LMFDB - Embedded newform 31.5.h.a.11.4

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			11.4
Character	$\chi$	$=$	31.11
Dual form			31.5.h.a.17.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.848371 - 2.61102i) q^{2} +(1.78506 - 1.60727i) q^{3} +(6.84659 - 4.97434i) q^{4} +(0.623819 + 1.08049i) q^{5} +(-5.71100 - 3.29725i) q^{6} +(-7.64750 - 72.7611i) q^{7} +(-54.3336 - 39.4757i) q^{8} +(-7.86370 + 74.8181i) q^{9} +(2.29194 - 2.54546i) q^{10} +(73.3967 - 164.852i) q^{11} +(4.22643 - 19.8838i) q^{12} +(42.9718 + 202.166i) q^{13} +(-183.493 + 81.6962i) q^{14} +(2.85018 + 0.926081i) q^{15} +(-15.1340 + 46.5776i) q^{16} +(117.402 + 263.690i) q^{17} +(202.023 - 42.9413i) q^{18} +(509.785 + 108.358i) q^{19} +(9.64573 + 4.29456i) q^{20} +(-130.598 - 117.591i) q^{21} +(-492.698 - 51.7847i) q^{22} +(-572.667 + 788.208i) q^{23} +(-160.436 + 16.8626i) q^{24} +(311.722 - 539.918i) q^{25} +(491.404 - 283.712i) q^{26} +(220.578 + 303.599i) q^{27} +(-414.298 - 460.124i) q^{28} +(-204.415 + 66.4186i) q^{29} -8.22754i q^{30} +(217.191 - 936.135i) q^{31} -940.106 q^{32} +(-133.944 - 412.238i) q^{33} +(588.898 - 530.246i) q^{34} +(73.8467 - 53.6527i) q^{35} +(318.331 + 551.366i) q^{36} +(731.028 + 422.059i) q^{37} +(-149.562 - 1422.99i) q^{38} +(401.643 + 291.811i) q^{39} +(8.75858 - 83.3323i) q^{40} +(-488.964 + 543.050i) q^{41} +(-196.237 + 440.754i) q^{42} +(-21.9668 + 103.346i) q^{43} +(-317.511 - 1493.77i) q^{44} +(-85.7455 + 38.1763i) q^{45} +(2543.86 + 826.550i) q^{46} +(-662.829 + 2039.98i) q^{47} +(47.8478 + 107.468i) q^{48} +(-2887.16 + 613.685i) q^{49} +(-1674.19 - 355.860i) q^{50} +(633.390 + 282.004i) q^{51} +(1299.85 + 1170.39i) q^{52} +(702.492 + 73.8349i) q^{53} +(605.572 - 833.498i) q^{54} +(223.906 - 23.5335i) q^{55} +(-2456.78 + 4255.26i) q^{56} +(1084.16 - 625.937i) q^{57} +(346.840 + 477.385i) q^{58} +(-412.248 - 457.848i) q^{59} +(24.1207 - 7.83728i) q^{60} -1630.50i q^{61} +(-2628.52 + 227.101i) q^{62} +5503.99 q^{63} +(1039.70 + 3199.87i) q^{64} +(-191.631 + 172.546i) q^{65} +(-962.726 + 699.461i) q^{66} +(-3260.15 - 5646.75i) q^{67} +(2115.49 + 1221.38i) q^{68} +(244.622 + 2327.43i) q^{69} +(-202.738 - 147.298i) q^{70} +(559.505 - 5323.33i) q^{71} +(3380.76 - 3754.71i) q^{72} +(748.759 - 1681.74i) q^{73} +(481.821 - 2266.79i) q^{74} +(-311.354 - 1464.80i) q^{75} +(4029.30 - 1793.96i) q^{76} +(-12556.1 - 4079.72i) q^{77} +(421.181 - 1296.26i) q^{78} +(3763.34 + 8452.60i) q^{79} +(-59.7673 + 12.7039i) q^{80} +(-5078.78 - 1079.53i) q^{81} +(1832.74 + 815.986i) q^{82} +(-1286.37 - 1158.26i) q^{83} +(-1479.09 - 155.458i) q^{84} +(-211.675 + 291.346i) q^{85} +(288.474 - 30.3198i) q^{86} +(-258.140 + 447.112i) q^{87} +(-10495.5 + 6059.60i) q^{88} +(-4343.15 - 5977.84i) q^{89} +(172.423 + 191.495i) q^{90} +(14381.2 - 4672.74i) q^{91} +8245.18i q^{92} +(-1116.93 - 2020.14i) q^{93} +5888.74 q^{94} +(200.934 + 618.411i) q^{95} +(-1678.14 + 1511.00i) q^{96} +(-2897.95 + 2105.48i) q^{97} +(4051.72 + 7017.79i) q^{98} +(11756.7 + 6787.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) $ 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.848371	−	2.61102i	−0.212093	−	0.652755i	−0.999347	−	0.0361263i	$-0.988498\pi$
$2$	−0.848371	−	2.61102i	−0.212093	−	0.652755i	0.787254	−	0.616628i	$-0.211502\pi$
$3$	1.78506	−	1.60727i	0.198339	−	0.178586i	−0.563976	−	0.825791i	$-0.690729\pi$
$3$	1.78506	−	1.60727i	0.198339	−	0.178586i	0.762316	+	0.647205i	$0.224062\pi$
$4$	6.84659	−	4.97434i	0.427912	−	0.310896i
$5$	0.623819	+	1.08049i	0.0249528	+	0.0432194i	0.878232	−	0.478235i	$-0.158723\pi$
$5$	0.623819	+	1.08049i	0.0249528	+	0.0432194i	−0.853279	+	0.521454i	$0.825390\pi$
$6$	−5.71100	−	3.29725i	−0.158639	−	0.0915903i
$7$	−7.64750	−	72.7611i	−0.156071	−	1.48492i	−0.739721	−	0.672914i	$-0.765042\pi$
$7$	−7.64750	−	72.7611i	−0.156071	−	1.48492i	0.583649	−	0.812006i	$-0.301624\pi$
$8$	−54.3336	−	39.4757i	−0.848962	−	0.616807i
$9$	−7.86370	+	74.8181i	−0.0970828	+	0.923681i
$10$	2.29194	−	2.54546i	0.0229194	−	0.0254546i
$11$	73.3967	−	164.852i	0.606584	−	1.36241i	−0.305415	−	0.952219i	$-0.598795\pi$
$11$	73.3967	−	164.852i	0.606584	−	1.36241i	0.911999	−	0.410191i	$-0.134538\pi$
$12$	4.22643	−	19.8838i	0.0293502	−	0.138082i
$13$	42.9718	+	202.166i	0.254271	+	1.19625i	0.901099	+	0.433614i	$0.142762\pi$
$13$	42.9718	+	202.166i	0.254271	+	1.19625i	−0.646828	+	0.762636i	$0.723905\pi$
$14$	−183.493	+	81.6962i	−0.936187	+	0.416817i
$15$	2.85018	+	0.926081i	0.0126675	+	0.00411592i
$16$	−15.1340	+	46.5776i	−0.0591171	+	0.181944i
$17$	117.402	+	263.690i	0.406236	+	0.912421i	0.994596	+	0.103822i	$0.0331072\pi$
$17$	117.402	+	263.690i	0.406236	+	0.912421i	−0.588360	+	0.808599i	$0.700226\pi$
$18$	202.023	−	42.9413i	0.623527	−	0.132535i
$19$	509.785	+	108.358i	1.41215	+	0.300161i	0.849959	−	0.526849i	$-0.176627\pi$
$19$	509.785	+	108.358i	1.41215	+	0.300161i	0.562188	+	0.827010i	$0.309960\pi$
$20$	9.64573	+	4.29456i	0.0241143	+	0.0107364i
$21$	−130.598	−	117.591i	−0.296141	−	0.266646i
$22$	−492.698	−	51.7847i	−1.01797	−	0.106993i
$23$	−572.667	+	788.208i	−1.08255	+	1.49000i	−0.225859	+	0.974160i	$0.572519\pi$
$23$	−572.667	+	788.208i	−1.08255	+	1.49000i	−0.856687	+	0.515837i	$0.827481\pi$
$24$	−160.436	+	16.8626i	−0.278536	+	0.0292753i
$25$	311.722	−	539.918i	0.498755	−	0.863869i
$26$	491.404	−	283.712i	0.726929	−	0.419693i
$27$	220.578	+	303.599i	0.302576	+	0.416460i
$28$	−414.298	−	460.124i	−0.528441	−	0.586893i
$29$	−204.415	+	66.4186i	−0.243062	+	0.0789758i	−0.428015	−	0.903772i	$-0.640787\pi$
$29$	−204.415	+	66.4186i	−0.243062	+	0.0789758i	0.184952	+	0.982747i	$0.440787\pi$
$30$		−	8.22754i		−	0.00914172i
$31$	217.191	−	936.135i	0.226005	−	0.974126i
$31$	217.191	−	936.135i	0.226005	−	0.974126i
$32$	−940.106			−0.918072
$33$	−133.944	−	412.238i	−0.122997	−	0.378547i
$34$	588.898	−	530.246i	0.509427	−	0.458691i
$35$	73.8467	−	53.6527i	0.0602830	−	0.0437982i
$36$	318.331	+	551.366i	0.245626	+	0.425437i
$37$	731.028	+	422.059i	0.533987	+	0.308298i	0.742639	−	0.669692i	$-0.233574\pi$
$37$	731.028	+	422.059i	0.533987	+	0.308298i	−0.208651	+	0.977990i	$0.566907\pi$
$38$	−149.562	−	1422.99i	−0.103575	−	0.985447i
$39$	401.643	+	291.811i	0.264065	+	0.191855i
$40$	8.75858	−	83.3323i	0.00547411	−	0.0520827i
$41$	−488.964	+	543.050i	−0.290877	+	0.323051i	−0.870817	−	0.491608i	$-0.836409\pi$
$41$	−488.964	+	543.050i	−0.290877	+	0.323051i	0.579940	+	0.814659i	$0.303076\pi$
$42$	−196.237	+	440.754i	−0.111245	+	0.249861i
$43$	−21.9668	+	103.346i	−0.0118804	+	0.0558928i	−0.983688	−	0.179880i	$-0.942429\pi$
$43$	−21.9668	+	103.346i	−0.0118804	+	0.0558928i	0.971808	+	0.235773i	$0.0757623\pi$
$44$	−317.511	−	1493.77i	−0.164004	−	0.771576i
$45$	−85.7455	+	38.1763i	−0.0423434	+	0.0188525i
$46$	2543.86	+	826.550i	1.20220	+	0.390619i
$47$	−662.829	+	2039.98i	−0.300058	+	0.923485i	0.681417	+	0.731896i	$0.261364\pi$
$47$	−662.829	+	2039.98i	−0.300058	+	0.923485i	−0.981475	+	0.191589i	$0.938636\pi$
$48$	47.8478	+	107.468i	0.0207673	+	0.0466441i
$49$	−2887.16	+	613.685i	−1.20248	+	0.255595i
$50$	−1674.19	−	355.860i	−0.669676	−	0.142344i
$51$	633.390	+	282.004i	0.243518	+	0.108421i
$52$	1299.85	+	1170.39i	0.480715	+	0.432838i
$53$	702.492	+	73.8349i	0.250086	+	0.0262851i	0.228742	−	0.973487i	$-0.426539\pi$
$53$	702.492	+	73.8349i	0.250086	+	0.0262851i	0.0213441	+	0.999772i	$0.493205\pi$
$54$	605.572	−	833.498i	0.207672	−	0.285836i
$55$	223.906	−	23.5335i	0.0740186	−	0.00777967i
$56$	−2456.78	+	4255.26i	−0.783411	+	1.35691i
$57$	1084.16	−	625.937i	0.333689	−	0.192655i
$58$	346.840	+	477.385i	0.103104	+	0.141910i
$59$	−412.248	−	457.848i	−0.118428	−	0.131528i	0.681015	−	0.732269i	$-0.261539\pi$
$59$	−412.248	−	457.848i	−0.118428	−	0.131528i	−0.799443	+	0.600742i	$0.794872\pi$
$60$	24.1207	−	7.83728i	0.00670019	−	0.00217702i
$61$		−	1630.50i		−	0.438189i	−0.975704	−	0.219094i	$-0.929690\pi$
$61$		−	1630.50i		−	0.438189i	0.975704	−	0.219094i	$-0.0703103\pi$
$62$	−2628.52	+	227.101i	−0.683799	+	0.0590794i
$63$	5503.99			1.38674
$64$	1039.70	+	3199.87i	0.253834	+	0.781219i
$65$	−191.631	+	172.546i	−0.0453565	+	0.0408392i
$66$	−962.726	+	699.461i	−0.221011	+	0.160574i
$67$	−3260.15	−	5646.75i	−0.726254	−	1.25791i	−0.958456	−	0.285241i	$-0.907926\pi$
$67$	−3260.15	−	5646.75i	−0.726254	−	1.25791i	0.232202	−	0.972668i	$-0.425407\pi$
$68$	2115.49	+	1221.38i	0.457502	+	0.264139i
$69$	244.622	+	2327.43i	0.0513804	+	0.488852i
$70$	−202.738	−	147.298i	−0.0413750	−	0.0300607i
$71$	559.505	−	5323.33i	0.110991	−	1.05601i	−0.787289	−	0.616584i	$-0.788516\pi$
$71$	559.505	−	5323.33i	0.110991	−	1.05601i	0.898280	−	0.439423i	$-0.144817\pi$
$72$	3380.76	−	3754.71i	0.652152	−	0.724289i
$73$	748.759	−	1681.74i	0.140507	−	0.315583i	−0.829562	−	0.558415i	$-0.811410\pi$
$73$	748.759	−	1681.74i	0.140507	−	0.315583i	0.970068	+	0.242832i	$0.0780764\pi$
$74$	481.821	−	2266.79i	0.0879878	−	0.413950i
$75$	−311.354	−	1464.80i	−0.0553518	−	0.260410i
$76$	4029.30	−	1793.96i	0.697593	−	0.310588i
$77$	−12556.1	−	4079.72i	−2.11774	−	0.688096i
$78$	421.181	−	1296.26i	0.0692276	−	0.213061i
$79$	3763.34	+	8452.60i	0.603002	+	1.35437i	0.914680	+	0.404178i	$0.132442\pi$
$79$	3763.34	+	8452.60i	0.603002	+	1.35437i	−0.311678	+	0.950188i	$0.600891\pi$
$80$	−59.7673	+	12.7039i	−0.00933864	+	0.00198499i
$81$	−5078.78	−	1079.53i	−0.774086	−	0.164537i
$82$	1832.74	+	815.986i	0.272566	+	0.121354i
$83$	−1286.37	−	1158.26i	−0.186729	−	0.168131i	0.570465	−	0.821322i	$-0.306763\pi$
$83$	−1286.37	−	1158.26i	−0.186729	−	0.168131i	−0.757193	+	0.653191i	$0.773430\pi$
$84$	−1479.09	−	155.458i	−0.209621	−	0.0220321i
$85$	−211.675	+	291.346i	−0.0292976	+	0.0403247i
$86$	288.474	−	30.3198i	0.0390041	−	0.00409949i
$87$	−258.140	+	447.112i	−0.0341049	+	0.0590715i
$88$	−10495.5	+	6059.60i	−1.35531	+	0.782490i
$89$	−4343.15	−	5977.84i	−0.548309	−	0.754682i	0.441473	−	0.897275i	$-0.354456\pi$
$89$	−4343.15	−	5977.84i	−0.548309	−	0.754682i	−0.989781	+	0.142592i	$0.954456\pi$
$90$	172.423	+	191.495i	0.0212868	+	0.0236414i
$91$	14381.2	−	4672.74i	1.73665	−	0.564272i
$92$			8245.18i			0.974146i
$93$	−1116.93	−	2020.14i	−0.129139	−	0.233569i
$94$	5888.74			0.666449
$95$	200.934	+	618.411i	0.0222642	+	0.0685220i
$96$	−1678.14	+	1511.00i	−0.182090	+	0.163954i
$97$	−2897.95	+	2105.48i	−0.307998	+	0.223773i	−0.731037	−	0.682338i	$-0.760963\pi$
$97$	−2897.95	+	2105.48i	−0.307998	+	0.223773i	0.423039	+	0.906111i	$0.360963\pi$
$98$	4051.72	+	7017.79i	0.421879	+	0.730716i
$99$	11756.7	+	6787.75i	1.19954	+	0.692557i
$100$	−551.503	−	5247.20i	−0.0551503	−	0.524720i
$101$	5182.29	+	3765.15i	0.508017	+	0.369096i	0.812071	−	0.583559i	$-0.198340\pi$
$101$	5182.29	+	3765.15i	0.508017	+	0.369096i	−0.304054	+	0.952655i	$0.598340\pi$
$102$	198.966	−	1893.04i	0.0191240	−	0.181953i
$103$	−10256.4	+	11390.9i	−0.966767	+	1.07370i	0.0304787	+	0.999535i	$0.490297\pi$
$103$	−10256.4	+	11390.9i	−0.966767	+	1.07370i	−0.997246	+	0.0741681i	$0.976370\pi$
$104$	5645.84	−	12680.8i	0.521989	−	1.17241i
$105$	45.5859	−	214.465i	0.00413477	−	0.0194526i
$106$	−403.190	−	1896.86i	−0.0358837	−	0.168820i
$107$	−10569.8	+	4705.96i	−0.923204	+	0.411037i	−0.812596	−	0.582827i	$-0.801946\pi$
$107$	−10569.8	+	4705.96i	−0.923204	+	0.411037i	−0.110608	+	0.993864i	$0.535280\pi$
$108$	3020.41	+	981.391i	0.258952	+	0.0841385i
$109$	−4441.23	+	13668.7i	−0.373809	+	1.15047i	0.570469	+	0.821319i	$0.306761\pi$
$109$	−4441.23	+	13668.7i	−0.373809	+	1.15047i	−0.944279	+	0.329147i	$0.893239\pi$
$110$	−251.402	−	564.658i	−0.0207770	−	0.0466660i
$111$	1983.29	−	421.561i	0.160968	−	0.0342149i
$112$	3504.77	+	744.963i	0.279398	+	0.0593880i
$113$	14234.6	+	6337.63i	1.11477	+	0.496330i	0.879643	−	0.475634i	$-0.157781\pi$
$113$	14234.6	+	6337.63i	1.11477	+	0.496330i	0.235131	+	0.971964i	$0.424448\pi$
$114$	−2554.10	−	2299.72i	−0.196530	−	0.176956i
$115$	−1208.89	−	127.059i	−0.0914093	−	0.00960751i
$116$	−1069.16	+	1471.57i	−0.0794560	+	0.109362i
$117$	−15463.6	+	1625.29i	−1.12964	+	0.118730i
$118$	−845.710	+	1464.81i	−0.0607375	+	0.105201i
$119$	18288.5	−	10558.9i	1.29147	−	0.745631i
$120$	−118.303	−	162.830i	−0.00821549	−	0.0113077i
$121$	−11992.3	−	13318.8i	−0.819088	−	0.909689i
$122$	−4257.27	+	1383.27i	−0.286030	+	0.0929367i
$123$			1755.27i			0.116020i
$124$	−3169.64	−	7489.71i	−0.206142	−	0.487104i
$125$	1557.60			0.0996867
$126$	−4669.42	−	14371.0i	−0.294118	−	0.905203i
$127$	−7880.54	+	7095.67i	−0.488595	+	0.439933i	−0.876239	−	0.481876i	$-0.839955\pi$
$127$	−7880.54	+	7095.67i	−0.488595	+	0.439933i	0.387645	+	0.921809i	$0.373289\pi$
$128$	−4696.11	+	3411.92i	−0.286628	+	0.208247i
$129$	126.893	+	219.785i	0.00762531	+	0.0132074i
$130$	613.094	+	353.970i	0.0362778	+	0.0209450i
$131$	−567.862	−	5402.85i	−0.0330903	−	0.314833i	−0.998530	−	0.0542057i	$-0.982737\pi$
$131$	−567.862	−	5402.85i	−0.0330903	−	0.314833i	0.965440	−	0.260627i	$-0.0839293\pi$
$132$	−2967.67	−	2156.14i	−0.170321	−	0.123745i
$133$	3985.68	−	37921.2i	0.225319	−	2.14377i
$134$	−11978.0	+	13302.9i	−0.667072	+	0.740859i
$135$	−190.434	+	427.722i	−0.0104491	+	0.0234690i
$136$	4030.44	−	18961.7i	0.217909	−	1.02518i
$137$	−908.746	−	4275.31i	−0.0484174	−	0.227786i	0.947286	−	0.320390i	$-0.103814\pi$
$137$	−908.746	−	4275.31i	−0.0484174	−	0.227786i	−0.995703	+	0.0926046i	$0.970481\pi$
$138$	5869.42	−	2613.23i	0.308203	−	0.137221i
$139$	31524.3	+	10242.9i	1.63161	+	0.530142i	0.974641	−	0.223775i	$-0.0718381\pi$
$139$	31524.3	+	10242.9i	1.63161	+	0.530142i	0.656969	+	0.753917i	$0.271838\pi$
$140$	238.711	−	734.677i	0.0121791	−	0.0374835i
$141$	2095.61	+	4706.82i	0.105408	+	0.236750i
$142$	−14374.0	+	3055.28i	−0.712854	+	0.151522i
$143$	36481.5	+	7754.37i	1.78402	+	0.379205i
$144$	−3365.84	−	1498.57i	−0.162319	−	0.0722689i
$145$	−199.283	−	179.435i	−0.00947836	−	0.00853436i
$146$	−5026.28	−	528.284i	−0.235799	−	0.0247834i
$147$	−4167.38	+	5735.91i	−0.192854	+	0.265441i
$148$	7104.52	−	746.715i	0.324348	−	0.0340903i
$149$	−13616.4	+	23584.4i	−0.613326	+	1.06231i	0.377350	+	0.926071i	$0.376835\pi$
$149$	−13616.4	+	23584.4i	−0.613326	+	1.06231i	−0.990676	+	0.136241i	$0.956498\pi$
$150$	−3560.49	+	2055.65i	−0.158244	+	0.0913621i
$151$	−4511.82	−	6209.98i	−0.197878	−	0.272356i	0.698535	−	0.715576i	$-0.253836\pi$
$151$	−4511.82	−	6209.98i	−0.197878	−	0.272356i	−0.896413	+	0.443221i	$0.853836\pi$
$152$	−23420.9	−	26011.6i	−1.01372	−	1.12585i
$153$	−20652.0	+	6710.24i	−0.882225	+	0.286652i
$154$			36245.3i			1.52831i
$155$	1146.97	−	349.307i	0.0477406	−	0.0145393i
$156$	4201.45			0.172643
$157$	−4756.08	−	14637.7i	−0.192952	−	0.593846i	−0.999994	−	0.00335198i	$-0.998933\pi$
$157$	−4756.08	−	14637.7i	−0.192952	−	0.593846i	0.807042	−	0.590494i	$-0.201067\pi$
$158$	18877.2	−	16997.1i	0.756176	−	0.680864i
$159$	1372.66	−	997.295i	0.0542961	−	0.0394484i
$160$	−586.456	−	1015.77i	−0.0229084	−	0.0396785i
$161$	61730.4	+	35640.0i	2.38148	+	1.37495i
$162$	1490.02	+	14176.6i	0.0567758	+	0.540185i
$163$	−8497.30	−	6173.65i	−0.319820	−	0.232363i	0.416279	−	0.909237i	$-0.363334\pi$
$163$	−8497.30	−	6173.65i	−0.319820	−	0.232363i	−0.736099	+	0.676874i	$0.763334\pi$
$164$	−646.424	+	6150.31i	−0.0240342	+	0.228670i
$165$	361.860	−	401.886i	0.0132915	−	0.0147617i
$166$	−1932.90	+	4341.37i	−0.0701446	+	0.157547i
$167$	5486.72	−	25813.0i	0.196734	−	0.925562i	−0.763379	−	0.645951i	$-0.776461\pi$
$167$	5486.72	−	25813.0i	0.196734	−	0.925562i	0.960113	−	0.279611i	$-0.0902055\pi$
$168$	2453.88	+	11544.6i	0.0869429	+	0.409034i
$169$	−12932.9	+	5758.09i	−0.452816	+	0.201607i
$170$	940.289	+	305.519i	0.0325360	+	0.0105716i
$171$	−12116.0	+	37289.1i	−0.414348	+	1.27523i
$172$	363.679	+	816.837i	0.0122931	+	0.0276108i
$173$	−6828.04	+	1451.35i	−0.228141	+	0.0484930i	−0.320564	−	0.947227i	$-0.603872\pi$
$173$	−6828.04	+	1451.35i	−0.228141	+	0.0484930i	0.0924223	+	0.995720i	$0.470539\pi$
$174$	1386.42	+	294.692i	0.0457926	+	0.00973351i
$175$	−41668.9	−	18552.2i	−1.36062	−	0.605786i
$176$	6567.61	+	5913.51i	0.212023	+	0.190906i
$177$	−1471.77	−	154.689i	−0.0469779	−	0.00493758i
$178$	−11923.6	+	16411.5i	−0.376330	+	0.517974i
$179$	4746.95	−	498.924i	0.148152	−	0.0155714i	−0.0301620	−	0.999545i	$-0.509602\pi$
$179$	4746.95	−	498.924i	0.148152	−	0.0155714i	0.178314	+	0.983974i	$0.442936\pi$
$180$	−397.162	+	687.905i	−0.0122581	+	0.0212316i
$181$	−47127.7	+	27209.2i	−1.43853	+	0.830535i	−0.997748	−	0.0670790i	$-0.978632\pi$
$181$	−47127.7	+	27209.2i	−1.43853	+	0.830535i	−0.440782	+	0.897614i	$0.645299\pi$
$182$	−24401.2	−	33585.4i	−0.736663	−	1.01393i
$183$	−2620.66	−	2910.53i	−0.0782543	−	0.0869102i
$184$	62230.1	−	20219.8i	1.83808	−	0.597229i
$185$			1053.15i			0.0307715i
$186$	−4327.05	+	4630.14i	−0.125074	+	0.133835i
$187$	52086.6			1.48951
$188$	5609.42	+	17264.0i	0.158709	+	0.488457i
$189$	20403.4	−	18371.3i	0.571187	−	0.514299i
$190$	1444.22	−	1049.28i	0.0400060	−	0.0290661i
$191$	−7870.90	−	13632.8i	−0.215753	−	0.373696i	0.737752	−	0.675072i	$-0.235887\pi$
$191$	−7870.90	−	13632.8i	−0.215753	−	0.373696i	−0.953505	+	0.301376i	$0.902554\pi$
$192$	6998.99	+	4040.87i	0.189860	+	0.109616i
$193$	1896.04	+	18039.6i	0.0509018	+	0.484298i	0.990043	+	0.140766i	$0.0449566\pi$
$193$	1896.04	+	18039.6i	0.0509018	+	0.484298i	−0.939141	+	0.343532i	$0.888377\pi$
$194$	7955.99	+	5780.37i	0.211393	+	0.153586i
$195$	−64.7449	+	616.007i	−0.00170269	+	0.0162000i
$196$	−16714.5	+	18563.3i	−0.435093	+	0.483219i
$197$	10434.3	−	23435.8i	0.268863	−	0.603876i	−0.727774	−	0.685817i	$-0.759445\pi$
$197$	10434.3	−	23435.8i	0.268863	−	0.603876i	0.996637	+	0.0819407i	$0.0261118\pi$
$198$	7748.87	−	36455.6i	0.197655	−	0.929894i
$199$	−6343.62	−	29844.4i	−0.160188	−	0.753627i	−0.982748	−	0.184949i	$-0.940788\pi$
$199$	−6343.62	−	29844.4i	−0.160188	−	0.753627i	0.822560	−	0.568679i	$-0.192545\pi$
$200$	−38250.6	+	17030.2i	−0.956264	+	0.425756i
$201$	−14895.4	−	4839.81i	−0.368689	−	0.119794i
$202$	5434.38	−	16725.3i	0.133182	−	0.409893i
$203$	6395.96	+	14365.6i	0.155208	+	0.348602i
$204$	5739.34	−	1219.94i	0.137912	−	0.0293141i
$205$	−891.782	−	189.554i	−0.0212203	−	0.00451051i
$206$	38443.2	+	17116.0i	0.905909	+	0.403337i
$207$	−54469.0	−	49044.1i	−1.27118	−	1.14458i
$208$	−10066.8	−	1058.06i	−0.232682	−	0.0244559i
$209$	55279.6	−	76085.8i	1.26553	−	1.74185i
$210$	−598.645	+	62.9201i	−0.0135747	+	0.00142676i
$211$	−8521.69	+	14760.0i	−0.191408	+	0.331529i	−0.945717	−	0.324991i	$-0.894639\pi$
$211$	−8521.69	+	14760.0i	−0.191408	+	0.331529i	0.754309	+	0.656520i	$0.227972\pi$
$212$	5176.95	−	2988.92i	0.115187	−	0.0665031i
$213$	−7557.29	−	10401.7i	−0.166574	−	0.229269i
$214$	21254.4	+	23605.4i	0.464111	+	0.515447i
$215$	−125.367	+	40.7342i	−0.00271211	+	0.000881217i
$216$		−	25203.1i		−	0.540190i
$217$	−69775.2	−	8643.94i	−1.48177	−	0.183566i
$218$	39457.0			0.830254
$219$	−1366.44	−	4205.46i	−0.0284906	−	0.0876850i
$220$	1415.93	−	1274.91i	0.0292548	−	0.0263411i
$221$	−48264.2	+	35066.0i	−0.988190	+	0.717962i
$222$	−2783.27	−	4820.77i	−0.0564741	−	0.0978160i
$223$	−4274.31	−	2467.77i	−0.0859520	−	0.0496244i	0.456408	−	0.889771i	$-0.349136\pi$
$223$	−4274.31	−	2467.77i	−0.0859520	−	0.0496244i	−0.542360	+	0.840146i	$0.682469\pi$
$224$	7189.46	+	68403.1i	0.143285	+	1.36326i
$225$	37944.4	+	27568.2i	0.749518	+	0.544557i
$226$	4471.49	−	42543.3i	0.0875457	−	0.832942i
$227$	−30873.2	+	34288.1i	−0.599142	+	0.665414i	−0.964078	−	0.265618i	$-0.914424\pi$
$227$	−30873.2	+	34288.1i	−0.599142	+	0.665414i	0.364936	+	0.931032i	$0.381091\pi$
$228$	4309.14	−	9678.49i	0.0828936	−	0.186182i
$229$	2011.88	−	9465.15i	0.0383646	−	0.180491i	−0.954793	−	0.297271i	$-0.903924\pi$
$229$	2011.88	−	9465.15i	0.0383646	−	0.180491i	0.993158	+	0.116779i	$0.0372570\pi$
$230$	693.832	+	3264.22i	0.0131159	+	0.0617055i
$231$	−28970.5	+	12898.5i	−0.542916	+	0.241722i
$232$	13728.5	+	4460.67i	0.255064	+	0.0828752i
$233$	19145.0	−	58922.3i	0.352650	−	1.08535i	−0.604709	−	0.796446i	$-0.706711\pi$
$233$	19145.0	−	58922.3i	0.352650	−	1.08535i	0.957359	−	0.288900i	$-0.0932894\pi$
$234$	17362.6	+	38997.0i	0.317090	+	0.712195i
$235$	−2617.65	+	556.399i	−0.0473998	+	0.0100751i
$236$	−5099.98	−	1084.03i	−0.0915682	−	0.0194634i
$237$	20303.4	+	9039.64i	0.361469	+	0.160937i
$238$	−43084.9	−	38793.8i	−0.760626	−	0.684871i
$239$	−41853.7	−	4399.01i	−0.732721	−	0.0770121i	−0.269183	−	0.963089i	$-0.586754\pi$
$239$	−41853.7	−	4399.01i	−0.732721	−	0.0770121i	−0.463538	+	0.886077i	$0.653420\pi$
$240$	−86.2693	+	118.739i	−0.00149773	+	0.00206145i
$241$	51995.8	−	5464.98i	0.895229	−	0.0940924i	0.354272	−	0.935142i	$-0.384729\pi$
$241$	51995.8	−	5464.98i	0.895229	−	0.0940924i	0.540957	+	0.841050i	$0.318062\pi$
$242$	−24601.6	+	42611.3i	−0.420081	+	0.727602i
$243$	−37125.4	+	21434.4i	−0.628722	+	0.362993i
$244$	−8110.66	−	11163.4i	−0.136231	−	0.187506i
$245$	−2464.14	−	2736.71i	−0.0410519	−	0.0455928i
$246$	4583.04	−	1489.12i	0.0757328	−	0.0246071i
$247$			107718.i			1.76560i
$248$	−48755.3	+	42289.8i	−0.792718	+	0.687595i
$249$	−4157.88			−0.0670614
$250$	−1321.43	−	4066.93i	−0.0211428	−	0.0650710i
$251$	58115.8	−	52327.7i	0.922458	−	0.830585i	−0.0634312	−	0.997986i	$-0.520204\pi$
$251$	58115.8	−	52327.7i	0.922458	−	0.830585i	0.985889	+	0.167402i	$0.0535377\pi$
$252$	37683.5	−	27378.7i	0.593404	−	0.431133i
$253$	87905.6	+	152257.i	1.37333	+	2.37868i
$254$	25212.6	+	14556.5i	0.390795	+	0.225626i
$255$	90.4200	+	860.288i	0.00139054	+	0.0132301i
$256$	56444.2	+	41009.1i	0.861271	+	0.625750i
$257$	8311.98	−	79083.2i	0.125846	−	1.19734i	−0.731223	−	0.682139i	$-0.761050\pi$
$257$	8311.98	−	79083.2i	0.125846	−	1.19734i	0.857069	−	0.515202i	$-0.172283\pi$
$258$	466.210	−	517.778i	0.00700393	−	0.00777866i
$259$	25119.0	−	56418.1i	0.374457	−	0.841045i
$260$	−453.720	+	2134.59i	−0.00671184	+	0.0315767i
$261$	−3361.85	−	15816.3i	−0.0493512	−	0.232179i
$262$	−13625.2	+	6066.32i	−0.198490	+	0.0883736i
$263$	61819.8	+	20086.5i	0.893750	+	0.290397i	0.719655	−	0.694332i	$-0.244300\pi$
$263$	61819.8	+	20086.5i	0.893750	+	0.290397i	0.174095	+	0.984729i	$0.444300\pi$
$264$	−8995.69	+	27685.9i	−0.129070	+	0.397238i
$265$	358.450	+	805.092i	0.00510431	+	0.0114645i
$266$	−102394.	+	21764.6i	−1.44715	+	0.307600i
$267$	−17360.8	−	3690.15i	−0.243527	−	0.0517632i
$268$	−50409.8	−	22443.9i	−0.701852	−	0.312484i
$269$	15827.9	+	14251.5i	0.218736	+	0.196950i	0.771213	−	0.636578i	$-0.219651\pi$
$269$	15827.9	+	14251.5i	0.218736	+	0.196950i	−0.552477	+	0.833528i	$0.686317\pi$
$270$	1278.35	+	134.360i	0.0175357	+	0.00184307i
$271$	−21322.2	+	29347.5i	−0.290331	+	0.399607i	−0.929122	−	0.369774i	$-0.879435\pi$
$271$	−21322.2	+	29347.5i	−0.290331	+	0.399607i	0.638790	+	0.769381i	$0.279435\pi$
$272$	−14058.8	+	1477.64i	−0.190025	+	0.0199724i
$273$	18160.9	−	31455.6i	0.243676	−	0.422059i
$274$	−10392.0	+	5999.80i	−0.138419	+	0.0799164i
$275$	−66127.0	−	91016.0i	−0.874407	−	1.20352i
$276$	13252.2	+	14718.1i	0.173969	+	0.193212i
$277$	−30169.4	+	9802.65i	−0.393195	+	0.127757i	−0.498940	−	0.866637i	$-0.666277\pi$
$277$	−30169.4	+	9802.65i	−0.393195	+	0.127757i	0.105745	+	0.994393i	$0.466277\pi$
$278$		−	91000.4i		−	1.17748i
$279$	68332.0	+	23611.3i	0.877840	+	0.303327i
$280$	−6130.33			−0.0781930
$281$	16039.9	+	49365.7i	0.203137	+	0.625190i	0.999785	+	0.0207470i	$0.00660444\pi$
$281$	16039.9	+	49365.7i	0.203137	+	0.625190i	−0.796648	+	0.604443i	$0.793396\pi$
$282$	10511.7	−	9464.81i	0.132183	−	0.119018i
$283$	4813.35	−	3497.11i	0.0601001	−	0.0436652i	−0.557330	−	0.830291i	$-0.688174\pi$
$283$	4813.35	−	3497.11i	0.0601001	−	0.0436652i	0.617430	+	0.786626i	$0.288174\pi$
$284$	−22649.4	−	39229.8i	−0.280814	−	0.486384i
$285$	1352.63	+	780.943i	0.0166529	+	0.00961456i
$286$	−10703.0	−	101832.i	−0.130850	−	1.24495i
$287$	43252.2	+	31424.6i	0.525103	+	0.381510i
$288$	7392.71	−	70337.0i	0.0891290	−	0.848005i
$289$	137.449	−	152.652i	0.00164568	−	0.00182771i
$290$	−299.442	+	672.558i	−0.00356055	+	0.00799712i
$291$	−1788.92	+	8416.19i	−0.0211254	+	0.0993870i
$292$	−3239.10	−	15238.8i	−0.0379891	−	0.178725i
$293$	−71396.2	+	31787.6i	−0.831649	+	0.370274i	−0.777983	−	0.628285i	$-0.783757\pi$
$293$	−71396.2	+	31787.6i	−0.831649	+	0.370274i	−0.0536655	+	0.998559i	$0.517090\pi$
$294$	18512.0	+	6014.93i	0.214171	+	0.0695882i
$295$	237.530	−	731.042i	0.00272945	−	0.00840037i
$296$	−23058.3	−	51789.8i	−0.263175	−	0.591100i
$297$	66238.6	−	14079.4i	0.750928	−	0.159615i
$298$	73131.0	+	15544.5i	0.823511	+	0.175043i
$299$	−183958.	−	81903.2i	−2.05767	−	0.916133i
$300$	−9418.14	−	8480.13i	−0.104646	−	0.0942237i
$301$	7687.55	+	807.994i	0.0848506	+	0.00891816i
$302$	−12386.7	+	17048.8i	−0.135813	+	0.186930i
$303$	15302.3	−	1608.33i	0.166675	−	0.0175183i
$304$	−12762.1	+	22104.7i	−0.138094	+	0.239187i
$305$	1761.73	−	1017.14i	0.0189383	−	0.0109340i
$306$	35041.1	+	48230.0i	0.374227	+	0.515079i
$307$	−81629.0	−	90658.2i	−0.866100	−	0.961901i	0.133475	−	0.991052i	$-0.457386\pi$
$307$	−81629.0	−	90658.2i	−0.866100	−	0.961901i	−0.999575	+	0.0291512i	$0.990720\pi$
$308$	−106260.	+	34526.1i	−1.12013	+	0.363953i
$309$			36818.3i			0.385608i
$310$	−1885.10	−	2698.41i	−0.0196161	−	0.0280792i
$311$	14259.9			0.147433			0.0737165	−	0.997279i	$-0.476514\pi$
$311$	14259.9			0.147433			0.0737165	+	0.997279i	$0.476514\pi$
$312$	−10303.3	−	31710.2i	−0.105844	−	0.325754i
$313$	124052.	−	111697.i	1.26624	−	1.14012i	0.282740	−	0.959196i	$-0.408757\pi$
$313$	124052.	−	111697.i	1.26624	−	1.14012i	0.983496	−	0.180928i	$-0.0579101\pi$
$314$	−34184.4	+	24836.4i	−0.346712	+	0.251901i
$315$	3433.49	+	5946.98i	0.0346031	+	0.0599343i
$316$	67812.1	+	39151.3i	0.679099	+	0.392078i
$317$	6737.78	+	64105.7i	0.0670499	+	0.637937i	0.975508	+	0.219962i	$0.0705934\pi$
$317$	6737.78	+	64105.7i	0.0670499	+	0.637937i	−0.908459	+	0.417975i	$0.862740\pi$
$318$	−3768.48	−	2737.96i	−0.0372659	−	0.0270753i
$319$	−4054.20	+	38573.2i	−0.0398404	+	0.379056i
$320$	−2808.83	+	3119.53i	−0.0274300	+	0.0304641i
$321$	−11303.8	+	25388.9i	−0.109702	+	0.246396i
$322$	40686.5	−	191415.i	0.392409	−	1.84614i
$323$	31277.0	+	147147.i	0.299792	+	1.41041i
$324$	−40142.3	+	17872.5i	−0.382395	+	0.170253i
$325$	122548.	+	39818.4i	1.16022	+	0.376979i
$326$	−8910.65	+	27424.2i	−0.0838444	+	0.258047i
$327$	14041.5	+	31537.6i	0.131316	+	0.294940i
$328$	48004.4	−	10203.6i	0.446204	−	0.0948436i
$329$	153500.	+	32627.4i	1.41813	+	0.301433i
$330$	−1356.32	−	603.875i	−0.0124548	−	0.00554522i
$331$	−48902.8	−	44032.3i	−0.446352	−	0.401897i	0.415068	−	0.909790i	$-0.363758\pi$
$331$	−48902.8	−	44032.3i	−0.446352	−	0.401897i	−0.861420	+	0.507893i	$0.830424\pi$
$332$	−14568.8	−	1531.24i	−0.132175	−	0.0138921i
$333$	−37326.3	+	51375.2i	−0.336610	+	0.463303i
$334$	−72053.0	+	7573.07i	−0.645890	+	0.0678858i
$335$	4067.49	−	7045.10i	0.0362441	−	0.0627766i
$336$	7453.57	−	4303.32i	0.0660216	−	0.0381176i
$337$	66291.0	+	91241.7i	0.583707	+	0.803403i	0.994096	−	0.108507i	$-0.0346071\pi$
$337$	66291.0	+	91241.7i	0.583707	+	0.803403i	−0.410389	+	0.911911i	$0.634607\pi$
$338$	26006.4	+	28883.0i	0.227639	+	0.252818i
$339$	35595.8	−	11565.8i	0.309741	−	0.100641i
$340$			3047.67i			0.0263639i
$341$	−138382.	−	104514.i	−1.19007	−	0.898801i
$342$	107641.			0.920294
$343$	12449.5	+	38315.5i	0.105819	+	0.325676i
$344$	5273.18	−	4748.00i	0.0445611	−	0.0401230i
$345$	−2362.15	+	1716.20i	−0.0198458	+	0.0144188i
$346$	9582.21	+	16596.9i	0.0800412	+	0.138635i
$347$	−35940.4	−	20750.2i	−0.298486	−	0.172331i	0.343277	−	0.939234i	$-0.388463\pi$
$347$	−35940.4	−	20750.2i	−0.298486	−	0.172331i	−0.641763	+	0.766903i	$0.721797\pi$
$348$	456.706	+	4345.27i	0.00377119	+	0.0358805i
$349$	−160460.	−	116581.i	−1.31739	−	0.957141i	−0.999961	−	0.00885957i	$-0.997180\pi$
$349$	−160460.	−	116581.i	−1.31739	−	0.957141i	−0.317431	−	0.948281i	$-0.602820\pi$
$350$	−13089.4	+	124537.i	−0.106852	+	1.01663i
$351$	−51899.0	+	57639.6i	−0.421254	+	0.467850i
$352$	−69000.7	+	154978.i	−0.556888	+	1.25079i
$353$	−34266.5	+	161211.i	−0.274992	+	1.29374i	0.596216	+	0.802824i	$0.296670\pi$
$353$	−34266.5	+	161211.i	−0.274992	+	1.29374i	−0.871209	+	0.490913i	$0.836663\pi$
$354$	844.711	+	3974.05i	0.00674065	+	0.0317123i
$355$	6100.81	−	2716.26i	0.0484095	−	0.0215533i
$356$	−59471.6	−	19323.5i	−0.469256	−	0.152470i
$357$	15675.0	−	48242.8i	0.122991	−	0.378526i
$358$	−5329.87	−	11971.1i	−0.0415864	−	0.0934045i
$359$	6294.06	−	1337.84i	0.0488362	−	0.0103805i	−0.183429	−	0.983033i	$-0.558720\pi$
$359$	6294.06	−	1337.84i	0.0488362	−	0.0103805i	0.232265	+	0.972653i	$0.425386\pi$
$360$	6165.89	+	1310.60i	0.0475763	+	0.0101127i
$361$	129085.	+	57472.4i	0.990516	+	0.441006i
$362$	111025.	+	99967.7i	0.847237	+	0.762856i
$363$	−42813.7	−	4499.90i	−0.324915	−	0.0341499i
$364$	75218.5	−	103529.i	0.567704	−	0.781377i
$365$	2284.19	−	240.078i	0.0171453	−	0.00180205i
$366$	−5376.17	+	9311.80i	−0.0401338	+	0.0695138i
$367$	−31683.5	+	18292.5i	−0.235235	+	0.135813i	−0.612985	−	0.790095i	$-0.710031\pi$
$367$	−31683.5	+	18292.5i	−0.235235	+	0.135813i	0.377750	+	0.925908i	$0.376698\pi$
$368$	−28046.1	−	38602.2i	−0.207099	−	0.285047i
$369$	−36784.9	−	40853.8i	−0.270157	−	0.300040i
$370$	2749.81	−	893.466i	0.0200862	−	0.00652641i
$371$		−	51678.7i		−	0.375460i
$372$	−17696.0	−	8275.08i	−0.127876	−	0.0597980i
$373$	−89978.5			−0.646727			−0.323364	−	0.946275i	$-0.604814\pi$
$373$	−89978.5			−0.646727			−0.323364	+	0.946275i	$0.604814\pi$
$374$	−44188.8	−	135999.i	−0.315914	−	0.972284i
$375$	2780.41	−	2503.49i	0.0197718	−	0.0178026i
$376$	116543.	−	84673.7i	0.824350	−	0.598925i
$377$	−22211.7	−	38471.8i	−0.156278	−	0.270682i
$378$	−65277.3	−	37687.9i	−0.456855	−	0.263766i
$379$	18610.2	+	177064.i	0.129560	+	1.23268i	0.845291	+	0.534307i	$0.179427\pi$
$379$	18610.2	+	177064.i	0.129560	+	1.23268i	−0.715730	+	0.698377i	$0.753906\pi$
$380$	4451.90	+	3234.49i	0.0308303	+	0.0223995i
$381$	−2662.54	+	25332.3i	−0.0183419	+	0.174512i
$382$	−28918.0	+	32116.7i	−0.198172	+	0.220092i
$383$	93608.7	−	210249.i	0.638144	−	1.43330i	−0.247480	−	0.968893i	$-0.579602\pi$
$383$	93608.7	−	210249.i	0.638144	−	1.43330i	0.885624	−	0.464403i	$-0.153731\pi$
$384$	−2898.93	+	13638.4i	−0.0196596	+	0.0924912i
$385$	−3424.64	−	16111.7i	−0.0231044	−	0.108697i
$386$	45493.2	−	20254.9i	0.305332	−	0.135942i
$387$	−7559.41	−	2456.20i	−0.0504738	−	0.0163999i
$388$	−9367.68	+	28830.8i	−0.0622256	+	0.191511i
$389$	−58580.9	−	131575.i	−0.387130	−	0.869508i	−0.997029	−	0.0770289i	$-0.975457\pi$
$389$	−58580.9	−	131575.i	−0.387130	−	0.869508i	0.609899	−	0.792479i	$-0.291210\pi$
$390$	1663.33	−	353.552i	0.0109358	−	0.00232447i
$391$	−275075.	−	58469.0i	−1.79927	−	0.382447i
$392$	181095.	+	80628.8i	1.17851	+	0.524708i
$393$	−9697.51	−	8731.67i	−0.0627878	−	0.0565343i
$394$	−70043.5	−	7361.87i	−0.451207	−	0.0474237i
$395$	−6785.27	+	9339.12i	−0.0434883	+	0.0598566i
$396$	114258.	−	12009.0i	0.728612	−	0.0765802i
$397$	90151.9	−	156148.i	0.571997	−	0.990728i	−0.424363	−	0.905492i	$-0.639502\pi$
$397$	90151.9	−	156148.i	0.571997	−	0.990728i	0.996361	−	0.0852365i	$-0.0271646\pi$
$398$	−72542.5	+	41882.4i	−0.457959	+	0.264403i
$399$	−53834.9	−	74097.4i	−0.338157	−	0.465433i
$400$	20430.5	+	22690.4i	0.127691	+	0.141815i
$401$	148318.	−	48191.5i	0.922372	−	0.299697i	0.190932	−	0.981603i	$-0.438849\pi$
$401$	148318.	−	48191.5i	0.922372	−	0.299697i	0.731439	+	0.681906i	$0.238849\pi$
$402$			42998.2i			0.266071i
$403$	198588.	+	3681.25i	1.22277	+	0.0226665i
$404$	54210.1			0.332137
$405$	−2001.82	−	6160.98i	−0.0122044	−	0.0375612i
$406$	32082.6	−	28887.3i	0.194633	−	0.175249i
$407$	123232.	−	89533.5i	0.743936	−	0.540501i
$408$	−23282.1	−	40325.8i	−0.139863	−	0.242249i
$409$	−24488.0	−	14138.1i	−0.146388	−	0.0845173i	0.425017	−	0.905185i	$-0.360268\pi$
$409$	−24488.0	−	14138.1i	−0.146388	−	0.0845173i	−0.571405	+	0.820668i	$0.693601\pi$
$410$	261.633	+	2489.27i	0.00155641	+	0.0148083i
$411$	−8493.75	−	6171.07i	−0.0502824	−	0.0365323i
$412$	−13559.3	+	129008.i	−0.0798807	+	0.760015i
$413$	−30160.8	+	33497.0i	−0.176825	+	0.196384i
$414$	−81845.1	+	183827.i	−0.477521	+	1.07253i
$415$	449.015	−	2112.45i	0.00260714	−	0.0122656i
$416$	−40398.0	−	190058.i	−0.233439	−	1.09824i
$417$	72735.8	−	32384.0i	0.418288	−	0.186234i
$418$	−245559.	−	79787.0i	−1.40541	−	0.456646i
$419$	−9561.65	+	29427.7i	−0.0544634	+	0.167621i	−0.974588	−	0.224004i	$-0.928087\pi$
$419$	−9561.65	+	29427.7i	−0.0544634	+	0.167621i	0.920125	+	0.391625i	$0.128087\pi$
$420$	−754.712	−	1695.11i	−0.00427841	−	0.00960947i
$421$	−76911.1	+	16348.0i	−0.433935	+	0.0922358i	−0.419700	−	0.907663i	$-0.637865\pi$
$421$	−76911.1	+	16348.0i	−0.433935	+	0.0922358i	−0.0142352	+	0.999899i	$0.504531\pi$
$422$	45768.2	+	9728.33i	0.257003	+	0.0546277i
$423$	−147415.	−	65633.4i	−0.823875	−	0.366813i
$424$	−35254.2	−	31743.0i	−0.196101	−	0.176570i
$425$	178968.	+	18810.3i	0.990824	+	0.104140i
$426$	−20747.7	+	28556.7i	−0.114327	+	0.157358i
$427$	−118637.	+	12469.3i	−0.650676	+	0.0683888i
$428$	−48957.8	+	84797.3i	−0.267260	+	0.462908i
$429$	77584.8	−	44793.6i	0.421562	−	0.243389i
$430$	212.716	+	292.778i	0.00115044	+	0.00158344i
$431$	118849.	+	131996.i	0.639798	+	0.710567i	0.972615	−	0.232424i	$-0.0746657\pi$
$431$	118849.	+	131996.i	0.639798	+	0.710567i	−0.332817	+	0.942992i	$0.607999\pi$
$432$	−17479.2	+	5679.32i	−0.0936597	+	0.0304319i
$433$		−	41829.5i		−	0.223104i	−0.993759	−	0.111552i	$-0.964418\pi$
$433$		−	41829.5i		−	0.223104i	0.993759	−	0.111552i	$-0.0355821\pi$
$434$	36625.8	+	189518.i	0.194450	+	1.00617i
$435$	−644.131			−0.00340405
$436$	37585.4	+	115676.i	0.197718	+	0.608514i
$437$	−377346.	+	339764.i	−1.97595	+	1.77916i
$438$	−9821.28	+	7135.58i	−0.0511941	+	0.0371947i
$439$	−11624.6	−	20134.4i	−0.0603182	−	0.104474i	0.834289	−	0.551327i	$-0.185878\pi$
$439$	−11624.6	−	20134.4i	−0.0603182	−	0.104474i	−0.894608	+	0.446853i	$0.852545\pi$
$440$	−13094.6	−	7560.18i	−0.0676375	−	0.0390505i
$441$	−23211.0	−	220838.i	−0.119348	−	1.13552i
$442$	132504.	+	96269.7i	0.678241	+	0.492771i
$443$	27344.2	−	260163.i	0.139334	−	1.32568i	−0.671763	−	0.740766i	$-0.734463\pi$
$443$	27344.2	−	260163.i	0.139334	−	1.32568i	0.811097	−	0.584911i	$-0.198871\pi$
$444$	11481.8	−	12751.8i	0.0582429	−	0.0646853i
$445$	3749.63	−	8421.80i	0.0189351	−	0.0425290i
$446$	−2817.20	+	13253.9i	−0.0141628	+	0.0666306i
$447$	13600.4	+	63984.7i	0.0680669	+	0.320229i
$448$	224875.	−	100121.i	1.12043	−	0.498849i
$449$	−66654.7	−	21657.4i	−0.330627	−	0.107427i	0.138999	−	0.990292i	$-0.455611\pi$
$449$	−66654.7	−	21657.4i	−0.330627	−	0.107427i	−0.469626	+	0.882865i	$0.655611\pi$
$450$	39790.1	−	122461.i	0.196495	−	0.604748i
$451$	53634.3	+	120465.i	0.263687	+	0.592252i
$452$	128984.	−	27416.3i	0.631332	−	0.134194i
$453$	−18035.0	−	3833.45i	−0.0878858	−	0.0186807i
$454$	115719.	+	51521.4i	0.561426	+	0.249963i
$455$	14020.1	+	12623.8i	0.0677218	+	0.0609770i
$456$	−83615.3	−	8788.32i	−0.402120	−	0.0422646i
$457$	97020.3	−	133537.i	0.464547	−	0.639395i	−0.510897	−	0.859642i	$-0.670686\pi$
$457$	97020.3	−	133537.i	0.464547	−	0.639395i	0.975444	+	0.220247i	$0.0706865\pi$
$458$	−26420.5	+	2776.91i	−0.125953	+	0.0132382i
$459$	−54159.7	+	93807.4i	−0.257070	+	0.445258i
$460$	−8908.80	+	5143.50i	−0.0421021	+	0.0243076i
$461$	112064.	+	154243.i	0.527310	+	0.725779i	0.986717	−	0.162446i	$-0.0519384\pi$
$461$	112064.	+	154243.i	0.527310	+	0.725779i	−0.459408	+	0.888225i	$0.651938\pi$
$462$	58256.0	+	64699.9i	0.272933	+	0.303123i
$463$	−315553.	+	102529.i	−1.47201	+	0.478285i	−0.931715	−	0.363191i	$-0.881687\pi$
$463$	−315553.	+	102529.i	−1.47201	+	0.478285i	−0.540295	+	0.841476i	$0.681687\pi$
$464$		−	10526.4i		−	0.0488925i
$465$	1485.97	−	2467.02i	0.00687233	−	0.0114095i
$466$	−170089.			−0.783259
$467$	105871.	+	325839.i	0.485451	+	1.49406i	0.831327	+	0.555784i	$0.187582\pi$
$467$	105871.	+	325839.i	0.485451	+	1.49406i	−0.345876	+	0.938280i	$0.612418\pi$
$468$	−97788.3	+	88049.0i	−0.446473	+	0.402006i
$469$	−385932.	+	280396.i	−1.75455	+	1.27475i
$470$	3673.51	+	6362.70i	0.0166297	+	0.0288036i
$471$	−32016.6	−	18484.8i	−0.144322	−	0.0833245i
$472$	4325.07	+	41150.3i	0.0194137	+	0.184709i
$473$	15424.5	+	11206.5i	0.0689426	+	0.0500897i
$474$	6377.88	−	60681.5i	0.0283870	−	0.270084i
$475$	217416.	−	241464.i	0.963614	−	1.07020i
$476$	72690.5	−	163266.i	0.320822	−	0.720578i
$477$	−11048.4	+	51978.5i	−0.0485581	+	0.228448i
$478$	24021.6	+	113013.i	0.105135	+	0.494621i
$479$	247599.	−	110238.i	1.07914	−	0.480465i	0.211359	−	0.977409i	$-0.432211\pi$
$479$	247599.	−	110238.i	1.07914	−	0.480465i	0.867783	+	0.496944i	$0.165544\pi$
$480$	−2679.47	−	870.614i	−0.0116297	−	0.00377871i
$481$	−53912.6	+	165926.i	−0.233024	+	0.717173i
$482$	−58380.9	−	131126.i	−0.251291	−	0.564409i
$483$	167475.	−	35598.0i	0.717888	−	0.152592i
$484$	−148358.	−	31534.5i	−0.633316	−	0.134616i
$485$	−4082.74	−	1817.75i	−0.0173567	−	0.00772772i
$486$	87461.7	+	78750.9i	0.370293	+	0.333413i
$487$	455665.	+	47892.4i	1.92127	+	0.201933i	0.987688	−	0.156435i	$-0.0500000\pi$
$487$	455665.	+	47892.4i	1.92127	+	0.201933i	0.933580	+	0.358368i	$0.116667\pi$
$488$	−64365.1	+	88591.0i	−0.270278	+	0.372006i
$489$	−25090.9	+	2637.16i	−0.104930	+	0.0110285i
$490$	−5055.08	+	8755.66i	−0.0210541	+	0.0364667i
$491$	202970.	−	117185.i	0.841918	−	0.486081i	−0.0159980	−	0.999872i	$-0.505093\pi$
$491$	202970.	−	117185.i	0.841918	−	0.486081i	0.857916	+	0.513791i	$0.171759\pi$
$492$	8731.31	+	12017.6i	0.0360703	+	0.0496465i
$493$	−41512.7	−	46104.6i	−0.170800	−	0.189693i
$494$	281253.	−	91384.6i	1.15251	−	0.374472i
$495$			16937.3i			0.0691248i
$496$	40316.0	+	24283.7i	0.163875	+	0.0987077i
$497$	−391610.			−1.58541
$498$	3527.42	+	10856.3i	0.0142232	+	0.0437747i
$499$	−201286.	+	181239.i	−0.808374	+	0.727863i	−0.965693	−	0.259685i	$-0.916381\pi$
$499$	−201286.	+	181239.i	−0.808374	+	0.727863i	0.157320	+	0.987548i	$0.449715\pi$
$500$	10664.3	−	7748.05i	0.0426571	−	0.0309922i
$501$	−31694.4	−	54896.2i	−0.126272	−	0.218709i
$502$	−185932.	−	107348.i	−0.737815	−	0.425977i
$503$	−50624.3	−	481658.i	−0.200089	−	1.90372i	−0.388206	−	0.921572i	$-0.626905\pi$
$503$	−50624.3	−	481658.i	−0.200089	−	1.90372i	0.188118	−	0.982147i	$-0.439761\pi$
$504$	−299051.	−	217273.i	−1.17729	−	0.855353i
$505$	−835.385	+	7948.16i	−0.00327570	+	0.0311662i
$506$	322969.	−	358694.i	1.26142	−	1.40095i
$507$	−13831.1	+	31065.1i	−0.0538072	+	0.120853i
$508$	−18658.6	+	87781.7i	−0.0723021	+	0.340155i
$509$	−12767.2	−	60064.8i	−0.0492787	−	0.231838i	0.946615	−	0.322366i	$-0.104478\pi$
$509$	−12767.2	−	60064.8i	−0.0492787	−	0.231838i	−0.995894	+	0.0905275i	$0.971145\pi$
$510$	2169.52	−	965.932i	0.00834110	−	0.00371370i
$511$	−128091.	−	41619.4i	−0.490544	−	0.159388i
$512$	30489.9	−	93838.3i	0.116310	−	0.357965i
$513$	79549.8	+	178672.i	0.302277	+	0.678924i
$514$	−213539.	+	45389.2i	−0.808261	+	0.171801i
$515$	−18705.9	−	3976.06i	−0.0705284	−	0.0149913i
$516$	1962.07	+	873.568i	0.00736910	+	0.00328093i
$517$	287644.	+	258996.i	1.07615	+	0.968974i
$518$	−168619.	−	17722.6i	−0.628415	−	0.0660491i
$519$	−9855.73	+	13565.2i	−0.0365893	+	0.0503608i
$520$	17223.4	−	1810.25i	0.0636959	−	0.00669470i
$521$	172574.	−	298907.i	0.635770	−	1.10119i	−0.350582	−	0.936532i	$-0.614016\pi$
$521$	172574.	−	298907.i	0.635770	−	1.10119i	0.986351	−	0.164653i	$-0.0526506\pi$
$522$	−38444.5	+	22195.9i	−0.141089	+	0.0814578i
$523$	96940.2	+	133427.i	0.354406	+	0.487797i	0.948579	−	0.316539i	$-0.102521\pi$
$523$	96940.2	+	133427.i	0.354406	+	0.487797i	−0.594174	+	0.804337i	$0.702521\pi$
$524$	−30763.5	−	34166.3i	−0.112040	−	0.124433i
$525$	−104200.	+	33856.5i	−0.378049	+	0.122835i
$526$		−	178453.i		−	0.644991i
$527$	272348.	−	52633.4i	0.980625	−	0.189514i
$528$	21228.2			0.0761455
$529$	−206849.	−	636617.i	−0.739167	−	2.27492i
$530$	1798.01	−	1618.94i	0.00640090	−	0.00576339i
$531$	37497.1	−	27243.2i	0.132987	−	0.0966206i
$532$	−161344.	−	279457.i	−0.570073	−	0.987396i
$533$	−130798.	−	75516.3i	−0.460412	−	0.265819i
$534$	5093.34	+	48459.9i	0.0178616	+	0.169942i
$535$	−11678.3	−	8484.81i	−0.0408012	−	0.0296438i
$536$	−45773.4	+	435505.i	−0.159325	+	1.51588i
$537$	7671.65	−	8520.24i	0.0266036	−	0.0295463i
$538$	23783.0	−	53417.6i	0.0821680	−	0.184552i
$539$	−110741.	+	520995.i	−0.381181	+	1.79331i
$540$	823.810	+	3875.72i	0.00282514	+	0.0132912i
$541$	−518779.	+	230975.i	−1.77251	+	0.789171i	−0.787577	+	0.616217i	$0.788665\pi$
$541$	−518779.	+	230975.i	−1.77251	+	0.789171i	−0.984930	+	0.172954i	$0.944669\pi$
$542$	94716.1	+	30775.1i	0.322422	+	0.104761i
$543$	−40393.0	+	124317.i	−0.136995	+	0.421629i
$544$	−110371.	−	247896.i	−0.372954	−	0.837668i
$545$	−17539.3	+	3728.10i	−0.0590501	+	0.0125515i
$546$	−97538.3	−	20732.4i	−0.327183	−	0.0695448i
$547$	221643.	+	98681.6i	0.740762	+	0.329808i	0.742189	−	0.670191i	$-0.233788\pi$
$547$	221643.	+	98681.6i	0.740762	+	0.329808i	−0.00142729	+	0.999999i	$0.500454\pi$
$548$	−27488.7	−	24750.9i	−0.0915361	−	0.0824195i
$549$	121991.	+	12821.8i	0.404747	+	0.0425406i
$550$	−181544.	+	249874.i	−0.600146	+	0.826031i
$551$	−111405.	+	11709.1i	−0.366945	+	0.0385675i
$552$	78585.4	−	136114.i	0.257907	−	0.446709i
$553$	586240.	−	338466.i	1.91701	−	1.10679i
$554$	51189.8	+	70456.7i	0.166788	+	0.229563i
$555$	1692.70	+	1879.94i	0.00549535	+	0.00610320i
$556$	266786.	−	86683.9i	0.863004	−	0.280407i
$557$			88478.6i			0.285186i	0.989781	+	0.142593i	$0.0455440\pi$
$557$			88478.6i			0.285186i	−0.989781	+	0.142593i	$0.954456\pi$
$558$	3678.64	−	198447.i	0.0118146	−	0.637348i
$559$	−21837.0			−0.0698827
$560$	1381.42	+	4251.58i	0.00440504	+	0.0135573i
$561$	92977.5	−	83717.3i	0.295428	−	0.266005i
$562$	115287.	−	83760.8i	0.365012	−	0.265197i
$563$	71803.1	+	124367.i	0.226530	+	0.392362i	0.956777	−	0.290821i	$-0.0939284\pi$
$563$	71803.1	+	124367.i	0.226530	+	0.392362i	−0.730247	+	0.683183i	$0.760595\pi$
$564$	37761.1	+	21801.4i	0.118710	+	0.0685371i
$565$	2032.06	+	19333.8i	0.00636561	+	0.0605647i
$566$	−13214.5	−	9600.91i	−0.0412495	−	0.0299695i
$567$	−39707.7	+	377793.i	−0.123512	+	1.17514i
$568$	−240542.	+	267149.i	−0.745580	+	0.828050i
$569$	−212689.	+	477706.i	−0.656931	+	1.47549i	0.210327	+	0.977631i	$0.432547\pi$
$569$	−212689.	+	477706.i	−0.656931	+	1.47549i	−0.867258	+	0.497860i	$0.834119\pi$
$570$	891.521	−	4194.28i	0.00274399	−	0.0129094i
$571$	−30167.0	−	141925.i	−0.0925253	−	0.435297i	−0.999888	−	0.0149492i	$-0.995241\pi$
$571$	−30167.0	−	141925.i	−0.0925253	−	0.435297i	0.907363	−	0.420348i	$-0.138092\pi$
$572$	288346.	−	128380.i	0.881297	−	0.392379i
$573$	−35961.6	−	11684.6i	−0.109529	−	0.0355882i
$574$	45356.2	−	139592.i	0.137662	−	0.423679i
$575$	247055.	+	554895.i	0.747236	+	1.67832i
$576$	−247585.	+	52625.7i	−0.746240	+	0.158618i
$577$	122169.	+	25967.8i	0.366952	+	0.0779981i	0.387697	−	0.921787i	$-0.373271\pi$
$577$	122169.	+	25967.8i	0.366952	+	0.0779981i	−0.0207453	+	0.999785i	$0.506604\pi$
$578$	−515.186	−	229.375i	−0.00154208	−	0.000686580i
$579$	32379.1	+	29154.2i	0.0965845	+	0.0869650i
$580$	−2256.98	−	237.218i	−0.00670920	−	0.000705166i
$581$	−74438.4	+	102456.i	−0.220518	+	0.303517i
$582$	23492.5	−	2469.16i	0.0693559	−	0.00728960i
$583$	63732.4	−	110388.i	0.187509	−	0.324776i
$584$	−107071.	+	61817.2i	−0.313938	+	0.181252i
$585$	−11402.6	−	15694.3i	−0.0333190	−	0.0458597i
$586$	143569.	+	159449.i	0.418085	+	0.464330i
$587$	−177417.	+	57646.4i	−0.514896	+	0.167300i	−0.554928	−	0.831898i	$-0.687254\pi$
$587$	−177417.	+	57646.4i	−0.514896	+	0.167300i	0.0400316	+	0.999198i	$0.487254\pi$
$588$			60001.4i			0.173543i
$589$	212158.	−	453693.i	0.611547	−	1.30777i
$590$	−2110.28			−0.00606228
$591$	−19041.9	−	58605.0i	−0.0545175	−	0.167787i
$592$	−30721.9	+	27662.1i	−0.0876606	+	0.0789300i
$593$	159873.	−	116154.i	0.454637	−	0.330313i	−0.336787	−	0.941581i	$-0.609340\pi$
$593$	159873.	−	116154.i	0.454637	−	0.330313i	0.791424	+	0.611268i	$0.209340\pi$
$594$	−92956.6	−	161006.i	−0.263456	−	0.456318i
$595$	22817.4	+	13173.7i	0.0644515	+	0.0372111i
$596$	24090.5	+	229205.i	0.0678192	+	0.645256i
$597$	−59291.7	−	43078.0i	−0.166359	−	0.120867i
$598$	−57786.4	+	549801.i	−0.161593	+	1.53746i
$599$	354939.	−	394200.i	0.989237	−	1.09866i	−0.00588224	−	0.999983i	$-0.501872\pi$
$599$	354939.	−	394200.i	0.989237	−	1.09866i	0.995120	−	0.0986766i	$-0.0314609\pi$
$600$	−40907.1	+	91878.9i	−0.113631	+	0.255219i
$601$	−105903.	+	498236.i	−0.293198	+	1.37939i	0.547012	+	0.837125i	$0.315765\pi$
$601$	−105903.	+	498236.i	−0.293198	+	1.37939i	−0.840209	+	0.542262i	$0.817568\pi$
$602$	−4412.21	−	20757.8i	−0.0121748	−	0.0572781i
$603$	448116.	−	199514.i	1.23241	−	0.548706i
$604$	−61781.1	−	20073.9i	−0.169349	−	0.0550247i
$605$	6909.73	−	21266.0i	0.0188778	−	0.0580998i
$606$	−17181.4	−	38590.1i	−0.0467857	−	0.105083i
$607$	534067.	−	113520.i	1.44950	−	0.308101i	0.585124	−	0.810944i	$-0.301046\pi$
$607$	534067.	−	113520.i	1.44950	−	0.308101i	0.864378	+	0.502843i	$0.167713\pi$
$608$	−479252.	−	101868.i	−1.29645	−	0.275569i
$609$	34506.5	+	15363.3i	0.0930392	+	0.0414237i
$610$	−4150.37	−	3737.01i	−0.0111539	−	0.0100430i
$611$	−440898.	−	46340.2i	−1.18102	−	0.124130i
$612$	−108017.	+	148672.i	−0.288395	+	0.396942i
$613$	−211468.	+	22226.2i	−0.562760	+	0.0591485i	−0.381638	−	0.924312i	$-0.624640\pi$
$613$	−211468.	+	22226.2i	−0.562760	+	0.0591485i	−0.181123	+	0.983461i	$0.557973\pi$
$614$	−167459.	+	290047.i	−0.444192	+	0.769363i
$615$	−1896.55	+	1094.97i	−0.00501433	+	0.00289503i
$616$	521168.	+	717326.i	1.37346	+	1.89041i
$617$	−129964.	−	144339.i	−0.341390	−	0.379152i	0.547863	−	0.836568i	$-0.315442\pi$
$617$	−129964.	−	144339.i	−0.341390	−	0.379152i	−0.889253	+	0.457416i	$0.848775\pi$
$618$	96133.2	−	31235.6i	0.251708	−	0.0817848i
$619$		−	634620.i		−	1.65627i	−0.560526	−	0.828137i	$-0.689401\pi$
$619$		−	634620.i		−	1.65627i	0.560526	−	0.828137i	$-0.310599\pi$
$620$	6115.25	−	8096.97i	0.0159086	−	0.0210639i
$621$	−365617.			−0.948077
$622$	−12097.7	−	37232.8i	−0.0312695	−	0.0962376i
$623$	−401740.	+	361728.i	−1.03507	+	0.931979i
$624$	−19670.3	+	14291.3i	−0.0505175	+	0.0367031i
$625$	−193854.	−	335766.i	−0.496267	−	0.859560i
$626$	−396885.	−	229141.i	−1.01278	−	0.584730i
$627$	−23613.4	−	224667.i	−0.0600653	−	0.571483i
$628$	−105376.	−	76560.0i	−0.267191	−	0.194126i
$629$	−25468.4	+	242315.i	−0.0643724	+	0.612463i
$630$	12614.8	−	14010.2i	0.0317833	−	0.0352989i
$631$	−93099.1	+	209104.i	−0.233823	+	0.525174i	−0.991905	−	0.126985i	$-0.959470\pi$
$631$	−93099.1	+	209104.i	−0.233823	+	0.525174i	0.758082	+	0.652159i	$0.226137\pi$
$632$	129196.	−	607820.i	0.323456	−	1.52174i
$633$	8511.63	+	40044.1i	0.0212425	+	0.0999380i
$634$	161665.	−	71977.8i	0.402196	−	0.179069i
$635$	−12582.8	−	4088.40i	−0.0312054	−	0.0101393i
$636$	4437.15	−	13656.1i	0.0109696	−	0.0337609i
$637$	−248133.	−	557315.i	−0.611512	−	1.37348i
$638$	104155.	−	22138.8i	0.255881	−	0.0543891i
$639$	393882.	+	83722.2i	0.964638	+	0.205040i
$640$	−6616.05	−	2945.66i	−0.0161525	−	0.00719154i
$641$	−138421.	−	124634.i	−0.336887	−	0.303335i	0.483272	−	0.875470i	$-0.339448\pi$
$641$	−138421.	−	124634.i	−0.336887	−	0.303335i	−0.820159	+	0.572136i	$0.806115\pi$
$642$	75880.6	+	7975.38i	0.184103	+	0.0193500i
$643$	−84831.4	+	116760.i	−0.205180	+	0.282406i	−0.899189	−	0.437560i	$-0.855843\pi$
$643$	−84831.4	+	116760.i	−0.205180	+	0.282406i	0.694009	+	0.719966i	$0.255843\pi$
$644$	599928.	−	63055.0i	1.44653	−	0.152036i
$645$	−158.316	+	274.212i	−0.000380545	+	0.000659123i
$646$	357668.	−	206500.i	0.857067	−	0.494828i
$647$	−234549.	−	322829.i	−0.560306	−	0.771195i	0.431060	−	0.902323i	$-0.358140\pi$
$647$	−234549.	−	322829.i	−0.560306	−	0.771195i	−0.991365	+	0.131129i	$0.958140\pi$
$648$	233333.	+	259143.i	0.555682	+	0.617148i
$649$	−105735.	+	34355.3i	−0.251031	+	0.0815650i
$650$		−	353757.i		−	0.837295i
$651$	−138446.	+	96717.7i	−0.326676	+	0.228215i
$652$	−88887.3			−0.209096
$653$	135498.	+	417020.i	0.317765	+	0.977981i	0.974601	+	0.223947i	$0.0718944\pi$
$653$	135498.	+	417020.i	0.317765	+	0.977981i	−0.656836	+	0.754033i	$0.728106\pi$
$654$	70432.9	−	63418.1i	0.164672	−	0.148271i
$655$	5483.46	−	3983.97i	0.0127812	−	0.00928609i
$656$	−17894.0	−	30993.3i	−0.0415814	−	0.0720211i
$657$	119937.	+	69245.5i	0.277857	+	0.160421i
$658$	−45034.2	−	428471.i	−0.104014	−	0.989624i
$659$	−339983.	−	247012.i	−0.782864	−	0.568784i	0.122973	−	0.992410i	$-0.460757\pi$
$659$	−339983.	−	247012.i	−0.782864	−	0.568784i	−0.905837	+	0.423626i	$0.860757\pi$
$660$	478.389	−	4551.57i	0.00109823	−	0.0104490i
$661$	138336.	−	153638.i	0.316616	−	0.351638i	−0.563739	−	0.825953i	$-0.690638\pi$
$661$	138336.	−	153638.i	0.316616	−	0.351638i	0.880355	+	0.474315i	$0.157304\pi$
$662$	−73481.3	+	165042.i	−0.167672	+	0.376598i
$663$	−29793.7	+	140168.i	−0.0677794	+	0.318877i
$664$	24170.3	+	113713.i	0.0548210	+	0.257912i
$665$	43459.6	−	19349.5i	0.0982749	−	0.0437548i
$666$	165808.	+	53874.4i	0.373816	+	0.121460i
$667$	64710.3	−	199158.i	0.145453	−	0.447657i
$668$	−90837.2	−	204024.i	−0.203569	−	0.457223i
$669$	−11596.3	+	2464.86i	−0.0259099	+	0.00550732i
$670$	−21845.6	−	4643.43i	−0.0486648	−	0.0103440i
$671$	−268791.	−	119673.i	−0.596993	−	0.265799i
$672$	122776.	+	110548.i	0.271878	+	0.244800i
$673$	103361.	+	10863.7i	0.228206	+	0.0239854i	0.217941	−	0.975962i	$-0.430066\pi$
$673$	103361.	+	10863.7i	0.228206	+	0.0239854i	0.0102649	+	0.999947i	$0.496733\pi$
$674$	181994.	−	250494.i	0.400625	−	0.551413i
$675$	232678.	−	24455.4i	0.510678	−	0.0536744i
$676$	−59903.4	+	103756.i	−0.131087	+	0.227049i
$677$	−274770.	+	158639.i	−0.599504	+	0.346124i	−0.768847	−	0.639433i	$-0.779169\pi$
$677$	−274770.	+	158639.i	−0.599504	+	0.346124i	0.169342	+	0.985557i	$0.445836\pi$
$678$	−60396.8	−	83129.1i	−0.131388	−	0.180840i
$679$	175359.	+	194756.i	0.380355	+	0.422427i
$680$	23002.2	−	7473.85i	0.0497451	−	0.0161632i
$681$			110828.i			0.238976i
$682$	−155487.	+	449985.i	−0.334292	+	0.967452i
$683$	−161628.			−0.346477			−0.173239	−	0.984880i	$-0.555423\pi$
$683$	−161628.			−0.346477			−0.173239	+	0.984880i	$0.555423\pi$
$684$	102535.	+	315572.i	0.219160	+	0.674506i
$685$	4052.52	−	3648.91i	0.00863663	−	0.00777646i
$686$	89480.7	−	65011.5i	0.190143	−	0.138147i
$687$	−11621.7	−	20129.4i	−0.0246239	−	0.0426499i
$688$	−4481.16	−	2587.20i	−0.00946702	−	0.00546579i
$689$	15260.4	+	145193.i	0.0321460	+	0.305849i
$690$	6485.02	+	4711.64i	0.0136211	+	0.00989633i
$691$	38630.7	−	367546.i	0.0809052	−	0.769761i	−0.876576	−	0.481264i	$-0.840178\pi$
$691$	38630.7	−	367546.i	0.0809052	−	0.769761i	0.957481	−	0.288497i	$-0.0931556\pi$
$692$	−39529.3	+	43901.8i	−0.0825481	+	0.0916790i
$693$	403975.	−	907342.i	0.841177	−	1.88931i
$694$	−23688.3	+	111445.i	−0.0491831	+	0.231388i
$695$	8598.19	+	40451.3i	0.0178007	+	0.0837458i
$696$	31675.7	−	14102.9i	0.0653895	−	0.0291133i
$697$	−200602.	−	65179.6i	−0.412924	−	0.134167i
$698$	−168265.	+	517867.i	−0.345369	+	1.06294i
$699$	−60529.2	−	135951.i	−0.123883	−	0.278245i
$700$	−377575.	+	80256.0i	−0.770561	+	0.163788i
$701$	−789397.	−	167791.i	−1.60642	−	0.341455i	−0.684554	−	0.728962i	$-0.740003\pi$
$701$	−789397.	−	167791.i	−1.60642	−	0.341455i	−0.921867	+	0.387507i	$0.873336\pi$
$702$	194528.	+	86609.3i	0.394736	+	0.175748i
$703$	326934.	+	294372.i	0.661529	+	0.595644i
$704$	603816.	+	63463.6i	1.21831	+	0.128050i
$705$	−3778.37	+	5200.48i	−0.00760197	+	0.0104632i
$706$	449996.	−	47296.5i	0.902816	−	0.0948898i
$707$	234325.	−	405863.i	0.468792	−	0.811971i
$708$	−10846.1	+	6261.99i	−0.0216375	+	0.0124924i
$709$	238634.	+	328452.i	0.474723	+	0.653400i	0.977480	−	0.211028i	$-0.0676810\pi$
$709$	238634.	+	328452.i	0.474723	+	0.653400i	−0.502757	+	0.864428i	$0.667681\pi$
$710$	−12268.0	−	13624.9i	−0.0243363	−	0.0270283i
$711$	−662001.	+	215097.i	−1.30954	+	0.425496i
$712$			496246.i			0.978897i
$713$	613492.	+	707285.i	1.20678	+	1.39128i
$714$	−139261.			−0.273170
$715$	14379.3	+	44255.0i	0.0281272	+	0.0865666i
$716$	30018.6	−	27028.8i	0.0585550	−	0.0527232i
$717$	−81781.6	+	59417.8i	−0.159081	+	0.115579i
$718$	−8832.84	−	15298.9i	−0.0171337	−	0.0296764i
$719$	−499227.	−	288229.i	−0.965696	−	0.557545i	−0.0677748	−	0.997701i	$-0.521590\pi$
$719$	−499227.	−	288229.i	−0.965696	−	0.557545i	−0.897922	+	0.440156i	$0.854923\pi$
$720$	−480.492	−	4571.58i	−0.000926875	−	0.00881863i
$721$	907252.	+	659157.i	1.74525	+	1.26800i
$722$	40549.4	−	385801.i	0.0777875	−	0.740098i
$723$	84031.7	−	93326.6i	0.160756	−	0.178537i
$724$	−187316.	+	420719.i	−0.357353	+	0.802629i
$725$	−27860.1	+	131072.i	−0.0530038	+	0.249364i
$726$	24572.6	+	115605.i	0.0466206	+	0.219333i
$727$	−536545.	+	238885.i	−1.01517	+	0.451981i	−0.845759	−	0.533565i	$-0.820852\pi$
$727$	−536545.	+	238885.i	−1.01517	+	0.451981i	−0.169407	+	0.985546i	$0.554185\pi$
$728$	−965842.	−	313821.i	−1.82240	−	0.592133i
$729$	98143.7	−	302055.i	0.184675	−	0.568370i
$730$	−2564.69	−	5760.38i	−0.00481270	−	0.0108095i
$731$	−29830.2	+	6340.61i	−0.0558241	+	0.0118658i
$732$	−32420.5	−	6891.20i	−0.0605060	−	0.0128609i
$733$	−49347.4	−	21970.9i	−0.0918451	−	0.0408921i	0.360300	−	0.932837i	$-0.382674\pi$
$733$	−49347.4	−	21970.9i	−0.0918451	−	0.0408921i	−0.452145	+	0.891944i	$0.649341\pi$
$734$	74641.4	+	67207.4i	0.138544	+	0.124746i
$735$	−8797.26	−	924.629i	−0.0162844	−	0.00171156i
$736$	538367.	−	740999.i	0.993855	−	1.36792i
$737$	−1.17016e6	+	122989.i	−2.15432	+	0.226428i
$738$	−75462.7	+	130705.i	−0.138554	+	0.239983i
$739$	−606705.	+	350281.i	−1.11093	+	0.641398i	−0.939071	−	0.343723i	$-0.888312\pi$
$739$	−606705.	+	350281.i	−1.11093	+	0.641398i	−0.171863	+	0.985121i	$0.554979\pi$
$740$	5238.75	+	7210.52i	0.00956674	+	0.0131675i
$741$	173131.	+	192282.i	0.315311	+	0.350189i
$742$	−134934.	+	43842.7i	−0.245083	+	0.0796324i
$743$			52348.9i			0.0948265i	0.998875	+	0.0474132i	$0.0150978\pi$
$743$			52348.9i			0.0948265i	−0.998875	+	0.0474132i	$0.984902\pi$
$744$	−19059.7	+	153853.i	−0.0344326	+	0.277945i
$745$	−33976.8			−0.0612167
$746$	76335.2	+	234935.i	0.137166	+	0.422154i
$747$	96774.2	−	87135.8i	0.173428	−	0.156155i
$748$	356616.	−	259097.i	0.637379	−	0.463083i
$749$	423243.	+	733078.i	0.754442	+	1.30673i
$750$	−8895.49	−	5135.81i	−0.0158142	−	0.00913033i
$751$	9143.28	+	86992.5i	0.0162115	+	0.154242i	0.999633	−	0.0270929i	$-0.00862498\pi$
$751$	9143.28	+	86992.5i	0.0162115	+	0.154242i	−0.983421	+	0.181335i	$0.941958\pi$
$752$	−84986.0	−	61746.0i	−0.150284	−	0.109187i
$753$	19635.1	−	186816.i	0.0346293	−	0.329475i
$754$	−81606.8	+	90633.5i	−0.143544	+	0.159421i
$755$	3895.24	−	8748.86i	0.00683346	−	0.0153482i
$756$	48308.5	−	227274.i	0.0845240	−	0.397654i
$757$	−39322.2	−	184996.i	−0.0686193	−	0.322828i	0.930428	−	0.366475i	$-0.119436\pi$
$757$	−39322.2	−	184996.i	−0.0686193	−	0.322828i	−0.999047	+	0.0436472i	$0.986102\pi$
$758$	446529.	−	198807.i	0.777161	−	0.346014i
$759$	401635.	+	130499.i	0.697184	+	0.226529i
$760$	13494.7	−	41532.5i	0.0233634	−	0.0719053i
$761$	318469.	+	715293.i	0.549918	+	1.23514i	0.948142	+	0.317848i	$0.102960\pi$
$761$	318469.	+	715293.i	0.549918	+	1.23514i	−0.398224	+	0.917288i	$0.630373\pi$
$762$	68402.0	−	14539.3i	0.117804	−	0.0250399i
$763$	1.02851e6	+	218617.i	1.76669	+	0.375522i
$764$	−121703.	−	54185.7i	−0.208504	−	0.0928320i
$765$	−20133.4	−	18128.2i	−0.0344029	−	0.0309765i
$766$	−628378.	−	66045.2i	−1.07094	−	0.112560i
$767$	74846.4	−	103017.i	0.127227	−	0.175113i
$768$	166669.	−	17517.6i	0.282574	−	0.0296997i
$769$	584667.	−	1.01267e6i	0.988680	−	1.71244i	0.364402	−	0.931242i	$-0.381274\pi$
$769$	584667.	−	1.01267e6i	0.988680	−	1.71244i	0.624278	−	0.781202i	$-0.285393\pi$
$770$	−39162.5	+	22610.5i	−0.0660525	+	0.0381354i
$771$	−112271.	−	154527.i	−0.188868	−	0.259954i
$772$	102717.	+	114078.i	0.172348	+	0.191412i
$773$	491247.	−	159616.i	0.822131	−	0.267127i	0.132404	−	0.991196i	$-0.457730\pi$
$773$	491247.	−	159616.i	0.822131	−	0.267127i	0.689727	+	0.724069i	$0.257730\pi$
$774$			21821.5i			0.0364253i
$775$	−437733.	−	409079.i	−0.728796	−	0.681089i
$776$	240571.			0.399503
$777$	−45840.5	−	141082.i	−0.0759289	−	0.233685i
$778$	−293846.	+	264580.i	−0.485468	+	0.437117i
$779$	−308110.	+	223855.i	−0.507728	+	0.368886i
$780$	2620.94	+	4539.61i	0.00430793	+	0.00746155i
$781$	−836494.	−	482950.i	−1.37139	−	0.791772i
$782$	80702.1	+	767829.i	0.131969	+	1.25560i
$783$	−65254.2	−	47409.9i	−0.106435	−	0.0773296i
$784$	15110.2	−	143764.i	0.0245833	−	0.233894i
$785$	12848.9	−	14270.1i	0.0208510	−	0.0231574i
$786$	−14571.5	+	32728.1i	−0.0235862	+	0.0529755i
$787$	−73666.0	+	346571.i	−0.118937	+	0.559556i	0.877813	+	0.479003i	$0.159002\pi$
$787$	−73666.0	+	346571.i	−0.118937	+	0.559556i	−0.996750	+	0.0805524i	$0.974332\pi$
$788$	−45138.3	−	212359.i	−0.0726931	−	0.341994i
$789$	142636.	−	63505.7i	0.229127	−	0.102014i
$790$	30141.0	+	9793.42i	0.0482952	+	0.0156921i
$791$	352274.	−	1.08419e6i	0.563025	−	1.73281i
$792$	−370834.	−	832907.i	−0.591193	−	1.32784i
$793$	329632.	−	70065.5i	0.524184	−	0.111419i
$794$	−484187.	−	102917.i	−0.768019	−	0.163247i
$795$	1933.85	+	861.007i	0.00305977	+	0.00136230i
$796$	−191888.	−	172777.i	−0.302846	−	0.272684i
$797$	773634.	+	81312.2i	1.21792	+	0.128009i	0.691602	−	0.722279i	$-0.256905\pi$
$797$	773634.	+	81312.2i	1.21792	+	0.128009i	0.526318	+	0.850288i	$0.323572\pi$
$798$	−147798.	+	203426.i	−0.232093	+	0.319449i
$799$	−615739.	+	64716.8i	−0.964502	+	0.101373i
$800$	−293051.	+	507580.i	−0.457893	+	0.793093i
$801$	481404.	−	277939.i	0.750317	−	0.433196i
$802$	−251658.	−	346377.i	−0.391257	−	0.538519i
$803$	−222281.	−	246868.i	−0.344724	−	0.382855i
$804$	−126058.	+	40958.6i	−0.195010	+	0.0633626i
$805$			88931.7i			0.137235i
$806$	−158865.	−	521640.i	−0.244544	−	0.802973i
$807$	51159.8			0.0785564
$808$	−132940.	−	409148.i	−0.203626	−	0.626698i
$809$	534272.	−	481061.i	0.816329	−	0.735026i	−0.151004	−	0.988533i	$-0.548251\pi$
$809$	534272.	−	481061.i	0.816329	−	0.735026i	0.967334	+	0.253507i	$0.0815841\pi$
$810$	−14388.1	+	10453.6i	−0.0219298	+	0.0159329i
$811$	507804.	+	879543.i	0.772066	+	1.33726i	0.936429	+	0.350858i	$0.114110\pi$
$811$	507804.	+	879543.i	0.772066	+	1.33726i	−0.164362	+	0.986400i	$0.552557\pi$
$812$	115250.	+	66539.4i	0.174794	+	0.100918i
$813$	9108.07	+	86657.5i	0.0137799	+	0.131107i
$814$	−338320.	−	245804.i	−0.510598	−	0.370971i
$815$	1369.77	−	13032.5i	0.00206220	−	0.0196205i
$816$	−22720.8	+	25234.0i	−0.0341226	+	0.0378970i
$817$	−22396.7	+	50303.9i	−0.0335537	+	0.0753629i
$818$	−16140.0	+	75932.9i	−0.0241211	+	0.113481i
$819$	236516.	+	1.11272e6i	0.352609	+	1.65889i
$820$	−7048.57	+	3138.23i	−0.0104827	+	0.00466720i
$821$	839977.	+	272925.i	1.24618	+	0.404909i	0.856551	−	0.516063i	$-0.172603\pi$
$821$	839977.	+	272925.i	1.24618	+	0.404909i	0.389630	+	0.920971i	$0.372603\pi$
$822$	−8906.92	+	27412.7i	−0.0131821	+	0.0405703i
$823$	−39787.3	−	89363.7i	−0.0587415	−	0.131935i	0.881790	−	0.471643i	$-0.156339\pi$
$823$	−39787.3	−	89363.7i	−0.0587415	−	0.131935i	−0.940531	+	0.339707i	$0.889672\pi$
$824$	1.00693e6	−	214030.i	1.48302	−	0.315225i
$825$	−264328.	−	56184.6i	−0.388360	−	0.0825486i
$826$	113049.	+	50332.6i	0.165694	+	0.0737716i
$827$	−773634.	−	696583.i	−1.13116	−	1.01850i	−0.999630	−	0.0271894i	$-0.991344\pi$
$827$	−773634.	−	696583.i	−1.13116	−	1.01850i	−0.131530	−	0.991312i	$-0.541989\pi$
$828$	−616889.	−	64837.6i	−0.899800	−	0.0945728i
$829$	18429.6	−	25366.2i	0.0268168	−	0.0369102i	−0.795398	−	0.606087i	$-0.792738\pi$
$829$	18429.6	−	25366.2i	0.0268168	−	0.0369102i	0.822215	+	0.569177i	$0.192738\pi$
$830$	−5896.57	+	619.755i	−0.00855941	+	0.000899630i
$831$	−38098.6	+	65988.7i	−0.0551705	+	0.0955582i
$832$	−602229.	+	347697.i	−0.869992	+	0.502290i
$833$	−500781.	−	689266.i	−0.721702	−	0.993338i
$834$	−146262.	−	162441.i	−0.210281	−	0.233541i
$835$	31313.3	−	10174.3i	0.0449113	−	0.0145926i
$836$		−	795907.i		−	1.13881i
$837$	332118.	−	140552.i	0.474068	−	0.200625i
$838$	84948.2			0.120967
$839$	9472.81	+	29154.3i	0.0134572	+	0.0414170i	0.957560	−	0.288235i	$-0.0930685\pi$
$839$	9472.81	+	29154.3i	0.0134572	+	0.0414170i	−0.944102	+	0.329652i	$0.893069\pi$
$840$	−10943.0	+	9853.10i	−0.0155088	+	0.0139641i
$841$	−534828.	+	388575.i	−0.756175	+	0.549393i
$842$	107934.	+	186947.i	0.152242	+	0.263691i
$843$	107976.	+	62340.0i	0.151940	+	0.0877226i
$844$	15076.7	+	143445.i	0.0211652	+	0.201373i
$845$	−14289.3	−	10381.8i	−0.0200123	−	0.0145398i
$846$	−46307.3	+	440585.i	−0.0647007	+	0.615586i
$847$	−877377.	+	974426.i	−1.22298	+	1.35826i
$848$	−14070.5	+	31603.0i	−0.0195668	+	0.0439477i
$849$	2971.30	−	13978.9i	0.00412223	−	0.0193935i
$850$	−102717.	−	483246.i	−0.142169	−	0.668852i
$851$	−751306.	+	334503.i	−1.03743	+	0.461893i
$852$	−103483.	−	33623.8i	−0.142558	−	0.0463198i
$853$	−92760.8	+	285488.i	−0.127487	+	0.392365i	−0.994346	−	0.106189i	$-0.966135\pi$
$853$	−92760.8	+	285488.i	−0.127487	+	0.392365i	0.866859	+	0.498554i	$0.166135\pi$
$854$	133206.	+	299185.i	0.182645	+	0.410227i
$855$	−47848.5	+	10170.5i	−0.0654539	+	0.0139127i
$856$	760064.	+	161556.i	1.03730	+	0.220484i
$857$	−398748.	−	177534.i	−0.542921	−	0.241724i	0.116904	−	0.993143i	$-0.462703\pi$
$857$	−398748.	−	177534.i	−0.542921	−	0.241724i	−0.659825	+	0.751419i	$0.729370\pi$
$858$	−182778.	−	164574.i	−0.248284	−	0.223556i
$859$	350474.	+	36836.3i	0.474973	+	0.0499217i	0.338991	−	0.940790i	$-0.389914\pi$
$859$	350474.	+	36836.3i	0.474973	+	0.0499217i	0.135982	+	0.990711i	$0.456581\pi$
$860$	−655.711	+	902.509i	−0.000886575	+	0.00122027i
$861$	127715.	−	13423.4i	0.172281	−	0.0181074i
$862$	243815.	−	422300.i	0.328130	−	0.568337i
$863$	−456399.	+	263502.i	−0.612806	+	0.353804i	−0.774063	−	0.633109i	$-0.781779\pi$
$863$	−456399.	+	263502.i	−0.612806	+	0.353804i	0.161257	+	0.986912i	$0.448445\pi$
$864$	−207367.	−	285416.i	−0.277787	−	0.382340i
$865$	−5827.62	−	6472.23i	−0.00778859	−	0.00865011i
$866$	−109218.	+	35486.9i	−0.145632	+	0.0473187i
$867$		−	493.410i		−	0.000656402i
$868$	−520720.	+	287904.i	−0.691138	+	0.382127i
$869$	1.66964e6			2.21097
$870$	546.462	+	1681.84i	0.000721974	+	0.00222201i
$871$	1.00149e6	−	901744.i	1.32011	−	1.18863i
$872$	780888.	−	567348.i	1.02697	−	0.746134i
$873$	−134740.	−	233376.i	−0.176794	−	0.306216i
$874$	1.20726e6	+	697011.i	1.58044	+	0.912466i
$875$	−11911.8	−	113333.i	−0.0155582	−	0.148027i
$876$	−30274.8	−	21995.9i	−0.0394524	−	0.0286638i
$877$	1644.62	−	15647.5i	0.00213828	−	0.0203444i	−0.993401	−	0.114695i	$-0.963411\pi$
$877$	1644.62	−	15647.5i	0.00213828	−	0.0203444i	0.995539	+	0.0943508i	$0.0300775\pi$
$878$	−42709.2	+	47433.4i	−0.0554029	+	0.0615312i
$879$	−76354.8	+	171496.i	−0.0988231	+	0.221960i
$880$	−2292.46	+	10785.2i	−0.00296030	+	0.0139271i
$881$	209698.	+	986553.i	0.270174	+	1.27107i	0.878639	+	0.477487i	$0.158452\pi$
$881$	209698.	+	986553.i	0.270174	+	1.27107i	−0.608465	+	0.793580i	$0.708215\pi$
$882$	−556920.	+	247957.i	−0.715905	+	0.318741i
$883$	1.09535e6	+	355902.i	1.40486	+	0.456466i	0.910759	−	0.412939i	$-0.135498\pi$
$883$	1.09535e6	+	355902.i	1.40486	+	0.456466i	0.494100	+	0.869405i	$0.335498\pi$
$884$	−156015.	+	480165.i	−0.199647	+	0.614449i
$885$	−750.979	−	1686.73i	−0.000958829	−	0.00215356i
$886$	−702488.	+	149318.i	−0.894894	+	0.190216i
$887$	536962.	+	114135.i	0.682490	+	0.145068i	0.536094	−	0.844158i	$-0.319899\pi$
$887$	536962.	+	114135.i	0.682490	+	0.145068i	0.146396	+	0.989226i	$0.453233\pi$
$888$	−124401.	−	55386.7i	−0.157760	−	0.0702392i
$889$	576555.	+	519133.i	0.729520	+	0.656863i
$890$	−25170.6	−	2645.53i	−0.0317770	−	0.00333990i
$891$	−550728.	+	758012.i	−0.693716	+	0.954818i
$892$	−41540.0	+	4366.03i	−0.0522079	+	0.00548728i
$893$	−558948.	+	968127.i	−0.700921	+	1.21403i
$894$	155527.	−	89793.6i	0.194595	−	0.112349i
$895$	3500.32	+	4817.77i	0.00436980	+	0.00601451i
$896$	284168.	+	315601.i	0.353965	+	0.393118i
$897$	−460015.	+	149468.i	−0.571725	+	0.185765i
$898$			192410.i			0.238603i
$899$	17779.7	+	205786.i	0.0219991	+	0.254622i
$900$	396923.			0.490028
$901$	63004.6	+	193908.i	0.0776109	+	0.238862i
$902$	269033.	−	242239.i	0.330669	−	0.297736i
$903$	15021.4	−	10913.7i	0.0184219	−	0.0133843i
$904$	−523232.	−	906264.i	−0.640262	−	1.10897i
$905$	−58798.2	−	33947.2i	−0.0717905	−	0.0414483i
$906$	5291.14	+	50341.8i	0.00644603	+	0.0613299i
$907$	−769585.	−	559136.i	−0.935496	−	0.679677i	0.0118366	−	0.999930i	$-0.496232\pi$
$907$	−769585.	−	559136.i	−0.935496	−	0.679677i	−0.947332	+	0.320253i	$0.896232\pi$
$908$	−40815.2	+	388330.i	−0.0495051	+	0.471010i
$909$	−322454.	+	358121.i	−0.390247	+	0.433413i
$910$	21066.6	−	47316.4i	0.0254397	−	0.0571385i
$911$	184846.	−	869630.i	0.222727	−	1.04785i	−0.714637	−	0.699495i	$-0.753408\pi$
$911$	184846.	−	869630.i	0.222727	−	1.04785i	0.937364	−	0.348352i	$-0.113259\pi$
$912$	12747.1	+	59970.3i	0.0153257	+	0.0721018i
$913$	−285356.	+	127049.i	−0.342330	+	0.152415i
$914$	−430977.	−	140033.i	−0.515895	−	0.167624i
$915$	1509.98	−	4647.23i	0.00180355	−	0.00555075i
$916$	−33308.3	−	74811.7i	−0.0396974	−	0.0891618i
$917$	−388774.	+	82636.5i	−0.462337	+	0.0982728i
$918$	290880.	+	61828.5i	0.345167	+	0.0733675i
$919$	−383574.	−	170778.i	−0.454170	−	0.202210i	0.166885	−	0.985976i	$-0.446629\pi$
$919$	−383574.	−	170778.i	−0.454170	−	0.202210i	−0.621055	+	0.783767i	$0.713296\pi$
$920$	60667.5	+	54625.2i	0.0716771	+	0.0645383i
$921$	−291425.	−	30630.0i	−0.343563	−	0.0361100i
$922$	307660.	−	423458.i	0.361917	−	0.498136i
$923$	1.10024e6	−	115640.i	1.29147	−	0.135739i
$924$	−134188.	+	232420.i	−0.157170	+	0.272226i
$925$	455755.	−	263130.i	0.532657	−	0.307530i
$926$	535413.	+	736932.i	0.624405	+	0.859420i
$927$	−771594.	−	856942.i	−0.897903	−	0.997222i
$928$	192172.	−	62440.5i	0.223149	−	0.0725054i
$929$			1.25305e6i			1.45191i	0.687744	+	0.725953i	$0.258601\pi$
$929$			1.25305e6i			1.45191i	−0.687744	+	0.725953i	$0.741399\pi$
$930$	−7702.09	−	1786.95i	−0.00890518	−	0.00206607i
$931$	−1.53833e6			−1.77480
$932$	−162022.	−	498651.i	−0.186527	−	0.574070i
$933$	25454.6	−	22919.5i	0.0292418	−	0.0263294i
$934$	760953.	−	552865.i	0.872296	−	0.633760i
$935$	32492.6	+	56278.9i	0.0371674	+	0.0643757i
$936$	904354.	+	522129.i	1.03225	+	0.595972i
$937$	−54200.1	−	515680.i	−0.0617335	−	0.587355i	−0.981039	−	0.193811i	$-0.937915\pi$
$937$	−54200.1	−	515680.i	−0.0617335	−	0.587355i	0.919305	−	0.393545i	$-0.128751\pi$
$938$	1.05953e6	+	769795.i	1.20423	+	0.874922i
$939$	41912.4	−	398770.i	0.0475348	−	0.452263i
$940$	−15154.3	+	16830.5i	−0.0171506	+	0.0190477i
$941$	226546.	−	508831.i	0.255845	−	0.574638i	−0.739264	−	0.673416i	$-0.764826\pi$
$941$	226546.	−	508831.i	0.255845	−	0.574638i	0.995110	+	0.0987773i	$0.0314931\pi$
$942$	−21102.2	+	99277.9i	−0.0237807	+	0.111880i
$943$	−148023.	−	696392.i	−0.166458	−	0.783124i
$944$	27564.4	−	12272.5i	0.0309318	−	0.0137717i
$945$	32577.9	+	10585.2i	0.0364804	+	0.0118532i
$946$	16174.8	−	49780.8i	0.0180741	−	0.0556262i
$947$	−272786.	−	612688.i	−0.304174	−	0.683187i	0.695190	−	0.718826i	$-0.255320\pi$
$947$	−272786.	−	612688.i	−0.304174	−	0.683187i	−0.999365	+	0.0356390i	$0.988653\pi$
$948$	183975.	−	39105.1i	0.204712	−	0.0435128i
$949$	372167.	+	79106.5i	0.413243	+	0.0878375i
$950$	−814917.	−	362824.i	−0.902955	−	0.402022i
$951$	115062.	+	103603.i	0.127225	+	0.114554i
$952$	−1.41050e6	−	148249.i	−1.55632	−	0.163576i
$953$	−105706.	+	145491.i	−0.116389	+	0.160196i	−0.863237	−	0.504799i	$-0.831566\pi$
$953$	−105706.	+	145491.i	−0.116389	+	0.160196i	0.746848	+	0.664995i	$0.231566\pi$
$954$	145090.	−	15249.6i	0.159419	−	0.0167556i
$955$	9820.03	−	17008.8i	0.0107673	−	0.0186495i
$956$	−308438.	+	178077.i	−0.337483	+	0.194846i
$957$	54760.5	+	75371.4i	0.0597921	+	0.0822968i
$958$	−497890.	−	552963.i	−0.542504	−	0.602511i
$959$	−304127.	+	98816.8i	−0.330687	+	0.107447i
$960$			10083.1i			0.0109408i
$961$	−829177.	−	406640.i	−0.897844	−	0.440315i
$962$	478974.			0.517561
$963$	−268974.	−	827816.i	−0.290040	−	0.892650i
$964$	328809.	−	296061.i	0.353826	−	0.318587i
$965$	−18308.8	+	13302.1i	−0.0196609	+	0.0142845i
$966$	−235028.	−	407081.i	−0.251864	−	0.436241i
$967$	159169.	+	91896.5i	0.170218	+	0.0982757i	0.582689	−	0.812695i	$-0.302001\pi$
$967$	159169.	+	91896.5i	0.170218	+	0.0982757i	−0.412470	+	0.910971i	$0.635334\pi$
$968$	125816.	+	1.19706e6i	0.134272	+	1.27751i
$969$	292335.	+	212394.i	0.311339	+	0.226201i
$970$	−1282.51	+	12202.2i	−0.00136306	+	0.0129687i
$971$	753491.	−	836837.i	0.799171	−	0.887570i	−0.196501	−	0.980504i	$-0.562958\pi$
$971$	753491.	−	836837.i	0.799171	−	0.887570i	0.995672	+	0.0929341i	$0.0296246\pi$
$972$	−147561.	+	331427.i	−0.156185	+	0.350796i
$973$	504201.	−	2.37208e6i	0.532571	−	2.50555i
$974$	−261526.	−	1.23038e6i	−0.275674	−	1.29695i
$975$	282755.	−	125890.i	0.297441	−	0.132429i
$976$	75944.8	+	24676.0i	0.0797257	+	0.0259045i
$977$	−137372.	+	422787.i	−0.143916	+	0.442927i	−0.996870	−	0.0790585i	$-0.974809\pi$
$977$	−137372.	+	422787.i	−0.143916	+	0.442927i	0.852954	+	0.521986i	$0.174809\pi$
$978$	28172.0	+	63275.4i	0.0294538	+	0.0661542i
$979$	−1.30423e6	+	277223.i	−1.36078	+	0.289243i
$980$	−30484.3	−	6479.63i	−0.0317412	−	0.00674680i
$981$	−987741.	−	439771.i	−1.02637	−	0.456971i
$982$	−478166.	−	430543.i	−0.495856	−	0.446471i
$983$	−22155.7	−	2328.66i	−0.0229286	−	0.00240990i	0.0930572	−	0.995661i	$-0.470336\pi$
$983$	−22155.7	−	2328.66i	−0.0229286	−	0.00240990i	−0.115986	+	0.993251i	$0.537003\pi$
$984$	69290.5	−	95370.1i	0.0715621	−	0.0984968i
$985$	31831.2	−	3345.59i	0.0328080	−	0.00344826i
$986$	−85161.7	+	147504.i	−0.0875972	+	0.151723i
$987$	326447.	−	188474.i	0.335103	−	0.193472i
$988$	535824.	+	737499.i	0.548919	+	0.755523i
$989$	−68878.4	−	76497.2i	−0.0704191	−	0.0782083i
$990$	44223.6	−	14369.1i	0.0451215	−	0.0146609i
$991$			629151.i			0.640631i	0.947311	+	0.320315i	$0.103789\pi$
$991$			629151.i			0.640631i	−0.947311	+	0.320315i	$0.896211\pi$
$992$	−204182.	+	880066.i	−0.207489	+	0.894318i
$993$	−158066.			−0.160302
$994$	332231.	+	1.02250e6i	0.336254	+	1.03488i
$995$	28289.2	−	25471.7i	0.0285742	−	0.0257283i
$996$	−28467.3	+	20682.7i	−0.0286964	+	0.0208491i
$997$	895224.	+	1.55057e6i	0.900620	+	1.55992i	0.826691	+	0.562656i	$0.190220\pi$
$997$	895224.	+	1.55057e6i	0.900620	+	1.55992i	0.0739287	+	0.997264i	$0.476446\pi$
$998$	643983.	+	371804.i	0.646566	+	0.373295i
$999$	33111.7	+	315037.i	0.0331780	+	0.315668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.h.a.11.4	✓	80
31.17	odd	30	inner	31.5.h.a.17.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.h.a.11.4	✓	80	1.1	even	1	trivial
31.5.h.a.17.4	yes	80	31.17	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.848371 - 2.61102i) q^{2} +(1.78506 - 1.60727i) q^{3} +(6.84659 - 4.97434i) q^{4} +(0.623819 + 1.08049i) q^{5} +(-5.71100 - 3.29725i) q^{6} +(-7.64750 - 72.7611i) q^{7} +(-54.3336 - 39.4757i) q^{8} +(-7.86370 + 74.8181i) q^{9} +(2.29194 - 2.54546i) q^{10} +(73.3967 - 164.852i) q^{11} +(4.22643 - 19.8838i) q^{12} +(42.9718 + 202.166i) q^{13} +(-183.493 + 81.6962i) q^{14} +(2.85018 + 0.926081i) q^{15} +(-15.1340 + 46.5776i) q^{16} +(117.402 + 263.690i) q^{17} +(202.023 - 42.9413i) q^{18} +(509.785 + 108.358i) q^{19} +(9.64573 + 4.29456i) q^{20} +(-130.598 - 117.591i) q^{21} +(-492.698 - 51.7847i) q^{22} +(-572.667 + 788.208i) q^{23} +(-160.436 + 16.8626i) q^{24} +(311.722 - 539.918i) q^{25} +(491.404 - 283.712i) q^{26} +(220.578 + 303.599i) q^{27} +(-414.298 - 460.124i) q^{28} +(-204.415 + 66.4186i) q^{29} -8.22754i q^{30} +(217.191 - 936.135i) q^{31} -940.106 q^{32} +(-133.944 - 412.238i) q^{33} +(588.898 - 530.246i) q^{34} +(73.8467 - 53.6527i) q^{35} +(318.331 + 551.366i) q^{36} +(731.028 + 422.059i) q^{37} +(-149.562 - 1422.99i) q^{38} +(401.643 + 291.811i) q^{39} +(8.75858 - 83.3323i) q^{40} +(-488.964 + 543.050i) q^{41} +(-196.237 + 440.754i) q^{42} +(-21.9668 + 103.346i) q^{43} +(-317.511 - 1493.77i) q^{44} +(-85.7455 + 38.1763i) q^{45} +(2543.86 + 826.550i) q^{46} +(-662.829 + 2039.98i) q^{47} +(47.8478 + 107.468i) q^{48} +(-2887.16 + 613.685i) q^{49} +(-1674.19 - 355.860i) q^{50} +(633.390 + 282.004i) q^{51} +(1299.85 + 1170.39i) q^{52} +(702.492 + 73.8349i) q^{53} +(605.572 - 833.498i) q^{54} +(223.906 - 23.5335i) q^{55} +(-2456.78 + 4255.26i) q^{56} +(1084.16 - 625.937i) q^{57} +(346.840 + 477.385i) q^{58} +(-412.248 - 457.848i) q^{59} +(24.1207 - 7.83728i) q^{60} -1630.50i q^{61} +(-2628.52 + 227.101i) q^{62} +5503.99 q^{63} +(1039.70 + 3199.87i) q^{64} +(-191.631 + 172.546i) q^{65} +(-962.726 + 699.461i) q^{66} +(-3260.15 - 5646.75i) q^{67} +(2115.49 + 1221.38i) q^{68} +(244.622 + 2327.43i) q^{69} +(-202.738 - 147.298i) q^{70} +(559.505 - 5323.33i) q^{71} +(3380.76 - 3754.71i) q^{72} +(748.759 - 1681.74i) q^{73} +(481.821 - 2266.79i) q^{74} +(-311.354 - 1464.80i) q^{75} +(4029.30 - 1793.96i) q^{76} +(-12556.1 - 4079.72i) q^{77} +(421.181 - 1296.26i) q^{78} +(3763.34 + 8452.60i) q^{79} +(-59.7673 + 12.7039i) q^{80} +(-5078.78 - 1079.53i) q^{81} +(1832.74 + 815.986i) q^{82} +(-1286.37 - 1158.26i) q^{83} +(-1479.09 - 155.458i) q^{84} +(-211.675 + 291.346i) q^{85} +(288.474 - 30.3198i) q^{86} +(-258.140 + 447.112i) q^{87} +(-10495.5 + 6059.60i) q^{88} +(-4343.15 - 5977.84i) q^{89} +(172.423 + 191.495i) q^{90} +(14381.2 - 4672.74i) q^{91} +8245.18i q^{92} +(-1116.93 - 2020.14i) q^{93} +5888.74 q^{94} +(200.934 + 618.411i) q^{95} +(-1678.14 + 1511.00i) q^{96} +(-2897.95 + 2105.48i) q^{97} +(4051.72 + 7017.79i) q^{98} +(11756.7 + 6787.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 16 q^{3} - 138 q^{4} - q^{5} - 9 q^{6} + 288 q^{7} - 221 q^{8} - 182 q^{9} + 102 q^{10} - 49 q^{11} - 159 q^{12} + 527 q^{13} - 740 q^{14} + 1060 q^{15} - 1970 q^{16} + 848 q^{17} + 3 q^{18}+ \cdots + 75228 q^{99}+O(q^{100}) \) 80 * q - 6 * q^2 - 16 * q^3 - 138 * q^4 - q^5 - 9 * q^6 + 288 * q^7 - 221 * q^8 - 182 * q^9 + 102 * q^10 - 49 * q^11 - 159 * q^12 + 527 * q^13 - 740 * q^14 + 1060 * q^15 - 1970 * q^16 + 848 * q^17 + 3 * q^18 + 1534 * q^19 + 1165 * q^20 + 1367 * q^21 + 4579 * q^22 - 1375 * q^23 - 3828 * q^24 - 5997 * q^25 - 2547 * q^26 - 3235 * q^27 - 1564 * q^28 - 1150 * q^29 - 3587 * q^31 + 15718 * q^32 - 5029 * q^33 + 5958 * q^34 + 4959 * q^35 + 13555 * q^36 + 3462 * q^37 + 6118 * q^38 - 8143 * q^39 - 13011 * q^40 - 7290 * q^41 - 24735 * q^42 + 4687 * q^43 + 17051 * q^44 - 6093 * q^45 - 16530 * q^46 - 4302 * q^47 + 40344 * q^48 + 14300 * q^49 + 30081 * q^50 + 1348 * q^51 - 14433 * q^52 + 17996 * q^53 - 42200 * q^54 - 5289 * q^55 - 32470 * q^56 - 35847 * q^57 - 38475 * q^58 + 3552 * q^59 - 26585 * q^60 - 6327 * q^62 + 35814 * q^63 + 231 * q^64 + 18280 * q^65 + 85992 * q^66 + 2185 * q^67 + 56694 * q^68 + 57836 * q^69 + 6338 * q^70 - 3708 * q^71 - 25127 * q^72 + 5344 * q^73 + 5247 * q^74 + 13921 * q^75 - 10354 * q^76 - 37000 * q^77 - 98345 * q^78 + 53300 * q^79 + 65286 * q^80 + 20439 * q^81 - 26142 * q^82 - 59542 * q^83 - 77120 * q^84 + 4525 * q^85 - 100990 * q^86 - 55761 * q^87 - 82191 * q^88 - 26395 * q^89 - 61689 * q^90 - 12450 * q^91 + 9029 * q^93 + 67112 * q^94 - 3972 * q^95 + 210490 * q^96 + 5883 * q^97 + 107722 * q^98 + 75228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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