LMFDB - Embedded newform 100.5.b.c.51.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,5,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, 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("100.51");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	100.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:	$10.3369963084$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.7
Root			$-1.02661 + 1.71641i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.5.b.c.51.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 - 14.0967i) q^{4} +(53.4761 + 31.9849i) q^{6} +37.6230i q^{7} +(-63.9314 - 2.96235i) q^{8} -161.671 q^{9} +O(q^{10})$	\(q+(2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 - 14.0967i) q^{4} +(53.4761 + 31.9849i) q^{6} +37.6230i q^{7} +(-63.9314 - 2.96235i) q^{8} -161.671 q^{9} +26.6928i q^{11} +(219.597 - 117.902i) q^{12} -58.0144 q^{13} +(129.153 + 77.2486i) q^{14} +(-141.435 + 213.383i) q^{16} -467.816 q^{17} +(-331.947 + 554.987i) q^{18} +428.041i q^{19} -586.088 q^{21} +(91.6316 + 54.8064i) q^{22} +360.456i q^{23} +(46.1472 - 995.917i) q^{24} +(-119.117 + 199.153i) q^{26} -1256.68i q^{27} +(530.361 - 284.751i) q^{28} +964.509 q^{29} -417.993i q^{31} +(442.107 + 923.644i) q^{32} -415.818 q^{33} +(-960.531 + 1605.93i) q^{34} +(1223.61 + 2279.03i) q^{36} +1797.48 q^{37} +(1469.39 + 878.866i) q^{38} -903.742i q^{39} -469.722 q^{41} +(-1203.37 + 2011.93i) q^{42} -27.7492i q^{43} +(376.281 - 202.025i) q^{44} +(1237.38 + 740.097i) q^{46} -1538.96i q^{47} +(-3324.05 - 2203.26i) q^{48} +985.506 q^{49} -7287.58i q^{51} +(439.083 + 817.812i) q^{52} +276.057 q^{53} +(-4313.96 - 2580.25i) q^{54} +(111.453 - 2405.29i) q^{56} -6667.98 q^{57} +(1980.36 - 3310.99i) q^{58} +3813.72i q^{59} -2051.87 q^{61} +(-1434.90 - 858.234i) q^{62} -6082.55i q^{63} +(4078.45 + 378.775i) q^{64} +(-853.768 + 1427.43i) q^{66} -1165.73i q^{67} +(3540.67 + 6594.66i) q^{68} -5615.14 q^{69} +5689.40i q^{71} +(10335.8 + 478.926i) q^{72} +2001.05 q^{73} +(3690.64 - 6170.44i) q^{74} +(6033.98 - 3239.64i) q^{76} -1004.26 q^{77} +(-3102.38 - 1855.59i) q^{78} -705.728i q^{79} +6481.10 q^{81} +(-964.446 + 1612.47i) q^{82} +1626.53i q^{83} +(4435.82 + 8261.91i) q^{84} +(-95.2580 - 56.9753i) q^{86} +15025.0i q^{87} +(79.0735 - 1706.51i) q^{88} +7156.62 q^{89} -2182.68i q^{91} +(5081.24 - 2728.12i) q^{92} +6511.45 q^{93} +(-5282.97 - 3159.83i) q^{94} +(-14388.4 + 6887.10i) q^{96} +13005.4 q^{97} +(2023.47 - 3383.07i) q^{98} -4315.45i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 200 q^{12} - 352 q^{13} - 168 q^{14} - 272 q^{16} + 48 q^{17} - 286 q^{18} + 16 q^{21} - 800 q^{22} + 1552 q^{24} - 2172 q^{26} - 40 q^{28} + 1200 q^{29} + 2304 q^{32} + 1120 q^{33} - 2132 q^{34} - 1044 q^{36} + 5728 q^{37} + 3360 q^{38} + 4896 q^{41} - 12120 q^{42} + 7920 q^{44} + 728 q^{46} - 8640 q^{48} - 5768 q^{49} + 12488 q^{52} - 2592 q^{53} - 17776 q^{54} + 48 q^{56} - 3840 q^{57} + 7428 q^{58} + 7936 q^{61} - 25680 q^{62} + 18880 q^{64} - 8080 q^{66} - 2712 q^{68} - 2256 q^{69} + 36264 q^{72} + 14448 q^{73} - 18492 q^{74} + 12000 q^{76} - 2400 q^{77} + 14480 q^{78} - 936 q^{81} - 27412 q^{82} + 50464 q^{84} - 7392 q^{86} - 18080 q^{88} + 23760 q^{89} + 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 + 200 * q^12 - 352 * q^13 - 168 * q^14 - 272 * q^16 + 48 * q^17 - 286 * q^18 + 16 * q^21 - 800 * q^22 + 1552 * q^24 - 2172 * q^26 - 40 * q^28 + 1200 * q^29 + 2304 * q^32 + 1120 * q^33 - 2132 * q^34 - 1044 * q^36 + 5728 * q^37 + 3360 * q^38 + 4896 * q^41 - 12120 * q^42 + 7920 * q^44 + 728 * q^46 - 8640 * q^48 - 5768 * q^49 + 12488 * q^52 - 2592 * q^53 - 17776 * q^54 + 48 * q^56 - 3840 * q^57 + 7428 * q^58 + 7936 * q^61 - 25680 * q^62 + 18880 * q^64 - 8080 * q^66 - 2712 * q^68 - 2256 * q^69 + 36264 * q^72 + 14448 * q^73 - 18492 * q^74 + 12000 * q^76 - 2400 * q^77 + 14480 * q^78 - 936 * q^81 - 27412 * q^82 + 50464 * q^84 - 7392 * q^86 - 18080 * q^88 + 23760 * q^89 + 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 $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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
$5$		0			0
$5$		0			0
$6$	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
$10$		0			0
$11$			26.6928i			0.220602i	0.993898	+	0.110301i	$0.0351814\pi$
$11$			26.6928i			0.220602i	−0.993898	+	0.110301i	$0.964819\pi$
$12$	219.597	−	117.902i	1.52498	−	0.818762i
$13$	−58.0144			−0.343280			−0.171640	−	0.985160i	$-0.554907\pi$
$13$	−58.0144			−0.343280			−0.171640	+	0.985160i	$0.554907\pi$
$14$	129.153	+	77.2486i	0.658945	+	0.394126i
$15$		0			0
$16$	−141.435	+	213.383i	−0.552480	+	0.833526i
$17$	−467.816			−1.61874			−0.809370	−	0.587300i	$-0.800191\pi$
$17$	−467.816			−1.61874			−0.809370	+	0.587300i	$0.800191\pi$
$18$	−331.947	+	554.987i	−1.02453	+	1.71292i
$19$			428.041i			1.18571i	0.805309	+	0.592855i	$0.201999\pi$
$19$			428.041i			1.18571i	−0.805309	+	0.592855i	$0.798001\pi$
$20$		0			0
$21$	−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
$25$		0			0
$26$	−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	$0.305612\pi$
$30$		0			0
$31$		−	417.993i		−	0.434956i	−0.976065	−	0.217478i	$-0.930217\pi$
$31$		−	417.993i		−	0.434956i	0.976065	−	0.217478i	$-0.0697831\pi$
$32$	442.107	+	923.644i	0.431745	+	0.901996i
$33$	−415.818			−0.381834
$34$	−960.531	+	1605.93i	−0.830909	+	1.38921i
$35$		0			0
$36$	1223.61	+	2279.03i	0.944143	+	1.75851i
$37$	1797.48			1.31299			0.656495	−	0.754330i	$-0.272038\pi$
$37$	1797.48			1.31299			0.656495	+	0.754330i	$0.272038\pi$
$38$	1469.39	+	878.866i	1.01758	+	0.608633i
$39$		−	903.742i		−	0.594176i
$40$		0			0
$41$	−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
$45$		0			0
$46$	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
$50$		0			0
$51$		−	7287.58i		−	2.80184i
$52$	439.083	+	817.812i	0.162383	+	0.302445i
$53$	276.057			0.0982758			0.0491379	−	0.998792i	$-0.484353\pi$
$53$	276.057			0.0982758			0.0491379	+	0.998792i	$0.484353\pi$
$54$	−4313.96	−	2580.25i	−1.47941	−	0.884859i
$55$		0			0
$56$	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	$0.184531\pi$
$59$			3813.72i			1.09558i	−0.836616	+	0.547791i	$0.815469\pi$
$60$		0			0
$61$	−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
$65$		0			0
$66$	−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
$70$		0			0
$71$			5689.40i			1.12863i	0.825561	+	0.564313i	$0.190859\pi$
$71$			5689.40i			1.12863i	−0.825561	+	0.564313i	$0.809141\pi$
$72$	10335.8	+	478.926i	1.99380	+	0.0923854i
$73$	2001.05			0.375501			0.187751	−	0.982217i	$-0.439880\pi$
$73$	2001.05			0.375501			0.187751	+	0.982217i	$0.439880\pi$
$74$	3690.64	−	6170.44i	0.673967	−	1.12682i
$75$		0			0
$76$	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	$-0.981993\pi$
$79$		−	705.728i		−	0.113079i	0.998400	−	0.0565396i	$-0.0180067\pi$
$80$		0			0
$81$	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
$85$		0			0
$86$	−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	$0.350800\pi$
$90$		0			0
$91$		−	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
$95$		0			0
$96$	−14388.4	+	6887.10i	−1.56124	+	0.747298i
$97$	13005.4			1.38223			0.691113	−	0.722747i	$-0.257121\pi$
$97$	13005.4			1.38223			0.691113	+	0.722747i	$0.257121\pi$
$98$	2023.47	−	3383.07i	0.210690	−	0.352256i
$99$		−	4315.45i		−	0.440307i
$100$		0			0
$101$	−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
$105$		0			0
$106$	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	$0.554017\pi$
$110$		0			0
$111$			28001.0i			2.27262i
$112$	−8028.11	−	5321.21i	−0.639996	−	0.424204i
$113$	−22690.2			−1.77698			−0.888489	−	0.458897i	$-0.848245\pi$
$113$	−22690.2			−1.77698			−0.888489	+	0.458897i	$0.848245\pi$
$114$	−13690.9	+	22890.0i	−1.05347	+	1.76131i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	−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
$130$		0			0
$131$			4968.89i			0.289545i	0.989465	+	0.144773i	$0.0462451\pi$
$131$			4968.89i			0.289545i	−0.989465	+	0.144773i	$0.953755\pi$
$132$	3147.13	+	5861.66i	0.180620	+	0.336413i
$133$	−16104.2			−0.910409
$134$	−4001.75	−	2393.51i	−0.222864	−	0.133299i
$135$		0			0
$136$	29908.1	+	1385.83i	1.61700	+	0.0749262i
$137$	11945.1			0.636426			0.318213	−	0.948019i	$-0.396917\pi$
$137$	11945.1			0.636426			0.318213	+	0.948019i	$0.396917\pi$
$138$	−11529.2	+	19275.8i	−0.605395	+	1.01217i
$139$			20123.7i			1.04154i	0.853696	+	0.520772i	$0.174356\pi$
$139$			20123.7i			1.04154i	−0.853696	+	0.520772i	$0.825644\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	$0.544069\pi$
$150$		0			0
$151$			15290.9i			0.670626i	0.942107	+	0.335313i	$0.108842\pi$
$151$			15290.9i			0.670626i	−0.942107	+	0.335313i	$0.891158\pi$
$152$	1268.01	−	27365.3i	0.0548827	−	1.18444i
$153$	75632.1			3.23090
$154$	−2061.98	+	3447.46i	−0.0869448	+	0.145364i
$155$		0			0
$156$	−12739.8	+	6839.99i	−0.523496	+	0.281065i
$157$	−26931.5			−1.09260			−0.546300	−	0.837589i	$-0.683964\pi$
$157$	−26931.5			−1.09260			−0.546300	+	0.837589i	$0.683964\pi$
$158$	−2422.64	−	1449.02i	−0.0970452	−	0.0580443i
$159$			4300.38i			0.170103i
$160$		0			0
$161$	−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
$165$		0			0
$166$	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
$170$		0			0
$171$		−	69201.8i		−	2.36660i
$172$	−391.172	+	210.020i	−0.0132224	+	0.00709912i
$173$	−27260.4			−0.910835			−0.455417	−	0.890278i	$-0.650510\pi$
$173$	−27260.4			−0.910835			−0.455417	+	0.890278i	$0.650510\pi$
$174$	51578.2	+	30849.8i	1.70360	+	1.01895i
$175$		0			0
$176$	−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	$-0.807900\pi$
$179$		−	36368.3i		−	1.13505i	0.823355	−	0.567527i	$-0.192100\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	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
$190$		0			0
$191$		−	23694.9i		−	0.649513i	−0.945798	−	0.324757i	$-0.894718\pi$
$191$		−	23694.9i		−	0.649513i	0.945798	−	0.324757i	$-0.105282\pi$
$192$	−5900.51	+	63533.6i	−0.160062	+	1.72346i
$193$	17101.4			0.459111			0.229556	−	0.973296i	$-0.426273\pi$
$193$	17101.4			0.459111			0.229556	+	0.973296i	$0.426273\pi$
$194$	26703.0	−	44645.1i	0.709506	−	1.18623i
$195$		0			0
$196$	−7458.83	−	13892.4i	−0.194159	−	0.361631i
$197$	55597.2			1.43259			0.716293	−	0.697800i	$-0.245837\pi$
$197$	55597.2			1.43259			0.716293	+	0.697800i	$0.245837\pi$
$198$	−14814.2	−	8860.59i	−0.377874	−	0.226012i
$199$			58399.0i			1.47468i	0.675520	+	0.737342i	$0.263919\pi$
$199$			58399.0i			1.47468i	−0.675520	+	0.737342i	$0.736081\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	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
$210$		0			0
$211$			16960.3i			0.380951i	0.981692	+	0.190475i	$0.0610030\pi$
$211$			16960.3i			0.380951i	−0.981692	+	0.190475i	$0.938997\pi$
$212$	−2089.34	−	3891.49i	−0.0464877	−	0.0865854i
$213$	−88628.9			−1.95351
$214$	−76044.8	−	45483.6i	−1.66051	−	0.993179i
$215$		0			0
$216$	−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
$220$		0			0
$221$	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
$225$		0			0
$226$	−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	$0.349642\pi$
$230$		0			0
$231$		−	15644.3i		−	0.293179i
$232$	−61662.4	−	2857.22i	−1.14563	−	0.0530844i
$233$	15756.7			0.290237			0.145119	−	0.989414i	$-0.453644\pi$
$233$	15756.7			0.290237			0.145119	+	0.989414i	$0.453644\pi$
$234$	19257.7	−	32197.2i	0.351700	−	0.588012i
$235$		0			0
$236$	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	$-0.586060\pi$
$239$		−	110092.i		−	1.92735i	0.267083	−	0.963673i	$-0.413940\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$	−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
$250$		0			0
$251$			24402.1i			0.387329i	0.981068	+	0.193665i	$0.0620374\pi$
$251$			24402.1i			0.387329i	−0.981068	+	0.193665i	$0.937963\pi$
$252$	−85743.9	+	46035.9i	−1.35021	+	0.724929i
$253$	−9621.57			−0.150316
$254$	75655.5	+	45250.8i	1.17266	+	0.701388i
$255$		0			0
$256$	−25528.4	−	60359.5i	−0.389532	−	0.921013i
$257$	−30469.1			−0.461311			−0.230655	−	0.973036i	$-0.574087\pi$
$257$	−30469.1			−0.461311			−0.230655	+	0.973036i	$0.574087\pi$
$258$	887.556	−	1483.92i	0.0133339	−	0.0222931i
$259$			67626.8i			1.00814i
$260$		0			0
$261$	−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
$265$		0			0
$266$	−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	$0.582101\pi$
$270$		0			0
$271$		−	123746.i		−	1.68497i	−0.538720	−	0.842485i	$-0.681092\pi$
$271$		−	123746.i		−	1.68497i	0.538720	−	0.842485i	$-0.318908\pi$
$272$	66165.4	−	99823.8i	0.894321	−	1.34926i
$273$	34001.5			0.456219
$274$	24526.0	−	41005.4i	0.326682	−	0.546185i
$275$		0			0
$276$	42498.3	+	79155.0i	0.557896	+	1.03911i
$277$	−95245.1			−1.24132			−0.620659	−	0.784081i	$-0.713135\pi$
$277$	−95245.1			−1.24132			−0.620659	+	0.784081i	$0.713135\pi$
$278$	69080.9	+	41318.4i	0.893858	+	0.534631i
$279$			67577.2i			0.868144i
$280$		0			0
$281$	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
$285$		0			0
$286$	−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
$290$		0			0
$291$			202596.i			2.39246i
$292$	−15145.0	−	28208.2i	−0.177625	−	0.330834i
$293$	56264.5			0.655390			0.327695	−	0.944784i	$-0.393728\pi$
$293$	56264.5			0.655390			0.327695	+	0.944784i	$0.393728\pi$
$294$	52701.1	+	31521.4i	0.609712	+	0.364679i
$295$		0			0
$296$	−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
$300$		0			0
$301$	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
$305$		0			0
$306$	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
$310$		0			0
$311$		−	23621.0i		−	0.244218i	−0.992517	−	0.122109i	$-0.961034\pi$
$311$		−	23621.0i		−	0.244218i	0.992517	−	0.122109i	$-0.0389657\pi$
$312$	−2677.20	+	57777.5i	−0.0275025	+	0.593539i
$313$	132585.			1.35333			0.676667	−	0.736289i	$-0.263424\pi$
$313$	132585.			1.35333			0.676667	+	0.736289i	$0.263424\pi$
$314$	−55296.5	+	92451.1i	−0.560839	+	0.937676i
$315$		0			0
$316$	−9948.44	+	5341.32i	−0.0996279	+	0.0534902i
$317$	33855.0			0.336902			0.168451	−	0.985710i	$-0.446123\pi$
$317$	33855.0			0.336902			0.168451	+	0.985710i	$0.446123\pi$
$318$	14762.4	+	8829.66i	0.145984	+	0.0873151i
$319$			25745.5i			0.252999i
$320$		0			0
$321$	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
$325$		0			0
$326$	−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
$330$		0			0
$331$			24338.3i			0.222144i	0.993812	+	0.111072i	$0.0354283\pi$
$331$			24338.3i			0.222144i	−0.993812	+	0.111072i	$0.964572\pi$
$332$	22928.8	−	12310.5i	0.208020	−	0.111686i
$333$	−290601.			−2.62064
$334$	39873.0	+	23848.7i	0.357426	+	0.213782i
$335$		0			0
$336$	82893.2	−	125061.i	0.734244	−	1.10775i
$337$	−5373.65			−0.0473161			−0.0236581	−	0.999720i	$-0.507531\pi$
$337$	−5373.65			−0.0473161			−0.0236581	+	0.999720i	$0.507531\pi$
$338$	−51731.7	+	86491.1i	−0.452818	+	0.757073i
$339$		−	353466.i		−	3.07573i
$340$		0			0
$341$	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
$345$		0			0
$346$	−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	$0.305370\pi$
$350$		0			0
$351$			72905.5i			0.591761i
$352$	−24654.6	+	11801.1i	−0.198982	+	0.0952437i
$353$	35542.6			0.285233			0.142616	−	0.989778i	$-0.454448\pi$
$353$	35542.6			0.285233			0.142616	+	0.989778i	$0.454448\pi$
$354$	−121982.	+	203943.i	−0.973391	+	1.62743i
$355$		0			0
$356$	−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	$0.244375\pi$
$359$			179016.i			1.38900i	−0.719491	+	0.694502i	$0.755625\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−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
$370$		0			0
$371$			10386.1i			0.0754578i
$372$	−49282.1	−	91790.1i	−0.356125	−	0.663300i
$373$	204296.			1.46839			0.734196	−	0.678937i	$-0.237559\pi$
$373$	204296.			1.46839			0.734196	+	0.678937i	$0.237559\pi$
$374$	−42866.7	−	25639.3i	−0.306462	−	0.183300i
$375$		0			0
$376$	−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	$0.156811\pi$
$379$			135870.i			0.945903i	−0.881089	+	0.472951i	$0.843189\pi$
$380$		0			0
$381$	−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
$385$		0			0
$386$	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	$0.402368\pi$
$390$		0			0
$391$		−	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
$395$		0			0
$396$	−60833.6	+	32661.6i	−0.387930	+	0.208280i
$397$	177315.			1.12503			0.562515	−	0.826787i	$-0.309834\pi$
$397$	177315.			1.12503			0.562515	+	0.826787i	$0.309834\pi$
$398$	200473.	+	119906.i	1.26558	+	0.756965i
$399$		−	250870.i		−	1.57581i
$400$		0			0
$401$	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
$405$		0			0
$406$	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	$0.677196\pi$
$410$		0			0
$411$			186079.i			1.10158i
$412$	287073.	−	154129.i	1.69121	−	0.908011i
$413$	−143484.			−0.841206
$414$	−200048.	−	119652.i	−1.16717	−	0.698103i
$415$		0			0
$416$	−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	$-0.856679\pi$
$419$		−	152807.i		−	0.870390i	0.900336	−	0.435195i	$-0.143321\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$			230818.i			1.24255i	0.783592	+	0.621276i	$0.213385\pi$
$431$			230818.i			1.24255i	−0.783592	+	0.621276i	$0.786615\pi$
$432$	268154.	+	177738.i	1.43687	+	0.952388i
$433$	284920.			1.51966			0.759832	−	0.650119i	$-0.225281\pi$
$433$	284920.			1.51966			0.759832	+	0.650119i	$0.225281\pi$
$434$	32289.4	−	53985.1i	0.171427	−	0.286612i
$435$		0			0
$436$	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	$0.323754\pi$
$439$			327852.i			1.70118i	−0.525832	+	0.850588i	$0.676246\pi$
$440$		0			0
$441$	−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
$445$		0			0
$446$	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	$0.777820\pi$
$450$		0			0
$451$		−	12538.2i		−	0.0616428i
$452$	171732.	+	319858.i	0.840569	+	1.56560i
$453$	−238201.			−1.16077
$454$	−278198.	−	166395.i	−1.34972	−	0.807288i
$455$		0			0
$456$	426293.	+	19752.9i	2.05012	+	0.0949951i
$457$	−56777.8			−0.271861			−0.135930	−	0.990718i	$-0.543402\pi$
$457$	−56777.8			−0.271861			−0.135930	+	0.990718i	$0.543402\pi$
$458$	97981.3	−	163816.i	0.467102	−	0.780956i
$459$			587895.i			2.79045i
$460$		0			0
$461$	−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
$465$		0			0
$466$	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
$470$		0			0
$471$		−	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
$475$		0			0
$476$	−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	$-0.907712\pi$
$479$		−	131187.i		−	0.571770i	0.958264	−	0.285885i	$-0.0922875\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	−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
$490$		0			0
$491$		−	357740.i		−	1.48390i	−0.670456	−	0.741950i	$-0.733901\pi$
$491$		−	357740.i		−	1.48390i	0.670456	−	0.741950i	$-0.266099\pi$
$492$	−103150.	+	55381.0i	−0.426126	+	0.228787i
$493$	−451213.			−1.85647
$494$	−85245.7	−	50986.8i	−0.349316	−	0.208932i
$495$		0			0
$496$	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	$-0.843077\pi$
$499$		−	235685.i		−	0.946523i	0.880922	−	0.473261i	$-0.156923\pi$
$500$		0			0
$501$	−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
$505$		0			0
$506$	−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	$0.590733\pi$
$510$		0			0
$511$			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
$515$		0			0
$516$	−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
$520$		0			0
$521$	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
$525$		0			0
$526$	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
$530$		0			0
$531$		−	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
$535$		0			0
$536$	−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
$540$		0			0
$541$	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
$545$		0			0
$546$	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
$550$		0			0
$551$			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
$555$		0			0
$556$	283677.	−	152306.i	0.917646	−	0.492684i
$557$	2288.63			0.00737675			0.00368838	−	0.999993i	$-0.498826\pi$
$557$	2288.63			0.00737675			0.00368838	+	0.999993i	$0.498826\pi$
$558$	231981.	+	138751.i	0.745046	+	0.445624i
$559$			1609.85i			0.00515184i
$560$		0			0
$561$	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
$565$		0			0
$566$	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	$0.398606\pi$
$570$		0			0
$571$		−	412759.i		−	1.26597i	−0.774163	−	0.632986i	$-0.781829\pi$
$571$		−	412759.i		−	1.26597i	0.774163	−	0.632986i	$-0.218171\pi$
$572$	−21829.7	+	11720.4i	−0.0667199	+	0.0358219i
$573$	369116.			1.12423
$574$	−60666.1	−	36285.4i	−0.184129	−	0.110131i
$575$		0			0
$576$	−659366.	−	61236.8i	−1.98738	−	0.184573i
$577$	441255.			1.32537			0.662686	−	0.748897i	$-0.269416\pi$
$577$	441255.			1.32537			0.662686	+	0.748897i	$0.269416\pi$
$578$	277864.	−	464565.i	0.831719	−	1.39056i
$579$			266404.i			0.794665i
$580$		0			0
$581$	−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
$585$		0			0
$586$	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
$590$		0			0
$591$			866088.i			2.47963i
$592$	−254227.	+	383552.i	−0.725401	+	1.09441i
$593$	−342542.			−0.974101			−0.487051	−	0.873374i	$-0.661927\pi$
$593$	−342542.			−0.974101			−0.487051	+	0.873374i	$0.661927\pi$
$594$	68874.1	−	115152.i	0.195201	−	0.326360i
$595$		0			0
$596$	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	$0.228643\pi$
$599$			472260.i			1.31622i	−0.752923	+	0.658109i	$0.771357\pi$
$600$		0			0
$601$	−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
$605$		0			0
$606$	−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
$610$		0			0
$611$			89281.8i			0.239156i
$612$	−572423.	−	1.06616e6i	−1.52832	−	2.84657i
$613$	−164930.			−0.438915			−0.219457	−	0.975622i	$-0.570429\pi$
$613$	−164930.			−0.438915			−0.219457	+	0.975622i	$0.570429\pi$
$614$	601009.	+	359473.i	1.59421	+	0.953520i
$615$		0			0
$616$	64204.1	+	2974.99i	0.169200	+	0.00784013i
$617$	−32007.8			−0.0840787			−0.0420394	−	0.999116i	$-0.513385\pi$
$617$	−32007.8			−0.0840787			−0.0420394	+	0.999116i	$0.513385\pi$
$618$	−651358.	+	1.08902e6i	−1.70547	+	2.85139i
$619$		−	30448.1i		−	0.0794655i	−0.999210	−	0.0397328i	$-0.987349\pi$
$619$		−	30448.1i		−	0.0794655i	0.999210	−	0.0397328i	$-0.0126507\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	272227.	−	455140.i	0.694676	−	1.16144i
$627$		−	177987.i		−	0.452745i
$628$	203832.	+	379646.i	0.516836	+	0.962630i
$629$	−840891.			−2.12539
$630$		0			0
$631$			205747.i			0.516744i	0.966045	+	0.258372i	$0.0831861\pi$
$631$			205747.i			0.516744i	−0.966045	+	0.258372i	$0.916814\pi$
$632$	−2090.61	+	45118.2i	−0.00523407	+	0.112958i
$633$	−264206.			−0.659379
$634$	69511.9	−	116218.i	0.172934	−	0.289131i
$635$		0			0
$636$	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
$640$		0			0
$641$	−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
$645$		0			0
$646$	−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
$650$		0			0
$651$			244981.i			0.578056i
$652$	−281433.	+	151101.i	−0.662033	+	0.355445i
$653$	348146.			0.816461			0.408231	−	0.912879i	$-0.366146\pi$
$653$	348146.			0.816461			0.408231	+	0.912879i	$0.366146\pi$
$654$	−214602.	−	128357.i	−0.501739	−	0.300098i
$655$		0			0
$656$	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	$-0.976174\pi$
$659$		−	64952.7i		−	0.149564i	0.997200	−	0.0747818i	$-0.0238260\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	−596669.	+	997580.i	−1.34519	+	2.24905i
$667$			347663.i			0.781460i
$668$	163737.	−	87910.2i	0.366938	−	0.197009i
$669$	−261987.			−0.585367
$670$		0			0
$671$		−	54770.1i		−	0.121646i
$672$	−259114.	−	541336.i	−0.573788	−	1.19875i
$673$	−166579.			−0.367781			−0.183891	−	0.982947i	$-0.558869\pi$
$673$	−166579.			−0.367781			−0.183891	+	0.982947i	$0.558869\pi$
$674$	−11033.3	+	18446.8i	−0.0242877	+	0.0406070i
$675$		0			0
$676$	190692.	+	355171.i	0.417290	+	0.777221i
$677$	528530.			1.15317			0.576584	−	0.817038i	$-0.304385\pi$
$677$	528530.			1.15317			0.576584	+	0.817038i	$0.304385\pi$
$678$	−1.21339e6	−	725746.i	−2.63961	−	1.57879i
$679$			489301.i			1.06130i
$680$		0			0
$681$	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
$685$		0			0
$686$	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
$690$		0			0
$691$			893708.i			1.87171i	0.352380	+	0.935857i	$0.385372\pi$
$691$			893708.i			1.87171i	−0.352380	+	0.935857i	$0.614628\pi$
$692$	206321.	+	384282.i	0.430855	+	0.802486i
$693$	162360.			0.338075
$694$	270873.	+	162013.i	0.562401	+	0.336381i
$695$		0			0
$696$	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
$700$		0			0
$701$	−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
$705$		0			0
$706$	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	$0.252376\pi$
$710$		0			0
$711$			114096.i			0.225699i
$712$	−457533.	−	21200.4i	−0.902531	−	0.0418201i
$713$	150668.			0.296375
$714$	562956.	−	941215.i	1.10428	−	1.84626i
$715$		0			0
$716$	−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	$-0.863138\pi$
$719$		−	430977.i		−	0.833675i	0.908981	−	0.416837i	$-0.136862\pi$
$720$		0			0
$721$	−766176.			−1.47387
$722$	−108612.	+	181591.i	−0.208355	+	0.348353i
$723$		−	409084.i		−	0.782592i
$724$	349404.	+	650781.i	0.666579	+	1.24153i
$725$		0			0
$726$	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
$730$		0			0
$731$			12981.5i			0.0242935i
$732$	−450584.	+	241919.i	−0.840918	+	0.451489i
$733$	−99574.1			−0.185327			−0.0926634	−	0.995697i	$-0.529538\pi$
$733$	−99574.1			−0.185327			−0.0926634	+	0.995697i	$0.529538\pi$
$734$	−110539.	−	66115.4i	−0.205175	−	0.122719i
$735$		0			0
$736$	−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	$-0.869187\pi$
$739$		−	436339.i		−	0.798979i	0.916738	−	0.399490i	$-0.130813\pi$
$740$		0			0
$741$	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
$745$		0			0
$746$	419466.	−	701312.i	0.753736	−	1.26018i
$747$		−	262963.i		−	0.471252i
$748$	−176030.	+	94510.5i	−0.314618	+	0.168918i
$749$	833436.			1.48562
$750$		0			0
$751$		−	201164.i		−	0.356673i	−0.983970	−	0.178336i	$-0.942929\pi$
$751$		−	201164.i		−	0.356673i	0.983970	−	0.178336i	$-0.0570715\pi$
$752$	328387.	+	217663.i	0.580699	+	0.384900i
$753$	−380134.			−0.670420
$754$	−114889.	+	192085.i	−0.202086	+	0.337871i
$755$		0			0
$756$	−357841.	−	666495.i	−0.626104	−	1.16615i
$757$	−915352.			−1.59734			−0.798669	−	0.601771i	$-0.794462\pi$
$757$	−915352.			−1.59734			−0.798669	+	0.601771i	$0.794462\pi$
$758$	466419.	+	278973.i	0.811779	+	0.485538i
$759$		−	149884.i		−	0.260178i
$760$		0			0
$761$	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
$765$		0			0
$766$	−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	$0.526317\pi$
$770$		0			0
$771$		−	474645.i		−	0.798472i
$772$	−129433.	−	241074.i	−0.217175	−	0.404497i
$773$	−517767.			−0.866514			−0.433257	−	0.901270i	$-0.642636\pi$
$773$	−517767.			−0.866514			−0.433257	+	0.901270i	$0.642636\pi$
$774$	15400.4	+	9211.25i	0.0257070	+	0.0153758i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−151866.			−0.248977
$782$	−578866.	−	346229.i	−0.946595	−	0.566174i
$783$		−	1.21208e6i		−	1.97700i
$784$	−139385.	+	210290.i	−0.226769	+	0.342126i
$785$		0			0
$786$	−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
$790$		0			0
$791$		−	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
$795$		0			0
$796$	823234.	−	441994.i	1.29926	−	0.697574i
$797$	204919.			0.322600			0.161300	−	0.986905i	$-0.448431\pi$
$797$	204919.			0.322600			0.161300	+	0.986905i	$0.448431\pi$
$798$	−861191.	−	515092.i	−1.35236	−	0.808871i
$799$			719949.i			1.12774i
$800$		0			0
$801$	−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
$805$		0			0
$806$	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	$0.332097\pi$
$810$		0			0
$811$		−	464925.i		−	0.706872i	−0.935459	−	0.353436i	$-0.885013\pi$
$811$		−	464925.i		−	0.706872i	0.935459	−	0.353436i	$-0.114987\pi$
$812$	511539.	−	274645.i	0.775829	−	0.416543i
$813$	1.92770e6			2.91648
$814$	164706.	+	98513.6i	0.248577	+	0.148678i
$815$		0			0
$816$	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
$820$		0			0
$821$	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
$825$		0			0
$826$	−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	$0.707818\pi$
$830$		0			0
$831$		−	1.48372e6i		−	2.14857i
$832$	−236609.	−	21974.4i	−0.341809	−	0.0317446i
$833$	−461035.			−0.664422
$834$	−643654.	+	1.07614e6i	−0.925380	+	1.54716i
$835$		0			0
$836$	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	$0.316063\pi$
$839$			1.17926e6i			1.67527i	−0.546229	+	0.837636i	$0.683937\pi$
$840$		0			0
$841$	222997.			0.315288
$842$	403658.	−	674882.i	0.569363	−	0.951927i
$843$			914872.i			1.28738i
$844$	239085.	−	128365.i	0.335635	−	0.180202i
$845$		0			0
$846$	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
$850$		0			0
$851$			647913.i			0.894659i
$852$	670790.	+	1.24938e6i	0.924075	+	1.72113i
$853$	533912.			0.733790			0.366895	−	0.930262i	$-0.380421\pi$
$853$	533912.			0.733790			0.366895	+	0.930262i	$0.380421\pi$
$854$	−265005.	−	158504.i	−0.363361	−	0.217332i
$855$		0			0
$856$	−65622.8	+	1.41623e6i	−0.0895586	+	1.93279i
$857$	−155720.			−0.212023			−0.106011	−	0.994365i	$-0.533808\pi$
$857$	−155720.			−0.212023			−0.106011	+	0.994365i	$0.533808\pi$
$858$	49530.8	−	82811.3i	0.0672823	−	0.112490i
$859$		−	1.28910e6i		−	1.74703i	−0.486795	−	0.873516i	$-0.661834\pi$
$859$		−	1.28910e6i		−	1.74703i	0.486795	−	0.873516i	$-0.338166\pi$
$860$		0			0
$861$	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
$865$		0			0
$866$	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
$870$		0			0
$871$			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
$875$		0			0
$876$	439424.	−	235927.i	0.572632	−	0.307446i
$877$	−1.08498e6			−1.41066			−0.705328	−	0.708881i	$-0.749200\pi$
$877$	−1.08498e6			−1.41066			−0.705328	+	0.708881i	$0.749200\pi$
$878$	1.12546e6	+	673155.i	1.45996	+	0.873225i
$879$			876483.i			1.13440i
$880$		0			0
$881$	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
$885$		0			0
$886$	−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
$890$		0			0
$891$			172999.i			0.217915i
$892$	237077.	−	127287.i	0.297961	−	0.159975i
$893$	658738.			0.826057
$894$	−327684.	−	195993.i	−0.409997	−	0.245226i
$895$		0			0
$896$	497485.	+	363975.i	0.619675	+	0.453372i
$897$	325759.			0.404866
$898$	−634251.	+	1.06041e6i	−0.786518	+	1.31499i
$899$		−	403158.i		−	0.498834i
$900$		0			0
$901$	−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
$905$		0			0
$906$	−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
$910$		0			0
$911$		−	606030.i		−	0.730227i	−0.930963	−	0.365113i	$-0.881030\pi$
$911$		−	606030.i		−	0.730227i	0.930963	−	0.365113i	$-0.118970\pi$
$912$	943085.	−	1.42283e6i	1.13386	−	1.71066i
$913$	−43416.7			−0.0520853
$914$	−116578.	+	194908.i	−0.139548	+	0.233312i
$915$		0			0
$916$	−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	$-0.764461\pi$
$919$		−	1.13891e6i		−	1.34853i	0.738491	−	0.674263i	$-0.235539\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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	$0.445932\pi$
$930$		0			0
$931$			421837.i			0.486683i
$932$	−119255.	−	222117.i	−0.137292	−	0.255712i
$933$	367965.			0.422711
$934$	−360779.	−	215788.i	−0.413569	−	0.247362i
$935$		0			0
$936$	−599627.	−	27784.6i	−0.684431	−	0.0317141i
$937$	1.11462e6			1.26955			0.634774	−	0.772698i	$-0.281093\pi$
$937$	1.11462e6			1.26955			0.634774	+	0.772698i	$0.281093\pi$
$938$	90051.2	−	150558.i	0.102349	−	0.171119i
$939$			2.06539e6i			2.34246i
$940$		0			0
$941$	−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
$945$		0			0
$946$	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
$950$		0			0
$951$			527389.i			0.583136i
$952$	−52139.3	+	1.12523e6i	−0.0575296	+	1.24156i
$953$	146915.			0.161763			0.0808815	−	0.996724i	$-0.474226\pi$
$953$	146915.			0.161763			0.0808815	+	0.996724i	$0.474226\pi$
$954$	−91636.1	+	153208.i	−0.100686	+	0.168339i
$955$		0			0
$956$	−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
$960$		0			0
$961$	748803.			0.810813
$962$	−214110.	+	357974.i	−0.231359	+	0.386813i
$963$			3.58137e6i			3.86186i
$964$	198753.	+	370187.i	0.213875	+	0.398352i
$965$		0			0
$966$	−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
$970$		0			0
$971$			1.55163e6i			1.64569i	0.568265	+	0.822846i	$0.307615\pi$
$971$			1.55163e6i			1.64569i	−0.568265	+	0.822846i	$0.692385\pi$
$972$	−11689.3	+	6275.97i	−0.0123724	+	0.00664275i
$973$	−757113.			−0.799715
$974$	119563.	+	71512.4i	0.126031	+	0.0753813i
$975$		0			0
$976$	290206.	−	437833.i	0.304653	−	0.459630i
$977$	−13609.0			−0.0142572			−0.00712862	−	0.999975i	$-0.502269\pi$
$977$	−13609.0			−0.0142572			−0.00712862	+	0.999975i	$0.502269\pi$
$978$	638561.	−	1.06762e6i	0.667612	−	1.11619i
$979$			191030.i			0.199314i
$980$		0			0
$981$	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
$985$		0			0
$986$	−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
$990$		0			0
$991$		−	1.04471e6i		−	1.06377i	−0.846816	−	0.531886i	$-0.821484\pi$
$991$		−	1.04471e6i		−	1.06377i	0.846816	−	0.531886i	$-0.178516\pi$
$992$	386076.	−	184798.i	0.392329	−	0.187790i
$993$	−379139.			−0.384503
$994$	−439498.	+	734804.i	−0.444820	+	0.743702i
$995$		0			0
$996$	191771.	+	357182.i	0.193314	+	0.360057i
$997$	−100146.			−0.100750			−0.0503748	−	0.998730i	$-0.516042\pi$
$997$	−100146.			−0.100750			−0.0503748	+	0.998730i	$0.516042\pi$
$998$	−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	100.5.b.c.51.7		8
4.3	odd	2	inner	100.5.b.c.51.8		8
5.2	odd	4		100.5.d.c.99.14		16
5.3	odd	4		100.5.d.c.99.3		16
5.4	even	2		20.5.b.a.11.2	yes	8
15.14	odd	2		180.5.c.a.91.7		8
20.3	even	4		100.5.d.c.99.13		16
20.7	even	4		100.5.d.c.99.4		16
20.19	odd	2		20.5.b.a.11.1	✓	8
40.19	odd	2		320.5.b.d.191.1		8
40.29	even	2		320.5.b.d.191.8		8
60.59	even	2		180.5.c.a.91.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.1	✓	8	20.19	odd	2
20.5.b.a.11.2	yes	8	5.4	even	2
100.5.b.c.51.7		8	1.1	even	1	trivial
100.5.b.c.51.8		8	4.3	odd	2	inner
100.5.d.c.99.3		16	5.3	odd	4
100.5.d.c.99.4		16	20.7	even	4
100.5.d.c.99.13		16	20.3	even	4
100.5.d.c.99.14		16	5.2	odd	4
180.5.c.a.91.7		8	15.14	odd	2
180.5.c.a.91.8		8	60.59	even	2
320.5.b.d.191.1		8	40.19	odd	2
320.5.b.d.191.8		8	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 - 14.0967i) q^{4} +(53.4761 + 31.9849i) q^{6} +37.6230i q^{7} +(-63.9314 - 2.96235i) q^{8} -161.671 q^{9} +O(q^{10})\)	\(q+(2.05323 - 3.43282i) q^{2} +15.5779i q^{3} +(-7.56853 - 14.0967i) q^{4} +(53.4761 + 31.9849i) q^{6} +37.6230i q^{7} +(-63.9314 - 2.96235i) q^{8} -161.671 q^{9} +26.6928i q^{11} +(219.597 - 117.902i) q^{12} -58.0144 q^{13} +(129.153 + 77.2486i) q^{14} +(-141.435 + 213.383i) q^{16} -467.816 q^{17} +(-331.947 + 554.987i) q^{18} +428.041i q^{19} -586.088 q^{21} +(91.6316 + 54.8064i) q^{22} +360.456i q^{23} +(46.1472 - 995.917i) q^{24} +(-119.117 + 199.153i) q^{26} -1256.68i q^{27} +(530.361 - 284.751i) q^{28} +964.509 q^{29} -417.993i q^{31} +(442.107 + 923.644i) q^{32} -415.818 q^{33} +(-960.531 + 1605.93i) q^{34} +(1223.61 + 2279.03i) q^{36} +1797.48 q^{37} +(1469.39 + 878.866i) q^{38} -903.742i q^{39} -469.722 q^{41} +(-1203.37 + 2011.93i) q^{42} -27.7492i q^{43} +(376.281 - 202.025i) q^{44} +(1237.38 + 740.097i) q^{46} -1538.96i q^{47} +(-3324.05 - 2203.26i) q^{48} +985.506 q^{49} -7287.58i q^{51} +(439.083 + 817.812i) q^{52} +276.057 q^{53} +(-4313.96 - 2580.25i) q^{54} +(111.453 - 2405.29i) q^{56} -6667.98 q^{57} +(1980.36 - 3310.99i) q^{58} +3813.72i q^{59} -2051.87 q^{61} +(-1434.90 - 858.234i) q^{62} -6082.55i q^{63} +(4078.45 + 378.775i) q^{64} +(-853.768 + 1427.43i) q^{66} -1165.73i q^{67} +(3540.67 + 6594.66i) q^{68} -5615.14 q^{69} +5689.40i q^{71} +(10335.8 + 478.926i) q^{72} +2001.05 q^{73} +(3690.64 - 6170.44i) q^{74} +(6033.98 - 3239.64i) q^{76} -1004.26 q^{77} +(-3102.38 - 1855.59i) q^{78} -705.728i q^{79} +6481.10 q^{81} +(-964.446 + 1612.47i) q^{82} +1626.53i q^{83} +(4435.82 + 8261.91i) q^{84} +(-95.2580 - 56.9753i) q^{86} +15025.0i q^{87} +(79.0735 - 1706.51i) q^{88} +7156.62 q^{89} -2182.68i q^{91} +(5081.24 - 2728.12i) q^{92} +6511.45 q^{93} +(-5282.97 - 3159.83i) q^{94} +(-14388.4 + 6887.10i) q^{96} +13005.4 q^{97} +(2023.47 - 3383.07i) q^{98} -4315.45i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 20 q^{4} + 48 q^{6} - 216 q^{8} - 328 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 20 * q^4 + 48 * q^6 - 216 * q^8 - 328 * q^9	\( 8 q - 6 q^{2} - 20 q^{4} + 48 q^{6} - 216 q^{8} - 328 q^{9} + 200 q^{12} - 352 q^{13} - 168 q^{14} - 272 q^{16} + 48 q^{17} - 286 q^{18} + 16 q^{21} - 800 q^{22} + 1552 q^{24} - 2172 q^{26} - 40 q^{28} + 1200 q^{29} + 2304 q^{32} + 1120 q^{33} - 2132 q^{34} - 1044 q^{36} + 5728 q^{37} + 3360 q^{38} + 4896 q^{41} - 12120 q^{42} + 7920 q^{44} + 728 q^{46} - 8640 q^{48} - 5768 q^{49} + 12488 q^{52} - 2592 q^{53} - 17776 q^{54} + 48 q^{56} - 3840 q^{57} + 7428 q^{58} + 7936 q^{61} - 25680 q^{62} + 18880 q^{64} - 8080 q^{66} - 2712 q^{68} - 2256 q^{69} + 36264 q^{72} + 14448 q^{73} - 18492 q^{74} + 12000 q^{76} - 2400 q^{77} + 14480 q^{78} - 936 q^{81} - 27412 q^{82} + 50464 q^{84} - 7392 q^{86} - 18080 q^{88} + 23760 q^{89} + 52680 q^{92} - 11360 q^{93} - 43368 q^{94} + 2688 q^{96} + 4368 q^{97} + 21474 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 - 20 * q^4 + 48 * q^6 - 216 * q^8 - 328 * q^9 + 200 * q^12 - 352 * q^13 - 168 * q^14 - 272 * q^16 + 48 * q^17 - 286 * q^18 + 16 * q^21 - 800 * q^22 + 1552 * q^24 - 2172 * q^26 - 40 * q^28 + 1200 * q^29 + 2304 * q^32 + 1120 * q^33 - 2132 * q^34 - 1044 * q^36 + 5728 * q^37 + 3360 * q^38 + 4896 * q^41 - 12120 * q^42 + 7920 * q^44 + 728 * q^46 - 8640 * q^48 - 5768 * q^49 + 12488 * q^52 - 2592 * q^53 - 17776 * q^54 + 48 * q^56 - 3840 * q^57 + 7428 * q^58 + 7936 * q^61 - 25680 * q^62 + 18880 * q^64 - 8080 * q^66 - 2712 * q^68 - 2256 * q^69 + 36264 * q^72 + 14448 * q^73 - 18492 * q^74 + 12000 * q^76 - 2400 * q^77 + 14480 * q^78 - 936 * q^81 - 27412 * q^82 + 50464 * q^84 - 7392 * q^86 - 18080 * q^88 + 23760 * q^89 + 52680 * q^92 - 11360 * q^93 - 43368 * q^94 + 2688 * q^96 + 4368 * q^97 + 21474 * q^98

Introduction

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