LMFDB - Embedded newform 82.5.e.a.55.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(3,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.3"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.e (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.47633697288$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			55.2
Character	$\chi$	$=$	82.55
Dual form			82.5.e.a.3.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 2.00000i) q^{2} +(-3.50051 - 8.45098i) q^{3} +8.00000i q^{4} +(13.5876 - 13.5876i) q^{5} +(-9.90093 + 23.9030i) q^{6} +(-23.8235 - 57.5149i) q^{7} +(16.0000 - 16.0000i) q^{8} +(-1.88977 + 1.88977i) q^{9} -54.3502 q^{10} +(-20.9969 + 8.69721i) q^{11} +(67.6078 - 28.0041i) q^{12} +(-31.3597 - 75.7090i) q^{13} +(-67.3829 + 162.677i) q^{14} +(-162.392 - 67.2648i) q^{15} -64.0000 q^{16} +(-173.998 + 420.067i) q^{17} +7.55910 q^{18} +(-114.142 + 275.563i) q^{19} +(108.700 + 108.700i) q^{20} +(-402.663 + 402.663i) q^{21} +(59.3882 + 24.5994i) q^{22} -365.026i q^{23} +(-191.224 - 79.2075i) q^{24} +255.756i q^{25} +(-88.6986 + 214.137i) q^{26} +(-661.943 - 274.186i) q^{27} +(460.119 - 190.588i) q^{28} +(-224.336 - 541.596i) q^{29} +(190.253 + 459.313i) q^{30} -429.487i q^{31} +(128.000 + 128.000i) q^{32} +(147.000 + 147.000i) q^{33} +(1188.13 - 492.140i) q^{34} +(-1105.19 - 457.785i) q^{35} +(-15.1182 - 15.1182i) q^{36} +1399.28 q^{37} +(779.410 - 322.842i) q^{38} +(-530.040 + 530.040i) q^{39} -434.802i q^{40} +(-1617.49 + 457.680i) q^{41} +1610.65 q^{42} +(-157.183 - 157.183i) q^{43} +(-69.5776 - 167.975i) q^{44} +51.3548i q^{45} +(-730.052 + 730.052i) q^{46} +(1602.73 - 3869.33i) q^{47} +(224.033 + 540.862i) q^{48} +(-1042.65 + 1042.65i) q^{49} +(511.513 - 511.513i) q^{50} +4159.06 q^{51} +(605.672 - 250.877i) q^{52} +(3051.33 - 1263.90i) q^{53} +(775.515 + 1872.26i) q^{54} +(-167.123 + 403.471i) q^{55} +(-1301.41 - 539.064i) q^{56} +2728.33 q^{57} +(-634.519 + 1531.86i) q^{58} -1145.35 q^{59} +(538.118 - 1299.13i) q^{60} +(31.8770 + 31.8770i) q^{61} +(-858.974 + 858.974i) q^{62} +(153.711 + 63.6693i) q^{63} -512.000i q^{64} +(-1454.80 - 602.599i) q^{65} -587.999i q^{66} +(-831.888 + 2008.35i) q^{67} +(-3360.54 - 1391.98i) q^{68} +(-3084.82 + 1277.78i) q^{69} +(1294.81 + 3125.95i) q^{70} +(-2407.40 - 5811.98i) q^{71} +60.4728i q^{72} +(-1568.23 - 1568.23i) q^{73} +(-2798.55 - 2798.55i) q^{74} +(2161.39 - 895.277i) q^{75} +(-2204.50 - 913.136i) q^{76} +(1000.44 + 1000.44i) q^{77} +2120.16 q^{78} +(-4749.45 + 1967.29i) q^{79} +(-869.604 + 869.604i) q^{80} +6770.33i q^{81} +(4150.35 + 2319.63i) q^{82} +709.274 q^{83} +(-3221.30 - 3221.30i) q^{84} +(3343.49 + 8071.89i) q^{85} +628.731i q^{86} +(-3791.72 + 3791.72i) q^{87} +(-196.795 + 475.106i) q^{88} +(-786.436 - 1898.62i) q^{89} +(102.710 - 102.710i) q^{90} +(-3607.30 + 3607.30i) q^{91} +2920.21 q^{92} +(-3629.58 + 1503.42i) q^{93} +(-10944.1 + 4533.20i) q^{94} +(2193.32 + 5295.14i) q^{95} +(633.660 - 1529.79i) q^{96} +(12165.7 + 5039.21i) q^{97} +4170.59 q^{98} +(23.2437 - 56.1152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) $ 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	−3.50051	−	8.45098i	−0.388945	−	0.938997i	−0.990164	−	0.139913i	$-0.955318\pi$
$3$	−3.50051	−	8.45098i	−0.388945	−	0.938997i	0.601218	−	0.799085i	$-0.294682\pi$
$4$			8.00000i			0.500000i
$5$	13.5876	−	13.5876i	0.543502	−	0.543502i	−0.381051	−	0.924554i	$-0.624438\pi$
$5$	13.5876	−	13.5876i	0.543502	−	0.543502i	0.924554	+	0.381051i	$0.124438\pi$
$6$	−9.90093	+	23.9030i	−0.275026	+	0.663971i
$7$	−23.8235	−	57.5149i	−0.486193	−	1.17377i	−0.956621	−	0.291336i	$-0.905900\pi$
$7$	−23.8235	−	57.5149i	−0.486193	−	1.17377i	0.470428	−	0.882439i	$-0.344100\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	−1.88977	+	1.88977i	−0.0233305	+	0.0233305i
$10$	−54.3502			−0.543502
$11$	−20.9969	+	8.69721i	−0.173528	+	0.0718777i	−0.467756	−	0.883858i	$-0.654937\pi$
$11$	−20.9969	+	8.69721i	−0.173528	+	0.0718777i	0.294228	+	0.955735i	$0.404937\pi$
$12$	67.6078	−	28.0041i	0.469499	−	0.194473i
$13$	−31.3597	−	75.7090i	−0.185560	−	0.447982i	0.803535	−	0.595257i	$-0.202950\pi$
$13$	−31.3597	−	75.7090i	−0.185560	−	0.447982i	−0.989096	+	0.147275i	$0.952950\pi$
$14$	−67.3829	+	162.677i	−0.343791	+	0.829984i
$15$	−162.392	−	67.2648i	−0.721740	−	0.298955i
$16$	−64.0000			−0.250000
$17$	−173.998	+	420.067i	−0.602068	+	1.45352i	0.269381	+	0.963034i	$0.413181\pi$
$17$	−173.998	+	420.067i	−0.602068	+	1.45352i	−0.871449	+	0.490487i	$0.836819\pi$
$18$	7.55910			0.0233305
$19$	−114.142	+	275.563i	−0.316183	+	0.763333i	0.683267	+	0.730168i	$0.260558\pi$
$19$	−114.142	+	275.563i	−0.316183	+	0.763333i	−0.999450	+	0.0331642i	$0.989442\pi$
$20$	108.700	+	108.700i	0.271751	+	0.271751i
$21$	−402.663	+	402.663i	−0.913068	+	0.913068i
$22$	59.3882	+	24.5994i	0.122703	+	0.0508252i
$23$		−	365.026i		−	0.690030i	−0.938597	−	0.345015i	$-0.887874\pi$
$23$		−	365.026i		−	0.690030i	0.938597	−	0.345015i	$-0.112126\pi$
$24$	−191.224	−	79.2075i	−0.331986	−	0.137513i
$25$			255.756i			0.409210i
$26$	−88.6986	+	214.137i	−0.131211	+	0.316771i
$27$	−661.943	−	274.186i	−0.908016	−	0.376112i
$28$	460.119	−	190.588i	0.586887	−	0.243097i
$29$	−224.336	−	541.596i	−0.266750	−	0.643991i	0.732577	−	0.680684i	$-0.238317\pi$
$29$	−224.336	−	541.596i	−0.266750	−	0.643991i	−0.999327	+	0.0366937i	$0.988317\pi$
$30$	190.253	+	459.313i	0.211393	+	0.510347i
$31$		−	429.487i		−	0.446917i	−0.974713	−	0.223458i	$-0.928265\pi$
$31$		−	429.487i		−	0.446917i	0.974713	−	0.223458i	$-0.0717347\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	147.000	+	147.000i	0.134986	+	0.134986i
$34$	1188.13	−	492.140i	1.02779	−	0.425726i
$35$	−1105.19	−	457.785i	−0.902196	−	0.373702i
$36$	−15.1182	−	15.1182i	−0.0116653	−	0.0116653i
$37$	1399.28			1.02212			0.511058	−	0.859546i	$-0.329254\pi$
$37$	1399.28			1.02212			0.511058	+	0.859546i	$0.329254\pi$
$38$	779.410	−	322.842i	0.539758	−	0.223575i
$39$	−530.040	+	530.040i	−0.348481	+	0.348481i
$40$		−	434.802i		−	0.271751i
$41$	−1617.49	+	457.680i	−0.962222	+	0.272267i
$41$	−1617.49	+	457.680i	−0.962222	+	0.272267i
$42$	1610.65			0.913068
$43$	−157.183	−	157.183i	−0.0850096	−	0.0850096i	0.663323	−	0.748333i	$-0.269145\pi$
$43$	−157.183	−	157.183i	−0.0850096	−	0.0850096i	−0.748333	+	0.663323i	$0.769145\pi$
$44$	−69.5776	−	167.975i	−0.0359389	−	0.0867641i
$45$			51.3548i			0.0253604i
$46$	−730.052	+	730.052i	−0.345015	+	0.345015i
$47$	1602.73	−	3869.33i	0.725545	−	1.75162i	0.0686465	−	0.997641i	$-0.478132\pi$
$47$	1602.73	−	3869.33i	0.725545	−	1.75162i	0.656898	−	0.753979i	$-0.271868\pi$
$48$	224.033	+	540.862i	0.0972363	+	0.234749i
$49$	−1042.65	+	1042.65i	−0.434255	+	0.434255i
$50$	511.513	−	511.513i	0.204605	−	0.204605i
$51$	4159.06			1.59902
$52$	605.672	−	250.877i	0.223991	−	0.0927801i
$53$	3051.33	−	1263.90i	1.08627	−	0.449947i	0.233564	−	0.972341i	$-0.424961\pi$
$53$	3051.33	−	1263.90i	1.08627	−	0.449947i	0.852704	+	0.522395i	$0.174961\pi$
$54$	775.515	+	1872.26i	0.265952	+	0.642064i
$55$	−167.123	+	403.471i	−0.0552473	+	0.133379i
$56$	−1301.41	−	539.064i	−0.414992	−	0.171895i
$57$	2728.33			0.839745
$58$	−634.519	+	1531.86i	−0.188620	+	0.455370i
$59$	−1145.35			−0.329028			−0.164514	−	0.986375i	$-0.552606\pi$
$59$	−1145.35			−0.329028			−0.164514	+	0.986375i	$0.552606\pi$
$60$	538.118	−	1299.13i	0.149477	−	0.360870i
$61$	31.8770	+	31.8770i	0.00856677	+	0.00856677i	0.711377	−	0.702810i	$-0.248072\pi$
$61$	31.8770	+	31.8770i	0.00856677	+	0.00856677i	−0.702810	+	0.711377i	$0.748072\pi$
$62$	−858.974	+	858.974i	−0.223458	+	0.223458i
$63$	153.711	+	63.6693i	0.0387279	+	0.0160416i
$64$		−	512.000i		−	0.125000i
$65$	−1454.80	−	602.599i	−0.344332	−	0.142627i
$66$		−	587.999i		−	0.134986i
$67$	−831.888	+	2008.35i	−0.185317	+	0.447395i	−0.989047	−	0.147599i	$-0.952845\pi$
$67$	−831.888	+	2008.35i	−0.185317	+	0.447395i	0.803730	+	0.594994i	$0.202845\pi$
$68$	−3360.54	−	1391.98i	−0.726760	−	0.301034i
$69$	−3084.82	+	1277.78i	−0.647936	+	0.268384i
$70$	1294.81	+	3125.95i	0.264247	+	0.637949i
$71$	−2407.40	−	5811.98i	−0.477564	−	1.15294i	−0.960748	−	0.277423i	$-0.910520\pi$
$71$	−2407.40	−	5811.98i	−0.477564	−	1.15294i	0.483184	−	0.875519i	$-0.339480\pi$
$72$			60.4728i			0.0116653i
$73$	−1568.23	−	1568.23i	−0.294283	−	0.294283i	0.544487	−	0.838770i	$-0.316725\pi$
$73$	−1568.23	−	1568.23i	−0.294283	−	0.294283i	−0.838770	+	0.544487i	$0.816725\pi$
$74$	−2798.55	−	2798.55i	−0.511058	−	0.511058i
$75$	2161.39	−	895.277i	0.384247	−	0.159160i
$76$	−2204.50	−	913.136i	−0.381666	−	0.158091i
$77$	1000.44	+	1000.44i	0.168736	+	0.168736i
$78$	2120.16			0.348481
$79$	−4749.45	+	1967.29i	−0.761008	+	0.315220i	−0.729224	−	0.684275i	$-0.760119\pi$
$79$	−4749.45	+	1967.29i	−0.761008	+	0.315220i	−0.0317836	+	0.999495i	$0.510119\pi$
$80$	−869.604	+	869.604i	−0.135876	+	0.135876i
$81$			6770.33i			1.03191i
$82$	4150.35	+	2319.63i	0.617244	+	0.344978i
$83$	709.274			0.102958			0.0514788	−	0.998674i	$-0.483607\pi$
$83$	709.274			0.102958			0.0514788	+	0.998674i	$0.483607\pi$
$84$	−3221.30	−	3221.30i	−0.456534	−	0.456534i
$85$	3343.49	+	8071.89i	0.462767	+	1.11722i
$86$			628.731i			0.0850096i
$87$	−3791.72	+	3791.72i	−0.500954	+	0.500954i
$88$	−196.795	+	475.106i	−0.0254126	+	0.0613515i
$89$	−786.436	−	1898.62i	−0.0992849	−	0.239695i	0.866431	−	0.499297i	$-0.166408\pi$
$89$	−786.436	−	1898.62i	−0.0992849	−	0.239695i	−0.965716	+	0.259602i	$0.916408\pi$
$90$	102.710	−	102.710i	0.0126802	−	0.0126802i
$91$	−3607.30	+	3607.30i	−0.435612	+	0.435612i
$92$	2920.21			0.345015
$93$	−3629.58	+	1503.42i	−0.419654	+	0.173826i
$94$	−10944.1	+	4533.20i	−1.23858	+	0.513038i
$95$	2193.32	+	5295.14i	0.243027	+	0.586719i
$96$	633.660	−	1529.79i	0.0687565	−	0.165993i
$97$	12165.7	+	5039.21i	1.29299	+	0.535574i	0.919875	−	0.392212i	$-0.128290\pi$
$97$	12165.7	+	5039.21i	1.29299	+	0.535574i	0.373114	+	0.927785i	$0.378290\pi$
$98$	4170.59			0.434255
$99$	23.2437	−	56.1152i	0.00237156	−	0.00572545i
$100$	−2046.05			−0.204605
$101$	−1148.06	+	2771.66i	−0.112544	+	0.271705i	−0.970109	−	0.242671i	$-0.921976\pi$
$101$	−1148.06	+	2771.66i	−0.112544	+	0.271705i	0.857565	+	0.514376i	$0.171976\pi$
$102$	−8318.12	−	8318.12i	−0.799512	−	0.799512i
$103$	8516.35	−	8516.35i	0.802747	−	0.802747i	−0.180777	−	0.983524i	$-0.557861\pi$
$103$	8516.35	−	8516.35i	0.802747	−	0.802747i	0.983524	+	0.180777i	$0.0578611\pi$
$104$	−1713.10	−	709.589i	−0.158386	−	0.0656055i
$105$			10942.4i			0.992510i
$106$	−8630.45	−	3574.85i	−0.768107	−	0.318160i
$107$		−	17329.4i		−	1.51362i	−0.653635	−	0.756810i	$-0.726757\pi$
$107$		−	17329.4i		−	1.51362i	0.653635	−	0.756810i	$-0.273243\pi$
$108$	2193.49	−	5295.55i	0.188056	−	0.454008i
$109$	−14097.0	−	5839.17i	−1.18652	−	0.491472i	−0.299898	−	0.953971i	$-0.596953\pi$
$109$	−14097.0	−	5839.17i	−1.18652	−	0.491472i	−0.886619	+	0.462500i	$0.846953\pi$
$110$	1141.19	−	472.695i	0.0943130	−	0.0390657i
$111$	−4898.18	−	11825.2i	−0.397547	−	0.959763i
$112$	1524.70	+	3680.96i	0.121548	+	0.293444i
$113$		−	13462.0i		−	1.05427i	−0.849781	−	0.527136i	$-0.823266\pi$
$113$		−	13462.0i		−	1.05427i	0.849781	−	0.527136i	$-0.176734\pi$
$114$	−5456.66	−	5456.66i	−0.419873	−	0.419873i
$115$	−4959.81	−	4959.81i	−0.375033	−	0.375033i
$116$	4332.77	−	1794.69i	0.321995	−	0.133375i
$117$	202.336	+	83.8101i	0.0147809	+	0.00612244i
$118$	2290.69	+	2290.69i	0.164514	+	0.164514i
$119$	28305.4			1.99883
$120$	−3674.50	+	1522.03i	−0.255174	+	0.105696i
$121$	−9987.52	+	9987.52i	−0.682161	+	0.682161i
$122$		−	127.508i		−	0.00856677i
$123$	9529.90	+	12067.3i	0.629909	+	0.797627i
$124$	3435.90			0.223458
$125$	11967.3	+	11967.3i	0.765909	+	0.765909i
$126$	−180.084	−	434.761i	−0.0113432	−	0.0273848i
$127$			3051.70i			0.189206i	0.995515	+	0.0946028i	$0.0301581\pi$
$127$			3051.70i			0.189206i	−0.995515	+	0.0946028i	$0.969842\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$	−778.128	+	1878.57i	−0.0467597	+	0.112888i
$130$	1704.41	+	4114.80i	0.100852	+	0.243479i
$131$	5307.94	−	5307.94i	0.309303	−	0.309303i	−0.535336	−	0.844639i	$-0.679815\pi$
$131$	5307.94	−	5307.94i	0.309303	−	0.309303i	0.844639	+	0.535336i	$0.179815\pi$
$132$	−1176.00	+	1176.00i	−0.0674930	+	0.0674930i
$133$	18568.3			1.04971
$134$	5680.48	−	2352.93i	0.316356	−	0.131039i
$135$	−12719.7	+	5268.68i	−0.697927	+	0.289091i
$136$	3937.12	+	9505.04i	0.212863	+	0.513897i
$137$	2771.15	−	6690.16i	0.147645	−	0.356447i	−0.832704	−	0.553719i	$-0.813208\pi$
$137$	2771.15	−	6690.16i	0.147645	−	0.356447i	0.980349	+	0.197272i	$0.0632082\pi$
$138$	8725.20	+	3614.10i	0.458160	+	0.189776i
$139$	33006.6			1.70833			0.854165	−	0.520003i	$-0.174069\pi$
$139$	33006.6			1.70833			0.854165	+	0.520003i	$0.174069\pi$
$140$	3662.28	−	8841.52i	0.186851	−	0.451098i
$141$	−38310.0			−1.92696
$142$	−6809.16	+	16438.8i	−0.337689	+	0.815253i
$143$	1316.91	+	1316.91i	0.0643999	+	0.0643999i
$144$	120.946	−	120.946i	0.00583264	−	0.00583264i
$145$	−10407.2	−	4310.78i	−0.494989	−	0.205031i
$146$			6272.94i			0.294283i
$147$	12461.2	+	5161.59i	0.576666	+	0.238863i
$148$			11194.2i			0.511058i
$149$	6359.21	−	15352.5i	0.286438	−	0.691523i	−0.713520	−	0.700634i	$-0.752900\pi$
$149$	6359.21	−	15352.5i	0.286438	−	0.691523i	0.999958	+	0.00911176i	$0.00290040\pi$
$150$	−6113.34	−	2532.23i	−0.271704	−	0.112543i
$151$	35958.2	−	14894.4i	1.57705	−	0.653234i	0.589105	−	0.808057i	$-0.299481\pi$
$151$	35958.2	−	14894.4i	1.57705	−	0.653234i	0.987942	+	0.154823i	$0.0494806\pi$
$152$	2582.74	+	6235.28i	0.111787	+	0.269879i
$153$	−465.016	−	1122.65i	−0.0198649	−	0.0479580i
$154$		−	4001.75i		−	0.168736i
$155$	−5835.68	−	5835.68i	−0.242900	−	0.242900i
$156$	−4240.32	−	4240.32i	−0.174241	−	0.174241i
$157$	−28009.3	+	11601.8i	−1.13632	+	0.470681i	−0.869926	−	0.493182i	$-0.835834\pi$
$157$	−28009.3	+	11601.8i	−1.13632	+	0.470681i	−0.266398	+	0.963863i	$0.585834\pi$
$158$	13433.5	+	5564.33i	0.538114	+	0.222894i
$159$	−21362.4	−	21362.4i	−0.844998	−	0.844998i
$160$	3478.42			0.135876
$161$	−20994.4	+	8696.18i	−0.809939	+	0.335488i
$162$	13540.7	−	13540.7i	0.515953	−	0.515953i
$163$			2694.06i			0.101399i	0.998714	+	0.0506994i	$0.0161450\pi$
$163$			2694.06i			0.101399i	−0.998714	+	0.0506994i	$0.983855\pi$
$164$	−3661.44	−	12940.0i	−0.136133	−	0.481111i
$165$	3994.74			0.146730
$166$	−1418.55	−	1418.55i	−0.0514788	−	0.0514788i
$167$	−945.989	−	2283.82i	−0.0339198	−	0.0818896i	0.906012	−	0.423252i	$-0.139112\pi$
$167$	−945.989	−	2283.82i	−0.0339198	−	0.0818896i	−0.939932	+	0.341363i	$0.889112\pi$
$168$			12885.2i			0.456534i
$169$	15447.3	−	15447.3i	0.540851	−	0.540851i
$170$	9456.81	−	22830.8i	0.327225	−	0.789992i
$171$	−305.049	−	736.455i	−0.0104323	−	0.0251857i
$172$	1257.46	−	1257.46i	0.0425048	−	0.0425048i
$173$	−4921.64	+	4921.64i	−0.164444	+	0.164444i	−0.784532	−	0.620088i	$-0.787097\pi$
$173$	−4921.64	+	4921.64i	−0.164444	+	0.164444i	0.620088	+	0.784532i	$0.287097\pi$
$174$	15166.9			0.500954
$175$	14709.8	−	6093.00i	0.480320	−	0.198955i
$176$	1343.80	−	556.621i	0.0433821	−	0.0179694i
$177$	4009.29	+	9679.29i	0.127974	+	0.308956i
$178$	−2224.38	+	5370.12i	−0.0702050	+	0.169490i
$179$	−49674.5	−	20575.8i	−1.55034	−	0.642172i	−0.566963	−	0.823743i	$-0.691882\pi$
$179$	−49674.5	−	20575.8i	−1.55034	−	0.642172i	−0.983378	+	0.181571i	$0.941882\pi$
$180$	−410.839			−0.0126802
$181$	−23520.5	+	56783.5i	−0.717942	+	1.73326i	−0.0388116	+	0.999247i	$0.512357\pi$
$181$	−23520.5	+	56783.5i	−0.717942	+	1.73326i	−0.679130	+	0.734018i	$0.737643\pi$
$182$	14429.2			0.435612
$183$	157.806	−	380.977i	0.00471217	−	0.0113762i
$184$	−5840.41	−	5840.41i	−0.172507	−	0.172507i
$185$	19012.7	−	19012.7i	0.555522	−	0.555522i
$186$	10266.0	+	4252.32i	0.296740	+	0.122914i
$187$		−	10333.4i		−	0.295502i
$188$	30954.6	+	12821.8i	0.875810	+	0.362772i
$189$			44603.7i			1.24867i
$190$	6203.64	−	14976.9i	0.171846	−	0.414873i
$191$	−36074.0	−	14942.3i	−0.988844	−	0.409592i	−0.171149	−	0.985245i	$-0.554748\pi$
$191$	−36074.0	−	14942.3i	−0.988844	−	0.409592i	−0.817694	+	0.575653i	$0.804748\pi$
$192$	−4326.90	+	1792.26i	−0.117375	+	0.0486182i
$193$	−11019.8	−	26604.0i	−0.295840	−	0.714221i	−0.999991	−	0.00417123i	$-0.998672\pi$
$193$	−11019.8	−	26604.0i	−0.295840	−	0.714221i	0.704151	−	0.710050i	$-0.251328\pi$
$194$	−14253.0	−	34409.9i	−0.378708	−	0.914281i
$195$			14403.9i			0.378801i
$196$	−8341.17	−	8341.17i	−0.217128	−	0.217128i
$197$	−28106.5	−	28106.5i	−0.724227	−	0.724227i	0.245237	−	0.969463i	$-0.421134\pi$
$197$	−28106.5	−	28106.5i	−0.724227	−	0.724227i	−0.969463	+	0.245237i	$0.921134\pi$
$198$	−158.718	+	65.7430i	−0.00404851	+	0.00167695i
$199$	−32417.2	−	13427.6i	−0.818595	−	0.339073i	−0.0662174	−	0.997805i	$-0.521093\pi$
$199$	−32417.2	−	13427.6i	−0.818595	−	0.339073i	−0.752378	+	0.658732i	$0.771093\pi$
$200$	4092.10	+	4092.10i	0.102303	+	0.102303i
$201$	19884.6			0.492180
$202$	7839.44	−	3247.20i	0.192124	−	0.0795805i
$203$	−25805.4	+	25805.4i	−0.626208	+	0.626208i
$204$			33272.5i			0.799512i
$205$	−15759.0	+	28196.6i	−0.374992	+	0.670948i
$206$	−34065.4			−0.802747
$207$	689.816	+	689.816i	0.0160988	+	0.0160988i
$208$	2007.02	+	4845.37i	0.0463901	+	0.111996i
$209$		−	6778.69i		−	0.155186i
$210$	21884.8	−	21884.8i	0.496255	−	0.496255i
$211$	−5973.40	+	14421.1i	−0.134170	+	0.323916i	−0.976658	−	0.214799i	$-0.931090\pi$
$211$	−5973.40	+	14421.1i	−0.134170	+	0.323916i	0.842488	+	0.538716i	$0.181090\pi$
$212$	10111.2	+	24410.6i	0.224973	+	0.543134i
$213$	−40689.8	+	40689.8i	−0.896863	+	0.896863i
$214$	−34658.9	+	34658.9i	−0.756810	+	0.756810i
$215$	−4271.46			−0.0924059
$216$	−14978.1	+	6204.12i	−0.321032	+	0.132976i
$217$	−24701.9	+	10231.9i	−0.524579	+	0.217288i
$218$	16515.7	+	39872.4i	0.347523	+	0.838994i
$219$	−7763.49	+	18742.7i	−0.161871	+	0.390791i
$220$	−3227.77	−	1336.98i	−0.0666894	−	0.0276236i
$221$	37259.4			0.762871
$222$	−13854.1	+	33446.8i	−0.281108	+	0.678655i
$223$	59172.9			1.18991			0.594954	−	0.803760i	$-0.297170\pi$
$223$	59172.9			1.18991			0.594954	+	0.803760i	$0.297170\pi$
$224$	4312.51	−	10411.3i	0.0859476	−	0.207496i
$225$	−483.322	−	483.322i	−0.00954710	−	0.00954710i
$226$	−26924.0	+	26924.0i	−0.527136	+	0.527136i
$227$	−35342.7	−	14639.4i	−0.685880	−	0.284101i	0.0124027	−	0.999923i	$-0.496052\pi$
$227$	−35342.7	−	14639.4i	−0.685880	−	0.284101i	−0.698282	+	0.715822i	$0.746052\pi$
$228$			21826.7i			0.419873i
$229$	12813.3	+	5307.46i	0.244338	+	0.101208i	0.501492	−	0.865162i	$-0.332785\pi$
$229$	12813.3	+	5307.46i	0.244338	+	0.101208i	−0.257154	+	0.966371i	$0.582785\pi$
$230$			19839.2i			0.375033i
$231$	4952.64	−	11956.7i	0.0928138	−	0.224072i
$232$	−12254.9	−	5076.15i	−0.227685	−	0.0943102i
$233$	69669.8	−	28858.2i	1.28331	−	0.531566i	0.366328	−	0.930486i	$-0.380615\pi$
$233$	69669.8	−	28858.2i	1.28331	−	0.531566i	0.916986	+	0.398920i	$0.130615\pi$
$234$	−237.051	−	572.291i	−0.00432922	−	0.0104517i
$235$	−30797.6	−	74351.9i	−0.557674	−	1.34635i
$236$		−	9162.77i		−	0.164514i
$237$	33251.0	+	33251.0i	0.591981	+	0.591981i
$238$	−56610.7	−	56610.7i	−0.999413	−	0.999413i
$239$	−3870.95	+	1603.40i	−0.0677676	+	0.0280703i	−0.416310	−	0.909223i	$-0.636677\pi$
$239$	−3870.95	+	1603.40i	−0.0677676	+	0.0280703i	0.348542	+	0.937293i	$0.386677\pi$
$240$	10393.1	+	4304.95i	0.180435	+	0.0747386i
$241$	45540.4	+	45540.4i	0.784084	+	0.784084i	0.980517	−	0.196433i	$-0.0629359\pi$
$241$	45540.4	+	45540.4i	0.784084	+	0.784084i	−0.196433	+	0.980517i	$0.562936\pi$
$242$	39950.1			0.682161
$243$	3598.51	−	1490.55i	0.0609410	−	0.0252426i
$244$	−255.016	+	255.016i	−0.00428339	+	0.00428339i
$245$			28334.1i			0.472038i
$246$	5074.79	−	43194.4i	0.0838586	−	0.713768i
$247$	24442.1			0.400630
$248$	−6871.79	−	6871.79i	−0.111729	−	0.111729i
$249$	−2482.82	−	5994.06i	−0.0400449	−	0.0966768i
$250$		−	47869.3i		−	0.765909i
$251$	14490.2	−	14490.2i	0.229999	−	0.229999i	−0.582693	−	0.812692i	$-0.698001\pi$
$251$	14490.2	−	14490.2i	0.229999	−	0.229999i	0.812692	+	0.582693i	$0.198001\pi$
$252$	−509.354	+	1229.69i	−0.00802082	+	0.0193640i
$253$	3174.70	+	7664.41i	0.0495978	+	0.119740i
$254$	6103.39	−	6103.39i	0.0946028	−	0.0946028i
$255$	56511.5	−	56511.5i	0.869073	−	0.869073i
$256$	4096.00			0.0625000
$257$	63941.0	−	26485.2i	0.968084	−	0.400994i	0.158086	−	0.987425i	$-0.449468\pi$
$257$	63941.0	−	26485.2i	0.968084	−	0.400994i	0.809999	+	0.586432i	$0.199468\pi$
$258$	5313.39	−	2200.88i	0.0798238	−	0.0330641i
$259$	−33335.6	−	80479.3i	−0.496945	−	1.19973i
$260$	4820.79	−	11638.4i	0.0713135	−	0.172166i
$261$	1447.44	+	599.549i	0.0212481	+	0.00880124i
$262$	−21231.8			−0.309303
$263$	−29952.6	+	72311.9i	−0.433035	+	1.04544i	0.545269	+	0.838261i	$0.316428\pi$
$263$	−29952.6	+	72311.9i	−0.433035	+	1.04544i	−0.978304	+	0.207177i	$0.933572\pi$
$264$	4703.99			0.0674930
$265$	24286.8	−	58633.4i	0.345842	−	0.834936i
$266$	−37136.5	−	37136.5i	−0.524853	−	0.524853i
$267$	−13292.3	+	13292.3i	−0.186456	+	0.186456i
$268$	−16066.8	−	6655.10i	−0.223697	−	0.0926585i
$269$		−	130621.i		−	1.80513i	−0.430557	−	0.902563i	$-0.641683\pi$
$269$		−	130621.i		−	1.80513i	0.430557	−	0.902563i	$-0.358317\pi$
$270$	35976.8	+	14902.1i	0.493509	+	0.204418i
$271$			80395.2i			1.09469i	0.836907	+	0.547346i	$0.184362\pi$
$271$			80395.2i			1.09469i	−0.836907	+	0.547346i	$0.815638\pi$
$272$	11135.8	−	26884.3i	0.150517	−	0.363380i
$273$	43112.6	+	17857.8i	0.578467	+	0.239609i
$274$	−18922.6	+	7838.01i	−0.252046	+	0.104401i
$275$	−2224.37	−	5370.09i	−0.0294131	−	0.0710095i
$276$	−10222.2	−	24678.6i	−0.134192	−	0.323968i
$277$			44197.6i			0.576022i	0.957627	+	0.288011i	$0.0929940\pi$
$277$			44197.6i			0.576022i	−0.957627	+	0.288011i	$0.907006\pi$
$278$	−66013.3	−	66013.3i	−0.854165	−	0.854165i
$279$	811.633	+	811.633i	0.0104268	+	0.0104268i
$280$	−25007.6	+	10358.5i	−0.318975	+	0.132124i
$281$	140603.	+	58239.7i	1.78066	+	0.737575i	0.992520	+	0.122086i	$0.0389582\pi$
$281$	140603.	+	58239.7i	1.78066	+	0.737575i	0.788145	+	0.615490i	$0.211042\pi$
$282$	76619.9	+	76619.9i	0.963482	+	0.963482i
$283$	64706.3			0.807930			0.403965	−	0.914774i	$-0.367632\pi$
$283$	64706.3			0.807930			0.403965	+	0.914774i	$0.367632\pi$
$284$	46495.8	−	19259.2i	0.576471	−	0.238782i
$285$	37071.4	−	37071.4i	0.456404	−	0.456404i
$286$		−	5267.65i		−	0.0643999i
$287$	64857.8	+	82126.6i	0.787405	+	0.997057i
$288$	−483.782			−0.00583264
$289$	−87123.2	−	87123.2i	−1.04313	−	1.04313i
$290$	12192.7	+	29435.9i	0.144979	+	0.350010i
$291$		−	120452.i		−	1.42242i
$292$	12545.9	−	12545.9i	0.147141	−	0.147141i
$293$	−62590.9	+	151108.i	−0.729081	+	1.76016i	−0.0834453	+	0.996512i	$0.526592\pi$
$293$	−62590.9	+	151108.i	−0.729081	+	1.76016i	−0.645636	+	0.763645i	$0.723408\pi$
$294$	−14599.2	−	35245.5i	−0.168902	−	0.407764i
$295$	−15562.5	+	15562.5i	−0.178827	+	0.178827i
$296$	22388.4	−	22388.4i	0.255529	−	0.255529i
$297$	16283.4			0.184600
$298$	−43423.4	+	17986.6i	−0.488980	+	0.202542i
$299$	−27635.7	+	11447.1i	−0.309121	+	0.128042i
$300$	7162.22	+	17291.1i	0.0795802	+	0.192124i
$301$	−5295.72	+	12785.0i	−0.0584510	+	0.141113i
$302$	−101705.	−	42127.7i	−1.11514	−	0.461906i
$303$	27442.0			0.298904
$304$	7305.09	−	17636.0i	0.0790457	−	0.190833i
$305$	866.260			0.00931212
$306$	−1315.26	+	3175.33i	−0.0140466	+	0.0339114i
$307$	53731.5	+	53731.5i	0.570101	+	0.570101i	0.932157	−	0.362055i	$-0.117925\pi$
$307$	53731.5	+	53731.5i	0.570101	+	0.570101i	−0.362055	+	0.932157i	$0.617925\pi$
$308$	−8003.51	+	8003.51i	−0.0843682	+	0.0843682i
$309$	−101783.	−	42159.9i	−1.06600	−	0.441553i
$310$			23342.7i			0.242900i
$311$	150898.	+	62504.0i	1.56014	+	0.646230i	0.985113	−	0.171906i	$-0.0549927\pi$
$311$	150898.	+	62504.0i	1.56014	+	0.646230i	0.575024	+	0.818136i	$0.304993\pi$
$312$			16961.3i			0.174241i
$313$	40221.6	−	97103.4i	0.410554	−	0.991165i	−0.574436	−	0.818550i	$-0.694778\pi$
$313$	40221.6	−	97103.4i	0.410554	−	0.991165i	0.984989	−	0.172615i	$-0.0552216\pi$
$314$	79222.2	+	32814.9i	0.803503	+	0.332822i
$315$	2953.67	−	1223.45i	0.0297674	−	0.0123301i
$316$	−15738.3	−	37995.6i	−0.157610	−	0.380504i
$317$	−12014.9	−	29006.5i	−0.119564	−	0.288653i	0.852755	−	0.522312i	$-0.174930\pi$
$317$	−12014.9	−	29006.5i	−0.119564	−	0.288653i	−0.972319	+	0.233658i	$0.924930\pi$
$318$			85449.5i			0.844998i
$319$	9420.74	+	9420.74i	0.0925772	+	0.0925772i
$320$	−6956.83	−	6956.83i	−0.0679378	−	0.0679378i
$321$	−146451.	+	60661.8i	−1.42128	+	0.588715i
$322$	59381.2	+	24596.5i	0.572713	+	0.237226i
$323$	−95894.6	−	95894.6i	−0.919156	−	0.919156i
$324$	−54162.7			−0.515953
$325$	19363.1	−	8020.44i	0.183319	−	0.0759332i
$326$	5388.12	−	5388.12i	0.0506994	−	0.0506994i
$327$			139574.i			1.30529i
$328$	−18557.0	+	33202.8i	−0.172489	+	0.308622i
$329$	−260727.			−2.40876
$330$	−7989.47	−	7989.47i	−0.0733652	−	0.0733652i
$331$	71753.6	+	173229.i	0.654919	+	1.58111i	0.805552	+	0.592525i	$0.201869\pi$
$331$	71753.6	+	173229.i	0.654919	+	1.58111i	−0.150633	+	0.988590i	$0.548131\pi$
$332$			5674.20i			0.0514788i
$333$	−2644.32	+	2644.32i	−0.0238465	+	0.0238465i
$334$	−2675.66	+	6459.61i	−0.0239849	+	0.0579047i
$335$	15985.3	+	38592.0i	0.142440	+	0.343880i
$336$	25770.4	−	25770.4i	0.228267	−	0.228267i
$337$	61979.5	−	61979.5i	0.545743	−	0.545743i	−0.379464	−	0.925207i	$-0.623891\pi$
$337$	61979.5	−	61979.5i	0.545743	−	0.545743i	0.925207	+	0.379464i	$0.123891\pi$
$338$	−61789.0			−0.540851
$339$	−113767.	+	47123.9i	−0.989959	+	0.410054i
$340$	−64575.2	+	26747.9i	−0.558609	+	0.231383i
$341$	3735.34	+	9017.90i	0.0321234	+	0.0775527i
$342$	−862.810	+	2083.01i	−0.00737672	+	0.0178090i
$343$	−53286.1	−	22071.8i	−0.452925	−	0.187608i
$344$	−5029.85			−0.0425048
$345$	−24553.4	+	59277.1i	−0.206288	+	0.498022i
$346$	19686.6			0.164444
$347$	−33450.9	+	80757.7i	−0.277811	+	0.670695i	−0.999774	−	0.0212362i	$-0.993240\pi$
$347$	−33450.9	+	80757.7i	−0.277811	+	0.670695i	0.721964	+	0.691931i	$0.243240\pi$
$348$	−30333.8	−	30333.8i	−0.250477	−	0.250477i
$349$	148357.	−	148357.i	1.21802	−	1.21802i	0.249702	−	0.968323i	$-0.419667\pi$
$349$	148357.	−	148357.i	1.21802	−	1.21802i	0.968323	−	0.249702i	$-0.0803327\pi$
$350$	−41605.6	−	17233.6i	−0.339638	−	0.140683i
$351$			58713.4i			0.476566i
$352$	−3800.85	−	1574.36i	−0.0306757	−	0.0127063i
$353$			42075.8i			0.337663i	0.985645	+	0.168831i	$0.0539993\pi$
$353$			42075.8i			0.337663i	−0.985645	+	0.168831i	$0.946001\pi$
$354$	11340.0	−	27377.2i	0.0904912	−	0.218465i
$355$	−111681.	−	46259.9i	−0.886184	−	0.367069i
$356$	15189.0	−	6291.48i	0.119847	−	0.0496424i
$357$	−99083.2	−	239208.i	−0.777434	−	1.87689i
$358$	58197.3	+	140501.i	0.454084	+	1.09626i
$359$			21259.0i			0.164950i	0.996593	+	0.0824752i	$0.0262825\pi$
$359$			21259.0i			0.164950i	−0.996593	+	0.0824752i	$0.973717\pi$
$360$	821.677	+	821.677i	0.00634010	+	0.00634010i
$361$	29244.2	+	29244.2i	0.224402	+	0.224402i
$362$	160608.	−	66526.0i	1.22560	−	0.507661i
$363$	119366.	+	49442.9i	0.905871	+	0.375224i
$364$	−28858.4	−	28858.4i	−0.217806	−	0.217806i
$365$	−42616.9			−0.319887
$366$	−1077.57	+	446.342i	−0.00804418	+	0.00333201i
$367$	−9285.44	+	9285.44i	−0.0689399	+	0.0689399i	−0.740736	−	0.671796i	$-0.765523\pi$
$367$	−9285.44	+	9285.44i	−0.0689399	+	0.0689399i	0.671796	+	0.740736i	$0.265523\pi$
$368$			23361.6i			0.172507i
$369$	2191.79	−	3921.61i	0.0160970	−	0.0288013i
$370$	−76051.0			−0.555522
$371$	−145386.	−	145386.i	−1.05627	−	1.05627i
$372$	−12027.4	−	29036.7i	−0.0869131	−	0.209827i
$373$		−	83998.7i		−	0.603747i	−0.953348	−	0.301873i	$-0.902388\pi$
$373$		−	83998.7i		−	0.603747i	0.953348	−	0.301873i	$-0.0976120\pi$
$374$	−20666.8	+	20666.8i	−0.147751	+	0.147751i
$375$	59243.9	−	143027.i	0.421290	−	1.01708i
$376$	−36265.6	−	87552.9i	−0.256519	−	0.619291i
$377$	−33968.6	+	33968.6i	−0.238998	+	0.238998i
$378$	89207.4	−	89207.4i	0.624334	−	0.624334i
$379$	−121354.			−0.844845			−0.422422	−	0.906399i	$-0.638820\pi$
$379$	−121354.			−0.844845			−0.422422	+	0.906399i	$0.638820\pi$
$380$	−42361.1	+	17546.6i	−0.293360	+	0.121514i
$381$	25789.8	−	10682.5i	0.177663	−	0.0735906i
$382$	42263.3	+	102033.i	0.289626	+	0.699218i
$383$	−62013.5	+	149714.i	−0.422755	+	1.02062i	0.558776	+	0.829318i	$0.311271\pi$
$383$	−62013.5	+	149714.i	−0.422755	+	1.02062i	−0.981531	+	0.191302i	$0.938729\pi$
$384$	12238.3	+	5069.28i	0.0829964	+	0.0343782i
$385$	27187.0			0.183417
$386$	−31168.6	+	75247.6i	−0.209191	+	0.505031i
$387$	594.080			0.00396664
$388$	−40313.7	+	97325.9i	−0.267787	+	0.646495i
$389$	−62160.1	−	62160.1i	−0.410783	−	0.410783i	0.471228	−	0.882011i	$-0.343811\pi$
$389$	−62160.1	−	62160.1i	−0.410783	−	0.410783i	−0.882011	+	0.471228i	$0.843811\pi$
$390$	28807.8	−	28807.8i	0.189400	−	0.189400i
$391$	153335.	+	63513.6i	1.00297	+	0.415445i
$392$			33364.7i			0.217128i
$393$	−63437.8	−	26276.8i	−0.410736	−	0.170132i
$394$			112426.i			0.724227i
$395$	−37802.8	+	91264.0i	−0.242287	+	0.584932i
$396$	448.921	+	185.949i	0.00286273	+	0.00118578i
$397$	269795.	−	111753.i	1.71180	−	0.709051i	0.711823	−	0.702359i	$-0.247870\pi$
$397$	269795.	−	111753.i	1.71180	−	0.709051i	0.999978	−	0.00669256i	$-0.00213032\pi$
$398$	37979.1	+	91689.6i	0.239761	+	0.578834i
$399$	−64998.3	−	156920.i	−0.408278	−	0.985671i
$400$		−	16368.4i		−	0.102303i
$401$	78604.1	+	78604.1i	0.488828	+	0.488828i	0.907936	−	0.419108i	$-0.137657\pi$
$401$	78604.1	+	78604.1i	0.488828	+	0.488828i	−0.419108	+	0.907936i	$0.637657\pi$
$402$	−39769.2	−	39769.2i	−0.246090	−	0.246090i
$403$	−32516.0	+	13468.6i	−0.200211	+	0.0829300i
$404$	−22173.3	−	9184.48i	−0.135852	−	0.0562719i
$405$	91992.3	+	91992.3i	0.560843	+	0.560843i
$406$	103222.			0.626208
$407$	−29380.5	+	12169.8i	−0.177366	+	0.0734673i
$408$	66544.9	−	66544.9i	0.399756	−	0.399756i
$409$		−	53852.7i		−	0.321930i	−0.986960	−	0.160965i	$-0.948539\pi$
$409$		−	53852.7i		−	0.321930i	0.986960	−	0.160965i	$-0.0514606\pi$
$410$	87911.2	−	24875.0i	0.522970	−	0.147978i
$411$	−66238.8			−0.392129
$412$	68130.8	+	68130.8i	0.401374	+	0.401374i
$413$	27286.1	+	65874.5i	0.159971	+	0.386204i
$414$		−	2759.27i		−	0.0160988i
$415$	9637.31	−	9637.31i	0.0559577	−	0.0559577i
$416$	5676.71	−	13704.8i	0.0328027	−	0.0791928i
$417$	−115540.	−	278938.i	−0.664447	−	1.60412i
$418$	−13557.4	+	13557.4i	−0.0775931	+	0.0775931i
$419$	−154489.	+	154489.i	−0.879971	+	0.879971i	−0.993531	−	0.113560i	$-0.963774\pi$
$419$	−154489.	+	154489.i	−0.879971	+	0.879971i	0.113560	+	0.993531i	$0.463774\pi$
$420$	−87539.3			−0.496255
$421$	16999.3	−	7041.32i	0.0959104	−	0.0397274i	−0.334212	−	0.942498i	$-0.608470\pi$
$421$	16999.3	−	7041.32i	0.0959104	−	0.0397274i	0.430123	+	0.902770i	$0.358470\pi$
$422$	40788.9	−	16895.3i	0.229043	−	0.0948728i
$423$	4283.36	+	10341.0i	0.0239389	+	0.0577936i
$424$	28598.8	−	69043.6i	0.159080	−	0.384054i
$425$	−107435.	−	44501.0i	−0.594795	−	0.246372i
$426$	162759.			0.896863
$427$	1073.98	−	2592.82i	0.00589035	−	0.0142206i
$428$	138635.			0.756810
$429$	6519.33	−	15739.1i	0.0354233	−	0.0855193i
$430$	8542.92	+	8542.92i	0.0462029	+	0.0462029i
$431$	151315.	−	151315.i	0.814569	−	0.814569i	−0.170746	−	0.985315i	$-0.554618\pi$
$431$	151315.	−	151315.i	0.814569	−	0.814569i	0.985315	+	0.170746i	$0.0546178\pi$
$432$	42364.4	+	17547.9i	0.227004	+	0.0940281i
$433$			241028.i			1.28556i	0.766052	+	0.642778i	$0.222218\pi$
$433$			241028.i			1.28556i	−0.766052	+	0.642778i	$0.777782\pi$
$434$	69867.6	+	28940.1i	0.370934	+	0.153646i
$435$			103041.i			0.544540i
$436$	46713.4	−	112776.i	0.245736	−	0.593259i
$437$	100588.	+	41664.8i	0.526722	+	0.218176i
$438$	53012.4	−	21958.5i	0.276331	−	0.114460i
$439$	27291.7	+	65888.0i	0.141612	+	0.341883i	0.978734	−	0.205134i	$-0.0657632\pi$
$439$	27291.7	+	65888.0i	0.141612	+	0.341883i	−0.837121	+	0.547017i	$0.815763\pi$
$440$	3781.56	+	9129.50i	0.0195329	+	0.0471565i
$441$		−	3940.73i		−	0.0202628i
$442$	−74518.8	−	74518.8i	−0.381435	−	0.381435i
$443$	51338.6	+	51338.6i	0.261599	+	0.261599i	0.825703	−	0.564104i	$-0.190778\pi$
$443$	51338.6	+	51338.6i	0.261599	+	0.261599i	−0.564104	+	0.825703i	$0.690778\pi$
$444$	94602.0	−	39185.4i	0.479882	−	0.198774i
$445$	−36483.4	−	15111.9i	−0.184236	−	0.0763132i
$446$	−118346.	−	118346.i	−0.594954	−	0.594954i
$447$	−152004.			−0.760747
$448$	−29447.6	+	12197.6i	−0.146722	+	0.0607741i
$449$	−11184.9	+	11184.9i	−0.0554805	+	0.0554805i	−0.734303	−	0.678822i	$-0.762491\pi$
$449$	−11184.9	+	11184.9i	−0.0554805	+	0.0554805i	0.678822	+	0.734303i	$0.262491\pi$
$450$			1933.29i			0.00954710i
$451$	29981.9	−	23677.6i	0.147403	−	0.116408i
$452$	107696.			0.527136
$453$	−251744.	−	251744.i	−1.22677	−	1.22677i
$454$	41406.5	+	99964.2i	0.200889	+	0.484990i
$455$			98028.8i			0.473512i
$456$	43653.3	−	43653.3i	0.209936	−	0.209936i
$457$	64255.7	−	155127.i	0.307666	−	0.742771i	−0.692114	−	0.721788i	$-0.743321\pi$
$457$	64255.7	−	155127.i	0.307666	−	0.742771i	0.999780	−	0.0209826i	$-0.00667946\pi$
$458$	−15011.8	−	36241.6i	−0.0715650	−	0.172773i
$459$	230353.	−	230353.i	1.09337	−	1.09337i
$460$	39678.5	−	39678.5i	0.187516	−	0.187516i
$461$	221425.			1.04190			0.520950	−	0.853587i	$-0.325578\pi$
$461$	221425.			1.04190			0.520950	+	0.853587i	$0.325578\pi$
$462$	−33818.7	+	14008.2i	−0.158443	+	0.0656293i
$463$	−45021.3	+	18648.4i	−0.210018	+	0.0869922i	−0.485212	−	0.874396i	$-0.661258\pi$
$463$	−45021.3	+	18648.4i	−0.210018	+	0.0869922i	0.275195	+	0.961389i	$0.411258\pi$
$464$	14357.5	+	34662.1i	0.0666874	+	0.160998i
$465$	−28889.3	+	69745.0i	−0.133608	+	0.322558i
$466$	−197056.	−	81623.2i	−0.907439	−	0.375874i
$467$	−368422.			−1.68932			−0.844661	−	0.535302i	$-0.820198\pi$
$467$	−368422.			−1.68932			−0.844661	+	0.535302i	$0.820198\pi$
$468$	−670.481	+	1618.68i	−0.00306122	+	0.00739044i
$469$	135329.			0.615240
$470$	−87108.7	+	210299.i	−0.394335	+	0.952010i
$471$	196093.	+	196093.i	0.883936	+	0.883936i
$472$	−18325.5	+	18325.5i	−0.0822570	+	0.0822570i
$473$	4667.40	+	1933.30i	0.0208619	+	0.00864127i
$474$		−	133004.i		−	0.591981i
$475$	−70477.0	−	29192.5i	−0.312364	−	0.129385i
$476$			226443.i			0.999413i
$477$	−3377.83	+	8154.80i	−0.0148457	+	0.0358407i
$478$	10948.7	+	4535.10i	0.0479189	+	0.0198487i
$479$	296093.	−	122646.i	1.29050	−	0.534542i	0.371364	−	0.928487i	$-0.378890\pi$
$479$	296093.	−	122646.i	1.29050	−	0.534542i	0.919134	+	0.393946i	$0.128890\pi$
$480$	−12176.2	−	29396.0i	−0.0528482	−	0.127587i
$481$	−43880.8	−	105938.i	−0.189664	−	0.457889i
$482$		−	182162.i		−	0.784084i
$483$	146982.	+	146982.i	0.630044	+	0.630044i
$484$	−79900.2	−	79900.2i	−0.341081	−	0.341081i
$485$	233773.	−	96832.1i	0.993828	−	0.411657i
$486$	−10178.1	−	4215.91i	−0.0430918	−	0.0178492i
$487$	183899.	+	183899.i	0.775392	+	0.775392i	0.979043	−	0.203652i	$-0.0652809\pi$
$487$	183899.	+	183899.i	0.775392	+	0.775392i	−0.203652	+	0.979043i	$0.565281\pi$
$488$	1020.06			0.00428339
$489$	22767.5	−	9430.59i	0.0952131	−	0.0394386i
$490$	56668.1	−	56668.1i	0.236019	−	0.236019i
$491$			359076.i			1.48944i	0.667377	+	0.744720i	$0.267417\pi$
$491$			359076.i			1.48944i	−0.667377	+	0.744720i	$0.732583\pi$
$492$	−96538.4	+	76239.2i	−0.398813	+	0.314955i
$493$	266541.			1.09665
$494$	−48884.1	−	48884.1i	−0.200315	−	0.200315i
$495$	−446.644	−	1078.29i	−0.00182285	−	0.00440075i
$496$			27487.2i			0.111729i
$497$	−276923.	+	276923.i	−1.12110	+	1.12110i
$498$	−7022.48	+	16953.8i	−0.0283160	+	0.0683608i
$499$	−177235.	−	427884.i	−0.711786	−	1.71840i	−0.695491	−	0.718535i	$-0.744813\pi$
$499$	−177235.	−	427884.i	−0.711786	−	1.71840i	−0.0162950	−	0.999867i	$-0.505187\pi$
$500$	−95738.6	+	95738.6i	−0.382955	+	0.382955i
$501$	−15989.1	+	15989.1i	−0.0637012	+	0.0637012i
$502$	−57960.7			−0.229999
$503$	−419287.	+	173674.i	−1.65720	+	0.686436i	−0.997859	−	0.0654054i	$-0.979166\pi$
$503$	−419287.	+	173674.i	−1.65720	+	0.686436i	−0.659344	+	0.751841i	$0.729166\pi$
$504$	3478.09	−	1440.67i	0.0136924	−	0.00567158i
$505$	22060.8	+	53259.5i	0.0865044	+	0.208840i
$506$	8979.42	−	21678.2i	0.0350709	−	0.0846687i
$507$	−184618.	−	76471.1i	−0.718220	−	0.297496i
$508$	−24413.6			−0.0946028
$509$	134021.	−	323556.i	0.517295	−	1.24886i	−0.422263	−	0.906473i	$-0.638764\pi$
$509$	134021.	−	323556.i	0.517295	−	1.24886i	0.939559	−	0.342388i	$-0.111236\pi$
$510$	−226046.			−0.869073
$511$	−52836.1	+	127558.i	−0.202343	+	0.488500i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	151111.	−	151111.i	0.574198	−	0.574198i
$514$	−180852.	−	74911.5i	−0.684539	−	0.283545i
$515$		−	231433.i		−	0.872590i
$516$	−15028.5	−	6225.02i	−0.0564439	−	0.0233798i
$517$			95183.2i			0.356106i
$518$	−94287.3	+	227630.i	−0.351394	+	0.848339i
$519$	58820.9	+	24364.4i	0.218372	+	0.0904526i
$520$	−32918.4	+	13635.3i	−0.121740	+	0.0504262i
$521$	6002.14	+	14490.5i	0.0221121	+	0.0533834i	0.934550	−	0.355832i	$-0.115802\pi$
$521$	6002.14	+	14490.5i	0.0221121	+	0.0533834i	−0.912438	+	0.409215i	$0.865802\pi$
$522$	−1695.78	−	4093.98i	−0.00622341	−	0.0150246i
$523$		−	38540.2i		−	0.140900i	−0.997515	−	0.0704500i	$-0.977556\pi$
$523$		−	38540.2i		−	0.140900i	0.997515	−	0.0704500i	$-0.0224435\pi$
$524$	42463.5	+	42463.5i	0.154651	+	0.154651i
$525$	−102984.	−	102984.i	−0.373637	−	0.373637i
$526$	204529.	−	84718.7i	0.739236	−	0.306202i
$527$	180413.	+	74729.7i	0.649603	+	0.269074i
$528$	−9407.98	−	9407.98i	−0.0337465	−	0.0337465i
$529$	146597.			0.523859
$530$	−165840.	+	68693.3i	−0.590389	+	0.244547i
$531$	2164.45	−	2164.45i	0.00767640	−	0.00767640i
$532$			148546.i			0.524853i
$533$	85374.6	+	108106.i	0.300521	+	0.380536i
$534$	53169.2			0.186456
$535$	−235465.	−	235465.i	−0.822656	−	0.822656i
$536$	18823.5	+	45443.9i	0.0655194	+	0.158178i
$537$			491824.i			1.70554i
$538$	−261242.	+	261242.i	−0.902563	+	0.902563i
$539$	12824.3	−	30960.5i	0.0441423	−	0.106569i
$540$	−42149.4	−	101758.i	−0.144545	−	0.348963i
$541$	−182791.	+	182791.i	−0.624539	+	0.624539i	−0.946689	−	0.322149i	$-0.895595\pi$
$541$	−182791.	+	182791.i	−0.624539	+	0.624539i	0.322149	+	0.946689i	$0.395595\pi$
$542$	160790.	−	160790.i	0.547346	−	0.547346i
$543$	562209.			1.90677
$544$	−76040.3	+	31496.9i	−0.256949	+	0.106432i
$545$	−270884.	+	112204.i	−0.911991	+	0.377759i
$546$	−50509.5	−	121941.i	−0.169429	−	0.409038i
$547$	−86300.6	+	208348.i	−0.288429	+	0.696329i	−0.999980	−	0.00630503i	$-0.997993\pi$
$547$	−86300.6	+	208348.i	−0.288429	+	0.696329i	0.711551	+	0.702634i	$0.247993\pi$
$548$	53521.2	+	22169.2i	0.178224	+	0.0738226i
$549$	−120.481			−0.000399735
$550$	−6291.46	+	15188.9i	−0.0207982	+	0.0502113i
$551$	174850.			0.575921
$552$	−28912.8	+	69801.6i	−0.0948880	+	0.229080i
$553$	226297.	+	226297.i	0.739993	+	0.739993i
$554$	88395.2	−	88395.2i	0.288011	−	0.288011i
$555$	−227231.	−	94122.0i	−0.737702	−	0.305566i
$556$			264053.i			0.854165i
$557$	−481206.	−	199322.i	−1.55103	−	0.642459i	−0.567530	−	0.823353i	$-0.692101\pi$
$557$	−481206.	−	199322.i	−1.55103	−	0.642459i	−0.983503	+	0.180894i	$0.942101\pi$
$558$		−	3246.53i		−	0.0104268i
$559$	−6970.94	+	16829.3i	−0.0223084	+	0.0538572i
$560$	70732.2	+	29298.2i	0.225549	+	0.0934255i
$561$	−87327.4	+	36172.2i	−0.277476	+	0.114934i
$562$	−164727.	−	397685.i	−0.521545	−	1.25912i
$563$	−149330.	−	360514.i	−0.471118	−	1.13738i	−0.963670	−	0.267097i	$-0.913936\pi$
$563$	−149330.	−	360514.i	−0.471118	−	1.13738i	0.492552	−	0.870283i	$-0.336064\pi$
$564$		−	306480.i		−	0.963482i
$565$	−182916.	−	182916.i	−0.573000	−	0.573000i
$566$	−129413.	−	129413.i	−0.403965	−	0.403965i
$567$	389395.	−	161293.i	1.21122	−	0.501706i
$568$	−131510.	−	54473.2i	−0.407626	−	0.168844i
$569$	221363.	+	221363.i	0.683724	+	0.683724i	0.960837	−	0.277113i	$-0.0893777\pi$
$569$	221363.	+	221363.i	0.683724	+	0.683724i	−0.277113	+	0.960837i	$0.589378\pi$
$570$	−148286.			−0.456404
$571$	−41370.6	+	17136.3i	−0.126888	+	0.0525587i	−0.445224	−	0.895419i	$-0.646876\pi$
$571$	−41370.6	+	17136.3i	−0.126888	+	0.0525587i	0.318336	+	0.947978i	$0.396876\pi$
$572$	−10535.3	+	10535.3i	−0.0321999	+	0.0321999i
$573$			357166.i			1.08783i
$574$	34537.6	−	293969.i	0.104826	−	0.892231i
$575$	93357.7			0.282367
$576$	967.564	+	967.564i	0.00291632	+	0.00291632i
$577$	−103765.	−	250512.i	−0.311674	−	0.752448i	−0.999643	−	0.0267079i	$-0.991498\pi$
$577$	−103765.	−	250512.i	−0.311674	−	0.752448i	0.687969	−	0.725740i	$-0.258502\pi$
$578$			348493.i			1.04313i
$579$	−186255.	+	186255.i	−0.555586	+	0.555586i
$580$	34486.3	−	83257.2i	0.102516	−	0.247495i
$581$	−16897.4	−	40793.9i	−0.0500573	−	0.120849i
$582$	−240904.	+	240904.i	−0.711211	+	0.711211i
$583$	−53076.0	+	53076.0i	−0.156157	+	0.156157i
$584$	−50183.5			−0.147141
$585$	3888.02	−	1610.47i	0.0113610	−	0.00470589i
$586$	427397.	−	177034.i	1.24462	−	0.515538i
$587$	−93773.5	−	226389.i	−0.272147	−	0.657022i	0.727427	−	0.686185i	$-0.240716\pi$
$587$	−93773.5	−	226389.i	−0.272147	−	0.657022i	−0.999575	+	0.0291631i	$0.990716\pi$
$588$	−41292.7	+	99689.4i	−0.119431	+	0.288333i
$589$	118351.	+	49022.5i	0.341146	+	0.141307i
$590$	62249.8			0.178827
$591$	−139140.	+	335915.i	−0.398362	+	0.961732i
$592$	−89553.6			−0.255529
$593$	−33649.2	+	81236.4i	−0.0956898	+	0.231016i	−0.964475	−	0.264173i	$-0.914901\pi$
$593$	−33649.2	+	81236.4i	−0.0956898	+	0.231016i	0.868786	+	0.495189i	$0.164901\pi$
$594$	−32566.8	−	32566.8i	−0.0923002	−	0.0923002i
$595$	384601.	−	384601.i	1.08637	−	1.08637i
$596$	122820.	+	50873.7i	0.345761	+	0.143219i
$597$			320960.i			0.900539i
$598$	78165.6	+	32377.3i	0.218582	+	0.0905394i
$599$		−	645721.i		−	1.79966i	−0.436239	−	0.899831i	$-0.643690\pi$
$599$		−	645721.i		−	1.79966i	0.436239	−	0.899831i	$-0.356310\pi$
$600$	20257.8	−	48906.7i	0.0562717	−	0.135852i
$601$	−623543.	−	258280.i	−1.72630	−	0.715059i	−0.999605	−	0.0281036i	$-0.991053\pi$
$601$	−623543.	−	258280.i	−1.72630	−	0.715059i	−0.726700	−	0.686955i	$-0.758947\pi$
$602$	36161.4	−	14978.6i	0.0997821	−	0.0413311i
$603$	−2223.26	−	5367.42i	−0.00611441	−	0.0147615i
$604$	119155.	+	287666.i	0.326617	+	0.788523i
$605$			271412.i			0.741513i
$606$	−54884.1	−	54884.1i	−0.149452	−	0.149452i
$607$	−48624.4	−	48624.4i	−0.131971	−	0.131971i	0.638036	−	0.770007i	$-0.279747\pi$
$607$	−48624.4	−	48624.4i	−0.131971	−	0.131971i	−0.770007	+	0.638036i	$0.779747\pi$
$608$	−49882.2	+	20661.9i	−0.134939	+	0.0558937i
$609$	308413.	+	127749.i	0.831568	+	0.344447i
$610$	−1732.52	−	1732.52i	−0.00465606	−	0.00465606i
$611$	−343204.			−0.919327
$612$	8981.19	−	3720.13i	0.0239790	−	0.00993243i
$613$	329801.	−	329801.i	0.877670	−	0.877670i	−0.115624	−	0.993293i	$-0.536887\pi$
$613$	329801.	−	329801.i	0.877670	−	0.877670i	0.993293	+	0.115624i	$0.0368866\pi$
$614$		−	214926.i		−	0.570101i
$615$	293453.	+	34477.0i	0.775869	+	0.0911547i
$616$	32014.0			0.0843682
$617$	311237.	+	311237.i	0.817561	+	0.817561i	0.985754	−	0.168193i	$-0.0537931\pi$
$617$	311237.	+	311237.i	0.817561	+	0.817561i	−0.168193	+	0.985754i	$0.553793\pi$
$618$	119246.	+	287886.i	0.312225	+	0.753778i
$619$			491241.i			1.28207i	0.767510	+	0.641037i	$0.221495\pi$
$619$			491241.i			1.28207i	−0.767510	+	0.641037i	$0.778505\pi$
$620$	46685.4	−	46685.4i	0.121450	−	0.121450i
$621$	−100085.	+	241626.i	−0.259529	+	0.626558i
$622$	−176788.	−	426804.i	−0.456954	−	1.10318i
$623$	−90463.6	+	90463.6i	−0.233076	+	0.233076i
$624$	33922.6	−	33922.6i	0.0871203	−	0.0871203i
$625$	165366.			0.423337
$626$	−274650.	+	113764.i	−0.700859	+	0.290305i
$627$	−57286.5	+	23728.9i	−0.145719	+	0.0603590i
$628$	−92814.5	−	224074.i	−0.235341	−	0.568162i
$629$	−243471.	+	587790.i	−0.615383	+	1.48567i
$630$	−8354.24	−	3460.44i	−0.0210487	−	0.00871867i
$631$	−12479.5			−0.0313428			−0.0156714	−	0.999877i	$-0.504989\pi$
$631$	−12479.5			−0.0313428			−0.0156714	+	0.999877i	$0.504989\pi$
$632$	−44514.6	+	107468.i	−0.111447	+	0.269057i
$633$	142782.			0.356341
$634$	−33983.2	+	82042.7i	−0.0845446	+	0.204109i
$635$	41465.1	+	41465.1i	0.102834	+	0.102834i
$636$	170899.	−	170899.i	0.422499	−	0.422499i
$637$	111635.	+	46240.7i	0.275119	+	0.113958i
$638$		−	37683.0i		−	0.0925772i
$639$	15532.8	+	6433.88i	0.0380406	+	0.0157569i
$640$			27827.3i			0.0679378i
$641$	47945.0	−	115749.i	0.116688	−	0.281710i	−0.854735	−	0.519065i	$-0.826280\pi$
$641$	47945.0	−	115749.i	0.116688	−	0.281710i	0.971423	+	0.237354i	$0.0762803\pi$
$642$	414225.	+	171578.i	1.00500	+	0.416285i
$643$	141238.	−	58502.8i	0.341610	−	0.141500i	−0.205282	−	0.978703i	$-0.565811\pi$
$643$	141238.	−	58502.8i	0.341610	−	0.141500i	0.546892	+	0.837203i	$0.315811\pi$
$644$	−69569.4	−	167955.i	−0.167744	−	0.404970i
$645$	14952.3	+	36098.0i	0.0359408	+	0.0867688i
$646$			383579.i			0.919156i
$647$	−163961.	−	163961.i	−0.391681	−	0.391681i	0.483605	−	0.875286i	$-0.339327\pi$
$647$	−163961.	−	163961.i	−0.391681	−	0.391681i	−0.875286	+	0.483605i	$0.839327\pi$
$648$	108325.	+	108325.i	0.257976	+	0.257976i
$649$	24048.7	−	9961.31i	0.0570956	−	0.0236498i
$650$	−54767.0	−	22685.2i	−0.129626	−	0.0536928i
$651$	172939.	+	172939.i	0.408065	+	0.408065i
$652$	−21552.5			−0.0506994
$653$	412889.	−	171024.i	0.968294	−	0.401081i	0.158217	−	0.987404i	$-0.449425\pi$
$653$	412889.	−	171024.i	0.968294	−	0.401081i	0.810077	+	0.586324i	$0.199425\pi$
$654$	279147.	−	279147.i	0.652646	−	0.652646i
$655$		−	144244.i		−	0.336213i
$656$	103520.	−	29291.5i	0.240555	−	0.0680667i
$657$	5927.22			0.0137316
$658$	521454.	+	521454.i	1.20438	+	1.20438i
$659$	136019.	+	328379.i	0.313205	+	0.756144i	0.999582	+	0.0288984i	$0.00919992\pi$
$659$	136019.	+	328379.i	0.313205	+	0.756144i	−0.686377	+	0.727246i	$0.740800\pi$
$660$			31957.9i			0.0733652i
$661$	−403391.	+	403391.i	−0.923257	+	0.923257i	−0.997258	−	0.0740007i	$-0.976423\pi$
$661$	−403391.	+	403391.i	−0.923257	+	0.923257i	0.0740007	+	0.997258i	$0.476423\pi$
$662$	202950.	−	489964.i	0.463098	−	1.11802i
$663$	−130427.	−	314878.i	−0.296715	−	0.716334i
$664$	11348.4	−	11348.4i	0.0257394	−	0.0257394i
$665$	252297.	−	252297.i	0.570518	−	0.570518i
$666$	10577.3			0.0238465
$667$	−197697.	+	81888.6i	−0.444373	+	0.184065i
$668$	18270.5	−	7567.91i	0.0409448	−	0.0169599i
$669$	−207135.	−	500069.i	−0.462809	−	1.11732i
$670$	45213.3	−	109155.i	0.100720	−	0.243160i
$671$	−946.558	−	392.077i	−0.00210234	−	0.000870816i
$672$	−103082.			−0.228267
$673$	227584.	−	549437.i	0.502472	−	1.21307i	−0.445661	−	0.895202i	$-0.647031\pi$
$673$	227584.	−	549437.i	0.502472	−	1.21307i	0.948133	−	0.317873i	$-0.102969\pi$
$674$	−247918.			−0.545743
$675$	70124.8	−	169296.i	0.153909	−	0.371569i
$676$	123578.	+	123578.i	0.270426	+	0.270426i
$677$	404715.	−	404715.i	0.883023	−	0.883023i	−0.110817	−	0.993841i	$-0.535347\pi$
$677$	404715.	−	404715.i	0.883023	−	0.883023i	0.993841	+	0.110817i	$0.0353469\pi$
$678$	321782.	+	133286.i	0.700007	+	0.289952i
$679$		−	819763.i		−	1.77807i
$680$	182646.	+	75654.5i	0.394996	+	0.163613i
$681$			349926.i			0.754539i
$682$	10565.1	−	25506.5i	0.0227146	−	0.0548380i
$683$	274306.	+	113621.i	0.588023	+	0.243567i	0.656800	−	0.754065i	$-0.271910\pi$
$683$	274306.	+	113621.i	0.588023	+	0.243567i	−0.0687768	+	0.997632i	$0.521910\pi$
$684$	5891.64	−	2440.40i	0.0125928	−	0.00521613i
$685$	−53249.7	−	128556.i	−0.113484	−	0.273975i
$686$	62428.6	+	150716.i	0.132659	+	0.320266i
$687$		−	126864.i		−	0.268798i
$688$	10059.7	+	10059.7i	0.0212524	+	0.0212524i
$689$	−191377.	−	191377.i	−0.403136	−	0.403136i
$690$	167661.	−	69447.4i	0.352155	−	0.145867i
$691$	−192430.	−	79707.0i	−0.403010	−	0.166932i	0.171965	−	0.985103i	$-0.444988\pi$
$691$	−192430.	−	79707.0i	−0.403010	−	0.166932i	−0.574975	+	0.818171i	$0.694988\pi$
$692$	−39373.1	−	39373.1i	−0.0822219	−	0.0822219i
$693$	−3781.21			−0.00787343
$694$	228417.	−	94613.5i	0.474253	−	0.196442i
$695$	448480.	−	448480.i	0.928481	−	0.928481i
$696$			121335.i			0.250477i
$697$	89183.6	−	759092.i	0.183578	−	1.56253i
$698$	−593427.			−1.21802
$699$	−487759.	−	487759.i	−0.998277	−	0.998277i
$700$	48744.0	+	117678.i	0.0994776	+	0.240160i
$701$		−	39525.8i		−	0.0804348i	−0.999191	−	0.0402174i	$-0.987195\pi$
$701$		−	39525.8i		−	0.0804348i	0.999191	−	0.0402174i	$-0.0128051\pi$
$702$	117427.	−	117427.i	0.238283	−	0.238283i
$703$	−159716.	+	385589.i	−0.323175	+	0.780214i
$704$	4452.97	+	10750.4i	0.00898472	+	0.0216910i
$705$	−520539.	+	520539.i	−1.04731	+	1.04731i
$706$	84151.7	−	84151.7i	0.168831	−	0.168831i
$707$	186763.			0.373638
$708$	−77434.3	+	32074.3i	−0.154478	+	0.0639869i
$709$	−775739.	+	321322.i	−1.54320	+	0.639216i	−0.982071	−	0.188510i	$-0.939634\pi$
$709$	−775739.	+	321322.i	−1.54320	+	0.639216i	−0.561133	+	0.827726i	$0.689634\pi$
$710$	130843.	+	315882.i	0.259557	+	0.626627i
$711$	5257.66	−	12693.1i	0.0104005	−	0.0251090i
$712$	−42960.9	−	17795.0i	−0.0847449	−	0.0351025i
$713$	−156774.			−0.308386
$714$	−280250.	+	676582.i	−0.549729	+	1.32716i
$715$	35787.3			0.0700030
$716$	164607.	−	397396.i	0.321086	−	0.775170i
$717$	27100.6	+	27100.6i	0.0527158	+	0.0527158i
$718$	42517.9	−	42517.9i	0.0824752	−	0.0824752i
$719$	924051.	+	382754.i	1.78747	+	0.740393i	0.990693	+	0.136116i	$0.0434621\pi$
$719$	924051.	+	382754.i	1.78747	+	0.740393i	0.796775	+	0.604277i	$0.206538\pi$
$720$		−	3286.71i		−	0.00634010i
$721$	−692706.	−	286928.i	−1.33253	−	0.551954i
$722$		−	116977.i		−	0.224402i
$723$	225446.	−	544275.i	0.431287	−	1.04122i
$724$	−454268.	−	188164.i	−0.866632	−	0.358971i
$725$	138517.	−	57375.5i	0.263527	−	0.109157i
$726$	−139846.	−	337617.i	−0.265323	−	0.640547i
$727$	158325.	+	382229.i	0.299557	+	0.723194i	0.999955	+	0.00944241i	$0.00300566\pi$
$727$	158325.	+	382229.i	0.299557	+	0.723194i	−0.700398	+	0.713752i	$0.746994\pi$
$728$			115434.i			0.217806i
$729$	362582.	+	362582.i	0.682262	+	0.682262i
$730$	85233.9	+	85233.9i	0.159944	+	0.159944i
$731$	93376.8	−	38677.9i	0.174745	−	0.0723816i
$732$	3047.82	+	1262.45i	0.00568809	+	0.00235608i
$733$	−292945.	−	292945.i	−0.545228	−	0.545228i	0.379829	−	0.925057i	$-0.375983\pi$
$733$	−292945.	−	292945.i	−0.545228	−	0.545228i	−0.925057	+	0.379829i	$0.875983\pi$
$734$	37141.8			0.0689399
$735$	239450.	−	99183.6i	0.443242	−	0.183597i
$736$	46723.3	−	46723.3i	0.0862537	−	0.0862537i
$737$		−	49404.3i		−	0.0909557i
$738$	−12226.8	+	3459.65i	−0.0224492	+	0.00635213i
$739$	−681423.			−1.24775			−0.623875	−	0.781524i	$-0.714443\pi$
$739$	−681423.			−1.24775			−0.623875	+	0.781524i	$0.714443\pi$
$740$	152102.	+	152102.i	0.277761	+	0.277761i
$741$	−85559.6	−	206559.i	−0.155823	−	0.376191i
$742$			581545.i			1.05627i
$743$	−73104.4	+	73104.4i	−0.132424	+	0.132424i	−0.770212	−	0.637788i	$-0.779850\pi$
$743$	−73104.4	+	73104.4i	−0.132424	+	0.132424i	0.637788	+	0.770212i	$0.279850\pi$
$744$	−34018.6	+	82128.1i	−0.0614568	+	0.148370i
$745$	−122197.	−	295009.i	−0.220164	−	0.531524i
$746$	−167997.	+	167997.i	−0.301873	+	0.301873i
$747$	−1340.37	+	1340.37i	−0.00240206	+	0.00240206i
$748$	82667.3			0.147751
$749$	−996701.	+	412847.i	−1.77665	+	0.735911i
$750$	−404542.	+	167567.i	−0.719187	+	0.297897i
$751$	111566.	+	269345.i	0.197812	+	0.477561i	0.991395	−	0.130901i	$-0.0417869\pi$
$751$	111566.	+	269345.i	0.197812	+	0.477561i	−0.793583	+	0.608462i	$0.791787\pi$
$752$	−102575.	+	247637.i	−0.181386	+	0.437905i
$753$	−173179.	−	71733.1i	−0.305426	−	0.126511i
$754$	135874.			0.238998
$755$	286206.	−	690963.i	0.502094	−	1.21216i
$756$	−356830.			−0.624334
$757$	−262949.	+	634816.i	−0.458860	+	1.10779i	0.509999	+	0.860175i	$0.329646\pi$
$757$	−262949.	+	634816.i	−0.458860	+	1.10779i	−0.968859	+	0.247612i	$0.920354\pi$
$758$	242709.	+	242709.i	0.422422	+	0.422422i
$759$	53658.7	−	53658.7i	0.0931444	−	0.0931444i
$760$	119815.	+	49629.2i	0.207437	+	0.0859230i
$761$			355760.i			0.614310i	0.951659	+	0.307155i	$0.0993770\pi$
$761$			355760.i			0.614310i	−0.951659	+	0.307155i	$0.900623\pi$
$762$	−72944.6	−	30214.6i	−0.125627	−	0.0520364i
$763$			949898.i			1.63165i
$764$	119539.	−	288592.i	0.204796	−	0.494422i
$765$	−21572.5	−	8935.62i	−0.0368619	−	0.0152687i
$766$	423455.	−	175401.i	0.721688	−	0.298933i
$767$	35917.7	+	86713.0i	0.0610545	+	0.147399i
$768$	−14338.1	−	34615.2i	−0.0243091	−	0.0586873i
$769$			773280.i			1.30763i	0.756656	+	0.653814i	$0.226832\pi$
$769$			773280.i			1.30763i	−0.756656	+	0.653814i	$0.773168\pi$
$770$	−54374.1	−	54374.1i	−0.0917087	−	0.0917087i
$771$	−447652.	−	447652.i	−0.753064	−	0.753064i
$772$	212832.	−	88158.0i	0.357111	−	0.147920i
$773$	395666.	+	163890.i	0.662171	+	0.274280i	0.688352	−	0.725377i	$-0.258335\pi$
$773$	395666.	+	163890.i	0.662171	+	0.274280i	−0.0261807	+	0.999657i	$0.508335\pi$
$774$	−1188.16	−	1188.16i	−0.00198332	−	0.00198332i
$775$	109844.			0.182883
$776$	275279.	−	114024.i	0.457141	−	0.189354i
$777$	−563437.	+	563437.i	−0.933261	+	0.933261i
$778$			248640.i			0.410783i
$779$	58504.2	−	497962.i	0.0964078	−	0.820581i
$780$	−115231.			−0.189400
$781$	101096.	+	101096.i	0.165742	+	0.165742i
$782$	−179644.	−	433698.i	−0.293764	−	0.709209i
$783$			420016.i			0.685081i
$784$	66729.4	−	66729.4i	0.108564	−	0.108564i
$785$	−222937.	+	538218.i	−0.361779	+	0.873411i
$786$	74322.0	+	179429.i	0.120302	+	0.290434i
$787$	−756542.	+	756542.i	−1.22147	+	1.22147i	−0.254364	+	0.967109i	$0.581866\pi$
$787$	−756542.	+	756542.i	−1.22147	+	1.22147i	−0.967109	+	0.254364i	$0.918134\pi$
$788$	224852.	−	224852.i	0.362113	−	0.362113i
$789$	715955.			1.15009
$790$	258134.	−	106922.i	0.413609	−	0.171323i
$791$	−774266.	+	320712.i	−1.23748	+	0.512580i
$792$	−525.944	−	1269.74i	−0.000838473	−	0.00202425i
$793$	1413.72	−	3413.02i	0.00224811	−	0.00542741i
$794$	−763096.	−	316085.i	−1.21043	−	0.501375i
$795$	−580525.			−0.918517
$796$	107421.	−	259337.i	0.169537	−	0.409298i
$797$	105053.			0.165384			0.0826920	−	0.996575i	$-0.473648\pi$
$797$	105053.			0.165384			0.0826920	+	0.996575i	$0.473648\pi$
$798$	−183843.	+	443836.i	−0.288696	+	0.696975i
$799$	1.34651e6	+	1.34651e6i	2.10919	+	2.10919i
$800$	−32736.8	+	32736.8i	−0.0511513	+	0.0511513i
$801$	5074.15	+	2101.78i	0.00790858	+	0.00327584i
$802$		−	314416.i		−	0.488828i
$803$	46567.3	+	19288.8i	0.0722188	+	0.0299140i
$804$			159077.i			0.246090i
$805$	−167103.	+	403423.i	−0.257865	+	0.622542i
$806$	91969.2	+	38094.9i	0.141570	+	0.0586404i
$807$	−1.10387e6	+	457239.i	−1.69501	+	0.702096i
$808$	25977.6	+	62715.6i	0.0397903	+	0.0960622i
$809$	−358899.	−	866460.i	−0.548372	−	1.32389i	−0.918689	−	0.394982i	$-0.870751\pi$
$809$	−358899.	−	866460.i	−0.548372	−	1.32389i	0.370316	−	0.928906i	$-0.379249\pi$
$810$		−	367969.i		−	0.560843i
$811$	83903.4	+	83903.4i	0.127567	+	0.127567i	0.768008	−	0.640441i	$-0.221248\pi$
$811$	83903.4	+	83903.4i	0.127567	+	0.127567i	−0.640441	+	0.768008i	$0.721248\pi$
$812$	−206443.	−	206443.i	−0.313104	−	0.313104i
$813$	679418.	−	281424.i	1.02791	−	0.425775i
$814$	83100.5	+	34421.4i	0.125417	+	0.0519492i
$815$	36605.7	+	36605.7i	0.0551104	+	0.0551104i
$816$	−266180.			−0.399756
$817$	61254.9	−	25372.6i	0.0917692	−	0.0380120i
$818$	−107705.	+	107705.i	−0.160965	+	0.160965i
$819$		−	13634.0i		−	0.0203261i
$820$	−225573.	−	126072.i	−0.335474	−	0.187496i
$821$	36375.2			0.0539658			0.0269829	−	0.999636i	$-0.491410\pi$
$821$	36375.2			0.0539658			0.0269829	+	0.999636i	$0.491410\pi$
$822$	132478.	+	132478.i	0.196064	+	0.196064i
$823$	−202685.	−	489325.i	−0.299241	−	0.722433i	−0.999960	−	0.00899446i	$-0.997137\pi$
$823$	−202685.	−	489325.i	−0.299241	−	0.722433i	0.700718	−	0.713438i	$-0.252863\pi$
$824$		−	272523.i		−	0.401374i
$825$	−37596.1	+	37596.1i	−0.0552376	+	0.0552376i
$826$	77176.8	−	186321.i	0.113117	−	0.273088i
$827$	−315884.	−	762612.i	−0.461867	−	1.11505i	−0.967630	−	0.252373i	$-0.918789\pi$
$827$	−315884.	−	762612.i	−0.461867	−	1.11505i	0.505763	−	0.862673i	$-0.331211\pi$
$828$	−5518.53	+	5518.53i	−0.00804939	+	0.00804939i
$829$	−587410.	+	587410.i	−0.854737	+	0.854737i	−0.990712	−	0.135975i	$-0.956583\pi$
$829$	−587410.	+	587410.i	−0.854737	+	0.854737i	0.135975	+	0.990712i	$0.456583\pi$
$830$	−38549.2			−0.0559577
$831$	373513.	−	154714.i	0.540883	−	0.224041i
$832$	−38763.0	+	16056.2i	−0.0559978	+	0.0231950i
$833$	−256564.	−	619400.i	−0.369748	−	0.892650i
$834$	−326796.	+	788956.i	−0.469835	+	1.13428i
$835$	−43885.2	−	18177.8i	−0.0629427	−	0.0260717i
$836$	54229.5			0.0775931
$837$	−117759.	+	284296.i	−0.168091	+	0.405807i
$838$	617954.			0.879971
$839$	238961.	−	576903.i	0.339471	−	0.819556i	−0.658295	−	0.752760i	$-0.728722\pi$
$839$	238961.	−	576903.i	0.339471	−	0.819556i	0.997767	−	0.0667965i	$-0.0212778\pi$
$840$	175079.	+	175079.i	0.248127	+	0.248127i
$841$	257124.	−	257124.i	0.363538	−	0.363538i
$842$	−48081.2	−	19915.9i	−0.0678189	−	0.0280915i
$843$		−	1.39210e6i		−	1.95892i
$844$	−115369.	−	47787.2i	−0.161958	−	0.0670852i
$845$		−	419781.i		−	0.587908i
$846$	12115.2	−	29248.6i	0.0169274	−	0.0408663i
$847$	812369.	+	336494.i	1.13237	+	0.469041i
$848$	−195285.	+	80889.6i	−0.271567	+	0.112487i
$849$	−226505.	−	546831.i	−0.314241	−	0.758644i
$850$	125868.	+	303872.i	0.174212	+	0.420584i
$851$		−	510772.i		−	0.705290i
$852$	−325518.	−	325518.i	−0.448431	−	0.448431i
$853$	−189978.	−	189978.i	−0.261099	−	0.261099i	0.564402	−	0.825500i	$-0.309107\pi$
$853$	−189978.	−	189978.i	−0.261099	−	0.261099i	−0.825500	+	0.564402i	$0.809107\pi$
$854$	−7333.61	+	3037.68i	−0.0100555	+	0.00416511i
$855$	−14151.5	−	5861.74i	−0.0193584	−	0.00801853i
$856$	−277271.	−	277271.i	−0.378405	−	0.378405i
$857$	727698.			0.990809			0.495404	−	0.868663i	$-0.335020\pi$
$857$	727698.			0.990809			0.495404	+	0.868663i	$0.335020\pi$
$858$	−44516.8	+	18439.5i	−0.0604713	+	0.0250480i
$859$	146465.	−	146465.i	0.198494	−	0.198494i	−0.600860	−	0.799354i	$-0.705175\pi$
$859$	146465.	−	146465.i	0.198494	−	0.198494i	0.799354	+	0.600860i	$0.205175\pi$
$860$		−	34171.7i		−	0.0462029i
$861$	467014.	−	835596.i	0.629976	−	1.12717i
$862$	−605261.			−0.814569
$863$	−309546.	−	309546.i	−0.415627	−	0.415627i	0.468066	−	0.883693i	$-0.344951\pi$
$863$	−309546.	−	309546.i	−0.415627	−	0.415627i	−0.883693	+	0.468066i	$0.844951\pi$
$864$	−49633.0	−	119825.i	−0.0664879	−	0.160516i
$865$			133746.i			0.178751i
$866$	482055.	−	482055.i	0.642778	−	0.642778i
$867$	−431300.	+	1.04125e6i	−0.573775	+	1.38522i
$868$	−81854.9	−	197615.i	−0.108644	−	0.262290i
$869$	82613.9	−	82613.9i	0.109399	−	0.109399i
$870$	206081.	−	206081.i	0.272270	−	0.272270i
$871$	178138.			0.234812
$872$	−318979.	+	132125.i	−0.419497	+	0.173761i
$873$	−32513.5	+	13467.5i	−0.0426614	+	0.0176709i
$874$	−117846.	−	284505.i	−0.154273	−	0.372449i
$875$	403197.	−	973404.i	0.526625	−	1.27138i
$876$	−149942.	−	62107.9i	−0.195395	−	0.0809354i
$877$	269574.			0.350492			0.175246	−	0.984525i	$-0.443928\pi$
$877$	269574.			0.350492			0.175246	+	0.984525i	$0.443928\pi$
$878$	77192.6	−	186359.i	0.100135	−	0.241748i
$879$	1.49611e6			1.93636
$880$	10695.9	−	25822.1i	0.0138118	−	0.0333447i
$881$	546021.	+	546021.i	0.703489	+	0.703489i	0.965158	−	0.261668i	$-0.0842727\pi$
$881$	546021.	+	546021.i	0.703489	+	0.703489i	−0.261668	+	0.965158i	$0.584273\pi$
$882$	−7881.47	+	7881.47i	−0.0101314	+	0.0101314i
$883$	1.26534e6	+	524122.i	1.62288	+	0.672220i	0.994408	−	0.105610i	$-0.0336795\pi$
$883$	1.26534e6	+	524122.i	1.62288	+	0.672220i	0.628475	+	0.777830i	$0.283679\pi$
$884$			298075.i			0.381435i
$885$	185994.	+	77041.4i	0.237473	+	0.0983644i
$886$		−	205354.i		−	0.261599i
$887$	522786.	−	1.26212e6i	0.664472	−	1.60418i	−0.126246	−	0.991999i	$-0.540293\pi$
$887$	522786.	−	1.26212e6i	0.664472	−	1.60418i	0.790719	−	0.612179i	$-0.209707\pi$
$888$	−267575.	−	110833.i	−0.339328	−	0.140554i
$889$	175518.	−	72702.0i	0.222085	−	0.0919904i
$890$	42743.0	+	103191.i	0.0539616	+	0.130275i
$891$	−58883.0	−	142156.i	−0.0741710	−	0.179065i
$892$			473383.i			0.594954i
$893$	883306.	+	883306.i	1.10766	+	1.10766i
$894$	304008.	+	304008.i	0.380373	+	0.380373i
$895$	−954530.	+	395379.i	−1.19164	+	0.493592i
$896$	83290.5	+	34500.1i	0.103748	+	0.0429738i
$897$	193478.	+	193478.i	0.240462	+	0.240462i
$898$	44739.7			0.0554805
$899$	−232608.	+	96349.6i	−0.287810	+	0.119215i
$900$	3866.57	−	3866.57i	0.00477355	−	0.00477355i
$901$			1.50168e6i			1.84981i
$902$	−107319.	−	12608.6i	−0.131905	−	0.0154972i
$903$	126583.			0.155239
$904$	−215392.	−	215392.i	−0.263568	−	0.263568i
$905$	451963.	+	1.09114e6i	0.551830	+	1.33224i
$906$			1.00698e6i			1.22677i
$907$	1.12335e6	−	1.12335e6i	1.36553	−	1.36553i	0.498837	−	0.866696i	$-0.333761\pi$
$907$	1.12335e6	−	1.12335e6i	1.36553	−	1.36553i	0.866696	−	0.498837i	$-0.166239\pi$
$908$	117115.	−	282742.i	0.142050	−	0.342940i
$909$	−3068.24	−	7407.39i	−0.00371331	−	0.00896473i
$910$	196058.	−	196058.i	0.236756	−	0.236756i
$911$	741088.	−	741088.i	0.892962	−	0.892962i	−0.101838	−	0.994801i	$-0.532472\pi$
$911$	741088.	−	741088.i	0.892962	−	0.892962i	0.994801	+	0.101838i	$0.0324725\pi$
$912$	−174613.			−0.209936
$913$	−14892.6	+	6168.71i	−0.0178660	+	0.00740035i
$914$	−438765.	+	181742.i	−0.525218	+	0.217552i
$915$	−3032.35	−	7320.74i	−0.00362191	−	0.00874406i
$916$	−42459.7	+	102507.i	−0.0506041	+	0.122169i
$917$	−431740.	−	178832.i	−0.513432	−	0.212671i
$918$	−921413.			−1.09337
$919$	−503679.	+	1.21599e6i	−0.596379	+	1.43979i	0.280867	+	0.959747i	$0.409378\pi$
$919$	−503679.	+	1.21599e6i	−0.596379	+	1.43979i	−0.877246	+	0.480040i	$0.840622\pi$
$920$	−158714.			−0.187516
$921$	265996.	−	642171.i	0.313585	−	0.757062i
$922$	−442851.	−	442851.i	−0.520950	−	0.520950i
$923$	−364524.	+	364524.i	−0.427880	+	0.427880i
$924$	95653.8	+	39621.1i	0.112036	+	0.0464069i
$925$			357874.i			0.418260i
$926$	127339.	+	52745.7i	0.148505	+	0.0615128i
$927$			32187.9i			0.0374571i
$928$	40609.2	−	98039.4i	0.0471551	−	0.113843i
$929$	1.30370e6	+	540012.i	1.51059	+	0.625708i	0.975680	−	0.219199i	$-0.0703445\pi$
$929$	1.30370e6	+	540012.i	1.51059	+	0.625708i	0.534913	+	0.844907i	$0.320344\pi$
$930$	197269.	−	81711.4i	0.228083	−	0.0944750i
$931$	−168305.	−	406325.i	−0.194177	−	0.468785i
$932$	230865.	+	557358.i	0.265783	+	0.641657i
$933$		−	1.49403e6i		−	1.71631i
$934$	736845.	+	736845.i	0.844661	+	0.844661i
$935$	−140406.	−	140406.i	−0.160606	−	0.160606i
$936$	4578.33	−	1896.41i	0.00522583	−	0.00216461i
$937$	−565557.	−	234262.i	−0.644166	−	0.266822i	0.0365927	−	0.999330i	$-0.488350\pi$
$937$	−565557.	−	234262.i	−0.644166	−	0.266822i	−0.680758	+	0.732508i	$0.738350\pi$
$938$	−270658.	−	270658.i	−0.307620	−	0.307620i
$939$	−961414.			−1.09038
$940$	594815.	−	246381.i	0.673173	−	0.278837i
$941$	−342596.	+	342596.i	−0.386904	+	0.386904i	−0.873582	−	0.486678i	$-0.838209\pi$
$941$	−342596.	+	342596.i	−0.386904	+	0.386904i	0.486678	+	0.873582i	$0.338209\pi$
$942$		−	784373.i		−	0.883936i
$943$	167065.	+	590427.i	0.187872	+	0.663962i
$944$	73302.1			0.0822570
$945$	606055.	+	606055.i	0.678654	+	0.678654i
$946$	−5468.20	−	13201.4i	−0.00611030	−	0.0147516i
$947$		−	235507.i		−	0.262606i	−0.991342	−	0.131303i	$-0.958084\pi$
$947$		−	235507.i		−	0.262606i	0.991342	−	0.131303i	$-0.0419160\pi$
$948$	−266008.	+	266008.i	−0.295990	+	0.295990i
$949$	−69550.1	+	167909.i	−0.0772263	+	0.186441i
$950$	82569.0	+	199339.i	0.0914892	+	0.220874i
$951$	−203075.	+	203075.i	−0.224541	+	0.224541i
$952$	452886.	−	452886.i	0.499706	−	0.499706i
$953$	784737.			0.864049			0.432025	−	0.901862i	$-0.357799\pi$
$953$	784737.			0.864049			0.432025	+	0.901862i	$0.357799\pi$
$954$	23065.3	−	9553.95i	0.0253432	−	0.0104975i
$955$	−693188.	+	287128.i	−0.760053	+	0.314824i
$956$	−12827.2	−	30967.6i	−0.0140351	−	0.0338838i
$957$	46637.1	−	112592.i	0.0509222	−	0.122937i
$958$	−837478.	−	346895.i	−0.912520	−	0.377978i
$959$	−450802.			−0.490173
$960$	−34439.6	+	83144.5i	−0.0373693	+	0.0902175i
$961$	739062.			0.800265
$962$	−124114.	+	299637.i	−0.134113	+	0.323777i
$963$	32748.7	+	32748.7i	0.0353136	+	0.0353136i
$964$	−364323.	+	364323.i	−0.392042	+	0.392042i
$965$	−511215.	−	211752.i	−0.548971	−	0.227391i
$966$		−	587930.i		−	0.630044i
$967$	389561.	+	161361.i	0.416603	+	0.172563i	0.581131	−	0.813810i	$-0.302610\pi$
$967$	389561.	+	161361.i	0.416603	+	0.172563i	−0.164528	+	0.986372i	$0.552610\pi$
$968$			319601.i			0.341081i
$969$	−474723.	+	1.14608e6i	−0.505584	+	1.22059i
$970$	−661211.	−	273882.i	−0.702743	−	0.291086i
$971$	−953624.	+	395004.i	−1.01144	+	0.418951i	−0.825979	−	0.563701i	$-0.809377\pi$
$971$	−953624.	+	395004.i	−1.01144	+	0.418951i	−0.185458	+	0.982652i	$0.559377\pi$
$972$	11924.4	+	28788.1i	0.0126213	+	0.0304705i
$973$	−786332.	−	1.89837e6i	−0.830578	−	2.00519i
$974$		−	735596.i		−	0.775392i
$975$	−135561.	−	135561.i	−0.142602	−	0.142602i
$976$	−2040.13	−	2040.13i	−0.00214169	−	0.00214169i
$977$	385067.	−	159500.i	0.403410	−	0.167098i	−0.171747	−	0.985141i	$-0.554941\pi$
$977$	385067.	−	159500.i	0.403410	−	0.167098i	0.575157	+	0.818043i	$0.304941\pi$
$978$	−64396.1	−	26673.7i	−0.0673258	−	0.0278873i
$979$	33025.4	+	33025.4i	0.0344575	+	0.0344575i
$980$	−226672.			−0.236019
$981$	37674.9	−	15605.5i	0.0391484	−	0.0162158i
$982$	718151.	−	718151.i	0.744720	−	0.744720i
$983$			123239.i			0.127538i	0.997965	+	0.0637692i	$0.0203121\pi$
$983$			123239.i			0.127538i	−0.997965	+	0.0637692i	$0.979688\pi$
$984$	345555.	+	40598.3i	0.356884	+	0.0419293i
$985$	−763798.			−0.787238
$986$	−533082.	−	533082.i	−0.548327	−	0.548327i
$987$	912676.	+	2.20340e6i	0.936877	+	2.26182i
$988$			195536.i			0.200315i
$989$	−57375.8	+	57375.8i	−0.0586592	+	0.0586592i
$990$	−1263.30	+	3049.87i	−0.00128895	+	0.00311180i
$991$	−415003.	−	1.00191e6i	−0.422575	−	1.02019i	−0.981585	−	0.191026i	$-0.938819\pi$
$991$	−415003.	−	1.00191e6i	−0.422575	−	1.02019i	0.559010	−	0.829161i	$-0.311181\pi$
$992$	54974.3	−	54974.3i	0.0558646	−	0.0558646i
$993$	1.21278e6	−	1.21278e6i	1.22993	−	1.22993i
$994$	1.10769e6			1.12110
$995$	−622919.	+	258022.i	−0.629196	+	0.260621i
$996$	47952.5	−	19862.6i	0.0483384	−	0.0200224i
$997$	486918.	+	1.17553e6i	0.489853	+	1.18261i	0.954794	+	0.297268i	$0.0960756\pi$
$997$	486918.	+	1.17553e6i	0.489853	+	1.18261i	−0.464941	+	0.885342i	$0.653924\pi$
$998$	−501297.	+	1.21024e6i	−0.503308	+	1.21509i
$999$	−926241.	−	383662.i	−0.928097	−	0.384430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.e.a.55.2	yes	28
41.3	odd	8	inner	82.5.e.a.3.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.e.a.3.2	✓	28	41.3	odd	8	inner
82.5.e.a.55.2	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	82.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(-3.50051 - 8.45098i) q^{3} +8.00000i q^{4} +(13.5876 - 13.5876i) q^{5} +(-9.90093 + 23.9030i) q^{6} +(-23.8235 - 57.5149i) q^{7} +(16.0000 - 16.0000i) q^{8} +(-1.88977 + 1.88977i) q^{9} -54.3502 q^{10} +(-20.9969 + 8.69721i) q^{11} +(67.6078 - 28.0041i) q^{12} +(-31.3597 - 75.7090i) q^{13} +(-67.3829 + 162.677i) q^{14} +(-162.392 - 67.2648i) q^{15} -64.0000 q^{16} +(-173.998 + 420.067i) q^{17} +7.55910 q^{18} +(-114.142 + 275.563i) q^{19} +(108.700 + 108.700i) q^{20} +(-402.663 + 402.663i) q^{21} +(59.3882 + 24.5994i) q^{22} -365.026i q^{23} +(-191.224 - 79.2075i) q^{24} +255.756i q^{25} +(-88.6986 + 214.137i) q^{26} +(-661.943 - 274.186i) q^{27} +(460.119 - 190.588i) q^{28} +(-224.336 - 541.596i) q^{29} +(190.253 + 459.313i) q^{30} -429.487i q^{31} +(128.000 + 128.000i) q^{32} +(147.000 + 147.000i) q^{33} +(1188.13 - 492.140i) q^{34} +(-1105.19 - 457.785i) q^{35} +(-15.1182 - 15.1182i) q^{36} +1399.28 q^{37} +(779.410 - 322.842i) q^{38} +(-530.040 + 530.040i) q^{39} -434.802i q^{40} +(-1617.49 + 457.680i) q^{41} +1610.65 q^{42} +(-157.183 - 157.183i) q^{43} +(-69.5776 - 167.975i) q^{44} +51.3548i q^{45} +(-730.052 + 730.052i) q^{46} +(1602.73 - 3869.33i) q^{47} +(224.033 + 540.862i) q^{48} +(-1042.65 + 1042.65i) q^{49} +(511.513 - 511.513i) q^{50} +4159.06 q^{51} +(605.672 - 250.877i) q^{52} +(3051.33 - 1263.90i) q^{53} +(775.515 + 1872.26i) q^{54} +(-167.123 + 403.471i) q^{55} +(-1301.41 - 539.064i) q^{56} +2728.33 q^{57} +(-634.519 + 1531.86i) q^{58} -1145.35 q^{59} +(538.118 - 1299.13i) q^{60} +(31.8770 + 31.8770i) q^{61} +(-858.974 + 858.974i) q^{62} +(153.711 + 63.6693i) q^{63} -512.000i q^{64} +(-1454.80 - 602.599i) q^{65} -587.999i q^{66} +(-831.888 + 2008.35i) q^{67} +(-3360.54 - 1391.98i) q^{68} +(-3084.82 + 1277.78i) q^{69} +(1294.81 + 3125.95i) q^{70} +(-2407.40 - 5811.98i) q^{71} +60.4728i q^{72} +(-1568.23 - 1568.23i) q^{73} +(-2798.55 - 2798.55i) q^{74} +(2161.39 - 895.277i) q^{75} +(-2204.50 - 913.136i) q^{76} +(1000.44 + 1000.44i) q^{77} +2120.16 q^{78} +(-4749.45 + 1967.29i) q^{79} +(-869.604 + 869.604i) q^{80} +6770.33i q^{81} +(4150.35 + 2319.63i) q^{82} +709.274 q^{83} +(-3221.30 - 3221.30i) q^{84} +(3343.49 + 8071.89i) q^{85} +628.731i q^{86} +(-3791.72 + 3791.72i) q^{87} +(-196.795 + 475.106i) q^{88} +(-786.436 - 1898.62i) q^{89} +(102.710 - 102.710i) q^{90} +(-3607.30 + 3607.30i) q^{91} +2920.21 q^{92} +(-3629.58 + 1503.42i) q^{93} +(-10944.1 + 4533.20i) q^{94} +(2193.32 + 5295.14i) q^{95} +(633.660 - 1529.79i) q^{96} +(12165.7 + 5039.21i) q^{97} +4170.59 q^{98} +(23.2437 - 56.1152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 56 q^{2} + 16 q^{3} - 16 q^{6} + 448 q^{8} + 24 q^{9} + 328 q^{11} - 64 q^{12} - 348 q^{13} + 192 q^{14} + 1036 q^{15} - 1792 q^{16} - 1832 q^{17} - 96 q^{18} - 504 q^{19} + 2004 q^{21} - 856 q^{22}+ \cdots + 11544 q^{99}+O(q^{100}) \) 28 * q - 56 * q^2 + 16 * q^3 - 16 * q^6 + 448 * q^8 + 24 * q^9 + 328 * q^11 - 64 * q^12 - 348 * q^13 + 192 * q^14 + 1036 * q^15 - 1792 * q^16 - 1832 * q^17 - 96 * q^18 - 504 * q^19 + 2004 * q^21 - 856 * q^22 + 384 * q^24 + 384 * q^26 + 964 * q^27 - 768 * q^28 - 4 * q^29 - 4456 * q^30 + 3584 * q^32 - 748 * q^33 + 3576 * q^34 - 1104 * q^35 + 192 * q^36 + 5488 * q^37 + 256 * q^38 + 1232 * q^39 - 3760 * q^41 - 8016 * q^42 + 4756 * q^43 + 800 * q^44 - 2320 * q^46 - 4240 * q^47 - 1024 * q^48 + 2088 * q^49 - 6280 * q^50 + 29792 * q^51 + 1248 * q^52 - 10492 * q^53 - 1992 * q^54 + 14840 * q^55 + 1536 * q^56 - 33512 * q^57 + 2192 * q^58 - 11376 * q^59 + 9536 * q^60 - 3360 * q^61 + 2224 * q^62 - 13912 * q^63 + 41300 * q^65 + 15440 * q^67 + 352 * q^68 - 1004 * q^69 - 6792 * q^70 - 28392 * q^71 + 4284 * q^73 - 10976 * q^74 + 23812 * q^75 + 3008 * q^76 - 16524 * q^77 - 4928 * q^78 - 22236 * q^79 + 16752 * q^82 - 4024 * q^83 + 16032 * q^84 - 16616 * q^85 - 4628 * q^87 + 3648 * q^88 - 54412 * q^89 + 18336 * q^90 + 59948 * q^91 + 9280 * q^92 - 26800 * q^93 - 3240 * q^94 - 47636 * q^95 + 1024 * q^96 + 46764 * q^97 - 8352 * q^98 + 11544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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