LMFDB - Embedded newform 42.9.g.a.31.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 243x^{6} - 2x^{5} + 49033x^{4} - 23088x^{3} + 2105352x^{2} + 2056320x + 73410624 $ x^8 - 2x^7 + 243x^6 - 2x^5 + 49033x^4 - 23088x^3 + 2105352x^2 + 2056320*x + 73410624
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$7.26102 - 12.5765i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.65685 + 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-65.1898 + 37.6374i) q^{5} +529.090i q^{6} +(2247.80 + 843.923i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(5.65685 + 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-65.1898 + 37.6374i) q^{5} +529.090i q^{6} +(2247.80 + 843.923i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-737.539 - 425.818i) q^{10} +(-8036.72 + 13920.0i) q^{11} +(-5184.00 + 2992.98i) q^{12} +16361.2i q^{13} +(4446.74 + 26797.8i) q^{14} -3520.25 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-6128.46 - 3538.27i) q^{17} +(-12371.5 + 21428.1i) q^{18} +(-35967.2 + 20765.7i) q^{19} -9635.17i q^{20} +(71302.6 + 86738.4i) q^{21} -181850. q^{22} +(-15268.4 - 26445.7i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-192479. + 333384. i) q^{25} +(-160307. + 92553.1i) q^{26} +102276. i q^{27} +(-237409. + 195160. i) q^{28} -496195. q^{29} +(-19913.6 - 34491.3i) q^{30} +(-233622. - 134882. i) q^{31} +(92681.9 - 160530. i) q^{32} +(-650974. + 375840. i) q^{33} -80061.8i q^{34} +(-178297. + 29586.0i) q^{35} -279936. q^{36} +(746506. + 1.29299e6i) q^{37} +(-406923. - 234937. i) q^{38} +(-382570. + 662630. i) q^{39} +(94405.0 - 54504.7i) q^{40} +380396. i q^{41} +(-446511. + 1.18929e6i) q^{42} +3.70688e6 q^{43} +(-1.02870e6 - 1.78176e6i) q^{44} +(-142570. - 82312.9i) q^{45} +(172743. - 299199. i) q^{46} +(6.05143e6 - 3.49379e6i) q^{47} -766204. i q^{48} +(4.34039e6 + 3.79394e6i) q^{49} -4.35531e6 q^{50} +(-165468. - 286599. i) q^{51} +(-1.81366e6 - 1.04712e6i) q^{52} +(2.69774e6 - 4.67263e6i) q^{53} +(-1.00209e6 + 578560. i) q^{54} -1.20992e6i q^{55} +(-3.25516e6 - 1.22213e6i) q^{56} -1.94223e6 q^{57} +(-2.80690e6 - 4.86170e6i) q^{58} +(5.16467e6 + 2.98182e6i) q^{59} +(225296. - 390224. i) q^{60} +(2.18625e7 - 1.26223e7i) q^{61} -3.05202e6i q^{62} +(859579. + 5.18015e6i) q^{63} +2.09715e6 q^{64} +(-615794. - 1.06659e6i) q^{65} +(-7.36493e6 - 4.25214e6i) q^{66} +(1.57957e7 - 2.73589e7i) q^{67} +(784442. - 452898. i) q^{68} -1.42807e6i q^{69} +(-1.29848e6 - 1.57958e6i) q^{70} -2.18100e7 q^{71} +(-1.58356e6 - 2.74280e6i) q^{72} +(2.52288e7 + 1.45659e7i) q^{73} +(-8.44575e6 + 1.46285e7i) q^{74} +(-1.55908e7 + 9.00137e6i) q^{75} -5.31602e6i q^{76} +(-2.98123e7 + 2.45070e7i) q^{77} -8.65656e6 q^{78} +(1.26546e7 + 2.19185e7i) q^{79} +(1.06807e6 + 616651. i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(-3.72710e6 + 2.15184e6i) q^{82} +2.26197e7i q^{83} +(-1.41784e7 + 2.35273e6i) q^{84} +532684. q^{85} +(2.09693e7 + 3.63199e7i) q^{86} +(-2.00959e7 - 1.16024e7i) q^{87} +(1.16384e7 - 2.01583e7i) q^{88} +(-1.00410e8 + 5.79716e7i) q^{89} -1.86253e6i q^{90} +(-1.38076e7 + 3.67768e7i) q^{91} +3.90872e6 q^{92} +(-6.30778e6 - 1.09254e7i) q^{93} +(6.84641e7 + 3.95278e7i) q^{94} +(1.56313e6 - 2.70742e6i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} +3.41886e7i q^{97} +(-1.26199e7 + 6.39887e7i) q^{98} -3.51526e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9}+O(q^{10}) $ 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9} - 21888 q^{10} - 7434 q^{11} - 41472 q^{12} + 32256 q^{14} - 120204 q^{15} - 65536 q^{16} + 7932 q^{17} - 773082 q^{19} + 130410 q^{21} + 557568 q^{22} + 391200 q^{23} - 138886 q^{25} - 805632 q^{26} + 654080 q^{28} - 2318196 q^{29} - 590976 q^{30} - 3212544 q^{31} - 602154 q^{33} + 3340932 q^{35} - 2239488 q^{36} + 544802 q^{37} - 1570560 q^{38} + 1341522 q^{39} + 2801664 q^{40} - 72576 q^{42} + 552284 q^{43} - 951552 q^{44} - 4868262 q^{45} + 7878912 q^{46} - 15735252 q^{47} - 588196 q^{49} + 25400832 q^{50} + 214164 q^{51} + 6359808 q^{52} + 10935222 q^{53} - 8601600 q^{56} - 41746428 q^{57} - 8158848 q^{58} + 63840318 q^{59} + 7693056 q^{60} + 43108176 q^{61} + 10869390 q^{63} + 16777216 q^{64} - 9118644 q^{65} + 22581504 q^{66} + 48827290 q^{67} - 1015296 q^{68} + 11053056 q^{70} - 164526744 q^{71} + 150530022 q^{73} - 31064064 q^{74} - 11249766 q^{75} - 137090394 q^{77} - 43504128 q^{78} - 18689696 q^{79} + 36470784 q^{80} - 19131876 q^{81} - 33914880 q^{82} + 18144000 q^{84} - 190617576 q^{85} - 37077504 q^{86} - 93886938 q^{87} - 35684352 q^{88} - 191605284 q^{89} + 110138574 q^{91} - 100147200 q^{92} - 86738688 q^{93} + 302275584 q^{94} + 260649552 q^{95} - 282428160 q^{98} - 32516316 q^{99}+O(q^{100}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9 - 21888 * q^10 - 7434 * q^11 - 41472 * q^12 + 32256 * q^14 - 120204 * q^15 - 65536 * q^16 + 7932 * q^17 - 773082 * q^19 + 130410 * q^21 + 557568 * q^22 + 391200 * q^23 - 138886 * q^25 - 805632 * q^26 + 654080 * q^28 - 2318196 * q^29 - 590976 * q^30 - 3212544 * q^31 - 602154 * q^33 + 3340932 * q^35 - 2239488 * q^36 + 544802 * q^37 - 1570560 * q^38 + 1341522 * q^39 + 2801664 * q^40 - 72576 * q^42 + 552284 * q^43 - 951552 * q^44 - 4868262 * q^45 + 7878912 * q^46 - 15735252 * q^47 - 588196 * q^49 + 25400832 * q^50 + 214164 * q^51 + 6359808 * q^52 + 10935222 * q^53 - 8601600 * q^56 - 41746428 * q^57 - 8158848 * q^58 + 63840318 * q^59 + 7693056 * q^60 + 43108176 * q^61 + 10869390 * q^63 + 16777216 * q^64 - 9118644 * q^65 + 22581504 * q^66 + 48827290 * q^67 - 1015296 * q^68 + 11053056 * q^70 - 164526744 * q^71 + 150530022 * q^73 - 31064064 * q^74 - 11249766 * q^75 - 137090394 * q^77 - 43504128 * q^78 - 18689696 * q^79 + 36470784 * q^80 - 19131876 * q^81 - 33914880 * q^82 + 18144000 * q^84 - 190617576 * q^85 - 37077504 * q^86 - 93886938 * q^87 - 35684352 * q^88 - 191605284 * q^89 + 110138574 * q^91 - 100147200 * q^92 - 86738688 * q^93 + 302275584 * q^94 + 260649552 * q^95 - 282428160 * q^98 - 32516316 * 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
$5$	−65.1898	+	37.6374i	−0.104304	+	0.0602198i	−0.551244	−	0.834344i	$-0.685847\pi$
$5$	−65.1898	+	37.6374i	−0.104304	+	0.0602198i	0.446941	+	0.894564i	$0.352513\pi$
$6$			529.090i			0.408248i
$7$	2247.80	+	843.923i	0.936192	+	0.351488i
$7$	2247.80	+	843.923i	0.936192	+	0.351488i
$8$	−1448.15			−0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	−737.539	−	425.818i	−0.0737539	−	0.0425818i
$11$	−8036.72	+	13920.0i	−0.548919	+	0.950755i	0.449430	+	0.893315i	$0.351627\pi$
$11$	−8036.72	+	13920.0i	−0.548919	+	0.950755i	−0.998349	+	0.0574395i	$0.981706\pi$
$12$	−5184.00	+	2992.98i	−0.250000	+	0.144338i
$13$			16361.2i			0.572852i	0.958102	+	0.286426i	$0.0924673\pi$
$13$			16361.2i			0.572852i	−0.958102	+	0.286426i	$0.907533\pi$
$14$	4446.74	+	26797.8i	0.115752	+	0.697568i
$15$	−3520.25			−0.0695358
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	−6128.46	−	3538.27i	−0.0733762	−	0.0423638i	0.462863	−	0.886430i	$-0.346822\pi$
$17$	−6128.46	−	3538.27i	−0.0733762	−	0.0423638i	−0.536239	+	0.844066i	$0.680156\pi$
$18$	−12371.5	+	21428.1i	−0.117851	+	0.204124i
$19$	−35967.2	+	20765.7i	−0.275990	+	0.159343i	−0.631606	−	0.775289i	$-0.717604\pi$
$19$	−35967.2	+	20765.7i	−0.275990	+	0.159343i	0.355617	+	0.934632i	$0.384271\pi$
$20$		−	9635.17i		−	0.0602198i
$21$	71302.6	+	86738.4i	0.366630	+	0.445999i
$22$	−181850.			−0.776288
$23$	−15268.4	−	26445.7i	−0.0545611	−	0.0945027i	0.837455	−	0.546507i	$-0.184043\pi$
$23$	−15268.4	−	26445.7i	−0.0545611	−	0.0945027i	−0.892016	+	0.452004i	$0.850709\pi$
$24$	−58650.3	−	33861.7i	−0.176777	−	0.102062i
$25$	−192479.	+	333384.i	−0.492747	+	0.853463i
$26$	−160307.	+	92553.1i	−0.350799	+	0.202534i
$27$			102276.i			0.192450i
$28$	−237409.	+	195160.i	−0.386247	+	0.317511i
$29$	−496195.			−0.701552			−0.350776	−	0.936459i	$-0.614082\pi$
$29$	−496195.			−0.701552			−0.350776	+	0.936459i	$0.614082\pi$
$30$	−19913.6	−	34491.3i	−0.0245846	−	0.0425818i
$31$	−233622.	−	134882.i	−0.252968	−	0.146051i	0.368154	−	0.929765i	$-0.379990\pi$
$31$	−233622.	−	134882.i	−0.252968	−	0.146051i	−0.621123	+	0.783713i	$0.713323\pi$
$32$	92681.9	−	160530.i	0.0883883	−	0.153093i
$33$	−650974.	+	375840.i	−0.548919	+	0.316918i
$34$		−	80061.8i		−	0.0599114i
$35$	−178297.	+	29586.0i	−0.118815	+	0.0197158i
$36$	−279936.			−0.166667
$37$	746506.	+	1.29299e6i	0.398315	+	0.689901i	0.993518	−	0.113674i	$-0.0362619\pi$
$37$	746506.	+	1.29299e6i	0.398315	+	0.689901i	−0.595203	+	0.803575i	$0.702929\pi$
$38$	−406923.	−	234937.i	−0.195154	−	0.112672i
$39$	−382570.	+	662630.i	−0.165368	+	0.286426i
$40$	94405.0	−	54504.7i	0.0368769	−	0.0212909i
$41$			380396.i			0.134617i	0.997732	+	0.0673085i	$0.0214412\pi$
$41$			380396.i			0.134617i	−0.997732	+	0.0673085i	$0.978559\pi$
$42$	−446511.	+	1.18929e6i	−0.143494	+	0.382199i
$43$	3.70688e6			1.08426			0.542132	−	0.840294i	$-0.317617\pi$
$43$	3.70688e6			1.08426			0.542132	+	0.840294i	$0.317617\pi$
$44$	−1.02870e6	−	1.78176e6i	−0.274459	−	0.475377i
$45$	−142570.	−	82312.9i	−0.0347679	−	0.0200733i
$46$	172743.	−	299199.i	0.0385805	−	0.0668235i
$47$	6.05143e6	−	3.49379e6i	1.24013	−	0.715988i	0.271008	−	0.962577i	$-0.412643\pi$
$47$	6.05143e6	−	3.49379e6i	1.24013	−	0.715988i	0.969120	+	0.246589i	$0.0793097\pi$
$48$		−	766204.i		−	0.144338i
$49$	4.34039e6	+	3.79394e6i	0.752912	+	0.658121i
$50$	−4.35531e6			−0.696850
$51$	−165468.	−	286599.i	−0.0244587	−	0.0423638i
$52$	−1.81366e6	−	1.04712e6i	−0.248052	−	0.143213i
$53$	2.69774e6	−	4.67263e6i	0.341898	−	0.592186i	−0.642887	−	0.765961i	$-0.722263\pi$
$53$	2.69774e6	−	4.67263e6i	0.341898	−	0.592186i	0.984785	+	0.173776i	$0.0555968\pi$
$54$	−1.00209e6	+	578560.i	−0.117851	+	0.0680414i
$55$		−	1.20992e6i		−	0.132223i
$56$	−3.25516e6	−	1.22213e6i	−0.330994	−	0.124270i
$57$	−1.94223e6			−0.183993
$58$	−2.80690e6	−	4.86170e6i	−0.248036	−	0.429611i
$59$	5.16467e6	+	2.98182e6i	0.426220	+	0.246078i	0.697735	−	0.716356i	$-0.254191\pi$
$59$	5.16467e6	+	2.98182e6i	0.426220	+	0.246078i	−0.271515	+	0.962434i	$0.587525\pi$
$60$	225296.	−	390224.i	0.0173840	−	0.0301099i
$61$	2.18625e7	−	1.26223e7i	1.57899	−	0.911631i	0.583990	−	0.811761i	$-0.301491\pi$
$61$	2.18625e7	−	1.26223e7i	1.57899	−	0.911631i	0.995001	−	0.0998697i	$-0.0318426\pi$
$62$		−	3.05202e6i		−	0.206548i
$63$	859579.	+	5.18015e6i	0.0545662	+	0.328837i
$64$	2.09715e6			0.125000
$65$	−615794.	−	1.06659e6i	−0.0344971	−	0.0597507i
$66$	−7.36493e6	−	4.25214e6i	−0.388144	−	0.224095i
$67$	1.57957e7	−	2.73589e7i	0.783861	−	1.35769i	−0.145817	−	0.989312i	$-0.546581\pi$
$67$	1.57957e7	−	2.73589e7i	0.783861	−	1.35769i	0.929677	−	0.368375i	$-0.120086\pi$
$68$	784442.	−	452898.i	0.0366881	−	0.0211819i
$69$		−	1.42807e6i		−	0.0630018i
$70$	−1.29848e6	−	1.57958e6i	−0.0540808	−	0.0657884i
$71$	−2.18100e7			−0.858268			−0.429134	−	0.903241i	$-0.641181\pi$
$71$	−2.18100e7			−0.858268			−0.429134	+	0.903241i	$0.641181\pi$
$72$	−1.58356e6	−	2.74280e6i	−0.0589256	−	0.102062i
$73$	2.52288e7	+	1.45659e7i	0.888395	+	0.512915i	0.873417	−	0.486973i	$-0.161899\pi$
$73$	2.52288e7	+	1.45659e7i	0.888395	+	0.512915i	0.0149777	+	0.999888i	$0.495232\pi$
$74$	−8.44575e6	+	1.46285e7i	−0.281651	+	0.487834i
$75$	−1.55908e7	+	9.00137e6i	−0.492747	+	0.284488i
$76$		−	5.31602e6i		−	0.159343i
$77$	−2.98123e7	+	2.45070e7i	−0.848072	+	0.697151i
$78$	−8.65656e6			−0.233866
$79$	1.26546e7	+	2.19185e7i	0.324894	+	0.562733i	0.981491	−	0.191509i	$-0.0613380\pi$
$79$	1.26546e7	+	2.19185e7i	0.324894	+	0.562733i	−0.656597	+	0.754242i	$0.728005\pi$
$80$	1.06807e6	+	616651.i	0.0260759	+	0.0150549i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	−3.72710e6	+	2.15184e6i	−0.0824358	+	0.0475943i
$83$			2.26197e7i			0.476623i	0.971189	+	0.238311i	$0.0765939\pi$
$83$			2.26197e7i			0.476623i	−0.971189	+	0.238311i	$0.923406\pi$
$84$	−1.41784e7	+	2.35273e6i	−0.284781	+	0.0472557i
$85$	532684.			0.0102046
$86$	2.09693e7	+	3.63199e7i	0.383345	+	0.663973i
$87$	−2.00959e7	−	1.16024e7i	−0.350776	−	0.202521i
$88$	1.16384e7	−	2.01583e7i	0.194072	−	0.336143i
$89$	−1.00410e8	+	5.79716e7i	−1.60035	+	0.923964i	−0.608937	+	0.793219i	$0.708404\pi$
$89$	−1.00410e8	+	5.79716e7i	−1.60035	+	0.923964i	−0.991416	+	0.130745i	$0.958263\pi$
$90$		−	1.86253e6i		−	0.0283879i
$91$	−1.38076e7	+	3.67768e7i	−0.201351	+	0.536300i
$92$	3.90872e6			0.0545611
$93$	−6.30778e6	−	1.09254e7i	−0.0843228	−	0.146051i
$94$	6.84641e7	+	3.95278e7i	0.876903	+	0.506280i
$95$	1.56313e6	−	2.70742e6i	0.0191912	−	0.0332401i
$96$	7.50723e6	−	4.33430e6i	0.0883883	−	0.0510310i
$97$			3.41886e7i			0.386184i	0.981181	+	0.193092i	$0.0618516\pi$
$97$			3.41886e7i			0.386184i	−0.981181	+	0.193092i	$0.938148\pi$
$98$	−1.26199e7	+	6.39887e7i	−0.136820	+	0.693744i
$99$	−3.51526e7			−0.365946
$100$	−2.46374e7	−	4.26732e7i	−0.246374	−	0.426732i
$101$	−5.53413e7	−	3.19513e7i	−0.531819	−	0.307046i	0.209938	−	0.977715i	$-0.432674\pi$
$101$	−5.53413e7	−	3.19513e7i	−0.531819	−	0.307046i	−0.741757	+	0.670669i	$0.766007\pi$
$102$	1.87206e6	−	3.24250e6i	0.0172949	−	0.0299557i
$103$	6.36463e7	−	3.67462e7i	0.565489	−	0.326485i	−0.189856	−	0.981812i	$-0.560802\pi$
$103$	6.36463e7	−	3.67462e7i	0.565489	−	0.326485i	0.755346	+	0.655326i	$0.227469\pi$
$104$		−	2.36936e7i		−	0.202534i
$105$	−7.91281e6	−	2.97082e6i	−0.0650989	−	0.0244410i
$106$	6.10430e7			0.483517
$107$	−1.21474e8	−	2.10398e8i	−0.926716	−	1.60512i	−0.788777	−	0.614679i	$-0.789285\pi$
$107$	−1.21474e8	−	2.10398e8i	−0.926716	−	1.60512i	−0.137939	−	0.990441i	$-0.544048\pi$
$108$	−1.13374e7	−	6.54566e6i	−0.0833333	−	0.0481125i
$109$	1.06038e8	−	1.83663e8i	0.751199	−	1.30112i	−0.196042	−	0.980595i	$-0.562809\pi$
$109$	1.06038e8	−	1.83663e8i	0.751199	−	1.30112i	0.947242	−	0.320520i	$-0.103858\pi$
$110$	1.18548e7	−	6.84436e6i	0.0809698	−	0.0467479i
$111$			6.98213e7i			0.459934i
$112$	−6.43957e6	−	3.88073e7i	−0.0409246	−	0.246628i
$113$	1.32760e8			0.814243			0.407122	−	0.913374i	$-0.366533\pi$
$113$	1.32760e8			0.814243			0.407122	+	0.913374i	$0.366533\pi$
$114$	−1.09869e7	−	1.90299e7i	−0.0650514	−	0.112672i
$115$	1.99069e6	+	1.14933e6i	0.0113819	+	0.00657132i
$116$	3.17565e7	−	5.50038e7i	0.175388	−	0.303781i
$117$	−3.09881e7	+	1.78910e7i	−0.165368	+	0.0954754i
$118$			6.74709e7i			0.348007i
$119$	−1.07895e7	−	1.31252e7i	−0.0538039	−	0.0654515i
$120$	5.09787e6			0.0245846
$121$	−2.19982e7	−	3.81019e7i	−0.102623	−	0.177748i
$122$	2.47345e8	+	1.42805e8i	1.11651	+	0.644620i
$123$	−8.89467e6	+	1.54060e7i	−0.0388606	+	0.0673085i
$124$	2.99036e7	−	1.72648e7i	0.126484	−	0.0730257i
$125$		−	5.83819e7i		−	0.239132i
$126$	−4.58924e7	+	3.77255e7i	−0.182079	+	0.149676i
$127$	−7.17952e7			−0.275982			−0.137991	−	0.990434i	$-0.544064\pi$
$127$	−7.17952e7			−0.275982			−0.137991	+	0.990434i	$0.544064\pi$
$128$	1.18633e7	+	2.05478e7i	0.0441942	+	0.0765466i
$129$	1.50129e8	+	8.66768e7i	0.542132	+	0.313000i
$130$	6.96691e6	−	1.20670e7i	0.0243931	−	0.0422501i
$131$	−7.91936e7	+	4.57224e7i	−0.268909	+	0.155254i	−0.628392	−	0.777897i	$-0.716286\pi$
$131$	−7.91936e7	+	4.57224e7i	−0.268909	+	0.155254i	0.359483	+	0.933152i	$0.382953\pi$
$132$		−	9.62150e7i		−	0.316918i
$133$	−9.83717e7	+	1.63235e7i	−0.314386	+	0.0521683i
$134$	3.57415e8			1.10855
$135$	−3.84940e6	−	6.66735e6i	−0.0115893	−	0.0200733i
$136$	8.87495e6	+	5.12396e6i	0.0259424	+	0.0149779i
$137$	2.62671e8	−	4.54959e8i	0.745640	−	1.29149i	−0.204255	−	0.978918i	$-0.565477\pi$
$137$	2.62671e8	−	4.54959e8i	0.745640	−	1.29149i	0.949895	−	0.312568i	$-0.101189\pi$
$138$	1.39922e7	−	8.07838e6i	0.0385805	−	0.0222745i
$139$			6.12770e8i			1.64149i	0.571295	+	0.820745i	$0.306441\pi$
$139$			6.12770e8i			1.64149i	−0.571295	+	0.820745i	$0.693559\pi$
$140$	8.13134e6	−	2.16579e7i	0.0211665	−	0.0563773i
$141$	3.26777e8			0.826752
$142$	−1.23376e8	−	2.13694e8i	−0.303444	−	0.525580i
$143$	−2.27748e8	−	1.31491e8i	−0.544642	−	0.314449i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	3.23469e7	−	1.86755e7i	0.0731746	−	0.0422473i
$146$			3.29588e8i			0.725371i
$147$	8.70734e7	+	2.55144e8i	0.186473	+	0.546407i
$148$	−1.91106e8			−0.398315
$149$	−2.88118e8	−	4.99034e8i	−0.584554	−	1.01248i	−0.994931	−	0.100561i	$-0.967936\pi$
$149$	−2.88118e8	−	4.99034e8i	−0.584554	−	1.01248i	0.410377	−	0.911916i	$-0.365397\pi$
$150$	−1.76390e8	−	1.01839e8i	−0.348425	−	0.201163i
$151$	−2.65647e8	+	4.60113e8i	−0.510971	+	0.885028i	0.488948	+	0.872313i	$0.337381\pi$
$151$	−2.65647e8	+	4.60113e8i	−0.510971	+	0.885028i	−0.999919	+	0.0127150i	$0.995953\pi$
$152$	5.20861e7	−	3.00719e7i	0.0975771	−	0.0563361i
$153$		−	1.54764e7i		−	0.0282425i
$154$	−4.08762e8	−	1.53467e8i	−0.726755	−	0.272856i
$155$	2.03063e7			0.0351807
$156$	−4.89689e7	−	8.48167e7i	−0.0826841	−	0.143213i
$157$	−2.77240e8	−	1.60065e8i	−0.456308	−	0.263449i	0.254183	−	0.967156i	$-0.418194\pi$
$157$	−2.77240e8	−	1.60065e8i	−0.456308	−	0.263449i	−0.710490	+	0.703707i	$0.751527\pi$
$158$	−1.43171e8	+	2.47979e8i	−0.229735	+	0.397912i
$159$	2.18517e8	−	1.26161e8i	0.341898	−	0.197395i
$160$			1.39532e7i			0.0212909i
$161$	−1.20022e7	−	7.23300e7i	−0.0178632	−	0.107650i
$162$	−5.41131e7			−0.0785674
$163$	−2.43058e8	−	4.20989e8i	−0.344318	−	0.596376i	0.640912	−	0.767614i	$-0.278556\pi$
$163$	−2.43058e8	−	4.20989e8i	−0.344318	−	0.596376i	−0.985230	+	0.171239i	$0.945223\pi$
$164$	−4.21673e7	−	2.43453e7i	−0.0582909	−	0.0336543i
$165$	2.82913e7	−	4.90019e7i	0.0381695	−	0.0661115i
$166$	−2.21627e8	+	1.27956e8i	−0.291871	+	0.168512i
$167$			1.20758e9i			1.55257i	0.630381	+	0.776286i	$0.282899\pi$
$167$			1.20758e9i			1.55257i	−0.630381	+	0.776286i	$0.717101\pi$
$168$	−1.03257e8	−	1.25611e8i	−0.129623	−	0.157685i
$169$	5.48041e8			0.671840
$170$	3.01332e6	+	5.21922e6i	0.00360785	+	0.00624899i
$171$	−7.86603e7	−	4.54146e7i	−0.0919965	−	0.0531142i
$172$	−2.37240e8	+	4.10912e8i	−0.271066	+	0.469500i
$173$	5.54745e8	−	3.20282e8i	0.619311	−	0.357559i	−0.157290	−	0.987553i	$-0.550276\pi$
$173$	5.54745e8	−	3.20282e8i	0.619311	−	0.357559i	0.776601	+	0.629993i	$0.216942\pi$
$174$		−	2.62532e8i		−	0.286408i
$175$	−7.14005e8	+	5.86942e8i	−0.761288	+	0.625811i
$176$	2.63347e8			0.274459
$177$	1.39446e8	+	2.41528e8i	0.142073	+	0.246078i
$178$	−1.13601e9	−	6.55873e8i	−1.13162	−	0.653341i
$179$	−3.66666e8	+	6.35084e8i	−0.357156	+	0.618613i	−0.987485	−	0.157716i	$-0.949587\pi$
$179$	−3.66666e8	+	6.35084e8i	−0.357156	+	0.618613i	0.630328	+	0.776329i	$0.282920\pi$
$180$	1.82490e7	−	1.05361e7i	0.0173840	−	0.0100366i
$181$			1.50094e9i			1.39845i	0.714900	+	0.699227i	$0.246472\pi$
$181$			1.50094e9i			1.39845i	−0.714900	+	0.699227i	$0.753528\pi$
$182$	−4.38445e8	+	7.27542e7i	−0.399604	+	0.0663090i
$183$	1.18057e9			1.05266
$184$	2.21111e7	+	3.82975e7i	0.0192903	+	0.0334117i
$185$	−9.73292e7	−	5.61930e7i	−0.0830914	−	0.0479729i
$186$	7.13644e7	−	1.23607e8i	0.0596252	−	0.103274i
$187$	9.85053e7	−	5.68721e7i	0.0805551	−	0.0465085i
$188$			8.94411e8i			0.715988i
$189$	−8.63129e7	+	2.29895e8i	−0.0676439	+	0.180170i
$190$	3.53696e7			0.0271404
$191$	−3.59563e8	−	6.22781e8i	−0.270173	−	0.467953i	0.698733	−	0.715382i	$-0.253747\pi$
$191$	−3.59563e8	−	6.22781e8i	−0.270173	−	0.467953i	−0.968906	+	0.247430i	$0.920414\pi$
$192$	8.49347e7	+	4.90370e7i	0.0625000	+	0.0360844i
$193$	5.75366e8	−	9.96564e8i	0.414682	−	0.718250i	−0.580713	−	0.814108i	$-0.697226\pi$
$193$	5.75366e8	−	9.96564e8i	0.414682	−	0.718250i	0.995395	+	0.0958579i	$0.0305594\pi$
$194$	−3.34978e8	+	1.93400e8i	−0.236488	+	0.136537i
$195$		−	5.75957e7i		−	0.0398338i
$196$	−6.98347e8	+	2.38326e8i	−0.473203	+	0.161490i
$197$	2.89805e9			1.92416			0.962080	−	0.272766i	$-0.0879385\pi$
$197$	2.89805e9			1.92416			0.962080	+	0.272766i	$0.0879385\pi$
$198$	−1.98853e8	−	3.44424e8i	−0.129381	−	0.224095i
$199$	−1.24278e9	−	7.17517e8i	−0.792466	−	0.457530i	0.0483640	−	0.998830i	$-0.484599\pi$
$199$	−1.24278e9	−	7.17517e8i	−0.792466	−	0.457530i	−0.840830	+	0.541299i	$0.817933\pi$
$200$	2.78740e8	−	4.82792e8i	0.174212	−	0.301745i
$201$	1.27945e9	−	7.38690e8i	0.783861	−	0.452562i
$202$		−	7.22976e8i		−	0.434228i
$203$	−1.11535e9	−	4.18750e8i	−0.656788	−	0.246587i
$204$	4.23599e7			0.0244587
$205$	−1.43171e7	−	2.47979e7i	−0.00810661	−	0.0140411i
$206$	7.20076e8	+	4.15736e8i	0.399861	+	0.230860i
$207$	3.33921e7	−	5.78368e7i	0.0181870	−	0.0315009i
$208$	2.32149e8	−	1.34031e8i	0.124026	−	0.0716066i
$209$		−	6.67552e8i		−	0.349865i
$210$	−1.56537e7	−	9.43349e7i	−0.00804894	−	0.0485060i
$211$	1.85899e9			0.937879			0.468939	−	0.883230i	$-0.344636\pi$
$211$	1.85899e9			0.937879			0.468939	+	0.883230i	$0.344636\pi$
$212$	3.45311e8	+	5.98096e8i	0.170949	+	0.296093i
$213$	−8.83307e8	−	5.09977e8i	−0.429134	−	0.247761i
$214$	1.37432e9	−	2.38039e9i	0.655287	−	1.13499i
$215$	−2.41651e8	+	1.39517e8i	−0.113093	+	0.0652941i
$216$		−	1.48111e8i		−	0.0680414i
$217$	−4.11305e8	−	5.00345e8i	−0.185492	−	0.225648i
$218$	2.39936e9			1.06236
$219$	6.81179e8	+	1.17984e9i	0.296132	+	0.512915i
$220$	1.34122e8	+	7.74351e7i	0.0572543	+	0.0330558i
$221$	5.78904e7	−	1.00269e8i	0.0242682	−	0.0420337i
$222$	−6.84106e8	+	3.94969e8i	−0.281651	+	0.162611i
$223$			1.25015e9i			0.505526i	0.967528	+	0.252763i	$0.0813393\pi$
$223$			1.25015e9i			0.505526i	−0.967528	+	0.252763i	$0.918661\pi$
$224$	3.43805e8	−	2.82622e8i	0.136559	−	0.112257i
$225$	−8.41905e8			−0.328498
$226$	7.51005e8	+	1.30078e9i	0.287878	+	0.498620i
$227$	−2.20623e9	−	1.27377e9i	−0.830898	−	0.479719i	0.0232623	−	0.999729i	$-0.492595\pi$
$227$	−2.20623e9	−	1.27377e9i	−0.830898	−	0.479719i	−0.854160	+	0.520010i	$0.825928\pi$
$228$	1.24303e8	−	2.15299e8i	0.0459983	−	0.0796713i
$229$	3.39654e9	−	1.96099e9i	1.23508	−	0.713073i	0.266995	−	0.963698i	$-0.413969\pi$
$229$	3.39654e9	−	1.96099e9i	1.23508	−	0.713073i	0.968084	+	0.250625i	$0.0806360\pi$
$230$			2.60063e7i			0.00929325i
$231$	−1.78044e9	+	2.95441e8i	−0.625286	+	0.103758i
$232$	7.18567e8			0.248036
$233$	−2.63318e9	−	4.56080e9i	−0.893423	−	1.54745i	−0.835745	−	0.549118i	$-0.814964\pi$
$233$	−2.63318e9	−	4.56080e9i	−0.893423	−	1.54745i	−0.0576783	−	0.998335i	$-0.518370\pi$
$234$	−3.50591e8	−	2.02414e8i	−0.116933	−	0.0675113i
$235$	−2.62994e8	+	4.55520e8i	−0.0862333	+	0.149361i
$236$	−6.61077e8	+	3.81673e8i	−0.213110	+	0.123039i
$237$			1.18360e9i			0.375155i
$238$	6.75660e7	−	1.79963e8i	0.0210582	−	0.0560886i
$239$	−1.37382e9			−0.421054			−0.210527	−	0.977588i	$-0.567518\pi$
$239$	−1.37382e9			−0.421054			−0.210527	+	0.977588i	$0.567518\pi$
$240$	2.88379e7	+	4.99487e7i	0.00869198	+	0.0150549i
$241$	−7.07581e7	−	4.08522e7i	−0.0209753	−	0.0121101i	0.489476	−	0.872017i	$-0.337188\pi$
$241$	−7.07581e7	−	4.08522e7i	−0.0209753	−	0.0121101i	−0.510451	+	0.859907i	$0.670522\pi$
$242$	2.48881e8	−	4.31074e8i	0.0725655	−	0.125687i
$243$	−1.93710e8	+	1.11839e8i	−0.0555556	+	0.0320750i
$244$			3.23131e9i			0.911631i
$245$	−4.25743e8	−	8.39652e7i	−0.118163	−	0.0233042i
$246$	−2.01263e8			−0.0549572
$247$	−3.39752e8	−	5.88469e8i	−0.0912798	−	0.158101i
$248$	3.38320e8	+	1.95329e8i	0.0894378	+	0.0516370i
$249$	−5.28910e8	+	9.16099e8i	−0.137589	+	0.238311i
$250$	5.72023e8	−	3.30258e8i	0.146438	−	0.0845460i
$251$			3.09159e9i			0.778909i	0.921046	+	0.389455i	$0.127336\pi$
$251$			3.09159e9i			0.778909i	−0.921046	+	0.389455i	$0.872664\pi$
$252$	−6.29240e8	−	2.36244e8i	−0.156032	−	0.0585813i
$253$	4.90833e8			0.119798
$254$	−4.06135e8	−	7.03446e8i	−0.0975743	−	0.169004i
$255$	2.15737e7	+	1.24556e7i	0.00510228	+	0.00294580i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−1.11959e9	+	6.46393e8i	−0.256640	+	0.148171i	−0.622801	−	0.782380i	$-0.714005\pi$
$257$	−1.11959e9	+	6.46393e8i	−0.256640	+	0.148171i	0.366161	+	0.930552i	$0.380672\pi$
$258$			1.96127e9i			0.442649i
$259$	5.86814e8	+	3.53637e9i	0.130407	+	0.785883i
$260$	1.57643e8			0.0344971
$261$	−5.42589e8	−	9.39792e8i	−0.116925	−	0.202521i
$262$	−8.95973e8	−	5.17290e8i	−0.190147	−	0.109781i
$263$	−2.48111e9	+	4.29741e9i	−0.518589	+	0.898222i	0.481178	+	0.876623i	$0.340209\pi$
$263$	−2.48111e9	+	4.29741e9i	−0.518589	+	0.898222i	−0.999767	+	0.0215992i	$0.993124\pi$
$264$	9.42711e8	−	5.44274e8i	0.194072	−	0.112048i
$265$			4.06144e8i			0.0823562i
$266$	−7.16412e8	−	8.71502e8i	−0.143099	−	0.174077i
$267$	−5.42212e9			−1.06690
$268$	2.02185e9	+	3.50194e9i	0.391930	+	0.678843i
$269$	5.87633e9	+	3.39270e9i	1.12227	+	0.647943i	0.941979	−	0.335670i	$-0.108963\pi$
$269$	5.87633e9	+	3.39270e9i	1.12227	+	0.647943i	0.180291	+	0.983613i	$0.442296\pi$
$270$	4.35509e7	−	7.54324e7i	0.00819488	−	0.0141939i
$271$	−2.70650e9	+	1.56260e9i	−0.501801	+	0.289715i	−0.729457	−	0.684027i	$-0.760227\pi$
$271$	−2.70650e9	+	1.56260e9i	−0.501801	+	0.289715i	0.227656	+	0.973742i	$0.426894\pi$
$272$			1.15942e8i			0.0211819i
$273$	−1.41915e9	+	1.16660e9i	−0.255492	+	0.210025i
$274$	5.94356e9			1.05449
$275$	−3.09380e9	−	5.35863e9i	−0.540956	−	0.936963i
$276$	1.58303e8	+	9.13964e7i	0.0272806	+	0.0157504i
$277$	9.68598e8	−	1.67766e9i	0.164522	−	0.284961i	−0.771963	−	0.635667i	$-0.780725\pi$
$277$	9.68598e8	−	1.67766e9i	0.164522	−	0.284961i	0.936485	+	0.350706i	$0.114058\pi$
$278$	−6.00389e9	+	3.46635e9i	−1.00520	+	0.580354i
$279$		−	5.89972e8i		−	0.0973676i
$280$	2.58201e8	−	4.28451e7i	0.0420074	−	0.00697059i
$281$	−1.98235e9			−0.317947			−0.158973	−	0.987283i	$-0.550818\pi$
$281$	−1.98235e9			−0.317947			−0.158973	+	0.987283i	$0.550818\pi$
$282$	1.84853e9	+	3.20175e9i	0.292301	+	0.506280i
$283$	2.93982e8	+	1.69731e8i	0.0458327	+	0.0264615i	0.522741	−	0.852491i	$-0.324909\pi$
$283$	2.93982e8	+	1.69731e8i	0.0458327	+	0.0264615i	−0.476909	+	0.878953i	$0.658243\pi$
$284$	1.39584e9	−	2.41767e9i	0.214567	−	0.371641i
$285$	1.26614e8	−	7.31005e7i	0.0191912	−	0.0110800i
$286$		−	2.97529e9i		−	0.444698i
$287$	−3.21025e8	+	8.55052e8i	−0.0473163	+	0.126027i
$288$	4.05391e8			0.0589256
$289$	−3.46284e9	−	5.99781e9i	−0.496411	−	0.859808i
$290$	3.65963e8	+	2.11289e8i	0.0517422	+	0.0298734i
$291$	−7.99421e8	+	1.38464e9i	−0.111482	+	0.193092i
$292$	−3.22929e9	+	1.86443e9i	−0.444197	+	0.256457i
$293$			5.64108e9i			0.765406i	0.923871	+	0.382703i	$0.125007\pi$
$293$			5.64108e9i			0.765406i	−0.923871	+	0.382703i	$0.874993\pi$
$294$	−2.00733e9	+	2.29646e9i	−0.268677	+	0.307375i
$295$	−4.48912e8			−0.0592752
$296$	−1.08106e9	−	1.87244e9i	−0.140826	−	0.243917i
$297$	−1.42368e9	−	8.21962e8i	−0.182973	−	0.105639i
$298$	3.25968e9	−	5.64593e9i	0.413342	−	0.715930i
$299$	4.32685e8	−	2.49811e8i	0.0541361	−	0.0312555i
$300$		−	2.30435e9i		−	0.284488i
$301$	8.33232e9	+	3.12832e9i	1.01508	+	0.381106i
$302$	−6.01089e9			−0.722622
$303$	−1.49422e9	−	2.58806e9i	−0.177273	−	0.307046i
$304$	5.89287e8	+	3.40225e8i	0.0689974	+	0.0398357i
$305$	−9.50140e8	+	1.64569e9i	−0.109796	+	0.190173i
$306$	1.51637e8	−	8.75476e7i	0.0172949	−	0.00998524i
$307$		−	8.54835e9i		−	0.962340i	−0.876627	−	0.481170i	$-0.840212\pi$
$307$		−	8.54835e9i		−	0.962340i	0.876627	−	0.481170i	$-0.159788\pi$
$308$	−8.08641e8	−	4.87318e9i	−0.0898572	−	0.541514i
$309$	3.43690e9			0.376993
$310$	1.14870e8	+	1.98961e8i	0.0124383	+	0.0215437i
$311$	1.29373e10	+	7.46938e9i	1.38294	+	0.798441i	0.992507	−	0.122190i	$-0.0389919\pi$
$311$	1.29373e10	+	7.46938e9i	1.38294	+	0.798441i	0.390433	+	0.920631i	$0.372325\pi$
$312$	5.54020e8	−	9.59591e8i	0.0584665	−	0.101267i
$313$	8.96920e9	−	5.17837e9i	0.934494	−	0.539530i	0.0462639	−	0.998929i	$-0.485268\pi$
$313$	8.96920e9	−	5.17837e9i	0.934494	−	0.539530i	0.888230	+	0.459399i	$0.151935\pi$
$314$		−	3.62185e9i		−	0.372574i
$315$	−2.51003e8	−	3.05341e8i	−0.0254939	−	0.0310129i
$316$	−3.23959e9			−0.324894
$317$	−2.16403e9	−	3.74821e9i	−0.214302	−	0.371182i	0.738754	−	0.673975i	$-0.235414\pi$
$317$	−2.16403e9	−	3.74821e9i	−0.214302	−	0.371182i	−0.953057	+	0.302792i	$0.902081\pi$
$318$	2.47224e9	+	1.42735e9i	0.241759	+	0.139579i
$319$	3.98778e9	−	6.90703e9i	0.385095	−	0.667004i
$320$	−1.36713e8	+	7.89313e7i	−0.0130380	+	0.00752747i
$321$		−	1.13615e10i		−	1.07008i
$322$	6.40792e8	−	5.26758e8i	0.0596065	−	0.0489990i
$323$	2.93898e8			0.0270014
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	−5.45458e9	−	3.14920e9i	−0.488908	−	0.282271i
$326$	2.74989e9	−	4.76294e9i	0.243469	−	0.421701i
$327$	8.58907e9	−	4.95890e9i	0.751199	−	0.433705i
$328$		−	5.50872e8i		−	0.0475943i
$329$	1.65509e10	−	2.74640e9i	1.41266	−	0.234413i
$330$	6.40158e8			0.0539798
$331$	4.75966e9	+	8.24398e9i	0.396519	+	0.686791i	0.993294	−	0.115618i	$-0.0368847\pi$
$331$	4.75966e9	+	8.24398e9i	0.396519	+	0.686791i	−0.596775	+	0.802409i	$0.703551\pi$
$332$	−2.50743e9	−	1.44766e9i	−0.206384	−	0.119156i
$333$	−1.63261e9	+	2.82776e9i	−0.132772	+	0.229967i
$334$	−1.18319e10	+	6.83113e9i	−0.950752	+	0.548917i
$335$			2.37803e9i			0.188816i
$336$	6.46617e8	−	1.72227e9i	0.0507329	−	0.135128i
$337$	−1.32861e10			−1.03010			−0.515050	−	0.857160i	$-0.672227\pi$
$337$	−1.32861e10			−1.03010			−0.515050	+	0.857160i	$0.672227\pi$
$338$	3.10019e9	+	5.36968e9i	0.237531	+	0.411416i
$339$	5.37679e9	+	3.10429e9i	0.407122	+	0.235052i
$340$	−3.40918e7	+	5.90487e7i	−0.00255114	+	0.00441870i
$341$	3.75510e9	−	2.16801e9i	0.277718	−	0.160341i
$342$		−	1.02761e9i		−	0.0751148i
$343$	6.55453e9	+	1.21910e10i	0.473549	+	0.880767i
$344$	−5.36814e9			−0.383345
$345$	5.37488e7	+	9.30956e7i	0.00379395	+	0.00657132i
$346$	6.27622e9	+	3.62358e9i	0.437919	+	0.252833i
$347$	−4.79747e9	+	8.30945e9i	−0.330898	+	0.573132i	−0.982688	−	0.185267i	$-0.940685\pi$
$347$	−4.79747e9	+	8.30945e9i	−0.330898	+	0.573132i	0.651790	+	0.758399i	$0.274018\pi$
$348$	2.57227e9	−	1.48510e9i	0.175388	−	0.101260i
$349$		−	9.98908e8i		−	0.0673323i	−0.999433	−	0.0336662i	$-0.989282\pi$
$349$		−	9.98908e8i		−	0.0673323i	0.999433	−	0.0336662i	$-0.0107183\pi$
$350$	−9.78986e9	−	3.67555e9i	−0.652385	−	0.244934i
$351$	−1.67336e9			−0.110245
$352$	1.48972e9	+	2.58026e9i	0.0970360	+	0.168071i
$353$	1.38155e10	+	7.97640e9i	0.889752	+	0.513699i	0.873861	−	0.486175i	$-0.161608\pi$
$353$	1.38155e10	+	7.97640e9i	0.889752	+	0.513699i	0.0158906	+	0.999874i	$0.494942\pi$
$354$	−1.57765e9	+	2.73257e9i	−0.100461	+	0.174004i
$355$	1.42179e9	−	8.20873e8i	0.0895206	−	0.0516847i
$356$		−	1.48407e10i		−	0.923964i
$357$	−1.30071e8	−	7.83860e8i	−0.00800772	−	0.0482576i
$358$	−8.29670e9			−0.505095
$359$	6.19858e9	+	1.07363e10i	0.373176	+	0.646361i	0.990052	−	0.140700i	$-0.0449353\pi$
$359$	6.19858e9	+	1.07363e10i	0.373176	+	0.646361i	−0.616876	+	0.787060i	$0.711602\pi$
$360$	2.06464e8	+	1.19202e8i	0.0122923	+	0.00709697i
$361$	−7.62935e9	+	1.32144e10i	−0.449220	+	0.778072i
$362$	−1.47061e10	+	8.49058e9i	−0.856374	+	0.494428i
$363$		−	2.05751e9i		−	0.118499i
$364$	−3.19306e9	−	3.88430e9i	−0.181887	−	0.221262i
$365$	−2.19289e9			−0.123551
$366$	6.67833e9	+	1.15672e10i	0.372172	+	0.644620i
$367$	−2.55884e10	−	1.47735e10i	−1.41052	−	0.814363i	−0.415081	−	0.909785i	$-0.636247\pi$
$367$	−2.55884e10	−	1.47735e10i	−1.41052	−	0.814363i	−0.995437	+	0.0954220i	$0.969580\pi$
$368$	−2.50158e8	+	4.33287e8i	−0.0136403	+	0.0236257i
$369$	−7.20468e8	+	4.15963e8i	−0.0388606	+	0.0224362i
$370$		−	1.27150e9i		−	0.0678439i
$371$	1.00073e10	−	8.22644e9i	0.528229	−	0.434226i
$372$	1.61479e9			0.0843228
$373$	5.44701e9	+	9.43450e9i	0.281399	+	0.487398i	0.971730	−	0.236096i	$-0.0758681\pi$
$373$	5.44701e9	+	9.43450e9i	0.281399	+	0.487398i	−0.690330	+	0.723494i	$0.742535\pi$
$374$	1.11446e9	+	6.43434e8i	0.0569611	+	0.0328865i
$375$	1.36512e9	−	2.36447e9i	0.0690315	−	0.119566i
$376$	−8.76341e9	+	5.05955e9i	−0.438451	+	0.253140i
$377$		−	8.11836e9i		−	0.401886i
$378$	−2.74077e9	+	4.54795e8i	−0.134247	+	0.0222766i
$379$	−3.22524e10			−1.56316			−0.781582	−	0.623802i	$-0.785587\pi$
$379$	−3.22524e10			−1.56316			−0.781582	+	0.623802i	$0.785587\pi$
$380$	2.00081e8	+	3.46550e8i	0.00959558	+	0.0166200i
$381$	−2.90770e9	−	1.67876e9i	−0.137991	−	0.0796691i
$382$	4.06799e9	−	7.04596e9i	0.191041	−	0.330892i
$383$	6.16368e9	−	3.55860e9i	0.286448	−	0.165381i	−0.349891	−	0.936790i	$-0.613781\pi$
$383$	6.16368e9	−	3.55860e9i	0.286448	−	0.165381i	0.636339	+	0.771410i	$0.280448\pi$
$384$			1.10958e9i			0.0510310i
$385$	1.02108e9	−	2.71966e9i	0.0464748	−	0.123786i
$386$	1.30191e10			0.586449
$387$	4.05347e9	+	7.02082e9i	0.180711	+	0.313000i
$388$	−3.78985e9	−	2.18807e9i	−0.167223	−	0.0965460i
$389$	−4.15223e9	+	7.19187e9i	−0.181335	+	0.314082i	−0.942336	−	0.334670i	$-0.891375\pi$
$389$	−4.15223e9	+	7.19187e9i	−0.181335	+	0.314082i	0.761000	+	0.648752i	$0.224709\pi$
$390$	5.64320e8	−	3.25810e8i	0.0243931	−	0.0140834i
$391$			2.16095e8i			0.00924566i
$392$	−6.28556e9	−	5.49421e9i	−0.266195	−	0.232681i
$393$	−4.27645e9			−0.179272
$394$	1.63939e10	+	2.83950e10i	0.680294	+	1.17830i
$395$	−1.64991e9	−	9.52575e8i	−0.0677753	−	0.0391301i
$396$	2.24977e9	−	3.89671e9i	0.0914864	−	0.158459i
$397$	−3.42200e10	+	1.97569e10i	−1.37758	+	0.795349i	−0.991868	−	0.127269i	$-0.959379\pi$
$397$	−3.42200e10	+	1.97569e10i	−1.37758	+	0.795349i	−0.385716	+	0.922617i	$0.626046\pi$
$398$		−	1.62356e10i		−	0.647046i
$399$	−4.36574e9	−	1.63909e9i	−0.172253	−	0.0646714i
$400$	6.30716e9			0.246374
$401$	2.05921e9	+	3.56665e9i	0.0796384	+	0.137938i	0.903094	−	0.429443i	$-0.141290\pi$
$401$	2.05921e9	+	3.56665e9i	0.0796384	+	0.137938i	−0.823456	+	0.567381i	$0.807957\pi$
$402$	1.44753e10	+	8.35733e9i	0.554273	+	0.320010i
$403$	2.20683e9	−	3.82234e9i	0.0836659	−	0.144914i
$404$	7.08369e9	−	4.08977e9i	0.265910	−	0.153523i
$405$		−	3.60037e8i		−	0.0133822i
$406$	−2.20645e9	−	1.32969e10i	−0.0812064	−	0.489381i
$407$	−2.39978e10			−0.874569
$408$	2.39624e8	+	4.15040e8i	0.00864747	+	0.0149779i
$409$	−3.07436e10	−	1.77498e10i	−1.09866	−	0.634310i	−0.162789	−	0.986661i	$-0.552049\pi$
$409$	−3.07436e10	−	1.77498e10i	−1.09866	−	0.634310i	−0.935868	+	0.352351i	$0.885382\pi$
$410$	1.61979e8	−	2.80557e8i	0.00573224	−	0.00992853i
$411$	2.12763e10	−	1.22839e10i	0.745640	−	0.430495i
$412$			9.40703e9i			0.326485i
$413$	9.09270e9	+	1.10611e10i	0.312531	+	0.380188i
$414$	7.55577e8			0.0257204
$415$	−8.51347e8	−	1.47458e9i	−0.0287021	−	0.0497136i
$416$	2.62647e9	+	1.51639e9i	0.0876998	+	0.0506335i
$417$	−1.43282e10	+	2.48172e10i	−0.473857	+	0.820745i
$418$	6.54065e9	−	3.77624e9i	0.214247	−	0.123696i
$419$		−	5.26489e10i		−	1.70818i	−0.520126	−	0.854090i	$-0.674115\pi$
$419$		−	5.26489e10i		−	1.70818i	0.520126	−	0.854090i	$-0.325885\pi$
$420$	8.35739e8	−	6.87013e8i	0.0268580	−	0.0220784i
$421$	−4.94567e10			−1.57433			−0.787166	−	0.616741i	$-0.788453\pi$
$421$	−4.94567e10			−1.57433			−0.787166	+	0.616741i	$0.788453\pi$
$422$	1.05160e10	+	1.82143e10i	0.331590	+	0.574331i
$423$	1.32345e10	+	7.64093e9i	0.413376	+	0.238663i
$424$	−3.90675e9	+	6.76669e9i	−0.120879	+	0.209369i
$425$	2.35920e9	−	1.36209e9i	0.0723118	−	0.0417493i
$426$		−	1.15395e10i		−	0.350387i
$427$	5.97946e10	−	9.92214e9i	1.79867	−	0.298465i
$428$	3.10972e10			0.926716
$429$	−6.14921e9	−	1.06507e10i	−0.181547	−	0.314449i
$430$	−2.73397e9	−	1.57846e9i	−0.0799687	−	0.0461699i
$431$	−2.13099e10	+	3.69098e10i	−0.617550	+	1.06963i	0.372382	+	0.928080i	$0.378541\pi$
$431$	−2.13099e10	+	3.69098e10i	−0.617550	+	1.06963i	−0.989931	+	0.141548i	$0.954792\pi$
$432$	1.45119e9	−	8.37844e8i	0.0416667	−	0.0240563i
$433$			5.73277e10i			1.63085i	0.578865	+	0.815423i	$0.303496\pi$
$433$			5.73277e10i			1.63085i	−0.578865	+	0.815423i	$0.696504\pi$
$434$	2.57567e9	−	6.86033e9i	0.0725991	−	0.193369i
$435$	1.74673e9			0.0487830
$436$	1.35729e10	+	2.35089e10i	0.375600	+	0.650558i
$437$	1.09833e9	+	6.34120e8i	0.0301166	+	0.0173878i
$438$	−7.70666e9	+	1.33483e10i	−0.209397	+	0.362686i
$439$	5.66015e10	−	3.26789e10i	1.52395	−	0.879852i	0.524350	−	0.851503i	$-0.324308\pi$
$439$	5.66015e10	−	3.26789e10i	1.52395	−	0.879852i	0.999598	−	0.0283492i	$-0.00902505\pi$
$440$			1.75216e9i			0.0467479i
$441$	−2.43949e9	+	1.23694e10i	−0.0644977	+	0.327034i
$442$	1.30991e9			0.0343204
$443$	−1.45224e10	−	2.51536e10i	−0.377072	−	0.653108i	0.613563	−	0.789646i	$-0.289736\pi$
$443$	−1.45224e10	−	2.51536e10i	−0.377072	−	0.653108i	−0.990635	+	0.136538i	$0.956402\pi$
$444$	−7.73977e9	−	4.46856e9i	−0.199157	−	0.114984i
$445$	4.36380e9	−	7.55832e9i	0.111282	−	0.192746i
$446$	−1.22489e10	+	7.07193e9i	−0.309570	+	0.178731i
$447$		−	2.69478e10i		−	0.674985i
$448$	4.71397e9	+	1.76983e9i	0.117024	+	0.0439360i
$449$	1.21838e10			0.299775			0.149888	−	0.988703i	$-0.452109\pi$
$449$	1.21838e10			0.299775			0.149888	+	0.988703i	$0.452109\pi$
$450$	−4.76253e9	−	8.24895e9i	−0.116142	−	0.201163i
$451$	−5.29511e9	−	3.05713e9i	−0.127988	−	0.0738938i
$452$	−8.49665e9	+	1.47166e10i	−0.203561	+	0.352578i
$453$	−2.15174e10	+	1.24231e10i	−0.510971	+	0.295009i
$454$		−	2.88221e10i		−	0.678425i
$455$	−4.84064e8	−	2.91715e9i	−0.0112942	−	0.0680634i
$456$	2.81265e9			0.0650514
$457$	3.10193e9	+	5.37270e9i	0.0711160	+	0.123177i	0.899391	−	0.437146i	$-0.144011\pi$
$457$	3.10193e9	+	5.37270e9i	0.0711160	+	0.123177i	−0.828275	+	0.560322i	$0.810677\pi$
$458$	3.84275e10	+	2.21861e10i	0.873333	+	0.504219i
$459$	3.61879e8	−	6.26793e8i	0.00815291	−	0.0141213i
$460$	−2.54809e8	+	1.47114e8i	−0.00569093	+	0.00328566i
$461$		−	3.27410e10i		−	0.724916i	−0.932000	−	0.362458i	$-0.881938\pi$
$461$		−	3.27410e10i		−	0.724916i	0.932000	−	0.362458i	$-0.118062\pi$
$462$	−1.29664e10	−	1.57734e10i	−0.284611	−	0.346224i
$463$	6.85044e10			1.49071			0.745357	−	0.666665i	$-0.232279\pi$
$463$	6.85044e10			1.49071			0.745357	+	0.666665i	$0.232279\pi$
$464$	4.06483e9	+	7.04049e9i	0.0876941	+	0.151891i
$465$	8.22407e8	+	4.74817e8i	0.0175904	+	0.0101558i
$466$	2.97910e10	−	5.15996e10i	0.631745	−	1.09422i
$467$	4.41905e10	−	2.55134e10i	0.929098	−	0.536415i	0.0425720	−	0.999093i	$-0.486445\pi$
$467$	4.41905e10	−	2.55134e10i	0.929098	−	0.536415i	0.886526	+	0.462678i	$0.153111\pi$
$468$		−	4.58010e9i		−	0.0954754i
$469$	5.85943e10	−	4.81670e10i	1.21105	−	0.995538i
$470$	−5.95089e9			−0.121952
$471$	−7.48549e9	−	1.29652e10i	−0.152103	−	0.263449i
$472$	−7.47924e9	−	4.31814e9i	−0.150692	−	0.0870019i
$473$	−2.97912e10	+	5.15998e10i	−0.595172	+	1.03087i
$474$	−1.15969e10	+	6.69545e9i	−0.229735	+	0.132637i
$475$		−	1.59879e10i		−	0.314063i
$476$	2.14548e9	−	3.56014e8i	0.0417923	−	0.00693489i
$477$	1.17999e10			0.227932
$478$	−7.77149e9	−	1.34606e10i	−0.148865	−	0.257842i
$479$	−5.78542e10	−	3.34021e10i	−1.09899	−	0.634500i	−0.163032	−	0.986621i	$-0.552127\pi$
$479$	−5.78542e10	−	3.34021e10i	−1.09899	−	0.634500i	−0.935955	+	0.352120i	$0.885461\pi$
$480$	−3.26264e8	+	5.65105e8i	−0.00614616	+	0.0106455i
$481$	−2.11549e10	+	1.22138e10i	−0.395212	+	0.228176i
$482$		−	9.24380e8i		−	0.0171263i
$483$	1.20518e9	−	3.21001e9i	0.0221444	−	0.0589818i
$484$	5.63153e9			0.102623
$485$	−1.28677e9	−	2.22875e9i	−0.0232559	−	0.0402804i
$486$	−2.19158e9	−	1.26531e9i	−0.0392837	−	0.0226805i
$487$	2.04410e10	−	3.54048e10i	0.363401	−	0.629429i	−0.625117	−	0.780531i	$-0.714949\pi$
$487$	2.04410e10	−	3.54048e10i	0.363401	−	0.629429i	0.988518	+	0.151102i	$0.0482822\pi$
$488$	−3.16602e10	+	1.82790e10i	−0.558257	+	0.322310i
$489$		−	2.27334e10i		−	0.397584i
$490$	−1.58568e9	−	4.64639e9i	−0.0275062	−	0.0805994i
$491$	−6.76575e10			−1.16410			−0.582050	−	0.813153i	$-0.697749\pi$
$491$	−6.76575e10			−1.16410			−0.582050	+	0.813153i	$0.697749\pi$
$492$	−1.13852e9	−	1.97197e9i	−0.0194303	−	0.0336543i
$493$	3.04091e9	+	1.75567e9i	0.0514773	+	0.0297204i
$494$	3.84386e9	−	6.65776e9i	0.0645446	−	0.111794i
$495$	2.29159e9	−	1.32305e9i	0.0381695	−	0.0220372i
$496$			4.41980e9i			0.0730257i
$497$	−4.90246e10	−	1.84060e10i	−0.803504	−	0.301671i
$498$	−1.19679e10			−0.194581
$499$	−5.07579e9	−	8.79152e9i	−0.0818656	−	0.141795i	0.822186	−	0.569219i	$-0.192754\pi$
$499$	−5.07579e9	−	8.79152e9i	−0.0818656	−	0.141795i	−0.904051	+	0.427424i	$0.859421\pi$
$500$	6.47170e9	+	3.73644e9i	0.103547	+	0.0597830i
$501$	−2.82366e10	+	4.89072e10i	−0.448189	+	0.776286i
$502$	−3.02913e10	+	1.74887e10i	−0.476982	+	0.275386i
$503$			9.70483e10i			1.51606i	0.652220	+	0.758030i	$0.273838\pi$
$503$			9.70483e10i			1.51606i	−0.652220	+	0.758030i	$0.726162\pi$
$504$	−1.24480e9	−	7.50166e9i	−0.0192921	−	0.116261i
$505$	4.81025e9			0.0739610
$506$	2.77657e9	+	4.80916e9i	0.0423552	+	0.0733613i
$507$	2.21956e10	+	1.28147e10i	0.335920	+	0.193944i
$508$	4.59489e9	−	7.95858e9i	0.0689954	−	0.119504i
$509$	1.66528e10	−	9.61450e9i	0.248094	−	0.143237i	−0.370797	−	0.928714i	$-0.620916\pi$
$509$	1.66528e10	−	9.61450e9i	0.248094	−	0.143237i	0.618891	+	0.785477i	$0.287582\pi$
$510$			2.81838e8i			0.00416599i
$511$	4.44169e10	+	5.40324e10i	0.651425	+	0.792447i
$512$	−3.03700e9			−0.0441942
$513$	−2.12383e9	−	3.67858e9i	−0.0306655	−	0.0531142i
$514$	−1.26667e10	−	7.31310e9i	−0.181472	−	0.104773i
$515$	−2.76606e9	+	4.79096e9i	−0.0393218	+	0.0681073i
$516$	−1.92165e10	+	1.10946e10i	−0.271066	+	0.156500i
$517$			1.12315e11i			1.57208i
$518$	−3.13296e10	+	2.57543e10i	−0.435147	+	0.357709i
$519$	2.99562e10			0.412874
$520$	8.91765e8	+	1.54458e9i	0.0121966	+	0.0211250i
$521$	7.54500e10	+	4.35611e10i	1.02402	+	0.591218i	0.915266	−	0.402851i	$-0.131981\pi$
$521$	7.54500e10	+	4.35611e10i	1.02402	+	0.591218i	0.108754	+	0.994069i	$0.465314\pi$
$522$	6.13869e9	−	1.06325e10i	0.0826788	−	0.143204i
$523$	−3.03278e10	+	1.75098e10i	−0.405354	+	0.234031i	−0.688792	−	0.724959i	$-0.741858\pi$
$523$	−3.03278e10	+	1.75098e10i	−0.405354	+	0.234031i	0.283437	+	0.958991i	$0.408525\pi$
$524$		−	1.17049e10i		−	0.155254i
$525$	−4.26415e10	+	7.07580e9i	−0.561300	+	0.0931405i
$526$	−5.61411e10			−0.733395
$527$	9.54493e8	+	1.65323e9i	0.0123746	+	0.0214334i
$528$	1.06656e10	+	6.15776e9i	0.137230	+	0.0792296i
$529$	3.86892e10	−	6.70117e10i	0.494046	−	0.855713i
$530$	−3.97938e9	+	2.29750e9i	−0.0504327	+	0.0291173i
$531$			1.30425e10i			0.164052i
$532$	4.48631e9	−	1.19493e10i	0.0560070	−	0.149175i
$533$	−6.22374e9			−0.0771157
$534$	−3.06722e10	−	5.31258e10i	−0.377207	−	0.653341i
$535$	1.58377e10	+	9.14390e9i	0.193320	+	0.111613i
$536$	−2.28746e10	+	3.96199e10i	−0.277137	+	0.480015i
$537$	−2.96999e10	+	1.71473e10i	−0.357156	+	0.206204i
$538$			7.67681e10i			0.916330i
$539$	−8.76941e10	+	2.99274e10i	−1.03900	+	0.354580i
$540$	9.85445e8			0.0115893
$541$	−1.96007e10	−	3.39494e10i	−0.228814	−	0.396317i	0.728643	−	0.684894i	$-0.240151\pi$
$541$	−1.96007e10	−	3.39494e10i	−0.228814	−	0.396317i	−0.957457	+	0.288576i	$0.906818\pi$
$542$	−3.06206e10	−	1.76788e10i	−0.354827	−	0.204859i
$543$	−3.50959e10	+	6.07879e10i	−0.403699	+	0.699227i
$544$	−1.13599e9	+	6.55866e8i	−0.0129712	+	0.00748893i
$545$			1.59640e10i			0.180948i
$546$	−1.94582e10	−	7.30547e9i	−0.218944	−	0.0822011i
$547$	5.28053e10			0.589832			0.294916	−	0.955523i	$-0.404708\pi$
$547$	5.28053e10			0.589832			0.294916	+	0.955523i	$0.404708\pi$
$548$	3.36218e10	+	5.82347e10i	0.372820	+	0.645743i
$549$	4.78132e10	+	2.76050e10i	0.526330	+	0.303877i
$550$	3.50024e10	−	6.06259e10i	0.382514	−	0.662533i
$551$	1.78468e10	−	1.03038e10i	0.193621	−	0.111787i
$552$			2.06806e9i			0.0222745i
$553$	9.94757e9	+	5.99479e10i	0.106369	+	0.641023i
$554$	2.19169e10			0.232669
$555$	−2.62789e9	−	4.55164e9i	−0.0276971	−	0.0479729i
$556$	−6.79263e10	−	3.92173e10i	−0.710786	−	0.410372i
$557$	3.71900e10	−	6.44150e10i	0.386372	−	0.669216i	−0.605586	−	0.795780i	$-0.707061\pi$
$557$	3.71900e10	−	6.44150e10i	0.386372	−	0.669216i	0.991959	+	0.126563i	$0.0403947\pi$
$558$	5.78052e9	−	3.33738e9i	0.0596252	−	0.0344246i
$559$			6.06492e10i			0.621123i
$560$	1.88040e9	+	2.28748e9i	0.0191205	+	0.0232597i
$561$	5.31929e9			0.0537034
$562$	−1.12138e10	−	1.94229e10i	−0.112411	−	0.194702i
$563$	−1.61996e10	−	9.35287e9i	−0.161240	−	0.0930918i	0.417209	−	0.908811i	$-0.363008\pi$
$563$	−1.61996e10	−	9.35287e9i	−0.161240	−	0.0930918i	−0.578449	+	0.815719i	$0.696342\pi$
$564$	−2.09137e10	+	3.62237e10i	−0.206688	+	0.357994i
$565$	−8.65462e9	+	4.99674e9i	−0.0849286	+	0.0490336i
$566$			3.84057e9i			0.0374222i
$567$	−8.87125e9	+	7.29254e9i	−0.0858326	+	0.0705580i
$568$	3.15843e10			0.303444
$569$	−8.79917e10	−	1.52406e11i	−0.839446	−	1.45396i	−0.890359	−	0.455259i	$-0.849547\pi$
$569$	−8.79917e10	−	1.52406e11i	−0.839446	−	1.45396i	0.0509133	−	0.998703i	$-0.483787\pi$
$570$	1.43247e9	+	8.27037e8i	0.0135702	+	0.00783476i
$571$	5.89987e10	−	1.02189e11i	0.555006	−	0.961299i	−0.442897	−	0.896573i	$-0.646049\pi$
$571$	5.89987e10	−	1.02189e11i	0.555006	−	0.961299i	0.997903	−	0.0647264i	$-0.0206175\pi$
$572$	2.91518e10	−	1.68308e10i	0.272321	−	0.157225i
$573$		−	3.36302e10i		−	0.311968i
$574$	−1.01938e10	+	1.69152e9i	−0.0939046	+	0.0155822i
$575$	1.17554e10			0.107539
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	−1.04820e10	−	6.05177e9i	−0.0945671	−	0.0545983i	0.451971	−	0.892033i	$-0.350721\pi$
$577$	−1.04820e10	−	6.05177e9i	−0.0945671	−	0.0545983i	−0.546538	+	0.837434i	$0.684055\pi$
$578$	3.91776e10	−	6.78575e10i	0.351015	−	0.607976i
$579$	4.66047e10	−	2.69072e10i	0.414682	−	0.239417i
$580$			4.78092e9i			0.0422473i
$581$	−1.90893e10	+	5.08446e10i	−0.167527	+	0.446211i
$582$	−1.80888e10			−0.157659
$583$	4.33620e10	+	7.51052e10i	0.375349	+	0.650123i
$584$	−3.65353e10	−	2.10937e10i	−0.314095	−	0.181343i
$585$	1.34674e9	−	2.33262e9i	0.0114990	−	0.0199169i
$586$	−5.52711e10	+	3.19108e10i	−0.468713	+	0.270612i
$587$		−	2.26097e11i		−	1.90433i	−0.305585	−	0.952165i	$-0.598852\pi$
$587$		−	2.26097e11i		−	1.90433i	0.305585	−	0.952165i	$-0.401148\pi$
$588$	−3.38558e10	−	6.67705e9i	−0.283220	−	0.0558567i
$589$	1.12036e10			0.0930889
$590$	−2.53943e9	−	4.39842e9i	−0.0209569	−	0.0362985i
$591$	1.17371e11	+	6.77643e10i	0.962080	+	0.555457i
$592$	1.22308e10	−	2.11843e10i	0.0995787	−	0.172475i
$593$	1.46704e11	−	8.46998e10i	1.18638	−	0.684957i	0.228899	−	0.973450i	$-0.426488\pi$
$593$	1.46704e11	−	8.46998e10i	1.18638	−	0.684957i	0.957482	+	0.288493i	$0.0931542\pi$
$594$		−	1.85989e10i		−	0.149397i
$595$	1.19737e9	+	4.49544e8i	0.00955343	+	0.00358678i
$596$	7.37581e10			0.584554
$597$	−3.35550e10	−	5.81189e10i	−0.264155	−	0.457530i
$598$	4.89527e9	+	2.82628e9i	0.0382800	+	0.0221010i
$599$	3.81603e10	−	6.60957e10i	0.296418	−	0.513412i	−0.678896	−	0.734235i	$-0.737541\pi$
$599$	3.81603e10	−	6.60957e10i	0.296418	−	0.513412i	0.975314	+	0.220823i	$0.0708744\pi$
$600$	2.25779e10	−	1.30354e10i	0.174212	−	0.100582i
$601$			1.01542e11i			0.778300i	0.921174	+	0.389150i	$0.127231\pi$
$601$			1.01542e11i			0.778300i	−0.921174	+	0.389150i	$0.872769\pi$
$602$	1.64836e10	+	9.93362e10i	0.125506	+	0.756348i
$603$	6.90903e10			0.522574
$604$	−3.40028e10	−	5.88945e10i	−0.255486	−	0.442514i
$605$	2.86811e9	+	1.65591e9i	0.0214079	+	0.0123599i
$606$	1.69051e10	−	2.92805e10i	0.125351	−	0.217114i
$607$	−1.46253e11	+	8.44391e10i	−1.07733	+	0.621998i	−0.930175	−	0.367116i	$-0.880345\pi$
$607$	−1.46253e11	+	8.44391e10i	−1.07733	+	0.621998i	−0.147156	+	0.989113i	$0.547012\pi$
$608$			7.69842e9i			0.0563361i
$609$	−3.53800e10	−	4.30392e10i	−0.257210	−	0.312892i
$610$	−2.14992e10			−0.155276
$611$	5.71628e10	+	9.90089e10i	0.410156	+	0.710410i
$612$	1.71558e9	+	9.90488e8i	0.0122294	+	0.00706063i
$613$	4.74945e10	−	8.22628e10i	0.336357	−	0.582588i	−0.647387	−	0.762161i	$-0.724138\pi$
$613$	4.74945e10	−	8.22628e10i	0.336357	−	0.582588i	0.983745	+	0.179573i	$0.0574717\pi$
$614$	8.37563e10	−	4.83567e10i	0.589311	−	0.340239i
$615$		−	1.33909e9i		−	0.00936071i
$616$	4.31729e10	−	3.54899e10i	0.299839	−	0.246480i
$617$	2.23569e11			1.54267			0.771333	−	0.636432i	$-0.219590\pi$
$617$	2.23569e11			1.54267			0.771333	+	0.636432i	$0.219590\pi$
$618$	1.94421e10	+	3.36746e10i	0.133287	+	0.230860i
$619$	−2.37043e11	−	1.36857e11i	−1.61460	−	0.932189i	−0.988285	−	0.152617i	$-0.951230\pi$
$619$	−2.37043e11	−	1.36857e11i	−1.61460	−	0.932189i	−0.626313	−	0.779572i	$-0.715437\pi$
$620$	−1.29961e9	+	2.25098e9i	−0.00879519	+	0.0152337i
$621$	2.70476e9	−	1.56159e9i	0.0181870	−	0.0105003i
$622$			1.69013e11i			1.12917i
$623$	−2.74624e11	+	4.55703e10i	−1.82300	+	0.302503i
$624$	1.25360e10			0.0826841
$625$	−7.29899e10	−	1.26422e11i	−0.478347	−	0.828521i
$626$	1.01475e11	+	5.85866e10i	0.660787	+	0.381506i
$627$	1.56092e10	−	2.70359e10i	0.100997	−	0.174932i
$628$	3.54868e10	−	2.04883e10i	0.228154	−	0.131725i
$629$		−	1.05653e10i		−	0.0674965i
$630$	1.57183e9	−	4.18659e9i	0.00997800	−	0.0265765i
$631$	8.05763e8			0.00508265			0.00254132	−	0.999997i	$-0.499191\pi$
$631$	8.05763e8			0.00508265			0.00254132	+	0.999997i	$0.499191\pi$
$632$	−1.83259e10	−	3.17414e10i	−0.114867	−	0.198956i
$633$	7.52890e10	+	4.34681e10i	0.468939	+	0.270742i
$634$	2.44832e10	−	4.24062e10i	0.151535	−	0.262466i
$635$	4.68032e9	−	2.70218e9i	0.0287859	−	0.0166196i
$636$			3.22972e10i			0.197395i
$637$	−6.20735e10	+	7.10141e10i	−0.377006	+	0.431308i
$638$	9.02331e10			0.544607
$639$	−2.38493e10	−	4.13082e10i	−0.143045	−	0.247761i
$640$	−1.54673e9	−	8.93006e8i	−0.00921924	−	0.00532273i
$641$	2.55067e10	−	4.41790e10i	0.151086	−	0.261688i	−0.780541	−	0.625104i	$-0.785056\pi$
$641$	2.55067e10	−	4.41790e10i	0.151086	−	0.261688i	0.931627	+	0.363416i	$0.118390\pi$
$642$	1.11320e11	−	6.42705e10i	0.655287	−	0.378330i
$643$			4.90913e10i			0.287184i	0.989637	+	0.143592i	$0.0458654\pi$
$643$			4.90913e10i			0.287184i	−0.989637	+	0.143592i	$0.954135\pi$
$644$	8.78602e9	+	3.29866e9i	0.0510797	+	0.0191776i
$645$	−1.30492e10			−0.0753952
$646$	1.66254e9	+	2.87960e9i	0.00954645	+	0.0165349i
$647$	7.17022e10	+	4.13973e10i	0.409181	+	0.236241i	0.690438	−	0.723392i	$-0.257418\pi$
$647$	7.17022e10	+	4.13973e10i	0.409181	+	0.236241i	−0.281257	+	0.959633i	$0.590751\pi$
$648$	3.46324e9	−	5.99851e9i	0.0196419	−	0.0340207i
$649$	−8.30139e10	+	4.79281e10i	−0.467921	+	0.270154i
$650$		−	7.12583e10i		−	0.399192i
$651$	−4.95843e9	−	2.98814e10i	−0.0276071	−	0.166371i
$652$	6.22228e10			0.344318
$653$	5.30873e10	+	9.19499e10i	0.291970	+	0.505707i	0.974275	−	0.225360i	$-0.0723559\pi$
$653$	5.30873e10	+	9.19499e10i	0.291970	+	0.505707i	−0.682306	+	0.731067i	$0.739023\pi$
$654$	9.71742e10	+	5.61036e10i	0.531178	+	0.306676i
$655$	3.44174e9	−	5.96128e9i	0.0186988	−	0.0323872i
$656$	5.39742e9	−	3.11620e9i	0.0291454	−	0.0168271i
$657$			6.37112e10i			0.341943i
$658$	1.20535e11	+	1.46629e11i	0.642998	+	0.782197i
$659$	−2.86613e11			−1.51969			−0.759844	−	0.650106i	$-0.774724\pi$
$659$	−2.86613e11			−1.51969			−0.759844	+	0.650106i	$0.774724\pi$
$660$	3.62128e9	+	6.27224e9i	0.0190848	+	0.0330558i
$661$	−2.97934e11	−	1.72012e11i	−1.56068	−	0.901060i	−0.997188	−	0.0749405i	$-0.976123\pi$
$661$	−2.97934e11	−	1.72012e11i	−1.56068	−	0.901060i	−0.563494	−	0.826120i	$-0.690543\pi$
$662$	−5.38494e10	+	9.32699e10i	−0.280381	+	0.485635i
$663$	4.68912e9	−	2.70727e9i	0.0242682	−	0.0140112i
$664$		−	3.27569e10i		−	0.168512i
$665$	5.79846e9	−	4.76658e9i	0.0296501	−	0.0243736i
$666$	−3.69417e10			−0.187767
$667$	7.57612e9	+	1.31222e10i	0.0382775	+	0.0662986i
$668$	−1.33862e11	−	7.72854e10i	−0.672283	−	0.388143i
$669$	−2.92319e10	+	5.06312e10i	−0.145933	+	0.252763i
$670$	−2.32998e10	+	1.34522e10i	−0.115626	+	0.0667564i
$671$			4.05767e11i			2.00164i
$672$	2.05326e10	−	3.40711e9i	0.100685	−	0.0167074i
$673$	−2.05021e10			−0.0999397			−0.0499698	−	0.998751i	$-0.515913\pi$
$673$	−2.05021e10			−0.0999397			−0.0499698	+	0.998751i	$0.515913\pi$
$674$	−7.51578e10	−	1.30177e11i	−0.364195	−	0.630805i
$675$	−3.40971e10	−	1.96860e10i	−0.164249	−	0.0948292i
$676$	−3.50746e10	+	6.07510e10i	−0.167960	+	0.290915i
$677$	1.72677e11	−	9.96952e10i	0.822016	−	0.474591i	−0.0290952	−	0.999577i	$-0.509263\pi$
$677$	1.72677e11	−	9.96952e10i	0.822016	−	0.474591i	0.851111	+	0.524986i	$0.175929\pi$
$678$			7.02421e10i			0.332413i
$679$	−2.88525e10	+	7.68490e10i	−0.135739	+	0.361542i
$680$	−7.71409e8			−0.00360785
$681$	−5.95682e10	−	1.03175e11i	−0.276966	−	0.479719i
$682$	4.24841e10	+	2.45282e10i	0.196376	+	0.113378i
$683$	−1.77568e11	+	3.07558e11i	−0.815987	+	1.41333i	0.0926306	+	0.995701i	$0.470472\pi$
$683$	−1.77568e11	+	3.07558e11i	−0.815987	+	1.41333i	−0.908617	+	0.417630i	$0.862861\pi$
$684$	1.00685e10	−	5.81307e9i	0.0459983	−	0.0265571i
$685$			3.95449e10i			0.179609i
$686$	−8.23685e10	+	1.33183e11i	−0.371933	+	0.601387i
$687$	1.83413e11			0.823386
$688$	−3.03668e10	−	5.25968e10i	−0.135533	−	0.234750i
$689$	7.64500e10	+	4.41384e10i	0.339235	+	0.195857i
$690$	−6.08098e8	+	1.05326e9i	−0.00268273	+	0.00464663i
$691$	−7.91689e10	+	4.57082e10i	−0.347250	+	0.200485i	−0.663473	−	0.748200i	$-0.730918\pi$
$691$	−7.91689e10	+	4.57082e10i	−0.347250	+	0.200485i	0.316223	+	0.948685i	$0.397585\pi$
$692$			8.19922e10i			0.357559i
$693$	−7.90159e10	−	2.96661e10i	−0.342596	−	0.128626i
$694$	−1.08554e11			−0.467960
$695$	−2.30630e10	−	3.99464e10i	−0.0988502	−	0.171214i
$696$	2.91020e10	+	1.68020e10i	0.124018	+	0.0716019i
$697$	1.34594e9	−	2.33124e9i	0.00570289	−	0.00987769i
$698$	9.78726e9	−	5.65068e9i	0.0412325	−	0.0238056i
$699$		−	2.46283e11i		−	1.03164i
$700$	−1.93670e10	−	1.16713e11i	−0.0806620	−	0.486100i
$701$	3.17220e11			1.31368			0.656839	−	0.754031i	$-0.271893\pi$
$701$	3.17220e11			1.31368			0.656839	+	0.754031i	$0.271893\pi$
$702$	−9.46595e9	−	1.63955e10i	−0.0389777	−	0.0675113i
$703$	−5.36995e10	−	3.10034e10i	−0.219861	−	0.126937i
$704$	−1.68542e10	+	2.91924e10i	−0.0686148	+	0.118844i
$705$	−2.13026e10	+	1.22990e10i	−0.0862333	+	0.0497868i
$706$			1.80485e11i			0.726479i
$707$	−9.74316e10	−	1.18524e11i	−0.389962	−	0.474382i
$708$	−3.56982e10			−0.142073
$709$	−7.55268e10	−	1.30816e11i	−0.298893	−	0.517698i	0.676990	−	0.735992i	$-0.263284\pi$
$709$	−7.55268e10	−	1.30816e11i	−0.298893	−	0.517698i	−0.975883	+	0.218294i	$0.929951\pi$
$710$	1.60858e10	+	9.28711e9i	0.0633006	+	0.0365466i
$711$	−2.76757e10	+	4.79357e10i	−0.108298	+	0.187578i
$712$	1.45409e11	−	8.39518e10i	0.565810	−	0.326671i
$713$			8.23772e9i			0.0318749i
$714$	6.94443e9	−	5.70862e9i	0.0267205	−	0.0219653i
$715$	1.97958e10			0.0757443
$716$	−4.69332e10	−	8.12907e10i	−0.178578	−	0.309306i
$717$	−5.56397e10	−	3.21236e10i	−0.210527	−	0.121548i
$718$	−7.01289e10	+	1.21467e11i	−0.263876	+	0.457046i
$719$	−1.80260e11	+	1.04073e11i	−0.674504	+	0.389425i	−0.797781	−	0.602947i	$-0.793993\pi$
$719$	−1.80260e11	+	1.04073e11i	−0.674504	+	0.389425i	0.123277	+	0.992372i	$0.460660\pi$
$720$			2.69723e9i			0.0100366i
$721$	1.74075e11	−	2.88855e10i	0.644163	−	0.106890i
$722$	−1.72633e11			−0.635293
$723$	−1.91047e9	−	3.30903e9i	−0.00699176	−	0.0121101i
$724$	−1.66381e11	−	9.60599e10i	−0.605548	−	0.349613i
$725$	9.55072e10	−	1.65423e11i	0.345688	−	0.598749i
$726$	2.01594e10	−	1.16390e10i	0.0725655	−	0.0418957i
$727$			2.53916e11i			0.908977i	0.890753	+	0.454488i	$0.150178\pi$
$727$			2.53916e11i			0.908977i	−0.890753	+	0.454488i	$0.849822\pi$
$728$	1.99956e10	−	5.32584e10i	0.0711883	−	0.189611i
$729$	−1.04604e10			−0.0370370
$730$	−1.24048e10	−	2.14858e10i	−0.0436817	−	0.0756589i
$731$	−2.27175e10	−	1.31159e10i	−0.0795592	−	0.0459335i
$732$	−7.55566e10	+	1.30868e11i	−0.263165	+	0.455815i
$733$	−3.15711e11	+	1.82276e11i	−1.09364	+	0.631413i	−0.934543	−	0.355850i	$-0.884191\pi$
$733$	−3.15711e11	+	1.82276e11i	−1.09364	+	0.631413i	−0.159096	+	0.987263i	$0.550858\pi$
$734$		−	3.34285e11i		−	1.15168i
$735$	−1.52793e10	−	1.33556e10i	−0.0523544	−	0.0457630i
$736$	−5.66043e9			−0.0192903
$737$	2.53891e11	+	4.39751e11i	0.860551	+	1.49052i
$738$	−8.15117e9	−	4.70608e9i	−0.0274786	−	0.0158648i
$739$	2.75075e11	−	4.76444e11i	0.922303	−	1.59748i	0.126461	−	0.991972i	$-0.459638\pi$
$739$	2.75075e11	−	4.76444e11i	0.922303	−	1.59748i	0.795842	−	0.605504i	$-0.207029\pi$
$740$	1.24581e10	−	7.19271e9i	0.0415457	−	0.0239864i
$741$		−	3.17773e10i		−	0.105401i
$742$	1.37212e11	+	5.15156e10i	0.452665	+	0.169951i
$743$	−1.44734e11			−0.474914			−0.237457	−	0.971398i	$-0.576314\pi$
$743$	−1.44734e11			−0.474914			−0.237457	+	0.971398i	$0.576314\pi$
$744$	9.13465e9	+	1.58217e10i	0.0298126	+	0.0516370i
$745$	3.75647e10	+	2.16880e10i	0.121942	+	0.0704034i
$746$	−6.16259e10	+	1.06739e11i	−0.198979	+	0.344642i
$747$	−4.28417e10	+	2.47347e10i	−0.137589	+	0.0794372i
$748$			1.45592e10i			0.0465085i
$749$	−9.54881e10	−	5.75448e11i	−0.303404	−	1.82843i
$750$	3.08893e10			0.0976253
$751$	2.22640e11	+	3.85624e11i	0.699912	+	1.21228i	0.968496	+	0.249028i	$0.0801110\pi$
$751$	2.22640e11	+	3.85624e11i	0.699912	+	1.21228i	−0.268584	+	0.963256i	$0.586556\pi$
$752$	−9.91466e10	−	5.72423e10i	−0.310032	−	0.178997i
$753$	−7.22896e10	+	1.25209e11i	−0.224852	+	0.389455i
$754$	7.95434e10	−	4.59244e10i	0.246104	−	0.142088i
$755$		−	3.99929e10i		−	0.123082i
$756$	−1.99602e10	−	2.42812e10i	−0.0611051	−	0.0743332i
$757$	5.82709e11			1.77447			0.887234	−	0.461320i	$-0.152624\pi$
$757$	5.82709e11			1.77447			0.887234	+	0.461320i	$0.152624\pi$
$758$	−1.82447e11	−	3.16007e11i	−0.552662	−	0.957239i
$759$	1.98787e10	+	1.14770e10i	0.0598992	+	0.0345828i
$760$	−2.26366e9	+	3.92077e9i	−0.00678510	+	0.0117521i
$761$	2.17518e11	−	1.25584e11i	0.648570	−	0.374452i	−0.139338	−	0.990245i	$-0.544498\pi$
$761$	2.17518e11	−	1.25584e11i	0.648570	−	0.374452i	0.787908	+	0.615793i	$0.211164\pi$
$762$		−	3.79861e10i		−	0.112669i
$763$	3.93349e11	−	3.23350e11i	1.16059	−	0.954057i
$764$	9.20481e10			0.270173
$765$	5.82490e8	+	1.00890e9i	0.00170076	+	0.00294580i
$766$	6.97341e10	+	4.02610e10i	0.202549	+	0.116942i
$767$	−4.87863e10	+	8.45003e10i	−0.140967	+	0.244161i
$768$	−1.08716e10	+	6.27674e9i	−0.0312500	+	0.0180422i
$769$		−	3.29216e11i		−	0.941402i	−0.882293	−	0.470701i	$-0.844001\pi$
$769$		−	3.29216e11i		−	0.941402i	0.882293	−	0.470701i	$-0.155999\pi$
$770$	3.24233e10	−	5.38022e9i	0.0922346	−	0.0153051i
$771$	−6.04576e10			−0.171094
$772$	7.36469e10	+	1.27560e11i	0.207341	+	0.359125i
$773$	5.17803e11	+	2.98953e11i	1.45026	+	0.837309i	0.998496	−	0.0548279i	$-0.0174610\pi$
$773$	5.17803e11	+	2.98953e11i	1.45026	+	0.837309i	0.451766	+	0.892137i	$0.350794\pi$
$774$	−4.58598e10	+	7.94316e10i	−0.127782	+	0.221324i
$775$	8.99347e10	−	5.19238e10i	0.249299	−	0.143933i
$776$		−	4.95103e10i		−	0.136537i
$777$	−5.89238e10	+	1.56944e11i	−0.161661	+	0.430587i
$778$	−9.39542e10			−0.256447
$779$	−7.89918e9	−	1.36818e10i	−0.0214502	−	0.0371529i
$780$	6.38455e9	+	3.68612e9i	0.0172485	+	0.00995844i
$781$	1.75281e11	−	3.03596e11i	0.471119	−	0.816003i
$782$	−2.11729e9	+	1.22242e9i	−0.00566179	+	0.00326884i
$783$		−	5.07487e10i		−	0.135014i
$784$	1.82755e10	−	9.26655e10i	0.0483733	−	0.245275i
$785$	2.40977e10			0.0634595
$786$	−2.41913e10	−	4.19005e10i	−0.0633824	−	0.109781i
$787$	1.21139e11	+	6.99394e10i	0.315779	+	0.182315i	0.649510	−	0.760353i	$-0.274974\pi$
$787$	1.21139e11	+	6.99394e10i	0.315779	+	0.182315i	−0.333731	+	0.942669i	$0.608308\pi$
$788$	−1.85475e11	+	3.21253e11i	−0.481040	+	0.833186i
$789$	−2.00970e11	+	1.16030e11i	−0.518589	+	0.299407i
$790$		−	2.15543e10i		−	0.0553383i
$791$	2.98418e11	+	1.12039e11i	0.762288	+	0.286197i
$792$	5.09064e10			0.129381
$793$	2.06516e11	+	3.57697e11i	0.522230	+	0.904529i
$794$	−3.87155e11	−	2.23524e11i	−0.974099	−	0.562397i
$795$	−9.49674e9	+	1.64488e10i	−0.0237742	+	0.0411781i
$796$	1.59075e11	−	9.18422e10i	0.396233	−	0.228765i
$797$			1.10625e11i			0.274171i	0.990559	+	0.137085i	$0.0437734\pi$
$797$			1.10625e11i			0.274171i	−0.990559	+	0.137085i	$0.956227\pi$
$798$	−8.63660e9	−	5.20475e10i	−0.0212976	−	0.128348i
$799$	−4.94479e10			−0.121328
$800$	3.56787e10	+	6.17973e10i	0.0871062	+	0.150872i
$801$	−2.19596e11	−	1.26784e11i	−0.533451	−	0.307988i
$802$	−2.32973e10	+	4.03521e10i	−0.0563129	+	0.0975367i
$803$	−4.05514e11	+	2.34124e11i	−0.975313	+	0.563097i
$804$			1.89105e11i			0.452562i
$805$	3.50474e9	+	4.26345e9i	0.00834587	+	0.0101526i
$806$	4.99348e10			0.118321
$807$	1.58661e11	+	2.74809e11i	0.374090	+	0.647943i
$808$	8.01428e10	+	4.62705e10i	0.188026	+	0.108557i
$809$	1.31556e11	−	2.27862e11i	0.307127	−	0.531960i	−0.670606	−	0.741814i	$-0.733966\pi$
$809$	1.31556e11	−	2.27862e11i	0.307127	−	0.531960i	0.977733	+	0.209855i	$0.0672990\pi$
$810$	3.52763e9	−	2.03668e9i	0.00819488	−	0.00473131i
$811$		−	4.24610e11i		−	0.981536i	−0.871290	−	0.490768i	$-0.836716\pi$
$811$		−	4.24610e11i		−	0.981536i	0.871290	−	0.490768i	$-0.163284\pi$
$812$	1.17801e11	−	9.68374e10i	0.270972	−	0.222751i
$813$	−1.46151e11			−0.334534
$814$	−1.35752e11	−	2.35130e11i	−0.309207	−	0.535562i
$815$	3.16898e10	+	1.82961e10i	0.0718273	+	0.0414695i
$816$	−2.71103e9	+	4.69565e9i	−0.00611469	+	0.0105909i
$817$	−1.33326e11	+	7.69760e10i	−0.299245	+	0.172769i
$818$		−	4.01633e11i		−	0.897049i
$819$	−8.47537e10	+	1.40638e10i	−0.188375	+	0.0312584i
$820$	3.66518e9			0.00810661
$821$	−3.51036e10	−	6.08013e10i	−0.0772644	−	0.133826i	0.824804	−	0.565418i	$-0.191285\pi$
$821$	−3.51036e10	−	6.08013e10i	−0.0772644	−	0.133826i	−0.902069	+	0.431592i	$0.857952\pi$
$822$	2.40714e11	+	1.38976e11i	0.527247	+	0.304406i
$823$	−2.47334e11	+	4.28396e11i	−0.539120	+	0.933783i	0.459832	+	0.888006i	$0.347910\pi$
$823$	−2.47334e11	+	4.28396e11i	−0.539120	+	0.933783i	−0.998952	+	0.0457766i	$0.985424\pi$
$824$	−9.21697e10	+	5.32142e10i	−0.199931	+	0.115430i
$825$		−	2.89366e11i		−	0.624642i
$826$	−5.69402e10	+	1.51661e11i	−0.122320	+	0.325802i
$827$	−2.17717e11			−0.465448			−0.232724	−	0.972543i	$-0.574764\pi$
$827$	−2.17717e11			−0.465448			−0.232724	+	0.972543i	$0.574764\pi$
$828$	4.27419e9	+	7.40311e9i	0.00909352	+	0.0157504i
$829$	−8.83932e10	−	5.10339e10i	−0.187155	−	0.108054i	0.403495	−	0.914982i	$-0.367795\pi$
$829$	−8.83932e10	−	5.10339e10i	−0.187155	−	0.108054i	−0.590650	+	0.806928i	$0.701129\pi$
$830$	9.63189e9	−	1.66829e10i	0.0202955	−	0.0351528i
$831$	7.84564e10	−	4.52968e10i	0.164522	−	0.0949869i
$832$			3.43120e10i			0.0716066i
$833$	−1.31759e10	−	3.86084e10i	−0.0273654	−	0.0801866i
$834$	−3.24210e11			−0.670135
$835$	−4.54503e10	−	7.87223e10i	−0.0934956	−	0.161939i
$836$	7.39990e10	+	4.27233e10i	0.151496	+	0.0874661i
$837$	1.37951e10	−	2.38939e10i	0.0281076	−	0.0486838i
$838$	5.15852e11	−	2.97827e11i	1.04604	−	0.603933i
$839$		−	5.00964e11i		−	1.01102i	−0.862822	−	0.505509i	$-0.831305\pi$
$839$		−	5.00964e11i		−	1.01102i	0.862822	−	0.505509i	$-0.168695\pi$
$840$	1.14590e10	+	4.30221e9i	0.0230159	+	0.00864120i
$841$	−2.54037e11			−0.507824
$842$	−2.79769e11	−	4.84574e11i	−0.556611	−	0.964078i
$843$	−8.02850e10	−	4.63526e10i	−0.158973	−	0.0917833i
$844$	−1.18975e11	+	2.06071e11i	−0.234470	+	0.406113i
$845$	−3.57267e10	+	2.06268e10i	−0.0700754	+	0.0404581i
$846$			1.72894e11i			0.337520i
$847$	−1.72923e10	−	1.04210e11i	−0.0335985	−	0.202477i
$848$	−8.83997e10			−0.170949
$849$	7.93752e9	+	1.37482e10i	0.0152776	+	0.0264615i
$850$	2.66913e10	+	1.54102e10i	0.0511322	+	0.0295212i
$851$	2.27960e10	−	3.94838e10i	0.0434650	−	0.0752836i
$852$	1.13063e11	−	6.52771e10i	0.214567	−	0.123880i
$853$		−	1.01965e11i		−	0.192599i	−0.995352	−	0.0962997i	$-0.969299\pi$
$853$		−	1.01965e11i		−	0.192599i	0.995352	−	0.0962997i	$-0.0307007\pi$
$854$	4.35466e11	+	5.29737e11i	0.818696	+	0.995930i
$855$	6.83714e9			0.0127941
$856$	1.75913e11	+	3.04690e11i	0.327644	+	0.567496i
$857$	−3.63074e11	−	2.09621e11i	−0.673087	−	0.388607i	0.124158	−	0.992262i	$-0.460377\pi$
$857$	−3.63074e11	−	2.09621e11i	−0.673087	−	0.388607i	−0.797245	+	0.603655i	$0.793710\pi$
$858$	6.95703e10	−	1.20499e11i	0.128373	−	0.222349i
$859$	7.52565e10	−	4.34493e10i	0.138220	−	0.0798014i	−0.429295	−	0.903164i	$-0.641238\pi$
$859$	7.52565e10	−	4.34493e10i	0.138220	−	0.0798014i	0.567515	+	0.823363i	$0.307905\pi$
$860$		−	3.57164e10i		−	0.0652941i
$861$	−3.29949e10	+	2.71232e10i	−0.0600391	+	0.0493547i
$862$	−4.82188e11			−0.873347
$863$	4.21106e11	+	7.29377e11i	0.759186	+	1.31495i	0.943266	+	0.332038i	$0.107736\pi$
$863$	4.21106e11	+	7.29377e11i	0.759186	+	1.31495i	−0.184080	+	0.982911i	$0.558931\pi$
$864$	1.64183e10	+	9.47912e9i	0.0294628	+	0.0170103i
$865$	−2.41091e10	+	4.17583e10i	−0.0430643	+	0.0745896i
$866$	−5.61695e11	+	3.24295e11i	−0.998685	+	0.576591i
$867$		−	3.23882e11i		−	0.573206i
$868$	8.17874e10	−	1.35716e10i	0.144081	−	0.0239084i
$869$	−4.06807e11			−0.713361
$870$	9.88100e9	+	1.71144e10i	0.0172474	+	0.0298734i
$871$	4.47626e11	+	2.58437e11i	0.777754	+	0.449036i
$872$	−1.53559e11	+	2.65973e11i	−0.265589	+	0.460014i
$873$	−6.47531e10	+	3.73852e10i	−0.111482	+	0.0643640i
$874$			1.43485e10i			0.0245901i
$875$	4.92698e10	−	1.31231e11i	0.0840521	−	0.223874i
$876$	−1.74382e11			−0.296132
$877$	2.44195e11	+	4.22959e11i	0.412800	+	0.714990i	0.995195	−	0.0979160i	$-0.0312177\pi$
$877$	2.44195e11	+	4.22959e11i	0.412800	+	0.714990i	−0.582395	+	0.812906i	$0.697884\pi$
$878$	6.40373e11	+	3.69720e11i	1.07759	+	0.622149i
$879$	−1.31904e11	+	2.28464e11i	−0.220954	+	0.382703i
$880$	−1.71676e10	+	9.91169e9i	−0.0286271	+	0.0165279i
$881$			4.67856e11i			0.776620i	0.921529	+	0.388310i	$0.126941\pi$
$881$			4.67856e11i			0.776620i	−0.921529	+	0.388310i	$0.873059\pi$
$882$	−1.34994e11	+	4.60696e10i	−0.223070	+	0.0761273i
$883$	−8.30367e11			−1.36593			−0.682963	−	0.730453i	$-0.739309\pi$
$883$	−8.30367e11			−1.36593			−0.682963	+	0.730453i	$0.739309\pi$
$884$	7.40997e9	+	1.28344e10i	0.0121341	+	0.0210169i
$885$	−1.81809e10	−	1.04968e10i	−0.0296376	−	0.0171113i
$886$	1.64303e11	−	2.84580e11i	0.266630	−	0.461817i
$887$	−6.38839e11	+	3.68834e11i	−1.03204	+	0.595849i	−0.917569	−	0.397577i	$-0.869851\pi$
$887$	−6.38839e11	+	3.68834e11i	−1.03204	+	0.595849i	−0.114472	+	0.993426i	$0.536518\pi$
$888$		−	1.01112e11i		−	0.162611i
$889$	−1.61381e11	−	6.05896e10i	−0.258372	−	0.0970043i
$890$	9.87414e10			0.157376
$891$	−3.84394e10	−	6.65789e10i	−0.0609909	−	0.105639i
$892$	−1.38581e11	−	8.00098e10i	−0.218899	−	0.126382i
$893$	−1.45102e11	+	2.51324e11i	−0.228175	+	0.395211i
$894$	2.64034e11	−	1.52440e11i	0.413342	−	0.238643i
$895$		−	5.52013e10i		−	0.0860315i
$896$	9.32550e9	+	5.61990e10i	0.0144690	+	0.0871960i
$897$	2.33650e10			0.0360907
$898$	6.89217e10	+	1.19376e11i	0.105987	+	0.183574i
$899$	1.15922e11	+	6.69275e10i	0.177471	+	0.102463i
$900$	5.38819e10	−	9.33262e10i	0.0821245	−	0.142244i
$901$	−3.30660e10	+	1.90907e10i	−0.0501744	+	0.0289682i
$902$		−	6.91750e10i		−	0.104502i
$903$	2.64310e11	+	3.21529e11i	0.397524	+	0.483581i
$904$	−1.92257e11			−0.287878
$905$	−5.64913e10	−	9.78458e10i	−0.0842146	−	0.145864i
$906$	−2.43441e11	−	1.40551e11i	−0.361311	−	0.208603i
$907$	7.27246e10	−	1.25963e11i	0.107461	−	0.186129i	−0.807280	−	0.590169i	$-0.799061\pi$
$907$	7.27246e10	−	1.25963e11i	0.107461	−	0.186129i	0.914741	+	0.404040i	$0.132394\pi$
$908$	2.82398e11	−	1.63042e11i	0.415449	−	0.239859i
$909$		−	1.39755e11i		−	0.204697i
$910$	2.58439e10	−	2.12448e10i	0.0376870	−	0.0309803i
$911$	−6.99353e11			−1.01537			−0.507683	−	0.861544i	$-0.669498\pi$
$911$	−6.99353e11			−1.01537			−0.507683	+	0.861544i	$0.669498\pi$
$912$	1.59108e10	+	2.75582e10i	0.0229991	+	0.0398357i
$913$	−3.14867e11	−	1.81788e11i	−0.453152	−	0.261627i
$914$	−3.50943e10	+	6.07852e10i	−0.0502866	+	0.0870990i
$915$	−7.69613e10	+	4.44336e10i	−0.109796	+	0.0633910i
$916$			5.02014e11i			0.713073i
$917$	−2.16597e11	+	3.59415e10i	−0.306320	+	0.0508299i
$918$	8.18839e9			0.0115300
$919$	3.31377e11	+	5.73963e11i	0.464580	+	0.804677i	0.999182	−	0.0404269i	$-0.0128718\pi$
$919$	3.31377e11	+	5.73963e11i	0.464580	+	0.804677i	−0.534602	+	0.845104i	$0.679538\pi$
$920$	−2.88283e9	−	1.66440e9i	−0.00402410	−	0.00232331i
$921$	1.99883e11	−	3.46208e11i	0.277804	−	0.481170i
$922$	3.20795e11	−	1.85211e11i	0.443919	−	0.256297i
$923$		−	3.56839e11i		−	0.491661i
$924$	8.11981e10	−	2.16272e11i	0.111393	−	0.296696i
$925$	−5.74748e11			−0.785074
$926$	3.87519e11	+	6.71203e11i	0.527047	+	0.912873i
$927$	1.39195e11	+	8.03640e10i	0.188496	+	0.108828i
$928$	−4.59883e10	+	7.96540e10i	−0.0620091	+	0.107403i
$929$	−1.59060e11	+	9.18331e10i	−0.213549	+	0.123292i	−0.602960	−	0.797772i	$-0.706012\pi$
$929$	−1.59060e11	+	9.18331e10i	−0.213549	+	0.123292i	0.389411	+	0.921064i	$0.372679\pi$
$930$			1.07439e10i			0.0143625i
$931$	−2.34896e11	−	4.63262e10i	−0.312663	−	0.0616635i
$932$	6.74094e11			0.893423
$933$	3.49308e11	+	6.05019e11i	0.460980	+	0.798441i
$934$	4.99959e11	+	2.88651e11i	0.656972	+	0.379303i
$935$	−4.28103e9	+	7.41496e9i	−0.00560147	+	0.00970203i
$936$	4.48756e10	−	2.59090e10i	0.0584665	−	0.0337557i
$937$		−	5.29506e11i		−	0.686930i	−0.939165	−	0.343465i	$-0.888399\pi$
$937$		−	5.29506e11i		−	0.686930i	0.939165	−	0.343465i	$-0.111601\pi$
$938$	8.03397e11	+	3.01631e11i	1.03781	+	0.389641i
$939$	4.84337e11			0.622996
$940$	−3.36633e10	−	5.83065e10i	−0.0431167	−	0.0746803i
$941$	5.87889e11	+	3.39418e11i	0.749785	+	0.432889i	0.825616	−	0.564232i	$-0.190828\pi$
$941$	5.87889e11	+	3.39418e11i	0.749785	+	0.432889i	−0.0758309	+	0.997121i	$0.524161\pi$
$942$	8.46886e10	−	1.46685e11i	0.107553	−	0.186287i
$943$	1.00598e10	−	5.80805e9i	0.0127217	−	0.00734486i
$944$		−	9.77083e10i		−	0.123039i
$945$	−3.02594e9	−	1.82354e10i	−0.00379431	−	0.0228659i
$946$	−6.74097e11			−0.841701
$947$	−7.74453e11	−	1.34139e12i	−0.962931	−	1.66784i	−0.715075	−	0.699048i	$-0.753608\pi$
$947$	−7.74453e11	−	1.34139e12i	−0.962931	−	1.66784i	−0.247855	−	0.968797i	$-0.579726\pi$
$948$	−1.31203e11	−	7.57503e10i	−0.162447	−	0.0937888i
$949$	−2.38316e11	+	4.12775e11i	−0.293825	+	0.508919i
$950$	1.56648e11	−	9.04410e10i	0.192323	−	0.111038i
$951$		−	2.02404e11i		−	0.247455i
$952$	1.56249e10	+	1.90074e10i	0.0190225	+	0.0231406i
$953$	−6.50547e11			−0.788692			−0.394346	−	0.918962i	$-0.629029\pi$
$953$	−6.50547e11			−0.788692			−0.394346	+	0.918962i	$0.629029\pi$
$954$	6.67505e10	+	1.15615e11i	0.0805862	+	0.139579i
$955$	4.68797e10	+	2.70660e10i	0.0563600	+	0.0325395i
$956$	8.79244e10	−	1.52290e11i	0.105264	−	0.182322i
$957$	3.23010e11	−	1.86490e11i	0.385095	−	0.222335i
$958$		−	7.55804e11i		−	0.897319i
$959$	9.74380e11	−	8.00982e11i	1.15200	−	0.946996i
$960$	−7.38250e9			−0.00869198
$961$	−3.90059e11	−	6.75603e11i	−0.457338	−	0.792133i
$962$	−2.39340e11	−	1.38183e11i	−0.279457	−	0.161344i
$963$	2.65663e11	−	4.60141e11i	0.308905	−	0.535040i
$964$	9.05704e9	−	5.22908e9i	0.0104876	−	0.00605504i
$965$			8.66211e10i			0.0998883i
$966$	3.82691e10	−	6.35026e9i	0.0439480	−	0.00729261i
$967$	−4.16425e10			−0.0476246			−0.0238123	−	0.999716i	$-0.507580\pi$
$967$	−4.16425e10			−0.0476246			−0.0238123	+	0.999716i	$0.507580\pi$
$968$	3.18568e10	+	5.51775e10i	0.0362827	+	0.0628436i
$969$	1.19029e10	+	6.87213e9i	0.0135007	+	0.00779464i
$970$	1.45581e10	−	2.52154e10i	0.0164444	−	0.0284826i
$971$	1.36377e12	−	7.87375e11i	1.53414	−	0.885737i	0.534977	−	0.844867i	$-0.320320\pi$
$971$	1.36377e12	−	7.87375e11i	1.53414	−	0.885737i	0.999164	−	0.0408702i	$-0.0130130\pi$
$972$		−	2.86307e10i		−	0.0320750i
$973$	−5.17130e11	+	1.37738e12i	−0.576964	+	1.53675i
$974$	4.62527e11			0.513926
$975$	−1.47274e11	−	2.55085e11i	−0.162969	−	0.282271i
$976$	−3.58194e11	−	2.06804e11i	−0.394748	−	0.227908i
$977$	5.00821e11	−	8.67447e11i	0.549672	−	0.952061i	−0.448624	−	0.893720i	$-0.648086\pi$
$977$	5.00821e11	−	8.67447e11i	0.549672	−	0.952061i	0.998297	−	0.0583402i	$-0.0185808\pi$
$978$	2.22741e11	−	1.28599e11i	0.243469	−	0.140567i
$979$		−	1.86360e12i		−	2.02872i
$980$	3.65552e10	−	4.18204e10i	0.0396319	−	0.0453402i
$981$	4.63810e11			0.500800
$982$	−3.82729e11	−	6.62905e11i	−0.411571	−	0.712862i
$983$	9.73305e11	+	5.61938e11i	1.04240	+	0.601831i	0.920512	−	0.390713i	$-0.127772\pi$
$983$	9.73305e11	+	5.61938e11i	1.04240	+	0.601831i	0.121889	+	0.992544i	$0.461105\pi$
$984$	1.28809e10	−	2.23103e10i	0.0137393	−	0.0237972i
$985$	−1.88924e11	+	1.09075e11i	−0.200697	+	0.115873i
$986$			3.97262e10i			0.0420310i
$987$	7.34529e11	+	2.75775e11i	0.773999	+	0.290593i
$988$	8.69766e10			0.0912798
$989$	−5.65983e10	−	9.80311e10i	−0.0591586	−	0.102466i
$990$	2.59264e10	+	1.49686e10i	0.0269899	+	0.0155826i
$991$	−1.26612e11	+	2.19298e11i	−0.131274	+	0.227374i	−0.924168	−	0.381986i	$-0.875240\pi$
$991$	−1.26612e11	+	2.19298e11i	−0.131274	+	0.227374i	0.792894	+	0.609360i	$0.208573\pi$
$992$	−4.33050e10	+	2.50022e10i	−0.0447189	+	0.0258185i
$993$			4.45175e11i			0.457861i
$994$	−9.69837e10	−	5.84461e11i	−0.0993466	−	0.598701i
$995$	1.08022e11			0.110210
$996$	−6.77005e10	−	1.17261e11i	−0.0687946	−	0.119156i
$997$	1.02352e11	+	5.90927e10i	0.103589	+	0.0598072i	0.550899	−	0.834572i	$-0.314285\pi$
$997$	1.02352e11	+	5.90927e10i	0.103589	+	0.0598072i	−0.447310	+	0.894379i	$0.647618\pi$
$998$	5.74260e10	−	9.94647e10i	0.0578877	−	0.100264i
$999$	−1.32241e11	+	7.63495e10i	−0.132772	+	0.0766557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.a.31.4	yes	8
3.2	odd	2		126.9.n.a.73.1		8
7.3	odd	6		294.9.c.a.97.3		8
7.4	even	3		294.9.c.a.97.2		8
7.5	odd	6	inner	42.9.g.a.19.4	✓	8
21.5	even	6		126.9.n.a.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.a.19.4	✓	8	7.5	odd	6	inner
42.9.g.a.31.4	yes	8	1.1	even	1	trivial
126.9.n.a.19.1		8	21.5	even	6
126.9.n.a.73.1		8	3.2	odd	2
294.9.c.a.97.2		8	7.4	even	3
294.9.c.a.97.3		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(5.65685 + 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-65.1898 + 37.6374i) q^{5} +529.090i q^{6} +(2247.80 + 843.923i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(5.65685 + 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-65.1898 + 37.6374i) q^{5} +529.090i q^{6} +(2247.80 + 843.923i) q^{7} -1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-737.539 - 425.818i) q^{10} +(-8036.72 + 13920.0i) q^{11} +(-5184.00 + 2992.98i) q^{12} +16361.2i q^{13} +(4446.74 + 26797.8i) q^{14} -3520.25 q^{15} +(-8192.00 - 14189.0i) q^{16} +(-6128.46 - 3538.27i) q^{17} +(-12371.5 + 21428.1i) q^{18} +(-35967.2 + 20765.7i) q^{19} -9635.17i q^{20} +(71302.6 + 86738.4i) q^{21} -181850. q^{22} +(-15268.4 - 26445.7i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-192479. + 333384. i) q^{25} +(-160307. + 92553.1i) q^{26} +102276. i q^{27} +(-237409. + 195160. i) q^{28} -496195. q^{29} +(-19913.6 - 34491.3i) q^{30} +(-233622. - 134882. i) q^{31} +(92681.9 - 160530. i) q^{32} +(-650974. + 375840. i) q^{33} -80061.8i q^{34} +(-178297. + 29586.0i) q^{35} -279936. q^{36} +(746506. + 1.29299e6i) q^{37} +(-406923. - 234937. i) q^{38} +(-382570. + 662630. i) q^{39} +(94405.0 - 54504.7i) q^{40} +380396. i q^{41} +(-446511. + 1.18929e6i) q^{42} +3.70688e6 q^{43} +(-1.02870e6 - 1.78176e6i) q^{44} +(-142570. - 82312.9i) q^{45} +(172743. - 299199. i) q^{46} +(6.05143e6 - 3.49379e6i) q^{47} -766204. i q^{48} +(4.34039e6 + 3.79394e6i) q^{49} -4.35531e6 q^{50} +(-165468. - 286599. i) q^{51} +(-1.81366e6 - 1.04712e6i) q^{52} +(2.69774e6 - 4.67263e6i) q^{53} +(-1.00209e6 + 578560. i) q^{54} -1.20992e6i q^{55} +(-3.25516e6 - 1.22213e6i) q^{56} -1.94223e6 q^{57} +(-2.80690e6 - 4.86170e6i) q^{58} +(5.16467e6 + 2.98182e6i) q^{59} +(225296. - 390224. i) q^{60} +(2.18625e7 - 1.26223e7i) q^{61} -3.05202e6i q^{62} +(859579. + 5.18015e6i) q^{63} +2.09715e6 q^{64} +(-615794. - 1.06659e6i) q^{65} +(-7.36493e6 - 4.25214e6i) q^{66} +(1.57957e7 - 2.73589e7i) q^{67} +(784442. - 452898. i) q^{68} -1.42807e6i q^{69} +(-1.29848e6 - 1.57958e6i) q^{70} -2.18100e7 q^{71} +(-1.58356e6 - 2.74280e6i) q^{72} +(2.52288e7 + 1.45659e7i) q^{73} +(-8.44575e6 + 1.46285e7i) q^{74} +(-1.55908e7 + 9.00137e6i) q^{75} -5.31602e6i q^{76} +(-2.98123e7 + 2.45070e7i) q^{77} -8.65656e6 q^{78} +(1.26546e7 + 2.19185e7i) q^{79} +(1.06807e6 + 616651. i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(-3.72710e6 + 2.15184e6i) q^{82} +2.26197e7i q^{83} +(-1.41784e7 + 2.35273e6i) q^{84} +532684. q^{85} +(2.09693e7 + 3.63199e7i) q^{86} +(-2.00959e7 - 1.16024e7i) q^{87} +(1.16384e7 - 2.01583e7i) q^{88} +(-1.00410e8 + 5.79716e7i) q^{89} -1.86253e6i q^{90} +(-1.38076e7 + 3.67768e7i) q^{91} +3.90872e6 q^{92} +(-6.30778e6 - 1.09254e7i) q^{93} +(6.84641e7 + 3.95278e7i) q^{94} +(1.56313e6 - 2.70742e6i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} +3.41886e7i q^{97} +(-1.26199e7 + 6.39887e7i) q^{98} -3.51526e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9}+O(q^{10}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9} - 21888 q^{10} - 7434 q^{11} - 41472 q^{12} + 32256 q^{14} - 120204 q^{15} - 65536 q^{16} + 7932 q^{17} - 773082 q^{19} + 130410 q^{21} + 557568 q^{22} + 391200 q^{23} - 138886 q^{25} - 805632 q^{26} + 654080 q^{28} - 2318196 q^{29} - 590976 q^{30} - 3212544 q^{31} - 602154 q^{33} + 3340932 q^{35} - 2239488 q^{36} + 544802 q^{37} - 1570560 q^{38} + 1341522 q^{39} + 2801664 q^{40} - 72576 q^{42} + 552284 q^{43} - 951552 q^{44} - 4868262 q^{45} + 7878912 q^{46} - 15735252 q^{47} - 588196 q^{49} + 25400832 q^{50} + 214164 q^{51} + 6359808 q^{52} + 10935222 q^{53} - 8601600 q^{56} - 41746428 q^{57} - 8158848 q^{58} + 63840318 q^{59} + 7693056 q^{60} + 43108176 q^{61} + 10869390 q^{63} + 16777216 q^{64} - 9118644 q^{65} + 22581504 q^{66} + 48827290 q^{67} - 1015296 q^{68} + 11053056 q^{70} - 164526744 q^{71} + 150530022 q^{73} - 31064064 q^{74} - 11249766 q^{75} - 137090394 q^{77} - 43504128 q^{78} - 18689696 q^{79} + 36470784 q^{80} - 19131876 q^{81} - 33914880 q^{82} + 18144000 q^{84} - 190617576 q^{85} - 37077504 q^{86} - 93886938 q^{87} - 35684352 q^{88} - 191605284 q^{89} + 110138574 q^{91} - 100147200 q^{92} - 86738688 q^{93} + 302275584 q^{94} + 260649552 q^{95} - 282428160 q^{98} - 32516316 q^{99}+O(q^{100}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9 - 21888 * q^10 - 7434 * q^11 - 41472 * q^12 + 32256 * q^14 - 120204 * q^15 - 65536 * q^16 + 7932 * q^17 - 773082 * q^19 + 130410 * q^21 + 557568 * q^22 + 391200 * q^23 - 138886 * q^25 - 805632 * q^26 + 654080 * q^28 - 2318196 * q^29 - 590976 * q^30 - 3212544 * q^31 - 602154 * q^33 + 3340932 * q^35 - 2239488 * q^36 + 544802 * q^37 - 1570560 * q^38 + 1341522 * q^39 + 2801664 * q^40 - 72576 * q^42 + 552284 * q^43 - 951552 * q^44 - 4868262 * q^45 + 7878912 * q^46 - 15735252 * q^47 - 588196 * q^49 + 25400832 * q^50 + 214164 * q^51 + 6359808 * q^52 + 10935222 * q^53 - 8601600 * q^56 - 41746428 * q^57 - 8158848 * q^58 + 63840318 * q^59 + 7693056 * q^60 + 43108176 * q^61 + 10869390 * q^63 + 16777216 * q^64 - 9118644 * q^65 + 22581504 * q^66 + 48827290 * q^67 - 1015296 * q^68 + 11053056 * q^70 - 164526744 * q^71 + 150530022 * q^73 - 31064064 * q^74 - 11249766 * q^75 - 137090394 * q^77 - 43504128 * q^78 - 18689696 * q^79 + 36470784 * q^80 - 19131876 * q^81 - 33914880 * q^82 + 18144000 * q^84 - 190617576 * q^85 - 37077504 * q^86 - 93886938 * q^87 - 35684352 * q^88 - 191605284 * q^89 + 110138574 * q^91 - 100147200 * q^92 - 86738688 * q^93 + 302275584 * q^94 + 260649552 * q^95 - 282428160 * q^98 - 32516316 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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