LMFDB - Embedded newform 74.5.d.a.43.3

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} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + \cdots + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-1.77388i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} -0.773882i q^{3} -8.00000i q^{4} +(2.70834 + 2.70834i) q^{5} +(1.54776 + 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 + 16.0000i) q^{8} +80.4011 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} -0.773882i q^{3} -8.00000i q^{4} +(2.70834 + 2.70834i) q^{5} +(1.54776 + 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 + 16.0000i) q^{8} +80.4011 q^{9} -10.8334 q^{10} -132.300i q^{11} -6.19106 q^{12} +(181.780 + 181.780i) q^{13} +(34.3199 - 34.3199i) q^{14} +(2.09593 - 2.09593i) q^{15} -64.0000 q^{16} +(261.124 + 261.124i) q^{17} +(-160.802 + 160.802i) q^{18} +(137.325 + 137.325i) q^{19} +(21.6667 - 21.6667i) q^{20} +13.2798i q^{21} +(264.600 + 264.600i) q^{22} +(543.359 + 543.359i) q^{23} +(12.3821 - 12.3821i) q^{24} -610.330i q^{25} -727.121 q^{26} -124.905i q^{27} +137.279i q^{28} +(-624.988 + 624.988i) q^{29} +8.38374i q^{30} +(833.169 - 833.169i) q^{31} +(128.000 - 128.000i) q^{32} -102.385 q^{33} -1044.49 q^{34} +(-46.4749 - 46.4749i) q^{35} -643.209i q^{36} +(1049.56 - 878.973i) q^{37} -549.301 q^{38} +(140.677 - 140.677i) q^{39} +86.6668i q^{40} -955.940i q^{41} +(-26.5595 - 26.5595i) q^{42} +(-1509.63 - 1509.63i) q^{43} -1058.40 q^{44} +(217.753 + 217.753i) q^{45} -2173.43 q^{46} -3094.13 q^{47} +49.5285i q^{48} -2106.54 q^{49} +(1220.66 + 1220.66i) q^{50} +(202.079 - 202.079i) q^{51} +(1454.24 - 1454.24i) q^{52} +4409.63 q^{53} +(249.811 + 249.811i) q^{54} +(358.313 - 358.313i) q^{55} +(-274.559 - 274.559i) q^{56} +(106.274 - 106.274i) q^{57} -2499.95i q^{58} +(1827.22 + 1827.22i) q^{59} +(-16.7675 - 16.7675i) q^{60} +(-4096.05 + 4096.05i) q^{61} +3332.68i q^{62} -1379.68 q^{63} +512.000i q^{64} +984.645i q^{65} +(204.769 - 204.769i) q^{66} -2455.82i q^{67} +(2088.99 - 2088.99i) q^{68} +(420.495 - 420.495i) q^{69} +185.900 q^{70} +6687.04 q^{71} +(1286.42 + 1286.42i) q^{72} +3245.28i q^{73} +(-341.165 + 3857.06i) q^{74} -472.323 q^{75} +(1098.60 - 1098.60i) q^{76} +2270.26i q^{77} +562.706i q^{78} +(-1773.15 - 1773.15i) q^{79} +(-173.334 - 173.334i) q^{80} +6415.83 q^{81} +(1911.88 + 1911.88i) q^{82} -5356.85 q^{83} +106.238 q^{84} +1414.42i q^{85} +6038.52 q^{86} +(483.667 + 483.667i) q^{87} +(2116.80 - 2116.80i) q^{88} +(-6276.92 + 6276.92i) q^{89} -871.014 q^{90} +(-3119.34 - 3119.34i) q^{91} +(4346.87 - 4346.87i) q^{92} +(-644.775 - 644.775i) q^{93} +(6188.25 - 6188.25i) q^{94} +743.847i q^{95} +(-99.0569 - 99.0569i) q^{96} +(430.923 + 430.923i) q^{97} +(4213.07 - 4213.07i) q^{98} -10637.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * 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
$3$		−	0.773882i		−	0.0859869i	−0.999075	−	0.0429935i	$-0.986311\pi$
$3$		−	0.773882i		−	0.0859869i	0.999075	−	0.0429935i	$-0.0136895\pi$
$4$		−	8.00000i		−	0.500000i
$5$	2.70834	+	2.70834i	0.108334	+	0.108334i	0.759196	−	0.650862i	$-0.225592\pi$
$5$	2.70834	+	2.70834i	0.108334	+	0.108334i	−0.650862	+	0.759196i	$0.725592\pi$
$6$	1.54776	+	1.54776i	0.0429935	+	0.0429935i
$7$	−17.1599			−0.350203			−0.175101	−	0.984550i	$-0.556025\pi$
$7$	−17.1599			−0.350203			−0.175101	+	0.984550i	$0.556025\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	80.4011			0.992606
$10$	−10.8334			−0.108334
$11$		−	132.300i		−	1.09339i	−0.837332	−	0.546695i	$-0.815886\pi$
$11$		−	132.300i		−	1.09339i	0.837332	−	0.546695i	$-0.184114\pi$
$12$	−6.19106			−0.0429935
$13$	181.780	+	181.780i	1.07562	+	1.07562i	0.996896	+	0.0787272i	$0.0250856\pi$
$13$	181.780	+	181.780i	1.07562	+	1.07562i	0.0787272	+	0.996896i	$0.474914\pi$
$14$	34.3199	−	34.3199i	0.175101	−	0.175101i
$15$	2.09593	−	2.09593i	0.00931527	−	0.00931527i
$16$	−64.0000			−0.250000
$17$	261.124	+	261.124i	0.903542	+	0.903542i	0.995741	−	0.0921990i	$-0.0293896\pi$
$17$	261.124	+	261.124i	0.903542	+	0.903542i	−0.0921990	+	0.995741i	$0.529390\pi$
$18$	−160.802	+	160.802i	−0.496303	+	0.496303i
$19$	137.325	+	137.325i	0.380402	+	0.380402i	0.871247	−	0.490845i	$-0.163312\pi$
$19$	137.325	+	137.325i	0.380402	+	0.380402i	−0.490845	+	0.871247i	$0.663312\pi$
$20$	21.6667	−	21.6667i	0.0541668	−	0.0541668i
$21$			13.2798i			0.0301128i
$22$	264.600	+	264.600i	0.546695	+	0.546695i
$23$	543.359	+	543.359i	1.02714	+	1.02714i	0.999621	+	0.0275216i	$0.00876152\pi$
$23$	543.359	+	543.359i	1.02714	+	1.02714i	0.0275216	+	0.999621i	$0.491238\pi$
$24$	12.3821	−	12.3821i	0.0214967	−	0.0214967i
$25$		−	610.330i		−	0.976528i
$26$	−727.121			−1.07562
$27$		−	124.905i		−	0.171338i
$28$			137.279i			0.175101i
$29$	−624.988	+	624.988i	−0.743148	+	0.743148i	−0.973183	−	0.230034i	$-0.926116\pi$
$29$	−624.988	+	624.988i	−0.743148	+	0.743148i	0.230034	+	0.973183i	$0.426116\pi$
$30$			8.38374i			0.00931527i
$31$	833.169	−	833.169i	0.866982	−	0.866982i	−0.125156	−	0.992137i	$-0.539943\pi$
$31$	833.169	−	833.169i	0.866982	−	0.866982i	0.992137	+	0.125156i	$0.0399430\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−102.385			−0.0940172
$34$	−1044.49			−0.903542
$35$	−46.4749	−	46.4749i	−0.0379387	−	0.0379387i
$36$		−	643.209i		−	0.496303i
$37$	1049.56	−	878.973i	0.766659	−	0.642055i
$37$	1049.56	−	878.973i	0.766659	−	0.642055i
$38$	−549.301			−0.380402
$39$	140.677	−	140.677i	0.0924895	−	0.0924895i
$40$			86.6668i			0.0541668i
$41$		−	955.940i		−	0.568674i	−0.958724	−	0.284337i	$-0.908227\pi$
$41$		−	955.940i		−	0.568674i	0.958724	−	0.284337i	$-0.0917734\pi$
$42$	−26.5595	−	26.5595i	−0.0150564	−	0.0150564i
$43$	−1509.63	−	1509.63i	−0.816458	−	0.816458i	0.169135	−	0.985593i	$-0.445903\pi$
$43$	−1509.63	−	1509.63i	−0.816458	−	0.816458i	−0.985593	+	0.169135i	$0.945903\pi$
$44$	−1058.40			−0.546695
$45$	217.753	+	217.753i	0.107533	+	0.107533i
$46$	−2173.43			−1.02714
$47$	−3094.13			−1.40069			−0.700346	−	0.713804i	$-0.746971\pi$
$47$	−3094.13			−1.40069			−0.700346	+	0.713804i	$0.746971\pi$
$48$			49.5285i			0.0214967i
$49$	−2106.54			−0.877358
$50$	1220.66	+	1220.66i	0.488264	+	0.488264i
$51$	202.079	−	202.079i	0.0776928	−	0.0776928i
$52$	1454.24	−	1454.24i	0.537812	−	0.537812i
$53$	4409.63			1.56982			0.784911	−	0.619609i	$-0.212709\pi$
$53$	4409.63			1.56982			0.784911	+	0.619609i	$0.212709\pi$
$54$	249.811	+	249.811i	0.0856690	+	0.0856690i
$55$	358.313	−	358.313i	0.118451	−	0.118451i
$56$	−274.559	−	274.559i	−0.0875507	−	0.0875507i
$57$	106.274	−	106.274i	0.0327096	−	0.0327096i
$58$		−	2499.95i		−	0.743148i
$59$	1827.22	+	1827.22i	0.524912	+	0.524912i	0.919051	−	0.394139i	$-0.128957\pi$
$59$	1827.22	+	1827.22i	0.524912	+	0.524912i	−0.394139	+	0.919051i	$0.628957\pi$
$60$	−16.7675	−	16.7675i	−0.00465763	−	0.00465763i
$61$	−4096.05	+	4096.05i	−1.10079	+	1.10079i	−0.106477	+	0.994315i	$0.533957\pi$
$61$	−4096.05	+	4096.05i	−1.10079	+	1.10079i	−0.994315	+	0.106477i	$0.966043\pi$
$62$			3332.68i			0.866982i
$63$	−1379.68			−0.347613
$64$			512.000i			0.125000i
$65$			984.645i			0.233052i
$66$	204.769	−	204.769i	0.0470086	−	0.0470086i
$67$		−	2455.82i		−	0.547076i	−0.961861	−	0.273538i	$-0.911806\pi$
$67$		−	2455.82i		−	0.547076i	0.961861	−	0.273538i	$-0.0881939\pi$
$68$	2088.99	−	2088.99i	0.451771	−	0.451771i
$69$	420.495	−	420.495i	0.0883208	−	0.0883208i
$70$	185.900			0.0379387
$71$	6687.04			1.32653			0.663265	−	0.748385i	$-0.269170\pi$
$71$	6687.04			1.32653			0.663265	+	0.748385i	$0.269170\pi$
$72$	1286.42	+	1286.42i	0.248152	+	0.248152i
$73$			3245.28i			0.608985i	0.952515	+	0.304493i	$0.0984869\pi$
$73$			3245.28i			0.608985i	−0.952515	+	0.304493i	$0.901513\pi$
$74$	−341.165	+	3857.06i	−0.0623019	+	0.704357i
$75$	−472.323			−0.0839686
$76$	1098.60	−	1098.60i	0.190201	−	0.190201i
$77$			2270.26i			0.382908i
$78$			562.706i			0.0924895i
$79$	−1773.15	−	1773.15i	−0.284113	−	0.284113i	0.550634	−	0.834747i	$-0.314386\pi$
$79$	−1773.15	−	1773.15i	−0.284113	−	0.284113i	−0.834747	+	0.550634i	$0.814386\pi$
$80$	−173.334	−	173.334i	−0.0270834	−	0.0270834i
$81$	6415.83			0.977873
$82$	1911.88	+	1911.88i	0.284337	+	0.284337i
$83$	−5356.85			−0.777595			−0.388798	−	0.921323i	$-0.627109\pi$
$83$	−5356.85			−0.777595			−0.388798	+	0.921323i	$0.627109\pi$
$84$	106.238			0.0150564
$85$			1414.42i			0.195768i
$86$	6038.52			0.816458
$87$	483.667	+	483.667i	0.0639010	+	0.0639010i
$88$	2116.80	−	2116.80i	0.273347	−	0.273347i
$89$	−6276.92	+	6276.92i	−0.792441	+	0.792441i	−0.981890	−	0.189450i	$-0.939330\pi$
$89$	−6276.92	+	6276.92i	−0.792441	+	0.792441i	0.189450	+	0.981890i	$0.439330\pi$
$90$	−871.014			−0.107533
$91$	−3119.34	−	3119.34i	−0.376686	−	0.376686i
$92$	4346.87	−	4346.87i	0.513571	−	0.513571i
$93$	−644.775	−	644.775i	−0.0745491	−	0.0745491i
$94$	6188.25	−	6188.25i	0.700346	−	0.700346i
$95$			743.847i			0.0824207i
$96$	−99.0569	−	99.0569i	−0.0107484	−	0.0107484i
$97$	430.923	+	430.923i	0.0457990	+	0.0457990i	0.729635	−	0.683836i	$-0.239690\pi$
$97$	430.923	+	430.923i	0.0457990	+	0.0457990i	−0.683836	+	0.729635i	$0.739690\pi$
$98$	4213.07	−	4213.07i	0.438679	−	0.438679i
$99$		−	10637.1i		−	1.08531i
$100$	−4882.64			−0.488264
$101$			9738.29i			0.954641i	0.878729	+	0.477321i	$0.158392\pi$
$101$			9738.29i			0.954641i	−0.878729	+	0.477321i	$0.841608\pi$
$102$			808.315i			0.0776928i
$103$	6805.12	−	6805.12i	0.641448	−	0.641448i	−0.309463	−	0.950911i	$-0.600149\pi$
$103$	6805.12	−	6805.12i	0.641448	−	0.641448i	0.950911	+	0.309463i	$0.100149\pi$
$104$			5816.97i			0.537812i
$105$	−35.9661	+	35.9661i	−0.00326223	+	0.00326223i
$106$	−8819.26	+	8819.26i	−0.784911	+	0.784911i
$107$	−2128.30			−0.185894			−0.0929468	−	0.995671i	$-0.529629\pi$
$107$	−2128.30			−0.185894			−0.0929468	+	0.995671i	$0.529629\pi$
$108$	−999.243			−0.0856690
$109$	−12788.1	−	12788.1i	−1.07635	−	1.07635i	−0.996833	−	0.0795192i	$-0.974662\pi$
$109$	−12788.1	−	12788.1i	−1.07635	−	1.07635i	−0.0795192	−	0.996833i	$-0.525338\pi$
$110$			1433.25i			0.118451i
$111$	−680.222	−	812.232i	−0.0552083	−	0.0659226i
$112$	1098.24			0.0875507
$113$	−4650.83	+	4650.83i	−0.364228	+	0.364228i	−0.865367	−	0.501139i	$-0.832915\pi$
$113$	−4650.83	+	4650.83i	−0.364228	+	0.364228i	0.501139	+	0.865367i	$0.332915\pi$
$114$			425.094i			0.0327096i
$115$			2943.20i			0.222548i
$116$	4999.90	+	4999.90i	0.371574	+	0.371574i
$117$	14615.3	+	14615.3i	1.06767	+	1.06767i
$118$	−7308.88			−0.524912
$119$	−4480.86	−	4480.86i	−0.316423	−	0.316423i
$120$	67.0699			0.00465763
$121$	−2862.32			−0.195500
$122$		−	16384.2i		−	1.10079i
$123$	−739.785			−0.0488985
$124$	−6665.35	−	6665.35i	−0.433491	−	0.433491i
$125$	3345.69	−	3345.69i	0.214124	−	0.214124i
$126$	2759.35	−	2759.35i	0.173807	−	0.173807i
$127$	−27171.0			−1.68460			−0.842302	−	0.539006i	$-0.818800\pi$
$127$	−27171.0			−1.68460			−0.842302	+	0.539006i	$0.818800\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−1168.28	+	1168.28i	−0.0702047	+	0.0702047i
$130$	−1969.29	−	1969.29i	−0.116526	−	0.116526i
$131$	−9032.72	+	9032.72i	−0.526352	+	0.526352i	−0.919483	−	0.393131i	$-0.871392\pi$
$131$	−9032.72	+	9032.72i	−0.526352	+	0.526352i	0.393131	+	0.919483i	$0.371392\pi$
$132$			819.078i			0.0470086i
$133$	−2356.49	−	2356.49i	−0.133218	−	0.133218i
$134$	4911.65	+	4911.65i	0.273538	+	0.273538i
$135$	338.286	−	338.286i	0.0185617	−	0.0185617i
$136$			8355.95i			0.451771i
$137$	10999.0			0.586019			0.293010	−	0.956109i	$-0.405343\pi$
$137$	10999.0			0.586019			0.293010	+	0.956109i	$0.405343\pi$
$138$			1681.98i			0.0883208i
$139$		−	11235.5i		−	0.581518i	−0.956796	−	0.290759i	$-0.906092\pi$
$139$		−	11235.5i		−	0.581518i	0.956796	−	0.290759i	$-0.0939079\pi$
$140$	−371.799	+	371.799i	−0.0189693	+	0.0189693i
$141$			2394.49i			0.120441i
$142$	−13374.1	+	13374.1i	−0.663265	+	0.663265i
$143$	24049.6	−	24049.6i	1.17608	−	1.17608i
$144$	−5145.67			−0.248152
$145$	−3385.36			−0.161016
$146$	−6490.56	−	6490.56i	−0.304493	−	0.304493i
$147$			1630.21i			0.0754413i
$148$	−7031.79	−	8396.45i	−0.321027	−	0.383329i
$149$	4400.81			0.198226			0.0991128	−	0.995076i	$-0.468400\pi$
$149$	4400.81			0.198226			0.0991128	+	0.995076i	$0.468400\pi$
$150$	944.647	−	944.647i	0.0419843	−	0.0419843i
$151$		−	32364.0i		−	1.41941i	−0.704497	−	0.709707i	$-0.748827\pi$
$151$		−	32364.0i		−	1.41941i	0.704497	−	0.709707i	$-0.251173\pi$
$152$			4394.41i			0.190201i
$153$	20994.6	+	20994.6i	0.896861	+	0.896861i
$154$	−4540.52	−	4540.52i	−0.191454	−	0.191454i
$155$	4513.01			0.187846
$156$	−1125.41	−	1125.41i	−0.0462448	−	0.0462448i
$157$	−5571.36			−0.226028			−0.113014	−	0.993593i	$-0.536050\pi$
$157$	−5571.36			−0.226028			−0.113014	+	0.993593i	$0.536050\pi$
$158$	7092.61			0.284113
$159$		−	3412.53i		−	0.134984i
$160$	693.335			0.0270834
$161$	−9324.00	−	9324.00i	−0.359708	−	0.359708i
$162$	−12831.7	+	12831.7i	−0.488937	+	0.488937i
$163$	22425.1	−	22425.1i	0.844034	−	0.844034i	−0.145347	−	0.989381i	$-0.546430\pi$
$163$	22425.1	−	22425.1i	0.844034	−	0.844034i	0.989381	+	0.145347i	$0.0464299\pi$
$164$	−7647.52			−0.284337
$165$	−277.292	−	277.292i	−0.0101852	−	0.0101852i
$166$	10713.7	−	10713.7i	0.388798	−	0.388798i
$167$	19640.7	+	19640.7i	0.704245	+	0.704245i	0.965319	−	0.261074i	$-0.0840767\pi$
$167$	19640.7	+	19640.7i	0.704245	+	0.704245i	−0.261074	+	0.965319i	$0.584077\pi$
$168$	−212.476	+	212.476i	−0.00752821	+	0.00752821i
$169$			37527.2i			1.31393i
$170$	−2828.84	−	2828.84i	−0.0978839	−	0.0978839i
$171$	11041.1	+	11041.1i	0.377590	+	0.377590i
$172$	−12077.0	+	12077.0i	−0.408229	+	0.408229i
$173$			10214.2i			0.341281i	0.985333	+	0.170641i	$0.0545837\pi$
$173$			10214.2i			0.341281i	−0.985333	+	0.170641i	$0.945416\pi$
$174$	−1934.67			−0.0639010
$175$			10473.2i			0.341983i
$176$			8467.21i			0.273347i
$177$	1414.05	−	1414.05i	0.0451356	−	0.0451356i
$178$		−	25107.7i		−	0.792441i
$179$	−19099.4	+	19099.4i	−0.596092	+	0.596092i	−0.939270	−	0.343178i	$-0.888497\pi$
$179$	−19099.4	+	19099.4i	−0.596092	+	0.596092i	0.343178	+	0.939270i	$0.388497\pi$
$180$	1742.03	−	1742.03i	0.0537663	−	0.0537663i
$181$	34247.7			1.04538			0.522691	−	0.852522i	$-0.324928\pi$
$181$	34247.7			1.04538			0.522691	+	0.852522i	$0.324928\pi$
$182$	12477.4			0.376686
$183$	3169.86	+	3169.86i	0.0946537	+	0.0946537i
$184$			17387.5i			0.513571i
$185$	5223.11	+	461.995i	0.152611	+	0.0134988i
$186$	2579.10			0.0745491
$187$	34546.7	−	34546.7i	0.987923	−	0.987923i
$188$			24753.0i			0.700346i
$189$			2143.37i			0.0600030i
$190$	−1487.69	−	1487.69i	−0.0412103	−	0.0412103i
$191$	−16792.2	−	16792.2i	−0.460300	−	0.460300i	0.438454	−	0.898754i	$-0.355526\pi$
$191$	−16792.2	−	16792.2i	−0.460300	−	0.460300i	−0.898754	+	0.438454i	$0.855526\pi$
$192$	396.228			0.0107484
$193$	22755.7	+	22755.7i	0.610907	+	0.610907i	0.943183	−	0.332275i	$-0.107816\pi$
$193$	22755.7	+	22755.7i	0.610907	+	0.610907i	−0.332275	+	0.943183i	$0.607816\pi$
$194$	−1723.69			−0.0457990
$195$	762.000			0.0200394
$196$			16852.3i			0.438679i
$197$	−8512.13			−0.219334			−0.109667	−	0.993968i	$-0.534978\pi$
$197$	−8512.13			−0.219334			−0.109667	+	0.993968i	$0.534978\pi$
$198$	21274.2	+	21274.2i	0.542653	+	0.542653i
$199$	−20588.3	+	20588.3i	−0.519894	+	0.519894i	−0.917539	−	0.397645i	$-0.869828\pi$
$199$	−20588.3	+	20588.3i	−0.519894	+	0.519894i	0.397645	+	0.917539i	$0.369828\pi$
$200$	9765.28	−	9765.28i	0.244132	−	0.244132i
$201$	−1900.52			−0.0470414
$202$	−19476.6	−	19476.6i	−0.477321	−	0.477321i
$203$	10724.7	−	10724.7i	0.260253	−	0.260253i
$204$	−1616.63	−	1616.63i	−0.0388464	−	0.0388464i
$205$	2589.01	−	2589.01i	0.0616064	−	0.0616064i
$206$			27220.5i			0.641448i
$207$	43686.6	+	43686.6i	1.01955	+	1.01955i
$208$	−11633.9	−	11633.9i	−0.268906	−	0.268906i
$209$	18168.1	−	18168.1i	0.415928	−	0.415928i
$210$		−	143.864i		−	0.00326223i
$211$	−42994.6			−0.965715			−0.482857	−	0.875699i	$-0.660401\pi$
$211$	−42994.6			−0.965715			−0.482857	+	0.875699i	$0.660401\pi$
$212$		−	35277.0i		−	0.784911i
$213$		−	5174.98i		−	0.114064i
$214$	4256.59	−	4256.59i	0.0929468	−	0.0929468i
$215$		−	8177.18i		−	0.176900i
$216$	1998.49	−	1998.49i	0.0428345	−	0.0428345i
$217$	−14297.1	+	14297.1i	−0.303619	+	0.303619i
$218$	51152.6			1.07635
$219$	2511.47			0.0523647
$220$	−2866.51	−	2866.51i	−0.0592254	−	0.0592254i
$221$			94934.3i			1.94374i
$222$	2984.91	+	264.021i	0.0605655	+	0.00535714i
$223$	−35757.6			−0.719048			−0.359524	−	0.933136i	$-0.617061\pi$
$223$	−35757.6			−0.719048			−0.359524	+	0.933136i	$0.617061\pi$
$224$	−2196.47	+	2196.47i	−0.0437753	+	0.0437753i
$225$		−	49071.2i		−	0.969307i
$226$		−	18603.3i		−	0.364228i
$227$	−55139.5	−	55139.5i	−1.07007	−	1.07007i	−0.997353	−	0.0727155i	$-0.976834\pi$
$227$	−55139.5	−	55139.5i	−1.07007	−	1.07007i	−0.0727155	−	0.997353i	$-0.523166\pi$
$228$	−850.189	−	850.189i	−0.0163548	−	0.0163548i
$229$	−72343.2			−1.37952			−0.689758	−	0.724040i	$-0.742283\pi$
$229$	−72343.2			−1.37952			−0.689758	+	0.724040i	$0.742283\pi$
$230$	−5886.40	−	5886.40i	−0.111274	−	0.111274i
$231$	1756.91			0.0329251
$232$	−19999.6			−0.371574
$233$		−	73555.4i		−	1.35489i	−0.735576	−	0.677443i	$-0.763088\pi$
$233$		−	73555.4i		−	1.35489i	0.735576	−	0.677443i	$-0.236912\pi$
$234$	−58461.4			−1.06767
$235$	−8379.94	−	8379.94i	−0.151742	−	0.151742i
$236$	14617.8	−	14617.8i	0.262456	−	0.262456i
$237$	−1372.21	+	1372.21i	−0.0244300	+	0.0244300i
$238$	17923.4			0.316423
$239$	2490.09	+	2490.09i	0.0435932	+	0.0435932i	0.728567	−	0.684974i	$-0.240187\pi$
$239$	2490.09	+	2490.09i	0.0435932	+	0.0435932i	−0.684974	+	0.728567i	$0.740187\pi$
$240$	−134.140	+	134.140i	−0.00232882	+	0.00232882i
$241$	−45627.5	−	45627.5i	−0.785584	−	0.785584i	0.195182	−	0.980767i	$-0.437470\pi$
$241$	−45627.5	−	45627.5i	−0.785584	−	0.785584i	−0.980767	+	0.195182i	$0.937470\pi$
$242$	5724.64	−	5724.64i	0.0977502	−	0.0977502i
$243$		−	15082.4i		−	0.255422i
$244$	32768.4	+	32768.4i	0.550396	+	0.550396i
$245$	−5705.21	−	5705.21i	−0.0950473	−	0.0950473i
$246$	1479.57	−	1479.57i	0.0244492	−	0.0244492i
$247$			49926.1i			0.818339i
$248$	26661.4			0.433491
$249$			4145.57i			0.0668630i
$250$			13382.8i			0.214124i
$251$	−65129.8	+	65129.8i	−1.03379	+	1.03379i	−0.0343813	+	0.999409i	$0.510946\pi$
$251$	−65129.8	+	65129.8i	−1.03379	+	1.03379i	−0.999409	+	0.0343813i	$0.989054\pi$
$252$			11037.4i			0.173807i
$253$	71886.4	−	71886.4i	1.12307	−	1.12307i
$254$	54342.0	−	54342.0i	0.842302	−	0.842302i
$255$	1094.60			0.0168335
$256$	4096.00			0.0625000
$257$	−72758.7	−	72758.7i	−1.10159	−	1.10159i	−0.994220	−	0.107367i	$-0.965758\pi$
$257$	−72758.7	−	72758.7i	−1.10159	−	1.10159i	−0.107367	−	0.994220i	$-0.534242\pi$
$258$		−	4673.10i		−	0.0702047i
$259$	−18010.3	+	15083.1i	−0.268486	+	0.224849i
$260$	7877.16			0.116526
$261$	−50249.7	+	50249.7i	−0.737654	+	0.737654i
$262$		−	36130.9i		−	0.526352i
$263$		−	50249.8i		−	0.726479i	−0.931696	−	0.363240i	$-0.881671\pi$
$263$		−	50249.8i		−	0.726479i	0.931696	−	0.363240i	$-0.118329\pi$
$264$	−1638.16	−	1638.16i	−0.0235043	−	0.0235043i
$265$	11942.8	+	11942.8i	0.170064	+	0.170064i
$266$	9425.97			0.133218
$267$	4857.60	+	4857.60i	0.0681395	+	0.0681395i
$268$	−19646.6			−0.273538
$269$	−101495.			−1.40262			−0.701309	−	0.712857i	$-0.747401\pi$
$269$	−101495.			−1.40262			−0.701309	+	0.712857i	$0.747401\pi$
$270$			1353.14i			0.0185617i
$271$	63036.3			0.858326			0.429163	−	0.903227i	$-0.358809\pi$
$271$	63036.3			0.858326			0.429163	+	0.903227i	$0.358809\pi$
$272$	−16711.9	−	16711.9i	−0.225885	−	0.225885i
$273$	−2414.00	+	2414.00i	−0.0323901	+	0.0323901i
$274$	−21998.0	+	21998.0i	−0.293010	+	0.293010i
$275$	−80746.7			−1.06773
$276$	−3363.96	−	3363.96i	−0.0441604	−	0.0441604i
$277$	36728.4	−	36728.4i	0.478677	−	0.478677i	−0.426031	−	0.904708i	$-0.640089\pi$
$277$	36728.4	−	36728.4i	0.478677	−	0.478677i	0.904708	+	0.426031i	$0.140089\pi$
$278$	22471.0	+	22471.0i	0.290759	+	0.290759i
$279$	66987.7	−	66987.7i	0.860571	−	0.860571i
$280$		−	1487.20i		−	0.0189693i
$281$	86416.0	+	86416.0i	1.09441	+	1.09441i	0.995051	+	0.0993620i	$0.0316802\pi$
$281$	86416.0	+	86416.0i	1.09441	+	1.09441i	0.0993620	+	0.995051i	$0.468320\pi$
$282$	−4788.98	−	4788.98i	−0.0602205	−	0.0602205i
$283$	17514.8	−	17514.8i	0.218691	−	0.218691i	−0.589256	−	0.807947i	$-0.700579\pi$
$283$	17514.8	−	17514.8i	0.218691	−	0.218691i	0.807947	+	0.589256i	$0.200579\pi$
$284$		−	53496.3i		−	0.663265i
$285$	575.650			0.00708710
$286$			96198.2i			1.17608i
$287$			16403.9i			0.199151i
$288$	10291.3	−	10291.3i	0.124076	−	0.124076i
$289$			52850.0i			0.632775i
$290$	6770.71	−	6770.71i	0.0805079	−	0.0805079i
$291$	333.484	−	333.484i	0.00393812	−	0.00393812i
$292$	25962.3			0.304493
$293$	29076.8			0.338697			0.169349	−	0.985556i	$-0.445834\pi$
$293$	29076.8			0.338697			0.169349	+	0.985556i	$0.445834\pi$
$294$	−3260.42	−	3260.42i	−0.0377207	−	0.0377207i
$295$			9897.46i			0.113731i
$296$	30856.5	+	2729.32i	0.352178	+	0.0311509i
$297$	−16525.0			−0.187339
$298$	−8801.61	+	8801.61i	−0.0991128	+	0.0991128i
$299$			197544.i			2.20964i
$300$			3778.59i			0.0419843i
$301$	25905.2	+	25905.2i	0.285926	+	0.285926i
$302$	64728.1	+	64728.1i	0.709707	+	0.709707i
$303$	7536.29			0.0820866
$304$	−8788.82	−	8788.82i	−0.0951006	−	0.0951006i
$305$	−22187.0			−0.238505
$306$	−83978.5			−0.896861
$307$			113505.i			1.20431i	0.798381	+	0.602153i	$0.205690\pi$
$307$			113505.i			1.20431i	−0.798381	+	0.602153i	$0.794310\pi$
$308$	18162.1			0.191454
$309$	−5266.36	−	5266.36i	−0.0551561	−	0.0551561i
$310$	−9026.02	+	9026.02i	−0.0939232	+	0.0939232i
$311$	121874.	−	121874.i	1.26006	−	1.26006i	0.308998	−	0.951063i	$-0.400006\pi$
$311$	121874.	−	121874.i	1.26006	−	1.26006i	0.951063	−	0.308998i	$-0.0999936\pi$
$312$	4501.65			0.0462448
$313$	−37218.8	−	37218.8i	−0.379904	−	0.379904i	0.491164	−	0.871067i	$-0.336572\pi$
$313$	−37218.8	−	37218.8i	−0.379904	−	0.379904i	−0.871067	+	0.491164i	$0.836572\pi$
$314$	11142.7	−	11142.7i	0.113014	−	0.113014i
$315$	−3736.63	−	3736.63i	−0.0376582	−	0.0376582i
$316$	−14185.2	+	14185.2i	−0.142057	+	0.142057i
$317$			11659.2i			0.116025i	0.998316	+	0.0580125i	$0.0184763\pi$
$317$			11659.2i			0.116025i	−0.998316	+	0.0580125i	$0.981524\pi$
$318$	6825.07	+	6825.07i	0.0674921	+	0.0674921i
$319$	82686.0	+	82686.0i	0.812551	+	0.812551i
$320$	−1386.67	+	1386.67i	−0.0135417	+	0.0135417i
$321$			1647.05i			0.0159844i
$322$	37296.0			0.359708
$323$			71717.7i			0.687419i
$324$		−	51326.6i		−	0.488937i
$325$	110946.	−	110946.i	1.05038	−	1.05038i
$326$			89700.5i			0.844034i
$327$	−9896.52	+	9896.52i	−0.0925522	+	0.0925522i
$328$	15295.0	−	15295.0i	0.142168	−	0.142168i
$329$	53095.0			0.490526
$330$	1109.17			0.0101852
$331$	−73581.9	−	73581.9i	−0.671607	−	0.671607i	0.286480	−	0.958086i	$-0.407515\pi$
$331$	−73581.9	−	73581.9i	−0.671607	−	0.671607i	−0.958086	+	0.286480i	$0.907515\pi$
$332$			42854.8i			0.388798i
$333$	84385.4	−	70670.4i	0.760990	−	0.637308i
$334$	−78562.7			−0.704245
$335$	6651.20	−	6651.20i	0.0592667	−	0.0592667i
$336$		−	849.905i		−	0.00752821i
$337$			157334.i			1.38536i	0.721243	+	0.692682i	$0.243571\pi$
$337$			157334.i			1.38536i	−0.721243	+	0.692682i	$0.756429\pi$
$338$	−75054.4	−	75054.4i	−0.656966	−	0.656966i
$339$	3599.19	+	3599.19i	0.0313188	+	0.0313188i
$340$	11315.4			0.0978839
$341$	−110228.	−	110228.i	−0.947949	−	0.947949i
$342$	−44164.4			−0.377590
$343$	77349.0			0.657456
$344$		−	48308.2i		−	0.408229i
$345$	2277.69			0.0191362
$346$	−20428.4	−	20428.4i	−0.170641	−	0.170641i
$347$	−129822.	+	129822.i	−1.07817	+	1.07817i	−0.0815002	+	0.996673i	$0.525971\pi$
$347$	−129822.	+	129822.i	−1.07817	+	1.07817i	−0.996673	+	0.0815002i	$0.974029\pi$
$348$	3869.34	−	3869.34i	0.0319505	−	0.0319505i
$349$	81437.9			0.668615			0.334307	−	0.942464i	$-0.391498\pi$
$349$	81437.9			0.668615			0.334307	+	0.942464i	$0.391498\pi$
$350$	−20946.4	−	20946.4i	−0.170991	−	0.170991i
$351$	22705.4	−	22705.4i	0.184295	−	0.184295i
$352$	−16934.4	−	16934.4i	−0.136674	−	0.136674i
$353$	115990.	−	115990.i	0.930829	−	0.930829i	−0.0669291	−	0.997758i	$-0.521320\pi$
$353$	115990.	−	115990.i	0.930829	−	0.930829i	0.997758	+	0.0669291i	$0.0213201\pi$
$354$			5656.21i			0.0451356i
$355$	18110.8	+	18110.8i	0.143708	+	0.143708i
$356$	50215.4	+	50215.4i	0.396220	+	0.396220i
$357$	−3467.66	+	3467.66i	−0.0272082	+	0.0272082i
$358$		−	76397.6i		−	0.596092i
$359$	92091.4			0.714546			0.357273	−	0.934000i	$-0.383707\pi$
$359$	92091.4			0.714546			0.357273	+	0.934000i	$0.383707\pi$
$360$			6968.11i			0.0537663i
$361$		−	92604.5i		−	0.710588i
$362$	−68495.5	+	68495.5i	−0.522691	+	0.522691i
$363$			2215.10i			0.0168105i
$364$	−24954.7	+	24954.7i	−0.188343	+	0.188343i
$365$	−8789.32	+	8789.32i	−0.0659735	+	0.0659735i
$366$	−12679.4			−0.0946537
$367$	244475.			1.81511			0.907553	−	0.419937i	$-0.137948\pi$
$367$	244475.			1.81511			0.907553	+	0.419937i	$0.137948\pi$
$368$	−34774.9	−	34774.9i	−0.256786	−	0.256786i
$369$		−	76858.7i		−	0.564469i
$370$	−11370.2	+	9522.23i	−0.0830548	+	0.0695561i
$371$	−75668.9			−0.549756
$372$	−5158.20	+	5158.20i	−0.0372745	+	0.0372745i
$373$		−	219454.i		−	1.57735i	−0.614813	−	0.788673i	$-0.710769\pi$
$373$		−	219454.i		−	1.57735i	0.614813	−	0.788673i	$-0.289231\pi$
$374$			138187.i			0.987923i
$375$	−2589.17	−	2589.17i	−0.0184119	−	0.0184119i
$376$	−49506.0	−	49506.0i	−0.350173	−	0.350173i
$377$	−227221.			−1.59870
$378$	−4286.74	−	4286.74i	−0.0300015	−	0.0300015i
$379$	−198641.			−1.38290			−0.691450	−	0.722424i	$-0.743028\pi$
$379$	−198641.			−1.38290			−0.691450	+	0.722424i	$0.743028\pi$
$380$	5950.77			0.0412103
$381$			21027.1i			0.144854i
$382$	67168.7			0.460300
$383$	67016.0	+	67016.0i	0.456858	+	0.456858i	0.897623	−	0.440765i	$-0.145293\pi$
$383$	67016.0	+	67016.0i	0.456858	+	0.456858i	−0.440765	+	0.897623i	$0.645293\pi$
$384$	−792.455	+	792.455i	−0.00537418	+	0.00537418i
$385$	−6148.63	+	6148.63i	−0.0414818	+	0.0414818i
$386$	−91022.8			−0.610907
$387$	−121376.	−	121376.i	−0.810421	−	0.810421i
$388$	3447.38	−	3447.38i	0.0228995	−	0.0228995i
$389$	−133025.	−	133025.i	−0.879092	−	0.879092i	0.114348	−	0.993441i	$-0.463522\pi$
$389$	−133025.	−	133025.i	−0.879092	−	0.879092i	−0.993441	+	0.114348i	$0.963522\pi$
$390$	−1524.00	+	1524.00i	−0.0100197	+	0.0100197i
$391$			283767.i			1.85613i
$392$	−33704.6	−	33704.6i	−0.219340	−	0.219340i
$393$	6990.26	+	6990.26i	0.0452594	+	0.0452594i
$394$	17024.3	−	17024.3i	0.109667	−	0.109667i
$395$		−	9604.59i		−	0.0615580i
$396$	−85096.6			−0.542653
$397$			136809.i			0.868029i	0.900906	+	0.434015i	$0.142903\pi$
$397$			136809.i			0.868029i	−0.900906	+	0.434015i	$0.857097\pi$
$398$		−	82353.3i		−	0.519894i
$399$	−1823.65	+	1823.65i	−0.0114550	+	0.0114550i
$400$			39061.1i			0.244132i
$401$	−106536.	+	106536.i	−0.662534	+	0.662534i	−0.955977	−	0.293443i	$-0.905199\pi$
$401$	−106536.	+	106536.i	−0.662534	+	0.662534i	0.293443	+	0.955977i	$0.405199\pi$
$402$	3801.04	−	3801.04i	0.0235207	−	0.0235207i
$403$	302908.			1.86509
$404$	77906.4			0.477321
$405$	17376.2	+	17376.2i	0.105936	+	0.105936i
$406$			42899.0i			0.260253i
$407$	−116288.	−	138856.i	−0.702016	−	0.838256i
$408$	6466.52			0.0388464
$409$	61457.4	−	61457.4i	0.367390	−	0.367390i	−0.499134	−	0.866525i	$-0.666349\pi$
$409$	61457.4	−	61457.4i	0.367390	−	0.367390i	0.866525	+	0.499134i	$0.166349\pi$
$410$			10356.0i			0.0616064i
$411$		−	8511.93i		−	0.0503900i
$412$	−54441.0	−	54441.0i	−0.320724	−	0.320724i
$413$	−31355.0	−	31355.0i	−0.183826	−	0.183826i
$414$	−174747.			−1.01955
$415$	−14508.2	−	14508.2i	−0.0842396	−	0.0842396i
$416$	46535.8			0.268906
$417$	−8694.97			−0.0500030
$418$			72672.6i			0.415928i
$419$	137264.			0.781857			0.390929	−	0.920421i	$-0.372154\pi$
$419$	137264.			0.781857			0.390929	+	0.920421i	$0.372154\pi$
$420$	287.729	+	287.729i	0.00163112	+	0.00163112i
$421$	−70605.1	+	70605.1i	−0.398357	+	0.398357i	−0.877653	−	0.479296i	$-0.840892\pi$
$421$	−70605.1	+	70605.1i	−0.398357	+	0.398357i	0.479296	+	0.877653i	$0.340892\pi$
$422$	85989.2	−	85989.2i	0.482857	−	0.482857i
$423$	−248771.			−1.39033
$424$	70554.1	+	70554.1i	0.392455	+	0.392455i
$425$	159371.	−	159371.i	0.882333	−	0.882333i
$426$	10350.0	+	10350.0i	0.0570321	+	0.0570321i
$427$	70287.9	−	70287.9i	0.385500	−	0.385500i
$428$			17026.4i			0.0929468i
$429$	−18611.5	−	18611.5i	−0.101127	−	0.101127i
$430$	16354.4	+	16354.4i	0.0884498	+	0.0884498i
$431$	−167786.	+	167786.i	−0.903236	+	0.903236i	−0.995715	−	0.0924783i	$-0.970521\pi$
$431$	−167786.	+	167786.i	−0.903236	+	0.903236i	0.0924783	+	0.995715i	$0.470521\pi$
$432$			7993.95i			0.0428345i
$433$	181141.			0.966143			0.483071	−	0.875581i	$-0.339521\pi$
$433$	181141.			0.966143			0.483071	+	0.875581i	$0.339521\pi$
$434$		−	57188.5i		−	0.303619i
$435$			2619.87i			0.0138452i
$436$	−102305.	+	102305.i	−0.538176	+	0.538176i
$437$			149234.i			0.781455i
$438$	−5022.93	+	5022.93i	−0.0261824	+	0.0261824i
$439$	61395.2	−	61395.2i	0.318570	−	0.318570i	−0.529648	−	0.848218i	$-0.677676\pi$
$439$	61395.2	−	61395.2i	0.318570	−	0.318570i	0.848218	+	0.529648i	$0.177676\pi$
$440$	11466.0			0.0592254
$441$	−169368.			−0.870871
$442$	−189869.	−	189869.i	−0.971871	−	0.971871i
$443$			33042.7i			0.168372i	0.996450	+	0.0841858i	$0.0268289\pi$
$443$			33042.7i			0.168372i	−0.996450	+	0.0841858i	$0.973171\pi$
$444$	−6497.86	+	5441.77i	−0.0329613	+	0.0276042i
$445$	−34000.1			−0.171696
$446$	71515.1	−	71515.1i	0.359524	−	0.359524i
$447$		−	3405.71i		−	0.0170448i
$448$		−	8785.88i		−	0.0437753i
$449$	−1694.29	−	1694.29i	−0.00840419	−	0.00840419i	0.702892	−	0.711296i	$-0.251892\pi$
$449$	−1694.29	−	1694.29i	−0.00840419	−	0.00840419i	−0.711296	+	0.702892i	$0.751892\pi$
$450$	98142.4	+	98142.4i	0.484654	+	0.484654i
$451$	−126471.			−0.621782
$452$	37206.6	+	37206.6i	0.182114	+	0.182114i
$453$	−25046.0			−0.122051
$454$	220558.			1.07007
$455$		−	16896.4i		−	0.0816155i
$456$	3400.75			0.0163548
$457$	−90594.5	−	90594.5i	−0.433780	−	0.433780i	0.456132	−	0.889912i	$-0.349234\pi$
$457$	−90594.5	−	90594.5i	−0.433780	−	0.433780i	−0.889912	+	0.456132i	$0.849234\pi$
$458$	144686.	−	144686.i	0.689758	−	0.689758i
$459$	32615.7	−	32615.7i	0.154811	−	0.154811i
$460$	23545.6			0.111274
$461$	73442.7	+	73442.7i	0.345579	+	0.345579i	0.858460	−	0.512881i	$-0.171422\pi$
$461$	73442.7	+	73442.7i	0.345579	+	0.345579i	−0.512881	+	0.858460i	$0.671422\pi$
$462$	−3513.83	+	3513.83i	−0.0164625	+	0.0164625i
$463$	−120453.	−	120453.i	−0.561896	−	0.561896i	0.367949	−	0.929846i	$-0.380060\pi$
$463$	−120453.	−	120453.i	−0.561896	−	0.561896i	−0.929846	+	0.367949i	$0.880060\pi$
$464$	39999.2	−	39999.2i	0.185787	−	0.185787i
$465$		−	3492.54i		−	0.0161523i
$466$	147111.	+	147111.i	0.677443	+	0.677443i
$467$	−39866.8	−	39866.8i	−0.182801	−	0.182801i	0.609774	−	0.792575i	$-0.291260\pi$
$467$	−39866.8	−	39866.8i	−0.182801	−	0.182801i	−0.792575	+	0.609774i	$0.791260\pi$
$468$	116923.	−	116923.i	0.533835	−	0.533835i
$469$			42141.8i			0.191587i
$470$	33519.8			0.151742
$471$			4311.57i			0.0194354i
$472$			58471.0i			0.262456i
$473$	−199724.	+	199724.i	−0.892706	+	0.892706i
$474$		−	5488.84i		−	0.0244300i
$475$	83813.7	−	83813.7i	0.371473	−	0.371473i
$476$	−35846.9	+	35846.9i	−0.158211	+	0.158211i
$477$	354539.			1.55821
$478$	−9960.35			−0.0435932
$479$	−23910.7	−	23910.7i	−0.104213	−	0.104213i	0.653078	−	0.757291i	$-0.273477\pi$
$479$	−23910.7	−	23910.7i	−0.104213	−	0.104213i	−0.757291	+	0.653078i	$0.773477\pi$
$480$		−	536.559i		−	0.00232882i
$481$	350569.	+	31008.5i	1.51525	+	0.134027i
$482$	182510.			0.785584
$483$	−7215.67	+	7215.67i	−0.0309302	+	0.0309302i
$484$			22898.6i			0.0977502i
$485$			2334.17i			0.00992314i
$486$	30164.9	+	30164.9i	0.127711	+	0.127711i
$487$	293325.	+	293325.i	1.23678	+	1.23678i	0.961311	+	0.275464i	$0.0888316\pi$
$487$	293325.	+	293325.i	1.23678	+	1.23678i	0.275464	+	0.961311i	$0.411168\pi$
$488$	−131074.			−0.550396
$489$	−17354.4	−	17354.4i	−0.0725758	−	0.0725758i
$490$	22820.9			0.0950473
$491$	−300745.			−1.24748			−0.623742	−	0.781630i	$-0.714388\pi$
$491$	−300745.			−1.24748			−0.623742	+	0.781630i	$0.714388\pi$
$492$			5918.28i			0.0244492i
$493$	−326398.			−1.34293
$494$	−99852.1	−	99852.1i	−0.409170	−	0.409170i
$495$	28808.8	−	28808.8i	0.117575	−	0.117575i
$496$	−53322.8	+	53322.8i	−0.216745	+	0.216745i
$497$	−114749.			−0.464554
$498$	−8291.15	−	8291.15i	−0.0334315	−	0.0334315i
$499$	−139954.	+	139954.i	−0.562061	+	0.562061i	−0.929892	−	0.367832i	$-0.880100\pi$
$499$	−139954.	+	139954.i	−0.562061	+	0.562061i	0.367832	+	0.929892i	$0.380100\pi$
$500$	−26765.5	−	26765.5i	−0.107062	−	0.107062i
$501$	15199.6	−	15199.6i	0.0605558	−	0.0605558i
$502$		−	260519.i		−	1.03379i
$503$	304523.	+	304523.i	1.20360	+	1.20360i	0.973062	+	0.230542i	$0.0740499\pi$
$503$	304523.	+	304523.i	1.20360	+	1.20360i	0.230542	+	0.973062i	$0.425950\pi$
$504$	−22074.8	−	22074.8i	−0.0869033	−	0.0869033i
$505$	−26374.6	+	26374.6i	−0.103420	+	0.103420i
$506$			287546.i			1.12307i
$507$	29041.6			0.112981
$508$			217368.i			0.842302i
$509$		−	427098.i		−	1.64851i	−0.566217	−	0.824256i	$-0.691594\pi$
$509$		−	427098.i		−	1.64851i	0.566217	−	0.824256i	$-0.308406\pi$
$510$	−2189.19	+	2189.19i	−0.00841673	+	0.00841673i
$511$		−	55688.8i		−	0.213268i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	17152.7	−	17152.7i	0.0651774	−	0.0651774i
$514$	291035.			1.10159
$515$	36861.2			0.138981
$516$	9346.21	+	9346.21i	0.0351023	+	0.0351023i
$517$			409353.i			1.53150i
$518$	5854.37	−	66186.8i	0.0218183	−	0.246668i
$519$	7904.59			0.0293457
$520$	−15754.3	+	15754.3i	−0.0582630	+	0.0582630i
$521$		−	310162.i		−	1.14265i	−0.820723	−	0.571326i	$-0.806429\pi$
$521$		−	310162.i		−	1.14265i	0.820723	−	0.571326i	$-0.193571\pi$
$522$		−	200999.i		−	0.737654i
$523$	−296372.	−	296372.i	−1.08351	−	1.08351i	−0.996179	−	0.0873340i	$-0.972165\pi$
$523$	−296372.	−	296372.i	−1.08351	−	1.08351i	−0.0873340	−	0.996179i	$-0.527835\pi$
$524$	72261.8	+	72261.8i	0.263176	+	0.263176i
$525$	8105.04			0.0294060
$526$	100500.	+	100500.i	0.363240	+	0.363240i
$527$	435120.			1.56671
$528$	6552.62			0.0235043
$529$			310636.i			1.11004i
$530$	−47771.1			−0.170064
$531$	146911.	+	146911.i	0.521031	+	0.521031i
$532$	−18851.9	+	18851.9i	−0.0666090	+	0.0666090i
$533$	173771.	−	173771.i	0.611679	−	0.611679i
$534$	−19430.4			−0.0681395
$535$	−5764.14	−	5764.14i	−0.0201385	−	0.0201385i
$536$	39293.2	−	39293.2i	0.136769	−	0.136769i
$537$	14780.7	+	14780.7i	0.0512561	+	0.0512561i
$538$	202990.	−	202990.i	0.701309	−	0.701309i
$539$			278695.i			0.959294i
$540$	−2706.29	−	2706.29i	−0.00928083	−	0.00928083i
$541$	10908.2	+	10908.2i	0.0372699	+	0.0372699i	0.725496	−	0.688226i	$-0.241610\pi$
$541$	10908.2	+	10908.2i	0.0372699	+	0.0372699i	−0.688226	+	0.725496i	$0.741610\pi$
$542$	−126073.	+	126073.i	−0.429163	+	0.429163i
$543$		−	26503.7i		−	0.0898891i
$544$	66847.6			0.225885
$545$		−	69269.2i		−	0.233210i
$546$		−	9656.00i		−	0.0323901i
$547$	−296475.	+	296475.i	−0.990863	+	0.990863i	−0.999959	−	0.00909537i	$-0.997105\pi$
$547$	−296475.	+	296475.i	−0.990863	+	0.990863i	0.00909537	+	0.999959i	$0.497105\pi$
$548$		−	87992.0i		−	0.293010i
$549$	−329327.	+	329327.i	−1.09265	+	1.09265i
$550$	161493.	−	161493.i	0.533863	−	0.533863i
$551$	−171653.			−0.565391
$552$	13455.9			0.0441604
$553$	30427.2	+	30427.2i	0.0994973	+	0.0994973i
$554$			146914.i			0.478677i
$555$	357.530	−	4042.07i	0.00116072	−	0.0131225i
$556$	−89884.1			−0.290759
$557$	−83744.8	+	83744.8i	−0.269928	+	0.269928i	−0.829071	−	0.559143i	$-0.811130\pi$
$557$	−83744.8	+	83744.8i	−0.269928	+	0.269928i	0.559143	+	0.829071i	$0.311130\pi$
$558$			267951.i			0.860571i
$559$		−	548842.i		−	1.75640i
$560$	2974.39	+	2974.39i	0.00948467	+	0.00948467i
$561$	−26735.1	−	26735.1i	−0.0849484	−	0.0849484i
$562$	−345664.			−1.09441
$563$	−301225.	−	301225.i	−0.950330	−	0.950330i	0.0484933	−	0.998824i	$-0.484558\pi$
$563$	−301225.	−	301225.i	−0.950330	−	0.950330i	−0.998824	+	0.0484933i	$0.984558\pi$
$564$	19155.9			0.0602205
$565$	−25192.0			−0.0789162
$566$			70059.0i			0.218691i
$567$	−110095.			−0.342454
$568$	106993.	+	106993.i	0.331633	+	0.331633i
$569$	−36629.3	+	36629.3i	−0.113137	+	0.113137i	−0.761409	−	0.648272i	$-0.775492\pi$
$569$	−36629.3	+	36629.3i	−0.113137	+	0.113137i	0.648272	+	0.761409i	$0.275492\pi$
$570$	−1151.30	+	1151.30i	−0.00354355	+	0.00354355i
$571$	−316415.			−0.970476			−0.485238	−	0.874382i	$-0.661267\pi$
$571$	−316415.			−0.970476			−0.485238	+	0.874382i	$0.661267\pi$
$572$	−192396.	−	192396.i	−0.588038	−	0.588038i
$573$	−12995.2	+	12995.2i	−0.0395797	+	0.0395797i
$574$	−32807.7	−	32807.7i	−0.0995755	−	0.0995755i
$575$	331628.	−	331628.i	1.00303	−	1.00303i
$576$			41165.4i			0.124076i
$577$	376706.	+	376706.i	1.13149	+	1.13149i	0.989929	+	0.141562i	$0.0452124\pi$
$577$	376706.	+	376706.i	1.13149	+	1.13149i	0.141562	+	0.989929i	$0.454788\pi$
$578$	−105700.	−	105700.i	−0.316388	−	0.316388i
$579$	17610.2	−	17610.2i	0.0525300	−	0.0525300i
$580$			27082.9i			0.0805079i
$581$	91923.2			0.272316
$582$			1333.93i			0.00393812i
$583$		−	583394.i		−	1.71643i
$584$	−51924.5	+	51924.5i	−0.152246	+	0.152246i
$585$			79166.6i			0.231329i
$586$	−58153.7	+	58153.7i	−0.169349	+	0.169349i
$587$	−78641.6	+	78641.6i	−0.228232	+	0.228232i	−0.811954	−	0.583722i	$-0.801596\pi$
$587$	−78641.6	+	78641.6i	−0.228232	+	0.228232i	0.583722	+	0.811954i	$0.301596\pi$
$588$	13041.7			0.0377207
$589$	228830.			0.659604
$590$	−19794.9	−	19794.9i	−0.0568656	−	0.0568656i
$591$			6587.38i			0.0188598i
$592$	−67171.6	+	56254.3i	−0.191665	+	0.160514i
$593$	30267.7			0.0860736			0.0430368	−	0.999073i	$-0.486297\pi$
$593$	30267.7			0.0860736			0.0430368	+	0.999073i	$0.486297\pi$
$594$	33050.0	−	33050.0i	0.0936696	−	0.0936696i
$595$		−	24271.4i		−	0.0685584i
$596$		−	35206.5i		−	0.0991128i
$597$	15932.9	+	15932.9i	0.0447041	+	0.0447041i
$598$	−395088.	−	395088.i	−1.10482	−	1.10482i
$599$	103433.			0.288273			0.144137	−	0.989558i	$-0.453960\pi$
$599$	103433.			0.288273			0.144137	+	0.989558i	$0.453960\pi$
$600$	−7557.17	−	7557.17i	−0.0209921	−	0.0209921i
$601$	−322765.			−0.893589			−0.446795	−	0.894637i	$-0.647435\pi$
$601$	−322765.			−0.893589			−0.446795	+	0.894637i	$0.647435\pi$
$602$	−103621.			−0.285926
$603$		−	197451.i		−	0.543031i
$604$	−258912.			−0.709707
$605$	−7752.13	−	7752.13i	−0.0211792	−	0.0211792i
$606$	−15072.6	+	15072.6i	−0.0410433	+	0.0410433i
$607$	90515.7	−	90515.7i	0.245667	−	0.245667i	−0.573523	−	0.819190i	$-0.694424\pi$
$607$	90515.7	−	90515.7i	0.245667	−	0.245667i	0.819190	+	0.573523i	$0.194424\pi$
$608$	35155.3			0.0951006
$609$	−8299.69	−	8299.69i	−0.0223783	−	0.0223783i
$610$	44373.9	−	44373.9i	0.119253	−	0.119253i
$611$	−562451.	−	562451.i	−1.50662	−	1.50662i
$612$	167957.	−	167957.i	0.448431	−	0.448431i
$613$			461596.i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$613$			461596.i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$614$	−227009.	−	227009.i	−0.602153	−	0.602153i
$615$	−2003.59	−	2003.59i	−0.00529735	−	0.00529735i
$616$	−36324.2	+	36324.2i	−0.0957270	+	0.0957270i
$617$		−	145059.i		−	0.381043i	−0.981683	−	0.190522i	$-0.938982\pi$
$617$		−	145059.i		−	0.381043i	0.981683	−	0.190522i	$-0.0610179\pi$
$618$	21065.5			0.0551561
$619$			353899.i			0.923629i	0.886977	+	0.461814i	$0.152801\pi$
$619$			353899.i			0.923629i	−0.886977	+	0.461814i	$0.847199\pi$
$620$		−	36104.1i		−	0.0939232i
$621$	67868.4	−	67868.4i	0.175989	−	0.175989i
$622$			487497.i			1.26006i
$623$	107712.	−	107712.i	0.277515	−	0.277515i
$624$	−9003.30	+	9003.30i	−0.0231224	+	0.0231224i
$625$	−363334.			−0.930134
$626$	148875.			0.379904
$627$	−14060.0	−	14060.0i	−0.0357644	−	0.0357644i
$628$			44570.8i			0.113014i
$629$	503584.	+	44543.1i	1.27283	+	0.112585i
$630$	14946.5			0.0376582
$631$	318155.	−	318155.i	0.799060	−	0.799060i	−0.183887	−	0.982947i	$-0.558868\pi$
$631$	318155.	−	318155.i	0.799060	−	0.799060i	0.982947	+	0.183887i	$0.0588681\pi$
$632$		−	56740.9i		−	0.142057i
$633$			33272.7i			0.0830388i
$634$	−23318.5	−	23318.5i	−0.0580125	−	0.0580125i
$635$	−73588.2	−	73588.2i	−0.182499	−	0.182499i
$636$	−27300.3			−0.0674921
$637$	−382927.	−	382927.i	−0.943707	−	0.943707i
$638$	−330744.			−0.812551
$639$	537645.			1.31672
$640$		−	5546.68i		−	0.0135417i
$641$	57302.6			0.139463			0.0697313	−	0.997566i	$-0.477786\pi$
$641$	57302.6			0.139463			0.0697313	+	0.997566i	$0.477786\pi$
$642$	−3294.10	−	3294.10i	−0.00799221	−	0.00799221i
$643$	313472.	−	313472.i	0.758188	−	0.758188i	−0.217805	−	0.975992i	$-0.569890\pi$
$643$	313472.	−	313472.i	0.758188	−	0.758188i	0.975992	+	0.217805i	$0.0698895\pi$
$644$	−74592.0	+	74592.0i	−0.179854	+	0.179854i
$645$	−6328.17			−0.0152110
$646$	−143435.	−	143435.i	−0.343709	−	0.343709i
$647$	246187.	−	246187.i	0.588108	−	0.588108i	−0.349011	−	0.937119i	$-0.613482\pi$
$647$	246187.	−	246187.i	0.588108	−	0.588108i	0.937119	+	0.349011i	$0.113482\pi$
$648$	102653.	+	102653.i	0.244468	+	0.244468i
$649$	241741.	−	241741.i	0.573934	−	0.573934i
$650$			443784.i			1.05038i
$651$	11064.3	+	11064.3i	0.0261073	+	0.0261073i
$652$	−179401.	−	179401.i	−0.422017	−	0.422017i
$653$	−114939.	+	114939.i	−0.269550	+	0.269550i	−0.828919	−	0.559369i	$-0.811044\pi$
$653$	−114939.	+	114939.i	−0.269550	+	0.269550i	0.559369	+	0.828919i	$0.311044\pi$
$654$		−	39586.1i		−	0.0925522i
$655$	−48927.3			−0.114043
$656$			61180.2i			0.142168i
$657$			260924.i			0.604482i
$658$	−106190.	+	106190.i	−0.245263	+	0.245263i
$659$			603251.i			1.38908i	0.719454	+	0.694540i	$0.244392\pi$
$659$			603251.i			1.38908i	−0.719454	+	0.694540i	$0.755608\pi$
$660$	−2218.34	+	2218.34i	−0.00509261	+	0.00509261i
$661$	147885.	−	147885.i	0.338471	−	0.338471i	−0.517320	−	0.855792i	$-0.673070\pi$
$661$	147885.	−	147885.i	0.338471	−	0.338471i	0.855792	+	0.517320i	$0.173070\pi$
$662$	294328.			0.671607
$663$	73467.9			0.167136
$664$	−85709.7	−	85709.7i	−0.194399	−	0.194399i
$665$		−	12764.4i		−	0.0288639i
$666$	−27430.0	+	310112.i	−0.0618412	+	0.699149i
$667$	−679185.			−1.52664
$668$	157125.	−	157125.i	0.352122	−	0.352122i
$669$			27672.1i			0.0618288i
$670$			26604.8i			0.0592667i
$671$	541908.	+	541908.i	1.20359	+	1.20359i
$672$	1699.81	+	1699.81i	0.00376411	+	0.00376411i
$673$	−338568.			−0.747509			−0.373754	−	0.927528i	$-0.621930\pi$
$673$	−338568.			−0.747509			−0.373754	+	0.927528i	$0.621930\pi$
$674$	−314669.	−	314669.i	−0.692682	−	0.692682i
$675$	−76233.5			−0.167316
$676$	300218.			0.656966
$677$			545608.i			1.19043i	0.803567	+	0.595214i	$0.202933\pi$
$677$			545608.i			1.19043i	−0.803567	+	0.595214i	$0.797067\pi$
$678$	−14396.8			−0.0313188
$679$	−7394.61	−	7394.61i	−0.0160389	−	0.0160389i
$680$	−22630.7	+	22630.7i	−0.0489419	+	0.0489419i
$681$	−42671.5	+	42671.5i	−0.0920119	+	0.0920119i
$682$	440914.			0.947949
$683$	347489.	+	347489.i	0.744903	+	0.744903i	0.973517	−	0.228614i	$-0.0734194\pi$
$683$	347489.	+	347489.i	0.744903	+	0.744903i	−0.228614	+	0.973517i	$0.573419\pi$
$684$	88328.8	−	88328.8i	0.188795	−	0.188795i
$685$	29789.0	+	29789.0i	0.0634855	+	0.0634855i
$686$	−154698.	+	154698.i	−0.328728	+	0.328728i
$687$			55985.1i			0.118620i
$688$	96616.4	+	96616.4i	0.204114	+	0.204114i
$689$	801584.	+	801584.i	1.68854	+	1.68854i
$690$	−4555.38	+	4555.38i	−0.00956811	+	0.00956811i
$691$			432975.i			0.906790i	0.891310	+	0.453395i	$0.149787\pi$
$691$			432975.i			0.906790i	−0.891310	+	0.453395i	$0.850213\pi$
$692$	81713.7			0.170641
$693$			182531.i			0.380077i
$694$		−	519287.i		−	1.07817i
$695$	30429.6	−	30429.6i	0.0629979	−	0.0629979i
$696$			15477.3i			0.0319505i
$697$	249619.	−	249619.i	0.513820	−	0.513820i
$698$	−162876.	+	162876.i	−0.334307	+	0.334307i
$699$	−56923.2			−0.116502
$700$	83785.7			0.170991
$701$	−485929.	−	485929.i	−0.988864	−	0.988864i	0.0110742	−	0.999939i	$-0.496475\pi$
$701$	−485929.	−	485929.i	−0.988864	−	0.988864i	−0.999939	+	0.0110742i	$0.996475\pi$
$702$			90821.4i			0.184295i
$703$	264836.	+	23425.3i	0.535878	+	0.0473995i
$704$	67737.7			0.136674
$705$	−6485.09	+	6485.09i	−0.0130478	+	0.0130478i
$706$			463959.i			0.930829i
$707$		−	167108.i		−	0.334318i
$708$	−11312.4	−	11312.4i	−0.0225678	−	0.0225678i
$709$	−81885.6	−	81885.6i	−0.162898	−	0.162898i	0.620951	−	0.783849i	$-0.286746\pi$
$709$	−81885.6	−	81885.6i	−0.162898	−	0.162898i	−0.783849	+	0.620951i	$0.786746\pi$
$710$	−72443.0			−0.143708
$711$	−142563.	−	142563.i	−0.282013	−	0.282013i
$712$	−200862.			−0.396220
$713$	905419.			1.78103
$714$		−	13870.6i		−	0.0272082i
$715$	130269.			0.254817
$716$	152795.	+	152795.i	0.298046	+	0.298046i
$717$	1927.03	−	1927.03i	0.00374844	−	0.00374844i
$718$	−184183.	+	184183.i	−0.357273	+	0.357273i
$719$	−430384.			−0.832526			−0.416263	−	0.909244i	$-0.636661\pi$
$719$	−430384.			−0.832526			−0.416263	+	0.909244i	$0.636661\pi$
$720$	−13936.2	−	13936.2i	−0.0268831	−	0.0268831i
$721$	−116775.	+	116775.i	−0.224637	+	0.224637i
$722$	185209.	+	185209.i	0.355294	+	0.355294i
$723$	−35310.3	+	35310.3i	−0.0675500	+	0.0675500i
$724$		−	273982.i		−	0.522691i
$725$	381449.	+	381449.i	0.725705	+	0.725705i
$726$	−4430.20	−	4430.20i	−0.00840524	−	0.00840524i
$727$	−115270.	+	115270.i	−0.218095	+	0.218095i	−0.807695	−	0.589600i	$-0.799285\pi$
$727$	−115270.	+	115270.i	−0.218095	+	0.218095i	0.589600	+	0.807695i	$0.299285\pi$
$728$		−	99818.8i		−	0.188343i
$729$	508010.			0.955910
$730$		−	35157.3i		−	0.0659735i
$731$		−	788400.i		−	1.47541i
$732$	25358.9	−	25358.9i	0.0473269	−	0.0473269i
$733$			514933.i			0.958391i	0.877708	+	0.479196i	$0.159072\pi$
$733$			514933.i			0.958391i	−0.877708	+	0.479196i	$0.840928\pi$
$734$	−488950.	+	488950.i	−0.907553	+	0.907553i
$735$	−4415.16	+	4415.16i	−0.00817282	+	0.00817282i
$736$	139100.			0.256786
$737$	−324906.			−0.598167
$738$	153717.	+	153717.i	0.282235	+	0.282235i
$739$		−	970067.i		−	1.77629i	−0.459567	−	0.888143i	$-0.651995\pi$
$739$		−	970067.i		−	1.77629i	0.459567	−	0.888143i	$-0.348005\pi$
$740$	3695.96	−	41784.9i	0.00674938	−	0.0763055i
$741$	38636.9			0.0703665
$742$	151338.	−	151338.i	0.274878	−	0.274878i
$743$			108671.i			0.196851i	0.995144	+	0.0984255i	$0.0313806\pi$
$743$			108671.i			0.196851i	−0.995144	+	0.0984255i	$0.968619\pi$
$744$		−	20632.8i		−	0.0372745i
$745$	11918.9	+	11918.9i	0.0214745	+	0.0214745i
$746$	438909.	+	438909.i	0.788673	+	0.788673i
$747$	−430697.			−0.771846
$748$	−276373.	−	276373.i	−0.493961	−	0.493961i
$749$	36521.4			0.0651004
$750$	10356.7			0.0184119
$751$			372158.i			0.659853i	0.944007	+	0.329927i	$0.107024\pi$
$751$			372158.i			0.659853i	−0.944007	+	0.329927i	$0.892976\pi$
$752$	198024.			0.350173
$753$	50402.8	+	50402.8i	0.0888924	+	0.0888924i
$754$	454442.	−	454442.i	0.799348	−	0.799348i
$755$	87652.8	−	87652.8i	0.153770	−	0.153770i
$756$	17146.9			0.0300015
$757$	−267014.	−	267014.i	−0.465953	−	0.465953i	0.434648	−	0.900600i	$-0.356873\pi$
$757$	−267014.	−	267014.i	−0.465953	−	0.465953i	−0.900600	+	0.434648i	$0.856873\pi$
$758$	397282.	−	397282.i	0.691450	−	0.691450i
$759$	−55631.6	−	55631.6i	−0.0965691	−	0.0965691i
$760$	−11901.5	+	11901.5i	−0.0206052	+	0.0206052i
$761$		−	275812.i		−	0.476260i	−0.971233	−	0.238130i	$-0.923466\pi$
$761$		−	275812.i		−	0.476260i	0.971233	−	0.238130i	$-0.0765345\pi$
$762$	−42054.3	−	42054.3i	−0.0724270	−	0.0724270i
$763$	219444.	+	219444.i	0.376942	+	0.376942i
$764$	−134337.	+	134337.i	−0.230150	+	0.230150i
$765$			113721.i			0.194320i
$766$	−268064.			−0.456858
$767$			664305.i			1.12922i
$768$		−	3169.82i		−	0.00537418i
$769$	−352671.	+	352671.i	−0.596372	+	0.596372i	−0.939345	−	0.342974i	$-0.888566\pi$
$769$	−352671.	+	352671.i	−0.596372	+	0.596372i	0.342974	+	0.939345i	$0.388566\pi$
$770$		−	24594.5i		−	0.0414818i
$771$	−56306.6	+	56306.6i	−0.0947220	+	0.0947220i
$772$	182046.	−	182046.i	0.305454	−	0.305454i
$773$	−294289.			−0.492511			−0.246255	−	0.969205i	$-0.579200\pi$
$773$	−294289.			−0.492511			−0.246255	+	0.969205i	$0.579200\pi$
$774$	485504.			0.810421
$775$	−508508.	−	508508.i	−0.846632	−	0.846632i
$776$			13789.5i			0.0228995i
$777$	11672.6	+	13937.9i	0.0193341	+	0.0230863i
$778$	532101.			0.879092
$779$	131275.	−	131275.i	0.216325	−	0.216325i
$780$		−	6096.00i		−	0.0100197i
$781$		−	884696.i		−	1.45041i
$782$	−567535.	−	567535.i	−0.928066	−	0.928066i
$783$	78064.4	+	78064.4i	0.127330	+	0.127330i
$784$	134818.			0.219340
$785$	−15089.1	−	15089.1i	−0.0244864	−	0.0244864i
$786$	−27961.0			−0.0452594
$787$	−831140.			−1.34191			−0.670957	−	0.741496i	$-0.734116\pi$
$787$	−831140.			−1.34191			−0.670957	+	0.741496i	$0.734116\pi$
$788$			68097.0i			0.109667i
$789$	−38887.4			−0.0624677
$790$	19209.2	+	19209.2i	0.0307790	+	0.0307790i
$791$	79807.8	−	79807.8i	0.127554	−	0.127554i
$792$	170193.	−	170193.i	0.271326	−	0.271326i
$793$	−1.48916e6			−2.36808
$794$	−273618.	−	273618.i	−0.434015	−	0.434015i
$795$	9242.29	−	9242.29i	0.0146233	−	0.0146233i
$796$	164707.	+	164707.i	0.259947	+	0.259947i
$797$	451637.	−	451637.i	0.711006	−	0.711006i	−0.255740	−	0.966746i	$-0.582319\pi$
$797$	451637.	−	451637.i	0.711006	−	0.711006i	0.966746	+	0.255740i	$0.0823191\pi$
$798$		−	7294.59i		−	0.0114550i
$799$	−807949.	−	807949.i	−1.26558	−	1.26558i
$800$	−78122.2	−	78122.2i	−0.122066	−	0.122066i
$801$	−504672.	+	504672.i	−0.786582	+	0.786582i
$802$		−	426145.i		−	0.662534i
$803$	429351.			0.665858
$804$			15204.1i			0.0235207i
$805$		−	50505.1i		−	0.0779369i
$806$	−605815.	+	605815.i	−0.932546	+	0.932546i
$807$			78545.1i			0.120607i
$808$	−155813.	+	155813.i	−0.238660	+	0.238660i
$809$	−527484.	+	527484.i	−0.805957	+	0.805957i	−0.984019	−	0.178062i	$-0.943017\pi$
$809$	−527484.	+	527484.i	−0.805957	+	0.805957i	0.178062	+	0.984019i	$0.443017\pi$
$810$	−69504.9			−0.105936
$811$	11885.4			0.0180705			0.00903527	−	0.999959i	$-0.497124\pi$
$811$	11885.4			0.0180705			0.00903527	+	0.999959i	$0.497124\pi$
$812$	−85798.0	−	85798.0i	−0.130126	−	0.130126i
$813$		−	48782.7i		−	0.0738048i
$814$	510289.	+	45136.2i	0.770136	+	0.0681202i
$815$	121470.			0.182874
$816$	−12933.0	+	12933.0i	−0.0194232	+	0.0194232i
$817$		−	414621.i		−	0.621165i
$818$			245830.i			0.367390i
$819$	−250798.	−	250798.i	−0.373901	−	0.373901i
$820$	−20712.1	−	20712.1i	−0.0308032	−	0.0308032i
$821$	442045.			0.655813			0.327906	−	0.944710i	$-0.393657\pi$
$821$	442045.			0.655813			0.327906	+	0.944710i	$0.393657\pi$
$822$	17023.9	+	17023.9i	0.0251950	+	0.0251950i
$823$	235451.			0.347617			0.173808	−	0.984780i	$-0.444393\pi$
$823$	235451.			0.347617			0.173808	+	0.984780i	$0.444393\pi$
$824$	217764.			0.320724
$825$			62488.4i			0.0918104i
$826$	125420.			0.183826
$827$	121779.	+	121779.i	0.178058	+	0.178058i	0.790509	−	0.612451i	$-0.209816\pi$
$827$	121779.	+	121779.i	0.178058	+	0.178058i	−0.612451	+	0.790509i	$0.709816\pi$
$828$	349493.	−	349493.i	0.509774	−	0.509774i
$829$	−378631.	+	378631.i	−0.550944	+	0.550944i	−0.926713	−	0.375769i	$-0.877378\pi$
$829$	−378631.	+	378631.i	−0.550944	+	0.550944i	0.375769	+	0.926713i	$0.377378\pi$
$830$	58032.7			0.0842396
$831$	−28423.5	−	28423.5i	−0.0411600	−	0.0411600i
$832$	−93071.5	+	93071.5i	−0.134453	+	0.134453i
$833$	−550066.	−	550066.i	−0.792730	−	0.792730i
$834$	17389.9	−	17389.9i	0.0250015	−	0.0250015i
$835$			106387.i			0.152587i
$836$	−145345.	−	145345.i	−0.207964	−	0.207964i
$837$	−104067.	−	104067.i	−0.148547	−	0.148547i
$838$	−274527.	+	274527.i	−0.390929	+	0.390929i
$839$			691069.i			0.981743i	0.871232	+	0.490871i	$0.163321\pi$
$839$			691069.i			0.981743i	−0.871232	+	0.490871i	$0.836679\pi$
$840$	−1150.92			−0.00163112
$841$		−	73938.5i		−	0.104539i
$842$		−	282421.i		−	0.398357i
$843$	66875.8	−	66875.8i	0.0941052	−	0.0941052i
$844$			343957.i			0.482857i
$845$	−101636.	+	101636.i	−0.142343	+	0.142343i
$846$	497542.	−	497542.i	0.695167	−	0.695167i
$847$	49117.2			0.0684648
$848$	−282216.			−0.392455
$849$	−13554.4	−	13554.4i	−0.0188046	−	0.0188046i
$850$			637486.i			0.882333i
$851$	1.04788e6	+	92687.4i	1.44695	+	0.127986i
$852$	−41399.8			−0.0570321
$853$	367553.	−	367553.i	0.505151	−	0.505151i	−0.407883	−	0.913034i	$-0.633733\pi$
$853$	367553.	−	367553.i	0.505151	−	0.505151i	0.913034	+	0.407883i	$0.133733\pi$
$854$			281152.i			0.385500i
$855$			59806.1i			0.0818113i
$856$	−34052.7	−	34052.7i	−0.0464734	−	0.0464734i
$857$	193735.	+	193735.i	0.263782	+	0.263782i	0.826589	−	0.562806i	$-0.190278\pi$
$857$	193735.	+	193735.i	0.263782	+	0.263782i	−0.562806	+	0.826589i	$0.690278\pi$
$858$	74446.1			0.101127
$859$	−234817.	−	234817.i	−0.318232	−	0.318232i	0.529856	−	0.848088i	$-0.322246\pi$
$859$	−234817.	−	234817.i	−0.318232	−	0.318232i	−0.848088	+	0.529856i	$0.822246\pi$
$860$	−65417.4			−0.0884498
$861$	12694.7			0.0171244
$862$		−	671144.i		−	0.903236i
$863$	−1.11987e6			−1.50364			−0.751822	−	0.659366i	$-0.770825\pi$
$863$	−1.11987e6			−1.50364			−0.751822	+	0.659366i	$0.770825\pi$
$864$	−15987.9	−	15987.9i	−0.0214173	−	0.0214173i
$865$	−27663.5	+	27663.5i	−0.0369722	+	0.0369722i
$866$	−362282.	+	362282.i	−0.483071	+	0.483071i
$867$	40899.7			0.0544104
$868$	114377.	+	114377.i	0.151810	+	0.151810i
$869$	−234588.	+	234588.i	−0.310647	+	0.310647i
$870$	−5239.73	−	5239.73i	−0.00692262	−	0.00692262i
$871$	446420.	−	446420.i	0.588448	−	0.588448i
$872$		−	409221.i		−	0.538176i
$873$	34646.7	+	34646.7i	0.0454604	+	0.0454604i
$874$	−298467.	−	298467.i	−0.390728	−	0.390728i
$875$	−57411.8	+	57411.8i	−0.0749869	+	0.0749869i
$876$		−	20091.7i		−	0.0261824i
$877$	275814.			0.358606			0.179303	−	0.983794i	$-0.442616\pi$
$877$	275814.			0.358606			0.179303	+	0.983794i	$0.442616\pi$
$878$			245581.i			0.318570i
$879$		−	22502.0i		−	0.0291235i
$880$	−22932.1	+	22932.1i	−0.0296127	+	0.0296127i
$881$		−	1.25917e6i		−	1.62230i	−0.584837	−	0.811151i	$-0.698841\pi$
$881$		−	1.25917e6i		−	1.62230i	0.584837	−	0.811151i	$-0.301159\pi$
$882$	338736.	−	338736.i	0.435436	−	0.435436i
$883$	−1.04737e6	+	1.04737e6i	−1.34331	+	1.34331i	−0.450572	+	0.892740i	$0.648780\pi$
$883$	−1.04737e6	+	1.04737e6i	−1.34331	+	1.34331i	−0.892740	+	0.450572i	$0.851220\pi$
$884$	759474.			0.971871
$885$	7659.47			0.00977940
$886$	−66085.5	−	66085.5i	−0.0841858	−	0.0841858i
$887$			1.07135e6i			1.36171i	0.732417	+	0.680857i	$0.238392\pi$
$887$			1.07135e6i			1.36171i	−0.732417	+	0.680857i	$0.761608\pi$
$888$	2112.17	−	23879.3i	0.00267857	−	0.0302827i
$889$	466252.			0.589953
$890$	68000.1	−	68000.1i	0.0858479	−	0.0858479i
$891$		−	848815.i		−	1.06920i
$892$			286060.i			0.359524i
$893$	−424902.	−	424902.i	−0.532826	−	0.532826i
$894$	6811.41	+	6811.41i	0.00852240	+	0.00852240i
$895$	−103455.			−0.129154
$896$	17571.8	+	17571.8i	0.0218877	+	0.0218877i
$897$	152876.			0.190000
$898$	6777.17			0.00840419
$899$			1.04144e6i			1.28859i
$900$	−392570.			−0.484654
$901$	1.15146e6	+	1.15146e6i	1.41840	+	1.41840i
$902$	252942.	−	252942.i	0.310891	−	0.310891i
$903$	20047.5	−	20047.5i	0.0245859	−	0.0245859i
$904$	−148826.			−0.182114
$905$	92754.4	+	92754.4i	0.113250	+	0.113250i
$906$	50091.9	−	50091.9i	0.0610255	−	0.0610255i
$907$	−207316.	−	207316.i	−0.252010	−	0.252010i	0.569784	−	0.821794i	$-0.307027\pi$
$907$	−207316.	−	207316.i	−0.252010	−	0.252010i	−0.821794	+	0.569784i	$0.807027\pi$
$908$	−441116.	+	441116.i	−0.535034	+	0.535034i
$909$			782970.i			0.947583i
$910$	33792.9	+	33792.9i	0.0408077	+	0.0408077i
$911$	−204338.	−	204338.i	−0.246213	−	0.246213i	0.573201	−	0.819415i	$-0.305701\pi$
$911$	−204338.	−	204338.i	−0.246213	−	0.246213i	−0.819415	+	0.573201i	$0.805701\pi$
$912$	−6801.51	+	6801.51i	−0.00817741	+	0.00817741i
$913$			708712.i			0.850214i
$914$	362378.			0.433780
$915$			17170.1i			0.0205083i
$916$			578746.i			0.689758i
$917$	155001.	−	155001.i	0.184330	−	0.184330i
$918$			130463.i			0.154811i
$919$	39820.1	−	39820.1i	0.0471489	−	0.0471489i	−0.683139	−	0.730288i	$-0.739386\pi$
$919$	39820.1	−	39820.1i	0.0471489	−	0.0471489i	0.730288	+	0.683139i	$0.239386\pi$
$920$	−47091.2	+	47091.2i	−0.0556370	+	0.0556370i
$921$	87839.2			0.103554
$922$	−293771.			−0.345579
$923$	1.21557e6	+	1.21557e6i	1.42685	+	1.42685i
$924$		−	14055.3i		−	0.0164625i
$925$	−536464.	−	640575.i	−0.626984	−	0.748663i
$926$	481813.			0.561896
$927$	547140.	−	547140.i	0.636706	−	0.636706i
$928$			159997.i			0.185787i
$929$		−	1.26063e6i		−	1.46069i	−0.683080	−	0.730344i	$-0.739360\pi$
$929$		−	1.26063e6i		−	1.46069i	0.683080	−	0.730344i	$-0.260640\pi$
$930$	6985.07	+	6985.07i	0.00807616	+	0.00807616i
$931$	−289281.	−	289281.i	−0.333749	−	0.333749i
$932$	−588443.			−0.677443
$933$	−94316.4	−	94316.4i	−0.108349	−	0.108349i
$934$	159467.			0.182801
$935$	187128.			0.214050
$936$			467691.i			0.533835i
$937$	1.32991e6			1.51475			0.757377	−	0.652978i	$-0.226481\pi$
$937$	1.32991e6			1.51475			0.757377	+	0.652978i	$0.226481\pi$
$938$	−84283.5	−	84283.5i	−0.0957937	−	0.0957937i
$939$	−28803.0	+	28803.0i	−0.0326667	+	0.0326667i
$940$	−67039.5	+	67039.5i	−0.0758709	+	0.0758709i
$941$	831115.			0.938602			0.469301	−	0.883038i	$-0.344506\pi$
$941$	831115.			0.938602			0.469301	+	0.883038i	$0.344506\pi$
$942$	−8623.14	−	8623.14i	−0.00971771	−	0.00971771i
$943$	519418.	−	519418.i	0.584109	−	0.584109i
$944$	−116942.	−	116942.i	−0.131228	−	0.131228i
$945$	−5804.97	+	5804.97i	−0.00650034	+	0.00650034i
$946$		−	798897.i		−	0.892706i
$947$	680685.	+	680685.i	0.759008	+	0.759008i	0.976142	−	0.217134i	$-0.0696707\pi$
$947$	680685.	+	680685.i	0.759008	+	0.759008i	−0.217134	+	0.976142i	$0.569671\pi$
$948$	10977.7	+	10977.7i	0.0122150	+	0.0122150i
$949$	−589928.	+	589928.i	−0.655039	+	0.655039i
$950$			335255.i			0.371473i
$951$	9022.87			0.00997663
$952$		−	143388.i		−	0.158211i
$953$		−	1.54820e6i		−	1.70467i	−0.522996	−	0.852335i	$-0.675186\pi$
$953$		−	1.54820e6i		−	1.70467i	0.522996	−	0.852335i	$-0.324814\pi$
$954$	−709078.	+	709078.i	−0.779107	+	0.779107i
$955$		−	90957.8i		−	0.0997317i
$956$	19920.7	−	19920.7i	0.0217966	−	0.0217966i
$957$	63989.2	−	63989.2i	0.0698687	−	0.0698687i
$958$	95642.9			0.104213
$959$	−188742.			−0.205226
$960$	1073.12	+	1073.12i	0.00116441	+	0.00116441i
$961$		−	464821.i		−	0.503314i
$962$	−763154.	+	639120.i	−0.824636	+	0.690609i
$963$	−171117.			−0.184519
$964$	−365020.	+	365020.i	−0.392792	+	0.392792i
$965$			123260.i			0.132364i
$966$		−	28862.7i		−	0.0309302i
$967$	1.11911e6	+	1.11911e6i	1.19679	+	1.19679i	0.975121	+	0.221674i	$0.0711521\pi$
$967$	1.11911e6	+	1.11911e6i	1.19679	+	1.19679i	0.221674	+	0.975121i	$0.428848\pi$
$968$	−45797.1	−	45797.1i	−0.0488751	−	0.0488751i
$969$	55501.1			0.0591090
$970$	−4668.34	−	4668.34i	−0.00496157	−	0.00496157i
$971$	206634.			0.219161			0.109580	−	0.993978i	$-0.465049\pi$
$971$	206634.			0.219161			0.109580	+	0.993978i	$0.465049\pi$
$972$	−120659.			−0.127711
$973$			192801.i			0.203649i
$974$	−1.17330e6			−1.23678
$975$	−85859.1	−	85859.1i	−0.0903186	−	0.0903186i
$976$	262147.	−	262147.i	0.275198	−	0.275198i
$977$	739018.	−	739018.i	0.774223	−	0.774223i	−0.204619	−	0.978842i	$-0.565595\pi$
$977$	739018.	−	739018.i	0.774223	−	0.774223i	0.978842	+	0.204619i	$0.0655954\pi$
$978$	69417.6			0.0725758
$979$	830438.	+	830438.i	0.866446	+	0.866446i
$980$	−45641.7	+	45641.7i	−0.0475237	+	0.0475237i
$981$	−1.02818e6	−	1.02818e6i	−1.06839	−	1.06839i
$982$	601489.	−	601489.i	0.623742	−	0.623742i
$983$			991458.i			1.02605i	0.858375	+	0.513023i	$0.171475\pi$
$983$			991458.i			1.02605i	−0.858375	+	0.513023i	$0.828525\pi$
$984$	−11836.6	−	11836.6i	−0.0122246	−	0.0122246i
$985$	−23053.7	−	23053.7i	−0.0237612	−	0.0237612i
$986$	652796.	−	652796.i	0.671466	−	0.671466i
$987$		−	41089.3i		−	0.0421788i
$988$	399409.			0.409170
$989$		−	1.64054e6i		−	1.67724i
$990$			115235.i			0.117575i
$991$	−36831.1	+	36831.1i	−0.0375032	+	0.0375032i	−0.725610	−	0.688107i	$-0.758442\pi$
$991$	−36831.1	+	36831.1i	−0.0375032	+	0.0375032i	0.688107	+	0.725610i	$0.258442\pi$
$992$		−	213291.i		−	0.216745i
$993$	−56943.7	+	56943.7i	−0.0577494	+	0.0577494i
$994$	229498.	−	229498.i	0.232277	−	0.232277i
$995$	−111520.			−0.112644
$996$	33164.6			0.0334315
$997$	709771.	+	709771.i	0.714049	+	0.714049i	0.967380	−	0.253330i	$-0.0815260\pi$
$997$	709771.	+	709771.i	0.714049	+	0.714049i	−0.253330	+	0.967380i	$0.581526\pi$
$998$		−	559815.i		−	0.562061i
$999$	−109789.	−	131095.i	−0.110008	−	0.131358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.3	yes	14
37.31	odd	4	inner	74.5.d.a.31.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.5	✓	14	37.31	odd	4	inner
74.5.d.a.43.3	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} -0.773882i q^{3} -8.00000i q^{4} +(2.70834 + 2.70834i) q^{5} +(1.54776 + 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 + 16.0000i) q^{8} +80.4011 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} -0.773882i q^{3} -8.00000i q^{4} +(2.70834 + 2.70834i) q^{5} +(1.54776 + 1.54776i) q^{6} -17.1599 q^{7} +(16.0000 + 16.0000i) q^{8} +80.4011 q^{9} -10.8334 q^{10} -132.300i q^{11} -6.19106 q^{12} +(181.780 + 181.780i) q^{13} +(34.3199 - 34.3199i) q^{14} +(2.09593 - 2.09593i) q^{15} -64.0000 q^{16} +(261.124 + 261.124i) q^{17} +(-160.802 + 160.802i) q^{18} +(137.325 + 137.325i) q^{19} +(21.6667 - 21.6667i) q^{20} +13.2798i q^{21} +(264.600 + 264.600i) q^{22} +(543.359 + 543.359i) q^{23} +(12.3821 - 12.3821i) q^{24} -610.330i q^{25} -727.121 q^{26} -124.905i q^{27} +137.279i q^{28} +(-624.988 + 624.988i) q^{29} +8.38374i q^{30} +(833.169 - 833.169i) q^{31} +(128.000 - 128.000i) q^{32} -102.385 q^{33} -1044.49 q^{34} +(-46.4749 - 46.4749i) q^{35} -643.209i q^{36} +(1049.56 - 878.973i) q^{37} -549.301 q^{38} +(140.677 - 140.677i) q^{39} +86.6668i q^{40} -955.940i q^{41} +(-26.5595 - 26.5595i) q^{42} +(-1509.63 - 1509.63i) q^{43} -1058.40 q^{44} +(217.753 + 217.753i) q^{45} -2173.43 q^{46} -3094.13 q^{47} +49.5285i q^{48} -2106.54 q^{49} +(1220.66 + 1220.66i) q^{50} +(202.079 - 202.079i) q^{51} +(1454.24 - 1454.24i) q^{52} +4409.63 q^{53} +(249.811 + 249.811i) q^{54} +(358.313 - 358.313i) q^{55} +(-274.559 - 274.559i) q^{56} +(106.274 - 106.274i) q^{57} -2499.95i q^{58} +(1827.22 + 1827.22i) q^{59} +(-16.7675 - 16.7675i) q^{60} +(-4096.05 + 4096.05i) q^{61} +3332.68i q^{62} -1379.68 q^{63} +512.000i q^{64} +984.645i q^{65} +(204.769 - 204.769i) q^{66} -2455.82i q^{67} +(2088.99 - 2088.99i) q^{68} +(420.495 - 420.495i) q^{69} +185.900 q^{70} +6687.04 q^{71} +(1286.42 + 1286.42i) q^{72} +3245.28i q^{73} +(-341.165 + 3857.06i) q^{74} -472.323 q^{75} +(1098.60 - 1098.60i) q^{76} +2270.26i q^{77} +562.706i q^{78} +(-1773.15 - 1773.15i) q^{79} +(-173.334 - 173.334i) q^{80} +6415.83 q^{81} +(1911.88 + 1911.88i) q^{82} -5356.85 q^{83} +106.238 q^{84} +1414.42i q^{85} +6038.52 q^{86} +(483.667 + 483.667i) q^{87} +(2116.80 - 2116.80i) q^{88} +(-6276.92 + 6276.92i) q^{89} -871.014 q^{90} +(-3119.34 - 3119.34i) q^{91} +(4346.87 - 4346.87i) q^{92} +(-644.775 - 644.775i) q^{93} +(6188.25 - 6188.25i) q^{94} +743.847i q^{95} +(-99.0569 - 99.0569i) q^{96} +(430.923 + 430.923i) q^{97} +(4213.07 - 4213.07i) q^{98} -10637.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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