LMFDB - Embedded newform 22.12.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,12,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	22.a (trivial)

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:	yes
Analytic conductor:	$16.9035499723$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 331687x - 40657734 $ x^3 - 331687*x - 40657734
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$629.503$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-32.0000 q^{2} +163.327 q^{3} +1024.00 q^{4} -4579.34 q^{5} -5226.46 q^{6} +32606.6 q^{7} -32768.0 q^{8} -150471. q^{9} +O(q^{10})$	\(q-32.0000 q^{2} +163.327 q^{3} +1024.00 q^{4} -4579.34 q^{5} -5226.46 q^{6} +32606.6 q^{7} -32768.0 q^{8} -150471. q^{9} +146539. q^{10} +161051. q^{11} +167247. q^{12} +2.16817e6 q^{13} -1.04341e6 q^{14} -747929. q^{15} +1.04858e6 q^{16} -1.07938e7 q^{17} +4.81508e6 q^{18} -1.36089e7 q^{19} -4.68924e6 q^{20} +5.32553e6 q^{21} -5.15363e6 q^{22} -4.42810e7 q^{23} -5.35189e6 q^{24} -2.78578e7 q^{25} -6.93814e7 q^{26} -5.35089e7 q^{27} +3.33892e7 q^{28} +8.71135e7 q^{29} +2.39337e7 q^{30} -1.59768e8 q^{31} -3.35544e7 q^{32} +2.63039e7 q^{33} +3.45402e8 q^{34} -1.49317e8 q^{35} -1.54083e8 q^{36} +3.00616e8 q^{37} +4.35485e8 q^{38} +3.54120e8 q^{39} +1.50056e8 q^{40} -1.36646e9 q^{41} -1.70417e8 q^{42} +4.89353e8 q^{43} +1.64916e8 q^{44} +6.89059e8 q^{45} +1.41699e9 q^{46} -4.12802e8 q^{47} +1.71261e8 q^{48} -9.14136e8 q^{49} +8.91449e8 q^{50} -1.76292e9 q^{51} +2.22020e9 q^{52} +5.13984e9 q^{53} +1.71228e9 q^{54} -7.37507e8 q^{55} -1.06845e9 q^{56} -2.22270e9 q^{57} -2.78763e9 q^{58} -6.08338e9 q^{59} -7.65879e8 q^{60} -2.43444e8 q^{61} +5.11259e9 q^{62} -4.90636e9 q^{63} +1.07374e9 q^{64} -9.92878e9 q^{65} -8.41726e8 q^{66} +7.95036e9 q^{67} -1.10529e10 q^{68} -7.23228e9 q^{69} +4.77813e9 q^{70} +7.47651e9 q^{71} +4.93065e9 q^{72} -1.18341e10 q^{73} -9.61972e9 q^{74} -4.54992e9 q^{75} -1.39355e10 q^{76} +5.25133e9 q^{77} -1.13318e10 q^{78} -1.55816e10 q^{79} -4.80178e9 q^{80} +1.79161e10 q^{81} +4.37266e10 q^{82} +1.21214e10 q^{83} +5.45335e9 q^{84} +4.94286e10 q^{85} -1.56593e10 q^{86} +1.42280e10 q^{87} -5.27732e9 q^{88} +7.18701e10 q^{89} -2.20499e10 q^{90} +7.06966e10 q^{91} -4.53438e10 q^{92} -2.60945e10 q^{93} +1.32097e10 q^{94} +6.23198e10 q^{95} -5.48034e9 q^{96} -1.14740e10 q^{97} +2.92524e10 q^{98} -2.42336e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 96 q^{2} - 70 q^{3} + 3072 q^{4} - 5624 q^{5} + 2240 q^{6} - 30576 q^{7} - 98304 q^{8} + 533833 q^{9}+O(q^{10}) $ 3 * q - 96 * q^2 - 70 * q^3 + 3072 * q^4 - 5624 * q^5 + 2240 * q^6 - 30576 * q^7 - 98304 * q^8 + 533833 * q^9	\( 3 q - 96 q^{2} - 70 q^{3} + 3072 q^{4} - 5624 q^{5} + 2240 q^{6} - 30576 q^{7} - 98304 q^{8} + 533833 q^{9} + 179968 q^{10} + 483153 q^{11} - 71680 q^{12} + 423050 q^{13} + 978432 q^{14} - 581042 q^{15} + 3145728 q^{16} - 16823942 q^{17} - 17082656 q^{18} - 12737072 q^{19} - 5758976 q^{20} - 64101968 q^{21} - 15460896 q^{22} - 11397034 q^{23} + 2293760 q^{24} - 124966369 q^{25} - 13537600 q^{26} - 327990502 q^{27} - 31309824 q^{28} - 136849122 q^{29} + 18593344 q^{30} + 242041022 q^{31} - 100663296 q^{32} - 11273570 q^{33} + 538366144 q^{34} - 119732536 q^{35} + 546644992 q^{36} + 450661244 q^{37} + 407586304 q^{38} - 556451364 q^{39} + 184287232 q^{40} + 97726086 q^{41} + 2051262976 q^{42} - 712479248 q^{43} + 494748672 q^{44} + 321123482 q^{45} + 364705088 q^{46} - 3330549288 q^{47} - 73400320 q^{48} + 2958905187 q^{49} + 3998923808 q^{50} + 5871605992 q^{51} + 433203200 q^{52} - 3777184886 q^{53} + 10495696064 q^{54} - 905750824 q^{55} + 1001914368 q^{56} - 13176751420 q^{57} + 4379171904 q^{58} - 9293353002 q^{59} - 594987008 q^{60} + 2647736806 q^{61} - 7745312704 q^{62} - 8605254952 q^{63} + 3221225472 q^{64} - 9066838392 q^{65} + 360754240 q^{66} + 1632055702 q^{67} - 17227716608 q^{68} - 53633241046 q^{69} + 3831441152 q^{70} - 2119547430 q^{71} - 17492639744 q^{72} - 5284631794 q^{73} - 14421159808 q^{74} + 6732072508 q^{75} - 13042761728 q^{76} - 4924295376 q^{77} + 17806443648 q^{78} + 8982892548 q^{79} - 5897191424 q^{80} + 123128573251 q^{81} - 3127234752 q^{82} + 11489211392 q^{83} - 65640415232 q^{84} + 52886747204 q^{85} + 22799335936 q^{86} + 65580896304 q^{87} - 15831957504 q^{88} + 181048875488 q^{89} - 10275951424 q^{90} + 210430763032 q^{91} - 11670562816 q^{92} + 40878143418 q^{93} + 106577577216 q^{94} + 61381442860 q^{95} + 2348810240 q^{96} - 17159174540 q^{97} - 94684965984 q^{98} + 85974338483 q^{99}+O(q^{100}) \) 3 * q - 96 * q^2 - 70 * q^3 + 3072 * q^4 - 5624 * q^5 + 2240 * q^6 - 30576 * q^7 - 98304 * q^8 + 533833 * q^9 + 179968 * q^10 + 483153 * q^11 - 71680 * q^12 + 423050 * q^13 + 978432 * q^14 - 581042 * q^15 + 3145728 * q^16 - 16823942 * q^17 - 17082656 * q^18 - 12737072 * q^19 - 5758976 * q^20 - 64101968 * q^21 - 15460896 * q^22 - 11397034 * q^23 + 2293760 * q^24 - 124966369 * q^25 - 13537600 * q^26 - 327990502 * q^27 - 31309824 * q^28 - 136849122 * q^29 + 18593344 * q^30 + 242041022 * q^31 - 100663296 * q^32 - 11273570 * q^33 + 538366144 * q^34 - 119732536 * q^35 + 546644992 * q^36 + 450661244 * q^37 + 407586304 * q^38 - 556451364 * q^39 + 184287232 * q^40 + 97726086 * q^41 + 2051262976 * q^42 - 712479248 * q^43 + 494748672 * q^44 + 321123482 * q^45 + 364705088 * q^46 - 3330549288 * q^47 - 73400320 * q^48 + 2958905187 * q^49 + 3998923808 * q^50 + 5871605992 * q^51 + 433203200 * q^52 - 3777184886 * q^53 + 10495696064 * q^54 - 905750824 * q^55 + 1001914368 * q^56 - 13176751420 * q^57 + 4379171904 * q^58 - 9293353002 * q^59 - 594987008 * q^60 + 2647736806 * q^61 - 7745312704 * q^62 - 8605254952 * q^63 + 3221225472 * q^64 - 9066838392 * q^65 + 360754240 * q^66 + 1632055702 * q^67 - 17227716608 * q^68 - 53633241046 * q^69 + 3831441152 * q^70 - 2119547430 * q^71 - 17492639744 * q^72 - 5284631794 * q^73 - 14421159808 * q^74 + 6732072508 * q^75 - 13042761728 * q^76 - 4924295376 * q^77 + 17806443648 * q^78 + 8982892548 * q^79 - 5897191424 * q^80 + 123128573251 * q^81 - 3127234752 * q^82 + 11489211392 * q^83 - 65640415232 * q^84 + 52886747204 * q^85 + 22799335936 * q^86 + 65580896304 * q^87 - 15831957504 * q^88 + 181048875488 * q^89 - 10275951424 * q^90 + 210430763032 * q^91 - 11670562816 * q^92 + 40878143418 * q^93 + 106577577216 * q^94 + 61381442860 * q^95 + 2348810240 * q^96 - 17159174540 * q^97 - 94684965984 * q^98 + 85974338483 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	163.327	0.388053	0.194026	−	0.980996i	$-0.437845\pi$
$3$	163.327	0.388053	0.194026	+	0.980996i	$0.437845\pi$
$4$	1024.00	0.500000
$5$	−4579.34	−0.655342	−0.327671	−	0.944792i	$-0.606264\pi$
$5$	−4579.34	−0.655342	−0.327671	+	0.944792i	$0.606264\pi$
$6$	−5226.46	−0.274395
$7$	32606.6	0.733274	0.366637	−	0.930364i	$-0.380509\pi$
$7$	32606.6	0.733274	0.366637	+	0.930364i	$0.380509\pi$
$8$	−32768.0	−0.353553
$9$	−150471.	−0.849415
$10$	146539.	0.463397
$11$	161051.	0.301511
$11$	161051.	0.301511
$12$	167247.	0.194026
$13$	2.16817e6	1.61959	0.809794	−	0.586714i	$-0.199579\pi$
$13$	2.16817e6	1.61959	0.809794	+	0.586714i	$0.199579\pi$
$14$	−1.04341e6	−0.518503
$15$	−747929.	−0.254307
$16$	1.04858e6	0.250000
$17$	−1.07938e7	−1.84377	−0.921884	−	0.387467i	$-0.873350\pi$
$17$	−1.07938e7	−1.84377	−0.921884	+	0.387467i	$0.873350\pi$
$18$	4.81508e6	0.600627
$19$	−1.36089e7	−1.26089	−0.630447	−	0.776232i	$-0.717128\pi$
$19$	−1.36089e7	−1.26089	−0.630447	+	0.776232i	$0.717128\pi$
$20$	−4.68924e6	−0.327671
$21$	5.32553e6	0.284549
$22$	−5.15363e6	−0.213201
$23$	−4.42810e7	−1.43455	−0.717273	−	0.696792i	$-0.754610\pi$
$23$	−4.42810e7	−1.43455	−0.717273	+	0.696792i	$0.754610\pi$
$24$	−5.35189e6	−0.137197
$25$	−2.78578e7	−0.570527
$26$	−6.93814e7	−1.14522
$27$	−5.35089e7	−0.717670
$28$	3.33892e7	0.366637
$29$	8.71135e7	0.788672	0.394336	−	0.918966i	$-0.370975\pi$
$29$	8.71135e7	0.788672	0.394336	+	0.918966i	$0.370975\pi$
$30$	2.39337e7	0.179822
$31$	−1.59768e8	−1.00231	−0.501154	−	0.865358i	$-0.667091\pi$
$31$	−1.59768e8	−1.00231	−0.501154	+	0.865358i	$0.667091\pi$
$32$	−3.35544e7	−0.176777
$33$	2.63039e7	0.117002
$34$	3.45402e8	1.30374
$35$	−1.49317e8	−0.480545
$36$	−1.54083e8	−0.424708
$37$	3.00616e8	0.712694	0.356347	−	0.934354i	$-0.384022\pi$
$37$	3.00616e8	0.712694	0.356347	+	0.934354i	$0.384022\pi$
$38$	4.35485e8	0.891587
$39$	3.54120e8	0.628485
$40$	1.50056e8	0.231698
$41$	−1.36646e9	−1.84198	−0.920990	−	0.389586i	$-0.872618\pi$
$41$	−1.36646e9	−1.84198	−0.920990	+	0.389586i	$0.872618\pi$
$42$	−1.70417e8	−0.201206
$43$	4.89353e8	0.507629	0.253814	−	0.967253i	$-0.418315\pi$
$43$	4.89353e8	0.507629	0.253814	+	0.967253i	$0.418315\pi$
$44$	1.64916e8	0.150756
$45$	6.89059e8	0.556657
$46$	1.41699e9	1.01438
$47$	−4.12802e8	−0.262545	−0.131273	−	0.991346i	$-0.541906\pi$
$47$	−4.12802e8	−0.262545	−0.131273	+	0.991346i	$0.541906\pi$
$48$	1.71261e8	0.0970131
$49$	−9.14136e8	−0.462309
$50$	8.91449e8	0.403424
$51$	−1.76292e9	−0.715479
$52$	2.22020e9	0.809794
$53$	5.13984e9	1.68823	0.844116	−	0.536160i	$-0.180126\pi$
$53$	5.13984e9	1.68823	0.844116	+	0.536160i	$0.180126\pi$
$54$	1.71228e9	0.507470
$55$	−7.37507e8	−0.197593
$56$	−1.06845e9	−0.259252
$57$	−2.22270e9	−0.489293
$58$	−2.78763e9	−0.557675
$59$	−6.08338e9	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$59$	−6.08338e9	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$60$	−7.65879e8	−0.127153
$61$	−2.43444e8	−0.0369050	−0.0184525	−	0.999830i	$-0.505874\pi$
$61$	−2.43444e8	−0.0369050	−0.0184525	+	0.999830i	$0.505874\pi$
$62$	5.11259e9	0.708739
$63$	−4.90636e9	−0.622854
$64$	1.07374e9	0.125000
$65$	−9.92878e9	−1.06138
$66$	−8.41726e8	−0.0827331
$67$	7.95036e9	0.719408	0.359704	−	0.933066i	$-0.382878\pi$
$67$	7.95036e9	0.719408	0.359704	+	0.933066i	$0.382878\pi$
$68$	−1.10529e10	−0.921884
$69$	−7.23228e9	−0.556680
$70$	4.77813e9	0.339797
$71$	7.47651e9	0.491788	0.245894	−	0.969297i	$-0.420918\pi$
$71$	7.47651e9	0.491788	0.245894	+	0.969297i	$0.420918\pi$
$72$	4.93065e9	0.300314
$73$	−1.18341e10	−0.668126	−0.334063	−	0.942551i	$-0.608420\pi$
$73$	−1.18341e10	−0.668126	−0.334063	+	0.942551i	$0.608420\pi$
$74$	−9.61972e9	−0.503951
$75$	−4.54992e9	−0.221395
$76$	−1.39355e10	−0.630447
$77$	5.25133e9	0.221090
$78$	−1.13318e10	−0.444406
$79$	−1.55816e10	−0.569723	−0.284862	−	0.958569i	$-0.591948\pi$
$79$	−1.55816e10	−0.569723	−0.284862	+	0.958569i	$0.591948\pi$
$80$	−4.80178e9	−0.163835
$81$	1.79161e10	0.570921
$82$	4.37266e10	1.30248
$83$	1.21214e10	0.337772	0.168886	−	0.985636i	$-0.445983\pi$
$83$	1.21214e10	0.337772	0.168886	+	0.985636i	$0.445983\pi$
$84$	5.45335e9	0.142274
$85$	4.94286e10	1.20830
$86$	−1.56593e10	−0.358948
$87$	1.42280e10	0.306046
$88$	−5.27732e9	−0.106600
$89$	7.18701e10	1.36428	0.682140	−	0.731222i	$-0.261050\pi$
$89$	7.18701e10	1.36428	0.682140	+	0.731222i	$0.261050\pi$
$90$	−2.20499e10	−0.393616
$91$	7.06966e10	1.18760
$92$	−4.53438e10	−0.717273
$93$	−2.60945e10	−0.388948
$94$	1.32097e10	0.185647
$95$	6.23198e10	0.826317
$96$	−5.48034e9	−0.0685986
$97$	−1.14740e10	−0.135665	−0.0678327	−	0.997697i	$-0.521608\pi$
$97$	−1.14740e10	−0.135665	−0.0678327	+	0.997697i	$0.521608\pi$
$98$	2.92524e10	0.326902
$99$	−2.42336e10	−0.256108
$100$	−2.85264e10	−0.285264
$101$	2.71816e10	0.257340	0.128670	−	0.991687i	$-0.458929\pi$
$101$	2.71816e10	0.257340	0.128670	+	0.991687i	$0.458929\pi$
$102$	5.64134e10	0.505920
$103$	1.26027e11	1.07117	0.535586	−	0.844480i	$-0.320091\pi$
$103$	1.26027e11	1.07117	0.535586	+	0.844480i	$0.320091\pi$
$104$	−7.10466e10	−0.572611
$105$	−2.43874e10	−0.186477
$106$	−1.64475e11	−1.19376
$107$	−2.60572e11	−1.79605	−0.898024	−	0.439947i	$-0.854997\pi$
$107$	−2.60572e11	−1.79605	−0.898024	+	0.439947i	$0.854997\pi$
$108$	−5.47931e10	−0.358835
$109$	−2.16666e11	−1.34879	−0.674397	−	0.738369i	$-0.735596\pi$
$109$	−2.16666e11	−1.34879	−0.674397	+	0.738369i	$0.735596\pi$
$110$	2.36002e10	0.139719
$111$	4.90987e10	0.276563
$112$	3.41905e10	0.183319
$113$	−5.96096e10	−0.304358	−0.152179	−	0.988353i	$-0.548629\pi$
$113$	−5.96096e10	−0.304358	−0.152179	+	0.988353i	$0.548629\pi$
$114$	7.11264e10	0.345983
$115$	2.02778e11	0.940118
$116$	8.92042e10	0.394336
$117$	−3.26247e11	−1.37570
$118$	1.94668e11	0.783329
$119$	−3.51950e11	−1.35199
$120$	2.45081e10	0.0899111
$121$	2.59374e10	0.0909091
$122$	7.79022e9	0.0260958
$123$	−2.23179e11	−0.714785
$124$	−1.63603e11	−0.501154
$125$	3.51171e11	1.02923
$126$	1.57004e11	0.440424
$127$	5.44365e11	1.46208	0.731038	−	0.682337i	$-0.239036\pi$
$127$	5.44365e11	1.46208	0.731038	+	0.682337i	$0.239036\pi$
$128$	−3.43597e10	−0.0883883
$129$	7.99245e10	0.196987
$130$	3.17721e11	0.750512
$131$	−4.46705e11	−1.01165	−0.505824	−	0.862637i	$-0.668811\pi$
$131$	−4.46705e11	−1.01165	−0.505824	+	0.862637i	$0.668811\pi$
$132$	2.69352e10	0.0585011
$133$	−4.43741e11	−0.924581
$134$	−2.54412e11	−0.508698
$135$	2.45035e11	0.470319
$136$	3.53692e11	0.651870
$137$	−7.29713e11	−1.29178	−0.645891	−	0.763430i	$-0.723514\pi$
$137$	−7.29713e11	−1.29178	−0.645891	+	0.763430i	$0.723514\pi$
$138$	2.31433e11	0.393632
$139$	1.03702e12	1.69514	0.847568	−	0.530688i	$-0.178066\pi$
$139$	1.03702e12	1.69514	0.847568	+	0.530688i	$0.178066\pi$
$140$	−1.52900e11	−0.240273
$141$	−6.74217e10	−0.101881
$142$	−2.39248e11	−0.347747
$143$	3.49186e11	0.488324
$144$	−1.57781e11	−0.212354
$145$	−3.98922e11	−0.516849
$146$	3.78690e11	0.472436
$147$	−1.49303e11	−0.179400
$148$	3.07831e11	0.356347
$149$	−2.69283e11	−0.300389	−0.150195	−	0.988656i	$-0.547990\pi$
$149$	−2.69283e11	−0.300389	−0.150195	+	0.988656i	$0.547990\pi$
$150$	1.45598e11	0.156550
$151$	−1.95733e11	−0.202905	−0.101452	−	0.994840i	$-0.532349\pi$
$151$	−1.95733e11	−0.202905	−0.101452	+	0.994840i	$0.532349\pi$
$152$	4.45937e11	0.445793
$153$	1.62416e12	1.56612
$154$	−1.68042e11	−0.156335
$155$	7.31633e11	0.656855
$156$	3.62619e11	0.314243
$157$	−9.37460e11	−0.784340	−0.392170	−	0.919893i	$-0.628276\pi$
$157$	−9.37460e11	−0.784340	−0.392170	+	0.919893i	$0.628276\pi$
$158$	4.98612e11	0.402855
$159$	8.39473e11	0.655123
$160$	1.53657e11	0.115849
$161$	−1.44385e12	−1.05192
$162$	−5.73316e11	−0.403702
$163$	5.23044e11	0.356046	0.178023	−	0.984026i	$-0.443030\pi$
$163$	5.23044e11	0.356046	0.178023	+	0.984026i	$0.443030\pi$
$164$	−1.39925e12	−0.920990
$165$	−1.20455e11	−0.0766764
$166$	−3.87885e11	−0.238841
$167$	−1.64879e12	−0.982255	−0.491128	−	0.871088i	$-0.663415\pi$
$167$	−1.64879e12	−0.982255	−0.491128	+	0.871088i	$0.663415\pi$
$168$	−1.74507e11	−0.100603
$169$	2.90880e12	1.62307
$170$	−1.58171e12	−0.854395
$171$	2.04775e12	1.07102
$172$	5.01098e11	0.253814
$173$	−2.41420e12	−1.18446	−0.592229	−	0.805770i	$-0.701752\pi$
$173$	−2.41420e12	−1.18446	−0.592229	+	0.805770i	$0.701752\pi$
$174$	−4.55295e11	−0.216407
$175$	−9.08348e11	−0.418353
$176$	1.68874e11	0.0753778
$177$	−9.93579e11	−0.429882
$178$	−2.29984e12	−0.964691
$179$	2.28220e12	0.928245	0.464122	−	0.885771i	$-0.346370\pi$
$179$	2.28220e12	0.928245	0.464122	+	0.885771i	$0.346370\pi$
$180$	7.05597e11	0.278329
$181$	−1.95423e12	−0.747727	−0.373864	−	0.927484i	$-0.621967\pi$
$181$	−1.95423e12	−0.747727	−0.373864	+	0.927484i	$0.621967\pi$
$182$	−2.26229e12	−0.839762
$183$	−3.97610e10	−0.0143211
$184$	1.45100e12	0.507189
$185$	−1.37662e12	−0.467058
$186$	8.35023e11	0.275028
$187$	−1.73836e12	−0.555917
$188$	−4.22710e11	−0.131273
$189$	−1.74474e12	−0.526249
$190$	−1.99423e12	−0.584294
$191$	3.46782e12	0.987128	0.493564	−	0.869710i	$-0.335694\pi$
$191$	3.46782e12	0.987128	0.493564	+	0.869710i	$0.335694\pi$
$192$	1.75371e11	0.0485066
$193$	−1.71046e11	−0.0459776	−0.0229888	−	0.999736i	$-0.507318\pi$
$193$	−1.71046e11	−0.0459776	−0.0229888	+	0.999736i	$0.507318\pi$
$194$	3.67167e11	0.0959300
$195$	−1.62164e12	−0.411873
$196$	−9.36075e11	−0.231155
$197$	3.12254e12	0.749798	0.374899	−	0.927066i	$-0.377677\pi$
$197$	3.12254e12	0.749798	0.374899	+	0.927066i	$0.377677\pi$
$198$	7.75474e11	0.181096
$199$	−4.31515e11	−0.0980177	−0.0490088	−	0.998798i	$-0.515606\pi$
$199$	−4.31515e11	−0.0980177	−0.0490088	+	0.998798i	$0.515606\pi$
$200$	9.12844e11	0.201712
$201$	1.29851e12	0.279168
$202$	−8.69812e11	−0.181967
$203$	2.84047e12	0.578313
$204$	−1.80523e12	−0.357739
$205$	6.25747e12	1.20713
$206$	−4.03287e12	−0.757434
$207$	6.66303e12	1.21853
$208$	2.27349e12	0.404897
$209$	−2.19173e12	−0.380174
$210$	7.80397e11	0.131859
$211$	8.09032e12	1.33172	0.665859	−	0.746078i	$-0.268065\pi$
$211$	8.09032e12	1.33172	0.665859	+	0.746078i	$0.268065\pi$
$212$	5.26320e12	0.844116
$213$	1.22111e12	0.190840
$214$	8.33832e12	1.27000
$215$	−2.24091e12	−0.332670
$216$	1.75338e12	0.253735
$217$	−5.20950e12	−0.734967
$218$	6.93332e12	0.953741
$219$	−1.93282e12	−0.259268
$220$	−7.55207e11	−0.0987965
$221$	−2.34028e13	−2.98614
$222$	−1.57116e12	−0.195559
$223$	4.85388e12	0.589403	0.294702	−	0.955589i	$-0.404780\pi$
$223$	4.85388e12	0.589403	0.294702	+	0.955589i	$0.404780\pi$
$224$	−1.09410e12	−0.129626
$225$	4.19180e12	0.484615
$226$	1.90751e12	0.215214
$227$	3.29433e12	0.362765	0.181382	−	0.983413i	$-0.441943\pi$
$227$	3.29433e12	0.362765	0.181382	+	0.983413i	$0.441943\pi$
$228$	−2.27605e12	−0.244647
$229$	2.01527e12	0.211465	0.105732	−	0.994395i	$-0.466281\pi$
$229$	2.01527e12	0.211465	0.105732	+	0.994395i	$0.466281\pi$
$230$	−6.48889e12	−0.664764
$231$	8.57682e11	0.0857947
$232$	−2.85453e12	−0.278838
$233$	−1.35525e13	−1.29289	−0.646445	−	0.762961i	$-0.723745\pi$
$233$	−1.35525e13	−1.29289	−0.646445	+	0.762961i	$0.723745\pi$
$234$	1.04399e13	0.972769
$235$	1.89036e12	0.172057
$236$	−6.22938e12	−0.553897
$237$	−2.54490e12	−0.221083
$238$	1.12624e13	0.955999
$239$	−1.54257e13	−1.27955	−0.639774	−	0.768563i	$-0.720972\pi$
$239$	−1.54257e13	−1.27955	−0.639774	+	0.768563i	$0.720972\pi$
$240$	−7.84260e11	−0.0635767
$241$	−1.07788e13	−0.854040	−0.427020	−	0.904242i	$-0.640437\pi$
$241$	−1.07788e13	−0.854040	−0.427020	+	0.904242i	$0.640437\pi$
$242$	−8.29998e11	−0.0642824
$243$	1.24051e13	0.939218
$244$	−2.49287e11	−0.0184525
$245$	4.18614e12	0.302970
$246$	7.14173e12	0.505429
$247$	−2.95064e13	−2.04213
$248$	5.23529e12	0.354370
$249$	1.97975e12	0.131073
$250$	−1.12375e13	−0.727777
$251$	1.21903e13	0.772338	0.386169	−	0.922428i	$-0.373798\pi$
$251$	1.21903e13	0.772338	0.386169	+	0.922428i	$0.373798\pi$
$252$	−5.02411e12	−0.311427
$253$	−7.13151e12	−0.432532
$254$	−1.74197e13	−1.03384
$255$	8.07301e12	0.468883
$256$	1.09951e12	0.0625000
$257$	−9.04603e12	−0.503299	−0.251649	−	0.967818i	$-0.580973\pi$
$257$	−9.04603e12	−0.503299	−0.251649	+	0.967818i	$0.580973\pi$
$258$	−2.55758e12	−0.139291
$259$	9.80208e12	0.522600
$260$	−1.01671e13	−0.530692
$261$	−1.31081e13	−0.669910
$262$	1.42946e13	0.715343
$263$	1.12537e12	0.0551493	0.0275747	−	0.999620i	$-0.491222\pi$
$263$	1.12537e12	0.0551493	0.0275747	+	0.999620i	$0.491222\pi$
$264$	−8.61928e11	−0.0413665
$265$	−2.35371e13	−1.10637
$266$	1.41997e13	0.653778
$267$	1.17383e13	0.529412
$268$	8.14117e12	0.359704
$269$	2.06704e13	0.894768	0.447384	−	0.894342i	$-0.352356\pi$
$269$	2.06704e13	0.894768	0.447384	+	0.894342i	$0.352356\pi$
$270$	−7.84113e12	−0.332566
$271$	4.47130e13	1.85824	0.929122	−	0.369773i	$-0.120564\pi$
$271$	4.47130e13	1.85824	0.929122	+	0.369773i	$0.120564\pi$
$272$	−1.13181e13	−0.460942
$273$	1.15467e13	0.460852
$274$	2.33508e13	0.913427
$275$	−4.48652e12	−0.172020
$276$	−7.40586e12	−0.278340
$277$	2.11635e13	0.779739	0.389869	−	0.920870i	$-0.372520\pi$
$277$	2.11635e13	0.779739	0.389869	+	0.920870i	$0.372520\pi$
$278$	−3.31845e13	−1.19864
$279$	2.40406e13	0.851376
$280$	4.89281e12	0.169898
$281$	5.48987e12	0.186929	0.0934647	−	0.995623i	$-0.470206\pi$
$281$	5.48987e12	0.186929	0.0934647	+	0.995623i	$0.470206\pi$
$282$	2.15749e12	0.0720410
$283$	−4.95720e13	−1.62335	−0.811673	−	0.584113i	$-0.801443\pi$
$283$	−4.95720e13	−1.62335	−0.811673	+	0.584113i	$0.801443\pi$
$284$	7.65595e12	0.245894
$285$	1.01785e13	0.320654
$286$	−1.11739e13	−0.345297
$287$	−4.45555e13	−1.35068
$288$	5.04898e12	0.150157
$289$	8.22346e13	2.39948
$290$	1.27655e13	0.365468
$291$	−1.87401e12	−0.0526453
$292$	−1.21181e13	−0.334063
$293$	3.92359e13	1.06148	0.530739	−	0.847535i	$-0.321914\pi$
$293$	3.92359e13	1.06148	0.530739	+	0.847535i	$0.321914\pi$
$294$	4.77769e12	0.126855
$295$	2.78579e13	0.725983
$296$	−9.85059e12	−0.251975
$297$	−8.61766e12	−0.216386
$298$	8.61705e12	0.212407
$299$	−9.60088e13	−2.32338
$300$	−4.65912e12	−0.110697
$301$	1.59562e13	0.372231
$302$	6.26347e12	0.143475
$303$	4.43949e12	0.0998616
$304$	−1.42700e13	−0.315224
$305$	1.11481e12	0.0241854
$306$	−5.19731e13	−1.10742
$307$	1.51770e13	0.317632	0.158816	−	0.987308i	$-0.449232\pi$
$307$	1.51770e13	0.317632	0.158816	+	0.987308i	$0.449232\pi$
$308$	5.37736e12	0.110545
$309$	2.05836e13	0.415671
$310$	−2.34123e13	−0.464466
$311$	−8.28377e12	−0.161453	−0.0807264	−	0.996736i	$-0.525724\pi$
$311$	−8.28377e12	−0.161453	−0.0807264	+	0.996736i	$0.525724\pi$
$312$	−1.16038e13	−0.222203
$313$	−3.70588e12	−0.0697264	−0.0348632	−	0.999392i	$-0.511100\pi$
$313$	−3.70588e12	−0.0697264	−0.0348632	+	0.999392i	$0.511100\pi$
$314$	2.99987e13	0.554612
$315$	2.24679e13	0.408182
$316$	−1.59556e13	−0.284862
$317$	1.20613e13	0.211626	0.105813	−	0.994386i	$-0.466256\pi$
$317$	1.20613e13	0.211626	0.105813	+	0.994386i	$0.466256\pi$
$318$	−2.68632e13	−0.463242
$319$	1.40297e13	0.237793
$320$	−4.91703e12	−0.0819177
$321$	−4.25585e13	−0.696961
$322$	4.62033e13	0.743817
$323$	1.46892e14	2.32480
$324$	1.83461e13	0.285461
$325$	−6.04004e13	−0.924019
$326$	−1.67374e13	−0.251762
$327$	−3.53874e13	−0.523403
$328$	4.47761e13	0.651238
$329$	−1.34601e13	−0.192518
$330$	3.85455e12	0.0542184
$331$	−1.05197e14	−1.45528	−0.727642	−	0.685957i	$-0.759384\pi$
$331$	−1.05197e14	−1.45528	−0.727642	+	0.685957i	$0.759384\pi$
$332$	1.24123e13	0.168886
$333$	−4.52341e13	−0.605373
$334$	5.27612e13	0.694560
$335$	−3.64074e13	−0.471458
$336$	5.58423e12	0.0711372
$337$	−7.51399e13	−0.941686	−0.470843	−	0.882217i	$-0.656050\pi$
$337$	−7.51399e13	−0.941686	−0.470843	+	0.882217i	$0.656050\pi$
$338$	−9.30815e13	−1.14768
$339$	−9.73585e12	−0.118107
$340$	5.06148e13	0.604149
$341$	−2.57309e13	−0.302207
$342$	−6.55281e13	−0.757328
$343$	−9.42808e13	−1.07227
$344$	−1.60351e13	−0.179474
$345$	3.31191e13	0.364815
$346$	7.72543e13	0.837538
$347$	−3.71551e13	−0.396466	−0.198233	−	0.980155i	$-0.563520\pi$
$347$	−3.71551e13	−0.396466	−0.198233	+	0.980155i	$0.563520\pi$
$348$	1.45694e13	0.153023
$349$	4.93259e13	0.509959	0.254979	−	0.966946i	$-0.417931\pi$
$349$	4.93259e13	0.509959	0.254979	+	0.966946i	$0.417931\pi$
$350$	2.90671e13	0.295820
$351$	−1.16016e14	−1.16233
$352$	−5.40397e12	−0.0533002
$353$	9.93536e13	0.964768	0.482384	−	0.875960i	$-0.339771\pi$
$353$	9.93536e13	0.964768	0.482384	+	0.875960i	$0.339771\pi$
$354$	3.17945e13	0.303973
$355$	−3.42375e13	−0.322289
$356$	7.35950e13	0.682140
$357$	−5.74828e13	−0.524642
$358$	−7.30305e13	−0.656368
$359$	3.41271e13	0.302050	0.151025	−	0.988530i	$-0.451743\pi$
$359$	3.41271e13	0.302050	0.151025	+	0.988530i	$0.451743\pi$
$360$	−2.25791e13	−0.196808
$361$	6.87123e13	0.589855
$362$	6.25353e13	0.528723
$363$	4.23628e12	0.0352775
$364$	7.23933e13	0.593801
$365$	5.41922e13	0.437851
$366$	1.27235e12	0.0101265
$367$	−1.89060e14	−1.48230	−0.741149	−	0.671340i	$-0.765719\pi$
$367$	−1.89060e14	−1.48230	−0.741149	+	0.671340i	$0.765719\pi$
$368$	−4.64320e13	−0.358637
$369$	2.05613e14	1.56461
$370$	4.40520e13	0.330260
$371$	1.67593e14	1.23794
$372$	−2.67207e13	−0.194474
$373$	−7.85673e13	−0.563434	−0.281717	−	0.959497i	$-0.590904\pi$
$373$	−7.85673e13	−0.563434	−0.281717	+	0.959497i	$0.590904\pi$
$374$	5.56274e13	0.393092
$375$	5.73556e13	0.399396
$376$	1.35267e13	0.0928237
$377$	1.88877e14	1.27732
$378$	5.58318e13	0.372114
$379$	−9.21213e13	−0.605124	−0.302562	−	0.953130i	$-0.597842\pi$
$379$	−9.21213e13	−0.605124	−0.302562	+	0.953130i	$0.597842\pi$
$380$	6.38155e13	0.413158
$381$	8.89094e13	0.567362
$382$	−1.10970e14	−0.698005
$383$	−1.50371e14	−0.932335	−0.466168	−	0.884696i	$-0.654366\pi$
$383$	−1.50371e14	−0.932335	−0.466168	+	0.884696i	$0.654366\pi$
$384$	−5.61187e12	−0.0342993
$385$	−2.40476e13	−0.144890
$386$	5.47346e12	0.0325111
$387$	−7.36337e13	−0.431187
$388$	−1.17493e13	−0.0678327
$389$	2.60394e14	1.48221	0.741103	−	0.671391i	$-0.234303\pi$
$389$	2.60394e14	1.48221	0.741103	+	0.671391i	$0.234303\pi$
$390$	5.18923e13	0.291238
$391$	4.77962e14	2.64497
$392$	2.99544e13	0.163451
$393$	−7.29590e13	−0.392572
$394$	−9.99214e13	−0.530187
$395$	7.13536e13	0.373363
$396$	−2.48152e13	−0.128054
$397$	−1.76981e14	−0.900699	−0.450349	−	0.892852i	$-0.648701\pi$
$397$	−1.76981e14	−0.900699	−0.450349	+	0.892852i	$0.648701\pi$
$398$	1.38085e13	0.0693090
$399$	−7.24747e13	−0.358786
$400$	−2.92110e13	−0.142632
$401$	−6.50876e12	−0.0313476	−0.0156738	−	0.999877i	$-0.504989\pi$
$401$	−6.50876e12	−0.0313476	−0.0156738	+	0.999877i	$0.504989\pi$
$402$	−4.15522e13	−0.197402
$403$	−3.46405e14	−1.62333
$404$	2.78340e13	0.128670
$405$	−8.20440e13	−0.374149
$406$	−9.08952e13	−0.408929
$407$	4.84146e13	0.214885
$408$	5.77674e13	0.252960
$409$	−2.95601e13	−0.127711	−0.0638555	−	0.997959i	$-0.520340\pi$
$409$	−2.95601e13	−0.127711	−0.0638555	+	0.997959i	$0.520340\pi$
$410$	−2.00239e14	−0.853567
$411$	−1.19182e14	−0.501279
$412$	1.29052e14	0.535586
$413$	−1.98358e14	−0.812317
$414$	−2.13217e14	−0.861628
$415$	−5.55081e13	−0.221356
$416$	−7.27517e13	−0.286305
$417$	1.69373e14	0.657801
$418$	7.01353e13	0.268824
$419$	1.17276e14	0.443641	0.221820	−	0.975088i	$-0.428800\pi$
$419$	1.17276e14	0.443641	0.221820	+	0.975088i	$0.428800\pi$
$420$	−2.49727e13	−0.0932384
$421$	−1.41654e14	−0.522007	−0.261004	−	0.965338i	$-0.584053\pi$
$421$	−1.41654e14	−0.522007	−0.261004	+	0.965338i	$0.584053\pi$
$422$	−2.58890e14	−0.941666
$423$	6.21149e13	0.223010
$424$	−1.68422e14	−0.596880
$425$	3.00692e14	1.05192
$426$	−3.90757e13	−0.134944
$427$	−7.93789e12	−0.0270615
$428$	−2.66826e14	−0.898024
$429$	5.70314e13	0.189495
$430$	7.17093e13	0.235233
$431$	−1.10819e14	−0.358914	−0.179457	−	0.983766i	$-0.557434\pi$
$431$	−1.10819e14	−0.358914	−0.179457	+	0.983766i	$0.557434\pi$
$432$	−5.61081e13	−0.179418
$433$	−5.73405e14	−1.81042	−0.905208	−	0.424969i	$-0.860285\pi$
$433$	−5.73405e14	−1.81042	−0.905208	+	0.424969i	$0.860285\pi$
$434$	1.66704e14	0.519700
$435$	−6.51547e13	−0.200565
$436$	−2.21866e14	−0.674397
$437$	6.02617e14	1.80881
$438$	6.18503e13	0.183330
$439$	−1.33280e14	−0.390129	−0.195065	−	0.980790i	$-0.562492\pi$
$439$	−1.33280e14	−0.390129	−0.195065	+	0.980790i	$0.562492\pi$
$440$	2.41666e13	0.0698597
$441$	1.37551e14	0.392692
$442$	7.48890e14	2.11152
$443$	4.62346e14	1.28750	0.643750	−	0.765236i	$-0.277378\pi$
$443$	4.62346e14	1.28750	0.643750	+	0.765236i	$0.277378\pi$
$444$	5.02771e13	0.138281
$445$	−3.29118e14	−0.894069
$446$	−1.55324e14	−0.416771
$447$	−4.39811e13	−0.116567
$448$	3.50111e13	0.0916593
$449$	3.94698e13	0.102073	0.0510364	−	0.998697i	$-0.483748\pi$
$449$	3.94698e13	0.102073	0.0510364	+	0.998697i	$0.483748\pi$
$450$	−1.34138e14	−0.342674
$451$	−2.20069e14	−0.555378
$452$	−6.10403e13	−0.152179
$453$	−3.19685e13	−0.0787376
$454$	−1.05419e14	−0.256513
$455$	−3.23744e14	−0.778285
$456$	7.28335e13	0.172991
$457$	−5.56442e14	−1.30581	−0.652906	−	0.757439i	$-0.726451\pi$
$457$	−5.56442e14	−1.30581	−0.652906	+	0.757439i	$0.726451\pi$
$458$	−6.44886e13	−0.149528
$459$	5.77565e14	1.32322
$460$	2.07645e14	0.470059
$461$	3.95623e14	0.884965	0.442482	−	0.896777i	$-0.354098\pi$
$461$	3.95623e14	0.884965	0.442482	+	0.896777i	$0.354098\pi$
$462$	−2.74458e13	−0.0606660
$463$	8.19440e14	1.78987	0.894935	−	0.446196i	$-0.147222\pi$
$463$	8.19440e14	1.78987	0.894935	+	0.446196i	$0.147222\pi$
$464$	9.13451e13	0.197168
$465$	1.19495e14	0.254894
$466$	4.33679e14	0.914211
$467$	−7.69276e13	−0.160265	−0.0801326	−	0.996784i	$-0.525534\pi$
$467$	−7.69276e13	−0.160265	−0.0801326	+	0.996784i	$0.525534\pi$
$468$	−3.34077e14	−0.687852
$469$	2.59234e14	0.527523
$470$	−6.04916e13	−0.121662
$471$	−1.53112e14	−0.304365
$472$	1.99340e14	0.391664
$473$	7.88108e13	0.153056
$474$	8.14368e13	0.156329
$475$	3.79114e14	0.719375
$476$	−3.60397e14	−0.675993
$477$	−7.73399e14	−1.43401
$478$	4.93623e14	0.904777
$479$	6.39397e14	1.15858	0.579289	−	0.815122i	$-0.303330\pi$
$479$	6.39397e14	1.15858	0.579289	+	0.815122i	$0.303330\pi$
$480$	2.50963e13	0.0449556
$481$	6.51787e14	1.15427
$482$	3.44923e14	0.603897
$483$	−2.35820e14	−0.408199
$484$	2.65599e13	0.0454545
$485$	5.25432e13	0.0889072
$486$	−3.96964e14	−0.664127
$487$	−7.45580e14	−1.23335	−0.616673	−	0.787220i	$-0.711520\pi$
$487$	−7.45580e14	−1.23335	−0.616673	+	0.787220i	$0.711520\pi$
$488$	7.97718e12	0.0130479
$489$	8.54270e13	0.138165
$490$	−1.33956e14	−0.214232
$491$	−8.86317e14	−1.40165	−0.700827	−	0.713331i	$-0.747185\pi$
$491$	−8.86317e14	−1.40165	−0.700827	+	0.713331i	$0.747185\pi$
$492$	−2.28535e14	−0.357393
$493$	−9.40287e14	−1.45413
$494$	9.44206e14	1.44400
$495$	1.10974e14	0.167838
$496$	−1.67529e14	−0.250577
$497$	2.43784e14	0.360616
$498$	−6.33521e13	−0.0926828
$499$	−2.15718e14	−0.312128	−0.156064	−	0.987747i	$-0.549881\pi$
$499$	−2.15718e14	−0.312128	−0.156064	+	0.987747i	$0.549881\pi$
$500$	3.59599e14	0.514616
$501$	−2.69291e14	−0.381167
$502$	−3.90088e14	−0.546125
$503$	5.51900e14	0.764252	0.382126	−	0.924110i	$-0.375192\pi$
$503$	5.51900e14	0.764252	0.382126	+	0.924110i	$0.375192\pi$
$504$	1.60772e14	0.220212
$505$	−1.24474e14	−0.168646
$506$	2.28208e14	0.305846
$507$	4.75084e14	0.629835
$508$	5.57430e14	0.731038
$509$	−8.62266e14	−1.11865	−0.559324	−	0.828949i	$-0.688939\pi$
$509$	−8.62266e14	−1.11865	−0.559324	+	0.828949i	$0.688939\pi$
$510$	−2.58336e14	−0.331550
$511$	−3.85869e14	−0.489920
$512$	−3.51844e13	−0.0441942
$513$	7.28198e14	0.904906
$514$	2.89473e14	0.355886
$515$	−5.77121e14	−0.701984
$516$	8.18427e13	0.0984933
$517$	−6.64822e13	−0.0791603
$518$	−3.13666e14	−0.369534
$519$	−3.94303e14	−0.459632
$520$	3.25346e14	0.375256
$521$	−1.66754e15	−1.90313	−0.951567	−	0.307441i	$-0.900527\pi$
$521$	−1.66754e15	−1.90313	−0.951567	+	0.307441i	$0.900527\pi$
$522$	4.19459e14	0.473698
$523$	−9.49984e14	−1.06159	−0.530795	−	0.847500i	$-0.678107\pi$
$523$	−9.49984e14	−1.06159	−0.530795	+	0.847500i	$0.678107\pi$
$524$	−4.57426e14	−0.505824
$525$	−1.48358e14	−0.162343
$526$	−3.60120e13	−0.0389965
$527$	1.72451e15	1.84802
$528$	2.75817e13	0.0292506
$529$	1.00800e15	1.05792
$530$	7.53186e14	0.782321
$531$	9.15375e14	0.940977
$532$	−4.54390e14	−0.462291
$533$	−2.96271e15	−2.98325
$534$	−3.75626e14	−0.374351
$535$	1.19325e15	1.17702
$536$	−2.60517e14	−0.254349
$537$	3.72745e14	0.360208
$538$	−6.61452e14	−0.632697
$539$	−1.47223e14	−0.139391
$540$	2.50916e14	0.235160
$541$	−1.44230e14	−0.133804	−0.0669022	−	0.997760i	$-0.521312\pi$
$541$	−1.44230e14	−0.133804	−0.0669022	+	0.997760i	$0.521312\pi$
$542$	−1.43082e15	−1.31398
$543$	−3.19178e14	−0.290157
$544$	3.62180e14	0.325935
$545$	9.92188e14	0.883921
$546$	−3.69493e14	−0.325872
$547$	1.99446e15	1.74139	0.870693	−	0.491827i	$-0.163671\pi$
$547$	1.99446e15	1.74139	0.870693	+	0.491827i	$0.163671\pi$
$548$	−7.47226e14	−0.645891
$549$	3.66314e13	0.0313477
$550$	1.43569e14	0.121637
$551$	−1.18552e15	−0.994432
$552$	2.36987e14	0.196816
$553$	−5.08064e14	−0.417763
$554$	−6.77232e14	−0.551358
$555$	−2.24840e14	−0.181243
$556$	1.06190e15	0.847568
$557$	−5.48297e14	−0.433323	−0.216662	−	0.976247i	$-0.569517\pi$
$557$	−5.48297e14	−0.433323	−0.216662	+	0.976247i	$0.569517\pi$
$558$	−7.69298e14	−0.602014
$559$	1.06100e15	0.822149
$560$	−1.56570e14	−0.120136
$561$	−2.83920e14	−0.215725
$562$	−1.75676e14	−0.132179
$563$	−2.50467e13	−0.0186618	−0.00933092	−	0.999956i	$-0.502970\pi$
$563$	−2.50467e13	−0.0186618	−0.00933092	+	0.999956i	$0.502970\pi$
$564$	−6.90398e13	−0.0509407
$565$	2.72973e14	0.199459
$566$	1.58630e15	1.14788
$567$	5.84184e14	0.418642
$568$	−2.44990e14	−0.173873
$569$	9.27419e14	0.651866	0.325933	−	0.945393i	$-0.394322\pi$
$569$	9.27419e14	0.651866	0.325933	+	0.945393i	$0.394322\pi$
$570$	−3.25712e14	−0.226737
$571$	−1.08316e15	−0.746785	−0.373393	−	0.927673i	$-0.621806\pi$
$571$	−1.08316e15	−0.746785	−0.373393	+	0.927673i	$0.621806\pi$
$572$	3.57566e14	0.244162
$573$	5.66388e14	0.383057
$574$	1.42578e15	0.955072
$575$	1.23357e15	0.818448
$576$	−1.61567e14	−0.106177
$577$	1.56061e14	0.101585	0.0507923	−	0.998709i	$-0.483825\pi$
$577$	1.56061e14	0.101585	0.0507923	+	0.998709i	$0.483825\pi$
$578$	−2.63151e15	−1.69669
$579$	−2.79363e13	−0.0178417
$580$	−4.08496e14	−0.258425
$581$	3.95238e14	0.247680
$582$	5.99682e13	0.0372259
$583$	8.27776e14	0.509021
$584$	3.87779e14	0.236218
$585$	1.49400e15	0.901555
$586$	−1.25555e15	−0.750579
$587$	2.05777e15	1.21867	0.609336	−	0.792912i	$-0.291436\pi$
$587$	2.05777e15	1.21867	0.609336	+	0.792912i	$0.291436\pi$
$588$	−1.52886e14	−0.0897001
$589$	2.17427e15	1.26381
$590$	−8.91452e14	−0.513348
$591$	5.09995e14	0.290961
$592$	3.15219e14	0.178173
$593$	−2.11536e15	−1.18463	−0.592317	−	0.805705i	$-0.701787\pi$
$593$	−2.11536e15	−1.18463	−0.592317	+	0.805705i	$0.701787\pi$
$594$	2.75765e14	0.153008
$595$	1.61170e15	0.886013
$596$	−2.75746e14	−0.150195
$597$	−7.04780e13	−0.0380360
$598$	3.07228e15	1.64287
$599$	−1.50597e14	−0.0797938	−0.0398969	−	0.999204i	$-0.512703\pi$
$599$	−1.50597e14	−0.0797938	−0.0398969	+	0.999204i	$0.512703\pi$
$600$	1.49092e14	0.0782748
$601$	−2.57205e15	−1.33804	−0.669022	−	0.743243i	$-0.733287\pi$
$601$	−2.57205e15	−1.33804	−0.669022	+	0.743243i	$0.733287\pi$
$602$	−5.10597e14	−0.263207
$603$	−1.19630e15	−0.611076
$604$	−2.00431e14	−0.101452
$605$	−1.18776e14	−0.0595765
$606$	−1.42064e14	−0.0706128
$607$	−3.32238e15	−1.63648	−0.818241	−	0.574875i	$-0.805051\pi$
$607$	−3.32238e15	−1.63648	−0.818241	+	0.574875i	$0.805051\pi$
$608$	4.56639e14	0.222897
$609$	4.63926e14	0.224416
$610$	−3.56740e13	−0.0171017
$611$	−8.95025e14	−0.425215
$612$	1.66314e15	0.783062
$613$	1.16878e15	0.545382	0.272691	−	0.962102i	$-0.412086\pi$
$613$	1.16878e15	0.545382	0.272691	+	0.962102i	$0.412086\pi$
$614$	−4.85664e14	−0.224600
$615$	1.02201e15	0.468428
$616$	−1.72075e14	−0.0781673
$617$	−9.04898e14	−0.407409	−0.203705	−	0.979032i	$-0.565298\pi$
$617$	−9.04898e14	−0.407409	−0.203705	+	0.979032i	$0.565298\pi$
$618$	−6.58676e14	−0.293924
$619$	3.51267e15	1.55360	0.776800	−	0.629748i	$-0.216842\pi$
$619$	3.51267e15	1.55360	0.776800	+	0.629748i	$0.216842\pi$
$620$	7.49193e14	0.328427
$621$	2.36943e15	1.02953
$622$	2.65081e14	0.114164
$623$	2.34344e15	1.00039
$624$	3.71322e14	0.157121
$625$	−2.47887e14	−0.103971
$626$	1.18588e14	0.0493040
$627$	−3.57968e14	−0.147527
$628$	−9.59959e14	−0.392170
$629$	−3.24480e15	−1.31404
$630$	−7.18972e14	−0.288628
$631$	−2.79712e15	−1.11314	−0.556569	−	0.830801i	$-0.687882\pi$
$631$	−2.79712e15	−1.11314	−0.556569	+	0.830801i	$0.687882\pi$
$632$	5.10579e14	0.201428
$633$	1.32137e15	0.516776
$634$	−3.85961e14	−0.149642
$635$	−2.49283e15	−0.958159
$636$	8.59621e14	0.327561
$637$	−1.98200e15	−0.748750
$638$	−4.48951e14	−0.168145
$639$	−1.12500e15	−0.417732
$640$	1.57345e14	0.0579246
$641$	5.48716e14	0.200276	0.100138	−	0.994974i	$-0.468072\pi$
$641$	5.48716e14	0.200276	0.100138	+	0.994974i	$0.468072\pi$
$642$	1.36187e15	0.492826
$643$	−3.24976e15	−1.16598	−0.582990	−	0.812479i	$-0.698117\pi$
$643$	−3.24976e15	−1.16598	−0.582990	+	0.812479i	$0.698117\pi$
$644$	−1.47851e15	−0.525958
$645$	−3.66001e14	−0.129093
$646$	−4.70055e15	−1.64388
$647$	−4.53810e15	−1.57362	−0.786810	−	0.617195i	$-0.788269\pi$
$647$	−4.53810e15	−1.57362	−0.786810	+	0.617195i	$0.788269\pi$
$648$	−5.87075e14	−0.201851
$649$	−9.79735e14	−0.334012
$650$	1.93281e15	0.653380
$651$	−8.50852e14	−0.285206
$652$	5.35597e14	0.178023
$653$	−1.99694e15	−0.658177	−0.329088	−	0.944299i	$-0.606741\pi$
$653$	−1.99694e15	−0.658177	−0.329088	+	0.944299i	$0.606741\pi$
$654$	1.13240e15	0.370102
$655$	2.04562e15	0.662975
$656$	−1.43283e15	−0.460495
$657$	1.78069e15	0.567516
$658$	4.30723e14	0.136130
$659$	2.40727e15	0.754492	0.377246	−	0.926113i	$-0.376871\pi$
$659$	2.40727e15	0.754492	0.377246	+	0.926113i	$0.376871\pi$
$660$	−1.23346e14	−0.0383382
$661$	−2.97484e15	−0.916971	−0.458485	−	0.888702i	$-0.651608\pi$
$661$	−2.97484e15	−0.916971	−0.458485	+	0.888702i	$0.651608\pi$
$662$	3.36629e15	1.02904
$663$	−3.82231e15	−1.15878
$664$	−3.97194e14	−0.119420
$665$	2.03204e15	0.605917
$666$	1.44749e15	0.428063
$667$	−3.85747e15	−1.13139
$668$	−1.68836e15	−0.491128
$669$	7.92769e14	0.228719
$670$	1.16504e15	0.333371
$671$	−3.92069e13	−0.0111273
$672$	−1.78695e14	−0.0503016
$673$	−3.52092e15	−0.983044	−0.491522	−	0.870865i	$-0.663559\pi$
$673$	−3.52092e15	−0.983044	−0.491522	+	0.870865i	$0.663559\pi$
$674$	2.40448e15	0.665873
$675$	1.49064e15	0.409451
$676$	2.97861e15	0.811533
$677$	1.45805e15	0.394034	0.197017	−	0.980400i	$-0.436875\pi$
$677$	1.45805e15	0.394034	0.197017	+	0.980400i	$0.436875\pi$
$678$	3.11547e14	0.0835143
$679$	−3.74127e14	−0.0994800
$680$	−1.61967e15	−0.427198
$681$	5.38052e14	0.140772
$682$	8.23387e14	0.213693
$683$	3.84905e14	0.0990923	0.0495462	−	0.998772i	$-0.484223\pi$
$683$	3.84905e14	0.0990923	0.0495462	+	0.998772i	$0.484223\pi$
$684$	2.09690e15	0.535511
$685$	3.34160e15	0.846558
$686$	3.01699e15	0.758212
$687$	3.29147e14	0.0820594
$688$	5.13124e14	0.126907
$689$	1.11440e16	2.73424
$690$	−1.05981e15	−0.257963
$691$	5.53939e15	1.33762	0.668810	−	0.743433i	$-0.266804\pi$
$691$	5.53939e15	1.33762	0.668810	+	0.743433i	$0.266804\pi$
$692$	−2.47214e15	−0.592229
$693$	−7.90174e14	−0.187798
$694$	1.18896e15	0.280344
$695$	−4.74885e15	−1.11089
$696$	−4.66222e14	−0.108204
$697$	1.47493e16	3.39618
$698$	−1.57843e15	−0.360595
$699$	−2.21348e15	−0.501709
$700$	−9.30148e14	−0.209176
$701$	−6.74120e15	−1.50414	−0.752069	−	0.659084i	$-0.770944\pi$
$701$	−6.74120e15	−1.50414	−0.752069	+	0.659084i	$0.770944\pi$
$702$	3.71252e15	0.821892
$703$	−4.09106e15	−0.898632
$704$	1.72927e14	0.0376889
$705$	3.08747e14	0.0667671
$706$	−3.17932e15	−0.682194
$707$	8.86301e14	0.188701
$708$	−1.01742e15	−0.214941
$709$	−3.58177e15	−0.750834	−0.375417	−	0.926856i	$-0.622500\pi$
$709$	−3.58177e15	−0.750834	−0.375417	+	0.926856i	$0.622500\pi$
$710$	1.09560e15	0.227893
$711$	2.34459e15	0.483932
$712$	−2.35504e15	−0.482346
$713$	7.07471e15	1.43786
$714$	1.83945e15	0.370978
$715$	−1.59904e15	−0.320019
$716$	2.33698e15	0.464122
$717$	−2.51943e15	−0.496532
$718$	−1.09207e15	−0.213582
$719$	2.33087e15	0.452386	0.226193	−	0.974083i	$-0.427372\pi$
$719$	2.33087e15	0.452386	0.226193	+	0.974083i	$0.427372\pi$
$720$	7.22531e14	0.139164
$721$	4.10932e15	0.785463
$722$	−2.19879e15	−0.417090
$723$	−1.76047e15	−0.331412
$724$	−2.00113e15	−0.373864
$725$	−2.42679e15	−0.449959
$726$	−1.35561e14	−0.0249450
$727$	−3.49003e15	−0.637367	−0.318683	−	0.947861i	$-0.603241\pi$
$727$	−3.49003e15	−0.637367	−0.318683	+	0.947861i	$0.603241\pi$
$728$	−2.31659e15	−0.419881
$729$	−1.14770e15	−0.206456
$730$	−1.73415e15	−0.309607
$731$	−5.28199e15	−0.935949
$732$	−4.07152e13	−0.00716054
$733$	2.25132e15	0.392976	0.196488	−	0.980506i	$-0.437046\pi$
$733$	2.25132e15	0.392976	0.196488	+	0.980506i	$0.437046\pi$
$734$	6.04991e15	1.04814
$735$	6.83709e14	0.117568
$736$	1.48583e15	0.253594
$737$	1.28041e15	0.216910
$738$	−6.57961e15	−1.10634
$739$	8.73290e15	1.45752	0.728760	−	0.684770i	$-0.240097\pi$
$739$	8.73290e15	1.45752	0.728760	+	0.684770i	$0.240097\pi$
$740$	−1.40966e15	−0.233529
$741$	−4.81919e15	−0.792454
$742$	−5.36297e15	−0.875354
$743$	2.11892e15	0.343301	0.171651	−	0.985158i	$-0.445090\pi$
$743$	2.11892e15	0.343301	0.171651	+	0.985158i	$0.445090\pi$
$744$	8.55063e14	0.137514
$745$	1.23314e15	0.196857
$746$	2.51415e15	0.398408
$747$	−1.82393e15	−0.286909
$748$	−1.78008e15	−0.277958
$749$	−8.49638e15	−1.31699
$750$	−1.83538e15	−0.282416
$751$	1.02581e16	1.56691	0.783457	−	0.621446i	$-0.213454\pi$
$751$	1.02581e16	1.56691	0.783457	+	0.621446i	$0.213454\pi$
$752$	−4.32855e14	−0.0656363
$753$	1.99100e15	0.299708
$754$	−6.04405e15	−0.903204
$755$	8.96330e14	0.132972
$756$	−1.78662e15	−0.263125
$757$	−4.23672e15	−0.619445	−0.309722	−	0.950827i	$-0.600236\pi$
$757$	−4.23672e15	−0.619445	−0.309722	+	0.950827i	$0.600236\pi$
$758$	2.94788e15	0.427887
$759$	−1.16477e15	−0.167845
$760$	−2.04210e15	−0.292147
$761$	3.84745e15	0.546458	0.273229	−	0.961949i	$-0.411908\pi$
$761$	3.84745e15	0.546458	0.273229	+	0.961949i	$0.411908\pi$
$762$	−2.84510e15	−0.401186
$763$	−7.06475e15	−0.989035
$764$	3.55105e15	0.493564
$765$	−7.43758e15	−1.02635
$766$	4.81189e15	0.659261
$767$	−1.31898e16	−1.79417
$768$	1.79580e14	0.0242533
$769$	6.95972e15	0.933248	0.466624	−	0.884456i	$-0.345470\pi$
$769$	6.95972e15	0.933248	0.466624	+	0.884456i	$0.345470\pi$
$770$	7.69523e14	0.102453
$771$	−1.47746e15	−0.195306
$772$	−1.75151e14	−0.0229888
$773$	4.40267e15	0.573758	0.286879	−	0.957967i	$-0.407382\pi$
$773$	4.40267e15	0.573758	0.286879	+	0.957967i	$0.407382\pi$
$774$	2.35628e15	0.304896
$775$	4.45079e15	0.571844
$776$	3.75979e14	0.0479650
$777$	1.60094e15	0.202796
$778$	−8.33262e15	−1.04808
$779$	1.85960e16	2.32254
$780$	−1.66056e15	−0.205936
$781$	1.20410e15	0.148280
$782$	−1.52948e16	−1.87028
$783$	−4.66134e15	−0.566006
$784$	−9.58541e14	−0.115577
$785$	4.29295e15	0.514011
$786$	2.33469e15	0.277591
$787$	−9.10246e15	−1.07473	−0.537363	−	0.843351i	$-0.680579\pi$
$787$	−9.10246e15	−1.07473	−0.537363	+	0.843351i	$0.680579\pi$
$788$	3.19749e15	0.374899
$789$	1.83804e14	0.0214008
$790$	−2.28331e15	−0.264008
$791$	−1.94367e15	−0.223178
$792$	7.94085e14	0.0905480
$793$	−5.27828e14	−0.0597710
$794$	5.66340e15	0.636890
$795$	−3.84423e15	−0.429329
$796$	−4.41872e14	−0.0490088
$797$	−3.31416e14	−0.0365050	−0.0182525	−	0.999833i	$-0.505810\pi$
$797$	−3.31416e14	−0.0365050	−0.0182525	+	0.999833i	$0.505810\pi$
$798$	2.31919e15	0.253700
$799$	4.45571e15	0.484072
$800$	9.34752e14	0.100856
$801$	−1.08144e16	−1.15884
$802$	2.08280e14	0.0221661
$803$	−1.90589e15	−0.201448
$804$	1.32967e15	0.139584
$805$	6.61190e15	0.689364
$806$	1.10850e16	1.14787
$807$	3.37603e15	0.347217
$808$	−8.90688e14	−0.0909836
$809$	−9.00501e14	−0.0913624	−0.0456812	−	0.998956i	$-0.514546\pi$
$809$	−9.00501e14	−0.0913624	−0.0456812	+	0.998956i	$0.514546\pi$
$810$	2.62541e15	0.264563
$811$	−1.73535e15	−0.173689	−0.0868444	−	0.996222i	$-0.527678\pi$
$811$	−1.73535e15	−0.173689	−0.0868444	+	0.996222i	$0.527678\pi$
$812$	2.90865e15	0.289156
$813$	7.30283e15	0.721097
$814$	−1.54927e15	−0.151947
$815$	−2.39519e15	−0.233332
$816$	−1.84856e15	−0.178870
$817$	−6.65957e15	−0.640066
$818$	9.45925e14	0.0903053
$819$	−1.06378e16	−1.00877
$820$	6.40765e15	0.603563
$821$	−1.28041e16	−1.19802	−0.599008	−	0.800743i	$-0.704438\pi$
$821$	−1.28041e16	−1.19802	−0.599008	+	0.800743i	$0.704438\pi$
$822$	3.81381e15	0.354458
$823$	−6.61590e15	−0.610787	−0.305394	−	0.952226i	$-0.598788\pi$
$823$	−6.61590e15	−0.610787	−0.305394	+	0.952226i	$0.598788\pi$
$824$	−4.12966e15	−0.378717
$825$	−7.32770e14	−0.0667530
$826$	6.34747e15	0.574395
$827$	6.29898e15	0.566227	0.283113	−	0.959086i	$-0.408633\pi$
$827$	6.29898e15	0.566227	0.283113	+	0.959086i	$0.408633\pi$
$828$	6.82294e15	0.609263
$829$	1.23443e16	1.09501	0.547504	−	0.836803i	$-0.315578\pi$
$829$	1.23443e16	1.09501	0.547504	+	0.836803i	$0.315578\pi$
$830$	1.77626e15	0.156522
$831$	3.45657e15	0.302580
$832$	2.32805e15	0.202449
$833$	9.86702e15	0.852390
$834$	−5.41992e15	−0.465136
$835$	7.55036e15	0.643713
$836$	−2.24433e15	−0.190087
$837$	8.54902e15	0.719327
$838$	−3.75283e15	−0.313702
$839$	1.57186e16	1.30534	0.652671	−	0.757642i	$-0.273649\pi$
$839$	1.57186e16	1.30534	0.652671	+	0.757642i	$0.273649\pi$
$840$	7.99127e14	0.0659295
$841$	−4.61176e15	−0.377997
$842$	4.53292e15	0.369115
$843$	8.96643e14	0.0725384
$844$	8.28448e15	0.665859
$845$	−1.33204e16	−1.06366
$846$	−1.98768e15	−0.157692
$847$	8.45731e14	0.0666613
$848$	5.38951e15	0.422058
$849$	−8.09643e15	−0.629943
$850$	−9.62214e15	−0.743819
$851$	−1.33116e16	−1.02239
$852$	1.25042e15	0.0954198
$853$	−1.20945e16	−0.916998	−0.458499	−	0.888695i	$-0.651613\pi$
$853$	−1.20945e16	−0.916998	−0.458499	+	0.888695i	$0.651613\pi$
$854$	2.54013e14	0.0191354
$855$	−9.37735e15	−0.701886
$856$	8.53844e15	0.634999
$857$	4.08926e15	0.302170	0.151085	−	0.988521i	$-0.451723\pi$
$857$	4.08926e15	0.302170	0.151085	+	0.988521i	$0.451723\pi$
$858$	−1.82500e15	−0.133994
$859$	−1.16373e16	−0.848968	−0.424484	−	0.905435i	$-0.639544\pi$
$859$	−1.16373e16	−0.848968	−0.424484	+	0.905435i	$0.639544\pi$
$860$	−2.29470e15	−0.166335
$861$	−7.27711e15	−0.524133
$862$	3.54622e15	0.253791
$863$	1.83940e16	1.30803	0.654013	−	0.756483i	$-0.273084\pi$
$863$	1.83940e16	1.30803	0.654013	+	0.756483i	$0.273084\pi$
$864$	1.79546e15	0.126867
$865$	1.10554e16	0.776224
$866$	1.83490e16	1.28016
$867$	1.34311e16	0.931123
$868$	−5.33453e15	−0.367483
$869$	−2.50944e15	−0.171778
$870$	2.08495e15	0.141821
$871$	1.72377e16	1.16515
$872$	7.09972e15	0.476871
$873$	1.72650e15	0.115236
$874$	−1.92837e16	−1.27902
$875$	1.14505e16	0.754709
$876$	−1.97921e15	−0.129634
$877$	−1.18388e16	−0.770567	−0.385284	−	0.922798i	$-0.625896\pi$
$877$	−1.18388e16	−0.770567	−0.385284	+	0.922798i	$0.625896\pi$
$878$	4.26495e15	0.275863
$879$	6.40827e15	0.411910
$880$	−7.73332e14	−0.0493982
$881$	1.46483e16	0.929862	0.464931	−	0.885347i	$-0.346079\pi$
$881$	1.46483e16	0.929862	0.464931	+	0.885347i	$0.346079\pi$
$882$	−4.40164e15	−0.277675
$883$	−2.54366e16	−1.59469	−0.797344	−	0.603525i	$-0.793762\pi$
$883$	−2.54366e16	−1.59469	−0.797344	+	0.603525i	$0.793762\pi$
$884$	−2.39645e16	−1.49307
$885$	4.54994e15	0.281720
$886$	−1.47951e16	−0.910400
$887$	−1.87344e16	−1.14567	−0.572834	−	0.819671i	$-0.694156\pi$
$887$	−1.87344e16	−1.14567	−0.572834	+	0.819671i	$0.694156\pi$
$888$	−1.60887e15	−0.0977797
$889$	1.77499e16	1.07210
$890$	1.05318e16	0.632202
$891$	2.88541e15	0.172139
$892$	4.97037e15	0.294702
$893$	5.61779e15	0.331042
$894$	1.40740e15	0.0824251
$895$	−1.04510e16	−0.608317
$896$	−1.12035e15	−0.0648129
$897$	−1.56808e16	−0.901592
$898$	−1.26303e15	−0.0721763
$899$	−1.39180e16	−0.790492
$900$	4.29240e15	0.242307
$901$	−5.54785e16	−3.11271
$902$	7.04222e15	0.392711
$903$	2.60607e15	0.144445
$904$	1.95329e15	0.107607
$905$	8.94908e15	0.490017
$906$	1.02299e15	0.0556759
$907$	2.70606e16	1.46385	0.731925	−	0.681385i	$-0.238622\pi$
$907$	2.70606e16	1.46385	0.731925	+	0.681385i	$0.238622\pi$
$908$	3.37339e15	0.181382
$909$	−4.09006e15	−0.218589
$910$	1.03598e16	0.550331
$911$	−2.60833e16	−1.37724	−0.688622	−	0.725120i	$-0.741784\pi$
$911$	−2.60833e16	−1.37724	−0.688622	+	0.725120i	$0.741784\pi$
$912$	−2.33067e15	−0.122323
$913$	1.95217e15	0.101842
$914$	1.78062e16	0.923349
$915$	1.82079e14	0.00938521
$916$	2.06363e15	0.105732
$917$	−1.45655e16	−0.741815
$918$	−1.84821e16	−0.935656
$919$	5.28619e15	0.266016	0.133008	−	0.991115i	$-0.457536\pi$
$919$	5.28619e15	0.266016	0.133008	+	0.991115i	$0.457536\pi$
$920$	−6.64463e15	−0.332382
$921$	2.47881e15	0.123258
$922$	−1.26599e16	−0.625765
$923$	1.62103e16	0.796494
$924$	8.78267e14	0.0428974
$925$	−8.37450e15	−0.406611
$926$	−2.62221e16	−1.26563
$927$	−1.89635e16	−0.909870
$928$	−2.92304e15	−0.139419
$929$	1.00624e16	0.477105	0.238553	−	0.971130i	$-0.423327\pi$
$929$	1.00624e16	0.477105	0.238553	+	0.971130i	$0.423327\pi$
$930$	−3.82385e15	−0.180237
$931$	1.24404e16	0.582923
$932$	−1.38777e16	−0.646445
$933$	−1.35296e15	−0.0626522
$934$	2.46168e15	0.113325
$935$	7.96052e15	0.364315
$936$	1.06905e16	0.486384
$937$	−1.01157e16	−0.457540	−0.228770	−	0.973481i	$-0.573470\pi$
$937$	−1.01157e16	−0.457540	−0.228770	+	0.973481i	$0.573470\pi$
$938$	−8.29550e15	−0.373015
$939$	−6.05269e14	−0.0270575
$940$	1.93573e15	0.0860284
$941$	2.22056e16	0.981113	0.490557	−	0.871409i	$-0.336793\pi$
$941$	2.22056e16	0.981113	0.490557	+	0.871409i	$0.336793\pi$
$942$	4.89959e15	0.215219
$943$	6.05082e16	2.64241
$944$	−6.37889e15	−0.276948
$945$	7.98977e15	0.344873
$946$	−2.52195e15	−0.108227
$947$	2.44306e16	1.04234	0.521170	−	0.853453i	$-0.325496\pi$
$947$	2.44306e16	1.04234	0.521170	+	0.853453i	$0.325496\pi$
$948$	−2.60598e15	−0.110541
$949$	−2.56583e16	−1.08209
$950$	−1.21317e16	−0.508675
$951$	1.96993e15	0.0821218
$952$	1.15327e16	0.477999
$953$	−4.09198e16	−1.68625	−0.843127	−	0.537714i	$-0.819288\pi$
$953$	−4.09198e16	−1.68625	−0.843127	+	0.537714i	$0.819288\pi$
$954$	2.47488e16	1.01400
$955$	−1.58803e16	−0.646906
$956$	−1.57959e16	−0.639774
$957$	2.29143e15	0.0922764
$958$	−2.04607e16	−0.819238
$959$	−2.37935e16	−0.947230
$960$	−8.03082e14	−0.0317884
$961$	1.17453e14	0.00462257
$962$	−2.08572e16	−0.816193
$963$	3.92087e16	1.52559
$964$	−1.10375e16	−0.427020
$965$	7.83276e14	0.0301311
$966$	7.54624e15	0.288640
$967$	4.55259e16	1.73146	0.865731	−	0.500509i	$-0.166854\pi$
$967$	4.55259e16	1.73146	0.865731	+	0.500509i	$0.166854\pi$
$968$	−8.49918e14	−0.0321412
$969$	2.39914e16	0.902143
$970$	−1.68138e15	−0.0628669
$971$	−1.47484e16	−0.548328	−0.274164	−	0.961683i	$-0.588401\pi$
$971$	−1.47484e16	−0.548328	−0.274164	+	0.961683i	$0.588401\pi$
$972$	1.27028e16	0.469609
$973$	3.38136e16	1.24300
$974$	2.38585e16	0.872107
$975$	−9.86500e15	−0.358568
$976$	−2.55270e14	−0.00922626
$977$	3.04602e15	0.109474	0.0547371	−	0.998501i	$-0.482568\pi$
$977$	3.04602e15	0.109474	0.0547371	+	0.998501i	$0.482568\pi$
$978$	−2.73366e15	−0.0976971
$979$	1.15748e16	0.411346
$980$	4.28661e15	0.151485
$981$	3.26021e16	1.14569
$982$	2.83621e16	0.991119
$983$	4.63572e16	1.61092	0.805458	−	0.592653i	$-0.201920\pi$
$983$	4.63572e16	1.61092	0.805458	+	0.592653i	$0.201920\pi$
$984$	7.31313e15	0.252715
$985$	−1.42992e16	−0.491374
$986$	3.00892e16	1.02822
$987$	−2.19839e15	−0.0747069
$988$	−3.02146e16	−1.02106
$989$	−2.16691e16	−0.728217
$990$	−3.55116e15	−0.118680
$991$	3.89171e16	1.29341	0.646703	−	0.762742i	$-0.276147\pi$
$991$	3.89171e16	1.29341	0.646703	+	0.762742i	$0.276147\pi$
$992$	5.36094e15	0.177185
$993$	−1.71814e16	−0.564727
$994$	−7.80108e15	−0.254994
$995$	1.97606e15	0.0642351
$996$	2.02727e15	0.0655367
$997$	−2.36600e16	−0.760662	−0.380331	−	0.924850i	$-0.624190\pi$
$997$	−2.36600e16	−0.760662	−0.380331	+	0.924850i	$0.624190\pi$
$998$	6.90297e15	0.220708
$999$	−1.60856e16	−0.511479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.12.a.b.1.2	✓	3
3.2	odd	2		198.12.a.l.1.3		3
4.3	odd	2		176.12.a.d.1.2		3
11.10	odd	2		242.12.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.12.a.b.1.2	✓	3	1.1	even	1	trivial
176.12.a.d.1.2		3	4.3	odd	2
198.12.a.l.1.3		3	3.2	odd	2
242.12.a.c.1.2		3	11.10	odd	2

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} +163.327 q^{3} +1024.00 q^{4} -4579.34 q^{5} -5226.46 q^{6} +32606.6 q^{7} -32768.0 q^{8} -150471. q^{9} +O(q^{10})\)	\(q-32.0000 q^{2} +163.327 q^{3} +1024.00 q^{4} -4579.34 q^{5} -5226.46 q^{6} +32606.6 q^{7} -32768.0 q^{8} -150471. q^{9} +146539. q^{10} +161051. q^{11} +167247. q^{12} +2.16817e6 q^{13} -1.04341e6 q^{14} -747929. q^{15} +1.04858e6 q^{16} -1.07938e7 q^{17} +4.81508e6 q^{18} -1.36089e7 q^{19} -4.68924e6 q^{20} +5.32553e6 q^{21} -5.15363e6 q^{22} -4.42810e7 q^{23} -5.35189e6 q^{24} -2.78578e7 q^{25} -6.93814e7 q^{26} -5.35089e7 q^{27} +3.33892e7 q^{28} +8.71135e7 q^{29} +2.39337e7 q^{30} -1.59768e8 q^{31} -3.35544e7 q^{32} +2.63039e7 q^{33} +3.45402e8 q^{34} -1.49317e8 q^{35} -1.54083e8 q^{36} +3.00616e8 q^{37} +4.35485e8 q^{38} +3.54120e8 q^{39} +1.50056e8 q^{40} -1.36646e9 q^{41} -1.70417e8 q^{42} +4.89353e8 q^{43} +1.64916e8 q^{44} +6.89059e8 q^{45} +1.41699e9 q^{46} -4.12802e8 q^{47} +1.71261e8 q^{48} -9.14136e8 q^{49} +8.91449e8 q^{50} -1.76292e9 q^{51} +2.22020e9 q^{52} +5.13984e9 q^{53} +1.71228e9 q^{54} -7.37507e8 q^{55} -1.06845e9 q^{56} -2.22270e9 q^{57} -2.78763e9 q^{58} -6.08338e9 q^{59} -7.65879e8 q^{60} -2.43444e8 q^{61} +5.11259e9 q^{62} -4.90636e9 q^{63} +1.07374e9 q^{64} -9.92878e9 q^{65} -8.41726e8 q^{66} +7.95036e9 q^{67} -1.10529e10 q^{68} -7.23228e9 q^{69} +4.77813e9 q^{70} +7.47651e9 q^{71} +4.93065e9 q^{72} -1.18341e10 q^{73} -9.61972e9 q^{74} -4.54992e9 q^{75} -1.39355e10 q^{76} +5.25133e9 q^{77} -1.13318e10 q^{78} -1.55816e10 q^{79} -4.80178e9 q^{80} +1.79161e10 q^{81} +4.37266e10 q^{82} +1.21214e10 q^{83} +5.45335e9 q^{84} +4.94286e10 q^{85} -1.56593e10 q^{86} +1.42280e10 q^{87} -5.27732e9 q^{88} +7.18701e10 q^{89} -2.20499e10 q^{90} +7.06966e10 q^{91} -4.53438e10 q^{92} -2.60945e10 q^{93} +1.32097e10 q^{94} +6.23198e10 q^{95} -5.48034e9 q^{96} -1.14740e10 q^{97} +2.92524e10 q^{98} -2.42336e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 96 q^{2} - 70 q^{3} + 3072 q^{4} - 5624 q^{5} + 2240 q^{6} - 30576 q^{7} - 98304 q^{8} + 533833 q^{9}+O(q^{10}) \) 3 * q - 96 * q^2 - 70 * q^3 + 3072 * q^4 - 5624 * q^5 + 2240 * q^6 - 30576 * q^7 - 98304 * q^8 + 533833 * q^9	\( 3 q - 96 q^{2} - 70 q^{3} + 3072 q^{4} - 5624 q^{5} + 2240 q^{6} - 30576 q^{7} - 98304 q^{8} + 533833 q^{9} + 179968 q^{10} + 483153 q^{11} - 71680 q^{12} + 423050 q^{13} + 978432 q^{14} - 581042 q^{15} + 3145728 q^{16} - 16823942 q^{17} - 17082656 q^{18} - 12737072 q^{19} - 5758976 q^{20} - 64101968 q^{21} - 15460896 q^{22} - 11397034 q^{23} + 2293760 q^{24} - 124966369 q^{25} - 13537600 q^{26} - 327990502 q^{27} - 31309824 q^{28} - 136849122 q^{29} + 18593344 q^{30} + 242041022 q^{31} - 100663296 q^{32} - 11273570 q^{33} + 538366144 q^{34} - 119732536 q^{35} + 546644992 q^{36} + 450661244 q^{37} + 407586304 q^{38} - 556451364 q^{39} + 184287232 q^{40} + 97726086 q^{41} + 2051262976 q^{42} - 712479248 q^{43} + 494748672 q^{44} + 321123482 q^{45} + 364705088 q^{46} - 3330549288 q^{47} - 73400320 q^{48} + 2958905187 q^{49} + 3998923808 q^{50} + 5871605992 q^{51} + 433203200 q^{52} - 3777184886 q^{53} + 10495696064 q^{54} - 905750824 q^{55} + 1001914368 q^{56} - 13176751420 q^{57} + 4379171904 q^{58} - 9293353002 q^{59} - 594987008 q^{60} + 2647736806 q^{61} - 7745312704 q^{62} - 8605254952 q^{63} + 3221225472 q^{64} - 9066838392 q^{65} + 360754240 q^{66} + 1632055702 q^{67} - 17227716608 q^{68} - 53633241046 q^{69} + 3831441152 q^{70} - 2119547430 q^{71} - 17492639744 q^{72} - 5284631794 q^{73} - 14421159808 q^{74} + 6732072508 q^{75} - 13042761728 q^{76} - 4924295376 q^{77} + 17806443648 q^{78} + 8982892548 q^{79} - 5897191424 q^{80} + 123128573251 q^{81} - 3127234752 q^{82} + 11489211392 q^{83} - 65640415232 q^{84} + 52886747204 q^{85} + 22799335936 q^{86} + 65580896304 q^{87} - 15831957504 q^{88} + 181048875488 q^{89} - 10275951424 q^{90} + 210430763032 q^{91} - 11670562816 q^{92} + 40878143418 q^{93} + 106577577216 q^{94} + 61381442860 q^{95} + 2348810240 q^{96} - 17159174540 q^{97} - 94684965984 q^{98} + 85974338483 q^{99}+O(q^{100}) \) 3 * q - 96 * q^2 - 70 * q^3 + 3072 * q^4 - 5624 * q^5 + 2240 * q^6 - 30576 * q^7 - 98304 * q^8 + 533833 * q^9 + 179968 * q^10 + 483153 * q^11 - 71680 * q^12 + 423050 * q^13 + 978432 * q^14 - 581042 * q^15 + 3145728 * q^16 - 16823942 * q^17 - 17082656 * q^18 - 12737072 * q^19 - 5758976 * q^20 - 64101968 * q^21 - 15460896 * q^22 - 11397034 * q^23 + 2293760 * q^24 - 124966369 * q^25 - 13537600 * q^26 - 327990502 * q^27 - 31309824 * q^28 - 136849122 * q^29 + 18593344 * q^30 + 242041022 * q^31 - 100663296 * q^32 - 11273570 * q^33 + 538366144 * q^34 - 119732536 * q^35 + 546644992 * q^36 + 450661244 * q^37 + 407586304 * q^38 - 556451364 * q^39 + 184287232 * q^40 + 97726086 * q^41 + 2051262976 * q^42 - 712479248 * q^43 + 494748672 * q^44 + 321123482 * q^45 + 364705088 * q^46 - 3330549288 * q^47 - 73400320 * q^48 + 2958905187 * q^49 + 3998923808 * q^50 + 5871605992 * q^51 + 433203200 * q^52 - 3777184886 * q^53 + 10495696064 * q^54 - 905750824 * q^55 + 1001914368 * q^56 - 13176751420 * q^57 + 4379171904 * q^58 - 9293353002 * q^59 - 594987008 * q^60 + 2647736806 * q^61 - 7745312704 * q^62 - 8605254952 * q^63 + 3221225472 * q^64 - 9066838392 * q^65 + 360754240 * q^66 + 1632055702 * q^67 - 17227716608 * q^68 - 53633241046 * q^69 + 3831441152 * q^70 - 2119547430 * q^71 - 17492639744 * q^72 - 5284631794 * q^73 - 14421159808 * q^74 + 6732072508 * q^75 - 13042761728 * q^76 - 4924295376 * q^77 + 17806443648 * q^78 + 8982892548 * q^79 - 5897191424 * q^80 + 123128573251 * q^81 - 3127234752 * q^82 + 11489211392 * q^83 - 65640415232 * q^84 + 52886747204 * q^85 + 22799335936 * q^86 + 65580896304 * q^87 - 15831957504 * q^88 + 181048875488 * q^89 - 10275951424 * q^90 + 210430763032 * q^91 - 11670562816 * q^92 + 40878143418 * q^93 + 106577577216 * q^94 + 61381442860 * q^95 + 2348810240 * q^96 - 17159174540 * q^97 - 94684965984 * q^98 + 85974338483 * q^99

Introduction

L-functions

Modular forms

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