LMFDB - Embedded newform 138.5.h.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,5,Mod(7,138)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	138.h (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.2650549056$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	138.19
Dual form			138.5.h.a.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17497 - 2.57283i) q^{2} +(-4.98567 + 1.46393i) q^{3} +(-5.23889 + 6.04600i) q^{4} +(7.54204 - 11.7356i) q^{5} +(9.62445 + 11.1072i) q^{6} +(-12.2007 + 1.75419i) q^{7} +(21.7108 + 6.37488i) q^{8} +(22.7138 - 14.5973i) q^{9} +O(q^{10})$	\(q+(-1.17497 - 2.57283i) q^{2} +(-4.98567 + 1.46393i) q^{3} +(-5.23889 + 6.04600i) q^{4} +(7.54204 - 11.7356i) q^{5} +(9.62445 + 11.1072i) q^{6} +(-12.2007 + 1.75419i) q^{7} +(21.7108 + 6.37488i) q^{8} +(22.7138 - 14.5973i) q^{9} +(-39.0554 - 5.61533i) q^{10} +(-144.954 - 66.1982i) q^{11} +(17.2685 - 37.8127i) q^{12} +(-20.3922 + 141.831i) q^{13} +(18.8487 + 29.3291i) q^{14} +(-20.4220 + 69.5510i) q^{15} +(-9.10815 - 63.3486i) q^{16} +(-64.5945 + 55.9715i) q^{17} +(-64.2445 - 41.2874i) q^{18} +(355.496 + 308.039i) q^{19} +(31.4418 + 107.081i) q^{20} +(58.2605 - 26.6067i) q^{21} +450.722i q^{22} +(515.098 - 120.478i) q^{23} -117.576 q^{24} +(178.792 + 391.499i) q^{25} +(388.867 - 114.182i) q^{26} +(-91.8744 + 106.029i) q^{27} +(53.3120 - 82.9552i) q^{28} +(818.014 + 944.038i) q^{29} +(202.938 - 29.1781i) q^{30} +(-1005.38 - 295.208i) q^{31} +(-152.283 + 97.8664i) q^{32} +(819.601 + 117.841i) q^{33} +(219.902 + 100.426i) q^{34} +(-71.4313 + 156.413i) q^{35} +(-30.7400 + 213.801i) q^{36} +(1052.14 + 1637.16i) q^{37} +(374.833 - 1276.57i) q^{38} +(-105.961 - 736.976i) q^{39} +(238.557 - 206.711i) q^{40} +(1218.06 + 782.802i) q^{41} +(-136.909 - 118.632i) q^{42} +(-170.993 - 582.349i) q^{43} +(1159.63 - 529.585i) q^{44} -376.655i q^{45} +(-915.195 - 1183.70i) q^{46} +4020.99 q^{47} +(138.148 + 302.502i) q^{48} +(-2157.96 + 633.635i) q^{49} +(797.184 - 920.000i) q^{50} +(240.109 - 373.617i) q^{51} +(-750.678 - 866.328i) q^{52} +(-3676.46 + 528.595i) q^{53} +(380.743 + 111.796i) q^{54} +(-1870.12 + 1201.86i) q^{55} +(-276.069 - 39.6928i) q^{56} +(-2223.33 - 1015.36i) q^{57} +(1467.71 - 3213.83i) q^{58} +(-510.720 + 3552.14i) q^{59} +(-313.517 - 487.841i) q^{60} +(146.583 - 499.217i) q^{61} +(421.780 + 2933.54i) q^{62} +(-251.517 + 217.941i) q^{63} +(430.722 + 276.808i) q^{64} +(1510.68 + 1309.01i) q^{65} +(-659.823 - 2247.15i) q^{66} +(1143.96 - 522.430i) q^{67} -683.766i q^{68} +(-2391.74 + 1354.73i) q^{69} +486.353 q^{70} +(330.477 + 723.644i) q^{71} +(586.193 - 172.122i) q^{72} +(-5895.70 + 6804.00i) q^{73} +(2975.90 - 4630.60i) q^{74} +(-1464.52 - 1690.15i) q^{75} +(-3724.80 + 535.546i) q^{76} +(1884.66 + 553.385i) q^{77} +(-1771.61 + 1138.55i) q^{78} +(-8771.06 - 1261.09i) q^{79} +(-812.130 - 370.887i) q^{80} +(302.838 - 663.122i) q^{81} +(582.825 - 4053.64i) q^{82} +(-3239.40 - 5040.61i) q^{83} +(-144.356 + 491.632i) q^{84} +(169.687 + 1180.20i) q^{85} +(-1297.37 + 1124.18i) q^{86} +(-5460.35 - 3509.15i) q^{87} +(-2725.06 - 2361.28i) q^{88} +(-208.821 - 711.179i) q^{89} +(-969.068 + 442.559i) q^{90} -1766.20i q^{91} +(-1970.13 + 3745.45i) q^{92} +5444.68 q^{93} +(-4724.55 - 10345.3i) q^{94} +(6296.19 - 1848.73i) q^{95} +(615.965 - 710.861i) q^{96} +(1095.34 - 1704.39i) q^{97} +(4165.78 + 4807.57i) q^{98} +(-4258.77 + 612.319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) $ 160 * q - 128 * q^4 - 432 * q^9	$ 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) $ 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.17497	−	2.57283i	−0.293743	−	0.643207i
$2$	−1.17497	−	2.57283i	−0.293743	−	0.643207i
$3$	−4.98567	+	1.46393i	−0.553964	+	0.162658i
$3$	−4.98567	+	1.46393i	−0.553964	+	0.162658i
$4$	−5.23889	+	6.04600i	−0.327430	+	0.377875i
$5$	7.54204	−	11.7356i	0.301681	−	0.469426i	−0.657007	−	0.753885i	$-0.728178\pi$
$5$	7.54204	−	11.7356i	0.301681	−	0.469426i	0.958688	+	0.284459i	$0.0918140\pi$
$6$	9.62445	+	11.1072i	0.267346	+	0.308533i
$7$	−12.2007	+	1.75419i	−0.248993	+	0.0357998i	−0.265681	−	0.964061i	$-0.585597\pi$
$7$	−12.2007	+	1.75419i	−0.248993	+	0.0357998i	0.0166881	+	0.999861i	$0.494688\pi$
$8$	21.7108	+	6.37488i	0.339232	+	0.0996075i
$9$	22.7138	−	14.5973i	0.280418	−	0.180214i
$10$	−39.0554	−	5.61533i	−0.390554	−	0.0561533i
$11$	−144.954	−	66.1982i	−1.19796	−	0.547092i	−0.286345	−	0.958127i	$-0.592440\pi$
$11$	−144.954	−	66.1982i	−1.19796	−	0.547092i	−0.911620	+	0.411034i	$0.865168\pi$
$12$	17.2685	−	37.8127i	0.119920	−	0.262588i
$13$	−20.3922	+	141.831i	−0.120664	+	0.839237i	0.836143	+	0.548512i	$0.184806\pi$
$13$	−20.3922	+	141.831i	−0.120664	+	0.839237i	−0.956807	+	0.290725i	$0.906104\pi$
$14$	18.8487	+	29.3291i	0.0961666	+	0.149638i
$15$	−20.4220	+	69.5510i	−0.0907645	+	0.309116i
$16$	−9.10815	−	63.3486i	−0.0355787	−	0.247455i
$17$	−64.5945	+	55.9715i	−0.223510	+	0.193673i	−0.759417	−	0.650605i	$-0.774516\pi$
$17$	−64.5945	+	55.9715i	−0.223510	+	0.193673i	0.535906	+	0.844278i	$0.319970\pi$
$18$	−64.2445	−	41.2874i	−0.198285	−	0.127430i
$19$	355.496	+	308.039i	0.984752	+	0.853293i	0.989181	−	0.146697i	$-0.0468644\pi$
$19$	355.496	+	308.039i	0.984752	+	0.853293i	−0.00442911	+	0.999990i	$0.501410\pi$
$20$	31.4418	+	107.081i	0.0786044	+	0.267702i
$21$	58.2605	−	26.6067i	0.132110	−	0.0603326i
$22$			450.722i			0.931244i
$23$	515.098	−	120.478i	0.973720	−	0.227747i
$23$	515.098	−	120.478i	0.973720	−	0.227747i
$24$	−117.576			−0.204124
$25$	178.792	+	391.499i	0.286066	+	0.626398i
$26$	388.867	−	114.182i	0.575247	−	0.168908i
$27$	−91.8744	+	106.029i	−0.126028	+	0.145444i
$28$	53.3120	−	82.9552i	0.0680001	−	0.105810i
$29$	818.014	+	944.038i	0.972668	+	1.12252i	0.992442	+	0.122714i	$0.0391598\pi$
$29$	818.014	+	944.038i	0.972668	+	1.12252i	−0.0197742	+	0.999804i	$0.506295\pi$
$30$	202.938	−	29.1781i	0.225487	−	0.0324201i
$31$	−1005.38	−	295.208i	−1.04619	−	0.307188i	−0.286910	−	0.957957i	$-0.592628\pi$
$31$	−1005.38	−	295.208i	−1.04619	−	0.307188i	−0.759275	+	0.650770i	$0.774446\pi$
$32$	−152.283	+	97.8664i	−0.148714	+	0.0955727i
$33$	819.601	+	117.841i	0.752618	+	0.108210i
$34$	219.902	+	100.426i	0.190226	+	0.0868734i
$35$	−71.4313	+	156.413i	−0.0583113	+	0.127684i
$36$	−30.7400	+	213.801i	−0.0237191	+	0.164970i
$37$	1052.14	+	1637.16i	0.768547	+	1.19588i	0.976028	+	0.217644i	$0.0698371\pi$
$37$	1052.14	+	1637.16i	0.768547	+	1.19588i	−0.207481	+	0.978239i	$0.566526\pi$
$38$	374.833	−	1276.57i	0.259580	−	0.884048i
$39$	−105.961	−	736.976i	−0.0696654	−	0.484534i
$40$	238.557	−	206.711i	0.149098	−	0.129194i
$41$	1218.06	+	782.802i	0.724607	+	0.465677i	0.850237	−	0.526401i	$-0.176459\pi$
$41$	1218.06	+	782.802i	0.724607	+	0.465677i	−0.125630	+	0.992077i	$0.540095\pi$
$42$	−136.909	−	118.632i	−0.0776127	−	0.0672518i
$43$	−170.993	−	582.349i	−0.0924787	−	0.314954i	0.900242	−	0.435389i	$-0.143389\pi$
$43$	−170.993	−	582.349i	−0.0924787	−	0.314954i	−0.992721	+	0.120435i	$0.961571\pi$
$44$	1159.63	−	529.585i	0.598982	−	0.273546i
$45$		−	376.655i		−	0.186002i
$46$	−915.195	−	1183.70i	−0.432512	−	0.559404i
$47$	4020.99			1.82028			0.910138	−	0.414306i	$-0.135976\pi$
$47$	4020.99			1.82028			0.910138	+	0.414306i	$0.135976\pi$
$48$	138.148	+	302.502i	0.0599600	+	0.131294i
$49$	−2157.96	+	633.635i	−0.898777	+	0.263905i
$50$	797.184	−	920.000i	0.318874	−	0.368000i
$51$	240.109	−	373.617i	0.0923141	−	0.143644i
$52$	−750.678	−	866.328i	−0.277618	−	0.320388i
$53$	−3676.46	+	528.595i	−1.30881	+	0.188179i	−0.761181	−	0.648539i	$-0.775380\pi$
$53$	−3676.46	+	528.595i	−1.30881	+	0.188179i	−0.547633	+	0.836718i	$0.684471\pi$
$54$	380.743	+	111.796i	0.130570	+	0.0383389i
$55$	−1870.12	+	1201.86i	−0.618223	+	0.397308i
$56$	−276.069	−	39.6928i	−0.0880323	−	0.0126571i
$57$	−2223.33	−	1015.36i	−0.684312	−	0.312515i
$58$	1467.71	−	3213.83i	0.436298	−	0.955358i
$59$	−510.720	+	3552.14i	−0.146717	+	1.02044i	0.774830	+	0.632169i	$0.217835\pi$
$59$	−510.720	+	3552.14i	−0.146717	+	1.02044i	−0.921547	+	0.388267i	$0.873074\pi$
$60$	−313.517	−	487.841i	−0.0870879	−	0.135511i
$61$	146.583	−	499.217i	0.0393935	−	0.134162i	−0.937448	−	0.348124i	$-0.886819\pi$
$61$	146.583	−	499.217i	0.0393935	−	0.134162i	0.976842	+	0.213962i	$0.0686369\pi$
$62$	421.780	+	2933.54i	0.109724	+	0.763148i
$63$	−251.517	+	217.941i	−0.0633705	+	0.0549108i
$64$	430.722	+	276.808i	0.105157	+	0.0675801i
$65$	1510.68	+	1309.01i	0.357557	+	0.309825i
$66$	−659.823	−	2247.15i	−0.151475	−	0.515875i
$67$	1143.96	−	522.430i	0.254837	−	0.116380i	−0.283901	−	0.958854i	$-0.591629\pi$
$67$	1143.96	−	522.430i	0.254837	−	0.116380i	0.538738	+	0.842474i	$0.318901\pi$
$68$		−	683.766i		−	0.147873i
$69$	−2391.74	+	1354.73i	−0.502360	+	0.284547i
$70$	486.353			0.0992556
$71$	330.477	+	723.644i	0.0655579	+	0.143552i	0.939575	−	0.342344i	$-0.111221\pi$
$71$	330.477	+	723.644i	0.0655579	+	0.143552i	−0.874017	+	0.485896i	$0.838494\pi$
$72$	586.193	−	172.122i	0.113077	−	0.0332025i
$73$	−5895.70	+	6804.00i	−1.10634	+	1.27679i	−0.148683	+	0.988885i	$0.547504\pi$
$73$	−5895.70	+	6804.00i	−1.10634	+	1.27679i	−0.957660	+	0.287903i	$0.907042\pi$
$74$	2975.90	−	4630.60i	0.543445	−	0.845617i
$75$	−1464.52	−	1690.15i	−0.260359	−	0.300471i
$76$	−3724.80	+	535.546i	−0.644876	+	0.0927191i
$77$	1884.66	+	553.385i	0.317871	+	0.0933353i
$78$	−1771.61	+	1138.55i	−0.291192	+	0.187138i
$79$	−8771.06	−	1261.09i	−1.40539	−	0.202065i	−0.602468	−	0.798143i	$-0.705816\pi$
$79$	−8771.06	−	1261.09i	−1.40539	−	0.202065i	−0.802926	+	0.596078i	$0.796725\pi$
$80$	−812.130	−	370.887i	−0.126895	−	0.0579511i
$81$	302.838	−	663.122i	0.0461572	−	0.101070i
$82$	582.825	−	4053.64i	0.0866784	−	0.602861i
$83$	−3239.40	−	5040.61i	−0.470228	−	0.731690i	0.522425	−	0.852686i	$-0.325028\pi$
$83$	−3239.40	−	5040.61i	−0.470228	−	0.731690i	−0.992653	+	0.120996i	$0.961391\pi$
$84$	−144.356	+	491.632i	−0.0204586	+	0.0696757i
$85$	169.687	+	1180.20i	0.0234860	+	0.163349i
$86$	−1297.37	+	1124.18i	−0.175415	+	0.151998i
$87$	−5460.35	−	3509.15i	−0.721410	−	0.463622i
$88$	−2725.06	−	2361.28i	−0.351893	−	0.304917i
$89$	−208.821	−	711.179i	−0.0263630	−	0.0897840i	0.945261	−	0.326316i	$-0.105807\pi$
$89$	−208.821	−	711.179i	−0.0263630	−	0.0897840i	−0.971624	+	0.236532i	$0.923989\pi$
$90$	−969.068	+	442.559i	−0.119638	+	0.0546369i
$91$		−	1766.20i		−	0.213284i
$92$	−1970.13	+	3745.45i	−0.232766	+	0.442516i
$93$	5444.68			0.629515
$94$	−4724.55	−	10345.3i	−0.534693	−	1.17081i
$95$	6296.19	−	1848.73i	0.697639	−	0.204845i
$96$	615.965	−	710.861i	0.0668364	−	0.0771334i
$97$	1095.34	−	1704.39i	0.116414	−	0.181144i	−0.778157	−	0.628070i	$-0.783845\pi$
$97$	1095.34	−	1704.39i	0.116414	−	0.181144i	0.894571	+	0.446926i	$0.147481\pi$
$98$	4165.78	+	4807.57i	0.433755	+	0.500580i
$99$	−4258.77	+	612.319i	−0.434524	+	0.0624751i
$100$	−3303.67	−	970.045i	−0.330367	−	0.0970045i
$101$	14954.5	−	9610.68i	1.46599	−	0.942131i	0.467682	−	0.883897i	$-0.345089\pi$
$101$	14954.5	−	9610.68i	1.46599	−	0.942131i	0.998303	−	0.0582347i	$-0.0185472\pi$
$102$	−1243.37	−	178.770i	−0.119509	−	0.0171828i
$103$	−1540.74	−	703.631i	−0.145229	−	0.0663240i	0.341475	−	0.939891i	$-0.389074\pi$
$103$	−1540.74	−	703.631i	−0.145229	−	0.0663240i	−0.486704	+	0.873567i	$0.661801\pi$
$104$	−1346.89	+	2949.28i	−0.124527	+	0.272677i
$105$	127.156	−	884.392i	0.0115335	−	0.0802170i
$106$	5679.72	+	8837.82i	0.505493	+	0.786562i
$107$	−1162.65	+	3959.62i	−0.101550	+	0.345848i	−0.994557	−	0.104195i	$-0.966773\pi$
$107$	−1162.65	+	3959.62i	−0.101550	+	0.345848i	0.893007	+	0.450043i	$0.148592\pi$
$108$	−159.730	−	1110.94i	−0.0136943	−	0.0952456i
$109$	408.492	−	353.960i	0.0343819	−	0.0297921i	−0.637500	−	0.770450i	$-0.720032\pi$
$109$	408.492	−	353.960i	0.0343819	−	0.0297921i	0.671882	+	0.740658i	$0.265486\pi$
$110$	5289.51	+	3399.36i	0.437150	+	0.280939i
$111$	−7642.32	−	6622.10i	−0.620268	−	0.537465i
$112$	222.251	+	756.917i	0.0177177	+	0.0603410i
$113$	−7964.29	+	3637.17i	−0.623721	+	0.284844i	−0.702098	−	0.712080i	$-0.747753\pi$
$113$	−7964.29	+	3637.17i	−0.623721	+	0.284844i	0.0783774	+	0.996924i	$0.475026\pi$
$114$			6913.26i			0.531953i
$115$	2471.00	−	6953.66i	0.186843	−	0.525796i
$116$	−9993.13			−0.742652
$117$	1607.17	+	3519.20i	0.117406	+	0.257082i
$118$	9739.12	−	2859.66i	0.699449	−	0.205377i
$119$	689.911	−	796.200i	0.0487191	−	0.0562248i
$120$	−886.759	+	1379.82i	−0.0615805	+	0.0958211i
$121$	7041.57	+	8126.41i	0.480949	+	0.555045i
$122$	−1456.63	+	209.432i	−0.0978655	+	0.0140709i
$123$	−7218.83	−	2119.64i	−0.477152	−	0.140104i
$124$	7051.92	−	4531.99i	0.458632	−	0.294745i
$125$	14573.1	+	2095.29i	0.932676	+	0.134099i
$126$	856.251	+	391.037i	0.0539337	+	0.0246307i
$127$	2141.02	−	4688.18i	0.132743	−	0.290667i	−0.831575	−	0.555412i	$-0.812560\pi$
$127$	2141.02	−	4688.18i	0.132743	−	0.290667i	0.964319	+	0.264745i	$0.0852877\pi$
$128$	206.094	−	1433.41i	0.0125790	−	0.0874887i
$129$	1705.03	+	2653.08i	0.102460	+	0.159430i
$130$	1592.86	−	5424.77i	0.0942518	−	0.320992i
$131$	968.180	+	6733.84i	0.0564174	+	0.392392i	0.998391	+	0.0567048i	$0.0180594\pi$
$131$	968.180	+	6733.84i	0.0564174	+	0.392392i	−0.941974	+	0.335687i	$0.891032\pi$
$132$	−5006.26	+	4337.95i	−0.287320	+	0.248964i
$133$	−4877.64	−	3134.67i	−0.275744	−	0.177210i
$134$	−2688.24	−	2329.38i	−0.149713	−	0.129727i
$135$	551.395	+	1877.88i	0.0302548	+	0.103039i
$136$	−1759.21	+	803.405i	−0.0951131	+	0.0434367i
$137$			8305.68i			0.442521i	0.975215	+	0.221261i	$0.0710171\pi$
$137$			8305.68i			0.442521i	−0.975215	+	0.221261i	$0.928983\pi$
$138$	6295.71	+	4561.76i	0.330588	+	0.239538i
$139$	20281.8			1.04973			0.524863	−	0.851187i	$-0.324116\pi$
$139$	20281.8			1.04973			0.524863	+	0.851187i	$0.324116\pi$
$140$	−571.450	−	1251.30i	−0.0291556	−	0.0638419i
$141$	−20047.3	+	5886.43i	−1.00837	+	0.296083i
$142$	1473.51	−	1700.52i	0.0730763	−	0.0843346i
$143$	12344.9	−	19209.0i	0.603691	−	0.939362i
$144$	−1131.60	−	1305.94i	−0.0545717	−	0.0629791i
$145$	17248.4	−	2479.94i	0.820375	−	0.117952i
$146$	24432.8	+	7174.12i	1.14622	+	0.336560i
$147$	9831.30	−	6318.20i	0.454963	−	0.292387i
$148$	−15410.3	−	2215.67i	−0.703540	−	0.101154i
$149$	24000.4	+	10960.6i	1.08105	+	0.493698i	0.874643	−	0.484768i	$-0.161096\pi$
$149$	24000.4	+	10960.6i	1.08105	+	0.493698i	0.206406	+	0.978466i	$0.433823\pi$
$150$	−2627.69	+	5753.83i	−0.116786	+	0.255726i
$151$	−5238.45	+	36434.2i	−0.229746	+	1.59792i	0.469429	+	0.882970i	$0.344460\pi$
$151$	−5238.45	+	36434.2i	−0.229746	+	1.59792i	−0.699175	+	0.714951i	$0.746449\pi$
$152$	5754.40	+	8954.02i	0.249065	+	0.387553i
$153$	−650.157	+	2214.23i	−0.0277738	+	0.0945889i
$154$	−790.652	−	5499.11i	−0.0333383	−	0.231873i
$155$	−11047.1	+	9572.36i	−0.459817	+	0.398433i
$156$	5010.87	+	3220.29i	0.205904	+	0.132326i
$157$	−10941.1	−	9480.48i	−0.443874	−	0.384619i	0.404050	−	0.914737i	$-0.367602\pi$
$157$	−10941.1	−	9480.48i	−0.443874	−	0.384619i	−0.847924	+	0.530118i	$0.822148\pi$
$158$	7061.18	+	24048.2i	0.282855	+	0.963314i
$159$	17555.8	−	8017.47i	0.694427	−	0.317134i
$160$			2525.25i			0.0986427i
$161$	−6073.19	+	2373.50i	−0.234296	+	0.0915665i
$162$	−2061.92			−0.0785674
$163$	−9715.26	−	21273.5i	−0.365662	−	0.800687i	−0.999627	−	0.0273254i	$-0.991301\pi$
$163$	−9715.26	−	21273.5i	−0.365662	−	0.800687i	0.633965	−	0.773362i	$-0.281426\pi$
$164$	−11114.1	+	3263.40i	−0.413226	+	0.121334i
$165$	7564.40	−	8729.78i	0.277847	−	0.320653i
$166$	−9162.42	+	14257.0i	−0.332502	+	0.517383i
$167$	−14392.9	−	16610.3i	−0.516079	−	0.595587i	0.436566	−	0.899672i	$-0.356195\pi$
$167$	−14392.9	−	16610.3i	−0.516079	−	0.595587i	−0.952645	+	0.304086i	$0.901649\pi$
$168$	1434.50	−	206.250i	0.0508255	−	0.00730760i
$169$	7703.86	+	2262.06i	0.269734	+	0.0792010i
$170$	2837.07	−	1823.27i	0.0981683	−	0.0630890i
$171$	12571.2	+	1807.47i	0.429917	+	0.0618127i
$172$	4416.69	+	2017.04i	0.149293	+	0.0681800i
$173$	−9931.04	+	21745.9i	−0.331820	+	0.726584i	−0.999846	−	0.0175536i	$-0.994412\pi$
$173$	−9931.04	+	21745.9i	−0.331820	+	0.726584i	0.668026	+	0.744138i	$0.267139\pi$
$174$	−2612.69	+	18171.7i	−0.0862959	+	0.600201i
$175$	−2868.14	−	4462.91i	−0.0936535	−	0.145728i
$176$	−2873.30	+	9785.55i	−0.0927589	+	0.315908i
$177$	−2653.78	−	18457.5i	−0.0847069	−	0.589149i
$178$	−1584.38	+	1372.88i	−0.0500058	+	0.0433302i
$179$	−29962.1	−	19255.5i	−0.935117	−	0.600963i	−0.0181107	−	0.999836i	$-0.505765\pi$
$179$	−29962.1	−	19255.5i	−0.935117	−	0.600963i	−0.917006	+	0.398873i	$0.869402\pi$
$180$	2277.25	+	1973.25i	0.0702856	+	0.0609028i
$181$	13648.0	+	46480.9i	0.416593	+	1.41879i	0.854352	+	0.519694i	$0.173954\pi$
$181$	13648.0	+	46480.9i	0.416593	+	1.41879i	−0.437759	+	0.899092i	$0.644228\pi$
$182$	−4544.14	+	2075.24i	−0.137186	+	0.0626506i
$183$			2703.52i			0.0807286i
$184$	11951.2	+	668.001i	0.353002	+	0.0197306i
$185$	27148.4			0.793234
$186$	−6397.34	−	14008.2i	−0.184916	−	0.404909i
$187$	13068.4	−	3837.23i	0.373714	−	0.109732i
$188$	−21065.5	+	24310.9i	−0.596014	+	0.687836i
$189$	934.934	−	1454.79i	0.0261732	−	0.0407263i
$190$	−12154.3	−	14026.8i	−0.336684	−	0.388554i
$191$	−6363.43	+	914.923i	−0.174431	+	0.0250794i	−0.228977	−	0.973432i	$-0.573538\pi$
$191$	−6363.43	+	914.923i	−0.174431	+	0.0250794i	0.0545456	+	0.998511i	$0.482629\pi$
$192$	−2552.66	−	749.530i	−0.0692454	−	0.0203323i
$193$	−10651.2	+	6845.11i	−0.285946	+	0.183766i	−0.675749	−	0.737132i	$-0.736180\pi$
$193$	−10651.2	+	6845.11i	−0.285946	+	0.183766i	0.389803	+	0.920898i	$0.372543\pi$
$194$	−5672.09	−	815.523i	−0.150709	−	0.0216687i
$195$	−9448.05	−	4314.78i	−0.248469	−	0.113472i
$196$	7474.37	−	16366.6i	0.194564	−	0.426036i
$197$	6085.99	−	42329.0i	0.156819	−	1.09070i	−0.747629	−	0.664117i	$-0.768808\pi$
$197$	6085.99	−	42329.0i	0.156819	−	1.09070i	0.904448	−	0.426584i	$-0.140283\pi$
$198$	6579.32	+	10237.6i	0.167823	+	0.261137i
$199$	−15606.9	+	53152.2i	−0.394104	+	1.34219i	0.488700	+	0.872452i	$0.337471\pi$
$199$	−15606.9	+	53152.2i	−0.394104	+	1.34219i	−0.882804	+	0.469742i	$0.844347\pi$
$200$	1385.96	+	9639.54i	0.0346489	+	0.240989i
$201$	−4938.62	+	4279.34i	−0.122240	+	0.105922i
$202$	−42297.8	−	27183.1i	−1.03661	−	0.666187i
$203$	−11636.3	−	10082.9i	−0.282374	−	0.244678i
$204$	1000.98	+	3409.03i	0.0240528	+	0.0819164i
$205$	18373.4	−	8390.84i	0.437201	−	0.199663i
$206$			4790.80i			0.112895i
$207$	9941.20	−	10255.6i	0.232005	−	0.239342i
$208$	9170.53			0.211967
$209$	−31138.8	−	68184.5i	−0.712869	−	1.56096i
$210$	−2424.79	+	711.984i	−0.0549840	+	0.0161448i
$211$	−10674.6	+	12319.1i	−0.239765	+	0.276704i	−0.862860	−	0.505442i	$-0.831329\pi$
$211$	−10674.6	+	12319.1i	−0.239765	+	0.276704i	0.623095	+	0.782146i	$0.285875\pi$
$212$	16064.7	−	24997.1i	0.357438	−	0.556184i
$213$	−2707.01	−	3124.06i	−0.0596666	−	0.0688589i
$214$	11553.5	−	1661.14i	0.252282	−	0.0362726i
$215$	−8123.87	−	2385.38i	−0.175746	−	0.0516038i
$216$	−2670.59	+	1716.29i	−0.0572401	+	0.0367859i
$217$	12784.2	+	1838.09i	0.271490	+	0.0390344i
$218$	−1390.64	−	635.086i	−0.0292619	−	0.0133635i
$219$	19433.5	−	42553.4i	0.405193	−	0.887250i
$220$	2530.95	−	17603.1i	0.0522924	−	0.363701i
$221$	−6621.27	−	10302.9i	−0.135568	−	0.210948i
$222$	−8058.03	+	27443.1i	−0.163502	+	0.556837i
$223$	−7562.06	−	52595.3i	−0.152065	−	1.05764i	−0.912751	−	0.408517i	$-0.866046\pi$
$223$	−7562.06	−	52595.3i	−0.152065	−	1.05764i	0.760685	−	0.649121i	$-0.224863\pi$
$224$	1686.28	−	1461.17i	0.0336073	−	0.0291209i
$225$	9775.87	+	6282.57i	0.193104	+	0.124100i
$226$	18715.6	+	16217.2i	0.366427	+	0.317511i
$227$	−25382.0	−	86443.1i	−0.492577	−	1.67756i	−0.712200	−	0.701977i	$-0.752301\pi$
$227$	−25382.0	−	86443.1i	−0.492577	−	1.67756i	0.219623	−	0.975585i	$-0.429517\pi$
$228$	17786.6	−	8122.89i	0.342156	−	0.156257i
$229$			57476.7i			1.09603i	0.836470	+	0.548013i	$0.184616\pi$
$229$			57476.7i			1.09603i	−0.836470	+	0.548013i	$0.815384\pi$
$230$	−20793.9	+	1812.89i	−0.393080	+	0.0342702i
$231$	−10206.4			−0.191271
$232$	11741.6	+	25710.6i	0.218149	+	0.477679i
$233$	−316.096	+	92.8141i	−0.00582247	+	0.00170963i	−0.284642	−	0.958634i	$-0.591875\pi$
$233$	−316.096	+	92.8141i	−0.00582247	+	0.00170963i	0.278820	+	0.960343i	$0.410057\pi$
$234$	7165.93	−	8269.92i	0.130870	−	0.151032i
$235$	30326.4	−	47188.9i	0.549143	−	0.854484i
$236$	−18800.6	−	21697.1i	−0.337558	−	0.389562i
$237$	45575.8	−	6552.81i	0.811405	−	0.116662i
$238$	−2859.11	−	839.511i	−0.0504751	−	0.0148208i
$239$	12756.2	−	8197.89i	0.223318	−	0.143518i	−0.424198	−	0.905569i	$-0.639444\pi$
$239$	12756.2	−	8197.89i	0.223318	−	0.143518i	0.647517	+	0.762051i	$0.275808\pi$
$240$	4591.96	+	660.225i	0.0797216	+	0.0114622i
$241$	3715.18	+	1696.67i	0.0639655	+	0.0292121i	0.447141	−	0.894464i	$-0.352442\pi$
$241$	3715.18	+	1696.67i	0.0639655	+	0.0292121i	−0.383175	+	0.923676i	$0.625170\pi$
$242$	12634.2	−	27665.1i	0.215733	−	0.472390i
$243$	−539.088	+	3749.44i	−0.00912950	+	0.0634971i
$244$	2250.33	+	3501.58i	0.0377978	+	0.0588145i
$245$	−8839.33	+	30104.0i	−0.147261	+	0.501524i
$246$	3028.45	+	21063.3i	0.0500438	+	0.348062i
$247$	−50938.8	+	44138.7i	−0.834939	+	0.723479i
$248$	−19945.8	−	12818.4i	−0.324301	−	0.208416i
$249$	23529.7	+	20388.6i	0.379505	+	0.328843i
$250$	−11732.1	−	39955.9i	−0.187714	−	0.639294i
$251$	−62797.0	+	28678.4i	−0.996761	+	0.455206i	−0.845895	−	0.533349i	$-0.820933\pi$
$251$	−62797.0	+	28678.4i	−0.996761	+	0.455206i	−0.150866	+	0.988554i	$0.548206\pi$
$252$		−	2662.44i		−	0.0419256i
$253$	−82640.8	−	16634.7i	−1.29108	−	0.259881i
$254$	−14577.5			−0.225952
$255$	−2573.72	−	5635.66i	−0.0395805	−	0.0866692i
$256$	−3930.08	+	1153.98i	−0.0599683	+	0.0176083i
$257$	−22096.3	+	25500.5i	−0.334544	+	0.386085i	−0.897951	−	0.440095i	$-0.854945\pi$
$257$	−22096.3	+	25500.5i	−0.334544	+	0.386085i	0.563407	+	0.826180i	$0.309490\pi$
$258$	4822.56	−	7504.04i	0.0724499	−	0.112734i
$259$	−15708.7	−	18128.8i	−0.234175	−	0.270253i
$260$	−15828.6	+	2275.80i	−0.234150	+	0.0336657i
$261$	32360.6	+	9501.94i	0.475047	+	0.139486i
$262$	16187.4	−	10403.0i	0.235817	−	0.151550i
$263$	−38907.1	−	5593.99i	−0.562493	−	0.0808742i	−0.144797	−	0.989461i	$-0.546253\pi$
$263$	−38907.1	−	5593.99i	−0.562493	−	0.0808742i	−0.417695	+	0.908587i	$0.637162\pi$
$264$	17043.0	+	7783.28i	0.244534	+	0.111675i
$265$	−21524.6	+	47132.3i	−0.306509	+	0.671161i
$266$	−2333.88	+	16232.5i	−0.0329849	+	0.229415i
$267$	2082.23	+	3240.01i	0.0292082	+	0.0454489i
$268$	−2834.48	+	9653.34i	−0.0394642	+	0.134403i
$269$	10429.8	+	72540.9i	0.144136	+	1.00249i	0.925591	+	0.378525i	$0.123569\pi$
$269$	10429.8	+	72540.9i	0.144136	+	1.00249i	−0.781455	+	0.623961i	$0.785522\pi$
$270$	4183.58	−	3625.09i	0.0573880	−	0.0497270i
$271$	62176.6	+	39958.5i	0.846620	+	0.544090i	0.890519	−	0.454946i	$-0.150342\pi$
$271$	62176.6	+	39958.5i	0.846620	+	0.544090i	−0.0438987	+	0.999036i	$0.513978\pi$
$272$	4134.05	+	3582.17i	0.0558776	+	0.0484182i
$273$	2585.59	+	8805.72i	0.0346924	+	0.118152i
$274$	21369.1	−	9758.94i	0.284633	−	0.129987i
$275$		−	68584.9i		−	0.906907i
$276$	4339.35	−	21557.7i	0.0569648	−	0.282999i
$277$	86588.2			1.12849			0.564247	−	0.825606i	$-0.309167\pi$
$277$	86588.2			1.12849			0.564247	+	0.825606i	$0.309167\pi$
$278$	−23830.5	−	52181.5i	−0.308350	−	0.675191i
$279$	−27145.4	+	7970.60i	−0.348729	+	0.102396i
$280$	−2547.95	+	2940.49i	−0.0324993	+	0.0375062i
$281$	51866.1	−	80705.2i	0.656857	−	1.02209i	−0.339809	−	0.940495i	$-0.610362\pi$
$281$	51866.1	−	80705.2i	0.656857	−	1.02209i	0.996666	−	0.0815948i	$-0.0260013\pi$
$282$	38699.8	+	44661.9i	0.486643	+	0.561616i
$283$	−54337.7	+	7812.59i	−0.678467	+	0.0975488i	−0.472929	−	0.881100i	$-0.656803\pi$
$283$	−54337.7	+	7812.59i	−0.678467	+	0.0975488i	−0.205538	+	0.978649i	$0.565894\pi$
$284$	−6106.48	−	1793.03i	−0.0757102	−	0.0222305i
$285$	−28684.3	+	18434.3i	−0.353147	+	0.226954i
$286$	−63926.4	−	9191.23i	−0.781534	−	0.112368i
$287$	−16234.4	−	7413.99i	−0.197093	−	0.0900095i
$288$	−2030.35	+	4445.85i	−0.0244786	+	0.0536006i
$289$	−10846.6	+	75440.0i	−0.129867	+	0.903246i
$290$	−26646.8	−	41463.2i	−0.316847	−	0.493023i
$291$	−2965.92	+	10101.0i	−0.0350247	+	0.119283i
$292$	−10250.1	−	71290.8i	−0.120216	−	0.836118i
$293$	−118965.	+	103084.i	−1.38575	+	1.20076i	−0.431369	+	0.902176i	$0.641969\pi$
$293$	−118965.	+	103084.i	−1.38575	+	1.20076i	−0.954383	+	0.298585i	$0.903485\pi$
$294$	−27807.1	−	17870.6i	−0.321708	−	0.206749i
$295$	37834.7	+	32784.0i	0.434757	+	0.376719i
$296$	12406.2	+	42251.5i	0.141597	+	0.482235i
$297$	20336.4	−	9287.34i	0.230548	−	0.105288i
$298$		−	74627.2i		−	0.840358i
$299$	6583.58	+	75513.7i	0.0736410	+	0.844663i
$300$	17891.1			0.198790
$301$	3107.78	+	6805.09i	0.0343018	+	0.0751105i
$302$	99893.9	−	29331.5i	1.09528	−	0.321603i
$303$	−60489.0	+	69808.0i	−0.658857	+	0.760361i
$304$	16275.9	−	25325.8i	0.176116	−	0.274041i
$305$	−4753.09	−	5485.36i	−0.0510948	−	0.0589665i
$306$	6460.75	−	928.916i	0.0689986	−	0.00992050i
$307$	171789.	+	50441.7i	1.82271	+	0.535196i	0.999472	−	0.0325009i	$-0.0103472\pi$
$307$	171789.	+	50441.7i	1.82271	+	0.535196i	0.823238	+	0.567697i	$0.192165\pi$
$308$	−13219.3	+	8495.50i	−0.139350	+	0.0895545i
$309$	8711.68	+	1252.55i	0.0912399	+	0.0131183i
$310$	37608.1	+	17175.0i	0.391343	+	0.178720i
$311$	27724.6	−	60708.5i	0.286645	−	0.627666i	−0.710457	−	0.703741i	$-0.751512\pi$
$311$	27724.6	−	60708.5i	0.286645	−	0.627666i	0.997102	+	0.0760750i	$0.0242388\pi$
$312$	2397.63	−	16675.9i	0.0246305	−	0.171309i
$313$	41664.3	+	64831.0i	0.425281	+	0.661750i	0.986093	−	0.166193i	$-0.0531475\pi$
$313$	41664.3	+	64831.0i	0.425281	+	0.661750i	−0.560812	+	0.827943i	$0.689511\pi$
$314$	−11536.2	+	39288.7i	−0.117005	+	0.398482i
$315$	660.724	+	4595.44i	0.00665885	+	0.0463133i
$316$	53575.1	−	46423.1i	0.536524	−	0.464901i
$317$	−31838.8	−	20461.5i	−0.316838	−	0.203620i	0.372549	−	0.928012i	$-0.378484\pi$
$317$	−31838.8	−	20461.5i	−0.316838	−	0.203620i	−0.689387	+	0.724393i	$0.742120\pi$
$318$	−41255.1	−	35747.8i	−0.407966	−	0.353504i
$319$	−56080.6	−	190993.i	−0.551101	−	1.87688i
$320$	6497.04	−	2967.10i	0.0634476	−	0.0289756i
$321$		−	21443.4i		−	0.208105i
$322$	13242.4	+	12836.5i	0.127719	+	0.123804i
$323$	−40204.4			−0.385362
$324$	2422.70	+	5304.97i	0.0230786	+	0.0505351i
$325$	−59172.7	+	17374.7i	−0.560215	+	0.164494i
$326$	−43317.8	+	49991.4i	−0.407597	+	0.470392i
$327$	−1518.43	+	2362.73i	−0.0142004	+	0.0220962i
$328$	21454.9	+	24760.3i	0.199425	+	0.230149i
$329$	−49058.7	+	7053.58i	−0.453236	+	0.0651655i
$330$	−31348.2	−	9204.65i	−0.287862	−	0.0845239i
$331$	−119419.	+	76746.2i	−1.08998	+	0.700489i	−0.956842	−	0.290609i	$-0.906142\pi$
$331$	−119419.	+	76746.2i	−1.08998	+	0.700489i	−0.133140	+	0.991097i	$0.542506\pi$
$332$	47446.4	+	6821.76i	0.430454	+	0.0618900i
$333$	47796.3	+	21827.9i	0.431029	+	0.196844i
$334$	−25824.2	+	56547.1i	−0.231491	+	0.506895i
$335$	2496.75	−	17365.3i	0.0222477	−	0.154736i
$336$	−2216.14	−	3448.38i	−0.0196299	−	0.0305448i
$337$	3824.53	−	13025.1i	0.0336758	−	0.114689i	−0.940940	−	0.338574i	$-0.890056\pi$
$337$	3824.53	−	13025.1i	0.0336758	−	0.114689i	0.974616	+	0.223884i	$0.0718738\pi$
$338$	−3231.93	−	22478.6i	−0.0282897	−	0.196759i
$339$	34382.8	−	29792.9i	0.299186	−	0.259247i
$340$	−8024.43	−	5156.99i	−0.0694155	−	0.0446106i
$341$	126192.	+	109346.i	1.08523	+	0.940360i
$342$	−10120.5	−	34467.3i	−0.0865266	−	0.294683i
$343$	52137.6	−	23810.5i	0.443163	−	0.202386i
$344$		−	13733.4i		−	0.116054i
$345$	−2139.95	+	38286.0i	−0.0179790	+	0.321664i
$346$	67617.2			0.564814
$347$	53332.5	+	116782.i	0.442928	+	0.969877i	0.991052	+	0.133479i	$0.0426150\pi$
$347$	53332.5	+	116782.i	0.442928	+	0.969877i	−0.548124	+	0.836397i	$0.684658\pi$
$348$	49822.5	−	14629.2i	0.411402	−	0.120799i
$349$	83462.5	−	96320.8i	0.685236	−	0.790805i	−0.301443	−	0.953484i	$-0.597468\pi$
$349$	83462.5	−	96320.8i	0.685236	−	0.790805i	0.986679	+	0.162679i	$0.0520136\pi$
$350$	−8112.32	+	12623.0i	−0.0662230	+	0.103045i
$351$	−13164.6	−	15192.8i	−0.106855	−	0.123317i
$352$	28552.6	−	4105.24i	0.230441	−	0.0331324i
$353$	184119.	+	54062.3i	1.47758	+	0.433856i	0.918554	−	0.395296i	$-0.129358\pi$
$353$	184119.	+	54062.3i	1.47758	+	0.433856i	0.559024	+	0.829152i	$0.311176\pi$
$354$	−44369.7	+	28514.7i	−0.354063	+	0.227542i
$355$	10984.9	+	1579.39i	0.0871644	+	0.0125324i
$356$	5393.77	+	2463.25i	0.0425591	+	0.0194361i
$357$	−2274.09	+	4979.57i	−0.0178432	+	0.0390711i
$358$	−14336.4	+	99711.9i	−0.111860	+	0.778002i
$359$	49990.8	+	77787.2i	0.387883	+	0.603558i	0.979204	−	0.202878i	$-0.0650296\pi$
$359$	49990.8	+	77787.2i	0.387883	+	0.603558i	−0.591321	+	0.806436i	$0.701393\pi$
$360$	2401.13	−	8177.50i	0.0185272	−	0.0630980i
$361$	12942.7	+	90018.3i	0.0993138	+	0.690743i
$362$	103551.	−	89727.7i	0.790202	−	0.684714i
$363$	−47003.4	−	30207.3i	−0.356711	−	0.229244i
$364$	10678.5	+	9252.95i	0.0805947	+	0.0698357i
$365$	35383.7	+	120506.i	0.265594	+	0.904529i
$366$	6955.69	−	3176.56i	0.0519252	−	0.0237134i
$367$			58681.6i			0.435682i	0.975984	+	0.217841i	$0.0699015\pi$
$367$			58681.6i			0.435682i	−0.975984	+	0.217841i	$0.930099\pi$
$368$	−12323.7	−	31533.4i	−0.0910010	−	0.232849i
$369$	39093.7			0.287114
$370$	−31898.6	−	69848.3i	−0.233007	−	0.510214i
$371$	43928.0	−	12898.4i	0.319149	−	0.0937106i
$372$	−28524.1	+	32918.5i	−0.206122	+	0.237878i
$373$	74033.8	−	115199.i	0.532124	−	0.828000i	−0.466271	−	0.884642i	$-0.654403\pi$
$373$	74033.8	−	115199.i	0.532124	−	0.828000i	0.998395	+	0.0566415i	$0.0180392\pi$
$374$	−25227.6	−	29114.2i	−0.180357	−	0.208143i
$375$	−75723.8	+	10887.4i	−0.538481	+	0.0774218i
$376$	87299.1	+	25633.3i	0.617496	+	0.181313i
$377$	−150575.	+	96768.7i	−1.05943	+	0.680851i
$378$	−4841.43	−	696.093i	−0.0338837	−	0.00487174i
$379$	117111.	+	53482.7i	0.815302	+	0.372336i	0.779015	−	0.627005i	$-0.215720\pi$
$379$	117111.	+	53482.7i	0.815302	+	0.372336i	0.0362871	+	0.999341i	$0.488447\pi$
$380$	−21807.6	+	47752.0i	−0.151022	+	0.330693i
$381$	−3811.27	+	26508.0i	−0.0262555	+	0.182611i
$382$	9830.79	+	15297.0i	0.0673692	+	0.104829i
$383$	13426.0	−	45724.9i	0.0915272	−	0.311713i	−0.900986	−	0.433847i	$-0.857156\pi$
$383$	13426.0	−	45724.9i	0.0915272	−	0.311713i	0.992514	+	0.122134i	$0.0389739\pi$
$384$	1070.90	+	7448.24i	0.00726247	+	0.0505116i
$385$	20708.5	−	17944.0i	0.139710	−	0.121059i
$386$	30126.1	+	19360.9i	0.202194	+	0.129942i
$387$	−12384.6	−	10731.3i	−0.0826916	−	0.0716527i
$388$	4566.34	+	15551.5i	0.0303323	+	0.103302i
$389$	252301.	−	115222.i	1.66732	−	0.761442i	0.667466	−	0.744641i	$-0.267379\pi$
$389$	252301.	−	115222.i	1.66732	−	0.761442i	0.999859	−	0.0168010i	$-0.00534819\pi$
$390$			29377.9i			0.193149i
$391$	−26529.1	+	36613.0i	−0.173528	+	0.239487i
$392$	−50890.6			−0.331181
$393$	−14684.9	−	32155.4i	−0.0950790	−	0.208194i
$394$	−116056.	+	34077.1i	−0.747611	+	0.219518i
$395$	−80951.4	+	93422.9i	−0.518836	+	0.598768i
$396$	18609.1	−	28956.4i	0.118669	−	0.184652i
$397$	−107945.	−	124575.i	−0.684888	−	0.790403i	0.301740	−	0.953390i	$-0.402433\pi$
$397$	−107945.	−	124575.i	−0.684888	−	0.790403i	−0.986628	+	0.162987i	$0.947887\pi$
$398$	155089.	−	22298.5i	0.979074	−	0.140770i
$399$	28907.2	+	8487.93i	0.181577	+	0.0533158i
$400$	23172.4	−	14892.0i	0.144828	−	0.0930751i
$401$	−119803.	−	17225.1i	−0.745038	−	0.107120i	−0.240668	−	0.970608i	$-0.577366\pi$
$401$	−119803.	−	17225.1i	−0.745038	−	0.107120i	−0.504371	+	0.863487i	$0.668275\pi$
$402$	16812.7	+	7678.12i	0.104037	+	0.0475119i
$403$	62371.6	−	136575.i	0.384041	−	0.840932i
$404$	−20238.8	+	140764.i	−0.124000	+	0.862441i
$405$	−5498.14	−	8555.28i	−0.0335202	−	0.0521584i
$406$	−12269.3	+	41785.4i	−0.0744334	+	0.253497i
$407$	−44134.6	−	306963.i	−0.266434	−	1.85309i
$408$	7594.73	−	6580.87i	0.0456239	−	0.0395333i
$409$	−176437.	−	113389.i	−1.05473	−	0.677836i	−0.106145	−	0.994351i	$-0.533851\pi$
$409$	−176437.	−	113389.i	−1.05473	−	0.677836i	−0.948587	+	0.316515i	$0.897487\pi$
$410$	−43176.4	−	37412.5i	−0.256849	−	0.222561i
$411$	−12158.9	−	41409.4i	−0.0719798	−	0.245141i
$412$	12325.9	−	5629.05i	0.0726147	−	0.0331620i
$413$		−	44234.3i		−	0.259334i
$414$	−38066.4	−	13527.0i	−0.222096	−	0.0789225i
$415$	−83586.5			−0.485333
$416$	−10775.1	−	23594.2i	−0.0622637	−	0.136339i
$417$	−101118.	+	29691.0i	−0.581510	+	0.170747i
$418$	−138840.	+	160230.i	−0.794623	+	0.917044i
$419$	99107.4	−	154214.i	0.564519	−	0.878408i	−0.435241	−	0.900314i	$-0.643337\pi$
$419$	99107.4	−	154214.i	0.564519	−	0.878408i	0.999760	+	0.0219057i	$0.00697337\pi$
$420$	4680.88	+	5402.02i	0.0265356	+	0.0306237i
$421$	285074.	−	40987.5i	1.60840	−	0.231253i	0.721229	−	0.692697i	$-0.243578\pi$
$421$	285074.	−	40987.5i	1.60840	−	0.231253i	0.887169	+	0.461444i	$0.152669\pi$
$422$	44237.3	+	12989.2i	0.248407	+	0.0729389i
$423$	91332.1	−	58695.6i	0.510438	−	0.328038i
$424$	−83188.8	−	11960.7i	−0.462736	−	0.0665314i
$425$	−33461.7	−	15281.4i	−0.185255	−	0.0846032i
$426$	−4857.00	+	10635.4i	−0.0267639	+	0.0586048i
$427$	−912.692	+	6347.91i	−0.00500574	+	0.0348157i
$428$	−17848.8	−	27773.3i	−0.0974367	−	0.151614i
$429$	−33427.0	+	113842.i	−0.181628	+	0.618568i
$430$	3408.13	+	23704.1i	0.0184323	+	0.128199i
$431$	−216404.	+	187515.i	−1.16496	+	1.00944i	−0.165230	+	0.986255i	$0.552837\pi$
$431$	−216404.	+	187515.i	−1.16496	+	1.00944i	−0.999731	+	0.0231897i	$0.992618\pi$
$432$	7553.57	+	4854.39i	0.0404748	+	0.0260116i
$433$	−179402.	−	155452.i	−0.956864	−	0.829128i	0.0284992	−	0.999594i	$-0.490927\pi$
$433$	−179402.	−	155452.i	−0.956864	−	0.829128i	−0.985364	+	0.170466i	$0.945473\pi$
$434$	−10292.0	−	35051.3i	−0.0546411	−	0.186091i
$435$	−82364.3	+	37614.5i	−0.435272	+	0.198782i
$436$			4324.09i			0.0227469i
$437$	220227.	+	115841.i	1.15321	+	0.606594i
$438$	−132316.			−0.689708
$439$	−90835.4	−	198902.i	−0.471331	−	1.03207i	−0.984757	−	0.173937i	$-0.944351\pi$
$439$	−90835.4	−	198902.i	−0.471331	−	1.03207i	0.513425	−	0.858134i	$-0.328376\pi$
$440$	−48263.7	+	14171.5i	−0.249296	+	0.0731998i
$441$	−39766.3	+	45892.7i	−0.204474	+	0.235975i
$442$	−18727.8	+	29141.0i	−0.0958609	+	0.149162i
$443$	−69742.6	−	80487.2i	−0.355378	−	0.410128i	0.549708	−	0.835357i	$-0.314739\pi$
$443$	−69742.6	−	80487.2i	−0.355378	−	0.410128i	−0.905086	+	0.425229i	$0.860194\pi$
$444$	80074.4	−	11513.0i	0.406189	−	0.0584011i
$445$	−9921.07	−	2913.09i	−0.0501001	−	0.0147107i
$446$	−126433.	+	81253.8i	−0.635612	+	0.408483i
$447$	−135703.	−	19511.2i	−0.679166	−	0.0976493i
$448$	−5740.66	−	2621.67i	−0.0286026	−	0.0130624i
$449$	−77081.7	+	168785.i	−0.382348	+	0.837225i	0.616411	+	0.787424i	$0.288586\pi$
$449$	−77081.7	+	168785.i	−0.382348	+	0.837225i	−0.998759	+	0.0498009i	$0.984141\pi$
$450$	4677.61	−	32533.5i	0.0230993	−	0.160659i
$451$	−124743.	−	194104.i	−0.613285	−	0.954291i
$452$	19733.7	−	67206.8i	0.0965899	−	0.328955i
$453$	−27219.8	−	189318.i	−0.132644	−	0.922560i
$454$	−192580.	+	166872.i	−0.934329	+	0.809600i
$455$	−20727.5	−	13320.8i	−0.100121	−	0.0643438i
$456$	−41797.6	−	36217.8i	−0.201012	−	0.174178i
$457$	−93127.6	−	317164.i	−0.445909	−	1.51863i	−0.809530	−	0.587079i	$-0.800278\pi$
$457$	−93127.6	−	317164.i	−0.445909	−	1.51863i	0.363621	−	0.931547i	$-0.381540\pi$
$458$	147878.	−	67533.4i	0.704971	−	0.321950i
$459$		−	11991.2i		−	0.0569165i
$460$	29096.5	+	51369.1i	0.137507	+	0.242765i
$461$	169050.			0.795451			0.397726	−	0.917504i	$-0.369800\pi$
$461$	169050.			0.795451			0.397726	+	0.917504i	$0.369800\pi$
$462$	11992.2	+	26259.3i	0.0561843	+	0.123027i
$463$	−176743.	+	51896.4i	−0.824480	+	0.242089i	−0.666644	−	0.745376i	$-0.732270\pi$
$463$	−176743.	+	51896.4i	−0.824480	+	0.242089i	−0.157836	+	0.987465i	$0.550452\pi$
$464$	52352.9	−	60418.4i	0.243167	−	0.280630i
$465$	41064.0	−	63896.8i	0.189913	−	0.295511i
$466$	610.198	+	704.207i	0.00280995	+	0.00324286i
$467$	358912.	−	51603.7i	1.64571	−	0.236618i	0.743758	−	0.668449i	$-0.233041\pi$
$467$	358912.	−	51603.7i	1.64571	−	0.236618i	0.901955	+	0.431831i	$0.142132\pi$
$468$	−29696.8	−	8719.78i	−0.135587	−	0.0398120i
$469$	−13040.6	+	8380.71i	−0.0592862	+	0.0381009i
$470$	−157042.	−	22579.2i	−0.710917	−	0.102214i
$471$	68427.2	+	31249.7i	0.308452	+	0.140865i
$472$	−33732.6	+	73864.2i	−0.151414	+	0.331551i
$473$	−13764.3	+	95733.1i	−0.0615224	+	0.427898i
$474$	−70409.5	−	109559.i	−0.313382	−	0.487632i
$475$	−57037.2	+	194251.i	−0.252796	+	0.860945i
$476$	1199.46	+	8342.40i	0.00529383	+	0.0368194i
$477$	−75790.5	+	65672.8i	−0.333103	+	0.288635i
$478$	−36079.9	−	23187.1i	−0.157910	−	0.101483i
$479$	−111238.	−	96388.1i	−0.484821	−	0.420100i	0.377849	−	0.925867i	$-0.376664\pi$
$479$	−111238.	−	96388.1i	−0.484821	−	0.420100i	−0.862670	+	0.505768i	$0.831209\pi$
$480$	−3696.78	−	12590.1i	−0.0160451	−	0.0546444i
$481$	−253656.	+	115841.i	−1.09637	+	0.500693i
$482$		−	11552.1i		−	0.0497239i
$483$	26804.3	−	20724.2i	0.114898	−	0.0888348i
$484$	−86022.2			−0.367215
$485$	−11740.9	−	25709.1i	−0.0499137	−	0.109296i
$486$	10280.1	−	3018.50i	0.0435235	−	0.0127796i
$487$	−37165.9	+	42891.7i	−0.156706	+	0.180849i	−0.828674	−	0.559732i	$-0.810904\pi$
$487$	−37165.9	+	42891.7i	−0.156706	+	0.180849i	0.671967	+	0.740581i	$0.265449\pi$
$488$	6364.90	−	9903.97i	0.0267271	−	0.0415882i
$489$	79579.9	+	91840.0i	0.332802	+	0.384074i
$490$	87838.3	−	12629.2i	0.365841	−	0.0525999i
$491$	169203.	+	49682.5i	0.701851	+	0.206082i	0.613139	−	0.789975i	$-0.289907\pi$
$491$	169203.	+	49682.5i	0.701851	+	0.206082i	0.0887125	+	0.996057i	$0.471725\pi$
$492$	50634.0	−	32540.5i	0.209176	−	0.134429i
$493$	−105678.	−	15194.3i	−0.434803	−	0.0625152i
$494$	173413.	+	79195.1i	0.710604	+	0.324522i
$495$	−24933.9	+	54597.5i	−0.101760	+	0.222824i
$496$	−9543.78	+	66378.5i	−0.0387933	+	0.269814i
$497$	−5301.45	−	8249.22i	−0.0214626	−	0.0333964i
$498$	24809.6	−	84493.8i	0.100037	−	0.340695i
$499$	51905.4	+	361010.i	0.208455	+	1.44983i	0.778202	+	0.628014i	$0.216132\pi$
$499$	51905.4	+	361010.i	0.208455	+	1.44983i	−0.569747	+	0.821820i	$0.692959\pi$
$500$	−89014.7	+	77131.7i	−0.356059	+	0.308527i
$501$	96074.6	+	61743.4i	0.382766	+	0.245989i
$502$	147569.	+	127869.i	0.585583	+	0.507410i
$503$	−54909.5	−	187005.i	−0.217026	−	0.739122i	−0.993980	−	0.109564i	$-0.965054\pi$
$503$	−54909.5	−	187005.i	−0.217026	−	0.739122i	0.776954	−	0.629557i	$-0.216764\pi$
$504$	−6850.01	+	3128.29i	−0.0269668	+	0.0123153i
$505$		−	247985.i		−	0.972394i
$506$	54302.2	+	232166.i	0.212088	+	0.906771i
$507$	−41720.4			−0.162305
$508$	17128.1	+	37505.4i	0.0663717	+	0.145334i
$509$	−496.585	+	145.810i	−0.00191672	+	0.000562799i	−0.282691	−	0.959211i	$-0.591227\pi$
$509$	−496.585	+	145.810i	−0.00191672	+	0.000562799i	0.280774	+	0.959774i	$0.409409\pi$
$510$	−11475.5	+	13243.5i	−0.0441197	+	0.0509169i
$511$	59995.9	−	93355.5i	0.229763	−	0.357518i
$512$	7586.72	+	8755.54i	0.0289410	+	0.0333997i
$513$	−65321.9	+	9391.87i	−0.248213	+	0.0356876i
$514$	91571.0	+	26887.7i	0.346602	+	0.101772i
$515$	−19877.9	+	12774.7i	−0.0749472	+	0.0481656i
$516$	−24973.0	−	3590.57i	−0.0937931	−	0.0134854i
$517$	−582857.	−	266182.i	−2.18063	−	0.995859i
$518$	−28185.1	+	61716.7i	−0.105041	+	0.230008i
$519$	17678.5	−	122956.i	0.0656311	−	0.456475i
$520$	24453.3	+	38050.1i	0.0904340	+	0.140718i
$521$	47340.2	−	161226.i	0.174403	−	0.593963i	−0.825174	−	0.564879i	$-0.808923\pi$
$521$	47340.2	−	161226.i	0.174403	−	0.593963i	0.999577	−	0.0290838i	$-0.00925898\pi$
$522$	−13576.0	−	94422.9i	−0.0498230	−	0.346526i
$523$	339410.	−	294100.i	1.24086	−	1.07521i	0.246496	−	0.969144i	$-0.420721\pi$
$523$	339410.	−	294100.i	1.24086	−	1.07521i	0.994359	−	0.106063i	$-0.0338246\pi$
$524$	−45784.9	−	29424.2i	−0.166748	−	0.107162i
$525$	20833.0	+	18051.9i	0.0755844	+	0.0654943i
$526$	31322.3	+	106674.i	0.113209	+	0.385555i
$527$	81465.5	−	37204.0i	0.293327	−	0.133958i
$528$		−	52993.9i		−	0.190089i
$529$	250811.	−	124116.i	0.896262	−	0.443524i
$530$	146554.			0.521730
$531$	40251.2	+	88137.9i	0.142755	+	0.312589i
$532$	44505.6	−	13068.0i	0.157250	−	0.0461728i
$533$	−135865.	+	156796.i	−0.478247	+	0.551927i
$534$	5889.42	−	9164.12i	0.0206533	−	0.0321372i
$535$	37699.9	+	43508.0i	0.131714	+	0.152006i
$536$	28166.8	−	4049.77i	0.0980411	−	0.0140962i
$537$	177570.	+	52139.2i	0.615772	+	0.180807i
$538$	174381.	−	112068.i	0.602468	−	0.387182i
$539$	354750.	+	51005.4i	1.22108	+	0.175565i
$540$	−14242.3	−	6504.26i	−0.0488420	−	0.0223054i
$541$	−196694.	+	430700.i	−0.672043	+	1.47157i	0.198817	+	0.980037i	$0.436290\pi$
$541$	−196694.	+	430700.i	−0.672043	+	1.47157i	−0.870860	+	0.491532i	$0.836437\pi$
$542$	29750.6	−	206920.i	0.101274	−	0.704374i
$543$	−136089.	−	211759.i	−0.461555	−	0.718194i
$544$	4358.93	−	14845.1i	0.0147293	−	0.0501634i
$545$	−1073.09	−	7463.49i	−0.00361278	−	0.0251275i
$546$	19617.6	−	16998.7i	0.0658053	−	0.0570206i
$547$	362788.	+	233150.i	1.21249	+	0.779220i	0.981074	−	0.193635i	$-0.0620276\pi$
$547$	362788.	+	233150.i	1.21249	+	0.779220i	0.231416	+	0.972855i	$0.425664\pi$
$548$	−50216.1	−	43512.5i	−0.167218	−	0.144895i
$549$	−3957.75	−	13478.9i	−0.0131312	−	0.0447207i
$550$	−176457.	+	80585.2i	−0.583329	+	0.266398i
$551$			587581.i			1.93537i
$552$	−60562.9	+	14165.3i	−0.198760	+	0.0464887i
$553$	109225.			0.357167
$554$	−101739.	−	222776.i	−0.331487	−	0.725855i
$555$	−135353.	+	39743.3i	−0.439423	+	0.129026i
$556$	−106254.	+	122623.i	−0.343712	+	0.396665i
$557$	264516.	−	411594.i	0.852591	−	1.32666i	−0.0911042	−	0.995841i	$-0.529040\pi$
$557$	264516.	−	411594.i	0.852591	−	1.32666i	0.943695	−	0.330816i	$-0.107324\pi$
$558$	52402.0	+	60475.2i	0.168298	+	0.194227i
$559$	86082.1	−	12376.7i	0.275480	−	0.0396080i
$560$	10559.1	+	3100.44i	0.0336707	+	0.00988661i
$561$	−59537.4	+	38262.4i	−0.189175	+	0.121576i
$562$	−268582.	−	38616.2i	−0.850362	−	0.122264i
$563$	−296498.	−	135406.i	−0.935416	−	0.427190i	−0.111412	−	0.993774i	$-0.535537\pi$
$563$	−296498.	−	135406.i	−0.935416	−	0.427190i	−0.824004	+	0.566584i	$0.808265\pi$
$564$	69436.4	−	152044.i	0.218287	−	0.477983i
$565$	−17382.5	+	120898.i	−0.0544521	+	0.378723i
$566$	83945.7	+	130622.i	0.262039	+	0.407740i
$567$	−2531.58	+	8621.76i	−0.00787454	+	0.0268182i
$568$	2561.80	+	17817.7i	0.00794050	+	0.0552274i
$569$	39911.6	−	34583.6i	0.123275	−	0.106818i	−0.591042	−	0.806641i	$-0.701283\pi$
$569$	39911.6	−	34583.6i	0.123275	−	0.106818i	0.714317	+	0.699823i	$0.246738\pi$
$570$	81131.6	+	52140.1i	0.249712	+	0.160480i
$571$	381575.	+	330636.i	1.17033	+	1.01409i	0.999586	+	0.0287788i	$0.00916183\pi$
$571$	381575.	+	330636.i	1.17033	+	1.01409i	0.170742	+	0.985316i	$0.445384\pi$
$572$	51464.2	+	175271.i	0.157294	+	0.535696i
$573$	30386.6	−	13877.1i	0.0925492	−	0.0422658i
$574$			50479.5i			0.153211i
$575$	139262.	+	180120.i	0.421209	+	0.544786i
$576$	13824.0			0.0416667
$577$	−201803.	−	441887.i	−0.606144	−	1.32727i	−0.925180	−	0.379528i	$-0.876086\pi$
$577$	−201803.	−	441887.i	−0.606144	−	1.32727i	0.319036	−	0.947743i	$-0.396641\pi$
$578$	206839.	−	60733.3i	0.619121	−	0.181790i
$579$	43082.7	−	49720.0i	0.128512	−	0.148311i
$580$	−75368.6	+	117276.i	−0.224044	+	0.348620i
$581$	48365.1	+	55816.3i	0.143278	+	0.165352i
$582$	29473.0	−	4237.58i	0.0870119	−	0.0125104i
$583$	567909.	+	166753.i	1.67087	+	0.490610i
$584$	−171375.	+	110136.i	−0.502485	+	0.322927i
$585$	53421.4	+	7680.83i	0.156100	+	0.0224438i
$586$	404999.	+	184957.i	1.17939	+	0.538610i
$587$	62547.8	−	136961.i	0.181525	−	0.397484i	−0.796893	−	0.604120i	$-0.793525\pi$
$587$	62547.8	−	136961.i	0.181525	−	0.397484i	0.978418	+	0.206637i	$0.0662519\pi$
$588$	−13305.3	+	92540.3i	−0.0384831	+	0.267656i
$589$	−266474.	−	414642.i	−0.768113	−	1.19521i
$590$	39892.8	−	135863.i	0.114602	−	0.390297i
$591$	31623.7	+	219948.i	0.0905395	+	0.629716i
$592$	94128.9	−	81563.2i	0.268584	−	0.232729i
$593$	164320.	+	105602.i	0.467284	+	0.300305i	0.753014	−	0.658005i	$-0.228599\pi$
$593$	164320.	+	105602.i	0.467284	+	0.300305i	−0.285729	+	0.958310i	$0.592236\pi$
$594$	−47789.5	−	41409.8i	−0.135444	−	0.117363i
$595$	−4140.58	−	14101.5i	−0.0116957	−	0.0398320i
$596$	−192003.	+	87684.8i	−0.540524	+	0.246849i
$597$		−	287847.i		−	0.807631i
$598$	186548.	−	105665.i	0.521662	−	0.295480i
$599$	−347269.			−0.967861			−0.483930	−	0.875106i	$-0.660791\pi$
$599$	−347269.			−0.967861			−0.483930	+	0.875106i	$0.660791\pi$
$600$	−21021.5	−	46030.7i	−0.0583931	−	0.127863i
$601$	−91201.3	+	26779.1i	−0.252495	+	0.0741391i	−0.405531	−	0.914082i	$-0.632913\pi$
$601$	−91201.3	+	26779.1i	−0.252495	+	0.0741391i	0.153036	+	0.988221i	$0.451095\pi$
$602$	13856.8	−	15991.6i	0.0382357	−	0.0441263i
$603$	18357.7	−	28565.1i	0.0504875	−	0.0785601i
$604$	−192837.	−	222546.i	−0.528588	−	0.610023i
$605$	148476.	−	21347.7i	0.405646	−	0.0583230i
$606$	250677.	+	73605.3i	0.682604	+	0.200431i
$607$	−60585.9	+	38936.2i	−0.164435	+	0.105676i	−0.620270	−	0.784388i	$-0.712977\pi$
$607$	−60585.9	+	38936.2i	−0.164435	+	0.105676i	0.455835	+	0.890064i	$0.349341\pi$
$608$	−84282.6	−	12118.0i	−0.227998	−	0.0327812i
$609$	72775.6	+	33235.5i	0.196224	+	0.0896123i
$610$	−8528.14	+	18674.0i	−0.0229190	+	0.0501855i
$611$	−81996.9	+	570301.i	−0.219642	+	1.52764i
$612$	−9981.14	−	15531.0i	−0.0266488	−	0.0414663i
$613$	−78121.9	+	266059.i	−0.207899	+	0.708038i	0.787845	+	0.615873i	$0.211197\pi$
$613$	−78121.9	+	266059.i	−0.207899	+	0.708038i	−0.995744	+	0.0921644i	$0.970621\pi$
$614$	−72068.8	−	501250.i	−0.191166	−	1.32959i
$615$	−79320.0	+	68731.2i	−0.209716	+	0.181720i
$616$	37389.7	+	24028.9i	0.0985350	+	0.0633246i
$617$	407837.	+	353393.i	1.07131	+	0.928297i	0.997618	−	0.0689836i	$-0.0219756\pi$
$617$	407837.	+	353393.i	1.07131	+	0.928297i	0.0736944	+	0.997281i	$0.476521\pi$
$618$	−7013.37	−	23885.4i	−0.0183633	−	0.0625396i
$619$	250861.	−	114564.i	0.654714	−	0.298998i	−0.0602247	−	0.998185i	$-0.519182\pi$
$619$	250861.	−	114564.i	0.654714	−	0.298998i	0.714939	+	0.699187i	$0.246454\pi$
$620$		−	116939.i		−	0.304212i
$621$	−34550.2	+	65684.1i	−0.0895915	+	0.170324i
$622$	−188768.			−0.487919
$623$	3795.30	+	8310.54i	0.00977844	+	0.0214118i
$624$	−45721.3	+	13425.0i	−0.117422	+	0.0344782i
$625$	−41654.4	+	48071.7i	−0.106635	+	0.123064i
$626$	117845.	−	183370.i	0.300719	−	0.467928i
$627$	255065.	+	294361.i	0.648807	+	0.748764i
$628$	114638.	−	16482.4i	0.290676	−	0.0417929i
$629$	−159597.	−	46861.9i	−0.403388	−	0.118446i
$630$	11046.9	−	7099.44i	0.0278331	−	0.0178872i
$631$	−363151.	−	52213.3i	−0.912071	−	0.131136i	−0.329725	−	0.944077i	$-0.606956\pi$
$631$	−363151.	−	52213.3i	−0.912071	−	0.131136i	−0.582346	+	0.812941i	$0.697865\pi$
$632$	−182388.	−	83293.8i	−0.456627	−	0.208535i
$633$	35185.7	−	77045.9i	0.0878130	−	0.192284i
$634$	−15234.4	+	105957.i	−0.0379006	+	0.263604i
$635$	−38871.1	−	60484.6i	−0.0964005	−	0.150002i
$636$	−43499.3	+	148145.i	−0.107539	+	0.366246i
$637$	−45863.5	−	318988.i	−0.113029	−	0.786131i
$638$	−425499.	+	368697.i	−1.04534	+	0.905791i
$639$	18069.7	+	11612.7i	0.0442536	+	0.0284400i
$640$	−15267.7	−	13229.5i	−0.0372746	−	0.0322986i
$641$	−81539.1	−	277697.i	−0.198450	−	0.675857i	−0.997240	−	0.0742475i	$-0.976345\pi$
$641$	−81539.1	−	277697.i	−0.198450	−	0.675857i	0.798790	−	0.601610i	$-0.205474\pi$
$642$	−55170.1	+	25195.4i	−0.133855	+	0.0611294i
$643$			130662.i			0.316030i	0.987437	+	0.158015i	$0.0505095\pi$
$643$			130662.i			0.316030i	−0.987437	+	0.158015i	$0.949491\pi$
$644$	17466.6	−	49153.0i	0.0421150	−	0.118516i
$645$	43995.0			0.105751
$646$	47239.0	+	103439.i	0.113197	+	0.247868i
$647$	−532736.	+	156425.i	−1.27263	+	0.373679i	−0.847182	−	0.531302i	$-0.821703\pi$
$647$	−532736.	+	156425.i	−1.27263	+	0.373679i	−0.425451	+	0.904981i	$0.639885\pi$
$648$	10802.2	−	12466.4i	0.0257254	−	0.0296886i
$649$	309176.	−	481087.i	0.734034	−	1.14218i
$650$	114228.	+	131826.i	0.270363	+	0.312015i
$651$	−66428.7	+	9551.00i	−0.156745	+	0.0225365i
$652$	179516.	+	52710.8i	0.422288	+	0.123995i
$653$	−205440.	+	132028.i	−0.481791	+	0.309628i	−0.758897	−	0.651211i	$-0.774261\pi$
$653$	−205440.	+	132028.i	−0.481791	+	0.309628i	0.277105	+	0.960840i	$0.410625\pi$
$654$	7863.01	+	1130.53i	0.0183837	+	0.00264318i
$655$	86327.9	+	39424.6i	0.201219	+	0.0918936i
$656$	38495.1	−	84292.5i	0.0894536	−	0.195876i
$657$	−34594.0	+	240606.i	−0.0801438	+	0.557412i
$658$	75790.2	+	117932.i	0.175050	+	0.272383i
$659$	−143823.	+	489817.i	−0.331176	+	1.12788i	0.610684	+	0.791875i	$0.290895\pi$
$659$	−143823.	+	489817.i	−0.331176	+	1.12788i	−0.941860	+	0.336007i	$0.890924\pi$
$660$	13151.2	+	91468.6i	0.0301910	+	0.209983i
$661$	−335193.	+	290447.i	−0.767172	+	0.664758i	−0.947826	−	0.318789i	$-0.896724\pi$
$661$	−335193.	+	290447.i	−0.767172	+	0.664758i	0.180654	+	0.983547i	$0.442179\pi$
$662$	337769.	+	217071.i	0.770733	+	0.495320i
$663$	48094.1	+	41673.8i	0.109412	+	0.0948060i
$664$	−38196.9	−	130087.i	−0.0866347	−	0.295051i
$665$	−73574.7	+	33600.4i	−0.166374	+	0.0759804i
$666$		−	148619.i		−	0.335062i
$667$	535093.	+	387719.i	1.20276	+	0.871497i
$668$	175829.			0.394037
$669$	114698.	+	251153.i	0.256272	+	0.561158i
$670$	−47611.5	+	13980.0i	−0.106063	+	0.0311428i
$671$	−54295.0	+	62659.8i	−0.120591	+	0.139169i
$672$	−6268.19	+	9753.49i	−0.0138805	+	0.0215984i
$673$	271381.	+	313191.i	0.599169	+	0.691478i	0.971613	−	0.236577i	$-0.0760254\pi$
$673$	271381.	+	313191.i	0.599169	+	0.691478i	−0.372443	+	0.928055i	$0.621480\pi$
$674$	−38005.2	+	5464.32i	−0.0836610	+	0.0120286i
$675$	−57936.5	−	17011.7i	−0.127158	−	0.0373370i
$676$	−54036.1	+	34726.9i	−0.118247	+	0.0759928i
$677$	−506964.	−	72890.5i	−1.10611	−	0.159035i	−0.435030	−	0.900416i	$-0.643262\pi$
$677$	−506964.	−	72890.5i	−1.10611	−	0.159035i	−0.671085	+	0.741381i	$0.734171\pi$
$678$	−117051.	−	53455.3i	−0.254633	−	0.116287i
$679$	−10374.1	+	22716.1i	−0.0225014	+	0.0492713i
$680$	−3839.57	+	26704.8i	−0.00830357	+	0.0577526i
$681$	253092.	+	393819.i	0.545739	+	0.849186i
$682$	133057.	−	453149.i	0.286067	−	0.974254i
$683$	−81638.4	−	567807.i	−0.175006	−	1.21719i	−0.868116	−	0.496361i	$-0.834669\pi$
$683$	−81638.4	−	567807.i	−0.175006	−	1.21719i	0.693110	−	0.720832i	$-0.256240\pi$
$684$	−76787.0	+	66536.4i	−0.164125	+	0.142215i
$685$	97472.5	+	62641.8i	0.207731	+	0.133500i
$686$	−122520.	−	106165.i	−0.260352	−	0.225596i
$687$	−84141.6	−	286560.i	−0.178278	−	0.607158i
$688$	−35333.5	+	16136.3i	−0.0746467	+	0.0340900i
$689$		−	532216.i		−	1.12111i
$690$	101018.	−	39479.2i	0.212177	−	0.0829221i
$691$	357553.			0.748831			0.374416	−	0.927261i	$-0.377843\pi$
$691$	357553.			0.748831			0.374416	+	0.927261i	$0.377843\pi$
$692$	−79448.3	−	173968.i	−0.165910	−	0.363292i
$693$	50885.7	−	14941.4i	0.105957	−	0.0311118i
$694$	237796.	−	274431.i	0.493725	−	0.569788i
$695$	152966.	−	238019.i	0.316683	−	0.492768i
$696$	−96178.4	−	110996.i	−0.198545	−	0.229133i
$697$	−122495.	+	17612.1i	−0.252146	+	0.0362531i
$698$	−345883.	−	101560.i	−0.709935	−	0.208456i
$699$	1440.08	−	925.482i	0.00294735	−	0.00189415i
$700$	42008.6	+	6039.92i	0.0857318	+	0.0123264i
$701$	−777908.	−	355259.i	−1.58304	−	0.722951i	−0.586813	−	0.809722i	$-0.699618\pi$
$701$	−777908.	−	355259.i	−1.58304	−	0.722951i	−0.996228	+	0.0867715i	$0.972345\pi$
$702$	−23620.4	+	51721.5i	−0.0479306	+	0.104953i
$703$	−130278.	+	906105.i	−0.263609	+	1.83344i
$704$	−44110.6	−	68637.4i	−0.0890015	−	0.138489i
$705$	−82116.7	+	279664.i	−0.165216	+	0.562676i
$706$	−77241.9	−	537229.i	−0.154969	−	1.07783i
$707$	−165596.	+	143490.i	−0.331292	+	0.287066i
$708$	125497.	+	80651.7i	0.250360	+	0.160897i
$709$	−54370.9	−	47112.6i	−0.108162	−	0.0937227i	0.599101	−	0.800673i	$-0.295525\pi$
$709$	−54370.9	−	47112.6i	−0.108162	−	0.0937227i	−0.707263	+	0.706951i	$0.750070\pi$
$710$	−8843.44	−	30118.0i	−0.0175430	−	0.0597461i
$711$	−217633.	+	99389.7i	−0.430512	+	0.196608i
$712$		−	16771.5i		−	0.0330835i
$713$	−553438.	−	30933.7i	−1.08865	−	0.0608490i
$714$	15483.6			0.0303721
$715$	−132324.	−	289750.i	−0.258838	−	0.566776i
$716$	273386.	−	80273.5i	0.533275	−	0.156584i
$717$	−51597.0	+	59546.1i	−0.100366	+	0.115828i
$718$	141395.	−	220015.i	0.274275	−	0.426780i
$719$	−50235.8	−	57975.2i	−0.0971753	−	0.112146i	0.705079	−	0.709129i	$-0.250912\pi$
$719$	−50235.8	−	57975.2i	−0.0971753	−	0.112146i	−0.802254	+	0.596983i	$0.796366\pi$
$720$	−23860.5	+	3430.63i	−0.0460273	+	0.00661773i
$721$	20032.3	+	5882.02i	0.0385355	+	0.0113150i
$722$	216394.	−	139068.i	0.415118	−	0.266780i
$723$	−21006.5	−	3020.27i	−0.0401861	−	0.00577790i
$724$	−352524.	−	160992.i	−0.672529	−	0.307134i
$725$	−223336.	+	489037.i	−0.424896	+	0.930392i
$726$	−22490.4	+	156424.i	−0.0426702	+	0.296778i
$727$	65018.6	+	101171.i	0.123018	+	0.191420i	0.897300	−	0.441421i	$-0.145525\pi$
$727$	65018.6	+	101171.i	0.123018	+	0.191420i	−0.774282	+	0.632840i	$0.781889\pi$
$728$	11259.3	−	38345.8i	0.0212447	−	0.0723528i
$729$	−2801.18	−	19482.7i	−0.00527092	−	0.0366601i
$730$	268466.	−	232627.i	0.503783	−	0.436530i
$731$	43640.1	+	28045.8i	0.0816679	+	0.0524848i
$732$	−16345.5	−	14163.4i	−0.0305053	−	0.0264330i
$733$	−173635.	−	591346.i	−0.323168	−	1.10061i	−0.947581	−	0.319516i	$-0.896480\pi$
$733$	−173635.	−	591346.i	−0.323168	−	1.10061i	0.624413	−	0.781095i	$-0.285338\pi$
$734$	150978.	−	68949.2i	0.280234	−	0.127979i
$735$		−	163029.i		−	0.301779i
$736$	−66650.0	+	68757.6i	−0.123039	+	0.126930i
$737$	−200405.			−0.368956
$738$	−45934.0	−	100581.i	−0.0843376	−	0.184674i
$739$	169155.	−	49668.3i	0.309739	−	0.0909475i	−0.123169	−	0.992386i	$-0.539306\pi$
$739$	169155.	−	49668.3i	0.309739	−	0.0909475i	0.432908	+	0.901438i	$0.357488\pi$
$740$	−142228.	+	164139.i	−0.259729	+	0.299743i
$741$	189348.	−	294632.i	0.344846	−	0.536591i
$742$	−84799.5	−	97863.9i	−0.154023	−	0.177752i
$743$	−286490.	+	41191.1i	−0.518958	+	0.0746149i	−0.396817	−	0.917898i	$-0.629885\pi$
$743$	−286490.	+	41191.1i	−0.518958	+	0.0746149i	−0.122141	+	0.992513i	$0.538976\pi$
$744$	118209.	+	34709.2i	0.213552	+	0.0627045i
$745$	309641.	−	198994.i	0.557887	−	0.358532i
$746$	−383374.	−	55120.9i	−0.688883	−	0.0990464i
$747$	−147159.	−	67205.1i	−0.263721	−	0.120437i
$748$	−45264.1	+	99114.5i	−0.0809003	+	0.177147i
$749$	7239.16	−	50349.4i	0.0129040	−	0.0897493i
$750$	116985.	+	182032.i	0.207973	+	0.323612i
$751$	−40637.3	+	138398.i	−0.0720519	+	0.245386i	−0.987642	−	0.156727i	$-0.949906\pi$
$751$	−40637.3	+	138398.i	−0.0720519	+	0.245386i	0.915590	+	0.402113i	$0.131724\pi$
$752$	−36623.8	−	254724.i	−0.0647631	−	0.450437i
$753$	271102.	−	234911.i	0.478126	−	0.414299i
$754$	425891.	+	273703.i	0.749127	+	0.481435i
$755$	388070.	+	336265.i	0.680795	+	0.589912i
$756$	3897.62	+	13274.1i	0.00681955	+	0.0232252i
$757$	418468.	−	191108.i	0.730248	−	0.333493i	−0.0153560	−	0.999882i	$-0.504888\pi$
$757$	418468.	−	191108.i	0.730248	−	0.333493i	0.745604	+	0.666389i	$0.232161\pi$
$758$		−	364147.i		−	0.633779i
$759$	436372.	−	38044.6i	0.757484	−	0.0660404i
$760$	148481.			0.257066
$761$	−206031.	−	451145.i	−0.355765	−	0.779016i	−0.999901	−	0.0141051i	$-0.995510\pi$
$761$	−206031.	−	451145.i	−0.355765	−	0.779016i	0.644136	−	0.764911i	$-0.277217\pi$
$762$	72678.7	−	21340.4i	0.125169	−	0.0367529i
$763$	−4362.95	+	5035.12i	−0.00749431	+	0.00864889i
$764$	27805.7	−	43266.5i	0.0476372	−	0.0741250i
$765$	21081.9	+	24329.8i	0.0360236	+	0.0415735i
$766$	−133417.	+	19182.5i	−0.227382	+	0.0326925i
$767$	−493389.	−	144872.i	−0.838685	−	0.246260i
$768$	17904.8	−	11506.7i	0.0303561	−	0.0195087i
$769$	−698035.	−	100362.i	−1.18039	−	0.169714i	−0.475945	−	0.879475i	$-0.657894\pi$
$769$	−698035.	−	100362.i	−1.18039	−	0.169714i	−0.704442	+	0.709761i	$0.748803\pi$
$770$	−70498.6	−	32195.6i	−0.118905	−	0.0543020i
$771$	72834.2	−	159485.i	0.122525	−	0.268293i
$772$	14414.9	−	100258.i	0.0241867	−	0.168222i
$773$	−428673.	−	667028.i	−0.717409	−	1.11631i	−0.988125	−	0.153651i	$-0.950897\pi$
$773$	−428673.	−	667028.i	−0.717409	−	1.11631i	0.270716	−	0.962659i	$-0.412739\pi$
$774$	−13058.3	+	44472.6i	−0.0217974	+	0.0742353i
$775$	−64180.8	−	446387.i	−0.106857	−	0.743205i
$776$	34646.1	−	30021.0i	0.0575348	−	0.0498542i
$777$	104858.	+	67388.0i	0.173683	+	0.111620i
$778$	−592893.	−	513745.i	−0.979529	−	0.848767i
$779$	191883.	+	653494.i	0.316200	+	1.07688i
$780$	75584.4	−	34518.2i	0.124235	−	0.0567361i
$781$		−	126772.i		−	0.207836i
$782$	125370.	+	25235.7i	0.205012	+	0.0412669i
$783$	−175250.			−0.285847
$784$	59794.9	+	130933.i	0.0972820	+	0.213018i
$785$	−193777.	+	56898.1i	−0.314459	+	0.0923334i
$786$	−65475.9	+	75563.2i	−0.105983	+	0.122311i
$787$	−529650.	+	824151.i	−0.855144	+	1.33063i	0.0872709	+	0.996185i	$0.472185\pi$
$787$	−529650.	+	824151.i	−0.855144	+	1.33063i	−0.942415	+	0.334446i	$0.891451\pi$
$788$	224037.	+	258553.i	0.360801	+	0.416387i
$789$	202167.	−	29067.2i	0.324755	−	0.0466928i
$790$	335476.	+	98504.8i	0.537536	+	0.157835i
$791$	90789.4	−	58346.8i	0.145105	−	0.0932532i
$792$	−96365.0	−	13855.2i	−0.153627	−	0.0220883i
$793$	67815.3	+	30970.2i	0.107840	+	0.0492491i
$794$	−193677.	+	424094.i	−0.307212	+	0.672700i
$795$	38316.4	−	266497.i	0.0606248	−	0.421655i
$796$	−239595.	−	372818.i	−0.378140	−	0.588397i
$797$	249320.	−	849105.i	0.392500	−	1.33673i	−0.492163	−	0.870503i	$-0.663794\pi$
$797$	249320.	−	849105.i	0.392500	−	1.33673i	0.884663	−	0.466231i	$-0.154388\pi$
$798$	−12127.2	−	84346.4i	−0.0190438	−	0.132453i
$799$	−259734.	+	225061.i	−0.406850	+	0.352538i
$800$	−65541.5	−	42121.0i	−0.102409	−	0.0658140i
$801$	−15124.4	−	13105.4i	−0.0235729	−	0.0204261i
$802$	96447.8	+	328471.i	0.149949	+	0.510680i
$803$	1.30502e6	−	595981.i	2.02388	−	0.924275i
$804$		−	52277.8i		−	0.0808734i
$805$	−17949.8	+	89173.8i	−0.0276992	+	0.137609i
$806$	−424668.			−0.653702
$807$	−158194.	−	346397.i	−0.242909	−	0.531896i
$808$	385942.	−	113323.i	0.591152	−	0.173578i
$809$	153961.	−	177681.i	0.235242	−	0.271484i	−0.625838	−	0.779953i	$-0.715243\pi$
$809$	153961.	−	177681.i	0.235242	−	0.271484i	0.861080	+	0.508469i	$0.169788\pi$
$810$	−15551.1	+	24198.0i	−0.0237023	+	0.0368816i
$811$	140582.	+	162241.i	0.213742	+	0.246671i	0.852489	−	0.522746i	$-0.175092\pi$
$811$	140582.	+	162241.i	0.213742	+	0.246671i	−0.638747	+	0.769417i	$0.720547\pi$
$812$	121923.	−	17529.9i	0.184915	−	0.0265868i
$813$	−368489.	−	108198.i	−0.557497	−	0.163696i
$814$	−737906.	+	474223.i	−1.11366	+	0.715705i
$815$	−322930.	−	46430.4i	−0.486176	−	0.0699016i
$816$	−25855.0	−	11807.6i	−0.0388298	−	0.0177330i
$817$	118599.	−	259695.i	0.177679	−	0.389063i
$818$	−84422.3	+	587170.i	−0.126168	+	0.877521i
$819$	−25781.8	−	40117.3i	−0.0384367	−	0.0598086i
$820$	−45525.0	+	155044.i	−0.0677053	+	0.230583i
$821$	127008.	+	883363.i	0.188428	+	1.31055i	0.836078	+	0.548610i	$0.184843\pi$
$821$	127008.	+	883363.i	0.188428	+	1.31055i	−0.647650	+	0.761938i	$0.724248\pi$
$822$	−92252.9	+	79937.6i	−0.136533	+	0.118306i
$823$	395093.	+	253911.i	0.583310	+	0.374870i	0.798765	−	0.601643i	$-0.205487\pi$
$823$	395093.	+	253911.i	0.583310	+	0.374870i	−0.215455	+	0.976514i	$0.569123\pi$
$824$	−28965.2	−	25098.5i	−0.0426601	−	0.0369652i
$825$	100403.	+	341942.i	0.147516	+	0.502394i
$826$	−113807.	+	51974.1i	−0.166805	+	0.0761775i
$827$		−	1.22380e6i		−	1.78937i	−0.446696	−	0.894686i	$-0.647400\pi$
$827$		−	1.22380e6i		−	1.78937i	0.446696	−	0.894686i	$-0.352600\pi$
$828$	9924.33	+	113832.i	0.0144757	+	0.166037i
$829$	4174.52			0.00607431			0.00303716	−	0.999995i	$-0.499033\pi$
$829$	4174.52			0.00607431			0.00303716	+	0.999995i	$0.499033\pi$
$830$	98211.7	+	215054.i	0.142563	+	0.312170i
$831$	−431700.	+	126759.i	−0.625144	+	0.183559i
$832$	−48043.4	+	55445.0i	−0.0694044	+	0.0800969i
$833$	103927.	−	161714.i	0.149775	−	0.233054i
$834$	195201.	+	225274.i	0.280640	+	0.323876i
$835$	−303485.	+	43634.5i	−0.435275	+	0.0625831i
$836$	575376.	+	168946.i	0.823264	+	0.241732i
$837$	123670.	−	79477.6i	0.176527	−	0.113447i
$838$	−513215.	−	73789.2i	−0.730821	−	0.105076i
$839$	−20026.9	−	9146.00i	−0.0284506	−	0.0129929i	0.401139	−	0.916017i	$-0.368614\pi$
$839$	−20026.9	−	9146.00i	−0.0284506	−	0.0129929i	−0.429589	+	0.903024i	$0.641342\pi$
$840$	8398.57	−	18390.3i	0.0119027	−	0.0260634i
$841$	−121405.	+	844390.i	−0.171650	+	1.19385i
$842$	−440408.	−	685287.i	−0.621199	−	0.966604i
$843$	−140441.	+	478298.i	−0.197623	+	0.673044i
$844$	−18558.5	−	129077.i	−0.0260530	−	0.181202i
$845$	84649.5	−	73349.2i	0.118553	−	0.102726i
$846$	−258326.	−	166016.i	−0.360934	−	0.231958i
$847$	−100167.	−	86795.3i	−0.139623	−	0.120984i
$848$	66971.5	+	228084.i	0.0931319	+	0.317178i
$849$	259473.	−	118497.i	0.359979	−	0.164397i
$850$			104046.i			0.144009i
$851$	739199.	+	716540.i	1.02071	+	0.989421i
$852$	33069.8			0.0455567
$853$	−392500.	−	859456.i	−0.539439	−	1.18121i	−0.961542	−	0.274658i	$-0.911435\pi$
$853$	−392500.	−	859456.i	−0.539439	−	1.18121i	0.422103	−	0.906548i	$-0.361292\pi$
$854$	17404.5	−	5110.41i	0.0238641	−	0.00700713i
$855$	116024.	−	133899.i	0.158714	−	0.183166i
$856$	−50484.2	+	78554.9i	−0.0688982	+	0.107208i
$857$	−214590.	−	247650.i	−0.292178	−	0.337192i	0.590615	−	0.806953i	$-0.298885\pi$
$857$	−214590.	−	247650.i	−0.292178	−	0.337192i	−0.882793	+	0.469762i	$0.844340\pi$
$858$	332171.	−	47759.0i	0.451219	−	0.0648755i
$859$	1.32754e6	+	389801.i	1.79913	+	0.528271i	0.997571	−	0.0696503i	$-0.0221884\pi$
$859$	1.32754e6	+	389801.i	1.79913	+	0.528271i	0.801555	+	0.597921i	$0.204007\pi$
$860$	56982.1	−	36620.2i	0.0770444	−	0.0495135i
$861$	91792.8	+	13197.8i	0.123823	+	0.0178031i
$862$	736714.	+	336446.i	0.991481	+	0.452794i
$863$	−612185.	+	1.34050e6i	−0.821979	+	1.79988i	−0.278568	+	0.960417i	$0.589860\pi$
$863$	−612185.	+	1.34050e6i	−0.821979	+	1.79988i	−0.543412	+	0.839466i	$0.682868\pi$
$864$	3614.27	−	25137.8i	0.00484165	−	0.0336744i
$865$	180302.	+	280556.i	0.240973	+	0.374962i
$866$	−189160.	+	644221.i	−0.252229	+	0.859012i
$867$	−56360.8	−	391998.i	−0.0749788	−	0.521489i
$868$	−78088.1	+	67663.7i	−0.103644	+	0.0898083i
$869$	1.18792e6	+	763428.i	1.57306	+	1.01095i
$870$	193551.	+	167713.i	0.255716	+	0.221579i
$871$	50768.9	+	172903.i	0.0669208	+	0.227911i
$872$	11125.1	−	5080.69i	0.0146310	−	0.00668174i
$873$		−	54702.2i		−	0.0717755i
$874$	39277.5	−	702716.i	0.0514186	−	0.919934i
$875$	−181476.			−0.237030
$876$	155468.	+	340427.i	0.202597	+	0.443625i
$877$	−761979.	+	223737.i	−0.990704	+	0.290897i	−0.736636	−	0.676290i	$-0.763587\pi$
$877$	−761979.	+	223737.i	−0.990704	+	0.290897i	−0.254068	+	0.967186i	$0.581769\pi$
$878$	−405011.	+	467408.i	−0.525385	+	0.606327i
$879$	442215.	−	688100.i	0.572342	−	0.890582i
$880$	93169.2	+	107523.i	0.120311	+	0.138847i
$881$	−512668.	+	73710.6i	−0.660518	+	0.0949681i	−0.464418	−	0.885616i	$-0.653737\pi$
$881$	−512668.	+	73710.6i	−0.660518	+	0.0949681i	−0.196099	+	0.980584i	$0.562828\pi$
$882$	164798.	+	48389.2i	0.211844	+	0.0622029i
$883$	318109.	−	204436.i	0.407995	−	0.262203i	−0.320507	−	0.947246i	$-0.603853\pi$
$883$	318109.	−	204436.i	0.407995	−	0.262203i	0.728502	+	0.685044i	$0.240217\pi$
$884$	96979.3	+	13943.5i	0.124101	+	0.0178430i
$885$	−236625.	−	108063.i	−0.302116	−	0.137972i
$886$	−125134.	+	274006.i	−0.159407	+	0.349054i
$887$	90369.5	−	628534.i	0.114862	−	0.798880i	−0.848215	−	0.529652i	$-0.822323\pi$
$887$	90369.5	−	628534.i	0.114862	−	0.798880i	0.963077	−	0.269228i	$-0.0867684\pi$
$888$	−123706.	−	192490.i	−0.156879	−	0.244109i
$889$	−17897.9	+	60954.6i	−0.0226463	+	0.0771264i
$890$	4162.10	+	28948.0i	0.00525451	+	0.0365459i
$891$	−87794.9	+	76074.7i	−0.110589	+	0.0958263i
$892$	357608.	+	229821.i	0.449446	+	0.288841i
$893$	1.42944e6	+	1.23862e6i	1.79252	+	1.55323i
$894$	109249.	+	372067.i	0.136691	+	0.465528i
$895$	−451950.	+	206399.i	−0.564215	+	0.257668i
$896$			17850.1i			0.0222344i
$897$	−143370.	−	366849.i	−0.178186	−	0.455934i
$898$	524825.			0.650821
$899$	−543731.	−	1.19061e6i	−0.672767	−	1.47315i
$900$	−89199.1	+	26191.2i	−0.110122	+	0.0323348i
$901$	207893.	−	239921.i	0.256088	−	0.295542i
$902$	−352826.	+	549008.i	−0.433658	+	0.674786i
$903$	−25456.5	−	29378.4i	−0.0312193	−	0.0360290i
$904$	−196098.	+	28194.6i	−0.239959	+	0.0345009i
$905$	648416.	+	190392.i	0.791693	+	0.232462i
$906$	−455099.	+	292475.i	−0.554434	+	0.356313i
$907$	1.00023e6	+	143811.i	1.21586	+	0.174814i	0.720240	−	0.693725i	$-0.244032\pi$
$907$	1.00023e6	+	143811.i	1.21586	+	0.174814i	0.495621	+	0.868539i	$0.334941\pi$
$908$	655608.	+	299406.i	0.795193	+	0.363152i
$909$	199384.	−	436591.i	0.241303	−	0.528381i
$910$	−9917.82	+	68979.9i	−0.0119766	+	0.0832990i
$911$	−652578.	−	1.01543e6i	−0.786313	−	1.22353i	−0.970610	−	0.240656i	$-0.922637\pi$
$911$	−652578.	−	1.01543e6i	−0.786313	−	1.22353i	0.184297	−	0.982871i	$-0.440999\pi$
$912$	−44071.2	+	150093.i	−0.0529865	+	0.180456i
$913$	135885.	+	945098.i	0.163015	+	1.13380i
$914$	−706585.	+	612259.i	−0.845808	+	0.732897i
$915$	31727.5	+	20390.0i	0.0378960	+	0.0243543i
$916$	−347504.	−	301114.i	−0.414160	−	0.358872i
$917$	−23624.9	−	80458.9i	−0.0280951	−	0.0956831i
$918$	−30851.3	+	14089.3i	−0.0366091	+	0.0167188i
$919$		−	735715.i		−	0.871121i	−0.900159	−	0.435561i	$-0.856550\pi$
$919$		−	735715.i		−	0.871121i	0.900159	−	0.435561i	$-0.143450\pi$
$920$	97976.2	−	135217.i	0.115756	−	0.159756i
$921$	−930324.			−1.09677
$922$	−198629.	−	434937.i	−0.233658	−	0.511640i
$923$	−109374.	+	32115.2i	−0.128384	+	0.0376971i
$924$	53470.1	−	61707.8i	0.0626278	−	0.0722763i
$925$	−452834.	+	704623.i	−0.529243	+	0.823518i
$926$	341188.	+	393752.i	0.397898	+	0.459199i
$927$	−45267.2	+	6508.44i	−0.0526774	+	0.00757386i
$928$	−216959.	−	63705.0i	−0.251931	−	0.0739738i
$929$	802748.	−	515895.i	0.930139	−	0.597764i	0.0145565	−	0.999894i	$-0.495366\pi$
$929$	802748.	−	515895.i	0.930139	−	0.597764i	0.915583	+	0.402130i	$0.131730\pi$
$930$	−212644.	−	30573.6i	−0.245860	−	0.0353493i
$931$	−962331.	−	439482.i	−1.11026	−	0.507039i
$932$	1094.84	−	2397.36i	0.00126043	−	0.00275995i
$933$	−49353.2	+	343259.i	−0.0566960	+	0.394329i
$934$	−554479.	−	862786.i	−0.635610	−	0.989029i
$935$	53530.1	−	182307.i	0.0612315	−	0.208535i
$936$	12458.4	+	86650.3i	0.0142204	+	0.0989051i
$937$	−776065.	+	672464.i	−0.883932	+	0.765932i	−0.973172	−	0.230079i	$-0.926102\pi$
$937$	−776065.	+	672464.i	−0.883932	+	0.765932i	0.0892399	+	0.996010i	$0.471556\pi$
$938$	36884.5	+	23704.2i	0.0419217	+	0.0269414i
$939$	−302632.	−	262233.i	−0.343229	−	0.297410i
$940$	126427.	+	430571.i	0.143082	+	0.487291i
$941$	372947.	−	170319.i	0.421180	−	0.192346i	−0.193539	−	0.981093i	$-0.561997\pi$
$941$	372947.	−	170319.i	0.421180	−	0.192346i	0.614719	+	0.788746i	$0.289269\pi$
$942$		−	212769.i		−	0.239776i
$943$	721733.	+	256470.i	0.811621	+	0.288411i
$944$	229675.			0.257732
$945$	−10021.5	−	21944.1i	−0.0112220	−	0.0245728i
$946$	262477.	−	77070.3i	0.293298	−	0.0861202i
$947$	−23013.1	+	26558.6i	−0.0256611	+	0.0296145i	−0.768435	−	0.639928i	$-0.778964\pi$
$947$	−23013.1	+	26558.6i	−0.0256611	+	0.0296145i	0.742774	+	0.669542i	$0.233510\pi$
$948$	−199148.	+	309880.i	−0.221595	+	0.344808i
$949$	−844793.	−	974943.i	−0.938032	−	1.08255i
$950$	566791.	−	81492.2i	0.628023	−	0.0902961i
$951$	188692.	+	55404.9i	0.208637	+	0.0612614i
$952$	20054.2	−	12888.1i	0.0221275	−	0.0142205i
$953$	1.32248e6	+	190143.i	1.45614	+	0.209361i	0.824482	−	0.565888i	$-0.191467\pi$
$953$	1.32248e6	+	190143.i	1.45614	+	0.209361i	0.631655	+	0.775249i	$0.282376\pi$
$954$	258017.	+	117832.i	0.283499	+	0.129469i
$955$	−37256.0	+	81579.3i	−0.0408498	+	0.0894485i
$956$	−17263.7	+	120072.i	−0.0188894	+	0.131379i
$957$	559199.	+	870130.i	0.610579	+	0.950080i
$958$	−117289.	+	399449.i	−0.127798	+	0.435241i
$959$	−14569.7	−	101335.i	−0.0158422	−	0.110185i
$960$	−28048.5	+	24304.2i	−0.0304346	+	0.0263717i
$961$	146735.	+	94301.1i	0.158887	+	0.102110i
$962$	596077.	+	516504.i	0.644099	+	0.558115i
$963$	31391.5	+	106910.i	0.0338501	+	0.115283i
$964$	−29721.4	+	13573.3i	−0.0319828	+	0.0146060i
$965$			176625.i			0.189669i
$966$	−84814.0	−	44612.6i	−0.0908895	−	0.0478083i
$967$	−530501.			−0.567327			−0.283663	−	0.958924i	$-0.591550\pi$
$967$	−530501.			−0.567327			−0.283663	+	0.958924i	$0.591550\pi$
$968$	101074.	+	221320.i	0.107867	+	0.236195i
$969$	200446.	−	58856.3i	0.213476	−	0.0626823i
$970$	−52349.8	+	60414.9i	−0.0556380	+	0.0642097i
$971$	751634.	−	1.16957e6i	0.797202	−	1.24047i	−0.169744	−	0.985488i	$-0.554294\pi$
$971$	751634.	−	1.16957e6i	0.797202	−	1.24047i	0.966946	−	0.254982i	$-0.0820695\pi$
$972$	−19844.9	−	22902.2i	−0.0210047	−	0.0242407i
$973$	−247451.	+	35578.1i	−0.261375	+	0.0375800i
$974$	154022.	+	45224.9i	0.162354	+	0.0476716i
$975$	269580.	−	173249.i	0.283582	−	0.182247i
$976$	−32959.8	−	4738.90i	−0.0346007	−	0.00497483i
$977$	817416.	+	373301.i	0.856355	+	0.391084i	0.794692	−	0.607013i	$-0.207632\pi$
$977$	817416.	+	373301.i	0.856355	+	0.391084i	0.0616628	+	0.998097i	$0.480360\pi$
$978$	142785.	−	312655.i	0.149281	−	0.326879i
$979$	−16809.4	+	116912.i	−0.0175382	+	0.121981i
$980$	−135700.	−	211154.i	−0.141296	−	0.219860i
$981$	4111.55	−	14002.7i	0.00427236	−	0.0145503i
$982$	−70984.2	−	493706.i	−0.0736103	−	0.511971i
$983$	−168648.	+	146134.i	−0.174531	+	0.151232i	−0.737746	−	0.675078i	$-0.764110\pi$
$983$	−168648.	+	146134.i	−0.174531	+	0.151232i	0.563215	+	0.826311i	$0.309564\pi$
$984$	−143215.	−	92038.4i	−0.147910	−	0.0950558i
$985$	−450857.	−	390670.i	−0.464693	−	0.402659i
$986$	85076.8	+	289745.i	0.0875099	+	0.298032i
$987$	234265.	−	106985.i	0.240477	−	0.109822i
$988$		−	539214.i		−	0.552391i
$989$	−158239.	−	279366.i	−0.161778	−	0.285615i
$990$	169767.			0.173214
$991$	687804.	+	1.50608e6i	0.700354	+	1.53356i	0.839542	+	0.543295i	$0.182823\pi$
$991$	687804.	+	1.50608e6i	0.700354	+	1.53356i	−0.139188	+	0.990266i	$0.544449\pi$
$992$	181994.	−	53438.3i	0.184941	−	0.0543037i
$993$	483036.	−	557453.i	0.489870	−	0.565340i
$994$	−14994.8	+	23332.3i	−0.0151763	+	0.0236148i
$995$	506068.	+	584033.i	0.511166	+	0.589918i
$996$	−246539.	+	35446.9i	−0.248523	+	0.0357322i
$997$	628979.	+	184685.i	0.632770	+	0.185798i	0.582361	−	0.812931i	$-0.302129\pi$
$997$	628979.	+	184685.i	0.632770	+	0.185798i	0.0504096	+	0.998729i	$0.483947\pi$
$998$	867829.	−	557720.i	0.871311	−	0.559958i
$999$	−270251.	−	38856.3i	−0.270793	−	0.0389341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.5.h.a.19.3	✓	160
23.17	odd	22	inner	138.5.h.a.109.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.5.h.a.19.3	✓	160	1.1	even	1	trivial
138.5.h.a.109.3	yes	160	23.17	odd	22	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	138.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17497 - 2.57283i) q^{2} +(-4.98567 + 1.46393i) q^{3} +(-5.23889 + 6.04600i) q^{4} +(7.54204 - 11.7356i) q^{5} +(9.62445 + 11.1072i) q^{6} +(-12.2007 + 1.75419i) q^{7} +(21.7108 + 6.37488i) q^{8} +(22.7138 - 14.5973i) q^{9} +O(q^{10})\)	\(q+(-1.17497 - 2.57283i) q^{2} +(-4.98567 + 1.46393i) q^{3} +(-5.23889 + 6.04600i) q^{4} +(7.54204 - 11.7356i) q^{5} +(9.62445 + 11.1072i) q^{6} +(-12.2007 + 1.75419i) q^{7} +(21.7108 + 6.37488i) q^{8} +(22.7138 - 14.5973i) q^{9} +(-39.0554 - 5.61533i) q^{10} +(-144.954 - 66.1982i) q^{11} +(17.2685 - 37.8127i) q^{12} +(-20.3922 + 141.831i) q^{13} +(18.8487 + 29.3291i) q^{14} +(-20.4220 + 69.5510i) q^{15} +(-9.10815 - 63.3486i) q^{16} +(-64.5945 + 55.9715i) q^{17} +(-64.2445 - 41.2874i) q^{18} +(355.496 + 308.039i) q^{19} +(31.4418 + 107.081i) q^{20} +(58.2605 - 26.6067i) q^{21} +450.722i q^{22} +(515.098 - 120.478i) q^{23} -117.576 q^{24} +(178.792 + 391.499i) q^{25} +(388.867 - 114.182i) q^{26} +(-91.8744 + 106.029i) q^{27} +(53.3120 - 82.9552i) q^{28} +(818.014 + 944.038i) q^{29} +(202.938 - 29.1781i) q^{30} +(-1005.38 - 295.208i) q^{31} +(-152.283 + 97.8664i) q^{32} +(819.601 + 117.841i) q^{33} +(219.902 + 100.426i) q^{34} +(-71.4313 + 156.413i) q^{35} +(-30.7400 + 213.801i) q^{36} +(1052.14 + 1637.16i) q^{37} +(374.833 - 1276.57i) q^{38} +(-105.961 - 736.976i) q^{39} +(238.557 - 206.711i) q^{40} +(1218.06 + 782.802i) q^{41} +(-136.909 - 118.632i) q^{42} +(-170.993 - 582.349i) q^{43} +(1159.63 - 529.585i) q^{44} -376.655i q^{45} +(-915.195 - 1183.70i) q^{46} +4020.99 q^{47} +(138.148 + 302.502i) q^{48} +(-2157.96 + 633.635i) q^{49} +(797.184 - 920.000i) q^{50} +(240.109 - 373.617i) q^{51} +(-750.678 - 866.328i) q^{52} +(-3676.46 + 528.595i) q^{53} +(380.743 + 111.796i) q^{54} +(-1870.12 + 1201.86i) q^{55} +(-276.069 - 39.6928i) q^{56} +(-2223.33 - 1015.36i) q^{57} +(1467.71 - 3213.83i) q^{58} +(-510.720 + 3552.14i) q^{59} +(-313.517 - 487.841i) q^{60} +(146.583 - 499.217i) q^{61} +(421.780 + 2933.54i) q^{62} +(-251.517 + 217.941i) q^{63} +(430.722 + 276.808i) q^{64} +(1510.68 + 1309.01i) q^{65} +(-659.823 - 2247.15i) q^{66} +(1143.96 - 522.430i) q^{67} -683.766i q^{68} +(-2391.74 + 1354.73i) q^{69} +486.353 q^{70} +(330.477 + 723.644i) q^{71} +(586.193 - 172.122i) q^{72} +(-5895.70 + 6804.00i) q^{73} +(2975.90 - 4630.60i) q^{74} +(-1464.52 - 1690.15i) q^{75} +(-3724.80 + 535.546i) q^{76} +(1884.66 + 553.385i) q^{77} +(-1771.61 + 1138.55i) q^{78} +(-8771.06 - 1261.09i) q^{79} +(-812.130 - 370.887i) q^{80} +(302.838 - 663.122i) q^{81} +(582.825 - 4053.64i) q^{82} +(-3239.40 - 5040.61i) q^{83} +(-144.356 + 491.632i) q^{84} +(169.687 + 1180.20i) q^{85} +(-1297.37 + 1124.18i) q^{86} +(-5460.35 - 3509.15i) q^{87} +(-2725.06 - 2361.28i) q^{88} +(-208.821 - 711.179i) q^{89} +(-969.068 + 442.559i) q^{90} -1766.20i q^{91} +(-1970.13 + 3745.45i) q^{92} +5444.68 q^{93} +(-4724.55 - 10345.3i) q^{94} +(6296.19 - 1848.73i) q^{95} +(615.965 - 710.861i) q^{96} +(1095.34 - 1704.39i) q^{97} +(4165.78 + 4807.57i) q^{98} +(-4258.77 + 612.319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 128 q^{4} - 432 q^{9}+O(q^{10}) \) 160 * q - 128 * q^4 - 432 * q^9	\( 160 q - 128 q^{4} - 432 q^{9} + 208 q^{13} - 1024 q^{16} - 1980 q^{17} - 3828 q^{19} - 3168 q^{20} + 3120 q^{23} + 9768 q^{25} + 4416 q^{26} + 5280 q^{28} - 828 q^{29} - 7748 q^{31} + 16464 q^{35} - 3456 q^{36} - 3520 q^{37} - 9072 q^{39} - 5472 q^{41} - 7216 q^{43} - 1280 q^{46} + 6960 q^{47} + 13888 q^{49} - 7296 q^{50} + 17424 q^{51} + 1664 q^{52} + 14784 q^{53} + 37316 q^{55} - 15840 q^{57} - 9984 q^{58} - 29808 q^{59} - 44968 q^{61} - 8192 q^{64} - 5852 q^{67} - 10584 q^{69} + 4352 q^{70} + 30048 q^{71} + 17084 q^{73} + 4176 q^{75} - 14160 q^{77} - 6912 q^{78} + 28424 q^{79} - 11664 q^{81} - 128 q^{82} - 35904 q^{83} - 91892 q^{85} + 8064 q^{87} - 15312 q^{89} - 6720 q^{92} + 11952 q^{93} + 21248 q^{94} + 224268 q^{95} + 41712 q^{97} + 62976 q^{98} + 17820 q^{99}+O(q^{100}) \) 160 * q - 128 * q^4 - 432 * q^9 + 208 * q^13 - 1024 * q^16 - 1980 * q^17 - 3828 * q^19 - 3168 * q^20 + 3120 * q^23 + 9768 * q^25 + 4416 * q^26 + 5280 * q^28 - 828 * q^29 - 7748 * q^31 + 16464 * q^35 - 3456 * q^36 - 3520 * q^37 - 9072 * q^39 - 5472 * q^41 - 7216 * q^43 - 1280 * q^46 + 6960 * q^47 + 13888 * q^49 - 7296 * q^50 + 17424 * q^51 + 1664 * q^52 + 14784 * q^53 + 37316 * q^55 - 15840 * q^57 - 9984 * q^58 - 29808 * q^59 - 44968 * q^61 - 8192 * q^64 - 5852 * q^67 - 10584 * q^69 + 4352 * q^70 + 30048 * q^71 + 17084 * q^73 + 4176 * q^75 - 14160 * q^77 - 6912 * q^78 + 28424 * q^79 - 11664 * q^81 - 128 * q^82 - 35904 * q^83 - 91892 * q^85 + 8064 * q^87 - 15312 * q^89 - 6720 * q^92 + 11952 * q^93 + 21248 * q^94 + 224268 * q^95 + 41712 * q^97 + 62976 * q^98 + 17820 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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