LMFDB - Embedded newform 177.10.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,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, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} -31808.2 q^{10} +35617.8 q^{11} +462.534 q^{12} -147759. q^{13} -76300.2 q^{14} -113235. q^{15} -265035. q^{16} +65139.2 q^{17} +149284. q^{18} +699375. q^{19} -7982.78 q^{20} -271624. q^{21} +810421. q^{22} +996679. q^{23} -933099. q^{24} +1179.05 q^{25} -3.36199e6 q^{26} +531441. q^{27} -19148.8 q^{28} -3.88707e6 q^{29} -2.57647e6 q^{30} +2.43647e6 q^{31} -132304. q^{32} +2.88504e6 q^{33} +1.48213e6 q^{34} +4.68790e6 q^{35} +37465.2 q^{36} +1.41307e7 q^{37} +1.59131e7 q^{38} -1.19684e7 q^{39} +1.61042e7 q^{40} -1.02547e7 q^{41} -6.18032e6 q^{42} +2.85692e7 q^{43} +203388. q^{44} -9.17204e6 q^{45} +2.26777e7 q^{46} +2.87214e7 q^{47} -2.14678e7 q^{48} -2.91085e7 q^{49} +26827.2 q^{50} +5.27627e6 q^{51} -843744. q^{52} +7.51619e7 q^{53} +1.20920e7 q^{54} -4.97924e7 q^{55} +3.86300e7 q^{56} +5.66494e7 q^{57} -8.84436e7 q^{58} -1.21174e7 q^{59} -646605. q^{60} +1.55086e8 q^{61} +5.54377e7 q^{62} -2.20015e7 q^{63} +1.32688e8 q^{64} +2.06561e8 q^{65} +6.56441e7 q^{66} -1.39101e8 q^{67} +371964. q^{68} +8.07310e7 q^{69} +1.06665e8 q^{70} +1.41817e8 q^{71} -7.55810e7 q^{72} +2.22968e8 q^{73} +3.21520e8 q^{74} +95503.2 q^{75} +3.99364e6 q^{76} -1.19440e8 q^{77} -2.72321e8 q^{78} -7.34739e7 q^{79} +3.70510e8 q^{80} +4.30467e7 q^{81} -2.33328e8 q^{82} -1.06550e8 q^{83} -1.55105e6 q^{84} -9.10622e7 q^{85} +6.50041e8 q^{86} -3.14853e8 q^{87} -4.10308e8 q^{88} -1.11107e7 q^{89} -2.08694e8 q^{90} +4.95490e8 q^{91} +5.69133e6 q^{92} +1.97354e8 q^{93} +6.53506e8 q^{94} -9.77702e8 q^{95} -1.07166e7 q^{96} -1.97748e8 q^{97} -6.62312e8 q^{98} +2.33688e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	22.7532	1.00556	0.502780	−	0.864414i	$-0.332310\pi$
$2$	22.7532	1.00556	0.502780	+	0.864414i	$0.332310\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	5.71029	0.0111529
$5$	−1397.96	−1.00030	−0.500151	−	0.865938i	$-0.666722\pi$
$5$	−1397.96	−1.00030	−0.500151	+	0.865938i	$0.666722\pi$
$6$	1843.01	0.580561
$7$	−3353.38	−0.527887	−0.263944	−	0.964538i	$-0.585023\pi$
$7$	−3353.38	−0.527887	−0.263944	+	0.964538i	$0.585023\pi$
$8$	−11519.7	−0.994346
$9$	6561.00	0.333333
$10$	−31808.2	−1.00586
$11$	35617.8	0.733500	0.366750	−	0.930320i	$-0.380470\pi$
$11$	35617.8	0.733500	0.366750	+	0.930320i	$0.380470\pi$
$12$	462.534	0.00643914
$13$	−147759.	−1.43485	−0.717427	−	0.696634i	$-0.754680\pi$
$13$	−147759.	−1.43485	−0.717427	+	0.696634i	$0.754680\pi$
$14$	−76300.2	−0.530823
$15$	−113235.	−0.577525
$16$	−265035.	−1.01103
$17$	65139.2	0.189157	0.0945784	−	0.995517i	$-0.469850\pi$
$17$	65139.2	0.189157	0.0945784	+	0.995517i	$0.469850\pi$
$18$	149284.	0.335187
$19$	699375.	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$19$	699375.	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$20$	−7982.78	−0.0111563
$21$	−271624.	−0.304776
$22$	810421.	0.737579
$23$	996679.	0.742643	0.371321	−	0.928504i	$-0.378905\pi$
$23$	996679.	0.742643	0.371321	+	0.928504i	$0.378905\pi$
$24$	−933099.	−0.574086
$25$	1179.05	0.000603674 0
$26$	−3.36199e6	−1.44283
$27$	531441.	0.192450
$28$	−19148.8	−0.00588748
$29$	−3.88707e6	−1.02054	−0.510272	−	0.860013i	$-0.670455\pi$
$29$	−3.88707e6	−1.02054	−0.510272	+	0.860013i	$0.670455\pi$
$30$	−2.57647e6	−0.580736
$31$	2.43647e6	0.473843	0.236921	−	0.971529i	$-0.423862\pi$
$31$	2.43647e6	0.473843	0.236921	+	0.971529i	$0.423862\pi$
$32$	−132304.	−0.0223048
$33$	2.88504e6	0.423486
$34$	1.48213e6	0.190209
$35$	4.68790e6	0.528047
$36$	37465.2	0.00371764
$37$	1.41307e7	1.23953	0.619765	−	0.784787i	$-0.287228\pi$
$37$	1.41307e7	1.23953	0.619765	+	0.784787i	$0.287228\pi$
$38$	1.59131e7	1.23802
$39$	−1.19684e7	−0.828413
$40$	1.61042e7	0.994646
$41$	−1.02547e7	−0.566755	−0.283378	−	0.959008i	$-0.591455\pi$
$41$	−1.02547e7	−0.566755	−0.283378	+	0.959008i	$0.591455\pi$
$42$	−6.18032e6	−0.306471
$43$	2.85692e7	1.27435	0.637176	−	0.770718i	$-0.280102\pi$
$43$	2.85692e7	1.27435	0.637176	+	0.770718i	$0.280102\pi$
$44$	203388.	0.00818066
$45$	−9.17204e6	−0.333434
$46$	2.26777e7	0.746773
$47$	2.87214e7	0.858550	0.429275	−	0.903174i	$-0.358769\pi$
$47$	2.87214e7	0.858550	0.429275	+	0.903174i	$0.358769\pi$
$48$	−2.14678e7	−0.583718
$49$	−2.91085e7	−0.721335
$50$	26827.2	0.000607031 0
$51$	5.27627e6	0.109210
$52$	−843744.	−0.0160028
$53$	7.51619e7	1.30845	0.654224	−	0.756301i	$-0.272996\pi$
$53$	7.51619e7	1.30845	0.654224	+	0.756301i	$0.272996\pi$
$54$	1.20920e7	0.193520
$55$	−4.97924e7	−0.733721
$56$	3.86300e7	0.524903
$57$	5.66494e7	0.710818
$58$	−8.84436e7	−1.02622
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−646605.	−0.00644108
$61$	1.55086e8	1.43413	0.717064	−	0.697008i	$-0.245486\pi$
$61$	1.55086e8	1.43413	0.717064	+	0.697008i	$0.245486\pi$
$62$	5.54377e7	0.476478
$63$	−2.20015e7	−0.175962
$64$	1.32688e8	0.988600
$65$	2.06561e8	1.43529
$66$	6.56441e7	0.425841
$67$	−1.39101e8	−0.843321	−0.421660	−	0.906754i	$-0.638553\pi$
$67$	−1.39101e8	−0.843321	−0.421660	+	0.906754i	$0.638553\pi$
$68$	371964.	0.00210965
$69$	8.07310e7	0.428765
$70$	1.06665e8	0.530983
$71$	1.41817e8	0.662318	0.331159	−	0.943575i	$-0.392560\pi$
$71$	1.41817e8	0.662318	0.331159	+	0.943575i	$0.392560\pi$
$72$	−7.55810e7	−0.331449
$73$	2.22968e8	0.918947	0.459474	−	0.888191i	$-0.348038\pi$
$73$	2.22968e8	0.918947	0.459474	+	0.888191i	$0.348038\pi$
$74$	3.21520e8	1.24642
$75$	95503.2	0.000348532 0
$76$	3.99364e6	0.0137312
$77$	−1.19440e8	−0.387205
$78$	−2.72321e8	−0.833020
$79$	−7.34739e7	−0.212232	−0.106116	−	0.994354i	$-0.533842\pi$
$79$	−7.34739e7	−0.212232	−0.106116	+	0.994354i	$0.533842\pi$
$80$	3.70510e8	1.01133
$81$	4.30467e7	0.111111
$82$	−2.33328e8	−0.569907
$83$	−1.06550e8	−0.246435	−0.123218	−	0.992380i	$-0.539321\pi$
$83$	−1.06550e8	−0.246435	−0.123218	+	0.992380i	$0.539321\pi$
$84$	−1.55105e6	−0.00339914
$85$	−9.10622e7	−0.189214
$86$	6.50041e8	1.28144
$87$	−3.14853e8	−0.589211
$88$	−4.10308e8	−0.729353
$89$	−1.11107e7	−0.0187710	−0.00938552	−	0.999956i	$-0.502988\pi$
$89$	−1.11107e7	−0.0187710	−0.00938552	+	0.999956i	$0.502988\pi$
$90$	−2.08694e8	−0.335288
$91$	4.95490e8	0.757441
$92$	5.69133e6	0.00828263
$93$	1.97354e8	0.273573
$94$	6.53506e8	0.863325
$95$	−9.77702e8	−1.23154
$96$	−1.07166e7	−0.0128777
$97$	−1.97748e8	−0.226798	−0.113399	−	0.993550i	$-0.536174\pi$
$97$	−1.97748e8	−0.226798	−0.113399	+	0.993550i	$0.536174\pi$
$98$	−6.62312e8	−0.725346
$99$	2.33688e8	0.244500
$100$	6732.73	6.73273e−6 0
$101$	1.98613e8	0.189916	0.0949580	−	0.995481i	$-0.469728\pi$
$101$	1.98613e8	0.189916	0.0949580	+	0.995481i	$0.469728\pi$
$102$	1.20052e8	0.109817
$103$	2.21392e7	0.0193818	0.00969090	−	0.999953i	$-0.496915\pi$
$103$	2.21392e7	0.0193818	0.00969090	+	0.999953i	$0.496915\pi$
$104$	1.70214e9	1.42674
$105$	3.79720e8	0.304868
$106$	1.71018e9	1.31572
$107$	−1.02274e9	−0.754293	−0.377146	−	0.926154i	$-0.623095\pi$
$107$	−1.02274e9	−0.754293	−0.377146	+	0.926154i	$0.623095\pi$
$108$	3.03468e6	0.00214638
$109$	1.36334e8	0.0925092	0.0462546	−	0.998930i	$-0.485271\pi$
$109$	1.36334e8	0.0925092	0.0462546	+	0.998930i	$0.485271\pi$
$110$	−1.13294e9	−0.737801
$111$	1.14459e9	0.715643
$112$	8.88763e8	0.533709
$113$	−4.89261e8	−0.282285	−0.141143	−	0.989989i	$-0.545078\pi$
$113$	−4.89261e8	−0.282285	−0.141143	+	0.989989i	$0.545078\pi$
$114$	1.28896e9	0.714771
$115$	−1.39332e9	−0.742867
$116$	−2.21963e7	−0.0113820
$117$	−9.69444e8	−0.478284
$118$	−2.75709e8	−0.130913
$119$	−2.18436e8	−0.0998535
$120$	1.30444e9	0.574259
$121$	−1.08932e9	−0.461978
$122$	3.52871e9	1.44210
$123$	−8.30631e8	−0.327216
$124$	1.39130e7	0.00528472
$125$	2.72875e9	0.999698
$126$	−5.00606e8	−0.176941
$127$	2.13822e9	0.729348	0.364674	−	0.931135i	$-0.381180\pi$
$127$	2.13822e9	0.729348	0.364674	+	0.931135i	$0.381180\pi$
$128$	3.08681e9	1.01640
$129$	2.31410e9	0.735747
$130$	4.69994e9	1.44327
$131$	−1.28564e9	−0.381415	−0.190708	−	0.981647i	$-0.561078\pi$
$131$	−1.28564e9	−0.381415	−0.190708	+	0.981647i	$0.561078\pi$
$132$	1.64744e7	0.00472311
$133$	−2.34527e9	−0.649921
$134$	−3.16499e9	−0.848011
$135$	−7.42936e8	−0.192508
$136$	−7.50386e8	−0.188087
$137$	−3.57302e9	−0.866548	−0.433274	−	0.901262i	$-0.642642\pi$
$137$	−3.57302e9	−0.866548	−0.433274	+	0.901262i	$0.642642\pi$
$138$	1.83689e9	0.431149
$139$	2.69381e9	0.612068	0.306034	−	0.952021i	$-0.400998\pi$
$139$	2.69381e9	0.612068	0.306034	+	0.952021i	$0.400998\pi$
$140$	2.67693e7	0.00588926
$141$	2.32644e9	0.495684
$142$	3.22680e9	0.666001
$143$	−5.26283e9	−1.05246
$144$	−1.73890e9	−0.337010
$145$	5.43399e9	1.02085
$146$	5.07326e9	0.924057
$147$	−2.35779e9	−0.416463
$148$	8.06907e7	0.0138244
$149$	9.84181e9	1.63582	0.817912	−	0.575343i	$-0.195132\pi$
$149$	9.84181e9	1.63582	0.817912	+	0.575343i	$0.195132\pi$
$150$	2.17301e6	0.000350470 0
$151$	−9.15733e9	−1.43342	−0.716708	−	0.697373i	$-0.754352\pi$
$151$	−9.15733e9	−1.43342	−0.716708	+	0.697373i	$0.754352\pi$
$152$	−8.05662e9	−1.22421
$153$	4.27378e8	0.0630523
$154$	−2.71765e9	−0.389359
$155$	−3.40610e9	−0.473986
$156$	−6.83433e7	−0.00923922
$157$	6.83830e9	0.898255	0.449128	−	0.893468i	$-0.351735\pi$
$157$	6.83830e9	0.898255	0.449128	+	0.893468i	$0.351735\pi$
$158$	−1.67177e9	−0.213412
$159$	6.08811e9	0.755432
$160$	1.84956e8	0.0223115
$161$	−3.34224e9	−0.392032
$162$	9.79453e8	0.111729
$163$	3.20037e9	0.355104	0.177552	−	0.984111i	$-0.443182\pi$
$163$	3.20037e9	0.355104	0.177552	+	0.984111i	$0.443182\pi$
$164$	−5.85573e7	−0.00632097
$165$	−4.03319e9	−0.423614
$166$	−2.42436e9	−0.247806
$167$	−2.62703e9	−0.261361	−0.130680	−	0.991425i	$-0.541716\pi$
$167$	−2.62703e9	−0.261361	−0.130680	+	0.991425i	$0.541716\pi$
$168$	3.12903e9	0.303053
$169$	1.12281e10	1.05880
$170$	−2.07196e9	−0.190266
$171$	4.58860e9	0.410391
$172$	1.63138e8	0.0142127
$173$	3.99041e9	0.338696	0.169348	−	0.985556i	$-0.445834\pi$
$173$	3.99041e9	0.338696	0.169348	+	0.985556i	$0.445834\pi$
$174$	−7.16393e9	−0.592488
$175$	−3.95380e6	−0.000318672 0
$176$	−9.43997e9	−0.741589
$177$	−9.81506e8	−0.0751646
$178$	−2.52806e8	−0.0188754
$179$	1.49455e10	1.08811	0.544055	−	0.839050i	$-0.316888\pi$
$179$	1.49455e10	1.08811	0.544055	+	0.839050i	$0.316888\pi$
$180$	−5.23750e7	−0.00371876
$181$	−1.02993e8	−0.00713271	−0.00356636	−	0.999994i	$-0.501135\pi$
$181$	−1.02993e8	−0.00713271	−0.00356636	+	0.999994i	$0.501135\pi$
$182$	1.12740e10	0.761653
$183$	1.25619e10	0.827994
$184$	−1.14815e10	−0.738444
$185$	−1.97543e10	−1.23990
$186$	4.49045e9	0.275094
$187$	2.32011e9	0.138747
$188$	1.64008e8	0.00957534
$189$	−1.78212e9	−0.101592
$190$	−2.22459e10	−1.23839
$191$	−7.24464e9	−0.393883	−0.196941	−	0.980415i	$-0.563101\pi$
$191$	−7.24464e9	−0.393883	−0.196941	+	0.980415i	$0.563101\pi$
$192$	1.07477e10	0.570768
$193$	2.51260e10	1.30351	0.651756	−	0.758429i	$-0.274033\pi$
$193$	2.51260e10	1.30351	0.651756	+	0.758429i	$0.274033\pi$
$194$	−4.49942e9	−0.228060
$195$	1.67315e10	0.828663
$196$	−1.66218e8	−0.00804499
$197$	3.06233e9	0.144862	0.0724309	−	0.997373i	$-0.476924\pi$
$197$	3.06233e9	0.144862	0.0724309	+	0.997373i	$0.476924\pi$
$198$	5.31717e9	0.245860
$199$	4.33802e10	1.96089	0.980444	−	0.196800i	$-0.0630550\pi$
$199$	4.33802e10	1.96089	0.980444	+	0.196800i	$0.0630550\pi$
$200$	−1.35824e7	−0.000600261 0
$201$	−1.12672e10	−0.486891
$202$	4.51909e9	0.190972
$203$	1.30348e10	0.538732
$204$	3.01291e7	0.00121801
$205$	1.43357e10	0.566926
$206$	5.03738e8	0.0194896
$207$	6.53921e9	0.247548
$208$	3.91612e10	1.45068
$209$	2.49102e10	0.903065
$210$	8.63987e9	0.306563
$211$	4.08132e10	1.41752	0.708761	−	0.705449i	$-0.249254\pi$
$211$	4.08132e10	1.41752	0.708761	+	0.705449i	$0.249254\pi$
$212$	4.29196e8	0.0145930
$213$	1.14872e10	0.382389
$214$	−2.32707e10	−0.758487
$215$	−3.99387e10	−1.27474
$216$	−6.12206e9	−0.191362
$217$	−8.17042e9	−0.250136
$218$	3.10204e9	0.0930237
$219$	1.80604e10	0.530554
$220$	−2.84329e8	−0.00818313
$221$	−9.62487e9	−0.271412
$222$	2.60431e10	0.719623
$223$	−3.62409e10	−0.981357	−0.490678	−	0.871341i	$-0.663251\pi$
$223$	−3.62409e10	−0.981357	−0.490678	+	0.871341i	$0.663251\pi$
$224$	4.43665e8	0.0117744
$225$	7.73576e6	0.000201225 0
$226$	−1.11323e10	−0.283855
$227$	−7.23329e10	−1.80809	−0.904044	−	0.427440i	$-0.859416\pi$
$227$	−7.23329e10	−1.80809	−0.904044	+	0.427440i	$0.859416\pi$
$228$	3.23485e8	0.00792769
$229$	−4.66680e10	−1.12140	−0.560698	−	0.828020i	$-0.689467\pi$
$229$	−4.66680e10	−1.12140	−0.560698	+	0.828020i	$0.689467\pi$
$230$	−3.17026e10	−0.746998
$231$	−9.67464e9	−0.223553
$232$	4.47781e10	1.01477
$233$	−6.49657e10	−1.44405	−0.722025	−	0.691867i	$-0.756789\pi$
$233$	−6.49657e10	−1.44405	−0.722025	+	0.691867i	$0.756789\pi$
$234$	−2.20580e10	−0.480944
$235$	−4.01515e10	−0.858809
$236$	−6.91937e7	−0.00145199
$237$	−5.95139e9	−0.122532
$238$	−4.97013e9	−0.100409
$239$	1.27226e10	0.252223	0.126111	−	0.992016i	$-0.459750\pi$
$239$	1.27226e10	0.252223	0.126111	+	0.992016i	$0.459750\pi$
$240$	3.00113e10	0.583894
$241$	−3.06114e10	−0.584530	−0.292265	−	0.956337i	$-0.594409\pi$
$241$	−3.06114e10	−0.584530	−0.292265	+	0.956337i	$0.594409\pi$
$242$	−2.47856e10	−0.464547
$243$	3.48678e9	0.0641500
$244$	8.85585e8	0.0159947
$245$	4.06926e10	0.721553
$246$	−1.88995e10	−0.329036
$247$	−1.03339e11	−1.76655
$248$	−2.80675e10	−0.471163
$249$	−8.63057e9	−0.142280
$250$	6.20879e10	1.00526
$251$	−5.69376e9	−0.0905455	−0.0452728	−	0.998975i	$-0.514416\pi$
$251$	−5.69376e9	−0.0905455	−0.0452728	+	0.998975i	$0.514416\pi$
$252$	−1.25635e8	−0.00196249
$253$	3.54995e10	0.544728
$254$	4.86514e10	0.733404
$255$	−7.37604e9	−0.109243
$256$	2.29898e9	0.0334546
$257$	8.08853e10	1.15657	0.578283	−	0.815836i	$-0.303723\pi$
$257$	8.08853e10	1.15657	0.578283	+	0.815836i	$0.303723\pi$
$258$	5.26533e10	0.739839
$259$	−4.73857e10	−0.654333
$260$	1.17952e9	0.0160076
$261$	−2.55031e10	−0.340181
$262$	−2.92525e10	−0.383536
$263$	1.13968e10	0.146886	0.0734432	−	0.997299i	$-0.476601\pi$
$263$	1.13968e10	0.146886	0.0734432	+	0.997299i	$0.476601\pi$
$264$	−3.32349e10	−0.421092
$265$	−1.05074e11	−1.30884
$266$	−5.33625e10	−0.653535
$267$	−8.99970e8	−0.0108375
$268$	−7.94306e8	−0.00940548
$269$	6.01816e10	0.700775	0.350387	−	0.936605i	$-0.386050\pi$
$269$	6.01816e10	0.700775	0.350387	+	0.936605i	$0.386050\pi$
$270$	−1.69042e10	−0.193579
$271$	−1.89338e10	−0.213244	−0.106622	−	0.994300i	$-0.534003\pi$
$271$	−1.89338e10	−0.213244	−0.106622	+	0.994300i	$0.534003\pi$
$272$	−1.72642e10	−0.191243
$273$	4.01347e10	0.437309
$274$	−8.12978e10	−0.871367
$275$	4.19952e7	0.000442795 0
$276$	4.60997e8	0.00478198
$277$	1.06645e11	1.08838	0.544192	−	0.838960i	$-0.316836\pi$
$277$	1.06645e11	1.08838	0.544192	+	0.838960i	$0.316836\pi$
$278$	6.12929e10	0.615472
$279$	1.59857e10	0.157948
$280$	−5.40034e10	−0.525061
$281$	8.24661e10	0.789036	0.394518	−	0.918888i	$-0.370912\pi$
$281$	8.24661e10	0.789036	0.394518	+	0.918888i	$0.370912\pi$
$282$	5.29340e10	0.498441
$283$	−1.52295e11	−1.41139	−0.705695	−	0.708516i	$-0.749365\pi$
$283$	−1.52295e11	−1.41139	−0.705695	+	0.708516i	$0.749365\pi$
$284$	8.09817e8	0.00738677
$285$	−7.91938e10	−0.711033
$286$	−1.19747e11	−1.05832
$287$	3.43879e10	0.299183
$288$	−8.68047e8	−0.00743493
$289$	−1.14345e11	−0.964220
$290$	1.23641e11	1.02653
$291$	−1.60176e10	−0.130942
$292$	1.27321e9	0.0102489
$293$	1.93446e10	0.153340	0.0766700	−	0.997057i	$-0.475571\pi$
$293$	1.93446e10	0.153340	0.0766700	+	0.997057i	$0.475571\pi$
$294$	−5.36473e10	−0.418779
$295$	1.69396e10	0.130228
$296$	−1.62782e11	−1.23252
$297$	1.89288e10	0.141162
$298$	2.23933e11	1.64492
$299$	−1.47268e11	−1.06558
$300$	545351.	3.88714e−6 0
$301$	−9.58032e10	−0.672714
$302$	−2.08359e11	−1.44139
$303$	1.60877e10	0.109648
$304$	−1.85359e11	−1.24475
$305$	−2.16804e11	−1.43456
$306$	9.72424e9	0.0634029
$307$	1.74407e10	0.112057	0.0560287	−	0.998429i	$-0.482156\pi$
$307$	1.74407e10	0.112057	0.0560287	+	0.998429i	$0.482156\pi$
$308$	−6.82037e8	−0.00431847
$309$	1.79327e9	0.0111901
$310$	−7.74999e10	−0.476621
$311$	−4.21904e10	−0.255736	−0.127868	−	0.991791i	$-0.540813\pi$
$311$	−4.21904e10	−0.255736	−0.127868	+	0.991791i	$0.540813\pi$
$312$	1.37873e11	0.823729
$313$	−6.79419e10	−0.400118	−0.200059	−	0.979784i	$-0.564113\pi$
$313$	−6.79419e10	−0.400118	−0.200059	+	0.979784i	$0.564113\pi$
$314$	1.55594e11	0.903251
$315$	3.07573e10	0.176016
$316$	−4.19557e8	−0.00236701
$317$	−1.45150e11	−0.807328	−0.403664	−	0.914907i	$-0.632264\pi$
$317$	−1.45150e11	−0.807328	−0.403664	+	0.914907i	$0.632264\pi$
$318$	1.38524e11	0.759633
$319$	−1.38449e11	−0.748569
$320$	−1.85493e11	−0.988898
$321$	−8.28423e10	−0.435491
$322$	−7.60468e10	−0.394212
$323$	4.55567e10	0.232885
$324$	2.45809e8	0.00123921
$325$	−1.74215e8	−0.000866184 0
$326$	7.28188e10	0.357079
$327$	1.10431e10	0.0534102
$328$	1.18131e11	0.563551
$329$	−9.63138e10	−0.453218
$330$	−9.17681e10	−0.425970
$331$	2.49225e10	0.114121	0.0570606	−	0.998371i	$-0.481827\pi$
$331$	2.49225e10	0.114121	0.0570606	+	0.998371i	$0.481827\pi$
$332$	−6.08433e8	−0.00274847
$333$	9.27118e10	0.413177
$334$	−5.97734e10	−0.262814
$335$	1.94458e11	0.843575
$336$	7.19898e10	0.308137
$337$	−4.53476e11	−1.91522	−0.957612	−	0.288060i	$-0.906990\pi$
$337$	−4.53476e11	−1.91522	−0.957612	+	0.288060i	$0.906990\pi$
$338$	2.55475e11	1.06469
$339$	−3.96302e10	−0.162977
$340$	−5.19992e8	−0.00211029
$341$	8.67818e10	0.347563
$342$	1.04406e11	0.412673
$343$	2.32933e11	0.908671
$344$	−3.29109e11	−1.26715
$345$	−1.12859e11	−0.428894
$346$	9.07948e10	0.340580
$347$	2.24806e10	0.0832387	0.0416194	−	0.999134i	$-0.486748\pi$
$347$	2.24806e10	0.0832387	0.0416194	+	0.999134i	$0.486748\pi$
$348$	−1.79790e9	−0.00657142
$349$	6.47369e9	0.0233581	0.0116790	−	0.999932i	$-0.496282\pi$
$349$	6.47369e9	0.0233581	0.0116790	+	0.999932i	$0.496282\pi$
$350$	−8.99619e7	−0.000320444 0
$351$	−7.85249e10	−0.276138
$352$	−4.71238e9	−0.0163606
$353$	2.09469e11	0.718016	0.359008	−	0.933335i	$-0.383115\pi$
$353$	2.09469e11	0.718016	0.359008	+	0.933335i	$0.383115\pi$
$354$	−2.23325e10	−0.0755826
$355$	−1.98255e11	−0.662517
$356$	−6.34456e7	−0.000209352 0
$357$	−1.76933e10	−0.0576505
$358$	3.40059e11	1.09416
$359$	4.81083e11	1.52860	0.764301	−	0.644859i	$-0.223084\pi$
$359$	4.81083e11	1.52860	0.764301	+	0.644859i	$0.223084\pi$
$360$	1.05660e11	0.331549
$361$	1.66438e11	0.515787
$362$	−2.34343e9	−0.00717238
$363$	−8.82349e10	−0.266723
$364$	2.82939e9	0.00844767
$365$	−3.11702e11	−0.919224
$366$	2.85825e11	0.832598
$367$	−1.18448e11	−0.340823	−0.170412	−	0.985373i	$-0.554510\pi$
$367$	−1.18448e11	−0.340823	−0.170412	+	0.985373i	$0.554510\pi$
$368$	−2.64155e11	−0.750833
$369$	−6.72811e10	−0.188918
$370$	−4.49474e11	−1.24680
$371$	−2.52046e11	−0.690713
$372$	1.12695e9	0.00305114
$373$	2.72138e11	0.727946	0.363973	−	0.931409i	$-0.381420\pi$
$373$	2.72138e11	0.727946	0.363973	+	0.931409i	$0.381420\pi$
$374$	5.27901e10	0.139518
$375$	2.21029e11	0.577176
$376$	−3.30863e11	−0.853696
$377$	5.74348e11	1.46433
$378$	−4.05491e10	−0.102157
$379$	−3.37404e11	−0.839991	−0.419995	−	0.907526i	$-0.637968\pi$
$379$	−3.37404e11	−0.839991	−0.419995	+	0.907526i	$0.637968\pi$
$380$	−5.58296e9	−0.0137353
$381$	1.73196e11	0.421089
$382$	−1.64839e11	−0.396073
$383$	5.80008e11	1.37733	0.688667	−	0.725077i	$-0.258196\pi$
$383$	5.80008e11	1.37733	0.688667	+	0.725077i	$0.258196\pi$
$384$	2.50032e11	0.586820
$385$	1.66973e11	0.387322
$386$	5.71698e11	1.31076
$387$	1.87442e11	0.424784
$388$	−1.12920e9	−0.00252946
$389$	−4.48244e11	−0.992525	−0.496262	−	0.868173i	$-0.665295\pi$
$389$	−4.48244e11	−0.992525	−0.496262	+	0.868173i	$0.665295\pi$
$390$	3.80695e11	0.833271
$391$	6.49228e10	0.140476
$392$	3.35322e11	0.717257
$393$	−1.04137e11	−0.220210
$394$	6.96779e10	0.145667
$395$	1.02714e11	0.212296
$396$	1.33443e9	0.00272689
$397$	4.48520e11	0.906200	0.453100	−	0.891460i	$-0.350318\pi$
$397$	4.48520e11	0.906200	0.453100	+	0.891460i	$0.350318\pi$
$398$	9.87040e11	1.97179
$399$	−1.89967e11	−0.375232
$400$	−3.12490e8	−0.000610332 0
$401$	2.37587e11	0.458852	0.229426	−	0.973326i	$-0.426315\pi$
$401$	2.37587e11	0.458852	0.229426	+	0.973326i	$0.426315\pi$
$402$	−2.56364e11	−0.489599
$403$	−3.60010e11	−0.679895
$404$	1.13414e9	0.00211812
$405$	−6.01778e10	−0.111145
$406$	2.96585e11	0.541728
$407$	5.03306e11	0.909196
$408$	−6.07813e10	−0.108592
$409$	9.97089e11	1.76189	0.880946	−	0.473217i	$-0.156907\pi$
$409$	9.97089e11	1.76189	0.880946	+	0.473217i	$0.156907\pi$
$410$	3.26184e11	0.570079
$411$	−2.89415e11	−0.500302
$412$	1.26421e8	0.000216164 0
$413$	4.06341e10	0.0687251
$414$	1.48788e11	0.248924
$415$	1.48953e11	0.246510
$416$	1.95490e10	0.0320041
$417$	2.18198e11	0.353378
$418$	5.66788e11	0.908087
$419$	9.76087e11	1.54713	0.773563	−	0.633720i	$-0.218473\pi$
$419$	9.76087e11	1.54713	0.773563	+	0.633720i	$0.218473\pi$
$420$	2.16831e9	0.00340017
$421$	1.69685e11	0.263254	0.131627	−	0.991299i	$-0.457980\pi$
$421$	1.69685e11	0.263254	0.131627	+	0.991299i	$0.457980\pi$
$422$	9.28633e11	1.42541
$423$	1.88441e11	0.286183
$424$	−8.65845e11	−1.30105
$425$	7.68024e7	0.000114189 0
$426$	2.61371e11	0.384516
$427$	−5.20061e11	−0.757058
$428$	−5.84017e9	−0.00841256
$429$	−4.26290e11	−0.607641
$430$	−9.08734e11	−1.28183
$431$	9.50235e11	1.32643	0.663214	−	0.748430i	$-0.269192\pi$
$431$	9.50235e11	1.32643	0.663214	+	0.748430i	$0.269192\pi$
$432$	−1.40850e11	−0.194573
$433$	1.24774e12	1.70581	0.852903	−	0.522069i	$-0.174840\pi$
$433$	1.24774e12	1.70581	0.852903	+	0.522069i	$0.174840\pi$
$434$	−1.85903e11	−0.251527
$435$	4.40153e11	0.589389
$436$	7.78507e8	0.00103175
$437$	6.97053e11	0.914322
$438$	4.10934e11	0.533505
$439$	−8.46452e11	−1.08771	−0.543854	−	0.839180i	$-0.683035\pi$
$439$	−8.46452e11	−1.08771	−0.543854	+	0.839180i	$0.683035\pi$
$440$	5.73595e11	0.729573
$441$	−1.90981e11	−0.240445
$442$	−2.18997e11	−0.272922
$443$	−9.24332e11	−1.14028	−0.570140	−	0.821548i	$-0.693111\pi$
$443$	−9.24332e11	−1.14028	−0.570140	+	0.821548i	$0.693111\pi$
$444$	6.53594e9	0.00798151
$445$	1.55324e10	0.0187767
$446$	−8.24598e11	−0.986814
$447$	7.97186e11	0.944444
$448$	−4.44952e11	−0.521869
$449$	1.46015e12	1.69547	0.847734	−	0.530421i	$-0.177966\pi$
$449$	1.46015e12	1.69547	0.847734	+	0.530421i	$0.177966\pi$
$450$	1.76014e8	0.000202344 0
$451$	−3.65250e11	−0.415715
$452$	−2.79382e9	−0.00314830
$453$	−7.41744e11	−0.827584
$454$	−1.64581e12	−1.81814
$455$	−6.92678e11	−0.757670
$456$	−6.52586e11	−0.706799
$457$	−1.36049e12	−1.45905	−0.729527	−	0.683953i	$-0.760260\pi$
$457$	−1.36049e12	−1.45905	−0.729527	+	0.683953i	$0.760260\pi$
$458$	−1.06185e12	−1.12763
$459$	3.46176e10	0.0364033
$460$	−7.95627e9	−0.00828513
$461$	1.78435e12	1.84003	0.920017	−	0.391878i	$-0.128174\pi$
$461$	1.78435e12	1.84003	0.920017	+	0.391878i	$0.128174\pi$
$462$	−2.20129e11	−0.224796
$463$	−1.15110e12	−1.16412	−0.582059	−	0.813146i	$-0.697753\pi$
$463$	−1.15110e12	−1.16412	−0.582059	+	0.813146i	$0.697753\pi$
$464$	1.03021e12	1.03180
$465$	−2.75894e11	−0.273656
$466$	−1.47818e12	−1.45208
$467$	7.32203e11	0.712370	0.356185	−	0.934416i	$-0.384077\pi$
$467$	7.32203e11	0.712370	0.356185	+	0.934416i	$0.384077\pi$
$468$	−5.53581e9	−0.00533426
$469$	4.66457e11	0.445178
$470$	−9.13578e11	−0.863585
$471$	5.53903e11	0.518608
$472$	1.39589e11	0.129453
$473$	1.01757e12	0.934737
$474$	−1.35413e11	−0.123214
$475$	8.24599e8	0.000743228 0
$476$	−1.24733e9	−0.00111366
$477$	4.93137e11	0.436149
$478$	2.89480e11	0.253625
$479$	5.44537e11	0.472626	0.236313	−	0.971677i	$-0.424061\pi$
$479$	5.44537e11	0.472626	0.236313	+	0.971677i	$0.424061\pi$
$480$	1.49815e10	0.0128816
$481$	−2.08794e12	−1.77854
$482$	−6.96509e11	−0.587781
$483$	−2.70722e11	−0.226340
$484$	−6.22033e9	−0.00515240
$485$	2.76445e11	0.226867
$486$	7.93357e10	0.0645068
$487$	−3.03937e11	−0.244852	−0.122426	−	0.992478i	$-0.539067\pi$
$487$	−3.03937e11	−0.244852	−0.122426	+	0.992478i	$0.539067\pi$
$488$	−1.78655e12	−1.42602
$489$	2.59230e11	0.205019
$490$	9.25889e11	0.725565
$491$	6.20518e11	0.481823	0.240912	−	0.970547i	$-0.422554\pi$
$491$	6.20518e11	0.481823	0.240912	+	0.970547i	$0.422554\pi$
$492$	−4.74314e9	−0.00364941
$493$	−2.53201e11	−0.193043
$494$	−2.35129e12	−1.77638
$495$	−3.26688e11	−0.244574
$496$	−6.45751e11	−0.479068
$497$	−4.75567e11	−0.349629
$498$	−1.96374e11	−0.143071
$499$	−2.20381e12	−1.59119	−0.795593	−	0.605831i	$-0.792841\pi$
$499$	−2.20381e12	−1.59119	−0.795593	+	0.605831i	$0.792841\pi$
$500$	1.55820e10	0.0111495
$501$	−2.12789e11	−0.150897
$502$	−1.29551e11	−0.0910491
$503$	2.05035e12	1.42815	0.714073	−	0.700072i	$-0.246849\pi$
$503$	2.05035e12	1.42815	0.714073	+	0.700072i	$0.246849\pi$
$504$	2.53452e11	0.174968
$505$	−2.77654e11	−0.189973
$506$	8.07729e11	0.547758
$507$	9.09475e11	0.611301
$508$	1.22098e10	0.00813436
$509$	9.88432e11	0.652705	0.326352	−	0.945248i	$-0.394180\pi$
$509$	9.88432e11	0.652705	0.326352	+	0.945248i	$0.394180\pi$
$510$	−1.67829e11	−0.109850
$511$	−7.47697e11	−0.485101
$512$	−1.52814e12	−0.982761
$513$	3.71677e11	0.236939
$514$	1.84040e12	1.16300
$515$	−3.09498e10	−0.0193876
$516$	1.32142e10	0.00820573
$517$	1.02299e12	0.629747
$518$	−1.07818e12	−0.657971
$519$	3.23223e11	0.195546
$520$	−2.37953e12	−1.42717
$521$	−2.84286e11	−0.169039	−0.0845193	−	0.996422i	$-0.526935\pi$
$521$	−2.84286e11	−0.169039	−0.0845193	+	0.996422i	$0.526935\pi$
$522$	−5.80278e11	−0.342073
$523$	2.36673e12	1.38322	0.691609	−	0.722273i	$-0.256902\pi$
$523$	2.36673e12	1.38322	0.691609	+	0.722273i	$0.256902\pi$
$524$	−7.34137e9	−0.00425389
$525$	−3.20258e8	−0.000183985 0
$526$	2.59314e11	0.147703
$527$	1.58710e11	0.0896306
$528$	−7.64637e11	−0.428157
$529$	−8.07784e11	−0.448482
$530$	−2.39077e12	−1.31612
$531$	−7.95020e10	−0.0433963
$532$	−1.33922e10	−0.00724851
$533$	1.51522e12	0.813211
$534$	−2.04773e10	−0.0108977
$535$	1.42976e12	0.754520
$536$	1.60240e12	0.838553
$537$	1.21059e12	0.628220
$538$	1.36933e12	0.704672
$539$	−1.03678e12	−0.529099
$540$	−4.24238e9	−0.00214703
$541$	2.27027e12	1.13943	0.569717	−	0.821841i	$-0.307053\pi$
$541$	2.27027e12	1.13943	0.569717	+	0.821841i	$0.307053\pi$
$542$	−4.30806e11	−0.214430
$543$	−8.34245e9	−0.00411807
$544$	−8.61817e9	−0.00421910
$545$	−1.90590e11	−0.0925372
$546$	9.13195e11	0.439741
$547$	2.45903e12	1.17441	0.587206	−	0.809437i	$-0.300228\pi$
$547$	2.45903e12	1.17441	0.587206	+	0.809437i	$0.300228\pi$
$548$	−2.04030e10	−0.00966454
$549$	1.01752e12	0.478043
$550$	9.55528e8	0.000445257 0
$551$	−2.71852e12	−1.25647
$552$	−9.30000e11	−0.426341
$553$	2.46386e11	0.112035
$554$	2.42653e12	1.09444
$555$	−1.60010e12	−0.715859
$556$	1.53824e10	0.00682635
$557$	3.65527e12	1.60906	0.804529	−	0.593914i	$-0.202418\pi$
$557$	3.65527e12	1.60906	0.804529	+	0.593914i	$0.202418\pi$
$558$	3.63727e11	0.158826
$559$	−4.22134e12	−1.82851
$560$	−1.24246e12	−0.533870
$561$	1.87929e11	0.0801053
$562$	1.87637e12	0.793424
$563$	−4.28647e12	−1.79809	−0.899047	−	0.437852i	$-0.855739\pi$
$563$	−4.28647e12	−1.79809	−0.899047	+	0.437852i	$0.855739\pi$
$564$	1.32846e10	0.00552832
$565$	6.83970e11	0.282370
$566$	−3.46521e12	−1.41924
$567$	−1.44352e11	−0.0586542
$568$	−1.63370e12	−0.658573
$569$	−2.55612e12	−1.02230	−0.511148	−	0.859493i	$-0.670779\pi$
$569$	−2.55612e12	−1.02230	−0.511148	+	0.859493i	$0.670779\pi$
$570$	−1.80192e12	−0.714987
$571$	−3.28901e12	−1.29480	−0.647400	−	0.762150i	$-0.724144\pi$
$571$	−3.28901e12	−1.29480	−0.647400	+	0.762150i	$0.724144\pi$
$572$	−3.00523e10	−0.0117380
$573$	−5.86816e11	−0.227408
$574$	7.82436e11	0.300847
$575$	1.17514e9	0.000448314 0
$576$	8.70563e11	0.329533
$577$	−2.30318e12	−0.865040	−0.432520	−	0.901624i	$-0.642375\pi$
$577$	−2.30318e12	−0.865040	−0.432520	+	0.901624i	$0.642375\pi$
$578$	−2.60171e12	−0.969582
$579$	2.03520e12	0.752583
$580$	3.10297e10	0.0113855
$581$	3.57303e11	0.130090
$582$	−3.64453e11	−0.131670
$583$	2.67710e12	0.959746
$584$	−2.56854e12	−0.913751
$585$	1.35525e12	0.478429
$586$	4.40152e11	0.154193
$587$	1.35652e12	0.471579	0.235790	−	0.971804i	$-0.424232\pi$
$587$	1.35652e12	0.471579	0.235790	+	0.971804i	$0.424232\pi$
$588$	−1.34636e10	−0.00464477
$589$	1.70401e12	0.583382
$590$	3.85432e11	0.130952
$591$	2.48049e11	0.0836360
$592$	−3.74514e12	−1.25320
$593$	−1.38959e12	−0.461468	−0.230734	−	0.973017i	$-0.574113\pi$
$593$	−1.38959e12	−0.461468	−0.230734	+	0.973017i	$0.574113\pi$
$594$	4.30691e11	0.141947
$595$	3.05366e11	0.0998836
$596$	5.61996e10	0.0182442
$597$	3.51380e12	1.13212
$598$	−3.35082e12	−1.07151
$599$	1.04751e12	0.332459	0.166230	−	0.986087i	$-0.446841\pi$
$599$	1.04751e12	0.332459	0.166230	+	0.986087i	$0.446841\pi$
$600$	−1.10017e9	−0.000346561 0
$601$	3.83855e12	1.20014	0.600071	−	0.799947i	$-0.295139\pi$
$601$	3.83855e12	1.20014	0.600071	+	0.799947i	$0.295139\pi$
$602$	−2.17983e12	−0.676455
$603$	−9.12640e11	−0.281107
$604$	−5.22910e10	−0.0159868
$605$	1.52283e12	0.462117
$606$	3.66047e11	0.110258
$607$	−5.75921e11	−0.172192	−0.0860962	−	0.996287i	$-0.527439\pi$
$607$	−5.75921e11	−0.172192	−0.0860962	+	0.996287i	$0.527439\pi$
$608$	−9.25302e10	−0.0274611
$609$	1.05582e12	0.311037
$610$	−4.93300e12	−1.44254
$611$	−4.24384e12	−1.23189
$612$	2.44045e9	0.000703217 0
$613$	5.65749e12	1.61827	0.809137	−	0.587620i	$-0.199935\pi$
$613$	5.65749e12	1.61827	0.809137	+	0.587620i	$0.199935\pi$
$614$	3.96832e11	0.112681
$615$	1.16119e12	0.327315
$616$	1.37592e12	0.385016
$617$	4.56000e12	1.26672	0.633361	−	0.773856i	$-0.281675\pi$
$617$	4.56000e12	1.26672	0.633361	+	0.773856i	$0.281675\pi$
$618$	4.08028e10	0.0112523
$619$	2.72974e12	0.747332	0.373666	−	0.927563i	$-0.378101\pi$
$619$	2.72974e12	0.747332	0.373666	+	0.927563i	$0.378101\pi$
$620$	−1.94498e10	−0.00528632
$621$	5.29676e11	0.142922
$622$	−9.59968e11	−0.257158
$623$	3.72585e10	0.00990899
$624$	3.17206e12	0.837549
$625$	−3.81700e12	−1.00060
$626$	−1.54590e12	−0.402343
$627$	2.01773e12	0.521385
$628$	3.90487e10	0.0100182
$629$	9.20465e11	0.234466
$630$	6.99829e11	0.176994
$631$	−2.98551e12	−0.749698	−0.374849	−	0.927086i	$-0.622306\pi$
$631$	−2.98551e12	−0.749698	−0.374849	+	0.927086i	$0.622306\pi$
$632$	8.46400e11	0.211032
$633$	3.30587e12	0.818407
$634$	−3.30263e12	−0.811817
$635$	−2.98915e12	−0.729568
$636$	3.47649e10	0.00842527
$637$	4.30102e12	1.03501
$638$	−3.15016e12	−0.752732
$639$	9.30463e11	0.220773
$640$	−4.31526e12	−1.01671
$641$	3.08549e12	0.721878	0.360939	−	0.932590i	$-0.382456\pi$
$641$	3.08549e12	0.721878	0.360939	+	0.932590i	$0.382456\pi$
$642$	−1.88493e12	−0.437913
$643$	4.78998e11	0.110506	0.0552528	−	0.998472i	$-0.482404\pi$
$643$	4.78998e11	0.110506	0.0552528	+	0.998472i	$0.482404\pi$
$644$	−1.90852e10	−0.00437230
$645$	−3.23503e12	−0.735970
$646$	1.03656e12	0.234180
$647$	−5.97540e11	−0.134060	−0.0670298	−	0.997751i	$-0.521352\pi$
$647$	−5.97540e11	−0.134060	−0.0670298	+	0.997751i	$0.521352\pi$
$648$	−4.95887e11	−0.110483
$649$	−4.31594e11	−0.0954935
$650$	−3.96395e9	−0.000871001 0
$651$	−6.61804e11	−0.144416
$652$	1.82750e10	0.00396044
$653$	5.25724e12	1.13148	0.565742	−	0.824582i	$-0.308590\pi$
$653$	5.25724e12	1.13148	0.565742	+	0.824582i	$0.308590\pi$
$654$	2.51265e11	0.0537072
$655$	1.79728e12	0.381530
$656$	2.71785e12	0.573006
$657$	1.46290e12	0.306316
$658$	−2.19145e12	−0.455738
$659$	−4.38391e11	−0.0905476	−0.0452738	−	0.998975i	$-0.514416\pi$
$659$	−4.38391e11	−0.0905476	−0.0452738	+	0.998975i	$0.514416\pi$
$660$	−2.30307e10	−0.00472453
$661$	−1.47713e12	−0.300963	−0.150482	−	0.988613i	$-0.548082\pi$
$661$	−1.47713e12	−0.300963	−0.150482	+	0.988613i	$0.548082\pi$
$662$	5.67069e11	0.114756
$663$	−7.79614e11	−0.156700
$664$	1.22743e12	0.245042
$665$	3.27860e12	0.650117
$666$	2.10950e12	0.415475
$667$	−3.87416e12	−0.757900
$668$	−1.50011e10	−0.00291493
$669$	−2.93551e12	−0.566587
$670$	4.42455e12	0.848266
$671$	5.52382e12	1.05193
$672$	3.59369e10	0.00679796
$673$	6.94568e12	1.30511	0.652555	−	0.757742i	$-0.273697\pi$
$673$	6.94568e12	1.30511	0.652555	+	0.757742i	$0.273697\pi$
$674$	−1.03181e13	−1.92588
$675$	6.26596e8	0.000116177 0
$676$	6.41156e10	0.0118087
$677$	−2.09846e12	−0.383930	−0.191965	−	0.981402i	$-0.561486\pi$
$677$	−2.09846e12	−0.383930	−0.191965	+	0.981402i	$0.561486\pi$
$678$	−9.01715e11	−0.163884
$679$	6.63125e11	0.119724
$680$	1.04901e12	0.188144
$681$	−5.85896e12	−1.04390
$682$	1.97457e12	0.349496
$683$	−8.36376e12	−1.47065	−0.735323	−	0.677717i	$-0.762970\pi$
$683$	−8.36376e12	−1.47065	−0.735323	+	0.677717i	$0.762970\pi$
$684$	2.62023e10	0.00457706
$685$	4.99495e12	0.866810
$686$	5.29997e12	0.913724
$687$	−3.78011e12	−0.647439
$688$	−7.57183e12	−1.28841
$689$	−1.11058e13	−1.87743
$690$	−2.56791e12	−0.431280
$691$	−2.29427e12	−0.382819	−0.191410	−	0.981510i	$-0.561306\pi$
$691$	−2.29427e12	−0.382819	−0.191410	+	0.981510i	$0.561306\pi$
$692$	2.27864e10	0.00377745
$693$	−7.83645e11	−0.129068
$694$	5.11507e11	0.0837016
$695$	−3.76585e12	−0.612253
$696$	3.62702e12	0.585880
$697$	−6.67983e11	−0.107206
$698$	1.47297e11	0.0234880
$699$	−5.26222e12	−0.833723
$700$	−2.25774e7	−3.55412e−6 0
$701$	−8.27605e12	−1.29447	−0.647235	−	0.762291i	$-0.724075\pi$
$701$	−8.27605e12	−1.29447	−0.647235	+	0.762291i	$0.724075\pi$
$702$	−1.78670e12	−0.277673
$703$	9.88269e12	1.52608
$704$	4.72604e12	0.725138
$705$	−3.25227e12	−0.495834
$706$	4.76610e12	0.722008
$707$	−6.66025e11	−0.100254
$708$	−5.60469e9	−0.000838304 0
$709$	6.39004e11	0.0949720	0.0474860	−	0.998872i	$-0.484879\pi$
$709$	6.39004e11	0.0949720	0.0474860	+	0.998872i	$0.484879\pi$
$710$	−4.51095e12	−0.666202
$711$	−4.82062e11	−0.0707441
$712$	1.27993e11	0.0186649
$713$	2.42838e12	0.351896
$714$	−4.02581e11	−0.0579710
$715$	7.35725e12	1.05278
$716$	8.53433e10	0.0121356
$717$	1.03053e12	0.145621
$718$	1.09462e13	1.53710
$719$	6.07965e12	0.848396	0.424198	−	0.905569i	$-0.360556\pi$
$719$	6.07965e12	0.848396	0.424198	+	0.905569i	$0.360556\pi$
$720$	2.43091e12	0.337111
$721$	−7.42411e10	−0.0102314
$722$	3.78701e12	0.518655
$723$	−2.47953e12	−0.337479
$724$	−5.88121e8	−7.95505e−5 0
$725$	−4.58306e9	−0.000616076 0
$726$	−2.00763e12	−0.268206
$727$	2.87181e12	0.381286	0.190643	−	0.981659i	$-0.438943\pi$
$727$	2.87181e12	0.381286	0.190643	+	0.981659i	$0.438943\pi$
$728$	−5.70792e12	−0.753158
$729$	2.82430e11	0.0370370
$730$	−7.09223e12	−0.924336
$731$	1.86097e12	0.241052
$732$	7.17324e10	0.00923454
$733$	8.02066e11	0.102622	0.0513112	−	0.998683i	$-0.483660\pi$
$733$	8.02066e11	0.102622	0.0513112	+	0.998683i	$0.483660\pi$
$734$	−2.69507e12	−0.342719
$735$	3.29610e12	0.416589
$736$	−1.31865e11	−0.0165645
$737$	−4.95446e12	−0.618576
$738$	−1.53086e12	−0.189969
$739$	1.42081e13	1.75241	0.876204	−	0.481941i	$-0.160068\pi$
$739$	1.42081e13	1.75241	0.876204	+	0.481941i	$0.160068\pi$
$740$	−1.12803e11	−0.0138286
$741$	−8.37043e12	−1.01992
$742$	−5.73487e12	−0.694554
$743$	−8.54638e12	−1.02880	−0.514402	−	0.857549i	$-0.671986\pi$
$743$	−8.54638e12	−1.02880	−0.514402	+	0.857549i	$0.671986\pi$
$744$	−2.27347e12	−0.272026
$745$	−1.37585e13	−1.63632
$746$	6.19202e12	0.731994
$747$	−6.99076e11	−0.0821451
$748$	1.32485e10	0.00154743
$749$	3.42965e12	0.398182
$750$	5.02912e12	0.580386
$751$	1.18674e13	1.36136	0.680682	−	0.732579i	$-0.261684\pi$
$751$	1.18674e13	1.36136	0.680682	+	0.732579i	$0.261684\pi$
$752$	−7.61219e12	−0.868019
$753$	−4.61194e11	−0.0522765
$754$	1.30683e13	1.47247
$755$	1.28016e13	1.43385
$756$	−1.01764e10	−0.00113305
$757$	−1.14291e13	−1.26498	−0.632488	−	0.774570i	$-0.717966\pi$
$757$	−1.14291e13	−1.26498	−0.632488	+	0.774570i	$0.717966\pi$
$758$	−7.67705e12	−0.844662
$759$	2.87546e12	0.314499
$760$	1.12629e13	1.22458
$761$	8.11619e12	0.877246	0.438623	−	0.898671i	$-0.355466\pi$
$761$	8.11619e12	0.877246	0.438623	+	0.898671i	$0.355466\pi$
$762$	3.94076e12	0.423431
$763$	−4.57180e11	−0.0488345
$764$	−4.13690e10	−0.00439294
$765$	−5.97459e11	−0.0630713
$766$	1.31971e13	1.38499
$767$	1.79044e12	0.186802
$768$	1.86218e11	0.0193150
$769$	−7.35224e12	−0.758143	−0.379072	−	0.925367i	$-0.623757\pi$
$769$	−7.35224e12	−0.758143	−0.379072	+	0.925367i	$0.623757\pi$
$770$	3.79917e12	0.389476
$771$	6.55171e12	0.667744
$772$	1.43477e11	0.0145380
$773$	1.27079e13	1.28017	0.640085	−	0.768304i	$-0.278899\pi$
$773$	1.27079e13	1.28017	0.640085	+	0.768304i	$0.278899\pi$
$774$	4.26492e12	0.427146
$775$	2.87273e9	0.000286047 0
$776$	2.27801e12	0.225516
$777$	−3.83824e12	−0.377779
$778$	−1.01990e13	−0.998044
$779$	−7.17188e12	−0.697774
$780$	9.55415e10	0.00924200
$781$	5.05122e12	0.485810
$782$	1.47721e12	0.141257
$783$	−2.06575e12	−0.196404
$784$	7.71476e12	0.729290
$785$	−9.55970e12	−0.898527
$786$	−2.36945e12	−0.221435
$787$	−1.81646e13	−1.68787	−0.843935	−	0.536445i	$-0.819767\pi$
$787$	−1.81646e13	−1.68787	−0.843935	+	0.536445i	$0.819767\pi$
$788$	1.74868e10	0.00161563
$789$	9.23140e11	0.0848049
$790$	2.33708e12	0.213477
$791$	1.64068e12	0.149015
$792$	−2.69203e12	−0.243118
$793$	−2.29152e13	−2.05776
$794$	1.02053e13	0.911240
$795$	−8.51096e12	−0.755660
$796$	2.47714e11	0.0218696
$797$	2.04779e13	1.79773	0.898863	−	0.438230i	$-0.144394\pi$
$797$	2.04779e13	1.79773	0.898863	+	0.438230i	$0.144394\pi$
$798$	−4.32236e12	−0.377319
$799$	1.87089e12	0.162401
$800$	−1.55993e8	−1.34648e−5 0
$801$	−7.28976e10	−0.00625701
$802$	5.40587e12	0.461404
$803$	7.94165e12	0.674048
$804$	−6.43388e10	−0.00543026
$805$	4.67233e12	0.392150
$806$	−8.19139e12	−0.683675
$807$	4.87471e12	0.404593
$808$	−2.28797e12	−0.188842
$809$	2.77264e12	0.227575	0.113788	−	0.993505i	$-0.463702\pi$
$809$	2.77264e12	0.227575	0.113788	+	0.993505i	$0.463702\pi$
$810$	−1.36924e12	−0.111763
$811$	4.45984e12	0.362014	0.181007	−	0.983482i	$-0.442064\pi$
$811$	4.45984e12	0.362014	0.181007	+	0.983482i	$0.442064\pi$
$812$	7.44327e10	0.00600844
$813$	−1.53364e12	−0.123116
$814$	1.14518e13	0.914252
$815$	−4.47400e12	−0.355211
$816$	−1.39840e12	−0.110414
$817$	1.99806e13	1.56895
$818$	2.26870e13	1.77169
$819$	3.25091e12	0.252480
$820$	8.18610e10	0.00632288
$821$	−7.92103e12	−0.608468	−0.304234	−	0.952597i	$-0.598400\pi$
$821$	−7.92103e12	−0.608468	−0.304234	+	0.952597i	$0.598400\pi$
$822$	−6.58512e12	−0.503084
$823$	9.57400e12	0.727435	0.363718	−	0.931509i	$-0.381507\pi$
$823$	9.57400e12	0.727435	0.363718	+	0.931509i	$0.381507\pi$
$824$	−2.55038e11	−0.0192722
$825$	3.40161e9	0.000255648 0
$826$	9.24557e11	0.0691073
$827$	−1.26247e13	−0.938524	−0.469262	−	0.883059i	$-0.655480\pi$
$827$	−1.26247e13	−0.938524	−0.469262	+	0.883059i	$0.655480\pi$
$828$	3.73408e10	0.00276088
$829$	4.32575e12	0.318101	0.159051	−	0.987270i	$-0.449157\pi$
$829$	4.32575e12	0.318101	0.159051	+	0.987270i	$0.449157\pi$
$830$	3.38917e12	0.247881
$831$	8.63826e12	0.628379
$832$	−1.96057e13	−1.41850
$833$	−1.89610e12	−0.136445
$834$	4.96472e12	0.355343
$835$	3.67249e12	0.261440
$836$	1.42245e11	0.0100718
$837$	1.29484e12	0.0911910
$838$	2.22092e13	1.55573
$839$	2.32435e11	0.0161947	0.00809735	−	0.999967i	$-0.497423\pi$
$839$	2.32435e11	0.0161947	0.00809735	+	0.999967i	$0.497423\pi$
$840$	−4.37427e12	−0.303144
$841$	6.02196e11	0.0415103
$842$	3.86089e12	0.264718
$843$	6.67975e12	0.455550
$844$	2.33055e11	0.0158095
$845$	−1.56965e13	−1.05912
$846$	4.28765e12	0.287775
$847$	3.65290e12	0.243872
$848$	−1.99205e13	−1.32288
$849$	−1.23359e13	−0.814866
$850$	1.74750e9	0.000114824 0
$851$	1.40838e13	0.920529
$852$	6.55952e10	0.00426475
$853$	−1.00294e13	−0.648644	−0.324322	−	0.945947i	$-0.605136\pi$
$853$	−1.00294e13	−0.648644	−0.324322	+	0.945947i	$0.605136\pi$
$854$	−1.18331e13	−0.761268
$855$	−6.41470e12	−0.410515
$856$	1.17817e13	0.750028
$857$	1.21511e13	0.769487	0.384743	−	0.923024i	$-0.374290\pi$
$857$	1.21511e13	0.769487	0.384743	+	0.923024i	$0.374290\pi$
$858$	−9.69947e12	−0.611020
$859$	−1.02223e13	−0.640588	−0.320294	−	0.947318i	$-0.603782\pi$
$859$	−1.02223e13	−0.640588	−0.320294	+	0.947318i	$0.603782\pi$
$860$	−2.28061e11	−0.0142170
$861$	2.78542e12	0.172733
$862$	2.16209e13	1.33380
$863$	1.52014e13	0.932897	0.466449	−	0.884548i	$-0.345533\pi$
$863$	1.52014e13	0.932897	0.466449	+	0.884548i	$0.345533\pi$
$864$	−7.03118e10	−0.00429256
$865$	−5.57845e12	−0.338798
$866$	2.83902e13	1.71529
$867$	−9.26193e12	−0.556692
$868$	−4.66555e10	−0.00278974
$869$	−2.61698e12	−0.155672
$870$	1.00149e13	0.592667
$871$	2.05533e13	1.21004
$872$	−1.57053e12	−0.0919862
$873$	−1.29743e12	−0.0755994
$874$	1.58602e13	0.919406
$875$	−9.15053e12	−0.527728
$876$	1.03130e11	0.00591723
$877$	−5.03270e12	−0.287278	−0.143639	−	0.989630i	$-0.545880\pi$
$877$	−5.03270e12	−0.287278	−0.143639	+	0.989630i	$0.545880\pi$
$878$	−1.92595e13	−1.09376
$879$	1.56691e12	0.0885308
$880$	1.31967e13	0.741813
$881$	1.51352e13	0.846439	0.423220	−	0.906027i	$-0.360900\pi$
$881$	1.51352e13	0.846439	0.423220	+	0.906027i	$0.360900\pi$
$882$	−4.34543e12	−0.241782
$883$	3.10810e13	1.72057	0.860283	−	0.509817i	$-0.170287\pi$
$883$	3.10810e13	1.72057	0.860283	+	0.509817i	$0.170287\pi$
$884$	−5.49608e10	−0.00302704
$885$	1.37211e12	0.0751873
$886$	−2.10316e13	−1.14662
$887$	2.22009e13	1.20424	0.602122	−	0.798404i	$-0.294322\pi$
$887$	2.22009e13	1.20424	0.602122	+	0.798404i	$0.294322\pi$
$888$	−1.31854e13	−0.711597
$889$	−7.17025e12	−0.385014
$890$	3.53413e11	0.0188811
$891$	1.53323e12	0.0815000
$892$	−2.06946e11	−0.0109450
$893$	2.00871e13	1.05702
$894$	1.81386e13	0.949696
$895$	−2.08933e13	−1.08844
$896$	−1.03513e13	−0.536546
$897$	−1.19287e13	−0.615215
$898$	3.32232e13	1.70490
$899$	−9.47075e12	−0.483577
$900$	4.41734e7	2.24424e−6 0
$901$	4.89598e12	0.247502
$902$	−8.31062e12	−0.418027
$903$	−7.76006e12	−0.388392
$904$	5.63616e12	0.280689
$905$	1.43981e11	0.00713487
$906$	−1.68771e13	−0.832186
$907$	−2.69908e13	−1.32429	−0.662145	−	0.749376i	$-0.730354\pi$
$907$	−2.69908e13	−1.32429	−0.662145	+	0.749376i	$0.730354\pi$
$908$	−4.13042e11	−0.0201654
$909$	1.30310e12	0.0633054
$910$	−1.57607e13	−0.761883
$911$	−6.41073e12	−0.308372	−0.154186	−	0.988042i	$-0.549276\pi$
$911$	−6.41073e12	−0.308372	−0.154186	+	0.988042i	$0.549276\pi$
$912$	−1.50141e13	−0.718657
$913$	−3.79509e12	−0.180760
$914$	−3.09555e13	−1.46717
$915$	−1.75612e13	−0.828244
$916$	−2.66488e11	−0.0125068
$917$	4.31123e12	0.201344
$918$	7.87663e11	0.0366057
$919$	−3.08233e13	−1.42548	−0.712738	−	0.701431i	$-0.752545\pi$
$919$	−3.08233e13	−1.42548	−0.712738	+	0.701431i	$0.752545\pi$
$920$	1.60507e13	0.738667
$921$	1.41269e12	0.0646964
$922$	4.05998e13	1.85027
$923$	−2.09547e13	−0.950329
$924$	−5.52450e10	−0.00249327
$925$	1.66609e10	0.000748273 0
$926$	−2.61912e13	−1.17059
$927$	1.45255e11	0.00646060
$928$	5.14275e11	0.0227630
$929$	−1.27614e13	−0.562119	−0.281060	−	0.959690i	$-0.590686\pi$
$929$	−1.27614e13	−0.562119	−0.281060	+	0.959690i	$0.590686\pi$
$930$	−6.27749e12	−0.275177
$931$	−2.03577e13	−0.888088
$932$	−3.70973e11	−0.0161054
$933$	−3.41742e12	−0.147649
$934$	1.66600e13	0.716331
$935$	−3.24344e12	−0.138788
$936$	1.11677e13	0.475580
$937$	−4.60555e13	−1.95188	−0.975940	−	0.218037i	$-0.930035\pi$
$937$	−4.60555e13	−1.95188	−0.975940	+	0.218037i	$0.930035\pi$
$938$	1.06134e13	0.447654
$939$	−5.50329e12	−0.231008
$940$	−2.29277e11	−0.00957823
$941$	−2.31569e12	−0.0962782	−0.0481391	−	0.998841i	$-0.515329\pi$
$941$	−2.31569e12	−0.0962782	−0.0481391	+	0.998841i	$0.515329\pi$
$942$	1.26031e13	0.521492
$943$	−1.02206e13	−0.420897
$944$	3.21153e12	0.131625
$945$	2.49134e12	0.101623
$946$	2.31530e13	0.939935
$947$	1.36583e13	0.551853	0.275926	−	0.961179i	$-0.411015\pi$
$947$	1.36583e13	0.551853	0.275926	+	0.961179i	$0.411015\pi$
$948$	−3.39842e10	−0.00136659
$949$	−3.29455e13	−1.31855
$950$	1.87623e10	0.000747361 0
$951$	−1.17571e13	−0.466111
$952$	2.51633e12	0.0992889
$953$	3.99596e13	1.56929	0.784645	−	0.619946i	$-0.212845\pi$
$953$	3.99596e13	1.56929	0.784645	+	0.619946i	$0.212845\pi$
$954$	1.12205e13	0.438575
$955$	1.01278e13	0.394001
$956$	7.26495e10	0.00281302
$957$	−1.12144e13	−0.432186
$958$	1.23900e13	0.475254
$959$	1.19817e13	0.457440
$960$	−1.50249e13	−0.570941
$961$	−2.05032e13	−0.775473
$962$	−4.75074e13	−1.78844
$963$	−6.71022e12	−0.251431
$964$	−1.74800e11	−0.00651921
$965$	−3.51252e13	−1.30391
$966$	−6.15979e12	−0.227598
$967$	2.52200e13	0.927525	0.463762	−	0.885960i	$-0.346499\pi$
$967$	2.52200e13	0.927525	0.463762	+	0.885960i	$0.346499\pi$
$968$	1.25487e13	0.459366
$969$	3.69009e12	0.134456
$970$	6.29002e12	0.228128
$971$	3.42705e13	1.23718	0.618591	−	0.785713i	$-0.287704\pi$
$971$	3.42705e13	1.23718	0.618591	+	0.785713i	$0.287704\pi$
$972$	1.99106e10	0.000715460 0
$973$	−9.03335e12	−0.323103
$974$	−6.91556e12	−0.246213
$975$	−1.41114e10	−0.000500092 0
$976$	−4.11032e13	−1.44994
$977$	1.42817e13	0.501481	0.250741	−	0.968054i	$-0.419326\pi$
$977$	1.42817e13	0.501481	0.250741	+	0.968054i	$0.419326\pi$
$978$	5.89832e12	0.206160
$979$	−3.95740e11	−0.0137686
$980$	2.32367e11	0.00804741
$981$	8.94488e11	0.0308364
$982$	1.41188e13	0.484503
$983$	−2.29765e13	−0.784863	−0.392431	−	0.919781i	$-0.628366\pi$
$983$	−2.29765e13	−0.784863	−0.392431	+	0.919781i	$0.628366\pi$
$984$	9.56864e12	0.325366
$985$	−4.28103e12	−0.144905
$986$	−5.76114e12	−0.194116
$987$	−7.80142e12	−0.261665
$988$	−5.90094e11	−0.0197022
$989$	2.84743e13	0.946388
$990$	−7.43321e12	−0.245934
$991$	6.00264e12	0.197702	0.0988510	−	0.995102i	$-0.468483\pi$
$991$	6.00264e12	0.197702	0.0988510	+	0.995102i	$0.468483\pi$
$992$	−3.22355e11	−0.0105690
$993$	2.01873e12	0.0658879
$994$	−1.08207e13	−0.351573
$995$	−6.06440e13	−1.96148
$996$	−4.92831e10	−0.00158683
$997$	−3.23900e13	−1.03820	−0.519102	−	0.854712i	$-0.673734\pi$
$997$	−3.23900e13	−1.03820	−0.519102	+	0.854712i	$0.673734\pi$
$998$	−5.01438e13	−1.60004
$999$	7.50966e12	0.238548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.16	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.16	✓	22	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+22.7532 q^{2} +81.0000 q^{3} +5.71029 q^{4} -1397.96 q^{5} +1843.01 q^{6} -3353.38 q^{7} -11519.7 q^{8} +6561.00 q^{9} -31808.2 q^{10} +35617.8 q^{11} +462.534 q^{12} -147759. q^{13} -76300.2 q^{14} -113235. q^{15} -265035. q^{16} +65139.2 q^{17} +149284. q^{18} +699375. q^{19} -7982.78 q^{20} -271624. q^{21} +810421. q^{22} +996679. q^{23} -933099. q^{24} +1179.05 q^{25} -3.36199e6 q^{26} +531441. q^{27} -19148.8 q^{28} -3.88707e6 q^{29} -2.57647e6 q^{30} +2.43647e6 q^{31} -132304. q^{32} +2.88504e6 q^{33} +1.48213e6 q^{34} +4.68790e6 q^{35} +37465.2 q^{36} +1.41307e7 q^{37} +1.59131e7 q^{38} -1.19684e7 q^{39} +1.61042e7 q^{40} -1.02547e7 q^{41} -6.18032e6 q^{42} +2.85692e7 q^{43} +203388. q^{44} -9.17204e6 q^{45} +2.26777e7 q^{46} +2.87214e7 q^{47} -2.14678e7 q^{48} -2.91085e7 q^{49} +26827.2 q^{50} +5.27627e6 q^{51} -843744. q^{52} +7.51619e7 q^{53} +1.20920e7 q^{54} -4.97924e7 q^{55} +3.86300e7 q^{56} +5.66494e7 q^{57} -8.84436e7 q^{58} -1.21174e7 q^{59} -646605. q^{60} +1.55086e8 q^{61} +5.54377e7 q^{62} -2.20015e7 q^{63} +1.32688e8 q^{64} +2.06561e8 q^{65} +6.56441e7 q^{66} -1.39101e8 q^{67} +371964. q^{68} +8.07310e7 q^{69} +1.06665e8 q^{70} +1.41817e8 q^{71} -7.55810e7 q^{72} +2.22968e8 q^{73} +3.21520e8 q^{74} +95503.2 q^{75} +3.99364e6 q^{76} -1.19440e8 q^{77} -2.72321e8 q^{78} -7.34739e7 q^{79} +3.70510e8 q^{80} +4.30467e7 q^{81} -2.33328e8 q^{82} -1.06550e8 q^{83} -1.55105e6 q^{84} -9.10622e7 q^{85} +6.50041e8 q^{86} -3.14853e8 q^{87} -4.10308e8 q^{88} -1.11107e7 q^{89} -2.08694e8 q^{90} +4.95490e8 q^{91} +5.69133e6 q^{92} +1.97354e8 q^{93} +6.53506e8 q^{94} -9.77702e8 q^{95} -1.07166e7 q^{96} -1.97748e8 q^{97} -6.62312e8 q^{98} +2.33688e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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