LMFDB - Embedded newform 177.12.a.a.1.14

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} -86350.1 q^{10} -908857. q^{11} +475188. q^{12} -1.01344e6 q^{13} +18614.0 q^{14} +2.18177e6 q^{15} +3.63457e6 q^{16} +1.33915e6 q^{17} +567902. q^{18} +1.42736e7 q^{19} +1.75574e7 q^{20} -470311. q^{21} -8.74091e6 q^{22} +7.93240e6 q^{23} +9.35637e6 q^{24} +3.17848e7 q^{25} -9.74668e6 q^{26} -1.43489e7 q^{27} -3.78475e6 q^{28} +6.25466e6 q^{29} +2.09831e7 q^{30} -1.62098e8 q^{31} +1.13811e8 q^{32} +2.20852e8 q^{33} +1.28792e7 q^{34} -1.73772e7 q^{35} -1.15471e8 q^{36} +1.71173e8 q^{37} +1.37276e8 q^{38} +2.46265e8 q^{39} +3.45703e8 q^{40} +5.36286e8 q^{41} -4.52320e6 q^{42} +1.25115e9 q^{43} +1.77727e9 q^{44} -5.30170e8 q^{45} +7.62896e7 q^{46} +1.92164e9 q^{47} -8.83200e8 q^{48} -1.97358e9 q^{49} +3.05689e8 q^{50} -3.25413e8 q^{51} +1.98178e9 q^{52} +3.11202e9 q^{53} -1.38000e8 q^{54} +8.16015e9 q^{55} -7.45211e7 q^{56} -3.46849e9 q^{57} +6.01540e7 q^{58} +7.14924e8 q^{59} -4.26646e9 q^{60} -8.48149e9 q^{61} -1.55897e9 q^{62} +1.14285e8 q^{63} -6.34902e9 q^{64} +9.09910e9 q^{65} +2.12404e9 q^{66} +4.77009e9 q^{67} -2.61871e9 q^{68} -1.92757e9 q^{69} -1.67125e8 q^{70} +5.10131e8 q^{71} -2.27360e9 q^{72} +1.18698e10 q^{73} +1.64625e9 q^{74} -7.72370e9 q^{75} -2.79122e10 q^{76} -1.75903e9 q^{77} +2.36844e9 q^{78} -2.99691e10 q^{79} -3.26328e10 q^{80} +3.48678e9 q^{81} +5.15771e9 q^{82} +5.44332e10 q^{83} +9.19694e8 q^{84} -1.20235e10 q^{85} +1.20329e10 q^{86} -1.51988e9 q^{87} +3.49943e10 q^{88} -2.89450e10 q^{89} -5.09889e9 q^{90} -1.96144e9 q^{91} -1.55118e10 q^{92} +3.93898e10 q^{93} +1.84814e10 q^{94} -1.28155e11 q^{95} -2.76560e10 q^{96} +1.91150e10 q^{97} -1.89808e10 q^{98} -5.36671e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	9.61747	0.212518	0.106259	−	0.994338i	$-0.466113\pi$
$2$	9.61747	0.212518	0.106259	+	0.994338i	$0.466113\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1955.50	−0.954836
$5$	−8978.47	−1.28489	−0.642447	−	0.766330i	$-0.722081\pi$
$5$	−8978.47	−1.28489	−0.642447	+	0.766330i	$0.722081\pi$
$6$	−2337.04	−0.122697
$7$	1935.43	0.0435250	0.0217625	−	0.999763i	$-0.493072\pi$
$7$	1935.43	0.0435250	0.0217625	+	0.999763i	$0.493072\pi$
$8$	−38503.6	−0.415438
$9$	59049.0	0.333333
$10$	−86350.1	−0.273063
$11$	−908857.	−1.70152	−0.850758	−	0.525558i	$-0.823857\pi$
$11$	−908857.	−1.70152	−0.850758	+	0.525558i	$0.823857\pi$
$12$	475188.	0.551275
$13$	−1.01344e6	−0.757020	−0.378510	−	0.925597i	$-0.623564\pi$
$13$	−1.01344e6	−0.757020	−0.378510	+	0.925597i	$0.623564\pi$
$14$	18614.0	0.00924986
$15$	2.18177e6	0.741834
$16$	3.63457e6	0.866548
$17$	1.33915e6	0.228750	0.114375	−	0.993438i	$-0.463514\pi$
$17$	1.33915e6	0.228750	0.114375	+	0.993438i	$0.463514\pi$
$18$	567902.	0.0708393
$19$	1.42736e7	1.32248	0.661241	−	0.750174i	$-0.270030\pi$
$19$	1.42736e7	1.32248	0.661241	+	0.750174i	$0.270030\pi$
$20$	1.75574e7	1.22686
$21$	−470311.	−0.0251292
$22$	−8.74091e6	−0.361603
$23$	7.93240e6	0.256981	0.128491	−	0.991711i	$-0.458987\pi$
$23$	7.93240e6	0.256981	0.128491	+	0.991711i	$0.458987\pi$
$24$	9.35637e6	0.239853
$25$	3.17848e7	0.650952
$26$	−9.74668e6	−0.160880
$27$	−1.43489e7	−0.192450
$28$	−3.78475e6	−0.0415593
$29$	6.25466e6	0.0566258	0.0283129	−	0.999599i	$-0.490987\pi$
$29$	6.25466e6	0.0566258	0.0283129	+	0.999599i	$0.490987\pi$
$30$	2.09831e7	0.157653
$31$	−1.62098e8	−1.01692	−0.508462	−	0.861084i	$-0.669786\pi$
$31$	−1.62098e8	−1.01692	−0.508462	+	0.861084i	$0.669786\pi$
$32$	1.13811e8	0.599595
$33$	2.20852e8	0.982371
$34$	1.28792e7	0.0486134
$35$	−1.73772e7	−0.0559251
$36$	−1.15471e8	−0.318279
$37$	1.71173e8	0.405813	0.202907	−	0.979198i	$-0.434961\pi$
$37$	1.71173e8	0.405813	0.202907	+	0.979198i	$0.434961\pi$
$38$	1.37276e8	0.281051
$39$	2.46265e8	0.437066
$40$	3.45703e8	0.533794
$41$	5.36286e8	0.722912	0.361456	−	0.932389i	$-0.382280\pi$
$41$	5.36286e8	0.722912	0.361456	+	0.932389i	$0.382280\pi$
$42$	−4.52320e6	−0.00534041
$43$	1.25115e9	1.29788	0.648938	−	0.760841i	$-0.275213\pi$
$43$	1.25115e9	1.29788	0.648938	+	0.760841i	$0.275213\pi$
$44$	1.77727e9	1.62467
$45$	−5.30170e8	−0.428298
$46$	7.62896e7	0.0546132
$47$	1.92164e9	1.22218	0.611090	−	0.791562i	$-0.290732\pi$
$47$	1.92164e9	1.22218	0.611090	+	0.791562i	$0.290732\pi$
$48$	−8.83200e8	−0.500302
$49$	−1.97358e9	−0.998106
$50$	3.05689e8	0.138339
$51$	−3.25413e8	−0.132069
$52$	1.98178e9	0.722830
$53$	3.11202e9	1.02217	0.511087	−	0.859529i	$-0.329243\pi$
$53$	3.11202e9	1.02217	0.511087	+	0.859529i	$0.329243\pi$
$54$	−1.38000e8	−0.0408991
$55$	8.16015e9	2.18627
$56$	−7.45211e7	−0.0180820
$57$	−3.46849e9	−0.763535
$58$	6.01540e7	0.0120340
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−4.26646e9	−0.708330
$61$	−8.48149e9	−1.28575	−0.642877	−	0.765969i	$-0.722259\pi$
$61$	−8.48149e9	−1.28575	−0.642877	+	0.765969i	$0.722259\pi$
$62$	−1.55897e9	−0.216115
$63$	1.14285e8	0.0145083
$64$	−6.34902e9	−0.739123
$65$	9.09910e9	0.972691
$66$	2.12404e9	0.208771
$67$	4.77009e9	0.431634	0.215817	−	0.976434i	$-0.430759\pi$
$67$	4.77009e9	0.431634	0.215817	+	0.976434i	$0.430759\pi$
$68$	−2.61871e9	−0.218418
$69$	−1.92757e9	−0.148368
$70$	−1.67125e8	−0.0118851
$71$	5.10131e8	0.0335553	0.0167776	−	0.999859i	$-0.494659\pi$
$71$	5.10131e8	0.0335553	0.0167776	+	0.999859i	$0.494659\pi$
$72$	−2.27360e9	−0.138479
$73$	1.18698e10	0.670144	0.335072	−	0.942192i	$-0.391239\pi$
$73$	1.18698e10	0.670144	0.335072	+	0.942192i	$0.391239\pi$
$74$	1.64625e9	0.0862426
$75$	−7.72370e9	−0.375827
$76$	−2.79122e10	−1.26275
$77$	−1.75903e9	−0.0740585
$78$	2.36844e9	0.0928844
$79$	−2.99691e10	−1.09578	−0.547891	−	0.836550i	$-0.684569\pi$
$79$	−2.99691e10	−1.09578	−0.547891	+	0.836550i	$0.684569\pi$
$80$	−3.26328e10	−1.11342
$81$	3.48678e9	0.111111
$82$	5.15771e9	0.153632
$83$	5.44332e10	1.51682	0.758411	−	0.651777i	$-0.225976\pi$
$83$	5.44332e10	1.51682	0.758411	+	0.651777i	$0.225976\pi$
$84$	9.19694e8	0.0239943
$85$	−1.20235e10	−0.293919
$86$	1.20329e10	0.275822
$87$	−1.51988e9	−0.0326929
$88$	3.49943e10	0.706874
$89$	−2.89450e10	−0.549451	−0.274725	−	0.961523i	$-0.588587\pi$
$89$	−2.89450e10	−0.549451	−0.274725	+	0.961523i	$0.588587\pi$
$90$	−5.09889e9	−0.0910210
$91$	−1.96144e9	−0.0329493
$92$	−1.55118e10	−0.245375
$93$	3.93898e10	0.587121
$94$	1.84814e10	0.259735
$95$	−1.28155e11	−1.69925
$96$	−2.76560e10	−0.346176
$97$	1.91150e10	0.226011	0.113005	−	0.993594i	$-0.463952\pi$
$97$	1.91150e10	0.226011	0.113005	+	0.993594i	$0.463952\pi$
$98$	−1.89808e10	−0.212115
$99$	−5.36671e10	−0.567172
$100$	−6.21553e10	−0.621553
$101$	6.28414e10	0.594947	0.297474	−	0.954730i	$-0.403856\pi$
$101$	6.28414e10	0.594947	0.297474	+	0.954730i	$0.403856\pi$
$102$	−3.12965e9	−0.0280670
$103$	−1.47830e11	−1.25649	−0.628243	−	0.778017i	$-0.716226\pi$
$103$	−1.47830e11	−1.25649	−0.628243	+	0.778017i	$0.716226\pi$
$104$	3.90209e10	0.314495
$105$	4.22267e9	0.0322884
$106$	2.99297e10	0.217230
$107$	8.34678e10	0.575319	0.287659	−	0.957733i	$-0.407123\pi$
$107$	8.34678e10	0.575319	0.287659	+	0.957733i	$0.407123\pi$
$108$	2.80593e10	0.183758
$109$	−1.65315e11	−1.02912	−0.514559	−	0.857455i	$-0.672044\pi$
$109$	−1.65315e11	−1.02912	−0.514559	+	0.857455i	$0.672044\pi$
$110$	7.84800e10	0.464621
$111$	−4.15951e10	−0.234296
$112$	7.03446e9	0.0377165
$113$	2.12923e10	0.108716	0.0543578	−	0.998522i	$-0.482689\pi$
$113$	2.12923e10	0.108716	0.0543578	+	0.998522i	$0.482689\pi$
$114$	−3.33581e10	−0.162265
$115$	−7.12208e10	−0.330194
$116$	−1.22310e10	−0.0540684
$117$	−5.98423e10	−0.252340
$118$	6.87576e9	0.0276675
$119$	2.59184e9	0.00995633
$120$	−8.40059e10	−0.308186
$121$	5.40710e11	1.89516
$122$	−8.15704e10	−0.273246
$123$	−1.30318e11	−0.417373
$124$	3.16983e11	0.970996
$125$	1.53023e11	0.448489
$126$	1.09914e9	0.00308329
$127$	−5.38389e10	−0.144602	−0.0723012	−	0.997383i	$-0.523034\pi$
$127$	−5.38389e10	−0.144602	−0.0723012	+	0.997383i	$0.523034\pi$
$128$	−2.94146e11	−0.756672
$129$	−3.04030e11	−0.749329
$130$	8.75103e10	0.206714
$131$	−5.33391e11	−1.20796	−0.603981	−	0.796999i	$-0.706420\pi$
$131$	−5.33391e11	−1.20796	−0.603981	+	0.796999i	$0.706420\pi$
$132$	−4.31878e11	−0.938003
$133$	2.76257e10	0.0575611
$134$	4.58762e10	0.0917299
$135$	1.28831e11	0.247278
$136$	−5.15621e10	−0.0950312
$137$	−1.81390e11	−0.321107	−0.160554	−	0.987027i	$-0.551328\pi$
$137$	−1.81390e11	−0.321107	−0.160554	+	0.987027i	$0.551328\pi$
$138$	−1.85384e10	−0.0315309
$139$	−6.69082e11	−1.09370	−0.546850	−	0.837231i	$-0.684173\pi$
$139$	−6.69082e11	−1.09370	−0.546850	+	0.837231i	$0.684173\pi$
$140$	3.39813e10	0.0533993
$141$	−4.66960e11	−0.705625
$142$	4.90617e9	0.00713110
$143$	9.21068e11	1.28808
$144$	2.14617e11	0.288849
$145$	−5.61573e10	−0.0727582
$146$	1.14158e11	0.142418
$147$	4.79580e11	0.576257
$148$	−3.34730e11	−0.387485
$149$	−1.17113e12	−1.30641	−0.653205	−	0.757181i	$-0.726576\pi$
$149$	−1.17113e12	−1.30641	−0.653205	+	0.757181i	$0.726576\pi$
$150$	−7.42824e10	−0.0798701
$151$	−6.40012e11	−0.663460	−0.331730	−	0.943374i	$-0.607632\pi$
$151$	−6.40012e11	−0.663460	−0.331730	+	0.943374i	$0.607632\pi$
$152$	−5.49586e11	−0.549409
$153$	7.90755e10	0.0762498
$154$	−1.69174e10	−0.0157388
$155$	1.45539e12	1.30664
$156$	−4.81572e11	−0.417326
$157$	−4.28861e11	−0.358813	−0.179407	−	0.983775i	$-0.557418\pi$
$157$	−4.28861e11	−0.358813	−0.179407	+	0.983775i	$0.557418\pi$
$158$	−2.88227e11	−0.232874
$159$	−7.56220e11	−0.590152
$160$	−1.02185e12	−0.770416
$161$	1.53526e10	0.0111851
$162$	3.35340e10	0.0236131
$163$	1.51544e12	1.03159	0.515793	−	0.856713i	$-0.327497\pi$
$163$	1.51544e12	1.03159	0.515793	+	0.856713i	$0.327497\pi$
$164$	−1.04871e12	−0.690262
$165$	−1.98292e12	−1.26224
$166$	5.23510e11	0.322352
$167$	2.00802e11	0.119626	0.0598132	−	0.998210i	$-0.480949\pi$
$167$	2.00802e11	0.119626	0.0598132	+	0.998210i	$0.480949\pi$
$168$	1.81086e10	0.0104396
$169$	−7.65109e11	−0.426920
$170$	−1.15636e11	−0.0624631
$171$	8.42844e11	0.440827
$172$	−2.44663e12	−1.23926
$173$	−9.66265e9	−0.00474070	−0.00237035	−	0.999997i	$-0.500755\pi$
$173$	−9.66265e9	−0.00474070	−0.00237035	+	0.999997i	$0.500755\pi$
$174$	−1.46174e10	−0.00694784
$175$	6.15174e10	0.0283327
$176$	−3.30330e12	−1.47445
$177$	−1.73727e11	−0.0751646
$178$	−2.78378e11	−0.116768
$179$	1.75496e12	0.713797	0.356899	−	0.934143i	$-0.383834\pi$
$179$	1.75496e12	0.713797	0.356899	+	0.934143i	$0.383834\pi$
$180$	1.03675e12	0.408954
$181$	3.25190e12	1.24424	0.622121	−	0.782921i	$-0.286271\pi$
$181$	3.25190e12	1.24424	0.622121	+	0.782921i	$0.286271\pi$
$182$	−1.88641e10	−0.00700233
$183$	2.06100e12	0.742331
$184$	−3.05426e11	−0.106760
$185$	−1.53687e12	−0.521427
$186$	3.78830e11	0.124774
$187$	−1.21710e12	−0.389221
$188$	−3.75778e12	−1.16698
$189$	−2.77714e10	−0.00837640
$190$	−1.23253e12	−0.361121
$191$	2.17402e12	0.618843	0.309421	−	0.950925i	$-0.399865\pi$
$191$	2.17402e12	0.618843	0.309421	+	0.950925i	$0.399865\pi$
$192$	1.54281e12	0.426733
$193$	4.37751e12	1.17669	0.588345	−	0.808610i	$-0.299780\pi$
$193$	4.37751e12	1.17669	0.588345	+	0.808610i	$0.299780\pi$
$194$	1.83838e11	0.0480314
$195$	−2.21108e12	−0.561583
$196$	3.85935e12	0.953027
$197$	−1.77709e12	−0.426721	−0.213361	−	0.976974i	$-0.568441\pi$
$197$	−1.77709e12	−0.426721	−0.213361	+	0.976974i	$0.568441\pi$
$198$	−5.16142e11	−0.120534
$199$	6.76559e12	1.53679	0.768393	−	0.639978i	$-0.221057\pi$
$199$	6.76559e12	1.53679	0.768393	+	0.639978i	$0.221057\pi$
$200$	−1.22383e12	−0.270430
$201$	−1.15913e12	−0.249204
$202$	6.04375e11	0.126437
$203$	1.21055e10	0.00246464
$204$	6.36347e11	0.126104
$205$	−4.81503e12	−0.928865
$206$	−1.42175e12	−0.267026
$207$	4.68400e11	0.0856604
$208$	−3.68340e12	−0.655995
$209$	−1.29727e13	−2.25022
$210$	4.06114e10	0.00686186
$211$	2.79045e12	0.459326	0.229663	−	0.973270i	$-0.426238\pi$
$211$	2.79045e12	0.459326	0.229663	+	0.973270i	$0.426238\pi$
$212$	−6.08556e12	−0.976008
$213$	−1.23962e11	−0.0193732
$214$	8.02749e11	0.122266
$215$	−1.12334e13	−1.66763
$216$	5.52484e11	0.0799511
$217$	−3.13730e11	−0.0442617
$218$	−1.58991e12	−0.218706
$219$	−2.88437e12	−0.386908
$220$	−1.59572e13	−2.08753
$221$	−1.35714e12	−0.173168
$222$	−4.00039e11	−0.0497922
$223$	−1.46989e13	−1.78488	−0.892438	−	0.451171i	$-0.851006\pi$
$223$	−1.46989e13	−1.78488	−0.892438	+	0.451171i	$0.851006\pi$
$224$	2.20273e11	0.0260974
$225$	1.87686e12	0.216984
$226$	2.04778e11	0.0231040
$227$	7.12599e12	0.784698	0.392349	−	0.919816i	$-0.371662\pi$
$227$	7.12599e12	0.784698	0.392349	+	0.919816i	$0.371662\pi$
$228$	6.78265e12	0.729051
$229$	4.09823e12	0.430033	0.215016	−	0.976610i	$-0.431019\pi$
$229$	4.09823e12	0.430033	0.215016	+	0.976610i	$0.431019\pi$
$230$	−6.84964e11	−0.0701721
$231$	4.27445e11	0.0427577
$232$	−2.40827e11	−0.0235245
$233$	−4.91911e11	−0.0469276	−0.0234638	−	0.999725i	$-0.507469\pi$
$233$	−4.91911e11	−0.0469276	−0.0234638	+	0.999725i	$0.507469\pi$
$234$	−5.75532e11	−0.0536268
$235$	−1.72534e13	−1.57037
$236$	−1.39804e12	−0.124309
$237$	7.28249e12	0.632650
$238$	2.49269e10	0.00211590
$239$	−6.14857e12	−0.510018	−0.255009	−	0.966939i	$-0.582078\pi$
$239$	−6.14857e12	−0.510018	−0.255009	+	0.966939i	$0.582078\pi$
$240$	7.92978e12	0.642835
$241$	4.98321e12	0.394835	0.197417	−	0.980320i	$-0.436745\pi$
$241$	4.98321e12	0.394835	0.197417	+	0.980320i	$0.436745\pi$
$242$	5.20026e12	0.402755
$243$	−8.47289e11	−0.0641500
$244$	1.65856e13	1.22768
$245$	1.77197e13	1.28246
$246$	−1.25332e12	−0.0886994
$247$	−1.44654e13	−1.00115
$248$	6.24135e12	0.422469
$249$	−1.32273e13	−0.875737
$250$	1.47170e12	0.0953120
$251$	−3.17460e12	−0.201133	−0.100567	−	0.994930i	$-0.532066\pi$
$251$	−3.17460e12	−0.201133	−0.100567	+	0.994930i	$0.532066\pi$
$252$	−2.23486e11	−0.0138531
$253$	−7.20942e12	−0.437258
$254$	−5.17793e11	−0.0307306
$255$	2.92171e12	0.169694
$256$	1.01739e13	0.578317
$257$	−2.00280e13	−1.11431	−0.557153	−	0.830410i	$-0.688106\pi$
$257$	−2.00280e13	−1.11431	−0.557153	+	0.830410i	$0.688106\pi$
$258$	−2.92400e12	−0.159246
$259$	3.31294e11	0.0176630
$260$	−1.77933e13	−0.928760
$261$	3.69331e11	0.0188753
$262$	−5.12987e12	−0.256714
$263$	1.25346e13	0.614260	0.307130	−	0.951668i	$-0.400631\pi$
$263$	1.25346e13	0.614260	0.307130	+	0.951668i	$0.400631\pi$
$264$	−8.50360e12	−0.408114
$265$	−2.79411e13	−1.31338
$266$	2.65689e11	0.0122328
$267$	7.03364e12	0.317226
$268$	−9.32794e12	−0.412140
$269$	2.94360e13	1.27421	0.637105	−	0.770777i	$-0.280132\pi$
$269$	2.94360e13	1.27421	0.637105	+	0.770777i	$0.280132\pi$
$270$	1.23903e12	0.0525510
$271$	5.64401e11	0.0234562	0.0117281	−	0.999931i	$-0.496267\pi$
$271$	5.64401e11	0.0234562	0.0117281	+	0.999931i	$0.496267\pi$
$272$	4.86723e12	0.198222
$273$	4.76629e11	0.0190233
$274$	−1.74451e12	−0.0682411
$275$	−2.88878e13	−1.10761
$276$	3.76938e12	0.141667
$277$	−5.72696e12	−0.211002	−0.105501	−	0.994419i	$-0.533645\pi$
$277$	−5.72696e12	−0.211002	−0.105501	+	0.994419i	$0.533645\pi$
$278$	−6.43487e12	−0.232431
$279$	−9.57173e12	−0.338975
$280$	6.69086e11	0.0232334
$281$	3.08258e13	1.04961	0.524806	−	0.851222i	$-0.324138\pi$
$281$	3.08258e13	1.04961	0.524806	+	0.851222i	$0.324138\pi$
$282$	−4.49097e12	−0.149958
$283$	−4.57961e12	−0.149969	−0.0749847	−	0.997185i	$-0.523891\pi$
$283$	−4.57961e12	−0.149969	−0.0749847	+	0.997185i	$0.523891\pi$
$284$	−9.97564e11	−0.0320398
$285$	3.11418e13	0.981062
$286$	8.85834e12	0.273741
$287$	1.03795e12	0.0314648
$288$	6.72040e12	0.199865
$289$	−3.24786e13	−0.947674
$290$	−5.40091e11	−0.0154624
$291$	−4.64494e12	−0.130487
$292$	−2.32115e13	−0.639878
$293$	−2.28588e13	−0.618417	−0.309209	−	0.950994i	$-0.600064\pi$
$293$	−2.28588e13	−0.618417	−0.309209	+	0.950994i	$0.600064\pi$
$294$	4.61235e12	0.122465
$295$	−6.41893e12	−0.167279
$296$	−6.59078e12	−0.168590
$297$	1.30411e13	0.327457
$298$	−1.12633e13	−0.277635
$299$	−8.03898e12	−0.194540
$300$	1.51037e13	0.358854
$301$	2.42152e12	0.0564901
$302$	−6.15529e12	−0.140997
$303$	−1.52705e13	−0.343493
$304$	5.18785e13	1.14599
$305$	7.61508e13	1.65206
$306$	7.60506e11	0.0162045
$307$	1.67173e13	0.349870	0.174935	−	0.984580i	$-0.444029\pi$
$307$	1.67173e13	0.349870	0.174935	+	0.984580i	$0.444029\pi$
$308$	3.43980e12	0.0707138
$309$	3.59227e13	0.725433
$310$	1.39972e13	0.277684
$311$	−1.89410e13	−0.369166	−0.184583	−	0.982817i	$-0.559093\pi$
$311$	−1.89410e13	−0.369166	−0.184583	+	0.982817i	$0.559093\pi$
$312$	−9.48207e12	−0.181574
$313$	−1.17436e13	−0.220956	−0.110478	−	0.993879i	$-0.535238\pi$
$313$	−1.17436e13	−0.220956	−0.110478	+	0.993879i	$0.535238\pi$
$314$	−4.12456e12	−0.0762543
$315$	−1.02611e12	−0.0186417
$316$	5.86047e13	1.04629
$317$	8.62862e13	1.51396	0.756982	−	0.653436i	$-0.226673\pi$
$317$	8.62862e13	1.51396	0.756982	+	0.653436i	$0.226673\pi$
$318$	−7.27292e12	−0.125418
$319$	−5.68459e12	−0.0963497
$320$	5.70045e13	0.949695
$321$	−2.02827e13	−0.332160
$322$	1.47654e11	0.00237704
$323$	1.91145e13	0.302517
$324$	−6.81842e12	−0.106093
$325$	−3.22118e13	−0.492784
$326$	1.45747e13	0.219231
$327$	4.01714e13	0.594162
$328$	−2.06489e13	−0.300325
$329$	3.71922e12	0.0531954
$330$	−1.90706e13	−0.268249
$331$	2.92656e13	0.404859	0.202430	−	0.979297i	$-0.435116\pi$
$331$	2.92656e13	0.404859	0.202430	+	0.979297i	$0.435116\pi$
$332$	−1.06444e14	−1.44832
$333$	1.01076e13	0.135271
$334$	1.93120e12	0.0254228
$335$	−4.28281e13	−0.554604
$336$	−1.70937e12	−0.0217757
$337$	1.32340e14	1.65855	0.829274	−	0.558842i	$-0.188754\pi$
$337$	1.32340e14	1.65855	0.829274	+	0.558842i	$0.188754\pi$
$338$	−7.35841e12	−0.0907282
$339$	−5.17404e12	−0.0627670
$340$	2.35120e13	0.280644
$341$	1.47324e14	1.73031
$342$	8.10602e12	0.0936837
$343$	−7.64672e12	−0.0869676
$344$	−4.81738e13	−0.539187
$345$	1.73067e13	0.190637
$346$	−9.29302e10	−0.00100748
$347$	3.67543e13	0.392190	0.196095	−	0.980585i	$-0.437174\pi$
$347$	3.67543e13	0.392190	0.196095	+	0.980585i	$0.437174\pi$
$348$	2.97214e12	0.0312164
$349$	−1.29785e14	−1.34180	−0.670898	−	0.741550i	$-0.734091\pi$
$349$	−1.29785e14	−1.34180	−0.670898	+	0.741550i	$0.734091\pi$
$350$	5.91641e11	0.00602121
$351$	1.45417e13	0.145689
$352$	−1.03438e14	−1.02022
$353$	1.04977e14	1.01937	0.509687	−	0.860360i	$-0.329761\pi$
$353$	1.04977e14	1.01937	0.509687	+	0.860360i	$0.329761\pi$
$354$	−1.67081e12	−0.0159738
$355$	−4.58020e12	−0.0431150
$356$	5.66021e13	0.524636
$357$	−6.29816e11	−0.00574829
$358$	1.68782e13	0.151695
$359$	9.26261e13	0.819811	0.409906	−	0.912128i	$-0.365562\pi$
$359$	9.26261e13	0.819811	0.409906	+	0.912128i	$0.365562\pi$
$360$	2.04134e13	0.177931
$361$	8.72464e13	0.748958
$362$	3.12750e13	0.264424
$363$	−1.31393e14	−1.09417
$364$	3.83560e12	0.0314612
$365$	−1.06573e14	−0.861064
$366$	1.98216e13	0.157759
$367$	2.10505e14	1.65044	0.825219	−	0.564813i	$-0.191052\pi$
$367$	2.10505e14	1.65044	0.825219	+	0.564813i	$0.191052\pi$
$368$	2.88308e13	0.222687
$369$	3.16672e13	0.240971
$370$	−1.47808e13	−0.110813
$371$	6.02310e12	0.0444902
$372$	−7.70270e13	−0.560605
$373$	−3.70839e13	−0.265942	−0.132971	−	0.991120i	$-0.542452\pi$
$373$	−3.70839e13	−0.265942	−0.132971	+	0.991120i	$0.542452\pi$
$374$	−1.17054e13	−0.0827165
$375$	−3.71846e13	−0.258935
$376$	−7.39902e13	−0.507739
$377$	−6.33869e12	−0.0428669
$378$	−2.67090e11	−0.00178014
$379$	4.29231e13	0.281952	0.140976	−	0.990013i	$-0.454976\pi$
$379$	4.29231e13	0.281952	0.140976	+	0.990013i	$0.454976\pi$
$380$	2.50608e14	1.62250
$381$	1.30828e13	0.0834862
$382$	2.09086e13	0.131515
$383$	1.09831e14	0.680975	0.340488	−	0.940249i	$-0.389408\pi$
$383$	1.09831e14	0.680975	0.340488	+	0.940249i	$0.389408\pi$
$384$	7.14774e13	0.436865
$385$	1.57934e13	0.0951574
$386$	4.21006e13	0.250068
$387$	7.38792e13	0.432625
$388$	−3.73794e13	−0.215803
$389$	−2.86161e14	−1.62887	−0.814436	−	0.580253i	$-0.802954\pi$
$389$	−2.86161e14	−1.62887	−0.814436	+	0.580253i	$0.802954\pi$
$390$	−2.12650e13	−0.119347
$391$	1.06227e13	0.0587844
$392$	7.59899e13	0.414651
$393$	1.29614e14	0.697417
$394$	−1.70911e13	−0.0906860
$395$	2.69076e14	1.40796
$396$	1.04946e14	0.541556
$397$	−1.19227e14	−0.606775	−0.303387	−	0.952867i	$-0.598118\pi$
$397$	−1.19227e14	−0.606775	−0.303387	+	0.952867i	$0.598118\pi$
$398$	6.50678e13	0.326595
$399$	−6.71304e12	−0.0332329
$400$	1.15524e14	0.564081
$401$	7.47737e13	0.360126	0.180063	−	0.983655i	$-0.442370\pi$
$401$	7.47737e13	0.360126	0.180063	+	0.983655i	$0.442370\pi$
$402$	−1.11479e13	−0.0529603
$403$	1.64276e14	0.769832
$404$	−1.22887e14	−0.568077
$405$	−3.13060e13	−0.142766
$406$	1.16424e11	0.000523781 0
$407$	−1.55572e14	−0.690497
$408$	1.25296e13	0.0548663
$409$	2.85390e14	1.23299	0.616495	−	0.787358i	$-0.288552\pi$
$409$	2.85390e14	1.23299	0.616495	+	0.787358i	$0.288552\pi$
$410$	−4.63084e13	−0.197401
$411$	4.40778e13	0.185391
$412$	2.89082e14	1.19974
$413$	1.38369e12	0.00566648
$414$	4.50483e12	0.0182044
$415$	−4.88727e14	−1.94895
$416$	−1.15340e14	−0.453906
$417$	1.62587e14	0.631448
$418$	−1.24764e14	−0.478213
$419$	−1.04792e13	−0.0396416	−0.0198208	−	0.999804i	$-0.506310\pi$
$419$	−1.04792e13	−0.0396416	−0.0198208	+	0.999804i	$0.506310\pi$
$420$	−8.25745e12	−0.0308301
$421$	−1.74954e14	−0.644721	−0.322361	−	0.946617i	$-0.604476\pi$
$421$	−1.74954e14	−0.644721	−0.322361	+	0.946617i	$0.604476\pi$
$422$	2.68371e13	0.0976151
$423$	1.13471e14	0.407393
$424$	−1.19824e14	−0.424650
$425$	4.25646e13	0.148905
$426$	−1.19220e12	−0.00411714
$427$	−1.64154e13	−0.0559625
$428$	−1.63222e14	−0.549335
$429$	−2.23820e14	−0.743675
$430$	−1.08037e14	−0.354402
$431$	−3.00307e14	−0.972613	−0.486306	−	0.873788i	$-0.661656\pi$
$431$	−3.00307e14	−0.972613	−0.486306	+	0.873788i	$0.661656\pi$
$432$	−5.21521e13	−0.166767
$433$	2.80926e14	0.886968	0.443484	−	0.896282i	$-0.353742\pi$
$433$	2.80926e14	0.886968	0.443484	+	0.896282i	$0.353742\pi$
$434$	−3.01729e12	−0.00940640
$435$	1.36462e13	0.0420070
$436$	3.23273e14	0.982639
$437$	1.13224e14	0.339853
$438$	−2.77403e13	−0.0822249
$439$	−5.81821e14	−1.70308	−0.851540	−	0.524290i	$-0.824331\pi$
$439$	−5.81821e14	−1.70308	−0.851540	+	0.524290i	$0.824331\pi$
$440$	−3.14195e14	−0.908258
$441$	−1.16538e14	−0.332702
$442$	−1.30523e13	−0.0368013
$443$	−5.40109e13	−0.150404	−0.0752022	−	0.997168i	$-0.523960\pi$
$443$	−5.40109e13	−0.150404	−0.0752022	+	0.997168i	$0.523960\pi$
$444$	8.13393e13	0.223715
$445$	2.59882e14	0.705986
$446$	−1.41366e14	−0.379318
$447$	2.84584e14	0.754256
$448$	−1.22881e13	−0.0321704
$449$	−6.26344e14	−1.61979	−0.809894	−	0.586576i	$-0.800476\pi$
$449$	−6.26344e14	−1.61979	−0.809894	+	0.586576i	$0.800476\pi$
$450$	1.80506e13	0.0461130
$451$	−4.87408e14	−1.23005
$452$	−4.16372e13	−0.103806
$453$	1.55523e14	0.383049
$454$	6.85339e13	0.166763
$455$	1.76107e13	0.0423364
$456$	1.33549e14	0.317201
$457$	1.70392e14	0.399861	0.199931	−	0.979810i	$-0.435928\pi$
$457$	1.70392e14	0.399861	0.199931	+	0.979810i	$0.435928\pi$
$458$	3.94146e13	0.0913897
$459$	−1.92153e13	−0.0440229
$460$	1.39273e14	0.315281
$461$	3.38574e14	0.757354	0.378677	−	0.925529i	$-0.376379\pi$
$461$	3.38574e14	0.757354	0.378677	+	0.925529i	$0.376379\pi$
$462$	4.11094e12	0.00908679
$463$	2.87373e14	0.627697	0.313849	−	0.949473i	$-0.398382\pi$
$463$	2.87373e14	0.627697	0.313849	+	0.949473i	$0.398382\pi$
$464$	2.27330e13	0.0490690
$465$	−3.53660e14	−0.754389
$466$	−4.73093e12	−0.00997296
$467$	7.74798e14	1.61416	0.807078	−	0.590444i	$-0.201048\pi$
$467$	7.74798e14	1.61416	0.807078	+	0.590444i	$0.201048\pi$
$468$	1.17022e14	0.240943
$469$	9.23220e12	0.0187869
$470$	−1.65934e14	−0.333732
$471$	1.04213e14	0.207161
$472$	−2.75271e13	−0.0540854
$473$	−1.13712e15	−2.20836
$474$	7.00391e13	0.134450
$475$	4.53684e14	0.860873
$476$	−5.06835e12	−0.00950667
$477$	1.83761e14	0.340725
$478$	−5.91336e13	−0.108388
$479$	−7.02364e13	−0.127267	−0.0636337	−	0.997973i	$-0.520269\pi$
$479$	−7.02364e13	−0.127267	−0.0636337	+	0.997973i	$0.520269\pi$
$480$	2.48308e14	0.444800
$481$	−1.73473e14	−0.307209
$482$	4.79258e13	0.0839094
$483$	−3.73069e12	−0.00645773
$484$	−1.05736e15	−1.80956
$485$	−1.71623e14	−0.290400
$486$	−8.14877e12	−0.0136330
$487$	−5.05024e14	−0.835416	−0.417708	−	0.908581i	$-0.637166\pi$
$487$	−5.05024e14	−0.835416	−0.417708	+	0.908581i	$0.637166\pi$
$488$	3.26568e14	0.534151
$489$	−3.68251e14	−0.595587
$490$	1.70419e14	0.272546
$491$	6.74170e14	1.06616	0.533079	−	0.846066i	$-0.321035\pi$
$491$	6.74170e14	1.06616	0.533079	+	0.846066i	$0.321035\pi$
$492$	2.54836e14	0.398523
$493$	8.37593e12	0.0129531
$494$	−1.39121e14	−0.212761
$495$	4.81849e14	0.728756
$496$	−5.89156e14	−0.881213
$497$	9.87325e11	0.00146050
$498$	−1.27213e14	−0.186110
$499$	−2.91391e13	−0.0421622	−0.0210811	−	0.999778i	$-0.506711\pi$
$499$	−2.91391e13	−0.0421622	−0.0210811	+	0.999778i	$0.506711\pi$
$500$	−2.99237e14	−0.428234
$501$	−4.87948e13	−0.0690663
$502$	−3.05316e13	−0.0427444
$503$	1.55483e14	0.215307	0.107654	−	0.994188i	$-0.465666\pi$
$503$	1.55483e14	0.215307	0.107654	+	0.994188i	$0.465666\pi$
$504$	−4.40040e12	−0.00602732
$505$	−5.64220e14	−0.764444
$506$	−6.93364e13	−0.0929252
$507$	1.85922e14	0.246482
$508$	1.05282e14	0.138072
$509$	−7.58496e14	−0.984024	−0.492012	−	0.870588i	$-0.663738\pi$
$509$	−7.58496e14	−0.984024	−0.492012	+	0.870588i	$0.663738\pi$
$510$	2.80995e13	0.0360631
$511$	2.29733e13	0.0291681
$512$	7.00257e14	0.879575
$513$	−2.04811e14	−0.254512
$514$	−1.92618e14	−0.236810
$515$	1.32729e15	1.61445
$516$	5.94531e14	0.715487
$517$	−1.74650e15	−2.07956
$518$	3.18621e12	0.00375371
$519$	2.34802e12	0.00273705
$520$	−3.50348e14	−0.404093
$521$	1.45929e15	1.66546	0.832728	−	0.553682i	$-0.186778\pi$
$521$	1.45929e15	1.66546	0.832728	+	0.553682i	$0.186778\pi$
$522$	3.55203e12	0.00401134
$523$	−1.72020e15	−1.92229	−0.961146	−	0.276039i	$-0.910978\pi$
$523$	−1.72020e15	−1.92229	−0.961146	+	0.276039i	$0.910978\pi$
$524$	1.04305e15	1.15341
$525$	−1.49487e13	−0.0163579
$526$	1.20551e14	0.130541
$527$	−2.17074e14	−0.232621
$528$	8.02702e14	0.851271
$529$	−8.89887e14	−0.933961
$530$	−2.68723e14	−0.279118
$531$	4.22156e13	0.0433963
$532$	−5.40221e13	−0.0549614
$533$	−5.43491e14	−0.547259
$534$	6.76458e13	0.0674162
$535$	−7.49413e14	−0.739223
$536$	−1.83666e14	−0.179317
$537$	−4.26455e14	−0.412111
$538$	2.83099e14	0.270792
$539$	1.79370e15	1.69829
$540$	−2.51930e14	−0.236110
$541$	−2.14899e15	−1.99365	−0.996826	−	0.0796149i	$-0.974631\pi$
$541$	−2.14899e15	−1.99365	−0.996826	+	0.0796149i	$0.974631\pi$
$542$	5.42811e12	0.00498485
$543$	−7.90212e14	−0.718364
$544$	1.52410e14	0.137157
$545$	1.48427e15	1.32231
$546$	4.58397e12	0.00404280
$547$	−1.09027e15	−0.951930	−0.475965	−	0.879464i	$-0.657901\pi$
$547$	−1.09027e15	−0.951930	−0.475965	+	0.879464i	$0.657901\pi$
$548$	3.54709e14	0.306605
$549$	−5.00823e14	−0.428585
$550$	−2.77828e14	−0.235386
$551$	8.92767e13	0.0748866
$552$	7.42185e13	0.0616378
$553$	−5.80032e13	−0.0476940
$554$	−5.50789e13	−0.0448416
$555$	3.73460e14	0.301046
$556$	1.30839e15	1.04430
$557$	1.71044e15	1.35177	0.675887	−	0.737006i	$-0.263761\pi$
$557$	1.71044e15	1.35177	0.675887	+	0.737006i	$0.263761\pi$
$558$	−9.20558e13	−0.0720382
$559$	−1.26796e15	−0.982519
$560$	−6.31587e13	−0.0484618
$561$	2.95754e14	0.224717
$562$	2.96466e14	0.223062
$563$	2.29132e15	1.70722	0.853610	−	0.520912i	$-0.174408\pi$
$563$	2.29132e15	1.70722	0.853610	+	0.520912i	$0.174408\pi$
$564$	9.13142e14	0.673757
$565$	−1.91172e14	−0.139688
$566$	−4.40442e13	−0.0318712
$567$	6.74844e12	0.00483612
$568$	−1.96419e13	−0.0139401
$569$	−2.79540e15	−1.96484	−0.982418	−	0.186693i	$-0.940223\pi$
$569$	−2.79540e15	−1.96484	−0.982418	+	0.186693i	$0.940223\pi$
$570$	2.99505e14	0.208493
$571$	−8.74818e14	−0.603142	−0.301571	−	0.953444i	$-0.597511\pi$
$571$	−8.74818e14	−0.603142	−0.301571	+	0.953444i	$0.597511\pi$
$572$	−1.80115e15	−1.22991
$573$	−5.28287e14	−0.357289
$574$	9.98242e12	0.00668683
$575$	2.52130e14	0.167283
$576$	−3.74903e14	−0.246374
$577$	−1.83319e15	−1.19328	−0.596638	−	0.802510i	$-0.703497\pi$
$577$	−1.83319e15	−1.19328	−0.596638	+	0.802510i	$0.703497\pi$
$578$	−3.12362e14	−0.201398
$579$	−1.06374e15	−0.679363
$580$	1.09816e14	0.0694721
$581$	1.05352e14	0.0660197
$582$	−4.46726e13	−0.0277309
$583$	−2.82838e15	−1.73924
$584$	−4.57030e14	−0.278403
$585$	5.37293e14	0.324230
$586$	−2.19844e14	−0.131425
$587$	−2.67588e15	−1.58473	−0.792367	−	0.610044i	$-0.791152\pi$
$587$	−2.67588e15	−1.58473	−0.792367	+	0.610044i	$0.791152\pi$
$588$	−9.37821e14	−0.550231
$589$	−2.31373e15	−1.34486
$590$	−6.17338e13	−0.0355498
$591$	4.31832e14	0.246368
$592$	6.22140e14	0.351657
$593$	5.40731e14	0.302817	0.151409	−	0.988471i	$-0.451619\pi$
$593$	5.40731e14	0.302817	0.151409	+	0.988471i	$0.451619\pi$
$594$	1.25422e14	0.0695905
$595$	−2.32707e13	−0.0127928
$596$	2.29014e15	1.24741
$597$	−1.64404e15	−0.887264
$598$	−7.73146e13	−0.0413433
$599$	3.38091e15	1.79138	0.895688	−	0.444683i	$-0.146684\pi$
$599$	3.38091e15	1.79138	0.895688	+	0.444683i	$0.146684\pi$
$600$	2.97390e14	0.156133
$601$	−2.57256e15	−1.33831	−0.669153	−	0.743125i	$-0.733343\pi$
$601$	−2.57256e15	−1.33831	−0.669153	+	0.743125i	$0.733343\pi$
$602$	2.32889e13	0.0120052
$603$	2.81669e14	0.143878
$604$	1.25155e15	0.633496
$605$	−4.85475e15	−2.43507
$606$	−1.46863e14	−0.0729985
$607$	−3.05746e14	−0.150599	−0.0752997	−	0.997161i	$-0.523991\pi$
$607$	−3.05746e14	−0.150599	−0.0752997	+	0.997161i	$0.523991\pi$
$608$	1.62449e15	0.792953
$609$	−2.94163e12	−0.00142296
$610$	7.32378e14	0.351092
$611$	−1.94746e15	−0.925214
$612$	−1.54632e14	−0.0728061
$613$	3.74944e15	1.74958	0.874789	−	0.484504i	$-0.161000\pi$
$613$	3.74944e15	1.74958	0.874789	+	0.484504i	$0.161000\pi$
$614$	1.60778e14	0.0743536
$615$	1.17005e15	0.536280
$616$	6.77291e13	0.0307667
$617$	−1.74630e15	−0.786232	−0.393116	−	0.919489i	$-0.628603\pi$
$617$	−1.74630e15	−0.786232	−0.393116	+	0.919489i	$0.628603\pi$
$618$	3.45485e14	0.154167
$619$	−2.66563e15	−1.17896	−0.589482	−	0.807781i	$-0.700668\pi$
$619$	−2.66563e15	−1.17896	−0.589482	+	0.807781i	$0.700668\pi$
$620$	−2.84603e15	−1.24763
$621$	−1.13821e14	−0.0494561
$622$	−1.82165e14	−0.0784544
$623$	−5.60212e13	−0.0239149
$624$	8.95066e14	0.378739
$625$	−2.92590e15	−1.22721
$626$	−1.12943e14	−0.0469571
$627$	3.15237e15	1.29917
$628$	8.38639e14	0.342608
$629$	2.29227e14	0.0928296
$630$	−9.86856e12	−0.00396169
$631$	−3.39794e15	−1.35224	−0.676121	−	0.736791i	$-0.736340\pi$
$631$	−3.39794e15	−1.35224	−0.676121	+	0.736791i	$0.736340\pi$
$632$	1.15392e15	0.455230
$633$	−6.78080e14	−0.265192
$634$	8.29855e14	0.321745
$635$	4.83390e14	0.185799
$636$	1.47879e15	0.563499
$637$	2.00010e15	0.755586
$638$	−5.46714e13	−0.0204761
$639$	3.01227e13	0.0111851
$640$	2.64098e15	0.972243
$641$	2.60956e15	0.952464	0.476232	−	0.879320i	$-0.342002\pi$
$641$	2.60956e15	0.952464	0.476232	+	0.879320i	$0.342002\pi$
$642$	−1.95068e14	−0.0705900
$643$	4.18378e15	1.50109	0.750547	−	0.660817i	$-0.229790\pi$
$643$	4.18378e15	1.50109	0.750547	+	0.660817i	$0.229790\pi$
$644$	−3.00222e13	−0.0106800
$645$	2.72972e15	0.962809
$646$	1.83833e14	0.0642903
$647$	1.52285e15	0.528059	0.264030	−	0.964515i	$-0.414948\pi$
$647$	1.52285e15	0.528059	0.264030	+	0.964515i	$0.414948\pi$
$648$	−1.34254e14	−0.0461598
$649$	−6.49764e14	−0.221518
$650$	−3.09796e14	−0.104725
$651$	7.62364e13	0.0255545
$652$	−2.96344e15	−0.984996
$653$	2.27823e14	0.0750888	0.0375444	−	0.999295i	$-0.488046\pi$
$653$	2.27823e14	0.0750888	0.0375444	+	0.999295i	$0.488046\pi$
$654$	3.86347e14	0.126270
$655$	4.78903e15	1.55210
$656$	1.94917e15	0.626438
$657$	7.00901e14	0.223381
$658$	3.57694e13	0.0113050
$659$	2.20006e15	0.689549	0.344774	−	0.938686i	$-0.387955\pi$
$659$	2.20006e15	0.689549	0.344774	+	0.938686i	$0.387955\pi$
$660$	3.87760e15	1.20523
$661$	4.21838e15	1.30028	0.650141	−	0.759814i	$-0.274710\pi$
$661$	4.21838e15	1.30028	0.650141	+	0.759814i	$0.274710\pi$
$662$	2.81461e14	0.0860398
$663$	3.29785e14	0.0999786
$664$	−2.09587e15	−0.630145
$665$	−2.48036e14	−0.0739599
$666$	9.72095e13	0.0287475
$667$	4.96145e13	0.0145518
$668$	−3.92669e14	−0.114224
$669$	3.57183e15	1.03050
$670$	−4.11898e14	−0.117863
$671$	7.70846e15	2.18773
$672$	−5.35263e13	−0.0150673
$673$	−2.92053e15	−0.815414	−0.407707	−	0.913113i	$-0.633672\pi$
$673$	−2.92053e15	−0.815414	−0.407707	+	0.913113i	$0.633672\pi$
$674$	1.27278e15	0.352471
$675$	−4.56077e14	−0.125276
$676$	1.49617e15	0.407639
$677$	2.76749e15	0.747910	0.373955	−	0.927447i	$-0.378002\pi$
$677$	2.76749e15	0.747910	0.373955	+	0.927447i	$0.378002\pi$
$678$	−4.97611e13	−0.0133391
$679$	3.69958e13	0.00983713
$680$	4.62948e14	0.122105
$681$	−1.73161e15	−0.453046
$682$	1.41688e15	0.367722
$683$	−5.44228e15	−1.40109	−0.700547	−	0.713606i	$-0.747061\pi$
$683$	−5.44228e15	−1.40109	−0.700547	+	0.713606i	$0.747061\pi$
$684$	−1.64818e15	−0.420918
$685$	1.62860e15	0.412589
$686$	−7.35421e13	−0.0184822
$687$	−9.95871e14	−0.248280
$688$	4.54739e15	1.12467
$689$	−3.15383e15	−0.773806
$690$	1.66446e14	0.0405139
$691$	−2.91161e15	−0.703079	−0.351540	−	0.936173i	$-0.614342\pi$
$691$	−2.91161e15	−0.703079	−0.351540	+	0.936173i	$0.614342\pi$
$692$	1.88954e13	0.00452659
$693$	−1.03869e14	−0.0246862
$694$	3.53484e14	0.0833474
$695$	6.00733e15	1.40529
$696$	5.85209e13	0.0135819
$697$	7.18168e14	0.165366
$698$	−1.24821e15	−0.285156
$699$	1.19534e14	0.0270937
$700$	−1.20297e14	−0.0270531
$701$	−5.11697e15	−1.14173	−0.570865	−	0.821044i	$-0.693392\pi$
$701$	−5.11697e15	−1.14173	−0.570865	+	0.821044i	$0.693392\pi$
$702$	1.39854e14	0.0309615
$703$	2.44326e15	0.536681
$704$	5.77035e15	1.25763
$705$	4.19258e15	0.906654
$706$	1.00961e15	0.216635
$707$	1.21625e14	0.0258951
$708$	3.39723e14	0.0717699
$709$	4.25185e14	0.0891300	0.0445650	−	0.999006i	$-0.485810\pi$
$709$	4.25185e14	0.0891300	0.0445650	+	0.999006i	$0.485810\pi$
$710$	−4.40499e13	−0.00916271
$711$	−1.76964e15	−0.365261
$712$	1.11449e15	0.228263
$713$	−1.28583e15	−0.261330
$714$	−6.05724e12	−0.00122162
$715$	−8.26978e15	−1.65505
$716$	−3.43183e15	−0.681559
$717$	1.49410e15	0.294459
$718$	8.90828e14	0.174225
$719$	1.41112e15	0.273877	0.136938	−	0.990580i	$-0.456274\pi$
$719$	1.41112e15	0.273877	0.136938	+	0.990580i	$0.456274\pi$
$720$	−1.92694e15	−0.371141
$721$	−2.86115e14	−0.0546886
$722$	8.39089e14	0.159167
$723$	−1.21092e15	−0.227958
$724$	−6.35911e15	−1.18805
$725$	1.98803e14	0.0368607
$726$	−1.26366e15	−0.232531
$727$	−6.89870e14	−0.125988	−0.0629938	−	0.998014i	$-0.520065\pi$
$727$	−6.89870e14	−0.125988	−0.0629938	+	0.998014i	$0.520065\pi$
$728$	7.55223e13	0.0136884
$729$	2.05891e14	0.0370370
$730$	−1.02496e15	−0.182992
$731$	1.67548e15	0.296889
$732$	−4.03030e15	−0.708804
$733$	−4.64231e15	−0.810330	−0.405165	−	0.914244i	$-0.632786\pi$
$733$	−4.64231e15	−0.810330	−0.405165	+	0.914244i	$0.632786\pi$
$734$	2.02453e15	0.350748
$735$	−4.30590e15	−0.740428
$736$	9.02792e14	0.154085
$737$	−4.33533e15	−0.734432
$738$	3.04558e14	0.0512106
$739$	5.83938e15	0.974592	0.487296	−	0.873237i	$-0.337983\pi$
$739$	5.83938e15	0.974592	0.487296	+	0.873237i	$0.337983\pi$
$740$	3.00536e15	0.497877
$741$	3.51509e15	0.578012
$742$	5.79270e13	0.00945496
$743$	−1.97794e15	−0.320460	−0.160230	−	0.987080i	$-0.551224\pi$
$743$	−1.97794e15	−0.320460	−0.160230	+	0.987080i	$0.551224\pi$
$744$	−1.51665e15	−0.243912
$745$	1.05149e16	1.67860
$746$	−3.56653e14	−0.0565175
$747$	3.21423e15	0.505607
$748$	2.38004e15	0.371642
$749$	1.61547e14	0.0250408
$750$	−3.57622e14	−0.0550284
$751$	−5.77666e15	−0.882384	−0.441192	−	0.897413i	$-0.645444\pi$
$751$	−5.77666e15	−0.882384	−0.441192	+	0.897413i	$0.645444\pi$
$752$	6.98434e15	1.05908
$753$	7.71428e14	0.116124
$754$	−6.09621e13	−0.00910999
$755$	5.74633e15	0.852476
$756$	5.43070e13	0.00799809
$757$	6.34073e15	0.927069	0.463535	−	0.886079i	$-0.346581\pi$
$757$	6.34073e15	0.927069	0.463535	+	0.886079i	$0.346581\pi$
$758$	4.12812e14	0.0599200
$759$	1.75189e15	0.252451
$760$	4.93444e15	0.705932
$761$	−1.27884e16	−1.81635	−0.908176	−	0.418589i	$-0.862525\pi$
$761$	−1.27884e16	−1.81635	−0.908176	+	0.418589i	$0.862525\pi$
$762$	1.25824e14	0.0177423
$763$	−3.19955e14	−0.0447924
$764$	−4.25131e15	−0.590893
$765$	−7.09977e14	−0.0979730
$766$	1.05629e15	0.144719
$767$	−7.24529e14	−0.0985557
$768$	−2.47225e15	−0.333891
$769$	−7.46048e15	−1.00040	−0.500198	−	0.865911i	$-0.666739\pi$
$769$	−7.46048e15	−1.00040	−0.500198	+	0.865911i	$0.666739\pi$
$770$	1.51893e14	0.0202227
$771$	4.86679e15	0.643345
$772$	−8.56025e15	−1.12355
$773$	−6.32191e15	−0.823874	−0.411937	−	0.911212i	$-0.635148\pi$
$773$	−6.32191e15	−0.823874	−0.411937	+	0.911212i	$0.635148\pi$
$774$	7.10531e14	0.0919407
$775$	−5.15225e15	−0.661969
$776$	−7.35995e14	−0.0938935
$777$	−8.05045e13	−0.0101978
$778$	−2.75214e15	−0.346165
$779$	7.65475e15	0.956038
$780$	4.32378e15	0.536220
$781$	−4.63636e14	−0.0570948
$782$	1.02163e14	0.0124927
$783$	−8.97475e13	−0.0108976
$784$	−7.17311e15	−0.864906
$785$	3.85051e15	0.461037
$786$	1.24656e15	0.148214
$787$	3.28483e15	0.387839	0.193920	−	0.981017i	$-0.437880\pi$
$787$	3.28483e15	0.387839	0.193920	+	0.981017i	$0.437880\pi$
$788$	3.47510e15	0.407449
$789$	−3.04590e15	−0.354643
$790$	2.58783e15	0.299218
$791$	4.12099e13	0.00473185
$792$	2.06638e15	0.235625
$793$	8.59544e15	0.973342
$794$	−1.14666e15	−0.128951
$795$	6.78970e15	0.758283
$796$	−1.32301e16	−1.46738
$797$	−1.22059e16	−1.34446	−0.672232	−	0.740341i	$-0.734664\pi$
$797$	−1.22059e16	−1.34446	−0.672232	+	0.740341i	$0.734664\pi$
$798$	−6.45624e13	−0.00706259
$799$	2.57337e15	0.279573
$800$	3.61745e15	0.390308
$801$	−1.70917e15	−0.183150
$802$	7.19134e14	0.0765333
$803$	−1.07880e16	−1.14026
$804$	2.26669e15	0.237949
$805$	−1.37843e14	−0.0143717
$806$	1.57992e15	0.163603
$807$	−7.15294e15	−0.735665
$808$	−2.41962e15	−0.247164
$809$	1.51655e16	1.53865	0.769324	−	0.638859i	$-0.220593\pi$
$809$	1.51655e16	1.53865	0.769324	+	0.638859i	$0.220593\pi$
$810$	−3.01084e14	−0.0303403
$811$	1.41376e15	0.141502	0.0707509	−	0.997494i	$-0.477460\pi$
$811$	1.41376e15	0.141502	0.0707509	+	0.997494i	$0.477460\pi$
$812$	−2.36723e13	−0.00235333
$813$	−1.37149e14	−0.0135424
$814$	−1.49621e15	−0.146743
$815$	−1.36063e16	−1.32548
$816$	−1.18274e15	−0.114444
$817$	1.78585e16	1.71642
$818$	2.74472e15	0.262033
$819$	−1.15821e14	−0.0109831
$820$	9.41581e15	0.886914
$821$	2.57332e15	0.240772	0.120386	−	0.992727i	$-0.461587\pi$
$821$	2.57332e15	0.240772	0.120386	+	0.992727i	$0.461587\pi$
$822$	4.23917e14	0.0393990
$823$	−1.91485e16	−1.76781	−0.883906	−	0.467665i	$-0.845095\pi$
$823$	−1.91485e16	−1.76781	−0.883906	+	0.467665i	$0.845095\pi$
$824$	5.69198e15	0.521992
$825$	7.01974e15	0.639476
$826$	1.33076e13	0.00120423
$827$	−1.88291e16	−1.69258	−0.846289	−	0.532724i	$-0.821168\pi$
$827$	−1.88291e16	−1.69258	−0.846289	+	0.532724i	$0.821168\pi$
$828$	−9.15959e14	−0.0817917
$829$	6.78530e15	0.601892	0.300946	−	0.953641i	$-0.402698\pi$
$829$	6.78530e15	0.601892	0.300946	+	0.953641i	$0.402698\pi$
$830$	−4.70031e15	−0.414188
$831$	1.39165e15	0.121822
$832$	6.43432e15	0.559531
$833$	−2.64292e15	−0.228316
$834$	1.56367e15	0.134194
$835$	−1.80289e15	−0.153707
$836$	2.53682e16	2.14859
$837$	2.32593e15	0.195707
$838$	−1.00783e14	−0.00842456
$839$	4.04318e15	0.335762	0.167881	−	0.985807i	$-0.446308\pi$
$839$	4.04318e15	0.335762	0.167881	+	0.985807i	$0.446308\pi$
$840$	−1.62588e14	−0.0134138
$841$	−1.21614e16	−0.996794
$842$	−1.68261e15	−0.137015
$843$	−7.49066e15	−0.605994
$844$	−5.45675e15	−0.438581
$845$	6.86951e15	0.548547
$846$	1.09131e15	0.0865783
$847$	1.04651e15	0.0824867
$848$	1.13108e16	0.885763
$849$	1.11284e15	0.0865849
$850$	4.09364e14	0.0316450
$851$	1.35781e15	0.104286
$852$	2.42408e14	0.0184982
$853$	−1.59369e16	−1.20833	−0.604164	−	0.796860i	$-0.706493\pi$
$853$	−1.59369e16	−1.20833	−0.604164	+	0.796860i	$0.706493\pi$
$854$	−1.57874e14	−0.0118930
$855$	−7.56745e15	−0.566416
$856$	−3.21381e15	−0.239009
$857$	−2.96888e15	−0.219381	−0.109690	−	0.993966i	$-0.534986\pi$
$857$	−2.96888e15	−0.219381	−0.109690	+	0.993966i	$0.534986\pi$
$858$	−2.15258e15	−0.158044
$859$	1.55831e16	1.13682	0.568411	−	0.822745i	$-0.307558\pi$
$859$	1.55831e16	1.13682	0.568411	+	0.822745i	$0.307558\pi$
$860$	2.19670e16	1.59232
$861$	−2.52221e14	−0.0181662
$862$	−2.88819e15	−0.206698
$863$	4.27803e15	0.304218	0.152109	−	0.988364i	$-0.451394\pi$
$863$	4.27803e15	0.304218	0.152109	+	0.988364i	$0.451394\pi$
$864$	−1.63306e15	−0.115392
$865$	8.67558e13	0.00609130
$866$	2.70179e15	0.188497
$867$	7.89229e15	0.547140
$868$	6.13501e14	0.0422626
$869$	2.72376e16	1.86449
$870$	1.31242e14	0.00892723
$871$	−4.83418e15	−0.326756
$872$	6.36520e15	0.427535
$873$	1.12872e15	0.0753369
$874$	1.08893e15	0.0722249
$875$	2.96166e14	0.0195205
$876$	5.64039e15	0.369434
$877$	−1.12838e16	−0.734441	−0.367221	−	0.930134i	$-0.619691\pi$
$877$	−1.12838e16	−0.734441	−0.367221	+	0.930134i	$0.619691\pi$
$878$	−5.59565e15	−0.361935
$879$	5.55469e15	0.357043
$880$	2.96586e16	1.89451
$881$	−5.86659e15	−0.372407	−0.186204	−	0.982511i	$-0.559618\pi$
$881$	−5.86659e15	−0.372407	−0.186204	+	0.982511i	$0.559618\pi$
$882$	−1.12080e15	−0.0707051
$883$	1.09029e16	0.683530	0.341765	−	0.939785i	$-0.388975\pi$
$883$	1.09029e16	0.683530	0.341765	+	0.939785i	$0.388975\pi$
$884$	2.65390e15	0.165347
$885$	1.55980e15	0.0965785
$886$	−5.19448e14	−0.0319636
$887$	−2.39091e16	−1.46212	−0.731062	−	0.682311i	$-0.760975\pi$
$887$	−2.39091e16	−1.46212	−0.731062	+	0.682311i	$0.760975\pi$
$888$	1.60156e15	0.0973356
$889$	−1.04202e14	−0.00629382
$890$	2.49941e15	0.150035
$891$	−3.16899e15	−0.189057
$892$	2.87437e16	1.70426
$893$	2.74288e16	1.61631
$894$	2.73697e15	0.160293
$895$	−1.57568e16	−0.917154
$896$	−5.69300e14	−0.0329342
$897$	1.95347e15	0.112318
$898$	−6.02385e15	−0.344234
$899$	−1.01387e15	−0.0575842
$900$	−3.67021e15	−0.207184
$901$	4.16746e15	0.233822
$902$	−4.68763e15	−0.261407
$903$	−5.88430e14	−0.0326146
$904$	−8.19831e14	−0.0451646
$905$	−2.91971e16	−1.59872
$906$	1.49574e15	0.0814048
$907$	−5.18038e15	−0.280234	−0.140117	−	0.990135i	$-0.544748\pi$
$907$	−5.18038e15	−0.280234	−0.140117	+	0.990135i	$0.544748\pi$
$908$	−1.39349e16	−0.749258
$909$	3.71072e15	0.198316
$910$	1.69370e14	0.00899725
$911$	−3.53724e16	−1.86773	−0.933863	−	0.357631i	$-0.883584\pi$
$911$	−3.53724e16	−1.86773	−0.933863	+	0.357631i	$0.883584\pi$
$912$	−1.26065e16	−0.661640
$913$	−4.94720e16	−2.58090
$914$	1.63874e15	0.0849777
$915$	−1.85046e16	−0.953816
$916$	−8.01412e15	−0.410611
$917$	−1.03234e15	−0.0525766
$918$	−1.84803e14	−0.00935565
$919$	−2.34017e16	−1.17764	−0.588820	−	0.808264i	$-0.700407\pi$
$919$	−2.34017e16	−1.17764	−0.588820	+	0.808264i	$0.700407\pi$
$920$	2.74226e15	0.137175
$921$	−4.06231e15	−0.201997
$922$	3.25623e15	0.160951
$923$	−5.16985e14	−0.0254020
$924$	−8.35871e14	−0.0408266
$925$	5.44070e15	0.264165
$926$	2.76380e15	0.133397
$927$	−8.72921e15	−0.418829
$928$	7.11847e14	0.0339526
$929$	−9.47653e15	−0.449328	−0.224664	−	0.974436i	$-0.572128\pi$
$929$	−9.47653e15	−0.449328	−0.224664	+	0.974436i	$0.572128\pi$
$930$	−3.40132e15	−0.160321
$931$	−2.81702e16	−1.31998
$932$	9.61933e14	0.0448082
$933$	4.60267e15	0.213138
$934$	7.45159e15	0.343037
$935$	1.09277e16	0.500108
$936$	2.30414e15	0.104832
$937$	−1.38527e16	−0.626566	−0.313283	−	0.949660i	$-0.601429\pi$
$937$	−1.38527e16	−0.626566	−0.313283	+	0.949660i	$0.601429\pi$
$938$	8.87904e13	0.00399255
$939$	2.85368e15	0.127569
$940$	3.37391e16	1.49945
$941$	−4.29714e16	−1.89862	−0.949308	−	0.314348i	$-0.898214\pi$
$941$	−4.29714e16	−1.89862	−0.949308	+	0.314348i	$0.898214\pi$
$942$	1.00227e15	0.0440254
$943$	4.25404e15	0.185775
$944$	2.59844e15	0.112815
$945$	2.49344e14	0.0107628
$946$	−1.09362e16	−0.469316
$947$	4.38038e15	0.186890	0.0934452	−	0.995624i	$-0.470212\pi$
$947$	4.38038e15	0.186890	0.0934452	+	0.995624i	$0.470212\pi$
$948$	−1.42409e16	−0.604077
$949$	−1.20293e16	−0.507313
$950$	4.36329e15	0.182951
$951$	−2.09676e16	−0.874088
$952$	−9.97950e13	−0.00413624
$953$	−3.70592e16	−1.52716	−0.763580	−	0.645713i	$-0.776560\pi$
$953$	−3.70592e16	−1.52716	−0.763580	+	0.645713i	$0.776560\pi$
$954$	1.76732e15	0.0724101
$955$	−1.95194e16	−0.795147
$956$	1.20236e16	0.486984
$957$	1.38136e15	0.0556275
$958$	−6.75496e14	−0.0270466
$959$	−3.51068e14	−0.0139762
$960$	−1.38521e16	−0.548307
$961$	8.67298e14	0.0341342
$962$	−1.66837e15	−0.0652874
$963$	4.92869e15	0.191773
$964$	−9.74468e15	−0.377002
$965$	−3.93034e16	−1.51192
$966$	−3.58798e13	−0.00137238
$967$	−3.18540e15	−0.121148	−0.0605742	−	0.998164i	$-0.519293\pi$
$967$	−3.18540e15	−0.121148	−0.0605742	+	0.998164i	$0.519293\pi$
$968$	−2.08193e16	−0.787319
$969$	−4.64483e15	−0.174658
$970$	−1.65058e15	−0.0617152
$971$	−1.07743e16	−0.400575	−0.200287	−	0.979737i	$-0.564188\pi$
$971$	−1.07743e16	−0.400575	−0.200287	+	0.979737i	$0.564188\pi$
$972$	1.65688e15	0.0612528
$973$	−1.29496e15	−0.0476033
$974$	−4.85705e15	−0.177541
$975$	7.82747e15	0.284509
$976$	−3.08265e16	−1.11417
$977$	5.03107e16	1.80817	0.904087	−	0.427348i	$-0.140552\pi$
$977$	5.03107e16	1.80817	0.904087	+	0.427348i	$0.140552\pi$
$978$	−3.54164e15	−0.126573
$979$	2.63069e16	0.934899
$980$	−3.46510e16	−1.22454
$981$	−9.76166e15	−0.343039
$982$	6.48381e15	0.226578
$983$	1.83781e16	0.638639	0.319319	−	0.947647i	$-0.396546\pi$
$983$	1.83781e16	0.638639	0.319319	+	0.947647i	$0.396546\pi$
$984$	5.01769e15	0.173393
$985$	1.59555e16	0.548292
$986$	8.05552e13	0.00275277
$987$	−9.03770e14	−0.0307124
$988$	2.82872e16	0.955930
$989$	9.92463e15	0.333530
$990$	4.63416e15	0.154874
$991$	−2.39571e16	−0.796214	−0.398107	−	0.917339i	$-0.630333\pi$
$991$	−2.39571e16	−0.796214	−0.398107	+	0.917339i	$0.630333\pi$
$992$	−1.84485e16	−0.609742
$993$	−7.11155e15	−0.233745
$994$	9.49557e12	0.000310382 0
$995$	−6.07446e16	−1.97461
$996$	2.58660e16	0.836186
$997$	5.69539e16	1.83105	0.915526	−	0.402260i	$-0.131775\pi$
$997$	5.69539e16	1.83105	0.915526	+	0.402260i	$0.131775\pi$
$998$	−2.80244e14	−0.00896023
$999$	−2.45615e15	−0.0780988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.14	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.14	✓	26	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)

\(f(q)\)	\(=\)	\(q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+9.61747 q^{2} -243.000 q^{3} -1955.50 q^{4} -8978.47 q^{5} -2337.04 q^{6} +1935.43 q^{7} -38503.6 q^{8} +59049.0 q^{9} -86350.1 q^{10} -908857. q^{11} +475188. q^{12} -1.01344e6 q^{13} +18614.0 q^{14} +2.18177e6 q^{15} +3.63457e6 q^{16} +1.33915e6 q^{17} +567902. q^{18} +1.42736e7 q^{19} +1.75574e7 q^{20} -470311. q^{21} -8.74091e6 q^{22} +7.93240e6 q^{23} +9.35637e6 q^{24} +3.17848e7 q^{25} -9.74668e6 q^{26} -1.43489e7 q^{27} -3.78475e6 q^{28} +6.25466e6 q^{29} +2.09831e7 q^{30} -1.62098e8 q^{31} +1.13811e8 q^{32} +2.20852e8 q^{33} +1.28792e7 q^{34} -1.73772e7 q^{35} -1.15471e8 q^{36} +1.71173e8 q^{37} +1.37276e8 q^{38} +2.46265e8 q^{39} +3.45703e8 q^{40} +5.36286e8 q^{41} -4.52320e6 q^{42} +1.25115e9 q^{43} +1.77727e9 q^{44} -5.30170e8 q^{45} +7.62896e7 q^{46} +1.92164e9 q^{47} -8.83200e8 q^{48} -1.97358e9 q^{49} +3.05689e8 q^{50} -3.25413e8 q^{51} +1.98178e9 q^{52} +3.11202e9 q^{53} -1.38000e8 q^{54} +8.16015e9 q^{55} -7.45211e7 q^{56} -3.46849e9 q^{57} +6.01540e7 q^{58} +7.14924e8 q^{59} -4.26646e9 q^{60} -8.48149e9 q^{61} -1.55897e9 q^{62} +1.14285e8 q^{63} -6.34902e9 q^{64} +9.09910e9 q^{65} +2.12404e9 q^{66} +4.77009e9 q^{67} -2.61871e9 q^{68} -1.92757e9 q^{69} -1.67125e8 q^{70} +5.10131e8 q^{71} -2.27360e9 q^{72} +1.18698e10 q^{73} +1.64625e9 q^{74} -7.72370e9 q^{75} -2.79122e10 q^{76} -1.75903e9 q^{77} +2.36844e9 q^{78} -2.99691e10 q^{79} -3.26328e10 q^{80} +3.48678e9 q^{81} +5.15771e9 q^{82} +5.44332e10 q^{83} +9.19694e8 q^{84} -1.20235e10 q^{85} +1.20329e10 q^{86} -1.51988e9 q^{87} +3.49943e10 q^{88} -2.89450e10 q^{89} -5.09889e9 q^{90} -1.96144e9 q^{91} -1.55118e10 q^{92} +3.93898e10 q^{93} +1.84814e10 q^{94} -1.28155e11 q^{95} -2.76560e10 q^{96} +1.91150e10 q^{97} -1.89808e10 q^{98} -5.36671e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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