LMFDB - Embedded newform 177.12.a.a.1.4

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			1.4
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)

$f(q)$	$=$	$q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +842068. q^{10} +995461. q^{11} -631686. q^{12} -2.04259e6 q^{13} -3.20647e6 q^{14} +3.00153e6 q^{15} -2.76058e6 q^{16} +4.93058e6 q^{17} -4.02554e6 q^{18} -7.46358e6 q^{19} -3.21093e7 q^{20} -1.14294e7 q^{21} -6.78634e7 q^{22} -6.09728e7 q^{23} +9.13666e6 q^{24} +1.03743e8 q^{25} +1.39249e8 q^{26} -1.43489e7 q^{27} +1.22267e8 q^{28} -1.21948e7 q^{29} -2.04623e8 q^{30} -9.81146e7 q^{31} +2.65200e8 q^{32} -2.41897e8 q^{33} -3.36132e8 q^{34} -5.80968e8 q^{35} +1.53500e8 q^{36} +5.10983e8 q^{37} +5.08813e8 q^{38} +4.96349e8 q^{39} +4.64427e8 q^{40} +9.11904e8 q^{41} +7.79172e8 q^{42} -5.23146e8 q^{43} +2.58773e9 q^{44} -7.29371e8 q^{45} +4.15669e9 q^{46} -2.51018e9 q^{47} +6.70821e8 q^{48} +2.34909e8 q^{49} -7.07245e9 q^{50} -1.19813e9 q^{51} -5.30977e9 q^{52} +2.99867e9 q^{53} +9.78205e8 q^{54} -1.22959e10 q^{55} -1.76847e9 q^{56} +1.81365e9 q^{57} +8.31353e8 q^{58} +7.14924e8 q^{59} +7.80257e9 q^{60} -5.25954e9 q^{61} +6.68875e9 q^{62} +2.77733e9 q^{63} -1.24258e10 q^{64} +2.52300e10 q^{65} +1.64908e10 q^{66} +4.16427e9 q^{67} +1.28172e10 q^{68} +1.48164e10 q^{69} +3.96062e10 q^{70} -2.59373e9 q^{71} -2.22021e9 q^{72} -5.20691e9 q^{73} -3.48351e10 q^{74} -2.52095e10 q^{75} -1.94018e10 q^{76} +4.68209e10 q^{77} -3.38375e10 q^{78} +1.63649e10 q^{79} +3.40986e10 q^{80} +3.48678e9 q^{81} -6.21671e10 q^{82} +5.97866e10 q^{83} -2.97110e10 q^{84} -6.09024e10 q^{85} +3.56644e10 q^{86} +2.96333e9 q^{87} -3.74288e10 q^{88} +8.53534e10 q^{89} +4.97233e10 q^{90} -9.60719e10 q^{91} -1.58501e11 q^{92} +2.38419e10 q^{93} +1.71126e11 q^{94} +9.21900e10 q^{95} -6.44437e10 q^{96} +9.77581e10 q^{97} -1.60144e10 q^{98} +5.87810e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−68.1728	−1.50642	−0.753210	−	0.657780i	$-0.771496\pi$
$2$	−68.1728	−1.50642	−0.753210	+	0.657780i	$0.771496\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2599.53	1.26930
$5$	−12352.0	−1.76767	−0.883835	−	0.467799i	$-0.845047\pi$
$5$	−12352.0	−1.76767	−0.883835	+	0.467799i	$0.845047\pi$
$6$	16566.0	0.869732
$7$	47034.4	1.05773	0.528867	−	0.848705i	$-0.322617\pi$
$7$	47034.4	1.05773	0.528867	+	0.848705i	$0.322617\pi$
$8$	−37599.4	−0.405682
$9$	59049.0	0.333333
$10$	842068.	2.66285
$11$	995461.	1.86365	0.931825	−	0.362907i	$-0.118216\pi$
$11$	995461.	1.86365	0.931825	+	0.362907i	$0.118216\pi$
$12$	−631686.	−0.732832
$13$	−2.04259e6	−1.52578	−0.762891	−	0.646527i	$-0.776221\pi$
$13$	−2.04259e6	−1.52578	−0.762891	+	0.646527i	$0.776221\pi$
$14$	−3.20647e6	−1.59339
$15$	3.00153e6	1.02056
$16$	−2.76058e6	−0.658174
$17$	4.93058e6	0.842227	0.421113	−	0.907008i	$-0.361639\pi$
$17$	4.93058e6	0.842227	0.421113	+	0.907008i	$0.361639\pi$
$18$	−4.02554e6	−0.502140
$19$	−7.46358e6	−0.691517	−0.345758	−	0.938324i	$-0.612378\pi$
$19$	−7.46358e6	−0.691517	−0.345758	+	0.938324i	$0.612378\pi$
$20$	−3.21093e7	−2.24371
$21$	−1.14294e7	−0.610683
$22$	−6.78634e7	−2.80744
$23$	−6.09728e7	−1.97530	−0.987650	−	0.156675i	$-0.949923\pi$
$23$	−6.09728e7	−1.97530	−0.987650	+	0.156675i	$0.949923\pi$
$24$	9.13666e6	0.234221
$25$	1.03743e8	2.12466
$26$	1.39249e8	2.29847
$27$	−1.43489e7	−0.192450
$28$	1.22267e8	1.34258
$29$	−1.21948e7	−0.110404	−0.0552021	−	0.998475i	$-0.517580\pi$
$29$	−1.21948e7	−0.110404	−0.0552021	+	0.998475i	$0.517580\pi$
$30$	−2.04623e8	−1.53740
$31$	−9.81146e7	−0.615523	−0.307762	−	0.951463i	$-0.599580\pi$
$31$	−9.81146e7	−0.615523	−0.307762	+	0.951463i	$0.599580\pi$
$32$	2.65200e8	1.39717
$33$	−2.41897e8	−1.07598
$34$	−3.36132e8	−1.26875
$35$	−5.80968e8	−1.86972
$36$	1.53500e8	0.423101
$37$	5.10983e8	1.21143	0.605713	−	0.795683i	$-0.292888\pi$
$37$	5.10983e8	1.21143	0.605713	+	0.795683i	$0.292888\pi$
$38$	5.08813e8	1.04171
$39$	4.96349e8	0.880910
$40$	4.64427e8	0.717113
$41$	9.11904e8	1.22924	0.614622	−	0.788822i	$-0.289309\pi$
$41$	9.11904e8	1.22924	0.614622	+	0.788822i	$0.289309\pi$
$42$	7.79172e8	0.919945
$43$	−5.23146e8	−0.542684	−0.271342	−	0.962483i	$-0.587467\pi$
$43$	−5.23146e8	−0.542684	−0.271342	+	0.962483i	$0.587467\pi$
$44$	2.58773e9	2.36554
$45$	−7.29371e8	−0.589223
$46$	4.15669e9	2.97563
$47$	−2.51018e9	−1.59649	−0.798246	−	0.602331i	$-0.794239\pi$
$47$	−2.51018e9	−1.59649	−0.798246	+	0.602331i	$0.794239\pi$
$48$	6.70821e8	0.379997
$49$	2.34909e8	0.118801
$50$	−7.07245e9	−3.20063
$51$	−1.19813e9	−0.486260
$52$	−5.30977e9	−1.93668
$53$	2.99867e9	0.984945	0.492472	−	0.870328i	$-0.336093\pi$
$53$	2.99867e9	0.984945	0.492472	+	0.870328i	$0.336093\pi$
$54$	9.78205e8	0.289911
$55$	−1.22959e10	−3.29432
$56$	−1.76847e9	−0.429104
$57$	1.81365e9	0.399247
$58$	8.31353e8	0.166315
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	7.80257e9	1.29541
$61$	−5.25954e9	−0.797322	−0.398661	−	0.917098i	$-0.630525\pi$
$61$	−5.25954e9	−0.797322	−0.398661	+	0.917098i	$0.630525\pi$
$62$	6.68875e9	0.927237
$63$	2.77733e9	0.352578
$64$	−1.24258e10	−1.44655
$65$	2.52300e10	2.69708
$66$	1.64908e10	1.62088
$67$	4.16427e9	0.376814	0.188407	−	0.982091i	$-0.439668\pi$
$67$	4.16427e9	0.376814	0.188407	+	0.982091i	$0.439668\pi$
$68$	1.28172e10	1.06904
$69$	1.48164e10	1.14044
$70$	3.96062e10	2.81659
$71$	−2.59373e9	−0.170610	−0.0853050	−	0.996355i	$-0.527186\pi$
$71$	−2.59373e9	−0.170610	−0.0853050	+	0.996355i	$0.527186\pi$
$72$	−2.22021e9	−0.135227
$73$	−5.20691e9	−0.293971	−0.146985	−	0.989139i	$-0.546957\pi$
$73$	−5.20691e9	−0.293971	−0.146985	+	0.989139i	$0.546957\pi$
$74$	−3.48351e10	−1.82492
$75$	−2.52095e10	−1.22667
$76$	−1.94018e10	−0.877744
$77$	4.68209e10	1.97125
$78$	−3.38375e10	−1.32702
$79$	1.63649e10	0.598364	0.299182	−	0.954196i	$-0.403286\pi$
$79$	1.63649e10	0.598364	0.299182	+	0.954196i	$0.403286\pi$
$80$	3.40986e10	1.16343
$81$	3.48678e9	0.111111
$82$	−6.21671e10	−1.85176
$83$	5.97866e10	1.66600	0.832999	−	0.553274i	$-0.186622\pi$
$83$	5.97866e10	1.66600	0.832999	+	0.553274i	$0.186622\pi$
$84$	−2.97110e10	−0.775141
$85$	−6.09024e10	−1.48878
$86$	3.56644e10	0.817510
$87$	2.96333e9	0.0637419
$88$	−3.74288e10	−0.756050
$89$	8.53534e10	1.62023	0.810113	−	0.586273i	$-0.199405\pi$
$89$	8.53534e10	1.62023	0.810113	+	0.586273i	$0.199405\pi$
$90$	4.97233e10	0.887618
$91$	−9.60719e10	−1.61387
$92$	−1.58501e11	−2.50725
$93$	2.38419e10	0.355373
$94$	1.71126e11	2.40499
$95$	9.21900e10	1.22237
$96$	−6.44437e10	−0.806656
$97$	9.77581e10	1.15587	0.577934	−	0.816083i	$-0.303859\pi$
$97$	9.77581e10	1.15587	0.577934	+	0.816083i	$0.303859\pi$
$98$	−1.60144e10	−0.178965
$99$	5.87810e10	0.621217
$100$	2.69683e11	2.69683
$101$	7.15210e10	0.677121	0.338560	−	0.940945i	$-0.390060\pi$
$101$	7.15210e10	0.677121	0.338560	+	0.940945i	$0.390060\pi$
$102$	8.16800e10	0.732512
$103$	−2.26703e11	−1.92687	−0.963436	−	0.267940i	$-0.913657\pi$
$103$	−2.26703e11	−1.92687	−0.963436	+	0.267940i	$0.913657\pi$
$104$	7.68001e10	0.618983
$105$	1.41175e11	1.07949
$106$	−2.04428e11	−1.48374
$107$	6.09715e10	0.420258	0.210129	−	0.977674i	$-0.432612\pi$
$107$	6.09715e10	0.420258	0.210129	+	0.977674i	$0.432612\pi$
$108$	−3.73004e10	−0.244277
$109$	1.22518e10	0.0762698	0.0381349	−	0.999273i	$-0.487858\pi$
$109$	1.22518e10	0.0762698	0.0381349	+	0.999273i	$0.487858\pi$
$110$	8.38246e11	4.96263
$111$	−1.24169e11	−0.699417
$112$	−1.29842e11	−0.696173
$113$	5.27228e10	0.269195	0.134598	−	0.990900i	$-0.457026\pi$
$113$	5.27228e10	0.269195	0.134598	+	0.990900i	$0.457026\pi$
$114$	−1.23642e11	−0.601434
$115$	7.53134e11	3.49168
$116$	−3.17007e10	−0.140136
$117$	−1.20613e11	−0.508594
$118$	−4.87384e10	−0.196119
$119$	2.31907e11	0.890852
$120$	−1.12856e11	−0.414025
$121$	7.05631e11	2.47319
$122$	3.58557e11	1.20110
$123$	−2.21593e11	−0.709704
$124$	−2.55052e11	−0.781285
$125$	−6.78307e11	−1.98802
$126$	−1.89339e11	−0.531131
$127$	−6.29747e11	−1.69140	−0.845699	−	0.533660i	$-0.820816\pi$
$127$	−6.29747e11	−1.69140	−0.845699	+	0.533660i	$0.820816\pi$
$128$	3.03970e11	0.781943
$129$	1.27125e11	0.313319
$130$	−1.72000e12	−4.06293
$131$	2.40547e11	0.544763	0.272381	−	0.962189i	$-0.412189\pi$
$131$	2.40547e11	0.544763	0.272381	+	0.962189i	$0.412189\pi$
$132$	−6.28819e11	−1.36574
$133$	−3.51045e11	−0.731441
$134$	−2.83890e11	−0.567641
$135$	1.77237e11	0.340188
$136$	−1.85387e11	−0.341677
$137$	−5.62152e11	−0.995154	−0.497577	−	0.867420i	$-0.665777\pi$
$137$	−5.62152e11	−0.995154	−0.497577	+	0.867420i	$0.665777\pi$
$138$	−1.01008e12	−1.71798
$139$	−7.08735e11	−1.15852	−0.579259	−	0.815144i	$-0.696658\pi$
$139$	−7.08735e11	−1.15852	−0.579259	+	0.815144i	$0.696658\pi$
$140$	−1.51024e12	−2.37325
$141$	6.09974e11	0.921735
$142$	1.76822e11	0.257010
$143$	−2.03332e12	−2.84352
$144$	−1.63010e11	−0.219391
$145$	1.50630e11	0.195158
$146$	3.54970e11	0.442844
$147$	−5.70829e10	−0.0685900
$148$	1.32832e12	1.53767
$149$	1.07853e12	1.20312	0.601558	−	0.798829i	$-0.294547\pi$
$149$	1.07853e12	1.20312	0.601558	+	0.798829i	$0.294547\pi$
$150$	1.71861e12	1.84788
$151$	−1.63944e11	−0.169950	−0.0849751	−	0.996383i	$-0.527081\pi$
$151$	−1.63944e11	−0.169950	−0.0849751	+	0.996383i	$0.527081\pi$
$152$	2.80626e11	0.280536
$153$	2.91146e11	0.280742
$154$	−3.19191e12	−2.96953
$155$	1.21191e12	1.08804
$156$	1.29027e12	1.11814
$157$	−3.34239e11	−0.279646	−0.139823	−	0.990177i	$-0.544653\pi$
$157$	−3.34239e11	−0.279646	−0.139823	+	0.990177i	$0.544653\pi$
$158$	−1.11564e12	−0.901388
$159$	−7.28677e11	−0.568658
$160$	−3.27574e12	−2.46973
$161$	−2.86782e12	−2.08934
$162$	−2.37704e11	−0.167380
$163$	−1.10253e12	−0.750511	−0.375256	−	0.926921i	$-0.622445\pi$
$163$	−1.10253e12	−0.750511	−0.375256	+	0.926921i	$0.622445\pi$
$164$	2.37052e12	1.56028
$165$	2.98791e12	1.90198
$166$	−4.07582e12	−2.50969
$167$	−4.93688e11	−0.294112	−0.147056	−	0.989128i	$-0.546980\pi$
$167$	−4.93688e11	−0.294112	−0.147056	+	0.989128i	$0.546980\pi$
$168$	4.29737e11	0.247743
$169$	2.38001e12	1.32801
$170$	4.15189e12	2.24273
$171$	−4.40717e11	−0.230506
$172$	−1.35994e12	−0.688830
$173$	−1.44961e11	−0.0711210	−0.0355605	−	0.999368i	$-0.511322\pi$
$173$	−1.44961e11	−0.0711210	−0.0355605	+	0.999368i	$0.511322\pi$
$174$	−2.02019e11	−0.0960221
$175$	4.87949e12	2.24732
$176$	−2.74805e12	−1.22661
$177$	−1.73727e11	−0.0751646
$178$	−5.81878e12	−2.44074
$179$	4.44571e12	1.80821	0.904106	−	0.427309i	$-0.140538\pi$
$179$	4.44571e12	1.80821	0.904106	+	0.427309i	$0.140538\pi$
$180$	−1.89602e12	−0.747902
$181$	−1.76207e12	−0.674205	−0.337102	−	0.941468i	$-0.609447\pi$
$181$	−1.76207e12	−0.674205	−0.337102	+	0.941468i	$0.609447\pi$
$182$	6.54949e12	2.43117
$183$	1.27807e12	0.460334
$184$	2.29254e12	0.801345
$185$	−6.31165e12	−2.14140
$186$	−1.62537e12	−0.535340
$187$	4.90820e12	1.56962
$188$	−6.52529e12	−2.02643
$189$	−6.74892e11	−0.203561
$190$	−6.28485e12	−1.84141
$191$	2.15378e12	0.613080	0.306540	−	0.951858i	$-0.400829\pi$
$191$	2.15378e12	0.613080	0.306540	+	0.951858i	$0.400829\pi$
$192$	3.01946e12	0.835166
$193$	6.89616e12	1.85371	0.926855	−	0.375418i	$-0.122501\pi$
$193$	6.89616e12	1.85371	0.926855	+	0.375418i	$0.122501\pi$
$194$	−6.66445e12	−1.74122
$195$	−6.13089e12	−1.55716
$196$	6.10653e11	0.150795
$197$	3.06746e12	0.736571	0.368285	−	0.929713i	$-0.379945\pi$
$197$	3.06746e12	0.736571	0.368285	+	0.929713i	$0.379945\pi$
$198$	−4.00726e12	−0.935814
$199$	3.48181e12	0.790885	0.395442	−	0.918491i	$-0.370591\pi$
$199$	3.48181e12	0.790885	0.395442	+	0.918491i	$0.370591\pi$
$200$	−3.90068e12	−0.861936
$201$	−1.01192e12	−0.217554
$202$	−4.87579e12	−1.02003
$203$	−5.73575e11	−0.116778
$204$	−3.11458e12	−0.617211
$205$	−1.12638e13	−2.17290
$206$	1.54550e13	2.90268
$207$	−3.60038e12	−0.658433
$208$	5.63873e12	1.00423
$209$	−7.42971e12	−1.28875
$210$	−9.62430e12	−1.62616
$211$	−4.77189e12	−0.785483	−0.392741	−	0.919649i	$-0.628473\pi$
$211$	−4.77189e12	−0.785483	−0.392741	+	0.919649i	$0.628473\pi$
$212$	7.79514e12	1.25019
$213$	6.30278e11	0.0985018
$214$	−4.15660e12	−0.633086
$215$	6.46189e12	0.959285
$216$	5.39510e11	0.0780736
$217$	−4.61476e12	−0.651060
$218$	−8.35236e11	−0.114894
$219$	1.26528e12	0.169724
$220$	−3.19636e13	−4.18149
$221$	−1.00711e13	−1.28505
$222$	8.46494e12	1.05362
$223$	1.33120e13	1.61647	0.808234	−	0.588862i	$-0.200424\pi$
$223$	1.33120e13	1.61647	0.808234	+	0.588862i	$0.200424\pi$
$224$	1.24735e13	1.47783
$225$	6.12592e12	0.708219
$226$	−3.59426e12	−0.405521
$227$	−6.30597e12	−0.694400	−0.347200	−	0.937791i	$-0.612868\pi$
$227$	−6.30597e12	−0.694400	−0.347200	+	0.937791i	$0.612868\pi$
$228$	4.71464e12	0.506765
$229$	1.17737e12	0.123543	0.0617714	−	0.998090i	$-0.480325\pi$
$229$	1.17737e12	0.123543	0.0617714	+	0.998090i	$0.480325\pi$
$230$	−5.13433e13	−5.25994
$231$	−1.13775e13	−1.13810
$232$	4.58517e11	0.0447890
$233$	5.71269e11	0.0544983	0.0272492	−	0.999629i	$-0.491325\pi$
$233$	5.71269e11	0.0544983	0.0272492	+	0.999629i	$0.491325\pi$
$234$	8.22251e12	0.766156
$235$	3.10057e13	2.82207
$236$	1.85847e12	0.165249
$237$	−3.97668e12	−0.345466
$238$	−1.58098e13	−1.34200
$239$	1.35214e12	0.112159	0.0560793	−	0.998426i	$-0.482140\pi$
$239$	1.35214e12	0.112159	0.0560793	+	0.998426i	$0.482140\pi$
$240$	−8.28597e12	−0.671709
$241$	1.11511e13	0.883533	0.441766	−	0.897130i	$-0.354352\pi$
$241$	1.11511e13	0.883533	0.441766	+	0.897130i	$0.354352\pi$
$242$	−4.81049e13	−3.72567
$243$	−8.47289e11	−0.0641500
$244$	−1.36723e13	−1.01204
$245$	−2.90159e12	−0.210002
$246$	1.51066e13	1.06911
$247$	1.52450e13	1.05510
$248$	3.68905e12	0.249707
$249$	−1.45281e13	−0.961864
$250$	4.62421e13	2.99480
$251$	−2.00365e13	−1.26945	−0.634727	−	0.772737i	$-0.718887\pi$
$251$	−2.00365e13	−1.26945	−0.634727	+	0.772737i	$0.718887\pi$
$252$	7.21977e12	0.447528
$253$	−6.06961e13	−3.68127
$254$	4.29316e13	2.54796
$255$	1.47993e13	0.859547
$256$	4.72552e12	0.268615
$257$	−2.97578e13	−1.65565	−0.827824	−	0.560987i	$-0.810422\pi$
$257$	−2.97578e13	−1.65565	−0.827824	+	0.560987i	$0.810422\pi$
$258$	−8.66644e12	−0.471989
$259$	2.40338e13	1.28137
$260$	6.55861e13	3.42341
$261$	−7.20090e11	−0.0368014
$262$	−1.63987e13	−0.820641
$263$	−1.52340e12	−0.0746549	−0.0373274	−	0.999303i	$-0.511884\pi$
$263$	−1.52340e12	−0.0746549	−0.0373274	+	0.999303i	$0.511884\pi$
$264$	9.09519e12	0.436506
$265$	−3.70395e13	−1.74106
$266$	2.39317e13	1.10186
$267$	−2.07409e13	−0.935438
$268$	1.08251e13	0.478291
$269$	−6.67744e12	−0.289050	−0.144525	−	0.989501i	$-0.546165\pi$
$269$	−6.67744e12	−0.289050	−0.144525	+	0.989501i	$0.546165\pi$
$270$	−1.20828e13	−0.512466
$271$	−4.15385e13	−1.72631	−0.863157	−	0.504935i	$-0.831516\pi$
$271$	−4.15385e13	−1.72631	−0.863157	+	0.504935i	$0.831516\pi$
$272$	−1.36113e13	−0.554332
$273$	2.33455e13	0.931769
$274$	3.83235e13	1.49912
$275$	1.03272e14	3.95962
$276$	3.85157e13	1.44756
$277$	7.23607e12	0.266602	0.133301	−	0.991076i	$-0.457442\pi$
$277$	7.23607e12	0.266602	0.133301	+	0.991076i	$0.457442\pi$
$278$	4.83165e13	1.74521
$279$	−5.79357e12	−0.205174
$280$	2.18440e13	0.758514
$281$	1.29866e13	0.442192	0.221096	−	0.975252i	$-0.429037\pi$
$281$	1.29866e13	0.442192	0.221096	+	0.975252i	$0.429037\pi$
$282$	−4.15836e13	−1.38852
$283$	−2.31296e13	−0.757431	−0.378716	−	0.925513i	$-0.623634\pi$
$283$	−2.31296e13	−0.757431	−0.378716	+	0.925513i	$0.623634\pi$
$284$	−6.74249e12	−0.216556
$285$	−2.24022e13	−0.705737
$286$	1.38617e14	4.28354
$287$	4.28909e13	1.30021
$288$	1.56598e13	0.465723
$289$	−9.96126e12	−0.290654
$290$	−1.02688e13	−0.293990
$291$	−2.37552e13	−0.667341
$292$	−1.35355e13	−0.373138
$293$	−2.67762e13	−0.724398	−0.362199	−	0.932101i	$-0.617974\pi$
$293$	−2.67762e13	−0.724398	−0.362199	+	0.932101i	$0.617974\pi$
$294$	3.89150e12	0.103325
$295$	−8.83072e12	−0.230131
$296$	−1.92127e13	−0.491454
$297$	−1.42838e13	−0.358660
$298$	−7.35263e13	−1.81240
$299$	1.24542e14	3.01388
$300$	−6.55330e13	−1.55702
$301$	−2.46059e13	−0.574015
$302$	1.11765e13	0.256016
$303$	−1.73796e13	−0.390936
$304$	2.06038e13	0.455138
$305$	6.49657e13	1.40940
$306$	−1.98482e13	−0.422916
$307$	4.45166e13	0.931667	0.465834	−	0.884872i	$-0.345755\pi$
$307$	4.45166e13	0.931667	0.465834	+	0.884872i	$0.345755\pi$
$308$	1.21712e14	2.50211
$309$	5.50889e13	1.11248
$310$	−8.26192e13	−1.63905
$311$	−2.12268e13	−0.413717	−0.206858	−	0.978371i	$-0.566324\pi$
$311$	−2.12268e13	−0.413717	−0.206858	+	0.978371i	$0.566324\pi$
$312$	−1.86624e13	−0.357370
$313$	−5.80501e12	−0.109222	−0.0546109	−	0.998508i	$-0.517392\pi$
$313$	−5.80501e12	−0.109222	−0.0546109	+	0.998508i	$0.517392\pi$
$314$	2.27860e13	0.421264
$315$	−3.43056e13	−0.623242
$316$	4.25412e13	0.759505
$317$	6.96405e13	1.22190	0.610951	−	0.791669i	$-0.290787\pi$
$317$	6.96405e13	1.22190	0.610951	+	0.791669i	$0.290787\pi$
$318$	4.96760e13	0.856638
$319$	−1.21394e13	−0.205755
$320$	1.53483e14	2.55702
$321$	−1.48161e13	−0.242636
$322$	1.95507e14	3.14743
$323$	−3.67998e13	−0.582414
$324$	9.06400e12	0.141034
$325$	−2.11904e14	−3.24176
$326$	7.51623e13	1.13059
$327$	−2.97718e12	−0.0440344
$328$	−3.42871e13	−0.498683
$329$	−1.18065e14	−1.68866
$330$	−2.03694e14	−2.86518
$331$	−9.83540e13	−1.36062	−0.680312	−	0.732923i	$-0.738156\pi$
$331$	−9.83540e13	−1.36062	−0.680312	+	0.732923i	$0.738156\pi$
$332$	1.55417e14	2.11466
$333$	3.01730e13	0.403809
$334$	3.36561e13	0.443056
$335$	−5.14369e13	−0.666083
$336$	3.15517e13	0.401936
$337$	6.68819e13	0.838194	0.419097	−	0.907942i	$-0.362347\pi$
$337$	6.68819e13	0.838194	0.419097	+	0.907942i	$0.362347\pi$
$338$	−1.62252e14	−2.00054
$339$	−1.28116e13	−0.155420
$340$	−1.58318e14	−1.88971
$341$	−9.76693e13	−1.14712
$342$	3.00449e13	0.347238
$343$	−8.19536e13	−0.932074
$344$	1.96700e13	0.220157
$345$	−1.83012e14	−2.01592
$346$	9.88240e12	0.107138
$347$	−3.55484e13	−0.379322	−0.189661	−	0.981850i	$-0.560739\pi$
$347$	−3.55484e13	−0.379322	−0.189661	+	0.981850i	$0.560739\pi$
$348$	7.70328e12	0.0809077
$349$	2.76566e13	0.285929	0.142965	−	0.989728i	$-0.454336\pi$
$349$	2.76566e13	0.285929	0.142965	+	0.989728i	$0.454336\pi$
$350$	−3.32649e14	−3.38541
$351$	2.93089e13	0.293637
$352$	2.63997e14	2.60384
$353$	−4.16636e13	−0.404572	−0.202286	−	0.979327i	$-0.564837\pi$
$353$	−4.16636e13	−0.404572	−0.202286	+	0.979327i	$0.564837\pi$
$354$	1.18434e13	0.113229
$355$	3.20377e13	0.301582
$356$	2.21879e14	2.05656
$357$	−5.63534e13	−0.514334
$358$	−3.03076e14	−2.72393
$359$	4.61181e13	0.408180	0.204090	−	0.978952i	$-0.434577\pi$
$359$	4.61181e13	0.408180	0.204090	+	0.978952i	$0.434577\pi$
$360$	2.74239e13	0.239038
$361$	−6.07852e13	−0.521805
$362$	1.20125e14	1.01564
$363$	−1.71468e14	−1.42790
$364$	−2.49742e14	−2.04849
$365$	6.43156e13	0.519644
$366$	−8.71295e13	−0.693456
$367$	3.82762e13	0.300099	0.150050	−	0.988678i	$-0.452057\pi$
$367$	3.82762e13	0.300099	0.150050	+	0.988678i	$0.452057\pi$
$368$	1.68320e14	1.30009
$369$	5.38470e13	0.409748
$370$	4.30283e14	3.22585
$371$	1.41041e14	1.04181
$372$	6.19776e13	0.451075
$373$	7.22448e13	0.518093	0.259047	−	0.965865i	$-0.416592\pi$
$373$	7.22448e13	0.518093	0.259047	+	0.965865i	$0.416592\pi$
$374$	−3.34606e14	−2.36450
$375$	1.64829e14	1.14778
$376$	9.43813e13	0.647669
$377$	2.49089e13	0.168453
$378$	4.60093e13	0.306648
$379$	2.32060e13	0.152435	0.0762176	−	0.997091i	$-0.475716\pi$
$379$	2.32060e13	0.152435	0.0762176	+	0.997091i	$0.475716\pi$
$380$	2.39651e14	1.55156
$381$	1.53029e14	0.976529
$382$	−1.46829e14	−0.923556
$383$	2.17383e14	1.34782	0.673911	−	0.738812i	$-0.264613\pi$
$383$	2.17383e14	1.34782	0.673911	+	0.738812i	$0.264613\pi$
$384$	−7.38646e13	−0.451455
$385$	−5.78331e14	−3.48451
$386$	−4.70130e14	−2.79247
$387$	−3.08913e13	−0.180895
$388$	2.54125e14	1.46715
$389$	1.17108e13	0.0666598	0.0333299	−	0.999444i	$-0.489389\pi$
$389$	1.17108e13	0.0666598	0.0333299	+	0.999444i	$0.489389\pi$
$390$	4.17960e14	2.34574
$391$	−3.00631e14	−1.66365
$392$	−8.83244e12	−0.0481956
$393$	−5.84528e13	−0.314519
$394$	−2.09117e14	−1.10958
$395$	−2.02139e14	−1.05771
$396$	1.52803e14	0.788512
$397$	2.63187e14	1.33942	0.669709	−	0.742624i	$-0.266419\pi$
$397$	2.63187e14	1.33942	0.669709	+	0.742624i	$0.266419\pi$
$398$	−2.37365e14	−1.19141
$399$	8.53040e13	0.422297
$400$	−2.86391e14	−1.39839
$401$	1.45838e14	0.702389	0.351194	−	0.936303i	$-0.385776\pi$
$401$	1.45838e14	0.702389	0.351194	+	0.936303i	$0.385776\pi$
$402$	6.89852e13	0.327727
$403$	2.00408e14	0.939154
$404$	1.85921e14	0.859471
$405$	−4.30687e13	−0.196408
$406$	3.91022e13	0.175917
$407$	5.08664e14	2.25768
$408$	4.50490e13	0.197267
$409$	1.92954e14	0.833634	0.416817	−	0.908991i	$-0.363146\pi$
$409$	1.92954e14	0.833634	0.416817	+	0.908991i	$0.363146\pi$
$410$	7.67886e14	3.27330
$411$	1.36603e14	0.574553
$412$	−5.89322e14	−2.44578
$413$	3.36260e13	0.137705
$414$	2.45448e14	0.991878
$415$	−7.38482e14	−2.94493
$416$	−5.41695e14	−2.13178
$417$	1.72223e14	0.668871
$418$	5.06504e14	1.94139
$419$	−8.40554e13	−0.317972	−0.158986	−	0.987281i	$-0.550822\pi$
$419$	−8.40554e13	−0.317972	−0.158986	+	0.987281i	$0.550822\pi$
$420$	3.66989e14	1.37019
$421$	2.11462e14	0.779256	0.389628	−	0.920972i	$-0.372604\pi$
$421$	2.11462e14	0.779256	0.389628	+	0.920972i	$0.372604\pi$
$422$	3.25313e14	1.18327
$423$	−1.48224e14	−0.532164
$424$	−1.12748e14	−0.399575
$425$	5.11513e14	1.78944
$426$	−4.29678e13	−0.148385
$427$	−2.47379e14	−0.843354
$428$	1.58497e14	0.533435
$429$	4.94096e14	1.64171
$430$	−4.40525e14	−1.44509
$431$	−4.79806e14	−1.55396	−0.776982	−	0.629523i	$-0.783250\pi$
$431$	−4.79806e14	−1.55396	−0.776982	+	0.629523i	$0.783250\pi$
$432$	3.96113e13	0.126666
$433$	−3.62226e14	−1.14366	−0.571829	−	0.820373i	$-0.693766\pi$
$433$	−3.62226e14	−1.14366	−0.571829	+	0.820373i	$0.693766\pi$
$434$	3.14601e14	0.980770
$435$	−3.66030e13	−0.112675
$436$	3.18488e13	0.0968094
$437$	4.55076e14	1.36595
$438$	−8.62576e13	−0.255676
$439$	4.61354e14	1.35045	0.675226	−	0.737611i	$-0.264046\pi$
$439$	4.61354e14	1.35045	0.675226	+	0.737611i	$0.264046\pi$
$440$	4.62319e14	1.33645
$441$	1.38711e13	0.0396005
$442$	6.86578e14	1.93583
$443$	9.15313e13	0.254888	0.127444	−	0.991846i	$-0.459323\pi$
$443$	9.15313e13	0.254888	0.127444	+	0.991846i	$0.459323\pi$
$444$	−3.22781e14	−0.887772
$445$	−1.05428e15	−2.86403
$446$	−9.07517e14	−2.43508
$447$	−2.62083e14	−0.694619
$448$	−5.84439e14	−1.53007
$449$	−2.98662e14	−0.772370	−0.386185	−	0.922421i	$-0.626207\pi$
$449$	−2.98662e14	−0.772370	−0.386185	+	0.922421i	$0.626207\pi$
$450$	−4.17621e14	−1.06688
$451$	9.07765e14	2.29088
$452$	1.37055e14	0.341690
$453$	3.98383e13	0.0981207
$454$	4.29896e14	1.04606
$455$	1.18668e15	2.85279
$456$	−6.81922e13	−0.161968
$457$	−2.09616e14	−0.491911	−0.245955	−	0.969281i	$-0.579102\pi$
$457$	−2.09616e14	−0.491911	−0.245955	+	0.969281i	$0.579102\pi$
$458$	−8.02645e13	−0.186107
$459$	−7.07485e13	−0.162087
$460$	1.95780e15	4.43200
$461$	2.81206e14	0.629028	0.314514	−	0.949253i	$-0.398158\pi$
$461$	2.81206e14	0.629028	0.314514	+	0.949253i	$0.398158\pi$
$462$	7.75635e14	1.71446
$463$	−4.32113e14	−0.943848	−0.471924	−	0.881639i	$-0.656440\pi$
$463$	−4.32113e14	−0.943848	−0.471924	+	0.881639i	$0.656440\pi$
$464$	3.36647e13	0.0726652
$465$	−2.94494e14	−0.628181
$466$	−3.89450e13	−0.0820974
$467$	−5.36221e14	−1.11712	−0.558562	−	0.829463i	$-0.688647\pi$
$467$	−5.36221e14	−1.11712	−0.558562	+	0.829463i	$0.688647\pi$
$468$	−3.13537e14	−0.645559
$469$	1.95864e14	0.398569
$470$	−2.11374e15	−4.25123
$471$	8.12200e13	0.161454
$472$	−2.68807e13	−0.0528153
$473$	−5.20772e14	−1.01137
$474$	2.71102e14	0.520417
$475$	−7.74295e14	−1.46924
$476$	6.02849e14	1.13076
$477$	1.77069e14	0.328315
$478$	−9.21790e13	−0.168958
$479$	−8.10801e14	−1.46916	−0.734579	−	0.678523i	$-0.762621\pi$
$479$	−8.10801e14	−1.46916	−0.734579	+	0.678523i	$0.762621\pi$
$480$	7.96006e14	1.42590
$481$	−1.04373e15	−1.84837
$482$	−7.60200e14	−1.33097
$483$	6.96880e14	1.20628
$484$	1.83431e15	3.13923
$485$	−1.20751e15	−2.04319
$486$	5.77620e13	0.0966369
$487$	−2.25678e14	−0.373319	−0.186659	−	0.982425i	$-0.559766\pi$
$487$	−2.25678e14	−0.373319	−0.186659	+	0.982425i	$0.559766\pi$
$488$	1.97756e14	0.323459
$489$	2.67914e14	0.433308
$490$	1.97810e14	0.316351
$491$	−3.53313e14	−0.558743	−0.279371	−	0.960183i	$-0.590126\pi$
$491$	−3.53313e14	−0.558743	−0.279371	+	0.960183i	$0.590126\pi$
$492$	−5.76037e14	−0.900829
$493$	−6.01274e13	−0.0929854
$494$	−1.03930e15	−1.58943
$495$	−7.26061e14	−1.09811
$496$	2.70853e14	0.405121
$497$	−1.21995e14	−0.180460
$498$	9.90425e14	1.44897
$499$	1.05969e15	1.53330	0.766649	−	0.642067i	$-0.221923\pi$
$499$	1.05969e15	1.53330	0.766649	+	0.642067i	$0.221923\pi$
$500$	−1.76328e15	−2.52340
$501$	1.19966e14	0.169805
$502$	1.36595e15	1.91233
$503$	−8.41626e14	−1.16545	−0.582727	−	0.812668i	$-0.698014\pi$
$503$	−8.41626e14	−1.16545	−0.582727	+	0.812668i	$0.698014\pi$
$504$	−1.04426e14	−0.143035
$505$	−8.83425e14	−1.19693
$506$	4.13782e15	5.54554
$507$	−5.78342e14	−0.766727
$508$	−1.63705e15	−2.14690
$509$	−1.34537e14	−0.174540	−0.0872698	−	0.996185i	$-0.527814\pi$
$509$	−1.34537e14	−0.174540	−0.0872698	+	0.996185i	$0.527814\pi$
$510$	−1.00891e15	−1.29484
$511$	−2.44904e14	−0.310943
$512$	−9.44682e14	−1.18659
$513$	1.07094e14	0.133082
$514$	2.02867e15	2.49410
$515$	2.80023e15	3.40607
$516$	3.30464e14	0.397696
$517$	−2.49879e15	−2.97530
$518$	−1.63845e15	−1.93028
$519$	3.52255e13	0.0410617
$520$	−9.48633e14	−1.09416
$521$	−1.89622e14	−0.216411	−0.108206	−	0.994129i	$-0.534511\pi$
$521$	−1.89622e14	−0.216411	−0.108206	+	0.994129i	$0.534511\pi$
$522$	4.90906e13	0.0554384
$523$	1.54008e12	0.00172101	0.000860506	−	1.00000i	$-0.499726\pi$
$523$	1.54008e12	0.00172101	0.000860506		1.00000i	$0.499726\pi$
$524$	6.25309e14	0.691468
$525$	−1.18572e15	−1.29749
$526$	1.03855e14	0.112462
$527$	−4.83762e14	−0.518410
$528$	6.67777e14	0.708182
$529$	2.76487e15	2.90181
$530$	2.52509e15	2.62276
$531$	4.22156e13	0.0433963
$532$	−9.12553e14	−0.928419
$533$	−1.86264e15	−1.87556
$534$	1.41396e15	1.40916
$535$	−7.53118e14	−0.742878
$536$	−1.56574e14	−0.152867
$537$	−1.08031e15	−1.04397
$538$	4.55220e14	0.435430
$539$	2.33843e14	0.221404
$540$	4.60734e14	0.431802
$541$	2.38586e14	0.221340	0.110670	−	0.993857i	$-0.464700\pi$
$541$	2.38586e14	0.221340	0.110670	+	0.993857i	$0.464700\pi$
$542$	2.83180e15	2.60056
$543$	4.28184e14	0.389252
$544$	1.30759e15	1.17673
$545$	−1.51333e14	−0.134820
$546$	−1.59153e15	−1.40364
$547$	4.04060e14	0.352789	0.176395	−	0.984320i	$-0.443557\pi$
$547$	4.04060e14	0.352789	0.176395	+	0.984320i	$0.443557\pi$
$548$	−1.46133e15	−1.26315
$549$	−3.10570e14	−0.265774
$550$	−7.04035e15	−5.96485
$551$	9.10169e13	0.0763463
$552$	−5.57088e14	−0.462657
$553$	7.69716e14	0.632910
$554$	−4.93303e14	−0.401615
$555$	1.53373e15	1.23634
$556$	−1.84238e15	−1.47051
$557$	−5.90750e14	−0.466875	−0.233437	−	0.972372i	$-0.574997\pi$
$557$	−5.90750e14	−0.466875	−0.233437	+	0.972372i	$0.574997\pi$
$558$	3.94964e14	0.309079
$559$	1.06857e15	0.828017
$560$	1.60381e15	1.23060
$561$	−1.19269e15	−0.906219
$562$	−8.85334e14	−0.666127
$563$	−1.48992e15	−1.11011	−0.555056	−	0.831813i	$-0.687303\pi$
$563$	−1.48992e15	−1.11011	−0.555056	+	0.831813i	$0.687303\pi$
$564$	1.58565e15	1.16996
$565$	−6.51231e14	−0.475848
$566$	1.57681e15	1.14101
$567$	1.63999e14	0.117526
$568$	9.75229e13	0.0692135
$569$	−1.08556e15	−0.763018	−0.381509	−	0.924365i	$-0.624596\pi$
$569$	−1.08556e15	−0.763018	−0.381509	+	0.924365i	$0.624596\pi$
$570$	1.52722e15	1.06314
$571$	−7.39126e14	−0.509589	−0.254794	−	0.966995i	$-0.582008\pi$
$571$	−7.39126e14	−0.509589	−0.254794	+	0.966995i	$0.582008\pi$
$572$	−5.28567e15	−3.60929
$573$	−5.23368e14	−0.353962
$574$	−2.92399e15	−1.95867
$575$	−6.32550e15	−4.19684
$576$	−7.33729e14	−0.482183
$577$	3.01763e15	1.96426	0.982130	−	0.188205i	$-0.0602671\pi$
$577$	3.01763e15	1.96426	0.982130	+	0.188205i	$0.0602671\pi$
$578$	6.79087e14	0.437847
$579$	−1.67577e15	−1.07024
$580$	3.91567e14	0.247715
$581$	2.81203e15	1.76218
$582$	1.61946e15	1.00530
$583$	2.98506e15	1.83559
$584$	1.95777e14	0.119259
$585$	1.48981e15	0.899026
$586$	1.82541e15	1.09125
$587$	−1.18221e15	−0.700140	−0.350070	−	0.936723i	$-0.613842\pi$
$587$	−1.18221e15	−0.700140	−0.350070	+	0.936723i	$0.613842\pi$
$588$	−1.48389e14	−0.0870614
$589$	7.32287e14	0.425645
$590$	6.02015e14	0.346674
$591$	−7.45392e14	−0.425259
$592$	−1.41061e15	−0.797329
$593$	−1.94166e13	−0.0108736	−0.00543678	−	0.999985i	$-0.501731\pi$
$593$	−1.94166e13	−0.0108736	−0.00543678	+	0.999985i	$0.501731\pi$
$594$	9.73765e14	0.540292
$595$	−2.86451e15	−1.57473
$596$	2.80367e15	1.52712
$597$	−8.46080e14	−0.456618
$598$	−8.49040e15	−4.54017
$599$	−1.33131e15	−0.705392	−0.352696	−	0.935738i	$-0.614735\pi$
$599$	−1.33131e15	−0.705392	−0.352696	+	0.935738i	$0.614735\pi$
$600$	9.47864e14	0.497639
$601$	−9.07370e14	−0.472036	−0.236018	−	0.971749i	$-0.575842\pi$
$601$	−9.07370e14	−0.472036	−0.236018	+	0.971749i	$0.575842\pi$
$602$	1.67745e15	0.864708
$603$	2.45896e14	0.125605
$604$	−4.26177e14	−0.215718
$605$	−8.71594e15	−4.37179
$606$	1.18482e15	0.588914
$607$	−2.22958e15	−1.09821	−0.549106	−	0.835753i	$-0.685032\pi$
$607$	−2.22958e15	−1.09821	−0.549106	+	0.835753i	$0.685032\pi$
$608$	−1.97934e15	−0.966166
$609$	1.39379e14	0.0674220
$610$	−4.42889e15	−2.12315
$611$	5.12727e15	2.43590
$612$	7.56843e14	0.356347
$613$	1.27510e15	0.594992	0.297496	−	0.954723i	$-0.403848\pi$
$613$	1.27510e15	0.594992	0.297496	+	0.954723i	$0.403848\pi$
$614$	−3.03482e15	−1.40348
$615$	2.73711e15	1.25452
$616$	−1.76044e15	−0.799700
$617$	6.25132e14	0.281452	0.140726	−	0.990049i	$-0.455056\pi$
$617$	6.25132e14	0.281452	0.140726	+	0.990049i	$0.455056\pi$
$618$	−3.75556e15	−1.67586
$619$	4.18398e15	1.85051	0.925255	−	0.379345i	$-0.123851\pi$
$619$	4.18398e15	1.85051	0.925255	+	0.379345i	$0.123851\pi$
$620$	3.15039e15	1.38105
$621$	8.74893e14	0.380147
$622$	1.44709e15	0.623231
$623$	4.01455e15	1.71377
$624$	−1.37021e15	−0.579792
$625$	3.31285e15	1.38951
$626$	3.95744e14	0.164534
$627$	1.80542e15	0.744058
$628$	−8.68864e14	−0.354955
$629$	2.51944e15	1.02030
$630$	2.33871e15	0.938864
$631$	−3.91655e15	−1.55863	−0.779314	−	0.626633i	$-0.784432\pi$
$631$	−3.91655e15	−1.55863	−0.779314	+	0.626633i	$0.784432\pi$
$632$	−6.15312e14	−0.242746
$633$	1.15957e15	0.453499
$634$	−4.74759e15	−1.84070
$635$	7.77862e15	2.98983
$636$	−1.89422e15	−0.721799
$637$	−4.79823e14	−0.181265
$638$	8.27580e14	0.309953
$639$	−1.53157e14	−0.0568700
$640$	−3.75462e15	−1.38222
$641$	−2.88221e15	−1.05198	−0.525988	−	0.850492i	$-0.676304\pi$
$641$	−2.88221e15	−1.05198	−0.525988	+	0.850492i	$0.676304\pi$
$642$	1.01005e15	0.365512
$643$	−1.52329e15	−0.546541	−0.273271	−	0.961937i	$-0.588105\pi$
$643$	−1.52329e15	−0.546541	−0.273271	+	0.961937i	$0.588105\pi$
$644$	−7.45499e15	−2.65201
$645$	−1.57024e15	−0.553844
$646$	2.50875e15	0.877360
$647$	−1.29862e15	−0.450307	−0.225154	−	0.974323i	$-0.572288\pi$
$647$	−1.29862e15	−0.450307	−0.225154	+	0.974323i	$0.572288\pi$
$648$	−1.31101e14	−0.0450758
$649$	7.11679e14	0.242627
$650$	1.44461e16	4.88346
$651$	1.12139e15	0.375890
$652$	−2.86605e15	−0.952626
$653$	−3.31342e15	−1.09208	−0.546040	−	0.837759i	$-0.683865\pi$
$653$	−3.31342e15	−1.09208	−0.546040	+	0.837759i	$0.683865\pi$
$654$	2.02962e14	0.0663343
$655$	−2.97123e15	−0.962960
$656$	−2.51739e15	−0.809056
$657$	−3.07463e14	−0.0979903
$658$	8.04881e15	2.54384
$659$	1.50578e15	0.471945	0.235972	−	0.971760i	$-0.424173\pi$
$659$	1.50578e15	0.471945	0.235972	+	0.971760i	$0.424173\pi$
$660$	7.76715e15	2.41418
$661$	−1.62543e15	−0.501025	−0.250513	−	0.968113i	$-0.580599\pi$
$661$	−1.62543e15	−0.501025	−0.250513	+	0.968113i	$0.580599\pi$
$662$	6.70507e15	2.04967
$663$	2.44729e15	0.741926
$664$	−2.24794e15	−0.675866
$665$	4.33610e15	1.29295
$666$	−2.05698e15	−0.608306
$667$	7.43551e14	0.218081
$668$	−1.28336e15	−0.373316
$669$	−3.23482e15	−0.933268
$670$	3.50660e15	1.00340
$671$	−5.23567e15	−1.48593
$672$	−3.03107e15	−0.853228
$673$	−5.30873e15	−1.48220	−0.741101	−	0.671393i	$-0.765696\pi$
$673$	−5.30873e15	−1.48220	−0.741101	+	0.671393i	$0.765696\pi$
$674$	−4.55953e15	−1.26267
$675$	−1.48860e15	−0.408890
$676$	6.18690e15	1.68565
$677$	−4.75556e15	−1.28518	−0.642590	−	0.766210i	$-0.722140\pi$
$677$	−4.75556e15	−1.28518	−0.642590	+	0.766210i	$0.722140\pi$
$678$	8.73406e14	0.234128
$679$	4.59800e15	1.22260
$680$	2.28989e15	0.603971
$681$	1.53235e15	0.400912
$682$	6.65839e15	1.72805
$683$	5.31997e15	1.36961	0.684803	−	0.728728i	$-0.259888\pi$
$683$	5.31997e15	1.36961	0.684803	+	0.728728i	$0.259888\pi$
$684$	−1.14566e15	−0.292581
$685$	6.94368e15	1.75910
$686$	5.58701e15	1.40409
$687$	−2.86101e14	−0.0713274
$688$	1.44419e15	0.357180
$689$	−6.12505e15	−1.50281
$690$	1.24764e16	3.03683
$691$	−4.37423e15	−1.05626	−0.528132	−	0.849162i	$-0.677107\pi$
$691$	−4.37423e15	−1.05626	−0.528132	+	0.849162i	$0.677107\pi$
$692$	−3.76831e14	−0.0902740
$693$	2.76473e15	0.657082
$694$	2.42343e15	0.571418
$695$	8.75428e15	2.04788
$696$	−1.11420e14	−0.0258590
$697$	4.49622e15	1.03530
$698$	−1.88543e15	−0.430730
$699$	−1.38818e14	−0.0314646
$700$	1.26844e16	2.85253
$701$	3.30107e15	0.736555	0.368278	−	0.929716i	$-0.379948\pi$
$701$	3.30107e15	0.736555	0.368278	+	0.929716i	$0.379948\pi$
$702$	−1.99807e15	−0.442340
$703$	−3.81377e15	−0.837722
$704$	−1.23694e16	−2.69586
$705$	−7.53438e15	−1.62932
$706$	2.84032e15	0.609455
$707$	3.36395e15	0.716214
$708$	−4.51608e14	−0.0954066
$709$	−1.78661e15	−0.374520	−0.187260	−	0.982310i	$-0.559961\pi$
$709$	−1.78661e15	−0.374520	−0.187260	+	0.982310i	$0.559961\pi$
$710$	−2.18410e15	−0.454310
$711$	9.66334e14	0.199455
$712$	−3.20924e15	−0.657298
$713$	5.98233e15	1.21584
$714$	3.84177e15	0.774803
$715$	2.51155e16	5.02641
$716$	1.15568e16	2.29517
$717$	−3.28569e14	−0.0647548
$718$	−3.14400e15	−0.614890
$719$	−3.21462e15	−0.623908	−0.311954	−	0.950097i	$-0.600983\pi$
$719$	−3.21462e15	−0.623908	−0.311954	+	0.950097i	$0.600983\pi$
$720$	2.01349e15	0.387811
$721$	−1.06628e16	−2.03812
$722$	4.14390e15	0.786057
$723$	−2.70971e15	−0.510108
$724$	−4.58056e15	−0.855770
$725$	−1.26512e15	−0.234571
$726$	1.16895e16	2.15102
$727$	−5.04622e15	−0.921567	−0.460784	−	0.887513i	$-0.652432\pi$
$727$	−5.04622e15	−0.921567	−0.460784	+	0.887513i	$0.652432\pi$
$728$	3.61225e15	0.654719
$729$	2.05891e14	0.0370370
$730$	−4.38457e15	−0.782802
$731$	−2.57942e15	−0.457063
$732$	3.32238e15	0.584303
$733$	−4.67581e15	−0.816178	−0.408089	−	0.912942i	$-0.633805\pi$
$733$	−4.67581e15	−0.816178	−0.408089	+	0.912942i	$0.633805\pi$
$734$	−2.60939e15	−0.452076
$735$	7.05086e14	0.121244
$736$	−1.61700e16	−2.75983
$737$	4.14537e15	0.702250
$738$	−3.67090e15	−0.617253
$739$	8.34283e15	1.39242	0.696208	−	0.717840i	$-0.254869\pi$
$739$	8.34283e15	1.39242	0.696208	+	0.717840i	$0.254869\pi$
$740$	−1.64073e16	−2.71809
$741$	−3.70454e15	−0.609164
$742$	−9.61515e15	−1.56940
$743$	−5.43413e15	−0.880423	−0.440212	−	0.897894i	$-0.645097\pi$
$743$	−5.43413e15	−0.880423	−0.440212	+	0.897894i	$0.645097\pi$
$744$	−8.96440e14	−0.144168
$745$	−1.33220e16	−2.12671
$746$	−4.92513e15	−0.780467
$747$	3.53034e15	0.555333
$748$	1.27590e16	1.99232
$749$	2.86776e15	0.444521
$750$	−1.12368e16	−1.72905
$751$	5.91094e15	0.902895	0.451447	−	0.892298i	$-0.350908\pi$
$751$	5.91094e15	0.902895	0.451447	+	0.892298i	$0.350908\pi$
$752$	6.92956e15	1.05077
$753$	4.86888e15	0.732919
$754$	−1.69811e15	−0.253761
$755$	2.02503e15	0.300416
$756$	−1.75440e15	−0.258380
$757$	−7.83452e15	−1.14547	−0.572737	−	0.819739i	$-0.694118\pi$
$757$	−7.83452e15	−1.14547	−0.572737	+	0.819739i	$0.694118\pi$
$758$	−1.58202e15	−0.229631
$759$	1.47491e16	2.12538
$760$	−3.46629e15	−0.495895
$761$	1.16409e16	1.65337	0.826687	−	0.562662i	$-0.190223\pi$
$761$	1.16409e16	1.65337	0.826687	+	0.562662i	$0.190223\pi$
$762$	−1.04324e16	−1.47106
$763$	5.76254e14	0.0806731
$764$	5.59881e15	0.778184
$765$	−3.59623e15	−0.496260
$766$	−1.48196e16	−2.03039
$767$	−1.46030e15	−0.198640
$768$	−1.14830e15	−0.155085
$769$	3.72079e15	0.498930	0.249465	−	0.968384i	$-0.419745\pi$
$769$	3.72079e15	0.498930	0.249465	+	0.968384i	$0.419745\pi$
$770$	3.94264e16	5.24914
$771$	7.23114e15	0.955889
$772$	1.79268e16	2.35292
$773$	7.08772e13	0.00923676	0.00461838	−	0.999989i	$-0.498530\pi$
$773$	7.08772e13	0.00923676	0.00461838	+	0.999989i	$0.498530\pi$
$774$	2.10594e15	0.272503
$775$	−1.01787e16	−1.30778
$776$	−3.67565e15	−0.468915
$777$	−5.84021e15	−0.739798
$778$	−7.98358e14	−0.100418
$779$	−6.80607e15	−0.850042
$780$	−1.59374e16	−1.97651
$781$	−2.58196e15	−0.317958
$782$	2.04949e16	2.50616
$783$	1.74982e14	0.0212473
$784$	−6.48486e14	−0.0781920
$785$	4.12851e15	0.494322
$786$	3.98489e15	0.473798
$787$	−7.47370e15	−0.882419	−0.441209	−	0.897404i	$-0.645450\pi$
$787$	−7.47370e15	−0.882419	−0.441209	+	0.897404i	$0.645450\pi$
$788$	7.97395e15	0.934931
$789$	3.70187e14	0.0431020
$790$	1.37804e16	1.59336
$791$	2.47979e15	0.284737
$792$	−2.21013e15	−0.252017
$793$	1.07431e16	1.21654
$794$	−1.79422e16	−2.01773
$795$	9.00060e15	1.00520
$796$	9.05108e15	1.00387
$797$	9.45897e15	1.04189	0.520946	−	0.853589i	$-0.325579\pi$
$797$	9.45897e15	1.04189	0.520946	+	0.853589i	$0.325579\pi$
$798$	−5.81541e15	−0.636158
$799$	−1.23767e16	−1.34461
$800$	2.75127e16	2.96850
$801$	5.04003e15	0.540076
$802$	−9.94221e15	−1.05809
$803$	−5.18328e15	−0.547859
$804$	−2.63051e15	−0.276142
$805$	3.54232e16	3.69327
$806$	−1.36624e16	−1.41476
$807$	1.62262e15	0.166883
$808$	−2.68915e15	−0.274696
$809$	−8.07445e15	−0.819212	−0.409606	−	0.912263i	$-0.634334\pi$
$809$	−8.07445e15	−0.819212	−0.409606	+	0.912263i	$0.634334\pi$
$810$	2.93611e15	0.295873
$811$	−9.74910e15	−0.975776	−0.487888	−	0.872906i	$-0.662232\pi$
$811$	−9.74910e15	−0.975776	−0.487888	+	0.872906i	$0.662232\pi$
$812$	−1.49103e15	−0.148227
$813$	1.00939e16	0.996688
$814$	−3.46770e16	−3.40101
$815$	1.36184e16	1.32666
$816$	3.30754e15	0.320044
$817$	3.90455e15	0.375275
$818$	−1.31542e16	−1.25580
$819$	−5.67295e15	−0.537957
$820$	−2.92806e16	−2.75806
$821$	8.93636e15	0.836129	0.418064	−	0.908417i	$-0.362709\pi$
$821$	8.93636e15	0.836129	0.418064	+	0.908417i	$0.362709\pi$
$822$	−9.31260e15	−0.865518
$823$	−1.99105e16	−1.83815	−0.919077	−	0.394077i	$-0.871064\pi$
$823$	−1.99105e16	−1.83815	−0.919077	+	0.394077i	$0.871064\pi$
$824$	8.52390e15	0.781698
$825$	−2.50951e16	−2.28609
$826$	−2.29238e15	−0.207442
$827$	−6.19967e15	−0.557299	−0.278649	−	0.960393i	$-0.589887\pi$
$827$	−6.19967e15	−0.557299	−0.278649	+	0.960393i	$0.589887\pi$
$828$	−9.35931e15	−0.835751
$829$	−1.71179e16	−1.51845	−0.759227	−	0.650826i	$-0.774423\pi$
$829$	−1.71179e16	−1.51845	−0.759227	+	0.650826i	$0.774423\pi$
$830$	5.03444e16	4.43631
$831$	−1.75836e15	−0.153923
$832$	2.53807e16	2.20712
$833$	1.15824e15	0.100058
$834$	−1.17409e16	−1.00760
$835$	6.09802e15	0.519892
$836$	−1.93138e16	−1.63581
$837$	1.40784e15	0.118458
$838$	5.73029e15	0.478999
$839$	−6.25974e15	−0.519835	−0.259918	−	0.965631i	$-0.583695\pi$
$839$	−6.25974e15	−0.519835	−0.259918	+	0.965631i	$0.583695\pi$
$840$	−5.30810e15	−0.437928
$841$	−1.20518e16	−0.987811
$842$	−1.44159e16	−1.17389
$843$	−3.15575e15	−0.255300
$844$	−1.24047e16	−0.997015
$845$	−2.93978e16	−2.34748
$846$	1.01048e16	0.801663
$847$	3.31890e16	2.61598
$848$	−8.27808e15	−0.648265
$849$	5.62050e15	0.437303
$850$	−3.48713e16	−2.69565
$851$	−3.11561e16	−2.39293
$852$	1.63843e15	0.125029
$853$	6.28237e14	0.0476326	0.0238163	−	0.999716i	$-0.492418\pi$
$853$	6.28237e14	0.0476326	0.0238163	+	0.999716i	$0.492418\pi$
$854$	1.68645e16	1.27045
$855$	5.44372e15	0.407458
$856$	−2.29249e15	−0.170491
$857$	−1.48020e16	−1.09377	−0.546885	−	0.837208i	$-0.684186\pi$
$857$	−1.48020e16	−1.09377	−0.546885	+	0.837208i	$0.684186\pi$
$858$	−3.36839e16	−2.47310
$859$	2.02138e16	1.47464	0.737319	−	0.675545i	$-0.236092\pi$
$859$	2.02138e16	1.47464	0.737319	+	0.675545i	$0.236092\pi$
$860$	1.67979e16	1.21762
$861$	−1.04225e16	−0.750678
$862$	3.27097e16	2.34092
$863$	−1.72387e16	−1.22587	−0.612935	−	0.790133i	$-0.710011\pi$
$863$	−1.72387e16	−1.22587	−0.612935	+	0.790133i	$0.710011\pi$
$864$	−3.80533e15	−0.268885
$865$	1.79055e15	0.125718
$866$	2.46939e16	1.72283
$867$	2.42059e15	0.167809
$868$	−1.19962e16	−0.826392
$869$	1.62907e16	1.11514
$870$	2.49533e15	0.169735
$871$	−8.50589e15	−0.574936
$872$	−4.60659e14	−0.0309413
$873$	5.77252e15	0.385289
$874$	−3.10238e16	−2.05770
$875$	−3.19038e16	−2.10280
$876$	3.28913e15	0.215431
$877$	−8.38600e15	−0.545830	−0.272915	−	0.962038i	$-0.587988\pi$
$877$	−8.38600e15	−0.545830	−0.272915	+	0.962038i	$0.587988\pi$
$878$	−3.14518e16	−2.03435
$879$	6.50662e15	0.418232
$880$	3.39439e16	2.16824
$881$	−3.07062e15	−0.194921	−0.0974603	−	0.995239i	$-0.531072\pi$
$881$	−3.07062e15	−0.194921	−0.0974603	+	0.995239i	$0.531072\pi$
$882$	−9.45635e14	−0.0596549
$883$	1.96212e14	0.0123010	0.00615051	−	0.999981i	$-0.498042\pi$
$883$	1.96212e14	0.0123010	0.00615051	+	0.999981i	$0.498042\pi$
$884$	−2.61803e16	−1.63112
$885$	2.14587e15	0.132866
$886$	−6.23995e15	−0.383968
$887$	4.87530e15	0.298141	0.149070	−	0.988827i	$-0.452372\pi$
$887$	4.87530e15	0.298141	0.149070	+	0.988827i	$0.452372\pi$
$888$	4.66868e15	0.283741
$889$	−2.96198e16	−1.78905
$890$	7.18734e16	4.31443
$891$	3.47096e15	0.207072
$892$	3.46050e16	2.05179
$893$	1.87349e16	1.10400
$894$	1.78669e16	1.04639
$895$	−5.49132e16	−3.19632
$896$	1.42970e16	0.827088
$897$	−3.02638e16	−1.74006
$898$	2.03606e16	1.16351
$899$	1.19649e15	0.0679563
$900$	1.59245e16	0.898944
$901$	1.47852e16	0.829547
$902$	−6.18849e16	−3.45103
$903$	5.97923e15	0.331408
$904$	−1.98235e15	−0.109208
$905$	2.17651e16	1.19177
$906$	−2.71589e15	−0.147811
$907$	−2.14404e16	−1.15983	−0.579914	−	0.814678i	$-0.696914\pi$
$907$	−2.14404e16	−1.15983	−0.579914	+	0.814678i	$0.696914\pi$
$908$	−1.63926e16	−0.881404
$909$	4.22325e15	0.225707
$910$	−8.08991e16	−4.29750
$911$	1.14567e16	0.604932	0.302466	−	0.953160i	$-0.402190\pi$
$911$	1.14567e16	0.604932	0.302466	+	0.953160i	$0.402190\pi$
$912$	−5.00673e15	−0.262774
$913$	5.95153e16	3.10484
$914$	1.42901e16	0.741024
$915$	−1.57867e16	−0.813718
$916$	3.06061e15	0.156813
$917$	1.13140e16	0.576214
$918$	4.82312e15	0.244171
$919$	−1.48996e16	−0.749792	−0.374896	−	0.927067i	$-0.622322\pi$
$919$	−1.48996e16	−0.749792	−0.374896	+	0.927067i	$0.622322\pi$
$920$	−2.83174e16	−1.41651
$921$	−1.08175e16	−0.537898
$922$	−1.91706e16	−0.947581
$923$	5.29793e15	0.260314
$924$	−2.95761e16	−1.44459
$925$	5.30109e16	2.57387
$926$	2.94584e16	1.42183
$927$	−1.33866e16	−0.642290
$928$	−3.23406e15	−0.154253
$929$	−9.94200e15	−0.471398	−0.235699	−	0.971826i	$-0.575738\pi$
$929$	−9.94200e15	−0.471398	−0.235699	+	0.971826i	$0.575738\pi$
$930$	2.00765e16	0.946305
$931$	−1.75326e15	−0.0821531
$932$	1.48503e15	0.0691749
$933$	5.15812e15	0.238859
$934$	3.65557e16	1.68286
$935$	−6.06260e16	−2.77456
$936$	4.53497e15	0.206328
$937$	−1.00880e16	−0.456287	−0.228144	−	0.973627i	$-0.573266\pi$
$937$	−1.00880e16	−0.456287	−0.228144	+	0.973627i	$0.573266\pi$
$938$	−1.33526e16	−0.600413
$939$	1.41062e15	0.0630592
$940$	8.06002e16	3.58206
$941$	2.92727e16	1.29336	0.646681	−	0.762761i	$-0.276157\pi$
$941$	2.92727e16	1.29336	0.646681	+	0.762761i	$0.276157\pi$
$942$	−5.53699e15	−0.243217
$943$	−5.56014e16	−2.42813
$944$	−1.97361e15	−0.0856870
$945$	8.33625e15	0.359829
$946$	3.55025e16	1.52355
$947$	−2.79988e16	−1.19458	−0.597289	−	0.802026i	$-0.703755\pi$
$947$	−2.79988e16	−1.19458	−0.597289	+	0.802026i	$0.703755\pi$
$948$	−1.03375e16	−0.438500
$949$	1.06356e16	0.448535
$950$	5.27858e16	2.21329
$951$	−1.69227e16	−0.705465
$952$	−8.71957e15	−0.361403
$953$	2.95213e16	1.21653	0.608267	−	0.793732i	$-0.291865\pi$
$953$	2.95213e16	1.21653	0.608267	+	0.793732i	$0.291865\pi$
$954$	−1.20713e16	−0.494580
$955$	−2.66034e16	−1.08372
$956$	3.51492e15	0.142363
$957$	2.94989e15	0.118793
$958$	5.52746e16	2.21317
$959$	−2.64405e16	−1.05261
$960$	−3.72963e16	−1.47630
$961$	−1.57820e16	−0.621131
$962$	7.11539e16	2.78443
$963$	3.60031e15	0.140086
$964$	2.89875e16	1.12147
$965$	−8.51811e16	−3.27675
$966$	−4.75083e16	−1.81717
$967$	4.26808e15	0.162326	0.0811629	−	0.996701i	$-0.474137\pi$
$967$	4.26808e15	0.162326	0.0811629	+	0.996701i	$0.474137\pi$
$968$	−2.65313e16	−1.00333
$969$	8.94235e15	0.336257
$970$	8.23190e16	3.07791
$971$	−4.89156e16	−1.81862	−0.909310	−	0.416120i	$-0.863390\pi$
$971$	−4.89156e16	−1.81862	−0.909310	+	0.416120i	$0.863390\pi$
$972$	−2.20255e15	−0.0814258
$973$	−3.33349e16	−1.22540
$974$	1.53851e16	0.562375
$975$	5.14927e16	1.87163
$976$	1.45194e16	0.524776
$977$	−4.27989e16	−1.53820	−0.769100	−	0.639129i	$-0.779295\pi$
$977$	−4.27989e16	−1.53820	−0.769100	+	0.639129i	$0.779295\pi$
$978$	−1.82644e16	−0.652744
$979$	8.49660e16	3.01954
$980$	−7.54277e15	−0.266555
$981$	7.23454e14	0.0254233
$982$	2.40864e16	0.841701
$983$	−4.05053e16	−1.40756	−0.703780	−	0.710418i	$-0.748506\pi$
$983$	−4.05053e16	−1.40756	−0.703780	+	0.710418i	$0.748506\pi$
$984$	8.33176e15	0.287914
$985$	−3.78891e16	−1.30201
$986$	4.09906e15	0.140075
$987$	2.86898e16	0.974951
$988$	3.96299e16	1.33925
$989$	3.18977e16	1.07196
$990$	4.94976e16	1.65421
$991$	4.18063e16	1.38943	0.694715	−	0.719285i	$-0.255530\pi$
$991$	4.18063e16	1.38943	0.694715	+	0.719285i	$0.255530\pi$
$992$	−2.60200e16	−0.859990
$993$	2.39000e16	0.785556
$994$	8.31673e15	0.271849
$995$	−4.30072e16	−1.39802
$996$	−3.77664e16	−1.22090
$997$	4.00612e16	1.28795	0.643977	−	0.765045i	$-0.277283\pi$
$997$	4.00612e16	1.28795	0.643977	+	0.765045i	$0.277283\pi$
$998$	−7.22421e16	−2.30979
$999$	−7.33205e15	−0.233139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-68.1728 q^{2} -243.000 q^{3} +2599.53 q^{4} -12352.0 q^{5} +16566.0 q^{6} +47034.4 q^{7} -37599.4 q^{8} +59049.0 q^{9} +842068. q^{10} +995461. q^{11} -631686. q^{12} -2.04259e6 q^{13} -3.20647e6 q^{14} +3.00153e6 q^{15} -2.76058e6 q^{16} +4.93058e6 q^{17} -4.02554e6 q^{18} -7.46358e6 q^{19} -3.21093e7 q^{20} -1.14294e7 q^{21} -6.78634e7 q^{22} -6.09728e7 q^{23} +9.13666e6 q^{24} +1.03743e8 q^{25} +1.39249e8 q^{26} -1.43489e7 q^{27} +1.22267e8 q^{28} -1.21948e7 q^{29} -2.04623e8 q^{30} -9.81146e7 q^{31} +2.65200e8 q^{32} -2.41897e8 q^{33} -3.36132e8 q^{34} -5.80968e8 q^{35} +1.53500e8 q^{36} +5.10983e8 q^{37} +5.08813e8 q^{38} +4.96349e8 q^{39} +4.64427e8 q^{40} +9.11904e8 q^{41} +7.79172e8 q^{42} -5.23146e8 q^{43} +2.58773e9 q^{44} -7.29371e8 q^{45} +4.15669e9 q^{46} -2.51018e9 q^{47} +6.70821e8 q^{48} +2.34909e8 q^{49} -7.07245e9 q^{50} -1.19813e9 q^{51} -5.30977e9 q^{52} +2.99867e9 q^{53} +9.78205e8 q^{54} -1.22959e10 q^{55} -1.76847e9 q^{56} +1.81365e9 q^{57} +8.31353e8 q^{58} +7.14924e8 q^{59} +7.80257e9 q^{60} -5.25954e9 q^{61} +6.68875e9 q^{62} +2.77733e9 q^{63} -1.24258e10 q^{64} +2.52300e10 q^{65} +1.64908e10 q^{66} +4.16427e9 q^{67} +1.28172e10 q^{68} +1.48164e10 q^{69} +3.96062e10 q^{70} -2.59373e9 q^{71} -2.22021e9 q^{72} -5.20691e9 q^{73} -3.48351e10 q^{74} -2.52095e10 q^{75} -1.94018e10 q^{76} +4.68209e10 q^{77} -3.38375e10 q^{78} +1.63649e10 q^{79} +3.40986e10 q^{80} +3.48678e9 q^{81} -6.21671e10 q^{82} +5.97866e10 q^{83} -2.97110e10 q^{84} -6.09024e10 q^{85} +3.56644e10 q^{86} +2.96333e9 q^{87} -3.74288e10 q^{88} +8.53534e10 q^{89} +4.97233e10 q^{90} -9.60719e10 q^{91} -1.58501e11 q^{92} +2.38419e10 q^{93} +1.71126e11 q^{94} +9.21900e10 q^{95} -6.44437e10 q^{96} +9.77581e10 q^{97} -1.60144e10 q^{98} +5.87810e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 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

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