LMFDB - Embedded newform 20.5.b.a.11.6

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43519 + 3.17330i) q^{2} +3.20523i q^{3} +(-4.13968 + 15.4552i) q^{4} +11.1803 q^{5} +(-10.1712 + 7.80536i) q^{6} -30.6227i q^{7} +(-59.1249 + 24.4999i) q^{8} +70.7265 q^{9} +O(q^{10})$	\(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	$0.0569849\pi$
$3$			3.20523i			0.356137i	−0.984018	+	0.178069i	$0.943015\pi$
$4$	−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	$-0.898842\pi$
$7$		−	30.6227i		−	0.624953i	0.949926	−	0.312476i	$-0.101158\pi$
$8$	−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	$-0.755745\pi$
$11$		−	168.004i		−	1.38846i	0.719752	−	0.694231i	$-0.244255\pi$
$12$	−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	$0.0671424\pi$
$19$			151.168i			0.418747i	−0.977836	+	0.209373i	$0.932858\pi$
$20$	−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	$0.333199\pi$
$23$			916.032i			1.73163i	−0.500365	+	0.865814i	$0.666801\pi$
$24$	−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	$-0.643948\pi$
$31$		−	1728.79i		−	1.79895i	0.436969	−	0.899477i	$-0.356052\pi$
$32$	−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	$-0.852472\pi$
$43$		−	1653.22i		−	0.894113i	0.894506	−	0.447057i	$-0.147528\pi$
$44$	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	$0.206117\pi$
$47$			2665.04i			1.20645i	−0.797573	+	0.603223i	$0.793883\pi$
$48$	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	$0.155338\pi$
$59$			3264.26i			0.937737i	−0.883268	+	0.468869i	$0.844662\pi$
$60$	−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	$0.0664069\pi$
$67$			1859.46i			0.414227i	−0.978317	+	0.207113i	$0.933593\pi$
$68$	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	$0.0887398\pi$
$71$			2774.43i			0.550374i	−0.961391	+	0.275187i	$0.911260\pi$
$72$	−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	$-0.976860\pi$
$79$		−	906.591i		−	0.145264i	0.997359	−	0.0726318i	$-0.0231398\pi$
$80$	−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	$0.0897416\pi$
$83$			3833.20i			0.556423i	−0.960520	+	0.278211i	$0.910258\pi$
$84$	−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	$0.0209251\pi$
$103$			1393.83i			0.131382i	−0.997840	+	0.0656908i	$0.979075\pi$
$104$	−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	$-0.682890\pi$
$107$		−	19221.2i		−	1.67886i	0.543470	−	0.839429i	$-0.317110\pi$
$108$	−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	$0.0322464\pi$
$127$			3262.31i			0.202264i	−0.994873	+	0.101132i	$0.967754\pi$
$128$	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	$0.257926\pi$
$131$			24866.0i			1.44899i	−0.689282	+	0.724493i	$0.742074\pi$
$132$	−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	$-0.981582\pi$
$139$		−	2234.68i		−	0.115661i	0.998326	−	0.0578304i	$-0.0184183\pi$
$140$	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	$0.0194166\pi$
$151$			2779.95i			0.121922i	−0.998140	+	0.0609611i	$0.980583\pi$
$152$	−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	$-0.725868\pi$
$163$		−	40312.2i		−	1.51726i	0.651520	−	0.758632i	$-0.274132\pi$
$164$	−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	$-0.871760\pi$
$167$		−	21868.7i		−	0.784135i	0.919936	−	0.392068i	$-0.128240\pi$
$168$	−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	$0.0482986\pi$
$179$			9686.18i			0.302306i	−0.988510	+	0.151153i	$0.951701\pi$
$180$	−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	$-0.885926\pi$
$191$		−	25591.6i		−	0.701504i	0.936468	−	0.350752i	$-0.114074\pi$
$192$	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	$0.0955928\pi$
$199$			23429.5i			0.591640i	−0.955244	+	0.295820i	$0.904407\pi$
$200$	−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	$-0.806193\pi$
$211$		−	50926.3i		−	1.14387i	0.820299	−	0.571935i	$-0.193807\pi$
$212$	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	$-0.998340\pi$
$223$		−	518.539i		−	0.0104273i	0.999986	−	0.00521365i	$-0.00165956\pi$
$224$	−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	$-0.912528\pi$
$227$		−	27965.3i		−	0.542711i	0.962479	−	0.271355i	$-0.0874719\pi$
$228$	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	$0.0146652\pi$
$239$			5261.50i			0.0921115i	−0.998939	+	0.0460558i	$0.985335\pi$
$240$	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	$-0.722851\pi$
$251$		−	96363.0i		−	1.52955i	0.644299	−	0.764774i	$-0.277149\pi$
$252$	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	$0.112082\pi$
$263$			47710.6i			0.689769i	−0.938645	+	0.344884i	$0.887918\pi$
$264$	−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	$0.0341000\pi$
$271$			15705.1i			0.213847i	−0.994267	+	0.106924i	$0.965900\pi$
$272$	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	$-0.886360\pi$
$283$		−	55978.1i		−	0.698949i	0.936946	−	0.349475i	$-0.113640\pi$
$284$	−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	$-0.988509\pi$
$307$		−	6803.29i		−	0.0721842i	0.999348	−	0.0360921i	$-0.0114910\pi$
$308$	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	$0.360583\pi$
$311$			175182.i			1.81121i	−0.424120	+	0.905606i	$0.639417\pi$
$312$	−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	$0.214864\pi$
$331$			136931.i			1.24982i	−0.780698	+	0.624908i	$0.785136\pi$
$332$	−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	$0.0911271\pi$
$347$			68004.5i			0.564779i	−0.959300	+	0.282390i	$0.908873\pi$
$348$	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	$-0.761421\pi$
$359$		−	175609.i		−	1.36257i	0.732018	−	0.681285i	$-0.238579\pi$
$360$	−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	$-0.748582\pi$
$367$		−	191326.i		−	1.42050i	0.703950	−	0.710250i	$-0.251418\pi$
$368$	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	$-0.868808\pi$
$379$		−	115080.i		−	0.801167i	0.916260	−	0.400583i	$-0.131192\pi$
$380$	−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	$0.125569\pi$
$383$			112755.i			0.768670i	−0.923194	+	0.384335i	$0.874431\pi$
$384$	−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	$0.0873523\pi$
$419$			95151.9i			0.541987i	−0.962581	+	0.270994i	$0.912648\pi$
$420$	−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	$0.0392719\pi$
$431$			45720.8i			0.246127i	−0.992399	+	0.123063i	$0.960728\pi$
$432$	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	$0.291332\pi$
$439$			305545.i			1.58543i	−0.609595	+	0.792713i	$0.708668\pi$
$440$	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	$0.278972\pi$
$443$			301615.i			1.53690i	−0.639909	+	0.768451i	$0.721028\pi$
$444$	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	$-0.825785\pi$
$463$		−	223112.i		−	1.04079i	0.853927	−	0.520393i	$-0.174215\pi$
$464$	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	$0.111572\pi$
$467$			149775.i			0.686760i	−0.939197	+	0.343380i	$0.888428\pi$
$468$	−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	$-0.811706\pi$
$479$		−	255892.i		−	1.11528i	0.830081	−	0.557642i	$-0.188294\pi$
$480$	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	$0.0599339\pi$
$487$			88785.3i			0.374354i	−0.982326	+	0.187177i	$0.940066\pi$
$488$	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	$-0.862897\pi$
$491$		−	201316.i		−	0.835055i	0.908664	−	0.417528i	$-0.137103\pi$
$492$	−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	$0.254823\pi$
$499$			357435.i			1.43548i	−0.696313	+	0.717739i	$0.745177\pi$
$500$	−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	$-0.843710\pi$
$503$		−	238591.i		−	0.943015i	0.881862	−	0.471507i	$-0.156290\pi$
$504$	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	$-0.838647\pi$
$523$		−	265583.i		−	0.970948i	0.874251	−	0.485474i	$-0.161353\pi$
$524$	−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	$0.0515266\pi$
$547$			96446.8i			0.322339i	−0.986927	+	0.161170i	$0.948473\pi$
$548$	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	$-0.771201\pi$
$563$		−	417434.i		−	1.31696i	0.752600	−	0.658478i	$-0.228799\pi$
$564$	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	$0.380138\pi$
$571$			606394.i			1.85987i	−0.367723	+	0.929935i	$0.619862\pi$
$572$	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	$-0.958473\pi$
$587$		−	89650.3i		−	0.260181i	0.991502	−	0.130090i	$-0.0415268\pi$
$588$	−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	$-0.884909\pi$
$599$		−	253846.i		−	0.707485i	0.935343	−	0.353742i	$-0.115091\pi$
$600$	−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	$-0.954616\pi$
$607$		−	104709.i		−	0.284190i	0.989853	−	0.142095i	$-0.0453838\pi$
$608$	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	$0.327779\pi$
$619$			656868.i			1.71434i	−0.515034	+	0.857169i	$0.672221\pi$
$620$	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	$0.0443046\pi$
$631$			110480.i			0.277476i	−0.990329	+	0.138738i	$0.955695\pi$
$632$	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	$0.0155099\pi$
$643$			40275.4i			0.0974133i	−0.998813	+	0.0487066i	$0.984490\pi$
$644$	−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	$-0.741863\pi$
$647$		−	606942.i		−	1.44990i	0.688801	−	0.724951i	$-0.258137\pi$
$648$	−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	$-0.722700\pi$
$659$		−	664518.i		−	1.53016i	0.643937	−	0.765079i	$-0.277300\pi$
$660$	−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	$0.0720609\pi$
$683$			209414.i			0.448914i	−0.974484	+	0.224457i	$0.927939\pi$
$684$	−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	$-0.985790\pi$
$691$		−	42616.4i		−	0.0892525i	0.999004	−	0.0446263i	$-0.0142097\pi$
$692$	−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	$0.129977\pi$
$719$			410551.i			0.794163i	−0.917783	+	0.397082i	$0.870023\pi$
$720$	−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	$0.236393\pi$
$727$			714829.i			1.35249i	−0.736678	+	0.676244i	$0.763607\pi$
$728$	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	$-0.961177\pi$
$739$		−	132886.i		−	0.243326i	0.992571	−	0.121663i	$-0.0388227\pi$
$740$	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	$0.0494026\pi$
$743$			170672.i			0.309161i	−0.987980	+	0.154581i	$0.950597\pi$
$744$	−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	$0.0572893\pi$
$751$			201923.i			0.358019i	−0.983847	+	0.179010i	$0.942711\pi$
$752$	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	$-0.891689\pi$
$787$		−	413419.i		−	0.667484i	0.942664	−	0.333742i	$-0.108311\pi$
$788$	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	$-0.851705\pi$
$811$		−	590910.i		−	0.898420i	0.893426	−	0.449210i	$-0.148295\pi$
$812$	−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	$-0.736289\pi$
$823$		−	998248.i		−	1.47380i	0.676002	−	0.736900i	$-0.263711\pi$
$824$	−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	$0.258393\pi$
$827$			992385.i			1.45101i	−0.688219	+	0.725503i	$0.741607\pi$
$828$	−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	$0.237083\pi$
$839$			954288.i			1.35568i	−0.735212	+	0.677838i	$0.762917\pi$
$840$	−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	$-0.879459\pi$
$859$		−	545595.i		−	0.739407i	0.929150	−	0.369704i	$-0.120541\pi$
$860$	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	$0.0427454\pi$
$863$			199428.i			0.267771i	−0.990997	+	0.133885i	$0.957255\pi$
$864$	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	$0.266278\pi$
$883$			1.15757e6i			1.48465i	−0.670039	+	0.742326i	$0.733722\pi$
$884$	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	$-0.804141\pi$
$887$		−	908264.i		−	1.15442i	0.816595	−	0.577211i	$-0.195859\pi$
$888$	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	$0.250441\pi$
$907$			1.16501e6i			1.41617i	−0.706127	+	0.708085i	$0.749559\pi$
$908$	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	$-0.913307\pi$
$911$		−	446494.i		−	0.537996i	0.963141	−	0.268998i	$-0.0866925\pi$
$912$	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	$-0.736173\pi$
$919$		−	1.24513e6i		−	1.47429i	0.675734	−	0.737146i	$-0.263827\pi$
$920$	−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	$-0.815281\pi$
$947$		−	983414.i		−	1.09657i	0.836291	−	0.548285i	$-0.184719\pi$
$948$	−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	$0.0426000\pi$
$967$			249543.i			0.266865i	−0.991058	+	0.133433i	$0.957400\pi$
$968$	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	$0.0121325\pi$
$971$			71856.1i			0.0762123i	−0.999274	+	0.0381062i	$0.987867\pi$
$972$	−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	$0.275875\pi$
$983$			1.47299e6i			1.52438i	−0.647355	+	0.762188i	$0.724125\pi$
$984$	−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	$0.00479022\pi$
$991$			29557.4i			0.0300967i	−0.999887	+	0.0150483i	$0.995210\pi$
$992$	−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.11.6	yes	8
3.2	odd	2		180.5.c.a.91.3		8
4.3	odd	2	inner	20.5.b.a.11.5	✓	8
5.2	odd	4		100.5.d.c.99.6		16
5.3	odd	4		100.5.d.c.99.11		16
5.4	even	2		100.5.b.c.51.3		8
8.3	odd	2		320.5.b.d.191.5		8
8.5	even	2		320.5.b.d.191.4		8
12.11	even	2		180.5.c.a.91.4		8
20.3	even	4		100.5.d.c.99.5		16
20.7	even	4		100.5.d.c.99.12		16
20.19	odd	2		100.5.b.c.51.4		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
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

Modular forms

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