LMFDB - Embedded newform 177.14.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +3.63027e6 q^{10} -6.55650e6 q^{11} +1.49801e7 q^{12} +3.19555e6 q^{13} -6.12269e7 q^{14} -1.56105e7 q^{15} +1.86812e8 q^{16} +2.70339e7 q^{17} -9.00959e7 q^{18} -6.84109e7 q^{19} -4.40025e8 q^{20} +2.63281e8 q^{21} +1.11153e9 q^{22} -5.78204e8 q^{23} -1.52717e9 q^{24} -7.62162e8 q^{25} -5.41746e8 q^{26} +3.87420e8 q^{27} +7.42131e9 q^{28} +3.44992e9 q^{29} +2.64647e9 q^{30} +9.42535e9 q^{31} -1.45092e10 q^{32} -4.77969e9 q^{33} -4.58309e9 q^{34} -7.73360e9 q^{35} +1.09205e10 q^{36} +1.03645e10 q^{37} +1.15978e10 q^{38} +2.32956e9 q^{39} +4.48589e10 q^{40} -2.19371e9 q^{41} -4.46344e10 q^{42} -2.12752e10 q^{43} -1.34729e11 q^{44} -1.13801e10 q^{45} +9.80237e10 q^{46} +3.14969e10 q^{47} +1.36186e11 q^{48} +3.35431e10 q^{49} +1.29210e11 q^{50} +1.97077e10 q^{51} +6.56650e10 q^{52} -2.87264e11 q^{53} -6.56799e10 q^{54} +1.40398e11 q^{55} -7.56575e11 q^{56} -4.98715e10 q^{57} -5.84870e11 q^{58} +4.21805e10 q^{59} -3.20779e11 q^{60} -5.01289e10 q^{61} -1.59789e12 q^{62} +1.91932e11 q^{63} +9.29400e11 q^{64} -6.84282e10 q^{65} +8.10307e11 q^{66} -5.06275e11 q^{67} +5.55516e11 q^{68} -4.21511e11 q^{69} +1.31109e12 q^{70} -1.47759e12 q^{71} -1.11331e12 q^{72} -5.72451e11 q^{73} -1.75710e12 q^{74} -5.55616e11 q^{75} -1.40577e12 q^{76} -2.36790e12 q^{77} -3.94933e11 q^{78} +1.61549e12 q^{79} -4.00031e12 q^{80} +2.82430e11 q^{81} +3.71903e11 q^{82} +2.15856e12 q^{83} +5.41014e12 q^{84} -5.78892e11 q^{85} +3.60682e12 q^{86} +2.51499e12 q^{87} +1.37351e13 q^{88} +1.78420e12 q^{89} +1.92928e12 q^{90} +1.15409e12 q^{91} -1.18815e13 q^{92} +6.87108e12 q^{93} -5.33972e12 q^{94} +1.46492e12 q^{95} -1.05772e13 q^{96} -3.76742e11 q^{97} -5.68661e12 q^{98} -3.48439e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−169.531	−1.87308	−0.936538	−	0.350567i	$-0.885989\pi$
$2$	−169.531	−1.87308	−0.936538	+	0.350567i	$0.885989\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	20548.9	2.50841
$5$	−21413.6	−0.612892	−0.306446	−	0.951888i	$-0.599140\pi$
$5$	−21413.6	−0.612892	−0.306446	+	0.951888i	$0.599140\pi$
$6$	−123588.	−1.08142
$7$	361154.	1.16026	0.580130	−	0.814524i	$-0.303002\pi$
$7$	361154.	1.16026	0.580130	+	0.814524i	$0.303002\pi$
$8$	−2.09488e6	−2.82537
$9$	531441.	0.333333
$10$	3.63027e6	1.14799
$11$	−6.55650e6	−1.11589	−0.557943	−	0.829880i	$-0.688409\pi$
$11$	−6.55650e6	−1.11589	−0.557943	+	0.829880i	$0.688409\pi$
$12$	1.49801e7	1.44823
$13$	3.19555e6	0.183617	0.0918087	−	0.995777i	$-0.470735\pi$
$13$	3.19555e6	0.183617	0.0918087	+	0.995777i	$0.470735\pi$
$14$	−6.12269e7	−2.17325
$15$	−1.56105e7	−0.353854
$16$	1.86812e8	2.78371
$17$	2.70339e7	0.271638	0.135819	−	0.990734i	$-0.456633\pi$
$17$	2.70339e7	0.271638	0.135819	+	0.990734i	$0.456633\pi$
$18$	−9.00959e7	−0.624358
$19$	−6.84109e7	−0.333601	−0.166800	−	0.985991i	$-0.553344\pi$
$19$	−6.84109e7	−0.333601	−0.166800	+	0.985991i	$0.553344\pi$
$20$	−4.40025e8	−1.53739
$21$	2.63281e8	0.669876
$22$	1.11153e9	2.09014
$23$	−5.78204e8	−0.814423	−0.407212	−	0.913334i	$-0.633499\pi$
$23$	−5.78204e8	−0.814423	−0.407212	+	0.913334i	$0.633499\pi$
$24$	−1.52717e9	−1.63123
$25$	−7.62162e8	−0.624363
$26$	−5.41746e8	−0.343929
$27$	3.87420e8	0.192450
$28$	7.42131e9	2.91041
$29$	3.44992e9	1.07702	0.538508	−	0.842620i	$-0.318988\pi$
$29$	3.44992e9	1.07702	0.538508	+	0.842620i	$0.318988\pi$
$30$	2.64647e9	0.662794
$31$	9.42535e9	1.90742	0.953710	−	0.300727i	$-0.0972293\pi$
$31$	9.42535e9	1.90742	0.953710	+	0.300727i	$0.0972293\pi$
$32$	−1.45092e10	−2.38874
$33$	−4.77969e9	−0.644257
$34$	−4.58309e9	−0.508798
$35$	−7.73360e9	−0.711114
$36$	1.09205e10	0.836137
$37$	1.03645e10	0.664103	0.332052	−	0.943261i	$-0.392259\pi$
$37$	1.03645e10	0.664103	0.332052	+	0.943261i	$0.392259\pi$
$38$	1.15978e10	0.624859
$39$	2.32956e9	0.106012
$40$	4.48589e10	1.73164
$41$	−2.19371e9	−0.0721248	−0.0360624	−	0.999350i	$-0.511482\pi$
$41$	−2.19371e9	−0.0721248	−0.0360624	+	0.999350i	$0.511482\pi$
$42$	−4.46344e10	−1.25473
$43$	−2.12752e10	−0.513250	−0.256625	−	0.966511i	$-0.582611\pi$
$43$	−2.12752e10	−0.513250	−0.256625	+	0.966511i	$0.582611\pi$
$44$	−1.34729e11	−2.79910
$45$	−1.13801e10	−0.204297
$46$	9.80237e10	1.52548
$47$	3.14969e10	0.426219	0.213109	−	0.977028i	$-0.431641\pi$
$47$	3.14969e10	0.426219	0.213109	+	0.977028i	$0.431641\pi$
$48$	1.36186e11	1.60718
$49$	3.35431e10	0.346201
$50$	1.29210e11	1.16948
$51$	1.97077e10	0.156830
$52$	6.56650e10	0.460588
$53$	−2.87264e11	−1.78028	−0.890138	−	0.455691i	$-0.849392\pi$
$53$	−2.87264e11	−1.78028	−0.890138	+	0.455691i	$0.849392\pi$
$54$	−6.56799e10	−0.360473
$55$	1.40398e11	0.683917
$56$	−7.56575e11	−3.27816
$57$	−4.98715e10	−0.192604
$58$	−5.84870e11	−2.01733
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−3.20779e11	−0.887610
$61$	−5.01289e10	−0.124579	−0.0622894	−	0.998058i	$-0.519840\pi$
$61$	−5.01289e10	−0.124579	−0.0622894	+	0.998058i	$0.519840\pi$
$62$	−1.59789e12	−3.57274
$63$	1.91932e11	0.386753
$64$	9.29400e11	1.69057
$65$	−6.84282e10	−0.112538
$66$	8.10307e11	1.20674
$67$	−5.06275e11	−0.683755	−0.341878	−	0.939744i	$-0.611063\pi$
$67$	−5.06275e11	−0.683755	−0.341878	+	0.939744i	$0.611063\pi$
$68$	5.55516e11	0.681379
$69$	−4.21511e11	−0.470207
$70$	1.31109e12	1.33197
$71$	−1.47759e12	−1.36891	−0.684454	−	0.729056i	$-0.739959\pi$
$71$	−1.47759e12	−1.36891	−0.684454	+	0.729056i	$0.739959\pi$
$72$	−1.11331e12	−0.941789
$73$	−5.72451e11	−0.442731	−0.221365	−	0.975191i	$-0.571051\pi$
$73$	−5.72451e11	−0.442731	−0.221365	+	0.975191i	$0.571051\pi$
$74$	−1.75710e12	−1.24392
$75$	−5.55616e11	−0.360476
$76$	−1.40577e12	−0.836807
$77$	−2.36790e12	−1.29472
$78$	−3.94933e11	−0.198568
$79$	1.61549e12	0.747702	0.373851	−	0.927489i	$-0.378037\pi$
$79$	1.61549e12	0.747702	0.373851	+	0.927489i	$0.378037\pi$
$80$	−4.00031e12	−1.70612
$81$	2.82430e11	0.111111
$82$	3.71903e11	0.135095
$83$	2.15856e12	0.724697	0.362348	−	0.932043i	$-0.381975\pi$
$83$	2.15856e12	0.724697	0.362348	+	0.932043i	$0.381975\pi$
$84$	5.41014e12	1.68032
$85$	−5.78892e11	−0.166485
$86$	3.60682e12	0.961355
$87$	2.51499e12	0.621816
$88$	1.37351e13	3.15278
$89$	1.78420e12	0.380547	0.190274	−	0.981731i	$-0.439062\pi$
$89$	1.78420e12	0.380547	0.190274	+	0.981731i	$0.439062\pi$
$90$	1.92928e12	0.382664
$91$	1.15409e12	0.213044
$92$	−1.18815e13	−2.04291
$93$	6.87108e12	1.10125
$94$	−5.33972e12	−0.798339
$95$	1.46492e12	0.204461
$96$	−1.05772e13	−1.37914
$97$	−3.76742e11	−0.0459227	−0.0229613	−	0.999736i	$-0.507309\pi$
$97$	−3.76742e11	−0.0459227	−0.0229613	+	0.999736i	$0.507309\pi$
$98$	−5.68661e12	−0.648461
$99$	−3.48439e12	−0.371962
$100$	−1.56616e13	−1.56616
$101$	−1.25220e13	−1.17377	−0.586887	−	0.809669i	$-0.699647\pi$
$101$	−1.25220e13	−1.17377	−0.586887	+	0.809669i	$0.699647\pi$
$102$	−3.34107e12	−0.293755
$103$	−3.17368e12	−0.261892	−0.130946	−	0.991390i	$-0.541801\pi$
$103$	−3.17368e12	−0.261892	−0.130946	+	0.991390i	$0.541801\pi$
$104$	−6.69430e12	−0.518786
$105$	−5.63779e12	−0.410562
$106$	4.87002e13	3.33459
$107$	−8.62759e12	−0.555770	−0.277885	−	0.960614i	$-0.589633\pi$
$107$	−8.62759e12	−0.555770	−0.277885	+	0.960614i	$0.589633\pi$
$108$	7.96106e12	0.482744
$109$	1.98524e13	1.13381	0.566906	−	0.823783i	$-0.308140\pi$
$109$	1.98524e13	1.13381	0.566906	+	0.823783i	$0.308140\pi$
$110$	−2.38019e13	−1.28103
$111$	7.55569e12	0.383420
$112$	6.74678e13	3.22983
$113$	3.65518e13	1.65158	0.825789	−	0.563979i	$-0.190730\pi$
$113$	3.65518e13	1.65158	0.825789	+	0.563979i	$0.190730\pi$
$114$	8.45479e12	0.360762
$115$	1.23814e13	0.499154
$116$	7.08921e13	2.70160
$117$	1.69825e12	0.0612058
$118$	−7.15093e12	−0.243854
$119$	9.76338e12	0.315170
$120$	3.27022e13	0.999766
$121$	8.46495e12	0.245199
$122$	8.49842e12	0.233345
$123$	−1.59922e12	−0.0416412
$124$	1.93681e14	4.78459
$125$	4.24602e13	0.995560
$126$	−3.25385e13	−0.724418
$127$	6.84567e13	1.44774	0.723872	−	0.689934i	$-0.242360\pi$
$127$	6.84567e13	1.44774	0.723872	+	0.689934i	$0.242360\pi$
$128$	−3.87033e13	−0.777827
$129$	−1.55096e13	−0.296325
$130$	1.16007e13	0.210792
$131$	5.40307e13	0.934065	0.467032	−	0.884240i	$-0.345323\pi$
$131$	5.40307e13	0.934065	0.467032	+	0.884240i	$0.345323\pi$
$132$	−9.82173e13	−1.61606
$133$	−2.47069e13	−0.387063
$134$	8.58296e13	1.28072
$135$	−8.29606e12	−0.117951
$136$	−5.66327e13	−0.767476
$137$	−3.82436e13	−0.494168	−0.247084	−	0.968994i	$-0.579472\pi$
$137$	−3.82436e13	−0.494168	−0.247084	+	0.968994i	$0.579472\pi$
$138$	7.14593e13	0.880734
$139$	−1.12280e14	−1.32040	−0.660201	−	0.751089i	$-0.729529\pi$
$139$	−1.12280e14	−1.32040	−0.660201	+	0.751089i	$0.729529\pi$
$140$	−1.58917e14	−1.78377
$141$	2.29613e13	0.246077
$142$	2.50498e14	2.56407
$143$	−2.09516e13	−0.204896
$144$	9.92794e13	0.927904
$145$	−7.38752e13	−0.660095
$146$	9.70484e13	0.829268
$147$	2.44529e13	0.199879
$148$	2.12978e14	1.66584
$149$	−3.45852e13	−0.258928	−0.129464	−	0.991584i	$-0.541326\pi$
$149$	−3.45852e13	−0.258928	−0.129464	+	0.991584i	$0.541326\pi$
$150$	9.41944e13	0.675199
$151$	−1.39958e14	−0.960831	−0.480416	−	0.877041i	$-0.659514\pi$
$151$	−1.39958e14	−0.960831	−0.480416	+	0.877041i	$0.659514\pi$
$152$	1.43313e14	0.942543
$153$	1.43669e13	0.0905459
$154$	4.01434e14	2.42510
$155$	−2.01830e14	−1.16904
$156$	4.78698e13	0.265920
$157$	9.14522e13	0.487356	0.243678	−	0.969856i	$-0.421646\pi$
$157$	9.14522e13	0.487356	0.243678	+	0.969856i	$0.421646\pi$
$158$	−2.73876e14	−1.40050
$159$	−2.09415e14	−1.02784
$160$	3.10693e14	1.46404
$161$	−2.08821e14	−0.944942
$162$	−4.78807e13	−0.208119
$163$	−2.06673e14	−0.863108	−0.431554	−	0.902087i	$-0.642035\pi$
$163$	−2.06673e14	−0.863108	−0.431554	+	0.902087i	$0.642035\pi$
$164$	−4.50783e13	−0.180918
$165$	1.02350e14	0.394860
$166$	−3.65943e14	−1.35741
$167$	−1.94548e13	−0.0694016	−0.0347008	−	0.999398i	$-0.511048\pi$
$167$	−1.94548e13	−0.0694016	−0.0347008	+	0.999398i	$0.511048\pi$
$168$	−5.51543e14	−1.89264
$169$	−2.92664e14	−0.966285
$170$	9.81403e13	0.311838
$171$	−3.63563e13	−0.111200
$172$	−4.37182e14	−1.28744
$173$	4.09717e14	1.16194	0.580971	−	0.813925i	$-0.302673\pi$
$173$	4.09717e14	1.16194	0.580971	+	0.813925i	$0.302673\pi$
$174$	−4.26370e14	−1.16471
$175$	−2.75258e14	−0.724423
$176$	−1.22483e15	−3.10630
$177$	3.07496e13	0.0751646
$178$	−3.02478e14	−0.712794
$179$	7.18549e14	1.63272	0.816360	−	0.577543i	$-0.195988\pi$
$179$	7.18549e14	1.63272	0.816360	+	0.577543i	$0.195988\pi$
$180$	−2.33848e14	−0.512462
$181$	−4.94149e14	−1.04459	−0.522297	−	0.852764i	$-0.674925\pi$
$181$	−4.94149e14	−1.04459	−0.522297	+	0.852764i	$0.674925\pi$
$182$	−1.95654e14	−0.399047
$183$	−3.65440e13	−0.0719256
$184$	1.21127e15	2.30104
$185$	−2.21940e14	−0.407024
$186$	−1.16486e15	−2.06272
$187$	−1.77247e14	−0.303116
$188$	6.47227e14	1.06913
$189$	1.39918e14	0.223292
$190$	−2.48350e14	−0.382971
$191$	−7.56869e14	−1.12799	−0.563993	−	0.825780i	$-0.690735\pi$
$191$	−7.56869e14	−1.12799	−0.563993	+	0.825780i	$0.690735\pi$
$192$	6.77533e14	0.976050
$193$	5.42119e13	0.0755044	0.0377522	−	0.999287i	$-0.487980\pi$
$193$	5.42119e13	0.0755044	0.0377522	+	0.999287i	$0.487980\pi$
$194$	6.38695e13	0.0860166
$195$	−4.98841e13	−0.0649737
$196$	6.89274e14	0.868415
$197$	−3.73102e14	−0.454775	−0.227388	−	0.973804i	$-0.573018\pi$
$197$	−3.73102e14	−0.454775	−0.227388	+	0.973804i	$0.573018\pi$
$198$	5.90714e14	0.696712
$199$	−3.01874e14	−0.344573	−0.172286	−	0.985047i	$-0.555115\pi$
$199$	−3.01874e14	−0.344573	−0.172286	+	0.985047i	$0.555115\pi$
$200$	1.59664e15	1.76405
$201$	−3.69075e14	−0.394766
$202$	2.12287e15	2.19857
$203$	1.24595e15	1.24962
$204$	4.04971e14	0.393394
$205$	4.69752e13	0.0442047
$206$	5.38039e14	0.490543
$207$	−3.07281e14	−0.271474
$208$	5.96966e14	0.511138
$209$	4.48536e14	0.372260
$210$	9.55783e14	0.769013
$211$	1.87437e15	1.46225	0.731123	−	0.682246i	$-0.238997\pi$
$211$	1.87437e15	1.46225	0.731123	+	0.682246i	$0.238997\pi$
$212$	−5.90295e15	−4.46566
$213$	−1.07716e15	−0.790339
$214$	1.46265e15	1.04100
$215$	4.55578e14	0.314567
$216$	−8.11600e14	−0.543742
$217$	3.40400e15	2.21310
$218$	−3.36561e15	−2.12371
$219$	−4.17317e14	−0.255611
$220$	2.88503e15	1.71555
$221$	8.63880e13	0.0498774
$222$	−1.28093e15	−0.718175
$223$	1.88601e14	0.102698	0.0513490	−	0.998681i	$-0.483648\pi$
$223$	1.88601e14	0.102698	0.0513490	+	0.998681i	$0.483648\pi$
$224$	−5.24005e15	−2.77155
$225$	−4.05044e14	−0.208121
$226$	−6.19668e15	−3.09353
$227$	−3.16490e15	−1.53529	−0.767647	−	0.640873i	$-0.778573\pi$
$227$	−3.16490e15	−1.53529	−0.767647	+	0.640873i	$0.778573\pi$
$228$	−1.02480e15	−0.483131
$229$	2.86580e15	1.31315	0.656577	−	0.754259i	$-0.272004\pi$
$229$	2.86580e15	1.31315	0.656577	+	0.754259i	$0.272004\pi$
$230$	−2.09904e15	−0.934952
$231$	−1.72620e15	−0.747505
$232$	−7.22718e15	−3.04297
$233$	−1.63684e14	−0.0670183	−0.0335092	−	0.999438i	$-0.510668\pi$
$233$	−1.63684e14	−0.0670183	−0.0335092	+	0.999438i	$0.510668\pi$
$234$	−2.87906e14	−0.114643
$235$	−6.74462e14	−0.261226
$236$	8.66763e14	0.326567
$237$	1.17769e15	0.431686
$238$	−1.65520e15	−0.590337
$239$	−1.56852e15	−0.544381	−0.272191	−	0.962243i	$-0.587748\pi$
$239$	−1.56852e15	−0.544381	−0.272191	+	0.962243i	$0.587748\pi$
$240$	−2.91622e15	−0.985026
$241$	−1.53250e15	−0.503835	−0.251918	−	0.967749i	$-0.581061\pi$
$241$	−1.53250e15	−0.503835	−0.251918	+	0.967749i	$0.581061\pi$
$242$	−1.43507e15	−0.459277
$243$	2.05891e14	0.0641500
$244$	−1.03009e15	−0.312495
$245$	−7.18278e14	−0.212184
$246$	2.71117e14	0.0779972
$247$	−2.18610e14	−0.0612549
$248$	−1.97450e16	−5.38916
$249$	1.57359e15	0.418404
$250$	−7.19834e15	−1.86476
$251$	−5.07634e15	−1.28136	−0.640680	−	0.767808i	$-0.721348\pi$
$251$	−5.07634e15	−1.28136	−0.640680	+	0.767808i	$0.721348\pi$
$252$	3.94399e15	0.970135
$253$	3.79099e15	0.908803
$254$	−1.16056e16	−2.71173
$255$	−4.22012e14	−0.0961200
$256$	−1.05222e15	−0.233640
$257$	5.57883e15	1.20775	0.603876	−	0.797078i	$-0.293622\pi$
$257$	5.57883e15	1.20775	0.603876	+	0.797078i	$0.293622\pi$
$258$	2.62937e15	0.555039
$259$	3.74317e15	0.770532
$260$	−1.40612e15	−0.282291
$261$	1.83343e15	0.359006
$262$	−9.15990e15	−1.74957
$263$	1.41314e15	0.263313	0.131656	−	0.991295i	$-0.457970\pi$
$263$	1.41314e15	0.263313	0.131656	+	0.991295i	$0.457970\pi$
$264$	1.00129e16	1.82026
$265$	6.15134e15	1.09112
$266$	4.18859e15	0.724998
$267$	1.30068e15	0.219709
$268$	−1.04034e16	−1.71514
$269$	4.22038e15	0.679144	0.339572	−	0.940580i	$-0.389718\pi$
$269$	4.22038e15	0.679144	0.339572	+	0.940580i	$0.389718\pi$
$270$	1.40644e15	0.220931
$271$	−2.83121e15	−0.434181	−0.217091	−	0.976151i	$-0.569657\pi$
$271$	−2.83121e15	−0.434181	−0.217091	+	0.976151i	$0.569657\pi$
$272$	5.05024e15	0.756161
$273$	8.41328e14	0.123001
$274$	6.48348e15	0.925614
$275$	4.99711e15	0.696717
$276$	−8.66158e15	−1.17947
$277$	5.67990e15	0.755479	0.377740	−	0.925912i	$-0.376701\pi$
$277$	5.67990e15	0.755479	0.377740	+	0.925912i	$0.376701\pi$
$278$	1.90350e16	2.47321
$279$	5.00902e15	0.635807
$280$	1.62010e16	2.00916
$281$	−6.84857e15	−0.829868	−0.414934	−	0.909852i	$-0.636195\pi$
$281$	−6.84857e15	−0.829868	−0.414934	+	0.909852i	$0.636195\pi$
$282$	−3.89266e15	−0.460921
$283$	−1.19895e16	−1.38736	−0.693678	−	0.720285i	$-0.744011\pi$
$283$	−1.19895e16	−1.38736	−0.693678	+	0.720285i	$0.744011\pi$
$284$	−3.03628e16	−3.43378
$285$	1.06793e15	0.118046
$286$	3.55196e15	0.383785
$287$	−7.92267e14	−0.0836834
$288$	−7.71077e15	−0.796245
$289$	−9.17375e15	−0.926213
$290$	1.25242e16	1.23641
$291$	−2.74645e14	−0.0265135
$292$	−1.17632e16	−1.11055
$293$	1.17508e16	1.08499	0.542496	−	0.840058i	$-0.317479\pi$
$293$	1.17508e16	1.08499	0.542496	+	0.840058i	$0.317479\pi$
$294$	−4.14554e15	−0.374389
$295$	−9.03236e14	−0.0797918
$296$	−2.17123e16	−1.87633
$297$	−2.54012e15	−0.214752
$298$	5.86328e15	0.484992
$299$	−1.84768e15	−0.149542
$300$	−1.14173e16	−0.904222
$301$	−7.68362e15	−0.595503
$302$	2.37273e16	1.79971
$303$	−9.12853e15	−0.677679
$304$	−1.27800e16	−0.928648
$305$	1.07344e15	0.0763534
$306$	−2.43564e15	−0.169599
$307$	1.55258e16	1.05841	0.529206	−	0.848493i	$-0.322490\pi$
$307$	1.55258e16	1.05841	0.529206	+	0.848493i	$0.322490\pi$
$308$	−4.86578e16	−3.24768
$309$	−2.31361e15	−0.151203
$310$	3.42166e16	2.18971
$311$	−2.18300e15	−0.136808	−0.0684041	−	0.997658i	$-0.521791\pi$
$311$	−2.18300e15	−0.136808	−0.0684041	+	0.997658i	$0.521791\pi$
$312$	−4.88014e15	−0.299521
$313$	−2.13942e16	−1.28605	−0.643024	−	0.765846i	$-0.722320\pi$
$313$	−2.13942e16	−1.28605	−0.643024	+	0.765846i	$0.722320\pi$
$314$	−1.55040e16	−0.912854
$315$	−4.10995e15	−0.237038
$316$	3.31966e16	1.87554
$317$	5.87276e15	0.325055	0.162528	−	0.986704i	$-0.448035\pi$
$317$	5.87276e15	0.325055	0.162528	+	0.986704i	$0.448035\pi$
$318$	3.55024e16	1.92523
$319$	−2.26194e16	−1.20183
$320$	−1.99018e16	−1.03614
$321$	−6.28951e15	−0.320874
$322$	3.54016e16	1.76995
$323$	−1.84941e15	−0.0906185
$324$	5.80362e15	0.278712
$325$	−2.43553e15	−0.114644
$326$	3.50376e16	1.61667
$327$	1.44724e16	0.654606
$328$	4.59557e15	0.203779
$329$	1.13752e16	0.494524
$330$	−1.73516e16	−0.739602
$331$	−5.76612e15	−0.240991	−0.120496	−	0.992714i	$-0.538448\pi$
$331$	−5.76612e15	−0.240991	−0.120496	+	0.992714i	$0.538448\pi$
$332$	4.43560e16	1.81784
$333$	5.50810e15	0.221368
$334$	3.29820e15	0.129994
$335$	1.08412e16	0.419068
$336$	4.91840e16	1.86474
$337$	−1.33634e16	−0.496961	−0.248481	−	0.968637i	$-0.579931\pi$
$337$	−1.33634e16	−0.496961	−0.248481	+	0.968637i	$0.579931\pi$
$338$	4.96157e16	1.80992
$339$	2.66463e16	0.953539
$340$	−1.18956e16	−0.417612
$341$	−6.17973e16	−2.12846
$342$	6.16354e15	0.208286
$343$	−2.28776e16	−0.758576
$344$	4.45690e16	1.45012
$345$	9.02605e15	0.288187
$346$	−6.94599e16	−2.17640
$347$	−4.82874e15	−0.148488	−0.0742441	−	0.997240i	$-0.523654\pi$
$347$	−4.82874e15	−0.148488	−0.0742441	+	0.997240i	$0.523654\pi$
$348$	5.16804e16	1.55977
$349$	3.20684e16	0.949974	0.474987	−	0.879993i	$-0.342453\pi$
$349$	3.20684e16	0.949974	0.474987	+	0.879993i	$0.342453\pi$
$350$	4.66648e16	1.35690
$351$	1.23802e15	0.0353372
$352$	9.51294e16	2.66555
$353$	−5.60978e16	−1.54316	−0.771579	−	0.636134i	$-0.780533\pi$
$353$	−5.60978e16	−1.54316	−0.771579	+	0.636134i	$0.780533\pi$
$354$	−5.21302e15	−0.140789
$355$	3.16404e16	0.838993
$356$	3.66634e16	0.954569
$357$	7.11750e15	0.181964
$358$	−1.21817e17	−3.05821
$359$	−3.53481e16	−0.871470	−0.435735	−	0.900075i	$-0.643512\pi$
$359$	−3.53481e16	−0.871470	−0.435735	+	0.900075i	$0.643512\pi$
$360$	2.38399e16	0.577215
$361$	−3.73729e16	−0.888711
$362$	8.37738e16	1.95660
$363$	6.17095e15	0.141566
$364$	2.37152e16	0.534401
$365$	1.22582e16	0.271346
$366$	6.19535e15	0.134722
$367$	4.60564e16	0.983922	0.491961	−	0.870617i	$-0.336280\pi$
$367$	4.60564e16	0.983922	0.491961	+	0.870617i	$0.336280\pi$
$368$	−1.08015e17	−2.26712
$369$	−1.16583e15	−0.0240416
$370$	3.76258e16	0.762386
$371$	−1.03746e17	−2.06558
$372$	1.41193e17	2.76239
$373$	−9.12768e16	−1.75490	−0.877451	−	0.479666i	$-0.840758\pi$
$373$	−9.12768e16	−1.75490	−0.877451	+	0.479666i	$0.840758\pi$
$374$	3.00490e16	0.567760
$375$	3.09535e16	0.574787
$376$	−6.59824e16	−1.20422
$377$	1.10244e16	0.197759
$378$	−2.37206e16	−0.418243
$379$	−2.08075e16	−0.360633	−0.180317	−	0.983609i	$-0.557712\pi$
$379$	−2.08075e16	−0.360633	−0.180317	+	0.983609i	$0.557712\pi$
$380$	3.01025e16	0.512873
$381$	4.99049e16	0.835856
$382$	1.28313e17	2.11280
$383$	−4.14608e16	−0.671191	−0.335595	−	0.942006i	$-0.608937\pi$
$383$	−4.14608e16	−0.671191	−0.335595	+	0.942006i	$0.608937\pi$
$384$	−2.82147e16	−0.449079
$385$	5.07053e16	0.793521
$386$	−9.19062e15	−0.141425
$387$	−1.13065e16	−0.171083
$388$	−7.74162e15	−0.115193
$389$	1.25116e17	1.83080	0.915398	−	0.402551i	$-0.131876\pi$
$389$	1.25116e17	1.83080	0.915398	+	0.402551i	$0.131876\pi$
$390$	8.45693e15	0.121701
$391$	−1.56311e16	−0.221228
$392$	−7.02689e16	−0.978146
$393$	3.93884e16	0.539283
$394$	6.32525e16	0.851829
$395$	−3.45934e16	−0.458261
$396$	−7.16004e16	−0.933032
$397$	−1.83934e16	−0.235789	−0.117894	−	0.993026i	$-0.537614\pi$
$397$	−1.83934e16	−0.235789	−0.117894	+	0.993026i	$0.537614\pi$
$398$	5.11771e16	0.645411
$399$	−1.80113e16	−0.223471
$400$	−1.42381e17	−1.73805
$401$	−1.57173e17	−1.88773	−0.943864	−	0.330333i	$-0.892839\pi$
$401$	−1.57173e17	−1.88773	−0.943864	+	0.330333i	$0.892839\pi$
$402$	6.25698e16	0.739427
$403$	3.01192e16	0.350236
$404$	−2.57313e17	−2.94431
$405$	−6.04783e15	−0.0680992
$406$	−2.11228e17	−2.34063
$407$	−6.79546e16	−0.741063
$408$	−4.12853e16	−0.443102
$409$	3.84365e16	0.406015	0.203008	−	0.979177i	$-0.434928\pi$
$409$	3.84365e16	0.406015	0.203008	+	0.979177i	$0.434928\pi$
$410$	−7.96377e15	−0.0827987
$411$	−2.78796e16	−0.285308
$412$	−6.52157e16	−0.656931
$413$	1.52337e16	0.151053
$414$	5.20938e16	0.508492
$415$	−4.62225e16	−0.444161
$416$	−4.63648e16	−0.438613
$417$	−8.18522e16	−0.762335
$418$	−7.60409e16	−0.697271
$419$	−1.88832e17	−1.70484	−0.852419	−	0.522859i	$-0.824866\pi$
$419$	−1.88832e17	−1.70484	−0.852419	+	0.522859i	$0.824866\pi$
$420$	−1.15850e17	−1.02986
$421$	−4.66069e16	−0.407959	−0.203979	−	0.978975i	$-0.565388\pi$
$421$	−4.66069e16	−0.407959	−0.203979	+	0.978975i	$0.565388\pi$
$422$	−3.17765e17	−2.73890
$423$	1.67388e16	0.142073
$424$	6.01783e17	5.02993
$425$	−2.06042e16	−0.169600
$426$	1.82613e17	1.48036
$427$	−1.81042e16	−0.144544
$428$	−1.77287e17	−1.39410
$429$	−1.52737e16	−0.118297
$430$	−7.72348e16	−0.589207
$431$	−4.58448e16	−0.344499	−0.172250	−	0.985053i	$-0.555104\pi$
$431$	−4.58448e16	−0.344499	−0.172250	+	0.985053i	$0.555104\pi$
$432$	7.23747e16	0.535726
$433$	−1.55194e17	−1.13163	−0.565814	−	0.824533i	$-0.691438\pi$
$433$	−1.55194e17	−1.13163	−0.565814	+	0.824533i	$0.691438\pi$
$434$	−5.77085e17	−4.14531
$435$	−5.38550e16	−0.381106
$436$	4.07945e17	2.84406
$437$	3.95554e16	0.271692
$438$	7.07483e16	0.478778
$439$	2.33386e17	1.55617	0.778083	−	0.628162i	$-0.216192\pi$
$439$	2.33386e17	1.55617	0.778083	+	0.628162i	$0.216192\pi$
$440$	−2.94117e17	−1.93232
$441$	1.78262e16	0.115400
$442$	−1.46455e16	−0.0934241
$443$	−1.78080e17	−1.11942	−0.559708	−	0.828690i	$-0.689087\pi$
$443$	−1.78080e17	−1.11942	−0.559708	+	0.828690i	$0.689087\pi$
$444$	1.55261e17	0.961775
$445$	−3.82061e16	−0.233235
$446$	−3.19738e16	−0.192361
$447$	−2.52126e16	−0.149492
$448$	3.35656e17	1.96150
$449$	7.79242e15	0.0448819	0.0224409	−	0.999748i	$-0.492856\pi$
$449$	7.79242e15	0.0448819	0.0224409	+	0.999748i	$0.492856\pi$
$450$	6.86677e16	0.389826
$451$	1.43831e16	0.0804829
$452$	7.51099e17	4.14283
$453$	−1.02029e17	−0.554736
$454$	5.36550e17	2.87572
$455$	−2.47131e16	−0.130573
$456$	1.04475e17	0.544178
$457$	−2.40369e17	−1.23431	−0.617155	−	0.786842i	$-0.711715\pi$
$457$	−2.40369e17	−1.23431	−0.617155	+	0.786842i	$0.711715\pi$
$458$	−4.85844e17	−2.45964
$459$	1.04735e16	0.0522767
$460$	2.54424e17	1.25208
$461$	2.59508e17	1.25920	0.629599	−	0.776920i	$-0.283219\pi$
$461$	2.59508e17	1.25920	0.629599	+	0.776920i	$0.283219\pi$
$462$	2.92646e17	1.40013
$463$	5.00655e16	0.236190	0.118095	−	0.993002i	$-0.462321\pi$
$463$	5.00655e16	0.236190	0.118095	+	0.993002i	$0.462321\pi$
$464$	6.44486e17	2.99810
$465$	−1.47134e17	−0.674948
$466$	2.77496e16	0.125530
$467$	−2.14821e17	−0.958332	−0.479166	−	0.877724i	$-0.659061\pi$
$467$	−2.14821e17	−0.958332	−0.479166	+	0.877724i	$0.659061\pi$
$468$	3.48971e16	0.153529
$469$	−1.82843e17	−0.793333
$470$	1.14343e17	0.489296
$471$	6.66686e16	0.281375
$472$	−8.83632e16	−0.367831
$473$	1.39491e17	0.572728
$474$	−1.99656e17	−0.808580
$475$	5.21402e16	0.208288
$476$	2.00627e17	0.790576
$477$	−1.52664e17	−0.593425
$478$	2.65913e17	1.01967
$479$	−3.43840e17	−1.30069	−0.650347	−	0.759637i	$-0.725377\pi$
$479$	−3.43840e17	−1.30069	−0.650347	+	0.759637i	$0.725377\pi$
$480$	2.26496e17	0.845262
$481$	3.31202e16	0.121941
$482$	2.59806e17	0.943721
$483$	−1.52230e17	−0.545563
$484$	1.73945e17	0.615061
$485$	8.06739e15	0.0281457
$486$	−3.49050e16	−0.120158
$487$	2.26271e17	0.768583	0.384291	−	0.923212i	$-0.374446\pi$
$487$	2.26271e17	0.768583	0.384291	+	0.923212i	$0.374446\pi$
$488$	1.05014e17	0.351981
$489$	−1.50665e17	−0.498315
$490$	1.21771e17	0.397437
$491$	−2.91151e17	−0.937754	−0.468877	−	0.883264i	$-0.655341\pi$
$491$	−2.91151e17	−0.937754	−0.468877	+	0.883264i	$0.655341\pi$
$492$	−3.28621e16	−0.104453
$493$	9.32647e16	0.292558
$494$	3.70613e16	0.114735
$495$	7.46133e16	0.227972
$496$	1.76077e18	5.30971
$497$	−5.33637e17	−1.58829
$498$	−2.66773e17	−0.783702
$499$	1.03775e17	0.300911	0.150455	−	0.988617i	$-0.451926\pi$
$499$	1.03775e17	0.300911	0.150455	+	0.988617i	$0.451926\pi$
$500$	8.72511e17	2.49727
$501$	−1.41825e16	−0.0400690
$502$	8.60599e17	2.40008
$503$	2.61519e17	0.719965	0.359983	−	0.932959i	$-0.382783\pi$
$503$	2.61519e17	0.719965	0.359983	+	0.932959i	$0.382783\pi$
$504$	−4.02075e17	−1.09272
$505$	2.68141e17	0.719397
$506$	−6.42692e17	−1.70226
$507$	−2.13352e17	−0.557885
$508$	1.40671e18	3.63154
$509$	4.60629e17	1.17405	0.587024	−	0.809569i	$-0.300299\pi$
$509$	4.60629e17	1.17405	0.587024	+	0.809569i	$0.300299\pi$
$510$	7.15443e16	0.180040
$511$	−2.06743e17	−0.513682
$512$	4.95442e17	1.21545
$513$	−2.65038e16	−0.0642015
$514$	−9.45787e17	−2.26221
$515$	6.79599e16	0.160511
$516$	−3.18706e17	−0.743304
$517$	−2.06510e17	−0.475611
$518$	−6.34584e17	−1.44326
$519$	2.98684e17	0.670847
$520$	1.43349e17	0.317960
$521$	−3.91504e17	−0.857611	−0.428806	−	0.903397i	$-0.641066\pi$
$521$	−3.91504e17	−0.857611	−0.428806	+	0.903397i	$0.641066\pi$
$522$	−3.10824e17	−0.672444
$523$	−2.55045e17	−0.544949	−0.272475	−	0.962163i	$-0.587842\pi$
$523$	−2.55045e17	−0.544949	−0.272475	+	0.962163i	$0.587842\pi$
$524$	1.11027e18	2.34302
$525$	−2.00663e17	−0.418246
$526$	−2.39571e17	−0.493205
$527$	2.54804e17	0.518127
$528$	−8.92901e17	−1.79342
$529$	−1.69717e17	−0.336715
$530$	−1.04285e18	−2.04375
$531$	2.24165e16	0.0433963
$532$	−5.07699e17	−0.970913
$533$	−7.01011e15	−0.0132434
$534$	−2.20506e17	−0.411532
$535$	1.84747e17	0.340627
$536$	1.06059e18	1.93186
$537$	5.23823e17	0.942652
$538$	−7.15487e17	−1.27209
$539$	−2.19925e17	−0.386321
$540$	−1.70475e17	−0.295870
$541$	2.32630e17	0.398918	0.199459	−	0.979906i	$-0.436081\pi$
$541$	2.32630e17	0.398918	0.199459	+	0.979906i	$0.436081\pi$
$542$	4.79978e17	0.813254
$543$	−3.60235e17	−0.603097
$544$	−3.92239e17	−0.648870
$545$	−4.25111e17	−0.694904
$546$	−1.42632e17	−0.230390
$547$	−6.70986e16	−0.107102	−0.0535508	−	0.998565i	$-0.517054\pi$
$547$	−6.70986e16	−0.107102	−0.0535508	+	0.998565i	$0.517054\pi$
$548$	−7.85863e17	−1.23958
$549$	−2.66405e16	−0.0415263
$550$	−8.47167e17	−1.30500
$551$	−2.36012e17	−0.359293
$552$	8.83015e17	1.32851
$553$	5.83441e17	0.867528
$554$	−9.62922e17	−1.41507
$555$	−1.61794e17	−0.234995
$556$	−2.30723e18	−3.31211
$557$	−3.30516e17	−0.468958	−0.234479	−	0.972121i	$-0.575338\pi$
$557$	−3.30516e17	−0.468958	−0.234479	+	0.972121i	$0.575338\pi$
$558$	−8.49186e17	−1.19091
$559$	−6.79860e16	−0.0942416
$560$	−1.44473e18	−1.97954
$561$	−1.29213e17	−0.175004
$562$	1.16105e18	1.55440
$563$	5.93581e17	0.785553	0.392777	−	0.919634i	$-0.371515\pi$
$563$	5.93581e17	0.785553	0.392777	+	0.919634i	$0.371515\pi$
$564$	4.71829e17	0.617263
$565$	−7.82705e17	−1.01224
$566$	2.03259e18	2.59862
$567$	1.02001e17	0.128918
$568$	3.09537e18	3.86766
$569$	4.04856e17	0.500116	0.250058	−	0.968231i	$-0.419550\pi$
$569$	4.04856e17	0.500116	0.250058	+	0.968231i	$0.419550\pi$
$570$	−1.81047e17	−0.221109
$571$	3.47447e17	0.419521	0.209760	−	0.977753i	$-0.432732\pi$
$571$	3.47447e17	0.419521	0.209760	+	0.977753i	$0.432732\pi$
$572$	−4.30533e17	−0.513963
$573$	−5.51757e17	−0.651243
$574$	1.34314e17	0.156745
$575$	4.40685e17	0.508496
$576$	4.93921e17	0.563523
$577$	−6.95052e17	−0.784106	−0.392053	−	0.919943i	$-0.628235\pi$
$577$	−6.95052e17	−0.784106	−0.392053	+	0.919943i	$0.628235\pi$
$578$	1.55524e18	1.73487
$579$	3.95205e16	0.0435925
$580$	−1.51805e18	−1.65579
$581$	7.79572e17	0.840836
$582$	4.65609e16	0.0496617
$583$	1.88344e18	1.98658
$584$	1.19922e18	1.25088
$585$	−3.63655e16	−0.0375126
$586$	−1.99212e18	−2.03227
$587$	−9.96401e17	−1.00528	−0.502639	−	0.864496i	$-0.667638\pi$
$587$	−9.96401e17	−1.00528	−0.502639	+	0.864496i	$0.667638\pi$
$588$	5.02481e17	0.501380
$589$	−6.44796e17	−0.636316
$590$	1.53127e17	0.149456
$591$	−2.71991e17	−0.262565
$592$	1.93620e18	1.84867
$593$	−1.57234e18	−1.48488	−0.742440	−	0.669912i	$-0.766332\pi$
$593$	−1.57234e18	−1.48488	−0.742440	+	0.669912i	$0.766332\pi$
$594$	4.30630e17	0.402247
$595$	−2.09069e17	−0.193165
$596$	−7.10688e17	−0.649499
$597$	−2.20066e17	−0.198939
$598$	3.13240e17	0.280104
$599$	2.19233e18	1.93924	0.969622	−	0.244609i	$-0.0786595\pi$
$599$	2.19233e18	1.93924	0.969622	+	0.244609i	$0.0786595\pi$
$600$	1.16395e18	1.01848
$601$	−2.21514e18	−1.91742	−0.958710	−	0.284385i	$-0.908211\pi$
$601$	−2.21514e18	−1.91742	−0.958710	+	0.284385i	$0.908211\pi$
$602$	1.30262e18	1.11542
$603$	−2.69056e17	−0.227918
$604$	−2.87598e18	−2.41016
$605$	−1.81265e17	−0.150281
$606$	1.54757e18	1.26934
$607$	1.51399e18	1.22856	0.614280	−	0.789088i	$-0.289447\pi$
$607$	1.51399e18	1.22856	0.614280	+	0.789088i	$0.289447\pi$
$608$	9.92586e17	0.796883
$609$	9.08300e17	0.721468
$610$	−1.81982e17	−0.143016
$611$	1.00650e17	0.0782611
$612$	2.95224e17	0.227126
$613$	−3.48013e17	−0.264912	−0.132456	−	0.991189i	$-0.542286\pi$
$613$	−3.48013e17	−0.264912	−0.132456	+	0.991189i	$0.542286\pi$
$614$	−2.63211e18	−1.98249
$615$	3.42449e16	0.0255216
$616$	4.96048e18	3.65805
$617$	−3.95948e17	−0.288925	−0.144462	−	0.989510i	$-0.546145\pi$
$617$	−3.95948e17	−0.288925	−0.144462	+	0.989510i	$0.546145\pi$
$618$	3.92230e17	0.283215
$619$	5.67935e17	0.405797	0.202899	−	0.979200i	$-0.434964\pi$
$619$	5.67935e17	0.405797	0.202899	+	0.979200i	$0.434964\pi$
$620$	−4.14739e18	−2.93244
$621$	−2.24008e17	−0.156736
$622$	3.70088e17	0.256252
$623$	6.44371e17	0.441534
$624$	4.35188e17	0.295106
$625$	2.11478e16	0.0141920
$626$	3.62698e18	2.40886
$627$	3.26983e17	0.214924
$628$	1.87924e18	1.22249
$629$	2.80191e17	0.180395
$630$	6.96766e17	0.443990
$631$	−1.34988e18	−0.851344	−0.425672	−	0.904878i	$-0.639962\pi$
$631$	−1.34988e18	−0.851344	−0.425672	+	0.904878i	$0.639962\pi$
$632$	−3.38426e18	−2.11253
$633$	1.36642e18	0.844228
$634$	−9.95617e17	−0.608853
$635$	−1.46590e18	−0.887312
$636$	−4.30325e18	−2.57825
$637$	1.07189e17	0.0635686
$638$	3.83470e18	2.25111
$639$	−7.85251e17	−0.456302
$640$	8.28776e17	0.476724
$641$	−2.93146e18	−1.66920	−0.834598	−	0.550859i	$-0.814300\pi$
$641$	−2.93146e18	−1.66920	−0.834598	+	0.550859i	$0.814300\pi$
$642$	1.06627e18	0.601021
$643$	−2.95486e18	−1.64879	−0.824397	−	0.566013i	$-0.808485\pi$
$643$	−2.95486e18	−1.64879	−0.824397	+	0.566013i	$0.808485\pi$
$644$	−4.29103e18	−2.37030
$645$	3.32117e17	0.181615
$646$	3.13533e17	0.169735
$647$	1.50205e18	0.805021	0.402510	−	0.915415i	$-0.368138\pi$
$647$	1.50205e18	0.805021	0.402510	+	0.915415i	$0.368138\pi$
$648$	−5.91657e17	−0.313930
$649$	−2.76557e17	−0.145276
$650$	4.12898e17	0.214737
$651$	2.48152e18	1.27774
$652$	−4.24691e18	−2.16503
$653$	−2.58043e18	−1.30243	−0.651217	−	0.758892i	$-0.725741\pi$
$653$	−2.58043e18	−1.30243	−0.651217	+	0.758892i	$0.725741\pi$
$654$	−2.45353e18	−1.22613
$655$	−1.15699e18	−0.572481
$656$	−4.09811e17	−0.200775
$657$	−3.04224e17	−0.147577
$658$	−1.92846e18	−0.926280
$659$	−1.84356e18	−0.876804	−0.438402	−	0.898779i	$-0.644455\pi$
$659$	−1.84356e18	−0.876804	−0.438402	+	0.898779i	$0.644455\pi$
$660$	2.10318e18	0.990471
$661$	−1.41603e18	−0.660334	−0.330167	−	0.943922i	$-0.607105\pi$
$661$	−1.41603e18	−0.660334	−0.330167	+	0.943922i	$0.607105\pi$
$662$	9.77538e17	0.451395
$663$	6.29769e16	0.0287967
$664$	−4.52193e18	−2.04753
$665$	5.29062e17	0.237228
$666$	−9.33796e17	−0.414638
$667$	−1.99476e18	−0.877147
$668$	−3.99774e17	−0.174088
$669$	1.37490e17	0.0592927
$670$	−1.83792e18	−0.784946
$671$	3.28670e17	0.139016
$672$	−3.81999e18	−1.60016
$673$	1.59678e18	0.662439	0.331220	−	0.943554i	$-0.392540\pi$
$673$	1.59678e18	0.662439	0.331220	+	0.943554i	$0.392540\pi$
$674$	2.26552e18	0.930846
$675$	−2.95277e17	−0.120159
$676$	−6.01391e18	−2.42384
$677$	1.26442e18	0.504737	0.252368	−	0.967631i	$-0.418791\pi$
$677$	1.26442e18	0.504737	0.252368	+	0.967631i	$0.418791\pi$
$678$	−4.51738e18	−1.78605
$679$	−1.36062e17	−0.0532822
$680$	1.21271e18	0.470380
$681$	−2.30721e18	−0.886403
$682$	1.04766e19	3.98677
$683$	2.94317e18	1.10938	0.554691	−	0.832056i	$-0.312836\pi$
$683$	2.94317e18	1.10938	0.554691	+	0.832056i	$0.312836\pi$
$684$	−7.47083e17	−0.278936
$685$	8.18932e17	0.302872
$686$	3.87847e18	1.42087
$687$	2.08917e18	0.758150
$688$	−3.97446e18	−1.42874
$689$	−9.17965e17	−0.326890
$690$	−1.53020e18	−0.539795
$691$	4.80100e18	1.67774	0.838870	−	0.544333i	$-0.183217\pi$
$691$	4.80100e18	1.67774	0.838870	+	0.544333i	$0.183217\pi$
$692$	8.41923e18	2.91462
$693$	−1.25840e18	−0.431572
$694$	8.18622e17	0.278129
$695$	2.40432e18	0.809265
$696$	−5.26862e18	−1.75686
$697$	−5.93045e16	−0.0195918
$698$	−5.43660e18	−1.77937
$699$	−1.19326e17	−0.0386931
$700$	−5.65624e18	−1.81715
$701$	2.27265e18	0.723378	0.361689	−	0.932299i	$-0.382200\pi$
$701$	2.27265e18	0.723378	0.361689	+	0.932299i	$0.382200\pi$
$702$	−2.09884e17	−0.0661892
$703$	−7.09042e17	−0.221545
$704$	−6.09361e18	−1.88648
$705$	−4.91683e17	−0.150819
$706$	9.51034e18	2.89045
$707$	−4.52236e18	−1.36188
$708$	6.31871e17	0.188544
$709$	−4.95978e18	−1.46643	−0.733216	−	0.679996i	$-0.761982\pi$
$709$	−4.95978e18	−1.46643	−0.733216	+	0.679996i	$0.761982\pi$
$710$	−5.36405e18	−1.57150
$711$	8.58538e17	0.249234
$712$	−3.73769e18	−1.07519
$713$	−5.44977e18	−1.55345
$714$	−1.20664e18	−0.340831
$715$	4.48649e17	0.125579
$716$	1.47654e19	4.09553
$717$	−1.14345e18	−0.314299
$718$	5.99262e18	1.63233
$719$	8.04577e17	0.217185	0.108592	−	0.994086i	$-0.465366\pi$
$719$	8.04577e17	0.217185	0.108592	+	0.994086i	$0.465366\pi$
$720$	−2.12593e18	−0.568705
$721$	−1.14619e18	−0.303862
$722$	6.33589e18	1.66462
$723$	−1.11719e18	−0.290889
$724$	−1.01542e19	−2.62027
$725$	−2.62940e18	−0.672449
$726$	−1.04617e18	−0.265164
$727$	−2.49801e18	−0.627509	−0.313755	−	0.949504i	$-0.601587\pi$
$727$	−2.49801e18	−0.627509	−0.313755	+	0.949504i	$0.601587\pi$
$728$	−2.41767e18	−0.601926
$729$	1.50095e17	0.0370370
$730$	−2.07815e18	−0.508252
$731$	−5.75151e17	−0.139418
$732$	−7.50938e17	−0.180419
$733$	−4.59618e18	−1.09451	−0.547256	−	0.836965i	$-0.684328\pi$
$733$	−4.59618e18	−1.09451	−0.547256	+	0.836965i	$0.684328\pi$
$734$	−7.80801e18	−1.84296
$735$	−5.23625e17	−0.122505
$736$	8.38927e18	1.94544
$737$	3.31939e18	0.762992
$738$	1.97644e17	0.0450317
$739$	−4.80740e18	−1.08573	−0.542864	−	0.839820i	$-0.682660\pi$
$739$	−4.80740e18	−1.08573	−0.542864	+	0.839820i	$0.682660\pi$
$740$	−4.56063e18	−1.02098
$741$	−1.59367e17	−0.0353655
$742$	1.75883e19	3.86899
$743$	−9.31952e17	−0.203220	−0.101610	−	0.994824i	$-0.532399\pi$
$743$	−9.31952e17	−0.203220	−0.101610	+	0.994824i	$0.532399\pi$
$744$	−1.43941e19	−3.11143
$745$	7.40593e17	0.158695
$746$	1.54743e19	3.28706
$747$	1.14715e18	0.241566
$748$	−3.64224e18	−0.760340
$749$	−3.11589e18	−0.644837
$750$	−5.24759e18	−1.07662
$751$	−4.00906e18	−0.815422	−0.407711	−	0.913111i	$-0.633673\pi$
$751$	−4.00906e18	−0.815422	−0.407711	+	0.913111i	$0.633673\pi$
$752$	5.88400e18	1.18647
$753$	−3.70065e18	−0.739794
$754$	−1.86898e18	−0.370417
$755$	2.99700e18	0.588886
$756$	2.87517e18	0.560108
$757$	−3.00730e18	−0.580835	−0.290418	−	0.956900i	$-0.593794\pi$
$757$	−3.00730e18	−0.580835	−0.290418	+	0.956900i	$0.593794\pi$
$758$	3.52753e18	0.675493
$759$	2.76363e18	0.524697
$760$	−3.06884e18	−0.577678
$761$	7.28236e18	1.35916	0.679582	−	0.733600i	$-0.262161\pi$
$761$	7.28236e18	1.35916	0.679582	+	0.733600i	$0.262161\pi$
$762$	−8.46046e18	−1.56562
$763$	7.16977e18	1.31551
$764$	−1.55528e19	−2.82945
$765$	−3.07647e17	−0.0554949
$766$	7.02891e18	1.25719
$767$	1.34790e17	0.0239049
$768$	−7.67071e17	−0.134892
$769$	−2.34981e18	−0.409744	−0.204872	−	0.978789i	$-0.565678\pi$
$769$	−2.34981e18	−0.409744	−0.204872	+	0.978789i	$0.565678\pi$
$770$	−8.59614e18	−1.48633
$771$	4.06697e18	0.697296
$772$	1.11399e18	0.189396
$773$	−5.57007e18	−0.939061	−0.469530	−	0.882916i	$-0.655577\pi$
$773$	−5.57007e18	−0.939061	−0.469530	+	0.882916i	$0.655577\pi$
$774$	1.91681e18	0.320452
$775$	−7.18364e18	−1.19092
$776$	7.89229e17	0.129748
$777$	2.72877e18	0.444867
$778$	−2.12111e19	−3.42922
$779$	1.50074e17	0.0240609
$780$	−1.02506e18	−0.162981
$781$	9.68780e18	1.52754
$782$	2.64996e18	0.414377
$783$	1.33657e18	0.207272
$784$	6.26625e18	0.963725
$785$	−1.95832e18	−0.298697
$786$	−6.67757e18	−1.01012
$787$	−9.32424e18	−1.39887	−0.699435	−	0.714696i	$-0.746565\pi$
$787$	−9.32424e18	−1.39887	−0.699435	+	0.714696i	$0.746565\pi$
$788$	−7.66683e18	−1.14076
$789$	1.03018e18	0.152024
$790$	5.86467e18	0.858357
$791$	1.32008e19	1.91626
$792$	7.29939e18	1.05093
$793$	−1.60189e17	−0.0228748
$794$	3.11825e18	0.441650
$795$	4.48433e18	0.629957
$796$	−6.20318e18	−0.864330
$797$	−8.06553e18	−1.11469	−0.557345	−	0.830281i	$-0.688180\pi$
$797$	−8.06553e18	−1.11469	−0.557345	+	0.830281i	$0.688180\pi$
$798$	3.05348e18	0.418578
$799$	8.51484e17	0.115777
$800$	1.10583e19	1.49144
$801$	9.48197e17	0.126849
$802$	2.66458e19	3.53586
$803$	3.75327e18	0.494037
$804$	−7.58408e18	−0.990236
$805$	4.47160e18	0.579148
$806$	−5.10615e18	−0.656017
$807$	3.07666e18	0.392104
$808$	2.62321e19	3.31634
$809$	−4.86012e18	−0.609511	−0.304756	−	0.952431i	$-0.598575\pi$
$809$	−4.86012e18	−0.609511	−0.304756	+	0.952431i	$0.598575\pi$
$810$	1.02530e18	0.127555
$811$	9.37387e18	1.15687	0.578433	−	0.815730i	$-0.303664\pi$
$811$	9.37387e18	1.15687	0.578433	+	0.815730i	$0.303664\pi$
$812$	2.56030e19	3.13456
$813$	−2.06395e18	−0.250675
$814$	1.15204e19	1.38807
$815$	4.42562e18	0.528992
$816$	3.68163e18	0.436570
$817$	1.45546e18	0.171220
$818$	−6.51619e18	−0.760497
$819$	6.13328e17	0.0710146
$820$	9.65289e17	0.110884
$821$	7.55050e18	0.860489	0.430245	−	0.902712i	$-0.358427\pi$
$821$	7.55050e18	0.860489	0.430245	+	0.902712i	$0.358427\pi$
$822$	4.72646e18	0.534403
$823$	2.08667e18	0.234075	0.117038	−	0.993127i	$-0.462660\pi$
$823$	2.08667e18	0.234075	0.117038	+	0.993127i	$0.462660\pi$
$824$	6.64849e18	0.739939
$825$	3.64289e18	0.402250
$826$	−2.58258e18	−0.282933
$827$	−1.53200e19	−1.66523	−0.832613	−	0.553856i	$-0.813156\pi$
$827$	−1.53200e19	−1.66523	−0.832613	+	0.553856i	$0.813156\pi$
$828$	−6.31429e18	−0.680969
$829$	1.39829e19	1.49621	0.748107	−	0.663578i	$-0.230963\pi$
$829$	1.39829e19	1.49621	0.748107	+	0.663578i	$0.230963\pi$
$830$	7.83616e18	0.831947
$831$	4.14065e18	0.436176
$832$	2.96994e18	0.310418
$833$	9.06800e17	0.0940413
$834$	1.38765e19	1.42791
$835$	4.16597e17	0.0425357
$836$	9.21691e18	0.933780
$837$	3.65157e18	0.367083
$838$	3.20129e19	3.19329
$839$	−1.92209e18	−0.190249	−0.0951244	−	0.995465i	$-0.530325\pi$
$839$	−1.92209e18	−0.190249	−0.0951244	+	0.995465i	$0.530325\pi$
$840$	1.18105e19	1.15999
$841$	1.64134e18	0.159965
$842$	7.90133e18	0.764137
$843$	−4.99261e18	−0.479124
$844$	3.85163e19	3.66791
$845$	6.26697e18	0.592228
$846$	−2.83775e18	−0.266113
$847$	3.05715e18	0.284495
$848$	−5.36642e19	−4.95577
$849$	−8.74032e18	−0.800990
$850$	3.49305e18	0.317674
$851$	−5.99277e18	−0.540861
$852$	−2.21345e19	−1.98249
$853$	−1.89443e19	−1.68387	−0.841937	−	0.539575i	$-0.818585\pi$
$853$	−1.89443e19	−1.68387	−0.841937	+	0.539575i	$0.818585\pi$
$854$	3.06924e18	0.270741
$855$	7.78519e17	0.0681537
$856$	1.80738e19	1.57025
$857$	7.63925e18	0.658681	0.329341	−	0.944211i	$-0.393174\pi$
$857$	7.63925e18	0.658681	0.329341	+	0.944211i	$0.393174\pi$
$858$	2.58938e18	0.221579
$859$	2.24819e19	1.90931	0.954656	−	0.297712i	$-0.0962235\pi$
$859$	2.24819e19	1.90931	0.954656	+	0.297712i	$0.0962235\pi$
$860$	9.36163e18	0.789063
$861$	−5.77563e17	−0.0483146
$862$	7.77214e18	0.645273
$863$	−8.51970e18	−0.702028	−0.351014	−	0.936370i	$-0.614163\pi$
$863$	−8.51970e18	−0.702028	−0.351014	+	0.936370i	$0.614163\pi$
$864$	−5.62115e18	−0.459712
$865$	−8.77350e18	−0.712145
$866$	2.63102e19	2.11962
$867$	−6.68766e18	−0.534749
$868$	6.99485e19	5.55137
$869$	−1.05920e19	−0.834349
$870$	9.13012e18	0.713841
$871$	−1.61783e18	−0.125549
$872$	−4.15884e19	−3.20343
$873$	−2.00216e17	−0.0153076
$874$	−6.70589e18	−0.508900
$875$	1.53347e19	1.15511
$876$	−8.57540e18	−0.641177
$877$	−2.01059e19	−1.49220	−0.746099	−	0.665835i	$-0.768076\pi$
$877$	−2.01059e19	−1.49220	−0.746099	+	0.665835i	$0.768076\pi$
$878$	−3.95663e19	−2.91482
$879$	8.56630e18	0.626420
$880$	2.62280e19	1.90383
$881$	−1.11063e18	−0.0800249	−0.0400125	−	0.999199i	$-0.512740\pi$
$881$	−1.11063e18	−0.0800249	−0.0400125	+	0.999199i	$0.512740\pi$
$882$	−3.02210e18	−0.216154
$883$	4.92034e18	0.349342	0.174671	−	0.984627i	$-0.444114\pi$
$883$	4.92034e18	0.349342	0.174671	+	0.984627i	$0.444114\pi$
$884$	1.77518e18	0.125113
$885$	−6.58459e17	−0.0460678
$886$	3.01902e19	2.09675
$887$	−2.53874e19	−1.75031	−0.875155	−	0.483842i	$-0.839241\pi$
$887$	−2.53874e19	−1.75031	−0.875155	+	0.483842i	$0.839241\pi$
$888$	−1.58283e19	−1.08330
$889$	2.47234e19	1.67976
$890$	6.47714e18	0.436866
$891$	−1.85175e18	−0.123987
$892$	3.87554e18	0.257609
$893$	−2.15473e18	−0.142187
$894$	4.27433e18	0.280010
$895$	−1.53867e19	−1.00068
$896$	−1.39778e19	−0.902481
$897$	−1.34696e18	−0.0863383
$898$	−1.32106e18	−0.0840671
$899$	3.25167e19	2.05432
$900$	−8.32321e18	−0.522053
$901$	−7.76584e18	−0.483590
$902$	−2.43838e18	−0.150751
$903$	−5.60136e18	−0.343814
$904$	−7.65717e19	−4.66631
$905$	1.05815e19	0.640224
$906$	1.72972e19	1.03906
$907$	−8.19639e18	−0.488850	−0.244425	−	0.969668i	$-0.578599\pi$
$907$	−8.19639e18	−0.488850	−0.244425	+	0.969668i	$0.578599\pi$
$908$	−6.50352e19	−3.85115
$909$	−6.65470e18	−0.391258
$910$	4.18965e18	0.244573
$911$	4.68189e18	0.271364	0.135682	−	0.990752i	$-0.456677\pi$
$911$	4.68189e18	0.271364	0.135682	+	0.990752i	$0.456677\pi$
$912$	−9.31659e18	−0.536155
$913$	−1.41526e19	−0.808678
$914$	4.07502e19	2.31195
$915$	7.82537e17	0.0440827
$916$	5.88891e19	3.29393
$917$	1.95134e19	1.08376
$918$	−1.77558e18	−0.0979182
$919$	−8.45116e18	−0.462770	−0.231385	−	0.972862i	$-0.574326\pi$
$919$	−8.45116e18	−0.462770	−0.231385	+	0.972862i	$0.574326\pi$
$920$	−2.59376e19	−1.41029
$921$	1.13183e19	0.611075
$922$	−4.39947e19	−2.35857
$923$	−4.72170e18	−0.251355
$924$	−3.54716e19	−1.87505
$925$	−7.89940e18	−0.414642
$926$	−8.48767e18	−0.442402
$927$	−1.68662e18	−0.0872972
$928$	−5.00556e19	−2.57271
$929$	1.21984e19	0.622587	0.311293	−	0.950314i	$-0.399238\pi$
$929$	1.21984e19	0.622587	0.311293	+	0.950314i	$0.399238\pi$
$930$	2.49439e19	1.26423
$931$	−2.29471e18	−0.115493
$932$	−3.36353e18	−0.168109
$933$	−1.59141e18	−0.0789862
$934$	3.64188e19	1.79503
$935$	3.79550e18	0.185778
$936$	−3.55763e18	−0.172929
$937$	−3.13677e19	−1.51417	−0.757086	−	0.653315i	$-0.773378\pi$
$937$	−3.13677e19	−1.51417	−0.757086	+	0.653315i	$0.773378\pi$
$938$	3.09977e19	1.48597
$939$	−1.55963e19	−0.742500
$940$	−1.38595e19	−0.655262
$941$	2.61583e19	1.22822	0.614111	−	0.789220i	$-0.289515\pi$
$941$	2.61583e19	1.22822	0.614111	+	0.789220i	$0.289515\pi$
$942$	−1.13024e19	−0.527037
$943$	1.26841e18	0.0587401
$944$	7.87982e18	0.362408
$945$	−2.99615e18	−0.136854
$946$	−2.36481e19	−1.07276
$947$	8.37461e18	0.377303	0.188651	−	0.982044i	$-0.439588\pi$
$947$	8.37461e18	0.377303	0.188651	+	0.982044i	$0.439588\pi$
$948$	2.42003e19	1.08285
$949$	−1.82930e18	−0.0812931
$950$	−8.83939e18	−0.390139
$951$	4.28124e18	0.187671
$952$	−2.04531e19	−0.890471
$953$	−2.89783e19	−1.25305	−0.626525	−	0.779401i	$-0.715524\pi$
$953$	−2.89783e19	−1.25305	−0.626525	+	0.779401i	$0.715524\pi$
$954$	2.58813e19	1.11153
$955$	1.62073e19	0.691334
$956$	−3.22313e19	−1.36553
$957$	−1.64896e19	−0.693875
$958$	5.82916e19	2.43630
$959$	−1.38118e19	−0.573363
$960$	−1.45084e19	−0.598214
$961$	6.44197e19	2.63825
$962$	−5.61491e18	−0.228404
$963$	−4.58505e18	−0.185257
$964$	−3.14911e19	−1.26383
$965$	−1.16087e18	−0.0462761
$966$	2.58078e19	1.02188
$967$	−4.09484e19	−1.61052	−0.805258	−	0.592924i	$-0.797973\pi$
$967$	−4.09484e19	−1.61052	−0.805258	+	0.592924i	$0.797973\pi$
$968$	−1.77331e19	−0.692778
$969$	−1.34822e18	−0.0523186
$970$	−1.36768e18	−0.0527189
$971$	−6.74802e18	−0.258376	−0.129188	−	0.991620i	$-0.541237\pi$
$971$	−6.74802e18	−0.258376	−0.129188	+	0.991620i	$0.541237\pi$
$972$	4.23084e18	0.160915
$973$	−4.05504e19	−1.53201
$974$	−3.83600e19	−1.43961
$975$	−1.77550e18	−0.0661897
$976$	−9.36466e18	−0.346791
$977$	4.29813e19	1.58112	0.790560	−	0.612384i	$-0.209789\pi$
$977$	4.29813e19	1.58112	0.790560	+	0.612384i	$0.209789\pi$
$978$	2.55424e19	0.933382
$979$	−1.16981e19	−0.424647
$980$	−1.47598e19	−0.532245
$981$	1.05504e19	0.377937
$982$	4.93593e19	1.75648
$983$	3.22411e19	1.13976	0.569878	−	0.821729i	$-0.306990\pi$
$983$	3.22411e19	1.13976	0.569878	+	0.821729i	$0.306990\pi$
$984$	3.35017e18	0.117652
$985$	7.98945e18	0.278728
$986$	−1.58113e19	−0.547984
$987$	8.29255e18	0.285514
$988$	−4.49220e18	−0.153652
$989$	1.23014e19	0.418003
$990$	−1.26493e19	−0.427010
$991$	−3.08700e18	−0.103528	−0.0517639	−	0.998659i	$-0.516484\pi$
$991$	−3.08700e18	−0.103528	−0.0517639	+	0.998659i	$0.516484\pi$
$992$	−1.36754e20	−4.55632
$993$	−4.20350e18	−0.139136
$994$	9.04681e19	2.97498
$995$	6.46421e18	0.211186
$996$	3.23355e19	1.04953
$997$	4.33114e19	1.39664	0.698318	−	0.715787i	$-0.253932\pi$
$997$	4.33114e19	1.39664	0.698318	+	0.715787i	$0.253932\pi$
$998$	−1.75931e19	−0.563628
$999$	4.01541e18	0.127807

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-169.531 q^{2} +729.000 q^{3} +20548.9 q^{4} -21413.6 q^{5} -123588. q^{6} +361154. q^{7} -2.09488e6 q^{8} +531441. q^{9} +3.63027e6 q^{10} -6.55650e6 q^{11} +1.49801e7 q^{12} +3.19555e6 q^{13} -6.12269e7 q^{14} -1.56105e7 q^{15} +1.86812e8 q^{16} +2.70339e7 q^{17} -9.00959e7 q^{18} -6.84109e7 q^{19} -4.40025e8 q^{20} +2.63281e8 q^{21} +1.11153e9 q^{22} -5.78204e8 q^{23} -1.52717e9 q^{24} -7.62162e8 q^{25} -5.41746e8 q^{26} +3.87420e8 q^{27} +7.42131e9 q^{28} +3.44992e9 q^{29} +2.64647e9 q^{30} +9.42535e9 q^{31} -1.45092e10 q^{32} -4.77969e9 q^{33} -4.58309e9 q^{34} -7.73360e9 q^{35} +1.09205e10 q^{36} +1.03645e10 q^{37} +1.15978e10 q^{38} +2.32956e9 q^{39} +4.48589e10 q^{40} -2.19371e9 q^{41} -4.46344e10 q^{42} -2.12752e10 q^{43} -1.34729e11 q^{44} -1.13801e10 q^{45} +9.80237e10 q^{46} +3.14969e10 q^{47} +1.36186e11 q^{48} +3.35431e10 q^{49} +1.29210e11 q^{50} +1.97077e10 q^{51} +6.56650e10 q^{52} -2.87264e11 q^{53} -6.56799e10 q^{54} +1.40398e11 q^{55} -7.56575e11 q^{56} -4.98715e10 q^{57} -5.84870e11 q^{58} +4.21805e10 q^{59} -3.20779e11 q^{60} -5.01289e10 q^{61} -1.59789e12 q^{62} +1.91932e11 q^{63} +9.29400e11 q^{64} -6.84282e10 q^{65} +8.10307e11 q^{66} -5.06275e11 q^{67} +5.55516e11 q^{68} -4.21511e11 q^{69} +1.31109e12 q^{70} -1.47759e12 q^{71} -1.11331e12 q^{72} -5.72451e11 q^{73} -1.75710e12 q^{74} -5.55616e11 q^{75} -1.40577e12 q^{76} -2.36790e12 q^{77} -3.94933e11 q^{78} +1.61549e12 q^{79} -4.00031e12 q^{80} +2.82430e11 q^{81} +3.71903e11 q^{82} +2.15856e12 q^{83} +5.41014e12 q^{84} -5.78892e11 q^{85} +3.60682e12 q^{86} +2.51499e12 q^{87} +1.37351e13 q^{88} +1.78420e12 q^{89} +1.92928e12 q^{90} +1.15409e12 q^{91} -1.18815e13 q^{92} +6.87108e12 q^{93} -5.33972e12 q^{94} +1.46492e12 q^{95} -1.05772e13 q^{96} -3.76742e11 q^{97} -5.68661e12 q^{98} -3.48439e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 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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