LMFDB - Embedded newform 177.14.a.d.1.3

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:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-163.348 q^{2} -729.000 q^{3} +18490.4 q^{4} -43774.8 q^{5} +119080. q^{6} -199445. q^{7} -1.68222e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-163.348 q^{2} -729.000 q^{3} +18490.4 q^{4} -43774.8 q^{5} +119080. q^{6} -199445. q^{7} -1.68222e6 q^{8} +531441. q^{9} +7.15050e6 q^{10} -2.23470e6 q^{11} -1.34795e7 q^{12} -5.61298e6 q^{13} +3.25788e7 q^{14} +3.19118e7 q^{15} +1.23313e8 q^{16} +1.65791e8 q^{17} -8.68096e7 q^{18} +1.96251e8 q^{19} -8.09414e8 q^{20} +1.45395e8 q^{21} +3.65032e8 q^{22} -1.17850e9 q^{23} +1.22634e9 q^{24} +6.95528e8 q^{25} +9.16867e8 q^{26} -3.87420e8 q^{27} -3.68781e9 q^{28} +3.91572e9 q^{29} -5.21272e9 q^{30} -4.87132e9 q^{31} -6.36214e9 q^{32} +1.62909e9 q^{33} -2.70815e10 q^{34} +8.73064e9 q^{35} +9.82657e9 q^{36} +2.62956e10 q^{37} -3.20571e10 q^{38} +4.09187e9 q^{39} +7.36388e10 q^{40} -3.31161e10 q^{41} -2.37499e10 q^{42} +7.22500e10 q^{43} -4.13205e10 q^{44} -2.32637e10 q^{45} +1.92504e11 q^{46} +2.41258e10 q^{47} -8.98953e10 q^{48} -5.71109e10 q^{49} -1.13613e11 q^{50} -1.20862e11 q^{51} -1.03786e11 q^{52} -1.23154e11 q^{53} +6.32842e10 q^{54} +9.78234e10 q^{55} +3.35510e11 q^{56} -1.43067e11 q^{57} -6.39622e11 q^{58} +4.21805e10 q^{59} +5.90063e11 q^{60} +6.38875e11 q^{61} +7.95717e11 q^{62} -1.05993e11 q^{63} +2.90593e10 q^{64} +2.45707e11 q^{65} -2.66108e11 q^{66} +1.16548e12 q^{67} +3.06554e12 q^{68} +8.59123e11 q^{69} -1.42613e12 q^{70} +5.09862e11 q^{71} -8.94001e11 q^{72} +1.14227e12 q^{73} -4.29533e12 q^{74} -5.07040e11 q^{75} +3.62876e12 q^{76} +4.45698e11 q^{77} -6.68396e11 q^{78} -1.10281e12 q^{79} -5.39801e12 q^{80} +2.82430e11 q^{81} +5.40944e12 q^{82} -4.10174e12 q^{83} +2.68842e12 q^{84} -7.25746e12 q^{85} -1.18019e13 q^{86} -2.85456e12 q^{87} +3.75925e12 q^{88} -1.70286e12 q^{89} +3.80007e12 q^{90} +1.11948e12 q^{91} -2.17909e13 q^{92} +3.55119e12 q^{93} -3.94089e12 q^{94} -8.59083e12 q^{95} +4.63800e12 q^{96} -5.45730e12 q^{97} +9.32892e12 q^{98} -1.18761e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) $ 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * 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 $

$2$	−163.348	−1.80475	−0.902376	−	0.430949i	$-0.858179\pi$
$2$	−163.348	−1.80475	−0.902376	+	0.430949i	$0.858179\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	18490.4	2.25713
$5$	−43774.8	−1.25291	−0.626454	−	0.779459i	$-0.715494\pi$
$5$	−43774.8	−1.25291	−0.626454	+	0.779459i	$0.715494\pi$
$6$	119080.	1.04197
$7$	−199445.	−0.640744	−0.320372	−	0.947292i	$-0.603808\pi$
$7$	−199445.	−0.640744	−0.320372	+	0.947292i	$0.603808\pi$
$8$	−1.68222e6	−2.26881
$9$	531441.	0.333333
$10$	7.15050e6	2.26119
$11$	−2.23470e6	−0.380335	−0.190167	−	0.981752i	$-0.560903\pi$
$11$	−2.23470e6	−0.380335	−0.190167	+	0.981752i	$0.560903\pi$
$12$	−1.34795e7	−1.30316
$13$	−5.61298e6	−0.322524	−0.161262	−	0.986912i	$-0.551556\pi$
$13$	−5.61298e6	−0.322524	−0.161262	+	0.986912i	$0.551556\pi$
$14$	3.25788e7	1.15638
$15$	3.19118e7	0.723366
$16$	1.23313e8	1.83751
$17$	1.65791e8	1.66588	0.832938	−	0.553366i	$-0.186657\pi$
$17$	1.65791e8	1.66588	0.832938	+	0.553366i	$0.186657\pi$
$18$	−8.68096e7	−0.601584
$19$	1.96251e8	0.957001	0.478501	−	0.878087i	$-0.341180\pi$
$19$	1.96251e8	0.957001	0.478501	+	0.878087i	$0.341180\pi$
$20$	−8.09414e8	−2.82798
$21$	1.45395e8	0.369934
$22$	3.65032e8	0.686410
$23$	−1.17850e9	−1.65996	−0.829979	−	0.557795i	$-0.811647\pi$
$23$	−1.17850e9	−1.65996	−0.829979	+	0.557795i	$0.811647\pi$
$24$	1.22634e9	1.30990
$25$	6.95528e8	0.569777
$26$	9.16867e8	0.582076
$27$	−3.87420e8	−0.192450
$28$	−3.68781e9	−1.44624
$29$	3.91572e9	1.22243	0.611215	−	0.791465i	$-0.290681\pi$
$29$	3.91572e9	1.22243	0.611215	+	0.791465i	$0.290681\pi$
$30$	−5.21272e9	−1.30550
$31$	−4.87132e9	−0.985815	−0.492907	−	0.870082i	$-0.664066\pi$
$31$	−4.87132e9	−0.985815	−0.492907	+	0.870082i	$0.664066\pi$
$32$	−6.36214e9	−1.04744
$33$	1.62909e9	0.219586
$34$	−2.70815e10	−3.00649
$35$	8.73064e9	0.802793
$36$	9.82657e9	0.752377
$37$	2.62956e10	1.68489	0.842446	−	0.538780i	$-0.181115\pi$
$37$	2.62956e10	1.68489	0.842446	+	0.538780i	$0.181115\pi$
$38$	−3.20571e10	−1.72715
$39$	4.09187e9	0.186209
$40$	7.36388e10	2.84261
$41$	−3.31161e10	−1.08879	−0.544396	−	0.838829i	$-0.683241\pi$
$41$	−3.31161e10	−1.08879	−0.544396	+	0.838829i	$0.683241\pi$
$42$	−2.37499e10	−0.667639
$43$	7.22500e10	1.74298	0.871491	−	0.490412i	$-0.163154\pi$
$43$	7.22500e10	1.74298	0.871491	+	0.490412i	$0.163154\pi$
$44$	−4.13205e10	−0.858466
$45$	−2.32637e10	−0.417636
$46$	1.92504e11	2.99581
$47$	2.41258e10	0.326472	0.163236	−	0.986587i	$-0.447807\pi$
$47$	2.41258e10	0.326472	0.163236	+	0.986587i	$0.447807\pi$
$48$	−8.98953e10	−1.06089
$49$	−5.71109e10	−0.589447
$50$	−1.13613e11	−1.02831
$51$	−1.20862e11	−0.961794
$52$	−1.03786e11	−0.727979
$53$	−1.23154e11	−0.763228	−0.381614	−	0.924322i	$-0.624632\pi$
$53$	−1.23154e11	−0.763228	−0.381614	+	0.924322i	$0.624632\pi$
$54$	6.32842e10	0.347325
$55$	9.78234e10	0.476524
$56$	3.35510e11	1.45373
$57$	−1.43067e11	−0.552525
$58$	−6.39622e11	−2.20618
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	5.90063e11	1.63273
$61$	6.38875e11	1.58771	0.793857	−	0.608105i	$-0.208070\pi$
$61$	6.38875e11	1.58771	0.793857	+	0.608105i	$0.208070\pi$
$62$	7.95717e11	1.77915
$63$	−1.05993e11	−0.213581
$64$	2.90593e10	0.0528585
$65$	2.45707e11	0.404093
$66$	−2.66108e11	−0.396299
$67$	1.16548e12	1.57404	0.787022	−	0.616925i	$-0.211622\pi$
$67$	1.16548e12	1.57404	0.787022	+	0.616925i	$0.211622\pi$
$68$	3.06554e12	3.76010
$69$	8.59123e11	0.958377
$70$	−1.42613e12	−1.44884
$71$	5.09862e11	0.472360	0.236180	−	0.971709i	$-0.424104\pi$
$71$	5.09862e11	0.472360	0.236180	+	0.971709i	$0.424104\pi$
$72$	−8.94001e11	−0.756270
$73$	1.14227e12	0.883428	0.441714	−	0.897156i	$-0.354371\pi$
$73$	1.14227e12	0.883428	0.441714	+	0.897156i	$0.354371\pi$
$74$	−4.29533e12	−3.04081
$75$	−5.07040e11	−0.328961
$76$	3.62876e12	2.16008
$77$	4.45698e11	0.243697
$78$	−6.68396e11	−0.336062
$79$	−1.10281e12	−0.510416	−0.255208	−	0.966886i	$-0.582144\pi$
$79$	−1.10281e12	−0.510416	−0.255208	+	0.966886i	$0.582144\pi$
$80$	−5.39801e12	−2.30223
$81$	2.82430e11	0.111111
$82$	5.40944e12	1.96500
$83$	−4.10174e12	−1.37709	−0.688543	−	0.725196i	$-0.741749\pi$
$83$	−4.10174e12	−1.37709	−0.688543	+	0.725196i	$0.741749\pi$
$84$	2.68842e12	0.834989
$85$	−7.25746e12	−2.08719
$86$	−1.18019e13	−3.14565
$87$	−2.85456e12	−0.705770
$88$	3.75925e12	0.862908
$89$	−1.70286e12	−0.363199	−0.181600	−	0.983373i	$-0.558128\pi$
$89$	−1.70286e12	−0.363199	−0.181600	+	0.983373i	$0.558128\pi$
$90$	3.80007e12	0.753729
$91$	1.11948e12	0.206655
$92$	−2.17909e13	−3.74674
$93$	3.55119e12	0.569160
$94$	−3.94089e12	−0.589201
$95$	−8.59083e12	−1.19903
$96$	4.63800e12	0.604739
$97$	−5.45730e12	−0.665214	−0.332607	−	0.943065i	$-0.607928\pi$
$97$	−5.45730e12	−0.665214	−0.332607	+	0.943065i	$0.607928\pi$
$98$	9.32892e12	1.06381
$99$	−1.18761e12	−0.126778
$100$	1.28606e13	1.28606
$101$	7.36088e11	0.0689987	0.0344994	−	0.999405i	$-0.489016\pi$
$101$	7.36088e11	0.0689987	0.0344994	+	0.999405i	$0.489016\pi$
$102$	1.97424e13	1.73580
$103$	−4.48749e12	−0.370307	−0.185153	−	0.982710i	$-0.559278\pi$
$103$	−4.48749e12	−0.370307	−0.185153	+	0.982710i	$0.559278\pi$
$104$	9.44228e12	0.731746
$105$	−6.36464e12	−0.463493
$106$	2.01168e13	1.37744
$107$	−2.90016e13	−1.86822	−0.934108	−	0.356989i	$-0.883803\pi$
$107$	−2.90016e13	−1.86822	−0.934108	+	0.356989i	$0.883803\pi$
$108$	−7.16357e12	−0.434385
$109$	−1.11195e13	−0.635058	−0.317529	−	0.948249i	$-0.602853\pi$
$109$	−1.11195e13	−0.635058	−0.317529	+	0.948249i	$0.602853\pi$
$110$	−1.59792e13	−0.860008
$111$	−1.91695e13	−0.972773
$112$	−2.45941e13	−1.17737
$113$	−3.02969e13	−1.36895	−0.684477	−	0.729035i	$-0.739969\pi$
$113$	−3.02969e13	−1.36895	−0.684477	+	0.729035i	$0.739969\pi$
$114$	2.33696e13	0.997171
$115$	5.15884e13	2.07977
$116$	7.24032e13	2.75919
$117$	−2.98297e12	−0.107508
$118$	−6.89009e12	−0.234959
$119$	−3.30661e13	−1.06740
$120$	−5.36827e13	−1.64118
$121$	−2.95288e13	−0.855345
$122$	−1.04359e14	−2.86543
$123$	2.41417e13	0.628614
$124$	−9.00727e13	−2.22511
$125$	2.29894e13	0.539030
$126$	1.73137e13	0.385462
$127$	3.77770e13	0.798921	0.399461	−	0.916750i	$-0.369197\pi$
$127$	3.77770e13	0.798921	0.399461	+	0.916750i	$0.369197\pi$
$128$	4.73719e13	0.952042
$129$	−5.26702e13	−1.00631
$130$	−4.01357e13	−0.729287
$131$	−7.40111e13	−1.27948	−0.639740	−	0.768591i	$-0.720958\pi$
$131$	−7.40111e13	−1.27948	−0.639740	+	0.768591i	$0.720958\pi$
$132$	3.01226e13	0.495635
$133$	−3.91411e13	−0.613193
$134$	−1.90378e14	−2.84076
$135$	1.69592e13	0.241122
$136$	−2.78897e14	−3.77956
$137$	−7.73464e13	−0.999439	−0.499719	−	0.866187i	$-0.666564\pi$
$137$	−7.73464e13	−0.999439	−0.499719	+	0.866187i	$0.666564\pi$
$138$	−1.40336e14	−1.72963
$139$	3.36925e13	0.396220	0.198110	−	0.980180i	$-0.436520\pi$
$139$	3.36925e13	0.396220	0.198110	+	0.980180i	$0.436520\pi$
$140$	1.61433e14	1.81201
$141$	−1.75877e13	−0.188489
$142$	−8.32847e13	−0.852493
$143$	1.25433e13	0.122667
$144$	6.55337e13	0.612503
$145$	−1.71410e14	−1.53159
$146$	−1.86587e14	−1.59437
$147$	4.16338e13	0.340317
$148$	4.86217e14	3.80302
$149$	−7.50681e13	−0.562011	−0.281005	−	0.959706i	$-0.590668\pi$
$149$	−7.50681e13	−0.562011	−0.281005	+	0.959706i	$0.590668\pi$
$150$	8.28237e13	0.593692
$151$	−1.01949e14	−0.699893	−0.349946	−	0.936770i	$-0.613800\pi$
$151$	−1.01949e14	−0.699893	−0.349946	+	0.936770i	$0.613800\pi$
$152$	−3.30137e14	−2.17125
$153$	8.81081e13	0.555292
$154$	−7.28037e13	−0.439814
$155$	2.13241e14	1.23513
$156$	7.56603e13	0.420299
$157$	−9.57418e13	−0.510216	−0.255108	−	0.966913i	$-0.582111\pi$
$157$	−9.57418e13	−0.510216	−0.255108	+	0.966913i	$0.582111\pi$
$158$	1.80141e14	0.921175
$159$	8.97790e13	0.440650
$160$	2.78501e14	1.31234
$161$	2.35044e14	1.06361
$162$	−4.61342e13	−0.200528
$163$	3.90303e14	1.62998	0.814990	−	0.579476i	$-0.196743\pi$
$163$	3.90303e14	1.62998	0.814990	+	0.579476i	$0.196743\pi$
$164$	−6.12331e14	−2.45754
$165$	−7.13132e13	−0.275121
$166$	6.70010e14	2.48530
$167$	4.97541e14	1.77489	0.887446	−	0.460912i	$-0.152478\pi$
$167$	4.97541e14	1.77489	0.887446	+	0.460912i	$0.152478\pi$
$168$	−2.44587e14	−0.839310
$169$	−2.71370e14	−0.895978
$170$	1.18549e15	3.76686
$171$	1.04296e14	0.319000
$172$	1.33593e15	3.93414
$173$	−3.56296e14	−1.01044	−0.505222	−	0.862990i	$-0.668589\pi$
$173$	−3.56296e14	−1.01044	−0.505222	+	0.862990i	$0.668589\pi$
$174$	4.66285e14	1.27374
$175$	−1.38719e14	−0.365081
$176$	−2.75567e14	−0.698869
$177$	−3.07496e13	−0.0751646
$178$	2.78159e14	0.655485
$179$	2.80606e13	0.0637606	0.0318803	−	0.999492i	$-0.489850\pi$
$179$	2.80606e13	0.0637606	0.0318803	+	0.999492i	$0.489850\pi$
$180$	−4.30156e14	−0.942659
$181$	6.34497e13	0.134128	0.0670639	−	0.997749i	$-0.478637\pi$
$181$	6.34497e13	0.134128	0.0670639	+	0.997749i	$0.478637\pi$
$182$	−1.82864e14	−0.372962
$183$	−4.65740e14	−0.916667
$184$	1.98249e15	3.76613
$185$	−1.15109e15	−2.11101
$186$	−5.80078e14	−1.02719
$187$	−3.70492e14	−0.633591
$188$	4.46097e14	0.736890
$189$	7.72689e13	0.123311
$190$	1.40329e15	2.16396
$191$	9.47339e14	1.41185	0.705925	−	0.708287i	$-0.250532\pi$
$191$	9.47339e14	1.41185	0.705925	+	0.708287i	$0.250532\pi$
$192$	−2.11842e13	−0.0305179
$193$	−1.10219e14	−0.153509	−0.0767547	−	0.997050i	$-0.524456\pi$
$193$	−1.10219e14	−0.153509	−0.0767547	+	0.997050i	$0.524456\pi$
$194$	8.91437e14	1.20055
$195$	−1.79121e14	−0.233303
$196$	−1.05600e15	−1.33046
$197$	−9.69782e14	−1.18207	−0.591035	−	0.806646i	$-0.701281\pi$
$197$	−9.69782e14	−1.18207	−0.591035	+	0.806646i	$0.701281\pi$
$198$	1.93993e14	0.228803
$199$	−7.30022e14	−0.833280	−0.416640	−	0.909072i	$-0.636792\pi$
$199$	−7.30022e14	−0.833280	−0.416640	+	0.909072i	$0.636792\pi$
$200$	−1.17003e15	−1.29271
$201$	−8.49631e14	−0.908775
$202$	−1.20238e14	−0.124526
$203$	−7.80968e14	−0.783265
$204$	−2.23478e15	−2.17089
$205$	1.44965e15	1.36415
$206$	7.33021e14	0.668312
$207$	−6.26301e14	−0.553319
$208$	−6.92155e14	−0.592641
$209$	−4.38561e14	−0.363981
$210$	1.03965e15	0.836490
$211$	5.10536e14	0.398281	0.199141	−	0.979971i	$-0.436185\pi$
$211$	5.10536e14	0.398281	0.199141	+	0.979971i	$0.436185\pi$
$212$	−2.27716e15	−1.72270
$213$	−3.71689e14	−0.272717
$214$	4.73734e15	3.37167
$215$	−3.16273e15	−2.18379
$216$	6.51727e14	0.436633
$217$	9.71557e14	0.631655
$218$	1.81635e15	1.14612
$219$	−8.32717e14	−0.510047
$220$	1.80879e15	1.07558
$221$	−9.30582e14	−0.537285
$222$	3.13129e15	1.75562
$223$	2.91184e15	1.58557	0.792786	−	0.609501i	$-0.208630\pi$
$223$	2.91184e15	1.58557	0.792786	+	0.609501i	$0.208630\pi$
$224$	1.26889e15	0.671141
$225$	3.69632e14	0.189926
$226$	4.94893e15	2.47062
$227$	9.23883e14	0.448176	0.224088	−	0.974569i	$-0.428060\pi$
$227$	9.23883e14	0.448176	0.224088	+	0.974569i	$0.428060\pi$
$228$	−2.64536e15	−1.24712
$229$	−5.77614e14	−0.264672	−0.132336	−	0.991205i	$-0.542248\pi$
$229$	−5.77614e14	−0.264672	−0.132336	+	0.991205i	$0.542248\pi$
$230$	−8.42683e15	−3.75347
$231$	−3.24914e14	−0.140699
$232$	−6.58710e15	−2.77346
$233$	2.49779e15	1.02269	0.511344	−	0.859376i	$-0.329148\pi$
$233$	2.49779e15	1.02269	0.511344	+	0.859376i	$0.329148\pi$
$234$	4.87261e14	0.194025
$235$	−1.05610e15	−0.409039
$236$	7.79936e14	0.293853
$237$	8.03948e14	0.294689
$238$	5.40126e15	1.92639
$239$	−2.26977e15	−0.787764	−0.393882	−	0.919161i	$-0.628868\pi$
$239$	−2.26977e15	−0.787764	−0.393882	+	0.919161i	$0.628868\pi$
$240$	3.93515e15	1.32919
$241$	−4.23806e15	−1.39334	−0.696669	−	0.717392i	$-0.745335\pi$
$241$	−4.23806e15	−1.39334	−0.696669	+	0.717392i	$0.745335\pi$
$242$	4.82346e15	1.54369
$243$	−2.05891e14	−0.0641500
$244$	1.18131e16	3.58368
$245$	2.50002e15	0.738522
$246$	−3.94348e15	−1.13449
$247$	−1.10155e15	−0.308656
$248$	8.19463e15	2.23663
$249$	2.99017e15	0.795061
$250$	−3.75527e15	−0.972816
$251$	3.26942e15	0.825261	0.412631	−	0.910898i	$-0.364610\pi$
$251$	3.26942e15	0.825261	0.412631	+	0.910898i	$0.364610\pi$
$252$	−1.95985e15	−0.482081
$253$	2.63358e15	0.631340
$254$	−6.17079e15	−1.44185
$255$	5.29069e15	1.20504
$256$	−7.97614e15	−1.77106
$257$	1.49257e15	0.323123	0.161562	−	0.986863i	$-0.448347\pi$
$257$	1.49257e15	0.323123	0.161562	+	0.986863i	$0.448347\pi$
$258$	8.60355e15	1.81614
$259$	−5.24452e15	−1.07959
$260$	4.54323e15	0.912090
$261$	2.08097e15	0.407477
$262$	1.20895e16	2.30914
$263$	2.20397e15	0.410670	0.205335	−	0.978692i	$-0.434172\pi$
$263$	2.20397e15	0.410670	0.205335	+	0.978692i	$0.434172\pi$
$264$	−2.74050e15	−0.498200
$265$	5.39102e15	0.956253
$266$	6.39360e15	1.10666
$267$	1.24139e15	0.209693
$268$	2.15501e16	3.55282
$269$	−5.46614e15	−0.879611	−0.439806	−	0.898093i	$-0.644953\pi$
$269$	−5.46614e15	−0.879611	−0.439806	+	0.898093i	$0.644953\pi$
$270$	−2.77025e15	−0.435166
$271$	−4.18110e15	−0.641195	−0.320597	−	0.947216i	$-0.603884\pi$
$271$	−4.18110e15	−0.641195	−0.320597	+	0.947216i	$0.603884\pi$
$272$	2.04442e16	3.06106
$273$	−8.16100e14	−0.119313
$274$	1.26343e16	1.80374
$275$	−1.55429e15	−0.216706
$276$	1.58855e16	2.16318
$277$	−1.20938e16	−1.60858	−0.804290	−	0.594236i	$-0.797454\pi$
$277$	−1.20938e16	−1.60858	−0.804290	+	0.594236i	$0.797454\pi$
$278$	−5.50358e15	−0.715080
$279$	−2.58882e15	−0.328605
$280$	−1.46869e16	−1.82139
$281$	−1.12960e16	−1.36877	−0.684387	−	0.729119i	$-0.739930\pi$
$281$	−1.12960e16	−1.36877	−0.684387	+	0.729119i	$0.739930\pi$
$282$	2.87291e15	0.340176
$283$	−1.23220e16	−1.42584	−0.712918	−	0.701247i	$-0.752627\pi$
$283$	−1.23220e16	−1.42584	−0.712918	+	0.701247i	$0.752627\pi$
$284$	9.42756e15	1.06618
$285$	6.26271e15	0.692263
$286$	−2.04892e15	−0.221384
$287$	6.60483e15	0.697637
$288$	−3.38110e15	−0.349146
$289$	1.75820e16	1.77514
$290$	2.79993e16	2.76414
$291$	3.97837e15	0.384062
$292$	2.11211e16	1.99401
$293$	2.09343e16	1.93294	0.966472	−	0.256773i	$-0.0826592\pi$
$293$	2.09343e16	1.93294	0.966472	+	0.256773i	$0.0826592\pi$
$294$	−6.80079e15	−0.614188
$295$	−1.84644e15	−0.163115
$296$	−4.42351e16	−3.82270
$297$	8.65767e14	0.0731955
$298$	1.22622e16	1.01429
$299$	6.61488e15	0.535376
$300$	−9.37538e15	−0.742507
$301$	−1.44099e16	−1.11681
$302$	1.66531e16	1.26313
$303$	−5.36608e14	−0.0398364
$304$	2.42003e16	1.75850
$305$	−2.79666e16	−1.98926
$306$	−1.43922e16	−1.00216
$307$	1.02631e16	0.699648	0.349824	−	0.936815i	$-0.386241\pi$
$307$	1.02631e16	0.699648	0.349824	+	0.936815i	$0.386241\pi$
$308$	8.24114e15	0.550057
$309$	3.27138e15	0.213797
$310$	−3.48324e16	−2.22911
$311$	−2.57416e16	−1.61322	−0.806609	−	0.591086i	$-0.798700\pi$
$311$	−2.57416e16	−1.61322	−0.806609	+	0.591086i	$0.798700\pi$
$312$	−6.88342e15	−0.422474
$313$	−4.32942e15	−0.260250	−0.130125	−	0.991498i	$-0.541538\pi$
$313$	−4.32942e15	−0.260250	−0.130125	+	0.991498i	$0.541538\pi$
$314$	1.56392e16	0.920813
$315$	4.63982e15	0.267598
$316$	−2.03914e16	−1.15208
$317$	6.65782e15	0.368508	0.184254	−	0.982879i	$-0.441013\pi$
$317$	6.65782e15	0.368508	0.184254	+	0.982879i	$0.441013\pi$
$318$	−1.46652e16	−0.795264
$319$	−8.75044e15	−0.464933
$320$	−1.27206e15	−0.0662268
$321$	2.11422e16	1.07862
$322$	−3.83939e16	−1.91955
$323$	3.25366e16	1.59425
$324$	5.22224e15	0.250792
$325$	−3.90399e15	−0.183767
$326$	−6.37550e16	−2.94171
$327$	8.10613e15	0.366651
$328$	5.57087e16	2.47026
$329$	−4.81176e15	−0.209185
$330$	1.16488e16	0.496526
$331$	6.28360e15	0.262619	0.131310	−	0.991341i	$-0.458082\pi$
$331$	6.28360e15	0.262619	0.131310	+	0.991341i	$0.458082\pi$
$332$	−7.58430e16	−3.10826
$333$	1.39746e16	0.561631
$334$	−8.12721e16	−3.20324
$335$	−5.10184e16	−1.97213
$336$	1.79291e16	0.679757
$337$	−1.56276e16	−0.581162	−0.290581	−	0.956850i	$-0.593849\pi$
$337$	−1.56276e16	−0.581162	−0.290581	+	0.956850i	$0.593849\pi$
$338$	4.43275e16	1.61702
$339$	2.20865e16	0.790366
$340$	−1.34193e17	−4.71106
$341$	1.08859e16	0.374940
$342$	−1.70364e16	−0.575717
$343$	3.07144e16	1.01843
$344$	−1.21540e17	−3.95449
$345$	−3.76079e16	−1.20076
$346$	5.82001e16	1.82360
$347$	3.86714e16	1.18918	0.594591	−	0.804028i	$-0.297314\pi$
$347$	3.86714e16	1.18918	0.594591	+	0.804028i	$0.297314\pi$
$348$	−5.27819e16	−1.59302
$349$	−9.63869e15	−0.285531	−0.142765	−	0.989757i	$-0.545599\pi$
$349$	−9.63869e15	−0.285531	−0.142765	+	0.989757i	$0.545599\pi$
$350$	2.26594e16	0.658881
$351$	2.17459e15	0.0620698
$352$	1.42175e16	0.398377
$353$	5.34091e16	1.46920	0.734598	−	0.678502i	$-0.237371\pi$
$353$	5.34091e16	1.46920	0.734598	+	0.678502i	$0.237371\pi$
$354$	5.02287e15	0.135653
$355$	−2.23191e16	−0.591823
$356$	−3.14867e16	−0.819789
$357$	2.41052e16	0.616264
$358$	−4.58363e15	−0.115072
$359$	−1.74370e16	−0.429891	−0.214945	−	0.976626i	$-0.568957\pi$
$359$	−1.74370e16	−0.429891	−0.214945	+	0.976626i	$0.568957\pi$
$360$	3.91347e16	0.947536
$361$	−3.53868e15	−0.0841482
$362$	−1.03644e16	−0.242067
$363$	2.15265e16	0.493834
$364$	2.06996e16	0.466448
$365$	−5.00027e16	−1.10685
$366$	7.60775e16	1.65436
$367$	4.43678e16	0.947848	0.473924	−	0.880566i	$-0.342837\pi$
$367$	4.43678e16	0.947848	0.473924	+	0.880566i	$0.342837\pi$
$368$	−1.45324e17	−3.05019
$369$	−1.75993e16	−0.362930
$370$	1.88027e17	3.80986
$371$	2.45623e16	0.489034
$372$	6.56630e16	1.28467
$373$	4.39633e16	0.845246	0.422623	−	0.906306i	$-0.361109\pi$
$373$	4.39633e16	0.845246	0.422623	+	0.906306i	$0.361109\pi$
$374$	6.05190e16	1.14347
$375$	−1.67593e16	−0.311209
$376$	−4.05850e16	−0.740703
$377$	−2.19788e16	−0.394263
$378$	−1.26217e16	−0.222546
$379$	1.03121e15	0.0178728	0.00893639	−	0.999960i	$-0.497155\pi$
$379$	1.03121e15	0.0178728	0.00893639	+	0.999960i	$0.497155\pi$
$380$	−1.58848e17	−2.70638
$381$	−2.75395e16	−0.461257
$382$	−1.54746e17	−2.54804
$383$	8.19067e15	0.132595	0.0662976	−	0.997800i	$-0.478881\pi$
$383$	8.19067e15	0.132595	0.0662976	+	0.997800i	$0.478881\pi$
$384$	−3.45341e16	−0.549662
$385$	−1.95103e16	−0.305330
$386$	1.80040e16	0.277046
$387$	3.83966e16	0.580994
$388$	−1.00908e17	−1.50148
$389$	3.42360e16	0.500968	0.250484	−	0.968121i	$-0.419410\pi$
$389$	3.42360e16	0.500968	0.250484	+	0.968121i	$0.419410\pi$
$390$	2.92589e16	0.421054
$391$	−1.95384e17	−2.76528
$392$	9.60731e16	1.33734
$393$	5.39541e16	0.738708
$394$	1.58411e17	2.13335
$395$	4.82752e16	0.639504
$396$	−2.19594e16	−0.286155
$397$	9.66808e16	1.23937	0.619686	−	0.784849i	$-0.287260\pi$
$397$	9.66808e16	1.23937	0.619686	+	0.784849i	$0.287260\pi$
$398$	1.19247e17	1.50386
$399$	2.85339e16	0.354027
$400$	8.57677e16	1.04697
$401$	1.05522e17	1.26738	0.633689	−	0.773588i	$-0.281540\pi$
$401$	1.05522e17	1.26738	0.633689	+	0.773588i	$0.281540\pi$
$402$	1.38785e17	1.64011
$403$	2.73426e16	0.317949
$404$	1.36106e16	0.155739
$405$	−1.23633e16	−0.139212
$406$	1.27569e17	1.41360
$407$	−5.87628e16	−0.640824
$408$	2.03316e17	2.18213
$409$	−1.33674e17	−1.41203	−0.706015	−	0.708197i	$-0.749509\pi$
$409$	−1.33674e17	−1.41203	−0.706015	+	0.708197i	$0.749509\pi$
$410$	−2.36797e17	−2.46196
$411$	5.63855e16	0.577026
$412$	−8.29756e16	−0.835831
$413$	−8.41268e15	−0.0834178
$414$	1.02305e17	0.998604
$415$	1.79553e17	1.72536
$416$	3.57106e16	0.337824
$417$	−2.45618e16	−0.228758
$418$	7.16378e16	0.656896
$419$	5.31742e16	0.480076	0.240038	−	0.970763i	$-0.422840\pi$
$419$	5.31742e16	0.480076	0.240038	+	0.970763i	$0.422840\pi$
$420$	−1.17685e17	−1.04616
$421$	2.22689e17	1.94924	0.974619	−	0.223869i	$-0.0718686\pi$
$421$	2.22689e17	1.94924	0.974619	+	0.223869i	$0.0718686\pi$
$422$	−8.33947e16	−0.718799
$423$	1.28215e16	0.108824
$424$	2.07172e17	1.73162
$425$	1.15312e17	0.949177
$426$	6.07145e16	0.492187
$427$	−1.27420e17	−1.01732
$428$	−5.36252e17	−4.21681
$429$	−9.14408e15	−0.0708219
$430$	5.16624e17	3.94121
$431$	5.54586e16	0.416741	0.208371	−	0.978050i	$-0.433184\pi$
$431$	5.54586e16	0.416741	0.208371	+	0.978050i	$0.433184\pi$
$432$	−4.77740e16	−0.353629
$433$	−5.13432e16	−0.374379	−0.187189	−	0.982324i	$-0.559938\pi$
$433$	−5.13432e16	−0.374379	−0.187189	+	0.982324i	$0.559938\pi$
$434$	−1.58701e17	−1.13998
$435$	1.24958e17	0.884265
$436$	−2.05604e17	−1.43341
$437$	−2.31280e17	−1.58858
$438$	1.36022e17	0.920509
$439$	−1.69330e16	−0.112906	−0.0564528	−	0.998405i	$-0.517979\pi$
$439$	−1.69330e16	−0.112906	−0.0564528	+	0.998405i	$0.517979\pi$
$440$	−1.64560e17	−1.08114
$441$	−3.03511e16	−0.196482
$442$	1.52008e17	0.969666
$443$	−1.55676e17	−0.978581	−0.489290	−	0.872121i	$-0.662744\pi$
$443$	−1.55676e17	−0.978581	−0.489290	+	0.872121i	$0.662744\pi$
$444$	−3.54452e17	−2.19568
$445$	7.45425e16	0.455055
$446$	−4.75642e17	−2.86156
$447$	5.47246e16	0.324477
$448$	−5.79571e15	−0.0338688
$449$	−6.17658e16	−0.355752	−0.177876	−	0.984053i	$-0.556923\pi$
$449$	−6.17658e16	−0.355752	−0.177876	+	0.984053i	$0.556923\pi$
$450$	−6.03785e16	−0.342769
$451$	7.40045e16	0.414105
$452$	−5.60203e17	−3.08991
$453$	7.43206e16	0.404083
$454$	−1.50914e17	−0.808847
$455$	−4.90049e16	−0.258920
$456$	2.40670e17	1.25357
$457$	−1.73026e17	−0.888497	−0.444249	−	0.895904i	$-0.646529\pi$
$457$	−1.73026e17	−0.888497	−0.444249	+	0.895904i	$0.646529\pi$
$458$	9.43519e16	0.477667
$459$	−6.42308e16	−0.320598
$460$	9.53890e17	4.69432
$461$	3.16127e17	1.53393	0.766966	−	0.641687i	$-0.221765\pi$
$461$	3.16127e17	1.53393	0.766966	+	0.641687i	$0.221765\pi$
$462$	5.30739e16	0.253926
$463$	1.57071e17	0.741004	0.370502	−	0.928832i	$-0.379186\pi$
$463$	1.57071e17	0.741004	0.370502	+	0.928832i	$0.379186\pi$
$464$	4.82859e17	2.24623
$465$	−1.55453e17	−0.713105
$466$	−4.08008e17	−1.84570
$467$	−1.32242e17	−0.589944	−0.294972	−	0.955506i	$-0.595310\pi$
$467$	−1.32242e17	−0.589944	−0.294972	+	0.955506i	$0.595310\pi$
$468$	−5.51564e16	−0.242660
$469$	−2.32448e17	−1.00856
$470$	1.72512e17	0.738215
$471$	6.97958e16	0.294573
$472$	−7.09570e16	−0.295374
$473$	−1.61457e17	−0.662917
$474$	−1.31323e17	−0.531840
$475$	1.36498e17	0.545277
$476$	−6.11406e17	−2.40926
$477$	−6.54489e16	−0.254409
$478$	3.70762e17	1.42172
$479$	−1.69518e17	−0.641261	−0.320631	−	0.947204i	$-0.603895\pi$
$479$	−1.69518e17	−0.641261	−0.320631	+	0.947204i	$0.603895\pi$
$480$	−2.03028e17	−0.757682
$481$	−1.47597e17	−0.543418
$482$	6.92277e17	2.51463
$483$	−1.71347e17	−0.614075
$484$	−5.46001e17	−1.93063
$485$	2.38892e17	0.833452
$486$	3.36318e16	0.115775
$487$	3.38240e17	1.14891	0.574456	−	0.818535i	$-0.305214\pi$
$487$	3.38240e17	1.14891	0.574456	+	0.818535i	$0.305214\pi$
$488$	−1.07473e18	−3.60222
$489$	−2.84531e17	−0.941069
$490$	−4.08372e17	−1.33285
$491$	4.57399e17	1.47321	0.736606	−	0.676322i	$-0.236427\pi$
$491$	4.57399e17	1.47321	0.736606	+	0.676322i	$0.236427\pi$
$492$	4.46389e17	1.41886
$493$	6.49190e17	2.03642
$494$	1.79936e17	0.557048
$495$	5.19873e16	0.158841
$496$	−6.00697e17	−1.81144
$497$	−1.01689e17	−0.302662
$498$	−4.88437e17	−1.43489
$499$	1.17811e17	0.341611	0.170805	−	0.985305i	$-0.445363\pi$
$499$	1.17811e17	0.341611	0.170805	+	0.985305i	$0.445363\pi$
$500$	4.25084e17	1.21666
$501$	−3.62707e17	−1.02473
$502$	−5.34052e17	−1.48939
$503$	−9.47641e16	−0.260887	−0.130443	−	0.991456i	$-0.541640\pi$
$503$	−9.47641e16	−0.260887	−0.130443	+	0.991456i	$0.541640\pi$
$504$	1.78304e17	0.484576
$505$	−3.22221e16	−0.0864490
$506$	−4.30189e17	−1.13941
$507$	1.97828e17	0.517293
$508$	6.98513e17	1.80327
$509$	−2.12435e17	−0.541453	−0.270726	−	0.962656i	$-0.587264\pi$
$509$	−2.12435e17	−0.541453	−0.270726	+	0.962656i	$0.587264\pi$
$510$	−8.64221e17	−2.17480
$511$	−2.27820e17	−0.566052
$512$	9.14812e17	2.24428
$513$	−7.60315e16	−0.184175
$514$	−2.43807e17	−0.583158
$515$	1.96439e17	0.463960
$516$	−9.73895e17	−2.27138
$517$	−5.39139e16	−0.124169
$518$	8.56679e17	1.94838
$519$	2.59740e17	0.583380
$520$	−4.13334e17	−0.916809
$521$	8.52584e17	1.86763	0.933817	−	0.357751i	$-0.116456\pi$
$521$	8.52584e17	1.86763	0.933817	+	0.357751i	$0.116456\pi$
$522$	−3.39922e17	−0.735395
$523$	2.95617e17	0.631637	0.315819	−	0.948820i	$-0.397721\pi$
$523$	2.95617e17	0.631637	0.315819	+	0.948820i	$0.397721\pi$
$524$	−1.36850e18	−2.88795
$525$	1.01126e17	0.210780
$526$	−3.60012e17	−0.741157
$527$	−8.07620e17	−1.64225
$528$	2.00889e17	0.403492
$529$	8.84815e17	1.75546
$530$	−8.80610e17	−1.72580
$531$	2.24165e16	0.0433963
$532$	−7.23735e17	−1.38406
$533$	1.85880e17	0.351161
$534$	−2.02778e17	−0.378444
$535$	1.26954e18	2.34070
$536$	−1.96059e18	−3.57121
$537$	−2.04562e16	−0.0368122
$538$	8.92880e17	1.58748
$539$	1.27626e17	0.224187
$540$	3.13584e17	0.544244
$541$	4.52896e15	0.00776634	0.00388317	−	0.999992i	$-0.498764\pi$
$541$	4.52896e15	0.00776634	0.00388317	+	0.999992i	$0.498764\pi$
$542$	6.82972e17	1.15720
$543$	−4.62548e16	−0.0774387
$544$	−1.05479e18	−1.74490
$545$	4.86754e17	0.795669
$546$	1.33308e17	0.215330
$547$	−4.36370e17	−0.696526	−0.348263	−	0.937397i	$-0.613228\pi$
$547$	−4.36370e17	−0.696526	−0.348263	+	0.937397i	$0.613228\pi$
$548$	−1.43017e18	−2.25586
$549$	3.39524e17	0.529238
$550$	2.53890e17	0.391100
$551$	7.68461e17	1.16987
$552$	−1.44523e18	−2.17437
$553$	2.19949e17	0.327046
$554$	1.97549e18	2.90309
$555$	8.39141e17	1.21879
$556$	6.22988e17	0.894321
$557$	2.80287e17	0.397690	0.198845	−	0.980031i	$-0.436281\pi$
$557$	2.80287e17	0.397690	0.198845	+	0.980031i	$0.436281\pi$
$558$	4.22877e17	0.593050
$559$	−4.05538e17	−0.562153
$560$	1.07660e18	1.47514
$561$	2.70089e17	0.365804
$562$	1.84517e18	2.47030
$563$	−7.09044e17	−0.938358	−0.469179	−	0.883103i	$-0.655450\pi$
$563$	−7.09044e17	−0.938358	−0.469179	+	0.883103i	$0.655450\pi$
$564$	−3.25204e17	−0.425444
$565$	1.32624e18	1.71517
$566$	2.01277e18	2.57328
$567$	−5.63290e16	−0.0711938
$568$	−8.57700e17	−1.07170
$569$	−1.56278e18	−1.93049	−0.965246	−	0.261341i	$-0.915835\pi$
$569$	−1.56278e18	−1.93049	−0.965246	+	0.261341i	$0.915835\pi$
$570$	−1.02300e18	−1.24936
$571$	1.19306e18	1.44055	0.720275	−	0.693688i	$-0.244015\pi$
$571$	1.19306e18	1.44055	0.720275	+	0.693688i	$0.244015\pi$
$572$	2.31931e17	0.276876
$573$	−6.90610e17	−0.815132
$574$	−1.07888e18	−1.25906
$575$	−8.19677e17	−0.945805
$576$	1.54433e16	0.0176195
$577$	−1.44180e18	−1.62653	−0.813263	−	0.581897i	$-0.802311\pi$
$577$	−1.44180e18	−1.62653	−0.813263	+	0.581897i	$0.802311\pi$
$578$	−2.87198e18	−3.20369
$579$	8.03498e16	0.0886287
$580$	−3.16943e18	−3.45700
$581$	8.18070e17	0.882360
$582$	−6.49857e17	−0.693136
$583$	2.75211e17	0.290282
$584$	−1.92155e18	−2.00433
$585$	1.30579e17	0.134698
$586$	−3.41957e18	−3.48848
$587$	−6.03376e17	−0.608751	−0.304376	−	0.952552i	$-0.598448\pi$
$587$	−6.03376e17	−0.608751	−0.304376	+	0.952552i	$0.598448\pi$
$588$	7.69827e17	0.768140
$589$	−9.55999e17	−0.943426
$590$	3.01612e17	0.294382
$591$	7.06971e17	0.682469
$592$	3.24260e18	3.09601
$593$	−9.11832e17	−0.861111	−0.430556	−	0.902564i	$-0.641682\pi$
$593$	−9.11832e17	−0.861111	−0.430556	+	0.902564i	$0.641682\pi$
$594$	−1.41421e17	−0.132100
$595$	1.44746e18	1.33735
$596$	−1.38804e18	−1.26853
$597$	5.32186e17	0.481095
$598$	−1.08052e18	−0.966221
$599$	−9.49895e17	−0.840236	−0.420118	−	0.907469i	$-0.638011\pi$
$599$	−9.49895e17	−0.840236	−0.420118	+	0.907469i	$0.638011\pi$
$600$	8.52953e17	0.746349
$601$	2.45128e16	0.0212182	0.0106091	−	0.999944i	$-0.496623\pi$
$601$	2.45128e16	0.0212182	0.0106091	+	0.999944i	$0.496623\pi$
$602$	2.35382e18	2.01556
$603$	6.19381e17	0.524681
$604$	−1.88507e18	−1.57975
$605$	1.29262e18	1.07167
$606$	8.76537e16	0.0718949
$607$	1.31186e18	1.06454	0.532270	−	0.846574i	$-0.321339\pi$
$607$	1.31186e18	1.06454	0.532270	+	0.846574i	$0.321339\pi$
$608$	−1.24857e18	−1.00240
$609$	5.69326e17	0.452218
$610$	4.56828e18	3.59012
$611$	−1.35418e17	−0.105295
$612$	1.62916e18	1.25337
$613$	5.66034e17	0.430874	0.215437	−	0.976518i	$-0.430882\pi$
$613$	5.66034e17	0.430874	0.215437	+	0.976518i	$0.430882\pi$
$614$	−1.67645e18	−1.26269
$615$	−1.05680e18	−0.787595
$616$	−7.49763e17	−0.552903
$617$	3.27134e17	0.238711	0.119355	−	0.992852i	$-0.461917\pi$
$617$	3.27134e17	0.238711	0.119355	+	0.992852i	$0.461917\pi$
$618$	−5.34372e17	−0.385850
$619$	1.10990e18	0.793042	0.396521	−	0.918026i	$-0.370217\pi$
$619$	1.10990e18	0.793042	0.396521	+	0.918026i	$0.370217\pi$
$620$	3.94291e18	2.78786
$621$	4.56573e17	0.319459
$622$	4.20483e18	2.91146
$623$	3.39627e17	0.232718
$624$	5.04581e17	0.342161
$625$	−1.85539e18	−1.24513
$626$	7.07199e17	0.469687
$627$	3.19711e17	0.210145
$628$	−1.77031e18	−1.15162
$629$	4.35958e18	2.80682
$630$	−7.57903e17	−0.482948
$631$	−1.40364e18	−0.885250	−0.442625	−	0.896707i	$-0.645953\pi$
$631$	−1.40364e18	−0.885250	−0.442625	+	0.896707i	$0.645953\pi$
$632$	1.85517e18	1.15804
$633$	−3.72180e17	−0.229948
$634$	−1.08754e18	−0.665066
$635$	−1.65368e18	−1.00097
$636$	1.66005e18	0.994604
$637$	3.20563e17	0.190111
$638$	1.42936e18	0.839089
$639$	2.70961e17	0.157453
$640$	−2.07370e18	−1.19282
$641$	1.58364e18	0.901735	0.450867	−	0.892591i	$-0.351115\pi$
$641$	1.58364e18	0.901735	0.450867	+	0.892591i	$0.351115\pi$
$642$	−3.45352e18	−1.94663
$643$	9.12608e17	0.509229	0.254614	−	0.967043i	$-0.418051\pi$
$643$	9.12608e17	0.509229	0.254614	+	0.967043i	$0.418051\pi$
$644$	4.34607e18	2.40070
$645$	2.30563e18	1.26081
$646$	−5.31477e18	−2.87722
$647$	−7.34102e17	−0.393440	−0.196720	−	0.980460i	$-0.563029\pi$
$647$	−7.34102e17	−0.393440	−0.196720	+	0.980460i	$0.563029\pi$
$648$	−4.75109e17	−0.252090
$649$	−9.42607e16	−0.0495154
$650$	6.37707e17	0.331653
$651$	−7.08265e17	−0.364686
$652$	7.21686e18	3.67908
$653$	−7.18118e17	−0.362460	−0.181230	−	0.983441i	$-0.558008\pi$
$653$	−7.18118e17	−0.362460	−0.181230	+	0.983441i	$0.558008\pi$
$654$	−1.32412e18	−0.661714
$655$	3.23982e18	1.60307
$656$	−4.08365e18	−2.00066
$657$	6.07050e17	0.294476
$658$	7.85990e17	0.377527
$659$	−1.83322e18	−0.871883	−0.435942	−	0.899975i	$-0.643585\pi$
$659$	−1.83322e18	−0.871883	−0.435942	+	0.899975i	$0.643585\pi$
$660$	−1.31861e18	−0.620985
$661$	−3.21751e18	−1.50041	−0.750206	−	0.661204i	$-0.770046\pi$
$661$	−3.21751e18	−1.50041	−0.750206	+	0.661204i	$0.770046\pi$
$662$	−1.02641e18	−0.473963
$663$	6.78394e17	0.310202
$664$	6.90004e18	3.12435
$665$	1.71339e18	0.768274
$666$	−2.28271e18	−1.01360
$667$	−4.61465e18	−2.02918
$668$	9.19974e18	4.00616
$669$	−2.12273e18	−0.915430
$670$	8.33373e18	3.55921
$671$	−1.42769e18	−0.603863
$672$	−9.25024e17	−0.387483
$673$	−3.12308e18	−1.29564	−0.647821	−	0.761793i	$-0.724319\pi$
$673$	−3.12308e18	−1.29564	−0.647821	+	0.761793i	$0.724319\pi$
$674$	2.55273e18	1.04885
$675$	−2.69462e17	−0.109654
$676$	−5.01774e18	−2.02234
$677$	5.53269e16	0.0220856	0.0110428	−	0.999939i	$-0.496485\pi$
$677$	5.53269e16	0.0220856	0.0110428	+	0.999939i	$0.496485\pi$
$678$	−3.60777e18	−1.42641
$679$	1.08843e18	0.426232
$680$	1.22087e19	4.73543
$681$	−6.73511e17	−0.258755
$682$	−1.77819e18	−0.676673
$683$	2.21983e18	0.836729	0.418365	−	0.908279i	$-0.362603\pi$
$683$	2.21983e18	0.836729	0.418365	+	0.908279i	$0.362603\pi$
$684$	1.92847e18	0.720026
$685$	3.38582e18	1.25220
$686$	−5.01713e18	−1.83801
$687$	4.21081e17	0.152808
$688$	8.90937e18	3.20274
$689$	6.91259e17	0.246159
$690$	6.14316e18	2.16707
$691$	1.28668e18	0.449638	0.224819	−	0.974401i	$-0.427821\pi$
$691$	1.28668e18	0.449638	0.224819	+	0.974401i	$0.427821\pi$
$692$	−6.58807e18	−2.28070
$693$	2.36862e17	0.0812325
$694$	−6.31688e18	−2.14618
$695$	−1.47488e18	−0.496427
$696$	4.80199e18	1.60126
$697$	−5.49035e18	−1.81379
$698$	1.57446e18	0.515312
$699$	−1.82089e18	−0.590449
$700$	−2.56498e18	−0.824036
$701$	−2.09365e18	−0.666403	−0.333202	−	0.942856i	$-0.608129\pi$
$701$	−2.09365e18	−0.666403	−0.333202	+	0.942856i	$0.608129\pi$
$702$	−3.55213e17	−0.112021
$703$	5.16053e18	1.61245
$704$	−6.49387e16	−0.0201039
$705$	7.69899e17	0.236159
$706$	−8.72425e18	−2.65154
$707$	−1.46809e17	−0.0442105
$708$	−5.68573e17	−0.169656
$709$	4.68214e18	1.38434	0.692172	−	0.721733i	$-0.256654\pi$
$709$	4.68214e18	1.38434	0.692172	+	0.721733i	$0.256654\pi$
$710$	3.64577e18	1.06809
$711$	−5.86078e17	−0.170139
$712$	2.86459e18	0.824030
$713$	5.74082e18	1.63641
$714$	−3.93752e18	−1.11220
$715$	−5.49081e17	−0.153691
$716$	5.18852e17	0.143916
$717$	1.65466e18	0.454816
$718$	2.84829e18	0.775846
$719$	−1.93581e18	−0.522548	−0.261274	−	0.965265i	$-0.584143\pi$
$719$	−1.93581e18	−0.522548	−0.261274	+	0.965265i	$0.584143\pi$
$720$	−2.86872e18	−0.767409
$721$	8.95006e17	0.237272
$722$	5.78035e17	0.151867
$723$	3.08955e18	0.804444
$724$	1.17321e18	0.302744
$725$	2.72349e18	0.696512
$726$	−3.51630e18	−0.891248
$727$	2.65448e18	0.666816	0.333408	−	0.942783i	$-0.391801\pi$
$727$	2.65448e18	0.666816	0.333408	+	0.942783i	$0.391801\pi$
$728$	−1.88321e18	−0.468862
$729$	1.50095e17	0.0370370
$730$	8.16782e18	1.99760
$731$	1.19784e19	2.90359
$732$	−8.61173e18	−2.06904
$733$	−3.22155e18	−0.767165	−0.383583	−	0.923507i	$-0.625310\pi$
$733$	−3.22155e18	−0.767165	−0.383583	+	0.923507i	$0.625310\pi$
$734$	−7.24737e18	−1.71063
$735$	−1.82251e18	−0.426386
$736$	7.49776e18	1.73870
$737$	−2.60448e18	−0.598664
$738$	2.87480e18	0.654999
$739$	−7.21327e18	−1.62908	−0.814542	−	0.580105i	$-0.803012\pi$
$739$	−7.21327e18	−1.62908	−0.814542	+	0.580105i	$0.803012\pi$
$740$	−2.12840e19	−4.76484
$741$	8.03031e17	0.178203
$742$	−4.01219e18	−0.882585
$743$	3.19289e18	0.696236	0.348118	−	0.937451i	$-0.386821\pi$
$743$	3.19289e18	0.696236	0.348118	+	0.937451i	$0.386821\pi$
$744$	−5.97389e18	−1.29132
$745$	3.28609e18	0.704147
$746$	−7.18130e18	−1.52546
$747$	−2.17983e18	−0.459029
$748$	−6.85056e18	−1.43010
$749$	5.78421e18	1.19705
$750$	2.73759e18	0.561655
$751$	1.91443e18	0.389386	0.194693	−	0.980864i	$-0.437629\pi$
$751$	1.91443e18	0.389386	0.194693	+	0.980864i	$0.437629\pi$
$752$	2.97503e18	0.599895
$753$	−2.38341e18	−0.476465
$754$	3.59019e18	0.711547
$755$	4.46278e18	0.876901
$756$	1.42873e18	0.278330
$757$	−3.09751e17	−0.0598259	−0.0299130	−	0.999553i	$-0.509523\pi$
$757$	−3.09751e17	−0.0598259	−0.0299130	+	0.999553i	$0.509523\pi$
$758$	−1.68445e17	−0.0322559
$759$	−1.91988e18	−0.364504
$760$	1.44517e19	2.72038
$761$	4.65705e18	0.869182	0.434591	−	0.900628i	$-0.356893\pi$
$761$	4.65705e18	0.869182	0.434591	+	0.900628i	$0.356893\pi$
$762$	4.49850e18	0.832455
$763$	2.21773e18	0.406910
$764$	1.75167e19	3.18673
$765$	−3.85691e18	−0.695729
$766$	−1.33793e18	−0.239301
$767$	−2.36759e17	−0.0419891
$768$	5.81461e18	1.02252
$769$	6.98089e18	1.21728	0.608638	−	0.793448i	$-0.291716\pi$
$769$	6.98089e18	1.21728	0.608638	+	0.793448i	$0.291716\pi$
$770$	3.18696e18	0.551046
$771$	−1.08808e18	−0.186555
$772$	−2.03800e18	−0.346491
$773$	8.05119e18	1.35735	0.678677	−	0.734437i	$-0.262554\pi$
$773$	8.05119e18	1.35735	0.678677	+	0.734437i	$0.262554\pi$
$774$	−6.27199e18	−1.04855
$775$	−3.38814e18	−0.561694
$776$	9.18039e18	1.50925
$777$	3.82325e18	0.623299
$778$	−5.59236e18	−0.904123
$779$	−6.49906e18	−1.04197
$780$	−3.31201e18	−0.526595
$781$	−1.13939e18	−0.179655
$782$	3.19155e19	4.99065
$783$	−1.51703e18	−0.235257
$784$	−7.04252e18	−1.08311
$785$	4.19107e18	0.639253
$786$	−8.81327e18	−1.33319
$787$	2.30816e18	0.346283	0.173141	−	0.984897i	$-0.444608\pi$
$787$	2.30816e18	0.346283	0.173141	+	0.984897i	$0.444608\pi$
$788$	−1.79317e19	−2.66809
$789$	−1.60669e18	−0.237100
$790$	−7.88564e18	−1.15415
$791$	6.04256e18	0.877149
$792$	1.99782e18	0.287636
$793$	−3.58600e18	−0.512076
$794$	−1.57926e19	−2.23676
$795$	−3.93006e18	−0.552093
$796$	−1.34984e19	−1.88082
$797$	−5.02879e18	−0.694999	−0.347500	−	0.937680i	$-0.612969\pi$
$797$	−5.02879e18	−0.694999	−0.347500	+	0.937680i	$0.612969\pi$
$798$	−4.66094e18	−0.638932
$799$	3.99984e18	0.543862
$800$	−4.42505e18	−0.596806
$801$	−9.04972e17	−0.121066
$802$	−1.72368e19	−2.28730
$803$	−2.55263e18	−0.335998
$804$	−1.57100e19	−2.05122
$805$	−1.02890e19	−1.33260
$806$	−4.46635e18	−0.573819
$807$	3.98481e18	0.507844
$808$	−1.23826e18	−0.156545
$809$	−1.05941e19	−1.32861	−0.664307	−	0.747460i	$-0.731273\pi$
$809$	−1.05941e19	−1.32861	−0.664307	+	0.747460i	$0.731273\pi$
$810$	2.01951e18	0.251243
$811$	−1.43060e18	−0.176556	−0.0882782	−	0.996096i	$-0.528136\pi$
$811$	−1.43060e18	−0.176556	−0.0882782	+	0.996096i	$0.528136\pi$
$812$	−1.44404e19	−1.76793
$813$	3.04802e18	0.370194
$814$	9.59875e18	1.15653
$815$	−1.70854e19	−2.04221
$816$	−1.49038e19	−1.76731
$817$	1.41791e19	1.66804
$818$	2.18352e19	2.54836
$819$	5.94937e17	0.0688852
$820$	2.68047e19	3.07907
$821$	−4.95271e18	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$821$	−4.95271e18	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$822$	−9.21043e18	−1.04139
$823$	2.92750e18	0.328396	0.164198	−	0.986427i	$-0.447496\pi$
$823$	2.92750e18	0.328396	0.164198	+	0.986427i	$0.447496\pi$
$824$	7.54896e18	0.840156
$825$	1.13308e18	0.125115
$826$	1.37419e18	0.150548
$827$	−1.56273e19	−1.69863	−0.849315	−	0.527887i	$-0.822985\pi$
$827$	−1.56273e19	−1.69863	−0.849315	+	0.527887i	$0.822985\pi$
$828$	−1.15806e19	−1.24891
$829$	−1.47793e19	−1.58143	−0.790713	−	0.612187i	$-0.790290\pi$
$829$	−1.47793e19	−1.58143	−0.790713	+	0.612187i	$0.790290\pi$
$830$	−2.93295e19	−3.11385
$831$	8.81635e18	0.928715
$832$	−1.63109e17	−0.0170481
$833$	−9.46847e18	−0.981945
$834$	4.01211e18	0.412851
$835$	−2.17797e19	−2.22377
$836$	−8.10917e18	−0.821553
$837$	1.88725e18	0.189720
$838$	−8.68588e18	−0.866419
$839$	−7.39045e17	−0.0731506	−0.0365753	−	0.999331i	$-0.511645\pi$
$839$	−7.39045e17	−0.0731506	−0.0365753	+	0.999331i	$0.511645\pi$
$840$	1.07067e19	1.05158
$841$	5.07220e18	0.494336
$842$	−3.63757e19	−3.51789
$843$	8.23475e18	0.790262
$844$	9.44002e18	0.898973
$845$	1.18791e19	1.12258
$846$	−2.09435e18	−0.196400
$847$	5.88937e18	0.548058
$848$	−1.51865e19	−1.40244
$849$	8.98274e18	0.823207
$850$	−1.88360e19	−1.71303
$851$	−3.09893e19	−2.79685
$852$	−6.87269e18	−0.615558
$853$	1.53235e19	1.36204	0.681020	−	0.732265i	$-0.261537\pi$
$853$	1.53235e19	1.36204	0.681020	+	0.732265i	$0.261537\pi$
$854$	2.08138e19	1.83601
$855$	−4.56552e18	−0.399678
$856$	4.87871e19	4.23863
$857$	−1.86519e19	−1.60823	−0.804113	−	0.594477i	$-0.797359\pi$
$857$	−1.86519e19	−1.60823	−0.804113	+	0.594477i	$0.797359\pi$
$858$	1.49366e18	0.127816
$859$	−1.87304e19	−1.59071	−0.795354	−	0.606145i	$-0.792715\pi$
$859$	−1.87304e19	−1.59071	−0.795354	+	0.606145i	$0.792715\pi$
$860$	−5.84801e19	−4.92911
$861$	−4.81492e18	−0.402781
$862$	−9.05902e18	−0.752115
$863$	−8.08436e18	−0.666156	−0.333078	−	0.942899i	$-0.608087\pi$
$863$	−8.08436e18	−0.666156	−0.333078	+	0.942899i	$0.608087\pi$
$864$	2.46483e18	0.201580
$865$	1.55968e19	1.26599
$866$	8.38678e18	0.675661
$867$	−1.28173e19	−1.02488
$868$	1.79645e19	1.42573
$869$	2.46444e18	0.194129
$870$	−2.04115e19	−1.59588
$871$	−6.54179e18	−0.507667
$872$	1.87055e19	1.44083
$873$	−2.90023e18	−0.221738
$874$	3.77791e19	2.86700
$875$	−4.58511e18	−0.345381
$876$	−1.53973e19	−1.15124
$877$	2.38788e18	0.177221	0.0886104	−	0.996066i	$-0.471757\pi$
$877$	2.38788e18	0.177221	0.0886104	+	0.996066i	$0.471757\pi$
$878$	2.76597e18	0.203767
$879$	−1.52611e19	−1.11599
$880$	1.20629e19	0.875618
$881$	1.27994e19	0.922246	0.461123	−	0.887336i	$-0.347447\pi$
$881$	1.27994e19	0.922246	0.461123	+	0.887336i	$0.347447\pi$
$882$	4.95777e18	0.354602
$883$	−1.26661e19	−0.899284	−0.449642	−	0.893209i	$-0.648448\pi$
$883$	−1.26661e19	−0.899284	−0.449642	+	0.893209i	$0.648448\pi$
$884$	−1.72068e19	−1.21272
$885$	1.34606e18	0.0941743
$886$	2.54292e19	1.76610
$887$	1.74734e19	1.20468	0.602342	−	0.798238i	$-0.294234\pi$
$887$	1.74734e19	1.20468	0.602342	+	0.798238i	$0.294234\pi$
$888$	3.22474e19	2.20704
$889$	−7.53443e18	−0.511904
$890$	−1.21763e19	−0.821262
$891$	−6.31144e17	−0.0422594
$892$	5.38411e19	3.57884
$893$	4.73471e18	0.312434
$894$	−8.93913e18	−0.585601
$895$	−1.22835e18	−0.0798861
$896$	−9.44807e18	−0.610016
$897$	−4.82224e18	−0.309100
$898$	1.00893e19	0.642044
$899$	−1.90747e19	−1.20509
$900$	6.83465e18	0.428687
$901$	−2.04178e19	−1.27144
$902$	−1.20885e19	−0.747357
$903$	1.05048e19	0.644788
$904$	5.09661e19	3.10590
$905$	−2.77750e18	−0.168050
$906$	−1.21401e19	−0.729270
$907$	2.42850e19	1.44840	0.724202	−	0.689588i	$-0.242208\pi$
$907$	2.42850e19	1.44840	0.724202	+	0.689588i	$0.242208\pi$
$908$	1.70830e19	1.01159
$909$	3.91188e17	0.0229996
$910$	8.00484e18	0.467287
$911$	3.36195e19	1.94860	0.974298	−	0.225263i	$-0.0723242\pi$
$911$	3.36195e19	1.94860	0.974298	+	0.225263i	$0.0723242\pi$
$912$	−1.76420e19	−1.01527
$913$	9.16615e18	0.523754
$914$	2.82634e19	1.60352
$915$	2.03877e19	1.14850
$916$	−1.06803e19	−0.597398
$917$	1.47611e19	0.819820
$918$	1.04919e19	0.578600
$919$	−1.17242e19	−0.641998	−0.320999	−	0.947079i	$-0.604019\pi$
$919$	−1.17242e19	−0.641998	−0.320999	+	0.947079i	$0.604019\pi$
$920$	−8.67830e19	−4.71861
$921$	−7.48181e18	−0.403942
$922$	−5.16386e19	−2.76837
$923$	−2.86185e18	−0.152347
$924$	−6.00779e18	−0.317576
$925$	1.82893e19	0.960013
$926$	−2.56572e19	−1.33733
$927$	−2.38484e18	−0.123436
$928$	−2.49123e19	−1.28042
$929$	8.44176e18	0.430855	0.215427	−	0.976520i	$-0.430886\pi$
$929$	8.44176e18	0.430855	0.215427	+	0.976520i	$0.430886\pi$
$930$	2.53928e19	1.28698
$931$	−1.12080e19	−0.564101
$932$	4.61852e19	2.30834
$933$	1.87656e19	0.931392
$934$	2.16014e19	1.06470
$935$	1.62182e19	0.793830
$936$	5.01801e18	0.243915
$937$	−3.03662e19	−1.46583	−0.732915	−	0.680320i	$-0.761841\pi$
$937$	−3.03662e19	−1.46583	−0.732915	+	0.680320i	$0.761841\pi$
$938$	3.79697e19	1.82020
$939$	3.15614e18	0.150256
$940$	−1.95278e19	−0.923255
$941$	2.91646e19	1.36938	0.684690	−	0.728835i	$-0.259938\pi$
$941$	2.91646e19	1.36938	0.684690	+	0.728835i	$0.259938\pi$
$942$	−1.14010e19	−0.531631
$943$	3.90272e19	1.80735
$944$	5.20141e18	0.239223
$945$	−3.38243e18	−0.154498
$946$	2.63736e19	1.19640
$947$	8.29619e18	0.373769	0.186885	−	0.982382i	$-0.440161\pi$
$947$	8.29619e18	0.373769	0.186885	+	0.982382i	$0.440161\pi$
$948$	1.48653e19	0.665151
$949$	−6.41156e18	−0.284927
$950$	−2.22966e19	−0.984090
$951$	−4.85355e18	−0.212758
$952$	5.56245e19	2.42173
$953$	7.06895e18	0.305669	0.152834	−	0.988252i	$-0.451160\pi$
$953$	7.06895e18	0.305669	0.152834	+	0.988252i	$0.451160\pi$
$954$	1.06909e19	0.459146
$955$	−4.14696e19	−1.76892
$956$	−4.19690e19	−1.77809
$957$	6.37907e18	0.268429
$958$	2.76903e19	1.15732
$959$	1.54263e19	0.640385
$960$	9.27334e17	0.0382361
$961$	−6.87826e17	−0.0281693
$962$	2.41096e19	0.980736
$963$	−1.54126e19	−0.622739
$964$	−7.83636e19	−3.14495
$965$	4.82482e18	0.192333
$966$	2.79892e19	1.10825
$967$	−2.44434e19	−0.961367	−0.480683	−	0.876894i	$-0.659611\pi$
$967$	−2.44434e19	−0.961367	−0.480683	+	0.876894i	$0.659611\pi$
$968$	4.96740e19	1.94062
$969$	−2.37192e19	−0.920438
$970$	−3.90224e19	−1.50417
$971$	7.74581e18	0.296580	0.148290	−	0.988944i	$-0.452623\pi$
$971$	7.74581e18	0.296580	0.148290	+	0.988944i	$0.452623\pi$
$972$	−3.80701e18	−0.144795
$973$	−6.71978e18	−0.253876
$974$	−5.52507e19	−2.07350
$975$	2.84601e18	0.106098
$976$	7.87817e19	2.91744
$977$	−2.51559e19	−0.925392	−0.462696	−	0.886517i	$-0.653118\pi$
$977$	−2.51559e19	−0.925392	−0.462696	+	0.886517i	$0.653118\pi$
$978$	4.64774e19	1.69840
$979$	3.80539e18	0.138137
$980$	4.62264e19	1.66694
$981$	−5.90937e18	−0.211686
$982$	−7.47149e19	−2.65878
$983$	1.56952e19	0.554841	0.277421	−	0.960749i	$-0.410520\pi$
$983$	1.56952e19	0.554841	0.277421	+	0.960749i	$0.410520\pi$
$984$	−4.06116e19	−1.42621
$985$	4.24520e19	1.48103
$986$	−1.06044e20	−3.67523
$987$	3.50778e18	0.120773
$988$	−2.03681e19	−0.696677
$989$	−8.51463e19	−2.89328
$990$	−8.49200e18	−0.286669
$991$	−1.70313e19	−0.571174	−0.285587	−	0.958353i	$-0.592189\pi$
$991$	−1.70313e19	−0.571174	−0.285587	+	0.958353i	$0.592189\pi$
$992$	3.09920e19	1.03258
$993$	−4.58075e18	−0.151623
$994$	1.66107e19	0.546230
$995$	3.19566e19	1.04402
$996$	5.52895e19	1.79456
$997$	−1.98108e19	−0.638827	−0.319413	−	0.947615i	$-0.603486\pi$
$997$	−1.98108e19	−0.638827	−0.319413	+	0.947615i	$0.603486\pi$
$998$	−1.92441e19	−0.616523
$999$	−1.01875e19	−0.324258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.3	✓	32	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)

\(f(q)\)	\(=\)	\(q-163.348 q^{2} -729.000 q^{3} +18490.4 q^{4} -43774.8 q^{5} +119080. q^{6} -199445. q^{7} -1.68222e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-163.348 q^{2} -729.000 q^{3} +18490.4 q^{4} -43774.8 q^{5} +119080. q^{6} -199445. q^{7} -1.68222e6 q^{8} +531441. q^{9} +7.15050e6 q^{10} -2.23470e6 q^{11} -1.34795e7 q^{12} -5.61298e6 q^{13} +3.25788e7 q^{14} +3.19118e7 q^{15} +1.23313e8 q^{16} +1.65791e8 q^{17} -8.68096e7 q^{18} +1.96251e8 q^{19} -8.09414e8 q^{20} +1.45395e8 q^{21} +3.65032e8 q^{22} -1.17850e9 q^{23} +1.22634e9 q^{24} +6.95528e8 q^{25} +9.16867e8 q^{26} -3.87420e8 q^{27} -3.68781e9 q^{28} +3.91572e9 q^{29} -5.21272e9 q^{30} -4.87132e9 q^{31} -6.36214e9 q^{32} +1.62909e9 q^{33} -2.70815e10 q^{34} +8.73064e9 q^{35} +9.82657e9 q^{36} +2.62956e10 q^{37} -3.20571e10 q^{38} +4.09187e9 q^{39} +7.36388e10 q^{40} -3.31161e10 q^{41} -2.37499e10 q^{42} +7.22500e10 q^{43} -4.13205e10 q^{44} -2.32637e10 q^{45} +1.92504e11 q^{46} +2.41258e10 q^{47} -8.98953e10 q^{48} -5.71109e10 q^{49} -1.13613e11 q^{50} -1.20862e11 q^{51} -1.03786e11 q^{52} -1.23154e11 q^{53} +6.32842e10 q^{54} +9.78234e10 q^{55} +3.35510e11 q^{56} -1.43067e11 q^{57} -6.39622e11 q^{58} +4.21805e10 q^{59} +5.90063e11 q^{60} +6.38875e11 q^{61} +7.95717e11 q^{62} -1.05993e11 q^{63} +2.90593e10 q^{64} +2.45707e11 q^{65} -2.66108e11 q^{66} +1.16548e12 q^{67} +3.06554e12 q^{68} +8.59123e11 q^{69} -1.42613e12 q^{70} +5.09862e11 q^{71} -8.94001e11 q^{72} +1.14227e12 q^{73} -4.29533e12 q^{74} -5.07040e11 q^{75} +3.62876e12 q^{76} +4.45698e11 q^{77} -6.68396e11 q^{78} -1.10281e12 q^{79} -5.39801e12 q^{80} +2.82430e11 q^{81} +5.40944e12 q^{82} -4.10174e12 q^{83} +2.68842e12 q^{84} -7.25746e12 q^{85} -1.18019e13 q^{86} -2.85456e12 q^{87} +3.75925e12 q^{88} -1.70286e12 q^{89} +3.80007e12 q^{90} +1.11948e12 q^{91} -2.17909e13 q^{92} +3.55119e12 q^{93} -3.94089e12 q^{94} -8.59083e12 q^{95} +4.63800e12 q^{96} -5.45730e12 q^{97} +9.32892e12 q^{98} -1.18761e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9} + 6145337 q^{10} + 400846 q^{11} - 101457846 q^{12} + 9411686 q^{13} - 36368387 q^{14} - 1630044 q^{15} + 734877786 q^{16} + 228113833 q^{17} + 6377292 q^{18} + 524233755 q^{19} - 420745331 q^{20} - 544450005 q^{21} - 1844479318 q^{22} - 399937087 q^{23} + 534588093 q^{24} + 8617402914 q^{25} - 499433574 q^{26} - 12397455648 q^{27} + 12648993070 q^{28} - 225284149 q^{29} - 4479950673 q^{30} + 9454638761 q^{31} + 11648295118 q^{32} - 292216734 q^{33} + 39279537096 q^{34} + 17608963479 q^{35} + 73962769734 q^{36} + 37463929597 q^{37} + 65554547351 q^{38} - 6861119094 q^{39} + 144414252742 q^{40} + 22650227173 q^{41} + 26512554123 q^{42} + 96253617602 q^{43} - 132186868002 q^{44} + 1188302076 q^{45} + 327853892309 q^{46} + 239981844027 q^{47} - 535725905994 q^{48} + 286262776863 q^{49} - 671840368399 q^{50} - 166294984257 q^{51} - 952971648498 q^{52} - 47446514136 q^{53} - 4649045868 q^{54} - 474454082548 q^{55} - 1167728875984 q^{56} - 382166407395 q^{57} + 547596592762 q^{58} + 1349777076512 q^{59} + 306723346299 q^{60} + 661498471821 q^{61} + 555821093242 q^{62} + 396904053645 q^{63} + 3522679273173 q^{64} + 1269187682756 q^{65} + 1344625422822 q^{66} + 2838711491386 q^{67} + 1395029358261 q^{68} + 291554136423 q^{69} + 5677102514386 q^{70} + 1912914480734 q^{71} - 389714719797 q^{72} + 2403595726697 q^{73} - 742136417562 q^{74} - 6282086724306 q^{75} - 4020161987188 q^{76} - 4878303804101 q^{77} + 364087075446 q^{78} - 1705546365970 q^{79} - 4347383766449 q^{80} + 9037745167392 q^{81} - 6943720239935 q^{82} - 2549647313691 q^{83} - 9221115948030 q^{84} - 8455706309615 q^{85} - 33993832711012 q^{86} + 164232144621 q^{87} - 42970239360587 q^{88} - 17356719361241 q^{89} + 3265884040617 q^{90} - 30776775043291 q^{91} - 13184590997480 q^{92} - 6892431656769 q^{93} - 35604563339520 q^{94} + 219501126195 q^{95} - 8491607141022 q^{96} - 4427131429152 q^{97} - 32707332037060 q^{98} + 213025999086 q^{99}+O(q^{100}) \) 32 * q + 12 * q^2 - 23328 * q^3 + 139174 * q^4 + 2236 * q^5 - 8748 * q^6 + 746845 * q^7 - 733317 * q^8 + 17006112 * q^9 + 6145337 * q^10 + 400846 * q^11 - 101457846 * q^12 + 9411686 * q^13 - 36368387 * q^14 - 1630044 * q^15 + 734877786 * q^16 + 228113833 * q^17 + 6377292 * q^18 + 524233755 * q^19 - 420745331 * q^20 - 544450005 * q^21 - 1844479318 * q^22 - 399937087 * q^23 + 534588093 * q^24 + 8617402914 * q^25 - 499433574 * q^26 - 12397455648 * q^27 + 12648993070 * q^28 - 225284149 * q^29 - 4479950673 * q^30 + 9454638761 * q^31 + 11648295118 * q^32 - 292216734 * q^33 + 39279537096 * q^34 + 17608963479 * q^35 + 73962769734 * q^36 + 37463929597 * q^37 + 65554547351 * q^38 - 6861119094 * q^39 + 144414252742 * q^40 + 22650227173 * q^41 + 26512554123 * q^42 + 96253617602 * q^43 - 132186868002 * q^44 + 1188302076 * q^45 + 327853892309 * q^46 + 239981844027 * q^47 - 535725905994 * q^48 + 286262776863 * q^49 - 671840368399 * q^50 - 166294984257 * q^51 - 952971648498 * q^52 - 47446514136 * q^53 - 4649045868 * q^54 - 474454082548 * q^55 - 1167728875984 * q^56 - 382166407395 * q^57 + 547596592762 * q^58 + 1349777076512 * q^59 + 306723346299 * q^60 + 661498471821 * q^61 + 555821093242 * q^62 + 396904053645 * q^63 + 3522679273173 * q^64 + 1269187682756 * q^65 + 1344625422822 * q^66 + 2838711491386 * q^67 + 1395029358261 * q^68 + 291554136423 * q^69 + 5677102514386 * q^70 + 1912914480734 * q^71 - 389714719797 * q^72 + 2403595726697 * q^73 - 742136417562 * q^74 - 6282086724306 * q^75 - 4020161987188 * q^76 - 4878303804101 * q^77 + 364087075446 * q^78 - 1705546365970 * q^79 - 4347383766449 * q^80 + 9037745167392 * q^81 - 6943720239935 * q^82 - 2549647313691 * q^83 - 9221115948030 * q^84 - 8455706309615 * q^85 - 33993832711012 * q^86 + 164232144621 * q^87 - 42970239360587 * q^88 - 17356719361241 * q^89 + 3265884040617 * q^90 - 30776775043291 * q^91 - 13184590997480 * q^92 - 6892431656769 * q^93 - 35604563339520 * q^94 + 219501126195 * q^95 - 8491607141022 * q^96 - 4427131429152 * q^97 - 32707332037060 * q^98 + 213025999086 * q^99

Introduction

L-functions

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