LMFDB - Embedded newform 49.6.c.d.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.6.c.d.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.13746 + 7.16629i) q^{2} +(-12.8248 - 22.2131i) q^{3} +(-18.2371 - 31.5876i) q^{4} +(14.3746 - 24.8975i) q^{5} +212.248 q^{6} +37.0241 q^{8} +(-207.449 + 359.311i) q^{9} +O(q^{10})$	\(q+(-4.13746 + 7.16629i) q^{2} +(-12.8248 - 22.2131i) q^{3} +(-18.2371 - 31.5876i) q^{4} +(14.3746 - 24.8975i) q^{5} +212.248 q^{6} +37.0241 q^{8} +(-207.449 + 359.311i) q^{9} +(118.949 + 206.025i) q^{10} +(135.045 + 233.905i) q^{11} +(-467.773 + 810.207i) q^{12} -300.640 q^{13} -737.402 q^{15} +(430.402 - 745.479i) q^{16} +(306.553 + 530.966i) q^{17} +(-1716.62 - 2973.27i) q^{18} +(-850.474 + 1473.06i) q^{19} -1048.60 q^{20} -2234.97 q^{22} +(-1594.08 + 2761.02i) q^{23} +(-474.825 - 822.421i) q^{24} +(1149.24 + 1990.55i) q^{25} +(1243.88 - 2154.47i) q^{26} +4409.07 q^{27} +4299.28 q^{29} +(3050.97 - 5284.44i) q^{30} +(1014.23 + 1756.69i) q^{31} +(4153.93 + 7194.82i) q^{32} +(3463.83 - 5999.54i) q^{33} -5073.40 q^{34} +15133.1 q^{36} +(-2577.23 + 4463.89i) q^{37} +(-7037.60 - 12189.5i) q^{38} +(3855.63 + 6678.14i) q^{39} +(532.206 - 921.808i) q^{40} +7146.21 q^{41} -19584.3 q^{43} +(4925.66 - 8531.49i) q^{44} +(5963.97 + 10329.9i) q^{45} +(-13190.9 - 22847.2i) q^{46} +(9999.19 - 17319.1i) q^{47} -22079.2 q^{48} -19019.8 q^{50} +(7862.94 - 13619.0i) q^{51} +(5482.80 + 9496.49i) q^{52} +(-1974.41 - 3419.78i) q^{53} +(-18242.4 + 31596.7i) q^{54} +7764.86 q^{55} +43628.5 q^{57} +(-17788.1 + 30809.9i) q^{58} +(-14853.8 - 25727.5i) q^{59} +(13448.1 + 23292.8i) q^{60} +(-25259.6 + 43751.0i) q^{61} -16785.3 q^{62} -41201.1 q^{64} +(-4321.57 + 7485.18i) q^{65} +(28662.9 + 49645.7i) q^{66} +(-2526.78 - 4376.51i) q^{67} +(11181.3 - 19366.6i) q^{68} +81774.5 q^{69} +32853.3 q^{71} +(-7680.59 + 13303.2i) q^{72} +(-5557.48 - 9625.84i) q^{73} +(-21326.3 - 36938.3i) q^{74} +(29477.5 - 51056.5i) q^{75} +62040.8 q^{76} -63810.0 q^{78} +(-40944.7 + 70918.3i) q^{79} +(-12373.7 - 21431.9i) q^{80} +(-6135.28 - 10626.6i) q^{81} +(-29567.1 + 51211.8i) q^{82} -118234. q^{83} +17626.3 q^{85} +(81029.2 - 140347. i) q^{86} +(-55137.2 - 95500.4i) q^{87} +(4999.91 + 8660.10i) q^{88} +(-20847.7 + 36109.2i) q^{89} -98702.8 q^{90} +116286. q^{92} +(26014.4 - 45058.3i) q^{93} +(82742.5 + 143314. i) q^{94} +(24450.4 + 42349.4i) q^{95} +(106546. - 184544. i) q^{96} -43682.8 q^{97} -112059. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9}+O(q^{10}) $ 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9} + 204 q^{10} - 396 q^{11} - 1554 q^{12} + 700 q^{13} - 3312 q^{15} - 113 q^{16} + 1800 q^{17} - 3537 q^{18} - 3266 q^{19} - 5040 q^{20} - 3504 q^{22} - 2088 q^{23} - 1854 q^{24} + 3238 q^{25} + 2016 q^{26} + 12744 q^{27} + 13392 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 20016 q^{33} - 11868 q^{34} + 21258 q^{36} - 6232 q^{37} - 15210 q^{38} + 20496 q^{39} + 3216 q^{40} + 12096 q^{41} - 6040 q^{43} + 30816 q^{44} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} - 82428 q^{48} - 39402 q^{50} - 7596 q^{51} + 31444 q^{52} - 9468 q^{53} - 37908 q^{54} + 77808 q^{55} + 25752 q^{57} - 37314 q^{58} - 43938 q^{59} - 2016 q^{60} - 64754 q^{61} - 30600 q^{62} - 141566 q^{64} - 39060 q^{65} + 66816 q^{66} - 24784 q^{67} - 14994 q^{68} + 206784 q^{69} + 194832 q^{71} - 8775 q^{72} + 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 25564 q^{76} - 146160 q^{78} - 51256 q^{79} - 70272 q^{80} + 61074 q^{81} - 58338 q^{82} - 235116 q^{83} - 75720 q^{85} + 150048 q^{86} - 63180 q^{87} + 40656 q^{88} + 84276 q^{89} - 187704 q^{90} + 301824 q^{92} + 92280 q^{93} + 159468 q^{94} - 24264 q^{95} + 255906 q^{96} - 41552 q^{97} - 33480 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9 + 204 * q^10 - 396 * q^11 - 1554 * q^12 + 700 * q^13 - 3312 * q^15 - 113 * q^16 + 1800 * q^17 - 3537 * q^18 - 3266 * q^19 - 5040 * q^20 - 3504 * q^22 - 2088 * q^23 - 1854 * q^24 + 3238 * q^25 + 2016 * q^26 + 12744 * q^27 + 13392 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 20016 * q^33 - 11868 * q^34 + 21258 * q^36 - 6232 * q^37 - 15210 * q^38 + 20496 * q^39 + 3216 * q^40 + 12096 * q^41 - 6040 * q^43 + 30816 * q^44 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 - 82428 * q^48 - 39402 * q^50 - 7596 * q^51 + 31444 * q^52 - 9468 * q^53 - 37908 * q^54 + 77808 * q^55 + 25752 * q^57 - 37314 * q^58 - 43938 * q^59 - 2016 * q^60 - 64754 * q^61 - 30600 * q^62 - 141566 * q^64 - 39060 * q^65 + 66816 * q^66 - 24784 * q^67 - 14994 * q^68 + 206784 * q^69 + 194832 * q^71 - 8775 * q^72 + 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 25564 * q^76 - 146160 * q^78 - 51256 * q^79 - 70272 * q^80 + 61074 * q^81 - 58338 * q^82 - 235116 * q^83 - 75720 * q^85 + 150048 * q^86 - 63180 * q^87 + 40656 * q^88 + 84276 * q^89 - 187704 * q^90 + 301824 * q^92 + 92280 * q^93 + 159468 * q^94 - 24264 * q^95 + 255906 * q^96 - 41552 * q^97 - 33480 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−4.13746	+	7.16629i	−0.731406	+	1.26683i	0.224876	+	0.974387i	$0.427802\pi$
$2$	−4.13746	+	7.16629i	−0.731406	+	1.26683i	−0.956282	+	0.292445i	$0.905531\pi$
$3$	−12.8248	−	22.2131i	−0.822708	−	1.42497i	−0.903658	−	0.428254i	$-0.859129\pi$
$3$	−12.8248	−	22.2131i	−0.822708	−	1.42497i	0.0809501	−	0.996718i	$-0.474205\pi$
$4$	−18.2371	−	31.5876i	−0.569910	−	0.987113i
$5$	14.3746	−	24.8975i	0.257140	−	0.445380i	−0.708334	−	0.705877i	$-0.750553\pi$
$5$	14.3746	−	24.8975i	0.257140	−	0.445380i	0.965475	+	0.260497i	$0.0838864\pi$
$6$	212.248			2.40694
$7$		0			0
$7$		0			0
$8$	37.0241			0.204531
$9$	−207.449	+	359.311i	−0.853698	+	1.47865i
$10$	118.949	+	206.025i	0.376148	+	0.651508i
$11$	135.045	+	233.905i	0.336509	+	0.582850i	0.983773	−	0.179415i	$-0.0574205\pi$
$11$	135.045	+	233.905i	0.336509	+	0.582850i	−0.647265	+	0.762265i	$0.724087\pi$
$12$	−467.773	+	810.207i	−0.937740	+	1.62421i
$13$	−300.640			−0.493387			−0.246694	−	0.969094i	$-0.579344\pi$
$13$	−300.640			−0.493387			−0.246694	+	0.969094i	$0.579344\pi$
$14$		0			0
$15$	−737.402			−0.846206
$16$	430.402	−	745.479i	0.420315	−	0.728007i
$17$	306.553	+	530.966i	0.257267	+	0.445599i	0.965509	−	0.260371i	$-0.0838448\pi$
$17$	306.553	+	530.966i	0.257267	+	0.445599i	−0.708242	+	0.705970i	$0.750511\pi$
$18$	−1716.62	−	2973.27i	−1.24880	−	2.16298i
$19$	−850.474	+	1473.06i	−0.540477	+	0.936134i	0.458400	+	0.888746i	$0.348423\pi$
$19$	−850.474	+	1473.06i	−0.540477	+	0.936134i	−0.998877	+	0.0473873i	$0.984910\pi$
$20$	−1048.60			−0.586188
$21$		0			0
$22$	−2234.97			−0.984498
$23$	−1594.08	+	2761.02i	−0.628333	+	1.08830i	0.359554	+	0.933124i	$0.382929\pi$
$23$	−1594.08	+	2761.02i	−0.628333	+	1.08830i	−0.987886	+	0.155180i	$0.950404\pi$
$24$	−474.825	−	822.421i	−0.168269	−	0.291451i
$25$	1149.24	+	1990.55i	0.367758	+	0.636975i
$26$	1243.88	−	2154.47i	0.360866	−	0.625039i
$27$	4409.07			1.16396
$28$		0			0
$29$	4299.28			0.949294			0.474647	−	0.880176i	$-0.342576\pi$
$29$	4299.28			0.949294			0.474647	+	0.880176i	$0.342576\pi$
$30$	3050.97	−	5284.44i	0.618920	−	1.07200i
$31$	1014.23	+	1756.69i	0.189553	+	0.328316i	0.945101	−	0.326777i	$-0.105963\pi$
$31$	1014.23	+	1756.69i	0.189553	+	0.328316i	−0.755548	+	0.655093i	$0.772629\pi$
$32$	4153.93	+	7194.82i	0.717107	+	1.24207i
$33$	3463.83	−	5999.54i	0.553697	−	0.959031i
$34$	−5073.40			−0.752666
$35$		0			0
$36$	15133.1			1.94612
$37$	−2577.23	+	4463.89i	−0.309491	+	0.536055i	−0.978251	−	0.207424i	$-0.933492\pi$
$37$	−2577.23	+	4463.89i	−0.309491	+	0.536055i	0.668760	+	0.743478i	$0.266825\pi$
$38$	−7037.60	−	12189.5i	−0.790616	−	1.36939i
$39$	3855.63	+	6678.14i	0.405914	+	0.703063i
$40$	532.206	−	921.808i	0.0525932	−	0.0910941i
$41$	7146.21			0.663921			0.331960	−	0.943293i	$-0.392290\pi$
$41$	7146.21			0.663921			0.331960	+	0.943293i	$0.392290\pi$
$42$		0			0
$43$	−19584.3			−1.61524			−0.807620	−	0.589703i	$-0.799245\pi$
$43$	−19584.3			−1.61524			−0.807620	+	0.589703i	$0.799245\pi$
$44$	4925.66	−	8531.49i	0.383560	−	0.664345i
$45$	5963.97	+	10329.9i	0.439040	+	0.760440i
$46$	−13190.9	−	22847.2i	−0.919133	−	1.59198i
$47$	9999.19	−	17319.1i	0.660268	−	1.14362i	−0.320277	−	0.947324i	$-0.603776\pi$
$47$	9999.19	−	17319.1i	0.660268	−	1.14362i	0.980545	−	0.196294i	$-0.0628907\pi$
$48$	−22079.2			−1.38319
$49$		0			0
$50$	−19019.8			−1.07592
$51$	7862.94	−	13619.0i	0.423311	−	0.733196i
$52$	5482.80	+	9496.49i	0.281186	+	0.487029i
$53$	−1974.41	−	3419.78i	−0.0965489	−	0.167228i	0.813705	−	0.581278i	$-0.197447\pi$
$53$	−1974.41	−	3419.78i	−0.0965489	−	0.167228i	−0.910254	+	0.414050i	$0.864114\pi$
$54$	−18242.4	+	31596.7i	−0.851327	+	1.47454i
$55$	7764.86			0.346120
$56$		0			0
$57$	43628.5			1.77862
$58$	−17788.1	+	30809.9i	−0.694319	+	1.20260i
$59$	−14853.8	−	25727.5i	−0.555530	−	0.962206i	−0.997862	−	0.0653544i	$-0.979182\pi$
$59$	−14853.8	−	25727.5i	−0.555530	−	0.962206i	0.442332	−	0.896851i	$-0.354151\pi$
$60$	13448.1	+	23292.8i	0.482262	+	0.835301i
$61$	−25259.6	+	43751.0i	−0.869165	+	1.50544i	−0.00631412	+	0.999980i	$0.502010\pi$
$61$	−25259.6	+	43751.0i	−0.869165	+	1.50544i	−0.862851	+	0.505458i	$0.831323\pi$
$62$	−16785.3			−0.554562
$63$		0			0
$64$	−41201.1			−1.25736
$65$	−4321.57	+	7485.18i	−0.126870	+	0.219745i
$66$	28662.9	+	49645.7i	0.809955	+	1.40288i
$67$	−2526.78	−	4376.51i	−0.0687671	−	0.119108i	0.829592	−	0.558370i	$-0.188573\pi$
$67$	−2526.78	−	4376.51i	−0.0687671	−	0.119108i	−0.898359	+	0.439262i	$0.855240\pi$
$68$	11181.3	−	19366.6i	0.293238	−	0.507903i
$69$	81774.5			2.06774
$70$		0			0
$71$	32853.3			0.773453			0.386726	−	0.922195i	$-0.373606\pi$
$71$	32853.3			0.773453			0.386726	+	0.922195i	$0.373606\pi$
$72$	−7680.59	+	13303.2i	−0.174608	+	0.302429i
$73$	−5557.48	−	9625.84i	−0.122059	−	0.211413i	0.798520	−	0.601968i	$-0.205616\pi$
$73$	−5557.48	−	9625.84i	−0.122059	−	0.211413i	−0.920580	+	0.390555i	$0.872283\pi$
$74$	−21326.3	−	36938.3i	−0.452728	−	0.784148i
$75$	29477.5	−	51056.5i	0.605114	−	1.04809i
$76$	62040.8			1.23209
$77$		0			0
$78$	−63810.0			−1.18755
$79$	−40944.7	+	70918.3i	−0.738125	+	1.27847i	0.215214	+	0.976567i	$0.430955\pi$
$79$	−40944.7	+	70918.3i	−0.738125	+	1.27847i	−0.953339	+	0.301903i	$0.902378\pi$
$80$	−12373.7	−	21431.9i	−0.216160	−	0.374400i
$81$	−6135.28	−	10626.6i	−0.103902	−	0.179963i
$82$	−29567.1	+	51211.8i	−0.485596	+	0.841076i
$83$	−118234.			−1.88385			−0.941926	−	0.335819i	$-0.890987\pi$
$83$	−118234.			−1.88385			−0.941926	+	0.335819i	$0.890987\pi$
$84$		0			0
$85$	17626.3			0.264615
$86$	81029.2	−	140347.i	1.18140	−	2.04624i
$87$	−55137.2	−	95500.4i	−0.780992	−	1.35272i
$88$	4999.91	+	8660.10i	0.0688265	+	0.119211i
$89$	−20847.7	+	36109.2i	−0.278986	+	0.483218i	−0.971133	−	0.238538i	$-0.923332\pi$
$89$	−20847.7	+	36109.2i	−0.278986	+	0.483218i	0.692147	+	0.721757i	$0.256665\pi$
$90$	−98702.8			−1.28447
$91$		0			0
$92$	116286.			1.43237
$93$	26014.4	−	45058.3i	0.311894	−	0.540216i
$94$	82742.5	+	143314.i	0.965849	+	1.67290i
$95$	24450.4	+	42349.4i	0.277957	+	0.481436i
$96$	106546.	−	184544.i	1.17994	−	2.04372i
$97$	−43682.8			−0.471391			−0.235695	−	0.971827i	$-0.575737\pi$
$97$	−43682.8			−0.471391			−0.235695	+	0.971827i	$0.575737\pi$
$98$		0			0
$99$	−112059.			−1.14911
$100$	41917.8	−	72603.7i	0.419178	−	0.726037i
$101$	12824.0	+	22211.9i	0.125090	+	0.216662i	0.921768	−	0.387742i	$-0.126745\pi$
$101$	12824.0	+	22211.9i	0.125090	+	0.216662i	−0.796678	+	0.604404i	$0.793411\pi$
$102$	65065.1	+	112696.i	0.619224	+	1.07253i
$103$	−7160.02	+	12401.5i	−0.0664999	+	0.115181i	−0.897358	−	0.441303i	$-0.854517\pi$
$103$	−7160.02	+	12401.5i	−0.0664999	+	0.115181i	0.830858	+	0.556484i	$0.187850\pi$
$104$	−11130.9			−0.100913
$105$		0			0
$106$	32676.1			0.282466
$107$	−8600.89	+	14897.2i	−0.0726247	+	0.125790i	−0.900051	−	0.435785i	$-0.856471\pi$
$107$	−8600.89	+	14897.2i	−0.0726247	+	0.125790i	0.827426	+	0.561574i	$0.189804\pi$
$108$	−80408.8	−	139272.i	−0.663352	−	1.14896i
$109$	43008.8	+	74493.4i	0.346730	+	0.600553i	0.985666	−	0.168706i	$-0.0539588\pi$
$109$	43008.8	+	74493.4i	0.346730	+	0.600553i	−0.638937	+	0.769259i	$0.720625\pi$
$110$	−32126.8	+	55645.2i	−0.253154	+	0.438476i
$111$	132209.			1.01848
$112$		0			0
$113$	137568.			1.01349			0.506745	−	0.862096i	$-0.330848\pi$
$113$	137568.			1.01349			0.506745	+	0.862096i	$0.330848\pi$
$114$	−180511.	+	312654.i	−1.30089	+	2.25321i
$115$	45828.4	+	79377.1i	0.323139	+	0.559694i
$116$	−78406.5	−	135804.i	−0.541012	−	0.937061i
$117$	62367.2	−	108023.i	0.421203	−	0.729546i
$118$	245828.			1.62527
$119$		0			0
$120$	−27301.6			−0.173075
$121$	44051.3	−	76299.0i	0.273524	−	0.473757i
$122$	−209021.	−	362036.i	−1.27143	−	2.20217i
$123$	−91648.4	−	158740.i	−0.546213	−	0.946068i
$124$	36993.2	−	64074.1i	0.216057	−	0.374221i
$125$	155921.			0.892542
$126$		0			0
$127$	−70567.1			−0.388233			−0.194117	−	0.980978i	$-0.562184\pi$
$127$	−70567.1			−0.388233			−0.194117	+	0.980978i	$0.562184\pi$
$128$	37542.1	−	65024.8i	0.202532	−	0.350795i
$129$	251164.	+	435029.i	1.32887	+	2.30167i
$130$	−35760.6	−	61939.2i	−0.185587	−	0.321446i
$131$	−86856.2	+	150439.i	−0.442204	+	0.765920i	−0.997853	−	0.0654972i	$-0.979137\pi$
$131$	−86856.2	+	150439.i	−0.442204	+	0.765920i	0.555649	+	0.831417i	$0.312470\pi$
$132$	−252682.			−1.26223
$133$		0			0
$134$	41817.8			0.201187
$135$	63378.6	−	109775.i	0.299301	−	0.518405i
$136$	11349.9	+	19658.5i	0.0526190	+	0.0911388i
$137$	994.971	+	1723.34i	0.00452907	+	0.00784457i	0.868281	−	0.496073i	$-0.165225\pi$
$137$	994.971	+	1723.34i	0.00452907	+	0.00784457i	−0.863752	+	0.503917i	$0.831892\pi$
$138$	−338339.	+	586020.i	−1.51236	+	2.61948i
$139$	−366409.			−1.60853			−0.804264	−	0.594272i	$-0.797440\pi$
$139$	−366409.			−1.60853			−0.804264	+	0.594272i	$0.797440\pi$
$140$		0			0
$141$	−512949.			−2.17283
$142$	−135929.	+	235437.i	−0.565708	+	0.979835i
$143$	−40599.8	−	70321.0i	−0.166029	−	0.287571i
$144$	178573.	+	309297.i	0.717644	+	1.24300i
$145$	61800.4	−	107041.i	0.244102	−	0.422797i
$146$	91975.4			0.357100
$147$		0			0
$148$	188005.			0.705529
$149$	−70359.3	+	121866.i	−0.259631	+	0.449693i	−0.966143	−	0.258007i	$-0.916934\pi$
$149$	−70359.3	+	121866.i	−0.259631	+	0.449693i	0.706512	+	0.707701i	$0.250267\pi$
$150$	243924.	+	422489.i	0.885169	+	1.53316i
$151$	−25032.3	−	43357.2i	−0.0893425	−	0.154746i	0.817891	−	0.575373i	$-0.195143\pi$
$151$	−25032.3	−	43357.2i	−0.0893425	−	0.154746i	−0.907233	+	0.420628i	$0.861810\pi$
$152$	−31488.0	+	54538.9i	−0.110544	+	0.191468i
$153$	−254376.			−0.878512
$154$		0			0
$155$	58316.4			0.194967
$156$	140631.	−	243580.i	0.462669	−	0.801366i
$157$	−44897.3	−	77764.4i	−0.145369	−	0.251786i	0.784142	−	0.620582i	$-0.213104\pi$
$157$	−44897.3	−	77764.4i	−0.145369	−	0.251786i	−0.929510	+	0.368796i	$0.879770\pi$
$158$	−338814.	−	586843.i	−1.07974	−	1.87016i
$159$	−50642.6	+	87715.6i	−0.158863	+	0.275159i
$160$	238844.			0.737589
$161$		0			0
$162$	101538.			0.303977
$163$	240615.	−	416758.i	0.709339	−	1.22861i	−0.255764	−	0.966739i	$-0.582327\pi$
$163$	240615.	−	416758.i	0.709339	−	1.22861i	0.965103	−	0.261872i	$-0.0843398\pi$
$164$	−130326.	−	225732.i	−0.378375	−	0.655365i
$165$	−99582.4	−	172482.i	−0.284756	−	0.493211i
$166$	489188.	−	847299.i	1.37786	−	2.38653i
$167$	86572.7			0.240209			0.120105	−	0.992761i	$-0.461677\pi$
$167$	86572.7			0.240209			0.120105	+	0.992761i	$0.461677\pi$
$168$		0			0
$169$	−280909.			−0.756569
$170$	−72928.1	+	126315.i	−0.193541	+	0.335222i
$171$	−352859.	−	611170.i	−0.922808	−	1.59835i
$172$	357161.	+	618622.i	0.920542	+	1.59442i
$173$	−29068.7	+	50348.5i	−0.0738432	+	0.127900i	−0.900583	−	0.434685i	$-0.856860\pi$
$173$	−29068.7	+	50348.5i	−0.0738432	+	0.127900i	0.826739	+	0.562585i	$0.190193\pi$
$174$	912511.			2.28489
$175$		0			0
$176$	232495.			0.565759
$177$	−380992.	+	659898.i	−0.914078	+	1.58323i
$178$	−172513.	−	298801.i	−0.408105	−	0.706858i
$179$	104690.	+	181328.i	0.244215	+	0.422993i	0.961911	−	0.273364i	$-0.0881363\pi$
$179$	104690.	+	181328.i	0.244215	+	0.422993i	−0.717695	+	0.696357i	$0.754803\pi$
$180$	217531.	−	376776.i	0.500427	−	0.866765i
$181$	−278996.			−0.632996			−0.316498	−	0.948593i	$-0.602507\pi$
$181$	−278996.			−0.632996			−0.316498	+	0.948593i	$0.602507\pi$
$182$		0			0
$183$	1.29579e6			2.86028
$184$	−59019.2	+	102224.i	−0.128514	+	0.222592i
$185$	74093.2	+	128333.i	0.159165	+	0.275683i
$186$	215267.	+	372854.i	0.456242	+	0.790235i
$187$	−82796.9	+	143408.i	−0.173145	+	0.299896i
$188$	−729426.			−1.50517
$189$		0			0
$190$	−404651.			−0.813198
$191$	222566.	−	385496.i	0.441444	−	0.764604i	−0.556353	−	0.830946i	$-0.687800\pi$
$191$	222566.	−	385496.i	0.441444	−	0.764604i	0.997797	+	0.0663425i	$0.0211330\pi$
$192$	528394.	+	915205.i	1.03444	+	1.79170i
$193$	363405.	+	629437.i	0.702260	+	1.21635i	0.967671	+	0.252215i	$0.0811590\pi$
$193$	363405.	+	629437.i	0.702260	+	1.21635i	−0.265411	+	0.964135i	$0.585508\pi$
$194$	180736.	−	313043.i	0.344778	−	0.597173i
$195$	221692.			0.417507
$196$		0			0
$197$	−364897.			−0.669892			−0.334946	−	0.942237i	$-0.608718\pi$
$197$	−364897.			−0.669892			−0.334946	+	0.942237i	$0.608718\pi$
$198$	463641.	−	803050.i	0.840464	−	1.45573i
$199$	144654.	+	250547.i	0.258938	+	0.448494i	0.965958	−	0.258700i	$-0.0832940\pi$
$199$	144654.	+	250547.i	0.258938	+	0.448494i	−0.707019	+	0.707194i	$0.749961\pi$
$200$	42549.7	+	73698.2i	0.0752179	+	0.130281i
$201$	−64810.7	+	112255.i	−0.113150	+	0.195982i
$202$	−212236.			−0.365965
$203$		0			0
$204$	−573589.			−0.964997
$205$	102724.	−	177923.i	0.170721	−	0.295697i
$206$	−59248.5	−	102621.i	−0.0972769	−	0.168488i
$207$	−661378.	−	1.14554e6i	−1.07281	−	1.85816i
$208$	−129396.	+	224120.i	−0.207378	+	0.359189i
$209$	−459409.			−0.727501
$210$		0			0
$211$	750147.			1.15995			0.579976	−	0.814633i	$-0.303062\pi$
$211$	750147.			1.15995			0.579976	+	0.814633i	$0.303062\pi$
$212$	−72015.1	+	124734.i	−0.110048	+	0.190609i
$213$	−421336.	−	729775.i	−0.636326	−	1.10215i
$214$	−71171.7	−	123273.i	−0.106236	−	0.184007i
$215$	−281516.	+	487600.i	−0.415343	+	0.719396i
$216$	163242.			0.238066
$217$		0			0
$218$	−711788.			−1.01440
$219$	−142547.	+	246898.i	−0.200838	+	0.347862i
$220$	−141609.	−	245273.i	−0.197257	−	0.341660i
$221$	−92162.0	−	159629.i	−0.126932	−	0.219853i
$222$	−547010.	+	947449.i	−0.744926	+	1.29025i
$223$	−534398.			−0.719619			−0.359810	−	0.933026i	$-0.617158\pi$
$223$	−534398.			−0.719619			−0.359810	+	0.933026i	$0.617158\pi$
$224$		0			0
$225$	−953635.			−1.25582
$226$	−569180.	+	985849.i	−0.741273	+	1.28392i
$227$	−205312.	−	355610.i	−0.264453	−	0.458047i	0.702967	−	0.711223i	$-0.251858\pi$
$227$	−205312.	−	355610.i	−0.264453	−	0.458047i	−0.967420	+	0.253176i	$0.918525\pi$
$228$	−795658.	−	1.37812e6i	−1.01365	−	1.75570i
$229$	515181.	−	892320.i	0.649189	−	1.12443i	−0.334128	−	0.942528i	$-0.608442\pi$
$229$	515181.	−	892320.i	0.649189	−	1.12443i	0.983317	−	0.181901i	$-0.0582250\pi$
$230$	−758452.			−0.945385
$231$		0			0
$232$	159177.			0.194160
$233$	59605.5	−	103240.i	0.0719278	−	0.124583i	−0.827818	−	0.560996i	$-0.810418\pi$
$233$	59605.5	−	103240.i	0.0719278	−	0.124583i	0.899746	+	0.436414i	$0.143752\pi$
$234$	516084.	+	893883.i	0.616142	+	1.06719i
$235$	−287469.	−	497910.i	−0.339563	−	0.588141i
$236$	−541781.	+	938392.i	−0.633204	+	1.09674i
$237$	2.10042e6			2.42905
$238$		0			0
$239$	−254090.			−0.287735			−0.143868	−	0.989597i	$-0.545954\pi$
$239$	−254090.			−0.287735			−0.143868	+	0.989597i	$0.545954\pi$
$240$	−317380.	+	549718.i	−0.355673	+	0.616044i
$241$	706254.	+	1.22327e6i	0.783282	+	1.35668i	0.930020	+	0.367509i	$0.119789\pi$
$241$	706254.	+	1.22327e6i	0.783282	+	1.35668i	−0.146738	+	0.989175i	$0.546877\pi$
$242$	364521.	+	631368.i	0.400114	+	0.693018i
$243$	378335.	−	655296.i	0.411019	−	0.711905i
$244$	1.84265e6			1.98138
$245$		0			0
$246$	1.51677e6			1.59801
$247$	255686.	−	442862.i	0.266664	−	0.461876i
$248$	37550.9	+	65040.0i	0.0387695	+	0.0671508i
$249$	1.51632e6	+	2.62635e6i	1.54986	+	2.68444i
$250$	−645115.	+	1.11737e6i	−0.652811	+	1.13070i
$251$	1.67542e6			1.67857			0.839286	−	0.543690i	$-0.182973\pi$
$251$	1.67542e6			1.67857			0.839286	+	0.543690i	$0.182973\pi$
$252$		0			0
$253$	−861087.			−0.845758
$254$	291968.	−	505704.i	0.283956	−	0.491827i
$255$	−226053.	−	391535.i	−0.217701	−	0.377069i
$256$	−348560.	−	603724.i	−0.332413	−	0.575756i
$257$	363498.	−	629597.i	0.343296	−	0.594607i	−0.641746	−	0.766917i	$-0.721790\pi$
$257$	363498.	−	629597.i	0.343296	−	0.594607i	0.985043	+	0.172310i	$0.0551232\pi$
$258$	−4.15672e6			−3.88778
$259$		0			0
$260$	315252.			0.289217
$261$	−891879.	+	1.54478e6i	−0.810410	+	1.40367i
$262$	−718728.	−	1.24487e6i	−0.646862	−	1.12040i
$263$	112940.	+	195618.i	0.100684	+	0.174389i	0.911967	−	0.410265i	$-0.134564\pi$
$263$	112940.	+	195618.i	0.100684	+	0.174389i	−0.811283	+	0.584654i	$0.801230\pi$
$264$	128245.	−	222127.i	0.113248	−	0.196152i
$265$	−113525.			−0.0993065
$266$		0			0
$267$	1.06947e6			0.918097
$268$	−92162.4	+	159630.i	−0.0783821	+	0.135762i
$269$	902635.	+	1.56341e6i	0.760557	+	1.31732i	0.942564	+	0.334025i	$0.108407\pi$
$269$	902635.	+	1.56341e6i	0.760557	+	1.31732i	−0.182008	+	0.983297i	$0.558260\pi$
$270$	524453.	+	908379.i	0.437821	+	0.758329i
$271$	−856898.	+	1.48419e6i	−0.708771	+	1.22763i	0.256543	+	0.966533i	$0.417417\pi$
$271$	−856898.	+	1.48419e6i	−0.708771	+	1.22763i	−0.965313	+	0.261094i	$0.915917\pi$
$272$	527765.			0.432532
$273$		0			0
$274$	−16466.6			−0.0132504
$275$	−310399.	+	537626.i	−0.247507	+	0.428695i
$276$	−1.49133e6	−	2.58306e6i	−1.17842	−	2.04109i
$277$	−1.11527e6	−	1.93171e6i	−0.873338	−	1.51267i	−0.858523	−	0.512775i	$-0.828617\pi$
$277$	−1.11527e6	−	1.93171e6i	−0.873338	−	1.51267i	−0.0148147	−	0.999890i	$-0.504716\pi$
$278$	1.51600e6	−	2.62579e6i	1.17649	−	2.03774i
$279$	−841600.			−0.647285
$280$		0			0
$281$	1.67140e6			1.26274			0.631371	−	0.775481i	$-0.282493\pi$
$281$	1.67140e6			1.26274			0.631371	+	0.775481i	$0.282493\pi$
$282$	2.12230e6	−	3.67594e6i	1.58922	−	2.75262i
$283$	−198076.	−	343078.i	−0.147016	−	0.254640i	0.783107	−	0.621887i	$-0.213634\pi$
$283$	−198076.	−	343078.i	−0.147016	−	0.254640i	−0.930123	+	0.367247i	$0.880300\pi$
$284$	−599151.	−	1.03776e6i	−0.440799	−	0.763486i
$285$	627141.	−	1.08624e6i	0.457355	−	0.792162i
$286$	671920.			0.485739
$287$		0			0
$288$	−3.44691e6			−2.44877
$289$	521979.	−	904094.i	0.367628	−	0.636750i
$290$	511393.	+	885758.i	0.357075	+	0.618472i
$291$	560221.	+	970331.i	0.387817	+	0.671718i
$292$	−202705.	+	351095.i	−0.139126	+	0.240973i
$293$	929465.			0.632505			0.316252	−	0.948675i	$-0.397575\pi$
$293$	929465.			0.632505			0.316252	+	0.948675i	$0.397575\pi$
$294$		0			0
$295$	−854068.			−0.571397
$296$	−95419.5	+	165271.i	−0.0633006	+	0.109640i
$297$	595423.	+	1.03130e6i	0.391683	+	0.678414i
$298$	−582217.	−	1.00843e6i	−0.379791	−	0.657817i
$299$	479242.	−	830072.i	0.310011	−	0.536955i
$300$	−2.15034e6			−1.37944
$301$		0			0
$302$	414280.			0.261383
$303$	328930.	−	569724.i	0.205825	−	0.356499i
$304$	732092.	+	1.26802e6i	0.454341	+	0.786942i
$305$	726193.	+	1.25780e6i	0.446995	+	0.774218i
$306$	1.05247e6	−	1.82293e6i	0.642549	−	1.11293i
$307$	−1.83295e6			−1.10995			−0.554976	−	0.831866i	$-0.687273\pi$
$307$	−1.83295e6			−1.10995			−0.554976	+	0.831866i	$0.687273\pi$
$308$		0			0
$309$	367302.			0.218840
$310$	−241282.	+	417912.i	−0.142600	+	0.246991i
$311$	−1.14842e6	−	1.98913e6i	−0.673289	−	1.16617i	−0.976966	−	0.213396i	$-0.931548\pi$
$311$	−1.14842e6	−	1.98913e6i	−0.673289	−	1.16617i	0.303677	−	0.952775i	$-0.401786\pi$
$312$	142751.	+	247252.i	0.0830220	+	0.143798i
$313$	−1.71235e6	+	2.96588e6i	−0.987943	+	1.71117i	−0.359897	+	0.932992i	$0.617188\pi$
$313$	−1.71235e6	+	2.96588e6i	−0.987943	+	1.71117i	−0.628047	+	0.778176i	$0.716145\pi$
$314$	743043.			0.425295
$315$		0			0
$316$	2.98685e6			1.68266
$317$	−1.47153e6	+	2.54876e6i	−0.822470	+	1.42456i	0.0813671	+	0.996684i	$0.474071\pi$
$317$	−1.47153e6	+	2.54876e6i	−0.822470	+	1.42456i	−0.903837	+	0.427876i	$0.859262\pi$
$318$	−419063.	−	725839.i	−0.232387	−	0.402506i
$319$	580596.	+	1.00562e6i	0.319446	+	0.553296i
$320$	−592249.	+	1.02580e6i	−0.323317	+	0.560002i
$321$	441217.			0.238996
$322$		0			0
$323$	−1.04286e6			−0.556187
$324$	−223780.	+	387598.i	−0.118429	+	0.205125i
$325$	−345508.	−	598437.i	−0.181447	−	0.314275i
$326$	1.99107e6	+	3.44863e6i	1.03763	+	1.79723i
$327$	1.10315e6	−	1.91072e6i	0.570515	−	0.988160i
$328$	264582.			0.135792
$329$		0			0
$330$	1.64807e6			0.833089
$331$	−483082.	+	836722.i	−0.242354	+	0.419770i	−0.961384	−	0.275209i	$-0.911253\pi$
$331$	−483082.	+	836722.i	−0.242354	+	0.419770i	0.719030	+	0.694979i	$0.244586\pi$
$332$	2.15625e6	+	3.73473e6i	1.07363	+	1.85958i
$333$	−1.06928e6	−	1.85205e6i	−0.528424	−	0.915257i
$334$	−358191.	+	620405.i	−0.175691	+	0.304305i
$335$	−145286.			−0.0707312
$336$		0			0
$337$	136417.			0.0654327			0.0327163	−	0.999465i	$-0.489584\pi$
$337$	136417.			0.0654327			0.0327163	+	0.999465i	$0.489584\pi$
$338$	1.16225e6	−	2.01307e6i	0.553359	−	0.958447i
$339$	−1.76427e6	−	3.05580e6i	−0.833807	−	1.44420i
$340$	−321453.	−	556773.i	−0.150807	−	0.261205i
$341$	−273932.	+	474465.i	−0.127573	+	0.220962i
$342$	5.83976e6			2.69979
$343$		0			0
$344$	−725091.			−0.330367
$345$	1.17548e6	−	2.03598e6i	0.531699	−	0.920929i
$346$	−240541.	−	416630.i	−0.108019	−	0.187094i
$347$	−177704.	−	307792.i	−0.0792270	−	0.137225i	0.823690	−	0.567041i	$-0.191912\pi$
$347$	−177704.	−	307792.i	−0.0792270	−	0.137225i	−0.902917	+	0.429816i	$0.858579\pi$
$348$	−2.01109e6	+	3.48331e6i	−0.890190	+	1.54186i
$349$	140128.			0.0615830			0.0307915	−	0.999526i	$-0.490197\pi$
$349$	140128.			0.0615830			0.0307915	+	0.999526i	$0.490197\pi$
$350$		0			0
$351$	−1.32554e6			−0.574283
$352$	−1.12193e6	+	1.94325e6i	−0.482626	+	0.835933i
$353$	1.74071e6	+	3.01499e6i	0.743514	+	1.28780i	0.950886	+	0.309541i	$0.100175\pi$
$353$	1.74071e6	+	3.01499e6i	0.743514	+	1.28780i	−0.207373	+	0.978262i	$0.566491\pi$
$354$	−3.15268e6	−	5.46060e6i	−1.33712	−	2.31597i
$355$	472253.	−	817967.i	0.198886	−	0.344481i
$356$	1.52081e6			0.635988
$357$		0			0
$358$	−1.73260e6			−0.714482
$359$	−876427.	+	1.51802e6i	−0.358905	+	0.621642i	−0.987778	−	0.155866i	$-0.950183\pi$
$359$	−876427.	+	1.51802e6i	−0.358905	+	0.621642i	0.628873	+	0.777508i	$0.283517\pi$
$360$	220811.	+	382455.i	0.0897974	+	0.155534i
$361$	−208563.	−	361242.i	−0.0842306	−	0.145892i
$362$	1.15433e6	−	1.99936e6i	0.462977	−	0.801900i
$363$	−2.25979e6			−0.900121
$364$		0			0
$365$	−319546.			−0.125546
$366$	−5.36129e6	+	9.28603e6i	−2.09202	+	3.62349i
$367$	−884695.	−	1.53234e6i	−0.342869	−	0.593867i	0.642095	−	0.766625i	$-0.278065\pi$
$367$	−884695.	−	1.53234e6i	−0.342869	−	0.593867i	−0.984964	+	0.172758i	$0.944732\pi$
$368$	1.37219e6	+	2.37670e6i	0.528195	+	0.914861i
$369$	−1.48247e6	+	2.56771e6i	−0.566787	+	0.981705i
$370$	−1.22623e6			−0.465658
$371$		0			0
$372$	−1.89771e6			−0.711006
$373$	2.08106e6	−	3.60451e6i	0.774485	−	1.34145i	−0.160598	−	0.987020i	$-0.551342\pi$
$373$	2.08106e6	−	3.60451e6i	0.774485	−	1.34145i	0.935083	−	0.354428i	$-0.115324\pi$
$374$	−685137.	−	1.18669e6i	−0.253279	−	0.438691i
$375$	−1.99964e6	−	3.46349e6i	−0.734302	−	1.27185i
$376$	370211.	−	641224.i	0.135045	−	0.233905i
$377$	−1.29253e6			−0.468369
$378$		0			0
$379$	618163.			0.221057			0.110529	−	0.993873i	$-0.464746\pi$
$379$	618163.			0.221057			0.110529	+	0.993873i	$0.464746\pi$
$380$	891811.	−	1.54466e6i	0.316821	−	0.548750i
$381$	905005.	+	1.56751e6i	0.319403	+	0.553222i
$382$	1.84172e6	+	3.18995e6i	0.645750	+	1.11847i
$383$	−2.05582e6	+	3.56078e6i	−0.716123	+	1.24036i	0.246402	+	0.969168i	$0.420752\pi$
$383$	−2.05582e6	+	3.56078e6i	−0.716123	+	1.24036i	−0.962525	+	0.271194i	$0.912582\pi$
$384$	−1.92587e6			−0.666498
$385$		0			0
$386$	−6.01430e6			−2.05455
$387$	4.06273e6	−	7.03686e6i	1.37893	−	2.38837i
$388$	796648.	+	1.37984e6i	0.268650	+	0.465316i
$389$	−2.31038e6	−	4.00169e6i	−0.774122	−	1.34082i	−0.935287	−	0.353891i	$-0.884858\pi$
$389$	−2.31038e6	−	4.00169e6i	−0.774122	−	1.34082i	0.161165	−	0.986927i	$-0.448475\pi$
$390$	−917242.	+	1.58871e6i	−0.305367	+	0.528912i
$391$	−1.95468e6			−0.646596
$392$		0			0
$393$	4.45564e6			1.45522
$394$	1.50975e6	−	2.61496e6i	0.489963	−	0.848641i
$395$	1.17713e6	+	2.03884e6i	0.379603	+	0.657492i
$396$	2.04364e6	+	3.53969e6i	0.654888	+	1.13430i
$397$	2.53675e6	−	4.39377e6i	0.807794	−	1.39914i	−0.106595	−	0.994303i	$-0.533995\pi$
$397$	2.53675e6	−	4.39377e6i	0.807794	−	1.39914i	0.914389	−	0.404838i	$-0.132672\pi$
$398$	−2.39399e6			−0.757557
$399$		0			0
$400$	1.97855e6			0.618296
$401$	740279.	−	1.28220e6i	0.229898	−	0.398194i	−0.727880	−	0.685705i	$-0.759494\pi$
$401$	740279.	−	1.28220e6i	0.229898	−	0.398194i	0.957778	+	0.287510i	$0.0928275\pi$
$402$	−536303.	−	928904.i	−0.165518	−	0.286685i
$403$	−304917.	−	528132.i	−0.0935231	−	0.161987i
$404$	467747.	−	810162.i	0.142580	−	0.246955i
$405$	−352768.			−0.106869
$406$		0			0
$407$	−1.39217e6			−0.416586
$408$	291118.	−	504231.i	0.0865802	−	0.149961i
$409$	−2.26690e6	−	3.92638e6i	−0.670075	−	1.16060i	−0.977882	−	0.209155i	$-0.932929\pi$
$409$	−2.26690e6	−	3.92638e6i	−0.670075	−	1.16060i	0.307808	−	0.951449i	$-0.400405\pi$
$410$	850031.	+	1.47230e6i	0.249733	+	0.432549i
$411$	25520.5	−	44202.8i	0.00745220	−	0.0129076i
$412$	522313.			0.151596
$413$		0			0
$414$	1.09457e7			3.13865
$415$	−1.69956e6	+	2.94373e6i	−0.484415	+	0.839031i
$416$	−1.24884e6	−	2.16305e6i	−0.353812	−	0.612820i
$417$	4.69910e6	+	8.13908e6i	1.32335	+	2.29211i
$418$	1.90078e6	−	3.29226e6i	0.532099	−	0.921622i
$419$	−111026.			−0.0308952			−0.0154476	−	0.999881i	$-0.504917\pi$
$419$	−111026.			−0.0308952			−0.0154476	+	0.999881i	$0.504917\pi$
$420$		0			0
$421$	−1.41151e6			−0.388132			−0.194066	−	0.980988i	$-0.562168\pi$
$421$	−1.41151e6			−0.388132			−0.194066	+	0.980988i	$0.562168\pi$
$422$	−3.10370e6	+	5.37577e6i	−0.848396	+	1.46947i
$423$	4.14864e6	+	7.18565e6i	1.12734	+	1.95261i
$424$	−73100.7	−	126614.i	−0.0197473	−	0.0342033i
$425$	−704608.	+	1.22042e6i	−0.189224	+	0.327745i
$426$	6.97304e6			1.86165
$427$		0			0
$428$	627422.			0.165558
$429$	−1.04137e6	+	1.80370e6i	−0.273187	+	0.473174i
$430$	−2.32952e6	−	4.03485e6i	−0.607570	−	1.05234i
$431$	−538200.	−	932189.i	−0.139557	−	0.241719i	0.787772	−	0.615967i	$-0.211234\pi$
$431$	−538200.	−	932189.i	−0.139557	−	0.241719i	−0.927329	+	0.374248i	$0.877901\pi$
$432$	1.89768e6	−	3.28687e6i	0.489230	−	0.847370i
$433$	310172.			0.0795029			0.0397515	−	0.999210i	$-0.487343\pi$
$433$	310172.			0.0795029			0.0397515	+	0.999210i	$0.487343\pi$
$434$		0			0
$435$	−3.17030e6			−0.803298
$436$	1.56871e6	−	2.71709e6i	0.395210	−	0.684523i
$437$	−2.71144e6	−	4.69636e6i	−0.679199	−	1.17641i
$438$	−1.17956e6	−	2.04306e6i	−0.293789	−	0.508857i
$439$	2.83825e6	−	4.91599e6i	0.702893	−	1.21745i	−0.264553	−	0.964371i	$-0.585225\pi$
$439$	2.83825e6	−	4.91599e6i	0.702893	−	1.21745i	0.967447	−	0.253075i	$-0.0814421\pi$
$440$	287487.			0.0707923
$441$		0			0
$442$	1.52527e6			0.371356
$443$	−2.02983e6	+	3.51577e6i	−0.491417	+	0.851159i	−0.999951	−	0.00988261i	$-0.996854\pi$
$443$	−2.02983e6	+	3.51577e6i	−0.491417	+	0.851159i	0.508534	+	0.861042i	$0.330188\pi$
$444$	−2.41112e6	−	4.17618e6i	−0.580445	−	1.00536i
$445$	599354.	+	1.03811e6i	0.143477	+	0.248510i
$446$	2.21105e6	−	3.82965e6i	0.526334	−	0.911637i
$447$	3.60936e6			0.854401
$448$		0			0
$449$	−6.96544e6			−1.63054			−0.815272	−	0.579078i	$-0.803413\pi$
$449$	−6.96544e6			−1.63054			−0.815272	+	0.579078i	$0.803413\pi$
$450$	3.94562e6	−	6.83402e6i	0.918511	−	1.59091i
$451$	965059.	+	1.67153e6i	0.223415	+	0.386966i
$452$	−2.50884e6	−	4.34543e6i	−0.577599	−	1.00043i
$453$	−642066.	+	1.11209e6i	−0.147006	+	0.254621i
$454$	3.39788e6			0.773692
$455$		0			0
$456$	1.61530e6			0.363783
$457$	−897615.	+	1.55472e6i	−0.201048	+	0.348225i	−0.948866	−	0.315678i	$-0.897768\pi$
$457$	−897615.	+	1.55472e6i	−0.201048	+	0.348225i	0.747818	+	0.663903i	$0.231101\pi$
$458$	4.26308e6	+	7.38387e6i	0.949642	+	1.64483i
$459$	1.35162e6	+	2.34107e6i	0.299448	+	0.518659i
$460$	1.67156e6	−	2.89522e6i	0.368321	−	0.637950i
$461$	2.11294e6			0.463058			0.231529	−	0.972828i	$-0.425627\pi$
$461$	2.11294e6			0.463058			0.231529	+	0.972828i	$0.425627\pi$
$462$		0			0
$463$	1.26223e6			0.273643			0.136822	−	0.990596i	$-0.456311\pi$
$463$	1.26223e6			0.273643			0.136822	+	0.990596i	$0.456311\pi$
$464$	1.85042e6	−	3.20502e6i	0.399002	−	0.691092i
$465$	−747893.	−	1.29539e6i	−0.160401	−	0.277823i
$466$	493231.	+	854301.i	0.105217	+	0.182241i
$467$	−1.79463e6	+	3.10839e6i	−0.380788	+	0.659544i	−0.991175	−	0.132559i	$-0.957681\pi$
$467$	−1.79463e6	+	3.10839e6i	−0.380788	+	0.659544i	0.610387	+	0.792103i	$0.291014\pi$
$468$	−4.54960e6			−0.960192
$469$		0			0
$470$	4.75756e6			0.993435
$471$	−1.15159e6	+	1.99462e6i	−0.239192	+	0.414293i
$472$	−549948.	−	952538.i	−0.113623	−	0.196801i
$473$	−2.64476e6	−	4.58086e6i	−0.543542	−	0.941443i
$474$	−8.69041e6	+	1.50522e7i	−1.77662	+	3.07719i
$475$	−3.90960e6			−0.795058
$476$		0			0
$477$	1.63835e6			0.329694
$478$	1.05129e6	−	1.82088e6i	0.210451	−	0.364512i
$479$	−1.20847e6	−	2.09312e6i	−0.240655	−	0.416827i	0.720246	−	0.693719i	$-0.244029\pi$
$479$	−1.20847e6	−	2.09312e6i	−0.240655	−	0.416827i	−0.960901	+	0.276892i	$0.910696\pi$
$480$	−3.06312e6	−	5.30547e6i	−0.606821	−	1.05104i
$481$	774817.	−	1.34202e6i	0.152699	−	0.264482i
$482$	−1.16884e7			−2.29159
$483$		0			0
$484$	−3.21347e6			−0.623536
$485$	−627922.	+	1.08759e6i	−0.121214	+	0.209948i
$486$	3.13069e6	+	5.42252e6i	0.601243	+	1.04138i
$487$	2.59701e6	+	4.49816e6i	0.496194	+	0.859434i	0.999990	−	0.00438895i	$-0.00139705\pi$
$487$	2.59701e6	+	4.49816e6i	0.496194	+	0.859434i	−0.503796	+	0.863823i	$0.668064\pi$
$488$	−935215.	+	1.61984e6i	−0.177771	+	0.307909i
$489$	−1.23433e7			−2.33432
$490$		0			0
$491$	5.38961e6			1.00891			0.504456	−	0.863437i	$-0.331693\pi$
$491$	5.38961e6			1.00891			0.504456	+	0.863437i	$0.331693\pi$
$492$	−3.34281e6	+	5.78991e6i	−0.622585	+	1.07835i
$493$	1.31796e6	+	2.28277e6i	0.244222	+	0.423004i
$494$	2.11578e6	+	3.66464e6i	0.390080	+	0.675638i
$495$	−1.61081e6	+	2.79000e6i	−0.295482	+	0.511790i
$496$	1.74610e6			0.318688
$497$		0			0
$498$	−2.50949e7			−4.53431
$499$	1.64803e6	−	2.85448e6i	0.296288	−	0.513186i	−0.678996	−	0.734142i	$-0.737584\pi$
$499$	1.64803e6	−	2.85448e6i	0.296288	−	0.513186i	0.975284	+	0.220956i	$0.0709178\pi$
$500$	−2.84355e6	−	4.92517e6i	−0.508669	−	0.881040i
$501$	−1.11027e6	−	1.92305e6i	−0.197622	−	0.342292i
$502$	−6.93199e6	+	1.20066e7i	−1.22772	+	2.12647i
$503$	1.06512e7			1.87706			0.938528	−	0.345204i	$-0.112190\pi$
$503$	1.06512e7			1.87706			0.938528	+	0.345204i	$0.112190\pi$
$504$		0			0
$505$	737361.			0.128662
$506$	3.56271e6	−	6.17080e6i	0.618592	−	1.07143i
$507$	3.60259e6	+	6.23986e6i	0.622436	+	1.07809i
$508$	1.28694e6	+	2.22905e6i	0.221258	+	0.383230i
$509$	−1.37134e6	+	2.37523e6i	−0.234612	+	0.406360i	−0.959160	−	0.282864i	$-0.908715\pi$
$509$	−1.37134e6	+	2.37523e6i	−0.234612	+	0.406360i	0.724548	+	0.689225i	$0.242049\pi$
$510$	3.74114e6			0.636910
$511$		0			0
$512$	8.17130e6			1.37758
$513$	−3.74980e6	+	6.49485e6i	−0.629093	+	1.08962i
$514$	3.00792e6	+	5.20986e6i	0.502178	+	0.869798i
$515$	205845.	+	356533.i	0.0341996	+	0.0592355i
$516$	9.16101e6	−	1.58673e7i	1.51467	−	2.62349i
$517$	5.40136e6			0.888744
$518$		0			0
$519$	1.49120e6			0.243006
$520$	−160002.	+	277132.i	−0.0259488	+	0.0449447i
$521$	2.48538e6	+	4.30481e6i	0.401143	+	0.694800i	0.993864	−	0.110608i	$-0.0352797\pi$
$521$	2.48538e6	+	4.30481e6i	0.401143	+	0.694800i	−0.592721	+	0.805408i	$0.701946\pi$
$522$	−7.38023e6	−	1.27829e7i	−1.18548	−	2.05331i
$523$	1.20789e6	−	2.09213e6i	0.193096	−	0.334453i	−0.753178	−	0.657816i	$-0.771480\pi$
$523$	1.20789e6	−	2.09213e6i	0.193096	−	0.334453i	0.946275	+	0.323363i	$0.104814\pi$
$524$	6.33603e6			1.00807
$525$		0			0
$526$	−1.86914e6			−0.294563
$527$	−621829.	+	1.07704e6i	−0.0975314	+	0.168929i
$528$	−2.98169e6	−	5.16443e6i	−0.465454	−	0.806190i
$529$	−1.86399e6	−	3.22852e6i	−0.289604	−	0.501608i
$530$	469706.	−	813555.i	0.0726334	−	0.125805i
$531$	1.23256e7			1.89702
$532$		0			0
$533$	−2.14843e6			−0.327570
$534$	−4.42487e6	+	7.66410e6i	−0.671502	+	1.16308i
$535$	247269.	+	428282.i	0.0373495	+	0.0646912i
$536$	−93551.7	−	162036.i	−0.0140650	−	0.0243613i
$537$	2.68525e6	−	4.65099e6i	0.401836	−	0.696000i
$538$	−1.49385e7			−2.22510
$539$		0			0
$540$	−4.62337e6			−0.682299
$541$	−236083.	+	408907.i	−0.0346794	+	0.0600664i	−0.882844	−	0.469666i	$-0.844374\pi$
$541$	−236083.	+	408907.i	−0.0346794	+	0.0600664i	0.848165	+	0.529732i	$0.177708\pi$
$542$	−7.09076e6	−	1.22816e7i	−1.03680	−	1.79579i
$543$	3.57805e6	+	6.19736e6i	0.520771	+	0.902002i
$544$	−2.54680e6	+	4.41119e6i	−0.368976	+	0.639085i
$545$	2.47293e6			0.356633
$546$		0			0
$547$	7.63716e6			1.09135			0.545675	−	0.837997i	$-0.316273\pi$
$547$	7.63716e6			1.09135			0.545675	+	0.837997i	$0.316273\pi$
$548$	36290.8	−	62857.5i	0.00516232	−	0.00894141i
$549$	−1.04801e7	−	1.81521e7i	−1.48401	−	2.57038i
$550$	−2.56852e6	−	4.44881e6i	−0.362057	−	0.627101i
$551$	−3.65643e6	+	6.33312e6i	−0.513071	+	0.888666i
$552$	3.02763e6			0.422917
$553$		0			0
$554$	1.84576e7			2.55506
$555$	1.90045e6	−	3.29168e6i	0.261893	−	0.453613i
$556$	6.68224e6	+	1.15740e7i	0.916717	+	1.58780i
$557$	2.24404e6	+	3.88679e6i	0.306473	+	0.530827i	0.977588	−	0.210526i	$-0.0675178\pi$
$557$	2.24404e6	+	3.88679e6i	0.306473	+	0.530827i	−0.671115	+	0.741353i	$0.734184\pi$
$558$	3.48209e6	−	6.03115e6i	0.473428	−	0.820001i
$559$	5.88782e6			0.796938
$560$		0			0
$561$	4.24740e6			0.569791
$562$	−6.91535e6	+	1.19777e7i	−0.923577	+	1.59968i
$563$	−1.08250e6	−	1.87494e6i	−0.143932	−	0.249297i	0.785042	−	0.619442i	$-0.212641\pi$
$563$	−1.08250e6	−	1.87494e6i	−0.143932	−	0.249297i	−0.928974	+	0.370145i	$0.879308\pi$
$564$	9.35471e6	+	1.62028e7i	1.23832	+	2.14483i
$565$	1.97748e6	−	3.42509e6i	0.260609	−	0.451389i
$566$	3.27812e6			0.430115
$567$		0			0
$568$	1.21637e6			0.158195
$569$	5.66627e6	−	9.81426e6i	0.733696	−	1.27080i	−0.221597	−	0.975138i	$-0.571127\pi$
$569$	5.66627e6	−	9.81426e6i	0.733696	−	1.27080i	0.955293	−	0.295661i	$-0.0955398\pi$
$570$	5.18954e6	+	8.98855e6i	0.669024	+	1.15878i
$571$	421887.	+	730729.i	0.0541509	+	0.0937921i	0.891830	−	0.452370i	$-0.149421\pi$
$571$	421887.	+	730729.i	0.0541509	+	0.0937921i	−0.837679	+	0.546162i	$0.816088\pi$
$572$	−1.48085e6	+	2.56490e6i	−0.189243	+	0.327779i
$573$	−1.14174e7			−1.45272
$574$		0			0
$575$	−7.32792e6			−0.924296
$576$	8.54711e6	−	1.48040e7i	1.07340	−	1.85919i
$577$	−1.11892e6	−	1.93803e6i	−0.139914	−	0.242338i	0.787550	−	0.616251i	$-0.211349\pi$
$577$	−1.11892e6	−	1.93803e6i	−0.139914	−	0.242338i	−0.927464	+	0.373913i	$0.878016\pi$
$578$	4.31933e6	+	7.48130e6i	0.537770	+	0.931446i
$579$	9.32117e6	−	1.61447e7i	1.15551	−	2.00140i
$580$	−4.50824e6			−0.556464
$581$		0			0
$582$	−9.27156e6			−1.13461
$583$	533267.	−	923646.i	0.0649791	−	0.112547i
$584$	−205761.	−	356388.i	−0.0249649	−	0.0432405i
$585$	−1.79301e6	−	3.10558e6i	−0.216617	−	0.375191i
$586$	−3.84562e6	+	6.66081e6i	−0.462618	+	0.801278i
$587$	−1.21190e7			−1.45168			−0.725839	−	0.687864i	$-0.758548\pi$
$587$	−1.21190e7			−1.45168			−0.725839	+	0.687864i	$0.758548\pi$
$588$		0			0
$589$	−3.45030e6			−0.409797
$590$	3.53367e6	−	6.12050e6i	0.417923	−	0.723864i
$591$	4.67971e6	+	8.10550e6i	0.551125	+	0.954577i
$592$	2.21849e6	+	3.84254e6i	0.260168	+	0.450624i
$593$	4.00084e6	−	6.92965e6i	0.467212	−	0.809235i	−0.532086	−	0.846690i	$-0.678592\pi$
$593$	4.00084e6	−	6.92965e6i	0.467212	−	0.809235i	0.999298	+	0.0374552i	$0.0119251\pi$
$594$	−9.85415e6			−1.14592
$595$		0			0
$596$	5.13261e6			0.591865
$597$	3.71029e6	−	6.42641e6i	0.426061	−	0.737960i
$598$	3.96569e6	+	6.86878e6i	0.453488	+	0.785465i
$599$	−7.29493e6	−	1.26352e7i	−0.830719	−	1.43885i	−0.897469	−	0.441078i	$-0.854596\pi$
$599$	−7.29493e6	−	1.26352e7i	−0.830719	−	1.43885i	0.0667499	−	0.997770i	$-0.478737\pi$
$600$	1.09138e6	−	1.89032e6i	0.123765	−	0.214367i
$601$	8.67178e6			0.979314			0.489657	−	0.871915i	$-0.337122\pi$
$601$	8.67178e6			0.979314			0.489657	+	0.871915i	$0.337122\pi$
$602$		0			0
$603$	2.09671e6			0.234825
$604$	−913034.	+	1.58142e6i	−0.101834	+	0.176382i
$605$	−1.26644e6	−	2.19353e6i	−0.140668	−	0.243644i
$606$	2.72187e6	+	4.71442e6i	0.301083	+	0.521491i
$607$	−6.65297e6	+	1.15233e7i	−0.732898	+	1.26942i	0.222742	+	0.974878i	$0.428499\pi$
$607$	−6.65297e6	+	1.15233e7i	−0.732898	+	1.26942i	−0.955639	+	0.294539i	$0.904834\pi$
$608$	−1.41312e7			−1.55032
$609$		0			0
$610$	−1.20184e7			−1.30774
$611$	−3.00615e6	+	5.20681e6i	−0.325768	+	0.564246i
$612$	4.63909e6	+	8.03513e6i	0.500673	+	0.867191i
$613$	−1.17551e6	−	2.03604e6i	−0.126350	−	0.218844i	0.795910	−	0.605415i	$-0.206993\pi$
$613$	−1.17551e6	−	2.03604e6i	−0.126350	−	0.218844i	−0.922260	+	0.386571i	$0.873659\pi$
$614$	7.58375e6	−	1.31354e7i	0.811826	−	1.40612i
$615$	−5.26963e6			−0.561814
$616$		0			0
$617$	9.63523e6			1.01894			0.509470	−	0.860488i	$-0.329841\pi$
$617$	9.63523e6			1.01894			0.509470	+	0.860488i	$0.329841\pi$
$618$	−1.51970e6	+	2.63219e6i	−0.160061	+	0.277234i
$619$	−2.43074e6	−	4.21016e6i	−0.254983	−	0.441644i	0.709908	−	0.704295i	$-0.248737\pi$
$619$	−2.43074e6	−	4.21016e6i	−0.254983	−	0.441644i	−0.964891	+	0.262651i	$0.915403\pi$
$620$	−1.06352e6	−	1.84208e6i	−0.111114	−	0.192455i
$621$	−7.02840e6	+	1.21735e7i	−0.731354	+	1.26674i
$622$	1.90062e7			1.96979
$623$		0			0
$624$	6.63789e6			0.682446
$625$	−1.35009e6	+	2.33842e6i	−0.138249	+	0.239454i
$626$	−1.41696e7	−	2.45424e7i	−1.44518	−	2.50312i
$627$	5.89180e6	+	1.02049e7i	0.598521	+	1.03667i
$628$	−1.63760e6	+	2.83640e6i	−0.165694	+	0.286991i
$629$	−3.16023e6			−0.318487
$630$		0			0
$631$	−6.59770e6			−0.659659			−0.329829	−	0.944041i	$-0.606991\pi$
$631$	−6.59770e6			−0.659659			−0.329829	+	0.944041i	$0.606991\pi$
$632$	−1.51594e6	+	2.62568e6i	−0.150969	+	0.261487i
$633$	−9.62045e6	−	1.66631e7i	−0.954302	−	1.65290i
$634$	−1.21768e7	−	2.10908e7i	−1.20312	−	2.08386i
$635$	−1.01437e6	+	1.75694e6i	−0.0998305	+	0.172911i
$636$	3.69430e6			0.362151
$637$		0			0
$638$	−9.60876e6			−0.934578
$639$	−6.81538e6	+	1.18046e7i	−0.660295	+	1.14366i
$640$	−1.07930e6	−	1.86941e6i	−0.104158	−	0.180407i
$641$	−7.22623e6	−	1.25162e7i	−0.694651	−	1.20317i	−0.970298	−	0.241911i	$-0.922226\pi$
$641$	−7.22623e6	−	1.25162e7i	−0.694651	−	1.20317i	0.275648	−	0.961259i	$-0.411108\pi$
$642$	−1.82552e6	+	3.16189e6i	−0.174803	+	0.302767i
$643$	1.54720e7			1.47577			0.737886	−	0.674926i	$-0.235824\pi$
$643$	1.54720e7			1.47577			0.737886	+	0.674926i	$0.235824\pi$
$644$		0			0
$645$	1.44415e7			1.36683
$646$	4.31480e6	−	7.47345e6i	0.406798	−	0.704596i
$647$	8.33234e6	+	1.44320e7i	0.782540	+	1.35540i	0.930458	+	0.366399i	$0.119410\pi$
$647$	8.33234e6	+	1.44320e7i	0.782540	+	1.35540i	−0.147918	+	0.989000i	$0.547257\pi$
$648$	−227153.	−	393441.i	−0.0212511	−	0.0368080i
$649$	4.01186e6	−	6.94874e6i	0.373881	−	0.647581i
$650$	5.71810e6			0.530845
$651$		0			0
$652$	−1.75525e7			−1.61704
$653$	6.67253e6	−	1.15572e7i	0.612361	−	1.06064i	−0.378481	−	0.925609i	$-0.623553\pi$
$653$	6.67253e6	−	1.15572e7i	0.612361	−	1.06064i	0.990841	−	0.135031i	$-0.0431133\pi$
$654$	9.12851e6	+	1.58110e7i	0.834556	+	1.44549i
$655$	2.49704e6	+	4.32501e6i	0.227417	+	0.393898i
$656$	3.07575e6	−	5.32735e6i	0.279056	−	0.483339i
$657$	4.61157e6			0.416807
$658$		0			0
$659$	−4.00667e6			−0.359393			−0.179697	−	0.983722i	$-0.557512\pi$
$659$	−4.00667e6			−0.359393			−0.179697	+	0.983722i	$0.557512\pi$
$660$	−3.63219e6	+	6.29114e6i	−0.324570	+	0.562173i
$661$	5.40024e6	+	9.35349e6i	0.480739	+	0.832664i	0.999756	−	0.0220996i	$-0.00703509\pi$
$661$	5.40024e6	+	9.35349e6i	0.480739	+	0.832664i	−0.519017	+	0.854764i	$0.673702\pi$
$662$	−3.99746e6	−	6.92381e6i	−0.354519	−	0.614045i
$663$	−2.36391e6	+	4.09441e6i	−0.208856	+	0.361749i
$664$	−4.37750e6			−0.385307
$665$		0			0
$666$	1.76965e7			1.54597
$667$	−6.85338e6	+	1.18704e7i	−0.596472	+	1.03312i
$668$	−1.57884e6	−	2.73463e6i	−0.136898	−	0.237114i
$669$	6.85352e6	+	1.18706e7i	0.592036	+	1.02544i
$670$	601114.	−	1.04116e6i	0.0517332	−	0.0896046i
$671$	−1.36447e7			−1.16993
$672$		0			0
$673$	1.09119e7			0.928676			0.464338	−	0.885658i	$-0.346292\pi$
$673$	1.09119e7			0.928676			0.464338	+	0.885658i	$0.346292\pi$
$674$	−564421.	+	977606.i	−0.0478579	+	0.0828923i
$675$	5.06709e6	+	8.77647e6i	0.428055	+	0.741413i
$676$	5.12297e6	+	8.87325e6i	0.431177	+	0.746820i
$677$	−6.78826e6	+	1.17576e7i	−0.569229	+	0.985933i	0.427414	+	0.904056i	$0.359425\pi$
$677$	−6.78826e6	+	1.17576e7i	−0.569229	+	0.985933i	−0.996642	+	0.0818771i	$0.973908\pi$
$678$	2.91984e7			2.43941
$679$		0			0
$680$	652598.			0.0541219
$681$	−5.26615e6	+	9.12123e6i	−0.435136	+	0.753678i
$682$	−2.26677e6	−	3.92616e6i	−0.186615	−	0.323226i
$683$	6.33631e6	+	1.09748e7i	0.519738	+	0.900213i	0.999737	+	0.0229436i	$0.00730382\pi$
$683$	6.33631e6	+	1.09748e7i	0.519738	+	0.900213i	−0.479999	+	0.877269i	$0.659363\pi$
$684$	−1.28703e7	+	2.22920e7i	−1.05184	+	1.82183i
$685$	57209.2			0.00465843
$686$		0			0
$687$	−2.64283e7			−2.13637
$688$	−8.42913e6	+	1.45997e7i	−0.678909	+	1.17591i
$689$	593585.	+	1.02812e6i	0.0476360	+	0.0825079i
$690$	9.72696e6	+	1.68476e7i	0.777776	+	1.34715i
$691$	3.55982e6	−	6.16579e6i	0.283617	−	0.491240i	−0.688656	−	0.725089i	$-0.741799\pi$
$691$	3.55982e6	−	6.16579e6i	0.283617	−	0.491240i	0.972273	+	0.233849i	$0.0751321\pi$
$692$	2.12052e6			0.168336
$693$		0			0
$694$	2.94097e6			0.231789
$695$	−5.26697e6	+	9.12267e6i	−0.413618	+	0.716407i
$696$	−2.04140e6	−	3.53582e6i	−0.159737	−	0.276673i
$697$	2.19069e6	+	3.79439e6i	0.170805	+	0.295842i
$698$	−579773.	+	1.00420e6i	−0.0450422	+	0.0780153i
$699$	−3.05770e6			−0.236702
$700$		0			0
$701$	−1.00155e7			−0.769803			−0.384902	−	0.922958i	$-0.625765\pi$
$701$	−1.00155e7			−0.769803			−0.384902	+	0.922958i	$0.625765\pi$
$702$	5.48437e6	−	9.49922e6i	0.420034	−	0.727520i
$703$	−4.38373e6	−	7.59285e6i	−0.334546	−	0.579450i
$704$	−5.56400e6	−	9.63713e6i	−0.423112	−	0.732851i
$705$	−7.37343e6	+	1.27711e7i	−0.558723	+	0.967737i
$706$	−2.88084e7			−2.17524
$707$		0			0
$708$	2.77928e7			2.08377
$709$	4.42227e6	−	7.65959e6i	0.330392	−	0.572256i	−0.652197	−	0.758050i	$-0.726152\pi$
$709$	4.42227e6	−	7.65959e6i	0.330392	−	0.572256i	0.982589	+	0.185794i	$0.0594857\pi$
$710$	3.90786e6	+	6.76861e6i	0.290933	+	0.503910i
$711$	−1.69878e7	−	2.94238e7i	−1.26027	−	2.18285i
$712$	−771866.	+	1.33691e6i	−0.0570614	+	0.0988332i
$713$	−6.46703e6			−0.476410
$714$		0			0
$715$	−2.33442e6			−0.170771
$716$	3.81849e6	−	6.61382e6i	0.278362	−	0.482136i
$717$	3.25864e6	+	5.64413e6i	0.236722	+	0.410015i
$718$	−7.25236e6	−	1.25615e7i	−0.525011	−	0.909346i
$719$	3.29043e6	−	5.69920e6i	0.237373	−	0.411142i	−0.722587	−	0.691280i	$-0.757047\pi$
$719$	3.29043e6	−	5.69920e6i	0.237373	−	0.411142i	0.959960	+	0.280139i	$0.0903804\pi$
$720$	1.02676e7			0.738141
$721$		0			0
$722$	3.45169e6			0.246427
$723$	1.81151e7	−	3.13762e7i	1.28883	−	2.23231i
$724$	5.08808e6	+	8.81281e6i	0.360751	+	0.624839i
$725$	4.94091e6	+	8.55791e6i	0.349110	+	0.604676i
$726$	9.34977e6	−	1.61943e7i	0.658354	−	1.14030i
$727$	−1.88401e7			−1.32205			−0.661023	−	0.750365i	$-0.729878\pi$
$727$	−1.88401e7			−1.32205			−0.661023	+	0.750365i	$0.729878\pi$
$728$		0			0
$729$	−2.23900e7			−1.56040
$730$	1.32211e6	−	2.28996e6i	0.0918248	−	0.159045i
$731$	−6.00363e6	−	1.03986e7i	−0.415547	−	0.719749i
$732$	−2.36316e7	−	4.09311e7i	−1.63010	−	2.82342i
$733$	−1.39165e6	+	2.41041e6i	−0.0956687	+	0.165703i	−0.909887	−	0.414855i	$-0.863832\pi$
$733$	−1.39165e6	+	2.41041e6i	−0.0956687	+	0.165703i	0.814219	+	0.580558i	$0.197166\pi$
$734$	1.46416e7			1.00311
$735$		0			0
$736$	−2.64867e7			−1.80233
$737$	682457.	−	1.18205e6i	0.0462814	−	0.0801618i
$738$	−1.22673e7	−	2.12476e7i	−0.829104	−	1.43605i
$739$	1.24485e7	+	2.15614e7i	0.838505	+	1.45233i	0.891144	+	0.453720i	$0.149903\pi$
$739$	1.24485e7	+	2.15614e7i	0.838505	+	1.45233i	−0.0526394	+	0.998614i	$0.516763\pi$
$740$	2.70249e6	−	4.68085e6i	0.181420	−	0.314229i
$741$	−1.31164e7			−0.877548
$742$		0			0
$743$	−3.86085e6			−0.256573			−0.128286	−	0.991737i	$-0.540948\pi$
$743$	−3.86085e6			−0.256573			−0.128286	+	0.991737i	$0.540948\pi$
$744$	963161.	−	1.66824e6i	0.0637920	−	0.110491i
$745$	2.02277e6	+	3.50354e6i	0.133523	+	0.231269i
$746$	1.72206e7	+	2.98270e7i	1.13293	+	1.96229i
$747$	2.45275e7	−	4.24828e7i	1.60824	−	2.78555i
$748$	6.03991e6			0.394708
$749$		0			0
$750$	3.30938e7			2.14829
$751$	−3.36368e6	+	5.82607e6i	−0.217628	+	0.376943i	−0.954082	−	0.299544i	$-0.903165\pi$
$751$	−3.36368e6	+	5.82607e6i	−0.217628	+	0.376943i	0.736454	+	0.676488i	$0.236499\pi$
$752$	−8.60736e6	−	1.49084e7i	−0.555041	−	0.961359i
$753$	−2.14869e7	−	3.72164e7i	−1.38097	−	2.39192i
$754$	5.34780e6	−	9.26267e6i	0.342568	−	0.593346i
$755$	−1.43932e6			−0.0918943
$756$		0			0
$757$	2.17782e7			1.38128			0.690642	−	0.723197i	$-0.257328\pi$
$757$	2.17782e7			1.38128			0.690642	+	0.723197i	$0.257328\pi$
$758$	−2.55762e6	+	4.42994e6i	−0.161683	+	0.280043i
$759$	1.10432e7	+	1.91274e7i	0.695812	+	1.20518i
$760$	905255.	+	1.56795e6i	0.0568508	+	0.0984686i
$761$	−1.28537e7	+	2.22633e7i	−0.804575	+	1.39356i	0.112003	+	0.993708i	$0.464273\pi$
$761$	−1.28537e7	+	2.22633e7i	−0.804575	+	1.39356i	−0.916578	+	0.399856i	$0.869060\pi$
$762$	−1.49777e7			−0.934453
$763$		0			0
$764$	−1.62359e7			−1.00633
$765$	−3.65655e6	+	6.33333e6i	−0.225901	+	0.391272i
$766$	−1.70117e7	−	2.94652e7i	−1.04755	−	1.81442i
$767$	4.46564e6	+	7.73471e6i	0.274091	+	0.474740i
$768$	−8.94039e6	+	1.54852e7i	−0.546957	+	0.947358i
$769$	1.34375e7			0.819413			0.409706	−	0.912217i	$-0.365631\pi$
$769$	1.34375e7			0.819413			0.409706	+	0.912217i	$0.365631\pi$
$770$		0			0
$771$	−1.86471e7			−1.12973
$772$	1.32549e7	−	2.29582e7i	0.800451	−	1.38642i
$773$	1.52786e7	+	2.64633e7i	0.919674	+	1.59292i	0.799910	+	0.600121i	$0.204881\pi$
$773$	1.52786e7	+	2.64633e7i	0.919674	+	1.59292i	0.119765	+	0.992802i	$0.461786\pi$
$774$	3.36188e7	+	5.82295e7i	2.01711	+	3.49374i
$775$	−2.33119e6	+	4.03773e6i	−0.139419	+	0.241481i
$776$	−1.61731e6			−0.0964140
$777$		0			0
$778$	3.82364e7			2.26479
$779$	−6.07767e6	+	1.05268e7i	−0.358834	+	0.621518i
$780$	−4.04303e6	−	7.00273e6i	−0.237942	−	0.412127i
$781$	4.43668e6	+	7.68455e6i	0.260274	+	0.450807i
$782$	8.08739e6	−	1.40078e7i	0.472924	−	0.819129i
$783$	1.89558e7			1.10494
$784$		0			0
$785$	−2.58152e6			−0.149521
$786$	−1.84350e7	+	3.19304e7i	−1.06436	+	1.84352i
$787$	−1.03836e6	−	1.79849e6i	−0.0597602	−	0.103508i	0.834598	−	0.550860i	$-0.185700\pi$
$787$	−1.03836e6	−	1.79849e6i	−0.0597602	−	0.103508i	−0.894358	+	0.447353i	$0.852367\pi$
$788$	6.65467e6	+	1.15262e7i	0.381778	+	0.661259i
$789$	2.89686e6	−	5.01751e6i	0.165666	−	0.286943i
$790$	−1.94812e7			−1.11058
$791$		0			0
$792$	−4.14890e6			−0.235028
$793$	7.59404e6	−	1.31533e7i	0.428835	−	0.742764i
$794$	2.09914e7	+	3.63581e7i	1.18165	+	2.04668i
$795$	1.45593e6	+	2.52175e6i	0.0817003	+	0.141509i
$796$	5.27613e6	−	9.13853e6i	0.295143	−	0.511203i
$797$	5.98563e6			0.333783			0.166892	−	0.985975i	$-0.446627\pi$
$797$	5.98563e6			0.333783			0.166892	+	0.985975i	$0.446627\pi$
$798$		0			0
$799$	1.22611e7			0.679460
$800$	−9.54775e6	+	1.65372e7i	−0.527443	+	0.913559i
$801$	−8.64964e6	−	1.49816e7i	−0.476340	−	0.825045i
$802$	6.12575e6	+	1.06101e7i	0.336297	+	0.582484i
$803$	1.50102e6	−	2.59984e6i	0.0821481	−	0.142285i
$804$	4.72784e6			0.257942
$805$		0			0
$806$	5.04633e6			0.273614
$807$	2.31521e7	−	4.01007e7i	1.25143	−	2.16754i
$808$	474798.	+	822375.i	0.0255847	+	0.0443141i
$809$	−9.84321e6	−	1.70489e7i	−0.528769	−	0.915854i	−0.999437	−	0.0335439i	$-0.989321\pi$
$809$	−9.84321e6	−	1.70489e7i	−0.528769	−	0.915854i	0.470669	−	0.882310i	$-0.344013\pi$
$810$	1.45956e6	−	2.52804e6i	0.0781647	−	0.135385i
$811$	−8.50101e6			−0.453856			−0.226928	−	0.973912i	$-0.572868\pi$
$811$	−8.50101e6			−0.453856			−0.226928	+	0.973912i	$0.572868\pi$
$812$		0			0
$813$	4.39580e7			2.33245
$814$	5.76003e6	−	9.97666e6i	0.304694	−	0.527745i
$815$	−6.91749e6	−	1.19814e7i	−0.364800	−	0.631851i
$816$	−6.76845e6	−	1.17233e7i	−0.355848	−	0.616346i
$817$	1.66559e7	−	2.88489e7i	0.873000	−	1.51208i
$818$	3.75168e7			1.96039
$819$		0			0
$820$	−7.49355e6			−0.389182
$821$	680993.	−	1.17952e6i	0.0352602	−	0.0610725i	−0.847857	−	0.530225i	$-0.822107\pi$
$821$	680993.	−	1.17952e6i	0.0352602	−	0.0610725i	0.883117	+	0.469153i	$0.155441\pi$
$822$	211180.	+	365775.i	0.0109012	+	0.0188814i
$823$	679670.	+	1.17722e6i	0.0349783	+	0.0605842i	0.882985	−	0.469402i	$-0.155530\pi$
$823$	679670.	+	1.17722e6i	0.0349783	+	0.0605842i	−0.848006	+	0.529986i	$0.822197\pi$
$824$	−265093.	+	459155.i	−0.0136013	+	0.0235581i
$825$	1.59231e7			0.814505
$826$		0			0
$827$	1.00727e7			0.512132			0.256066	−	0.966659i	$-0.417574\pi$
$827$	1.00727e7			0.512132			0.256066	+	0.966659i	$0.417574\pi$
$828$	−2.41233e7	+	4.17827e7i	−1.22281	+	2.11797i
$829$	−2.81992e6	−	4.88425e6i	−0.142512	−	0.246837i	0.785930	−	0.618315i	$-0.212185\pi$
$829$	−2.81992e6	−	4.88425e6i	−0.142512	−	0.246837i	−0.928442	+	0.371478i	$0.878851\pi$
$830$	−1.40638e7	−	2.43591e7i	−0.708608	−	1.22734i
$831$	−2.86062e7	+	4.95474e7i	−1.43700	+	2.48896i
$832$	1.23867e7			0.620364
$833$		0			0
$834$	−7.77693e7			−3.87163
$835$	1.24445e6	−	2.15544e6i	0.0617675	−	0.106984i
$836$	8.37830e6	+	1.45116e7i	0.414610	+	0.718126i
$837$	4.47180e6	+	7.74539e6i	0.220632	+	0.382146i
$838$	459366.	−	795646.i	0.0225969	−	0.0391390i
$839$	1.16351e7			0.570642			0.285321	−	0.958432i	$-0.407900\pi$
$839$	1.16351e7			0.570642			0.285321	+	0.958432i	$0.407900\pi$
$840$		0			0
$841$	−2.02735e6			−0.0988413
$842$	5.84007e6	−	1.01153e7i	0.283882	−	0.491698i
$843$	−2.14353e7	−	3.71270e7i	−1.03887	−	1.79937i
$844$	−1.36805e7	−	2.36954e7i	−0.661069	−	1.14500i
$845$	−4.03795e6	+	6.99393e6i	−0.194545	+	0.336961i
$846$	−6.86592e7			−3.29817
$847$		0			0
$848$	−3.39916e6			−0.162324
$849$	−5.08055e6	+	8.79977e6i	−0.241903	+	0.418989i
$850$	−5.83057e6	−	1.00988e7i	−0.276799	−	0.479429i
$851$	−8.21660e6	−	1.42316e7i	−0.388927	−	0.673641i
$852$	−1.53679e7	+	2.66180e7i	−0.725297	+	1.25625i
$853$	−2.85205e7			−1.34210			−0.671049	−	0.741413i	$-0.734156\pi$
$853$	−2.85205e7			−1.34210			−0.671049	+	0.741413i	$0.734156\pi$
$854$		0			0
$855$	−2.02888e7			−0.949165
$856$	−318440.	+	551555.i	−0.0148540	+	0.0257279i
$857$	−4.97862e6	−	8.62323e6i	−0.231557	−	0.401068i	0.726710	−	0.686945i	$-0.241049\pi$
$857$	−4.97862e6	−	8.62323e6i	−0.231557	−	0.401068i	−0.958266	+	0.285877i	$0.907715\pi$
$858$	−8.61721e6	−	1.49255e7i	−0.399621	−	0.692164i
$859$	−7.46610e6	+	1.29317e7i	−0.345232	+	0.597959i	−0.985396	−	0.170279i	$-0.945533\pi$
$859$	−7.46610e6	+	1.29317e7i	−0.345232	+	0.597959i	0.640164	+	0.768238i	$0.278866\pi$
$860$	2.05362e7			0.946834
$861$		0			0
$862$	8.90711e6			0.408290
$863$	−1.92467e7	+	3.33362e7i	−0.879687	+	1.52366i	−0.0280024	+	0.999608i	$0.508915\pi$
$863$	−1.92467e7	+	3.33362e7i	−0.879687	+	1.52366i	−0.851685	+	0.524055i	$0.824419\pi$
$864$	1.83150e7	+	3.17225e7i	0.834684	+	1.44572i
$865$	835701.	+	1.44748e6i	0.0379761	+	0.0657766i
$866$	−1.28332e6	+	2.22278e6i	−0.0581489	+	0.100717i
$867$	−2.67770e7			−1.20980
$868$		0			0
$869$	−2.21175e7			−0.993542
$870$	1.31170e7	−	2.27193e7i	0.587537	−	1.01764i
$871$	759650.	+	1.31575e6i	0.0339288	+	0.0587664i
$872$	1.59236e6	+	2.75805e6i	0.0709170	+	0.122832i
$873$	9.06193e6	−	1.56957e7i	0.402425	−	0.697020i
$874$	4.48739e7			1.98708
$875$		0			0
$876$	1.03986e7			0.457839
$877$	−4.70156e6	+	8.14334e6i	−0.206416	+	0.357523i	−0.950583	−	0.310471i	$-0.899513\pi$
$877$	−4.70156e6	+	8.14334e6i	−0.206416	+	0.357523i	0.744167	+	0.667993i	$0.232847\pi$
$878$	2.34863e7	+	4.06794e7i	1.02820	+	1.78090i
$879$	−1.19202e7	−	2.06463e7i	−0.520367	−	0.901302i
$880$	3.34201e6	−	5.78854e6i	0.145479	−	0.251978i
$881$	−1.10395e6			−0.0479194			−0.0239597	−	0.999713i	$-0.507627\pi$
$881$	−1.10395e6			−0.0479194			−0.0239597	+	0.999713i	$0.507627\pi$
$882$		0			0
$883$	8.06579e6			0.348133			0.174067	−	0.984734i	$-0.444309\pi$
$883$	8.06579e6			0.348133			0.174067	+	0.984734i	$0.444309\pi$
$884$	−3.36154e6	+	5.82236e6i	−0.144680	+	0.250593i
$885$	1.09532e7	+	1.89715e7i	0.470093	+	0.814224i
$886$	−1.67967e7	−	2.90927e7i	−0.718851	−	1.24509i
$887$	−7.49509e6	+	1.29819e7i	−0.319866	+	0.554024i	−0.980460	−	0.196719i	$-0.936971\pi$
$887$	−7.49509e6	+	1.29819e7i	−0.319866	+	0.554024i	0.660594	+	0.750743i	$0.270305\pi$
$888$	4.89493e6			0.208312
$889$		0			0
$890$	−9.91920e6			−0.419761
$891$	1.65708e6	−	2.87014e6i	0.0699275	−	0.121118i
$892$	9.74588e6	+	1.68804e7i	0.410118	+	0.710346i
$893$	1.70081e7	+	2.94589e7i	0.713719	+	1.23620i
$894$	−1.49336e7	+	2.58657e7i	−0.624914	+	1.08238i
$895$	6.01950e6			0.251190
$896$		0			0
$897$	−2.45847e7			−1.02019
$898$	2.88192e7	−	4.99163e7i	1.19259	−	2.06563i
$899$	4.36045e6	+	7.55252e6i	0.179942	+	0.311668i
$900$	1.73916e7	+	3.01231e7i	0.715702	+	1.23963i
$901$	1.21052e6	−	2.09669e6i	0.0496776	−	0.0860442i
$902$	−1.59716e7			−0.653629
$903$		0			0
$904$	5.09331e6			0.207290
$905$	−4.01045e6	+	6.94630e6i	−0.162769	+	0.281924i
$906$	−5.31304e6	−	9.20246e6i	−0.215042	−	0.372463i
$907$	−2.06311e6	−	3.57341e6i	−0.0832730	−	0.144233i	0.821381	−	0.570380i	$-0.193204\pi$
$907$	−2.06311e6	−	3.57341e6i	−0.0832730	−	0.144233i	−0.904654	+	0.426147i	$0.859871\pi$
$908$	−7.48859e6	+	1.29706e7i	−0.301429	+	0.522091i
$909$	−1.06413e7			−0.427155
$910$		0			0
$911$	4.04272e7			1.61391			0.806953	−	0.590616i	$-0.201115\pi$
$911$	4.04272e7			1.61391			0.806953	+	0.590616i	$0.201115\pi$
$912$	1.87778e7	−	3.25241e7i	0.747580	−	1.29485i
$913$	−1.59669e7	−	2.76555e7i	−0.633933	−	1.09800i
$914$	−7.42769e6	−	1.28651e7i	−0.294096	−	0.509388i
$915$	1.86265e7	−	3.22620e7i	0.735493	−	1.27391i
$916$	−3.75817e7			−1.47992
$917$		0			0
$918$	−2.23690e7			−0.876072
$919$	−1.09273e7	+	1.89267e7i	−0.426800	+	0.739240i	−0.996587	−	0.0825532i	$-0.973693\pi$
$919$	−1.09273e7	+	1.89267e7i	−0.426800	+	0.739240i	0.569786	+	0.821793i	$0.307026\pi$
$920$	1.69675e6	+	2.93886e6i	0.0660921	+	0.114475i
$921$	2.35071e7	+	4.07155e7i	0.913167	+	1.58165i
$922$	−8.74220e6	+	1.51419e7i	−0.338683	+	0.586616i
$923$	−9.87702e6			−0.381612
$924$		0			0
$925$	−1.18474e7			−0.455271
$926$	−5.22241e6	+	9.04548e6i	−0.200144	+	0.346660i
$927$	−2.97067e6	−	5.14535e6i	−0.113542	−	0.196660i
$928$	1.78589e7	+	3.09325e7i	0.680746	+	1.17909i
$929$	5.34215e6	−	9.25288e6i	0.203085	−	0.351753i	−0.746436	−	0.665457i	$-0.768237\pi$
$929$	5.34215e6	−	9.25288e6i	0.203085	−	0.351753i	0.949521	+	0.313704i	$0.101570\pi$
$930$	1.23775e7			0.469274
$931$		0			0
$932$	−4.34813e6			−0.163970
$933$	−2.94565e7	+	5.10202e7i	−1.10784	+	1.91884i
$934$	−1.48504e7	−	2.57217e7i	−0.557021	−	0.964789i
$935$	2.38034e6	+	4.12287e6i	0.0890451	+	0.154231i
$936$	2.30909e6	−	3.99946e6i	0.0861492	−	0.149215i
$937$	3.99105e7			1.48504			0.742521	−	0.669823i	$-0.233630\pi$
$937$	3.99105e7			1.48504			0.742521	+	0.669823i	$0.233630\pi$
$938$		0			0
$939$	8.78419e7			3.25116
$940$	−1.04852e7	+	1.81609e7i	−0.387041	+	0.670375i
$941$	661751.	+	1.14619e6i	0.0243624	+	0.0421969i	0.877950	−	0.478753i	$-0.158911\pi$
$941$	661751.	+	1.14619e6i	0.0243624	+	0.0421969i	−0.853587	+	0.520950i	$0.825578\pi$
$942$	−9.52934e6	−	1.65053e7i	−0.349893	−	0.606033i
$943$	−1.13916e7	+	1.97308e7i	−0.417163	+	0.722547i
$944$	−2.55724e7			−0.933990
$945$		0			0
$946$	4.37703e7			1.59020
$947$	1.38161e7	−	2.39301e7i	0.500622	−	0.867102i	−0.499378	−	0.866384i	$-0.666438\pi$
$947$	1.38161e7	−	2.39301e7i	0.500622	−	0.867102i	1.00000		0.000718120i	$-0.000228585\pi$
$948$	−3.83057e7	−	6.63473e7i	−1.38434	−	2.39774i
$949$	1.67080e6	+	2.89391e6i	0.0602225	+	0.104308i
$950$	1.61758e7	−	2.80174e7i	0.581510	−	1.00721i
$951$	7.54879e7			2.70661
$952$		0			0
$953$	−3.07901e7			−1.09819			−0.549096	−	0.835759i	$-0.685028\pi$
$953$	−3.07901e7			−1.09819			−0.549096	+	0.835759i	$0.685028\pi$
$954$	−6.77862e6	+	1.17409e7i	−0.241140	+	0.417668i
$955$	−6.39859e6	−	1.10827e7i	−0.227026	−	0.393221i
$956$	4.63387e6	+	8.02610e6i	0.163983	+	0.284027i
$957$	1.48920e7	−	2.57937e7i	0.525621	−	0.910403i
$958$	1.99999e7			0.704068
$959$		0			0
$960$	3.03818e7			1.06398
$961$	1.22573e7	−	2.12302e7i	0.428139	−	0.741559i
$962$	6.41154e6	+	1.11051e7i	0.223370	+	0.386888i
$963$	−3.56849e6	−	6.18080e6i	−0.123999	−	0.214773i
$964$	2.57601e7	−	4.46178e7i	0.892801	−	1.54638i
$965$	2.08952e7			0.722318
$966$		0			0
$967$	2.92557e6			0.100611			0.0503055	−	0.998734i	$-0.483981\pi$
$967$	2.92557e6			0.100611			0.0503055	+	0.998734i	$0.483981\pi$
$968$	1.63096e6	−	2.82490e6i	0.0559441	−	0.0968980i
$969$	1.33744e7	+	2.31652e7i	0.457579	+	0.792551i
$970$	−5.19600e6	−	8.99974e6i	−0.177313	−	0.307115i
$971$	1.39055e6	−	2.40850e6i	0.0473301	−	0.0819781i	−0.841390	−	0.540429i	$-0.818262\pi$
$971$	1.39055e6	−	2.40850e6i	0.0473301	−	0.0819781i	0.888720	+	0.458451i	$0.151595\pi$
$972$	−2.75990e7			−0.936975
$973$		0			0
$974$	−4.29801e7			−1.45168
$975$	−8.86210e6	+	1.53496e7i	−0.298556	+	0.517114i
$976$	2.17436e7	+	3.76610e7i	0.730646	+	1.26552i
$977$	−3.74337e6	−	6.48370e6i	−0.125466	−	0.217313i	0.796449	−	0.604706i	$-0.206709\pi$
$977$	−3.74337e6	−	6.48370e6i	−0.125466	−	0.217313i	−0.921915	+	0.387392i	$0.873376\pi$
$978$	5.10700e7	−	8.84558e7i	1.70733	−	2.95719i
$979$	−1.12615e7			−0.375525
$980$		0			0
$981$	−3.56884e7			−1.18401
$982$	−2.22993e7	+	3.86235e7i	−0.737925	+	1.27812i
$983$	8.99073e6	+	1.55724e7i	0.296764	+	0.514010i	0.975394	−	0.220470i	$-0.0707592\pi$
$983$	8.99073e6	+	1.55724e7i	0.296764	+	0.514010i	−0.678630	+	0.734481i	$0.737426\pi$
$984$	−3.39320e6	−	5.87719e6i	−0.111718	−	0.193500i
$985$	−5.24524e6	+	9.08502e6i	−0.172256	+	0.298357i
$986$	−2.18120e7			−0.714501
$987$		0			0
$988$	−1.86519e7			−0.607899
$989$	3.12189e7	−	5.40727e7i	1.01491	−	1.75787i
$990$	−1.33293e7	−	2.30870e7i	−0.432234	−	0.748652i
$991$	−1.86389e7	−	3.22835e7i	−0.602888	−	1.04423i	−0.992381	−	0.123203i	$-0.960683\pi$
$991$	−1.86389e7	−	3.22835e7i	−0.602888	−	1.04423i	0.389494	−	0.921029i	$-0.372650\pi$
$992$	−8.42606e6	+	1.45944e7i	−0.271860	+	0.470875i
$993$	2.47816e7			0.797548
$994$		0			0
$995$	8.31734e6			0.266334
$996$	5.53067e7	−	9.57940e7i	1.76656	−	3.05978i
$997$	2.43711e7	+	4.22119e7i	0.776492	+	1.34492i	0.933952	+	0.357398i	$0.116336\pi$
$997$	2.43711e7	+	4.22119e7i	0.776492	+	1.34492i	−0.157461	+	0.987525i	$0.550331\pi$
$998$	1.36373e7	+	2.36205e7i	0.433414	+	0.750695i
$999$	−1.13632e7	+	1.96816e7i	−0.360235	+	0.623946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.d.30.1		4
7.2	even	3		49.6.a.f.1.2		2
7.3	odd	6		49.6.c.e.18.1		4
7.4	even	3	inner	49.6.c.d.18.1		4
7.5	odd	6		7.6.a.b.1.2	✓	2
7.6	odd	2		49.6.c.e.30.1		4
21.2	odd	6		441.6.a.l.1.1		2
21.5	even	6		63.6.a.f.1.1		2
28.19	even	6		112.6.a.h.1.2		2
28.23	odd	6		784.6.a.v.1.1		2
35.12	even	12		175.6.b.c.99.4		4
35.19	odd	6		175.6.a.c.1.1		2
35.33	even	12		175.6.b.c.99.1		4
56.5	odd	6		448.6.a.w.1.2		2
56.19	even	6		448.6.a.u.1.1		2
77.54	even	6		847.6.a.c.1.1		2
84.47	odd	6		1008.6.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.b.1.2	✓	2	7.5	odd	6
49.6.a.f.1.2		2	7.2	even	3
49.6.c.d.18.1		4	7.4	even	3	inner
49.6.c.d.30.1		4	1.1	even	1	trivial
49.6.c.e.18.1		4	7.3	odd	6
49.6.c.e.30.1		4	7.6	odd	2
63.6.a.f.1.1		2	21.5	even	6
112.6.a.h.1.2		2	28.19	even	6
175.6.a.c.1.1		2	35.19	odd	6
175.6.b.c.99.1		4	35.33	even	12
175.6.b.c.99.4		4	35.12	even	12
441.6.a.l.1.1		2	21.2	odd	6
448.6.a.u.1.1		2	56.19	even	6
448.6.a.w.1.2		2	56.5	odd	6
784.6.a.v.1.1		2	28.23	odd	6
847.6.a.c.1.1		2	77.54	even	6
1008.6.a.bq.1.1		2	84.47	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-4.13746 + 7.16629i) q^{2} +(-12.8248 - 22.2131i) q^{3} +(-18.2371 - 31.5876i) q^{4} +(14.3746 - 24.8975i) q^{5} +212.248 q^{6} +37.0241 q^{8} +(-207.449 + 359.311i) q^{9} +O(q^{10})\)	\(q+(-4.13746 + 7.16629i) q^{2} +(-12.8248 - 22.2131i) q^{3} +(-18.2371 - 31.5876i) q^{4} +(14.3746 - 24.8975i) q^{5} +212.248 q^{6} +37.0241 q^{8} +(-207.449 + 359.311i) q^{9} +(118.949 + 206.025i) q^{10} +(135.045 + 233.905i) q^{11} +(-467.773 + 810.207i) q^{12} -300.640 q^{13} -737.402 q^{15} +(430.402 - 745.479i) q^{16} +(306.553 + 530.966i) q^{17} +(-1716.62 - 2973.27i) q^{18} +(-850.474 + 1473.06i) q^{19} -1048.60 q^{20} -2234.97 q^{22} +(-1594.08 + 2761.02i) q^{23} +(-474.825 - 822.421i) q^{24} +(1149.24 + 1990.55i) q^{25} +(1243.88 - 2154.47i) q^{26} +4409.07 q^{27} +4299.28 q^{29} +(3050.97 - 5284.44i) q^{30} +(1014.23 + 1756.69i) q^{31} +(4153.93 + 7194.82i) q^{32} +(3463.83 - 5999.54i) q^{33} -5073.40 q^{34} +15133.1 q^{36} +(-2577.23 + 4463.89i) q^{37} +(-7037.60 - 12189.5i) q^{38} +(3855.63 + 6678.14i) q^{39} +(532.206 - 921.808i) q^{40} +7146.21 q^{41} -19584.3 q^{43} +(4925.66 - 8531.49i) q^{44} +(5963.97 + 10329.9i) q^{45} +(-13190.9 - 22847.2i) q^{46} +(9999.19 - 17319.1i) q^{47} -22079.2 q^{48} -19019.8 q^{50} +(7862.94 - 13619.0i) q^{51} +(5482.80 + 9496.49i) q^{52} +(-1974.41 - 3419.78i) q^{53} +(-18242.4 + 31596.7i) q^{54} +7764.86 q^{55} +43628.5 q^{57} +(-17788.1 + 30809.9i) q^{58} +(-14853.8 - 25727.5i) q^{59} +(13448.1 + 23292.8i) q^{60} +(-25259.6 + 43751.0i) q^{61} -16785.3 q^{62} -41201.1 q^{64} +(-4321.57 + 7485.18i) q^{65} +(28662.9 + 49645.7i) q^{66} +(-2526.78 - 4376.51i) q^{67} +(11181.3 - 19366.6i) q^{68} +81774.5 q^{69} +32853.3 q^{71} +(-7680.59 + 13303.2i) q^{72} +(-5557.48 - 9625.84i) q^{73} +(-21326.3 - 36938.3i) q^{74} +(29477.5 - 51056.5i) q^{75} +62040.8 q^{76} -63810.0 q^{78} +(-40944.7 + 70918.3i) q^{79} +(-12373.7 - 21431.9i) q^{80} +(-6135.28 - 10626.6i) q^{81} +(-29567.1 + 51211.8i) q^{82} -118234. q^{83} +17626.3 q^{85} +(81029.2 - 140347. i) q^{86} +(-55137.2 - 95500.4i) q^{87} +(4999.91 + 8660.10i) q^{88} +(-20847.7 + 36109.2i) q^{89} -98702.8 q^{90} +116286. q^{92} +(26014.4 - 45058.3i) q^{93} +(82742.5 + 143314. i) q^{94} +(24450.4 + 42349.4i) q^{95} +(106546. - 184544. i) q^{96} -43682.8 q^{97} -112059. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9}+O(q^{10}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9} + 204 q^{10} - 396 q^{11} - 1554 q^{12} + 700 q^{13} - 3312 q^{15} - 113 q^{16} + 1800 q^{17} - 3537 q^{18} - 3266 q^{19} - 5040 q^{20} - 3504 q^{22} - 2088 q^{23} - 1854 q^{24} + 3238 q^{25} + 2016 q^{26} + 12744 q^{27} + 13392 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 20016 q^{33} - 11868 q^{34} + 21258 q^{36} - 6232 q^{37} - 15210 q^{38} + 20496 q^{39} + 3216 q^{40} + 12096 q^{41} - 6040 q^{43} + 30816 q^{44} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} - 82428 q^{48} - 39402 q^{50} - 7596 q^{51} + 31444 q^{52} - 9468 q^{53} - 37908 q^{54} + 77808 q^{55} + 25752 q^{57} - 37314 q^{58} - 43938 q^{59} - 2016 q^{60} - 64754 q^{61} - 30600 q^{62} - 141566 q^{64} - 39060 q^{65} + 66816 q^{66} - 24784 q^{67} - 14994 q^{68} + 206784 q^{69} + 194832 q^{71} - 8775 q^{72} + 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 25564 q^{76} - 146160 q^{78} - 51256 q^{79} - 70272 q^{80} + 61074 q^{81} - 58338 q^{82} - 235116 q^{83} - 75720 q^{85} + 150048 q^{86} - 63180 q^{87} + 40656 q^{88} + 84276 q^{89} - 187704 q^{90} + 301824 q^{92} + 92280 q^{93} + 159468 q^{94} - 24264 q^{95} + 255906 q^{96} - 41552 q^{97} - 33480 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9 + 204 * q^10 - 396 * q^11 - 1554 * q^12 + 700 * q^13 - 3312 * q^15 - 113 * q^16 + 1800 * q^17 - 3537 * q^18 - 3266 * q^19 - 5040 * q^20 - 3504 * q^22 - 2088 * q^23 - 1854 * q^24 + 3238 * q^25 + 2016 * q^26 + 12744 * q^27 + 13392 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 20016 * q^33 - 11868 * q^34 + 21258 * q^36 - 6232 * q^37 - 15210 * q^38 + 20496 * q^39 + 3216 * q^40 + 12096 * q^41 - 6040 * q^43 + 30816 * q^44 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 - 82428 * q^48 - 39402 * q^50 - 7596 * q^51 + 31444 * q^52 - 9468 * q^53 - 37908 * q^54 + 77808 * q^55 + 25752 * q^57 - 37314 * q^58 - 43938 * q^59 - 2016 * q^60 - 64754 * q^61 - 30600 * q^62 - 141566 * q^64 - 39060 * q^65 + 66816 * q^66 - 24784 * q^67 - 14994 * q^68 + 206784 * q^69 + 194832 * q^71 - 8775 * q^72 + 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 25564 * q^76 - 146160 * q^78 - 51256 * q^79 - 70272 * q^80 + 61074 * q^81 - 58338 * q^82 - 235116 * q^83 - 75720 * q^85 + 150048 * q^86 - 63180 * q^87 + 40656 * q^88 + 84276 * q^89 - 187704 * q^90 + 301824 * q^92 + 92280 * q^93 + 159468 * q^94 - 24264 * q^95 + 255906 * q^96 - 41552 * q^97 - 33480 * q^99

Introduction

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