LMFDB - Embedded newform 28.5.c.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,5,Mod(15,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, 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("28.15");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	28.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:	$2.89435896635$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 10 x^{10} - 29 x^{9} + 174 x^{8} - 96 x^{7} + 88 x^{6} - 3030 x^{5} - 399 x^{4} + \cdots + 117656 $ x^12 - 6x^11 + 10x^10 - 29x^9 + 174x^8 - 96x^7 + 88x^6 - 3030x^5 - 399x^4 + 5790x^3 + 52966x^2 + 89019*x + 117656
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.3
Root			$3.63313 + 1.03277i$ of defining polynomial
Character	$\chi$	$=$	28.15
Dual form			28.5.c.a.15.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.68279 - 2.96693i) q^{2} +5.27316i q^{3} +(-1.60531 + 15.9193i) q^{4} +36.6030 q^{5} +(15.6451 - 14.1468i) q^{6} -18.5203i q^{7} +(51.5380 - 37.9452i) q^{8} +53.1938 q^{9} +O(q^{10})$	\(q+(-2.68279 - 2.96693i) q^{2} +5.27316i q^{3} +(-1.60531 + 15.9193i) q^{4} +36.6030 q^{5} +(15.6451 - 14.1468i) q^{6} -18.5203i q^{7} +(51.5380 - 37.9452i) q^{8} +53.1938 q^{9} +(-98.1982 - 108.599i) q^{10} +162.995i q^{11} +(-83.9448 - 8.46505i) q^{12} +134.614 q^{13} +(-54.9483 + 49.6859i) q^{14} +193.014i q^{15} +(-250.846 - 51.1107i) q^{16} -386.598 q^{17} +(-142.708 - 157.822i) q^{18} -137.042i q^{19} +(-58.7592 + 582.693i) q^{20} +97.6603 q^{21} +(483.593 - 437.280i) q^{22} -649.210i q^{23} +(200.091 + 271.768i) q^{24} +714.782 q^{25} +(-361.142 - 399.391i) q^{26} +707.625i q^{27} +(294.829 + 29.7307i) q^{28} -508.809 q^{29} +(572.657 - 517.815i) q^{30} -573.575i q^{31} +(521.325 + 881.361i) q^{32} -859.496 q^{33} +(1037.16 + 1147.01i) q^{34} -677.898i q^{35} +(-85.3924 + 846.806i) q^{36} -237.647 q^{37} +(-406.593 + 367.654i) q^{38} +709.843i q^{39} +(1886.45 - 1388.91i) q^{40} -1617.06 q^{41} +(-262.002 - 289.751i) q^{42} -2895.64i q^{43} +(-2594.75 - 261.657i) q^{44} +1947.05 q^{45} +(-1926.16 + 1741.69i) q^{46} +2487.83i q^{47} +(269.515 - 1322.75i) q^{48} -343.000 q^{49} +(-1917.61 - 2120.71i) q^{50} -2038.59i q^{51} +(-216.098 + 2142.96i) q^{52} +823.204 q^{53} +(2099.47 - 1898.41i) q^{54} +5966.09i q^{55} +(-702.754 - 954.497i) q^{56} +722.643 q^{57} +(1365.03 + 1509.60i) q^{58} +1795.12i q^{59} +(-3072.64 - 309.847i) q^{60} -2831.89 q^{61} +(-1701.75 + 1538.78i) q^{62} -985.163i q^{63} +(1216.33 - 3911.23i) q^{64} +4927.30 q^{65} +(2305.85 + 2550.06i) q^{66} -6139.35i q^{67} +(620.609 - 6154.36i) q^{68} +3423.39 q^{69} +(-2011.27 + 1818.66i) q^{70} +7650.03i q^{71} +(2741.50 - 2018.45i) q^{72} +4654.29 q^{73} +(637.556 + 705.081i) q^{74} +3769.16i q^{75} +(2181.60 + 219.994i) q^{76} +3018.70 q^{77} +(2106.05 - 1904.36i) q^{78} -4283.86i q^{79} +(-9181.72 - 1870.81i) q^{80} +577.275 q^{81} +(4338.22 + 4797.69i) q^{82} -8058.77i q^{83} +(-156.775 + 1554.68i) q^{84} -14150.7 q^{85} +(-8591.14 + 7768.37i) q^{86} -2683.03i q^{87} +(6184.85 + 8400.41i) q^{88} -13380.9 q^{89} +(-5223.53 - 5776.77i) q^{90} -2493.09i q^{91} +(10334.9 + 1042.18i) q^{92} +3024.55 q^{93} +(7381.21 - 6674.32i) q^{94} -5016.14i q^{95} +(-4647.56 + 2749.03i) q^{96} -7290.90 q^{97} +(920.196 + 1017.66i) q^{98} +8670.30i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 31 q^{4} + 24 q^{5} + 30 q^{6} + 171 q^{8} - 436 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 31 * q^4 + 24 * q^5 + 30 * q^6 + 171 * q^8 - 436 * q^9	$ 12 q + 3 q^{2} - 31 q^{4} + 24 q^{5} + 30 q^{6} + 171 q^{8} - 436 q^{9} + 52 q^{10} + 390 q^{12} + 120 q^{13} + 147 q^{14} - 911 q^{16} - 648 q^{17} + 631 q^{18} + 912 q^{20} - 628 q^{22} - 1174 q^{24} + 2340 q^{25} - 2280 q^{26} + 245 q^{28} + 24 q^{29} + 800 q^{30} + 1443 q^{32} - 1120 q^{33} + 1634 q^{34} + 421 q^{36} - 424 q^{37} + 2970 q^{38} - 4936 q^{40} + 7320 q^{41} - 2450 q^{42} - 2244 q^{44} + 888 q^{45} - 7512 q^{46} + 3550 q^{48} - 4116 q^{49} - 5451 q^{50} - 3484 q^{52} - 7080 q^{53} + 11620 q^{54} + 3087 q^{56} - 9152 q^{57} + 4666 q^{58} + 15856 q^{60} + 9752 q^{61} - 5964 q^{62} + 6329 q^{64} - 11280 q^{65} + 30264 q^{66} - 7314 q^{68} - 10464 q^{69} - 7644 q^{70} - 10553 q^{72} + 13752 q^{73} - 2838 q^{74} + 11202 q^{76} + 4704 q^{77} - 34600 q^{78} - 49272 q^{80} + 3340 q^{81} - 11950 q^{82} + 11662 q^{84} + 23152 q^{85} + 30612 q^{86} + 20740 q^{88} - 12552 q^{89} - 40508 q^{90} + 47880 q^{92} + 13632 q^{93} + 71340 q^{94} - 11110 q^{96} + 19704 q^{97} - 1029 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 31 * q^4 + 24 * q^5 + 30 * q^6 + 171 * q^8 - 436 * q^9 + 52 * q^10 + 390 * q^12 + 120 * q^13 + 147 * q^14 - 911 * q^16 - 648 * q^17 + 631 * q^18 + 912 * q^20 - 628 * q^22 - 1174 * q^24 + 2340 * q^25 - 2280 * q^26 + 245 * q^28 + 24 * q^29 + 800 * q^30 + 1443 * q^32 - 1120 * q^33 + 1634 * q^34 + 421 * q^36 - 424 * q^37 + 2970 * q^38 - 4936 * q^40 + 7320 * q^41 - 2450 * q^42 - 2244 * q^44 + 888 * q^45 - 7512 * q^46 + 3550 * q^48 - 4116 * q^49 - 5451 * q^50 - 3484 * q^52 - 7080 * q^53 + 11620 * q^54 + 3087 * q^56 - 9152 * q^57 + 4666 * q^58 + 15856 * q^60 + 9752 * q^61 - 5964 * q^62 + 6329 * q^64 - 11280 * q^65 + 30264 * q^66 - 7314 * q^68 - 10464 * q^69 - 7644 * q^70 - 10553 * q^72 + 13752 * q^73 - 2838 * q^74 + 11202 * q^76 + 4704 * q^77 - 34600 * q^78 - 49272 * q^80 + 3340 * q^81 - 11950 * q^82 + 11662 * q^84 + 23152 * q^85 + 30612 * q^86 + 20740 * q^88 - 12552 * q^89 - 40508 * q^90 + 47880 * q^92 + 13632 * q^93 + 71340 * q^94 - 11110 * q^96 + 19704 * q^97 - 1029 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.68279	−	2.96693i	−0.670697	−	0.741732i
$2$	−2.68279	−	2.96693i	−0.670697	−	0.741732i
$3$			5.27316i			0.585907i	0.956127	+	0.292953i	$0.0946381\pi$
$3$			5.27316i			0.585907i	−0.956127	+	0.292953i	$0.905362\pi$
$4$	−1.60531	+	15.9193i	−0.100332	+	0.994954i
$5$	36.6030			1.46412			0.732061	−	0.681239i	$-0.238559\pi$
$5$	36.6030			1.46412			0.732061	+	0.681239i	$0.238559\pi$
$6$	15.6451	−	14.1468i	0.434586	−	0.392966i
$7$		−	18.5203i		−	0.377964i
$7$		−	18.5203i		−	0.377964i
$8$	51.5380	−	37.9452i	0.805281	−	0.592893i
$9$	53.1938			0.656713
$10$	−98.1982	−	108.599i	−0.981982	−	1.08599i
$11$			162.995i			1.34706i	0.739159	+	0.673531i	$0.235223\pi$
$11$			162.995i			1.34706i	−0.739159	+	0.673531i	$0.764777\pi$
$12$	−83.9448	−	8.46505i	−0.582950	−	0.0587851i
$13$	134.614			0.796535			0.398268	−	0.917269i	$-0.369612\pi$
$13$	134.614			0.796535			0.398268	+	0.917269i	$0.369612\pi$
$14$	−54.9483	+	49.6859i	−0.280348	+	0.253500i
$15$			193.014i			0.857839i
$16$	−250.846	−	51.1107i	−0.979867	−	0.199651i
$17$	−386.598			−1.33771			−0.668855	−	0.743393i	$-0.733215\pi$
$17$	−386.598			−1.33771			−0.668855	+	0.743393i	$0.733215\pi$
$18$	−142.708	−	157.822i	−0.440455	−	0.487105i
$19$		−	137.042i		−	0.379617i	−0.981821	−	0.189809i	$-0.939213\pi$
$19$		−	137.042i		−	0.379617i	0.981821	−	0.189809i	$-0.0607867\pi$
$20$	−58.7592	+	582.693i	−0.146898	+	1.45673i
$21$	97.6603			0.221452
$22$	483.593	−	437.280i	0.999159	−	0.903470i
$23$		−	649.210i		−	1.22724i	−0.789602	−	0.613620i	$-0.789713\pi$
$23$		−	649.210i		−	1.22724i	0.789602	−	0.613620i	$-0.210287\pi$
$24$	200.091	+	271.768i	0.347380	+	0.471820i
$25$	714.782			1.14365
$26$	−361.142	−	399.391i	−0.534233	−	0.590815i
$27$			707.625i			0.970679i
$28$	294.829	+	29.7307i	0.376057	+	0.0379219i
$29$	−508.809			−0.605004			−0.302502	−	0.953149i	$-0.597822\pi$
$29$	−508.809			−0.605004			−0.302502	+	0.953149i	$0.597822\pi$
$30$	572.657	−	517.815i	0.636286	−	0.575350i
$31$		−	573.575i		−	0.596852i	−0.954433	−	0.298426i	$-0.903538\pi$
$31$		−	573.575i		−	0.596852i	0.954433	−	0.298426i	$-0.0964616\pi$
$32$	521.325	+	881.361i	0.509106	+	0.860704i
$33$	−859.496			−0.789253
$34$	1037.16	+	1147.01i	0.897197	+	0.992221i
$35$		−	677.898i		−	0.553386i
$36$	−85.3924	+	846.806i	−0.0658892	+	0.653400i
$37$	−237.647			−0.173592			−0.0867958	−	0.996226i	$-0.527663\pi$
$37$	−237.647			−0.173592			−0.0867958	+	0.996226i	$0.527663\pi$
$38$	−406.593	+	367.654i	−0.281574	+	0.254608i
$39$			709.843i			0.466695i
$40$	1886.45	−	1388.91i	1.17903	−	0.868068i
$41$	−1617.06			−0.961962			−0.480981	−	0.876731i	$-0.659719\pi$
$41$	−1617.06			−0.961962			−0.480981	+	0.876731i	$0.659719\pi$
$42$	−262.002	−	289.751i	−0.148527	−	0.164258i
$43$		−	2895.64i		−	1.56605i	−0.621987	−	0.783027i	$-0.713674\pi$
$43$		−	2895.64i		−	1.56605i	0.621987	−	0.783027i	$-0.286326\pi$
$44$	−2594.75	−	261.657i	−1.34026	−	0.135153i
$45$	1947.05			0.961508
$46$	−1926.16	+	1741.69i	−0.910282	+	0.823106i
$47$			2487.83i			1.12623i	0.826380	+	0.563113i	$0.190396\pi$
$47$			2487.83i			1.12623i	−0.826380	+	0.563113i	$0.809604\pi$
$48$	269.515	−	1322.75i	0.116977	−	0.574111i
$49$	−343.000			−0.142857
$50$	−1917.61	−	2120.71i	−0.767044	−	0.848283i
$51$		−	2038.59i		−	0.783773i
$52$	−216.098	+	2142.96i	−0.0799178	+	0.792516i
$53$	823.204			0.293060			0.146530	−	0.989206i	$-0.453190\pi$
$53$	823.204			0.293060			0.146530	+	0.989206i	$0.453190\pi$
$54$	2099.47	−	1898.41i	0.719984	−	0.651032i
$55$			5966.09i			1.97226i
$56$	−702.754	−	954.497i	−0.224093	−	0.304368i
$57$	722.643			0.222420
$58$	1365.03	+	1509.60i	0.405774	+	0.448751i
$59$			1795.12i			0.515690i	0.966186	+	0.257845i	$0.0830123\pi$
$59$			1795.12i			0.515690i	−0.966186	+	0.257845i	$0.916988\pi$
$60$	−3072.64	−	309.847i	−0.853510	−	0.0860685i
$61$	−2831.89			−0.761056			−0.380528	−	0.924769i	$-0.624258\pi$
$61$	−2831.89			−0.761056			−0.380528	+	0.924769i	$0.624258\pi$
$62$	−1701.75	+	1538.78i	−0.442704	+	0.400307i
$63$		−	985.163i		−	0.248214i
$64$	1216.33	−	3911.23i	0.296955	−	0.954891i
$65$	4927.30			1.16622
$66$	2305.85	+	2550.06i	0.529349	+	0.585414i
$67$		−	6139.35i		−	1.36764i	−0.729650	−	0.683821i	$-0.760317\pi$
$67$		−	6139.35i		−	1.36764i	0.729650	−	0.683821i	$-0.239683\pi$
$68$	620.609	−	6154.36i	0.134215	−	1.33096i
$69$	3423.39			0.719048
$70$	−2011.27	+	1818.66i	−0.410464	+	0.371154i
$71$			7650.03i			1.51756i	0.651346	+	0.758781i	$0.274205\pi$
$71$			7650.03i			1.51756i	−0.651346	+	0.758781i	$0.725795\pi$
$72$	2741.50	−	2018.45i	0.528839	−	0.389361i
$73$	4654.29			0.873389			0.436694	−	0.899610i	$-0.356149\pi$
$73$	4654.29			0.873389			0.436694	+	0.899610i	$0.356149\pi$
$74$	637.556	+	705.081i	0.116427	+	0.128758i
$75$			3769.16i			0.670073i
$76$	2181.60	+	219.994i	0.377701	+	0.0380877i
$77$	3018.70			0.509142
$78$	2106.05	−	1904.36i	0.346163	−	0.313011i
$79$		−	4283.86i		−	0.686406i	−0.939261	−	0.343203i	$-0.888488\pi$
$79$		−	4283.86i		−	0.686406i	0.939261	−	0.343203i	$-0.111512\pi$
$80$	−9181.72	−	1870.81i	−1.43464	−	0.292313i
$81$	577.275			0.0879858
$82$	4338.22	+	4797.69i	0.645185	+	0.713518i
$83$		−	8058.77i		−	1.16980i	−0.811104	−	0.584902i	$-0.801133\pi$
$83$		−	8058.77i		−	1.16980i	0.811104	−	0.584902i	$-0.198867\pi$
$84$	−156.775	+	1554.68i	−0.0222187	+	0.220334i
$85$	−14150.7			−1.95857
$86$	−8591.14	+	7768.37i	−1.16159	+	1.05035i
$87$		−	2683.03i		−	0.354476i
$88$	6184.85	+	8400.41i	0.798664	+	1.08476i
$89$	−13380.9			−1.68929			−0.844645	−	0.535327i	$-0.820189\pi$
$89$	−13380.9			−1.68929			−0.844645	+	0.535327i	$0.820189\pi$
$90$	−5223.53	−	5776.77i	−0.644880	−	0.713181i
$91$		−	2493.09i		−	0.301062i
$92$	10334.9	+	1042.18i	1.22105	+	0.123131i
$93$	3024.55			0.349699
$94$	7381.21	−	6674.32i	0.835357	−	0.755356i
$95$		−	5016.14i		−	0.555805i
$96$	−4647.56	+	2749.03i	−0.504292	+	0.298289i
$97$	−7290.90			−0.774886			−0.387443	−	0.921894i	$-0.626642\pi$
$97$	−7290.90			−0.774886			−0.387443	+	0.921894i	$0.626642\pi$
$98$	920.196	+	1017.66i	0.0958138	+	0.105962i
$99$			8670.30i			0.884634i
$100$	−1147.45	+	11378.8i	−0.114745	+	1.13788i
$101$	−11013.8			−1.07968			−0.539839	−	0.841768i	$-0.681515\pi$
$101$	−11013.8			−1.07968			−0.539839	+	0.841768i	$0.681515\pi$
$102$	−6048.36	+	5469.11i	−0.581349	+	0.525674i
$103$			10763.7i			1.01458i	0.861776	+	0.507289i	$0.169352\pi$
$103$			10763.7i			1.01458i	−0.861776	+	0.507289i	$0.830648\pi$
$104$	6937.76	−	5107.97i	0.641435	−	0.472260i
$105$	3574.66			0.324233
$106$	−2208.48	−	2442.39i	−0.196554	−	0.217372i
$107$		−	3947.85i		−	0.344821i	−0.985025	−	0.172410i	$-0.944845\pi$
$107$		−	3947.85i		−	0.344821i	0.985025	−	0.172410i	$-0.0551555\pi$
$108$	−11264.9	−	1135.96i	−0.965781	−	0.0973900i
$109$	8101.80			0.681912			0.340956	−	0.940079i	$-0.389249\pi$
$109$	8101.80			0.681912			0.340956	+	0.940079i	$0.389249\pi$
$110$	17701.0	−	16005.8i	1.46289	−	1.32279i
$111$		−	1253.15i		−	0.101708i
$112$	−946.583	+	4645.73i	−0.0754610	+	0.370355i
$113$	21181.3			1.65880			0.829402	−	0.558652i	$-0.188681\pi$
$113$	21181.3			1.65880			0.829402	+	0.558652i	$0.188681\pi$
$114$	−1938.70	−	2144.03i	−0.149176	−	0.164976i
$115$		−	23763.0i		−	1.79683i
$116$	816.795	−	8099.86i	0.0607012	−	0.601952i
$117$	7160.65			0.523095
$118$	5325.98	−	4815.91i	0.382503	−	0.345871i
$119$			7159.90i			0.505607i
$120$	7323.94	+	9947.54i	0.508607	+	0.690801i
$121$	−11926.2			−0.814577
$122$	7597.36	+	8402.01i	0.510438	+	0.564499i
$123$		−	8527.01i		−	0.563620i
$124$	9130.89	+	920.764i	0.593840	+	0.0598832i
$125$	3286.31			0.210324
$126$	−2922.91	+	2642.98i	−0.184108	+	0.166477i
$127$			7257.46i			0.449963i	0.974363	+	0.224982i	$0.0722322\pi$
$127$			7257.46i			0.449963i	−0.974363	+	0.224982i	$0.927768\pi$
$128$	−14867.5	+	6884.25i	−0.907440	+	0.420181i
$129$	15269.1			0.917562
$130$	−13218.9	−	14618.9i	−0.782183	−	0.865025i
$131$			18489.6i			1.07742i	0.842492	+	0.538709i	$0.181088\pi$
$131$			18489.6i			1.07742i	−0.842492	+	0.538709i	$0.818912\pi$
$132$	1379.76	−	13682.5i	0.0791871	−	0.785270i
$133$	−2538.05			−0.143482
$134$	−18215.0	+	16470.6i	−1.01442	+	0.917273i
$135$			25901.2i			1.42119i
$136$	−19924.5	+	14669.5i	−1.07723	+	0.793119i
$137$	18700.0			0.996322			0.498161	−	0.867085i	$-0.334009\pi$
$137$	18700.0			0.996322			0.498161	+	0.867085i	$0.334009\pi$
$138$	−9184.22	−	10156.9i	−0.482263	−	0.533341i
$139$		−	8538.53i		−	0.441930i	−0.975282	−	0.220965i	$-0.929079\pi$
$139$		−	8538.53i		−	0.441930i	0.975282	−	0.220965i	$-0.0709206\pi$
$140$	10791.6	+	1088.24i	0.550594	+	0.0555222i
$141$	−13118.7			−0.659863
$142$	22697.1	−	20523.4i	1.12562	−	1.01782i
$143$			21941.4i			1.07298i
$144$	−13343.4	−	2718.77i	−0.643492	−	0.131114i
$145$	−18623.9			−0.885800
$146$	−12486.5	−	13808.9i	−0.585779	−	0.647820i
$147$		−	1808.69i		−	0.0837010i
$148$	381.497	−	3783.16i	0.0174168	−	0.172716i
$149$	32698.3			1.47283			0.736414	−	0.676531i	$-0.236518\pi$
$149$	32698.3			1.47283			0.736414	+	0.676531i	$0.236518\pi$
$150$	11182.8	−	10111.9i	0.497015	−	0.449416i
$151$		−	4989.64i		−	0.218834i	−0.993996	−	0.109417i	$-0.965102\pi$
$151$		−	4989.64i		−	0.218834i	0.993996	−	0.109417i	$-0.0348985\pi$
$152$	−5200.07	−	7062.86i	−0.225072	−	0.305698i
$153$	−20564.6			−0.878492
$154$	−8098.53	−	8956.26i	−0.341480	−	0.377646i
$155$		−	20994.6i		−	0.873864i
$156$	−11300.2	−	1139.52i	−0.464340	−	0.0468244i
$157$	954.944			0.0387417			0.0193708	−	0.999812i	$-0.493834\pi$
$157$	954.944			0.0387417			0.0193708	+	0.999812i	$0.493834\pi$
$158$	−12709.9	+	11492.7i	−0.509129	+	0.460370i
$159$			4340.89i			0.171706i
$160$	19082.1	+	32260.5i	0.745393	+	1.26017i
$161$	−12023.5			−0.463853
$162$	−1548.70	−	1712.73i	−0.0590118	−	0.0652618i
$163$		−	8360.43i		−	0.314669i	−0.987545	−	0.157334i	$-0.949710\pi$
$163$		−	8360.43i		−	0.314669i	0.987545	−	0.157334i	$-0.0502900\pi$
$164$	2595.88	−	25742.4i	0.0965154	−	0.957108i
$165$	−31460.2			−1.15556
$166$	−23909.8	+	21620.0i	−0.867680	+	0.784583i
$167$		−	12298.6i		−	0.440983i	−0.975389	−	0.220491i	$-0.929234\pi$
$167$		−	12298.6i		−	0.440983i	0.975389	−	0.220491i	$-0.0707661\pi$
$168$	5033.22	−	3705.74i	0.178331	−	0.131297i
$169$	−10440.0			−0.365532
$170$	37963.2	+	41984.0i	1.31361	+	1.45273i
$171$		−	7289.77i		−	0.249300i
$172$	46096.4	+	4648.39i	1.55815	+	0.157125i
$173$	29255.6			0.977500			0.488750	−	0.872424i	$-0.337453\pi$
$173$	29255.6			0.977500			0.488750	+	0.872424i	$0.337453\pi$
$174$	−7960.35	+	7198.00i	−0.262926	+	0.237746i
$175$		−	13238.0i		−	0.432260i
$176$	8330.76	−	40886.5i	0.268942	−	1.31994i
$177$	−9465.93			−0.302146
$178$	35898.0	+	39700.1i	1.13300	+	1.25300i
$179$			52927.8i			1.65188i	0.563759	+	0.825939i	$0.309355\pi$
$179$			52927.8i			1.65188i	−0.563759	+	0.825939i	$0.690645\pi$
$180$	−3125.62	+	30995.7i	−0.0964698	+	0.956656i
$181$	22781.5			0.695384			0.347692	−	0.937609i	$-0.386965\pi$
$181$	22781.5			0.695384			0.347692	+	0.937609i	$0.386965\pi$
$182$	−7396.83	+	6688.44i	−0.223307	+	0.201921i
$183$		−	14933.0i		−	0.445908i
$184$	−24634.4	−	33459.0i	−0.727622	−	0.988273i
$185$	−8698.60			−0.254159
$186$	−8114.23	−	8973.62i	−0.234542	−	0.259383i
$187$		−	63013.4i		−	1.80198i
$188$	−39604.5	−	3993.74i	−1.12054	−	0.112996i
$189$	13105.4			0.366882
$190$	−14882.5	+	13457.2i	−0.412259	+	0.372777i
$191$		−	30096.8i		−	0.824998i	−0.910958	−	0.412499i	$-0.864656\pi$
$191$		−	30096.8i		−	0.824998i	0.910958	−	0.412499i	$-0.135344\pi$
$192$	20624.6	+	6413.90i	0.559477	+	0.173988i
$193$	−11403.3			−0.306136			−0.153068	−	0.988216i	$-0.548915\pi$
$193$	−11403.3			−0.306136			−0.153068	+	0.988216i	$0.548915\pi$
$194$	19559.9	+	21631.6i	0.519713	+	0.574757i
$195$			25982.4i			0.683299i
$196$	550.621	−	5460.31i	0.0143331	−	0.142136i
$197$	−4048.86			−0.104328			−0.0521639	−	0.998639i	$-0.516612\pi$
$197$	−4048.86			−0.104328			−0.0521639	+	0.998639i	$0.516612\pi$
$198$	25724.1	−	23260.6i	0.656161	−	0.593321i
$199$			40535.2i			1.02359i	0.859107	+	0.511795i	$0.171019\pi$
$199$			40535.2i			1.02359i	−0.859107	+	0.511795i	$0.828981\pi$
$200$	36838.4	−	27122.5i	0.920961	−	0.678063i
$201$	32373.8			0.801311
$202$	29547.7	+	32677.1i	0.724137	+	0.800831i
$203$			9423.27i			0.228670i
$204$	32452.9	+	3272.57i	0.779818	+	0.0786373i
$205$	−59189.3			−1.40843
$206$	31935.0	−	28876.6i	0.752545	−	0.680474i
$207$		−	34533.9i		−	0.805945i
$208$	−33767.5	−	6880.23i	−0.780498	−	0.159029i
$209$	22337.1			0.511368
$210$	−9590.06	−	10605.8i	−0.217462	−	0.240494i
$211$			18045.2i			0.405318i	0.979249	+	0.202659i	$0.0649584\pi$
$211$			18045.2i			0.405318i	−0.979249	+	0.202659i	$0.935042\pi$
$212$	−1321.50	+	13104.8i	−0.0294032	+	0.291581i
$213$	−40339.8			−0.889150
$214$	−11713.0	+	10591.2i	−0.255764	+	0.231270i
$215$		−	105989.i		−	2.29289i
$216$	26851.0	+	36469.6i	0.575509	+	0.781670i
$217$	−10622.8			−0.225589
$218$	−21735.4	−	24037.4i	−0.457356	−	0.505796i
$219$			24542.8i			0.511724i
$220$	−94975.8	−	9577.42i	−1.96231	−	0.197881i
$221$	−52041.7			−1.06553
$222$	−3718.00	+	3361.93i	−0.0754404	+	0.0682155i
$223$			72931.4i			1.46658i	0.679918	+	0.733288i	$0.262015\pi$
$223$			72931.4i			1.46658i	−0.679918	+	0.733288i	$0.737985\pi$
$224$	16323.0	−	9655.07i	0.325315	−	0.192424i
$225$	38022.0			0.751051
$226$	−56824.9	−	62843.3i	−1.11255	−	1.23039i
$227$			46488.9i			0.902190i	0.892476	+	0.451095i	$0.148966\pi$
$227$			46488.9i			0.902190i	−0.892476	+	0.451095i	$0.851034\pi$
$228$	−1160.07	+	11503.9i	−0.0223158	+	0.221298i
$229$	61009.5			1.16339			0.581696	−	0.813406i	$-0.302389\pi$
$229$	61009.5			1.16339			0.581696	+	0.813406i	$0.302389\pi$
$230$	−70503.2	+	63751.2i	−1.33276	+	1.20513i
$231$			15918.1i			0.298310i
$232$	−26223.0	+	19306.8i	−0.487199	+	0.358703i
$233$	−13636.0			−0.251175			−0.125587	−	0.992083i	$-0.540082\pi$
$233$	−13636.0			−0.251175			−0.125587	+	0.992083i	$0.540082\pi$
$234$	−19210.5	−	21245.1i	−0.350838	−	0.387996i
$235$			91062.2i			1.64893i
$236$	−28576.9	−	2881.71i	−0.513087	−	0.0517401i
$237$	22589.5			0.402170
$238$	21242.9	−	19208.5i	0.375024	−	0.339109i
$239$		−	64369.5i		−	1.12690i	−0.826151	−	0.563448i	$-0.809474\pi$
$239$		−	64369.5i		−	1.12690i	0.826151	−	0.563448i	$-0.190526\pi$
$240$	9865.06	−	48416.7i	0.171268	−	0.840568i
$241$	36372.5			0.626238			0.313119	−	0.949714i	$-0.398626\pi$
$241$	36372.5			0.626238			0.313119	+	0.949714i	$0.398626\pi$
$242$	31995.5	+	35384.2i	0.546334	+	0.604197i
$243$			60361.7i			1.02223i
$244$	4546.06	−	45081.6i	0.0763581	−	0.757216i
$245$	−12554.8			−0.209160
$246$	−25299.0	+	22876.1i	−0.418055	+	0.378018i
$247$		−	18447.8i		−	0.302378i
$248$	−21764.4	−	29560.9i	−0.353869	−	0.480634i
$249$	42495.2			0.685395
$250$	−8816.46	−	9750.23i	−0.141063	−	0.156004i
$251$		−	15521.4i		−	0.246368i	−0.992384	−	0.123184i	$-0.960689\pi$
$251$		−	15521.4i		−	0.246368i	0.992384	−	0.123184i	$-0.0393106\pi$
$252$	15683.1	+	1581.49i	0.246962	+	0.0249038i
$253$	105818.			1.65317
$254$	21532.4	−	19470.2i	0.333752	−	0.301789i
$255$		−	74618.7i		−	1.14754i
$256$	60311.4	+	25641.8i	0.920279	+	0.391263i
$257$	−67225.9			−1.01782			−0.508910	−	0.860820i	$-0.669951\pi$
$257$	−67225.9			−1.01782			−0.508910	+	0.860820i	$0.669951\pi$
$258$	−40963.9	−	45302.4i	−0.615406	−	0.680585i
$259$			4401.28i			0.0656114i
$260$	−7909.83	+	78438.9i	−0.117009	+	1.16034i
$261$	−27065.5			−0.397314
$262$	54857.2	−	49603.6i	0.799155	−	0.722621i
$263$			26906.8i			0.389001i	0.980902	+	0.194501i	$0.0623086\pi$
$263$			26906.8i			0.389001i	−0.980902	+	0.194501i	$0.937691\pi$
$264$	−44296.7	+	32613.7i	−0.635570	+	0.467943i
$265$	30131.8			0.429075
$266$	6809.04	+	7530.20i	0.0962327	+	0.106425i
$267$		−	70559.5i		−	0.989767i
$268$	97733.9	+	9855.54i	1.36074	+	0.137218i
$269$	−10793.8			−0.149166			−0.0745829	−	0.997215i	$-0.523763\pi$
$269$	−10793.8			−0.149166			−0.0745829	+	0.997215i	$0.523763\pi$
$270$	76847.1	−	69487.5i	1.05414	−	0.953189i
$271$		−	12743.9i		−	0.173526i	−0.996229	−	0.0867629i	$-0.972348\pi$
$271$		−	12743.9i		−	0.173526i	0.996229	−	0.0867629i	$-0.0276522\pi$
$272$	96976.5	+	19759.3i	1.31078	+	0.267075i
$273$	13146.5			0.176394
$274$	−50168.0	−	55481.4i	−0.668230	−	0.739004i
$275$			116506.i			1.54057i
$276$	−5495.59	+	54497.8i	−0.0721434	+	0.715420i
$277$	18003.7			0.234640			0.117320	−	0.993094i	$-0.462570\pi$
$277$	18003.7			0.234640			0.117320	+	0.993094i	$0.462570\pi$
$278$	−25333.2	+	22907.0i	−0.327793	+	0.296401i
$279$		−	30510.6i		−	0.391961i
$280$	−25722.9	−	34937.5i	−0.328099	−	0.445631i
$281$	−26862.5			−0.340199			−0.170100	−	0.985427i	$-0.554409\pi$
$281$	−26862.5			−0.340199			−0.170100	+	0.985427i	$0.554409\pi$
$282$	35194.8	+	38922.3i	0.442568	+	0.489441i
$283$		−	7280.61i		−	0.0909065i	−0.998966	−	0.0454533i	$-0.985527\pi$
$283$		−	7280.61i		−	0.0909065i	0.998966	−	0.0454533i	$-0.0144732\pi$
$284$	−121783.	−	12280.7i	−1.50990	−	0.152260i
$285$	26450.9			0.325650
$286$	65098.6	−	58864.1i	0.795865	−	0.719646i
$287$			29948.3i			0.363588i
$288$	27731.2	+	46882.9i	0.334337	+	0.565236i
$289$	65937.0			0.789466
$290$	49964.1	+	55255.9i	0.594103	+	0.657026i
$291$		−	38446.1i		−	0.454011i
$292$	−7471.57	+	74092.9i	−0.0876287	+	0.868982i
$293$	−120150.			−1.39955			−0.699775	−	0.714364i	$-0.746716\pi$
$293$	−120150.			−1.39955			−0.699775	+	0.714364i	$0.746716\pi$
$294$	−5366.26	+	4852.34i	−0.0620837	+	0.0561380i
$295$			65706.7i			0.755032i
$296$	−12247.8	+	9017.55i	−0.139790	+	0.102921i
$297$	−115339.			−1.30757
$298$	−87722.5	−	97013.4i	−0.987821	−	1.09244i
$299$		−	87393.0i		−	0.977539i
$300$	−60002.3	−	6050.67i	−0.666692	−	0.0672297i
$301$	−53627.9			−0.591913
$302$	−14803.9	+	13386.2i	−0.162316	+	0.146772i
$303$		−	58077.5i		−	0.632591i
$304$	−7004.30	+	34376.4i	−0.0757909	+	0.371974i
$305$	−103656.			−1.11428
$306$	55170.5	+	61013.7i	0.589201	+	0.651605i
$307$		−	67713.1i		−	0.718449i	−0.933251	−	0.359225i	$-0.883041\pi$
$307$		−	67713.1i		−	0.718449i	0.933251	−	0.359225i	$-0.116959\pi$
$308$	−4845.95	+	48055.5i	−0.0510831	+	0.506573i
$309$	−56758.5			−0.594448
$310$	−62289.4	+	56324.0i	−0.648172	+	0.586097i
$311$			35397.3i			0.365973i	0.983115	+	0.182986i	$0.0585765\pi$
$311$			35397.3i			0.365973i	−0.983115	+	0.182986i	$0.941424\pi$
$312$	26935.1	+	36583.9i	0.276700	+	0.375821i
$313$	63615.0			0.649338			0.324669	−	0.945828i	$-0.394747\pi$
$313$	63615.0			0.649338			0.324669	+	0.945828i	$0.394747\pi$
$314$	−2561.91	−	2833.25i	−0.0259839	−	0.0287359i
$315$		−	36059.9i		−	0.363416i
$316$	68195.9	+	6876.92i	0.682942	+	0.0688683i
$317$	−71715.2			−0.713663			−0.356831	−	0.934169i	$-0.616143\pi$
$317$	−71715.2			−0.713663			−0.356831	+	0.934169i	$0.616143\pi$
$318$	12879.1	−	11645.7i	0.127359	−	0.115162i
$319$		−	82933.0i		−	0.814979i
$320$	44521.4	−	143163.i	0.434779	−	1.39808i
$321$	20817.6			0.202033
$322$	32256.6	+	35672.9i	0.311105	+	0.344054i
$323$			52980.1i			0.507817i
$324$	−926.704	+	9189.79i	−0.00882777	+	0.0875418i
$325$	96220.0			0.910959
$326$	−24804.8	+	22429.3i	−0.233400	+	0.211047i
$327$			42722.1i			0.399537i
$328$	−83340.0	+	61359.5i	−0.774650	+	0.570341i
$329$	46075.3			0.425673
$330$	84400.9	+	93340.0i	0.775032	+	0.857117i
$331$			2135.50i			0.0194914i	0.999953	+	0.00974571i	$0.00310221\pi$
$331$			2135.50i			0.0194914i	−0.999953	+	0.00974571i	$0.996898\pi$
$332$	128290.	+	12936.8i	1.16390	+	0.117368i
$333$	−12641.3			−0.114000
$334$	−36488.9	+	32994.4i	−0.327091	+	0.295766i
$335$		−	224719.i		−	2.00239i
$336$	−24497.7	−	4991.48i	−0.216993	−	0.0442131i
$337$	−210757.			−1.85576			−0.927880	−	0.372880i	$-0.878370\pi$
$337$	−210757.			−1.85576			−0.927880	+	0.372880i	$0.878370\pi$
$338$	28008.2	+	30974.6i	0.245161	+	0.271127i
$339$			111692.i			0.971905i
$340$	22716.2	−	225268.i	0.196507	−	1.94869i
$341$	93489.5			0.803997
$342$	−21628.2	+	19556.9i	−0.184913	+	0.167204i
$343$			6352.45i			0.0539949i
$344$	−109875.	−	149235.i	−0.928503	−	1.26111i
$345$	125306.			1.05277
$346$	−78486.6	−	86799.3i	−0.655606	−	0.725043i
$347$		−	11109.0i		−	0.0922602i	−0.998935	−	0.0461301i	$-0.985311\pi$
$347$		−	11109.0i		−	0.0922602i	0.998935	−	0.0461301i	$-0.0146889\pi$
$348$	42711.9	+	4307.09i	0.352687	+	0.0355652i
$349$	55087.5			0.452275			0.226137	−	0.974095i	$-0.427390\pi$
$349$	55087.5			0.452275			0.226137	+	0.974095i	$0.427390\pi$
$350$	−39276.0	+	35514.6i	−0.320621	+	0.289915i
$351$			95256.6i			0.773180i
$352$	−143657.	+	84973.1i	−1.15942	+	0.685798i
$353$	112398.			0.902003			0.451001	−	0.892523i	$-0.351067\pi$
$353$	112398.			0.902003			0.451001	+	0.892523i	$0.351067\pi$
$354$	25395.1	+	28084.7i	0.202648	+	0.224111i
$355$			280014.i			2.22190i
$356$	21480.4	−	213014.i	0.169490	−	1.68077i
$357$	−37755.3			−0.296238
$358$	157033.	−	141994.i	1.22525	−	1.10791i
$359$			216236.i			1.67779i	0.544290	+	0.838897i	$0.316799\pi$
$359$			216236.i			1.67779i	−0.544290	+	0.838897i	$0.683201\pi$
$360$	100347.	−	73881.3i	0.774284	−	0.570072i
$361$	111541.			0.855891
$362$	−61117.9	−	67591.0i	−0.466392	−	0.515788i
$363$		−	62888.8i		−	0.477266i
$364$	39688.2	+	4002.19i	0.299543	+	0.0302061i
$365$	170361.			1.27875
$366$	−44305.1	+	40062.1i	−0.330744	+	0.299069i
$367$		−	173238.i		−	1.28621i	−0.765778	−	0.643105i	$-0.777646\pi$
$367$		−	173238.i		−	1.28621i	0.765778	−	0.643105i	$-0.222354\pi$
$368$	−33181.5	+	162852.i	−0.245020	+	1.20253i
$369$	−86017.5			−0.631733
$370$	23336.5	+	25808.1i	0.170464	+	0.188518i
$371$		−	15246.0i		−	0.110766i
$372$	−4855.34	+	48148.6i	−0.0350860	+	0.347935i
$373$	46116.1			0.331463			0.165731	−	0.986171i	$-0.447002\pi$
$373$	46116.1			0.331463			0.165731	+	0.986171i	$0.447002\pi$
$374$	−186956.	+	169051.i	−1.33658	+	1.20858i
$375$			17329.2i			0.123230i
$376$	94401.2	+	128218.i	0.667731	+	0.906928i
$377$	−68493.0			−0.481907
$378$	−35159.0	−	38882.8i	−0.246067	−	0.272128i
$379$			103679.i			0.721791i	0.932606	+	0.360896i	$0.117529\pi$
$379$			103679.i			0.721791i	−0.932606	+	0.360896i	$0.882471\pi$
$380$	79853.3	+	8052.46i	0.553001	+	0.0557650i
$381$	−38269.8			−0.263637
$382$	−89294.9	+	80743.2i	−0.611927	+	0.553324i
$383$		−	65887.8i		−	0.449166i	−0.974455	−	0.224583i	$-0.927898\pi$
$383$		−	65887.8i		−	0.449166i	0.974455	−	0.224583i	$-0.0721021\pi$
$384$	−36301.7	−	78398.7i	−0.246187	−	0.531675i
$385$	110494.			0.745445
$386$	30592.5	+	33832.6i	0.205324	+	0.227071i
$387$		−	154030.i		−	1.02845i
$388$	11704.1	−	116066.i	0.0777457	−	0.770976i
$389$	223507.			1.47704			0.738518	−	0.674234i	$-0.235526\pi$
$389$	223507.			1.47704			0.738518	+	0.674234i	$0.235526\pi$
$390$	77088.0	−	69705.3i	0.506824	−	0.458286i
$391$			250983.i			1.64169i
$392$	−17677.5	+	13015.2i	−0.115040	+	0.0846990i
$393$	−97498.5			−0.631267
$394$	10862.2	+	12012.7i	0.0699724	+	0.0773833i
$395$		−	156802.i		−	1.00498i
$396$	−138025.	−	13918.5i	−0.880170	−	0.0887569i
$397$	−293103.			−1.85968			−0.929842	−	0.367958i	$-0.880057\pi$
$397$	−293103.			−1.85968			−0.929842	+	0.367958i	$0.880057\pi$
$398$	120265.	−	108747.i	0.759230	−	0.686519i
$399$		−	13383.5i		−	0.0840669i
$400$	−179300.	−	36533.0i	−1.12063	−	0.228331i
$401$	−8960.63			−0.0557250			−0.0278625	−	0.999612i	$-0.508870\pi$
$401$	−8960.63			−0.0557250			−0.0278625	+	0.999612i	$0.508870\pi$
$402$	−86851.9	−	96050.5i	−0.537436	−	0.594357i
$403$		−	77211.4i		−	0.475413i
$404$	17680.5	−	175332.i	0.108326	−	1.07423i
$405$	21130.0			0.128822
$406$	27958.1	−	25280.6i	0.169612	−	0.153368i
$407$		−	38735.1i		−	0.233839i
$408$	−77354.7	−	105065.i	−0.464694	−	0.631158i
$409$	−7602.46			−0.0454473			−0.0227236	−	0.999742i	$-0.507234\pi$
$409$	−7602.46			−0.0454473			−0.0227236	+	0.999742i	$0.507234\pi$
$410$	158792.	+	175610.i	0.944629	+	1.04468i
$411$			98607.9i			0.583752i
$412$	−171350.	−	17279.0i	−1.00946	−	0.101794i
$413$	33246.0			0.194912
$414$	−102460.	+	92647.1i	−0.597795	+	0.540544i
$415$		−	294976.i		−	1.71273i
$416$	70177.8	+	118644.i	0.405521	+	0.685581i
$417$	45025.0			0.258930
$418$	−59925.6	−	66272.4i	−0.342973	−	0.379298i
$419$			236440.i			1.34677i	0.739292	+	0.673385i	$0.235160\pi$
$419$			236440.i			1.34677i	−0.739292	+	0.673385i	$0.764840\pi$
$420$	−5738.44	+	56906.0i	−0.0325308	+	0.322596i
$421$	234204.			1.32139			0.660693	−	0.750656i	$-0.270263\pi$
$421$	234204.			1.32139			0.660693	+	0.750656i	$0.270263\pi$
$422$	53538.7	−	48411.4i	0.300638	−	0.271846i
$423$			132337.i			0.739607i
$424$	42426.3	−	31236.6i	0.235995	−	0.173753i
$425$	−276333.			−1.52987
$426$	108223.	+	119685.i	0.596350	+	0.659511i
$427$			52447.3i			0.287652i
$428$	62846.9	+	6337.52i	0.343081	+	0.0345965i
$429$	−115701.			−0.628667
$430$	−314462.	+	284346.i	−1.70071	+	1.53784i
$431$		−	118274.i		−	0.636701i	−0.947973	−	0.318350i	$-0.896871\pi$
$431$		−	118274.i		−	0.636701i	0.947973	−	0.318350i	$-0.103129\pi$
$432$	36167.2	−	177505.i	0.193797	−	0.951137i
$433$	−153529.			−0.818869			−0.409435	−	0.912339i	$-0.634274\pi$
$433$	−153529.			−0.818869			−0.409435	+	0.912339i	$0.634274\pi$
$434$	28498.6	+	31516.9i	0.151302	+	0.167326i
$435$		−	98207.0i		−	0.518996i
$436$	−13005.9	+	128975.i	−0.0684175	+	0.678471i
$437$	−88968.8			−0.465881
$438$	72816.7	−	65843.1i	0.379562	−	0.343212i
$439$			245393.i			1.27331i	0.771150	+	0.636653i	$0.219682\pi$
$439$			245393.i			1.27331i	−0.771150	+	0.636653i	$0.780318\pi$
$440$	226384.	+	307481.i	1.16934	+	1.58823i
$441$	−18245.5			−0.0938162
$442$	139617.	+	154404.i	0.714649	+	0.790339i
$443$		−	74591.2i		−	0.380085i	−0.981776	−	0.190042i	$-0.939137\pi$
$443$		−	74591.2i		−	0.380085i	0.981776	−	0.190042i	$-0.0608625\pi$
$444$	19949.2	+	2011.69i	0.101195	+	0.0102046i
$445$	−489780.			−2.47333
$446$	216382.	−	195659.i	1.08781	−	0.983628i
$447$			172423.i			0.862940i
$448$	−72437.1	−	22526.7i	−0.360915	−	0.112239i
$449$	−124024.			−0.615194			−0.307597	−	0.951517i	$-0.599525\pi$
$449$	−124024.			−0.615194			−0.307597	+	0.951517i	$0.599525\pi$
$450$	−102005.	−	112808.i	−0.503728	−	0.557079i
$451$		−	263572.i		−	1.29582i
$452$	−34002.5	+	337190.i	−0.166431	+	1.65043i
$453$	26311.2			0.128217
$454$	137929.	−	124720.i	0.669183	−	0.605096i
$455$		−	91254.8i		−	0.440791i
$456$	37243.6	−	27420.8i	0.179111	−	0.131871i
$457$	289814.			1.38767			0.693836	−	0.720133i	$-0.255919\pi$
$457$	289814.			1.38767			0.693836	+	0.720133i	$0.255919\pi$
$458$	−163675.	−	181011.i	−0.780284	−	0.862925i
$459$		−	273567.i		−	1.29849i
$460$	378290.	+	38147.0i	1.78776	+	0.180279i
$461$	250030.			1.17650			0.588249	−	0.808680i	$-0.299818\pi$
$461$	250030.			1.17650			0.588249	+	0.808680i	$0.299818\pi$
$462$	47227.8	−	42704.9i	0.221266	−	0.200075i
$463$		−	14643.0i		−	0.0683076i	−0.999417	−	0.0341538i	$-0.989126\pi$
$463$		−	14643.0i		−	0.0683076i	0.999417	−	0.0341538i	$-0.0108736\pi$
$464$	127633.	+	26005.6i	0.592824	+	0.120790i
$465$	110708.			0.512003
$466$	36582.5	+	40457.1i	0.168462	+	0.186304i
$467$		−	364513.i		−	1.67140i	−0.549189	−	0.835698i	$-0.685063\pi$
$467$		−	364513.i		−	1.67140i	0.549189	−	0.835698i	$-0.314937\pi$
$468$	−11495.1	+	113992.i	−0.0524831	+	0.520456i
$469$	−113702.			−0.516920
$470$	270175.	−	244300.i	1.22306	−	1.10593i
$471$			5035.57i			0.0226990i
$472$	68115.9	+	92516.6i	0.305749	+	0.415275i
$473$	471973.			2.10957
$474$	−60602.8	−	67021.3i	−0.269734	−	0.298302i
$475$		−	97955.0i		−	0.434150i
$476$	−113980.	−	11493.8i	−0.503055	−	0.0507284i
$477$	43789.3			0.192456
$478$	−190979.	+	172690.i	−0.835855	+	0.755806i
$479$			356405.i			1.55336i	0.629893	+	0.776682i	$0.283099\pi$
$479$			356405.i			1.55336i	−0.629893	+	0.776682i	$0.716901\pi$
$480$	−170115.	+	100623.i	−0.738345	+	0.436731i
$481$	−31990.7			−0.138272
$482$	−97579.7	−	107915.i	−0.420016	−	0.464500i
$483$		−	63402.0i		−	0.271775i
$484$	19145.3	−	189857.i	0.0817279	−	0.810466i
$485$	−266869.			−1.13453
$486$	179089.	−	161938.i	0.758221	−	0.685607i
$487$			238920.i			1.00738i	0.863884	+	0.503691i	$0.168025\pi$
$487$			238920.i			1.00738i	−0.863884	+	0.503691i	$0.831975\pi$
$488$	−145950.	+	107457.i	−0.612864	+	0.451225i
$489$	44085.9			0.184366
$490$	33682.0	+	37249.3i	0.140283	+	0.155141i
$491$		−	108162.i		−	0.448654i	−0.974514	−	0.224327i	$-0.927982\pi$
$491$		−	108162.i		−	0.448654i	0.974514	−	0.224327i	$-0.0720184\pi$
$492$	135744.	+	13688.5i	0.560776	+	0.0565490i
$493$	196704.			0.809320
$494$	−54733.3	+	49491.5i	−0.224284	+	0.202804i
$495$			317359.i			1.29521i
$496$	−29315.8	+	143879.i	−0.119162	+	0.584835i
$497$	141681.			0.573585
$498$	−114006.	−	126080.i	−0.459692	−	0.508380i
$499$		−	246397.i		−	0.989540i	−0.869024	−	0.494770i	$-0.835252\pi$
$499$		−	246397.i		−	0.989540i	0.869024	−	0.494770i	$-0.164748\pi$
$500$	−5275.54	+	52315.6i	−0.0211021	+	0.209262i
$501$	64852.3			0.258375
$502$	−46051.0	+	41640.7i	−0.182739	+	0.165238i
$503$			144372.i			0.570621i	0.958435	+	0.285310i	$0.0920967\pi$
$503$			144372.i			0.570621i	−0.958435	+	0.285310i	$0.907903\pi$
$504$	−37382.2	−	50773.3i	−0.147165	−	0.199882i
$505$	−403138.			−1.58078
$506$	−283886.	−	313953.i	−1.10877	−	1.22621i
$507$		−	55051.6i		−	0.214168i
$508$	−115533.	−	11650.5i	−0.447693	−	0.0451456i
$509$	302399.			1.16720			0.583599	−	0.812042i	$-0.301644\pi$
$509$	302399.			1.16720			0.583599	+	0.812042i	$0.301644\pi$
$510$	−221388.	+	200186.i	−0.851166	+	0.769650i
$511$		−	86198.6i		−	0.330110i
$512$	−85725.3	−	247731.i	−0.327016	−	0.945019i
$513$	96974.2			0.368486
$514$	180353.	+	199454.i	0.682648	+	0.754949i
$515$			393983.i			1.48547i
$516$	−24511.7	+	243074.i	−0.0920606	+	0.912932i
$517$	−405503.			−1.51710
$518$	13058.3	−	11807.7i	0.0486661	−	0.0440054i
$519$			154270.i			0.572724i
$520$	253943.	−	186967.i	0.939138	−	0.691446i
$521$	−46951.9			−0.172973			−0.0864865	−	0.996253i	$-0.527564\pi$
$521$	−46951.9			−0.172973			−0.0864865	+	0.996253i	$0.527564\pi$
$522$	72610.9	+	80301.2i	0.266478	+	0.294701i
$523$		−	209351.i		−	0.765370i	−0.923879	−	0.382685i	$-0.875000\pi$
$523$		−	209351.i		−	0.765370i	0.923879	−	0.382685i	$-0.125000\pi$
$524$	−294340.	−	29681.5i	−1.07198	−	0.108099i
$525$	69805.9			0.253264
$526$	79830.6	−	72185.3i	0.288535	−	0.260902i
$527$			221743.i			0.798414i
$528$	215601.	+	43929.4i	0.773363	+	0.157575i
$529$	−141632.			−0.506117
$530$	−80837.1	−	89398.8i	−0.287779	−	0.318258i
$531$			95489.0i			0.338660i
$532$	4074.35	−	40403.9i	0.0143958	−	0.142758i
$533$	−217679.			−0.766237
$534$	−209345.	+	189296.i	−0.734141	+	0.663833i
$535$		−	144503.i		−	0.504859i
$536$	−232958.	−	316410.i	−0.810866	−	1.10134i
$537$	−279097.			−0.967847
$538$	28957.4	+	32024.4i	0.100045	+	0.110641i
$539$		−	55907.1i		−	0.192437i
$540$	−412329.	−	41579.5i	−1.41402	−	0.142591i
$541$	249074.			0.851007			0.425503	−	0.904957i	$-0.360097\pi$
$541$	249074.			0.851007			0.425503	+	0.904957i	$0.360097\pi$
$542$	−37810.2	+	34189.2i	−0.128710	+	0.116383i
$543$			120130.i			0.407430i
$544$	−201543.	−	340732.i	−0.681036	−	1.15137i
$545$	296550.			0.998402
$546$	−35269.2	−	39004.7i	−0.118307	−	0.130837i
$547$			344310.i			1.15073i	0.817895	+	0.575367i	$0.195141\pi$
$547$			344310.i			1.15073i	−0.817895	+	0.575367i	$0.804859\pi$
$548$	−30019.2	+	297690.i	−0.0999628	+	0.991295i
$549$	−150639.			−0.499796
$550$	345664.	−	312560.i	1.14269	−	1.03326i
$551$			69728.0i			0.229670i
$552$	176434.	−	129901.i	0.579036	−	0.426319i
$553$	−79338.2			−0.259437
$554$	−48300.1	−	53415.7i	−0.157372	−	0.174040i
$555$		−	45869.1i		−	0.148914i
$556$	135927.	+	13707.0i	0.439700	+	0.0443396i
$557$	−87168.8			−0.280964			−0.140482	−	0.990083i	$-0.544865\pi$
$557$	−87168.8			−0.280964			−0.140482	+	0.990083i	$0.544865\pi$
$558$	−90522.7	+	81853.4i	−0.290730	+	0.262887i
$559$		−	389794.i		−	1.24742i
$560$	−34647.8	+	170048.i	−0.110484	+	0.542245i
$561$	332280.			1.05579
$562$	72066.3	+	79699.0i	0.228171	+	0.252337i
$563$			566730.i			1.78797i	0.448101	+	0.893983i	$0.352100\pi$
$563$			566730.i			1.78797i	−0.448101	+	0.893983i	$0.647900\pi$
$564$	21059.6	−	208841.i	0.0662052	−	0.656533i
$565$	775299.			2.42869
$566$	−21601.0	+	19532.3i	−0.0674282	+	0.0609707i
$567$		−	10691.3i		−	0.0332555i
$568$	290282.	+	394267.i	0.899752	+	1.22206i
$569$	89918.1			0.277730			0.138865	−	0.990311i	$-0.455655\pi$
$569$	89918.1			0.277730			0.138865	+	0.990311i	$0.455655\pi$
$570$	−70962.2	−	78478.0i	−0.218412	−	0.241545i
$571$		−	395133.i		−	1.21191i	−0.795498	−	0.605956i	$-0.792791\pi$
$571$		−	395133.i		−	1.21191i	0.795498	−	0.605956i	$-0.207209\pi$
$572$	−349291.	−	35222.7i	−1.06757	−	0.107654i
$573$	158705.			0.483372
$574$	88854.5	−	80345.0i	0.269684	−	0.243857i
$575$		−	464044.i		−	1.40353i
$576$	64701.2	−	208053.i	0.195015	−	0.627090i
$577$	360542.			1.08294			0.541469	−	0.840721i	$-0.317868\pi$
$577$	360542.			1.08294			0.541469	+	0.840721i	$0.317868\pi$
$578$	−176895.	−	195630.i	−0.529492	−	0.585572i
$579$		−	60131.2i		−	0.179367i
$580$	29897.2	−	296479.i	0.0888739	−	0.881330i
$581$	−149251.			−0.442144
$582$	−114067.	+	103143.i	−0.336754	+	0.304504i
$583$			134178.i			0.394769i
$584$	239873.	−	176608.i	0.703324	−	0.517826i
$585$	262102.			0.765875
$586$	322337.	+	356476.i	0.938673	+	1.03809i
$587$			56841.2i			0.164963i	0.996593	+	0.0824816i	$0.0262846\pi$
$587$			56841.2i			0.164963i	−0.996593	+	0.0824816i	$0.973715\pi$
$588$	28793.1	+	2903.51i	0.0832786	+	0.00839787i
$589$	−78603.7			−0.226575
$590$	194947.	−	176277.i	0.560031	−	0.506398i
$591$		−	21350.3i		−	0.0611264i
$592$	59612.8	+	12146.3i	0.170097	+	0.0346577i
$593$	−554159.			−1.57589			−0.787943	−	0.615748i	$-0.788854\pi$
$593$	−554159.			−1.57589			−0.787943	+	0.615748i	$0.788854\pi$
$594$	309430.	+	342203.i	0.876980	+	0.969863i
$595$			262074.i			0.740270i
$596$	−52490.8	+	520532.i	−0.147772	+	1.46540i
$597$	−213749.			−0.599729
$598$	−259289.	+	234457.i	−0.725072	+	0.655632i
$599$		−	106614.i		−	0.297138i	−0.988902	−	0.148569i	$-0.952533\pi$
$599$		−	106614.i		−	0.297138i	0.988902	−	0.148569i	$-0.0474668\pi$
$600$	143021.	+	194255.i	0.397282	+	0.539597i
$601$	−550910.			−1.52522			−0.762608	−	0.646861i	$-0.776081\pi$
$601$	−550910.			−1.52522			−0.762608	+	0.646861i	$0.776081\pi$
$602$	143872.	+	159110.i	0.396994	+	0.439041i
$603$		−	326575.i		−	0.898149i
$604$	79431.5	+	8009.92i	0.217730	+	0.0219561i
$605$	−436536.			−1.19264
$606$	−172312.	+	155810.i	−0.469213	+	0.424276i
$607$		−	405496.i		−	1.10055i	−0.834984	−	0.550275i	$-0.814523\pi$
$607$		−	405496.i		−	1.10055i	0.834984	−	0.550275i	$-0.185477\pi$
$608$	120783.	−	71443.2i	0.326738	−	0.193265i
$609$	−49690.4			−0.133979
$610$	278086.	+	307539.i	0.747343	+	0.826496i
$611$			334898.i			0.897078i
$612$	33012.5	−	327373.i	0.0881406	−	0.874059i
$613$	−258201.			−0.687126			−0.343563	−	0.939130i	$-0.611634\pi$
$613$	−258201.			−0.687126			−0.343563	+	0.939130i	$0.611634\pi$
$614$	−200900.	+	181660.i	−0.532897	+	0.481862i
$615$		−	312114.i		−	0.825208i
$616$	155578.	−	114545.i	0.410002	−	0.301867i
$617$	389033.			1.02192			0.510959	−	0.859605i	$-0.329290\pi$
$617$	389033.			1.02192			0.510959	+	0.859605i	$0.329290\pi$
$618$	152271.	+	168398.i	0.398695	+	0.440921i
$619$		−	493034.i		−	1.28675i	−0.765549	−	0.643377i	$-0.777533\pi$
$619$		−	493034.i		−	1.28675i	0.765549	−	0.643377i	$-0.222467\pi$
$620$	334218.	+	33702.8i	0.869454	+	0.0876763i
$621$	459397.			1.19126
$622$	105021.	−	94963.3i	0.271454	−	0.245457i
$623$			247817.i			0.638492i
$624$	36280.6	−	178061.i	0.0931762	−	0.457299i
$625$	−326450.			−0.835712
$626$	−170666.	−	188741.i	−0.435509	−	0.481635i
$627$			117787.i			0.299614i
$628$	−1532.98	+	15202.0i	−0.00388702	+	0.0385462i
$629$	91873.8			0.232215
$630$	−106987.	+	96741.1i	−0.269557	+	0.243742i
$631$			201101.i			0.505075i	0.967587	+	0.252538i	$0.0812651\pi$
$631$			201101.i			0.505075i	−0.967587	+	0.252538i	$0.918735\pi$
$632$	−162552.	−	220782.i	−0.406965	−	0.552750i
$633$	−95155.1			−0.237479
$634$	192397.	+	212774.i	0.478651	+	0.529346i
$635$			265645.i			0.658801i
$636$	−69103.7	−	6968.47i	−0.170839	−	0.0172275i
$637$	−46172.7			−0.113791
$638$	−246056.	+	222492.i	−0.604495	+	0.546603i
$639$			406934.i			0.996603i
$640$	−544196.	+	251984.i	−1.32860	+	0.615196i
$641$	−360516.			−0.877422			−0.438711	−	0.898628i	$-0.644565\pi$
$641$	−360516.			−0.877422			−0.438711	+	0.898628i	$0.644565\pi$
$642$	−55849.3	−	61764.4i	−0.135503	−	0.149854i
$643$		−	268055.i		−	0.648339i	−0.945999	−	0.324169i	$-0.894915\pi$
$643$		−	268055.i		−	0.648339i	0.945999	−	0.324169i	$-0.105085\pi$
$644$	19301.5	−	191406.i	0.0465392	−	0.461512i
$645$	558897.			1.34342
$646$	157188.	−	142134.i	0.376664	−	0.340591i
$647$		−	724695.i		−	1.73120i	−0.500738	−	0.865599i	$-0.666938\pi$
$647$		−	724695.i		−	1.73120i	0.500738	−	0.865599i	$-0.333062\pi$
$648$	29751.6	−	21904.8i	0.0708533	−	0.0521662i
$649$	−292594.			−0.694666
$650$	−258138.	−	285478.i	−0.610977	−	0.675687i
$651$		−	56015.5i		−	0.132174i
$652$	133092.	+	13421.1i	0.313081	+	0.0315713i
$653$	−507722.			−1.19069			−0.595346	−	0.803469i	$-0.702985\pi$
$653$	−507722.			−1.19069			−0.595346	+	0.803469i	$0.702985\pi$
$654$	126753.	−	114614.i	0.296349	−	0.267968i
$655$			676775.i			1.57747i
$656$	405633.	+	82648.9i	0.942595	+	0.192057i
$657$	247579.			0.573566
$658$	−123610.	−	136702.i	−0.285498	−	0.315735i
$659$		−	270657.i		−	0.623229i	−0.950209	−	0.311615i	$-0.899130\pi$
$659$		−	270657.i		−	0.623229i	0.950209	−	0.311615i	$-0.100870\pi$
$660$	50503.3	−	500823.i	0.115940	−	1.14973i
$661$	−763718.			−1.74796			−0.873978	−	0.485966i	$-0.838468\pi$
$661$	−763718.			−1.74796			−0.873978	+	0.485966i	$0.838468\pi$
$662$	6335.87	−	5729.09i	0.0144574	−	0.0130728i
$663$		−	274424.i		−	0.624303i
$664$	−305791.	−	415333.i	−0.693568	−	0.942020i
$665$	−92900.3			−0.210075
$666$	33914.0	+	37505.9i	0.0764594	+	0.0845573i
$667$			330324.i			0.742485i
$668$	195784.	+	19743.0i	0.438757	+	0.0442446i
$669$	−384579.			−0.859277
$670$	−666724.	+	602872.i	−1.48524	+	1.34300i
$671$		−	461582.i		−	1.02519i
$672$	50912.7	+	86073.9i	0.112743	+	0.190604i
$673$	136675.			0.301758			0.150879	−	0.988552i	$-0.451790\pi$
$673$	136675.			0.301758			0.150879	+	0.988552i	$0.451790\pi$
$674$	565415.	+	625300.i	1.24465	+	1.37648i
$675$			505798.i			1.11012i
$676$	16759.4	−	166196.i	0.0366745	−	0.363687i
$677$	756709.			1.65102			0.825508	−	0.564390i	$-0.190889\pi$
$677$	756709.			1.65102			0.825508	+	0.564390i	$0.190889\pi$
$678$	331383.	−	299647.i	0.720893	−	0.651853i
$679$			135029.i			0.292879i
$680$	−729297.	+	536949.i	−1.57720	+	1.16122i
$681$	−245144.			−0.528599
$682$	−250812.	−	277377.i	−0.539238	−	0.596350i
$683$		−	255354.i		−	0.547395i	−0.961816	−	0.273697i	$-0.911753\pi$
$683$		−	255354.i		−	0.547395i	0.961816	−	0.273697i	$-0.0882467\pi$
$684$	116048.	+	11702.3i	0.248042	+	0.0250127i
$685$	684476.			1.45874
$686$	18847.3	−	17042.3i	0.0400497	−	0.0362142i
$687$			321713.i			0.681640i
$688$	−147998.	+	726358.i	−0.312665	+	1.53453i
$689$	110815.			0.233432
$690$	−336170.	−	371775.i	−0.706092	−	0.780875i
$691$		−	203246.i		−	0.425663i	−0.977089	−	0.212832i	$-0.931731\pi$
$691$		−	203246.i		−	0.425663i	0.977089	−	0.212832i	$-0.0682686\pi$
$692$	−46964.3	+	465728.i	−0.0980744	+	0.972568i
$693$	160576.			0.334360
$694$	−32959.4	+	29803.0i	−0.0684323	+	0.0618786i
$695$		−	312536.i		−	0.647039i
$696$	−101808.	−	138278.i	−0.210166	−	0.285453i
$697$	625152.			1.28683
$698$	−147788.	−	163441.i	−0.303339	−	0.335466i
$699$		−	71904.9i		−	0.147165i
$700$	210739.	+	21251.0i	0.430079	+	0.0433694i
$701$	1565.31			0.00318539			0.00159270	−	0.999999i	$-0.499493\pi$
$701$	1565.31			0.00318539			0.00159270	+	0.999999i	$0.499493\pi$
$702$	282619.	−	255553.i	0.573492	−	0.518569i
$703$			32567.5i			0.0658983i
$704$	637510.	+	198255.i	1.28630	+	0.400017i
$705$	−480186.			−0.966120
$706$	−301539.	−	333476.i	−0.604970	−	0.669044i
$707$			203978.i			0.408080i
$708$	15195.7	−	150691.i	0.0303148	−	0.300621i
$709$	307124.			0.610972			0.305486	−	0.952197i	$-0.401181\pi$
$709$	307124.			0.610972			0.305486	+	0.952197i	$0.401181\pi$
$710$	830782.	−	751219.i	1.64805	−	1.49022i
$711$		−	227875.i		−	0.450772i
$712$	−689623.	+	507739.i	−1.36035	+	1.00157i
$713$	−372370.			−0.732480
$714$	101289.	+	112017.i	0.198686	+	0.219729i
$715$			803122.i			1.57098i
$716$	−842572.	−	84965.5i	−1.64354	−	0.165736i
$717$	339430.			0.660256
$718$	641556.	−	580114.i	1.24447	−	1.12529i
$719$		−	339092.i		−	0.655933i	−0.944689	−	0.327967i	$-0.893637\pi$
$719$		−	339092.i		−	0.655933i	0.944689	−	0.327967i	$-0.106363\pi$
$720$	−488411.	−	99515.2i	−0.942150	−	0.191966i
$721$	199346.			0.383475
$722$	−299240.	−	330933.i	−0.574043	−	0.634841i
$723$			191798.i			0.366917i
$724$	−36571.3	+	362664.i	−0.0697691	+	0.691875i
$725$	−363687.			−0.691914
$726$	−186587.	+	168717.i	−0.354003	+	0.320101i
$727$			772438.i			1.46149i	0.682653	+	0.730743i	$0.260826\pi$
$727$			772438.i			1.46149i	−0.682653	+	0.730743i	$0.739174\pi$
$728$	−94600.9	−	128489.i	−0.178498	−	0.242440i
$729$	−271538.			−0.510946
$730$	−457043.	−	505449.i	−0.857652	−	0.948487i
$731$			1.11945e6i			2.09493i
$732$	237722.	+	23972.1i	0.443658	+	0.0447387i
$733$	924879.			1.72138			0.860690	−	0.509129i	$-0.170032\pi$
$733$	924879.			1.72138			0.860690	+	0.509129i	$0.170032\pi$
$734$	−513985.	+	464761.i	−0.954022	+	0.862656i
$735$		−	66203.7i		−	0.122548i
$736$	572188.	−	338449.i	1.05629	−	0.624795i
$737$	1.00068e6			1.84230
$738$	230767.	+	255208.i	0.423702	+	0.468577i
$739$		−	124602.i		−	0.228158i	−0.993472	−	0.114079i	$-0.963608\pi$
$739$		−	124602.i		−	0.228158i	0.993472	−	0.114079i	$-0.0363917\pi$
$740$	13963.9	−	138475.i	0.0255002	−	0.252877i
$741$	97278.2			0.177165
$742$	−45233.6	+	40901.7i	−0.0821587	+	0.0742905i
$743$		−	275837.i		−	0.499660i	−0.968290	−	0.249830i	$-0.919625\pi$
$743$		−	275837.i		−	0.499660i	0.968290	−	0.249830i	$-0.0803747\pi$
$744$	155879.	−	114767.i	0.281606	−	0.207334i
$745$	1.19686e6			2.15640
$746$	−123720.	−	136823.i	−0.222311	−	0.245856i
$747$		−	428677.i		−	0.768225i
$748$	1.00313e6	+	101156.i	1.79288	+	0.180796i
$749$	−73115.2			−0.130330
$750$	51414.5	−	46490.6i	0.0914036	−	0.0826500i
$751$		−	265528.i		−	0.470793i	−0.971899	−	0.235396i	$-0.924361\pi$
$751$		−	265528.i		−	0.470793i	0.971899	−	0.235396i	$-0.0756388\pi$
$752$	127155.	−	624063.i	0.224852	−	1.10355i
$753$	81847.1			0.144349
$754$	183752.	+	203214.i	0.323214	+	0.357446i
$755$		−	182636.i		−	0.320400i
$756$	−21038.2	+	208628.i	−0.0368100	+	0.365031i
$757$	−617266.			−1.07716			−0.538580	−	0.842574i	$-0.681039\pi$
$757$	−617266.			−1.07716			−0.538580	+	0.842574i	$0.681039\pi$
$758$	307607.	−	278148.i	0.535375	−	0.484103i
$759$			557993.i			0.968602i
$760$	−190338.	−	258522.i	−0.329533	−	0.447580i
$761$	152689.			0.263657			0.131829	−	0.991273i	$-0.457915\pi$
$761$	152689.			0.263657			0.131829	+	0.991273i	$0.457915\pi$
$762$	102670.	+	113544.i	0.176820	+	0.195548i
$763$		−	150047.i		−	0.257739i
$764$	479118.	+	48314.6i	0.820835	+	0.0827736i
$765$	−752727.			−1.28622
$766$	−195484.	+	176763.i	−0.333161	+	0.301254i
$767$			241648.i			0.410765i
$768$	−135213.	+	318032.i	−0.229244	+	0.539198i
$769$	−281434.			−0.475909			−0.237954	−	0.971276i	$-0.576477\pi$
$769$	−281434.			−0.475909			−0.237954	+	0.971276i	$0.576477\pi$
$770$	−296431.	−	327826.i	−0.499968	−	0.552920i
$771$		−	354493.i		−	0.596347i
$772$	18305.8	−	181532.i	0.0307152	−	0.304591i
$773$	−573828.			−0.960335			−0.480167	−	0.877177i	$-0.659424\pi$
$773$	−573828.			−0.960335			−0.480167	+	0.877177i	$0.659424\pi$
$774$	−456995.	+	413229.i	−0.762833	+	0.689777i
$775$		−	409981.i		−	0.682591i
$776$	−375758.	+	276654.i	−0.624001	+	0.459424i
$777$	−23208.7			−0.0384422
$778$	−599621.	−	663128.i	−0.990643	−	1.09556i
$779$			221605.i			0.365177i
$780$	−413621.	−	41709.8i	−0.679851	−	0.0685566i
$781$	−1.24691e6			−2.04425
$782$	744649.	−	673334.i	1.21769	−	1.10108i
$783$		−	360046.i		−	0.587265i
$784$	86040.2	+	17531.0i	0.139981	+	0.0285216i
$785$	34953.8			0.0567225
$786$	261568.	+	289271.i	0.423389	+	0.468231i
$787$		−	630450.i		−	1.01789i	−0.860799	−	0.508945i	$-0.830036\pi$
$787$		−	630450.i		−	1.01789i	0.860799	−	0.508945i	$-0.169964\pi$
$788$	6499.67	−	64454.9i	0.0104674	−	0.103801i
$789$	−141884.			−0.227918
$790$	−465221.	+	420667.i	−0.745427	+	0.674038i
$791$		−	392283.i		−	0.626969i
$792$	328996.	+	446850.i	0.524493	+	0.712379i
$793$	−381213.			−0.606208
$794$	786333.	+	869615.i	1.24728	+	1.37939i
$795$			158890.i			0.251398i
$796$	−645291.	−	65071.6i	−1.01843	−	0.102699i
$797$	492028.			0.774592			0.387296	−	0.921955i	$-0.373409\pi$
$797$	492028.			0.774592			0.387296	+	0.921955i	$0.373409\pi$
$798$	−39708.0	+	35905.2i	−0.0623551	+	0.0563834i
$799$		−	961791.i		−	1.50656i
$800$	372634.	+	629981.i	0.582240	+	0.984345i
$801$	−711779.			−1.10938
$802$	24039.5	+	26585.5i	0.0373746	+	0.0413330i
$803$			758624.i			1.17651i
$804$	−51969.9	+	515366.i	−0.0803969	+	0.797267i
$805$	−440098.			−0.679137
$806$	−229081.	+	207142.i	−0.352629	+	0.318858i
$807$		−	56917.3i		−	0.0873972i
$808$	−567629.	+	417920.i	−0.869444	+	0.640134i
$809$	423402.			0.646928			0.323464	−	0.946241i	$-0.395153\pi$
$809$	423402.			0.646928			0.323464	+	0.946241i	$0.395153\pi$
$810$	−56687.3	−	62691.2i	−0.0864004	−	0.0955513i
$811$			1.16771e6i			1.77538i	0.460440	+	0.887691i	$0.347692\pi$
$811$			1.16771e6i			1.77538i	−0.460440	+	0.887691i	$0.652308\pi$
$812$	−150012.	−	15127.3i	−0.227516	−	0.0229429i
$813$	67200.6			0.101670
$814$	−114924.	+	103918.i	−0.173446	+	0.156835i
$815$		−	306017.i		−	0.460713i
$816$	−104194.	+	511373.i	−0.156481	+	0.767993i
$817$	−396823.			−0.594501
$818$	20395.8	+	22555.9i	0.0304813	+	0.0337097i
$819$		−	132617.i		−	0.197711i
$820$	95017.0	−	942249.i	0.141310	−	1.40132i
$821$	302231.			0.448386			0.224193	−	0.974545i	$-0.428025\pi$
$821$	302231.			0.448386			0.224193	+	0.974545i	$0.428025\pi$
$822$	292562.	−	264544.i	0.432987	−	0.391520i
$823$			326584.i			0.482165i	0.970505	+	0.241083i	$0.0775024\pi$
$823$			326584.i			0.482165i	−0.970505	+	0.241083i	$0.922498\pi$
$824$	408429.	+	554738.i	0.601537	+	0.817021i
$825$	−614353.			−0.902630
$826$	−89191.9	−	98638.4i	−0.130727	−	0.144573i
$827$			395430.i			0.578173i	0.957303	+	0.289087i	$0.0933516\pi$
$827$			395430.i			0.578173i	−0.957303	+	0.289087i	$0.906648\pi$
$828$	549755.	+	55437.6i	0.801878	+	0.0808619i
$829$	603244.			0.877777			0.438888	−	0.898542i	$-0.355372\pi$
$829$	603244.			0.877777			0.438888	+	0.898542i	$0.355372\pi$
$830$	−875171.	+	791357.i	−1.27039	+	1.14872i
$831$			94936.4i			0.137477i
$832$	163735.	−	526509.i	0.236535	−	0.760604i
$833$	132603.			0.191101
$834$	−120793.	−	133586.i	−0.173663	−	0.192056i
$835$		−	450165.i		−	0.645652i
$836$	−35857.9	+	355589.i	−0.0513064	+	0.508787i
$837$	405876.			0.579352
$838$	701501.	−	634319.i	0.998941	−	0.903274i
$839$		−	925717.i		−	1.31509i	−0.753417	−	0.657543i	$-0.771596\pi$
$839$		−	925717.i		−	1.31509i	0.753417	−	0.657543i	$-0.228404\pi$
$840$	184231.	−	135641.i	0.261098	−	0.192235i
$841$	−448395.			−0.633970
$842$	−628319.	−	694865.i	−0.886249	−	0.980114i
$843$		−	141650.i		−	0.199325i
$844$	−287266.	−	28968.1i	−0.403273	−	0.0406663i
$845$	−382134.			−0.535183
$846$	392635.	−	355032.i	0.548590	−	0.496052i
$847$			220877.i			0.307881i
$848$	−206497.	−	42074.5i	−0.287159	−	0.0585096i
$849$	38391.8			0.0532627
$850$	741344.	+	819861.i	1.02608	+	1.13476i
$851$			154283.i			0.213038i
$852$	64757.9	−	642181.i	0.0892100	−	0.884663i
$853$	272516.			0.374536			0.187268	−	0.982309i	$-0.440037\pi$
$853$	272516.			0.374536			0.187268	+	0.982309i	$0.440037\pi$
$854$	155607.	−	140705.i	0.213361	−	0.192927i
$855$		−	266828.i		−	0.365005i
$856$	−149802.	−	203464.i	−0.204442	−	0.277677i
$857$	−473133.			−0.644201			−0.322100	−	0.946706i	$-0.604389\pi$
$857$	−473133.			−0.644201			−0.322100	+	0.946706i	$0.604389\pi$
$858$	310400.	+	343275.i	0.421645	+	0.466303i
$859$			163985.i			0.222237i	0.993807	+	0.111119i	$0.0354434\pi$
$859$			163985.i			0.222237i	−0.993807	+	0.111119i	$0.964557\pi$
$860$	1.68727e6	+	170145.i	2.28132	+	0.230050i
$861$	−157922.			−0.213028
$862$	−350911.	+	317304.i	−0.472261	+	0.427033i
$863$		−	1.24638e6i		−	1.67351i	−0.547576	−	0.836756i	$-0.684449\pi$
$863$		−	1.24638e6i		−	1.67351i	0.547576	−	0.836756i	$-0.315551\pi$
$864$	−623673.	+	368903.i	−0.835467	+	0.494179i
$865$	1.07084e6			1.43118
$866$	411886.	+	455509.i	0.549213	+	0.607381i
$867$			347696.i			0.462554i
$868$	17052.8	−	169106.i	0.0226337	−	0.224450i
$869$	698246.			0.924632
$870$	−291373.	+	263469.i	−0.384956	+	0.348089i
$871$		−	826444.i		−	1.08937i
$872$	417550.	−	307424.i	0.549131	−	0.404301i
$873$	−387831.			−0.508878
$874$	238684.	+	263964.i	0.312465	+	0.345559i
$875$		−	60863.3i		−	0.0794949i
$876$	−390704.	−	39398.8i	−0.509142	−	0.0513422i
$877$	208681.			0.271322			0.135661	−	0.990755i	$-0.456684\pi$
$877$	208681.			0.271322			0.135661	+	0.990755i	$0.456684\pi$
$878$	728063.	−	658337.i	0.944452	−	0.854002i
$879$		−	633570.i		−	0.820005i
$880$	304931.	−	1.49657e6i	0.393764	−	1.93256i
$881$	−477077.			−0.614663			−0.307331	−	0.951603i	$-0.599436\pi$
$881$	−477077.			−0.614663			−0.307331	+	0.951603i	$0.599436\pi$
$882$	48948.7	+	54133.0i	0.0629222	+	0.0695864i
$883$		−	874317.i		−	1.12137i	−0.828030	−	0.560683i	$-0.810538\pi$
$883$		−	874317.i		−	1.12137i	0.828030	−	0.560683i	$-0.189462\pi$
$884$	83542.9	−	828465.i	0.106907	−	1.06016i
$885$	−346482.			−0.442378
$886$	−221307.	+	200112.i	−0.281921	+	0.254922i
$887$			1.09986e6i			1.39794i	0.715151	+	0.698970i	$0.246358\pi$
$887$			1.09986e6i			1.39794i	−0.715151	+	0.698970i	$0.753642\pi$
$888$	−47551.0	−	64584.8i	−0.0603022	−	0.0819039i
$889$	134410.			0.170070
$890$	1.31398e6	+	1.45314e6i	1.65885	+	1.83454i
$891$			94092.6i			0.118522i
$892$	−1.16101e6	−	117077.i	−1.45918	−	0.147144i
$893$	340937.			0.427534
$894$	511567.	−	462575.i	0.640070	−	0.578771i
$895$			1.93732e6i			2.41855i
$896$	127498.	+	275350.i	0.158814	+	0.342980i
$897$	460837.			0.572747
$898$	332729.	+	367969.i	0.412609	+	0.456309i
$899$			291840.i			0.361098i
$900$	−61037.0	+	605282.i	−0.0753543	+	0.747262i
$901$	−318249.			−0.392028
$902$	−781998.	+	707107.i	−0.961153	+	0.869104i
$903$		−	282789.i		−	0.346806i
$904$	1.09164e6	−	803727.i	1.33580	−	0.983494i
$905$	833871.			1.01813
$906$	−70587.3	−	78063.4i	−0.0859944	−	0.0951023i
$907$			1.45628e6i			1.77023i	0.465368	+	0.885117i	$0.345922\pi$
$907$			1.45628e6i			1.77023i	−0.465368	+	0.885117i	$0.654078\pi$
$908$	−740069.	−	74629.1i	−0.897637	−	0.0905183i
$909$	−585865.			−0.709039
$910$	−270746.	+	244817.i	−0.326949	+	0.295637i
$911$			450623.i			0.542971i	0.962443	+	0.271485i	$0.0875148\pi$
$911$			450623.i			0.542971i	−0.962443	+	0.271485i	$0.912485\pi$
$912$	−181272.	−	36934.8i	−0.217942	−	0.0444064i
$913$	1.31354e6			1.57580
$914$	−777509.	−	859857.i	−0.930707	−	1.02928i
$915$		−	546593.i		−	0.652863i
$916$	−97939.0	+	971226.i	−0.116725	+	1.15752i
$917$	342432.			0.407226
$918$	−811652.	+	733921.i	−0.963129	+	0.870891i
$919$			943888.i			1.11761i	0.829300	+	0.558804i	$0.188740\pi$
$919$			943888.i			1.11761i	−0.829300	+	0.558804i	$0.811260\pi$
$920$	−901693.	−	1.22470e6i	−1.06533	−	1.44695i
$921$	357062.			0.420944
$922$	−670778.	−	741822.i	−0.789073	−	0.872645i
$923$			1.02980e6i			1.20879i
$924$	−253404.	−	25553.5i	−0.296804	−	0.0299299i
$925$	−169866.			−0.198528
$926$	−43444.8	+	39284.1i	−0.0506659	+	0.0458137i
$927$			572560.i			0.666287i
$928$	−265255.	−	448444.i	−0.308011	−	0.520730i
$929$	−1.44545e6			−1.67483			−0.837415	−	0.546568i	$-0.815934\pi$
$929$	−1.44545e6			−1.67483			−0.837415	+	0.546568i	$0.815934\pi$
$930$	−297005.	−	328462.i	−0.343398	−	0.379769i
$931$			47005.3i			0.0542310i
$932$	21890.0	−	217075.i	0.0252008	−	0.249907i
$933$	−186655.			−0.214426
$934$	−1.08148e6	+	977911.i	−1.23973	+	1.12100i
$935$		−	2.30648e6i		−	2.63831i
$936$	369046.	−	271712.i	0.421239	−	0.310140i
$937$	725855.			0.826743			0.413372	−	0.910562i	$-0.364351\pi$
$937$	725855.			0.826743			0.413372	+	0.910562i	$0.364351\pi$
$938$	305039.	+	337346.i	0.346697	+	0.383416i
$939$			335452.i			0.380452i
$940$	−1.44964e6	−	146183.i	−1.64061	−	0.165440i
$941$	155306.			0.175392			0.0876958	−	0.996147i	$-0.472050\pi$
$941$	155306.			0.175392			0.0876958	+	0.996147i	$0.472050\pi$
$942$	14940.2	−	13509.4i	0.0168366	−	0.0152241i
$943$			1.04981e6i			1.18056i
$944$	91749.5	−	450297.i	0.102958	−	0.505307i
$945$	479698.			0.537160
$946$	−1.26620e6	−	1.40031e6i	−1.41488	−	1.56474i
$947$		−	1.35751e6i		−	1.51372i	−0.653579	−	0.756858i	$-0.726733\pi$
$947$		−	1.35751e6i		−	1.51372i	0.653579	−	0.756858i	$-0.273267\pi$
$948$	−36263.1	+	359608.i	−0.0403504	+	0.400141i
$949$	626534.			0.695685
$950$	−290625.	+	262792.i	−0.322023	+	0.291183i
$951$		−	378166.i		−	0.418140i
$952$	271683.	+	369007.i	0.299771	+	0.407155i
$953$	−1.14440e6			−1.26007			−0.630033	−	0.776568i	$-0.716959\pi$
$953$	−1.14440e6			−1.26007			−0.630033	+	0.776568i	$0.716959\pi$
$954$	−117477.	−	129920.i	−0.129080	−	0.142751i
$955$		−	1.10163e6i		−	1.20790i
$956$	1.02471e6	+	103333.i	1.12121	+	0.113064i
$957$	437319.			0.477501
$958$	1.05743e6	−	956160.i	1.15218	−	1.04184i
$959$		−	346328.i		−	0.376574i
$960$	754922.	+	234768.i	0.819143	+	0.254740i
$961$	594533.			0.643768
$962$	85824.2	+	94914.0i	0.0927384	+	0.102561i
$963$		−	210001.i		−	0.226448i
$964$	−58389.1	+	579024.i	−0.0628316	+	0.623078i
$965$	−417394.			−0.448220
$966$	−188109.	+	170094.i	−0.201584	+	0.182278i
$967$			1.54142e6i			1.64842i	0.566284	+	0.824210i	$0.308381\pi$
$967$			1.54142e6i			1.64842i	−0.566284	+	0.824210i	$0.691619\pi$
$968$	−614653.	+	452542.i	−0.655963	+	0.482957i
$969$	−279372.			−0.297534
$970$	715953.	+	791781.i	0.760923	+	0.841515i
$971$			930841.i			0.987272i	0.869669	+	0.493636i	$0.164333\pi$
$971$			930841.i			0.987272i	−0.869669	+	0.493636i	$0.835667\pi$
$972$	−960914.	−	96899.2i	−1.01707	−	0.102562i
$973$	−158136.			−0.167034
$974$	708857.	−	640971.i	0.747207	−	0.675648i
$975$			507384.i			0.533737i
$976$	710368.	+	144740.i	0.745734	+	0.151946i
$977$	−423734.			−0.443920			−0.221960	−	0.975056i	$-0.571245\pi$
$977$	−423734.			−0.443920			−0.221960	+	0.975056i	$0.571245\pi$
$978$	−118273.	−	130800.i	−0.123654	−	0.136750i
$979$		−	2.18101e6i		−	2.27558i
$980$	20154.4	−	199864.i	0.0209854	−	0.208105i
$981$	430965.			0.447821
$982$	−320909.	+	290175.i	−0.332781	+	0.300911i
$983$			195100.i			0.201907i	0.994891	+	0.100953i	$0.0321893\pi$
$983$			195100.i			0.201907i	−0.994891	+	0.100953i	$0.967811\pi$
$984$	−323559.	−	439465.i	−0.334167	−	0.453873i
$985$	−148201.			−0.152749
$986$	−527716.	−	583608.i	−0.542808	−	0.600298i
$987$			242962.i			0.249405i
$988$	293675.	+	29614.4i	0.300852	+	0.0303382i
$989$	−1.87987e6			−1.92192
$990$	941581.	−	851407.i	0.960699	−	0.868694i
$991$			969204.i			0.986888i	0.869778	+	0.493444i	$0.164262\pi$
$991$			969204.i			0.986888i	−0.869778	+	0.493444i	$0.835738\pi$
$992$	505526.	−	299019.i	0.513713	−	0.303861i
$993$	−11260.8			−0.0114202
$994$	−380099.	−	420356.i	−0.384701	−	0.425446i
$995$			1.48371e6i			1.49866i
$996$	−68217.9	+	676492.i	−0.0687670	+	0.681937i
$997$	−135435.			−0.136251			−0.0681256	−	0.997677i	$-0.521702\pi$
$997$	−135435.			−0.136251			−0.0681256	+	0.997677i	$0.521702\pi$
$998$	−731041.	+	661029.i	−0.733973	+	0.663682i
$999$		−	168165.i		−	0.168502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.5.c.a.15.3	✓	12
3.2	odd	2		252.5.g.a.127.10		12
4.3	odd	2	inner	28.5.c.a.15.4	yes	12
7.6	odd	2		196.5.c.f.99.3		12
8.3	odd	2		448.5.d.e.127.7		12
8.5	even	2		448.5.d.e.127.6		12
12.11	even	2		252.5.g.a.127.9		12
28.27	even	2		196.5.c.f.99.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.5.c.a.15.3	✓	12	1.1	even	1	trivial
28.5.c.a.15.4	yes	12	4.3	odd	2	inner
196.5.c.f.99.3		12	7.6	odd	2
196.5.c.f.99.4		12	28.27	even	2
252.5.g.a.127.9		12	12.11	even	2
252.5.g.a.127.10		12	3.2	odd	2
448.5.d.e.127.6		12	8.5	even	2
448.5.d.e.127.7		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68279 - 2.96693i) q^{2} +5.27316i q^{3} +(-1.60531 + 15.9193i) q^{4} +36.6030 q^{5} +(15.6451 - 14.1468i) q^{6} -18.5203i q^{7} +(51.5380 - 37.9452i) q^{8} +53.1938 q^{9} +O(q^{10})\)	\(q+(-2.68279 - 2.96693i) q^{2} +5.27316i q^{3} +(-1.60531 + 15.9193i) q^{4} +36.6030 q^{5} +(15.6451 - 14.1468i) q^{6} -18.5203i q^{7} +(51.5380 - 37.9452i) q^{8} +53.1938 q^{9} +(-98.1982 - 108.599i) q^{10} +162.995i q^{11} +(-83.9448 - 8.46505i) q^{12} +134.614 q^{13} +(-54.9483 + 49.6859i) q^{14} +193.014i q^{15} +(-250.846 - 51.1107i) q^{16} -386.598 q^{17} +(-142.708 - 157.822i) q^{18} -137.042i q^{19} +(-58.7592 + 582.693i) q^{20} +97.6603 q^{21} +(483.593 - 437.280i) q^{22} -649.210i q^{23} +(200.091 + 271.768i) q^{24} +714.782 q^{25} +(-361.142 - 399.391i) q^{26} +707.625i q^{27} +(294.829 + 29.7307i) q^{28} -508.809 q^{29} +(572.657 - 517.815i) q^{30} -573.575i q^{31} +(521.325 + 881.361i) q^{32} -859.496 q^{33} +(1037.16 + 1147.01i) q^{34} -677.898i q^{35} +(-85.3924 + 846.806i) q^{36} -237.647 q^{37} +(-406.593 + 367.654i) q^{38} +709.843i q^{39} +(1886.45 - 1388.91i) q^{40} -1617.06 q^{41} +(-262.002 - 289.751i) q^{42} -2895.64i q^{43} +(-2594.75 - 261.657i) q^{44} +1947.05 q^{45} +(-1926.16 + 1741.69i) q^{46} +2487.83i q^{47} +(269.515 - 1322.75i) q^{48} -343.000 q^{49} +(-1917.61 - 2120.71i) q^{50} -2038.59i q^{51} +(-216.098 + 2142.96i) q^{52} +823.204 q^{53} +(2099.47 - 1898.41i) q^{54} +5966.09i q^{55} +(-702.754 - 954.497i) q^{56} +722.643 q^{57} +(1365.03 + 1509.60i) q^{58} +1795.12i q^{59} +(-3072.64 - 309.847i) q^{60} -2831.89 q^{61} +(-1701.75 + 1538.78i) q^{62} -985.163i q^{63} +(1216.33 - 3911.23i) q^{64} +4927.30 q^{65} +(2305.85 + 2550.06i) q^{66} -6139.35i q^{67} +(620.609 - 6154.36i) q^{68} +3423.39 q^{69} +(-2011.27 + 1818.66i) q^{70} +7650.03i q^{71} +(2741.50 - 2018.45i) q^{72} +4654.29 q^{73} +(637.556 + 705.081i) q^{74} +3769.16i q^{75} +(2181.60 + 219.994i) q^{76} +3018.70 q^{77} +(2106.05 - 1904.36i) q^{78} -4283.86i q^{79} +(-9181.72 - 1870.81i) q^{80} +577.275 q^{81} +(4338.22 + 4797.69i) q^{82} -8058.77i q^{83} +(-156.775 + 1554.68i) q^{84} -14150.7 q^{85} +(-8591.14 + 7768.37i) q^{86} -2683.03i q^{87} +(6184.85 + 8400.41i) q^{88} -13380.9 q^{89} +(-5223.53 - 5776.77i) q^{90} -2493.09i q^{91} +(10334.9 + 1042.18i) q^{92} +3024.55 q^{93} +(7381.21 - 6674.32i) q^{94} -5016.14i q^{95} +(-4647.56 + 2749.03i) q^{96} -7290.90 q^{97} +(920.196 + 1017.66i) q^{98} +8670.30i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 31 q^{4} + 24 q^{5} + 30 q^{6} + 171 q^{8} - 436 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 31 * q^4 + 24 * q^5 + 30 * q^6 + 171 * q^8 - 436 * q^9	\( 12 q + 3 q^{2} - 31 q^{4} + 24 q^{5} + 30 q^{6} + 171 q^{8} - 436 q^{9} + 52 q^{10} + 390 q^{12} + 120 q^{13} + 147 q^{14} - 911 q^{16} - 648 q^{17} + 631 q^{18} + 912 q^{20} - 628 q^{22} - 1174 q^{24} + 2340 q^{25} - 2280 q^{26} + 245 q^{28} + 24 q^{29} + 800 q^{30} + 1443 q^{32} - 1120 q^{33} + 1634 q^{34} + 421 q^{36} - 424 q^{37} + 2970 q^{38} - 4936 q^{40} + 7320 q^{41} - 2450 q^{42} - 2244 q^{44} + 888 q^{45} - 7512 q^{46} + 3550 q^{48} - 4116 q^{49} - 5451 q^{50} - 3484 q^{52} - 7080 q^{53} + 11620 q^{54} + 3087 q^{56} - 9152 q^{57} + 4666 q^{58} + 15856 q^{60} + 9752 q^{61} - 5964 q^{62} + 6329 q^{64} - 11280 q^{65} + 30264 q^{66} - 7314 q^{68} - 10464 q^{69} - 7644 q^{70} - 10553 q^{72} + 13752 q^{73} - 2838 q^{74} + 11202 q^{76} + 4704 q^{77} - 34600 q^{78} - 49272 q^{80} + 3340 q^{81} - 11950 q^{82} + 11662 q^{84} + 23152 q^{85} + 30612 q^{86} + 20740 q^{88} - 12552 q^{89} - 40508 q^{90} + 47880 q^{92} + 13632 q^{93} + 71340 q^{94} - 11110 q^{96} + 19704 q^{97} - 1029 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 31 * q^4 + 24 * q^5 + 30 * q^6 + 171 * q^8 - 436 * q^9 + 52 * q^10 + 390 * q^12 + 120 * q^13 + 147 * q^14 - 911 * q^16 - 648 * q^17 + 631 * q^18 + 912 * q^20 - 628 * q^22 - 1174 * q^24 + 2340 * q^25 - 2280 * q^26 + 245 * q^28 + 24 * q^29 + 800 * q^30 + 1443 * q^32 - 1120 * q^33 + 1634 * q^34 + 421 * q^36 - 424 * q^37 + 2970 * q^38 - 4936 * q^40 + 7320 * q^41 - 2450 * q^42 - 2244 * q^44 + 888 * q^45 - 7512 * q^46 + 3550 * q^48 - 4116 * q^49 - 5451 * q^50 - 3484 * q^52 - 7080 * q^53 + 11620 * q^54 + 3087 * q^56 - 9152 * q^57 + 4666 * q^58 + 15856 * q^60 + 9752 * q^61 - 5964 * q^62 + 6329 * q^64 - 11280 * q^65 + 30264 * q^66 - 7314 * q^68 - 10464 * q^69 - 7644 * q^70 - 10553 * q^72 + 13752 * q^73 - 2838 * q^74 + 11202 * q^76 + 4704 * q^77 - 34600 * q^78 - 49272 * q^80 + 3340 * q^81 - 11950 * q^82 + 11662 * q^84 + 23152 * q^85 + 30612 * q^86 + 20740 * q^88 - 12552 * q^89 - 40508 * q^90 + 47880 * q^92 + 13632 * q^93 + 71340 * q^94 - 11110 * q^96 + 19704 * q^97 - 1029 * q^98

Introduction

L-functions

Modular forms

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Database

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