LMFDB - Embedded newform 74.5.d.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 $ x^14 + 727x^12 + 207381x^10 + 29788577x^8 + 2302194203x^6 + 92916575085x^4 + 1658451585508x^2 + 6531254919424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$-9.34569i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.b.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 2.00000i) q^{2} -8.34569i q^{3} -8.00000i q^{4} +(-6.01044 - 6.01044i) q^{5} +(-16.6914 - 16.6914i) q^{6} -74.3653 q^{7} +(-16.0000 - 16.0000i) q^{8} +11.3495 q^{9} +O(q^{10})$	\(q+(2.00000 - 2.00000i) q^{2} -8.34569i q^{3} -8.00000i q^{4} +(-6.01044 - 6.01044i) q^{5} +(-16.6914 - 16.6914i) q^{6} -74.3653 q^{7} +(-16.0000 - 16.0000i) q^{8} +11.3495 q^{9} -24.0418 q^{10} -29.8441i q^{11} -66.7655 q^{12} +(74.7512 + 74.7512i) q^{13} +(-148.731 + 148.731i) q^{14} +(-50.1612 + 50.1612i) q^{15} -64.0000 q^{16} +(-128.547 - 128.547i) q^{17} +(22.6990 - 22.6990i) q^{18} +(-356.064 - 356.064i) q^{19} +(-48.0835 + 48.0835i) q^{20} +620.629i q^{21} +(-59.6881 - 59.6881i) q^{22} +(274.279 + 274.279i) q^{23} +(-133.531 + 133.531i) q^{24} -552.749i q^{25} +299.005 q^{26} -770.720i q^{27} +594.922i q^{28} +(861.481 - 861.481i) q^{29} +200.645i q^{30} +(-456.584 + 456.584i) q^{31} +(-128.000 + 128.000i) q^{32} -249.069 q^{33} -514.187 q^{34} +(446.968 + 446.968i) q^{35} -90.7962i q^{36} +(1353.78 - 203.559i) q^{37} -1424.26 q^{38} +(623.850 - 623.850i) q^{39} +192.334i q^{40} -669.356i q^{41} +(1241.26 + 1241.26i) q^{42} +(116.504 + 116.504i) q^{43} -238.753 q^{44} +(-68.2156 - 68.2156i) q^{45} +1097.12 q^{46} +1803.51 q^{47} +534.124i q^{48} +3129.20 q^{49} +(-1105.50 - 1105.50i) q^{50} +(-1072.81 + 1072.81i) q^{51} +(598.009 - 598.009i) q^{52} +275.703 q^{53} +(-1541.44 - 1541.44i) q^{54} +(-179.376 + 179.376i) q^{55} +(1189.84 + 1189.84i) q^{56} +(-2971.60 + 2971.60i) q^{57} -3445.92i q^{58} +(444.380 + 444.380i) q^{59} +(401.290 + 401.290i) q^{60} +(3467.51 - 3467.51i) q^{61} +1826.34i q^{62} -844.011 q^{63} +512.000i q^{64} -898.575i q^{65} +(-498.138 + 498.138i) q^{66} +2630.98i q^{67} +(-1028.37 + 1028.37i) q^{68} +(2289.05 - 2289.05i) q^{69} +1787.87 q^{70} -4706.12 q^{71} +(-181.592 - 181.592i) q^{72} +7254.78i q^{73} +(2300.44 - 3114.68i) q^{74} -4613.07 q^{75} +(-2848.51 + 2848.51i) q^{76} +2219.36i q^{77} -2495.40i q^{78} +(-6842.87 - 6842.87i) q^{79} +(384.668 + 384.668i) q^{80} -5512.88 q^{81} +(-1338.71 - 1338.71i) q^{82} +238.677 q^{83} +4965.04 q^{84} +1545.24i q^{85} +466.014 q^{86} +(-7189.65 - 7189.65i) q^{87} +(-477.505 + 477.505i) q^{88} +(-10365.4 + 10365.4i) q^{89} -272.863 q^{90} +(-5558.89 - 5558.89i) q^{91} +(2194.23 - 2194.23i) q^{92} +(3810.51 + 3810.51i) q^{93} +(3607.02 - 3607.02i) q^{94} +4280.21i q^{95} +(1068.25 + 1068.25i) q^{96} +(-2982.33 - 2982.33i) q^{97} +(6258.39 - 6258.39i) q^{98} -338.716i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$2$	2.00000	−	2.00000i	0.500000	−	0.500000i
$3$		−	8.34569i		−	0.927298i	−0.886019	−	0.463649i	$-0.846540\pi$
$3$		−	8.34569i		−	0.927298i	0.886019	−	0.463649i	$-0.153460\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−6.01044	−	6.01044i	−0.240418	−	0.240418i	0.576605	−	0.817023i	$-0.304377\pi$
$5$	−6.01044	−	6.01044i	−0.240418	−	0.240418i	−0.817023	+	0.576605i	$0.804377\pi$
$6$	−16.6914	−	16.6914i	−0.463649	−	0.463649i
$7$	−74.3653			−1.51766			−0.758830	−	0.651289i	$-0.774228\pi$
$7$	−74.3653			−1.51766			−0.758830	+	0.651289i	$0.774228\pi$
$8$	−16.0000	−	16.0000i	−0.250000	−	0.250000i
$9$	11.3495			0.140118
$10$	−24.0418			−0.240418
$11$		−	29.8441i		−	0.246645i	−0.992367	−	0.123323i	$-0.960645\pi$
$11$		−	29.8441i		−	0.246645i	0.992367	−	0.123323i	$-0.0393550\pi$
$12$	−66.7655			−0.463649
$13$	74.7512	+	74.7512i	0.442315	+	0.442315i	0.892789	−	0.450475i	$-0.148745\pi$
$13$	74.7512	+	74.7512i	0.442315	+	0.442315i	−0.450475	+	0.892789i	$0.648745\pi$
$14$	−148.731	+	148.731i	−0.758830	+	0.758830i
$15$	−50.1612	+	50.1612i	−0.222939	+	0.222939i
$16$	−64.0000			−0.250000
$17$	−128.547	−	128.547i	−0.444798	−	0.444798i	0.448823	−	0.893621i	$-0.351843\pi$
$17$	−128.547	−	128.547i	−0.444798	−	0.444798i	−0.893621	+	0.448823i	$0.851843\pi$
$18$	22.6990	−	22.6990i	0.0700588	−	0.0700588i
$19$	−356.064	−	356.064i	−0.986328	−	0.986328i	0.0135800	−	0.999908i	$-0.495677\pi$
$19$	−356.064	−	356.064i	−0.986328	−	0.986328i	−0.999908	+	0.0135800i	$0.995677\pi$
$20$	−48.0835	+	48.0835i	−0.120209	+	0.120209i
$21$			620.629i			1.40732i
$22$	−59.6881	−	59.6881i	−0.123323	−	0.123323i
$23$	274.279	+	274.279i	0.518486	+	0.518486i	0.917113	−	0.398627i	$-0.130513\pi$
$23$	274.279	+	274.279i	0.518486	+	0.518486i	−0.398627	+	0.917113i	$0.630513\pi$
$24$	−133.531	+	133.531i	−0.231825	+	0.231825i
$25$		−	552.749i		−	0.884399i
$26$	299.005			0.442315
$27$		−	770.720i		−	1.05723i
$28$			594.922i			0.758830i
$29$	861.481	−	861.481i	1.02435	−	1.02435i	0.0246569	−	0.999696i	$-0.492151\pi$
$29$	861.481	−	861.481i	1.02435	−	1.02435i	0.999696	−	0.0246569i	$-0.00784934\pi$
$30$			200.645i			0.222939i
$31$	−456.584	+	456.584i	−0.475113	+	0.475113i	−0.903565	−	0.428451i	$-0.859059\pi$
$31$	−456.584	+	456.584i	−0.475113	+	0.475113i	0.428451	+	0.903565i	$0.359059\pi$
$32$	−128.000	+	128.000i	−0.125000	+	0.125000i
$33$	−249.069			−0.228714
$34$	−514.187			−0.444798
$35$	446.968	+	446.968i	0.364872	+	0.364872i
$36$		−	90.7962i		−	0.0700588i
$37$	1353.78	−	203.559i	0.988884	−	0.148692i
$37$	1353.78	−	203.559i	0.988884	−	0.148692i
$38$	−1424.26			−0.986328
$39$	623.850	−	623.850i	0.410158	−	0.410158i
$40$			192.334i			0.120209i
$41$		−	669.356i		−	0.398189i	−0.979980	−	0.199095i	$-0.936200\pi$
$41$		−	669.356i		−	0.398189i	0.979980	−	0.199095i	$-0.0638001\pi$
$42$	1241.26	+	1241.26i	0.703661	+	0.703661i
$43$	116.504	+	116.504i	0.0630090	+	0.0630090i	0.737909	−	0.674900i	$-0.235813\pi$
$43$	116.504	+	116.504i	0.0630090	+	0.0630090i	−0.674900	+	0.737909i	$0.735813\pi$
$44$	−238.753			−0.123323
$45$	−68.2156	−	68.2156i	−0.0336867	−	0.0336867i
$46$	1097.12			0.518486
$47$	1803.51			0.816438			0.408219	−	0.912884i	$-0.366150\pi$
$47$	1803.51			0.816438			0.408219	+	0.912884i	$0.366150\pi$
$48$			534.124i			0.231825i
$49$	3129.20			1.30329
$50$	−1105.50	−	1105.50i	−0.442199	−	0.442199i
$51$	−1072.81	+	1072.81i	−0.412461	+	0.412461i
$52$	598.009	−	598.009i	0.221157	−	0.221157i
$53$	275.703			0.0981499			0.0490749	−	0.998795i	$-0.484373\pi$
$53$	275.703			0.0981499			0.0490749	+	0.998795i	$0.484373\pi$
$54$	−1541.44	−	1541.44i	−0.528615	−	0.528615i
$55$	−179.376	+	179.376i	−0.0592978	+	0.0592978i
$56$	1189.84	+	1189.84i	0.379415	+	0.379415i
$57$	−2971.60	+	2971.60i	−0.914620	+	0.914620i
$58$		−	3445.92i		−	1.02435i
$59$	444.380	+	444.380i	0.127659	+	0.127659i	0.768049	−	0.640391i	$-0.221227\pi$
$59$	444.380	+	444.380i	0.127659	+	0.127659i	−0.640391	+	0.768049i	$0.721227\pi$
$60$	401.290	+	401.290i	0.111469	+	0.111469i
$61$	3467.51	−	3467.51i	0.931877	−	0.931877i	−0.0659464	−	0.997823i	$-0.521007\pi$
$61$	3467.51	−	3467.51i	0.931877	−	0.931877i	0.997823	+	0.0659464i	$0.0210066\pi$
$62$			1826.34i			0.475113i
$63$	−844.011			−0.212651
$64$			512.000i			0.125000i
$65$		−	898.575i		−	0.212680i
$66$	−498.138	+	498.138i	−0.114357	+	0.114357i
$67$			2630.98i			0.586095i	0.956098	+	0.293048i	$0.0946695\pi$
$67$			2630.98i			0.586095i	−0.956098	+	0.293048i	$0.905331\pi$
$68$	−1028.37	+	1028.37i	−0.222399	+	0.222399i
$69$	2289.05	−	2289.05i	0.480791	−	0.480791i
$70$	1787.87			0.364872
$71$	−4706.12			−0.933569			−0.466785	−	0.884371i	$-0.654588\pi$
$71$	−4706.12			−0.933569			−0.466785	+	0.884371i	$0.654588\pi$
$72$	−181.592	−	181.592i	−0.0350294	−	0.0350294i
$73$			7254.78i			1.36138i	0.732573	+	0.680688i	$0.238319\pi$
$73$			7254.78i			1.36138i	−0.732573	+	0.680688i	$0.761681\pi$
$74$	2300.44	−	3114.68i	0.420096	−	0.568788i
$75$	−4613.07			−0.820102
$76$	−2848.51	+	2848.51i	−0.493164	+	0.493164i
$77$			2219.36i			0.374323i
$78$		−	2495.40i		−	0.410158i
$79$	−6842.87	−	6842.87i	−1.09644	−	1.09644i	−0.994824	−	0.101615i	$-0.967599\pi$
$79$	−6842.87	−	6842.87i	−1.09644	−	1.09644i	−0.101615	−	0.994824i	$-0.532401\pi$
$80$	384.668	+	384.668i	0.0601044	+	0.0601044i
$81$	−5512.88			−0.840249
$82$	−1338.71	−	1338.71i	−0.199095	−	0.199095i
$83$	238.677			0.0346461			0.0173230	−	0.999850i	$-0.494486\pi$
$83$	238.677			0.0346461			0.0173230	+	0.999850i	$0.494486\pi$
$84$	4965.04			0.703661
$85$			1545.24i			0.213875i
$86$	466.014			0.0630090
$87$	−7189.65	−	7189.65i	−0.949881	−	0.949881i
$88$	−477.505	+	477.505i	−0.0616613	+	0.0616613i
$89$	−10365.4	+	10365.4i	−1.30860	+	1.30860i	−0.386176	+	0.922425i	$0.626204\pi$
$89$	−10365.4	+	10365.4i	−1.30860	+	1.30860i	−0.922425	+	0.386176i	$0.873796\pi$
$90$	−272.863			−0.0336867
$91$	−5558.89	−	5558.89i	−0.671283	−	0.671283i
$92$	2194.23	−	2194.23i	0.259243	−	0.259243i
$93$	3810.51	+	3810.51i	0.440572	+	0.440572i
$94$	3607.02	−	3607.02i	0.408219	−	0.408219i
$95$			4280.21i			0.474261i
$96$	1068.25	+	1068.25i	0.115912	+	0.115912i
$97$	−2982.33	−	2982.33i	−0.316966	−	0.316966i	0.530635	−	0.847601i	$-0.321954\pi$
$97$	−2982.33	−	2982.33i	−0.316966	−	0.316966i	−0.847601	+	0.530635i	$0.821954\pi$
$98$	6258.39	−	6258.39i	0.651645	−	0.651645i
$99$		−	338.716i		−	0.0345593i
$100$	−4421.99			−0.442199
$101$			6107.65i			0.598730i	0.954139	+	0.299365i	$0.0967748\pi$
$101$			6107.65i			0.598730i	−0.954139	+	0.299365i	$0.903225\pi$
$102$			4291.24i			0.412461i
$103$	8256.15	−	8256.15i	0.778221	−	0.778221i	−0.201307	−	0.979528i	$-0.564519\pi$
$103$	8256.15	−	8256.15i	0.778221	−	0.778221i	0.979528	+	0.201307i	$0.0645190\pi$
$104$		−	2392.04i		−	0.221157i
$105$	3730.26	−	3730.26i	0.338345	−	0.338345i
$106$	551.406	−	551.406i	0.0490749	−	0.0490749i
$107$	1644.11			0.143603			0.0718015	−	0.997419i	$-0.477125\pi$
$107$	1644.11			0.143603			0.0718015	+	0.997419i	$0.477125\pi$
$108$	−6165.76			−0.528615
$109$	11086.3	+	11086.3i	0.933111	+	0.933111i	0.997899	−	0.0647877i	$-0.0206370\pi$
$109$	11086.3	+	11086.3i	0.933111	+	0.933111i	−0.0647877	+	0.997899i	$0.520637\pi$
$110$			717.504i			0.0592978i
$111$	−1698.84	−	11298.2i	−0.137882	−	0.916990i
$112$	4759.38			0.379415
$113$	1486.82	−	1486.82i	0.116440	−	0.116440i	−0.646486	−	0.762926i	$-0.723762\pi$
$113$	1486.82	−	1486.82i	0.116440	−	0.116440i	0.762926	+	0.646486i	$0.223762\pi$
$114$			11886.4i			0.914620i
$115$		−	3297.08i		−	0.249306i
$116$	−6891.85	−	6891.85i	−0.512176	−	0.512176i
$117$	848.390	+	848.390i	0.0619761	+	0.0619761i
$118$	1777.52			0.127659
$119$	9559.41	+	9559.41i	0.675052	+	0.675052i
$120$	1605.16			0.111469
$121$	13750.3			0.939166
$122$		−	13870.1i		−	0.931877i
$123$	−5586.24			−0.369240
$124$	3652.67	+	3652.67i	0.237557	+	0.237557i
$125$	−7078.79	+	7078.79i	−0.453043	+	0.453043i
$126$	−1688.02	+	1688.02i	−0.106325	+	0.106325i
$127$	27811.7			1.72433			0.862163	−	0.506631i	$-0.169109\pi$
$127$	27811.7			1.72433			0.862163	+	0.506631i	$0.169109\pi$
$128$	1024.00	+	1024.00i	0.0625000	+	0.0625000i
$129$	972.303	−	972.303i	0.0584281	−	0.0584281i
$130$	−1797.15	−	1797.15i	−0.106340	−	0.106340i
$131$	−9101.69	+	9101.69i	−0.530371	+	0.530371i	−0.920683	−	0.390312i	$-0.872367\pi$
$131$	−9101.69	+	9101.69i	−0.530371	+	0.530371i	0.390312	+	0.920683i	$0.372367\pi$
$132$			1992.55i			0.114357i
$133$	26478.8	+	26478.8i	1.49691	+	1.49691i
$134$	5261.96	+	5261.96i	0.293048	+	0.293048i
$135$	−4632.37	+	4632.37i	−0.254177	+	0.254177i
$136$			4113.49i			0.222399i
$137$	14140.7			0.753405			0.376702	−	0.926334i	$-0.377058\pi$
$137$	14140.7			0.753405			0.376702	+	0.926334i	$0.377058\pi$
$138$		−	9156.19i		−	0.480791i
$139$			5163.48i			0.267247i	0.991032	+	0.133623i	$0.0426613\pi$
$139$			5163.48i			0.267247i	−0.991032	+	0.133623i	$0.957339\pi$
$140$	3575.75	−	3575.75i	0.182436	−	0.182436i
$141$		−	15051.5i		−	0.757082i
$142$	−9412.25	+	9412.25i	−0.466785	+	0.466785i
$143$	2230.88	−	2230.88i	0.109095	−	0.109095i
$144$	−726.370			−0.0350294
$145$	−10355.8			−0.492545
$146$	14509.6	+	14509.6i	0.680688	+	0.680688i
$147$		−	26115.3i		−	1.20854i
$148$	−1628.47	−	10830.3i	−0.0743460	−	0.494442i
$149$	−39331.5			−1.77161			−0.885805	−	0.464057i	$-0.846393\pi$
$149$	−39331.5			−1.77161			−0.885805	+	0.464057i	$0.846393\pi$
$150$	−9226.14	+	9226.14i	−0.410051	+	0.410051i
$151$		−	17638.6i		−	0.773589i	−0.922166	−	0.386795i	$-0.873582\pi$
$151$		−	17638.6i		−	0.773589i	0.922166	−	0.386795i	$-0.126418\pi$
$152$			11394.1i			0.493164i
$153$	−1458.94	−	1458.94i	−0.0623240	−	0.0623240i
$154$	4438.73	+	4438.73i	0.187162	+	0.187162i
$155$	5488.54			0.228451
$156$	−4990.80	−	4990.80i	−0.205079	−	0.205079i
$157$	17202.3			0.697891			0.348945	−	0.937143i	$-0.386540\pi$
$157$	17202.3			0.697891			0.348945	+	0.937143i	$0.386540\pi$
$158$	−27371.5			−1.09644
$159$		−	2300.93i		−	0.0910142i
$160$	1538.67			0.0601044
$161$	−20396.9	−	20396.9i	−0.786885	−	0.786885i
$162$	−11025.8	+	11025.8i	−0.420125	+	0.420125i
$163$	23313.5	−	23313.5i	0.877468	−	0.877468i	−0.115804	−	0.993272i	$-0.536944\pi$
$163$	23313.5	−	23313.5i	0.877468	−	0.877468i	0.993272	+	0.115804i	$0.0369443\pi$
$164$	−5354.85			−0.199095
$165$	1497.02	+	1497.02i	0.0549868	+	0.0549868i
$166$	477.353	−	477.353i	0.0173230	−	0.0173230i
$167$	−30843.4	−	30843.4i	−1.10593	−	1.10593i	−0.993680	−	0.112253i	$-0.964193\pi$
$167$	−30843.4	−	30843.4i	−1.10593	−	1.10593i	−0.112253	−	0.993680i	$-0.535807\pi$
$168$	9930.07	−	9930.07i	0.351831	−	0.351831i
$169$		−	17385.5i		−	0.608716i
$170$	3090.49	+	3090.49i	0.106937	+	0.106937i
$171$	−4041.16	−	4041.16i	−0.138202	−	0.138202i
$172$	932.029	−	932.029i	0.0315045	−	0.0315045i
$173$		−	10251.3i		−	0.342521i	−0.985226	−	0.171260i	$-0.945216\pi$
$173$		−	10251.3i		−	0.342521i	0.985226	−	0.171260i	$-0.0547839\pi$
$174$	−28758.6			−0.949881
$175$			41105.4i			1.34222i
$176$			1910.02i			0.0616613i
$177$	3708.66	−	3708.66i	0.118378	−	0.118378i
$178$			41461.7i			1.30860i
$179$	−5460.59	+	5460.59i	−0.170425	+	0.170425i	−0.787166	−	0.616741i	$-0.788453\pi$
$179$	−5460.59	+	5460.59i	−0.170425	+	0.170425i	0.616741	+	0.787166i	$0.288453\pi$
$180$	−545.725	+	545.725i	−0.0168434	+	0.0168434i
$181$	6594.71			0.201298			0.100649	−	0.994922i	$-0.467908\pi$
$181$	6594.71			0.201298			0.100649	+	0.994922i	$0.467908\pi$
$182$	−22235.6			−0.671283
$183$	−28938.8	−	28938.8i	−0.864128	−	0.864128i
$184$		−	8776.94i		−	0.259243i
$185$	−9360.30	−	6913.34i	−0.273493	−	0.201997i
$186$	15242.0			0.440572
$187$	−3836.35	+	3836.35i	−0.109707	+	0.109707i
$188$		−	14428.1i		−	0.408219i
$189$			57314.8i			1.60451i
$190$	8560.41	+	8560.41i	0.237131	+	0.237131i
$191$	−28282.8	−	28282.8i	−0.775276	−	0.775276i	0.203748	−	0.979023i	$-0.434688\pi$
$191$	−28282.8	−	28282.8i	−0.775276	−	0.775276i	−0.979023	+	0.203748i	$0.934688\pi$
$192$	4272.99			0.115912
$193$	36855.1	+	36855.1i	0.989426	+	0.989426i	0.999945	−	0.0105184i	$-0.00334816\pi$
$193$	36855.1	+	36855.1i	0.989426	+	0.989426i	−0.0105184	+	0.999945i	$0.503348\pi$
$194$	−11929.3			−0.316966
$195$	−7499.22			−0.197218
$196$		−	25033.6i		−	0.651645i
$197$	68484.2			1.76465			0.882324	−	0.470643i	$-0.155978\pi$
$197$	68484.2			1.76465			0.882324	+	0.470643i	$0.155978\pi$
$198$	−677.432	−	677.432i	−0.0172797	−	0.0172797i
$199$	−20724.0	+	20724.0i	−0.523320	+	0.523320i	−0.918573	−	0.395252i	$-0.870657\pi$
$199$	−20724.0	+	20724.0i	−0.523320	+	0.523320i	0.395252	+	0.918573i	$0.370657\pi$
$200$	−8843.99	+	8843.99i	−0.221100	+	0.221100i
$201$	21957.3			0.543485
$202$	12215.3	+	12215.3i	0.299365	+	0.299365i
$203$	−64064.3	+	64064.3i	−1.55462	+	1.55462i
$204$	8582.48	+	8582.48i	0.206230	+	0.206230i
$205$	−4023.13	+	4023.13i	−0.0957317	+	0.0957317i
$206$		−	33024.6i		−	0.778221i
$207$	3112.94	+	3112.94i	0.0726490	+	0.0726490i
$208$	−4784.07	−	4784.07i	−0.110579	−	0.110579i
$209$	−10626.4	+	10626.4i	−0.243273	+	0.243273i
$210$		−	14921.0i		−	0.338345i
$211$	−63864.2			−1.43447			−0.717237	−	0.696829i	$-0.754593\pi$
$211$	−63864.2			−1.43447			−0.717237	+	0.696829i	$0.754593\pi$
$212$		−	2205.62i		−	0.0490749i
$213$			39275.8i			0.865697i
$214$	3288.22	−	3288.22i	0.0718015	−	0.0718015i
$215$		−	1400.48i		−	0.0302969i
$216$	−12331.5	+	12331.5i	−0.264307	+	0.264307i
$217$	33954.0	−	33954.0i	0.721060	−	0.721060i
$218$	44345.2			0.933111
$219$	60546.1			1.26240
$220$	1435.01	+	1435.01i	0.0296489	+	0.0296489i
$221$		−	19218.0i		−	0.393481i
$222$	−25994.2	−	19198.8i	−0.527436	−	0.389554i
$223$	87323.9			1.75600			0.877998	−	0.478664i	$-0.158879\pi$
$223$	87323.9			1.75600			0.877998	+	0.478664i	$0.158879\pi$
$224$	9518.76	−	9518.76i	0.189707	−	0.189707i
$225$		−	6273.44i		−	0.123920i
$226$		−	5947.29i		−	0.116440i
$227$	2204.77	+	2204.77i	0.0427869	+	0.0427869i	0.728177	−	0.685390i	$-0.240368\pi$
$227$	2204.77	+	2204.77i	0.0427869	+	0.0427869i	−0.685390	+	0.728177i	$0.740368\pi$
$228$	23772.8	+	23772.8i	0.457310	+	0.457310i
$229$	22716.7			0.433185			0.216593	−	0.976262i	$-0.430506\pi$
$229$	22716.7			0.433185			0.216593	+	0.976262i	$0.430506\pi$
$230$	−6594.16	−	6594.16i	−0.124653	−	0.124653i
$231$	18522.1			0.347109
$232$	−27567.4			−0.512176
$233$		−	66960.1i		−	1.23340i	−0.787198	−	0.616701i	$-0.788469\pi$
$233$		−	66960.1i		−	1.23340i	0.787198	−	0.616701i	$-0.211531\pi$
$234$	3393.56			0.0619761
$235$	−10839.9	−	10839.9i	−0.196286	−	0.196286i
$236$	3555.04	−	3555.04i	0.0638294	−	0.0638294i
$237$	−57108.5	+	57108.5i	−1.01673	+	1.01673i
$238$	38237.6			0.675052
$239$	10205.6	+	10205.6i	0.178666	+	0.178666i	0.790774	−	0.612108i	$-0.209678\pi$
$239$	10205.6	+	10205.6i	0.178666	+	0.178666i	−0.612108	+	0.790774i	$0.709678\pi$
$240$	3210.32	−	3210.32i	0.0557347	−	0.0557347i
$241$	−33637.4	−	33637.4i	−0.579147	−	0.579147i	0.355521	−	0.934668i	$-0.384303\pi$
$241$	−33637.4	−	33637.4i	−0.579147	−	0.579147i	−0.934668	+	0.355521i	$0.884303\pi$
$242$	27500.7	−	27500.7i	0.469583	−	0.469583i
$243$		−	16419.6i		−	0.278067i
$244$	−27740.1	−	27740.1i	−0.465938	−	0.465938i
$245$	−18807.9	−	18807.9i	−0.313334	−	0.313334i
$246$	−11172.5	+	11172.5i	−0.184620	+	0.184620i
$247$		−	53232.4i		−	0.872534i
$248$	14610.7			0.237557
$249$		−	1991.92i		−	0.0321272i
$250$			28315.2i			0.453043i
$251$	31829.4	−	31829.4i	0.505221	−	0.505221i	−0.407835	−	0.913056i	$-0.633716\pi$
$251$	31829.4	−	31829.4i	0.505221	−	0.505221i	0.913056	+	0.407835i	$0.133716\pi$
$252$			6752.09i			0.106325i
$253$	8185.61	−	8185.61i	0.127882	−	0.127882i
$254$	55623.3	−	55623.3i	0.862163	−	0.862163i
$255$	12896.1			0.198326
$256$	4096.00			0.0625000
$257$	1686.62	+	1686.62i	0.0255359	+	0.0255359i	0.719759	−	0.694224i	$-0.244252\pi$
$257$	1686.62	+	1686.62i	0.0255359	+	0.0255359i	−0.694224	+	0.719759i	$0.744252\pi$
$258$		−	3889.21i		−	0.0584281i
$259$	−100674.	+	15137.7i	−1.50079	+	0.225664i
$260$	−7188.60			−0.106340
$261$	9777.40	−	9777.40i	0.143530	−	0.143530i
$262$			36406.8i			0.530371i
$263$			125286.i			1.81130i	0.424030	+	0.905648i	$0.360615\pi$
$263$			125286.i			1.81130i	−0.424030	+	0.905648i	$0.639385\pi$
$264$	3985.11	+	3985.11i	0.0571784	+	0.0571784i
$265$	−1657.10	−	1657.10i	−0.0235970	−	0.0235970i
$266$	105915.			1.49691
$267$	86506.6	+	86506.6i	1.21346	+	1.21346i
$268$	21047.9			0.293048
$269$	−61012.3			−0.843165			−0.421582	−	0.906790i	$-0.638525\pi$
$269$	−61012.3			−0.843165			−0.421582	+	0.906790i	$0.638525\pi$
$270$			18529.5i			0.254177i
$271$	44825.9			0.610366			0.305183	−	0.952294i	$-0.401282\pi$
$271$	44825.9			0.610366			0.305183	+	0.952294i	$0.401282\pi$
$272$	8226.99	+	8226.99i	0.111200	+	0.111200i
$273$	−46392.8	+	46392.8i	−0.622479	+	0.622479i
$274$	28281.3	−	28281.3i	0.376702	−	0.376702i
$275$	−16496.3			−0.218133
$276$	−18312.4	−	18312.4i	−0.240396	−	0.240396i
$277$	23839.9	−	23839.9i	0.310703	−	0.310703i	−0.534479	−	0.845182i	$-0.679492\pi$
$277$	23839.9	−	23839.9i	0.310703	−	0.310703i	0.845182	+	0.534479i	$0.179492\pi$
$278$	10327.0	+	10327.0i	0.133623	+	0.133623i
$279$	−5182.01	+	5182.01i	−0.0665718	+	0.0665718i
$280$		−	14303.0i		−	0.182436i
$281$	21675.2	+	21675.2i	0.274506	+	0.274506i	0.830911	−	0.556405i	$-0.187820\pi$
$281$	21675.2	+	21675.2i	0.274506	+	0.274506i	−0.556405	+	0.830911i	$0.687820\pi$
$282$	−30103.1	−	30103.1i	−0.378541	−	0.378541i
$283$	−54911.3	+	54911.3i	−0.685628	+	0.685628i	−0.961263	−	0.275634i	$-0.911112\pi$
$283$	−54911.3	+	54911.3i	−0.685628	+	0.685628i	0.275634	+	0.961263i	$0.411112\pi$
$284$			37649.0i			0.466785i
$285$	35721.3			0.439782
$286$		−	8923.51i		−	0.109095i
$287$			49776.9i			0.604316i
$288$	−1452.74	+	1452.74i	−0.0175147	+	0.0175147i
$289$		−	50472.5i		−	0.604309i
$290$	−20711.5	+	20711.5i	−0.246272	+	0.246272i
$291$	−24889.6	+	24889.6i	−0.293922	+	0.293922i
$292$	58038.2			0.680688
$293$	−100313.			−1.16848			−0.584241	−	0.811580i	$-0.698608\pi$
$293$	−100313.			−1.16848			−0.584241	+	0.811580i	$0.698608\pi$
$294$	−52230.6	−	52230.6i	−0.604269	−	0.604269i
$295$		−	5341.84i		−	0.0613829i
$296$	−24917.5	−	18403.6i	−0.284394	−	0.210048i
$297$	−23001.4			−0.260760
$298$	−78663.0	+	78663.0i	−0.885805	+	0.885805i
$299$			41005.4i			0.458668i
$300$			36904.6i			0.410051i
$301$	−8663.83	−	8663.83i	−0.0956262	−	0.0956262i
$302$	−35277.2	−	35277.2i	−0.386795	−	0.386795i
$303$	50972.5			0.555201
$304$	22788.1	+	22788.1i	0.246582	+	0.246582i
$305$	−41682.6			−0.448079
$306$	−5835.77			−0.0623240
$307$		−	143403.i		−	1.52154i	−0.649023	−	0.760768i	$-0.724822\pi$
$307$		−	143403.i		−	1.52154i	0.649023	−	0.760768i	$-0.275178\pi$
$308$	17754.9			0.187162
$309$	−68903.2	−	68903.2i	−0.721643	−	0.721643i
$310$	10977.1	−	10977.1i	0.114226	−	0.114226i
$311$	120451.	−	120451.i	1.24534	−	1.24534i	0.287592	−	0.957753i	$-0.407145\pi$
$311$	120451.	−	120451.i	1.24534	−	1.24534i	0.957753	−	0.287592i	$-0.0928547\pi$
$312$	−19963.2			−0.205079
$313$	−23085.0	−	23085.0i	−0.235636	−	0.235636i	0.579405	−	0.815040i	$-0.303285\pi$
$313$	−23085.0	−	23085.0i	−0.235636	−	0.235636i	−0.815040	+	0.579405i	$0.803285\pi$
$314$	34404.6	−	34404.6i	0.348945	−	0.348945i
$315$	5072.88	+	5072.88i	0.0511250	+	0.0511250i
$316$	−54743.0	+	54743.0i	−0.548219	+	0.548219i
$317$			51058.1i			0.508096i	0.967192	+	0.254048i	$0.0817622\pi$
$317$			51058.1i			0.508096i	−0.967192	+	0.254048i	$0.918238\pi$
$318$	−4601.86	−	4601.86i	−0.0455071	−	0.0455071i
$319$	−25710.1	−	25710.1i	−0.252652	−	0.252652i
$320$	3077.35	−	3077.35i	0.0300522	−	0.0300522i
$321$		−	13721.2i		−	0.133163i
$322$	−81587.4			−0.786885
$323$			91541.7i			0.877433i
$324$			44103.0i			0.420125i
$325$	41318.6	−	41318.6i	0.391182	−	0.391182i
$326$		−	93253.8i		−	0.877468i
$327$	92522.7	−	92522.7i	0.865273	−	0.865273i
$328$	−10709.7	+	10709.7i	−0.0995473	+	0.0995473i
$329$	−134119.			−1.23907
$330$	5988.06			0.0549868
$331$	110379.	+	110379.i	1.00747	+	1.00747i	0.999972	+	0.00749690i	$0.00238636\pi$
$331$	110379.	+	110379.i	1.00747	+	1.00747i	0.00749690	+	0.999972i	$0.497614\pi$
$332$		−	1909.41i		−	0.0173230i
$333$	15364.8	−	2310.30i	0.138560	−	0.0208344i
$334$	−123373.			−1.10593
$335$	15813.4	−	15813.4i	0.140908	−	0.140908i
$336$		−	39720.3i		−	0.351831i
$337$		−	31530.2i		−	0.277631i	−0.990318	−	0.138815i	$-0.955671\pi$
$337$		−	31530.2i		−	0.277631i	0.990318	−	0.138815i	$-0.0443294\pi$
$338$	−34771.1	−	34771.1i	−0.304358	−	0.304358i
$339$	−12408.6	−	12408.6i	−0.107975	−	0.107975i
$340$	12362.0			0.106937
$341$	13626.3	+	13626.3i	0.117184	+	0.117184i
$342$	−16164.6			−0.138202
$343$	−54152.6			−0.460290
$344$		−	3728.12i		−	0.0315045i
$345$	−27516.4			−0.231181
$346$	−20502.6	−	20502.6i	−0.171260	−	0.171260i
$347$	−78078.6	+	78078.6i	−0.648445	+	0.648445i	−0.952617	−	0.304172i	$-0.901620\pi$
$347$	−78078.6	+	78078.6i	−0.648445	+	0.648445i	0.304172	+	0.952617i	$0.401620\pi$
$348$	−57517.2	+	57517.2i	−0.474940	+	0.474940i
$349$	−85545.1			−0.702335			−0.351167	−	0.936313i	$-0.614215\pi$
$349$	−85545.1			−0.702335			−0.351167	+	0.936313i	$0.614215\pi$
$350$	82210.7	+	82210.7i	0.671108	+	0.671108i
$351$	57612.2	−	57612.2i	0.467628	−	0.467628i
$352$	3820.04	+	3820.04i	0.0308306	+	0.0308306i
$353$	−116125.	+	116125.i	−0.931915	+	0.931915i	−0.997826	−	0.0659107i	$-0.979005\pi$
$353$	−116125.	+	116125.i	−0.931915	+	0.931915i	0.0659107	+	0.997826i	$0.479005\pi$
$354$		−	14834.6i		−	0.118378i
$355$	28285.9	+	28285.9i	0.224447	+	0.224447i
$356$	82923.4	+	82923.4i	0.654300	+	0.654300i
$357$	79779.8	−	79779.8i	0.625975	−	0.625975i
$358$			21842.4i			0.170425i
$359$	−19405.0			−0.150565			−0.0752827	−	0.997162i	$-0.523986\pi$
$359$	−19405.0			−0.150565			−0.0752827	+	0.997162i	$0.523986\pi$
$360$			2182.90i			0.0168434i
$361$			123243.i			0.945685i
$362$	13189.4	−	13189.4i	0.100649	−	0.100649i
$363$		−	114756.i		−	0.870887i
$364$	−44471.1	+	44471.1i	−0.335641	+	0.335641i
$365$	43604.4	−	43604.4i	0.327299	−	0.327299i
$366$	−115755.			−0.864128
$367$	−167595.			−1.24431			−0.622156	−	0.782893i	$-0.713743\pi$
$367$	−167595.			−1.24431			−0.622156	+	0.782893i	$0.713743\pi$
$368$	−17553.9	−	17553.9i	−0.129622	−	0.129622i
$369$		−	7596.87i		−	0.0557933i
$370$	−32547.3	+	4893.92i	−0.237745	+	0.0357482i
$371$	−20502.7			−0.148958
$372$	30484.1	−	30484.1i	0.220286	−	0.220286i
$373$		−	110011.i		−	0.790715i	−0.918527	−	0.395357i	$-0.870621\pi$
$373$		−	110011.i		−	0.790715i	0.918527	−	0.395357i	$-0.129379\pi$
$374$			15345.4i			0.109707i
$375$	59077.4	+	59077.4i	0.420106	+	0.420106i
$376$	−28856.2	−	28856.2i	−0.204110	−	0.204110i
$377$	128793.			0.906172
$378$	114630.	+	114630.i	0.802257	+	0.802257i
$379$	126561.			0.881092			0.440546	−	0.897730i	$-0.354785\pi$
$379$	126561.			0.881092			0.440546	+	0.897730i	$0.354785\pi$
$380$	34241.7			0.237131
$381$		−	232107.i		−	1.59897i
$382$	−113131.			−0.775276
$383$	174105.	+	174105.i	1.18690	+	1.18690i	0.977921	+	0.208977i	$0.0670133\pi$
$383$	174105.	+	174105.i	1.18690	+	1.18690i	0.208977	+	0.977921i	$0.432987\pi$
$384$	8545.98	−	8545.98i	0.0579562	−	0.0579562i
$385$	13339.3	−	13339.3i	0.0899939	−	0.0899939i
$386$	147421.			0.989426
$387$	1322.26	+	1322.26i	0.00882867	+	0.00882867i
$388$	−23858.7	+	23858.7i	−0.158483	+	0.158483i
$389$	207222.	+	207222.i	1.36942	+	1.36942i	0.861265	+	0.508157i	$0.169673\pi$
$389$	207222.	+	207222.i	1.36942	+	1.36942i	0.508157	+	0.861265i	$0.330327\pi$
$390$	−14998.4	+	14998.4i	−0.0986091	+	0.0986091i
$391$		−	70515.3i		−	0.461243i
$392$	−50067.2	−	50067.2i	−0.325822	−	0.325822i
$393$	75959.9	+	75959.9i	0.491812	+	0.491812i
$394$	136968.	−	136968.i	0.882324	−	0.882324i
$395$			82257.4i			0.527206i
$396$	−2709.73			−0.0172797
$397$		−	224815.i		−	1.42641i	−0.700956	−	0.713204i	$-0.747243\pi$
$397$		−	224815.i		−	1.42641i	0.700956	−	0.713204i	$-0.252757\pi$
$398$			82896.0i			0.523320i
$399$	220984.	−	220984.i	1.38808	−	1.38808i
$400$			35375.9i			0.221100i
$401$	189685.	−	189685.i	1.17963	−	1.17963i	0.199789	−	0.979839i	$-0.435974\pi$
$401$	189685.	−	189685.i	1.17963	−	1.17963i	0.979839	−	0.199789i	$-0.0640257\pi$
$402$	43914.7	−	43914.7i	0.271743	−	0.271743i
$403$	−68260.4			−0.420299
$404$	48861.2			0.299365
$405$	33134.8	+	33134.8i	0.202011	+	0.202011i
$406$			256257.i			1.55462i
$407$	−6075.04	−	40402.3i	−0.0366742	−	0.243903i
$408$	34329.9			0.206230
$409$	−155073.	+	155073.i	−0.927023	+	0.927023i	−0.997513	−	0.0704894i	$-0.977544\pi$
$409$	−155073.	+	155073.i	−0.927023	+	0.927023i	0.0704894	+	0.997513i	$0.477544\pi$
$410$			16092.5i			0.0957317i
$411$		−	118013.i		−	0.698631i
$412$	−66049.2	−	66049.2i	−0.389110	−	0.389110i
$413$	−33046.5	−	33046.5i	−0.193743	−	0.193743i
$414$	12451.8			0.0726490
$415$	−1434.55	−	1434.55i	−0.00832952	−	0.00832952i
$416$	−19136.3			−0.110579
$417$	43092.8			0.247818
$418$			42505.6i			0.243273i
$419$	137786.			0.784834			0.392417	−	0.919787i	$-0.371639\pi$
$419$	137786.			0.784834			0.392417	+	0.919787i	$0.371639\pi$
$420$	−29842.0	−	29842.0i	−0.169173	−	0.169173i
$421$	−160090.	+	160090.i	−0.903231	+	0.903231i	−0.995714	−	0.0924831i	$-0.970520\pi$
$421$	−160090.	+	160090.i	−0.903231	+	0.903231i	0.0924831	+	0.995714i	$0.470520\pi$
$422$	−127728.	+	127728.i	−0.717237	+	0.717237i
$423$	20469.0			0.114397
$424$	−4411.25	−	4411.25i	−0.0245375	−	0.0245375i
$425$	−71054.1	+	71054.1i	−0.393379	+	0.393379i
$426$	78551.6	+	78551.6i	0.432849	+	0.432849i
$427$	−257863.	+	257863.i	−1.41427	+	1.41427i
$428$		−	13152.9i		−	0.0718015i
$429$	−18618.2	−	18618.2i	−0.101163	−	0.101163i
$430$	−2800.95	−	2800.95i	−0.0151485	−	0.0151485i
$431$	157580.	−	157580.i	0.848295	−	0.848295i	−0.141625	−	0.989920i	$-0.545233\pi$
$431$	157580.	−	157580.i	0.848295	−	0.848295i	0.989920	+	0.141625i	$0.0452327\pi$
$432$			49326.1i			0.264307i
$433$	−132955.			−0.709134			−0.354567	−	0.935031i	$-0.615372\pi$
$433$	−132955.			−0.709134			−0.354567	+	0.935031i	$0.615372\pi$
$434$		−	135816.i		−	0.721060i
$435$			86425.9i			0.456736i
$436$	88690.4	−	88690.4i	0.466556	−	0.466556i
$437$		−	195322.i		−	1.02279i
$438$	121092.	−	121092.i	0.631201	−	0.631201i
$439$	−34598.1	+	34598.1i	−0.179524	+	0.179524i	−0.791148	−	0.611624i	$-0.790516\pi$
$439$	−34598.1	+	34598.1i	−0.179524	+	0.179524i	0.611624	+	0.791148i	$0.290516\pi$
$440$	5740.03			0.0296489
$441$	35514.9			0.182614
$442$	−38436.0	−	38436.0i	−0.196741	−	0.196741i
$443$			123857.i			0.631123i	0.948905	+	0.315561i	$0.102193\pi$
$443$			123857.i			0.631123i	−0.948905	+	0.315561i	$0.897807\pi$
$444$	−90385.9	+	13590.7i	−0.458495	+	0.0689409i
$445$	124602.			0.629221
$446$	174648.	−	174648.i	0.877998	−	0.877998i
$447$			328249.i			1.64281i
$448$		−	38075.0i		−	0.189707i
$449$	188229.	+	188229.i	0.933671	+	0.933671i	0.997933	−	0.0642622i	$-0.0204694\pi$
$449$	188229.	+	188229.i	0.933671	+	0.933671i	−0.0642622	+	0.997933i	$0.520469\pi$
$450$	−12546.9	−	12546.9i	−0.0619599	−	0.0619599i
$451$	−19976.3			−0.0982115
$452$	−11894.6	−	11894.6i	−0.0582200	−	0.0582200i
$453$	−147206.			−0.717348
$454$	8819.06			0.0427869
$455$			66822.8i			0.322776i
$456$	95091.2			0.457310
$457$	−113566.	−	113566.i	−0.543771	−	0.543771i	0.380861	−	0.924632i	$-0.375628\pi$
$457$	−113566.	−	113566.i	−0.543771	−	0.543771i	−0.924632	+	0.380861i	$0.875628\pi$
$458$	45433.3	−	45433.3i	0.216593	−	0.216593i
$459$	−99073.5	+	99073.5i	−0.470254	+	0.470254i
$460$	−26376.6			−0.124653
$461$	−287290.	−	287290.i	−1.35182	−	1.35182i	−0.883625	−	0.468196i	$-0.844904\pi$
$461$	−287290.	−	287290.i	−1.35182	−	1.35182i	−0.468196	−	0.883625i	$-0.655096\pi$
$462$	37044.2	−	37044.2i	0.173555	−	0.173555i
$463$	238340.	+	238340.i	1.11182	+	1.11182i	0.992904	+	0.118917i	$0.0379423\pi$
$463$	238340.	+	238340.i	1.11182	+	1.11182i	0.118917	+	0.992904i	$0.462058\pi$
$464$	−55134.8	+	55134.8i	−0.256088	+	0.256088i
$465$		−	45805.7i		−	0.211843i
$466$	−133920.	−	133920.i	−0.616701	−	0.616701i
$467$	−102704.	−	102704.i	−0.470927	−	0.470927i	0.431287	−	0.902215i	$-0.358059\pi$
$467$	−102704.	−	102704.i	−0.470927	−	0.470927i	−0.902215	+	0.431287i	$0.858059\pi$
$468$	6787.12	−	6787.12i	0.0309880	−	0.0309880i
$469$		−	195654.i		−	0.889493i
$470$	−43359.6			−0.196286
$471$		−	143565.i		−	0.647153i
$472$		−	14220.2i		−	0.0638294i
$473$	3476.94	−	3476.94i	0.0155409	−	0.0155409i
$474$			228434.i			1.01673i
$475$	−196814.	+	196814.i	−0.872307	+	0.872307i
$476$	76475.3	−	76475.3i	0.337526	−	0.337526i
$477$	3129.10			0.0137525
$478$	40822.4			0.178666
$479$	−62677.4	−	62677.4i	−0.273174	−	0.273174i	0.557202	−	0.830377i	$-0.311875\pi$
$479$	−62677.4	−	62677.4i	−0.273174	−	0.273174i	−0.830377	+	0.557202i	$0.811875\pi$
$480$		−	12841.3i		−	0.0557347i
$481$	116413.	+	85980.5i	0.503166	+	0.371629i
$482$	−134550.			−0.579147
$483$	−170226.	+	170226.i	−0.729678	+	0.729678i
$484$		−	110003.i		−	0.469583i
$485$			35850.3i			0.152408i
$486$	−32839.2	−	32839.2i	−0.139034	−	0.139034i
$487$	16951.0	+	16951.0i	0.0714721	+	0.0714721i	0.741939	−	0.670467i	$-0.233906\pi$
$487$	16951.0	+	16951.0i	0.0714721	+	0.0714721i	−0.670467	+	0.741939i	$0.733906\pi$
$488$	−110960.			−0.465938
$489$	−194567.	−	194567.i	−0.813675	−	0.813675i
$490$	−75231.4			−0.313334
$491$	−361863.			−1.50100			−0.750502	−	0.660868i	$-0.770188\pi$
$491$	−361863.			−1.50100			−0.750502	+	0.660868i	$0.770188\pi$
$492$			44689.9i			0.184620i
$493$	−221481.			−0.911260
$494$	−106465.	−	106465.i	−0.436267	−	0.436267i
$495$	−2035.83	+	2035.83i	−0.00830867	+	0.00830867i
$496$	29221.4	−	29221.4i	0.118778	−	0.118778i
$497$	349972.			1.41684
$498$	−3983.84	−	3983.84i	−0.0160636	−	0.0160636i
$499$	96829.0	−	96829.0i	0.388870	−	0.388870i	−0.485414	−	0.874284i	$-0.661331\pi$
$499$	96829.0	−	96829.0i	0.388870	−	0.388870i	0.874284	+	0.485414i	$0.161331\pi$
$500$	56630.3	+	56630.3i	0.226521	+	0.226521i
$501$	−257409.	+	257409.i	−1.02553	+	1.02553i
$502$		−	127318.i		−	0.505221i
$503$	−143731.	−	143731.i	−0.568085	−	0.568085i	0.363507	−	0.931592i	$-0.381579\pi$
$503$	−143731.	−	143731.i	−0.568085	−	0.568085i	−0.931592	+	0.363507i	$0.881579\pi$
$504$	13504.2	+	13504.2i	0.0531627	+	0.0531627i
$505$	36709.6	−	36709.6i	0.143945	−	0.143945i
$506$		−	32742.4i		−	0.127882i
$507$	−145094.			−0.564461
$508$		−	222493.i		−	0.862163i
$509$			473753.i			1.82859i	0.405051	+	0.914294i	$0.367254\pi$
$509$			473753.i			1.82859i	−0.405051	+	0.914294i	$0.632746\pi$
$510$	25792.2	−	25792.2i	0.0991628	−	0.0991628i
$511$		−	539504.i		−	2.06611i
$512$	8192.00	−	8192.00i	0.0312500	−	0.0312500i
$513$	−274426.	+	274426.i	−1.04277	+	1.04277i
$514$	6746.47			0.0255359
$515$	−99246.1			−0.374196
$516$	−7778.42	−	7778.42i	−0.0292141	−	0.0292141i
$517$		−	53824.1i		−	0.201371i
$518$	−171073.	+	231624.i	−0.637562	+	0.863226i
$519$	−85554.1			−0.317619
$520$	−14377.2	+	14377.2i	−0.0531701	+	0.0531701i
$521$		−	247802.i		−	0.912914i	−0.889746	−	0.456457i	$-0.849118\pi$
$521$		−	247802.i		−	0.912914i	0.889746	−	0.456457i	$-0.150882\pi$
$522$		−	39109.6i		−	0.143530i
$523$	262988.	+	262988.i	0.961461	+	0.961461i	0.999284	−	0.0378231i	$-0.0120424\pi$
$523$	262988.	+	262988.i	0.961461	+	0.961461i	−0.0378231	+	0.999284i	$0.512042\pi$
$524$	72813.5	+	72813.5i	0.265185	+	0.265185i
$525$	343052.			1.24463
$526$	250571.	+	250571.i	0.905648	+	0.905648i
$527$	117385.			0.422659
$528$	15940.4			0.0571784
$529$		−	129383.i		−	0.462344i
$530$	−6628.39			−0.0235970
$531$	5043.51	+	5043.51i	0.0178873	+	0.0178873i
$532$	211831.	−	211831.i	0.748455	−	0.748455i
$533$	50035.2	−	50035.2i	0.176125	−	0.176125i
$534$	346026.			1.21346
$535$	−9881.83	−	9881.83i	−0.0345247	−	0.0345247i
$536$	42095.7	−	42095.7i	0.146524	−	0.146524i
$537$	45572.4	+	45572.4i	0.158035	+	0.158035i
$538$	−122025.	+	122025.i	−0.421582	+	0.421582i
$539$		−	93388.0i		−	0.321450i
$540$	37058.9	+	37058.9i	0.127088	+	0.127088i
$541$	57019.9	+	57019.9i	0.194819	+	0.194819i	0.797775	−	0.602955i	$-0.206010\pi$
$541$	57019.9	+	57019.9i	0.194819	+	0.194819i	−0.602955	+	0.797775i	$0.706010\pi$
$542$	89651.8	−	89651.8i	0.305183	−	0.305183i
$543$		−	55037.4i		−	0.186663i
$544$	32907.9			0.111200
$545$		−	133267.i		−	0.448673i
$546$			185571.i			0.622479i
$547$	155564.	−	155564.i	0.519918	−	0.519918i	−0.397628	−	0.917547i	$-0.630167\pi$
$547$	155564.	−	155564.i	0.519918	−	0.519918i	0.917547	+	0.397628i	$0.130167\pi$
$548$		−	113125.i		−	0.376702i
$549$	39354.6	−	39354.6i	0.130572	−	0.130572i
$550$	−32992.6	+	32992.6i	−0.109066	+	0.109066i
$551$	−613485.			−2.02070
$552$	−73249.5			−0.240396
$553$	508872.	+	508872.i	1.66402	+	1.66402i
$554$		−	95359.7i		−	0.310703i
$555$	−57696.6	+	78118.2i	−0.187311	+	0.253610i
$556$	41307.8			0.133623
$557$	−171093.	+	171093.i	−0.551470	+	0.551470i	−0.926865	−	0.375395i	$-0.877507\pi$
$557$	−171093.	+	171093.i	−0.551470	+	0.551470i	0.375395	+	0.926865i	$0.377507\pi$
$558$			20728.0i			0.0665718i
$559$			17417.6i			0.0557396i
$560$	−28606.0	−	28606.0i	−0.0912180	−	0.0912180i
$561$	32017.0	+	32017.0i	0.101731	+	0.101731i
$562$	86701.0			0.274506
$563$	209933.	+	209933.i	0.662316	+	0.662316i	0.955925	−	0.293610i	$-0.0948566\pi$
$563$	209933.	+	209933.i	0.662316	+	0.662316i	−0.293610	+	0.955925i	$0.594857\pi$
$564$	−120412.			−0.378541
$565$	−17872.9			−0.0559885
$566$			219645.i			0.685628i
$567$	409967.			1.27521
$568$	75298.0	+	75298.0i	0.233392	+	0.233392i
$569$	202625.	−	202625.i	0.625847	−	0.625847i	−0.321173	−	0.947020i	$-0.604077\pi$
$569$	202625.	−	202625.i	0.625847	−	0.625847i	0.947020	+	0.321173i	$0.104077\pi$
$570$	71442.5	−	71442.5i	0.219891	−	0.219891i
$571$	−532914.			−1.63450			−0.817250	−	0.576283i	$-0.804503\pi$
$571$	−532914.			−1.63450			−0.817250	+	0.576283i	$0.804503\pi$
$572$	−17847.0	−	17847.0i	−0.0545474	−	0.0545474i
$573$	−236040.	+	236040.i	−0.718912	+	0.718912i
$574$	99553.7	+	99553.7i	0.302158	+	0.302158i
$575$	151608.	−	151608.i	0.458549	−	0.458549i
$576$			5810.96i			0.0175147i
$577$	−164555.	−	164555.i	−0.494266	−	0.494266i	0.415381	−	0.909647i	$-0.363648\pi$
$577$	−164555.	−	164555.i	−0.494266	−	0.494266i	−0.909647	+	0.415381i	$0.863648\pi$
$578$	−100945.	−	100945.i	−0.302155	−	0.302155i
$579$	307581.	−	307581.i	0.917494	−	0.917494i
$580$			82846.1i			0.246272i
$581$	−17749.3			−0.0525809
$582$			99558.5i			0.293922i
$583$		−	8228.10i		−	0.0242082i
$584$	116076.	−	116076.i	0.340344	−	0.340344i
$585$		−	10198.4i		−	0.0298003i
$586$	−200626.	+	200626.i	−0.584241	+	0.584241i
$587$	−477611.	+	477611.i	−1.38611	+	1.38611i	−0.552793	+	0.833318i	$0.686438\pi$
$587$	−477611.	+	477611.i	−1.38611	+	1.38611i	−0.833318	+	0.552793i	$0.813562\pi$
$588$	−208922.			−0.604269
$589$	325147.			0.937235
$590$	−10683.7	−	10683.7i	−0.0306914	−	0.0306914i
$591$		−	571548.i		−	1.63635i
$592$	−86642.0	+	13027.8i	−0.247221	+	0.0371730i
$593$	466216.			1.32580			0.662900	−	0.748708i	$-0.269325\pi$
$593$	466216.			1.32580			0.662900	+	0.748708i	$0.269325\pi$
$594$	−46002.8	+	46002.8i	−0.130380	+	0.130380i
$595$		−	114913.i		−	0.324589i
$596$			314652.i			0.885805i
$597$	172956.	+	172956.i	0.485274	+	0.485274i
$598$	82010.8	+	82010.8i	0.229334	+	0.229334i
$599$	233855.			0.651767			0.325884	−	0.945410i	$-0.394338\pi$
$599$	233855.			0.651767			0.325884	+	0.945410i	$0.394338\pi$
$600$	73809.1	+	73809.1i	0.205025	+	0.205025i
$601$	294459.			0.815221			0.407610	−	0.913156i	$-0.366362\pi$
$601$	294459.			0.815221			0.407610	+	0.913156i	$0.366362\pi$
$602$	−34655.3			−0.0956262
$603$			29860.4i			0.0821223i
$604$	−141109.			−0.386795
$605$	−82645.6	−	82645.6i	−0.225792	−	0.225792i
$606$	101945.	−	101945.i	0.277601	−	0.277601i
$607$	58823.3	−	58823.3i	0.159651	−	0.159651i	−0.622761	−	0.782412i	$-0.713989\pi$
$607$	58823.3	−	58823.3i	0.159651	−	0.159651i	0.782412	+	0.622761i	$0.213989\pi$
$608$	91152.5			0.246582
$609$	534660.	+	534660.i	1.44160	+	1.44160i
$610$	−83365.1	+	83365.1i	−0.224040	+	0.224040i
$611$	134815.	+	134815.i	0.361122	+	0.361122i
$612$	−11671.5	+	11671.5i	−0.0311620	+	0.0311620i
$613$			239371.i			0.637016i	0.947920	+	0.318508i	$0.103182\pi$
$613$			239371.i			0.637016i	−0.947920	+	0.318508i	$0.896818\pi$
$614$	−286807.	−	286807.i	−0.760768	−	0.760768i
$615$	33575.7	+	33575.7i	0.0887719	+	0.0887719i
$616$	35509.8	−	35509.8i	0.0935808	−	0.0935808i
$617$		−	507125.i		−	1.33212i	−0.745896	−	0.666062i	$-0.767979\pi$
$617$		−	507125.i		−	1.33212i	0.745896	−	0.666062i	$-0.232021\pi$
$618$	−275613.			−0.721643
$619$		−	605945.i		−	1.58144i	−0.612181	−	0.790718i	$-0.709707\pi$
$619$		−	605945.i		−	1.58144i	0.612181	−	0.790718i	$-0.290293\pi$
$620$		−	43908.3i		−	0.114226i
$621$	211393.	−	211393.i	0.548159	−	0.548159i
$622$		−	481804.i		−	1.24534i
$623$	770828.	−	770828.i	1.98601	−	1.98601i
$624$	−39926.4	+	39926.4i	−0.102539	+	0.102539i
$625$	−260375.			−0.666560
$626$	−92339.9			−0.235636
$627$	88684.7	+	88684.7i	0.225587	+	0.225587i
$628$		−	137618.i		−	0.348945i
$629$	−200191.	−	147857.i	−0.505991	−	0.373716i
$630$	20291.5			0.0511250
$631$	198378.	−	198378.i	0.498234	−	0.498234i	−0.412654	−	0.910888i	$-0.635398\pi$
$631$	198378.	−	198378.i	0.498234	−	0.498234i	0.910888	+	0.412654i	$0.135398\pi$
$632$			218972.i			0.548219i
$633$			532991.i			1.33019i
$634$	102116.	+	102116.i	0.254048	+	0.254048i
$635$	−167160.	−	167160.i	−0.414558	−	0.414558i
$636$	−18407.4			−0.0455071
$637$	233911.	+	233911.i	0.576464	+	0.576464i
$638$	−102840.			−0.252652
$639$	−53412.3			−0.130809
$640$		−	12309.4i		−	0.0300522i
$641$	−544243.			−1.32457			−0.662287	−	0.749250i	$-0.730414\pi$
$641$	−544243.			−1.32457			−0.662287	+	0.749250i	$0.730414\pi$
$642$	−27442.5	−	27442.5i	−0.0665814	−	0.0665814i
$643$	−292685.	+	292685.i	−0.707910	+	0.707910i	−0.966095	−	0.258185i	$-0.916876\pi$
$643$	−292685.	+	292685.i	−0.707910	+	0.707910i	0.258185	+	0.966095i	$0.416876\pi$
$644$	−163175.	+	163175.i	−0.393443	+	0.393443i
$645$	−11687.9			−0.0280943
$646$	183083.	+	183083.i	0.438717	+	0.438717i
$647$	−350912.	+	350912.i	−0.838281	+	0.838281i	−0.988633	−	0.150352i	$-0.951959\pi$
$647$	−350912.	+	350912.i	−0.838281	+	0.838281i	0.150352	+	0.988633i	$0.451959\pi$
$648$	88206.0	+	88206.0i	0.210062	+	0.210062i
$649$	13262.1	−	13262.1i	0.0314864	−	0.0314864i
$650$		−	165275.i		−	0.391182i
$651$	−283369.	−	283369.i	−0.668638	−	0.668638i
$652$	−186508.	−	186508.i	−0.438734	−	0.438734i
$653$	−468773.	+	468773.i	−1.09935	+	1.09935i	−0.104863	+	0.994487i	$0.533440\pi$
$653$	−468773.	+	468773.i	−1.09935	+	1.09935i	−0.994487	+	0.104863i	$0.966560\pi$
$654$		−	370091.i		−	0.865273i
$655$	109410.			0.255021
$656$			42838.8i			0.0995473i
$657$			82338.3i			0.190753i
$658$	−268237.	+	268237.i	−0.619537	+	0.619537i
$659$		−	82131.4i		−	0.189120i	−0.995519	−	0.0945602i	$-0.969856\pi$
$659$		−	82131.4i		−	0.189120i	0.995519	−	0.0945602i	$-0.0301445\pi$
$660$	11976.1	−	11976.1i	0.0274934	−	0.0274934i
$661$	82904.6	−	82904.6i	0.189747	−	0.189747i	−0.605840	−	0.795587i	$-0.707163\pi$
$661$	82904.6	−	82904.6i	0.189747	−	0.189747i	0.795587	+	0.605840i	$0.207163\pi$
$662$	441517.			1.00747
$663$	−160388.			−0.364875
$664$	−3818.83	−	3818.83i	−0.00866151	−	0.00866151i
$665$		−	318299.i		−	0.719767i
$666$	26109.0	−	35350.2i	0.0588628	−	0.0796972i
$667$	472573.			1.06223
$668$	−246747.	+	246747.i	−0.552966	+	0.552966i
$669$		−	728778.i		−	1.62833i
$670$		−	63253.4i		−	0.140908i
$671$	−103485.	−	103485.i	−0.229843	−	0.229843i
$672$	−79440.6	−	79440.6i	−0.175915	−	0.175915i
$673$	266396.			0.588164			0.294082	−	0.955780i	$-0.404986\pi$
$673$	266396.			0.588164			0.294082	+	0.955780i	$0.404986\pi$
$674$	−63060.5	−	63060.5i	−0.138815	−	0.138815i
$675$	−426015.			−0.935012
$676$	−139084.			−0.304358
$677$			252631.i			0.551201i	0.961272	+	0.275600i	$0.0888766\pi$
$677$			252631.i			0.551201i	−0.961272	+	0.275600i	$0.911123\pi$
$678$	−49634.2			−0.107975
$679$	221782.	+	221782.i	0.481047	+	0.481047i
$680$	24723.9	−	24723.9i	0.0534686	−	0.0534686i
$681$	18400.3	−	18400.3i	0.0396762	−	0.0396762i
$682$	54505.3			0.117184
$683$	403845.	+	403845.i	0.865711	+	0.865711i	0.991994	−	0.126283i	$-0.0403048\pi$
$683$	403845.	+	403845.i	0.865711	+	0.865711i	−0.126283	+	0.991994i	$0.540305\pi$
$684$	−32329.3	+	32329.3i	−0.0691009	+	0.0691009i
$685$	−84991.6	−	84991.6i	−0.181132	−	0.181132i
$686$	−108305.	+	108305.i	−0.230145	+	0.230145i
$687$		−	189586.i		−	0.401692i
$688$	−7456.23	−	7456.23i	−0.0157522	−	0.0157522i
$689$	20609.1	+	20609.1i	0.0434131	+	0.0434131i
$690$	−55032.8	+	55032.8i	−0.115591	+	0.115591i
$691$			508793.i			1.06558i	0.846248	+	0.532789i	$0.178856\pi$
$691$			508793.i			1.06558i	−0.846248	+	0.532789i	$0.821144\pi$
$692$	−82010.4			−0.171260
$693$			25188.7i			0.0524493i
$694$			312315.i			0.648445i
$695$	31034.8	−	31034.8i	0.0642509	−	0.0642509i
$696$			230069.i			0.474940i
$697$	−86043.5	+	86043.5i	−0.177114	+	0.177114i
$698$	−171090.	+	171090.i	−0.351167	+	0.351167i
$699$	−558828.			−1.14373
$700$	328843.			0.671108
$701$	296359.	+	296359.i	0.603089	+	0.603089i	0.941131	−	0.338042i	$-0.109765\pi$
$701$	296359.	+	296359.i	0.603089	+	0.603089i	−0.338042	+	0.941131i	$0.609765\pi$
$702$		−	230449.i		−	0.467628i
$703$	−554514.	−	409553.i	−1.12202	−	0.828704i
$704$	15280.2			0.0308306
$705$	−90466.4	+	90466.4i	−0.182016	+	0.182016i
$706$			464500.i			0.931915i
$707$		−	454197.i		−	0.908668i
$708$	−29669.3	−	29669.3i	−0.0591889	−	0.0591889i
$709$	444479.	+	444479.i	0.884217	+	0.884217i	0.993960	−	0.109743i	$-0.0350028\pi$
$709$	444479.	+	444479.i	0.884217	+	0.884217i	−0.109743	+	0.993960i	$0.535003\pi$
$710$	113143.			0.224447
$711$	−77663.4	−	77663.4i	−0.153630	−	0.153630i
$712$	331694.			0.654300
$713$	−250463.			−0.492680
$714$		−	319119.i		−	0.625975i
$715$	−26817.1			−0.0524566
$716$	43684.7	+	43684.7i	0.0852126	+	0.0852126i
$717$	85172.7	−	85172.7i	0.165677	−	0.165677i
$718$	−38810.0	+	38810.0i	−0.0752827	+	0.0752827i
$719$	819951.			1.58610			0.793050	−	0.609157i	$-0.208492\pi$
$719$	819951.			1.58610			0.793050	+	0.609157i	$0.208492\pi$
$720$	4365.80	+	4365.80i	0.00842168	+	0.00842168i
$721$	−613971.	+	613971.i	−1.18107	+	1.18107i
$722$	246485.	+	246485.i	0.472842	+	0.472842i
$723$	−280727.	+	280727.i	−0.537042	+	0.537042i
$724$		−	52757.7i		−	0.100649i
$725$	−476183.	−	476183.i	−0.905936	−	0.905936i
$726$	−229512.	−	229512.i	−0.435444	−	0.435444i
$727$	62586.0	−	62586.0i	0.118415	−	0.118415i	−0.645416	−	0.763831i	$-0.723316\pi$
$727$	62586.0	−	62586.0i	0.118415	−	0.118415i	0.763831	+	0.645416i	$0.223316\pi$
$728$			177885.i			0.335641i
$729$	−583576.			−1.09810
$730$		−	174418.i		−	0.327299i
$731$		−	29952.3i		−	0.0560526i
$732$	−231510.	+	231510.i	−0.432064	+	0.432064i
$733$		−	763799.i		−	1.42158i	−0.703405	−	0.710789i	$-0.748338\pi$
$733$		−	763799.i		−	1.42158i	0.703405	−	0.710789i	$-0.251662\pi$
$734$	−335191.	+	335191.i	−0.622156	+	0.622156i
$735$	−156964.	+	156964.i	−0.290554	+	0.290554i
$736$	−70215.5			−0.129622
$737$	78519.2			0.144558
$738$	−15193.7	−	15193.7i	−0.0278967	−	0.0278967i
$739$		−	343008.i		−	0.628081i	−0.949410	−	0.314040i	$-0.898317\pi$
$739$		−	343008.i		−	0.628081i	0.949410	−	0.314040i	$-0.101683\pi$
$740$	−55306.7	+	74882.4i	−0.100998	+	0.136747i
$741$	−444261.			−0.809100
$742$	−41005.5	+	41005.5i	−0.0744790	+	0.0744790i
$743$			207508.i			0.375886i	0.982180	+	0.187943i	$0.0601821\pi$
$743$			207508.i			0.375886i	−0.982180	+	0.187943i	$0.939818\pi$
$744$		−	121936.i		−	0.220286i
$745$	236400.	+	236400.i	0.425926	+	0.425926i
$746$	−220023.	−	220023.i	−0.395357	−	0.395357i
$747$	2708.87			0.00485452
$748$	30690.8	+	30690.8i	0.0548536	+	0.0548536i
$749$	−122265.			−0.217940
$750$	236309.			0.420106
$751$			306333.i			0.543143i	0.962418	+	0.271572i	$0.0875434\pi$
$751$			306333.i			0.543143i	−0.962418	+	0.271572i	$0.912457\pi$
$752$	−115425.			−0.204110
$753$	−265638.	−	265638.i	−0.468490	−	0.468490i
$754$	257587.	−	257587.i	0.453086	−	0.453086i
$755$	−106016.	+	106016.i	−0.185985	+	0.185985i
$756$	458519.			0.802257
$757$	747474.	+	747474.i	1.30438	+	1.30438i	0.925408	+	0.378973i	$0.123723\pi$
$757$	747474.	+	747474.i	1.30438	+	1.30438i	0.378973	+	0.925408i	$0.376277\pi$
$758$	253122.	−	253122.i	0.440546	−	0.440546i
$759$	−68314.5	−	68314.5i	−0.118585	−	0.118585i
$760$	68483.3	−	68483.3i	0.118565	−	0.118565i
$761$		−	930613.i		−	1.60694i	−0.595344	−	0.803471i	$-0.702984\pi$
$761$		−	930613.i		−	1.60694i	0.595344	−	0.803471i	$-0.297016\pi$
$762$	−464215.	−	464215.i	−0.799483	−	0.799483i
$763$	−824436.	−	824436.i	−1.41614	−	1.41614i
$764$	−226263.	+	226263.i	−0.387638	+	0.387638i
$765$			17537.8i			0.0299676i
$766$	696419.			1.18690
$767$			66435.9i			0.112931i
$768$		−	34183.9i		−	0.0579562i
$769$	−21198.2	+	21198.2i	−0.0358465	+	0.0358465i	−0.724803	−	0.688956i	$-0.758069\pi$
$769$	−21198.2	+	21198.2i	−0.0358465	+	0.0358465i	0.688956	+	0.724803i	$0.258069\pi$
$770$		−	53357.4i		−	0.0899939i
$771$	14076.0	−	14076.0i	0.0236794	−	0.0236794i
$772$	294841.	−	294841.i	0.494713	−	0.494713i
$773$	166836.			0.279211			0.139605	−	0.990207i	$-0.455417\pi$
$773$	166836.			0.279211			0.139605	+	0.990207i	$0.455417\pi$
$774$	5289.04			0.00882867
$775$	252376.	+	252376.i	0.420190	+	0.420190i
$776$			95434.7i			0.158483i
$777$	126335.	+	840197.i	0.209258	+	1.39168i
$778$	828889.			1.36942
$779$	−238334.	+	238334.i	−0.392745	+	0.392745i
$780$			59993.8i			0.0986091i
$781$			140450.i			0.230260i
$782$	−141031.	−	141031.i	−0.230622	−	0.230622i
$783$	−663961.	−	663961.i	−1.08298	−	1.08298i
$784$	−200269.			−0.325822
$785$	−103393.	−	103393.i	−0.167785	−	0.167785i
$786$	303839.			0.491812
$787$	721213.			1.16443			0.582216	−	0.813034i	$-0.302186\pi$
$787$	721213.			1.16443			0.582216	+	0.813034i	$0.302186\pi$
$788$		−	547874.i		−	0.882324i
$789$	1.04559e6			1.67961
$790$	164515.	+	164515.i	0.263603	+	0.263603i
$791$	−110568.	+	110568.i	−0.176716	+	0.176716i
$792$	−5419.46	+	5419.46i	−0.00863983	+	0.00863983i
$793$	518401.			0.824365
$794$	−449630.	−	449630.i	−0.713204	−	0.713204i
$795$	−13829.6	+	13829.6i	−0.0218814	+	0.0218814i
$796$	165792.	+	165792.i	0.261660	+	0.261660i
$797$	−502348.	+	502348.i	−0.790839	+	0.790839i	−0.981631	−	0.190791i	$-0.938895\pi$
$797$	−502348.	+	502348.i	−0.790839	+	0.790839i	0.190791	+	0.981631i	$0.438895\pi$
$798$		−	883936.i		−	1.38808i
$799$	−231835.	−	231835.i	−0.363150	−	0.363150i
$800$	70751.9	+	70751.9i	0.110550	+	0.110550i
$801$	−117643.	+	117643.i	−0.183358	+	0.183358i
$802$		−	758741.i		−	1.17963i
$803$	216512.			0.335777
$804$		−	175659.i		−	0.271743i
$805$			245188.i			0.378362i
$806$	−136521.	+	136521.i	−0.210150	+	0.210150i
$807$			509189.i			0.781866i
$808$	97722.3	−	97722.3i	0.149683	−	0.149683i
$809$	104843.	−	104843.i	0.160193	−	0.160193i	−0.622459	−	0.782652i	$-0.713866\pi$
$809$	104843.	−	104843.i	0.160193	−	0.160193i	0.782652	+	0.622459i	$0.213866\pi$
$810$	132539.			0.202011
$811$	−890921.			−1.35456			−0.677279	−	0.735726i	$-0.736841\pi$
$811$	−890921.			−1.35456			−0.677279	+	0.735726i	$0.736841\pi$
$812$	512514.	+	512514.i	0.777309	+	0.777309i
$813$		−	374103.i		−	0.565992i
$814$	−92954.8	−	68654.6i	−0.140289	−	0.103615i
$815$	−280248.			−0.421918
$816$	68659.8	−	68659.8i	0.103115	−	0.103115i
$817$		−	82965.6i		−	0.124295i
$818$			620293.i			0.927023i
$819$	−63090.8	−	63090.8i	−0.0940585	−	0.0940585i
$820$	32185.0	+	32185.0i	0.0478659	+	0.0478659i
$821$	1.13659e6			1.68623			0.843114	−	0.537734i	$-0.180720\pi$
$821$	1.13659e6			1.68623			0.843114	+	0.537734i	$0.180720\pi$
$822$	−236027.	−	236027.i	−0.349316	−	0.349316i
$823$	1.20219e6			1.77489			0.887446	−	0.460912i	$-0.152478\pi$
$823$	1.20219e6			1.77489			0.887446	+	0.460912i	$0.152478\pi$
$824$	−264197.			−0.389110
$825$			137673.i			0.202274i
$826$	−132186.			−0.193743
$827$	439174.	+	439174.i	0.642134	+	0.642134i	0.951080	−	0.308946i	$-0.0999761\pi$
$827$	439174.	+	439174.i	0.642134	+	0.642134i	−0.308946	+	0.951080i	$0.599976\pi$
$828$	24903.5	−	24903.5i	0.0363245	−	0.0363245i
$829$	−365913.	+	365913.i	−0.532438	+	0.532438i	−0.921297	−	0.388859i	$-0.872869\pi$
$829$	−365913.	+	365913.i	−0.532438	+	0.532438i	0.388859	+	0.921297i	$0.372869\pi$
$830$	−5738.21			−0.00832952
$831$	−198960.	−	198960.i	−0.288114	−	0.288114i
$832$	−38272.6	+	38272.6i	−0.0552893	+	0.0552893i
$833$	−402248.	−	402248.i	−0.579701	−	0.579701i
$834$	86185.5	−	86185.5i	0.123909	−	0.123909i
$835$			370764.i			0.531771i
$836$	85011.3	+	85011.3i	0.121636	+	0.121636i
$837$	351899.	+	351899.i	0.502304	+	0.502304i
$838$	275572.	−	275572.i	0.392417	−	0.392417i
$839$			496276.i			0.705017i	0.935809	+	0.352509i	$0.114671\pi$
$839$			496276.i			0.705017i	−0.935809	+	0.352509i	$0.885329\pi$
$840$	−119368.			−0.169173
$841$		−	777017.i		−	1.09860i
$842$			640358.i			0.903231i
$843$	180895.	−	180895.i	0.254549	−	0.254549i
$844$			510914.i			0.717237i
$845$	−104495.	+	104495.i	−0.146346	+	0.146346i
$846$	40938.0	−	40938.0i	0.0571987	−	0.0571987i
$847$	−1.02255e6			−1.42533
$848$	−17645.0			−0.0245375
$849$	458272.	+	458272.i	0.635782	+	0.635782i
$850$			284216.i			0.393379i
$851$	427146.	+	315482.i	0.589817	+	0.435628i
$852$	314207.			0.432849
$853$	260430.	−	260430.i	0.357926	−	0.357926i	−0.505122	−	0.863048i	$-0.668553\pi$
$853$	260430.	−	260430.i	0.357926	−	0.357926i	0.863048	+	0.505122i	$0.168553\pi$
$854$			1.03145e6i			1.41427i
$855$			48578.3i			0.0664523i
$856$	−26305.8	−	26305.8i	−0.0359007	−	0.0359007i
$857$	75697.4	+	75697.4i	0.103067	+	0.103067i	0.756760	−	0.653693i	$-0.226781\pi$
$857$	75697.4	+	75697.4i	0.103067	+	0.103067i	−0.653693	+	0.756760i	$0.726781\pi$
$858$	−74472.8			−0.101163
$859$	1.00008e6	+	1.00008e6i	1.35533	+	1.35533i	0.879576	+	0.475758i	$0.157826\pi$
$859$	1.00008e6	+	1.00008e6i	1.35533	+	1.35533i	0.475758	+	0.879576i	$0.342174\pi$
$860$	−11203.8			−0.0151485
$861$	415422.			0.560381
$862$		−	630321.i		−	0.848295i
$863$	837840.			1.12497			0.562483	−	0.826809i	$-0.309846\pi$
$863$	837840.			1.12497			0.562483	+	0.826809i	$0.309846\pi$
$864$	98652.2	+	98652.2i	0.132154	+	0.132154i
$865$	−61614.8	+	61614.8i	−0.0823480	+	0.0823480i
$866$	−265910.	+	265910.i	−0.354567	+	0.354567i
$867$	−421228.			−0.560375
$868$	−271632.	−	271632.i	−0.360530	−	0.360530i
$869$	−204219.	+	204219.i	−0.270431	+	0.270431i
$870$	172852.	+	172852.i	0.228368	+	0.228368i
$871$	−196669.	+	196669.i	−0.259239	+	0.259239i
$872$		−	354761.i		−	0.466556i
$873$	−33848.1	−	33848.1i	−0.0444125	−	0.0444125i
$874$	−390644.	−	390644.i	−0.511397	−	0.511397i
$875$	526416.	−	526416.i	0.687564	−	0.687564i
$876$		−	484369.i		−	0.631201i
$877$	810184.			1.05338			0.526689	−	0.850058i	$-0.323433\pi$
$877$	810184.			1.05338			0.526689	+	0.850058i	$0.323433\pi$
$878$			138392.i			0.179524i
$879$			837181.i			1.08353i
$880$	11480.1	−	11480.1i	0.0148245	−	0.0148245i
$881$		−	177217.i		−	0.228325i	−0.993462	−	0.114163i	$-0.963582\pi$
$881$		−	177217.i		−	0.228325i	0.993462	−	0.114163i	$-0.0364185\pi$
$882$	71029.8	−	71029.8i	0.0913069	−	0.0913069i
$883$	214145.	−	214145.i	0.274654	−	0.274654i	−0.556316	−	0.830971i	$-0.687786\pi$
$883$	214145.	−	214145.i	0.274654	−	0.274654i	0.830971	+	0.556316i	$0.187786\pi$
$884$	−153744.			−0.196741
$885$	−44581.4			−0.0569202
$886$	247714.	+	247714.i	0.315561	+	0.315561i
$887$		−	717553.i		−	0.912025i	−0.889973	−	0.456012i	$-0.849277\pi$
$887$		−	717553.i		−	0.912025i	0.889973	−	0.456012i	$-0.150723\pi$
$888$	−153590.	+	207953.i	−0.194777	+	0.263718i
$889$	−2.06822e6			−2.61694
$890$	249203.	−	249203.i	0.314611	−	0.314611i
$891$			164527.i			0.207243i
$892$		−	698591.i		−	0.877998i
$893$	−642166.	−	642166.i	−0.805276	−	0.805276i
$894$	656497.	+	656497.i	0.821406	+	0.821406i
$895$	65641.1			0.0819464
$896$	−76150.1	−	76150.1i	−0.0948537	−	0.0948537i
$897$	342218.			0.425322
$898$	752916.			0.933671
$899$			786677.i			0.973368i
$900$	−50187.5			−0.0619599
$901$	−35440.7	−	35440.7i	−0.0436569	−	0.0436569i
$902$	−39952.6	+	39952.6i	−0.0491057	+	0.0491057i
$903$	−72305.6	+	72305.6i	−0.0886740	+	0.0886740i
$904$	−47578.3			−0.0582200
$905$	−39637.1	−	39637.1i	−0.0483955	−	0.0483955i
$906$	−294413.	+	294413.i	−0.358674	+	0.358674i
$907$	−1.03176e6	−	1.03176e6i	−1.25419	−	1.25419i	−0.953824	−	0.300365i	$-0.902892\pi$
$907$	−1.03176e6	−	1.03176e6i	−1.25419	−	1.25419i	−0.300365	−	0.953824i	$-0.597108\pi$
$908$	17638.1	−	17638.1i	0.0213934	−	0.0213934i
$909$			69318.9i			0.0838926i
$910$	133646.	+	133646.i	0.161388	+	0.161388i
$911$	887826.	+	887826.i	1.06977	+	1.06977i	0.997376	+	0.0723956i	$0.0230644\pi$
$911$	887826.	+	887826.i	1.06977	+	1.06977i	0.0723956	+	0.997376i	$0.476936\pi$
$912$	190182.	−	190182.i	0.228655	−	0.228655i
$913$		−	7123.08i		−	0.00854528i
$914$	−454264.			−0.543771
$915$			347870.i			0.415503i
$916$		−	181733.i		−	0.216593i
$917$	676850.	−	676850.i	0.804922	−	0.804922i
$918$			396294.i			0.470254i
$919$	−450589.	+	450589.i	−0.533519	+	0.533519i	−0.921618	−	0.388099i	$-0.873132\pi$
$919$	−450589.	+	450589.i	−0.533519	+	0.533519i	0.388099	+	0.921618i	$0.373132\pi$
$920$	−52753.2	+	52753.2i	−0.0623266	+	0.0623266i
$921$	−1.19680e6			−1.41092
$922$	−1.14916e6			−1.35182
$923$	−351788.	−	351788.i	−0.412931	−	0.412931i
$924$		−	148177.i		−	0.173555i
$925$	−112517.	−	748302.i	−0.131503	−	0.874567i
$926$	953360.			1.11182
$927$	93703.3	−	93703.3i	0.109042	−	0.109042i
$928$			220539.i			0.256088i
$929$		−	1.70436e6i		−	1.97483i	−0.158166	−	0.987413i	$-0.550558\pi$
$929$		−	1.70436e6i		−	1.97483i	0.158166	−	0.987413i	$-0.449442\pi$
$930$	−91611.3	−	91611.3i	−0.105921	−	0.105921i
$931$	−1.11420e6	−	1.11420e6i	−1.28547	−	1.28547i
$932$	−535681.			−0.616701
$933$	−1.00525e6	−	1.00525e6i	−1.15481	−	1.15481i
$934$	−410816.			−0.470927
$935$	46116.4			0.0527511
$936$		−	27148.5i		−	0.0309880i
$937$	−244966.			−0.279014			−0.139507	−	0.990221i	$-0.544552\pi$
$937$	−244966.			−0.279014			−0.139507	+	0.990221i	$0.544552\pi$
$938$	−391308.	−	391308.i	−0.444746	−	0.444746i
$939$	−192660.	+	192660.i	−0.218504	+	0.218504i
$940$	−86719.2	+	86719.2i	−0.0981430	+	0.0981430i
$941$	−276724.			−0.312512			−0.156256	−	0.987717i	$-0.549943\pi$
$941$	−276724.			−0.312512			−0.156256	+	0.987717i	$0.549943\pi$
$942$	−287130.	−	287130.i	−0.323576	−	0.323576i
$943$	183590.	−	183590.i	0.206456	−	0.206456i
$944$	−28440.3	−	28440.3i	−0.0319147	−	0.0319147i
$945$	344487.	−	344487.i	0.385753	−	0.385753i
$946$		−	13907.8i		−	0.0155409i
$947$	301290.	+	301290.i	0.335958	+	0.335958i	0.854844	−	0.518886i	$-0.173653\pi$
$947$	301290.	+	301290.i	0.335958	+	0.335958i	−0.518886	+	0.854844i	$0.673653\pi$
$948$	456868.	+	456868.i	0.508363	+	0.508363i
$949$	−542303.	+	542303.i	−0.602157	+	0.602157i
$950$			787257.i			0.872307i
$951$	426115.			0.471157
$952$		−	305901.i		−	0.337526i
$953$		−	1.13569e6i		−	1.25048i	−0.780434	−	0.625238i	$-0.785002\pi$
$953$		−	1.13569e6i		−	1.25048i	0.780434	−	0.625238i	$-0.214998\pi$
$954$	6258.20	−	6258.20i	0.00687626	−	0.00687626i
$955$			339985.i			0.372780i
$956$	81644.8	−	81644.8i	0.0893331	−	0.0893331i
$957$	−214568.	+	214568.i	−0.234284	+	0.234284i
$958$	−250709.			−0.273174
$959$	−1.05157e6			−1.14341
$960$	−25682.6	−	25682.6i	−0.0278674	−	0.0278674i
$961$			506583.i			0.548534i
$962$	404787.	−	60865.2i	0.437398	−	0.0657686i
$963$	18659.9			0.0201213
$964$	−269099.	+	269099.i	−0.289573	+	0.289573i
$965$		−	443031.i		−	0.475751i
$966$			680903.i			0.729678i
$967$	407188.	+	407188.i	0.435453	+	0.435453i	0.890479	−	0.455025i	$-0.150370\pi$
$967$	407188.	+	407188.i	0.435453	+	0.435453i	−0.455025	+	0.890479i	$0.650370\pi$
$968$	−220005.	−	220005.i	−0.234792	−	0.234792i
$969$	763979.			0.813643
$970$	71700.6	+	71700.6i	0.0762042	+	0.0762042i
$971$	1.53972e6			1.63307			0.816533	−	0.577299i	$-0.195893\pi$
$971$	1.53972e6			1.63307			0.816533	+	0.577299i	$0.195893\pi$
$972$	−131357.			−0.139034
$973$		−	383984.i		−	0.405590i
$974$	67803.9			0.0714721
$975$	−344832.	−	344832.i	−0.362743	−	0.362743i
$976$	−221921.	+	221921.i	−0.232969	+	0.232969i
$977$	−1.30683e6	+	1.30683e6i	−1.36908	+	1.36908i	−0.507336	+	0.861748i	$0.669370\pi$
$977$	−1.30683e6	+	1.30683e6i	−1.36908	+	1.36908i	−0.861748	+	0.507336i	$0.830630\pi$
$978$	−778267.			−0.813675
$979$	309347.	+	309347.i	0.322760	+	0.322760i
$980$	−150463.	+	150463.i	−0.156667	+	0.156667i
$981$	125824.	+	125824.i	0.130745	+	0.130745i
$982$	−723727.	+	723727.i	−0.750502	+	0.750502i
$983$			549994.i			0.569182i	0.958649	+	0.284591i	$0.0918578\pi$
$983$			549994.i			0.569182i	−0.958649	+	0.284591i	$0.908142\pi$
$984$	89379.8	+	89379.8i	0.0923101	+	0.0923101i
$985$	−411620.	−	411620.i	−0.424252	−	0.424252i
$986$	−442962.	+	442962.i	−0.455630	+	0.455630i
$987$			1.11931e6i			1.14899i
$988$	−425860.			−0.436267
$989$			63909.0i			0.0653386i
$990$			8143.33i			0.00830867i
$991$	471250.	−	471250.i	0.479848	−	0.479848i	−0.425235	−	0.905083i	$-0.639808\pi$
$991$	471250.	−	471250.i	0.479848	−	0.479848i	0.905083	+	0.425235i	$0.139808\pi$
$992$		−	116886.i		−	0.118778i
$993$	921191.	−	921191.i	0.934224	−	0.934224i
$994$	699944.	−	699944.i	0.708420	−	0.708420i
$995$	249121.			0.251631
$996$	−15935.4			−0.0160636
$997$	559243.	+	559243.i	0.562614	+	0.562614i	0.930049	−	0.367435i	$-0.119764\pi$
$997$	559243.	+	559243.i	0.562614	+	0.562614i	−0.367435	+	0.930049i	$0.619764\pi$
$998$		−	387316.i		−	0.388870i
$999$	−156887.	−	1.04339e6i	−0.157202	−	1.04548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.b.43.2	yes	14
37.31	odd	4	inner	74.5.d.b.31.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.b.31.6	✓	14	37.31	odd	4	inner
74.5.d.b.43.2	yes	14	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{2} -8.34569i q^{3} -8.00000i q^{4} +(-6.01044 - 6.01044i) q^{5} +(-16.6914 - 16.6914i) q^{6} -74.3653 q^{7} +(-16.0000 - 16.0000i) q^{8} +11.3495 q^{9} +O(q^{10})\)	\(q+(2.00000 - 2.00000i) q^{2} -8.34569i q^{3} -8.00000i q^{4} +(-6.01044 - 6.01044i) q^{5} +(-16.6914 - 16.6914i) q^{6} -74.3653 q^{7} +(-16.0000 - 16.0000i) q^{8} +11.3495 q^{9} -24.0418 q^{10} -29.8441i q^{11} -66.7655 q^{12} +(74.7512 + 74.7512i) q^{13} +(-148.731 + 148.731i) q^{14} +(-50.1612 + 50.1612i) q^{15} -64.0000 q^{16} +(-128.547 - 128.547i) q^{17} +(22.6990 - 22.6990i) q^{18} +(-356.064 - 356.064i) q^{19} +(-48.0835 + 48.0835i) q^{20} +620.629i q^{21} +(-59.6881 - 59.6881i) q^{22} +(274.279 + 274.279i) q^{23} +(-133.531 + 133.531i) q^{24} -552.749i q^{25} +299.005 q^{26} -770.720i q^{27} +594.922i q^{28} +(861.481 - 861.481i) q^{29} +200.645i q^{30} +(-456.584 + 456.584i) q^{31} +(-128.000 + 128.000i) q^{32} -249.069 q^{33} -514.187 q^{34} +(446.968 + 446.968i) q^{35} -90.7962i q^{36} +(1353.78 - 203.559i) q^{37} -1424.26 q^{38} +(623.850 - 623.850i) q^{39} +192.334i q^{40} -669.356i q^{41} +(1241.26 + 1241.26i) q^{42} +(116.504 + 116.504i) q^{43} -238.753 q^{44} +(-68.2156 - 68.2156i) q^{45} +1097.12 q^{46} +1803.51 q^{47} +534.124i q^{48} +3129.20 q^{49} +(-1105.50 - 1105.50i) q^{50} +(-1072.81 + 1072.81i) q^{51} +(598.009 - 598.009i) q^{52} +275.703 q^{53} +(-1541.44 - 1541.44i) q^{54} +(-179.376 + 179.376i) q^{55} +(1189.84 + 1189.84i) q^{56} +(-2971.60 + 2971.60i) q^{57} -3445.92i q^{58} +(444.380 + 444.380i) q^{59} +(401.290 + 401.290i) q^{60} +(3467.51 - 3467.51i) q^{61} +1826.34i q^{62} -844.011 q^{63} +512.000i q^{64} -898.575i q^{65} +(-498.138 + 498.138i) q^{66} +2630.98i q^{67} +(-1028.37 + 1028.37i) q^{68} +(2289.05 - 2289.05i) q^{69} +1787.87 q^{70} -4706.12 q^{71} +(-181.592 - 181.592i) q^{72} +7254.78i q^{73} +(2300.44 - 3114.68i) q^{74} -4613.07 q^{75} +(-2848.51 + 2848.51i) q^{76} +2219.36i q^{77} -2495.40i q^{78} +(-6842.87 - 6842.87i) q^{79} +(384.668 + 384.668i) q^{80} -5512.88 q^{81} +(-1338.71 - 1338.71i) q^{82} +238.677 q^{83} +4965.04 q^{84} +1545.24i q^{85} +466.014 q^{86} +(-7189.65 - 7189.65i) q^{87} +(-477.505 + 477.505i) q^{88} +(-10365.4 + 10365.4i) q^{89} -272.863 q^{90} +(-5558.89 - 5558.89i) q^{91} +(2194.23 - 2194.23i) q^{92} +(3810.51 + 3810.51i) q^{93} +(3607.02 - 3607.02i) q^{94} +4280.21i q^{95} +(1068.25 + 1068.25i) q^{96} +(-2982.33 - 2982.33i) q^{97} +(6258.39 - 6258.39i) q^{98} -338.716i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more