LMFDB - Embedded newform 42.9.g.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.g (of order $6$, degree $2$, 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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 6683 x^{10} + 105006 x^{9} + 34690411 x^{8} + 548172728 x^{7} + \cdots + 30\!\cdots\!24 $ x^12 - 2x^11 + 6683x^10 + 105006x^9 + 34690411x^8 + 548172728x^7 + 69245553226x^6 + 2257669296800x^5 + 109555419264148x^4 + 2043640985398464x^3 + 35697604660076192x^2 + 112120335940899328*x + 305636965993402624
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$-32.5038 - 56.2982i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-1036.40 + 598.368i) q^{5} +529.090i q^{6} +(-2203.25 - 954.186i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-1036.40 + 598.368i) q^{5} +529.090i q^{6} +(-2203.25 - 954.186i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(11725.6 + 6769.76i) q^{10} +(1470.98 - 2547.82i) q^{11} +(5184.00 - 2992.98i) q^{12} +17133.5i q^{13} +(3114.42 + 26985.1i) q^{14} +55965.8 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-105255. - 60768.8i) q^{17} +(12371.5 - 21428.1i) q^{18} +(92898.9 - 53635.2i) q^{19} -153182. i q^{20} +(66920.4 + 90162.5i) q^{21} -33284.5 q^{22} +(134603. + 233139. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(520776. - 902010. i) q^{25} +(167873. - 96921.8i) q^{26} -102276. i q^{27} +(246781. - 183166. i) q^{28} +122955. q^{29} +(-316590. - 548351. i) q^{30} +(-468669. - 270586. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-119150. + 68791.0i) q^{33} +1.37504e6i q^{34} +(2.85442e6 - 329435. i) q^{35} -279936. q^{36} +(-1.01710e6 - 1.76166e6i) q^{37} +(-1.05103e6 - 606813. i) q^{38} +(400628. - 693907. i) q^{39} +(-1.50087e6 + 866529. i) q^{40} +3.23405e6i q^{41} +(504850. - 1.16572e6i) q^{42} +6.67132e6 q^{43} +(188286. + 326120. i) q^{44} +(-2.26662e6 - 1.30863e6i) q^{45} +(1.52286e6 - 2.63767e6i) q^{46} +(-3.92844e6 + 2.26809e6i) q^{47} +766204. i q^{48} +(3.94386e6 + 4.20463e6i) q^{49} -1.17838e7 q^{50} +(2.84188e6 + 4.92228e6i) q^{51} +(-1.89927e6 - 1.09654e6i) q^{52} +(-6.27661e6 + 1.08714e7i) q^{53} +(-1.00209e6 + 578560. i) q^{54} +3.52075e6i q^{55} +(-3.19065e6 - 1.38181e6i) q^{56} -5.01654e6 q^{57} +(-695539. - 1.20471e6i) q^{58} +(-499865. - 288597. i) q^{59} +(-3.58181e6 + 6.20388e6i) q^{60} +(8.77059e6 - 5.06370e6i) q^{61} +6.12266e6i q^{62} +(-602034. - 5.21636e6i) q^{63} +2.09715e6 q^{64} +(-1.02521e7 - 1.77572e7i) q^{65} +(1.34802e6 + 778282. i) q^{66} +(-1.18488e6 + 2.05228e6i) q^{67} +(1.34726e7 - 7.77841e6i) q^{68} -1.25895e7i q^{69} +(-1.93748e7 - 2.61039e7i) q^{70} +2.95099e7 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(1.72712e7 + 9.97155e6i) q^{73} +(-1.15071e7 + 1.99309e7i) q^{74} +(-4.21829e7 + 2.43543e7i) q^{75} +1.37306e7i q^{76} +(-5.67204e6 + 4.20990e6i) q^{77} -9.06517e6 q^{78} +(-6014.57 - 10417.5i) q^{79} +(1.69804e7 + 9.80366e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(3.16871e7 - 1.82945e7i) q^{82} -1.41766e7i q^{83} +(-1.42775e7 + 1.64781e6i) q^{84} +1.45449e8 q^{85} +(-3.77387e7 - 6.53653e7i) q^{86} +(-4.97968e6 - 2.87502e6i) q^{87} +(2.13021e6 - 3.68963e6i) q^{88} +(6.90485e7 - 3.98652e7i) q^{89} +2.96109e7i q^{90} +(1.63485e7 - 3.77495e7i) q^{91} -3.44583e7 q^{92} +(1.26541e7 + 2.19175e7i) q^{93} +(4.44453e7 + 2.56605e7i) q^{94} +(-6.41871e7 + 1.11175e8i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} -1.14316e8i q^{97} +(1.88869e7 - 6.24268e7i) q^{98} +6.43408e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) $ 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$3$	−40.5000	−	23.3827i	−0.500000	−	0.288675i
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	−1036.40	+	598.368i	−1.65825	+	0.957389i	−0.684722	+	0.728804i	$0.740076\pi$
$5$	−1036.40	+	598.368i	−1.65825	+	0.957389i	−0.973524	+	0.228584i	$0.926590\pi$
$6$			529.090i			0.408248i
$7$	−2203.25	−	954.186i	−0.917640	−	0.397412i
$7$	−2203.25	−	954.186i	−0.917640	−	0.397412i
$8$	1448.15			0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	11725.6	+	6769.76i	1.17256	+	0.676976i
$11$	1470.98	−	2547.82i	0.100470	−	0.174019i	−0.811408	−	0.584480i	$-0.801299\pi$
$11$	1470.98	−	2547.82i	0.100470	−	0.174019i	0.911878	+	0.410460i	$0.134632\pi$
$12$	5184.00	−	2992.98i	0.250000	−	0.144338i
$13$			17133.5i			0.599892i	0.953956	+	0.299946i	$0.0969686\pi$
$13$			17133.5i			0.599892i	−0.953956	+	0.299946i	$0.903031\pi$
$14$	3114.42	+	26985.1i	0.0810709	+	0.702444i
$15$	55965.8			1.10550
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−105255.	−	60768.8i	−1.26022	−	0.727588i	−0.287102	−	0.957900i	$-0.592692\pi$
$17$	−105255.	−	60768.8i	−1.26022	−	0.727588i	−0.973117	+	0.230312i	$0.926025\pi$
$18$	12371.5	−	21428.1i	0.117851	−	0.204124i
$19$	92898.9	−	53635.2i	0.712846	−	0.411562i	−0.0992677	−	0.995061i	$-0.531650\pi$
$19$	92898.9	−	53635.2i	0.712846	−	0.411562i	0.812114	+	0.583499i	$0.198317\pi$
$20$		−	153182.i		−	0.957389i
$21$	66920.4	+	90162.5i	0.344097	+	0.463606i
$22$	−33284.5			−0.142086
$23$	134603.	+	233139.i	0.480998	+	0.833113i	0.999762	−	0.0218045i	$-0.00694115\pi$
$23$	134603.	+	233139.i	0.480998	+	0.833113i	−0.518764	+	0.854917i	$0.673608\pi$
$24$	−58650.3	−	33861.7i	−0.176777	−	0.102062i
$25$	520776.	−	902010.i	1.33319	−	2.30915i
$26$	167873.	−	96921.8i	0.367357	−	0.212094i
$27$		−	102276.i		−	0.192450i
$28$	246781.	−	183166.i	0.401494	−	0.297997i
$29$	122955.			0.173842			0.0869210	−	0.996215i	$-0.472297\pi$
$29$	122955.			0.173842			0.0869210	+	0.996215i	$0.472297\pi$
$30$	−316590.	−	548351.i	−0.390852	−	0.676976i
$31$	−468669.	−	270586.i	−0.507480	−	0.292994i	0.224317	−	0.974516i	$-0.427985\pi$
$31$	−468669.	−	270586.i	−0.507480	−	0.292994i	−0.731797	+	0.681522i	$0.761318\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$	−119150.	+	68791.0i	−0.100470	+	0.0580064i
$34$			1.37504e6i			1.02896i
$35$	2.85442e6	−	329435.i	1.90215	−	0.219532i
$36$	−279936.			−0.166667
$37$	−1.01710e6	−	1.76166e6i	−0.542694	−	0.939974i	−0.998748	−	0.0500218i	$-0.984071\pi$
$37$	−1.01710e6	−	1.76166e6i	−0.542694	−	0.939974i	0.456054	−	0.889952i	$-0.349262\pi$
$38$	−1.05103e6	−	606813.i	−0.504059	−	0.291018i
$39$	400628.	−	693907.i	0.173174	−	0.299946i
$40$	−1.50087e6	+	866529.i	−0.586279	+	0.338488i
$41$			3.23405e6i			1.14449i	0.820084	+	0.572244i	$0.193927\pi$
$41$			3.23405e6i			1.14449i	−0.820084	+	0.572244i	$0.806073\pi$
$42$	504850.	−	1.16572e6i	0.162243	−	0.374625i
$43$	6.67132e6			1.95136			0.975681	−	0.219197i	$-0.0703437\pi$
$43$	6.67132e6			1.95136			0.975681	+	0.219197i	$0.0703437\pi$
$44$	188286.	+	326120.i	0.0502350	+	0.0870096i
$45$	−2.26662e6	−	1.30863e6i	−0.552749	−	0.319130i
$46$	1.52286e6	−	2.63767e6i	0.340117	−	0.589100i
$47$	−3.92844e6	+	2.26809e6i	−0.805062	+	0.464803i	−0.845238	−	0.534390i	$-0.820541\pi$
$47$	−3.92844e6	+	2.26809e6i	−0.805062	+	0.464803i	0.0401762	+	0.999193i	$0.487208\pi$
$48$			766204.i			0.144338i
$49$	3.94386e6	+	4.20463e6i	0.684128	+	0.729362i
$50$	−1.17838e7			−1.88541
$51$	2.84188e6	+	4.92228e6i	0.420073	+	0.727588i
$52$	−1.89927e6	−	1.09654e6i	−0.259761	−	0.149973i
$53$	−6.27661e6	+	1.08714e7i	−0.795467	+	1.37779i	0.127076	+	0.991893i	$0.459441\pi$
$53$	−6.27661e6	+	1.08714e7i	−0.795467	+	1.37779i	−0.922542	+	0.385896i	$0.873893\pi$
$54$	−1.00209e6	+	578560.i	−0.117851	+	0.0680414i
$55$			3.52075e6i			0.384756i
$56$	−3.19065e6	−	1.38181e6i	−0.324435	−	0.140506i
$57$	−5.01654e6			−0.475231
$58$	−695539.	−	1.20471e6i	−0.0614624	−	0.106456i
$59$	−499865.	−	288597.i	−0.0412520	−	0.0238168i	0.479232	−	0.877688i	$-0.340915\pi$
$59$	−499865.	−	288597.i	−0.0412520	−	0.0238168i	−0.520484	+	0.853871i	$0.674249\pi$
$60$	−3.58181e6	+	6.20388e6i	−0.276374	+	0.478694i
$61$	8.77059e6	−	5.06370e6i	0.633446	−	0.365720i	−0.148640	−	0.988891i	$-0.547489\pi$
$61$	8.77059e6	−	5.06370e6i	0.633446	−	0.365720i	0.782085	+	0.623171i	$0.214156\pi$
$62$			6.12266e6i			0.414356i
$63$	−602034.	−	5.21636e6i	−0.0382172	−	0.331135i
$64$	2.09715e6			0.125000
$65$	−1.02521e7	−	1.77572e7i	−0.574330	−	0.994768i
$66$	1.34802e6	+	778282.i	0.0710431	+	0.0410167i
$67$	−1.18488e6	+	2.05228e6i	−0.0587998	+	0.101844i	−0.893927	−	0.448213i	$-0.852061\pi$
$67$	−1.18488e6	+	2.05228e6i	−0.0587998	+	0.101844i	0.835127	+	0.550057i	$0.185394\pi$
$68$	1.34726e7	−	7.77841e6i	0.630109	−	0.363794i
$69$		−	1.25895e7i		−	0.555408i
$70$	−1.93748e7	−	2.61039e7i	−0.806947	−	1.08721i
$71$	2.95099e7			1.16127			0.580636	−	0.814163i	$-0.302804\pi$
$71$	2.95099e7			1.16127			0.580636	+	0.814163i	$0.302804\pi$
$72$	1.58356e6	+	2.74280e6i	0.0589256	+	0.102062i
$73$	1.72712e7	+	9.97155e6i	0.608180	+	0.351133i	0.772253	−	0.635316i	$-0.219130\pi$
$73$	1.72712e7	+	9.97155e6i	0.608180	+	0.351133i	−0.164073	+	0.986448i	$0.552463\pi$
$74$	−1.15071e7	+	1.99309e7i	−0.383743	+	0.664662i
$75$	−4.21829e7	+	2.43543e7i	−1.33319	+	0.769716i
$76$			1.37306e7i			0.411562i
$77$	−5.67204e6	+	4.20990e6i	−0.161353	+	0.119759i
$78$	−9.06517e6			−0.244905
$79$	−6014.57	−	10417.5i	−0.000154417	−	0.000267459i	0.865948	−	0.500134i	$-0.166716\pi$
$79$	−6014.57	−	10417.5i	−0.000154417	−	0.000267459i	−0.866103	+	0.499866i	$0.833382\pi$
$80$	1.69804e7	+	9.80366e6i	0.414562	+	0.239347i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	3.16871e7	−	1.82945e7i	0.700853	−	0.404637i
$83$		−	1.41766e7i		−	0.298716i	−0.988783	−	0.149358i	$-0.952279\pi$
$83$		−	1.41766e7i		−	0.298716i	0.988783	−	0.149358i	$-0.0477207\pi$
$84$	−1.42775e7	+	1.64781e6i	−0.286772	+	0.0330970i
$85$	1.45449e8			2.78634
$86$	−3.77387e7	−	6.53653e7i	−0.689910	−	1.19496i
$87$	−4.97968e6	−	2.87502e6i	−0.0869210	−	0.0501839i
$88$	2.13021e6	−	3.68963e6i	0.0355215	−	0.0615251i
$89$	6.90485e7	−	3.98652e7i	1.10051	−	0.635380i	0.164156	−	0.986434i	$-0.447510\pi$
$89$	6.90485e7	−	3.98652e7i	1.10051	−	0.635380i	0.936355	+	0.351054i	$0.114177\pi$
$90$			2.96109e7i			0.451317i
$91$	1.63485e7	−	3.77495e7i	0.238404	−	0.550485i
$92$	−3.44583e7			−0.480998
$93$	1.26541e7	+	2.19175e7i	0.169160	+	0.292994i
$94$	4.44453e7	+	2.56605e7i	0.569265	+	0.328665i
$95$	−6.41871e7	+	1.11175e8i	−0.788050	+	1.36494i
$96$	7.50723e6	−	4.33430e6i	0.0883883	−	0.0510310i
$97$		−	1.14316e8i		−	1.29128i	−0.763643	−	0.645639i	$-0.776591\pi$
$97$		−	1.14316e8i		−	1.29128i	0.763643	−	0.645639i	$-0.223409\pi$
$98$	1.88869e7	−	6.24268e7i	0.204766	−	0.676809i
$99$	6.43408e6			0.0669800
$100$	6.66593e7	+	1.15457e8i	0.666593	+	1.15457i
$101$	−1.53837e8	−	8.88178e7i	−1.47834	−	0.853522i	−0.478643	−	0.878010i	$-0.658871\pi$
$101$	−1.53837e8	−	8.88178e7i	−1.47834	−	0.853522i	−0.999700	+	0.0244879i	$0.992204\pi$
$102$	3.21522e7	−	5.56892e7i	0.297036	−	0.514482i
$103$	−1.38944e8	+	8.02194e7i	−1.23450	+	0.712739i	−0.967965	−	0.251086i	$-0.919212\pi$
$103$	−1.38944e8	+	8.02194e7i	−1.23450	+	0.712739i	−0.266535	+	0.963825i	$0.585879\pi$
$104$			2.48120e7i			0.212094i
$105$	−1.23307e8	−	5.34018e7i	−1.01445	−	0.439338i
$106$	1.42024e8			1.12496
$107$	−4.78052e7	−	8.28011e7i	−0.364704	−	0.631686i	0.624025	−	0.781405i	$-0.285496\pi$
$107$	−4.78052e7	−	8.28011e7i	−0.364704	−	0.631686i	−0.988729	+	0.149719i	$0.952163\pi$
$108$	1.13374e7	+	6.54566e6i	0.0833333	+	0.0481125i
$109$	9.15619e7	−	1.58590e8i	0.648647	−	1.12349i	−0.334799	−	0.942290i	$-0.608668\pi$
$109$	9.15619e7	−	1.58590e8i	0.648647	−	1.12349i	0.983446	−	0.181200i	$-0.0579983\pi$
$110$	3.44962e7	−	1.99164e7i	0.235614	−	0.136032i
$111$			9.51298e7i			0.626649i
$112$	4.51016e6	+	3.90786e7i	0.0286629	+	0.248351i
$113$	−3.19567e7			−0.195997			−0.0979983	−	0.995187i	$-0.531244\pi$
$113$	−3.19567e7			−0.195997			−0.0979983	+	0.995187i	$0.531244\pi$
$114$	2.83778e7	+	4.91518e7i	0.168020	+	0.291018i
$115$	−2.79006e8	−	1.61084e8i	−1.59523	−	0.921004i
$116$	−7.86913e6	+	1.36297e7i	−0.0434605	+	0.0752758i
$117$	−3.24508e7	+	1.87355e7i	−0.173174	+	0.0999820i
$118$			6.53021e6i			0.0336821i
$119$	1.73918e8	+	2.34322e8i	0.867276	+	1.16849i
$120$	8.10471e7			0.390852
$121$	1.02852e8	+	1.78145e8i	0.479812	+	0.831058i
$122$	−9.92279e7	−	5.72892e7i	−0.447914	−	0.258603i
$123$	7.56207e7	−	1.30979e8i	0.330385	−	0.572244i
$124$	5.99896e7	−	3.46350e7i	0.253740	−	0.146497i
$125$			7.78988e8i			3.19073i
$126$	−4.77041e7	+	3.54069e7i	−0.189266	+	0.140477i
$127$	−2.35388e8			−0.904835			−0.452417	−	0.891806i	$-0.649438\pi$
$127$	−2.35388e8			−0.904835			−0.452417	+	0.891806i	$0.649438\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$	−2.70188e8	−	1.55993e8i	−0.975681	−	0.563310i
$130$	−1.15990e8	+	2.00900e8i	−0.406112	+	0.703407i
$131$	2.27634e8	−	1.31424e8i	0.772950	−	0.446263i	−0.0609761	−	0.998139i	$-0.519421\pi$
$131$	2.27634e8	−	1.31424e8i	0.772950	−	0.446263i	0.833926	+	0.551876i	$0.186088\pi$
$132$		−	1.76105e7i		−	0.0580064i
$133$	−2.55858e8	+	2.95292e7i	−0.817696	+	0.0943724i
$134$	2.68108e7			0.0831555
$135$	6.11986e7	+	1.05999e8i	0.184250	+	0.319130i
$136$	−1.52425e8	−	8.80027e7i	−0.445555	−	0.257241i
$137$	2.35009e7	−	4.07048e7i	0.0667117	−	0.115548i	−0.830740	−	0.556660i	$-0.812083\pi$
$137$	2.35009e7	−	4.07048e7i	0.0667117	−	0.115548i	0.897452	+	0.441112i	$0.145416\pi$
$138$	−1.23352e8	+	7.12170e7i	−0.340117	+	0.196367i
$139$			3.63001e8i			0.972408i	0.873845	+	0.486204i	$0.161619\pi$
$139$			3.63001e8i			0.972408i	−0.873845	+	0.486204i	$0.838381\pi$
$140$	−1.46164e8	+	3.37499e8i	−0.380478	+	0.878539i
$141$	2.12136e8			0.536708
$142$	−1.66933e8	−	2.89136e8i	−0.410572	−	0.711131i
$143$	4.36530e7	+	2.52031e7i	0.104393	+	0.0602712i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	−1.27431e8	+	7.35724e7i	−0.288273	+	0.166434i
$146$		−	2.25630e8i		−	0.496577i
$147$	−6.14109e7	−	2.62505e8i	−0.131515	−	0.562172i
$148$	2.60377e8			0.542694
$149$	−3.03723e8	−	5.26064e8i	−0.616216	−	1.06732i	−0.990170	−	0.139870i	$-0.955332\pi$
$149$	−3.03723e8	−	5.26064e8i	−0.616216	−	1.06732i	0.373954	−	0.927447i	$-0.378002\pi$
$150$	4.77245e8	+	2.75537e8i	0.942705	+	0.544271i
$151$	2.67491e8	−	4.63308e8i	0.514519	−	0.891172i	−0.485339	−	0.874326i	$-0.661304\pi$
$151$	2.67491e8	−	4.63308e8i	0.514519	−	0.891172i	0.999858	−	0.0168466i	$-0.00536270\pi$
$152$	1.34532e8	−	7.76720e7i	0.252029	−	0.145509i
$153$		−	2.65803e8i		−	0.485058i
$154$	7.33343e7	+	3.17596e7i	0.130384	+	0.0564667i
$155$	6.47640e8			1.12204
$156$	5.12803e7	+	8.88201e7i	0.0865869	+	0.149973i
$157$	5.42643e8	+	3.13295e8i	0.893132	+	0.515650i	0.874966	−	0.484185i	$-0.160884\pi$
$157$	5.42643e8	+	3.13295e8i	0.893132	+	0.515650i	0.0181660	+	0.999835i	$0.494217\pi$
$158$	−68047.0	+	117861.i	−0.000109190	+	0.000189122i
$159$	5.08406e8	−	2.93528e8i	0.795467	−	0.459263i
$160$		−	2.21832e8i		−	0.338488i
$161$	−7.41065e7	−	6.42101e8i	−0.110294	−	0.955652i
$162$	5.41131e7			0.0785674
$163$	−4.29035e8	−	7.43110e8i	−0.607774	−	1.05270i	−0.991606	−	0.129293i	$-0.958729\pi$
$163$	−4.29035e8	−	7.43110e8i	−0.607774	−	1.05270i	0.383832	−	0.923403i	$-0.374604\pi$
$164$	−3.58498e8	−	2.06979e8i	−0.495578	−	0.286122i
$165$	8.23247e7	−	1.42591e8i	0.111069	−	0.192378i
$166$	−1.38901e8	+	8.01948e7i	−0.182926	+	0.105612i
$167$			9.16729e8i			1.17862i	0.807906	+	0.589312i	$0.200601\pi$
$167$			9.16729e8i			1.17862i	−0.807906	+	0.589312i	$0.799399\pi$
$168$	9.69111e7	+	1.30569e8i	0.121657	+	0.163909i
$169$	5.22174e8			0.640130
$170$	−8.22781e8	−	1.42510e9i	−0.985119	−	1.70628i
$171$	2.03170e8	+	1.17300e8i	0.237615	+	0.137187i
$172$	−4.26964e8	+	7.39524e8i	−0.487840	+	0.844964i
$173$	1.37843e9	−	7.95835e8i	1.53886	−	0.888461i	0.539954	−	0.841695i	$-0.318442\pi$
$173$	1.37843e9	−	7.95835e8i	1.53886	−	0.888461i	0.998906	−	0.0467666i	$-0.0148917\pi$
$174$			6.50543e7i			0.0709707i
$175$	−2.00809e9	+	1.49044e9i	−2.14107	+	1.58914i
$176$	−4.82011e7			−0.0502350
$177$	1.34964e7	+	2.33764e7i	0.0137507	+	0.0238168i
$178$	−7.81195e8	−	4.51023e8i	−0.778179	−	0.449282i
$179$	2.95445e8	−	5.11726e8i	0.287783	−	0.498455i	−0.685497	−	0.728075i	$-0.740415\pi$
$179$	2.95445e8	−	5.11726e8i	0.287783	−	0.498455i	0.973280	+	0.229620i	$0.0737485\pi$
$180$	2.90127e8	−	1.67505e8i	0.276374	−	0.159565i
$181$		−	2.02577e8i		−	0.188745i	−0.995537	−	0.0943726i	$-0.969915\pi$
$181$		−	2.02577e8i		−	0.188745i	0.995537	−	0.0943726i	$-0.0300845\pi$
$182$	−4.62349e8	+	5.33609e7i	−0.421390	+	0.0486338i
$183$	−4.73612e8			−0.422297
$184$	1.94926e8	+	3.37621e8i	0.170058	+	0.294550i
$185$	2.10824e9	+	1.21720e9i	1.79984	+	1.03914i
$186$	1.43164e8	−	2.47968e8i	0.119614	−	0.207178i
$187$	−3.09656e8	+	1.78780e8i	−0.253229	+	0.146202i
$188$		−	5.80631e8i		−	0.464803i
$189$	−9.75902e7	+	2.25340e8i	−0.0764819	+	0.176600i
$190$	1.45239e9			1.11447
$191$	8.00808e8	+	1.38704e9i	0.601721	+	1.04221i	0.992561	+	0.121752i	$0.0388514\pi$
$191$	8.00808e8	+	1.38704e9i	0.601721	+	1.04221i	−0.390840	+	0.920459i	$0.627815\pi$
$192$	−8.49347e7	−	4.90370e7i	−0.0625000	−	0.0360844i
$193$	2.44627e8	−	4.23706e8i	0.176309	−	0.305376i	−0.764305	−	0.644855i	$-0.776918\pi$
$193$	2.44627e8	−	4.23706e8i	0.176309	−	0.305376i	0.940613	+	0.339479i	$0.110251\pi$
$194$	−1.12006e9	+	6.46668e8i	−0.790743	+	0.456536i
$195$			9.58891e8i			0.663179i
$196$	−7.18495e8	+	1.68086e8i	−0.486855	+	0.113895i
$197$	1.99149e9			1.32225			0.661125	−	0.750276i	$-0.270079\pi$
$197$	1.99149e9			1.32225			0.661125	+	0.750276i	$0.270079\pi$
$198$	−3.63966e7	−	6.30408e7i	−0.0236810	−	0.0410167i
$199$	−4.38208e8	−	2.52999e8i	−0.279426	−	0.161327i	0.353737	−	0.935345i	$-0.384911\pi$
$199$	−4.38208e8	−	2.52999e8i	−0.279426	−	0.161327i	−0.633164	+	0.774018i	$0.718244\pi$
$200$	7.54164e8	−	1.30625e9i	0.471353	−	0.816407i
$201$	9.59755e7	−	5.54115e7i	0.0587998	−	0.0339481i
$202$			2.00972e9i			1.20706i
$203$	−2.70902e8	−	1.17322e8i	−0.159524	−	0.0690869i
$204$	−7.27521e8			−0.420073
$205$	−1.93515e9	−	3.35178e9i	−1.09572	−	1.89784i
$206$	1.57197e9	+	9.07579e8i	0.872923	+	0.503983i
$207$	−2.94377e8	+	5.09875e8i	−0.160333	+	0.277704i
$208$	2.43107e8	−	1.40358e8i	0.129880	−	0.0749865i
$209$		−	3.15586e8i		−	0.165399i
$210$	1.74301e8	+	1.51024e9i	0.0896236	+	0.776550i
$211$	−8.15773e8			−0.411566			−0.205783	−	0.978598i	$-0.565974\pi$
$211$	−8.15773e8			−0.411566			−0.205783	+	0.978598i	$0.565974\pi$
$212$	−8.03407e8	−	1.39154e9i	−0.397733	−	0.688894i
$213$	−1.19515e9	−	6.90020e8i	−0.580636	−	0.335230i
$214$	−5.40855e8	+	9.36788e8i	−0.257885	+	0.446669i
$215$	−6.91418e9	+	3.99190e9i	−3.23584	+	1.86821i
$216$		−	1.48111e8i		−	0.0680414i
$217$	7.74407e8	+	1.04337e9i	0.349245	+	0.470542i
$218$	−2.07181e9			−0.917326
$219$	−4.66323e8	−	8.07696e8i	−0.202727	−	0.351133i
$220$	−3.90280e8	−	2.25328e8i	−0.166604	−	0.0961889i
$221$	1.04118e9	−	1.80338e9i	0.436474	−	0.755995i
$222$	9.32078e8	−	5.38135e8i	0.383743	−	0.221554i
$223$			4.55344e9i			1.84128i	0.390412	+	0.920640i	$0.372333\pi$
$223$			4.55344e9i			1.84128i	−0.390412	+	0.920640i	$0.627667\pi$
$224$	3.57377e8	−	2.65252e8i	0.141950	−	0.105358i
$225$	2.27787e9			0.888791
$226$	1.80775e8	+	3.13111e8i	0.0692952	+	0.120023i
$227$	−2.90949e9	−	1.67980e9i	−1.09576	−	0.632635i	−0.160653	−	0.987011i	$-0.551360\pi$
$227$	−2.90949e9	−	1.67980e9i	−1.09576	−	0.632635i	−0.935103	+	0.354376i	$0.884693\pi$
$228$	3.21058e8	−	5.56090e8i	0.118808	−	0.205781i
$229$	2.19926e8	−	1.26974e8i	0.0799714	−	0.0461715i	−0.459481	−	0.888188i	$-0.651965\pi$
$229$	2.19926e8	−	1.26974e8i	0.0799714	−	0.0461715i	0.539452	+	0.842016i	$0.318631\pi$
$230$			3.64492e9i			1.30250i
$231$	3.28156e8	−	3.78734e7i	0.115248	−	0.0133010i
$232$	1.78058e8			0.0614624
$233$	−2.55401e8	−	4.42368e8i	−0.0866561	−	0.150093i	0.819440	−	0.573166i	$-0.194285\pi$
$233$	−2.55401e8	−	4.42368e8i	−0.0866561	−	0.150093i	−0.906096	+	0.423073i	$0.860951\pi$
$234$	3.67139e8	+	2.11968e8i	0.122452	+	0.0706979i
$235$	2.71430e9	−	4.70131e9i	0.889994	−	1.54151i
$236$	6.39828e7	−	3.69405e7i	0.0206260	−	0.0119084i
$237$			562547.i			0.000178306i
$238$	1.31205e9	−	3.02957e9i	0.408923	−	0.944219i
$239$	5.10104e9			1.56339			0.781694	−	0.623662i	$-0.214356\pi$
$239$	5.10104e9			1.56339			0.781694	+	0.623662i	$0.214356\pi$
$240$	−4.58472e8	−	7.94097e8i	−0.138187	−	0.239347i
$241$	2.64383e9	+	1.52642e9i	0.783728	+	0.452486i	0.837750	−	0.546054i	$-0.183871\pi$
$241$	2.64383e9	+	1.52642e9i	0.783728	+	0.452486i	−0.0540217	+	0.998540i	$0.517204\pi$
$242$	1.16364e9	−	2.01548e9i	0.339278	−	0.587647i
$243$	1.93710e8	−	1.11839e8i	0.0555556	−	0.0320750i
$244$			1.29631e9i			0.365720i
$245$	−6.60335e9	−	1.99781e9i	−1.83274	−	0.554486i
$246$	−1.71110e9			−0.467235
$247$	9.18959e8	+	1.59168e9i	0.246893	+	0.427631i
$248$	−6.78705e8	−	3.91850e8i	−0.179421	−	0.103589i
$249$	−3.31486e8	+	5.74151e8i	−0.0862319	+	0.149358i
$250$	7.63249e9	−	4.40662e9i	1.95392	−	1.12809i
$251$			3.88447e9i			0.978671i	0.872096	+	0.489336i	$0.162761\pi$
$251$			3.88447e9i			0.978671i	−0.872096	+	0.489336i	$0.837239\pi$
$252$	6.16770e8	+	2.67111e8i	0.152940	+	0.0662353i
$253$	7.91994e8			0.193304
$254$	1.33155e9	+	2.30632e9i	0.319907	+	0.554096i
$255$	−5.89067e9	−	3.40098e9i	−1.39317	−	0.804346i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−3.04402e9	+	1.75747e9i	−0.697774	+	0.402860i	−0.806518	−	0.591210i	$-0.798651\pi$
$257$	−3.04402e9	+	1.75747e9i	−0.697774	+	0.402860i	0.108744	+	0.994070i	$0.465317\pi$
$258$			3.52973e9i			0.796640i
$259$	5.59969e8	+	4.85189e9i	0.124441	+	1.07823i
$260$	2.62455e9			0.574330
$261$	1.34451e8	+	2.32877e8i	0.0289737	+	0.0501839i
$262$	−2.57538e9	−	1.48690e9i	−0.546558	−	0.315555i
$263$	5.26263e8	−	9.11515e8i	0.109997	−	0.190520i	−0.805772	−	0.592226i	$-0.798249\pi$
$263$	5.26263e8	−	9.11515e8i	0.109997	−	0.190520i	0.915769	+	0.401706i	$0.131583\pi$
$264$	−1.72547e8	+	9.96201e7i	−0.0355215	+	0.0205084i
$265$		−	1.50229e10i		−	3.04628i
$266$	1.73668e9	+	2.33984e9i	0.346890	+	0.467369i
$267$	−3.72862e9			−0.733674
$268$	−1.51665e8	−	2.62691e8i	−0.0293999	−	0.0509222i
$269$	1.51989e9	+	8.77508e8i	0.290270	+	0.167588i	0.638064	−	0.769984i	$-0.279736\pi$
$269$	1.51989e9	+	8.77508e8i	0.290270	+	0.167588i	−0.347794	+	0.937571i	$0.613069\pi$
$270$	6.92383e8	−	1.19924e9i	0.130284	−	0.225659i
$271$	5.91326e9	−	3.41402e9i	1.09635	−	0.632979i	0.161092	−	0.986939i	$-0.448499\pi$
$271$	5.91326e9	−	3.41402e9i	1.09635	−	0.632979i	0.935260	+	0.353960i	$0.115165\pi$
$272$			1.99127e9i			0.363794i
$273$	−1.54480e9	+	1.14658e9i	−0.278113	+	0.206421i
$274$	−5.31765e8			−0.0943447
$275$	−1.53210e9	−	2.65368e9i	−0.267891	−	0.464000i
$276$	1.39556e9	+	8.05729e8i	0.240499	+	0.138852i
$277$	−2.49712e9	+	4.32513e9i	−0.424150	+	0.734650i	−0.996341	−	0.0854712i	$-0.972760\pi$
$277$	−2.49712e9	+	4.32513e9i	−0.424150	+	0.734650i	0.572191	+	0.820121i	$0.306094\pi$
$278$	3.55667e9	−	2.05344e9i	0.595476	−	0.343798i
$279$		−	1.18354e9i		−	0.195329i
$280$	4.13364e9	−	4.77074e8i	0.672512	−	0.0776163i
$281$	6.44185e9			1.03320			0.516601	−	0.856226i	$-0.327197\pi$
$281$	6.44185e9			1.03320			0.516601	+	0.856226i	$0.327197\pi$
$282$	−1.20002e9	−	2.07850e9i	−0.189755	−	0.328665i
$283$	3.46126e9	+	1.99836e9i	0.539621	+	0.311550i	0.744925	−	0.667148i	$-0.232485\pi$
$283$	3.46126e9	+	1.99836e9i	0.539621	+	0.311550i	−0.205304	+	0.978698i	$0.565818\pi$
$284$	−1.88863e9	+	3.27121e9i	−0.290318	+	0.502845i
$285$	5.19916e9	−	3.00174e9i	0.788050	−	0.454981i
$286$		−	5.70281e8i		−	0.0852363i
$287$	3.08588e9	−	7.12543e9i	0.454833	−	1.05023i
$288$	−4.05391e8			−0.0589256
$289$	3.89783e9	+	6.75124e9i	0.558768	+	0.967814i
$290$	1.44172e9	+	8.32377e8i	0.203840	+	0.117687i
$291$	−2.67301e9	+	4.62979e9i	−0.372760	+	0.645639i
$292$	−2.21072e9	+	1.27636e9i	−0.304090	+	0.175566i
$293$		−	3.95148e9i		−	0.536154i	−0.963397	−	0.268077i	$-0.913612\pi$
$293$		−	3.95148e9i		−	0.536154i	0.963397	−	0.268077i	$-0.0863882\pi$
$294$	−2.22463e9	+	2.08666e9i	−0.297761	+	0.279294i
$295$	6.90750e8			0.0912079
$296$	−1.47291e9	−	2.55116e9i	−0.191871	−	0.332331i
$297$	−2.60580e8	−	1.50446e8i	−0.0334900	−	0.0193355i
$298$	−3.43623e9	+	5.95173e9i	−0.435730	+	0.754707i
$299$	−3.99449e9	+	2.30622e9i	−0.499778	+	0.288547i
$300$		−	6.23470e9i		−	0.769716i
$301$	−1.46986e10	−	6.36567e9i	−1.79065	−	0.775494i
$302$	−6.05263e9			−0.727639
$303$	4.15360e9	+	7.19424e9i	0.492781	+	0.853522i
$304$	−1.52205e9	−	8.78759e8i	−0.178212	−	0.102891i
$305$	−6.05991e9	+	1.04961e10i	−0.700273	+	1.21291i
$306$	−2.60433e9	+	1.50361e9i	−0.297036	+	0.171494i
$307$			3.15707e9i			0.355410i	0.984084	+	0.177705i	$0.0568674\pi$
$307$			3.15707e9i			0.355410i	−0.984084	+	0.177705i	$0.943133\pi$
$308$	−1.03662e8	−	8.98186e8i	−0.0115190	−	0.0998075i
$309$	7.50298e9			0.823000
$310$	−3.66360e9	−	6.34555e9i	−0.396700	−	0.687104i
$311$	−6.06279e9	−	3.50035e9i	−0.648084	−	0.374171i	0.139638	−	0.990203i	$-0.455406\pi$
$311$	−6.06279e9	−	3.50035e9i	−0.648084	−	0.374171i	−0.787722	+	0.616031i	$0.788739\pi$
$312$	5.80171e8	−	1.00488e9i	0.0612262	−	0.106047i
$313$	5.73783e9	−	3.31274e9i	0.597820	−	0.345151i	−0.170364	−	0.985381i	$-0.554494\pi$
$313$	5.73783e9	−	3.31274e9i	0.597820	−	0.345151i	0.768183	+	0.640230i	$0.221161\pi$
$314$		−	7.08906e9i		−	0.729239i
$315$	3.74525e9	+	5.04602e9i	0.380399	+	0.512515i
$316$	1.53973e6			0.000154417
$317$	−3.68994e9	−	6.39117e9i	−0.365412	−	0.632912i	0.623430	−	0.781879i	$-0.285738\pi$
$317$	−3.68994e9	−	6.39117e9i	−0.365412	−	0.632912i	−0.988842	+	0.148967i	$0.952405\pi$
$318$	−5.75195e9	−	3.32089e9i	−0.562480	−	0.324748i
$319$	1.80865e8	−	3.13267e8i	0.0174659	−	0.0302519i
$320$	−2.17350e9	+	1.25487e9i	−0.207281	+	0.119674i
$321$			4.47126e9i			0.421124i
$322$	−5.87207e9	+	4.35836e9i	−0.546220	+	0.405415i
$323$	−1.30374e10			−1.19779
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	1.54546e10	+	8.92272e9i	1.38524	+	0.799768i
$326$	−4.85398e9	+	8.40734e9i	−0.429761	+	0.744368i
$327$	−7.41651e9	+	4.28192e9i	−0.648647	+	0.374497i
$328$			4.68340e9i			0.404637i
$329$	1.08195e10	−	1.24871e9i	0.923475	−	0.106581i
$330$	−1.86280e9			−0.157076
$331$	7.16497e9	+	1.24101e10i	0.596901	+	1.03386i	0.993276	+	0.115774i	$0.0369350\pi$
$331$	7.16497e9	+	1.24101e10i	0.596901	+	1.03386i	−0.396374	+	0.918089i	$0.629732\pi$
$332$	1.57149e9	+	9.07300e8i	0.129348	+	0.0746790i
$333$	2.22439e9	−	3.85276e9i	0.180898	−	0.313325i
$334$	8.98207e9	−	5.18580e9i	0.721756	−	0.416706i
$335$		−	2.83598e9i		−	0.225177i
$336$	7.31101e8	−	1.68814e9i	0.0573614	−	0.132450i
$337$	−2.42707e9			−0.188175			−0.0940877	−	0.995564i	$-0.529993\pi$
$337$	−2.42707e9			−0.188175			−0.0940877	+	0.995564i	$0.529993\pi$
$338$	−2.95386e9	−	5.11623e9i	−0.226320	−	0.391998i
$339$	1.29425e9	+	7.47234e8i	0.0979983	+	0.0565793i
$340$	−9.30871e9	+	1.61232e10i	−0.696584	+	1.20652i
$341$	−1.37881e9	+	7.96054e8i	−0.101973	+	0.0588742i
$342$		−	2.65420e9i		−	0.194012i
$343$	−4.67733e9	−	1.30270e10i	−0.337926	−	0.941173i
$344$	9.66110e9			0.689910
$345$	7.53316e9	+	1.30478e10i	0.531742	+	0.921004i
$346$	−1.55951e10	−	9.00384e9i	−1.08814	−	0.628237i
$347$	9.33878e9	−	1.61752e10i	0.644128	−	1.11566i	−0.340374	−	0.940290i	$-0.610554\pi$
$347$	9.33878e9	−	1.61752e10i	0.644128	−	1.11566i	0.984502	−	0.175372i	$-0.0561128\pi$
$348$	6.37400e8	−	3.68003e8i	0.0434605	−	0.0250919i
$349$			8.48814e9i			0.572151i	0.958207	+	0.286076i	$0.0923509\pi$
$349$			8.48814e9i			0.572151i	−0.958207	+	0.286076i	$0.907649\pi$
$350$	2.59627e10	+	1.12439e10i	1.73013	+	0.749284i
$351$	1.75234e9			0.115449
$352$	2.72667e8	+	4.72273e8i	0.0177608	+	0.0307625i
$353$	2.37153e9	+	1.36920e9i	0.152732	+	0.0881798i	0.574418	−	0.818562i	$-0.305228\pi$
$353$	2.37153e9	+	1.36920e9i	0.152732	+	0.0881798i	−0.421686	+	0.906742i	$0.638562\pi$
$354$	1.52694e8	−	2.64474e8i	0.00972319	−	0.0168411i
$355$	−3.05841e10	+	1.76578e10i	−1.92567	+	1.11179i
$356$			1.02055e10i			0.635380i
$357$	−1.56461e9	−	1.35567e10i	−0.0963240	−	0.834606i
$358$	−6.68517e9			−0.406987
$359$	1.46342e10	+	2.53472e10i	0.881032	+	1.52599i	0.850195	+	0.526468i	$0.176484\pi$
$359$	1.46342e10	+	2.53472e10i	0.881032	+	1.52599i	0.0308370	+	0.999524i	$0.490183\pi$
$360$	−3.28241e9	−	1.89510e9i	−0.195426	−	0.112829i
$361$	−2.73832e9	+	4.74290e9i	−0.161233	+	0.279264i
$362$	−1.98484e9	+	1.14595e9i	−0.115582	+	0.0667315i
$363$		−	9.61981e9i		−	0.554039i
$364$	3.13827e9	+	4.22822e9i	0.178766	+	0.240853i
$365$	−2.38666e10			−1.34468
$366$	2.67915e9	+	4.64043e9i	0.149305	+	0.258603i
$367$	−1.70244e10	−	9.82903e9i	−0.938441	−	0.541809i	−0.0489698	−	0.998800i	$-0.515594\pi$
$367$	−1.70244e10	−	9.82903e9i	−0.938441	−	0.541809i	−0.889471	+	0.456991i	$0.848927\pi$
$368$	2.20533e9	−	3.81975e9i	0.120249	−	0.208278i
$369$	−6.12528e9	+	3.53643e9i	−0.330385	+	0.190748i
$370$		−	2.75420e10i		−	1.46956i
$371$	2.42023e10	−	1.79634e10i	1.27750	−	0.948187i
$372$	−3.23944e9			−0.169160
$373$	7.90854e9	+	1.36980e10i	0.408565	+	0.707655i	0.994729	−	0.102537i	$-0.0326960\pi$
$373$	7.90854e9	+	1.36980e10i	0.408565	+	0.707655i	−0.586164	+	0.810192i	$0.699363\pi$
$374$	3.50335e9	+	2.02266e9i	0.179060	+	0.103380i
$375$	1.82148e10	−	3.15490e10i	0.921086	−	1.59537i
$376$	−5.68900e9	+	3.28454e9i	−0.284632	+	0.164333i
$377$			2.10665e9i			0.104286i
$378$	2.75992e9	−	3.18530e8i	0.135185	−	0.0156021i
$379$	2.21212e9			0.107214			0.0536069	−	0.998562i	$-0.482928\pi$
$379$	2.21212e9			0.107214			0.0536069	+	0.998562i	$0.482928\pi$
$380$	−8.21596e9	−	1.42305e10i	−0.394025	−	0.682471i
$381$	9.53321e9	+	5.50400e9i	0.452417	+	0.261203i
$382$	9.06011e9	−	1.56926e10i	0.425481	−	0.736955i
$383$	3.02281e10	−	1.74522e10i	1.40481	−	0.811065i	0.409925	−	0.912119i	$-0.365555\pi$
$383$	3.02281e10	−	1.74522e10i	1.40481	−	0.811065i	0.994881	+	0.101054i	$0.0322214\pi$
$384$			1.10958e9i			0.0510310i
$385$	3.35945e9	−	7.75712e9i	0.152906	−	0.353067i
$386$	−5.53527e9			−0.249338
$387$	7.29508e9	+	1.26355e10i	0.325227	+	0.563310i
$388$	1.26721e10	+	7.31622e9i	0.559140	+	0.322819i
$389$	3.35160e9	−	5.80515e9i	0.146371	−	0.253522i	−0.783513	−	0.621376i	$-0.786574\pi$
$389$	3.35160e9	−	5.80515e9i	0.146371	−	0.253522i	0.929884	+	0.367854i	$0.119907\pi$
$390$	9.39517e9	−	5.42431e9i	0.406112	−	0.234469i
$391$		−	3.27187e10i		−	1.39987i
$392$	5.71132e9	+	6.08895e9i	0.241876	+	0.257868i
$393$	−1.22922e10			−0.515300
$394$	−1.12656e10	−	1.95126e10i	−0.467486	−	0.809710i
$395$	1.24670e7	+	7.19785e6i	0.000512124	+	0.000295675i
$396$	−4.11781e8	+	7.13225e8i	−0.0167450	+	0.0290032i
$397$	−6.14520e9	+	3.54794e9i	−0.247386	+	0.142828i	−0.618567	−	0.785732i	$-0.712286\pi$
$397$	−6.14520e9	+	3.54794e9i	−0.247386	+	0.142828i	0.371181	+	0.928561i	$0.378953\pi$
$398$			5.72472e9i			0.228151i
$399$	1.10527e10	+	4.78671e9i	0.436091	+	0.188862i
$400$	−1.70648e10			−0.666593
$401$	−1.64715e10	−	2.85295e10i	−0.637025	−	1.10336i	−0.986082	−	0.166258i	$-0.946831\pi$
$401$	−1.64715e10	−	2.85295e10i	−0.637025	−	1.10336i	0.349057	−	0.937101i	$-0.386502\pi$
$402$	−1.08584e9	−	6.26909e8i	−0.0415778	−	0.0240049i
$403$	4.63609e9	−	8.02994e9i	0.175765	−	0.304433i
$404$	1.96911e10	−	1.13687e10i	0.739172	−	0.426761i
$405$		−	5.72395e9i		−	0.212753i
$406$	3.82934e8	+	3.31796e9i	0.0140935	+	0.122114i
$407$	−5.98452e9			−0.218098
$408$	4.11548e9	+	7.12822e9i	0.148518	+	0.257241i
$409$	3.01927e10	+	1.74318e10i	1.07897	+	0.622944i	0.930618	−	0.365991i	$-0.119270\pi$
$409$	3.01927e10	+	1.74318e10i	1.07897	+	0.622944i	0.148352	+	0.988935i	$0.452603\pi$
$410$	−2.18937e10	+	3.79211e10i	−0.774791	+	1.34198i
$411$	−1.90357e9	+	1.09903e9i	−0.0667117	+	0.0385160i
$412$		−	2.05362e10i		−	0.712739i
$413$	8.25955e8	+	1.11282e9i	0.0283894	+	0.0382493i
$414$	6.66098e9			0.226745
$415$	8.48280e9	+	1.46926e10i	0.285987	+	0.495345i
$416$	−2.75044e9	−	1.58797e9i	−0.0918393	−	0.0530234i
$417$	8.48794e9	−	1.47015e10i	0.280710	−	0.486204i
$418$	−3.09209e9	+	1.78522e9i	−0.101286	+	0.0584773i
$419$			6.77305e9i			0.219750i	0.993945	+	0.109875i	$0.0350450\pi$
$419$			6.77305e9i			0.219750i	−0.993945	+	0.109875i	$0.964955\pi$
$420$	1.38113e10	−	1.02510e10i	0.443851	−	0.329435i
$421$	−3.10072e10			−0.987040			−0.493520	−	0.869735i	$-0.664290\pi$
$421$	−3.10072e10			−0.987040			−0.493520	+	0.869735i	$0.664290\pi$
$422$	4.61471e9	+	7.99291e9i	0.145511	+	0.252032i
$423$	−8.59151e9	−	4.96031e9i	−0.268354	−	0.154934i
$424$	−9.08951e9	+	1.57435e10i	−0.281240	+	0.487122i
$425$	−1.09628e11	+	6.32939e10i	−3.36021	+	1.94002i
$426$			1.56134e10i			0.474087i
$427$	−2.41556e10	+	2.78785e9i	−0.726617	+	0.0838607i
$428$	1.22381e10			0.364704
$429$	−1.17863e9	−	2.04145e9i	−0.0347976	−	0.0602712i
$430$	7.82250e10	+	4.51632e10i	2.28808	+	1.32103i
$431$	6.62616e9	−	1.14769e10i	0.192023	−	0.332593i	−0.753898	−	0.656992i	$-0.771829\pi$
$431$	6.62616e9	−	1.14769e10i	0.192023	−	0.332593i	0.945921	+	0.324398i	$0.105162\pi$
$432$	−1.45119e9	+	8.37844e8i	−0.0416667	+	0.0240563i
$433$		−	5.78082e10i		−	1.64451i	−0.569116	−	0.822257i	$-0.692715\pi$
$433$		−	5.78082e10i		−	1.64451i	0.569116	−	0.822257i	$-0.307285\pi$
$434$	5.84216e9	−	1.34898e10i	0.164670	−	0.380230i
$435$	6.88128e9			0.192182
$436$	1.17199e10	+	2.02995e10i	0.324324	+	0.561745i
$437$	2.50089e10	+	1.44389e10i	0.685755	+	0.395921i
$438$	−5.27585e9	+	9.13803e9i	−0.143349	+	0.248288i
$439$	−3.21334e9	+	1.85522e9i	−0.0865164	+	0.0499503i	−0.542634	−	0.839969i	$-0.682573\pi$
$439$	−3.21334e9	+	1.85522e9i	−0.0865164	+	0.0499503i	0.456118	+	0.889919i	$0.349240\pi$
$440$			5.09860e9i			0.136032i
$441$	−3.65094e9	+	1.20674e10i	−0.0965274	+	0.319051i
$442$	−2.35593e10			−0.617267
$443$	1.29870e9	+	2.24942e9i	0.0337205	+	0.0584057i	0.882393	−	0.470513i	$-0.155931\pi$
$443$	1.29870e9	+	2.24942e9i	0.0337205	+	0.0584057i	−0.848673	+	0.528918i	$0.822598\pi$
$444$	−1.05453e10	−	6.08831e9i	−0.271347	−	0.156662i
$445$	−4.77081e10	+	8.26328e10i	−1.21661	+	2.10723i
$446$	4.46144e10	−	2.57581e10i	1.12755	−	0.650991i
$447$			2.84074e10i			0.711545i
$448$	−4.62056e9	−	2.00107e9i	−0.114705	−	0.0496765i
$449$	−2.26612e10			−0.557569			−0.278784	−	0.960354i	$-0.589931\pi$
$449$	−2.26612e10			−0.557569			−0.278784	+	0.960354i	$0.589931\pi$
$450$	−1.28856e10	−	2.23185e10i	−0.314235	−	0.544271i
$451$	8.23976e9	+	4.75723e9i	0.199163	+	0.114987i
$452$	2.04523e9	−	3.54244e9i	0.0489991	−	0.0848690i
$453$	−2.16668e10	+	1.25093e10i	−0.514519	+	0.297057i
$454$			3.80094e10i			0.894681i
$455$	5.64439e9	+	4.89062e10i	0.131696	+	1.14108i
$456$	−7.26472e9			−0.168020
$457$	−2.53876e9	−	4.39726e9i	−0.0582045	−	0.100813i	0.835455	−	0.549559i	$-0.185204\pi$
$457$	−2.53876e9	−	4.39726e9i	−0.0582045	−	0.100813i	−0.893659	+	0.448746i	$0.851871\pi$
$458$	−2.48818e9	−	1.43655e9i	−0.0565483	−	0.0326482i
$459$	−6.21519e9	+	1.07650e10i	−0.140024	+	0.242529i
$460$	3.57128e10	−	2.06188e10i	0.797613	−	0.460502i
$461$		−	5.39866e10i		−	1.19531i	−0.801752	−	0.597657i	$-0.796098\pi$
$461$		−	5.39866e10i		−	1.19531i	0.801752	−	0.597657i	$-0.203902\pi$
$462$	−2.22741e9	−	3.00102e9i	−0.0488915	−	0.0658720i
$463$	2.10169e10			0.457347			0.228673	−	0.973503i	$-0.426561\pi$
$463$	2.10169e10			0.457347			0.228673	+	0.973503i	$0.426561\pi$
$464$	−1.00725e9	−	1.74461e9i	−0.0217303	−	0.0376379i
$465$	−2.62294e10	−	1.51436e10i	−0.561018	−	0.323904i
$466$	−2.88953e9	+	5.00482e9i	−0.0612751	+	0.106132i
$467$	3.20664e10	−	1.85136e10i	0.674191	−	0.389244i	−0.123472	−	0.992348i	$-0.539403\pi$
$467$	3.20664e10	−	1.85136e10i	0.674191	−	0.389244i	0.797663	+	0.603104i	$0.206070\pi$
$468$		−	4.79629e9i		−	0.0999820i
$469$	4.56885e9	−	3.39109e9i	0.0944312	−	0.0700887i
$470$	−6.14177e10			−1.25864
$471$	−1.46514e10	−	2.53769e10i	−0.297711	−	0.515650i
$472$	−7.23882e8	−	4.17934e8i	−0.0145848	−	0.00842053i
$473$	9.81339e9	−	1.69973e10i	0.196053	−	0.339574i
$474$	5.51181e6	−	3.18225e6i	0.000109190	−	6.30406e-5i
$475$		−	1.11728e11i		−	2.19476i
$476$	−3.71056e10	+	4.28246e9i	−0.722790	+	0.0834190i
$477$	−2.74539e10			−0.530311
$478$	−2.88558e10	−	4.99797e10i	−0.552741	−	0.957376i
$479$	7.60097e9	+	4.38842e9i	0.144387	+	0.0833617i	0.570453	−	0.821330i	$-0.306768\pi$
$479$	7.60097e9	+	4.38842e9i	0.144387	+	0.0833617i	−0.426066	+	0.904692i	$0.640101\pi$
$480$	−5.18702e9	+	8.98418e9i	−0.0977131	+	0.169244i
$481$	3.01835e10	−	1.74264e10i	0.563883	−	0.325558i
$482$		−	3.45389e10i		−	0.639911i
$483$	−1.20127e10	+	2.77379e10i	−0.220726	+	0.509665i
$484$	−2.63301e10			−0.479812
$485$	6.84030e10	+	1.18477e11i	1.23625	+	2.14126i
$486$	−2.19158e9	−	1.26531e9i	−0.0392837	−	0.0226805i
$487$	−3.06327e10	+	5.30574e10i	−0.544589	+	0.943257i	0.454043	+	0.890980i	$0.349981\pi$
$487$	−3.06327e10	+	5.30574e10i	−0.544589	+	0.943257i	−0.998633	+	0.0522769i	$0.983352\pi$
$488$	1.27012e10	−	7.33302e9i	0.223957	−	0.129302i
$489$			4.01280e10i			0.701797i
$490$	1.77797e10	+	7.60007e10i	0.308418	+	1.31836i
$491$	1.19728e10			0.206002			0.103001	−	0.994681i	$-0.467156\pi$
$491$	1.19728e10			0.206002			0.103001	+	0.994681i	$0.467156\pi$
$492$	9.67945e9	+	1.67653e10i	0.165193	+	0.286122i
$493$	−1.29416e10	−	7.47184e9i	−0.219079	−	0.126485i
$494$	1.03968e10	−	1.80078e10i	0.174580	−	0.302381i
$495$	−6.66830e9	+	3.84995e9i	−0.111069	+	0.0641259i
$496$			8.86656e9i			0.146497i
$497$	−6.50177e10	−	2.81579e10i	−1.06563	−	0.461503i
$498$	7.50068e9			0.121950
$499$	−4.24587e9	−	7.35406e9i	−0.0684801	−	0.118611i	0.829752	−	0.558132i	$-0.188482\pi$
$499$	−4.24587e9	−	7.35406e9i	−0.0684801	−	0.118611i	−0.898232	+	0.439521i	$0.855148\pi$
$500$	−8.63518e10	−	4.98552e10i	−1.38163	−	0.797683i
$501$	2.14356e10	−	3.71275e10i	0.340239	−	0.589312i
$502$	3.80599e10	−	2.19739e10i	0.599311	−	0.346013i
$503$			1.28168e10i			0.200220i	0.994976	+	0.100110i	$0.0319195\pi$
$503$			1.28168e10i			0.200220i	−0.994976	+	0.100110i	$0.968081\pi$
$504$	−8.71838e8	−	7.55410e9i	−0.0135118	−	0.117074i
$505$	2.12583e11			3.26861
$506$	−4.48019e9	−	7.75992e9i	−0.0683431	−	0.118374i
$507$	−2.11480e10	−	1.22098e10i	−0.320065	−	0.184790i
$508$	1.50648e10	−	2.60930e10i	0.226209	−	0.391805i
$509$	−7.98797e9	+	4.61185e9i	−0.119005	+	0.0687075i	−0.558321	−	0.829625i	$-0.688554\pi$
$509$	−7.98797e9	+	4.61185e9i	−0.119005	+	0.0687075i	0.439316	+	0.898333i	$0.355221\pi$
$510$			7.69553e10i			1.13752i
$511$	−2.85382e10	−	3.84498e10i	−0.418546	−	0.563911i
$512$	3.03700e9			0.0441942
$513$	−5.48558e9	−	9.50131e9i	−0.0792052	−	0.137187i
$514$	3.44391e10	+	1.98834e10i	0.493401	+	0.284865i
$515$	9.60015e10	−	1.66279e11i	1.36474	−	2.36379i
$516$	3.45841e10	−	1.99671e10i	0.487840	−	0.281655i
$517$			1.33453e10i			0.186795i
$518$	4.43709e10	−	3.29330e10i	0.616282	−	0.457417i
$519$	−7.44350e10			−1.02591
$520$	−1.48467e10	−	2.57152e10i	−0.203056	−	0.351704i
$521$	−3.66823e10	−	2.11785e10i	−0.497858	−	0.287438i	0.229971	−	0.973198i	$-0.426137\pi$
$521$	−3.66823e10	−	2.11785e10i	−0.497858	−	0.287438i	−0.727828	+	0.685759i	$0.759470\pi$
$522$	1.52114e9	−	2.63470e9i	0.0204875	−	0.0354854i
$523$	5.57062e10	−	3.21620e10i	0.744555	−	0.429869i	−0.0791679	−	0.996861i	$-0.525226\pi$
$523$	5.57062e10	−	3.21620e10i	0.744555	−	0.429869i	0.823723	+	0.566992i	$0.191893\pi$
$524$			3.36446e10i			0.446263i
$525$	1.16178e11	−	1.34084e10i	1.52928	−	0.176498i
$526$	−1.19080e10			−0.155559
$527$	3.28864e10	+	5.69609e10i	0.426357	+	0.738473i
$528$	1.95215e9	+	1.12707e9i	0.0251175	+	0.0145016i
$529$	2.91960e9	−	5.05690e9i	0.0372822	−	0.0645746i
$530$	−1.47194e11	+	8.49824e10i	−1.86546	+	1.07702i
$531$		−	1.26232e9i		−	0.0158779i
$532$	1.31015e10	−	3.02520e10i	0.163560	−	0.377666i
$533$	−5.54106e10			−0.686569
$534$	2.10923e10	+	3.65329e10i	0.259393	+	0.449282i
$535$	9.90911e10	+	5.72103e10i	1.20954	+	0.698327i
$536$	−1.71589e9	+	2.97201e9i	−0.0207889	+	0.0360074i
$537$	−2.39311e10	+	1.38166e10i	−0.287783	+	0.166152i
$538$		−	1.98557e10i		−	0.237005i
$539$	1.65140e10	−	3.86330e9i	0.195657	−	0.0457723i
$540$	−1.56668e10			−0.184250
$541$	−4.29991e10	−	7.44767e10i	−0.501962	−	0.869423i	−0.999997	−	0.00226685i	$-0.999278\pi$
$541$	−4.29991e10	−	7.44767e10i	−0.501962	−	0.869423i	0.498036	−	0.867157i	$-0.334055\pi$
$542$	−6.69009e10	−	3.86253e10i	−0.775238	−	0.447584i
$543$	−4.73680e9	+	8.20437e9i	−0.0544860	+	0.0943726i
$544$	1.95104e10	−	1.12643e10i	0.222777	−	0.128621i
$545$			2.19151e11i			2.48403i
$546$	1.99729e10	+	8.64985e9i	0.224735	+	0.0973281i
$547$	1.37838e10			0.153965			0.0769823	−	0.997032i	$-0.475472\pi$
$547$	1.37838e10			0.153965			0.0769823	+	0.997032i	$0.475472\pi$
$548$	3.00812e9	+	5.21021e9i	0.0333559	+	0.0577741i
$549$	1.91813e10	+	1.10743e10i	0.211149	+	0.121907i
$550$	−1.73338e10	+	3.00230e10i	−0.189427	+	0.328098i
$551$	1.14224e10	−	6.59472e9i	0.123923	−	0.0715468i
$552$		−	1.82316e10i		−	0.196367i
$553$	3.31136e6	+	2.86915e7i	3.54084e−5	+	0.000306798i
$554$	5.65033e10			0.599839
$555$	−5.69226e10	−	9.85929e10i	−0.599947	−	1.03914i
$556$	−4.02391e10	−	2.32321e10i	−0.421065	−	0.243102i
$557$	4.61407e10	−	7.99181e10i	0.479362	−	0.830280i	−0.520358	−	0.853948i	$-0.674201\pi$
$557$	4.61407e10	−	7.99181e10i	0.479362	−	0.830280i	0.999720	+	0.0236687i	$0.00753470\pi$
$558$	−1.15963e10	+	6.69513e9i	−0.119614	+	0.0690593i
$559$			1.14303e11i			1.17061i
$560$	−2.80577e10	−	3.78025e10i	−0.285299	−	0.384386i
$561$	1.67214e10			0.168819
$562$	−3.64406e10	−	6.31169e10i	−0.365292	−	0.632704i
$563$	−5.61712e10	−	3.24304e10i	−0.559087	−	0.322789i	0.193692	−	0.981062i	$-0.437954\pi$
$563$	−5.61712e10	−	3.24304e10i	−0.559087	−	0.322789i	−0.752779	+	0.658273i	$0.771287\pi$
$564$	−1.35767e10	+	2.35155e10i	−0.134177	+	0.232401i
$565$	3.31201e10	−	1.91219e10i	0.325011	−	0.187645i
$566$		−	4.52178e10i		−	0.440599i
$567$	9.22145e9	−	6.84434e9i	0.0892210	−	0.0662216i
$568$	4.27349e10			0.410572
$569$	7.06161e10	+	1.22311e11i	0.673682	+	1.16685i	0.976852	+	0.213915i	$0.0686214\pi$
$569$	7.06161e10	+	1.22311e11i	0.673682	+	1.16685i	−0.303171	+	0.952936i	$0.598045\pi$
$570$	−5.88218e10	−	3.39608e10i	−0.557235	−	0.321720i
$571$	−2.43023e10	+	4.20928e10i	−0.228614	+	0.395971i	−0.957398	−	0.288773i	$-0.906753\pi$
$571$	−2.43023e10	+	4.20928e10i	−0.228614	+	0.395971i	0.728784	+	0.684744i	$0.240086\pi$
$572$	−5.58759e9	+	3.22600e9i	−0.0521964	+	0.0301356i
$573$		−	7.49002e10i		−	0.694807i
$574$	−8.72711e10	+	1.00722e10i	−0.803938	+	0.0927846i
$575$	2.80392e11			2.56504
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	−6.75108e10	−	3.89774e10i	−0.609074	−	0.351649i	0.163529	−	0.986539i	$-0.447712\pi$
$577$	−6.75108e10	−	3.89774e10i	−0.609074	−	0.351649i	−0.772603	+	0.634889i	$0.781046\pi$
$578$	4.40989e10	−	7.63815e10i	0.395108	−	0.684348i
$579$	−1.98147e10	+	1.14401e10i	−0.176309	+	0.101792i
$580$		−	1.88345e10i		−	0.166434i
$581$	−1.35271e10	+	3.12346e10i	−0.118713	+	0.274114i
$582$	6.04834e10			0.527162
$583$	1.84656e10	+	3.19833e10i	0.159841	+	0.276853i
$584$	2.50114e10	+	1.44403e10i	0.215024	+	0.124144i
$585$	2.24214e10	−	3.88351e10i	0.191443	−	0.331589i
$586$	−3.87165e10	+	2.23530e10i	−0.328326	+	0.189559i
$587$		−	3.18178e10i		−	0.267990i	−0.990982	−	0.133995i	$-0.957219\pi$
$587$		−	3.18178e10i		−	0.267990i	0.990982	−	0.133995i	$-0.0427805\pi$
$588$	3.30294e10	+	9.99288e9i	0.276306	+	0.0835952i
$589$	−5.80517e10			−0.482341
$590$	−3.90747e9	−	6.76794e9i	−0.0322469	−	0.0558532i
$591$	−8.06554e10	−	4.65664e10i	−0.661125	−	0.381701i
$592$	−1.66641e10	+	2.88631e10i	−0.135674	+	0.234993i
$593$	−7.13590e9	+	4.11992e9i	−0.0577072	+	0.0333173i	−0.528576	−	0.848886i	$-0.677274\pi$
$593$	−7.13590e9	+	4.11992e9i	−0.0577072	+	0.0333173i	0.470869	+	0.882203i	$0.343941\pi$
$594$			3.40420e9i			0.0273445i
$595$	−3.20460e11	−	1.38785e11i	−2.55686	−	1.10732i
$596$	7.77531e10			0.616216
$597$	1.18316e10	+	2.04929e10i	0.0931422	+	0.161327i
$598$	4.51925e10	+	2.60919e10i	0.353396	+	0.204033i
$599$	−1.13008e11	+	1.95735e11i	−0.877809	+	1.52041i	−0.0240696	+	0.999710i	$0.507662\pi$
$599$	−1.13008e11	+	1.95735e11i	−0.877809	+	1.52041i	−0.853740	+	0.520700i	$0.825671\pi$
$600$	−6.10873e10	+	3.52688e10i	−0.471353	+	0.272136i
$601$			1.08158e11i			0.829008i	0.910047	+	0.414504i	$0.136045\pi$
$601$			1.08158e11i			0.829008i	−0.910047	+	0.414504i	$0.863955\pi$
$602$	2.07773e10	+	1.80026e11i	0.158199	+	1.37072i
$603$	−5.18268e9			−0.0391999
$604$	3.42388e10	+	5.93034e10i	0.257259	+	0.445586i
$605$	−2.13192e11	−	1.23087e11i	−1.59129	−	0.918732i
$606$	4.69926e10	−	8.13936e10i	0.348449	−	0.603531i
$607$	−9.17061e9	+	5.29465e9i	−0.0675528	+	0.0390016i	−0.533396	−	0.845866i	$-0.679084\pi$
$607$	−9.17061e9	+	5.29465e9i	−0.0675528	+	0.0390016i	0.465843	+	0.884867i	$0.345751\pi$
$608$			1.98840e10i			0.145509i
$609$	8.22821e9	+	1.10859e10i	0.0598186	+	0.0805942i
$610$	1.37120e11			0.990335
$611$	−3.88603e10	−	6.73081e10i	−0.278831	−	0.482950i
$612$	2.94646e10	+	1.70114e10i	0.210036	+	0.121265i
$613$	−1.06257e11	+	1.84042e11i	−0.752514	+	1.30339i	0.194087	+	0.980984i	$0.437825\pi$
$613$	−1.06257e11	+	1.84042e11i	−0.752514	+	1.30339i	−0.946601	+	0.322408i	$0.895508\pi$
$614$	3.09328e10	−	1.78591e10i	0.217644	−	0.125657i
$615$			1.80996e11i			1.26523i
$616$	−8.21399e9	+	6.09658e9i	−0.0570468	+	0.0423412i
$617$	−1.40829e11			−0.971741			−0.485870	−	0.874031i	$-0.661497\pi$
$617$	−1.40829e11			−0.971741			−0.485870	+	0.874031i	$0.661497\pi$
$618$	−4.24433e10	−	7.35139e10i	−0.290974	−	0.503983i
$619$	1.91894e11	+	1.10790e11i	1.30707	+	0.754635i	0.981606	−	0.190920i	$-0.0611472\pi$
$619$	1.91894e11	+	1.10790e11i	1.30707	+	0.754635i	0.325461	+	0.945555i	$0.394481\pi$
$620$	−4.14490e10	+	7.17917e10i	−0.280509	+	0.485856i
$621$	2.38445e10	−	1.37666e10i	0.160333	−	0.0925681i
$622$			7.92040e10i			0.529158i
$623$	−1.90170e11	+	2.19480e10i	−1.26238	+	0.145695i
$624$	−1.31278e10			−0.0865869
$625$	−2.62693e11	−	4.54998e11i	−1.72159	−	2.98187i
$626$	−6.49161e10	−	3.74793e10i	−0.422722	−	0.244059i
$627$	−7.37924e9	+	1.27812e10i	−0.0477465	+	0.0826993i
$628$	−6.94583e10	+	4.01018e10i	−0.446566	+	0.257825i
$629$			2.47231e11i			1.57943i
$630$	2.82543e10	−	6.52404e10i	0.179359	−	0.414147i
$631$	5.39299e9			0.0340182			0.0170091	−	0.999855i	$-0.494586\pi$
$631$	5.39299e9			0.0340182			0.0170091	+	0.999855i	$0.494586\pi$
$632$	−8.71002e6	−	1.50862e7i	−5.45948e−5	−	9.45609e-5i
$633$	3.30388e10	+	1.90750e10i	0.205783	+	0.118809i
$634$	−4.17469e10	+	7.23078e10i	−0.258385	+	0.447536i
$635$	2.43957e11	−	1.40849e11i	1.50044	−	0.866278i
$636$			7.51432e10i			0.459263i
$637$	−7.20400e10	+	6.75722e10i	−0.437538	+	0.410403i
$638$	−4.09250e9			−0.0247005
$639$	3.22690e10	+	5.58916e10i	0.193545	+	0.335230i
$640$	2.45903e10	+	1.41972e10i	0.146570	+	0.0846220i
$641$	5.28937e10	−	9.16145e10i	0.313308	−	0.542666i	−0.665768	−	0.746159i	$-0.731896\pi$
$641$	5.28937e10	−	9.16145e10i	0.313308	−	0.542666i	0.979076	+	0.203493i	$0.0652294\pi$
$642$	4.38092e10	−	2.52933e10i	0.257885	−	0.148890i
$643$		−	3.15633e11i		−	1.84646i	−0.384253	−	0.923228i	$-0.625541\pi$
$643$		−	3.15633e11i		−	1.84646i	0.384253	−	0.923228i	$-0.374459\pi$
$644$	7.59205e10	+	3.28797e10i	0.441383	+	0.191154i
$645$	3.73366e11			2.15722
$646$	7.37506e10	+	1.27740e11i	0.423483	+	0.733494i
$647$	2.81309e11	+	1.62414e11i	1.60534	+	0.926841i	0.990395	+	0.138269i	$0.0441538\pi$
$647$	2.81309e11	+	1.62414e11i	1.60534	+	0.926841i	0.614942	+	0.788573i	$0.289180\pi$
$648$	−3.46324e9	+	5.99851e9i	−0.0196419	+	0.0340207i
$649$	−1.47059e9	+	8.49043e8i	−0.00828918	+	0.00478576i
$650$		−	2.01898e11i		−	1.13104i
$651$	−6.96677e9	−	6.03641e10i	−0.0387889	−	0.336089i
$652$	1.09833e11			0.607774
$653$	−1.12986e11	−	1.95698e11i	−0.621403	−	1.07630i	−0.989225	−	0.146406i	$-0.953229\pi$
$653$	−1.12986e11	−	1.95698e11i	−0.621403	−	1.07630i	0.367821	−	0.929897i	$-0.380104\pi$
$654$	8.39082e10	+	4.84444e10i	0.458663	+	0.264809i
$655$	−1.57280e11	+	2.72417e11i	−0.854494	+	1.48003i
$656$	4.58878e10	−	2.64933e10i	0.247789	−	0.143061i
$657$			4.36156e10i			0.234088i
$658$	−7.34394e10	−	9.89456e10i	−0.391765	−	0.527829i
$659$	−1.28012e11			−0.678749			−0.339374	−	0.940651i	$-0.610215\pi$
$659$	−1.28012e11			−0.678749			−0.339374	+	0.940651i	$0.610215\pi$
$660$	1.05376e10	+	1.82516e10i	0.0555347	+	0.0961889i
$661$	2.01081e11	+	1.16094e11i	1.05333	+	0.608140i	0.923580	−	0.383406i	$-0.125249\pi$
$661$	2.01081e11	+	1.16094e11i	1.05333	+	0.608140i	0.129750	+	0.991547i	$0.458582\pi$
$662$	8.10624e10	−	1.40404e11i	0.422073	−	0.731052i
$663$	−8.43359e10	+	4.86913e10i	−0.436474	+	0.251998i
$664$		−	2.05299e10i		−	0.105612i
$665$	2.47503e11	−	1.83701e11i	1.26559	−	0.939346i
$666$	−5.03322e10			−0.255828
$667$	1.65501e10	+	2.86657e10i	0.0836176	+	0.144830i
$668$	−1.01621e11	−	5.86706e10i	−0.510359	−	0.294656i
$669$	1.06472e11	−	1.84414e11i	0.531532	−	0.920640i
$670$	−2.77869e10	+	1.60427e10i	−0.137892	+	0.0796122i
$671$		−	2.97945e10i		−	0.146976i
$672$	−2.06761e10	+	2.38628e9i	−0.101389	+	0.0117016i
$673$	−9.83689e10			−0.479510			−0.239755	−	0.970833i	$-0.577067\pi$
$673$	−9.83689e10			−0.479510			−0.239755	+	0.970833i	$0.577067\pi$
$674$	1.37296e10	+	2.37803e10i	0.0665300	+	0.115233i
$675$	−9.22539e10	−	5.32628e10i	−0.444396	−	0.256572i
$676$	−3.34191e10	+	5.78836e10i	−0.160032	+	0.277184i
$677$	1.14902e11	−	6.63388e10i	0.546982	−	0.315800i	−0.200922	−	0.979607i	$-0.564394\pi$
$677$	1.14902e11	−	6.63388e10i	0.546982	−	0.315800i	0.747904	+	0.663807i	$0.231060\pi$
$678$		−	1.69080e10i		−	0.0800153i
$679$	−1.09079e11	+	2.51867e11i	−0.513169	+	1.18493i
$680$	2.10632e11			0.985119
$681$	7.85563e10	+	1.36063e11i	0.365252	+	0.632635i
$682$	1.55994e10	+	9.00633e9i	0.0721059	+	0.0416304i
$683$	−1.20557e10	+	2.08811e10i	−0.0554000	+	0.0959556i	−0.892395	−	0.451254i	$-0.850977\pi$
$683$	−1.20557e10	+	2.08811e10i	−0.0554000	+	0.0959556i	0.836995	+	0.547210i	$0.184310\pi$
$684$	−2.60057e10	+	1.50144e10i	−0.118808	+	0.0685937i
$685$			5.62488e10i			0.255476i
$686$	−1.01179e11	+	1.19520e11i	−0.456873	+	0.539691i
$687$	−1.18760e10			−0.0533143
$688$	−5.46514e10	−	9.46590e10i	−0.243920	−	0.422482i
$689$	−1.86265e11	−	1.07540e11i	−0.826524	−	0.477194i
$690$	8.52280e10	−	1.47619e11i	0.375998	−	0.651248i
$691$	−1.22976e11	+	7.10003e10i	−0.539397	+	0.311421i	−0.744835	−	0.667249i	$-0.767472\pi$
$691$	−1.22976e11	+	7.10003e10i	−0.539397	+	0.311421i	0.205438	+	0.978670i	$0.434138\pi$
$692$			2.03734e11i			0.888461i
$693$	−1.41759e10	−	6.13930e9i	−0.0614636	−	0.0266187i
$694$	−2.11312e11			−0.910934
$695$	−2.17208e11	−	3.76216e11i	−0.930973	−	1.61249i
$696$	−7.21135e9	−	4.16348e9i	−0.0307312	−	0.0177427i
$697$	1.96529e11	−	3.40399e11i	0.832715	−	1.44230i
$698$	8.31664e10	−	4.80162e10i	0.350370	−	0.202286i
$699$			2.38879e10i			0.100062i
$700$	−3.66997e10	−	3.17987e11i	−0.152852	−	1.32440i
$701$	1.05031e11			0.434958			0.217479	−	0.976065i	$-0.430217\pi$
$701$	1.05031e11			0.434958			0.217479	+	0.976065i	$0.430217\pi$
$702$	−9.91276e9	−	1.71694e10i	−0.0408175	−	0.0706979i
$703$	−1.88974e11	−	1.09104e11i	−0.773715	−	0.446705i
$704$	3.08487e9	−	5.34316e9i	0.0125588	−	0.0217524i
$705$	−2.19859e11	+	1.26935e11i	−0.889994	+	0.513838i
$706$		−	3.09815e10i		−	0.124705i
$707$	2.54193e11	+	3.42477e11i	1.01739	+	1.37074i
$708$	−3.45507e9			−0.0137507
$709$	3.76112e10	+	6.51446e10i	0.148844	+	0.257806i	0.930801	−	0.365527i	$-0.119111\pi$
$709$	3.76112e10	+	6.51446e10i	0.148844	+	0.257806i	−0.781956	+	0.623333i	$0.785778\pi$
$710$	3.46020e11	+	1.99775e11i	1.36166	+	0.786153i
$711$	1.31539e7	−	2.27831e7i	5.14724e−5	−	8.91529e-5i
$712$	9.99929e10	−	5.77309e10i	0.389089	−	0.224641i
$713$		−	1.45687e11i		−	0.563718i
$714$	−1.23977e11	+	9.20184e10i	−0.477034	+	0.354064i
$715$	−6.03229e10			−0.230812
$716$	3.78170e10	+	6.55010e10i	0.143891	+	0.249227i
$717$	−2.06592e11	−	1.19276e11i	−0.781694	−	0.451311i
$718$	1.65567e11	−	2.86771e11i	0.622984	−	1.07904i
$719$	3.69314e11	−	2.13223e11i	1.38191	−	0.797847i	0.389525	−	0.921016i	$-0.372639\pi$
$719$	3.69314e11	−	2.13223e11i	1.38191	−	0.797847i	0.992386	+	0.123169i	$0.0393058\pi$
$720$			4.28812e10i			0.159565i
$721$	3.82673e11	−	4.41653e10i	1.41608	−	0.163433i
$722$	6.19610e10			0.228018
$723$	−7.13834e10	−	1.23640e11i	−0.261243	−	0.452486i
$724$	2.24559e10	+	1.29649e10i	0.0817291	+	0.0471863i
$725$	6.40321e10	−	1.10907e11i	0.231764	−	0.401427i
$726$	−9.42545e10	+	5.44179e10i	−0.339278	+	0.195882i
$727$			1.53706e11i			0.550240i	0.961410	+	0.275120i	$0.0887176\pi$
$727$			1.53706e11i			0.550240i	−0.961410	+	0.275120i	$0.911282\pi$
$728$	2.36752e10	−	5.46671e10i	0.0842886	−	0.194626i
$729$	−1.04604e10			−0.0370370
$730$	1.35010e11	+	2.33844e11i	0.475417	+	0.823446i
$731$	−7.02188e11	−	4.05408e11i	−2.45914	−	1.41979i
$732$	3.03112e10	−	5.25005e10i	0.105574	−	0.182860i
$733$	3.48191e11	−	2.01028e11i	1.20615	−	0.696372i	0.244235	−	0.969716i	$-0.421463\pi$
$733$	3.48191e11	−	2.01028e11i	1.20615	−	0.696372i	0.961916	+	0.273344i	$0.0881297\pi$
$734$			2.22406e11i			0.766234i
$735$	2.20721e11	+	2.35315e11i	0.756301	+	0.806308i
$736$	−4.99010e10			−0.170058
$737$	3.48588e9	+	6.03773e9i	0.0118152	+	0.0204646i
$738$	6.92996e10	+	4.00102e10i	0.233618	+	0.134879i
$739$	−3.43921e10	+	5.95688e10i	−0.115314	+	0.199729i	−0.917905	−	0.396800i	$-0.870121\pi$
$739$	−3.43921e10	+	5.95688e10i	−0.115314	+	0.199729i	0.802591	+	0.596529i	$0.203454\pi$
$740$	−2.69855e11	+	1.55801e11i	−0.899920	+	0.519569i
$741$		−	8.59509e10i		−	0.285087i
$742$	−3.12914e11	−	1.35517e11i	−1.03231	−	0.447072i
$743$	−3.37111e11			−1.10616			−0.553079	−	0.833129i	$-0.686547\pi$
$743$	−3.37111e11			−1.10616			−0.553079	+	0.833129i	$0.686547\pi$
$744$	1.83250e10	+	3.17399e10i	0.0598071	+	0.103589i
$745$	6.29560e11	+	3.63476e11i	2.04367	+	1.17992i
$746$	8.94749e10	−	1.54975e11i	0.288899	−	0.500388i
$747$	2.68504e10	−	1.55021e10i	0.0862319	−	0.0497860i
$748$		−	4.57676e10i		−	0.146202i
$749$	2.63195e10	+	2.28047e11i	0.0836277	+	0.724598i
$750$	−4.12154e11			−1.30261
$751$	1.27390e11	+	2.20646e11i	0.400476	+	0.693645i	0.993783	−	0.111331i	$-0.0355114\pi$
$751$	1.27390e11	+	2.20646e11i	0.400476	+	0.693645i	−0.593307	+	0.804976i	$0.702178\pi$
$752$	6.43636e10	+	3.71604e10i	0.201265	+	0.116201i
$753$	9.08293e10	−	1.57321e11i	0.282518	−	0.489336i
$754$	2.06409e10	−	1.19170e10i	0.0638621	−	0.0368708i
$755$			6.40232e11i			1.97038i
$756$	−1.87334e10	−	2.52397e10i	−0.0573496	−	0.0772676i
$757$	1.51138e11			0.460246			0.230123	−	0.973162i	$-0.426087\pi$
$757$	1.51138e11			0.460246			0.230123	+	0.973162i	$0.426087\pi$
$758$	−1.25136e10	−	2.16742e10i	−0.0379058	−	0.0656548i
$759$	−3.20758e10	−	1.85189e10i	−0.0966518	−	0.0558019i
$760$	−9.29529e10	+	1.60999e11i	−0.278618	+	0.482580i
$761$	−2.31170e11	+	1.33466e11i	−0.689276	+	0.397954i	−0.803341	−	0.595519i	$-0.796946\pi$
$761$	−2.31170e11	+	1.33466e11i	−0.689276	+	0.397954i	0.114065	+	0.993473i	$0.463613\pi$
$762$		−	1.24541e11i		−	0.369397i
$763$	−3.53058e11	+	2.62047e11i	−1.04171	+	0.773180i
$764$	−2.05007e11			−0.601721
$765$	1.59048e11	+	2.75479e11i	0.464390	+	0.804346i
$766$	−3.41992e11	−	1.97449e11i	−0.993348	−	0.573510i
$767$	4.94469e9	−	8.56445e9i	0.0142875	−	0.0247467i
$768$	1.08716e10	−	6.27674e9i	0.0312500	−	0.0180422i
$769$		−	4.78074e11i		−	1.36707i	−0.729919	−	0.683533i	$-0.760442\pi$
$769$		−	4.78074e11i		−	1.36707i	0.729919	−	0.683533i	$-0.239558\pi$
$770$	−9.50079e10	+	1.09651e10i	−0.270269	+	0.0311925i
$771$	1.64377e11			0.465183
$772$	3.13122e10	+	5.42343e10i	0.0881545	+	0.152688i
$773$	−1.83294e11	−	1.05825e11i	−0.513370	−	0.296394i	0.220848	−	0.975308i	$-0.429118\pi$
$773$	−1.83294e11	−	1.05825e11i	−0.513370	−	0.296394i	−0.734218	+	0.678914i	$0.762451\pi$
$774$	8.25345e10	−	1.42954e11i	0.229970	−	0.398320i
$775$	−4.88143e11	+	2.81829e11i	−1.35313	+	0.781231i
$776$		−	1.65547e11i		−	0.456536i
$777$	9.07715e10	−	2.09595e11i	0.249038	−	0.575039i
$778$	−7.58382e10			−0.207000
$779$	1.73459e11	+	3.00439e11i	0.471028	+	0.815844i
$780$	−1.06294e11	−	6.13690e10i	−0.287165	−	0.165795i
$781$	4.34085e10	−	7.51857e10i	0.116673	−	0.202084i
$782$	−3.20576e11	+	1.85085e11i	−0.857243	+	0.494930i
$783$		−	1.25753e10i		−	0.0334559i
$784$	2.73512e10	−	9.04036e10i	0.0723956	−	0.239288i
$785$	−7.49863e11			−1.97471
$786$	6.95353e10	+	1.20439e11i	0.182186	+	0.315555i
$787$	2.76336e11	+	1.59542e11i	0.720341	+	0.415889i	0.814878	−	0.579632i	$-0.196804\pi$
$787$	2.76336e11	+	1.59542e11i	0.720341	+	0.415889i	−0.0945374	+	0.995521i	$0.530137\pi$
$788$	−1.27455e11	+	2.20759e11i	−0.330563	+	0.572551i
$789$	−4.26273e10	+	2.46109e10i	−0.109997	+	0.0635067i
$790$		−	1.62869e8i		−	0.000418147i
$791$	7.04088e10	+	3.04926e10i	0.179854	+	0.0778913i
$792$	9.31754e9			0.0236810
$793$	8.67590e10	+	1.50271e11i	0.219392	+	0.379999i
$794$	6.95250e10	+	4.01403e10i	0.174928	+	0.100995i
$795$	−3.51276e11	+	6.08427e11i	−0.879386	+	1.52314i
$796$	5.60906e10	−	3.23839e10i	0.139713	−	0.0806635i
$797$		−	3.68732e11i		−	0.913856i	−0.889504	−	0.456928i	$-0.848950\pi$
$797$		−	3.68732e11i		−	0.913856i	0.889504	−	0.456928i	$-0.151050\pi$
$798$	−1.56236e10	−	1.35372e11i	−0.0385274	−	0.333823i
$799$	5.51317e11			1.35274
$800$	9.65330e10	+	1.67200e11i	0.235676	+	0.408203i
$801$	1.51009e11	+	8.71851e10i	0.366837	+	0.211793i
$802$	−1.86354e11	+	3.22775e11i	−0.450445	+	0.780193i
$803$	5.08113e10	−	2.93359e10i	0.122208	−	0.0705566i
$804$			1.41853e10i			0.0339481i
$805$	4.61017e11	+	6.21133e11i	1.09783	+	1.47911i
$806$	−1.04903e11			−0.248569
$807$	−4.10370e10	−	7.10781e10i	−0.0967567	−	0.167588i
$808$	−2.22780e11	−	1.28622e11i	−0.522673	−	0.301766i
$809$	−3.63130e11	+	6.28960e11i	−0.847751	+	1.46835i	0.0354595	+	0.999371i	$0.488711\pi$
$809$	−3.63130e11	+	6.28960e11i	−0.847751	+	1.46835i	−0.883211	+	0.468977i	$0.844623\pi$
$810$	−5.60830e10	+	3.23796e10i	−0.130284	+	0.0752196i
$811$		−	4.74637e11i		−	1.09718i	−0.836091	−	0.548591i	$-0.815165\pi$
$811$		−	4.74637e11i		−	1.09718i	0.836091	−	0.548591i	$-0.184835\pi$
$812$	3.03430e10	−	2.25212e10i	0.0697966	−	0.0518044i
$813$	−3.19316e11			−0.730901
$814$	3.38536e10	+	5.86361e10i	0.0771093	+	0.133557i
$815$	8.89307e11	+	5.13442e11i	2.01568	+	1.16375i
$816$	4.65613e10	−	8.06466e10i	0.105018	−	0.181897i
$817$	6.19758e11	−	3.57817e11i	1.39102	−	0.803106i
$818$		−	3.94436e11i		−	0.880975i
$819$	8.93746e10	−	1.03150e10i	0.198645	−	0.0229262i
$820$	4.95399e11			1.09572
$821$	−1.48524e10	−	2.57251e10i	−0.0326907	−	0.0566220i	0.849217	−	0.528044i	$-0.177074\pi$
$821$	−1.48524e10	−	2.57251e10i	−0.0326907	−	0.0566220i	−0.881908	+	0.471422i	$0.843741\pi$
$822$	2.15365e10	+	1.24341e10i	0.0471723	+	0.0272350i
$823$	4.42125e11	−	7.65782e11i	0.963708	−	1.66919i	0.250660	−	0.968075i	$-0.419352\pi$
$823$	4.42125e11	−	7.65782e11i	0.963708	−	1.66919i	0.713047	−	0.701116i	$-0.247314\pi$
$824$	−2.01213e11	+	1.16170e11i	−0.436462	+	0.251991i
$825$			1.43299e11i			0.309334i
$826$	6.23103e9	−	1.43877e10i	0.0133857	−	0.0309081i
$827$	4.55180e10			0.0973109			0.0486554	−	0.998816i	$-0.484506\pi$
$827$	4.55180e10			0.0973109			0.0486554	+	0.998816i	$0.484506\pi$
$828$	−3.76802e10	−	6.52640e10i	−0.0801663	−	0.138852i
$829$	−3.75631e11	−	2.16871e11i	−0.795323	−	0.459180i	0.0465102	−	0.998918i	$-0.485190\pi$
$829$	−3.75631e11	−	2.16871e11i	−0.795323	−	0.459180i	−0.841833	+	0.539738i	$0.818523\pi$
$830$	9.59720e10	−	1.66228e11i	0.202224	−	0.350262i
$831$	2.02266e11	−	1.16779e11i	0.424150	−	0.244883i
$832$			3.59316e10i			0.0749865i
$833$	−1.59600e11	−	6.82221e11i	−0.331476	−	1.41692i
$834$	−1.92060e11			−0.396984
$835$	−5.48541e11	−	9.50101e11i	−1.12840	−	1.95445i
$836$	3.49831e10	+	2.01975e10i	0.0716197	+	0.0413497i
$837$	−2.76744e10	+	4.79335e10i	−0.0563867	+	0.0976646i
$838$	6.63621e10	−	3.83142e10i	0.134569	−	0.0776933i
$839$			3.20676e10i			0.0647171i	0.999476	+	0.0323585i	$0.0103018\pi$
$839$			3.20676e10i			0.0647171i	−0.999476	+	0.0323585i	$0.989698\pi$
$840$	−1.78567e11	−	7.73340e10i	−0.358662	−	0.155329i
$841$	−4.85128e11			−0.969779
$842$	1.75403e11	+	3.03808e11i	0.348971	+	0.604436i
$843$	−2.60895e11	−	1.50628e11i	−0.516601	−	0.298260i
$844$	5.22095e10	−	9.04295e10i	0.102892	−	0.178213i
$845$	−5.41183e11	+	3.12452e11i	−1.06149	+	0.612853i
$846$			1.12239e11i			0.219110i
$847$	−5.66258e10	−	4.90638e11i	−0.110022	−	0.953295i
$848$	2.05672e11			0.397733
$849$	−9.34541e10	−	1.61867e11i	−0.179874	−	0.311550i
$850$	1.24030e12	+	7.16089e11i	2.37603	+	1.37180i
$851$	2.73808e11	−	4.74250e11i	0.522069	−	0.904251i
$852$	1.52979e11	−	8.83226e10i	0.290318	−	0.167615i
$853$		−	6.74482e11i		−	1.27401i	−0.770858	−	0.637007i	$-0.780172\pi$
$853$		−	6.74482e11i		−	1.27401i	0.770858	−	0.637007i	$-0.219828\pi$
$854$	1.63960e11	+	2.20905e11i	0.308252	+	0.415311i
$855$	−2.80755e11			−0.525367
$856$	−6.92294e10	−	1.19909e11i	−0.128942	−	0.223335i
$857$	4.61976e11	+	2.66722e11i	0.856438	+	0.494465i	0.862818	−	0.505515i	$-0.168697\pi$
$857$	4.61976e11	+	2.66722e11i	0.856438	+	0.494465i	−0.00638000	+	0.999980i	$0.502031\pi$
$858$	−1.33347e10	+	2.30964e10i	−0.0246056	+	0.0426182i
$859$	−1.81156e11	+	1.04590e11i	−0.332720	+	0.192096i	−0.657048	−	0.753849i	$-0.728195\pi$
$859$	−1.81156e11	+	1.04590e11i	−0.332720	+	0.192096i	0.324328	+	0.945945i	$0.394862\pi$
$860$		−	1.02193e12i		−	1.86821i
$861$	−2.91590e11	+	2.16424e11i	−0.530591	+	0.393815i
$862$	−1.49933e11			−0.271561
$863$	8.84866e10	+	1.53263e11i	0.159527	+	0.276309i	0.934698	−	0.355442i	$-0.115670\pi$
$863$	8.84866e10	+	1.53263e11i	0.159527	+	0.276309i	−0.775171	+	0.631751i	$0.782336\pi$
$864$	1.64183e10	+	9.47912e9i	0.0294628	+	0.0170103i
$865$	−9.52404e11	+	1.64961e12i	−1.70121	+	2.94657i
$866$	−5.66402e11	+	3.27012e11i	−1.00706	+	0.581424i
$867$		−	3.64567e11i		−	0.645209i
$868$	−1.65221e11	+	1.90685e10i	−0.291062	+	0.0335922i
$869$	−3.53893e7			−6.20573e−5
$870$	−3.89264e10	−	6.74225e10i	−0.0679466	−	0.117687i
$871$	−3.51627e10	−	2.03012e10i	−0.0610956	−	0.0352735i
$872$	1.32596e11	−	2.29663e11i	0.229331	−	0.397214i
$873$	2.16514e11	−	1.25004e11i	0.372760	−	0.215213i
$874$		−	3.26715e11i		−	0.559917i
$875$	7.43299e11	−	1.71631e12i	1.26804	−	2.92795i
$876$	1.19379e11			0.202727
$877$	1.08864e11	+	1.88559e11i	0.184030	+	0.318749i	0.943249	−	0.332086i	$-0.107752\pi$
$877$	1.08864e11	+	1.88559e11i	0.184030	+	0.318749i	−0.759220	+	0.650835i	$0.774419\pi$
$878$	3.63548e10	+	2.09894e10i	0.0611763	+	0.0353202i
$879$	−9.23963e10	+	1.60035e11i	−0.154774	+	0.268077i
$880$	4.99558e10	−	2.88420e10i	0.0833020	−	0.0480945i
$881$		−	6.31061e10i		−	0.104753i	−0.998627	−	0.0523766i	$-0.983320\pi$
$881$		−	6.31061e10i		−	0.104753i	0.998627	−	0.0523766i	$-0.0166796\pi$
$882$	1.38889e11	−	3.24919e10i	0.229506	−	0.0536908i
$883$	−7.90938e10			−0.130107			−0.0650533	−	0.997882i	$-0.520722\pi$
$883$	−7.90938e10			−0.130107			−0.0650533	+	0.997882i	$0.520722\pi$
$884$	1.33272e11	+	2.30833e11i	0.218237	+	0.377997i
$885$	−2.79754e10	−	1.61516e10i	−0.0456040	−	0.0263295i
$886$	1.46931e10	−	2.54492e10i	0.0238440	−	0.0412990i
$887$	2.73865e11	−	1.58116e11i	0.442427	−	0.255435i	−0.262199	−	0.965014i	$-0.584448\pi$
$887$	2.73865e11	−	1.58116e11i	0.442427	−	0.255435i	0.704627	+	0.709578i	$0.251115\pi$
$888$			1.37763e11i			0.221554i
$889$	5.18619e11	+	2.24604e11i	0.830313	+	0.359592i
$890$	1.07951e12			1.72055
$891$	7.03566e9	+	1.21861e10i	0.0111633	+	0.0193355i
$892$	−5.04754e11	−	2.91420e11i	−0.797298	−	0.460320i
$893$	−2.43299e11	+	4.21406e11i	−0.382590	+	0.662666i
$894$	2.78335e11	−	1.60697e11i	0.435730	−	0.251569i
$895$			7.07140e11i			1.10208i
$896$	6.53141e9	+	5.65918e10i	0.0101339	+	0.0878055i
$897$	2.15703e11			0.333185
$898$	1.28191e11	+	2.22034e11i	0.197130	+	0.341440i
$899$	−5.76252e10	−	3.32699e10i	−0.0882214	−	0.0509346i
$900$	−1.45784e11	+	2.52505e11i	−0.222198	+	0.384858i
$901$	1.32129e12	−	7.62845e11i	2.00492	−	1.15754i
$902$		−	1.07644e11i		−	0.162616i
$903$	4.46447e11	+	6.01503e11i	0.671458	+	0.904663i
$904$	−4.62783e10			−0.0692952
$905$	1.21216e11	+	2.09952e11i	0.180703	+	0.312986i
$906$	2.45131e11	+	1.41527e11i	0.363820	+	0.210051i
$907$	−1.44966e11	+	2.51089e11i	−0.214209	+	0.371021i	−0.953028	−	0.302883i	$-0.902051\pi$
$907$	−1.44966e11	+	2.51089e11i	−0.214209	+	0.371021i	0.738819	+	0.673904i	$0.235384\pi$
$908$	3.72415e11	−	2.15014e11i	0.547878	−	0.316317i
$909$		−	3.88489e11i		−	0.569015i
$910$	4.47251e11	−	3.31958e11i	0.652208	−	0.484081i
$911$	−7.44580e11			−1.08103			−0.540515	−	0.841334i	$-0.681771\pi$
$911$	−7.44580e11			−1.08103			−0.540515	+	0.841334i	$0.681771\pi$
$912$	4.10955e10	+	7.11795e10i	0.0594039	+	0.102891i
$913$	−3.61193e10	−	2.08535e10i	−0.0519824	−	0.0300120i
$914$	−2.87228e10	+	4.97493e10i	−0.0411568	+	0.0712857i
$915$	4.90853e11	−	2.83394e11i	0.700273	−	0.404303i
$916$			3.25054e10i			0.0461715i
$917$	−6.26938e11	+	7.23565e10i	−0.886640	+	0.102329i
$918$	1.40634e11			0.198024
$919$	6.16321e11	+	1.06750e12i	0.864061	+	1.49660i	0.867976	+	0.496606i	$0.165421\pi$
$919$	6.16321e11	+	1.06750e12i	0.864061	+	1.49660i	−0.00391475	+	0.999992i	$0.501246\pi$
$920$	−4.04044e11	−	2.33275e11i	−0.563997	−	0.325624i
$921$	7.38207e10	−	1.27861e11i	0.102598	−	0.177705i
$922$	−5.28958e11	+	3.05394e11i	−0.731978	+	0.422607i
$923$			5.05608e11i			0.696637i
$924$	−1.68037e10	+	3.88004e10i	−0.0230524	+	0.0532290i
$925$	−2.11872e12			−2.89405
$926$	−1.18890e11	−	2.05923e11i	−0.161696	−	0.280066i
$927$	−3.03871e11	−	1.75440e11i	−0.411500	−	0.237580i
$928$	−1.13957e10	+	1.97380e10i	−0.0153656	+	0.0266140i
$929$	−2.15201e11	+	1.24246e11i	−0.288922	+	0.166809i	−0.637456	−	0.770487i	$-0.720013\pi$
$929$	−2.15201e11	+	1.24246e11i	−0.288922	+	0.166809i	0.348533	+	0.937296i	$0.386680\pi$
$930$			3.42660e11i			0.458069i
$931$	5.91896e11	+	1.79075e11i	0.787856	+	0.238362i
$932$	6.53827e10			0.0866561
$933$	1.63695e11	+	2.83529e11i	0.216028	+	0.374171i
$934$	−3.62790e11	−	2.09457e11i	−0.476725	−	0.275237i
$935$	2.13952e11	−	3.70576e11i	0.279943	−	0.484876i
$936$	−4.69938e10	+	2.71319e10i	−0.0612262	+	0.0353490i
$937$			3.46983e11i			0.450143i	0.974342	+	0.225071i	$0.0722615\pi$
$937$			3.46983e11i			0.450143i	−0.974342	+	0.225071i	$0.927738\pi$
$938$	−5.90711e10	−	2.55825e10i	−0.0763069	−	0.0330470i
$939$	−3.09843e11			−0.398546
$940$	3.47431e11	+	6.01768e11i	0.444997	+	0.770757i
$941$	−1.85964e10	−	1.07366e10i	−0.0237176	−	0.0136933i	0.488094	−	0.872791i	$-0.337692\pi$
$941$	−1.85964e10	−	1.07366e10i	−0.0237176	−	0.0136933i	−0.511812	+	0.859098i	$0.671026\pi$
$942$	−1.65761e11	+	2.87107e11i	−0.210513	+	0.364619i
$943$	−7.53983e11	+	4.35312e11i	−0.953487	+	0.550496i
$944$			9.45676e9i			0.0119084i
$945$	−3.36933e10	−	2.91938e11i	−0.0422490	−	0.366069i
$946$	−2.22052e11			−0.277261
$947$	−5.97454e11	−	1.03482e12i	−0.742856	−	1.28666i	−0.951190	−	0.308606i	$-0.900138\pi$
$947$	−5.97454e11	−	1.03482e12i	−0.742856	−	1.28666i	0.208334	−	0.978058i	$-0.433196\pi$
$948$	−6.23590e7	−	3.60030e7i	−7.72086e−5	−	4.45764e-5i
$949$	−1.70848e11	+	2.95917e11i	−0.210642	+	0.364842i
$950$	−1.09470e12	+	6.32027e11i	−1.34401	+	0.775963i
$951$			3.45123e11i			0.421941i
$952$	2.51860e11	+	3.39334e11i	0.306628	+	0.413123i
$953$	3.74144e11			0.453594			0.226797	−	0.973942i	$-0.427175\pi$
$953$	3.74144e11			0.453594			0.226797	+	0.973942i	$0.427175\pi$
$954$	1.55303e11	+	2.68992e11i	0.187493	+	0.324748i
$955$	−1.65992e12	−	9.58356e11i	−1.99560	−	1.15216i
$956$	−3.26466e11	+	5.65456e11i	−0.390847	+	0.676967i
$957$	−1.46501e10	+	8.45821e9i	−0.0174659	+	0.0100840i
$958$		−	9.92987e10i		−	0.117891i
$959$	−9.06184e10	+	6.72587e10i	−0.107138	+	0.0795196i
$960$	1.17369e11			0.138187
$961$	−2.80012e11	−	4.84995e11i	−0.328309	−	0.568648i
$962$	−3.41487e11	−	1.97158e11i	−0.398725	−	0.230204i
$963$	1.04550e11	−	1.81086e11i	0.121568	−	0.210562i
$964$	−3.38410e11	+	1.95381e11i	−0.391864	+	0.226243i
$965$			5.85507e11i			0.675185i
$966$	3.39729e11	−	3.92090e10i	0.390143	−	0.0450274i
$967$	2.62550e11			0.300265			0.150133	−	0.988666i	$-0.452030\pi$
$967$	2.62550e11			0.300265			0.150133	+	0.988666i	$0.452030\pi$
$968$	1.48945e11	+	2.57981e11i	0.169639	+	0.293823i
$969$	5.28014e11	+	3.04849e11i	0.598895	+	0.345772i
$970$	7.73891e11	−	1.34042e12i	0.874164	−	1.51410i
$971$	2.27809e11	−	1.31526e11i	0.256268	−	0.147957i	−0.366363	−	0.930472i	$-0.619397\pi$
$971$	2.27809e11	−	1.31526e11i	0.256268	−	0.147957i	0.622631	+	0.782516i	$0.286064\pi$
$972$			2.86307e10i			0.0320750i
$973$	3.46370e11	−	7.99783e11i	0.386446	−	0.892321i
$974$	6.93139e11			0.770166
$975$	−4.17274e11	−	7.22740e11i	−0.461746	−	0.799768i
$976$	−1.43697e11	−	8.29637e10i	−0.158361	−	0.0914300i
$977$	4.39954e11	−	7.62023e11i	0.482869	−	0.836353i	−0.516938	−	0.856023i	$-0.672928\pi$
$977$	4.39954e11	−	7.62023e11i	0.482869	−	0.836353i	0.999807	+	0.0196697i	$0.00626146\pi$
$978$	3.93172e11	−	2.26998e11i	0.429761	−	0.248123i
$979$		−	2.34564e11i		−	0.255347i
$980$	6.44074e11	−	6.04129e11i	0.698283	−	0.654976i
$981$	4.00492e11			0.432432
$982$	−6.77286e10	−	1.17309e11i	−0.0728327	−	0.126150i
$983$	7.13400e11	+	4.11882e11i	0.764046	+	0.441122i	0.830746	−	0.556651i	$-0.187914\pi$
$983$	7.13400e11	+	4.11882e11i	0.764046	+	0.441122i	−0.0667008	+	0.997773i	$0.521247\pi$
$984$	1.09511e11	−	1.89678e11i	0.116809	−	0.202319i
$985$	−2.06399e12	+	1.19165e12i	−2.19262	+	1.26591i
$986$			1.69069e11i			0.178877i
$987$	−4.67390e11	−	2.02417e11i	−0.492505	−	0.213294i
$988$	−2.35253e11			−0.246893
$989$	8.97979e11	+	1.55534e12i	0.938601	+	1.62570i
$990$	7.54432e10	+	4.35572e10i	0.0785379	+	0.0453439i
$991$	−2.13235e11	+	3.69335e11i	−0.221088	+	0.382935i	−0.955139	−	0.296159i	$-0.904294\pi$
$991$	−2.13235e11	+	3.69335e11i	−0.221088	+	0.382935i	0.734051	+	0.679095i	$0.237627\pi$
$992$	8.68742e10	−	5.01568e10i	0.0897107	−	0.0517945i
$993$		−	6.70145e11i		−	0.689242i
$994$	9.19061e10	+	7.96326e11i	0.0941453	+	0.815728i
$995$	6.05547e11			0.617810
$996$	−4.24302e10	−	7.34913e10i	−0.0431160	−	0.0746790i
$997$	−1.47698e12	−	8.52733e11i	−1.49483	−	0.863043i	−0.494852	−	0.868978i	$-0.664778\pi$
$997$	−1.47698e12	−	8.52733e11i	−1.49483	−	0.863043i	−0.999982	+	0.00593479i	$0.998111\pi$
$998$	−4.80365e10	+	8.32017e10i	−0.0484228	+	0.0838707i
$999$	−1.80176e11	+	1.04024e11i	−0.180898	+	0.104442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.b.31.1	yes	12
3.2	odd	2		126.9.n.c.73.6		12
7.3	odd	6		294.9.c.b.97.9		12
7.4	even	3		294.9.c.b.97.10		12
7.5	odd	6	inner	42.9.g.b.19.1	✓	12
21.5	even	6		126.9.n.c.19.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.b.19.1	✓	12	7.5	odd	6	inner
42.9.g.b.31.1	yes	12	1.1	even	1	trivial
126.9.n.c.19.6		12	21.5	even	6
126.9.n.c.73.6		12	3.2	odd	2
294.9.c.b.97.9		12	7.3	odd	6
294.9.c.b.97.10		12	7.4	even	3

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-1036.40 + 598.368i) q^{5} +529.090i q^{6} +(-2203.25 - 954.186i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-1036.40 + 598.368i) q^{5} +529.090i q^{6} +(-2203.25 - 954.186i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(11725.6 + 6769.76i) q^{10} +(1470.98 - 2547.82i) q^{11} +(5184.00 - 2992.98i) q^{12} +17133.5i q^{13} +(3114.42 + 26985.1i) q^{14} +55965.8 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-105255. - 60768.8i) q^{17} +(12371.5 - 21428.1i) q^{18} +(92898.9 - 53635.2i) q^{19} -153182. i q^{20} +(66920.4 + 90162.5i) q^{21} -33284.5 q^{22} +(134603. + 233139. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(520776. - 902010. i) q^{25} +(167873. - 96921.8i) q^{26} -102276. i q^{27} +(246781. - 183166. i) q^{28} +122955. q^{29} +(-316590. - 548351. i) q^{30} +(-468669. - 270586. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-119150. + 68791.0i) q^{33} +1.37504e6i q^{34} +(2.85442e6 - 329435. i) q^{35} -279936. q^{36} +(-1.01710e6 - 1.76166e6i) q^{37} +(-1.05103e6 - 606813. i) q^{38} +(400628. - 693907. i) q^{39} +(-1.50087e6 + 866529. i) q^{40} +3.23405e6i q^{41} +(504850. - 1.16572e6i) q^{42} +6.67132e6 q^{43} +(188286. + 326120. i) q^{44} +(-2.26662e6 - 1.30863e6i) q^{45} +(1.52286e6 - 2.63767e6i) q^{46} +(-3.92844e6 + 2.26809e6i) q^{47} +766204. i q^{48} +(3.94386e6 + 4.20463e6i) q^{49} -1.17838e7 q^{50} +(2.84188e6 + 4.92228e6i) q^{51} +(-1.89927e6 - 1.09654e6i) q^{52} +(-6.27661e6 + 1.08714e7i) q^{53} +(-1.00209e6 + 578560. i) q^{54} +3.52075e6i q^{55} +(-3.19065e6 - 1.38181e6i) q^{56} -5.01654e6 q^{57} +(-695539. - 1.20471e6i) q^{58} +(-499865. - 288597. i) q^{59} +(-3.58181e6 + 6.20388e6i) q^{60} +(8.77059e6 - 5.06370e6i) q^{61} +6.12266e6i q^{62} +(-602034. - 5.21636e6i) q^{63} +2.09715e6 q^{64} +(-1.02521e7 - 1.77572e7i) q^{65} +(1.34802e6 + 778282. i) q^{66} +(-1.18488e6 + 2.05228e6i) q^{67} +(1.34726e7 - 7.77841e6i) q^{68} -1.25895e7i q^{69} +(-1.93748e7 - 2.61039e7i) q^{70} +2.95099e7 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(1.72712e7 + 9.97155e6i) q^{73} +(-1.15071e7 + 1.99309e7i) q^{74} +(-4.21829e7 + 2.43543e7i) q^{75} +1.37306e7i q^{76} +(-5.67204e6 + 4.20990e6i) q^{77} -9.06517e6 q^{78} +(-6014.57 - 10417.5i) q^{79} +(1.69804e7 + 9.80366e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(3.16871e7 - 1.82945e7i) q^{82} -1.41766e7i q^{83} +(-1.42775e7 + 1.64781e6i) q^{84} +1.45449e8 q^{85} +(-3.77387e7 - 6.53653e7i) q^{86} +(-4.97968e6 - 2.87502e6i) q^{87} +(2.13021e6 - 3.68963e6i) q^{88} +(6.90485e7 - 3.98652e7i) q^{89} +2.96109e7i q^{90} +(1.63485e7 - 3.77495e7i) q^{91} -3.44583e7 q^{92} +(1.26541e7 + 2.19175e7i) q^{93} +(4.44453e7 + 2.56605e7i) q^{94} +(-6.41871e7 + 1.11175e8i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} -1.14316e8i q^{97} +(1.88869e7 - 6.24268e7i) q^{98} +6.43408e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9}+O(q^{10}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9	\( 12 q - 486 q^{3} - 768 q^{4} - 1122 q^{5} - 4434 q^{7} + 13122 q^{9} + 4224 q^{10} + 9606 q^{11} + 62208 q^{12} - 19968 q^{14} + 60588 q^{15} - 98304 q^{16} - 227388 q^{17} + 315408 q^{19} + 155358 q^{21} + 557568 q^{22} - 663480 q^{23} + 601008 q^{25} - 585984 q^{26} + 398592 q^{28} + 5944884 q^{29} - 114048 q^{30} - 3214278 q^{31} - 778086 q^{33} - 1019784 q^{35} - 3359232 q^{36} + 1607760 q^{37} - 986880 q^{38} + 903636 q^{39} - 540672 q^{40} + 2788992 q^{42} + 12627648 q^{43} + 1229568 q^{44} - 2453814 q^{45} - 4608768 q^{46} - 7830240 q^{47} + 16477242 q^{49} - 16565760 q^{50} + 6139476 q^{51} - 4283904 q^{52} - 33200358 q^{53} - 8110080 q^{56} - 17032032 q^{57} + 5576064 q^{58} - 29657382 q^{59} - 3877632 q^{60} + 58344096 q^{61} - 2886840 q^{63} + 25165824 q^{64} + 30909216 q^{65} - 22581504 q^{66} + 7977444 q^{67} + 29105664 q^{68} - 59774976 q^{70} + 117213264 q^{71} - 170286636 q^{73} - 80311296 q^{74} - 48681648 q^{75} - 3340686 q^{77} + 31643136 q^{78} + 35420490 q^{79} + 18382848 q^{80} - 28697814 q^{81} + 154232832 q^{82} - 26085888 q^{84} + 416634600 q^{85} - 71958528 q^{86} - 240767802 q^{87} - 35684352 q^{88} + 78064092 q^{89} + 335513292 q^{91} + 169850880 q^{92} + 86785506 q^{93} - 18456576 q^{94} - 250727796 q^{95} - 150533376 q^{98} + 42016644 q^{99}+O(q^{100}) \) 12 * q - 486 * q^3 - 768 * q^4 - 1122 * q^5 - 4434 * q^7 + 13122 * q^9 + 4224 * q^10 + 9606 * q^11 + 62208 * q^12 - 19968 * q^14 + 60588 * q^15 - 98304 * q^16 - 227388 * q^17 + 315408 * q^19 + 155358 * q^21 + 557568 * q^22 - 663480 * q^23 + 601008 * q^25 - 585984 * q^26 + 398592 * q^28 + 5944884 * q^29 - 114048 * q^30 - 3214278 * q^31 - 778086 * q^33 - 1019784 * q^35 - 3359232 * q^36 + 1607760 * q^37 - 986880 * q^38 + 903636 * q^39 - 540672 * q^40 + 2788992 * q^42 + 12627648 * q^43 + 1229568 * q^44 - 2453814 * q^45 - 4608768 * q^46 - 7830240 * q^47 + 16477242 * q^49 - 16565760 * q^50 + 6139476 * q^51 - 4283904 * q^52 - 33200358 * q^53 - 8110080 * q^56 - 17032032 * q^57 + 5576064 * q^58 - 29657382 * q^59 - 3877632 * q^60 + 58344096 * q^61 - 2886840 * q^63 + 25165824 * q^64 + 30909216 * q^65 - 22581504 * q^66 + 7977444 * q^67 + 29105664 * q^68 - 59774976 * q^70 + 117213264 * q^71 - 170286636 * q^73 - 80311296 * q^74 - 48681648 * q^75 - 3340686 * q^77 + 31643136 * q^78 + 35420490 * q^79 + 18382848 * q^80 - 28697814 * q^81 + 154232832 * q^82 - 26085888 * q^84 + 416634600 * q^85 - 71958528 * q^86 - 240767802 * q^87 - 35684352 * q^88 + 78064092 * q^89 + 335513292 * q^91 + 169850880 * q^92 + 86785506 * q^93 - 18456576 * q^94 - 250727796 * q^95 - 150533376 * q^98 + 42016644 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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