LMFDB - Embedded newform 177.12.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.2053 q^{2} +243.000 q^{3} -1010.82 q^{4} -5509.44 q^{5} +7825.90 q^{6} -36737.1 q^{7} -98510.2 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+32.2053 q^{2} +243.000 q^{3} -1010.82 q^{4} -5509.44 q^{5} +7825.90 q^{6} -36737.1 q^{7} -98510.2 q^{8} +59049.0 q^{9} -177433. q^{10} +785481. q^{11} -245628. q^{12} +1.64819e6 q^{13} -1.18313e6 q^{14} -1.33879e6 q^{15} -1.10240e6 q^{16} +14272.3 q^{17} +1.90169e6 q^{18} -8.87395e6 q^{19} +5.56903e6 q^{20} -8.92711e6 q^{21} +2.52967e7 q^{22} +2.97072e7 q^{23} -2.39380e7 q^{24} -1.84742e7 q^{25} +5.30806e7 q^{26} +1.43489e7 q^{27} +3.71344e7 q^{28} +6.76779e7 q^{29} -4.31163e7 q^{30} +6.05970e7 q^{31} +1.66246e8 q^{32} +1.90872e8 q^{33} +459646. q^{34} +2.02401e8 q^{35} -5.96877e7 q^{36} +1.57018e8 q^{37} -2.85789e8 q^{38} +4.00511e8 q^{39} +5.42736e8 q^{40} -1.38293e9 q^{41} -2.87501e8 q^{42} -1.09612e9 q^{43} -7.93977e8 q^{44} -3.25327e8 q^{45} +9.56729e8 q^{46} +1.74265e9 q^{47} -2.67884e8 q^{48} -6.27714e8 q^{49} -5.94967e8 q^{50} +3.46818e6 q^{51} -1.66602e9 q^{52} +3.03335e8 q^{53} +4.62111e8 q^{54} -4.32756e9 q^{55} +3.61898e9 q^{56} -2.15637e9 q^{57} +2.17959e9 q^{58} -7.14924e8 q^{59} +1.35327e9 q^{60} +1.62524e9 q^{61} +1.95155e9 q^{62} -2.16929e9 q^{63} +7.61172e9 q^{64} -9.08062e9 q^{65} +6.14710e9 q^{66} -1.24549e10 q^{67} -1.44267e7 q^{68} +7.21884e9 q^{69} +6.51839e9 q^{70} -8.29797e9 q^{71} -5.81693e9 q^{72} -2.93246e10 q^{73} +5.05681e9 q^{74} -4.48923e9 q^{75} +8.96993e9 q^{76} -2.88563e10 q^{77} +1.28986e10 q^{78} -1.88795e10 q^{79} +6.07363e9 q^{80} +3.48678e9 q^{81} -4.45377e10 q^{82} +2.23593e10 q^{83} +9.02366e9 q^{84} -7.86326e7 q^{85} -3.53009e10 q^{86} +1.64457e10 q^{87} -7.73779e10 q^{88} -9.79467e10 q^{89} -1.04773e10 q^{90} -6.05498e10 q^{91} -3.00285e10 q^{92} +1.47251e10 q^{93} +5.61227e10 q^{94} +4.88905e10 q^{95} +4.03977e10 q^{96} +2.14426e10 q^{97} -2.02157e10 q^{98} +4.63819e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	32.2053	0.711644	0.355822	−	0.934554i	$-0.384201\pi$
$2$	32.2053	0.711644	0.355822	+	0.934554i	$0.384201\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1010.82	−0.493562
$5$	−5509.44	−0.788447	−0.394224	−	0.919015i	$-0.628986\pi$
$5$	−5509.44	−0.788447	−0.394224	+	0.919015i	$0.628986\pi$
$6$	7825.90	0.410868
$7$	−36737.1	−0.826162	−0.413081	−	0.910694i	$-0.635547\pi$
$7$	−36737.1	−0.826162	−0.413081	+	0.910694i	$0.635547\pi$
$8$	−98510.2	−1.06289
$9$	59049.0	0.333333
$10$	−177433.	−0.561094
$11$	785481.	1.47054	0.735269	−	0.677776i	$-0.237056\pi$
$11$	785481.	1.47054	0.735269	+	0.677776i	$0.237056\pi$
$12$	−245628.	−0.284958
$13$	1.64819e6	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$13$	1.64819e6	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$14$	−1.18313e6	−0.587934
$15$	−1.33879e6	−0.455210
$16$	−1.10240e6	−0.262834
$17$	14272.3	0.00243796	0.00121898	−	0.999999i	$-0.499612\pi$
$17$	14272.3	0.00243796	0.00121898	+	0.999999i	$0.499612\pi$
$18$	1.90169e6	0.237215
$19$	−8.87395e6	−0.822190	−0.411095	−	0.911593i	$-0.634853\pi$
$19$	−8.87395e6	−0.822190	−0.411095	+	0.911593i	$0.634853\pi$
$20$	5.56903e6	0.389148
$21$	−8.92711e6	−0.476985
$22$	2.52967e7	1.04650
$23$	2.97072e7	0.962405	0.481203	−	0.876609i	$-0.340200\pi$
$23$	2.97072e7	0.962405	0.481203	+	0.876609i	$0.340200\pi$
$24$	−2.39380e7	−0.613657
$25$	−1.84742e7	−0.378351
$26$	5.30806e7	0.876158
$27$	1.43489e7	0.192450
$28$	3.71344e7	0.407763
$29$	6.76779e7	0.612714	0.306357	−	0.951917i	$-0.400890\pi$
$29$	6.76779e7	0.612714	0.306357	+	0.951917i	$0.400890\pi$
$30$	−4.31163e7	−0.323948
$31$	6.05970e7	0.380156	0.190078	−	0.981769i	$-0.439126\pi$
$31$	6.05970e7	0.380156	0.190078	+	0.981769i	$0.439126\pi$
$32$	1.66246e8	0.875841
$33$	1.90872e8	0.849015
$34$	459646.	0.00173496
$35$	2.02401e8	0.651385
$36$	−5.96877e7	−0.164521
$37$	1.57018e8	0.372254	0.186127	−	0.982526i	$-0.440406\pi$
$37$	1.57018e8	0.372254	0.186127	+	0.982526i	$0.440406\pi$
$38$	−2.85789e8	−0.585107
$39$	4.00511e8	0.710819
$40$	5.42736e8	0.838029
$41$	−1.38293e9	−1.86419	−0.932093	−	0.362220i	$-0.882019\pi$
$41$	−1.38293e9	−1.86419	−0.932093	+	0.362220i	$0.882019\pi$
$42$	−2.87501e8	−0.339444
$43$	−1.09612e9	−1.13706	−0.568528	−	0.822664i	$-0.692487\pi$
$43$	−1.09612e9	−1.13706	−0.568528	+	0.822664i	$0.692487\pi$
$44$	−7.93977e8	−0.725802
$45$	−3.25327e8	−0.262816
$46$	9.56729e8	0.684890
$47$	1.74265e9	1.10834	0.554170	−	0.832404i	$-0.313036\pi$
$47$	1.74265e9	1.10834	0.554170	+	0.832404i	$0.313036\pi$
$48$	−2.67884e8	−0.151747
$49$	−6.27714e8	−0.317456
$50$	−5.94967e8	−0.269252
$51$	3.46818e6	0.00140756
$52$	−1.66602e9	−0.607661
$53$	3.03335e8	0.0996336	0.0498168	−	0.998758i	$-0.484136\pi$
$53$	3.03335e8	0.0996336	0.0498168	+	0.998758i	$0.484136\pi$
$54$	4.62111e8	0.136956
$55$	−4.32756e9	−1.15944
$56$	3.61898e9	0.878116
$57$	−2.15637e9	−0.474691
$58$	2.17959e9	0.436034
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.35327e9	0.224675
$61$	1.62524e9	0.246378	0.123189	−	0.992383i	$-0.460688\pi$
$61$	1.62524e9	0.246378	0.123189	+	0.992383i	$0.460688\pi$
$62$	1.95155e9	0.270536
$63$	−2.16929e9	−0.275387
$64$	7.61172e9	0.886121
$65$	−9.08062e9	−0.970716
$66$	6.14710e9	0.604197
$67$	−1.24549e10	−1.12702	−0.563508	−	0.826111i	$-0.690549\pi$
$67$	−1.24549e10	−1.12702	−0.563508	+	0.826111i	$0.690549\pi$
$68$	−1.44267e7	−0.00120328
$69$	7.21884e9	0.555645
$70$	6.51839e9	0.463555
$71$	−8.29797e9	−0.545822	−0.272911	−	0.962039i	$-0.587986\pi$
$71$	−8.29797e9	−0.545822	−0.272911	+	0.962039i	$0.587986\pi$
$72$	−5.81693e9	−0.354295
$73$	−2.93246e10	−1.65560	−0.827801	−	0.561021i	$-0.810409\pi$
$73$	−2.93246e10	−1.65560	−0.827801	+	0.561021i	$0.810409\pi$
$74$	5.05681e9	0.264912
$75$	−4.48923e9	−0.218441
$76$	8.96993e9	0.405802
$77$	−2.88563e10	−1.21490
$78$	1.28986e10	0.505850
$79$	−1.88795e10	−0.690307	−0.345154	−	0.938546i	$-0.612173\pi$
$79$	−1.88795e10	−0.690307	−0.345154	+	0.938546i	$0.612173\pi$
$80$	6.07363e9	0.207230
$81$	3.48678e9	0.111111
$82$	−4.45377e10	−1.32664
$83$	2.23593e10	0.623057	0.311529	−	0.950237i	$-0.399159\pi$
$83$	2.23593e10	0.623057	0.311529	+	0.950237i	$0.399159\pi$
$84$	9.02366e9	0.235422
$85$	−7.86326e7	−0.00192220
$86$	−3.53009e10	−0.809179
$87$	1.64457e10	0.353750
$88$	−7.73779e10	−1.56301
$89$	−9.79467e10	−1.85928	−0.929640	−	0.368470i	$-0.879882\pi$
$89$	−9.79467e10	−1.85928	−0.929640	+	0.368470i	$0.879882\pi$
$90$	−1.04773e10	−0.187031
$91$	−6.05498e10	−1.01715
$92$	−3.00285e10	−0.475007
$93$	1.47251e10	0.219483
$94$	5.61227e10	0.788743
$95$	4.88905e10	0.648253
$96$	4.03977e10	0.505667
$97$	2.14426e10	0.253533	0.126766	−	0.991933i	$-0.459540\pi$
$97$	2.14426e10	0.253533	0.126766	+	0.991933i	$0.459540\pi$
$98$	−2.02157e10	−0.225916
$99$	4.63819e10	0.490179
$100$	1.86740e10	0.186740
$101$	−1.43434e11	−1.35795	−0.678977	−	0.734159i	$-0.737576\pi$
$101$	−1.43434e11	−1.35795	−0.678977	+	0.734159i	$0.737576\pi$
$102$	1.11694e8	0.00100168
$103$	−2.08419e10	−0.177147	−0.0885735	−	0.996070i	$-0.528231\pi$
$103$	−2.08419e10	−0.177147	−0.0885735	+	0.996070i	$0.528231\pi$
$104$	−1.62364e11	−1.30860
$105$	4.91834e10	0.376077
$106$	9.76902e9	0.0709037
$107$	1.99719e11	1.37660	0.688302	−	0.725424i	$-0.258356\pi$
$107$	1.99719e11	1.37660	0.688302	+	0.725424i	$0.258356\pi$
$108$	−1.45041e10	−0.0949861
$109$	8.05057e10	0.501165	0.250583	−	0.968095i	$-0.419378\pi$
$109$	8.05057e10	0.501165	0.250583	+	0.968095i	$0.419378\pi$
$110$	−1.39371e11	−0.825109
$111$	3.81553e10	0.214921
$112$	4.04991e10	0.217143
$113$	−9.30445e10	−0.475072	−0.237536	−	0.971379i	$-0.576340\pi$
$113$	−9.30445e10	−0.475072	−0.237536	+	0.971379i	$0.576340\pi$
$114$	−6.94466e10	−0.337811
$115$	−1.63670e11	−0.758805
$116$	−6.84099e10	−0.302412
$117$	9.73241e10	0.410391
$118$	−2.30244e10	−0.0926482
$119$	−5.24324e8	−0.00201415
$120$	1.31885e11	0.483836
$121$	3.31669e11	1.16248
$122$	5.23413e10	0.175334
$123$	−3.36052e11	−1.07629
$124$	−6.12524e10	−0.187631
$125$	3.70798e11	1.08676
$126$	−6.98627e10	−0.195978
$127$	2.11371e11	0.567709	0.283854	−	0.958867i	$-0.408387\pi$
$127$	2.11371e11	0.567709	0.283854	+	0.958867i	$0.408387\pi$
$128$	−9.53329e10	−0.245238
$129$	−2.66357e11	−0.656479
$130$	−2.92445e11	−0.690804
$131$	−4.56049e8	−0.00103281	−0.000516404	−	1.00000i	$-0.500164\pi$
$131$	−4.56049e8	−0.00103281	−0.000516404		1.00000i	$0.500164\pi$
$132$	−1.92936e11	−0.419042
$133$	3.26003e11	0.679262
$134$	−4.01116e11	−0.802035
$135$	−7.90545e10	−0.151737
$136$	−1.40597e9	−0.00259127
$137$	7.80465e11	1.38163	0.690813	−	0.723033i	$-0.257253\pi$
$137$	7.80465e11	1.38163	0.690813	+	0.723033i	$0.257253\pi$
$138$	2.32485e11	0.395422
$139$	−2.07582e11	−0.339319	−0.169659	−	0.985503i	$-0.554267\pi$
$139$	−2.07582e11	−0.339319	−0.169659	+	0.985503i	$0.554267\pi$
$140$	−2.04590e11	−0.321499
$141$	4.23465e11	0.639900
$142$	−2.67239e11	−0.388431
$143$	1.29462e12	1.81049
$144$	−6.50959e10	−0.0876113
$145$	−3.72867e11	−0.483092
$146$	−9.44408e11	−1.17820
$147$	−1.52534e11	−0.183283
$148$	−1.58716e11	−0.183731
$149$	−1.52018e12	−1.69578	−0.847889	−	0.530173i	$-0.822127\pi$
$149$	−1.52018e12	−1.69578	−0.847889	+	0.530173i	$0.822127\pi$
$150$	−1.44577e11	−0.155452
$151$	−8.72188e11	−0.904142	−0.452071	−	0.891982i	$-0.649315\pi$
$151$	−8.72188e11	−0.904142	−0.452071	+	0.891982i	$0.649315\pi$
$152$	8.74174e11	0.873893
$153$	8.42768e8	0.000812653 0
$154$	−9.29327e11	−0.864579
$155$	−3.33856e11	−0.299733
$156$	−4.04843e11	−0.350833
$157$	−1.28318e12	−1.07359	−0.536796	−	0.843712i	$-0.680366\pi$
$157$	−1.28318e12	−1.07359	−0.536796	+	0.843712i	$0.680366\pi$
$158$	−6.08022e11	−0.491253
$159$	7.37105e10	0.0575235
$160$	−9.15920e11	−0.690554
$161$	−1.09135e12	−0.795103
$162$	1.12293e11	0.0790716
$163$	−1.84584e12	−1.25650	−0.628250	−	0.778012i	$-0.716228\pi$
$163$	−1.84584e12	−1.25650	−0.628250	+	0.778012i	$0.716228\pi$
$164$	1.39789e12	0.920092
$165$	−1.05160e12	−0.669404
$166$	7.20088e11	0.443395
$167$	−2.58949e11	−0.154267	−0.0771335	−	0.997021i	$-0.524577\pi$
$167$	−2.58949e11	−0.154267	−0.0771335	+	0.997021i	$0.524577\pi$
$168$	8.79412e11	0.506980
$169$	9.24379e11	0.515790
$170$	−2.53239e9	−0.00136792
$171$	−5.23998e11	−0.274063
$172$	1.10798e12	0.561208
$173$	3.88764e12	1.90736	0.953680	−	0.300822i	$-0.0972611\pi$
$173$	3.88764e12	1.90736	0.953680	+	0.300822i	$0.0972611\pi$
$174$	5.29640e11	0.251745
$175$	6.78688e11	0.312580
$176$	−8.65918e11	−0.386507
$177$	−1.73727e11	−0.0751646
$178$	−3.15441e12	−1.32315
$179$	1.24427e11	0.0506083	0.0253041	−	0.999680i	$-0.491945\pi$
$179$	1.24427e11	0.0506083	0.0253041	+	0.999680i	$0.491945\pi$
$180$	3.28846e11	0.129716
$181$	−1.21291e12	−0.464085	−0.232043	−	0.972706i	$-0.574541\pi$
$181$	−1.21291e12	−0.464085	−0.232043	+	0.972706i	$0.574541\pi$
$182$	−1.95003e12	−0.723849
$183$	3.94933e11	0.142247
$184$	−2.92646e12	−1.02293
$185$	−8.65080e11	−0.293502
$186$	4.74226e11	0.156194
$187$	1.12107e10	0.00358511
$188$	−1.76150e12	−0.547035
$189$	−5.27137e11	−0.158995
$190$	1.57453e12	0.461326
$191$	−2.18790e12	−0.622793	−0.311397	−	0.950280i	$-0.600797\pi$
$191$	−2.18790e12	−0.622793	−0.311397	+	0.950280i	$0.600797\pi$
$192$	1.84965e12	0.511602
$193$	2.69207e12	0.723639	0.361819	−	0.932248i	$-0.382156\pi$
$193$	2.69207e12	0.723639	0.361819	+	0.932248i	$0.382156\pi$
$194$	6.90568e11	0.180425
$195$	−2.20659e12	−0.560443
$196$	6.34503e11	0.156684
$197$	−4.91992e12	−1.18139	−0.590696	−	0.806895i	$-0.701147\pi$
$197$	−4.91992e12	−1.18139	−0.590696	+	0.806895i	$0.701147\pi$
$198$	1.49374e12	0.348833
$199$	6.24859e12	1.41935	0.709676	−	0.704528i	$-0.248841\pi$
$199$	6.24859e12	1.41935	0.709676	+	0.704528i	$0.248841\pi$
$200$	1.81990e12	0.402144
$201$	−3.02655e12	−0.650683
$202$	−4.61935e12	−0.966380
$203$	−2.48629e12	−0.506201
$204$	−3.50569e9	−0.000694716 0
$205$	7.61917e12	1.46981
$206$	−6.71222e11	−0.126066
$207$	1.75418e12	0.320802
$208$	−1.81698e12	−0.323594
$209$	−6.97032e12	−1.20906
$210$	1.58397e12	0.267633
$211$	−6.22887e12	−1.02531	−0.512656	−	0.858594i	$-0.671338\pi$
$211$	−6.22887e12	−1.02531	−0.512656	+	0.858594i	$0.671338\pi$
$212$	−3.06616e11	−0.0491754
$213$	−2.01641e12	−0.315130
$214$	6.43202e12	0.979652
$215$	6.03901e12	0.896508
$216$	−1.41351e12	−0.204552
$217$	−2.22616e12	−0.314071
$218$	2.59271e12	0.356651
$219$	−7.12587e12	−0.955863
$220$	4.37437e12	0.572256
$221$	2.35236e10	0.00300155
$222$	1.22880e12	0.152947
$223$	−1.60743e13	−1.95188	−0.975942	−	0.218031i	$-0.930037\pi$
$223$	−1.60743e13	−1.95188	−0.975942	+	0.218031i	$0.930037\pi$
$224$	−6.10738e12	−0.723587
$225$	−1.09088e12	−0.126117
$226$	−2.99653e12	−0.338082
$227$	1.19496e13	1.31586	0.657931	−	0.753078i	$-0.271432\pi$
$227$	1.19496e13	1.31586	0.657931	+	0.753078i	$0.271432\pi$
$228$	2.17969e12	0.234290
$229$	−6.43549e12	−0.675284	−0.337642	−	0.941275i	$-0.609629\pi$
$229$	−6.43549e12	−0.675284	−0.337642	+	0.941275i	$0.609629\pi$
$230$	−5.27104e12	−0.540000
$231$	−7.01208e12	−0.701424
$232$	−6.66696e12	−0.651244
$233$	4.91366e12	0.468757	0.234379	−	0.972145i	$-0.424694\pi$
$233$	4.91366e12	0.468757	0.234379	+	0.972145i	$0.424694\pi$
$234$	3.13436e12	0.292053
$235$	−9.60104e12	−0.873867
$236$	7.22657e11	0.0642564
$237$	−4.58773e12	−0.398549
$238$	−1.68860e10	−0.00143336
$239$	2.43640e12	0.202097	0.101048	−	0.994882i	$-0.467780\pi$
$239$	2.43640e12	0.202097	0.101048	+	0.994882i	$0.467780\pi$
$240$	1.47589e12	0.119645
$241$	−1.61679e13	−1.28103	−0.640517	−	0.767944i	$-0.721280\pi$
$241$	−1.61679e13	−1.28103	−0.640517	+	0.767944i	$0.721280\pi$
$242$	1.06815e13	0.827273
$243$	8.47289e11	0.0641500
$244$	−1.64281e12	−0.121603
$245$	3.45835e12	0.250297
$246$	−1.08227e13	−0.765934
$247$	−1.46260e13	−1.01226
$248$	−5.96943e12	−0.404062
$249$	5.43330e12	0.359722
$250$	1.19417e13	0.773384
$251$	−3.03619e13	−1.92364	−0.961821	−	0.273680i	$-0.911759\pi$
$251$	−3.03619e13	−1.92364	−0.961821	+	0.273680i	$0.911759\pi$
$252$	2.19275e12	0.135921
$253$	2.33344e13	1.41525
$254$	6.80729e12	0.404007
$255$	−1.91077e10	−0.00110978
$256$	−1.86590e13	−1.06064
$257$	1.34863e13	0.750344	0.375172	−	0.926955i	$-0.377584\pi$
$257$	1.34863e13	0.750344	0.375172	+	0.926955i	$0.377584\pi$
$258$	−8.57812e12	−0.467180
$259$	−5.76837e12	−0.307542
$260$	9.17883e12	0.479109
$261$	3.99631e12	0.204238
$262$	−1.46872e10	−0.000734992 0
$263$	3.69926e13	1.81283	0.906417	−	0.422384i	$-0.138807\pi$
$263$	3.69926e13	1.81283	0.906417	+	0.422384i	$0.138807\pi$
$264$	−1.88028e13	−0.902406
$265$	−1.67121e12	−0.0785558
$266$	1.04990e13	0.483393
$267$	−2.38010e13	−1.07346
$268$	1.25896e13	0.556253
$269$	1.48939e13	0.644721	0.322361	−	0.946617i	$-0.395524\pi$
$269$	1.48939e13	0.644721	0.322361	+	0.946617i	$0.395524\pi$
$270$	−2.54598e12	−0.107983
$271$	−3.11925e13	−1.29634	−0.648171	−	0.761495i	$-0.724466\pi$
$271$	−3.11925e13	−1.29634	−0.648171	+	0.761495i	$0.724466\pi$
$272$	−1.57339e10	−0.000640778 0
$273$	−1.47136e13	−0.587252
$274$	2.51352e13	0.983226
$275$	−1.45111e13	−0.556380
$276$	−7.29692e12	−0.274245
$277$	2.20689e12	0.0813095	0.0406547	−	0.999173i	$-0.487056\pi$
$277$	2.20689e12	0.0813095	0.0406547	+	0.999173i	$0.487056\pi$
$278$	−6.68524e12	−0.241474
$279$	3.57819e12	0.126719
$280$	−1.99385e13	−0.692348
$281$	−1.29643e13	−0.441433	−0.220717	−	0.975338i	$-0.570840\pi$
$281$	−1.29643e13	−0.441433	−0.220717	+	0.975338i	$0.570840\pi$
$282$	1.36378e13	0.455381
$283$	8.26712e12	0.270725	0.135363	−	0.990796i	$-0.456780\pi$
$283$	8.26712e12	0.270725	0.135363	+	0.990796i	$0.456780\pi$
$284$	8.38772e12	0.269397
$285$	1.18804e13	0.374269
$286$	4.16938e13	1.28842
$287$	5.08048e13	1.54012
$288$	9.81664e12	0.291947
$289$	−3.42717e13	−0.999994
$290$	−1.20083e13	−0.343790
$291$	5.21056e12	0.146377
$292$	2.96418e13	0.817143
$293$	−5.87683e13	−1.58990	−0.794952	−	0.606672i	$-0.792504\pi$
$293$	−5.87683e13	−1.58990	−0.794952	+	0.606672i	$0.792504\pi$
$294$	−4.91242e12	−0.130432
$295$	3.93883e12	0.102647
$296$	−1.54679e13	−0.395663
$297$	1.12708e13	0.283005
$298$	−4.89578e13	−1.20679
$299$	4.89631e13	1.18489
$300$	4.53778e12	0.107814
$301$	4.02682e13	0.939392
$302$	−2.80891e13	−0.643428
$303$	−3.48545e13	−0.784015
$304$	9.78268e12	0.216099
$305$	−8.95415e12	−0.194256
$306$	2.71416e10	0.000578320 0
$307$	−2.77624e13	−0.581026	−0.290513	−	0.956871i	$-0.593826\pi$
$307$	−2.77624e13	−0.581026	−0.290513	+	0.956871i	$0.593826\pi$
$308$	2.91684e13	0.599630
$309$	−5.06459e12	−0.102276
$310$	−1.07519e13	−0.213303
$311$	−7.79725e13	−1.51971	−0.759853	−	0.650095i	$-0.774729\pi$
$311$	−7.79725e13	−1.51971	−0.759853	+	0.650095i	$0.774729\pi$
$312$	−3.94544e13	−0.755519
$313$	1.06582e13	0.200535	0.100268	−	0.994961i	$-0.468030\pi$
$313$	1.06582e13	0.200535	0.100268	+	0.994961i	$0.468030\pi$
$314$	−4.13252e13	−0.764016
$315$	1.19516e13	0.217128
$316$	1.90837e13	0.340710
$317$	3.75125e13	0.658189	0.329094	−	0.944297i	$-0.393257\pi$
$317$	3.75125e13	0.658189	0.329094	+	0.944297i	$0.393257\pi$
$318$	2.37387e12	0.0409362
$319$	5.31597e13	0.901019
$320$	−4.19363e13	−0.698659
$321$	4.85318e13	0.794783
$322$	−3.51474e13	−0.565830
$323$	−1.26652e11	−0.00200446
$324$	−3.52450e12	−0.0548403
$325$	−3.04490e13	−0.465816
$326$	−5.94459e13	−0.894181
$327$	1.95629e13	0.289348
$328$	1.36233e14	1.98141
$329$	−6.40200e13	−0.915668
$330$	−3.38671e13	−0.476377
$331$	4.84161e13	0.669785	0.334893	−	0.942256i	$-0.391300\pi$
$331$	4.84161e13	0.669785	0.334893	+	0.942256i	$0.391300\pi$
$332$	−2.26011e13	−0.307518
$333$	9.27174e12	0.124085
$334$	−8.33953e12	−0.109783
$335$	6.86197e13	0.888593
$336$	9.84129e12	0.125368
$337$	1.23301e13	0.154526	0.0772631	−	0.997011i	$-0.475382\pi$
$337$	1.23301e13	0.154526	0.0772631	+	0.997011i	$0.475382\pi$
$338$	2.97699e13	0.367059
$339$	−2.26098e13	−0.274283
$340$	7.94831e10	0.000948726 0
$341$	4.75978e13	0.559034
$342$	−1.68755e13	−0.195036
$343$	9.57016e13	1.08843
$344$	1.07979e14	1.20856
$345$	−3.97718e13	−0.438097
$346$	1.25203e14	1.35736
$347$	3.03658e13	0.324021	0.162011	−	0.986789i	$-0.448202\pi$
$347$	3.03658e13	0.324021	0.162011	+	0.986789i	$0.448202\pi$
$348$	−1.66236e13	−0.174598
$349$	1.22411e13	0.126555	0.0632775	−	0.997996i	$-0.479845\pi$
$349$	1.22411e13	0.126555	0.0632775	+	0.997996i	$0.479845\pi$
$350$	2.18574e13	0.222446
$351$	2.36498e13	0.236940
$352$	1.30583e14	1.28796
$353$	−1.60954e13	−0.156294	−0.0781468	−	0.996942i	$-0.524900\pi$
$353$	−1.60954e13	−0.156294	−0.0781468	+	0.996942i	$0.524900\pi$
$354$	−5.59493e12	−0.0534905
$355$	4.57172e13	0.430352
$356$	9.90060e13	0.917670
$357$	−1.27411e11	−0.00116287
$358$	4.00720e12	0.0360151
$359$	3.28329e13	0.290596	0.145298	−	0.989388i	$-0.453586\pi$
$359$	3.28329e13	0.290596	0.145298	+	0.989388i	$0.453586\pi$
$360$	3.20480e13	0.279343
$361$	−3.77433e13	−0.324004
$362$	−3.90623e13	−0.330263
$363$	8.05956e13	0.671158
$364$	6.12047e13	0.502027
$365$	1.61562e14	1.30535
$366$	1.27189e13	0.101229
$367$	3.18205e13	0.249484	0.124742	−	0.992189i	$-0.460190\pi$
$367$	3.18205e13	0.249484	0.124742	+	0.992189i	$0.460190\pi$
$368$	−3.27493e13	−0.252953
$369$	−8.16607e13	−0.621395
$370$	−2.78602e13	−0.208869
$371$	−1.11437e13	−0.0823135
$372$	−1.48843e13	−0.108329
$373$	−3.27361e13	−0.234763	−0.117381	−	0.993087i	$-0.537450\pi$
$373$	−3.27361e13	−0.234763	−0.117381	+	0.993087i	$0.537450\pi$
$374$	3.61043e11	0.00255132
$375$	9.01039e13	0.627439
$376$	−1.71669e14	−1.17804
$377$	1.11546e14	0.754358
$378$	−1.69766e13	−0.113148
$379$	2.74875e14	1.80559	0.902797	−	0.430066i	$-0.141510\pi$
$379$	2.74875e14	1.80559	0.902797	+	0.430066i	$0.141510\pi$
$380$	−4.94193e13	−0.319953
$381$	5.13632e13	0.327767
$382$	−7.04621e13	−0.443207
$383$	−3.66325e13	−0.227129	−0.113565	−	0.993531i	$-0.536227\pi$
$383$	−3.66325e13	−0.227129	−0.113565	+	0.993531i	$0.536227\pi$
$384$	−2.31659e13	−0.141588
$385$	1.58982e14	0.957886
$386$	8.66992e13	0.514973
$387$	−6.47248e13	−0.379018
$388$	−2.16746e13	−0.125134
$389$	1.92375e14	1.09503	0.547515	−	0.836796i	$-0.315574\pi$
$389$	1.92375e14	1.09503	0.547515	+	0.836796i	$0.315574\pi$
$390$	−7.10640e13	−0.398836
$391$	4.23991e11	0.00234630
$392$	6.18362e13	0.337419
$393$	−1.10820e11	−0.000596292 0
$394$	−1.58448e14	−0.840730
$395$	1.04016e14	0.544271
$396$	−4.68835e13	−0.241934
$397$	−3.10067e14	−1.57800	−0.789002	−	0.614391i	$-0.789402\pi$
$397$	−3.10067e14	−1.57800	−0.789002	+	0.614391i	$0.789402\pi$
$398$	2.01238e14	1.01007
$399$	7.92187e13	0.392172
$400$	2.03660e13	0.0994435
$401$	−4.61347e13	−0.222194	−0.111097	−	0.993810i	$-0.535437\pi$
$401$	−4.61347e13	−0.222194	−0.111097	+	0.993810i	$0.535437\pi$
$402$	−9.74711e13	−0.463055
$403$	9.98756e13	0.468038
$404$	1.44986e14	0.670235
$405$	−1.92102e13	−0.0876052
$406$	−8.00717e13	−0.360235
$407$	1.23334e14	0.547413
$408$	−3.41651e11	−0.00149607
$409$	1.71918e14	0.742751	0.371376	−	0.928483i	$-0.378886\pi$
$409$	1.71918e14	0.742751	0.371376	+	0.928483i	$0.378886\pi$
$410$	2.45378e14	1.04598
$411$	1.89653e14	0.797682
$412$	2.10674e13	0.0874331
$413$	2.62642e13	0.107557
$414$	5.64939e13	0.228297
$415$	−1.23187e14	−0.491248
$416$	2.74005e14	1.07831
$417$	−5.04424e13	−0.195906
$418$	−2.24482e14	−0.860421
$419$	6.18027e13	0.233792	0.116896	−	0.993144i	$-0.462706\pi$
$419$	6.18027e13	0.233792	0.116896	+	0.993144i	$0.462706\pi$
$420$	−4.97153e13	−0.185618
$421$	1.34130e14	0.494282	0.247141	−	0.968979i	$-0.420509\pi$
$421$	1.34130e14	0.494282	0.247141	+	0.968979i	$0.420509\pi$
$422$	−2.00603e14	−0.729657
$423$	1.02902e14	0.369446
$424$	−2.98816e13	−0.105899
$425$	−2.63670e11	−0.000922404 0
$426$	−6.49391e13	−0.224261
$427$	−5.97065e13	−0.203549
$428$	−2.01879e14	−0.679440
$429$	3.14594e14	1.04529
$430$	1.94488e14	0.637995
$431$	−2.17813e14	−0.705439	−0.352719	−	0.935729i	$-0.614743\pi$
$431$	−2.17813e14	−0.705439	−0.352719	+	0.935729i	$0.614743\pi$
$432$	−1.58183e13	−0.0505824
$433$	−1.77000e13	−0.0558844	−0.0279422	−	0.999610i	$-0.508895\pi$
$433$	−1.77000e13	−0.0558844	−0.0279422	+	0.999610i	$0.508895\pi$
$434$	−7.16942e13	−0.223507
$435$	−9.06067e13	−0.278914
$436$	−8.13765e13	−0.247356
$437$	−2.63620e14	−0.791280
$438$	−2.29491e14	−0.680234
$439$	3.27938e14	0.959925	0.479963	−	0.877289i	$-0.340650\pi$
$439$	3.27938e14	0.959925	0.479963	+	0.877289i	$0.340650\pi$
$440$	4.26309e14	1.23235
$441$	−3.70659e13	−0.105819
$442$	7.57585e11	0.00213604
$443$	1.89807e13	0.0528557	0.0264278	−	0.999651i	$-0.491587\pi$
$443$	1.89807e13	0.0528557	0.0264278	+	0.999651i	$0.491587\pi$
$444$	−3.85680e13	−0.106077
$445$	5.39631e14	1.46594
$446$	−5.17677e14	−1.38905
$447$	−3.69403e14	−0.979058
$448$	−2.79632e14	−0.732080
$449$	−2.96844e14	−0.767668	−0.383834	−	0.923402i	$-0.625397\pi$
$449$	−2.96844e14	−0.767668	−0.383834	+	0.923402i	$0.625397\pi$
$450$	−3.51322e13	−0.0897505
$451$	−1.08627e15	−2.74135
$452$	9.40509e13	0.234478
$453$	−2.11942e14	−0.522007
$454$	3.84840e14	0.936425
$455$	3.33596e14	0.801969
$456$	2.12424e14	0.504542
$457$	9.36083e13	0.219672	0.109836	−	0.993950i	$-0.464967\pi$
$457$	9.36083e13	0.219672	0.109836	+	0.993950i	$0.464967\pi$
$458$	−2.07257e14	−0.480562
$459$	2.04793e11	0.000469185 0
$460$	1.65440e14	0.374518
$461$	−6.28776e14	−1.40650	−0.703252	−	0.710941i	$-0.748269\pi$
$461$	−6.28776e14	−1.40650	−0.703252	+	0.710941i	$0.748269\pi$
$462$	−2.25826e14	−0.499165
$463$	−1.35375e14	−0.295694	−0.147847	−	0.989010i	$-0.547234\pi$
$463$	−1.35375e14	−0.295694	−0.147847	+	0.989010i	$0.547234\pi$
$464$	−7.46084e13	−0.161042
$465$	−8.11269e13	−0.173051
$466$	1.58246e14	0.333588
$467$	−6.74862e14	−1.40596	−0.702979	−	0.711211i	$-0.748147\pi$
$467$	−6.74862e14	−1.40596	−0.702979	+	0.711211i	$0.748147\pi$
$468$	−9.83768e13	−0.202554
$469$	4.57558e14	0.931098
$470$	−3.09205e14	−0.621882
$471$	−3.11813e14	−0.619839
$472$	7.04273e13	0.138376
$473$	−8.60982e14	−1.67208
$474$	−1.47749e14	−0.283625
$475$	1.63939e14	0.311077
$476$	5.29995e11	0.000994108 0
$477$	1.79116e13	0.0332112
$478$	7.84650e13	0.143821
$479$	−3.46511e14	−0.627873	−0.313936	−	0.949444i	$-0.601648\pi$
$479$	−3.46511e14	−0.627873	−0.313936	+	0.949444i	$0.601648\pi$
$480$	−2.22569e14	−0.398692
$481$	2.58795e14	0.458309
$482$	−5.20694e14	−0.911640
$483$	−2.65199e14	−0.459053
$484$	−3.35257e14	−0.573757
$485$	−1.18137e14	−0.199897
$486$	2.72872e13	0.0456520
$487$	−5.80006e14	−0.959453	−0.479726	−	0.877418i	$-0.659264\pi$
$487$	−5.80006e14	−0.959453	−0.479726	+	0.877418i	$0.659264\pi$
$488$	−1.60102e14	−0.261872
$489$	−4.48539e14	−0.725440
$490$	1.11377e14	0.178122
$491$	−1.01449e15	−1.60435	−0.802173	−	0.597092i	$-0.796323\pi$
$491$	−1.01449e15	−1.60435	−0.802173	+	0.597092i	$0.796323\pi$
$492$	3.39687e14	0.531215
$493$	9.65922e11	0.00149377
$494$	−4.71035e14	−0.720368
$495$	−2.55538e14	−0.386480
$496$	−6.68024e13	−0.0999179
$497$	3.04843e14	0.450937
$498$	1.74981e14	0.255994
$499$	1.32024e15	1.91029	0.955147	−	0.296131i	$-0.0956964\pi$
$499$	1.32024e15	1.91029	0.955147	+	0.296131i	$0.0956964\pi$
$500$	−3.74809e14	−0.536382
$501$	−6.29245e13	−0.0890661
$502$	−9.77817e14	−1.36895
$503$	3.47956e14	0.481838	0.240919	−	0.970545i	$-0.422551\pi$
$503$	3.47956e14	0.481838	0.240919	+	0.970545i	$0.422551\pi$
$504$	2.13697e14	0.292705
$505$	7.90242e14	1.07067
$506$	7.51493e14	1.00716
$507$	2.24624e14	0.297792
$508$	−2.13657e14	−0.280200
$509$	9.29904e14	1.20640	0.603199	−	0.797591i	$-0.293893\pi$
$509$	9.29904e14	1.20640	0.603199	+	0.797591i	$0.293893\pi$
$510$	−6.15371e11	−0.000789771 0
$511$	1.07730e15	1.36780
$512$	−4.05679e14	−0.509563
$513$	−1.27331e14	−0.158230
$514$	4.34331e14	0.533978
$515$	1.14827e14	0.139671
$516$	2.69238e14	0.324013
$517$	1.36882e15	1.62985
$518$	−1.85772e14	−0.218861
$519$	9.44697e14	1.10122
$520$	8.94534e14	1.03176
$521$	1.14862e15	1.31090	0.655449	−	0.755239i	$-0.272479\pi$
$521$	1.14862e15	1.31090	0.655449	+	0.755239i	$0.272479\pi$
$522$	1.28703e14	0.145345
$523$	−9.44210e14	−1.05514	−0.527569	−	0.849512i	$-0.676896\pi$
$523$	−9.44210e14	−1.05514	−0.527569	+	0.849512i	$0.676896\pi$
$524$	4.60981e11	0.000509755 0
$525$	1.64921e14	0.180468
$526$	1.19136e15	1.29009
$527$	8.64861e11	0.000926804 0
$528$	−2.10418e14	−0.223150
$529$	−7.02948e13	−0.0737763
$530$	−5.38218e13	−0.0559038
$531$	−4.22156e13	−0.0433963
$532$	−3.29529e14	−0.335258
$533$	−2.27934e15	−2.29514
$534$	−7.66521e14	−0.763918
$535$	−1.10034e15	−1.08538
$536$	1.22694e15	1.19789
$537$	3.02357e13	0.0292187
$538$	4.79664e14	0.458812
$539$	−4.93057e14	−0.466830
$540$	7.99095e13	0.0748915
$541$	−1.06941e15	−0.992108	−0.496054	−	0.868292i	$-0.665218\pi$
$541$	−1.06941e15	−0.992108	−0.496054	+	0.868292i	$0.665218\pi$
$542$	−1.00457e15	−0.922534
$543$	−2.94738e14	−0.267940
$544$	2.37271e12	0.00213526
$545$	−4.43542e14	−0.395142
$546$	−4.73857e14	−0.417914
$547$	2.04326e15	1.78400	0.891999	−	0.452038i	$-0.149303\pi$
$547$	2.04326e15	1.78400	0.891999	+	0.452038i	$0.149303\pi$
$548$	−7.88907e14	−0.681919
$549$	9.59686e13	0.0821261
$550$	−4.67336e14	−0.395944
$551$	−6.00570e14	−0.503767
$552$	−7.11129e14	−0.590587
$553$	6.93579e14	0.570306
$554$	7.10735e13	0.0578634
$555$	−2.10214e14	−0.169454
$556$	2.09827e14	0.167475
$557$	−2.42812e15	−1.91896	−0.959482	−	0.281771i	$-0.909078\pi$
$557$	−2.42812e15	−1.91896	−0.959482	+	0.281771i	$0.909078\pi$
$558$	1.15237e14	0.0901786
$559$	−1.80662e15	−1.39991
$560$	−2.23128e14	−0.171206
$561$	2.72419e12	0.00206986
$562$	−4.17520e14	−0.314143
$563$	−1.28449e15	−0.957049	−0.478524	−	0.878074i	$-0.658828\pi$
$563$	−1.28449e15	−0.957049	−0.478524	+	0.878074i	$0.658828\pi$
$564$	−4.28045e14	−0.315831
$565$	5.12623e14	0.374569
$566$	2.66245e14	0.192660
$567$	−1.28094e14	−0.0917958
$568$	8.17435e14	0.580146
$569$	−1.05248e15	−0.739772	−0.369886	−	0.929077i	$-0.620603\pi$
$569$	−1.05248e15	−0.739772	−0.369886	+	0.929077i	$0.620603\pi$
$570$	3.82612e14	0.266346
$571$	−9.54795e14	−0.658281	−0.329141	−	0.944281i	$-0.606759\pi$
$571$	−9.54795e14	−0.658281	−0.329141	+	0.944281i	$0.606759\pi$
$572$	−1.30863e15	−0.893589
$573$	−5.31660e14	−0.359570
$574$	1.63619e15	1.09602
$575$	−5.48815e14	−0.364127
$576$	4.49465e14	0.295374
$577$	2.48804e15	1.61954	0.809769	−	0.586749i	$-0.199593\pi$
$577$	2.48804e15	1.61954	0.809769	+	0.586749i	$0.199593\pi$
$578$	−1.10373e15	−0.711640
$579$	6.54174e14	0.417793
$580$	3.76900e14	0.238436
$581$	−8.21414e14	−0.514746
$582$	1.67808e14	0.104168
$583$	2.38264e14	0.146515
$584$	2.88877e15	1.75972
$585$	−5.36202e14	−0.323572
$586$	−1.89265e15	−1.13145
$587$	4.96923e14	0.294293	0.147146	−	0.989115i	$-0.452991\pi$
$587$	4.96923e14	0.294293	0.147146	+	0.989115i	$0.452991\pi$
$588$	1.54184e14	0.0904617
$589$	−5.37735e14	−0.312560
$590$	1.26851e14	0.0730482
$591$	−1.19554e15	−0.682076
$592$	−1.73097e14	−0.0978409
$593$	−1.40763e15	−0.788291	−0.394145	−	0.919048i	$-0.628959\pi$
$593$	−1.40763e15	−0.788291	−0.394145	+	0.919048i	$0.628959\pi$
$594$	3.62980e14	0.201399
$595$	2.88873e12	0.00158805
$596$	1.53662e15	0.836973
$597$	1.51841e15	0.819463
$598$	1.57687e15	0.843219
$599$	−1.58628e15	−0.840489	−0.420244	−	0.907411i	$-0.638056\pi$
$599$	−1.58628e15	−0.840489	−0.420244	+	0.907411i	$0.638056\pi$
$600$	4.42235e14	0.232178
$601$	1.44110e15	0.749695	0.374847	−	0.927087i	$-0.377695\pi$
$601$	1.44110e15	0.749695	0.374847	+	0.927087i	$0.377695\pi$
$602$	1.29685e15	0.668513
$603$	−7.35452e14	−0.375672
$604$	8.81621e14	0.446251
$605$	−1.82731e15	−0.916554
$606$	−1.12250e15	−0.557940
$607$	1.02307e15	0.503928	0.251964	−	0.967737i	$-0.418923\pi$
$607$	1.02307e15	0.503928	0.251964	+	0.967737i	$0.418923\pi$
$608$	−1.47525e15	−0.720107
$609$	−6.04168e14	−0.292255
$610$	−2.88371e14	−0.138241
$611$	2.87223e15	1.36456
$612$	−8.51883e11	−0.000401095 0
$613$	3.57680e15	1.66902	0.834511	−	0.550991i	$-0.185750\pi$
$613$	3.57680e15	1.66902	0.834511	+	0.550991i	$0.185750\pi$
$614$	−8.94097e14	−0.413484
$615$	1.85146e15	0.848596
$616$	2.84264e15	1.29130
$617$	−1.98761e15	−0.894876	−0.447438	−	0.894315i	$-0.647664\pi$
$617$	−1.98761e15	−0.894876	−0.447438	+	0.894315i	$0.647664\pi$
$618$	−1.63107e14	−0.0727840
$619$	9.32973e14	0.412639	0.206320	−	0.978485i	$-0.433851\pi$
$619$	9.32973e14	0.412639	0.206320	+	0.978485i	$0.433851\pi$
$620$	3.37467e14	0.147937
$621$	4.26265e14	0.185215
$622$	−2.51113e15	−1.08149
$623$	3.59827e15	1.53607
$624$	−4.41525e14	−0.186827
$625$	−1.14083e15	−0.478499
$626$	3.43251e14	0.142710
$627$	−1.69379e15	−0.698052
$628$	1.29706e15	0.529885
$629$	2.24101e12	0.000907539 0
$630$	3.84904e14	0.154518
$631$	2.34954e14	0.0935021	0.0467510	−	0.998907i	$-0.485113\pi$
$631$	2.34954e14	0.0935021	0.0467510	+	0.998907i	$0.485113\pi$
$632$	1.85983e15	0.733717
$633$	−1.51362e15	−0.591964
$634$	1.20810e15	0.468396
$635$	−1.16454e15	−0.447608
$636$	−7.45077e13	−0.0283914
$637$	−1.03459e15	−0.390843
$638$	1.71203e15	0.641205
$639$	−4.89987e14	−0.181941
$640$	5.25231e14	0.193357
$641$	−4.01924e15	−1.46698	−0.733490	−	0.679700i	$-0.762110\pi$
$641$	−4.01924e15	−1.46698	−0.733490	+	0.679700i	$0.762110\pi$
$642$	1.56298e15	0.565602
$643$	−3.67581e15	−1.31884	−0.659420	−	0.751774i	$-0.729198\pi$
$643$	−3.67581e15	−1.31884	−0.659420	+	0.751774i	$0.729198\pi$
$644$	1.10316e15	0.392433
$645$	1.46748e15	0.517599
$646$	−4.07887e12	−0.00142647
$647$	−2.25806e15	−0.783001	−0.391500	−	0.920178i	$-0.628044\pi$
$647$	−2.25806e15	−0.783001	−0.391500	+	0.920178i	$0.628044\pi$
$648$	−3.43484e14	−0.118098
$649$	−5.61560e14	−0.191448
$650$	−9.80621e14	−0.331496
$651$	−5.40956e14	−0.181329
$652$	1.86580e15	0.620161
$653$	−1.04171e15	−0.343339	−0.171669	−	0.985155i	$-0.554916\pi$
$653$	−1.04171e15	−0.343339	−0.171669	+	0.985155i	$0.554916\pi$
$654$	6.30030e14	0.205913
$655$	2.51257e12	0.000814314 0
$656$	1.52455e15	0.489971
$657$	−1.73159e15	−0.551868
$658$	−2.06179e15	−0.651630
$659$	5.09258e15	1.59613	0.798065	−	0.602572i	$-0.205857\pi$
$659$	5.09258e15	1.59613	0.798065	+	0.602572i	$0.205857\pi$
$660$	1.06297e15	0.330392
$661$	3.62635e15	1.11780	0.558898	−	0.829237i	$-0.311225\pi$
$661$	3.62635e15	1.11780	0.558898	+	0.829237i	$0.311225\pi$
$662$	1.55926e15	0.476649
$663$	5.71623e12	0.00173295
$664$	−2.20262e15	−0.662238
$665$	−1.79609e15	−0.535562
$666$	2.98600e14	0.0883041
$667$	2.01052e15	0.589679
$668$	2.61749e14	0.0761404
$669$	−3.90604e15	−1.12692
$670$	2.20992e15	0.632362
$671$	1.27659e15	0.362309
$672$	−1.48409e15	−0.417763
$673$	−1.04228e15	−0.291005	−0.145502	−	0.989358i	$-0.546480\pi$
$673$	−1.04228e15	−0.291005	−0.145502	+	0.989358i	$0.546480\pi$
$674$	3.97095e14	0.109968
$675$	−2.65084e14	−0.0728137
$676$	−9.34377e14	−0.254575
$677$	−2.30069e15	−0.621757	−0.310878	−	0.950450i	$-0.600623\pi$
$677$	−2.30069e15	−0.621757	−0.310878	+	0.950450i	$0.600623\pi$
$678$	−7.28157e14	−0.195192
$679$	−7.87740e14	−0.209459
$680$	7.74612e12	0.00204308
$681$	2.90375e15	0.759713
$682$	1.53290e15	0.397833
$683$	−1.97637e15	−0.508807	−0.254404	−	0.967098i	$-0.581879\pi$
$683$	−1.97637e15	−0.508807	−0.254404	+	0.967098i	$0.581879\pi$
$684$	5.29665e14	0.135267
$685$	−4.29993e15	−1.08934
$686$	3.08210e15	0.774577
$687$	−1.56382e15	−0.389876
$688$	1.20837e15	0.298856
$689$	4.99955e14	0.122666
$690$	−1.28086e15	−0.311769
$691$	1.81722e15	0.438813	0.219406	−	0.975634i	$-0.429588\pi$
$691$	1.81722e15	0.438813	0.219406	+	0.975634i	$0.429588\pi$
$692$	−3.92969e15	−0.941401
$693$	−1.70394e15	−0.404968
$694$	9.77942e14	0.230588
$695$	1.14366e15	0.267535
$696$	−1.62007e15	−0.375996
$697$	−1.97377e13	−0.00454480
$698$	3.94228e14	0.0900622
$699$	1.19402e15	0.270637
$700$	−6.86028e14	−0.154278
$701$	1.47361e14	0.0328801	0.0164401	−	0.999865i	$-0.494767\pi$
$701$	1.47361e14	0.0328801	0.0164401	+	0.999865i	$0.494767\pi$
$702$	7.61649e14	0.168617
$703$	−1.39337e15	−0.306063
$704$	5.97887e15	1.30307
$705$	−2.33305e15	−0.504527
$706$	−5.18358e14	−0.111225
$707$	5.26935e15	1.12189
$708$	1.75606e14	0.0370984
$709$	6.07023e14	0.127248	0.0636240	−	0.997974i	$-0.479734\pi$
$709$	6.07023e14	0.127248	0.0636240	+	0.997974i	$0.479734\pi$
$710$	1.47234e15	0.306257
$711$	−1.11482e15	−0.230102
$712$	9.64875e15	1.97620
$713$	1.80016e15	0.365864
$714$	−4.10331e12	−0.000827549 0
$715$	−7.13266e15	−1.42747
$716$	−1.25772e14	−0.0249783
$717$	5.92044e14	0.116681
$718$	1.05740e15	0.206801
$719$	−1.92770e15	−0.374137	−0.187069	−	0.982347i	$-0.559899\pi$
$719$	−1.92770e15	−0.374137	−0.187069	+	0.982347i	$0.559899\pi$
$720$	3.58642e14	0.0690768
$721$	7.65672e14	0.146352
$722$	−1.21554e15	−0.230576
$723$	−3.92881e15	−0.739605
$724$	1.22603e15	0.229055
$725$	−1.25029e15	−0.231821
$726$	2.59561e15	0.477626
$727$	9.80226e15	1.79014	0.895070	−	0.445926i	$-0.147126\pi$
$727$	9.80226e15	1.79014	0.895070	+	0.445926i	$0.147126\pi$
$728$	5.96477e15	1.08111
$729$	2.05891e14	0.0370370
$730$	5.20316e15	0.928948
$731$	−1.56442e13	−0.00277209
$732$	−3.99204e14	−0.0702076
$733$	−1.38846e14	−0.0242360	−0.0121180	−	0.999927i	$-0.503857\pi$
$733$	−1.38846e14	−0.0242360	−0.0121180	+	0.999927i	$0.503857\pi$
$734$	1.02479e15	0.177544
$735$	8.40379e14	0.144509
$736$	4.93868e15	0.842914
$737$	−9.78312e15	−1.65732
$738$	−2.62991e15	−0.442212
$739$	−7.72677e15	−1.28960	−0.644798	−	0.764353i	$-0.723058\pi$
$739$	−7.72677e15	−1.28960	−0.644798	+	0.764353i	$0.723058\pi$
$740$	8.74436e14	0.144862
$741$	−3.55411e15	−0.584428
$742$	−3.58885e14	−0.0585779
$743$	−5.06696e15	−0.820936	−0.410468	−	0.911875i	$-0.634635\pi$
$743$	−5.06696e15	−0.820936	−0.410468	+	0.911875i	$0.634635\pi$
$744$	−1.45057e15	−0.233285
$745$	8.37532e15	1.33703
$746$	−1.05428e15	−0.167067
$747$	1.32029e15	0.207686
$748$	−1.13319e13	−0.00176947
$749$	−7.33710e15	−1.13730
$750$	2.90183e15	0.446514
$751$	8.33127e15	1.27260	0.636300	−	0.771442i	$-0.280464\pi$
$751$	8.33127e15	1.27260	0.636300	+	0.771442i	$0.280464\pi$
$752$	−1.92111e15	−0.291309
$753$	−7.37795e15	−1.11061
$754$	3.59238e15	0.536834
$755$	4.80527e15	0.712868
$756$	5.32838e14	0.0784740
$757$	1.01977e15	0.149099	0.0745495	−	0.997217i	$-0.476248\pi$
$757$	1.01977e15	0.149099	0.0745495	+	0.997217i	$0.476248\pi$
$758$	8.85246e15	1.28494
$759$	5.67026e15	0.817097
$760$	−4.81621e15	−0.689018
$761$	−2.21417e15	−0.314482	−0.157241	−	0.987560i	$-0.550260\pi$
$761$	−2.21417e15	−0.314482	−0.157241	+	0.987560i	$0.550260\pi$
$762$	1.65417e15	0.233253
$763$	−2.95755e15	−0.414044
$764$	2.21156e15	0.307387
$765$	−4.64318e12	−0.000640733 0
$766$	−1.17976e15	−0.161635
$767$	−1.17833e15	−0.160285
$768$	−4.53415e15	−0.612363
$769$	−1.20942e16	−1.62174	−0.810871	−	0.585225i	$-0.801006\pi$
$769$	−1.20942e16	−1.62174	−0.810871	+	0.585225i	$0.801006\pi$
$770$	5.12007e15	0.681674
$771$	3.27717e15	0.433212
$772$	−2.72119e15	−0.357161
$773$	2.48533e15	0.323889	0.161945	−	0.986800i	$-0.448223\pi$
$773$	2.48533e15	0.323889	0.161945	+	0.986800i	$0.448223\pi$
$774$	−2.08448e15	−0.269726
$775$	−1.11948e15	−0.143833
$776$	−2.11232e15	−0.269476
$777$	−1.40171e15	−0.177560
$778$	6.19551e15	0.779272
$779$	1.22720e16	1.53271
$780$	2.23046e15	0.276614
$781$	−6.51790e15	−0.802651
$782$	1.36548e13	0.00166973
$783$	9.71103e14	0.117917
$784$	6.91994e14	0.0834381
$785$	7.06960e15	0.846471
$786$	−3.56899e12	−0.000424348 0
$787$	−4.29022e15	−0.506545	−0.253273	−	0.967395i	$-0.581507\pi$
$787$	−4.29022e15	−0.506545	−0.253273	+	0.967395i	$0.581507\pi$
$788$	4.97313e15	0.583090
$789$	8.98920e15	1.04664
$790$	3.34986e15	0.387327
$791$	3.41818e15	0.392487
$792$	−4.56909e15	−0.521004
$793$	2.67870e15	0.303335
$794$	−9.98582e15	−1.12298
$795$	−4.06104e14	−0.0453542
$796$	−6.31617e15	−0.700539
$797$	−5.62716e15	−0.619825	−0.309912	−	0.950765i	$-0.600300\pi$
$797$	−5.62716e15	−0.619825	−0.309912	+	0.950765i	$0.600300\pi$
$798$	2.55127e15	0.279087
$799$	2.48717e13	0.00270208
$800$	−3.07125e15	−0.331376
$801$	−5.78365e15	−0.619760
$802$	−1.48578e15	−0.158123
$803$	−2.30339e16	−2.43463
$804$	3.05928e15	0.321153
$805$	6.01275e15	0.626897
$806$	3.21653e15	0.333077
$807$	3.61923e15	0.372230
$808$	1.41297e16	1.44335
$809$	1.23571e15	0.125372	0.0626861	−	0.998033i	$-0.480033\pi$
$809$	1.23571e15	0.125372	0.0626861	+	0.998033i	$0.480033\pi$
$810$	−6.18672e14	−0.0623438
$811$	1.20094e16	1.20201	0.601004	−	0.799246i	$-0.294768\pi$
$811$	1.20094e16	1.20201	0.601004	+	0.799246i	$0.294768\pi$
$812$	2.51318e15	0.249842
$813$	−7.57979e15	−0.748443
$814$	3.97203e15	0.389564
$815$	1.01695e16	0.990683
$816$	−3.82334e12	−0.000369953 0
$817$	9.72691e15	0.934875
$818$	5.53668e15	0.528575
$819$	−3.57540e15	−0.339050
$820$	−7.70158e15	−0.725444
$821$	1.49862e15	0.140218	0.0701092	−	0.997539i	$-0.477665\pi$
$821$	1.49862e15	0.140218	0.0701092	+	0.997539i	$0.477665\pi$
$822$	6.10784e15	0.567666
$823$	−4.57801e15	−0.422647	−0.211323	−	0.977416i	$-0.567777\pi$
$823$	−4.57801e15	−0.422647	−0.211323	+	0.977416i	$0.567777\pi$
$824$	2.05314e15	0.188287
$825$	−3.52620e15	−0.321226
$826$	8.45849e14	0.0765425
$827$	8.74446e15	0.786055	0.393027	−	0.919527i	$-0.371428\pi$
$827$	8.74446e15	0.786055	0.393027	+	0.919527i	$0.371428\pi$
$828$	−1.77315e15	−0.158336
$829$	3.01144e15	0.267131	0.133566	−	0.991040i	$-0.457357\pi$
$829$	3.01144e15	0.267131	0.133566	+	0.991040i	$0.457357\pi$
$830$	−3.96728e15	−0.349593
$831$	5.36273e14	0.0469441
$832$	1.25456e16	1.09097
$833$	−8.95894e12	−0.000773944 0
$834$	−1.62451e15	−0.139415
$835$	1.42666e15	0.121631
$836$	7.04571e15	0.596747
$837$	8.69501e14	0.0731611
$838$	1.99038e15	0.166377
$839$	2.58723e15	0.214854	0.107427	−	0.994213i	$-0.465739\pi$
$839$	2.58723e15	0.214854	0.107427	+	0.994213i	$0.465739\pi$
$840$	−4.84507e15	−0.399727
$841$	−7.62022e15	−0.624582
$842$	4.31971e15	0.351753
$843$	−3.15033e15	−0.254862
$844$	6.29624e15	0.506055
$845$	−5.09281e15	−0.406673
$846$	3.31399e15	0.262914
$847$	−1.21846e16	−0.960398
$848$	−3.34398e14	−0.0261871
$849$	2.00891e15	0.156303
$850$	−8.49158e12	−0.000656424 0
$851$	4.66455e15	0.358259
$852$	2.03822e15	0.155536
$853$	−1.46066e16	−1.10746	−0.553732	−	0.832695i	$-0.686797\pi$
$853$	−1.46066e16	−1.10746	−0.553732	+	0.832695i	$0.686797\pi$
$854$	−1.92287e15	−0.144854
$855$	2.88693e15	0.216084
$856$	−1.96744e16	−1.46317
$857$	−1.21875e16	−0.900574	−0.450287	−	0.892884i	$-0.648678\pi$
$857$	−1.21875e16	−0.900574	−0.450287	+	0.892884i	$0.648678\pi$
$858$	1.01316e16	0.743872
$859$	2.33332e16	1.70220	0.851102	−	0.525001i	$-0.175935\pi$
$859$	2.33332e16	1.70220	0.851102	+	0.525001i	$0.175935\pi$
$860$	−6.10432e15	−0.442483
$861$	1.23456e16	0.889189
$862$	−7.01475e15	−0.502022
$863$	2.51263e16	1.78677	0.893387	−	0.449289i	$-0.148323\pi$
$863$	2.51263e16	1.78677	0.893387	+	0.449289i	$0.148323\pi$
$864$	2.38544e15	0.168556
$865$	−2.14187e16	−1.50385
$866$	−5.70035e14	−0.0397698
$867$	−8.32802e15	−0.577347
$868$	2.25024e15	0.155013
$869$	−1.48295e16	−1.01512
$870$	−2.91802e15	−0.198487
$871$	−2.05281e16	−1.38755
$872$	−7.93064e15	−0.532681
$873$	1.26617e15	0.0845109
$874$	−8.48996e15	−0.563110
$875$	−1.36220e16	−0.897838
$876$	7.20295e15	0.471778
$877$	−1.66456e16	−1.08343	−0.541717	−	0.840561i	$-0.682226\pi$
$877$	−1.66456e16	−1.08343	−0.541717	+	0.840561i	$0.682226\pi$
$878$	1.05614e16	0.683125
$879$	−1.42807e16	−0.917932
$880$	4.77073e15	0.304740
$881$	4.23358e15	0.268745	0.134372	−	0.990931i	$-0.457098\pi$
$881$	4.23358e15	0.268745	0.134372	+	0.990931i	$0.457098\pi$
$882$	−1.19372e15	−0.0753052
$883$	1.64624e16	1.03207	0.516035	−	0.856567i	$-0.327407\pi$
$883$	1.64624e16	1.03207	0.516035	+	0.856567i	$0.327407\pi$
$884$	−2.37780e13	−0.00148145
$885$	9.57136e14	0.0592633
$886$	6.11280e14	0.0376144
$887$	7.28714e15	0.445633	0.222817	−	0.974860i	$-0.428475\pi$
$887$	7.28714e15	0.445633	0.222817	+	0.974860i	$0.428475\pi$
$888$	−3.75869e15	−0.228436
$889$	−7.76516e15	−0.469020
$890$	1.73790e16	1.04323
$891$	2.73880e15	0.163393
$892$	1.62481e16	0.963376
$893$	−1.54642e16	−0.911265
$894$	−1.18967e16	−0.696741
$895$	−6.85521e14	−0.0399020
$896$	3.50225e15	0.202606
$897$	1.18980e16	0.684096
$898$	−9.55996e15	−0.546307
$899$	4.10108e15	0.232927
$900$	1.10268e15	0.0622467
$901$	4.32930e12	0.000242902 0
$902$	−3.49836e16	−1.95087
$903$	9.78518e15	0.542358
$904$	9.16583e15	0.504947
$905$	6.68247e15	0.365906
$906$	−6.82565e15	−0.371483
$907$	−3.31414e16	−1.79279	−0.896397	−	0.443253i	$-0.853824\pi$
$907$	−3.31414e16	−1.79279	−0.896397	+	0.443253i	$0.853824\pi$
$908$	−1.20788e16	−0.649460
$909$	−8.46964e15	−0.452651
$910$	1.07436e16	0.570717
$911$	8.72205e15	0.460540	0.230270	−	0.973127i	$-0.426039\pi$
$911$	8.72205e15	0.460540	0.230270	+	0.973127i	$0.426039\pi$
$912$	2.37719e15	0.124765
$913$	1.75628e16	0.916229
$914$	3.01469e15	0.156328
$915$	−2.17586e15	−0.112154
$916$	6.50510e15	0.333295
$917$	1.67539e13	0.000853267 0
$918$	6.59541e12	0.000333893 0
$919$	3.28544e16	1.65333	0.826664	−	0.562696i	$-0.190236\pi$
$919$	3.28544e16	1.65333	0.826664	+	0.562696i	$0.190236\pi$
$920$	1.61231e16	0.806523
$921$	−6.74626e15	−0.335456
$922$	−2.02500e16	−1.00093
$923$	−1.36767e16	−0.672002
$924$	7.08792e15	0.346197
$925$	−2.90077e15	−0.140843
$926$	−4.35979e15	−0.210429
$927$	−1.23070e15	−0.0590490
$928$	1.12511e16	0.536640
$929$	1.96092e16	0.929767	0.464884	−	0.885372i	$-0.346096\pi$
$929$	1.96092e16	0.929767	0.464884	+	0.885372i	$0.346096\pi$
$930$	−2.61272e15	−0.123151
$931$	5.57030e15	0.261009
$932$	−4.96681e15	−0.231361
$933$	−1.89473e16	−0.877403
$934$	−2.17342e16	−1.00054
$935$	−6.17645e13	−0.00282667
$936$	−9.58742e15	−0.436199
$937$	−2.05928e16	−0.931426	−0.465713	−	0.884936i	$-0.654202\pi$
$937$	−2.05928e16	−0.931426	−0.465713	+	0.884936i	$0.654202\pi$
$938$	1.47358e16	0.662611
$939$	2.58994e15	0.115779
$940$	9.70489e15	0.431308
$941$	−3.71778e16	−1.64263	−0.821317	−	0.570472i	$-0.806760\pi$
$941$	−3.71778e16	−1.64263	−0.821317	+	0.570472i	$0.806760\pi$
$942$	−1.00420e16	−0.441105
$943$	−4.10829e16	−1.79410
$944$	7.88136e14	0.0342180
$945$	2.90423e15	0.125359
$946$	−2.77282e16	−1.18993
$947$	1.22223e16	0.521469	0.260734	−	0.965411i	$-0.416035\pi$
$947$	1.22223e16	0.521469	0.260734	+	0.965411i	$0.416035\pi$
$948$	4.63735e15	0.196709
$949$	−4.83326e16	−2.03834
$950$	5.27971e15	0.221376
$951$	9.11554e15	0.380005
$952$	5.16513e13	0.00214081
$953$	1.36347e16	0.561870	0.280935	−	0.959727i	$-0.409355\pi$
$953$	1.36347e16	0.561870	0.280935	+	0.959727i	$0.409355\pi$
$954$	5.76851e14	0.0236346
$955$	1.20541e16	0.491040
$956$	−2.46275e15	−0.0997474
$957$	1.29178e16	0.520203
$958$	−1.11595e16	−0.446822
$959$	−2.86720e16	−1.14145
$960$	−1.01905e16	−0.403371
$961$	−2.17365e16	−0.855481
$962$	8.33460e15	0.326153
$963$	1.17932e16	0.458868
$964$	1.63428e16	0.632270
$965$	−1.48318e16	−0.570551
$966$	−8.54083e15	−0.326682
$967$	3.10975e16	1.18271	0.591356	−	0.806410i	$-0.298593\pi$
$967$	3.10975e16	1.18271	0.591356	+	0.806410i	$0.298593\pi$
$968$	−3.26728e16	−1.23558
$969$	−3.07764e13	−0.00115728
$970$	−3.80464e15	−0.142256
$971$	−3.17570e16	−1.18068	−0.590341	−	0.807154i	$-0.701007\pi$
$971$	−3.17570e16	−1.18068	−0.590341	+	0.807154i	$0.701007\pi$
$972$	−8.56453e14	−0.0316620
$973$	7.62595e15	0.280332
$974$	−1.86793e16	−0.682789
$975$	−7.39911e15	−0.268939
$976$	−1.79167e15	−0.0647565
$977$	2.35140e16	0.845098	0.422549	−	0.906340i	$-0.361135\pi$
$977$	2.35140e16	0.845098	0.422549	+	0.906340i	$0.361135\pi$
$978$	−1.44454e16	−0.516255
$979$	−7.69353e16	−2.73414
$980$	−3.49576e15	−0.123537
$981$	4.75378e15	0.167055
$982$	−3.26719e16	−1.14172
$983$	1.44138e16	0.500881	0.250440	−	0.968132i	$-0.419425\pi$
$983$	1.44138e16	0.500881	0.250440	+	0.968132i	$0.419425\pi$
$984$	3.31046e16	1.14397
$985$	2.71060e16	0.931464
$986$	3.11078e13	0.00106303
$987$	−1.55569e16	−0.528661
$988$	1.47842e16	0.499613
$989$	−3.25626e16	−1.09431
$990$	−8.22970e15	−0.275036
$991$	−2.26252e16	−0.751946	−0.375973	−	0.926631i	$-0.622691\pi$
$991$	−2.26252e16	−0.751946	−0.375973	+	0.926631i	$0.622691\pi$
$992$	1.00740e16	0.332956
$993$	1.17651e16	0.386701
$994$	9.81758e15	0.320907
$995$	−3.44262e16	−1.11908
$996$	−5.49206e15	−0.177545
$997$	3.70510e16	1.19118	0.595589	−	0.803290i	$-0.296919\pi$
$997$	3.70510e16	1.19118	0.595589	+	0.803290i	$0.296919\pi$
$998$	4.25188e16	1.35945
$999$	2.25303e15	0.0716403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.18	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.18	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+32.2053 q^{2} +243.000 q^{3} -1010.82 q^{4} -5509.44 q^{5} +7825.90 q^{6} -36737.1 q^{7} -98510.2 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+32.2053 q^{2} +243.000 q^{3} -1010.82 q^{4} -5509.44 q^{5} +7825.90 q^{6} -36737.1 q^{7} -98510.2 q^{8} +59049.0 q^{9} -177433. q^{10} +785481. q^{11} -245628. q^{12} +1.64819e6 q^{13} -1.18313e6 q^{14} -1.33879e6 q^{15} -1.10240e6 q^{16} +14272.3 q^{17} +1.90169e6 q^{18} -8.87395e6 q^{19} +5.56903e6 q^{20} -8.92711e6 q^{21} +2.52967e7 q^{22} +2.97072e7 q^{23} -2.39380e7 q^{24} -1.84742e7 q^{25} +5.30806e7 q^{26} +1.43489e7 q^{27} +3.71344e7 q^{28} +6.76779e7 q^{29} -4.31163e7 q^{30} +6.05970e7 q^{31} +1.66246e8 q^{32} +1.90872e8 q^{33} +459646. q^{34} +2.02401e8 q^{35} -5.96877e7 q^{36} +1.57018e8 q^{37} -2.85789e8 q^{38} +4.00511e8 q^{39} +5.42736e8 q^{40} -1.38293e9 q^{41} -2.87501e8 q^{42} -1.09612e9 q^{43} -7.93977e8 q^{44} -3.25327e8 q^{45} +9.56729e8 q^{46} +1.74265e9 q^{47} -2.67884e8 q^{48} -6.27714e8 q^{49} -5.94967e8 q^{50} +3.46818e6 q^{51} -1.66602e9 q^{52} +3.03335e8 q^{53} +4.62111e8 q^{54} -4.32756e9 q^{55} +3.61898e9 q^{56} -2.15637e9 q^{57} +2.17959e9 q^{58} -7.14924e8 q^{59} +1.35327e9 q^{60} +1.62524e9 q^{61} +1.95155e9 q^{62} -2.16929e9 q^{63} +7.61172e9 q^{64} -9.08062e9 q^{65} +6.14710e9 q^{66} -1.24549e10 q^{67} -1.44267e7 q^{68} +7.21884e9 q^{69} +6.51839e9 q^{70} -8.29797e9 q^{71} -5.81693e9 q^{72} -2.93246e10 q^{73} +5.05681e9 q^{74} -4.48923e9 q^{75} +8.96993e9 q^{76} -2.88563e10 q^{77} +1.28986e10 q^{78} -1.88795e10 q^{79} +6.07363e9 q^{80} +3.48678e9 q^{81} -4.45377e10 q^{82} +2.23593e10 q^{83} +9.02366e9 q^{84} -7.86326e7 q^{85} -3.53009e10 q^{86} +1.64457e10 q^{87} -7.73779e10 q^{88} -9.79467e10 q^{89} -1.04773e10 q^{90} -6.05498e10 q^{91} -3.00285e10 q^{92} +1.47251e10 q^{93} +5.61227e10 q^{94} +4.88905e10 q^{95} +4.03977e10 q^{96} +2.14426e10 q^{97} -2.02157e10 q^{98} +4.63819e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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