LMFDB - Embedded newform 177.14.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +O(q^{10})$	\(q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +1.94915e6 q^{10} +1.22717e6 q^{11} -5.23020e6 q^{12} -6.08798e6 q^{13} -7.55091e6 q^{14} +4.45454e7 q^{15} +4.31377e7 q^{16} +1.15524e8 q^{17} +1.69522e7 q^{18} -2.61499e8 q^{19} -4.38395e8 q^{20} -1.72566e8 q^{21} +3.91448e7 q^{22} -1.17829e9 q^{23} -3.57333e8 q^{24} +2.51309e9 q^{25} -1.94198e8 q^{26} +3.87420e8 q^{27} +1.69832e9 q^{28} -1.96230e8 q^{29} +1.42093e9 q^{30} +1.49325e9 q^{31} +5.39149e9 q^{32} +8.94604e8 q^{33} +3.68506e9 q^{34} -1.44645e10 q^{35} -3.81281e9 q^{36} +1.48696e10 q^{37} -8.34144e9 q^{38} -4.43814e9 q^{39} -2.99516e10 q^{40} -1.03207e10 q^{41} -5.50461e9 q^{42} -3.86482e10 q^{43} -8.80428e9 q^{44} +3.24736e10 q^{45} -3.75857e10 q^{46} -1.59891e10 q^{47} +3.14474e10 q^{48} -4.08543e10 q^{49} +8.01640e10 q^{50} +8.42173e10 q^{51} +4.36781e10 q^{52} -3.65459e10 q^{53} +1.23581e10 q^{54} +7.49857e10 q^{55} +1.16031e11 q^{56} -1.90633e11 q^{57} -6.25946e9 q^{58} +4.21805e10 q^{59} -3.19590e11 q^{60} -7.27065e11 q^{61} +4.76325e10 q^{62} -1.25801e11 q^{63} -1.81404e11 q^{64} -3.72005e11 q^{65} +2.85365e10 q^{66} +2.38478e11 q^{67} -8.28828e11 q^{68} -8.58973e11 q^{69} -4.61397e11 q^{70} -4.31528e11 q^{71} -2.60495e11 q^{72} -8.74060e11 q^{73} +4.74317e11 q^{74} +1.83205e12 q^{75} +1.87612e12 q^{76} -2.90491e11 q^{77} -1.41570e11 q^{78} +1.86554e12 q^{79} +2.63592e12 q^{80} +2.82430e11 q^{81} -3.29215e11 q^{82} +2.77153e11 q^{83} +1.23807e12 q^{84} +7.05910e12 q^{85} -1.23282e12 q^{86} -1.43052e11 q^{87} -6.01518e11 q^{88} -1.37556e12 q^{89} +1.03586e12 q^{90} +1.44113e12 q^{91} +8.45362e12 q^{92} +1.08858e12 q^{93} -5.10030e11 q^{94} -1.59789e13 q^{95} +3.93039e12 q^{96} +6.08837e12 q^{97} -1.30319e12 q^{98} +6.52166e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * 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 $

$2$	31.8985	0.352432	0.176216	−	0.984352i	$-0.443614\pi$
$2$	31.8985	0.352432	0.176216	+	0.984352i	$0.443614\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7174.48	−0.875792
$5$	61104.8	1.74892	0.874461	−	0.485096i	$-0.161215\pi$
$5$	61104.8	1.74892	0.874461	+	0.485096i	$0.161215\pi$
$6$	23254.0	0.203477
$7$	−236717.	−0.760486	−0.380243	−	0.924887i	$-0.624160\pi$
$7$	−236717.	−0.760486	−0.380243	+	0.924887i	$0.624160\pi$
$8$	−490168.	−0.661089
$9$	531441.	0.333333
$10$	1.94915e6	0.616376
$11$	1.22717e6	0.208858	0.104429	−	0.994532i	$-0.466699\pi$
$11$	1.22717e6	0.208858	0.104429	+	0.994532i	$0.466699\pi$
$12$	−5.23020e6	−0.505638
$13$	−6.08798e6	−0.349818	−0.174909	−	0.984585i	$-0.555963\pi$
$13$	−6.08798e6	−0.349818	−0.174909	+	0.984585i	$0.555963\pi$
$14$	−7.55091e6	−0.268020
$15$	4.45454e7	1.00974
$16$	4.31377e7	0.642802
$17$	1.15524e8	1.16080	0.580398	−	0.814333i	$-0.302897\pi$
$17$	1.15524e8	1.16080	0.580398	+	0.814333i	$0.302897\pi$
$18$	1.69522e7	0.117477
$19$	−2.61499e8	−1.27518	−0.637591	−	0.770375i	$-0.720069\pi$
$19$	−2.61499e8	−1.27518	−0.637591	+	0.770375i	$0.720069\pi$
$20$	−4.38395e8	−1.53169
$21$	−1.72566e8	−0.439067
$22$	3.91448e7	0.0736082
$23$	−1.17829e9	−1.65967	−0.829834	−	0.558010i	$-0.811565\pi$
$23$	−1.17829e9	−1.65967	−0.829834	+	0.558010i	$0.811565\pi$
$24$	−3.57333e8	−0.381680
$25$	2.51309e9	2.05873
$26$	−1.94198e8	−0.123287
$27$	3.87420e8	0.192450
$28$	1.69832e9	0.666028
$29$	−1.96230e8	−0.0612603	−0.0306301	−	0.999531i	$-0.509751\pi$
$29$	−1.96230e8	−0.0612603	−0.0306301	+	0.999531i	$0.509751\pi$
$30$	1.42093e9	0.355865
$31$	1.49325e9	0.302191	0.151096	−	0.988519i	$-0.451720\pi$
$31$	1.49325e9	0.302191	0.151096	+	0.988519i	$0.451720\pi$
$32$	5.39149e9	0.887634
$33$	8.94604e8	0.120584
$34$	3.68506e9	0.409102
$35$	−1.44645e10	−1.33003
$36$	−3.81281e9	−0.291931
$37$	1.48696e10	0.952767	0.476383	−	0.879238i	$-0.341947\pi$
$37$	1.48696e10	0.952767	0.476383	+	0.879238i	$0.341947\pi$
$38$	−8.34144e9	−0.449415
$39$	−4.43814e9	−0.201967
$40$	−2.99516e10	−1.15619
$41$	−1.03207e10	−0.339323	−0.169662	−	0.985502i	$-0.554267\pi$
$41$	−1.03207e10	−0.339323	−0.169662	+	0.985502i	$0.554267\pi$
$42$	−5.50461e9	−0.154741
$43$	−3.86482e10	−0.932362	−0.466181	−	0.884689i	$-0.654370\pi$
$43$	−3.86482e10	−0.932362	−0.466181	+	0.884689i	$0.654370\pi$
$44$	−8.80428e9	−0.182916
$45$	3.24736e10	0.582974
$46$	−3.75857e10	−0.584921
$47$	−1.59891e10	−0.216366	−0.108183	−	0.994131i	$-0.534503\pi$
$47$	−1.59891e10	−0.216366	−0.108183	+	0.994131i	$0.534503\pi$
$48$	3.14474e10	0.371122
$49$	−4.08543e10	−0.421660
$50$	8.01640e10	0.725562
$51$	8.42173e10	0.670186
$52$	4.36781e10	0.306367
$53$	−3.65459e10	−0.226488	−0.113244	−	0.993567i	$-0.536124\pi$
$53$	−3.65459e10	−0.226488	−0.113244	+	0.993567i	$0.536124\pi$
$54$	1.23581e10	0.0678256
$55$	7.49857e10	0.365276
$56$	1.16031e11	0.502750
$57$	−1.90633e11	−0.736226
$58$	−6.25946e9	−0.0215901
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−3.19590e11	−0.884322
$61$	−7.27065e11	−1.80688	−0.903440	−	0.428715i	$-0.858966\pi$
$61$	−7.27065e11	−1.80688	−0.903440	+	0.428715i	$0.858966\pi$
$62$	4.76325e10	0.106502
$63$	−1.25801e11	−0.253495
$64$	−1.81404e11	−0.329972
$65$	−3.72005e11	−0.611804
$66$	2.85365e10	0.0424977
$67$	2.38478e11	0.322079	0.161039	−	0.986948i	$-0.448515\pi$
$67$	2.38478e11	0.322079	0.161039	+	0.986948i	$0.448515\pi$
$68$	−8.28828e11	−1.01662
$69$	−8.58973e11	−0.958210
$70$	−4.61397e11	−0.468746
$71$	−4.31528e11	−0.399788	−0.199894	−	0.979818i	$-0.564060\pi$
$71$	−4.31528e11	−0.399788	−0.199894	+	0.979818i	$0.564060\pi$
$72$	−2.60495e11	−0.220363
$73$	−8.74060e11	−0.675994	−0.337997	−	0.941147i	$-0.609749\pi$
$73$	−8.74060e11	−0.675994	−0.337997	+	0.941147i	$0.609749\pi$
$74$	4.74317e11	0.335786
$75$	1.83205e12	1.18861
$76$	1.87612e12	1.11679
$77$	−2.90491e11	−0.158834
$78$	−1.41570e11	−0.0711798
$79$	1.86554e12	0.863433	0.431717	−	0.902009i	$-0.357908\pi$
$79$	1.86554e12	0.863433	0.431717	+	0.902009i	$0.357908\pi$
$80$	2.63592e12	1.12421
$81$	2.82430e11	0.111111
$82$	−3.29215e11	−0.119588
$83$	2.77153e11	0.0930491	0.0465245	−	0.998917i	$-0.485185\pi$
$83$	2.77153e11	0.0930491	0.0465245	+	0.998917i	$0.485185\pi$
$84$	1.23807e12	0.384531
$85$	7.05910e12	2.03014
$86$	−1.23282e12	−0.328594
$87$	−1.43052e11	−0.0353686
$88$	−6.01518e11	−0.138074
$89$	−1.37556e12	−0.293389	−0.146695	−	0.989182i	$-0.546863\pi$
$89$	−1.37556e12	−0.293389	−0.146695	+	0.989182i	$0.546863\pi$
$90$	1.03586e12	0.205459
$91$	1.44113e12	0.266032
$92$	8.45362e12	1.45352
$93$	1.08858e12	0.174470
$94$	−5.10030e11	−0.0762544
$95$	−1.59789e13	−2.23019
$96$	3.93039e12	0.512476
$97$	6.08837e12	0.742138	0.371069	−	0.928605i	$-0.378991\pi$
$97$	6.08837e12	0.742138	0.371069	+	0.928605i	$0.378991\pi$
$98$	−1.30319e12	−0.148607
$99$	6.52166e11	0.0696193
$100$	−1.80302e13	−1.80302
$101$	1.09470e13	1.02614	0.513071	−	0.858346i	$-0.328508\pi$
$101$	1.09470e13	1.02614	0.513071	+	0.858346i	$0.328508\pi$
$102$	2.68641e12	0.236195
$103$	−1.90541e13	−1.57234	−0.786168	−	0.618013i	$-0.787938\pi$
$103$	−1.90541e13	−1.57234	−0.786168	+	0.618013i	$0.787938\pi$
$104$	2.98414e12	0.231261
$105$	−1.05446e13	−0.767894
$106$	−1.16576e12	−0.0798218
$107$	−1.06552e13	−0.686381	−0.343191	−	0.939266i	$-0.611508\pi$
$107$	−1.06552e13	−0.686381	−0.343191	+	0.939266i	$0.611508\pi$
$108$	−2.77954e12	−0.168546
$109$	−8.24908e12	−0.471122	−0.235561	−	0.971860i	$-0.575693\pi$
$109$	−8.24908e12	−0.471122	−0.235561	+	0.971860i	$0.575693\pi$
$110$	2.39193e12	0.128735
$111$	1.08399e13	0.550080
$112$	−1.02114e13	−0.488842
$113$	3.64270e13	1.64594	0.822969	−	0.568086i	$-0.192316\pi$
$113$	3.64270e13	1.64594	0.822969	+	0.568086i	$0.192316\pi$
$114$	−6.08091e12	−0.259470
$115$	−7.19992e13	−2.90263
$116$	1.40785e12	0.0536512
$117$	−3.23540e12	−0.116606
$118$	1.34550e12	0.0458828
$119$	−2.73466e13	−0.882770
$120$	−2.18347e13	−0.667529
$121$	−3.30168e13	−0.956378
$122$	−2.31923e13	−0.636803
$123$	−7.52378e12	−0.195908
$124$	−1.07133e13	−0.264657
$125$	7.89713e13	1.85163
$126$	−4.01286e12	−0.0893400
$127$	4.28928e13	0.907111	0.453556	−	0.891228i	$-0.350155\pi$
$127$	4.28928e13	0.907111	0.453556	+	0.891228i	$0.350155\pi$
$128$	−4.99536e13	−1.00393
$129$	−2.81745e13	−0.538299
$130$	−1.18664e13	−0.215619
$131$	−5.87157e13	−1.01506	−0.507529	−	0.861635i	$-0.669441\pi$
$131$	−5.87157e13	−1.01506	−0.507529	+	0.861635i	$0.669441\pi$
$132$	−6.41832e12	−0.105607
$133$	6.19012e13	0.969758
$134$	7.60710e12	0.113511
$135$	2.36733e13	0.336580
$136$	−5.66264e13	−0.767390
$137$	−3.05025e13	−0.394142	−0.197071	−	0.980389i	$-0.563143\pi$
$137$	−3.05025e13	−0.394142	−0.197071	+	0.980389i	$0.563143\pi$
$138$	−2.74000e13	−0.337704
$139$	−8.80908e13	−1.03594	−0.517970	−	0.855399i	$-0.673312\pi$
$139$	−8.80908e13	−1.03594	−0.517970	+	0.855399i	$0.673312\pi$
$140$	1.03775e14	1.16483
$141$	−1.16561e13	−0.124919
$142$	−1.37651e13	−0.140898
$143$	−7.47097e12	−0.0730622
$144$	2.29252e13	0.214267
$145$	−1.19906e13	−0.107139
$146$	−2.78812e13	−0.238242
$147$	−2.97827e13	−0.243446
$148$	−1.06681e14	−0.834425
$149$	8.99670e13	0.673554	0.336777	−	0.941584i	$-0.390663\pi$
$149$	8.99670e13	0.673554	0.336777	+	0.941584i	$0.390663\pi$
$150$	5.84395e13	0.418903
$151$	−2.47335e13	−0.169799	−0.0848995	−	0.996390i	$-0.527057\pi$
$151$	−2.47335e13	−0.169799	−0.0848995	+	0.996390i	$0.527057\pi$
$152$	1.28179e14	0.843009
$153$	6.13944e13	0.386932
$154$	−9.26622e12	−0.0559781
$155$	9.12448e13	0.528509
$156$	3.18414e13	0.176881
$157$	−1.64598e14	−0.877157	−0.438578	−	0.898693i	$-0.644518\pi$
$157$	−1.64598e14	−0.877157	−0.438578	+	0.898693i	$0.644518\pi$
$158$	5.95080e13	0.304302
$159$	−2.66420e13	−0.130763
$160$	3.29446e14	1.55240
$161$	2.78921e14	1.26216
$162$	9.00909e12	0.0391591
$163$	−3.36300e14	−1.40446	−0.702228	−	0.711952i	$-0.747811\pi$
$163$	−3.36300e14	−1.40446	−0.702228	+	0.711952i	$0.747811\pi$
$164$	7.40456e13	0.297176
$165$	5.46646e13	0.210892
$166$	8.84078e12	0.0327935
$167$	5.17600e14	1.84645	0.923225	−	0.384261i	$-0.125544\pi$
$167$	5.17600e14	1.84645	0.923225	+	0.384261i	$0.125544\pi$
$168$	8.45866e13	0.290263
$169$	−2.65812e14	−0.877628
$170$	2.25175e14	0.715487
$171$	−1.38971e14	−0.425061
$172$	2.77281e14	0.816554
$173$	−1.12219e14	−0.318248	−0.159124	−	0.987259i	$-0.550867\pi$
$173$	−1.12219e14	−0.318248	−0.159124	+	0.987259i	$0.550867\pi$
$174$	−4.56314e12	−0.0124650
$175$	−5.94891e14	−1.56563
$176$	5.29371e13	0.134254
$177$	3.07496e13	0.0751646
$178$	−4.38783e13	−0.103400
$179$	−5.53289e14	−1.25721	−0.628605	−	0.777725i	$-0.716374\pi$
$179$	−5.53289e14	−1.25721	−0.628605	+	0.777725i	$0.716374\pi$
$180$	−2.32981e14	−0.510564
$181$	−6.06513e14	−1.28212	−0.641061	−	0.767490i	$-0.721505\pi$
$181$	−6.06513e14	−1.28212	−0.641061	+	0.767490i	$0.721505\pi$
$182$	4.59698e13	0.0937581
$183$	−5.30030e14	−1.04320
$184$	5.77560e14	1.09719
$185$	9.08601e14	1.66631
$186$	3.47241e13	0.0614889
$187$	1.41768e14	0.242441
$188$	1.14714e14	0.189492
$189$	−9.17089e13	−0.146356
$190$	−5.09702e14	−0.785992
$191$	8.16520e14	1.21689	0.608443	−	0.793597i	$-0.291794\pi$
$191$	8.16520e14	1.21689	0.608443	+	0.793597i	$0.291794\pi$
$192$	−1.32243e14	−0.190509
$193$	2.28230e14	0.317870	0.158935	−	0.987289i	$-0.449194\pi$
$193$	2.28230e14	0.317870	0.158935	+	0.987289i	$0.449194\pi$
$194$	1.94210e14	0.261554
$195$	−2.71192e14	−0.353225
$196$	2.93108e14	0.369287
$197$	−2.72506e14	−0.332158	−0.166079	−	0.986112i	$-0.553111\pi$
$197$	−2.72506e14	−0.332158	−0.166079	+	0.986112i	$0.553111\pi$
$198$	2.08031e13	0.0245361
$199$	−3.44397e14	−0.393110	−0.196555	−	0.980493i	$-0.562975\pi$
$199$	−3.44397e14	−0.393110	−0.196555	+	0.980493i	$0.562975\pi$
$200$	−1.23184e15	−1.36100
$201$	1.73850e14	0.185952
$202$	3.49194e14	0.361645
$203$	4.64510e13	0.0465876
$204$	−6.04216e14	−0.586943
$205$	−6.30644e14	−0.593450
$206$	−6.07796e14	−0.554142
$207$	−6.26192e14	−0.553223
$208$	−2.62622e14	−0.224864
$209$	−3.20903e14	−0.266332
$210$	−3.36358e14	−0.270631
$211$	−9.27119e14	−0.723268	−0.361634	−	0.932320i	$-0.617781\pi$
$211$	−9.27119e14	−0.723268	−0.361634	+	0.932320i	$0.617781\pi$
$212$	2.62198e14	0.198356
$213$	−3.14584e14	−0.230818
$214$	−3.39884e14	−0.241903
$215$	−2.36159e15	−1.63063
$216$	−1.89901e14	−0.127227
$217$	−3.53477e14	−0.229812
$218$	−2.63134e14	−0.166039
$219$	−6.37190e14	−0.390285
$220$	−5.37984e14	−0.319906
$221$	−7.03311e14	−0.406067
$222$	3.45777e14	0.193866
$223$	−3.07542e15	−1.67465	−0.837324	−	0.546708i	$-0.815881\pi$
$223$	−3.07542e15	−1.67465	−0.837324	+	0.546708i	$0.815881\pi$
$224$	−1.27625e15	−0.675033
$225$	1.33556e15	0.686242
$226$	1.16197e15	0.580082
$227$	6.53264e14	0.316899	0.158449	−	0.987367i	$-0.449351\pi$
$227$	6.53264e14	0.316899	0.158449	+	0.987367i	$0.449351\pi$
$228$	1.36769e15	0.644781
$229$	−3.20867e15	−1.47026	−0.735131	−	0.677926i	$-0.762879\pi$
$229$	−3.20867e15	−1.47026	−0.735131	+	0.677926i	$0.762879\pi$
$230$	−2.29667e15	−1.02298
$231$	−2.11768e14	−0.0917026
$232$	9.61858e13	0.0404985
$233$	5.16607e14	0.211518	0.105759	−	0.994392i	$-0.466273\pi$
$233$	5.16607e14	0.211518	0.105759	+	0.994392i	$0.466273\pi$
$234$	−1.03205e14	−0.0410957
$235$	−9.77014e14	−0.378407
$236$	−3.02624e14	−0.114018
$237$	1.35998e15	0.498503
$238$	−8.72315e14	−0.311117
$239$	−1.95374e15	−0.678080	−0.339040	−	0.940772i	$-0.610102\pi$
$239$	−1.95374e15	−0.678080	−0.339040	+	0.940772i	$0.610102\pi$
$240$	1.92159e15	0.649063
$241$	−2.51478e15	−0.826779	−0.413389	−	0.910554i	$-0.635655\pi$
$241$	−2.51478e15	−0.826779	−0.413389	+	0.910554i	$0.635655\pi$
$242$	−1.05319e15	−0.337059
$243$	2.05891e14	0.0641500
$244$	5.21632e15	1.58245
$245$	−2.49639e15	−0.737451
$246$	−2.39998e14	−0.0690444
$247$	1.59200e15	0.446081
$248$	−7.31944e14	−0.199775
$249$	2.02045e14	0.0537219
$250$	2.51907e15	0.652574
$251$	−5.01551e15	−1.26601	−0.633004	−	0.774149i	$-0.718178\pi$
$251$	−5.01551e15	−1.26601	−0.633004	+	0.774149i	$0.718178\pi$
$252$	9.02557e14	0.222009
$253$	−1.44596e15	−0.346635
$254$	1.36822e15	0.319695
$255$	5.14608e15	1.17210
$256$	−1.07386e14	−0.0238445
$257$	−2.61044e14	−0.0565130	−0.0282565	−	0.999601i	$-0.508996\pi$
$257$	−2.61044e14	−0.0565130	−0.0282565	+	0.999601i	$0.508996\pi$
$258$	−8.98726e14	−0.189714
$259$	−3.51987e15	−0.724566
$260$	2.66894e15	0.535812
$261$	−1.04285e14	−0.0204201
$262$	−1.87294e15	−0.357739
$263$	−6.79659e15	−1.26642	−0.633211	−	0.773979i	$-0.718264\pi$
$263$	−6.79659e15	−1.26642	−0.633211	+	0.773979i	$0.718264\pi$
$264$	−4.38506e14	−0.0797169
$265$	−2.23313e15	−0.396110
$266$	1.97456e15	0.341774
$267$	−1.00278e15	−0.169388
$268$	−1.71096e15	−0.282074
$269$	1.47692e15	0.237666	0.118833	−	0.992914i	$-0.462085\pi$
$269$	1.47692e15	0.237666	0.118833	+	0.992914i	$0.462085\pi$
$270$	7.55142e14	0.118622
$271$	−6.15043e15	−0.943203	−0.471601	−	0.881812i	$-0.656324\pi$
$271$	−6.15043e15	−0.943203	−0.471601	+	0.881812i	$0.656324\pi$
$272$	4.98346e15	0.746162
$273$	1.05058e15	0.153593
$274$	−9.72986e14	−0.138908
$275$	3.08398e15	0.429981
$276$	6.16269e15	0.839192
$277$	1.55873e15	0.207326	0.103663	−	0.994613i	$-0.466944\pi$
$277$	1.55873e15	0.207326	0.103663	+	0.994613i	$0.466944\pi$
$278$	−2.80997e15	−0.365098
$279$	7.93575e14	0.100730
$280$	7.09005e15	0.879270
$281$	1.02028e15	0.123631	0.0618157	−	0.998088i	$-0.480311\pi$
$281$	1.02028e15	0.123631	0.0618157	+	0.998088i	$0.480311\pi$
$282$	−3.71812e14	−0.0440255
$283$	−3.55832e15	−0.411750	−0.205875	−	0.978578i	$-0.566004\pi$
$283$	−3.55832e15	−0.411750	−0.205875	+	0.978578i	$0.566004\pi$
$284$	3.09599e15	0.350131
$285$	−1.16486e16	−1.28760
$286$	−2.38313e14	−0.0257495
$287$	2.44308e15	0.258051
$288$	2.86526e15	0.295878
$289$	3.44133e15	0.347448
$290$	−3.82483e14	−0.0377594
$291$	4.43842e15	0.428474
$292$	6.27093e15	0.592029
$293$	9.91796e15	0.915763	0.457881	−	0.889013i	$-0.348608\pi$
$293$	9.91796e15	0.915763	0.457881	+	0.889013i	$0.348608\pi$
$294$	−9.50026e14	−0.0857981
$295$	2.57743e15	0.227690
$296$	−7.28858e15	−0.629864
$297$	4.75429e14	0.0401947
$298$	2.86981e15	0.237382
$299$	7.17341e15	0.580581
$300$	−1.31440e16	−1.04097
$301$	9.14867e15	0.709048
$302$	−7.88961e14	−0.0598426
$303$	7.98038e15	0.592443
$304$	−1.12805e16	−0.819690
$305$	−4.44272e16	−3.16009
$306$	1.95839e15	0.136367
$307$	2.05391e15	0.140017	0.0700087	−	0.997546i	$-0.477697\pi$
$307$	2.05391e15	0.140017	0.0700087	+	0.997546i	$0.477697\pi$
$308$	2.08412e15	0.139105
$309$	−1.38904e16	−0.907789
$310$	2.91058e15	0.186264
$311$	−1.23258e16	−0.772452	−0.386226	−	0.922404i	$-0.626222\pi$
$311$	−1.23258e16	−0.772452	−0.386226	+	0.922404i	$0.626222\pi$
$312$	2.17544e15	0.133518
$313$	−1.78783e16	−1.07470	−0.537352	−	0.843358i	$-0.680575\pi$
$313$	−1.78783e16	−1.07470	−0.537352	+	0.843358i	$0.680575\pi$
$314$	−5.25044e15	−0.309138
$315$	−7.68704e15	−0.443344
$316$	−1.33843e16	−0.756188
$317$	−1.45191e15	−0.0803628	−0.0401814	−	0.999192i	$-0.512794\pi$
$317$	−1.45191e15	−0.0803628	−0.0401814	+	0.999192i	$0.512794\pi$
$318$	−8.49840e14	−0.0460851
$319$	−2.40807e14	−0.0127947
$320$	−1.10846e16	−0.577094
$321$	−7.76761e15	−0.396283
$322$	8.89716e15	0.444824
$323$	−3.02096e16	−1.48023
$324$	−2.02629e15	−0.0973102
$325$	−1.52997e16	−0.720179
$326$	−1.07275e16	−0.494975
$327$	−6.01358e15	−0.272002
$328$	5.05887e15	0.224323
$329$	3.78490e15	0.164544
$330$	1.74372e15	0.0743252
$331$	−1.14585e16	−0.478901	−0.239450	−	0.970909i	$-0.576967\pi$
$331$	−1.14585e16	−0.478901	−0.239450	+	0.970909i	$0.576967\pi$
$332$	−1.98843e15	−0.0814916
$333$	7.90229e15	0.317589
$334$	1.65107e16	0.650748
$335$	1.45722e16	0.563290
$336$	−7.44412e15	−0.282233
$337$	2.20633e16	0.820497	0.410248	−	0.911974i	$-0.365442\pi$
$337$	2.20633e16	0.820497	0.410248	+	0.911974i	$0.365442\pi$
$338$	−8.47900e15	−0.309304
$339$	2.65553e16	0.950283
$340$	−5.06454e16	−1.77798
$341$	1.83247e15	0.0631150
$342$	−4.43298e15	−0.149805
$343$	3.26061e16	1.08115
$344$	1.89441e16	0.616374
$345$	−5.24874e16	−1.67583
$346$	−3.57961e15	−0.112161
$347$	3.06253e16	0.941756	0.470878	−	0.882198i	$-0.343937\pi$
$347$	3.06253e16	0.941756	0.470878	+	0.882198i	$0.343937\pi$
$348$	1.02632e15	0.0309756
$349$	−2.42759e16	−0.719136	−0.359568	−	0.933119i	$-0.617076\pi$
$349$	−2.42759e16	−0.719136	−0.359568	+	0.933119i	$0.617076\pi$
$350$	−1.89761e16	−0.551780
$351$	−2.35861e15	−0.0673224
$352$	6.61625e15	0.185389
$353$	−2.83637e16	−0.780238	−0.390119	−	0.920765i	$-0.627566\pi$
$353$	−2.83637e16	−0.780238	−0.390119	+	0.920765i	$0.627566\pi$
$354$	9.80867e14	0.0264904
$355$	−2.63684e16	−0.699197
$356$	9.86892e15	0.256948
$357$	−1.99356e16	−0.509667
$358$	−1.76491e16	−0.443081
$359$	2.74348e16	0.676375	0.338187	−	0.941079i	$-0.390186\pi$
$359$	2.74348e16	0.676375	0.338187	+	0.941079i	$0.390186\pi$
$360$	−1.59175e16	−0.385398
$361$	2.63289e16	0.626088
$362$	−1.93469e16	−0.451861
$363$	−2.40692e16	−0.552165
$364$	−1.03393e16	−0.232988
$365$	−5.34093e16	−1.18226
$366$	−1.69072e16	−0.367658
$367$	−4.88581e16	−1.04377	−0.521887	−	0.853014i	$-0.674772\pi$
$367$	−4.88581e16	−1.04377	−0.521887	+	0.853014i	$0.674772\pi$
$368$	−5.08288e16	−1.06684
$369$	−5.48484e15	−0.113108
$370$	2.89830e16	0.587263
$371$	8.65102e15	0.172241
$372$	−7.81000e15	−0.152800
$373$	4.30144e16	0.827001	0.413500	−	0.910504i	$-0.364306\pi$
$373$	4.30144e16	0.827001	0.413500	+	0.910504i	$0.364306\pi$
$374$	4.52218e15	0.0854442
$375$	5.75701e16	1.06904
$376$	7.83737e15	0.143037
$377$	1.19465e15	0.0214299
$378$	−2.92538e15	−0.0515805
$379$	8.99296e16	1.55865	0.779323	−	0.626622i	$-0.215563\pi$
$379$	8.99296e16	1.55865	0.779323	+	0.626622i	$0.215563\pi$
$380$	1.14640e17	1.95318
$381$	3.12689e16	0.523721
$382$	2.60458e16	0.428870
$383$	5.93851e16	0.961359	0.480680	−	0.876896i	$-0.340390\pi$
$383$	5.93851e16	0.961359	0.480680	+	0.876896i	$0.340390\pi$
$384$	−3.64162e16	−0.579617
$385$	−1.77504e16	−0.277787
$386$	7.28020e15	0.112028
$387$	−2.05392e16	−0.310787
$388$	−4.36809e16	−0.649958
$389$	1.12825e17	1.65094	0.825471	−	0.564445i	$-0.190910\pi$
$389$	1.12825e17	1.65094	0.825471	+	0.564445i	$0.190910\pi$
$390$	−8.65062e15	−0.124488
$391$	−1.36121e17	−1.92654
$392$	2.00255e16	0.278755
$393$	−4.28038e16	−0.586044
$394$	−8.69253e15	−0.117063
$395$	1.13994e17	1.51008
$396$	−4.67896e15	−0.0609720
$397$	1.47653e17	1.89280	0.946400	−	0.322996i	$-0.104690\pi$
$397$	1.47653e17	1.89280	0.946400	+	0.322996i	$0.104690\pi$
$398$	−1.09858e16	−0.138545
$399$	4.51260e16	0.559890
$400$	1.08409e17	1.32335
$401$	1.58877e17	1.90819	0.954096	−	0.299501i	$-0.0968201\pi$
$401$	1.58877e17	1.90819	0.954096	+	0.299501i	$0.0968201\pi$
$402$	5.54557e15	0.0655356
$403$	−9.09089e15	−0.105712
$404$	−7.85392e16	−0.898686
$405$	1.72578e16	0.194325
$406$	1.48172e15	0.0164190
$407$	1.82474e16	0.198993
$408$	−4.12807e16	−0.443053
$409$	−4.33141e16	−0.457539	−0.228769	−	0.973481i	$-0.573470\pi$
$409$	−4.33141e16	−0.457539	−0.228769	+	0.973481i	$0.573470\pi$
$410$	−2.01166e16	−0.209151
$411$	−2.22364e16	−0.227558
$412$	1.36703e17	1.37704
$413$	−9.98483e15	−0.0990069
$414$	−1.99746e16	−0.194974
$415$	1.69354e16	0.162736
$416$	−3.28233e16	−0.310510
$417$	−6.42182e16	−0.598100
$418$	−1.02363e16	−0.0938639
$419$	−1.14548e17	−1.03418	−0.517088	−	0.855932i	$-0.672984\pi$
$419$	−1.14548e17	−1.03418	−0.517088	+	0.855932i	$0.672984\pi$
$420$	7.56523e16	0.672515
$421$	1.28806e16	0.112746	0.0563732	−	0.998410i	$-0.482046\pi$
$421$	1.28806e16	0.112746	0.0563732	+	0.998410i	$0.482046\pi$
$422$	−2.95737e16	−0.254903
$423$	−8.49729e15	−0.0721220
$424$	1.79136e16	0.149729
$425$	2.90324e17	2.38976
$426$	−1.00348e16	−0.0813475
$427$	1.72108e17	1.37411
$428$	7.64453e16	0.601127
$429$	−5.44633e15	−0.0421825
$430$	−7.53313e16	−0.574686
$431$	1.00330e17	0.753923	0.376962	−	0.926229i	$-0.376969\pi$
$431$	1.00330e17	0.753923	0.376962	+	0.926229i	$0.376969\pi$
$432$	1.67124e16	0.123707
$433$	−1.36706e17	−0.996820	−0.498410	−	0.866941i	$-0.666083\pi$
$433$	−1.36706e17	−0.996820	−0.498410	+	0.866941i	$0.666083\pi$
$434$	−1.12754e16	−0.0809933
$435$	−8.74115e15	−0.0618570
$436$	5.91829e16	0.412605
$437$	3.08122e17	2.11638
$438$	−2.03254e16	−0.137549
$439$	−2.05821e17	−1.37236	−0.686182	−	0.727430i	$-0.740715\pi$
$439$	−2.05821e17	−1.37236	−0.686182	+	0.727430i	$0.740715\pi$
$440$	−3.67556e16	−0.241480
$441$	−2.17116e16	−0.140553
$442$	−2.24346e16	−0.143111
$443$	5.17244e16	0.325141	0.162570	−	0.986697i	$-0.448022\pi$
$443$	5.17244e16	0.325141	0.162570	+	0.986697i	$0.448022\pi$
$444$	−7.77707e16	−0.481756
$445$	−8.40532e16	−0.513115
$446$	−9.81015e16	−0.590200
$447$	6.55859e16	0.388877
$448$	4.29413e16	0.250939
$449$	1.72646e17	0.994384	0.497192	−	0.867640i	$-0.334364\pi$
$449$	1.72646e17	0.994384	0.497192	+	0.867640i	$0.334364\pi$
$450$	4.26024e16	0.241854
$451$	−1.26652e16	−0.0708703
$452$	−2.61345e17	−1.44150
$453$	−1.80307e16	−0.0980335
$454$	2.08382e16	0.111685
$455$	8.80598e16	0.465268
$456$	9.34422e16	0.486712
$457$	2.70189e17	1.38744	0.693718	−	0.720247i	$-0.255972\pi$
$457$	2.70189e17	1.38744	0.693718	+	0.720247i	$0.255972\pi$
$458$	−1.02352e17	−0.518167
$459$	4.47565e16	0.223395
$460$	5.16557e17	2.54210
$461$	−2.84833e17	−1.38209	−0.691043	−	0.722814i	$-0.742848\pi$
$461$	−2.84833e17	−1.38209	−0.691043	+	0.722814i	$0.742848\pi$
$462$	−6.75507e15	−0.0323190
$463$	2.36098e17	1.11382	0.556912	−	0.830571i	$-0.311986\pi$
$463$	2.36098e17	1.11382	0.556912	+	0.830571i	$0.311986\pi$
$464$	−8.46493e15	−0.0393782
$465$	6.65175e16	0.305135
$466$	1.64790e16	0.0745457
$467$	−2.54803e17	−1.13670	−0.568348	−	0.822788i	$-0.692417\pi$
$467$	−2.54803e17	−1.13670	−0.568348	+	0.822788i	$0.692417\pi$
$468$	2.32124e16	0.102122
$469$	−5.64517e16	−0.244937
$470$	−3.11653e16	−0.133363
$471$	−1.19992e17	−0.506427
$472$	−2.06756e16	−0.0860665
$473$	−4.74278e16	−0.194731
$474$	4.33813e16	0.175689
$475$	−6.57172e17	−2.62525
$476$	1.96197e17	0.773122
$477$	−1.94220e16	−0.0754961
$478$	−6.23215e16	−0.238977
$479$	5.00063e16	0.189166	0.0945831	−	0.995517i	$-0.469848\pi$
$479$	5.00063e16	0.189166	0.0945831	+	0.995517i	$0.469848\pi$
$480$	2.40166e17	0.896279
$481$	−9.05256e16	−0.333295
$482$	−8.02178e16	−0.291384
$483$	2.03333e17	0.728706
$484$	2.36878e17	0.837588
$485$	3.72029e17	1.29794
$486$	6.56762e15	0.0226085
$487$	−5.46060e17	−1.85482	−0.927410	−	0.374046i	$-0.877970\pi$
$487$	−5.46060e17	−1.85482	−0.927410	+	0.374046i	$0.877970\pi$
$488$	3.56384e17	1.19451
$489$	−2.45163e17	−0.810863
$490$	−7.96312e16	−0.259901
$491$	−4.51729e16	−0.145495	−0.0727476	−	0.997350i	$-0.523177\pi$
$491$	−4.51729e16	−0.145495	−0.0727476	+	0.997350i	$0.523177\pi$
$492$	5.39793e16	0.171575
$493$	−2.26694e16	−0.0711107
$494$	5.07826e16	0.157213
$495$	3.98505e16	0.121759
$496$	6.44155e16	0.194249
$497$	1.02150e17	0.304033
$498$	6.44493e15	0.0189333
$499$	3.26679e17	0.947256	0.473628	−	0.880725i	$-0.342944\pi$
$499$	3.26679e17	0.947256	0.473628	+	0.880725i	$0.342944\pi$
$500$	−5.66578e17	−1.62164
$501$	3.77331e17	1.06605
$502$	−1.59987e17	−0.446182
$503$	3.73415e17	1.02802	0.514008	−	0.857786i	$-0.328160\pi$
$503$	3.73415e17	1.02802	0.514008	+	0.857786i	$0.328160\pi$
$504$	6.16636e16	0.167583
$505$	6.68916e17	1.79464
$506$	−4.61239e16	−0.122165
$507$	−1.93777e17	−0.506699
$508$	−3.07734e17	−0.794440
$509$	4.39988e17	1.12144	0.560719	−	0.828006i	$-0.310525\pi$
$509$	4.39988e17	1.12144	0.560719	+	0.828006i	$0.310525\pi$
$510$	1.64152e17	0.413087
$511$	2.06904e17	0.514084
$512$	4.05794e17	0.995523
$513$	−1.01310e17	−0.245409
$514$	−8.32691e15	−0.0199170
$515$	−1.16429e18	−2.74989
$516$	2.02138e17	0.471438
$517$	−1.96213e16	−0.0451898
$518$	−1.12279e17	−0.255361
$519$	−8.18074e16	−0.183740
$520$	1.82345e17	0.404457
$521$	1.37202e17	0.300549	0.150275	−	0.988644i	$-0.451984\pi$
$521$	1.37202e17	0.300549	0.150275	+	0.988644i	$0.451984\pi$
$522$	−3.32653e15	−0.00719670
$523$	4.14693e17	0.886065	0.443032	−	0.896506i	$-0.353903\pi$
$523$	4.14693e17	0.886065	0.443032	+	0.896506i	$0.353903\pi$
$524$	4.21255e17	0.888979
$525$	−4.33676e17	−0.903919
$526$	−2.16801e17	−0.446328
$527$	1.72507e17	0.350782
$528$	3.85912e16	0.0775118
$529$	8.84331e17	1.75450
$530$	−7.12336e16	−0.139602
$531$	2.24165e16	0.0433963
$532$	−4.44109e17	−0.849306
$533$	6.28322e16	0.118701
$534$	−3.19873e16	−0.0596979
$535$	−6.51082e17	−1.20043
$536$	−1.16894e17	−0.212923
$537$	−4.03348e17	−0.725850
$538$	4.71116e16	0.0837613
$539$	−5.01349e16	−0.0880671
$540$	−1.69843e17	−0.294774
$541$	−1.38315e17	−0.237186	−0.118593	−	0.992943i	$-0.537838\pi$
$541$	−1.38315e17	−0.237186	−0.118593	+	0.992943i	$0.537838\pi$
$542$	−1.96190e17	−0.332415
$543$	−4.42148e17	−0.740233
$544$	6.22849e17	1.03036
$545$	−5.04058e17	−0.823955
$546$	3.35120e16	0.0541313
$547$	2.79562e17	0.446232	0.223116	−	0.974792i	$-0.428377\pi$
$547$	2.79562e17	0.446232	0.223116	+	0.974792i	$0.428377\pi$
$548$	2.18840e17	0.345186
$549$	−3.86392e17	−0.602293
$550$	9.83745e16	0.151539
$551$	5.13141e16	0.0781180
$552$	4.21041e17	0.633462
$553$	−4.41605e17	−0.656629
$554$	4.97212e16	0.0730682
$555$	6.62370e17	0.962047
$556$	6.32006e17	0.907267
$557$	6.12643e17	0.869259	0.434629	−	0.900609i	$-0.356879\pi$
$557$	6.12643e17	0.869259	0.434629	+	0.900609i	$0.356879\pi$
$558$	2.53139e16	0.0355006
$559$	2.35290e17	0.326157
$560$	−6.23967e17	−0.854947
$561$	1.03349e17	0.139974
$562$	3.25455e16	0.0435717
$563$	−4.57103e17	−0.604935	−0.302468	−	0.953160i	$-0.597810\pi$
$563$	−4.57103e17	−0.604935	−0.302468	+	0.953160i	$0.597810\pi$
$564$	8.36264e16	0.109403
$565$	2.22586e18	2.87862
$566$	−1.13505e17	−0.145114
$567$	−6.68558e16	−0.0844985
$568$	2.11521e17	0.264295
$569$	−3.02816e17	−0.374067	−0.187033	−	0.982354i	$-0.559887\pi$
$569$	−3.02816e17	−0.374067	−0.187033	+	0.982354i	$0.559887\pi$
$570$	−3.71573e17	−0.453793
$571$	4.55065e17	0.549463	0.274732	−	0.961521i	$-0.411411\pi$
$571$	4.55065e17	0.549463	0.274732	+	0.961521i	$0.411411\pi$
$572$	5.36003e16	0.0639872
$573$	5.95243e17	0.702570
$574$	7.79306e16	0.0909454
$575$	−2.96115e18	−3.41680
$576$	−9.64054e16	−0.109991
$577$	−1.34983e18	−1.52278	−0.761391	−	0.648293i	$-0.775483\pi$
$577$	−1.34983e18	−1.52278	−0.761391	+	0.648293i	$0.775483\pi$
$578$	1.09773e17	0.122452
$579$	1.66380e17	0.183522
$580$	8.60264e16	0.0938318
$581$	−6.56067e16	−0.0707626
$582$	1.41579e17	0.151008
$583$	−4.48479e16	−0.0473038
$584$	4.28436e17	0.446892
$585$	−1.97699e17	−0.203935
$586$	3.16368e17	0.322744
$587$	−3.09629e17	−0.312388	−0.156194	−	0.987726i	$-0.549923\pi$
$587$	−3.09629e17	−0.312388	−0.156194	+	0.987726i	$0.549923\pi$
$588$	2.13676e17	0.213208
$589$	−3.90484e17	−0.385349
$590$	8.22163e16	0.0802454
$591$	−1.98657e17	−0.191772
$592$	6.41439e17	0.612441
$593$	−1.77955e18	−1.68056	−0.840282	−	0.542149i	$-0.817611\pi$
$593$	−1.77955e18	−1.68056	−0.840282	+	0.542149i	$0.817611\pi$
$594$	1.51655e16	0.0141659
$595$	−1.67101e18	−1.54390
$596$	−6.45467e17	−0.589893
$597$	−2.51065e17	−0.226962
$598$	2.28821e17	0.204616
$599$	1.80860e17	0.159981	0.0799906	−	0.996796i	$-0.474511\pi$
$599$	1.80860e17	0.159981	0.0799906	+	0.996796i	$0.474511\pi$
$600$	−8.98010e17	−0.785775
$601$	−5.00295e17	−0.433054	−0.216527	−	0.976277i	$-0.569473\pi$
$601$	−5.00295e17	−0.433054	−0.216527	+	0.976277i	$0.569473\pi$
$602$	2.91829e17	0.249892
$603$	1.26737e17	0.107360
$604$	1.77450e17	0.148708
$605$	−2.01748e18	−1.67263
$606$	2.54562e17	0.208796
$607$	−1.91470e18	−1.55373	−0.776864	−	0.629668i	$-0.783191\pi$
$607$	−1.91470e18	−1.55373	−0.776864	+	0.629668i	$0.783191\pi$
$608$	−1.40987e18	−1.13189
$609$	3.38627e16	0.0268974
$610$	−1.41716e18	−1.11372
$611$	9.73417e16	0.0756887
$612$	−4.40473e17	−0.338872
$613$	4.62799e17	0.352290	0.176145	−	0.984364i	$-0.443637\pi$
$613$	4.62799e17	0.352290	0.176145	+	0.984364i	$0.443637\pi$
$614$	6.55167e16	0.0493467
$615$	−4.59739e17	−0.342628
$616$	1.42389e17	0.105003
$617$	2.13534e18	1.55817	0.779083	−	0.626921i	$-0.215685\pi$
$617$	2.13534e18	1.55817	0.779083	+	0.626921i	$0.215685\pi$
$618$	−4.43083e17	−0.319934
$619$	−7.96416e16	−0.0569051	−0.0284525	−	0.999595i	$-0.509058\pi$
$619$	−7.96416e16	−0.0569051	−0.0284525	+	0.999595i	$0.509058\pi$
$620$	−6.54634e17	−0.462863
$621$	−4.56494e17	−0.319403
$622$	−3.93174e17	−0.272237
$623$	3.25618e17	0.223118
$624$	−1.91451e17	−0.129825
$625$	1.75778e18	1.17963
$626$	−5.70293e17	−0.378760
$627$	−2.33938e17	−0.153767
$628$	1.18091e18	0.768207
$629$	1.71780e18	1.10597
$630$	−2.45205e17	−0.156249
$631$	1.92195e18	1.21213	0.606067	−	0.795414i	$-0.292746\pi$
$631$	1.92195e18	1.21213	0.606067	+	0.795414i	$0.292746\pi$
$632$	−9.14429e17	−0.570807
$633$	−6.75869e17	−0.417579
$634$	−4.63139e16	−0.0283224
$635$	2.62096e18	1.58647
$636$	1.91142e17	0.114521
$637$	2.48720e17	0.147504
$638$	−7.68139e15	−0.00450926
$639$	−2.29332e17	−0.133263
$640$	−3.05240e18	−1.75579
$641$	1.47841e18	0.841819	0.420909	−	0.907103i	$-0.361711\pi$
$641$	1.47841e18	0.841819	0.420909	+	0.907103i	$0.361711\pi$
$642$	−2.47775e17	−0.139663
$643$	3.10088e18	1.73027	0.865135	−	0.501539i	$-0.167233\pi$
$643$	3.10088e18	1.73027	0.865135	+	0.501539i	$0.167233\pi$
$644$	−2.00111e18	−1.10538
$645$	−1.72160e18	−0.941443
$646$	−9.63641e17	−0.521679
$647$	−2.73452e18	−1.46556	−0.732780	−	0.680465i	$-0.761778\pi$
$647$	−2.73452e18	−1.46556	−0.732780	+	0.680465i	$0.761778\pi$
$648$	−1.38438e17	−0.0734544
$649$	5.17625e16	0.0271910
$650$	−4.88037e17	−0.253814
$651$	−2.57685e17	−0.132682
$652$	2.41278e18	1.23001
$653$	1.21786e18	0.614696	0.307348	−	0.951597i	$-0.400558\pi$
$653$	1.21786e18	0.614696	0.307348	+	0.951597i	$0.400558\pi$
$654$	−1.91824e17	−0.0958624
$655$	−3.58781e18	−1.77526
$656$	−4.45211e17	−0.218118
$657$	−4.64511e17	−0.225331
$658$	1.20733e17	0.0579904
$659$	1.74676e18	0.830766	0.415383	−	0.909647i	$-0.363648\pi$
$659$	1.74676e18	0.830766	0.415383	+	0.909647i	$0.363648\pi$
$660$	−3.92190e17	−0.184698
$661$	4.20821e18	1.96240	0.981201	−	0.192989i	$-0.0618181\pi$
$661$	4.20821e18	1.96240	0.981201	+	0.192989i	$0.0618181\pi$
$662$	−3.65509e17	−0.168780
$663$	−5.12714e17	−0.234443
$664$	−1.35852e17	−0.0615138
$665$	3.78246e18	1.69603
$666$	2.52071e17	0.111929
$667$	2.31216e17	0.101672
$668$	−3.71351e18	−1.61710
$669$	−2.24198e18	−0.966858
$670$	4.64830e17	0.198522
$671$	−8.92229e17	−0.377381
$672$	−9.30390e17	−0.389731
$673$	4.24735e18	1.76206	0.881030	−	0.473061i	$-0.156851\pi$
$673$	4.24735e18	1.76206	0.881030	+	0.473061i	$0.156851\pi$
$674$	7.03788e17	0.289170
$675$	9.73624e17	0.396202
$676$	1.90706e18	0.768619
$677$	−8.79869e17	−0.351230	−0.175615	−	0.984459i	$-0.556191\pi$
$677$	−8.79869e17	−0.351230	−0.175615	+	0.984459i	$0.556191\pi$
$678$	8.47074e17	0.334910
$679$	−1.44122e18	−0.564386
$680$	−3.46015e18	−1.34211
$681$	4.76229e17	0.182962
$682$	5.84530e16	0.0222438
$683$	5.01079e18	1.88874	0.944369	−	0.328887i	$-0.106673\pi$
$683$	5.01079e18	1.88874	0.944369	+	0.328887i	$0.106673\pi$
$684$	9.97048e17	0.372264
$685$	−1.86385e18	−0.689323
$686$	1.04009e18	0.381033
$687$	−2.33912e18	−0.848856
$688$	−1.66720e18	−0.599324
$689$	2.22491e17	0.0792296
$690$	−1.67427e18	−0.590618
$691$	3.55620e18	1.24274	0.621368	−	0.783519i	$-0.286577\pi$
$691$	3.55620e18	1.24274	0.621368	+	0.783519i	$0.286577\pi$
$692$	8.05111e17	0.278719
$693$	−1.54379e17	−0.0529445
$694$	9.76901e17	0.331905
$695$	−5.38277e18	−1.81178
$696$	7.01195e16	0.0233818
$697$	−1.19229e18	−0.393885
$698$	−7.74367e17	−0.253447
$699$	3.76607e17	0.122120
$700$	4.26804e18	1.37117
$701$	8.46551e17	0.269455	0.134727	−	0.990883i	$-0.456984\pi$
$701$	8.46551e17	0.269455	0.134727	+	0.990883i	$0.456984\pi$
$702$	−7.52362e16	−0.0237266
$703$	−3.88838e18	−1.21495
$704$	−2.22612e17	−0.0689171
$705$	−7.12243e17	−0.218474
$706$	−9.04759e17	−0.274981
$707$	−2.59134e18	−0.780366
$708$	−2.20613e17	−0.0658285
$709$	3.28062e18	0.969963	0.484982	−	0.874524i	$-0.338826\pi$
$709$	3.28062e18	0.969963	0.484982	+	0.874524i	$0.338826\pi$
$710$	−8.41114e17	−0.246420
$711$	9.91425e17	0.287811
$712$	6.74255e17	0.193956
$713$	−1.75948e18	−0.501537
$714$	−6.35918e17	−0.179623
$715$	−4.56512e17	−0.127780
$716$	3.96957e18	1.10105
$717$	−1.42428e18	−0.391489
$718$	8.75128e17	0.238376
$719$	4.73928e18	1.27931	0.639653	−	0.768664i	$-0.279078\pi$
$719$	4.73928e18	1.27931	0.639653	+	0.768664i	$0.279078\pi$
$720$	1.40084e18	0.374737
$721$	4.51041e18	1.19574
$722$	8.39852e17	0.220654
$723$	−1.83328e18	−0.477341
$724$	4.35142e18	1.12287
$725$	−4.93145e17	−0.126118
$726$	−7.67773e17	−0.194601
$727$	−4.27803e18	−1.07466	−0.537329	−	0.843373i	$-0.680567\pi$
$727$	−4.27803e18	−1.07466	−0.537329	+	0.843373i	$0.680567\pi$
$728$	−7.06395e17	−0.175871
$729$	1.50095e17	0.0370370
$730$	−1.70368e18	−0.416666
$731$	−4.46481e18	−1.08228
$732$	3.80269e18	0.913628
$733$	−6.99073e18	−1.66474	−0.832371	−	0.554219i	$-0.813017\pi$
$733$	−6.99073e18	−1.66474	−0.832371	+	0.554219i	$0.813017\pi$
$734$	−1.55850e18	−0.367860
$735$	−1.81987e18	−0.425767
$736$	−6.35274e18	−1.47318
$737$	2.92652e17	0.0672687
$738$	−1.74958e17	−0.0398628
$739$	−3.99272e18	−0.901736	−0.450868	−	0.892591i	$-0.648886\pi$
$739$	−3.99272e18	−0.901736	−0.450868	+	0.892591i	$0.648886\pi$
$740$	−6.51874e18	−1.45934
$741$	1.16057e18	0.257545
$742$	2.75955e17	0.0607034
$743$	−8.47400e18	−1.84783	−0.923913	−	0.382603i	$-0.875028\pi$
$743$	−8.47400e18	−1.84783	−0.923913	+	0.382603i	$0.875028\pi$
$744$	−5.33587e17	−0.115340
$745$	5.49741e18	1.17799
$746$	1.37209e18	0.291462
$747$	1.47291e17	0.0310164
$748$	−1.01711e18	−0.212328
$749$	2.52225e18	0.521984
$750$	1.83640e18	0.376764
$751$	1.30595e18	0.265624	0.132812	−	0.991141i	$-0.457599\pi$
$751$	1.30595e18	0.265624	0.132812	+	0.991141i	$0.457599\pi$
$752$	−6.89736e17	−0.139081
$753$	−3.65631e18	−0.730930
$754$	3.81075e16	0.00755260
$755$	−1.51133e18	−0.296965
$756$	6.57964e17	0.128177
$757$	−3.49982e18	−0.675963	−0.337982	−	0.941153i	$-0.609744\pi$
$757$	−3.49982e18	−0.675963	−0.337982	+	0.941153i	$0.609744\pi$
$758$	2.86862e18	0.549317
$759$	−1.05410e18	−0.200130
$760$	7.83233e18	1.47436
$761$	7.28338e18	1.35935	0.679677	−	0.733511i	$-0.262120\pi$
$761$	7.28338e18	1.35935	0.679677	+	0.733511i	$0.262120\pi$
$762$	9.97431e17	0.184576
$763$	1.95269e18	0.358282
$764$	−5.85811e18	−1.06574
$765$	3.75150e18	0.676714
$766$	1.89430e18	0.338814
$767$	−2.56794e17	−0.0455424
$768$	−7.82845e16	−0.0137666
$769$	−2.42836e18	−0.423440	−0.211720	−	0.977330i	$-0.567907\pi$
$769$	−2.42836e18	−0.423440	−0.211720	+	0.977330i	$0.567907\pi$
$770$	−5.66211e17	−0.0979013
$771$	−1.90301e17	−0.0326278
$772$	−1.63743e18	−0.278388
$773$	−9.57989e18	−1.61508	−0.807539	−	0.589814i	$-0.799201\pi$
$773$	−9.57989e18	−1.61508	−0.807539	+	0.589814i	$0.799201\pi$
$774$	−6.55172e17	−0.109531
$775$	3.75268e18	0.622129
$776$	−2.98433e18	−0.490620
$777$	−2.56599e18	−0.418329
$778$	3.59894e18	0.581845
$779$	2.69885e18	0.432699
$780$	1.94566e18	0.309351
$781$	−5.29556e17	−0.0834988
$782$	−4.34207e18	−0.678974
$783$	−7.60236e16	−0.0117895
$784$	−1.76236e18	−0.271044
$785$	−1.00577e19	−1.53408
$786$	−1.36538e18	−0.206541
$787$	−7.50361e18	−1.12573	−0.562865	−	0.826549i	$-0.690301\pi$
$787$	−7.50361e18	−1.12573	−0.562865	+	0.826549i	$0.690301\pi$
$788$	1.95509e18	0.290901
$789$	−4.95471e18	−0.731169
$790$	3.63623e18	0.532200
$791$	−8.62288e18	−1.25171
$792$	−3.19671e17	−0.0460246
$793$	4.42636e18	0.632078
$794$	4.70992e18	0.667084
$795$	−1.62795e18	−0.228694
$796$	2.47087e18	0.344283
$797$	1.11566e19	1.54189	0.770944	−	0.636903i	$-0.219785\pi$
$797$	1.11566e19	1.54189	0.770944	+	0.636903i	$0.219785\pi$
$798$	1.43945e18	0.197323
$799$	−1.84714e18	−0.251157
$800$	1.35493e19	1.82739
$801$	−7.31028e17	−0.0977964
$802$	5.06794e18	0.672508
$803$	−1.07262e18	−0.141187
$804$	−1.24729e18	−0.162855
$805$	1.70434e19	2.20741
$806$	−2.89986e17	−0.0372563
$807$	1.07668e18	0.137217
$808$	−5.36588e18	−0.678371
$809$	6.68924e17	0.0838902	0.0419451	−	0.999120i	$-0.486645\pi$
$809$	6.68924e17	0.0838902	0.0419451	+	0.999120i	$0.486645\pi$
$810$	5.50498e17	0.0684863
$811$	−7.52813e17	−0.0929077	−0.0464539	−	0.998920i	$-0.514792\pi$
$811$	−7.52813e17	−0.0929077	−0.0464539	+	0.998920i	$0.514792\pi$
$812$	−3.33262e17	−0.0408010
$813$	−4.48366e18	−0.544558
$814$	5.82065e17	0.0701315
$815$	−2.05496e19	−2.45628
$816$	3.63294e18	0.430797
$817$	1.01065e19	1.18893
$818$	−1.38166e18	−0.161251
$819$	7.65874e17	0.0886772
$820$	4.52454e18	0.519738
$821$	−4.89736e18	−0.558125	−0.279062	−	0.960273i	$-0.590024\pi$
$821$	−4.89736e18	−0.558125	−0.279062	+	0.960273i	$0.590024\pi$
$822$	−7.09307e17	−0.0801987
$823$	1.48706e19	1.66813	0.834065	−	0.551666i	$-0.186008\pi$
$823$	1.48706e19	1.66813	0.834065	+	0.551666i	$0.186008\pi$
$824$	9.33969e18	1.03945
$825$	2.24822e18	0.248250
$826$	−3.18501e17	−0.0348932
$827$	9.49478e18	1.03205	0.516023	−	0.856575i	$-0.327412\pi$
$827$	9.49478e18	1.03205	0.516023	+	0.856575i	$0.327412\pi$
$828$	4.49260e18	0.484508
$829$	−9.27501e18	−0.992453	−0.496227	−	0.868193i	$-0.665282\pi$
$829$	−9.27501e18	−0.992453	−0.496227	+	0.868193i	$0.665282\pi$
$830$	5.40214e17	0.0573533
$831$	1.13632e18	0.119699
$832$	1.10438e18	0.115430
$833$	−4.71967e18	−0.489462
$834$	−2.04847e18	−0.210790
$835$	3.16279e19	3.22929
$836$	2.30231e18	0.233251
$837$	5.78516e17	0.0581567
$838$	−3.65390e18	−0.364477
$839$	1.10658e19	1.09529	0.547646	−	0.836710i	$-0.315524\pi$
$839$	1.10658e19	1.09529	0.547646	+	0.836710i	$0.315524\pi$
$840$	5.16865e18	0.507647
$841$	−1.02221e19	−0.996247
$842$	4.10873e17	0.0397355
$843$	7.43785e17	0.0713787
$844$	6.65160e18	0.633432
$845$	−1.62424e19	−1.53490
$846$	−2.71051e17	−0.0254181
$847$	7.81562e18	0.727313
$848$	−1.57651e18	−0.145587
$849$	−2.59402e18	−0.237724
$850$	9.26090e18	0.842229
$851$	−1.75206e19	−1.58128
$852$	2.25698e18	0.202148
$853$	1.96256e19	1.74443	0.872217	−	0.489119i	$-0.162682\pi$
$853$	1.96256e19	1.74443	0.872217	+	0.489119i	$0.162682\pi$
$854$	5.49000e18	0.484280
$855$	−8.49182e18	−0.743398
$856$	5.22282e18	0.453760
$857$	−5.45242e18	−0.470126	−0.235063	−	0.971980i	$-0.575530\pi$
$857$	−5.45242e18	−0.470126	−0.235063	+	0.971980i	$0.575530\pi$
$858$	−1.73730e17	−0.0148665
$859$	−5.00600e18	−0.425144	−0.212572	−	0.977145i	$-0.568184\pi$
$859$	−5.00600e18	−0.425144	−0.212572	+	0.977145i	$0.568184\pi$
$860$	1.69432e19	1.42809
$861$	1.78100e18	0.148986
$862$	3.20037e18	0.265707
$863$	9.36860e18	0.771977	0.385989	−	0.922503i	$-0.373860\pi$
$863$	9.36860e18	0.771977	0.385989	+	0.922503i	$0.373860\pi$
$864$	2.08877e18	0.170825
$865$	−6.85710e18	−0.556591
$866$	−4.36073e18	−0.351312
$867$	2.50873e18	0.200599
$868$	2.53602e18	0.201268
$869$	2.28933e18	0.180335
$870$	−2.78830e17	−0.0218004
$871$	−1.45185e18	−0.112669
$872$	4.04344e18	0.311454
$873$	3.23561e18	0.247379
$874$	9.82864e18	0.745880
$875$	−1.86938e19	−1.40814
$876$	4.57151e18	0.341808
$877$	−1.78464e19	−1.32450	−0.662252	−	0.749281i	$-0.730399\pi$
$877$	−1.78464e19	−1.32450	−0.662252	+	0.749281i	$0.730399\pi$
$878$	−6.56537e18	−0.483666
$879$	7.23020e18	0.528716
$880$	3.23471e18	0.234800
$881$	1.66487e19	1.19960	0.599801	−	0.800149i	$-0.295246\pi$
$881$	1.66487e19	1.19960	0.599801	+	0.800149i	$0.295246\pi$
$882$	−6.92569e17	−0.0495356
$883$	9.29562e18	0.659985	0.329992	−	0.943984i	$-0.392954\pi$
$883$	9.29562e18	0.659985	0.329992	+	0.943984i	$0.392954\pi$
$884$	5.04590e18	0.355630
$885$	1.87895e18	0.131457
$886$	1.64993e18	0.114590
$887$	−2.31206e19	−1.59403	−0.797013	−	0.603962i	$-0.793588\pi$
$887$	−2.31206e19	−1.59403	−0.797013	+	0.603962i	$0.793588\pi$
$888$	−5.31338e18	−0.363652
$889$	−1.01534e19	−0.689846
$890$	−2.68117e18	−0.180838
$891$	3.46588e17	0.0232064
$892$	2.20646e19	1.46664
$893$	4.18115e18	0.275906
$894$	2.09209e18	0.137053
$895$	−3.38086e19	−2.19876
$896$	1.18248e19	0.763472
$897$	5.22942e18	0.335199
$898$	5.50714e18	0.350453
$899$	−2.93021e17	−0.0185123
$900$	−9.58196e18	−0.601005
$901$	−4.22195e18	−0.262907
$902$	−4.04001e17	−0.0249770
$903$	6.66938e18	0.409369
$904$	−1.78554e19	−1.08811
$905$	−3.70608e19	−2.24233
$906$	−5.75153e17	−0.0345502
$907$	5.63564e18	0.336121	0.168061	−	0.985777i	$-0.446250\pi$
$907$	5.63564e18	0.336121	0.168061	+	0.985777i	$0.446250\pi$
$908$	−4.68683e18	−0.277537
$909$	5.81770e18	0.342047
$910$	2.80898e18	0.163976
$911$	4.33976e18	0.251534	0.125767	−	0.992060i	$-0.459861\pi$
$911$	4.33976e18	0.251534	0.125767	+	0.992060i	$0.459861\pi$
$912$	−8.22347e18	−0.473248
$913$	3.40113e17	0.0194340
$914$	8.61864e18	0.488977
$915$	−3.23874e19	−1.82448
$916$	2.30206e19	1.28764
$917$	1.38990e19	0.771938
$918$	1.42767e18	0.0787317
$919$	−1.11553e19	−0.610844	−0.305422	−	0.952217i	$-0.598798\pi$
$919$	−1.11553e19	−0.610844	−0.305422	+	0.952217i	$0.598798\pi$
$920$	3.52917e19	1.91890
$921$	1.49730e18	0.0808391
$922$	−9.08577e18	−0.487091
$923$	2.62713e18	0.139853
$924$	1.51932e18	0.0803124
$925$	3.73686e19	1.96149
$926$	7.53119e18	0.392548
$927$	−1.01261e19	−0.524112
$928$	−1.05797e18	−0.0543767
$929$	1.47329e19	0.751944	0.375972	−	0.926631i	$-0.377309\pi$
$929$	1.47329e19	0.751944	0.375972	+	0.926631i	$0.377309\pi$
$930$	2.12181e18	0.107539
$931$	1.06834e19	0.537693
$932$	−3.70639e18	−0.185246
$933$	−8.98549e18	−0.445975
$934$	−8.12784e18	−0.400609
$935$	8.66269e18	0.424011
$936$	1.58589e18	0.0770869
$937$	−8.83941e18	−0.426694	−0.213347	−	0.976977i	$-0.568436\pi$
$937$	−8.83941e18	−0.426694	−0.213347	+	0.976977i	$0.568436\pi$
$938$	−1.80073e18	−0.0863235
$939$	−1.30333e19	−0.620481
$940$	7.00957e18	0.331406
$941$	−1.84886e19	−0.868102	−0.434051	−	0.900888i	$-0.642916\pi$
$941$	−1.84886e19	−0.868102	−0.434051	+	0.900888i	$0.642916\pi$
$942$	−3.82757e18	−0.178481
$943$	1.21608e19	0.563164
$944$	1.81957e18	0.0836857
$945$	−5.60385e18	−0.255965
$946$	−1.51288e18	−0.0686295
$947$	3.98813e19	1.79678	0.898389	−	0.439200i	$-0.144738\pi$
$947$	3.98813e19	1.79678	0.898389	+	0.439200i	$0.144738\pi$
$948$	−9.75715e18	−0.436585
$949$	5.32126e18	0.236475
$950$	−2.09628e19	−0.925223
$951$	−1.05844e18	−0.0463975
$952$	1.34044e19	0.583590
$953$	1.34098e19	0.579852	0.289926	−	0.957049i	$-0.406369\pi$
$953$	1.34098e19	0.579852	0.289926	+	0.957049i	$0.406369\pi$
$954$	−6.19533e17	−0.0266073
$955$	4.98933e19	2.12824
$956$	1.40171e19	0.593856
$957$	−1.75548e17	−0.00738702
$958$	1.59513e18	0.0666683
$959$	7.22046e18	0.299739
$960$	−8.08070e18	−0.333186
$961$	−2.21877e19	−0.908680
$962$	−2.88763e18	−0.117464
$963$	−5.66259e18	−0.228794
$964$	1.80423e19	0.724086
$965$	1.39459e19	0.555930
$966$	6.48603e18	0.256819
$967$	−4.28033e19	−1.68347	−0.841734	−	0.539892i	$-0.818465\pi$
$967$	−4.28033e19	−1.68347	−0.841734	+	0.539892i	$0.818465\pi$
$968$	1.61838e19	0.632252
$969$	−2.20228e19	−0.854609
$970$	1.18672e19	0.457437
$971$	−3.07681e19	−1.17808	−0.589041	−	0.808103i	$-0.700495\pi$
$971$	−3.07681e19	−1.17808	−0.589041	+	0.808103i	$0.700495\pi$
$972$	−1.47716e18	−0.0561821
$973$	2.08526e19	0.787818
$974$	−1.74185e19	−0.653698
$975$	−1.11535e19	−0.415795
$976$	−3.13639e19	−1.16147
$977$	3.07179e19	1.13000	0.564998	−	0.825093i	$-0.308877\pi$
$977$	3.07179e19	1.13000	0.564998	+	0.825093i	$0.308877\pi$
$978$	−7.82034e18	−0.285774
$979$	−1.68804e18	−0.0612766
$980$	1.79103e19	0.645853
$981$	−4.38390e18	−0.157041
$982$	−1.44095e18	−0.0512772
$983$	1.53784e18	0.0543641	0.0271820	−	0.999631i	$-0.491347\pi$
$983$	1.53784e18	0.0543641	0.0271820	+	0.999631i	$0.491347\pi$
$984$	3.68792e18	0.129513
$985$	−1.66514e19	−0.580919
$986$	−7.23120e17	−0.0250617
$987$	2.75919e18	0.0949992
$988$	−1.14218e19	−0.390674
$989$	4.55388e19	1.54741
$990$	1.27117e18	0.0429117
$991$	−1.73780e18	−0.0582803	−0.0291401	−	0.999575i	$-0.509277\pi$
$991$	−1.73780e18	−0.0582803	−0.0291401	+	0.999575i	$0.509277\pi$
$992$	8.05085e18	0.268235
$993$	−8.35324e18	−0.276493
$994$	3.25843e18	0.107151
$995$	−2.10443e19	−0.687519
$996$	−1.44957e18	−0.0470492
$997$	−2.74038e19	−0.883675	−0.441837	−	0.897095i	$-0.645673\pi$
$997$	−2.74038e19	−0.883675	−0.441837	+	0.897095i	$0.645673\pi$
$998$	1.04206e19	0.333843
$999$	5.76077e18	0.183360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.19	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.19	✓	30	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+31.8985 q^{2} +729.000 q^{3} -7174.48 q^{4} +61104.8 q^{5} +23254.0 q^{6} -236717. q^{7} -490168. q^{8} +531441. q^{9} +1.94915e6 q^{10} +1.22717e6 q^{11} -5.23020e6 q^{12} -6.08798e6 q^{13} -7.55091e6 q^{14} +4.45454e7 q^{15} +4.31377e7 q^{16} +1.15524e8 q^{17} +1.69522e7 q^{18} -2.61499e8 q^{19} -4.38395e8 q^{20} -1.72566e8 q^{21} +3.91448e7 q^{22} -1.17829e9 q^{23} -3.57333e8 q^{24} +2.51309e9 q^{25} -1.94198e8 q^{26} +3.87420e8 q^{27} +1.69832e9 q^{28} -1.96230e8 q^{29} +1.42093e9 q^{30} +1.49325e9 q^{31} +5.39149e9 q^{32} +8.94604e8 q^{33} +3.68506e9 q^{34} -1.44645e10 q^{35} -3.81281e9 q^{36} +1.48696e10 q^{37} -8.34144e9 q^{38} -4.43814e9 q^{39} -2.99516e10 q^{40} -1.03207e10 q^{41} -5.50461e9 q^{42} -3.86482e10 q^{43} -8.80428e9 q^{44} +3.24736e10 q^{45} -3.75857e10 q^{46} -1.59891e10 q^{47} +3.14474e10 q^{48} -4.08543e10 q^{49} +8.01640e10 q^{50} +8.42173e10 q^{51} +4.36781e10 q^{52} -3.65459e10 q^{53} +1.23581e10 q^{54} +7.49857e10 q^{55} +1.16031e11 q^{56} -1.90633e11 q^{57} -6.25946e9 q^{58} +4.21805e10 q^{59} -3.19590e11 q^{60} -7.27065e11 q^{61} +4.76325e10 q^{62} -1.25801e11 q^{63} -1.81404e11 q^{64} -3.72005e11 q^{65} +2.85365e10 q^{66} +2.38478e11 q^{67} -8.28828e11 q^{68} -8.58973e11 q^{69} -4.61397e11 q^{70} -4.31528e11 q^{71} -2.60495e11 q^{72} -8.74060e11 q^{73} +4.74317e11 q^{74} +1.83205e12 q^{75} +1.87612e12 q^{76} -2.90491e11 q^{77} -1.41570e11 q^{78} +1.86554e12 q^{79} +2.63592e12 q^{80} +2.82430e11 q^{81} -3.29215e11 q^{82} +2.77153e11 q^{83} +1.23807e12 q^{84} +7.05910e12 q^{85} -1.23282e12 q^{86} -1.43052e11 q^{87} -6.01518e11 q^{88} -1.37556e12 q^{89} +1.03586e12 q^{90} +1.44113e12 q^{91} +8.45362e12 q^{92} +1.08858e12 q^{93} -5.10030e11 q^{94} -1.59789e13 q^{95} +3.93039e12 q^{96} +6.08837e12 q^{97} -1.30319e12 q^{98} +6.52166e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

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