LMFDB - Embedded newform 20.5.b.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.246034965625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 21x^{5} + 49x^{4} - 84x^{3} + 112x^{2} - 192x + 256 $ x^8 - 3x^7 + 7x^6 - 21x^5 + 49x^4 - 84x^3 + 112x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$1.21760 - 1.58665i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.5.b.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43519 - 3.17330i) q^{2} -3.20523i q^{3} +(-4.13968 - 15.4552i) q^{4} +11.1803 q^{5} +(-10.1712 - 7.80536i) q^{6} +30.6227i q^{7} +(-59.1249 - 24.4999i) q^{8} +70.7265 q^{9} +O(q^{10})$	\(q+(2.43519 - 3.17330i) q^{2} -3.20523i q^{3} +(-4.13968 - 15.4552i) q^{4} +11.1803 q^{5} +(-10.1712 - 7.80536i) q^{6} +30.6227i q^{7} +(-59.1249 - 24.4999i) q^{8} +70.7265 q^{9} +(27.2263 - 35.4786i) q^{10} +168.004i q^{11} +(-49.5375 + 13.2686i) q^{12} +3.15282 q^{13} +(97.1750 + 74.5721i) q^{14} -35.8356i q^{15} +(-221.726 + 127.959i) q^{16} -229.376 q^{17} +(172.233 - 224.436i) q^{18} -151.168i q^{19} +(-46.2830 - 172.794i) q^{20} +98.1528 q^{21} +(533.127 + 409.122i) q^{22} -916.032i q^{23} +(-78.5280 + 189.509i) q^{24} +125.000 q^{25} +(7.67772 - 10.0048i) q^{26} -486.319i q^{27} +(473.279 - 126.768i) q^{28} -1004.39 q^{29} +(-113.717 - 87.2666i) q^{30} +1728.79i q^{31} +(-133.893 + 1015.21i) q^{32} +538.492 q^{33} +(-558.575 + 727.879i) q^{34} +342.372i q^{35} +(-292.785 - 1093.09i) q^{36} -841.993 q^{37} +(-479.700 - 368.122i) q^{38} -10.1055i q^{39} +(-661.036 - 273.917i) q^{40} +2525.54 q^{41} +(239.021 - 311.468i) q^{42} +1653.22i q^{43} +(2596.53 - 695.482i) q^{44} +790.746 q^{45} +(-2906.84 - 2230.71i) q^{46} -2665.04i q^{47} +(410.139 + 710.684i) q^{48} +1463.25 q^{49} +(304.399 - 396.663i) q^{50} +735.204i q^{51} +(-13.0517 - 48.7275i) q^{52} -3145.59 q^{53} +(-1543.24 - 1184.28i) q^{54} +1878.34i q^{55} +(750.253 - 1810.56i) q^{56} -484.527 q^{57} +(-2445.89 + 3187.24i) q^{58} -3264.26i q^{59} +(-553.846 + 148.348i) q^{60} -767.207 q^{61} +(5485.98 + 4209.95i) q^{62} +2165.83i q^{63} +(2895.51 + 2897.11i) q^{64} +35.2496 q^{65} +(1311.33 - 1708.80i) q^{66} -1859.46i q^{67} +(949.543 + 3545.05i) q^{68} -2936.10 q^{69} +(1086.45 + 833.741i) q^{70} -2774.43i q^{71} +(-4181.70 - 1732.79i) q^{72} +2252.97 q^{73} +(-2050.41 + 2671.90i) q^{74} -400.654i q^{75} +(-2336.32 + 625.785i) q^{76} -5144.73 q^{77} +(-32.0679 - 24.6089i) q^{78} +906.591i q^{79} +(-2478.97 + 1430.63i) q^{80} +4170.08 q^{81} +(6150.17 - 8014.30i) q^{82} -3833.20i q^{83} +(-406.321 - 1516.97i) q^{84} -2564.50 q^{85} +(5246.15 + 4025.90i) q^{86} +3219.31i q^{87} +(4116.08 - 9933.21i) q^{88} +1824.43 q^{89} +(1925.62 - 2509.28i) q^{90} +96.5478i q^{91} +(-14157.4 + 3792.08i) q^{92} +5541.19 q^{93} +(-8456.97 - 6489.88i) q^{94} -1690.10i q^{95} +(3253.98 + 429.158i) q^{96} +15831.0 q^{97} +(3563.30 - 4643.34i) q^{98} +11882.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	2.43519	−	3.17330i	0.608798	−	0.793325i
$2$	2.43519	−	3.17330i	0.608798	−	0.793325i
$3$		−	3.20523i		−	0.356137i	−0.984018	−	0.178069i	$-0.943015\pi$
$3$		−	3.20523i		−	0.356137i	0.984018	−	0.178069i	$-0.0569849\pi$
$4$	−4.13968	−	15.4552i	−0.258730	−	0.965950i
$5$	11.1803			0.447214
$5$	11.1803			0.447214
$6$	−10.1712	−	7.80536i	−0.282533	−	0.216816i
$7$			30.6227i			0.624953i	0.949926	+	0.312476i	$0.101158\pi$
$7$			30.6227i			0.624953i	−0.949926	+	0.312476i	$0.898842\pi$
$8$	−59.1249	−	24.4999i	−0.923827	−	0.382811i
$9$	70.7265			0.873166
$10$	27.2263	−	35.4786i	0.272263	−	0.354786i
$11$			168.004i			1.38846i	0.719752	+	0.694231i	$0.244255\pi$
$11$			168.004i			1.38846i	−0.719752	+	0.694231i	$0.755745\pi$
$12$	−49.5375	+	13.2686i	−0.344011	+	0.0921433i
$13$	3.15282			0.0186557			0.00932787	−	0.999956i	$-0.497031\pi$
$13$	3.15282			0.0186557			0.00932787	+	0.999956i	$0.497031\pi$
$14$	97.1750	+	74.5721i	0.495791	+	0.380470i
$15$		−	35.8356i		−	0.159269i
$16$	−221.726	+	127.959i	−0.866118	+	0.499840i
$17$	−229.376			−0.793689			−0.396844	−	0.917886i	$-0.629895\pi$
$17$	−229.376			−0.793689			−0.396844	+	0.917886i	$0.629895\pi$
$18$	172.233	−	224.436i	0.531582	−	0.692705i
$19$		−	151.168i		−	0.418747i	−0.977836	−	0.209373i	$-0.932858\pi$
$19$		−	151.168i		−	0.418747i	0.977836	−	0.209373i	$-0.0671424\pi$
$20$	−46.2830	−	172.794i	−0.115708	−	0.431986i
$21$	98.1528			0.222569
$22$	533.127	+	409.122i	1.10150	+	0.845293i
$23$		−	916.032i		−	1.73163i	−0.500365	−	0.865814i	$-0.666801\pi$
$23$		−	916.032i		−	1.73163i	0.500365	−	0.865814i	$-0.333199\pi$
$24$	−78.5280	+	189.509i	−0.136333	+	0.329009i
$25$	125.000			0.200000
$26$	7.67772	−	10.0048i	0.0113576	−	0.0148001i
$27$		−	486.319i		−	0.667104i
$28$	473.279	−	126.768i	0.603673	−	0.161694i
$29$	−1004.39			−1.19428			−0.597141	−	0.802136i	$-0.703697\pi$
$29$	−1004.39			−1.19428			−0.597141	+	0.802136i	$0.703697\pi$
$30$	−113.717	−	87.2666i	−0.126352	−	0.0969629i
$31$			1728.79i			1.79895i	0.436969	+	0.899477i	$0.356052\pi$
$31$			1728.79i			1.79895i	−0.436969	+	0.899477i	$0.643948\pi$
$32$	−133.893	+	1015.21i	−0.130755	+	0.991415i
$33$	538.492			0.494483
$34$	−558.575	+	727.879i	−0.483196	+	0.629653i
$35$			342.372i			0.279487i
$36$	−292.785	−	1093.09i	−0.225914	−	0.843435i
$37$	−841.993			−0.615042			−0.307521	−	0.951541i	$-0.599499\pi$
$37$	−841.993			−0.615042			−0.307521	+	0.951541i	$0.599499\pi$
$38$	−479.700	−	368.122i	−0.332202	−	0.254932i
$39$		−	10.1055i		−	0.00664400i
$40$	−661.036	−	273.917i	−0.413148	−	0.171198i
$41$	2525.54			1.50240			0.751202	−	0.660073i	$-0.229475\pi$
$41$	2525.54			1.50240			0.751202	+	0.660073i	$0.229475\pi$
$42$	239.021	−	311.468i	0.135499	−	0.176569i
$43$			1653.22i			0.894113i	0.894506	+	0.447057i	$0.147528\pi$
$43$			1653.22i			0.894113i	−0.894506	+	0.447057i	$0.852472\pi$
$44$	2596.53	−	695.482i	1.34118	−	0.359237i
$45$	790.746			0.390492
$46$	−2906.84	−	2230.71i	−1.37374	−	1.05421i
$47$		−	2665.04i		−	1.20645i	−0.797573	−	0.603223i	$-0.793883\pi$
$47$		−	2665.04i		−	1.20645i	0.797573	−	0.603223i	$-0.206117\pi$
$48$	410.139	+	710.684i	0.178012	+	0.308457i
$49$	1463.25			0.609434
$50$	304.399	−	396.663i	0.121760	−	0.158665i
$51$			735.204i			0.282662i
$52$	−13.0517	−	48.7275i	−0.00482680	−	0.0180205i
$53$	−3145.59			−1.11982			−0.559912	−	0.828552i	$-0.689165\pi$
$53$	−3145.59			−1.11982			−0.559912	+	0.828552i	$0.689165\pi$
$54$	−1543.24	−	1184.28i	−0.529230	−	0.406132i
$55$			1878.34i			0.620939i
$56$	750.253	−	1810.56i	0.239239	−	0.577348i
$57$	−484.527			−0.149131
$58$	−2445.89	+	3187.24i	−0.727077	+	0.947454i
$59$		−	3264.26i		−	0.937737i	−0.883268	−	0.468869i	$-0.844662\pi$
$59$		−	3264.26i		−	0.937737i	0.883268	−	0.468869i	$-0.155338\pi$
$60$	−553.846	+	148.348i	−0.153846	+	0.0412077i
$61$	−767.207			−0.206183			−0.103091	−	0.994672i	$-0.532873\pi$
$61$	−767.207			−0.206183			−0.103091	+	0.994672i	$0.532873\pi$
$62$	5485.98	+	4209.95i	1.42716	+	1.09520i
$63$			2165.83i			0.545688i
$64$	2895.51	+	2897.11i	0.706911	+	0.707302i
$65$	35.2496			0.00834310
$66$	1311.33	−	1708.80i	0.301040	−	0.392286i
$67$		−	1859.46i		−	0.414227i	−0.978317	−	0.207113i	$-0.933593\pi$
$67$		−	1859.46i		−	0.414227i	0.978317	−	0.207113i	$-0.0664069\pi$
$68$	949.543	+	3545.05i	0.205351	+	0.766663i
$69$	−2936.10			−0.616697
$70$	1086.45	+	833.741i	0.221724	+	0.170151i
$71$		−	2774.43i		−	0.550374i	−0.961391	−	0.275187i	$-0.911260\pi$
$71$		−	2774.43i		−	0.550374i	0.961391	−	0.275187i	$-0.0887398\pi$
$72$	−4181.70	−	1732.79i	−0.806654	−	0.334258i
$73$	2252.97			0.422776			0.211388	−	0.977402i	$-0.432202\pi$
$73$	2252.97			0.422776			0.211388	+	0.977402i	$0.432202\pi$
$74$	−2050.41	+	2671.90i	−0.374437	+	0.487929i
$75$		−	400.654i		−	0.0712274i
$76$	−2336.32	+	625.785i	−0.404488	+	0.108342i
$77$	−5144.73			−0.867723
$78$	−32.0679	−	24.6089i	−0.00527086	−	0.00404486i
$79$			906.591i			0.145264i	0.997359	+	0.0726318i	$0.0231398\pi$
$79$			906.591i			0.145264i	−0.997359	+	0.0726318i	$0.976860\pi$
$80$	−2478.97	+	1430.63i	−0.387340	+	0.223535i
$81$	4170.08			0.635586
$82$	6150.17	−	8014.30i	0.914660	−	1.19189i
$83$		−	3833.20i		−	0.556423i	−0.960520	−	0.278211i	$-0.910258\pi$
$83$		−	3833.20i		−	0.556423i	0.960520	−	0.278211i	$-0.0897416\pi$
$84$	−406.321	−	1516.97i	−0.0575852	−	0.214990i
$85$	−2564.50			−0.354948
$86$	5246.15	+	4025.90i	0.709323	+	0.544334i
$87$			3219.31i			0.425328i
$88$	4116.08	−	9933.21i	0.531519	−	1.28270i
$89$	1824.43			0.230329			0.115164	−	0.993346i	$-0.463261\pi$
$89$	1824.43			0.230329			0.115164	+	0.993346i	$0.463261\pi$
$90$	1925.62	−	2509.28i	0.237731	−	0.309787i
$91$			96.5478i			0.0116590i
$92$	−14157.4	+	3792.08i	−1.67267	+	0.448024i
$93$	5541.19			0.640674
$94$	−8456.97	−	6489.88i	−0.957104	−	0.734482i
$95$		−	1690.10i		−	0.187269i
$96$	3253.98	+	429.158i	0.353080	+	0.0465667i
$97$	15831.0			1.68253			0.841267	−	0.540620i	$-0.181810\pi$
$97$	15831.0			1.68253			0.841267	+	0.540620i	$0.181810\pi$
$98$	3563.30	−	4643.34i	0.371022	−	0.483480i
$99$			11882.3i			1.21236i
$100$	−517.460	−	1931.90i	−0.0517460	−	0.193190i
$101$	−12246.1			−1.20048			−0.600240	−	0.799820i	$-0.704928\pi$
$101$	−12246.1			−1.20048			−0.600240	+	0.799820i	$0.704928\pi$
$102$	2333.02	+	1790.36i	0.224243	+	0.172084i
$103$		−	1393.83i		−	0.131382i	−0.997840	−	0.0656908i	$-0.979075\pi$
$103$		−	1393.83i		−	0.131382i	0.997840	−	0.0656908i	$-0.0209251\pi$
$104$	−186.410	−	77.2439i	−0.0172347	−	0.00714163i
$105$	1097.38			0.0995358
$106$	−7660.11	+	9981.89i	−0.681747	+	0.888385i
$107$			19221.2i			1.67886i	0.543470	+	0.839429i	$0.317110\pi$
$107$			19221.2i			1.67886i	−0.543470	+	0.839429i	$0.682890\pi$
$108$	−7516.15	+	2013.20i	−0.644389	+	0.172600i
$109$	3429.78			0.288678			0.144339	−	0.989528i	$-0.453894\pi$
$109$	3429.78			0.288678			0.144339	+	0.989528i	$0.453894\pi$
$110$	5960.54	+	4574.12i	0.492607	+	0.378027i
$111$			2698.78i			0.219039i
$112$	−3918.45	−	6789.85i	−0.312376	−	0.541282i
$113$	−6436.39			−0.504064			−0.252032	−	0.967719i	$-0.581099\pi$
$113$	−6436.39			−0.504064			−0.252032	+	0.967719i	$0.581099\pi$
$114$	−1179.92	+	1537.55i	−0.0907908	+	0.118310i
$115$		−	10241.5i		−	0.774408i
$116$	4157.86	+	15523.1i	0.308997	+	1.15362i
$117$	222.988			0.0162896
$118$	−10358.5	−	7949.11i	−0.743931	−	0.570893i
$119$		−	7024.11i		−	0.496018i
$120$	−877.970	+	2118.78i	−0.0609701	+	0.147137i
$121$	−13584.3			−0.927827
$122$	−1868.30	+	2434.58i	−0.125524	+	0.163570i
$123$		−	8094.94i		−	0.535061i
$124$	26718.9	−	7156.65i	1.73770	−	0.465443i
$125$	1397.54			0.0894427
$126$	6872.84	+	5274.22i	0.432908	+	0.332213i
$127$		−	3262.31i		−	0.202264i	−0.994873	−	0.101132i	$-0.967754\pi$
$127$		−	3262.31i		−	0.202264i	0.994873	−	0.101132i	$-0.0322464\pi$
$128$	16244.5	−	2133.30i	0.991487	−	0.130206i
$129$	5298.94			0.318427
$130$	85.8396	−	111.858i	0.00507926	−	0.00661879i
$131$		−	24866.0i		−	1.44899i	−0.689282	−	0.724493i	$-0.742074\pi$
$131$		−	24866.0i		−	1.44899i	0.689282	−	0.724493i	$-0.257926\pi$
$132$	−2229.18	−	8322.50i	−0.127938	−	0.477646i
$133$	4629.16			0.261697
$134$	−5900.64	−	4528.15i	−0.328617	−	0.252181i
$135$		−	5437.21i		−	0.298338i
$136$	13561.8	+	5619.69i	0.733231	+	0.303833i
$137$	−4464.13			−0.237846			−0.118923	−	0.992903i	$-0.537944\pi$
$137$	−4464.13			−0.237846			−0.118923	+	0.992903i	$0.537944\pi$
$138$	−7149.96	+	9317.12i	−0.375444	+	0.489242i
$139$			2234.68i			0.115661i	0.998326	+	0.0578304i	$0.0184183\pi$
$139$			2234.68i			0.115661i	−0.998326	+	0.0578304i	$0.981582\pi$
$140$	5291.42	−	1417.31i	0.269971	−	0.0723117i
$141$	−8542.07			−0.429660
$142$	−8804.12	−	6756.28i	−0.436626	−	0.335067i
$143$			529.686i			0.0259028i
$144$	−15681.9	+	9050.10i	−0.756265	+	0.436444i
$145$	−11229.4			−0.534099
$146$	5486.42	−	7149.36i	0.257385	−	0.335399i
$147$		−	4690.06i		−	0.217042i
$148$	3485.58	+	13013.2i	0.159130	+	0.594100i
$149$	5918.85			0.266603			0.133301	−	0.991076i	$-0.457442\pi$
$149$	5918.85			0.266603			0.133301	+	0.991076i	$0.457442\pi$
$150$	−1271.40	−	975.670i	−0.0565065	−	0.0433631i
$151$		−	2779.95i		−	0.121922i	−0.998140	−	0.0609611i	$-0.980583\pi$
$151$		−	2779.95i		−	0.121922i	0.998140	−	0.0609611i	$-0.0194166\pi$
$152$	−3703.59	+	8937.77i	−0.160301	+	0.386849i
$153$	−16223.0			−0.693022
$154$	−12528.4	+	16325.8i	−0.528268	+	0.688386i
$155$			19328.5i			0.804516i
$156$	−156.183	+	41.8336i	−0.00641777	+	0.00171900i
$157$	15602.7			0.632995			0.316497	−	0.948593i	$-0.397493\pi$
$157$	15602.7			0.632995			0.316497	+	0.948593i	$0.397493\pi$
$158$	2876.89	+	2207.72i	0.115241	+	0.0884363i
$159$			10082.3i			0.398811i
$160$	−1496.97	+	11350.4i	−0.0584754	+	0.443374i
$161$	28051.3			1.08219
$162$	10154.9	−	13232.9i	0.386943	−	0.504226i
$163$			40312.2i			1.51726i	0.651520	+	0.758632i	$0.274132\pi$
$163$			40312.2i			1.51726i	−0.651520	+	0.758632i	$0.725868\pi$
$164$	−10454.9	−	39032.7i	−0.388717	−	1.45125i
$165$	6020.52			0.221139
$166$	−12163.9	−	9334.57i	−0.441424	−	0.338749i
$167$			21868.7i			0.784135i	0.919936	+	0.392068i	$0.128240\pi$
$167$			21868.7i			0.784135i	−0.919936	+	0.392068i	$0.871760\pi$
$168$	−5803.28	−	2404.74i	−0.205615	−	0.0852018i
$169$	−28551.1			−0.999652
$170$	−6245.05	+	8137.94i	−0.216092	+	0.281590i
$171$		−	10691.6i		−	0.365636i
$172$	25550.8	−	6843.78i	0.863669	−	0.231334i
$173$	43256.9			1.44532			0.722659	−	0.691205i	$-0.242920\pi$
$173$	43256.9			1.44532			0.722659	+	0.691205i	$0.242920\pi$
$174$	10215.8	+	7839.64i	0.337424	+	0.258939i
$175$			3827.83i			0.124991i
$176$	−21497.6	−	37250.9i	−0.694009	−	1.20257i
$177$	−10462.7			−0.333963
$178$	4442.85	−	5789.48i	0.140224	−	0.182726i
$179$		−	9686.18i		−	0.302306i	−0.988510	−	0.151153i	$-0.951701\pi$
$179$		−	9686.18i		−	0.302306i	0.988510	−	0.151153i	$-0.0482986\pi$
$180$	−3273.43	−	12221.1i	−0.101032	−	0.377196i
$181$	18040.2			0.550661			0.275330	−	0.961350i	$-0.411213\pi$
$181$	18040.2			0.550661			0.275330	+	0.961350i	$0.411213\pi$
$182$	306.375	+	235.112i	0.00924934	+	0.00709795i
$183$			2459.08i			0.0734294i
$184$	−22442.7	+	54160.3i	−0.662887	+	1.59972i
$185$	−9413.77			−0.275055
$186$	13493.9	−	17583.9i	0.390041	−	0.508263i
$187$		−	38536.1i		−	1.10201i
$188$	−41188.7	+	11032.4i	−1.16537	+	0.312144i
$189$	14892.4			0.416908
$190$	−5363.21	−	4115.73i	−0.148565	−	0.114009i
$191$			25591.6i			0.701504i	0.936468	+	0.350752i	$0.114074\pi$
$191$			25591.6i			0.701504i	−0.936468	+	0.350752i	$0.885926\pi$
$192$	9285.92	−	9280.78i	0.251897	−	0.251757i
$193$	−37818.2			−1.01528			−0.507641	−	0.861569i	$-0.669482\pi$
$193$	−37818.2			−1.01528			−0.507641	+	0.861569i	$0.669482\pi$
$194$	38551.4	−	50236.4i	1.02432	−	1.33480i
$195$		−	112.983i		−	0.00297129i
$196$	−6057.39	−	22614.8i	−0.157679	−	0.588683i
$197$	−13762.7			−0.354625			−0.177313	−	0.984155i	$-0.556740\pi$
$197$	−13762.7			−0.354625			−0.177313	+	0.984155i	$0.556740\pi$
$198$	37706.2	+	28935.7i	0.961795	+	0.738081i
$199$		−	23429.5i		−	0.591640i	−0.955244	−	0.295820i	$-0.904407\pi$
$199$		−	23429.5i		−	0.591640i	0.955244	−	0.295820i	$-0.0955928\pi$
$200$	−7390.61	−	3062.49i	−0.184765	−	0.0765623i
$201$	−5960.02			−0.147522
$202$	−29821.6	+	38860.6i	−0.730850	+	0.952372i
$203$		−	30757.2i		−	0.746370i
$204$	11362.7	−	3043.51i	0.273037	−	0.0731331i
$205$	28236.4			0.671895
$206$	−4423.03	−	3394.24i	−0.104228	−	0.0799848i
$207$		−	64787.7i		−	1.51200i
$208$	−699.063	+	403.432i	−0.0161581	+	0.00932489i
$209$	25396.7			0.581414
$210$	2672.34	−	3482.32i	0.0605972	−	0.0789643i
$211$			50926.3i			1.14387i	0.820299	+	0.571935i	$0.193807\pi$
$211$			50926.3i			1.14387i	−0.820299	+	0.571935i	$0.806193\pi$
$212$	13021.7	+	48615.7i	0.289732	+	1.08169i
$213$	−8892.71			−0.196009
$214$	60994.8	+	46807.4i	1.33188	+	1.02208i
$215$			18483.5i			0.399860i
$216$	−11914.8	+	28753.6i	−0.255375	+	0.616288i
$217$	−52940.3			−1.12426
$218$	8352.18	−	10883.7i	0.175747	−	0.229016i
$219$		−	7221.30i		−	0.150566i
$220$	29030.1	−	7775.73i	0.599796	−	0.160656i
$221$	−723.182			−0.0148069
$222$	8564.05	+	6572.06i	0.173769	+	0.133351i
$223$			518.539i			0.0104273i	0.999986	+	0.00521365i	$0.00165956\pi$
$223$			518.539i			0.0104273i	−0.999986	+	0.00521365i	$0.998340\pi$
$224$	−31088.4	−	4100.16i	−0.619587	−	0.0817156i
$225$	8840.81			0.174633
$226$	−15673.9	+	20424.6i	−0.306873	+	0.399887i
$227$			27965.3i			0.542711i	0.962479	+	0.271355i	$0.0874719\pi$
$227$			27965.3i			0.542711i	−0.962479	+	0.271355i	$0.912528\pi$
$228$	2005.79	+	7488.47i	0.0385847	+	0.144053i
$229$	−69032.7			−1.31639			−0.658194	−	0.752848i	$-0.728679\pi$
$229$	−69032.7			−1.31639			−0.658194	+	0.752848i	$0.728679\pi$
$230$	−32499.5	−	24940.1i	−0.614357	−	0.471458i
$231$			16490.1i			0.309028i
$232$	59384.6	+	24607.5i	1.10331	+	0.457185i
$233$	−73445.5			−1.35286			−0.676431	−	0.736506i	$-0.736474\pi$
$233$	−73445.5			−1.35286			−0.676431	+	0.736506i	$0.736474\pi$
$234$	543.018	−	707.608i	0.00991706	−	0.0129229i
$235$		−	29796.0i		−	0.539539i
$236$	−50449.8	+	13513.0i	−0.905807	+	0.242621i
$237$	2905.84			0.0517338
$238$	−22289.6	−	17105.1i	−0.393503	−	0.301975i
$239$		−	5261.50i		−	0.0921115i	−0.998939	−	0.0460558i	$-0.985335\pi$
$239$		−	5261.50i		−	0.0921115i	0.998939	−	0.0460558i	$-0.0146652\pi$
$240$	4585.49	+	7945.69i	0.0796092	+	0.137946i
$241$	83930.3			1.44506			0.722528	−	0.691342i	$-0.242980\pi$
$241$	83930.3			1.44506			0.722528	+	0.691342i	$0.242980\pi$
$242$	−33080.4	+	43107.1i	−0.564859	+	0.736069i
$243$		−	52757.9i		−	0.893460i
$244$	3175.99	+	11857.3i	0.0533457	+	0.199162i
$245$	16359.7			0.272547
$246$	−25687.7	−	19712.7i	−0.424478	−	0.325744i
$247$		−	476.604i		−	0.00781203i
$248$	42355.3	−	102215.i	0.688660	−	1.66192i
$249$	−12286.3			−0.198163
$250$	3403.28	−	4434.82i	0.0544526	−	0.0709572i
$251$			96363.0i			1.52955i	0.644299	+	0.764774i	$0.277149\pi$
$251$			96363.0i			1.52955i	−0.644299	+	0.764774i	$0.722851\pi$
$252$	33473.4	−	8965.86i	0.527107	−	0.141186i
$253$	153897.			2.40430
$254$	−10352.3	−	7944.36i	−0.160461	−	0.123138i
$255$			8219.83i			0.126410i
$256$	32788.9	−	56743.7i	0.500320	−	0.865841i
$257$	60685.4			0.918794			0.459397	−	0.888231i	$-0.348066\pi$
$257$	60685.4			0.918794			0.459397	+	0.888231i	$0.348066\pi$
$258$	12903.9	−	16815.1i	0.193858	−	0.252616i
$259$		−	25784.1i		−	0.384372i
$260$	−145.922	−	544.790i	−0.00215861	−	0.00805902i
$261$	−71037.1			−1.04281
$262$	−78907.4	−	60553.6i	−1.14952	−	0.882140i
$263$		−	47710.6i		−	0.689769i	−0.938645	−	0.344884i	$-0.887918\pi$
$263$		−	47710.6i		−	0.689769i	0.938645	−	0.344884i	$-0.112082\pi$
$264$	−31838.3	−	13193.0i	−0.456816	−	0.189294i
$265$	−35168.7			−0.500801
$266$	11272.9	−	14689.7i	0.159321	−	0.207611i
$267$		−	5847.74i		−	0.0820286i
$268$	−28738.4	+	7697.59i	−0.400122	+	0.107173i
$269$	65980.8			0.911828			0.455914	−	0.890024i	$-0.349313\pi$
$269$	65980.8			0.911828			0.455914	+	0.890024i	$0.349313\pi$
$270$	−17253.9	−	13240.7i	−0.236679	−	0.181628i
$271$		−	15705.1i		−	0.213847i	−0.994267	−	0.106924i	$-0.965900\pi$
$271$		−	15705.1i		−	0.213847i	0.994267	−	0.106924i	$-0.0341000\pi$
$272$	50858.7	−	29350.7i	0.687428	−	0.396717i
$273$	309.458			0.00415219
$274$	−10871.0	+	14166.0i	−0.144800	+	0.188689i
$275$			21000.5i			0.277692i
$276$	12154.5	+	45377.9i	0.159558	+	0.595699i
$277$	−90555.4			−1.18020			−0.590099	−	0.807331i	$-0.700911\pi$
$277$	−90555.4			−1.18020			−0.590099	+	0.807331i	$0.700911\pi$
$278$	7091.32	+	5441.88i	0.0917566	+	0.0704140i
$279$			122272.i			1.57079i
$280$	8388.08	−	20242.7i	0.106991	−	0.258198i
$281$	24002.4			0.303978			0.151989	−	0.988382i	$-0.451432\pi$
$281$	24002.4			0.303978			0.151989	+	0.988382i	$0.451432\pi$
$282$	−20801.6	+	27106.6i	−0.261576	+	0.340860i
$283$			55978.1i			0.698949i	0.936946	+	0.349475i	$0.113640\pi$
$283$			55978.1i			0.698949i	−0.936946	+	0.349475i	$0.886360\pi$
$284$	−42879.4	+	11485.3i	−0.531634	+	0.142398i
$285$	−5417.18			−0.0666935
$286$	1680.85	+	1289.89i	0.0205493	+	0.0157696i
$287$			77338.8i			0.938931i
$288$	−9469.78	+	71802.1i	−0.114171	+	0.865670i
$289$	−30907.6			−0.370058
$290$	−27345.8	+	35634.4i	−0.325159	+	0.423715i
$291$		−	50741.9i		−	0.599213i
$292$	−9326.58	−	34820.1i	−0.109385	−	0.408380i
$293$	−5265.22			−0.0613312			−0.0306656	−	0.999530i	$-0.509763\pi$
$293$	−5265.22			−0.0613312			−0.0306656	+	0.999530i	$0.509763\pi$
$294$	−14883.0	−	11421.2i	−0.172185	−	0.132135i
$295$		−	36495.6i		−	0.419369i
$296$	49782.7	+	20628.8i	0.568192	+	0.235445i
$297$	81703.5			0.926249
$298$	14413.5	−	18782.3i	0.162307	−	0.211503i
$299$		−	2888.08i		−	0.0323048i
$300$	−6192.19	+	1658.58i	−0.0688021	+	0.0184287i
$301$	−50625.9			−0.558778
$302$	−8821.62	−	6769.71i	−0.0967240	−	0.0742260i
$303$			39251.6i			0.427536i
$304$	19343.3	+	33517.8i	0.209306	+	0.362684i
$305$	−8577.63			−0.0922078
$306$	−39506.0	+	51480.3i	−0.421911	+	0.549792i
$307$			6803.29i			0.0721842i	0.999348	+	0.0360921i	$0.0114910\pi$
$307$			6803.29i			0.0721842i	−0.999348	+	0.0360921i	$0.988509\pi$
$308$	21297.5	+	79512.8i	0.224506	+	0.838177i
$309$	−4467.54			−0.0467898
$310$	61335.2	+	47068.6i	0.638243	+	0.489788i
$311$		−	175182.i		−	1.81121i	−0.424120	−	0.905606i	$-0.639417\pi$
$311$		−	175182.i		−	1.81121i	0.424120	−	0.905606i	$-0.360583\pi$
$312$	−247.585	+	597.488i	−0.00254340	+	0.00613791i
$313$	−100372.			−1.02453			−0.512264	−	0.858828i	$-0.671193\pi$
$313$	−100372.			−1.02453			−0.512264	+	0.858828i	$0.671193\pi$
$314$	37995.5	−	49512.0i	0.385366	−	0.502171i
$315$			24214.8i			0.244039i
$316$	14011.5	−	3752.99i	0.140317	−	0.0375841i
$317$	−50852.5			−0.506051			−0.253025	−	0.967460i	$-0.581426\pi$
$317$	−50852.5			−0.506051			−0.253025	+	0.967460i	$0.581426\pi$
$318$	31994.3	+	24552.4i	0.316387	+	0.242795i
$319$		−	168742.i		−	1.65822i
$320$	32372.8	+	32390.7i	0.316140	+	0.316315i
$321$	61608.6			0.597903
$322$	68310.4	−	89015.3i	0.658833	−	0.858525i
$323$			34674.2i			0.332355i
$324$	−17262.8	−	64449.4i	−0.164445	−	0.613944i
$325$	394.103			0.00373115
$326$	127923.	+	98167.9i	1.20368	+	0.923707i
$327$		−	10993.3i		−	0.102809i
$328$	−149322.	−	61875.5i	−1.38796	−	0.575137i
$329$	81610.6			0.753971
$330$	14661.1	−	19104.9i	0.134629	−	0.175436i
$331$		−	136931.i		−	1.24982i	−0.780698	−	0.624908i	$-0.785136\pi$
$331$		−	136931.i		−	1.24982i	0.780698	−	0.624908i	$-0.214864\pi$
$332$	−59242.8	+	15868.2i	−0.537477	+	0.143963i
$333$	−59551.2			−0.537034
$334$	69396.1	+	53254.6i	0.622074	+	0.477380i
$335$		−	20789.4i		−	0.185248i
$336$	−21763.0	+	12559.5i	−0.192771	+	0.111249i
$337$	196912.			1.73385			0.866926	−	0.498437i	$-0.166093\pi$
$337$	196912.			1.73385			0.866926	+	0.498437i	$0.166093\pi$
$338$	−69527.3	+	90601.1i	−0.608586	+	0.793049i
$339$			20630.1i			0.179516i
$340$	10616.2	+	39634.9i	0.0918358	+	0.342862i
$341$	−290444.			−2.49778
$342$	−33927.5	−	26036.0i	−0.290068	−	0.222598i
$343$			118334.i			1.00582i
$344$	40503.7	−	97746.2i	0.342277	−	0.826006i
$345$	−32826.5			−0.275795
$346$	105339.	−	137267.i	0.879907	−	1.14661i
$347$		−	68004.5i		−	0.564779i	−0.959300	−	0.282390i	$-0.908873\pi$
$347$		−	68004.5i		−	0.564779i	0.959300	−	0.282390i	$-0.0911271\pi$
$348$	49755.1	−	13326.9i	0.410846	−	0.110045i
$349$	−25273.0			−0.207494			−0.103747	−	0.994604i	$-0.533083\pi$
$349$	−25273.0			−0.207494			−0.103747	+	0.994604i	$0.533083\pi$
$350$	12146.9	+	9321.51i	0.0991581	+	0.0760940i
$351$		−	1533.28i		−	0.0124453i
$352$	−170559.	−	22494.5i	−1.37654	−	0.181548i
$353$	−23471.6			−0.188362			−0.0941810	−	0.995555i	$-0.530023\pi$
$353$	−23471.6			−0.188362			−0.0941810	+	0.995555i	$0.530023\pi$
$354$	−25478.8	+	33201.4i	−0.203316	+	0.264941i
$355$		−	31019.1i		−	0.246135i
$356$	−7552.57	−	28197.0i	−0.0595929	−	0.222486i
$357$	−22513.9			−0.176650
$358$	−30737.2	−	23587.7i	−0.239827	−	0.184043i
$359$			175609.i			1.36257i	0.732018	+	0.681285i	$0.238579\pi$
$359$			175609.i			1.36257i	−0.732018	+	0.681285i	$0.761421\pi$
$360$	−46752.8	−	19373.2i	−0.360747	−	0.149485i
$361$	107469.			0.824651
$362$	43931.4	−	57247.0i	0.335241	−	0.436853i
$363$			43540.9i			0.330434i
$364$	1492.17	−	399.677i	0.0112620	−	0.00301652i
$365$	25189.0			0.189071
$366$	7803.39	+	5988.33i	0.0582534	+	0.0447037i
$367$			191326.i			1.42050i	0.703950	+	0.710250i	$0.251418\pi$
$367$			191326.i			1.42050i	−0.703950	+	0.710250i	$0.748582\pi$
$368$	117215.	+	203108.i	0.865538	+	1.49979i
$369$	178623.			1.31185
$370$	−22924.3	+	29872.7i	−0.167453	+	0.218208i
$371$		−	96326.3i		−	0.699837i
$372$	−22938.7	−	85640.2i	−0.165762	−	0.618859i
$373$	227739.			1.63689			0.818446	−	0.574584i	$-0.194836\pi$
$373$	227739.			1.63689			0.818446	+	0.574584i	$0.194836\pi$
$374$	−122287.	−	93842.7i	−0.874250	−	0.670899i
$375$		−	4479.45i		−	0.0318539i
$376$	−65293.2	+	157570.i	−0.461841	+	1.11455i
$377$	−3166.67			−0.0222802
$378$	36265.8	−	47258.0i	0.253813	−	0.330744i
$379$			115080.i			0.801167i	0.916260	+	0.400583i	$0.131192\pi$
$379$			115080.i			0.801167i	−0.916260	+	0.400583i	$0.868808\pi$
$380$	−26120.9	+	6996.49i	−0.180893	+	0.0484522i
$381$	−10456.5			−0.0720336
$382$	81209.8	+	62320.4i	0.556521	+	0.427074i
$383$		−	112755.i		−	0.768670i	−0.923194	−	0.384335i	$-0.874431\pi$
$383$		−	112755.i		−	0.768670i	0.923194	−	0.384335i	$-0.125569\pi$
$384$	−6837.71	−	52067.5i	−0.0463712	−	0.353105i
$385$	−57519.8			−0.388057
$386$	−92094.7	+	120009.i	−0.618102	+	0.805449i
$387$			116926.i			0.780710i
$388$	−65535.1	−	244671.i	−0.435322	−	1.62524i
$389$	−183416.			−1.21210			−0.606049	−	0.795427i	$-0.707246\pi$
$389$	−183416.			−1.21210			−0.606049	+	0.795427i	$0.707246\pi$
$390$	−358.530	−	275.136i	−0.00235720	−	0.00180891i
$391$			210116.i			1.37437i
$392$	−86514.6	−	35849.6i	−0.563012	−	0.233298i
$393$	−79701.5			−0.516038
$394$	−33514.7	+	43673.1i	−0.215895	+	0.281333i
$395$			10136.0i			0.0649639i
$396$	183644.	−	49189.0i	1.17108	−	0.313673i
$397$	64357.2			0.408335			0.204167	−	0.978936i	$-0.434551\pi$
$397$	64357.2			0.408335			0.204167	+	0.978936i	$0.434551\pi$
$398$	−74349.0	−	57055.4i	−0.469363	−	0.360189i
$399$		−	14837.5i		−	0.0932000i
$400$	−27715.8	+	15994.9i	−0.173224	+	0.0999680i
$401$	95942.1			0.596651			0.298326	−	0.954464i	$-0.403572\pi$
$401$	95942.1			0.596651			0.298326	+	0.954464i	$0.403572\pi$
$402$	−14513.8	+	18912.9i	−0.0898108	+	0.117033i
$403$			5450.58i			0.0335608i
$404$	50694.9	+	189266.i	0.310600	+	1.15960i
$405$	46622.9			0.284243
$406$	−97601.7	−	74899.6i	−0.592114	−	0.454389i
$407$		−	141458.i		−	0.853963i
$408$	18012.4	−	43468.9i	0.108206	−	0.261131i
$409$	−115605.			−0.691084			−0.345542	−	0.938403i	$-0.612305\pi$
$409$	−115605.			−0.691084			−0.345542	+	0.938403i	$0.612305\pi$
$410$	68761.0	−	89602.6i	0.409048	−	0.533031i
$411$			14308.6i			0.0847058i
$412$	−21541.9	+	5769.99i	−0.126908	+	0.0339923i
$413$	99960.5			0.586041
$414$	−205591.	−	157770.i	−1.19951	−	0.920503i
$415$		−	42856.5i		−	0.248840i
$416$	−422.141	+	3200.77i	−0.00243933	+	0.0184956i
$417$	7162.68			0.0411911
$418$	61846.0	−	80591.5i	0.353964	−	0.461250i
$419$		−	95151.9i		−	0.541987i	−0.962581	−	0.270994i	$-0.912648\pi$
$419$		−	95151.9i		−	0.541987i	0.962581	−	0.270994i	$-0.0873523\pi$
$420$	−4542.81	−	16960.3i	−0.0257529	−	0.0961466i
$421$	−91153.3			−0.514290			−0.257145	−	0.966373i	$-0.582782\pi$
$421$	−91153.3			−0.514290			−0.257145	+	0.966373i	$0.582782\pi$
$422$	161604.	+	124015.i	0.907461	+	0.696386i
$423$		−	188489.i		−	1.05343i
$424$	185983.	+	77066.6i	1.03452	+	0.428681i
$425$	−28672.0			−0.158738
$426$	−21655.5	+	28219.3i	−0.119330	+	0.155499i
$427$		−	23493.9i		−	0.128855i
$428$	297068.	−	79569.7i	1.62169	−	0.434371i
$429$	1697.77			0.00922495
$430$	58653.7	+	45010.9i	0.317219	+	0.243434i
$431$		−	45720.8i		−	0.246127i	−0.992399	−	0.123063i	$-0.960728\pi$
$431$		−	45720.8i		−	0.246127i	0.992399	−	0.123063i	$-0.0392719\pi$
$432$	62228.9	+	107830.i	0.333445	+	0.577791i
$433$	−41171.0			−0.219592			−0.109796	−	0.993954i	$-0.535020\pi$
$433$	−41171.0			−0.219592			−0.109796	+	0.993954i	$0.535020\pi$
$434$	−128920.	+	167995.i	−0.684448	+	0.891904i
$435$			35993.0i			0.190213i
$436$	−14198.2	−	53008.0i	−0.0746896	−	0.278848i
$437$	−138474.			−0.725114
$438$	−22915.4	−	17585.3i	−0.119448	−	0.0916644i
$439$		−	305545.i		−	1.58543i	−0.609595	−	0.792713i	$-0.708668\pi$
$439$		−	305545.i		−	1.58543i	0.609595	−	0.792713i	$-0.291332\pi$
$440$	46019.2	−	111057.i	0.237703	−	0.573640i
$441$	103491.			0.532138
$442$	−1761.09	+	2294.87i	−0.00901438	+	0.0117467i
$443$		−	301615.i		−	1.53690i	−0.639909	−	0.768451i	$-0.721028\pi$
$443$		−	301615.i		−	1.53690i	0.639909	−	0.768451i	$-0.278972\pi$
$444$	41710.2	−	11172.1i	0.211581	−	0.0566720i
$445$	20397.8			0.103006
$446$	1645.48	+	1262.74i	0.00827224	+	0.00634812i
$447$		−	18971.3i		−	0.0949472i
$448$	−88717.3	+	88668.2i	−0.442030	+	0.441786i
$449$	44795.9			0.222201			0.111100	−	0.993809i	$-0.464563\pi$
$449$	44795.9			0.222201			0.111100	+	0.993809i	$0.464563\pi$
$450$	21529.1	−	28054.5i	0.106316	−	0.138541i
$451$			424301.i			2.08603i
$452$	26644.6	+	99475.7i	0.130416	+	0.486900i
$453$	−8910.39			−0.0434210
$454$	88742.5	+	68101.0i	0.430546	+	0.330401i
$455$			1079.44i			0.00521404i
$456$	28647.6	+	11870.9i	0.137771	+	0.0570891i
$457$	−260232.			−1.24603			−0.623014	−	0.782211i	$-0.714092\pi$
$457$	−260232.			−1.24603			−0.623014	+	0.782211i	$0.714092\pi$
$458$	−168108.	+	219062.i	−0.801414	+	1.04432i
$459$			111550.i			0.529473i
$460$	−158285.	+	42396.7i	−0.748039	+	0.200363i
$461$	40597.5			0.191028			0.0955140	−	0.995428i	$-0.469551\pi$
$461$	40597.5			0.191028			0.0955140	+	0.995428i	$0.469551\pi$
$462$	52327.9	+	40156.5i	0.245160	+	0.188136i
$463$			223112.i			1.04079i	0.853927	+	0.520393i	$0.174215\pi$
$463$			223112.i			1.04079i	−0.853927	+	0.520393i	$0.825785\pi$
$464$	222700.	−	128521.i	1.03439	−	0.596950i
$465$	61952.4			0.286518
$466$	−178854.	+	233065.i	−0.823619	+	1.07326i
$467$		−	149775.i		−	0.686760i	−0.939197	−	0.343380i	$-0.888428\pi$
$467$		−	149775.i		−	0.686760i	0.939197	−	0.343380i	$-0.111572\pi$
$468$	−923.098	−	3446.32i	−0.00421460	−	0.0157349i
$469$	56941.8			0.258872
$470$	−94551.8	−	72559.1i	−0.428030	−	0.328470i
$471$		−	50010.3i		−	0.225433i
$472$	−79974.2	+	192999.i	−0.358976	+	0.866307i
$473$	−277747.			−1.24144
$474$	7076.27	−	9221.09i	0.0314954	−	0.0410417i
$475$		−	18895.9i		−	0.0837494i
$476$	−108559.	+	29077.5i	−0.479128	+	0.128335i
$477$	−222476.			−0.977793
$478$	−16696.3	−	12812.8i	−0.0730744	−	0.0560773i
$479$			255892.i			1.11528i	0.830081	+	0.557642i	$0.188294\pi$
$479$			255892.i			1.11528i	−0.830081	+	0.557642i	$0.811706\pi$
$480$	36380.6	+	4798.14i	0.157902	+	0.0208252i
$481$	−2654.65			−0.0114741
$482$	204386.	−	266336.i	0.879747	−	1.14640i
$483$		−	89911.1i		−	0.385406i
$484$	56234.7	+	209948.i	0.240057	+	0.896234i
$485$	176995.			0.752452
$486$	−167417.	−	128476.i	−0.708804	−	0.543937i
$487$		−	88785.3i		−	0.374354i	−0.982326	−	0.187177i	$-0.940066\pi$
$487$		−	88785.3i		−	0.374354i	0.982326	−	0.187177i	$-0.0599339\pi$
$488$	45361.0	+	18796.5i	0.190477	+	0.0789292i
$489$	129210.			0.540354
$490$	39838.9	−	51914.1i	0.165926	−	0.216219i
$491$			201316.i			0.835055i	0.908664	+	0.417528i	$0.137103\pi$
$491$			201316.i			0.835055i	−0.908664	+	0.417528i	$0.862897\pi$
$492$	−125109.	+	33510.5i	−0.516842	+	0.138436i
$493$	230383.			0.947889
$494$	−1512.41	−	1160.62i	−0.00619748	−	0.00475595i
$495$			132848.i			0.542183i
$496$	−221215.	−	383319.i	−0.899189	−	1.55811i
$497$	84960.6			0.343958
$498$	−29919.5	+	38988.1i	−0.120641	+	0.157208i
$499$		−	357435.i		−	1.43548i	−0.696313	−	0.717739i	$-0.745177\pi$
$499$		−	357435.i		−	1.43548i	0.696313	−	0.717739i	$-0.254823\pi$
$500$	−5785.38	−	21599.3i	−0.0231415	−	0.0863972i
$501$	70094.4			0.279260
$502$	305789.	+	234662.i	1.21343	+	0.931185i
$503$			238591.i			0.943015i	0.881862	+	0.471507i	$0.156290\pi$
$503$			238591.i			0.943015i	−0.881862	+	0.471507i	$0.843710\pi$
$504$	53062.8	−	128055.i	0.208895	−	0.504121i
$505$	−136916.			−0.536871
$506$	374769.	−	488361.i	1.46373	−	1.90739i
$507$			91512.8i			0.356013i
$508$	−50419.7	+	13504.9i	−0.195377	+	0.0523317i
$509$	108780.			0.419870			0.209935	−	0.977715i	$-0.432675\pi$
$509$	108780.			0.419870			0.209935	+	0.977715i	$0.432675\pi$
$510$	26084.0	+	20016.9i	0.100284	+	0.0769583i
$511$			68992.0i			0.264215i
$512$	−100218.	−	242231.i	−0.382300	−	0.924038i
$513$	−73515.6			−0.279348
$514$	147781.	−	192573.i	0.559360	−	0.728902i
$515$		−	15583.5i		−	0.0587556i
$516$	−21935.9	−	81896.2i	−0.0823866	−	0.307584i
$517$	447737.			1.67510
$518$	−81820.6	−	62789.2i	−0.304932	−	0.234005i
$519$		−	138649.i		−	0.514731i
$520$	−2084.13	−	863.613i	−0.00770758	−	0.00319383i
$521$	318609.			1.17377			0.586884	−	0.809671i	$-0.300354\pi$
$521$	318609.			1.17377			0.586884	+	0.809671i	$0.300354\pi$
$522$	−172989.	+	225422.i	−0.634859	+	0.827285i
$523$			265583.i			0.970948i	0.874251	+	0.485474i	$0.161353\pi$
$523$			265583.i			0.970948i	−0.874251	+	0.485474i	$0.838647\pi$
$524$	−384310.	+	102937.i	−1.39965	+	0.374896i
$525$	12269.1			0.0445138
$526$	−151400.	−	116185.i	−0.547211	−	0.419930i
$527$		−	396544.i		−	1.42781i
$528$	−119398.	+	68904.9i	−0.428280	+	0.247162i
$529$	−559273.			−1.99854
$530$	−85642.6	+	111601.i	−0.304887	+	0.397298i
$531$		−	230870.i		−	0.818801i
$532$	−19163.2	−	71544.5i	−0.0677088	−	0.252786i
$533$	7962.57			0.0280284
$534$	−18556.6	−	14240.4i	−0.0650754	−	0.0499388i
$535$			214900.i			0.750808i
$536$	−45556.7	+	109941.i	−0.158571	+	0.382674i
$537$	−31046.5			−0.107662
$538$	160676.	−	209377.i	0.555119	−	0.723376i
$539$			245832.i			0.846176i
$540$	−84033.1	+	22508.3i	−0.288179	+	0.0771890i
$541$	169497.			0.579118			0.289559	−	0.957160i	$-0.406491\pi$
$541$	169497.			0.579118			0.289559	+	0.957160i	$0.406491\pi$
$542$	−49837.2	−	38245.1i	−0.169650	−	0.130190i
$543$		−	57823.1i		−	0.196111i
$544$	30711.8	−	232865.i	0.103779	−	0.786875i
$545$	38346.1			0.129101
$546$	753.590	−	982.004i	0.00252784	−	0.00329403i
$547$		−	96446.8i		−	0.322339i	−0.986927	−	0.161170i	$-0.948473\pi$
$547$		−	96446.8i		−	0.322339i	0.986927	−	0.161170i	$-0.0515266\pi$
$548$	18480.1	+	68994.0i	0.0615379	+	0.229747i
$549$	−54261.8			−0.180032
$550$	66640.9	+	51140.2i	0.220300	+	0.169059i
$551$			151831.i			0.500102i
$552$	173596.	+	71934.1i	0.569721	+	0.236079i
$553$	−27762.2			−0.0907829
$554$	−220520.	+	287360.i	−0.718502	+	0.936281i
$555$			30173.3i			0.0979574i
$556$	34537.4	−	9250.86i	0.111722	−	0.0299249i
$557$	−200938.			−0.647668			−0.323834	−	0.946114i	$-0.604972\pi$
$557$	−200938.			−0.647668			−0.323834	+	0.946114i	$0.604972\pi$
$558$	388004.	+	297755.i	1.24614	+	0.956291i
$559$			5212.29i			0.0166804i
$560$	−43809.6	−	75912.8i	−0.139699	−	0.242069i
$561$	−123517.			−0.392465
$562$	58450.5	−	76166.8i	0.185061	−	0.241153i
$563$			417434.i			1.31696i	0.752600	+	0.658478i	$0.228799\pi$
$563$			417434.i			1.31696i	−0.752600	+	0.658478i	$0.771201\pi$
$564$	35361.4	+	132019.i	0.111166	+	0.415030i
$565$	−71961.1			−0.225424
$566$	177635.	+	136317.i	0.554494	+	0.425519i
$567$			127699.i			0.397211i
$568$	−67973.4	+	164038.i	−0.210689	+	0.508450i
$569$	−424.191			−0.00131020			−0.000655100	−	1.00000i	$-0.500209\pi$
$569$	−424.191			−0.00131020			−0.000655100		1.00000i	$0.500209\pi$
$570$	−13191.9	+	17190.3i	−0.0406029	+	0.0529097i
$571$		−	606394.i		−	1.85987i	−0.367723	−	0.929935i	$-0.619862\pi$
$571$		−	606394.i		−	1.85987i	0.367723	−	0.929935i	$-0.380138\pi$
$572$	8186.40	−	2192.73i	0.0250208	−	0.00670183i
$573$	82027.0			0.249832
$574$	245419.	+	188335.i	0.744877	+	0.571619i
$575$		−	114504.i		−	0.346326i
$576$	204789.	+	204902.i	0.617251	+	0.617593i
$577$	−228321.			−0.685795			−0.342897	−	0.939373i	$-0.611408\pi$
$577$	−228321.			−0.685795			−0.342897	+	0.939373i	$0.611408\pi$
$578$	−75266.0	+	98079.2i	−0.225291	+	0.293577i
$579$			121216.i			0.361580i
$580$	46486.3	+	173553.i	0.138187	+	0.515913i
$581$	117383.			0.347738
$582$	−161019.	−	123566.i	−0.475370	−	0.364799i
$583$		−	528471.i		−	1.55483i
$584$	−133207.	−	55197.7i	−0.390572	−	0.161843i
$585$	2493.08			0.00728492
$586$	−12821.8	+	16708.1i	−0.0373383	+	0.0486556i
$587$			89650.3i			0.260181i	0.991502	+	0.130090i	$0.0415268\pi$
$587$			89650.3i			0.260181i	−0.991502	+	0.130090i	$0.958473\pi$
$588$	−72485.9	+	19415.4i	−0.209652	+	0.0561553i
$589$	261338.			0.753306
$590$	−115811.	−	88873.7i	−0.332696	−	0.255311i
$591$			44112.5i			0.126295i
$592$	186692.	−	107741.i	0.532699	−	0.307423i
$593$	−326334.			−0.928012			−0.464006	−	0.885832i	$-0.653588\pi$
$593$	−326334.			−0.928012			−0.464006	+	0.885832i	$0.653588\pi$
$594$	198964.	−	259270.i	0.563898	−	0.734816i
$595$		−	78531.9i		−	0.221826i
$596$	−24502.1	−	91477.0i	−0.0689782	−	0.257525i
$597$	−75097.1			−0.210705
$598$	−9164.76	−	7033.04i	−0.0256282	−	0.0196671i
$599$			253846.i			0.707485i	0.935343	+	0.353742i	$0.115091\pi$
$599$			253846.i			0.707485i	−0.935343	+	0.353742i	$0.884909\pi$
$600$	−9816.00	+	23688.6i	−0.0272667	+	0.0658018i
$601$	−468553.			−1.29721			−0.648604	−	0.761126i	$-0.724647\pi$
$601$	−468553.			−1.29721			−0.648604	+	0.761126i	$0.724647\pi$
$602$	−123284.	+	160651.i	−0.340183	+	0.443293i
$603$		−	131513.i		−	0.361689i
$604$	−42964.7	+	11508.1i	−0.117771	+	0.0315449i
$605$	−151877.			−0.414937
$606$	124557.	+	95585.2i	0.339175	+	0.260283i
$607$			104709.i			0.284190i	0.989853	+	0.142095i	$0.0453838\pi$
$607$			104709.i			0.284190i	−0.989853	+	0.142095i	$0.954616\pi$
$608$	153467.	+	20240.3i	0.415152	+	0.0547532i
$609$	−98583.9			−0.265810
$610$	−20888.2	+	27219.4i	−0.0561359	+	0.0731508i
$611$		−	8402.39i		−	0.0225071i
$612$	67157.8	+	250729.i	0.179306	+	0.669425i
$613$	352323.			0.937604			0.468802	−	0.883303i	$-0.344686\pi$
$613$	352323.			0.937604			0.468802	+	0.883303i	$0.344686\pi$
$614$	21588.9	+	16567.3i	0.0572656	+	0.0439456i
$615$		−	90504.2i		−	0.239287i
$616$	304182.	+	126045.i	0.801625	+	0.332174i
$617$	543388.			1.42738			0.713690	−	0.700461i	$-0.247022\pi$
$617$	543388.			1.42738			0.713690	+	0.700461i	$0.247022\pi$
$618$	−10879.3	+	14176.8i	−0.0284856	+	0.0371196i
$619$		−	656868.i		−	1.71434i	−0.515034	−	0.857169i	$-0.672221\pi$
$619$		−	656868.i		−	1.71434i	0.515034	−	0.857169i	$-0.327779\pi$
$620$	298726.	−	80013.8i	0.777122	−	0.208152i
$621$	−445483.			−1.15518
$622$	−555906.	−	426602.i	−1.43688	−	1.10266i
$623$			55869.0i			0.143945i
$624$	1293.09	+	2240.66i	0.00332094	+	0.00575449i
$625$	15625.0			0.0400000
$626$	−244425.	+	318510.i	−0.623730	+	0.812784i
$627$		−	81402.5i		−	0.207063i
$628$	−64590.1	−	241143.i	−0.163775	−	0.611441i
$629$	193133.			0.488152
$630$	76840.7	+	58967.6i	0.193602	+	0.148570i
$631$		−	110480.i		−	0.277476i	−0.990329	−	0.138738i	$-0.955695\pi$
$631$		−	110480.i		−	0.277476i	0.990329	−	0.138738i	$-0.0443046\pi$
$632$	22211.4	−	53602.1i	0.0556086	−	0.134198i
$633$	163231.			0.407375
$634$	−123836.	+	161370.i	−0.308083	+	0.401463i
$635$		−	36473.8i		−	0.0904551i
$636$	155825.	−	41737.7i	0.385231	−	0.103184i
$637$	4613.37			0.0113695
$638$	−535468.	−	410918.i	−1.31550	−	1.00952i
$639$		−	196226.i		−	0.480568i
$640$	181619.	−	23851.0i	0.443406	−	0.0582299i
$641$	−282590.			−0.687766			−0.343883	−	0.939013i	$-0.611742\pi$
$641$	−282590.			−0.687766			−0.343883	+	0.939013i	$0.611742\pi$
$642$	150029.	−	195503.i	0.364002	−	0.474332i
$643$		−	40275.4i		−	0.0974133i	−0.998813	−	0.0487066i	$-0.984490\pi$
$643$		−	40275.4i		−	0.0974133i	0.998813	−	0.0487066i	$-0.0155099\pi$
$644$	−116124.	−	433539.i	−0.279994	−	1.04534i
$645$	59244.0			0.142405
$646$	110032.	+	84438.4i	0.263665	+	0.202337i
$647$			606942.i			1.44990i	0.688801	+	0.724951i	$0.258137\pi$
$647$			606942.i			1.44990i	−0.688801	+	0.724951i	$0.741863\pi$
$648$	−246555.	−	102167.i	−0.587171	−	0.243309i
$649$	548409.			1.30201
$650$	959.716	−	1250.61i	0.00227152	−	0.00296001i
$651$			169686.i			0.400391i
$652$	623033.	−	166879.i	1.46560	−	0.392562i
$653$	−95017.0			−0.222831			−0.111415	−	0.993774i	$-0.535538\pi$
$653$	−95017.0			−0.222831			−0.111415	+	0.993774i	$0.535538\pi$
$654$	−34884.9	−	26770.7i	−0.0815609	−	0.0625899i
$655$		−	278011.i		−	0.648006i
$656$	−559978.	+	323166.i	−1.30126	+	0.750961i
$657$	159345.			0.369154
$658$	198738.	−	258975.i	0.459016	−	0.598144i
$659$			664518.i			1.53016i	0.643937	+	0.765079i	$0.277300\pi$
$659$			664518.i			1.53016i	−0.643937	+	0.765079i	$0.722700\pi$
$660$	−24923.0	−	93048.3i	−0.0572154	−	0.213610i
$661$	323882.			0.741283			0.370642	−	0.928776i	$-0.379138\pi$
$661$	323882.			0.741283			0.370642	+	0.928776i	$0.379138\pi$
$662$	−434524.	−	333454.i	−0.991511	−	0.760886i
$663$			2317.97i			0.00527327i
$664$	−93913.1	+	226637.i	−0.213005	+	0.514038i
$665$	51755.5			0.117034
$666$	−145019.	+	188974.i	−0.326945	+	0.426043i
$667$			920054.i			2.06805i
$668$	337986.	−	90529.6i	0.757435	−	0.202879i
$669$	1662.04			0.00371355
$670$	−65971.2	−	50626.3i	−0.146962	−	0.112779i
$671$		−	128894.i		−	0.286277i
$672$	−13142.0	+	99645.6i	−0.0291020	+	0.220658i
$673$	−301219.			−0.665047			−0.332524	−	0.943095i	$-0.607900\pi$
$673$	−301219.			−0.665047			−0.332524	+	0.943095i	$0.607900\pi$
$674$	479518.	−	624860.i	1.05557	−	1.37551i
$675$		−	60789.9i		−	0.133421i
$676$	118192.	+	441262.i	0.258640	+	0.965614i
$677$	458020.			0.999325			0.499662	−	0.866220i	$-0.333457\pi$
$677$	458020.			0.999325			0.499662	+	0.866220i	$0.333457\pi$
$678$	65465.7	+	50238.4i	0.142414	+	0.109289i
$679$			484786.i			1.05150i
$680$	151626.	+	62830.1i	0.327911	+	0.135878i
$681$	89635.5			0.193279
$682$	−707287.	+	921667.i	−1.52064	+	1.98155i
$683$		−	209414.i		−	0.448914i	−0.974484	−	0.224457i	$-0.927939\pi$
$683$		−	209414.i		−	0.448914i	0.974484	−	0.224457i	$-0.0720609\pi$
$684$	−165240.	+	44259.6i	−0.353186	+	0.0946009i
$685$	−49910.5			−0.106368
$686$	375509.	+	288165.i	0.797942	+	0.612341i
$687$			221266.i			0.468815i
$688$	−211544.	−	366561.i	−0.446914	−	0.774407i
$689$	−9917.47			−0.0208912
$690$	−79938.9	+	104169.i	−0.167904	+	0.218795i
$691$			42616.4i			0.0892525i	0.999004	+	0.0446263i	$0.0142097\pi$
$691$			42616.4i			0.0892525i	−0.999004	+	0.0446263i	$0.985790\pi$
$692$	−179070.	−	668544.i	−0.373947	−	1.39610i
$693$	−363869.			−0.757666
$694$	−215799.	−	165604.i	−0.448053	−	0.343836i
$695$			24984.5i			0.0517251i
$696$	78872.8	−	190341.i	0.162820	−	0.392930i
$697$	−579298.			−1.19244
$698$	−61544.5	+	80198.8i	−0.126322	+	0.164610i
$699$			235410.i			0.481804i
$700$	59159.9	−	15846.0i	0.120735	−	0.0323388i
$701$	−496713.			−1.01081			−0.505405	−	0.862882i	$-0.668657\pi$
$701$	−496713.			−1.01081			−0.505405	+	0.862882i	$0.668657\pi$
$702$	−4865.55	−	3733.82i	−0.00987319	−	0.00757669i
$703$			127282.i			0.257547i
$704$	−486726.	+	486457.i	−0.982063	+	0.981519i
$705$	−95503.3			−0.192150
$706$	−57157.9	+	74482.5i	−0.114674	+	0.149432i
$707$		−	375008.i		−	0.750243i
$708$	43312.3	+	161704.i	0.0864062	+	0.322591i
$709$	−309547.			−0.615792			−0.307896	−	0.951420i	$-0.599625\pi$
$709$	−309547.			−0.615792			−0.307896	+	0.951420i	$0.599625\pi$
$710$	−98433.0	−	75537.5i	−0.195265	−	0.149846i
$711$			64120.0i			0.126839i
$712$	−107869.	−	44698.5i	−0.212784	−	0.0881724i
$713$	1.58363e6			3.11512
$714$	−54825.7	+	71443.4i	−0.107544	+	0.140141i
$715$			5922.07i			0.0115841i
$716$	−149702.	+	40097.7i	−0.292012	+	0.0782156i
$717$	−16864.3			−0.0328043
$718$	557262.	+	427643.i	1.08096	+	0.829530i
$719$		−	410551.i		−	0.794163i	−0.917783	−	0.397082i	$-0.870023\pi$
$719$		−	410551.i		−	0.794163i	0.917783	−	0.397082i	$-0.129977\pi$
$720$	−175329.	+	101183.i	−0.338212	+	0.195184i
$721$	42682.7			0.0821072
$722$	261709.	−	341033.i	0.502046	−	0.654217i
$723$		−	269016.i		−	0.514638i
$724$	−74680.6	−	278815.i	−0.142472	−	0.531911i
$725$	−125549.			−0.238857
$726$	138168.	+	106030.i	0.262141	+	0.201167i
$727$		−	714829.i		−	1.35249i	−0.736678	−	0.676244i	$-0.763607\pi$
$727$		−	714829.i		−	1.35249i	0.736678	−	0.676244i	$-0.236393\pi$
$728$	2365.41	−	5708.38i	0.00446318	−	0.0107709i
$729$	168675.			0.317392
$730$	61340.1	−	79932.3i	0.115106	−	0.149995i
$731$		−	379208.i		−	0.709648i
$732$	38005.5	−	10179.8i	0.0709291	−	0.0189984i
$733$	−664653.			−1.23705			−0.618525	−	0.785765i	$-0.712269\pi$
$733$	−664653.			−1.23705			−0.618525	+	0.785765i	$0.712269\pi$
$734$	607134.	+	465915.i	1.12692	+	0.864798i
$735$		−	52436.5i		−	0.0970642i
$736$	929963.	+	122650.i	1.71676	+	0.226419i
$737$	312397.			0.575138
$738$	434980.	−	566823.i	0.798650	−	1.04072i
$739$			132886.i			0.243326i	0.992571	+	0.121663i	$0.0388227\pi$
$739$			132886.i			0.243326i	−0.992571	+	0.121663i	$0.961177\pi$
$740$	38970.0	+	145492.i	0.0711650	+	0.265690i
$741$	−1527.63			−0.00278215
$742$	−305672.	−	234573.i	−0.555198	−	0.426059i
$743$		−	170672.i		−	0.309161i	−0.987980	−	0.154581i	$-0.950597\pi$
$743$		−	170672.i		−	0.309161i	0.987980	−	0.154581i	$-0.0494026\pi$
$744$	−327622.	−	135759.i	−0.591872	−	0.245257i
$745$	66174.8			0.119228
$746$	554588.	−	722685.i	0.996536	−	1.29859i
$747$		−	271109.i		−	0.485850i
$748$	−595582.	+	159527.i	−1.06448	+	0.285122i
$749$	−588606.			−1.04921
$750$	−14214.6	−	10908.3i	−0.0252705	−	0.0193926i
$751$		−	201923.i		−	0.358019i	−0.983847	−	0.179010i	$-0.942711\pi$
$751$		−	201923.i		−	0.358019i	0.983847	−	0.179010i	$-0.0572893\pi$
$752$	341016.	+	590909.i	0.603030	+	1.04492i
$753$	308866.			0.544728
$754$	−7711.44	+	10048.8i	−0.0135642	+	0.0176755i
$755$		−	31080.8i		−	0.0545253i
$756$	−61649.7	−	230165.i	−0.107867	−	0.402712i
$757$	363133.			0.633686			0.316843	−	0.948478i	$-0.397377\pi$
$757$	363133.			0.633686			0.316843	+	0.948478i	$0.397377\pi$
$758$	365185.	+	280243.i	0.635586	+	0.487749i
$759$		−	493276.i		−	0.856261i
$760$	−41407.4	+	99927.3i	−0.0716888	+	0.173004i
$761$	−106273.			−0.183508			−0.0917539	−	0.995782i	$-0.529247\pi$
$761$	−106273.			−0.183508			−0.0917539	+	0.995782i	$0.529247\pi$
$762$	−25463.5	+	33181.5i	−0.0438539	+	0.0571461i
$763$			105029.i			0.180410i
$764$	395523.	−	105941.i	0.677618	−	0.181500i
$765$	−181378.			−0.309929
$766$	−357807.	−	274581.i	−0.609805	−	0.467965i
$767$		−	10291.6i		−	0.0174942i
$768$	−181877.	−	105096.i	−0.308358	−	0.178182i
$769$	−573093.			−0.969109			−0.484554	−	0.874761i	$-0.661018\pi$
$769$	−573093.			−0.969109			−0.484554	+	0.874761i	$0.661018\pi$
$770$	−140072.	+	182528.i	−0.236249	+	0.307856i
$771$		−	194511.i		−	0.327217i
$772$	156555.	+	584488.i	0.262684	+	0.980711i
$773$	−890302.			−1.48997			−0.744986	−	0.667080i	$-0.767544\pi$
$773$	−890302.			−1.48997			−0.744986	+	0.667080i	$0.767544\pi$
$774$	371042.	+	284738.i	0.619357	+	0.475295i
$775$			216099.i			0.359791i
$776$	−936004.	−	387857.i	−1.55437	−	0.644093i
$777$	−82644.0			−0.136889
$778$	−446653.	+	582034.i	−0.737923	+	0.961588i
$779$		−	381780.i		−	0.629126i
$780$	−1746.18	+	467.714i	−0.00287012	+	0.000768761i
$781$	466116.			0.764173
$782$	666760.	+	511672.i	1.09033	+	0.836716i
$783$			488455.i			0.796711i
$784$	−324441.	+	187236.i	−0.527842	+	0.304620i
$785$	174443.			0.283084
$786$	−194088.	+	252917.i	−0.314163	+	0.409386i
$787$			413419.i			0.667484i	0.942664	+	0.333742i	$0.108311\pi$
$787$			413419.i			0.667484i	−0.942664	+	0.333742i	$0.891689\pi$
$788$	56973.0	+	212705.i	0.0917522	+	0.342550i
$789$	−152924.			−0.245652
$790$	32164.6	+	24683.1i	0.0515375	+	0.0395499i
$791$		−	197100.i		−	0.315016i
$792$	291116.	−	702541.i	0.464104	−	1.12001i
$793$	−2418.87			−0.00384650
$794$	156722.	−	204225.i	0.248593	−	0.323942i
$795$			112724.i			0.178354i
$796$	−362108.	+	96990.7i	−0.571494	+	0.153075i
$797$	−1.06112e6			−1.67051			−0.835254	−	0.549865i	$-0.814679\pi$
$797$	−1.06112e6			−1.67051			−0.835254	+	0.549865i	$0.814679\pi$
$798$	−47083.9	−	36132.2i	−0.0739379	−	0.0567399i
$799$			611296.i			0.957542i
$800$	−16736.6	+	126901.i	−0.0261510	+	0.198283i
$801$	129036.			0.201115
$802$	233638.	−	304453.i	0.363240	−	0.473339i
$803$			378508.i			0.587008i
$804$	24672.6	+	92113.3i	0.0381682	+	0.142498i
$805$	313623.			0.483968
$806$	17296.3	+	13273.2i	0.0266246	+	0.0204318i
$807$		−	211484.i		−	0.324736i
$808$	724050.	+	300029.i	1.10904	+	0.459558i
$809$	817968.			1.24980			0.624898	−	0.780706i	$-0.285140\pi$
$809$	817968.			1.24980			0.624898	+	0.780706i	$0.285140\pi$
$810$	113536.	−	147948.i	0.173046	−	0.225497i
$811$			590910.i			0.898420i	0.893426	+	0.449210i	$0.148295\pi$
$811$			590910.i			0.898420i	−0.893426	+	0.449210i	$0.851705\pi$
$812$	−475358.	+	127325.i	−0.720956	+	0.193108i
$813$	−50338.7			−0.0761589
$814$	−448889.	−	344478.i	−0.677470	−	0.519891i
$815$			450704.i			0.678541i
$816$	−94076.0	−	163014.i	−0.141286	−	0.244819i
$817$	249913.			0.374407
$818$	−281521.	+	366850.i	−0.420730	+	0.548254i
$819$			6828.49i			0.0101802i
$820$	−116890.	−	436399.i	−0.173839	−	0.649017i
$821$	646976.			0.959846			0.479923	−	0.877311i	$-0.340665\pi$
$821$	646976.			0.959846			0.479923	+	0.877311i	$0.340665\pi$
$822$	45405.4	+	34844.1i	0.0671992	+	0.0515687i
$823$			998248.i			1.47380i	0.676002	+	0.736900i	$0.263711\pi$
$823$			998248.i			1.47380i	−0.676002	+	0.736900i	$0.736289\pi$
$824$	−34148.6	+	82409.9i	−0.0502943	+	0.121374i
$825$	67311.5			0.0988966
$826$	243423.	−	317205.i	0.356781	−	0.464921i
$827$		−	992385.i		−	1.45101i	−0.688219	−	0.725503i	$-0.741607\pi$
$827$		−	992385.i		−	1.45101i	0.688219	−	0.725503i	$-0.258393\pi$
$828$	−1.00131e6	+	268200.i	−1.46052	+	0.391200i
$829$	725129.			1.05513			0.527565	−	0.849514i	$-0.323105\pi$
$829$	725129.			1.05513			0.527565	+	0.849514i	$0.323105\pi$
$830$	−135996.	−	104364.i	−0.197411	−	0.151493i
$831$			290251.i			0.420312i
$832$	9129.02	+	9134.07i	0.0131880	+	0.0131953i
$833$	−335635.			−0.483701
$834$	17442.5	−	22729.3i	0.0250770	−	0.0326779i
$835$			244500.i			0.350676i
$836$	−105134.	−	392512.i	−0.150429	−	0.561617i
$837$	840745.			1.20009
$838$	−301945.	−	231713.i	−0.429972	−	0.329961i
$839$		−	954288.i		−	1.35568i	−0.735212	−	0.677838i	$-0.762917\pi$
$839$		−	954288.i		−	1.35568i	0.735212	−	0.677838i	$-0.237083\pi$
$840$	−64882.6	−	26885.8i	−0.0919538	−	0.0381034i
$841$	301521.			0.426311
$842$	−221976.	+	289257.i	−0.313099	+	0.407999i
$843$		−	76933.3i		−	0.108258i
$844$	787075.	−	210818.i	1.10492	−	0.295954i
$845$	−319211.			−0.447058
$846$	−598132.	−	459006.i	−0.835711	−	0.641325i
$847$		−	415988.i		−	0.579848i
$848$	697459.	−	402506.i	0.969900	−	0.559733i
$849$	179423.			0.248922
$850$	−69821.8	+	90984.9i	−0.0966392	+	0.125931i
$851$			771292.i			1.06502i
$852$	36813.0	+	137439.i	0.0507133	+	0.189334i
$853$	−327068.			−0.449511			−0.224756	−	0.974415i	$-0.572158\pi$
$853$	−327068.			−0.449511			−0.224756	+	0.974415i	$0.572158\pi$
$854$	−74553.3	−	57212.2i	−0.102224	−	0.0784464i
$855$		−	119535.i		−	0.163517i
$856$	470919.	−	1.13645e6i	0.642686	−	1.55097i
$857$	−1.26713e6			−1.72527			−0.862637	−	0.505823i	$-0.831189\pi$
$857$	−1.26713e6			−1.72527			−0.862637	+	0.505823i	$0.831189\pi$
$858$	4134.39	−	5387.53i	0.00561613	−	0.00731838i
$859$			545595.i			0.739407i	0.929150	+	0.369704i	$0.120541\pi$
$859$			545595.i			0.739407i	−0.929150	+	0.369704i	$0.879459\pi$
$860$	285666.	−	76515.8i	0.386244	−	0.103456i
$861$	247889.			0.334388
$862$	−145086.	−	111339.i	−0.195259	−	0.149842i
$863$		−	199428.i		−	0.267771i	−0.990997	−	0.133885i	$-0.957255\pi$
$863$		−	199428.i		−	0.267771i	0.990997	−	0.133885i	$-0.0427454\pi$
$864$	493715.	+	65114.7i	0.661377	+	0.0872271i
$865$	483627.			0.646366
$866$	−100259.	+	130648.i	−0.133687	+	0.174208i
$867$			99066.2i			0.131791i
$868$	219156.	+	818203.i	0.290880	+	1.08598i
$869$	−152311.			−0.201693
$870$	114217.	+	87649.8i	0.150900	+	0.115801i
$871$		−	5862.56i		−	0.00772771i
$872$	−202786.	−	84029.4i	−0.266688	−	0.110509i
$873$	1.11967e6			1.46913
$874$	−337211.	+	439421.i	−0.441448	+	0.575251i
$875$			42796.5i			0.0558975i
$876$	−111607.	+	29893.9i	−0.145439	+	0.0389560i
$877$	−966378.			−1.25646			−0.628229	−	0.778028i	$-0.716220\pi$
$877$	−966378.			−1.25646			−0.628229	+	0.778028i	$0.716220\pi$
$878$	−969586.	−	744060.i	−1.25776	−	0.965204i
$879$			16876.3i			0.0218423i
$880$	−240351.	−	416477.i	−0.310370	−	0.537806i
$881$	−410709.			−0.529154			−0.264577	−	0.964365i	$-0.585232\pi$
$881$	−410709.			−0.529154			−0.264577	+	0.964365i	$0.585232\pi$
$882$	252020.	−	328407.i	0.323964	−	0.422158i
$883$		−	1.15757e6i		−	1.48465i	−0.670039	−	0.742326i	$-0.733722\pi$
$883$		−	1.15757e6i		−	1.48465i	0.670039	−	0.742326i	$-0.266278\pi$
$884$	2993.74	+	11176.9i	0.00383098	+	0.0143027i
$885$	−116977.			−0.149353
$886$	−957116.	−	734491.i	−1.21926	−	0.935662i
$887$			908264.i			1.15442i	0.816595	+	0.577211i	$0.195859\pi$
$887$			908264.i			1.15442i	−0.816595	+	0.577211i	$0.804141\pi$
$888$	66120.0	−	159565.i	0.0838507	−	0.202354i
$889$	99900.7			0.126405
$890$	49672.5	−	64728.3i	0.0627099	−	0.0817174i
$891$			700590.i			0.882487i
$892$	8014.13	−	2146.59i	0.0100723	−	0.00269786i
$893$	−402867.			−0.505195
$894$	−60201.7	−	46198.8i	−0.0753240	−	0.0578037i
$895$		−	108295.i		−	0.135195i
$896$	65327.2	+	497451.i	0.0813726	+	0.619632i
$897$	−9256.98			−0.0115049
$898$	109087.	−	142151.i	0.135275	−	0.176277i
$899$		−	1.73639e6i		−	2.14846i
$900$	−36598.1	−	136636.i	−0.0451829	−	0.168687i
$901$	721522.			0.888792
$902$	1.34643e6	+	1.03325e6i	1.65490	+	1.26997i
$903$			162268.i			0.199002i
$904$	380551.	+	157691.i	0.465668	+	0.192961i
$905$	201696.			0.246263
$906$	−21698.5	+	28275.3i	−0.0264346	+	0.0344470i
$907$		−	1.16501e6i		−	1.41617i	−0.706127	−	0.708085i	$-0.749559\pi$
$907$		−	1.16501e6i		−	1.41617i	0.706127	−	0.708085i	$-0.250441\pi$
$908$	432210.	−	115768.i	0.524231	−	0.140416i
$909$	−866124.			−1.04822
$910$	3425.38	+	2628.64i	0.00413643	+	0.00317430i
$911$			446494.i			0.537996i	0.963141	+	0.268998i	$0.0866925\pi$
$911$			446494.i			0.537996i	−0.963141	+	0.268998i	$0.913307\pi$
$912$	107432.	−	61999.7i	0.129165	−	0.0745418i
$913$	643992.			0.772572
$914$	−633714.	+	825794.i	−0.758580	+	0.988506i
$915$			27493.3i			0.0328386i
$916$	285773.	+	1.06691e6i	0.340589	+	1.27156i
$917$	761465.			0.905547
$918$	353981.	+	271645.i	0.420044	+	0.322342i
$919$			1.24513e6i			1.47429i	0.675734	+	0.737146i	$0.263827\pi$
$919$			1.24513e6i			1.47429i	−0.675734	+	0.737146i	$0.736173\pi$
$920$	−250917.	+	605530.i	−0.296452	+	0.715419i
$921$	21806.1			0.0257075
$922$	98862.6	−	128828.i	0.116297	−	0.151547i
$923$		−	8747.30i		−	0.0102676i
$924$	254857.	−	68263.5i	0.298506	−	0.0799549i
$925$	−105249.			−0.123008
$926$	708003.	+	543321.i	0.825682	+	0.633629i
$927$		−	98580.4i		−	0.114718i
$928$	134481.	−	1.01967e6i	0.156158	−	1.18403i
$929$	−1.65942e6			−1.92276			−0.961378	−	0.275231i	$-0.911246\pi$
$929$	−1.65942e6			−1.92276			−0.961378	+	0.275231i	$0.911246\pi$
$930$	150866.	−	196594.i	0.174432	−	0.227302i
$931$		−	221196.i		−	0.255199i
$932$	304041.	+	1.13511e6i	0.350026	+	1.30680i
$933$	−561500.			−0.645040
$934$	−475280.	−	364730.i	−0.544824	−	0.418098i
$935$		−	430846.i		−	0.492832i
$936$	−13184.1	−	5463.19i	−0.0150487	−	0.00623583i
$937$	44504.5			0.0506902			0.0253451	−	0.999679i	$-0.491932\pi$
$937$	44504.5			0.0506902			0.0253451	+	0.999679i	$0.491932\pi$
$938$	138664.	−	180693.i	0.157601	−	0.205370i
$939$			321716.i			0.364872i
$940$	−460504.	+	123346.i	−0.521167	+	0.139595i
$941$	439028.			0.495807			0.247904	−	0.968785i	$-0.420258\pi$
$941$	439028.			0.495807			0.247904	+	0.968785i	$0.420258\pi$
$942$	−158698.	−	121785.i	−0.178842	−	0.137243i
$943$		−	2.31347e6i		−	2.60160i
$944$	417692.	+	723772.i	0.468719	+	0.812191i
$945$	166502.			0.186447
$946$	−676367.	+	881374.i	−0.755788	+	0.984868i
$947$			983414.i			1.09657i	0.836291	+	0.548285i	$0.184719\pi$
$947$			983414.i			1.09657i	−0.836291	+	0.548285i	$0.815281\pi$
$948$	−12029.2	−	44910.3i	−0.0133851	−	0.0499722i
$949$	7103.22			0.00788720
$950$	−59962.5	−	46015.3i	−0.0664405	−	0.0509864i
$951$			162994.i			0.180223i
$952$	−172090.	+	415300.i	−0.189881	+	0.458234i
$953$	455101.			0.501097			0.250549	−	0.968104i	$-0.419389\pi$
$953$	455101.			0.501097			0.250549	+	0.968104i	$0.419389\pi$
$954$	−541772.	+	705984.i	−0.595279	+	0.775708i
$955$			286123.i			0.313722i
$956$	−81317.5	+	21780.9i	−0.0889751	+	0.0238320i
$957$	−540857.			−0.590552
$958$	812022.	+	623146.i	0.884784	+	0.678983i
$959$		−	136704.i		−	0.148642i
$960$	103820.	−	103762.i	0.112652	−	0.112589i
$961$	−2.06521e6			−2.23623
$962$	−6464.59	+	8424.01i	−0.00698539	+	0.00910267i
$963$			1.35945e6i			1.46592i
$964$	−347444.	−	1.29716e6i	−0.373879	−	1.39585i
$965$	−422821.			−0.454048
$966$	−285315.	−	218951.i	−0.305753	−	0.234635i
$967$		−	249543.i		−	0.266865i	−0.991058	−	0.133433i	$-0.957400\pi$
$967$		−	249543.i		−	0.266865i	0.991058	−	0.133433i	$-0.0426000\pi$
$968$	803171.	+	332815.i	0.857151	+	0.355183i
$969$	111139.			0.118364
$970$	431018.	−	561660.i	0.458091	−	0.596939i
$971$		−	71856.1i		−	0.0762123i	−0.999274	−	0.0381062i	$-0.987867\pi$
$971$		−	71856.1i		−	0.0762123i	0.999274	−	0.0381062i	$-0.0121325\pi$
$972$	−815384.	+	218401.i	−0.863037	+	0.231165i
$973$	−68431.9			−0.0722825
$974$	−281742.	−	216209.i	−0.296985	−	0.227906i
$975$		−	1263.19i		−	0.00132880i
$976$	170110.	−	98171.1i	0.178579	−	0.103059i
$977$	279175.			0.292474			0.146237	−	0.989250i	$-0.453284\pi$
$977$	279175.			0.292474			0.146237	+	0.989250i	$0.453284\pi$
$978$	314651.	−	410022.i	0.328966	−	0.428676i
$979$			306512.i			0.319803i
$980$	−67723.7	−	252842.i	−0.0705161	−	0.263267i
$981$	242576.			0.252064
$982$	638836.	+	490243.i	0.662470	+	0.508380i
$983$		−	1.47299e6i		−	1.52438i	−0.647355	−	0.762188i	$-0.724125\pi$
$983$		−	1.47299e6i		−	1.52438i	0.647355	−	0.762188i	$-0.275875\pi$
$984$	−198326.	+	478613.i	−0.204828	+	0.494304i
$985$	−153871.			−0.158593
$986$	561028.	−	731076.i	0.577073	−	0.751984i
$987$		−	261581.i		−	0.268517i
$988$	−7366.01	+	1972.99i	−0.00754603	+	0.00202121i
$989$	1.51440e6			1.54827
$990$	421568.	+	323511.i	0.430128	+	0.330080i
$991$		−	29557.4i		−	0.0300967i	−0.999887	−	0.0150483i	$-0.995210\pi$
$991$		−	29557.4i		−	0.0300967i	0.999887	−	0.0150483i	$-0.00479022\pi$
$992$	−1.75509e6	−	231473.i	−1.78351	−	0.235222i
$993$	−438896.			−0.445106
$994$	206895.	−	269606.i	0.209401	−	0.272870i
$995$		−	261950.i		−	0.264589i
$996$	50861.3	+	189887.i	0.0512707	+	0.191415i
$997$	1.37172e6			1.37999			0.689994	−	0.723815i	$-0.257613\pi$
$997$	1.37172e6			1.37999			0.689994	+	0.723815i	$0.257613\pi$
$998$	−1.13425e6	−	870424.i	−1.13880	−	0.873916i
$999$			409477.i			0.410297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.b.a.11.5	✓	8
3.2	odd	2		180.5.c.a.91.4		8
4.3	odd	2	inner	20.5.b.a.11.6	yes	8
5.2	odd	4		100.5.d.c.99.12		16
5.3	odd	4		100.5.d.c.99.5		16
5.4	even	2		100.5.b.c.51.4		8
8.3	odd	2		320.5.b.d.191.4		8
8.5	even	2		320.5.b.d.191.5		8
12.11	even	2		180.5.c.a.91.3		8
20.3	even	4		100.5.d.c.99.11		16
20.7	even	4		100.5.d.c.99.6		16
20.19	odd	2		100.5.b.c.51.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.5	✓	8	1.1	even	1	trivial
20.5.b.a.11.6	yes	8	4.3	odd	2	inner
100.5.b.c.51.3		8	20.19	odd	2
100.5.b.c.51.4		8	5.4	even	2
100.5.d.c.99.5		16	5.3	odd	4
100.5.d.c.99.6		16	20.7	even	4
100.5.d.c.99.11		16	20.3	even	4
100.5.d.c.99.12		16	5.2	odd	4
180.5.c.a.91.3		8	12.11	even	2
180.5.c.a.91.4		8	3.2	odd	2
320.5.b.d.191.4		8	8.3	odd	2
320.5.b.d.191.5		8	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.43519 - 3.17330i) q^{2} -3.20523i q^{3} +(-4.13968 - 15.4552i) q^{4} +11.1803 q^{5} +(-10.1712 - 7.80536i) q^{6} +30.6227i q^{7} +(-59.1249 - 24.4999i) q^{8} +70.7265 q^{9} +O(q^{10})\)	\(q+(2.43519 - 3.17330i) q^{2} -3.20523i q^{3} +(-4.13968 - 15.4552i) q^{4} +11.1803 q^{5} +(-10.1712 - 7.80536i) q^{6} +30.6227i q^{7} +(-59.1249 - 24.4999i) q^{8} +70.7265 q^{9} +(27.2263 - 35.4786i) q^{10} +168.004i q^{11} +(-49.5375 + 13.2686i) q^{12} +3.15282 q^{13} +(97.1750 + 74.5721i) q^{14} -35.8356i q^{15} +(-221.726 + 127.959i) q^{16} -229.376 q^{17} +(172.233 - 224.436i) q^{18} -151.168i q^{19} +(-46.2830 - 172.794i) q^{20} +98.1528 q^{21} +(533.127 + 409.122i) q^{22} -916.032i q^{23} +(-78.5280 + 189.509i) q^{24} +125.000 q^{25} +(7.67772 - 10.0048i) q^{26} -486.319i q^{27} +(473.279 - 126.768i) q^{28} -1004.39 q^{29} +(-113.717 - 87.2666i) q^{30} +1728.79i q^{31} +(-133.893 + 1015.21i) q^{32} +538.492 q^{33} +(-558.575 + 727.879i) q^{34} +342.372i q^{35} +(-292.785 - 1093.09i) q^{36} -841.993 q^{37} +(-479.700 - 368.122i) q^{38} -10.1055i q^{39} +(-661.036 - 273.917i) q^{40} +2525.54 q^{41} +(239.021 - 311.468i) q^{42} +1653.22i q^{43} +(2596.53 - 695.482i) q^{44} +790.746 q^{45} +(-2906.84 - 2230.71i) q^{46} -2665.04i q^{47} +(410.139 + 710.684i) q^{48} +1463.25 q^{49} +(304.399 - 396.663i) q^{50} +735.204i q^{51} +(-13.0517 - 48.7275i) q^{52} -3145.59 q^{53} +(-1543.24 - 1184.28i) q^{54} +1878.34i q^{55} +(750.253 - 1810.56i) q^{56} -484.527 q^{57} +(-2445.89 + 3187.24i) q^{58} -3264.26i q^{59} +(-553.846 + 148.348i) q^{60} -767.207 q^{61} +(5485.98 + 4209.95i) q^{62} +2165.83i q^{63} +(2895.51 + 2897.11i) q^{64} +35.2496 q^{65} +(1311.33 - 1708.80i) q^{66} -1859.46i q^{67} +(949.543 + 3545.05i) q^{68} -2936.10 q^{69} +(1086.45 + 833.741i) q^{70} -2774.43i q^{71} +(-4181.70 - 1732.79i) q^{72} +2252.97 q^{73} +(-2050.41 + 2671.90i) q^{74} -400.654i q^{75} +(-2336.32 + 625.785i) q^{76} -5144.73 q^{77} +(-32.0679 - 24.6089i) q^{78} +906.591i q^{79} +(-2478.97 + 1430.63i) q^{80} +4170.08 q^{81} +(6150.17 - 8014.30i) q^{82} -3833.20i q^{83} +(-406.321 - 1516.97i) q^{84} -2564.50 q^{85} +(5246.15 + 4025.90i) q^{86} +3219.31i q^{87} +(4116.08 - 9933.21i) q^{88} +1824.43 q^{89} +(1925.62 - 2509.28i) q^{90} +96.5478i q^{91} +(-14157.4 + 3792.08i) q^{92} +5541.19 q^{93} +(-8456.97 - 6489.88i) q^{94} -1690.10i q^{95} +(3253.98 + 429.158i) q^{96} +15831.0 q^{97} +(3563.30 - 4643.34i) q^{98} +11882.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Introduction

L-functions

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