LMFDB - Embedded newform 50.6.d.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, 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:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	50.31
Dual form			50.6.d.b.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(-7.20148 + 5.23218i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-5.94028 - 55.5852i) q^{5} +(28.8059 + 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 + 37.6183i) q^{8} +(-50.6055 + 155.748i) q^{9} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.20148 + 5.23218i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-5.94028 - 55.5852i) q^{5} +(28.8059 + 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 + 37.6183i) q^{8} +(-50.6055 + 155.748i) q^{9} +(-204.116 + 91.3052i) q^{10} +(158.710 + 488.460i) q^{11} +(44.0116 - 135.454i) q^{12} +(-161.333 + 496.533i) q^{13} +(20.8783 + 64.2569i) q^{14} +(333.611 + 369.215i) q^{15} +(79.1084 - 243.470i) q^{16} +(479.260 + 348.203i) q^{17} +655.052 q^{18} +(498.551 + 362.218i) q^{19} +(599.647 + 663.644i) q^{20} +(121.640 - 88.3764i) q^{21} +(1662.04 - 1207.54i) q^{22} +(442.325 + 1361.34i) q^{23} -569.697 q^{24} +(-3054.43 + 660.383i) q^{25} +2088.34 q^{26} +(-1118.89 - 3443.59i) q^{27} +(218.641 - 158.852i) q^{28} +(-6398.09 + 4648.49i) q^{29} +(992.212 - 1725.51i) q^{30} +(-460.025 - 334.228i) q^{31} -1024.00 q^{32} +(-3698.66 - 2687.23i) q^{33} +(732.245 - 2253.62i) q^{34} +(100.337 + 938.885i) q^{35} +(-809.688 - 2491.96i) q^{36} +(2908.55 - 8951.60i) q^{37} +(761.718 - 2344.33i) q^{38} +(-1436.11 - 4419.90i) q^{39} +(1783.45 - 3101.50i) q^{40} +(-2948.88 + 9075.73i) q^{41} +(-486.559 - 353.506i) q^{42} -1668.25 q^{43} +(-6648.14 - 4830.16i) q^{44} +(8957.88 + 1887.73i) q^{45} +(4632.09 - 3365.41i) q^{46} +(7201.89 - 5232.48i) q^{47} +(704.185 + 2167.26i) q^{48} -16521.7 q^{49} +(6287.72 + 10803.4i) q^{50} -5273.25 q^{51} +(-2581.33 - 7944.52i) q^{52} +(8259.40 - 6000.81i) q^{53} +(-11717.2 + 8513.03i) q^{54} +(26208.4 - 11723.5i) q^{55} +(-874.563 - 635.407i) q^{56} -5485.50 q^{57} +(25592.4 + 18593.9i) q^{58} +(-2401.25 + 7390.29i) q^{59} +(-7790.66 - 1641.76i) q^{60} +(16982.0 + 52265.2i) q^{61} +(-702.856 + 2163.17i) q^{62} +(854.774 - 2630.72i) q^{63} +(1265.73 + 3895.53i) q^{64} +(28558.2 + 6018.20i) q^{65} +(-5651.05 + 17392.1i) q^{66} +(-36904.6 - 26812.7i) q^{67} -9478.37 q^{68} +(-10308.2 - 7489.32i) q^{69} +(3447.71 - 1542.23i) q^{70} +(-46500.9 + 33784.9i) q^{71} +(-8479.17 + 6160.47i) q^{72} +(17212.3 + 52974.0i) q^{73} -37649.1 q^{74} +(18541.2 - 20737.1i) q^{75} -9859.88 q^{76} +(-2680.76 - 8250.54i) q^{77} +(-15039.2 + 10926.6i) q^{78} +(69422.4 - 50438.4i) q^{79} +(-14003.3 - 2950.97i) q^{80} +(-6119.13 - 4445.81i) q^{81} +38171.2 q^{82} +(38076.0 + 27663.8i) q^{83} +(-743.396 + 2287.94i) q^{84} +(16508.0 - 28708.2i) q^{85} +(2062.08 + 6346.41i) q^{86} +(21754.0 - 66952.0i) q^{87} +(-10157.5 + 31261.4i) q^{88} +(-9809.24 - 30189.7i) q^{89} +(-3891.19 - 36411.2i) q^{90} +(2725.07 - 8386.90i) q^{91} +(-18528.4 - 13461.6i) q^{92} +5061.61 q^{93} +(-28807.6 - 20929.9i) q^{94} +(17172.4 - 29863.7i) q^{95} +(7374.32 - 5357.76i) q^{96} +(17366.2 - 12617.3i) q^{97} +(20421.9 + 62852.3i) q^{98} -84108.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$	−7.20148	+	5.23218i	−0.461975	+	0.335645i	−0.794306	−	0.607518i	$-0.792165\pi$
$3$	−7.20148	+	5.23218i	−0.461975	+	0.335645i	0.332330	+	0.943163i	$0.392165\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−5.94028	−	55.5852i	−0.106263	−	0.994338i
$5$	−5.94028	−	55.5852i	−0.106263	−	0.994338i
$6$	28.8059	+	20.9287i	0.326666	+	0.237337i
$7$	−16.8909			−0.130289			−0.0651446	−	0.997876i	$-0.520751\pi$
$7$	−16.8909			−0.130289			−0.0651446	+	0.997876i	$0.520751\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	−50.6055	+	155.748i	−0.208253	+	0.640937i
$10$	−204.116	+	91.3052i	−0.645472	+	0.288732i
$11$	158.710	+	488.460i	0.395479	+	1.21716i	0.928588	+	0.371112i	$0.121024\pi$
$11$	158.710	+	488.460i	0.395479	+	1.21716i	−0.533109	+	0.846046i	$0.678976\pi$
$12$	44.0116	−	135.454i	0.0882294	−	0.271542i
$13$	−161.333	+	496.533i	−0.264768	+	0.814872i	0.726979	+	0.686660i	$0.240924\pi$
$13$	−161.333	+	496.533i	−0.264768	+	0.814872i	−0.991747	+	0.128212i	$0.959076\pi$
$14$	20.8783	+	64.2569i	0.0284692	+	0.0876193i
$15$	333.611	+	369.215i	0.382835	+	0.423693i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	479.260	+	348.203i	0.402207	+	0.292220i	0.770439	−	0.637514i	$-0.220037\pi$
$17$	479.260	+	348.203i	0.402207	+	0.292220i	−0.368233	+	0.929734i	$0.620037\pi$
$18$	655.052			0.476534
$19$	498.551	+	362.218i	0.316829	+	0.230190i	0.734821	−	0.678261i	$-0.237266\pi$
$19$	498.551	+	362.218i	0.316829	+	0.230190i	−0.417992	+	0.908451i	$0.637266\pi$
$20$	599.647	+	663.644i	0.335213	+	0.370988i
$21$	121.640	−	88.3764i	0.0601904	−	0.0437309i
$22$	1662.04	−	1207.54i	0.732122	−	0.531918i
$23$	442.325	+	1361.34i	0.174350	+	0.536594i	0.999603	−	0.0281688i	$-0.00896760\pi$
$23$	442.325	+	1361.34i	0.174350	+	0.536594i	−0.825253	+	0.564763i	$0.808968\pi$
$24$	−569.697			−0.201891
$25$	−3054.43	+	660.383i	−0.977416	+	0.211323i
$26$	2088.34			0.605854
$27$	−1118.89	−	3443.59i	−0.295378	−	0.909081i
$28$	218.641	−	158.852i	0.0527031	−	0.0382910i
$29$	−6398.09	+	4648.49i	−1.41272	+	1.02640i	−0.419797	+	0.907618i	$0.637899\pi$
$29$	−6398.09	+	4648.49i	−1.41272	+	1.02640i	−0.992920	+	0.118782i	$0.962101\pi$
$30$	992.212	−	1725.51i	0.201280	−	0.350036i
$31$	−460.025	−	334.228i	−0.0859761	−	0.0624653i	0.543967	−	0.839107i	$-0.316922\pi$
$31$	−460.025	−	334.228i	−0.0859761	−	0.0624653i	−0.629943	+	0.776641i	$0.716922\pi$
$32$	−1024.00			−0.176777
$33$	−3698.66	−	2687.23i	−0.591234	−	0.429557i
$34$	732.245	−	2253.62i	0.108632	−	0.334336i
$35$	100.337	+	938.885i	0.0138449	+	0.129552i
$36$	−809.688	−	2491.96i	−0.104127	−	0.320469i
$37$	2908.55	−	8951.60i	0.349279	−	1.07497i	−0.609974	−	0.792421i	$-0.708820\pi$
$37$	2908.55	−	8951.60i	0.349279	−	1.07497i	0.959253	−	0.282549i	$-0.0911798\pi$
$38$	761.718	−	2344.33i	0.0855727	−	0.263366i
$39$	−1436.11	−	4419.90i	−0.151191	−	0.465319i
$40$	1783.45	−	3101.50i	0.176242	−	0.306494i
$41$	−2948.88	+	9075.73i	−0.273967	+	0.843183i	0.715524	+	0.698588i	$0.246188\pi$
$41$	−2948.88	+	9075.73i	−0.273967	+	0.843183i	−0.989491	+	0.144595i	$0.953812\pi$
$42$	−486.559	−	353.506i	−0.0425610	−	0.0309224i
$43$	−1668.25			−0.137591			−0.0687957	−	0.997631i	$-0.521916\pi$
$43$	−1668.25			−0.137591			−0.0687957	+	0.997631i	$0.521916\pi$
$44$	−6648.14	−	4830.16i	−0.517689	−	0.376123i
$45$	8957.88	+	1887.73i	0.659438	+	0.138966i
$46$	4632.09	−	3365.41i	0.322762	−	0.234500i
$47$	7201.89	−	5232.48i	0.475556	−	0.345512i	−0.324047	−	0.946041i	$-0.605043\pi$
$47$	7201.89	−	5232.48i	0.475556	−	0.345512i	0.799603	+	0.600529i	$0.205043\pi$
$48$	704.185	+	2167.26i	0.0441147	+	0.135771i
$49$	−16521.7			−0.983025
$50$	6287.72	+	10803.4i	0.355687	+	0.611135i
$51$	−5273.25			−0.283892
$52$	−2581.33	−	7944.52i	−0.132384	−	0.407436i
$53$	8259.40	−	6000.81i	0.403886	−	0.293440i	−0.367236	−	0.930128i	$-0.619696\pi$
$53$	8259.40	−	6000.81i	0.403886	−	0.293440i	0.771122	+	0.636687i	$0.219696\pi$
$54$	−11717.2	+	8513.03i	−0.546813	+	0.397283i
$55$	26208.4	−	11723.5i	1.16824	−	0.522579i
$56$	−874.563	−	635.407i	−0.0372667	−	0.0270758i
$57$	−5485.50			−0.223629
$58$	25592.4	+	18593.9i	0.998942	+	0.725774i
$59$	−2401.25	+	7390.29i	−0.0898064	+	0.276396i	−0.985865	−	0.167539i	$-0.946418\pi$
$59$	−2401.25	+	7390.29i	−0.0898064	+	0.276396i	0.896059	+	0.443935i	$0.146418\pi$
$60$	−7790.66	−	1641.76i	−0.279380	−	0.0588750i
$61$	16982.0	+	52265.2i	0.584338	+	1.79841i	0.601913	+	0.798562i	$0.294406\pi$
$61$	16982.0	+	52265.2i	0.584338	+	1.79841i	−0.0175745	+	0.999846i	$0.505594\pi$
$62$	−702.856	+	2163.17i	−0.0232213	+	0.0714680i
$63$	854.774	−	2630.72i	0.0271331	−	0.0835072i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	28558.2	+	6018.20i	0.838393	+	0.176678i
$66$	−5651.05	+	17392.1i	−0.159687	+	0.491466i
$67$	−36904.6	−	26812.7i	−1.00437	−	0.729716i	−0.0413478	−	0.999145i	$-0.513165\pi$
$67$	−36904.6	−	26812.7i	−1.00437	−	0.729716i	−0.963020	+	0.269429i	$0.913165\pi$
$68$	−9478.37			−0.248577
$69$	−10308.2	−	7489.32i	−0.260650	−	0.189374i
$70$	3447.71	−	1542.23i	0.0840980	−	0.0376187i
$71$	−46500.9	+	33784.9i	−1.09475	+	0.795384i	−0.980195	−	0.198033i	$-0.936545\pi$
$71$	−46500.9	+	33784.9i	−1.09475	+	0.795384i	−0.114556	+	0.993417i	$0.536545\pi$
$72$	−8479.17	+	6160.47i	−0.192762	+	0.140050i
$73$	17212.3	+	52974.0i	0.378035	+	1.16347i	0.941408	+	0.337269i	$0.109503\pi$
$73$	17212.3	+	52974.0i	0.378035	+	1.16347i	−0.563373	+	0.826202i	$0.690497\pi$
$74$	−37649.1			−0.799236
$75$	18541.2	−	20737.1i	0.380613	−	0.425691i
$76$	−9859.88			−0.195811
$77$	−2680.76	−	8250.54i	−0.0515266	−	0.158583i
$78$	−15039.2	+	10926.6i	−0.279890	+	0.203352i
$79$	69422.4	−	50438.4i	1.25150	−	0.909271i	0.253196	−	0.967415i	$-0.418518\pi$
$79$	69422.4	−	50438.4i	1.25150	−	0.909271i	0.998308	+	0.0581445i	$0.0185184\pi$
$80$	−14003.3	−	2950.97i	−0.244627	−	0.0515513i
$81$	−6119.13	−	4445.81i	−0.103628	−	0.0752902i
$82$	38171.2			0.626903
$83$	38076.0	+	27663.8i	0.606674	+	0.440775i	0.848242	−	0.529609i	$-0.177661\pi$
$83$	38076.0	+	27663.8i	0.606674	+	0.440775i	−0.241567	+	0.970384i	$0.577661\pi$
$84$	−743.396	+	2287.94i	−0.0114953	+	0.0353790i
$85$	16508.0	−	28708.2i	0.247826	−	0.430982i
$86$	2062.08	+	6346.41i	0.0300648	+	0.0925300i
$87$	21754.0	−	66952.0i	0.308135	−	0.948343i
$88$	−10157.5	+	31261.4i	−0.139823	+	0.430331i
$89$	−9809.24	−	30189.7i	−0.131268	−	0.404003i	0.863723	−	0.503968i	$-0.168127\pi$
$89$	−9809.24	−	30189.7i	−0.131268	−	0.404003i	−0.994991	+	0.0999650i	$0.968127\pi$
$90$	−3891.19	−	36411.2i	−0.0506379	−	0.473836i
$91$	2725.07	−	8386.90i	0.0344964	−	0.106169i
$92$	−18528.4	−	13461.6i	−0.228227	−	0.165817i
$93$	5061.61			0.0606850
$94$	−28807.6	−	20929.9i	−0.336269	−	0.244314i
$95$	17172.4	−	29863.7i	0.195219	−	0.339496i
$96$	7374.32	−	5357.76i	0.0816665	−	0.0593342i
$97$	17366.2	−	12617.3i	0.187403	−	0.136156i	−0.490128	−	0.871650i	$-0.663050\pi$
$97$	17366.2	−	12617.3i	0.187403	−	0.136156i	0.677531	+	0.735494i	$0.263050\pi$
$98$	20421.9	+	62852.3i	0.214799	+	0.661083i
$99$	−84108.2			−0.862482
$100$	33326.7	−	37273.7i	0.333267	−	0.372737i
$101$	−125521.			−1.22437			−0.612184	−	0.790716i	$-0.709709\pi$
$101$	−125521.			−1.22437			−0.612184	+	0.790716i	$0.709709\pi$
$102$	6518.09	+	20060.6i	0.0620326	+	0.190917i
$103$	147304.	−	107023.i	1.36811	−	0.993992i	0.370231	−	0.928940i	$-0.379278\pi$
$103$	147304.	−	107023.i	1.36811	−	0.993992i	0.997882	−	0.0650528i	$-0.0207216\pi$
$104$	−27032.1	+	19639.9i	−0.245073	+	0.178056i
$105$	−5634.99	−	6236.39i	−0.0498793	−	0.0552026i
$106$	−33037.6	−	24003.2i	−0.285591	−	0.207494i
$107$	−153788.			−1.29856			−0.649280	−	0.760550i	$-0.724930\pi$
$107$	−153788.			−1.29856			−0.649280	+	0.760550i	$0.724930\pi$
$108$	46868.7	+	34052.1i	0.386655	+	0.280921i
$109$	−8833.67	+	27187.3i	−0.0712156	+	0.219179i	−0.980329	−	0.197369i	$-0.936760\pi$
$109$	−8833.67	+	27187.3i	−0.0712156	+	0.219179i	0.909114	+	0.416548i	$0.136760\pi$
$110$	−76994.3	−	85211.4i	−0.606704	−	0.671454i
$111$	25890.5	+	79682.9i	0.199450	+	0.613843i
$112$	−1336.21	+	4112.44i	−0.0100654	+	0.0309781i
$113$	−31449.7	+	96792.1i	−0.231697	+	0.713089i	0.765846	+	0.643024i	$0.222321\pi$
$113$	−31449.7	+	96792.1i	−0.231697	+	0.713089i	−0.997542	+	0.0700649i	$0.977679\pi$
$114$	6780.45	+	20868.1i	0.0488648	+	0.150390i
$115$	73042.6	−	32673.4i	0.515029	−	0.230383i
$116$	39101.7	−	120343.i	0.269805	−	0.830375i
$117$	−69169.5	−	50254.6i	−0.467143	−	0.339399i
$118$	31082.4			0.205499
$119$	−8095.15	−	5881.47i	−0.0524032	−	0.0380731i
$120$	3384.16	+	31666.7i	0.0214535	+	0.200748i
$121$	−83111.2	+	60383.8i	−0.516055	+	0.374936i
$122$	177838.	−	129207.i	1.08174	−	0.785933i
$123$	−26249.6	−	80787.8i	−0.156444	−	0.481485i
$124$	9097.96			0.0531361
$125$	54851.7	+	165858.i	0.313989	+	0.949427i
$126$	−11064.4			−0.0620873
$127$	19292.3	+	59375.5i	0.106139	+	0.326662i	0.989996	−	0.141095i	$-0.0450623\pi$
$127$	19292.3	+	59375.5i	0.106139	+	0.326662i	−0.883857	+	0.467757i	$0.845062\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	12013.9	−	8728.61i	0.0635638	−	0.0461818i
$130$	−12405.3	−	116081.i	−0.0643798	−	0.602424i
$131$	−24021.6	−	17452.7i	−0.122299	−	0.0888557i	0.524954	−	0.851131i	$-0.324082\pi$
$131$	−24021.6	−	17452.7i	−0.122299	−	0.0888557i	−0.647254	+	0.762275i	$0.724082\pi$
$132$	73148.8			0.365403
$133$	−8420.99	−	6118.20i	−0.0412794	−	0.0299913i
$134$	−56385.1	+	173536.i	−0.271271	+	0.834885i
$135$	−184766.	+	82649.7i	−0.872546	+	0.390308i
$136$	11715.9	+	36057.9i	0.0543161	+	0.167168i
$137$	−93020.5	+	286288.i	−0.423426	+	1.30317i	0.481068	+	0.876683i	$0.340249\pi$
$137$	−93020.5	+	286288.i	−0.423426	+	1.30317i	−0.904494	+	0.426487i	$0.859751\pi$
$138$	−15749.5	+	48471.9i	−0.0703993	+	0.216667i
$139$	−20199.9	−	62168.9i	−0.0886772	−	0.272921i	0.896877	−	0.442280i	$-0.145830\pi$
$139$	−20199.9	−	62168.9i	−0.0886772	−	0.272921i	−0.985554	+	0.169359i	$0.945830\pi$
$140$	−10128.6	−	11209.6i	−0.0436746	−	0.0483358i
$141$	−24487.0	+	75363.2i	−0.103726	+	0.319236i
$142$	186004.	+	135140.i	0.774106	+	0.562421i
$143$	−268142.			−1.09654
$144$	33916.7	+	24641.9i	0.136303	+	0.0990303i
$145$	296393.	+	328026.i	1.17071	+	1.29565i
$146$	180250.	−	130959.i	0.699829	−	0.508456i
$147$	118981.	−	86444.6i	0.454133	−	0.329947i
$148$	46536.8	+	143226.i	0.174639	+	0.537485i
$149$	361011.			1.33215			0.666077	−	0.745883i	$-0.267972\pi$
$149$	361011.			1.33215			0.666077	+	0.745883i	$0.267972\pi$
$150$	−101807.	−	44902.3i	−0.369443	−	0.162945i
$151$	403121.			1.43878			0.719388	−	0.694609i	$-0.244423\pi$
$151$	403121.			1.43878			0.719388	+	0.694609i	$0.244423\pi$
$152$	12187.5	+	37509.2i	0.0427863	+	0.131683i
$153$	−78485.1	+	57022.7i	−0.271056	+	0.196933i
$154$	−28073.3	+	20396.5i	−0.0953876	+	0.0693032i
$155$	−15845.5	+	27556.0i	−0.0529755	+	0.0921270i
$156$	60156.6	+	43706.3i	0.197912	+	0.143791i
$157$	−286202.			−0.926667			−0.463334	−	0.886184i	$-0.653347\pi$
$157$	−286202.			−0.926667			−0.463334	+	0.886184i	$0.653347\pi$
$158$	−277690.	−	201753.i	−0.884947	−	0.642951i
$159$	−28082.6	+	86429.4i	−0.0880937	+	0.271125i
$160$	6082.85	+	56919.2i	0.0187848	+	0.175776i
$161$	−7471.28	−	22994.2i	−0.0227159	−	0.0699124i
$162$	−9349.20	+	28773.9i	−0.0279890	+	0.0861412i
$163$	194402.	−	598308.i	0.573102	−	1.76383i	−0.0694500	−	0.997585i	$-0.522124\pi$
$163$	194402.	−	598308.i	0.573102	−	1.76383i	0.642552	−	0.766242i	$-0.277876\pi$
$164$	−47182.1	−	145212.i	−0.136983	−	0.421592i
$165$	−127399.	+	221554.i	−0.364299	+	0.633533i
$166$	58174.9	−	179044.i	0.163857	−	0.504300i
$167$	−62082.2	−	45105.4i	−0.172257	−	0.125152i	0.498316	−	0.866995i	$-0.333952\pi$
$167$	−62082.2	−	45105.4i	−0.172257	−	0.125152i	−0.670573	+	0.741843i	$0.733952\pi$
$168$	9622.72			0.0263042
$169$	79866.1	+	58026.1i	0.215103	+	0.156281i
$170$	−129617.	−	27314.8i	−0.343986	−	0.0724897i
$171$	−81644.1	+	59317.9i	−0.213518	+	0.155130i
$172$	21594.3	−	15689.2i	0.0556569	−	0.0404371i
$173$	−132775.	−	408641.i	−0.337289	−	1.03807i	−0.965583	−	0.260094i	$-0.916246\pi$
$173$	−132775.	−	408641.i	−0.337289	−	1.03807i	0.628294	−	0.777976i	$-0.283754\pi$
$174$	−281590.			−0.705089
$175$	51592.1	−	11154.5i	0.127347	−	0.0275330i
$176$	131481.			0.319949
$177$	−21374.8	−	65784.8i	−0.0512824	−	0.157831i
$178$	−102724.	+	74633.1i	−0.243008	+	0.176556i
$179$	528551.	−	384015.i	1.23298	−	0.895809i	0.235866	−	0.971786i	$-0.424207\pi$
$179$	528551.	−	384015.i	1.23298	−	0.895809i	0.997110	+	0.0759766i	$0.0242074\pi$
$180$	−133707.	+	59809.6i	−0.307589	+	0.137591i
$181$	−89305.6	−	64884.3i	−0.202620	−	0.147212i	0.481848	−	0.876255i	$-0.339966\pi$
$181$	−89305.6	−	64884.3i	−0.202620	−	0.147212i	−0.684468	+	0.729043i	$0.739966\pi$
$182$	−35274.0			−0.0789363
$183$	−395757.	−	287534.i	−0.873576	−	0.634690i
$184$	−28308.8	+	87125.5i	−0.0616420	+	0.189715i
$185$	−514854.	−	108497.i	−1.10600	−	0.233072i
$186$	−6256.49	−	19255.5i	−0.0132602	−	0.0408106i
$187$	−94019.7	+	289363.i	−0.196614	+	0.605116i
$188$	−44014.0	+	135461.i	−0.0908231	+	0.279525i
$189$	18899.1	+	58165.5i	0.0384846	+	0.118443i
$190$	−134835.	−	28414.3i	−0.270968	−	0.0571022i
$191$	113065.	−	347979.i	0.224257	−	0.690192i	−0.774109	−	0.633052i	$-0.781802\pi$
$191$	113065.	−	347979.i	0.224257	−	0.690192i	0.998366	−	0.0571397i	$-0.0181980\pi$
$192$	−29497.3	−	21431.0i	−0.0577469	−	0.0419556i
$193$	−619378.			−1.19691			−0.598457	−	0.801155i	$-0.704219\pi$
$193$	−619378.			−1.19691			−0.598457	+	0.801155i	$0.704219\pi$
$194$	−69465.0	−	50469.3i	−0.132514	−	0.0962770i
$195$	−237150.	+	106082.i	−0.446618	+	0.199781i
$196$	213861.	−	155379.i	0.397642	−	0.288904i
$197$	503197.	−	365594.i	0.923788	−	0.671171i	−0.0206758	−	0.999786i	$-0.506582\pi$
$197$	503197.	−	365594.i	0.923788	−	0.671171i	0.944464	+	0.328615i	$0.106582\pi$
$198$	103963.	+	319966.i	0.188459	+	0.580018i
$199$	612135.			1.09576			0.547879	−	0.836558i	$-0.315435\pi$
$199$	612135.			1.09576			0.547879	+	0.836558i	$0.315435\pi$
$200$	−182992.	−	80709.5i	−0.323487	−	0.142676i
$201$	406057.			0.708919
$202$	155152.	+	477509.i	0.267534	+	0.823385i
$203$	108070.	−	78517.2i	0.184062	−	0.133729i
$204$	68258.4	−	49592.6i	0.114837	−	0.0834337i
$205$	521993.	+	110002.i	0.867522	+	0.182817i
$206$	−589217.	−	428091.i	−0.967402	−	0.702859i
$207$	−234409.			−0.380232
$208$	108128.	+	78559.8i	0.173293	+	0.125905i
$209$	−97804.0	+	301010.i	−0.154878	+	0.476667i
$210$	−16759.4	+	29145.4i	−0.0262247	+	0.0456060i
$211$	−16676.0	−	51323.4i	−0.0257861	−	0.0793614i	0.937335	−	0.348429i	$-0.113285\pi$
$211$	−16676.0	−	51323.4i	−0.0257861	−	0.0793614i	−0.963121	+	0.269067i	$0.913285\pi$
$212$	−50477.0	+	155352.i	−0.0771354	+	0.237398i
$213$	158107.	−	486603.i	0.238782	−	0.734895i
$214$	190092.	+	585043.i	0.283746	+	0.873279i
$215$	9909.89	+	92730.2i	0.0146209	+	0.136812i
$216$	71609.1	−	220390.i	0.104432	−	0.321409i
$217$	7770.26	+	5645.42i	0.0112018	+	0.00813855i
$218$	114345.			0.162959
$219$	−401124.	−	291434.i	−0.565156	−	0.410610i
$220$	−228993.	+	398231.i	−0.318982	+	0.554725i
$221$	−250215.	+	181792.i	−0.344614	+	0.250376i
$222$	271129.	−	196987.i	0.369227	−	0.268259i
$223$	30995.9	+	95395.6i	0.0417390	+	0.128459i	0.969755	−	0.244082i	$-0.0784865\pi$
$223$	30995.9	+	95395.6i	0.0417390	+	0.128459i	−0.928016	+	0.372541i	$0.878487\pi$
$224$	17296.3			0.0230321
$225$	51717.6	−	509139.i	0.0681055	−	0.670471i
$226$	407093.			0.530179
$227$	335115.	+	1.03138e6i	0.431647	+	1.32847i	0.896484	+	0.443076i	$0.146113\pi$
$227$	335115.	+	1.03138e6i	0.431647	+	1.32847i	−0.464837	+	0.885396i	$0.653887\pi$
$228$	71005.8	−	51588.7i	0.0904600	−	0.0657230i
$229$	942748.	−	684947.i	1.18797	−	0.863114i	0.194926	−	0.980818i	$-0.437553\pi$
$229$	942748.	−	684947.i	1.18797	−	0.863114i	0.993049	+	0.117704i	$0.0375534\pi$
$230$	−214583.	−	237484.i	−0.267470	−	0.296016i
$231$	62473.8	+	45389.9i	0.0770315	+	0.0559666i
$232$	−506142.			−0.617380
$233$	382634.	+	278000.i	0.461736	+	0.335471i	0.794212	−	0.607641i	$-0.207884\pi$
$233$	382634.	+	278000.i	0.461736	+	0.335471i	−0.332476	+	0.943112i	$0.607884\pi$
$234$	−105682.	+	325254.i	−0.126171	+	0.388315i
$235$	−333630.	−	369236.i	−0.394089	−	0.436148i
$236$	−38420.0	−	118245.i	−0.0449032	−	0.138198i
$237$	−236042.	+	726462.i	−0.272972	+	0.840121i
$238$	−12368.3	+	38065.7i	−0.0141536	+	0.0435603i
$239$	494526.	+	1.52199e6i	0.560008	+	1.72353i	0.682337	+	0.731038i	$0.260964\pi$
$239$	494526.	+	1.52199e6i	0.560008	+	1.72353i	−0.122328	+	0.992490i	$0.539036\pi$
$240$	116284.	−	52016.4i	0.130315	−	0.0582924i
$241$	36524.9	−	112412.i	0.0405085	−	0.124672i	−0.928757	−	0.370689i	$-0.879122\pi$
$241$	36524.9	−	112412.i	0.0405085	−	0.124672i	0.969266	+	0.246016i	$0.0791217\pi$
$242$	332445.	+	241535.i	0.364906	+	0.265120i
$243$	947185.			1.02901
$244$	−711351.	−	516827.i	−0.764908	−	0.555739i
$245$	98143.5	+	918362.i	0.104459	+	0.977459i
$246$	−274889.	+	199719.i	−0.289614	+	0.210417i
$247$	−260286.	+	189109.i	−0.271462	+	0.197228i
$248$	−11245.7	−	34610.7i	−0.0116107	−	0.0357340i
$249$	−418946.			−0.428212
$250$	563161.	−	413680.i	0.569879	−	0.418615i
$251$	−489205.			−0.490125			−0.245062	−	0.969507i	$-0.578808\pi$
$251$	−489205.			−0.490125			−0.245062	+	0.969507i	$0.578808\pi$
$252$	13676.4	+	42091.6i	0.0135666	+	0.0417536i
$253$	−594757.	+	432116.i	−0.584169	+	0.424423i
$254$	202031.	−	146784.i	0.196487	−	0.142756i
$255$	31324.6	+	293114.i	0.0301672	+	0.282284i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	225164.			0.212651			0.106325	−	0.994331i	$-0.466091\pi$
$257$	225164.			0.212651			0.106325	+	0.994331i	$0.466091\pi$
$258$	−48055.6	−	34914.4i	−0.0449464	−	0.0326555i
$259$	−49128.1	+	151201.i	−0.0455073	+	0.140057i
$260$	−426264.	+	190676.i	−0.391062	+	0.174930i
$261$	−400212.	−	1.23173e6i	−0.363655	−	1.11921i
$262$	−36701.8	+	112957.i	−0.0330319	+	0.101662i
$263$	−412733.	+	1.27026e6i	−0.367943	+	1.13241i	0.580175	+	0.814492i	$0.302984\pi$
$263$	−412733.	+	1.27026e6i	−0.367943	+	1.13241i	−0.948118	+	0.317919i	$0.897016\pi$
$264$	−90416.8	−	278274.i	−0.0798435	−	0.245733i
$265$	−382619.	−	423454.i	−0.334697	−	0.370417i
$266$	−12866.1	+	39597.8i	−0.0111492	+	0.0343137i
$267$	228599.	+	166087.i	0.196244	+	0.142580i
$268$	729865.			0.620734
$269$	−491227.	−	356898.i	−0.413906	−	0.300720i	0.361275	−	0.932459i	$-0.382342\pi$
$269$	−491227.	−	356898.i	−0.413906	−	0.300720i	−0.775181	+	0.631739i	$0.782342\pi$
$270$	542802.	+	600732.i	0.453140	+	0.501501i
$271$	−1.53712e6	+	1.11679e6i	−1.27141	+	0.923734i	−0.999258	−	0.0385206i	$-0.987735\pi$
$271$	−1.53712e6	+	1.11679e6i	−1.27141	+	0.923734i	−0.272152	+	0.962254i	$0.587735\pi$
$272$	122691.	−	89140.0i	0.100552	−	0.0730550i
$273$	24257.3	+	74656.2i	0.0196986	+	0.0606260i
$274$	1.20408e6			0.968902
$275$	−807339.	−	1.38716e6i	−0.643761	−	1.10610i
$276$	203865.			0.161091
$277$	−660581.	−	2.03306e6i	−0.517281	−	1.59203i	−0.779093	−	0.626908i	$-0.784320\pi$
$277$	−660581.	−	2.03306e6i	−0.517281	−	1.59203i	0.261813	−	0.965119i	$-0.415680\pi$
$278$	−211536.	+	153690.i	−0.164162	+	0.119271i
$279$	75335.1	−	54734.2i	0.0579411	−	0.0420967i
$280$	−30124.1	+	52387.2i	−0.0229625	+	0.0399329i
$281$	345196.	+	250800.i	0.260796	+	0.189479i	0.710498	−	0.703700i	$-0.248470\pi$
$281$	345196.	+	250800.i	0.260796	+	0.189479i	−0.449702	+	0.893179i	$0.648470\pi$
$282$	316966.			0.237351
$283$	144371.	+	104892.i	0.107155	+	0.0778529i	0.640073	−	0.768314i	$-0.278904\pi$
$283$	144371.	+	104892.i	0.107155	+	0.0778529i	−0.532917	+	0.846167i	$0.678904\pi$
$284$	284188.	−	874642.i	0.209079	−	0.643479i
$285$	32585.4	+	304912.i	0.0237635	+	0.222363i
$286$	331441.	+	1.02007e6i	0.239603	+	0.737421i
$287$	49809.4	−	153298.i	0.0356949	−	0.109858i
$288$	51820.0	−	159486.i	0.0368143	−	0.113303i
$289$	−330315.	−	1.01660e6i	−0.232639	−	0.715991i
$290$	881522.	−	1.53301e6i	0.615514	−	1.07041i
$291$	−59046.6	+	181727.i	−0.0408754	+	0.125802i
$292$	−720998.	−	523836.i	−0.494854	−	0.359533i
$293$	165122.			0.112366			0.0561831	−	0.998420i	$-0.482107\pi$
$293$	165122.			0.112366			0.0561831	+	0.998420i	$0.482107\pi$
$294$	−475923.	−	345778.i	−0.321121	−	0.233308i
$295$	425055.	+	89573.6i	0.284374	+	0.0599273i
$296$	487340.	−	354073.i	0.323298	−	0.234890i
$297$	1.50448e6	−	1.09307e6i	0.989680	−	0.719045i
$298$	−446234.	−	1.37337e6i	−0.291087	−	0.895872i
$299$	−747310.			−0.483418
$300$	−44978.8	+	442798.i	−0.0288539	+	0.284055i
$301$	28178.4			0.0179267
$302$	−498285.	−	1.53356e6i	−0.314384	−	0.967574i
$303$	903935.	−	656747.i	0.565627	−	0.410952i
$304$	127629.	−	92727.9i	0.0792073	−	0.0575475i
$305$	2.80429e6	−	1.25442e6i	1.72613	−	0.772134i
$306$	313940.	+	228091.i	0.191665	+	0.139253i
$307$	−3.07543e6			−1.86234			−0.931171	−	0.364583i	$-0.881211\pi$
$307$	−3.07543e6			−1.86234			−0.931171	+	0.364583i	$0.881211\pi$
$308$	112293.	+	81585.8i	0.0674492	+	0.0490047i
$309$	−500846.	+	1.54145e6i	−0.298406	+	0.918400i
$310$	124415.	+	26218.6i	0.0735309	+	0.0154955i
$311$	849084.	+	2.61321e6i	0.497794	+	1.53205i	0.812557	+	0.582882i	$0.198075\pi$
$311$	849084.	+	2.61321e6i	0.497794	+	1.53205i	−0.314763	+	0.949170i	$0.601925\pi$
$312$	91911.1	−	282873.i	0.0534542	−	0.164515i
$313$	−400062.	+	1.23126e6i	−0.230816	+	0.710380i	0.766833	+	0.641847i	$0.221832\pi$
$313$	−400062.	+	1.23126e6i	−0.230816	+	0.710380i	−0.997649	+	0.0685325i	$0.978168\pi$
$314$	353765.	+	1.08878e6i	0.202484	+	0.623182i
$315$	−151307.	−	31885.5i	−0.0859176	−	0.0181058i
$316$	−424272.	+	1.30578e6i	−0.239016	+	0.735615i
$317$	89655.4	+	65138.4i	0.0501104	+	0.0364074i	0.612559	−	0.790425i	$-0.290140\pi$
$317$	89655.4	+	65138.4i	0.0501104	+	0.0364074i	−0.562448	+	0.826833i	$0.690140\pi$
$318$	363509.			0.201580
$319$	−3.28604e6	−	2.38745e6i	−1.80799	−	1.31358i
$320$	209015.	−	93496.6i	0.114104	−	0.0510412i
$321$	1.10750e6	−	804645.i	0.599903	−	0.435855i
$322$	−78240.3	+	56844.9i	−0.0420524	+	0.0305528i
$323$	112810.	+	347194.i	0.0601647	+	0.185168i
$324$	121019.			0.0640457
$325$	164879.	−	1.62316e6i	0.0865877	−	0.852421i
$326$	−2.51639e6			−1.31140
$327$	−78633.2	−	242008.i	−0.0406665	−	0.125158i
$328$	−494098.	+	358983.i	−0.253588	+	0.184242i
$329$	−121647.	+	88381.4i	−0.0619598	+	0.0450164i
$330$	1.00031e6	+	210801.i	0.505652	+	0.106558i
$331$	364874.	+	265097.i	0.183051	+	0.132995i	0.675537	−	0.737326i	$-0.263912\pi$
$331$	364874.	+	265097.i	0.183051	+	0.132995i	−0.492486	+	0.870320i	$0.663912\pi$
$332$	−753032.			−0.374945
$333$	1.24700e6	+	906001.i	0.616250	+	0.447732i
$334$	−94853.2	+	291928.i	−0.0465249	+	0.143189i
$335$	−1.27117e6	+	2.21062e6i	−0.618857	+	1.07622i
$336$	−11894.3	−	36607.0i	−0.00574767	−	0.0176895i
$337$	−123025.	+	378632.i	−0.0590090	+	0.181611i	−0.976216	−	0.216800i	$-0.930438\pi$
$337$	−123025.	+	378632.i	−0.0590090	+	0.181611i	0.917207	+	0.398411i	$0.130438\pi$
$338$	122025.	−	375553.i	0.0580972	−	0.178805i
$339$	−279950.	−	861597.i	−0.132306	−	0.407198i
$340$	56304.2	+	526857.i	0.0264146	+	0.247170i
$341$	90246.3	−	277749.i	0.0420284	−	0.129350i
$342$	326576.	+	237272.i	0.150980	+	0.109693i
$343$	562953.			0.258367
$344$	−86377.3	−	62756.8i	−0.0393553	−	0.0285933i
$345$	−355062.	+	617470.i	−0.160604	+	0.279298i
$346$	−1.39044e6	+	1.01022e6i	−0.624400	+	0.453653i
$347$	3.46313e6	−	2.51611e6i	1.54399	−	1.12178i	0.596224	−	0.802818i	$-0.296667\pi$
$347$	3.46313e6	−	2.51611e6i	1.54399	−	1.12178i	0.947769	−	0.318959i	$-0.103333\pi$
$348$	348064.	+	1.07123e6i	0.154068	+	0.474171i
$349$	−2.26805e6			−0.996755			−0.498378	−	0.866960i	$-0.666071\pi$
$349$	−2.26805e6			−0.996755			−0.498378	+	0.866960i	$0.666071\pi$
$350$	−106205.	−	182480.i	−0.0463422	−	0.0796243i
$351$	1.89037e6			0.818991
$352$	−162519.	−	500183.i	−0.0699114	−	0.215165i
$353$	−1.37199e6	+	996812.i	−0.586024	+	0.425771i	−0.840891	−	0.541205i	$-0.817968\pi$
$353$	−1.37199e6	+	996812.i	−0.586024	+	0.425771i	0.254867	+	0.966976i	$0.417968\pi$
$354$	−223840.	+	162629.i	−0.0949356	+	0.0689747i
$355$	2.15417e6	+	2.38407e6i	0.907212	+	1.00403i
$356$	410895.	+	298533.i	0.171833	+	0.124844i
$357$	89070.0			0.0369880
$358$	−2.11420e6	−	1.53606e6i	−0.871845	−	0.633433i
$359$	−1.25482e6	+	3.86194e6i	−0.513861	+	1.58150i	0.271484	+	0.962443i	$0.412486\pi$
$359$	−1.25482e6	+	3.86194e6i	−0.513861	+	1.58150i	−0.785345	+	0.619058i	$0.787514\pi$
$360$	392800.	+	434721.i	0.159740	+	0.176789i
$361$	−647806.	−	1.99374e6i	−0.261624	−	0.805195i
$362$	−136447.	+	419940.i	−0.0547258	+	0.168429i
$363$	282585.	−	869706.i	0.112559	−	0.346422i
$364$	43601.1	+	134190.i	0.0172482	+	0.0530845i
$365$	2.84233e6	−	1.27143e6i	1.11671	−	0.499528i
$366$	−604663.	+	1.86096e6i	−0.235945	+	0.726163i
$367$	3.67128e6	+	2.66734e6i	1.42283	+	1.03375i	0.991296	+	0.131649i	$0.0420272\pi$
$367$	3.67128e6	+	2.66734e6i	1.42283	+	1.03375i	0.431533	+	0.902097i	$0.357973\pi$
$368$	366437.			0.141052
$369$	−1.26430e6	−	918564.i	−0.483373	−	0.351191i
$370$	223646.	+	2.09273e6i	0.0849292	+	0.794711i
$371$	−139509.	+	101359.i	−0.0526220	+	0.0382321i
$372$	−65518.8	+	47602.2i	−0.0245476	+	0.0178349i
$373$	22176.0	+	68250.8i	0.00825300	+	0.0254001i	0.955098	−	0.296289i	$-0.0957493\pi$
$373$	22176.0	+	68250.8i	0.00825300	+	0.0254001i	−0.946845	+	0.321689i	$0.895749\pi$
$374$	1.21702e6			0.449902
$375$	−1.26281e6	−	907430.i	−0.463725	−	0.333223i
$376$	569730.			0.207826
$377$	−1.27590e6	−	3.92682e6i	−0.462342	−	1.42294i
$378$	197914.	−	143793.i	0.0712438	−	0.0517617i
$379$	1.96297e6	−	1.42618e6i	0.701964	−	0.510007i	−0.178607	−	0.983921i	$-0.557159\pi$
$379$	1.96297e6	−	1.42618e6i	0.701964	−	0.510007i	0.880571	+	0.473913i	$0.157159\pi$
$380$	58570.5	+	548063.i	0.0208075	+	0.194703i
$381$	−449597.	−	326651.i	−0.158676	−	0.115285i
$382$	−1.46355e6			−0.513155
$383$	3.97141e6	+	2.88540e6i	1.38340	+	1.00510i	0.996553	+	0.0829534i	$0.0264353\pi$
$383$	3.97141e6	+	2.88540e6i	1.38340	+	1.00510i	0.386845	+	0.922145i	$0.373565\pi$
$384$	−45067.8	+	138705.i	−0.0155969	+	0.0480024i
$385$	−442683.	+	198021.i	−0.152209	+	0.0680863i
$386$	765594.	+	2.35626e6i	0.261535	+	0.804922i
$387$	84422.8	−	259827.i	0.0286538	−	0.0881874i
$388$	−106133.	+	326644.i	−0.0357908	+	0.110153i
$389$	1.34644e6	+	4.14390e6i	0.451140	+	1.38847i	0.875608	+	0.483023i	$0.160461\pi$
$389$	1.34644e6	+	4.14390e6i	0.451140	+	1.38847i	−0.424467	+	0.905443i	$0.639539\pi$
$390$	696693.	+	771047.i	0.231942	+	0.256696i
$391$	−262033.	+	806454.i	−0.0866789	+	0.266770i
$392$	−855445.	−	621517.i	−0.281175	−	0.204286i
$393$	264307.			0.0863233
$394$	−2.01279e6	−	1.46238e6i	−0.653217	−	0.474590i
$395$	−3.21601e6	−	3.55924e6i	−1.03711	−	1.14780i
$396$	1.08872e6	−	791001.i	0.348881	−	0.253477i
$397$	−1.79497e6	+	1.30412e6i	−0.571584	+	0.415280i	−0.835680	−	0.549216i	$-0.814926\pi$
$397$	−1.79497e6	+	1.30412e6i	−0.571584	+	0.415280i	0.264096	+	0.964496i	$0.414926\pi$
$398$	−756641.	−	2.32870e6i	−0.239432	−	0.736896i
$399$	92655.2			0.0291365
$400$	−80846.9	+	795904.i	−0.0252646	+	0.248720i
$401$	−415051.			−0.128896			−0.0644481	−	0.997921i	$-0.520529\pi$
$401$	−415051.			−0.128896			−0.0644481	+	0.997921i	$0.520529\pi$
$402$	−501914.	−	1.54473e6i	−0.154904	−	0.476747i
$403$	240173.	−	174496.i	0.0736649	−	0.0535207i
$404$	1.62477e6	−	1.18047e6i	0.495267	−	0.359832i
$405$	−210772.	+	366543.i	−0.0638521	+	0.111042i
$406$	−432279.	−	314069.i	−0.130151	−	0.0945605i
$407$	4.83411e6			1.44654
$408$	−273033.	−	198370.i	−0.0812017	−	0.0589965i
$409$	−1.14046e6	+	3.50996e6i	−0.337109	+	1.03751i	0.628565	+	0.777757i	$0.283643\pi$
$409$	−1.14046e6	+	3.50996e6i	−0.337109	+	1.03751i	−0.965674	+	0.259757i	$0.916357\pi$
$410$	−226747.	−	2.12175e6i	−0.0666166	−	0.623354i
$411$	−828024.	−	2.54840e6i	−0.241790	−	0.744153i
$412$	−900243.	+	2.77066e6i	−0.261286	+	0.804157i
$413$	40559.4	−	124829.i	0.0117008	−	0.0360114i
$414$	289746.	+	891746.i	0.0830838	+	0.255706i
$415$	1.31152e6	−	2.28079e6i	0.373812	−	0.650077i
$416$	165205.	−	508449.i	0.0468048	−	0.144050i
$417$	470748.	+	342019.i	0.132571	+	0.0963185i
$418$	1.26600e6			0.354400
$419$	−4.52052e6	−	3.28435e6i	−1.25792	−	0.913932i	−0.259266	−	0.965806i	$-0.583481\pi$
$419$	−4.52052e6	−	3.28435e6i	−1.25792	−	0.913932i	−0.998654	+	0.0518739i	$0.983481\pi$
$420$	131591.	+	27730.8i	0.0364002	+	0.00767078i
$421$	3.35679e6	−	2.43885e6i	0.923037	−	0.670625i	−0.0212413	−	0.999774i	$-0.506762\pi$
$421$	3.35679e6	−	2.43885e6i	0.923037	−	0.670625i	0.944278	+	0.329149i	$0.106762\pi$
$422$	−174633.	+	126879.i	−0.0477360	+	0.0346822i
$423$	450492.	+	1.38647e6i	0.122415	+	0.376756i
$424$	653388.			0.176505
$425$	−1.69381e6	−	747065.i	−0.454876	−	0.200625i
$426$	−2.04658e6			−0.546392
$427$	−286842.	−	882808.i	−0.0761329	−	0.234313i
$428$	1.99067e6	−	1.44631e6i	0.525278	−	0.381637i
$429$	1.93102e6	−	1.40297e6i	0.506574	−	0.368048i
$430$	340517.	−	152320.i	0.0888113	−	0.0397271i
$431$	−1.26566e6	−	919558.i	−0.328190	−	0.238444i	0.411472	−	0.911422i	$-0.365015\pi$
$431$	−1.26566e6	−	919558.i	−0.328190	−	0.238444i	−0.739662	+	0.672978i	$0.765015\pi$
$432$	−926927.			−0.238966
$433$	−263625.	−	191535.i	−0.0675721	−	0.0490940i	0.553486	−	0.832858i	$-0.313297\pi$
$433$	−263625.	−	191535.i	−0.0675721	−	0.0490940i	−0.621059	+	0.783764i	$0.713297\pi$
$434$	11871.9	−	36537.9i	0.00302549	−	0.00931150i
$435$	−3.85076e6	−	811488.i	−0.975717	−	0.205617i
$436$	−141339.	−	434996.i	−0.0356078	−	0.109590i
$437$	−272580.	+	838914.i	−0.0682794	+	0.210142i
$438$	−612863.	+	1.88620e6i	−0.152643	+	0.469788i
$439$	−359917.	−	1.10771e6i	−0.0891335	−	0.274325i	0.896547	−	0.442949i	$-0.146068\pi$
$439$	−359917.	−	1.10771e6i	−0.0891335	−	0.274325i	−0.985680	+	0.168624i	$0.946068\pi$
$440$	1.79801e6	+	378902.i	0.442752	+	0.0933030i
$441$	836089.	−	2.57322e6i	0.204718	−	0.630057i
$442$	1.00086e6	+	727167.i	0.243679	+	0.177043i
$443$	−6.07467e6			−1.47066			−0.735332	−	0.677707i	$-0.762974\pi$
$443$	−6.07467e6			−1.47066			−0.735332	+	0.677707i	$0.762974\pi$
$444$	−1.08452e6	−	787948.i	−0.261083	−	0.189688i
$445$	−1.61983e6	+	724584.i	−0.387766	+	0.173456i
$446$	324593.	−	235831.i	0.0772685	−	0.0561388i
$447$	−2.59981e6	+	1.88888e6i	−0.615423	+	0.447131i
$448$	−21379.4	−	65799.1i	−0.00503270	−	0.0154890i
$449$	5.21186e6			1.22005			0.610024	−	0.792383i	$-0.291160\pi$
$449$	5.21186e6			1.22005			0.610024	+	0.792383i	$0.291160\pi$
$450$	−2.00081e6	+	432585.i	−0.465772	+	0.100702i
$451$	−4.90115e6			−1.13464
$452$	−503195.	−	1.54867e6i	−0.115848	−	0.356545i
$453$	−2.90307e6	+	2.10920e6i	−0.664679	+	0.482917i
$454$	3.50937e6	−	2.54970e6i	0.799078	−	0.580564i
$455$	−482375.	−	101653.i	−0.109234	−	0.0230193i
$456$	−284023.	−	206355.i	−0.0639649	−	0.0464732i
$457$	−5.36086e6			−1.20073			−0.600363	−	0.799727i	$-0.704977\pi$
$457$	−5.36086e6			−1.20073			−0.600363	+	0.799727i	$0.704977\pi$
$458$	−3.77099e6	−	2.73979e6i	−0.840025	−	0.610314i
$459$	662830.	−	2.03998e6i	0.146849	−	0.451954i
$460$	−638204.	+	1.10987e6i	−0.140626	+	0.244555i
$461$	353023.	+	1.08649e6i	0.0773662	+	0.238109i	0.982258	−	0.187532i	$-0.0600488\pi$
$461$	353023.	+	1.08649e6i	0.0773662	+	0.238109i	−0.904892	+	0.425641i	$0.860049\pi$
$462$	95451.5	−	293770.i	0.0208055	−	0.0640327i
$463$	1.07672e6	−	3.31379e6i	0.233426	−	0.718411i	−0.763900	−	0.645334i	$-0.776718\pi$
$463$	1.07672e6	−	3.31379e6i	0.233426	−	0.718411i	0.997326	−	0.0730770i	$-0.0232819\pi$
$464$	625626.	+	1.92548e6i	0.134903	+	0.415187i
$465$	−30067.4	−	281350.i	−0.00644856	−	0.0603414i
$466$	584612.	−	1.79925e6i	0.124711	−	0.383820i
$467$	6.00353e6	+	4.36182e6i	1.27384	+	0.925498i	0.999348	−	0.0360922i	$-0.0114910\pi$
$467$	6.00353e6	+	4.36182e6i	1.27384	+	0.925498i	0.274490	+	0.961590i	$0.411491\pi$
$468$	1.36797e6			0.288710
$469$	623352.	+	452892.i	0.130858	+	0.0950741i
$470$	−992268.	+	1.72560e6i	−0.207197	+	0.360326i
$471$	2.06108e6	−	1.49746e6i	0.428097	−	0.311031i
$472$	−402340.	+	292317.i	−0.0831262	+	0.0603947i
$473$	−264769.	−	814875.i	−0.0544145	−	0.167470i
$474$	3.05539e6			0.624627
$475$	−1.76199e6	−	777135.i	−0.358319	−	0.158038i
$476$	160099.			0.0323869
$477$	516641.	+	1.59006e6i	0.103966	+	0.319976i
$478$	5.17874e6	−	3.76258e6i	1.03670	−	0.753209i
$479$	6.61576e6	−	4.80663e6i	1.31747	−	0.957198i	0.317511	−	0.948255i	$-0.397153\pi$
$479$	6.61576e6	−	4.80663e6i	1.31747	−	0.957198i	0.999960	−	0.00894376i	$-0.00284693\pi$
$480$	−341617.	−	378076.i	−0.0676763	−	0.0748991i
$481$	3.97552e6	+	2.88838e6i	0.783485	+	0.569235i
$482$	−472788.			−0.0926934
$483$	174114.	+	126501.i	0.0339599	+	0.0246733i
$484$	507930.	−	1.56325e6i	0.0985577	−	0.303330i
$485$	−804496.	−	890355.i	−0.155299	−	0.171874i
$486$	−1.17078e6	−	3.60331e6i	−0.224847	−	0.692007i
$487$	−2.30500e6	+	7.09405e6i	−0.440400	+	1.35541i	0.447050	+	0.894509i	$0.352475\pi$
$487$	−2.30500e6	+	7.09405e6i	−0.440400	+	1.35541i	−0.887450	+	0.460904i	$0.847525\pi$
$488$	−1.08685e6	+	3.34497e6i	−0.206595	+	0.635833i
$489$	1.73048e6	+	5.32586e6i	0.327260	+	1.00720i
$490$	3.37234e6	−	1.50852e6i	0.634515	−	0.283831i
$491$	−1.17515e6	+	3.61675e6i	−0.219984	+	0.677041i	0.778778	+	0.627299i	$0.215840\pi$
$491$	−1.17515e6	+	3.61675e6i	−0.219984	+	0.677041i	−0.998762	+	0.0497414i	$0.984160\pi$
$492$	1.09956e6	+	798874.i	0.204788	+	0.148787i
$493$	−4.68497e6			−0.868139
$494$	1.04114e6	+	756436.i	0.191952	+	0.139462i
$495$	499626.	+	4.67517e6i	0.0916499	+	0.857599i
$496$	−117767.	+	85562.4i	−0.0214940	+	0.0156163i
$497$	785444.	−	570658.i	0.142634	−	0.103630i
$498$	517845.	+	1.59376e6i	0.0935678	+	0.287972i
$499$	3.80253e6			0.683630			0.341815	−	0.939767i	$-0.388958\pi$
$499$	3.80253e6			0.683630			0.341815	+	0.939767i	$0.388958\pi$
$500$	−2.26984e6	−	1.63106e6i	−0.406041	−	0.291772i
$501$	683084.			0.121585
$502$	604691.	+	1.86105e6i	0.107096	+	0.329608i
$503$	621806.	−	451769.i	0.109581	−	0.0796152i	−0.531645	−	0.846967i	$-0.678426\pi$
$503$	621806.	−	451769.i	0.109581	−	0.0796152i	0.641226	+	0.767352i	$0.278426\pi$
$504$	143221.	−	104056.i	0.0251148	−	0.0182470i
$505$	745628.	+	6.97709e6i	0.130105	+	1.21743i
$506$	2.37903e6	+	1.72846e6i	0.413070	+	0.300113i
$507$	−878758.			−0.151827
$508$	−808125.	−	587137.i	−0.138938	−	0.100944i
$509$	−3.29945e6	+	1.01547e7i	−0.564479	+	1.73729i	0.105017	+	0.994470i	$0.466510\pi$
$509$	−3.29945e6	+	1.01547e7i	−0.564479	+	1.73729i	−0.669496	+	0.742816i	$0.733490\pi$
$510$	1.07635e6	−	481475.i	0.183244	−	0.0819688i
$511$	−290732.	−	894780.i	−0.0492539	−	0.151588i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	689509.	−	2.12209e6i	0.115677	−	0.356017i
$514$	−278319.	−	856576.i	−0.0464659	−	0.143007i
$515$	−6.82391e6	−	7.55219e6i	−1.13374	−	1.25474i
$516$	−73422.4	+	225971.i	−0.0121396	+	0.0373619i
$517$	3.69887e6	+	2.68739e6i	0.608615	+	0.442185i
$518$	635928.			0.104132
$519$	3.09427e6	+	2.24812e6i	0.504242	+	0.366353i
$520$	1.25227e6	+	1.38592e6i	0.203090	+	0.224765i
$521$	−1.03133e6	+	749308.i	−0.166458	+	0.120939i	−0.667896	−	0.744255i	$-0.732805\pi$
$521$	−1.03133e6	+	749308.i	−0.166458	+	0.120939i	0.501437	+	0.865194i	$0.332805\pi$
$522$	−4.19108e6	+	3.04500e6i	−0.673209	+	0.489115i
$523$	−281561.	−	866556.i	−0.0450110	−	0.138529i	0.926025	−	0.377461i	$-0.123203\pi$
$523$	−281561.	−	866556.i	−0.0450110	−	0.138529i	−0.971036	+	0.238932i	$0.923203\pi$
$524$	475078.			0.0755852
$525$	−313177.	+	350268.i	−0.0495898	+	0.0554629i
$526$	5.34253e6			0.841943
$527$	−104093.	−	320365.i	−0.0163265	−	0.0502479i
$528$	−946857.	+	687932.i	−0.147809	+	0.107389i
$529$	3.54953e6	−	2.57888e6i	0.551482	−	0.400675i
$530$	−1.13797e6	+	1.97899e6i	−0.175971	+	0.306023i
$531$	−1.02950e6	−	747979.i	−0.158450	−	0.115121i
$532$	166543.			0.0255121
$533$	−4.03064e6	−	2.92843e6i	−0.614549	−	0.446496i
$534$	349269.	−	1.07494e6i	0.0530037	−	0.163129i
$535$	913541.	+	8.54831e6i	0.137989	+	1.29121i
$536$	−902162.	−	2.77657e6i	−0.135635	−	0.417442i
$537$	−1.79712e6	+	5.53095e6i	−0.268931	+	0.827683i
$538$	−750529.	+	2.30989e6i	−0.111792	+	0.344061i
$539$	−2.62216e6	−	8.07019e6i	−0.388766	−	1.19650i
$540$	1.61438e6	−	2.80749e6i	0.238244	−	0.414318i
$541$	2.46082e6	−	7.57364e6i	0.361483	−	1.11253i	−0.590672	−	0.806912i	$-0.701137\pi$
$541$	2.46082e6	−	7.57364e6i	0.361483	−	1.11253i	0.952154	−	0.305617i	$-0.0988628\pi$
$542$	6.14850e6	+	4.46714e6i	0.899023	+	0.653178i
$543$	982620.			0.143016
$544$	−490763.	−	356560.i	−0.0711008	−	0.0516577i
$545$	1.56368e6	+	329522.i	0.225506	+	0.0475218i
$546$	254025.	−	184560.i	0.0364666	−	0.0264945i
$547$	188546.	−	136986.i	0.0269431	−	0.0195753i	−0.574232	−	0.818692i	$-0.694699\pi$
$547$	188546.	−	136986.i	0.0269431	−	0.0195753i	0.601175	+	0.799117i	$0.294699\pi$
$548$	−1.48833e6	−	4.58060e6i	−0.211713	−	0.651585i
$549$	−8.99957e6			−1.27436
$550$	−4.27913e6	+	4.78592e6i	−0.603182	+	0.674619i
$551$	−4.87354e6			−0.683857
$552$	−251991.	−	775550.i	−0.0351996	−	0.108333i
$553$	−1.17261e6	+	851951.i	−0.163057	+	0.118468i
$554$	−6.91769e6	+	5.02600e6i	−0.957606	+	0.695741i
$555$	4.27539e6	−	1.91247e6i	0.589174	−	0.263549i
$556$	846144.	+	614760.i	0.116080	+	0.0843371i
$557$	−1.89788e6			−0.259197			−0.129599	−	0.991567i	$-0.541369\pi$
$557$	−1.89788e6			−0.259197			−0.129599	+	0.991567i	$0.541369\pi$
$558$	−301340.	−	218937.i	−0.0409706	−	0.0297669i
$559$	269145.	−	828343.i	0.0364298	−	0.112119i
$560$	236528.	+	49844.6i	0.0318723	+	0.00671658i
$561$	−836918.	−	2.57577e6i	−0.112273	−	0.345541i
$562$	527413.	−	1.62321e6i	0.0704385	−	0.216787i
$563$	4.06727e6	−	1.25178e7i	0.540794	−	1.66439i	−0.189992	−	0.981786i	$-0.560846\pi$
$563$	4.06727e6	−	1.25178e7i	0.540794	−	1.66439i	0.730786	−	0.682606i	$-0.239154\pi$
$564$	−391792.	−	1.20581e6i	−0.0518630	−	0.159618i
$565$	5.56703e6	+	1.17316e6i	0.733673	+	0.154610i
$566$	220579.	−	678873.i	0.0289417	−	0.0890733i
$567$	103358.	+	75093.9i	0.0135016	+	0.00980950i
$568$	−3.67861e6			−0.478424
$569$	7.58893e6	+	5.51368e6i	0.982652	+	0.713938i	0.958300	−	0.285765i	$-0.0922477\pi$
$569$	7.58893e6	+	5.51368e6i	0.982652	+	0.713938i	0.0243521	+	0.999703i	$0.492248\pi$
$570$	1.11968e6	−	500855.i	0.144346	−	0.0645691i
$571$	5.49114e6	−	3.98954e6i	0.704810	−	0.512074i	−0.176685	−	0.984267i	$-0.556537\pi$
$571$	5.49114e6	−	3.98954e6i	0.704810	−	0.512074i	0.881495	+	0.472193i	$0.156537\pi$
$572$	3.47090e6	−	2.52175e6i	0.443559	−	0.322265i
$573$	1.00645e6	+	3.09754e6i	0.128058	+	0.394122i
$574$	−644746.			−0.0816787
$575$	−2.25005e6	−	3.86600e6i	−0.283807	−	0.487632i
$576$	−670773.			−0.0842402
$577$	−4.16497e6	−	1.28185e7i	−0.520802	−	1.60286i	−0.772471	−	0.635050i	$-0.780979\pi$
$577$	−4.16497e6	−	1.28185e7i	−0.520802	−	1.60286i	0.251669	−	0.967813i	$-0.419021\pi$
$578$	−3.45910e6	+	2.51318e6i	−0.430669	+	0.312899i
$579$	4.46044e6	−	3.24070e6i	0.552945	−	0.401738i
$580$	−6.92154e6	−	1.45860e6i	−0.854343	−	0.180039i
$581$	−643138.	−	467267.i	−0.0790431	−	0.0574282i
$582$	764315.			0.0935330
$583$	4.24201e6	+	3.08200e6i	0.516892	+	0.375544i
$584$	−1.10159e6	+	3.39034e6i	−0.133656	+	0.411349i
$585$	−2.38252e6	+	4.14333e6i	−0.287838	+	0.500564i
$586$	−204102.	−	628161.i	−0.0245529	−	0.0755660i
$587$	2.14573e6	−	6.60389e6i	0.257028	−	0.791051i	−0.736395	−	0.676552i	$-0.763474\pi$
$587$	2.14573e6	−	6.60389e6i	0.257028	−	0.791051i	0.993423	−	0.114499i	$-0.0365264\pi$
$588$	−727145.	+	2.23792e6i	−0.0867317	+	0.266933i
$589$	−108283.	−	333259.i	−0.0128609	−	0.0395817i
$590$	−184638.	−	1.72772e6i	−0.0218369	−	0.204336i
$591$	−1.71091e6	+	5.26564e6i	−0.201492	+	0.620129i
$592$	−1.94936e6	−	1.41629e6i	−0.228606	−	0.166092i
$593$	−1.09158e7			−1.27474			−0.637369	−	0.770559i	$-0.719977\pi$
$593$	−1.09158e7			−1.27474			−0.637369	+	0.770559i	$0.719977\pi$
$594$	−6.01791e6	−	4.37227e6i	−0.699809	−	0.508441i
$595$	−278835.	+	484908.i	−0.0322891	+	0.0561522i
$596$	−4.67302e6	+	3.39515e6i	−0.538868	+	0.391510i
$597$	−4.40828e6	+	3.20280e6i	−0.506213	+	0.367786i
$598$	923726.	+	2.84294e6i	0.105631	+	0.325098i
$599$	−5.98857e6			−0.681955			−0.340978	−	0.940071i	$-0.610758\pi$
$599$	−5.98857e6			−0.681955			−0.340978	+	0.940071i	$0.610758\pi$
$600$	1.74010e6	−	376219.i	0.197331	−	0.0426640i
$601$	6.79095e6			0.766910			0.383455	−	0.923560i	$-0.374734\pi$
$601$	6.79095e6			0.766910			0.383455	+	0.923560i	$0.374734\pi$
$602$	−34830.4	−	107197.i	−0.00391712	−	0.0120557i
$603$	6.04360e6	−	4.39093e6i	0.676865	−	0.491771i
$604$	−5.21811e6	+	3.79118e6i	−0.581997	+	0.422845i
$605$	3.85015e6	+	4.26105e6i	0.427651	+	0.473291i
$606$	−3.61574e6	−	2.62699e6i	−0.399959	−	0.290587i
$607$	8.98882e6			0.990219			0.495109	−	0.868831i	$-0.335128\pi$
$607$	8.98882e6			0.990219			0.495109	+	0.868831i	$0.335128\pi$
$608$	−510516.	−	370912.i	−0.0560080	−	0.0406922i
$609$	−367446.	+	1.13088e6i	−0.0401467	+	0.123559i
$610$	−8.23839e6	−	9.11762e6i	−0.896432	−	0.992104i
$611$	1.43619e6	+	4.42015e6i	0.155636	+	0.478998i
$612$	479658.	−	1.47624e6i	0.0517670	−	0.159322i
$613$	2.19871e6	−	6.76693e6i	0.236329	−	0.727345i	−0.760614	−	0.649205i	$-0.775102\pi$
$613$	2.19871e6	−	6.76693e6i	0.236329	−	0.727345i	0.996942	−	0.0781402i	$-0.0248982\pi$
$614$	3.80144e6	+	1.16996e7i	0.406937	+	1.25242i
$615$	−4.33468e6	+	1.93899e6i	−0.462135	+	0.206722i
$616$	171569.	−	528035.i	0.0182174	−	0.0560674i
$617$	−6.89367e6	−	5.00854e6i	−0.729016	−	0.529661i	0.160236	−	0.987079i	$-0.448775\pi$
$617$	−6.89367e6	−	5.00854e6i	−0.729016	−	0.529661i	−0.889252	+	0.457417i	$0.848775\pi$
$618$	6.48309e6			0.682827
$619$	−4.80501e6	−	3.49104e6i	−0.504043	−	0.366209i	0.306516	−	0.951865i	$-0.400837\pi$
$619$	−4.80501e6	−	3.49104e6i	−0.504043	−	0.366209i	−0.810559	+	0.585657i	$0.800837\pi$
$620$	−54044.4	−	505712.i	−0.00564640	−	0.0528353i
$621$	4.19298e6	−	3.04638e6i	0.436308	−	0.316997i
$622$	8.89172e6	−	6.46021e6i	0.921531	−	0.669531i
$623$	165687.	+	509933.i	0.0171029	+	0.0526372i
$624$	−1.18972e6			−0.122316
$625$	8.89341e6	−	4.03418e6i	0.910686	−	0.413100i
$626$	5.17851e6			0.528165
$627$	−870605.	−	2.67945e6i	−0.0884407	−	0.272193i
$628$	3.70468e6	−	2.69161e6i	0.374845	−	0.272341i
$629$	4.51093e6	−	3.27738e6i	0.454610	−	0.330294i
$630$	65725.8	+	615018.i	0.00659758	+	0.0617357i
$631$	5.30615e6	+	3.85514e6i	0.530525	+	0.385449i	0.820554	−	0.571569i	$-0.193665\pi$
$631$	5.30615e6	+	3.85514e6i	0.530525	+	0.385449i	−0.290029	+	0.957018i	$0.593665\pi$
$632$	5.49189e6			0.546927
$633$	388626.	+	282353.i	0.0385498	+	0.0280081i
$634$	136981.	−	421585.i	0.0135344	−	0.0416545i
$635$	3.18580e6	−	1.42507e6i	0.313534	−	0.140250i
$636$	−449322.	−	1.38287e6i	−0.0440468	−	0.135562i
$637$	2.66550e6	−	8.20356e6i	0.260273	−	0.801039i
$638$	−5.02062e6	+	1.54519e7i	−0.488322	+	1.50290i
$639$	−2.90872e6	−	8.95211e6i	−0.281806	−	0.867308i
$640$	−614039.	−	679572.i	−0.0592578	−	0.0655821i
$641$	−3.35196e6	+	1.03163e7i	−0.322221	+	0.991694i	0.650459	+	0.759542i	$0.274577\pi$
$641$	−3.35196e6	+	1.03163e7i	−0.322221	+	0.991694i	−0.972679	+	0.232152i	$0.925423\pi$
$642$	−4.43000e6	−	3.21858e6i	−0.424195	−	0.308196i
$643$	1.31460e7			1.25391			0.626957	−	0.779054i	$-0.284300\pi$
$643$	1.31460e7			1.25391			0.626957	+	0.779054i	$0.284300\pi$
$644$	312961.	+	227380.i	0.0297355	+	0.0216041i
$645$	−556547.	−	615945.i	−0.0526748	−	0.0582965i
$646$	1.18136e6	−	858310.i	0.111379	−	0.0809213i
$647$	4.96469e6	−	3.60706e6i	0.466263	−	0.338760i	−0.329720	−	0.944079i	$-0.606954\pi$
$647$	4.96469e6	−	3.60706e6i	0.466263	−	0.338760i	0.795983	+	0.605319i	$0.206954\pi$
$648$	−149587.	−	460382.i	−0.0139945	−	0.0430706i
$649$	−3.99096e6			−0.371934
$650$	−6.37868e6	+	1.37911e6i	−0.592172	+	0.128031i
$651$	−85495.3			−0.00790660
$652$	3.11043e6	+	9.57293e6i	0.286551	+	0.881914i
$653$	−1.08472e7	+	7.88093e6i	−0.995482	+	0.723260i	−0.961115	−	0.276149i	$-0.910942\pi$
$653$	−1.08472e7	+	7.88093e6i	−0.995482	+	0.723260i	−0.0343675	+	0.999409i	$0.510942\pi$
$654$	−823457.	+	598277.i	−0.0752829	+	0.0546963i
$655$	−827419.	+	1.43892e6i	−0.0753567	+	0.131049i
$656$	1.97639e6	+	1.43593e6i	0.179314	+	0.130279i
$657$	−9.12162e6			−0.824439
$658$	486586.	+	353526.i	0.0438122	+	0.0318314i
$659$	257156.	−	791446.i	0.0230666	−	0.0709917i	−0.938861	−	0.344298i	$-0.888117\pi$
$659$	257156.	−	791446.i	0.0230666	−	0.0709917i	0.961927	+	0.273306i	$0.0881171\pi$
$660$	−434524.	−	4.06599e6i	−0.0388288	−	0.363334i
$661$	−715387.	−	2.20173e6i	−0.0636850	−	0.196002i	0.914151	−	0.405373i	$-0.132858\pi$
$661$	−715387.	−	2.20173e6i	−0.0636850	−	0.196002i	−0.977836	+	0.209371i	$0.932858\pi$
$662$	557478.	−	1.71574e6i	0.0494405	−	0.152162i
$663$	850750.	−	2.61834e6i	0.0751654	−	0.231335i
$664$	930798.	+	2.86470e6i	0.0819286	+	0.252150i
$665$	−290059.	+	504426.i	−0.0254350	+	0.0442327i
$666$	1.90525e6	−	5.86376e6i	0.166443	−	0.512260i
$667$	−9.15819e6	−	6.65381e6i	−0.797067	−	0.579103i
$668$	1.22781e6			0.106461
$669$	−722343.	−	524813.i	−0.0623991	−	0.0453356i
$670$	9.98095e6	+	2.10333e6i	0.858984	+	0.181017i
$671$	−2.28342e7	+	1.65901e7i	−1.95785	+	1.42246i
$672$	−124559.	+	90497.5i	−0.0106403	+	0.00773060i
$673$	5.44341e6	+	1.67531e7i	0.463270	+	1.42580i	0.861146	+	0.508358i	$0.169747\pi$
$673$	5.44341e6	+	1.67531e7i	0.463270	+	1.42580i	−0.397876	+	0.917439i	$0.630253\pi$
$674$	1.59247e6			0.135027
$675$	5.69166e6	+	9.77931e6i	0.480817	+	0.826131i
$676$	−1.57952e6			−0.132941
$677$	2.04533e6	+	6.29487e6i	0.171511	+	0.527855i	0.999457	−	0.0329520i	$-0.0104908\pi$
$677$	2.04533e6	+	6.29487e6i	0.171511	+	0.527855i	−0.827946	+	0.560807i	$0.810491\pi$
$678$	−2.93167e6	+	2.12999e6i	−0.244930	+	0.177952i
$679$	−293332.	+	213118.i	−0.0244166	+	0.0177397i
$680$	1.93469e6	−	865425.i	0.160450	−	0.0717724i
$681$	−7.80967e6	−	5.67406e6i	−0.645305	−	0.468842i
$682$	−1.16817e6			−0.0961714
$683$	−9.43175e6	−	6.85257e6i	−0.773643	−	0.562085i	0.129421	−	0.991590i	$-0.458688\pi$
$683$	−9.43175e6	−	6.85257e6i	−0.773643	−	0.562085i	−0.903064	+	0.429505i	$0.858688\pi$
$684$	498964.	−	1.53565e6i	0.0407783	−	0.125503i
$685$	1.64659e7	+	3.46993e6i	1.34079	+	0.282550i
$686$	−695848.	−	2.14160e6i	−0.0564552	−	0.173751i
$687$	−3.20542e6	+	9.86527e6i	−0.259115	+	0.797475i
$688$	−131973.	+	406171.i	−0.0106295	+	0.0327143i
$689$	1.64708e6	+	5.06919e6i	0.132180	+	0.406809i
$690$	2.78787e6	+	587501.i	0.222921	+	0.0469770i
$691$	−5.05220e6	+	1.55491e7i	−0.402518	+	1.23882i	0.520432	+	0.853903i	$0.325771\pi$
$691$	−5.05220e6	+	1.55491e7i	−0.402518	+	1.23882i	−0.922950	+	0.384920i	$0.874229\pi$
$692$	5.56177e6	+	4.04086e6i	0.441518	+	0.320781i
$693$	1.42066e6			0.112372
$694$	−1.38525e7	−	1.00644e7i	−1.09177	−	0.793216i
$695$	−3.33568e6	+	1.49212e6i	−0.261952	+	0.117176i
$696$	3.64498e6	−	2.64823e6i	0.285214	−	0.207220i
$697$	−4.57348e6	+	3.32283e6i	−0.356586	+	0.259075i
$698$	2.80346e6	+	8.62817e6i	0.217799	+	0.670317i
$699$	−4.21008e6			−0.325910
$700$	−562919.	+	629588.i	−0.0434211	+	0.0485636i
$701$	3.15730e6			0.242672			0.121336	−	0.992611i	$-0.461282\pi$
$701$	3.15730e6			0.242672			0.121336	+	0.992611i	$0.461282\pi$
$702$	−2.33663e6	−	7.19140e6i	−0.178956	−	0.550770i
$703$	4.69249e6	−	3.40930e6i	0.358109	−	0.260182i
$704$	−1.70192e6	+	1.23652e6i	−0.129422	+	0.0940307i
$705$	4.33454e6	+	913436.i	0.328451	+	0.0692158i
$706$	5.48797e6	+	3.98725e6i	0.414381	+	0.301066i
$707$	2.12016e6			0.159522
$708$	895359.	+	650516.i	0.0671296	+	0.0487725i
$709$	−1.38088e6	+	4.24992e6i	−0.103167	+	0.317516i	−0.989296	−	0.145923i	$-0.953385\pi$
$709$	−1.38088e6	+	4.24992e6i	−0.103167	+	0.317516i	0.886129	+	0.463439i	$0.153385\pi$
$710$	6.40684e6	−	1.11418e7i	0.476978	−	0.829488i
$711$	4.34250e6	+	1.33648e7i	0.322156	+	0.991494i
$712$	627791.	−	1.93214e6i	0.0464104	−	0.142837i
$713$	251516.	−	774087.i	0.0185286	−	0.0570251i
$714$	−110097.	−	338843.i	−0.00808218	−	0.0248744i
$715$	1.59284e6	+	1.49047e7i	0.116521	+	1.09033i
$716$	−3.23022e6	+	9.94159e6i	−0.235477	+	0.724725i
$717$	−1.15247e7	−	8.37317e6i	−0.837203	−	0.608264i
$718$	1.62427e7			1.17584
$719$	6.14151e6	+	4.46207e6i	0.443050	+	0.321895i	0.786846	−	0.617150i	$-0.211713\pi$
$719$	6.14151e6	+	4.46207e6i	0.443050	+	0.321895i	−0.343796	+	0.939045i	$0.611713\pi$
$720$	1.16825e6	−	2.03164e6i	0.0839855	−	0.146055i
$721$	−2.48810e6	+	1.80771e6i	−0.178250	+	0.129506i
$722$	−6.78391e6	+	4.92880e6i	−0.484325	+	0.351883i
$723$	325127.	+	1.00064e6i	0.0231317	+	0.0711921i
$724$	1.76620e6			0.125226
$725$	1.64727e7	−	1.84236e7i	1.16391	−	1.30176i
$726$	−3.65785e6			−0.257564
$727$	4.40017e6	+	1.35423e7i	0.308769	+	0.950292i	0.978244	+	0.207458i	$0.0665189\pi$
$727$	4.40017e6	+	1.35423e7i	0.308769	+	0.950292i	−0.669476	+	0.742834i	$0.733481\pi$
$728$	456597.	−	331737.i	0.0319304	−	0.0231988i
$729$	−5.33419e6	+	3.87551e6i	−0.371749	+	0.270091i
$730$	−8.35011e6	−	9.24127e6i	−0.579943	−	0.641837i
$731$	−799528.	−	580891.i	−0.0553401	−	0.0402070i
$732$	7.82692e6			0.539900
$733$	2.16307e7	+	1.57156e7i	1.48700	+	1.08037i	0.975218	+	0.221248i	$0.0710129\pi$
$733$	2.16307e7	+	1.57156e7i	1.48700	+	1.08037i	0.511778	+	0.859118i	$0.328987\pi$
$734$	5.60922e6	−	1.72634e7i	0.384293	−	1.18273i
$735$	−5.51182e6	−	6.10006e6i	−0.376336	−	0.416501i
$736$	−452941.	−	1.39401e6i	−0.0308210	−	0.0948573i
$737$	7.23981e6	−	2.22819e7i	0.490974	−	1.51106i
$738$	−1.93167e6	+	5.94507e6i	−0.130555	+	0.401806i
$739$	−5.45632e6	−	1.67928e7i	−0.367527	−	1.13113i	−0.948384	−	0.317125i	$-0.897283\pi$
$739$	−5.45632e6	−	1.67928e7i	−0.367527	−	1.13113i	0.580857	−	0.814005i	$-0.302717\pi$
$740$	7.68478e6	−	3.43756e6i	0.515884	−	0.230765i
$741$	884993.	−	2.72373e6i	0.0592099	−	0.182229i
$742$	558036.	+	405437.i	0.0372094	+	0.0270342i
$743$	1.47880e6			0.0982737			0.0491368	−	0.998792i	$-0.484353\pi$
$743$	1.47880e6			0.0982737			0.0491368	+	0.998792i	$0.484353\pi$
$744$	262075.	+	190409.i	0.0173578	+	0.0126112i
$745$	−2.14451e6	−	2.00669e7i	−0.141559	−	1.32461i
$746$	232230.	−	168725.i	0.0152782	−	0.0111003i
$747$	−6.23543e6	+	4.53030e6i	−0.408851	+	0.297047i
$748$	−1.50432e6	−	4.62981e6i	−0.0983071	−	0.302558i
$749$	2.59762e6			0.169188
$750$	−1.89115e6	+	5.92567e6i	−0.122764	+	0.384666i
$751$	−1.60998e7			−1.04165			−0.520824	−	0.853664i	$-0.674375\pi$
$751$	−1.60998e7			−1.04165			−0.520824	+	0.853664i	$0.674375\pi$
$752$	−704224.	−	2.16738e6i	−0.0454116	−	0.139762i
$753$	3.52300e6	−	2.55961e6i	0.226426	−	0.164508i
$754$	−1.33614e7	+	9.70762e6i	−0.855901	+	0.621848i
$755$	−2.39465e6	−	2.24076e7i	−0.152888	−	1.43063i
$756$	−791656.	−	575172.i	−0.0503770	−	0.0366010i
$757$	−2.65168e7			−1.68183			−0.840914	−	0.541168i	$-0.817982\pi$
$757$	−2.65168e7			−1.68183			−0.840914	+	0.541168i	$0.817982\pi$
$758$	−7.85187e6	−	5.70472e6i	−0.496364	−	0.360629i
$759$	2.02222e6	−	6.22375e6i	0.127416	−	0.392146i
$760$	2.01256e6	−	900259.i	0.126391	−	0.0565371i
$761$	4.98907e6	+	1.53548e7i	0.312290	+	0.961130i	0.976856	+	0.213900i	$0.0686166\pi$
$761$	4.98907e6	+	1.53548e7i	0.312290	+	0.961130i	−0.664566	+	0.747230i	$0.731383\pi$
$762$	−686923.	+	2.11413e6i	−0.0428569	+	0.131900i
$763$	149209.	−	459218.i	0.00927862	−	0.0285567i
$764$	1.80904e6	+	5.56766e6i	0.112128	+	0.345096i
$765$	3.63584e6	+	4.02388e6i	0.224622	+	0.248594i
$766$	6.06777e6	−	1.86747e7i	0.373643	−	1.14996i
$767$	−3.28212e6	−	2.38460e6i	−0.201449	−	0.146362i
$768$	583370.			0.0356896
$769$	1.30116e7	+	9.45346e6i	0.793440	+	0.576468i	0.908982	−	0.416835i	$-0.136861\pi$
$769$	1.30116e7	+	9.45346e6i	0.793440	+	0.576468i	−0.115542	+	0.993303i	$0.536861\pi$
$770$	1.30050e6	+	1.43930e6i	0.0790469	+	0.0874832i
$771$	−1.62152e6	+	1.17810e6i	−0.0982394	+	0.0713751i
$772$	8.01740e6	−	5.82498e6i	0.484162	−	0.351764i
$773$	−8.17027e6	−	2.51455e7i	−0.491799	−	1.51360i	−0.821886	−	0.569652i	$-0.807078\pi$
$773$	−8.17027e6	−	2.51455e7i	−0.491799	−	1.51360i	0.330087	−	0.943951i	$-0.392922\pi$
$774$	−1.09279e6			−0.0655670
$775$	1.62583e6	+	717082.i	0.0972348	+	0.0428859i
$776$	1.37381e6			0.0818981
$777$	−437315.	−	1.34592e6i	−0.0259861	−	0.0799771i
$778$	1.41001e7	−	1.02443e7i	0.835164	−	0.606782i
$779$	−4.75757e6	+	3.45657e6i	−0.280893	+	0.204081i
$780$	2.07208e6	−	3.60344e6i	0.121947	−	0.212071i
$781$	−2.38827e7	−	1.73518e7i	−1.40106	−	1.01793i
$782$	3.39182e6			0.198343
$783$	2.31663e7	+	1.68313e7i	1.35037	+	0.981099i
$784$	−1.30700e6	+	4.02255e6i	−0.0759428	+	0.233728i
$785$	1.70012e6	+	1.59086e7i	0.0984704	+	0.921421i
$786$	−326702.	−	1.00548e6i	−0.0188623	−	0.0580523i
$787$	−3.15846e6	+	9.72074e6i	−0.181777	+	0.559451i	−0.999878	−	0.0156229i	$-0.995027\pi$
$787$	−3.15846e6	+	9.72074e6i	−0.181777	+	0.559451i	0.818101	+	0.575074i	$0.195027\pi$
$788$	−3.07527e6	+	9.46470e6i	−0.176428	+	0.542989i
$789$	−3.67395e6	−	1.13073e7i	−0.210107	−	0.646644i
$790$	−9.56495e6	+	1.66339e7i	−0.545274	+	0.948258i
$791$	531214.	−	1.63491e6i	0.0301876	−	0.0929078i
$792$	−4.35488e6	−	3.16400e6i	−0.246696	−	0.179235i
$793$	−2.86911e7			−1.62019
$794$	7.17986e6	+	5.21648e6i	0.404171	+	0.293647i
$795$	4.97101e6	+	1.04756e6i	0.278951	+	0.0587844i
$796$	−7.92365e6	+	5.75687e6i	−0.443244	+	0.322035i
$797$	2.29781e7	−	1.66946e7i	1.28135	−	0.930958i	0.281761	−	0.959485i	$-0.409082\pi$
$797$	2.29781e7	−	1.66946e7i	1.28135	−	0.930958i	0.999593	+	0.0285266i	$0.00908154\pi$
$798$	−114528.	−	352481.i	−0.00636656	−	0.0195943i
$799$	5.27354e6			0.292237
$800$	3.12773e6	−	676232.i	0.172784	−	0.0373569i
$801$	5.19839e6			0.286277
$802$	513031.	+	1.57895e6i	0.0281649	+	0.0866826i
$803$	−2.31439e7	+	1.68150e7i	−1.26662	+	0.920257i
$804$	−5.25611e6	+	3.81879e6i	−0.286764	+	0.208346i
$805$	−1.23376e6	+	551885.i	−0.0671027	+	0.0300164i
$806$	−960690.	−	697982.i	−0.0520890	−	0.0378449i
$807$	5.40492e6			0.292150
$808$	−6.49909e6	−	4.72187e6i	−0.350207	−	0.254440i
$809$	1.07447e7	−	3.30688e7i	0.577196	−	1.77643i	−0.0513817	−	0.998679i	$-0.516363\pi$
$809$	1.07447e7	−	3.30688e7i	0.577196	−	1.77643i	0.628578	−	0.777747i	$-0.283637\pi$
$810$	1.65494e6	+	348752.i	0.0886277	+	0.0186769i
$811$	−931001.	−	2.86533e6i	−0.0497048	−	0.152976i	0.923123	−	0.384504i	$-0.125627\pi$
$811$	−931001.	−	2.86533e6i	−0.0497048	−	0.152976i	−0.972828	+	0.231528i	$0.925627\pi$
$812$	−660463.	+	2.03270e6i	−0.0351527	+	0.108189i
$813$	5.22634e6	−	1.60850e7i	0.277314	−	0.853484i
$814$	−5.97529e6	−	1.83901e7i	−0.316081	−	0.972797i
$815$	−3.44119e7	−	7.25176e6i	−1.81474	−	0.382428i
$816$	−417158.	+	1.28388e6i	−0.0219318	+	0.0674993i
$817$	−831709.	−	604272.i	−0.0435930	−	0.0316721i
$818$	1.47624e7			0.771388
$819$	1.16834e6	+	848846.i	0.0608637	+	0.0442201i
$820$	−7.79134e6	+	3.48523e6i	−0.404648	+	0.181007i
$821$	−5.50752e6	+	4.00145e6i	−0.285166	+	0.207185i	−0.721168	−	0.692761i	$-0.756394\pi$
$821$	−5.50752e6	+	4.00145e6i	−0.285166	+	0.207185i	0.436001	+	0.899946i	$0.356394\pi$
$822$	−8.67118e6	+	6.29998e6i	−0.447609	+	0.325207i
$823$	414188.	+	1.27474e6i	0.0213156	+	0.0656028i	0.961149	−	0.276032i	$-0.0890195\pi$
$823$	414188.	+	1.27474e6i	0.0213156	+	0.0656028i	−0.939833	+	0.341635i	$0.889019\pi$
$824$	1.16530e7			0.597887
$825$	1.30719e7	+	5.76543e6i	0.668657	+	0.294915i
$826$	−525011.			−0.0267743
$827$	7.10278e6	+	2.18601e7i	0.361131	+	1.11145i	0.952369	+	0.304949i	$0.0986394\pi$
$827$	7.10278e6	+	2.18601e7i	0.361131	+	1.11145i	−0.591238	+	0.806497i	$0.701361\pi$
$828$	3.03426e6	−	2.20452e6i	0.153807	−	0.111747i
$829$	−2.22988e7	+	1.62010e7i	−1.12693	+	0.818760i	−0.985245	−	0.171153i	$-0.945251\pi$
$829$	−2.22988e7	+	1.62010e7i	−1.12693	+	0.818760i	−0.141681	+	0.989912i	$0.545251\pi$
$830$	−1.02978e7	−	2.17009e6i	−0.518857	−	0.109341i
$831$	1.53945e7	+	1.11848e7i	0.773326	+	0.561855i
$832$	−2.13846e6			−0.107101
$833$	−7.91819e6	−	5.75290e6i	−0.395379	−	0.287260i
$834$	719239.	−	2.21359e6i	0.0358062	−	0.110200i
$835$	−2.13841e6	+	3.71879e6i	−0.106139	+	0.184580i
$836$	−1.56486e6	−	4.81616e6i	−0.0774392	−	0.238333i
$837$	−636227.	+	1.95811e6i	−0.0313905	+	0.0966101i
$838$	−6.90673e6	+	2.12567e7i	−0.339752	+	1.04565i
$839$	2.36854e6	+	7.28961e6i	0.116165	+	0.357519i	0.992188	−	0.124750i	$-0.0398128\pi$
$839$	2.36854e6	+	7.28961e6i	0.116165	+	0.357519i	−0.876023	+	0.482269i	$0.839813\pi$
$840$	−57161.6	−	534881.i	−0.00279516	−	0.0261552i
$841$	1.29889e7	−	3.99756e7i	0.633258	−	1.94897i
$842$	−1.34272e7	−	9.75540e6i	−0.652686	−	0.474204i
$843$	−3.79816e6			−0.184079
$844$	698533.	+	507514.i	0.0337544	+	0.0245240i
$845$	2.75097e6	−	4.78406e6i	0.132539	−	0.230492i
$846$	4.71761e6	−	3.42754e6i	0.226619	−	0.164648i
$847$	1.40382e6	−	1.01994e6i	0.0672364	−	0.0488501i
$848$	−807632.	−	2.48563e6i	−0.0385677	−	0.118699i
$849$	−1.58850e6			−0.0756341
$850$	−748337.	+	7.36707e6i	−0.0355263	+	0.349742i
$851$	1.34727e7			0.637719
$852$	2.52971e6	+	7.78564e6i	0.119391	+	0.367448i
$853$	−5.64819e6	+	4.10365e6i	−0.265789	+	0.193107i	−0.712695	−	0.701474i	$-0.752526\pi$
$853$	−5.64819e6	+	4.10365e6i	−0.265789	+	0.193107i	0.446906	+	0.894581i	$0.352526\pi$
$854$	−3.00384e6	+	2.18242e6i	−0.140940	+	0.102399i
$855$	3.78219e6	+	4.18584e6i	0.176941	+	0.195825i
$856$	−7.96267e6	−	5.78522e6i	−0.371428	−	0.269858i
$857$	2.99029e7			1.39079			0.695394	−	0.718629i	$-0.255230\pi$
$857$	2.99029e7			1.39079			0.695394	+	0.718629i	$0.255230\pi$
$858$	−7.72407e6	−	5.61186e6i	−0.358202	−	0.260249i
$859$	−9.23253e6	+	2.84148e7i	−0.426912	+	1.31390i	0.474240	+	0.880395i	$0.342723\pi$
$859$	−9.23253e6	+	2.84148e7i	−0.426912	+	1.31390i	−0.901152	+	0.433503i	$0.857277\pi$
$860$	−1.00036e6	−	1.10713e6i	−0.0461224	−	0.0510448i
$861$	443379.	+	1.36458e6i	0.0203830	+	0.0627324i
$862$	−1.93376e6	+	5.95151e6i	−0.0886410	+	0.272809i
$863$	6.97915e6	−	2.14796e7i	0.318989	−	0.981746i	−0.655093	−	0.755548i	$-0.727370\pi$
$863$	6.97915e6	−	2.14796e7i	0.318989	−	0.981746i	0.974081	−	0.226198i	$-0.0726295\pi$
$864$	1.14574e6	+	3.52624e6i	0.0522160	+	0.160704i
$865$	−2.19257e7	+	9.80779e6i	−0.996351	+	0.445688i
$866$	−402784.	+	1.23964e6i	−0.0182506	+	0.0561696i
$867$	7.69782e6	+	5.59279e6i	0.347792	+	0.252686i
$868$	−153673.			−0.00692307
$869$	3.56552e7	+	2.59050e7i	1.60167	+	1.16368i
$870$	1.67272e6	+	1.56522e7i	0.0749248	+	0.701097i
$871$	1.92673e7	−	1.39985e7i	0.860550	−	0.625226i
$872$	−1.48012e6	+	1.07537e6i	−0.0659182	+	0.0478924i
$873$	1.08629e6	+	3.34326e6i	0.0482403	+	0.148469i
$874$	3.52834e6			0.156240
$875$	−926495.	−	2.80150e6i	−0.0409094	−	0.123700i
$876$	7.93306e6			0.349286
$877$	−200629.	−	617472.i	−0.00880835	−	0.0271093i	0.946556	−	0.322540i	$-0.104537\pi$
$877$	−200629.	−	617472.i	−0.00880835	−	0.0271093i	−0.955364	+	0.295431i	$0.904537\pi$
$878$	−3.76910e6	+	2.73841e6i	−0.165007	+	0.119884i
$879$	−1.18912e6	+	863948.i	−0.0519104	+	0.0377151i
$880$	−781033.	−	7.30839e6i	−0.0339987	−	0.318138i
$881$	1.35066e7	+	9.81310e6i	0.586281	+	0.425958i	0.840983	−	0.541062i	$-0.181977\pi$
$881$	1.35066e7	+	9.81310e6i	0.586281	+	0.425958i	−0.254702	+	0.967020i	$0.581977\pi$
$882$	−1.08226e7			−0.468445
$883$	2.29791e7	+	1.66953e7i	0.991818	+	0.720598i	0.960319	−	0.278906i	$-0.0899716\pi$
$883$	2.29791e7	+	1.66953e7i	0.991818	+	0.720598i	0.0314998	+	0.999504i	$0.489972\pi$
$884$	1.52918e6	−	4.70632e6i	0.0658153	−	0.202559i
$885$	−3.52969e6	+	1.57890e6i	−0.151488	+	0.0677637i
$886$	7.50871e6	+	2.31094e7i	0.321352	+	0.989019i
$887$	6.79384e6	−	2.09093e7i	0.289939	−	0.892339i	−0.694936	−	0.719071i	$-0.744567\pi$
$887$	6.79384e6	−	2.09093e7i	0.289939	−	0.892339i	0.984875	−	0.173268i	$-0.0554326\pi$
$888$	−1.65699e6	+	5.09970e6i	−0.0705161	+	0.217026i
$889$	−325864.	−	1.00291e6i	−0.0138287	−	0.0425605i
$890$	4.75870e6	+	5.26657e6i	0.201379	+	0.222871i
$891$	1.20043e6	−	3.69455e6i	0.0506574	−	0.155907i
$892$	−1.29837e6	−	943323.i	−0.0546371	−	0.0396961i
$893$	5.48581e6			0.230203
$894$	1.03993e7	+	7.55550e6i	0.435170	+	0.316169i
$895$	−2.44853e7	−	2.70985e7i	−1.02176	−	1.13080i
$896$	−223888.	+	162664.i	−0.00931668	+	0.00676896i
$897$	5.38174e6	−	3.91006e6i	0.223327	−	0.162257i
$898$	−6.44221e6	−	1.98271e7i	−0.266590	−	0.820480i
$899$	4.49694e6			0.185574
$900$	4.11878e6	+	7.07682e6i	0.169497	+	0.291227i
$901$	6.04790e6			0.248195
$902$	6.05815e6	+	1.86451e7i	0.247927	+	0.763041i
$903$	−202926.	+	147434.i	−0.00828168	+	0.00601699i
$904$	−5.26952e6	+	3.82853e6i	−0.214462	+	0.155816i
$905$	−3.07611e6	+	5.34950e6i	−0.124848	+	0.217116i
$906$	1.16123e7	+	8.43681e6i	0.469999	+	0.341474i
$907$	1.03369e7			0.417227			0.208613	−	0.977998i	$-0.433105\pi$
$907$	1.03369e7			0.417227			0.208613	+	0.977998i	$0.433105\pi$
$908$	−1.40375e7	−	1.01988e7i	−0.565033	−	0.410521i
$909$	6.35204e6	−	1.95496e7i	0.254978	−	0.784743i
$910$	209538.	+	1.96071e6i	0.00838800	+	0.0784893i
$911$	770915.	+	2.37263e6i	0.0307759	+	0.0947185i	0.965265	−	0.261274i	$-0.0841427\pi$
$911$	770915.	+	2.37263e6i	0.0307759	+	0.0947185i	−0.934489	+	0.355993i	$0.884143\pi$
$912$	−433949.	+	1.33556e6i	−0.0172763	+	0.0531711i
$913$	−7.46962e6	+	2.29891e7i	−0.296566	+	0.912736i
$914$	6.62639e6	+	2.03939e7i	0.262368	+	0.807487i
$915$	−1.36317e7	+	2.37062e7i	−0.538268	+	0.936074i
$916$	−5.76157e6	+	1.77323e7i	−0.226883	+	0.698274i
$917$	405748.	+	294793.i	0.0159343	+	0.0115769i
$918$	−8.57985e6			−0.336026
$919$	2.06836e7	+	1.50275e7i	0.807861	+	0.586946i	0.913210	−	0.407490i	$-0.133596\pi$
$919$	2.06836e7	+	1.50275e7i	0.807861	+	0.586946i	−0.105349	+	0.994435i	$0.533596\pi$
$920$	5.01105e6	+	1.05600e6i	0.195191	+	0.0411334i
$921$	2.21476e7	−	1.60912e7i	0.860356	−	0.625085i
$922$	3.69691e6	−	2.68596e6i	0.143223	−	0.104057i
$923$	−9.27316e6	−	2.85398e7i	−0.358281	−	1.10267i
$924$	−1.23555e6			−0.0476081
$925$	−2.97247e6	+	2.92628e7i	−0.114226	+	1.12450i
$926$	−1.39373e7			−0.534136
$927$	9.21415e6	+	2.83582e7i	0.352173	+	1.08388i
$928$	6.55165e6	−	4.76005e6i	0.249736	−	0.181444i
$929$	−1.90227e7	+	1.38208e7i	−0.723158	+	0.525405i	−0.887391	−	0.461017i	$-0.847485\pi$
$929$	−1.90227e7	+	1.38208e7i	−0.723158	+	0.525405i	0.164234	+	0.986421i	$0.447485\pi$
$930$	−1.03316e6	+	462151.i	−0.0391704	+	0.0175217i
$931$	−8.23691e6	−	5.98446e6i	−0.311451	−	0.226282i
$932$	−7.56738e6			−0.285368
$933$	−1.97875e7	−	1.43764e7i	−0.744194	−	0.540688i
$934$	9.17257e6	−	2.82303e7i	0.344052	−	1.05888i
$935$	1.66428e7	+	3.50721e6i	0.622583	+	0.131200i
$936$	−1.69091e6	−	5.20407e6i	−0.0630855	−	0.194157i
$937$	−312690.	+	962361.i	−0.0116350	+	0.0358088i	−0.956705	−	0.291058i	$-0.905993\pi$
$937$	−312690.	+	962361.i	−0.0116350	+	0.0358088i	0.945070	+	0.326867i	$0.105993\pi$
$938$	952397.	−	2.93118e6i	0.0353436	−	0.108776i
$939$	−3.56116e6	−	1.09601e7i	−0.131804	−	0.405650i
$940$	7.79109e6	+	1.64185e6i	0.287593	+	0.0606058i
$941$	5.56408e6	−	1.71245e7i	0.204842	−	0.630439i	−0.794878	−	0.606769i	$-0.792465\pi$
$941$	5.56408e6	−	1.71245e7i	0.204842	−	0.630439i	0.999720	−	0.0236693i	$-0.00753488\pi$
$942$	−8.24432e6	−	5.98985e6i	−0.302711	−	0.219932i
$943$	−1.36595e7			−0.500213
$944$	1.60936e6	+	1.16927e6i	0.0587791	+	0.0427055i
$945$	3.12087e6	−	1.39603e6i	0.113683	−	0.0508528i
$946$	−2.77270e6	+	2.01448e6i	−0.100734	+	0.0731873i
$947$	−3.05159e7	+	2.21711e7i	−1.10574	+	0.803365i	−0.981987	−	0.188949i	$-0.939492\pi$
$947$	−3.05159e7	+	2.21711e7i	−1.10574	+	0.803365i	−0.123750	+	0.992313i	$0.539492\pi$
$948$	−3.77667e6	−	1.16234e7i	−0.136486	−	0.420061i
$949$	−2.90802e7			−1.04817
$950$	−778458.	+	7.66360e6i	−0.0279850	+	0.275501i
$951$	−986468.			−0.0353697
$952$	−197893.	−	609051.i	−0.00707681	−	0.0217802i
$953$	−7.15157e6	+	5.19592e6i	−0.255076	+	0.185323i	−0.707973	−	0.706239i	$-0.750390\pi$
$953$	−7.15157e6	+	5.19592e6i	−0.255076	+	0.185323i	0.452898	+	0.891563i	$0.350390\pi$
$954$	5.41033e6	−	3.93084e6i	0.192466	−	0.139834i
$955$	−2.00141e7	−	4.21766e6i	−0.710114	−	0.149645i
$956$	−2.07150e7	−	1.50503e7i	−0.733060	−	0.532599i
$957$	3.61559e7			1.27614
$958$	−2.64630e7	−	1.92265e7i	−0.931592	−	0.676842i
$959$	1.57120e6	−	4.83566e6i	0.0551678	−	0.169789i
$960$	−1.01603e6	+	1.76692e6i	−0.0355817	+	0.0618783i
$961$	−8.74698e6	−	2.69204e7i	−0.305527	−	0.940315i
$962$	6.07405e6	−	1.86940e7i	0.211612	−	0.651275i
$963$	7.78250e6	−	2.39521e7i	0.270429	−	0.832295i
$964$	584398.	+	1.79859e6i	0.0202543	+	0.0623362i
$965$	3.67928e6	+	3.44283e7i	0.127188	+	1.19014i
$966$	266023.	−	818735.i	0.00917226	−	0.0282293i
$967$	−2.97462e7	−	2.16119e7i	−1.02297	−	0.743235i	−0.0560841	−	0.998426i	$-0.517862\pi$
$967$	−2.97462e7	−	2.16119e7i	−1.02297	−	0.743235i	−0.966891	+	0.255191i	$0.917862\pi$
$968$	−6.57479e6			−0.225524
$969$	−2.62898e6	−	1.91007e6i	−0.0899452	−	0.0653490i
$970$	−2.39270e6	+	4.16102e6i	−0.0816506	+	0.141994i
$971$	652637.	−	474168.i	0.0222138	−	0.0161393i	−0.576623	−	0.817010i	$-0.695630\pi$
$971$	652637.	−	474168.i	0.0222138	−	0.0161393i	0.598837	+	0.800871i	$0.295630\pi$
$972$	−1.22606e7	+	8.90786e6i	−0.416243	+	0.302418i
$973$	341195.	+	1.05009e6i	0.0115537	+	0.0355586i
$974$	2.98365e7			1.00774
$975$	7.30532e6	+	1.25519e7i	0.246109	+	0.422860i
$976$	1.40685e7			0.472739
$977$	1.07937e7	+	3.32196e7i	0.361771	+	1.11342i	0.951979	+	0.306165i	$0.0990458\pi$
$977$	1.07937e7	+	3.32196e7i	0.361771	+	1.11342i	−0.590208	+	0.807251i	$0.700954\pi$
$978$	1.81218e7	−	1.31662e7i	0.605834	−	0.440164i
$979$	1.31896e7	−	9.58284e6i	0.439822	−	0.319549i
$980$	−9.90719e6	−	1.09645e7i	−0.329523	−	0.364691i
$981$	−3.78732e6	−	2.75165e6i	−0.125649	−	0.0912895i
$982$	1.52115e7			0.503377
$983$	−5.38823e6	−	3.91478e6i	−0.177853	−	0.129218i	0.495297	−	0.868724i	$-0.335059\pi$
$983$	−5.38823e6	−	3.91478e6i	−0.177853	−	0.129218i	−0.673150	+	0.739506i	$0.735059\pi$
$984$	1.67997e6	−	5.17042e6i	0.0553113	−	0.170231i
$985$	−2.33107e7	−	2.57986e7i	−0.765536	−	0.847237i
$986$	5.79094e6	+	1.78227e7i	0.189695	+	0.583822i
$987$	413608.	−	1.27295e6i	0.0135144	−	0.0415930i
$988$	1.59073e6	−	4.89575e6i	0.0518446	−	0.159561i
$989$	−737910.	−	2.27105e6i	−0.0239890	−	0.0738307i
$990$	1.71678e7	−	7.67951e6i	0.556708	−	0.249027i
$991$	1.37702e7	−	4.23803e7i	0.445405	−	1.37082i	−0.436633	−	0.899640i	$-0.643829\pi$
$991$	1.37702e7	−	4.23803e7i	0.445405	−	1.37082i	0.882038	−	0.471177i	$-0.156171\pi$
$992$	471066.	+	342250.i	0.0151986	+	0.0110424i
$993$	−4.01467e6			−0.129204
$994$	−3.14177e6	−	2.28263e6i	−0.100858	−	0.0732774i
$995$	−3.63625e6	−	3.40257e7i	−0.116438	−	1.08955i
$996$	5.42294e6	−	3.94000e6i	0.173216	−	0.125848i
$997$	−3.41613e7	+	2.48197e7i	−1.08842	+	0.790784i	−0.979132	−	0.203226i	$-0.934857\pi$
$997$	−3.41613e7	+	2.48197e7i	−1.08842	+	0.790784i	−0.109289	+	0.994010i	$0.534857\pi$
$998$	−4.70018e6	−	1.44657e7i	−0.149379	−	0.459740i
$999$	−3.40800e7			−1.08040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.b.31.3	yes	28
25.21	even	5	inner	50.6.d.b.21.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.b.21.3	✓	28	25.21	even	5	inner
50.6.d.b.31.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.20148 + 5.23218i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-5.94028 - 55.5852i) q^{5} +(28.8059 + 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 + 37.6183i) q^{8} +(-50.6055 + 155.748i) q^{9} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(-7.20148 + 5.23218i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-5.94028 - 55.5852i) q^{5} +(28.8059 + 20.9287i) q^{6} -16.8909 q^{7} +(51.7771 + 37.6183i) q^{8} +(-50.6055 + 155.748i) q^{9} +(-204.116 + 91.3052i) q^{10} +(158.710 + 488.460i) q^{11} +(44.0116 - 135.454i) q^{12} +(-161.333 + 496.533i) q^{13} +(20.8783 + 64.2569i) q^{14} +(333.611 + 369.215i) q^{15} +(79.1084 - 243.470i) q^{16} +(479.260 + 348.203i) q^{17} +655.052 q^{18} +(498.551 + 362.218i) q^{19} +(599.647 + 663.644i) q^{20} +(121.640 - 88.3764i) q^{21} +(1662.04 - 1207.54i) q^{22} +(442.325 + 1361.34i) q^{23} -569.697 q^{24} +(-3054.43 + 660.383i) q^{25} +2088.34 q^{26} +(-1118.89 - 3443.59i) q^{27} +(218.641 - 158.852i) q^{28} +(-6398.09 + 4648.49i) q^{29} +(992.212 - 1725.51i) q^{30} +(-460.025 - 334.228i) q^{31} -1024.00 q^{32} +(-3698.66 - 2687.23i) q^{33} +(732.245 - 2253.62i) q^{34} +(100.337 + 938.885i) q^{35} +(-809.688 - 2491.96i) q^{36} +(2908.55 - 8951.60i) q^{37} +(761.718 - 2344.33i) q^{38} +(-1436.11 - 4419.90i) q^{39} +(1783.45 - 3101.50i) q^{40} +(-2948.88 + 9075.73i) q^{41} +(-486.559 - 353.506i) q^{42} -1668.25 q^{43} +(-6648.14 - 4830.16i) q^{44} +(8957.88 + 1887.73i) q^{45} +(4632.09 - 3365.41i) q^{46} +(7201.89 - 5232.48i) q^{47} +(704.185 + 2167.26i) q^{48} -16521.7 q^{49} +(6287.72 + 10803.4i) q^{50} -5273.25 q^{51} +(-2581.33 - 7944.52i) q^{52} +(8259.40 - 6000.81i) q^{53} +(-11717.2 + 8513.03i) q^{54} +(26208.4 - 11723.5i) q^{55} +(-874.563 - 635.407i) q^{56} -5485.50 q^{57} +(25592.4 + 18593.9i) q^{58} +(-2401.25 + 7390.29i) q^{59} +(-7790.66 - 1641.76i) q^{60} +(16982.0 + 52265.2i) q^{61} +(-702.856 + 2163.17i) q^{62} +(854.774 - 2630.72i) q^{63} +(1265.73 + 3895.53i) q^{64} +(28558.2 + 6018.20i) q^{65} +(-5651.05 + 17392.1i) q^{66} +(-36904.6 - 26812.7i) q^{67} -9478.37 q^{68} +(-10308.2 - 7489.32i) q^{69} +(3447.71 - 1542.23i) q^{70} +(-46500.9 + 33784.9i) q^{71} +(-8479.17 + 6160.47i) q^{72} +(17212.3 + 52974.0i) q^{73} -37649.1 q^{74} +(18541.2 - 20737.1i) q^{75} -9859.88 q^{76} +(-2680.76 - 8250.54i) q^{77} +(-15039.2 + 10926.6i) q^{78} +(69422.4 - 50438.4i) q^{79} +(-14003.3 - 2950.97i) q^{80} +(-6119.13 - 4445.81i) q^{81} +38171.2 q^{82} +(38076.0 + 27663.8i) q^{83} +(-743.396 + 2287.94i) q^{84} +(16508.0 - 28708.2i) q^{85} +(2062.08 + 6346.41i) q^{86} +(21754.0 - 66952.0i) q^{87} +(-10157.5 + 31261.4i) q^{88} +(-9809.24 - 30189.7i) q^{89} +(-3891.19 - 36411.2i) q^{90} +(2725.07 - 8386.90i) q^{91} +(-18528.4 - 13461.6i) q^{92} +5061.61 q^{93} +(-28807.6 - 20929.9i) q^{94} +(17172.4 - 29863.7i) q^{95} +(7374.32 - 5357.76i) q^{96} +(17366.2 - 12617.3i) q^{97} +(20421.9 + 62852.3i) q^{98} -84108.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Introduction

L-functions

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