LMFDB - Embedded newform 177.14.a.d.1.27

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			1.27
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)

$f(q)$	$=$	$q+119.478 q^{2} -729.000 q^{3} +6083.02 q^{4} -42747.4 q^{5} -87099.5 q^{6} -107876. q^{7} -251977. q^{8} +531441. q^{9} +O(q^{10})$	\(q+119.478 q^{2} -729.000 q^{3} +6083.02 q^{4} -42747.4 q^{5} -87099.5 q^{6} -107876. q^{7} -251977. q^{8} +531441. q^{9} -5.10737e6 q^{10} +416621. q^{11} -4.43452e6 q^{12} -2.56022e7 q^{13} -1.28889e7 q^{14} +3.11628e7 q^{15} -7.99378e7 q^{16} +3.06528e7 q^{17} +6.34956e7 q^{18} -2.89661e8 q^{19} -2.60033e8 q^{20} +7.86419e7 q^{21} +4.97771e7 q^{22} -7.92872e8 q^{23} +1.83691e8 q^{24} +6.06634e8 q^{25} -3.05890e9 q^{26} -3.87420e8 q^{27} -6.56214e8 q^{28} +3.60791e8 q^{29} +3.72328e9 q^{30} -4.30096e9 q^{31} -7.48662e9 q^{32} -3.03717e8 q^{33} +3.66234e9 q^{34} +4.61143e9 q^{35} +3.23276e9 q^{36} -1.34271e10 q^{37} -3.46081e10 q^{38} +1.86640e10 q^{39} +1.07714e10 q^{40} +4.43199e10 q^{41} +9.39598e9 q^{42} -5.79206e10 q^{43} +2.53431e9 q^{44} -2.27177e10 q^{45} -9.47309e10 q^{46} +2.75213e10 q^{47} +5.82747e10 q^{48} -8.52517e10 q^{49} +7.24795e10 q^{50} -2.23459e10 q^{51} -1.55739e11 q^{52} -8.97453e10 q^{53} -4.62883e10 q^{54} -1.78095e10 q^{55} +2.71824e10 q^{56} +2.11163e11 q^{57} +4.31067e10 q^{58} +4.21805e10 q^{59} +1.89564e11 q^{60} -7.82250e11 q^{61} -5.13870e11 q^{62} -5.73299e10 q^{63} -2.39637e11 q^{64} +1.09443e12 q^{65} -3.62875e10 q^{66} +1.53282e11 q^{67} +1.86462e11 q^{68} +5.78004e11 q^{69} +5.50965e11 q^{70} +1.97048e12 q^{71} -1.33911e11 q^{72} +3.47895e11 q^{73} -1.60425e12 q^{74} -4.42236e11 q^{75} -1.76201e12 q^{76} -4.49436e10 q^{77} +2.22994e12 q^{78} +4.07214e11 q^{79} +3.41713e12 q^{80} +2.82430e11 q^{81} +5.29526e12 q^{82} -3.54766e12 q^{83} +4.78380e11 q^{84} -1.31033e12 q^{85} -6.92025e12 q^{86} -2.63017e11 q^{87} -1.04979e11 q^{88} +6.13782e12 q^{89} -2.71427e12 q^{90} +2.76187e12 q^{91} -4.82306e12 q^{92} +3.13540e12 q^{93} +3.28819e12 q^{94} +1.23822e13 q^{95} +5.45775e12 q^{96} +1.40507e12 q^{97} -1.01857e13 q^{98} +2.21410e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	119.478	1.32006	0.660030	−	0.751240i	$-0.270544\pi$
$2$	119.478	1.32006	0.660030	+	0.751240i	$0.270544\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	6083.02	0.742556
$5$	−42747.4	−1.22350	−0.611751	−	0.791051i	$-0.709534\pi$
$5$	−42747.4	−1.22350	−0.611751	+	0.791051i	$0.709534\pi$
$6$	−87099.5	−0.762136
$7$	−107876.	−0.346568	−0.173284	−	0.984872i	$-0.555438\pi$
$7$	−107876.	−0.346568	−0.173284	+	0.984872i	$0.555438\pi$
$8$	−251977.	−0.339841
$9$	531441.	0.333333
$10$	−5.10737e6	−1.61509
$11$	416621.	0.0709070	0.0354535	−	0.999371i	$-0.488712\pi$
$11$	416621.	0.0709070	0.0354535	+	0.999371i	$0.488712\pi$
$12$	−4.43452e6	−0.428715
$13$	−2.56022e7	−1.47111	−0.735556	−	0.677464i	$-0.763079\pi$
$13$	−2.56022e7	−1.47111	−0.735556	+	0.677464i	$0.763079\pi$
$14$	−1.28889e7	−0.457491
$15$	3.11628e7	0.706389
$16$	−7.99378e7	−1.19117
$17$	3.06528e7	0.308001	0.154000	−	0.988071i	$-0.450784\pi$
$17$	3.06528e7	0.308001	0.154000	+	0.988071i	$0.450784\pi$
$18$	6.34956e7	0.440020
$19$	−2.89661e8	−1.41251	−0.706254	−	0.707958i	$-0.749616\pi$
$19$	−2.89661e8	−1.41251	−0.706254	+	0.707958i	$0.749616\pi$
$20$	−2.60033e8	−0.908518
$21$	7.86419e7	0.200091
$22$	4.97771e7	0.0936014
$23$	−7.92872e8	−1.11679	−0.558396	−	0.829575i	$-0.688583\pi$
$23$	−7.92872e8	−1.11679	−0.558396	+	0.829575i	$0.688583\pi$
$24$	1.83691e8	0.196208
$25$	6.06634e8	0.496955
$26$	−3.05890e9	−1.94195
$27$	−3.87420e8	−0.192450
$28$	−6.56214e8	−0.257346
$29$	3.60791e8	0.112634	0.0563170	−	0.998413i	$-0.482064\pi$
$29$	3.60791e8	0.112634	0.0563170	+	0.998413i	$0.482064\pi$
$30$	3.72328e9	0.932475
$31$	−4.30096e9	−0.870390	−0.435195	−	0.900336i	$-0.643321\pi$
$31$	−4.30096e9	−0.870390	−0.435195	+	0.900336i	$0.643321\pi$
$32$	−7.48662e9	−1.23257
$33$	−3.03717e8	−0.0409382
$34$	3.66234e9	0.406580
$35$	4.61143e9	0.424027
$36$	3.23276e9	0.247519
$37$	−1.34271e10	−0.860343	−0.430172	−	0.902747i	$-0.641547\pi$
$37$	−1.34271e10	−0.860343	−0.430172	+	0.902747i	$0.641547\pi$
$38$	−3.46081e10	−1.86459
$39$	1.86640e10	0.849347
$40$	1.07714e10	0.415796
$41$	4.43199e10	1.45715	0.728574	−	0.684967i	$-0.240184\pi$
$41$	4.43199e10	1.45715	0.728574	+	0.684967i	$0.240184\pi$
$42$	9.39598e9	0.264132
$43$	−5.79206e10	−1.39730	−0.698648	−	0.715466i	$-0.746215\pi$
$43$	−5.79206e10	−1.39730	−0.698648	+	0.715466i	$0.746215\pi$
$44$	2.53431e9	0.0526524
$45$	−2.27177e10	−0.407834
$46$	−9.47309e10	−1.47423
$47$	2.75213e10	0.372420	0.186210	−	0.982510i	$-0.440380\pi$
$47$	2.75213e10	0.372420	0.186210	+	0.982510i	$0.440380\pi$
$48$	5.82747e10	0.687720
$49$	−8.52517e10	−0.879890
$50$	7.24795e10	0.656010
$51$	−2.23459e10	−0.177824
$52$	−1.55739e11	−1.09238
$53$	−8.97453e10	−0.556184	−0.278092	−	0.960554i	$-0.589702\pi$
$53$	−8.97453e10	−0.556184	−0.278092	+	0.960554i	$0.589702\pi$
$54$	−4.62883e10	−0.254045
$55$	−1.78095e10	−0.0867548
$56$	2.71824e10	0.117778
$57$	2.11163e11	0.815512
$58$	4.31067e10	0.148683
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	1.89564e11	0.524533
$61$	−7.82250e11	−1.94403	−0.972013	−	0.234929i	$-0.924514\pi$
$61$	−7.82250e11	−1.94403	−0.972013	+	0.234929i	$0.924514\pi$
$62$	−5.13870e11	−1.14897
$63$	−5.73299e10	−0.115523
$64$	−2.39637e11	−0.435897
$65$	1.09443e12	1.79991
$66$	−3.62875e10	−0.0540408
$67$	1.53282e11	0.207016	0.103508	−	0.994629i	$-0.466993\pi$
$67$	1.53282e11	0.207016	0.103508	+	0.994629i	$0.466993\pi$
$68$	1.86462e11	0.228708
$69$	5.78004e11	0.644780
$70$	5.50965e11	0.559740
$71$	1.97048e12	1.82555	0.912774	−	0.408465i	$-0.133936\pi$
$71$	1.97048e12	1.82555	0.912774	+	0.408465i	$0.133936\pi$
$72$	−1.33911e11	−0.113280
$73$	3.47895e11	0.269060	0.134530	−	0.990910i	$-0.457048\pi$
$73$	3.47895e11	0.269060	0.134530	+	0.990910i	$0.457048\pi$
$74$	−1.60425e12	−1.13570
$75$	−4.42236e11	−0.286917
$76$	−1.76201e12	−1.04887
$77$	−4.49436e10	−0.0245741
$78$	2.22994e12	1.12119
$79$	4.07214e11	0.188472	0.0942360	−	0.995550i	$-0.469959\pi$
$79$	4.07214e11	0.188472	0.0942360	+	0.995550i	$0.469959\pi$
$80$	3.41713e12	1.45739
$81$	2.82430e11	0.111111
$82$	5.29526e12	1.92352
$83$	−3.54766e12	−1.19106	−0.595531	−	0.803332i	$-0.703058\pi$
$83$	−3.54766e12	−1.19106	−0.595531	+	0.803332i	$0.703058\pi$
$84$	4.78380e11	0.148579
$85$	−1.31033e12	−0.376840
$86$	−6.92025e12	−1.84451
$87$	−2.63017e11	−0.0650292
$88$	−1.04979e11	−0.0240971
$89$	6.13782e12	1.30912	0.654559	−	0.756011i	$-0.272854\pi$
$89$	6.13782e12	1.30912	0.654559	+	0.756011i	$0.272854\pi$
$90$	−2.71427e12	−0.538365
$91$	2.76187e12	0.509841
$92$	−4.82306e12	−0.829281
$93$	3.13540e12	0.502520
$94$	3.28819e12	0.491616
$95$	1.23822e13	1.72821
$96$	5.45775e12	0.711624
$97$	1.40507e12	0.171270	0.0856350	−	0.996327i	$-0.472708\pi$
$97$	1.40507e12	0.171270	0.0856350	+	0.996327i	$0.472708\pi$
$98$	−1.01857e13	−1.16151
$99$	2.21410e11	0.0236357
$100$	3.69017e12	0.369017
$101$	1.03972e13	0.974607	0.487303	−	0.873233i	$-0.337981\pi$
$101$	1.03972e13	0.974607	0.487303	+	0.873233i	$0.337981\pi$
$102$	−2.66984e12	−0.234739
$103$	−2.81402e12	−0.232212	−0.116106	−	0.993237i	$-0.537041\pi$
$103$	−2.81402e12	−0.232212	−0.116106	+	0.993237i	$0.537041\pi$
$104$	6.45117e12	0.499945
$105$	−3.36173e12	−0.244812
$106$	−1.07226e13	−0.734196
$107$	−6.86428e12	−0.442181	−0.221091	−	0.975253i	$-0.570962\pi$
$107$	−6.86428e12	−0.442181	−0.221091	+	0.975253i	$0.570962\pi$
$108$	−2.35669e12	−0.142905
$109$	−2.64518e13	−1.51071	−0.755357	−	0.655313i	$-0.772537\pi$
$109$	−2.64518e13	−1.51071	−0.755357	+	0.655313i	$0.772537\pi$
$110$	−2.12784e12	−0.114521
$111$	9.78837e12	0.496719
$112$	8.62340e12	0.412821
$113$	1.33884e13	0.604947	0.302473	−	0.953158i	$-0.402188\pi$
$113$	1.33884e13	0.604947	0.302473	+	0.953158i	$0.402188\pi$
$114$	2.52293e13	1.07652
$115$	3.38932e13	1.36640
$116$	2.19470e12	0.0836370
$117$	−1.36061e13	−0.490371
$118$	5.03965e12	0.171857
$119$	−3.30671e12	−0.106743
$120$	−7.85232e12	−0.240060
$121$	−3.43491e13	−0.994972
$122$	−9.34618e13	−2.56623
$123$	−3.23092e13	−0.841285
$124$	−2.61628e13	−0.646314
$125$	2.62498e13	0.615476
$126$	−6.84967e12	−0.152497
$127$	8.97367e13	1.89778	0.948890	−	0.315608i	$-0.102208\pi$
$127$	8.97367e13	1.89778	0.948890	+	0.315608i	$0.102208\pi$
$128$	3.26991e13	0.657159
$129$	4.22241e13	0.806729
$130$	1.30760e14	2.37598
$131$	−1.66086e13	−0.287124	−0.143562	−	0.989641i	$-0.545856\pi$
$131$	−1.66086e13	−0.287124	−0.143562	+	0.989641i	$0.545856\pi$
$132$	−1.84752e12	−0.0303989
$133$	3.12475e13	0.489531
$134$	1.83138e13	0.273274
$135$	1.65612e13	0.235463
$136$	−7.72381e12	−0.104672
$137$	−3.08228e13	−0.398280	−0.199140	−	0.979971i	$-0.563815\pi$
$137$	−3.08228e13	−0.398280	−0.199140	+	0.979971i	$0.563815\pi$
$138$	6.90588e13	0.851148
$139$	3.91867e13	0.460832	0.230416	−	0.973092i	$-0.425991\pi$
$139$	3.91867e13	0.460832	0.230416	+	0.973092i	$0.425991\pi$
$140$	2.80514e13	0.314864
$141$	−2.00630e13	−0.215017
$142$	2.35430e14	2.40983
$143$	−1.06664e13	−0.104312
$144$	−4.24822e13	−0.397056
$145$	−1.54229e13	−0.137808
$146$	4.15658e13	0.355175
$147$	6.21485e13	0.508005
$148$	−8.16774e13	−0.638853
$149$	−1.71786e14	−1.28611	−0.643054	−	0.765821i	$-0.722333\pi$
$149$	−1.71786e14	−1.28611	−0.643054	+	0.765821i	$0.722333\pi$
$150$	−5.28376e13	−0.378747
$151$	2.29060e13	0.157253	0.0786265	−	0.996904i	$-0.474947\pi$
$151$	2.29060e13	0.157253	0.0786265	+	0.996904i	$0.474947\pi$
$152$	7.29879e13	0.480029
$153$	1.62902e13	0.102667
$154$	−5.36977e12	−0.0324393
$155$	1.83855e14	1.06492
$156$	1.13533e14	0.630687
$157$	2.55812e14	1.36324	0.681620	−	0.731706i	$-0.261276\pi$
$157$	2.55812e14	1.36324	0.681620	+	0.731706i	$0.261276\pi$
$158$	4.86532e13	0.248794
$159$	6.54243e13	0.321113
$160$	3.20033e14	1.50805
$161$	8.55322e13	0.387045
$162$	3.37441e13	0.146673
$163$	4.76791e14	1.99117	0.995585	−	0.0938624i	$-0.0299214\pi$
$163$	4.76791e14	1.99117	0.995585	+	0.0938624i	$0.0299214\pi$
$164$	2.69599e14	1.08201
$165$	1.29831e13	0.0500879
$166$	−4.23868e14	−1.57227
$167$	9.16154e12	0.0326822	0.0163411	−	0.999866i	$-0.494798\pi$
$167$	9.16154e12	0.0326822	0.0163411	+	0.999866i	$0.494798\pi$
$168$	−1.98160e13	−0.0679993
$169$	3.52598e14	1.16417
$170$	−1.56555e14	−0.497450
$171$	−1.53938e14	−0.470836
$172$	−3.52332e14	−1.03757
$173$	−3.13114e13	−0.0887980	−0.0443990	−	0.999014i	$-0.514137\pi$
$173$	−3.13114e13	−0.0887980	−0.0443990	+	0.999014i	$0.514137\pi$
$174$	−3.14248e13	−0.0858424
$175$	−6.54415e13	−0.172229
$176$	−3.33038e13	−0.0844620
$177$	−3.07496e13	−0.0751646
$178$	7.33335e14	1.72811
$179$	−4.55148e14	−1.03421	−0.517104	−	0.855923i	$-0.672990\pi$
$179$	−4.55148e14	−1.03421	−0.517104	+	0.855923i	$0.672990\pi$
$180$	−1.38192e14	−0.302839
$181$	−8.78555e14	−1.85720	−0.928599	−	0.371086i	$-0.878986\pi$
$181$	−8.78555e14	−1.85720	−0.928599	+	0.371086i	$0.878986\pi$
$182$	3.29983e14	0.673020
$183$	5.70261e14	1.12238
$184$	1.99786e14	0.379532
$185$	5.73974e14	1.05263
$186$	3.74611e14	0.663356
$187$	1.27706e13	0.0218394
$188$	1.67413e14	0.276543
$189$	4.17935e13	0.0666971
$190$	1.47941e15	2.28133
$191$	3.31318e14	0.493774	0.246887	−	0.969044i	$-0.420592\pi$
$191$	3.31318e14	0.493774	0.246887	+	0.969044i	$0.420592\pi$
$192$	1.74695e14	0.251665
$193$	−3.46500e14	−0.482592	−0.241296	−	0.970452i	$-0.577573\pi$
$193$	−3.46500e14	−0.482592	−0.241296	+	0.970452i	$0.577573\pi$
$194$	1.67875e14	0.226086
$195$	−7.97837e14	−1.03918
$196$	−5.18588e14	−0.653368
$197$	−1.26757e15	−1.54504	−0.772521	−	0.634990i	$-0.781004\pi$
$197$	−1.26757e15	−1.54504	−0.772521	+	0.634990i	$0.781004\pi$
$198$	2.64536e13	0.0312005
$199$	8.80092e14	1.00458	0.502288	−	0.864700i	$-0.332492\pi$
$199$	8.80092e14	1.00458	0.502288	+	0.864700i	$0.332492\pi$
$200$	−1.52858e14	−0.168886
$201$	−1.11743e14	−0.119521
$202$	1.24224e15	1.28654
$203$	−3.89209e13	−0.0390354
$204$	−1.35930e14	−0.132045
$205$	−1.89456e15	−1.78282
$206$	−3.36214e14	−0.306534
$207$	−4.21365e14	−0.372264
$208$	2.04659e15	1.75234
$209$	−1.20679e14	−0.100157
$210$	−4.01653e14	−0.323166
$211$	−2.32986e15	−1.81758	−0.908792	−	0.417248i	$-0.862995\pi$
$211$	−2.32986e15	−1.81758	−0.908792	+	0.417248i	$0.862995\pi$
$212$	−5.45922e14	−0.412998
$213$	−1.43648e15	−1.05398
$214$	−8.20131e14	−0.583705
$215$	2.47595e15	1.70959
$216$	9.76211e13	0.0654025
$217$	4.63972e14	0.301650
$218$	−3.16041e15	−1.99423
$219$	−2.53615e14	−0.155342
$220$	−1.08335e14	−0.0644203
$221$	−7.84779e14	−0.453104
$222$	1.16950e15	0.655699
$223$	−2.97551e15	−1.62024	−0.810120	−	0.586265i	$-0.800598\pi$
$223$	−2.97551e15	−1.62024	−0.810120	+	0.586265i	$0.800598\pi$
$224$	8.07630e14	0.427169
$225$	3.22390e14	0.165652
$226$	1.59962e15	0.798566
$227$	−2.02707e15	−0.983334	−0.491667	−	0.870783i	$-0.663612\pi$
$227$	−2.02707e15	−0.983334	−0.491667	+	0.870783i	$0.663612\pi$
$228$	1.28451e15	0.605563
$229$	4.58030e14	0.209876	0.104938	−	0.994479i	$-0.466536\pi$
$229$	4.58030e14	0.209876	0.104938	+	0.994479i	$0.466536\pi$
$230$	4.04950e15	1.80372
$231$	3.27639e13	0.0141879
$232$	−9.09112e13	−0.0382777
$233$	−4.56950e15	−1.87092	−0.935460	−	0.353433i	$-0.885014\pi$
$233$	−4.56950e15	−1.87092	−0.935460	+	0.353433i	$0.885014\pi$
$234$	−1.62563e15	−0.647318
$235$	−1.17646e15	−0.455656
$236$	2.56585e14	0.0966725
$237$	−2.96859e14	−0.108814
$238$	−3.95080e14	−0.140908
$239$	−2.34262e15	−0.813046	−0.406523	−	0.913641i	$-0.633259\pi$
$239$	−2.34262e15	−0.813046	−0.406523	+	0.913641i	$0.633259\pi$
$240$	−2.49109e15	−0.841427
$241$	−1.55997e15	−0.512869	−0.256435	−	0.966562i	$-0.582548\pi$
$241$	−1.55997e15	−0.512869	−0.256435	+	0.966562i	$0.582548\pi$
$242$	−4.10397e15	−1.31342
$243$	−2.05891e14	−0.0641500
$244$	−4.75844e15	−1.44355
$245$	3.64429e15	1.07655
$246$	−3.86024e15	−1.11055
$247$	7.41595e15	2.07796
$248$	1.08374e15	0.295795
$249$	2.58625e15	0.687661
$250$	3.13628e15	0.812465
$251$	−2.40913e15	−0.608109	−0.304055	−	0.952655i	$-0.598341\pi$
$251$	−2.40913e15	−0.608109	−0.304055	+	0.952655i	$0.598341\pi$
$252$	−3.48739e14	−0.0857821
$253$	−3.30327e14	−0.0791884
$254$	1.07216e16	2.50518
$255$	9.55228e14	0.217568
$256$	5.86993e15	1.30339
$257$	7.86488e15	1.70266	0.851328	−	0.524634i	$-0.175798\pi$
$257$	7.86488e15	1.70266	0.851328	+	0.524634i	$0.175798\pi$
$258$	5.04486e15	1.06493
$259$	1.44847e15	0.298168
$260$	6.65742e15	1.33653
$261$	1.91739e14	0.0375446
$262$	−1.98436e15	−0.379021
$263$	5.07640e15	0.945897	0.472948	−	0.881090i	$-0.343190\pi$
$263$	5.07640e15	0.945897	0.472948	+	0.881090i	$0.343190\pi$
$264$	7.65297e13	0.0139125
$265$	3.83637e15	0.680492
$266$	3.73340e15	0.646210
$267$	−4.47447e15	−0.755820
$268$	9.32417e14	0.153721
$269$	1.91269e15	0.307790	0.153895	−	0.988087i	$-0.450818\pi$
$269$	1.91269e15	0.307790	0.153895	+	0.988087i	$0.450818\pi$
$270$	1.97870e15	0.310825
$271$	9.58060e15	1.46924	0.734619	−	0.678480i	$-0.237361\pi$
$271$	9.58060e15	1.46924	0.734619	+	0.678480i	$0.237361\pi$
$272$	−2.45032e15	−0.366881
$273$	−2.01341e15	−0.294357
$274$	−3.68265e15	−0.525754
$275$	2.52737e14	0.0352376
$276$	3.51601e15	0.478785
$277$	6.89502e15	0.917101	0.458550	−	0.888668i	$-0.348369\pi$
$277$	6.89502e15	0.917101	0.458550	+	0.888668i	$0.348369\pi$
$278$	4.68196e15	0.608326
$279$	−2.28571e15	−0.290130
$280$	−1.16198e15	−0.144102
$281$	−4.84288e13	−0.00586830	−0.00293415	−	0.999996i	$-0.500934\pi$
$281$	−4.84288e13	−0.00586830	−0.00293415	+	0.999996i	$0.500934\pi$
$282$	−2.39709e15	−0.283835
$283$	−3.82205e15	−0.442267	−0.221134	−	0.975244i	$-0.570976\pi$
$283$	−3.82205e15	−0.442267	−0.221134	+	0.975244i	$0.570976\pi$
$284$	1.19865e16	1.35557
$285$	−9.02664e15	−0.997780
$286$	−1.27440e15	−0.137698
$287$	−4.78107e15	−0.505001
$288$	−3.97870e15	−0.410856
$289$	−8.96498e15	−0.905135
$290$	−1.84270e15	−0.181914
$291$	−1.02429e15	−0.0988827
$292$	2.11625e15	0.199792
$293$	7.94239e15	0.733350	0.366675	−	0.930349i	$-0.380496\pi$
$293$	7.94239e15	0.733350	0.366675	+	0.930349i	$0.380496\pi$
$294$	7.42538e15	0.670596
$295$	−1.80311e15	−0.159286
$296$	3.38333e15	0.292380
$297$	−1.61408e14	−0.0136461
$298$	−2.05247e16	−1.69774
$299$	2.02993e16	1.64293
$300$	−2.69013e15	−0.213052
$301$	6.24827e15	0.484259
$302$	2.73676e15	0.207583
$303$	−7.57959e15	−0.562689
$304$	2.31548e16	1.68253
$305$	3.34391e16	2.37852
$306$	1.94632e15	0.135527
$307$	−2.63285e16	−1.79484	−0.897422	−	0.441174i	$-0.854562\pi$
$307$	−2.63285e16	−1.79484	−0.897422	+	0.441174i	$0.854562\pi$
$308$	−2.73393e14	−0.0182477
$309$	2.05142e15	0.134068
$310$	2.19666e16	1.40576
$311$	−1.62017e16	−1.01536	−0.507679	−	0.861546i	$-0.669496\pi$
$311$	−1.62017e16	−1.01536	−0.507679	+	0.861546i	$0.669496\pi$
$312$	−4.70291e15	−0.288643
$313$	1.62608e16	0.977471	0.488736	−	0.872432i	$-0.337458\pi$
$313$	1.62608e16	0.977471	0.488736	+	0.872432i	$0.337458\pi$
$314$	3.05639e16	1.79956
$315$	2.45070e15	0.141342
$316$	2.47709e15	0.139951
$317$	2.22405e16	1.23101	0.615503	−	0.788135i	$-0.288953\pi$
$317$	2.22405e16	1.23101	0.615503	+	0.788135i	$0.288953\pi$
$318$	7.81677e15	0.423888
$319$	1.50313e14	0.00798653
$320$	1.02438e16	0.533320
$321$	5.00406e15	0.255293
$322$	1.02192e16	0.510922
$323$	−8.87891e15	−0.435054
$324$	1.71802e15	0.0825062
$325$	−1.55312e16	−0.731076
$326$	5.69661e16	2.62846
$327$	1.92833e16	0.872211
$328$	−1.11676e16	−0.495199
$329$	−2.96890e15	−0.129069
$330$	1.55120e15	0.0661190
$331$	−2.54935e16	−1.06549	−0.532743	−	0.846277i	$-0.678839\pi$
$331$	−2.54935e16	−1.06549	−0.532743	+	0.846277i	$0.678839\pi$
$332$	−2.15805e16	−0.884431
$333$	−7.13572e15	−0.286781
$334$	1.09460e15	0.0431424
$335$	−6.55240e15	−0.253285
$336$	−6.28646e15	−0.238342
$337$	2.31187e16	0.859743	0.429871	−	0.902890i	$-0.358559\pi$
$337$	2.31187e16	0.859743	0.429871	+	0.902890i	$0.358559\pi$
$338$	4.21277e16	1.53677
$339$	−9.76011e15	−0.349266
$340$	−7.97074e15	−0.279824
$341$	−1.79187e15	−0.0617168
$342$	−1.83922e16	−0.621531
$343$	1.96487e16	0.651511
$344$	1.45947e16	0.474859
$345$	−2.47081e16	−0.788889
$346$	−3.74103e15	−0.117219
$347$	−3.57148e16	−1.09826	−0.549131	−	0.835736i	$-0.685041\pi$
$347$	−3.57148e16	−1.09826	−0.549131	+	0.835736i	$0.685041\pi$
$348$	−1.59994e15	−0.0482878
$349$	5.84649e15	0.173193	0.0865964	−	0.996243i	$-0.472401\pi$
$349$	5.84649e15	0.173193	0.0865964	+	0.996243i	$0.472401\pi$
$350$	−7.81882e15	−0.227352
$351$	9.91882e15	0.283116
$352$	−3.11909e15	−0.0873977
$353$	−4.39427e16	−1.20879	−0.604396	−	0.796684i	$-0.706585\pi$
$353$	−4.39427e16	−1.20879	−0.604396	+	0.796684i	$0.706585\pi$
$354$	−3.67391e15	−0.0992217
$355$	−8.42329e16	−2.23356
$356$	3.73365e16	0.972094
$357$	2.41059e15	0.0616283
$358$	−5.43802e16	−1.36522
$359$	3.17332e16	0.782348	0.391174	−	0.920317i	$-0.372069\pi$
$359$	3.17332e16	0.782348	0.391174	+	0.920317i	$0.372069\pi$
$360$	5.72434e15	0.138599
$361$	4.18503e16	0.995180
$362$	−1.04968e17	−2.45161
$363$	2.50405e16	0.574447
$364$	1.68005e16	0.378585
$365$	−1.48716e16	−0.329195
$366$	6.81337e16	1.48161
$367$	−6.97383e16	−1.48985	−0.744924	−	0.667149i	$-0.767514\pi$
$367$	−6.97383e16	−1.48985	−0.744924	+	0.667149i	$0.767514\pi$
$368$	6.33805e16	1.33029
$369$	2.35534e16	0.485716
$370$	6.85773e16	1.38953
$371$	9.68139e15	0.192756
$372$	1.90727e16	0.373149
$373$	2.69782e16	0.518686	0.259343	−	0.965785i	$-0.416494\pi$
$373$	2.69782e16	0.518686	0.259343	+	0.965785i	$0.416494\pi$
$374$	1.52581e15	0.0288293
$375$	−1.91361e16	−0.355345
$376$	−6.93474e15	−0.126564
$377$	−9.23706e15	−0.165697
$378$	4.99341e15	0.0880441
$379$	−5.91378e16	−1.02497	−0.512484	−	0.858697i	$-0.671275\pi$
$379$	−5.91378e16	−1.02497	−0.512484	+	0.858697i	$0.671275\pi$
$380$	7.53213e16	1.28329
$381$	−6.54180e16	−1.09568
$382$	3.95852e16	0.651810
$383$	4.85252e16	0.785553	0.392776	−	0.919634i	$-0.371515\pi$
$383$	4.85252e16	0.785553	0.392776	+	0.919634i	$0.371515\pi$
$384$	−2.38376e16	−0.379411
$385$	1.92122e15	0.0300665
$386$	−4.13991e16	−0.637050
$387$	−3.07814e16	−0.465765
$388$	8.54705e15	0.127177
$389$	−3.93773e16	−0.576201	−0.288100	−	0.957600i	$-0.593024\pi$
$389$	−3.93773e16	−0.576201	−0.288100	+	0.957600i	$0.593024\pi$
$390$	−9.53241e16	−1.37177
$391$	−2.43038e16	−0.343973
$392$	2.14815e16	0.299023
$393$	1.21077e16	0.165771
$394$	−1.51446e17	−2.03955
$395$	−1.74073e16	−0.230596
$396$	1.34684e15	0.0175508
$397$	4.96288e15	0.0636202	0.0318101	−	0.999494i	$-0.489873\pi$
$397$	4.96288e15	0.0636202	0.0318101	+	0.999494i	$0.489873\pi$
$398$	1.05152e17	1.32610
$399$	−2.27794e16	−0.282631
$400$	−4.84930e16	−0.591956
$401$	6.78323e16	0.814701	0.407351	−	0.913272i	$-0.366453\pi$
$401$	6.78323e16	0.814701	0.407351	+	0.913272i	$0.366453\pi$
$402$	−1.33508e16	−0.157775
$403$	1.10114e17	1.28044
$404$	6.32466e16	0.723700
$405$	−1.20731e16	−0.135945
$406$	−4.65019e15	−0.0515290
$407$	−5.59402e15	−0.0610043
$408$	5.63066e15	0.0604321
$409$	−7.30349e16	−0.771487	−0.385744	−	0.922606i	$-0.626055\pi$
$409$	−7.30349e16	−0.771487	−0.385744	+	0.922606i	$0.626055\pi$
$410$	−2.26358e17	−2.35343
$411$	2.24699e16	0.229947
$412$	−1.71177e16	−0.172431
$413$	−4.55028e15	−0.0451194
$414$	−5.03439e16	−0.491410
$415$	1.51653e17	1.45727
$416$	1.91674e17	1.81325
$417$	−2.85671e16	−0.266062
$418$	−1.44185e16	−0.132213
$419$	−8.82801e16	−0.797024	−0.398512	−	0.917163i	$-0.630473\pi$
$419$	−8.82801e16	−0.797024	−0.398512	+	0.917163i	$0.630473\pi$
$420$	−2.04495e16	−0.181787
$421$	1.49378e16	0.130753	0.0653767	−	0.997861i	$-0.479175\pi$
$421$	1.49378e16	0.130753	0.0653767	+	0.997861i	$0.479175\pi$
$422$	−2.78368e17	−2.39932
$423$	1.46260e16	0.124140
$424$	2.26138e16	0.189014
$425$	1.85950e16	0.153063
$426$	−1.71628e17	−1.39132
$427$	8.43863e16	0.673738
$428$	−4.17555e16	−0.328344
$429$	7.77582e15	0.0602246
$430$	2.95822e17	2.25676
$431$	−9.79364e16	−0.735939	−0.367969	−	0.929838i	$-0.619947\pi$
$431$	−9.79364e16	−0.735939	−0.367969	+	0.929838i	$0.619947\pi$
$432$	3.09696e16	0.229240
$433$	−4.09319e16	−0.298463	−0.149231	−	0.988802i	$-0.547680\pi$
$433$	−4.09319e16	−0.298463	−0.149231	+	0.988802i	$0.547680\pi$
$434$	5.54344e16	0.398196
$435$	1.12433e16	0.0795633
$436$	−1.60907e17	−1.12179
$437$	2.29664e17	1.57748
$438$	−3.03015e16	−0.205061
$439$	−1.74520e16	−0.116366	−0.0581831	−	0.998306i	$-0.518531\pi$
$439$	−1.74520e16	−0.116366	−0.0581831	+	0.998306i	$0.518531\pi$
$440$	4.48758e15	0.0294829
$441$	−4.53063e16	−0.293297
$442$	−9.37639e16	−0.598124
$443$	−1.48032e17	−0.930534	−0.465267	−	0.885171i	$-0.654042\pi$
$443$	−1.48032e17	−0.930534	−0.465267	+	0.885171i	$0.654042\pi$
$444$	5.95428e16	0.368842
$445$	−2.62376e17	−1.60171
$446$	−3.55508e17	−2.13881
$447$	1.25232e17	0.742534
$448$	2.58512e16	0.151068
$449$	−1.61796e17	−0.931897	−0.465948	−	0.884812i	$-0.654287\pi$
$449$	−1.61796e17	−0.931897	−0.465948	+	0.884812i	$0.654287\pi$
$450$	3.85186e16	0.218670
$451$	1.84646e16	0.103322
$452$	8.14416e16	0.449207
$453$	−1.66985e16	−0.0907901
$454$	−2.42191e17	−1.29806
$455$	−1.18063e17	−0.623791
$456$	−5.32082e16	−0.277145
$457$	−1.45094e17	−0.745063	−0.372532	−	0.928020i	$-0.621510\pi$
$457$	−1.45094e17	−0.745063	−0.372532	+	0.928020i	$0.621510\pi$
$458$	5.47246e16	0.277049
$459$	−1.18755e16	−0.0592748
$460$	2.06173e17	1.01463
$461$	−1.07176e17	−0.520048	−0.260024	−	0.965602i	$-0.583730\pi$
$461$	−1.07176e17	−0.520048	−0.260024	+	0.965602i	$0.583730\pi$
$462$	3.91457e15	0.0187288
$463$	−1.43063e17	−0.674919	−0.337460	−	0.941340i	$-0.609568\pi$
$463$	−1.43063e17	−0.674919	−0.337460	+	0.941340i	$0.609568\pi$
$464$	−2.88409e16	−0.134166
$465$	−1.34030e17	−0.614834
$466$	−5.45955e17	−2.46972
$467$	3.15097e17	1.40568	0.702838	−	0.711350i	$-0.251916\pi$
$467$	3.15097e17	1.40568	0.702838	+	0.711350i	$0.251916\pi$
$468$	−8.27659e16	−0.364128
$469$	−1.65355e16	−0.0717453
$470$	−1.40562e17	−0.601493
$471$	−1.86487e17	−0.787068
$472$	−1.06285e16	−0.0442436
$473$	−2.41310e16	−0.0990780
$474$	−3.54682e16	−0.143641
$475$	−1.75718e17	−0.701953
$476$	−2.01148e16	−0.0792630
$477$	−4.76943e16	−0.185395
$478$	−2.79891e17	−1.07327
$479$	1.71433e17	0.648506	0.324253	−	0.945970i	$-0.394887\pi$
$479$	1.71433e17	0.648506	0.324253	+	0.945970i	$0.394887\pi$
$480$	−2.33304e17	−0.870673
$481$	3.43764e17	1.26566
$482$	−1.86383e17	−0.677017
$483$	−6.23530e16	−0.223460
$484$	−2.08946e17	−0.738822
$485$	−6.00630e16	−0.209549
$486$	−2.45995e16	−0.0846818
$487$	−1.46410e17	−0.497316	−0.248658	−	0.968591i	$-0.579990\pi$
$487$	−1.46410e17	−0.497316	−0.248658	+	0.968591i	$0.579990\pi$
$488$	1.97109e17	0.660660
$489$	−3.47580e17	−1.14960
$490$	4.35412e17	1.42111
$491$	2.38736e17	0.768934	0.384467	−	0.923139i	$-0.374385\pi$
$491$	2.38736e17	0.768934	0.384467	+	0.923139i	$0.374385\pi$
$492$	−1.96537e17	−0.624701
$493$	1.10593e16	0.0346914
$494$	8.86044e17	2.74303
$495$	−9.46468e15	−0.0289183
$496$	3.43809e17	1.03678
$497$	−2.12568e17	−0.632677
$498$	3.09000e17	0.907752
$499$	−5.82602e17	−1.68935	−0.844673	−	0.535283i	$-0.820205\pi$
$499$	−5.82602e17	−1.68935	−0.844673	+	0.535283i	$0.820205\pi$
$500$	1.59678e17	0.457026
$501$	−6.67876e15	−0.0188691
$502$	−2.87839e17	−0.802740
$503$	−5.25377e17	−1.44637	−0.723184	−	0.690655i	$-0.757322\pi$
$503$	−5.25377e17	−1.44637	−0.723184	+	0.690655i	$0.757322\pi$
$504$	1.44458e16	0.0392594
$505$	−4.44455e17	−1.19243
$506$	−3.94669e16	−0.104533
$507$	−2.57044e17	−0.672134
$508$	5.45870e17	1.40921
$509$	−7.38641e15	−0.0188264	−0.00941321	−	0.999956i	$-0.502996\pi$
$509$	−7.38641e15	−0.0188264	−0.00941321	+	0.999956i	$0.502996\pi$
$510$	1.14129e17	0.287203
$511$	−3.75296e16	−0.0932477
$512$	4.33457e17	1.06339
$513$	1.12220e17	0.271837
$514$	9.39681e17	2.24761
$515$	1.20292e17	0.284112
$516$	2.56850e17	0.599041
$517$	1.14660e16	0.0264072
$518$	1.73060e17	0.393599
$519$	2.28260e16	0.0512675
$520$	−2.75771e17	−0.611683
$521$	−9.97310e16	−0.218467	−0.109233	−	0.994016i	$-0.534840\pi$
$521$	−9.97310e16	−0.218467	−0.109233	+	0.994016i	$0.534840\pi$
$522$	2.29087e16	0.0495611
$523$	−3.81983e17	−0.816174	−0.408087	−	0.912943i	$-0.633804\pi$
$523$	−3.81983e17	−0.816174	−0.408087	+	0.912943i	$0.633804\pi$
$524$	−1.01030e17	−0.213206
$525$	4.77068e16	0.0994363
$526$	6.06519e17	1.24864
$527$	−1.31836e17	−0.268081
$528$	2.42785e16	0.0487642
$529$	1.24610e17	0.247225
$530$	4.58363e17	0.898289
$531$	2.24165e16	0.0433963
$532$	1.90079e17	0.363504
$533$	−1.13469e18	−2.14363
$534$	−5.34601e17	−0.997727
$535$	2.93430e17	0.541009
$536$	−3.86235e16	−0.0703527
$537$	3.31803e17	0.597100
$538$	2.28525e17	0.406301
$539$	−3.55177e16	−0.0623904
$540$	1.00742e17	0.174844
$541$	−2.49163e17	−0.427269	−0.213634	−	0.976914i	$-0.568530\pi$
$541$	−2.49163e17	−0.427269	−0.213634	+	0.976914i	$0.568530\pi$
$542$	1.14467e18	1.93948
$543$	6.40466e17	1.07225
$544$	−2.29486e17	−0.379632
$545$	1.13074e18	1.84836
$546$	−2.40558e17	−0.388568
$547$	6.73885e17	1.07564	0.537821	−	0.843059i	$-0.319248\pi$
$547$	6.73885e17	1.07564	0.537821	+	0.843059i	$0.319248\pi$
$548$	−1.87496e17	−0.295745
$549$	−4.15720e17	−0.648008
$550$	3.01965e16	0.0465157
$551$	−1.04507e17	−0.159096
$552$	−1.45644e17	−0.219123
$553$	−4.39288e16	−0.0653184
$554$	8.23804e17	1.21063
$555$	−4.18427e17	−0.607737
$556$	2.38374e17	0.342194
$557$	−7.59749e17	−1.07798	−0.538991	−	0.842312i	$-0.681194\pi$
$557$	−7.59749e17	−1.07798	−0.538991	+	0.842312i	$0.681194\pi$
$558$	−2.73092e17	−0.382989
$559$	1.48290e18	2.05558
$560$	−3.68628e17	−0.505087
$561$	−9.30977e15	−0.0126090
$562$	−5.78618e15	−0.00774651
$563$	8.92763e17	1.18149	0.590747	−	0.806857i	$-0.298833\pi$
$563$	8.92763e17	1.18149	0.590747	+	0.806857i	$0.298833\pi$
$564$	−1.22044e17	−0.159662
$565$	−5.72317e17	−0.740153
$566$	−4.56652e17	−0.583819
$567$	−3.04675e16	−0.0385076
$568$	−4.96517e17	−0.620397
$569$	2.58170e17	0.318915	0.159458	−	0.987205i	$-0.449025\pi$
$569$	2.58170e17	0.318915	0.159458	+	0.987205i	$0.449025\pi$
$570$	−1.07849e18	−1.31713
$571$	−1.88749e17	−0.227902	−0.113951	−	0.993486i	$-0.536351\pi$
$571$	−1.88749e17	−0.227902	−0.113951	+	0.993486i	$0.536351\pi$
$572$	−6.48840e16	−0.0774576
$573$	−2.41531e17	−0.285080
$574$	−5.71233e17	−0.666632
$575$	−4.80983e17	−0.554995
$576$	−1.27353e17	−0.145299
$577$	1.08259e17	0.122130	0.0610649	−	0.998134i	$-0.480550\pi$
$577$	1.08259e17	0.122130	0.0610649	+	0.998134i	$0.480550\pi$
$578$	−1.07112e18	−1.19483
$579$	2.52598e17	0.278625
$580$	−9.38177e16	−0.102330
$581$	3.82709e17	0.412785
$582$	−1.22381e17	−0.130531
$583$	−3.73898e16	−0.0394373
$584$	−8.76616e16	−0.0914378
$585$	5.81623e17	0.599969
$586$	9.48942e17	0.968066
$587$	1.15860e18	1.16892	0.584462	−	0.811421i	$-0.301306\pi$
$587$	1.15860e18	1.16892	0.584462	+	0.811421i	$0.301306\pi$
$588$	3.78050e17	0.377222
$589$	1.24582e18	1.22943
$590$	−2.15432e17	−0.210267
$591$	9.24056e17	0.892030
$592$	1.07334e18	1.02481
$593$	−1.76287e18	−1.66481	−0.832404	−	0.554169i	$-0.813036\pi$
$593$	−1.76287e18	−1.66481	−0.832404	+	0.554169i	$0.813036\pi$
$594$	−1.92847e16	−0.0180136
$595$	1.41353e17	0.130601
$596$	−1.04498e18	−0.955006
$597$	−6.41587e17	−0.579993
$598$	2.42532e18	2.16876
$599$	−1.29312e18	−1.14383	−0.571917	−	0.820311i	$-0.693800\pi$
$599$	−1.29312e18	−1.14383	−0.571917	+	0.820311i	$0.693800\pi$
$600$	1.11433e17	0.0975063
$601$	−9.02036e17	−0.780800	−0.390400	−	0.920645i	$-0.627663\pi$
$601$	−9.02036e17	−0.780800	−0.390400	+	0.920645i	$0.627663\pi$
$602$	7.46531e17	0.639250
$603$	8.14603e16	0.0690055
$604$	1.39338e17	0.116769
$605$	1.46834e18	1.21735
$606$	−9.05595e17	−0.742783
$607$	1.89107e18	1.53455	0.767275	−	0.641318i	$-0.221612\pi$
$607$	1.89107e18	1.53455	0.767275	+	0.641318i	$0.221612\pi$
$608$	2.16858e18	1.74101
$609$	2.83733e16	0.0225371
$610$	3.99525e18	3.13978
$611$	−7.04606e17	−0.547871
$612$	9.90933e16	0.0762360
$613$	5.21411e17	0.396906	0.198453	−	0.980110i	$-0.436408\pi$
$613$	5.21411e17	0.396906	0.198453	+	0.980110i	$0.436408\pi$
$614$	−3.14568e18	−2.36930
$615$	1.38113e18	1.02931
$616$	1.13248e16	0.00835131
$617$	−1.94041e18	−1.41593	−0.707963	−	0.706250i	$-0.750385\pi$
$617$	−1.94041e18	−1.41593	−0.707963	+	0.706250i	$0.750385\pi$
$618$	2.45100e17	0.176977
$619$	1.10530e18	0.789751	0.394876	−	0.918735i	$-0.370788\pi$
$619$	1.10530e18	0.789751	0.394876	+	0.918735i	$0.370788\pi$
$620$	1.11839e18	0.790765
$621$	3.07175e17	0.214927
$622$	−1.93575e18	−1.34033
$623$	−6.62125e17	−0.453699
$624$	−1.49196e18	−1.01171
$625$	−1.86263e18	−1.24999
$626$	1.94281e18	1.29032
$627$	8.79748e16	0.0578255
$628$	1.55611e18	1.01228
$629$	−4.11579e17	−0.264987
$630$	2.92805e17	0.186580
$631$	−3.06106e18	−1.93055	−0.965275	−	0.261236i	$-0.915870\pi$
$631$	−3.06106e18	−1.93055	−0.965275	+	0.261236i	$0.915870\pi$
$632$	−1.02609e17	−0.0640506
$633$	1.69847e18	1.04938
$634$	2.65726e18	1.62500
$635$	−3.83601e18	−2.32193
$636$	3.97977e17	0.238444
$637$	2.18263e18	1.29442
$638$	1.79592e16	0.0105427
$639$	1.04720e18	0.608516
$640$	−1.39780e18	−0.804035
$641$	−2.23247e18	−1.27119	−0.635593	−	0.772024i	$-0.719244\pi$
$641$	−2.23247e18	−1.27119	−0.635593	+	0.772024i	$0.719244\pi$
$642$	5.97875e17	0.337002
$643$	−2.00490e18	−1.11872	−0.559360	−	0.828925i	$-0.688953\pi$
$643$	−2.00490e18	−1.11872	−0.559360	+	0.828925i	$0.688953\pi$
$644$	5.20294e17	0.287402
$645$	−1.80497e18	−0.987034
$646$	−1.06084e18	−0.574297
$647$	−8.05563e16	−0.0431739	−0.0215870	−	0.999767i	$-0.506872\pi$
$647$	−8.05563e16	−0.0431739	−0.0215870	+	0.999767i	$0.506872\pi$
$648$	−7.11658e16	−0.0377602
$649$	1.75733e16	0.00923130
$650$	−1.85564e18	−0.965063
$651$	−3.38235e17	−0.174158
$652$	2.90033e18	1.47856
$653$	2.38604e18	1.20432	0.602160	−	0.798375i	$-0.294307\pi$
$653$	2.38604e18	1.20432	0.602160	+	0.798375i	$0.294307\pi$
$654$	2.30394e18	1.15137
$655$	7.09974e17	0.351296
$656$	−3.54284e18	−1.73571
$657$	1.84886e17	0.0896867
$658$	−3.54718e17	−0.170379
$659$	2.97088e18	1.41296	0.706480	−	0.707733i	$-0.250282\pi$
$659$	2.97088e18	1.41296	0.706480	+	0.707733i	$0.250282\pi$
$660$	7.89764e16	0.0371931
$661$	1.26785e18	0.591233	0.295616	−	0.955307i	$-0.404475\pi$
$661$	1.26785e18	0.591233	0.295616	+	0.955307i	$0.404475\pi$
$662$	−3.04592e18	−1.40651
$663$	5.72104e17	0.261600
$664$	8.93930e17	0.404773
$665$	−1.33575e18	−0.598941
$666$	−8.52563e17	−0.378568
$667$	−2.86061e17	−0.125789
$668$	5.57298e16	0.0242684
$669$	2.16914e18	0.935445
$670$	−7.82868e17	−0.334351
$671$	−3.25902e17	−0.137845
$672$	−5.88762e17	−0.246626
$673$	−1.58705e18	−0.658405	−0.329202	−	0.944259i	$-0.606780\pi$
$673$	−1.58705e18	−0.658405	−0.329202	+	0.944259i	$0.606780\pi$
$674$	2.76218e18	1.13491
$675$	−2.35023e17	−0.0956390
$676$	2.14486e18	0.864461
$677$	2.24728e17	0.0897080	0.0448540	−	0.998994i	$-0.485718\pi$
$677$	2.24728e17	0.0897080	0.0448540	+	0.998994i	$0.485718\pi$
$678$	−1.16612e18	−0.461052
$679$	−1.51574e17	−0.0593568
$680$	3.30172e17	0.128066
$681$	1.47773e18	0.567728
$682$	−2.14089e17	−0.0814698
$683$	−4.77481e16	−0.0179979	−0.00899894	−	0.999960i	$-0.502864\pi$
$683$	−4.77481e16	−0.0179979	−0.00899894	+	0.999960i	$0.502864\pi$
$684$	−9.36405e17	−0.349622
$685$	1.31760e18	0.487297
$686$	2.34759e18	0.860032
$687$	−3.33904e17	−0.121172
$688$	4.63005e18	1.66441
$689$	2.29768e18	0.818209
$690$	−2.95208e18	−1.04138
$691$	−2.87840e18	−1.00588	−0.502938	−	0.864322i	$-0.667748\pi$
$691$	−2.87840e18	−1.00588	−0.502938	+	0.864322i	$0.667748\pi$
$692$	−1.90468e17	−0.0659375
$693$	−2.38849e16	−0.00819137
$694$	−4.26713e18	−1.44977
$695$	−1.67513e18	−0.563829
$696$	6.62743e16	0.0220996
$697$	1.35853e18	0.448803
$698$	6.98528e17	0.228625
$699$	3.33116e18	1.08018
$700$	−3.98082e17	−0.127890
$701$	−3.76047e17	−0.119695	−0.0598474	−	0.998208i	$-0.519061\pi$
$701$	−3.76047e17	−0.119695	−0.0598474	+	0.998208i	$0.519061\pi$
$702$	1.18508e18	0.373729
$703$	3.88931e18	1.21524
$704$	−9.98378e16	−0.0309081
$705$	8.57642e17	0.263073
$706$	−5.25019e18	−1.59568
$707$	−1.12162e18	−0.337768
$708$	−1.87050e17	−0.0558139
$709$	3.32581e18	0.983325	0.491663	−	0.870786i	$-0.336389\pi$
$709$	3.32581e18	0.983325	0.491663	+	0.870786i	$0.336389\pi$
$710$	−1.00640e19	−2.94843
$711$	2.16410e17	0.0628240
$712$	−1.54659e18	−0.444893
$713$	3.41011e18	0.972045
$714$	2.88013e17	0.0813531
$715$	4.55962e17	0.127626
$716$	−2.76867e18	−0.767957
$717$	1.70777e18	0.469412
$718$	3.79142e18	1.03275
$719$	−4.89049e18	−1.32012	−0.660062	−	0.751211i	$-0.729470\pi$
$719$	−4.89049e18	−1.32012	−0.660062	+	0.751211i	$0.729470\pi$
$720$	1.81600e18	0.485798
$721$	3.03566e17	0.0804775
$722$	5.00019e18	1.31370
$723$	1.13722e18	0.296105
$724$	−5.34426e18	−1.37907
$725$	2.18868e17	0.0559739
$726$	2.99179e18	0.758305
$727$	4.08570e18	1.02634	0.513172	−	0.858286i	$-0.328470\pi$
$727$	4.08570e18	1.02634	0.513172	+	0.858286i	$0.328470\pi$
$728$	−6.95929e17	−0.173265
$729$	1.50095e17	0.0370370
$730$	−1.77683e18	−0.434557
$731$	−1.77543e18	−0.430368
$732$	3.46891e18	0.833432
$733$	5.62648e18	1.33986	0.669932	−	0.742422i	$-0.266323\pi$
$733$	5.62648e18	1.33986	0.669932	+	0.742422i	$0.266323\pi$
$734$	−8.33220e18	−1.96669
$735$	−2.65668e18	−0.621545
$736$	5.93594e18	1.37652
$737$	6.38605e16	0.0146789
$738$	2.81412e18	0.641174
$739$	−4.37876e18	−0.988923	−0.494462	−	0.869199i	$-0.664635\pi$
$739$	−4.37876e18	−0.988923	−0.494462	+	0.869199i	$0.664635\pi$
$740$	3.49149e18	0.781637
$741$	−5.40623e18	−1.19971
$742$	1.15671e18	0.254449
$743$	2.55838e18	0.557875	0.278938	−	0.960309i	$-0.410018\pi$
$743$	2.55838e18	0.557875	0.278938	+	0.960309i	$0.410018\pi$
$744$	−7.90049e17	−0.170777
$745$	7.34340e18	1.57355
$746$	3.22330e18	0.684697
$747$	−1.88537e18	−0.397021
$748$	7.76838e16	0.0162170
$749$	7.40493e17	0.153246
$750$	−2.28635e18	−0.469077
$751$	6.33861e17	0.128924	0.0644621	−	0.997920i	$-0.479467\pi$
$751$	6.33861e17	0.128924	0.0644621	+	0.997920i	$0.479467\pi$
$752$	−2.19999e18	−0.443614
$753$	1.75626e18	0.351092
$754$	−1.10363e18	−0.218730
$755$	−9.79171e17	−0.192399
$756$	2.54231e17	0.0495263
$757$	1.87341e18	0.361834	0.180917	−	0.983498i	$-0.442093\pi$
$757$	1.87341e18	0.361834	0.180917	+	0.983498i	$0.442093\pi$
$758$	−7.06567e18	−1.35302
$759$	2.40809e17	0.0457194
$760$	−3.12004e18	−0.587316
$761$	−2.24015e18	−0.418097	−0.209049	−	0.977905i	$-0.567037\pi$
$761$	−2.24015e18	−0.418097	−0.209049	+	0.977905i	$0.567037\pi$
$762$	−7.81602e18	−1.44637
$763$	2.85352e18	0.523566
$764$	2.01541e18	0.366655
$765$	−6.96361e17	−0.125613
$766$	5.79770e18	1.03698
$767$	−1.07991e18	−0.191522
$768$	−4.27918e18	−0.752510
$769$	4.33439e18	0.755799	0.377899	−	0.925847i	$-0.376646\pi$
$769$	4.33439e18	0.755799	0.377899	+	0.925847i	$0.376646\pi$
$770$	2.29544e17	0.0396895
$771$	−5.73350e18	−0.983029
$772$	−2.10776e18	−0.358352
$773$	8.30934e18	1.40088	0.700439	−	0.713713i	$-0.252988\pi$
$773$	8.30934e18	1.40088	0.700439	+	0.713713i	$0.252988\pi$
$774$	−3.67770e18	−0.614838
$775$	−2.60911e18	−0.432545
$776$	−3.54045e17	−0.0582046
$777$	−1.05593e18	−0.172147
$778$	−4.70473e18	−0.760619
$779$	−1.28377e19	−2.05823
$780$	−4.85326e18	−0.771647
$781$	8.20945e17	0.129444
$782$	−2.90377e18	−0.454065
$783$	−1.39778e17	−0.0216764
$784$	6.81484e18	1.04810
$785$	−1.09353e19	−1.66793
$786$	1.44660e18	0.218828
$787$	5.22885e18	0.784459	0.392229	−	0.919867i	$-0.371704\pi$
$787$	5.22885e18	0.784459	0.392229	+	0.919867i	$0.371704\pi$
$788$	−7.71063e18	−1.14728
$789$	−3.70070e18	−0.546114
$790$	−2.07979e18	−0.304400
$791$	−1.44429e18	−0.209656
$792$	−5.57902e16	−0.00803238
$793$	2.00273e19	2.85988
$794$	5.92955e17	0.0839824
$795$	−2.79672e18	−0.392882
$796$	5.35362e18	0.745954
$797$	1.19564e19	1.65243	0.826213	−	0.563357i	$-0.190491\pi$
$797$	1.19564e19	1.65243	0.826213	+	0.563357i	$0.190491\pi$
$798$	−2.72165e18	−0.373089
$799$	8.43605e17	0.114706
$800$	−4.54164e18	−0.612531
$801$	3.26189e18	0.436373
$802$	8.10448e18	1.07545
$803$	1.44940e17	0.0190782
$804$	−6.79732e17	−0.0887510
$805$	−3.65628e18	−0.473550
$806$	1.31562e19	1.69026
$807$	−1.39435e18	−0.177703
$808$	−2.61987e18	−0.331212
$809$	−8.65418e18	−1.08533	−0.542663	−	0.839950i	$-0.682584\pi$
$809$	−8.65418e18	−1.08533	−0.542663	+	0.839950i	$0.682584\pi$
$810$	−1.44247e18	−0.179455
$811$	1.48926e19	1.83796	0.918979	−	0.394305i	$-0.129015\pi$
$811$	1.48926e19	1.83796	0.918979	+	0.394305i	$0.129015\pi$
$812$	−2.36756e17	−0.0289859
$813$	−6.98426e18	−0.848265
$814$	−6.68363e17	−0.0805293
$815$	−2.03815e19	−2.43620
$816$	1.78628e18	0.211819
$817$	1.67773e19	1.97369
$818$	−8.72607e18	−1.01841
$819$	1.46777e18	0.169947
$820$	−1.15246e19	−1.32384
$821$	5.03269e18	0.573548	0.286774	−	0.957998i	$-0.407417\pi$
$821$	5.03269e18	0.573548	0.286774	+	0.957998i	$0.407417\pi$
$822$	2.68466e18	0.303544
$823$	6.18465e18	0.693771	0.346886	−	0.937907i	$-0.387239\pi$
$823$	6.18465e18	0.693771	0.346886	+	0.937907i	$0.387239\pi$
$824$	7.09069e17	0.0789154
$825$	−1.84245e17	−0.0203444
$826$	−5.43659e17	−0.0595602
$827$	3.69281e18	0.401394	0.200697	−	0.979653i	$-0.435679\pi$
$827$	3.69281e18	0.401394	0.200697	+	0.979653i	$0.435679\pi$
$828$	−2.56317e18	−0.276427
$829$	2.69471e18	0.288341	0.144171	−	0.989553i	$-0.453949\pi$
$829$	2.69471e18	0.288341	0.144171	+	0.989553i	$0.453949\pi$
$830$	1.81192e19	1.92368
$831$	−5.02647e18	−0.529488
$832$	6.13523e18	0.641253
$833$	−2.61320e18	−0.271007
$834$	−3.41315e18	−0.351217
$835$	−3.91632e17	−0.0399867
$836$	−7.34091e17	−0.0743719
$837$	1.66628e18	0.167507
$838$	−1.05475e19	−1.05212
$839$	1.53523e19	1.51957	0.759786	−	0.650174i	$-0.225304\pi$
$839$	1.53523e19	1.51957	0.759786	+	0.650174i	$0.225304\pi$
$840$	8.47080e17	0.0831973
$841$	−1.01305e19	−0.987314
$842$	1.78474e18	0.172602
$843$	3.53046e16	0.00338807
$844$	−1.41726e19	−1.34966
$845$	−1.50726e19	−1.42436
$846$	1.74748e18	0.163872
$847$	3.70546e18	0.344826
$848$	7.17404e18	0.662508
$849$	2.78628e18	0.255343
$850$	2.22170e18	0.202052
$851$	1.06460e19	0.960824
$852$	−8.73814e18	−0.782640
$853$	−3.54078e18	−0.314724	−0.157362	−	0.987541i	$-0.550299\pi$
$853$	−3.54078e18	−0.314724	−0.157362	+	0.987541i	$0.550299\pi$
$854$	1.00823e19	0.889374
$855$	6.58042e18	0.576068
$856$	1.72964e18	0.150272
$857$	1.76765e19	1.52413	0.762064	−	0.647502i	$-0.224186\pi$
$857$	1.76765e19	1.52413	0.762064	+	0.647502i	$0.224186\pi$
$858$	9.29041e17	0.0795000
$859$	1.81966e19	1.54538	0.772690	−	0.634783i	$-0.218911\pi$
$859$	1.81966e19	1.54538	0.772690	+	0.634783i	$0.218911\pi$
$860$	1.50613e19	1.26947
$861$	3.48540e18	0.291563
$862$	−1.17013e19	−0.971483
$863$	−2.16635e19	−1.78508	−0.892542	−	0.450964i	$-0.851080\pi$
$863$	−2.16635e19	−1.78508	−0.892542	+	0.450964i	$0.851080\pi$
$864$	2.90047e18	0.237208
$865$	1.33848e18	0.108644
$866$	−4.89046e18	−0.393989
$867$	6.53547e18	0.522580
$868$	2.82235e18	0.223992
$869$	1.69654e17	0.0133640
$870$	1.34333e18	0.105028
$871$	−3.92436e18	−0.304544
$872$	6.66524e18	0.513403
$873$	7.46711e17	0.0570900
$874$	2.74398e19	2.08236
$875$	−2.83174e18	−0.213305
$876$	−1.54275e18	−0.115350
$877$	−1.48158e19	−1.09958	−0.549790	−	0.835303i	$-0.685292\pi$
$877$	−1.48158e19	−1.09958	−0.549790	+	0.835303i	$0.685292\pi$
$878$	−2.08514e18	−0.153610
$879$	−5.79000e18	−0.423400
$880$	1.42365e18	0.103339
$881$	2.30353e18	0.165978	0.0829890	−	0.996550i	$-0.473553\pi$
$881$	2.30353e18	0.165978	0.0829890	+	0.996550i	$0.473553\pi$
$882$	−5.41310e18	−0.387169
$883$	−1.73519e18	−0.123198	−0.0615989	−	0.998101i	$-0.519620\pi$
$883$	−1.73519e18	−0.123198	−0.0615989	+	0.998101i	$0.519620\pi$
$884$	−4.77383e18	−0.336455
$885$	1.31446e18	0.0919640
$886$	−1.76866e19	−1.22836
$887$	9.68715e18	0.667871	0.333936	−	0.942596i	$-0.391623\pi$
$887$	9.68715e18	0.667871	0.333936	+	0.942596i	$0.391623\pi$
$888$	−2.46645e18	−0.168806
$889$	−9.68046e18	−0.657710
$890$	−3.13481e19	−2.11435
$891$	1.17666e17	0.00787855
$892$	−1.81001e19	−1.20312
$893$	−7.97184e18	−0.526046
$894$	1.49625e19	0.980189
$895$	1.94564e19	1.26535
$896$	−3.52746e18	−0.227751
$897$	−1.47982e19	−0.948544
$898$	−1.93311e19	−1.23016
$899$	−1.55175e18	−0.0980355
$900$	1.96111e18	0.123006
$901$	−2.75094e18	−0.171305
$902$	2.20612e18	0.136391
$903$	−4.55499e18	−0.279587
$904$	−3.37356e18	−0.205586
$905$	3.75559e19	2.27228
$906$	−1.99510e18	−0.119848
$907$	−1.23901e19	−0.738968	−0.369484	−	0.929237i	$-0.620466\pi$
$907$	−1.23901e19	−0.738968	−0.369484	+	0.929237i	$0.620466\pi$
$908$	−1.23307e19	−0.730180
$909$	5.52552e18	0.324869
$910$	−1.41059e19	−0.823441
$911$	2.95236e19	1.71120	0.855598	−	0.517642i	$-0.173190\pi$
$911$	2.95236e19	1.71120	0.855598	+	0.517642i	$0.173190\pi$
$912$	−1.68799e19	−0.971411
$913$	−1.47803e18	−0.0844547
$914$	−1.73355e19	−0.983527
$915$	−2.43771e19	−1.37324
$916$	2.78620e18	0.155845
$917$	1.79167e18	0.0995081
$918$	−1.41886e18	−0.0782463
$919$	1.57660e19	0.863317	0.431659	−	0.902037i	$-0.357929\pi$
$919$	1.57660e19	0.863317	0.431659	+	0.902037i	$0.357929\pi$
$920$	−8.54032e18	−0.464358
$921$	1.91935e19	1.03625
$922$	−1.28052e19	−0.686493
$923$	−5.04487e19	−2.68559
$924$	1.99303e17	0.0105353
$925$	−8.14535e18	−0.427552
$926$	−1.70929e19	−0.890933
$927$	−1.49549e18	−0.0774041
$928$	−2.70111e18	−0.138829
$929$	1.64535e19	0.839762	0.419881	−	0.907579i	$-0.362072\pi$
$929$	1.64535e19	0.839762	0.419881	+	0.907579i	$0.362072\pi$
$930$	−1.60137e19	−0.811617
$931$	2.46941e19	1.24285
$932$	−2.77963e19	−1.38926
$933$	1.18111e19	0.586217
$934$	3.76472e19	1.85557
$935$	−5.45910e17	−0.0267206
$936$	3.42842e18	0.166648
$937$	−1.70096e19	−0.821083	−0.410542	−	0.911842i	$-0.634660\pi$
$937$	−1.70096e19	−0.821083	−0.410542	+	0.911842i	$0.634660\pi$
$938$	−1.97563e18	−0.0947081
$939$	−1.18541e19	−0.564343
$940$	−7.15645e18	−0.338350
$941$	−3.77340e19	−1.77174	−0.885869	−	0.463935i	$-0.846437\pi$
$941$	−3.77340e19	−1.77174	−0.885869	+	0.463935i	$0.846437\pi$
$942$	−2.22811e19	−1.03898
$943$	−3.51400e19	−1.62733
$944$	−3.37182e18	−0.155077
$945$	−1.78656e18	−0.0816040
$946$	−2.88312e18	−0.130789
$947$	5.91926e18	0.266681	0.133341	−	0.991070i	$-0.457430\pi$
$947$	5.91926e18	0.266681	0.133341	+	0.991070i	$0.457430\pi$
$948$	−1.80580e18	−0.0808007
$949$	−8.90687e18	−0.395817
$950$	−2.09945e19	−0.926619
$951$	−1.62134e19	−0.710722
$952$	8.33216e17	0.0362758
$953$	1.25870e19	0.544276	0.272138	−	0.962258i	$-0.412269\pi$
$953$	1.25870e19	0.544276	0.272138	+	0.962258i	$0.412269\pi$
$954$	−5.69843e18	−0.244732
$955$	−1.41630e19	−0.604133
$956$	−1.42502e19	−0.603732
$957$	−1.09578e17	−0.00461103
$958$	2.04825e19	0.856066
$959$	3.32506e18	0.138031
$960$	−7.46776e18	−0.307913
$961$	−5.91931e18	−0.242420
$962$	4.10723e19	1.67075
$963$	−3.64796e18	−0.147394
$964$	−9.48935e18	−0.380834
$965$	1.48120e19	0.590452
$966$	−7.44981e18	−0.294981
$967$	7.23048e18	0.284378	0.142189	−	0.989840i	$-0.454586\pi$
$967$	7.23048e18	0.284378	0.142189	+	0.989840i	$0.454586\pi$
$968$	8.65520e18	0.338133
$969$	6.47272e18	0.251179
$970$	−7.17621e18	−0.276617
$971$	2.91241e19	1.11514	0.557568	−	0.830131i	$-0.311735\pi$
$971$	2.91241e19	1.11514	0.557568	+	0.830131i	$0.311735\pi$
$972$	−1.25244e18	−0.0476350
$973$	−4.22732e18	−0.159710
$974$	−1.74928e19	−0.656487
$975$	1.13222e19	0.422087
$976$	6.25314e19	2.31566
$977$	−1.69348e19	−0.622968	−0.311484	−	0.950251i	$-0.600826\pi$
$977$	−1.69348e19	−0.622968	−0.311484	+	0.950251i	$0.600826\pi$
$978$	−4.15283e19	−1.51754
$979$	2.55715e18	0.0928256
$980$	2.21683e19	0.799396
$981$	−1.40575e19	−0.503571
$982$	2.85238e19	1.01504
$983$	−1.73582e19	−0.613632	−0.306816	−	0.951769i	$-0.599264\pi$
$983$	−1.73582e19	−0.613632	−0.306816	+	0.951769i	$0.599264\pi$
$984$	8.14118e18	0.285903
$985$	5.41851e19	1.89036
$986$	1.32134e18	0.0457946
$987$	2.16433e18	0.0745180
$988$	4.51114e19	1.54300
$989$	4.59237e19	1.56049
$990$	−1.13082e18	−0.0381738
$991$	−5.36207e19	−1.79826	−0.899132	−	0.437677i	$-0.855801\pi$
$991$	−5.36207e19	−1.79826	−0.899132	+	0.437677i	$0.855801\pi$
$992$	3.21997e19	1.07282
$993$	1.85848e19	0.615159
$994$	−2.53973e19	−0.835172
$995$	−3.76216e19	−1.22910
$996$	1.57322e19	0.510626
$997$	1.51048e19	0.487077	0.243539	−	0.969891i	$-0.421692\pi$
$997$	1.51048e19	0.487077	0.243539	+	0.969891i	$0.421692\pi$
$998$	−6.96082e19	−2.23004
$999$	5.20194e18	0.165573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.27	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.27	✓	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)

\(f(q)\)	\(=\)	\(q+119.478 q^{2} -729.000 q^{3} +6083.02 q^{4} -42747.4 q^{5} -87099.5 q^{6} -107876. q^{7} -251977. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+119.478 q^{2} -729.000 q^{3} +6083.02 q^{4} -42747.4 q^{5} -87099.5 q^{6} -107876. q^{7} -251977. q^{8} +531441. q^{9} -5.10737e6 q^{10} +416621. q^{11} -4.43452e6 q^{12} -2.56022e7 q^{13} -1.28889e7 q^{14} +3.11628e7 q^{15} -7.99378e7 q^{16} +3.06528e7 q^{17} +6.34956e7 q^{18} -2.89661e8 q^{19} -2.60033e8 q^{20} +7.86419e7 q^{21} +4.97771e7 q^{22} -7.92872e8 q^{23} +1.83691e8 q^{24} +6.06634e8 q^{25} -3.05890e9 q^{26} -3.87420e8 q^{27} -6.56214e8 q^{28} +3.60791e8 q^{29} +3.72328e9 q^{30} -4.30096e9 q^{31} -7.48662e9 q^{32} -3.03717e8 q^{33} +3.66234e9 q^{34} +4.61143e9 q^{35} +3.23276e9 q^{36} -1.34271e10 q^{37} -3.46081e10 q^{38} +1.86640e10 q^{39} +1.07714e10 q^{40} +4.43199e10 q^{41} +9.39598e9 q^{42} -5.79206e10 q^{43} +2.53431e9 q^{44} -2.27177e10 q^{45} -9.47309e10 q^{46} +2.75213e10 q^{47} +5.82747e10 q^{48} -8.52517e10 q^{49} +7.24795e10 q^{50} -2.23459e10 q^{51} -1.55739e11 q^{52} -8.97453e10 q^{53} -4.62883e10 q^{54} -1.78095e10 q^{55} +2.71824e10 q^{56} +2.11163e11 q^{57} +4.31067e10 q^{58} +4.21805e10 q^{59} +1.89564e11 q^{60} -7.82250e11 q^{61} -5.13870e11 q^{62} -5.73299e10 q^{63} -2.39637e11 q^{64} +1.09443e12 q^{65} -3.62875e10 q^{66} +1.53282e11 q^{67} +1.86462e11 q^{68} +5.78004e11 q^{69} +5.50965e11 q^{70} +1.97048e12 q^{71} -1.33911e11 q^{72} +3.47895e11 q^{73} -1.60425e12 q^{74} -4.42236e11 q^{75} -1.76201e12 q^{76} -4.49436e10 q^{77} +2.22994e12 q^{78} +4.07214e11 q^{79} +3.41713e12 q^{80} +2.82430e11 q^{81} +5.29526e12 q^{82} -3.54766e12 q^{83} +4.78380e11 q^{84} -1.31033e12 q^{85} -6.92025e12 q^{86} -2.63017e11 q^{87} -1.04979e11 q^{88} +6.13782e12 q^{89} -2.71427e12 q^{90} +2.76187e12 q^{91} -4.82306e12 q^{92} +3.13540e12 q^{93} +3.28819e12 q^{94} +1.23822e13 q^{95} +5.45775e12 q^{96} +1.40507e12 q^{97} -1.01857e13 q^{98} +2.21410e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 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

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