LMFDB - Embedded newform 50.6.d.b.21.5

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			21.5
Character	$\chi$	$=$	50.21
Dual form			50.6.d.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(6.10314 + 4.43419i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(17.4261 - 53.1162i) q^{5} +(-24.4126 + 17.7368i) q^{6} -227.988 q^{7} +(51.7771 - 37.6183i) q^{8} +(-57.5049 - 176.982i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(6.10314 + 4.43419i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(17.4261 - 53.1162i) q^{5} +(-24.4126 + 17.7368i) q^{6} -227.988 q^{7} +(51.7771 - 37.6183i) q^{8} +(-57.5049 - 176.982i) q^{9} +(180.526 + 131.948i) q^{10} +(-92.0846 + 283.407i) q^{11} +(-37.2991 - 114.795i) q^{12} +(-259.699 - 799.271i) q^{13} +(281.809 - 867.318i) q^{14} +(341.881 - 246.905i) q^{15} +(79.1084 + 243.470i) q^{16} +(1071.58 - 778.546i) q^{17} +744.359 q^{18} +(-544.162 + 395.357i) q^{19} +(-725.103 + 523.665i) q^{20} +(-1391.44 - 1010.94i) q^{21} +(-964.323 - 700.622i) q^{22} +(74.8426 - 230.342i) q^{23} +482.809 q^{24} +(-2517.66 - 1851.22i) q^{25} +3361.61 q^{26} +(1000.29 - 3078.58i) q^{27} +(2951.14 + 2144.13i) q^{28} +(1125.11 + 817.440i) q^{29} +(516.692 + 1605.79i) q^{30} +(-5826.62 + 4233.28i) q^{31} -1024.00 q^{32} +(-1818.69 + 1321.35i) q^{33} +(1637.22 + 5038.86i) q^{34} +(-3972.95 + 12109.9i) q^{35} +(-920.078 + 2831.71i) q^{36} +(1171.06 + 3604.15i) q^{37} +(-831.406 - 2558.80i) q^{38} +(1959.14 - 6029.61i) q^{39} +(-1095.86 - 3405.74i) q^{40} +(4428.31 + 13628.9i) q^{41} +(5565.77 - 4043.77i) q^{42} -287.464 q^{43} +(3857.29 - 2802.49i) q^{44} +(-10402.7 - 29.6712i) q^{45} +(783.762 + 569.436i) q^{46} +(-23653.6 - 17185.4i) q^{47} +(-596.785 + 1836.72i) q^{48} +35171.6 q^{49} +(10154.5 - 7289.51i) q^{50} +9992.21 q^{51} +(-4155.18 + 12788.3i) q^{52} +(-17710.9 - 12867.7i) q^{53} +(10475.2 + 7610.66i) q^{54} +(13448.8 + 9829.88i) q^{55} +(-11804.6 + 8576.52i) q^{56} -5074.19 q^{57} +(-4500.44 + 3269.76i) q^{58} +(-6390.88 - 19669.1i) q^{59} +(-6747.44 - 19.2454i) q^{60} +(11865.4 - 36518.1i) q^{61} +(-8902.28 - 27398.4i) q^{62} +(13110.4 + 40349.7i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-46979.8 - 133.998i) q^{65} +(-2778.71 - 8551.98i) q^{66} +(51586.7 - 37479.9i) q^{67} -21192.7 q^{68} +(1478.15 - 1073.94i) q^{69} +(-41157.8 - 30082.6i) q^{70} +(42932.7 + 31192.5i) q^{71} +(-9635.18 - 7000.37i) q^{72} +(-15367.6 + 47296.6i) q^{73} -15158.5 q^{74} +(-7156.96 - 22462.0i) q^{75} +10761.9 q^{76} +(20994.2 - 64613.5i) q^{77} +(20516.4 + 14906.0i) q^{78} +(2349.03 + 1706.67i) q^{79} +(14310.8 + 40.8180i) q^{80} +(-16827.7 + 12226.0i) q^{81} -57321.2 q^{82} +(-15035.2 + 10923.7i) q^{83} +(8503.74 + 26171.8i) q^{84} +(-22680.0 - 70485.2i) q^{85} +(355.325 - 1093.58i) q^{86} +(3242.02 + 9977.90i) q^{87} +(5893.42 + 18138.1i) q^{88} +(4004.23 - 12323.7i) q^{89} +(12971.3 - 39537.5i) q^{90} +(59208.2 + 182224. i) q^{91} +(-3135.05 + 2277.75i) q^{92} -54331.8 q^{93} +(94614.5 - 68741.4i) q^{94} +(11517.2 + 35793.4i) q^{95} +(-6249.61 - 4540.61i) q^{96} +(83232.1 + 60471.6i) q^{97} +(-43474.5 + 133801. i) q^{98} +55453.3 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 $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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
$3$	6.10314	+	4.43419i	0.391517	+	0.284453i	0.766077	−	0.642749i	$-0.222206\pi$
$3$	6.10314	+	4.43419i	0.391517	+	0.284453i	−0.374560	+	0.927203i	$0.622206\pi$
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	17.4261	−	53.1162i	0.311728	−	0.950171i
$5$	17.4261	−	53.1162i	0.311728	−	0.950171i
$6$	−24.4126	+	17.7368i	−0.276844	+	0.201139i
$7$	−227.988			−1.75860			−0.879300	−	0.476268i	$-0.841989\pi$
$7$	−227.988			−1.75860			−0.879300	+	0.476268i	$0.841989\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	−57.5049	−	176.982i	−0.236646	−	0.728320i
$10$	180.526	+	131.948i	0.570874	+	0.417257i
$11$	−92.0846	+	283.407i	−0.229459	+	0.706203i	0.768349	+	0.640031i	$0.221079\pi$
$11$	−92.0846	+	283.407i	−0.229459	+	0.706203i	−0.997808	+	0.0661717i	$0.978921\pi$
$12$	−37.2991	−	114.795i	−0.0747730	−	0.230128i
$13$	−259.699	−	799.271i	−0.426198	−	1.31170i	−0.901842	−	0.432065i	$-0.857785\pi$
$13$	−259.699	−	799.271i	−0.426198	−	1.31170i	0.475644	−	0.879638i	$-0.342215\pi$
$14$	281.809	−	867.318i	0.384268	−	1.18266i
$15$	341.881	−	246.905i	0.392326	−	0.283336i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	1071.58	−	778.546i	0.899293	−	0.653375i	−0.0389913	−	0.999240i	$-0.512414\pi$
$17$	1071.58	−	778.546i	0.899293	−	0.653375i	0.938284	+	0.345865i	$0.112414\pi$
$18$	744.359			0.541503
$19$	−544.162	+	395.357i	−0.345815	+	0.251250i	−0.747111	−	0.664699i	$-0.768560\pi$
$19$	−544.162	+	395.357i	−0.345815	+	0.251250i	0.401296	+	0.915948i	$0.368560\pi$
$20$	−725.103	+	523.665i	−0.405345	+	0.292738i
$21$	−1391.44	−	1010.94i	−0.688521	−	0.500240i
$22$	−964.323	−	700.622i	−0.424782	−	0.308622i
$23$	74.8426	−	230.342i	0.0295005	−	0.0907932i	−0.935222	−	0.354061i	$-0.884800\pi$
$23$	74.8426	−	230.342i	0.0295005	−	0.0907932i	0.964723	+	0.263268i	$0.0848004\pi$
$24$	482.809			0.171099
$25$	−2517.66	−	1851.22i	−0.805651	−	0.592391i
$26$	3361.61			0.975246
$27$	1000.29	−	3078.58i	0.264069	−	0.812719i
$28$	2951.14	+	2144.13i	0.711369	+	0.516840i
$29$	1125.11	+	817.440i	0.248428	+	0.180493i	0.705030	−	0.709178i	$-0.250934\pi$
$29$	1125.11	+	817.440i	0.248428	+	0.180493i	−0.456602	+	0.889671i	$0.650934\pi$
$30$	516.692	+	1605.79i	0.104816	+	0.325750i
$31$	−5826.62	+	4233.28i	−1.08896	+	0.791176i	−0.979223	−	0.202784i	$-0.935001\pi$
$31$	−5826.62	+	4233.28i	−1.08896	+	0.791176i	−0.109737	+	0.993961i	$0.535001\pi$
$32$	−1024.00			−0.176777
$33$	−1818.69	+	1321.35i	−0.290719	+	0.211220i
$34$	1637.22	+	5038.86i	0.242891	+	0.747541i
$35$	−3972.95	+	12109.9i	−0.548206	+	1.67097i
$36$	−920.078	+	2831.71i	−0.118323	+	0.364160i
$37$	1171.06	+	3604.15i	0.140629	+	0.432811i	0.996423	−	0.0845053i	$-0.0269310\pi$
$37$	1171.06	+	3604.15i	0.140629	+	0.432811i	−0.855794	+	0.517317i	$0.826931\pi$
$38$	−831.406	−	2558.80i	−0.0934016	−	0.287460i
$39$	1959.14	−	6029.61i	0.206255	−	0.634787i
$40$	−1095.86	−	3405.74i	−0.108294	−	0.336560i
$41$	4428.31	+	13628.9i	0.411413	+	1.26620i	0.915420	+	0.402500i	$0.131859\pi$
$41$	4428.31	+	13628.9i	0.411413	+	1.26620i	−0.504007	+	0.863700i	$0.668141\pi$
$42$	5565.77	−	4043.77i	0.486858	−	0.353723i
$43$	−287.464			−0.0237089			−0.0118545	−	0.999930i	$-0.503773\pi$
$43$	−287.464			−0.0237089			−0.0118545	+	0.999930i	$0.503773\pi$
$44$	3857.29	−	2802.49i	0.300366	−	0.218229i
$45$	−10402.7	−	29.6712i	−0.765798	−	0.00218425i
$46$	783.762	+	569.436i	0.0546122	+	0.0396781i
$47$	−23653.6	−	17185.4i	−1.56190	−	1.13479i	−0.934431	−	0.356143i	$-0.884091\pi$
$47$	−23653.6	−	17185.4i	−1.56190	−	1.13479i	−0.627468	−	0.778643i	$-0.715909\pi$
$48$	−596.785	+	1836.72i	−0.0373865	+	0.115064i
$49$	35171.6			2.09267
$50$	10154.5	−	7289.51i	0.574423	−	0.412357i
$51$	9992.21			0.537943
$52$	−4155.18	+	12788.3i	−0.213099	+	0.655851i
$53$	−17710.9	−	12867.7i	−0.866066	−	0.629234i	0.0634626	−	0.997984i	$-0.479786\pi$
$53$	−17710.9	−	12867.7i	−0.866066	−	0.629234i	−0.929528	+	0.368751i	$0.879786\pi$
$54$	10475.2	+	7610.66i	0.488851	+	0.355171i
$55$	13448.8	+	9829.88i	0.599485	+	0.438169i
$56$	−11804.6	+	8576.52i	−0.503014	+	0.365461i
$57$	−5074.19			−0.206861
$58$	−4500.44	+	3269.76i	−0.175665	+	0.127628i
$59$	−6390.88	−	19669.1i	−0.239018	−	0.735621i	−0.996563	−	0.0828386i	$-0.973601\pi$
$59$	−6390.88	−	19669.1i	−0.239018	−	0.735621i	0.757545	−	0.652783i	$-0.226399\pi$
$60$	−6747.44	−	19.2454i	−0.241970	−	0.000690160i
$61$	11865.4	−	36518.1i	0.408281	−	1.25656i	−0.509843	−	0.860268i	$-0.670296\pi$
$61$	11865.4	−	36518.1i	0.408281	−	1.25656i	0.918124	−	0.396293i	$-0.129704\pi$
$62$	−8902.28	−	27398.4i	−0.294118	−	0.905203i
$63$	13110.4	+	40349.7i	0.416165	+	1.28082i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	−46979.8	−	133.998i	−1.37920	−	0.00393384i
$66$	−2778.71	−	8551.98i	−0.0785205	−	0.241661i
$67$	51586.7	−	37479.9i	1.40395	−	1.02003i	0.409778	−	0.912185i	$-0.365606\pi$
$67$	51586.7	−	37479.9i	1.40395	−	1.02003i	0.994168	−	0.107841i	$-0.0343938\pi$
$68$	−21192.7			−0.555794
$69$	1478.15	−	1073.94i	0.0373764	−	0.0271555i
$70$	−41157.8	−	30082.6i	−1.00394	−	0.733788i
$71$	42932.7	+	31192.5i	1.01075	+	0.734351i	0.964366	−	0.264573i	$-0.0852309\pi$
$71$	42932.7	+	31192.5i	1.01075	+	0.734351i	0.0463819	+	0.998924i	$0.485231\pi$
$72$	−9635.18	−	7000.37i	−0.219043	−	0.159144i
$73$	−15367.6	+	47296.6i	−0.337519	+	1.03878i	0.627949	+	0.778255i	$0.283895\pi$
$73$	−15367.6	+	47296.6i	−0.337519	+	1.03878i	−0.965468	+	0.260523i	$0.916105\pi$
$74$	−15158.5			−0.321793
$75$	−7156.96	−	22462.0i	−0.146918	−	0.461101i
$76$	10761.9			0.213726
$77$	20994.2	−	64613.5i	0.403527	−	1.24193i
$78$	20516.4	+	14906.0i	0.381825	+	0.277412i
$79$	2349.03	+	1706.67i	0.0423468	+	0.0307667i	0.608757	−	0.793357i	$-0.291668\pi$
$79$	2349.03	+	1706.67i	0.0423468	+	0.0307667i	−0.566411	+	0.824123i	$0.691668\pi$
$80$	14310.8	+	40.8180i	0.249999	+	0.000713062i
$81$	−16827.7	+	12226.0i	−0.284978	+	0.207049i
$82$	−57321.2			−0.941415
$83$	−15035.2	+	10923.7i	−0.239559	+	0.174050i	−0.701087	−	0.713076i	$-0.747301\pi$
$83$	−15035.2	+	10923.7i	−0.239559	+	0.174050i	0.461528	+	0.887126i	$0.347301\pi$
$84$	8503.74	+	26171.8i	0.131496	+	0.404703i
$85$	−22680.0	−	70485.2i	−0.340483	−	1.05816i
$86$	355.325	−	1093.58i	0.00518059	−	0.0159442i
$87$	3242.02	+	9977.90i	0.0459216	+	0.141332i
$88$	5893.42	+	18138.1i	0.0811261	+	0.249680i
$89$	4004.23	−	12323.7i	0.0535851	−	0.164918i	−0.920683	−	0.390312i	$-0.872367\pi$
$89$	4004.23	−	12323.7i	0.0535851	−	0.164918i	0.974268	+	0.225394i	$0.0723671\pi$
$90$	12971.3	−	39537.5i	0.168802	−	0.514521i
$91$	59208.2	+	182224.i	0.749512	+	2.30676i
$92$	−3135.05	+	2277.75i	−0.0386167	+	0.0280566i
$93$	−54331.8			−0.651399
$94$	94614.5	−	68741.4i	1.10443	−	0.802415i
$95$	11517.2	+	35793.4i	0.130930	+	0.406906i
$96$	−6249.61	−	4540.61i	−0.0692110	−	0.0502847i
$97$	83232.1	+	60471.6i	0.898176	+	0.652563i	0.937997	−	0.346644i	$-0.112679\pi$
$97$	83232.1	+	60471.6i	0.898176	+	0.652563i	−0.0398209	+	0.999207i	$0.512679\pi$
$98$	−43474.5	+	133801.i	−0.457266	+	1.40732i
$99$	55453.3			0.568642
$100$	15179.3	+	47640.2i	0.151793	+	0.476402i
$101$	67884.4			0.662165			0.331083	−	0.943602i	$-0.392586\pi$
$101$	67884.4			0.662165			0.331083	+	0.943602i	$0.392586\pi$
$102$	−12351.0	+	38012.6i	−0.117545	+	0.361766i
$103$	16790.9	+	12199.3i	0.155948	+	0.113303i	0.663023	−	0.748599i	$-0.269273\pi$
$103$	16790.9	+	12199.3i	0.155948	+	0.113303i	−0.507075	+	0.861902i	$0.669273\pi$
$104$	−43513.6	−	31614.5i	−0.394495	−	0.286618i
$105$	−77944.9	+	56291.3i	−0.689945	+	0.498274i
$106$	70843.6	−	51470.9i	0.612401	−	0.444935i
$107$	32902.4			0.277823			0.138912	−	0.990305i	$-0.455640\pi$
$107$	32902.4			0.277823			0.138912	+	0.990305i	$0.455640\pi$
$108$	−41900.7	+	30442.6i	−0.345670	+	0.251144i
$109$	−37079.6	−	114119.i	−0.298930	−	0.920011i	−0.981873	−	0.189540i	$-0.939300\pi$
$109$	−37079.6	−	114119.i	−0.298930	−	0.920011i	0.682943	−	0.730471i	$-0.260700\pi$
$110$	−54018.8	+	39012.0i	−0.425660	+	0.307409i
$111$	−8834.35	+	27189.3i	−0.0680561	+	0.209455i
$112$	−18035.8	−	55508.4i	−0.135859	−	0.418132i
$113$	−71302.8	−	219448.i	−0.525304	−	1.61672i	−0.763714	−	0.645555i	$-0.776626\pi$
$113$	−71302.8	−	219448.i	−0.525304	−	1.61672i	0.238410	−	0.971165i	$-0.423374\pi$
$114$	6272.04	−	19303.4i	0.0452009	−	0.139114i
$115$	−10930.7	−	7989.32i	−0.0770729	−	0.0563333i
$116$	−6876.06	−	21162.3i	−0.0474454	−	0.146022i
$117$	−126522.	+	91923.9i	−0.854482	+	0.620817i
$118$	82725.2			0.546932
$119$	−244307.	+	177499.i	−1.58150	+	1.14902i
$120$	8413.50	−	25645.0i	0.0533364	−	0.162573i
$121$	58452.8	+	42468.5i	0.362946	+	0.263696i
$122$	124257.	+	90277.7i	0.755822	+	0.549137i
$123$	−33406.7	+	102815.i	−0.199100	+	0.612766i
$124$	115233.			0.673015
$125$	−142203.	+	101469.i	−0.814017	+	0.580841i
$126$	−169705.			−0.952287
$127$	75735.8	−	233091.i	0.416670	−	1.28238i	−0.494079	−	0.869417i	$-0.664495\pi$
$127$	75735.8	−	233091.i	0.416670	−	1.28238i	0.910749	−	0.412961i	$-0.135505\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−1754.43	−	1274.67i	−0.00928243	−	0.00674408i
$130$	58579.9	−	178556.i	0.304012	−	0.926651i
$131$	77096.9	−	56014.2i	0.392517	−	0.285180i	−0.373969	−	0.927441i	$-0.622003\pi$
$131$	77096.9	−	56014.2i	0.392517	−	0.285180i	0.766486	+	0.642261i	$0.222003\pi$
$132$	35968.3			0.179674
$133$	124063.	−	90136.7i	0.608151	−	0.441848i
$134$	78817.4	+	242575.i	0.379193	+	1.16704i
$135$	−146091.	−	106779.i	−0.689905	−	0.504258i
$136$	26195.6	−	80621.7i	0.121445	−	0.373770i
$137$	−83107.9	−	255780.i	−0.378304	−	1.16430i	−0.941222	−	0.337787i	$-0.890322\pi$
$137$	−83107.9	−	255780.i	−0.378304	−	1.16430i	0.562919	−	0.826512i	$-0.309678\pi$
$138$	2258.42	+	6950.70i	0.0100950	+	0.0310692i
$139$	67340.4	−	207252.i	0.295623	−	0.909835i	−0.687388	−	0.726290i	$-0.741243\pi$
$139$	67340.4	−	207252.i	0.295623	−	0.909835i	0.983011	−	0.183545i	$-0.0587572\pi$
$140$	165315.	−	119389.i	0.712840	−	0.514809i
$141$	−68158.2	−	209769.i	−0.288716	−	0.888575i
$142$	−171731.	+	124770.i	−0.714707	+	0.519265i
$143$	250433.			1.02412
$144$	38540.7	−	28001.5i	0.154887	−	0.112532i
$145$	63025.6	−	45516.7i	0.248941	−	0.179784i
$146$	−160931.	−	116924.i	−0.624826	−	0.453962i
$147$	214657.	+	155957.i	0.819317	+	0.595268i
$148$	18737.0	−	57666.4i	0.0703145	−	0.216406i
$149$	−185311.			−0.683809			−0.341904	−	0.939735i	$-0.611072\pi$
$149$	−185311.			−0.683809			−0.341904	+	0.939735i	$0.611072\pi$
$150$	94297.1	+	537.924i	0.342192	+	0.00195206i
$151$	−88626.2			−0.316315			−0.158157	−	0.987414i	$-0.550555\pi$
$151$	−88626.2			−0.316315			−0.158157	+	0.987414i	$0.550555\pi$
$152$	−13302.5	+	40940.9i	−0.0467008	+	0.143730i
$153$	−199409.	−	144879.i	−0.688680	−	0.500355i
$154$	219854.	+	159733.i	0.747021	+	0.542743i
$155$	123320.	+	383257.i	0.412293	+	1.28133i
$156$	−82065.5	+	59624.1i	−0.269991	+	0.196160i
$157$	44271.7			0.143343			0.0716716	−	0.997428i	$-0.477167\pi$
$157$	44271.7			0.143343			0.0716716	+	0.997428i	$0.477167\pi$
$158$	−9396.11	+	6826.68i	−0.0299437	+	0.0217554i
$159$	−51034.1	−	157067.i	−0.160091	−	0.492711i
$160$	−17844.4	+	54391.0i	−0.0551063	+	0.167968i
$161$	−17063.2	+	52515.2i	−0.0518796	+	0.159669i
$162$	−25710.4	−	79128.5i	−0.0769700	−	0.236889i
$163$	−52218.3	−	160712.i	−0.153941	−	0.473781i	0.844111	−	0.536168i	$-0.180129\pi$
$163$	−52218.3	−	160712.i	−0.153941	−	0.473781i	−0.998052	+	0.0623868i	$0.980129\pi$
$164$	70852.9	−	218063.i	0.205707	−	0.633100i
$165$	38492.6	+	119628.i	0.110069	+	0.342076i
$166$	−22971.7	−	70699.5i	−0.0647027	−	0.199134i
$167$	−419997.	+	305145.i	−1.16535	+	0.846673i	−0.990444	−	0.137913i	$-0.955961\pi$
$167$	−419997.	+	305145.i	−1.16535	+	0.846673i	−0.174901	+	0.984586i	$0.555961\pi$
$168$	−110075.			−0.300895
$169$	−271008.	+	196899.i	−0.729902	+	0.530305i
$170$	296175.	+	844.769i	0.786008	+	0.00224190i
$171$	101263.	+	73571.9i	0.264826	+	0.192407i
$172$	3721.01	+	2703.47i	0.00959046	+	0.00696788i
$173$	177363.	−	545867.i	0.450555	−	1.38667i	−0.425720	−	0.904855i	$-0.639979\pi$
$173$	177363.	−	545867.i	0.450555	−	1.38667i	0.876275	−	0.481811i	$-0.160021\pi$
$174$	−41965.5			−0.105080
$175$	573996.	+	422056.i	1.41682	+	1.04178i
$176$	−76286.0			−0.185636
$177$	48212.1	−	148382.i	0.115671	−	0.355997i
$178$	41932.8	+	30466.0i	0.0991983	+	0.0720718i
$179$	193034.	+	140247.i	0.450299	+	0.327161i	0.789714	−	0.613476i	$-0.210229\pi$
$179$	193034.	+	140247.i	0.450299	+	0.327161i	−0.339415	+	0.940637i	$0.610229\pi$
$180$	134376.	+	98216.8i	0.309130	+	0.225946i
$181$	−688478.	+	500209.i	−1.56205	+	1.13489i	−0.627738	+	0.778425i	$0.716019\pi$
$181$	−688478.	+	500209.i	−1.56205	+	1.13489i	−0.934308	+	0.356468i	$0.883981\pi$
$182$	−766407.			−1.71507
$183$	234345.	−	170261.i	0.517282	−	0.375827i
$184$	−4789.93	−	14741.9i	−0.0104300	−	0.0321002i
$185$	211846.	+	604.239i	0.455083	+	0.00129801i
$186$	67157.8	−	206691.i	0.142336	−	0.438065i
$187$	121970.	+	375385.i	0.255064	+	0.785006i
$188$	144558.	+	444904.i	0.298296	+	0.918061i
$189$	−228054.	+	701879.i	−0.464391	+	1.42925i
$190$	−150402.	−	428.986i	−0.302253	−	0.000862103i
$191$	−17240.2	−	53059.9i	−0.0341947	−	0.105241i	0.932502	−	0.361164i	$-0.117621\pi$
$191$	−17240.2	−	53059.9i	−0.0341947	−	0.105241i	−0.966697	+	0.255923i	$0.917621\pi$
$192$	24998.5	−	18162.4i	0.0489396	−	0.0355567i
$193$	274104.			0.529691			0.264846	−	0.964291i	$-0.414679\pi$
$193$	274104.			0.529691			0.264846	+	0.964291i	$0.414679\pi$
$194$	−332928.	+	241887.i	−0.635106	+	0.461432i
$195$	−286130.	−	209135.i	−0.538861	−	0.393858i
$196$	−455270.	−	330773.i	−0.846505	−	0.615022i
$197$	668942.	+	486015.i	1.22807	+	0.892245i	0.996744	−	0.0806315i	$-0.0256937\pi$
$197$	668942.	+	486015.i	1.22807	+	0.892245i	0.231326	+	0.972876i	$0.425694\pi$
$198$	−68544.0	+	210957.i	−0.124253	+	0.382411i
$199$	−319487.			−0.571901			−0.285951	−	0.958244i	$-0.592309\pi$
$199$	−319487.			−0.571901			−0.285951	+	0.958244i	$0.592309\pi$
$200$	−199997.	−	1140.89i	−0.353548	−	0.00201684i
$201$	481034.			0.839818
$202$	−83909.7	+	258247.i	−0.144688	+	0.445305i
$203$	−256512.	−	186367.i	−0.436885	−	0.317415i
$204$	−129342.	−	93972.4i	−0.217602	−	0.158097i
$205$	801085.	+	2284.90i	1.33136	+	0.00379737i
$206$	−67163.4	+	48797.1i	−0.110272	+	0.0801172i
$207$	−45070.1			−0.0731077
$208$	174054.	−	126458.i	0.278950	−	0.202669i
$209$	−61938.1	−	190626.i	−0.0980827	−	0.301867i
$210$	−117800.	−	366100.i	−0.184330	−	0.572864i
$211$	227967.	−	701611.i	0.352506	−	1.08490i	−0.604936	−	0.796274i	$-0.706801\pi$
$211$	227967.	−	701611.i	0.352506	−	1.08490i	0.957442	−	0.288627i	$-0.0931986\pi$
$212$	108239.	+	333126.i	0.165404	+	0.509061i
$213$	123711.	+	380744.i	0.186836	+	0.575021i
$214$	−40669.6	+	125168.i	−0.0607066	+	0.186836i
$215$	−5009.38	+	15269.0i	−0.00739074	+	0.0225275i
$216$	−64018.6	−	197029.i	−0.0933623	−	0.287340i
$217$	1.32840e6	−	965138.i	1.91505	−	1.39136i
$218$	479969.			0.684025
$219$	−303512.	+	220515.i	−0.427628	+	0.310690i
$220$	−81639.7	−	253721.i	−0.113722	−	0.353427i
$221$	−900557.	−	654293.i	−1.24031	−	0.901138i
$222$	−92514.5	−	67215.7i	−0.125987	−	0.0915353i
$223$	322486.	−	992508.i	0.434258	−	1.33651i	−0.459587	−	0.888133i	$-0.652002\pi$
$223$	322486.	−	992508.i	0.434258	−	1.33651i	0.893845	−	0.448376i	$-0.147998\pi$
$224$	233460.			0.310880
$225$	−182855.	+	552034.i	−0.240796	+	0.726958i
$226$	922963.			1.20202
$227$	−354328.	+	1.09051e6i	−0.456395	+	1.40464i	0.413095	+	0.910688i	$0.364448\pi$
$227$	−354328.	+	1.09051e6i	−0.456395	+	1.40464i	−0.869490	+	0.493951i	$0.835552\pi$
$228$	65681.6	+	47720.5i	0.0836772	+	0.0607950i
$229$	−425605.	−	309220.i	−0.536312	−	0.389654i	0.286401	−	0.958110i	$-0.407541\pi$
$229$	−425605.	−	309220.i	−0.536312	−	0.389654i	−0.822714	+	0.568456i	$0.807541\pi$
$230$	43904.2	−	31707.4i	0.0547251	−	0.0395222i
$231$	414639.	−	301253.i	0.511258	−	0.371451i
$232$	89005.5			0.108567
$233$	−137605.	+	99975.8i	−0.166052	+	0.120644i	−0.667708	−	0.744424i	$-0.732724\pi$
$233$	−137605.	+	99975.8i	−0.166052	+	0.120644i	0.501656	+	0.865067i	$0.332724\pi$
$234$	−193309.	−	594944.i	−0.230788	−	0.710291i
$235$	−1.32501e6	+	956915.i	−1.56513	+	1.13033i
$236$	−102254.	+	314706.i	−0.119509	+	0.367811i
$237$	6768.75	+	20832.1i	0.00782776	+	0.0240914i
$238$	−373268.	−	1.14880e6i	−0.427148	−	1.31463i
$239$	370832.	−	1.14130e6i	0.419936	−	1.29243i	−0.487825	−	0.872941i	$-0.662210\pi$
$239$	370832.	−	1.14130e6i	0.419936	−	1.29243i	0.907761	−	0.419488i	$-0.137790\pi$
$240$	87159.7	+	63705.8i	0.0976759	+	0.0713922i
$241$	277146.	+	852968.i	0.307373	+	0.945997i	0.978781	+	0.204909i	$0.0656899\pi$
$241$	277146.	+	852968.i	0.307373	+	0.945997i	−0.671408	+	0.741088i	$0.734310\pi$
$242$	−233811.	+	169874.i	−0.256642	+	0.186461i
$243$	−943507.			−1.02501
$244$	−497026.	+	361111.i	−0.534447	+	0.388299i
$245$	612905.	−	1.86818e6i	0.652346	−	1.98840i
$246$	−349839.	−	254173.i	−0.368579	−	0.267789i
$247$	457315.	+	332259.i	0.476951	+	0.346525i
$248$	−142436.	+	438374.i	−0.147059	+	0.452601i
$249$	−140199.			−0.143300
$250$	−210238.	−	666394.i	−0.212746	−	0.674344i
$251$	225589.			0.226013			0.113006	−	0.993594i	$-0.463952\pi$
$251$	225589.			0.226013			0.113006	+	0.993594i	$0.463952\pi$
$252$	209767.	−	645596.i	0.208082	−	0.640412i
$253$	58388.7	+	42421.9i	0.0573492	+	0.0416667i
$254$	793116.	+	576232.i	0.771352	+	0.560420i
$255$	174126.	−	530748.i	0.167692	−	0.511138i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	−1.48313e6			−1.40071			−0.700353	−	0.713797i	$-0.746974\pi$
$257$	−1.48313e6			−1.40071			−0.700353	+	0.713797i	$0.746974\pi$
$258$	7017.72	−	5098.67i	0.00656367	−	0.00476879i
$259$	−266988.	−	821703.i	−0.247310	−	0.761142i
$260$	606858.	+	443559.i	0.556742	+	0.406928i
$261$	79972.7	−	246131.i	0.0726675	−	0.223648i
$262$	117794.	+	362531.i	0.106015	+	0.326281i
$263$	29342.1	+	90305.8i	0.0261579	+	0.0805056i	0.963283	−	0.268487i	$-0.0865237\pi$
$263$	29342.1	+	90305.8i	0.0261579	+	0.0805056i	−0.937125	+	0.348993i	$0.886524\pi$
$264$	−44459.3	+	136832.i	−0.0392602	+	0.120831i
$265$	−992117.	+	716500.i	−0.867857	+	0.626761i
$266$	189551.	+	583377.i	0.164256	+	0.505528i
$267$	79084.2	−	57458.0i	0.0678909	−	0.0493256i
$268$	−1.02023e6			−0.867686
$269$	−456963.	+	332003.i	−0.385035	+	0.279745i	−0.763418	−	0.645905i	$-0.776480\pi$
$269$	−456963.	+	332003.i	−0.385035	+	0.279745i	0.378383	+	0.925649i	$0.376480\pi$
$270$	586791.	−	423777.i	0.489862	−	0.353776i
$271$	543685.	+	395011.i	0.449702	+	0.326727i	0.789478	−	0.613779i	$-0.210351\pi$
$271$	543685.	+	395011.i	0.449702	+	0.326727i	−0.339776	+	0.940506i	$0.610351\pi$
$272$	274324.	+	199308.i	0.224823	+	0.163344i
$273$	−446661.	+	1.37468e6i	−0.362720	+	1.11634i
$274$	1.07577e6			0.865652
$275$	756487.	−	543054.i	0.603212	−	0.433023i
$276$	−29233.6			−0.0230999
$277$	−247412.	+	761457.i	−0.193741	+	0.596274i	0.806248	+	0.591578i	$0.201495\pi$
$277$	−247412.	+	761457.i	−0.193741	+	0.596274i	−0.999989	+	0.00469599i	$0.998505\pi$
$278$	705198.	+	512356.i	0.547267	+	0.397612i
$279$	1.08427e6	+	787770.i	0.833927	+	0.605884i
$280$	249844.	+	776469.i	0.190447	+	0.591874i
$281$	148888.	−	108174.i	0.112485	−	0.0817251i	−0.530121	−	0.847922i	$-0.677853\pi$
$281$	148888.	−	108174.i	0.112485	−	0.0817251i	0.642606	+	0.766197i	$0.277853\pi$
$282$	882258.			0.660652
$283$	−1.15336e6	+	837962.i	−0.856046	+	0.621954i	−0.926806	−	0.375540i	$-0.877457\pi$
$283$	−1.15336e6	+	837962.i	−0.856046	+	0.621954i	0.0707605	+	0.997493i	$0.477457\pi$
$284$	−262382.	−	807527.i	−0.193036	−	0.594103i
$285$	−88423.5	+	269521.i	−0.0644845	+	0.196554i
$286$	−309553.	+	952705.i	−0.223779	+	0.688721i
$287$	−1.00960e6	−	3.10724e6i	−0.723511	−	2.22674i
$288$	58885.0	+	181229.i	0.0418334	+	0.128750i
$289$	103383.	−	318181.i	0.0728125	−	0.224094i
$290$	95251.9	+	296025.i	0.0665087	+	0.206697i
$291$	239834.	+	738134.i	0.166027	+	0.510978i
$292$	643726.	−	467694.i	0.441818	−	0.321000i
$293$	1.50495e6			1.02412			0.512061	−	0.858949i	$-0.328882\pi$
$293$	1.50495e6			1.02412			0.512061	+	0.858949i	$0.328882\pi$
$294$	−858628.	+	623830.i	−0.579344	+	0.420918i
$295$	−1.15612e6	−	3297.54i	−0.773475	−	0.00220615i
$296$	196216.	+	142559.i	0.130168	+	0.0945727i
$297$	780380.	+	566979.i	0.513352	+	0.372972i
$298$	229057.	−	704964.i	0.149418	−	0.459861i
$299$	−203542.			−0.131667
$300$	−118604.	+	358063.i	−0.0760845	+	0.229697i
$301$	65538.3			0.0416945
$302$	109548.	−	337154.i	0.0691173	−	0.212721i
$303$	414308.	+	301012.i	0.259249	+	0.188355i
$304$	−139306.	−	101211.i	−0.0864539	−	0.0628124i
$305$	−1.73293e6	−	1.26662e6i	−1.06667	−	0.779643i
$306$	797638.	−	579518.i	0.486970	−	0.353804i
$307$	−1.42172e6			−0.860930			−0.430465	−	0.902607i	$-0.641650\pi$
$307$	−1.42172e6			−0.860930			−0.430465	+	0.902607i	$0.641650\pi$
$308$	−879417.	+	638934.i	−0.528224	+	0.383777i
$309$	48383.1	+	148908.i	0.0288268	+	0.0887199i
$310$	−1.61043e6	−	4593.37i	−0.951783	−	0.00271473i
$311$	9366.90	−	28828.3i	0.00549155	−	0.0169012i	−0.948273	−	0.317455i	$-0.897172\pi$
$311$	9366.90	−	28828.3i	0.00549155	−	0.0169012i	0.953765	+	0.300554i	$0.0971716\pi$
$312$	−125385.	−	385895.i	−0.0729221	−	0.224431i
$313$	861019.	+	2.64995e6i	0.496766	+	1.52889i	0.814186	+	0.580604i	$0.197184\pi$
$313$	861019.	+	2.64995e6i	0.496766	+	1.52889i	−0.317420	+	0.948285i	$0.602816\pi$
$314$	−54722.8	+	168420.i	−0.0313216	+	0.0963981i
$315$	2.37169e6	+	6764.67i	1.34673	+	0.00384123i
$316$	−14356.0	−	44183.2i	−0.00808752	−	0.0248908i
$317$	291887.	−	212068.i	0.163142	−	0.118530i	−0.503219	−	0.864159i	$-0.667851\pi$
$317$	291887.	−	212068.i	0.163142	−	0.118530i	0.666361	+	0.745629i	$0.267851\pi$
$318$	660600.			0.366328
$319$	−335274.	+	243591.i	−0.184469	+	0.134024i
$320$	−184859.	−	135115.i	−0.100917	−	0.0737613i
$321$	200808.	+	145896.i	0.108772	+	0.0790277i
$322$	−178688.	−	129825.i	−0.0960410	−	0.0697779i
$323$	−275308.	+	847311.i	−0.146829	+	0.451894i
$324$	332802.			0.176126
$325$	−825794.	+	2.49305e6i	−0.433674	+	1.30925i
$326$	675928.			0.352255
$327$	279725.	−	860904.i	0.144664	−	0.445231i
$328$	741982.	+	539081.i	0.380810	+	0.276675i
$329$	5.39274e6	+	3.91806e6i	2.74676	+	1.99563i
$330$	−502671.	−	1433.75i	−0.254097	−	0.000724749i
$331$	−1.61612e6	+	1.17418e6i	−0.810782	+	0.589068i	−0.914057	−	0.405585i	$-0.867068\pi$
$331$	−1.61612e6	+	1.17418e6i	−0.810782	+	0.589068i	0.103275	+	0.994653i	$0.467068\pi$
$332$	297352.			0.148056
$333$	570527.	−	414512.i	0.281946	−	0.204846i
$334$	−641698.	−	1.97494e6i	−0.314749	−	0.968698i
$335$	−1.09183e6	−	3.39322e6i	−0.531550	−	1.65196i
$336$	136060.	−	418749.i	0.0657479	−	0.202351i
$337$	−538752.	−	1.65811e6i	−0.258413	−	0.795312i	−0.993138	−	0.116948i	$-0.962689\pi$
$337$	−538752.	−	1.65811e6i	−0.258413	−	0.795312i	0.734725	−	0.678365i	$-0.237311\pi$
$338$	−414063.	−	1.27435e6i	−0.197140	−	0.606734i
$339$	537901.	−	1.65549e6i	0.254216	−	0.782397i
$340$	−369307.	+	1.12567e6i	−0.173257	+	0.528099i
$341$	−663202.	−	2.04113e6i	−0.308859	−	0.950570i
$342$	−405052.	+	294287.i	−0.187260	+	0.136052i
$343$	−4.18691e6			−1.92158
$344$	−14884.0	+	10813.9i	−0.00678148	+	0.00492703i
$345$	−31285.2	−	97228.6i	−0.0141511	−	0.0439791i
$346$	1.85737e6	+	1.34946e6i	0.834081	+	0.605995i
$347$	−445849.	−	323928.i	−0.198776	−	0.144419i	0.483945	−	0.875099i	$-0.339204\pi$
$347$	−445849.	−	323928.i	−0.198776	−	0.144419i	−0.682721	+	0.730679i	$0.739204\pi$
$348$	51872.2	−	159646.i	0.0229608	−	0.0706661i
$349$	2.64681e6			1.16321			0.581606	−	0.813471i	$-0.302425\pi$
$349$	2.64681e6			1.16321			0.581606	+	0.813471i	$0.302425\pi$
$350$	−2.31510e6	+	1.66192e6i	−1.01018	+	0.725171i
$351$	−2.72039e6			−1.17859
$352$	94294.7	−	290209.i	0.0405630	−	0.124840i
$353$	−1.76601e6	−	1.28308e6i	−0.754320	−	0.548046i	0.142843	−	0.989745i	$-0.454376\pi$
$353$	−1.76601e6	−	1.28308e6i	−0.754320	−	0.548046i	−0.897163	+	0.441700i	$0.854376\pi$
$354$	504884.	+	366819.i	0.214133	+	0.155577i
$355$	2.40498e6	−	1.73686e6i	1.01284	−	0.731465i
$356$	−167731.	+	121864.i	−0.0701438	+	0.0509624i
$357$	−2.27810e6			−0.946026
$358$	−772135.	+	560989.i	−0.318409	+	0.231338i
$359$	−962680.	−	2.96282e6i	−0.394227	−	1.21330i	−0.929562	−	0.368665i	$-0.879815\pi$
$359$	−962680.	−	2.96282e6i	−0.394227	−	1.21330i	0.535336	−	0.844639i	$-0.320185\pi$
$360$	−539737.	+	389795.i	−0.219496	+	0.158518i
$361$	−625351.	+	1.92463e6i	−0.252555	+	0.777284i
$362$	−1.05190e6	−	3.23742e6i	−0.421894	−	1.29846i
$363$	168433.	+	518382.i	0.0670902	+	0.206483i
$364$	947332.	−	2.91559e6i	0.374756	−	1.15338i
$365$	2.24442e6	+	1.64046e6i	0.881802	+	0.644517i
$366$	358047.	+	1.10195e6i	0.139713	+	0.429993i
$367$	−129962.	+	94423.0i	−0.0503676	+	0.0365942i	−0.612684	−	0.790328i	$-0.709910\pi$
$367$	−129962.	+	94423.0i	−0.0503676	+	0.0365942i	0.562317	+	0.826922i	$0.309910\pi$
$368$	62002.1			0.0238664
$369$	2.15742e6	−	1.56746e6i	0.824840	−	0.599281i
$370$	−264154.	+	805162.i	−0.100312	+	0.305759i
$371$	4.03787e6	+	2.93369e6i	1.52306	+	1.10657i
$372$	703286.	+	510967.i	0.263496	+	0.191441i
$373$	1.00108e6	−	3.08100e6i	0.372560	−	1.14662i	−0.572551	−	0.819869i	$-0.694046\pi$
$373$	1.00108e6	−	3.08100e6i	0.372560	−	1.14662i	0.945110	−	0.326751i	$-0.105954\pi$
$374$	−1.57881e6			−0.583649
$375$	−1.31782e6	−	11276.5i	−0.483923	−	0.00414091i
$376$	−1.87120e6			−0.682575
$377$	361166.	−	1.11155e6i	0.130874	−	0.402789i
$378$	−2.38822e6	−	1.73514e6i	−0.859694	−	0.624604i
$379$	1.30670e6	+	949371.i	0.467280	+	0.339499i	0.796380	−	0.604796i	$-0.206745\pi$
$379$	1.30670e6	+	949371.i	0.467280	+	0.339499i	−0.329100	+	0.944295i	$0.606745\pi$
$380$	187539.	−	571633.i	0.0666244	−	0.203076i
$381$	1.49580e6	−	1.08676e6i	0.527910	−	0.383549i
$382$	223162.			0.0782460
$383$	2.30710e6	−	1.67621e6i	0.803656	−	0.583890i	−0.108328	−	0.994115i	$-0.534550\pi$
$383$	2.30710e6	−	1.67621e6i	0.803656	−	0.583890i	0.911984	+	0.410225i	$0.134550\pi$
$384$	38194.2	+	117550.i	0.0132181	+	0.0406812i
$385$	−3.06618e6	−	2.24110e6i	−1.05425	−	0.770564i
$386$	−338812.	+	1.04276e6i	−0.115742	+	0.356217i
$387$	16530.6	+	50875.8i	0.00561061	+	0.0172677i
$388$	−508669.	−	1.56552e6i	−0.171536	−	0.527935i
$389$	−883476.	+	2.71906e6i	−0.296020	+	0.911055i	0.686857	+	0.726792i	$0.258990\pi$
$389$	−883476.	+	2.71906e6i	−0.296020	+	0.911055i	−0.982877	+	0.184263i	$0.941010\pi$
$390$	1.14927e6	−	829997.i	0.382615	−	0.276322i
$391$	−99132.2	−	305098.i	−0.0327924	−	0.100925i
$392$	1.82108e6	−	1.32309e6i	0.598569	−	0.434886i
$393$	718910.			0.234797
$394$	−2.67577e6	+	1.94406e6i	−0.868376	+	0.630912i
$395$	131586.	−	95030.8i	0.0424344	−	0.0306458i
$396$	−717802.	−	521514.i	−0.230021	−	0.167120i
$397$	1.70719e6	+	1.24035e6i	0.543633	+	0.394972i	0.825432	−	0.564501i	$-0.190931\pi$
$397$	1.70719e6	+	1.24035e6i	0.543633	+	0.394972i	−0.281800	+	0.959473i	$0.590931\pi$
$398$	394908.	−	1.21540e6i	0.124965	−	0.384603i
$399$	1.15685e6			0.363786
$400$	251550.	−	759423.i	0.0786093	−	0.237320i
$401$	2.79242e6			0.867200			0.433600	−	0.901105i	$-0.357243\pi$
$401$	2.79242e6			0.867200			0.433600	+	0.901105i	$0.357243\pi$
$402$	−594590.	+	1.82996e6i	−0.183507	+	0.564776i
$403$	4.89670e6	+	3.55766e6i	1.50190	+	1.09119i
$404$	−878714.	−	638423.i	−0.267851	−	0.194605i
$405$	356158.	+	1.10687e6i	0.107896	+	0.335321i
$406$	1.02605e6	−	745466.i	0.308924	−	0.224447i
$407$	−1.12928e6			−0.337921
$408$	517367.	−	375889.i	0.153868	−	0.111792i
$409$	−935149.	−	2.87809e6i	−0.276422	−	0.850739i	−0.988840	−	0.148984i	$-0.952400\pi$
$409$	−935149.	−	2.87809e6i	−0.276422	−	0.850739i	0.712418	−	0.701756i	$-0.247600\pi$
$410$	−998888.	+	3.04469e6i	−0.293466	+	0.894505i
$411$	626957.	−	1.92958e6i	0.183077	−	0.563452i
$412$	−102617.	−	315821.i	−0.0297834	−	0.0916640i
$413$	1.45704e6	+	4.48432e6i	0.420337	+	1.29366i
$414$	55709.7	−	171457.i	0.0159746	−	0.0491648i
$415$	318219.	+	988968.i	0.0906998	+	0.281878i
$416$	265932.	+	818453.i	0.0753419	+	0.231878i
$417$	1.32998e6	−	966290.i	0.374547	−	0.272124i
$418$	801744.			0.224437
$419$	−4.28582e6	+	3.11383e6i	−1.19261	+	0.866482i	−0.993538	−	0.113503i	$-0.963793\pi$
$419$	−4.28582e6	+	3.11383e6i	−1.19261	+	0.866482i	−0.199073	+	0.979985i	$0.563793\pi$
$420$	1.53834e6	+	4387.73i	0.425528	+	0.00121372i
$421$	−4.45155e6	−	3.23424e6i	−1.22407	−	0.889338i	−0.227637	−	0.973746i	$-0.573100\pi$
$421$	−4.45155e6	−	3.23424e6i	−1.22407	−	0.889338i	−0.996431	+	0.0844081i	$0.973100\pi$
$422$	2.38730e6	+	1.73448e6i	0.652569	+	0.474119i
$423$	−1.68130e6	+	5.17450e6i	−0.456871	+	1.40610i
$424$	−1.40108e6			−0.378485
$425$	−4.13913e6	−	23611.9i	−1.11157	−	0.00634102i
$426$	−1.60135e6			−0.427526
$427$	−2.70518e6	+	8.32569e6i	−0.718004	+	2.20979i
$428$	−425898.	−	309433.i	−0.112382	−	0.0816502i
$429$	1.52843e6	+	1.11047e6i	0.400961	+	0.291315i
$430$	−51894.7	−	37930.3i	−0.0135348	−	0.00989271i
$431$	62896.4	−	45696.9i	0.0163092	−	0.0118493i	−0.579601	−	0.814901i	$-0.696791\pi$
$431$	62896.4	−	45696.9i	0.0163092	−	0.0118493i	0.595910	+	0.803051i	$0.296791\pi$
$432$	828674.			0.213636
$433$	−1.57701e6	+	1.14576e6i	−0.404216	+	0.293680i	−0.771256	−	0.636525i	$-0.780371\pi$
$433$	−1.57701e6	+	1.14576e6i	−0.404216	+	0.293680i	0.367040	+	0.930205i	$0.380371\pi$
$434$	2.02961e6	+	6.24651e6i	0.517236	+	1.59189i
$435$	586484.	+	1672.80i	0.148605	+	0.000423859i
$436$	−593274.	+	1.82591e6i	−0.149465	+	0.460005i
$437$	50340.8	+	154933.i	0.0126100	+	0.0388097i
$438$	−463726.	−	1.42720e6i	−0.115498	−	0.355468i
$439$	1.17305e6	−	3.61029e6i	0.290507	−	0.894088i	−0.694187	−	0.719795i	$-0.744236\pi$
$439$	1.17305e6	−	3.61029e6i	0.290507	−	0.894088i	0.984694	−	0.174293i	$-0.0557641\pi$
$440$	1.06612e6	+	3040.86i	0.262528	+	0.000748799i
$441$	−2.02254e6	−	6.22473e6i	−0.495222	−	1.52414i
$442$	3.60223e6	−	2.61717e6i	0.877032	−	0.637201i
$443$	−1.66201e6			−0.402370			−0.201185	−	0.979553i	$-0.564479\pi$
$443$	−1.66201e6			−0.402370			−0.201185	+	0.979553i	$0.564479\pi$
$444$	370058.	−	268863.i	0.0890866	−	0.0647252i
$445$	−584812.	−	427445.i	−0.139996	−	0.102325i
$446$	3.37711e6	+	2.45362e6i	0.803912	+	0.584076i
$447$	−1.13098e6	−	821703.i	−0.267723	−	0.194512i
$448$	−288572.	+	888134.i	−0.0679297	+	0.209066i
$449$	−1.41249e6			−0.330650			−0.165325	−	0.986239i	$-0.552867\pi$
$449$	−1.41249e6			−0.330650			−0.165325	+	0.986239i	$0.552867\pi$
$450$	−1.87404e6	−	1.37797e6i	−0.436262	−	0.320781i
$451$	−4.27032e6			−0.988596
$452$	−1.14085e6	+	3.51116e6i	−0.262652	+	0.808360i
$453$	−540898.	−	392985.i	−0.123842	−	0.0899768i
$454$	−3.71057e6	−	2.69589e6i	−0.844891	−	0.613850i
$455$	1.07108e7	+	30550.0i	2.42546	+	0.00691805i
$456$	−262727.	+	190882.i	−0.0591687	+	0.0429886i
$457$	3.69934e6			0.828578			0.414289	−	0.910145i	$-0.364030\pi$
$457$	3.69934e6			0.828578			0.414289	+	0.910145i	$0.364030\pi$
$458$	1.70242e6	−	1.23688e6i	0.379230	−	0.275527i
$459$	−1.32493e6	−	4.07771e6i	−0.293535	−	0.903408i
$460$	66353.4	+	206214.i	0.0146207	+	0.0454385i
$461$	−722211.	+	2.22274e6i	−0.158275	+	0.487120i	−0.998478	−	0.0551519i	$-0.982436\pi$
$461$	−722211.	+	2.22274e6i	−0.158275	+	0.487120i	0.840203	+	0.542272i	$0.182436\pi$
$462$	633512.	+	1.94975e6i	0.138086	+	0.424985i
$463$	−2.32566e6	−	7.15766e6i	−0.504190	−	1.55174i	−0.802127	−	0.597153i	$-0.796298\pi$
$463$	−2.32566e6	−	7.15766e6i	−0.504190	−	1.55174i	0.297937	−	0.954586i	$-0.403702\pi$
$464$	−110017.	+	338597.i	−0.0237227	+	0.0730110i
$465$	−946794.	+	2.88590e6i	−0.203060	+	0.618940i
$466$	−210242.	−	647057.i	−0.0448491	−	0.138031i
$467$	763862.	−	554978.i	0.162077	−	0.117756i	−0.503790	−	0.863826i	$-0.668062\pi$
$467$	763862.	−	554978.i	0.162077	−	0.117756i	0.665868	+	0.746070i	$0.268062\pi$
$468$	2.50224e6			0.528099
$469$	−1.17611e7	+	8.54497e6i	−2.46898	+	1.79382i
$470$	−2.00252e6	−	6.22346e6i	−0.418150	−	1.29953i
$471$	270196.	+	196309.i	0.0561212	+	0.0407745i
$472$	−1.07082e6	−	777995.i	−0.221238	−	0.160739i
$473$	26471.0	−	81469.3i	0.00544023	−	0.0167433i
$474$	−87616.6			−0.0179118
$475$	2.10191e6	+	11990.5i	0.427444	+	0.00243838i
$476$	4.83168e6			0.977419
$477$	−1.25889e6	+	3.87446e6i	−0.253333	+	0.779678i
$478$	3.88341e6	+	2.82146e6i	0.777398	+	0.564812i
$479$	1.48719e6	+	1.08051e6i	0.296161	+	0.215174i	0.725936	−	0.687762i	$-0.241407\pi$
$479$	1.48719e6	+	1.08051e6i	0.296161	+	0.215174i	−0.429775	+	0.902936i	$0.641407\pi$
$480$	−350087.	+	252830.i	−0.0693541	+	0.0500871i
$481$	2.57657e6	−	1.87199e6i	0.507784	−	0.368927i
$482$	−3.58745e6			−0.703345
$483$	−337002.	+	244846.i	−0.0657301	+	0.0477557i
$484$	−357232.	−	1.09945e6i	−0.0693165	−	0.213334i
$485$	4.66244e6	−	3.36718e6i	0.900034	−	0.649999i
$486$	1.16624e6	−	3.58931e6i	0.223974	−	0.689320i
$487$	2.16968e6	+	6.67759e6i	0.414547	+	1.27584i	0.912656	+	0.408729i	$0.134028\pi$
$487$	2.16968e6	+	6.67759e6i	0.414547	+	1.27584i	−0.498109	+	0.867115i	$0.665972\pi$
$488$	−759389.	−	2.33716e6i	−0.144349	−	0.444261i
$489$	393930.	−	1.21239e6i	0.0744983	−	0.229282i
$490$	6.34939e6	+	4.64083e6i	1.19465	+	0.873183i
$491$	2.03950e6	+	6.27693e6i	0.381786	+	1.17502i	0.938785	+	0.344503i	$0.111952\pi$
$491$	2.03950e6	+	6.27693e6i	0.381786	+	1.17502i	−0.557000	+	0.830513i	$0.688048\pi$
$492$	1.39936e6	−	1.01669e6i	0.260625	−	0.189355i
$493$	1.84206e6			0.341339
$494$	−1.82926e6	+	1.32904e6i	−0.337255	+	0.245030i
$495$	966337.	−	2.94547e6i	0.177262	−	0.540307i
$496$	−1.49161e6	−	1.08372e6i	−0.272240	−	0.197794i
$497$	−9.78815e6	−	7.11151e6i	−1.77750	−	1.29143i
$498$	173296.	−	533350.i	0.0313123	−	0.0963693i
$499$	2.10162e6			0.377835			0.188918	−	0.981993i	$-0.439502\pi$
$499$	2.10162e6			0.377835			0.188918	+	0.981993i	$0.439502\pi$
$500$	2.79498e6	+	23916.6i	0.499982	+	0.00427833i
$501$	−3.91637e6			−0.697091
$502$	−278843.	+	858190.i	−0.0493856	+	0.151993i
$503$	−6.17891e6	−	4.48924e6i	−1.08891	−	0.791140i	−0.109696	−	0.993965i	$-0.534988\pi$
$503$	−6.17891e6	−	4.48924e6i	−1.08891	−	0.791140i	−0.979215	+	0.202825i	$0.934988\pi$
$504$	2.19671e6	+	1.59600e6i	0.385208	+	0.279870i
$505$	1.18296e6	−	3.60576e6i	0.206416	−	0.629170i
$506$	−233555.	+	169688.i	−0.0405520	+	0.0294628i
$507$	−2.52708e6			−0.436616
$508$	−3.17246e6	+	2.30493e6i	−0.545428	+	0.396277i
$509$	−2.07653e6	−	6.39090e6i	−0.355258	−	1.09337i	−0.955860	−	0.293823i	$-0.905072\pi$
$509$	−2.07653e6	−	6.39090e6i	−0.355258	−	1.09337i	0.600602	−	0.799548i	$-0.294928\pi$
$510$	1.80385e6	+	1.31845e6i	0.307097	+	0.224460i
$511$	3.50363e6	−	1.07831e7i	0.593561	−	1.82679i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	672817.	+	2.07072e6i	0.112876	+	0.347398i
$514$	1.83325e6	−	5.64217e6i	0.306065	−	0.941972i
$515$	940579.	−	679280.i	0.156271	−	0.112858i
$516$	10722.1	+	32999.3i	0.00177279	+	0.00545608i
$517$	7.04859e6	−	5.12110e6i	1.15978	−	0.842630i
$518$	3.45596e6			0.565906
$519$	3.50295e6	−	2.54504e6i	0.570841	−	0.414741i
$520$	−2.43752e6	+	1.76036e6i	−0.395311	+	0.285491i
$521$	−7.82842e6	−	5.68768e6i	−1.26351	−	0.917996i	−0.264589	−	0.964361i	$-0.585236\pi$
$521$	−7.82842e6	−	5.68768e6i	−1.26351	−	0.917996i	−0.998925	+	0.0463654i	$0.985236\pi$
$522$	837485.	+	608468.i	0.134524	+	0.0977376i
$523$	2.23896e6	−	6.89082e6i	0.357925	−	1.10158i	−0.596368	−	0.802711i	$-0.703390\pi$
$523$	2.23896e6	−	6.89082e6i	0.357925	−	1.10158i	0.954294	−	0.298870i	$-0.0966098\pi$
$524$	−1.52475e6			−0.242589
$525$	1.63170e6	+	5.12108e6i	0.258370	+	0.810892i
$526$	−379813.			−0.0598556
$527$	−2.94786e6	+	9.07258e6i	−0.462360	+	1.42300i
$528$	−465584.	−	338267.i	−0.0726797	−	0.0528049i
$529$	5.15965e6	+	3.74871e6i	0.801644	+	0.582428i
$530$	−1.49941e6	−	4.65988e6i	−0.231862	−	0.720585i
$531$	−3.11357e6	+	2.26214e6i	−0.479205	+	0.348163i
$532$	−2.45360e6			−0.375858
$533$	9.74318e6	−	7.07883e6i	1.48553	−	1.07930i
$534$	120830.	+	371876.i	0.0183367	+	0.0564346i
$535$	573362.	−	1.74765e6i	0.0866053	−	0.263980i
$536$	1.26108e6	−	3.88120e6i	0.189596	−	0.583518i
$537$	556229.	+	1.71190e6i	0.0832373	+	0.256178i
$538$	−698178.	−	2.14877e6i	−0.103994	−	0.320062i
$539$	−3.23876e6	+	9.96788e6i	−0.480183	+	1.47785i
$540$	886829.	+	2.75610e6i	0.130875	+	0.406735i
$541$	−1.61911e6	−	4.98311e6i	−0.237839	−	0.731994i	−0.996732	−	0.0807784i	$-0.974259\pi$
$541$	−1.61911e6	−	4.98311e6i	−0.237839	−	0.731994i	0.758893	−	0.651216i	$-0.225741\pi$
$542$	−2.17474e6	+	1.58004e6i	−0.317987	+	0.231031i
$543$	−6.41990e6			−0.934391
$544$	−1.09730e6	+	797232.i	−0.158974	+	0.115501i
$545$	−6.70774e6	−	19132.2i	−0.967353	−	0.00275914i
$546$	−4.67749e6	−	3.39840e6i	−0.671477	−	0.487857i
$547$	1.04762e7	+	7.61141e6i	1.49705	+	1.08767i	0.971539	+	0.236881i	$0.0761251\pi$
$547$	1.04762e7	+	7.61141e6i	1.49705	+	1.08767i	0.525509	+	0.850788i	$0.323875\pi$
$548$	−1.32973e6	+	4.09248e6i	−0.189152	+	0.582150i
$549$	−7.14536e6			−1.01180
$550$	1.13083e6	+	3.54910e6i	0.159401	+	0.500278i
$551$	−935423.			−0.131259
$552$	36134.7	−	111211.i	0.00504751	−	0.0155346i
$553$	−535551.	−	389100.i	−0.0744711	−	0.0541064i
$554$	−2.59094e6	−	1.88242e6i	−0.358659	−	0.260581i
$555$	1.29024e6	+	943052.i	0.177803	+	0.129958i
$556$	−2.82079e6	+	2.04942e6i	−0.386976	+	0.281154i
$557$	3.70427e6			0.505899			0.252950	−	0.967479i	$-0.418599\pi$
$557$	3.70427e6			0.505899			0.252950	+	0.967479i	$0.418599\pi$
$558$	−4.33709e6	+	3.15108e6i	−0.589676	+	0.428424i
$559$	74653.9	+	229761.i	0.0101047	+	0.0310990i
$560$	−3.26269e6	−	9306.03i	−0.439648	−	0.00125399i
$561$	−920129.	+	2.83187e6i	−0.123436	+	0.379897i
$562$	227481.	+	700115.i	0.0303812	+	0.0935036i
$563$	1.63120e6	+	5.02031e6i	0.216888	+	0.667513i	0.999014	+	0.0443926i	$0.0141352\pi$
$563$	1.63120e6	+	5.02031e6i	0.216888	+	0.667513i	−0.782126	+	0.623120i	$0.785865\pi$
$564$	−1.09053e6	+	3.35631e6i	−0.144358	+	0.444287i
$565$	−1.28988e7	−	36790.6i	−1.69991	−	0.00484859i
$566$	−1.76217e6	−	5.42340e6i	−0.231210	−	0.711591i
$567$	3.83651e6	−	2.78739e6i	0.501163	−	0.364116i
$568$	3.39634e6			0.441713
$569$	−5.94846e6	+	4.32181e6i	−0.770236	+	0.559609i	−0.902033	−	0.431668i	$-0.857925\pi$
$569$	−5.94846e6	+	4.32181e6i	−0.770236	+	0.559609i	0.131797	+	0.991277i	$0.457925\pi$
$570$	−916023.	−	669530.i	−0.118092	−	0.0863143i
$571$	9.84887e6	+	7.15562e6i	1.26414	+	0.918454i	0.998953	−	0.0457425i	$-0.0145654\pi$
$571$	9.84887e6	+	7.15562e6i	1.26414	+	0.918454i	0.265190	+	0.964196i	$0.414565\pi$
$572$	−3.24168e6	−	2.35522e6i	−0.414267	−	0.300982i
$573$	130058.	−	400279.i	0.0165482	−	0.0509302i
$574$	1.30686e7			1.65557
$575$	−614842.	+	441372.i	−0.0775521	+	0.0556718i
$576$	−762223.			−0.0957251
$577$	2.04300e6	−	6.28770e6i	0.255463	−	0.786235i	−0.738275	−	0.674500i	$-0.764359\pi$
$577$	2.04300e6	−	6.28770e6i	0.255463	−	0.786235i	0.993738	−	0.111735i	$-0.0356407\pi$
$578$	1.08264e6	+	786587.i	0.134793	+	0.0979326i
$579$	1.67290e6	+	1.21543e6i	0.207383	+	0.150673i
$580$	−1.24389e6	−	3547.88i	−0.153536	−	0.000437925i
$581$	3.42784e6	−	2.49047e6i	0.421289	−	0.306084i
$582$	−3.10448e6			−0.379910
$583$	5.27771e6	−	3.83448e6i	0.643093	−	0.467235i
$584$	983526.	+	3.02698e6i	0.119331	+	0.367263i
$585$	2.67785e6	+	8.32227e6i	0.323516	+	1.00543i
$586$	−1.86022e6	+	5.72516e6i	−0.223779	+	0.688721i
$587$	−406334.	−	1.25057e6i	−0.0486730	−	0.149800i	0.923766	−	0.382957i	$-0.125094\pi$
$587$	−406334.	−	1.25057e6i	−0.0486730	−	0.149800i	−0.972439	+	0.233157i	$0.925094\pi$
$588$	−1.31187e6	−	4.03751e6i	−0.156476	−	0.481582i
$589$	1.49697e6	−	4.60719e6i	0.177797	−	0.547202i
$590$	1.44158e6	−	4.39405e6i	0.170494	−	0.519679i
$591$	1.92756e6	+	5.93243e6i	0.227007	+	0.698657i
$592$	−784864.	+	570237.i	−0.0920428	+	0.0668730i
$593$	1.55074e7			1.81093			0.905466	−	0.424419i	$-0.139522\pi$
$593$	1.55074e7			1.81093			0.905466	+	0.424419i	$0.139522\pi$
$594$	−3.12152e6	+	2.26792e6i	−0.362994	+	0.263731i
$595$	5.17076e6	+	1.60698e7i	0.598773	+	1.86088i
$596$	2.39871e6	+	1.74277e6i	0.276607	+	0.200966i
$597$	−1.94988e6	−	1.41667e6i	−0.223909	−	0.162679i
$598$	251592.	−	774320.i	0.0287702	−	0.0885457i
$599$	−5.48671e6			−0.624805			−0.312403	−	0.949950i	$-0.601134\pi$
$599$	−5.48671e6			−0.624805			−0.312403	+	0.949950i	$0.601134\pi$
$600$	−1.21555e6	−	893787.i	−0.137846	−	0.101357i
$601$	2.05927e6			0.232556			0.116278	−	0.993217i	$-0.462904\pi$
$601$	2.05927e6			0.232556			0.116278	+	0.993217i	$0.462904\pi$
$602$	−81009.8	+	249322.i	−0.00911058	+	0.0280395i
$603$	−9.59974e6	−	6.97462e6i	−1.07514	−	0.781137i
$604$	1.14720e6	+	833490.i	0.127952	+	0.0929626i
$605$	3.27437e6	−	2.36473e6i	0.363697	−	0.262660i
$606$	−1.65723e6	+	1.20405e6i	−0.183316	+	0.133187i
$607$	−3.22534e6			−0.355307			−0.177654	−	0.984093i	$-0.556851\pi$
$607$	−3.22534e6			−0.355307			−0.177654	+	0.984093i	$0.556851\pi$
$608$	557222.	−	404846.i	0.0611321	−	0.0444151i
$609$	−739141.	−	2.27484e6i	−0.0807577	−	0.248547i
$610$	6.96052e6	−	5.02684e6i	0.757386	−	0.546979i
$611$	−7.59294e6	+	2.33687e7i	−0.822824	+	2.53239i
$612$	1.21868e6	+	3.75072e6i	0.131526	+	0.404796i
$613$	3.10893e6	+	9.56831e6i	0.334164	+	1.02845i	0.967132	+	0.254274i	$0.0818364\pi$
$613$	3.10893e6	+	9.56831e6i	0.334164	+	1.02845i	−0.632968	+	0.774178i	$0.718164\pi$
$614$	1.75734e6	−	5.40854e6i	0.188120	−	0.578974i
$615$	4.87900e6	+	3.56611e6i	0.520168	+	0.380195i
$616$	−1.34363e6	−	4.13526e6i	−0.142668	−	0.439088i
$617$	−7.89826e6	+	5.73843e6i	−0.835254	+	0.606848i	−0.921041	−	0.389466i	$-0.872660\pi$
$617$	−7.89826e6	+	5.73843e6i	−0.835254	+	0.606848i	0.0857865	+	0.996314i	$0.472660\pi$
$618$	−626283.			−0.0659629
$619$	1.00963e7	−	7.33540e6i	1.05910	−	0.769479i	0.0851763	−	0.996366i	$-0.472855\pi$
$619$	1.00963e7	−	7.33540e6i	1.05910	−	0.769479i	0.973921	+	0.226887i	$0.0728547\pi$
$620$	2.00808e6	−	6.12076e6i	0.209798	−	0.639479i
$621$	−634261.	−	460817.i	−0.0659992	−	0.0479512i
$622$	98091.4	+	71267.6i	0.0101661	+	0.00738612i
$623$	−912916.	+	2.80967e6i	−0.0942347	+	0.290025i
$624$	1.62302e6			0.166864
$625$	2.91159e6	+	9.32149e6i	0.298147	+	0.954520i
$626$	−1.11453e7			−1.13672
$627$	467255.	−	1.43806e6i	0.0474662	−	0.146086i
$628$	−573065.	−	416356.i	−0.0579836	−	0.0421275i
$629$	4.06088e6	+	2.95040e6i	0.409255	+	0.297341i
$630$	−2.95730e6	+	9.01408e6i	−0.296855	+	0.904836i
$631$	1.03951e7	−	7.55246e6i	1.03933	−	0.755118i	0.0691764	−	0.997604i	$-0.477963\pi$
$631$	1.03951e7	−	7.55246e6i	1.03933	−	0.755118i	0.970155	+	0.242486i	$0.0779629\pi$
$632$	185828.			0.0185062
$633$	4.50239e6	−	3.27118e6i	0.446615	−	0.324485i
$634$	445963.	+	1.37253e6i	0.0440632	+	0.135613i
$635$	−1.10611e7	−	8.08467e6i	−1.08859	−	0.795661i
$636$	−816546.	+	2.51307e6i	−0.0800457	+	0.246355i
$637$	−9.13401e6	−	2.81116e7i	−0.891894	−	2.74497i
$638$	−512253.	−	1.57655e6i	−0.0498233	−	0.153340i
$639$	3.05166e6	−	9.39203e6i	0.295654	−	0.909929i
$640$	742506.	−	536233.i	0.0716556	−	0.0517492i
$641$	1.51239e6	+	4.65465e6i	0.145385	+	0.447448i	0.997060	−	0.0766215i	$-0.0244133\pi$
$641$	1.51239e6	+	4.65465e6i	0.145385	+	0.447448i	−0.851676	+	0.524069i	$0.824413\pi$
$642$	−803232.	+	583582.i	−0.0769137	+	0.0558810i
$643$	−1.46595e7			−1.39827			−0.699134	−	0.714991i	$-0.746431\pi$
$643$	−1.46595e7			−1.39827			−0.699134	+	0.714991i	$0.746431\pi$
$644$	714754.	−	519299.i	0.0679112	−	0.0493404i
$645$	−98278.5	+	70976.1i	−0.00930163	+	0.00671758i
$646$	−2.88306e6	−	2.09467e6i	−0.271815	−	0.197485i
$647$	343334.	+	249447.i	0.0322445	+	0.0234270i	0.603791	−	0.797143i	$-0.293656\pi$
$647$	343334.	+	249447.i	0.0322445	+	0.0234270i	−0.571546	+	0.820570i	$0.693656\pi$
$648$	−411366.	+	1.26606e6i	−0.0384850	+	0.118445i
$649$	6.16287e6			0.574343
$650$	−8.46339e6	−	6.22308e6i	−0.785708	−	0.577727i
$651$	1.23870e7			1.14555
$652$	−835494.	+	2.57138e6i	−0.0769705	+	0.236891i
$653$	4.04766e6	+	2.94080e6i	0.371468	+	0.269887i	0.757819	−	0.652464i	$-0.226265\pi$
$653$	4.04766e6	+	2.94080e6i	0.371468	+	0.269887i	−0.386351	+	0.922352i	$0.626265\pi$
$654$	2.92932e6	+	2.12827e6i	0.267807	+	0.194573i
$655$	−1.63176e6	−	5.07120e6i	−0.148611	−	0.461857i
$656$	−2.96793e6	+	2.15633e6i	−0.269273	+	0.195639i
$657$	9.25434e6			0.836435
$658$	−2.15710e7	+	1.56722e7i	−1.94225	+	1.41113i
$659$	−634632.	−	1.95320e6i	−0.0569257	−	0.175199i	0.918551	−	0.395303i	$-0.129360\pi$
$659$	−634632.	−	1.95320e6i	−0.0569257	−	0.175199i	−0.975476	+	0.220104i	$0.929360\pi$
$660$	626790.	−	1.91050e6i	0.0560095	−	0.170721i
$661$	−3.93699e6	+	1.21168e7i	−0.350478	+	1.07866i	0.608108	+	0.793855i	$0.291929\pi$
$661$	−3.93699e6	+	1.21168e7i	−0.350478	+	1.07866i	−0.958585	+	0.284805i	$0.908071\pi$
$662$	−2.46921e6	−	7.59946e6i	−0.218985	−	0.673966i
$663$	−2.59496e6	−	7.98648e6i	−0.229270	−	0.705621i
$664$	−367547.	+	1.13119e6i	−0.0323513	+	0.0995672i
$665$	−2.62579e6	−	8.16046e6i	−0.230253	−	0.715584i
$666$	871688.	+	2.68278e6i	0.0761510	+	0.234369i
$667$	272497.	−	197980.i	0.0237163	−	0.0172309i
$668$	8.30631e6			0.720223
$669$	6.36914e6	−	4.62745e6i	0.550194	−	0.399739i
$670$	1.42581e7	+	40667.9i	1.22709	+	0.00349998i
$671$	9.25687e6	+	6.72551e6i	0.793703	+	0.576659i
$672$	1.42484e6	+	1.03521e6i	0.121714	+	0.0884307i
$673$	155969.	−	480024.i	0.0132740	−	0.0408531i	−0.944200	−	0.329372i	$-0.893163\pi$
$673$	155969.	−	480024.i	0.0132740	−	0.0408531i	0.957474	+	0.288519i	$0.0931629\pi$
$674$	6.97375e6			0.591312
$675$	−8.21752e6	+	5.89905e6i	−0.694194	+	0.498336i
$676$	5.35974e6			0.451104
$677$	4.01589e6	−	1.23596e7i	0.336752	−	1.03642i	−0.629101	−	0.777324i	$-0.716577\pi$
$677$	4.01589e6	−	1.23596e7i	0.336752	−	1.03642i	0.965853	−	0.259092i	$-0.0834233\pi$
$678$	5.63297e6	+	4.09259e6i	0.470613	+	0.341920i
$679$	−1.89759e7	−	1.37868e7i	−1.57953	−	1.14760i
$680$	−3.82583e6	−	2.79634e6i	−0.317288	−	0.231909i
$681$	−6.99804e6	+	5.08437e6i	−0.578240	+	0.420116i
$682$	8.58467e6			0.706745
$683$	2.42490e6	−	1.76180e6i	0.198904	−	0.144512i	−0.483875	−	0.875137i	$-0.660771\pi$
$683$	2.42490e6	−	1.76180e6i	0.198904	−	0.144512i	0.682779	+	0.730625i	$0.260771\pi$
$684$	−618864.	−	1.90467e6i	−0.0505772	−	0.155661i
$685$	−1.50343e7	−	42881.7i	−1.22421	−	0.00349177i
$686$	5.17530e6	−	1.59279e7i	0.419880	−	1.29226i
$687$	−1.22638e6	−	3.77442e6i	−0.0991368	−	0.305112i
$688$	−22740.8	−	69988.9i	−0.00183161	−	0.00563713i
$689$	−5.68529e6	+	1.74975e7i	−0.456252	+	1.40420i
$690$	408550.	+	1165.29i	0.0326680	+	9.31776e-5i
$691$	−4.67594e6	−	1.43910e7i	−0.372540	−	1.14656i	−0.945123	−	0.326714i	$-0.894058\pi$
$691$	−4.67594e6	−	1.43910e7i	−0.372540	−	1.14656i	0.572583	−	0.819847i	$-0.305942\pi$
$692$	−7.42948e6	+	5.39783e6i	−0.589784	+	0.428503i
$693$	−1.26427e7			−1.00001
$694$	1.78340e6	−	1.29571e6i	0.140556	−	0.102120i
$695$	−9.83497e6	−	7.18847e6i	−0.772345	−	0.564514i
$696$	543213.	+	394667.i	0.0425057	+	0.0308822i
$697$	1.53560e7	+	1.11568e7i	1.19728	+	0.869878i
$698$	−3.27163e6	+	1.00691e7i	−0.254171	+	0.782258i
$699$	−1.28313e6			−0.0993296
$700$	−3.46071e6	−	1.08614e7i	−0.266944	−	0.837800i
$701$	1.15030e7			0.884128			0.442064	−	0.896984i	$-0.354246\pi$
$701$	1.15030e7			0.884128			0.442064	+	0.896984i	$0.354246\pi$
$702$	3.36259e6	−	1.03490e7i	0.257532	−	0.792601i
$703$	−2.06217e6	−	1.49826e6i	−0.157375	−	0.114340i
$704$	987467.	+	717436.i	0.0750915	+	0.0545572i
$705$	−1.23299e7	−	35168.0i	−0.934299	−	0.00266486i
$706$	7.06403e6	−	5.13232e6i	0.533385	−	0.387527i
$707$	−1.54768e7			−1.16448
$708$	−2.01953e6	+	1.46728e6i	−0.151415	+	0.110009i
$709$	4.05949e6	+	1.24938e7i	0.303288	+	0.933425i	0.980310	+	0.197462i	$0.0632701\pi$
$709$	4.05949e6	+	1.24938e7i	0.303288	+	0.933425i	−0.677022	+	0.735963i	$0.736730\pi$
$710$	3.63469e6	+	1.12960e7i	0.270596	+	0.840963i
$711$	166969.	−	513877.i	0.0123869	−	0.0381228i
$712$	−256271.	−	788720.i	−0.0189452	−	0.0583073i
$713$	539023.	+	1.65894e6i	0.0397085	+	0.122210i
$714$	2.81589e6	−	8.66643e6i	0.206714	−	0.636201i
$715$	4.36409e6	−	1.33021e7i	0.319248	−	0.973092i
$716$	−1.17972e6	−	3.63080e6i	−0.0859994	−	0.264679i
$717$	7.32400e6	−	5.32120e6i	0.532048	−	0.386555i
$718$	1.24612e7			0.902087
$719$	7.34843e6	−	5.33895e6i	0.530118	−	0.385153i	−0.290284	−	0.956941i	$-0.593750\pi$
$719$	7.34843e6	−	5.33895e6i	0.530118	−	0.385153i	0.820402	+	0.571787i	$0.193750\pi$
$720$	−815715.	−	2.53509e6i	−0.0586418	−	0.182248i
$721$	−3.82812e6	−	2.78129e6i	−0.274250	−	0.199254i
$722$	−6.54876e6	−	4.75796e6i	−0.467537	−	0.339686i
$723$	−2.09076e6	+	6.43470e6i	−0.148751	+	0.457807i
$724$	1.36161e7			0.965397
$725$	−1.31938e6	−	4.14086e6i	−0.0932234	−	0.292581i
$726$	−2.18024e6			−0.153519
$727$	5.52010e6	−	1.69891e7i	0.387357	−	1.19216i	−0.547399	−	0.836872i	$-0.684382\pi$
$727$	5.52010e6	−	1.69891e7i	0.387357	−	1.19216i	0.934756	−	0.355290i	$-0.115618\pi$
$728$	9.92059e6	+	7.20773e6i	0.693759	+	0.504046i
$729$	−1.66923e6	−	1.21277e6i	−0.116331	−	0.0845197i
$730$	−9.01495e6	+	6.51054e6i	−0.626118	+	0.452178i
$731$	−308039.	+	223804.i	−0.0213213	+	0.0154908i
$732$	−4.63465e6			−0.319698
$733$	−1.68776e7	+	1.22623e7i	−1.16025	+	0.842972i	−0.989810	−	0.142396i	$-0.954519\pi$
$733$	−1.68776e7	+	1.22623e7i	−1.16025	+	0.842972i	−0.170441	+	0.985368i	$0.554519\pi$
$734$	−198564.	−	611118.i	−0.0136038	−	0.0418683i
$735$	1.20245e7	−	8.68403e6i	0.821011	−	0.592929i
$736$	−76638.8	+	235870.i	−0.00521500	+	0.0160501i
$737$	5.87174e6	+	1.80714e7i	0.398197	+	1.22553i
$738$	3.29625e6	+	1.01448e7i	0.222782	+	0.685651i
$739$	−1.08640e6	+	3.34359e6i	−0.0731776	+	0.225217i	−0.980955	−	0.194235i	$-0.937778\pi$
$739$	−1.08640e6	+	3.34359e6i	−0.0731776	+	0.225217i	0.907778	+	0.419452i	$0.137778\pi$
$740$	−2.73651e6	−	2.00014e6i	−0.183703	−	0.134271i
$741$	1.31776e6	+	4.05565e6i	0.0881639	+	0.271341i
$742$	−1.61515e7	+	1.17347e7i	−1.07697	+	0.782463i
$743$	−7.89235e6			−0.524487			−0.262243	−	0.965002i	$-0.584462\pi$
$743$	−7.89235e6			−0.524487			−0.262243	+	0.965002i	$0.584462\pi$
$744$	−2.81314e6	+	2.04387e6i	−0.186320	+	0.135369i
$745$	−3.22925e6	+	9.84300e6i	−0.213163	+	0.649736i
$746$	1.04834e7	+	7.61665e6i	0.689693	+	0.501091i
$747$	2.79789e6	+	2.03278e6i	0.183455	+	0.133288i
$748$	1.95152e6	−	6.00616e6i	0.127532	−	0.392503i
$749$	−7.50136e6			−0.488580
$750$	1.67181e6	−	4.99933e6i	0.108526	−	0.324533i
$751$	7.17825e6			0.464429			0.232214	−	0.972665i	$-0.425403\pi$
$751$	7.17825e6			0.464429			0.232214	+	0.972665i	$0.425403\pi$
$752$	2.31293e6	−	7.11846e6i	0.149148	−	0.459031i
$753$	1.37680e6	+	1.00030e6i	0.0884877	+	0.0642901i
$754$	3.78218e6	+	2.74791e6i	0.242278	+	0.176025i
$755$	−1.54441e6	+	4.70748e6i	−0.0986043	+	0.300553i
$756$	9.55286e6	−	6.94056e6i	0.607896	−	0.441662i
$757$	1.52975e7			0.970240			0.485120	−	0.874447i	$-0.338776\pi$
$757$	1.52975e7			0.970240			0.485120	+	0.874447i	$0.338776\pi$
$758$	−5.22679e6	+	3.79749e6i	−0.330417	+	0.240062i
$759$	168248.	+	517813.i	0.0106010	+	0.0326264i
$760$	1.94281e6	+	1.42002e6i	0.122010	+	0.0891785i
$761$	8.28287e6	−	2.54921e7i	0.518465	−	1.59567i	−0.258423	−	0.966032i	$-0.583203\pi$
$761$	8.28287e6	−	2.54921e7i	0.518465	−	1.59567i	0.776888	−	0.629639i	$-0.216797\pi$
$762$	2.28537e6	+	7.03365e6i	0.142584	+	0.438827i
$763$	8.45371e6	+	2.60179e7i	0.525698	+	1.61793i
$764$	−275843.	+	848959.i	−0.0170974	+	0.0526203i
$765$	−1.11704e7	+	8.06718e6i	−0.690104	+	0.498389i
$766$	3.52494e6	+	1.08487e7i	0.217060	+	0.668042i
$767$	−1.40612e7	+	1.02161e7i	−0.863048	+	0.627041i
$768$	−494397.			−0.0302463
$769$	1.93688e7	−	1.40723e7i	1.18110	−	0.858120i	0.188805	−	0.982015i	$-0.439539\pi$
$769$	1.93688e7	−	1.40723e7i	1.18110	−	0.858120i	0.992295	+	0.123895i	$0.0395386\pi$
$770$	1.23156e7	−	8.89428e6i	0.748566	−	0.540610i
$771$	−9.05176e6	−	6.57649e6i	−0.548399	−	0.398435i
$772$	−3.54808e6	−	2.57783e6i	−0.214265	−	0.155672i
$773$	4.52454e6	−	1.39251e7i	0.272349	−	0.838203i	−0.717560	−	0.696497i	$-0.754741\pi$
$773$	4.52454e6	−	1.39251e7i	0.272349	−	0.838203i	0.989909	−	0.141706i	$-0.0452589\pi$
$774$	−213976.			−0.0128385
$775$	2.25062e7	+	128388.i	1.34601	+	0.00767839i
$776$	6.58435e6			0.392517
$777$	2.01413e6	−	6.19884e6i	0.119683	−	0.368348i
$778$	−9.25188e6	−	6.72188e6i	−0.548001	−	0.398146i
$779$	−7.79801e6	−	5.66559e6i	−0.460405	−	0.334504i
$780$	1.73692e6	+	5.39803e6i	0.102222	+	0.317686i
$781$	−1.27936e7	+	9.29511e6i	−0.750526	+	0.545289i
$782$	1.28319e6			0.0750370
$783$	3.64199e6	−	2.64606e6i	0.212292	−	0.154239i
$784$	2.78237e6	+	8.56324e6i	0.161668	+	0.497563i
$785$	771485.	−	2.35154e6i	0.0446842	−	0.136201i
$786$	−888622.	+	2.73490e6i	−0.0513051	+	0.157901i
$787$	2.97718e6	+	9.16281e6i	0.171344	+	0.527341i	0.999448	−	0.0332331i	$-0.0105804\pi$
$787$	2.97718e6	+	9.16281e6i	0.171344	+	0.527341i	−0.828104	+	0.560574i	$0.810580\pi$
$788$	−4.08821e6	−	1.25822e7i	−0.234540	−	0.721841i
$789$	−221354.	+	681257.i	−0.0126589	+	0.0389600i
$790$	198869.	+	618048.i	0.0113370	+	0.0352334i
$791$	1.62562e7	+	5.00314e7i	0.923800	+	2.84316i
$792$	2.87121e6	−	2.08605e6i	0.162649	−	0.118171i
$793$	−3.22693e7			−1.82224
$794$	−6.82876e6	+	4.96139e6i	−0.384406	+	0.279288i
$795$	−9.23213e6	−	26332.4i	−0.518065	−	0.00147765i
$796$	4.13553e6	+	3.00464e6i	0.231339	+	0.168078i
$797$	−1.14658e7	−	8.33040e6i	−0.639380	−	0.464537i	0.220257	−	0.975442i	$-0.429310\pi$
$797$	−1.14658e7	−	8.33040e6i	−0.639380	−	0.464537i	−0.859637	+	0.510905i	$0.829310\pi$
$798$	−1.42995e6	+	4.40093e6i	−0.0794902	+	0.244646i
$799$	−3.87263e7			−2.14605
$800$	2.57808e6	+	1.89565e6i	0.142420	+	0.104721i
$801$	−2.41134e6			−0.132794
$802$	−3.45162e6	+	1.06230e7i	−0.189490	+	0.583191i
$803$	−1.19891e7	−	8.71057e6i	−0.656141	−	0.476714i
$804$	−6.22663e6	−	4.52391e6i	−0.339714	−	0.246816i
$805$	2.49206e6	+	1.82147e6i	0.135540	+	0.0990678i
$806$	−1.95868e7	+	1.42307e7i	−1.06200	+	0.771591i
$807$	−4.26108e6			−0.230322
$808$	3.51485e6	−	2.55369e6i	0.189400	−	0.137607i
$809$	7.16789e6	+	2.20605e7i	0.385053	+	1.18507i	0.936442	+	0.350822i	$0.114098\pi$
$809$	7.16789e6	+	2.20605e7i	0.385053	+	1.18507i	−0.551390	+	0.834248i	$0.685902\pi$
$810$	−4.65104e6	−	13266.0i	−0.249079	−	0.000710438i
$811$	2.76554e6	−	8.51147e6i	0.147648	−	0.454415i	−0.849694	−	0.527276i	$-0.823213\pi$
$811$	2.76554e6	−	8.51147e6i	0.147648	−	0.454415i	0.997342	+	0.0728619i	$0.0232132\pi$
$812$	1.56766e6	+	4.82476e6i	0.0834375	+	0.256794i
$813$	1.56664e6	+	4.82161e6i	0.0831269	+	0.255838i
$814$	1.39587e6	−	4.29603e6i	0.0738385	−	0.227251i
$815$	−9.44635e6	−	26943.4i	−0.498161	−	0.00142089i
$816$	790467.	+	2.43281e6i	0.0415584	+	0.127903i
$817$	156427.	−	113651.i	0.00819891	−	0.00595686i
$818$	1.21048e7			0.632521
$819$	2.88456e7	−	2.09576e7i	1.50269	−	1.09177i
$820$	−1.03480e7	−	7.56344e6i	−0.537429	−	0.392812i
$821$	1.54887e7	+	1.12532e7i	0.801966	+	0.582662i	0.911490	−	0.411322i	$-0.134933\pi$
$821$	1.54887e7	+	1.12532e7i	0.801966	+	0.582662i	−0.109525	+	0.993984i	$0.534933\pi$
$822$	6.56558e6	+	4.77017e6i	0.338917	+	0.246238i
$823$	−3.89747e6	+	1.19952e7i	−0.200578	+	0.617315i	0.799288	+	0.600948i	$0.205210\pi$
$823$	−3.89747e6	+	1.19952e7i	−0.200578	+	0.617315i	−0.999866	+	0.0163674i	$0.994790\pi$
$824$	1.32830e6			0.0681518
$825$	7.02495e6	+	40074.3i	0.359342	+	0.00204989i
$826$	−1.88604e7			−0.961834
$827$	87959.4	−	270711.i	0.00447217	−	0.0137639i	−0.948796	−	0.315891i	$-0.897697\pi$
$827$	87959.4	−	270711.i	0.00447217	−	0.0137639i	0.953268	+	0.302127i	$0.0976966\pi$
$828$	583400.	+	423865.i	0.0295727	+	0.0214858i
$829$	2.12617e7	+	1.54475e7i	1.07451	+	0.780680i	0.976718	−	0.214527i	$-0.0688210\pi$
$829$	2.12617e7	+	1.54475e7i	1.07451	+	0.780680i	0.0977952	+	0.995207i	$0.468821\pi$
$830$	−4.15560e6	−	11852.8i	−0.209381	−	0.000597210i
$831$	−4.88644e6	+	3.55020e6i	−0.245465	+	0.178341i
$832$	−3.44229e6			−0.172401
$833$	3.76891e7	−	2.73827e7i	1.88193	−	1.36730i
$834$	2.03203e6	+	6.25396e6i	0.101162	+	0.311344i
$835$	8.88924e6	+	2.76261e7i	0.441213	+	1.37121i
$836$	−991010.	+	3.05001e6i	−0.0490413	+	0.150934i
$837$	7.20418e6	+	2.21722e7i	0.355444	+	1.09394i
$838$	−6.54815e6	−	2.01531e7i	−0.322113	−	0.991362i
$839$	2.72454e6	−	8.38527e6i	0.133625	−	0.411256i	−0.861748	−	0.507336i	$-0.830630\pi$
$839$	2.72454e6	−	8.38527e6i	0.133625	−	0.411256i	0.995374	+	0.0960797i	$0.0306304\pi$
$840$	−1.91818e6	+	5.84675e6i	−0.0937974	+	0.285902i
$841$	−5.74063e6	−	1.76678e7i	−0.279879	−	0.861378i
$842$	1.78062e7	−	1.29370e7i	0.865547	−	0.628857i
$843$	1.38835e6			0.0672867
$844$	−9.54921e6	+	6.93791e6i	−0.461436	+	0.335253i
$845$	5.73588e6	+	1.78261e7i	0.276349	+	0.858843i
$846$	−1.76068e7	−	1.27921e7i	−0.845773	−	0.614490i
$847$	−1.33266e7	−	9.68231e6i	−0.638277	−	0.463736i
$848$	1.73183e6	−	5.33002e6i	0.0827019	−	0.254530i
$849$	−1.07548e7			−0.512073
$850$	5.20607e6	−	1.57170e7i	0.247151	−	0.746143i
$851$	917832.			0.0434449
$852$	1.97938e6	−	6.09190e6i	0.0934179	−	0.287511i
$853$	2.71212e7	+	1.97047e7i	1.27625	+	0.927252i	0.999433	−	0.0336696i	$-0.0107194\pi$
$853$	2.71212e7	+	1.97047e7i	1.27625	+	0.927252i	0.276820	+	0.960922i	$0.410719\pi$
$854$	−2.83290e7	−	2.05822e7i	−1.32919	−	0.965713i
$855$	5.67248e6	−	4.09663e6i	0.265374	−	0.191651i
$856$	1.70359e6	−	1.23773e6i	0.0794659	−	0.0577354i
$857$	9.70165e6			0.451225			0.225613	−	0.974217i	$-0.427562\pi$
$857$	9.70165e6			0.451225			0.225613	+	0.974217i	$0.427562\pi$
$858$	−6.11372e6	+	4.44188e6i	−0.283522	+	0.205991i
$859$	−1.13832e7	−	3.50339e7i	−0.526358	−	1.61996i	−0.761615	−	0.648030i	$-0.775593\pi$
$859$	−1.13832e7	−	3.50339e7i	−0.526358	−	1.61996i	0.235257	−	0.971933i	$-0.424407\pi$
$860$	208441.	−	150535.i	0.00961029	−	0.00694049i
$861$	7.61633e6	−	2.34407e7i	0.350137	−	1.07761i
$862$	96097.1	+	295756.i	0.00440496	+	0.0135571i
$863$	2.32250e6	+	7.14793e6i	0.106152	+	0.326703i	0.989999	−	0.141073i	$-0.0450553\pi$
$863$	2.32250e6	+	7.14793e6i	0.106152	+	0.326703i	−0.883847	+	0.467776i	$0.845055\pi$
$864$	−1.02430e6	+	3.15246e6i	−0.0466812	+	0.143670i
$865$	−2.59036e7	−	1.89332e7i	−1.17712	−	0.860367i
$866$	−2.40945e6	−	7.41552e6i	−0.109175	−	0.336006i
$867$	2.04184e6	−	1.48348e6i	0.0922516	−	0.0670247i
$868$	−2.62719e7			−1.18356
$869$	−699992.	+	508574.i	−0.0314444	+	0.0228457i
$870$	−731297.	+	2.22905e6i	−0.0327564	+	0.0998439i
$871$	−4.33536e7	−	3.14982e7i	−1.93633	−	1.40683i
$872$	−6.21285e6	−	4.51390e6i	−0.276694	−	0.201030i
$873$	5.91613e6	−	1.82080e7i	0.262725	−	0.808586i
$874$	−651624.			−0.0288548
$875$	3.24206e7	−	2.31337e7i	1.43153	−	1.02147i
$876$	6.00259e6			0.264289
$877$	1.31607e6	−	4.05045e6i	0.0577804	−	0.177830i	−0.918001	−	0.396578i	$-0.870197\pi$
$877$	1.31607e6	−	4.05045e6i	0.0577804	−	0.177830i	0.975781	+	0.218749i	$0.0701975\pi$
$878$	1.22844e7	+	8.92512e6i	0.537795	+	0.390731i
$879$	9.18490e6	+	6.67322e6i	0.400961	+	0.291315i
$880$	−1.32937e6	+	4.05202e6i	−0.0578681	+	0.176386i
$881$	1.33901e7	−	9.72849e6i	0.581226	−	0.422285i	−0.257940	−	0.966161i	$-0.583044\pi$
$881$	1.33901e7	−	9.72849e6i	0.581226	−	0.422285i	0.839166	+	0.543876i	$0.183044\pi$
$882$	2.61803e7			1.13319
$883$	1.72681e7	−	1.25460e7i	0.745319	−	0.541506i	−0.149053	−	0.988829i	$-0.547623\pi$
$883$	1.72681e7	−	1.25460e7i	0.745319	−	0.541506i	0.894372	+	0.447323i	$0.147623\pi$
$884$	5.50371e6	+	1.69387e7i	0.236878	+	0.729036i
$885$	−7.04131e6	−	5.14656e6i	−0.302201	−	0.220881i
$886$	2.05436e6	−	6.32268e6i	0.0879210	−	0.270593i
$887$	−645261.	−	1.98591e6i	−0.0275376	−	0.0847521i	0.936343	−	0.351086i	$-0.114188\pi$
$887$	−645261.	−	1.98591e6i	−0.0275376	−	0.0847521i	−0.963881	+	0.266334i	$0.914188\pi$
$888$	565398.	+	1.74012e6i	0.0240615	+	0.0740536i
$889$	−1.72669e7	+	5.31420e7i	−0.732756	+	2.25519i
$890$	2.34896e6	−	1.69641e6i	0.0994034	−	0.0717885i
$891$	−1.91537e6	−	5.89491e6i	−0.0808275	−	0.248762i
$892$	−1.35084e7	+	9.81446e6i	−0.568451	+	0.413004i
$893$	1.96658e7			0.825243
$894$	4.52391e6	−	3.28681e6i	0.189308	−	0.137541i
$895$	1.08132e7	−	7.80925e6i	0.451230	−	0.325875i
$896$	−3.02197e6	−	2.19559e6i	−0.125753	−	0.0913652i
$897$	−1.24225e6	−	902544.i	−0.0515497	−	0.0374531i
$898$	1.74593e6	−	5.37342e6i	0.0722498	−	0.222362i
$899$	−1.00160e7			−0.413330
$900$	7.55856e6	−	5.42601e6i	0.311052	−	0.223293i
$901$	−2.89967e7			−1.18997
$902$	5.27841e6	−	1.62453e7i	0.216016	−	0.664830i
$903$	399989.	+	290609.i	0.0163241	+	0.0118601i
$904$	−1.19471e7	−	8.68007e6i	−0.486229	−	0.353266i
$905$	1.45717e7	+	4.52860e7i	0.591408	+	1.83799i
$906$	2.16359e6	−	1.57194e6i	0.0875699	−	0.0636232i
$907$	−8.80226e6			−0.355284			−0.177642	−	0.984095i	$-0.556847\pi$
$907$	−8.80226e6			−0.355284			−0.177642	+	0.984095i	$0.556847\pi$
$908$	1.48423e7	−	1.07835e7i	0.597428	−	0.434057i
$909$	−3.90368e6	−	1.20143e7i	−0.156698	−	0.482268i
$910$	−1.33555e7	+	4.07086e7i	−0.534635	+	1.62961i
$911$	−3.15547e6	+	9.71155e6i	−0.125970	+	0.387697i	−0.994077	−	0.108681i	$-0.965337\pi$
$911$	−3.15547e6	+	9.71155e6i	−0.125970	+	0.387697i	0.868106	+	0.496379i	$0.165337\pi$
$912$	−401410.	−	1.23541e6i	−0.0159809	−	0.0491842i
$913$	−1.71134e6	−	5.26698e6i	−0.0679455	−	0.209115i
$914$	−4.57263e6	+	1.40731e7i	−0.181051	+	0.557218i
$915$	−4.95991e6	−	1.54145e7i	−0.195849	−	0.608662i
$916$	2.60106e6	+	8.00525e6i	0.102426	+	0.315236i
$917$	−1.75772e7	+	1.27706e7i	−0.690280	+	0.501518i
$918$	1.71502e7			0.671681
$919$	1.87376e7	−	1.36137e7i	0.731857	−	0.531725i	−0.158294	−	0.987392i	$-0.550599\pi$
$919$	1.87376e7	−	1.36137e7i	0.731857	−	0.531725i	0.890150	+	0.455667i	$0.150599\pi$
$920$	−866502.	−	2471.49i	−0.0337521	−	9.62696e-5i
$921$	−8.67694e6	−	6.30417e6i	−0.337068	−	0.244894i
$922$	−7.56309e6	−	5.49491e6i	−0.293003	−	0.212879i
$923$	1.37816e7	−	4.24155e7i	0.532472	−	1.63878i
$924$	−8.20035e6			−0.315975
$925$	3.72375e6	−	1.12419e7i	0.143096	−	0.432002i
$926$	3.01040e7			1.15371
$927$	1.19349e6	−	3.67319e6i	0.0456164	−	0.140393i
$928$	−1.15211e6	−	837058.i	−0.0439162	−	0.0319070i
$929$	−3.31096e7	−	2.40555e7i	−1.25868	−	0.914483i	−0.259985	−	0.965613i	$-0.583718\pi$
$929$	−3.31096e7	−	2.40555e7i	−1.25868	−	0.914483i	−0.998692	+	0.0511301i	$0.983718\pi$
$930$	−9.80831e6	−	7.16899e6i	−0.371866	−	0.271801i
$931$	−1.91390e7	+	1.39053e7i	−0.723679	+	0.525784i
$932$	2.72142e6			0.102626
$933$	184998.	−	134409.i	0.00695765	−	0.00505503i
$934$	1.16708e6	+	3.59189e6i	0.0437756	+	0.134728i
$935$	2.20645e7	+	62933.6i	0.825401	+	0.00235426i
$936$	−3.09294e6	+	9.51910e6i	−0.115394	+	0.355146i
$937$	6.66127e6	+	2.05013e7i	0.247861	+	0.762837i	0.995153	+	0.0983412i	$0.0313537\pi$
$937$	6.66127e6	+	2.05013e7i	0.247861	+	0.762837i	−0.747292	+	0.664496i	$0.768646\pi$
$938$	−1.79694e7	−	5.53042e7i	−0.666849	−	2.05235i
$939$	−6.49544e6	+	1.99909e7i	−0.240406	+	0.739892i
$940$	2.61507e7	+	74588.5i	0.965303	+	0.00275329i
$941$	2.07027e6	+	6.37162e6i	0.0762170	+	0.234572i	0.981905	−	0.189372i	$-0.0606453\pi$
$941$	2.07027e6	+	6.37162e6i	0.0762170	+	0.234572i	−0.905688	+	0.423944i	$0.860645\pi$
$942$	−1.08079e6	+	785237.i	−0.0396837	+	0.0288319i
$943$	3.47074e6			0.127099
$944$	4.28327e6	−	3.11198e6i	0.156439	−	0.113660i
$945$	3.33070e7	+	2.43444e7i	1.21327	+	0.886788i
$946$	277208.	+	201403.i	0.0100711	+	0.00731709i
$947$	−3.67232e6	−	2.66810e6i	−0.133065	−	0.0966777i	0.519261	−	0.854615i	$-0.326207\pi$
$947$	−3.67232e6	−	2.66810e6i	−0.133065	−	0.0966777i	−0.652327	+	0.757938i	$0.726207\pi$
$948$	108300.	−	333313.i	0.00391388	−	0.0120457i
$949$	4.17937e7			1.50642
$950$	−2.64372e6	+	7.98131e6i	−0.0950399	+	0.286923i
$951$	2.72178e6			0.0975891
$952$	−5.97228e6	+	1.83808e7i	−0.213574	+	0.657313i
$953$	−1.46050e7	−	1.06112e7i	−0.520919	−	0.378470i	0.296031	−	0.955178i	$-0.404337\pi$
$953$	−1.46050e7	−	1.06112e7i	−0.520919	−	0.378470i	−0.816950	+	0.576708i	$0.804337\pi$
$954$	−1.31833e7	−	9.57820e6i	−0.468977	−	0.340732i
$955$	−3.11877e6	−	8895.55i	−0.110656	−	0.000315620i
$956$	−1.55336e7	+	1.12858e7i	−0.549703	+	0.399383i
$957$	−3.12635e6			−0.110346
$958$	−5.94877e6	+	4.32203e6i	−0.209418	+	0.152151i
$959$	1.89476e7	+	5.83147e7i	0.665285	+	2.04754i
$960$	−529093.	−	1.64432e6i	−0.0185291	−	0.0575850i
$961$	7.18186e6	−	2.21035e7i	0.250858	−	0.772063i
$962$	3.93665e6	+	1.21158e7i	0.137148	+	0.422097i
$963$	−1.89205e6	−	5.82313e6i	−0.0657456	−	0.202344i
$964$	4.43434e6	−	1.36475e7i	0.153687	−	0.472999i
$965$	4.77658e6	−	1.45594e7i	0.165120	−	0.503297i
$966$	−514893.	−	1.58468e6i	−0.0177531	−	0.0546384i
$967$	−4.07907e7	+	2.96362e7i	−1.40280	+	1.01919i	−0.408476	+	0.912769i	$0.633940\pi$
$967$	−4.07907e7	+	2.96362e7i	−1.40280	+	1.01919i	−0.994321	+	0.106423i	$0.966060\pi$
$968$	4.62411e6			0.158613
$969$	−5.43738e6	+	3.95049e6i	−0.186029	+	0.135158i
$970$	7.04644e6	+	2.18990e7i	0.240458	+	0.747301i
$971$	1.09394e7	+	7.94795e6i	0.372346	+	0.270525i	0.758183	−	0.652042i	$-0.226087\pi$
$971$	1.09394e7	+	7.94795e6i	0.372346	+	0.270525i	−0.385837	+	0.922567i	$0.626087\pi$
$972$	1.22130e7	+	8.87327e6i	0.414626	+	0.301244i
$973$	−1.53528e7	+	4.72511e7i	−0.519883	+	1.60004i
$974$	−2.80849e7			−0.948585
$975$	−1.60946e7	+	1.15537e7i	−0.542211	+	0.389233i
$976$	9.82973e6			0.330307
$977$	−435236.	+	1.33952e6i	−0.0145878	+	0.0448965i	−0.958085	−	0.286483i	$-0.907514\pi$
$977$	−435236.	+	1.33952e6i	−0.0145878	+	0.0448965i	0.943498	+	0.331379i	$0.107514\pi$
$978$	4.12529e6	+	2.99720e6i	0.137914	+	0.100200i
$979$	3.12391e6	+	2.26966e6i	0.104170	+	0.0756838i
$980$	−2.55030e7	+	1.84181e7i	−0.848255	+	0.612605i
$981$	−1.80648e7	+	1.31248e7i	−0.599322	+	0.435433i
$982$	−2.63998e7			−0.873619
$983$	−3.80550e7	+	2.76486e7i	−1.25611	+	0.912619i	−0.998560	−	0.0536460i	$-0.982916\pi$
$983$	−3.80550e7	+	2.76486e7i	−1.25611	+	0.912619i	−0.257552	+	0.966265i	$0.582916\pi$
$984$	2.13803e6	+	6.58018e6i	0.0703924	+	0.216646i
$985$	3.74723e7	−	2.70623e7i	1.23061	−	0.888738i
$986$	−2.27691e6	+	7.00760e6i	−0.0745853	+	0.229550i
$987$	1.55393e7	+	4.78249e7i	0.507735	+	1.56265i
$988$	−2.79486e6	−	8.60171e6i	−0.0910895	−	0.280345i
$989$	−21514.5	+	66214.9i	−0.000699425	+	0.00215261i
$990$	1.00108e7	+	7.31696e6i	0.324623	+	0.237270i
$991$	−1.55765e7	−	4.79394e7i	−0.503831	−	1.55063i	−0.802728	−	0.596346i	$-0.796619\pi$
$991$	−1.55765e7	−	4.79394e7i	−0.503831	−	1.55063i	0.298897	−	0.954285i	$-0.403381\pi$
$992$	5.96645e6	−	4.33488e6i	0.192503	−	0.139862i
$993$	−1.50700e7			−0.484997
$994$	3.91526e7	−	2.84460e7i	1.25688	−	0.913179i
$995$	−5.56743e6	+	1.69700e7i	−0.178278	+	0.543404i
$996$	1.81478e6	+	1.31851e6i	0.0579662	+	0.0421149i
$997$	−5.32632e6	−	3.86980e6i	−0.169703	−	0.123296i	0.499692	−	0.866203i	$-0.333447\pi$
$997$	−5.32632e6	−	3.86980e6i	−0.169703	−	0.123296i	−0.669395	+	0.742907i	$0.733447\pi$
$998$	−2.59774e6	+	7.99503e6i	−0.0825600	+	0.254094i
$999$	1.22671e7			0.388890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.b.21.5	✓	28
25.6	even	5	inner	50.6.d.b.31.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.b.21.5	✓	28	1.1	even	1	trivial
50.6.d.b.31.5	yes	28	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(6.10314 + 4.43419i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(17.4261 - 53.1162i) q^{5} +(-24.4126 + 17.7368i) q^{6} -227.988 q^{7} +(51.7771 - 37.6183i) q^{8} +(-57.5049 - 176.982i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(6.10314 + 4.43419i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(17.4261 - 53.1162i) q^{5} +(-24.4126 + 17.7368i) q^{6} -227.988 q^{7} +(51.7771 - 37.6183i) q^{8} +(-57.5049 - 176.982i) q^{9} +(180.526 + 131.948i) q^{10} +(-92.0846 + 283.407i) q^{11} +(-37.2991 - 114.795i) q^{12} +(-259.699 - 799.271i) q^{13} +(281.809 - 867.318i) q^{14} +(341.881 - 246.905i) q^{15} +(79.1084 + 243.470i) q^{16} +(1071.58 - 778.546i) q^{17} +744.359 q^{18} +(-544.162 + 395.357i) q^{19} +(-725.103 + 523.665i) q^{20} +(-1391.44 - 1010.94i) q^{21} +(-964.323 - 700.622i) q^{22} +(74.8426 - 230.342i) q^{23} +482.809 q^{24} +(-2517.66 - 1851.22i) q^{25} +3361.61 q^{26} +(1000.29 - 3078.58i) q^{27} +(2951.14 + 2144.13i) q^{28} +(1125.11 + 817.440i) q^{29} +(516.692 + 1605.79i) q^{30} +(-5826.62 + 4233.28i) q^{31} -1024.00 q^{32} +(-1818.69 + 1321.35i) q^{33} +(1637.22 + 5038.86i) q^{34} +(-3972.95 + 12109.9i) q^{35} +(-920.078 + 2831.71i) q^{36} +(1171.06 + 3604.15i) q^{37} +(-831.406 - 2558.80i) q^{38} +(1959.14 - 6029.61i) q^{39} +(-1095.86 - 3405.74i) q^{40} +(4428.31 + 13628.9i) q^{41} +(5565.77 - 4043.77i) q^{42} -287.464 q^{43} +(3857.29 - 2802.49i) q^{44} +(-10402.7 - 29.6712i) q^{45} +(783.762 + 569.436i) q^{46} +(-23653.6 - 17185.4i) q^{47} +(-596.785 + 1836.72i) q^{48} +35171.6 q^{49} +(10154.5 - 7289.51i) q^{50} +9992.21 q^{51} +(-4155.18 + 12788.3i) q^{52} +(-17710.9 - 12867.7i) q^{53} +(10475.2 + 7610.66i) q^{54} +(13448.8 + 9829.88i) q^{55} +(-11804.6 + 8576.52i) q^{56} -5074.19 q^{57} +(-4500.44 + 3269.76i) q^{58} +(-6390.88 - 19669.1i) q^{59} +(-6747.44 - 19.2454i) q^{60} +(11865.4 - 36518.1i) q^{61} +(-8902.28 - 27398.4i) q^{62} +(13110.4 + 40349.7i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-46979.8 - 133.998i) q^{65} +(-2778.71 - 8551.98i) q^{66} +(51586.7 - 37479.9i) q^{67} -21192.7 q^{68} +(1478.15 - 1073.94i) q^{69} +(-41157.8 - 30082.6i) q^{70} +(42932.7 + 31192.5i) q^{71} +(-9635.18 - 7000.37i) q^{72} +(-15367.6 + 47296.6i) q^{73} -15158.5 q^{74} +(-7156.96 - 22462.0i) q^{75} +10761.9 q^{76} +(20994.2 - 64613.5i) q^{77} +(20516.4 + 14906.0i) q^{78} +(2349.03 + 1706.67i) q^{79} +(14310.8 + 40.8180i) q^{80} +(-16827.7 + 12226.0i) q^{81} -57321.2 q^{82} +(-15035.2 + 10923.7i) q^{83} +(8503.74 + 26171.8i) q^{84} +(-22680.0 - 70485.2i) q^{85} +(355.325 - 1093.58i) q^{86} +(3242.02 + 9977.90i) q^{87} +(5893.42 + 18138.1i) q^{88} +(4004.23 - 12323.7i) q^{89} +(12971.3 - 39537.5i) q^{90} +(59208.2 + 182224. i) q^{91} +(-3135.05 + 2277.75i) q^{92} -54331.8 q^{93} +(94614.5 - 68741.4i) q^{94} +(11517.2 + 35793.4i) q^{95} +(-6249.61 - 4540.61i) q^{96} +(83232.1 + 60471.6i) q^{97} +(-43474.5 + 133801. i) q^{98} +55453.3 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

Modular forms

Varieties

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Database

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