LMFDB - Embedded newform 294.8.e.z.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,8,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.e (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:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 22015x^{4} - 28740x^{3} + 484660225x^{2} - 316355550x + 206496900 $ x^6 + 22015x^4 - 28740x^3 + 484660225x^2 - 316355550x + 206496900
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$0.326375 + 0.565298i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.8.e.z.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 + 6.92820i) q^{2} +(13.5000 + 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(154.404 - 267.436i) q^{5} -216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})$	\(q+(-4.00000 + 6.92820i) q^{2} +(13.5000 + 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(154.404 - 267.436i) q^{5} -216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(1235.23 + 2139.49i) q^{10} +(-3241.58 - 5614.58i) q^{11} +(864.000 - 1496.49i) q^{12} -993.626 q^{13} +8337.82 q^{15} +(-2048.00 + 3547.24i) q^{16} +(15459.7 + 26777.0i) q^{17} +(-2916.00 - 5050.66i) q^{18} +(-7794.64 + 13500.7i) q^{19} -19763.7 q^{20} +51865.2 q^{22} +(40551.3 - 70236.9i) q^{23} +(6912.00 + 11971.9i) q^{24} +(-8618.77 - 14928.1i) q^{25} +(3974.50 - 6884.04i) q^{26} -19683.0 q^{27} -34651.6 q^{29} +(-33351.3 + 57766.1i) q^{30} +(80255.8 + 139007. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(87522.6 - 151594. i) q^{33} -247356. q^{34} +46656.0 q^{36} +(5542.31 - 9599.55i) q^{37} +(-62357.1 - 108006. i) q^{38} +(-13413.9 - 23233.6i) q^{39} +(79054.9 - 136927. i) q^{40} +459665. q^{41} +455951. q^{43} +(-207461. + 359333. i) q^{44} +(112561. + 194961. i) q^{45} +(324410. + 561895. i) q^{46} +(149997. - 259803. i) q^{47} -110592. q^{48} +137900. q^{50} +(-417413. + 722980. i) q^{51} +(31796.0 + 55072.3i) q^{52} +(-948986. - 1.64369e6i) q^{53} +(78732.0 - 136368. i) q^{54} -2.00205e6 q^{55} -420911. q^{57} +(138606. - 240073. i) q^{58} +(-1.48133e6 - 2.56574e6i) q^{59} +(-266810. - 462129. i) q^{60} +(-1.19185e6 + 2.06435e6i) q^{61} -1.28409e6 q^{62} +262144. q^{64} +(-153420. + 265731. i) q^{65} +(700181. + 1.21275e6i) q^{66} +(-2.26696e6 - 3.92649e6i) q^{67} +(989423. - 1.71373e6i) q^{68} +2.18977e6 q^{69} -4.00697e6 q^{71} +(-186624. + 323242. i) q^{72} +(-1.73655e6 - 3.00779e6i) q^{73} +(44338.4 + 76796.4i) q^{74} +(232707. - 403060. i) q^{75} +997714. q^{76} +214623. q^{78} +(346434. - 600041. i) q^{79} +(632439. + 1.09542e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-1.83866e6 + 3.18465e6i) q^{82} -2.65827e6 q^{83} +9.54818e6 q^{85} +(-1.82381e6 + 3.15892e6i) q^{86} +(-467797. - 810248. i) q^{87} +(-1.65969e6 - 2.87466e6i) q^{88} +(-686791. + 1.18956e6i) q^{89} -1.80097e6 q^{90} -5.19057e6 q^{92} +(-2.16691e6 + 3.75319e6i) q^{93} +(1.19998e6 + 2.07842e6i) q^{94} +(2.40705e6 + 4.16913e6i) q^{95} +(442368. - 766204. i) q^{96} -299539. q^{97} +4.72622e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} + 81 q^{3} - 192 q^{4} - 70 q^{5} - 1296 q^{6} + 3072 q^{8} - 2187 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 + 81 * q^3 - 192 * q^4 - 70 * q^5 - 1296 * q^6 + 3072 * q^8 - 2187 * q^9	\( 6 q - 24 q^{2} + 81 q^{3} - 192 q^{4} - 70 q^{5} - 1296 q^{6} + 3072 q^{8} - 2187 q^{9} - 560 q^{10} - 2428 q^{11} + 5184 q^{12} + 3838 q^{13} - 3780 q^{15} - 12288 q^{16} + 24508 q^{17} - 17496 q^{18} - 1353 q^{19} + 8960 q^{20} + 38848 q^{22} - 96628 q^{23} + 41472 q^{24} - 135175 q^{25} - 15352 q^{26} - 118098 q^{27} - 228224 q^{29} + 15120 q^{30} + 221395 q^{31} - 98304 q^{32} + 65556 q^{33} - 392128 q^{34} + 279936 q^{36} - 249987 q^{37} - 10824 q^{38} + 51813 q^{39} - 35840 q^{40} - 1221852 q^{41} + 1200486 q^{43} - 155392 q^{44} - 51030 q^{45} - 773024 q^{46} - 123114 q^{47} - 663552 q^{48} + 2162800 q^{50} - 661716 q^{51} - 122816 q^{52} - 3004752 q^{53} + 472392 q^{54} - 4492720 q^{55} - 73062 q^{57} + 912896 q^{58} - 2852938 q^{59} + 120960 q^{60} + 665386 q^{61} - 3542320 q^{62} + 1572864 q^{64} - 5835930 q^{65} + 524448 q^{66} - 10545857 q^{67} + 1568512 q^{68} - 5217912 q^{69} - 2039524 q^{71} - 1119744 q^{72} - 6858031 q^{73} - 1999896 q^{74} + 3649725 q^{75} + 173184 q^{76} - 829008 q^{78} - 1723021 q^{79} - 286720 q^{80} - 1594323 q^{81} + 4887408 q^{82} - 5271608 q^{83} + 1474120 q^{85} - 4801944 q^{86} - 3081024 q^{87} - 1243136 q^{88} - 976224 q^{89} + 816480 q^{90} + 12368384 q^{92} - 5977665 q^{93} - 984912 q^{94} - 11136310 q^{95} + 2654208 q^{96} + 16971584 q^{97} + 3540024 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 + 81 * q^3 - 192 * q^4 - 70 * q^5 - 1296 * q^6 + 3072 * q^8 - 2187 * q^9 - 560 * q^10 - 2428 * q^11 + 5184 * q^12 + 3838 * q^13 - 3780 * q^15 - 12288 * q^16 + 24508 * q^17 - 17496 * q^18 - 1353 * q^19 + 8960 * q^20 + 38848 * q^22 - 96628 * q^23 + 41472 * q^24 - 135175 * q^25 - 15352 * q^26 - 118098 * q^27 - 228224 * q^29 + 15120 * q^30 + 221395 * q^31 - 98304 * q^32 + 65556 * q^33 - 392128 * q^34 + 279936 * q^36 - 249987 * q^37 - 10824 * q^38 + 51813 * q^39 - 35840 * q^40 - 1221852 * q^41 + 1200486 * q^43 - 155392 * q^44 - 51030 * q^45 - 773024 * q^46 - 123114 * q^47 - 663552 * q^48 + 2162800 * q^50 - 661716 * q^51 - 122816 * q^52 - 3004752 * q^53 + 472392 * q^54 - 4492720 * q^55 - 73062 * q^57 + 912896 * q^58 - 2852938 * q^59 + 120960 * q^60 + 665386 * q^61 - 3542320 * q^62 + 1572864 * q^64 - 5835930 * q^65 + 524448 * q^66 - 10545857 * q^67 + 1568512 * q^68 - 5217912 * q^69 - 2039524 * q^71 - 1119744 * q^72 - 6858031 * q^73 - 1999896 * q^74 + 3649725 * q^75 + 173184 * q^76 - 829008 * q^78 - 1723021 * q^79 - 286720 * q^80 - 1594323 * q^81 + 4887408 * q^82 - 5271608 * q^83 + 1474120 * q^85 - 4801944 * q^86 - 3081024 * q^87 - 1243136 * q^88 - 976224 * q^89 + 816480 * q^90 + 12368384 * q^92 - 5977665 * q^93 - 984912 * q^94 - 11136310 * q^95 + 2654208 * q^96 + 16971584 * q^97 + 3540024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$	13.5000	+	23.3827i	0.288675	+	0.500000i
$3$	13.5000	+	23.3827i	0.288675	+	0.500000i
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	154.404	−	267.436i	0.552413	−	0.956807i	−0.445687	−	0.895189i	$-0.647040\pi$
$5$	154.404	−	267.436i	0.552413	−	0.956807i	0.998100	−	0.0616184i	$-0.0196262\pi$
$6$	−216.000			−0.408248
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	−364.500	+	631.333i	−0.166667	+	0.288675i
$10$	1235.23	+	2139.49i	0.390615	+	0.676565i
$11$	−3241.58	−	5614.58i	−0.734314	−	1.27187i	−0.955023	−	0.296530i	$-0.904170\pi$
$11$	−3241.58	−	5614.58i	−0.734314	−	1.27187i	0.220709	−	0.975340i	$-0.429163\pi$
$12$	864.000	−	1496.49i	0.144338	−	0.250000i
$13$	−993.626			−0.125436			−0.0627178	−	0.998031i	$-0.519977\pi$
$13$	−993.626			−0.125436			−0.0627178	+	0.998031i	$0.519977\pi$
$14$		0			0
$15$	8337.82			0.637872
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	15459.7	+	26777.0i	0.763186	+	1.32188i	0.941200	+	0.337850i	$0.109699\pi$
$17$	15459.7	+	26777.0i	0.763186	+	1.32188i	−0.178014	+	0.984028i	$0.556967\pi$
$18$	−2916.00	−	5050.66i	−0.117851	−	0.204124i
$19$	−7794.64	+	13500.7i	−0.260710	+	0.451564i	−0.966431	−	0.256927i	$-0.917290\pi$
$19$	−7794.64	+	13500.7i	−0.260710	+	0.451564i	0.705720	+	0.708490i	$0.250623\pi$
$20$	−19763.7			−0.552413
$21$		0			0
$22$	51865.2			1.03848
$23$	40551.3	−	70236.9i	0.694956	−	1.20370i	−0.275239	−	0.961376i	$-0.588757\pi$
$23$	40551.3	−	70236.9i	0.694956	−	1.20370i	0.970195	−	0.242324i	$-0.0779096\pi$
$24$	6912.00	+	11971.9i	0.102062	+	0.176777i
$25$	−8618.77	−	14928.1i	−0.110320	−	0.191080i
$26$	3974.50	−	6884.04i	0.0443482	−	0.0768134i
$27$	−19683.0			−0.192450
$28$		0			0
$29$	−34651.6			−0.263834			−0.131917	−	0.991261i	$-0.542113\pi$
$29$	−34651.6			−0.263834			−0.131917	+	0.991261i	$0.542113\pi$
$30$	−33351.3	+	57766.1i	−0.225522	+	0.390615i
$31$	80255.8	+	139007.i	0.483850	+	0.838052i	0.999828	−	0.0185496i	$-0.00590485\pi$
$31$	80255.8	+	139007.i	0.483850	+	0.838052i	−0.515978	+	0.856602i	$0.672572\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$	87522.6	−	151594.i	0.423957	−	0.734314i
$34$	−247356.			−1.07931
$35$		0			0
$36$	46656.0			0.166667
$37$	5542.31	−	9599.55i	0.0179881	−	0.0311562i	−0.856891	−	0.515497i	$-0.827607\pi$
$37$	5542.31	−	9599.55i	0.0179881	−	0.0311562i	0.874879	+	0.484341i	$0.160941\pi$
$38$	−62357.1	−	108006.i	−0.184350	−	0.319304i
$39$	−13413.9	−	23233.6i	−0.0362102	−	0.0627178i
$40$	79054.9	−	136927.i	0.195307	−	0.338282i
$41$	459665.			1.04159			0.520796	−	0.853681i	$-0.325635\pi$
$41$	459665.			1.04159			0.520796	+	0.853681i	$0.325635\pi$
$42$		0			0
$43$	455951.			0.874538			0.437269	−	0.899331i	$-0.355946\pi$
$43$	455951.			0.874538			0.437269	+	0.899331i	$0.355946\pi$
$44$	−207461.	+	359333.i	−0.367157	+	0.635935i
$45$	112561.	+	194961.i	0.184138	+	0.318936i
$46$	324410.	+	561895.i	0.491408	+	0.851144i
$47$	149997.	−	259803.i	0.210737	−	0.365007i	−0.741208	−	0.671275i	$-0.765747\pi$
$47$	149997.	−	259803.i	0.210737	−	0.365007i	0.951945	+	0.306268i	$0.0990803\pi$
$48$	−110592.			−0.144338
$49$		0			0
$50$	137900.			0.156016
$51$	−417413.	+	722980.i	−0.440626	+	0.763186i
$52$	31796.0	+	55072.3i	0.0313589	+	0.0543152i
$53$	−948986.	−	1.64369e6i	−0.875577	−	1.51654i	−0.856147	−	0.516733i	$-0.827148\pi$
$53$	−948986.	−	1.64369e6i	−0.875577	−	1.51654i	−0.0194308	−	0.999811i	$-0.506185\pi$
$54$	78732.0	−	136368.i	0.0680414	−	0.117851i
$55$	−2.00205e6			−1.62258
$56$		0			0
$57$	−420911.			−0.301042
$58$	138606.	−	240073.i	0.0932794	−	0.161565i
$59$	−1.48133e6	−	2.56574e6i	−0.939011	−	1.62641i	−0.767321	−	0.641264i	$-0.778410\pi$
$59$	−1.48133e6	−	2.56574e6i	−0.939011	−	1.62641i	−0.171690	−	0.985151i	$-0.554923\pi$
$60$	−266810.	−	462129.i	−0.159468	−	0.276206i
$61$	−1.19185e6	+	2.06435e6i	−0.672309	+	1.16447i	0.304939	+	0.952372i	$0.401364\pi$
$61$	−1.19185e6	+	2.06435e6i	−0.672309	+	1.16447i	−0.977248	+	0.212101i	$0.931969\pi$
$62$	−1.28409e6			−0.684267
$63$		0			0
$64$	262144.			0.125000
$65$	−153420.	+	265731.i	−0.0692923	+	0.120018i
$66$	700181.	+	1.21275e6i	0.299783	+	0.519239i
$67$	−2.26696e6	−	3.92649e6i	−0.920835	−	1.59493i	−0.798127	−	0.602489i	$-0.794176\pi$
$67$	−2.26696e6	−	3.92649e6i	−0.920835	−	1.59493i	−0.122708	−	0.992443i	$-0.539158\pi$
$68$	989423.	−	1.71373e6i	0.381593	−	0.660939i
$69$	2.18977e6			0.802466
$70$		0			0
$71$	−4.00697e6			−1.32866			−0.664328	−	0.747441i	$-0.731282\pi$
$71$	−4.00697e6			−1.32866			−0.664328	+	0.747441i	$0.731282\pi$
$72$	−186624.	+	323242.i	−0.0589256	+	0.102062i
$73$	−1.73655e6	−	3.00779e6i	−0.522465	−	0.904936i	−0.999658	−	0.0261377i	$-0.991679\pi$
$73$	−1.73655e6	−	3.00779e6i	−0.522465	−	0.904936i	0.477193	−	0.878798i	$-0.341654\pi$
$74$	44338.4	+	76796.4i	0.0127195	+	0.0220308i
$75$	232707.	−	403060.i	0.0636934	−	0.110320i
$76$	997714.			0.260710
$77$		0			0
$78$	214623.			0.0512089
$79$	346434.	−	600041.i	0.0790543	−	0.136926i	−0.823788	−	0.566898i	$-0.808143\pi$
$79$	346434.	−	600041.i	0.0790543	−	0.136926i	0.902842	+	0.429972i	$0.141477\pi$
$80$	632439.	+	1.09542e6i	0.138103	+	0.239202i
$81$	−265720.	−	460241.i	−0.0555556	−	0.0962250i
$82$	−1.83866e6	+	3.18465e6i	−0.368259	+	0.637842i
$83$	−2.65827e6			−0.510301			−0.255151	−	0.966901i	$-0.582125\pi$
$83$	−2.65827e6			−0.510301			−0.255151	+	0.966901i	$0.582125\pi$
$84$		0			0
$85$	9.54818e6			1.68638
$86$	−1.82381e6	+	3.15892e6i	−0.309196	+	0.535543i
$87$	−467797.	−	810248.i	−0.0761623	−	0.131917i
$88$	−1.65969e6	−	2.87466e6i	−0.259619	−	0.449674i
$89$	−686791.	+	1.18956e6i	−0.103267	+	0.178863i	−0.913029	−	0.407895i	$-0.866263\pi$
$89$	−686791.	+	1.18956e6i	−0.103267	+	0.178863i	0.809762	+	0.586758i	$0.199596\pi$
$90$	−1.80097e6			−0.260410
$91$		0			0
$92$	−5.19057e6			−0.694956
$93$	−2.16691e6	+	3.75319e6i	−0.279351	+	0.483850i
$94$	1.19998e6	+	2.07842e6i	0.149014	+	0.258099i
$95$	2.40705e6	+	4.16913e6i	0.288040	+	0.498899i
$96$	442368.	−	766204.i	0.0510310	−	0.0883883i
$97$	−299539.			−0.0333236			−0.0166618	−	0.999861i	$-0.505304\pi$
$97$	−299539.			−0.0333236			−0.0166618	+	0.999861i	$0.505304\pi$
$98$		0			0
$99$	4.72622e6			0.489543
$100$	−551601.	+	955401.i	−0.0551601	+	0.0955401i
$101$	709804.	+	1.22942e6i	0.0685509	+	0.118734i	0.898264	−	0.439457i	$-0.144829\pi$
$101$	709804.	+	1.22942e6i	0.0685509	+	0.118734i	−0.829713	+	0.558191i	$0.811496\pi$
$102$	−3.33930e6	−	5.78384e6i	−0.311570	−	0.539654i
$103$	9.35929e6	−	1.62108e7i	0.843942	−	1.46175i	−0.0425955	−	0.999092i	$-0.513563\pi$
$103$	9.35929e6	−	1.62108e7i	0.843942	−	1.46175i	0.886537	−	0.462657i	$-0.153104\pi$
$104$	−508736.			−0.0443482
$105$		0			0
$106$	1.51838e7			1.23825
$107$	−2.10297e6	+	3.64245e6i	−0.165955	+	0.287442i	−0.936994	−	0.349346i	$-0.886404\pi$
$107$	−2.10297e6	+	3.64245e6i	−0.165955	+	0.287442i	0.771039	+	0.636788i	$0.219737\pi$
$108$	629856.	+	1.09094e6i	0.0481125	+	0.0833333i
$109$	−5.45235e6	−	9.44375e6i	−0.403265	−	0.698476i	0.590853	−	0.806780i	$-0.298792\pi$
$109$	−5.45235e6	−	9.44375e6i	−0.403265	−	0.698476i	−0.994118	+	0.108303i	$0.965458\pi$
$110$	8.00821e6	−	1.38706e7i	0.573668	−	0.993623i
$111$	299284.			0.0207708
$112$		0			0
$113$	7.18622e6			0.468517			0.234259	−	0.972174i	$-0.424734\pi$
$113$	7.18622e6			0.468517			0.234259	+	0.972174i	$0.424734\pi$
$114$	1.68364e6	−	2.91615e6i	0.106435	−	0.184350i
$115$	−1.25226e7	−	2.16897e7i	−0.767806	−	1.32988i
$116$	1.10885e6	+	1.92059e6i	0.0659585	+	0.114243i
$117$	362177.	−	627308.i	0.0209059	−	0.0362102i
$118$	2.37013e7			1.32796
$119$		0			0
$120$	4.26897e6			0.225522
$121$	−1.12721e7	+	1.95238e7i	−0.578435	+	1.00188i
$122$	−9.53484e6	−	1.65148e7i	−0.475394	−	0.823407i
$123$	6.20548e6	+	1.07482e7i	0.300682	+	0.520796i
$124$	5.13637e6	−	8.89645e6i	0.241925	−	0.419026i
$125$	1.88026e7			0.861057
$126$		0			0
$127$	−1.62113e7			−0.702270			−0.351135	−	0.936325i	$-0.614204\pi$
$127$	−1.62113e7			−0.702270			−0.351135	+	0.936325i	$0.614204\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$	6.15534e6	+	1.06614e7i	0.252457	+	0.437269i
$130$	−1.22736e6	−	2.12585e6i	−0.0489971	−	0.0848654i
$131$	3.37734e6	−	5.84973e6i	0.131258	−	0.227346i	−0.792904	−	0.609347i	$-0.791432\pi$
$131$	3.37734e6	−	5.84973e6i	0.131258	−	0.227346i	0.924162	+	0.382001i	$0.124765\pi$
$132$	−1.12029e7			−0.423957
$133$		0			0
$134$	3.62713e7			1.30226
$135$	−3.03914e6	+	5.26394e6i	−0.106312	+	0.184138i
$136$	7.91538e6	+	1.37098e7i	0.269827	+	0.467354i
$137$	−2.76387e7	−	4.78716e7i	−0.918322	−	1.59058i	−0.801963	−	0.597374i	$-0.796211\pi$
$137$	−2.76387e7	−	4.78716e7i	−0.918322	−	1.59058i	−0.116359	−	0.993207i	$-0.537122\pi$
$138$	−8.75908e6	+	1.51712e7i	−0.283715	+	0.491408i
$139$	3.26212e7			1.03026			0.515132	−	0.857111i	$-0.327743\pi$
$139$	3.26212e7			1.03026			0.515132	+	0.857111i	$0.327743\pi$
$140$		0			0
$141$	8.09985e6			0.243338
$142$	1.60279e7	−	2.77611e7i	0.469751	−	0.813632i
$143$	3.22092e6	+	5.57879e6i	0.0921092	+	0.159538i
$144$	−1.49299e6	−	2.58594e6i	−0.0416667	−	0.0721688i
$145$	−5.35035e6	+	9.26708e6i	−0.145745	+	0.252438i
$146$	2.77848e7			0.738877
$147$		0			0
$148$	−709415.			−0.0179881
$149$	3.21298e7	−	5.56505e7i	0.795713	−	1.37822i	−0.126673	−	0.991945i	$-0.540430\pi$
$149$	3.21298e7	−	5.56505e7i	0.795713	−	1.37822i	0.922386	−	0.386270i	$-0.126237\pi$
$150$	1.86165e6	+	3.22448e6i	0.0450380	+	0.0780082i
$151$	−3.11266e7	−	5.39128e7i	−0.735719	−	1.27430i	−0.954407	−	0.298508i	$-0.903511\pi$
$151$	−3.11266e7	−	5.39128e7i	−0.735719	−	1.27430i	0.218688	−	0.975795i	$-0.429822\pi$
$152$	−3.99086e6	+	6.91236e6i	−0.0921751	+	0.159652i
$153$	−2.25403e7			−0.508791
$154$		0			0
$155$	4.95673e7			1.06914
$156$	−858493.	+	1.48695e6i	−0.0181051	+	0.0313589i
$157$	8.89893e6	+	1.54134e7i	0.183522	+	0.317870i	0.943078	−	0.332573i	$-0.107917\pi$
$157$	8.89893e6	+	1.54134e7i	0.183522	+	0.317870i	−0.759555	+	0.650443i	$0.774583\pi$
$158$	2.77147e6	+	4.80033e6i	0.0558999	+	0.0968214i
$159$	2.56226e7	−	4.43797e7i	0.505515	−	0.875577i
$160$	−1.01190e7			−0.195307
$161$		0			0
$162$	4.25153e6			0.0785674
$163$	−1.92169e7	+	3.32846e7i	−0.347557	+	0.601986i	−0.985815	−	0.167836i	$-0.946322\pi$
$163$	−1.92169e7	+	3.32846e7i	−0.347557	+	0.601986i	0.638258	+	0.769823i	$0.279655\pi$
$164$	−1.47093e7	−	2.54772e7i	−0.260398	−	0.451023i
$165$	−2.70277e7	−	4.68134e7i	−0.468398	−	0.811290i
$166$	1.06331e7	−	1.84171e7i	0.180419	−	0.312494i
$167$	5.42631e7			0.901566			0.450783	−	0.892634i	$-0.351145\pi$
$167$	5.42631e7			0.901566			0.450783	+	0.892634i	$0.351145\pi$
$168$		0			0
$169$	−6.17612e7			−0.984266
$170$	−3.81927e7	+	6.61517e7i	−0.596224	+	1.03269i
$171$	−5.68229e6	−	9.84202e6i	−0.0869035	−	0.150521i
$172$	−1.45904e7	−	2.52714e7i	−0.218635	−	0.378686i
$173$	8.55530e6	−	1.48182e7i	0.125624	−	0.217588i	−0.796352	−	0.604833i	$-0.793240\pi$
$173$	8.55530e6	−	1.48182e7i	0.125624	−	0.217588i	0.921977	+	0.387245i	$0.126573\pi$
$174$	7.48475e6			0.107710
$175$		0			0
$176$	2.65550e7			0.367157
$177$	3.99960e7	−	6.92751e7i	0.542138	−	0.939011i
$178$	−5.49433e6	−	9.51646e6i	−0.0730205	−	0.126475i
$179$	3.20119e7	+	5.54463e7i	0.417182	+	0.722581i	0.995655	−	0.0931208i	$-0.0296843\pi$
$179$	3.20119e7	+	5.54463e7i	0.417182	+	0.722581i	−0.578472	+	0.815702i	$0.696351\pi$
$180$	7.20388e6	−	1.24775e7i	0.0920688	−	0.159468i
$181$	−6.60928e6			−0.0828475			−0.0414237	−	0.999142i	$-0.513189\pi$
$181$	−6.60928e6			−0.0828475			−0.0414237	+	0.999142i	$0.513189\pi$
$182$		0			0
$183$	−6.43601e7			−0.776315
$184$	2.07623e7	−	3.59613e7i	0.245704	−	0.425572i
$185$	−1.71151e6	−	2.96442e6i	−0.0198737	−	0.0344222i
$186$	−1.73352e7	−	3.00255e7i	−0.197531	−	0.342133i
$187$	1.00228e8	−	1.73600e8i	1.12084	−	1.94135i
$188$	−1.91996e7			−0.210737
$189$		0			0
$190$	−3.85128e7			−0.407350
$191$	−1.13085e7	+	1.95869e7i	−0.117432	+	0.203399i	−0.918749	−	0.394841i	$-0.870800\pi$
$191$	−1.13085e7	+	1.95869e7i	−0.117432	+	0.203399i	0.801317	+	0.598240i	$0.204133\pi$
$192$	3.53894e6	+	6.12963e6i	0.0360844	+	0.0625000i
$193$	−8.00169e6	−	1.38593e7i	−0.0801182	−	0.138769i	0.823182	−	0.567777i	$-0.192196\pi$
$193$	−8.00169e6	−	1.38593e7i	−0.0801182	−	0.138769i	−0.903301	+	0.429008i	$0.858863\pi$
$194$	1.19816e6	−	2.07527e6i	0.0117817	−	0.0204065i
$195$	−8.28468e6			−0.0800119
$196$		0			0
$197$	−1.29465e7			−0.120648			−0.0603242	−	0.998179i	$-0.519213\pi$
$197$	−1.29465e7			−0.120648			−0.0603242	+	0.998179i	$0.519213\pi$
$198$	−1.89049e7	+	3.27442e7i	−0.173080	+	0.299783i
$199$	−1.01406e8	−	1.75640e8i	−0.912173	−	1.57993i	−0.810989	−	0.585062i	$-0.801070\pi$
$199$	−1.01406e8	−	1.75640e8i	−0.912173	−	1.57993i	−0.101184	−	0.994868i	$-0.532263\pi$
$200$	−4.41281e6	−	7.64321e6i	−0.0390041	−	0.0675571i
$201$	6.12079e7	−	1.06015e8i	0.531644	−	0.920835i
$202$	−1.13569e7			−0.0969457
$203$		0			0
$204$	5.34288e7			0.440626
$205$	7.09741e7	−	1.22931e8i	0.575389	−	0.996603i
$206$	7.48743e7	+	1.29686e8i	0.596757	+	1.03361i
$207$	2.95619e7	+	5.12027e7i	0.231652	+	0.401233i
$208$	2.03495e6	−	3.52463e6i	0.0156795	−	0.0271576i
$209$	1.01068e8			0.765774
$210$		0			0
$211$	2.54584e8			1.86570			0.932851	−	0.360262i	$-0.117313\pi$
$211$	2.54584e8			1.86570			0.932851	+	0.360262i	$0.117313\pi$
$212$	−6.07351e7	+	1.05196e8i	−0.437789	+	0.758272i
$213$	−5.40942e7	−	9.36938e7i	−0.383550	−	0.664328i
$214$	−1.68237e7	−	2.91396e7i	−0.117348	−	0.203252i
$215$	7.04008e7	−	1.21938e8i	0.483106	−	0.836765i
$216$	−1.00777e7			−0.0680414
$217$		0			0
$218$	8.72376e7			0.570303
$219$	4.68868e7	−	8.12104e7i	0.301645	−	0.522465i
$220$	6.40657e7	+	1.10965e8i	0.405645	+	0.702597i
$221$	−1.53612e7	−	2.66063e7i	−0.0957308	−	0.165811i
$222$	−1.19714e6	+	2.07350e6i	−0.00734360	+	0.0127195i
$223$	−1.97491e8			−1.19256			−0.596280	−	0.802777i	$-0.703355\pi$
$223$	−1.97491e8			−1.19256			−0.596280	+	0.802777i	$0.703355\pi$
$224$		0			0
$225$	1.25662e7			0.0735468
$226$	−2.87449e7	+	4.97876e7i	−0.165646	+	0.286907i
$227$	3.09513e7	+	5.36092e7i	0.175626	+	0.304193i	0.940378	−	0.340132i	$-0.110472\pi$
$227$	3.09513e7	+	5.36092e7i	0.175626	+	0.304193i	−0.764752	+	0.644325i	$0.777138\pi$
$228$	1.34691e7	+	2.33292e7i	0.0752606	+	0.130355i
$229$	−1.55203e8	+	2.68819e8i	−0.854035	+	1.47923i	0.0235015	+	0.999724i	$0.492519\pi$
$229$	−1.55203e8	+	2.68819e8i	−0.854035	+	1.47923i	−0.877537	+	0.479509i	$0.840815\pi$
$230$	2.00361e8			1.08584
$231$		0			0
$232$	−1.77416e7			−0.0932794
$233$	−6.17555e7	+	1.06964e8i	−0.319838	+	0.553976i	−0.980454	−	0.196748i	$-0.936962\pi$
$233$	−6.17555e7	+	1.06964e8i	−0.319838	+	0.553976i	0.660616	+	0.750724i	$0.270295\pi$
$234$	2.89741e6	+	5.01847e6i	0.0147827	+	0.0256045i
$235$	−4.63204e7	−	8.02293e7i	−0.232828	−	0.403269i
$236$	−9.48053e7	+	1.64208e8i	−0.469505	+	0.813207i
$237$	1.87074e7			0.0912841
$238$		0			0
$239$	1.86771e8			0.884944			0.442472	−	0.896782i	$-0.354102\pi$
$239$	1.86771e8			0.884944			0.442472	+	0.896782i	$0.354102\pi$
$240$	−1.70759e7	+	2.95763e7i	−0.0797339	+	0.138103i
$241$	−5.46575e7	−	9.46695e7i	−0.251530	−	0.435663i	0.712417	−	0.701756i	$-0.247600\pi$
$241$	−5.46575e7	−	9.46695e7i	−0.251530	−	0.435663i	−0.963947	+	0.266093i	$0.914267\pi$
$242$	−9.01765e7	−	1.56190e8i	−0.409016	−	0.708436i
$243$	7.17445e6	−	1.24265e7i	0.0320750	−	0.0555556i
$244$	1.52557e8			0.672309
$245$		0			0
$246$	−9.92876e7			−0.425228
$247$	7.74495e6	−	1.34147e7i	0.0327024	−	0.0566422i
$248$	4.10910e7	+	7.11716e7i	0.171067	+	0.296296i
$249$	−3.58867e7	−	6.21576e7i	−0.147311	−	0.255151i
$250$	−7.52102e7	+	1.30268e8i	−0.304430	+	0.527287i
$251$	1.32241e8			0.527846			0.263923	−	0.964544i	$-0.414984\pi$
$251$	1.32241e8			0.527846			0.263923	+	0.964544i	$0.414984\pi$
$252$		0			0
$253$	−5.25801e8			−2.04127
$254$	6.48451e7	−	1.12315e8i	0.248290	−	0.430051i
$255$	1.28900e8	+	2.23262e8i	0.486815	+	0.843188i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−6.22242e7	+	1.07775e8i	−0.228662	+	0.396053i	−0.957412	−	0.288726i	$-0.906768\pi$
$257$	−6.22242e7	+	1.07775e8i	−0.228662	+	0.396053i	0.728750	+	0.684780i	$0.240102\pi$
$258$	−9.84855e7			−0.357029
$259$		0			0
$260$	1.96377e7			0.0692923
$261$	1.26305e7	−	2.18767e7i	0.0439723	−	0.0761623i
$262$	2.70188e7	+	4.67979e7i	0.0928134	+	0.160758i
$263$	2.43121e8	+	4.21098e8i	0.824095	+	1.42737i	0.902609	+	0.430461i	$0.141649\pi$
$263$	2.43121e8	+	4.21098e8i	0.824095	+	1.42737i	−0.0785143	+	0.996913i	$0.525018\pi$
$264$	4.48116e7	−	7.76159e7i	0.149891	−	0.259619i
$265$	−5.86110e8			−1.93472
$266$		0			0
$267$	−3.70867e7			−0.119242
$268$	−1.45085e8	+	2.51295e8i	−0.460417	+	0.797466i
$269$	−2.90735e8	−	5.03568e8i	−0.910676	−	1.57734i	−0.813111	−	0.582109i	$-0.802228\pi$
$269$	−2.90735e8	−	5.03568e8i	−0.910676	−	1.57734i	−0.0975655	−	0.995229i	$-0.531106\pi$
$270$	−2.43131e7	−	4.21115e7i	−0.0751739	−	0.130205i
$271$	−1.20919e8	+	2.09437e8i	−0.369064	+	0.639237i	−0.989419	−	0.145084i	$-0.953655\pi$
$271$	−1.20919e8	+	2.09437e8i	−0.369064	+	0.639237i	0.620356	+	0.784321i	$0.286988\pi$
$272$	−1.26646e8			−0.381593
$273$		0			0
$274$	4.42219e8			1.29870
$275$	−5.58768e7	+	9.67815e7i	−0.162019	+	0.280626i
$276$	−7.00727e7	−	1.21369e8i	−0.200617	−	0.347478i
$277$	−1.23766e8	−	2.14369e8i	−0.349882	−	0.606013i	0.636346	−	0.771403i	$-0.280445\pi$
$277$	−1.23766e8	−	2.14369e8i	−0.349882	−	0.606013i	−0.986228	+	0.165390i	$0.947112\pi$
$278$	−1.30485e8	+	2.26007e8i	−0.364254	+	0.630906i
$279$	−1.17013e8			−0.322566
$280$		0			0
$281$	−3.68601e8			−0.991026			−0.495513	−	0.868601i	$-0.665020\pi$
$281$	−3.68601e8			−0.991026			−0.495513	+	0.868601i	$0.665020\pi$
$282$	−3.23994e7	+	5.61174e7i	−0.0860330	+	0.149014i
$283$	8.30769e7	+	1.43893e8i	0.217885	+	0.377388i	0.954161	−	0.299293i	$-0.0967508\pi$
$283$	8.30769e7	+	1.43893e8i	0.217885	+	0.377388i	−0.736276	+	0.676681i	$0.763417\pi$
$284$	1.28223e8	+	2.22089e8i	0.332164	+	0.575325i
$285$	−6.49903e7	+	1.12567e8i	−0.166300	+	0.288040i
$286$	−5.15346e7			−0.130262
$287$		0			0
$288$	2.38879e7			0.0589256
$289$	−2.72837e8	+	4.72567e8i	−0.664907	+	1.15165i
$290$	−4.28028e7	−	7.41367e7i	−0.103057	−	0.178501i
$291$	−4.04378e6	−	7.00403e6i	−0.00961970	−	0.0166618i
$292$	−1.11139e8	+	1.92499e8i	−0.261233	+	0.452468i
$293$	2.64915e7			0.0615276			0.0307638	−	0.999527i	$-0.490206\pi$
$293$	2.64915e7			0.0615276			0.0307638	+	0.999527i	$0.490206\pi$
$294$		0			0
$295$	−9.14896e8			−2.07489
$296$	2.83766e6	−	4.91497e6i	0.00635974	−	0.0110154i
$297$	6.38040e7	+	1.10512e8i	0.141319	+	0.244771i
$298$	2.57039e8	+	4.45204e8i	0.562654	+	0.974545i
$299$	−4.02928e7	+	6.97892e7i	−0.0871723	+	0.150987i
$300$	−2.97865e7			−0.0636934
$301$		0			0
$302$	4.98025e8			1.04046
$303$	−1.91647e7	+	3.31942e7i	−0.0395779	+	0.0685509i
$304$	−3.19268e7	−	5.52989e7i	−0.0651776	−	0.112891i
$305$	3.68054e8	+	6.37489e8i	0.742784	+	1.28654i
$306$	9.01611e7	−	1.56164e8i	0.179885	−	0.311570i
$307$	7.09759e8			1.39999			0.699997	−	0.714146i	$-0.253185\pi$
$307$	7.09759e8			1.39999			0.699997	+	0.714146i	$0.253185\pi$
$308$		0			0
$309$	5.05401e8			0.974500
$310$	−1.98269e8	+	3.43412e8i	−0.377998	+	0.654711i
$311$	2.11645e7	+	3.66581e7i	0.0398977	+	0.0691048i	0.885285	−	0.465049i	$-0.153963\pi$
$311$	2.11645e7	+	3.66581e7i	0.0398977	+	0.0691048i	−0.845387	+	0.534154i	$0.820630\pi$
$312$	−6.86794e6	−	1.18956e7i	−0.0128022	−	0.0221741i
$313$	−4.05048e6	+	7.01564e6i	−0.00746623	+	0.0129319i	−0.869734	−	0.493520i	$-0.835710\pi$
$313$	−4.05048e6	+	7.01564e6i	−0.00746623	+	0.0129319i	0.862268	+	0.506452i	$0.169043\pi$
$314$	−1.42383e8			−0.259540
$315$		0			0
$316$	−4.43435e7			−0.0790543
$317$	2.37441e8	−	4.11260e8i	0.418648	−	0.725119i	−0.577156	−	0.816634i	$-0.695838\pi$
$317$	2.37441e8	−	4.11260e8i	0.418648	−	0.725119i	0.995804	+	0.0915148i	$0.0291709\pi$
$318$	2.04981e8	+	3.55038e8i	0.357453	+	0.619127i
$319$	1.12326e8	+	1.94554e8i	0.193737	+	0.335562i
$320$	4.04761e7	−	7.01067e7i	0.0690516	−	0.119601i
$321$	−1.13560e8			−0.191628
$322$		0			0
$323$	−4.82012e8			−0.795883
$324$	−1.70061e7	+	2.94555e7i	−0.0277778	+	0.0481125i
$325$	8.56383e6	+	1.48330e7i	0.0138381	+	0.0239683i
$326$	−1.53735e8	−	2.66277e8i	−0.245760	−	0.425669i
$327$	1.47213e8	−	2.54981e8i	0.232825	−	0.403265i
$328$	2.35348e8			0.368259
$329$		0			0
$330$	4.32443e8			0.662415
$331$	4.55018e8	−	7.88114e8i	0.689653	−	1.19451i	−0.282298	−	0.959327i	$-0.591097\pi$
$331$	4.55018e8	−	7.88114e8i	0.689653	−	1.19451i	0.971950	−	0.235186i	$-0.0755700\pi$
$332$	8.50648e7	+	1.47337e8i	0.127575	+	0.220967i
$333$	4.04034e6	+	6.99807e6i	0.00599602	+	0.0103854i
$334$	−2.17053e8	+	3.75946e8i	−0.318752	+	0.552094i
$335$	−1.40011e9			−2.03472
$336$		0			0
$337$	−1.34422e9			−1.91323			−0.956614	−	0.291359i	$-0.905893\pi$
$337$	−1.34422e9			−1.91323			−0.956614	+	0.291359i	$0.905893\pi$
$338$	2.47045e8	−	4.27894e8i	0.347991	−	0.602737i
$339$	9.70139e7	+	1.68033e8i	0.135249	+	0.234259i
$340$	−3.05542e8	−	5.29214e8i	−0.421594	−	0.730222i
$341$	5.20311e8	−	9.01205e8i	0.710595	−	1.23079i
$342$	9.09167e7			0.122900
$343$		0			0
$344$	2.33447e8			0.309196
$345$	3.38110e8	−	5.85623e8i	0.443293	−	0.767806i
$346$	6.84424e7	+	1.18546e8i	0.0888298	+	0.153858i
$347$	2.38413e8	+	4.12943e8i	0.306320	+	0.530563i	0.977554	−	0.210683i	$-0.0675688\pi$
$347$	2.38413e8	+	4.12943e8i	0.306320	+	0.530563i	−0.671234	+	0.741246i	$0.734235\pi$
$348$	−2.99390e7	+	5.18559e7i	−0.0380811	+	0.0659585i
$349$	−9.67291e8			−1.21806			−0.609029	−	0.793148i	$-0.708441\pi$
$349$	−9.67291e8			−1.21806			−0.609029	+	0.793148i	$0.708441\pi$
$350$		0			0
$351$	1.95575e7			0.0241401
$352$	−1.06220e8	+	1.83978e8i	−0.129810	+	0.224837i
$353$	3.41483e8	+	5.91465e8i	0.413197	+	0.715678i	0.995237	−	0.0974819i	$-0.0310788\pi$
$353$	3.41483e8	+	5.91465e8i	0.413197	+	0.715678i	−0.582040	+	0.813160i	$0.697745\pi$
$354$	3.19968e8	+	5.54201e8i	0.383350	+	0.663981i
$355$	−6.18693e8	+	1.07161e9i	−0.733967	+	1.27127i
$356$	8.79093e7			0.103267
$357$		0			0
$358$	−5.12191e8			−0.589985
$359$	5.63400e8	−	9.75838e8i	0.642668	−	1.11313i	−0.342167	−	0.939639i	$-0.611161\pi$
$359$	5.63400e8	−	9.75838e8i	0.642668	−	1.11313i	0.984835	−	0.173494i	$-0.0555057\pi$
$360$	5.76310e7	+	9.98199e7i	0.0651025	+	0.112761i
$361$	3.25423e8	+	5.63649e8i	0.364060	+	0.630571i
$362$	2.64371e7	−	4.57904e7i	0.0292910	−	0.0507335i
$363$	−6.08692e8			−0.667920
$364$		0			0
$365$	−1.07252e9			−1.15447
$366$	2.57441e8	−	4.45900e8i	0.274469	−	0.475394i
$367$	−5.12152e8	−	8.87073e8i	−0.540838	−	0.936760i	−0.998856	−	0.0478166i	$-0.984774\pi$
$367$	−5.12152e8	−	8.87073e8i	−0.540838	−	0.936760i	0.458018	−	0.888943i	$-0.348560\pi$
$368$	1.66098e8	+	2.87690e8i	0.173739	+	0.300925i
$369$	−1.67548e8	+	2.90201e8i	−0.173599	+	0.300682i
$370$	2.73842e7			0.0281056
$371$		0			0
$372$	2.77364e8			0.279351
$373$	3.50582e8	−	6.07226e8i	0.349791	−	0.605856i	−0.636421	−	0.771342i	$-0.719586\pi$
$373$	3.50582e8	−	6.07226e8i	0.349791	−	0.605856i	0.986212	+	0.165486i	$0.0529193\pi$
$374$	8.01823e8	+	1.38880e9i	0.792552	+	1.37274i
$375$	2.53834e8	+	4.39654e8i	0.248566	+	0.430528i
$376$	7.67986e7	−	1.33019e8i	0.0745068	−	0.129050i
$377$	3.44307e7			0.0330942
$378$		0			0
$379$	3.40034e8			0.320838			0.160419	−	0.987049i	$-0.448715\pi$
$379$	3.40034e8			0.320838			0.160419	+	0.987049i	$0.448715\pi$
$380$	1.54051e8	−	2.66824e8i	0.144020	−	0.249450i
$381$	−2.18852e8	−	3.79063e8i	−0.202728	−	0.351135i
$382$	−9.04679e7	−	1.56695e8i	−0.0830372	−	0.143825i
$383$	−4.29964e8	+	7.44719e8i	−0.391053	+	0.677324i	−0.992589	−	0.121522i	$-0.961223\pi$
$383$	−4.29964e8	+	7.44719e8i	−0.391053	+	0.677324i	0.601535	+	0.798846i	$0.294556\pi$
$384$	−5.66231e7			−0.0510310
$385$		0			0
$386$	1.28027e8			0.113304
$387$	−1.66194e8	+	2.87857e8i	−0.145756	+	0.252457i
$388$	9.58525e6	+	1.66021e7i	0.00833091	+	0.0144296i
$389$	−9.65248e6	−	1.67186e7i	−0.00831410	−	0.0144004i	0.861838	−	0.507183i	$-0.169313\pi$
$389$	−9.65248e6	−	1.67186e7i	−0.00831410	−	0.0144004i	−0.870153	+	0.492782i	$0.835980\pi$
$390$	3.31387e7	−	5.73979e7i	0.0282885	−	0.0489971i
$391$	2.50765e9			2.12152
$392$		0			0
$393$	1.82377e8			0.151564
$394$	5.17862e7	−	8.96963e7i	0.0426557	−	0.0738818i
$395$	−1.06982e8	−	1.85298e8i	−0.0873413	−	0.151280i
$396$	−1.51239e8	−	2.61954e8i	−0.122386	−	0.211978i
$397$	−3.26680e8	+	5.65827e8i	−0.262033	+	0.453855i	−0.966782	−	0.255602i	$-0.917726\pi$
$397$	−3.26680e8	+	5.65827e8i	−0.262033	+	0.453855i	0.704749	+	0.709457i	$0.251060\pi$
$398$	1.62249e9			1.29001
$399$		0			0
$400$	7.06049e7			0.0551601
$401$	−8.65527e8	+	1.49914e9i	−0.670309	+	1.16101i	0.307507	+	0.951546i	$0.400505\pi$
$401$	−8.65527e8	+	1.49914e9i	−0.670309	+	1.16101i	−0.977816	+	0.209464i	$0.932828\pi$
$402$	4.89663e8	+	8.48121e8i	0.375929	+	0.651128i
$403$	−7.97442e7	−	1.38121e8i	−0.0606920	−	0.105122i
$404$	4.54274e7	−	7.86826e7i	0.0342755	−	0.0593669i
$405$	−1.64113e8			−0.122758
$406$		0			0
$407$	−7.18633e7			−0.0528356
$408$	−2.13715e8	+	3.70166e8i	−0.155785	+	0.269827i
$409$	−8.98363e8	−	1.55601e9i	−0.649262	−	1.12456i	−0.983299	−	0.181996i	$-0.941744\pi$
$409$	−8.98363e8	−	1.55601e9i	−0.649262	−	1.12456i	0.334037	−	0.942560i	$-0.391589\pi$
$410$	5.67793e8	+	9.83447e8i	0.406862	+	0.704705i
$411$	7.46244e8	−	1.29253e9i	0.530194	−	0.918322i
$412$	−1.19799e9			−0.843942
$413$		0			0
$414$	−4.72990e8			−0.327606
$415$	−4.10448e8	+	7.10918e8i	−0.281897	+	0.488260i
$416$	1.62796e7	+	2.81970e7i	0.0110871	+	0.0192033i
$417$	4.40387e8	+	7.62772e8i	0.297412	+	0.515132i
$418$	−4.04271e8	+	7.00218e8i	−0.270742	+	0.468939i
$419$	−1.18733e9			−0.788536			−0.394268	−	0.918995i	$-0.629002\pi$
$419$	−1.18733e9			−0.788536			−0.394268	+	0.918995i	$0.629002\pi$
$420$		0			0
$421$	−3.66435e8			−0.239337			−0.119669	−	0.992814i	$-0.538183\pi$
$421$	−3.66435e8			−0.239337			−0.119669	+	0.992814i	$0.538183\pi$
$422$	−1.01834e9	+	1.76381e9i	−0.659625	+	1.14250i
$423$	1.09348e8	+	1.89396e8i	0.0702457	+	0.121669i
$424$	−4.85881e8	−	8.41571e8i	−0.309563	−	0.536179i
$425$	2.66488e8	−	4.61570e8i	0.168390	−	0.291660i
$426$	8.65507e8			0.542421
$427$		0			0
$428$	2.69180e8			0.165955
$429$	−8.69647e7	+	1.50627e8i	−0.0531793	+	0.0921092i
$430$	5.63206e8	+	9.75502e8i	0.341608	+	0.591682i
$431$	3.26720e7	+	5.65896e7i	0.0196565	+	0.0340460i	0.875686	−	0.482880i	$-0.160409\pi$
$431$	3.26720e7	+	5.65896e7i	0.0196565	+	0.0340460i	−0.856030	+	0.516926i	$0.827076\pi$
$432$	4.03108e7	−	6.98203e7i	0.0240563	−	0.0416667i
$433$	1.55564e9			0.920874			0.460437	−	0.887692i	$-0.347693\pi$
$433$	1.55564e9			0.920874			0.460437	+	0.887692i	$0.347693\pi$
$434$		0			0
$435$	−2.88919e8			−0.168292
$436$	−3.48950e8	+	6.04400e8i	−0.201633	+	0.349238i
$437$	6.32166e8	+	1.09494e9i	0.362365	+	0.627634i
$438$	3.75095e8	+	6.49683e8i	0.213295	+	0.369439i
$439$	−1.33630e9	+	2.31454e9i	−0.753839	+	1.30569i	0.192111	+	0.981373i	$0.438467\pi$
$439$	−1.33630e9	+	2.31454e9i	−0.753839	+	1.30569i	−0.945950	+	0.324314i	$0.894867\pi$
$440$	−1.02505e9			−0.573668
$441$		0			0
$442$	2.45779e8			0.135384
$443$	1.17317e9	−	2.03199e9i	0.641133	−	1.11048i	−0.344047	−	0.938952i	$-0.611798\pi$
$443$	1.17317e9	−	2.03199e9i	0.641133	−	1.11048i	0.985180	−	0.171523i	$-0.0548687\pi$
$444$	−9.57710e6	−	1.65880e7i	−0.00519271	−	0.00899403i
$445$	2.12087e8	+	3.67345e8i	0.114092	+	0.197612i
$446$	7.89964e8	−	1.36826e9i	0.421633	−	0.730291i
$447$	1.73501e9			0.918810
$448$		0			0
$449$	2.07584e9			1.08226			0.541129	−	0.840940i	$-0.317997\pi$
$449$	2.07584e9			1.08226			0.541129	+	0.840940i	$0.317997\pi$
$450$	−5.02646e7	+	8.70609e7i	−0.0260027	+	0.0450380i
$451$	−1.49004e9	−	2.58082e9i	−0.764856	−	1.32477i
$452$	−2.29959e8	−	3.98300e8i	−0.117129	−	0.202874i
$453$	8.40417e8	−	1.45565e9i	0.424768	−	0.735719i
$454$	−4.95220e8			−0.248372
$455$		0			0
$456$	−2.15506e8			−0.106435
$457$	8.35072e8	−	1.44639e9i	0.409277	−	0.708889i	−0.585532	−	0.810649i	$-0.699114\pi$
$457$	8.35072e8	−	1.44639e9i	0.409277	−	0.708889i	0.994809	+	0.101761i	$0.0324476\pi$
$458$	−1.24162e9	−	2.15056e9i	−0.603894	−	1.04598i
$459$	−3.04294e8	−	5.27052e8i	−0.146875	−	0.254395i
$460$	−8.01445e8	+	1.38814e9i	−0.383903	+	0.664939i
$461$	1.80273e8			0.0856995			0.0428498	−	0.999082i	$-0.486356\pi$
$461$	1.80273e8			0.0856995			0.0428498	+	0.999082i	$0.486356\pi$
$462$		0			0
$463$	−2.76184e9			−1.29320			−0.646598	−	0.762831i	$-0.723809\pi$
$463$	−2.76184e9			−1.29320			−0.646598	+	0.762831i	$0.723809\pi$
$464$	7.09665e7	−	1.22918e8i	0.0329792	−	0.0571217i
$465$	6.69158e8	+	1.15902e9i	0.308634	+	0.534570i
$466$	−4.94044e8	−	8.55710e8i	−0.226160	−	0.391720i
$467$	1.22566e9	−	2.12291e9i	0.556880	−	0.964545i	−0.440874	−	0.897569i	$-0.645332\pi$
$467$	1.22566e9	−	2.12291e9i	0.556880	−	0.964545i	0.997755	−	0.0669761i	$-0.0213351\pi$
$468$	−4.63586e7			−0.0209059
$469$		0			0
$470$	7.41126e8			0.329268
$471$	−2.40271e8	+	4.16162e8i	−0.105957	+	0.183522i
$472$	−7.58442e8	−	1.31366e9i	−0.331991	−	0.575024i
$473$	−1.47800e9	−	2.55997e9i	−0.642186	−	1.11230i
$474$	−7.48297e7	+	1.29609e8i	−0.0322738	+	0.0558999i
$475$	2.68721e8			0.115047
$476$		0			0
$477$	1.38362e9			0.583718
$478$	−7.47083e8	+	1.29399e9i	−0.312875	+	0.541916i
$479$	1.71553e9	+	2.97138e9i	0.713220	+	1.23533i	0.963642	+	0.267197i	$0.0860974\pi$
$479$	1.71553e9	+	2.97138e9i	0.713220	+	1.23533i	−0.250422	+	0.968137i	$0.580569\pi$
$480$	−1.36607e8	−	2.36610e8i	−0.0563804	−	0.0976537i
$481$	−5.50698e6	+	9.53836e6i	−0.00225634	+	0.00390810i
$482$	8.74520e8			0.355717
$483$		0			0
$484$	1.44282e9			0.578435
$485$	−4.62501e7	+	8.01075e7i	−0.0184084	+	0.0318843i
$486$	5.73956e7	+	9.94121e7i	0.0226805	+	0.0392837i
$487$	−9.49694e8	−	1.64492e9i	−0.372591	−	0.645346i	0.617372	−	0.786671i	$-0.288197\pi$
$487$	−9.49694e8	−	1.64492e9i	−0.372591	−	0.645346i	−0.989963	+	0.141325i	$0.954864\pi$
$488$	−6.10230e8	+	1.05695e9i	−0.237697	+	0.411703i
$489$	−1.03771e9			−0.401324
$490$		0			0
$491$	5.21957e9			1.98998			0.994991	−	0.0999634i	$-0.0318726\pi$
$491$	5.21957e9			1.98998			0.994991	+	0.0999634i	$0.0318726\pi$
$492$	3.97150e8	−	6.87885e8i	0.150341	−	0.260398i
$493$	−5.35705e8	−	9.27868e8i	−0.201354	−	0.348756i
$494$	6.19596e7	+	1.07317e8i	0.0231241	+	0.0400521i
$495$	7.29748e8	−	1.26396e9i	0.270430	−	0.468398i
$496$	−6.57455e8			−0.241925
$497$		0			0
$498$	5.74187e8			0.208330
$499$	−8.59078e8	+	1.48797e9i	−0.309514	+	0.536095i	−0.978256	−	0.207400i	$-0.933500\pi$
$499$	−8.59078e8	+	1.48797e9i	−0.309514	+	0.536095i	0.668742	+	0.743495i	$0.266833\pi$
$500$	−6.01682e8	−	1.04214e9i	−0.215264	−	0.372848i
$501$	7.32552e8	+	1.26882e9i	0.260260	+	0.450783i
$502$	−5.28963e8	+	9.16190e8i	−0.186622	+	0.323238i
$503$	1.00189e9			0.351020			0.175510	−	0.984478i	$-0.443843\pi$
$503$	1.00189e9			0.351020			0.175510	+	0.984478i	$0.443843\pi$
$504$		0			0
$505$	4.38386e8			0.151474
$506$	2.10320e9	−	3.64286e9i	0.721696	−	1.25001i
$507$	−8.33777e8	−	1.44414e9i	−0.284133	−	0.492133i
$508$	5.18761e8	+	8.98520e8i	0.175568	+	0.304092i
$509$	1.97093e9	−	3.41376e9i	0.662461	−	1.14742i	−0.317507	−	0.948256i	$-0.602846\pi$
$509$	1.97093e9	−	3.41376e9i	0.662461	−	1.14742i	0.979967	−	0.199159i	$-0.0638211\pi$
$510$	−2.06241e9			−0.688460
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	1.53422e8	−	2.65735e8i	0.0501737	−	0.0869035i
$514$	−4.97793e8	−	8.62203e8i	−0.161688	−	0.280052i
$515$	−2.89022e9	−	5.00602e9i	−0.932409	−	1.61498i
$516$	3.93942e8	−	6.82327e8i	0.126229	−	0.218635i
$517$	−1.94491e9			−0.618989
$518$		0			0
$519$	4.61986e8			0.145059
$520$	−7.85510e7	+	1.36054e8i	−0.0244985	+	0.0424327i
$521$	1.90088e9	+	3.29241e9i	0.588873	+	1.01996i	0.994380	+	0.105867i	$0.0337616\pi$
$521$	1.90088e9	+	3.29241e9i	0.588873	+	1.01996i	−0.405507	+	0.914092i	$0.632905\pi$
$522$	1.01044e8	+	1.75014e8i	0.0310931	+	0.0538549i
$523$	−8.92625e8	+	1.54607e9i	−0.272843	+	0.472578i	−0.969589	−	0.244740i	$-0.921297\pi$
$523$	−8.92625e8	+	1.54607e9i	−0.272843	+	0.472578i	0.696745	+	0.717318i	$0.254631\pi$
$524$	−4.32300e8			−0.131258
$525$		0			0
$526$	−3.88993e9			−1.16545
$527$	−2.48146e9	+	4.29802e9i	−0.738535	+	1.27918i
$528$	3.58493e8	+	6.20927e8i	0.105989	+	0.183579i
$529$	−1.58640e9	−	2.74773e9i	−0.465928	−	0.807012i
$530$	2.34444e9	−	4.06069e9i	0.684027	−	1.18477i
$531$	2.15978e9			0.626007
$532$		0			0
$533$	−4.56735e8			−0.130653
$534$	1.48347e8	−	2.56944e8i	0.0421584	−	0.0730205i
$535$	6.49414e8	+	1.12482e9i	0.183351	+	0.317573i
$536$	−1.16068e9	−	2.01036e9i	−0.325564	−	0.563894i
$537$	−8.64322e8	+	1.49705e9i	−0.240860	+	0.417182i
$538$	4.65176e9			1.28789
$539$		0			0
$540$	3.89009e8			0.106312
$541$	−1.95081e9	+	3.37891e9i	−0.529695	+	0.917458i	0.469705	+	0.882823i	$0.344360\pi$
$541$	−1.95081e9	+	3.37891e9i	−0.529695	+	0.917458i	−0.999400	+	0.0346347i	$0.988973\pi$
$542$	−9.67350e8	−	1.67550e9i	−0.260967	−	0.452009i
$543$	−8.92253e7	−	1.54543e8i	−0.0239160	−	0.0414237i
$544$	5.06584e8	−	8.77430e8i	0.134914	−	0.233677i
$545$	−3.36746e9			−0.891076
$546$		0			0
$547$	1.55347e9			0.405833			0.202917	−	0.979196i	$-0.434958\pi$
$547$	1.55347e9			0.405833			0.202917	+	0.979196i	$0.434958\pi$
$548$	−1.76887e9	+	3.06378e9i	−0.459161	+	0.795291i
$549$	−8.68862e8	−	1.50491e9i	−0.224103	−	0.388158i
$550$	−4.47014e8	−	7.74252e8i	−0.114565	−	0.198432i
$551$	2.70097e8	−	4.67822e8i	0.0687842	−	0.119138i
$552$	1.12116e9			0.283715
$553$		0			0
$554$	1.98025e9			0.494808
$555$	4.62108e7	−	8.00394e7i	0.0114741	−	0.0198737i
$556$	−1.04388e9	−	1.80805e9i	−0.257566	−	0.446118i
$557$	1.07718e9	+	1.86574e9i	0.264117	+	0.457464i	0.967332	−	0.253513i	$-0.0815861\pi$
$557$	1.07718e9	+	1.86574e9i	0.264117	+	0.457464i	−0.703215	+	0.710977i	$0.748253\pi$
$558$	4.68052e8	−	8.10689e8i	0.114044	−	0.197531i
$559$	−4.53045e8			−0.109698
$560$		0			0
$561$	5.41230e9			1.29423
$562$	1.47441e9	−	2.55375e9i	0.350380	−	0.606877i
$563$	−2.15812e9	−	3.73798e9i	−0.509679	−	0.882790i	−0.999937	−	0.0112127i	$-0.996431\pi$
$563$	−2.15812e9	−	3.73798e9i	−0.509679	−	0.882790i	0.490258	−	0.871577i	$-0.336903\pi$
$564$	−2.59195e8	−	4.48939e8i	−0.0608345	−	0.105368i
$565$	1.10958e9	−	1.92185e9i	0.258815	−	0.448281i
$566$	−1.32923e9			−0.308136
$567$		0			0
$568$	−2.05157e9			−0.469751
$569$	1.29318e9	−	2.23985e9i	0.294282	−	0.509712i	−0.680535	−	0.732715i	$-0.738253\pi$
$569$	1.29318e9	−	2.23985e9i	0.294282	−	0.509712i	0.974818	+	0.223003i	$0.0715860\pi$
$570$	−5.19923e8	−	9.00532e8i	−0.117592	−	0.203675i
$571$	−1.86709e9	−	3.23390e9i	−0.419701	−	0.726943i	0.576208	−	0.817303i	$-0.304532\pi$
$571$	−1.86709e9	−	3.23390e9i	−0.419701	−	0.726943i	−0.995909	+	0.0903597i	$0.971198\pi$
$572$	2.06139e8	−	3.57042e8i	0.0460546	−	0.0797689i
$573$	−6.10658e8			−0.135599
$574$		0			0
$575$	−1.39801e9			−0.306671
$576$	−9.55515e7	+	1.65500e8i	−0.0208333	+	0.0360844i
$577$	−2.23301e9	−	3.86770e9i	−0.483923	−	0.838179i	0.515907	−	0.856645i	$-0.327455\pi$
$577$	−2.23301e9	−	3.86770e9i	−0.483923	−	0.838179i	−0.999829	+	0.0184657i	$0.994122\pi$
$578$	−2.18270e9	−	3.78054e9i	−0.470160	−	0.814341i
$579$	2.16046e8	−	3.74202e8i	0.0462563	−	0.0801182i
$580$	6.84845e8			0.145745
$581$		0			0
$582$	6.47004e7			0.0136043
$583$	−6.15243e9	+	1.06563e10i	−1.28590	+	2.22724i
$584$	−8.89114e8	−	1.53999e9i	−0.184719	−	0.319943i
$585$	−1.11843e8	−	1.93718e8i	−0.0230974	−	0.0400059i
$586$	−1.05966e8	+	1.83539e8i	−0.0217533	+	0.0376778i
$587$	−7.59680e9			−1.55023			−0.775117	−	0.631818i	$-0.782309\pi$
$587$	−7.59680e9			−1.55023			−0.775117	+	0.631818i	$0.782309\pi$
$588$		0			0
$589$	−2.50226e9			−0.504579
$590$	3.65958e9	−	6.33858e9i	0.733583	−	1.27060i
$591$	−1.74778e8	−	3.02725e8i	−0.0348282	−	0.0603242i
$592$	2.27013e7	+	3.93198e7i	0.00449702	+	0.00778906i
$593$	3.78292e9	−	6.55221e9i	0.744965	−	1.29032i	−0.205246	−	0.978711i	$-0.565799\pi$
$593$	3.78292e9	−	6.55221e9i	0.744965	−	1.29032i	0.950211	−	0.311607i	$-0.100867\pi$
$594$	−1.02086e9			−0.199855
$595$		0			0
$596$	−4.11262e9			−0.795713
$597$	2.73796e9	−	4.74228e9i	0.526643	−	0.912173i
$598$	−3.22343e8	−	5.58314e8i	−0.0616401	−	0.106764i
$599$	2.56777e9	+	4.44751e9i	0.488161	+	0.845519i	0.999907	−	0.0136173i	$-0.00433466\pi$
$599$	2.56777e9	+	4.44751e9i	0.488161	+	0.845519i	−0.511747	+	0.859136i	$0.671001\pi$
$600$	1.19146e8	−	2.06367e8i	0.0225190	−	0.0390041i
$601$	5.69082e9			1.06934			0.534668	−	0.845062i	$-0.320437\pi$
$601$	5.69082e9			1.06934			0.534668	+	0.845062i	$0.320437\pi$
$602$		0			0
$603$	3.30522e9			0.613890
$604$	−1.99210e9	+	3.45042e9i	−0.367860	+	0.637151i
$605$	3.48091e9	+	6.02911e9i	0.639070	+	1.10690i
$606$	−1.53318e8	−	2.65554e8i	−0.0279858	−	0.0484728i
$607$	1.43923e9	−	2.49281e9i	0.261197	−	0.452407i	−0.705363	−	0.708846i	$-0.749216\pi$
$607$	1.43923e9	−	2.49281e9i	0.261197	−	0.452407i	0.966560	+	0.256439i	$0.0825494\pi$
$608$	5.10830e8			0.0921751
$609$		0			0
$610$	−5.88887e9			−1.05046
$611$	−1.49041e8	+	2.58147e8i	−0.0264339	+	0.0457849i
$612$	7.21289e8	+	1.24931e9i	0.127198	+	0.220313i
$613$	−4.36739e9	−	7.56455e9i	−0.765792	−	1.32639i	−0.939827	−	0.341651i	$-0.889014\pi$
$613$	−4.36739e9	−	7.56455e9i	−0.765792	−	1.32639i	0.174035	−	0.984739i	$-0.444319\pi$
$614$	−2.83903e9	+	4.91735e9i	−0.494973	+	0.857318i
$615$	3.83260e9			0.664402
$616$		0			0
$617$	−2.09281e9			−0.358701			−0.179350	−	0.983785i	$-0.557400\pi$
$617$	−2.09281e9			−0.358701			−0.179350	+	0.983785i	$0.557400\pi$
$618$	−2.02161e9	+	3.50152e9i	−0.344538	+	0.596757i
$619$	1.35754e9	+	2.35132e9i	0.230057	+	0.398470i	0.957825	−	0.287354i	$-0.0927755\pi$
$619$	1.35754e9	+	2.35132e9i	0.230057	+	0.398470i	−0.727768	+	0.685823i	$0.759442\pi$
$620$	−1.58615e9	−	2.74730e9i	−0.267285	−	0.462951i
$621$	−7.98171e8	+	1.38247e9i	−0.133744	+	0.231652i
$622$	−3.38633e8			−0.0564238
$623$		0			0
$624$	1.09887e8			0.0181051
$625$	3.57653e9	−	6.19474e9i	0.585979	−	1.01495i
$626$	−3.24039e7	−	5.61251e7i	−0.00527942	−	0.00914423i
$627$	1.36441e9	+	2.36323e9i	0.221060	+	0.382887i
$628$	5.69532e8	−	9.86458e8i	0.0917612	−	0.158935i
$629$	3.42730e8			0.0549130
$630$		0			0
$631$	5.11357e9			0.810254			0.405127	−	0.914260i	$-0.367227\pi$
$631$	5.11357e9			0.810254			0.405127	+	0.914260i	$0.367227\pi$
$632$	1.77374e8	−	3.07221e8i	0.0279499	−	0.0484107i
$633$	3.43688e9	+	5.95286e9i	0.538582	+	0.932851i
$634$	1.89953e9	+	3.29008e9i	0.296029	+	0.512737i
$635$	−2.50309e9	+	4.33548e9i	−0.387943	+	0.671937i
$636$	−3.27970e9			−0.505515
$637$		0			0
$638$	−1.79721e9			−0.273986
$639$	1.46054e9	−	2.52973e9i	0.221443	−	0.383550i
$640$	3.23809e8	+	5.60853e8i	0.0488269	+	0.0845706i
$641$	1.99007e9	+	3.44691e9i	0.298446	+	0.516923i	0.975781	−	0.218752i	$-0.0701984\pi$
$641$	1.99007e9	+	3.44691e9i	0.298446	+	0.516923i	−0.677335	+	0.735675i	$0.736865\pi$
$642$	4.54241e8	−	7.86769e8i	0.0677507	−	0.117348i
$643$	1.15835e10			1.71830			0.859152	−	0.511721i	$-0.170992\pi$
$643$	1.15835e10			1.71830			0.859152	+	0.511721i	$0.170992\pi$
$644$		0			0
$645$	3.80164e9			0.557843
$646$	1.92805e9	−	3.33948e9i	0.281387	−	0.487377i
$647$	−3.14313e9	−	5.44406e9i	−0.456244	−	0.790237i	0.542515	−	0.840046i	$-0.317472\pi$
$647$	−3.14313e9	−	5.44406e9i	−0.456244	−	0.790237i	−0.998759	+	0.0498088i	$0.984139\pi$
$648$	−1.36049e8	−	2.35644e8i	−0.0196419	−	0.0340207i
$649$	−9.60371e9	+	1.66341e10i	−1.37906	+	2.38860i
$650$	−1.37021e8			−0.0195700
$651$		0			0
$652$	2.45976e9			0.347557
$653$	−1.69599e9	+	2.93753e9i	−0.238356	+	0.412845i	−0.960243	−	0.279167i	$-0.909942\pi$
$653$	−1.69599e9	+	2.93753e9i	−0.238356	+	0.412845i	0.721887	+	0.692011i	$0.243275\pi$
$654$	1.17771e9	+	2.03985e9i	0.164632	+	0.285152i
$655$	−1.04295e9	−	1.80645e9i	−0.145017	−	0.251177i
$656$	−9.41394e8	+	1.63054e9i	−0.130199	+	0.225511i
$657$	2.53189e9			0.348310
$658$		0			0
$659$	1.04865e10			1.42735			0.713676	−	0.700476i	$-0.247029\pi$
$659$	1.04865e10			1.42735			0.713676	+	0.700476i	$0.247029\pi$
$660$	−1.72977e9	+	2.99605e9i	−0.234199	+	0.405645i
$661$	3.12980e9	+	5.42097e9i	0.421513	+	0.730082i	0.996088	−	0.0883702i	$-0.0281659\pi$
$661$	3.12980e9	+	5.42097e9i	0.421513	+	0.730082i	−0.574575	+	0.818452i	$0.694833\pi$
$662$	3.64014e9	+	6.30491e9i	0.487658	+	0.844648i
$663$	4.14752e8	−	7.18371e8i	0.0552702	−	0.0957308i
$664$	−1.36104e9			−0.180419
$665$		0			0
$666$	−6.46454e7			−0.00847965
$667$	−1.40517e9	+	2.43382e9i	−0.183353	+	0.317577i
$668$	−1.73642e9	−	3.00757e9i	−0.225391	−	0.390389i
$669$	−2.66613e9	−	4.61787e9i	−0.344262	−	0.596280i
$670$	5.60044e9	−	9.70025e9i	0.719384	−	1.24601i
$671$	1.54540e10			1.97474
$672$		0			0
$673$	5.20341e9			0.658014			0.329007	−	0.944327i	$-0.393286\pi$
$673$	5.20341e9			0.658014			0.329007	+	0.944327i	$0.393286\pi$
$674$	5.37689e9	−	9.31305e9i	0.676428	−	1.17161i
$675$	1.69643e8	+	2.93831e8i	0.0212311	+	0.0367734i
$676$	1.97636e9	+	3.42315e9i	0.246066	+	0.426200i
$677$	−3.15953e9	+	5.47247e9i	−0.391347	+	0.677833i	−0.992628	−	0.121205i	$-0.961324\pi$
$677$	−3.15953e9	+	5.47247e9i	−0.391347	+	0.677833i	0.601280	+	0.799038i	$0.294658\pi$
$678$	−1.55222e9			−0.191271
$679$		0			0
$680$	4.88867e9			0.596224
$681$	−8.35685e8	+	1.44745e9i	−0.101398	+	0.175626i
$682$	4.16249e9	+	7.20964e9i	0.502467	+	0.870298i
$683$	3.27270e9	+	5.66848e9i	0.393037	+	0.680760i	0.992849	−	0.119381i	$-0.0380910\pi$
$683$	3.27270e9	+	5.66848e9i	0.393037	+	0.680760i	−0.599811	+	0.800141i	$0.704758\pi$
$684$	−3.63667e8	+	6.29889e8i	−0.0434517	+	0.0752606i
$685$	−1.70701e10			−2.02917
$686$		0			0
$687$	−8.38096e9			−0.986155
$688$	−9.33788e8	+	1.61737e9i	−0.109317	+	0.189343i
$689$	9.42937e8	+	1.63322e9i	0.109829	+	0.190229i
$690$	2.70488e9	+	4.68498e9i	0.313455	+	0.542921i
$691$	−1.35415e9	+	2.34545e9i	−0.156132	+	0.270429i	−0.933471	−	0.358653i	$-0.883236\pi$
$691$	−1.35415e9	+	2.34545e9i	−0.156132	+	0.270429i	0.777338	+	0.629083i	$0.216569\pi$
$692$	−1.09508e9			−0.125624
$693$		0			0
$694$	−3.81460e9			−0.433203
$695$	5.03686e9	−	8.72409e9i	0.569132	−	0.985765i
$696$	−2.39512e8	−	4.14847e8i	−0.0269274	−	0.0466397i
$697$	7.10629e9	+	1.23085e10i	0.794929	+	1.37686i
$698$	3.86916e9	−	6.70159e9i	0.430649	−	0.745905i
$699$	−3.33480e9			−0.369317
$700$		0			0
$701$	−8.01526e9			−0.878830			−0.439415	−	0.898284i	$-0.644814\pi$
$701$	−8.01526e9			−0.878830			−0.439415	+	0.898284i	$0.644814\pi$
$702$	−7.82301e7	+	1.35499e8i	−0.00853482	+	0.0147827i
$703$	8.64005e7	+	1.49650e8i	0.00937935	+	0.0162455i
$704$	−8.49760e8	−	1.47183e9i	−0.0917893	−	0.158984i
$705$	1.25065e9	−	2.16619e9i	0.134423	−	0.232828i
$706$	−5.46372e9			−0.584349
$707$		0			0
$708$	−5.11949e9			−0.542138
$709$	6.99354e9	−	1.21132e10i	0.736945	−	1.27643i	−0.216919	−	0.976190i	$-0.569601\pi$
$709$	6.99354e9	−	1.21132e10i	0.736945	−	1.27643i	0.953865	−	0.300237i	$-0.0970658\pi$
$710$	−4.94955e9	−	8.57287e9i	−0.518993	−	0.898922i
$711$	2.52550e8	+	4.37430e8i	0.0263514	+	0.0456420i
$712$	−3.51637e8	+	6.09053e8i	−0.0365102	+	0.0632376i
$713$	1.30179e10			1.34502
$714$		0			0
$715$	1.98929e9			0.203529
$716$	2.04876e9	−	3.54856e9i	0.208591	−	0.361291i
$717$	2.52140e9	+	4.36720e9i	0.255461	+	0.442472i
$718$	4.50720e9	+	7.80670e9i	0.454435	+	0.787104i
$719$	9.24603e9	−	1.60146e10i	0.927693	−	1.60681i	0.140520	−	0.990078i	$-0.455122\pi$
$719$	9.24603e9	−	1.60146e10i	0.927693	−	1.60681i	0.787172	−	0.616733i	$-0.211544\pi$
$720$	−9.22096e8			−0.0920688
$721$		0			0
$722$	−5.20677e9			−0.514859
$723$	1.47575e9	−	2.55608e9i	0.145221	−	0.251530i
$724$	2.11497e8	+	3.66324e8i	0.0207119	+	0.0358740i
$725$	2.98654e8	+	5.17284e8i	0.0291062	+	0.0504134i
$726$	2.43477e9	−	4.21714e9i	0.236145	−	0.409016i
$727$	6.52913e8			0.0630210			0.0315105	−	0.999503i	$-0.489968\pi$
$727$	6.52913e8			0.0630210			0.0315105	+	0.999503i	$0.489968\pi$
$728$		0			0
$729$	3.87420e8			0.0370370
$730$	4.29009e9	−	7.43065e9i	0.408165	−	0.706963i
$731$	7.04888e9	+	1.22090e10i	0.667436	+	1.15603i
$732$	2.05952e9	+	3.56720e9i	0.194079	+	0.336154i
$733$	−2.99898e9	+	5.19439e9i	−0.281261	+	0.487159i	−0.971696	−	0.236236i	$-0.924086\pi$
$733$	−2.99898e9	+	5.19439e9i	−0.281261	+	0.487159i	0.690434	+	0.723395i	$0.257419\pi$
$734$	8.19443e9			0.764861
$735$		0			0
$736$	−2.65757e9			−0.245704
$737$	−1.46970e10	+	2.54560e10i	−1.35236	+	2.34236i
$738$	−1.34038e9	−	2.32161e9i	−0.122753	−	0.212614i
$739$	−1.54303e9	−	2.67261e9i	−0.140644	−	0.243602i	0.787096	−	0.616831i	$-0.211584\pi$
$739$	−1.54303e9	−	2.67261e9i	−0.140644	−	0.243602i	−0.927739	+	0.373229i	$0.878250\pi$
$740$	−1.09537e8	+	1.89723e8i	−0.00993684	+	0.0172111i
$741$	4.18228e8			0.0377615
$742$		0			0
$743$	−1.65397e10			−1.47933			−0.739667	−	0.672974i	$-0.765017\pi$
$743$	−1.65397e10			−1.47933			−0.739667	+	0.672974i	$0.765017\pi$
$744$	−1.10946e9	+	1.92163e9i	−0.0987654	+	0.171067i
$745$	−9.92195e9	−	1.71853e10i	−0.879124	−	1.52269i
$746$	2.80466e9	+	4.85781e9i	0.247340	+	0.428405i
$747$	9.68941e8	−	1.67825e9i	0.0850502	−	0.147311i
$748$	−1.28292e10			−1.12084
$749$		0			0
$750$	−4.06135e9			−0.351525
$751$	9.01861e8	−	1.56207e9i	0.0776962	−	0.134574i	−0.824559	−	0.565775i	$-0.808577\pi$
$751$	9.01861e8	−	1.56207e9i	0.0776962	−	0.134574i	0.902256	+	0.431202i	$0.141910\pi$
$752$	6.14389e8	+	1.06415e9i	0.0526842	+	0.0912518i
$753$	1.78525e9	+	3.09214e9i	0.152376	+	0.263923i
$754$	−1.37723e8	+	2.38543e8i	−0.0117006	+	0.0202660i
$755$	−1.92243e10			−1.62568
$756$		0			0
$757$	−8.71019e9			−0.729780			−0.364890	−	0.931051i	$-0.618893\pi$
$757$	−8.71019e9			−0.729780			−0.364890	+	0.931051i	$0.618893\pi$
$758$	−1.36014e9	+	2.35583e9i	−0.113433	+	0.196472i
$759$	−7.09831e9	−	1.22946e10i	−0.589263	−	1.02063i
$760$	1.23241e9	+	2.13460e9i	0.101837	+	0.176388i
$761$	−1.14245e10	+	1.97879e10i	−0.939707	+	1.62762i	−0.173690	+	0.984800i	$0.555569\pi$
$761$	−1.14245e10	+	1.97879e10i	−0.939707	+	1.62762i	−0.766017	+	0.642820i	$0.777764\pi$
$762$	3.50164e9			0.286701
$763$		0			0
$764$	1.44749e9			0.117432
$765$	−3.48031e9	+	6.02808e9i	−0.281063	+	0.486815i
$766$	−3.43971e9	−	5.95775e9i	−0.276516	−	0.478941i
$767$	1.47189e9	+	2.54939e9i	0.117785	+	0.204010i
$768$	2.26492e8	−	3.92296e8i	0.0180422	−	0.0312500i
$769$	1.04328e10			0.827288			0.413644	−	0.910439i	$-0.364256\pi$
$769$	1.04328e10			0.827288			0.413644	+	0.910439i	$0.364256\pi$
$770$		0			0
$771$	−3.36010e9			−0.264036
$772$	−5.12108e8	+	8.86998e8i	−0.0400591	+	0.0693844i
$773$	9.22414e9	+	1.59767e10i	0.718286	+	1.24411i	0.961678	+	0.274180i	$0.0884065\pi$
$773$	9.22414e9	+	1.59767e10i	0.718286	+	1.24411i	−0.243392	+	0.969928i	$0.578260\pi$
$774$	−1.32955e9	−	2.30286e9i	−0.103065	−	0.178514i
$775$	1.38341e9	−	2.39614e9i	0.106757	−	0.184908i
$776$	−1.53364e8			−0.0117817
$777$		0			0
$778$	1.54440e8			0.0117579
$779$	−3.58292e9	+	6.20580e9i	−0.271554	+	0.470345i
$780$	2.65110e8	+	4.59183e8i	0.0200030	+	0.0346461i
$781$	1.29889e10	+	2.24975e10i	0.975651	+	1.68988i
$782$	−1.00306e10	+	1.73735e10i	−0.750072	+	1.29916i
$783$	6.82048e8			0.0507749
$784$		0			0
$785$	5.49613e9			0.405521
$786$	−7.29506e8	+	1.26354e9i	−0.0535859	+	0.0928134i
$787$	8.74207e9	+	1.51417e10i	0.639297	+	1.10730i	0.985587	+	0.169168i	$0.0541080\pi$
$787$	8.74207e9	+	1.51417e10i	0.639297	+	1.10730i	−0.346290	+	0.938128i	$0.612559\pi$
$788$	4.14289e8	+	7.17570e8i	0.0301621	+	0.0522423i
$789$	−6.56426e9	+	1.13696e10i	−0.475791	+	0.824095i
$790$	1.71171e9			0.123519
$791$		0			0
$792$	2.41982e9			0.173080
$793$	1.18426e9	−	2.05119e9i	0.0843315	−	0.146066i
$794$	−2.61344e9	−	4.52662e9i	−0.185285	−	0.320924i
$795$	−7.91248e9	−	1.37048e10i	−0.558506	−	0.967361i
$796$	−6.48997e9	+	1.12410e10i	−0.456086	+	0.789965i
$797$	−8.77363e9			−0.613869			−0.306934	−	0.951731i	$-0.599303\pi$
$797$	−8.77363e9			−0.613869			−0.306934	+	0.951731i	$0.599303\pi$
$798$		0			0
$799$	9.27567e9			0.643326
$800$	−2.82420e8	+	4.89165e8i	−0.0195020	+	0.0337785i
$801$	−5.00671e8	−	8.67187e8i	−0.0344222	−	0.0596210i
$802$	−6.92421e9	−	1.19931e10i	−0.473980	−	0.820958i
$803$	−1.12583e10	+	1.95000e10i	−0.767307	+	1.32902i
$804$	−7.83461e9			−0.531644
$805$		0			0
$806$	1.27591e9			0.0858315
$807$	7.84984e9	−	1.35963e10i	0.525779	−	0.910676i
$808$	3.63419e8	+	6.29461e8i	0.0242364	+	0.0419787i
$809$	1.23018e10	+	2.13073e10i	0.816862	+	1.41485i	0.907983	+	0.419007i	$0.137622\pi$
$809$	1.23018e10	+	2.13073e10i	0.816862	+	1.41485i	−0.0911204	+	0.995840i	$0.529045\pi$
$810$	6.56453e8	−	1.13701e9i	0.0434017	−	0.0751739i
$811$	−2.27226e10			−1.49584			−0.747921	−	0.663788i	$-0.768948\pi$
$811$	−2.27226e10			−1.49584			−0.747921	+	0.663788i	$0.768948\pi$
$812$		0			0
$813$	−6.52961e9			−0.426158
$814$	2.87453e8	−	4.97883e8i	0.0186802	−	0.0323550i
$815$	5.93433e9	+	1.02786e10i	0.383990	+	0.665090i
$816$	−1.70972e9	−	2.96133e9i	−0.110156	−	0.190797i
$817$	−3.55398e9	+	6.15567e9i	−0.228001	+	0.394910i
$818$	1.43738e10			0.918196
$819$		0			0
$820$	−9.08469e9			−0.575389
$821$	−6.78361e9	+	1.17496e10i	−0.427819	+	0.741004i	−0.996679	−	0.0814306i	$-0.974051\pi$
$821$	−6.78361e9	+	1.17496e10i	−0.427819	+	0.741004i	0.568860	+	0.822434i	$0.307384\pi$
$822$	5.96995e9	+	1.03403e10i	0.374904	+	0.649352i
$823$	−1.20715e10	−	2.09085e10i	−0.754854	−	1.30744i	−0.945447	−	0.325776i	$-0.894375\pi$
$823$	−1.20715e10	−	2.09085e10i	−0.754854	−	1.30744i	0.190593	−	0.981669i	$-0.438959\pi$
$824$	4.79195e9	−	8.29991e9i	0.298378	−	0.516807i
$825$	−3.01735e9			−0.187084
$826$		0			0
$827$	5.22827e9			0.321432			0.160716	−	0.987001i	$-0.448620\pi$
$827$	5.22827e9			0.321432			0.160716	+	0.987001i	$0.448620\pi$
$828$	1.89196e9	−	3.27697e9i	0.115826	−	0.200617i
$829$	−4.00404e9	−	6.93520e9i	−0.244094	−	0.422784i	0.717782	−	0.696268i	$-0.245157\pi$
$829$	−4.00404e9	−	6.93520e9i	−0.244094	−	0.422784i	−0.961877	+	0.273484i	$0.911824\pi$
$830$	−3.28359e9	−	5.68734e9i	−0.199331	−	0.345252i
$831$	3.34168e9	−	5.78795e9i	0.202004	−	0.349882i
$832$	−2.60473e8			−0.0156795
$833$		0			0
$834$	−7.04619e9			−0.420604
$835$	8.37845e9	−	1.45119e10i	0.498036	−	0.862624i
$836$	−3.23417e9	−	5.60174e9i	−0.191443	−	0.331590i
$837$	−1.57967e9	−	2.73608e9i	−0.0931169	−	0.161283i
$838$	4.74931e9	−	8.22605e9i	0.278790	−	0.482878i
$839$	−1.13828e10			−0.665397			−0.332699	−	0.943033i	$-0.607959\pi$
$839$	−1.13828e10			−0.665397			−0.332699	+	0.943033i	$0.607959\pi$
$840$		0			0
$841$	−1.60491e10			−0.930392
$842$	1.46574e9	−	2.53874e9i	0.0846185	−	0.146563i
$843$	−4.97612e9	−	8.61889e9i	−0.286084	−	0.495513i
$844$	−8.14669e9	−	1.41105e10i	−0.466426	−	0.807873i
$845$	−9.53619e9	+	1.65172e10i	−0.543721	+	0.941753i
$846$	−1.74957e9			−0.0993424
$847$		0			0
$848$	7.77410e9			0.437789
$849$	−2.24308e9	+	3.88512e9i	−0.125796	+	0.217885i
$850$	2.13190e9	+	3.69256e9i	0.119070	+	0.206234i
$851$	−4.49495e8	−	7.78549e8i	−0.0250018	−	0.0433044i
$852$	−3.46203e9	+	5.99641e9i	−0.191775	+	0.332164i
$853$	−2.07865e9			−0.114673			−0.0573364	−	0.998355i	$-0.518261\pi$
$853$	−2.07865e9			−0.114673			−0.0573364	+	0.998355i	$0.518261\pi$
$854$		0			0
$855$	−3.50948e9			−0.192026
$856$	−1.07672e9	+	1.86493e9i	−0.0586738	+	0.101626i
$857$	5.94941e9	+	1.03047e10i	0.322880	+	0.559244i	0.981081	−	0.193598i	$-0.0620157\pi$
$857$	5.94941e9	+	1.03047e10i	0.322880	+	0.559244i	−0.658201	+	0.752842i	$0.728682\pi$
$858$	−6.95718e8	−	1.20502e9i	−0.0376034	−	0.0651311i
$859$	1.27030e10	−	2.20023e10i	0.683803	−	1.18438i	−0.290009	−	0.957024i	$-0.593658\pi$
$859$	1.27030e10	−	2.20023e10i	0.683803	−	1.18438i	0.973811	−	0.227357i	$-0.0730085\pi$
$860$	−9.01130e9			−0.483106
$861$		0			0
$862$	−5.22753e8			−0.0277985
$863$	−2.99783e9	+	5.19239e9i	−0.158770	+	0.274998i	−0.934425	−	0.356159i	$-0.884086\pi$
$863$	−2.99783e9	+	5.19239e9i	−0.158770	+	0.274998i	0.775655	+	0.631157i	$0.217420\pi$
$864$	3.22486e8	+	5.58563e8i	0.0170103	+	0.0294628i
$865$	−2.64195e9	−	4.57599e9i	−0.138793	−	0.240397i
$866$	−6.22254e9	+	1.07778e10i	−0.325578	+	0.563918i
$867$	−1.47332e10			−0.767768
$868$		0			0
$869$	−4.49197e9			−0.232203
$870$	1.15568e9	−	2.00169e9i	0.0595002	−	0.103057i
$871$	2.25251e9	+	3.90146e9i	0.115506	+	0.200061i
$872$	−2.79160e9	−	4.83520e9i	−0.142576	−	0.246949i
$873$	1.09182e8	−	1.89109e8i	0.00555394	−	0.00961970i
$874$	−1.01147e10			−0.512461
$875$		0			0
$876$	−6.00152e9			−0.301645
$877$	4.41384e9	−	7.64499e9i	0.220962	−	0.382718i	−0.734138	−	0.679000i	$-0.762414\pi$
$877$	4.41384e9	−	7.64499e9i	0.220962	−	0.382718i	0.955100	+	0.296282i	$0.0957470\pi$
$878$	−1.06904e10	−	1.85163e10i	−0.533044	−	0.923260i
$879$	3.57636e8	+	6.19443e8i	0.0177615	+	0.0307638i
$880$	4.10020e9	−	7.10176e9i	0.202822	−	0.351299i
$881$	−7.07937e9			−0.348802			−0.174401	−	0.984675i	$-0.555799\pi$
$881$	−7.07937e9			−0.348802			−0.174401	+	0.984675i	$0.555799\pi$
$882$		0			0
$883$	3.43253e10			1.67785			0.838923	−	0.544251i	$-0.183186\pi$
$883$	3.43253e10			1.67785			0.838923	+	0.544251i	$0.183186\pi$
$884$	−9.83116e8	+	1.70281e9i	−0.0478654	+	0.0829053i
$885$	−1.23511e10	−	2.13927e10i	−0.598968	−	1.03744i
$886$	9.38537e9	+	1.62559e10i	0.453350	+	0.785225i
$887$	5.23222e9	−	9.06247e9i	0.251741	−	0.436028i	−0.712264	−	0.701911i	$-0.752330\pi$
$887$	5.23222e9	−	9.06247e9i	0.251741	−	0.436028i	0.964005	+	0.265884i	$0.0856637\pi$
$888$	1.53234e8			0.00734360
$889$		0			0
$890$	−3.39339e9			−0.161350
$891$	−1.72271e9	+	2.98382e9i	−0.0815905	+	0.141319i
$892$	6.31971e9	+	1.09461e10i	0.298140	+	0.516393i
$893$	2.33835e9	+	4.05014e9i	0.109883	+	0.190322i
$894$	−6.94004e9	+	1.20205e10i	−0.324848	+	0.562654i
$895$	1.97711e10			0.921828
$896$		0			0
$897$	−2.17581e9			−0.100658
$898$	−8.30334e9	+	1.43818e10i	−0.382636	+	0.662745i
$899$	−2.78099e9	−	4.81682e9i	−0.127656	−	0.221107i
$900$	−4.02117e8	−	6.96487e8i	−0.0183867	−	0.0318467i
$901$	2.93421e10	−	5.08221e10i	1.33646	−	2.31481i
$902$	2.38406e10			1.08167
$903$		0			0
$904$	3.67934e9			0.165646
$905$	−1.02050e9	+	1.76756e9i	−0.0457660	+	0.0792691i
$906$	6.72334e9	+	1.16452e10i	0.300356	+	0.520232i
$907$	1.54783e10	+	2.68092e10i	0.688806	+	1.19305i	0.972224	+	0.234051i	$0.0751983\pi$
$907$	1.54783e10	+	2.68092e10i	0.688806	+	1.19305i	−0.283418	+	0.958996i	$0.591468\pi$
$908$	1.98088e9	−	3.43099e9i	0.0878129	−	0.152096i
$909$	−1.03489e9			−0.0457006
$910$		0			0
$911$	1.55078e10			0.679572			0.339786	−	0.940503i	$-0.389645\pi$
$911$	1.55078e10			0.679572			0.339786	+	0.940503i	$0.389645\pi$
$912$	8.62025e8	−	1.49307e9i	0.0376303	−	0.0651776i
$913$	8.61700e9	+	1.49251e10i	0.374721	+	0.649036i
$914$	6.68058e9	+	1.15711e10i	0.289403	+	0.501260i
$915$	−9.93747e9	+	1.72122e10i	−0.428847	+	0.742784i
$916$	1.98660e10			0.854035
$917$		0			0
$918$	4.86870e9			0.207713
$919$	−1.66116e10	+	2.87721e10i	−0.706003	+	1.22283i	0.260325	+	0.965521i	$0.416170\pi$
$919$	−1.66116e10	+	2.87721e10i	−0.706003	+	1.22283i	−0.966328	+	0.257312i	$0.917163\pi$
$920$	−6.41156e9	−	1.11051e10i	−0.271460	−	0.470183i
$921$	9.58174e9	+	1.65961e10i	0.404144	+	0.699997i
$922$	−7.21094e8	+	1.24897e9i	−0.0302994	+	0.0524800i
$923$	3.98143e9			0.166661
$924$		0			0
$925$	−1.91071e8			−0.00793779
$926$	1.10473e10	−	1.91346e10i	0.457214	−	0.791918i
$927$	6.82292e9	+	1.18176e10i	0.281314	+	0.487250i
$928$	5.67732e8	+	9.83341e8i	0.0233198	+	0.0403911i
$929$	1.77847e8	−	3.08039e8i	0.00727764	−	0.0126052i	−0.862364	−	0.506289i	$-0.831017\pi$
$929$	1.77847e8	−	3.08039e8i	0.00727764	−	0.0126052i	0.869641	+	0.493684i	$0.164350\pi$
$930$	−1.07065e10			−0.436474
$931$		0			0
$932$	7.90471e9			0.319838
$933$	−5.71443e8	+	9.89768e8i	−0.0230349	+	0.0398977i
$934$	9.80530e9	+	1.69833e10i	0.393774	+	0.682036i
$935$	−3.09512e10	−	5.36090e10i	−1.23833	−	2.14485i
$936$	1.85434e8	−	3.21182e8i	0.00739137	−	0.0128022i
$937$	−4.28321e9			−0.170091			−0.0850454	−	0.996377i	$-0.527104\pi$
$937$	−4.28321e9			−0.170091			−0.0850454	+	0.996377i	$0.527104\pi$
$938$		0			0
$939$	−2.18726e8			−0.00862126
$940$	−2.96450e9	+	5.13467e9i	−0.116414	+	0.201635i
$941$	−1.65059e10	−	2.85890e10i	−0.645765	−	1.11850i	−0.984124	−	0.177481i	$-0.943205\pi$
$941$	−1.65059e10	−	2.85890e10i	−0.645765	−	1.11850i	0.338359	−	0.941017i	$-0.390128\pi$
$942$	−1.92217e9	−	3.32930e9i	−0.0749227	−	0.129770i
$943$	1.86400e10	−	3.22854e10i	0.723861	−	1.25376i
$944$	1.21351e10			0.469505
$945$		0			0
$946$	2.36480e10			0.908188
$947$	−3.68911e9	+	6.38973e9i	−0.141155	+	0.244488i	−0.927932	−	0.372750i	$-0.878415\pi$
$947$	−3.68911e9	+	6.38973e9i	−0.141155	+	0.244488i	0.786777	+	0.617238i	$0.211748\pi$
$948$	−5.98638e8	−	1.03687e9i	−0.0228210	−	0.0395272i
$949$	1.72548e9	+	2.98862e9i	0.0655358	+	0.113511i
$950$	−1.07488e9	+	1.86175e9i	−0.0406751	+	0.0704513i
$951$	1.28218e10			0.483413
$952$		0			0
$953$	−6.89038e9			−0.257880			−0.128940	−	0.991652i	$-0.541158\pi$
$953$	−6.89038e9			−0.257880			−0.128940	+	0.991652i	$0.541158\pi$
$954$	−5.53449e9	+	9.58602e9i	−0.206376	+	0.357453i
$955$	3.49215e9	+	6.04859e9i	0.129742	+	0.224720i
$956$	−5.97666e9	−	1.03519e10i	−0.221236	−	0.383192i
$957$	−3.03280e9	+	5.25296e9i	−0.111854	+	0.193737i
$958$	−2.74485e10			−1.00865
$959$		0			0
$960$	2.18571e9			0.0797339
$961$	8.74329e8	−	1.51438e9i	0.0317792	−	0.0550432i
$962$	−4.40558e7	−	7.63069e7i	−0.00159548	−	0.00276345i
$963$	−1.53306e9	−	2.65534e9i	−0.0553182	−	0.0958140i
$964$	−3.49808e9	+	6.05885e9i	−0.125765	+	0.217831i
$965$	−4.94198e9			−0.177033
$966$		0			0
$967$	2.74855e10			0.977489			0.488744	−	0.872427i	$-0.337455\pi$
$967$	2.74855e10			0.977489			0.488744	+	0.872427i	$0.337455\pi$
$968$	−5.77130e9	+	9.99618e9i	−0.204508	+	0.354218i
$969$	−6.50716e9	−	1.12707e10i	−0.229752	−	0.397941i
$970$	−3.70001e8	−	6.40860e8i	−0.0130167	−	0.0225456i
$971$	2.81796e9	−	4.88085e9i	0.0987797	−	0.171091i	−0.812400	−	0.583100i	$-0.801839\pi$
$971$	2.81796e9	−	4.88085e9i	0.0987797	−	0.171091i	0.911180	+	0.412009i	$0.135173\pi$
$972$	−9.18330e8			−0.0320750
$973$		0			0
$974$	1.51951e10			0.526923
$975$	−2.31223e8	+	4.00491e8i	−0.00798942	+	0.0138381i
$976$	−4.88184e9	−	8.45559e9i	−0.168077	−	0.291118i
$977$	1.54612e10	+	2.67796e10i	0.530411	+	0.918699i	0.999370	+	0.0354794i	$0.0112958\pi$
$977$	1.54612e10	+	2.67796e10i	0.530411	+	0.918699i	−0.468959	+	0.883220i	$0.655371\pi$
$978$	4.15084e9	−	7.18947e9i	0.141890	−	0.245760i
$979$	8.90515e9			0.303320
$980$		0			0
$981$	7.94953e9			0.268844
$982$	−2.08783e10	+	3.61622e10i	−0.703565	+	1.21861i
$983$	−5.51561e9	−	9.55332e9i	−0.185207	−	0.320787i	0.758440	−	0.651743i	$-0.225962\pi$
$983$	−5.51561e9	−	9.55332e9i	−0.185207	−	0.320787i	−0.943646	+	0.330956i	$0.892629\pi$
$984$	3.17720e9	+	5.50308e9i	0.106307	+	0.184129i
$985$	−1.99900e9	+	3.46237e9i	−0.0666478	+	0.115437i
$986$	8.57127e9			0.284758
$987$		0			0
$988$	−9.91354e8			−0.0327024
$989$	1.84894e10	−	3.20246e10i	0.607766	−	1.05268i
$990$	5.83798e9	+	1.01117e10i	0.191223	+	0.331208i
$991$	−1.80670e10	−	3.12929e10i	−0.589695	−	1.02138i	−0.994272	−	0.106877i	$-0.965915\pi$
$991$	−1.80670e10	−	3.12929e10i	−0.589695	−	1.02138i	0.404578	−	0.914504i	$-0.367419\pi$
$992$	2.62982e9	−	4.55498e9i	0.0855333	−	0.148148i
$993$	2.45710e10			0.796342
$994$		0			0
$995$	−6.26299e10			−2.01558
$996$	−2.29675e9	+	3.97809e9i	−0.0736556	+	0.127575i
$997$	1.16908e9	+	2.02490e9i	0.0373603	+	0.0647099i	0.884101	−	0.467296i	$-0.154772\pi$
$997$	1.16908e9	+	2.02490e9i	0.0373603	+	0.0647099i	−0.846741	+	0.532006i	$0.821438\pi$
$998$	−6.87263e9	−	1.19037e10i	−0.218860	−	0.379076i
$999$	−1.09089e8	+	1.88948e8i	−0.00346180	+	0.00599602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.e.z.79.3		6
7.2	even	3		294.8.a.x.1.1		3
7.3	odd	6		42.8.e.d.25.1	✓	6
7.4	even	3	inner	294.8.e.z.67.3		6
7.5	odd	6		294.8.a.y.1.3		3
7.6	odd	2		42.8.e.d.37.1	yes	6
21.17	even	6		126.8.g.k.109.3		6
21.20	even	2		126.8.g.k.37.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.d.25.1	✓	6	7.3	odd	6
42.8.e.d.37.1	yes	6	7.6	odd	2
126.8.g.k.37.3		6	21.20	even	2
126.8.g.k.109.3		6	21.17	even	6
294.8.a.x.1.1		3	7.2	even	3
294.8.a.y.1.3		3	7.5	odd	6
294.8.e.z.67.3		6	7.4	even	3	inner
294.8.e.z.79.3		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(13.5000 + 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(154.404 - 267.436i) q^{5} -216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +O(q^{10})\)	\(q+(-4.00000 + 6.92820i) q^{2} +(13.5000 + 23.3827i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(154.404 - 267.436i) q^{5} -216.000 q^{6} +512.000 q^{8} +(-364.500 + 631.333i) q^{9} +(1235.23 + 2139.49i) q^{10} +(-3241.58 - 5614.58i) q^{11} +(864.000 - 1496.49i) q^{12} -993.626 q^{13} +8337.82 q^{15} +(-2048.00 + 3547.24i) q^{16} +(15459.7 + 26777.0i) q^{17} +(-2916.00 - 5050.66i) q^{18} +(-7794.64 + 13500.7i) q^{19} -19763.7 q^{20} +51865.2 q^{22} +(40551.3 - 70236.9i) q^{23} +(6912.00 + 11971.9i) q^{24} +(-8618.77 - 14928.1i) q^{25} +(3974.50 - 6884.04i) q^{26} -19683.0 q^{27} -34651.6 q^{29} +(-33351.3 + 57766.1i) q^{30} +(80255.8 + 139007. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(87522.6 - 151594. i) q^{33} -247356. q^{34} +46656.0 q^{36} +(5542.31 - 9599.55i) q^{37} +(-62357.1 - 108006. i) q^{38} +(-13413.9 - 23233.6i) q^{39} +(79054.9 - 136927. i) q^{40} +459665. q^{41} +455951. q^{43} +(-207461. + 359333. i) q^{44} +(112561. + 194961. i) q^{45} +(324410. + 561895. i) q^{46} +(149997. - 259803. i) q^{47} -110592. q^{48} +137900. q^{50} +(-417413. + 722980. i) q^{51} +(31796.0 + 55072.3i) q^{52} +(-948986. - 1.64369e6i) q^{53} +(78732.0 - 136368. i) q^{54} -2.00205e6 q^{55} -420911. q^{57} +(138606. - 240073. i) q^{58} +(-1.48133e6 - 2.56574e6i) q^{59} +(-266810. - 462129. i) q^{60} +(-1.19185e6 + 2.06435e6i) q^{61} -1.28409e6 q^{62} +262144. q^{64} +(-153420. + 265731. i) q^{65} +(700181. + 1.21275e6i) q^{66} +(-2.26696e6 - 3.92649e6i) q^{67} +(989423. - 1.71373e6i) q^{68} +2.18977e6 q^{69} -4.00697e6 q^{71} +(-186624. + 323242. i) q^{72} +(-1.73655e6 - 3.00779e6i) q^{73} +(44338.4 + 76796.4i) q^{74} +(232707. - 403060. i) q^{75} +997714. q^{76} +214623. q^{78} +(346434. - 600041. i) q^{79} +(632439. + 1.09542e6i) q^{80} +(-265720. - 460241. i) q^{81} +(-1.83866e6 + 3.18465e6i) q^{82} -2.65827e6 q^{83} +9.54818e6 q^{85} +(-1.82381e6 + 3.15892e6i) q^{86} +(-467797. - 810248. i) q^{87} +(-1.65969e6 - 2.87466e6i) q^{88} +(-686791. + 1.18956e6i) q^{89} -1.80097e6 q^{90} -5.19057e6 q^{92} +(-2.16691e6 + 3.75319e6i) q^{93} +(1.19998e6 + 2.07842e6i) q^{94} +(2.40705e6 + 4.16913e6i) q^{95} +(442368. - 766204. i) q^{96} -299539. q^{97} +4.72622e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} + 81 q^{3} - 192 q^{4} - 70 q^{5} - 1296 q^{6} + 3072 q^{8} - 2187 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 + 81 * q^3 - 192 * q^4 - 70 * q^5 - 1296 * q^6 + 3072 * q^8 - 2187 * q^9	\( 6 q - 24 q^{2} + 81 q^{3} - 192 q^{4} - 70 q^{5} - 1296 q^{6} + 3072 q^{8} - 2187 q^{9} - 560 q^{10} - 2428 q^{11} + 5184 q^{12} + 3838 q^{13} - 3780 q^{15} - 12288 q^{16} + 24508 q^{17} - 17496 q^{18} - 1353 q^{19} + 8960 q^{20} + 38848 q^{22} - 96628 q^{23} + 41472 q^{24} - 135175 q^{25} - 15352 q^{26} - 118098 q^{27} - 228224 q^{29} + 15120 q^{30} + 221395 q^{31} - 98304 q^{32} + 65556 q^{33} - 392128 q^{34} + 279936 q^{36} - 249987 q^{37} - 10824 q^{38} + 51813 q^{39} - 35840 q^{40} - 1221852 q^{41} + 1200486 q^{43} - 155392 q^{44} - 51030 q^{45} - 773024 q^{46} - 123114 q^{47} - 663552 q^{48} + 2162800 q^{50} - 661716 q^{51} - 122816 q^{52} - 3004752 q^{53} + 472392 q^{54} - 4492720 q^{55} - 73062 q^{57} + 912896 q^{58} - 2852938 q^{59} + 120960 q^{60} + 665386 q^{61} - 3542320 q^{62} + 1572864 q^{64} - 5835930 q^{65} + 524448 q^{66} - 10545857 q^{67} + 1568512 q^{68} - 5217912 q^{69} - 2039524 q^{71} - 1119744 q^{72} - 6858031 q^{73} - 1999896 q^{74} + 3649725 q^{75} + 173184 q^{76} - 829008 q^{78} - 1723021 q^{79} - 286720 q^{80} - 1594323 q^{81} + 4887408 q^{82} - 5271608 q^{83} + 1474120 q^{85} - 4801944 q^{86} - 3081024 q^{87} - 1243136 q^{88} - 976224 q^{89} + 816480 q^{90} + 12368384 q^{92} - 5977665 q^{93} - 984912 q^{94} - 11136310 q^{95} + 2654208 q^{96} + 16971584 q^{97} + 3540024 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 + 81 * q^3 - 192 * q^4 - 70 * q^5 - 1296 * q^6 + 3072 * q^8 - 2187 * q^9 - 560 * q^10 - 2428 * q^11 + 5184 * q^12 + 3838 * q^13 - 3780 * q^15 - 12288 * q^16 + 24508 * q^17 - 17496 * q^18 - 1353 * q^19 + 8960 * q^20 + 38848 * q^22 - 96628 * q^23 + 41472 * q^24 - 135175 * q^25 - 15352 * q^26 - 118098 * q^27 - 228224 * q^29 + 15120 * q^30 + 221395 * q^31 - 98304 * q^32 + 65556 * q^33 - 392128 * q^34 + 279936 * q^36 - 249987 * q^37 - 10824 * q^38 + 51813 * q^39 - 35840 * q^40 - 1221852 * q^41 + 1200486 * q^43 - 155392 * q^44 - 51030 * q^45 - 773024 * q^46 - 123114 * q^47 - 663552 * q^48 + 2162800 * q^50 - 661716 * q^51 - 122816 * q^52 - 3004752 * q^53 + 472392 * q^54 - 4492720 * q^55 - 73062 * q^57 + 912896 * q^58 - 2852938 * q^59 + 120960 * q^60 + 665386 * q^61 - 3542320 * q^62 + 1572864 * q^64 - 5835930 * q^65 + 524448 * q^66 - 10545857 * q^67 + 1568512 * q^68 - 5217912 * q^69 - 2039524 * q^71 - 1119744 * q^72 - 6858031 * q^73 - 1999896 * q^74 + 3649725 * q^75 + 173184 * q^76 - 829008 * q^78 - 1723021 * q^79 - 286720 * q^80 - 1594323 * q^81 + 4887408 * q^82 - 5271608 * q^83 + 1474120 * q^85 - 4801944 * q^86 - 3081024 * q^87 - 1243136 * q^88 - 976224 * q^89 + 816480 * q^90 + 12368384 * q^92 - 5977665 * q^93 - 984912 * q^94 - 11136310 * q^95 + 2654208 * q^96 + 16971584 * q^97 + 3540024 * q^99

Introduction

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