LMFDB - Embedded newform 177.14.a.d.1.13

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			1.13
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)

$f(q)$	$=$	$q-36.3263 q^{2} -729.000 q^{3} -6872.40 q^{4} +50926.0 q^{5} +26481.8 q^{6} -312829. q^{7} +547233. q^{8} +531441. q^{9} +O(q^{10})$	\(q-36.3263 q^{2} -729.000 q^{3} -6872.40 q^{4} +50926.0 q^{5} +26481.8 q^{6} -312829. q^{7} +547233. q^{8} +531441. q^{9} -1.84995e6 q^{10} -2.56725e6 q^{11} +5.00998e6 q^{12} -1.52376e7 q^{13} +1.13639e7 q^{14} -3.71251e7 q^{15} +3.64198e7 q^{16} -1.84400e8 q^{17} -1.93053e7 q^{18} -6.07523e7 q^{19} -3.49984e8 q^{20} +2.28052e8 q^{21} +9.32584e7 q^{22} +4.01014e8 q^{23} -3.98933e8 q^{24} +1.37276e9 q^{25} +5.53525e8 q^{26} -3.87420e8 q^{27} +2.14989e9 q^{28} -1.21250e9 q^{29} +1.34862e9 q^{30} +1.48417e9 q^{31} -5.80593e9 q^{32} +1.87152e9 q^{33} +6.69856e9 q^{34} -1.59311e10 q^{35} -3.65228e9 q^{36} -1.10503e10 q^{37} +2.20690e9 q^{38} +1.11082e10 q^{39} +2.78684e10 q^{40} +3.77778e10 q^{41} -8.28429e9 q^{42} -3.35887e10 q^{43} +1.76431e10 q^{44} +2.70642e10 q^{45} -1.45673e10 q^{46} -1.15649e10 q^{47} -2.65500e10 q^{48} +9.72922e8 q^{49} -4.98672e10 q^{50} +1.34428e11 q^{51} +1.04719e11 q^{52} +3.78314e10 q^{53} +1.40735e10 q^{54} -1.30740e11 q^{55} -1.71190e11 q^{56} +4.42885e10 q^{57} +4.40456e10 q^{58} +4.21805e10 q^{59} +2.55139e11 q^{60} -2.93008e11 q^{61} -5.39142e10 q^{62} -1.66250e11 q^{63} -8.74432e10 q^{64} -7.75991e11 q^{65} -6.79854e10 q^{66} -6.83114e11 q^{67} +1.26727e12 q^{68} -2.92339e11 q^{69} +5.78719e11 q^{70} +4.11493e11 q^{71} +2.90822e11 q^{72} -7.22231e11 q^{73} +4.01415e11 q^{74} -1.00074e12 q^{75} +4.17515e11 q^{76} +8.03109e11 q^{77} -4.03520e11 q^{78} -4.04241e12 q^{79} +1.85472e12 q^{80} +2.82430e11 q^{81} -1.37233e12 q^{82} +1.70460e12 q^{83} -1.56727e12 q^{84} -9.39076e12 q^{85} +1.22015e12 q^{86} +8.83914e11 q^{87} -1.40488e12 q^{88} -4.85952e12 q^{89} -9.83141e11 q^{90} +4.76676e12 q^{91} -2.75593e12 q^{92} -1.08196e12 q^{93} +4.20109e11 q^{94} -3.09388e12 q^{95} +4.23252e12 q^{96} -2.65734e12 q^{97} -3.53426e10 q^{98} -1.36434e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−36.3263	−0.401352	−0.200676	−	0.979658i	$-0.564314\pi$
$2$	−36.3263	−0.401352	−0.200676	+	0.979658i	$0.564314\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−6872.40	−0.838916
$5$	50926.0	1.45759	0.728794	−	0.684733i	$-0.240081\pi$
$5$	50926.0	1.45759	0.728794	+	0.684733i	$0.240081\pi$
$6$	26481.8	0.231721
$7$	−312829.	−1.00501	−0.502504	−	0.864575i	$-0.667588\pi$
$7$	−312829.	−1.00501	−0.502504	+	0.864575i	$0.667588\pi$
$8$	547233.	0.738053
$9$	531441.	0.333333
$10$	−1.84995e6	−0.585006
$11$	−2.56725e6	−0.436933	−0.218467	−	0.975844i	$-0.570105\pi$
$11$	−2.56725e6	−0.436933	−0.218467	+	0.975844i	$0.570105\pi$
$12$	5.00998e6	0.484349
$13$	−1.52376e7	−0.875558	−0.437779	−	0.899083i	$-0.644235\pi$
$13$	−1.52376e7	−0.875558	−0.437779	+	0.899083i	$0.644235\pi$
$14$	1.13639e7	0.403362
$15$	−3.71251e7	−0.841539
$16$	3.64198e7	0.542697
$17$	−1.84400e8	−1.85286	−0.926431	−	0.376466i	$-0.877139\pi$
$17$	−1.84400e8	−1.85286	−0.926431	+	0.376466i	$0.877139\pi$
$18$	−1.93053e7	−0.133784
$19$	−6.07523e7	−0.296254	−0.148127	−	0.988968i	$-0.547324\pi$
$19$	−6.07523e7	−0.296254	−0.148127	+	0.988968i	$0.547324\pi$
$20$	−3.49984e8	−1.22279
$21$	2.28052e8	0.580242
$22$	9.32584e7	0.175364
$23$	4.01014e8	0.564844	0.282422	−	0.959290i	$-0.408862\pi$
$23$	4.01014e8	0.564844	0.282422	+	0.959290i	$0.408862\pi$
$24$	−3.98933e8	−0.426115
$25$	1.37276e9	1.12456
$26$	5.53525e8	0.351407
$27$	−3.87420e8	−0.192450
$28$	2.14989e9	0.843118
$29$	−1.21250e9	−0.378526	−0.189263	−	0.981926i	$-0.560610\pi$
$29$	−1.21250e9	−0.378526	−0.189263	+	0.981926i	$0.560610\pi$
$30$	1.34862e9	0.337754
$31$	1.48417e9	0.300353	0.150176	−	0.988659i	$-0.452016\pi$
$31$	1.48417e9	0.300353	0.150176	+	0.988659i	$0.452016\pi$
$32$	−5.80593e9	−0.955866
$33$	1.87152e9	0.252263
$34$	6.69856e9	0.743650
$35$	−1.59311e10	−1.46489
$36$	−3.65228e9	−0.279639
$37$	−1.10503e10	−0.708047	−0.354023	−	0.935237i	$-0.615187\pi$
$37$	−1.10503e10	−0.708047	−0.354023	+	0.935237i	$0.615187\pi$
$38$	2.20690e9	0.118902
$39$	1.11082e10	0.505504
$40$	2.78684e10	1.07578
$41$	3.77778e10	1.24206	0.621028	−	0.783788i	$-0.286715\pi$
$41$	3.77778e10	1.24206	0.621028	+	0.783788i	$0.286715\pi$
$42$	−8.28429e9	−0.232881
$43$	−3.35887e10	−0.810306	−0.405153	−	0.914249i	$-0.632782\pi$
$43$	−3.35887e10	−0.810306	−0.405153	+	0.914249i	$0.632782\pi$
$44$	1.76431e10	0.366550
$45$	2.70642e10	0.485863
$46$	−1.45673e10	−0.226701
$47$	−1.15649e10	−0.156497	−0.0782484	−	0.996934i	$-0.524933\pi$
$47$	−1.15649e10	−0.156497	−0.0782484	+	0.996934i	$0.524933\pi$
$48$	−2.65500e10	−0.313326
$49$	9.72922e8	0.0100416
$50$	−4.98672e10	−0.451346
$51$	1.34428e11	1.06975
$52$	1.04719e11	0.734520
$53$	3.78314e10	0.234455	0.117228	−	0.993105i	$-0.462599\pi$
$53$	3.78314e10	0.234455	0.117228	+	0.993105i	$0.462599\pi$
$54$	1.40735e10	0.0772403
$55$	−1.30740e11	−0.636869
$56$	−1.71190e11	−0.741750
$57$	4.42885e10	0.171042
$58$	4.40456e10	0.151922
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	2.55139e11	0.705981
$61$	−2.93008e11	−0.728174	−0.364087	−	0.931365i	$-0.618619\pi$
$61$	−2.93008e11	−0.728174	−0.364087	+	0.931365i	$0.618619\pi$
$62$	−5.39142e10	−0.120547
$63$	−1.66250e11	−0.335003
$64$	−8.74432e10	−0.159058
$65$	−7.75991e11	−1.27620
$66$	−6.79854e10	−0.101247
$67$	−6.83114e11	−0.922586	−0.461293	−	0.887248i	$-0.652614\pi$
$67$	−6.83114e11	−0.922586	−0.461293	+	0.887248i	$0.652614\pi$
$68$	1.26727e12	1.55440
$69$	−2.92339e11	−0.326113
$70$	5.78719e11	0.587936
$71$	4.11493e11	0.381227	0.190613	−	0.981665i	$-0.438952\pi$
$71$	4.11493e11	0.381227	0.190613	+	0.981665i	$0.438952\pi$
$72$	2.90822e11	0.246018
$73$	−7.22231e11	−0.558570	−0.279285	−	0.960208i	$-0.590097\pi$
$73$	−7.22231e11	−0.558570	−0.279285	+	0.960208i	$0.590097\pi$
$74$	4.01415e11	0.284176
$75$	−1.00074e12	−0.649267
$76$	4.17515e11	0.248533
$77$	8.03109e11	0.439121
$78$	−4.03520e11	−0.202885
$79$	−4.04241e12	−1.87096	−0.935478	−	0.353384i	$-0.885031\pi$
$79$	−4.04241e12	−1.87096	−0.935478	+	0.353384i	$0.885031\pi$
$80$	1.85472e12	0.791029
$81$	2.82430e11	0.111111
$82$	−1.37233e12	−0.498502
$83$	1.70460e12	0.572290	0.286145	−	0.958186i	$-0.407626\pi$
$83$	1.70460e12	0.572290	0.286145	+	0.958186i	$0.407626\pi$
$84$	−1.56727e12	−0.486774
$85$	−9.39076e12	−2.70071
$86$	1.22015e12	0.325218
$87$	8.83914e11	0.218542
$88$	−1.40488e12	−0.322480
$89$	−4.85952e12	−1.03647	−0.518237	−	0.855237i	$-0.673411\pi$
$89$	−4.85952e12	−1.03647	−0.518237	+	0.855237i	$0.673411\pi$
$90$	−9.83141e11	−0.195002
$91$	4.76676e12	0.879943
$92$	−2.75593e12	−0.473857
$93$	−1.08196e12	−0.173409
$94$	4.20109e11	0.0628103
$95$	−3.09388e12	−0.431817
$96$	4.23252e12	0.551869
$97$	−2.65734e12	−0.323915	−0.161958	−	0.986798i	$-0.551781\pi$
$97$	−2.65734e12	−0.323915	−0.161958	+	0.986798i	$0.551781\pi$
$98$	−3.53426e10	−0.00403022
$99$	−1.36434e12	−0.145644
$100$	−9.43415e12	−0.943415
$101$	−7.72459e12	−0.724080	−0.362040	−	0.932163i	$-0.617920\pi$
$101$	−7.72459e12	−0.724080	−0.362040	+	0.932163i	$0.617920\pi$
$102$	−4.88325e12	−0.429346
$103$	−1.99440e13	−1.64578	−0.822889	−	0.568202i	$-0.807639\pi$
$103$	−1.99440e13	−1.64578	−0.822889	+	0.568202i	$0.807639\pi$
$104$	−8.33853e12	−0.646208
$105$	1.16138e13	0.845754
$106$	−1.37427e12	−0.0940991
$107$	6.99480e12	0.450589	0.225295	−	0.974291i	$-0.427666\pi$
$107$	6.99480e12	0.450589	0.225295	+	0.974291i	$0.427666\pi$
$108$	2.66251e12	0.161450
$109$	1.10349e13	0.630227	0.315113	−	0.949054i	$-0.397957\pi$
$109$	1.10349e13	0.630227	0.315113	+	0.949054i	$0.397957\pi$
$110$	4.74928e12	0.255609
$111$	8.05565e12	0.408791
$112$	−1.13932e13	−0.545415
$113$	5.76810e12	0.260629	0.130314	−	0.991473i	$-0.458401\pi$
$113$	5.76810e12	0.260629	0.130314	+	0.991473i	$0.458401\pi$
$114$	−1.60883e12	−0.0686483
$115$	2.04221e13	0.823310
$116$	8.33280e12	0.317551
$117$	−8.09789e12	−0.291853
$118$	−1.53226e12	−0.0522516
$119$	5.76856e13	1.86214
$120$	−2.03161e13	−0.621101
$121$	−2.79320e13	−0.809089
$122$	1.06439e13	0.292254
$123$	−2.75400e13	−0.717102
$124$	−1.01998e13	−0.251971
$125$	7.74358e12	0.181563
$126$	6.03924e12	0.134454
$127$	8.41152e13	1.77890	0.889448	−	0.457037i	$-0.151089\pi$
$127$	8.41152e13	1.77890	0.889448	+	0.457037i	$0.151089\pi$
$128$	5.07387e13	1.01970
$129$	2.44862e13	0.467830
$130$	2.81888e13	0.512207
$131$	−5.69154e12	−0.0983936	−0.0491968	−	0.998789i	$-0.515666\pi$
$131$	−5.69154e12	−0.0983936	−0.0491968	+	0.998789i	$0.515666\pi$
$132$	−1.28619e13	−0.211628
$133$	1.90051e13	0.297738
$134$	2.48150e13	0.370282
$135$	−1.97298e13	−0.280513
$136$	−1.00910e14	−1.36751
$137$	1.47831e14	1.91021	0.955107	−	0.296262i	$-0.0957400\pi$
$137$	1.47831e14	1.91021	0.955107	+	0.296262i	$0.0957400\pi$
$138$	1.06196e13	0.130886
$139$	−4.53301e13	−0.533077	−0.266539	−	0.963824i	$-0.585880\pi$
$139$	−4.53301e13	−0.533077	−0.266539	+	0.963824i	$0.585880\pi$
$140$	1.09485e14	1.22892
$141$	8.43080e12	0.0903534
$142$	−1.49480e13	−0.153006
$143$	3.91187e13	0.382560
$144$	1.93550e13	0.180899
$145$	−6.17479e13	−0.551735
$146$	2.62359e13	0.224183
$147$	−7.09260e11	−0.00579753
$148$	7.59419e13	0.593992
$149$	−1.32139e14	−0.989282	−0.494641	−	0.869097i	$-0.664701\pi$
$149$	−1.32139e14	−0.989282	−0.494641	+	0.869097i	$0.664701\pi$
$150$	3.63532e13	0.260585
$151$	−4.46794e13	−0.306731	−0.153365	−	0.988170i	$-0.549011\pi$
$151$	−4.46794e13	−0.306731	−0.153365	+	0.988170i	$0.549011\pi$
$152$	−3.32457e13	−0.218651
$153$	−9.79977e13	−0.617620
$154$	−2.91739e13	−0.176242
$155$	7.55827e13	0.437790
$156$	−7.63401e13	−0.424075
$157$	−1.40554e14	−0.749026	−0.374513	−	0.927222i	$-0.622190\pi$
$157$	−1.40554e14	−0.749026	−0.374513	+	0.927222i	$0.622190\pi$
$158$	1.46845e14	0.750913
$159$	−2.75791e13	−0.135363
$160$	−2.95673e14	−1.39326
$161$	−1.25449e14	−0.567673
$162$	−1.02596e13	−0.0445947
$163$	−3.69083e14	−1.54136	−0.770680	−	0.637222i	$-0.780083\pi$
$163$	−3.69083e14	−1.54136	−0.770680	+	0.637222i	$0.780083\pi$
$164$	−2.59624e14	−1.04198
$165$	9.53092e13	0.367696
$166$	−6.19219e13	−0.229690
$167$	2.53897e14	0.905733	0.452866	−	0.891578i	$-0.350401\pi$
$167$	2.53897e14	0.905733	0.452866	+	0.891578i	$0.350401\pi$
$168$	1.24798e14	0.428249
$169$	−7.06905e13	−0.233398
$170$	3.41131e14	1.08394
$171$	−3.22863e13	−0.0987514
$172$	2.30835e14	0.679779
$173$	1.50705e14	0.427393	0.213697	−	0.976900i	$-0.431450\pi$
$173$	1.50705e14	0.427393	0.213697	+	0.976900i	$0.431450\pi$
$174$	−3.21093e13	−0.0877123
$175$	−4.29439e14	−1.13020
$176$	−9.34985e13	−0.237122
$177$	−3.07496e13	−0.0751646
$178$	1.76528e14	0.415991
$179$	−7.04181e14	−1.60007	−0.800036	−	0.599952i	$-0.795186\pi$
$179$	−7.04181e14	−1.60007	−0.800036	+	0.599952i	$0.795186\pi$
$180$	−1.85996e14	−0.407598
$181$	3.97397e14	0.840066	0.420033	−	0.907509i	$-0.362018\pi$
$181$	3.97397e14	0.840066	0.420033	+	0.907509i	$0.362018\pi$
$182$	−1.73159e14	−0.353167
$183$	2.13603e14	0.420411
$184$	2.19448e14	0.416885
$185$	−5.62747e14	−1.03204
$186$	3.93034e13	0.0695979
$187$	4.73400e14	0.809576
$188$	7.94786e13	0.131288
$189$	1.21196e14	0.193414
$190$	1.12389e14	0.173311
$191$	8.25658e14	1.23050	0.615252	−	0.788330i	$-0.289054\pi$
$191$	8.25658e14	1.23050	0.615252	+	0.788330i	$0.289054\pi$
$192$	6.37461e13	0.0918323
$193$	2.73306e14	0.380651	0.190325	−	0.981721i	$-0.439046\pi$
$193$	2.73306e14	0.380651	0.190325	+	0.981721i	$0.439046\pi$
$194$	9.65313e13	0.130004
$195$	5.65697e14	0.736816
$196$	−6.68631e12	−0.00842408
$197$	1.26446e15	1.54126	0.770628	−	0.637285i	$-0.219943\pi$
$197$	1.26446e15	1.54126	0.770628	+	0.637285i	$0.219943\pi$
$198$	4.95614e13	0.0584547
$199$	−1.87735e14	−0.214289	−0.107145	−	0.994243i	$-0.534171\pi$
$199$	−1.87735e14	−0.214289	−0.107145	+	0.994243i	$0.534171\pi$
$200$	7.51219e14	0.829988
$201$	4.97990e14	0.532655
$202$	2.80605e14	0.290611
$203$	3.79306e14	0.380421
$204$	−9.23840e14	−0.897431
$205$	1.92387e15	1.81041
$206$	7.24492e14	0.660537
$207$	2.13115e14	0.188281
$208$	−5.54950e14	−0.475163
$209$	1.55966e14	0.129443
$210$	−4.21886e14	−0.339445
$211$	1.08127e15	0.843527	0.421763	−	0.906706i	$-0.361411\pi$
$211$	1.08127e15	0.843527	0.421763	+	0.906706i	$0.361411\pi$
$212$	−2.59993e14	−0.196688
$213$	−2.99979e14	−0.220101
$214$	−2.54095e14	−0.180845
$215$	−1.71054e15	−1.18109
$216$	−2.12009e14	−0.142038
$217$	−4.64290e14	−0.301857
$218$	−4.00857e14	−0.252943
$219$	5.26506e14	0.322490
$220$	8.98496e14	0.534280
$221$	2.80981e15	1.62229
$222$	−2.92632e14	−0.164069
$223$	1.27828e15	0.696054	0.348027	−	0.937484i	$-0.386852\pi$
$223$	1.27828e15	0.696054	0.348027	+	0.937484i	$0.386852\pi$
$224$	1.81626e15	0.960653
$225$	7.29540e14	0.374855
$226$	−2.09533e14	−0.104604
$227$	3.09769e15	1.50269	0.751345	−	0.659909i	$-0.229405\pi$
$227$	3.09769e15	1.50269	0.751345	+	0.659909i	$0.229405\pi$
$228$	−3.04368e14	−0.143490
$229$	−8.82595e14	−0.404418	−0.202209	−	0.979342i	$-0.564812\pi$
$229$	−8.82595e14	−0.404418	−0.202209	+	0.979342i	$0.564812\pi$
$230$	−7.41857e14	−0.330437
$231$	−5.85466e14	−0.253527
$232$	−6.63521e14	−0.279372
$233$	−7.35380e14	−0.301091	−0.150546	−	0.988603i	$-0.548103\pi$
$233$	−7.35380e14	−0.301091	−0.150546	+	0.988603i	$0.548103\pi$
$234$	2.94166e14	0.117136
$235$	−5.88954e14	−0.228108
$236$	−2.89882e14	−0.109218
$237$	2.94691e15	1.08020
$238$	−2.09550e15	−0.747374
$239$	1.29429e15	0.449205	0.224603	−	0.974450i	$-0.427892\pi$
$239$	1.29429e15	0.449205	0.224603	+	0.974450i	$0.427892\pi$
$240$	−1.35209e15	−0.456701
$241$	1.63898e14	0.0538845	0.0269422	−	0.999637i	$-0.491423\pi$
$241$	1.63898e14	0.0538845	0.0269422	+	0.999637i	$0.491423\pi$
$242$	1.01466e15	0.324730
$243$	−2.05891e14	−0.0641500
$244$	2.01367e15	0.610877
$245$	4.95471e13	0.0146365
$246$	1.00043e15	0.287810
$247$	9.25720e14	0.259388
$248$	8.12185e14	0.221676
$249$	−1.24266e15	−0.330412
$250$	−2.81295e14	−0.0728706
$251$	4.68428e14	0.118240	0.0591199	−	0.998251i	$-0.481171\pi$
$251$	4.68428e14	0.118240	0.0591199	+	0.998251i	$0.481171\pi$
$252$	1.14254e15	0.281039
$253$	−1.02950e15	−0.246799
$254$	−3.05559e15	−0.713964
$255$	6.84586e15	1.55925
$256$	−1.12681e15	−0.250202
$257$	7.26066e15	1.57185	0.785924	−	0.618323i	$-0.212188\pi$
$257$	7.26066e15	1.57185	0.785924	+	0.618323i	$0.212188\pi$
$258$	−8.89492e14	−0.187765
$259$	3.45685e15	0.711593
$260$	5.33292e15	1.07063
$261$	−6.44373e14	−0.126175
$262$	2.06753e14	0.0394905
$263$	−5.54009e14	−0.103230	−0.0516148	−	0.998667i	$-0.516437\pi$
$263$	−5.54009e14	−0.103230	−0.0516148	+	0.998667i	$0.516437\pi$
$264$	1.02416e15	0.186184
$265$	1.92661e15	0.341739
$266$	−6.90384e14	−0.119498
$267$	3.54259e15	0.598408
$268$	4.69463e15	0.773972
$269$	−1.06588e16	−1.71521	−0.857607	−	0.514305i	$-0.828050\pi$
$269$	−1.06588e16	−1.71521	−0.857607	+	0.514305i	$0.828050\pi$
$270$	7.16709e14	0.112585
$271$	9.70653e15	1.48855	0.744275	−	0.667873i	$-0.232795\pi$
$271$	9.70653e15	1.48855	0.744275	+	0.667873i	$0.232795\pi$
$272$	−6.71581e15	−1.00554
$273$	−3.47497e15	−0.508035
$274$	−5.37015e15	−0.766669
$275$	−3.52421e15	−0.491359
$276$	2.00907e15	0.273581
$277$	2.99781e15	0.398736	0.199368	−	0.979925i	$-0.436111\pi$
$277$	2.99781e15	0.398736	0.199368	+	0.979925i	$0.436111\pi$
$278$	1.64667e15	0.213952
$279$	7.88746e14	0.100118
$280$	−8.71805e15	−1.08117
$281$	1.10311e16	1.33668	0.668341	−	0.743855i	$-0.267005\pi$
$281$	1.10311e16	1.33668	0.668341	+	0.743855i	$0.267005\pi$
$282$	−3.06259e14	−0.0362636
$283$	−9.71964e15	−1.12470	−0.562352	−	0.826898i	$-0.690103\pi$
$283$	−9.71964e15	−1.12470	−0.562352	+	0.826898i	$0.690103\pi$
$284$	−2.82795e15	−0.319817
$285$	2.25544e15	0.249310
$286$	−1.42104e15	−0.153541
$287$	−1.18180e16	−1.24828
$288$	−3.08551e15	−0.318622
$289$	2.40988e16	2.43309
$290$	2.24307e15	0.221440
$291$	1.93720e15	0.187013
$292$	4.96346e15	0.468593
$293$	1.25827e16	1.16181	0.580905	−	0.813972i	$-0.302699\pi$
$293$	1.25827e16	1.16181	0.580905	+	0.813972i	$0.302699\pi$
$294$	2.57648e13	0.00232685
$295$	2.14809e15	0.189762
$296$	−6.04708e15	−0.522576
$297$	9.94604e14	0.0840878
$298$	4.80012e15	0.397051
$299$	−6.11049e15	−0.494554
$300$	6.87749e15	0.544681
$301$	1.05075e16	0.814364
$302$	1.62304e15	0.123107
$303$	5.63122e15	0.418048
$304$	−2.21259e15	−0.160776
$305$	−1.49217e16	−1.06138
$306$	3.55989e15	0.247883
$307$	3.65631e15	0.249255	0.124627	−	0.992204i	$-0.460226\pi$
$307$	3.65631e15	0.249255	0.124627	+	0.992204i	$0.460226\pi$
$308$	−5.51929e15	−0.368386
$309$	1.45392e16	0.950190
$310$	−2.74564e15	−0.175708
$311$	−1.18435e15	−0.0742231	−0.0371116	−	0.999311i	$-0.511816\pi$
$311$	−1.18435e15	−0.0742231	−0.0371116	+	0.999311i	$0.511816\pi$
$312$	6.07879e15	0.373089
$313$	8.09973e15	0.486892	0.243446	−	0.969915i	$-0.421722\pi$
$313$	8.09973e15	0.486892	0.243446	+	0.969915i	$0.421722\pi$
$314$	5.10582e15	0.300623
$315$	−8.46646e15	−0.488296
$316$	2.77810e16	1.56958
$317$	−9.55268e14	−0.0528737	−0.0264369	−	0.999650i	$-0.508416\pi$
$317$	−9.55268e14	−0.0528737	−0.0264369	+	0.999650i	$0.508416\pi$
$318$	1.00185e15	0.0543281
$319$	3.11279e15	0.165390
$320$	−4.45313e15	−0.231841
$321$	−5.09921e15	−0.260148
$322$	4.55708e15	0.227837
$323$	1.12027e16	0.548918
$324$	−1.94097e15	−0.0932129
$325$	−2.09176e16	−0.984621
$326$	1.34074e16	0.618628
$327$	−8.04445e15	−0.363862
$328$	2.06733e16	0.916704
$329$	3.61783e15	0.157281
$330$	−3.46223e15	−0.147576
$331$	−8.44548e15	−0.352974	−0.176487	−	0.984303i	$-0.556473\pi$
$331$	−8.44548e15	−0.352974	−0.176487	+	0.984303i	$0.556473\pi$
$332$	−1.17147e16	−0.480103
$333$	−5.87257e15	−0.236016
$334$	−9.22312e15	−0.363518
$335$	−3.47883e16	−1.34475
$336$	8.30562e15	0.314896
$337$	−3.51975e15	−0.130893	−0.0654467	−	0.997856i	$-0.520847\pi$
$337$	−3.51975e15	−0.130893	−0.0654467	+	0.997856i	$0.520847\pi$
$338$	2.56792e15	0.0936748
$339$	−4.20494e15	−0.150474
$340$	6.45371e16	2.26567
$341$	−3.81022e15	−0.131234
$342$	1.17284e15	0.0396341
$343$	3.00053e16	0.994916
$344$	−1.83809e16	−0.598049
$345$	−1.48877e16	−0.475338
$346$	−5.47454e15	−0.171535
$347$	4.17690e16	1.28444	0.642218	−	0.766522i	$-0.278014\pi$
$347$	4.17690e16	1.28444	0.642218	+	0.766522i	$0.278014\pi$
$348$	−6.07461e15	−0.183338
$349$	−3.76108e16	−1.11416	−0.557080	−	0.830459i	$-0.688078\pi$
$349$	−3.76108e16	−1.11416	−0.557080	+	0.830459i	$0.688078\pi$
$350$	1.55999e16	0.453607
$351$	5.90336e15	0.168501
$352$	1.49053e16	0.417649
$353$	1.35249e16	0.372048	0.186024	−	0.982545i	$-0.440440\pi$
$353$	1.35249e16	0.372048	0.186024	+	0.982545i	$0.440440\pi$
$354$	1.11702e15	0.0301675
$355$	2.09557e16	0.555672
$356$	3.33966e16	0.869514
$357$	−4.20528e16	−1.07511
$358$	2.55803e16	0.642192
$359$	2.12459e15	0.0523795	0.0261897	−	0.999657i	$-0.491663\pi$
$359$	2.12459e15	0.0523795	0.0261897	+	0.999657i	$0.491663\pi$
$360$	1.48104e16	0.358593
$361$	−3.83621e16	−0.912233
$362$	−1.44359e16	−0.337162
$363$	2.03624e16	0.467128
$364$	−3.27591e16	−0.738199
$365$	−3.67804e16	−0.814165
$366$	−7.75938e15	−0.168733
$367$	1.67707e16	0.358280	0.179140	−	0.983824i	$-0.442668\pi$
$367$	1.67707e16	0.358280	0.179140	+	0.983824i	$0.442668\pi$
$368$	1.46048e16	0.306539
$369$	2.00767e16	0.414019
$370$	2.04425e16	0.414212
$371$	−1.18348e16	−0.235629
$372$	7.43564e15	0.145475
$373$	−4.40990e16	−0.847854	−0.423927	−	0.905696i	$-0.639349\pi$
$373$	−4.40990e16	−0.847854	−0.423927	+	0.905696i	$0.639349\pi$
$374$	−1.71969e16	−0.324925
$375$	−5.64507e15	−0.104825
$376$	−6.32869e15	−0.115503
$377$	1.84756e16	0.331421
$378$	−4.40261e15	−0.0776271
$379$	−5.24548e16	−0.909140	−0.454570	−	0.890711i	$-0.650207\pi$
$379$	−5.24548e16	−0.909140	−0.454570	+	0.890711i	$0.650207\pi$
$380$	2.12624e16	0.362258
$381$	−6.13200e16	−1.02705
$382$	−2.99931e16	−0.493866
$383$	−1.98205e16	−0.320865	−0.160433	−	0.987047i	$-0.551289\pi$
$383$	−1.98205e16	−0.320865	−0.160433	+	0.987047i	$0.551289\pi$
$384$	−3.69885e16	−0.588727
$385$	4.08991e16	0.640058
$386$	−9.92818e15	−0.152775
$387$	−1.78504e16	−0.270102
$388$	1.82623e16	0.271738
$389$	2.47515e16	0.362183	0.181092	−	0.983466i	$-0.442037\pi$
$389$	2.47515e16	0.362183	0.181092	+	0.983466i	$0.442037\pi$
$390$	−2.05497e16	−0.295723
$391$	−7.39470e16	−1.04658
$392$	5.32415e14	0.00741125
$393$	4.14914e15	0.0568076
$394$	−4.59331e16	−0.618587
$395$	−2.05864e17	−2.72709
$396$	9.37629e15	0.122183
$397$	4.57878e16	0.586965	0.293482	−	0.955965i	$-0.405186\pi$
$397$	4.57878e16	0.586965	0.293482	+	0.955965i	$0.405186\pi$
$398$	6.81971e15	0.0860054
$399$	−1.38547e16	−0.171899
$400$	4.99956e16	0.610297
$401$	−1.65516e15	−0.0198793	−0.00993967	−	0.999951i	$-0.503164\pi$
$401$	−1.65516e15	−0.0198793	−0.00993967	+	0.999951i	$0.503164\pi$
$402$	−1.80901e16	−0.213782
$403$	−2.26151e16	−0.262976
$404$	5.30865e16	0.607442
$405$	1.43830e16	0.161954
$406$	−1.37788e16	−0.152683
$407$	2.83688e16	0.309369
$408$	7.35633e16	0.789532
$409$	−1.01655e17	−1.07381	−0.536904	−	0.843643i	$-0.680406\pi$
$409$	−1.01655e17	−1.07381	−0.536904	+	0.843643i	$0.680406\pi$
$410$	−6.98871e16	−0.726611
$411$	−1.07769e17	−1.10286
$412$	1.37064e17	1.38067
$413$	−1.31953e16	−0.130841
$414$	−7.74168e15	−0.0755671
$415$	8.68087e16	0.834163
$416$	8.84685e16	0.836916
$417$	3.30456e16	0.307772
$418$	−5.66567e15	−0.0519524
$419$	−2.81598e16	−0.254237	−0.127118	−	0.991888i	$-0.540573\pi$
$419$	−2.81598e16	−0.254237	−0.127118	+	0.991888i	$0.540573\pi$
$420$	−7.98147e16	−0.709517
$421$	−1.05741e17	−0.925569	−0.462784	−	0.886471i	$-0.653150\pi$
$421$	−1.05741e17	−0.925569	−0.462784	+	0.886471i	$0.653150\pi$
$422$	−3.92786e16	−0.338551
$423$	−6.14605e15	−0.0521656
$424$	2.07026e16	0.173040
$425$	−2.53137e17	−2.08366
$426$	1.08971e16	0.0883382
$427$	9.16612e16	0.731820
$428$	−4.80711e16	−0.378007
$429$	−2.85175e16	−0.220871
$430$	6.21376e16	0.474034
$431$	4.83171e16	0.363077	0.181539	−	0.983384i	$-0.441892\pi$
$431$	4.83171e16	0.363077	0.181539	+	0.983384i	$0.441892\pi$
$432$	−1.41098e16	−0.104442
$433$	−1.06363e17	−0.775564	−0.387782	−	0.921751i	$-0.626759\pi$
$433$	−1.06363e17	−0.775564	−0.387782	+	0.921751i	$0.626759\pi$
$434$	1.68659e16	0.121151
$435$	4.50142e16	0.318544
$436$	−7.58364e16	−0.528708
$437$	−2.43625e16	−0.167337
$438$	−1.91260e16	−0.129432
$439$	2.54396e17	1.69625	0.848126	−	0.529794i	$-0.177731\pi$
$439$	2.54396e17	1.69625	0.848126	+	0.529794i	$0.177731\pi$
$440$	−7.15451e16	−0.470043
$441$	5.17051e14	0.00334720
$442$	−1.02070e17	−0.651109
$443$	2.50718e17	1.57602	0.788010	−	0.615662i	$-0.211111\pi$
$443$	2.50718e17	1.57602	0.788010	+	0.615662i	$0.211111\pi$
$444$	−5.53617e16	−0.342941
$445$	−2.47476e17	−1.51075
$446$	−4.64350e16	−0.279363
$447$	9.63293e16	0.571162
$448$	2.73547e16	0.159855
$449$	−1.21253e17	−0.698377	−0.349188	−	0.937053i	$-0.613543\pi$
$449$	−1.21253e17	−0.698377	−0.349188	+	0.937053i	$0.613543\pi$
$450$	−2.65015e16	−0.150449
$451$	−9.69849e16	−0.542696
$452$	−3.96407e16	−0.218646
$453$	3.25713e16	0.177091
$454$	−1.12527e17	−0.603108
$455$	2.42752e17	1.28259
$456$	2.42361e16	0.126238
$457$	2.67425e17	1.37324	0.686621	−	0.727016i	$-0.259093\pi$
$457$	2.67425e17	1.37324	0.686621	+	0.727016i	$0.259093\pi$
$458$	3.20614e16	0.162314
$459$	7.14403e16	0.356583
$460$	−1.40349e17	−0.690688
$461$	−6.04177e16	−0.293162	−0.146581	−	0.989199i	$-0.546827\pi$
$461$	−6.04177e16	−0.293162	−0.146581	+	0.989199i	$0.546827\pi$
$462$	2.12678e16	0.101754
$463$	−1.86342e17	−0.879091	−0.439545	−	0.898220i	$-0.644860\pi$
$463$	−1.86342e17	−0.879091	−0.439545	+	0.898220i	$0.644860\pi$
$464$	−4.41590e16	−0.205425
$465$	−5.50998e16	−0.252758
$466$	2.67136e16	0.120844
$467$	4.17180e17	1.86107	0.930537	−	0.366198i	$-0.119341\pi$
$467$	4.17180e17	1.86107	0.930537	+	0.366198i	$0.119341\pi$
$468$	5.56520e16	0.244840
$469$	2.13698e17	0.927206
$470$	2.13945e16	0.0915516
$471$	1.02464e17	0.432450
$472$	2.30826e16	0.0960863
$473$	8.62306e16	0.354049
$474$	−1.07050e17	−0.433540
$475$	−8.33983e16	−0.333157
$476$	−3.96439e17	−1.56218
$477$	2.01052e16	0.0781517
$478$	−4.70167e16	−0.180290
$479$	3.44872e17	1.30460	0.652300	−	0.757961i	$-0.273804\pi$
$479$	3.44872e17	1.30460	0.652300	+	0.757961i	$0.273804\pi$
$480$	2.15546e17	0.804398
$481$	1.68380e17	0.619936
$482$	−5.95381e15	−0.0216267
$483$	9.14522e16	0.327746
$484$	1.91960e17	0.678758
$485$	−1.35328e17	−0.472135
$486$	7.47925e15	0.0257468
$487$	4.38311e16	0.148883	0.0744413	−	0.997225i	$-0.476283\pi$
$487$	4.38311e16	0.148883	0.0744413	+	0.997225i	$0.476283\pi$
$488$	−1.60344e17	−0.537431
$489$	2.69061e17	0.889905
$490$	−1.79986e15	−0.00587441
$491$	9.30984e16	0.299856	0.149928	−	0.988697i	$-0.452096\pi$
$491$	9.30984e16	0.299856	0.149928	+	0.988697i	$0.452096\pi$
$492$	1.89266e17	0.601589
$493$	2.23585e17	0.701355
$494$	−3.36279e16	−0.104106
$495$	−6.94804e16	−0.212290
$496$	5.40530e16	0.163000
$497$	−1.28727e17	−0.383136
$498$	4.51410e16	0.132611
$499$	−2.12032e17	−0.614820	−0.307410	−	0.951577i	$-0.599462\pi$
$499$	−2.12032e17	−0.614820	−0.307410	+	0.951577i	$0.599462\pi$
$500$	−5.32170e16	−0.152316
$501$	−1.85091e17	−0.522925
$502$	−1.70162e16	−0.0474558
$503$	4.55107e17	1.25292	0.626458	−	0.779455i	$-0.284504\pi$
$503$	4.55107e17	1.25292	0.626458	+	0.779455i	$0.284504\pi$
$504$	−9.09776e16	−0.247250
$505$	−3.93383e17	−1.05541
$506$	3.73979e16	0.0990534
$507$	5.15333e16	0.134752
$508$	−5.78074e17	−1.49234
$509$	−5.17262e17	−1.31839	−0.659196	−	0.751971i	$-0.729103\pi$
$509$	−5.17262e17	−1.31839	−0.659196	+	0.751971i	$0.729103\pi$
$510$	−2.48685e17	−0.625810
$511$	2.25935e17	0.561367
$512$	−3.74718e17	−0.919285
$513$	2.35367e16	0.0570142
$514$	−2.63752e17	−0.630865
$515$	−1.01567e18	−2.39887
$516$	−1.68279e17	−0.392470
$517$	2.96899e16	0.0683786
$518$	−1.25574e17	−0.285599
$519$	−1.09864e17	−0.246756
$520$	−4.24648e17	−0.941906
$521$	−5.56431e17	−1.21889	−0.609447	−	0.792826i	$-0.708609\pi$
$521$	−5.56431e17	−1.21889	−0.609447	+	0.792826i	$0.708609\pi$
$522$	2.34077e16	0.0506407
$523$	−6.88297e17	−1.47067	−0.735335	−	0.677704i	$-0.762975\pi$
$523$	−6.88297e17	−1.47067	−0.735335	+	0.677704i	$0.762975\pi$
$524$	3.91146e16	0.0825440
$525$	3.13061e17	0.652519
$526$	2.01251e16	0.0414314
$527$	−2.73680e17	−0.556511
$528$	6.81604e16	0.136903
$529$	−3.43224e17	−0.680951
$530$	−6.99864e16	−0.137158
$531$	2.24165e16	0.0433963
$532$	−1.30611e17	−0.249777
$533$	−5.75643e17	−1.08749
$534$	−1.28689e17	−0.240172
$535$	3.56217e17	0.656773
$536$	−3.73823e17	−0.680917
$537$	5.13348e17	0.923802
$538$	3.87194e17	0.688405
$539$	−2.49773e15	−0.00438751
$540$	1.35591e17	0.235327
$541$	−5.63177e17	−0.965745	−0.482873	−	0.875691i	$-0.660407\pi$
$541$	−5.63177e17	−0.965745	−0.482873	+	0.875691i	$0.660407\pi$
$542$	−3.52602e17	−0.597433
$543$	−2.89702e17	−0.485012
$544$	1.07061e18	1.77109
$545$	5.61965e17	0.918611
$546$	1.26233e17	0.203901
$547$	−8.01616e17	−1.27953	−0.639763	−	0.768572i	$-0.720967\pi$
$547$	−8.01616e17	−1.27953	−0.639763	+	0.768572i	$0.720967\pi$
$548$	−1.01595e18	−1.60251
$549$	−1.55716e17	−0.242725
$550$	1.28021e17	0.197208
$551$	7.36623e16	0.112140
$552$	−1.59978e17	−0.240689
$553$	1.26458e18	1.88033
$554$	−1.08899e17	−0.160034
$555$	4.10242e17	0.595849
$556$	3.11527e17	0.447207
$557$	−1.26903e18	−1.80058	−0.900289	−	0.435293i	$-0.856645\pi$
$557$	−1.26903e18	−1.80058	−0.900289	+	0.435293i	$0.856645\pi$
$558$	−2.86522e16	−0.0401824
$559$	5.11812e17	0.709470
$560$	−5.80209e17	−0.794991
$561$	−3.45109e17	−0.467409
$562$	−4.00719e17	−0.536480
$563$	1.09966e18	1.45530	0.727652	−	0.685947i	$-0.240612\pi$
$563$	1.09966e18	1.45530	0.727652	+	0.685947i	$0.240612\pi$
$564$	−5.79399e16	−0.0757990
$565$	2.93746e17	0.379890
$566$	3.53078e17	0.451403
$567$	−8.83521e16	−0.111668
$568$	2.25183e17	0.281366
$569$	7.84486e17	0.969070	0.484535	−	0.874772i	$-0.338989\pi$
$569$	7.84486e17	0.969070	0.484535	+	0.874772i	$0.338989\pi$
$570$	−8.19315e16	−0.100061
$571$	4.14712e17	0.500740	0.250370	−	0.968150i	$-0.419448\pi$
$571$	4.14712e17	0.500740	0.250370	+	0.968150i	$0.419448\pi$
$572$	−2.68839e17	−0.320936
$573$	−6.01905e17	−0.710432
$574$	4.29303e17	0.500999
$575$	5.50495e17	0.635203
$576$	−4.64709e16	−0.0530194
$577$	1.19712e18	1.35050	0.675249	−	0.737589i	$-0.264036\pi$
$577$	1.19712e18	1.35050	0.675249	+	0.737589i	$0.264036\pi$
$578$	−8.75418e17	−0.976528
$579$	−1.99240e17	−0.219769
$580$	4.24357e17	0.462859
$581$	−5.33249e17	−0.575156
$582$	−7.03713e16	−0.0750579
$583$	−9.71226e16	−0.102441
$584$	−3.95229e17	−0.412254
$585$	−4.12393e17	−0.425401
$586$	−4.57083e17	−0.466295
$587$	1.68308e18	1.69807	0.849036	−	0.528336i	$-0.177184\pi$
$587$	1.68308e18	1.69807	0.849036	+	0.528336i	$0.177184\pi$
$588$	4.87432e15	0.00486364
$589$	−9.01665e16	−0.0889807
$590$	−7.80320e16	−0.0761613
$591$	−9.21792e17	−0.889845
$592$	−4.02449e17	−0.384255
$593$	1.54207e18	1.45630	0.728148	−	0.685420i	$-0.240381\pi$
$593$	1.54207e18	1.45630	0.728148	+	0.685420i	$0.240381\pi$
$594$	−3.61302e16	−0.0337488
$595$	2.93770e18	2.71423
$596$	9.08112e17	0.829925
$597$	1.36859e17	0.123720
$598$	2.21971e17	0.198490
$599$	6.70837e17	0.593393	0.296697	−	0.954972i	$-0.404115\pi$
$599$	6.70837e17	0.593393	0.296697	+	0.954972i	$0.404115\pi$
$600$	−5.47639e17	−0.479194
$601$	3.45763e17	0.299292	0.149646	−	0.988740i	$-0.452187\pi$
$601$	3.45763e17	0.299292	0.149646	+	0.988740i	$0.452187\pi$
$602$	−3.81699e17	−0.326847
$603$	−3.63035e17	−0.307529
$604$	3.07055e17	0.257322
$605$	−1.42246e18	−1.17932
$606$	−2.04561e17	−0.167784
$607$	1.30301e18	1.05736	0.528678	−	0.848822i	$-0.322688\pi$
$607$	1.30301e18	1.05736	0.528678	+	0.848822i	$0.322688\pi$
$608$	3.52724e17	0.283179
$609$	−2.76514e17	−0.219636
$610$	5.42050e17	0.425986
$611$	1.76221e17	0.137022
$612$	6.73480e17	0.518132
$613$	−3.58329e17	−0.272765	−0.136383	−	0.990656i	$-0.543548\pi$
$613$	−3.58329e17	−0.272765	−0.136383	+	0.990656i	$0.543548\pi$
$614$	−1.32820e17	−0.100039
$615$	−1.40250e18	−1.04524
$616$	4.39488e17	0.324095
$617$	5.14752e17	0.375616	0.187808	−	0.982206i	$-0.439862\pi$
$617$	5.14752e17	0.375616	0.187808	+	0.982206i	$0.439862\pi$
$618$	−5.28155e17	−0.381361
$619$	−1.68141e18	−1.20139	−0.600697	−	0.799477i	$-0.705110\pi$
$619$	−1.68141e18	−1.20139	−0.600697	+	0.799477i	$0.705110\pi$
$620$	−5.19435e17	−0.367269
$621$	−1.55361e17	−0.108704
$622$	4.30232e16	0.0297896
$623$	1.52020e18	1.04166
$624$	4.04559e17	0.274335
$625$	−1.28138e18	−0.859920
$626$	−2.94233e17	−0.195415
$627$	−1.13699e17	−0.0747341
$628$	9.65947e17	0.628370
$629$	2.03767e18	1.31191
$630$	3.07555e17	0.195979
$631$	1.12331e18	0.708447	0.354223	−	0.935161i	$-0.384745\pi$
$631$	1.12331e18	0.708447	0.354223	+	0.935161i	$0.384745\pi$
$632$	−2.21214e18	−1.38087
$633$	−7.88247e17	−0.487010
$634$	3.47013e16	0.0212210
$635$	4.28365e18	2.59290
$636$	1.89535e17	0.113558
$637$	−1.48250e16	−0.00879202
$638$	−1.13076e17	−0.0663798
$639$	2.18684e17	0.127076
$640$	2.58392e18	1.48631
$641$	2.62258e18	1.49332	0.746658	−	0.665208i	$-0.231657\pi$
$641$	2.62258e18	1.49332	0.746658	+	0.665208i	$0.231657\pi$
$642$	1.85235e17	0.104411
$643$	9.29999e17	0.518933	0.259466	−	0.965752i	$-0.416453\pi$
$643$	9.29999e17	0.518933	0.259466	+	0.965752i	$0.416453\pi$
$644$	8.62134e17	0.476230
$645$	1.24698e18	0.681904
$646$	−4.06953e17	−0.220309
$647$	1.87154e18	1.00305	0.501523	−	0.865144i	$-0.332773\pi$
$647$	1.87154e18	1.00305	0.501523	+	0.865144i	$0.332773\pi$
$648$	1.54555e17	0.0820059
$649$	−1.08288e17	−0.0568839
$650$	7.59856e17	0.395180
$651$	3.38467e17	0.174277
$652$	2.53648e18	1.29307
$653$	−1.03343e18	−0.521611	−0.260806	−	0.965391i	$-0.583988\pi$
$653$	−1.03343e18	−0.521611	−0.260806	+	0.965391i	$0.583988\pi$
$654$	2.92225e17	0.146037
$655$	−2.89848e17	−0.143417
$656$	1.37586e18	0.674061
$657$	−3.83823e17	−0.186190
$658$	−1.31422e17	−0.0631249
$659$	8.76849e16	0.0417032	0.0208516	−	0.999783i	$-0.493362\pi$
$659$	8.76849e16	0.0417032	0.0208516	+	0.999783i	$0.493362\pi$
$660$	−6.55003e17	−0.308466
$661$	−7.05143e16	−0.0328827	−0.0164414	−	0.999865i	$-0.505234\pi$
$661$	−7.05143e16	−0.0328827	−0.0164414	+	0.999865i	$0.505234\pi$
$662$	3.06793e17	0.141667
$663$	−2.04835e18	−0.936628
$664$	9.32816e17	0.422380
$665$	9.67854e17	0.433979
$666$	2.13328e17	0.0947254
$667$	−4.86230e17	−0.213808
$668$	−1.74488e18	−0.759834
$669$	−9.31863e17	−0.401867
$670$	1.26373e18	0.539718
$671$	7.52222e17	0.318163
$672$	−1.32406e18	−0.554633
$673$	−4.87826e17	−0.202380	−0.101190	−	0.994867i	$-0.532265\pi$
$673$	−4.87826e17	−0.202380	−0.101190	+	0.994867i	$0.532265\pi$
$674$	1.27859e17	0.0525344
$675$	−5.31835e17	−0.216422
$676$	4.85813e17	0.195801
$677$	−3.11098e18	−1.24186	−0.620928	−	0.783868i	$-0.713244\pi$
$677$	−3.11098e18	−1.24186	−0.620928	+	0.783868i	$0.713244\pi$
$678$	1.52750e17	0.0603932
$679$	8.31294e17	0.325537
$680$	−5.13894e18	−1.99327
$681$	−2.25821e18	−0.867579
$682$	1.38411e17	0.0526710
$683$	−2.38520e17	−0.0899063	−0.0449531	−	0.998989i	$-0.514314\pi$
$683$	−2.38520e17	−0.0899063	−0.0449531	+	0.998989i	$0.514314\pi$
$684$	2.21884e17	0.0828442
$685$	7.52845e18	2.78431
$686$	−1.08998e18	−0.399312
$687$	6.43412e17	0.233491
$688$	−1.22329e18	−0.439750
$689$	−5.76461e17	−0.205279
$690$	5.40814e17	0.190778
$691$	−3.99664e18	−1.39665	−0.698326	−	0.715780i	$-0.746071\pi$
$691$	−3.99664e18	−1.39665	−0.698326	+	0.715780i	$0.746071\pi$
$692$	−1.03570e18	−0.358547
$693$	4.26805e17	0.146374
$694$	−1.51731e18	−0.515512
$695$	−2.30848e18	−0.777007
$696$	4.83707e17	0.161296
$697$	−6.96622e18	−2.30136
$698$	1.36626e18	0.447170
$699$	5.36092e17	0.173835
$700$	2.95127e18	0.948140
$701$	−1.68919e18	−0.537666	−0.268833	−	0.963187i	$-0.586638\pi$
$701$	−1.68919e18	−0.537666	−0.268833	+	0.963187i	$0.586638\pi$
$702$	−2.14447e17	−0.0676283
$703$	6.71330e17	0.209762
$704$	2.24488e17	0.0694978
$705$	4.29347e17	0.131698
$706$	−4.91310e17	−0.149322
$707$	2.41647e18	0.727706
$708$	2.11324e17	0.0630568
$709$	6.28329e18	1.85775	0.928873	−	0.370399i	$-0.120779\pi$
$709$	6.28329e18	1.85775	0.928873	+	0.370399i	$0.120779\pi$
$710$	−7.61243e17	−0.223020
$711$	−2.14830e18	−0.623652
$712$	−2.65929e18	−0.764972
$713$	5.95171e17	0.169652
$714$	1.52762e18	0.431497
$715$	1.99216e18	0.557615
$716$	4.83941e18	1.34233
$717$	−9.43537e17	−0.259349
$718$	−7.71784e16	−0.0210226
$719$	6.67528e18	1.80190	0.900952	−	0.433918i	$-0.142869\pi$
$719$	6.67528e18	1.80190	0.900952	+	0.433918i	$0.142869\pi$
$720$	9.85672e17	0.263676
$721$	6.23907e18	1.65402
$722$	1.39355e18	0.366127
$723$	−1.19482e17	−0.0311102
$724$	−2.73107e18	−0.704745
$725$	−1.66447e18	−0.425676
$726$	−7.39690e17	−0.187483
$727$	1.34273e18	0.337299	0.168650	−	0.985676i	$-0.446059\pi$
$727$	1.34273e18	0.337299	0.168650	+	0.985676i	$0.446059\pi$
$728$	2.60853e18	0.649445
$729$	1.50095e17	0.0370370
$730$	1.33609e18	0.326767
$731$	6.19376e18	1.50138
$732$	−1.46796e18	−0.352690
$733$	1.83105e18	0.436039	0.218019	−	0.975944i	$-0.430040\pi$
$733$	1.83105e18	0.436039	0.218019	+	0.975944i	$0.430040\pi$
$734$	−6.09218e17	−0.143796
$735$	−3.61198e16	−0.00845041
$736$	−2.32826e18	−0.539915
$737$	1.75372e18	0.403108
$738$	−7.29310e17	−0.166167
$739$	6.24792e18	1.41106	0.705532	−	0.708678i	$-0.250708\pi$
$739$	6.24792e18	1.41106	0.705532	+	0.708678i	$0.250708\pi$
$740$	3.86742e18	0.865796
$741$	−6.74850e17	−0.149758
$742$	4.29913e17	0.0945704
$743$	−2.65165e18	−0.578215	−0.289108	−	0.957297i	$-0.593359\pi$
$743$	−2.65165e18	−0.578215	−0.289108	+	0.957297i	$0.593359\pi$
$744$	−5.92083e17	−0.127985
$745$	−6.72932e18	−1.44197
$746$	1.60195e18	0.340288
$747$	9.05896e17	0.190763
$748$	−3.25340e18	−0.679167
$749$	−2.18818e18	−0.452846
$750$	2.05064e17	0.0420718
$751$	4.55881e18	0.927239	0.463619	−	0.886034i	$-0.346551\pi$
$751$	4.55881e18	0.927239	0.463619	+	0.886034i	$0.346551\pi$
$752$	−4.21191e17	−0.0849303
$753$	−3.41484e17	−0.0682658
$754$	−6.71150e17	−0.133017
$755$	−2.27535e18	−0.447087
$756$	−8.32910e17	−0.162258
$757$	7.82344e18	1.51104	0.755518	−	0.655128i	$-0.227385\pi$
$757$	7.82344e18	1.51104	0.755518	+	0.655128i	$0.227385\pi$
$758$	1.90549e18	0.364885
$759$	7.50507e17	0.142490
$760$	−1.69307e18	−0.318704
$761$	−8.54000e18	−1.59389	−0.796943	−	0.604054i	$-0.793551\pi$
$761$	−8.54000e18	−1.59389	−0.796943	+	0.604054i	$0.793551\pi$
$762$	2.22753e18	0.412207
$763$	−3.45204e18	−0.633383
$764$	−5.67425e18	−1.03229
$765$	−4.99064e18	−0.900236
$766$	7.20004e17	0.128780
$767$	−6.42730e17	−0.113988
$768$	8.21446e17	0.144454
$769$	−1.55655e18	−0.271420	−0.135710	−	0.990749i	$-0.543331\pi$
$769$	−1.55655e18	−0.271420	−0.135710	+	0.990749i	$0.543331\pi$
$770$	−1.48571e18	−0.256889
$771$	−5.29302e18	−0.907507
$772$	−1.87827e18	−0.319334
$773$	−2.50000e18	−0.421476	−0.210738	−	0.977543i	$-0.567587\pi$
$773$	−2.50000e18	−0.421476	−0.210738	+	0.977543i	$0.567587\pi$
$774$	6.48440e17	0.108406
$775$	2.03740e18	0.337766
$776$	−1.45419e18	−0.239067
$777$	−2.52004e18	−0.410838
$778$	−8.99128e17	−0.145363
$779$	−2.29509e18	−0.367965
$780$	−3.88770e18	−0.618127
$781$	−1.05640e18	−0.166571
$782$	2.68622e18	0.420046
$783$	4.69748e17	0.0728473
$784$	3.54336e16	0.00544956
$785$	−7.15788e18	−1.09177
$786$	−1.50723e17	−0.0227998
$787$	9.21565e18	1.38258	0.691290	−	0.722577i	$-0.257043\pi$
$787$	9.21565e18	1.38258	0.691290	+	0.722577i	$0.257043\pi$
$788$	−8.68988e18	−1.29298
$789$	4.03872e17	0.0595996
$790$	7.47826e18	1.09452
$791$	−1.80443e18	−0.261934
$792$	−7.46612e17	−0.107493
$793$	4.46473e18	0.637558
$794$	−1.66330e18	−0.235580
$795$	−1.40450e18	−0.197303
$796$	1.29019e18	0.179771
$797$	−6.60016e18	−0.912169	−0.456085	−	0.889936i	$-0.650749\pi$
$797$	−6.60016e18	−0.912169	−0.456085	+	0.889936i	$0.650749\pi$
$798$	5.03290e17	0.0689921
$799$	2.13256e18	0.289967
$800$	−7.97014e18	−1.07493
$801$	−2.58255e18	−0.345491
$802$	6.01258e16	0.00797862
$803$	1.85414e18	0.244058
$804$	−3.42239e18	−0.446853
$805$	−6.38861e18	−0.827433
$806$	8.21523e17	0.105546
$807$	7.77027e18	0.990280
$808$	−4.22715e18	−0.534409
$809$	−1.26447e19	−1.58578	−0.792891	−	0.609363i	$-0.791425\pi$
$809$	−1.26447e19	−1.58578	−0.792891	+	0.609363i	$0.791425\pi$
$810$	−5.22481e17	−0.0650007
$811$	1.32265e19	1.63233	0.816166	−	0.577818i	$-0.196096\pi$
$811$	1.32265e19	1.63233	0.816166	+	0.577818i	$0.196096\pi$
$812$	−2.60674e18	−0.319142
$813$	−7.07606e18	−0.859415
$814$	−1.03053e18	−0.124166
$815$	−1.87959e19	−2.24667
$816$	4.89582e18	0.580550
$817$	2.04059e18	0.240056
$818$	3.69274e18	0.430975
$819$	2.53325e18	0.293314
$820$	−1.32216e19	−1.51878
$821$	1.13991e19	1.29909	0.649546	−	0.760322i	$-0.274959\pi$
$821$	1.13991e19	1.29909	0.649546	+	0.760322i	$0.274959\pi$
$822$	3.91484e18	0.442636
$823$	−3.52165e18	−0.395045	−0.197523	−	0.980298i	$-0.563290\pi$
$823$	−3.52165e18	−0.395045	−0.197523	+	0.980298i	$0.563290\pi$
$824$	−1.09140e19	−1.21467
$825$	2.56915e18	0.283686
$826$	4.79336e17	0.0525133
$827$	2.87539e18	0.312544	0.156272	−	0.987714i	$-0.450052\pi$
$827$	2.87539e18	0.312544	0.156272	+	0.987714i	$0.450052\pi$
$828$	−1.46461e18	−0.157952
$829$	−5.87262e18	−0.628387	−0.314193	−	0.949359i	$-0.601734\pi$
$829$	−5.87262e18	−0.628387	−0.314193	+	0.949359i	$0.601734\pi$
$830$	−3.15344e18	−0.334793
$831$	−2.18540e18	−0.230210
$832$	1.33242e18	0.139265
$833$	−1.79407e17	−0.0186057
$834$	−1.20042e18	−0.123525
$835$	1.29300e19	1.32019
$836$	−1.07186e18	−0.108592
$837$	−5.74996e17	−0.0578029
$838$	1.02294e18	0.102039
$839$	6.55877e18	0.649187	0.324593	−	0.945854i	$-0.394773\pi$
$839$	6.55877e18	0.649187	0.324593	+	0.945854i	$0.394773\pi$
$840$	6.35546e18	0.624211
$841$	−8.79047e18	−0.856718
$842$	3.84117e18	0.371479
$843$	−8.04167e18	−0.771733
$844$	−7.43094e18	−0.707649
$845$	−3.59999e18	−0.340198
$846$	2.23263e17	0.0209368
$847$	8.73793e18	0.813142
$848$	1.37781e18	0.127238
$849$	7.08562e18	0.649348
$850$	9.19551e18	0.836282
$851$	−4.43131e18	−0.399936
$852$	2.06157e18	0.184647
$853$	−3.55348e18	−0.315853	−0.157926	−	0.987451i	$-0.550481\pi$
$853$	−3.55348e18	−0.315853	−0.157926	+	0.987451i	$0.550481\pi$
$854$	−3.32971e18	−0.293718
$855$	−1.64421e18	−0.143939
$856$	3.82779e18	0.332559
$857$	−3.28482e18	−0.283228	−0.141614	−	0.989922i	$-0.545229\pi$
$857$	−3.28482e18	−0.283228	−0.141614	+	0.989922i	$0.545229\pi$
$858$	1.03593e18	0.0886472
$859$	1.47163e19	1.24981	0.624906	−	0.780700i	$-0.285137\pi$
$859$	1.47163e19	1.24981	0.624906	+	0.780700i	$0.285137\pi$
$860$	1.17555e19	0.990837
$861$	8.61531e18	0.720693
$862$	−1.75518e18	−0.145722
$863$	−1.84115e19	−1.51712	−0.758558	−	0.651605i	$-0.774096\pi$
$863$	−1.84115e19	−1.51712	−0.758558	+	0.651605i	$0.774096\pi$
$864$	2.24934e18	0.183956
$865$	7.67480e18	0.622963
$866$	3.86375e18	0.311274
$867$	−1.75680e19	−1.40475
$868$	3.19079e18	0.253233
$869$	1.03778e19	0.817483
$870$	−1.63520e18	−0.127848
$871$	1.04090e19	0.807777
$872$	6.03867e18	0.465141
$873$	−1.41222e18	−0.107972
$874$	8.85000e17	0.0671613
$875$	−2.42241e18	−0.182472
$876$	−3.61836e18	−0.270542
$877$	1.04014e19	0.771962	0.385981	−	0.922507i	$-0.373863\pi$
$877$	1.04014e19	0.771962	0.385981	+	0.922507i	$0.373863\pi$
$878$	−9.24125e18	−0.680795
$879$	−9.17280e18	−0.670771
$880$	−4.76151e18	−0.345627
$881$	−2.97901e18	−0.214649	−0.107324	−	0.994224i	$-0.534228\pi$
$881$	−2.97901e18	−0.214649	−0.107324	+	0.994224i	$0.534228\pi$
$882$	−1.87825e16	−0.00134341
$883$	−1.44020e18	−0.102253	−0.0511266	−	0.998692i	$-0.516281\pi$
$883$	−1.44020e18	−0.102253	−0.0511266	+	0.998692i	$0.516281\pi$
$884$	−1.93102e19	−1.36096
$885$	−1.56596e18	−0.109559
$886$	−9.10766e18	−0.632539
$887$	1.58018e19	1.08944	0.544720	−	0.838618i	$-0.316636\pi$
$887$	1.58018e19	1.08944	0.544720	+	0.838618i	$0.316636\pi$
$888$	4.40832e18	0.301709
$889$	−2.63137e19	−1.78780
$890$	8.98988e18	0.606343
$891$	−7.25066e17	−0.0485481
$892$	−8.78483e18	−0.583931
$893$	7.02594e17	0.0463628
$894$	−3.49928e18	−0.229237
$895$	−3.58611e19	−2.33225
$896$	−1.58725e19	−1.02481
$897$	4.45455e18	0.285531
$898$	4.40465e18	0.280295
$899$	−1.79955e18	−0.113691
$900$	−5.01369e18	−0.314472
$901$	−6.97612e18	−0.434413
$902$	3.52310e18	0.217812
$903$	−7.65999e18	−0.470173
$904$	3.15650e18	0.192358
$905$	2.02378e19	1.22447
$906$	−1.18319e18	−0.0710759
$907$	2.54563e19	1.51827	0.759134	−	0.650934i	$-0.225623\pi$
$907$	2.54563e19	1.51827	0.759134	+	0.650934i	$0.225623\pi$
$908$	−2.12886e19	−1.26063
$909$	−4.10516e18	−0.241360
$910$	−8.81829e18	−0.514772
$911$	2.37904e19	1.37890	0.689450	−	0.724333i	$-0.257852\pi$
$911$	2.37904e19	1.37890	0.689450	+	0.724333i	$0.257852\pi$
$912$	1.61298e18	0.0928242
$913$	−4.37614e18	−0.250052
$914$	−9.71456e18	−0.551154
$915$	1.08779e19	0.612786
$916$	6.06555e18	0.339273
$917$	1.78048e18	0.0988864
$918$	−2.59516e18	−0.143115
$919$	3.74959e18	0.205321	0.102660	−	0.994716i	$-0.467265\pi$
$919$	3.74959e18	0.205321	0.102660	+	0.994716i	$0.467265\pi$
$920$	1.11756e19	0.607647
$921$	−2.66545e18	−0.143907
$922$	2.19475e18	0.117661
$923$	−6.27017e18	−0.333786
$924$	4.02356e18	0.212688
$925$	−1.51694e19	−0.796243
$926$	6.76910e18	0.352825
$927$	−1.05991e19	−0.548593
$928$	7.03970e18	0.361820
$929$	−3.23817e19	−1.65271	−0.826356	−	0.563148i	$-0.809590\pi$
$929$	−3.23817e19	−1.65271	−0.826356	+	0.563148i	$0.809590\pi$
$930$	2.00157e18	0.101445
$931$	−5.91073e16	−0.00297487
$932$	5.05383e18	0.252591
$933$	8.63394e17	0.0428527
$934$	−1.51546e19	−0.746946
$935$	2.41084e19	1.18003
$936$	−4.43144e18	−0.215403
$937$	1.22720e19	0.592392	0.296196	−	0.955127i	$-0.404282\pi$
$937$	1.22720e19	0.592392	0.296196	+	0.955127i	$0.404282\pi$
$938$	−7.76284e18	−0.372136
$939$	−5.90470e18	−0.281107
$940$	4.04753e18	0.191363
$941$	3.45719e18	0.162327	0.0811636	−	0.996701i	$-0.474136\pi$
$941$	3.45719e18	0.162327	0.0811636	+	0.996701i	$0.474136\pi$
$942$	−3.72214e18	−0.173565
$943$	1.51494e19	0.701568
$944$	1.53621e18	0.0706531
$945$	6.17205e18	0.281918
$946$	−3.13243e18	−0.142098
$947$	−1.69144e19	−0.762048	−0.381024	−	0.924565i	$-0.624428\pi$
$947$	−1.69144e19	−0.762048	−0.381024	+	0.924565i	$0.624428\pi$
$948$	−2.02524e19	−0.906195
$949$	1.10051e19	0.489060
$950$	3.02955e18	0.133713
$951$	6.96390e17	0.0305267
$952$	3.15675e19	1.37436
$953$	2.62570e19	1.13538	0.567689	−	0.823243i	$-0.307837\pi$
$953$	2.62570e19	1.13538	0.567689	+	0.823243i	$0.307837\pi$
$954$	−7.30346e17	−0.0313664
$955$	4.20475e19	1.79357
$956$	−8.89488e18	−0.376846
$957$	−2.26922e18	−0.0954882
$958$	−1.25279e19	−0.523604
$959$	−4.62458e19	−1.91978
$960$	3.24633e18	0.133854
$961$	−2.22148e19	−0.909788
$962$	−6.11660e18	−0.248813
$963$	3.71732e18	0.150196
$964$	−1.12638e18	−0.0452046
$965$	1.39184e19	0.554832
$966$	−3.32211e18	−0.131542
$967$	−8.65776e18	−0.340513	−0.170256	−	0.985400i	$-0.554460\pi$
$967$	−8.65776e18	−0.340513	−0.170256	+	0.985400i	$0.554460\pi$
$968$	−1.52853e19	−0.597151
$969$	−8.16679e18	−0.316918
$970$	4.91596e18	0.189492
$971$	3.56223e19	1.36394	0.681972	−	0.731378i	$-0.261122\pi$
$971$	3.56223e19	1.36394	0.681972	+	0.731378i	$0.261122\pi$
$972$	1.41497e18	0.0538165
$973$	1.41806e19	0.535747
$974$	−1.59222e18	−0.0597544
$975$	1.52489e19	0.568471
$976$	−1.06713e19	−0.395178
$977$	−1.66093e19	−0.610994	−0.305497	−	0.952193i	$-0.598823\pi$
$977$	−1.66093e19	−0.610994	−0.305497	+	0.952193i	$0.598823\pi$
$978$	−9.77399e18	−0.357165
$979$	1.24756e19	0.452870
$980$	−3.40507e17	−0.0122788
$981$	5.86441e18	0.210076
$982$	−3.38192e18	−0.120348
$983$	−2.95232e19	−1.04367	−0.521837	−	0.853045i	$-0.674753\pi$
$983$	−2.95232e19	−1.04367	−0.521837	+	0.853045i	$0.674753\pi$
$984$	−1.50708e19	−0.529259
$985$	6.43940e19	2.24652
$986$	−8.12202e18	−0.281491
$987$	−2.63740e18	−0.0908059
$988$	−6.36192e18	−0.217605
$989$	−1.34696e19	−0.457696
$990$	2.52396e18	0.0852029
$991$	−2.47165e19	−0.828913	−0.414457	−	0.910069i	$-0.636028\pi$
$991$	−2.47165e19	−0.828913	−0.414457	+	0.910069i	$0.636028\pi$
$992$	−8.61696e18	−0.287097
$993$	6.15675e18	0.203789
$994$	4.67617e18	0.153773
$995$	−9.56060e18	−0.312345
$996$	8.54003e18	0.277188
$997$	−8.99194e18	−0.289958	−0.144979	−	0.989435i	$-0.546311\pi$
$997$	−8.99194e18	−0.289958	−0.144979	+	0.989435i	$0.546311\pi$
$998$	7.70233e18	0.246759
$999$	4.28110e18	0.136264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.d.1.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.d.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-36.3263 q^{2} -729.000 q^{3} -6872.40 q^{4} +50926.0 q^{5} +26481.8 q^{6} -312829. q^{7} +547233. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-36.3263 q^{2} -729.000 q^{3} -6872.40 q^{4} +50926.0 q^{5} +26481.8 q^{6} -312829. q^{7} +547233. q^{8} +531441. q^{9} -1.84995e6 q^{10} -2.56725e6 q^{11} +5.00998e6 q^{12} -1.52376e7 q^{13} +1.13639e7 q^{14} -3.71251e7 q^{15} +3.64198e7 q^{16} -1.84400e8 q^{17} -1.93053e7 q^{18} -6.07523e7 q^{19} -3.49984e8 q^{20} +2.28052e8 q^{21} +9.32584e7 q^{22} +4.01014e8 q^{23} -3.98933e8 q^{24} +1.37276e9 q^{25} +5.53525e8 q^{26} -3.87420e8 q^{27} +2.14989e9 q^{28} -1.21250e9 q^{29} +1.34862e9 q^{30} +1.48417e9 q^{31} -5.80593e9 q^{32} +1.87152e9 q^{33} +6.69856e9 q^{34} -1.59311e10 q^{35} -3.65228e9 q^{36} -1.10503e10 q^{37} +2.20690e9 q^{38} +1.11082e10 q^{39} +2.78684e10 q^{40} +3.77778e10 q^{41} -8.28429e9 q^{42} -3.35887e10 q^{43} +1.76431e10 q^{44} +2.70642e10 q^{45} -1.45673e10 q^{46} -1.15649e10 q^{47} -2.65500e10 q^{48} +9.72922e8 q^{49} -4.98672e10 q^{50} +1.34428e11 q^{51} +1.04719e11 q^{52} +3.78314e10 q^{53} +1.40735e10 q^{54} -1.30740e11 q^{55} -1.71190e11 q^{56} +4.42885e10 q^{57} +4.40456e10 q^{58} +4.21805e10 q^{59} +2.55139e11 q^{60} -2.93008e11 q^{61} -5.39142e10 q^{62} -1.66250e11 q^{63} -8.74432e10 q^{64} -7.75991e11 q^{65} -6.79854e10 q^{66} -6.83114e11 q^{67} +1.26727e12 q^{68} -2.92339e11 q^{69} +5.78719e11 q^{70} +4.11493e11 q^{71} +2.90822e11 q^{72} -7.22231e11 q^{73} +4.01415e11 q^{74} -1.00074e12 q^{75} +4.17515e11 q^{76} +8.03109e11 q^{77} -4.03520e11 q^{78} -4.04241e12 q^{79} +1.85472e12 q^{80} +2.82430e11 q^{81} -1.37233e12 q^{82} +1.70460e12 q^{83} -1.56727e12 q^{84} -9.39076e12 q^{85} +1.22015e12 q^{86} +8.83914e11 q^{87} -1.40488e12 q^{88} -4.85952e12 q^{89} -9.83141e11 q^{90} +4.76676e12 q^{91} -2.75593e12 q^{92} -1.08196e12 q^{93} +4.20109e11 q^{94} -3.09388e12 q^{95} +4.23252e12 q^{96} -2.65734e12 q^{97} -3.53426e10 q^{98} -1.36434e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{2} - 23328 q^{3} + 139174 q^{4} + 2236 q^{5} - 8748 q^{6} + 746845 q^{7} - 733317 q^{8} + 17006112 q^{9}+O(q^{10}) \) 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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