LMFDB - Embedded newform 49.6.c.g.18.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,6,Mod(18,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.18"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-13})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 13x^{2} + 169 $ x^4 - 13*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.2
Root			$3.12250 - 1.80278i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.g.30.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(12.4900 - 21.6333i) q^{3} +(14.0000 - 24.2487i) q^{4} +(37.4700 + 64.8999i) q^{5} +49.9600 q^{6} +120.000 q^{8} +(-190.500 - 329.956i) q^{9} +(-74.9400 + 129.800i) q^{10} +(142.000 - 245.951i) q^{11} +(-349.720 - 605.733i) q^{12} -524.580 q^{13} +1872.00 q^{15} +(-328.000 - 568.113i) q^{16} +(-74.9400 + 129.800i) q^{17} +(381.000 - 659.911i) q^{18} +(1086.63 + 1882.10i) q^{19} +2098.32 q^{20} +568.000 q^{22} +(-748.000 - 1295.57i) q^{23} +(1498.80 - 2596.00i) q^{24} +(-1245.50 + 2157.27i) q^{25} +(-524.580 - 908.599i) q^{26} -3447.24 q^{27} -4366.00 q^{29} +(1872.00 + 3242.40i) q^{30} +(-3222.42 + 5581.39i) q^{31} +(2576.00 - 4461.76i) q^{32} +(-3547.16 - 6143.86i) q^{33} -299.760 q^{34} -10668.0 q^{36} +(6315.00 + 10937.9i) q^{37} +(-2173.26 + 3764.20i) q^{38} +(-6552.00 + 11348.4i) q^{39} +(4496.40 + 7787.99i) q^{40} +9442.44 q^{41} -1356.00 q^{43} +(-3976.00 - 6886.63i) q^{44} +(14276.1 - 24726.9i) q^{45} +(1496.00 - 2591.15i) q^{46} +(5020.98 + 8696.59i) q^{47} -16386.9 q^{48} -4982.00 q^{50} +(1872.00 + 3242.40i) q^{51} +(-7344.12 + 12720.4i) q^{52} +(-7075.00 + 12254.3i) q^{53} +(-3447.24 - 5970.79i) q^{54} +21283.0 q^{55} +54288.0 q^{57} +(-4366.00 - 7562.13i) q^{58} +(-18697.5 + 32385.1i) q^{59} +(26208.0 - 45393.6i) q^{60} +(-17798.2 - 30827.5i) q^{61} -12889.7 q^{62} -10688.0 q^{64} +(-19656.0 - 34045.2i) q^{65} +(7094.32 - 12287.7i) q^{66} +(1822.00 - 3155.80i) q^{67} +(2098.32 + 3634.40i) q^{68} -37370.1 q^{69} +35632.0 q^{71} +(-22860.0 - 39594.7i) q^{72} +(20383.7 - 35305.6i) q^{73} +(-12630.0 + 21875.8i) q^{74} +(31112.6 + 53888.6i) q^{75} +60851.3 q^{76} -26208.0 q^{78} +(27308.0 + 47298.8i) q^{79} +(24580.3 - 42574.3i) q^{80} +(3235.50 - 5604.05i) q^{81} +(9442.44 + 16354.8i) q^{82} +524.580 q^{83} -11232.0 q^{85} +(-1356.00 - 2348.66i) q^{86} +(-54531.3 + 94451.0i) q^{87} +(17040.0 - 29514.1i) q^{88} +(-10191.8 - 17652.8i) q^{89} +57104.3 q^{90} -41888.0 q^{92} +(80496.0 + 139423. i) q^{93} +(-10042.0 + 17393.2i) q^{94} +(-81432.0 + 141044. i) q^{95} +(-64348.5 - 111455. i) q^{96} -183603. q^{97} -108204. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 56 q^{4} + 480 q^{8} - 762 q^{9} + 568 q^{11} + 7488 q^{15} - 1312 q^{16} + 1524 q^{18} + 2272 q^{22} - 2992 q^{23} - 4982 q^{25} - 17464 q^{29} + 7488 q^{30} + 10304 q^{32} - 42672 q^{36}+ \cdots - 432816 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 56 * q^4 + 480 * q^8 - 762 * q^9 + 568 * q^11 + 7488 * q^15 - 1312 * q^16 + 1524 * q^18 + 2272 * q^22 - 2992 * q^23 - 4982 * q^25 - 17464 * q^29 + 7488 * q^30 + 10304 * q^32 - 42672 * q^36 + 25260 * q^37 - 26208 * q^39 - 5424 * q^43 - 15904 * q^44 + 5984 * q^46 - 19928 * q^50 + 7488 * q^51 - 28300 * q^53 + 217152 * q^57 - 17464 * q^58 + 104832 * q^60 - 42752 * q^64 - 78624 * q^65 + 7288 * q^67 + 142528 * q^71 - 91440 * q^72 - 50520 * q^74 - 104832 * q^78 + 109232 * q^79 + 12942 * q^81 - 44928 * q^85 - 5424 * q^86 + 68160 * q^88 - 167552 * q^92 + 321984 * q^93 - 325728 * q^95 - 432816 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	1.00000	+	1.73205i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	12.4900	−	21.6333i	0.801234	−	1.38778i	−0.117571	−	0.993064i	$-0.537511\pi$
$3$	12.4900	−	21.6333i	0.801234	−	1.38778i	0.918805	−	0.394713i	$-0.129156\pi$
$4$	14.0000	−	24.2487i	0.437500	−	0.757772i
$5$	37.4700	+	64.8999i	0.670284	+	1.16097i	0.977824	+	0.209430i	$0.0671608\pi$
$5$	37.4700	+	64.8999i	0.670284	+	1.16097i	−0.307540	+	0.951535i	$0.599506\pi$
$6$	49.9600			0.566558
$7$		0			0
$7$		0			0
$8$	120.000			0.662913
$9$	−190.500	−	329.956i	−0.783951	−	1.35784i
$10$	−74.9400	+	129.800i	−0.236981	+	0.410463i
$11$	142.000	−	245.951i	0.353840	−	0.612868i	−0.633079	−	0.774087i	$-0.718209\pi$
$11$	142.000	−	245.951i	0.353840	−	0.612868i	0.986919	+	0.161219i	$0.0515425\pi$
$12$	−349.720	−	605.733i	−0.701079	−	1.21431i
$13$	−524.580			−0.860901			−0.430450	−	0.902614i	$-0.641645\pi$
$13$	−524.580			−0.860901			−0.430450	+	0.902614i	$0.641645\pi$
$14$		0			0
$15$	1872.00			2.14821
$16$	−328.000	−	568.113i	−0.320312	−	0.554798i
$17$	−74.9400	+	129.800i	−0.0628914	+	0.108931i	−0.895757	−	0.444545i	$-0.853366\pi$
$17$	−74.9400	+	129.800i	−0.0628914	+	0.108931i	0.832865	+	0.553476i	$0.186699\pi$
$18$	381.000	−	659.911i	0.277168	−	0.480070i
$19$	1086.63	+	1882.10i	0.690554	+	1.19607i	0.971657	+	0.236397i	$0.0759665\pi$
$19$	1086.63	+	1882.10i	0.690554	+	1.19607i	−0.281103	+	0.959678i	$0.590700\pi$
$20$	2098.32			1.17300
$21$		0			0
$22$	568.000			0.250202
$23$	−748.000	−	1295.57i	−0.294837	−	0.510673i	0.680110	−	0.733110i	$-0.261932\pi$
$23$	−748.000	−	1295.57i	−0.294837	−	0.510673i	−0.974947	+	0.222437i	$0.928599\pi$
$24$	1498.80	−	2596.00i	0.531148	−	0.919975i
$25$	−1245.50	+	2157.27i	−0.398560	+	0.690326i
$26$	−524.580	−	908.599i	−0.152187	−	0.263596i
$27$	−3447.24			−0.910043
$28$		0			0
$29$	−4366.00			−0.964026			−0.482013	−	0.876164i	$-0.660094\pi$
$29$	−4366.00			−0.964026			−0.482013	+	0.876164i	$0.660094\pi$
$30$	1872.00	+	3242.40i	0.379754	+	0.657754i
$31$	−3222.42	+	5581.39i	−0.602251	+	1.04313i	0.390228	+	0.920718i	$0.372396\pi$
$31$	−3222.42	+	5581.39i	−0.602251	+	1.04313i	−0.992479	+	0.122412i	$0.960937\pi$
$32$	2576.00	−	4461.76i	0.444704	−	0.770250i
$33$	−3547.16	−	6143.86i	−0.567017	−	0.982102i
$34$	−299.760			−0.0444709
$35$		0			0
$36$	−10668.0			−1.37191
$37$	6315.00	+	10937.9i	0.758349	+	1.31350i	0.943692	+	0.330825i	$0.107327\pi$
$37$	6315.00	+	10937.9i	0.758349	+	1.31350i	−0.185343	+	0.982674i	$0.559340\pi$
$38$	−2173.26	+	3764.20i	−0.244148	+	0.422876i
$39$	−6552.00	+	11348.4i	−0.689783	+	1.19474i
$40$	4496.40	+	7787.99i	0.444339	+	0.769618i
$41$	9442.44			0.877252			0.438626	−	0.898670i	$-0.355465\pi$
$41$	9442.44			0.877252			0.438626	+	0.898670i	$0.355465\pi$
$42$		0			0
$43$	−1356.00			−0.111838			−0.0559189	−	0.998435i	$-0.517809\pi$
$43$	−1356.00			−0.111838			−0.0559189	+	0.998435i	$0.517809\pi$
$44$	−3976.00	−	6886.63i	−0.309610	−	0.536260i
$45$	14276.1	−	24726.9i	1.05094	−	1.82028i
$46$	1496.00	−	2591.15i	0.104241	−	0.180550i
$47$	5020.98	+	8696.59i	0.331546	+	0.574254i	0.982815	−	0.184592i	$-0.0590965\pi$
$47$	5020.98	+	8696.59i	0.331546	+	0.574254i	−0.651269	+	0.758847i	$0.725763\pi$
$48$	−16386.9			−1.02658
$49$		0			0
$50$	−4982.00			−0.281824
$51$	1872.00	+	3242.40i	0.100781	+	0.174559i
$52$	−7344.12	+	12720.4i	−0.376644	+	0.652367i
$53$	−7075.00	+	12254.3i	−0.345969	+	0.599235i	−0.985529	−	0.169505i	$-0.945783\pi$
$53$	−7075.00	+	12254.3i	−0.345969	+	0.599235i	0.639561	+	0.768741i	$0.279116\pi$
$54$	−3447.24	−	5970.79i	−0.160874	−	0.278643i
$55$	21283.0			0.948692
$56$		0			0
$57$	54288.0			2.21318
$58$	−4366.00	−	7562.13i	−0.170417	−	0.295171i
$59$	−18697.5	+	32385.1i	−0.699285	+	1.21120i	0.269430	+	0.963020i	$0.413165\pi$
$59$	−18697.5	+	32385.1i	−0.699285	+	1.21120i	−0.968715	+	0.248177i	$0.920169\pi$
$60$	26208.0	−	45393.6i	0.939844	−	1.62786i
$61$	−17798.2	−	30827.5i	−0.612425	−	1.06075i	−0.990831	−	0.135111i	$-0.956861\pi$
$61$	−17798.2	−	30827.5i	−0.612425	−	1.06075i	0.378406	−	0.925640i	$-0.376472\pi$
$62$	−12889.7			−0.425856
$63$		0			0
$64$	−10688.0			−0.326172
$65$	−19656.0	−	34045.2i	−0.577048	−	0.999476i
$66$	7094.32	−	12287.7i	0.200471	−	0.347225i
$67$	1822.00	−	3155.80i	0.0495863	−	0.0858859i	−0.840167	−	0.542328i	$-0.817543\pi$
$67$	1822.00	−	3155.80i	0.0495863	−	0.0858859i	0.889753	+	0.456442i	$0.150876\pi$
$68$	2098.32	+	3634.40i	0.0550300	+	0.0953147i
$69$	−37370.1			−0.944933
$70$		0			0
$71$	35632.0			0.838869			0.419435	−	0.907786i	$-0.362228\pi$
$71$	35632.0			0.838869			0.419435	+	0.907786i	$0.362228\pi$
$72$	−22860.0	−	39594.7i	−0.519691	−	0.900131i
$73$	20383.7	−	35305.6i	0.447688	−	0.775418i	−0.550547	−	0.834804i	$-0.685581\pi$
$73$	20383.7	−	35305.6i	0.447688	−	0.775418i	0.998235	+	0.0593859i	$0.0189143\pi$
$74$	−12630.0	+	21875.8i	−0.268117	+	0.464392i
$75$	31112.6	+	53888.6i	0.638679	+	1.10623i
$76$	60851.3			1.20847
$77$		0			0
$78$	−26208.0			−0.487750
$79$	27308.0	+	47298.8i	0.492291	+	0.852674i	0.999961	−	0.00887848i	$-0.00282614\pi$
$79$	27308.0	+	47298.8i	0.492291	+	0.852674i	−0.507669	+	0.861552i	$0.669493\pi$
$80$	24580.3	−	42574.3i	0.429400	−	0.743743i
$81$	3235.50	−	5604.05i	0.0547935	−	0.0949051i
$82$	9442.44	+	16354.8i	0.155078	+	0.268603i
$83$	524.580			0.00835827			0.00417913	−	0.999991i	$-0.498670\pi$
$83$	524.580			0.00835827			0.00417913	+	0.999991i	$0.498670\pi$
$84$		0			0
$85$	−11232.0			−0.168620
$86$	−1356.00	−	2348.66i	−0.0197703	−	0.0342432i
$87$	−54531.3	+	94451.0i	−0.772410	+	1.33785i
$88$	17040.0	−	29514.1i	0.234565	−	0.406278i
$89$	−10191.8	−	17652.8i	−0.136388	−	0.236232i	0.789739	−	0.613444i	$-0.210216\pi$
$89$	−10191.8	−	17652.8i	−0.136388	−	0.236232i	−0.926127	+	0.377212i	$0.876883\pi$
$90$	57104.3			0.743126
$91$		0			0
$92$	−41888.0			−0.515965
$93$	80496.0	+	139423.i	0.965088	+	1.67158i
$94$	−10042.0	+	17393.2i	−0.117219	+	0.203030i
$95$	−81432.0	+	141044.i	−0.925734	+	1.60342i
$96$	−64348.5	−	111455.i	−0.712623	−	1.23430i
$97$	−183603.			−1.98130			−0.990650	−	0.136427i	$-0.956438\pi$
$97$	−183603.			−1.98130			−0.990650	+	0.136427i	$0.956438\pi$
$98$		0			0
$99$	−108204.			−1.10957
$100$	34874.0	+	60403.5i	0.348740	+	0.604035i
$101$	37957.1	−	65743.6i	0.370245	−	0.641284i	−0.619358	−	0.785109i	$-0.712607\pi$
$101$	37957.1	−	65743.6i	0.370245	−	0.641284i	0.989603	+	0.143825i	$0.0459403\pi$
$102$	−3744.00	+	6484.80i	−0.0356316	+	0.0617158i
$103$	−5470.62	−	9475.39i	−0.0508093	−	0.0880043i	0.839502	−	0.543356i	$-0.182847\pi$
$103$	−5470.62	−	9475.39i	−0.0508093	−	0.0880043i	−0.890311	+	0.455352i	$0.849513\pi$
$104$	−62949.6			−0.570702
$105$		0			0
$106$	−28300.0			−0.244637
$107$	−109094.	−	188956.i	−0.921173	−	1.59552i	−0.797602	−	0.603184i	$-0.793899\pi$
$107$	−109094.	−	188956.i	−0.921173	−	1.59552i	−0.123571	−	0.992336i	$-0.539435\pi$
$108$	−48261.3	+	83591.1i	−0.398144	+	0.689605i
$109$	48015.0	−	83164.4i	0.387089	−	0.670458i	−0.604968	−	0.796250i	$-0.706814\pi$
$109$	48015.0	−	83164.4i	0.387089	−	0.670458i	0.992057	+	0.125792i	$0.0401473\pi$
$110$	21283.0	+	36863.2i	0.167707	+	0.290476i
$111$	315497.			2.43046
$112$		0			0
$113$	−137422.			−1.01242			−0.506209	−	0.862411i	$-0.668954\pi$
$113$	−137422.			−1.01242			−0.506209	+	0.862411i	$0.668954\pi$
$114$	54288.0	+	94029.6i	0.391239	+	0.677645i
$115$	56055.1	−	97090.3i	0.395249	−	0.684591i
$116$	−61124.0	+	105870.i	−0.421761	+	0.730512i
$117$	99932.5	+	173088.i	0.674904	+	1.16897i
$118$	−74790.1			−0.494469
$119$		0			0
$120$	224640.			1.42408
$121$	40197.5	+	69624.1i	0.249595	+	0.432311i
$122$	35596.5	−	61654.9i	0.216525	−	0.375032i
$123$	117936.	−	204271.i	0.702884	−	1.21743i
$124$	90227.7	+	156279.i	0.526970	+	0.912739i
$125$	47511.9			0.271974
$126$		0			0
$127$	170368.			0.937300			0.468650	−	0.883384i	$-0.344741\pi$
$127$	170368.			0.937300			0.468650	+	0.883384i	$0.344741\pi$
$128$	−93120.0	−	161289.i	−0.502363	−	0.870119i
$129$	−16936.4	+	29334.8i	−0.0896082	+	0.155206i
$130$	39312.0	−	68090.4i	0.204017	−	0.353368i
$131$	−174123.	−	301590.i	−0.886498	−	1.53546i	−0.843986	−	0.536364i	$-0.819797\pi$
$131$	−174123.	−	301590.i	−0.886498	−	1.53546i	−0.0425120	−	0.999096i	$-0.513536\pi$
$132$	−198641.			−0.992279
$133$		0			0
$134$	7288.00			0.0350628
$135$	−129168.	−	223726.i	−0.609987	−	1.05653i
$136$	−8992.80	+	15576.0i	−0.0416915	+	0.0722118i
$137$	37781.0	−	65438.6i	0.171978	−	0.297874i	−0.767134	−	0.641487i	$-0.778318\pi$
$137$	37781.0	−	65438.6i	0.171978	−	0.297874i	0.939111	+	0.343613i	$0.111651\pi$
$138$	−37370.1	−	64726.9i	−0.167042	−	0.289326i
$139$	−97047.3			−0.426036			−0.213018	−	0.977048i	$-0.568329\pi$
$139$	−97047.3			−0.426036			−0.213018	+	0.977048i	$0.568329\pi$
$140$		0			0
$141$	250848.			1.06258
$142$	35632.0	+	61716.4i	0.148293	+	0.256850i
$143$	−74490.3	+	129021.i	−0.304621	+	0.527619i
$144$	−124968.	+	216451.i	−0.502218	+	0.869868i
$145$	−163594.	−	283353.i	−0.646171	−	1.11920i
$146$	81534.7			0.316563
$147$		0			0
$148$	353640.			1.32711
$149$	−180515.	−	312661.i	−0.666113	−	1.15374i	−0.978982	−	0.203945i	$-0.934624\pi$
$149$	−180515.	−	312661.i	−0.666113	−	1.15374i	0.312870	−	0.949796i	$-0.398710\pi$
$150$	−62225.2	+	107777.i	−0.225807	+	0.391110i
$151$	−16140.0	+	27955.3i	−0.0576051	+	0.0997750i	−0.893390	−	0.449282i	$-0.851680\pi$
$151$	−16140.0	+	27955.3i	−0.0576051	+	0.0997750i	0.835785	+	0.549057i	$0.185013\pi$
$152$	130396.	+	225852.i	0.457777	+	0.792893i
$153$	57104.3			0.197215
$154$		0			0
$155$	−482976.			−1.61472
$156$	183456.	+	317755.i	0.603560	+	1.04540i
$157$	−66434.3	+	115068.i	−0.215101	+	0.372566i	−0.953304	−	0.302013i	$-0.902342\pi$
$157$	−66434.3	+	115068.i	−0.215101	+	0.372566i	0.738203	+	0.674579i	$0.235675\pi$
$158$	−54616.0	+	94597.7i	−0.174051	+	0.301466i
$159$	176733.	+	306111.i	0.554403	+	0.960255i
$160$	386091.			1.19231
$161$		0			0
$162$	12942.0			0.0387448
$163$	30682.0	+	53142.8i	0.0904513	+	0.156666i	0.907701	−	0.419617i	$-0.137836\pi$
$163$	30682.0	+	53142.8i	0.0904513	+	0.156666i	−0.817250	+	0.576284i	$0.804502\pi$
$164$	132194.	−	228967.i	0.383798	−	0.664757i
$165$	265824.	−	460421.i	0.760124	−	1.31657i
$166$	524.580	+	908.599i	0.00147755	+	0.00255919i
$167$	−380845.			−1.05671			−0.528356	−	0.849023i	$-0.677192\pi$
$167$	−380845.			−1.05671			−0.528356	+	0.849023i	$0.677192\pi$
$168$		0			0
$169$	−96109.0			−0.258849
$170$	−11232.0	−	19454.4i	−0.0298081	−	0.0516292i
$171$	414006.	−	717079.i	1.08272	−	1.87533i
$172$	−18984.0	+	32881.3i	−0.0489290	+	0.0847476i
$173$	258655.	+	448004.i	0.657062	+	1.13806i	0.981373	+	0.192114i	$0.0615343\pi$
$173$	258655.	+	448004.i	0.657062	+	1.13806i	−0.324311	+	0.945951i	$0.605132\pi$
$174$	−218125.			−0.546176
$175$		0			0
$176$	−186304.			−0.453357
$177$	467064.	+	808979.i	1.12058	+	1.94090i
$178$	20383.7	−	35305.6i	0.0482206	−	0.0835205i
$179$	−305282.	+	528764.i	−0.712145	+	1.23347i	0.251905	+	0.967752i	$0.418943\pi$
$179$	−305282.	+	528764.i	−0.712145	+	1.23347i	−0.964050	+	0.265720i	$0.914390\pi$
$180$	−399730.	−	692352.i	−0.919571	−	1.59274i
$181$	433828.			0.984285			0.492142	−	0.870515i	$-0.336214\pi$
$181$	433828.			0.984285			0.492142	+	0.870515i	$0.336214\pi$
$182$		0			0
$183$	−889200.			−1.96278
$184$	−89760.0	−	155469.i	−0.195451	−	0.338531i
$185$	−473246.	+	819686.i	−1.01662	+	1.76083i
$186$	−160992.	+	278846.i	−0.341210	+	0.590993i
$187$	21283.0	+	36863.2i	0.0445070	+	0.0770883i
$188$	281175.			0.580205
$189$		0			0
$190$	−325728.			−0.654593
$191$	−170596.	−	295481.i	−0.338365	−	0.586065i	0.645760	−	0.763540i	$-0.276541\pi$
$191$	−170596.	−	295481.i	−0.338365	−	0.586065i	−0.984125	+	0.177475i	$0.943207\pi$
$192$	−133493.	+	231217.i	−0.261340	+	0.452654i
$193$	308079.	−	533608.i	0.595345	−	1.03117i	−0.398153	−	0.917319i	$-0.630349\pi$
$193$	308079.	−	533608.i	0.595345	−	1.03117i	0.993498	−	0.113849i	$-0.0363180\pi$
$194$	−183603.	−	318010.i	−0.350248	−	0.606647i
$195$	−982013.			−1.84940
$196$		0			0
$197$	231478.			0.424956			0.212478	−	0.977166i	$-0.431847\pi$
$197$	231478.			0.424956			0.212478	+	0.977166i	$0.431847\pi$
$198$	−108204.	−	187415.i	−0.196146	−	0.339736i
$199$	−202563.	+	350849.i	−0.362599	+	0.628040i	−0.988388	−	0.151952i	$-0.951444\pi$
$199$	−202563.	+	350849.i	−0.362599	+	0.628040i	0.625789	+	0.779993i	$0.284777\pi$
$200$	−149460.	+	258872.i	−0.264210	+	0.457626i
$201$	−45513.5	−	78831.8i	−0.0794604	−	0.137629i
$202$	151828.			0.261803
$203$		0			0
$204$	104832.			0.176367
$205$	353808.	+	612813.i	0.588008	+	1.01846i
$206$	10941.2	−	18950.8i	0.0179638	−	0.0311142i
$207$	−284988.	+	493614.i	−0.462275	+	0.800684i
$208$	172062.	+	298020.i	0.275757	+	0.477626i
$209$	617206.			0.977382
$210$		0			0
$211$	776820.			1.20120			0.600599	−	0.799551i	$-0.294929\pi$
$211$	776820.			1.20120			0.600599	+	0.799551i	$0.294929\pi$
$212$	198100.	+	343119.i	0.302723	+	0.524331i
$213$	445044.	−	770838.i	0.672130	−	1.16416i
$214$	218188.	−	377913.i	0.325684	−	0.564101i
$215$	−50809.3	−	88004.3i	−0.0749630	−	0.129840i
$216$	−413669.			−0.603279
$217$		0			0
$218$	192060.			0.273713
$219$	−509184.	−	881933.i	−0.717405	−	1.24258i
$220$	297961.	−	516084.i	0.415053	−	0.718892i
$221$	39312.0	−	68090.4i	0.0541433	−	0.0937789i
$222$	315497.	+	546457.i	0.429648	+	0.744173i
$223$	−81834.5			−0.110198			−0.0550990	−	0.998481i	$-0.517547\pi$
$223$	−81834.5			−0.110198			−0.0550990	+	0.998481i	$0.517547\pi$
$224$		0			0
$225$	949071.			1.24981
$226$	−137422.	−	238022.i	−0.178972	−	0.309989i
$227$	376836.	−	652699.i	0.485386	−	0.840713i	−0.514473	−	0.857507i	$-0.672012\pi$
$227$	376836.	−	652699.i	0.485386	−	0.840713i	0.999859	+	0.0167932i	$0.00534570\pi$
$228$	760032.	−	1.31641e6i	0.968266	−	1.67709i
$229$	13152.0	+	22779.9i	0.0165730	+	0.0287053i	0.874193	−	0.485579i	$-0.161391\pi$
$229$	13152.0	+	22779.9i	0.0165730	+	0.0287053i	−0.857620	+	0.514284i	$0.828058\pi$
$230$	224220.			0.279483
$231$		0			0
$232$	−523920.			−0.639065
$233$	−23771.0	−	41172.6i	−0.0286852	−	0.0496842i	0.851326	−	0.524636i	$-0.175799\pi$
$233$	−23771.0	−	41172.6i	−0.0286852	−	0.0496842i	−0.880012	+	0.474952i	$0.842465\pi$
$234$	−199865.	+	346176.i	−0.238615	+	0.413293i
$235$	−376272.	+	651722.i	−0.444460	+	0.769827i
$236$	523531.	+	906782.i	0.611874	+	1.05980i
$237$	1.36431e6			1.57776
$238$		0			0
$239$	1.08899e6			1.23319			0.616595	−	0.787281i	$-0.288512\pi$
$239$	1.08899e6			1.23319			0.616595	+	0.787281i	$0.288512\pi$
$240$	−614016.	−	1.06351e6i	−0.688100	−	1.19182i
$241$	−674685.	+	1.16859e6i	−0.748270	+	1.29604i	0.200382	+	0.979718i	$0.435782\pi$
$241$	−674685.	+	1.16859e6i	−0.748270	+	1.29604i	−0.948651	+	0.316323i	$0.897552\pi$
$242$	−80395.0	+	139248.i	−0.0882451	+	0.152845i
$243$	−499662.	−	865440.i	−0.542826	−	0.940203i
$244$	−996702.			−1.07174
$245$		0			0
$246$	471744.			0.497014
$247$	−570024.	−	987311.i	−0.594498	−	1.02970i
$248$	−386690.	+	669767.i	−0.399240	+	0.691504i
$249$	6552.00	−	11348.4i	0.00669693	−	0.0115994i
$250$	47511.9	+	82293.1i	0.0480787	+	0.0832748i
$251$	−630020.			−0.631205			−0.315602	−	0.948892i	$-0.602207\pi$
$251$	−630020.			−0.631205			−0.315602	+	0.948892i	$0.602207\pi$
$252$		0			0
$253$	−424864.			−0.417300
$254$	170368.	+	295086.i	0.165693	+	0.286988i
$255$	−140288.	+	242985.i	−0.135104	+	0.234007i
$256$	15232.0	−	26382.6i	0.0145264	−	0.0251604i
$257$	−967025.	−	1.67494e6i	−0.913282	−	1.58185i	−0.809397	−	0.587262i	$-0.800206\pi$
$257$	−967025.	−	1.67494e6i	−0.913282	−	1.58185i	−0.103886	−	0.994589i	$-0.533128\pi$
$258$	−67745.7			−0.0633626
$259$		0			0
$260$	−1.10074e6			−1.00983
$261$	831723.	+	1.44059e6i	0.755749	+	1.30900i
$262$	348246.	−	603180.i	0.313425	−	0.542867i
$263$	558560.	−	967454.i	0.497944	−	0.862464i	−0.502053	−	0.864837i	$-0.667422\pi$
$263$	558560.	−	967454.i	0.497944	−	0.862464i	0.999997	+	0.00237250i	$0.000755190\pi$
$264$	−425659.	−	737263.i	−0.375882	−	0.651048i
$265$	−1.06040e6			−0.927588
$266$		0			0
$267$	−509184.			−0.437116
$268$	−51016.0	−	88362.3i	−0.0433880	−	0.0751502i
$269$	760304.	−	1.31688e6i	0.640629	−	1.10960i	−0.344664	−	0.938726i	$-0.612007\pi$
$269$	760304.	−	1.31688e6i	0.640629	−	1.10960i	0.985293	−	0.170875i	$-0.0546595\pi$
$270$	258336.	−	447451.i	0.215663	−	0.373539i
$271$	510191.	+	883677.i	0.421997	+	0.730921i	0.996135	−	0.0878380i	$-0.0279958\pi$
$271$	510191.	+	883677.i	0.421997	+	0.730921i	−0.574137	+	0.818759i	$0.694662\pi$
$272$	98321.2			0.0805796
$273$		0			0
$274$	151124.			0.121607
$275$	353722.	+	612664.i	0.282053	+	0.488530i
$276$	−523181.	+	906176.i	−0.413408	+	0.716044i
$277$	−948211.	+	1.64235e6i	−0.742516	+	1.28607i	0.208831	+	0.977952i	$0.433034\pi$
$277$	−948211.	+	1.64235e6i	−0.742516	+	1.28607i	−0.951347	+	0.308123i	$0.900299\pi$
$278$	−97047.3	−	168091.i	−0.0753132	−	0.130446i
$279$	2.45548e6			1.88854
$280$		0			0
$281$	1.31911e6			0.996587			0.498293	−	0.867008i	$-0.333960\pi$
$281$	1.31911e6			0.996587			0.498293	+	0.867008i	$0.333960\pi$
$282$	250848.	+	434481.i	0.187840	+	0.325348i
$283$	239396.	−	414646.i	0.177685	−	0.307759i	−0.763402	−	0.645923i	$-0.776473\pi$
$283$	239396.	−	414646.i	0.177685	−	0.307759i	0.941087	+	0.338164i	$0.109806\pi$
$284$	498848.	−	864030.i	0.367005	−	0.635672i
$285$	2.03417e6	+	3.52329e6i	1.48346	+	2.56942i
$286$	−297961.			−0.215400
$287$		0			0
$288$	−1.96291e6			−1.39450
$289$	698696.	+	1.21018e6i	0.492089	+	0.852324i
$290$	327188.	−	566706.i	0.228456	−	0.395697i
$291$	−2.29320e6	+	3.97194e6i	−1.58748	+	2.74960i
$292$	−570743.	−	988556.i	−0.391727	−	0.678491i
$293$	−1.50187e6			−1.02203			−0.511015	−	0.859572i	$-0.670730\pi$
$293$	−1.50187e6			−1.02203			−0.511015	+	0.859572i	$0.670730\pi$
$294$		0			0
$295$	−2.80238e6			−1.87488
$296$	757800.	+	1.31255e6i	0.502719	+	0.870735i
$297$	−489508.	+	847853.i	−0.322009	+	0.557737i
$298$	361030.	−	625322.i	0.235506	−	0.407909i
$299$	392386.	+	679632.i	0.253825	+	0.439639i
$300$	1.74230e6			1.11769
$301$		0			0
$302$	−64560.0			−0.0407330
$303$	−948168.	−	1.64228e6i	−0.593306	−	1.02764i
$304$	712829.	−	1.23466e6i	0.442386	−	0.766235i
$305$	1.33380e6	−	2.31021e6i	0.820996	−	1.42201i
$306$	57104.3	+	98907.5i	0.0348630	+	0.0603845i
$307$	1.19657e6			0.724588			0.362294	−	0.932064i	$-0.381994\pi$
$307$	1.19657e6			0.724588			0.362294	+	0.932064i	$0.381994\pi$
$308$		0			0
$309$	−273312.			−0.162841
$310$	−482976.	−	836539.i	−0.285444	−	0.494404i
$311$	−657373.	+	1.13860e6i	−0.385400	+	0.667532i	−0.991825	−	0.127609i	$-0.959270\pi$
$311$	−657373.	+	1.13860e6i	−0.385400	+	0.667532i	0.606425	+	0.795141i	$0.292603\pi$
$312$	−786240.	+	1.36181e6i	−0.457266	+	0.792007i
$313$	−1.32636e6	−	2.29733e6i	−0.765247	−	1.32545i	−0.940116	−	0.340854i	$-0.889284\pi$
$313$	−1.32636e6	−	2.29733e6i	−0.765247	−	1.32545i	0.174869	−	0.984592i	$-0.444050\pi$
$314$	−265737.			−0.152100
$315$		0			0
$316$	1.52925e6			0.861510
$317$	799961.	+	1.38557e6i	0.447116	+	0.774428i	0.998197	−	0.0600237i	$-0.0191176\pi$
$317$	799961.	+	1.38557e6i	0.447116	+	0.774428i	−0.551080	+	0.834452i	$0.685784\pi$
$318$	−353467.	+	612223.i	−0.196011	+	0.339501i
$319$	−619972.	+	1.07382e6i	−0.341111	+	0.590821i
$320$	−400479.	−	693650.i	−0.218628	−	0.378674i
$321$	−5.45033e6			−2.95230
$322$		0			0
$323$	−325728.			−0.173720
$324$	−90594.0	−	156913.i	−0.0479443	−	0.0830419i
$325$	653364.	−	1.13166e6i	0.343121	−	0.594302i
$326$	−61364.0	+	106286.i	−0.0319794	+	0.0553899i
$327$	−1.19941e6	−	2.07745e6i	−0.620297	−	1.07439i
$328$	1.13309e6			0.581542
$329$		0			0
$330$	1.06330e6			0.537489
$331$	55854.0	+	96742.0i	0.0280210	+	0.0485339i	0.879696	−	0.475537i	$-0.157746\pi$
$331$	55854.0	+	96742.0i	0.0280210	+	0.0485339i	−0.851675	+	0.524071i	$0.824413\pi$
$332$	7344.12	−	12720.4i	0.00365674	−	0.00633366i
$333$	2.40602e6	−	4.16734e6i	1.18902	−	2.05944i
$334$	−380845.	−	659643.i	−0.186802	−	0.323551i
$335$	273081.			0.132947
$336$		0			0
$337$	1.59301e6			0.764087			0.382043	−	0.924144i	$-0.375220\pi$
$337$	1.59301e6			0.764087			0.382043	+	0.924144i	$0.375220\pi$
$338$	−96109.0	−	166466.i	−0.0457586	−	0.0792561i
$339$	−1.71640e6	+	2.97289e6i	−0.811184	+	1.40501i
$340$	−157248.	+	272362.i	−0.0737714	+	0.127776i
$341$	915167.	+	1.58512e6i	0.426201	+	0.738202i
$342$	1.65602e6			0.765599
$343$		0			0
$344$	−162720.			−0.0741387
$345$	−1.40026e6	−	2.42531e6i	−0.633373	−	1.09703i
$346$	−517311.	+	896008.i	−0.232306	+	0.402366i
$347$	1.66838e6	−	2.88972e6i	0.743827	−	1.28835i	−0.206914	−	0.978359i	$-0.566342\pi$
$347$	1.66838e6	−	2.88972e6i	0.743827	−	1.28835i	0.950741	−	0.309987i	$-0.100325\pi$
$348$	1.52688e6	+	2.64463e6i	0.675859	+	1.17062i
$349$	1.60259e6			0.704303			0.352151	−	0.935943i	$-0.385450\pi$
$349$	1.60259e6			0.704303			0.352151	+	0.935943i	$0.385450\pi$
$350$		0			0
$351$	1.80835e6			0.783457
$352$	−731584.	−	1.26714e6i	−0.314708	−	0.545090i
$353$	904825.	−	1.56720e6i	0.386481	−	0.669404i	−0.605493	−	0.795851i	$-0.707024\pi$
$353$	904825.	−	1.56720e6i	0.386481	−	0.669404i	0.991973	+	0.126447i	$0.0403572\pi$
$354$	−934128.	+	1.61796e6i	−0.396185	+	0.686213i
$355$	1.33513e6	+	2.31251e6i	0.562280	+	0.973898i
$356$	−570743.			−0.238680
$357$		0			0
$358$	−1.22113e6			−0.503563
$359$	−460396.	−	797429.i	−0.188536	−	0.326555i	0.756226	−	0.654310i	$-0.227041\pi$
$359$	−460396.	−	797429.i	−0.188536	−	0.326555i	−0.944763	+	0.327756i	$0.893708\pi$
$360$	1.71313e6	−	2.96722e6i	0.696680	−	1.20669i
$361$	−1.12348e6	+	1.94592e6i	−0.453729	+	0.785882i
$362$	433828.	+	751411.i	0.173999	+	0.301374i
$363$	2.00827e6			0.799935
$364$		0			0
$365$	3.05510e6			1.20031
$366$	−889200.	−	1.54014e6i	−0.346974	−	0.600976i
$367$	674010.	−	1.16742e6i	0.261217	−	0.452441i	−0.705349	−	0.708861i	$-0.749210\pi$
$367$	674010.	−	1.16742e6i	0.261217	−	0.452441i	0.966566	+	0.256420i	$0.0825429\pi$
$368$	−490688.	+	849897.i	−0.188880	+	0.327150i
$369$	−1.79878e6	−	3.11559e6i	−0.687722	−	1.19117i
$370$	−1.89298e6			−0.718857
$371$		0			0
$372$	4.50778e6			1.68890
$373$	−1.56887e6	−	2.71736e6i	−0.583867	−	1.01129i	−0.995016	−	0.0997192i	$-0.968206\pi$
$373$	−1.56887e6	−	2.71736e6i	−0.583867	−	1.01129i	0.411148	−	0.911568i	$-0.365128\pi$
$374$	−42565.9	+	73726.3i	−0.0157356	+	0.0272548i
$375$	593424.	−	1.02784e6i	0.217915	−	0.377440i
$376$	602517.	+	1.04359e6i	0.219786	+	0.380680i
$377$	2.29032e6			0.829931
$378$		0			0
$379$	−1.83188e6			−0.655088			−0.327544	−	0.944836i	$-0.606221\pi$
$379$	−1.83188e6			−0.655088			−0.327544	+	0.944836i	$0.606221\pi$
$380$	2.28010e6	+	3.94924e6i	0.810017	+	1.40299i
$381$	2.12790e6	−	3.68562e6i	0.750996	−	1.30076i
$382$	341192.	−	590962.i	0.119630	−	0.207205i
$383$	−13863.9	−	24013.0i	−0.00482935	−	0.00836467i	0.863601	−	0.504177i	$-0.168204\pi$
$383$	−13863.9	−	24013.0i	−0.00482935	−	0.00836467i	−0.868430	+	0.495812i	$0.834871\pi$
$384$	−4.65227e6			−1.61004
$385$		0			0
$386$	1.23232e6			0.420973
$387$	258318.	+	447420.i	0.0876753	+	0.151858i
$388$	−2.57044e6	+	4.45213e6i	−0.866819	+	1.50137i
$389$	274171.	−	474878.i	0.0918645	−	0.159114i	−0.816431	−	0.577443i	$-0.804051\pi$
$389$	274171.	−	474878.i	0.0918645	−	0.159114i	0.908296	+	0.418329i	$0.137384\pi$
$390$	−982013.	−	1.70090e6i	−0.326931	−	0.566261i
$391$	224220.			0.0741708
$392$		0			0
$393$	−8.69918e6			−2.84117
$394$	231478.	+	400932.i	0.0751224	+	0.130116i
$395$	−2.04646e6	+	3.54457e6i	−0.659950	+	1.14307i
$396$	−1.51486e6	+	2.62381e6i	−0.485438	+	0.840803i
$397$	−201926.	−	349746.i	−0.0643007	−	0.111372i	0.832083	−	0.554651i	$-0.187148\pi$
$397$	−201926.	−	349746.i	−0.0643007	−	0.111372i	−0.896384	+	0.443279i	$0.853815\pi$
$398$	−810251.			−0.256396
$399$		0			0
$400$	1.63410e6			0.510655
$401$	2.08214e6	+	3.60637e6i	0.646619	+	1.11998i	0.983925	+	0.178582i	$0.0571509\pi$
$401$	2.08214e6	+	3.60637e6i	0.646619	+	1.11998i	−0.337306	+	0.941395i	$0.609516\pi$
$402$	91027.1	−	157664.i	0.0280935	−	0.0486593i
$403$	1.69042e6	−	2.92789e6i	0.518479	−	0.898032i
$404$	−1.06280e6	−	1.84082e6i	−0.323965	−	0.561123i
$405$	484937.			0.146909
$406$		0			0
$407$	3.58692e6			1.07334
$408$	224640.	+	389088.i	0.0668093	+	0.115717i
$409$	−1.27061e6	+	2.20076e6i	−0.375581	+	0.650525i	−0.990414	−	0.138133i	$-0.955890\pi$
$409$	−1.27061e6	+	2.20076e6i	−0.375581	+	0.650525i	0.614833	+	0.788657i	$0.289223\pi$
$410$	−707616.	+	1.22563e6i	−0.207892	+	0.360080i
$411$	−943769.	−	1.63466e6i	−0.275589	−	0.477333i
$412$	−306355.			−0.0889163
$413$		0			0
$414$	−1.13995e6			−0.326878
$415$	19656.0	+	34045.2i	0.00560241	+	0.00970366i
$416$	−1.35132e6	+	2.34055e6i	−0.382846	+	0.663109i
$417$	−1.21212e6	+	2.09945e6i	−0.341354	+	0.591243i
$418$	617206.	+	1.06903e6i	0.172778	+	0.299261i
$419$	2.30133e6			0.640389			0.320195	−	0.947352i	$-0.396252\pi$
$419$	2.30133e6			0.640389			0.320195	+	0.947352i	$0.396252\pi$
$420$		0			0
$421$	−2.79991e6			−0.769909			−0.384955	−	0.922936i	$-0.625783\pi$
$421$	−2.79991e6			−0.769909			−0.384955	+	0.922936i	$0.625783\pi$
$422$	776820.	+	1.34549e6i	0.212344	+	0.367790i
$423$	1.91299e6	−	3.31340e6i	0.519831	−	0.900374i
$424$	−849000.	+	1.47051e6i	−0.229347	+	0.397241i
$425$	−186675.	−	323331.i	−0.0501320	−	0.0868312i
$426$	1.78017e6			0.475268
$427$		0			0
$428$	−6.10926e6			−1.61205
$429$	1.86077e6	+	3.22294e6i	0.488145	+	0.845492i
$430$	101619.	−	176009.i	0.0265034	−	0.0459053i
$431$	−477160.	+	826465.i	−0.123729	+	0.214305i	−0.921235	−	0.389006i	$-0.872819\pi$
$431$	−477160.	+	826465.i	−0.123729	+	0.214305i	0.797507	+	0.603310i	$0.206152\pi$
$432$	1.13069e6	+	1.95842e6i	0.291498	+	0.504890i
$433$	−519334.			−0.133115			−0.0665575	−	0.997783i	$-0.521202\pi$
$433$	−519334.			−0.133115			−0.0665575	+	0.997783i	$0.521202\pi$
$434$		0			0
$435$	−8.17315e6			−2.07093
$436$	−1.34442e6	−	2.32860e6i	−0.338703	−	0.586650i
$437$	1.62560e6	−	2.81562e6i	0.407202	−	0.705294i
$438$	1.01837e6	−	1.76387e6i	0.253641	−	0.439319i
$439$	2.99040e6	+	5.17953e6i	0.740574	+	1.28271i	0.952234	+	0.305369i	$0.0987798\pi$
$439$	2.99040e6	+	5.17953e6i	0.740574	+	1.28271i	−0.211660	+	0.977343i	$0.567887\pi$
$440$	2.55395e6			0.628900
$441$		0			0
$442$	157248.			0.0382851
$443$	−1.87410e6	−	3.24604e6i	−0.453716	−	0.785859i	0.544898	−	0.838503i	$-0.316569\pi$
$443$	−1.87410e6	−	3.24604e6i	−0.453716	−	0.785859i	−0.998613	+	0.0526438i	$0.983235\pi$
$444$	4.41696e6	−	7.65040e6i	1.06333	−	1.84173i
$445$	763776.	−	1.32290e6i	0.182838	−	0.316684i
$446$	−81834.5	−	141741.i	−0.0194805	−	0.0337411i
$447$	−9.01853e6			−2.13485
$448$		0			0
$449$	99458.0			0.0232822			0.0116411	−	0.999932i	$-0.496294\pi$
$449$	99458.0			0.0232822			0.0116411	+	0.999932i	$0.496294\pi$
$450$	949071.	+	1.64384e6i	0.220936	+	0.382673i
$451$	1.34083e6	−	2.32238e6i	0.310407	−	0.537640i
$452$	−1.92391e6	+	3.33231e6i	−0.442933	+	0.767183i
$453$	403177.	+	698323.i	0.0923103	+	0.159886i
$454$	1.50734e6			0.343220
$455$		0			0
$456$	6.51456e6			1.46714
$457$	80907.0	+	140135.i	0.0181216	+	0.0313875i	0.874944	−	0.484224i	$-0.160898\pi$
$457$	80907.0	+	140135.i	0.0181216	+	0.0313875i	−0.856822	+	0.515612i	$0.827565\pi$
$458$	−26303.9	+	45559.7i	−0.00585945	+	0.0101489i
$459$	258336.	−	447451.i	0.0572339	−	0.0991320i
$460$	−1.56954e6	−	2.71853e6i	−0.345843	−	0.599017i
$461$	4.49198e6			0.984431			0.492215	−	0.870473i	$-0.336187\pi$
$461$	4.49198e6			0.984431			0.492215	+	0.870473i	$0.336187\pi$
$462$		0			0
$463$	3.59382e6			0.779118			0.389559	−	0.921001i	$-0.372627\pi$
$463$	3.59382e6			0.779118			0.389559	+	0.921001i	$0.372627\pi$
$464$	1.43205e6	+	2.48038e6i	0.308790	+	0.534839i
$465$	−6.03237e6	+	1.04484e7i	−1.29377	+	2.24087i
$466$	47542.0	−	82345.2i	0.0101417	−	0.0175660i
$467$	1.02612e6	+	1.77728e6i	0.217723	+	0.377107i	0.954111	−	0.299452i	$-0.0968038\pi$
$467$	1.02612e6	+	1.77728e6i	0.217723	+	0.377107i	−0.736389	+	0.676559i	$0.763470\pi$
$468$	5.59622e6			1.18108
$469$		0			0
$470$	−1.50509e6			−0.314280
$471$	1.65953e6	+	2.87439e6i	0.344693	+	0.597026i
$472$	−2.24370e6	+	3.88621e6i	−0.463565	+	0.802918i
$473$	−192552.	+	333510.i	−0.0395727	+	0.0685418i
$474$	1.36431e6	+	2.36305e6i	0.278911	+	0.483089i
$475$	−5.41359e6			−1.10091
$476$		0			0
$477$	5.39115e6			1.08489
$478$	1.08899e6	+	1.88619e6i	0.217999	+	0.377586i
$479$	−999924.	+	1.73192e6i	−0.199126	+	0.344897i	−0.948245	−	0.317539i	$-0.897144\pi$
$479$	−999924.	+	1.73192e6i	−0.199126	+	0.344897i	0.749119	+	0.662435i	$0.230477\pi$
$480$	4.82227e6	−	8.35242e6i	0.955319	−	1.65466i
$481$	−3.31272e6	−	5.73780e6i	−0.652863	−	1.13079i
$482$	−2.69874e6			−0.529107
$483$		0			0
$484$	2.25106e6			0.436791
$485$	−6.87960e6	−	1.19158e7i	−1.32803	−	2.30022i
$486$	999325.	−	1.73088e6i	0.191918	−	0.332412i
$487$	−1.08563e6	+	1.88036e6i	−0.207424	+	0.359269i	−0.950902	−	0.309491i	$-0.899841\pi$
$487$	−1.08563e6	+	1.88036e6i	−0.207424	+	0.359269i	0.743478	+	0.668760i	$0.233175\pi$
$488$	−2.13579e6	−	3.69930e6i	−0.405984	−	0.703185i
$489$	1.53287e6			0.289890
$490$		0			0
$491$	3.04555e6			0.570114			0.285057	−	0.958511i	$-0.407987\pi$
$491$	3.04555e6			0.570114			0.285057	+	0.958511i	$0.407987\pi$
$492$	−3.30221e6	−	5.71959e6i	−0.615023	−	1.06525i
$493$	327188.	−	566706.i	0.0606289	−	0.105012i
$494$	1.14005e6	−	1.97462e6i	0.210187	−	0.364054i
$495$	−4.05440e6	−	7.02243e6i	−0.743728	−	1.28817i
$496$	4.22781e6			0.771635
$497$		0			0
$498$	26208.0			0.00473544
$499$	3.99613e6	+	6.92149e6i	0.718436	+	1.24437i	0.961619	+	0.274387i	$0.0884748\pi$
$499$	3.99613e6	+	6.92149e6i	0.718436	+	1.24437i	−0.243184	+	0.969980i	$0.578192\pi$
$500$	665167.	−	1.15210e6i	0.118989	−	0.206095i
$501$	−4.75675e6	+	8.23894e6i	−0.846674	+	1.46648i
$502$	−630020.	−	1.09123e6i	−0.111582	−	0.193266i
$503$	−9.47811e6			−1.67033			−0.835164	−	0.550001i	$-0.814627\pi$
$503$	−9.47811e6			−1.67033			−0.835164	+	0.550001i	$0.814627\pi$
$504$		0			0
$505$	5.68901e6			0.992677
$506$	−424864.	−	735886.i	−0.0737690	−	0.127772i
$507$	−1.20040e6	+	2.07916e6i	−0.207399	+	0.359225i
$508$	2.38515e6	−	4.13120e6i	0.410069	−	0.710260i
$509$	5.05017e6	+	8.74715e6i	0.863995	+	1.49648i	0.868041	+	0.496492i	$0.165379\pi$
$509$	5.05017e6	+	8.74715e6i	0.863995	+	1.49648i	−0.00404624	+	0.999992i	$0.501288\pi$
$510$	−561151.			−0.0955331
$511$		0			0
$512$	−5.89875e6			−0.994455
$513$	−3.74587e6	−	6.48804e6i	−0.628434	−	1.08848i
$514$	1.93405e6	−	3.34987e6i	0.322894	−	0.559269i
$515$	409968.	−	710085.i	0.0681133	−	0.117976i
$516$	474220.	+	821373.i	0.0784072	+	0.135805i
$517$	2.85192e6			0.469257
$518$		0			0
$519$	1.29224e7			2.10584
$520$	−2.35872e6	−	4.08542e6i	−0.382532	−	0.662565i
$521$	2.55987e6	−	4.43383e6i	0.413166	−	0.715624i	−0.582068	−	0.813140i	$-0.697756\pi$
$521$	2.55987e6	−	4.43383e6i	0.413166	−	0.715624i	0.995234	+	0.0975158i	$0.0310897\pi$
$522$	−1.66345e6	+	2.88117e6i	−0.267198	+	0.462800i
$523$	1.75738e6	+	3.04387e6i	0.280939	+	0.486600i	0.971616	−	0.236563i	$-0.0760209\pi$
$523$	1.75738e6	+	3.04387e6i	0.280939	+	0.486600i	−0.690678	+	0.723163i	$0.742688\pi$
$524$	−9.75089e6			−1.55137
$525$		0			0
$526$	2.23424e6			0.352100
$527$	−482976.	−	836539.i	−0.0757529	−	0.131208i
$528$	−2.32694e6	+	4.03037e6i	−0.363245	+	0.629159i
$529$	2.09916e6	−	3.63586e6i	0.326142	−	0.564895i
$530$	−1.06040e6	−	1.83667e6i	−0.163976	−	0.284015i
$531$	1.42475e7			2.19282
$532$		0			0
$533$	−4.95331e6			−0.755227
$534$	−509184.	−	881933.i	−0.0772719	−	0.133839i
$535$	8.17550e6	−	1.41604e7i	1.23489	−	2.13890i
$536$	218640.	−	378696.i	0.0328714	−	0.0569349i
$537$	7.62594e6	+	1.32085e7i	1.14119	+	1.97660i
$538$	3.04121e6			0.452993
$539$		0			0
$540$	−7.23341e6			−1.06748
$541$	1.73774e6	+	3.00985e6i	0.255265	+	0.442132i	0.964967	−	0.262370i	$-0.0845040\pi$
$541$	1.73774e6	+	3.00985e6i	0.255265	+	0.442132i	−0.709703	+	0.704501i	$0.751171\pi$
$542$	−1.02038e6	+	1.76735e6i	−0.149199	+	0.258420i
$543$	5.41850e6	−	9.38512e6i	0.788642	−	1.36597i
$544$	386091.	+	668729.i	0.0559361	+	0.0968842i
$545$	7.19649e6			1.03784
$546$		0			0
$547$	−7.85765e6			−1.12286			−0.561429	−	0.827525i	$-0.689748\pi$
$547$	−7.85765e6			−1.12286			−0.561429	+	0.827525i	$0.689748\pi$
$548$	−1.05787e6	−	1.83228e6i	−0.150480	−	0.260640i
$549$	−6.78113e6	+	1.17453e7i	−0.960221	+	1.66315i
$550$	−707444.	+	1.22533e6i	−0.0997207	+	0.172721i
$551$	−4.74423e6	−	8.21724e6i	−0.665712	−	1.15305i
$552$	−4.48441e6			−0.626408
$553$		0			0
$554$	−3.79284e6			−0.525038
$555$	1.18217e7	+	2.04758e7i	1.62910	+	2.82168i
$556$	−1.35866e6	+	2.35327e6i	−0.186391	+	0.322838i
$557$	−4.53269e6	+	7.85084e6i	−0.619039	+	1.07221i	0.370623	+	0.928783i	$0.379144\pi$
$557$	−4.53269e6	+	7.85084e6i	−0.619039	+	1.07221i	−0.989661	+	0.143423i	$0.954189\pi$
$558$	2.45548e6	+	4.25302e6i	0.333850	+	0.578245i
$559$	711330.			0.0962813
$560$		0			0
$561$	1.06330e6			0.142642
$562$	1.31911e6	+	2.28477e6i	0.176173	+	0.305141i
$563$	2.90479e6	−	5.03124e6i	0.386227	−	0.668966i	−0.605711	−	0.795685i	$-0.707111\pi$
$563$	2.90479e6	−	5.03124e6i	0.386227	−	0.668966i	0.991939	+	0.126719i	$0.0404446\pi$
$564$	3.51187e6	−	6.08274e6i	0.464880	−	0.805196i
$565$	−5.14920e6	−	8.91868e6i	−0.678608	−	1.17538i
$566$	957583.			0.125642
$567$		0			0
$568$	4.27584e6			0.556097
$569$	−5.27797e6	−	9.14171e6i	−0.683418	−	1.18371i	−0.973931	−	0.226844i	$-0.927159\pi$
$569$	−5.27797e6	−	9.14171e6i	−0.683418	−	1.18371i	0.290513	−	0.956871i	$-0.406174\pi$
$570$	−4.06834e6	+	7.04657e6i	−0.524482	+	0.908429i
$571$	−3.99792e6	+	6.92460e6i	−0.513150	+	0.888801i	0.486734	+	0.873550i	$0.338188\pi$
$571$	−3.99792e6	+	6.92460e6i	−0.513150	+	0.888801i	−0.999884	+	0.0152511i	$0.995145\pi$
$572$	2.08573e6	+	3.61259e6i	0.266543	+	0.461667i
$573$	−8.52297e6			−1.08444
$574$		0			0
$575$	3.72654e6			0.470041
$576$	2.03606e6	+	3.52657e6i	0.255703	+	0.442890i
$577$	−1.30470e6	+	2.25982e6i	−0.163145	+	0.282575i	−0.935995	−	0.352014i	$-0.885497\pi$
$577$	−1.30470e6	+	2.25982e6i	−0.163145	+	0.282575i	0.772850	+	0.634588i	$0.218830\pi$
$578$	−1.39739e6	+	2.42036e6i	−0.173980	+	0.301342i
$579$	−7.69581e6	−	1.33295e7i	−0.954021	−	1.65241i
$580$	−9.16126e6			−1.13080
$581$		0			0
$582$	−9.17280e6			−1.12252
$583$	2.00930e6	+	3.48021e6i	0.244835	+	0.424067i
$584$	2.44604e6	−	4.23667e6i	0.296778	−	0.514034i
$585$	−7.48894e6	+	1.29712e7i	−0.904754	+	1.56708i
$586$	−1.50187e6	−	2.60132e6i	−0.180671	−	0.312932i
$587$	−4.41749e6			−0.529151			−0.264576	−	0.964365i	$-0.585232\pi$
$587$	−4.41749e6			−0.529151			−0.264576	+	0.964365i	$0.585232\pi$
$588$		0			0
$589$	−1.40063e7			−1.66355
$590$	−2.80238e6	−	4.85387e6i	−0.331434	−	0.574061i
$591$	2.89116e6	−	5.00763e6i	0.340489	−	0.589745i
$592$	4.14264e6	−	7.17526e6i	0.485817	−	0.841460i
$593$	−2.77053e6	−	4.79870e6i	−0.323539	−	0.560386i	0.657677	−	0.753300i	$-0.271539\pi$
$593$	−2.77053e6	−	4.79870e6i	−0.323539	−	0.560386i	−0.981216	+	0.192915i	$0.938206\pi$
$594$	−1.95803e6			−0.227695
$595$		0			0
$596$	−1.01088e7			−1.16570
$597$	5.06002e6	+	8.76420e6i	0.581053	+	1.00641i
$598$	−784771.	+	1.35926e6i	−0.0897409	+	0.155436i
$599$	−2.54306e6	+	4.40470e6i	−0.289594	+	0.501591i	−0.973713	−	0.227779i	$-0.926853\pi$
$599$	−2.54306e6	+	4.40470e6i	−0.289594	+	0.501591i	0.684119	+	0.729370i	$0.260187\pi$
$600$	3.73351e6	+	6.46663e6i	0.423389	+	0.733331i
$601$	−2.41307e6			−0.272511			−0.136255	−	0.990674i	$-0.543507\pi$
$601$	−2.41307e6			−0.272511			−0.136255	+	0.990674i	$0.543507\pi$
$602$		0			0
$603$	−1.38836e6			−0.155493
$604$	451920.	+	782748.i	0.0504045	+	0.0873031i
$605$	−3.01240e6	+	5.21763e6i	−0.334599	+	0.579542i
$606$	1.89634e6	−	3.28455e6i	0.209765	−	0.363324i
$607$	3.81085e6	+	6.60058e6i	0.419807	+	0.727127i	0.995920	−	0.0902430i	$-0.0287644\pi$
$607$	3.81085e6	+	6.60058e6i	0.419807	+	0.727127i	−0.576113	+	0.817370i	$0.695431\pi$
$608$	1.11966e7			1.22837
$609$		0			0
$610$	5.33520e6			0.580532
$611$	−2.63390e6	−	4.56206e6i	−0.285428	−	0.494376i
$612$	799460.	−	1.38470e6i	0.0862816	−	0.149444i
$613$	−1.80063e6	+	3.11878e6i	−0.193541	+	0.335223i	−0.946421	−	0.322935i	$-0.895331\pi$
$613$	−1.80063e6	+	3.11878e6i	−0.193541	+	0.335223i	0.752880	+	0.658158i	$0.228664\pi$
$614$	1.19657e6	+	2.07251e6i	0.128090	+	0.221859i
$615$	1.76762e7			1.88453
$616$		0			0
$617$	7.22901e6			0.764480			0.382240	−	0.924063i	$-0.375153\pi$
$617$	7.22901e6			0.764480			0.382240	+	0.924063i	$0.375153\pi$
$618$	−273312.	−	473390.i	−0.0287864	−	0.0498595i
$619$	−6.29162e6	+	1.08974e7i	−0.659988	+	1.14313i	0.320630	+	0.947204i	$0.396105\pi$
$619$	−6.29162e6	+	1.08974e7i	−0.659988	+	1.14313i	−0.980618	+	0.195928i	$0.937228\pi$
$620$	−6.76166e6	+	1.17115e7i	−0.706439	+	1.22359i
$621$	2.57853e6	+	4.46615e6i	0.268314	+	0.464734i
$622$	−2.62949e6			−0.272519
$623$		0			0
$624$	8.59622e6			0.883784
$625$	5.67246e6	+	9.82499e6i	0.580860	+	1.00608i
$626$	2.65273e6	−	4.59465e6i	0.270556	−	0.468616i
$627$	7.70890e6	−	1.33522e7i	0.783111	−	1.35639i
$628$	1.86016e6	+	3.22189e6i	0.188214	+	0.325996i
$629$	−1.89298e6			−0.190774
$630$		0			0
$631$	5.98350e6			0.598249			0.299125	−	0.954214i	$-0.403305\pi$
$631$	5.98350e6			0.598249			0.299125	+	0.954214i	$0.403305\pi$
$632$	3.27696e6	+	5.67586e6i	0.326346	+	0.565248i
$633$	9.70248e6	−	1.68052e7i	0.962439	−	1.66699i
$634$	−1.59992e6	+	2.77115e6i	−0.158080	+	0.273802i
$635$	6.38369e6	+	1.10569e7i	0.628257	+	1.08817i
$636$	9.89707e6			0.970206
$637$		0			0
$638$	−2.47989e6			−0.241202
$639$	−6.78790e6	−	1.17570e7i	−0.657632	−	1.13905i
$640$	6.97841e6	−	1.20870e7i	0.673452	−	1.16645i
$641$	3.87000e6	−	6.70304e6i	0.372020	−	0.644357i	−0.617856	−	0.786291i	$-0.711999\pi$
$641$	3.87000e6	−	6.70304e6i	0.372020	−	0.644357i	0.989876	+	0.141934i	$0.0453320\pi$
$642$	−5.45033e6	−	9.44026e6i	−0.521898	−	0.903954i
$643$	−6.81377e6			−0.649920			−0.324960	−	0.945728i	$-0.605351\pi$
$643$	−6.81377e6			−0.649920			−0.324960	+	0.945728i	$0.605351\pi$
$644$		0			0
$645$	−2.53843e6			−0.240252
$646$	−325728.	−	564177.i	−0.0307096	−	0.0531905i
$647$	−5.35604e6	+	9.27692e6i	−0.503017	+	0.871251i	0.496977	+	0.867764i	$0.334443\pi$
$647$	−5.35604e6	+	9.27692e6i	−0.503017	+	0.871251i	−0.999994	+	0.00348730i	$0.998890\pi$
$648$	388260.	−	672486.i	0.0363233	−	0.0629138i
$649$	5.31010e6	+	9.19736e6i	0.494870	+	0.857139i
$650$	2.61346e6			0.242623
$651$		0			0
$652$	1.71819e6			0.158290
$653$	−6.70834e6	−	1.16192e7i	−0.615647	−	1.06633i	−0.990271	−	0.139155i	$-0.955561\pi$
$653$	−6.70834e6	−	1.16192e7i	−0.615647	−	1.06633i	0.374623	−	0.927177i	$-0.377772\pi$
$654$	2.39883e6	−	4.15489e6i	0.219308	−	0.379853i
$655$	1.30488e7	−	2.26011e7i	1.18841	−	2.05839i
$656$	−3.09712e6	−	5.36437e6i	−0.280995	−	0.486697i
$657$	−1.55324e7			−1.40386
$658$		0			0
$659$	1.38574e7			1.24299			0.621494	−	0.783419i	$-0.286526\pi$
$659$	1.38574e7			1.24299			0.621494	+	0.783419i	$0.286526\pi$
$660$	−7.44307e6	−	1.28918e7i	−0.665108	−	1.15200i
$661$	−6.03668e6	+	1.04558e7i	−0.537396	+	0.930797i	0.461647	+	0.887064i	$0.347259\pi$
$661$	−6.03668e6	+	1.04558e7i	−0.537396	+	0.930797i	−0.999043	+	0.0437334i	$0.986075\pi$
$662$	−111708.	+	193484.i	−0.00990693	+	0.0171593i
$663$	−982013.	−	1.70090e6i	−0.0867628	−	0.150278i
$664$	62949.6			0.00554080
$665$		0			0
$666$	9.62406e6			0.840761
$667$	3.26577e6	+	5.65648e6i	0.284231	+	0.492302i
$668$	−5.33183e6	+	9.23500e6i	−0.462312	+	0.800748i
$669$	−1.02211e6	+	1.77035e6i	−0.0882944	+	0.152930i
$670$	273081.	+	472991.i	0.0235020	+	0.0407067i
$671$	−1.01094e7			−0.866801
$672$		0			0
$673$	−5.32490e6			−0.453183			−0.226592	−	0.973990i	$-0.572758\pi$
$673$	−5.32490e6			−0.453183			−0.226592	+	0.973990i	$0.572758\pi$
$674$	1.59301e6	+	2.75917e6i	0.135073	+	0.233953i
$675$	4.29354e6	−	7.43662e6i	0.362707	−	0.628227i
$676$	−1.34553e6	+	2.33052e6i	−0.113247	+	0.196149i
$677$	−1.17259e7	−	2.03098e7i	−0.983274	−	1.70308i	−0.649370	−	0.760472i	$-0.724967\pi$
$677$	−1.17259e7	−	2.03098e7i	−0.983274	−	1.70308i	−0.333903	−	0.942607i	$-0.608366\pi$
$678$	−6.86560e6			−0.573594
$679$		0			0
$680$	−1.34784e6			−0.111781
$681$	−9.41335e6	−	1.63044e7i	−0.777815	−	1.34722i
$682$	−1.83033e6	+	3.17023e6i	−0.150685	+	0.260994i
$683$	−9.11349e6	+	1.57850e7i	−0.747538	+	1.29477i	0.201462	+	0.979496i	$0.435431\pi$
$683$	−9.11349e6	+	1.57850e7i	−0.747538	+	1.29477i	−0.949000	+	0.315277i	$0.897903\pi$
$684$	−1.15922e7	−	2.00782e7i	−0.947380	−	1.64091i
$685$	5.66261e6			0.461095
$686$		0			0
$687$	657072.			0.0531155
$688$	444768.	+	770361.i	0.0358230	+	0.0620473i
$689$	3.71140e6	−	6.42834e6i	0.297845	−	0.515882i
$690$	2.80051e6	−	4.85063e6i	0.223931	−	0.387860i
$691$	3.80429e6	+	6.58922e6i	0.303095	+	0.524976i	0.976835	−	0.213992i	$-0.0686468\pi$
$691$	3.80429e6	+	6.58922e6i	0.303095	+	0.524976i	−0.673740	+	0.738968i	$0.735313\pi$
$692$	1.44847e7			1.14986
$693$		0			0
$694$	6.67353e6			0.525965
$695$	−3.63636e6	−	6.29836e6i	−0.285565	−	0.494613i
$696$	−6.54376e6	+	1.13341e7i	−0.512040	+	0.886880i
$697$	−707616.	+	1.22563e6i	−0.0551716	+	0.0955600i
$698$	1.60259e6	+	2.77577e6i	0.124504	+	0.215648i
$699$	−1.18760e6			−0.0919341
$700$		0			0
$701$	314162.			0.0241467			0.0120734	−	0.999927i	$-0.496157\pi$
$701$	314162.			0.0241467			0.0120734	+	0.999927i	$0.496157\pi$
$702$	1.80835e6	+	3.13216e6i	0.138497	+	0.239884i
$703$	−1.37241e7	+	2.37709e7i	−1.04736	+	1.81408i
$704$	−1.51770e6	+	2.62873e6i	−0.115413	+	0.199900i
$705$	9.39927e6	+	1.62800e7i	0.712232	+	1.23362i
$706$	3.61930e6			0.273283
$707$		0			0
$708$	2.61556e7			1.96102
$709$	−1.24143e7	−	2.15021e7i	−0.927482	−	1.60645i	−0.787521	−	0.616288i	$-0.788636\pi$
$709$	−1.24143e7	−	2.15021e7i	−0.927482	−	1.60645i	−0.139961	−	0.990157i	$-0.544698\pi$
$710$	−2.67026e6	+	4.62503e6i	−0.198796	+	0.344325i
$711$	1.04043e7	−	1.80209e7i	0.771864	−	1.33691i
$712$	−1.22302e6	−	2.11833e6i	−0.0904136	−	0.156601i
$713$	9.64148e6			0.710264
$714$		0			0
$715$	−1.11646e7			−0.816730
$716$	8.54790e6	+	1.48054e7i	0.623127	+	1.07929i
$717$	1.36015e7	−	2.35585e7i	0.988073	−	1.71139i
$718$	920792.	−	1.59486e6i	0.0666577	−	0.115455i
$719$	8.59659e6	+	1.48897e7i	0.620160	+	1.07415i	0.989456	+	0.144837i	$0.0462658\pi$
$719$	8.59659e6	+	1.48897e7i	0.620160	+	1.07415i	−0.369295	+	0.929312i	$0.620401\pi$
$720$	−1.87302e7			−1.34651
$721$		0			0
$722$	−4.49391e6			−0.320835
$723$	1.68536e7	+	2.91913e7i	1.19908	+	2.07686i
$724$	6.07359e6	−	1.05198e7i	0.430624	−	0.745863i
$725$	5.43785e6	−	9.41864e6i	0.384222	−	0.665492i
$726$	2.00827e6	+	3.47842e6i	0.141410	+	0.244929i
$727$	2.12927e7			1.49415			0.747076	−	0.664739i	$-0.231457\pi$
$727$	2.12927e7			1.49415			0.747076	+	0.664739i	$0.231457\pi$
$728$		0			0
$729$	−2.33907e7			−1.63014
$730$	3.05510e6	+	5.29160e6i	0.212187	+	0.367519i
$731$	101619.	−	176009.i	0.00703363	−	0.0121826i
$732$	−1.24488e7	+	2.15620e7i	−0.858716	+	1.48734i
$733$	−9.80121e6	−	1.69762e7i	−0.673783	−	1.16703i	−0.976823	−	0.214048i	$-0.931335\pi$
$733$	−9.80121e6	−	1.69762e7i	−0.673783	−	1.16703i	0.303040	−	0.952978i	$-0.401998\pi$
$734$	2.69604e6			0.184708
$735$		0			0
$736$	−7.70739e6			−0.524461
$737$	−517448.	−	896246.i	−0.0350912	−	0.0607797i
$738$	3.59757e6	−	6.23117e6i	0.243147	−	0.421142i
$739$	−7.20905e6	+	1.24864e7i	−0.485587	+	0.841061i	−0.999863	−	0.0165639i	$-0.994727\pi$
$739$	−7.20905e6	+	1.24864e7i	−0.485587	+	0.841061i	0.514276	+	0.857625i	$0.328061\pi$
$740$	1.32509e7	+	2.29512e7i	0.889540	+	1.54073i
$741$	−2.84784e7			−1.90533
$742$		0			0
$743$	5.57521e6			0.370501			0.185250	−	0.982691i	$-0.440690\pi$
$743$	5.57521e6			0.370501			0.185250	+	0.982691i	$0.440690\pi$
$744$	9.65952e6	+	1.67308e7i	0.639769	+	1.10811i
$745$	1.35278e7	−	2.34308e7i	0.892969	−	1.54667i
$746$	3.13773e6	−	5.43471e6i	0.206428	−	0.357544i
$747$	−99932.5	−	173088.i	−0.00655247	−	0.0113492i
$748$	1.19185e6			0.0778872
$749$		0			0
$750$	2.37370e6			0.154089
$751$	−254400.	−	440634.i	−0.0164595	−	0.0285087i	0.857678	−	0.514187i	$-0.171906\pi$
$751$	−254400.	−	440634.i	−0.0164595	−	0.0285087i	−0.874138	+	0.485678i	$0.838573\pi$
$752$	3.29376e6	−	5.70496e6i	0.212397	−	0.367882i
$753$	−7.86895e6	+	1.36294e7i	−0.505743	+	0.875972i
$754$	2.29032e6	+	3.96694e6i	0.146712	+	0.254113i
$755$	−2.41906e6			−0.154447
$756$		0			0
$757$	1.10466e7			0.700631			0.350316	−	0.936632i	$-0.386074\pi$
$757$	1.10466e7			0.700631			0.350316	+	0.936632i	$0.386074\pi$
$758$	−1.83188e6	−	3.17292e6i	−0.115804	−	0.200579i
$759$	−5.30655e6	+	9.19121e6i	−0.334355	+	0.579120i
$760$	−9.77184e6	+	1.69253e7i	−0.613681	+	1.06293i
$761$	−3.38586e6	−	5.86449e6i	−0.211937	−	0.367086i	0.740383	−	0.672185i	$-0.234644\pi$
$761$	−3.38586e6	−	5.86449e6i	−0.211937	−	0.367086i	−0.952321	+	0.305098i	$0.901311\pi$
$762$	8.51158e6			0.531035
$763$		0			0
$764$	−9.55338e6			−0.592139
$765$	2.13970e6	+	3.70606e6i	0.132190	+	0.228960i
$766$	27727.8	−	48025.9i	0.00170743	−	0.00295736i
$767$	9.80834e6	−	1.69886e7i	0.602015	−	1.04272i
$768$	−380495.	−	659037.i	−0.0232780	−	0.0403187i
$769$	2.48053e7			1.51261			0.756307	−	0.654216i	$-0.227001\pi$
$769$	2.48053e7			1.51261			0.756307	+	0.654216i	$0.227001\pi$
$770$		0			0
$771$	−4.83126e7			−2.92701
$772$	−8.62621e6	−	1.49410e7i	−0.520927	−	0.902272i
$773$	−8.14759e6	+	1.41120e7i	−0.490434	+	0.849456i	−0.999939	−	0.0110113i	$-0.996495\pi$
$773$	−8.14759e6	+	1.41120e7i	−0.490434	+	0.849456i	0.509506	+	0.860467i	$0.329828\pi$
$774$	−516636.	+	894840.i	−0.0309979	+	0.0536899i
$775$	−8.02705e6	−	1.39033e7i	−0.480067	−	0.831500i
$776$	−2.20324e7			−1.31343
$777$		0			0
$778$	1.09668e6			0.0649580
$779$	1.02604e7	+	1.77716e7i	0.605790	+	1.04926i
$780$	−1.37482e7	+	2.38126e7i	−0.809113	+	1.40142i
$781$	5.05974e6	−	8.76373e6i	0.296825	−	0.514117i
$782$	224220.	+	388361.i	0.0131117	+	0.0227101i
$783$	1.50506e7			0.877305
$784$		0			0
$785$	−9.95717e6			−0.576716
$786$	−8.69918e6	−	1.50674e7i	−0.502253	−	0.869927i
$787$	−7.21069e6	+	1.24893e7i	−0.414992	+	0.718787i	−0.995428	−	0.0955188i	$-0.969549\pi$
$787$	−7.21069e6	+	1.24893e7i	−0.414992	+	0.718787i	0.580436	+	0.814306i	$0.302882\pi$
$788$	3.24069e6	−	5.61304e6i	0.185918	−	0.322020i
$789$	−1.39528e7	−	2.41670e7i	−0.797939	−	1.38207i
$790$	−8.18584e6			−0.466655
$791$		0			0
$792$	−1.29845e7			−0.735549
$793$	9.33660e6	+	1.61715e7i	0.527237	+	0.913201i
$794$	403852.	−	699491.i	0.0227337	−	0.0393760i
$795$	−1.32444e7	+	2.29400e7i	−0.743215	+	1.28729i
$796$	5.67176e6	+	9.82377e6i	0.317274	+	0.549535i
$797$	1.10109e6			0.0614014			0.0307007	−	0.999529i	$-0.490226\pi$
$797$	1.10109e6			0.0614014			0.0307007	+	0.999529i	$0.490226\pi$
$798$		0			0
$799$	−1.50509e6			−0.0834055
$800$	6.41682e6	+	1.11143e7i	0.354482	+	0.613981i
$801$	−3.88309e6	+	6.72571e6i	−0.213844	+	0.370388i
$802$	−4.16427e6	+	7.21273e6i	−0.228614	+	0.395972i
$803$	−5.78896e6	−	1.00268e7i	−0.316820	−	0.548748i
$804$	−2.54876e6			−0.139056
$805$		0			0
$806$	6.76166e6			0.366620
$807$	−1.89924e7	−	3.28958e7i	−1.02659	−	1.77810i
$808$	4.55485e6	−	7.88923e6i	0.245440	−	0.425115i
$809$	1.22573e7	−	2.12302e7i	0.658450	−	1.14047i	−0.322567	−	0.946547i	$-0.604546\pi$
$809$	1.22573e7	−	2.12302e7i	0.658450	−	1.14047i	0.981017	−	0.193922i	$-0.0621208\pi$
$810$	484937.	+	839935.i	0.0259700	+	0.0449814i
$811$	−3.03580e7			−1.62077			−0.810383	−	0.585900i	$-0.800741\pi$
$811$	−3.03580e7			−1.62077			−0.810383	+	0.585900i	$0.800741\pi$
$812$		0			0
$813$	2.54892e7			1.35247
$814$	3.58692e6	+	6.21273e6i	0.189741	+	0.328641i
$815$	−2.29931e6	+	3.98252e6i	−0.121256	+	0.210022i
$816$	1.22803e6	−	2.12701e6i	0.0645631	−	0.111827i
$817$	−1.47347e6	−	2.55212e6i	−0.0772300	−	0.133766i
$818$	−5.08243e6			−0.265576
$819$		0			0
$820$	1.98132e7			1.02901
$821$	1.27299e7	+	2.20489e7i	0.659126	+	1.14164i	0.980842	+	0.194804i	$0.0624072\pi$
$821$	1.27299e7	+	2.20489e7i	0.659126	+	1.14164i	−0.321716	+	0.946836i	$0.604260\pi$
$822$	1.88754e6	−	3.26931e6i	0.0974353	−	0.168763i
$823$	−2.97616e6	+	5.15486e6i	−0.153164	+	0.265288i	−0.932389	−	0.361456i	$-0.882280\pi$
$823$	−2.97616e6	+	5.15486e6i	−0.153164	+	0.265288i	0.779225	+	0.626744i	$0.215613\pi$
$824$	−656474.	−	1.13705e6i	−0.0336821	−	0.0583392i
$825$	1.76719e7			0.903961
$826$		0			0
$827$	−7.85900e6			−0.399580			−0.199790	−	0.979839i	$-0.564026\pi$
$827$	−7.85900e6			−0.399580			−0.199790	+	0.979839i	$0.564026\pi$
$828$	7.97966e6	+	1.38212e7i	0.404491	+	0.700599i
$829$	5.63208e6	−	9.75504e6i	0.284631	−	0.492995i	−0.687889	−	0.725816i	$-0.741462\pi$
$829$	5.63208e6	−	9.75504e6i	0.284631	−	0.492995i	0.972520	+	0.232821i	$0.0747956\pi$
$830$	−39312.0	+	68090.4i	−0.00198075	+	0.00343076i
$831$	2.36863e7	+	4.10259e7i	1.18986	+	2.06089i
$832$	5.60671e6			0.280802
$833$		0			0
$834$	−4.84848e6			−0.241374
$835$	−1.42703e7	−	2.47168e7i	−0.708297	−	1.22681i
$836$	8.64088e6	−	1.49664e7i	0.427604	−	0.740633i
$837$	1.11084e7	−	1.92404e7i	0.548075	−	0.949293i
$838$	2.30133e6	+	3.98602e6i	0.113206	+	0.196078i
$839$	7.80470e6			0.382782			0.191391	−	0.981514i	$-0.438700\pi$
$839$	7.80470e6			0.382782			0.191391	+	0.981514i	$0.438700\pi$
$840$		0			0
$841$	−1.44919e6			−0.0706539
$842$	−2.79991e6	−	4.84959e6i	−0.136102	−	0.235736i
$843$	1.64757e7	−	2.85367e7i	0.798499	−	1.38304i
$844$	1.08755e7	−	1.88369e7i	0.525524	−	0.910234i
$845$	−3.60120e6	−	6.23747e6i	−0.173503	−	0.300515i
$846$	7.65197e6			0.367576
$847$		0			0
$848$	9.28240e6			0.443272
$849$	−5.98010e6	−	1.03578e7i	−0.284734	−	0.493174i
$850$	373351.	−	646663.i	0.0177243	−	0.0306994i
$851$	9.44724e6	−	1.63631e7i	0.447179	−	0.774536i
$852$	−1.24612e7	−	2.15835e7i	−0.588114	−	1.01864i
$853$	−1.50581e7			−0.708593			−0.354296	−	0.935133i	$-0.615280\pi$
$853$	−1.50581e7			−0.708593			−0.354296	+	0.935133i	$0.615280\pi$
$854$		0			0
$855$	6.20512e7			2.90292
$856$	−1.30913e7	−	2.26748e7i	−0.610658	−	1.05769i
$857$	1.14368e7	−	1.98091e7i	0.531928	−	0.921327i	−0.467377	−	0.884058i	$-0.654801\pi$
$857$	1.14368e7	−	1.98091e7i	0.531928	−	0.921327i	0.999305	−	0.0372686i	$-0.0118657\pi$
$858$	−3.72154e6	+	6.44589e6i	−0.172585	+	0.298927i
$859$	4.11432e6	+	7.12621e6i	0.190246	+	0.329515i	0.945332	−	0.326111i	$-0.105738\pi$
$859$	4.11432e6	+	7.12621e6i	0.190246	+	0.329515i	−0.755086	+	0.655626i	$0.772405\pi$
$860$	−2.84532e6			−0.131185
$861$		0			0
$862$	−1.90864e6			−0.0874895
$863$	−2.04951e6	−	3.54985e6i	−0.0936748	−	0.162249i	0.815380	−	0.578926i	$-0.196528\pi$
$863$	−2.04951e6	−	3.54985e6i	−0.0936748	−	0.162249i	−0.909055	+	0.416677i	$0.863195\pi$
$864$	−8.88009e6	+	1.53808e7i	−0.404700	+	0.700960i
$865$	−1.93836e7	+	3.35734e7i	−0.880835	+	1.52565i
$866$	−519334.	−	899513.i	−0.0235316	−	0.0407580i
$867$	3.49069e7			1.57711
$868$		0			0
$869$	1.55109e7			0.696769
$870$	−8.17315e6	−	1.41563e7i	−0.366093	−	0.634092i
$871$	−955784.	+	1.65547e6i	−0.0426889	+	0.0739393i
$872$	5.76180e6	−	9.97973e6i	0.256606	−	0.444455i
$873$	3.49764e7	+	6.05808e7i	1.55324	+	2.69029i
$874$	6.50239e6			0.287935
$875$		0			0
$876$	−2.85143e7			−1.25546
$877$	−393889.	−	682236.i	−0.0172932	−	0.0299527i	0.857249	−	0.514902i	$-0.172172\pi$
$877$	−393889.	−	682236.i	−0.0172932	−	0.0299527i	−0.874542	+	0.484949i	$0.838838\pi$
$878$	−5.98081e6	+	1.03591e7i	−0.261833	+	0.453507i
$879$	−1.87584e7	+	3.24905e7i	−0.818885	+	1.41835i
$880$	−6.98081e6	−	1.20911e7i	−0.303878	−	0.526332i
$881$	−1.73321e7			−0.752336			−0.376168	−	0.926551i	$-0.622758\pi$
$881$	−1.73321e7			−0.752336			−0.376168	+	0.926551i	$0.622758\pi$
$882$		0			0
$883$	1.23991e7			0.535164			0.267582	−	0.963535i	$-0.413775\pi$
$883$	1.23991e7			0.535164			0.267582	+	0.963535i	$0.413775\pi$
$884$	−1.10074e6	−	1.90653e6i	−0.0473754	−	0.0820565i
$885$	−3.50018e7	+	6.06248e7i	−1.50221	+	2.60191i
$886$	3.74820e6	−	6.49208e6i	0.160413	−	0.277843i
$887$	−8.37776e6	−	1.45107e7i	−0.357535	−	0.619270i	0.630013	−	0.776585i	$-0.283050\pi$
$887$	−8.37776e6	−	1.45107e7i	−0.357535	−	0.619270i	−0.987548	+	0.157315i	$0.949716\pi$
$888$	3.78597e7			1.61118
$889$		0			0
$890$	3.05510e6			0.129286
$891$	−918882.	−	1.59155e6i	−0.0387762	−	0.0671624i
$892$	−1.14568e6	+	1.98438e6i	−0.0482117	+	0.0835050i
$893$	−1.09119e7	+	1.88999e7i	−0.457901	+	0.793107i
$894$	−9.01853e6	−	1.56205e7i	−0.377391	−	0.653661i
$895$	−4.57557e7			−1.90936
$896$		0			0
$897$	1.96036e7			0.813494
$898$	99458.0	+	172266.i	0.00411575	+	0.00712869i
$899$	1.40691e7	−	2.43684e7i	0.580586	−	1.00560i
$900$	1.32870e7	−	2.30137e7i	0.546790	−	0.947068i
$901$	−1.06040e6	−	1.83667e6i	−0.0435169	−	0.0753735i
$902$	5.36330e6			0.219491
$903$		0			0
$904$	−1.64906e7			−0.671145
$905$	1.62555e7	+	2.81554e7i	0.659750	+	1.14272i
$906$	−806354.	+	1.39665e6i	−0.0326366	+	0.0565283i
$907$	1.98271e7	−	3.43416e7i	0.800280	−	1.38613i	−0.119152	−	0.992876i	$-0.538018\pi$
$907$	1.98271e7	−	3.43416e7i	0.800280	−	1.38613i	0.919432	−	0.393249i	$-0.128649\pi$
$908$	−1.05514e7	−	1.82756e7i	−0.424713	−	0.735624i
$909$	−2.89233e7			−1.16102
$910$		0			0
$911$	2.99138e7			1.19419			0.597097	−	0.802169i	$-0.296321\pi$
$911$	2.99138e7			1.19419			0.597097	+	0.802169i	$0.296321\pi$
$912$	−1.78065e7	−	3.08417e7i	−0.708909	−	1.22787i
$913$	74490.3	−	129021.i	0.00295749	−	0.00512252i
$914$	−161814.	+	280270.i	−0.00640694	+	0.0110971i
$915$	−3.33183e7	−	5.77090e7i	−1.31562	−	2.27872i
$916$	736510.			0.0290028
$917$		0			0
$918$	1.03334e6			0.0404705
$919$	−9.94985e6	−	1.72336e7i	−0.388622	−	0.673113i	0.603642	−	0.797255i	$-0.293716\pi$
$919$	−9.94985e6	−	1.72336e7i	−0.388622	−	0.673113i	−0.992264	+	0.124142i	$0.960382\pi$
$920$	6.72661e6	−	1.16508e7i	0.262015	−	0.453824i
$921$	1.49451e7	−	2.58857e7i	0.580564	−	1.00557i
$922$	4.49198e6	+	7.78033e6i	0.174024	+	0.301419i
$923$	−1.86918e7			−0.722183
$924$		0			0
$925$	−3.14613e7			−1.20899
$926$	3.59382e6	+	6.22467e6i	0.137730	+	0.238555i
$927$	−2.08431e6	+	3.61012e6i	−0.0796640	+	0.137982i
$928$	−1.12468e7	+	1.94801e7i	−0.428706	+	0.742541i
$929$	5.98313e6	+	1.03631e7i	0.227452	+	0.393958i	0.957052	−	0.289916i	$-0.0936273\pi$
$929$	5.98313e6	+	1.03631e7i	0.227452	+	0.393958i	−0.729600	+	0.683874i	$0.760294\pi$
$930$	−2.41295e7			−0.914830
$931$		0			0
$932$	−1.33118e6			−0.0501991
$933$	1.64212e7	+	2.84423e7i	0.617590	+	1.06970i
$934$	−2.05223e6	+	3.55457e6i	−0.0769767	+	0.133327i
$935$	−1.59494e6	+	2.76252e6i	−0.0596646	+	0.103342i
$936$	1.19919e7	+	2.07706e7i	0.447402	+	0.774923i
$937$	6.18165e6			0.230015			0.115007	−	0.993365i	$-0.463311\pi$
$937$	6.18165e6			0.230015			0.115007	+	0.993365i	$0.463311\pi$
$938$		0			0
$939$	−6.62651e7			−2.45257
$940$	1.05356e7	+	1.82482e7i	0.388902	+	0.673598i
$941$	−1.49713e7	+	2.59311e7i	−0.551171	+	0.954656i	0.447020	+	0.894524i	$0.352485\pi$
$941$	−1.49713e7	+	2.59311e7i	−0.551171	+	0.954656i	−0.998190	+	0.0601315i	$0.980848\pi$
$942$	−3.31906e6	+	5.74877e6i	−0.121867	+	0.211080i
$943$	−7.06294e6	−	1.22334e7i	−0.258646	−	0.447989i
$944$	2.45312e7			0.895959
$945$		0			0
$946$	−770208.			−0.0279821
$947$	2.42139e7	+	4.19398e7i	0.877386	+	1.51968i	0.854199	+	0.519946i	$0.174048\pi$
$947$	2.42139e7	+	4.19398e7i	0.877386	+	1.51968i	0.0231865	+	0.999731i	$0.492619\pi$
$948$	1.91003e7	−	3.30827e7i	0.690271	−	1.19558i
$949$	−1.06929e7	+	1.85206e7i	−0.385415	+	0.667558i
$950$	−5.41359e6	−	9.37661e6i	−0.194615	−	0.337083i
$951$	3.99660e7			1.43298
$952$		0			0
$953$	2.26780e7			0.808860			0.404430	−	0.914569i	$-0.367470\pi$
$953$	2.26780e7			0.808860			0.404430	+	0.914569i	$0.367470\pi$
$954$	5.39115e6	+	9.33775e6i	0.191783	+	0.332178i
$955$	1.27845e7	−	2.21433e7i	0.453601	−	0.785660i
$956$	1.52459e7	−	2.64067e7i	0.539521	−	0.934477i
$957$	1.54869e7	+	2.68241e7i	0.546619	+	0.946771i
$958$	−3.99970e6			−0.140803
$959$		0			0
$960$	−2.00079e7			−0.700687
$961$	−6.45339e6	−	1.11776e7i	−0.225413	−	0.390427i
$962$	6.62544e6	−	1.14756e7i	0.230822	−	0.399795i
$963$	−4.15648e7	+	7.19924e7i	−1.44431	+	2.50162i
$964$	1.88912e7	+	3.27205e7i	0.654736	+	1.13404i
$965$	4.61749e7			1.59620
$966$		0			0
$967$	−3.60431e6			−0.123953			−0.0619764	−	0.998078i	$-0.519740\pi$
$967$	−3.60431e6			−0.123953			−0.0619764	+	0.998078i	$0.519740\pi$
$968$	4.82370e6	+	8.35489e6i	0.165460	+	0.286584i
$969$	−4.06834e6	+	7.04657e6i	−0.139190	+	0.241084i
$970$	1.37592e7	−	2.38316e7i	0.469531	−	0.813251i
$971$	1.45403e7	+	2.51846e7i	0.494910	+	0.857210i	0.999983	−	0.00586710i	$-0.00186757\pi$
$971$	1.45403e7	+	2.51846e7i	0.494910	+	0.857210i	−0.505072	+	0.863077i	$0.668534\pi$
$972$	−2.79811e7			−0.949946
$973$		0			0
$974$	−4.34251e6			−0.146671
$975$	−1.63210e7	−	2.82689e7i	−0.549840	−	0.952350i
$976$	−1.16756e7	+	2.02228e7i	−0.392334	+	0.679543i
$977$	9.09799e6	−	1.57582e7i	0.304936	−	0.528165i	−0.672311	−	0.740269i	$-0.734698\pi$
$977$	9.09799e6	−	1.57582e7i	0.304936	−	0.528165i	0.977247	+	0.212104i	$0.0680315\pi$
$978$	1.53287e6	+	2.65501e6i	0.0512459	+	0.0887604i
$979$	−5.78896e6			−0.193039
$980$		0			0
$981$	−3.65874e7			−1.21383
$982$	3.04555e6	+	5.27504e6i	0.100783	+	0.174561i
$983$	−1.66404e6	+	2.88221e6i	−0.0549263	+	0.0951352i	−0.892181	−	0.451678i	$-0.850826\pi$
$983$	−1.66404e6	+	2.88221e6i	−0.0549263	+	0.0951352i	0.837255	+	0.546813i	$0.184159\pi$
$984$	1.41523e7	−	2.45125e7i	0.465951	−	0.807050i
$985$	8.67348e6	+	1.50229e7i	0.284841	+	0.493359i
$986$	1.30875e6			0.0428711
$987$		0			0
$988$	−3.19213e7			−1.04037
$989$	1.01429e6	+	1.75680e6i	0.0329739	+	0.0571125i
$990$	8.10881e6	−	1.40449e7i	0.262947	−	0.455438i
$991$	−2.62710e7	+	4.55027e7i	−0.849753	+	1.47182i	0.0316758	+	0.999498i	$0.489916\pi$
$991$	−2.62710e7	+	4.55027e7i	−0.849753	+	1.47182i	−0.881429	+	0.472317i	$0.843418\pi$
$992$	1.66019e7	+	2.87553e7i	0.535647	+	0.927768i
$993$	2.79046e6			0.0898056
$994$		0			0
$995$	−3.03601e7			−0.972177
$996$	−183456.	−	317755.i	−0.00585981	−	0.0101495i
$997$	614995.	−	1.06520e6i	0.0195945	−	0.0339386i	−0.856062	−	0.516873i	$-0.827096\pi$
$997$	614995.	−	1.06520e6i	0.0195945	−	0.0339386i	0.875656	+	0.482935i	$0.160429\pi$
$998$	−7.99225e6	+	1.38430e7i	−0.254005	+	0.439950i
$999$	−2.17693e7	−	3.77056e7i	−0.690130	−	1.19534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.g.18.2		4
7.2	even	3	inner	49.6.c.g.30.2		4
7.3	odd	6		49.6.a.c.1.2	yes	2
7.4	even	3		49.6.a.c.1.1	✓	2
7.5	odd	6	inner	49.6.c.g.30.1		4
7.6	odd	2	inner	49.6.c.g.18.1		4
21.11	odd	6		441.6.a.u.1.2		2
21.17	even	6		441.6.a.u.1.1		2
28.3	even	6		784.6.a.z.1.1		2
28.11	odd	6		784.6.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.a.c.1.1	✓	2	7.4	even	3
49.6.a.c.1.2	yes	2	7.3	odd	6
49.6.c.g.18.1		4	7.6	odd	2	inner
49.6.c.g.18.2		4	1.1	even	1	trivial
49.6.c.g.30.1		4	7.5	odd	6	inner
49.6.c.g.30.2		4	7.2	even	3	inner
441.6.a.u.1.1		2	21.17	even	6
441.6.a.u.1.2		2	21.11	odd	6
784.6.a.z.1.1		2	28.3	even	6
784.6.a.z.1.2		2	28.11	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(12.4900 - 21.6333i) q^{3} +(14.0000 - 24.2487i) q^{4} +(37.4700 + 64.8999i) q^{5} +49.9600 q^{6} +120.000 q^{8} +(-190.500 - 329.956i) q^{9} +(-74.9400 + 129.800i) q^{10} +(142.000 - 245.951i) q^{11} +(-349.720 - 605.733i) q^{12} -524.580 q^{13} +1872.00 q^{15} +(-328.000 - 568.113i) q^{16} +(-74.9400 + 129.800i) q^{17} +(381.000 - 659.911i) q^{18} +(1086.63 + 1882.10i) q^{19} +2098.32 q^{20} +568.000 q^{22} +(-748.000 - 1295.57i) q^{23} +(1498.80 - 2596.00i) q^{24} +(-1245.50 + 2157.27i) q^{25} +(-524.580 - 908.599i) q^{26} -3447.24 q^{27} -4366.00 q^{29} +(1872.00 + 3242.40i) q^{30} +(-3222.42 + 5581.39i) q^{31} +(2576.00 - 4461.76i) q^{32} +(-3547.16 - 6143.86i) q^{33} -299.760 q^{34} -10668.0 q^{36} +(6315.00 + 10937.9i) q^{37} +(-2173.26 + 3764.20i) q^{38} +(-6552.00 + 11348.4i) q^{39} +(4496.40 + 7787.99i) q^{40} +9442.44 q^{41} -1356.00 q^{43} +(-3976.00 - 6886.63i) q^{44} +(14276.1 - 24726.9i) q^{45} +(1496.00 - 2591.15i) q^{46} +(5020.98 + 8696.59i) q^{47} -16386.9 q^{48} -4982.00 q^{50} +(1872.00 + 3242.40i) q^{51} +(-7344.12 + 12720.4i) q^{52} +(-7075.00 + 12254.3i) q^{53} +(-3447.24 - 5970.79i) q^{54} +21283.0 q^{55} +54288.0 q^{57} +(-4366.00 - 7562.13i) q^{58} +(-18697.5 + 32385.1i) q^{59} +(26208.0 - 45393.6i) q^{60} +(-17798.2 - 30827.5i) q^{61} -12889.7 q^{62} -10688.0 q^{64} +(-19656.0 - 34045.2i) q^{65} +(7094.32 - 12287.7i) q^{66} +(1822.00 - 3155.80i) q^{67} +(2098.32 + 3634.40i) q^{68} -37370.1 q^{69} +35632.0 q^{71} +(-22860.0 - 39594.7i) q^{72} +(20383.7 - 35305.6i) q^{73} +(-12630.0 + 21875.8i) q^{74} +(31112.6 + 53888.6i) q^{75} +60851.3 q^{76} -26208.0 q^{78} +(27308.0 + 47298.8i) q^{79} +(24580.3 - 42574.3i) q^{80} +(3235.50 - 5604.05i) q^{81} +(9442.44 + 16354.8i) q^{82} +524.580 q^{83} -11232.0 q^{85} +(-1356.00 - 2348.66i) q^{86} +(-54531.3 + 94451.0i) q^{87} +(17040.0 - 29514.1i) q^{88} +(-10191.8 - 17652.8i) q^{89} +57104.3 q^{90} -41888.0 q^{92} +(80496.0 + 139423. i) q^{93} +(-10042.0 + 17393.2i) q^{94} +(-81432.0 + 141044. i) q^{95} +(-64348.5 - 111455. i) q^{96} -183603. q^{97} -108204. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 56 q^{4} + 480 q^{8} - 762 q^{9} + 568 q^{11} + 7488 q^{15} - 1312 q^{16} + 1524 q^{18} + 2272 q^{22} - 2992 q^{23} - 4982 q^{25} - 17464 q^{29} + 7488 q^{30} + 10304 q^{32} - 42672 q^{36}+ \cdots - 432816 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 56 * q^4 + 480 * q^8 - 762 * q^9 + 568 * q^11 + 7488 * q^15 - 1312 * q^16 + 1524 * q^18 + 2272 * q^22 - 2992 * q^23 - 4982 * q^25 - 17464 * q^29 + 7488 * q^30 + 10304 * q^32 - 42672 * q^36 + 25260 * q^37 - 26208 * q^39 - 5424 * q^43 - 15904 * q^44 + 5984 * q^46 - 19928 * q^50 + 7488 * q^51 - 28300 * q^53 + 217152 * q^57 - 17464 * q^58 + 104832 * q^60 - 42752 * q^64 - 78624 * q^65 + 7288 * q^67 + 142528 * q^71 - 91440 * q^72 - 50520 * q^74 - 104832 * q^78 + 109232 * q^79 + 12942 * q^81 - 44928 * q^85 - 5424 * q^86 + 68160 * q^88 - 167552 * q^92 + 321984 * q^93 - 325728 * q^95 - 432816 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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