LMFDB - Embedded newform 31.5.h.a.11.1

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			11.1
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.1

$q$-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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.06958	−	6.36951i	−0.517395	−	1.59238i	−0.778881	−	0.627171i	$-0.784213\pi$
$2$	−2.06958	−	6.36951i	−0.517395	−	1.59238i	0.261486	−	0.965207i	$-0.415787\pi$
$3$	1.99917	−	1.80007i	0.222131	−	0.200007i	−0.550550	−	0.834802i	$-0.685582\pi$
$3$	1.99917	−	1.80007i	0.222131	−	0.200007i	0.772681	+	0.634795i	$0.218915\pi$
$4$	−23.3433	+	16.9599i	−1.45895	+	1.05999i
$5$	−16.3958	−	28.3984i	−0.655833	−	1.13594i	−0.981684	−	0.190516i	$-0.938984\pi$
$5$	−16.3958	−	28.3984i	−0.655833	−	1.13594i	0.325851	−	0.945421i	$-0.394349\pi$
$6$	−15.6030	−	9.00839i	−0.433416	−	0.250233i
$7$	2.86136	+	27.2240i	0.0583950	+	0.555591i	0.984134	+	0.177428i	$0.0567776\pi$
$7$	2.86136	+	27.2240i	0.0583950	+	0.555591i	−0.925739	+	0.378164i	$0.876556\pi$
$8$	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	−0.637500	−	0.770451i	$-0.720031\pi$
$11$	43.7569	−	98.2796i	0.361627	−	0.812228i	0.999127	−	0.0417777i	$-0.0133021\pi$
$12$	−16.1384	+	75.9252i	−0.112072	+	0.527258i
$13$	−53.5234	−	251.808i	−0.316707	−	1.48999i	−0.792196	−	0.610266i	$-0.791062\pi$
$13$	−53.5234	−	251.808i	−0.316707	−	1.48999i	0.475490	−	0.879721i	$-0.342271\pi$
$14$	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	−0.977803	−	0.209526i	$-0.932808\pi$
$17$	−138.498	−	311.072i	−0.479233	−	1.07638i	0.498570	−	0.866849i	$-0.333859\pi$
$18$	483.218	−	102.711i	1.49141	−	0.317010i
$19$	−49.9620	−	10.6197i	−0.138399	−	0.0294176i	0.138191	−	0.990406i	$-0.455871\pi$
$19$	−49.9620	−	10.6197i	−0.138399	−	0.0294176i	−0.276590	+	0.960988i	$0.589204\pi$
$20$	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	−0.462886	−	0.886418i	$-0.653186\pi$
$23$	276.766	−	380.935i	0.523187	−	0.720105i	0.986073	+	0.166313i	$0.0531862\pi$
$24$	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	0.0641386	−	0.997941i	$-0.479570\pi$
$29$	590.889	−	191.991i	0.702603	−	0.228290i	0.638464	+	0.769651i	$0.279570\pi$
$30$			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	0.374719	−	0.927138i	$-0.377739\pi$
$37$	−329.720	−	190.364i	−0.240847	−	0.139053i	−0.615566	+	0.788085i	$0.711073\pi$
$38$	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	−0.0579964	+	0.998317i	$0.518471\pi$
$41$	−1756.28	+	1950.54i	−1.04478	+	1.16035i	−0.986786	+	0.162031i	$0.948195\pi$
$42$	200.599	−	450.552i	0.113718	−	0.255415i
$43$	536.106	−	2522.18i	0.289944	−	1.36408i	−0.556166	−	0.831071i	$-0.687728\pi$
$43$	536.106	−	2522.18i	0.289944	−	1.36408i	0.846110	−	0.533008i	$-0.178938\pi$
$44$	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	0.341991	+	0.939703i	$0.388899\pi$
$47$	−1075.85	+	3311.12i	−0.487029	+	1.49892i	−0.829020	+	0.559219i	$0.811101\pi$
$48$	−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	0.964455	−	0.264245i	$-0.0851229\pi$
$53$	5204.78	+	547.045i	1.85290	+	0.194747i	0.888440	+	0.458993i	$0.151790\pi$
$54$	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	0.175295	−	0.984516i	$-0.443912\pi$
$59$	−2861.91	−	3178.47i	−0.822151	−	0.913091i	−0.997446	+	0.0714248i	$0.977245\pi$
$60$	2420.76	−	786.552i	0.672433	−	0.218487i
$61$			1231.90i			0.331068i	0.986204	+	0.165534i	$0.0529347\pi$
$61$			1231.90i			0.331068i	−0.986204	+	0.165534i	$0.947065\pi$
$62$	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	0.959010	−	0.283373i	$-0.0914535\pi$
$67$	1050.86	+	1820.14i	0.234096	+	0.405467i	−0.724913	+	0.688840i	$0.758120\pi$
$68$	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	−0.277908	−	0.960608i	$-0.589641\pi$
$71$	976.182	−	9287.76i	0.193649	−	1.84244i	0.471557	−	0.881836i	$-0.343692\pi$
$72$	−4248.97	+	4718.96i	−0.819632	+	0.910293i
$73$	−718.637	+	1614.09i	−0.134854	+	0.302887i	−0.968332	−	0.249665i	$-0.919679\pi$
$73$	−718.637	+	1614.09i	−0.134854	+	0.302887i	0.833478	+	0.552552i	$0.186346\pi$
$74$	−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	0.980533	−	0.196357i	$-0.0629111\pi$
$79$	1114.06	+	2502.22i	0.178507	+	0.400932i	−0.802026	+	0.597289i	$0.796244\pi$
$80$	−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	0.308577	−	0.951199i	$-0.400147\pi$
$83$	−4168.92	−	3753.71i	−0.605156	−	0.544885i	−0.913733	+	0.406314i	$0.866814\pi$
$84$	−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	0.939906	−	0.341432i	$-0.110912\pi$
$89$	2572.25	+	3540.40i	0.324738	+	0.446963i	−0.615169	+	0.788396i	$0.710912\pi$
$90$	−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	−0.730465	−	0.682950i	$-0.760696\pi$
$97$	−2885.42	+	2096.38i	−0.306666	+	0.222806i	0.423798	+	0.905757i	$0.360696\pi$
$98$	−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	0.602769	−	0.797916i	$-0.294064\pi$
$101$	307.775	+	223.612i	0.0301711	+	0.0219206i	−0.572598	+	0.819837i	$0.694064\pi$
$102$	−641.273	+	6101.31i	−0.0616372	+	0.586439i
$103$	4985.52	−	5536.98i	0.469933	−	0.521914i	−0.460854	−	0.887476i	$-0.652457\pi$
$103$	4985.52	−	5536.98i	0.469933	−	0.521914i	0.930787	+	0.365562i	$0.119123\pi$
$104$	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	−0.00603816	−	0.999982i	$-0.501922\pi$
$107$	8392.72	−	3736.68i	0.733053	−	0.326376i	0.739091	+	0.673606i	$0.235255\pi$
$108$	−11425.0	−	3712.20i	−0.979507	−	0.318261i
$109$	−4991.49	+	15362.2i	−0.420124	+	1.29301i	0.487462	+	0.873144i	$0.337923\pi$
$109$	−4991.49	+	15362.2i	−0.420124	+	1.29301i	−0.907587	+	0.419865i	$0.862077\pi$
$110$	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	0.629271	−	0.777186i	$-0.283353\pi$
$113$	6036.86	+	2687.78i	0.472775	+	0.210493i	−0.156497	+	0.987678i	$0.550020\pi$
$114$	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	−0.700636	−	0.713519i	$-0.747100\pi$
$127$	−1036.47	+	933.243i	−0.0642614	+	0.0578612i	0.636374	+	0.771380i	$0.280433\pi$
$128$	−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	−0.848084	−	0.529862i	$-0.822244\pi$
$131$	−2208.57	−	21013.2i	−0.128697	−	1.22447i	0.719387	−	0.694610i	$-0.244423\pi$
$132$	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	0.945609	−	0.325307i	$-0.105468\pi$
$137$	−948.999	−	4464.69i	−0.0505620	−	0.237876i	−0.996171	+	0.0874311i	$0.972134\pi$
$138$	−7749.99	+	3450.52i	−0.406952	+	0.181187i
$139$	−22272.2	−	7236.69i	−1.15275	−	0.374550i	−0.330570	−	0.943781i	$-0.607241\pi$
$139$	−22272.2	−	7236.69i	−1.15275	−	0.374550i	−0.822178	+	0.569231i	$0.807241\pi$
$140$	−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	−0.769638	−	0.638481i	$-0.779563\pi$
$149$	3732.47	−	6464.82i	0.168122	−	0.291195i	0.937759	+	0.347286i	$0.112897\pi$
$150$	7025.93	−	4056.42i	0.312264	−	0.180285i
$151$	3620.76	+	4983.55i	0.158798	+	0.218567i	0.881001	−	0.473114i	$-0.156870\pi$
$151$	3620.76	+	4983.55i	0.158798	+	0.218567i	−0.722203	+	0.691681i	$0.756870\pi$
$152$	−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	0.975875	+	0.218331i	$0.0700614\pi$
$157$	7757.22	+	23874.3i	0.314707	+	0.968570i	−0.661167	+	0.750239i	$0.729939\pi$
$158$	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	0.929154	−	0.369693i	$-0.120537\pi$
$163$	22973.7	+	16691.4i	0.864680	+	0.628227i	−0.0644742	+	0.997919i	$0.520537\pi$
$164$	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	−0.989257	−	0.146184i	$-0.953301\pi$
$167$	−726.994	+	3420.24i	−0.0260674	+	0.122638i	0.963190	+	0.268822i	$0.0866342\pi$
$168$	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	−0.280739	−	0.959784i	$-0.590580\pi$
$173$	−4394.43	+	934.064i	−0.146828	+	0.0312093i	0.133911	+	0.990993i	$0.457246\pi$
$174$	−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	−0.183283	−	0.983060i	$-0.558672\pi$
$179$	−5067.96	+	532.664i	−0.158171	+	0.0166245i	0.0251119	+	0.999685i	$0.492006\pi$
$180$	−34896.1	+	60441.8i	−1.07704	+	1.86549i
$181$	11617.9	−	6707.62i	0.354627	−	0.204744i	−0.312094	−	0.950051i	$-0.601030\pi$
$181$	11617.9	−	6707.62i	0.354627	−	0.204744i	0.666721	+	0.745307i	$0.267697\pi$
$182$	−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	0.940902	+	0.338679i	$0.109980\pi$
$191$	27862.6	+	48259.4i	0.763756	+	1.32286i	−0.177146	+	0.984185i	$0.556687\pi$
$192$	−13768.5	−	7949.26i	−0.373495	−	0.215637i
$193$	882.049	+	8392.14i	0.0236798	+	0.225298i	0.999961	+	0.00879339i	$0.00279906\pi$
$193$	882.049	+	8392.14i	0.0236798	+	0.225298i	−0.976282	+	0.216505i	$0.930534\pi$
$194$	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	0.0463284	−	0.998926i	$-0.485248\pi$
$197$	29404.6	−	66043.9i	0.757676	−	1.70177i	0.711347	−	0.702841i	$-0.248085\pi$
$198$	11049.7	−	51984.8i	0.281852	−	1.32601i
$199$	−5475.07	−	25758.2i	−0.138256	−	0.650443i	−0.991627	−	0.129138i	$-0.958779\pi$
$199$	−5475.07	−	25758.2i	−0.138256	−	0.650443i	0.853371	−	0.521305i	$-0.174554\pi$
$200$	−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	−0.714484	−	0.699652i	$-0.753339\pi$
$211$	11071.2	−	19175.9i	0.248674	−	0.430716i	0.963158	+	0.268935i	$0.0866718\pi$
$212$	−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	0.688600	−	0.725142i	$-0.258226\pi$
$223$	20135.7	+	11625.3i	0.404908	+	0.233774i	−0.283691	+	0.958916i	$0.591559\pi$
$224$	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	0.0186719	+	0.999826i	$0.494056\pi$
$227$	−50376.2	+	55948.5i	−0.977628	+	1.08577i	−0.996300	+	0.0859406i	$0.972610\pi$
$228$	1612.61	−	3621.99i	0.0310213	−	0.0696750i
$229$	−21352.1	+	100454.i	−0.407164	+	1.91556i	−0.00500362	+	0.999987i	$0.501593\pi$
$229$	−21352.1	+	100454.i	−0.407164	+	1.91556i	−0.402161	+	0.915569i	$0.631741\pi$
$230$	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	−0.332748	−	0.943016i	$-0.607976\pi$
$233$	26641.9	−	81995.2i	0.490742	−	1.51035i	0.823490	−	0.567331i	$-0.192024\pi$
$234$	−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	0.191502	−	0.981492i	$-0.438664\pi$
$239$	9982.22	+	1049.17i	0.174756	+	0.0183676i	−0.0167464	+	0.999860i	$0.505331\pi$
$240$	−5956.88	+	8198.94i	−0.103418	+	0.142343i
$241$	57500.5	−	6043.55i	0.990006	−	0.104054i	0.404342	−	0.914608i	$-0.367501\pi$
$241$	57500.5	−	6043.55i	0.990006	−	0.104054i	0.585664	+	0.810554i	$0.300834\pi$
$242$	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	−0.702558	−	0.711627i	$-0.747959\pi$
$251$	−4300.85	+	3872.50i	−0.0682663	+	0.0614673i	0.634291	+	0.773094i	$0.281292\pi$
$252$	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	−0.872253	−	0.489054i	$-0.837342\pi$
$257$	5456.92	−	51919.1i	0.0826193	−	0.786070i	0.954873	−	0.297016i	$-0.0959914\pi$
$258$	−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	0.328226	−	0.944599i	$-0.393549\pi$
$263$	2666.09	+	866.264i	0.0385445	+	0.0125239i	−0.289681	+	0.957123i	$0.593549\pi$
$264$	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	0.175382	−	0.984501i	$-0.443884\pi$
$269$	−56831.8	−	51171.6i	−0.785393	−	0.707171i	−0.960775	+	0.277329i	$0.910551\pi$
$270$	−90933.2	−	9557.47i	−1.24737	−	0.131104i
$271$	85791.2	−	118081.i	1.16816	−	1.60784i	0.493414	−	0.869795i	$-0.335749\pi$
$271$	85791.2	−	118081.i	1.16816	−	1.60784i	0.674751	−	0.738046i	$-0.264251\pi$
$272$	−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	−0.799939	−	0.600082i	$-0.795135\pi$
$277$	−83971.0	+	27283.8i	−1.09438	+	0.355587i	−0.294445	+	0.955668i	$0.595135\pi$
$278$			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	0.964533	−	0.263964i	$-0.0850300\pi$
$281$	2294.23	+	7060.91i	0.0290552	+	0.0894228i	−0.935477	+	0.353387i	$0.885030\pi$
$282$	46614.3	−	41971.7i	0.586167	−	0.527787i
$283$	79707.4	−	57910.8i	0.995235	−	0.723081i	0.0341737	−	0.999416i	$-0.489120\pi$
$283$	79707.4	−	57910.8i	0.995235	−	0.723081i	0.961061	+	0.276335i	$0.0891201\pi$
$284$	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	−0.0648992	−	0.997892i	$-0.520673\pi$
$293$	54364.1	−	24204.5i	0.633253	−	0.281942i	0.698152	+	0.715949i	$0.254006\pi$
$294$	−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	0.923762	−	0.382968i	$-0.125098\pi$
$307$	42066.3	+	46719.4i	0.446332	+	0.495702i	−0.477430	+	0.878670i	$0.658431\pi$
$308$	−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	−0.328353	−	0.944555i	$-0.606493\pi$
$313$	56499.3	−	50872.2i	0.576706	−	0.519268i	0.905059	+	0.425287i	$0.139827\pi$
$314$	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	0.982706	+	0.185175i	$0.0592852\pi$
$317$	6026.78	+	57341.0i	0.0599745	+	0.570620i	−0.922731	+	0.385445i	$0.874048\pi$
$318$	−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	0.562785	−	0.826603i	$-0.309730\pi$
$331$	−21962.9	−	19775.5i	−0.200463	−	0.180498i	−0.763248	+	0.646106i	$0.776397\pi$
$332$	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	0.782244	−	0.622972i	$-0.214075\pi$
$337$	−5901.45	−	8122.65i	−0.0519636	−	0.0715217i	−0.834208	+	0.551450i	$0.814075\pi$
$338$	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	0.599965	−	0.800026i	$-0.295181\pi$
$347$	24937.4	+	14397.6i	0.207105	+	0.119572i	−0.392860	+	0.919598i	$0.628514\pi$
$348$	5040.99	+	47961.8i	0.0416253	+	0.396038i
$349$	96818.9	+	70343.0i	0.794894	+	0.577524i	0.909412	−	0.415897i	$-0.136532\pi$
$349$	96818.9	+	70343.0i	0.794894	+	0.577524i	−0.114518	+	0.993421i	$0.536532\pi$
$350$	−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	0.665945	+	0.746001i	$0.268028\pi$
$353$	−30635.4	+	144128.i	−0.245852	+	1.15664i	−0.911797	+	0.410641i	$0.865305\pi$
$354$	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	−0.279308	−	0.960201i	$-0.590105\pi$
$359$	−18548.6	+	3942.62i	−0.143920	+	0.0305911i	0.135388	+	0.990793i	$0.456772\pi$
$360$	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	−0.143551	−	0.989643i	$-0.545852\pi$
$367$	86433.9	−	49902.6i	0.641730	−	0.370503i	0.785280	+	0.619140i	$0.212519\pi$
$368$	−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	0.982986	−	0.183679i	$-0.0588006\pi$
$379$	−2400.00	−	22834.5i	−0.0167083	−	0.158969i	−0.999695	+	0.0247095i	$0.992134\pi$
$380$	−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	−0.998044	−	0.0625179i	$-0.980087\pi$
$383$	−41624.8	+	93490.9i	−0.283762	+	0.637341i	0.714282	+	0.699858i	$0.246754\pi$
$384$	−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	0.671335	+	0.741154i	$0.265721\pi$
$389$	116957.	+	262690.i	0.772909	+	1.73598i	0.101573	+	0.994828i	$0.467612\pi$
$390$	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	−0.629446	−	0.777044i	$-0.716718\pi$
$397$	56458.2	−	97788.5i	0.358217	−	0.620450i	0.987663	+	0.156594i	$0.0500514\pi$
$398$	−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	−0.919995	−	0.391930i	$-0.871807\pi$
$401$	−230575.	+	74918.4i	−1.43392	+	0.465907i	−0.513921	+	0.857838i	$0.671807\pi$
$402$		−	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	0.247334	−	0.968930i	$-0.420445\pi$
$409$	−78307.0	−	45210.6i	−0.468117	−	0.270267i	−0.715451	+	0.698663i	$0.753779\pi$
$410$	−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	0.656382	+	0.754429i	$0.272086\pi$
$419$	−55843.2	+	171868.i	−0.318084	+	0.978963i	−0.974466	+	0.224534i	$0.927914\pi$
$420$	28339.7	+	63652.1i	0.160656	+	0.360839i
$421$	25390.9	−	5397.01i	0.143257	−	0.0304501i	−0.135725	−	0.990747i	$-0.543336\pi$
$421$	25390.9	−	5397.01i	0.143257	−	0.0304501i	0.278982	+	0.960296i	$0.410003\pi$
$422$	−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	0.501165	−	0.865352i	$-0.332905\pi$
$431$	−76502.5	−	84964.6i	−0.411833	−	0.457387i	−0.912997	+	0.407965i	$0.866238\pi$
$432$	45489.4	−	14780.4i	0.243749	−	0.0791988i
$433$		−	39335.7i		−	0.209803i	−0.994483	−	0.104901i	$-0.966547\pi$
$433$		−	39335.7i		−	0.209803i	0.994483	−	0.104901i	$-0.0334527\pi$
$434$	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	0.996816	+	0.0797391i	$0.0254087\pi$
$439$	109362.	+	189421.i	0.567464	+	0.982876i	−0.429352	+	0.903137i	$0.641258\pi$
$440$	−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	−0.923489	−	0.383624i	$-0.874676\pi$
$443$	11692.4	−	111246.i	0.0595795	−	0.566861i	0.983069	−	0.183237i	$-0.0586575\pi$
$444$	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	−0.183992	−	0.982928i	$-0.558902\pi$
$449$	−183577.	−	59647.7i	−0.910595	−	0.295870i	−0.726603	+	0.687057i	$0.758902\pi$
$450$	−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	−0.955677	−	0.294416i	$-0.904875\pi$
$457$	−79435.8	+	109334.i	−0.380350	+	0.523507i	0.575327	+	0.817924i	$0.304875\pi$
$458$	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	0.991720	−	0.128416i	$-0.0409893\pi$
$461$	119677.	+	164721.i	0.563131	+	0.775083i	−0.428589	+	0.903499i	$0.640989\pi$
$462$	−35502.5	−	39429.5i	−0.166332	−	0.184730i
$463$	362237.	−	117698.i	1.68978	−	0.549043i	0.703012	−	0.711178i	$-0.251838\pi$
$463$	362237.	−	117698.i	1.68978	−	0.549043i	0.986769	+	0.162135i	$0.0518381\pi$
$464$		−	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	−0.969022	−	0.246973i	$-0.920564\pi$
$467$	−72020.4	−	221656.i	−0.330234	−	1.01636i	0.638788	−	0.769383i	$-0.279436\pi$
$468$	−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	0.00964186	−	0.999954i	$-0.496931\pi$
$479$	174192.	−	77555.5i	0.759204	−	0.338019i	0.749562	+	0.661934i	$0.230264\pi$
$480$	−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	0.690719	−	0.723123i	$-0.257294\pi$
$487$	288397.	+	30311.8i	1.21600	+	0.127807i	0.525279	+	0.850930i	$0.323961\pi$
$488$	−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	−0.278462	−	0.960447i	$-0.589825\pi$
$491$	99826.6	−	57634.9i	0.414079	−	0.239069i	0.692541	+	0.721379i	$0.256491\pi$
$492$	−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	−0.967126	−	0.254298i	$-0.918156\pi$
$499$	−203014.	+	182794.i	−0.815313	+	0.734111i	0.151813	+	0.988409i	$0.451489\pi$
$500$	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	0.923491	+	0.383621i	$0.125323\pi$
$503$	25285.6	+	240577.i	0.0999397	+	0.950863i	−0.823551	+	0.567242i	$0.808010\pi$
$504$	−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	0.982297	−	0.187329i	$-0.0599829\pi$
$509$	2261.96	+	10641.7i	0.00873070	+	0.0410747i	−0.973567	+	0.228403i	$0.926650\pi$
$510$	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	−0.982417	−	0.186701i	$-0.940220\pi$
$521$	−89445.4	+	154924.i	−0.329520	+	0.570746i	0.652896	+	0.757447i	$0.273554\pi$
$522$	265809.	−	153465.i	0.975502	−	0.563206i
$523$	−73007.0	−	100486.i	−0.266908	−	0.367367i	0.654435	−	0.756118i	$-0.272907\pi$
$523$	−73007.0	−	100486.i	−0.266908	−	0.367367i	−0.921343	+	0.388751i	$0.872907\pi$
$524$	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	−0.166719	−	0.986004i	$-0.553317\pi$
$541$	133014.	−	59221.8i	0.454468	−	0.202342i	0.621187	+	0.783662i	$0.286651\pi$
$542$	−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	0.166347	−	0.986067i	$-0.446803\pi$
$547$	−136181.	−	60631.6i	−0.455136	−	0.202639i	−0.621483	+	0.783428i	$0.713469\pi$
$548$	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	$0.245350\pi$
$557$			432302.i			1.39340i	−0.717362	+	0.696701i	$0.754650\pi$
$558$	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	−0.902243	−	0.431229i	$-0.858080\pi$
$563$	−261365.	−	452698.i	−0.824576	−	1.42821i	0.0776664	−	0.996979i	$-0.475253\pi$
$564$	−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	−0.306433	−	0.951892i	$-0.599135\pi$
$569$	196201.	−	440674.i	0.606005	−	1.36111i	0.912437	−	0.409216i	$-0.134198\pi$
$570$	6274.15	−	29517.6i	0.0193110	−	0.0908512i
$571$	13077.5	+	61524.7i	0.0401099	+	0.188702i	0.993641	−	0.112591i	$-0.0359150\pi$
$571$	13077.5	+	61524.7i	0.0401099	+	0.188702i	−0.953531	+	0.301293i	$0.902582\pi$
$572$	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	0.151940	−	0.988390i	$-0.451448\pi$
$577$	−37044.9	−	7874.14i	−0.111270	−	0.0236511i	−0.263210	+	0.964739i	$0.584781\pi$
$578$	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	−0.697985	−	0.716112i	$-0.745920\pi$
$587$	−290040.	+	94239.6i	−0.841746	+	0.273500i	−0.143761	+	0.989612i	$0.545920\pi$
$588$			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	−0.332869	+	0.942973i	$0.608017\pi$
$593$	−468591.	+	340451.i	−1.33255	+	0.968156i	−0.999683	+	0.0251830i	$0.991983\pi$
$594$	−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	−0.975715	−	0.219042i	$-0.929707\pi$
$599$	−235332.	+	261362.i	−0.655883	+	0.728432i	0.319832	+	0.947474i	$0.396373\pi$
$600$	−42415.1	+	95265.9i	−0.117820	+	0.264627i
$601$	−87151.8	+	410017.i	−0.241284	+	1.13515i	0.675996	+	0.736905i	$0.263714\pi$
$601$	−87151.8	+	410017.i	−0.241284	+	1.13515i	−0.917279	+	0.398244i	$0.869620\pi$
$602$	−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	0.00698972	−	0.999976i	$-0.497775\pi$
$607$	154786.	−	32900.8i	0.420102	−	0.0892954i	0.413112	+	0.910680i	$0.364442\pi$
$608$	−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	−0.984355	−	0.176198i	$-0.943620\pi$
$613$	−717931.	+	75457.6i	−1.91057	+	0.200808i	−0.926211	+	0.377007i	$0.876953\pi$
$614$	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	0.553976	−	0.832533i	$-0.313110\pi$
$617$	−126352.	−	140328.i	−0.331902	−	0.368615i	−0.885878	+	0.463918i	$0.846443\pi$
$618$	−127668.	+	41482.0i	−0.334277	+	0.108613i
$619$			560378.i			1.46251i	0.682102	+	0.731257i	$0.261066\pi$
$619$			560378.i			1.46251i	−0.682102	+	0.731257i	$0.738934\pi$
$620$	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	−0.697654	−	0.716435i	$-0.745773\pi$
$631$	120079.	−	269701.i	0.301583	−	0.677366i	0.999237	+	0.0390689i	$0.0124392\pi$
$632$	−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	0.960911	−	0.276856i	$-0.0892924\pi$
$641$	322959.	+	290793.i	0.786015	+	0.707731i	−0.174897	+	0.984587i	$0.555959\pi$
$642$	−164613.	−	17301.5i	−0.399387	−	0.0419773i
$643$	237659.	−	327109.i	0.574820	−	0.791172i	−0.418296	−	0.908311i	$-0.637372\pi$
$643$	237659.	−	327109.i	0.574820	−	0.791172i	0.993115	+	0.117139i	$0.0373724\pi$
$644$	−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	0.770881	−	0.636979i	$-0.219816\pi$
$647$	−30615.9	−	42139.2i	−0.0731372	−	0.100665i	−0.844018	+	0.536314i	$0.819816\pi$
$648$	−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	0.999380	+	0.0351965i	$0.0112057\pi$
$653$	90208.0	+	277632.i	0.211553	+	0.651092i	−0.787828	+	0.615896i	$0.788794\pi$
$654$	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	0.912754	−	0.408509i	$-0.133951\pi$
$659$	350159.	+	254405.i	0.806295	+	0.585808i	−0.106459	+	0.994317i	$0.533951\pi$
$660$	28622.9	−	272328.i	0.0657090	−	0.625180i
$661$	−16666.0	+	18509.4i	−0.0381441	+	0.0423634i	−0.761915	−	0.647677i	$-0.775741\pi$
$661$	−16666.0	+	18509.4i	−0.0381441	+	0.0423634i	0.723771	+	0.690040i	$0.242407\pi$
$662$	−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	−0.620258	−	0.784398i	$-0.712972\pi$
$673$	−629593.	−	66172.8i	−1.39005	−	0.146100i	−0.769789	+	0.638298i	$0.779639\pi$
$674$	−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	−0.579082	−	0.815269i	$-0.696589\pi$
$677$	−74514.9	+	43021.2i	−0.162579	+	0.0938653i	0.416503	+	0.909134i	$0.363256\pi$
$678$	−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	−0.950196	−	0.311654i	$-0.899117\pi$
$691$	21024.6	−	200036.i	0.0440324	−	0.418940i	0.994228	−	0.107287i	$-0.0342163\pi$
$692$	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	0.522763	−	0.852478i	$-0.324901\pi$
$701$	321178.	+	68268.4i	0.653596	+	0.138926i	0.130833	+	0.991404i	$0.458235\pi$
$702$	−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	0.999972	−	0.00749783i	$-0.00238666\pi$
$709$	343750.	+	473131.i	0.683833	+	0.941215i	−0.316139	+	0.948713i	$0.602387\pi$
$710$	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	0.672441	−	0.740151i	$-0.265246\pi$
$719$	190072.	+	109738.i	0.367672	+	0.212275i	−0.304769	+	0.952426i	$0.598579\pi$
$720$	−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	−0.854986	−	0.518652i	$-0.826434\pi$
$727$	−550542.	+	245117.i	−1.04165	+	0.463772i	−0.186664	+	0.982424i	$0.559767\pi$
$728$	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	0.184930	−	0.982752i	$-0.440794\pi$
$733$	−226550.	−	100867.i	−0.421654	−	0.187732i	−0.606584	+	0.795019i	$0.707461\pi$
$734$	−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	0.0280932	−	0.999605i	$-0.491056\pi$
$739$	495781.	−	286240.i	0.907823	−	0.524132i	0.879730	+	0.475473i	$0.157723\pi$
$740$	−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	$-0.574858\pi$
$743$		−	1.07371e6i		−	1.94495i	0.233011	−	0.972474i	$-0.425142\pi$
$744$	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	0.843063	+	0.537814i	$0.180750\pi$
$751$	73456.0	+	698887.i	0.130241	+	1.23916i	−0.712823	+	0.701344i	$0.752583\pi$
$752$	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	−0.868547	−	0.495607i	$-0.834946\pi$
$757$	−158546.	−	745901.i	−0.276671	−	1.30164i	0.591876	−	0.806029i	$-0.298388\pi$
$758$	−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	0.977352	+	0.211621i	$0.0678741\pi$
$761$	278349.	+	625182.i	0.480641	+	1.07954i	−0.496711	+	0.867916i	$0.665459\pi$
$762$	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	−0.314629	−	0.949215i	$-0.601880\pi$
$769$	393095.	−	680861.i	0.664730	−	1.15135i	0.979359	−	0.202131i	$-0.0647866\pi$
$770$	−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	−0.458289	−	0.888803i	$-0.651538\pi$
$773$	−183219.	+	59531.4i	−0.306628	+	0.0996294i	0.151662	+	0.988432i	$0.451538\pi$
$774$		−	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	−0.768177	−	0.640237i	$-0.778836\pi$
$787$	120155.	−	565284.i	0.193995	−	0.912677i	0.962173	−	0.272440i	$-0.0878305\pi$
$788$	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	0.100270	−	0.994960i	$-0.468029\pi$
$797$	−5408.67	−	568.474i	−0.00851479	−	0.000894941i	−0.108785	+	0.994065i	$0.534696\pi$
$798$	−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	−0.506938	−	0.861982i	$-0.669223\pi$
$809$	194599.	−	175217.i	0.297333	−	0.267720i	0.804271	+	0.594263i	$0.202556\pi$
$810$	862566.	−	626691.i	1.31469	−	0.955176i
$811$	440428.	+	762844.i	0.669628	+	1.15983i	0.978008	+	0.208566i	$0.0668797\pi$
$811$	440428.	+	762844.i	0.669628	+	1.15983i	−0.308380	+	0.951263i	$0.599787\pi$
$812$	−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	0.00489751	−	0.999988i	$-0.498441\pi$
$821$	−390215.	−	126788.i	−0.578919	−	0.188102i	−0.583816	+	0.811886i	$0.698441\pi$
$822$	−25412.4	+	78211.5i	−0.0376100	+	0.115752i
$823$	−193041.	−	433578.i	−0.285004	−	0.640129i	0.713140	−	0.701021i	$-0.247272\pi$
$823$	−193041.	−	433578.i	−0.285004	−	0.640129i	−0.998144	+	0.0608919i	$0.980606\pi$
$824$	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	0.507627	−	0.861577i	$-0.330523\pi$
$827$	−202558.	−	182384.i	−0.296168	−	0.266671i	−0.803795	+	0.594906i	$0.797189\pi$
$828$	−996669.	−	104754.i	−1.45375	−	0.152796i
$829$	−237652.	+	327101.i	−0.345807	+	0.475962i	−0.946126	−	0.323798i	$-0.895040\pi$
$829$	−237652.	+	327101.i	−0.345807	+	0.475962i	0.600320	+	0.799760i	$0.295040\pi$
$830$	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	−0.999863	−	0.0165537i	$-0.994731\pi$
$839$	−141268.	−	434777.i	−0.200687	−	0.617651i	0.799176	−	0.601097i	$-0.205269\pi$
$840$	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	−0.576531	−	0.817075i	$-0.695594\pi$
$853$	269330.	−	828912.i	0.370157	−	1.13923i	0.946688	−	0.322152i	$-0.104406\pi$
$854$	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	0.500240	−	0.865887i	$-0.333245\pi$
$857$	140636.	+	62615.4i	0.191486	+	0.0852549i	−0.308754	+	0.951142i	$0.599912\pi$
$858$	370808.	+	333877.i	0.503703	+	0.453536i
$859$	−129280.	−	13587.9i	−0.175204	−	0.0184147i	0.0165200	−	0.999864i	$-0.494741\pi$
$859$	−129280.	−	13587.9i	−0.175204	−	0.0184147i	−0.191724	+	0.981449i	$0.561408\pi$
$860$	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	−0.698461	−	0.715648i	$-0.746132\pi$
$863$	−318704.	+	184004.i	−0.427923	+	0.247062i	0.270538	+	0.962709i	$0.412798\pi$
$864$	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	0.925510	+	0.378724i	$0.123637\pi$
$877$	−45006.8	+	428211.i	−0.0585166	+	0.556748i	−0.984026	+	0.178024i	$0.943030\pi$
$878$	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	−0.999716	−	0.0238463i	$-0.992409\pi$
$881$	−74611.7	−	351020.i	−0.0961291	−	0.452252i	0.903587	−	0.428406i	$-0.140925\pi$
$882$	745404.	−	331875.i	0.958196	−	0.426617i
$883$	775832.	+	252083.i	0.995053	+	0.323312i	0.760887	−	0.648884i	$-0.224764\pi$
$883$	775832.	+	252083.i	0.995053	+	0.323312i	0.234166	+	0.972197i	$0.424764\pi$
$884$	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	0.694130	−	0.719849i	$-0.255789\pi$
$887$	814669.	+	173163.i	1.03546	+	0.220094i	0.341331	+	0.939943i	$0.389122\pi$
$888$	−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	0.802724	−	0.596351i	$-0.203383\pi$
$907$	397847.	+	289053.i	0.483617	+	0.351368i	−0.319108	+	0.947718i	$0.603383\pi$
$908$	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	0.850877	+	0.525364i	$0.176071\pi$
$911$	−116291.	+	547105.i	−0.140123	+	0.659225i	−0.991000	+	0.133861i	$0.957262\pi$
$912$	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	0.830426	−	0.557128i	$-0.188097\pi$
$919$	820967.	+	365518.i	0.972063	+	0.432790i	0.141637	+	0.989919i	$0.454763\pi$
$920$	−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	$0.287075\pi$
$929$			1.35409e6i			1.56898i	−0.620143	+	0.784489i	$0.712925\pi$
$930$	−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	0.987662	−	0.156602i	$-0.0500541\pi$
$937$	−9637.18	−	91691.7i	−0.0109767	−	0.104436i	−0.998638	+	0.0521662i	$0.983387\pi$
$938$	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	−0.337382	−	0.941368i	$-0.609541\pi$
$941$	520613.	−	1.16932e6i	0.587943	−	1.32054i	0.925325	−	0.379174i	$-0.123792\pi$
$942$	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	0.913581	+	0.406657i	$0.133306\pi$
$947$	542104.	+	1.21759e6i	0.604481	+	1.35769i	−0.309100	+	0.951030i	$0.600028\pi$
$948$	−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	0.150179	+	0.988659i	$0.452015\pi$
$953$	−759716.	+	1.04566e6i	−0.836499	+	1.15134i	−0.986678	+	0.162684i	$0.947985\pi$
$954$	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	−0.999869	−	0.0162101i	$-0.994840\pi$
$967$	−1.41558e6	−	817283.i	−1.51384	−	0.874017i	−0.513973	−	0.857807i	$-0.671827\pi$
$968$	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	−0.968210	−	0.250137i	$-0.919524\pi$
$971$	−582900.	+	647376.i	−0.618238	+	0.686623i	0.349972	+	0.936760i	$0.386191\pi$
$972$	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	0.407045	+	0.913408i	$0.366559\pi$
$977$	−438271.	+	1.34886e6i	−0.459149	+	1.41312i	−0.866194	+	0.499708i	$0.833441\pi$
$978$	−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	0.191600	−	0.981473i	$-0.438632\pi$
$983$	169056.	+	17768.5i	0.174954	+	0.0183884i	−0.0166466	+	0.999861i	$0.505299\pi$
$984$	−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	$-0.787625\pi$
$991$		−	1.21540e6i		−	1.23757i	0.785559	−	0.618786i	$-0.212375\pi$
$992$	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	0.970882	−	0.239557i	$-0.0770021\pi$
$997$	276314.	+	478589.i	0.277979	+	0.481474i	−0.692903	+	0.721031i	$0.743669\pi$
$998$	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.11.1	✓	80
31.17	odd	30	inner	31.5.h.a.17.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.1	✓	80	1.1	even	1	trivial
31.5.h.a.17.1	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+(-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

Varieties

Fields

Representations

Groups

Database

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