LMFDB - Embedded newform 100.5.d.c.99.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,5,Mod(99,100)]

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, 1]))

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

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + 21x^{12} + 35x^{10} - 199x^{8} + 560x^{6} + 5376x^{4} - 20480x^{2} + 65536 $ x^16 - 5x^14 + 21x^12 + 35x^10 - 199x^8 + 560x^6 + 5376x^4 - 20480*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{37}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.13
Root			$-1.71641 - 1.02661i$ of defining polynomial
Character	$\chi$	$=$	100.99
Dual form			100.5.d.c.99.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.43282 - 2.05323i) q^{2} +15.5779 q^{3} +(7.56853 - 14.0967i) q^{4} +(53.4761 - 31.9849i) q^{6} -37.6230 q^{7} +(-2.96235 - 63.9314i) q^{8} +161.671 q^{9} +O(q^{10})$	\(q+(3.43282 - 2.05323i) q^{2} +15.5779 q^{3} +(7.56853 - 14.0967i) q^{4} +(53.4761 - 31.9849i) q^{6} -37.6230 q^{7} +(-2.96235 - 63.9314i) q^{8} +161.671 q^{9} -26.6928i q^{11} +(117.902 - 219.597i) q^{12} -58.0144i q^{13} +(-129.153 + 77.2486i) q^{14} +(-141.435 - 213.383i) q^{16} +467.816i q^{17} +(554.987 - 331.947i) q^{18} +428.041i q^{19} -586.088 q^{21} +(-54.8064 - 91.6316i) q^{22} +360.456 q^{23} +(-46.1472 - 995.917i) q^{24} +(-119.117 - 199.153i) q^{26} +1256.68 q^{27} +(-284.751 + 530.361i) q^{28} -964.509 q^{29} +417.993i q^{31} +(-923.644 - 442.107i) q^{32} -415.818i q^{33} +(960.531 + 1605.93i) q^{34} +(1223.61 - 2279.03i) q^{36} -1797.48i q^{37} +(878.866 + 1469.39i) q^{38} -903.742i q^{39} -469.722 q^{41} +(-2011.93 + 1203.37i) q^{42} -27.7492 q^{43} +(-376.281 - 202.025i) q^{44} +(1237.38 - 740.097i) q^{46} +1538.96 q^{47} +(-2203.26 - 3324.05i) q^{48} -985.506 q^{49} +7287.58i q^{51} +(-817.812 - 439.083i) q^{52} +276.057i q^{53} +(4313.96 - 2580.25i) q^{54} +(111.453 + 2405.29i) q^{56} +6667.98i q^{57} +(-3310.99 + 1980.36i) q^{58} +3813.72i q^{59} -2051.87 q^{61} +(858.234 + 1434.90i) q^{62} -6082.55 q^{63} +(-4078.45 + 378.775i) q^{64} +(-853.768 - 1427.43i) q^{66} +1165.73 q^{67} +(6594.66 + 3540.67i) q^{68} +5615.14 q^{69} -5689.40i q^{71} +(-478.926 - 10335.8i) q^{72} +2001.05i q^{73} +(-3690.64 - 6170.44i) q^{74} +(6033.98 + 3239.64i) q^{76} +1004.26i q^{77} +(-1855.59 - 3102.38i) q^{78} -705.728i q^{79} +6481.10 q^{81} +(-1612.47 + 964.446i) q^{82} +1626.53 q^{83} +(-4435.82 + 8261.91i) q^{84} +(-95.2580 + 56.9753i) q^{86} -15025.0 q^{87} +(-1706.51 + 79.0735i) q^{88} -7156.62 q^{89} +2182.68i q^{91} +(2728.12 - 5081.24i) q^{92} +6511.45i q^{93} +(5282.97 - 3159.83i) q^{94} +(-14388.4 - 6887.10i) q^{96} -13005.4i q^{97} +(-3383.07 + 2023.47i) q^{98} -4315.45i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{4} + 96 q^{6} + 656 q^{9}+O(q^{10}) $ 16 * q + 40 * q^4 + 96 * q^6 + 656 * q^9	$ 16 q + 40 q^{4} + 96 q^{6} + 656 q^{9} + 336 q^{14} - 544 q^{16} + 32 q^{21} - 3104 q^{24} - 4344 q^{26} - 2400 q^{29} + 4264 q^{34} - 2088 q^{36} + 9792 q^{41} - 15840 q^{44} + 1456 q^{46} + 11536 q^{49} + 35552 q^{54} + 96 q^{56} + 15872 q^{61} - 37760 q^{64} - 16160 q^{66} + 4512 q^{69} + 36984 q^{74} + 24000 q^{76} - 1872 q^{81} - 100928 q^{84} - 14784 q^{86} - 47520 q^{89} + 86736 q^{94} + 5376 q^{96}+O(q^{100}) $ 16 * q + 40 * q^4 + 96 * q^6 + 656 * q^9 + 336 * q^14 - 544 * q^16 + 32 * q^21 - 3104 * q^24 - 4344 * q^26 - 2400 * q^29 + 4264 * q^34 - 2088 * q^36 + 9792 * q^41 - 15840 * q^44 + 1456 * q^46 + 11536 * q^49 + 35552 * q^54 + 96 * q^56 + 15872 * q^61 - 37760 * q^64 - 16160 * q^66 + 4512 * q^69 + 36984 * q^74 + 24000 * q^76 - 1872 * q^81 - 100928 * q^84 - 14784 * q^86 - 47520 * q^89 + 86736 * q^94 + 5376 * q^96

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 $

$2$	3.43282	−	2.05323i	0.858205	−	0.513307i
$2$	3.43282	−	2.05323i	0.858205	−	0.513307i
$3$	15.5779			1.73088			0.865438	−	0.501015i	$-0.167040\pi$
$3$	15.5779			1.73088			0.865438	+	0.501015i	$0.167040\pi$
$4$	7.56853	−	14.0967i	0.473033	−	0.881045i
$5$		0			0
$5$		0			0
$6$	53.4761	−	31.9849i	1.48545	−	0.888470i
$7$	−37.6230			−0.767817			−0.383909	−	0.923371i	$-0.625422\pi$
$7$	−37.6230			−0.767817			−0.383909	+	0.923371i	$0.625422\pi$
$8$	−2.96235	−	63.9314i	−0.0462868	−	0.998928i
$9$	161.671			1.99594
$10$		0			0
$11$		−	26.6928i		−	0.220602i	−0.993898	−	0.110301i	$-0.964819\pi$
$11$		−	26.6928i		−	0.220602i	0.993898	−	0.110301i	$-0.0351814\pi$
$12$	117.902	−	219.597i	0.818762	−	1.52498i
$13$		−	58.0144i		−	0.343280i	−0.985160	−	0.171640i	$-0.945093\pi$
$13$		−	58.0144i		−	0.343280i	0.985160	−	0.171640i	$-0.0549066\pi$
$14$	−129.153	+	77.2486i	−0.658945	+	0.394126i
$15$		0			0
$16$	−141.435	−	213.383i	−0.552480	−	0.833526i
$17$			467.816i			1.61874i	0.587300	+	0.809370i	$0.300191\pi$
$17$			467.816i			1.61874i	−0.587300	+	0.809370i	$0.699809\pi$
$18$	554.987	−	331.947i	1.71292	−	1.02453i
$19$			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
$22$	−54.8064	−	91.6316i	−0.113236	−	0.189322i
$23$	360.456			0.681391			0.340695	−	0.940174i	$-0.389338\pi$
$23$	360.456			0.681391			0.340695	+	0.940174i	$0.389338\pi$
$24$	−46.1472	−	995.917i	−0.0801167	−	1.72902i
$25$		0			0
$26$	−119.117	−	199.153i	−0.176208	−	0.294605i
$27$	1256.68			1.72384
$28$	−284.751	+	530.361i	−0.363203	+	0.676481i
$29$	−964.509			−1.14686			−0.573430	−	0.819255i	$-0.694388\pi$
$29$	−964.509			−1.14686			−0.573430	+	0.819255i	$0.694388\pi$
$30$		0			0
$31$			417.993i			0.434956i	0.976065	+	0.217478i	$0.0697831\pi$
$31$			417.993i			0.434956i	−0.976065	+	0.217478i	$0.930217\pi$
$32$	−923.644	−	442.107i	−0.901996	−	0.431745i
$33$		−	415.818i		−	0.381834i
$34$	960.531	+	1605.93i	0.830909	+	1.38921i
$35$		0			0
$36$	1223.61	−	2279.03i	0.944143	−	1.75851i
$37$		−	1797.48i		−	1.31299i	−0.754330	−	0.656495i	$-0.772038\pi$
$37$		−	1797.48i		−	1.31299i	0.754330	−	0.656495i	$-0.227962\pi$
$38$	878.866	+	1469.39i	0.608633	+	1.01758i
$39$		−	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	$0.544619\pi$
$42$	−2011.93	+	1203.37i	−1.14055	+	0.682183i
$43$	−27.7492			−0.0150077			−0.00750384	−	0.999972i	$-0.502389\pi$
$43$	−27.7492			−0.0150077			−0.00750384	+	0.999972i	$0.502389\pi$
$44$	−376.281	−	202.025i	−0.194360	−	0.104352i
$45$		0			0
$46$	1237.38	−	740.097i	0.584773	−	0.349762i
$47$	1538.96			0.696677			0.348339	−	0.937369i	$-0.386746\pi$
$47$	1538.96			0.696677			0.348339	+	0.937369i	$0.386746\pi$
$48$	−2203.26	−	3324.05i	−0.956275	−	1.44273i
$49$	−985.506			−0.410457
$50$		0			0
$51$			7287.58i			2.80184i
$52$	−817.812	−	439.083i	−0.302445	−	0.162383i
$53$			276.057i			0.0982758i	0.998792	+	0.0491379i	$0.0156474\pi$
$53$			276.057i			0.0982758i	−0.998792	+	0.0491379i	$0.984353\pi$
$54$	4313.96	−	2580.25i	1.47941	−	0.884859i
$55$		0			0
$56$	111.453	+	2405.29i	0.0355398	+	0.766994i
$57$			6667.98i			2.05232i
$58$	−3310.99	+	1980.36i	−0.984241	+	0.588691i
$59$			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	$0.588914\pi$
$62$	858.234	+	1434.90i	0.223266	+	0.373282i
$63$	−6082.55			−1.53251
$64$	−4078.45	+	378.775i	−0.995715	+	0.0924743i
$65$		0			0
$66$	−853.768	−	1427.43i	−0.195998	−	0.327692i
$67$	1165.73			0.259686			0.129843	−	0.991535i	$-0.458553\pi$
$67$	1165.73			0.259686			0.129843	+	0.991535i	$0.458553\pi$
$68$	6594.66	+	3540.67i	1.42618	+	0.765717i
$69$	5615.14			1.17940
$70$		0			0
$71$		−	5689.40i		−	1.12863i	−0.825561	−	0.564313i	$-0.809141\pi$
$71$		−	5689.40i		−	1.12863i	0.825561	−	0.564313i	$-0.190859\pi$
$72$	−478.926	−	10335.8i	−0.0923854	−	1.99380i
$73$			2001.05i			0.375501i	0.982217	+	0.187751i	$0.0601197\pi$
$73$			2001.05i			0.375501i	−0.982217	+	0.187751i	$0.939880\pi$
$74$	−3690.64	−	6170.44i	−0.673967	−	1.12682i
$75$		0			0
$76$	6033.98	+	3239.64i	1.04466	+	0.560880i
$77$			1004.26i			0.169382i
$78$	−1855.59	−	3102.38i	−0.304994	−	0.509925i
$79$		−	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
$82$	−1612.47	+	964.446i	−0.239809	+	0.143433i
$83$	1626.53			0.236106			0.118053	−	0.993007i	$-0.462335\pi$
$83$	1626.53			0.236106			0.118053	+	0.993007i	$0.462335\pi$
$84$	−4435.82	+	8261.91i	−0.628659	+	1.17091i
$85$		0			0
$86$	−95.2580	+	56.9753i	−0.0128797	+	0.00770354i
$87$	−15025.0			−1.98507
$88$	−1706.51	+	79.0735i	−0.220365	+	0.0102109i
$89$	−7156.62			−0.903499			−0.451750	−	0.892145i	$-0.649200\pi$
$89$	−7156.62			−0.903499			−0.451750	+	0.892145i	$0.649200\pi$
$90$		0			0
$91$			2182.68i			0.263577i
$92$	2728.12	−	5081.24i	0.322320	−	0.600336i
$93$			6511.45i			0.752856i
$94$	5282.97	−	3159.83i	0.597892	−	0.357609i
$95$		0			0
$96$	−14388.4	−	6887.10i	−1.56124	−	0.747298i
$97$		−	13005.4i		−	1.38223i	−0.722747	−	0.691113i	$-0.757121\pi$
$97$		−	13005.4i		−	1.38223i	0.722747	−	0.691113i	$-0.242879\pi$
$98$	−3383.07	+	2023.47i	−0.352256	+	0.210690i
$99$		−	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	$0.656275\pi$
$102$	14963.1	+	25017.0i	1.43820	+	2.40455i
$103$	20364.5			1.91955			0.959776	−	0.280767i	$-0.0905888\pi$
$103$	20364.5			1.91955			0.959776	+	0.280767i	$0.0905888\pi$
$104$	−3708.94	+	171.859i	−0.342912	+	0.0158893i
$105$		0			0
$106$	566.807	+	947.653i	0.0504456	+	0.0843408i
$107$	22152.3			1.93486			0.967432	−	0.253129i	$-0.0814598\pi$
$107$	22152.3			1.93486			0.967432	+	0.253129i	$0.0814598\pi$
$108$	9511.22	−	17715.1i	0.815433	−	1.51878i
$109$	4013.04			0.337770			0.168885	−	0.985636i	$-0.445983\pi$
$109$	4013.04			0.337770			0.168885	+	0.985636i	$0.445983\pi$
$110$		0			0
$111$		−	28001.0i		−	2.27262i
$112$	5321.21	+	8028.11i	0.424204	+	0.639996i
$113$		−	22690.2i		−	1.77698i	−0.458897	−	0.888489i	$-0.651755\pi$
$113$		−	22690.2i		−	1.77698i	0.458897	−	0.888489i	$-0.348245\pi$
$114$	13690.9	+	22890.0i	1.05347	+	1.76131i
$115$		0			0
$116$	−7299.91	+	13596.4i	−0.542502	+	1.01044i
$117$		−	9379.23i		−	0.685165i
$118$	7830.42	+	13091.8i	0.562369	+	0.940234i
$119$		−	17600.6i		−	1.24290i
$120$		0			0
$121$	13928.5			0.951335
$122$	−7043.69	+	4212.95i	−0.473239	+	0.283052i
$123$	−7317.28			−0.483659
$124$	5892.33	+	3163.59i	0.383216	+	0.205749i
$125$		0			0
$126$	−20880.3	+	12488.8i	−1.31521	+	0.786649i
$127$	−22038.9			−1.36641			−0.683206	−	0.730225i	$-0.739415\pi$
$127$	−22038.9			−1.36641			−0.683206	+	0.730225i	$0.739415\pi$
$128$	−13222.9	+	9674.24i	−0.807060	+	0.590469i
$129$	−432.274			−0.0259764
$130$		0			0
$131$		−	4968.89i		−	0.289545i	−0.989465	−	0.144773i	$-0.953755\pi$
$131$		−	4968.89i		−	0.289545i	0.989465	−	0.144773i	$-0.0462451\pi$
$132$	−5861.66	−	3147.13i	−0.336413	−	0.180620i
$133$		−	16104.2i		−	0.910409i
$134$	4001.75	−	2393.51i	0.222864	−	0.133299i
$135$		0			0
$136$	29908.1	−	1385.83i	1.61700	−	0.0749262i
$137$		−	11945.1i		−	0.636426i	−0.948019	−	0.318213i	$-0.896917\pi$
$137$		−	11945.1i		−	0.636426i	0.948019	−	0.318213i	$-0.103083\pi$
$138$	19275.8	−	11529.2i	1.01217	−	0.605395i
$139$			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
$142$	−11681.6	−	19530.7i	−0.579331	−	0.968592i
$143$	−1548.57			−0.0757282
$144$	−22865.9	−	34497.7i	−1.10271	−	1.66366i
$145$		0			0
$146$	4108.60	+	6869.24i	0.192747	+	0.322257i
$147$	−15352.1			−0.710450
$148$	−25338.6	−	13604.3i	−1.15680	−	0.621088i
$149$	6127.67			0.276009			0.138004	−	0.990432i	$-0.455931\pi$
$149$	6127.67			0.276009			0.138004	+	0.990432i	$0.455931\pi$
$150$		0			0
$151$		−	15290.9i		−	0.670626i	−0.942107	−	0.335313i	$-0.891158\pi$
$151$		−	15290.9i		−	0.670626i	0.942107	−	0.335313i	$-0.108842\pi$
$152$	27365.3	−	1268.01i	1.18444	−	0.0548827i
$153$			75632.1i			3.23090i
$154$	2061.98	+	3447.46i	0.0869448	+	0.145364i
$155$		0			0
$156$	−12739.8	−	6839.99i	−0.523496	−	0.281065i
$157$			26931.5i			1.09260i	0.837589	+	0.546300i	$0.183964\pi$
$157$			26931.5i			1.09260i	−0.837589	+	0.546300i	$0.816036\pi$
$158$	−1449.02	−	2422.64i	−0.0580443	−	0.0970452i
$159$			4300.38i			0.170103i
$160$		0			0
$161$	−13561.4			−0.523183
$162$	22248.5	−	13307.2i	0.847754	−	0.507055i
$163$	−19964.4			−0.751418			−0.375709	−	0.926738i	$-0.622601\pi$
$163$	−19964.4			−0.751418			−0.375709	+	0.926738i	$0.622601\pi$
$164$	−3555.10	+	6621.54i	−0.132180	+	0.246191i
$165$		0			0
$166$	5583.60	−	3339.64i	0.202627	−	0.121195i
$167$	−11615.2			−0.416481			−0.208240	−	0.978078i	$-0.566774\pi$
$167$	−11615.2			−0.416481			−0.208240	+	0.978078i	$0.566774\pi$
$168$	1736.20	+	37469.4i	0.0615150	+	1.32757i
$169$	25195.3			0.882159
$170$		0			0
$171$			69201.8i			2.36660i
$172$	−210.020	+	391.172i	−0.00709912	+	0.0132224i
$173$		−	27260.4i		−	0.910835i	−0.890278	−	0.455417i	$-0.849490\pi$
$173$		−	27260.4i		−	0.910835i	0.890278	−	0.455417i	$-0.150510\pi$
$174$	−51578.2	+	30849.8i	−1.70360	+	1.01895i
$175$		0			0
$176$	−5695.78	+	3775.29i	−0.183877	+	0.121878i
$177$			59409.7i			1.89632i
$178$	−24567.4	+	14694.2i	−0.775388	+	0.463772i
$179$		−	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	$0.748864\pi$
$182$	4481.53	+	7492.74i	0.135296	+	0.226203i
$183$	−31963.8			−0.954456
$184$	−1067.80	−	23044.4i	−0.0315394	−	0.680660i
$185$		0			0
$186$	13369.5	+	22352.6i	0.386446	+	0.646105i
$187$	12487.3			0.357097
$188$	11647.7	−	21694.3i	0.329551	−	0.613804i
$189$	−47280.1			−1.32360
$190$		0			0
$191$			23694.9i			0.649513i	0.945798	+	0.324757i	$0.105282\pi$
$191$			23694.9i			0.649513i	−0.945798	+	0.324757i	$0.894718\pi$
$192$	−63533.6	+	5900.51i	−1.72346	+	0.160062i
$193$			17101.4i			0.459111i	0.973296	+	0.229556i	$0.0737272\pi$
$193$			17101.4i			0.459111i	−0.973296	+	0.229556i	$0.926273\pi$
$194$	−26703.0	−	44645.1i	−0.709506	−	1.18623i
$195$		0			0
$196$	−7458.83	+	13892.4i	−0.194159	+	0.361631i
$197$		−	55597.2i		−	1.43259i	−0.697800	−	0.716293i	$-0.745837\pi$
$197$		−	55597.2i		−	1.43259i	0.697800	−	0.716293i	$-0.254163\pi$
$198$	−8860.59	−	14814.2i	−0.226012	−	0.377874i
$199$			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
$202$	−33019.8	+	19749.7i	−0.809230	+	0.484014i
$203$	36287.8			0.880579
$204$	102731.	+	55156.2i	2.46855	+	1.32536i
$205$		0			0
$206$	69907.8	−	41813.0i	1.64737	−	0.985319i
$207$	58275.1			1.36001
$208$	−12379.3	+	8205.25i	−0.286133	+	0.189655i
$209$	11425.6			0.261570
$210$		0			0
$211$		−	16960.3i		−	0.380951i	−0.981692	−	0.190475i	$-0.938997\pi$
$211$		−	16960.3i		−	0.380951i	0.981692	−	0.190475i	$-0.0610030\pi$
$212$	3891.49	+	2089.34i	0.0865854	+	0.0464877i
$213$		−	88628.9i		−	1.95351i
$214$	76044.8	−	45483.6i	1.66051	−	0.993179i
$215$		0			0
$216$	−3722.73	−	80341.3i	−0.0797910	−	1.72199i
$217$		−	15726.2i		−	0.333967i
$218$	13776.1	−	8239.68i	0.289876	−	0.173379i
$219$			31172.1i			0.649947i
$220$		0			0
$221$	27140.0			0.555681
$222$	−57492.4	−	96122.5i	−1.16655	−	1.95038i
$223$	16817.9			0.338191			0.169095	−	0.985600i	$-0.445915\pi$
$223$	16817.9			0.338191			0.169095	+	0.985600i	$0.445915\pi$
$224$	34750.3	+	16633.4i	0.692568	+	0.331501i
$225$		0			0
$226$	−46588.2	−	77891.6i	−0.912135	−	1.52501i
$227$	81040.8			1.57272			0.786361	−	0.617768i	$-0.211963\pi$
$227$	81040.8			1.57272			0.786361	+	0.617768i	$0.211963\pi$
$228$	93996.7	+	50466.8i	1.80818	+	0.970814i
$229$	−47720.6			−0.909987			−0.454994	−	0.890495i	$-0.650358\pi$
$229$	−47720.6			−0.909987			−0.454994	+	0.890495i	$0.650358\pi$
$230$		0			0
$231$			15644.3i			0.293179i
$232$	2857.22	+	61662.4i	0.0530844	+	1.14563i
$233$			15756.7i			0.290237i	0.989414	+	0.145119i	$0.0463564\pi$
$233$			15756.7i			0.290237i	−0.989414	+	0.145119i	$0.953644\pi$
$234$	−19257.7	−	32197.2i	−0.351700	−	0.588012i
$235$		0			0
$236$	53760.9	+	28864.2i	0.965256	+	0.518246i
$237$		−	10993.8i		−	0.195726i
$238$	−36138.1	−	60419.9i	−0.637987	−	1.06666i
$239$		−	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	$0.572587\pi$
$242$	47814.0	−	28598.3i	0.816441	−	0.488326i
$243$	−829.219			−0.0140429
$244$	−15529.6	+	28924.6i	−0.260844	+	0.485834i
$245$		0			0
$246$	−25118.9	+	15024.0i	−0.415079	+	0.248266i
$247$	24832.5			0.407031
$248$	26722.9	−	1238.24i	0.434490	−	0.0201327i
$249$	25338.0			0.408670
$250$		0			0
$251$		−	24402.1i		−	0.387329i	−0.981068	−	0.193665i	$-0.937963\pi$
$251$		−	24402.1i		−	0.387329i	0.981068	−	0.193665i	$-0.0620374\pi$
$252$	−46035.9	+	85743.9i	−0.724929	+	1.35021i
$253$		−	9621.57i		−	0.150316i
$254$	−75655.5	+	45250.8i	−1.17266	+	0.701388i
$255$		0			0
$256$	−25528.4	+	60359.5i	−0.389532	+	0.921013i
$257$			30469.1i			0.461311i	0.973036	+	0.230655i	$0.0740870\pi$
$257$			30469.1i			0.461311i	−0.973036	+	0.230655i	$0.925913\pi$
$258$	−1483.92	+	887.556i	−0.0222931	+	0.0133339i
$259$			67626.8i			1.00814i
$260$		0			0
$261$	−155933.			−2.28906
$262$	−10202.2	−	17057.3i	−0.148625	−	0.248489i
$263$	45832.0			0.662610			0.331305	−	0.943524i	$-0.392511\pi$
$263$	45832.0			0.662610			0.331305	+	0.943524i	$0.392511\pi$
$264$	−26583.8	+	1231.80i	−0.381425	+	0.0176739i
$265$		0			0
$266$	−33065.6	−	55282.9i	−0.467319	−	0.781318i
$267$	−111485.			−1.56385
$268$	8822.87	−	16433.0i	0.122840	−	0.228795i
$269$	36915.5			0.510157			0.255078	−	0.966920i	$-0.417899\pi$
$269$	36915.5			0.510157			0.255078	+	0.966920i	$0.417899\pi$
$270$		0			0
$271$			123746.i			1.68497i	0.538720	+	0.842485i	$0.318908\pi$
$271$			123746.i			1.68497i	−0.538720	+	0.842485i	$0.681092\pi$
$272$	99823.8	−	66165.4i	1.34926	−	0.894321i
$273$			34001.5i			0.456219i
$274$	−24526.0	−	41005.4i	−0.326682	−	0.546185i
$275$		0			0
$276$	42498.3	−	79155.0i	0.557896	−	1.03911i
$277$			95245.1i			1.24132i	0.784081	+	0.620659i	$0.213135\pi$
$277$			95245.1i			1.24132i	−0.784081	+	0.620659i	$0.786865\pi$
$278$	41318.4	+	69080.9i	0.534631	+	0.893858i
$279$			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	$0.378711\pi$
$282$	82297.6	−	49223.5i	1.03488	−	0.618977i
$283$	71397.1			0.891472			0.445736	−	0.895164i	$-0.352942\pi$
$283$	71397.1			0.891472			0.445736	+	0.895164i	$0.352942\pi$
$284$	−80201.9	−	43060.4i	−0.994369	−	0.533877i
$285$		0			0
$286$	−5315.95	+	3179.56i	−0.0649904	+	0.0388718i
$287$	17672.4			0.214551
$288$	−149326.	−	71475.8i	−1.80032	−	0.861735i
$289$	−135330.			−1.62032
$290$		0			0
$291$		−	202596.i		−	2.39246i
$292$	28208.2	+	15145.0i	0.330834	+	0.177625i
$293$			56264.5i			0.655390i	0.944784	+	0.327695i	$0.106272\pi$
$293$			56264.5i			0.655390i	−0.944784	+	0.327695i	$0.893728\pi$
$294$	−52701.1	+	31521.4i	−0.609712	+	0.364679i
$295$		0			0
$296$	−114916.	+	5324.78i	−1.31158	+	0.0607741i
$297$		−	33544.3i		−	0.380282i
$298$	21035.2	−	12581.5i	0.236872	−	0.141677i
$299$		−	20911.6i		−	0.233908i
$300$		0			0
$301$	1044.01			0.0115231
$302$	−31395.7	−	52491.0i	−0.344236	−	0.575534i
$303$	−149842.			−1.63210
$304$	91336.6	−	60540.0i	0.988320	−	0.655081i
$305$		0			0
$306$	155290.	+	259632.i	1.65844	+	2.77277i
$307$	−175077.			−1.85760			−0.928802	−	0.370577i	$-0.879160\pi$
$307$	−175077.			−1.85760			−0.928802	+	0.370577i	$0.879160\pi$
$308$	14156.8	+	7600.80i	0.149233	+	0.0801232i
$309$	317236.			3.32251
$310$		0			0
$311$			23621.0i			0.244218i	0.992517	+	0.122109i	$0.0389657\pi$
$311$			23621.0i			0.244218i	−0.992517	+	0.122109i	$0.961034\pi$
$312$	−57777.5	+	2677.20i	−0.593539	+	0.0275025i
$313$			132585.i			1.35333i	0.736289	+	0.676667i	$0.236576\pi$
$313$			132585.i			1.35333i	−0.736289	+	0.676667i	$0.763424\pi$
$314$	55296.5	+	92451.1i	0.560839	+	0.937676i
$315$		0			0
$316$	−9948.44	−	5341.32i	−0.0996279	−	0.0534902i
$317$		−	33855.0i		−	0.336902i	−0.985710	−	0.168451i	$-0.946123\pi$
$317$		−	33855.0i		−	0.336902i	0.985710	−	0.168451i	$-0.0538765\pi$
$318$	8829.66	+	14762.4i	0.0873151	+	0.145984i
$319$			25745.5i			0.252999i
$320$		0			0
$321$	345086.			3.34901
$322$	−46554.0	+	27844.7i	−0.448999	+	0.268553i
$323$	−200244.			−1.91936
$324$	49052.4	−	91362.2i	0.467272	−	0.870315i
$325$		0			0
$326$	−68534.3	+	40991.5i	−0.644871	+	0.385708i
$327$	62514.8			0.584638
$328$	1391.48	+	30030.0i	0.0129339	+	0.279131i
$329$	−57900.4			−0.534921
$330$		0			0
$331$		−	24338.3i		−	0.222144i	−0.993812	−	0.111072i	$-0.964572\pi$
$331$		−	24338.3i		−	0.222144i	0.993812	−	0.111072i	$-0.0354283\pi$
$332$	12310.5	−	22928.8i	0.111686	−	0.208020i
$333$		−	290601.i		−	2.62064i
$334$	−39873.0	+	23848.7i	−0.357426	+	0.213782i
$335$		0			0
$336$	82893.2	+	125061.i	0.734244	+	1.10775i
$337$			5373.65i			0.0473161i	0.999720	+	0.0236581i	$0.00753130\pi$
$337$			5373.65i			0.0473161i	−0.999720	+	0.0236581i	$0.992469\pi$
$338$	86491.1	−	51731.7i	0.757073	−	0.452818i
$339$		−	353466.i		−	3.07573i
$340$		0			0
$341$	11157.4			0.0959521
$342$	142087.	+	237557.i	1.21479	+	2.03103i
$343$	127411.			1.08297
$344$	82.2029	+	1774.04i	0.000694656	+	0.0149916i
$345$		0			0
$346$	−55971.7	−	93580.0i	−0.467537	−	0.781683i
$347$	−78906.7			−0.655322			−0.327661	−	0.944795i	$-0.606260\pi$
$347$	−78906.7			−0.655322			−0.327661	+	0.944795i	$0.606260\pi$
$348$	−113717.	+	211803.i	−0.939005	+	1.74894i
$349$	−139841.			−1.14811			−0.574053	−	0.818818i	$-0.694630\pi$
$349$	−139841.			−1.14811			−0.574053	+	0.818818i	$0.694630\pi$
$350$		0			0
$351$		−	72905.5i		−	0.591761i
$352$	−11801.1	+	24654.6i	−0.0952437	+	0.198982i
$353$			35542.6i			0.285233i	0.989778	+	0.142616i	$0.0455515\pi$
$353$			35542.6i			0.285233i	−0.989778	+	0.142616i	$0.954448\pi$
$354$	121982.	+	203943.i	0.973391	+	1.62743i
$355$		0			0
$356$	−54165.0	+	100885.i	−0.427385	+	0.796023i
$357$		−	274181.i		−	2.15130i
$358$	−74672.3	−	124846.i	−0.582631	−	0.974110i
$359$			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
$362$	−158478.	+	94788.1i	−1.20935	+	0.723331i
$363$	216977.			1.64664
$364$	30768.6	+	16519.6i	0.232223	+	0.124680i
$365$		0			0
$366$	−109726.	+	65628.8i	−0.819119	+	0.489928i
$367$	32200.7			0.239075			0.119537	−	0.992830i	$-0.461859\pi$
$367$	32200.7			0.239075			0.119537	+	0.992830i	$0.461859\pi$
$368$	−50981.0	−	76915.0i	−0.376455	−	0.567957i
$369$	−75940.3			−0.557725
$370$		0			0
$371$		−	10386.1i		−	0.0754578i
$372$	91790.1	+	49282.1i	0.663300	+	0.356125i
$373$			204296.i			1.46839i	0.678937	+	0.734196i	$0.262441\pi$
$373$			204296.i			1.46839i	−0.678937	+	0.734196i	$0.737559\pi$
$374$	42866.7	−	25639.3i	0.306462	−	0.183300i
$375$		0			0
$376$	−4558.94	−	98387.9i	−0.0322469	−	0.695930i
$377$			55955.4i			0.393694i
$378$	−162304.	+	97076.8i	−1.13592	+	0.679410i
$379$			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
$382$	48651.0	+	81340.3i	0.333399	+	0.557416i
$383$	−155856.			−1.06249			−0.531245	−	0.847218i	$-0.678276\pi$
$383$	−155856.			−1.06249			−0.531245	+	0.847218i	$0.678276\pi$
$384$	−205985.	+	150704.i	−1.39692	+	1.02203i
$385$		0			0
$386$	35113.1	+	58706.1i	0.235665	+	0.394012i
$387$	−4486.23			−0.0299543
$388$	−183333.	−	98431.4i	−1.21780	−	0.653838i
$389$	−91378.0			−0.603869			−0.301934	−	0.953329i	$-0.597632\pi$
$389$	−91378.0			−0.603869			−0.301934	+	0.953329i	$0.597632\pi$
$390$		0			0
$391$			168627.i			1.10299i
$392$	2919.42	+	63004.8i	0.0189987	+	0.410017i
$393$		−	77404.8i		−	0.501167i
$394$	−114154.	−	190855.i	−0.735356	−	1.22945i
$395$		0			0
$396$	−60833.6	−	32661.6i	−0.387930	−	0.208280i
$397$		−	177315.i		−	1.12503i	−0.826787	−	0.562515i	$-0.809834\pi$
$397$		−	177315.i		−	1.12503i	0.826787	−	0.562515i	$-0.190166\pi$
$398$	119906.	+	200473.i	0.756965	+	1.26558i
$399$		−	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	$0.288724\pi$
$402$	62338.8	−	37285.9i	0.385751	−	0.230724i
$403$	24249.6			0.149312
$404$	−72800.6	+	135594.i	−0.446038	+	0.830767i
$405$		0			0
$406$	124569.	−	74507.0i	0.755718	−	0.452007i
$407$	−47979.9			−0.289648
$408$	465905.	−	21588.4i	2.79884	−	0.129688i
$409$	176772.			1.05674			0.528370	−	0.849014i	$-0.322804\pi$
$409$	176772.			1.05674			0.528370	+	0.849014i	$0.322804\pi$
$410$		0			0
$411$		−	186079.i		−	1.10158i
$412$	154129.	−	287073.i	0.908011	−	1.69121i
$413$		−	143484.i		−	0.841206i
$414$	200048.	−	119652.i	1.16717	−	0.698103i
$415$		0			0
$416$	−25648.6	+	53584.6i	−0.148210	+	0.309637i
$417$			313484.i			1.80278i
$418$	39222.1	−	23459.4i	0.224480	−	0.134265i
$419$		−	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	$0.312870\pi$
$422$	−34823.4	−	58221.7i	−0.195545	−	0.326934i
$423$	248805.			1.39052
$424$	17648.7	−	817.777i	0.0981705	−	0.00454887i
$425$		0			0
$426$	−181975.	−	304247.i	−1.00275	−	1.67651i
$427$	77197.5			0.423397
$428$	167660.	−	312274.i	0.915255	−	1.70470i
$429$	−24123.4			−0.131076
$430$		0			0
$431$		−	230818.i		−	1.24255i	−0.783592	−	0.621276i	$-0.786615\pi$
$431$		−	230818.i		−	1.24255i	0.783592	−	0.621276i	$-0.213385\pi$
$432$	−177738.	−	268154.i	−0.952388	−	1.43687i
$433$			284920.i			1.51966i	0.650119	+	0.759832i	$0.274719\pi$
$433$			284920.i			1.51966i	−0.650119	+	0.759832i	$0.725281\pi$
$434$	−32289.4	−	53985.1i	−0.171427	−	0.286612i
$435$		0			0
$436$	30372.8	−	56570.7i	0.159776	−	0.297590i
$437$			154290.i			0.807932i
$438$	64003.4	+	107008.i	0.333622	+	0.557788i
$439$			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
$442$	93166.9	−	55724.6i	0.476889	−	0.285235i
$443$	−179147.			−0.912854			−0.456427	−	0.889761i	$-0.650871\pi$
$443$	−179147.			−0.912854			−0.456427	+	0.889761i	$0.650871\pi$
$444$	−394722.	−	211926.i	−2.00228	−	1.07503i
$445$		0			0
$446$	57732.8	−	34530.9i	0.290237	−	0.173596i
$447$	95456.2			0.477737
$448$	153444.	−	14250.7i	0.764527	−	0.0710034i
$449$	308905.			1.53226			0.766129	−	0.642687i	$-0.222180\pi$
$449$	308905.			1.53226			0.766129	+	0.642687i	$0.222180\pi$
$450$		0			0
$451$			12538.2i			0.0616428i
$452$	−319858.	−	171732.i	−1.56560	−	0.840569i
$453$		−	238201.i		−	1.16077i
$454$	278198.	−	166395.i	1.34972	−	0.807288i
$455$		0			0
$456$	426293.	−	19752.9i	2.05012	−	0.0949951i
$457$			56777.8i			0.271861i	0.990718	+	0.135930i	$0.0434023\pi$
$457$			56777.8i			0.271861i	−0.990718	+	0.135930i	$0.956598\pi$
$458$	−163816.	+	97981.3i	−0.780956	+	0.467102i
$459$			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	$0.709266\pi$
$462$	32121.3	+	53704.2i	0.150491	+	0.251608i
$463$	64677.1			0.301709			0.150855	−	0.988556i	$-0.451797\pi$
$463$	64677.1			0.301709			0.150855	+	0.988556i	$0.451797\pi$
$464$	136415.	+	205810.i	0.633617	+	0.955938i
$465$		0			0
$466$	32352.0	+	54089.9i	0.148981	+	0.249083i
$467$	105097.			0.481899			0.240950	−	0.970538i	$-0.422541\pi$
$467$	105097.			0.481899			0.240950	+	0.970538i	$0.422541\pi$
$468$	−132216.	−	70986.9i	−0.603661	−	0.324106i
$469$	−43858.4			−0.199392
$470$		0			0
$471$			419536.i			1.89116i
$472$	243816.	−	11297.6i	1.09441	−	0.0507109i
$473$			740.704i			0.00331072i
$474$	−22572.7	−	37739.6i	−0.100468	−	0.167973i
$475$		0			0
$476$	−248111.	−	133211.i	−1.09505	−	0.587931i
$477$			44630.3i			0.196152i
$478$	−226044.	−	377926.i	−0.989320	−	1.65406i
$479$		−	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
$482$	−90147.7	+	53918.8i	−0.388026	+	0.232084i
$483$	−211259.			−0.905566
$484$	105418.	−	196346.i	0.450013	−	0.838169i
$485$		0			0
$486$	−2846.56	+	1702.57i	−0.0120517	+	0.00720831i
$487$	−34829.3			−0.146854			−0.0734271	−	0.997301i	$-0.523394\pi$
$487$	−34829.3			−0.146854			−0.0734271	+	0.997301i	$0.523394\pi$
$488$	6078.35	+	131179.i	0.0255239	+	0.550838i
$489$	−311004.			−1.30061
$490$		0			0
$491$			357740.i			1.48390i	0.670456	+	0.741950i	$0.266099\pi$
$491$			357740.i			1.48390i	−0.670456	+	0.741950i	$0.733901\pi$
$492$	−55381.0	+	103150.i	−0.228787	+	0.426126i
$493$		−	451213.i		−	1.85647i
$494$	85245.7	−	50986.8i	0.349316	−	0.208932i
$495$		0			0
$496$	89192.5	−	59118.8i	0.362547	−	0.240305i
$497$			214053.i			0.866578i
$498$	86980.7	−	52024.5i	0.350723	−	0.209773i
$499$		−	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
$502$	−50103.1	−	83768.2i	−0.198819	−	0.332408i
$503$	94290.4			0.372676			0.186338	−	0.982486i	$-0.440338\pi$
$503$	94290.4			0.372676			0.186338	+	0.982486i	$0.440338\pi$
$504$	18018.6	+	388866.i	0.0709351	+	1.53087i
$505$		0			0
$506$	−19755.3	−	33029.1i	−0.0771581	−	0.129002i
$507$	392490.			1.52691
$508$	−166802.	+	310676.i	−0.646358	+	1.20387i
$509$	145708.			0.562405			0.281202	−	0.959649i	$-0.409267\pi$
$509$	145708.			0.562405			0.281202	+	0.959649i	$0.409267\pi$
$510$		0			0
$511$		−	75285.5i		−	0.288316i
$512$	36297.4	+	259619.i	0.138464	+	0.990368i
$513$			537911.i			2.04398i
$514$	62560.0	+	104595.i	0.236794	+	0.395899i
$515$		0			0
$516$	−3271.68	+	6093.64i	−0.0122877	+	0.0228864i
$517$		−	41079.2i		−	0.153688i
$518$	138853.	+	232151.i	0.517483	+	0.865188i
$519$		−	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	$0.431829\pi$
$522$	−535290.	+	320166.i	−1.96448	+	1.17499i
$523$	339555.			1.24139			0.620693	−	0.784054i	$-0.286851\pi$
$523$	339555.			1.24139			0.620693	+	0.784054i	$0.286851\pi$
$524$	−70045.0	−	37607.1i	−0.255102	−	0.136964i
$525$		0			0
$526$	157333.	−	94103.5i	0.568655	−	0.340122i
$527$	−195544.			−0.704081
$528$	−88728.3	+	58811.1i	−0.318269	+	0.210956i
$529$	−149913.			−0.535707
$530$		0			0
$531$			616567.i			2.18671i
$532$	−227017.	−	121885.i	−0.802111	−	0.430653i
$533$			27250.6i			0.0959229i
$534$	−382708.	+	228904.i	−1.34210	+	0.802733i
$535$		0			0
$536$	−3453.31	−	74526.9i	−0.0120200	−	0.259408i
$537$		−	566541.i		−	1.96464i
$538$	126724.	−	75795.8i	0.437819	−	0.261867i
$539$			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	$0.344517\pi$
$542$	254078.	+	424798.i	0.864906	+	1.44605i
$543$	−719161.			−2.43908
$544$	206825.	−	432095.i	0.698883	−	1.46010i
$545$		0			0
$546$	69812.8	+	116721.i	0.234180	+	0.391529i
$547$	354189.			1.18375			0.591875	−	0.806029i	$-0.298388\pi$
$547$	354189.			1.18375			0.591875	+	0.806029i	$0.298388\pi$
$548$	−168387.	−	90406.7i	−0.560720	−	0.301051i
$549$	−331727.			−1.10062
$550$		0			0
$551$		−	412850.i		−	1.35984i
$552$	−16634.0	−	358984.i	−0.0545907	−	1.17814i
$553$			26551.6i			0.0868242i
$554$	195560.	+	326959.i	0.637177	+	1.06531i
$555$		0			0
$556$	283677.	+	152306.i	0.917646	+	0.492684i
$557$		−	2288.63i		−	0.00737675i	−0.999993	−	0.00368838i	$-0.998826\pi$
$557$		−	2288.63i		−	0.00737675i	0.999993	−	0.00368838i	$-0.00117405\pi$
$558$	138751.	+	231981.i	0.445624	+	0.745046i
$559$			1609.85i			0.00515184i
$560$		0			0
$561$	194526.			0.618090
$562$	201606.	−	120584.i	0.638308	−	0.381782i
$563$	−48825.1			−0.154037			−0.0770187	−	0.997030i	$-0.524540\pi$
$563$	−48825.1			−0.154037			−0.0770187	+	0.997030i	$0.524540\pi$
$564$	181446.	−	337951.i	0.570413	−	1.06242i
$565$		0			0
$566$	245093.	−	146594.i	0.765066	−	0.457598i
$567$	−243839.			−0.758467
$568$	−363731.	+	16854.0i	−1.12742	+	0.0522404i
$569$	−202790.			−0.626356			−0.313178	−	0.949695i	$-0.601394\pi$
$569$	−202790.			−0.626356			−0.313178	+	0.949695i	$0.601394\pi$
$570$		0			0
$571$			412759.i			1.26597i	0.774163	+	0.632986i	$0.218171\pi$
$571$			412759.i			1.26597i	−0.774163	+	0.632986i	$0.781829\pi$
$572$	−11720.4	+	21829.7i	−0.0358219	+	0.0667199i
$573$			369116.i			1.12423i
$574$	60666.1	−	36285.4i	0.184129	−	0.110131i
$575$		0			0
$576$	−659366.	+	61236.8i	−1.98738	+	0.184573i
$577$		−	441255.i		−	1.32537i	−0.748897	−	0.662686i	$-0.769416\pi$
$577$		−	441255.i		−	1.32537i	0.748897	−	0.662686i	$-0.230584\pi$
$578$	−464565.	+	277864.i	−1.39056	+	0.831719i
$579$			266404.i			0.794665i
$580$		0			0
$581$	−61195.1			−0.181286
$582$	−415976.	−	695477.i	−1.22807	−	2.05322i
$583$	7368.73			0.0216798
$584$	127930.	−	5927.81i	0.375099	−	0.0173807i
$585$		0			0
$586$	115524.	+	193146.i	0.336416	+	0.562459i
$587$	−416031.			−1.20739			−0.603697	−	0.797214i	$-0.706306\pi$
$587$	−416031.			−1.20739			−0.603697	+	0.797214i	$0.706306\pi$
$588$	−116193.	+	216414.i	−0.336066	+	0.625938i
$589$	−178918.			−0.515732
$590$		0			0
$591$		−	866088.i		−	2.47963i
$592$	−383552.	+	254227.i	−1.09441	+	0.725401i
$593$		−	342542.i		−	0.974101i	−0.873374	−	0.487051i	$-0.838073\pi$
$593$		−	342542.i		−	0.974101i	0.873374	−	0.487051i	$-0.161927\pi$
$594$	−68874.1	−	115152.i	−0.195201	−	0.326360i
$595$		0			0
$596$	46377.4	−	86380.1i	0.130561	−	0.243176i
$597$			909733.i			2.55250i
$598$	−42936.3	−	71785.8i	−0.120066	−	0.200741i
$599$			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	$0.594667\pi$
$602$	3583.90	−	2143.59i	0.00988923	−	0.00591491i
$603$	188465.			0.518317
$604$	−215552.	−	115730.i	−0.590851	−	0.317228i
$605$		0			0
$606$	−514380.	+	307659.i	−1.40068	+	0.837768i
$607$	9168.57			0.0248842			0.0124421	−	0.999923i	$-0.496039\pi$
$607$	9168.57			0.0248842			0.0124421	+	0.999923i	$0.496039\pi$
$608$	189240.	−	395358.i	0.511925	−	1.06951i
$609$	565287.			1.52417
$610$		0			0
$611$		−	89281.8i		−	0.239156i
$612$	1.06616e6	+	572423.i	2.84657	+	1.52832i
$613$		−	164930.i		−	0.438915i	−0.975622	−	0.219457i	$-0.929571\pi$
$613$		−	164930.i		−	0.438915i	0.975622	−	0.219457i	$-0.0704286\pi$
$614$	−601009.	+	359473.i	−1.59421	+	0.953520i
$615$		0			0
$616$	64204.1	−	2974.99i	0.169200	−	0.00784013i
$617$			32007.8i			0.0840787i	0.999116	+	0.0420394i	$0.0133855\pi$
$617$			32007.8i			0.0840787i	−0.999116	+	0.0420394i	$0.986615\pi$
$618$	1.08902e6	−	651358.i	2.85139	−	1.70547i
$619$		−	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
$622$	48499.2	+	81086.6i	0.125359	+	0.209589i
$623$	269254.			0.693722
$624$	−192843.	+	127821.i	−0.495261	+	0.328270i
$625$		0			0
$626$	272227.	+	455140.i	0.694676	+	1.16144i
$627$	177987.			0.452745
$628$	379646.	+	203832.i	0.962630	+	0.516836i
$629$	840891.			2.12539
$630$		0			0
$631$		−	205747.i		−	0.516744i	−0.966045	−	0.258372i	$-0.916814\pi$
$631$		−	205747.i		−	0.516744i	0.966045	−	0.258372i	$-0.0831861\pi$
$632$	−45118.2	+	2090.61i	−0.112958	+	0.00523407i
$633$		−	264206.i		−	0.659379i
$634$	−69511.9	−	116218.i	−0.172934	−	0.289131i
$635$		0			0
$636$	60621.3	+	32547.5i	0.149869	+	0.0804644i
$637$			57173.5i			0.140902i
$638$	52861.3	+	88379.6i	0.129866	+	0.217125i
$639$		−	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	$0.754359\pi$
$642$	1.18462e6	−	708539.i	2.87414	−	1.71907i
$643$	−231907.			−0.560909			−0.280454	−	0.959867i	$-0.590485\pi$
$643$	−231907.			−0.560909			−0.280454	+	0.959867i	$0.590485\pi$
$644$	−102640.	+	191172.i	−0.247483	+	0.460948i
$645$		0			0
$646$	−687403.	+	411147.i	−1.64720	+	0.985218i
$647$	−427586.			−1.02144			−0.510722	−	0.859746i	$-0.670622\pi$
$647$	−427586.			−1.02144			−0.510722	+	0.859746i	$0.670622\pi$
$648$	−19199.3	−	414346.i	−0.0457231	−	0.986763i
$649$	101799.			0.241687
$650$		0			0
$651$		−	244981.i		−	0.578056i
$652$	−151101.	+	281433.i	−0.355445	+	0.662033i
$653$			348146.i			0.816461i	0.912879	+	0.408231i	$0.133854\pi$
$653$			348146.i			0.816461i	−0.912879	+	0.408231i	$0.866146\pi$
$654$	214602.	−	128357.i	0.501739	−	0.300098i
$655$		0			0
$656$	66435.1	+	100231.i	0.154380	+	0.232912i
$657$			323511.i			0.749477i
$658$	−198762.	+	118883.i	−0.459072	+	0.274578i
$659$		−	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	$0.564427\pi$
$662$	−49972.0	−	83548.9i	−0.114028	−	0.190645i
$663$	422784.			0.961816
$664$	−4818.36	−	103987.i	−0.0109286	−	0.235853i
$665$		0			0
$666$	−596669.	−	997580.i	−1.34519	−	2.24905i
$667$	−347663.			−0.781460
$668$	−87910.2	+	163737.i	−0.197009	+	0.366938i
$669$	261987.			0.585367
$670$		0			0
$671$			54770.1i			0.121646i
$672$	541336.	+	259114.i	1.19875	+	0.573788i
$673$		−	166579.i		−	0.367781i	−0.982947	−	0.183891i	$-0.941131\pi$
$673$		−	166579.i		−	0.367781i	0.982947	−	0.183891i	$-0.0588692\pi$
$674$	11033.3	+	18446.8i	0.0242877	+	0.0406070i
$675$		0			0
$676$	190692.	−	355171.i	0.417290	−	0.777221i
$677$		−	528530.i		−	1.15317i	−0.817038	−	0.576584i	$-0.804385\pi$
$677$		−	528530.i		−	1.15317i	0.817038	−	0.576584i	$-0.195615\pi$
$678$	−725746.	−	1.21339e6i	−1.57879	−	2.63961i
$679$			489301.i			1.06130i
$680$		0			0
$681$	1.26244e6			2.72219
$682$	38301.4	−	22908.7i	0.0823466	−	0.0492528i
$683$	144855.			0.310521			0.155261	−	0.987874i	$-0.450378\pi$
$683$	144855.			0.310521			0.155261	+	0.987874i	$0.450378\pi$
$684$	975518.	+	523755.i	2.08508	+	1.11948i
$685$		0			0
$686$	437378.	−	261603.i	0.929413	−	0.555897i
$687$	−743387.			−1.57508
$688$	3924.70	+	5921.20i	0.00829144	+	0.0125093i
$689$	16015.3			0.0337361
$690$		0			0
$691$		−	893708.i		−	1.87171i	−0.352380	−	0.935857i	$-0.614628\pi$
$691$		−	893708.i		−	1.87171i	0.352380	−	0.935857i	$-0.385372\pi$
$692$	−384282.	−	206321.i	−0.802486	−	0.430855i
$693$			162360.i			0.338075i
$694$	−270873.	+	162013.i	−0.562401	+	0.336381i
$695$		0			0
$696$	44509.4	+	960571.i	0.0918826	+	1.98295i
$697$		−	219743.i		−	0.452325i
$698$	−480048.	+	287124.i	−0.985311	+	0.589331i
$699$			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	$0.507927\pi$
$702$	−149691.	−	250272.i	−0.303755	−	0.507852i
$703$	769397.			1.55683
$704$	10110.6	+	108865.i	0.0204000	+	0.219656i
$705$		0			0
$706$	72977.0	+	122011.i	0.146412	+	0.244788i
$707$	361891.			0.724001
$708$	837482.	+	449644.i	1.67074	+	0.897020i
$709$	−705573.			−1.40362			−0.701809	−	0.712365i	$-0.747624\pi$
$709$	−705573.			−1.40362			−0.701809	+	0.712365i	$0.747624\pi$
$710$		0			0
$711$		−	114096.i		−	0.225699i
$712$	21200.4	+	457533.i	0.0418201	+	0.902531i
$713$			150668.i			0.296375i
$714$	−562956.	−	941215.i	−1.10428	−	1.84626i
$715$		0			0
$716$	−512673.	−	275254.i	−1.00003	−	0.536918i
$717$		−	1.71500e6i		−	3.33600i
$718$	367561.	+	614530.i	0.712984	+	1.19205i
$719$		−	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
$722$	−181591.	+	108612.i	−0.348353	+	0.208355i
$723$	−409084.			−0.782592
$724$	−349404.	+	650781.i	−0.666579	+	1.24153i
$725$		0			0
$726$	744842.	−	445502.i	1.41316	−	0.845233i
$727$	709623.			1.34264			0.671319	−	0.741168i	$-0.265728\pi$
$727$	709623.			1.34264			0.671319	+	0.741168i	$0.265728\pi$
$728$	139542.	−	6465.86i	0.263294	−	0.0122001i
$729$	−537887.			−1.01213
$730$		0			0
$731$		−	12981.5i		−	0.0242935i
$732$	−241919.	+	450584.i	−0.451489	+	0.840918i
$733$		−	99574.1i		−	0.185327i	−0.995697	−	0.0926634i	$-0.970462\pi$
$733$		−	99574.1i		−	0.185327i	0.995697	−	0.0926634i	$-0.0295381\pi$
$734$	110539.	−	66115.4i	0.205175	−	0.122719i
$735$		0			0
$736$	−332933.	−	159360.i	−0.614611	−	0.294187i
$737$		−	31116.7i		−	0.0572873i
$738$	−260690.	+	155923.i	−0.478642	+	0.286284i
$739$		−	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
$742$	−21325.0	−	35653.6i	−0.0387330	−	0.0647583i
$743$	−220581.			−0.399568			−0.199784	−	0.979840i	$-0.564024\pi$
$743$	−220581.			−0.399568			−0.199784	+	0.979840i	$0.564024\pi$
$744$	416286.	−	19289.2i	0.752049	−	0.0348472i
$745$		0			0
$746$	419466.	+	701312.i	0.753736	+	1.26018i
$747$	262963.			0.471252
$748$	94510.5	−	176030.i	0.168918	−	0.314618i
$749$	−833436.			−1.48562
$750$		0			0
$751$			201164.i			0.356673i	0.983970	+	0.178336i	$0.0570715\pi$
$751$			201164.i			0.356673i	−0.983970	+	0.178336i	$0.942929\pi$
$752$	−217663.	−	328387.i	−0.384900	−	0.580699i
$753$		−	380134.i		−	0.670420i
$754$	114889.	+	192085.i	0.202086	+	0.337871i
$755$		0			0
$756$	−357841.	+	666495.i	−0.626104	+	1.16615i
$757$			915352.i			1.59734i	0.601771	+	0.798669i	$0.294462\pi$
$757$			915352.i			1.59734i	−0.601771	+	0.798669i	$0.705538\pi$
$758$	278973.	+	466419.i	0.485538	+	0.811779i
$759$		−	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	$0.398396\pi$
$762$	−1.17855e6	+	704912.i	−2.02973	+	1.21402i
$763$	−150983.			−0.259345
$764$	334020.	+	179335.i	0.572250	+	0.307241i
$765$		0			0
$766$	−535025.	+	320007.i	−0.911835	+	0.545383i
$767$	221250.			0.376091
$768$	−397678.	+	940274.i	−0.674232	+	1.59416i
$769$	97671.8			0.165164			0.0825822	−	0.996584i	$-0.473683\pi$
$769$	97671.8			0.165164			0.0825822	+	0.996584i	$0.473683\pi$
$770$		0			0
$771$			474645.i			0.798472i
$772$	241074.	+	129433.i	0.404497	+	0.217175i
$773$		−	517767.i		−	0.866514i	−0.901270	−	0.433257i	$-0.857364\pi$
$773$		−	517767.i		−	0.866514i	0.901270	−	0.433257i	$-0.142636\pi$
$774$	−15400.4	+	9211.25i	−0.0257070	+	0.0153758i
$775$		0			0
$776$	−831451.	+	38526.5i	−1.38074	+	0.0639788i
$777$			1.05348e6i			1.74496i
$778$	−313684.	+	187620.i	−0.518243	+	0.309970i
$779$		−	201061.i		−	0.331323i
$780$		0			0
$781$	−151866.			−0.248977
$782$	346229.	+	578866.i	0.566174	+	0.946595i
$783$	−1.21208e6			−1.97700
$784$	139385.	+	210290.i	0.226769	+	0.342126i
$785$		0			0
$786$	−158929.	−	265717.i	−0.257252	−	0.430104i
$787$	−199421.			−0.321974			−0.160987	−	0.986957i	$-0.551468\pi$
$787$	−199421.			−0.321974			−0.160987	+	0.986957i	$0.551468\pi$
$788$	−783738.	−	420789.i	−1.26217	−	0.677660i
$789$	713967.			1.14690
$790$		0			0
$791$			853676.i			1.36440i
$792$	−275893.	+	12783.9i	−0.439835	+	0.0203804i
$793$			119038.i			0.189295i
$794$	−364067.	−	608690.i	−0.577485	−	0.965507i
$795$		0			0
$796$	823234.	+	441994.i	1.29926	+	0.697574i
$797$		−	204919.i		−	0.322600i	−0.986905	−	0.161300i	$-0.948431\pi$
$797$		−	204919.i		−	0.322600i	0.986905	−	0.161300i	$-0.0515687\pi$
$798$	−515092.	−	861191.i	−0.808871	−	1.35236i
$799$			719949.i			1.12774i
$800$		0			0
$801$	−1.15702e6			−1.80333
$802$	680143.	−	406804.i	1.05743	−	0.632465i
$803$	53413.6			0.0828363
$804$	137442.	−	255991.i	0.212621	−	0.396017i
$805$		0			0
$806$	83244.5	−	49789.9i	0.128140	−	0.0766428i
$807$	575065.			0.883019
$808$	28494.5	+	614947.i	0.0436453	+	0.941923i
$809$	−658877.			−1.00672			−0.503359	−	0.864078i	$-0.667903\pi$
$809$	−658877.			−1.00672			−0.503359	+	0.864078i	$0.667903\pi$
$810$		0			0
$811$			464925.i			0.706872i	0.935459	+	0.353436i	$0.114987\pi$
$811$			464925.i			0.706872i	−0.935459	+	0.353436i	$0.885013\pi$
$812$	274645.	−	511539.i	0.416543	−	0.775829i
$813$			1.92770e6i			2.91648i
$814$	−164706.	+	98513.6i	−0.248577	+	0.148678i
$815$		0			0
$816$	1.55504e6	−	1.03072e6i	2.33541	−	1.54796i
$817$		−	11877.8i		−	0.0177947i
$818$	606828.	−	362954.i	0.906899	−	0.542431i
$819$			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	$0.451974\pi$
$822$	−382063.	−	638777.i	−0.565446	−	0.945378i
$823$	−316525.			−0.467313			−0.233656	−	0.972319i	$-0.575069\pi$
$823$	−316525.			−0.467313			−0.233656	+	0.972319i	$0.575069\pi$
$824$	−60326.9	−	1.30193e6i	−0.0888498	−	1.91749i
$825$		0			0
$826$	−294604.	−	492554.i	−0.431797	−	0.721928i
$827$	148466.			0.217077			0.108539	−	0.994092i	$-0.465383\pi$
$827$	148466.			0.217077			0.108539	+	0.994092i	$0.465383\pi$
$828$	441057.	−	821488.i	0.643330	−	1.19823i
$829$	834966.			1.21495			0.607477	−	0.794337i	$-0.292182\pi$
$829$	834966.			1.21495			0.607477	+	0.794337i	$0.292182\pi$
$830$		0			0
$831$			1.48372e6i			2.14857i
$832$	21974.4	+	236609.i	0.0317446	+	0.341809i
$833$		−	461035.i		−	0.664422i
$834$	643654.	+	1.07614e6i	0.925380	+	1.54716i
$835$		0			0
$836$	86475.1	−	161064.i	0.123731	−	0.230455i
$837$			525283.i			0.749796i
$838$	−313746.	−	524558.i	−0.446777	−	0.746973i
$839$			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
$842$	674882.	−	403658.i	0.951927	−	0.569363i
$843$	914872.			1.28738
$844$	−239085.	−	128365.i	−0.335635	−	0.180202i
$845$		0			0
$846$	854102.	−	510852.i	1.19335	−	0.713764i
$847$	−524032.			−0.730451
$848$	58905.7	−	39044.0i	0.0819154	−	0.0542954i
$849$	1.11222e6			1.54303
$850$		0			0
$851$		−	647913.i		−	0.894659i
$852$	−1.24938e6	−	670790.i	−1.72113	−	0.924075i
$853$			533912.i			0.733790i	0.930262	+	0.366895i	$0.119579\pi$
$853$			533912.i			0.733790i	−0.930262	+	0.366895i	$0.880421\pi$
$854$	265005.	−	158504.i	0.363361	−	0.217332i
$855$		0			0
$856$	−65622.8	−	1.41623e6i	−0.0895586	−	1.93279i
$857$			155720.i			0.212023i	0.994365	+	0.106011i	$0.0338080\pi$
$857$			155720.i			0.212023i	−0.994365	+	0.106011i	$0.966192\pi$
$858$	−82811.3	+	49530.8i	−0.112490	+	0.0672823i
$859$		−	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
$862$	−473921.	−	792356.i	−0.637810	−	1.06636i
$863$	573138.			0.769551			0.384776	−	0.923010i	$-0.374279\pi$
$863$	573138.			0.769551			0.384776	+	0.923010i	$0.374279\pi$
$864$	−1.16072e6	−	555587.i	−1.55490	−	0.744260i
$865$		0			0
$866$	585006.	+	978081.i	0.780054	+	1.30418i
$867$	−2.10816e6			−2.80457
$868$	−221687.	−	119024.i	−0.294240	−	0.157977i
$869$	−18837.9			−0.0249455
$870$		0			0
$871$		−	67629.2i		−	0.0891452i
$872$	−11888.0	−	256559.i	−0.0156343	−	0.337408i
$873$		−	2.10259e6i		−	2.75883i
$874$	316792.	+	529650.i	0.414717	+	0.693371i
$875$		0			0
$876$	439424.	+	235927.i	0.572632	+	0.307446i
$877$			1.08498e6i			1.41066i	0.708881	+	0.705328i	$0.249200\pi$
$877$			1.08498e6i			1.41066i	−0.708881	+	0.705328i	$0.750800\pi$
$878$	673155.	+	1.12546e6i	0.873225	+	1.45996i
$879$			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	$0.407700\pi$
$882$	−546943.	+	327135.i	−0.703080	+	0.420524i
$883$	−1.21061e6			−1.55269			−0.776344	−	0.630310i	$-0.782928\pi$
$883$	−1.21061e6			−1.55269			−0.776344	+	0.630310i	$0.782928\pi$
$884$	205410.	−	382585.i	0.262855	−	0.489580i
$885$		0			0
$886$	−614978.	+	367829.i	−0.783416	+	0.468574i
$887$	1.17188e6			1.48949			0.744743	−	0.667352i	$-0.232572\pi$
$887$	1.17188e6			1.48949			0.744743	+	0.667352i	$0.232572\pi$
$888$	−1.79014e6	+	82948.9i	−2.27019	+	0.105192i
$889$	829169.			1.04916
$890$		0			0
$891$		−	172999.i		−	0.217915i
$892$	127287.	−	237077.i	0.159975	−	0.297961i
$893$			658738.i			0.826057i
$894$	327684.	−	195993.i	0.409997	−	0.245226i
$895$		0			0
$896$	497485.	−	363975.i	0.619675	−	0.453372i
$897$		−	325759.i		−	0.404866i
$898$	1.06041e6	−	634251.i	1.31499	−	0.786518i
$899$		−	403158.i		−	0.498834i
$900$		0			0
$901$	−129144.			−0.159083
$902$	25743.8	+	43041.4i	0.0316416	+	0.0529022i
$903$	16263.5			0.0199452
$904$	−1.45062e6	+	67216.5i	−1.77507	+	0.0822506i
$905$		0			0
$906$	−489080.	−	817700.i	−0.595831	−	0.996179i
$907$	201406.			0.244827			0.122413	−	0.992479i	$-0.460937\pi$
$907$	201406.			0.244827			0.122413	+	0.992479i	$0.460937\pi$
$908$	613359.	−	1.14241e6i	0.743949	−	1.38564i
$909$	−1.55509e6			−1.88203
$910$		0			0
$911$			606030.i			0.730227i	0.930963	+	0.365113i	$0.118970\pi$
$911$			606030.i			0.730227i	−0.930963	+	0.365113i	$0.881030\pi$
$912$	1.42283e6	−	943085.i	1.71066	−	1.13386i
$913$		−	43416.7i		−	0.0520853i
$914$	116578.	+	194908.i	0.139548	+	0.233312i
$915$		0			0
$916$	−361175.	+	672704.i	−0.430454	+	0.801740i
$917$			186945.i			0.222318i
$918$	1.20708e6	+	2.01814e6i	1.43236	+	2.39478i
$919$		−	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
$922$	−891629.	+	533297.i	−1.04887	+	0.627347i
$923$	−330067.			−0.387435
$924$	220534.	+	118404.i	0.258304	+	0.138683i
$925$		0			0
$926$	222025.	−	132797.i	0.258928	−	0.154869i
$927$	3.29235e6			3.83130
$928$	890863.	+	426416.i	1.03446	+	0.495151i
$929$	−291783.			−0.338087			−0.169043	−	0.985609i	$-0.554068\pi$
$929$	−291783.			−0.338087			−0.169043	+	0.985609i	$0.554068\pi$
$930$		0			0
$931$		−	421837.i		−	0.486683i
$932$	222117.	+	119255.i	0.255712	+	0.137292i
$933$			367965.i			0.422711i
$934$	360779.	−	215788.i	0.413569	−	0.247362i
$935$		0			0
$936$	−599627.	+	27784.6i	−0.684431	+	0.0317141i
$937$		−	1.11462e6i		−	1.26955i	−0.772698	−	0.634774i	$-0.781093\pi$
$937$		−	1.11462e6i		−	1.26955i	0.772698	−	0.634774i	$-0.218907\pi$
$938$	−150558.	+	90051.2i	−0.171119	+	0.102349i
$939$			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	$0.545918\pi$
$942$	861403.	+	1.44019e6i	0.970743	+	1.62300i
$943$	−169314.			−0.190401
$944$	813781.	−	539393.i	0.913196	−	0.605287i
$945$		0			0
$946$	1520.83	+	2542.70i	0.00169941	+	0.00284128i
$947$	997643.			1.11244			0.556218	−	0.831036i	$-0.312252\pi$
$947$	997643.			1.11244			0.556218	+	0.831036i	$0.312252\pi$
$948$	−154976.	−	83206.5i	−0.172444	−	0.0925850i
$949$	116089.			0.128902
$950$		0			0
$951$		−	527389.i		−	0.583136i
$952$	−1.12523e6	+	52139.3i	−1.24156	+	0.0575296i
$953$			146915.i			0.161763i	0.996724	+	0.0808815i	$0.0257735\pi$
$953$			146915.i			0.161763i	−0.996724	+	0.0808815i	$0.974226\pi$
$954$	91636.1	+	153208.i	0.100686	+	0.168339i
$955$		0			0
$956$	−1.55194e6	−	833234.i	−1.69808	−	0.911698i
$957$			401060.i			0.437911i
$958$	−269357.	−	450343.i	−0.293493	−	0.490696i
$959$			449411.i			0.488659i
$960$		0			0
$961$	748803.			0.810813
$962$	−357974.	+	214110.i	−0.386813	+	0.231359i
$963$	3.58137e6			3.86186
$964$	−198753.	+	370187.i	−0.213875	+	0.398352i
$965$		0			0
$966$	−725213.	+	433762.i	−0.777162	+	0.464833i
$967$	−1.47654e6			−1.57904			−0.789518	−	0.613727i	$-0.789669\pi$
$967$	−1.47654e6			−1.57904			−0.789518	+	0.613727i	$0.789669\pi$
$968$	−41261.1	−	890468.i	−0.0440342	−	0.950315i
$969$	−3.11939e6			−3.32217
$970$		0			0
$971$		−	1.55163e6i		−	1.64569i	−0.568265	−	0.822846i	$-0.692385\pi$
$971$		−	1.55163e6i		−	1.64569i	0.568265	−	0.822846i	$-0.307615\pi$
$972$	−6275.97	+	11689.3i	−0.00664275	+	0.0123724i
$973$		−	757113.i		−	0.799715i
$974$	−119563.	+	71512.4i	−0.126031	+	0.0753813i
$975$		0			0
$976$	290206.	+	437833.i	0.304653	+	0.459630i
$977$			13609.0i			0.0142572i	0.999975	+	0.00712862i	$0.00226913\pi$
$977$			13609.0i			0.0142572i	−0.999975	+	0.00712862i	$0.997731\pi$
$978$	−1.06762e6	+	638561.i	−1.11619	+	0.667612i
$979$			191030.i			0.199314i
$980$		0			0
$981$	648792.			0.674167
$982$	734521.	+	1.22806e6i	0.761695	+	1.27349i
$983$	179673.			0.185941			0.0929706	−	0.995669i	$-0.470364\pi$
$983$	179673.			0.185941			0.0929706	+	0.995669i	$0.470364\pi$
$984$	21676.4	+	467804.i	0.0223870	+	0.483141i
$985$		0			0
$986$	−926441.	−	1.54893e6i	−0.952937	−	1.59323i
$987$	−901966.			−0.925882
$988$	187946.	−	350057.i	0.192539	−	0.358612i
$989$	−10002.3			−0.0102261
$990$		0			0
$991$			1.04471e6i			1.06377i	0.846816	+	0.531886i	$0.178516\pi$
$991$			1.04471e6i			1.06377i	−0.846816	+	0.531886i	$0.821484\pi$
$992$	184798.	−	386076.i	0.187790	−	0.392329i
$993$		−	379139.i		−	0.384503i
$994$	439498.	+	734804.i	0.444820	+	0.743702i
$995$		0			0
$996$	191771.	−	357182.i	0.193314	−	0.360057i
$997$			100146.i			0.100750i	0.998730	+	0.0503748i	$0.0160416\pi$
$997$			100146.i			0.100750i	−0.998730	+	0.0503748i	$0.983958\pi$
$998$	−483915.	−	809065.i	−0.485856	−	0.812311i
$999$		−	2.25886e6i		−	2.26339i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.1	✓	8	5.3	odd	4
20.5.b.a.11.2	yes	8	20.3	even	4
100.5.b.c.51.7		8	20.7	even	4
100.5.b.c.51.8		8	5.2	odd	4
100.5.d.c.99.3		16	4.3	odd	2	inner
100.5.d.c.99.4		16	5.4	even	2	inner
100.5.d.c.99.13		16	1.1	even	1	trivial
100.5.d.c.99.14		16	20.19	odd	2	inner
180.5.c.a.91.7		8	60.23	odd	4
180.5.c.a.91.8		8	15.8	even	4
320.5.b.d.191.1		8	40.13	odd	4
320.5.b.d.191.8		8	40.3	even	4

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.43282 - 2.05323i) q^{2} +15.5779 q^{3} +(7.56853 - 14.0967i) q^{4} +(53.4761 - 31.9849i) q^{6} -37.6230 q^{7} +(-2.96235 - 63.9314i) q^{8} +161.671 q^{9} +O(q^{10})\)	\(q+(3.43282 - 2.05323i) q^{2} +15.5779 q^{3} +(7.56853 - 14.0967i) q^{4} +(53.4761 - 31.9849i) q^{6} -37.6230 q^{7} +(-2.96235 - 63.9314i) q^{8} +161.671 q^{9} -26.6928i q^{11} +(117.902 - 219.597i) q^{12} -58.0144i q^{13} +(-129.153 + 77.2486i) q^{14} +(-141.435 - 213.383i) q^{16} +467.816i q^{17} +(554.987 - 331.947i) q^{18} +428.041i q^{19} -586.088 q^{21} +(-54.8064 - 91.6316i) q^{22} +360.456 q^{23} +(-46.1472 - 995.917i) q^{24} +(-119.117 - 199.153i) q^{26} +1256.68 q^{27} +(-284.751 + 530.361i) q^{28} -964.509 q^{29} +417.993i q^{31} +(-923.644 - 442.107i) q^{32} -415.818i q^{33} +(960.531 + 1605.93i) q^{34} +(1223.61 - 2279.03i) q^{36} -1797.48i q^{37} +(878.866 + 1469.39i) q^{38} -903.742i q^{39} -469.722 q^{41} +(-2011.93 + 1203.37i) q^{42} -27.7492 q^{43} +(-376.281 - 202.025i) q^{44} +(1237.38 - 740.097i) q^{46} +1538.96 q^{47} +(-2203.26 - 3324.05i) q^{48} -985.506 q^{49} +7287.58i q^{51} +(-817.812 - 439.083i) q^{52} +276.057i q^{53} +(4313.96 - 2580.25i) q^{54} +(111.453 + 2405.29i) q^{56} +6667.98i q^{57} +(-3310.99 + 1980.36i) q^{58} +3813.72i q^{59} -2051.87 q^{61} +(858.234 + 1434.90i) q^{62} -6082.55 q^{63} +(-4078.45 + 378.775i) q^{64} +(-853.768 - 1427.43i) q^{66} +1165.73 q^{67} +(6594.66 + 3540.67i) q^{68} +5615.14 q^{69} -5689.40i q^{71} +(-478.926 - 10335.8i) q^{72} +2001.05i q^{73} +(-3690.64 - 6170.44i) q^{74} +(6033.98 + 3239.64i) q^{76} +1004.26i q^{77} +(-1855.59 - 3102.38i) q^{78} -705.728i q^{79} +6481.10 q^{81} +(-1612.47 + 964.446i) q^{82} +1626.53 q^{83} +(-4435.82 + 8261.91i) q^{84} +(-95.2580 + 56.9753i) q^{86} -15025.0 q^{87} +(-1706.51 + 79.0735i) q^{88} -7156.62 q^{89} +2182.68i q^{91} +(2728.12 - 5081.24i) q^{92} +6511.45i q^{93} +(5282.97 - 3159.83i) q^{94} +(-14388.4 - 6887.10i) q^{96} -13005.4i q^{97} +(-3383.07 + 2023.47i) q^{98} -4315.45i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{4} + 96 q^{6} + 656 q^{9}+O(q^{10}) \) 16 * q + 40 * q^4 + 96 * q^6 + 656 * q^9	\( 16 q + 40 q^{4} + 96 q^{6} + 656 q^{9} + 336 q^{14} - 544 q^{16} + 32 q^{21} - 3104 q^{24} - 4344 q^{26} - 2400 q^{29} + 4264 q^{34} - 2088 q^{36} + 9792 q^{41} - 15840 q^{44} + 1456 q^{46} + 11536 q^{49} + 35552 q^{54} + 96 q^{56} + 15872 q^{61} - 37760 q^{64} - 16160 q^{66} + 4512 q^{69} + 36984 q^{74} + 24000 q^{76} - 1872 q^{81} - 100928 q^{84} - 14784 q^{86} - 47520 q^{89} + 86736 q^{94} + 5376 q^{96}+O(q^{100}) \) 16 * q + 40 * q^4 + 96 * q^6 + 656 * q^9 + 336 * q^14 - 544 * q^16 + 32 * q^21 - 3104 * q^24 - 4344 * q^26 - 2400 * q^29 + 4264 * q^34 - 2088 * q^36 + 9792 * q^41 - 15840 * q^44 + 1456 * q^46 + 11536 * q^49 + 35552 * q^54 + 96 * q^56 + 15872 * q^61 - 37760 * q^64 - 16160 * q^66 + 4512 * q^69 + 36984 * q^74 + 24000 * q^76 - 1872 * q^81 - 100928 * q^84 - 14784 * q^86 - 47520 * q^89 + 86736 * q^94 + 5376 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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