LMFDB - Embedded newform 177.14.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} +O(q^{10})$	\(q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} -2.23492e6 q^{10} +2.81280e6 q^{11} -4.18717e6 q^{12} -3.96387e6 q^{13} -5.74029e6 q^{14} +3.29274e7 q^{15} +1.29339e7 q^{16} -9.19750e7 q^{17} -2.62958e7 q^{18} +2.77273e8 q^{19} -2.59432e8 q^{20} +8.45727e7 q^{21} -1.39178e8 q^{22} -6.95853e8 q^{23} +5.02676e8 q^{24} +8.19439e8 q^{25} +1.96133e8 q^{26} +3.87420e8 q^{27} -6.66339e8 q^{28} -4.72216e9 q^{29} -1.62925e9 q^{30} +1.19494e9 q^{31} -6.28869e9 q^{32} +2.05053e9 q^{33} +4.55094e9 q^{34} +5.24002e9 q^{35} -3.05244e9 q^{36} -1.10540e10 q^{37} -1.37195e10 q^{38} -2.88966e9 q^{39} +3.11452e10 q^{40} -4.13527e10 q^{41} -4.18467e9 q^{42} -4.95977e10 q^{43} -1.61559e10 q^{44} +2.40041e10 q^{45} +3.44309e10 q^{46} +1.54159e10 q^{47} +9.42878e9 q^{48} -8.34302e10 q^{49} -4.05460e10 q^{50} -6.70498e10 q^{51} +2.27673e10 q^{52} +1.00986e11 q^{53} -1.91696e10 q^{54} +1.27048e11 q^{55} +7.99950e10 q^{56} +2.02132e11 q^{57} +2.33653e11 q^{58} +4.21805e10 q^{59} -1.89126e11 q^{60} -4.41939e11 q^{61} -5.91257e10 q^{62} +6.16535e10 q^{63} +2.05212e11 q^{64} -1.79040e11 q^{65} -1.01461e11 q^{66} -1.19202e12 q^{67} +5.28278e11 q^{68} -5.07277e11 q^{69} -2.59277e11 q^{70} +2.02385e12 q^{71} +3.66451e11 q^{72} -1.19897e11 q^{73} +5.46952e11 q^{74} +5.97371e11 q^{75} -1.59258e12 q^{76} +3.26318e11 q^{77} +1.42981e11 q^{78} -1.71085e11 q^{79} +5.84195e11 q^{80} +2.82430e11 q^{81} +2.04614e12 q^{82} -5.24484e12 q^{83} -4.85761e11 q^{84} -4.15432e12 q^{85} +2.45410e12 q^{86} -3.44245e12 q^{87} +1.93954e12 q^{88} +2.52640e12 q^{89} -1.18773e12 q^{90} -4.59856e11 q^{91} +3.99678e12 q^{92} +8.71109e11 q^{93} -7.62781e11 q^{94} +1.25239e13 q^{95} -4.58446e12 q^{96} -6.11249e12 q^{97} +4.12814e12 q^{98} +1.49484e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) $ 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−49.4802	−0.546684	−0.273342	−	0.961917i	$-0.588129\pi$
$2$	−49.4802	−0.546684	−0.273342	+	0.961917i	$0.588129\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−5743.71	−0.701137
$5$	45167.9	1.29278	0.646391	−	0.763007i	$-0.276278\pi$
$5$	45167.9	1.29278	0.646391	+	0.763007i	$0.276278\pi$
$6$	−36071.0	−0.315628
$7$	116012.	0.372705	0.186353	−	0.982483i	$-0.440333\pi$
$7$	116012.	0.372705	0.186353	+	0.982483i	$0.440333\pi$
$8$	689542.	0.929984
$9$	531441.	0.333333
$10$	−2.23492e6	−0.706743
$11$	2.81280e6	0.478725	0.239362	−	0.970930i	$-0.423062\pi$
$11$	2.81280e6	0.478725	0.239362	+	0.970930i	$0.423062\pi$
$12$	−4.18717e6	−0.404801
$13$	−3.96387e6	−0.227765	−0.113883	−	0.993494i	$-0.536329\pi$
$13$	−3.96387e6	−0.227765	−0.113883	+	0.993494i	$0.536329\pi$
$14$	−5.74029e6	−0.203752
$15$	3.29274e7	0.746388
$16$	1.29339e7	0.192729
$17$	−9.19750e7	−0.924170	−0.462085	−	0.886836i	$-0.652899\pi$
$17$	−9.19750e7	−0.924170	−0.462085	+	0.886836i	$0.652899\pi$
$18$	−2.62958e7	−0.182228
$19$	2.77273e8	1.35210	0.676051	−	0.736855i	$-0.263690\pi$
$19$	2.77273e8	1.35210	0.676051	+	0.736855i	$0.263690\pi$
$20$	−2.59432e8	−0.906417
$21$	8.45727e7	0.215181
$22$	−1.39178e8	−0.261711
$23$	−6.95853e8	−0.980136	−0.490068	−	0.871684i	$-0.663028\pi$
$23$	−6.95853e8	−0.980136	−0.490068	+	0.871684i	$0.663028\pi$
$24$	5.02676e8	0.536927
$25$	8.19439e8	0.671284
$26$	1.96133e8	0.124516
$27$	3.87420e8	0.192450
$28$	−6.66339e8	−0.261317
$29$	−4.72216e9	−1.47419	−0.737095	−	0.675789i	$-0.763803\pi$
$29$	−4.72216e9	−1.47419	−0.737095	+	0.675789i	$0.763803\pi$
$30$	−1.62925e9	−0.408038
$31$	1.19494e9	0.241821	0.120910	−	0.992663i	$-0.461419\pi$
$31$	1.19494e9	0.241821	0.120910	+	0.992663i	$0.461419\pi$
$32$	−6.28869e9	−1.03535
$33$	2.05053e9	0.276392
$34$	4.55094e9	0.505229
$35$	5.24002e9	0.481826
$36$	−3.05244e9	−0.233712
$37$	−1.10540e10	−0.708283	−0.354142	−	0.935192i	$-0.615227\pi$
$37$	−1.10540e10	−0.708283	−0.354142	+	0.935192i	$0.615227\pi$
$38$	−1.37195e10	−0.739173
$39$	−2.88966e9	−0.131500
$40$	3.11452e10	1.20227
$41$	−4.13527e10	−1.35959	−0.679796	−	0.733402i	$-0.737932\pi$
$41$	−4.13527e10	−1.35959	−0.679796	+	0.733402i	$0.737932\pi$
$42$	−4.18467e9	−0.117636
$43$	−4.95977e10	−1.19651	−0.598255	−	0.801306i	$-0.704139\pi$
$43$	−4.95977e10	−1.19651	−0.598255	+	0.801306i	$0.704139\pi$
$44$	−1.61559e10	−0.335652
$45$	2.40041e10	0.430927
$46$	3.44309e10	0.535825
$47$	1.54159e10	0.208609	0.104304	−	0.994545i	$-0.466738\pi$
$47$	1.54159e10	0.208609	0.104304	+	0.994545i	$0.466738\pi$
$48$	9.42878e9	0.111272
$49$	−8.34302e10	−0.861091
$50$	−4.05460e10	−0.366980
$51$	−6.70498e10	−0.533570
$52$	2.27673e10	0.159695
$53$	1.00986e11	0.625848	0.312924	−	0.949778i	$-0.398691\pi$
$53$	1.00986e11	0.625848	0.312924	+	0.949778i	$0.398691\pi$
$54$	−1.91696e10	−0.105209
$55$	1.27048e11	0.618887
$56$	7.99950e10	0.346610
$57$	2.02132e11	0.780637
$58$	2.33653e11	0.805916
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	−1.89126e11	−0.523320
$61$	−4.41939e11	−1.09829	−0.549147	−	0.835726i	$-0.685047\pi$
$61$	−4.41939e11	−1.09829	−0.549147	+	0.835726i	$0.685047\pi$
$62$	−5.91257e10	−0.132200
$63$	6.16535e10	0.124235
$64$	2.05212e11	0.373278
$65$	−1.79040e11	−0.294451
$66$	−1.01461e11	−0.151099
$67$	−1.19202e12	−1.60990	−0.804948	−	0.593346i	$-0.797807\pi$
$67$	−1.19202e12	−1.60990	−0.804948	+	0.593346i	$0.797807\pi$
$68$	5.28278e11	0.647970
$69$	−5.07277e11	−0.565882
$70$	−2.59277e11	−0.263407
$71$	2.02385e12	1.87499	0.937493	−	0.348004i	$-0.113140\pi$
$71$	2.02385e12	1.87499	0.937493	+	0.348004i	$0.113140\pi$
$72$	3.66451e11	0.309995
$73$	−1.19897e11	−0.0927278	−0.0463639	−	0.998925i	$-0.514763\pi$
$73$	−1.19897e11	−0.0927278	−0.0463639	+	0.998925i	$0.514763\pi$
$74$	5.46952e11	0.387207
$75$	5.97371e11	0.387566
$76$	−1.59258e12	−0.948009
$77$	3.26318e11	0.178423
$78$	1.42981e11	0.0718892
$79$	−1.71085e11	−0.0791838	−0.0395919	−	0.999216i	$-0.512606\pi$
$79$	−1.71085e11	−0.0791838	−0.0395919	+	0.999216i	$0.512606\pi$
$80$	5.84195e11	0.249157
$81$	2.82430e11	0.111111
$82$	2.04614e12	0.743267
$83$	−5.24484e12	−1.76086	−0.880430	−	0.474176i	$-0.842746\pi$
$83$	−5.24484e12	−1.76086	−0.880430	+	0.474176i	$0.842746\pi$
$84$	−4.85761e11	−0.150872
$85$	−4.15432e12	−1.19475
$86$	2.45410e12	0.654113
$87$	−3.44245e12	−0.851124
$88$	1.93954e12	0.445206
$89$	2.52640e12	0.538849	0.269425	−	0.963021i	$-0.413166\pi$
$89$	2.52640e12	0.538849	0.269425	+	0.963021i	$0.413166\pi$
$90$	−1.18773e12	−0.235581
$91$	−4.59856e11	−0.0848893
$92$	3.99678e12	0.687209
$93$	8.71109e11	0.139615
$94$	−7.62781e11	−0.114043
$95$	1.25239e13	1.74797
$96$	−4.58446e12	−0.597757
$97$	−6.11249e12	−0.745078	−0.372539	−	0.928016i	$-0.621513\pi$
$97$	−6.11249e12	−0.745078	−0.372539	+	0.928016i	$0.621513\pi$
$98$	4.12814e12	0.470745
$99$	1.49484e12	0.159575
$100$	−4.70662e12	−0.470662
$101$	−1.01497e12	−0.0951407	−0.0475703	−	0.998868i	$-0.515148\pi$
$101$	−1.01497e12	−0.0951407	−0.0475703	+	0.998868i	$0.515148\pi$
$102$	3.31764e12	0.291694
$103$	2.30285e13	1.90031	0.950153	−	0.311785i	$-0.100927\pi$
$103$	2.30285e13	1.90031	0.950153	+	0.311785i	$0.100927\pi$
$104$	−2.73325e12	−0.211818
$105$	3.81997e12	0.278183
$106$	−4.99681e12	−0.342141
$107$	−4.93765e12	−0.318072	−0.159036	−	0.987273i	$-0.550839\pi$
$107$	−4.93765e12	−0.318072	−0.159036	+	0.987273i	$0.550839\pi$
$108$	−2.22523e12	−0.134934
$109$	2.12524e13	1.21377	0.606883	−	0.794791i	$-0.292420\pi$
$109$	2.12524e13	1.21377	0.606883	+	0.794791i	$0.292420\pi$
$110$	−6.28637e12	−0.338335
$111$	−8.05834e12	−0.408927
$112$	1.50048e12	0.0718312
$113$	−2.30395e13	−1.04103	−0.520514	−	0.853853i	$-0.674260\pi$
$113$	−2.30395e13	−1.04103	−0.520514	+	0.853853i	$0.674260\pi$
$114$	−1.00015e13	−0.426762
$115$	−3.14302e13	−1.26710
$116$	2.71227e13	1.03361
$117$	−2.10656e12	−0.0759218
$118$	−2.08710e12	−0.0711722
$119$	−1.06702e13	−0.344443
$120$	2.27048e13	0.694129
$121$	−2.66109e13	−0.770822
$122$	2.18672e13	0.600420
$123$	−3.01461e13	−0.784960
$124$	−6.86337e12	−0.169549
$125$	−1.81243e13	−0.424958
$126$	−3.05063e12	−0.0679173
$127$	5.96752e13	1.26203	0.631015	−	0.775771i	$-0.282639\pi$
$127$	5.96752e13	1.26203	0.631015	+	0.775771i	$0.282639\pi$
$128$	4.13631e13	0.831281
$129$	−3.61567e13	−0.690806
$130$	8.85893e12	0.160972
$131$	2.82008e13	0.487527	0.243763	−	0.969835i	$-0.421618\pi$
$131$	2.82008e13	0.487527	0.243763	+	0.969835i	$0.421618\pi$
$132$	−1.17776e13	−0.193789
$133$	3.21670e13	0.503935
$134$	5.89814e13	0.880104
$135$	1.74990e13	0.248796
$136$	−6.34206e13	−0.859464
$137$	−3.39933e13	−0.439248	−0.219624	−	0.975585i	$-0.570483\pi$
$137$	−3.39933e13	−0.439248	−0.219624	+	0.975585i	$0.570483\pi$
$138$	2.51001e13	0.309358
$139$	−5.29965e13	−0.623234	−0.311617	−	0.950208i	$-0.600871\pi$
$139$	−5.29965e13	−0.623234	−0.311617	+	0.950208i	$0.600871\pi$
$140$	−3.00972e13	−0.337826
$141$	1.12382e13	0.120440
$142$	−1.00140e14	−1.02502
$143$	−1.11496e13	−0.109037
$144$	6.87358e12	0.0642431
$145$	−2.13290e14	−1.90581
$146$	5.93253e12	0.0506928
$147$	−6.08207e13	−0.497151
$148$	6.34908e13	0.496603
$149$	2.05324e13	0.153720	0.0768598	−	0.997042i	$-0.475511\pi$
$149$	2.05324e13	0.153720	0.0768598	+	0.997042i	$0.475511\pi$
$150$	−2.95580e13	−0.211876
$151$	1.23313e14	0.846565	0.423282	−	0.905998i	$-0.360878\pi$
$151$	1.23313e14	0.846565	0.423282	+	0.905998i	$0.360878\pi$
$152$	1.91191e14	1.25743
$153$	−4.88793e13	−0.308057
$154$	−1.61463e13	−0.0975411
$155$	5.39728e13	0.312622
$156$	1.65974e13	0.0921998
$157$	3.04482e14	1.62261	0.811306	−	0.584622i	$-0.198757\pi$
$157$	3.04482e14	1.62261	0.811306	+	0.584622i	$0.198757\pi$
$158$	8.46532e12	0.0432885
$159$	7.36189e13	0.361333
$160$	−2.84047e14	−1.33848
$161$	−8.07272e13	−0.365302
$162$	−1.39747e13	−0.0607427
$163$	1.60383e14	0.669791	0.334895	−	0.942255i	$-0.391299\pi$
$163$	1.60383e14	0.669791	0.334895	+	0.942255i	$0.391299\pi$
$164$	2.37518e14	0.953259
$165$	9.26182e13	0.357314
$166$	2.59516e14	0.962634
$167$	−2.25333e14	−0.803837	−0.401919	−	0.915675i	$-0.631657\pi$
$167$	−2.25333e14	−0.803837	−0.401919	+	0.915675i	$0.631657\pi$
$168$	5.83164e13	0.200115
$169$	−2.87163e14	−0.948123
$170$	2.05557e14	0.653151
$171$	1.47354e14	0.450701
$172$	2.84875e14	0.838917
$173$	3.94268e14	1.11813	0.559064	−	0.829125i	$-0.311161\pi$
$173$	3.94268e14	1.11813	0.559064	+	0.829125i	$0.311161\pi$
$174$	1.70333e14	0.465296
$175$	9.50646e13	0.250191
$176$	3.63803e13	0.0922644
$177$	3.07496e13	0.0751646
$178$	−1.25007e14	−0.294580
$179$	8.16873e14	1.85614	0.928068	−	0.372410i	$-0.121468\pi$
$179$	8.16873e14	1.85614	0.928068	+	0.372410i	$0.121468\pi$
$180$	−1.37873e14	−0.302139
$181$	4.65273e14	0.983552	0.491776	−	0.870722i	$-0.336348\pi$
$181$	4.65273e14	0.983552	0.491776	+	0.870722i	$0.336348\pi$
$182$	2.27538e13	0.0464076
$183$	−3.22174e14	−0.634101
$184$	−4.79819e14	−0.911511
$185$	−4.99285e14	−0.915655
$186$	−4.31026e13	−0.0763255
$187$	−2.58707e14	−0.442423
$188$	−8.85445e13	−0.146263
$189$	4.49454e13	0.0717271
$190$	−6.19683e14	−0.955589
$191$	1.56260e14	0.232879	0.116439	−	0.993198i	$-0.462852\pi$
$191$	1.56260e14	0.232879	0.116439	+	0.993198i	$0.462852\pi$
$192$	1.49599e14	0.215512
$193$	−1.36488e15	−1.90095	−0.950475	−	0.310801i	$-0.899403\pi$
$193$	−1.36488e15	−1.90095	−0.950475	+	0.310801i	$0.899403\pi$
$194$	3.02447e14	0.407322
$195$	−1.30520e14	−0.170001
$196$	4.79199e14	0.603742
$197$	−1.12615e15	−1.37266	−0.686332	−	0.727288i	$-0.740780\pi$
$197$	−1.12615e15	−1.37266	−0.686332	+	0.727288i	$0.740780\pi$
$198$	−7.39647e13	−0.0872371
$199$	−1.46375e15	−1.67080	−0.835398	−	0.549646i	$-0.814763\pi$
$199$	−1.46375e15	−1.67080	−0.835398	+	0.549646i	$0.814763\pi$
$200$	5.65037e14	0.624284
$201$	−8.68983e14	−0.929474
$202$	5.02211e13	0.0520119
$203$	−5.47826e14	−0.549438
$204$	3.85115e14	0.374105
$205$	−1.86781e15	−1.75765
$206$	−1.13945e15	−1.03887
$207$	−3.69805e14	−0.326712
$208$	−5.12681e13	−0.0438971
$209$	7.79914e14	0.647285
$210$	−1.89013e14	−0.152078
$211$	−7.23736e14	−0.564605	−0.282302	−	0.959325i	$-0.591098\pi$
$211$	−7.23736e14	−0.564605	−0.282302	+	0.959325i	$0.591098\pi$
$212$	−5.80036e14	−0.438805
$213$	1.47538e15	1.08252
$214$	2.44316e14	0.173885
$215$	−2.24022e15	−1.54683
$216$	2.67143e14	0.178976
$217$	1.38627e14	0.0901279
$218$	−1.05157e15	−0.663546
$219$	−8.74050e13	−0.0535364
$220$	−7.29728e14	−0.433924
$221$	3.64577e14	0.210494
$222$	3.98728e14	0.223554
$223$	−3.59902e15	−1.95976	−0.979880	−	0.199586i	$-0.936040\pi$
$223$	−3.59902e15	−1.95976	−0.979880	+	0.199586i	$0.936040\pi$
$224$	−7.29563e14	−0.385879
$225$	4.35483e14	0.223761
$226$	1.14000e15	0.569114
$227$	−2.80159e15	−1.35905	−0.679526	−	0.733651i	$-0.737815\pi$
$227$	−2.80159e15	−1.35905	−0.679526	+	0.733651i	$0.737815\pi$
$228$	−1.16099e15	−0.547333
$229$	−1.81469e15	−0.831520	−0.415760	−	0.909474i	$-0.636484\pi$
$229$	−1.81469e15	−0.831520	−0.415760	+	0.909474i	$0.636484\pi$
$230$	1.55517e15	0.692704
$231$	2.37886e14	0.103013
$232$	−3.25612e15	−1.37097
$233$	−4.57053e15	−1.87134	−0.935672	−	0.352872i	$-0.885205\pi$
$233$	−4.57053e15	−1.87134	−0.935672	+	0.352872i	$0.885205\pi$
$234$	1.04233e14	0.0415052
$235$	6.96304e14	0.269686
$236$	−2.42273e14	−0.0912802
$237$	−1.24721e14	−0.0457168
$238$	5.27963e14	0.188301
$239$	3.93199e15	1.36466	0.682332	−	0.731042i	$-0.260966\pi$
$239$	3.93199e15	1.36466	0.682332	+	0.731042i	$0.260966\pi$
$240$	4.25878e14	0.143851
$241$	−2.65595e15	−0.873190	−0.436595	−	0.899658i	$-0.643816\pi$
$241$	−2.65595e15	−0.873190	−0.436595	+	0.899658i	$0.643816\pi$
$242$	1.31671e15	0.421396
$243$	2.05891e14	0.0641500
$244$	2.53837e15	0.770055
$245$	−3.76837e15	−1.11320
$246$	1.49163e15	0.429125
$247$	−1.09908e15	−0.307962
$248$	8.23958e14	0.224890
$249$	−3.82349e15	−1.01663
$250$	8.96793e14	0.232318
$251$	1.62523e14	0.0410238	0.0205119	−	0.999790i	$-0.493470\pi$
$251$	1.62523e14	0.0410238	0.0205119	+	0.999790i	$0.493470\pi$
$252$	−3.54120e14	−0.0871057
$253$	−1.95729e15	−0.469216
$254$	−2.95274e15	−0.689931
$255$	−3.02850e15	−0.689789
$256$	−3.72775e15	−0.827726
$257$	−8.58304e15	−1.85813	−0.929064	−	0.369918i	$-0.879386\pi$
$257$	−8.58304e15	−1.85813	−0.929064	+	0.369918i	$0.879386\pi$
$258$	1.78904e15	0.377652
$259$	−1.28239e15	−0.263981
$260$	1.02835e15	0.206450
$261$	−2.50955e15	−0.491397
$262$	−1.39538e15	−0.266523
$263$	9.79891e14	0.182585	0.0912926	−	0.995824i	$-0.470900\pi$
$263$	9.79891e14	0.182585	0.0912926	+	0.995824i	$0.470900\pi$
$264$	1.41393e15	0.257040
$265$	4.56134e15	0.809085
$266$	−1.59163e15	−0.275493
$267$	1.84175e15	0.311105
$268$	6.84663e15	1.12876
$269$	3.73415e15	0.600900	0.300450	−	0.953798i	$-0.402863\pi$
$269$	3.73415e15	0.600900	0.300450	+	0.953798i	$0.402863\pi$
$270$	−8.65853e14	−0.136013
$271$	9.60543e15	1.47305	0.736523	−	0.676413i	$-0.236466\pi$
$271$	9.60543e15	1.47305	0.736523	+	0.676413i	$0.236466\pi$
$272$	−1.18959e15	−0.178115
$273$	−3.35235e14	−0.0490109
$274$	1.68199e15	0.240130
$275$	2.30491e15	0.321360
$276$	2.91365e15	0.396761
$277$	−2.83716e15	−0.377369	−0.188684	−	0.982038i	$-0.560422\pi$
$277$	−2.83716e15	−0.377369	−0.188684	+	0.982038i	$0.560422\pi$
$278$	2.62228e15	0.340712
$279$	6.35038e14	0.0806070
$280$	3.61321e15	0.448091
$281$	−8.61754e15	−1.04422	−0.522110	−	0.852878i	$-0.674855\pi$
$281$	−8.61754e15	−1.04422	−0.522110	+	0.852878i	$0.674855\pi$
$282$	−5.56068e14	−0.0658428
$283$	9.38782e15	1.08631	0.543154	−	0.839633i	$-0.317230\pi$
$283$	9.38782e15	1.08631	0.543154	+	0.839633i	$0.317230\pi$
$284$	−1.16244e16	−1.31462
$285$	9.12989e15	1.00919
$286$	5.51683e14	0.0596088
$287$	−4.79740e15	−0.506727
$288$	−3.34207e15	−0.345115
$289$	−1.44517e15	−0.145909
$290$	1.05536e16	1.04187
$291$	−4.45601e15	−0.430171
$292$	6.88655e14	0.0650149
$293$	−1.06056e16	−0.979258	−0.489629	−	0.871931i	$-0.662868\pi$
$293$	−1.06056e16	−0.979258	−0.489629	+	0.871931i	$0.662868\pi$
$294$	3.00942e15	0.271784
$295$	1.90521e15	0.168306
$296$	−7.62217e15	−0.658692
$297$	1.08974e15	0.0921306
$298$	−1.01595e15	−0.0840361
$299$	2.75827e15	0.223241
$300$	−3.43113e15	−0.271737
$301$	−5.75392e15	−0.445945
$302$	−6.10157e15	−0.462803
$303$	−7.39916e14	−0.0549295
$304$	3.58621e15	0.260590
$305$	−1.99615e16	−1.41985
$306$	2.41856e15	0.168410
$307$	−7.13186e15	−0.486187	−0.243093	−	0.970003i	$-0.578162\pi$
$307$	−7.13186e15	−0.486187	−0.243093	+	0.970003i	$0.578162\pi$
$308$	−1.87428e15	−0.125099
$309$	1.67878e16	1.09714
$310$	−2.67058e15	−0.170905
$311$	2.89266e16	1.81282	0.906409	−	0.422402i	$-0.138813\pi$
$311$	2.89266e16	1.81282	0.906409	+	0.422402i	$0.138813\pi$
$312$	−1.99254e15	−0.122293
$313$	−3.69552e15	−0.222145	−0.111073	−	0.993812i	$-0.535429\pi$
$313$	−3.69552e15	−0.222145	−0.111073	+	0.993812i	$0.535429\pi$
$314$	−1.50658e16	−0.887055
$315$	2.78476e15	0.160609
$316$	9.82664e14	0.0555187
$317$	−7.31483e15	−0.404873	−0.202437	−	0.979295i	$-0.564886\pi$
$317$	−7.31483e15	−0.404873	−0.202437	+	0.979295i	$0.564886\pi$
$318$	−3.64268e15	−0.197535
$319$	−1.32825e16	−0.705731
$320$	9.26898e15	0.482566
$321$	−3.59955e15	−0.183639
$322$	3.99440e15	0.199705
$323$	−2.55022e16	−1.24957
$324$	−1.62219e15	−0.0779041
$325$	−3.24815e15	−0.152895
$326$	−7.93578e15	−0.366164
$327$	1.54930e16	0.700768
$328$	−2.85144e16	−1.26440
$329$	1.78843e15	0.0777496
$330$	−4.58276e15	−0.195338
$331$	1.60515e16	0.670862	0.335431	−	0.942065i	$-0.391118\pi$
$331$	1.60515e16	0.670862	0.335431	+	0.942065i	$0.391118\pi$
$332$	3.01249e16	1.23460
$333$	−5.87453e15	−0.236094
$334$	1.11495e16	0.439445
$335$	−5.38411e16	−2.08124
$336$	1.09385e15	0.0414718
$337$	5.53045e15	0.205668	0.102834	−	0.994699i	$-0.467209\pi$
$337$	5.53045e15	0.205668	0.102834	+	0.994699i	$0.467209\pi$
$338$	1.42089e16	0.518324
$339$	−1.67958e16	−0.601038
$340$	2.38612e16	0.837683
$341$	3.36111e15	0.115766
$342$	−7.29112e15	−0.246391
$343$	−2.09192e16	−0.693638
$344$	−3.41997e16	−1.11274
$345$	−2.29126e16	−0.731562
$346$	−1.95084e16	−0.611262
$347$	−1.39023e16	−0.427507	−0.213754	−	0.976888i	$-0.568569\pi$
$347$	−1.39023e16	−0.427507	−0.213754	+	0.976888i	$0.568569\pi$
$348$	1.97725e16	0.596754
$349$	−6.02345e15	−0.178435	−0.0892174	−	0.996012i	$-0.528437\pi$
$349$	−6.02345e15	−0.178435	−0.0892174	+	0.996012i	$0.528437\pi$
$350$	−4.70382e15	−0.136775
$351$	−1.53569e15	−0.0438335
$352$	−1.76888e16	−0.495646
$353$	−5.04897e16	−1.38889	−0.694444	−	0.719547i	$-0.744350\pi$
$353$	−5.04897e16	−1.38889	−0.694444	+	0.719547i	$0.744350\pi$
$354$	−1.52150e15	−0.0410913
$355$	9.14129e16	2.42395
$356$	−1.45109e16	−0.377807
$357$	−7.77858e15	−0.198864
$358$	−4.04190e16	−1.01472
$359$	5.12566e16	1.26368	0.631838	−	0.775100i	$-0.282301\pi$
$359$	5.12566e16	1.26368	0.631838	+	0.775100i	$0.282301\pi$
$360$	1.65518e16	0.400755
$361$	3.48275e16	0.828181
$362$	−2.30218e16	−0.537692
$363$	−1.93993e16	−0.445035
$364$	2.64128e15	0.0595190
$365$	−5.41550e15	−0.119877
$366$	1.59412e16	0.346653
$367$	3.05992e16	0.653703	0.326851	−	0.945076i	$-0.394012\pi$
$367$	3.05992e16	0.653703	0.326851	+	0.945076i	$0.394012\pi$
$368$	−9.00006e15	−0.188901
$369$	−2.19765e16	−0.453197
$370$	2.47047e16	0.500574
$371$	1.17156e16	0.233257
$372$	−5.00340e15	−0.0978894
$373$	−3.50925e16	−0.674695	−0.337347	−	0.941380i	$-0.609530\pi$
$373$	−3.50925e16	−0.674695	−0.337347	+	0.941380i	$0.609530\pi$
$374$	1.28009e16	0.241866
$375$	−1.32126e16	−0.245350
$376$	1.06299e16	0.194003
$377$	1.87180e16	0.335769
$378$	−2.22391e15	−0.0392121
$379$	−4.01424e16	−0.695742	−0.347871	−	0.937542i	$-0.613095\pi$
$379$	−4.01424e16	−0.695742	−0.347871	+	0.937542i	$0.613095\pi$
$380$	−7.19334e16	−1.22557
$381$	4.35032e16	0.728633
$382$	−7.73176e15	−0.127311
$383$	1.16199e17	1.88109	0.940543	−	0.339675i	$-0.110317\pi$
$383$	1.16199e17	1.88109	0.940543	+	0.339675i	$0.110317\pi$
$384$	3.01537e16	0.479940
$385$	1.47391e16	0.230662
$386$	6.75343e16	1.03922
$387$	−2.63582e16	−0.398837
$388$	3.51084e16	0.522402
$389$	7.91494e16	1.15818	0.579089	−	0.815265i	$-0.303409\pi$
$389$	7.91494e16	1.15818	0.579089	+	0.815265i	$0.303409\pi$
$390$	6.45816e15	0.0929370
$391$	6.40011e16	0.905813
$392$	−5.75286e16	−0.800801
$393$	2.05584e16	0.281474
$394$	5.57219e16	0.750414
$395$	−7.72756e15	−0.102367
$396$	−8.58591e15	−0.111884
$397$	−3.88974e16	−0.498634	−0.249317	−	0.968422i	$-0.580206\pi$
$397$	−3.88974e16	−0.498634	−0.249317	+	0.968422i	$0.580206\pi$
$398$	7.24268e16	0.913397
$399$	2.34497e16	0.290947
$400$	1.05985e16	0.129376
$401$	6.84850e16	0.822540	0.411270	−	0.911513i	$-0.365085\pi$
$401$	6.84850e16	0.822540	0.411270	+	0.911513i	$0.365085\pi$
$402$	4.29974e16	0.508128
$403$	−4.73657e15	−0.0550784
$404$	5.82972e15	0.0667066
$405$	1.27568e16	0.143642
$406$	2.71065e16	0.300369
$407$	−3.10926e16	−0.339073
$408$	−4.62336e16	−0.496212
$409$	1.49171e17	1.57573	0.787864	−	0.615849i	$-0.211187\pi$
$409$	1.49171e17	1.57573	0.787864	+	0.615849i	$0.211187\pi$
$410$	9.24198e16	0.960881
$411$	−2.47811e16	−0.253600
$412$	−1.32269e17	−1.33237
$413$	4.89344e15	0.0485221
$414$	1.82980e16	0.178608
$415$	−2.36899e17	−2.27641
$416$	2.49276e16	0.235816
$417$	−3.86344e16	−0.359824
$418$	−3.85903e16	−0.353860
$419$	−1.77108e17	−1.59899	−0.799496	−	0.600672i	$-0.794900\pi$
$419$	−1.77108e17	−1.59899	−0.799496	+	0.600672i	$0.794900\pi$
$420$	−2.19408e16	−0.195044
$421$	1.06774e17	0.934610	0.467305	−	0.884096i	$-0.345225\pi$
$421$	1.06774e17	0.934610	0.467305	+	0.884096i	$0.345225\pi$
$422$	3.58106e16	0.308660
$423$	8.19264e15	0.0695363
$424$	6.96342e16	0.582029
$425$	−7.53679e16	−0.620381
$426$	−7.30022e16	−0.591798
$427$	−5.12702e16	−0.409340
$428$	2.83605e16	0.223012
$429$	−8.12804e15	−0.0629525
$430$	1.10847e17	0.845625
$431$	−5.54125e16	−0.416395	−0.208198	−	0.978087i	$-0.566760\pi$
$431$	−5.54125e16	−0.416395	−0.208198	+	0.978087i	$0.566760\pi$
$432$	5.01084e15	0.0370908
$433$	2.63489e17	1.92128	0.960641	−	0.277793i	$-0.0896029\pi$
$433$	2.63489e17	1.92128	0.960641	+	0.277793i	$0.0896029\pi$
$434$	−6.85928e15	−0.0492715
$435$	−1.55488e17	−1.10032
$436$	−1.22067e17	−0.851016
$437$	−1.92941e17	−1.32524
$438$	4.32481e15	0.0292675
$439$	−2.30044e16	−0.153388	−0.0766941	−	0.997055i	$-0.524436\pi$
$439$	−2.30044e16	−0.153388	−0.0766941	+	0.997055i	$0.524436\pi$
$440$	8.76050e16	0.575555
$441$	−4.43383e16	−0.287030
$442$	−1.80393e16	−0.115074
$443$	1.69714e17	1.06682	0.533412	−	0.845856i	$-0.320910\pi$
$443$	1.69714e17	1.06682	0.533412	+	0.845856i	$0.320910\pi$
$444$	4.62848e16	0.286714
$445$	1.14112e17	0.696614
$446$	1.78080e17	1.07137
$447$	1.49681e16	0.0887501
$448$	2.38070e16	0.139122
$449$	2.77603e16	0.159891	0.0799453	−	0.996799i	$-0.474525\pi$
$449$	2.77603e16	0.159891	0.0799453	+	0.996799i	$0.474525\pi$
$450$	−2.15478e16	−0.122327
$451$	−1.16317e17	−0.650870
$452$	1.32332e17	0.729903
$453$	8.98955e16	0.488764
$454$	1.38623e17	0.742972
$455$	−2.07708e16	−0.109743
$456$	1.39379e17	0.725980
$457$	−1.57594e17	−0.809254	−0.404627	−	0.914482i	$-0.632599\pi$
$457$	−1.57594e17	−0.809254	−0.404627	+	0.914482i	$0.632599\pi$
$458$	8.97914e16	0.454579
$459$	−3.56330e16	−0.177857
$460$	1.80526e17	0.888412
$461$	−8.30522e16	−0.402991	−0.201495	−	0.979489i	$-0.564580\pi$
$461$	−8.30522e16	−0.402991	−0.201495	+	0.979489i	$0.564580\pi$
$462$	−1.17706e16	−0.0563154
$463$	−1.07084e17	−0.505184	−0.252592	−	0.967573i	$-0.581283\pi$
$463$	−1.07084e17	−0.505184	−0.252592	+	0.967573i	$0.581283\pi$
$464$	−6.10757e16	−0.284120
$465$	3.93462e16	0.180492
$466$	2.26151e17	1.02303
$467$	1.05563e17	0.470926	0.235463	−	0.971883i	$-0.424339\pi$
$467$	1.05563e17	0.470926	0.235463	+	0.971883i	$0.424339\pi$
$468$	1.20995e16	0.0532316
$469$	−1.38289e17	−0.600016
$470$	−3.44532e16	−0.147433
$471$	2.21968e17	0.936815
$472$	2.90852e16	0.121074
$473$	−1.39508e17	−0.572799
$474$	6.17122e15	0.0249926
$475$	2.27208e17	0.907645
$476$	6.12866e16	0.241502
$477$	5.36682e16	0.208616
$478$	−1.94555e17	−0.746040
$479$	−2.85877e17	−1.08143	−0.540716	−	0.841205i	$-0.681846\pi$
$479$	−2.85877e17	−1.08143	−0.540716	+	0.841205i	$0.681846\pi$
$480$	−2.07070e17	−0.772770
$481$	4.38165e16	0.161322
$482$	1.31417e17	0.477359
$483$	−5.88501e16	−0.210907
$484$	1.52845e17	0.540452
$485$	−2.76089e17	−0.963224
$486$	−1.01875e16	−0.0350698
$487$	−1.47491e17	−0.500989	−0.250495	−	0.968118i	$-0.580593\pi$
$487$	−1.47491e17	−0.500989	−0.250495	+	0.968118i	$0.580593\pi$
$488$	−3.04736e17	−1.02140
$489$	1.16919e17	0.386704
$490$	1.86460e17	0.608570
$491$	−4.91532e17	−1.58315	−0.791575	−	0.611072i	$-0.790739\pi$
$491$	−4.91532e17	−1.58315	−0.791575	+	0.611072i	$0.790739\pi$
$492$	1.73150e17	0.550365
$493$	4.34320e17	1.36240
$494$	5.43825e16	0.168358
$495$	6.75186e16	0.206296
$496$	1.54551e16	0.0466060
$497$	2.34790e17	0.698817
$498$	1.89187e17	0.555777
$499$	3.38522e17	0.981598	0.490799	−	0.871273i	$-0.336705\pi$
$499$	3.38522e17	0.981598	0.490799	+	0.871273i	$0.336705\pi$
$500$	1.04101e17	0.297954
$501$	−1.64268e17	−0.464096
$502$	−8.04166e15	−0.0224270
$503$	−2.54609e17	−0.700942	−0.350471	−	0.936574i	$-0.613978\pi$
$503$	−2.54609e17	−0.700942	−0.350471	+	0.936574i	$0.613978\pi$
$504$	4.25126e16	0.115537
$505$	−4.58443e16	−0.122996
$506$	9.68472e16	0.256513
$507$	−2.09342e17	−0.547399
$508$	−3.42757e17	−0.884855
$509$	1.95923e17	0.499366	0.249683	−	0.968328i	$-0.419674\pi$
$509$	1.95923e17	0.499366	0.249683	+	0.968328i	$0.419674\pi$
$510$	1.49851e17	0.377097
$511$	−1.39095e16	−0.0345601
$512$	−1.54397e17	−0.378777
$513$	1.07421e17	0.260212
$514$	4.24690e17	1.01581
$515$	1.04015e18	2.45668
$516$	2.07674e17	0.484349
$517$	4.33618e16	0.0998662
$518$	6.34530e16	0.144314
$519$	2.87421e17	0.645551
$520$	−1.23455e17	−0.273835
$521$	−7.64099e16	−0.167380	−0.0836902	−	0.996492i	$-0.526671\pi$
$521$	−7.64099e16	−0.167380	−0.0836902	+	0.996492i	$0.526671\pi$
$522$	1.24173e17	0.268639
$523$	6.49832e17	1.38848	0.694240	−	0.719743i	$-0.255741\pi$
$523$	6.49832e17	1.38848	0.694240	+	0.719743i	$0.255741\pi$
$524$	−1.61977e17	−0.341823
$525$	6.93021e16	0.144448
$526$	−4.84852e16	−0.0998163
$527$	−1.09904e17	−0.223484
$528$	2.65212e16	0.0532689
$529$	−1.98253e16	−0.0393332
$530$	−2.25696e17	−0.442314
$531$	2.24165e16	0.0433963
$532$	−1.84758e17	−0.353328
$533$	1.63917e17	0.309668
$534$	−9.11299e16	−0.170076
$535$	−2.23024e17	−0.411198
$536$	−8.21948e17	−1.49718
$537$	5.95501e17	1.07164
$538$	−1.84766e17	−0.328502
$539$	−2.34672e17	−0.412226
$540$	−1.00509e17	−0.174440
$541$	−1.92053e16	−0.0329336	−0.0164668	−	0.999864i	$-0.505242\pi$
$541$	−1.92053e16	−0.0329336	−0.0164668	+	0.999864i	$0.505242\pi$
$542$	−4.75278e17	−0.805290
$543$	3.39184e17	0.567854
$544$	5.78403e17	0.956836
$545$	9.59925e17	1.56913
$546$	1.65875e16	0.0267935
$547$	4.09634e17	0.653851	0.326926	−	0.945050i	$-0.393987\pi$
$547$	4.09634e17	0.653851	0.326926	+	0.945050i	$0.393987\pi$
$548$	1.95248e17	0.307973
$549$	−2.34865e17	−0.366098
$550$	−1.14048e17	−0.175683
$551$	−1.30933e18	−1.99326
$552$	−3.49788e17	−0.526261
$553$	−1.98479e16	−0.0295122
$554$	1.40383e17	0.206301
$555$	−3.63979e17	−0.528654
$556$	3.04397e17	0.436972
$557$	−3.51029e16	−0.0498063	−0.0249031	−	0.999690i	$-0.507928\pi$
$557$	−3.51029e16	−0.0498063	−0.0249031	+	0.999690i	$0.507928\pi$
$558$	−3.14218e16	−0.0440665
$559$	1.96599e17	0.272524
$560$	6.77736e16	0.0928621
$561$	−1.88598e17	−0.255433
$562$	4.26397e17	0.570858
$563$	7.47411e17	0.989134	0.494567	−	0.869140i	$-0.335327\pi$
$563$	7.47411e17	0.989134	0.494567	+	0.869140i	$0.335327\pi$
$564$	−6.45489e16	−0.0844452
$565$	−1.04065e18	−1.34582
$566$	−4.64511e17	−0.593867
$567$	3.27652e16	0.0414117
$568$	1.39553e18	1.74371
$569$	8.74316e17	1.08004	0.540018	−	0.841653i	$-0.318417\pi$
$569$	8.74316e17	1.08004	0.540018	+	0.841653i	$0.318417\pi$
$570$	−4.51749e17	−0.551709
$571$	−7.66178e17	−0.925114	−0.462557	−	0.886590i	$-0.653068\pi$
$571$	−7.66178e17	−0.925114	−0.462557	+	0.886590i	$0.653068\pi$
$572$	6.40399e16	0.0764498
$573$	1.13913e17	0.134453
$574$	2.37376e17	0.277019
$575$	−5.70209e17	−0.657950
$576$	1.09058e17	0.124426
$577$	−1.54561e17	−0.174364	−0.0871821	−	0.996192i	$-0.527786\pi$
$577$	−1.54561e17	−0.174364	−0.0871821	+	0.996192i	$0.527786\pi$
$578$	7.15073e16	0.0797663
$579$	−9.94995e17	−1.09751
$580$	1.22508e18	1.33623
$581$	−6.08464e17	−0.656282
$582$	2.20484e17	0.235168
$583$	2.84054e17	0.299609
$584$	−8.26740e16	−0.0862354
$585$	−9.51491e16	−0.0981503
$586$	5.24769e17	0.535345
$587$	1.29963e18	1.31121	0.655605	−	0.755104i	$-0.272414\pi$
$587$	1.29963e18	1.31121	0.655605	+	0.755104i	$0.272414\pi$
$588$	3.49336e17	0.348571
$589$	3.31324e17	0.326967
$590$	−9.42700e16	−0.0920101
$591$	−8.20961e17	−0.792508
$592$	−1.42970e17	−0.136507
$593$	−1.73461e18	−1.63812	−0.819062	−	0.573705i	$-0.805506\pi$
$593$	−1.73461e18	−1.63812	−0.819062	+	0.573705i	$0.805506\pi$
$594$	−5.39203e16	−0.0503663
$595$	−4.81951e17	−0.445289
$596$	−1.17932e17	−0.107779
$597$	−1.06708e18	−0.964634
$598$	−1.36480e17	−0.122042
$599$	−5.57315e17	−0.492976	−0.246488	−	0.969146i	$-0.579277\pi$
$599$	−5.57315e17	−0.492976	−0.246488	+	0.969146i	$0.579277\pi$
$600$	4.11912e17	0.360430
$601$	−1.84473e18	−1.59679	−0.798395	−	0.602134i	$-0.794317\pi$
$601$	−1.84473e18	−1.59679	−0.798395	+	0.602134i	$0.794317\pi$
$602$	2.84705e17	0.243791
$603$	−6.33489e17	−0.536632
$604$	−7.08277e17	−0.593558
$605$	−1.20196e18	−0.996505
$606$	3.66112e16	0.0300291
$607$	1.87633e18	1.52259	0.761295	−	0.648405i	$-0.224564\pi$
$607$	1.87633e18	1.52259	0.761295	+	0.648405i	$0.224564\pi$
$608$	−1.74369e18	−1.39989
$609$	−3.99365e17	−0.317218
$610$	9.87698e17	0.776212
$611$	−6.11066e16	−0.0475139
$612$	2.80749e17	0.215990
$613$	−1.43070e18	−1.08907	−0.544535	−	0.838738i	$-0.683294\pi$
$613$	−1.43070e18	−1.08907	−0.544535	+	0.838738i	$0.683294\pi$
$614$	3.52885e17	0.265790
$615$	−1.36164e18	−1.01478
$616$	2.25010e17	0.165931
$617$	9.18832e17	0.670475	0.335238	−	0.942134i	$-0.391183\pi$
$617$	9.18832e17	0.670475	0.335238	+	0.942134i	$0.391183\pi$
$618$	−8.30661e17	−0.599790
$619$	1.60857e18	1.14935	0.574674	−	0.818383i	$-0.305129\pi$
$619$	1.60857e18	1.14935	0.574674	+	0.818383i	$0.305129\pi$
$620$	−3.10004e17	−0.219190
$621$	−2.69588e17	−0.188627
$622$	−1.43129e18	−0.991038
$623$	2.93093e17	0.200832
$624$	−3.73745e16	−0.0253440
$625$	−1.81893e18	−1.22066
$626$	1.82855e17	0.121443
$627$	5.68557e17	0.373710
$628$	−1.74886e18	−1.13767
$629$	1.01669e18	0.654574
$630$	−1.37790e17	−0.0878022
$631$	−1.14567e18	−0.722550	−0.361275	−	0.932459i	$-0.617658\pi$
$631$	−1.14567e18	−0.722550	−0.361275	+	0.932459i	$0.617658\pi$
$632$	−1.17970e17	−0.0736396
$633$	−5.27604e17	−0.325975
$634$	3.61939e17	0.221338
$635$	2.69540e18	1.63153
$636$	−4.22846e17	−0.253344
$637$	3.30707e17	0.196127
$638$	6.57219e17	0.385812
$639$	1.07555e18	0.624995
$640$	1.86828e18	1.07467
$641$	2.85339e18	1.62474	0.812371	−	0.583141i	$-0.198177\pi$
$641$	2.85339e18	1.62474	0.812371	+	0.583141i	$0.198177\pi$
$642$	1.78106e17	0.100393
$643$	−2.71854e18	−1.51693	−0.758464	−	0.651715i	$-0.774050\pi$
$643$	−2.71854e18	−1.51693	−0.758464	+	0.651715i	$0.774050\pi$
$644$	4.63674e17	0.256126
$645$	−1.63312e18	−0.893061
$646$	1.26185e18	0.683121
$647$	−3.14020e18	−1.68298	−0.841491	−	0.540272i	$-0.818322\pi$
$647$	−3.14020e18	−1.68298	−0.841491	+	0.540272i	$0.818322\pi$
$648$	1.94747e17	0.103332
$649$	1.18645e17	0.0623247
$650$	1.60719e17	0.0835854
$651$	1.01059e17	0.0520353
$652$	−9.21194e17	−0.469615
$653$	2.80797e18	1.41728	0.708642	−	0.705568i	$-0.249308\pi$
$653$	2.80797e18	1.41728	0.708642	+	0.705568i	$0.249308\pi$
$654$	−7.66595e17	−0.383099
$655$	1.27377e18	0.630265
$656$	−5.34849e17	−0.262033
$657$	−6.37182e16	−0.0309093
$658$	−8.84917e16	−0.0425044
$659$	−2.36009e18	−1.12247	−0.561233	−	0.827658i	$-0.689673\pi$
$659$	−2.36009e18	−1.12247	−0.561233	+	0.827658i	$0.689673\pi$
$660$	−5.31972e17	−0.250526
$661$	5.16477e17	0.240847	0.120424	−	0.992723i	$-0.461575\pi$
$661$	5.16477e17	0.240847	0.120424	+	0.992723i	$0.461575\pi$
$662$	−7.94230e17	−0.366749
$663$	2.65777e17	0.121529
$664$	−3.61654e18	−1.63757
$665$	1.45292e18	0.651478
$666$	2.90673e17	0.129069
$667$	3.28593e18	1.44491
$668$	1.29425e18	0.563600
$669$	−2.62369e18	−1.13147
$670$	2.66407e18	1.13778
$671$	−1.24309e18	−0.525781
$672$	−5.31852e17	−0.222787
$673$	1.59299e18	0.660870	0.330435	−	0.943829i	$-0.392805\pi$
$673$	1.59299e18	0.660870	0.330435	+	0.943829i	$0.392805\pi$
$674$	−2.73648e17	−0.112435
$675$	3.17467e17	0.129189
$676$	1.64938e18	0.664764
$677$	−1.54364e18	−0.616198	−0.308099	−	0.951354i	$-0.599693\pi$
$677$	−1.54364e18	−0.616198	−0.308099	+	0.951354i	$0.599693\pi$
$678$	8.31058e17	0.328578
$679$	−7.09122e17	−0.277694
$680$	−2.86458e18	−1.11110
$681$	−2.04236e18	−0.784650
$682$	−1.66309e17	−0.0632872
$683$	−5.23911e17	−0.197480	−0.0987399	−	0.995113i	$-0.531481\pi$
$683$	−5.23911e17	−0.197480	−0.0987399	+	0.995113i	$0.531481\pi$
$684$	−8.46361e17	−0.316003
$685$	−1.53541e18	−0.567851
$686$	1.03508e18	0.379201
$687$	−1.32291e18	−0.480078
$688$	−6.41489e17	−0.230603
$689$	−4.00296e17	−0.142547
$690$	1.13372e18	0.399933
$691$	9.33605e17	0.326254	0.163127	−	0.986605i	$-0.447842\pi$
$691$	9.33605e17	0.326254	0.163127	+	0.986605i	$0.447842\pi$
$692$	−2.26456e18	−0.783960
$693$	1.73419e17	0.0594744
$694$	6.87886e17	0.233711
$695$	−2.39374e18	−0.805705
$696$	−2.37371e18	−0.791532
$697$	3.80341e18	1.25649
$698$	2.98041e17	0.0975475
$699$	−3.33192e18	−1.08042
$700$	−5.46024e17	−0.175418
$701$	−4.26621e17	−0.135792	−0.0678962	−	0.997692i	$-0.521629\pi$
$701$	−4.26621e17	−0.135792	−0.0678962	+	0.997692i	$0.521629\pi$
$702$	7.59860e16	0.0239631
$703$	−3.06497e18	−0.957671
$704$	5.77218e17	0.178697
$705$	5.07606e17	0.155703
$706$	2.49824e18	0.759283
$707$	−1.17749e17	−0.0354594
$708$	−1.76617e17	−0.0527007
$709$	−3.18574e18	−0.941910	−0.470955	−	0.882157i	$-0.656091\pi$
$709$	−3.18574e18	−0.941910	−0.470955	+	0.882157i	$0.656091\pi$
$710$	−4.52313e18	−1.32513
$711$	−9.09217e16	−0.0263946
$712$	1.74206e18	0.501121
$713$	−8.31500e17	−0.237017
$714$	3.84885e17	0.108716
$715$	−5.03603e17	−0.140961
$716$	−4.69189e18	−1.30141
$717$	2.86642e18	0.787889
$718$	−2.53619e18	−0.690832
$719$	9.40698e17	0.253929	0.126965	−	0.991907i	$-0.459477\pi$
$719$	9.40698e17	0.253929	0.126965	+	0.991907i	$0.459477\pi$
$720$	3.10465e17	0.0830523
$721$	2.67158e18	0.708253
$722$	−1.72327e18	−0.452753
$723$	−1.93619e18	−0.504137
$724$	−2.67239e18	−0.689604
$725$	−3.86952e18	−0.989600
$726$	9.59882e17	0.243293
$727$	−5.82825e18	−1.46408	−0.732040	−	0.681262i	$-0.761432\pi$
$727$	−5.82825e18	−1.46408	−0.732040	+	0.681262i	$0.761432\pi$
$728$	−3.17090e17	−0.0789457
$729$	1.50095e17	0.0370370
$730$	2.67960e17	0.0655347
$731$	4.56175e18	1.10578
$732$	1.85047e18	0.444591
$733$	3.47252e18	0.826931	0.413466	−	0.910520i	$-0.364318\pi$
$733$	3.47252e18	0.826931	0.413466	+	0.910520i	$0.364318\pi$
$734$	−1.51405e18	−0.357369
$735$	−2.74714e18	−0.642708
$736$	4.37600e18	1.01478
$737$	−3.35291e18	−0.770697
$738$	1.08740e18	0.247756
$739$	−1.68498e18	−0.380545	−0.190273	−	0.981731i	$-0.560937\pi$
$739$	−1.68498e18	−0.380545	−0.190273	+	0.981731i	$0.560937\pi$
$740$	2.86775e18	0.642000
$741$	−8.01226e17	−0.177802
$742$	−5.79690e17	−0.127518
$743$	2.87648e18	0.627241	0.313620	−	0.949548i	$-0.398458\pi$
$743$	2.87648e18	0.627241	0.313620	+	0.949548i	$0.398458\pi$
$744$	6.00666e17	0.129840
$745$	9.27407e17	0.198726
$746$	1.73639e18	0.368845
$747$	−2.78732e18	−0.586953
$748$	1.48594e18	0.310199
$749$	−5.72827e17	−0.118547
$750$	6.53762e17	0.134129
$751$	−1.25091e18	−0.254429	−0.127215	−	0.991875i	$-0.540604\pi$
$751$	−1.25091e18	−0.254429	−0.127215	+	0.991875i	$0.540604\pi$
$752$	1.99387e17	0.0402051
$753$	1.18479e17	0.0236851
$754$	−9.26171e17	−0.183560
$755$	5.56981e18	1.09442
$756$	−2.58153e17	−0.0502905
$757$	9.78014e18	1.88896	0.944478	−	0.328574i	$-0.106568\pi$
$757$	9.78014e18	1.88896	0.944478	+	0.328574i	$0.106568\pi$
$758$	1.98625e18	0.380351
$759$	−1.42687e18	−0.270902
$760$	8.63572e18	1.62559
$761$	−2.61183e18	−0.487467	−0.243734	−	0.969842i	$-0.578372\pi$
$761$	−2.61183e18	−0.487467	−0.243734	+	0.969842i	$0.578372\pi$
$762$	−2.15255e18	−0.398332
$763$	2.46553e18	0.452377
$764$	−8.97511e17	−0.163280
$765$	−2.20778e18	−0.398250
$766$	−5.74952e18	−1.02836
$767$	−1.67198e17	−0.0296525
$768$	−2.71753e18	−0.477888
$769$	4.05338e18	0.706799	0.353400	−	0.935472i	$-0.385026\pi$
$769$	4.05338e18	0.706799	0.353400	+	0.935472i	$0.385026\pi$
$770$	−7.29294e17	−0.126099
$771$	−6.25704e18	−1.07279
$772$	7.83945e18	1.33283
$773$	1.38763e18	0.233941	0.116970	−	0.993135i	$-0.462682\pi$
$773$	1.38763e18	0.233941	0.116970	+	0.993135i	$0.462682\pi$
$774$	1.30421e18	0.218038
$775$	9.79177e17	0.162331
$776$	−4.21482e18	−0.692911
$777$	−9.34863e17	−0.152409
$778$	−3.91632e18	−0.633157
$779$	−1.14660e19	−1.83831
$780$	7.49670e17	0.119194
$781$	5.69267e18	0.897603
$782$	−3.16678e18	−0.495193
$783$	−1.82946e18	−0.283708
$784$	−1.07907e18	−0.165958
$785$	1.37528e19	2.09768
$786$	−1.01723e18	−0.153877
$787$	−2.36169e18	−0.354313	−0.177157	−	0.984183i	$-0.556690\pi$
$787$	−2.36169e18	−0.354313	−0.177157	+	0.984183i	$0.556690\pi$
$788$	6.46826e18	0.962426
$789$	7.14340e17	0.105416
$790$	3.82361e17	0.0559626
$791$	−2.67285e18	−0.387997
$792$	1.03075e18	0.148402
$793$	1.75179e18	0.250154
$794$	1.92465e18	0.272595
$795$	3.32521e18	0.467125
$796$	8.40739e18	1.17146
$797$	−9.88256e18	−1.36581	−0.682905	−	0.730507i	$-0.739284\pi$
$797$	−9.88256e18	−1.36581	−0.682905	+	0.730507i	$0.739284\pi$
$798$	−1.16030e18	−0.159056
$799$	−1.41788e18	−0.192790
$800$	−5.15320e18	−0.695011
$801$	1.34263e18	0.179616
$802$	−3.38865e18	−0.449670
$803$	−3.37246e17	−0.0443911
$804$	4.99119e18	0.651688
$805$	−3.64628e18	−0.472255
$806$	2.34367e17	0.0301105
$807$	2.72220e18	0.346930
$808$	−6.99867e17	−0.0884793
$809$	9.16850e18	1.14983	0.574914	−	0.818214i	$-0.305035\pi$
$809$	9.16850e18	1.14983	0.574914	+	0.818214i	$0.305035\pi$
$810$	−6.31207e17	−0.0785270
$811$	1.02083e19	1.25984	0.629921	−	0.776659i	$-0.283087\pi$
$811$	1.02083e19	1.25984	0.629921	+	0.776659i	$0.283087\pi$
$812$	3.14656e18	0.385231
$813$	7.00236e18	0.850463
$814$	1.53847e18	0.185366
$815$	7.24417e18	0.865893
$816$	−8.67212e17	−0.102835
$817$	−1.37521e19	−1.61780
$818$	−7.38098e18	−0.861426
$819$	−2.44387e17	−0.0282964
$820$	1.07282e19	1.23236
$821$	−7.37435e18	−0.840414	−0.420207	−	0.907428i	$-0.638043\pi$
$821$	−7.37435e18	−0.840414	−0.420207	+	0.907428i	$0.638043\pi$
$822$	1.22617e18	0.138639
$823$	6.15624e18	0.690584	0.345292	−	0.938495i	$-0.387780\pi$
$823$	6.15624e18	0.690584	0.345292	+	0.938495i	$0.387780\pi$
$824$	1.58791e19	1.76725
$825$	1.68028e18	0.185538
$826$	−2.42128e17	−0.0265262
$827$	−1.23456e19	−1.34191	−0.670957	−	0.741496i	$-0.734117\pi$
$827$	−1.23456e19	−1.34191	−0.670957	+	0.741496i	$0.734117\pi$
$828$	2.12405e18	0.229070
$829$	2.56859e18	0.274847	0.137423	−	0.990512i	$-0.456118\pi$
$829$	2.56859e18	0.274847	0.137423	+	0.990512i	$0.456118\pi$
$830$	1.17218e19	1.24448
$831$	−2.06829e18	−0.217874
$832$	−8.13432e17	−0.0850197
$833$	7.67350e18	0.795795
$834$	1.91164e18	0.196710
$835$	−1.01778e19	−1.03919
$836$	−4.47960e18	−0.453835
$837$	4.62943e17	0.0465384
$838$	8.76332e18	0.874143
$839$	−6.60491e18	−0.653754	−0.326877	−	0.945067i	$-0.605996\pi$
$839$	−6.60491e18	−0.653754	−0.326877	+	0.945067i	$0.605996\pi$
$840$	2.63403e18	0.258705
$841$	1.20381e19	1.17323
$842$	−5.28318e18	−0.510936
$843$	−6.28219e18	−0.602881
$844$	4.15693e18	0.395865
$845$	−1.29705e19	−1.22572
$846$	−4.05373e17	−0.0380144
$847$	−3.08718e18	−0.287289
$848$	1.30614e18	0.120619
$849$	6.84372e18	0.627180
$850$	3.72922e18	0.339152
$851$	7.69193e18	0.694214
$852$	−8.47418e18	−0.758997
$853$	1.36136e18	0.121006	0.0605028	−	0.998168i	$-0.480730\pi$
$853$	1.36136e18	0.121006	0.0605028	+	0.998168i	$0.480730\pi$
$854$	2.53686e18	0.223780
$855$	6.65569e18	0.582658
$856$	−3.40472e18	−0.295802
$857$	−4.49699e18	−0.387745	−0.193873	−	0.981027i	$-0.562105\pi$
$857$	−4.49699e18	−0.387745	−0.193873	+	0.981027i	$0.562105\pi$
$858$	4.02177e17	0.0344151
$859$	3.76827e17	0.0320027	0.0160013	−	0.999872i	$-0.494906\pi$
$859$	3.76827e17	0.0320027	0.0160013	+	0.999872i	$0.494906\pi$
$860$	1.28672e19	1.08454
$861$	−3.49731e18	−0.292559
$862$	2.74182e18	0.227637
$863$	7.43499e18	0.612647	0.306323	−	0.951928i	$-0.400901\pi$
$863$	7.43499e18	0.612647	0.306323	+	0.951928i	$0.400901\pi$
$864$	−2.43637e18	−0.199252
$865$	1.78082e19	1.44549
$866$	−1.30375e19	−1.05033
$867$	−1.05353e18	−0.0842408
$868$	−7.96233e17	−0.0631920
$869$	−4.81228e17	−0.0379072
$870$	7.69359e18	0.601526
$871$	4.72502e18	0.366679
$872$	1.46544e19	1.12878
$873$	−3.24843e18	−0.248359
$874$	9.54677e18	0.724490
$875$	−2.10263e18	−0.158384
$876$	5.02029e17	0.0375364
$877$	−1.41996e18	−0.105385	−0.0526925	−	0.998611i	$-0.516780\pi$
$877$	−1.41996e18	−0.105385	−0.0526925	+	0.998611i	$0.516780\pi$
$878$	1.13826e18	0.0838549
$879$	−7.73151e18	−0.565375
$880$	1.64322e18	0.119278
$881$	5.51464e17	0.0397350	0.0198675	−	0.999803i	$-0.493676\pi$
$881$	5.51464e17	0.0397350	0.0198675	+	0.999803i	$0.493676\pi$
$882$	2.19386e18	0.156915
$883$	7.55926e18	0.536704	0.268352	−	0.963321i	$-0.413521\pi$
$883$	7.55926e18	0.536704	0.268352	+	0.963321i	$0.413521\pi$
$884$	−2.09403e18	−0.147585
$885$	1.38890e18	0.0971714
$886$	−8.39746e18	−0.583215
$887$	−1.17171e19	−0.807826	−0.403913	−	0.914797i	$-0.632350\pi$
$887$	−1.17171e19	−0.807826	−0.403913	+	0.914797i	$0.632350\pi$
$888$	−5.55656e18	−0.380296
$889$	6.92303e18	0.470365
$890$	−5.64630e18	−0.380828
$891$	7.94417e17	0.0531917
$892$	2.06718e19	1.37406
$893$	4.27442e18	0.282061
$894$	−7.40626e17	−0.0485183
$895$	3.68965e19	2.39958
$896$	4.79861e18	0.309823
$897$	2.01078e18	0.128888
$898$	−1.37358e18	−0.0874096
$899$	−5.64268e18	−0.356490
$900$	−2.50129e18	−0.156887
$901$	−9.28821e18	−0.578390
$902$	5.75537e18	0.355820
$903$	−4.19461e18	−0.257467
$904$	−1.58867e19	−0.968140
$905$	2.10154e19	1.27152
$906$	−4.44805e18	−0.267200
$907$	1.34218e19	0.800502	0.400251	−	0.916406i	$-0.368923\pi$
$907$	1.34218e19	0.800502	0.400251	+	0.916406i	$0.368923\pi$
$908$	1.60915e19	0.952882
$909$	−5.39399e17	−0.0317136
$910$	1.02774e18	0.0599949
$911$	2.44836e19	1.41908	0.709538	−	0.704667i	$-0.248904\pi$
$911$	2.44836e19	1.41908	0.709538	+	0.704667i	$0.248904\pi$
$912$	2.61435e18	0.150452
$913$	−1.47527e19	−0.842968
$914$	7.79779e18	0.442406
$915$	−1.45519e19	−0.819754
$916$	1.04231e19	0.583009
$917$	3.27163e18	0.181704
$918$	1.76313e18	0.0972314
$919$	−2.13400e19	−1.16854	−0.584270	−	0.811559i	$-0.698619\pi$
$919$	−2.13400e19	−1.16854	−0.584270	+	0.811559i	$0.698619\pi$
$920$	−2.16724e19	−1.17838
$921$	−5.19912e18	−0.280700
$922$	4.10944e18	0.220309
$923$	−8.02227e18	−0.427057
$924$	−1.36635e18	−0.0722260
$925$	−9.05805e18	−0.475459
$926$	5.29855e18	0.276176
$927$	1.22383e19	0.633435
$928$	2.96962e19	1.52630
$929$	−3.42915e19	−1.75018	−0.875092	−	0.483956i	$-0.839199\pi$
$929$	−3.42915e19	−1.75018	−0.875092	+	0.483956i	$0.839199\pi$
$930$	−1.94686e18	−0.0986721
$931$	−2.31330e19	−1.16428
$932$	2.62518e19	1.31207
$933$	2.10875e19	1.04663
$934$	−5.22329e18	−0.257448
$935$	−1.16853e19	−0.571957
$936$	−1.45256e18	−0.0706061
$937$	−3.23335e18	−0.156080	−0.0780398	−	0.996950i	$-0.524866\pi$
$937$	−3.23335e18	−0.156080	−0.0780398	+	0.996950i	$0.524866\pi$
$938$	6.84255e18	0.328019
$939$	−2.69404e18	−0.128256
$940$	−3.99937e18	−0.189087
$941$	1.33516e19	0.626902	0.313451	−	0.949604i	$-0.398515\pi$
$941$	1.33516e19	0.626902	0.313451	+	0.949604i	$0.398515\pi$
$942$	−1.09830e19	−0.512142
$943$	2.87754e19	1.33258
$944$	5.45557e17	0.0250912
$945$	2.03009e18	0.0927275
$946$	6.90289e18	0.313140
$947$	−2.64881e19	−1.19337	−0.596686	−	0.802474i	$-0.703516\pi$
$947$	−2.64881e19	−1.19337	−0.596686	+	0.802474i	$0.703516\pi$
$948$	7.16362e17	0.0320537
$949$	4.75257e17	0.0211202
$950$	−1.12423e19	−0.496195
$951$	−5.33251e18	−0.233754
$952$	−7.35755e18	−0.320326
$953$	−1.90636e19	−0.824328	−0.412164	−	0.911110i	$-0.635227\pi$
$953$	−1.90636e19	−0.824328	−0.412164	+	0.911110i	$0.635227\pi$
$954$	−2.65551e18	−0.114047
$955$	7.05793e18	0.301062
$956$	−2.25842e19	−0.956816
$957$	−9.68292e18	−0.407454
$958$	1.41453e19	0.591201
$959$	−3.94363e18	−0.163710
$960$	6.75709e18	0.278610
$961$	−2.29897e19	−0.941523
$962$	−2.16805e18	−0.0881924
$963$	−2.62407e18	−0.106024
$964$	1.52550e19	0.612226
$965$	−6.16486e19	−2.45751
$966$	2.91191e18	0.115299
$967$	1.19401e19	0.469607	0.234803	−	0.972043i	$-0.424555\pi$
$967$	1.19401e19	0.469607	0.234803	+	0.972043i	$0.424555\pi$
$968$	−1.83493e19	−0.716853
$969$	−1.85911e19	−0.721441
$970$	1.36609e19	0.526579
$971$	−2.27579e19	−0.871378	−0.435689	−	0.900097i	$-0.643495\pi$
$971$	−2.27579e19	−0.871378	−0.435689	+	0.900097i	$0.643495\pi$
$972$	−1.18258e18	−0.0449779
$973$	−6.14822e18	−0.232282
$974$	7.29790e18	0.273883
$975$	−2.36790e18	−0.0882742
$976$	−5.71598e18	−0.211674
$977$	1.73613e18	0.0638657	0.0319328	−	0.999490i	$-0.489834\pi$
$977$	1.73613e18	0.0638657	0.0319328	+	0.999490i	$0.489834\pi$
$978$	−5.78519e18	−0.211405
$979$	7.10625e18	0.257961
$980$	2.16444e19	0.780507
$981$	1.12944e19	0.404589
$982$	2.43211e19	0.865483
$983$	4.30016e19	1.52015	0.760075	−	0.649835i	$-0.225162\pi$
$983$	4.30016e19	1.52015	0.760075	+	0.649835i	$0.225162\pi$
$984$	−2.07870e19	−0.730001
$985$	−5.08657e19	−1.77456
$986$	−2.14903e19	−0.744803
$987$	1.30376e18	0.0448887
$988$	6.31277e18	0.215924
$989$	3.45127e19	1.17274
$990$	−3.34083e18	−0.112778
$991$	7.41012e17	0.0248512	0.0124256	−	0.999923i	$-0.496045\pi$
$991$	7.41012e17	0.0248512	0.0124256	+	0.999923i	$0.496045\pi$
$992$	−7.51459e18	−0.250368
$993$	1.17015e19	0.387322
$994$	−1.16175e19	−0.382032
$995$	−6.61148e19	−2.15997
$996$	2.19610e19	0.712799
$997$	5.06954e19	1.63474	0.817372	−	0.576110i	$-0.195430\pi$
$997$	5.06954e19	1.63474	0.817372	+	0.576110i	$0.195430\pi$
$998$	−1.67501e19	−0.536624
$999$	−4.28253e18	−0.136309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.11	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.11	✓	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} -2.23492e6 q^{10} +2.81280e6 q^{11} -4.18717e6 q^{12} -3.96387e6 q^{13} -5.74029e6 q^{14} +3.29274e7 q^{15} +1.29339e7 q^{16} -9.19750e7 q^{17} -2.62958e7 q^{18} +2.77273e8 q^{19} -2.59432e8 q^{20} +8.45727e7 q^{21} -1.39178e8 q^{22} -6.95853e8 q^{23} +5.02676e8 q^{24} +8.19439e8 q^{25} +1.96133e8 q^{26} +3.87420e8 q^{27} -6.66339e8 q^{28} -4.72216e9 q^{29} -1.62925e9 q^{30} +1.19494e9 q^{31} -6.28869e9 q^{32} +2.05053e9 q^{33} +4.55094e9 q^{34} +5.24002e9 q^{35} -3.05244e9 q^{36} -1.10540e10 q^{37} -1.37195e10 q^{38} -2.88966e9 q^{39} +3.11452e10 q^{40} -4.13527e10 q^{41} -4.18467e9 q^{42} -4.95977e10 q^{43} -1.61559e10 q^{44} +2.40041e10 q^{45} +3.44309e10 q^{46} +1.54159e10 q^{47} +9.42878e9 q^{48} -8.34302e10 q^{49} -4.05460e10 q^{50} -6.70498e10 q^{51} +2.27673e10 q^{52} +1.00986e11 q^{53} -1.91696e10 q^{54} +1.27048e11 q^{55} +7.99950e10 q^{56} +2.02132e11 q^{57} +2.33653e11 q^{58} +4.21805e10 q^{59} -1.89126e11 q^{60} -4.41939e11 q^{61} -5.91257e10 q^{62} +6.16535e10 q^{63} +2.05212e11 q^{64} -1.79040e11 q^{65} -1.01461e11 q^{66} -1.19202e12 q^{67} +5.28278e11 q^{68} -5.07277e11 q^{69} -2.59277e11 q^{70} +2.02385e12 q^{71} +3.66451e11 q^{72} -1.19897e11 q^{73} +5.46952e11 q^{74} +5.97371e11 q^{75} -1.59258e12 q^{76} +3.26318e11 q^{77} +1.42981e11 q^{78} -1.71085e11 q^{79} +5.84195e11 q^{80} +2.82430e11 q^{81} +2.04614e12 q^{82} -5.24484e12 q^{83} -4.85761e11 q^{84} -4.15432e12 q^{85} +2.45410e12 q^{86} -3.44245e12 q^{87} +1.93954e12 q^{88} +2.52640e12 q^{89} -1.18773e12 q^{90} -4.59856e11 q^{91} +3.99678e12 q^{92} +8.71109e11 q^{93} -7.62781e11 q^{94} +1.25239e13 q^{95} -4.58446e12 q^{96} -6.11249e12 q^{97} +4.12814e12 q^{98} +1.49484e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9}+O(q^{10}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9	\( 30 q - 138 q^{2} + 21870 q^{3} + 114598 q^{4} - 137742 q^{5} - 100602 q^{6} - 879443 q^{7} - 872301 q^{8} + 15943230 q^{9} - 5352519 q^{10} - 13950782 q^{11} + 83541942 q^{12} - 17256988 q^{13} + 33780109 q^{14} - 100413918 q^{15} + 499996762 q^{16} - 317583695 q^{17} - 73338858 q^{18} - 863401469 q^{19} - 1841280623 q^{20} - 641113947 q^{21} - 2723764842 q^{22} - 3142075981 q^{23} - 635907429 q^{24} + 5435751692 q^{25} - 6441414040 q^{26} + 11622614670 q^{27} - 7538400046 q^{28} - 4604589283 q^{29} - 3901986351 q^{30} + 4308675373 q^{31} + 6094556360 q^{32} - 10170120078 q^{33} + 38097713432 q^{34} - 15447827315 q^{35} + 60902075718 q^{36} - 19633376949 q^{37} - 18152222923 q^{38} - 12580344252 q^{39} + 14680384170 q^{40} - 103644439493 q^{41} + 24625699461 q^{42} - 64494894924 q^{43} - 199714496208 q^{44} - 73201746222 q^{45} - 265425792847 q^{46} - 293365585139 q^{47} + 364497639498 q^{48} + 414396765797 q^{49} - 126058522207 q^{50} - 231518513655 q^{51} + 156029960316 q^{52} - 76747013118 q^{53} - 53464027482 q^{54} - 433465885754 q^{55} - 502955241518 q^{56} - 629419670901 q^{57} - 1755031845830 q^{58} + 1265416009230 q^{59} - 1342293574167 q^{60} - 2022612531219 q^{61} - 3816005187046 q^{62} - 467372067363 q^{63} - 3570205594131 q^{64} - 3889749040576 q^{65} - 1985624569818 q^{66} - 502618987776 q^{67} - 8953998390517 q^{68} - 2290573390149 q^{69} - 6805178272420 q^{70} - 1599540605456 q^{71} - 463576515741 q^{72} - 3826795087235 q^{73} - 7573387813210 q^{74} + 3962662983468 q^{75} - 19498723328388 q^{76} - 9088623115219 q^{77} - 4695790835160 q^{78} - 8595482172338 q^{79} - 17452527463963 q^{80} + 8472886094430 q^{81} - 11181116792901 q^{82} - 13548556984389 q^{83} - 5495493633534 q^{84} - 12851795888367 q^{85} + 8539949468848 q^{86} - 3356745587307 q^{87} - 25134826741387 q^{88} - 21826401667403 q^{89} - 2844548049879 q^{90} - 26577050621355 q^{91} - 34908210763168 q^{92} + 3141024346917 q^{93} - 26426808959500 q^{94} - 29105233533993 q^{95} + 4442931586440 q^{96} + 417815797414 q^{97} + 29159956938360 q^{98} - 7414017536862 q^{99}+O(q^{100}) \) 30 * q - 138 * q^2 + 21870 * q^3 + 114598 * q^4 - 137742 * q^5 - 100602 * q^6 - 879443 * q^7 - 872301 * q^8 + 15943230 * q^9 - 5352519 * q^10 - 13950782 * q^11 + 83541942 * q^12 - 17256988 * q^13 + 33780109 * q^14 - 100413918 * q^15 + 499996762 * q^16 - 317583695 * q^17 - 73338858 * q^18 - 863401469 * q^19 - 1841280623 * q^20 - 641113947 * q^21 - 2723764842 * q^22 - 3142075981 * q^23 - 635907429 * q^24 + 5435751692 * q^25 - 6441414040 * q^26 + 11622614670 * q^27 - 7538400046 * q^28 - 4604589283 * q^29 - 3901986351 * q^30 + 4308675373 * q^31 + 6094556360 * q^32 - 10170120078 * q^33 + 38097713432 * q^34 - 15447827315 * q^35 + 60902075718 * q^36 - 19633376949 * q^37 - 18152222923 * q^38 - 12580344252 * q^39 + 14680384170 * q^40 - 103644439493 * q^41 + 24625699461 * q^42 - 64494894924 * q^43 - 199714496208 * q^44 - 73201746222 * q^45 - 265425792847 * q^46 - 293365585139 * q^47 + 364497639498 * q^48 + 414396765797 * q^49 - 126058522207 * q^50 - 231518513655 * q^51 + 156029960316 * q^52 - 76747013118 * q^53 - 53464027482 * q^54 - 433465885754 * q^55 - 502955241518 * q^56 - 629419670901 * q^57 - 1755031845830 * q^58 + 1265416009230 * q^59 - 1342293574167 * q^60 - 2022612531219 * q^61 - 3816005187046 * q^62 - 467372067363 * q^63 - 3570205594131 * q^64 - 3889749040576 * q^65 - 1985624569818 * q^66 - 502618987776 * q^67 - 8953998390517 * q^68 - 2290573390149 * q^69 - 6805178272420 * q^70 - 1599540605456 * q^71 - 463576515741 * q^72 - 3826795087235 * q^73 - 7573387813210 * q^74 + 3962662983468 * q^75 - 19498723328388 * q^76 - 9088623115219 * q^77 - 4695790835160 * q^78 - 8595482172338 * q^79 - 17452527463963 * q^80 + 8472886094430 * q^81 - 11181116792901 * q^82 - 13548556984389 * q^83 - 5495493633534 * q^84 - 12851795888367 * q^85 + 8539949468848 * q^86 - 3356745587307 * q^87 - 25134826741387 * q^88 - 21826401667403 * q^89 - 2844548049879 * q^90 - 26577050621355 * q^91 - 34908210763168 * q^92 + 3141024346917 * q^93 - 26426808959500 * q^94 - 29105233533993 * q^95 + 4442931586440 * q^96 + 417815797414 * q^97 + 29159956938360 * q^98 - 7414017536862 * q^99

Introduction

L-functions

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