LMFDB - Embedded newform 177.12.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} -34509.2 q^{10} +210488. q^{11} +494983. q^{12} -165388. q^{13} -119610. q^{14} -2.52444e6 q^{15} +4.12663e6 q^{16} +1.10693e7 q^{17} -196151. q^{18} +6.36628e6 q^{19} -2.11613e7 q^{20} -8.74979e6 q^{21} -699203. q^{22} +3.65341e7 q^{23} -3.29740e6 q^{24} +5.90953e7 q^{25} +549389. q^{26} -1.43489e7 q^{27} -7.33458e7 q^{28} +4.69684e7 q^{29} +8.38574e6 q^{30} +2.92595e8 q^{31} -4.14984e7 q^{32} -5.11485e7 q^{33} -3.67704e7 q^{34} +3.74067e8 q^{35} -1.20281e8 q^{36} -8.53685e7 q^{37} -2.11477e7 q^{38} +4.01892e7 q^{39} +1.40969e8 q^{40} -1.98363e8 q^{41} +2.90653e7 q^{42} -1.07429e9 q^{43} -4.28756e8 q^{44} +6.13438e8 q^{45} -1.21360e8 q^{46} +4.33042e8 q^{47} -1.00277e9 q^{48} -6.80797e8 q^{49} -1.96305e8 q^{50} -2.68984e9 q^{51} +3.36889e8 q^{52} +5.70841e7 q^{53} +4.76646e7 q^{54} +2.18668e9 q^{55} +4.88604e8 q^{56} -1.54701e9 q^{57} -1.56021e8 q^{58} -7.14924e8 q^{59} +5.14219e9 q^{60} -7.10908e9 q^{61} -9.71951e8 q^{62} +2.12620e9 q^{63} -8.31349e9 q^{64} -1.71815e9 q^{65} +1.69906e8 q^{66} -1.47067e10 q^{67} -2.25478e10 q^{68} -8.87779e9 q^{69} -1.24259e9 q^{70} -4.78497e8 q^{71} +8.01268e8 q^{72} +1.94031e10 q^{73} +2.83579e8 q^{74} -1.43602e10 q^{75} -1.29679e10 q^{76} +7.57910e9 q^{77} -1.33501e8 q^{78} -1.66351e10 q^{79} +4.28700e10 q^{80} +3.48678e9 q^{81} +6.58929e8 q^{82} +1.27453e10 q^{83} +1.78230e10 q^{84} +1.14995e11 q^{85} +3.56860e9 q^{86} -1.14133e10 q^{87} +2.85622e9 q^{88} +2.31158e10 q^{89} -2.03773e9 q^{90} -5.95517e9 q^{91} -7.44188e10 q^{92} -7.11007e10 q^{93} -1.43849e9 q^{94} +6.61369e10 q^{95} +1.00841e10 q^{96} -7.93508e10 q^{97} +2.26149e9 q^{98} +1.24291e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * 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 $

$2$	−3.32183	−0.0734027	−0.0367013	−	0.999326i	$-0.511685\pi$
$2$	−3.32183	−0.0734027	−0.0367013	+	0.999326i	$0.511685\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−2036.97	−0.994612
$5$	10388.6	1.48670	0.743349	−	0.668903i	$-0.233236\pi$
$5$	10388.6	1.48670	0.743349	+	0.668903i	$0.233236\pi$
$6$	807.204	0.0423791
$7$	36007.4	0.809752	0.404876	−	0.914372i	$-0.367315\pi$
$7$	36007.4	0.809752	0.404876	+	0.914372i	$0.367315\pi$
$8$	13569.5	0.146410
$9$	59049.0	0.333333
$10$	−34509.2	−0.109128
$11$	210488.	0.394064	0.197032	−	0.980397i	$-0.436870\pi$
$11$	210488.	0.394064	0.197032	+	0.980397i	$0.436870\pi$
$12$	494983.	0.574240
$13$	−165388.	−0.123542	−0.0617710	−	0.998090i	$-0.519675\pi$
$13$	−165388.	−0.123542	−0.0617710	+	0.998090i	$0.519675\pi$
$14$	−119610.	−0.0594380
$15$	−2.52444e6	−0.858346
$16$	4.12663e6	0.983865
$17$	1.10693e7	1.89083	0.945413	−	0.325873i	$-0.105658\pi$
$17$	1.10693e7	1.89083	0.945413	+	0.325873i	$0.105658\pi$
$18$	−196151.	−0.0244676
$19$	6.36628e6	0.589849	0.294925	−	0.955521i	$-0.404705\pi$
$19$	6.36628e6	0.589849	0.294925	+	0.955521i	$0.404705\pi$
$20$	−2.11613e7	−1.47869
$21$	−8.74979e6	−0.467511
$22$	−699203.	−0.0289254
$23$	3.65341e7	1.18357	0.591787	−	0.806094i	$-0.298423\pi$
$23$	3.65341e7	1.18357	0.591787	+	0.806094i	$0.298423\pi$
$24$	−3.29740e6	−0.0845298
$25$	5.90953e7	1.21027
$26$	549389.	0.00906831
$27$	−1.43489e7	−0.192450
$28$	−7.33458e7	−0.805389
$29$	4.69684e7	0.425223	0.212612	−	0.977137i	$-0.431803\pi$
$29$	4.69684e7	0.425223	0.212612	+	0.977137i	$0.431803\pi$
$30$	8.38574e6	0.0630049
$31$	2.92595e8	1.83560	0.917800	−	0.397043i	$-0.129964\pi$
$31$	2.92595e8	1.83560	0.917800	+	0.397043i	$0.129964\pi$
$32$	−4.14984e7	−0.218628
$33$	−5.11485e7	−0.227513
$34$	−3.67704e7	−0.138792
$35$	3.74067e8	1.20386
$36$	−1.20281e8	−0.331537
$37$	−8.53685e7	−0.202390	−0.101195	−	0.994867i	$-0.532267\pi$
$37$	−8.53685e7	−0.202390	−0.101195	+	0.994867i	$0.532267\pi$
$38$	−2.11477e7	−0.0432965
$39$	4.01892e7	0.0713270
$40$	1.40969e8	0.217667
$41$	−1.98363e8	−0.267393	−0.133697	−	0.991022i	$-0.542685\pi$
$41$	−1.98363e8	−0.267393	−0.133697	+	0.991022i	$0.542685\pi$
$42$	2.90653e7	0.0343165
$43$	−1.07429e9	−1.11441	−0.557203	−	0.830376i	$-0.688126\pi$
$43$	−1.07429e9	−1.11441	−0.557203	+	0.830376i	$0.688126\pi$
$44$	−4.28756e8	−0.391941
$45$	6.13438e8	0.495566
$46$	−1.21360e8	−0.0868776
$47$	4.33042e8	0.275418	0.137709	−	0.990473i	$-0.456026\pi$
$47$	4.33042e8	0.275418	0.137709	+	0.990473i	$0.456026\pi$
$48$	−1.00277e9	−0.568035
$49$	−6.80797e8	−0.344302
$50$	−1.96305e8	−0.0888373
$51$	−2.68984e9	−1.09167
$52$	3.36889e8	0.122876
$53$	5.70841e7	0.0187498	0.00937492	−	0.999956i	$-0.497016\pi$
$53$	5.70841e7	0.0187498	0.00937492	+	0.999956i	$0.497016\pi$
$54$	4.76646e7	0.0141264
$55$	2.18668e9	0.585854
$56$	4.88604e8	0.118556
$57$	−1.54701e9	−0.340550
$58$	−1.56021e8	−0.0312125
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	5.14219e9	0.853721
$61$	−7.10908e9	−1.07770	−0.538852	−	0.842401i	$-0.681142\pi$
$61$	−7.10908e9	−1.07770	−0.538852	+	0.842401i	$0.681142\pi$
$62$	−9.71951e8	−0.134738
$63$	2.12620e9	0.269917
$64$	−8.31349e9	−0.967817
$65$	−1.71815e9	−0.183670
$66$	1.69906e8	0.0167001
$67$	−1.47067e10	−1.33077	−0.665385	−	0.746500i	$-0.731733\pi$
$67$	−1.47067e10	−1.33077	−0.665385	+	0.746500i	$0.731733\pi$
$68$	−2.25478e10	−1.88064
$69$	−8.87779e9	−0.683337
$70$	−1.24259e9	−0.0883664
$71$	−4.78497e8	−0.0314745	−0.0157372	−	0.999876i	$-0.505010\pi$
$71$	−4.78497e8	−0.0314745	−0.0157372	+	0.999876i	$0.505010\pi$
$72$	8.01268e8	0.0488033
$73$	1.94031e10	1.09546	0.547730	−	0.836655i	$-0.315492\pi$
$73$	1.94031e10	1.09546	0.547730	+	0.836655i	$0.315492\pi$
$74$	2.83579e8	0.0148559
$75$	−1.43602e10	−0.698751
$76$	−1.29679e10	−0.586671
$77$	7.57910e9	0.319094
$78$	−1.33501e8	−0.00523559
$79$	−1.66351e10	−0.608240	−0.304120	−	0.952634i	$-0.598362\pi$
$79$	−1.66351e10	−0.608240	−0.304120	+	0.952634i	$0.598362\pi$
$80$	4.28700e10	1.46271
$81$	3.48678e9	0.111111
$82$	6.58929e8	0.0196274
$83$	1.27453e10	0.355158	0.177579	−	0.984107i	$-0.443173\pi$
$83$	1.27453e10	0.355158	0.177579	+	0.984107i	$0.443173\pi$
$84$	1.78230e10	0.464992
$85$	1.14995e11	2.81109
$86$	3.56860e9	0.0818005
$87$	−1.14133e10	−0.245503
$88$	2.85622e9	0.0576949
$89$	2.31158e10	0.438797	0.219399	−	0.975635i	$-0.429590\pi$
$89$	2.31158e10	0.438797	0.219399	+	0.975635i	$0.429590\pi$
$90$	−2.03773e9	−0.0363759
$91$	−5.95517e9	−0.100038
$92$	−7.44188e10	−1.17720
$93$	−7.11007e10	−1.05978
$94$	−1.43849e9	−0.0202164
$95$	6.61369e10	0.876928
$96$	1.00841e10	0.126225
$97$	−7.93508e10	−0.938224	−0.469112	−	0.883139i	$-0.655426\pi$
$97$	−7.93508e10	−0.938224	−0.469112	+	0.883139i	$0.655426\pi$
$98$	2.26149e9	0.0252727
$99$	1.24291e10	0.131355
$100$	−1.20375e11	−1.20375
$101$	1.11992e11	1.06028	0.530138	−	0.847911i	$-0.322140\pi$
$101$	1.11992e11	1.06028	0.530138	+	0.847911i	$0.322140\pi$
$102$	8.93520e9	0.0801315
$103$	−1.05658e10	−0.0898042	−0.0449021	−	0.998991i	$-0.514298\pi$
$103$	−1.05658e10	−0.0898042	−0.0449021	+	0.998991i	$0.514298\pi$
$104$	−2.24423e9	−0.0180878
$105$	−9.08982e10	−0.695047
$106$	−1.89623e8	−0.00137629
$107$	1.96255e11	1.35273	0.676363	−	0.736568i	$-0.263555\pi$
$107$	1.96255e11	1.35273	0.676363	+	0.736568i	$0.263555\pi$
$108$	2.92282e10	0.191413
$109$	1.50533e11	0.937103	0.468552	−	0.883436i	$-0.344776\pi$
$109$	1.50533e11	0.937103	0.468552	+	0.883436i	$0.344776\pi$
$110$	−7.26376e9	−0.0430033
$111$	2.07446e10	0.116850
$112$	1.48589e11	0.796687
$113$	3.57354e11	1.82460	0.912299	−	0.409525i	$-0.134305\pi$
$113$	3.57354e11	1.82460	0.912299	+	0.409525i	$0.134305\pi$
$114$	5.13889e9	0.0249973
$115$	3.79539e11	1.75962
$116$	−9.56731e10	−0.422932
$117$	−9.76597e9	−0.0411806
$118$	2.37485e9	0.00955622
$119$	3.98577e11	1.53110
$120$	−3.42554e10	−0.125670
$121$	−2.41007e11	−0.844714
$122$	2.36151e10	0.0791063
$123$	4.82023e10	0.154379
$124$	−5.96007e11	−1.82571
$125$	1.06662e11	0.312612
$126$	−7.06286e9	−0.0198127
$127$	−5.29513e11	−1.42219	−0.711093	−	0.703098i	$-0.751799\pi$
$127$	−5.29513e11	−1.42219	−0.711093	+	0.703098i	$0.751799\pi$
$128$	1.12605e11	0.289669
$129$	2.61052e11	0.643403
$130$	5.70739e9	0.0134818
$131$	−1.60022e11	−0.362400	−0.181200	−	0.983446i	$-0.557998\pi$
$131$	−1.60022e11	−0.362400	−0.181200	+	0.983446i	$0.557998\pi$
$132$	1.04188e11	0.226287
$133$	2.29233e11	0.477631
$134$	4.88531e10	0.0976822
$135$	−1.49065e11	−0.286115
$136$	1.50206e11	0.276836
$137$	4.42732e11	0.783750	0.391875	−	0.920019i	$-0.371827\pi$
$137$	4.42732e11	0.783750	0.391875	+	0.920019i	$0.371827\pi$
$138$	2.94905e10	0.0501588
$139$	−9.70500e11	−1.58641	−0.793203	−	0.608958i	$-0.791588\pi$
$139$	−9.70500e11	−1.58641	−0.793203	+	0.608958i	$0.791588\pi$
$140$	−7.61961e11	−1.19737
$141$	−1.05229e11	−0.159013
$142$	1.58948e9	0.00231031
$143$	−3.48120e10	−0.0486834
$144$	2.43673e11	0.327955
$145$	4.87937e11	0.632179
$146$	−6.44539e10	−0.0804097
$147$	1.65434e11	0.198783
$148$	1.73893e11	0.201299
$149$	−5.89226e11	−0.657290	−0.328645	−	0.944453i	$-0.606592\pi$
$149$	−5.89226e11	−0.657290	−0.328645	+	0.944453i	$0.606592\pi$
$150$	4.77020e10	0.0512902
$151$	−6.30046e11	−0.653129	−0.326564	−	0.945175i	$-0.605891\pi$
$151$	−6.30046e11	−0.653129	−0.326564	+	0.945175i	$0.605891\pi$
$152$	8.63875e10	0.0863597
$153$	6.53632e11	0.630276
$154$	−2.51765e10	−0.0234224
$155$	3.03966e12	2.72898
$156$	−8.18640e10	−0.0709427
$157$	−1.65494e12	−1.38463	−0.692315	−	0.721595i	$-0.743409\pi$
$157$	−1.65494e12	−1.38463	−0.692315	+	0.721595i	$0.743409\pi$
$158$	5.52588e10	0.0446465
$159$	−1.38714e10	−0.0108252
$160$	−4.31111e11	−0.325034
$161$	1.31550e12	0.958402
$162$	−1.15825e10	−0.00815586
$163$	3.03764e11	0.206778	0.103389	−	0.994641i	$-0.467031\pi$
$163$	3.03764e11	0.206778	0.103389	+	0.994641i	$0.467031\pi$
$164$	4.04059e11	0.265952
$165$	−5.31362e11	−0.338243
$166$	−4.23378e10	−0.0260696
$167$	1.80369e12	1.07454	0.537269	−	0.843411i	$-0.319456\pi$
$167$	1.80369e12	1.07454	0.537269	+	0.843411i	$0.319456\pi$
$168$	−1.18731e11	−0.0684482
$169$	−1.76481e12	−0.984737
$170$	−3.81993e11	−0.206342
$171$	3.75922e11	0.196616
$172$	2.18829e12	1.10840
$173$	1.00023e12	0.490735	0.245367	−	0.969430i	$-0.421091\pi$
$173$	1.00023e12	0.490735	0.245367	+	0.969430i	$0.421091\pi$
$174$	3.79131e10	0.0180206
$175$	2.12787e12	0.980021
$176$	8.68604e11	0.387706
$177$	1.73727e11	0.0751646
$178$	−7.67867e10	−0.0322089
$179$	1.77601e12	0.722359	0.361180	−	0.932496i	$-0.382374\pi$
$179$	1.77601e12	0.722359	0.361180	+	0.932496i	$0.382374\pi$
$180$	−1.24955e12	−0.492896
$181$	9.10888e11	0.348524	0.174262	−	0.984699i	$-0.444246\pi$
$181$	9.10888e11	0.348524	0.174262	+	0.984699i	$0.444246\pi$
$182$	1.97820e10	0.00734308
$183$	1.72751e12	0.622212
$184$	4.95752e11	0.173287
$185$	−8.86861e11	−0.300892
$186$	2.36184e11	0.0777910
$187$	2.32995e12	0.745107
$188$	−8.82092e11	−0.273934
$189$	−5.16666e11	−0.155837
$190$	−2.19695e11	−0.0643689
$191$	2.56867e12	0.731182	0.365591	−	0.930776i	$-0.380867\pi$
$191$	2.56867e12	0.731182	0.365591	+	0.930776i	$0.380867\pi$
$192$	2.02018e12	0.558770
$193$	2.96998e12	0.798341	0.399171	−	0.916877i	$-0.369298\pi$
$193$	2.96998e12	0.798341	0.399171	+	0.916877i	$0.369298\pi$
$194$	2.63590e11	0.0688682
$195$	4.17510e11	0.106042
$196$	1.38676e12	0.342446
$197$	−3.59827e12	−0.864032	−0.432016	−	0.901866i	$-0.642198\pi$
$197$	−3.59827e12	−0.864032	−0.432016	+	0.901866i	$0.642198\pi$
$198$	−4.12873e10	−0.00964179
$199$	7.64364e12	1.73623	0.868117	−	0.496360i	$-0.165330\pi$
$199$	7.64364e12	1.73623	0.868117	+	0.496360i	$0.165330\pi$
$200$	8.01897e11	0.177196
$201$	3.57372e12	0.768321
$202$	−3.72018e11	−0.0778271
$203$	1.69121e12	0.344326
$204$	5.47912e12	1.08579
$205$	−2.06072e12	−0.397533
$206$	3.50977e10	0.00659187
$207$	2.15730e12	0.394525
$208$	−6.82493e11	−0.121549
$209$	1.34002e12	0.232438
$210$	3.01948e11	0.0510183
$211$	6.08970e12	1.00240	0.501201	−	0.865331i	$-0.332892\pi$
$211$	6.08970e12	1.00240	0.501201	+	0.865331i	$0.332892\pi$
$212$	−1.16278e11	−0.0186488
$213$	1.16275e11	0.0181718
$214$	−6.51925e11	−0.0992938
$215$	−1.11604e13	−1.65679
$216$	−1.94708e11	−0.0281766
$217$	1.05356e13	1.48638
$218$	−5.00046e11	−0.0687859
$219$	−4.71496e12	−0.632464
$220$	−4.45418e12	−0.582698
$221$	−1.83073e12	−0.233596
$222$	−6.89098e10	−0.00857708
$223$	6.69853e12	0.813397	0.406698	−	0.913562i	$-0.366680\pi$
$223$	6.69853e12	0.813397	0.406698	+	0.913562i	$0.366680\pi$
$224$	−1.49425e12	−0.177035
$225$	3.48952e12	0.403424
$226$	−1.18707e12	−0.133930
$227$	−1.28260e13	−1.41237	−0.706184	−	0.708028i	$-0.749585\pi$
$227$	−1.28260e13	−1.41237	−0.706184	+	0.708028i	$0.749585\pi$
$228$	3.15120e12	0.338715
$229$	−1.17983e13	−1.23801	−0.619007	−	0.785385i	$-0.712465\pi$
$229$	−1.17983e13	−1.23801	−0.619007	+	0.785385i	$0.712465\pi$
$230$	−1.26076e12	−0.129161
$231$	−1.84172e12	−0.184229
$232$	6.37341e11	0.0622569
$233$	−4.42287e12	−0.421936	−0.210968	−	0.977493i	$-0.567662\pi$
$233$	−4.42287e12	−0.421936	−0.210968	+	0.977493i	$0.567662\pi$
$234$	3.24409e10	0.00302277
$235$	4.49871e12	0.409463
$236$	1.45628e12	0.129487
$237$	4.04232e12	0.351168
$238$	−1.32400e12	−0.112387
$239$	2.33707e13	1.93858	0.969291	−	0.245917i	$-0.0790892\pi$
$239$	2.33707e13	1.93858	0.969291	+	0.245917i	$0.0790892\pi$
$240$	−1.04174e13	−0.844497
$241$	8.46901e12	0.671026	0.335513	−	0.942036i	$-0.391090\pi$
$241$	8.46901e12	0.671026	0.335513	+	0.942036i	$0.391090\pi$
$242$	8.00582e11	0.0620043
$243$	−8.47289e11	−0.0641500
$244$	1.44809e13	1.07190
$245$	−7.07254e12	−0.511873
$246$	−1.60120e11	−0.0113319
$247$	−1.05290e12	−0.0728711
$248$	3.97039e12	0.268750
$249$	−3.09712e12	−0.205051
$250$	−3.54314e11	−0.0229466
$251$	−1.99261e13	−1.26246	−0.631229	−	0.775597i	$-0.717449\pi$
$251$	−1.99261e13	−1.26246	−0.631229	+	0.775597i	$0.717449\pi$
$252$	−4.33099e12	−0.268463
$253$	7.68998e12	0.466404
$254$	1.75895e12	0.104392
$255$	−2.79438e13	−1.62298
$256$	1.66520e13	0.946555
$257$	2.25882e11	0.0125675	0.00628375	−	0.999980i	$-0.498000\pi$
$257$	2.25882e11	0.0125675	0.00628375	+	0.999980i	$0.498000\pi$
$258$	−8.67169e11	−0.0472275
$259$	−3.07390e12	−0.163885
$260$	3.49981e12	0.182680
$261$	2.77344e12	0.141741
$262$	5.31566e11	0.0266011
$263$	−1.12859e13	−0.553070	−0.276535	−	0.961004i	$-0.589186\pi$
$263$	−1.12859e13	−0.553070	−0.276535	+	0.961004i	$0.589186\pi$
$264$	−6.94062e11	−0.0333101
$265$	5.93025e11	0.0278754
$266$	−7.61472e11	−0.0350594
$267$	−5.61714e12	−0.253340
$268$	2.99570e13	1.32360
$269$	2.12970e13	0.921894	0.460947	−	0.887428i	$-0.347510\pi$
$269$	2.12970e13	0.921894	0.460947	+	0.887428i	$0.347510\pi$
$270$	4.95169e11	0.0210016
$271$	5.21661e12	0.216799	0.108399	−	0.994107i	$-0.465427\pi$
$271$	5.21661e12	0.216799	0.108399	+	0.994107i	$0.465427\pi$
$272$	4.56790e13	1.86032
$273$	1.44711e12	0.0577572
$274$	−1.47068e12	−0.0575293
$275$	1.24388e13	0.476925
$276$	1.80838e13	0.679655
$277$	−3.60809e13	−1.32935	−0.664674	−	0.747134i	$-0.731430\pi$
$277$	−3.60809e13	−1.32935	−0.664674	+	0.747134i	$0.731430\pi$
$278$	3.22383e12	0.116446
$279$	1.72775e13	0.611867
$280$	5.07592e12	0.176257
$281$	−9.47322e12	−0.322562	−0.161281	−	0.986909i	$-0.551563\pi$
$281$	−9.47322e12	−0.322562	−0.161281	+	0.986909i	$0.551563\pi$
$282$	3.49553e11	0.0116719
$283$	1.23634e12	0.0404867	0.0202434	−	0.999795i	$-0.493556\pi$
$283$	1.23634e12	0.0404867	0.0202434	+	0.999795i	$0.493556\pi$
$284$	9.74682e11	0.0313049
$285$	−1.60713e13	−0.506294
$286$	1.15640e11	0.00357349
$287$	−7.14254e12	−0.216522
$288$	−2.45044e12	−0.0728761
$289$	8.82579e13	2.57523
$290$	−1.62084e12	−0.0464037
$291$	1.92822e13	0.541684
$292$	−3.95235e13	−1.08956
$293$	−1.31349e12	−0.0355348	−0.0177674	−	0.999842i	$-0.505656\pi$
$293$	−1.31349e12	−0.0355348	−0.0177674	+	0.999842i	$0.505656\pi$
$294$	−5.49542e11	−0.0145912
$295$	−7.42708e12	−0.193552
$296$	−1.15841e12	−0.0296318
$297$	−3.02027e12	−0.0758376
$298$	1.95731e12	0.0482469
$299$	−6.04229e12	−0.146221
$300$	2.92512e13	0.694986
$301$	−3.86822e13	−0.902393
$302$	2.09290e12	0.0479414
$303$	−2.72140e13	−0.612151
$304$	2.62713e13	0.580332
$305$	−7.38535e13	−1.60222
$306$	−2.17125e12	−0.0462639
$307$	−1.49170e13	−0.312192	−0.156096	−	0.987742i	$-0.549891\pi$
$307$	−1.49170e13	−0.312192	−0.156096	+	0.987742i	$0.549891\pi$
$308$	−1.54384e13	−0.317375
$309$	2.56748e12	0.0518485
$310$	−1.00972e13	−0.200315
$311$	8.39872e13	1.63693	0.818466	−	0.574555i	$-0.194825\pi$
$311$	8.39872e13	1.63693	0.818466	+	0.574555i	$0.194825\pi$
$312$	5.45349e11	0.0104430
$313$	2.97502e13	0.559752	0.279876	−	0.960036i	$-0.409707\pi$
$313$	2.97502e13	0.559752	0.279876	+	0.960036i	$0.409707\pi$
$314$	5.49742e12	0.101636
$315$	2.20883e13	0.401286
$316$	3.38850e13	0.604963
$317$	−9.01607e13	−1.58195	−0.790973	−	0.611852i	$-0.790425\pi$
$317$	−9.01607e13	−1.58195	−0.790973	+	0.611852i	$0.790425\pi$
$318$	4.60785e10	0.000794601 0
$319$	9.88628e12	0.167565
$320$	−8.63657e13	−1.43885
$321$	−4.76900e13	−0.780997
$322$	−4.36986e12	−0.0703493
$323$	7.04704e13	1.11530
$324$	−7.10246e12	−0.110512
$325$	−9.77363e12	−0.149519
$326$	−1.00905e12	−0.0151781
$327$	−3.65796e13	−0.541037
$328$	−2.69170e12	−0.0391490
$329$	1.55927e13	0.223020
$330$	1.76509e12	0.0248280
$331$	−9.26480e13	−1.28169	−0.640844	−	0.767671i	$-0.721415\pi$
$331$	−9.26480e13	−1.28169	−0.640844	+	0.767671i	$0.721415\pi$
$332$	−2.59618e13	−0.353245
$333$	−5.04093e12	−0.0674632
$334$	−5.99156e12	−0.0788741
$335$	−1.52782e14	−1.97846
$336$	−3.61071e13	−0.459967
$337$	−3.89814e13	−0.488533	−0.244266	−	0.969708i	$-0.578547\pi$
$337$	−3.89814e13	−0.488533	−0.244266	+	0.969708i	$0.578547\pi$
$338$	5.86238e12	0.0722824
$339$	−8.68370e13	−1.05343
$340$	−2.34241e14	−2.79594
$341$	6.15877e13	0.723344
$342$	−1.24875e12	−0.0144322
$343$	−9.57120e13	−1.08855
$344$	−1.45776e13	−0.163160
$345$	−9.22280e13	−1.01592
$346$	−3.32259e12	−0.0360212
$347$	6.88496e13	0.734665	0.367333	−	0.930090i	$-0.380271\pi$
$347$	6.88496e13	0.734665	0.367333	+	0.930090i	$0.380271\pi$
$348$	2.32486e13	0.244180
$349$	4.87913e12	0.0504431	0.0252216	−	0.999682i	$-0.491971\pi$
$349$	4.87913e12	0.0504431	0.0252216	+	0.999682i	$0.491971\pi$
$350$	−7.06841e12	−0.0719362
$351$	2.37313e12	0.0237757
$352$	−8.73489e12	−0.0861535
$353$	1.21783e14	1.18257	0.591285	−	0.806463i	$-0.298621\pi$
$353$	1.21783e14	1.18257	0.591285	+	0.806463i	$0.298621\pi$
$354$	−5.77090e11	−0.00551728
$355$	−4.97092e12	−0.0467930
$356$	−4.70861e13	−0.436433
$357$	−9.68542e13	−0.883982
$358$	−5.89959e12	−0.0530231
$359$	−1.59489e14	−1.41160	−0.705799	−	0.708412i	$-0.749412\pi$
$359$	−1.59489e14	−1.41160	−0.705799	+	0.708412i	$0.749412\pi$
$360$	8.32407e12	0.0725558
$361$	−7.59607e13	−0.652078
$362$	−3.02581e12	−0.0255826
$363$	5.85646e13	0.487696
$364$	1.21305e13	0.0994993
$365$	2.01572e14	1.62862
$366$	−5.73848e12	−0.0456721
$367$	−1.62158e14	−1.27138	−0.635689	−	0.771945i	$-0.719284\pi$
$367$	−1.62158e14	−1.27138	−0.635689	+	0.771945i	$0.719284\pi$
$368$	1.50763e14	1.16448
$369$	−1.17132e13	−0.0891310
$370$	2.94600e12	0.0220863
$371$	2.05545e12	0.0151827
$372$	1.44830e14	1.05407
$373$	−6.90596e13	−0.495251	−0.247625	−	0.968856i	$-0.579650\pi$
$373$	−6.90596e13	−0.495251	−0.247625	+	0.968856i	$0.579650\pi$
$374$	−7.73970e12	−0.0546928
$375$	−2.59189e13	−0.180487
$376$	5.87619e12	0.0403239
$377$	−7.76800e12	−0.0525329
$378$	1.71628e12	0.0114388
$379$	1.83874e14	1.20782	0.603912	−	0.797051i	$-0.293608\pi$
$379$	1.83874e14	1.20782	0.603912	+	0.797051i	$0.293608\pi$
$380$	−1.34719e14	−0.872203
$381$	1.28672e14	0.821099
$382$	−8.53269e12	−0.0536707
$383$	9.17114e13	0.568630	0.284315	−	0.958731i	$-0.408234\pi$
$383$	9.17114e13	0.568630	0.284315	+	0.958731i	$0.408234\pi$
$384$	−2.73629e13	−0.167240
$385$	7.87364e13	0.474397
$386$	−9.86577e12	−0.0586004
$387$	−6.34356e13	−0.371469
$388$	1.61635e14	0.933169
$389$	−2.04127e14	−1.16193	−0.580963	−	0.813930i	$-0.697324\pi$
$389$	−2.04127e14	−1.16193	−0.580963	+	0.813930i	$0.697324\pi$
$390$	−1.38690e12	−0.00778375
$391$	4.04408e14	2.23793
$392$	−9.23810e12	−0.0504092
$393$	3.88854e13	0.209232
$394$	1.19528e13	0.0634223
$395$	−1.72815e14	−0.904270
$396$	−2.53176e13	−0.130647
$397$	1.05923e14	0.539065	0.269533	−	0.962991i	$-0.413131\pi$
$397$	1.05923e14	0.539065	0.269533	+	0.962991i	$0.413131\pi$
$398$	−2.53908e13	−0.127444
$399$	−5.57036e13	−0.275761
$400$	2.43865e14	1.19075
$401$	−3.46025e14	−1.66653	−0.833267	−	0.552871i	$-0.813532\pi$
$401$	−3.46025e14	−1.66653	−0.833267	+	0.552871i	$0.813532\pi$
$402$	−1.18713e13	−0.0563968
$403$	−4.83916e13	−0.226774
$404$	−2.28124e14	−1.05456
$405$	3.62229e13	0.165189
$406$	−5.61791e12	−0.0252744
$407$	−1.79690e13	−0.0797545
$408$	−3.65000e13	−0.159831
$409$	2.63269e14	1.13742	0.568710	−	0.822538i	$-0.307443\pi$
$409$	2.63269e14	1.13742	0.568710	+	0.822538i	$0.307443\pi$
$410$	6.84536e12	0.0291800
$411$	−1.07584e14	−0.452498
$412$	2.15221e13	0.0893204
$413$	−2.57425e13	−0.105421
$414$	−7.16619e12	−0.0289592
$415$	1.32407e14	0.528013
$416$	6.86332e12	0.0270098
$417$	2.35832e14	0.915912
$418$	−4.45132e12	−0.0170616
$419$	−4.94698e14	−1.87138	−0.935692	−	0.352819i	$-0.885223\pi$
$419$	−4.94698e14	−1.87138	−0.935692	+	0.352819i	$0.885223\pi$
$420$	1.85157e14	0.691302
$421$	−2.14561e14	−0.790679	−0.395339	−	0.918535i	$-0.629373\pi$
$421$	−2.14561e14	−0.790679	−0.395339	+	0.918535i	$0.629373\pi$
$422$	−2.02289e13	−0.0735790
$423$	2.55707e13	0.0918059
$424$	7.74605e11	0.00274516
$425$	6.54145e14	2.28842
$426$	−3.86245e11	−0.00133386
$427$	−2.55979e14	−0.872672
$428$	−3.99765e14	−1.34544
$429$	8.45932e12	0.0281074
$430$	3.70728e13	0.121613
$431$	6.20114e12	0.0200838	0.0100419	−	0.999950i	$-0.496804\pi$
$431$	6.20114e12	0.0200838	0.0100419	+	0.999950i	$0.496804\pi$
$432$	−5.92126e13	−0.189345
$433$	5.25433e13	0.165895	0.0829476	−	0.996554i	$-0.473567\pi$
$433$	5.25433e13	0.165895	0.0829476	+	0.996554i	$0.473567\pi$
$434$	−3.49974e13	−0.109104
$435$	−1.18569e14	−0.364989
$436$	−3.06632e14	−0.932054
$437$	2.32586e14	0.698130
$438$	1.56623e13	0.0464246
$439$	4.16478e14	1.21909	0.609547	−	0.792750i	$-0.291351\pi$
$439$	4.16478e14	1.21909	0.609547	+	0.792750i	$0.291351\pi$
$440$	2.96722e13	0.0857749
$441$	−4.02004e13	−0.114767
$442$	6.08136e12	0.0171466
$443$	3.80244e14	1.05887	0.529433	−	0.848352i	$-0.322405\pi$
$443$	3.80244e14	1.05887	0.529433	+	0.848352i	$0.322405\pi$
$444$	−4.22559e13	−0.116220
$445$	2.40141e14	0.652359
$446$	−2.22513e13	−0.0597055
$447$	1.43182e14	0.379487
$448$	−2.99347e14	−0.783692
$449$	2.25663e14	0.583586	0.291793	−	0.956481i	$-0.405748\pi$
$449$	2.25663e14	0.583586	0.291793	+	0.956481i	$0.405748\pi$
$450$	−1.15916e13	−0.0296124
$451$	−4.17530e13	−0.105370
$452$	−7.27918e14	−1.81477
$453$	1.53101e14	0.377084
$454$	4.26057e13	0.103672
$455$	−6.18660e13	−0.148727
$456$	−2.09922e13	−0.0498598
$457$	−1.96353e14	−0.460786	−0.230393	−	0.973098i	$-0.574001\pi$
$457$	−1.96353e14	−0.460786	−0.230393	+	0.973098i	$0.574001\pi$
$458$	3.91920e13	0.0908736
$459$	−1.58833e14	−0.363890
$460$	−7.73108e14	−1.75014
$461$	8.18485e14	1.83086	0.915431	−	0.402475i	$-0.131850\pi$
$461$	8.18485e14	1.83086	0.915431	+	0.402475i	$0.131850\pi$
$462$	6.11788e12	0.0135229
$463$	5.09865e14	1.11368	0.556840	−	0.830620i	$-0.312014\pi$
$463$	5.09865e14	1.11368	0.556840	+	0.830620i	$0.312014\pi$
$464$	1.93821e14	0.418363
$465$	−7.38638e14	−1.57558
$466$	1.46920e13	0.0309713
$467$	−1.23439e14	−0.257164	−0.128582	−	0.991699i	$-0.541042\pi$
$467$	−1.23439e14	−0.257164	−0.128582	+	0.991699i	$0.541042\pi$
$468$	1.98929e13	0.0409588
$469$	−5.29549e14	−1.07759
$470$	−1.49439e13	−0.0300557
$471$	4.02150e14	0.799417
$472$	−9.70120e12	−0.0190609
$473$	−2.26124e14	−0.439148
$474$	−1.34279e13	−0.0257767
$475$	3.76217e14	0.713878
$476$	−8.11887e14	−1.52285
$477$	3.37076e12	0.00624995
$478$	−7.76336e13	−0.142297
$479$	−5.23224e14	−0.948073	−0.474037	−	0.880505i	$-0.657204\pi$
$479$	−5.23224e14	−0.948073	−0.474037	+	0.880505i	$0.657204\pi$
$480$	1.04760e14	0.187659
$481$	1.41189e13	0.0250036
$482$	−2.81326e13	−0.0492551
$483$	−3.19666e14	−0.553334
$484$	4.90922e14	0.840162
$485$	−8.24345e14	−1.39486
$486$	2.81455e12	0.00470879
$487$	−5.93984e14	−0.982574	−0.491287	−	0.870998i	$-0.663473\pi$
$487$	−5.93984e14	−0.982574	−0.491287	+	0.870998i	$0.663473\pi$
$488$	−9.64670e13	−0.157786
$489$	−7.38146e13	−0.119383
$490$	2.34938e13	0.0375728
$491$	3.03016e14	0.479200	0.239600	−	0.970872i	$-0.422984\pi$
$491$	3.03016e14	0.479200	0.239600	+	0.970872i	$0.422984\pi$
$492$	−9.81864e13	−0.153548
$493$	5.19909e14	0.804024
$494$	3.49756e12	0.00534893
$495$	1.29121e14	0.195285
$496$	1.20743e15	1.80598
$497$	−1.72294e13	−0.0254865
$498$	1.02881e13	0.0150513
$499$	7.21812e14	1.04441	0.522205	−	0.852820i	$-0.325110\pi$
$499$	7.21812e14	1.04441	0.522205	+	0.852820i	$0.325110\pi$
$500$	−2.17267e14	−0.310928
$501$	−4.38298e14	−0.620385
$502$	6.61911e13	0.0926678
$503$	1.05026e15	1.45436	0.727180	−	0.686446i	$-0.240830\pi$
$503$	1.05026e15	1.45436	0.727180	+	0.686446i	$0.240830\pi$
$504$	2.88516e13	0.0395186
$505$	1.16344e15	1.57631
$506$	−2.55448e13	−0.0342353
$507$	4.28848e14	0.568538
$508$	1.07860e15	1.41452
$509$	−1.00418e15	−1.30276	−0.651378	−	0.758753i	$-0.725809\pi$
$509$	−1.00418e15	−1.30276	−0.651378	+	0.758753i	$0.725809\pi$
$510$	9.28244e13	0.119131
$511$	6.98656e14	0.887051
$512$	−2.85929e14	−0.359148
$513$	−9.13491e13	−0.113517
$514$	−7.50340e11	−0.000922488 0
$515$	−1.09764e14	−0.133512
$516$	−5.31753e14	−0.639936
$517$	9.11500e13	0.108532
$518$	1.02109e13	0.0120296
$519$	−2.43056e14	−0.283326
$520$	−2.33145e13	−0.0268910
$521$	−6.69577e14	−0.764176	−0.382088	−	0.924126i	$-0.624795\pi$
$521$	−6.69577e14	−0.764176	−0.382088	+	0.924126i	$0.624795\pi$
$522$	−9.21289e12	−0.0104042
$523$	−7.80796e12	−0.00872525	−0.00436263	−	0.999990i	$-0.501389\pi$
$523$	−7.80796e12	−0.00872525	−0.00436263	+	0.999990i	$0.501389\pi$
$524$	3.25960e14	0.360448
$525$	−5.17072e14	−0.565815
$526$	3.74899e13	0.0405968
$527$	3.23883e15	3.47080
$528$	−2.11071e14	−0.223842
$529$	3.81933e14	0.400849
$530$	−1.96993e12	−0.00204613
$531$	−4.22156e13	−0.0433963
$532$	−4.66940e14	−0.475058
$533$	3.28068e13	0.0330343
$534$	1.86592e13	0.0185958
$535$	2.03882e15	2.01110
$536$	−1.99563e14	−0.194838
$537$	−4.31570e14	−0.417054
$538$	−7.07450e13	−0.0676695
$539$	−1.43299e14	−0.135677
$540$	3.03641e14	0.284574
$541$	−1.78557e15	−1.65651	−0.828253	−	0.560354i	$-0.810665\pi$
$541$	−1.78557e15	−1.65651	−0.828253	+	0.560354i	$0.810665\pi$
$542$	−1.73287e13	−0.0159136
$543$	−2.21346e14	−0.201220
$544$	−4.59359e14	−0.413388
$545$	1.56384e15	1.39319
$546$	−4.80704e12	−0.00423953
$547$	1.41356e15	1.23420	0.617100	−	0.786885i	$-0.288307\pi$
$547$	1.41356e15	1.23420	0.617100	+	0.786885i	$0.288307\pi$
$548$	−9.01829e14	−0.779527
$549$	−4.19784e14	−0.359234
$550$	−4.13197e13	−0.0350076
$551$	2.99014e14	0.250818
$552$	−1.20468e14	−0.100047
$553$	−5.98985e14	−0.492524
$554$	1.19855e14	0.0975777
$555$	2.15507e14	0.173720
$556$	1.97688e15	1.57786
$557$	1.23222e15	0.973832	0.486916	−	0.873449i	$-0.338122\pi$
$557$	1.23222e15	0.973832	0.486916	+	0.873449i	$0.338122\pi$
$558$	−5.73927e13	−0.0449127
$559$	1.77674e14	0.137676
$560$	1.54364e15	1.18443
$561$	−5.66179e14	−0.430188
$562$	3.14684e13	0.0236769
$563$	−1.66422e15	−1.23998	−0.619991	−	0.784609i	$-0.712864\pi$
$563$	−1.66422e15	−1.23998	−0.619991	+	0.784609i	$0.712864\pi$
$564$	2.14348e14	0.158156
$565$	3.71242e15	2.71263
$566$	−4.10691e12	−0.00297184
$567$	1.25550e14	0.0899725
$568$	−6.49299e12	−0.00460817
$569$	1.26849e15	0.891598	0.445799	−	0.895133i	$-0.352920\pi$
$569$	1.26849e15	0.891598	0.445799	+	0.895133i	$0.352920\pi$
$570$	5.33859e13	0.0371634
$571$	−3.62621e14	−0.250009	−0.125004	−	0.992156i	$-0.539894\pi$
$571$	−3.62621e14	−0.250009	−0.125004	+	0.992156i	$0.539894\pi$
$572$	7.09109e13	0.0484211
$573$	−6.24188e14	−0.422148
$574$	2.37263e13	0.0158933
$575$	2.15900e15	1.43245
$576$	−4.90903e14	−0.322606
$577$	−2.06852e15	−1.34646	−0.673228	−	0.739435i	$-0.735093\pi$
$577$	−2.06852e15	−1.34646	−0.673228	+	0.739435i	$0.735093\pi$
$578$	−2.93177e14	−0.189029
$579$	−7.21706e14	−0.460923
$580$	−9.93912e14	−0.628773
$581$	4.58926e14	0.287590
$582$	−6.40523e13	−0.0397611
$583$	1.20155e13	0.00738864
$584$	2.63292e14	0.160386
$585$	−1.01455e14	−0.0612232
$586$	4.36318e12	0.00260835
$587$	−8.38675e14	−0.496688	−0.248344	−	0.968672i	$-0.579886\pi$
$587$	−8.38675e14	−0.496688	−0.248344	+	0.968672i	$0.579886\pi$
$588$	−3.36983e14	−0.197712
$589$	1.86274e15	1.08273
$590$	2.46715e13	0.0142072
$591$	8.74380e14	0.498849
$592$	−3.52284e14	−0.199124
$593$	−1.65943e15	−0.929303	−0.464652	−	0.885494i	$-0.653820\pi$
$593$	−1.65943e15	−0.929303	−0.464652	+	0.885494i	$0.653820\pi$
$594$	1.00328e13	0.00556669
$595$	4.14067e15	2.27629
$596$	1.20023e15	0.653749
$597$	−1.85740e15	−1.00242
$598$	2.00714e13	0.0107330
$599$	2.76061e15	1.46271	0.731354	−	0.681998i	$-0.238889\pi$
$599$	2.76061e15	1.46271	0.731354	+	0.681998i	$0.238889\pi$
$600$	−1.94861e14	−0.102304
$601$	8.93942e14	0.465050	0.232525	−	0.972590i	$-0.425301\pi$
$601$	8.93942e14	0.465050	0.232525	+	0.972590i	$0.425301\pi$
$602$	1.28496e14	0.0662381
$603$	−8.68415e14	−0.443590
$604$	1.28338e15	0.649610
$605$	−2.50373e15	−1.25583
$606$	9.04003e13	0.0449335
$607$	9.27961e14	0.457080	0.228540	−	0.973535i	$-0.426605\pi$
$607$	9.27961e14	0.457080	0.228540	+	0.973535i	$0.426605\pi$
$608$	−2.64190e14	−0.128958
$609$	−4.10964e14	−0.198796
$610$	2.45329e14	0.117607
$611$	−7.16198e13	−0.0340256
$612$	−1.33143e15	−0.626880
$613$	−2.04765e15	−0.955485	−0.477743	−	0.878500i	$-0.658545\pi$
$613$	−2.04765e15	−0.955485	−0.477743	+	0.878500i	$0.658545\pi$
$614$	4.95518e13	0.0229157
$615$	5.00755e14	0.229516
$616$	1.02845e14	0.0467185
$617$	1.00220e15	0.451217	0.225609	−	0.974218i	$-0.427563\pi$
$617$	1.00220e15	0.451217	0.225609	+	0.974218i	$0.427563\pi$
$618$	−8.52874e12	−0.00380582
$619$	2.85171e15	1.26126	0.630632	−	0.776082i	$-0.282796\pi$
$619$	2.85171e15	1.26126	0.630632	+	0.776082i	$0.282796\pi$
$620$	−6.19169e15	−2.71428
$621$	−5.24225e14	−0.227779
$622$	−2.78991e14	−0.120155
$623$	8.32339e14	0.355317
$624$	1.65846e14	0.0701761
$625$	−1.77744e15	−0.745513
$626$	−9.88249e13	−0.0410873
$627$	−3.25626e14	−0.134198
$628$	3.37105e15	1.37717
$629$	−9.44971e14	−0.382684
$630$	−7.33734e13	−0.0294555
$631$	7.28646e14	0.289971	0.144986	−	0.989434i	$-0.453686\pi$
$631$	7.28646e14	0.289971	0.144986	+	0.989434i	$0.453686\pi$
$632$	−2.25730e14	−0.0890524
$633$	−1.47980e15	−0.578737
$634$	2.99498e14	0.116119
$635$	−5.50091e15	−2.11436
$636$	2.82556e13	0.0107669
$637$	1.12595e14	0.0425357
$638$	−3.28405e13	−0.0122997
$639$	−2.82548e13	−0.0104915
$640$	1.16981e15	0.430650
$641$	−2.42963e15	−0.886790	−0.443395	−	0.896326i	$-0.646226\pi$
$641$	−2.42963e15	−0.886790	−0.443395	+	0.896326i	$0.646226\pi$
$642$	1.58418e14	0.0573273
$643$	−5.36655e15	−1.92546	−0.962730	−	0.270464i	$-0.912823\pi$
$643$	−5.36655e15	−1.92546	−0.962730	+	0.270464i	$0.912823\pi$
$644$	−2.67962e15	−0.953238
$645$	2.71197e15	0.956547
$646$	−2.34090e14	−0.0818662
$647$	2.30015e14	0.0797595	0.0398797	−	0.999204i	$-0.487303\pi$
$647$	2.30015e14	0.0797595	0.0398797	+	0.999204i	$0.487303\pi$
$648$	4.73141e13	0.0162678
$649$	−1.50483e14	−0.0513028
$650$	3.24663e13	0.0109751
$651$	−2.56015e15	−0.858163
$652$	−6.18756e14	−0.205664
$653$	−2.22055e14	−0.0731876	−0.0365938	−	0.999330i	$-0.511651\pi$
$653$	−2.22055e14	−0.0731876	−0.0365938	+	0.999330i	$0.511651\pi$
$654$	1.21511e14	0.0397136
$655$	−1.66241e15	−0.538780
$656$	−8.18572e14	−0.263079
$657$	1.14574e15	0.365153
$658$	−5.17963e13	−0.0163703
$659$	1.70683e15	0.534958	0.267479	−	0.963564i	$-0.413809\pi$
$659$	1.70683e15	0.534958	0.267479	+	0.963564i	$0.413809\pi$
$660$	1.08237e15	0.336421
$661$	3.88940e14	0.119888	0.0599438	−	0.998202i	$-0.480908\pi$
$661$	3.88940e14	0.119888	0.0599438	+	0.998202i	$0.480908\pi$
$662$	3.07761e14	0.0940793
$663$	4.44867e14	0.134867
$664$	1.72948e14	0.0519987
$665$	2.38141e15	0.710094
$666$	1.67451e13	0.00495198
$667$	1.71595e15	0.503284
$668$	−3.67406e15	−1.06875
$669$	−1.62774e15	−0.469615
$670$	5.07516e14	0.145224
$671$	−1.49637e15	−0.424684
$672$	3.63102e14	0.102211
$673$	2.57391e14	0.0718639	0.0359320	−	0.999354i	$-0.488560\pi$
$673$	2.57391e14	0.0718639	0.0359320	+	0.999354i	$0.488560\pi$
$674$	1.29490e14	0.0358596
$675$	−8.47954e14	−0.232917
$676$	3.59485e15	0.979432
$677$	−6.09512e15	−1.64719	−0.823596	−	0.567177i	$-0.808036\pi$
$677$	−6.09512e15	−1.64719	−0.823596	+	0.567177i	$0.808036\pi$
$678$	2.88458e14	0.0773248
$679$	−2.85721e15	−0.759729
$680$	1.56043e15	0.411571
$681$	3.11671e15	0.815432
$682$	−2.04584e14	−0.0530954
$683$	8.80864e14	0.226775	0.113388	−	0.993551i	$-0.463830\pi$
$683$	8.80864e14	0.226775	0.113388	+	0.993551i	$0.463830\pi$
$684$	−7.65741e14	−0.195557
$685$	4.59937e15	1.16520
$686$	3.17939e14	0.0799026
$687$	2.86700e15	0.714768
$688$	−4.43318e15	−1.09643
$689$	−9.44099e12	−0.00231639
$690$	3.06366e14	0.0745710
$691$	9.96161e14	0.240547	0.120274	−	0.992741i	$-0.461623\pi$
$691$	9.96161e14	0.240547	0.120274	+	0.992741i	$0.461623\pi$
$692$	−2.03744e15	−0.488091
$693$	4.47538e14	0.106365
$694$	−2.28707e14	−0.0539264
$695$	−1.00822e16	−2.35851
$696$	−1.54874e14	−0.0359441
$697$	−2.19575e15	−0.505594
$698$	−1.62076e13	−0.00370266
$699$	1.07476e15	0.243605
$700$	−4.33439e15	−0.974741
$701$	1.99748e15	0.445691	0.222846	−	0.974854i	$-0.428465\pi$
$701$	1.99748e15	0.445691	0.222846	+	0.974854i	$0.428465\pi$
$702$	−7.88313e12	−0.00174520
$703$	−5.43480e14	−0.119379
$704$	−1.74989e15	−0.381382
$705$	−1.09319e15	−0.236404
$706$	−4.04543e14	−0.0868038
$707$	4.03253e15	0.858561
$708$	−3.53875e14	−0.0747596
$709$	1.18551e15	0.248513	0.124257	−	0.992250i	$-0.460345\pi$
$709$	1.18551e15	0.248513	0.124257	+	0.992250i	$0.460345\pi$
$710$	1.65126e13	0.00343474
$711$	−9.82284e14	−0.202747
$712$	3.13671e14	0.0642443
$713$	1.06897e16	2.17257
$714$	3.21733e14	0.0648866
$715$	−3.61649e14	−0.0723776
$716$	−3.61767e15	−0.718467
$717$	−5.67909e15	−1.11924
$718$	5.29795e14	0.103615
$719$	−3.16369e15	−0.614023	−0.307011	−	0.951706i	$-0.599329\pi$
$719$	−3.16369e15	−0.614023	−0.307011	+	0.951706i	$0.599329\pi$
$720$	2.53143e15	0.487570
$721$	−3.80446e14	−0.0727192
$722$	2.52328e14	0.0478643
$723$	−2.05797e15	−0.387417
$724$	−1.85545e15	−0.346646
$725$	2.77562e15	0.514636
$726$	−1.94542e14	−0.0357982
$727$	−1.22235e15	−0.223231	−0.111616	−	0.993751i	$-0.535603\pi$
$727$	−1.22235e15	−0.223231	−0.111616	+	0.993751i	$0.535603\pi$
$728$	−8.08089e13	−0.0146466
$729$	2.05891e14	0.0370370
$730$	−6.69587e14	−0.119545
$731$	−1.18916e16	−2.10715
$732$	−3.51887e15	−0.618860
$733$	1.08174e15	0.188822	0.0944108	−	0.995533i	$-0.469903\pi$
$733$	1.08174e15	0.188822	0.0944108	+	0.995533i	$0.469903\pi$
$734$	5.38660e14	0.0933225
$735$	1.71863e15	0.295530
$736$	−1.51611e15	−0.258763
$737$	−3.09557e15	−0.524409
$738$	3.89091e13	0.00654246
$739$	9.51167e15	1.58749	0.793747	−	0.608248i	$-0.208127\pi$
$739$	9.51167e15	1.58749	0.793747	+	0.608248i	$0.208127\pi$
$740$	1.80651e15	0.299271
$741$	2.55855e14	0.0420721
$742$	−6.82784e12	−0.00111445
$743$	8.40092e15	1.36110	0.680548	−	0.732704i	$-0.261742\pi$
$743$	8.40092e15	1.36110	0.680548	+	0.732704i	$0.261742\pi$
$744$	−9.64804e14	−0.155163
$745$	−6.12124e15	−0.977192
$746$	2.29404e14	0.0363528
$747$	7.52600e14	0.118386
$748$	−4.74604e15	−0.741092
$749$	7.06662e15	1.09537
$750$	8.60982e13	0.0132482
$751$	5.38899e15	0.823167	0.411583	−	0.911372i	$-0.364976\pi$
$751$	5.38899e15	0.823167	0.411583	+	0.911372i	$0.364976\pi$
$752$	1.78700e15	0.270974
$753$	4.84204e15	0.728880
$754$	2.58039e13	0.00385606
$755$	−6.54531e15	−0.971006
$756$	1.05243e15	0.154997
$757$	−7.91662e15	−1.15748	−0.578739	−	0.815513i	$-0.696455\pi$
$757$	−7.91662e15	−1.15748	−0.578739	+	0.815513i	$0.696455\pi$
$758$	−6.10796e14	−0.0886575
$759$	−1.86867e15	−0.269279
$760$	8.97447e14	0.128391
$761$	−4.02627e15	−0.571857	−0.285928	−	0.958251i	$-0.592302\pi$
$761$	−4.02627e15	−0.571857	−0.285928	+	0.958251i	$0.592302\pi$
$762$	−4.27425e14	−0.0602709
$763$	5.42031e15	0.758821
$764$	−5.23230e15	−0.727242
$765$	6.79034e15	0.937030
$766$	−3.04649e14	−0.0417390
$767$	1.18240e14	0.0160838
$768$	−4.04643e15	−0.546494
$769$	−1.17462e16	−1.57508	−0.787541	−	0.616263i	$-0.788646\pi$
$769$	−1.17462e16	−1.57508	−0.787541	+	0.616263i	$0.788646\pi$
$770$	−2.61549e14	−0.0348220
$771$	−5.48892e13	−0.00725585
$772$	−6.04975e15	−0.794040
$773$	5.51156e15	0.718270	0.359135	−	0.933286i	$-0.383072\pi$
$773$	5.51156e15	0.718270	0.359135	+	0.933286i	$0.383072\pi$
$774$	2.10722e14	0.0272668
$775$	1.72910e16	2.22158
$776$	−1.07675e15	−0.137365
$777$	7.46957e14	0.0946193
$778$	6.78076e14	0.0852885
$779$	−1.26284e15	−0.157722
$780$	−8.50454e14	−0.105470
$781$	−1.00718e14	−0.0124030
$782$	−1.34337e15	−0.164270
$783$	−6.73946e14	−0.0818343
$784$	−2.80940e15	−0.338746
$785$	−1.71925e16	−2.05853
$786$	−1.29171e14	−0.0153582
$787$	−7.24348e15	−0.855237	−0.427618	−	0.903959i	$-0.640647\pi$
$787$	−7.24348e15	−0.855237	−0.427618	+	0.903959i	$0.640647\pi$
$788$	7.32955e15	0.859376
$789$	2.74248e15	0.319315
$790$	5.74063e14	0.0663759
$791$	1.28674e16	1.47747
$792$	1.68657e14	0.0192316
$793$	1.17575e15	0.133142
$794$	−3.51857e14	−0.0395689
$795$	−1.44105e14	−0.0160938
$796$	−1.55698e16	−1.72688
$797$	−9.01023e15	−0.992465	−0.496233	−	0.868190i	$-0.665284\pi$
$797$	−9.01023e15	−0.992465	−0.496233	+	0.868190i	$0.665284\pi$
$798$	1.85038e14	0.0202416
$799$	4.79348e15	0.520767
$800$	−2.45236e15	−0.264600
$801$	1.36496e15	0.146266
$802$	1.14944e15	0.122328
$803$	4.08412e15	0.431681
$804$	−7.27955e15	−0.764181
$805$	1.36662e16	1.42485
$806$	1.60749e14	0.0166458
$807$	−5.17517e15	−0.532256
$808$	1.51968e15	0.155235
$809$	−6.21630e15	−0.630689	−0.315345	−	0.948977i	$-0.602120\pi$
$809$	−6.21630e15	−0.630689	−0.315345	+	0.948977i	$0.602120\pi$
$810$	−1.20326e14	−0.0121253
$811$	9.36711e15	0.937542	0.468771	−	0.883320i	$-0.344697\pi$
$811$	9.36711e15	0.937542	0.468771	+	0.883320i	$0.344697\pi$
$812$	−3.44494e15	−0.342470
$813$	−1.26764e15	−0.125169
$814$	5.96900e13	0.00585419
$815$	3.15569e15	0.307416
$816$	−1.11000e16	−1.07406
$817$	−6.83921e15	−0.657332
$818$	−8.74533e14	−0.0834897
$819$	−3.51647e14	−0.0333461
$820$	4.19762e15	0.395391
$821$	1.82498e16	1.70754	0.853768	−	0.520654i	$-0.174312\pi$
$821$	1.82498e16	1.70754	0.853768	+	0.520654i	$0.174312\pi$
$822$	3.57375e14	0.0332146
$823$	1.96146e16	1.81084	0.905422	−	0.424513i	$-0.139555\pi$
$823$	1.96146e16	1.81084	0.905422	+	0.424513i	$0.139555\pi$
$824$	−1.43373e14	−0.0131482
$825$	−3.02264e15	−0.275353
$826$	8.55123e13	0.00773817
$827$	−1.78609e15	−0.160555	−0.0802773	−	0.996773i	$-0.525581\pi$
$827$	−1.78609e15	−0.160555	−0.0802773	+	0.996773i	$0.525581\pi$
$828$	−4.39435e15	−0.392399
$829$	1.19781e16	1.06252	0.531261	−	0.847208i	$-0.321718\pi$
$829$	1.19781e16	1.06252	0.531261	+	0.847208i	$0.321718\pi$
$830$	−4.39832e14	−0.0387576
$831$	8.76766e15	0.767499
$832$	1.37495e15	0.119566
$833$	−7.53595e15	−0.651015
$834$	−7.83392e14	−0.0672304
$835$	1.87379e16	1.59752
$836$	−2.72958e15	−0.231186
$837$	−4.19842e15	−0.353261
$838$	1.64330e15	0.137365
$839$	1.03328e15	0.0858076	0.0429038	−	0.999079i	$-0.486339\pi$
$839$	1.03328e15	0.0858076	0.0429038	+	0.999079i	$0.486339\pi$
$840$	−1.23345e15	−0.101762
$841$	−9.99447e15	−0.819185
$842$	7.12736e14	0.0580380
$843$	2.30199e15	0.186231
$844$	−1.24045e16	−0.997001
$845$	−1.83339e16	−1.46401
$846$	−8.49415e13	−0.00673880
$847$	−8.67801e15	−0.684009
$848$	2.35565e14	0.0184473
$849$	−3.00431e14	−0.0233750
$850$	−2.17296e15	−0.167976
$851$	−3.11886e15	−0.239543
$852$	−2.36848e14	−0.0180739
$853$	−4.84684e15	−0.367484	−0.183742	−	0.982974i	$-0.558821\pi$
$853$	−4.84684e15	−0.367484	−0.183742	+	0.982974i	$0.558821\pi$
$854$	8.50318e14	0.0640565
$855$	3.90532e15	0.292309
$856$	2.66309e15	0.198053
$857$	2.05524e16	1.51868	0.759342	−	0.650692i	$-0.225521\pi$
$857$	2.05524e16	1.51868	0.759342	+	0.650692i	$0.225521\pi$
$858$	−2.81004e13	−0.00206316
$859$	7.33281e15	0.534944	0.267472	−	0.963566i	$-0.413812\pi$
$859$	7.33281e15	0.534944	0.267472	+	0.963566i	$0.413812\pi$
$860$	2.27333e16	1.64786
$861$	1.73564e15	0.125009
$862$	−2.05991e13	−0.00147421
$863$	1.33948e16	0.952526	0.476263	−	0.879303i	$-0.341991\pi$
$863$	1.33948e16	0.952526	0.476263	+	0.879303i	$0.341991\pi$
$864$	5.95456e14	0.0420750
$865$	1.03910e16	0.729574
$866$	−1.74540e14	−0.0121772
$867$	−2.14467e16	−1.48681
$868$	−2.14606e16	−1.47837
$869$	−3.50147e15	−0.239686
$870$	3.93865e14	0.0267912
$871$	2.43230e15	0.164406
$872$	2.04267e15	0.137201
$873$	−4.68559e15	−0.312741
$874$	−7.72612e14	−0.0512447
$875$	3.84063e15	0.253138
$876$	9.60422e15	0.629056
$877$	7.59948e15	0.494636	0.247318	−	0.968934i	$-0.420451\pi$
$877$	7.59948e15	0.494636	0.247318	+	0.968934i	$0.420451\pi$
$878$	−1.38347e15	−0.0894848
$879$	3.19177e14	0.0205160
$880$	9.02360e15	0.576402
$881$	−2.82049e16	−1.79043	−0.895213	−	0.445638i	$-0.852977\pi$
$881$	−2.82049e16	−1.79043	−0.895213	+	0.445638i	$0.852977\pi$
$882$	1.33539e14	0.00842422
$883$	−7.08941e15	−0.444453	−0.222227	−	0.974995i	$-0.571332\pi$
$883$	−7.08941e15	−0.444453	−0.222227	+	0.974995i	$0.571332\pi$
$884$	3.72913e15	0.232338
$885$	1.80478e15	0.111747
$886$	−1.26310e15	−0.0777237
$887$	−2.49307e15	−0.152459	−0.0762296	−	0.997090i	$-0.524288\pi$
$887$	−2.49307e15	−0.152459	−0.0762296	+	0.997090i	$0.524288\pi$
$888$	2.81494e14	0.0171080
$889$	−1.90664e16	−1.15162
$890$	−7.97708e14	−0.0478849
$891$	7.33925e14	0.0437849
$892$	−1.36447e16	−0.809014
$893$	2.75687e15	0.162455
$894$	−4.75625e14	−0.0278553
$895$	1.84503e16	1.07393
$896$	4.05460e15	0.234560
$897$	1.46828e15	0.0844208
$898$	−7.49613e14	−0.0428368
$899$	1.37428e16	0.780540
$900$	−7.10803e15	−0.401251
$901$	6.31882e14	0.0354527
$902$	1.38696e14	0.00773444
$903$	9.39978e15	0.520997
$904$	4.84913e15	0.267139
$905$	9.46287e15	0.518150
$906$	−5.08575e14	−0.0276790
$907$	5.93175e15	0.320880	0.160440	−	0.987046i	$-0.448709\pi$
$907$	5.93175e15	0.320880	0.160440	+	0.987046i	$0.448709\pi$
$908$	2.61261e16	1.40476
$909$	6.61301e15	0.353425
$910$	2.05508e14	0.0109170
$911$	1.05821e16	0.558754	0.279377	−	0.960182i	$-0.409872\pi$
$911$	1.05821e16	0.558754	0.279377	+	0.960182i	$0.409872\pi$
$912$	−6.38392e15	−0.335055
$913$	2.68274e15	0.139955
$914$	6.52252e14	0.0338230
$915$	1.79464e16	0.925042
$916$	2.40328e16	1.23134
$917$	−5.76198e15	−0.293454
$918$	5.27614e14	0.0267105
$919$	6.28506e15	0.316282	0.158141	−	0.987417i	$-0.449450\pi$
$919$	6.28506e15	0.316282	0.158141	+	0.987417i	$0.449450\pi$
$920$	5.15018e15	0.257626
$921$	3.62484e15	0.180244
$922$	−2.71887e15	−0.134390
$923$	7.91374e13	0.00388842
$924$	3.75152e15	0.183236
$925$	−5.04488e15	−0.244947
$926$	−1.69368e15	−0.0817471
$927$	−6.23899e14	−0.0299347
$928$	−1.94911e15	−0.0929659
$929$	1.25567e13	0.000595374 0	0.000297687	−	1.00000i	$-0.499905\pi$
$929$	1.25567e13	0.000595374 0	0.000297687		1.00000i	$0.499905\pi$
$930$	2.45363e15	0.115652
$931$	−4.33414e15	−0.203086
$932$	9.00924e15	0.419663
$933$	−2.04089e16	−0.945083
$934$	4.10043e14	0.0188765
$935$	2.42050e16	1.10775
$936$	−1.32520e14	−0.00602925
$937$	−1.43024e16	−0.646907	−0.323453	−	0.946244i	$-0.604844\pi$
$937$	−1.43024e16	−0.646907	−0.323453	+	0.946244i	$0.604844\pi$
$938$	1.75907e15	0.0790983
$939$	−7.22929e15	−0.323173
$940$	−9.16372e15	−0.407257
$941$	8.90168e15	0.393304	0.196652	−	0.980473i	$-0.436993\pi$
$941$	8.90168e15	0.393304	0.196652	+	0.980473i	$0.436993\pi$
$942$	−1.33587e15	−0.0586793
$943$	−7.24703e15	−0.316480
$944$	−2.95023e15	−0.128088
$945$	−5.36745e15	−0.231682
$946$	7.51145e14	0.0322346
$947$	−7.97878e15	−0.340417	−0.170209	−	0.985408i	$-0.554444\pi$
$947$	−7.97878e15	−0.340417	−0.170209	+	0.985408i	$0.554444\pi$
$948$	−8.23406e15	−0.349276
$949$	−3.20904e15	−0.135335
$950$	−1.24973e15	−0.0524006
$951$	2.19091e16	0.913336
$952$	5.40851e15	0.224168
$953$	−3.43098e16	−1.41386	−0.706932	−	0.707282i	$-0.749921\pi$
$953$	−3.43098e16	−1.41386	−0.706932	+	0.707282i	$0.749921\pi$
$954$	−1.11971e13	−0.000458763 0
$955$	2.66850e16	1.08705
$956$	−4.76054e16	−1.92814
$957$	−2.40236e15	−0.0967438
$958$	1.73806e15	0.0695911
$959$	1.59416e16	0.634643
$960$	2.09869e16	0.830722
$961$	6.02036e16	2.36943
$962$	−4.69005e13	−0.00183533
$963$	1.15887e16	0.450909
$964$	−1.72511e16	−0.667410
$965$	3.08540e16	1.18689
$966$	1.06187e15	0.0406162
$967$	−3.86522e16	−1.47004	−0.735019	−	0.678047i	$-0.762827\pi$
$967$	−3.86522e16	−1.47004	−0.735019	+	0.678047i	$0.762827\pi$
$968$	−3.27035e15	−0.123674
$969$	−1.71243e16	−0.643920
$970$	2.73833e15	0.102386
$971$	−1.63748e16	−0.608794	−0.304397	−	0.952545i	$-0.598455\pi$
$971$	−1.63748e16	−0.608794	−0.304397	+	0.952545i	$0.598455\pi$
$972$	1.72590e15	0.0638044
$973$	−3.49452e16	−1.28460
$974$	1.97311e15	0.0721236
$975$	2.37499e15	0.0863251
$976$	−2.93365e16	−1.06031
$977$	3.71306e16	1.33448	0.667239	−	0.744844i	$-0.267476\pi$
$977$	3.71306e16	1.33448	0.667239	+	0.744844i	$0.267476\pi$
$978$	2.45199e14	0.00876305
$979$	4.86559e15	0.172914
$980$	1.44065e16	0.509115
$981$	8.88885e15	0.312368
$982$	−1.00657e15	−0.0351746
$983$	−4.04066e16	−1.40413	−0.702066	−	0.712112i	$-0.747739\pi$
$983$	−4.04066e16	−1.40413	−0.702066	+	0.712112i	$0.747739\pi$
$984$	6.54083e14	0.0226027
$985$	−3.73811e16	−1.28455
$986$	−1.72705e15	−0.0590175
$987$	−3.78903e15	−0.128761
$988$	2.14473e15	0.0724785
$989$	−3.92481e16	−1.31898
$990$	−4.28918e14	−0.0143344
$991$	2.25060e16	0.747987	0.373993	−	0.927431i	$-0.377988\pi$
$991$	2.25060e16	0.747987	0.373993	+	0.927431i	$0.377988\pi$
$992$	−1.21422e16	−0.401314
$993$	2.25135e16	0.739983
$994$	5.72331e13	0.00187078
$995$	7.94069e16	2.58126
$996$	6.30872e15	0.203946
$997$	3.07794e16	0.989548	0.494774	−	0.869022i	$-0.335251\pi$
$997$	3.07794e16	0.989548	0.494774	+	0.869022i	$0.335251\pi$
$998$	−2.39773e15	−0.0766625
$999$	1.22494e15	0.0389499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.15	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-3.32183 q^{2} -243.000 q^{3} -2036.97 q^{4} +10388.6 q^{5} +807.204 q^{6} +36007.4 q^{7} +13569.5 q^{8} +59049.0 q^{9} -34509.2 q^{10} +210488. q^{11} +494983. q^{12} -165388. q^{13} -119610. q^{14} -2.52444e6 q^{15} +4.12663e6 q^{16} +1.10693e7 q^{17} -196151. q^{18} +6.36628e6 q^{19} -2.11613e7 q^{20} -8.74979e6 q^{21} -699203. q^{22} +3.65341e7 q^{23} -3.29740e6 q^{24} +5.90953e7 q^{25} +549389. q^{26} -1.43489e7 q^{27} -7.33458e7 q^{28} +4.69684e7 q^{29} +8.38574e6 q^{30} +2.92595e8 q^{31} -4.14984e7 q^{32} -5.11485e7 q^{33} -3.67704e7 q^{34} +3.74067e8 q^{35} -1.20281e8 q^{36} -8.53685e7 q^{37} -2.11477e7 q^{38} +4.01892e7 q^{39} +1.40969e8 q^{40} -1.98363e8 q^{41} +2.90653e7 q^{42} -1.07429e9 q^{43} -4.28756e8 q^{44} +6.13438e8 q^{45} -1.21360e8 q^{46} +4.33042e8 q^{47} -1.00277e9 q^{48} -6.80797e8 q^{49} -1.96305e8 q^{50} -2.68984e9 q^{51} +3.36889e8 q^{52} +5.70841e7 q^{53} +4.76646e7 q^{54} +2.18668e9 q^{55} +4.88604e8 q^{56} -1.54701e9 q^{57} -1.56021e8 q^{58} -7.14924e8 q^{59} +5.14219e9 q^{60} -7.10908e9 q^{61} -9.71951e8 q^{62} +2.12620e9 q^{63} -8.31349e9 q^{64} -1.71815e9 q^{65} +1.69906e8 q^{66} -1.47067e10 q^{67} -2.25478e10 q^{68} -8.87779e9 q^{69} -1.24259e9 q^{70} -4.78497e8 q^{71} +8.01268e8 q^{72} +1.94031e10 q^{73} +2.83579e8 q^{74} -1.43602e10 q^{75} -1.29679e10 q^{76} +7.57910e9 q^{77} -1.33501e8 q^{78} -1.66351e10 q^{79} +4.28700e10 q^{80} +3.48678e9 q^{81} +6.58929e8 q^{82} +1.27453e10 q^{83} +1.78230e10 q^{84} +1.14995e11 q^{85} +3.56860e9 q^{86} -1.14133e10 q^{87} +2.85622e9 q^{88} +2.31158e10 q^{89} -2.03773e9 q^{90} -5.95517e9 q^{91} -7.44188e10 q^{92} -7.11007e10 q^{93} -1.43849e9 q^{94} +6.61369e10 q^{95} +1.00841e10 q^{96} -7.93508e10 q^{97} +2.26149e9 q^{98} +1.24291e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more