LMFDB - Embedded newform 42.9.g.b.31.3

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			31.3
Root			$-1.61905 - 2.80427i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(537.676 - 310.427i) q^{5} +529.090i q^{6} +(-2285.79 + 734.809i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(537.676 - 310.427i) q^{5} +529.090i q^{6} +(-2285.79 + 734.809i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-6083.11 - 3512.08i) q^{10} +(-10951.6 + 18968.8i) q^{11} +(5184.00 - 2992.98i) q^{12} -5805.39i q^{13} +(20130.0 + 18239.4i) q^{14} -29034.5 q^{15} +(-8192.00 - 14189.0i) q^{16} +(132646. + 76583.4i) q^{17} +(12371.5 - 21428.1i) q^{18} +(115221. - 66522.9i) q^{19} +79469.4i q^{20} +(109756. + 23688.2i) q^{21} +247807. q^{22} +(-235279. - 407515. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-2582.29 + 4472.67i) q^{25} +(-56881.0 + 32840.3i) q^{26} -102276. i q^{27} +(64836.3 - 300411. i) q^{28} +1.18753e6 q^{29} +(164244. + 284479. i) q^{30} +(1.33485e6 + 770678. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(887082. - 512157. i) q^{33} -1.73288e6i q^{34} +(-1.00091e6 + 1.10466e6i) q^{35} -279936. q^{36} +(964693. + 1.67090e6i) q^{37} +(-1.30358e6 - 752621. i) q^{38} +(-135746. + 235118. i) q^{39} +(778638. - 449547. i) q^{40} +54261.2i q^{41} +(-388780. - 1.20939e6i) q^{42} -730259. q^{43} +(-1.40181e6 - 2.42800e6i) q^{44} +(1.17590e6 + 678904. i) q^{45} +(-2.66188e6 + 4.61051e6i) q^{46} +(-3.34816e6 + 1.93306e6i) q^{47} +766204. i q^{48} +(4.68491e6 - 3.35925e6i) q^{49} +58430.7 q^{50} +(-3.58145e6 - 6.20325e6i) q^{51} +(643535. + 371545. i) q^{52} +(-6.89945e6 + 1.19502e7i) q^{53} +(-1.00209e6 + 578560. i) q^{54} +1.35987e7i q^{55} +(-3.31018e6 + 1.06412e6i) q^{56} -6.22194e6 q^{57} +(-6.71766e6 - 1.16353e7i) q^{58} +(-3.84372e6 - 2.21917e6i) q^{59} +(1.85821e6 - 3.21851e6i) q^{60} +(8.07548e6 - 4.66238e6i) q^{61} -1.74385e7i q^{62} +(-3.89124e6 - 3.52578e6i) q^{63} +2.09715e6 q^{64} +(-1.80215e6 - 3.12142e6i) q^{65} +(-1.00362e7 - 5.79440e6i) q^{66} +(4.06537e6 - 7.04142e6i) q^{67} +(-1.69787e7 + 9.80267e6i) q^{68} +2.20058e7i q^{69} +(1.64854e7 + 3.55798e6i) q^{70} +9.55170e6 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(1.92373e6 + 1.11066e6i) q^{73} +(1.09143e7 - 1.89040e7i) q^{74} +(209166. - 120762. i) q^{75} +1.70299e7i q^{76} +(1.10947e7 - 5.14061e7i) q^{77} +3.07157e6 q^{78} +(3.28239e7 + 5.68527e7i) q^{79} +(-8.80928e6 - 5.08604e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(531649. - 306948. i) q^{82} +5.08211e7i q^{83} +(-9.65029e6 + 1.06506e7i) q^{84} +9.50943e7 q^{85} +(4.13097e6 + 7.15505e6i) q^{86} +(-4.80948e7 - 2.77675e7i) q^{87} +(-1.58597e7 + 2.74697e7i) q^{88} +(-1.61978e7 + 9.35180e6i) q^{89} -1.53619e7i q^{90} +(4.26585e6 + 1.32699e7i) q^{91} +6.02314e7 q^{92} +(-3.60411e7 - 6.24249e7i) q^{93} +(3.78801e7 + 2.18701e7i) q^{94} +(4.13011e7 - 7.15355e7i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} -7.35915e6i q^{97} +(-5.94156e7 - 2.68998e7i) q^{98} -4.79024e7 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
$5$	537.676	−	310.427i	0.860281	−	0.496684i	−0.00382515	−	0.999993i	$-0.501218\pi$
$5$	537.676	−	310.427i	0.860281	−	0.496684i	0.864106	+	0.503309i	$0.167884\pi$
$6$			529.090i			0.408248i
$7$	−2285.79	+	734.809i	−0.952018	+	0.306043i
$7$	−2285.79	+	734.809i	−0.952018	+	0.306043i
$8$	1448.15			0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	−6083.11	−	3512.08i	−0.608311	−	0.351208i
$11$	−10951.6	+	18968.8i	−0.748011	+	1.29559i	0.200764	+	0.979640i	$0.435658\pi$
$11$	−10951.6	+	18968.8i	−0.748011	+	1.29559i	−0.948775	+	0.315953i	$0.897676\pi$
$12$	5184.00	−	2992.98i	0.250000	−	0.144338i
$13$		−	5805.39i		−	0.203263i	−0.994822	−	0.101631i	$-0.967594\pi$
$13$		−	5805.39i		−	0.203263i	0.994822	−	0.101631i	$-0.0324062\pi$
$14$	20130.0	+	18239.4i	0.524001	+	0.474787i
$15$	−29034.5			−0.573521
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	132646.	+	76583.4i	1.58818	+	0.916936i	0.993607	+	0.112893i	$0.0360118\pi$
$17$	132646.	+	76583.4i	1.58818	+	0.916936i	0.594572	+	0.804042i	$0.297322\pi$
$18$	12371.5	−	21428.1i	0.117851	−	0.204124i
$19$	115221.	−	66522.9i	0.884133	−	0.510454i	0.0121139	−	0.999927i	$-0.496144\pi$
$19$	115221.	−	66522.9i	0.884133	−	0.510454i	0.872019	+	0.489472i	$0.162811\pi$
$20$			79469.4i			0.496684i
$21$	109756.	+	23688.2i	0.564356	+	0.121802i
$22$	247807.			1.05785
$23$	−235279.	−	407515.i	−0.840760	−	1.45624i	−0.889253	−	0.457415i	$-0.848775\pi$
$23$	−235279.	−	407515.i	−0.840760	−	1.45624i	0.0484938	−	0.998823i	$-0.484558\pi$
$24$	−58650.3	−	33861.7i	−0.176777	−	0.102062i
$25$	−2582.29	+	4472.67i	−0.00661067	+	0.0114500i
$26$	−56881.0	+	32840.3i	−0.124473	+	0.0718643i
$27$		−	102276.i		−	0.192450i
$28$	64836.3	−	300411.i	0.105484	−	0.488746i
$29$	1.18753e6			1.67900			0.839501	−	0.543358i	$-0.182848\pi$
$29$	1.18753e6			1.67900			0.839501	+	0.543358i	$0.182848\pi$
$30$	164244.	+	284479.i	0.202770	+	0.351208i
$31$	1.33485e6	+	770678.i	1.44540	+	0.834500i	0.998202	−	0.0599367i	$-0.0190899\pi$
$31$	1.33485e6	+	770678.i	1.44540	+	0.834500i	0.447194	+	0.894437i	$0.352423\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$	887082.	−	512157.i	0.748011	−	0.431864i
$34$		−	1.73288e6i		−	1.29674i
$35$	−1.00091e6	+	1.10466e6i	−0.666997	+	0.736135i
$36$	−279936.			−0.166667
$37$	964693.	+	1.67090e6i	0.514733	+	0.891544i	0.999854	+	0.0170966i	$0.00544229\pi$
$37$	964693.	+	1.67090e6i	0.514733	+	0.891544i	−0.485121	+	0.874447i	$0.661224\pi$
$38$	−1.30358e6	−	752621.i	−0.625176	−	0.360946i
$39$	−135746.	+	235118.i	−0.0586769	+	0.101631i
$40$	778638.	−	449547.i	0.304155	−	0.175604i
$41$			54261.2i			0.0192023i	0.999954	+	0.00960116i	$0.00305619\pi$
$41$			54261.2i			0.0192023i	−0.999954	+	0.00960116i	$0.996944\pi$
$42$	−388780.	−	1.20939e6i	−0.124942	−	0.388660i
$43$	−730259.			−0.213601			−0.106800	−	0.994280i	$-0.534061\pi$
$43$	−730259.			−0.213601			−0.106800	+	0.994280i	$0.534061\pi$
$44$	−1.40181e6	−	2.42800e6i	−0.374006	−	0.647797i
$45$	1.17590e6	+	678904.i	0.286760	+	0.165561i
$46$	−2.66188e6	+	4.61051e6i	−0.594507	+	1.02972i
$47$	−3.34816e6	+	1.93306e6i	−0.686143	+	0.396145i	−0.802165	−	0.597102i	$-0.796319\pi$
$47$	−3.34816e6	+	1.93306e6i	−0.686143	+	0.396145i	0.116023	+	0.993247i	$0.462985\pi$
$48$			766204.i			0.144338i
$49$	4.68491e6	−	3.35925e6i	0.812675	−	0.582717i
$50$	58430.7			0.00934891
$51$	−3.58145e6	−	6.20325e6i	−0.529393	−	0.916936i
$52$	643535.	+	371545.i	0.0880154	+	0.0508157i
$53$	−6.89945e6	+	1.19502e7i	−0.874402	+	1.51451i	−0.0170028	+	0.999855i	$0.505412\pi$
$53$	−6.89945e6	+	1.19502e7i	−0.874402	+	1.51451i	−0.857399	+	0.514653i	$0.827921\pi$
$54$	−1.00209e6	+	578560.i	−0.117851	+	0.0680414i
$55$			1.35987e7i			1.48610i
$56$	−3.31018e6	+	1.06412e6i	−0.336589	+	0.108203i
$57$	−6.22194e6			−0.589422
$58$	−6.71766e6	−	1.16353e7i	−0.593617	−	1.02817i
$59$	−3.84372e6	−	2.21917e6i	−0.317208	−	0.183140i	0.332939	−	0.942948i	$-0.391960\pi$
$59$	−3.84372e6	−	2.21917e6i	−0.317208	−	0.183140i	−0.650147	+	0.759808i	$0.725293\pi$
$60$	1.85821e6	−	3.21851e6i	0.143380	−	0.248342i
$61$	8.07548e6	−	4.66238e6i	0.583243	−	0.336735i	−0.179178	−	0.983817i	$-0.557344\pi$
$61$	8.07548e6	−	4.66238e6i	0.583243	−	0.336735i	0.762421	+	0.647081i	$0.224011\pi$
$62$		−	1.74385e7i		−	1.18016i
$63$	−3.89124e6	−	3.52578e6i	−0.247017	−	0.223817i
$64$	2.09715e6			0.125000
$65$	−1.80215e6	−	3.12142e6i	−0.100957	−	0.174863i
$66$	−1.00362e7	−	5.79440e6i	−0.528924	−	0.305374i
$67$	4.06537e6	−	7.04142e6i	0.201744	−	0.349431i	−0.747347	−	0.664434i	$-0.768672\pi$
$67$	4.06537e6	−	7.04142e6i	0.201744	−	0.349431i	0.949090	+	0.315004i	$0.102006\pi$
$68$	−1.69787e7	+	9.80267e6i	−0.794090	+	0.458468i
$69$			2.20058e7i			0.970826i
$70$	1.64854e7	+	3.55798e6i	0.686607	+	0.148187i
$71$	9.55170e6			0.375878			0.187939	−	0.982181i	$-0.439819\pi$
$71$	9.55170e6			0.375878			0.187939	+	0.982181i	$0.439819\pi$
$72$	1.58356e6	+	2.74280e6i	0.0589256	+	0.102062i
$73$	1.92373e6	+	1.11066e6i	0.0677410	+	0.0391103i	0.533488	−	0.845808i	$-0.320881\pi$
$73$	1.92373e6	+	1.11066e6i	0.0677410	+	0.0391103i	−0.465747	+	0.884918i	$0.654214\pi$
$74$	1.09143e7	−	1.89040e7i	0.363971	−	0.630417i
$75$	209166.	−	120762.i	0.00661067	−	0.00381667i
$76$			1.70299e7i			0.510454i
$77$	1.10947e7	−	5.14061e7i	0.315613	−	1.46235i
$78$	3.07157e6			0.0829817
$79$	3.28239e7	+	5.68527e7i	0.842717	+	1.45963i	0.887589	+	0.460636i	$0.152379\pi$
$79$	3.28239e7	+	5.68527e7i	0.842717	+	1.45963i	−0.0448721	+	0.998993i	$0.514288\pi$
$80$	−8.80928e6	−	5.08604e6i	−0.215070	−	0.124171i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	531649.	−	306948.i	0.0117590	−	0.00678905i
$83$			5.08211e7i			1.07086i	0.844581	+	0.535429i	$0.179850\pi$
$83$			5.08211e7i			1.07086i	−0.844581	+	0.535429i	$0.820150\pi$
$84$	−9.65029e6	+	1.06506e7i	−0.193831	+	0.213923i
$85$	9.50943e7			1.82171
$86$	4.13097e6	+	7.15505e6i	0.0755193	+	0.130803i
$87$	−4.80948e7	−	2.77675e7i	−0.839501	−	0.484686i
$88$	−1.58597e7	+	2.74697e7i	−0.264462	+	0.458061i
$89$	−1.61978e7	+	9.35180e6i	−0.258164	+	0.149051i	−0.623497	−	0.781826i	$-0.714289\pi$
$89$	−1.61978e7	+	9.35180e6i	−0.258164	+	0.149051i	0.365333	+	0.930877i	$0.380955\pi$
$90$		−	1.53619e7i		−	0.234139i
$91$	4.26585e6	+	1.32699e7i	0.0622072	+	0.193510i
$92$	6.02314e7			0.840760
$93$	−3.60411e7	−	6.24249e7i	−0.481799	−	0.834500i
$94$	3.78801e7	+	2.18701e7i	0.485176	+	0.280117i
$95$	4.13011e7	−	7.15355e7i	0.507069	−	0.878268i
$96$	7.50723e6	−	4.33430e6i	0.0883883	−	0.0510310i
$97$		−	7.35915e6i		−	0.0831267i	−0.999136	−	0.0415633i	$-0.986766\pi$
$97$		−	7.35915e6i		−	0.0831267i	0.999136	−	0.0415633i	$-0.0132338\pi$
$98$	−5.94156e7	−	2.68998e7i	−0.644164	−	0.291639i
$99$	−4.79024e7			−0.498674
$100$	−330534.	−	572501.i	−0.00330534	−	0.00572501i
$101$	−2.30521e7	−	1.33092e7i	−0.221526	−	0.127898i	0.385130	−	0.922862i	$-0.374156\pi$
$101$	−2.30521e7	−	1.33092e7i	−0.221526	−	0.127898i	−0.606657	+	0.794964i	$0.707490\pi$
$102$	−4.05195e7	+	7.01818e7i	−0.374337	+	0.648371i
$103$	6.93143e7	−	4.00187e7i	0.615849	−	0.355561i	−0.159402	−	0.987214i	$-0.550957\pi$
$103$	6.93143e7	−	4.00187e7i	0.615849	−	0.355561i	0.775251	+	0.631653i	$0.217623\pi$
$104$		−	8.40711e6i		−	0.0718643i
$105$	6.63669e7	−	2.13348e7i	0.546002	−	0.175522i
$106$	1.56117e8			1.23659
$107$	3.62780e7	+	6.28354e7i	0.276763	+	0.479368i	0.970579	−	0.240785i	$-0.0774048\pi$
$107$	3.62780e7	+	6.28354e7i	0.276763	+	0.479368i	−0.693815	+	0.720153i	$0.744071\pi$
$108$	1.13374e7	+	6.54566e6i	0.0833333	+	0.0481125i
$109$	−2.97382e7	+	5.15081e7i	−0.210673	+	0.364896i	−0.951925	−	0.306330i	$-0.900899\pi$
$109$	−2.97382e7	+	5.15081e7i	−0.210673	+	0.364896i	0.741252	+	0.671226i	$0.234232\pi$
$110$	1.33240e8	−	7.69261e7i	0.910046	−	0.525416i
$111$		−	9.02284e7i		−	0.594363i
$112$	2.91514e7	+	2.64135e7i	0.185262	+	0.167863i
$113$	−1.39211e7			−0.0853808			−0.0426904	−	0.999088i	$-0.513593\pi$
$113$	−1.39211e7			−0.0853808			−0.0426904	+	0.999088i	$0.513593\pi$
$114$	3.51966e7	+	6.09623e7i	0.208392	+	0.360946i
$115$	−2.53008e8	−	1.46074e8i	−1.44658	−	0.835183i
$116$	−7.60017e7	+	1.31639e8i	−0.419750	+	0.727029i
$117$	1.09954e7	−	6.34820e6i	0.0586769	−	0.0338772i
$118$			5.02142e7i			0.258999i
$119$	−3.59476e8	−	7.75842e7i	−1.79260	−	0.386888i
$120$	−4.20464e7			−0.202770
$121$	−1.32697e8	−	2.29838e8i	−0.619041	−	1.07221i
$122$	−9.13637e7	−	5.27488e7i	−0.412415	−	0.238108i
$123$	1.26877e6	−	2.19758e6i	0.00554323	−	0.00960116i
$124$	−1.70861e8	+	9.86468e7i	−0.722698	+	0.417250i
$125$			2.45728e8i			1.00650i
$126$	−1.25332e7	+	5.80710e7i	−0.0497256	+	0.230397i
$127$	1.37879e8			0.530009			0.265005	−	0.964247i	$-0.414627\pi$
$127$	1.37879e8			0.530009			0.265005	+	0.964247i	$0.414627\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$	2.95755e7	+	1.70754e7i	0.106800	+	0.0616613i
$130$	−2.03890e7	+	3.53148e7i	−0.0713876	+	0.123647i
$131$	−4.01806e8	+	2.31983e8i	−1.36437	+	0.787717i	−0.990202	−	0.139645i	$-0.955404\pi$
$131$	−4.01806e8	+	2.31983e8i	−1.36437	+	0.787717i	−0.374164	+	0.927362i	$0.622070\pi$
$132$			1.31112e8i			0.431864i
$133$	−2.14490e8	+	2.36723e8i	−0.685489	+	0.756544i
$134$	−9.19887e7			−0.285309
$135$	−3.17492e7	−	5.49913e7i	−0.0955868	−	0.165561i
$136$	1.92092e8	+	1.10905e8i	0.561506	+	0.324186i
$137$	6.12586e7	−	1.06103e8i	0.173894	−	0.301193i	−0.765884	−	0.642979i	$-0.777698\pi$
$137$	6.12586e7	−	1.06103e8i	0.173894	−	0.301193i	0.939778	+	0.341786i	$0.111032\pi$
$138$	2.15612e8	−	1.24484e8i	0.594507	−	0.343239i
$139$			2.30753e7i			0.0618141i	0.999522	+	0.0309071i	$0.00983959\pi$
$139$			2.30753e7i			0.0618141i	−0.999522	+	0.0309071i	$0.990160\pi$
$140$	−5.83948e7	−	1.81651e8i	−0.152007	−	0.472852i
$141$	1.80801e8			0.457429
$142$	−5.40326e7	−	9.35871e7i	−0.132893	−	0.230177i
$143$	1.10121e8	+	6.35785e7i	0.263346	+	0.152043i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	6.38504e8	−	3.68640e8i	1.44441	−	0.833933i
$146$		−	2.51314e7i		−	0.0553103i
$147$	−2.68287e8	+	2.65036e7i	−0.574554	+	0.0567591i
$148$	−2.46961e8			−0.514733
$149$	1.51934e8	+	2.63158e8i	0.308256	+	0.533915i	0.977981	−	0.208694i	$-0.0669214\pi$
$149$	1.51934e8	+	2.63158e8i	0.308256	+	0.533915i	−0.669725	+	0.742609i	$0.733588\pi$
$150$	−2.36644e6	−	1.36627e6i	−0.00467445	−	0.00269880i
$151$	−1.43153e6	+	2.47948e6i	−0.00275354	+	0.00476927i	−0.867399	−	0.497613i	$-0.834210\pi$
$151$	−1.43153e6	+	2.47948e6i	−0.00275354	+	0.00476927i	0.864645	+	0.502383i	$0.167543\pi$
$152$	1.66858e8	−	9.63355e7i	0.312588	−	0.180473i
$153$			3.34976e8i			0.611290i
$154$	−5.66436e8	+	1.82091e8i	−1.00709	+	0.323747i
$155$	9.56958e8			1.65793
$156$	−1.73754e7	−	3.00952e7i	−0.0293385	−	0.0508157i
$157$	−9.83943e8	−	5.68080e8i	−1.61946	−	0.934998i	−0.987059	−	0.160360i	$-0.948734\pi$
$157$	−9.83943e8	−	5.68080e8i	−1.61946	−	0.934998i	−0.632405	−	0.774638i	$-0.717932\pi$
$158$	3.71360e8	−	6.43214e8i	0.595891	−	1.03211i
$159$	5.58855e8	−	3.22655e8i	0.874402	−	0.504836i
$160$			1.15084e8i			0.175604i
$161$	8.37245e8	+	7.58611e8i	1.24609	+	1.12906i
$162$	5.41131e7			0.0785674
$163$	−3.50903e8	−	6.07783e8i	−0.497093	−	0.860989i	0.502902	−	0.864344i	$-0.332266\pi$
$163$	−3.50903e8	−	6.07783e8i	−0.497093	−	0.860989i	−0.999994	+	0.00335404i	$0.998932\pi$
$164$	−6.01492e6	−	3.47272e6i	−0.00831485	−	0.00480058i
$165$	3.17975e8	−	5.50749e8i	0.429000	−	0.743050i
$166$	4.97943e8	−	2.87487e8i	0.655763	−	0.378605i
$167$			1.16592e9i			1.49901i	0.662001	+	0.749503i	$0.269708\pi$
$167$			1.16592e9i			1.49901i	−0.662001	+	0.749503i	$0.730292\pi$
$168$	1.58944e8	+	3.43042e7i	0.199530	+	0.0430636i
$169$	7.82028e8			0.958684
$170$	−5.37934e8	−	9.31730e8i	−0.644071	−	1.11556i
$171$	2.51988e8	+	1.45486e8i	0.294711	+	0.170151i
$172$	4.67366e7	−	8.09501e7i	0.0534002	−	0.0924919i
$173$	5.12432e7	−	2.95853e7i	0.0572073	−	0.0330287i	−0.471124	−	0.882067i	$-0.656151\pi$
$173$	5.12432e7	−	2.95853e7i	0.0572073	−	0.0330287i	0.528331	+	0.849039i	$0.322818\pi$
$174$			6.28308e8i			0.685450i
$175$	2.61604e6	−	1.21211e7i	0.00278928	−	0.0129238i
$176$	3.58863e8			0.374006
$177$	1.03781e8	+	1.79753e8i	0.105736	+	0.183140i
$178$	1.83257e8	+	1.05804e8i	0.182550	+	0.105395i
$179$	2.44003e8	−	4.22625e8i	0.237675	−	0.411664i	−0.722372	−	0.691505i	$-0.756948\pi$
$179$	2.44003e8	−	4.22625e8i	0.237675	−	0.411664i	0.960047	+	0.279840i	$0.0902815\pi$
$180$	−1.50515e8	+	8.68998e7i	−0.143380	+	0.0827806i
$181$			5.50366e8i			0.512787i	0.966572	+	0.256394i	$0.0825343\pi$
$181$			5.50366e8i			0.512787i	−0.966572	+	0.256394i	$0.917466\pi$
$182$	1.05887e8	−	1.16863e8i	0.0965066	−	0.106510i
$183$	−4.36076e8			−0.388828
$184$	−3.40720e8	−	5.90145e8i	−0.297253	−	0.514858i
$185$	1.03738e9	+	5.98934e8i	0.885630	+	0.511319i
$186$	−4.07758e8	+	7.06258e8i	−0.340683	+	0.590081i
$187$	−2.90539e9	+	1.67743e9i	−2.37595	+	1.37176i
$188$		−	4.94863e8i		−	0.396145i
$189$	7.51532e7	+	2.33782e8i	0.0588980	+	0.183216i
$190$	−9.34536e8			−0.717103
$191$	−7.99193e8	−	1.38424e9i	−0.600507	−	1.04011i	−0.992744	−	0.120244i	$-0.961632\pi$
$191$	−7.99193e8	−	1.38424e9i	−0.600507	−	1.04011i	0.392237	−	0.919864i	$-0.371701\pi$
$192$	−8.49347e7	−	4.90370e7i	−0.0625000	−	0.0360844i
$193$	9.01236e8	−	1.56099e9i	0.649545	−	1.12504i	−0.333687	−	0.942684i	$-0.608293\pi$
$193$	9.01236e8	−	1.56099e9i	0.649545	−	1.12504i	0.983232	−	0.182361i	$-0.0583739\pi$
$194$	−7.21046e7	+	4.16296e7i	−0.0509045	+	0.0293897i
$195$			1.68557e8i			0.116576i
$196$	7.25421e7	+	7.34320e8i	0.0491548	+	0.497578i
$197$	1.75822e9			1.16737			0.583685	−	0.811980i	$-0.301610\pi$
$197$	1.75822e9			1.16737			0.583685	+	0.811980i	$0.301610\pi$
$198$	2.70977e8	+	4.69346e8i	0.176308	+	0.305374i
$199$	8.65820e8	+	4.99882e8i	0.552097	+	0.318753i	0.749967	−	0.661475i	$-0.230069\pi$
$199$	8.65820e8	+	4.99882e8i	0.552097	+	0.318753i	−0.197870	+	0.980228i	$0.563402\pi$
$200$	−3.73956e6	+	6.47711e6i	−0.00233723	+	0.00404819i
$201$	−3.29295e8	+	1.90118e8i	−0.201744	+	0.116477i
$202$			3.01152e8i			0.180876i
$203$	−2.71444e9	+	8.72605e8i	−1.59844	+	0.513847i
$204$	9.16851e8			0.529393
$205$	1.68442e7	+	2.91749e7i	0.00953748	+	0.0165194i
$206$	−7.84202e8	−	4.52759e8i	−0.435471	−	0.251419i
$207$	5.14555e8	−	8.91236e8i	0.280253	−	0.485413i
$208$	−8.23725e7	+	4.75578e7i	−0.0440077	+	0.0254079i
$209$			2.91414e9i			1.52730i
$210$	−5.84465e8	−	5.29572e8i	−0.300526	−	0.272300i
$211$	6.12135e7			0.0308828			0.0154414	−	0.999881i	$-0.495085\pi$
$211$	6.12135e7			0.0308828			0.0154414	+	0.999881i	$0.495085\pi$
$212$	−8.83130e8	−	1.52963e9i	−0.437201	−	0.757254i
$213$	−3.86844e8	−	2.23344e8i	−0.187939	−	0.108507i
$214$	4.10439e8	−	7.10902e8i	0.195701	−	0.338965i
$215$	−3.92643e8	+	2.26692e8i	−0.183757	+	0.106092i
$216$		−	1.48111e8i		−	0.0680414i
$217$	−3.61750e9	−	7.80750e8i	−1.63144	−	0.352105i
$218$	6.72899e8			0.297937
$219$	−5.19406e7	−	8.99637e7i	−0.0225803	−	0.0391103i
$220$	−1.50744e9	−	8.70319e8i	−0.643500	−	0.371525i
$221$	4.44597e8	−	7.70064e8i	0.186379	−	0.322818i
$222$	−8.84054e8	+	5.10409e8i	−0.363971	+	0.210139i
$223$		−	1.75314e9i		−	0.708918i	−0.935072	−	0.354459i	$-0.884665\pi$
$223$		−	1.75314e9i		−	0.708918i	0.935072	−	0.354459i	$-0.115335\pi$
$224$	9.38931e7	−	4.35042e8i	0.0372942	−	0.172798i
$225$	−1.12950e7			−0.00440712
$226$	7.87497e7	+	1.36398e8i	0.0301867	+	0.0522848i
$227$	1.17341e9	+	6.77469e8i	0.441923	+	0.255144i	0.704413	−	0.709790i	$-0.251210\pi$
$227$	1.17341e9	+	6.77469e8i	0.441923	+	0.255144i	−0.262490	+	0.964935i	$0.584544\pi$
$228$	3.98204e8	−	6.89709e8i	0.147355	−	0.255227i
$229$	2.35852e9	−	1.36169e9i	0.857625	−	0.495150i	−0.00559138	−	0.999984i	$-0.501780\pi$
$229$	2.35852e9	−	1.36169e9i	0.857625	−	0.495150i	0.863216	+	0.504834i	$0.168446\pi$
$230$			3.30528e9i			1.18113i
$231$	−1.65135e9	+	1.82252e9i	−0.579951	+	0.640066i
$232$	1.71972e9			0.593617
$233$	−2.21156e9	−	3.83054e9i	−0.750370	−	1.29968i	−0.947644	−	0.319330i	$-0.896542\pi$
$233$	−2.21156e9	−	3.83054e9i	−0.750370	−	1.29968i	0.197274	−	0.980348i	$-0.436791\pi$
$234$	−1.24399e8	−	7.18216e7i	−0.0414909	−	0.0239548i
$235$	−1.20015e9	+	2.07872e9i	−0.393517	+	0.681592i
$236$	4.91997e8	−	2.84054e8i	0.158604	−	0.0915701i
$237$		−	3.07004e9i		−	0.973086i
$238$	1.27334e9	+	3.96102e9i	0.396859	+	1.23452i
$239$	−4.36594e9			−1.33809			−0.669046	−	0.743221i	$-0.733297\pi$
$239$	−4.36594e9			−1.33809			−0.669046	+	0.743221i	$0.733297\pi$
$240$	2.37851e8	+	4.11969e8i	0.0716901	+	0.124171i
$241$	2.64504e9	+	1.52712e9i	0.784087	+	0.452693i	0.837877	−	0.545859i	$-0.183797\pi$
$241$	2.64504e9	+	1.52712e9i	0.784087	+	0.452693i	−0.0537897	+	0.998552i	$0.517130\pi$
$242$	−1.50129e9	+	2.60032e9i	−0.437728	+	0.758167i
$243$	1.93710e8	−	1.11839e8i	0.0555556	−	0.0320750i
$244$			1.19357e9i			0.336735i
$245$	1.47616e9	−	3.26051e9i	0.409704	−	0.904943i
$246$	−2.87090e7			−0.00783932
$247$	−3.86192e8	−	6.68903e8i	−0.103756	−	0.179711i
$248$	1.93308e9	+	1.11606e9i	0.511025	+	0.295040i
$249$	1.18833e9	−	2.05825e9i	0.309130	−	0.535429i
$250$	2.40763e9	−	1.39005e9i	0.616353	−	0.355852i
$251$			7.58622e8i			0.191131i	0.995423	+	0.0955653i	$0.0304659\pi$
$251$			7.58622e8i			0.191131i	−0.995423	+	0.0955653i	$0.969534\pi$
$252$	6.39876e8	−	2.05700e8i	0.158670	−	0.0510072i
$253$	1.03068e10			2.51559
$254$	−7.79962e8	−	1.35093e9i	−0.187387	−	0.324563i
$255$	−3.85132e9	−	2.22356e9i	−0.910854	−	0.525882i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−1.91693e9	+	1.10674e9i	−0.439414	+	0.253696i	−0.703349	−	0.710845i	$-0.748313\pi$
$257$	−1.91693e9	+	1.10674e9i	−0.439414	+	0.253696i	0.263935	+	0.964540i	$0.414980\pi$
$258$		−	3.86372e8i		−	0.0872022i
$259$	−3.43288e9	−	3.11046e9i	−0.762886	−	0.691235i
$260$	4.61351e8			0.100957
$261$	1.29856e9	+	2.24917e9i	0.279834	+	0.484686i
$262$	4.54591e9	+	2.62458e9i	0.964752	+	0.557000i
$263$	−8.56479e8	+	1.48347e9i	−0.179017	+	0.310066i	−0.941544	−	0.336890i	$-0.890625\pi$
$263$	−8.56479e8	+	1.48347e9i	−0.179017	+	0.310066i	0.762527	+	0.646956i	$0.223958\pi$
$264$	1.28463e9	−	7.41683e8i	0.264462	−	0.152687i
$265$			8.56711e9i			1.73720i
$266$	3.53274e9	+	7.62456e8i	0.705644	+	0.152296i
$267$	8.74681e8			0.172109
$268$	5.20367e8	+	9.01302e8i	0.100872	+	0.174715i
$269$	−1.24205e9	−	7.17097e8i	−0.237208	−	0.136952i	0.376685	−	0.926341i	$-0.377064\pi$
$269$	−1.24205e9	−	7.17097e8i	−0.237208	−	0.136952i	−0.613893	+	0.789389i	$0.710397\pi$
$270$	−3.59201e8	+	6.22155e8i	−0.0675901	+	0.117069i
$271$	7.15365e9	−	4.13016e9i	1.32633	−	0.765755i	0.341598	−	0.939846i	$-0.389032\pi$
$271$	7.15365e9	−	4.13016e9i	1.32633	−	0.765755i	0.984730	+	0.174091i	$0.0556986\pi$
$272$		−	2.50948e9i		−	0.458468i
$273$	1.37520e8	−	6.37179e8i	0.0247579	−	0.114713i
$274$	−1.38612e9			−0.245923
$275$	−5.65607e7	−	9.79660e7i	−0.00988972	−	0.0171295i
$276$	−2.43937e9	−	1.40837e9i	−0.420380	−	0.242706i
$277$	3.03150e9	−	5.25071e9i	0.514918	−	0.891864i	−0.484932	−	0.874552i	$-0.661156\pi$
$277$	3.03150e9	−	5.25071e9i	0.514918	−	0.891864i	0.999850	−	0.0173124i	$-0.00551098\pi$
$278$	2.26091e8	−	1.30533e8i	0.0378533	−	0.0218546i
$279$			3.37095e9i			0.556333i
$280$	−1.44947e9	+	1.59972e9i	−0.235819	+	0.260263i
$281$	4.73743e8			0.0759832			0.0379916	−	0.999278i	$-0.487904\pi$
$281$	4.73743e8			0.0759832			0.0379916	+	0.999278i	$0.487904\pi$
$282$	−1.02276e9	−	1.77148e9i	−0.161725	−	0.280117i
$283$	−5.97536e9	−	3.44987e9i	−0.931575	−	0.537845i	−0.0442659	−	0.999020i	$-0.514095\pi$
$283$	−5.97536e9	−	3.44987e9i	−0.931575	−	0.537845i	−0.887309	+	0.461174i	$0.847428\pi$
$284$	−6.11309e8	+	1.05882e9i	−0.0939696	+	0.162760i
$285$	−3.34539e9	+	1.93146e9i	−0.507069	+	0.292756i
$286$		−	1.43862e9i		−	0.215021i
$287$	−3.98716e7	−	1.24030e8i	−0.00587674	−	0.0182810i
$288$	−4.05391e8			−0.0589256
$289$	8.24215e9	+	1.42758e10i	1.18154	+	2.04649i
$290$	−7.22385e9	−	4.17069e9i	−1.02135	−	0.589679i
$291$	−1.72077e8	+	2.98045e8i	−0.0239966	+	0.0415633i
$292$	−2.46237e8	+	1.42165e8i	−0.0338705	+	0.0195551i
$293$		−	6.88140e9i		−	0.933698i	−0.884337	−	0.466849i	$-0.845389\pi$
$293$		−	6.88140e9i		−	0.933698i	0.884337	−	0.466849i	$-0.154611\pi$
$294$	1.77734e9	+	2.47874e9i	0.237893	+	0.331773i
$295$	−2.75557e9			−0.363851
$296$	1.39702e9	+	2.41972e9i	0.181986	+	0.315208i
$297$	1.94005e9	+	1.12009e9i	0.249337	+	0.143955i
$298$	1.71894e9	−	2.97730e9i	0.217970	−	0.377535i
$299$	−2.36579e9	+	1.36589e9i	−0.295999	+	0.170895i
$300$			3.09151e7i			0.00381667i
$301$	1.66922e9	−	5.36601e8i	0.203352	−	0.0653710i
$302$	3.23918e7			0.00389410
$303$	6.22408e8	+	1.07804e9i	0.0738422	+	0.127898i
$304$	−1.88778e9	−	1.08991e9i	−0.221033	−	0.127614i
$305$	2.89466e9	−	5.01370e9i	0.334502	−	0.579374i
$306$	3.28208e9	−	1.89491e9i	0.374337	−	0.216124i
$307$		−	1.19655e10i		−	1.34704i	−0.739171	−	0.673518i	$-0.764782\pi$
$307$		−	1.19655e10i		−	1.34704i	0.739171	−	0.673518i	$-0.235218\pi$
$308$	4.98837e9	+	4.51986e9i	0.554313	+	0.502252i
$309$	−3.74297e9			−0.410566
$310$	−5.41337e9	−	9.37624e9i	−0.586167	−	1.01527i
$311$	−6.96905e8	−	4.02358e8i	−0.0744958	−	0.0430102i	0.462289	−	0.886729i	$-0.347028\pi$
$311$	−6.96905e8	−	4.02358e8i	−0.0744958	−	0.0430102i	−0.536785	+	0.843719i	$0.680361\pi$
$312$	−1.96581e8	+	3.40488e8i	−0.0207454	+	0.0359321i
$313$	−4.07155e9	+	2.35071e9i	−0.424211	+	0.244918i	−0.696877	−	0.717190i	$-0.745428\pi$
$313$	−4.07155e9	+	2.35071e9i	−0.424211	+	0.244918i	0.272666	+	0.962109i	$0.412095\pi$
$314$			1.28542e10i			1.32229i
$315$	−3.18672e9	−	6.87776e8i	−0.323670	−	0.0698562i
$316$	−8.40292e9			−0.842717
$317$	−2.03035e9	−	3.51667e9i	−0.201064	−	0.348252i	0.747808	−	0.663915i	$-0.231106\pi$
$317$	−2.03035e9	−	3.51667e9i	−0.201064	−	0.348252i	−0.948871	+	0.315663i	$0.897773\pi$
$318$	−6.32273e9	−	3.65043e9i	−0.618295	−	0.356973i
$319$	−1.30053e10	+	2.25259e10i	−1.25591	+	2.17530i
$320$	1.12759e9	−	6.51013e8i	0.107535	−	0.0620855i
$321$		−	3.39311e9i		−	0.319579i
$322$	2.69666e9	−	1.24946e10i	0.250844	−	1.16225i
$323$	2.03782e10			1.87221
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	2.59656e7	+	1.49912e7i	0.00232737	+	0.00134370i
$326$	−3.97002e9	+	6.87628e9i	−0.351497	+	0.608811i
$327$	2.40879e9	−	1.39072e9i	0.210673	−	0.121632i
$328$			7.85786e7i			0.00678905i
$329$	6.23277e9	−	6.87884e9i	0.531983	−	0.587126i
$330$	−7.19495e9			−0.606698
$331$	4.90035e9	+	8.48765e9i	0.408239	+	0.707091i	0.994693	−	0.102892i	$-0.0328095\pi$
$331$	4.90035e9	+	8.48765e9i	0.408239	+	0.707091i	−0.586453	+	0.809983i	$0.699476\pi$
$332$	−5.63358e9	−	3.25255e9i	−0.463695	−	0.267714i
$333$	−2.10978e9	+	3.65425e9i	−0.171578	+	0.297181i
$334$	1.14237e10	−	6.59545e9i	0.917950	−	0.529979i
$335$		−	5.04800e9i		−	0.400812i
$336$	−5.63014e8	−	1.75138e9i	−0.0441735	−	0.137412i
$337$	−2.32945e10			−1.80607			−0.903033	−	0.429570i	$-0.858665\pi$
$337$	−2.32945e10			−1.80607			−0.903033	+	0.429570i	$0.858665\pi$
$338$	−4.42382e9	−	7.66228e9i	−0.338946	−	0.587072i
$339$	5.63805e8	+	3.25513e8i	0.0426904	+	0.0246473i
$340$	−6.08603e9	+	1.05413e10i	−0.455427	+	0.788823i
$341$	−2.92377e10	+	1.68804e10i	−2.16235	+	1.24843i
$342$		−	3.29196e9i		−	0.240630i
$343$	−8.24034e9	+	1.11211e10i	−0.595345	+	0.803470i
$344$	−1.05753e9			−0.0755193
$345$	6.83121e9	+	1.18320e10i	0.482193	+	0.835183i
$346$	−5.79750e8	−	3.34719e8i	−0.0404517	−	0.0233548i
$347$	7.55095e9	−	1.30786e10i	0.520815	−	0.902079i	−0.478892	−	0.877874i	$-0.658961\pi$
$347$	7.55095e9	−	1.30786e10i	0.520815	−	0.902079i	0.999707	−	0.0242047i	$-0.00770535\pi$
$348$	6.15613e9	−	3.55425e9i	0.419750	−	0.242343i
$349$		−	4.82490e9i		−	0.325227i	−0.986690	−	0.162614i	$-0.948008\pi$
$349$		−	4.82490e9i		−	0.325227i	0.986690	−	0.162614i	$-0.0519924\pi$
$350$	−1.33560e8	+	4.29354e7i	−0.00890032	+	0.00286117i
$351$	−5.93751e8			−0.0391180
$352$	−2.03004e9	−	3.51613e9i	−0.132231	−	0.229031i
$353$	−1.56875e9	−	9.05716e8i	−0.101031	−	0.0583301i	0.448633	−	0.893716i	$-0.351911\pi$
$353$	−1.56875e9	−	9.05716e8i	−0.101031	−	0.0583301i	−0.549664	+	0.835386i	$0.685244\pi$
$354$	1.17414e9	−	2.03367e9i	0.0747666	−	0.129500i
$355$	5.13572e9	−	2.96511e9i	0.323361	−	0.186693i
$356$		−	2.39406e9i		−	0.149051i
$357$	1.27447e10	+	1.15477e10i	0.784613	+	0.710922i
$358$	−5.52115e9			−0.336123
$359$	1.24701e10	+	2.15989e10i	0.750745	+	1.30033i	0.947462	+	0.319868i	$0.103639\pi$
$359$	1.24701e10	+	2.15989e10i	0.750745	+	1.30033i	−0.196717	+	0.980460i	$0.563028\pi$
$360$	1.70288e9	+	9.83159e8i	0.101385	+	0.0585347i
$361$	3.58812e8	−	6.21481e8i	0.0211270	−	0.0365931i
$362$	5.39246e9	−	3.11334e9i	0.314017	−	0.181298i
$363$			1.24112e10i			0.714807i
$364$	−1.74400e9	−	3.76400e8i	−0.0993440	−	0.0214410i
$365$	1.37912e9			0.0777018
$366$	2.46682e9	+	4.27266e9i	0.137472	+	0.238108i
$367$	2.27098e10	+	1.31115e10i	1.25184	+	0.722749i	0.971474	−	0.237144i	$-0.0762114\pi$
$367$	2.27098e10	+	1.31115e10i	1.25184	+	0.722749i	0.280364	+	0.959894i	$0.409545\pi$
$368$	−3.85481e9	+	6.67673e9i	−0.210190	+	0.364060i
$369$	−1.02771e8	+	5.93346e7i	−0.00554323	+	0.00320039i
$370$		−	1.35523e10i		−	0.723114i
$371$	6.98961e9	−	3.23855e10i	0.368941	−	1.70944i
$372$	9.22651e9			0.481799
$373$	−5.51286e9	−	9.54855e9i	−0.284801	−	0.493290i	0.687760	−	0.725938i	$-0.258594\pi$
$373$	−5.51286e9	−	9.54855e9i	−0.284801	−	0.493290i	−0.972561	+	0.232649i	$0.925261\pi$
$374$	3.28707e10	+	1.89779e10i	1.68005	+	0.969978i
$375$	5.74578e9	−	9.95198e9i	0.290552	−	0.503250i
$376$	−4.84865e9	+	2.79937e9i	−0.242588	+	0.140058i
$377$		−	6.89405e9i		−	0.341279i
$378$	1.86545e9	−	2.05882e9i	0.0913728	−	0.100844i
$379$	8.51183e9			0.412540			0.206270	−	0.978495i	$-0.433868\pi$
$379$	8.51183e9			0.412540			0.206270	+	0.978495i	$0.433868\pi$
$380$	5.28653e9	+	9.15655e9i	0.253534	+	0.439134i
$381$	−5.58410e9	−	3.22398e9i	−0.265005	−	0.153001i
$382$	−9.04183e9	+	1.56609e10i	−0.424622	+	0.735468i
$383$	−1.22700e10	+	7.08407e9i	−0.570228	+	0.329221i	−0.757240	−	0.653136i	$-0.773453\pi$
$383$	−1.22700e10	+	7.08407e9i	−0.570228	+	0.329221i	0.187013	+	0.982358i	$0.440119\pi$
$384$			1.10958e9i			0.0510310i
$385$	−9.99248e9	−	3.10839e10i	−0.454810	−	1.41479i
$386$	−2.03926e10			−0.918595
$387$	−7.98538e8	−	1.38311e9i	−0.0356001	−	0.0616613i
$388$	8.15771e8	+	4.70985e8i	0.0359949	+	0.0207817i
$389$	3.84581e9	−	6.66114e9i	0.167954	−	0.290904i	−0.769747	−	0.638350i	$-0.779617\pi$
$389$	3.84581e9	−	6.66114e9i	0.167954	−	0.290904i	0.937700	+	0.347445i	$0.112951\pi$
$390$	1.65151e9	−	9.53500e8i	0.0713876	−	0.0412157i
$391$		−	7.20738e10i		−	3.08369i
$392$	6.78448e9	−	4.86471e9i	0.287324	−	0.206021i
$393$	2.16975e10			0.909577
$394$	−9.94599e9	−	1.72270e10i	−0.412727	−	0.714865i
$395$	3.52972e10	+	2.03789e10i	1.44995	+	0.837128i
$396$	3.06576e9	−	5.31004e9i	0.124669	−	0.215932i
$397$	−1.65923e10	+	9.57957e9i	−0.667951	+	0.385642i	−0.795300	−	0.606216i	$-0.792687\pi$
$397$	−1.65923e10	+	9.57957e9i	−0.667951	+	0.385642i	0.127349	+	0.991858i	$0.459353\pi$
$398$		−	1.13110e10i		−	0.450785i
$399$	1.42221e10	−	4.57194e9i	0.561140	−	0.180388i
$400$	8.46166e7			0.00330534
$401$	1.68968e10	+	2.92661e10i	0.653471	+	1.13184i	0.982275	+	0.187447i	$0.0600212\pi$
$401$	1.68968e10	+	2.92661e10i	0.653471	+	1.13184i	−0.328804	+	0.944398i	$0.606646\pi$
$402$	3.72554e9	+	2.15094e9i	0.142654	+	0.0823616i
$403$	4.47409e9	−	7.74935e9i	0.169623	−	0.293796i
$404$	2.95067e9	−	1.70357e9i	0.110763	−	0.0639492i
$405$			2.96953e9i			0.110374i
$406$	2.39049e10	+	2.16598e10i	0.879799	+	0.797168i
$407$	−4.22598e10			−1.54010
$408$	−5.18649e9	−	8.98327e9i	−0.187169	−	0.324186i
$409$	1.39418e10	+	8.04933e9i	0.498227	+	0.287651i	0.727981	−	0.685597i	$-0.240459\pi$
$409$	1.39418e10	+	8.04933e9i	0.498227	+	0.287651i	−0.229754	+	0.973249i	$0.573792\pi$
$410$	1.90570e8	−	3.30077e8i	0.00674402	−	0.0116810i
$411$	−4.96194e9	+	2.86478e9i	−0.173894	+	0.100398i
$412$			1.02448e10i			0.355561i
$413$	1.04166e10	+	2.24817e9i	0.358036	+	0.0772734i
$414$	−1.16431e10			−0.396338
$415$	1.57762e10	+	2.73253e10i	0.531877	+	0.921238i
$416$	9.31938e8	+	5.38055e8i	0.0311181	+	0.0179661i
$417$	5.39562e8	−	9.34549e8i	0.0178442	−	0.0309071i
$418$	2.85526e10	−	1.64848e10i	0.935277	−	0.539983i
$419$			9.98987e9i			0.324118i	0.986781	+	0.162059i	$0.0518136\pi$
$419$			9.98987e9i			0.324118i	−0.986781	+	0.162059i	$0.948186\pi$
$420$	−1.88249e9	+	8.72228e9i	−0.0604973	+	0.280306i
$421$	−1.58205e10			−0.503607			−0.251803	−	0.967778i	$-0.581024\pi$
$421$	−1.58205e10			−0.503607			−0.251803	+	0.967778i	$0.581024\pi$
$422$	−3.46276e8	−	5.99767e8i	−0.0109187	−	0.0189118i
$423$	−7.32242e9	−	4.22760e9i	−0.228714	−	0.132048i
$424$	−9.99147e9	+	1.73057e10i	−0.309148	+	0.535459i
$425$	−6.85064e8	+	3.95522e8i	−0.0209979	+	0.0121231i
$426$			5.05371e9i			0.153452i
$427$	−1.50329e10	+	1.65912e10i	−0.452202	+	0.499075i
$428$	−9.28718e9			−0.276763
$429$	−2.97327e9	−	5.14986e9i	−0.0877820	−	0.152043i
$430$	4.44224e9	+	2.56473e9i	0.129936	+	0.0750184i
$431$	1.22870e10	−	2.12817e10i	0.356071	−	0.616734i	−0.631229	−	0.775596i	$-0.717449\pi$
$431$	1.22870e10	−	2.12817e10i	0.356071	−	0.616734i	0.987301	+	0.158862i	$0.0507826\pi$
$432$	−1.45119e9	+	8.37844e8i	−0.0416667	+	0.0240563i
$433$		−	7.20216e8i		−	0.0204885i	−0.999948	−	0.0102443i	$-0.996739\pi$
$433$		−	7.20216e8i		−	0.0204885i	0.999948	−	0.0102443i	$-0.00326091\pi$
$434$	1.28139e10	+	3.98607e10i	0.361180	+	1.12353i
$435$	−3.44792e10			−0.962943
$436$	−3.80649e9	−	6.59303e9i	−0.105336	−	0.182448i
$437$	−5.42182e10	−	3.13029e10i	−1.48669	−	0.858339i
$438$	−5.87641e8	+	1.01782e9i	−0.0159667	+	0.0276552i
$439$	−5.53795e10	+	3.19734e10i	−1.49104	+	0.860855i	−0.999947	−	0.0102494i	$-0.996737\pi$
$439$	−5.53795e10	+	3.19734e10i	−1.49104	+	0.860855i	−0.491098	+	0.871105i	$0.663404\pi$
$440$			1.96931e10i			0.525416i
$441$	1.14854e10	+	5.19988e9i	0.303662	+	0.137480i
$442$	−1.00601e10			−0.263580
$443$	−7.05537e9	−	1.22203e10i	−0.183191	−	0.317297i	0.759774	−	0.650187i	$-0.225309\pi$
$443$	−7.05537e9	−	1.22203e10i	−0.183191	−	0.317297i	−0.942966	+	0.332890i	$0.891976\pi$
$444$	1.00019e10	+	5.77462e9i	0.257367	+	0.148591i
$445$	−5.80611e9	+	1.00565e10i	−0.148062	+	0.256452i
$446$	−1.71772e10	+	9.91723e9i	−0.434122	+	0.250640i
$447$		−	1.42105e10i		−	0.355943i
$448$	−4.79366e9	+	1.54101e9i	−0.119002	+	0.0382554i
$449$	−7.10052e10			−1.74705			−0.873524	−	0.486782i	$-0.838171\pi$
$449$	−7.10052e10			−1.74705			−0.873524	+	0.486782i	$0.838171\pi$
$450$	6.38939e7	+	1.10668e8i	0.00155815	+	0.00269880i
$451$	−1.02927e9	−	5.94248e8i	−0.0248784	−	0.0143636i
$452$	8.90951e8	−	1.54317e9i	0.0213452	−	0.0369710i
$453$	1.15954e8	−	6.69459e7i	0.00275354	−	0.00158976i
$454$		−	1.53294e10i		−	0.360828i
$455$	6.41300e9	+	5.81068e9i	0.149629	+	0.135576i
$456$	−9.01033e9			−0.208392
$457$	−2.12316e10	−	3.67743e10i	−0.486764	−	0.843101i	0.513120	−	0.858317i	$-0.328490\pi$
$457$	−2.12316e10	−	3.67743e10i	−0.486764	−	0.843101i	−0.999884	+	0.0152162i	$0.995156\pi$
$458$	−2.66836e10	−	1.54058e10i	−0.606432	−	0.350124i
$459$	7.83263e9	−	1.35665e10i	0.176464	−	0.305645i
$460$	3.23850e10	−	1.86975e10i	0.723290	−	0.417592i
$461$		−	7.62855e9i		−	0.168903i	−0.996428	−	0.0844516i	$-0.973086\pi$
$461$		−	7.62855e9i		−	0.168903i	0.996428	−	0.0844516i	$-0.0269138\pi$
$462$	2.71984e10	+	5.87012e9i	0.597002	+	0.128848i
$463$	2.77888e10			0.604709			0.302354	−	0.953196i	$-0.402227\pi$
$463$	2.77888e10			0.604709			0.302354	+	0.953196i	$0.402227\pi$
$464$	−9.72821e9	−	1.68498e10i	−0.209875	−	0.363515i
$465$	−3.87568e10	−	2.23763e10i	−0.828965	−	0.478603i
$466$	−2.50210e10	+	4.33376e10i	−0.530591	+	0.919011i
$467$	3.44755e10	−	1.99044e10i	0.724841	−	0.418487i	−0.0916908	−	0.995788i	$-0.529227\pi$
$467$	3.44755e10	−	1.99044e10i	0.724841	−	0.418487i	0.816532	+	0.577300i	$0.195894\pi$
$468$			1.62514e9i			0.0338772i
$469$	−4.11849e9	+	1.90825e10i	−0.0851230	+	0.394406i
$470$	2.71563e10			0.556517
$471$	2.65665e10	+	4.60145e10i	0.539821	+	0.934998i
$472$	−5.56631e9	−	3.21371e9i	−0.112150	−	0.0647498i
$473$	7.99752e9	−	1.38521e10i	0.159776	−	0.276740i
$474$	−3.00802e10	+	1.73668e10i	−0.595891	+	0.344038i
$475$			6.87127e8i			0.0134978i
$476$	3.16068e10	−	3.48830e10i	0.615676	−	0.679495i
$477$	−3.01782e10			−0.582934
$478$	2.46975e10	+	4.27773e10i	0.473087	+	0.819411i
$479$	1.76385e8	+	1.01836e8i	0.00335057	+	0.00193446i	0.501674	−	0.865057i	$-0.332718\pi$
$479$	1.76385e8	+	1.01836e8i	0.00335057	+	0.00193446i	−0.498324	+	0.866991i	$0.666051\pi$
$480$	2.69097e9	−	4.66090e9i	0.0506926	−	0.0878021i
$481$	9.70021e9	−	5.60042e9i	0.181218	−	0.104626i
$482$		−	3.45547e10i		−	0.640204i
$483$	−1.61701e10	−	5.03008e10i	−0.297114	−	0.924243i
$484$	3.39704e10			0.619041
$485$	−2.28448e9	−	3.95684e9i	−0.0412877	−	0.0715123i
$486$	−2.19158e9	−	1.26531e9i	−0.0392837	−	0.0226805i
$487$	1.78689e10	−	3.09498e10i	0.317674	−	0.550227i	−0.662329	−	0.749214i	$-0.730432\pi$
$487$	1.78689e10	−	3.09498e10i	0.317674	−	0.550227i	0.980002	+	0.198987i	$0.0637650\pi$
$488$	1.16945e10	−	6.75185e9i	0.206207	−	0.119054i
$489$			3.28203e10i			0.573993i
$490$	−4.02968e10	+	3.98085e9i	−0.699014	+	0.0690543i
$491$	6.76126e10			1.16333			0.581664	−	0.813429i	$-0.302402\pi$
$491$	6.76126e10			1.16333			0.581664	+	0.813429i	$0.302402\pi$
$492$	1.62403e8	+	2.81290e8i	0.00277162	+	0.00480058i
$493$	1.57521e11	+	9.09448e10i	2.66656	+	1.53954i
$494$	−4.36926e9	+	7.56778e9i	−0.0733669	+	0.127075i
$495$	−2.57560e10	+	1.48702e10i	−0.429000	+	0.247683i
$496$		−	2.52536e10i		−	0.417250i
$497$	−2.18332e10	+	7.01867e9i	−0.357843	+	0.115035i
$498$	−2.68889e10			−0.437176
$499$	4.80633e9	+	8.32481e9i	0.0775196	+	0.134268i	0.902179	−	0.431361i	$-0.141967\pi$
$499$	4.80633e9	+	8.32481e9i	0.0775196	+	0.134268i	−0.824660	+	0.565629i	$0.808633\pi$
$500$	−2.72392e10	−	1.57266e10i	−0.435828	−	0.251625i
$501$	2.72624e10	−	4.72198e10i	0.432726	−	0.749503i
$502$	7.43295e9	−	4.29141e9i	0.117043	−	0.0675749i
$503$			6.20461e10i			0.969266i	0.874718	+	0.484633i	$0.161047\pi$
$503$			6.20461e10i			0.969266i	−0.874718	+	0.484633i	$0.838953\pi$
$504$	−5.63512e9	−	5.10587e9i	−0.0873336	−	0.0791311i
$505$	−1.65261e10			−0.254100
$506$	−5.83038e10	−	1.00985e11i	−0.889395	−	1.54048i
$507$	−3.16721e10	−	1.82859e10i	−0.479342	−	0.276748i
$508$	−8.82426e9	+	1.52841e10i	−0.132502	+	0.229501i
$509$	−5.03694e10	+	2.90808e10i	−0.750404	+	0.433246i	−0.825840	−	0.563904i	$-0.809299\pi$
$509$	−5.03694e10	+	2.90808e10i	−0.750404	+	0.433246i	0.0754356	+	0.997151i	$0.475965\pi$
$510$			5.03134e10i			0.743709i
$511$	−5.21337e9	−	1.12518e9i	−0.0764601	−	0.0165020i
$512$	3.03700e9			0.0441942
$513$	−6.80369e9	−	1.17843e10i	−0.0982370	−	0.170151i
$514$	2.16876e10	+	1.25213e10i	0.310713	+	0.179390i
$515$	2.48458e10	−	4.30341e10i	0.353202	−	0.611764i
$516$	−3.78566e9	+	2.18565e9i	−0.0534002	+	0.0308306i
$517$		−	8.46806e10i		−	1.18528i
$518$	−1.10569e10	+	5.12306e10i	−0.153572	+	0.711559i
$519$	−2.76713e9			−0.0381382
$520$	−2.60979e9	−	4.52030e9i	−0.0356938	−	0.0618235i
$521$	−1.45782e10	−	8.41672e9i	−0.197857	−	0.114233i	0.397798	−	0.917473i	$-0.369774\pi$
$521$	−1.45782e10	−	8.41672e9i	−0.197857	−	0.114233i	−0.595656	+	0.803240i	$0.703108\pi$
$522$	1.46915e10	−	2.54465e10i	0.197872	−	0.342725i
$523$	1.19612e11	−	6.90581e10i	1.59871	−	0.923014i	0.606970	−	0.794725i	$-0.292385\pi$
$523$	1.19612e11	−	6.90581e10i	1.59871	−	0.923014i	0.991737	−	0.128289i	$-0.0409484\pi$
$524$		−	5.93875e10i		−	0.787717i
$525$	−3.89373e8	+	4.29734e8i	−0.00512541	+	0.00565669i
$526$	1.93799e10			0.253168
$527$	1.18042e11	+	2.04455e11i	1.53037	+	2.65067i
$528$	−1.45340e10	−	8.39118e9i	−0.187003	−	0.107966i
$529$	−7.15569e10	+	1.23940e11i	−0.913753	+	1.58267i
$530$	8.39402e10	−	4.84629e10i	1.06382	−	0.614194i
$531$		−	9.70667e9i		−	0.122093i
$532$	−1.25137e10	−	3.89268e10i	−0.156221	−	0.485961i
$533$	3.15007e8			0.00390312
$534$	−4.94794e9	−	8.57009e9i	−0.0608498	−	0.105395i
$535$	3.90117e10	+	2.25234e10i	0.476189	+	0.274928i
$536$	5.88728e9	−	1.01971e10i	0.0713272	−	0.123542i
$537$	−1.97642e10	+	1.14109e10i	−0.237675	+	0.137221i
$538$			1.62260e10i			0.193679i
$539$	1.24134e10	+	1.25656e11i	0.147073	+	1.48878i
$540$	8.12780e9			0.0955868
$541$	1.56243e10	+	2.70620e10i	0.182394	+	0.315916i	0.942695	−	0.333655i	$-0.108282\pi$
$541$	1.56243e10	+	2.70620e10i	0.182394	+	0.315916i	−0.760301	+	0.649571i	$0.774949\pi$
$542$	−8.09344e10	−	4.67275e10i	−0.937855	−	0.541471i
$543$	1.28690e10	−	2.22898e10i	0.148029	−	0.256394i
$544$	−2.45878e10	+	1.41958e10i	−0.280753	+	0.162093i
$545$			3.69262e10i			0.418551i
$546$	−7.02099e9	+	2.25702e9i	−0.0790001	+	0.0253960i
$547$	1.41283e11			1.57812			0.789061	−	0.614315i	$-0.210567\pi$
$547$	1.41283e11			1.57812			0.789061	+	0.614315i	$0.210567\pi$
$548$	7.84110e9	+	1.35812e10i	0.0869470	+	0.150597i
$549$	1.76611e10	+	1.01966e10i	0.194414	+	0.112245i
$550$	−6.39911e8	+	1.10836e9i	−0.00699308	+	0.0121124i
$551$	1.36828e11	−	7.89977e10i	1.48446	−	0.857054i
$552$			3.18678e10i			0.343239i
$553$	−1.16805e11	−	1.05834e11i	−1.24899	−	1.13168i
$554$	−6.85950e10			−0.728204
$555$	−2.80094e10	−	4.85136e10i	−0.295210	−	0.511319i
$556$	−2.55792e9	−	1.47682e9i	−0.0267663	−	0.0154535i
$557$	−6.06130e10	+	1.04985e11i	−0.629716	+	1.09070i	0.357892	+	0.933763i	$0.383496\pi$
$557$	−6.06130e10	+	1.04985e11i	−0.629716	+	1.09070i	−0.987609	+	0.156938i	$0.949838\pi$
$558$	3.30284e10	−	1.90690e10i	0.340683	−	0.196694i
$559$			4.23944e9i			0.0434171i
$560$	2.38735e10	+	5.15250e9i	0.242752	+	0.0523922i
$561$	1.56891e11			1.58397
$562$	−2.67989e9	−	4.64171e9i	−0.0268641	−	0.0465300i
$563$	−1.19841e11	−	6.91900e10i	−1.19281	−	0.688668i	−0.233866	−	0.972269i	$-0.575138\pi$
$563$	−1.19841e11	−	6.91900e10i	−1.19281	−	0.688668i	−0.958942	+	0.283601i	$0.908471\pi$
$564$	−1.15712e10	+	2.00420e10i	−0.114357	+	0.198072i
$565$	−7.48504e9	+	4.32149e9i	−0.0734515	+	0.0424072i
$566$			7.80617e10i			0.760628i
$567$	2.42274e9	−	1.12254e10i	0.0234409	−	0.108610i
$568$	1.38323e10			0.132893
$569$	−7.44655e10	−	1.28978e11i	−0.710405	−	1.23046i	−0.964705	−	0.263332i	$-0.915178\pi$
$569$	−7.44655e10	−	1.28978e11i	−0.710405	−	1.23046i	0.254300	−	0.967125i	$-0.418155\pi$
$570$	3.78487e10	+	2.18520e10i	0.358552	+	0.207010i
$571$	−3.28239e10	+	5.68527e10i	−0.308778	+	0.534818i	−0.978095	−	0.208158i	$-0.933253\pi$
$571$	−3.28239e10	+	5.68527e10i	−0.308778	+	0.534818i	0.669318	+	0.742976i	$0.266587\pi$
$572$	−1.40955e10	+	8.13805e9i	−0.131673	+	0.0760214i
$573$			7.47491e10i			0.693406i
$574$	−9.89692e8	+	1.09228e9i	−0.00911701	+	0.0100620i
$575$	2.43024e9			0.0222320
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	9.67509e10	+	5.58592e10i	0.872875	+	0.503954i	0.868302	−	0.496035i	$-0.165211\pi$
$577$	9.67509e10	+	5.58592e10i	0.872875	+	0.503954i	0.00457220	+	0.999990i	$0.498545\pi$
$578$	9.32493e10	−	1.61512e11i	0.835476	−	1.44709i
$579$	−7.30001e10	+	4.21466e10i	−0.649545	+	0.375015i
$580$			9.43720e10i			0.833933i
$581$	−3.73438e10	−	1.16167e11i	−0.327728	−	1.01947i
$582$	3.89365e9			0.0339363
$583$	−1.51120e11	−	2.61748e11i	−1.30812	−	2.26574i
$584$	2.78585e9	+	1.60841e9i	0.0239501	+	0.0138276i
$585$	3.94131e9	−	6.82654e9i	0.0336525	−	0.0582878i
$586$	−6.74237e10	+	3.89271e10i	−0.571771	+	0.330112i
$587$			9.40500e10i			0.792148i	0.918219	+	0.396074i	$0.129628\pi$
$587$			9.40500e10i			0.792148i	−0.918219	+	0.396074i	$0.870372\pi$
$588$	1.42324e10	−	3.14362e10i	0.119061	−	0.262979i
$589$	2.05071e11			1.70390
$590$	1.55879e10	+	2.69990e10i	0.128641	+	0.222812i
$591$	−7.12079e10	−	4.11119e10i	−0.583685	−	0.336990i
$592$	1.58055e10	−	2.73760e10i	0.128683	−	0.222886i
$593$	−1.04033e11	+	6.00632e10i	−0.841299	+	0.485724i	−0.857706	−	0.514141i	$-0.828111\pi$
$593$	−1.04033e11	+	6.00632e10i	−0.841299	+	0.485724i	0.0164066	+	0.999865i	$0.494777\pi$
$594$		−	2.53447e10i		−	0.203583i
$595$	−2.17366e11	+	6.98761e10i	−1.73430	+	0.557521i
$596$	−3.88952e10			−0.308256
$597$	−2.33772e10	−	4.04904e10i	−0.184032	−	0.318753i
$598$	2.67658e10	+	1.54532e10i	0.209303	+	0.120841i
$599$	−9.96550e9	+	1.72607e10i	−0.0774090	+	0.134076i	−0.902131	−	0.431462i	$-0.857998\pi$
$599$	−9.96550e9	+	1.72607e10i	−0.0774090	+	0.134076i	0.824722	+	0.565538i	$0.191331\pi$
$600$	3.02905e8	−	1.74882e8i	0.00233723	−	0.00134940i
$601$		−	8.86826e10i		−	0.679737i	−0.940473	−	0.339868i	$-0.889617\pi$
$601$		−	8.86826e10i		−	0.679737i	0.940473	−	0.339868i	$-0.110383\pi$
$602$	−1.47001e10	−	1.33195e10i	−0.111927	−	0.101415i
$603$	1.77819e10			0.134496
$604$	−1.83235e8	−	3.17373e8i	−0.00137677	−	0.00238464i
$605$	−1.42696e11	−	8.23855e10i	−1.06510	−	0.614935i
$606$	7.04174e9	−	1.21966e10i	0.0522143	−	0.0904378i
$607$	−1.41815e11	+	8.18770e10i	−1.04464	+	0.603125i	−0.921145	−	0.389220i	$-0.872745\pi$
$607$	−1.41815e11	+	8.18770e10i	−1.04464	+	0.603125i	−0.123498	+	0.992345i	$0.539411\pi$
$608$			2.46619e10i			0.180473i
$609$	1.30339e11	+	2.81304e10i	0.947554	+	0.204506i
$610$	−6.54987e10			−0.473057
$611$	1.12222e10	+	1.94374e10i	0.0805215	+	0.139467i
$612$	−3.71325e10	−	2.14384e10i	−0.264697	−	0.152823i
$613$	−1.48756e10	+	2.57653e10i	−0.105349	+	0.182471i	−0.913881	−	0.405982i	$-0.866929\pi$
$613$	−1.48756e10	+	2.57653e10i	−0.105349	+	0.182471i	0.808531	+	0.588453i	$0.200263\pi$
$614$	−1.17238e11	+	6.76874e10i	−0.824888	+	0.476249i
$615$		−	1.57545e9i		−	0.0110129i
$616$	1.60669e10	−	7.44440e10i	0.111586	−	0.517019i
$617$	1.16035e11			0.800659			0.400329	−	0.916371i	$-0.368896\pi$
$617$	1.16035e11			0.800659			0.400329	+	0.916371i	$0.368896\pi$
$618$	2.11735e10	+	3.66735e10i	0.145157	+	0.251419i
$619$	−2.33667e11	−	1.34908e11i	−1.59160	−	0.918912i	−0.993032	−	0.117842i	$-0.962402\pi$
$619$	−2.33667e11	−	1.34908e11i	−1.59160	−	0.918912i	−0.598570	−	0.801070i	$-0.704264\pi$
$620$	−6.12453e10	+	1.06080e11i	−0.414483	+	0.717905i
$621$	−4.16790e10	+	2.40634e10i	−0.280253	+	0.161804i
$622$			9.10432e9i			0.0608256i
$623$	3.01530e10	−	3.32786e10i	0.200161	−	0.220909i
$624$	4.44811e9			0.0293385
$625$	7.52719e10	+	1.30375e11i	0.493302	+	0.854424i
$626$	4.60643e10	+	2.65952e10i	0.299963	+	0.173183i
$627$	6.81403e10	−	1.18023e11i	0.440894	−	0.763651i
$628$	1.25945e11	−	7.27142e10i	0.809732	−	0.467499i
$629$			2.95518e11i			1.88791i
$630$	1.12880e10	+	3.51140e10i	0.0716566	+	0.222904i
$631$	−1.81139e11			−1.14260			−0.571299	−	0.820742i	$-0.693560\pi$
$631$	−1.81139e11			−1.14260			−0.571299	+	0.820742i	$0.693560\pi$
$632$	4.75341e10	+	8.23314e10i	0.297945	+	0.516057i
$633$	−2.47915e9	−	1.43134e9i	−0.0154414	−	0.00891511i
$634$	−2.29708e10	+	3.97865e10i	−0.142173	+	0.246252i
$635$	7.41342e10	−	4.28014e10i	0.455957	−	0.263247i
$636$			8.25998e10i			0.504836i
$637$	−1.95017e10	−	2.71978e10i	−0.118445	−	0.165187i
$638$	2.94277e11			1.77613
$639$	1.04448e10	+	1.80909e10i	0.0626464	+	0.108507i
$640$	−1.27572e10	−	7.36537e9i	−0.0760388	−	0.0439010i
$641$	1.51228e11	−	2.61935e11i	0.895780	−	1.55154i	0.0629433	−	0.998017i	$-0.479951\pi$
$641$	1.51228e11	−	2.61935e11i	0.895780	−	1.55154i	0.832837	−	0.553519i	$-0.186715\pi$
$642$	−3.32456e10	+	1.91943e10i	−0.195701	+	0.112988i
$643$		−	2.62802e10i		−	0.153739i	−0.997041	−	0.0768696i	$-0.975507\pi$
$643$		−	2.62802e10i		−	0.153739i	0.997041	−	0.0768696i	$-0.0244925\pi$
$644$	−1.37677e11	+	4.42586e10i	−0.800418	+	0.257309i
$645$	2.12027e10			0.122505
$646$	−1.15276e11	−	1.99665e11i	−0.661928	−	1.14649i
$647$	7.96062e10	+	4.59607e10i	0.454287	+	0.262283i	0.709639	−	0.704566i	$-0.248858\pi$
$647$	7.96062e10	+	4.59607e10i	0.454287	+	0.262283i	−0.255352	+	0.966848i	$0.582191\pi$
$648$	−3.46324e9	+	5.99851e9i	−0.0196419	+	0.0340207i
$649$	8.41901e10	−	4.86072e10i	0.474550	−	0.273982i
$650$		−	3.39213e8i		−	0.00190029i
$651$	1.28253e11	+	1.16207e11i	0.714074	+	0.647008i
$652$	8.98313e10			0.497093
$653$	−8.26701e10	−	1.43189e11i	−0.454670	−	0.787511i	0.543999	−	0.839086i	$-0.316909\pi$
$653$	−8.26701e10	−	1.43189e11i	−0.454670	−	0.787511i	−0.998669	+	0.0515746i	$0.983576\pi$
$654$	−2.72524e10	−	1.57342e10i	−0.148968	−	0.0860069i
$655$	−1.44027e11	+	2.49463e11i	−0.782492	+	1.35532i
$656$	7.69910e8	−	4.44508e8i	0.00415743	−	0.00240029i
$657$			4.85804e9i			0.0260735i
$658$	−1.02656e11	−	2.21559e10i	−0.547624	−	0.118191i
$659$	3.14934e10			0.166985			0.0834925	−	0.996508i	$-0.473393\pi$
$659$	3.14934e10			0.166985			0.0834925	+	0.996508i	$0.473393\pi$
$660$	4.07008e10	+	7.04959e10i	0.214500	+	0.371525i
$661$	1.99589e10	+	1.15233e10i	0.104552	+	0.0603628i	0.551364	−	0.834265i	$-0.314108\pi$
$661$	1.99589e10	+	1.15233e10i	0.104552	+	0.0603628i	−0.446812	+	0.894628i	$0.647441\pi$
$662$	5.54411e10	−	9.60268e10i	0.288669	−	0.499989i
$663$	−3.60123e10	+	2.07917e10i	−0.186379	+	0.107606i
$664$			7.35968e10i			0.378605i
$665$	−4.18408e10	+	1.93864e11i	−0.213950	+	0.991312i
$666$	4.77389e10			0.242647
$667$	−2.79400e11	−	4.83935e11i	−1.41164	−	2.44503i
$668$	−1.29244e11	−	7.46190e10i	−0.649089	−	0.374752i
$669$	−4.09930e10	+	7.10020e10i	−0.204647	+	0.354459i
$670$	−4.94601e10	+	2.85558e10i	−0.245446	+	0.141708i
$671$			2.04243e11i			1.00753i
$672$	−1.39751e10	+	1.54237e10i	−0.0685296	+	0.0756331i
$673$	1.07957e10			0.0526249			0.0263124	−	0.999654i	$-0.491624\pi$
$673$	1.07957e10			0.0526249			0.0263124	+	0.999654i	$0.491624\pi$
$674$	1.31774e11	+	2.28239e11i	0.638541	+	1.10599i
$675$	4.57446e8	+	2.64106e8i	0.00220356	+	0.00127222i
$676$	−5.00498e10	+	8.66888e10i	−0.239671	+	0.415122i
$677$	3.45829e11	−	1.99665e11i	1.64629	−	0.950487i	0.667764	−	0.744373i	$-0.267251\pi$
$677$	3.45829e11	−	1.99665e11i	1.64629	−	0.950487i	0.978528	−	0.206114i	$-0.0660819\pi$
$678$		−	7.36552e9i		−	0.0348566i
$679$	5.40757e9	+	1.68215e10i	0.0254403	+	0.0791381i
$680$	1.37711e11			0.644071
$681$	−3.16821e10	−	5.48750e10i	−0.147308	−	0.255144i
$682$	3.30786e11	+	1.90980e11i	1.52901	+	0.882774i
$683$	1.63717e11	−	2.83566e11i	0.752334	−	1.30308i	−0.194355	−	0.980931i	$-0.562261\pi$
$683$	1.63717e11	−	2.83566e11i	0.752334	−	1.30308i	0.946689	−	0.322149i	$-0.104405\pi$
$684$	−3.22545e10	+	1.86222e10i	−0.147355	+	0.0850757i
$685$		−	7.60653e10i		−	0.345481i
$686$	1.55578e11	+	1.78283e10i	0.702509	+	0.0805034i
$687$	−1.27360e11			−0.571750
$688$	5.98228e9	+	1.03616e10i	0.0267001	+	0.0462459i
$689$	6.93756e10	+	4.00540e10i	0.307843	+	0.177733i
$690$	7.72863e10	−	1.33864e11i	0.340962	−	0.590564i
$691$	3.29744e11	−	1.90378e11i	1.44632	−	0.835035i	0.448062	−	0.894002i	$-0.352114\pi$
$691$	3.29744e11	−	1.90378e11i	1.44632	−	0.835035i	0.998260	+	0.0589678i	$0.0187809\pi$
$692$			7.57383e9i			0.0330287i
$693$	1.09495e11	−	3.51991e10i	0.474747	−	0.152616i
$694$	−1.70859e11			−0.736544
$695$	7.16319e9	+	1.24070e10i	0.0307021	+	0.0531775i
$696$	−6.96487e10	−	4.02117e10i	−0.296808	−	0.171362i
$697$	−4.15550e9	+	7.19755e9i	−0.0176073	+	0.0304967i
$698$	−4.72742e10	+	2.72938e10i	−0.199160	+	0.114985i
$699$			2.06849e11i			0.866452i
$700$	1.17621e9	+	1.06574e9i	0.00489884	+	0.00443874i
$701$	−2.13418e11			−0.883809			−0.441904	−	0.897062i	$-0.645697\pi$
$701$	−2.13418e11			−0.883809			−0.441904	+	0.897062i	$0.645697\pi$
$702$	3.35877e9	+	5.81755e9i	0.0138303	+	0.0239548i
$703$	2.22306e11	+	1.28348e11i	0.910185	+	0.525495i
$704$	−2.29672e10	+	3.97804e10i	−0.0935014	+	0.161949i
$705$	9.72121e10	−	5.61254e10i	0.393517	−	0.227197i
$706$			2.04940e10i			0.0824913i
$707$	6.24721e10	+	1.34831e10i	0.250039	+	0.0539649i
$708$	−2.65678e10			−0.105736
$709$	6.57127e10	+	1.13818e11i	0.260055	+	0.450428i	0.966256	−	0.257583i	$-0.0829261\pi$
$709$	6.57127e10	+	1.13818e11i	0.260055	+	0.450428i	−0.706202	+	0.708011i	$0.749593\pi$
$710$	−5.81040e10	−	3.35464e10i	−0.228651	−	0.132012i
$711$	−7.17859e10	+	1.24337e11i	−0.280906	+	0.486543i
$712$	−2.34569e10	+	1.35429e10i	−0.0912748	+	0.0526975i
$713$		−	7.25298e11i		−	2.80646i
$714$	4.10490e10	−	1.90195e11i	0.157946	−	0.731824i
$715$	7.89460e10			0.302069
$716$	3.12324e10	+	5.40960e10i	0.118837	+	0.205832i
$717$	1.76821e11	+	1.02087e11i	0.669046	+	0.386274i
$718$	1.41083e11	−	2.44363e11i	0.530857	−	0.919471i
$719$	−2.74912e11	+	1.58721e11i	−1.02868	+	0.593906i	−0.916605	−	0.399794i	$-0.869081\pi$
$719$	−2.74912e11	+	1.58721e11i	−1.02868	+	0.593906i	−0.112070	+	0.993700i	$0.535748\pi$
$720$		−	2.22463e10i		−	0.0827806i
$721$	−1.29032e11	+	1.42407e11i	−0.477482	+	0.526976i
$722$	−8.11900e9			−0.0298781
$723$	−7.14161e10	−	1.23696e11i	−0.261362	−	0.452693i
$724$	−6.10088e10	−	3.52234e10i	−0.222043	−	0.128197i
$725$	−3.06654e9	+	5.31141e9i	−0.0110993	+	0.0192246i
$726$	1.21605e11	−	7.02086e10i	0.437728	−	0.252722i
$727$			4.92748e11i			1.76395i	0.471293	+	0.881977i	$0.343788\pi$
$727$			4.92748e11i			1.76395i	−0.471293	+	0.881977i	$0.656212\pi$
$728$	6.17762e9	+	1.92169e10i	0.0219936	+	0.0684161i
$729$	−1.04604e10			−0.0370370
$730$	−7.80149e9	−	1.35126e10i	−0.0274717	−	0.0475824i
$731$	−9.68661e10	−	5.59257e10i	−0.339236	−	0.195858i
$732$	2.79089e10	−	4.83396e10i	0.0972071	−	0.168368i
$733$	1.58090e11	−	9.12732e10i	0.547631	−	0.316175i	−0.200535	−	0.979687i	$-0.564268\pi$
$733$	1.58090e11	−	9.12732e10i	0.547631	−	0.316175i	0.748166	+	0.663512i	$0.230935\pi$
$734$		−	2.96679e11i		−	1.02212i
$735$	−1.36024e11	+	9.75340e10i	−0.466086	+	0.334200i
$736$	8.72244e10			0.297253
$737$	8.90448e10	+	1.54230e11i	0.301813	+	0.522756i
$738$	1.16272e9	+	6.71294e8i	0.00391966	+	0.00226302i
$739$	−9.21547e10	+	1.59617e11i	−0.308987	+	0.535181i	−0.978141	−	0.207943i	$-0.933323\pi$
$739$	−9.21547e10	+	1.59617e11i	−0.308987	+	0.535181i	0.669154	+	0.743124i	$0.266657\pi$
$740$	−1.32785e11	+	7.66635e10i	−0.442815	+	0.255659i
$741$			3.61208e10i			0.119808i
$742$	−3.56851e11	+	1.14716e11i	−1.17726	+	0.378450i
$743$	−1.39124e11			−0.456507			−0.228253	−	0.973602i	$-0.573301\pi$
$743$	−1.39124e11			−0.456507			−0.228253	+	0.973602i	$0.573301\pi$
$744$	−5.21930e10	−	9.04010e10i	−0.170342	−	0.295040i
$745$	1.63383e11	+	9.43292e10i	0.530373	+	0.306211i
$746$	−6.23708e10	+	1.08029e11i	−0.201385	+	0.348808i
$747$	−9.62550e10	+	5.55728e10i	−0.309130	+	0.178476i
$748$		−	4.29421e11i		−	1.37176i
$749$	−1.29096e11	−	1.16971e11i	−0.410191	−	0.371666i
$750$	−1.30012e11			−0.410902
$751$	1.12421e11	+	1.94719e11i	0.353418	+	0.612138i	0.986846	−	0.161664i	$-0.0516860\pi$
$751$	1.12421e11	+	1.94719e11i	0.353418	+	0.612138i	−0.633428	+	0.773802i	$0.718353\pi$
$752$	5.48562e10	+	3.16713e10i	0.171536	+	0.0990362i
$753$	1.77386e10	−	3.07242e10i	0.0551747	−	0.0955653i
$754$	−6.75477e10	+	3.89987e10i	−0.208990	+	0.120660i
$755$			1.77754e9i			0.00547056i
$756$	−3.07248e10	−	6.63119e9i	−0.0940593	−	0.0203004i
$757$	1.15204e11			0.350819			0.175410	−	0.984496i	$-0.443875\pi$
$757$	1.15204e11			0.350819			0.175410	+	0.984496i	$0.443875\pi$
$758$	−4.81502e10	−	8.33985e10i	−0.145855	−	0.252628i
$759$	−4.17424e11	−	2.41000e11i	−1.25779	−	0.726188i
$760$	5.98103e10	−	1.03594e11i	0.179276	−	0.310515i
$761$	1.93352e10	−	1.11632e10i	0.0576513	−	0.0332850i	−0.470897	−	0.882188i	$-0.656070\pi$
$761$	1.93352e10	−	1.11632e10i	0.0576513	−	0.0332850i	0.528549	+	0.848903i	$0.322736\pi$
$762$			7.29504e10i			0.216375i
$763$	3.01268e10	−	1.39589e11i	0.0888905	−	0.411863i
$764$	2.04593e11			0.600507
$765$	1.03986e11	+	1.80108e11i	0.303618	+	0.525882i
$766$	1.38819e11	+	8.01471e10i	0.403212	+	0.232794i
$767$	−1.28832e10	+	2.23143e10i	−0.0372256	+	0.0644766i
$768$	1.08716e10	−	6.27674e9i	0.0312500	−	0.0180422i
$769$		−	3.04933e10i		−	0.0871964i	−0.999049	−	0.0435982i	$-0.986118\pi$
$769$		−	3.04933e10i		−	0.0871964i	0.999049	−	0.0435982i	$-0.0138821\pi$
$770$	−2.48033e11	+	2.73743e11i	−0.705581	+	0.778718i
$771$	1.03514e11			0.292943
$772$	1.15358e11	+	1.99806e11i	0.324772	+	0.562522i
$773$	2.15578e11	+	1.24464e11i	0.603792	+	0.348599i	0.770532	−	0.637401i	$-0.219991\pi$
$773$	2.15578e11	+	1.24464e11i	0.603792	+	0.348599i	−0.166740	+	0.986001i	$0.553324\pi$
$774$	−9.03443e9	+	1.56481e10i	−0.0251731	+	0.0436011i
$775$	−6.89397e9	+	3.98024e9i	−0.0191101	+	0.0110332i
$776$		−	1.06572e10i		−	0.0293897i
$777$	6.63007e10	+	2.06244e11i	0.181900	+	0.565844i
$778$	−8.70208e10			−0.237522
$779$	3.60961e9	+	6.25203e9i	0.00980191	+	0.0169774i
$780$	−1.86847e10	−	1.07876e10i	−0.0504787	−	0.0291439i
$781$	−1.04607e11	+	1.81184e11i	−0.281161	+	0.486985i
$782$	−7.06177e11	+	4.07711e11i	−1.88837	+	1.09025i
$783$		−	1.21455e11i		−	0.323124i
$784$	−8.60430e10	−	3.89551e10i	−0.227746	−	0.103110i
$785$	−7.05390e11			−1.85759
$786$	−1.22740e11	−	2.12591e11i	−0.321584	−	0.557000i
$787$	3.14298e10	+	1.81460e10i	0.0819299	+	0.0473023i	0.540405	−	0.841405i	$-0.318271\pi$
$787$	3.14298e10	+	1.81460e10i	0.0819299	+	0.0473023i	−0.458475	+	0.888707i	$0.651604\pi$
$788$	−1.12526e11	+	1.94901e11i	−0.291842	+	0.505486i
$789$	6.93748e10	−	4.00536e10i	0.179017	−	0.103355i
$790$		−	4.61121e11i		−	1.18388i
$791$	3.18208e10	−	1.02294e10i	0.0812840	−	0.0261302i
$792$	−6.93701e10			−0.176308
$793$	−2.70670e10	−	4.68813e10i	−0.0684458	−	0.118552i
$794$	1.87720e11	+	1.08380e11i	0.472313	+	0.272690i
$795$	2.00322e11	−	3.46968e11i	0.501488	−	0.868602i
$796$	−1.10825e11	+	6.39848e10i	−0.276049	+	0.159377i
$797$			7.21635e11i			1.78848i	0.447587	+	0.894240i	$0.352284\pi$
$797$			7.21635e11i			1.78848i	−0.447587	+	0.894240i	$0.647716\pi$
$798$	−1.25248e11	−	1.13484e11i	−0.308858	−	0.279850i
$799$	−5.92161e11			−1.45296
$800$	−4.78664e8	−	8.29070e8i	−0.00116861	−	0.00202410i
$801$	−3.54246e10	−	2.04524e10i	−0.0860547	−	0.0496837i
$802$	1.91165e11	−	3.31108e11i	0.462074	−	0.800335i
$803$	−4.21359e10	+	2.43272e10i	−0.101342	+	0.0585099i
$804$		−	4.86703e10i		−	0.116477i
$805$	6.85660e11	+	1.47983e11i	1.63277	+	0.352394i
$806$	−1.01237e11			−0.239883
$807$	3.35353e10	+	5.80848e10i	0.0790693	+	0.136952i
$808$	−3.33831e10	−	1.92737e10i	−0.0783214	−	0.0452189i
$809$	−1.59556e11	+	2.76359e11i	−0.372494	+	0.645178i	−0.989949	−	0.141428i	$-0.954831\pi$
$809$	−1.59556e11	+	2.76359e11i	−0.372494	+	0.645178i	0.617455	+	0.786606i	$0.288164\pi$
$810$	2.90953e10	−	1.67982e10i	0.0675901	−	0.0390232i
$811$		−	5.77386e11i		−	1.33470i	−0.744745	−	0.667349i	$-0.767429\pi$
$811$		−	5.77386e11i		−	1.33470i	0.744745	−	0.667349i	$-0.232571\pi$
$812$	7.69948e10	−	3.56746e11i	0.177108	−	0.820606i
$813$	−3.86297e11			−0.884218
$814$	2.39058e11	+	4.14060e11i	0.544509	+	0.943117i
$815$	−3.77345e11	−	2.17860e11i	−0.855279	−	0.493795i
$816$	−5.86785e10	+	1.01634e11i	−0.132348	+	0.229234i
$817$	−8.41412e10	+	4.85789e10i	−0.188851	+	0.109033i
$818$		−	1.82135e11i		−	0.406800i
$819$	−2.04685e10	+	2.25902e10i	−0.0454936	+	0.0502093i
$820$	−4.31210e9			−0.00953748
$821$	−3.63982e11	−	6.30435e11i	−0.801138	−	1.38761i	−0.918868	−	0.394565i	$-0.870895\pi$
$821$	−3.63982e11	−	6.30435e11i	−0.801138	−	1.38761i	0.117730	−	0.993046i	$-0.462438\pi$
$822$	5.61380e10	+	3.24113e10i	0.122962	+	0.0709919i
$823$	−3.48957e11	+	6.04411e11i	−0.760628	+	1.31745i	0.181900	+	0.983317i	$0.441775\pi$
$823$	−3.48957e11	+	6.04411e11i	−0.760628	+	1.31745i	−0.942527	+	0.334129i	$0.891558\pi$
$824$	1.00378e11	−	5.79532e10i	0.217736	−	0.125710i
$825$			5.29016e9i			0.0114197i
$826$	−3.68978e10	−	1.14779e11i	−0.0792649	−	0.246572i
$827$	1.05240e11			0.224989			0.112494	−	0.993652i	$-0.464116\pi$
$827$	1.05240e11			0.224989			0.112494	+	0.993652i	$0.464116\pi$
$828$	6.58631e10	+	1.14078e11i	0.140127	+	0.242706i
$829$	3.17670e11	+	1.83407e11i	0.672601	+	0.388326i	0.797062	−	0.603898i	$-0.206387\pi$
$829$	3.17670e11	+	1.83407e11i	0.672601	+	0.388326i	−0.124460	+	0.992225i	$0.539720\pi$
$830$	1.78488e11	−	3.09150e11i	0.376094	−	0.651414i
$831$	−2.45551e11	+	1.41769e11i	−0.514918	+	0.297288i
$832$		−	1.21748e10i		−	0.0254079i
$833$	8.78699e11	−	8.68050e10i	1.82499	−	0.180287i
$834$	−1.22089e10			−0.0252355
$835$	3.61934e11	+	6.26888e11i	0.744532	+	1.28957i
$836$	−3.23036e11	−	1.86505e11i	−0.661341	−	0.381825i
$837$	7.88218e10	−	1.36523e11i	0.160600	−	0.278167i
$838$	9.78803e10	−	5.65112e10i	0.198481	−	0.114593i
$839$			2.22293e11i			0.448620i	0.974518	+	0.224310i	$0.0720128\pi$
$839$			2.22293e11i			0.448620i	−0.974518	+	0.224310i	$0.927987\pi$
$840$	9.61095e10	−	3.08961e10i	0.193041	−	0.0620564i
$841$	9.09972e11			1.81905
$842$	8.94942e10	+	1.55008e11i	0.178052	+	0.308395i
$843$	−1.91866e10	−	1.10774e10i	−0.0379916	−	0.0219344i
$844$	−3.91766e9	+	6.78559e9i	−0.00772071	+	0.0133727i
$845$	4.20478e11	−	2.42763e11i	0.824738	−	0.476163i
$846$			9.56597e10i			0.186744i
$847$	4.72205e11	+	4.27855e11i	0.917481	+	0.831310i
$848$	2.26081e11			0.437201
$849$	1.61335e11	+	2.79440e11i	0.310525	+	0.537845i
$850$	7.75061e9	+	4.47482e9i	0.0148477	+	0.00857234i
$851$	4.53944e11	−	7.86254e11i	0.865533	−	1.49915i
$852$	4.95160e10	−	2.85881e10i	0.0939696	−	0.0542534i
$853$		−	8.52855e11i		−	1.61094i	−0.592637	−	0.805469i	$-0.701913\pi$
$853$		−	8.52855e11i		−	1.61094i	0.592637	−	0.805469i	$-0.298087\pi$
$854$	2.47599e11	+	5.34382e10i	0.465497	+	0.100466i
$855$	1.80651e11			0.338046
$856$	5.25362e10	+	9.09954e10i	0.0978507	+	0.169482i
$857$	−4.86704e11	−	2.80998e11i	−0.902280	−	0.520931i	−0.0243406	−	0.999704i	$-0.507749\pi$
$857$	−4.86704e11	−	2.80998e11i	−0.902280	−	0.520931i	−0.877939	+	0.478772i	$0.841082\pi$
$858$	−3.36387e10	+	5.82640e10i	−0.0620713	+	0.107511i
$859$	5.66982e11	−	3.27347e11i	1.04135	−	0.601223i	0.121134	−	0.992636i	$-0.461347\pi$
$859$	5.66982e11	−	3.27347e11i	1.04135	−	0.601223i	0.920215	+	0.391413i	$0.128014\pi$
$860$		−	5.80332e10i		−	0.106092i
$861$	−1.28535e9	+	5.95552e9i	−0.00233889	+	0.0108369i
$862$	−2.78023e11			−0.503561
$863$	9.24709e10	+	1.60164e11i	0.166710	+	0.288750i	0.937261	−	0.348628i	$-0.113352\pi$
$863$	9.24709e10	+	1.60164e11i	0.166710	+	0.288750i	−0.770551	+	0.637378i	$0.780019\pi$
$864$	1.64183e10	+	9.47912e9i	0.0294628	+	0.0170103i
$865$	1.83681e10	−	3.18146e10i	0.0328096	−	0.0568279i
$866$	−7.05665e9	+	4.07416e9i	−0.0125466	+	0.00724379i
$867$		−	7.70894e11i		−	1.36433i
$868$	3.18067e11	−	3.51037e11i	0.560325	−	0.618406i
$869$	−1.43790e12			−2.52145
$870$	1.95044e11	+	3.37826e11i	0.340452	+	0.589679i
$871$	−4.08782e10	−	2.36010e10i	−0.0710263	−	0.0410071i
$872$	−4.30655e10	+	7.45917e10i	−0.0744841	+	0.129010i
$873$	1.39382e10	−	8.04723e9i	0.0239966	−	0.0138544i
$874$			7.08303e11i			1.21387i
$875$	−1.80563e11	−	5.61683e11i	−0.308033	−	0.958207i
$876$	1.32968e10			0.0225803
$877$	−3.10378e11	−	5.37590e11i	−0.524677	−	0.908768i	−0.999587	−	0.0287332i	$-0.990853\pi$
$877$	−3.10378e11	−	5.37590e11i	−0.524677	−	0.908768i	0.474910	−	0.880034i	$-0.342481\pi$
$878$	6.26547e11	+	3.61737e11i	1.05433	+	0.608717i
$879$	−1.60906e11	+	2.78697e11i	−0.269535	+	0.466849i
$880$	1.92952e11	−	1.11401e11i	0.321750	−	0.185762i
$881$			2.18312e11i			0.362388i	0.983447	+	0.181194i	$0.0579963\pi$
$881$			2.18312e11i			0.362388i	−0.983447	+	0.181194i	$0.942004\pi$
$882$	−1.40228e10	−	1.41948e11i	−0.0231718	−	0.234560i
$883$	−2.37203e11			−0.390191			−0.195095	−	0.980784i	$-0.562502\pi$
$883$	−2.37203e11			−0.390191			−0.195095	+	0.980784i	$0.562502\pi$
$884$	5.69084e10	+	9.85682e10i	0.0931895	+	0.161409i
$885$	1.11601e11	+	6.44326e10i	0.181925	+	0.105035i
$886$	−7.98224e10	+	1.38256e11i	−0.129536	+	0.224363i
$887$	4.95974e11	−	2.86351e11i	0.801243	−	0.462598i	−0.0426623	−	0.999090i	$-0.513584\pi$
$887$	4.95974e11	−	2.86351e11i	0.801243	−	0.462598i	0.843906	+	0.536491i	$0.180251\pi$
$888$		−	1.30665e11i		−	0.210139i
$889$	−3.15163e11	+	1.01315e11i	−0.504578	+	0.162206i
$890$	1.31377e11			0.209392
$891$	−5.23813e10	−	9.07271e10i	−0.0831123	−	0.143955i
$892$	1.94337e11	+	1.12201e11i	0.306971	+	0.177230i
$893$	−2.57186e11	+	4.45458e11i	−0.404428	+	0.700489i
$894$	−1.39234e11	+	8.03870e10i	−0.217970	+	0.125845i
$895$		−	3.02981e11i		−	0.472196i
$896$	4.22157e10	+	3.82508e10i	0.0655002	+	0.0593484i
$897$	1.27752e11			0.197333
$898$	4.01666e11	+	6.95706e11i	0.617675	+	1.06984i
$899$	1.58517e12	+	9.15201e11i	2.42682	+	1.40113i
$900$	7.22877e8	−	1.25206e9i	0.00110178	−	0.00190834i
$901$	−1.83037e12	+	1.05677e12i	−2.77741	+	1.60354i
$902$			1.34463e10i			0.0203131i
$903$	−8.01506e10	−	1.72986e10i	−0.120547	−	0.0260171i
$904$	−2.01599e10			−0.0301867
$905$	1.70849e11	+	2.95918e11i	0.254693	+	0.441141i
$906$	−1.31187e9	−	7.57406e8i	−0.00194705	−	0.00112413i
$907$	4.89219e10	−	8.47352e10i	0.0722893	−	0.125209i	−0.827615	−	0.561296i	$-0.810303\pi$
$907$	4.89219e10	−	8.47352e10i	0.0722893	−	0.125209i	0.899904	+	0.436088i	$0.143636\pi$
$908$	−1.50196e11	+	8.67160e10i	−0.220961	+	0.127572i
$909$		−	5.82142e10i		−	0.0852656i
$910$	2.06555e10	−	9.57045e10i	0.0301210	−	0.139562i
$911$	1.02467e12			1.48769			0.743843	−	0.668355i	$-0.233001\pi$
$911$	1.02467e12			1.48769			0.743843	+	0.668355i	$0.233001\pi$
$912$	5.09701e10	+	8.82828e10i	0.0736777	+	0.127614i
$913$	−9.64014e11	−	5.56574e11i	−1.38740	−	0.801013i
$914$	−2.40209e11	+	4.16054e11i	−0.344194	+	0.596162i
$915$	−2.34468e11	+	1.35370e11i	−0.334502	+	0.193125i
$916$			3.48593e11i			0.495150i
$917$	7.47982e11	−	8.25515e11i	1.05783	−	1.16748i
$918$	−1.77232e11			−0.249558
$919$	−4.05429e11	−	7.02224e11i	−0.568399	−	0.984495i	−0.996725	−	0.0808709i	$-0.974230\pi$
$919$	−4.05429e11	−	7.02224e11i	−0.568399	−	0.984495i	0.428326	−	0.903624i	$-0.359103\pi$
$920$	−3.66394e11	−	2.11538e11i	−0.511443	−	0.295282i
$921$	−2.79787e11	+	4.84605e11i	−0.388856	+	0.673518i
$922$	−7.47442e10	+	4.31536e10i	−0.103432	+	0.0597163i
$923$		−	5.54513e10i		−	0.0764021i
$924$	−9.63424e10	−	2.99696e11i	−0.132169	−	0.411143i
$925$	−9.96448e9			−0.0136109
$926$	−1.57197e11	−	2.72274e11i	−0.213797	−	0.370307i
$927$	1.51590e11	+	8.75208e10i	0.205283	+	0.118520i
$928$	−1.10062e11	+	1.90633e11i	−0.148404	+	0.257044i
$929$	2.54570e11	−	1.46976e11i	0.341778	−	0.197325i	−0.319280	−	0.947660i	$-0.603441\pi$
$929$	2.54570e11	−	1.46976e11i	0.341778	−	0.197325i	0.661058	+	0.750335i	$0.270108\pi$
$930$			5.06317e11i			0.676847i
$931$	3.16334e11	−	6.98710e11i	0.421063	−	0.930032i
$932$	5.66160e11			0.750370
$933$	1.88164e10	+	3.25910e10i	0.0248319	+	0.0430102i
$934$	−3.90046e11	−	2.25193e11i	−0.512540	−	0.295915i
$935$	−1.04144e12	+	1.80382e12i	−1.36266	+	2.36019i
$936$	1.59230e10	−	9.19317e9i	0.0207454	−	0.0119774i
$937$		−	1.67151e10i		−	0.0216845i	−0.999941	−	0.0108423i	$-0.996549\pi$
$937$		−	1.67151e10i		−	0.0216845i	0.999941	−	0.0108423i	$-0.00345126\pi$
$938$	2.10267e11	−	6.75942e10i	0.271619	−	0.0873168i
$939$	2.19864e11			0.282807
$940$	−1.53619e11	−	2.66076e11i	−0.196759	−	0.340796i
$941$	1.18411e11	+	6.83646e10i	0.151020	+	0.0871912i	0.573606	−	0.819132i	$-0.305544\pi$
$941$	1.18411e11	+	6.83646e10i	0.151020	+	0.0871912i	−0.422586	+	0.906323i	$0.638878\pi$
$942$	3.00565e11	−	5.20594e11i	0.381711	−	0.661143i
$943$	2.21123e10	−	1.27665e10i	0.0279632	−	0.0161445i
$944$			7.27179e10i			0.0915701i
$945$	1.12980e11	+	1.02369e11i	0.141669	+	0.128364i
$946$	−1.80963e11			−0.225957
$947$	−4.98621e11	−	8.63636e11i	−0.619969	−	1.07382i	−0.989491	−	0.144596i	$-0.953812\pi$
$947$	−4.98621e11	−	8.63636e11i	−0.619969	−	1.07382i	0.369521	−	0.929222i	$-0.379522\pi$
$948$	3.40318e11	+	1.96483e11i	0.421359	+	0.243271i
$949$	6.44784e9	−	1.11680e10i	0.00794967	−	0.0137692i
$950$	6.73244e9	−	3.88698e9i	0.00826567	−	0.00477219i
$951$			1.89900e11i			0.232168i
$952$	−5.20577e11	−	1.12354e11i	−0.633778	−	0.136786i
$953$	−1.27182e12			−1.54190			−0.770948	−	0.636898i	$-0.780217\pi$
$953$	−1.27182e12			−1.54190			−0.770948	+	0.636898i	$0.780217\pi$
$954$	1.70714e11	+	2.95685e11i	0.206098	+	0.356973i
$955$	−8.59413e11	−	4.96182e11i	−1.03321	−	0.596524i
$956$	2.79420e11	−	4.83970e11i	0.334523	−	0.579411i
$957$	1.05343e12	−	6.08200e11i	1.25591	−	0.725101i
$958$		−	2.30428e9i		−	0.00273573i
$959$	−6.20591e10	+	2.87543e11i	−0.0733721	+	0.339960i
$960$	−6.08897e10			−0.0716901
$961$	7.61445e11	+	1.31886e12i	0.892781	+	1.54634i
$962$	−1.09745e11	−	6.33615e10i	−0.128140	−	0.0739818i
$963$	−7.93401e10	+	1.37421e11i	−0.0922545	+	0.159789i
$964$	−3.38565e11	+	1.95471e11i	−0.392044	+	0.226346i
$965$		−	1.11907e12i		−	1.29047i
$966$	−4.01373e11	+	4.42978e11i	−0.460935	+	0.508714i
$967$	−3.42799e11			−0.392043			−0.196021	−	0.980600i	$-0.562802\pi$
$967$	−3.42799e11			−0.392043			−0.196021	+	0.980600i	$0.562802\pi$
$968$	−1.92166e11	−	3.32841e11i	−0.218864	−	0.379084i
$969$	−8.25317e11	−	4.76497e11i	−0.936107	−	0.540462i
$970$	−2.58459e10	+	4.47665e10i	−0.0291948	+	0.0505669i
$971$	−1.01509e11	+	5.86060e10i	−0.114189	+	0.0659273i	−0.556007	−	0.831178i	$-0.687667\pi$
$971$	−1.01509e11	+	5.86060e10i	−0.114189	+	0.0659273i	0.441818	+	0.897105i	$0.354334\pi$
$972$			2.86307e10i			0.0320750i
$973$	−1.69559e10	−	5.27453e10i	−0.0189178	−	0.0588481i
$974$	−4.04326e11			−0.449258
$975$	−7.01071e8	−	1.21429e9i	−0.000775788	−	0.00134370i
$976$	−1.32309e11	−	7.63885e10i	−0.145811	−	0.0841838i
$977$	−6.10515e11	+	1.05744e12i	−0.670067	+	1.16059i	0.307817	+	0.951445i	$0.400401\pi$
$977$	−6.10515e11	+	1.05744e12i	−0.670067	+	1.16059i	−0.977885	+	0.209145i	$0.932932\pi$
$978$	3.21572e11	−	1.85659e11i	0.351497	−	0.202937i
$979$		−	4.09670e11i		−	0.445967i
$980$	2.66957e11	+	3.72307e11i	0.289426	+	0.403643i
$981$	−1.30075e11			−0.140449
$982$	−3.82475e11	−	6.62466e11i	−0.411298	−	0.712390i
$983$	9.09822e11	+	5.25286e11i	0.974412	+	0.562577i	0.900578	−	0.434694i	$-0.143143\pi$
$983$	9.09822e11	+	5.25286e11i	0.974412	+	0.562577i	0.0738334	+	0.997271i	$0.476477\pi$
$984$	1.83738e9	−	3.18243e9i	0.00195983	−	0.00339452i
$985$	9.45352e11	−	5.45799e11i	1.00427	−	0.579813i
$986$		−	2.05784e12i		−	2.17723i
$987$	−4.13273e11	+	1.32854e11i	−0.435480	+	0.139993i
$988$	9.88650e10			0.103756
$989$	1.71815e11	+	2.97592e11i	0.179587	+	0.311054i
$990$	2.91396e11	+	1.68237e11i	0.303349	+	0.175139i
$991$	7.74778e11	−	1.34196e12i	0.803310	−	1.39137i	−0.114117	−	0.993467i	$-0.536404\pi$
$991$	7.74778e11	−	1.34196e12i	0.803310	−	1.39137i	0.917426	−	0.397906i	$-0.130263\pi$
$992$	−2.47434e11	+	1.42856e11i	−0.255512	+	0.147520i
$993$		−	4.58333e11i		−	0.471394i
$994$	1.92276e11	+	1.74217e11i	0.196961	+	0.178462i
$995$	6.20708e11			0.633278
$996$	1.52107e11	+	2.63456e11i	0.154565	+	0.267714i
$997$	−1.33307e12	−	7.69646e11i	−1.34918	−	0.778951i	−0.361049	−	0.932547i	$-0.617581\pi$
$997$	−1.33307e12	−	7.69646e11i	−1.34918	−	0.778951i	−0.988134	+	0.153595i	$0.950915\pi$
$998$	5.43774e10	−	9.41845e10i	0.0548146	−	0.0949417i
$999$	1.70892e11	−	9.86648e10i	0.171578	−	0.0990604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.b.31.3	yes	12
3.2	odd	2		126.9.n.c.73.4		12
7.3	odd	6		294.9.c.b.97.7		12
7.4	even	3		294.9.c.b.97.12		12
7.5	odd	6	inner	42.9.g.b.19.3	✓	12
21.5	even	6		126.9.n.c.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.b.19.3	✓	12	7.5	odd	6	inner
42.9.g.b.31.3	yes	12	1.1	even	1	trivial
126.9.n.c.19.4		12	21.5	even	6
126.9.n.c.73.4		12	3.2	odd	2
294.9.c.b.97.7		12	7.3	odd	6
294.9.c.b.97.12		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)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(537.676 - 310.427i) q^{5} +529.090i q^{6} +(-2285.79 + 734.809i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(-40.5000 - 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(537.676 - 310.427i) q^{5} +529.090i q^{6} +(-2285.79 + 734.809i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(-6083.11 - 3512.08i) q^{10} +(-10951.6 + 18968.8i) q^{11} +(5184.00 - 2992.98i) q^{12} -5805.39i q^{13} +(20130.0 + 18239.4i) q^{14} -29034.5 q^{15} +(-8192.00 - 14189.0i) q^{16} +(132646. + 76583.4i) q^{17} +(12371.5 - 21428.1i) q^{18} +(115221. - 66522.9i) q^{19} +79469.4i q^{20} +(109756. + 23688.2i) q^{21} +247807. q^{22} +(-235279. - 407515. i) q^{23} +(-58650.3 - 33861.7i) q^{24} +(-2582.29 + 4472.67i) q^{25} +(-56881.0 + 32840.3i) q^{26} -102276. i q^{27} +(64836.3 - 300411. i) q^{28} +1.18753e6 q^{29} +(164244. + 284479. i) q^{30} +(1.33485e6 + 770678. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(887082. - 512157. i) q^{33} -1.73288e6i q^{34} +(-1.00091e6 + 1.10466e6i) q^{35} -279936. q^{36} +(964693. + 1.67090e6i) q^{37} +(-1.30358e6 - 752621. i) q^{38} +(-135746. + 235118. i) q^{39} +(778638. - 449547. i) q^{40} +54261.2i q^{41} +(-388780. - 1.20939e6i) q^{42} -730259. q^{43} +(-1.40181e6 - 2.42800e6i) q^{44} +(1.17590e6 + 678904. i) q^{45} +(-2.66188e6 + 4.61051e6i) q^{46} +(-3.34816e6 + 1.93306e6i) q^{47} +766204. i q^{48} +(4.68491e6 - 3.35925e6i) q^{49} +58430.7 q^{50} +(-3.58145e6 - 6.20325e6i) q^{51} +(643535. + 371545. i) q^{52} +(-6.89945e6 + 1.19502e7i) q^{53} +(-1.00209e6 + 578560. i) q^{54} +1.35987e7i q^{55} +(-3.31018e6 + 1.06412e6i) q^{56} -6.22194e6 q^{57} +(-6.71766e6 - 1.16353e7i) q^{58} +(-3.84372e6 - 2.21917e6i) q^{59} +(1.85821e6 - 3.21851e6i) q^{60} +(8.07548e6 - 4.66238e6i) q^{61} -1.74385e7i q^{62} +(-3.89124e6 - 3.52578e6i) q^{63} +2.09715e6 q^{64} +(-1.80215e6 - 3.12142e6i) q^{65} +(-1.00362e7 - 5.79440e6i) q^{66} +(4.06537e6 - 7.04142e6i) q^{67} +(-1.69787e7 + 9.80267e6i) q^{68} +2.20058e7i q^{69} +(1.64854e7 + 3.55798e6i) q^{70} +9.55170e6 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(1.92373e6 + 1.11066e6i) q^{73} +(1.09143e7 - 1.89040e7i) q^{74} +(209166. - 120762. i) q^{75} +1.70299e7i q^{76} +(1.10947e7 - 5.14061e7i) q^{77} +3.07157e6 q^{78} +(3.28239e7 + 5.68527e7i) q^{79} +(-8.80928e6 - 5.08604e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(531649. - 306948. i) q^{82} +5.08211e7i q^{83} +(-9.65029e6 + 1.06506e7i) q^{84} +9.50943e7 q^{85} +(4.13097e6 + 7.15505e6i) q^{86} +(-4.80948e7 - 2.77675e7i) q^{87} +(-1.58597e7 + 2.74697e7i) q^{88} +(-1.61978e7 + 9.35180e6i) q^{89} -1.53619e7i q^{90} +(4.26585e6 + 1.32699e7i) q^{91} +6.02314e7 q^{92} +(-3.60411e7 - 6.24249e7i) q^{93} +(3.78801e7 + 2.18701e7i) q^{94} +(4.13011e7 - 7.15355e7i) q^{95} +(7.50723e6 - 4.33430e6i) q^{96} -7.35915e6i q^{97} +(-5.94156e7 - 2.68998e7i) q^{98} -4.79024e7 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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