LMFDB - Embedded newform 177.10.a.a.1.10

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} -22189.8 q^{10} -73867.0 q^{11} -28288.0 q^{12} +162700. q^{13} -95800.9 q^{14} +140883. q^{15} +38628.6 q^{16} -663069. q^{17} -83705.0 q^{18} -716119. q^{19} -607420. q^{20} +608237. q^{21} +942393. q^{22} -1.59218e6 q^{23} +889995. q^{24} +1.07201e6 q^{25} -2.07572e6 q^{26} +531441. q^{27} -2.62244e6 q^{28} -2.50545e6 q^{29} -1.79738e6 q^{30} +2.91112e6 q^{31} -6.11847e6 q^{32} -5.98323e6 q^{33} +8.45942e6 q^{34} +1.30605e7 q^{35} -2.29133e6 q^{36} -1.43874e7 q^{37} +9.13622e6 q^{38} +1.31787e7 q^{39} +1.91106e7 q^{40} +1.18070e7 q^{41} -7.75987e6 q^{42} +1.63694e7 q^{43} +2.57969e7 q^{44} +1.14115e7 q^{45} +2.03130e7 q^{46} -5.19546e7 q^{47} +3.12891e6 q^{48} +1.60330e7 q^{49} -1.36767e7 q^{50} -5.37086e7 q^{51} -5.68204e7 q^{52} -1.54905e7 q^{53} -6.78011e6 q^{54} -1.28476e8 q^{55} +8.25070e7 q^{56} -5.80056e7 q^{57} +3.19645e7 q^{58} +1.21174e7 q^{59} -4.92010e7 q^{60} -1.00668e8 q^{61} -3.71399e7 q^{62} +4.92672e7 q^{63} +5.82814e7 q^{64} +2.82982e8 q^{65} +7.63338e7 q^{66} -2.65492e7 q^{67} +2.31567e8 q^{68} -1.28967e8 q^{69} -1.66626e8 q^{70} +1.72825e7 q^{71} +7.20896e7 q^{72} +5.63024e7 q^{73} +1.83554e8 q^{74} +8.68328e7 q^{75} +2.50093e8 q^{76} -5.54675e8 q^{77} -1.68133e8 q^{78} +5.55414e8 q^{79} +6.71863e7 q^{80} +4.30467e7 q^{81} -1.50634e8 q^{82} +6.01877e8 q^{83} -2.12417e8 q^{84} -1.15327e9 q^{85} -2.08841e8 q^{86} -2.02942e8 q^{87} -8.11621e8 q^{88} -4.74335e8 q^{89} -1.45587e8 q^{90} +1.22173e9 q^{91} +5.56044e8 q^{92} +2.35800e8 q^{93} +6.62835e8 q^{94} -1.24554e9 q^{95} -4.95596e8 q^{96} -5.39952e8 q^{97} -2.04549e8 q^{98} -4.84642e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	−12.7580	−0.563828	−0.281914	−	0.959440i	$-0.590969\pi$
$2$	−12.7580	−0.563828	−0.281914	+	0.959440i	$0.590969\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−349.234	−0.682098
$5$	1739.29	1.24454	0.622268	−	0.782804i	$-0.286211\pi$
$5$	1739.29	1.24454	0.622268	+	0.782804i	$0.286211\pi$
$6$	−1033.40	−0.325526
$7$	7509.10	1.18208	0.591040	−	0.806642i	$-0.298718\pi$
$7$	7509.10	1.18208	0.591040	+	0.806642i	$0.298718\pi$
$8$	10987.6	0.948414
$9$	6561.00	0.333333
$10$	−22189.8	−0.701704
$11$	−73867.0	−1.52119	−0.760595	−	0.649227i	$-0.775093\pi$
$11$	−73867.0	−1.52119	−0.760595	+	0.649227i	$0.775093\pi$
$12$	−28288.0	−0.393810
$13$	162700.	1.57995	0.789973	−	0.613142i	$-0.210095\pi$
$13$	162700.	1.57995	0.789973	+	0.613142i	$0.210095\pi$
$14$	−95800.9	−0.666490
$15$	140883.	0.718533
$16$	38628.6	0.147356
$17$	−663069.	−1.92548	−0.962740	−	0.270430i	$-0.912834\pi$
$17$	−663069.	−1.92548	−0.962740	+	0.270430i	$0.912834\pi$
$18$	−83705.0	−0.187943
$19$	−716119.	−1.26065	−0.630324	−	0.776332i	$-0.717078\pi$
$19$	−716119.	−1.26065	−0.630324	+	0.776332i	$0.717078\pi$
$20$	−607420.	−0.848896
$21$	608237.	0.682474
$22$	942393.	0.857689
$23$	−1.59218e6	−1.18636	−0.593181	−	0.805069i	$-0.702128\pi$
$23$	−1.59218e6	−1.18636	−0.593181	+	0.805069i	$0.702128\pi$
$24$	889995.	0.547567
$25$	1.07201e6	0.548869
$26$	−2.07572e6	−0.890817
$27$	531441.	0.192450
$28$	−2.62244e6	−0.806295
$29$	−2.50545e6	−0.657802	−0.328901	−	0.944364i	$-0.606678\pi$
$29$	−2.50545e6	−0.657802	−0.328901	+	0.944364i	$0.606678\pi$
$30$	−1.79738e6	−0.405129
$31$	2.91112e6	0.566150	0.283075	−	0.959098i	$-0.408645\pi$
$31$	2.91112e6	0.566150	0.283075	+	0.959098i	$0.408645\pi$
$32$	−6.11847e6	−1.03150
$33$	−5.98323e6	−0.878260
$34$	8.45942e6	1.08564
$35$	1.30605e7	1.47114
$36$	−2.29133e6	−0.227366
$37$	−1.43874e7	−1.26204	−0.631021	−	0.775766i	$-0.717364\pi$
$37$	−1.43874e7	−1.26204	−0.631021	+	0.775766i	$0.717364\pi$
$38$	9.13622e6	0.710788
$39$	1.31787e7	0.912182
$40$	1.91106e7	1.18033
$41$	1.18070e7	0.652550	0.326275	−	0.945275i	$-0.394206\pi$
$41$	1.18070e7	0.652550	0.326275	+	0.945275i	$0.394206\pi$
$42$	−7.75987e6	−0.384798
$43$	1.63694e7	0.730173	0.365086	−	0.930974i	$-0.381039\pi$
$43$	1.63694e7	0.730173	0.365086	+	0.930974i	$0.381039\pi$
$44$	2.57969e7	1.03760
$45$	1.14115e7	0.414845
$46$	2.03130e7	0.668904
$47$	−5.19546e7	−1.55304	−0.776521	−	0.630091i	$-0.783018\pi$
$47$	−5.19546e7	−1.55304	−0.776521	+	0.630091i	$0.783018\pi$
$48$	3.12891e6	0.0850762
$49$	1.60330e7	0.397313
$50$	−1.36767e7	−0.309468
$51$	−5.37086e7	−1.11168
$52$	−5.68204e7	−1.07768
$53$	−1.54905e7	−0.269664	−0.134832	−	0.990868i	$-0.543049\pi$
$53$	−1.54905e7	−0.269664	−0.134832	+	0.990868i	$0.543049\pi$
$54$	−6.78011e6	−0.108509
$55$	−1.28476e8	−1.89318
$56$	8.25070e7	1.12110
$57$	−5.80056e7	−0.727835
$58$	3.19645e7	0.370887
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−4.92010e7	−0.490110
$61$	−1.00668e8	−0.930908	−0.465454	−	0.885072i	$-0.654109\pi$
$61$	−1.00668e8	−0.930908	−0.465454	+	0.885072i	$0.654109\pi$
$62$	−3.71399e7	−0.319211
$63$	4.92672e7	0.394027
$64$	5.82814e7	0.434231
$65$	2.82982e8	1.96630
$66$	7.63338e7	0.495187
$67$	−2.65492e7	−0.160959	−0.0804793	−	0.996756i	$-0.525645\pi$
$67$	−2.65492e7	−0.160959	−0.0804793	+	0.996756i	$0.525645\pi$
$68$	2.31567e8	1.31337
$69$	−1.28967e8	−0.684947
$70$	−1.66626e8	−0.829470
$71$	1.72825e7	0.0807130	0.0403565	−	0.999185i	$-0.487151\pi$
$71$	1.72825e7	0.0807130	0.0403565	+	0.999185i	$0.487151\pi$
$72$	7.20896e7	0.316138
$73$	5.63024e7	0.232046	0.116023	−	0.993247i	$-0.462985\pi$
$73$	5.63024e7	0.232046	0.116023	+	0.993247i	$0.462985\pi$
$74$	1.83554e8	0.711574
$75$	8.68328e7	0.316890
$76$	2.50093e8	0.859886
$77$	−5.54675e8	−1.79817
$78$	−1.68133e8	−0.514313
$79$	5.55414e8	1.60433	0.802167	−	0.597099i	$-0.203680\pi$
$79$	5.55414e8	1.60433	0.802167	+	0.597099i	$0.203680\pi$
$80$	6.71863e7	0.183390
$81$	4.30467e7	0.111111
$82$	−1.50634e8	−0.367926
$83$	6.01877e8	1.39206	0.696028	−	0.718015i	$-0.254949\pi$
$83$	6.01877e8	1.39206	0.696028	+	0.718015i	$0.254949\pi$
$84$	−2.12417e8	−0.465514
$85$	−1.15327e9	−2.39633
$86$	−2.08841e8	−0.411692
$87$	−2.02942e8	−0.379782
$88$	−8.11621e8	−1.44272
$89$	−4.74335e8	−0.801365	−0.400682	−	0.916217i	$-0.631227\pi$
$89$	−4.74335e8	−0.801365	−0.400682	+	0.916217i	$0.631227\pi$
$90$	−1.45587e8	−0.233901
$91$	1.22173e9	1.86762
$92$	5.56044e8	0.809216
$93$	2.35800e8	0.326867
$94$	6.62835e8	0.875648
$95$	−1.24554e9	−1.56892
$96$	−4.95596e8	−0.595535
$97$	−5.39952e8	−0.619273	−0.309636	−	0.950855i	$-0.600207\pi$
$97$	−5.39952e8	−0.619273	−0.309636	+	0.950855i	$0.600207\pi$
$98$	−2.04549e8	−0.224016
$99$	−4.84642e8	−0.507063
$100$	−3.74383e8	−0.374383
$101$	8.61496e8	0.823772	0.411886	−	0.911235i	$-0.364870\pi$
$101$	8.61496e8	0.823772	0.411886	+	0.911235i	$0.364870\pi$
$102$	6.85213e8	0.626794
$103$	−1.81166e9	−1.58602	−0.793010	−	0.609209i	$-0.791487\pi$
$103$	−1.81166e9	−1.58602	−0.793010	+	0.609209i	$0.791487\pi$
$104$	1.78768e9	1.49844
$105$	1.05790e9	0.849364
$106$	1.97627e8	0.152044
$107$	−2.64093e9	−1.94774	−0.973868	−	0.227117i	$-0.927070\pi$
$107$	−2.64093e9	−1.94774	−0.973868	+	0.227117i	$0.927070\pi$
$108$	−1.85597e8	−0.131270
$109$	1.63965e9	1.11258	0.556291	−	0.830988i	$-0.312224\pi$
$109$	1.63965e9	1.11258	0.556291	+	0.830988i	$0.312224\pi$
$110$	1.63910e9	1.06742
$111$	−1.16538e9	−0.728640
$112$	2.90066e8	0.174187
$113$	−8.07127e8	−0.465682	−0.232841	−	0.972515i	$-0.574802\pi$
$113$	−8.07127e8	−0.465682	−0.232841	+	0.972515i	$0.574802\pi$
$114$	7.40034e8	0.410374
$115$	−2.76927e9	−1.47647
$116$	8.74990e8	0.448686
$117$	1.06747e9	0.526648
$118$	−1.54593e8	−0.0734041
$119$	−4.97906e9	−2.27607
$120$	1.54796e9	0.681467
$121$	3.09839e9	1.31402
$122$	1.28432e9	0.524872
$123$	9.56370e8	0.376750
$124$	−1.01666e9	−0.386170
$125$	−1.53252e9	−0.561449
$126$	−6.28550e8	−0.222163
$127$	−4.54461e9	−1.55017	−0.775086	−	0.631856i	$-0.782293\pi$
$127$	−4.54461e9	−1.55017	−0.775086	+	0.631856i	$0.782293\pi$
$128$	2.38911e9	0.786666
$129$	1.32592e9	0.421565
$130$	−3.61028e9	−1.10865
$131$	1.30881e9	0.388289	0.194145	−	0.980973i	$-0.437807\pi$
$131$	1.30881e9	0.388289	0.194145	+	0.980973i	$0.437807\pi$
$132$	2.08955e9	0.599059
$133$	−5.37741e9	−1.49019
$134$	3.38713e8	0.0907529
$135$	9.24331e8	0.239511
$136$	−7.28554e9	−1.82615
$137$	2.61531e9	0.634278	0.317139	−	0.948379i	$-0.397278\pi$
$137$	2.61531e9	0.634278	0.317139	+	0.948379i	$0.397278\pi$
$138$	1.64535e9	0.386192
$139$	−4.93205e9	−1.12063	−0.560314	−	0.828281i	$-0.689319\pi$
$139$	−4.93205e9	−1.12063	−0.560314	+	0.828281i	$0.689319\pi$
$140$	−4.56118e9	−1.00346
$141$	−4.20832e9	−0.896649
$142$	−2.20489e8	−0.0455082
$143$	−1.20182e10	−2.40340
$144$	2.53442e8	0.0491188
$145$	−4.35771e9	−0.818658
$146$	−7.18304e8	−0.130834
$147$	1.29867e9	0.229389
$148$	5.02456e9	0.860837
$149$	−7.57899e9	−1.25972	−0.629858	−	0.776710i	$-0.716887\pi$
$149$	−7.57899e9	−1.25972	−0.629858	+	0.776710i	$0.716887\pi$
$150$	−1.10781e9	−0.178671
$151$	1.47211e9	0.230432	0.115216	−	0.993340i	$-0.463244\pi$
$151$	1.47211e9	0.230432	0.115216	+	0.993340i	$0.463244\pi$
$152$	−7.86843e9	−1.19562
$153$	−4.35040e9	−0.641826
$154$	7.07653e9	1.01386
$155$	5.06328e9	0.704594
$156$	−4.60245e9	−0.622198
$157$	1.05021e10	1.37952	0.689762	−	0.724037i	$-0.257715\pi$
$157$	1.05021e10	1.37952	0.689762	+	0.724037i	$0.257715\pi$
$158$	−7.08596e9	−0.904569
$159$	−1.25473e9	−0.155691
$160$	−1.06418e10	−1.28374
$161$	−1.19559e10	−1.40238
$162$	−5.49189e8	−0.0626475
$163$	−1.68860e9	−0.187362	−0.0936811	−	0.995602i	$-0.529863\pi$
$163$	−1.68860e9	−0.187362	−0.0936811	+	0.995602i	$0.529863\pi$
$164$	−4.12342e9	−0.445103
$165$	−1.04066e10	−1.09303
$166$	−7.67873e9	−0.784879
$167$	−6.84704e8	−0.0681207	−0.0340603	−	0.999420i	$-0.510844\pi$
$167$	−6.84704e8	−0.0681207	−0.0340603	+	0.999420i	$0.510844\pi$
$168$	6.68307e9	0.647268
$169$	1.58667e10	1.49623
$170$	1.47134e10	1.35112
$171$	−4.69846e9	−0.420216
$172$	−5.71677e9	−0.498050
$173$	1.08407e10	0.920133	0.460067	−	0.887884i	$-0.347826\pi$
$173$	1.08407e10	0.920133	0.460067	+	0.887884i	$0.347826\pi$
$174$	2.58912e9	0.214132
$175$	8.04983e9	0.648807
$176$	−2.85338e9	−0.224157
$177$	9.81506e8	0.0751646
$178$	6.05155e9	0.451832
$179$	−2.45631e10	−1.78832	−0.894160	−	0.447747i	$-0.852226\pi$
$179$	−2.45631e10	−1.78832	−0.894160	+	0.447747i	$0.852226\pi$
$180$	−3.98528e9	−0.282965
$181$	6.62375e9	0.458723	0.229361	−	0.973341i	$-0.426336\pi$
$181$	6.62375e9	0.458723	0.229361	+	0.973341i	$0.426336\pi$
$182$	−1.55868e10	−1.05302
$183$	−8.15410e9	−0.537460
$184$	−1.74943e10	−1.12516
$185$	−2.50238e10	−1.57066
$186$	−3.00833e9	−0.184297
$187$	4.89790e10	2.92902
$188$	1.81443e10	1.05933
$189$	3.99065e9	0.227491
$190$	1.58905e10	0.884601
$191$	2.27509e9	0.123694	0.0618469	−	0.998086i	$-0.480301\pi$
$191$	2.27509e9	0.123694	0.0618469	+	0.998086i	$0.480301\pi$
$192$	4.72080e9	0.250703
$193$	4.96866e9	0.257769	0.128885	−	0.991660i	$-0.458860\pi$
$193$	4.96866e9	0.257769	0.128885	+	0.991660i	$0.458860\pi$
$194$	6.88869e9	0.349163
$195$	2.29216e10	1.13524
$196$	−5.59928e9	−0.271007
$197$	−1.44778e10	−0.684865	−0.342432	−	0.939543i	$-0.611251\pi$
$197$	−1.44778e10	−0.684865	−0.342432	+	0.939543i	$0.611251\pi$
$198$	6.18304e9	0.285896
$199$	−8.12208e9	−0.367137	−0.183569	−	0.983007i	$-0.558765\pi$
$199$	−8.12208e9	−0.367137	−0.183569	+	0.983007i	$0.558765\pi$
$200$	1.17788e10	0.520555
$201$	−2.15048e9	−0.0929295
$202$	−1.09909e10	−0.464466
$203$	−1.88137e10	−0.777574
$204$	1.87569e10	0.758272
$205$	2.05359e10	0.812122
$206$	2.31131e10	0.894242
$207$	−1.04463e10	−0.395454
$208$	6.28486e9	0.232815
$209$	5.28976e10	1.91769
$210$	−1.34967e10	−0.478895
$211$	4.43430e10	1.54012	0.770060	−	0.637972i	$-0.220226\pi$
$211$	4.43430e10	1.54012	0.770060	+	0.637972i	$0.220226\pi$
$212$	5.40980e9	0.183937
$213$	1.39988e9	0.0465997
$214$	3.36929e10	1.09819
$215$	2.84712e10	0.908726
$216$	5.83926e9	0.182522
$217$	2.18599e10	0.669235
$218$	−2.09186e10	−0.627305
$219$	4.56049e9	0.133972
$220$	4.48683e10	1.29133
$221$	−1.07881e11	−3.04215
$222$	1.48678e10	0.410828
$223$	4.53861e10	1.22900	0.614499	−	0.788918i	$-0.289358\pi$
$223$	4.53861e10	1.22900	0.614499	+	0.788918i	$0.289358\pi$
$224$	−4.59442e10	−1.21931
$225$	7.03346e9	0.182956
$226$	1.02973e10	0.262564
$227$	−4.69791e10	−1.17433	−0.587163	−	0.809469i	$-0.699755\pi$
$227$	−4.69791e10	−1.17433	−0.587163	+	0.809469i	$0.699755\pi$
$228$	2.02576e10	0.496455
$229$	−6.10936e10	−1.46803	−0.734017	−	0.679131i	$-0.762357\pi$
$229$	−6.10936e10	−1.46803	−0.734017	+	0.679131i	$0.762357\pi$
$230$	3.53302e10	0.832475
$231$	−4.49287e10	−1.03817
$232$	−2.75289e10	−0.623868
$233$	1.32852e10	0.295302	0.147651	−	0.989040i	$-0.452829\pi$
$233$	1.32852e10	0.295302	0.147651	+	0.989040i	$0.452829\pi$
$234$	−1.36188e10	−0.296939
$235$	−9.03641e10	−1.93282
$236$	−4.23180e9	−0.0888016
$237$	4.49885e10	0.926263
$238$	6.35226e10	1.28331
$239$	4.18144e10	0.828963	0.414481	−	0.910058i	$-0.363963\pi$
$239$	4.18144e10	0.828963	0.414481	+	0.910058i	$0.363963\pi$
$240$	5.44209e9	0.105880
$241$	−8.05400e10	−1.53792	−0.768962	−	0.639295i	$-0.779226\pi$
$241$	−8.05400e10	−1.53792	−0.768962	+	0.639295i	$0.779226\pi$
$242$	−3.95291e10	−0.740881
$243$	3.48678e9	0.0641500
$244$	3.51567e10	0.634971
$245$	2.78861e10	0.494471
$246$	−1.22013e10	−0.212422
$247$	−1.16512e11	−1.99176
$248$	3.19862e10	0.536945
$249$	4.87520e10	0.803703
$250$	1.95518e10	0.316560
$251$	−9.22880e9	−0.146762	−0.0733810	−	0.997304i	$-0.523379\pi$
$251$	−9.22880e9	−0.146762	−0.0733810	+	0.997304i	$0.523379\pi$
$252$	−1.72058e10	−0.268765
$253$	1.17610e11	1.80468
$254$	5.79800e10	0.874030
$255$	−9.34149e10	−1.38352
$256$	−6.03202e10	−0.877775
$257$	−1.68553e10	−0.241011	−0.120505	−	0.992713i	$-0.538451\pi$
$257$	−1.68553e10	−0.241011	−0.120505	+	0.992713i	$0.538451\pi$
$258$	−1.69161e10	−0.237690
$259$	−1.08036e11	−1.49183
$260$	−9.88272e10	−1.34121
$261$	−1.64383e10	−0.219267
$262$	−1.66977e10	−0.218928
$263$	1.22903e11	1.58403	0.792014	−	0.610503i	$-0.209033\pi$
$263$	1.22903e11	1.58403	0.792014	+	0.610503i	$0.209033\pi$
$264$	−6.57413e10	−0.832953
$265$	−2.69424e10	−0.335606
$266$	6.86048e10	0.840209
$267$	−3.84211e10	−0.462668
$268$	9.27188e9	0.109790
$269$	1.34363e11	1.56457	0.782286	−	0.622920i	$-0.214054\pi$
$269$	1.34363e11	1.56457	0.782286	+	0.622920i	$0.214054\pi$
$270$	−1.17926e10	−0.135043
$271$	1.88205e9	0.0211967	0.0105984	−	0.999944i	$-0.496626\pi$
$271$	1.88205e9	0.0211967	0.0105984	+	0.999944i	$0.496626\pi$
$272$	−2.56134e10	−0.283731
$273$	9.89601e10	1.07827
$274$	−3.33660e10	−0.357624
$275$	−7.91862e10	−0.834934
$276$	4.50396e10	0.467201
$277$	3.67108e10	0.374658	0.187329	−	0.982297i	$-0.440017\pi$
$277$	3.67108e10	0.374658	0.187329	+	0.982297i	$0.440017\pi$
$278$	6.29230e10	0.631841
$279$	1.90998e10	0.188717
$280$	1.43504e11	1.39525
$281$	1.92591e11	1.84271	0.921356	−	0.388720i	$-0.127083\pi$
$281$	1.92591e11	1.84271	0.921356	+	0.388720i	$0.127083\pi$
$282$	5.36896e10	0.505556
$283$	8.03371e10	0.744521	0.372261	−	0.928128i	$-0.378583\pi$
$283$	8.03371e10	0.744521	0.372261	+	0.928128i	$0.378583\pi$
$284$	−6.03564e9	−0.0550542
$285$	−1.00889e11	−0.905817
$286$	1.53327e11	1.35510
$287$	8.86603e10	0.771366
$288$	−4.01433e10	−0.343832
$289$	3.21073e11	2.70747
$290$	5.55955e10	0.461582
$291$	−4.37361e10	−0.357537
$292$	−1.96627e10	−0.158278
$293$	−1.17861e9	−0.00934253	−0.00467127	−	0.999989i	$-0.501487\pi$
$293$	−1.17861e9	−0.00934253	−0.00467127	+	0.999989i	$0.501487\pi$
$294$	−1.65685e10	−0.129336
$295$	2.10756e10	0.162025
$296$	−1.58083e11	−1.19694
$297$	−3.92560e10	−0.292753
$298$	9.66924e10	0.710263
$299$	−2.59048e11	−1.87439
$300$	−3.03250e10	−0.216150
$301$	1.22920e11	0.863123
$302$	−1.87811e10	−0.129924
$303$	6.97812e10	0.475605
$304$	−2.76626e10	−0.185764
$305$	−1.75091e11	−1.15855
$306$	5.55022e10	0.361880
$307$	−1.56337e11	−1.00447	−0.502237	−	0.864730i	$-0.667490\pi$
$307$	−1.56337e11	−1.00447	−0.502237	+	0.864730i	$0.667490\pi$
$308$	1.93712e11	1.22653
$309$	−1.46744e11	−0.915689
$310$	−6.45971e10	−0.397270
$311$	2.63103e9	0.0159479	0.00797396	−	0.999968i	$-0.497462\pi$
$311$	2.63103e9	0.0159479	0.00797396	+	0.999968i	$0.497462\pi$
$312$	1.44802e11	0.865126
$313$	−1.30025e10	−0.0765730	−0.0382865	−	0.999267i	$-0.512190\pi$
$313$	−1.30025e10	−0.0765730	−0.0382865	+	0.999267i	$0.512190\pi$
$314$	−1.33986e11	−0.777813
$315$	8.56901e10	0.490380
$316$	−1.93970e11	−1.09431
$317$	1.49671e10	0.0832472	0.0416236	−	0.999133i	$-0.486747\pi$
$317$	1.49671e10	0.0832472	0.0416236	+	0.999133i	$0.486747\pi$
$318$	1.60078e10	0.0877826
$319$	1.85070e11	1.00064
$320$	1.01368e11	0.540415
$321$	−2.13915e11	−1.12453
$322$	1.52532e11	0.790698
$323$	4.74836e11	2.42735
$324$	−1.50334e10	−0.0757887
$325$	1.74416e11	0.867183
$326$	2.15431e10	0.105640
$327$	1.32812e11	0.642349
$328$	1.29731e11	0.618887
$329$	−3.90132e11	−1.83582
$330$	1.32767e11	0.616278
$331$	−1.15965e11	−0.531009	−0.265504	−	0.964110i	$-0.585538\pi$
$331$	−1.15965e11	−0.531009	−0.265504	+	0.964110i	$0.585538\pi$
$332$	−2.10196e11	−0.949518
$333$	−9.43956e10	−0.420681
$334$	8.73543e9	0.0384083
$335$	−4.61767e10	−0.200319
$336$	2.34953e10	0.100567
$337$	4.01252e10	0.169466	0.0847329	−	0.996404i	$-0.472996\pi$
$337$	4.01252e10	0.169466	0.0847329	+	0.996404i	$0.472996\pi$
$338$	−2.02427e11	−0.843614
$339$	−6.53773e10	−0.268861
$340$	4.02762e11	1.63453
$341$	−2.15035e11	−0.861222
$342$	5.99427e10	0.236929
$343$	−1.82626e11	−0.712424
$344$	1.79861e11	0.692506
$345$	−2.24311e11	−0.852441
$346$	−1.38306e11	−0.518797
$347$	2.83797e11	1.05081	0.525406	−	0.850852i	$-0.323914\pi$
$347$	2.83797e11	1.05081	0.525406	+	0.850852i	$0.323914\pi$
$348$	7.08742e10	0.259049
$349$	−9.89684e10	−0.357094	−0.178547	−	0.983931i	$-0.557140\pi$
$349$	−9.89684e10	−0.357094	−0.178547	+	0.983931i	$0.557140\pi$
$350$	−1.02699e11	−0.365816
$351$	8.64654e10	0.304061
$352$	4.51953e11	1.56910
$353$	−4.13864e11	−1.41864	−0.709319	−	0.704888i	$-0.750997\pi$
$353$	−4.13864e11	−1.41864	−0.709319	+	0.704888i	$0.750997\pi$
$354$	−1.25220e10	−0.0423799
$355$	3.00593e10	0.100450
$356$	1.65654e11	0.546610
$357$	−4.03304e11	−1.31409
$358$	3.13376e11	1.00830
$359$	−5.20511e11	−1.65388	−0.826941	−	0.562288i	$-0.809921\pi$
$359$	−5.20511e11	−1.65388	−0.826941	+	0.562288i	$0.809921\pi$
$360$	1.25385e11	0.393445
$361$	1.90138e11	0.589233
$362$	−8.45056e10	−0.258641
$363$	2.50970e11	0.758649
$364$	−4.26670e11	−1.27390
$365$	9.79262e10	0.288789
$366$	1.04030e11	0.303035
$367$	−6.58062e11	−1.89352	−0.946759	−	0.321943i	$-0.895664\pi$
$367$	−6.58062e11	−1.89352	−0.946759	+	0.321943i	$0.895664\pi$
$368$	−6.15037e10	−0.174818
$369$	7.74660e10	0.217517
$370$	3.19253e11	0.885579
$371$	−1.16319e11	−0.318764
$372$	−8.23496e10	−0.222955
$373$	4.46324e10	0.119388	0.0596940	−	0.998217i	$-0.480988\pi$
$373$	4.46324e10	0.119388	0.0596940	+	0.998217i	$0.480988\pi$
$374$	−6.24872e11	−1.65146
$375$	−1.24134e11	−0.324152
$376$	−5.70856e11	−1.47293
$377$	−4.07637e11	−1.03929
$378$	−5.09125e10	−0.128266
$379$	−1.03766e11	−0.258332	−0.129166	−	0.991623i	$-0.541230\pi$
$379$	−1.03766e11	−0.258332	−0.129166	+	0.991623i	$0.541230\pi$
$380$	4.34985e11	1.07016
$381$	−3.68113e11	−0.894992
$382$	−2.90255e10	−0.0697419
$383$	−2.71556e11	−0.644860	−0.322430	−	0.946593i	$-0.604500\pi$
$383$	−2.71556e11	−0.644860	−0.322430	+	0.946593i	$0.604500\pi$
$384$	1.93518e11	0.454182
$385$	−9.64742e11	−2.23788
$386$	−6.33900e10	−0.145338
$387$	1.07400e11	0.243391
$388$	1.88570e11	0.422405
$389$	9.45844e10	0.209434	0.104717	−	0.994502i	$-0.466606\pi$
$389$	9.45844e10	0.209434	0.104717	+	0.994502i	$0.466606\pi$
$390$	−2.92433e11	−0.640081
$391$	1.05573e12	2.28432
$392$	1.76164e11	0.376817
$393$	1.06014e11	0.224179
$394$	1.84707e11	0.386146
$395$	9.66027e11	1.99665
$396$	1.69253e11	0.345867
$397$	5.98081e11	1.20838	0.604189	−	0.796841i	$-0.293497\pi$
$397$	5.98081e11	1.20838	0.604189	+	0.796841i	$0.293497\pi$
$398$	1.03621e11	0.207002
$399$	−4.35570e11	−0.860360
$400$	4.14102e10	0.0808793
$401$	7.44476e11	1.43781	0.718904	−	0.695109i	$-0.244644\pi$
$401$	7.44476e11	1.43781	0.718904	+	0.695109i	$0.244644\pi$
$402$	2.74358e10	0.0523962
$403$	4.73638e11	0.894487
$404$	−3.00864e11	−0.561894
$405$	7.48708e10	0.138282
$406$	2.40025e11	0.438418
$407$	1.06275e12	1.91981
$408$	−5.90129e11	−1.05433
$409$	1.01980e11	0.180202	0.0901010	−	0.995933i	$-0.471281\pi$
$409$	1.01980e11	0.180202	0.0901010	+	0.995933i	$0.471281\pi$
$410$	−2.61996e11	−0.457897
$411$	2.11840e11	0.366201
$412$	6.32693e11	1.08182
$413$	9.09905e10	0.153894
$414$	1.33274e11	0.222968
$415$	1.04684e12	1.73246
$416$	−9.95474e11	−1.62971
$417$	−3.99496e11	−0.646994
$418$	−6.74865e11	−1.08124
$419$	−1.11843e12	−1.77275	−0.886375	−	0.462968i	$-0.846784\pi$
$419$	−1.11843e12	−1.77275	−0.886375	+	0.462968i	$0.846784\pi$
$420$	−3.69456e11	−0.579349
$421$	3.12652e11	0.485056	0.242528	−	0.970144i	$-0.422023\pi$
$421$	3.12652e11	0.485056	0.242528	+	0.970144i	$0.422023\pi$
$422$	−5.65727e11	−0.868362
$423$	−3.40874e11	−0.517681
$424$	−1.70203e11	−0.255753
$425$	−7.10817e11	−1.05684
$426$	−1.78596e10	−0.0262742
$427$	−7.55926e11	−1.10041
$428$	9.22303e11	1.32855
$429$	−9.73470e11	−1.38760
$430$	−3.63235e11	−0.512365
$431$	6.75381e11	0.942760	0.471380	−	0.881930i	$-0.343756\pi$
$431$	6.75381e11	0.942760	0.471380	+	0.881930i	$0.343756\pi$
$432$	2.05288e10	0.0283587
$433$	−5.25804e10	−0.0718833	−0.0359417	−	0.999354i	$-0.511443\pi$
$433$	−5.25804e10	−0.0718833	−0.0359417	+	0.999354i	$0.511443\pi$
$434$	−2.78887e11	−0.377333
$435$	−3.52975e11	−0.472652
$436$	−5.72622e11	−0.758890
$437$	1.14019e12	1.49559
$438$	−5.81826e10	−0.0755370
$439$	−8.88917e11	−1.14228	−0.571138	−	0.820854i	$-0.693498\pi$
$439$	−8.88917e11	−1.14228	−0.571138	+	0.820854i	$0.693498\pi$
$440$	−1.41165e12	−1.79551
$441$	1.05193e11	0.132438
$442$	1.37635e12	1.71525
$443$	−1.05658e12	−1.30342	−0.651712	−	0.758467i	$-0.725949\pi$
$443$	−1.05658e12	−1.30342	−0.651712	+	0.758467i	$0.725949\pi$
$444$	4.06990e11	0.497004
$445$	−8.25007e11	−0.997327
$446$	−5.79034e11	−0.692943
$447$	−6.13898e11	−0.727298
$448$	4.37641e11	0.513295
$449$	−1.35032e12	−1.56793	−0.783966	−	0.620803i	$-0.786806\pi$
$449$	−1.35032e12	−1.56793	−0.783966	+	0.620803i	$0.786806\pi$
$450$	−8.97326e10	−0.103156
$451$	−8.72151e11	−0.992652
$452$	2.81877e11	0.317641
$453$	1.19241e11	0.133040
$454$	5.99358e11	0.662117
$455$	2.12494e12	2.32432
$456$	−6.37342e11	−0.690289
$457$	−5.30062e11	−0.568465	−0.284233	−	0.958755i	$-0.591739\pi$
$457$	−5.30062e11	−0.568465	−0.284233	+	0.958755i	$0.591739\pi$
$458$	7.79431e11	0.827719
$459$	−3.52382e11	−0.370559
$460$	9.67123e11	1.00710
$461$	2.63945e11	0.272181	0.136091	−	0.990696i	$-0.456546\pi$
$461$	2.63945e11	0.272181	0.136091	+	0.990696i	$0.456546\pi$
$462$	5.73199e11	0.585351
$463$	7.13021e11	0.721088	0.360544	−	0.932742i	$-0.382591\pi$
$463$	7.13021e11	0.721088	0.360544	+	0.932742i	$0.382591\pi$
$464$	−9.67820e10	−0.0969312
$465$	4.10126e11	0.406798
$466$	−1.69492e11	−0.166499
$467$	−1.27483e12	−1.24030	−0.620149	−	0.784484i	$-0.712928\pi$
$467$	−1.27483e12	−1.24030	−0.620149	+	0.784484i	$0.712928\pi$
$468$	−3.72798e11	−0.359226
$469$	−1.99360e11	−0.190266
$470$	1.15286e12	1.08978
$471$	8.50673e11	0.796468
$472$	1.33141e11	0.123473
$473$	−1.20916e12	−1.11073
$474$	−5.73962e11	−0.522253
$475$	−7.67686e11	−0.691931
$476$	1.73886e12	1.55250
$477$	−1.01633e11	−0.0898880
$478$	−5.33466e11	−0.467392
$479$	1.10751e12	0.961254	0.480627	−	0.876925i	$-0.340409\pi$
$479$	1.10751e12	0.961254	0.480627	+	0.876925i	$0.340409\pi$
$480$	−8.61986e11	−0.741165
$481$	−2.34082e12	−1.99396
$482$	1.02753e12	0.867124
$483$	−9.68424e11	−0.809662
$484$	−1.08206e12	−0.896290
$485$	−9.39133e11	−0.770707
$486$	−4.44843e10	−0.0361696
$487$	1.73479e12	1.39755	0.698775	−	0.715341i	$-0.253729\pi$
$487$	1.73479e12	1.39755	0.698775	+	0.715341i	$0.253729\pi$
$488$	−1.10610e12	−0.882886
$489$	−1.36776e11	−0.108174
$490$	−3.55770e11	−0.278796
$491$	−2.79615e11	−0.217117	−0.108559	−	0.994090i	$-0.534624\pi$
$491$	−2.79615e11	−0.217117	−0.108559	+	0.994090i	$0.534624\pi$
$492$	−3.33997e11	−0.256980
$493$	1.66129e12	1.26658
$494$	1.48646e12	1.12301
$495$	−8.42933e11	−0.631058
$496$	1.12452e11	0.0834258
$497$	1.29776e11	0.0954092
$498$	−6.21977e11	−0.453150
$499$	−1.73268e12	−1.25103	−0.625513	−	0.780214i	$-0.715110\pi$
$499$	−1.73268e12	−1.25103	−0.625513	+	0.780214i	$0.715110\pi$
$500$	5.35207e11	0.382963
$501$	−5.54610e10	−0.0393295
$502$	1.17741e11	0.0827485
$503$	−1.53274e12	−1.06761	−0.533805	−	0.845607i	$-0.679239\pi$
$503$	−1.53274e12	−1.06761	−0.533805	+	0.845607i	$0.679239\pi$
$504$	5.41328e11	0.373700
$505$	1.49839e12	1.02521
$506$	−1.50046e12	−1.01753
$507$	1.28521e12	0.863847
$508$	1.58713e12	1.05737
$509$	−1.22778e12	−0.810760	−0.405380	−	0.914148i	$-0.632861\pi$
$509$	−1.22778e12	−0.810760	−0.405380	+	0.914148i	$0.632861\pi$
$510$	1.19178e12	0.780067
$511$	4.22780e11	0.274297
$512$	−4.53659e11	−0.291752
$513$	−3.80575e11	−0.242612
$514$	2.15039e11	0.135889
$515$	−3.15100e12	−1.97386
$516$	−4.63058e11	−0.287549
$517$	3.83773e12	2.36247
$518$	1.37832e12	0.841138
$519$	8.78099e11	0.531239
$520$	3.10930e12	1.86486
$521$	8.56707e11	0.509404	0.254702	−	0.967020i	$-0.418023\pi$
$521$	8.56707e11	0.509404	0.254702	+	0.967020i	$0.418023\pi$
$522$	2.09719e11	0.123629
$523$	−1.42937e12	−0.835385	−0.417692	−	0.908589i	$-0.637161\pi$
$523$	−1.42937e12	−0.835385	−0.417692	+	0.908589i	$0.637161\pi$
$524$	−4.57081e11	−0.264851
$525$	6.52036e11	0.374589
$526$	−1.56800e12	−0.893119
$527$	−1.93027e12	−1.09011
$528$	−2.31124e11	−0.129417
$529$	7.33890e11	0.407456
$530$	3.43731e11	0.189224
$531$	7.95020e10	0.0433963
$532$	1.87798e12	1.01645
$533$	1.92100e12	1.03099
$534$	4.90176e11	0.260865
$535$	−4.59335e12	−2.42403
$536$	−2.91712e11	−0.152655
$537$	−1.98961e12	−1.03249
$538$	−1.71420e12	−0.882149
$539$	−1.18431e12	−0.604389
$540$	−3.22808e11	−0.163370
$541$	9.13135e11	0.458297	0.229149	−	0.973391i	$-0.426406\pi$
$541$	9.13135e11	0.458297	0.229149	+	0.973391i	$0.426406\pi$
$542$	−2.40111e10	−0.0119513
$543$	5.36524e11	0.264844
$544$	4.05697e12	1.98613
$545$	2.85183e12	1.38465
$546$	−1.26253e12	−0.607960
$547$	1.79117e12	0.855448	0.427724	−	0.903909i	$-0.359316\pi$
$547$	1.79117e12	0.855448	0.427724	+	0.903909i	$0.359316\pi$
$548$	−9.13354e11	−0.432640
$549$	−6.60482e11	−0.310303
$550$	1.01025e12	0.470759
$551$	1.79420e12	0.829257
$552$	−1.41703e12	−0.649613
$553$	4.17066e12	1.89645
$554$	−4.68355e11	−0.211242
$555$	−2.02693e12	−0.906819
$556$	1.72244e12	0.764378
$557$	−2.69969e12	−1.18841	−0.594203	−	0.804315i	$-0.702533\pi$
$557$	−2.69969e12	−1.18841	−0.594203	+	0.804315i	$0.702533\pi$
$558$	−2.43675e11	−0.106404
$559$	2.66330e12	1.15363
$560$	5.04509e11	0.216782
$561$	3.96730e12	1.69107
$562$	−2.45707e12	−1.03897
$563$	−2.13576e12	−0.895910	−0.447955	−	0.894056i	$-0.647847\pi$
$563$	−2.13576e12	−0.895910	−0.447955	+	0.894056i	$0.647847\pi$
$564$	1.46969e12	0.611603
$565$	−1.40383e12	−0.579557
$566$	−1.02494e12	−0.419782
$567$	3.23242e11	0.131342
$568$	1.89893e11	0.0765493
$569$	2.14904e12	0.859489	0.429744	−	0.902951i	$-0.358604\pi$
$569$	2.14904e12	0.859489	0.429744	+	0.902951i	$0.358604\pi$
$570$	1.28713e12	0.510725
$571$	2.27870e12	0.897067	0.448533	−	0.893766i	$-0.351947\pi$
$571$	2.27870e12	0.897067	0.448533	+	0.893766i	$0.351947\pi$
$572$	4.19715e12	1.63935
$573$	1.84282e11	0.0714146
$574$	−1.13112e12	−0.434918
$575$	−1.70683e12	−0.651158
$576$	3.82384e11	0.144744
$577$	−1.61675e12	−0.607228	−0.303614	−	0.952795i	$-0.598193\pi$
$577$	−1.61675e12	−0.607228	−0.303614	+	0.952795i	$0.598193\pi$
$578$	−4.09624e12	−1.52655
$579$	4.02461e11	0.148823
$580$	1.52186e12	0.558405
$581$	4.51956e12	1.64552
$582$	5.57984e11	0.201590
$583$	1.14423e12	0.410210
$584$	6.18628e11	0.220075
$585$	1.85665e12	0.655433
$586$	1.50366e10	0.00526758
$587$	−2.42203e12	−0.841993	−0.420996	−	0.907062i	$-0.638320\pi$
$587$	−2.42203e12	−0.841993	−0.420996	+	0.907062i	$0.638320\pi$
$588$	−4.53542e11	−0.156466
$589$	−2.08470e12	−0.713716
$590$	−2.68882e11	−0.0913541
$591$	−1.17270e12	−0.395407
$592$	−5.55764e11	−0.185970
$593$	−4.67893e12	−1.55382	−0.776910	−	0.629611i	$-0.783214\pi$
$593$	−4.67893e12	−1.55382	−0.776910	+	0.629611i	$0.783214\pi$
$594$	5.00826e11	0.165062
$595$	−8.66003e12	−2.83265
$596$	2.64684e12	0.859250
$597$	−6.57888e11	−0.211967
$598$	3.30492e12	1.05683
$599$	4.42395e12	1.40407	0.702036	−	0.712141i	$-0.252274\pi$
$599$	4.42395e12	1.40407	0.702036	+	0.712141i	$0.252274\pi$
$600$	9.54084e11	0.300543
$601$	1.93036e12	0.603536	0.301768	−	0.953381i	$-0.402423\pi$
$601$	1.93036e12	0.603536	0.301768	+	0.953381i	$0.402423\pi$
$602$	−1.56821e12	−0.486652
$603$	−1.74189e11	−0.0536529
$604$	−5.14110e11	−0.157177
$605$	5.38900e12	1.63534
$606$	−8.90266e11	−0.268159
$607$	2.14021e12	0.639893	0.319947	−	0.947436i	$-0.396335\pi$
$607$	2.14021e12	0.639893	0.319947	+	0.947436i	$0.396335\pi$
$608$	4.38155e12	1.30036
$609$	−1.52391e12	−0.448933
$610$	2.23380e12	0.653222
$611$	−8.45300e12	−2.45372
$612$	1.51931e12	0.437789
$613$	3.34392e12	0.956499	0.478249	−	0.878224i	$-0.341272\pi$
$613$	3.34392e12	0.956499	0.478249	+	0.878224i	$0.341272\pi$
$614$	1.99454e12	0.566351
$615$	1.66341e12	0.468879
$616$	−6.09455e12	−1.70541
$617$	1.60127e12	0.444817	0.222408	−	0.974954i	$-0.428608\pi$
$617$	1.60127e12	0.444817	0.222408	+	0.974954i	$0.428608\pi$
$618$	1.87216e12	0.516291
$619$	3.69026e12	1.01030	0.505148	−	0.863033i	$-0.331438\pi$
$619$	3.69026e12	1.01030	0.505148	+	0.863033i	$0.331438\pi$
$620$	−1.76827e12	−0.480603
$621$	−8.46151e11	−0.228316
$622$	−3.35666e10	−0.00899188
$623$	−3.56183e12	−0.947277
$624$	5.09074e11	0.134416
$625$	−4.75926e12	−1.24761
$626$	1.65885e11	0.0431740
$627$	4.28470e12	1.10718
$628$	−3.66770e12	−0.940970
$629$	9.53983e12	2.43004
$630$	−1.09323e12	−0.276490
$631$	−4.36858e12	−1.09700	−0.548502	−	0.836149i	$-0.684802\pi$
$631$	−4.36858e12	−1.09700	−0.548502	+	0.836149i	$0.684802\pi$
$632$	6.10267e12	1.52157
$633$	3.59179e12	0.889188
$634$	−1.90949e11	−0.0469371
$635$	−7.90440e12	−1.92924
$636$	4.38194e11	0.106196
$637$	2.60857e12	0.627733
$638$	−2.36112e12	−0.564190
$639$	1.13390e11	0.0269043
$640$	4.15535e12	0.979034
$641$	−4.25253e12	−0.994916	−0.497458	−	0.867488i	$-0.665733\pi$
$641$	−4.25253e12	−0.994916	−0.497458	+	0.867488i	$0.665733\pi$
$642$	2.72912e12	0.634039
$643$	5.18438e12	1.19604	0.598022	−	0.801479i	$-0.295953\pi$
$643$	5.18438e12	1.19604	0.598022	+	0.801479i	$0.295953\pi$
$644$	4.17540e12	0.956558
$645$	2.30617e12	0.524653
$646$	−6.05795e12	−1.36861
$647$	6.51180e12	1.46094	0.730468	−	0.682946i	$-0.239302\pi$
$647$	6.51180e12	1.46094	0.730468	+	0.682946i	$0.239302\pi$
$648$	4.72980e11	0.105379
$649$	−8.95073e11	−0.198042
$650$	−2.22519e12	−0.488942
$651$	1.77065e12	0.386383
$652$	5.89716e11	0.127799
$653$	7.98599e11	0.171878	0.0859388	−	0.996300i	$-0.472611\pi$
$653$	7.98599e11	0.171878	0.0859388	+	0.996300i	$0.472611\pi$
$654$	−1.69441e12	−0.362174
$655$	2.27640e12	0.483240
$656$	4.56089e11	0.0961573
$657$	3.69400e11	0.0773486
$658$	4.97729e12	1.03509
$659$	−2.53693e12	−0.523992	−0.261996	−	0.965069i	$-0.584381\pi$
$659$	−2.53693e12	−0.523992	−0.261996	+	0.965069i	$0.584381\pi$
$660$	3.63433e12	0.745551
$661$	−4.69117e12	−0.955817	−0.477909	−	0.878410i	$-0.658605\pi$
$661$	−4.69117e12	−0.955817	−0.477909	+	0.878410i	$0.658605\pi$
$662$	1.47948e12	0.299397
$663$	−8.73838e12	−1.75639
$664$	6.61318e12	1.32024
$665$	−9.35288e12	−1.85459
$666$	1.20430e12	0.237191
$667$	3.98913e12	0.780391
$668$	2.39122e11	0.0464650
$669$	3.67627e12	0.709562
$670$	5.89121e11	0.112945
$671$	7.43604e12	1.41609
$672$	−3.72148e12	−0.703970
$673$	−2.88094e12	−0.541336	−0.270668	−	0.962673i	$-0.587244\pi$
$673$	−2.88094e12	−0.541336	−0.270668	+	0.962673i	$0.587244\pi$
$674$	−5.11915e11	−0.0955495
$675$	5.69710e11	0.105630
$676$	−5.54121e12	−1.02057
$677$	−2.82495e12	−0.516847	−0.258424	−	0.966032i	$-0.583203\pi$
$677$	−2.82495e12	−0.516847	−0.258424	+	0.966032i	$0.583203\pi$
$678$	8.34082e11	0.151592
$679$	−4.05455e12	−0.732030
$680$	−1.26717e13	−2.27271
$681$	−3.80531e12	−0.677997
$682$	2.74341e12	0.485581
$683$	8.92345e12	1.56906	0.784530	−	0.620091i	$-0.212904\pi$
$683$	8.92345e12	1.56906	0.784530	+	0.620091i	$0.212904\pi$
$684$	1.64086e12	0.286629
$685$	4.54878e12	0.789382
$686$	2.32993e12	0.401684
$687$	−4.94858e12	−0.847570
$688$	6.32328e11	0.107596
$689$	−2.52030e12	−0.426054
$690$	2.86175e12	0.480630
$691$	5.24694e12	0.875498	0.437749	−	0.899097i	$-0.355776\pi$
$691$	5.24694e12	0.875498	0.437749	+	0.899097i	$0.355776\pi$
$692$	−3.78595e12	−0.627621
$693$	−3.63922e12	−0.599390
$694$	−3.62067e12	−0.592476
$695$	−8.57828e12	−1.39466
$696$	−2.22984e12	−0.360191
$697$	−7.82889e12	−1.25647
$698$	1.26263e12	0.201339
$699$	1.07610e12	0.170493
$700$	−2.81128e12	−0.442550
$701$	8.82988e12	1.38110	0.690548	−	0.723287i	$-0.257370\pi$
$701$	8.82988e12	1.38110	0.690548	+	0.723287i	$0.257370\pi$
$702$	−1.10312e12	−0.171438
$703$	1.03031e13	1.59099
$704$	−4.30508e12	−0.660547
$705$	−7.31949e12	−1.11591
$706$	5.28006e12	0.799867
$707$	6.46907e12	0.973765
$708$	−3.42776e11	−0.0512696
$709$	5.84677e12	0.868977	0.434488	−	0.900677i	$-0.356929\pi$
$709$	5.84677e12	0.868977	0.434488	+	0.900677i	$0.356929\pi$
$710$	−3.83495e11	−0.0566366
$711$	3.64407e12	0.534778
$712$	−5.21180e12	−0.760025
$713$	−4.63502e12	−0.671660
$714$	5.14533e12	0.740920
$715$	−2.09031e13	−2.99111
$716$	8.57829e12	1.21981
$717$	3.38696e12	0.478602
$718$	6.64066e12	0.932505
$719$	−1.95656e12	−0.273032	−0.136516	−	0.990638i	$-0.543590\pi$
$719$	−1.95656e12	−0.273032	−0.136516	+	0.990638i	$0.543590\pi$
$720$	4.40810e11	0.0611300
$721$	−1.36039e13	−1.87480
$722$	−2.42578e12	−0.332226
$723$	−6.52374e12	−0.887920
$724$	−2.31324e12	−0.312894
$725$	−2.68587e12	−0.361047
$726$	−3.20186e12	−0.427748
$727$	−3.82900e12	−0.508370	−0.254185	−	0.967156i	$-0.581807\pi$
$727$	−3.82900e12	−0.508370	−0.254185	+	0.967156i	$0.581807\pi$
$728$	1.34239e13	1.77128
$729$	2.82430e11	0.0370370
$730$	−1.24934e12	−0.162827
$731$	−1.08541e13	−1.40593
$732$	2.84769e12	0.366601
$733$	6.07535e12	0.777327	0.388663	−	0.921380i	$-0.372937\pi$
$733$	6.07535e12	0.777327	0.388663	+	0.921380i	$0.372937\pi$
$734$	8.39553e12	1.06762
$735$	2.25877e12	0.285483
$736$	9.74172e12	1.22373
$737$	1.96111e12	0.244849
$738$	−9.88308e11	−0.122642
$739$	−1.29264e13	−1.59433	−0.797167	−	0.603759i	$-0.793669\pi$
$739$	−1.29264e13	−1.59433	−0.797167	+	0.603759i	$0.793669\pi$
$740$	8.73918e12	1.07134
$741$	−9.43751e12	−1.14994
$742$	1.48400e12	0.179728
$743$	6.22278e12	0.749091	0.374546	−	0.927209i	$-0.377799\pi$
$743$	6.22278e12	0.749091	0.374546	+	0.927209i	$0.377799\pi$
$744$	2.59088e12	0.310005
$745$	−1.31821e13	−1.56776
$746$	−5.69419e11	−0.0673142
$747$	3.94892e12	0.464018
$748$	−1.71051e13	−1.99788
$749$	−1.98310e13	−2.30238
$750$	1.58369e12	0.182766
$751$	1.46813e12	0.168416	0.0842082	−	0.996448i	$-0.473164\pi$
$751$	1.46813e12	0.168416	0.0842082	+	0.996448i	$0.473164\pi$
$752$	−2.00693e12	−0.228851
$753$	−7.47533e11	−0.0847331
$754$	5.20061e12	0.585981
$755$	2.56042e12	0.286781
$756$	−1.39367e12	−0.155171
$757$	−3.31049e11	−0.0366405	−0.0183202	−	0.999832i	$-0.505832\pi$
$757$	−3.31049e11	−0.0366405	−0.0183202	+	0.999832i	$0.505832\pi$
$758$	1.32384e12	0.145655
$759$	9.52639e12	1.04193
$760$	−1.36855e13	−1.48799
$761$	−2.90517e10	−0.00314008	−0.00157004	−	0.999999i	$-0.500500\pi$
$761$	−2.90517e10	−0.00314008	−0.00157004	+	0.999999i	$0.500500\pi$
$762$	4.69638e12	0.504621
$763$	1.23123e13	1.31516
$764$	−7.94538e11	−0.0843713
$765$	−7.56661e12	−0.798776
$766$	3.46450e12	0.363590
$767$	1.97149e12	0.205691
$768$	−4.88594e12	−0.506783
$769$	−9.36673e12	−0.965872	−0.482936	−	0.875656i	$-0.660430\pi$
$769$	−9.36673e12	−0.965872	−0.482936	+	0.875656i	$0.660430\pi$
$770$	1.23081e13	1.26178
$771$	−1.36528e12	−0.139148
$772$	−1.73523e12	−0.175824
$773$	−5.92112e12	−0.596480	−0.298240	−	0.954491i	$-0.596400\pi$
$773$	−5.92112e12	−0.596480	−0.298240	+	0.954491i	$0.596400\pi$
$774$	−1.37020e12	−0.137231
$775$	3.12074e12	0.310742
$776$	−5.93277e12	−0.587327
$777$	−8.75094e12	−0.861311
$778$	−1.20670e12	−0.118084
$779$	−8.45524e12	−0.822636
$780$	−8.00500e12	−0.774347
$781$	−1.27661e12	−0.122780
$782$	−1.34689e13	−1.28796
$783$	−1.33150e12	−0.126594
$784$	6.19333e11	0.0585466
$785$	1.82663e13	1.71687
$786$	−1.35252e12	−0.126398
$787$	1.09623e13	1.01863	0.509315	−	0.860580i	$-0.329899\pi$
$787$	1.09623e13	1.01863	0.509315	+	0.860580i	$0.329899\pi$
$788$	5.05615e12	0.467145
$789$	9.95517e12	0.914539
$790$	−1.23245e13	−1.12577
$791$	−6.06080e12	−0.550473
$792$	−5.32505e12	−0.480906
$793$	−1.63787e13	−1.47078
$794$	−7.63030e12	−0.681317
$795$	−2.18234e12	−0.193762
$796$	2.83651e12	0.250424
$797$	1.23075e13	1.08046	0.540229	−	0.841518i	$-0.318338\pi$
$797$	1.23075e13	1.08046	0.540229	+	0.841518i	$0.318338\pi$
$798$	5.55699e12	0.485095
$799$	3.44495e13	2.99035
$800$	−6.55906e12	−0.566157
$801$	−3.11211e12	−0.267122
$802$	−9.49800e12	−0.810676
$803$	−4.15889e12	−0.352986
$804$	7.51022e11	0.0633871
$805$	−2.07947e13	−1.74531
$806$	−6.04266e12	−0.504336
$807$	1.08834e13	0.903306
$808$	9.46578e12	0.781277
$809$	6.04381e12	0.496069	0.248035	−	0.968751i	$-0.420215\pi$
$809$	6.04381e12	0.496069	0.248035	+	0.968751i	$0.420215\pi$
$810$	−9.55199e11	−0.0779671
$811$	−4.73277e12	−0.384169	−0.192084	−	0.981378i	$-0.561525\pi$
$811$	−4.73277e12	−0.384169	−0.192084	+	0.981378i	$0.561525\pi$
$812$	6.57039e12	0.530382
$813$	1.52446e11	0.0122379
$814$	−1.35586e13	−1.08244
$815$	−2.93696e12	−0.233179
$816$	−2.07469e12	−0.163812
$817$	−1.17225e13	−0.920491
$818$	−1.30106e12	−0.101603
$819$	8.01577e12	0.622541
$820$	−7.17184e12	−0.553947
$821$	9.83876e12	0.755781	0.377891	−	0.925850i	$-0.376650\pi$
$821$	9.83876e12	0.755781	0.377891	+	0.925850i	$0.376650\pi$
$822$	−2.70264e12	−0.206474
$823$	−1.89616e12	−0.144071	−0.0720355	−	0.997402i	$-0.522949\pi$
$823$	−1.89616e12	−0.144071	−0.0720355	+	0.997402i	$0.522949\pi$
$824$	−1.99058e13	−1.50420
$825$	−6.41408e12	−0.482049
$826$	−1.16085e12	−0.0867695
$827$	−1.24758e13	−0.927460	−0.463730	−	0.885977i	$-0.653489\pi$
$827$	−1.24758e13	−0.927460	−0.463730	+	0.885977i	$0.653489\pi$
$828$	3.64821e12	0.269739
$829$	−2.54424e13	−1.87095	−0.935475	−	0.353393i	$-0.885028\pi$
$829$	−2.54424e13	−1.87095	−0.935475	+	0.353393i	$0.885028\pi$
$830$	−1.33555e13	−0.976810
$831$	2.97357e12	0.216309
$832$	9.48238e12	0.686060
$833$	−1.06310e13	−0.765018
$834$	5.09676e12	0.364793
$835$	−1.19090e12	−0.0847786
$836$	−1.84736e13	−1.30805
$837$	1.54709e12	0.108956
$838$	1.42689e13	0.999526
$839$	6.98126e12	0.486413	0.243207	−	0.969975i	$-0.421801\pi$
$839$	6.98126e12	0.486413	0.243207	+	0.969975i	$0.421801\pi$
$840$	1.16238e13	0.805548
$841$	−8.22986e12	−0.567297
$842$	−3.98880e12	−0.273488
$843$	1.55999e13	1.06389
$844$	−1.54861e13	−1.05051
$845$	2.75969e13	1.86211
$846$	4.34886e12	0.291883
$847$	2.32661e13	1.55328
$848$	−5.98374e11	−0.0397367
$849$	6.50731e12	0.429850
$850$	9.06858e12	0.595873
$851$	2.29073e13	1.49724
$852$	−4.88886e11	−0.0317856
$853$	−1.84886e12	−0.119573	−0.0597866	−	0.998211i	$-0.519042\pi$
$853$	−1.84886e12	−0.119573	−0.0597866	+	0.998211i	$0.519042\pi$
$854$	9.64408e12	0.620441
$855$	−8.17198e12	−0.522974
$856$	−2.90175e13	−1.84726
$857$	1.45086e13	0.918782	0.459391	−	0.888234i	$-0.348068\pi$
$857$	1.45086e13	0.918782	0.459391	+	0.888234i	$0.348068\pi$
$858$	1.24195e13	0.782369
$859$	2.74113e13	1.71775	0.858875	−	0.512186i	$-0.171164\pi$
$859$	2.74113e13	1.71775	0.858875	+	0.512186i	$0.171164\pi$
$860$	−9.94313e12	−0.619840
$861$	7.18148e12	0.445348
$862$	−8.61649e12	−0.531554
$863$	−1.70047e13	−1.04357	−0.521783	−	0.853078i	$-0.674733\pi$
$863$	−1.70047e13	−1.04357	−0.521783	+	0.853078i	$0.674733\pi$
$864$	−3.25161e12	−0.198512
$865$	1.88552e13	1.14514
$866$	6.70819e11	0.0405298
$867$	2.60069e13	1.56316
$868$	−7.63422e12	−0.456484
$869$	−4.10268e13	−2.44050
$870$	4.50324e12	0.266495
$871$	−4.31955e12	−0.254306
$872$	1.80158e13	1.05519
$873$	−3.54262e12	−0.206424
$874$	−1.45465e13	−0.843253
$875$	−1.15078e13	−0.663677
$876$	−1.59268e12	−0.0913819
$877$	1.26828e13	0.723965	0.361983	−	0.932185i	$-0.382100\pi$
$877$	1.26828e13	0.723965	0.361983	+	0.932185i	$0.382100\pi$
$878$	1.13408e13	0.644047
$879$	−9.54672e10	−0.00539391
$880$	−4.96285e12	−0.278971
$881$	3.27635e13	1.83231	0.916155	−	0.400825i	$-0.131276\pi$
$881$	3.27635e13	1.83231	0.916155	+	0.400825i	$0.131276\pi$
$882$	−1.34204e12	−0.0746721
$883$	3.49858e13	1.93673	0.968364	−	0.249542i	$-0.0802802\pi$
$883$	3.49858e13	1.93673	0.968364	+	0.249542i	$0.0802802\pi$
$884$	3.76758e13	2.07505
$885$	1.70713e12	0.0935450
$886$	1.34798e13	0.734907
$887$	−1.92767e13	−1.04562	−0.522812	−	0.852448i	$-0.675117\pi$
$887$	−1.92767e13	−1.04562	−0.522812	+	0.852448i	$0.675117\pi$
$888$	−1.28047e13	−0.691052
$889$	−3.41259e13	−1.83243
$890$	1.05254e13	0.562321
$891$	−3.17973e12	−0.169021
$892$	−1.58504e13	−0.838297
$893$	3.72056e13	1.95784
$894$	7.83209e12	0.410071
$895$	−4.27225e13	−2.22563
$896$	1.79400e13	0.929902
$897$	−2.09829e13	−1.08218
$898$	1.72273e13	0.884044
$899$	−7.29366e12	−0.372415
$900$	−2.45632e12	−0.124794
$901$	1.02712e13	0.519232
$902$	1.11269e13	0.559685
$903$	9.95650e12	0.498324
$904$	−8.86839e12	−0.441659
$905$	1.15206e13	0.570897
$906$	−1.52127e12	−0.0750116
$907$	1.51666e13	0.744141	0.372070	−	0.928204i	$-0.378648\pi$
$907$	1.51666e13	0.744141	0.372070	+	0.928204i	$0.378648\pi$
$908$	1.64067e13	0.801005
$909$	5.65228e12	0.274591
$910$	−2.71100e13	−1.31052
$911$	−8.07083e12	−0.388227	−0.194113	−	0.980979i	$-0.562183\pi$
$911$	−8.07083e12	−0.388227	−0.194113	+	0.980979i	$0.562183\pi$
$912$	−2.24067e12	−0.107251
$913$	−4.44589e13	−2.11758
$914$	6.76251e12	0.320516
$915$	−1.41824e13	−0.668888
$916$	2.13360e13	1.00134
$917$	9.82798e12	0.458989
$918$	4.49568e12	0.208931
$919$	−5.04236e12	−0.233192	−0.116596	−	0.993179i	$-0.537198\pi$
$919$	−5.04236e12	−0.233192	−0.116596	+	0.993179i	$0.537198\pi$
$920$	−3.04276e13	−1.40030
$921$	−1.26633e13	−0.579934
$922$	−3.36740e12	−0.153463
$923$	2.81186e12	0.127522
$924$	1.56906e13	0.708136
$925$	−1.54234e13	−0.692696
$926$	−9.09670e12	−0.406569
$927$	−1.18863e13	−0.528673
$928$	1.53295e13	0.678521
$929$	3.27657e13	1.44328	0.721638	−	0.692271i	$-0.243390\pi$
$929$	3.27657e13	1.44328	0.721638	+	0.692271i	$0.243390\pi$
$930$	−5.23237e12	−0.229364
$931$	−1.14815e13	−0.500872
$932$	−4.63965e12	−0.201425
$933$	2.13114e11	0.00920754
$934$	1.62642e13	0.699314
$935$	8.51887e13	3.64527
$936$	1.17290e13	0.499481
$937$	2.31762e13	0.982230	0.491115	−	0.871095i	$-0.336589\pi$
$937$	2.31762e13	0.982230	0.491115	+	0.871095i	$0.336589\pi$
$938$	2.54343e12	0.107277
$939$	−1.05320e12	−0.0442095
$940$	3.15583e13	1.31837
$941$	−1.95362e12	−0.0812244	−0.0406122	−	0.999175i	$-0.512931\pi$
$941$	−1.95362e12	−0.0812244	−0.0406122	+	0.999175i	$0.512931\pi$
$942$	−1.08529e13	−0.449071
$943$	−1.87990e13	−0.774161
$944$	4.68076e11	0.0191842
$945$	6.94090e12	0.283121
$946$	1.54264e13	0.626261
$947$	−4.55372e13	−1.83989	−0.919945	−	0.392048i	$-0.871767\pi$
$947$	−4.55372e13	−1.83989	−0.919945	+	0.392048i	$0.871767\pi$
$948$	−1.57115e13	−0.631803
$949$	9.16039e12	0.366620
$950$	9.79412e12	0.390130
$951$	1.21233e12	0.0480628
$952$	−5.47079e13	−2.15866
$953$	−1.87415e11	−0.00736015	−0.00368007	−	0.999993i	$-0.501171\pi$
$953$	−1.87415e11	−0.00736015	−0.00368007	+	0.999993i	$0.501171\pi$
$954$	1.29663e12	0.0506813
$955$	3.95704e12	0.153941
$956$	−1.46030e13	−0.565434
$957$	1.49907e13	0.577721
$958$	−1.41296e13	−0.541982
$959$	1.96386e13	0.749768
$960$	8.21084e12	0.312009
$961$	−1.79650e13	−0.679474
$962$	2.98641e13	1.12425
$963$	−1.73271e13	−0.649245
$964$	2.81273e13	1.04901
$965$	8.64195e12	0.320803
$966$	1.23551e13	0.456510
$967$	8.34513e12	0.306912	0.153456	−	0.988155i	$-0.450960\pi$
$967$	8.34513e12	0.306912	0.153456	+	0.988155i	$0.450960\pi$
$968$	3.40439e13	1.24623
$969$	3.84617e13	1.40143
$970$	1.19814e13	0.434546
$971$	8.89056e11	0.0320954	0.0160477	−	0.999871i	$-0.494892\pi$
$971$	8.89056e11	0.0320954	0.0160477	+	0.999871i	$0.494892\pi$
$972$	−1.21770e12	−0.0437566
$973$	−3.70353e13	−1.32467
$974$	−2.21324e13	−0.787978
$975$	1.41277e13	0.500668
$976$	−3.88866e12	−0.137175
$977$	3.98018e13	1.39758	0.698791	−	0.715326i	$-0.253722\pi$
$977$	3.98018e13	1.39758	0.698791	+	0.715326i	$0.253722\pi$
$978$	1.74499e12	0.0609913
$979$	3.50377e13	1.21903
$980$	−9.73878e12	−0.337277
$981$	1.07577e13	0.370861
$982$	3.56732e12	0.122417
$983$	6.88619e12	0.235228	0.117614	−	0.993059i	$-0.462476\pi$
$983$	6.88619e12	0.235228	0.117614	+	0.993059i	$0.462476\pi$
$984$	1.05082e13	0.357315
$985$	−2.51811e13	−0.852338
$986$	−2.11947e13	−0.714135
$987$	−3.16007e13	−1.05991
$988$	4.06901e13	1.35857
$989$	−2.60631e13	−0.866249
$990$	1.07541e13	0.355808
$991$	1.66826e13	0.549455	0.274728	−	0.961522i	$-0.411412\pi$
$991$	1.66826e13	0.549455	0.274728	+	0.961522i	$0.411412\pi$
$992$	−1.78116e13	−0.583983
$993$	−9.39318e12	−0.306578
$994$	−1.65568e12	−0.0537944
$995$	−1.41267e13	−0.456915
$996$	−1.70259e13	−0.548205
$997$	−5.55920e13	−1.78190	−0.890952	−	0.454097i	$-0.849962\pi$
$997$	−5.55920e13	−1.78190	−0.890952	+	0.454097i	$0.849962\pi$
$998$	2.21055e13	0.705363
$999$	−7.64604e12	−0.242880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.10	✓	21	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)

\(f(q)\)	\(=\)	\(q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} -22189.8 q^{10} -73867.0 q^{11} -28288.0 q^{12} +162700. q^{13} -95800.9 q^{14} +140883. q^{15} +38628.6 q^{16} -663069. q^{17} -83705.0 q^{18} -716119. q^{19} -607420. q^{20} +608237. q^{21} +942393. q^{22} -1.59218e6 q^{23} +889995. q^{24} +1.07201e6 q^{25} -2.07572e6 q^{26} +531441. q^{27} -2.62244e6 q^{28} -2.50545e6 q^{29} -1.79738e6 q^{30} +2.91112e6 q^{31} -6.11847e6 q^{32} -5.98323e6 q^{33} +8.45942e6 q^{34} +1.30605e7 q^{35} -2.29133e6 q^{36} -1.43874e7 q^{37} +9.13622e6 q^{38} +1.31787e7 q^{39} +1.91106e7 q^{40} +1.18070e7 q^{41} -7.75987e6 q^{42} +1.63694e7 q^{43} +2.57969e7 q^{44} +1.14115e7 q^{45} +2.03130e7 q^{46} -5.19546e7 q^{47} +3.12891e6 q^{48} +1.60330e7 q^{49} -1.36767e7 q^{50} -5.37086e7 q^{51} -5.68204e7 q^{52} -1.54905e7 q^{53} -6.78011e6 q^{54} -1.28476e8 q^{55} +8.25070e7 q^{56} -5.80056e7 q^{57} +3.19645e7 q^{58} +1.21174e7 q^{59} -4.92010e7 q^{60} -1.00668e8 q^{61} -3.71399e7 q^{62} +4.92672e7 q^{63} +5.82814e7 q^{64} +2.82982e8 q^{65} +7.63338e7 q^{66} -2.65492e7 q^{67} +2.31567e8 q^{68} -1.28967e8 q^{69} -1.66626e8 q^{70} +1.72825e7 q^{71} +7.20896e7 q^{72} +5.63024e7 q^{73} +1.83554e8 q^{74} +8.68328e7 q^{75} +2.50093e8 q^{76} -5.54675e8 q^{77} -1.68133e8 q^{78} +5.55414e8 q^{79} +6.71863e7 q^{80} +4.30467e7 q^{81} -1.50634e8 q^{82} +6.01877e8 q^{83} -2.12417e8 q^{84} -1.15327e9 q^{85} -2.08841e8 q^{86} -2.02942e8 q^{87} -8.11621e8 q^{88} -4.74335e8 q^{89} -1.45587e8 q^{90} +1.22173e9 q^{91} +5.56044e8 q^{92} +2.35800e8 q^{93} +6.62835e8 q^{94} -1.24554e9 q^{95} -4.95596e8 q^{96} -5.39952e8 q^{97} -2.04549e8 q^{98} -4.84642e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more