LMFDB - Embedded newform 92.5.c.a.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,5,Mod(47,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("92.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.c (of order $2$, degree $1$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	92.47
Dual form			92.5.c.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.78901 + 1.28195i) q^{2} -8.06260i q^{3} +(12.7132 - 9.71463i) q^{4} +47.7328 q^{5} +(10.3358 + 30.5493i) q^{6} -53.2079i q^{7} +(-35.7169 + 53.1065i) q^{8} +15.9945 q^{9} +(-180.860 + 61.1909i) q^{10} +159.374i q^{11} +(-78.3252 - 102.502i) q^{12} +33.4299 q^{13} +(68.2097 + 201.605i) q^{14} -384.850i q^{15} +(67.2520 - 247.008i) q^{16} +83.4957 q^{17} +(-60.6032 + 20.5041i) q^{18} -338.682i q^{19} +(606.837 - 463.706i) q^{20} -428.994 q^{21} +(-204.309 - 603.868i) q^{22} +110.304i q^{23} +(428.177 + 287.971i) q^{24} +1653.42 q^{25} +(-126.666 + 42.8554i) q^{26} -782.028i q^{27} +(-516.895 - 676.443i) q^{28} +323.380 q^{29} +(493.358 + 1458.20i) q^{30} +651.984i q^{31} +(61.8331 + 1022.13i) q^{32} +1284.97 q^{33} +(-316.366 + 107.037i) q^{34} -2539.76i q^{35} +(203.341 - 155.380i) q^{36} -2668.49 q^{37} +(434.172 + 1283.27i) q^{38} -269.532i q^{39} +(-1704.87 + 2534.92i) q^{40} -2087.72 q^{41} +(1625.46 - 549.948i) q^{42} -1814.93i q^{43} +(1548.25 + 2026.15i) q^{44} +763.460 q^{45} +(-141.404 - 417.944i) q^{46} -2954.38i q^{47} +(-1991.53 - 542.226i) q^{48} -430.077 q^{49} +(-6264.82 + 2119.59i) q^{50} -673.193i q^{51} +(425.002 - 324.759i) q^{52} +2231.01 q^{53} +(1002.52 + 2963.11i) q^{54} +7607.34i q^{55} +(2825.68 + 1900.42i) q^{56} -2730.66 q^{57} +(-1225.29 + 414.556i) q^{58} +4317.42i q^{59} +(-3738.68 - 4892.69i) q^{60} +533.511 q^{61} +(-835.809 - 2470.37i) q^{62} -851.031i q^{63} +(-1544.61 - 3793.60i) q^{64} +1595.70 q^{65} +(-4868.75 + 1647.26i) q^{66} +3765.26i q^{67} +(1061.50 - 811.130i) q^{68} +889.338 q^{69} +(3255.84 + 9623.18i) q^{70} -1365.59i q^{71} +(-571.273 + 849.410i) q^{72} -2073.28 q^{73} +(10110.9 - 3420.86i) q^{74} -13330.8i q^{75} +(-3290.17 - 4305.74i) q^{76} +8479.93 q^{77} +(345.526 + 1021.26i) q^{78} +10499.3i q^{79} +(3210.13 - 11790.4i) q^{80} -5009.63 q^{81} +(7910.41 - 2676.35i) q^{82} +28.3130i q^{83} +(-5453.89 + 4167.52i) q^{84} +3985.48 q^{85} +(2326.64 + 6876.77i) q^{86} -2607.28i q^{87} +(-8463.77 - 5692.33i) q^{88} +5959.71 q^{89} +(-2892.76 + 978.715i) q^{90} -1778.73i q^{91} +(1071.56 + 1402.32i) q^{92} +5256.68 q^{93} +(3787.36 + 11194.2i) q^{94} -16166.2i q^{95} +(8241.04 - 498.536i) q^{96} -4425.37 q^{97} +(1629.57 - 551.336i) q^{98} +2549.09i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) $ 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$	−3.78901	+	1.28195i	−0.947253	+	0.320487i
$2$	−3.78901	+	1.28195i	−0.947253	+	0.320487i
$3$		−	8.06260i		−	0.895845i	−0.894072	−	0.447922i	$-0.852164\pi$
$3$		−	8.06260i		−	0.895845i	0.894072	−	0.447922i	$-0.147836\pi$
$4$	12.7132	−	9.71463i	0.794576	−	0.607164i
$5$	47.7328			1.90931			0.954655	−	0.297713i	$-0.0962238\pi$
$5$	47.7328			1.90931			0.954655	+	0.297713i	$0.0962238\pi$
$6$	10.3358	+	30.5493i	0.287106	+	0.848591i
$7$		−	53.2079i		−	1.08587i	−0.839773	−	0.542937i	$-0.817312\pi$
$7$		−	53.2079i		−	1.08587i	0.839773	−	0.542937i	$-0.182688\pi$
$8$	−35.7169	+	53.1065i	−0.558077	+	0.829789i
$9$	15.9945			0.197462
$10$	−180.860	+	61.1909i	−1.80860	+	0.611909i
$11$			159.374i			1.31714i	0.752521	+	0.658568i	$0.228838\pi$
$11$			159.374i			1.31714i	−0.752521	+	0.658568i	$0.771162\pi$
$12$	−78.3252	−	102.502i	−0.543925	−	0.711817i
$13$	33.4299			0.197810			0.0989050	−	0.995097i	$-0.468466\pi$
$13$	33.4299			0.197810			0.0989050	+	0.995097i	$0.468466\pi$
$14$	68.2097	+	201.605i	0.348009	+	1.02860i
$15$		−	384.850i		−	1.71045i
$16$	67.2520	−	247.008i	0.262703	−	0.964877i
$17$	83.4957			0.288913			0.144456	−	0.989511i	$-0.453857\pi$
$17$	83.4957			0.288913			0.144456	+	0.989511i	$0.453857\pi$
$18$	−60.6032	+	20.5041i	−0.187047	+	0.0632841i
$19$		−	338.682i		−	0.938177i	−0.883151	−	0.469088i	$-0.844583\pi$
$19$		−	338.682i		−	0.938177i	0.883151	−	0.469088i	$-0.155417\pi$
$20$	606.837	−	463.706i	1.51709	−	1.15927i
$21$	−428.994			−0.972775
$22$	−204.309	−	603.868i	−0.422125	−	1.24766i
$23$			110.304i			0.208514i
$23$			110.304i			0.208514i
$24$	428.177	+	287.971i	0.743362	+	0.499950i
$25$	1653.42			2.64547
$26$	−126.666	+	42.8554i	−0.187376	+	0.0633955i
$27$		−	782.028i		−	1.07274i
$28$	−516.895	−	676.443i	−0.659304	−	0.862810i
$29$	323.380			0.384518			0.192259	−	0.981344i	$-0.438419\pi$
$29$	323.380			0.384518			0.192259	+	0.981344i	$0.438419\pi$
$30$	493.358	+	1458.20i	0.548175	+	1.62022i
$31$			651.984i			0.678443i	0.940707	+	0.339221i	$0.110164\pi$
$31$			651.984i			0.678443i	−0.940707	+	0.339221i	$0.889836\pi$
$32$	61.8331	+	1022.13i	0.0603839	+	0.998175i
$33$	1284.97			1.17995
$34$	−316.366	+	107.037i	−0.273673	+	0.0925927i
$35$		−	2539.76i		−	2.07327i
$36$	203.341	−	155.380i	0.156899	−	0.119892i
$37$	−2668.49			−1.94923			−0.974613	−	0.223896i	$-0.928122\pi$
$37$	−2668.49			−1.94923			−0.974613	+	0.223896i	$0.928122\pi$
$38$	434.172	+	1283.27i	0.300673	+	0.888691i
$39$		−	269.532i		−	0.177207i
$40$	−1704.87	+	2534.92i	−1.06554	+	1.58433i
$41$	−2087.72			−1.24195			−0.620977	−	0.783829i	$-0.713264\pi$
$41$	−2087.72			−1.24195			−0.620977	+	0.783829i	$0.713264\pi$
$42$	1625.46	−	549.948i	0.921464	−	0.311762i
$43$		−	1814.93i		−	0.981571i	−0.871280	−	0.490786i	$-0.836710\pi$
$43$		−	1814.93i		−	0.981571i	0.871280	−	0.490786i	$-0.163290\pi$
$44$	1548.25	+	2026.15i	0.799718	+	1.04657i
$45$	763.460			0.377017
$46$	−141.404	−	417.944i	−0.0668261	−	0.197516i
$47$		−	2954.38i		−	1.33743i	−0.743519	−	0.668715i	$-0.766845\pi$
$47$		−	2954.38i		−	1.33743i	0.743519	−	0.668715i	$-0.233155\pi$
$48$	−1991.53	−	542.226i	−0.864380	−	0.235341i
$49$	−430.077			−0.179124
$50$	−6264.82	+	2119.59i	−2.50593	+	0.847838i
$51$		−	673.193i		−	0.258821i
$52$	425.002	−	324.759i	0.157175	−	0.120103i
$53$	2231.01			0.794235			0.397118	−	0.917768i	$-0.370010\pi$
$53$	2231.01			0.794235			0.397118	+	0.917768i	$0.370010\pi$
$54$	1002.52	+	2963.11i	0.343799	+	1.01616i
$55$			7607.34i			2.51482i
$56$	2825.68	+	1900.42i	0.901047	+	0.606001i
$57$	−2730.66			−0.840461
$58$	−1225.29	+	414.556i	−0.364236	+	0.123233i
$59$			4317.42i			1.24028i	0.784491	+	0.620140i	$0.212924\pi$
$59$			4317.42i			1.24028i	−0.784491	+	0.620140i	$0.787076\pi$
$60$	−3738.68	−	4892.69i	−1.03852	−	1.35908i
$61$	533.511			0.143378			0.0716891	−	0.997427i	$-0.477161\pi$
$61$	533.511			0.143378			0.0716891	+	0.997427i	$0.477161\pi$
$62$	−835.809	−	2470.37i	−0.217432	−	0.642657i
$63$		−	851.031i		−	0.214420i
$64$	−1544.61	−	3793.60i	−0.377101	−	0.926172i
$65$	1595.70			0.377681
$66$	−4868.75	+	1647.26i	−1.11771	+	0.378158i
$67$			3765.26i			0.838775i	0.907807	+	0.419387i	$0.137755\pi$
$67$			3765.26i			0.838775i	−0.907807	+	0.419387i	$0.862245\pi$
$68$	1061.50	−	811.130i	0.229563	−	0.175417i
$69$	889.338			0.186797
$70$	3255.84	+	9623.18i	0.664457	+	1.96391i
$71$		−	1365.59i		−	0.270896i	−0.990784	−	0.135448i	$-0.956753\pi$
$71$		−	1365.59i		−	0.270896i	0.990784	−	0.135448i	$-0.0432474\pi$
$72$	−571.273	+	849.410i	−0.110199	+	0.163852i
$73$	−2073.28			−0.389057			−0.194528	−	0.980897i	$-0.562318\pi$
$73$	−2073.28			−0.389057			−0.194528	+	0.980897i	$0.562318\pi$
$74$	10110.9	−	3420.86i	1.84641	−	0.624701i
$75$		−	13330.8i		−	2.36993i
$76$	−3290.17	−	4305.74i	−0.569627	−	0.745453i
$77$	8479.93			1.43025
$78$	345.526	+	1021.26i	0.0567925	+	0.167860i
$79$			10499.3i			1.68230i	0.540799	+	0.841152i	$0.318122\pi$
$79$			10499.3i			1.68230i	−0.540799	+	0.841152i	$0.681878\pi$
$80$	3210.13	−	11790.4i	0.501582	−	1.84225i
$81$	−5009.63			−0.763546
$82$	7910.41	−	2676.35i	1.17644	−	0.398030i
$83$			28.3130i			0.00410989i	0.999998	+	0.00205495i	$0.000654110\pi$
$83$			28.3130i			0.00410989i	−0.999998	+	0.00205495i	$0.999346\pi$
$84$	−5453.89	+	4167.52i	−0.772944	+	0.590634i
$85$	3985.48			0.551624
$86$	2326.64	+	6876.77i	0.314581	+	0.929796i
$87$		−	2607.28i		−	0.344468i
$88$	−8463.77	−	5692.33i	−1.09295	−	0.735063i
$89$	5959.71			0.752394			0.376197	−	0.926540i	$-0.377232\pi$
$89$	5959.71			0.752394			0.376197	+	0.926540i	$0.377232\pi$
$90$	−2892.76	+	978.715i	−0.357131	+	0.120829i
$91$		−	1778.73i		−	0.214797i
$92$	1071.56	+	1402.32i	0.126602	+	0.165681i
$93$	5256.68			0.607779
$94$	3787.36	+	11194.2i	0.428629	+	1.26688i
$95$		−	16166.2i		−	1.79127i
$96$	8241.04	−	498.536i	0.894210	−	0.0540946i
$97$	−4425.37			−0.470334			−0.235167	−	0.971955i	$-0.575564\pi$
$97$	−4425.37			−0.470334			−0.235167	+	0.971955i	$0.575564\pi$
$98$	1629.57	−	551.336i	0.169676	−	0.0574069i
$99$			2549.09i			0.260085i
$100$	21020.3	−	16062.3i	2.10203	−	1.60623i
$101$	−10761.3			−1.05493			−0.527463	−	0.849578i	$-0.676857\pi$
$101$	−10761.3			−1.05493			−0.527463	+	0.849578i	$0.676857\pi$
$102$	862.998	+	2550.74i	0.0829486	+	0.245169i
$103$			7156.01i			0.674523i	0.941411	+	0.337261i	$0.109501\pi$
$103$			7156.01i			0.674523i	−0.941411	+	0.337261i	$0.890499\pi$
$104$	−1194.01	+	1775.35i	−0.110393	+	0.164141i
$105$	−20477.1			−1.85733
$106$	−8453.31	+	2860.03i	−0.752342	+	0.254542i
$107$		−	1241.12i		−	0.108404i	−0.998530	−	0.0542022i	$-0.982738\pi$
$107$		−	1241.12i		−	0.108404i	0.998530	−	0.0542022i	$-0.0172616\pi$
$108$	−7597.11	−	9942.09i	−0.651330	−	0.852374i
$109$	−11066.7			−0.931465			−0.465732	−	0.884926i	$-0.654209\pi$
$109$	−11066.7			−0.931465			−0.465732	+	0.884926i	$0.654209\pi$
$110$	−9752.21	−	28824.3i	−0.805968	−	2.38217i
$111$			21515.0i			1.74620i
$112$	−13142.8	−	3578.34i	−1.04774	−	0.285263i
$113$	7186.11			0.562778			0.281389	−	0.959594i	$-0.409205\pi$
$113$	7186.11			0.562778			0.281389	+	0.959594i	$0.409205\pi$
$114$	10346.5	−	3500.56i	0.796129	−	0.269357i
$115$			5265.12i			0.398119i
$116$	4111.20	−	3141.51i	0.305529	−	0.233466i
$117$	534.693			0.0390601
$118$	−5534.70	−	16358.7i	−0.397493	−	1.17486i
$119$		−	4442.63i		−	0.313723i
$120$	20438.1	+	13745.7i	1.41931	+	0.954560i
$121$	−10758.9			−0.734849
$122$	−2021.48	+	683.932i	−0.135815	+	0.0459508i
$123$			16832.5i			1.11260i
$124$	6333.78	+	8288.81i	0.411926	+	0.539075i
$125$	49089.2			3.14171
$126$	1090.98	+	3224.57i	0.0687186	+	0.203110i
$127$			30094.9i			1.86589i	0.360019	+	0.932945i	$0.382770\pi$
$127$			30094.9i			1.86589i	−0.360019	+	0.932945i	$0.617230\pi$
$128$	10715.7	+	12393.9i	0.654036	+	0.756464i
$129$	−14633.0			−0.879335
$130$	−6046.13	+	2045.61i	−0.357759	+	0.121042i
$131$			20142.7i			1.17375i	0.809678	+	0.586874i	$0.199642\pi$
$131$			20142.7i			1.17375i	−0.809678	+	0.586874i	$0.800358\pi$
$132$	16336.1	−	12483.0i	0.937560	−	0.716423i
$133$	−18020.5			−1.01874
$134$	−4826.86	−	14266.6i	−0.268816	−	0.794532i
$135$		−	37328.3i		−	2.04819i
$136$	−2982.21	+	4434.17i	−0.161235	+	0.239737i
$137$	15776.1			0.840540			0.420270	−	0.907399i	$-0.361935\pi$
$137$	15776.1			0.840540			0.420270	+	0.907399i	$0.361935\pi$
$138$	−3369.71	+	1140.08i	−0.176944	+	0.0598658i
$139$		−	646.127i		−	0.0334417i	−0.999860	−	0.0167208i	$-0.994677\pi$
$139$		−	646.127i		−	0.0334417i	0.999860	−	0.0167208i	$-0.00532266\pi$
$140$	−24672.8	−	32288.5i	−1.25882	−	1.64737i
$141$	−23820.0			−1.19813
$142$	1750.61	+	5174.23i	0.0868186	+	0.256607i
$143$			5327.84i			0.260543i
$144$	1075.66	−	3950.77i	0.0518740	−	0.190527i
$145$	15435.8			0.734164
$146$	7855.70	−	2657.84i	0.368535	−	0.124688i
$147$			3467.54i			0.160467i
$148$	−33925.1	+	25923.4i	−1.54881	+	1.18350i
$149$	−32158.9			−1.44854			−0.724268	−	0.689519i	$-0.757822\pi$
$149$	−32158.9			−1.44854			−0.724268	+	0.689519i	$0.757822\pi$
$150$	17089.4	+	50510.7i	0.759531	+	2.24492i
$151$		−	33709.4i		−	1.47842i	−0.673477	−	0.739209i	$-0.735200\pi$
$151$		−	33709.4i		−	1.47842i	0.673477	−	0.739209i	$-0.264800\pi$
$152$	17986.2	+	12096.7i	0.778489	+	0.523575i
$153$	1335.47			0.0570494
$154$	−32130.5	+	10870.8i	−1.35480	+	0.458375i
$155$			31121.0i			1.29536i
$156$	−2618.40	−	3426.62i	−0.107594	−	0.140805i
$157$	37164.6			1.50775			0.753876	−	0.657016i	$-0.228182\pi$
$157$	37164.6			1.50775			0.753876	+	0.657016i	$0.228182\pi$
$158$	−13459.5	−	39781.8i	−0.539156	−	1.59357i
$159$		−	17987.7i		−	0.711512i
$160$	2951.47	+	48789.2i	0.115292	+	1.90583i
$161$	5869.05			0.226421
$162$	18981.5	−	6422.08i	0.723271	−	0.244706i
$163$			10018.5i			0.377074i	0.982066	+	0.188537i	$0.0603746\pi$
$163$			10018.5i			0.377074i	−0.982066	+	0.188537i	$0.939625\pi$
$164$	−26541.7	+	20281.5i	−0.986827	+	0.754070i
$165$	61335.0			2.25289
$166$	−36.2958	−	107.278i	−0.00131717	−	0.00389311i
$167$		−	17230.0i		−	0.617805i	−0.951094	−	0.308902i	$-0.900038\pi$
$167$		−	17230.0i		−	0.617805i	0.951094	−	0.308902i	$-0.0999616\pi$
$168$	15322.3	−	22782.4i	0.542883	−	0.807198i
$169$	−27443.4			−0.960871
$170$	−15101.0	+	5109.18i	−0.522527	+	0.176788i
$171$		−	5417.03i		−	0.185255i
$172$	−17631.3	−	23073.5i	−0.595975	−	0.779933i
$173$	−27874.9			−0.931368			−0.465684	−	0.884951i	$-0.654192\pi$
$173$	−27874.9			−0.931368			−0.465684	+	0.884951i	$0.654192\pi$
$174$	3342.40	+	9879.02i	0.110398	+	0.326299i
$175$		−	87974.8i		−	2.87265i
$176$	39366.6	+	10718.2i	1.27087	+	0.346016i
$177$	34809.6			1.11110
$178$	−22581.4	+	7640.04i	−0.712707	+	0.241132i
$179$			44935.8i			1.40245i	0.712941	+	0.701224i	$0.247363\pi$
$179$			44935.8i			1.40245i	−0.712941	+	0.701224i	$0.752637\pi$
$180$	9706.03	−	7416.73i	0.299569	−	0.228911i
$181$	56780.7			1.73318			0.866590	−	0.499021i	$-0.166307\pi$
$181$	56780.7			1.73318			0.866590	+	0.499021i	$0.166307\pi$
$182$	2280.24	+	6739.64i	0.0688396	+	0.203467i
$183$		−	4301.48i		−	0.128445i
$184$	−5857.87	−	3939.72i	−0.173023	−	0.116367i
$185$	−127374.			−3.72168
$186$	−19917.6	+	6738.79i	−0.575721	+	0.194785i
$187$			13307.0i			0.380537i
$188$	−28700.7	−	37559.7i	−0.812039	−	1.06269i
$189$	−41610.0			−1.16486
$190$	20724.2	+	61254.0i	0.574079	+	1.69679i
$191$			49264.7i			1.35042i	0.737625	+	0.675211i	$0.235947\pi$
$191$			49264.7i			1.35042i	−0.737625	+	0.675211i	$0.764053\pi$
$192$	−30586.3	+	12453.5i	−0.829706	+	0.337824i
$193$	14046.5			0.377098			0.188549	−	0.982064i	$-0.439621\pi$
$193$	14046.5			0.377098			0.188549	+	0.982064i	$0.439621\pi$
$194$	16767.8	−	5673.09i	0.445525	−	0.150736i
$195$		−	12865.5i		−	0.338343i
$196$	−5467.67	+	4178.04i	−0.142328	+	0.108758i
$197$	19636.7			0.505983			0.252991	−	0.967469i	$-0.418586\pi$
$197$	19636.7			0.505983			0.252991	+	0.967469i	$0.418586\pi$
$198$	−3267.80	−	9658.55i	−0.0833538	−	0.246366i
$199$		−	23070.4i		−	0.582572i	−0.956636	−	0.291286i	$-0.905917\pi$
$199$		−	23070.4i		−	0.582572i	0.956636	−	0.291286i	$-0.0940831\pi$
$200$	−59055.0	+	87807.3i	−1.47637	+	2.19518i
$201$	30357.8			0.751412
$202$	40774.7	−	13795.4i	0.999282	−	0.338090i
$203$		−	17206.3i		−	0.417538i
$204$	−6539.82	−	8558.45i	−0.157147	−	0.205653i
$205$	−99652.8			−2.37128
$206$	−9173.63	−	27114.2i	−0.216176	−	0.638944i
$207$			1764.25i			0.0411738i
$208$	2248.23	−	8257.47i	0.0519653	−	0.190862i
$209$	53976.9			1.23571
$210$	77587.8	−	26250.5i	1.75936	−	0.595250i
$211$			57411.2i			1.28953i	0.764381	+	0.644765i	$0.223045\pi$
$211$			57411.2i			1.28953i	−0.764381	+	0.644765i	$0.776955\pi$
$212$	28363.3	−	21673.4i	0.631081	−	0.482231i
$213$	−11010.2			−0.242681
$214$	1591.05	+	4702.62i	0.0347422	+	0.102686i
$215$		−	86631.4i		−	1.87412i
$216$	41530.8	+	27931.6i	0.890148	+	0.598671i
$217$	34690.7			0.736704
$218$	41932.0	−	14187.0i	0.882333	−	0.298522i
$219$			16716.1i			0.348535i
$220$	73902.5	+	96713.8i	1.52691	+	1.99822i
$221$	2791.25			0.0571498
$222$	−27581.1	−	81520.5i	−0.559635	−	1.65410i
$223$		−	32704.9i		−	0.657663i	−0.944389	−	0.328831i	$-0.893345\pi$
$223$		−	32704.9i		−	0.657663i	0.944389	−	0.328831i	$-0.106655\pi$
$224$	54385.4	−	3290.01i	1.08389	−	0.0655694i
$225$	26445.5			0.522381
$226$	−27228.3	+	9212.22i	−0.533093	+	0.180363i
$227$		−	27325.4i		−	0.530291i	−0.964208	−	0.265146i	$-0.914580\pi$
$227$		−	27325.4i		−	0.530291i	0.964208	−	0.265146i	$-0.0854200\pi$
$228$	−34715.4	+	26527.3i	−0.667810	+	0.510298i
$229$	−3463.88			−0.0660529			−0.0330264	−	0.999454i	$-0.510515\pi$
$229$	−3463.88			−0.0660529			−0.0330264	+	0.999454i	$0.510515\pi$
$230$	−6749.61	−	19949.6i	−0.127592	−	0.377119i
$231$		−	68370.3i		−	1.28128i
$232$	−11550.1	+	17173.6i	−0.214590	+	0.319069i
$233$	21643.1			0.398665			0.199332	−	0.979932i	$-0.436123\pi$
$233$	21643.1			0.398665			0.199332	+	0.979932i	$0.436123\pi$
$234$	−2025.96	+	685.448i	−0.0369998	+	0.0125182i
$235$		−	141021.i		−	2.55357i
$236$	41942.1	+	54888.3i	0.753054	+	0.985497i
$237$	84651.3			1.50708
$238$	5695.22	+	16833.2i	0.100544	+	0.297175i
$239$			41382.7i			0.724474i	0.932086	+	0.362237i	$0.117987\pi$
$239$			41382.7i			0.724474i	−0.932086	+	0.362237i	$0.882013\pi$
$240$	−95061.3	−	25882.0i	−1.65037	−	0.449340i
$241$	42308.9			0.728446			0.364223	−	0.931312i	$-0.381335\pi$
$241$	42308.9			0.728446			0.364223	+	0.931312i	$0.381335\pi$
$242$	40765.7	−	13792.4i	0.696088	−	0.235510i
$243$		−	22953.6i		−	0.388722i
$244$	6782.64	−	5182.86i	0.113925	−	0.0870542i
$245$	−20528.8			−0.342004
$246$	−21578.4	−	63778.5i	−0.356573	−	1.05391i
$247$		−	11322.1i		−	0.185581i
$248$	−34624.6	−	23286.8i	−0.562965	−	0.378623i
$249$	228.277			0.00368182
$250$	−186000.	+	62929.8i	−2.97599	+	1.00688i
$251$		−	9017.01i		−	0.143125i	−0.997436	−	0.0715624i	$-0.977201\pi$
$251$		−	9017.01i		−	0.143125i	0.997436	−	0.0715624i	$-0.0227985\pi$
$252$	−8267.45	−	10819.3i	−0.130188	−	0.170373i
$253$	−17579.6			−0.274642
$254$	−38580.1	−	114030.i	−0.597993	−	1.76747i
$255$		−	32133.4i		−	0.494169i
$256$	−56490.3	−	33223.6i	−0.861974	−	0.506952i
$257$	34980.9			0.529621			0.264811	−	0.964300i	$-0.414691\pi$
$257$	34980.9			0.529621			0.264811	+	0.964300i	$0.414691\pi$
$258$	55444.7	−	18758.8i	0.832953	−	0.281815i
$259$			141985.i			2.11662i
$260$	20286.5	−	15501.6i	0.300096	−	0.229314i
$261$	5172.28			0.0759279
$262$	−25821.9	−	76320.9i	−0.376171	−	1.11184i
$263$		−	17659.5i		−	0.255310i	−0.991819	−	0.127655i	$-0.959255\pi$
$263$		−	17659.5i		−	0.255310i	0.991819	−	0.127655i	$-0.0407450\pi$
$264$	−45895.0	+	68240.0i	−0.658502	+	0.979110i
$265$	106492.			1.51644
$266$	68280.0	−	23101.4i	0.965007	−	0.326494i
$267$		−	48050.8i		−	0.674028i
$268$	36578.1	+	47868.6i	0.509274	+	0.666470i
$269$	36997.7			0.511293			0.255646	−	0.966770i	$-0.417712\pi$
$269$	36997.7			0.511293			0.255646	+	0.966770i	$0.417712\pi$
$270$	47853.0	+	141438.i	0.656419	+	1.94016i
$271$		−	71704.4i		−	0.976354i	−0.872745	−	0.488177i	$-0.837662\pi$
$271$		−	71704.4i		−	0.976354i	0.872745	−	0.488177i	$-0.162338\pi$
$272$	5615.26	−	20624.1i	0.0758982	−	0.278765i
$273$	−14341.2			−0.192425
$274$	−59775.8	+	20224.1i	−0.796204	+	0.269382i
$275$			263511.i			3.48444i
$276$	11306.4	−	8639.59i	0.148424	−	0.113416i
$277$	−101568.			−1.32373			−0.661864	−	0.749624i	$-0.730234\pi$
$277$	−101568.			−1.32373			−0.661864	+	0.749624i	$0.730234\pi$
$278$	828.300	+	2448.18i	0.0107176	+	0.0316777i
$279$			10428.1i			0.133967i
$280$	134878.	+	90712.3i	1.72038	+	1.15705i
$281$	−107572.			−1.36234			−0.681171	−	0.732125i	$-0.738529\pi$
$281$	−107572.			−1.36234			−0.681171	+	0.732125i	$0.738529\pi$
$282$	90254.3	−	30536.0i	1.13493	−	0.383985i
$283$			52709.5i			0.658136i	0.944306	+	0.329068i	$0.106735\pi$
$283$			52709.5i			0.658136i	−0.944306	+	0.329068i	$0.893265\pi$
$284$	−13266.2	−	17361.0i	−0.164478	−	0.215248i
$285$	−130342.			−1.60470
$286$	−6830.01	−	20187.3i	−0.0835006	−	0.246800i
$287$			111083.i			1.34861i
$288$	988.987	+	16348.4i	0.0119236	+	0.197102i
$289$	−76549.5			−0.916530
$290$	−58486.4	+	19787.9i	−0.695439	+	0.235290i
$291$			35680.0i			0.421346i
$292$	−26358.1	+	20141.2i	−0.309135	+	0.236221i
$293$	−23189.8			−0.270123			−0.135062	−	0.990837i	$-0.543123\pi$
$293$	−23189.8			−0.270123			−0.135062	+	0.990837i	$0.543123\pi$
$294$	−4445.21	−	13138.6i	−0.0514277	−	0.152003i
$295$			206082.i			2.36808i
$296$	95310.2	−	141714.i	1.08782	−	1.61745i
$297$	124635.			1.41295
$298$	121851.	−	41226.1i	1.37213	−	0.464237i
$299$			3687.46i			0.0412462i
$300$	−129504.	−	169478.i	−1.43894	−	1.88309i
$301$	−96568.3			−1.06586
$302$	43213.7	+	127725.i	0.473813	+	1.40044i
$303$			86764.1i			0.945050i
$304$	−83657.3	−	22777.0i	−0.905225	−	0.246462i
$305$	25465.9			0.273754
$306$	−5060.11	+	1712.00i	−0.0540402	+	0.0182836i
$307$		−	45546.2i		−	0.483254i	−0.970369	−	0.241627i	$-0.922319\pi$
$307$		−	45546.2i		−	0.483254i	0.970369	−	0.241627i	$-0.0776810\pi$
$308$	107807.	−	82379.3i	1.13644	−	0.868394i
$309$	57696.1			0.604268
$310$	−39895.5	−	117918.i	−0.415145	−	1.22703i
$311$		−	101998.i		−	1.05456i	−0.849691	−	0.527280i	$-0.823212\pi$
$311$		−	101998.i		−	1.05456i	0.849691	−	0.527280i	$-0.176788\pi$
$312$	14313.9	+	9626.85i	0.147045	+	0.0988951i
$313$	−75462.9			−0.770273			−0.385137	−	0.922860i	$-0.625846\pi$
$313$	−75462.9			−0.770273			−0.385137	+	0.922860i	$0.625846\pi$
$314$	−140817.	+	47643.1i	−1.42822	+	0.483215i
$315$		−	40622.1i		−	0.409394i
$316$	101996.	+	133479.i	1.02143	+	1.33672i
$317$	12644.8			0.125833			0.0629165	−	0.998019i	$-0.479960\pi$
$317$	12644.8			0.125833			0.0629165	+	0.998019i	$0.479960\pi$
$318$	23059.3	+	68155.7i	0.228030	+	0.673981i
$319$			51538.2i			0.506463i
$320$	−73728.3	−	181079.i	−0.720003	−	1.76835i
$321$	−10006.7			−0.0971135
$322$	−22237.9	+	7523.81i	−0.214478	+	0.0725648i
$323$		−	28278.5i		−	0.271051i
$324$	−63688.5	+	48666.7i	−0.606696	+	0.463598i
$325$	55273.6			0.523300
$326$	−12843.2	−	37960.2i	−0.120847	−	0.357185i
$327$			89226.6i			0.834448i
$328$	74567.0	−	110872.i	0.693105	−	1.03056i
$329$	−157196.			−1.45228
$330$	−232399.	+	78628.2i	−2.13406	+	0.722022i
$331$			42516.4i			0.388062i	0.980995	+	0.194031i	$0.0621562\pi$
$331$			42516.4i			0.388062i	−0.980995	+	0.194031i	$0.937844\pi$
$332$	275.051	+	359.950i	0.00249538	+	0.00326562i
$333$	−42681.1			−0.384899
$334$	22087.9	+	65284.5i	0.197998	+	0.585217i
$335$			179726.i			1.60148i
$336$	−28850.7	+	105965.i	−0.255551	+	0.938608i
$337$	−127491.			−1.12258			−0.561291	−	0.827618i	$-0.689695\pi$
$337$	−127491.			−1.12258			−0.561291	+	0.827618i	$0.689695\pi$
$338$	103984.	−	35181.0i	0.910188	−	0.307947i
$339$		−	57938.7i		−	0.504162i
$340$	50668.3	−	38717.5i	0.438307	−	0.334926i
$341$	−103909.			−0.893602
$342$	6944.35	+	20525.2i	0.0593717	+	0.175483i
$343$		−	104869.i		−	0.891368i
$344$	96384.4	+	64823.5i	0.814497	+	0.547792i
$345$	42450.6			0.356653
$346$	105618.	−	35734.2i	0.882241	−	0.298491i
$347$		−	33075.9i		−	0.274697i	−0.990523	−	0.137348i	$-0.956142\pi$
$347$		−	33075.9i		−	0.274697i	0.990523	−	0.137348i	$-0.0438580\pi$
$348$	−25328.8	−	33146.9i	−0.209149	−	0.273706i
$349$	136029.			1.11681			0.558405	−	0.829568i	$-0.311413\pi$
$349$	136029.			1.11681			0.558405	+	0.829568i	$0.311413\pi$
$350$	112779.	+	333338.i	0.920646	+	2.72112i
$351$		−	26143.1i		−	0.212199i
$352$	−162901.	+	9854.56i	−1.31473	+	0.0795339i
$353$	10204.6			0.0818929			0.0409465	−	0.999161i	$-0.486963\pi$
$353$	10204.6			0.0818929			0.0409465	+	0.999161i	$0.486963\pi$
$354$	−131894.	+	44624.1i	−1.05249	+	0.356092i
$355$		−	65183.3i		−	0.517225i
$356$	75767.1	−	57896.4i	0.597834	−	0.456827i
$357$	−35819.1			−0.281047
$358$	−57605.4	−	170262.i	−0.449466	−	1.32847i
$359$		−	28543.1i		−	0.221469i	−0.993850	−	0.110734i	$-0.964680\pi$
$359$		−	28543.1i		−	0.221469i	0.993850	−	0.110734i	$-0.0353203\pi$
$360$	−27268.4	+	40544.7i	−0.210405	+	0.312845i
$361$	15615.6			0.119824
$362$	−215143.	+	72789.9i	−1.64176	+	0.555461i
$363$			86744.9i			0.658311i
$364$	−17279.7	−	22613.4i	−0.130417	−	0.170673i
$365$	−98963.6			−0.742831
$366$	5514.27	+	16298.4i	0.0411648	+	0.121670i
$367$		−	166509.i		−	1.23625i	−0.786080	−	0.618125i	$-0.787893\pi$
$367$		−	166509.i		−	1.23625i	0.786080	−	0.618125i	$-0.212107\pi$
$368$	27246.0	+	7418.18i	0.201191	+	0.0547774i
$369$	−33392.0			−0.245239
$370$	482623.	−	163287.i	3.52537	−	1.19275i
$371$		−	118707.i		−	0.862440i
$372$	66829.4	−	51066.7i	0.482927	−	0.369022i
$373$	236231.			1.69793			0.848965	−	0.528448i	$-0.177226\pi$
$373$	236231.			1.69793			0.848965	+	0.528448i	$0.177226\pi$
$374$	−17058.9	−	50420.4i	−0.121957	−	0.360465i
$375$		−	395787.i		−	2.81448i
$376$	156897.	+	105521.i	1.10978	+	0.746388i
$377$	10810.5			0.0760615
$378$	157661.	−	53341.9i	1.10342	−	0.373323i
$379$			49309.4i			0.343282i	0.985160	+	0.171641i	$0.0549069\pi$
$379$			49309.4i			0.343282i	−0.985160	+	0.171641i	$0.945093\pi$
$380$	−157049.	−	205525.i	−1.08760	−	1.42330i
$381$	242643.			1.67155
$382$	−63154.8	−	186665.i	−0.432792	−	1.27919i
$383$			34149.5i			0.232802i	0.993202	+	0.116401i	$0.0371358\pi$
$383$			34149.5i			0.232802i	−0.993202	+	0.116401i	$0.962864\pi$
$384$	99927.1	−	86396.6i	0.677674	−	0.585915i
$385$	404770.			2.73078
$386$	−53222.5	+	18006.9i	−0.357208	+	0.120855i
$387$		−	29028.7i		−	0.193823i
$388$	−56260.7	+	42990.8i	−0.373716	+	0.285570i
$389$	−169597.			−1.12078			−0.560389	−	0.828229i	$-0.689348\pi$
$389$	−169597.			−1.12078			−0.560389	+	0.828229i	$0.689348\pi$
$390$	16492.9	+	48747.6i	0.108435	+	0.320497i
$391$			9209.92i			0.0602424i
$392$	15361.0	−	22839.9i	0.0999650	−	0.148635i
$393$	162402.			1.05150
$394$	−74403.6	+	25173.2i	−0.479294	+	0.162161i
$395$			501158.i			3.21204i
$396$	24763.5	+	32407.2i	0.157914	+	0.206657i
$397$	197592.			1.25368			0.626842	−	0.779146i	$-0.284347\pi$
$397$	197592.			1.25368			0.626842	+	0.779146i	$0.284347\pi$
$398$	29575.1	+	87414.1i	0.186707	+	0.551843i
$399$			145292.i			0.912635i
$400$	111196.	−	408408.i	0.694973	−	2.55255i
$401$	−1712.54			−0.0106500			−0.00532502	−	0.999986i	$-0.501695\pi$
$401$	−1712.54			−0.0106500			−0.00532502	+	0.999986i	$0.501695\pi$
$402$	−115026.	+	38917.1i	−0.711777	+	0.240818i
$403$			21795.7i			0.134203i
$404$	−136811.	+	104542.i	−0.838220	+	0.640514i
$405$	−239123.			−1.45785
$406$	22057.6	+	65195.0i	0.133816	+	0.395514i
$407$		−	425287.i		−	2.56740i
$408$	35750.9	+	24044.4i	0.214767	+	0.144442i
$409$	−216801.			−1.29603			−0.648015	−	0.761628i	$-0.724400\pi$
$409$	−216801.			−1.29603			−0.648015	+	0.761628i	$0.724400\pi$
$410$	377586.	−	127750.i	2.24620	−	0.759963i
$411$		−	127196.i		−	0.752993i
$412$	69518.0	+	90976.0i	0.409546	+	0.535960i
$413$	229720.			1.34679
$414$	−2261.68	−	6684.78i	−0.0131957	−	0.0390020i
$415$			1351.46i			0.00784706i
$416$	2067.07	+	34169.8i	0.0119445	+	0.197449i
$417$	−5209.46			−0.0299585
$418$	−204519.	+	69195.6i	−1.17053	+	0.396028i
$419$			238060.i			1.35600i	0.735063	+	0.677999i	$0.237153\pi$
$419$			238060.i			1.35600i	−0.735063	+	0.677999i	$0.762847\pi$
$420$	−260329.	+	198927.i	−1.47579	+	1.12770i
$421$	−299217.			−1.68819			−0.844097	−	0.536190i	$-0.819863\pi$
$421$	−299217.			−1.68819			−0.844097	+	0.536190i	$0.819863\pi$
$422$	−73598.1	−	217532.i	−0.413278	−	1.22151i
$423$		−	47253.7i		−	0.264092i
$424$	−79684.7	+	118481.i	−0.443244	+	0.659048i
$425$	138053.			0.764309
$426$	41717.7	−	14114.5i	0.229880	−	0.0777760i
$427$		−	28387.0i		−	0.155691i
$428$	−12057.0	−	15778.7i	−0.0658193	−	0.0861356i
$429$	42956.3			0.233406
$430$	111057.	+	328247.i	0.600632	+	1.77527i
$431$		−	264960.i		−	1.42635i	−0.700986	−	0.713175i	$-0.747257\pi$
$431$		−	264960.i		−	1.42635i	0.700986	−	0.713175i	$-0.252743\pi$
$432$	−193167.	−	52592.9i	−1.03506	−	0.281812i
$433$	−317940.			−1.69578			−0.847889	−	0.530173i	$-0.822127\pi$
$433$	−317940.			−1.69578			−0.847889	+	0.530173i	$0.822127\pi$
$434$	−131443.	+	44471.6i	−0.697845	+	0.236104i
$435$		−	124453.i		−	0.657697i
$436$	−140694.	+	107509.i	−0.740120	+	0.565552i
$437$	37358.0			0.195623
$438$	−21429.1	−	63337.4i	−0.111701	−	0.330150i
$439$			261205.i			1.35535i	0.735361	+	0.677676i	$0.237013\pi$
$439$			261205.i			1.35535i	−0.735361	+	0.677676i	$0.762987\pi$
$440$	−403999.	−	271711.i	−2.08677	−	1.40346i
$441$	−6878.85			−0.0353703
$442$	−10576.1	+	3578.24i	−0.0541353	+	0.0183158i
$443$			219070.i			1.11629i	0.829745	+	0.558143i	$0.188486\pi$
$443$			219070.i			1.11629i	−0.829745	+	0.558143i	$0.811514\pi$
$444$	209010.	+	273525.i	1.06023	+	1.38749i
$445$	284474.			1.43655
$446$	41926.0	+	123919.i	0.210772	+	0.622973i
$447$			259285.i			1.29766i
$448$	−201849.	+	82185.1i	−1.00571	+	0.409484i
$449$	82842.7			0.410924			0.205462	−	0.978665i	$-0.434130\pi$
$449$	82842.7			0.410924			0.205462	+	0.978665i	$0.434130\pi$
$450$	−100202.	+	33901.8i	−0.494827	+	0.167416i
$451$		−	332728.i		−	1.63582i
$452$	91358.6	−	69810.4i	0.447170	−	0.341699i
$453$	−271785.			−1.32443
$454$	35029.7	+	103536.i	0.169951	+	0.502320i
$455$		−	84903.9i		−	0.410114i
$456$	97530.6	−	145016.i	0.469041	−	0.697405i
$457$	−347792.			−1.66528			−0.832640	−	0.553815i	$-0.813172\pi$
$457$	−347792.			−1.66528			−0.832640	+	0.553815i	$0.813172\pi$
$458$	13124.7	−	4440.51i	0.0625688	−	0.0211691i
$459$		−	65296.0i		−	0.309928i
$460$	51148.7	+	66936.7i	0.241724	+	0.316336i
$461$	−7736.17			−0.0364019			−0.0182010	−	0.999834i	$-0.505794\pi$
$461$	−7736.17			−0.0364019			−0.0182010	+	0.999834i	$0.505794\pi$
$462$	87647.1	+	259056.i	0.410633	+	1.21369i
$463$		−	281154.i		−	1.31154i	−0.754960	−	0.655771i	$-0.772344\pi$
$463$		−	281154.i		−	1.31154i	0.754960	−	0.655771i	$-0.227656\pi$
$464$	21747.9	−	79877.5i	0.101014	−	0.371012i
$465$	250916.			1.16044
$466$	−82006.0	+	27745.3i	−0.377636	+	0.127767i
$467$			227383.i			1.04262i	0.853368	+	0.521309i	$0.174556\pi$
$467$			227383.i			1.04262i	−0.853368	+	0.521309i	$0.825444\pi$
$468$	6797.67	−	5194.34i	0.0310362	−	0.0237159i
$469$	200341.			0.910804
$470$	180781.	+	534330.i	0.818385	+	2.41888i
$471$		−	299643.i		−	1.35071i
$472$	−229283.	−	154205.i	−1.02917	−	0.692171i
$473$	289251.			1.29286
$474$	−320745.	+	108519.i	−1.42759	+	0.483000i
$475$		−	559983.i		−	2.48192i
$476$	−43158.5	−	56480.1i	−0.190481	−	0.249277i
$477$	35683.8			0.156832
$478$	−53050.4	−	156799.i	−0.232184	−	0.686260i
$479$		−	208710.i		−	0.909644i	−0.890582	−	0.454822i	$-0.849703\pi$
$479$		−	208710.i		−	0.909644i	0.890582	−	0.454822i	$-0.150297\pi$
$480$	393368.	−	23796.5i	1.70732	−	0.103283i
$481$	−89207.4			−0.385576
$482$	−160309.	+	54237.8i	−0.690023	+	0.233457i
$483$		−	47319.8i		−	0.202838i
$484$	−136781.	+	104519.i	−0.583894	+	0.446174i
$485$	−211235.			−0.898013
$486$	29425.3	+	86971.5i	0.124580	+	0.368218i
$487$		−	377431.i		−	1.59140i	−0.605689	−	0.795701i	$-0.707102\pi$
$487$		−	377431.i		−	1.59140i	0.605689	−	0.795701i	$-0.292898\pi$
$488$	−19055.3	+	28332.9i	−0.0800161	+	0.118974i
$489$	80775.0			0.337800
$490$	77783.8	−	26316.8i	0.323964	−	0.109608i
$491$			252350.i			1.04674i	0.852104	+	0.523372i	$0.175326\pi$
$491$			252350.i			1.04674i	−0.852104	+	0.523372i	$0.824674\pi$
$492$	163521.	+	213995.i	0.675529	+	0.884044i
$493$	27000.8			0.111092
$494$	14514.3	+	42899.6i	0.0594762	+	0.175792i
$495$			121675.i			0.496583i
$496$	161045.	+	43847.2i	0.654614	+	0.178229i
$497$	−72660.0			−0.294159
$498$	−864.943	+	292.639i	−0.00348762	+	0.00117998i
$499$			84777.8i			0.340472i	0.985403	+	0.170236i	$0.0544530\pi$
$499$			84777.8i			0.340472i	−0.985403	+	0.170236i	$0.945547\pi$
$500$	624082.	−	476884.i	2.49633	−	1.90753i
$501$	−138918.			−0.553457
$502$	11559.3	+	34165.6i	0.0458696	+	0.135575i
$503$			134806.i			0.532811i	0.963861	+	0.266405i	$0.0858360\pi$
$503$			134806.i			0.532811i	−0.963861	+	0.266405i	$0.914164\pi$
$504$	45195.3	+	30396.2i	0.177923	+	0.119663i
$505$	−513667.			−2.01418
$506$	66609.2	−	22536.1i	0.260155	−	0.0880191i
$507$			221266.i			0.860791i
$508$	292361.	+	382604.i	1.13290	+	1.48259i
$509$	427066.			1.64839			0.824194	−	0.566308i	$-0.191629\pi$
$509$	427066.			1.64839			0.824194	+	0.566308i	$0.191629\pi$
$510$	41193.3	+	121754.i	0.158375	+	0.468103i
$511$			110315.i			0.422467i
$512$	256633.	+	53467.1i	0.978979	+	0.203961i
$513$	−264859.			−1.00642
$514$	−132543.	+	44843.7i	−0.501685	+	0.169737i
$515$			341576.i			1.28787i
$516$	−186033.	+	142154.i	−0.698699	+	0.533901i
$517$	470850.			1.76158
$518$	−182017.	−	537982.i	−0.678347	−	2.00497i
$519$			224744.i			0.834361i
$520$	−56993.5	+	84742.2i	−0.210775	+	0.313396i
$521$	10989.0			0.0404839			0.0202419	−	0.999795i	$-0.493556\pi$
$521$	10989.0			0.0404839			0.0202419	+	0.999795i	$0.493556\pi$
$522$	−19597.8	+	6630.59i	−0.0719229	+	0.0243339i
$523$			177050.i			0.647281i	0.946180	+	0.323640i	$0.104907\pi$
$523$			177050.i			0.647281i	−0.946180	+	0.323640i	$0.895093\pi$
$524$	195679.	+	256079.i	0.712658	+	0.932633i
$525$	−709306.			−2.57345
$526$	22638.6	+	66912.1i	0.0818233	+	0.241843i
$527$			54437.8i			0.196011i
$528$	86416.5	−	317397.i	0.309977	−	1.13851i
$529$	−12167.0			−0.0434783
$530$	−403500.	+	136517.i	−1.43645	+	0.486000i
$531$			69054.7i			0.244909i
$532$	−229099.	+	175063.i	−0.809469	+	0.618544i
$533$	−69792.4			−0.245671
$534$	61598.6	+	182065.i	0.216017	+	0.638475i
$535$		−	59242.2i		−	0.206978i
$536$	−199960.	−	134483.i	−0.696006	−	0.468101i
$537$	362300.			1.25638
$538$	−140185.	+	47429.1i	−0.484324	+	0.163863i
$539$		−	68542.9i		−	0.235931i
$540$	−362631.	−	474564.i	−1.24359	−	1.62745i
$541$	−132030.			−0.451107			−0.225553	−	0.974231i	$-0.572419\pi$
$541$	−132030.			−0.451107			−0.225553	+	0.974231i	$0.572419\pi$
$542$	91921.3	+	271689.i	0.312908	+	0.924854i
$543$		−	457800.i		−	1.55266i
$544$	5162.80	+	85343.6i	0.0174457	+	0.288385i
$545$	−528246.			−1.77846
$546$	54339.1	−	18384.7i	0.182275	−	0.0616696i
$547$			324514.i			1.08457i	0.840193	+	0.542287i	$0.182441\pi$
$547$			324514.i			1.08457i	−0.840193	+	0.542287i	$0.817559\pi$
$548$	200565.	−	153259.i	0.667873	−	0.510346i
$549$	8533.21			0.0283118
$550$	−337807.	−	998446.i	−1.11672	−	3.30065i
$551$		−	109523.i		−	0.360746i
$552$	−31764.4	+	47229.7i	−0.104247	+	0.155002i
$553$	558643.			1.82677
$554$	384844.	−	130205.i	1.25391	−	0.424237i
$555$			1.02697e6i			3.33405i
$556$	−6276.88	−	8214.35i	−0.0203046	−	0.0265720i
$557$	167844.			0.540998			0.270499	−	0.962720i	$-0.412811\pi$
$557$	167844.			0.540998			0.270499	+	0.962720i	$0.412811\pi$
$558$	−13368.3	−	39512.3i	−0.0429347	−	0.126901i
$559$		−	60672.8i		−	0.194165i
$560$	−627342.	−	170804.i	−2.00045	−	0.544655i
$561$	107289.			0.340902
$562$	407591.	−	137901.i	1.29048	−	0.436613i
$563$			1052.70i			0.00332115i	0.999999	+	0.00166057i	$0.000528577\pi$
$563$			1052.70i			0.00332115i	−0.999999	+	0.00166057i	$0.999471\pi$
$564$	−302829.	+	231402.i	−0.952005	+	0.727461i
$565$	343013.			1.07452
$566$	−67570.8	−	199717.i	−0.210924	−	0.623422i
$567$			266552.i			0.829116i
$568$	72521.6	+	48774.6i	0.224787	+	0.151181i
$569$	−298507.			−0.921998			−0.460999	−	0.887401i	$-0.652509\pi$
$569$	−298507.			−0.921998			−0.460999	+	0.887401i	$0.652509\pi$
$570$	493867.	−	167091.i	1.52006	−	0.514285i
$571$		−	471812.i		−	1.44709i	−0.690275	−	0.723547i	$-0.742510\pi$
$571$		−	471812.i		−	1.44709i	0.690275	−	0.723547i	$-0.257490\pi$
$572$	51758.0	+	67734.0i	0.158192	+	0.207021i
$573$	397202.			1.20977
$574$	−142403.	−	420896.i	−0.432211	−	1.27747i
$575$			182379.i			0.551618i
$576$	−24705.1	−	60676.6i	−0.0744633	−	0.182884i
$577$	−199903.			−0.600436			−0.300218	−	0.953871i	$-0.597060\pi$
$577$	−199903.			−0.600436			−0.300218	+	0.953871i	$0.597060\pi$
$578$	290047.	−	98132.4i	0.868185	−	0.293736i
$579$		−	113252.i		−	0.337822i
$580$	196239.	−	149953.i	0.583350	−	0.445758i
$581$	1506.48			0.00446283
$582$	−45739.9	−	135192.i	−0.135036	−	0.399121i
$583$			355564.i			1.04612i
$584$	74051.3	−	110105.i	0.217124	−	0.322835i
$585$	25522.4			0.0745778
$586$	87866.4	−	29728.1i	0.255875	−	0.0865709i
$587$		−	328527.i		−	0.953443i	−0.879054	−	0.476721i	$-0.841825\pi$
$587$		−	328527.i		−	0.953443i	0.879054	−	0.476721i	$-0.158175\pi$
$588$	33685.9	+	44083.6i	0.0974301	+	0.127504i
$589$	220815.			0.636499
$590$	−264187.	−	780848.i	−0.758939	−	2.24317i
$591$		−	158323.i		−	0.453282i
$592$	−179461.	+	659140.i	−0.512068	+	1.88076i
$593$	−18298.9			−0.0520374			−0.0260187	−	0.999661i	$-0.508283\pi$
$593$	−18298.9			−0.0520374			−0.0260187	+	0.999661i	$0.508283\pi$
$594$	−472242.	+	159775.i	−1.33842	+	0.452830i
$595$		−	212059.i		−	0.598994i
$596$	−408844.	+	312412.i	−1.15097	+	0.879499i
$597$	−186008.			−0.521894
$598$	−4727.12	−	13971.8i	−0.0132189	−	0.0390706i
$599$			98178.2i			0.273629i	0.990597	+	0.136814i	$0.0436864\pi$
$599$			98178.2i			0.273629i	−0.990597	+	0.136814i	$0.956314\pi$
$600$	707955.	+	476137.i	1.96654	+	1.32260i
$601$	74675.7			0.206743			0.103371	−	0.994643i	$-0.467037\pi$
$601$	74675.7			0.206743			0.103371	+	0.994643i	$0.467037\pi$
$602$	365898.	−	123795.i	1.00964	−	0.341595i
$603$			60223.3i			0.165626i
$604$	−327474.	−	428555.i	−0.897642	−	1.17472i
$605$	−513553.			−1.40306
$606$	−111227.	−	328750.i	−0.302876	−	0.895202i
$607$		−	513233.i		−	1.39296i	−0.717578	−	0.696478i	$-0.754749\pi$
$607$		−	513233.i		−	1.39296i	0.717578	−	0.696478i	$-0.245251\pi$
$608$	346177.	−	20941.8i	0.936465	−	0.0566508i
$609$	−138728.			−0.374049
$610$	−96490.7	+	32646.0i	−0.259314	+	0.0877345i
$611$		−	98764.7i		−	0.264557i
$612$	16978.1	−	12973.6i	0.0453301	−	0.0346383i
$613$	−286532.			−0.762520			−0.381260	−	0.924468i	$-0.624510\pi$
$613$	−286532.			−0.762520			−0.381260	+	0.924468i	$0.624510\pi$
$614$	58387.8	+	172575.i	0.154876	+	0.457763i
$615$			803461.i			2.12429i
$616$	−302877.	+	450339.i	−0.798187	+	1.18680i
$617$	−334406.			−0.878424			−0.439212	−	0.898383i	$-0.644742\pi$
$617$	−334406.			−0.878424			−0.439212	+	0.898383i	$0.644742\pi$
$618$	−218611.	+	73963.4i	−0.572394	+	0.193660i
$619$		−	622554.i		−	1.62478i	−0.583112	−	0.812392i	$-0.698165\pi$
$619$		−	622554.i		−	1.62478i	0.583112	−	0.812392i	$-0.301835\pi$
$620$	302329.	+	395648.i	0.786495	+	1.02926i
$621$	86260.9			0.223682
$622$	130756.	+	386472.i	0.337973	+	0.998936i
$623$		−	317104.i		−	0.817006i
$624$	−66576.7	−	18126.6i	−0.170983	−	0.0465529i
$625$	1.30978e6			3.35303
$626$	285930.	−	96739.5i	0.729644	−	0.246862i
$627$		−	435194.i		−	1.10700i
$628$	472482.	−	361040.i	1.19802	−	0.915454i
$629$	−222808.			−0.563156
$630$	52075.4	+	153918.i	0.131205	+	0.387799i
$631$			183455.i			0.460755i	0.973101	+	0.230378i	$0.0739962\pi$
$631$			183455.i			0.460755i	−0.973101	+	0.230378i	$0.926004\pi$
$632$	−557579.	−	375001.i	−1.39596	−	0.938854i
$633$	462883.			1.15522
$634$	−47911.5	+	16210.0i	−0.119196	+	0.0403279i
$635$			1.43651e6i			3.56256i
$636$	−174744.	−	228682.i	−0.432004	−	0.565350i
$637$	−14377.4			−0.0354326
$638$	−66069.2	−	195279.i	−0.162315	−	0.479748i
$639$		−	21841.8i		−	0.0534918i
$640$	511491.	+	591595.i	1.24876	+	1.44432i
$641$	610734.			1.48640			0.743201	−	0.669068i	$-0.233307\pi$
$641$	610734.			1.48640			0.743201	+	0.669068i	$0.233307\pi$
$642$	37915.4	−	12828.0i	0.0919910	−	0.0311236i
$643$		−	142502.i		−	0.344667i	−0.985039	−	0.172334i	$-0.944869\pi$
$643$		−	142502.i		−	0.344667i	0.985039	−	0.172334i	$-0.0551307\pi$
$644$	74614.5	−	57015.6i	0.179908	−	0.137474i
$645$	−698474.			−1.67892
$646$	36251.5	+	107148.i	0.0868683	+	0.256754i
$647$			57067.6i			0.136327i	0.997674	+	0.0681633i	$0.0217139\pi$
$647$			57067.6i			0.136327i	−0.997674	+	0.0681633i	$0.978286\pi$
$648$	178928.	−	266044.i	0.426117	−	0.633582i
$649$	−688082.			−1.63362
$650$	−209432.	+	70857.8i	−0.495698	+	0.167711i
$651$		−	279697.i		−	0.659972i
$652$	97325.8	+	127367.i	0.228946	+	0.299614i
$653$	85463.1			0.200425			0.100213	−	0.994966i	$-0.468048\pi$
$653$	85463.1			0.200425			0.100213	+	0.994966i	$0.468048\pi$
$654$	−114384.	−	338081.i	−0.267429	−	0.790433i
$655$			961467.i			2.24105i
$656$	−140404.	+	515685.i	−0.326265	+	1.19833i
$657$	−33161.1			−0.0768241
$658$	595619.	−	201517.i	1.37568	−	0.465437i
$659$		−	407272.i		−	0.937807i	−0.883250	−	0.468903i	$-0.844649\pi$
$659$		−	407272.i		−	0.937807i	0.883250	−	0.468903i	$-0.155351\pi$
$660$	779765.	−	595846.i	1.79009	−	1.36787i
$661$	156882.			0.359064			0.179532	−	0.983752i	$-0.442542\pi$
$661$	156882.			0.359064			0.179532	+	0.983752i	$0.442542\pi$
$662$	−54503.8	−	161095.i	−0.124369	−	0.367593i
$663$		−	22504.8i		−	0.0511973i
$664$	−1503.61	−	1011.25i	−0.00341034	−	0.00229363i
$665$	−860170.			−1.94510
$666$	161719.	−	54714.9i	0.364597	−	0.123355i
$667$			35670.1i			0.0801775i
$668$	−167383.	−	219048.i	−0.375109	−	0.490893i
$669$	−263687.			−0.589164
$670$	−230400.	−	680985.i	−0.513254	−	1.51701i
$671$			85027.5i			0.188849i
$672$	−26526.0	−	438488.i	−0.0587400	−	0.971000i
$673$	442095.			0.976080			0.488040	−	0.872821i	$-0.337712\pi$
$673$	442095.			0.976080			0.488040	+	0.872821i	$0.337712\pi$
$674$	483063.	−	163436.i	1.06337	−	0.359773i
$675$		−	1.29302e6i		−	2.83790i
$676$	−348895.	+	266603.i	−0.763486	+	0.583407i
$677$	263274.			0.574421			0.287210	−	0.957867i	$-0.407272\pi$
$677$	263274.			0.574421			0.287210	+	0.957867i	$0.407272\pi$
$678$	74274.4	+	219531.i	0.161577	+	0.477568i
$679$			235464.i			0.510723i
$680$	−142349.	+	211655.i	−0.307848	+	0.457732i
$681$	−220314.			−0.475058
$682$	393712.	−	133206.i	0.846467	−	0.286388i
$683$			345585.i			0.740821i	0.928868	+	0.370410i	$0.120783\pi$
$683$			345585.i			0.740821i	−0.928868	+	0.370410i	$0.879217\pi$
$684$	−52624.5	−	68867.9i	−0.112480	−	0.147199i
$685$	753037.			1.60485
$686$	134436.	+	397348.i	0.285672	+	0.844351i
$687$			27927.9i			0.0591731i
$688$	−448302.	−	122057.i	−0.947095	−	0.257862i
$689$	74582.3			0.157108
$690$	−160846.	+	54419.4i	−0.337840	+	0.114302i
$691$		−	232619.i		−	0.487179i	−0.969878	−	0.243589i	$-0.921675\pi$
$691$		−	232619.i		−	0.487179i	0.969878	−	0.243589i	$-0.0783249\pi$
$692$	−354380.	+	270795.i	−0.740043	+	0.565494i
$693$	135632.			0.282420
$694$	42401.6	+	125325.i	0.0880367	+	0.260207i
$695$		−	30841.4i		−	0.0638506i
$696$	138464.	+	93124.0i	0.285836	+	0.192240i
$697$	−174316.			−0.358816
$698$	−515414.	+	174382.i	−1.05790	+	0.357923i
$699$		−	174500.i		−	0.357142i
$700$	−854643.	−	1.11844e6i	−1.74417	−	2.28254i
$701$	479883.			0.976561			0.488281	−	0.872687i	$-0.337624\pi$
$701$	479883.			0.976561			0.488281	+	0.872687i	$0.337624\pi$
$702$	33514.1	+	99056.5i	0.0680069	+	0.201006i
$703$			903769.i			1.82872i
$704$	604600.	−	246169.i	1.21990	−	0.496693i
$705$	−1.13699e6			−2.28760
$706$	−38665.3	+	13081.8i	−0.0775733	+	0.0262456i
$707$			572586.i			1.14552i
$708$	442542.	−	338162.i	0.882852	−	0.674619i
$709$	111586.			0.221983			0.110991	−	0.993821i	$-0.464597\pi$
$709$	111586.			0.221983			0.110991	+	0.993821i	$0.464597\pi$
$710$	83561.5	+	246980.i	0.165764	+	0.489943i
$711$			167930.i			0.332192i
$712$	−212863.	+	316500.i	−0.419894	+	0.624329i
$713$	−71916.5			−0.141465
$714$	135719.	−	45918.3i	0.266223	−	0.0900718i
$715$			254313.i			0.497457i
$716$	436535.	+	571279.i	0.851516	+	1.11435i
$717$	333652.			0.649016
$718$	36590.8	+	108150.i	0.0709779	+	0.209787i
$719$		−	33918.8i		−	0.0656119i	−0.999462	−	0.0328059i	$-0.989556\pi$
$719$		−	33918.8i		−	0.0656119i	0.999462	−	0.0328059i	$-0.0104443\pi$
$720$	51344.2	−	188581.i	0.0990436	−	0.363775i
$721$	380756.			0.732448
$722$	−59167.7	+	20018.4i	−0.113504	+	0.0384021i
$723$		−	341120.i		−	0.652575i
$724$	721866.	−	551603.i	1.37714	−	1.05232i
$725$	534682.			1.01723
$726$	−111202.	−	328678.i	−0.210980	−	0.623587i
$727$			2235.91i			0.00423043i	0.999998	+	0.00211522i	$0.000673295\pi$
$727$			2235.91i			0.00423043i	−0.999998	+	0.00211522i	$0.999327\pi$
$728$	94462.4	+	63530.9i	0.178236	+	0.119873i
$729$	−590846.			−1.11178
$730$	374974.	−	126866.i	0.703649	−	0.238067i
$731$		−	151538.i		−	0.283588i
$732$	−41787.3	−	54685.7i	−0.0779870	−	0.102059i
$733$	−518923.			−0.965818			−0.482909	−	0.875671i	$-0.660420\pi$
$733$	−518923.			−0.965818			−0.482909	+	0.875671i	$0.660420\pi$
$734$	213456.	+	630906.i	0.396202	+	1.17104i
$735$			165515.i			0.306382i
$736$	−112745.	+	6820.45i	−0.208134	+	0.0125909i
$737$	−600083.			−1.10478
$738$	126523.	−	42806.8i	0.232304	−	0.0785959i
$739$		−	417443.i		−	0.764378i	−0.924084	−	0.382189i	$-0.875170\pi$
$739$		−	417443.i		−	0.764378i	0.924084	−	0.382189i	$-0.124830\pi$
$740$	−1.61934e6	+	1.23740e6i	−2.95716	+	2.25967i
$741$	−91285.6			−0.166252
$742$	152176.	+	449783.i	0.276401	+	0.816949i
$743$		−	190838.i		−	0.345690i	−0.984949	−	0.172845i	$-0.944704\pi$
$743$		−	190838.i		−	0.345690i	0.984949	−	0.172845i	$-0.0552960\pi$
$744$	−187752.	+	279164.i	−0.339187	+	0.504329i
$745$	−1.53504e6			−2.76570
$746$	−895084.	+	302836.i	−1.60837	+	0.544165i
$747$			452.852i			0.000811549i
$748$	129273.	+	169175.i	0.231049	+	0.302366i
$749$	−66037.4			−0.117714
$750$	507378.	+	1.49964e6i	0.902005	+	2.66603i
$751$		−	268214.i		−	0.475556i	−0.971319	−	0.237778i	$-0.923581\pi$
$751$		−	268214.i		−	0.475556i	0.971319	−	0.237778i	$-0.0764191\pi$
$752$	−729757.	−	198688.i	−1.29045	−	0.351347i
$753$	−72700.6			−0.128218
$754$	−40961.3	+	13858.6i	−0.0720495	+	0.0243767i
$755$		−	1.60904e6i		−	2.82276i
$756$	−528997.	+	404226.i	−0.925572	+	0.707262i
$757$	−516815.			−0.901868			−0.450934	−	0.892557i	$-0.648909\pi$
$757$	−516815.			−0.901868			−0.450934	+	0.892557i	$0.648909\pi$
$758$	−63212.0	−	186834.i	−0.110017	−	0.325175i
$759$			141737.i			0.246037i
$760$	858532.	+	577408.i	1.48638	+	0.999667i
$761$	498527.			0.860834			0.430417	−	0.902630i	$-0.358367\pi$
$761$	498527.			0.860834			0.430417	+	0.902630i	$0.358367\pi$
$762$	−919379.	+	311056.i	−1.58338	+	0.535709i
$763$			588837.i			1.01145i
$764$	478588.	+	626313.i	0.819928	+	1.07301i
$765$	63745.6			0.108925
$766$	−43777.9	−	129393.i	−0.0746100	−	0.220522i
$767$			144331.i			0.245340i
$768$	−267869.	+	455459.i	−0.454151	+	0.772195i
$769$	338826.			0.572959			0.286480	−	0.958086i	$-0.407515\pi$
$769$	338826.			0.572959			0.286480	+	0.958086i	$0.407515\pi$
$770$	−1.53368e6	+	518894.i	−2.58674	+	0.875180i
$771$		−	282037.i		−	0.474458i
$772$	178577.	−	136457.i	0.299634	−	0.228961i
$773$	−201809.			−0.337739			−0.168869	−	0.985638i	$-0.554012\pi$
$773$	−201809.			−0.337739			−0.168869	+	0.985638i	$0.554012\pi$
$774$	37213.3	+	109990.i	0.0621179	+	0.183600i
$775$			1.07800e6i			1.79480i
$776$	158060.	−	235016.i	0.262482	−	0.390278i
$777$	1.14477e6			1.89616
$778$	642606.	−	217415.i	1.06166	−	0.359195i
$779$			707074.i			1.16517i
$780$	−124984.	−	163562.i	−0.205430	−	0.268840i
$781$	217638.			0.356807
$782$	−11806.6	−	34896.5i	−0.0193069	−	0.0570648i
$783$		−	252892.i		−	0.412488i
$784$	−28923.6	+	106233.i	−0.0470565	+	0.172833i
$785$	1.77397e6			2.87877
$786$	−615345.	+	208191.i	−0.996033	+	0.336991i
$787$		−	998369.i		−	1.61191i	−0.591975	−	0.805956i	$-0.701652\pi$
$787$		−	998369.i		−	1.61191i	0.591975	−	0.805956i	$-0.298348\pi$
$788$	249645.	−	190763.i	0.402042	−	0.307215i
$789$	−142382.			−0.228718
$790$	−642459.	−	1.89890e6i	−1.02942	−	3.04261i
$791$		−	382358.i		−	0.611106i
$792$	−135373.	−	91045.7i	−0.215816	−	0.145147i
$793$	17835.2			0.0283617
$794$	−748678.	+	253302.i	−1.18756	+	0.401789i
$795$		−	858604.i		−	1.35850i
$796$	−224121.	−	293299.i	−0.353717	−	0.462898i
$797$	−237838.			−0.374425			−0.187212	−	0.982319i	$-0.559945\pi$
$797$	−237838.			−0.374425			−0.187212	+	0.982319i	$0.559945\pi$
$798$	−186257.	−	550515.i	−0.292488	−	0.864496i
$799$		−	246678.i		−	0.386400i
$800$	102236.	+	1.69001e6i	0.159744	+	2.64064i
$801$	95322.4			0.148570
$802$	6488.83	−	2195.38i	0.0100883	−	0.00341320i
$803$		−	330427.i		−	0.512441i
$804$	385945.	−	294915.i	0.597054	−	0.456230i
$805$	280146.			0.432307
$806$	−27941.0	−	82584.3i	−0.0430102	−	0.127124i
$807$		−	298297.i		−	0.458039i
$808$	384361.	−	571495.i	0.588730	−	0.875367i
$809$	520330.			0.795027			0.397513	−	0.917596i	$-0.369873\pi$
$809$	520330.			0.795027			0.397513	+	0.917596i	$0.369873\pi$
$810$	906041.	−	306544.i	1.38095	−	0.467221i
$811$			107019.i			0.162712i	0.996685	+	0.0813561i	$0.0259251\pi$
$811$			107019.i			0.162712i	−0.996685	+	0.0813561i	$0.974075\pi$
$812$	−167153.	−	218748.i	−0.253514	−	0.331766i
$813$	−578124.			−0.874661
$814$	545195.	+	1.61142e6i	0.822817	+	2.43197i
$815$			478210.i			0.719952i
$816$	−166284.	−	45273.6i	−0.249730	−	0.0679930i
$817$	−614682.			−0.920887
$818$	821462.	−	277928.i	1.22767	−	0.415360i
$819$		−	28449.9i		−	0.0424143i
$820$	−1.26691e6	+	968090.i	−1.88416	+	1.43975i
$821$	1.07705e6			1.59790			0.798950	−	0.601397i	$-0.205389\pi$
$821$	1.07705e6			1.59790			0.798950	+	0.601397i	$0.205389\pi$
$822$	163059.	+	481948.i	0.241324	+	0.713275i
$823$			48998.1i			0.0723402i	0.999346	+	0.0361701i	$0.0115158\pi$
$823$			48998.1i			0.0723402i	−0.999346	+	0.0361701i	$0.988484\pi$
$824$	−380031.	−	255591.i	−0.559712	−	0.376436i
$825$	2.12458e6			3.12152
$826$	−870414.	+	294490.i	−1.27575	+	0.431628i
$827$		−	675667.i		−	0.987920i	−0.869485	−	0.493960i	$-0.835549\pi$
$827$		−	675667.i		−	0.987920i	0.869485	−	0.493960i	$-0.164451\pi$
$828$	17139.1	+	22429.4i	0.0249992	+	0.0327157i
$829$	353332.			0.514131			0.257065	−	0.966394i	$-0.417244\pi$
$829$	353332.			0.514131			0.257065	+	0.966394i	$0.417244\pi$
$830$	−1732.50	−	5120.70i	−0.00251488	−	0.00743315i
$831$			818905.i			1.18585i
$832$	−51636.0	−	126820.i	−0.0745943	−	0.183206i
$833$	−35909.6			−0.0517512
$834$	19738.7	−	6678.26i	0.0283783	−	0.00960132i
$835$		−	822434.i		−	1.17958i
$836$	686221.	−	524366.i	0.981864	−	0.750277i
$837$	509869.			0.727793
$838$	−305181.	−	902014.i	−0.434580	−	1.28447i
$839$		−	803680.i		−	1.14172i	−0.821048	−	0.570860i	$-0.806610\pi$
$839$		−	803680.i		−	1.14172i	0.821048	−	0.570860i	$-0.193390\pi$
$840$	731377.	−	1.08747e6i	1.03653	−	1.54119i
$841$	−602707.			−0.852146
$842$	1.13374e6	−	383581.i	1.59915	−	0.541044i
$843$			867309.i			1.22045i
$844$	557728.	+	729881.i	0.782957	+	1.02463i
$845$	−1.30995e6			−1.83460
$846$	60576.8	+	179045.i	0.0846381	+	0.250162i
$847$			572460.i			0.797954i
$848$	150040.	−	551078.i	0.208648	−	0.766339i
$849$	424976.			0.589588
$850$	−523086.	+	176977.i	−0.723994	+	0.244951i
$851$		−	294345.i		−	0.406442i
$852$	−139975.	+	106960.i	−0.192828	+	0.147347i
$853$	−550338.			−0.756366			−0.378183	−	0.925731i	$-0.623451\pi$
$853$	−550338.			−0.756366			−0.378183	+	0.925731i	$0.623451\pi$
$854$	36390.6	+	107559.i	0.0498969	+	0.147479i
$855$		−	258570.i		−	0.353709i
$856$	65911.7	+	44329.0i	0.0899528	+	0.0604980i
$857$	−1.36973e6			−1.86498			−0.932492	−	0.361192i	$-0.882370\pi$
$857$	−1.36973e6			−1.86498			−0.932492	+	0.361192i	$0.882370\pi$
$858$	−162762.	+	55067.7i	−0.221094	+	0.0748035i
$859$			1.40361e6i			1.90222i	0.308856	+	0.951109i	$0.400054\pi$
$859$			1.40361e6i			1.90222i	−0.308856	+	0.951109i	$0.599946\pi$
$860$	−841592.	−	1.10136e6i	−1.13790	−	1.48914i
$861$	895621.			1.20814
$862$	339665.	+	1.00394e6i	0.457126	+	1.35111i
$863$		−	185129.i		−	0.248572i	−0.992246	−	0.124286i	$-0.960336\pi$
$863$		−	185129.i		−	0.248572i	0.992246	−	0.124286i	$-0.0396641\pi$
$864$	799335.	−	48355.2i	1.07078	−	0.0647762i
$865$	−1.33055e6			−1.77827
$866$	1.20468e6	−	407582.i	1.60633	−	0.543475i
$867$			617188.i			0.821068i
$868$	441030.	−	337007.i	0.585368	−	0.447300i
$869$	−1.67330e6			−2.21582
$870$	159542.	+	471553.i	0.210783	+	0.623006i
$871$			125872.i			0.165918i
$872$	395269.	−	587716.i	0.519829	−	0.772919i
$873$	−70781.4			−0.0928732
$874$	−141550.	+	47891.0i	−0.185305	+	0.0626947i
$875$		−	2.61193e6i		−	3.41150i
$876$	162390.	+	212515.i	0.211618	+	0.276937i
$877$	−991741.			−1.28943			−0.644717	−	0.764421i	$-0.723025\pi$
$877$	−991741.			−1.28943			−0.644717	+	0.764421i	$0.723025\pi$
$878$	−334851.	−	989708.i	−0.434372	−	1.28386i
$879$			186970.i			0.241988i
$880$	1.87908e6	+	511609.i	2.42649	+	0.660652i
$881$	853384.			1.09949			0.549747	−	0.835331i	$-0.314724\pi$
$881$	853384.			1.09949			0.549747	+	0.835331i	$0.314724\pi$
$882$	26064.1	−	8818.33i	0.0335046	−	0.0113357i
$883$			218646.i			0.280427i	0.990121	+	0.140214i	$0.0447789\pi$
$883$			218646.i			0.280427i	−0.990121	+	0.140214i	$0.955221\pi$
$884$	35485.8	−	27116.0i	0.0454099	−	0.0346993i
$885$	1.66156e6			2.12143
$886$	−280836.	−	830059.i	−0.357755	−	1.05741i
$887$		−	1.38562e6i		−	1.76115i	−0.473908	−	0.880575i	$-0.657157\pi$
$887$		−	1.38562e6i		−	1.76115i	0.473908	−	0.880575i	$-0.342843\pi$
$888$	−1.14259e6	−	768448.i	−1.44898	−	0.974515i
$889$	1.60129e6			2.02612
$890$	−1.07787e6	+	364680.i	−1.36078	+	0.460397i
$891$		−	798402.i		−	1.00569i
$892$	−317716.	−	415785.i	−0.399309	−	0.522563i
$893$	−1.00060e6			−1.25475
$894$	−332389.	−	982433.i	−0.415884	−	1.22921i
$895$			2.14491e6i			2.67771i
$896$	659453.	−	570161.i	0.821425	−	0.710201i
$897$	29730.5			0.0369502
$898$	−313892.	+	106200.i	−0.389249	+	0.131696i
$899$			210838.i			0.260873i
$900$	336208.	−	256908.i	0.415071	−	0.317171i
$901$	186280.			0.229465
$902$	426540.	+	1.26071e6i	0.524260	+	1.54954i
$903$			778592.i			0.954848i
$904$	−256666.	+	381629.i	−0.314073	+	0.466987i
$905$	2.71030e6			3.30918
$906$	1.02980e6	−	348415.i	1.25457	−	0.424463i
$907$		−	210955.i		−	0.256434i	−0.991746	−	0.128217i	$-0.959075\pi$
$907$		−	210955.i		−	0.256434i	0.991746	−	0.128217i	$-0.0409254\pi$
$908$	−265456.	−	347393.i	−0.321974	−	0.421357i
$909$	−172121.			−0.208308
$910$	108842.	+	321702.i	0.131436	+	0.388482i
$911$		−	1.09921e6i		−	1.32447i	−0.749295	−	0.662236i	$-0.769607\pi$
$911$		−	1.09921e6i		−	1.32447i	0.749295	−	0.662236i	$-0.230393\pi$
$912$	−183642.	+	674495.i	−0.220792	+	0.810941i
$913$	−4512.35			−0.00541329
$914$	1.31779e6	−	445851.i	1.57744	−	0.533700i
$915$		−	205322.i		−	0.245241i
$916$	−44037.1	+	33650.3i	−0.0524841	+	0.0401049i
$917$	1.07175e6			1.27454
$918$	83706.0	+	247407.i	0.0993279	+	0.293580i
$919$		−	1.51580e6i		−	1.79478i	−0.441234	−	0.897392i	$-0.645459\pi$
$919$		−	1.51580e6i		−	1.79478i	0.441234	−	0.897392i	$-0.354541\pi$
$920$	−279612.	−	188054.i	−0.330355	−	0.222181i
$921$	−367221.			−0.432920
$922$	29312.5	−	9917.37i	0.0344818	−	0.0116663i
$923$		−	45651.4i		−	0.0535860i
$924$	−664192.	−	869206.i	−0.777946	−	1.01807i
$925$	−4.41213e6			−5.15661
$926$	360424.	+	1.06530e6i	0.420332	+	1.24236i
$927$			114457.i			0.133193i
$928$	19995.6	+	330536.i	0.0232187	+	0.383816i
$929$	582526.			0.674969			0.337485	−	0.941331i	$-0.390424\pi$
$929$	582526.			0.674969			0.337485	+	0.941331i	$0.390424\pi$
$930$	−950724.	+	321661.i	−1.09923	+	0.371906i
$931$			145659.i			0.168050i
$932$	275154.	−	210255.i	0.316770	−	0.242055i
$933$	−822371.			−0.944722
$934$	−291493.	−	861558.i	−0.334145	−	0.987622i
$935$			635180.i			0.726564i
$936$	−19097.6	+	28395.7i	−0.0217985	+	0.0324116i
$937$	−637352.			−0.725939			−0.362970	−	0.931801i	$-0.618237\pi$
$937$	−637352.			−0.725939			−0.362970	+	0.931801i	$0.618237\pi$
$938$	−759096.	+	256827.i	−0.862762	+	0.291901i
$939$			608427.i			0.690045i
$940$	−1.36996e6	−	1.79283e6i	−1.55044	−	2.02901i
$941$	598400.			0.675790			0.337895	−	0.941184i	$-0.390285\pi$
$941$	598400.			0.675790			0.337895	+	0.941184i	$0.390285\pi$
$942$	384127.	+	1.13535e6i	0.432885	+	1.27947i
$943$		−	230285.i		−	0.258965i
$944$	1.06644e6	+	290355.i	1.19672	+	0.325826i
$945$	−1.98616e6			−2.22408
$946$	−1.09598e6	+	370805.i	−1.22467	+	0.414346i
$947$		−	173533.i		−	0.193500i	−0.995309	−	0.0967502i	$-0.969155\pi$
$947$		−	173533.i		−	0.193500i	0.995309	−	0.0967502i	$-0.0308448\pi$
$948$	1.07619e6	−	822356.i	1.19749	−	0.915046i
$949$	−69309.7			−0.0769594
$950$	717868.	+	2.12178e6i	0.795422	+	2.35100i
$951$		−	101950.i		−	0.112727i
$952$	235933.	+	158677.i	0.260324	+	0.175081i
$953$	385958.			0.424966			0.212483	−	0.977165i	$-0.431845\pi$
$953$	385958.			0.424966			0.212483	+	0.977165i	$0.431845\pi$
$954$	−135206.	+	45744.7i	−0.148559	+	0.0502625i
$955$			2.35154e6i			2.57837i
$956$	402017.	+	526107.i	0.439875	+	0.575650i
$957$	415532.			0.453712
$958$	267555.	+	790804.i	0.291529	+	0.861663i
$959$		−	839412.i		−	0.912721i
$960$	−1.45997e6	+	594442.i	−1.58417	+	0.645011i
$961$	498438.			0.539715
$962$	338008.	−	114359.i	0.365238	−	0.123572i
$963$		−	19851.1i		−	0.0214058i
$964$	537882.	−	411015.i	0.578806	−	0.442286i
$965$	670480.			0.719998
$966$	60661.5	+	179295.i	0.0650068	+	0.192139i
$967$			1.03952e6i			1.11168i	0.831290	+	0.555840i	$0.187603\pi$
$967$			1.03952e6i			1.11168i	−0.831290	+	0.555840i	$0.812397\pi$
$968$	384276.	−	571369.i	0.410102	−	0.609770i
$969$	−227998.			−0.242820
$970$	800372.	−	270792.i	0.850645	−	0.287801i
$971$			256268.i			0.271804i	0.990722	+	0.135902i	$0.0433933\pi$
$971$			256268.i			0.271804i	−0.990722	+	0.135902i	$0.956607\pi$
$972$	−222986.	−	291814.i	−0.236018	−	0.308869i
$973$	−34379.0			−0.0363135
$974$	483847.	+	1.43009e6i	0.510024	+	1.50746i
$975$		−	445649.i		−	0.468796i
$976$	35879.7	−	131782.i	0.0376659	−	0.138342i
$977$	95494.9			0.100044			0.0500220	−	0.998748i	$-0.484071\pi$
$977$	95494.9			0.100044			0.0500220	+	0.998748i	$0.484071\pi$
$978$	−306058.	+	103549.i	−0.319982	+	0.108260i
$979$			949821.i			0.991006i
$980$	−260987.	+	199429.i	−0.271748	+	0.207652i
$981$	−177006.			−0.183929
$982$	−323499.	−	956157.i	−0.335468	−	0.991531i
$983$			252122.i			0.260918i	0.991454	+	0.130459i	$0.0416451\pi$
$983$			252122.i			0.260918i	−0.991454	+	0.130459i	$0.958355\pi$
$984$	−893915.	−	601204.i	−0.923221	−	0.620915i
$985$	937313.			0.966078
$986$	−102306.	+	34613.6i	−0.105232	+	0.0356035i
$987$			1.26741e6i			1.30102i
$988$	−109990.	−	143940.i	−0.112678	−	0.147458i
$989$	200194.			0.204672
$990$	−155981.	−	461029.i	−0.159148	−	0.470390i
$991$			884004.i			0.900133i	0.892995	+	0.450067i	$0.148600\pi$
$991$			884004.i			0.900133i	−0.892995	+	0.450067i	$0.851400\pi$
$992$	−666413.	+	40314.2i	−0.677205	+	0.0409670i
$993$	342793.			0.347643
$994$	275310.	−	93146.3i	0.278643	−	0.0942742i
$995$		−	1.10122e6i		−	1.11231i
$996$	2902.13	−	2217.62i	0.00292549	−	0.00223547i
$997$	26841.2			0.0270030			0.0135015	−	0.999909i	$-0.495702\pi$
$997$	26841.2			0.0270030			0.0135015	+	0.999909i	$0.495702\pi$
$998$	−108681.	−	321224.i	−0.109117	−	0.322513i
$999$			2.08683e6i			2.09101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.c.a.47.4	yes	44
4.3	odd	2	inner	92.5.c.a.47.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.c.a.47.3	✓	44	4.3	odd	2	inner
92.5.c.a.47.4	yes	44	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.78901 + 1.28195i) q^{2} -8.06260i q^{3} +(12.7132 - 9.71463i) q^{4} +47.7328 q^{5} +(10.3358 + 30.5493i) q^{6} -53.2079i q^{7} +(-35.7169 + 53.1065i) q^{8} +15.9945 q^{9} +(-180.860 + 61.1909i) q^{10} +159.374i q^{11} +(-78.3252 - 102.502i) q^{12} +33.4299 q^{13} +(68.2097 + 201.605i) q^{14} -384.850i q^{15} +(67.2520 - 247.008i) q^{16} +83.4957 q^{17} +(-60.6032 + 20.5041i) q^{18} -338.682i q^{19} +(606.837 - 463.706i) q^{20} -428.994 q^{21} +(-204.309 - 603.868i) q^{22} +110.304i q^{23} +(428.177 + 287.971i) q^{24} +1653.42 q^{25} +(-126.666 + 42.8554i) q^{26} -782.028i q^{27} +(-516.895 - 676.443i) q^{28} +323.380 q^{29} +(493.358 + 1458.20i) q^{30} +651.984i q^{31} +(61.8331 + 1022.13i) q^{32} +1284.97 q^{33} +(-316.366 + 107.037i) q^{34} -2539.76i q^{35} +(203.341 - 155.380i) q^{36} -2668.49 q^{37} +(434.172 + 1283.27i) q^{38} -269.532i q^{39} +(-1704.87 + 2534.92i) q^{40} -2087.72 q^{41} +(1625.46 - 549.948i) q^{42} -1814.93i q^{43} +(1548.25 + 2026.15i) q^{44} +763.460 q^{45} +(-141.404 - 417.944i) q^{46} -2954.38i q^{47} +(-1991.53 - 542.226i) q^{48} -430.077 q^{49} +(-6264.82 + 2119.59i) q^{50} -673.193i q^{51} +(425.002 - 324.759i) q^{52} +2231.01 q^{53} +(1002.52 + 2963.11i) q^{54} +7607.34i q^{55} +(2825.68 + 1900.42i) q^{56} -2730.66 q^{57} +(-1225.29 + 414.556i) q^{58} +4317.42i q^{59} +(-3738.68 - 4892.69i) q^{60} +533.511 q^{61} +(-835.809 - 2470.37i) q^{62} -851.031i q^{63} +(-1544.61 - 3793.60i) q^{64} +1595.70 q^{65} +(-4868.75 + 1647.26i) q^{66} +3765.26i q^{67} +(1061.50 - 811.130i) q^{68} +889.338 q^{69} +(3255.84 + 9623.18i) q^{70} -1365.59i q^{71} +(-571.273 + 849.410i) q^{72} -2073.28 q^{73} +(10110.9 - 3420.86i) q^{74} -13330.8i q^{75} +(-3290.17 - 4305.74i) q^{76} +8479.93 q^{77} +(345.526 + 1021.26i) q^{78} +10499.3i q^{79} +(3210.13 - 11790.4i) q^{80} -5009.63 q^{81} +(7910.41 - 2676.35i) q^{82} +28.3130i q^{83} +(-5453.89 + 4167.52i) q^{84} +3985.48 q^{85} +(2326.64 + 6876.77i) q^{86} -2607.28i q^{87} +(-8463.77 - 5692.33i) q^{88} +5959.71 q^{89} +(-2892.76 + 978.715i) q^{90} -1778.73i q^{91} +(1071.56 + 1402.32i) q^{92} +5256.68 q^{93} +(3787.36 + 11194.2i) q^{94} -16166.2i q^{95} +(8241.04 - 498.536i) q^{96} -4425.37 q^{97} +(1629.57 - 551.336i) q^{98} +2549.09i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 24 q^{5} + 33 q^{6} - 27 q^{8} - 1300 q^{9} - 46 q^{10} + 145 q^{12} + 472 q^{13} - 264 q^{14} + 272 q^{16} - 648 q^{17} + 1313 q^{18} + 324 q^{20} - 288 q^{21} + 796 q^{22} - 1028 q^{24} + 5604 q^{25}+ \cdots + 57204 q^{98}+O(q^{100}) \) 44 * q + 24 * q^5 + 33 * q^6 - 27 * q^8 - 1300 * q^9 - 46 * q^10 + 145 * q^12 + 472 * q^13 - 264 * q^14 + 272 * q^16 - 648 * q^17 + 1313 * q^18 + 324 * q^20 - 288 * q^21 + 796 * q^22 - 1028 * q^24 + 5604 * q^25 - 3015 * q^26 - 510 * q^28 - 840 * q^29 + 1390 * q^30 + 4200 * q^32 + 320 * q^33 - 4302 * q^34 - 3741 * q^36 - 680 * q^37 + 5940 * q^38 - 626 * q^40 + 7320 * q^41 + 1320 * q^42 - 378 * q^44 - 3240 * q^45 - 8813 * q^48 - 19444 * q^49 - 6960 * q^50 + 1519 * q^52 + 4152 * q^53 - 14405 * q^54 + 13026 * q^56 + 3840 * q^57 + 6771 * q^58 - 180 * q^60 + 6360 * q^61 + 9309 * q^62 - 12765 * q^64 - 15792 * q^65 - 5610 * q^66 - 5484 * q^68 + 4236 * q^70 + 39063 * q^72 - 2888 * q^73 + 43854 * q^74 - 13712 * q^76 + 4320 * q^77 + 18907 * q^78 + 12174 * q^80 + 31628 * q^81 - 31507 * q^82 - 16642 * q^84 - 1904 * q^85 - 25470 * q^86 + 540 * q^88 - 9768 * q^89 - 42044 * q^90 - 11136 * q^93 - 2219 * q^94 + 24435 * q^96 - 3752 * q^97 + 57204 * q^98

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