LMFDB - Embedded newform 177.12.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q+18.0234 q^{2} -243.000 q^{3} -1723.16 q^{4} -3879.65 q^{5} -4379.69 q^{6} +32120.2 q^{7} -67969.1 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+18.0234 q^{2} -243.000 q^{3} -1723.16 q^{4} -3879.65 q^{5} -4379.69 q^{6} +32120.2 q^{7} -67969.1 q^{8} +59049.0 q^{9} -69924.5 q^{10} -362420. q^{11} +418727. q^{12} -286043. q^{13} +578915. q^{14} +942754. q^{15} +2.30399e6 q^{16} +9.02842e6 q^{17} +1.06426e6 q^{18} -2.13529e7 q^{19} +6.68524e6 q^{20} -7.80520e6 q^{21} -6.53205e6 q^{22} -5.38940e7 q^{23} +1.65165e7 q^{24} -3.37765e7 q^{25} -5.15548e6 q^{26} -1.43489e7 q^{27} -5.53480e7 q^{28} +1.58491e8 q^{29} +1.69917e7 q^{30} -1.44016e8 q^{31} +1.80727e8 q^{32} +8.80681e7 q^{33} +1.62723e8 q^{34} -1.24615e8 q^{35} -1.01751e8 q^{36} -1.68394e8 q^{37} -3.84852e8 q^{38} +6.95085e7 q^{39} +2.63696e8 q^{40} -1.21824e9 q^{41} -1.40676e8 q^{42} -6.48935e8 q^{43} +6.24507e8 q^{44} -2.29089e8 q^{45} -9.71354e8 q^{46} +1.87600e8 q^{47} -5.59869e8 q^{48} -9.45622e8 q^{49} -6.08767e8 q^{50} -2.19391e9 q^{51} +4.92897e8 q^{52} -2.62856e9 q^{53} -2.58616e8 q^{54} +1.40606e9 q^{55} -2.18318e9 q^{56} +5.18875e9 q^{57} +2.85655e9 q^{58} -7.14924e8 q^{59} -1.62451e9 q^{60} -3.26106e9 q^{61} -2.59565e9 q^{62} +1.89666e9 q^{63} -1.46126e9 q^{64} +1.10975e9 q^{65} +1.58729e9 q^{66} +1.11768e10 q^{67} -1.55574e10 q^{68} +1.30962e10 q^{69} -2.24599e9 q^{70} -1.81403e10 q^{71} -4.01351e9 q^{72} -4.66168e9 q^{73} -3.03503e9 q^{74} +8.20768e9 q^{75} +3.67943e10 q^{76} -1.16410e10 q^{77} +1.25278e9 q^{78} +3.85674e10 q^{79} -8.93866e9 q^{80} +3.48678e9 q^{81} -2.19569e10 q^{82} +4.48401e10 q^{83} +1.34496e10 q^{84} -3.50271e10 q^{85} -1.16960e10 q^{86} -3.85133e10 q^{87} +2.46334e10 q^{88} +8.91551e10 q^{89} -4.12897e9 q^{90} -9.18775e9 q^{91} +9.28678e10 q^{92} +3.49958e10 q^{93} +3.38120e9 q^{94} +8.28416e10 q^{95} -4.39165e10 q^{96} -1.14808e11 q^{97} -1.70434e10 q^{98} -2.14006e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	18.0234	0.398265	0.199133	−	0.979973i	$-0.436188\pi$
$2$	18.0234	0.398265	0.199133	+	0.979973i	$0.436188\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1723.16	−0.841385
$5$	−3879.65	−0.555210	−0.277605	−	0.960695i	$-0.589541\pi$
$5$	−3879.65	−0.555210	−0.277605	+	0.960695i	$0.589541\pi$
$6$	−4379.69	−0.229938
$7$	32120.2	0.722335	0.361167	−	0.932501i	$-0.382378\pi$
$7$	32120.2	0.722335	0.361167	+	0.932501i	$0.382378\pi$
$8$	−67969.1	−0.733359
$9$	59049.0	0.333333
$10$	−69924.5	−0.221121
$11$	−362420.	−0.678505	−0.339252	−	0.940695i	$-0.610174\pi$
$11$	−362420.	−0.678505	−0.339252	+	0.940695i	$0.610174\pi$
$12$	418727.	0.485774
$13$	−286043.	−0.213670	−0.106835	−	0.994277i	$-0.534072\pi$
$13$	−286043.	−0.213670	−0.106835	+	0.994277i	$0.534072\pi$
$14$	578915.	0.287681
$15$	942754.	0.320551
$16$	2.30399e6	0.549314
$17$	9.02842e6	1.54221	0.771104	−	0.636710i	$-0.219705\pi$
$17$	9.02842e6	1.54221	0.771104	+	0.636710i	$0.219705\pi$
$18$	1.06426e6	0.132755
$19$	−2.13529e7	−1.97839	−0.989194	−	0.146615i	$-0.953162\pi$
$19$	−2.13529e7	−1.97839	−0.989194	+	0.146615i	$0.953162\pi$
$20$	6.68524e6	0.467145
$21$	−7.80520e6	−0.417040
$22$	−6.53205e6	−0.270225
$23$	−5.38940e7	−1.74597	−0.872986	−	0.487745i	$-0.837820\pi$
$23$	−5.38940e7	−1.74597	−0.872986	+	0.487745i	$0.837820\pi$
$24$	1.65165e7	0.423405
$25$	−3.37765e7	−0.691742
$26$	−5.15548e6	−0.0850972
$27$	−1.43489e7	−0.192450
$28$	−5.53480e7	−0.607761
$29$	1.58491e8	1.43488	0.717440	−	0.696621i	$-0.245314\pi$
$29$	1.58491e8	1.43488	0.717440	+	0.696621i	$0.245314\pi$
$30$	1.69917e7	0.127664
$31$	−1.44016e8	−0.903483	−0.451742	−	0.892149i	$-0.649197\pi$
$31$	−1.44016e8	−0.903483	−0.451742	+	0.892149i	$0.649197\pi$
$32$	1.80727e8	0.952132
$33$	8.80681e7	0.391735
$34$	1.62723e8	0.614207
$35$	−1.24615e8	−0.401047
$36$	−1.01751e8	−0.280462
$37$	−1.68394e8	−0.399224	−0.199612	−	0.979875i	$-0.563968\pi$
$37$	−1.68394e8	−0.399224	−0.199612	+	0.979875i	$0.563968\pi$
$38$	−3.84852e8	−0.787923
$39$	6.95085e7	0.123362
$40$	2.63696e8	0.407168
$41$	−1.21824e9	−1.64219	−0.821093	−	0.570795i	$-0.806635\pi$
$41$	−1.21824e9	−1.64219	−0.821093	+	0.570795i	$0.806635\pi$
$42$	−1.40676e8	−0.166092
$43$	−6.48935e8	−0.673170	−0.336585	−	0.941653i	$-0.609272\pi$
$43$	−6.48935e8	−0.673170	−0.336585	+	0.941653i	$0.609272\pi$
$44$	6.24507e8	0.570884
$45$	−2.29089e8	−0.185070
$46$	−9.71354e8	−0.695360
$47$	1.87600e8	0.119315	0.0596576	−	0.998219i	$-0.480999\pi$
$47$	1.87600e8	0.119315	0.0596576	+	0.998219i	$0.480999\pi$
$48$	−5.59869e8	−0.317146
$49$	−9.45622e8	−0.478233
$50$	−6.08767e8	−0.275497
$51$	−2.19391e9	−0.890394
$52$	4.92897e8	0.179779
$53$	−2.62856e9	−0.863376	−0.431688	−	0.902023i	$-0.642082\pi$
$53$	−2.62856e9	−0.863376	−0.431688	+	0.902023i	$0.642082\pi$
$54$	−2.58616e8	−0.0766462
$55$	1.40606e9	0.376712
$56$	−2.18318e9	−0.529731
$57$	5.18875e9	1.14222
$58$	2.85655e9	0.571462
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.62451e9	−0.269706
$61$	−3.26106e9	−0.494361	−0.247181	−	0.968969i	$-0.579504\pi$
$61$	−3.26106e9	−0.494361	−0.247181	+	0.968969i	$0.579504\pi$
$62$	−2.59565e9	−0.359826
$63$	1.89666e9	0.240778
$64$	−1.46126e9	−0.170113
$65$	1.10975e9	0.118632
$66$	1.58729e9	0.156014
$67$	1.11768e10	1.01136	0.505681	−	0.862721i	$-0.331241\pi$
$67$	1.11768e10	1.01136	0.505681	+	0.862721i	$0.331241\pi$
$68$	−1.55574e10	−1.29759
$69$	1.30962e10	1.00804
$70$	−2.24599e9	−0.159723
$71$	−1.81403e10	−1.19323	−0.596614	−	0.802528i	$-0.703488\pi$
$71$	−1.81403e10	−1.19323	−0.596614	+	0.802528i	$0.703488\pi$
$72$	−4.01351e9	−0.244453
$73$	−4.66168e9	−0.263188	−0.131594	−	0.991304i	$-0.542010\pi$
$73$	−4.66168e9	−0.263188	−0.131594	+	0.991304i	$0.542010\pi$
$74$	−3.03503e9	−0.158997
$75$	8.20768e9	0.399377
$76$	3.67943e10	1.66459
$77$	−1.16410e10	−0.490107
$78$	1.25278e9	0.0491309
$79$	3.85674e10	1.41017	0.705085	−	0.709122i	$-0.250909\pi$
$79$	3.85674e10	1.41017	0.705085	+	0.709122i	$0.250909\pi$
$80$	−8.93866e9	−0.304984
$81$	3.48678e9	0.111111
$82$	−2.19569e10	−0.654025
$83$	4.48401e10	1.24950	0.624751	−	0.780824i	$-0.285201\pi$
$83$	4.48401e10	1.24950	0.624751	+	0.780824i	$0.285201\pi$
$84$	1.34496e10	0.350891
$85$	−3.50271e10	−0.856249
$86$	−1.16960e10	−0.268100
$87$	−3.85133e10	−0.828428
$88$	2.46334e10	0.497588
$89$	8.91551e10	1.69239	0.846197	−	0.532871i	$-0.178887\pi$
$89$	8.91551e10	1.69239	0.846197	+	0.532871i	$0.178887\pi$
$90$	−4.12897e9	−0.0737069
$91$	−9.18775e9	−0.154341
$92$	9.28678e10	1.46904
$93$	3.49958e10	0.521626
$94$	3.38120e9	0.0475190
$95$	8.28416e10	1.09842
$96$	−4.39165e10	−0.549713
$97$	−1.14808e11	−1.35746	−0.678731	−	0.734387i	$-0.737470\pi$
$97$	−1.14808e11	−1.35746	−0.678731	+	0.734387i	$0.737470\pi$
$98$	−1.70434e10	−0.190463
$99$	−2.14006e10	−0.226168
$100$	5.82021e10	0.582021
$101$	−1.27258e11	−1.20481	−0.602404	−	0.798192i	$-0.705790\pi$
$101$	−1.27258e11	−1.20481	−0.602404	+	0.798192i	$0.705790\pi$
$102$	−3.95417e10	−0.354613
$103$	1.39054e11	1.18189	0.590945	−	0.806712i	$-0.298755\pi$
$103$	1.39054e11	1.18189	0.590945	+	0.806712i	$0.298755\pi$
$104$	1.94421e10	0.156697
$105$	3.02814e10	0.231545
$106$	−4.73756e10	−0.343853
$107$	−2.97788e10	−0.205257	−0.102628	−	0.994720i	$-0.532725\pi$
$107$	−2.97788e10	−0.205257	−0.102628	+	0.994720i	$0.532725\pi$
$108$	2.47254e10	0.161925
$109$	1.33959e11	0.833924	0.416962	−	0.908924i	$-0.363095\pi$
$109$	1.33959e11	0.833924	0.416962	+	0.908924i	$0.363095\pi$
$110$	2.53421e10	0.150031
$111$	4.09197e10	0.230492
$112$	7.40044e10	0.396788
$113$	−1.64153e11	−0.838140	−0.419070	−	0.907954i	$-0.637644\pi$
$113$	−1.64153e11	−0.838140	−0.419070	+	0.907954i	$0.637644\pi$
$114$	9.35189e10	0.454907
$115$	2.09090e11	0.969381
$116$	−2.73105e11	−1.20729
$117$	−1.68906e10	−0.0712233
$118$	−1.28854e10	−0.0518497
$119$	2.89994e11	1.11399
$120$	−6.40782e10	−0.235079
$121$	−1.53963e11	−0.539632
$122$	−5.87754e10	−0.196887
$123$	2.96033e11	0.948116
$124$	2.48161e11	0.760177
$125$	3.20477e11	0.939272
$126$	3.41844e10	0.0958935
$127$	2.89349e11	0.777143	0.388571	−	0.921419i	$-0.372969\pi$
$127$	2.89349e11	0.777143	0.388571	+	0.921419i	$0.372969\pi$
$128$	−3.96465e11	−1.01988
$129$	1.57691e11	0.388655
$130$	2.00014e10	0.0472468
$131$	5.85181e11	1.32525	0.662625	−	0.748951i	$-0.269442\pi$
$131$	5.85181e11	1.32525	0.662625	+	0.748951i	$0.269442\pi$
$132$	−1.51755e11	−0.329600
$133$	−6.85857e11	−1.42906
$134$	2.01444e11	0.402790
$135$	5.56687e10	0.106850
$136$	−6.13654e11	−1.13099
$137$	2.05345e11	0.363514	0.181757	−	0.983344i	$-0.441822\pi$
$137$	2.05345e11	0.363514	0.181757	+	0.983344i	$0.441822\pi$
$138$	2.36039e11	0.401466
$139$	1.85933e11	0.303930	0.151965	−	0.988386i	$-0.451440\pi$
$139$	1.85933e11	0.303930	0.151965	+	0.988386i	$0.451440\pi$
$140$	2.14731e11	0.337435
$141$	−4.55869e10	−0.0688866
$142$	−3.26950e11	−0.475221
$143$	1.03668e11	0.144976
$144$	1.36048e11	0.183105
$145$	−6.14889e11	−0.796659
$146$	−8.40194e10	−0.104819
$147$	2.29786e11	0.276108
$148$	2.90169e11	0.335901
$149$	1.54005e11	0.171794	0.0858972	−	0.996304i	$-0.472624\pi$
$149$	1.54005e11	0.171794	0.0858972	+	0.996304i	$0.472624\pi$
$150$	1.47930e11	0.159058
$151$	4.71655e11	0.488935	0.244467	−	0.969658i	$-0.421387\pi$
$151$	4.71655e11	0.488935	0.244467	+	0.969658i	$0.421387\pi$
$152$	1.45134e12	1.45087
$153$	5.33119e11	0.514069
$154$	−2.09811e11	−0.195193
$155$	5.58730e11	0.501623
$156$	−1.19774e11	−0.103795
$157$	−2.47986e11	−0.207481	−0.103740	−	0.994604i	$-0.533081\pi$
$157$	−2.47986e11	−0.207481	−0.103740	+	0.994604i	$0.533081\pi$
$158$	6.95117e11	0.561622
$159$	6.38739e11	0.498470
$160$	−7.01155e11	−0.528633
$161$	−1.73108e12	−1.26118
$162$	6.28438e10	0.0442517
$163$	6.84742e11	0.466117	0.233059	−	0.972463i	$-0.425127\pi$
$163$	6.84742e11	0.466117	0.233059	+	0.972463i	$0.425127\pi$
$164$	2.09922e12	1.38171
$165$	−3.41673e11	−0.217495
$166$	8.08171e11	0.497633
$167$	1.79932e12	1.07193	0.535967	−	0.844239i	$-0.319947\pi$
$167$	1.79932e12	1.07193	0.535967	+	0.844239i	$0.319947\pi$
$168$	5.30513e11	0.305840
$169$	−1.71034e12	−0.954345
$170$	−6.31308e11	−0.341014
$171$	−1.26087e12	−0.659462
$172$	1.11822e12	0.566395
$173$	2.05890e11	0.101014	0.0505070	−	0.998724i	$-0.483916\pi$
$173$	2.05890e11	0.101014	0.0505070	+	0.998724i	$0.483916\pi$
$174$	−6.94141e11	−0.329934
$175$	−1.08491e12	−0.499669
$176$	−8.35012e11	−0.372712
$177$	1.73727e11	0.0751646
$178$	1.60688e12	0.674021
$179$	−3.45127e12	−1.40374	−0.701872	−	0.712304i	$-0.747652\pi$
$179$	−3.45127e12	−1.40374	−0.701872	+	0.712304i	$0.747652\pi$
$180$	3.94757e11	0.155715
$181$	−3.37062e12	−1.28967	−0.644834	−	0.764323i	$-0.723073\pi$
$181$	−3.37062e12	−1.28967	−0.644834	+	0.764323i	$0.723073\pi$
$182$	−1.65595e11	−0.0614687
$183$	7.92437e11	0.285420
$184$	3.66313e12	1.28043
$185$	6.53308e11	0.221653
$186$	6.30744e11	0.207746
$187$	−3.27208e12	−1.04639
$188$	−3.23265e11	−0.100390
$189$	−4.60889e11	−0.139013
$190$	1.49309e12	0.437462
$191$	2.38809e12	0.679778	0.339889	−	0.940465i	$-0.389610\pi$
$191$	2.38809e12	0.679778	0.339889	+	0.940465i	$0.389610\pi$
$192$	3.55085e11	0.0982146
$193$	5.57651e12	1.49899	0.749493	−	0.662012i	$-0.230297\pi$
$193$	5.57651e12	1.49899	0.749493	+	0.662012i	$0.230297\pi$
$194$	−2.06923e12	−0.540629
$195$	−2.69668e11	−0.0684920
$196$	1.62946e12	0.402378
$197$	−8.64153e11	−0.207504	−0.103752	−	0.994603i	$-0.533085\pi$
$197$	−8.64153e11	−0.207504	−0.103752	+	0.994603i	$0.533085\pi$
$198$	−3.85711e11	−0.0900749
$199$	3.45541e11	0.0784889	0.0392445	−	0.999230i	$-0.487505\pi$
$199$	3.45541e11	0.0784889	0.0392445	+	0.999230i	$0.487505\pi$
$200$	2.29576e12	0.507295
$201$	−2.71596e12	−0.583910
$202$	−2.29363e12	−0.479833
$203$	5.09075e12	1.03646
$204$	3.78044e12	0.749164
$205$	4.72635e12	0.911758
$206$	2.50622e12	0.470706
$207$	−3.18239e12	−0.581991
$208$	−6.59040e11	−0.117372
$209$	7.73871e12	1.34234
$210$	5.45775e11	0.0922162
$211$	6.76550e12	1.11364	0.556822	−	0.830632i	$-0.312021\pi$
$211$	6.76550e12	1.11364	0.556822	+	0.830632i	$0.312021\pi$
$212$	4.52941e12	0.726432
$213$	4.40809e12	0.688911
$214$	−5.36717e11	−0.0817465
$215$	2.51764e12	0.373751
$216$	9.75283e11	0.141135
$217$	−4.62580e12	−0.652617
$218$	2.41440e12	0.332123
$219$	1.13279e12	0.151952
$220$	−2.42287e12	−0.316960
$221$	−2.58252e12	−0.329523
$222$	7.37512e11	0.0917968
$223$	3.60649e12	0.437933	0.218967	−	0.975732i	$-0.429731\pi$
$223$	3.60649e12	0.437933	0.218967	+	0.975732i	$0.429731\pi$
$224$	5.80496e12	0.687758
$225$	−1.99447e12	−0.230581
$226$	−2.95859e12	−0.333802
$227$	−2.38826e12	−0.262990	−0.131495	−	0.991317i	$-0.541978\pi$
$227$	−2.38826e12	−0.262990	−0.131495	+	0.991317i	$0.541978\pi$
$228$	−8.94102e12	−0.961049
$229$	5.83285e12	0.612048	0.306024	−	0.952024i	$-0.401001\pi$
$229$	5.83285e12	0.612048	0.306024	+	0.952024i	$0.401001\pi$
$230$	3.76851e12	0.386071
$231$	2.82876e12	0.282964
$232$	−1.07725e13	−1.05228
$233$	−6.07236e12	−0.579295	−0.289648	−	0.957133i	$-0.593538\pi$
$233$	−6.07236e12	−0.579295	−0.289648	+	0.957133i	$0.593538\pi$
$234$	−3.04426e11	−0.0283657
$235$	−7.27823e11	−0.0662449
$236$	1.23193e12	0.109539
$237$	−9.37189e12	−0.814163
$238$	5.22669e12	0.443663
$239$	−5.24155e12	−0.434782	−0.217391	−	0.976085i	$-0.569755\pi$
$239$	−5.24155e12	−0.434782	−0.217391	+	0.976085i	$0.569755\pi$
$240$	2.17209e12	0.176083
$241$	1.50319e13	1.19103	0.595513	−	0.803346i	$-0.296949\pi$
$241$	1.50319e13	1.19103	0.595513	+	0.803346i	$0.296949\pi$
$242$	−2.77494e12	−0.214916
$243$	−8.47289e11	−0.0641500
$244$	5.61931e12	0.415948
$245$	3.66868e12	0.265520
$246$	5.33552e12	0.377602
$247$	6.10784e12	0.422722
$248$	9.78861e12	0.662578
$249$	−1.08961e13	−0.721400
$250$	5.77609e12	0.374079
$251$	2.00908e13	1.27289	0.636446	−	0.771321i	$-0.280404\pi$
$251$	2.00908e13	1.27289	0.636446	+	0.771321i	$0.280404\pi$
$252$	−3.26825e12	−0.202587
$253$	1.95323e13	1.18465
$254$	5.21505e12	0.309509
$255$	8.51158e12	0.494356
$256$	−4.15300e12	−0.236071
$257$	−1.74585e13	−0.971349	−0.485674	−	0.874140i	$-0.661426\pi$
$257$	−1.74585e13	−0.971349	−0.485674	+	0.874140i	$0.661426\pi$
$258$	2.84214e12	0.154788
$259$	−5.40883e12	−0.288373
$260$	−1.91227e12	−0.0998148
$261$	9.35873e12	0.478293
$262$	1.05470e13	0.527801
$263$	−1.19269e13	−0.584482	−0.292241	−	0.956345i	$-0.594401\pi$
$263$	−1.19269e13	−0.584482	−0.292241	+	0.956345i	$0.594401\pi$
$264$	−5.98592e12	−0.287282
$265$	1.01979e13	0.479355
$266$	−1.23615e13	−0.569144
$267$	−2.16647e13	−0.977104
$268$	−1.92594e13	−0.850944
$269$	−1.82284e13	−0.789063	−0.394531	−	0.918882i	$-0.629093\pi$
$269$	−1.82284e13	−0.789063	−0.394531	+	0.918882i	$0.629093\pi$
$270$	1.00334e12	0.0425547
$271$	5.45181e12	0.226574	0.113287	−	0.993562i	$-0.463862\pi$
$271$	5.45181e12	0.226574	0.113287	+	0.993562i	$0.463862\pi$
$272$	2.08014e13	0.847155
$273$	2.23262e12	0.0891089
$274$	3.70102e12	0.144775
$275$	1.22413e13	0.469350
$276$	−2.25669e13	−0.848148
$277$	−1.60314e13	−0.590652	−0.295326	−	0.955397i	$-0.595428\pi$
$277$	−1.60314e13	−0.590652	−0.295326	+	0.955397i	$0.595428\pi$
$278$	3.35114e12	0.121045
$279$	−8.50397e12	−0.301161
$280$	8.46996e12	0.294112
$281$	3.31008e13	1.12708	0.563538	−	0.826090i	$-0.309440\pi$
$281$	3.31008e13	1.12708	0.563538	+	0.826090i	$0.309440\pi$
$282$	−8.21632e11	−0.0274351
$283$	4.22069e13	1.38216	0.691079	−	0.722779i	$-0.257136\pi$
$283$	4.22069e13	1.38216	0.691079	+	0.722779i	$0.257136\pi$
$284$	3.12586e13	1.00396
$285$	−2.01305e13	−0.634173
$286$	1.86845e12	0.0577389
$287$	−3.91301e13	−1.18621
$288$	1.06717e13	0.317377
$289$	4.72405e13	1.37840
$290$	−1.10824e13	−0.317282
$291$	2.78983e13	0.783730
$292$	8.03280e12	0.221443
$293$	2.36378e13	0.639492	0.319746	−	0.947503i	$-0.396402\pi$
$293$	2.36378e13	0.639492	0.319746	+	0.947503i	$0.396402\pi$
$294$	4.14153e12	0.109964
$295$	2.77365e12	0.0722822
$296$	1.14456e13	0.292774
$297$	5.20034e12	0.130578
$298$	2.77569e12	0.0684197
$299$	1.54160e13	0.373062
$300$	−1.41431e13	−0.336030
$301$	−2.08439e13	−0.486254
$302$	8.50083e12	0.194726
$303$	3.09237e13	0.695596
$304$	−4.91967e13	−1.08675
$305$	1.26518e13	0.274474
$306$	9.60863e12	0.204736
$307$	−7.37980e12	−0.154449	−0.0772243	−	0.997014i	$-0.524606\pi$
$307$	−7.37980e12	−0.154449	−0.0772243	+	0.997014i	$0.524606\pi$
$308$	2.00593e13	0.412369
$309$	−3.37900e13	−0.682365
$310$	1.00702e13	0.199779
$311$	−2.70914e13	−0.528019	−0.264010	−	0.964520i	$-0.585045\pi$
$311$	−2.70914e13	−0.528019	−0.264010	+	0.964520i	$0.585045\pi$
$312$	−4.72443e12	−0.0904689
$313$	−6.62339e13	−1.24620	−0.623098	−	0.782144i	$-0.714126\pi$
$313$	−6.62339e13	−1.24620	−0.623098	+	0.782144i	$0.714126\pi$
$314$	−4.46955e12	−0.0826324
$315$	−7.35838e12	−0.133682
$316$	−6.64577e13	−1.18650
$317$	−2.57294e13	−0.451445	−0.225722	−	0.974192i	$-0.572474\pi$
$317$	−2.57294e13	−0.451445	−0.225722	+	0.974192i	$0.572474\pi$
$318$	1.15123e13	0.198523
$319$	−5.74403e13	−0.973572
$320$	5.66916e12	0.0944483
$321$	7.23626e12	0.118505
$322$	−3.12001e13	−0.502283
$323$	−1.92783e14	−3.05108
$324$	−6.00827e12	−0.0934872
$325$	9.66153e12	0.147804
$326$	1.23414e13	0.185638
$327$	−3.25521e13	−0.481466
$328$	8.28028e13	1.20431
$329$	6.02575e12	0.0861854
$330$	−6.15812e12	−0.0866207
$331$	−5.48873e13	−0.759308	−0.379654	−	0.925129i	$-0.623957\pi$
$331$	−5.48873e13	−0.759308	−0.379654	+	0.925129i	$0.623957\pi$
$332$	−7.72664e13	−1.05131
$333$	−9.94348e12	−0.133075
$334$	3.24299e13	0.426914
$335$	−4.33621e13	−0.561518
$336$	−1.79831e13	−0.229086
$337$	−9.79581e13	−1.22765	−0.613827	−	0.789441i	$-0.710371\pi$
$337$	−9.79581e13	−1.22765	−0.613827	+	0.789441i	$0.710371\pi$
$338$	−3.08262e13	−0.380082
$339$	3.98891e13	0.483901
$340$	6.03572e13	0.720435
$341$	5.21942e13	0.613017
$342$	−2.27251e13	−0.262641
$343$	−9.38856e13	−1.06778
$344$	4.41076e13	0.493676
$345$	−5.08088e13	−0.559673
$346$	3.71084e12	0.0402303
$347$	7.13794e12	0.0761659	0.0380829	−	0.999275i	$-0.487875\pi$
$347$	7.13794e12	0.0761659	0.0380829	+	0.999275i	$0.487875\pi$
$348$	6.63644e13	0.697027
$349$	−1.62450e14	−1.67950	−0.839748	−	0.542976i	$-0.817298\pi$
$349$	−1.62450e14	−1.67950	−0.839748	+	0.542976i	$0.817298\pi$
$350$	−1.95537e13	−0.199001
$351$	4.10441e12	0.0411208
$352$	−6.54990e13	−0.646026
$353$	1.51005e14	1.46632	0.733162	−	0.680054i	$-0.238044\pi$
$353$	1.51005e14	1.46632	0.733162	+	0.680054i	$0.238044\pi$
$354$	3.13115e12	0.0299354
$355$	7.03780e13	0.662492
$356$	−1.53628e14	−1.42395
$357$	−7.04686e13	−0.643162
$358$	−6.22037e13	−0.559062
$359$	2.50228e13	0.221471	0.110736	−	0.993850i	$-0.464679\pi$
$359$	2.50228e13	0.221471	0.110736	+	0.993850i	$0.464679\pi$
$360$	1.55710e13	0.135723
$361$	3.39455e14	2.91402
$362$	−6.07501e13	−0.513630
$363$	3.74131e13	0.311556
$364$	1.58319e13	0.129860
$365$	1.80857e13	0.146125
$366$	1.42824e13	0.113673
$367$	1.47297e14	1.15487	0.577433	−	0.816438i	$-0.304055\pi$
$367$	1.47297e14	1.15487	0.577433	+	0.816438i	$0.304055\pi$
$368$	−1.24171e14	−0.959086
$369$	−7.19359e13	−0.547395
$370$	1.17748e13	0.0882766
$371$	−8.44296e13	−0.623646
$372$	−6.03032e13	−0.438888
$373$	−7.52002e13	−0.539288	−0.269644	−	0.962960i	$-0.586906\pi$
$373$	−7.52002e13	−0.539288	−0.269644	+	0.962960i	$0.586906\pi$
$374$	−5.89741e13	−0.416743
$375$	−7.78758e13	−0.542289
$376$	−1.27510e13	−0.0875009
$377$	−4.53352e13	−0.306590
$378$	−8.30680e12	−0.0553642
$379$	1.75453e14	1.15251	0.576257	−	0.817269i	$-0.304513\pi$
$379$	1.75453e14	1.15251	0.576257	+	0.817269i	$0.304513\pi$
$380$	−1.42749e14	−0.924194
$381$	−7.03117e13	−0.448684
$382$	4.30416e13	0.270732
$383$	−2.55697e14	−1.58537	−0.792687	−	0.609629i	$-0.791319\pi$
$383$	−2.55697e14	−1.58537	−0.792687	+	0.609629i	$0.791319\pi$
$384$	9.63409e13	0.588829
$385$	4.51630e13	0.272112
$386$	1.00508e14	0.596994
$387$	−3.83190e13	−0.224390
$388$	1.97832e14	1.14215
$389$	2.60045e14	1.48022	0.740108	−	0.672488i	$-0.234774\pi$
$389$	2.60045e14	1.48022	0.740108	+	0.672488i	$0.234774\pi$
$390$	−4.86035e12	−0.0272780
$391$	−4.86578e14	−2.69265
$392$	6.42731e13	0.350716
$393$	−1.42199e14	−0.765134
$394$	−1.55750e13	−0.0826415
$395$	−1.49628e14	−0.782941
$396$	3.68765e13	0.190295
$397$	−1.25874e14	−0.640602	−0.320301	−	0.947316i	$-0.603784\pi$
$397$	−1.25874e14	−0.640602	−0.320301	+	0.947316i	$0.603784\pi$
$398$	6.22784e12	0.0312594
$399$	1.66663e14	0.825067
$400$	−7.78206e13	−0.379983
$401$	−3.18523e13	−0.153407	−0.0767037	−	0.997054i	$-0.524440\pi$
$401$	−3.18523e13	−0.153407	−0.0767037	+	0.997054i	$0.524440\pi$
$402$	−4.89510e13	−0.232551
$403$	4.11947e13	0.193047
$404$	2.19285e14	1.01371
$405$	−1.35275e13	−0.0616900
$406$	9.17528e13	0.412787
$407$	6.10293e13	0.270875
$408$	1.49118e14	0.652979
$409$	−2.50325e14	−1.08150	−0.540749	−	0.841184i	$-0.681859\pi$
$409$	−2.50325e14	−1.08150	−0.540749	+	0.841184i	$0.681859\pi$
$410$	8.51849e13	0.363121
$411$	−4.98988e13	−0.209875
$412$	−2.39611e14	−0.994425
$413$	−2.29635e13	−0.0940399
$414$	−5.73575e13	−0.231787
$415$	−1.73964e14	−0.693735
$416$	−5.16956e13	−0.203442
$417$	−4.51816e13	−0.175474
$418$	1.39478e14	0.534609
$419$	2.94744e13	0.111498	0.0557491	−	0.998445i	$-0.482245\pi$
$419$	2.94744e13	0.111498	0.0557491	+	0.998445i	$0.482245\pi$
$420$	−5.21796e13	−0.194818
$421$	4.40544e14	1.62344	0.811722	−	0.584044i	$-0.198530\pi$
$421$	4.40544e14	1.62344	0.811722	+	0.584044i	$0.198530\pi$
$422$	1.21937e14	0.443525
$423$	1.10776e13	0.0397717
$424$	1.78661e14	0.633165
$425$	−3.04948e14	−1.06681
$426$	7.94489e13	0.274369
$427$	−1.04746e14	−0.357094
$428$	5.13136e13	0.172700
$429$	−2.51913e13	−0.0837019
$430$	4.53765e13	0.148852
$431$	−1.08455e14	−0.351256	−0.175628	−	0.984457i	$-0.556196\pi$
$431$	−1.08455e14	−0.351256	−0.175628	+	0.984457i	$0.556196\pi$
$432$	−3.30597e13	−0.105715
$433$	−2.49683e14	−0.788326	−0.394163	−	0.919041i	$-0.628965\pi$
$433$	−2.49683e14	−0.788326	−0.394163	+	0.919041i	$0.628965\pi$
$434$	−8.33728e13	−0.259915
$435$	1.49418e14	0.459951
$436$	−2.30833e14	−0.701651
$437$	1.15079e15	3.45421
$438$	2.04167e13	0.0605171
$439$	5.41840e14	1.58605	0.793024	−	0.609190i	$-0.208505\pi$
$439$	5.41840e14	1.58605	0.793024	+	0.609190i	$0.208505\pi$
$440$	−9.55689e13	−0.276266
$441$	−5.58381e13	−0.159411
$442$	−4.65458e13	−0.131238
$443$	−3.54094e14	−0.986048	−0.493024	−	0.870016i	$-0.664109\pi$
$443$	−3.54094e14	−0.986048	−0.493024	+	0.870016i	$0.664109\pi$
$444$	−7.05110e13	−0.193932
$445$	−3.45890e14	−0.939633
$446$	6.50013e13	0.174413
$447$	−3.74231e13	−0.0991856
$448$	−4.69358e13	−0.122878
$449$	−4.79011e14	−1.23877	−0.619385	−	0.785087i	$-0.712618\pi$
$449$	−4.79011e14	−1.23877	−0.619385	+	0.785087i	$0.712618\pi$
$450$	−3.59471e13	−0.0918322
$451$	4.41515e14	1.11423
$452$	2.82861e14	0.705199
$453$	−1.14612e14	−0.282287
$454$	−4.30446e13	−0.104740
$455$	3.56452e13	0.0856917
$456$	−3.52675e14	−0.837659
$457$	1.22388e14	0.287210	0.143605	−	0.989635i	$-0.454131\pi$
$457$	1.22388e14	0.287210	0.143605	+	0.989635i	$0.454131\pi$
$458$	1.05128e14	0.243757
$459$	−1.29548e14	−0.296798
$460$	−3.60294e14	−0.815623
$461$	−8.45619e14	−1.89156	−0.945779	−	0.324812i	$-0.894699\pi$
$461$	−8.45619e14	−1.89156	−0.945779	+	0.324812i	$0.894699\pi$
$462$	5.09840e13	0.112695
$463$	7.32000e14	1.59888	0.799439	−	0.600747i	$-0.205130\pi$
$463$	7.32000e14	1.59888	0.799439	+	0.600747i	$0.205130\pi$
$464$	3.65161e14	0.788199
$465$	−1.35771e14	−0.289612
$466$	−1.09445e14	−0.230713
$467$	−1.14805e14	−0.239175	−0.119588	−	0.992824i	$-0.538157\pi$
$467$	−1.14805e14	−0.239175	−0.119588	+	0.992824i	$0.538157\pi$
$468$	2.91051e13	0.0599262
$469$	3.59001e14	0.730541
$470$	−1.31179e13	−0.0263830
$471$	6.02605e13	0.119789
$472$	4.85928e13	0.0954753
$473$	2.35187e14	0.456749
$474$	−1.68913e14	−0.324253
$475$	7.21224e14	1.36853
$476$	−4.99706e14	−0.937294
$477$	−1.55214e14	−0.287792
$478$	−9.44707e13	−0.173158
$479$	9.95247e14	1.80337	0.901686	−	0.432391i	$-0.142330\pi$
$479$	9.95247e14	1.80337	0.901686	+	0.432391i	$0.142330\pi$
$480$	1.70381e14	0.305206
$481$	4.81679e13	0.0853020
$482$	2.70927e14	0.474344
$483$	4.20653e14	0.728141
$484$	2.65303e14	0.454038
$485$	4.45414e14	0.753676
$486$	−1.52710e13	−0.0255487
$487$	−5.98697e13	−0.0990371	−0.0495186	−	0.998773i	$-0.515769\pi$
$487$	−5.98697e13	−0.0990371	−0.0495186	+	0.998773i	$0.515769\pi$
$488$	2.21651e14	0.362545
$489$	−1.66392e14	−0.269113
$490$	6.61222e13	0.105747
$491$	−5.55539e13	−0.0878550	−0.0439275	−	0.999035i	$-0.513987\pi$
$491$	−5.55539e13	−0.0878550	−0.0439275	+	0.999035i	$0.513987\pi$
$492$	−5.10111e14	−0.797731
$493$	1.43092e15	2.21288
$494$	1.10084e14	0.168355
$495$	8.30266e13	0.125571
$496$	−3.31810e14	−0.496296
$497$	−5.82669e14	−0.861910
$498$	−1.96386e14	−0.287308
$499$	1.10932e14	0.160510	0.0802550	−	0.996774i	$-0.474427\pi$
$499$	1.10932e14	0.160510	0.0802550	+	0.996774i	$0.474427\pi$
$500$	−5.52231e14	−0.790289
$501$	−4.37235e14	−0.618881
$502$	3.62105e14	0.506949
$503$	−6.51056e14	−0.901560	−0.450780	−	0.892635i	$-0.648854\pi$
$503$	−6.51056e14	−0.901560	−0.450780	+	0.892635i	$0.648854\pi$
$504$	−1.28915e14	−0.176577
$505$	4.93716e14	0.668921
$506$	3.52039e14	0.471805
$507$	4.15613e14	0.550991
$508$	−4.98593e14	−0.653876
$509$	−2.39761e13	−0.0311050	−0.0155525	−	0.999879i	$-0.504951\pi$
$509$	−2.39761e13	−0.0311050	−0.0155525	+	0.999879i	$0.504951\pi$
$510$	1.53408e14	0.196885
$511$	−1.49734e14	−0.190110
$512$	7.37109e14	0.925863
$513$	3.06390e14	0.380741
$514$	−3.14662e14	−0.386854
$515$	−5.39479e14	−0.656197
$516$	−2.71727e14	−0.327008
$517$	−6.79902e13	−0.0809559
$518$	−9.74856e13	−0.114849
$519$	−5.00312e13	−0.0583204
$520$	−7.54285e13	−0.0869996
$521$	−2.07535e14	−0.236856	−0.118428	−	0.992963i	$-0.537785\pi$
$521$	−2.07535e14	−0.236856	−0.118428	+	0.992963i	$0.537785\pi$
$522$	1.68676e14	0.190487
$523$	2.09577e14	0.234199	0.117099	−	0.993120i	$-0.462640\pi$
$523$	2.09577e14	0.234199	0.117099	+	0.993120i	$0.462640\pi$
$524$	−1.00836e15	−1.11505
$525$	2.63632e14	0.288484
$526$	−2.14964e14	−0.232779
$527$	−1.30023e15	−1.39336
$528$	2.02908e14	0.215185
$529$	1.95176e15	2.04842
$530$	1.83801e14	0.190910
$531$	−4.22156e13	−0.0433963
$532$	1.18184e15	1.20239
$533$	3.48470e14	0.350885
$534$	−3.90472e14	−0.389146
$535$	1.15531e14	0.113960
$536$	−7.59678e14	−0.741691
$537$	8.38659e14	0.810451
$538$	−3.28538e14	−0.314256
$539$	3.42713e14	0.324483
$540$	−9.59259e13	−0.0899021
$541$	−4.31551e12	−0.00400357	−0.00200178	−	0.999998i	$-0.500637\pi$
$541$	−4.31551e12	−0.00400357	−0.00200178	+	0.999998i	$0.500637\pi$
$542$	9.82602e13	0.0902364
$543$	8.19061e14	0.744590
$544$	1.63168e15	1.46838
$545$	−5.19714e14	−0.463003
$546$	4.02395e13	0.0354890
$547$	1.27963e15	1.11726	0.558630	−	0.829417i	$-0.311327\pi$
$547$	1.27963e15	1.11726	0.558630	+	0.829417i	$0.311327\pi$
$548$	−3.53841e14	−0.305855
$549$	−1.92562e14	−0.164787
$550$	2.20630e14	0.186926
$551$	−3.38423e15	−2.83875
$552$	−8.90141e14	−0.739254
$553$	1.23879e15	1.01862
$554$	−2.88940e14	−0.235236
$555$	−1.58754e14	−0.127971
$556$	−3.20391e14	−0.255722
$557$	−2.47444e14	−0.195557	−0.0977785	−	0.995208i	$-0.531174\pi$
$557$	−2.47444e14	−0.195557	−0.0977785	+	0.995208i	$0.531174\pi$
$558$	−1.53271e14	−0.119942
$559$	1.85624e14	0.143836
$560$	−2.87111e14	−0.220301
$561$	7.95116e14	0.604136
$562$	5.96589e14	0.448875
$563$	−7.22104e14	−0.538027	−0.269013	−	0.963136i	$-0.586698\pi$
$563$	−7.22104e14	−0.538027	−0.269013	+	0.963136i	$0.586698\pi$
$564$	7.85533e13	0.0579602
$565$	6.36855e14	0.465344
$566$	7.60712e14	0.550465
$567$	1.11996e14	0.0802594
$568$	1.23298e15	0.875065
$569$	9.44684e14	0.664002	0.332001	−	0.943279i	$-0.392276\pi$
$569$	9.44684e14	0.664002	0.332001	+	0.943279i	$0.392276\pi$
$570$	−3.62821e14	−0.252569
$571$	−9.77473e13	−0.0673916	−0.0336958	−	0.999432i	$-0.510728\pi$
$571$	−9.77473e13	−0.0673916	−0.0336958	+	0.999432i	$0.510728\pi$
$572$	−1.78636e14	−0.121981
$573$	−5.80306e14	−0.392470
$574$	−7.05258e14	−0.472425
$575$	1.82035e15	1.20776
$576$	−8.62858e13	−0.0567042
$577$	1.50543e14	0.0979924	0.0489962	−	0.998799i	$-0.484398\pi$
$577$	1.50543e14	0.0979924	0.0489962	+	0.998799i	$0.484398\pi$
$578$	8.51436e14	0.548970
$579$	−1.35509e15	−0.865440
$580$	1.05955e15	0.670297
$581$	1.44027e15	0.902558
$582$	5.02823e14	0.312132
$583$	9.52642e14	0.585805
$584$	3.16850e14	0.193012
$585$	6.55294e13	0.0395439
$586$	4.26034e14	0.254687
$587$	−6.10101e14	−0.361320	−0.180660	−	0.983546i	$-0.557823\pi$
$587$	−6.10101e14	−0.361320	−0.180660	+	0.983546i	$0.557823\pi$
$588$	−3.95958e14	−0.232313
$589$	3.07514e15	1.78744
$590$	4.99907e13	0.0287875
$591$	2.09989e14	0.119802
$592$	−3.87977e14	−0.219299
$593$	−7.60782e13	−0.0426049	−0.0213024	−	0.999773i	$-0.506781\pi$
$593$	−7.60782e13	−0.0426049	−0.0213024	+	0.999773i	$0.506781\pi$
$594$	9.37278e13	0.0520048
$595$	−1.12508e15	−0.618498
$596$	−2.65374e14	−0.144545
$597$	−8.39666e13	−0.0453156
$598$	2.77849e14	0.148577
$599$	3.07445e15	1.62899	0.814497	−	0.580168i	$-0.197013\pi$
$599$	3.07445e15	1.62899	0.814497	+	0.580168i	$0.197013\pi$
$600$	−5.57869e14	−0.292887
$601$	2.51066e15	1.30611	0.653053	−	0.757312i	$-0.273488\pi$
$601$	2.51066e15	1.30611	0.653053	+	0.757312i	$0.273488\pi$
$602$	−3.75678e14	−0.193658
$603$	6.59979e14	0.337121
$604$	−8.12735e14	−0.411382
$605$	5.97323e14	0.299609
$606$	5.57351e14	0.277032
$607$	3.18922e15	1.57089	0.785446	−	0.618931i	$-0.212434\pi$
$607$	3.18922e15	1.57089	0.785446	+	0.618931i	$0.212434\pi$
$608$	−3.85903e15	−1.88369
$609$	−1.23705e15	−0.598402
$610$	2.28028e14	0.109314
$611$	−5.36618e13	−0.0254940
$612$	−9.18648e14	−0.432530
$613$	1.38627e15	0.646868	0.323434	−	0.946251i	$-0.395163\pi$
$613$	1.38627e15	0.646868	0.323434	+	0.946251i	$0.395163\pi$
$614$	−1.33009e14	−0.0615115
$615$	−1.14850e15	−0.526403
$616$	7.91228e14	0.359425
$617$	1.52685e15	0.687429	0.343715	−	0.939074i	$-0.388315\pi$
$617$	1.52685e15	0.687429	0.343715	+	0.939074i	$0.388315\pi$
$618$	−6.09011e14	−0.271762
$619$	−4.10703e15	−1.81648	−0.908238	−	0.418455i	$-0.862572\pi$
$619$	−4.10703e15	−1.81648	−0.908238	+	0.418455i	$0.862572\pi$
$620$	−9.62778e14	−0.422058
$621$	7.73320e14	0.336013
$622$	−4.88280e14	−0.210292
$623$	2.86368e15	1.22247
$624$	1.60147e14	0.0677646
$625$	4.05905e14	0.170249
$626$	−1.19376e15	−0.496316
$627$	−1.88051e15	−0.775003
$628$	4.27318e14	0.174571
$629$	−1.52033e15	−0.615686
$630$	−1.32623e14	−0.0532410
$631$	−4.75010e14	−0.189035	−0.0945173	−	0.995523i	$-0.530131\pi$
$631$	−4.75010e14	−0.189035	−0.0945173	+	0.995523i	$0.530131\pi$
$632$	−2.62140e15	−1.03416
$633$	−1.64402e15	−0.642963
$634$	−4.63732e14	−0.179795
$635$	−1.12257e15	−0.431477
$636$	−1.10065e15	−0.419406
$637$	2.70489e14	0.102184
$638$	−1.03527e15	−0.387740
$639$	−1.07117e15	−0.397743
$640$	1.53814e15	0.566248
$641$	3.96744e15	1.44808	0.724038	−	0.689760i	$-0.242284\pi$
$641$	3.96744e15	1.44808	0.724038	+	0.689760i	$0.242284\pi$
$642$	1.30422e14	0.0471964
$643$	5.00082e15	1.79424	0.897120	−	0.441787i	$-0.145655\pi$
$643$	5.00082e15	1.79424	0.897120	+	0.441787i	$0.145655\pi$
$644$	2.98293e15	1.06113
$645$	−6.11786e14	−0.215785
$646$	−3.47460e15	−1.21514
$647$	−5.11962e14	−0.177527	−0.0887634	−	0.996053i	$-0.528292\pi$
$647$	−5.11962e14	−0.177527	−0.0887634	+	0.996053i	$0.528292\pi$
$648$	−2.36994e14	−0.0814844
$649$	2.59103e14	0.0883338
$650$	1.74134e14	0.0588653
$651$	1.12407e15	0.376789
$652$	−1.17992e15	−0.392184
$653$	−5.33380e15	−1.75798	−0.878990	−	0.476840i	$-0.841782\pi$
$653$	−5.33380e15	−1.75798	−0.878990	+	0.476840i	$0.841782\pi$
$654$	−5.86700e14	−0.191751
$655$	−2.27030e15	−0.735792
$656$	−2.80681e15	−0.902075
$657$	−2.75267e14	−0.0877294
$658$	1.08605e14	0.0343247
$659$	−3.31774e15	−1.03985	−0.519927	−	0.854211i	$-0.674041\pi$
$659$	−3.31774e15	−1.03985	−0.519927	+	0.854211i	$0.674041\pi$
$660$	5.88757e14	0.182997
$661$	−2.53460e15	−0.781270	−0.390635	−	0.920546i	$-0.627745\pi$
$661$	−2.53460e15	−0.781270	−0.390635	+	0.920546i	$0.627745\pi$
$662$	−9.89257e14	−0.302406
$663$	6.27552e14	0.190250
$664$	−3.04774e15	−0.916333
$665$	2.66088e15	0.793427
$666$	−1.79215e14	−0.0529989
$667$	−8.54171e15	−2.50526
$668$	−3.10051e15	−0.901909
$669$	−8.76377e14	−0.252841
$670$	−7.81533e14	−0.223633
$671$	1.18187e15	0.335426
$672$	−1.41061e15	−0.397077
$673$	5.86295e15	1.63694	0.818471	−	0.574548i	$-0.194822\pi$
$673$	5.86295e15	1.63694	0.818471	+	0.574548i	$0.194822\pi$
$674$	−1.76554e15	−0.488932
$675$	4.84655e14	0.133126
$676$	2.94718e15	0.802972
$677$	−1.87975e13	−0.00507999	−0.00254000	−	0.999997i	$-0.500809\pi$
$677$	−1.87975e13	−0.00507999	−0.00254000	+	0.999997i	$0.500809\pi$
$678$	7.18938e14	0.192721
$679$	−3.68765e15	−0.980541
$680$	2.38076e15	0.627938
$681$	5.80347e14	0.151837
$682$	9.40717e14	0.244143
$683$	−6.07603e15	−1.56425	−0.782125	−	0.623121i	$-0.785864\pi$
$683$	−6.07603e15	−1.56425	−0.782125	+	0.623121i	$0.785864\pi$
$684$	2.17267e15	0.554862
$685$	−7.96665e14	−0.201826
$686$	−1.69214e15	−0.425259
$687$	−1.41738e15	−0.353366
$688$	−1.49514e15	−0.369781
$689$	7.51881e14	0.184477
$690$	−9.15749e14	−0.222898
$691$	1.75688e15	0.424242	0.212121	−	0.977243i	$-0.431963\pi$
$691$	1.75688e15	0.424242	0.212121	+	0.977243i	$0.431963\pi$
$692$	−3.54780e14	−0.0849916
$693$	−6.87389e14	−0.163369
$694$	1.28650e14	0.0303342
$695$	−7.21352e14	−0.168745
$696$	2.61772e15	0.607535
$697$	−1.09988e16	−2.53259
$698$	−2.92790e15	−0.668885
$699$	1.47558e15	0.334456
$700$	1.86946e15	0.420414
$701$	−3.30315e15	−0.737020	−0.368510	−	0.929624i	$-0.620132\pi$
$701$	−3.30315e15	−0.737020	−0.368510	+	0.929624i	$0.620132\pi$
$702$	7.39755e13	0.0163770
$703$	3.59569e15	0.789819
$704$	5.29589e14	0.115422
$705$	1.76861e14	0.0382465
$706$	2.72162e15	0.583986
$707$	−4.08755e15	−0.870274
$708$	−2.99358e14	−0.0632424
$709$	4.88990e15	1.02505	0.512526	−	0.858672i	$-0.328710\pi$
$709$	4.88990e15	1.02505	0.512526	+	0.858672i	$0.328710\pi$
$710$	1.26845e15	0.263848
$711$	2.27737e15	0.470057
$712$	−6.05980e15	−1.24113
$713$	7.76158e15	1.57746
$714$	−1.27009e15	−0.256149
$715$	−4.02195e14	−0.0804921
$716$	5.94708e15	1.18109
$717$	1.27370e15	0.251021
$718$	4.50997e14	0.0882042
$719$	7.32137e15	1.42097	0.710483	−	0.703715i	$-0.248477\pi$
$719$	7.32137e15	1.42097	0.710483	+	0.703715i	$0.248477\pi$
$720$	−5.27819e14	−0.101661
$721$	4.46642e15	0.853720
$722$	6.11813e15	1.16055
$723$	−3.65276e15	−0.687639
$724$	5.80811e15	1.08511
$725$	−5.35326e15	−0.992566
$726$	6.74311e14	0.124082
$727$	8.09516e15	1.47838	0.739190	−	0.673497i	$-0.235209\pi$
$727$	8.09516e15	1.47838	0.739190	+	0.673497i	$0.235209\pi$
$728$	6.24483e14	0.113187
$729$	2.05891e14	0.0370370
$730$	3.25966e14	0.0581964
$731$	−5.85886e15	−1.03817
$732$	−1.36549e15	−0.240148
$733$	−3.29018e15	−0.574313	−0.287156	−	0.957884i	$-0.592710\pi$
$733$	−3.29018e15	−0.574313	−0.287156	+	0.957884i	$0.592710\pi$
$734$	2.65480e15	0.459942
$735$	−8.91490e14	−0.153298
$736$	−9.74008e15	−1.66240
$737$	−4.05070e15	−0.686213
$738$	−1.29653e15	−0.218008
$739$	2.17098e15	0.362336	0.181168	−	0.983452i	$-0.442012\pi$
$739$	2.17098e15	0.362336	0.181168	+	0.983452i	$0.442012\pi$
$740$	−1.12575e15	−0.186495
$741$	−1.48421e15	−0.244058
$742$	−1.52171e15	−0.248377
$743$	4.01946e15	0.651222	0.325611	−	0.945504i	$-0.394430\pi$
$743$	4.01946e15	0.651222	0.325611	+	0.945504i	$0.394430\pi$
$744$	−2.37863e15	−0.382539
$745$	−5.97483e14	−0.0953820
$746$	−1.35537e15	−0.214780
$747$	2.64776e15	0.416500
$748$	5.63831e15	0.880421
$749$	−9.56501e14	−0.148264
$750$	−1.40359e15	−0.215975
$751$	1.10261e16	1.68423	0.842116	−	0.539296i	$-0.181310\pi$
$751$	1.10261e16	1.68423	0.842116	+	0.539296i	$0.181310\pi$
$752$	4.32229e14	0.0655414
$753$	−4.88206e15	−0.734905
$754$	−8.17096e14	−0.122104
$755$	−1.82985e15	−0.271461
$756$	7.94184e14	0.116964
$757$	−1.19658e16	−1.74949	−0.874747	−	0.484579i	$-0.838973\pi$
$757$	−1.19658e16	−1.74949	−0.874747	+	0.484579i	$0.838973\pi$
$758$	3.16227e15	0.459006
$759$	−4.74635e15	−0.683958
$760$	−5.63067e15	−0.805537
$761$	4.06587e15	0.577481	0.288740	−	0.957407i	$-0.406764\pi$
$761$	4.06587e15	0.577481	0.288740	+	0.957407i	$0.406764\pi$
$762$	−1.26726e15	−0.178695
$763$	4.30279e15	0.602372
$764$	−4.11505e15	−0.571955
$765$	−2.06831e15	−0.285416
$766$	−4.60853e15	−0.631399
$767$	2.04499e14	0.0278174
$768$	1.00918e15	0.136295
$769$	−1.12489e16	−1.50839	−0.754195	−	0.656650i	$-0.771973\pi$
$769$	−1.12489e16	−1.50839	−0.754195	+	0.656650i	$0.771973\pi$
$770$	8.13991e14	0.108373
$771$	4.24242e15	0.560808
$772$	−9.60921e15	−1.26122
$773$	−1.25407e16	−1.63431	−0.817156	−	0.576417i	$-0.804451\pi$
$773$	−1.25407e16	−1.63431	−0.817156	+	0.576417i	$0.804451\pi$
$774$	−6.90639e14	−0.0893667
$775$	4.86434e15	0.624977
$776$	7.80340e15	0.995507
$777$	1.31435e15	0.166492
$778$	4.68689e15	0.589518
$779$	2.60129e16	3.24888
$780$	4.64681e14	0.0576281
$781$	6.57441e15	0.809611
$782$	−8.76980e15	−1.07239
$783$	−2.27417e15	−0.276143
$784$	−2.17870e15	−0.262700
$785$	9.62097e14	0.115196
$786$	−2.56291e15	−0.304726
$787$	1.32562e16	1.56516	0.782579	−	0.622551i	$-0.213904\pi$
$787$	1.32562e16	1.56516	0.782579	+	0.622551i	$0.213904\pi$
$788$	1.48907e15	0.174591
$789$	2.89824e15	0.337451
$790$	−2.69681e15	−0.311818
$791$	−5.27261e15	−0.605418
$792$	1.45458e15	0.165863
$793$	9.32804e14	0.105630
$794$	−2.26868e15	−0.255130
$795$	−2.47808e15	−0.276756
$796$	−5.95422e14	−0.0660394
$797$	1.25975e15	0.138759	0.0693797	−	0.997590i	$-0.477898\pi$
$797$	1.25975e15	0.138759	0.0693797	+	0.997590i	$0.477898\pi$
$798$	3.00384e15	0.328595
$799$	1.69374e15	0.184009
$800$	−6.10430e15	−0.658629
$801$	5.26452e15	0.564131
$802$	−5.74087e14	−0.0610968
$803$	1.68949e15	0.178574
$804$	4.68003e15	0.491293
$805$	6.71600e15	0.700218
$806$	7.42469e14	0.0768839
$807$	4.42951e15	0.455566
$808$	8.64962e15	0.883557
$809$	2.69532e15	0.273460	0.136730	−	0.990608i	$-0.456341\pi$
$809$	2.69532e15	0.273460	0.136730	+	0.990608i	$0.456341\pi$
$810$	−2.43812e14	−0.0245690
$811$	−7.63973e15	−0.764651	−0.382326	−	0.924028i	$-0.624877\pi$
$811$	−7.63973e15	−0.764651	−0.382326	+	0.924028i	$0.624877\pi$
$812$	−8.77216e15	−0.872064
$813$	−1.32479e15	−0.130812
$814$	1.09996e15	0.107880
$815$	−2.65656e15	−0.258793
$816$	−5.05473e15	−0.489105
$817$	1.38566e16	1.33179
$818$	−4.51171e15	−0.430723
$819$	−5.42528e14	−0.0514470
$820$	−8.14423e15	−0.767139
$821$	2.91872e15	0.273089	0.136545	−	0.990634i	$-0.456400\pi$
$821$	2.91872e15	0.273089	0.136545	+	0.990634i	$0.456400\pi$
$822$	−8.99347e14	−0.0835857
$823$	−6.18239e15	−0.570765	−0.285382	−	0.958414i	$-0.592121\pi$
$823$	−6.18239e15	−0.570765	−0.285382	+	0.958414i	$0.592121\pi$
$824$	−9.45135e15	−0.866750
$825$	−2.97463e15	−0.270979
$826$	−4.13880e14	−0.0374528
$827$	−5.31928e15	−0.478160	−0.239080	−	0.971000i	$-0.576846\pi$
$827$	−5.31928e15	−0.478160	−0.239080	+	0.971000i	$0.576846\pi$
$828$	5.48375e15	0.489678
$829$	−7.02110e15	−0.622809	−0.311405	−	0.950277i	$-0.600799\pi$
$829$	−7.02110e15	−0.622809	−0.311405	+	0.950277i	$0.600799\pi$
$830$	−3.13542e15	−0.276291
$831$	3.89562e15	0.341013
$832$	4.17983e14	0.0363480
$833$	−8.53748e15	−0.737534
$834$	−8.14327e14	−0.0698852
$835$	−6.98073e15	−0.595148
$836$	−1.33350e16	−1.12943
$837$	2.06647e15	0.173875
$838$	5.31229e14	0.0444058
$839$	−1.16618e16	−0.968443	−0.484222	−	0.874945i	$-0.660897\pi$
$839$	−1.16618e16	−0.968443	−0.484222	+	0.874945i	$0.660897\pi$
$840$	−2.05820e15	−0.169806
$841$	1.29189e16	1.05888
$842$	7.94010e15	0.646561
$843$	−8.04348e15	−0.650718
$844$	−1.16580e16	−0.937003
$845$	6.63551e15	0.529862
$846$	1.99657e14	0.0158397
$847$	−4.94532e15	−0.389795
$848$	−6.05616e15	−0.474264
$849$	−1.02563e16	−0.797989
$850$	−5.49621e15	−0.424873
$851$	9.07541e15	0.697033
$852$	−7.59583e15	−0.579639
$853$	−8.18494e15	−0.620577	−0.310289	−	0.950642i	$-0.600426\pi$
$853$	−8.18494e15	−0.620577	−0.310289	+	0.950642i	$0.600426\pi$
$854$	−1.88788e15	−0.142218
$855$	4.89171e15	0.366140
$856$	2.02404e15	0.150527
$857$	1.48309e16	1.09590	0.547952	−	0.836510i	$-0.315408\pi$
$857$	1.48309e16	1.09590	0.547952	+	0.836510i	$0.315408\pi$
$858$	−4.54033e14	−0.0333355
$859$	1.84576e16	1.34652	0.673262	−	0.739404i	$-0.264893\pi$
$859$	1.84576e16	1.34652	0.673262	+	0.739404i	$0.264893\pi$
$860$	−4.33829e15	−0.314468
$861$	9.50862e15	0.684857
$862$	−1.95473e15	−0.139893
$863$	1.57578e16	1.12056	0.560281	−	0.828303i	$-0.310693\pi$
$863$	1.57578e16	1.12056	0.560281	+	0.828303i	$0.310693\pi$
$864$	−2.59323e15	−0.183238
$865$	−7.98780e14	−0.0560840
$866$	−4.50014e15	−0.313963
$867$	−1.14794e16	−0.795822
$868$	7.97098e15	0.549102
$869$	−1.39776e16	−0.956807
$870$	2.69302e15	0.183183
$871$	−3.19705e15	−0.216097
$872$	−9.10509e15	−0.611566
$873$	−6.77929e15	−0.452487
$874$	2.07412e16	1.37569
$875$	1.02938e16	0.678469
$876$	−1.95197e15	−0.127850
$877$	−1.76366e16	−1.14794	−0.573968	−	0.818878i	$-0.694597\pi$
$877$	−1.76366e16	−1.14794	−0.573968	+	0.818878i	$0.694597\pi$
$878$	9.76582e15	0.631668
$879$	−5.74398e15	−0.369211
$880$	3.23955e15	0.206933
$881$	2.32278e16	1.47449	0.737243	−	0.675628i	$-0.236127\pi$
$881$	2.32278e16	1.47449	0.737243	+	0.675628i	$0.236127\pi$
$882$	−1.00639e15	−0.0634878
$883$	2.21922e16	1.39128	0.695642	−	0.718389i	$-0.255120\pi$
$883$	2.21922e16	1.39128	0.695642	+	0.718389i	$0.255120\pi$
$884$	4.45008e15	0.277256
$885$	−6.73998e14	−0.0417321
$886$	−6.38199e15	−0.392709
$887$	1.93898e16	1.18575	0.592875	−	0.805295i	$-0.297993\pi$
$887$	1.93898e16	1.18575	0.592875	+	0.805295i	$0.297993\pi$
$888$	−2.78127e15	−0.169033
$889$	9.29392e15	0.561357
$890$	−6.23413e15	−0.374223
$891$	−1.26368e15	−0.0753894
$892$	−6.21454e15	−0.368470
$893$	−4.00581e15	−0.236052
$894$	−6.74492e14	−0.0395021
$895$	1.33897e16	0.779372
$896$	−1.27345e16	−0.736696
$897$	−3.74609e15	−0.215387
$898$	−8.63342e15	−0.493359
$899$	−2.28252e16	−1.29639
$900$	3.43678e15	0.194007
$901$	−2.37317e16	−1.33151
$902$	7.95762e15	0.443759
$903$	5.06507e15	0.280739
$904$	1.11573e16	0.614658
$905$	1.30768e16	0.716036
$906$	−2.06570e15	−0.112425
$907$	−2.54420e16	−1.37629	−0.688146	−	0.725572i	$-0.741575\pi$
$907$	−2.54420e16	−1.37629	−0.688146	+	0.725572i	$0.741575\pi$
$908$	4.11534e15	0.221276
$909$	−7.51446e15	−0.401603
$910$	6.42449e14	0.0341280
$911$	−9.76594e15	−0.515659	−0.257830	−	0.966190i	$-0.583007\pi$
$911$	−9.76594e15	−0.515659	−0.257830	+	0.966190i	$0.583007\pi$
$912$	1.19548e16	0.627438
$913$	−1.62509e16	−0.847792
$914$	2.20585e15	0.114386
$915$	−3.07438e15	−0.158468
$916$	−1.00509e16	−0.514968
$917$	1.87961e16	0.957274
$918$	−2.33490e15	−0.118204
$919$	3.66644e16	1.84505	0.922527	−	0.385933i	$-0.126121\pi$
$919$	3.66644e16	1.84505	0.922527	+	0.385933i	$0.126121\pi$
$920$	−1.42117e16	−0.710905
$921$	1.79329e15	0.0891709
$922$	−1.52409e16	−0.753341
$923$	5.18891e15	0.254957
$924$	−4.87440e15	−0.238081
$925$	5.68774e15	0.276160
$926$	1.31931e16	0.636778
$927$	8.21097e15	0.393964
$928$	2.86435e16	1.36619
$929$	1.21481e16	0.576001	0.288001	−	0.957630i	$-0.407009\pi$
$929$	1.21481e16	0.576001	0.288001	+	0.957630i	$0.407009\pi$
$930$	−2.44706e15	−0.115342
$931$	2.01917e16	0.946130
$932$	1.04636e16	0.487410
$933$	6.58321e15	0.304852
$934$	−2.06917e15	−0.0952552
$935$	1.26945e16	0.580969
$936$	1.14804e15	0.0522322
$937$	−1.51708e16	−0.686183	−0.343091	−	0.939302i	$-0.611474\pi$
$937$	−1.51708e16	−0.686183	−0.343091	+	0.939302i	$0.611474\pi$
$938$	6.47042e15	0.290949
$939$	1.60948e16	0.719491
$940$	1.25415e15	0.0557375
$941$	−3.17507e16	−1.40285	−0.701423	−	0.712745i	$-0.747451\pi$
$941$	−3.17507e16	−1.40285	−0.701423	+	0.712745i	$0.747451\pi$
$942$	1.08610e15	0.0477079
$943$	6.56559e16	2.86721
$944$	−1.64718e15	−0.0715145
$945$	1.78809e15	0.0771816
$946$	4.23888e15	0.181907
$947$	2.85074e16	1.21628	0.608138	−	0.793831i	$-0.291917\pi$
$947$	2.85074e16	1.21628	0.608138	+	0.793831i	$0.291917\pi$
$948$	1.61492e16	0.685024
$949$	1.33344e15	0.0562354
$950$	1.29989e16	0.545039
$951$	6.25225e15	0.260642
$952$	−1.97107e16	−0.816955
$953$	−7.54001e15	−0.310714	−0.155357	−	0.987858i	$-0.549653\pi$
$953$	−7.54001e15	−0.310714	−0.155357	+	0.987858i	$0.549653\pi$
$954$	−2.79748e15	−0.114618
$955$	−9.26495e15	−0.377420
$956$	9.03201e15	0.365819
$957$	1.39580e16	0.562092
$958$	1.79378e16	0.718220
$959$	6.59571e15	0.262578
$960$	−1.37761e15	−0.0545297
$961$	−4.66800e15	−0.183718
$962$	8.68149e14	0.0339728
$963$	−1.75841e15	−0.0684188
$964$	−2.59024e16	−1.00211
$965$	−2.16349e16	−0.832252
$966$	7.58161e15	0.289993
$967$	4.65003e16	1.76852	0.884260	−	0.466995i	$-0.154663\pi$
$967$	4.65003e16	1.76852	0.884260	+	0.466995i	$0.154663\pi$
$968$	1.04647e16	0.395744
$969$	4.68462e16	1.76154
$970$	8.02789e15	0.300163
$971$	2.80464e15	0.104273	0.0521365	−	0.998640i	$-0.483397\pi$
$971$	2.80464e15	0.104273	0.0521365	+	0.998640i	$0.483397\pi$
$972$	1.46001e15	0.0539749
$973$	5.97218e15	0.219539
$974$	−1.07906e15	−0.0394430
$975$	−2.34775e15	−0.0853349
$976$	−7.51344e15	−0.271559
$977$	3.02212e16	1.08615	0.543077	−	0.839683i	$-0.317259\pi$
$977$	3.02212e16	1.08615	0.543077	+	0.839683i	$0.317259\pi$
$978$	−2.99896e15	−0.107178
$979$	−3.23116e16	−1.14830
$980$	−6.32171e15	−0.223404
$981$	7.91015e15	0.277975
$982$	−1.00127e15	−0.0349896
$983$	−6.55268e15	−0.227706	−0.113853	−	0.993498i	$-0.536319\pi$
$983$	−6.55268e15	−0.227706	−0.113853	+	0.993498i	$0.536319\pi$
$984$	−2.01211e16	−0.695310
$985$	3.35261e15	0.115208
$986$	2.57901e16	0.881313
$987$	−1.46426e15	−0.0497592
$988$	−1.05248e16	−0.355672
$989$	3.49737e16	1.17534
$990$	1.49642e15	0.0500105
$991$	−4.07952e16	−1.35583	−0.677913	−	0.735143i	$-0.737115\pi$
$991$	−4.07952e16	−1.35583	−0.677913	+	0.735143i	$0.737115\pi$
$992$	−2.60274e16	−0.860235
$993$	1.33376e16	0.438387
$994$	−1.05017e16	−0.343269
$995$	−1.34058e15	−0.0435778
$996$	1.87757e16	0.606975
$997$	−1.46734e16	−0.471746	−0.235873	−	0.971784i	$-0.575795\pi$
$997$	−1.46734e16	−0.471746	−0.235873	+	0.971784i	$0.575795\pi$
$998$	1.99937e15	0.0639255
$999$	2.41626e15	0.0768306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.17	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+18.0234 q^{2} -243.000 q^{3} -1723.16 q^{4} -3879.65 q^{5} -4379.69 q^{6} +32120.2 q^{7} -67969.1 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+18.0234 q^{2} -243.000 q^{3} -1723.16 q^{4} -3879.65 q^{5} -4379.69 q^{6} +32120.2 q^{7} -67969.1 q^{8} +59049.0 q^{9} -69924.5 q^{10} -362420. q^{11} +418727. q^{12} -286043. q^{13} +578915. q^{14} +942754. q^{15} +2.30399e6 q^{16} +9.02842e6 q^{17} +1.06426e6 q^{18} -2.13529e7 q^{19} +6.68524e6 q^{20} -7.80520e6 q^{21} -6.53205e6 q^{22} -5.38940e7 q^{23} +1.65165e7 q^{24} -3.37765e7 q^{25} -5.15548e6 q^{26} -1.43489e7 q^{27} -5.53480e7 q^{28} +1.58491e8 q^{29} +1.69917e7 q^{30} -1.44016e8 q^{31} +1.80727e8 q^{32} +8.80681e7 q^{33} +1.62723e8 q^{34} -1.24615e8 q^{35} -1.01751e8 q^{36} -1.68394e8 q^{37} -3.84852e8 q^{38} +6.95085e7 q^{39} +2.63696e8 q^{40} -1.21824e9 q^{41} -1.40676e8 q^{42} -6.48935e8 q^{43} +6.24507e8 q^{44} -2.29089e8 q^{45} -9.71354e8 q^{46} +1.87600e8 q^{47} -5.59869e8 q^{48} -9.45622e8 q^{49} -6.08767e8 q^{50} -2.19391e9 q^{51} +4.92897e8 q^{52} -2.62856e9 q^{53} -2.58616e8 q^{54} +1.40606e9 q^{55} -2.18318e9 q^{56} +5.18875e9 q^{57} +2.85655e9 q^{58} -7.14924e8 q^{59} -1.62451e9 q^{60} -3.26106e9 q^{61} -2.59565e9 q^{62} +1.89666e9 q^{63} -1.46126e9 q^{64} +1.10975e9 q^{65} +1.58729e9 q^{66} +1.11768e10 q^{67} -1.55574e10 q^{68} +1.30962e10 q^{69} -2.24599e9 q^{70} -1.81403e10 q^{71} -4.01351e9 q^{72} -4.66168e9 q^{73} -3.03503e9 q^{74} +8.20768e9 q^{75} +3.67943e10 q^{76} -1.16410e10 q^{77} +1.25278e9 q^{78} +3.85674e10 q^{79} -8.93866e9 q^{80} +3.48678e9 q^{81} -2.19569e10 q^{82} +4.48401e10 q^{83} +1.34496e10 q^{84} -3.50271e10 q^{85} -1.16960e10 q^{86} -3.85133e10 q^{87} +2.46334e10 q^{88} +8.91551e10 q^{89} -4.12897e9 q^{90} -9.18775e9 q^{91} +9.28678e10 q^{92} +3.49958e10 q^{93} +3.38120e9 q^{94} +8.28416e10 q^{95} -4.39165e10 q^{96} -1.14808e11 q^{97} -1.70434e10 q^{98} -2.14006e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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

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