LMFDB - Embedded newform 20.5.b.a.11.1

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			11.1
Root			$-1.02661 - 1.71641i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.5.b.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 + 14.0967i) q^{4} +11.1803 q^{5} +(53.4761 - 31.9849i) q^{6} +37.6230i q^{7} +(63.9314 - 2.96235i) q^{8} -161.671 q^{9} +O(q^{10})$	\(q+(-2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 + 14.0967i) q^{4} +11.1803 q^{5} +(53.4761 - 31.9849i) q^{6} +37.6230i q^{7} +(63.9314 - 2.96235i) q^{8} -161.671 q^{9} +(-22.9558 - 38.3801i) q^{10} -26.6928i q^{11} +(-219.597 - 117.902i) q^{12} +58.0144 q^{13} +(129.153 - 77.2486i) q^{14} +174.166i q^{15} +(-141.435 - 213.383i) q^{16} +467.816 q^{17} +(331.947 + 554.987i) q^{18} -428.041i q^{19} +(-84.6187 + 157.606i) q^{20} -586.088 q^{21} +(-91.6316 + 54.8064i) q^{22} +360.456i q^{23} +(46.1472 + 995.917i) q^{24} +125.000 q^{25} +(-119.117 - 199.153i) q^{26} -1256.68i q^{27} +(-530.361 - 284.751i) q^{28} +964.509 q^{29} +(597.881 - 357.602i) q^{30} +417.993i q^{31} +(-442.107 + 923.644i) q^{32} +415.818 q^{33} +(-960.531 - 1605.93i) q^{34} +420.638i q^{35} +(1223.61 - 2279.03i) q^{36} -1797.48 q^{37} +(-1469.39 + 878.866i) q^{38} +903.742i q^{39} +(714.775 - 33.1201i) q^{40} -469.722 q^{41} +(1203.37 + 2011.93i) q^{42} -27.7492i q^{43} +(376.281 + 202.025i) q^{44} -1807.53 q^{45} +(1237.38 - 740.097i) q^{46} -1538.96i q^{47} +(3324.05 - 2203.26i) q^{48} +985.506 q^{49} +(-256.653 - 429.103i) q^{50} +7287.58i q^{51} +(-439.083 + 817.812i) q^{52} -276.057 q^{53} +(-4313.96 + 2580.25i) q^{54} -298.435i q^{55} +(111.453 + 2405.29i) q^{56} +6667.98 q^{57} +(-1980.36 - 3310.99i) q^{58} -3813.72i q^{59} +(-2455.17 - 1318.18i) q^{60} -2051.87 q^{61} +(1434.90 - 858.234i) q^{62} -6082.55i q^{63} +(4078.45 - 378.775i) q^{64} +648.620 q^{65} +(-853.768 - 1427.43i) q^{66} -1165.73i q^{67} +(-3540.67 + 6594.66i) q^{68} -5615.14 q^{69} +(1443.98 - 863.666i) q^{70} -5689.40i q^{71} +(-10335.8 + 478.926i) q^{72} -2001.05 q^{73} +(3690.64 + 6170.44i) q^{74} +1947.24i q^{75} +(6033.98 + 3239.64i) q^{76} +1004.26 q^{77} +(3102.38 - 1855.59i) q^{78} +705.728i q^{79} +(-1581.29 - 2385.69i) q^{80} +6481.10 q^{81} +(964.446 + 1612.47i) q^{82} +1626.53i q^{83} +(4435.82 - 8261.91i) q^{84} +5230.34 q^{85} +(-95.2580 + 56.9753i) q^{86} +15025.0i q^{87} +(-79.0735 - 1706.51i) q^{88} +7156.62 q^{89} +(3711.28 + 6204.94i) q^{90} +2182.68i q^{91} +(-5081.24 - 2728.12i) q^{92} -6511.45 q^{93} +(-5282.97 + 3159.83i) q^{94} -4785.65i q^{95} +(-14388.4 - 6887.10i) q^{96} -13005.4 q^{97} +(-2023.47 - 3383.07i) q^{98} +4315.45i 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 $

$2$	−2.05323	−	3.43282i	−0.513307	−	0.858205i
$2$	−2.05323	−	3.43282i	−0.513307	−	0.858205i
$3$			15.5779i			1.73088i	0.501015	+	0.865438i	$0.332960\pi$
$3$			15.5779i			1.73088i	−0.501015	+	0.865438i	$0.667040\pi$
$4$	−7.56853	+	14.0967i	−0.473033	+	0.881045i
$5$	11.1803			0.447214
$5$	11.1803			0.447214
$6$	53.4761	−	31.9849i	1.48545	−	0.888470i
$7$			37.6230i			0.767817i	0.923371	+	0.383909i	$0.125422\pi$
$7$			37.6230i			0.767817i	−0.923371	+	0.383909i	$0.874578\pi$
$8$	63.9314	−	2.96235i	0.998928	−	0.0462868i
$9$	−161.671			−1.99594
$10$	−22.9558	−	38.3801i	−0.229558	−	0.383801i
$11$		−	26.6928i		−	0.220602i	−0.993898	−	0.110301i	$-0.964819\pi$
$11$		−	26.6928i		−	0.220602i	0.993898	−	0.110301i	$-0.0351814\pi$
$12$	−219.597	−	117.902i	−1.52498	−	0.818762i
$13$	58.0144			0.343280			0.171640	−	0.985160i	$-0.445093\pi$
$13$	58.0144			0.343280			0.171640	+	0.985160i	$0.445093\pi$
$14$	129.153	−	77.2486i	0.658945	−	0.394126i
$15$			174.166i			0.774072i
$16$	−141.435	−	213.383i	−0.552480	−	0.833526i
$17$	467.816			1.61874			0.809370	−	0.587300i	$-0.199809\pi$
$17$	467.816			1.61874			0.809370	+	0.587300i	$0.199809\pi$
$18$	331.947	+	554.987i	1.02453	+	1.71292i
$19$		−	428.041i		−	1.18571i	−0.805309	−	0.592855i	$-0.798001\pi$
$19$		−	428.041i		−	1.18571i	0.805309	−	0.592855i	$-0.201999\pi$
$20$	−84.6187	+	157.606i	−0.211547	+	0.394015i
$21$	−586.088			−1.32900
$22$	−91.6316	+	54.8064i	−0.189322	+	0.113236i
$23$			360.456i			0.681391i	0.940174	+	0.340695i	$0.110662\pi$
$23$			360.456i			0.681391i	−0.940174	+	0.340695i	$0.889338\pi$
$24$	46.1472	+	995.917i	0.0801167	+	1.72902i
$25$	125.000			0.200000
$26$	−119.117	−	199.153i	−0.176208	−	0.294605i
$27$		−	1256.68i		−	1.72384i
$28$	−530.361	−	284.751i	−0.676481	−	0.363203i
$29$	964.509			1.14686			0.573430	−	0.819255i	$-0.305612\pi$
$29$	964.509			1.14686			0.573430	+	0.819255i	$0.305612\pi$
$30$	597.881	−	357.602i	0.664312	−	0.397336i
$31$			417.993i			0.434956i	0.976065	+	0.217478i	$0.0697831\pi$
$31$			417.993i			0.434956i	−0.976065	+	0.217478i	$0.930217\pi$
$32$	−442.107	+	923.644i	−0.431745	+	0.901996i
$33$	415.818			0.381834
$34$	−960.531	−	1605.93i	−0.830909	−	1.38921i
$35$			420.638i			0.343378i
$36$	1223.61	−	2279.03i	0.944143	−	1.75851i
$37$	−1797.48			−1.31299			−0.656495	−	0.754330i	$-0.727962\pi$
$37$	−1797.48			−1.31299			−0.656495	+	0.754330i	$0.727962\pi$
$38$	−1469.39	+	878.866i	−1.01758	+	0.608633i
$39$			903.742i			0.594176i
$40$	714.775	−	33.1201i	0.446734	−	0.0207001i
$41$	−469.722			−0.279430			−0.139715	−	0.990192i	$-0.544619\pi$
$41$	−469.722			−0.279430			−0.139715	+	0.990192i	$0.544619\pi$
$42$	1203.37	+	2011.93i	0.682183	+	1.14055i
$43$		−	27.7492i		−	0.0150077i	−0.999972	−	0.00750384i	$-0.997611\pi$
$43$		−	27.7492i		−	0.0150077i	0.999972	−	0.00750384i	$-0.00238857\pi$
$44$	376.281	+	202.025i	0.194360	+	0.104352i
$45$	−1807.53			−0.892609
$46$	1237.38	−	740.097i	0.584773	−	0.349762i
$47$		−	1538.96i		−	0.696677i	−0.937369	−	0.348339i	$-0.886746\pi$
$47$		−	1538.96i		−	0.696677i	0.937369	−	0.348339i	$-0.113254\pi$
$48$	3324.05	−	2203.26i	1.44273	−	0.956275i
$49$	985.506			0.410457
$50$	−256.653	−	429.103i	−0.102661	−	0.171641i
$51$			7287.58i			2.80184i
$52$	−439.083	+	817.812i	−0.162383	+	0.302445i
$53$	−276.057			−0.0982758			−0.0491379	−	0.998792i	$-0.515647\pi$
$53$	−276.057			−0.0982758			−0.0491379	+	0.998792i	$0.515647\pi$
$54$	−4313.96	+	2580.25i	−1.47941	+	0.884859i
$55$		−	298.435i		−	0.0986561i
$56$	111.453	+	2405.29i	0.0355398	+	0.766994i
$57$	6667.98			2.05232
$58$	−1980.36	−	3310.99i	−0.588691	−	0.984241i
$59$		−	3813.72i		−	1.09558i	−0.836616	−	0.547791i	$-0.815469\pi$
$59$		−	3813.72i		−	1.09558i	0.836616	−	0.547791i	$-0.184531\pi$
$60$	−2455.17	−	1318.18i	−0.681992	−	0.366161i
$61$	−2051.87			−0.551429			−0.275714	−	0.961240i	$-0.588914\pi$
$61$	−2051.87			−0.551429			−0.275714	+	0.961240i	$0.588914\pi$
$62$	1434.90	−	858.234i	0.373282	−	0.223266i
$63$		−	6082.55i		−	1.53251i
$64$	4078.45	−	378.775i	0.995715	−	0.0924743i
$65$	648.620			0.153520
$66$	−853.768	−	1427.43i	−0.195998	−	0.327692i
$67$		−	1165.73i		−	0.259686i	−0.991535	−	0.129843i	$-0.958553\pi$
$67$		−	1165.73i		−	0.259686i	0.991535	−	0.129843i	$-0.0414474\pi$
$68$	−3540.67	+	6594.66i	−0.765717	+	1.42618i
$69$	−5615.14			−1.17940
$70$	1443.98	−	863.666i	0.294689	−	0.176258i
$71$		−	5689.40i		−	1.12863i	−0.825561	−	0.564313i	$-0.809141\pi$
$71$		−	5689.40i		−	1.12863i	0.825561	−	0.564313i	$-0.190859\pi$
$72$	−10335.8	+	478.926i	−1.99380	+	0.0923854i
$73$	−2001.05			−0.375501			−0.187751	−	0.982217i	$-0.560120\pi$
$73$	−2001.05			−0.375501			−0.187751	+	0.982217i	$0.560120\pi$
$74$	3690.64	+	6170.44i	0.673967	+	1.12682i
$75$			1947.24i			0.346175i
$76$	6033.98	+	3239.64i	1.04466	+	0.560880i
$77$	1004.26			0.169382
$78$	3102.38	−	1855.59i	0.509925	−	0.304994i
$79$			705.728i			0.113079i	0.998400	+	0.0565396i	$0.0180067\pi$
$79$			705.728i			0.113079i	−0.998400	+	0.0565396i	$0.981993\pi$
$80$	−1581.29	−	2385.69i	−0.247077	−	0.372764i
$81$	6481.10			0.987822
$82$	964.446	+	1612.47i	0.143433	+	0.239809i
$83$			1626.53i			0.236106i	0.993007	+	0.118053i	$0.0376652\pi$
$83$			1626.53i			0.236106i	−0.993007	+	0.118053i	$0.962335\pi$
$84$	4435.82	−	8261.91i	0.628659	−	1.17091i
$85$	5230.34			0.723922
$86$	−95.2580	+	56.9753i	−0.0128797	+	0.00770354i
$87$			15025.0i			1.98507i
$88$	−79.0735	−	1706.51i	−0.0102109	−	0.220365i
$89$	7156.62			0.903499			0.451750	−	0.892145i	$-0.350800\pi$
$89$	7156.62			0.903499			0.451750	+	0.892145i	$0.350800\pi$
$90$	3711.28	+	6204.94i	0.458182	+	0.766042i
$91$			2182.68i			0.263577i
$92$	−5081.24	−	2728.12i	−0.600336	−	0.322320i
$93$	−6511.45			−0.752856
$94$	−5282.97	+	3159.83i	−0.597892	+	0.357609i
$95$		−	4785.65i		−	0.530266i
$96$	−14388.4	−	6887.10i	−1.56124	−	0.747298i
$97$	−13005.4			−1.38223			−0.691113	−	0.722747i	$-0.742879\pi$
$97$	−13005.4			−1.38223			−0.691113	+	0.722747i	$0.742879\pi$
$98$	−2023.47	−	3383.07i	−0.210690	−	0.352256i
$99$			4315.45i			0.440307i
$100$	−946.066	+	1762.09i	−0.0946066	+	0.176209i
$101$	−9618.86			−0.942933			−0.471467	−	0.881884i	$-0.656275\pi$
$101$	−9618.86			−0.942933			−0.471467	+	0.881884i	$0.656275\pi$
$102$	25017.0	−	14963.1i	2.40455	−	1.43820i
$103$			20364.5i			1.91955i	0.280767	+	0.959776i	$0.409411\pi$
$103$			20364.5i			1.91955i	−0.280767	+	0.959776i	$0.590589\pi$
$104$	3708.94	−	171.859i	0.342912	−	0.0158893i
$105$	−6552.66			−0.594346
$106$	566.807	+	947.653i	0.0504456	+	0.0843408i
$107$		−	22152.3i		−	1.93486i	−0.253129	−	0.967432i	$-0.581460\pi$
$107$		−	22152.3i		−	1.93486i	0.253129	−	0.967432i	$-0.418540\pi$
$108$	17715.1	+	9511.22i	1.51878	+	0.815433i
$109$	−4013.04			−0.337770			−0.168885	−	0.985636i	$-0.554017\pi$
$109$	−4013.04			−0.337770			−0.168885	+	0.985636i	$0.554017\pi$
$110$	−1024.47	+	612.754i	−0.0846672	+	0.0506408i
$111$		−	28001.0i		−	2.27262i
$112$	8028.11	−	5321.21i	0.639996	−	0.424204i
$113$	22690.2			1.77698			0.888489	−	0.458897i	$-0.151755\pi$
$113$	22690.2			1.77698			0.888489	+	0.458897i	$0.151755\pi$
$114$	−13690.9	−	22890.0i	−1.05347	−	1.76131i
$115$			4030.02i			0.304727i
$116$	−7299.91	+	13596.4i	−0.542502	+	1.01044i
$117$	−9379.23			−0.685165
$118$	−13091.8	+	7830.42i	−0.940234	+	0.562369i
$119$			17600.6i			1.24290i
$120$	515.941	+	11134.7i	0.0358293	+	0.773242i
$121$	13928.5			0.951335
$122$	4212.95	+	7043.69i	0.283052	+	0.473239i
$123$		−	7317.28i		−	0.483659i
$124$	−5892.33	−	3163.59i	−0.383216	−	0.205749i
$125$	1397.54			0.0894427
$126$	−20880.3	+	12488.8i	−1.31521	+	0.786649i
$127$			22038.9i			1.36641i	0.730225	+	0.683206i	$0.239415\pi$
$127$			22038.9i			1.36641i	−0.730225	+	0.683206i	$0.760585\pi$
$128$	−9674.24	−	13222.9i	−0.590469	−	0.807060i
$129$	432.274			0.0259764
$130$	−1331.76	−	2226.60i	−0.0788026	−	0.131751i
$131$		−	4968.89i		−	0.289545i	−0.989465	−	0.144773i	$-0.953755\pi$
$131$		−	4968.89i		−	0.289545i	0.989465	−	0.144773i	$-0.0462451\pi$
$132$	−3147.13	+	5861.66i	−0.180620	+	0.336413i
$133$	16104.2			0.910409
$134$	−4001.75	+	2393.51i	−0.222864	+	0.133299i
$135$		−	14050.1i		−	0.770925i
$136$	29908.1	−	1385.83i	1.61700	−	0.0749262i
$137$	−11945.1			−0.636426			−0.318213	−	0.948019i	$-0.603083\pi$
$137$	−11945.1			−0.636426			−0.318213	+	0.948019i	$0.603083\pi$
$138$	11529.2	+	19275.8i	0.605395	+	1.01217i
$139$		−	20123.7i		−	1.04154i	−0.853696	−	0.520772i	$-0.825644\pi$
$139$		−	20123.7i		−	1.04154i	0.853696	−	0.520772i	$-0.174356\pi$
$140$	−5929.62	−	3183.61i	−0.302532	−	0.162429i
$141$	23973.8			1.20586
$142$	−19530.7	+	11681.6i	−0.968592	+	0.579331i
$143$		−	1548.57i		−	0.0757282i
$144$	22865.9	+	34497.7i	1.10271	+	1.66366i
$145$	10783.5			0.512891
$146$	4108.60	+	6869.24i	0.192747	+	0.322257i
$147$			15352.1i			0.710450i
$148$	13604.3	−	25338.6i	0.621088	−	1.15680i
$149$	−6127.67			−0.276009			−0.138004	−	0.990432i	$-0.544069\pi$
$149$	−6127.67			−0.276009			−0.138004	+	0.990432i	$0.544069\pi$
$150$	6684.52	−	3998.12i	0.297090	−	0.177694i
$151$		−	15290.9i		−	0.670626i	−0.942107	−	0.335313i	$-0.891158\pi$
$151$		−	15290.9i		−	0.670626i	0.942107	−	0.335313i	$-0.108842\pi$
$152$	−1268.01	−	27365.3i	−0.0548827	−	1.18444i
$153$	−75632.1			−3.23090
$154$	−2061.98	−	3447.46i	−0.0869448	−	0.145364i
$155$			4673.30i			0.194518i
$156$	−12739.8	−	6839.99i	−0.523496	−	0.281065i
$157$	26931.5			1.09260			0.546300	−	0.837589i	$-0.316036\pi$
$157$	26931.5			1.09260			0.546300	+	0.837589i	$0.316036\pi$
$158$	2422.64	−	1449.02i	0.0970452	−	0.0580443i
$159$		−	4300.38i		−	0.170103i
$160$	−4942.91	+	10326.6i	−0.193082	+	0.403385i
$161$	−13561.4			−0.523183
$162$	−13307.2	−	22248.5i	−0.507055	−	0.847754i
$163$		−	19964.4i		−	0.751418i	−0.926738	−	0.375709i	$-0.877399\pi$
$163$		−	19964.4i		−	0.751418i	0.926738	−	0.375709i	$-0.122601\pi$
$164$	3555.10	−	6621.54i	0.132180	−	0.246191i
$165$	4648.98			0.170762
$166$	5583.60	−	3339.64i	0.202627	−	0.121195i
$167$			11615.2i			0.416481i	0.978078	+	0.208240i	$0.0667737\pi$
$167$			11615.2i			0.416481i	−0.978078	+	0.208240i	$0.933226\pi$
$168$	−37469.4	+	1736.20i	−1.32757	+	0.0615150i
$169$	−25195.3			−0.882159
$170$	−10739.1	−	17954.8i	−0.371594	−	0.621274i
$171$			69201.8i			2.36660i
$172$	391.172	+	210.020i	0.0132224	+	0.00709912i
$173$	27260.4			0.910835			0.455417	−	0.890278i	$-0.349490\pi$
$173$	27260.4			0.910835			0.455417	+	0.890278i	$0.349490\pi$
$174$	51578.2	−	30849.8i	1.70360	−	1.01895i
$175$			4702.88i			0.153563i
$176$	−5695.78	+	3775.29i	−0.183877	+	0.121878i
$177$	59409.7			1.89632
$178$	−14694.2	−	24567.4i	−0.463772	−	0.775388i
$179$			36368.3i			1.13505i	0.823355	+	0.567527i	$0.192100\pi$
$179$			36368.3i			1.13505i	−0.823355	+	0.567527i	$0.807900\pi$
$180$	13680.4	−	25480.3i	0.422234	−	0.786429i
$181$	−46165.5			−1.40916			−0.704580	−	0.709625i	$-0.748864\pi$
$181$	−46165.5			−1.40916			−0.704580	+	0.709625i	$0.748864\pi$
$182$	7492.74	−	4481.53i	0.226203	−	0.135296i
$183$		−	31963.8i		−	0.954456i
$184$	1067.80	+	23044.4i	0.0315394	+	0.680660i
$185$	−20096.5			−0.587187
$186$	13369.5	+	22352.6i	0.386446	+	0.646105i
$187$		−	12487.3i		−	0.357097i
$188$	21694.3	+	11647.7i	0.613804	+	0.329551i
$189$	47280.1			1.32360
$190$	−16428.3	+	9826.02i	−0.455077	+	0.272189i
$191$			23694.9i			0.649513i	0.945798	+	0.324757i	$0.105282\pi$
$191$			23694.9i			0.649513i	−0.945798	+	0.324757i	$0.894718\pi$
$192$	5900.51	+	63533.6i	0.160062	+	1.72346i
$193$	−17101.4			−0.459111			−0.229556	−	0.973296i	$-0.573727\pi$
$193$	−17101.4			−0.459111			−0.229556	+	0.973296i	$0.573727\pi$
$194$	26703.0	+	44645.1i	0.709506	+	1.18623i
$195$			10104.1i			0.265724i
$196$	−7458.83	+	13892.4i	−0.194159	+	0.361631i
$197$	−55597.2			−1.43259			−0.716293	−	0.697800i	$-0.754163\pi$
$197$	−55597.2			−1.43259			−0.716293	+	0.697800i	$0.754163\pi$
$198$	14814.2	−	8860.59i	0.377874	−	0.226012i
$199$		−	58399.0i		−	1.47468i	−0.675520	−	0.737342i	$-0.736081\pi$
$199$		−	58399.0i		−	1.47468i	0.675520	−	0.737342i	$-0.263919\pi$
$200$	7991.43	−	370.294i	0.199786	−	0.00925735i
$201$	18159.7			0.449485
$202$	19749.7	+	33019.8i	0.484014	+	0.809230i
$203$			36287.8i			0.880579i
$204$	−102731.	−	55156.2i	−2.46855	−	1.32536i
$205$	−5251.65			−0.124965
$206$	69907.8	−	41813.0i	1.64737	−	0.985319i
$207$		−	58275.1i		−	1.36001i
$208$	−8205.25	−	12379.3i	−0.189655	−	0.286133i
$209$	−11425.6			−0.261570
$210$	13454.1	+	22494.1i	0.305081	+	0.510071i
$211$		−	16960.3i		−	0.380951i	−0.981692	−	0.190475i	$-0.938997\pi$
$211$		−	16960.3i		−	0.380951i	0.981692	−	0.190475i	$-0.0610030\pi$
$212$	2089.34	−	3891.49i	0.0464877	−	0.0865854i
$213$	88628.9			1.95351
$214$	−76044.8	+	45483.6i	−1.66051	+	0.993179i
$215$		−	310.245i		−	0.00671163i
$216$	−3722.73	−	80341.3i	−0.0797910	−	1.72199i
$217$	−15726.2			−0.333967
$218$	8239.68	+	13776.1i	0.173379	+	0.289876i
$219$		−	31172.1i		−	0.649947i
$220$	4206.95	+	2258.71i	0.0869204	+	0.0466676i
$221$	27140.0			0.555681
$222$	−96122.5	+	57492.4i	−1.95038	+	1.16655i
$223$			16817.9i			0.338191i	0.985600	+	0.169095i	$0.0540846\pi$
$223$			16817.9i			0.338191i	−0.985600	+	0.169095i	$0.945915\pi$
$224$	−34750.3	−	16633.4i	−0.692568	−	0.331501i
$225$	−20208.8			−0.399187
$226$	−46588.2	−	77891.6i	−0.912135	−	1.52501i
$227$		−	81040.8i		−	1.57272i	−0.617768	−	0.786361i	$-0.711963\pi$
$227$		−	81040.8i		−	1.57272i	0.617768	−	0.786361i	$-0.288037\pi$
$228$	−50466.8	+	93996.7i	−0.970814	+	1.80818i
$229$	47720.6			0.909987			0.454994	−	0.890495i	$-0.349642\pi$
$229$	47720.6			0.909987			0.454994	+	0.890495i	$0.349642\pi$
$230$	13834.3	−	8274.53i	0.261518	−	0.156418i
$231$			15644.3i			0.293179i
$232$	61662.4	−	2857.22i	1.14563	−	0.0530844i
$233$	−15756.7			−0.290237			−0.145119	−	0.989414i	$-0.546356\pi$
$233$	−15756.7			−0.290237			−0.145119	+	0.989414i	$0.546356\pi$
$234$	19257.7	+	32197.2i	0.351700	+	0.588012i
$235$		−	17206.1i		−	0.311563i
$236$	53760.9	+	28864.2i	0.965256	+	0.518246i
$237$	−10993.8			−0.195726
$238$	60419.9	−	36138.1i	1.06666	−	0.637987i
$239$			110092.i			1.92735i	0.267083	+	0.963673i	$0.413940\pi$
$239$			110092.i			1.92735i	−0.267083	+	0.963673i	$0.586060\pi$
$240$	37164.0	−	24633.2i	0.645209	−	0.427659i
$241$	−26260.5			−0.452136			−0.226068	−	0.974112i	$-0.572587\pi$
$241$	−26260.5			−0.452136			−0.226068	+	0.974112i	$0.572587\pi$
$242$	−28598.3	−	47814.0i	−0.488326	−	0.816441i
$243$		−	829.219i		−	0.0140429i
$244$	15529.6	−	28924.6i	0.260844	−	0.485834i
$245$	11018.3			0.183562
$246$	−25118.9	+	15024.0i	−0.415079	+	0.248266i
$247$		−	24832.5i		−	0.407031i
$248$	1238.24	+	26722.9i	0.0201327	+	0.434490i
$249$	−25338.0			−0.408670
$250$	−2869.47	−	4797.51i	−0.0459115	−	0.0767602i
$251$		−	24402.1i		−	0.387329i	−0.981068	−	0.193665i	$-0.937963\pi$
$251$		−	24402.1i		−	0.387329i	0.981068	−	0.193665i	$-0.0620374\pi$
$252$	85743.9	+	46035.9i	1.35021	+	0.724929i
$253$	9621.57			0.150316
$254$	75655.5	−	45250.8i	1.17266	−	0.701388i
$255$			81477.6i			1.25302i
$256$	−25528.4	+	60359.5i	−0.389532	+	0.921013i
$257$	30469.1			0.461311			0.230655	−	0.973036i	$-0.425913\pi$
$257$	30469.1			0.461311			0.230655	+	0.973036i	$0.425913\pi$
$258$	−887.556	−	1483.92i	−0.0133339	−	0.0222931i
$259$		−	67626.8i		−	1.00814i
$260$	−4909.10	+	9143.42i	−0.0726198	+	0.135258i
$261$	−155933.			−2.28906
$262$	−17057.3	+	10202.2i	−0.248489	+	0.148625i
$263$			45832.0i			0.662610i	0.943524	+	0.331305i	$0.107489\pi$
$263$			45832.0i			0.662610i	−0.943524	+	0.331305i	$0.892511\pi$
$264$	26583.8	−	1231.80i	0.381425	−	0.0176739i
$265$	−3086.41			−0.0439503
$266$	−33065.6	−	55282.9i	−0.467319	−	0.781318i
$267$			111485.i			1.56385i
$268$	16433.0	+	8822.87i	0.228795	+	0.122840i
$269$	−36915.5			−0.510157			−0.255078	−	0.966920i	$-0.582101\pi$
$269$	−36915.5			−0.510157			−0.255078	+	0.966920i	$0.582101\pi$
$270$	−48231.5	+	28848.1i	−0.661612	+	0.395721i
$271$			123746.i			1.68497i	0.538720	+	0.842485i	$0.318908\pi$
$271$			123746.i			1.68497i	−0.538720	+	0.842485i	$0.681092\pi$
$272$	−66165.4	−	99823.8i	−0.894321	−	1.34926i
$273$	−34001.5			−0.456219
$274$	24526.0	+	41005.4i	0.326682	+	0.546185i
$275$		−	3336.60i		−	0.0441203i
$276$	42498.3	−	79155.0i	0.557896	−	1.03911i
$277$	95245.1			1.24132			0.620659	−	0.784081i	$-0.286865\pi$
$277$	95245.1			1.24132			0.620659	+	0.784081i	$0.286865\pi$
$278$	−69080.9	+	41318.4i	−0.893858	+	0.534631i
$279$		−	67577.2i		−	0.868144i
$280$	1246.08	+	26892.0i	0.0158939	+	0.343010i
$281$	58728.9			0.743771			0.371885	−	0.928279i	$-0.378711\pi$
$281$	58728.9			0.743771			0.371885	+	0.928279i	$0.378711\pi$
$282$	−49223.5	−	82297.6i	−0.618977	−	1.03488i
$283$			71397.1i			0.891472i	0.895164	+	0.445736i	$0.147058\pi$
$283$			71397.1i			0.891472i	−0.895164	+	0.445736i	$0.852942\pi$
$284$	80201.9	+	43060.4i	0.994369	+	0.533877i
$285$	74550.3			0.917825
$286$	−5315.95	+	3179.56i	−0.0649904	+	0.0388718i
$287$		−	17672.4i		−	0.214551i
$288$	71475.8	−	149326.i	0.861735	−	1.80032i
$289$	135330.			1.62032
$290$	−22141.0	−	37018.0i	−0.263270	−	0.440166i
$291$		−	202596.i		−	2.39246i
$292$	15145.0	−	28208.2i	0.177625	−	0.330834i
$293$	−56264.5			−0.655390			−0.327695	−	0.944784i	$-0.606272\pi$
$293$	−56264.5			−0.655390			−0.327695	+	0.944784i	$0.606272\pi$
$294$	52701.1	−	31521.4i	0.609712	−	0.364679i
$295$		−	42638.7i		−	0.489959i
$296$	−114916.	+	5324.78i	−1.31158	+	0.0607741i
$297$	−33544.3			−0.380282
$298$	12581.5	+	21035.2i	0.141677	+	0.236872i
$299$			20911.6i			0.233908i
$300$	−27449.6	−	14737.7i	−0.304996	−	0.163752i
$301$	1044.01			0.0115231
$302$	−52491.0	+	31395.7i	−0.575534	+	0.344236i
$303$		−	149842.i		−	1.63210i
$304$	−91336.6	+	60540.0i	−0.988320	+	0.655081i
$305$	−22940.6			−0.246607
$306$	155290.	+	259632.i	1.65844	+	2.77277i
$307$			175077.i			1.85760i	0.370577	+	0.928802i	$0.379160\pi$
$307$			175077.i			1.85760i	−0.370577	+	0.928802i	$0.620840\pi$
$308$	−7600.80	+	14156.8i	−0.0801232	+	0.149233i
$309$	−317236.			−3.32251
$310$	16042.6	−	9595.35i	0.166937	−	0.0998475i
$311$			23621.0i			0.244218i	0.992517	+	0.122109i	$0.0389657\pi$
$311$			23621.0i			0.244218i	−0.992517	+	0.122109i	$0.961034\pi$
$312$	2677.20	+	57777.5i	0.0275025	+	0.593539i
$313$	−132585.			−1.35333			−0.676667	−	0.736289i	$-0.736576\pi$
$313$	−132585.			−1.35333			−0.676667	+	0.736289i	$0.736576\pi$
$314$	−55296.5	−	92451.1i	−0.560839	−	0.937676i
$315$		−	68004.9i		−	0.685361i
$316$	−9948.44	−	5341.32i	−0.0996279	−	0.0534902i
$317$	−33855.0			−0.336902			−0.168451	−	0.985710i	$-0.553877\pi$
$317$	−33855.0			−0.336902			−0.168451	+	0.985710i	$0.553877\pi$
$318$	−14762.4	+	8829.66i	−0.145984	+	0.0873151i
$319$		−	25745.5i		−	0.252999i
$320$	45598.4	−	4234.83i	0.445297	−	0.0413558i
$321$	345086.			3.34901
$322$	27844.7	+	46554.0i	0.268553	+	0.448999i
$323$		−	200244.i		−	1.91936i
$324$	−49052.4	+	91362.2i	−0.467272	+	0.870315i
$325$	7251.80			0.0686561
$326$	−68534.3	+	40991.5i	−0.644871	+	0.385708i
$327$		−	62514.8i		−	0.584638i
$328$	−30030.0	+	1391.48i	−0.279131	+	0.0129339i
$329$	57900.4			0.534921
$330$	−9545.41	−	15959.1i	−0.0876530	−	0.146548i
$331$		−	24338.3i		−	0.222144i	−0.993812	−	0.111072i	$-0.964572\pi$
$331$		−	24338.3i		−	0.222144i	0.993812	−	0.111072i	$-0.0354283\pi$
$332$	−22928.8	−	12310.5i	−0.208020	−	0.111686i
$333$	290601.			2.62064
$334$	39873.0	−	23848.7i	0.357426	−	0.213782i
$335$		−	13033.3i		−	0.116135i
$336$	82893.2	+	125061.i	0.734244	+	1.10775i
$337$	5373.65			0.0473161			0.0236581	−	0.999720i	$-0.492469\pi$
$337$	5373.65			0.0473161			0.0236581	+	0.999720i	$0.492469\pi$
$338$	51731.7	+	86491.1i	0.452818	+	0.757073i
$339$			353466.i			3.07573i
$340$	−39585.9	+	73730.6i	−0.342439	+	0.637808i
$341$	11157.4			0.0959521
$342$	237557.	−	142087.i	2.03103	−	1.21479i
$343$			127411.i			1.08297i
$344$	−82.2029	−	1774.04i	−0.000694656	−	0.0149916i
$345$	−62779.2			−0.527445
$346$	−55971.7	−	93580.0i	−0.467537	−	0.781683i
$347$			78906.7i			0.655322i	0.944795	+	0.327661i	$0.106260\pi$
$347$			78906.7i			0.655322i	−0.944795	+	0.327661i	$0.893740\pi$
$348$	−211803.	−	113717.i	−1.74894	−	0.939005i
$349$	139841.			1.14811			0.574053	−	0.818818i	$-0.305370\pi$
$349$	139841.			1.14811			0.574053	+	0.818818i	$0.305370\pi$
$350$	16144.1	−	9656.08i	0.131789	−	0.0788251i
$351$		−	72905.5i		−	0.591761i
$352$	24654.6	+	11801.1i	0.198982	+	0.0952437i
$353$	−35542.6			−0.285233			−0.142616	−	0.989778i	$-0.545552\pi$
$353$	−35542.6			−0.285233			−0.142616	+	0.989778i	$0.545552\pi$
$354$	−121982.	−	203943.i	−0.973391	−	1.62743i
$355$		−	63609.4i		−	0.504737i
$356$	−54165.0	+	100885.i	−0.427385	+	0.796023i
$357$	−274181.			−2.15130
$358$	124846.	−	74672.3i	0.974110	−	0.582631i
$359$		−	179016.i		−	1.38900i	−0.719491	−	0.694502i	$-0.755625\pi$
$359$		−	179016.i		−	1.38900i	0.719491	−	0.694502i	$-0.244375\pi$
$360$	−115558.	+	5354.55i	−0.891653	+	0.0413160i
$361$	−52898.4			−0.405908
$362$	94788.1	+	158478.i	0.723331	+	1.20935i
$363$			216977.i			1.64664i
$364$	−30768.6	−	16519.6i	−0.232223	−	0.124680i
$365$	−22372.4			−0.167929
$366$	−109726.	+	65628.8i	−0.819119	+	0.489928i
$367$		−	32200.7i		−	0.239075i	−0.992830	−	0.119537i	$-0.961859\pi$
$367$		−	32200.7i		−	0.239075i	0.992830	−	0.119537i	$-0.0381411\pi$
$368$	76915.0	−	50981.0i	0.567957	−	0.376455i
$369$	75940.3			0.557725
$370$	41262.6	+	68987.6i	0.301407	+	0.503927i
$371$		−	10386.1i		−	0.0754578i
$372$	49282.1	−	91790.1i	0.356125	−	0.663300i
$373$	−204296.			−1.46839			−0.734196	−	0.678937i	$-0.762441\pi$
$373$	−204296.			−1.46839			−0.734196	+	0.678937i	$0.762441\pi$
$374$	−42866.7	+	25639.3i	−0.306462	+	0.183300i
$375$			21770.8i			0.154814i
$376$	−4558.94	−	98387.9i	−0.0322469	−	0.695930i
$377$	55955.4			0.393694
$378$	−97076.8	−	162304.i	−0.679410	−	1.13592i
$379$		−	135870.i		−	0.945903i	−0.881089	−	0.472951i	$-0.843189\pi$
$379$		−	135870.i		−	0.945903i	0.881089	−	0.472951i	$-0.156811\pi$
$380$	67461.9	+	36220.3i	0.467188	+	0.250833i
$381$	−343319.			−2.36509
$382$	81340.3	−	48651.0i	0.557416	−	0.333399i
$383$		−	155856.i		−	1.06249i	−0.847218	−	0.531245i	$-0.821724\pi$
$383$		−	155856.i		−	1.06249i	0.847218	−	0.531245i	$-0.178276\pi$
$384$	205985.	−	150704.i	1.39692	−	1.02203i
$385$	11228.0			0.0757498
$386$	35113.1	+	58706.1i	0.235665	+	0.394012i
$387$			4486.23i			0.0299543i
$388$	98431.4	−	183333.i	0.653838	−	1.21780i
$389$	91378.0			0.603869			0.301934	−	0.953329i	$-0.402368\pi$
$389$	91378.0			0.603869			0.301934	+	0.953329i	$0.402368\pi$
$390$	34685.7	−	20746.1i	0.228045	−	0.136398i
$391$			168627.i			1.10299i
$392$	63004.8	−	2919.42i	0.410017	−	0.0189987i
$393$	77404.8			0.501167
$394$	114154.	+	190855.i	0.735356	+	1.22945i
$395$			7890.28i			0.0505706i
$396$	−60833.6	−	32661.6i	−0.387930	−	0.208280i
$397$	−177315.			−1.12503			−0.562515	−	0.826787i	$-0.690166\pi$
$397$	−177315.			−1.12503			−0.562515	+	0.826787i	$0.690166\pi$
$398$	−200473.	+	119906.i	−1.26558	+	0.756965i
$399$			250870.i			1.57581i
$400$	−17679.4	−	26672.8i	−0.110496	−	0.166705i
$401$	198129.			1.23214			0.616070	−	0.787691i	$-0.288724\pi$
$401$	198129.			1.23214			0.616070	+	0.787691i	$0.288724\pi$
$402$	−37285.9	−	62338.8i	−0.230724	−	0.385751i
$403$			24249.6i			0.149312i
$404$	72800.6	−	135594.i	0.446038	−	0.830767i
$405$	72460.9			0.441767
$406$	124569.	−	74507.0i	0.755718	−	0.452007i
$407$			47979.9i			0.289648i
$408$	21588.4	+	465905.i	0.129688	+	2.79884i
$409$	−176772.			−1.05674			−0.528370	−	0.849014i	$-0.677196\pi$
$409$	−176772.			−1.05674			−0.528370	+	0.849014i	$0.677196\pi$
$410$	10782.8	+	18028.0i	0.0641454	+	0.107246i
$411$		−	186079.i		−	1.10158i
$412$	−287073.	−	154129.i	−1.69121	−	0.908011i
$413$	143484.			0.841206
$414$	−200048.	+	119652.i	−1.16717	+	0.698103i
$415$			18185.2i			0.105590i
$416$	−25648.6	+	53584.6i	−0.148210	+	0.309637i
$417$	313484.			1.80278
$418$	23459.4	+	39222.1i	0.134265	+	0.224480i
$419$			152807.i			0.870390i	0.900336	+	0.435195i	$0.143321\pi$
$419$			152807.i			0.870390i	−0.900336	+	0.435195i	$0.856679\pi$
$420$	49594.0	−	92371.0i	0.281145	−	0.523645i
$421$	196597.			1.10921			0.554604	−	0.832115i	$-0.312870\pi$
$421$	196597.			1.10921			0.554604	+	0.832115i	$0.312870\pi$
$422$	−58221.7	+	34823.4i	−0.326934	+	0.195545i
$423$			248805.i			1.39052i
$424$	−17648.7	+	817.777i	−0.0981705	+	0.00454887i
$425$	58477.0			0.323748
$426$	−181975.	−	304247.i	−1.00275	−	1.67651i
$427$		−	77197.5i		−	0.423397i
$428$	312274.	+	167660.i	1.70470	+	0.915255i
$429$	24123.4			0.131076
$430$	−1065.02	+	637.004i	−0.00575996	+	0.00344513i
$431$		−	230818.i		−	1.24255i	−0.783592	−	0.621276i	$-0.786615\pi$
$431$		−	230818.i		−	1.24255i	0.783592	−	0.621276i	$-0.213385\pi$
$432$	−268154.	+	177738.i	−1.43687	+	0.952388i
$433$	−284920.			−1.51966			−0.759832	−	0.650119i	$-0.774719\pi$
$433$	−284920.			−1.51966			−0.759832	+	0.650119i	$0.774719\pi$
$434$	32289.4	+	53985.1i	0.171427	+	0.286612i
$435$			167985.i			0.887752i
$436$	30372.8	−	56570.7i	0.159776	−	0.297590i
$437$	154290.			0.807932
$438$	−107008.	+	64003.4i	−0.557788	+	0.333622i
$439$		−	327852.i		−	1.70118i	−0.525832	−	0.850588i	$-0.676246\pi$
$439$		−	327852.i		−	1.70118i	0.525832	−	0.850588i	$-0.323754\pi$
$440$	−884.069	−	19079.3i	−0.00456647	−	0.0985503i
$441$	−159328.			−0.819245
$442$	−55724.6	−	93166.9i	−0.285235	−	0.476889i
$443$		−	179147.i		−	0.912854i	−0.889761	−	0.456427i	$-0.849129\pi$
$443$		−	179147.i		−	0.912854i	0.889761	−	0.456427i	$-0.150871\pi$
$444$	394722.	+	211926.i	2.00228	+	1.07503i
$445$	80013.4			0.404057
$446$	57732.8	−	34530.9i	0.290237	−	0.173596i
$447$		−	95456.2i		−	0.477737i
$448$	14250.7	+	153444.i	0.0710034	+	0.764527i
$449$	−308905.			−1.53226			−0.766129	−	0.642687i	$-0.777820\pi$
$449$	−308905.			−1.53226			−0.766129	+	0.642687i	$0.777820\pi$
$450$	41493.3	+	69373.3i	0.204905	+	0.342584i
$451$			12538.2i			0.0616428i
$452$	−171732.	+	319858.i	−0.840569	+	1.56560i
$453$	238201.			1.16077
$454$	−278198.	+	166395.i	−1.34972	+	0.807288i
$455$			24403.1i			0.117875i
$456$	426293.	−	19752.9i	2.05012	−	0.0949951i
$457$	56777.8			0.271861			0.135930	−	0.990718i	$-0.456598\pi$
$457$	56777.8			0.271861			0.135930	+	0.990718i	$0.456598\pi$
$458$	−97981.3	−	163816.i	−0.467102	−	0.780956i
$459$		−	587895.i		−	2.79045i
$460$	−56810.0	−	30501.3i	−0.268478	−	0.144146i
$461$	−259736.			−1.22217			−0.611084	−	0.791566i	$-0.709266\pi$
$461$	−259736.			−1.22217			−0.611084	+	0.791566i	$0.709266\pi$
$462$	53704.2	−	32121.3i	0.251608	−	0.150491i
$463$			64677.1i			0.301709i	0.988556	+	0.150855i	$0.0482025\pi$
$463$			64677.1i			0.301709i	−0.988556	+	0.150855i	$0.951797\pi$
$464$	−136415.	−	205810.i	−0.633617	−	0.955938i
$465$	−72800.2			−0.336687
$466$	32352.0	+	54089.9i	0.148981	+	0.249083i
$467$		−	105097.i		−	0.481899i	−0.970538	−	0.240950i	$-0.922541\pi$
$467$		−	105097.i		−	0.481899i	0.970538	−	0.240950i	$-0.0774589\pi$
$468$	70986.9	−	132216.i	0.324106	−	0.603661i
$469$	43858.4			0.199392
$470$	−59065.4	+	35328.0i	−0.267385	+	0.159928i
$471$			419536.i			1.89116i
$472$	−11297.6	−	243816.i	−0.0507109	−	1.09441i
$473$	−740.704			−0.00331072
$474$	22572.7	+	37739.6i	0.100468	+	0.167973i
$475$		−	53505.2i		−	0.237142i
$476$	−248111.	−	133211.i	−1.09505	−	0.587931i
$477$	44630.3			0.196152
$478$	377926.	−	226044.i	1.65406	−	0.989320i
$479$			131187.i			0.571770i	0.958264	+	0.285885i	$0.0922875\pi$
$479$			131187.i			0.571770i	−0.958264	+	0.285885i	$0.907712\pi$
$480$	−160867.	−	77000.1i	−0.698209	−	0.334202i
$481$	−104280.			−0.450724
$482$	53918.8	+	90147.7i	0.232084	+	0.388026i
$483$		−	211259.i		−	0.905566i
$484$	−105418.	+	196346.i	−0.450013	+	0.838169i
$485$	−145404.			−0.618150
$486$	−2846.56	+	1702.57i	−0.0120517	+	0.00720831i
$487$			34829.3i			0.146854i	0.997301	+	0.0734271i	$0.0233936\pi$
$487$			34829.3i			0.146854i	−0.997301	+	0.0734271i	$0.976606\pi$
$488$	−131179.	+	6078.35i	−0.550838	+	0.0255239i
$489$	311004.			1.30061
$490$	−22623.1	−	37823.8i	−0.0942235	−	0.157534i
$491$			357740.i			1.48390i	0.670456	+	0.741950i	$0.266099\pi$
$491$			357740.i			1.48390i	−0.670456	+	0.741950i	$0.733901\pi$
$492$	103150.	+	55381.0i	0.426126	+	0.228787i
$493$	451213.			1.85647
$494$	−85245.7	+	50986.8i	−0.349316	+	0.208932i
$495$			48248.2i			0.196911i
$496$	89192.5	−	59118.8i	0.362547	−	0.240305i
$497$	214053.			0.866578
$498$	52024.5	+	86980.7i	0.209773	+	0.350723i
$499$			235685.i			0.946523i	0.880922	+	0.473261i	$0.156923\pi$
$499$			235685.i			0.946523i	−0.880922	+	0.473261i	$0.843077\pi$
$500$	−10577.3	+	19700.8i	−0.0423093	+	0.0788030i
$501$	−180941.			−0.720877
$502$	−83768.2	+	50103.1i	−0.332408	+	0.198819i
$503$			94290.4i			0.372676i	0.982486	+	0.186338i	$0.0596619\pi$
$503$			94290.4i			0.372676i	−0.982486	+	0.186338i	$0.940338\pi$
$504$	−18018.6	−	388866.i	−0.0709351	−	1.53087i
$505$	−107542.			−0.421693
$506$	−19755.3	−	33029.1i	−0.0771581	−	0.129002i
$507$		−	392490.i		−	1.52691i
$508$	−310676.	−	166802.i	−1.20387	−	0.646358i
$509$	−145708.			−0.562405			−0.281202	−	0.959649i	$-0.590733\pi$
$509$	−145708.			−0.562405			−0.281202	+	0.959649i	$0.590733\pi$
$510$	279698.	−	167292.i	1.07535	−	0.643183i
$511$		−	75285.5i		−	0.288316i
$512$	259619.	−	36297.4i	0.990368	−	0.138464i
$513$	−537911.			−2.04398
$514$	−62560.0	−	104595.i	−0.236794	−	0.395899i
$515$			227682.i			0.858450i
$516$	−3271.68	+	6093.64i	−0.0122877	+	0.0228864i
$517$	−41079.2			−0.153688
$518$	−232151.	+	138853.i	−0.865188	+	0.517483i
$519$			424659.i			1.57654i
$520$	41467.2	−	1921.44i	0.153355	−	0.00710592i
$521$	115380.			0.425064			0.212532	−	0.977154i	$-0.431829\pi$
$521$	115380.			0.425064			0.212532	+	0.977154i	$0.431829\pi$
$522$	320166.	+	535290.i	1.17499	+	1.96448i
$523$			339555.i			1.24139i	0.784054	+	0.620693i	$0.213149\pi$
$523$			339555.i			1.24139i	−0.784054	+	0.620693i	$0.786851\pi$
$524$	70045.0	+	37607.1i	0.255102	+	0.136964i
$525$	−73261.0			−0.265799
$526$	157333.	−	94103.5i	0.568655	−	0.340122i
$527$			195544.i			0.704081i
$528$	−58811.1	−	88728.3i	−0.210956	−	0.318269i
$529$	149913.			0.535707
$530$	6337.09	+	10595.1i	0.0225600	+	0.0377184i
$531$			616567.i			2.18671i
$532$	−121885.	+	227017.i	−0.430653	+	0.802111i
$533$	−27250.6			−0.0959229
$534$	382708.	−	228904.i	1.34210	−	0.802733i
$535$		−	247670.i		−	0.865298i
$536$	−3453.31	−	74526.9i	−0.0120200	−	0.259408i
$537$	−566541.			−1.96464
$538$	75795.8	+	126724.i	0.261867	+	0.437819i
$539$		−	26305.9i		−	0.0905474i
$540$	198060.	+	106339.i	0.679220	+	0.364673i
$541$	274692.			0.938539			0.469269	−	0.883055i	$-0.344517\pi$
$541$	274692.			0.938539			0.469269	+	0.883055i	$0.344517\pi$
$542$	424798.	−	254078.i	1.44605	−	0.864906i
$543$		−	719161.i		−	2.43908i
$544$	−206825.	+	432095.i	−0.698883	+	1.46010i
$545$	−44867.2			−0.151055
$546$	69812.8	+	116721.i	0.234180	+	0.391529i
$547$		−	354189.i		−	1.18375i	−0.806029	−	0.591875i	$-0.798388\pi$
$547$		−	354189.i		−	1.18375i	0.806029	−	0.591875i	$-0.201612\pi$
$548$	90406.7	−	168387.i	0.301051	−	0.560720i
$549$	331727.			1.10062
$550$	−11454.0	+	6850.80i	−0.0378643	+	0.0226473i
$551$		−	412850.i		−	1.35984i
$552$	−358984.	+	16634.0i	−1.17814	+	0.0545907i
$553$	−26551.6			−0.0868242
$554$	−195560.	−	326959.i	−0.637177	−	1.06531i
$555$		−	313061.i		−	1.01635i
$556$	283677.	+	152306.i	0.917646	+	0.492684i
$557$	−2288.63			−0.00737675			−0.00368838	−	0.999993i	$-0.501174\pi$
$557$	−2288.63			−0.00737675			−0.00368838	+	0.999993i	$0.501174\pi$
$558$	−231981.	+	138751.i	−0.745046	+	0.445624i
$559$		−	1609.85i		−	0.00515184i
$560$	89757.0	−	59492.9i	0.286215	−	0.189710i
$561$	194526.			0.618090
$562$	−120584.	−	201606.i	−0.381782	−	0.638308i
$563$		−	48825.1i		−	0.154037i	−0.997030	−	0.0770187i	$-0.975460\pi$
$563$		−	48825.1i		−	0.154037i	0.997030	−	0.0770187i	$-0.0245401\pi$
$564$	−181446.	+	337951.i	−0.570413	+	1.06242i
$565$	253685.			0.794689
$566$	245093.	−	146594.i	0.765066	−	0.457598i
$567$			243839.i			0.758467i
$568$	−16854.0	−	363731.i	−0.0522404	−	1.12742i
$569$	202790.			0.626356			0.313178	−	0.949695i	$-0.398606\pi$
$569$	202790.			0.626356			0.313178	+	0.949695i	$0.398606\pi$
$570$	−153069.	−	255918.i	−0.471125	−	0.787682i
$571$			412759.i			1.26597i	0.774163	+	0.632986i	$0.218171\pi$
$571$			412759.i			1.26597i	−0.774163	+	0.632986i	$0.781829\pi$
$572$	21829.7	+	11720.4i	0.0667199	+	0.0358219i
$573$	−369116.			−1.12423
$574$	−60666.1	+	36285.4i	−0.184129	+	0.110131i
$575$			45057.0i			0.136278i
$576$	−659366.	+	61236.8i	−1.98738	+	0.184573i
$577$	−441255.			−1.32537			−0.662686	−	0.748897i	$-0.730584\pi$
$577$	−441255.			−1.32537			−0.662686	+	0.748897i	$0.730584\pi$
$578$	−277864.	−	464565.i	−0.831719	−	1.39056i
$579$		−	266404.i		−	0.794665i
$580$	−81615.5	+	152013.i	−0.242614	+	0.451880i
$581$	−61195.1			−0.181286
$582$	−695477.	+	415976.i	−2.05322	+	1.22807i
$583$			7368.73i			0.0216798i
$584$	−127930.	+	5927.81i	−0.375099	+	0.0173807i
$585$	−104863.			−0.306415
$586$	115524.	+	193146.i	0.336416	+	0.562459i
$587$			416031.i			1.20739i	0.797214	+	0.603697i	$0.206306\pi$
$587$			416031.i			1.20739i	−0.797214	+	0.603697i	$0.793694\pi$
$588$	−216414.	−	116193.i	−0.625938	−	0.336066i
$589$	178918.			0.515732
$590$	−146371.	+	87546.8i	−0.420485	+	0.251499i
$591$		−	866088.i		−	2.47963i
$592$	254227.	+	383552.i	0.725401	+	1.09441i
$593$	342542.			0.974101			0.487051	−	0.873374i	$-0.338073\pi$
$593$	342542.			0.974101			0.487051	+	0.873374i	$0.338073\pi$
$594$	68874.1	+	115152.i	0.195201	+	0.326360i
$595$			196781.i			0.555840i
$596$	46377.4	−	86380.1i	0.130561	−	0.243176i
$597$	909733.			2.55250
$598$	71785.8	−	42936.3i	0.200741	−	0.120066i
$599$		−	472260.i		−	1.31622i	−0.752923	−	0.658109i	$-0.771357\pi$
$599$		−	472260.i		−	1.31622i	0.752923	−	0.658109i	$-0.228643\pi$
$600$	5768.40	+	124490.i	0.0160233	+	0.345804i
$601$	−211692.			−0.586078			−0.293039	−	0.956101i	$-0.594667\pi$
$601$	−211692.			−0.586078			−0.293039	+	0.956101i	$0.594667\pi$
$602$	−2143.59	−	3583.90i	−0.00591491	−	0.00988923i
$603$			188465.i			0.518317i
$604$	215552.	+	115730.i	0.590851	+	0.317228i
$605$	155725.			0.425450
$606$	−514380.	+	307659.i	−1.40068	+	0.837768i
$607$		−	9168.57i		−	0.0248842i	−0.999923	−	0.0124421i	$-0.996039\pi$
$607$		−	9168.57i		−	0.0248842i	0.999923	−	0.0124421i	$-0.00396055\pi$
$608$	395358.	+	189240.i	1.06951	+	0.511925i
$609$	−565287.			−1.52417
$610$	47102.2	+	78750.9i	0.126585	+	0.211639i
$611$		−	89281.8i		−	0.239156i
$612$	572423.	−	1.06616e6i	1.52832	−	2.84657i
$613$	164930.			0.438915			0.219457	−	0.975622i	$-0.429571\pi$
$613$	164930.			0.438915			0.219457	+	0.975622i	$0.429571\pi$
$614$	601009.	−	359473.i	1.59421	−	0.953520i
$615$		−	81809.7i		−	0.216299i
$616$	64204.1	−	2974.99i	0.169200	−	0.00784013i
$617$	32007.8			0.0840787			0.0420394	−	0.999116i	$-0.486615\pi$
$617$	32007.8			0.0840787			0.0420394	+	0.999116i	$0.486615\pi$
$618$	651358.	+	1.08902e6i	1.70547	+	2.85139i
$619$			30448.1i			0.0794655i	0.999210	+	0.0397328i	$0.0126507\pi$
$619$			30448.1i			0.0794655i	−0.999210	+	0.0397328i	$0.987349\pi$
$620$	−65878.2	−	35370.0i	−0.171379	−	0.0920136i
$621$	452977.			1.17461
$622$	81086.6	−	48499.2i	0.209589	−	0.125359i
$623$			269254.i			0.693722i
$624$	192843.	−	127821.i	0.495261	−	0.328270i
$625$	15625.0			0.0400000
$626$	272227.	+	455140.i	0.694676	+	1.16144i
$627$		−	177987.i		−	0.452745i
$628$	−203832.	+	379646.i	−0.516836	+	0.962630i
$629$	−840891.			−2.12539
$630$	−233449.	+	139630.i	−0.588180	+	0.351800i
$631$		−	205747.i		−	0.516744i	−0.966045	−	0.258372i	$-0.916814\pi$
$631$		−	205747.i		−	0.516744i	0.966045	−	0.258372i	$-0.0831861\pi$
$632$	2090.61	+	45118.2i	0.00523407	+	0.112958i
$633$	264206.			0.659379
$634$	69511.9	+	116218.i	0.172934	+	0.289131i
$635$			246402.i			0.611078i
$636$	60621.3	+	32547.5i	0.149869	+	0.0804644i
$637$	57173.5			0.140902
$638$	−88379.6	+	52861.3i	−0.217125	+	0.129866i
$639$			919809.i			2.25266i
$640$	−108161.	−	147836.i	−0.264066	−	0.360928i
$641$	−588976.			−1.43345			−0.716723	−	0.697358i	$-0.754359\pi$
$641$	−588976.			−1.43345			−0.716723	+	0.697358i	$0.754359\pi$
$642$	−708539.	−	1.18462e6i	−1.71907	−	2.87414i
$643$		−	231907.i		−	0.560909i	−0.959867	−	0.280454i	$-0.909515\pi$
$643$		−	231907.i		−	0.560909i	0.959867	−	0.280454i	$-0.0904852\pi$
$644$	102640.	−	191172.i	0.247483	−	0.460948i
$645$	4832.97			0.0116170
$646$	−687403.	+	411147.i	−1.64720	+	0.985218i
$647$			427586.i			1.02144i	0.859746	+	0.510722i	$0.170622\pi$
$647$			427586.i			1.02144i	−0.859746	+	0.510722i	$0.829378\pi$
$648$	414346.	−	19199.3i	0.986763	−	0.0457231i
$649$	−101799.			−0.241687
$650$	−14889.6	−	24894.1i	−0.0352416	−	0.0589210i
$651$		−	244981.i		−	0.578056i
$652$	281433.	+	151101.i	0.662033	+	0.355445i
$653$	−348146.			−0.816461			−0.408231	−	0.912879i	$-0.633854\pi$
$653$	−348146.			−0.816461			−0.408231	+	0.912879i	$0.633854\pi$
$654$	−214602.	+	128357.i	−0.501739	+	0.300098i
$655$		−	55553.8i		−	0.129489i
$656$	66435.1	+	100231.i	0.154380	+	0.232912i
$657$	323511.			0.749477
$658$	−118883.	−	198762.i	−0.274578	−	0.459072i
$659$			64952.7i			0.149564i	0.997200	+	0.0747818i	$0.0238260\pi$
$659$			64952.7i			0.149564i	−0.997200	+	0.0747818i	$0.976174\pi$
$660$	−35185.9	+	65535.4i	−0.0807758	+	0.150449i
$661$	−175663.			−0.402048			−0.201024	−	0.979586i	$-0.564427\pi$
$661$	−175663.			−0.402048			−0.201024	+	0.979586i	$0.564427\pi$
$662$	−83548.9	+	49972.0i	−0.190645	+	0.114028i
$663$			422784.i			0.961816i
$664$	4818.36	+	103987.i	0.0109286	+	0.235853i
$665$	180051.			0.407147
$666$	−596669.	−	997580.i	−1.34519	−	2.24905i
$667$			347663.i			0.781460i
$668$	−163737.	−	87910.2i	−0.366938	−	0.197009i
$669$	−261987.			−0.585367
$670$	−44740.9	+	26760.3i	−0.0996679	+	0.0596130i
$671$			54770.1i			0.121646i
$672$	259114.	−	541336.i	0.573788	−	1.19875i
$673$	166579.			0.367781			0.183891	−	0.982947i	$-0.441131\pi$
$673$	166579.			0.367781			0.183891	+	0.982947i	$0.441131\pi$
$674$	−11033.3	−	18446.8i	−0.0242877	−	0.0406070i
$675$		−	157085.i		−	0.344768i
$676$	190692.	−	355171.i	0.417290	−	0.777221i
$677$	−528530.			−1.15317			−0.576584	−	0.817038i	$-0.695615\pi$
$677$	−528530.			−1.15317			−0.576584	+	0.817038i	$0.695615\pi$
$678$	1.21339e6	−	725746.i	2.63961	−	1.57879i
$679$		−	489301.i		−	1.06130i
$680$	334383.	−	15494.1i	0.723146	−	0.0335080i
$681$	1.26244e6			2.72219
$682$	−22908.7	−	38301.4i	−0.0492528	−	0.0823466i
$683$			144855.i			0.310521i	0.987874	+	0.155261i	$0.0496217\pi$
$683$			144855.i			0.310521i	−0.987874	+	0.155261i	$0.950378\pi$
$684$	−975518.	−	523755.i	−2.08508	−	1.11948i
$685$	−133550.			−0.284619
$686$	437378.	−	261603.i	0.929413	−	0.555897i
$687$			743387.i			1.57508i
$688$	−5921.20	+	3924.70i	−0.0125093	+	0.00829144i
$689$	−16015.3			−0.0337361
$690$	128900.	+	215510.i	0.270741	+	0.452656i
$691$		−	893708.i		−	1.87171i	−0.352380	−	0.935857i	$-0.614628\pi$
$691$		−	893708.i		−	1.87171i	0.352380	−	0.935857i	$-0.385372\pi$
$692$	−206321.	+	384282.i	−0.430855	+	0.802486i
$693$	−162360.			−0.338075
$694$	270873.	−	162013.i	0.562401	−	0.336381i
$695$		−	224989.i		−	0.465792i
$696$	44509.4	+	960571.i	0.0918826	+	1.98295i
$697$	−219743.			−0.452325
$698$	−287124.	−	480048.i	−0.589331	−	0.985311i
$699$		−	245456.i		−	0.502365i
$700$	−66295.2	−	35593.9i	−0.135296	−	0.0726406i
$701$	−24472.5			−0.0498015			−0.0249008	−	0.999690i	$-0.507927\pi$
$701$	−24472.5			−0.0498015			−0.0249008	+	0.999690i	$0.507927\pi$
$702$	−250272.	+	149691.i	−0.507852	+	0.303755i
$703$			769397.i			1.55683i
$704$	−10110.6	−	108865.i	−0.0204000	−	0.219656i
$705$	268035.			0.539278
$706$	72977.0	+	122011.i	0.146412	+	0.244788i
$707$		−	361891.i		−	0.724001i
$708$	−449644.	+	837482.i	−0.897020	+	1.67074i
$709$	705573.			1.40362			0.701809	−	0.712365i	$-0.252376\pi$
$709$	705573.			1.40362			0.701809	+	0.712365i	$0.252376\pi$
$710$	−218360.	+	130605.i	−0.433168	+	0.259085i
$711$		−	114096.i		−	0.225699i
$712$	457533.	−	21200.4i	0.902531	−	0.0418201i
$713$	−150668.			−0.296375
$714$	562956.	+	941215.i	1.10428	+	1.84626i
$715$		−	17313.5i		−	0.0338667i
$716$	−512673.	−	275254.i	−1.00003	−	0.536918i
$717$	−1.71500e6			−3.33600
$718$	−614530.	+	367561.i	−1.19205	+	0.712984i
$719$			430977.i			0.833675i	0.908981	+	0.416837i	$0.136862\pi$
$719$			430977.i			0.833675i	−0.908981	+	0.416837i	$0.863138\pi$
$720$	255648.	+	385696.i	0.493149	+	0.744013i
$721$	−766176.			−1.47387
$722$	108612.	+	181591.i	0.208355	+	0.348353i
$723$		−	409084.i		−	0.782592i
$724$	349404.	−	650781.i	0.666579	−	1.24153i
$725$	120564.			0.229372
$726$	744842.	−	445502.i	1.41316	−	0.845233i
$727$		−	709623.i		−	1.34264i	−0.741168	−	0.671319i	$-0.765728\pi$
$727$		−	709623.i		−	1.34264i	0.741168	−	0.671319i	$-0.234272\pi$
$728$	6465.86	+	139542.i	0.0122001	+	0.263294i
$729$	537887.			1.01213
$730$	45935.6	+	76800.4i	0.0861992	+	0.144118i
$731$		−	12981.5i		−	0.0242935i
$732$	450584.	+	241919.i	0.840918	+	0.451489i
$733$	99574.1			0.185327			0.0926634	−	0.995697i	$-0.470462\pi$
$733$	99574.1			0.185327			0.0926634	+	0.995697i	$0.470462\pi$
$734$	−110539.	+	66115.4i	−0.205175	+	0.122719i
$735$			171642.i			0.317723i
$736$	−332933.	−	159360.i	−0.614611	−	0.294187i
$737$	−31116.7			−0.0572873
$738$	−155923.	−	260690.i	−0.286284	−	0.478642i
$739$			436339.i			0.798979i	0.916738	+	0.399490i	$0.130813\pi$
$739$			436339.i			0.798979i	−0.916738	+	0.399490i	$0.869187\pi$
$740$	152101.	−	283294.i	0.277759	−	0.517338i
$741$	386839.			0.704520
$742$	−35653.6	+	21325.0i	−0.0647583	+	0.0387330i
$743$		−	220581.i		−	0.399568i	−0.979840	−	0.199784i	$-0.935976\pi$
$743$		−	220581.i		−	0.399568i	0.979840	−	0.199784i	$-0.0640240\pi$
$744$	−416286.	+	19289.2i	−0.752049	+	0.0348472i
$745$	−68509.5			−0.123435
$746$	419466.	+	701312.i	0.753736	+	1.26018i
$747$		−	262963.i		−	0.471252i
$748$	176030.	+	94510.5i	0.314618	+	0.168918i
$749$	833436.			1.48562
$750$	74735.2	−	44700.3i	0.132862	−	0.0794672i
$751$			201164.i			0.356673i	0.983970	+	0.178336i	$0.0570715\pi$
$751$			201164.i			0.356673i	−0.983970	+	0.178336i	$0.942929\pi$
$752$	−328387.	+	217663.i	−0.580699	+	0.384900i
$753$	380134.			0.670420
$754$	−114889.	−	192085.i	−0.202086	−	0.337871i
$755$		−	170958.i		−	0.299913i
$756$	−357841.	+	666495.i	−0.626104	+	1.16615i
$757$	915352.			1.59734			0.798669	−	0.601771i	$-0.205538\pi$
$757$	915352.			1.59734			0.798669	+	0.601771i	$0.205538\pi$
$758$	−466419.	+	278973.i	−0.811779	+	0.485538i
$759$			149884.i			0.260178i
$760$	−14176.8	−	305953.i	−0.0245443	−	0.529697i
$761$	363462.			0.627610			0.313805	−	0.949488i	$-0.398396\pi$
$761$	363462.			0.627610			0.313805	+	0.949488i	$0.398396\pi$
$762$	704912.	+	1.17855e6i	1.21402	+	2.02973i
$763$		−	150983.i		−	0.259345i
$764$	−334020.	−	179335.i	−0.572250	−	0.307241i
$765$	−845593.			−1.44490
$766$	−535025.	+	320007.i	−0.911835	+	0.545383i
$767$		−	221250.i		−	0.376091i
$768$	−940274.	−	397678.i	−1.59416	−	0.674232i
$769$	−97671.8			−0.165164			−0.0825822	−	0.996584i	$-0.526317\pi$
$769$	−97671.8			−0.165164			−0.0825822	+	0.996584i	$0.526317\pi$
$770$	−23053.7	−	38543.8i	−0.0388829	−	0.0650089i
$771$			474645.i			0.798472i
$772$	129433.	−	241074.i	0.217175	−	0.404497i
$773$	517767.			0.866514			0.433257	−	0.901270i	$-0.357364\pi$
$773$	517767.			0.866514			0.433257	+	0.901270i	$0.357364\pi$
$774$	15400.4	−	9211.25i	0.0257070	−	0.0153758i
$775$			52249.1i			0.0869912i
$776$	−831451.	+	38526.5i	−1.38074	+	0.0639788i
$777$	1.05348e6			1.74496
$778$	−187620.	−	313684.i	−0.309970	−	0.518243i
$779$			201061.i			0.331323i
$780$	−142435.	−	76473.4i	−0.234114	−	0.125696i
$781$	−151866.			−0.248977
$782$	578866.	−	346229.i	0.946595	−	0.566174i
$783$		−	1.21208e6i		−	1.97700i
$784$	−139385.	−	210290.i	−0.226769	−	0.342126i
$785$	301103.			0.488626
$786$	−158929.	−	265717.i	−0.257252	−	0.430104i
$787$			199421.i			0.321974i	0.986957	+	0.160987i	$0.0514677\pi$
$787$			199421.i			0.321974i	−0.986957	+	0.160987i	$0.948532\pi$
$788$	420789.	−	783738.i	0.677660	−	1.26217i
$789$	−713967.			−1.14690
$790$	27085.9	−	16200.5i	0.0434000	−	0.0259582i
$791$			853676.i			1.36440i
$792$	12783.9	+	275893.i	0.0203804	+	0.439835i
$793$	−119038.			−0.189295
$794$	364067.	+	608690.i	0.577485	+	0.965507i
$795$		−	48079.7i		−	0.0760725i
$796$	823234.	+	441994.i	1.29926	+	0.697574i
$797$	−204919.			−0.322600			−0.161300	−	0.986905i	$-0.551569\pi$
$797$	−204919.			−0.322600			−0.161300	+	0.986905i	$0.551569\pi$
$798$	861191.	−	515092.i	1.35236	−	0.808871i
$799$		−	719949.i		−	1.12774i
$800$	−55263.4	+	115455.i	−0.0863490	+	0.180399i
$801$	−1.15702e6			−1.80333
$802$	−406804.	−	680143.i	−0.632465	−	1.05743i
$803$			53413.6i			0.0828363i
$804$	−137442.	+	255991.i	−0.212621	+	0.396017i
$805$	−151621.			−0.233975
$806$	83244.5	−	49789.9i	0.128140	−	0.0766428i
$807$		−	575065.i		−	0.883019i
$808$	−614947.	+	28494.5i	−0.941923	+	0.0436453i
$809$	658877.			1.00672			0.503359	−	0.864078i	$-0.332097\pi$
$809$	658877.			1.00672			0.503359	+	0.864078i	$0.332097\pi$
$810$	−148779.	−	248745.i	−0.226762	−	0.379127i
$811$			464925.i			0.706872i	0.935459	+	0.353436i	$0.114987\pi$
$811$			464925.i			0.706872i	−0.935459	+	0.353436i	$0.885013\pi$
$812$	−511539.	−	274645.i	−0.775829	−	0.416543i
$813$	−1.92770e6			−2.91648
$814$	164706.	−	98513.6i	0.248577	−	0.148678i
$815$		−	223209.i		−	0.336044i
$816$	1.55504e6	−	1.03072e6i	2.33541	−	1.54796i
$817$	−11877.8			−0.0177947
$818$	362954.	+	606828.i	0.542431	+	0.906899i
$819$		−	352875.i		−	0.526082i
$820$	39747.3	−	74031.1i	0.0591126	−	0.110100i
$821$	202623.			0.300610			0.150305	−	0.988640i	$-0.451974\pi$
$821$	202623.			0.300610			0.150305	+	0.988640i	$0.451974\pi$
$822$	−638777.	+	382063.i	−0.945378	+	0.565446i
$823$		−	316525.i		−	0.467313i	−0.972319	−	0.233656i	$-0.924931\pi$
$823$		−	316525.i		−	0.467313i	0.972319	−	0.233656i	$-0.0750691\pi$
$824$	60326.9	+	1.30193e6i	0.0888498	+	1.91749i
$825$	51977.2			0.0763669
$826$	−294604.	−	492554.i	−0.431797	−	0.721928i
$827$		−	148466.i		−	0.217077i	−0.994092	−	0.108539i	$-0.965383\pi$
$827$		−	148466.i		−	0.217077i	0.994092	−	0.108539i	$-0.0346171\pi$
$828$	821488.	+	441057.i	1.19823	+	0.643330i
$829$	−834966.			−1.21495			−0.607477	−	0.794337i	$-0.707818\pi$
$829$	−834966.			−1.21495			−0.607477	+	0.794337i	$0.707818\pi$
$830$	62426.5	−	37338.3i	0.0906176	−	0.0541999i
$831$			1.48372e6i			2.14857i
$832$	236609.	−	21974.4i	0.341809	−	0.0317446i
$833$	461035.			0.664422
$834$	−643654.	−	1.07614e6i	−0.925380	−	1.54716i
$835$			129862.i			0.186256i
$836$	86475.1	−	161064.i	0.123731	−	0.230455i
$837$	525283.			0.749796
$838$	524558.	−	313746.i	0.746973	−	0.446777i
$839$		−	1.17926e6i		−	1.67527i	−0.546229	−	0.837636i	$-0.683937\pi$
$839$		−	1.17926e6i		−	1.67527i	0.546229	−	0.837636i	$-0.316063\pi$
$840$	−418921.	+	19411.3i	−0.593709	+	0.0275103i
$841$	222997.			0.315288
$842$	−403658.	−	674882.i	−0.569363	−	0.951927i
$843$			914872.i			1.28738i
$844$	239085.	+	128365.i	0.335635	+	0.180202i
$845$	−281692.			−0.394513
$846$	854102.	−	510852.i	1.19335	−	0.713764i
$847$			524032.i			0.730451i
$848$	39044.0	+	58905.7i	0.0542954	+	0.0819154i
$849$	−1.11222e6			−1.54303
$850$	−120066.	−	200741.i	−0.166182	−	0.277842i
$851$		−	647913.i		−	0.894659i
$852$	−670790.	+	1.24938e6i	−0.924075	+	1.72113i
$853$	−533912.			−0.733790			−0.366895	−	0.930262i	$-0.619579\pi$
$853$	−533912.			−0.733790			−0.366895	+	0.930262i	$0.619579\pi$
$854$	−265005.	+	158504.i	−0.363361	+	0.217332i
$855$			773699.i			1.05838i
$856$	−65622.8	−	1.41623e6i	−0.0895586	−	1.93279i
$857$	155720.			0.212023			0.106011	−	0.994365i	$-0.466192\pi$
$857$	155720.			0.212023			0.106011	+	0.994365i	$0.466192\pi$
$858$	−49530.8	−	82811.3i	−0.0672823	−	0.112490i
$859$			1.28910e6i			1.74703i	0.486795	+	0.873516i	$0.338166\pi$
$859$			1.28910e6i			1.74703i	−0.486795	+	0.873516i	$0.661834\pi$
$860$	4373.44	+	2348.10i	0.00591325	+	0.00317482i
$861$	275298.			0.371362
$862$	−792356.	+	473921.i	−1.06636	+	0.637810i
$863$			573138.i			0.769551i	0.923010	+	0.384776i	$0.125721\pi$
$863$			573138.i			0.769551i	−0.923010	+	0.384776i	$0.874279\pi$
$864$	1.16072e6	+	555587.i	1.55490	+	0.744260i
$865$	304780.			0.407338
$866$	585006.	+	978081.i	0.780054	+	1.30418i
$867$			2.10816e6i			2.80457i
$868$	119024.	−	221687.i	0.157977	−	0.294240i
$869$	18837.9			0.0249455
$870$	576662.	−	344911.i	0.761873	−	0.455689i
$871$		−	67629.2i		−	0.0891452i
$872$	−256559.	+	11888.0i	−0.337408	+	0.0156343i
$873$	2.10259e6			2.75883
$874$	−316792.	−	529650.i	−0.414717	−	0.693371i
$875$			52579.8i			0.0686757i
$876$	439424.	+	235927.i	0.572632	+	0.307446i
$877$	1.08498e6			1.41066			0.705328	−	0.708881i	$-0.250800\pi$
$877$	1.08498e6			1.41066			0.705328	+	0.708881i	$0.250800\pi$
$878$	−1.12546e6	+	673155.i	−1.45996	+	0.873225i
$879$		−	876483.i		−	1.13440i
$880$	−63680.8	+	42209.1i	−0.0822324	+	0.0545055i
$881$	443843.			0.571844			0.285922	−	0.958253i	$-0.407700\pi$
$881$	443843.			0.571844			0.285922	+	0.958253i	$0.407700\pi$
$882$	327135.	+	546943.i	0.420524	+	0.703080i
$883$		−	1.21061e6i		−	1.55269i	−0.630310	−	0.776344i	$-0.717072\pi$
$883$		−	1.21061e6i		−	1.55269i	0.630310	−	0.776344i	$-0.282928\pi$
$884$	−205410.	+	382585.i	−0.262855	+	0.489580i
$885$	664220.			0.848058
$886$	−614978.	+	367829.i	−0.783416	+	0.468574i
$887$		−	1.17188e6i		−	1.48949i	−0.667352	−	0.744743i	$-0.732572\pi$
$887$		−	1.17188e6i		−	1.48949i	0.667352	−	0.744743i	$-0.267428\pi$
$888$	−82948.9	−	1.79014e6i	−0.105192	−	2.27019i
$889$	−829169.			−1.04916
$890$	−164286.	−	274672.i	−0.207405	−	0.346764i
$891$		−	172999.i		−	0.217915i
$892$	−237077.	−	127287.i	−0.297961	−	0.159975i
$893$	−658738.			−0.826057
$894$	−327684.	+	195993.i	−0.409997	+	0.245226i
$895$			406610.i			0.507612i
$896$	497485.	−	363975.i	0.619675	−	0.453372i
$897$	−325759.			−0.404866
$898$	634251.	+	1.06041e6i	0.786518	+	1.31499i
$899$			403158.i			0.498834i
$900$	152951.	−	284878.i	0.188829	−	0.351702i
$901$	−129144.			−0.159083
$902$	43041.4	−	25743.8i	0.0529022	−	0.0316416i
$903$			16263.5i			0.0199452i
$904$	1.45062e6	−	67216.5i	1.77507	−	0.0822506i
$905$	−516146.			−0.630195
$906$	−489080.	−	817700.i	−0.595831	−	0.996179i
$907$		−	201406.i		−	0.244827i	−0.992479	−	0.122413i	$-0.960937\pi$
$907$		−	201406.i		−	0.244827i	0.992479	−	0.122413i	$-0.0390634\pi$
$908$	1.14241e6	+	613359.i	1.38564	+	0.743949i
$909$	1.55509e6			1.88203
$910$	83771.4	−	50105.0i	0.101161	−	0.0605060i
$911$			606030.i			0.730227i	0.930963	+	0.365113i	$0.118970\pi$
$911$			606030.i			0.730227i	−0.930963	+	0.365113i	$0.881030\pi$
$912$	−943085.	−	1.42283e6i	−1.13386	−	1.71066i
$913$	43416.7			0.0520853
$914$	−116578.	−	194908.i	−0.139548	−	0.233312i
$915$		−	357366.i		−	0.426846i
$916$	−361175.	+	672704.i	−0.430454	+	0.801740i
$917$	186945.			0.222318
$918$	−2.01814e6	+	1.20708e6i	−2.39478	+	1.43236i
$919$			1.13891e6i			1.34853i	0.738491	+	0.674263i	$0.235539\pi$
$919$			1.13891e6i			1.34853i	−0.738491	+	0.674263i	$0.764461\pi$
$920$	11938.3	+	257645.i	0.0141048	+	0.304401i
$921$	−2.72733e6			−3.21528
$922$	533297.	+	891629.i	0.627347	+	1.04887i
$923$		−	330067.i		−	0.387435i
$924$	−220534.	−	118404.i	−0.258304	−	0.138683i
$925$	−224685.			−0.262598
$926$	222025.	−	132797.i	0.258928	−	0.154869i
$927$		−	3.29235e6i		−	3.83130i
$928$	−426416.	+	890863.i	−0.495151	+	1.03446i
$929$	291783.			0.338087			0.169043	−	0.985609i	$-0.445932\pi$
$929$	291783.			0.338087			0.169043	+	0.985609i	$0.445932\pi$
$930$	149475.	+	249910.i	0.172824	+	0.288947i
$931$		−	421837.i		−	0.486683i
$932$	119255.	−	222117.i	0.137292	−	0.255712i
$933$	−367965.			−0.422711
$934$	−360779.	+	215788.i	−0.413569	+	0.247362i
$935$		−	139612.i		−	0.159698i
$936$	−599627.	+	27784.6i	−0.684431	+	0.0317141i
$937$	−1.11462e6			−1.26955			−0.634774	−	0.772698i	$-0.718907\pi$
$937$	−1.11462e6			−1.26955			−0.634774	+	0.772698i	$0.718907\pi$
$938$	−90051.2	−	150558.i	−0.102349	−	0.171119i
$939$		−	2.06539e6i		−	2.34246i
$940$	242549.	+	130225.i	0.274501	+	0.147380i
$941$	−254584.			−0.287509			−0.143755	−	0.989613i	$-0.545918\pi$
$941$	−254584.			−0.287509			−0.143755	+	0.989613i	$0.545918\pi$
$942$	1.44019e6	−	861403.i	1.62300	−	0.970743i
$943$		−	169314.i		−	0.190401i
$944$	−813781.	+	539393.i	−0.913196	+	0.605287i
$945$	528608.			0.591930
$946$	1520.83	+	2542.70i	0.00169941	+	0.00284128i
$947$		−	997643.i		−	1.11244i	−0.831036	−	0.556218i	$-0.812252\pi$
$947$		−	997643.i		−	1.11244i	0.831036	−	0.556218i	$-0.187748\pi$
$948$	83206.5	−	154976.i	0.0925850	−	0.172444i
$949$	−116089.			−0.128902
$950$	−183674.	+	109858.i	−0.203517	+	0.121727i
$951$		−	527389.i		−	0.583136i
$952$	52139.3	+	1.12523e6i	0.0575296	+	1.24156i
$953$	−146915.			−0.161763			−0.0808815	−	0.996724i	$-0.525774\pi$
$953$	−146915.			−0.161763			−0.0808815	+	0.996724i	$0.525774\pi$
$954$	−91636.1	−	153208.i	−0.100686	−	0.168339i
$955$			264917.i			0.290471i
$956$	−1.55194e6	−	833234.i	−1.69808	−	0.911698i
$957$	401060.			0.437911
$958$	450343.	−	269357.i	0.490696	−	0.293493i
$959$		−	449411.i		−	0.488659i
$960$	65969.7	+	710328.i	0.0715817	+	0.770755i
$961$	748803.			0.810813
$962$	214110.	+	357974.i	0.231359	+	0.386813i
$963$			3.58137e6i			3.86186i
$964$	198753.	−	370187.i	0.213875	−	0.398352i
$965$	−191200.			−0.205321
$966$	−725213.	+	433762.i	−0.777162	+	0.464833i
$967$			1.47654e6i			1.57904i	0.613727	+	0.789518i	$0.289669\pi$
$967$			1.47654e6i			1.57904i	−0.613727	+	0.789518i	$0.710331\pi$
$968$	890468.	−	41261.1i	0.950315	−	0.0440342i
$969$	3.11939e6			3.32217
$970$	298548.	+	499147.i	0.317301	+	0.530500i
$971$		−	1.55163e6i		−	1.64569i	−0.568265	−	0.822846i	$-0.692385\pi$
$971$		−	1.55163e6i		−	1.64569i	0.568265	−	0.822846i	$-0.307615\pi$
$972$	11689.3	+	6275.97i	0.0123724	+	0.00664275i
$973$	757113.			0.799715
$974$	119563.	−	71512.4i	0.126031	−	0.0753813i
$975$			112968.i			0.118835i
$976$	290206.	+	437833.i	0.304653	+	0.459630i
$977$	13609.0			0.0142572			0.00712862	−	0.999975i	$-0.497731\pi$
$977$	13609.0			0.0142572			0.00712862	+	0.999975i	$0.497731\pi$
$978$	−638561.	−	1.06762e6i	−0.667612	−	1.11619i
$979$		−	191030.i		−	0.199314i
$980$	−83392.3	+	155322.i	−0.0868308	+	0.161726i
$981$	648792.			0.674167
$982$	1.22806e6	−	734521.i	1.27349	−	0.761695i
$983$			179673.i			0.185941i	0.995669	+	0.0929706i	$0.0296363\pi$
$983$			179673.i			0.185941i	−0.995669	+	0.0929706i	$0.970364\pi$
$984$	−21676.4	−	467804.i	−0.0223870	−	0.483141i
$985$	−621596.			−0.640672
$986$	−926441.	−	1.54893e6i	−0.952937	−	1.59323i
$987$			901966.i			0.925882i
$988$	350057.	+	187946.i	0.358612	+	0.192539i
$989$	10002.3			0.0102261
$990$	165627.	−	99064.4i	0.168990	−	0.101076i
$991$			1.04471e6i			1.06377i	0.846816	+	0.531886i	$0.178516\pi$
$991$			1.04471e6i			1.06377i	−0.846816	+	0.531886i	$0.821484\pi$
$992$	−386076.	−	184798.i	−0.392329	−	0.187790i
$993$	379139.			0.384503
$994$	−439498.	−	734804.i	−0.444820	−	0.743702i
$995$		−	652920.i		−	0.659499i
$996$	191771.	−	357182.i	0.193314	−	0.360057i
$997$	100146.			0.100750			0.0503748	−	0.998730i	$-0.483958\pi$
$997$	100146.			0.100750			0.0503748	+	0.998730i	$0.483958\pi$
$998$	809065.	−	483915.i	0.812311	−	0.485856i
$999$			2.25886e6i			2.26339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.b.a.11.1	✓	8
3.2	odd	2		180.5.c.a.91.8		8
4.3	odd	2	inner	20.5.b.a.11.2	yes	8
5.2	odd	4		100.5.d.c.99.13		16
5.3	odd	4		100.5.d.c.99.4		16
5.4	even	2		100.5.b.c.51.8		8
8.3	odd	2		320.5.b.d.191.8		8
8.5	even	2		320.5.b.d.191.1		8
12.11	even	2		180.5.c.a.91.7		8
20.3	even	4		100.5.d.c.99.14		16
20.7	even	4		100.5.d.c.99.3		16
20.19	odd	2		100.5.b.c.51.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.1	✓	8	1.1	even	1	trivial
20.5.b.a.11.2	yes	8	4.3	odd	2	inner
100.5.b.c.51.7		8	20.19	odd	2
100.5.b.c.51.8		8	5.4	even	2
100.5.d.c.99.3		16	20.7	even	4
100.5.d.c.99.4		16	5.3	odd	4
100.5.d.c.99.13		16	5.2	odd	4
100.5.d.c.99.14		16	20.3	even	4
180.5.c.a.91.7		8	12.11	even	2
180.5.c.a.91.8		8	3.2	odd	2
320.5.b.d.191.1		8	8.5	even	2
320.5.b.d.191.8		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)

\(f(q)\)	\(=\)	\(q+(-2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 + 14.0967i) q^{4} +11.1803 q^{5} +(53.4761 - 31.9849i) q^{6} +37.6230i q^{7} +(63.9314 - 2.96235i) q^{8} -161.671 q^{9} +O(q^{10})\)	\(q+(-2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 + 14.0967i) q^{4} +11.1803 q^{5} +(53.4761 - 31.9849i) q^{6} +37.6230i q^{7} +(63.9314 - 2.96235i) q^{8} -161.671 q^{9} +(-22.9558 - 38.3801i) q^{10} -26.6928i q^{11} +(-219.597 - 117.902i) q^{12} +58.0144 q^{13} +(129.153 - 77.2486i) q^{14} +174.166i q^{15} +(-141.435 - 213.383i) q^{16} +467.816 q^{17} +(331.947 + 554.987i) q^{18} -428.041i q^{19} +(-84.6187 + 157.606i) q^{20} -586.088 q^{21} +(-91.6316 + 54.8064i) q^{22} +360.456i q^{23} +(46.1472 + 995.917i) q^{24} +125.000 q^{25} +(-119.117 - 199.153i) q^{26} -1256.68i q^{27} +(-530.361 - 284.751i) q^{28} +964.509 q^{29} +(597.881 - 357.602i) q^{30} +417.993i q^{31} +(-442.107 + 923.644i) q^{32} +415.818 q^{33} +(-960.531 - 1605.93i) q^{34} +420.638i q^{35} +(1223.61 - 2279.03i) q^{36} -1797.48 q^{37} +(-1469.39 + 878.866i) q^{38} +903.742i q^{39} +(714.775 - 33.1201i) q^{40} -469.722 q^{41} +(1203.37 + 2011.93i) q^{42} -27.7492i q^{43} +(376.281 + 202.025i) q^{44} -1807.53 q^{45} +(1237.38 - 740.097i) q^{46} -1538.96i q^{47} +(3324.05 - 2203.26i) q^{48} +985.506 q^{49} +(-256.653 - 429.103i) q^{50} +7287.58i q^{51} +(-439.083 + 817.812i) q^{52} -276.057 q^{53} +(-4313.96 + 2580.25i) q^{54} -298.435i q^{55} +(111.453 + 2405.29i) q^{56} +6667.98 q^{57} +(-1980.36 - 3310.99i) q^{58} -3813.72i q^{59} +(-2455.17 - 1318.18i) q^{60} -2051.87 q^{61} +(1434.90 - 858.234i) q^{62} -6082.55i q^{63} +(4078.45 - 378.775i) q^{64} +648.620 q^{65} +(-853.768 - 1427.43i) q^{66} -1165.73i q^{67} +(-3540.67 + 6594.66i) q^{68} -5615.14 q^{69} +(1443.98 - 863.666i) q^{70} -5689.40i q^{71} +(-10335.8 + 478.926i) q^{72} -2001.05 q^{73} +(3690.64 + 6170.44i) q^{74} +1947.24i q^{75} +(6033.98 + 3239.64i) q^{76} +1004.26 q^{77} +(3102.38 - 1855.59i) q^{78} +705.728i q^{79} +(-1581.29 - 2385.69i) q^{80} +6481.10 q^{81} +(964.446 + 1612.47i) q^{82} +1626.53i q^{83} +(4435.82 - 8261.91i) q^{84} +5230.34 q^{85} +(-95.2580 + 56.9753i) q^{86} +15025.0i q^{87} +(-79.0735 - 1706.51i) q^{88} +7156.62 q^{89} +(3711.28 + 6204.94i) q^{90} +2182.68i q^{91} +(-5081.24 - 2728.12i) q^{92} -6511.45 q^{93} +(-5282.97 + 3159.83i) q^{94} -4785.65i q^{95} +(-14388.4 - 6887.10i) q^{96} -13005.4 q^{97} +(-2023.47 - 3383.07i) q^{98} +4315.45i 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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