	109362.	−	189421.i	0.567464	−	0.982876i	−0.429352	−	0.903137i	$-0.641258\pi$
$439$	109362.	−	189421.i	0.567464	−	0.982876i	0.996816	−	0.0797391i	$-0.0254087\pi$
$440$	−263003.	+	151845.i	−1.35849	+	0.784324i
$441$	12734.9	−	121165.i	0.0654816	−	0.623015i
$442$	474957.	−	345076.i	2.43114	−	1.76632i
$443$	11692.4	+	111246.i	0.0595795	+	0.566861i	0.983069	+	0.183237i	$0.0586575\pi$
$443$	11692.4	+	111246.i	0.0595795	+	0.566861i	−0.923489	+	0.383624i	$0.874676\pi$
$444$	19774.5	+	21961.8i	0.100309	+	0.111405i
$445$	58367.5	+	131096.i	0.294748	+	0.662015i
$446$	32375.4	+	152314.i	0.162759	+	0.765721i
$447$	−4175.25	+	19643.0i	−0.0208962	+	0.0983089i
$448$	147791.	+	65800.6i	0.736361	+	0.327849i
$449$	−183577.	+	59647.7i	−0.910595	+	0.295870i	−0.726603	−	0.687057i	$-0.758902\pi$
$449$	−183577.	+	59647.7i	−0.910595	+	0.295870i	−0.183992	+	0.982928i	$0.558902\pi$
$450$	−68741.2	−	211564.i	−0.339463	−	1.04476i
$451$	114850.	−	257956.i	0.564646	−	1.26822i
$452$	−186505.	−	39642.8i	−0.912878	−	0.194038i
$453$	16209.2	−	3445.38i	0.0789889	−	0.0167896i
$454$	460622.	−	205082.i	2.23477	−	0.994984i
$455$	−171727.	+	154624.i	−0.829500	+	0.746885i
$456$	−11764.2	+	1236.46i	−0.0565758	+	0.00594636i
$457$	−79435.8	−	109334.i	−0.380350	−	0.523507i	0.575327	−	0.817924i	$-0.304875\pi$
$457$	−79435.8	−	109334.i	−0.380350	−	0.523507i	−0.955677	+	0.294416i	$0.904875\pi$
$458$	684031.	+	71894.6i	3.26096	+	0.342740i
$459$	70883.7	+	122774.i	0.336450	+	0.582749i
$460$	385826.	+	222757.i	1.82338	+	1.05273i
$461$	119677.	−	164721.i	0.563131	−	0.775083i	−0.428589	−	0.903499i	$-0.640989\pi$
$461$	119677.	−	164721.i	0.563131	−	0.775083i	0.991720	+	0.128416i	$0.0409893\pi$
$462$	−35502.5	+	39429.5i	−0.166332	+	0.184730i
$463$	362237.	+	117698.i	1.68978	+	0.549043i	0.986769	−	0.162135i	$-0.0518381\pi$
$463$	362237.	+	117698.i	1.68978	+	0.549043i	0.703012	+	0.711178i	$0.251838\pi$
$464$			71377.1i			0.331530i
$465$	−55057.5	+	64462.0i	−0.254631	+	0.298125i
$466$	−577407.			−2.65895
$467$	−72020.4	+	221656.i	−0.330234	+	1.01636i	0.638788	+	0.769383i	$0.279436\pi$
$467$	−72020.4	+	221656.i	−0.330234	+	1.01636i	−0.969022	+	0.246973i	$0.920564\pi$
$468$	−407175.	−	366622.i	−1.85904	−	1.67389i
$469$	−46544.6	−	33816.6i	−0.211604	−	0.153739i
$470$	−382298.	+	662160.i	−1.73064	+	2.99755i
$471$	58483.3	−	33765.4i	0.263627	−	0.152205i
$472$	−38486.9	+	366179.i	−0.172754	+	1.64365i
$473$	−224421.	+	163051.i	−1.00309	+	0.728789i
$474$	5158.31	+	49078.0i	0.0229589	+	0.218439i
$475$	15390.1	+	17092.5i	0.0682111	+	0.0757561i
$476$	−109392.	−	245699.i	−0.482805	−	1.08440i
$477$	−80261.3	−	377600.i	−0.352752	−	1.65957i
$478$	−13976.3	+	65753.2i	−0.0611696	+	0.287780i
$479$	174192.	+	77555.5i	0.759204	+	0.338019i	0.749562	−	0.661934i	$-0.230264\pi$
$479$	174192.	+	77555.5i	0.759204	+	0.338019i	0.00964186	+	0.999954i	$0.496931\pi$
$480$	−51006.8	+	16573.1i	−0.221384	+	0.0719319i
$481$	−30287.4	−	93214.9i	−0.130910	−	0.402898i
$482$	−157496.	+	353743.i	−0.677917	+	1.52263i
$483$	33916.6	+	7209.20i	0.145385	+	0.0309025i
$484$	−86573.6	+	18401.8i	−0.369568	+	0.0785542i
$485$	106843.	−	47569.5i	0.454216	−	0.202230i
$486$	232844.	−	209654.i	0.985809	−	0.887627i
$487$	288397.	−	30311.8i	1.21600	−	0.127807i	0.525279	−	0.850930i	$-0.323961\pi$
$487$	288397.	−	30311.8i	1.21600	−	0.127807i	0.690719	+	0.723123i	$0.257294\pi$
$488$	−62334.5	−	85796.1i	−0.261751	−	0.360270i
$489$	75973.9	+	7985.18i	0.317722	+	0.0333939i
$490$	−181366.	−	314135.i	−0.755377	−	1.30835i
$491$	99826.6	+	57634.9i	0.414079	+	0.239069i	0.692541	−	0.721379i	$-0.256491\pi$
$491$	99826.6	+	57634.9i	0.414079	+	0.239069i	−0.278462	+	0.960447i	$0.589825\pi$
$492$	−119752.	+	164824.i	−0.494712	+	0.680913i
$493$	−141560.	+	157219.i	−0.582436	+	0.646861i
$494$	83754.2	+	27213.4i	0.343204	+	0.111514i
$495$			260217.i			1.06200i
$496$	83950.3	+	71702.6i	0.341239	+	0.291455i
$497$	255643.			1.03495
$498$	31232.7	−	96124.4i	0.125936	−	0.387592i
$499$	−203014.	−	182794.i	−0.815313	−	0.734111i	0.151813	−	0.988409i	$-0.451489\pi$
$499$	−203014.	−	182794.i	−0.815313	−	0.734111i	−0.967126	+	0.254298i	$0.918156\pi$
$500$	133731.	+	97161.6i	0.534926	+	0.388646i
$501$	4703.26	−	8146.29i	0.0187380	−	0.0324552i
$502$	33566.9	−	19379.8i	0.133200	−	0.0769029i
$503$	25285.6	−	240577.i	0.0999397	−	0.950863i	−0.823551	−	0.567242i	$-0.808010\pi$
$503$	25285.6	−	240577.i	0.0999397	−	0.950863i	0.923491	−	0.383621i	$-0.125323\pi$
$504$	−140627.	+	102171.i	−0.553614	+	0.402224i
$505$	1303.99	+	12406.6i	0.00511318	+	0.0486487i
$506$	−227006.	−	252116.i	−0.886619	−	0.984690i
$507$	−41262.8	−	92677.7i	−0.160525	−	0.360545i
$508$	8366.95	+	39363.4i	0.0324220	+	0.152533i
$509$	2261.96	−	10641.7i	0.00873070	−	0.0410747i	−0.973567	−	0.228403i	$-0.926650\pi$
$509$	2261.96	−	10641.7i	0.00873070	−	0.0410747i	0.982297	+	0.187329i	$0.0599829\pi$
$510$	183782.	+	81824.9i	0.706581	+	0.314590i
$511$	−45998.1	+	14945.7i	−0.176156	+	0.0572367i
$512$	70482.0	+	216921.i	0.268867	+	0.827489i
$513$	−8649.54	+	19427.2i	−0.0328669	+	0.0738202i
$514$	−341993.	−	72692.9i	−1.29447	−	0.275148i
$515$	−238983.	+	50797.5i	−0.901059	+	0.191526i
$516$	182845.	−	81407.9i	0.686727	−	0.305751i
$517$	278340.	−	250618.i	1.04134	−	0.937630i
$518$	−69417.0	+	7296.02i	−0.258706	+	0.0271911i
$519$	−7103.85	−	9777.61i	−0.0263730	−	0.0362993i
$520$	−722731.	−	75962.1i	−2.67282	−	0.280925i
$521$	−89445.4	−	154924.i	−0.329520	−	0.570746i	0.652896	−	0.757447i	$-0.273554\pi$
$521$	−89445.4	−	154924.i	−0.329520	−	0.570746i	−0.982417	+	0.186701i	$0.940220\pi$
$522$	265809.	+	153465.i	0.975502	+	0.563206i
$523$	−73007.0	+	100486.i	−0.266908	+	0.367367i	−0.921343	−	0.388751i	$-0.872907\pi$
$523$	−73007.0	+	100486.i	−0.266908	+	0.367367i	0.654435	+	0.756118i	$0.272907\pi$
$524$	407936.	−	453059.i	1.48569	−	1.65003i
$525$	−31536.8	−	10246.9i	−0.114419	−	0.0371770i
$526$			18774.5i			0.0678572i
$527$	42707.1	+	324432.i	0.153772	+	1.16816i
$528$	−33248.3			−0.119262
$529$	17963.1	−	55284.8i	0.0641905	−	0.197558i
$530$	−854133.	−	769065.i	−3.04070	−	2.73786i
$531$	255236.	+	185440.i	0.905216	+	0.657678i
$532$	20171.9	−	34938.7i	0.0712727	−	0.123448i
$533$	585165.	−	337845.i	2.05979	−	1.18922i
$534$	−8241.50	+	78412.6i	−0.0289017	+	0.274981i
$535$	−243722.	+	177074.i	−0.851503	+	0.618653i
$536$	−18912.2	−	179938.i	−0.0658284	−	0.626315i
$537$	−9172.91	−	10187.5i	−0.0318096	−	0.0353282i
$538$	−208320.	−	467895.i	−0.719726	−	1.61653i
$539$	36943.2	+	173804.i	0.127162	+	0.598250i
$540$	81901.4	−	385316.i	0.280869	−	1.32138i
$541$	133014.	+	59221.8i	0.454468	+	0.202342i	0.621187	−	0.783662i	$-0.286651\pi$
$541$	133014.	+	59221.8i	0.454468	+	0.202342i	−0.166719	+	0.986004i	$0.553317\pi$
$542$	−929673.	+	302069.i	−3.16469	+	1.02827i
$543$	11152.1	+	34322.8i	0.0378232	+	0.116408i
$544$	−84202.6	+	189122.i	−0.284530	+	0.639064i
$545$	518103.	+	110126.i	1.74431	+	0.370764i
$546$	−124189.	+	26397.2i	−0.416580	+	0.0885468i
$547$	−136181.	+	60631.6i	−0.455136	+	0.202639i	−0.621483	−	0.783428i	$-0.713469\pi$
$547$	−136181.	+	60631.6i	−0.455136	+	0.202639i	0.166347	+	0.986067i	$0.446803\pi$
$548$	97873.3	−	88125.6i	0.325914	−	0.293454i
$549$	−90371.1	+	9498.39i	−0.299837	+	0.0315141i
$550$	190699.	+	262474.i	0.630409	+	0.867684i
$551$	−31560.9	−	3317.18i	−0.103955	−	0.0109261i
$552$	54522.4	+	94435.6i	0.178936	+	0.309926i
$553$	−64932.6	−	37488.9i	−0.212331	−	0.122589i
$554$	347569.	−	478388.i	1.13246	−	1.55869i
$555$	22473.2	−	24959.1i	0.0729592	−	0.0810294i
$556$	642640.	+	208806.i	2.07883	+	0.675452i
$557$		−	432302.i		−	1.39340i	−0.717362	−	0.696701i	$-0.754650\pi$
$557$		−	432302.i		−	1.39340i	0.717362	−	0.696701i	$-0.245350\pi$
$558$	447519.	−	158467.i	1.43729	−	0.508943i
$559$	−663800.			−2.12429
$560$	−31867.1	+	98076.8i	−0.101617	+	0.312745i
$561$	−73234.5	−	65940.6i	−0.232697	−	0.209521i
$562$	40226.5	+	29226.3i	0.127362	+	0.0925338i
$563$	−261365.	+	452698.i	−0.824576	+	1.42821i	0.0776664	+	0.996979i	$0.475253\pi$
$563$	−261365.	+	452698.i	−0.824576	+	1.42821i	−0.902243	+	0.431229i	$0.858080\pi$
$564$	−234035.	+	135120.i	−0.735737	+	0.424778i
$565$	−22650.6	+	215506.i	−0.0709549	+	0.675091i
$566$	−533824.	+	387846.i	−1.66635	+	1.21067i
$567$	13891.3	+	132167.i	0.0432093	+	0.411109i
$568$	537949.	+	597453.i	1.66742	+	1.85186i
$569$	196201.	+	440674.i	0.606005	+	1.36111i	0.912437	+	0.409216i	$0.134198\pi$
$569$	196201.	+	440674.i	0.606005	+	1.36111i	−0.306433	+	0.951892i	$0.599135\pi$
$570$	6274.15	+	29517.6i	0.0193110	+	0.0908512i
$571$	13077.5	−	61524.7i	0.0401099	−	0.188702i	−0.953531	−	0.301293i	$-0.902582\pi$
$571$	13077.5	−	61524.7i	0.0401099	−	0.188702i	0.993641	+	0.112591i	$0.0359150\pi$
$572$	730016.	+	325024.i	2.23121	+	0.993399i
$573$	142572.	−	46324.5i	0.434236	−	0.141092i
$574$	−148697.	−	457642.i	−0.451314	−	1.38900i
$575$	86238.9	−	193696.i	0.260836	−	0.585847i
$576$	426405.	+	90635.2i	1.28522	+	0.273182i
$577$	−37044.9	+	7874.14i	−0.111270	+	0.0236511i	−0.263210	−	0.964739i	$-0.584781\pi$
$577$	−37044.9	+	7874.14i	−0.111270	+	0.0236511i	0.151940	+	0.988390i	$0.451448\pi$
$578$	198397.	−	88332.1i	0.593854	−	0.264401i
$579$	16869.8	−	15189.6i	0.0503213	−	0.0453095i
$580$	584631.	−	61447.2i	1.73790	−	0.182661i
$581$	90262.2	+	124235.i	0.267395	+	0.368038i
$582$	63906.3	+	6716.82i	0.188668	+	0.0198298i
$583$	281509.	+	487587.i	0.828237	+	1.43455i
$584$	−131723.	−	76050.2i	−0.386220	−	0.222984i
$585$	−366004.	+	503762.i	−1.06948	+	1.47202i
$586$	−266682.	+	296180.i	−0.776601	+	0.862503i
$587$	−290040.	−	94239.6i	−0.841746	−	0.273500i	−0.143761	−	0.989612i	$-0.545920\pi$
$587$	−290040.	−	94239.6i	−0.841746	−	0.273500i	−0.697985	+	0.716112i	$0.745920\pi$
$588$		−	128205.i		−	0.370808i
$589$	−35606.3	+	33788.1i	−0.102635	+	0.0973942i
$590$	939308.			2.69839
$591$	−60098.3	+	184964.i	−0.172063	+	0.529555i
$592$	−32504.7	−	29267.4i	−0.0927477	−	0.0835104i
$593$	−468591.	−	340451.i	−1.33255	−	0.968156i	−0.999683	−	0.0251830i	$-0.991983\pi$
$593$	−468591.	−	340451.i	−1.33255	−	0.968156i	−0.332869	−	0.942973i	$-0.608017\pi$
$594$	−149985.	+	259782.i	−0.425084	+	0.736268i
$595$	−264705.	+	152828.i	−0.747703	+	0.431686i
$596$	22514.6	−	214212.i	0.0633829	−	0.603048i
$597$	−57312.0	+	41639.6i	−0.160804	+	0.116831i
$598$	−84858.1	−	807371.i	−0.237296	−	2.25772i
$599$	−235332.	−	261362.i	−0.655883	−	0.728432i	0.319832	−	0.947474i	$-0.396373\pi$
$599$	−235332.	−	261362.i	−0.655883	−	0.728432i	−0.975715	+	0.219042i	$0.929707\pi$
$600$	−42415.1	−	95265.9i	−0.117820	−	0.264627i
$601$	−87151.8	−	410017.i	−0.241284	−	1.13515i	−0.917279	−	0.398244i	$-0.869620\pi$
$601$	−87151.8	−	410017.i	−0.241284	−	1.13515i	0.675996	−	0.736905i	$-0.263714\pi$
$602$	−98285.2	+	462396.i	−0.271203	+	1.27591i
$603$	−141626.	−	63056.1i	−0.389501	−	0.173417i
$604$	−169041.	+	54924.7i	−0.463359	+	0.150554i
$605$	31083.0	+	95663.6i	0.0849204	+	0.261358i
$606$	−2787.83	+	6261.57i	−0.00759139	+	0.0170505i
$607$	154786.	+	32900.8i	0.420102	+	0.0892954i	0.413112	−	0.910680i	$-0.364442\pi$
$607$	154786.	+	32900.8i	0.420102	+	0.0892954i	0.00698972	+	0.999976i	$0.497775\pi$
$608$	−30375.3	+	6456.47i	−0.0821700	+	0.0174658i
$609$	41796.9	−	18609.2i	0.112696	−	0.0501756i
$610$	−201054.	+	181030.i	−0.540323	+	0.486509i
$611$	891349.	−	93684.6i	2.38762	−	0.250949i
$612$	−425984.	−	586316.i	−1.13734	−	1.56541i
$613$	−717931.	−	75457.6i	−1.91057	−	0.200808i	−0.926211	−	0.377007i	$-0.876953\pi$
$613$	−717931.	−	75457.6i	−1.91057	−	0.200808i	−0.984355	+	0.176198i	$0.943620\pi$
$614$	210520.	+	364632.i	0.558415	+	0.967203i
$615$	200518.	+	115769.i	0.530156	+	0.306086i
$616$	149013.	−	205098.i	0.392701	−	0.540506i
$617$	−126352.	+	140328.i	−0.331902	+	0.368615i	−0.885878	−	0.463918i	$-0.846443\pi$
$617$	−126352.	+	140328.i	−0.331902	+	0.368615i	0.553976	+	0.832533i	$0.313110\pi$
$618$	−127668.	−	41482.0i	−0.334277	−	0.108613i
$619$		−	560378.i		−	1.46251i	−0.682102	−	0.731257i	$-0.738934\pi$
$619$		−	560378.i		−	1.46251i	0.682102	−	0.731257i	$-0.261066\pi$
$620$	515026.	−	749342.i	1.33982	−	1.94938i
$621$	196037.			0.508341
$622$	−30049.7	+	92483.6i	−0.0776712	+	0.239047i
$623$	−89023.6	−	80157.2i	−0.229366	−	0.206522i
$624$	−64366.4	−	46764.9i	−0.165306	−	0.120102i
$625$	234647.	−	406421.i	0.600696	−	1.04044i
$626$	−440961.	+	254589.i	−1.12526	+	0.649667i
$627$	1545.18	−	14701.5i	0.00393048	−	0.0373960i
$628$	−585984.	+	425742.i	−1.48582	+	1.07951i
$629$	−13551.3	−	128932.i	−0.0342514	−	0.325881i
$630$	296723.	+	329544.i	0.747601	+	0.830294i
$631$	120079.	+	269701.i	0.301583	+	0.677366i	0.999237	−	0.0390689i	$-0.0124392\pi$
$631$	120079.	+	269701.i	0.301583	+	0.677366i	−0.697654	+	0.716435i	$0.745773\pi$
$632$	−49023.9	−	230639.i	−0.122737	−	0.577430i
$633$	−12384.6	+	58264.9i	−0.0309082	+	0.145412i
$634$	352761.	+	157059.i	0.877612	+	0.390738i
$635$	43496.5	−	14132.9i	0.107871	−	0.0350496i
$636$	−125531.	−	386346.i	−0.310340	−	0.955129i
$637$	−172942.	+	388434.i	−0.426208	+	0.957280i
$638$	−437862.	−	93070.5i	−1.07571	−	0.228650i
$639$	673814.	−	143224.i	1.65021	−	0.350762i
$640$	894292.	−	398164.i	2.18333	−	0.972081i
$641$	322959.	−	290793.i	0.786015	−	0.707731i	−0.174897	−	0.984587i	$-0.555959\pi$
$641$	322959.	−	290793.i	0.786015	−	0.707731i	0.960911	+	0.276856i	$0.0892924\pi$
$642$	−164613.	+	17301.5i	−0.399387	+	0.0419773i
$643$	237659.	+	327109.i	0.574820	+	0.791172i	0.993115	−	0.117139i	$-0.0373724\pi$
$643$	237659.	+	327109.i	0.574820	+	0.791172i	−0.418296	+	0.908311i	$0.637372\pi$
$644$	−369870.	−	38874.9i	−0.891821	−	0.0937342i
$645$	−113732.	−	196990.i	−0.273378	−	0.473504i
$646$	100878.	+	58242.0i	0.241731	+	0.139563i
$647$	−30615.9	+	42139.2i	−0.0731372	+	0.100665i	−0.844018	−	0.536314i	$-0.819816\pi$
$647$	−30615.9	+	42139.2i	−0.0731372	+	0.100665i	0.770881	+	0.636979i	$0.219816\pi$
$648$	−279651.	+	310584.i	−0.665987	+	0.739654i
$649$	−437607.	−	142187.i	−1.03895	−	0.337576i
$650$			776356.i			1.83753i
$651$	20100.3	−	67853.6i	0.0474287	−	0.160107i
$652$	−819364.			−1.92744
$653$	90208.0	−	277632.i	0.211553	−	0.651092i	−0.787828	−	0.615896i	$-0.788794\pi$
$653$	90208.0	−	277632.i	0.211553	−	0.651092i	0.999380	−	0.0351965i	$-0.0112057\pi$
$654$	216271.	+	194732.i	0.505642	+	0.455282i
$655$	−560529.	−	407248.i	−1.30652	−	0.949241i
$656$	150769.	−	261139.i	0.350352	−	0.606827i
$657$	−112867.	+	65163.6i	−0.261478	+	0.150964i
$658$	66717.6	−	634775.i	0.154095	−	1.46612i
$659$	350159.	−	254405.i	0.806295	−	0.585808i	−0.106459	−	0.994317i	$-0.533951\pi$
$659$	350159.	−	254405.i	0.806295	−	0.585808i	0.912754	+	0.408509i	$0.133951\pi$
$660$	28622.9	+	272328.i	0.0657090	+	0.625180i
$661$	−16666.0	−	18509.4i	−0.0381441	−	0.0423634i	0.723771	−	0.690040i	$-0.242407\pi$
$661$	−16666.0	−	18509.4i	−0.0381441	−	0.0423634i	−0.761915	+	0.647677i	$0.775741\pi$
$662$	−80506.3	−	180820.i	−0.183702	−	0.412602i
$663$	−49028.9	−	230663.i	−0.111539	−	0.524748i
$664$	−100407.	+	472377.i	−0.227733	+	1.07140i
$665$	−41885.7	−	18648.7i	−0.0947159	−	0.0421702i
$666$	−178879.	+	58121.3i	−0.403284	+	0.131035i
$667$	90401.5	+	278227.i	0.203200	+	0.625386i
$668$	−41036.4	+	92169.3i	−0.0919637	+	0.206554i
$669$	61181.1	+	13004.4i	0.136699	+	0.0290563i
$670$	−451484.	+	95965.9i	−1.00576	+	0.213780i
$671$	121071.	−	53904.2i	0.268902	−	0.119723i
$672$	33271.2	−	29957.5i	0.0736767	−	0.0663388i
$673$	−629593.	+	66172.8i	−1.39005	+	0.146100i	−0.769789	−	0.638298i	$-0.779639\pi$
$673$	−629593.	+	66172.8i	−1.39005	+	0.146100i	−0.620258	+	0.784398i	$0.712972\pi$
$674$	−39523.8	−	54399.9i	−0.0870040	−	0.119751i
$675$	−186447.	−	19596.4i	−0.409211	−	0.0430098i
$676$	544054.	+	942329.i	1.19055	+	2.06210i
$677$	−74514.9	−	43021.2i	−0.162579	−	0.0938653i	0.416503	−	0.909134i	$-0.363256\pi$
$677$	−74514.9	−	43021.2i	−0.162579	−	0.0938653i	−0.579082	+	0.815269i	$0.696589\pi$
$678$	−69980.5	+	96319.9i	−0.152236	+	0.209535i
$679$	−65328.1	+	72554.2i	−0.141697	+	0.157370i
$680$	−914187.	−	297037.i	−1.97705	−	0.642382i
$681$		−	202531.i		−	0.436715i
$682$	−549324.	+	421497.i	−1.18103	+	0.906204i
$683$	−312476.			−0.669847			−0.334923	−	0.942245i	$-0.608710\pi$
$683$	−312476.			−0.669847			−0.334923	+	0.942245i	$0.608710\pi$
$684$	33593.9	−	103391.i	0.0718040	−	0.220990i
$685$	−111231.	−	100152.i	−0.237052	−	0.213442i
$686$	601085.	+	436714.i	1.27728	+	0.928001i
$687$	138137.	−	239260.i	0.292682	−	0.506939i
$688$	−256544.	+	148116.i	−0.541982	+	0.312913i
$689$	−140828.	+	1.33989e6i	−0.296653	+	2.82247i
$690$	225057.	−	163513.i	0.472709	−	0.343443i
$691$	21024.6	+	200036.i	0.0440324	+	0.418940i	0.994228	+	0.107287i	$0.0342163\pi$
$691$	21024.6	+	200036.i	0.0440324	+	0.418940i	−0.950196	+	0.311654i	$0.899117\pi$
$692$	86738.7	+	96333.1i	0.181134	+	0.201170i
$693$	−88353.3	−	198445.i	−0.183974	−	0.413212i
$694$	40095.8	+	188636.i	0.0832492	+	0.391656i
$695$	159661.	−	751148.i	0.330545	−	1.55509i
$696$	131444.	+	58522.7i	0.271345	+	0.120811i
$697$	850003.	−	276183.i	1.74966	−	0.568500i
$698$	247676.	+	762270.i	0.508363	+	1.56458i
$699$	−94335.0	+	211880.i	−0.193072	+	0.433646i
$700$	347890.	+	73946.3i	0.709979	+	0.150911i
$701$	321178.	−	68268.4i	0.653596	−	0.138926i	0.130833	−	0.991404i	$-0.458235\pi$
$701$	321178.	−	68268.4i	0.653596	−	0.138926i	0.522763	+	0.852478i	$0.324901\pi$
$702$	−655752.	+	291960.i	−1.33065	+	0.592446i
$703$	14451.8	−	13012.5i	0.0292423	−	0.0263299i
$704$	−632306.	+	66458.0i	−1.27580	+	0.134092i
$705$	180521.	+	248466.i	0.363203	+	0.499907i
$706$	981428.	+	103152.i	1.96901	+	0.206952i
$707$	−5206.95	−	9018.69i	−0.0104170	−	0.0180428i
$708$	287512.	+	165995.i	0.573575	+	0.331154i
$709$	343750.	−	473131.i	0.683833	−	0.941215i	−0.316139	−	0.948713i	$-0.602387\pi$
$709$	343750.	−	473131.i	0.683833	−	0.941215i	0.999972	+	0.00749783i	$0.00238666\pi$
$710$	1.37237e6	−	1.52417e6i	2.72241	−	3.02355i
$711$	−192150.	−	62433.3i	−0.380103	−	0.123503i
$712$		−	376728.i		−	0.743136i
$713$	418051.	+	173170.i	0.822338	+	0.340639i
$714$	−167937.			−0.329420
$715$	280637.	−	863711.i	0.548949	−	1.68949i
$716$	109269.	+	98386.1i	0.213143	+	0.191914i
$717$	21844.8	+	15871.2i	0.0424922	+	0.0308724i
$718$	63500.3	−	109986.i	0.123176	−	0.213347i
$719$	190072.	−	109738.i	0.367672	−	0.212275i	−0.304769	−	0.952426i	$-0.598579\pi$
$719$	190072.	−	109738.i	0.367672	−	0.212275i	0.672441	+	0.740151i	$0.265246\pi$
$720$	−29046.7	+	276361.i	−0.0560314	+	0.533103i
$721$	165004.	−	119882.i	0.317413	−	0.230614i
$722$	−89405.9	−	850641.i	−0.171511	−	1.63182i
$723$	104075.	+	115587.i	0.199099	+	0.221122i
$724$	−157440.	−	353617.i	−0.300358	−	0.674615i
$725$	−58166.7	−	273653.i	−0.110662	−	0.520624i
$726$	−11490.3	+	54057.8i	−0.0218002	+	0.102562i
$727$	−550542.	−	245117.i	−1.04165	−	0.463772i	−0.186664	−	0.982424i	$-0.559767\pi$
$727$	−550542.	−	245117.i	−1.04165	−	0.463772i	−0.854986	+	0.518652i	$0.826434\pi$
$728$	576956.	−	187464.i	1.08863	−	0.353717i
$729$	82626.2	+	254297.i	0.155476	+	0.478505i
$730$	−157824.	+	354479.i	−0.296161	+	0.665188i
$731$	−858831.	−	182550.i	−1.60721	−	0.341623i
$732$	−93532.4	+	19880.9i	−0.174558	+	0.0371035i
$733$	−226550.	+	100867.i	−0.421654	+	0.187732i	−0.606584	−	0.795019i	$-0.707461\pi$
$733$	−226550.	+	100867.i	−0.421654	+	0.187732i	0.184930	+	0.982752i	$0.440794\pi$
$734$	−496738.	+	447264.i	−0.922008	+	0.830180i
$735$	−144903.	+	15229.9i	−0.268227	+	0.0281918i
$736$	168265.	+	231597.i	0.310626	+	0.427540i
$737$	224865.	+	23634.3i	0.413988	+	0.0435118i
$738$	−648323.	−	1.12293e6i	−1.19036	−	2.06177i
$739$	495781.	+	286240.i	0.907823	+	0.524132i	0.879730	−	0.475473i	$-0.157723\pi$
$739$	495781.	+	286240.i	0.907823	+	0.524132i	0.0280932	+	0.999605i	$0.491056\pi$
$740$	−211739.	+	291433.i	−0.386667	+	0.532201i
$741$	23669.5	−	26287.6i	0.0431074	−	0.0478756i
$742$	912498.	+	296489.i	1.65739	+	0.538518i
$743$			1.07371e6i			1.94495i	0.233011	+	0.972474i	$0.425142\pi$
$743$			1.07371e6i			1.94495i	−0.233011	+	0.972474i	$0.574858\pi$
$744$	200875.	−	95808.6i	0.362894	−	0.173085i
$745$	−244788.			−0.441039
$746$	−49129.7	+	151206.i	−0.0882809	+	0.271701i
$747$	307512.	+	276885.i	0.551088	+	0.496202i
$748$	855119.	+	621280.i	1.52835	+	1.11041i
$749$	125742.	−	217791.i	0.224138	−	0.388219i
$750$	89388.1	−	51608.2i	0.158912	−	0.0917480i
$751$	73456.0	−	698887.i	0.130241	−	1.23916i	−0.712823	−	0.701344i	$-0.752583\pi$
$751$	73456.0	−	698887.i	0.130241	−	1.23916i	0.843063	−	0.537814i	$-0.180750\pi$
$752$	323583.	−	235097.i	0.572202	−	0.415729i
$753$	−1627.39	−	15483.6i	−0.00287014	−	0.0273075i
$754$	−716763.	−	796046.i	−1.26076	−	1.40022i
$755$	82159.5	+	184533.i	0.144133	+	0.323728i
$756$	68369.9	+	321655.i	0.119625	+	0.562791i
$757$	−158546.	+	745901.i	−0.276671	+	1.30164i	0.591876	+	0.806029i	$0.298388\pi$
$757$	−158546.	+	745901.i	−0.276671	+	1.30164i	−0.868547	+	0.495607i	$0.834946\pi$
$758$	−140478.	−	62544.7i	−0.244494	−	0.108856i
$759$	−129602.	+	42110.1i	−0.224971	+	0.0730976i
$760$	−44556.9	−	137132.i	−0.0771415	−	0.237417i
$761$	278349.	−	625182.i	0.480641	−	1.07954i	−0.496711	−	0.867916i	$-0.665459\pi$
$761$	278349.	−	625182.i	0.480641	−	1.07954i	0.977352	−	0.211621i	$-0.0678741\pi$
$762$	24579.1	+	5224.45i	0.0423307	+	0.00899767i
$763$	−432504.	+	91931.5i	−0.742918	+	0.157912i
$764$	−1.46888e6	+	653986.i	−2.51651	+	1.12042i
$765$	−612079.	+	551118.i	−1.04589	+	0.941720i
$766$	681637.	−	71643.0i	1.16170	−	0.122100i
$767$	−647185.	−	890773.i	−1.10011	−	1.51418i
$768$	281923.	+	29631.3i	0.477978	+	0.0502375i
$769$	393095.	+	680861.i	0.664730	+	1.15135i	0.979359	+	0.202131i	$0.0647866\pi$
$769$	393095.	+	680861.i	0.664730	+	1.15135i	−0.314629	+	0.949215i	$0.601880\pi$
$770$	−560099.	−	323373.i	−0.944677	−	0.545410i
$771$	−82548.5	+	113618.i	−0.138867	+	0.191135i
$772$	−162920.	+	180940.i	−0.273362	+	0.303600i
$773$	−183219.	−	59531.4i	−0.306628	−	0.0996294i	0.151662	−	0.988432i	$-0.451538\pi$
$773$	−183219.	−	59531.4i	−0.306628	−	0.0996294i	−0.458289	+	0.888803i	$0.651538\pi$
$774$			1.27383e6i			2.12632i
$775$	−380289.	−	206488.i	−0.633156	−	0.343789i
$776$	−307033.			−0.509873
$777$	−8663.85	+	26664.6i	−0.0143506	+	0.0441665i
$778$	1.43116e6	+	1.28862e6i	2.36444	+	2.12895i
$779$	108461.	+	78801.9i	0.178731	+	0.129856i
$780$	−327627.	+	567467.i	−0.538506	+	0.932720i
$781$	−870083.	+	502342.i	−1.42646	+	0.823565i
$782$	112243.	−	1.06792e6i	0.183547	−	1.74633i
$783$	209268.	−	152042.i	0.341333	−	0.247993i
$784$	19834.3	+	188711.i	0.0322689	+	0.307018i
$785$	550806.	+	611732.i	0.893839	+	0.992708i
$786$	−154834.	−	347764.i	−0.250624	−	0.562910i
$787$	120155.	+	565284.i	0.193995	+	0.912677i	0.962173	+	0.272440i	$0.0878305\pi$
$787$	120155.	+	565284.i	0.193995	+	0.912677i	−0.768177	+	0.640237i	$0.778836\pi$
$788$	433696.	−	2.04038e6i	0.698446	−	3.28593i
$789$	6889.30	+	3067.31i	0.0110668	+	0.00492725i
$790$	−572091.	+	185884.i	−0.916665	+	0.297843i
$791$	−55898.6	−	172038.i	−0.0893404	−	0.274961i
$792$	277856.	−	624074.i	0.442965	−	0.994915i
$793$	310203.	+	65935.6i	0.493286	+	0.104851i
$794$	−739710.	+	157230.i	−1.17333	+	0.249399i
$795$	−421754.	+	187777.i	−0.667306	+	0.297104i
$796$	564662.	−	508424.i	0.891174	−	0.802416i
$797$	−5408.67	+	568.474i	−0.00851479	+	0.000894941i	−0.108785	−	0.994065i	$-0.534696\pi$
$797$	−5408.67	+	568.474i	−0.00851479	+	0.000894941i	0.100270	+	0.994960i	$0.468029\pi$
$798$	−14807.0	−	20380.2i	−0.0232521	−	0.0320038i
$799$	1.17900e6	+	123918.i	1.84680	+	0.194107i
$800$	−136882.	−	237087.i	−0.213878	−	0.370448i
$801$	−279553.	−	161400.i	−0.435711	−	0.251558i
$802$	954387.	−	1.31360e6i	1.48380	−	2.04228i
$803$	127186.	−	141255.i	0.197247	−	0.219065i
$804$	−155154.	−	50412.5i	−0.240021	−	0.0779877i
$805$			422663.i			0.652233i
$806$	−1.65630e6	+	43345.2i	−2.54959	+	0.0667224i
$807$	−205729.			−0.315899
$808$	10120.3	−	31147.0i	0.0155013	−	0.0477082i
$809$	194599.	+	175217.i	0.297333	+	0.267720i	0.804271	−	0.594263i	$-0.202556\pi$
$809$	194599.	+	175217.i	0.297333	+	0.267720i	−0.506938	+	0.861982i	$0.669223\pi$
$810$	862566.	+	626691.i	1.31469	+	0.955176i
$811$	440428.	−	762844.i	0.669628	−	1.15983i	−0.308380	−	0.951263i	$-0.599787\pi$
$811$	440428.	−	762844.i	0.669628	−	1.15983i	0.978008	−	0.208566i	$-0.0668797\pi$
$812$	−424983.	+	245364.i	−0.644554	+	0.372134i
$813$	−41042.7	+	390495.i	−0.0620947	+	0.590792i
$814$	221924.	−	161238.i	0.334932	−	0.243342i
$815$	97335.5	+	926085.i	0.146540	+	1.39423i
$816$	−70417.2	−	78206.2i	−0.105754	−	0.117452i
$817$	−53569.9	−	120320.i	−0.0802558	−	0.180257i
$818$	−125907.	−	592344.i	−0.188166	−	0.885254i
$819$	108074.	−	508447.i	0.161121	−	0.758015i
$820$	−2.26872e6	−	1.01010e6i	−3.37406	−	1.50223i
$821$	−390215.	+	126788.i	−0.578919	+	0.188102i	−0.583816	−	0.811886i	$-0.698441\pi$
$821$	−390215.	+	126788.i	−0.578919	+	0.188102i	0.00489751	+	0.999988i	$0.498441\pi$
$822$	−25412.4	−	78211.5i	−0.0376100	−	0.115752i
$823$	−193041.	+	433578.i	−0.285004	+	0.640129i	−0.998144	−	0.0608919i	$-0.980606\pi$
$823$	−193041.	+	433578.i	−0.285004	+	0.640129i	0.713140	+	0.701021i	$0.247272\pi$
$824$	627390.	+	133356.i	0.924025	+	0.196407i
$825$	127471.	−	27094.8i	0.187285	−	0.0398087i
$826$	−716328.	+	318930.i	−1.04991	+	0.467450i
$827$	−202558.	+	182384.i	−0.296168	+	0.266671i	−0.803795	−	0.594906i	$-0.797189\pi$
$827$	−202558.	+	182384.i	−0.296168	+	0.266671i	0.507627	+	0.861577i	$0.330523\pi$
$828$	−996669.	+	104754.i	−1.45375	+	0.152796i
$829$	−237652.	−	327101.i	−0.345807	−	0.475962i	0.600320	−	0.799760i	$-0.295040\pi$
$829$	−237652.	−	327101.i	−0.345807	−	0.475962i	−0.946126	+	0.323798i	$0.895040\pi$
$830$	1.22526e6	+	128780.i	1.77857	+	0.186936i
$831$	−118760.	−	205698.i	−0.171976	−	0.297871i
$832$	−1.31757e6	−	760701.i	−1.90339	−	1.09892i
$833$	−330577.	+	455000.i	−0.476412	+	0.655725i
$834$	282323.	−	313551.i	0.405895	−	0.450792i
$835$	109049.	+	35432.2i	0.156404	+	0.0508189i
$836$			158552.i			0.226861i
$837$	31397.8	−	398866.i	0.0448176	−	0.569345i
$838$	1.21029e6			1.72346
$839$	−141268.	+	434777.i	−0.200687	+	0.617651i	0.799176	+	0.601097i	$0.205269\pi$
$839$	−141268.	+	434777.i	−0.200687	+	0.617651i	−0.999863	+	0.0165537i	$0.994731\pi$
$840$	154485.	+	139099.i	0.218941	+	0.197135i
$841$	−259913.	−	188838.i	−0.367482	−	0.266992i
$842$	−86924.9	+	150558.i	−0.122608	+	0.212364i
$843$	17296.7	−	9986.24i	0.0243393	−	0.0140523i
$844$	66782.7	−	635395.i	0.0937517	−	0.891988i
$845$	1.00044e6	−	726859.i	1.40112	−	1.01797i
$846$	−179780.	−	1.71049e6i	−0.251189	−	2.38991i
$847$	−56185.6	−	62400.4i	−0.0783174	−	0.0869803i
$848$	244546.	+	549260.i	0.340071	+	0.763811i
$849$	55105.8	+	259252.i	0.0764507	+	0.359672i
$850$	−213504.	+	1.00446e6i	−0.295507	+	1.39025i
$851$	−163771.	−	72915.7i	−0.226141	−	0.100684i
$852$	689420.	−	224006.i	0.949740	−	0.308589i
$853$	269330.	+	828912.i	0.370157	+	1.13923i	0.946688	+	0.322152i	$0.104406\pi$
$853$	269330.	+	828912.i	0.370157	+	1.13923i	−0.576531	+	0.817075i	$0.695594\pi$
$854$	91860.1	−	206321.i	0.125954	−	0.282897i
$855$	−120849.	−	25687.2i	−0.165314	−	0.0351386i
$856$	773590.	−	164432.i	1.05576	−	0.224408i
$857$	140636.	−	62615.4i	0.191486	−	0.0852549i	−0.308754	−	0.951142i	$-0.599912\pi$
$857$	140636.	−	62615.4i	0.191486	−	0.0852549i	0.500240	+	0.865887i	$0.333245\pi$
$858$	370808.	−	333877.i	0.503703	−	0.453536i
$859$	−129280.	+	13587.9i	−0.175204	+	0.0184147i	−0.191724	−	0.981449i	$-0.561408\pi$
$859$	−129280.	+	13587.9i	−0.175204	+	0.0184147i	0.0165200	+	0.999864i	$0.494741\pi$
$860$	1.43403e6	+	1.97377e6i	1.93893	+	2.66870i
$861$	−192226.	−	20203.7i	−0.259302	−	0.0272537i
$862$	−382855.	−	663125.i	−0.515253	−	0.892444i
$863$	−318704.	−	184004.i	−0.427923	−	0.247062i	0.270538	−	0.962709i	$-0.412798\pi$
$863$	−318704.	−	184004.i	−0.427923	−	0.247062i	−0.698461	+	0.715648i	$0.746132\pi$
$864$	148780.	−	204778.i	0.199304	−	0.274319i
$865$	98576.3	−	109480.i	0.131747	−	0.146320i
$866$	−250550.	−	81408.5i	−0.334086	−	0.108551i
$867$		−	87233.4i		−	0.116050i
$868$	−138336.	+	746328.i	−0.183610	+	0.990581i
$869$	294665.			0.390202
$870$	113429.	−	349098.i	0.149860	−	0.461220i
$871$	402080.	+	362035.i	0.530001	+	0.477215i
$872$	−1.12497e6	−	817336.i	−1.47947	−	1.07490i
$873$	−131541.	+	227836.i	−0.172597	+	0.298946i
$874$	139495.	−	80537.6i	0.182615	−	0.105433i
$875$	−16392.4	+	155964.i	−0.0214105	+	0.203708i
$876$	−110952.	+	80611.4i	−0.144586	+	0.105048i
$877$	−45006.8	−	428211.i	−0.0585166	−	0.556748i	−0.984026	−	0.178024i	$-0.943030\pi$
$877$	−45006.8	−	428211.i	−0.0585166	−	0.556748i	0.925510	−	0.378724i	$-0.123637\pi$
$878$	980185.	+	1.08861e6i	1.27151	+	1.41215i
$879$	65113.8	+	146248.i	0.0842743	+	0.189283i
$880$	−84262.6	−	396425.i	−0.108810	−	0.511912i
$881$	−74611.7	+	351020.i	−0.0961291	+	0.452252i	0.903587	+	0.428406i	$0.140925\pi$
$881$	−74611.7	+	351020.i	−0.0961291	+	0.452252i	−0.999716	+	0.0238463i	$0.992409\pi$
$882$	745404.	+	331875.i	0.958196	+	0.426617i
$883$	775832.	−	252083.i	0.995053	−	0.323312i	0.234166	−	0.972197i	$-0.424764\pi$
$883$	775832.	−	252083.i	0.995053	−	0.323312i	0.760887	+	0.648884i	$0.224764\pi$
$884$	781597.	+	2.40551e6i	1.00018	+	3.07824i
$885$	153461.	−	344680.i	0.195935	−	0.440078i
$886$	−732781.	−	155757.i	−0.933483	−	0.198418i
$887$	814669.	−	173163.i	1.03546	−	0.220094i	0.341331	−	0.939943i	$-0.389122\pi$
$887$	814669.	−	173163.i	1.03546	−	0.220094i	0.694130	+	0.719849i	$0.255789\pi$
$888$	−80548.1	+	35862.3i	−0.102148	+	0.0454792i
$889$	−28372.3	+	25546.5i	−0.0358997	+	0.0323243i
$890$	−955811.	+	100460.i	−1.20668	+	0.126827i
$891$	−306989.	−	422535.i	−0.386694	−	0.532239i
$892$	−667197.	−	70125.2i	−0.838541	−	0.0881342i
$893$	88914.7	+	154005.i	0.111499	+	0.193122i
$894$	−116475.	−	67247.1i	−0.145733	−	0.0841392i
$895$	98220.3	−	135189.i	0.122618	−	0.168769i
$896$	−546806.	+	607290.i	−0.681111	+	0.756450i
$897$	−310129.	−	100767.i	−0.385441	−	0.125237i
$898$		−	1.29274e6i		−	1.60309i
$899$	580572.	−	139373.i	0.718351	−	0.172449i
$900$	958383.			1.18319
$901$	−550684.	+	1.69483e6i	−0.678348	+	2.08774i
$902$	1.40537e6	+	1.26540e6i	1.72733	+	1.55530i
$903$	153619.	+	111611.i	0.188395	+	0.136877i
$904$	284436.	−	492658.i	0.348055	−	0.602849i
$905$	−380972.	+	219954.i	−0.465153	+	0.268556i
$906$	−11600.9	+	110375.i	−0.0141331	+	0.134467i
$907$	397847.	−	289053.i	0.483617	−	0.351368i	−0.319108	−	0.947718i	$-0.603383\pi$
$907$	397847.	−	289053.i	0.483617	−	0.351368i	0.802724	+	0.596351i	$0.203383\pi$
$908$	227067.	+	2.16039e6i	0.275411	+	2.62036i
$909$	−18777.0	−	20853.9i	−0.0227247	−	0.0252383i
$910$	−629476.	−	1.41383e6i	−0.760145	−	1.70731i
$911$	−116291.	−	547105.i	−0.140123	−	0.659225i	−0.991000	−	0.133861i	$-0.957262\pi$
$911$	−116291.	−	547105.i	−0.140123	−	0.659225i	0.850877	−	0.525364i	$-0.176071\pi$
$912$	3282.09	−	15441.0i	0.00394603	−	0.0185646i
$913$	−551332.	−	245469.i	−0.661412	−	0.294480i
$914$	860803.	−	279692.i	1.03041	−	0.334802i
$915$	33581.5	+	103353.i	0.0401104	+	0.123447i
$916$	−1.20526e6	+	2.70705e6i	−1.43644	+	3.22630i
$917$	565742.	+	120252.i	0.672791	+	0.143006i
$918$	−928711.	+	197404.i	−1.10203	+	0.234245i
$919$	820967.	−	365518.i	0.972063	−	0.432790i	0.141637	−	0.989919i	$-0.454763\pi$
$919$	820967.	−	365518.i	0.972063	−	0.432790i	0.830426	+	0.557128i	$0.188097\pi$
$920$	−987790.	+	889410.i	−1.16705	+	1.05082i
$921$	168196.	−	17678.1i	0.198288	−	0.0208409i
$922$	801514.	+	1.10319e6i	0.942865	+	1.29774i
$923$	−2.39098e6	−	251302.i	−2.80655	−	0.294980i
$924$	−114294.	−	197962.i	−0.133868	−	0.231867i
$925$	148471.	+	85719.6i	0.173523	+	0.100184i
$926$	−1.49936e6	+	2.06369e6i	−1.74857	+	2.40670i
$927$	367747.	−	408425.i	0.427947	−	0.475283i
$928$	359242.	+	116725.i	0.417148	+	0.135540i
$929$		−	1.35409e6i		−	1.56898i	−0.620143	−	0.784489i	$-0.712925\pi$
$929$		−	1.35409e6i		−	1.56898i	0.620143	−	0.784489i	$-0.287075\pi$
$930$	−296646.	−	484099.i	−0.342983	−	0.559717i
$931$	−84364.1			−0.0973326
$932$	768721.	−	2.36588e6i	0.884987	−	2.72371i
$933$	29027.5	+	26136.4i	0.0333462	+	0.0300250i
$934$	−1.26279e6	−	917470.i	−1.44756	−	1.05172i
$935$	600618.	−	1.04030e6i	0.687029	−	1.18997i
$936$	1.41569e6	−	817349.i	1.61591	−	0.932945i
$937$	−9637.18	+	91691.7i	−0.0109767	+	0.104436i	−0.998638	−	0.0521662i	$-0.983387\pi$
$937$	−9637.18	+	91691.7i	−0.0109767	+	0.104436i	0.987662	+	0.156602i	$0.0500541\pi$
$938$	311723.	−	226480.i	0.354294	−	0.257410i
$939$	21378.7	+	203405.i	0.0242466	+	0.230691i
$940$	−2.20418e6	−	2.44799e6i	−2.49455	−	2.77047i
$941$	520613.	+	1.16932e6i	0.587943	+	1.32054i	0.925325	+	0.379174i	$0.123792\pi$
$941$	520613.	+	1.16932e6i	0.587943	+	1.32054i	−0.337382	+	0.941368i	$0.609541\pi$
$942$	94033.0	+	442390.i	0.105969	+	0.498544i
$943$	256954.	−	1.20887e6i	0.288956	−	1.35943i
$944$	−448884.	−	199856.i	−0.503721	−	0.224271i
$945$	355428.	−	115486.i	0.398005	−	0.129320i
$946$	−574100.	−	1.76690e6i	−0.641513	−	1.97437i
$947$	542104.	−	1.21759e6i	0.604481	−	1.35769i	−0.309100	−	0.951030i	$-0.600028\pi$
$947$	542104.	−	1.21759e6i	0.604481	−	1.35769i	0.913581	−	0.406657i	$-0.133306\pi$
$948$	−207961.	−	44203.4i	−0.231401	−	0.0491857i
$949$	444903.	−	94567.1i	0.494007	−	0.105004i
$950$	−140722.	+	62653.4i	−0.155924	+	0.0694220i
$951$	115266.	−	103786.i	0.127450	−	0.114757i
$952$	798026.	−	83875.9i	0.880528	−	0.0925472i
$953$	−759716.	−	1.04566e6i	−0.836499	−	1.15134i	−0.986678	−	0.162684i	$-0.947985\pi$
$953$	−759716.	−	1.04566e6i	−0.836499	−	1.15134i	0.150179	−	0.988659i	$-0.452015\pi$
$954$	2.57123e6	+	270248.i	2.82517	+	0.296938i
$955$	913660.	+	1.58251e6i	1.00179	+	1.73516i
$956$	−250811.	−	144806.i	−0.274430	−	0.158442i
$957$	−105689.	+	145468.i	−0.115400	+	0.158834i
$958$	−854496.	+	949014.i	−0.931063	+	1.03405i
$959$	118831.	+	38610.6i	0.129209	+	0.0419826i
$960$		−	521339.i		−	0.565689i
$961$	419296.	−	822850.i	0.454019	−	0.890992i
$962$	656416.			0.709298
$963$	209408.	−	644493.i	0.225809	−	0.694969i
$964$	−1.23975e6	−	1.11628e6i	−1.33408	−	1.20121i
$965$	223861.	+	162645.i	0.240395	+	0.174657i
$966$	−116112.	+	201112.i	−0.124430	+	0.215519i
$967$	−1.41558e6	+	817283.i	−1.51384	+	0.874017i	−0.513973	+	0.857807i	$0.671827\pi$
$967$	−1.41558e6	+	817283.i	−1.51384	+	0.874017i	−0.999869	+	0.0162101i	$0.994840\pi$
$968$	27602.3	−	262618.i	0.0294574	−	0.280269i
$969$	37853.1	−	27501.9i	0.0403138	−	0.0292897i
$970$	81874.7	+	778986.i	0.0870175	+	0.827916i
$971$	−582900.	−	647376.i	−0.618238	−	0.686623i	0.349972	−	0.936760i	$-0.386191\pi$
$971$	−582900.	−	647376.i	−0.618238	−	0.686623i	−0.968210	+	0.250137i	$0.919524\pi$
$972$	549047.	+	1.23318e6i	0.581135	+	1.30525i
$973$	133283.	+	627046.i	0.140782	+	0.662329i
$974$	−403790.	+	1.89968e6i	−0.425635	+	2.00246i
$975$	284884.	+	126839.i	0.299681	+	0.133427i
$976$	134599.	−	43733.9i	0.141300	−	0.0459111i
$977$	−438271.	−	1.34886e6i	−0.459149	−	1.41312i	−0.866194	−	0.499708i	$-0.833441\pi$
$977$	−438271.	−	1.34886e6i	−0.459149	−	1.41312i	0.407045	−	0.913408i	$-0.366559\pi$
$978$	−208096.	+	467391.i	−0.217563	+	0.488655i
$979$	460502.	+	97882.8i	0.480470	+	0.102127i
$980$	1.52860e6	−	324915.i	1.59163	−	0.338312i
$981$	−1.08847e6	+	484619.i	−1.13104	+	0.503573i
$982$	−573705.	+	516567.i	−0.594930	+	0.535677i
$983$	169056.	−	17768.5i	0.174954	−	0.0183884i	−0.0166466	−	0.999861i	$-0.505299\pi$
$983$	169056.	−	17768.5i	0.174954	−	0.0183884i	0.191600	+	0.981473i	$0.438632\pi$
$984$	−357283.	−	491758.i	−0.368996	−	0.507880i
$985$	−2.35766e6	−	247800.i	−2.43001	−	0.255404i
$986$	−708437.	−	1.22705e6i	−0.728697	−	1.26214i
$987$	−222031.	−	128190.i	−0.227918	−	0.131589i
$988$	−223009.	+	306946.i	−0.228459	+	0.314447i
$989$	−812413.	+	902276.i	−0.830585	+	0.922458i
$990$	−1.65746e6	−	538540.i	−1.69111	−	0.549475i
$991$			1.21540e6i			1.23757i	0.785559	+	0.618786i	$0.212375\pi$
$991$			1.21540e6i			1.23757i	−0.785559	+	0.618786i	$0.787625\pi$
$992$	498166.	−	305266.i	0.506233	−	0.310209i
$993$	−79505.0			−0.0806298
$994$	−529074.	+	1.62832e6i	−0.535480	+	1.64804i
$995$	−641724.	−	577810.i	−0.648189	−	0.583632i
$996$	352281.	+	255947.i	0.355116	+	0.258007i
$997$	276314.	−	478589.i	0.277979	−	0.481474i	−0.692903	−	0.721031i	$-0.743669\pi$
$997$	276314.	−	478589.i	0.277979	−	0.481474i	0.970882	+	0.239557i	$0.0770021\pi$
$998$	1.58447e6	−	914792.i	1.59082	−	0.918462i
$999$	−16568.9	+	157642.i	−0.0166021	+	0.157958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.17.1	yes	80
31.11	odd	30	inner	31.5.h.a.11.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.1	✓	80	31.11	odd	30	inner
31.5.h.a.17.1	yes	80	1.1	even	1	trivial

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+(-2.06958 + 6.36951i) q^{2} +(1.99917 + 1.80007i) q^{3} +(-23.3433 - 16.9599i) q^{4} +(-16.3958 + 28.3984i) q^{5} +(-15.6030 + 9.00839i) q^{6} +(2.86136 - 27.2240i) q^{7} +(69.6453 - 50.6002i) q^{8} +(-7.71034 - 73.3590i) q^{9} +(-146.952 - 163.206i) q^{10} +(43.7569 + 98.2796i) q^{11} +(-16.1384 - 75.9252i) q^{12} +(-53.5234 + 251.808i) q^{13} +(167.482 + 74.5677i) q^{14} +(-83.8972 + 27.2598i) q^{15} +(35.5011 + 109.261i) q^{16} +(-138.498 + 311.072i) q^{17} +(483.218 + 102.711i) q^{18} +(-49.9620 + 10.6197i) q^{19} +(864.366 - 384.841i) q^{20} +(54.7253 - 49.2749i) q^{21} +(-716.552 + 75.3126i) q^{22} +(276.766 + 380.935i) q^{23} +(230.317 + 24.2073i) q^{24} +(-225.147 - 389.966i) q^{25} +(-1493.12 - 862.055i) q^{26} +(244.717 - 336.823i) q^{27} +(-528.509 + 586.969i) q^{28} +(590.889 + 191.991i) q^{29} -590.801i q^{30} +(819.395 - 502.108i) q^{31} +607.968 q^{32} +(-89.4320 + 275.243i) q^{33} +(-1694.75 - 1525.96i) q^{34} +(726.204 + 527.618i) q^{35} +(-1064.17 + 1843.21i) q^{36} +(-329.720 + 190.364i) q^{37} +(35.7577 - 340.212i) q^{38} +(-560.273 + 407.062i) q^{39} +(295.075 + 2807.45i) q^{40} +(-1756.28 - 1950.54i) q^{41} +(200.599 + 450.552i) q^{42} +(536.106 + 2522.18i) q^{43} +(645.381 - 3036.28i) q^{44} +(2209.70 + 983.820i) q^{45} +(-2999.16 + 974.487i) q^{46} +(-1075.85 - 3311.12i) q^{47} +(-125.704 + 282.336i) q^{48} +(1615.57 + 343.401i) q^{49} +(2949.85 - 627.011i) q^{50} +(-836.833 + 372.582i) q^{51} +(5520.04 - 4970.27i) q^{52} +(5204.78 - 547.045i) q^{53} +(1638.94 + 2255.81i) q^{54} +(-3508.42 - 368.750i) q^{55} +(-1178.26 - 2040.81i) q^{56} +(-118.999 - 68.7041i) q^{57} +(-2445.78 + 3366.33i) q^{58} +(-2861.91 + 3178.47i) q^{59} +(2420.76 + 786.552i) q^{60} -1231.90i q^{61} +(1502.38 + 6258.30i) q^{62} -2019.19 q^{63} +(-1826.26 + 5620.64i) q^{64} +(-6273.39 - 5648.58i) q^{65} +(-1568.08 - 1139.28i) q^{66} +(1050.86 - 1820.14i) q^{67} +(8508.76 - 4912.53i) q^{68} +(-132.405 + 1259.75i) q^{69} +(-4863.61 + 3533.62i) q^{70} +(976.182 + 9287.76i) q^{71} +(-4248.97 - 4718.96i) q^{72} +(-718.637 - 1614.09i) q^{73} +(-530.143 - 2494.13i) q^{74} +(251.856 - 1184.89i) q^{75} +(1346.39 + 599.449i) q^{76} +(2800.77 - 910.024i) q^{77} +(-1433.26 - 4411.12i) q^{78} +(1114.06 - 2502.22i) q^{79} +(-3684.91 - 783.252i) q^{80} +(-4748.71 + 1009.37i) q^{81} +(16058.8 - 7149.83i) q^{82} +(-4168.92 + 3753.71i) q^{83} +(-2113.16 + 222.102i) q^{84} +(-6563.17 - 9033.43i) q^{85} +(-17174.6 - 1805.12i) q^{86} +(835.693 + 1447.46i) q^{87} +(8020.43 + 4630.60i) q^{88} +(2572.25 - 3540.40i) q^{89} +(-10839.6 + 12038.6i) q^{90} +(6702.06 + 2177.63i) q^{91} -13586.2i q^{92} +(2541.94 + 471.163i) q^{93} +23316.8 q^{94} +(517.584 - 1592.96i) q^{95} +(1215.43 + 1094.38i) q^{96} +(-2885.42 - 2096.38i) q^{97} +(-5530.86 + 9579.73i) q^{98} +(6872.31 - 3967.73i) 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

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