LMFDB - Embedded newform 177.12.a.c.1.27

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			1.27
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)

$f(q)$	$=$	$q+89.5689 q^{2} -243.000 q^{3} +5974.59 q^{4} -2394.52 q^{5} -21765.2 q^{6} +82780.6 q^{7} +351700. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+89.5689 q^{2} -243.000 q^{3} +5974.59 q^{4} -2394.52 q^{5} -21765.2 q^{6} +82780.6 q^{7} +351700. q^{8} +59049.0 q^{9} -214474. q^{10} +779652. q^{11} -1.45182e6 q^{12} -367842. q^{13} +7.41457e6 q^{14} +581867. q^{15} +1.92654e7 q^{16} +3.35571e6 q^{17} +5.28895e6 q^{18} -1.92545e6 q^{19} -1.43062e7 q^{20} -2.01157e7 q^{21} +6.98326e7 q^{22} -3.41753e7 q^{23} -8.54631e7 q^{24} -4.30944e7 q^{25} -3.29472e7 q^{26} -1.43489e7 q^{27} +4.94580e8 q^{28} -2.65752e7 q^{29} +5.21172e7 q^{30} +1.71821e8 q^{31} +1.00530e9 q^{32} -1.89455e8 q^{33} +3.00567e8 q^{34} -1.98219e8 q^{35} +3.52793e8 q^{36} -7.07509e8 q^{37} -1.72460e8 q^{38} +8.93856e7 q^{39} -8.42151e8 q^{40} -2.76802e8 q^{41} -1.80174e9 q^{42} -9.77694e8 q^{43} +4.65810e9 q^{44} -1.41394e8 q^{45} -3.06105e9 q^{46} +2.45966e9 q^{47} -4.68150e9 q^{48} +4.87530e9 q^{49} -3.85992e9 q^{50} -8.15437e8 q^{51} -2.19770e9 q^{52} -3.75673e9 q^{53} -1.28522e9 q^{54} -1.86689e9 q^{55} +2.91140e10 q^{56} +4.67883e8 q^{57} -2.38031e9 q^{58} -7.14924e8 q^{59} +3.47642e9 q^{60} +1.05908e9 q^{61} +1.53898e10 q^{62} +4.88811e9 q^{63} +5.05882e10 q^{64} +8.80803e8 q^{65} -1.69693e10 q^{66} -4.59928e9 q^{67} +2.00490e10 q^{68} +8.30460e9 q^{69} -1.77543e10 q^{70} +1.72811e10 q^{71} +2.07675e10 q^{72} +2.89063e9 q^{73} -6.33708e10 q^{74} +1.04719e10 q^{75} -1.15037e10 q^{76} +6.45401e10 q^{77} +8.00617e9 q^{78} -5.08894e10 q^{79} -4.61314e10 q^{80} +3.48678e9 q^{81} -2.47928e10 q^{82} +3.23140e10 q^{83} -1.20183e11 q^{84} -8.03529e9 q^{85} -8.75709e10 q^{86} +6.45778e9 q^{87} +2.74204e11 q^{88} +1.57705e10 q^{89} -1.26645e10 q^{90} -3.04502e10 q^{91} -2.04183e11 q^{92} -4.17525e10 q^{93} +2.20309e11 q^{94} +4.61051e9 q^{95} -2.44288e11 q^{96} +1.26505e11 q^{97} +4.36676e11 q^{98} +4.60377e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	89.5689	1.97921	0.989606	−	0.143806i	$-0.0459343\pi$
$2$	89.5689	1.97921	0.989606	+	0.143806i	$0.0459343\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	5974.59	2.91728
$5$	−2394.52	−0.342675	−0.171338	−	0.985212i	$-0.554809\pi$
$5$	−2394.52	−0.342675	−0.171338	+	0.985212i	$0.554809\pi$
$6$	−21765.2	−1.14270
$7$	82780.6	1.86161	0.930807	−	0.365512i	$-0.119106\pi$
$7$	82780.6	1.86161	0.930807	+	0.365512i	$0.119106\pi$
$8$	351700.	3.79470
$9$	59049.0	0.333333
$10$	−214474.	−0.678227
$11$	779652.	1.45962	0.729812	−	0.683648i	$-0.239608\pi$
$11$	779652.	1.45962	0.729812	+	0.683648i	$0.239608\pi$
$12$	−1.45182e6	−1.68429
$13$	−367842.	−0.274772	−0.137386	−	0.990518i	$-0.543870\pi$
$13$	−367842.	−0.274772	−0.137386	+	0.990518i	$0.543870\pi$
$14$	7.41457e6	3.68453
$15$	581867.	0.197844
$16$	1.92654e7	4.59324
$17$	3.35571e6	0.573212	0.286606	−	0.958049i	$-0.407473\pi$
$17$	3.35571e6	0.573212	0.286606	+	0.958049i	$0.407473\pi$
$18$	5.28895e6	0.659737
$19$	−1.92545e6	−0.178397	−0.0891983	−	0.996014i	$-0.528430\pi$
$19$	−1.92545e6	−0.178397	−0.0891983	+	0.996014i	$0.528430\pi$
$20$	−1.43062e7	−0.999679
$21$	−2.01157e7	−1.07480
$22$	6.98326e7	2.88891
$23$	−3.41753e7	−1.10716	−0.553579	−	0.832797i	$-0.686738\pi$
$23$	−3.41753e7	−1.10716	−0.553579	+	0.832797i	$0.686738\pi$
$24$	−8.54631e7	−2.19087
$25$	−4.30944e7	−0.882574
$26$	−3.29472e7	−0.543833
$27$	−1.43489e7	−0.192450
$28$	4.94580e8	5.43084
$29$	−2.65752e7	−0.240596	−0.120298	−	0.992738i	$-0.538385\pi$
$29$	−2.65752e7	−0.240596	−0.120298	+	0.992738i	$0.538385\pi$
$30$	5.21172e7	0.391574
$31$	1.71821e8	1.07792	0.538960	−	0.842331i	$-0.318817\pi$
$31$	1.71821e8	1.07792	0.538960	+	0.842331i	$0.318817\pi$
$32$	1.00530e9	5.29629
$33$	−1.89455e8	−0.842714
$34$	3.00567e8	1.13451
$35$	−1.98219e8	−0.637928
$36$	3.52793e8	0.972426
$37$	−7.07509e8	−1.67735	−0.838673	−	0.544635i	$-0.816668\pi$
$37$	−7.07509e8	−1.67735	−0.838673	+	0.544635i	$0.816668\pi$
$38$	−1.72460e8	−0.353085
$39$	8.93856e7	0.158640
$40$	−8.42151e8	−1.30035
$41$	−2.76802e8	−0.373128	−0.186564	−	0.982443i	$-0.559735\pi$
$41$	−2.76802e8	−0.373128	−0.186564	+	0.982443i	$0.559735\pi$
$42$	−1.80174e9	−2.12726
$43$	−9.77694e8	−1.01421	−0.507103	−	0.861885i	$-0.669284\pi$
$43$	−9.77694e8	−1.01421	−0.507103	+	0.861885i	$0.669284\pi$
$44$	4.65810e9	4.25813
$45$	−1.41394e8	−0.114225
$46$	−3.06105e9	−2.19130
$47$	2.45966e9	1.56436	0.782180	−	0.623053i	$-0.214108\pi$
$47$	2.45966e9	1.56436	0.782180	+	0.623053i	$0.214108\pi$
$48$	−4.68150e9	−2.65191
$49$	4.87530e9	2.46560
$50$	−3.85992e9	−1.74680
$51$	−8.15437e8	−0.330944
$52$	−2.19770e9	−0.801587
$53$	−3.75673e9	−1.23394	−0.616968	−	0.786988i	$-0.711639\pi$
$53$	−3.75673e9	−1.23394	−0.616968	+	0.786988i	$0.711639\pi$
$54$	−1.28522e9	−0.380899
$55$	−1.86689e9	−0.500177
$56$	2.91140e10	7.06427
$57$	4.67883e8	0.102997
$58$	−2.38031e9	−0.476190
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	3.47642e9	0.577165
$61$	1.05908e9	0.160551	0.0802755	−	0.996773i	$-0.474420\pi$
$61$	1.05908e9	0.160551	0.0802755	+	0.996773i	$0.474420\pi$
$62$	1.53898e10	2.13343
$63$	4.88811e9	0.620538
$64$	5.05882e10	5.88924
$65$	8.80803e8	0.0941576
$66$	−1.69693e10	−1.66791
$67$	−4.59928e9	−0.416178	−0.208089	−	0.978110i	$-0.566724\pi$
$67$	−4.59928e9	−0.416178	−0.208089	+	0.978110i	$0.566724\pi$
$68$	2.00490e10	1.67222
$69$	8.30460e9	0.639218
$70$	−1.77543e10	−1.26260
$71$	1.72811e10	1.13671	0.568357	−	0.822782i	$-0.307579\pi$
$71$	1.72811e10	1.13671	0.568357	+	0.822782i	$0.307579\pi$
$72$	2.07675e10	1.26490
$73$	2.89063e9	0.163198	0.0815992	−	0.996665i	$-0.473997\pi$
$73$	2.89063e9	0.163198	0.0815992	+	0.996665i	$0.473997\pi$
$74$	−6.33708e10	−3.31982
$75$	1.04719e10	0.509554
$76$	−1.15037e10	−0.520433
$77$	6.45401e10	2.71726
$78$	8.00617e9	0.313982
$79$	−5.08894e10	−1.86071	−0.930355	−	0.366660i	$-0.880501\pi$
$79$	−5.08894e10	−1.86071	−0.930355	+	0.366660i	$0.880501\pi$
$80$	−4.61314e10	−1.57399
$81$	3.48678e9	0.111111
$82$	−2.47928e10	−0.738499
$83$	3.23140e10	0.900455	0.450227	−	0.892914i	$-0.351343\pi$
$83$	3.23140e10	0.900455	0.450227	+	0.892914i	$0.351343\pi$
$84$	−1.20183e11	−3.13550
$85$	−8.03529e9	−0.196425
$86$	−8.75709e10	−2.00733
$87$	6.45778e9	0.138908
$88$	2.74204e11	5.53884
$89$	1.57705e10	0.299364	0.149682	−	0.988734i	$-0.452175\pi$
$89$	1.57705e10	0.299364	0.149682	+	0.988734i	$0.452175\pi$
$90$	−1.26645e10	−0.226076
$91$	−3.04502e10	−0.511520
$92$	−2.04183e11	−3.22989
$93$	−4.17525e10	−0.622338
$94$	2.20309e11	3.09620
$95$	4.61051e9	0.0611321
$96$	−2.44288e11	−3.05781
$97$	1.26505e11	1.49576	0.747879	−	0.663835i	$-0.231072\pi$
$97$	1.26505e11	1.49576	0.747879	+	0.663835i	$0.231072\pi$
$98$	4.36676e11	4.87995
$99$	4.60377e10	0.486541
$100$	−2.57471e11	−2.57471
$101$	−1.00166e11	−0.948311	−0.474156	−	0.880441i	$-0.657247\pi$
$101$	−1.00166e11	−0.948311	−0.474156	+	0.880441i	$0.657247\pi$
$102$	−7.30378e10	−0.655008
$103$	−1.09210e11	−0.928232	−0.464116	−	0.885775i	$-0.653628\pi$
$103$	−1.09210e11	−0.928232	−0.464116	+	0.885775i	$0.653628\pi$
$104$	−1.29370e11	−1.04268
$105$	4.81673e10	0.368308
$106$	−3.36486e11	−2.44222
$107$	−1.15719e11	−0.797619	−0.398809	−	0.917034i	$-0.630577\pi$
$107$	−1.15719e11	−0.797619	−0.398809	+	0.917034i	$0.630577\pi$
$108$	−8.57288e10	−0.561431
$109$	2.81349e11	1.75146	0.875730	−	0.482801i	$-0.160381\pi$
$109$	2.81349e11	1.75146	0.875730	+	0.482801i	$0.160381\pi$
$110$	−1.67215e11	−0.989956
$111$	1.71925e11	0.968416
$112$	1.59480e12	8.55083
$113$	−3.92395e10	−0.200351	−0.100176	−	0.994970i	$-0.531940\pi$
$113$	−3.92395e10	−0.200351	−0.100176	+	0.994970i	$0.531940\pi$
$114$	4.19078e10	0.203854
$115$	8.18333e10	0.379395
$116$	−1.58776e11	−0.701885
$117$	−2.17207e10	−0.0915908
$118$	−6.40350e10	−0.257671
$119$	2.77788e11	1.06710
$120$	2.04643e11	0.750757
$121$	3.22546e11	1.13050
$122$	9.48602e10	0.317764
$123$	6.72628e10	0.215425
$124$	1.02656e12	3.14460
$125$	2.20110e11	0.645111
$126$	4.37823e11	1.22818
$127$	7.56882e10	0.203286	0.101643	−	0.994821i	$-0.467590\pi$
$127$	7.56882e10	0.203286	0.101643	+	0.994821i	$0.467590\pi$
$128$	2.47227e12	6.35976
$129$	2.37580e11	0.585552
$130$	7.88926e10	0.186358
$131$	3.15747e10	0.0715067	0.0357534	−	0.999361i	$-0.488617\pi$
$131$	3.15747e10	0.0715067	0.0357534	+	0.999361i	$0.488617\pi$
$132$	−1.13192e12	−2.45843
$133$	−1.59390e11	−0.332105
$134$	−4.11953e11	−0.823704
$135$	3.43587e10	0.0659479
$136$	1.18020e12	2.17517
$137$	−9.94887e10	−0.176121	−0.0880604	−	0.996115i	$-0.528067\pi$
$137$	−9.94887e10	−0.176121	−0.0880604	+	0.996115i	$0.528067\pi$
$138$	7.43834e11	1.26515
$139$	−9.15273e11	−1.49613	−0.748065	−	0.663626i	$-0.769017\pi$
$139$	−9.15273e11	−1.49613	−0.748065	+	0.663626i	$0.769017\pi$
$140$	−1.18428e12	−1.86102
$141$	−5.97697e11	−0.903183
$142$	1.54785e12	2.24980
$143$	−2.86789e11	−0.401064
$144$	1.13760e12	1.53108
$145$	6.36348e10	0.0824462
$146$	2.58910e11	0.323004
$147$	−1.18470e12	−1.42352
$148$	−4.22708e12	−4.89329
$149$	−3.25855e11	−0.363497	−0.181748	−	0.983345i	$-0.558176\pi$
$149$	−3.25855e11	−0.363497	−0.181748	+	0.983345i	$0.558176\pi$
$150$	9.37961e11	1.00852
$151$	3.19807e11	0.331524	0.165762	−	0.986166i	$-0.446992\pi$
$151$	3.19807e11	0.331524	0.165762	+	0.986166i	$0.446992\pi$
$152$	−6.77180e11	−0.676962
$153$	1.98151e11	0.191071
$154$	5.78078e12	5.37802
$155$	−4.11428e11	−0.369377
$156$	5.34042e11	0.462797
$157$	5.65929e11	0.473494	0.236747	−	0.971571i	$-0.423919\pi$
$157$	5.65929e11	0.473494	0.236747	+	0.971571i	$0.423919\pi$
$158$	−4.55811e12	−3.68274
$159$	9.12886e11	0.712414
$160$	−2.40721e12	−1.81491
$161$	−2.82905e12	−2.06110
$162$	3.12307e11	0.219912
$163$	2.04386e12	1.39130	0.695648	−	0.718383i	$-0.255117\pi$
$163$	2.04386e12	1.39130	0.695648	+	0.718383i	$0.255117\pi$
$164$	−1.65378e12	−1.08852
$165$	4.53654e11	0.288777
$166$	2.89433e12	1.78219
$167$	−1.64310e12	−0.978866	−0.489433	−	0.872041i	$-0.662796\pi$
$167$	−1.64310e12	−0.978866	−0.489433	+	0.872041i	$0.662796\pi$
$168$	−7.07469e12	−4.07856
$169$	−1.65685e12	−0.924500
$170$	−7.19712e11	−0.388767
$171$	−1.13696e11	−0.0594655
$172$	−5.84132e12	−2.95872
$173$	−3.57062e12	−1.75182	−0.875912	−	0.482471i	$-0.839740\pi$
$173$	−3.57062e12	−1.75182	−0.875912	+	0.482471i	$0.839740\pi$
$174$	5.78416e11	0.274928
$175$	−3.56738e12	−1.64301
$176$	1.50203e13	6.70440
$177$	1.73727e11	0.0751646
$178$	1.41254e12	0.592504
$179$	−1.07276e12	−0.436327	−0.218163	−	0.975912i	$-0.570007\pi$
$179$	−1.07276e12	−0.436327	−0.218163	+	0.975912i	$0.570007\pi$
$180$	−8.44769e11	−0.333226
$181$	3.26993e12	1.25114	0.625571	−	0.780167i	$-0.284866\pi$
$181$	3.26993e12	1.25114	0.625571	+	0.780167i	$0.284866\pi$
$182$	−2.72739e12	−1.01241
$183$	−2.57355e11	−0.0926941
$184$	−1.20195e13	−4.20133
$185$	1.69414e12	0.574785
$186$	−3.73972e12	−1.23174
$187$	2.61628e12	0.836674
$188$	1.46954e13	4.56367
$189$	−1.18781e12	−0.358268
$190$	4.12958e11	0.120993
$191$	2.80134e12	0.797411	0.398705	−	0.917079i	$-0.369460\pi$
$191$	2.80134e12	0.797411	0.398705	+	0.917079i	$0.369460\pi$
$192$	−1.22929e13	−3.40015
$193$	−3.03872e12	−0.816819	−0.408410	−	0.912799i	$-0.633917\pi$
$193$	−3.03872e12	−0.816819	−0.408410	+	0.912799i	$0.633917\pi$
$194$	1.13309e13	2.96042
$195$	−2.14035e11	−0.0543619
$196$	2.91279e13	7.19285
$197$	−7.58725e11	−0.182188	−0.0910941	−	0.995842i	$-0.529036\pi$
$197$	−7.58725e11	−0.182188	−0.0910941	+	0.995842i	$0.529036\pi$
$198$	4.12354e12	0.962968
$199$	2.00619e12	0.455700	0.227850	−	0.973696i	$-0.426830\pi$
$199$	2.00619e12	0.455700	0.227850	+	0.973696i	$0.426830\pi$
$200$	−1.51563e13	−3.34910
$201$	1.11763e12	0.240280
$202$	−8.97172e12	−1.87691
$203$	−2.19991e12	−0.447896
$204$	−4.87190e12	−0.965456
$205$	6.62806e11	0.127862
$206$	−9.78179e12	−1.83717
$207$	−2.01802e12	−0.369053
$208$	−7.08664e12	−1.26209
$209$	−1.50118e12	−0.260392
$210$	4.31429e12	0.728960
$211$	−9.56347e12	−1.57421	−0.787104	−	0.616820i	$-0.788420\pi$
$211$	−9.56347e12	−1.57421	−0.787104	+	0.616820i	$0.788420\pi$
$212$	−2.24449e13	−3.59974
$213$	−4.19932e12	−0.656282
$214$	−1.03649e13	−1.57866
$215$	2.34110e12	0.347543
$216$	−5.04651e12	−0.730291
$217$	1.42234e13	2.00667
$218$	2.52002e13	3.46651
$219$	−7.02422e11	−0.0942227
$220$	−1.11539e13	−1.45916
$221$	−1.23437e12	−0.157503
$222$	1.53991e13	1.91670
$223$	4.22311e12	0.512809	0.256404	−	0.966570i	$-0.417462\pi$
$223$	4.22311e12	0.512809	0.256404	+	0.966570i	$0.417462\pi$
$224$	8.32195e13	9.85964
$225$	−2.54468e12	−0.294191
$226$	−3.51463e12	−0.396537
$227$	8.54796e12	0.941283	0.470641	−	0.882325i	$-0.344023\pi$
$227$	8.54796e12	0.941283	0.470641	+	0.882325i	$0.344023\pi$
$228$	2.79541e12	0.300472
$229$	−1.10399e13	−1.15843	−0.579216	−	0.815174i	$-0.696641\pi$
$229$	−1.10399e13	−1.15843	−0.579216	+	0.815174i	$0.696641\pi$
$230$	7.32972e12	0.750904
$231$	−1.56832e13	−1.56881
$232$	−9.34651e12	−0.912989
$233$	−3.30039e11	−0.0314853	−0.0157427	−	0.999876i	$-0.505011\pi$
$233$	−3.30039e11	−0.0314853	−0.0157427	+	0.999876i	$0.505011\pi$
$234$	−1.94550e12	−0.181278
$235$	−5.88969e12	−0.536067
$236$	−4.27138e12	−0.379797
$237$	1.23661e13	1.07428
$238$	2.48811e13	2.11201
$239$	−1.78415e13	−1.47994	−0.739968	−	0.672642i	$-0.765159\pi$
$239$	−1.78415e13	−1.47994	−0.739968	+	0.672642i	$0.765159\pi$
$240$	1.12099e13	0.908742
$241$	1.77101e13	1.40323	0.701613	−	0.712559i	$-0.252464\pi$
$241$	1.77101e13	1.40323	0.701613	+	0.712559i	$0.252464\pi$
$242$	2.88901e13	2.23750
$243$	−8.47289e11	−0.0641500
$244$	6.32754e12	0.468372
$245$	−1.16740e13	−0.844901
$246$	6.02466e12	0.426372
$247$	7.08260e11	0.0490184
$248$	6.04294e13	4.09039
$249$	−7.85231e12	−0.519878
$250$	1.97150e13	1.27681
$251$	−2.85583e13	−1.80937	−0.904685	−	0.426081i	$-0.859894\pi$
$251$	−2.85583e13	−1.80937	−0.904685	+	0.426081i	$0.859894\pi$
$252$	2.92045e13	1.81028
$253$	−2.66449e13	−1.61603
$254$	6.77931e12	0.402346
$255$	1.95258e12	0.113406
$256$	1.17834e14	6.69807
$257$	2.79519e13	1.55517	0.777587	−	0.628776i	$-0.216444\pi$
$257$	2.79519e13	1.55517	0.777587	+	0.628776i	$0.216444\pi$
$258$	2.12797e13	1.15893
$259$	−5.85681e13	−3.12257
$260$	5.26244e12	0.274684
$261$	−1.56924e12	−0.0801986
$262$	2.82811e12	0.141527
$263$	−6.56787e12	−0.321861	−0.160930	−	0.986966i	$-0.551449\pi$
$263$	−6.56787e12	−0.321861	−0.160930	+	0.986966i	$0.551449\pi$
$264$	−6.66315e13	−3.19785
$265$	8.99555e12	0.422839
$266$	−1.42764e13	−0.657307
$267$	−3.83222e12	−0.172838
$268$	−2.74788e13	−1.21411
$269$	−2.47910e13	−1.07314	−0.536571	−	0.843855i	$-0.680281\pi$
$269$	−2.47910e13	−1.07314	−0.536571	+	0.843855i	$0.680281\pi$
$270$	3.07747e12	0.130525
$271$	3.75050e13	1.55869	0.779343	−	0.626598i	$-0.215553\pi$
$271$	3.75050e13	1.55869	0.779343	+	0.626598i	$0.215553\pi$
$272$	6.46492e13	2.63290
$273$	7.39940e12	0.295326
$274$	−8.91109e12	−0.348580
$275$	−3.35987e13	−1.28823
$276$	4.96166e13	1.86478
$277$	−3.84476e12	−0.141655	−0.0708273	−	0.997489i	$-0.522564\pi$
$277$	−3.84476e12	−0.141655	−0.0708273	+	0.997489i	$0.522564\pi$
$278$	−8.19800e13	−2.96116
$279$	1.01459e13	0.359307
$280$	−6.97138e13	−2.42075
$281$	2.69982e13	0.919283	0.459642	−	0.888104i	$-0.347978\pi$
$281$	2.69982e13	0.919283	0.459642	+	0.888104i	$0.347978\pi$
$282$	−5.35350e13	−1.78759
$283$	−2.83401e13	−0.928059	−0.464030	−	0.885820i	$-0.653597\pi$
$283$	−2.83401e13	−0.928059	−0.464030	+	0.885820i	$0.653597\pi$
$284$	1.03248e14	3.31611
$285$	−1.12035e12	−0.0352946
$286$	−2.56874e13	−0.793791
$287$	−2.29138e13	−0.694620
$288$	5.93621e13	1.76543
$289$	−2.30111e13	−0.671428
$290$	5.69970e12	0.163178
$291$	−3.07406e13	−0.863577
$292$	1.72703e13	0.476095
$293$	1.54553e13	0.418124	0.209062	−	0.977902i	$-0.432959\pi$
$293$	1.54553e13	0.418124	0.209062	+	0.977902i	$0.432959\pi$
$294$	−1.06112e14	−2.81744
$295$	1.71190e12	0.0446125
$296$	−2.48831e14	−6.36503
$297$	−1.11872e13	−0.280905
$298$	−2.91865e13	−0.719437
$299$	1.25711e13	0.304216
$300$	6.25655e13	1.48651
$301$	−8.09341e13	−1.88806
$302$	2.86448e13	0.656156
$303$	2.43402e13	0.547508
$304$	−3.70946e13	−0.819418
$305$	−2.53597e12	−0.0550168
$306$	1.77482e13	0.378169
$307$	6.40813e13	1.34113	0.670565	−	0.741851i	$-0.266052\pi$
$307$	6.40813e13	1.34113	0.670565	+	0.741851i	$0.266052\pi$
$308$	3.85600e14	7.92699
$309$	2.65379e13	0.535915
$310$	−3.68511e13	−0.731074
$311$	2.21297e13	0.431314	0.215657	−	0.976469i	$-0.430811\pi$
$311$	2.21297e13	0.431314	0.215657	+	0.976469i	$0.430811\pi$
$312$	3.14369e13	0.601991
$313$	−1.22687e13	−0.230836	−0.115418	−	0.993317i	$-0.536821\pi$
$313$	−1.22687e13	−0.230836	−0.115418	+	0.993317i	$0.536821\pi$
$314$	5.06897e13	0.937144
$315$	−1.17047e13	−0.212643
$316$	−3.04043e14	−5.42821
$317$	3.03961e13	0.533325	0.266663	−	0.963790i	$-0.414079\pi$
$317$	3.03961e13	0.533325	0.266663	+	0.963790i	$0.414079\pi$
$318$	8.17662e13	1.41002
$319$	−2.07194e13	−0.351179
$320$	−1.21134e14	−2.01810
$321$	2.81198e13	0.460506
$322$	−2.53395e14	−4.07935
$323$	−6.46123e12	−0.102259
$324$	2.08321e13	0.324142
$325$	1.58519e13	0.242507
$326$	1.83066e14	2.75367
$327$	−6.83679e13	−1.01121
$328$	−9.73512e13	−1.41591
$329$	2.03612e14	2.91223
$330$	4.06333e13	0.571551
$331$	−1.16696e13	−0.161436	−0.0807181	−	0.996737i	$-0.525721\pi$
$331$	−1.16696e13	−0.161436	−0.0807181	+	0.996737i	$0.525721\pi$
$332$	1.93063e14	2.62688
$333$	−4.17777e13	−0.559116
$334$	−1.47171e14	−1.93738
$335$	1.10131e13	0.142614
$336$	−3.87537e14	−4.93682
$337$	7.59043e13	0.951265	0.475633	−	0.879644i	$-0.342219\pi$
$337$	7.59043e13	0.951265	0.475633	+	0.879644i	$0.342219\pi$
$338$	−1.48402e14	−1.82978
$339$	9.53519e12	0.115673
$340$	−4.80075e13	−0.573028
$341$	1.33961e14	1.57336
$342$	−1.01836e13	−0.117695
$343$	2.39896e14	2.72839
$344$	−3.43855e14	−3.84861
$345$	−1.98855e13	−0.219044
$346$	−3.19817e14	−3.46723
$347$	−1.11797e14	−1.19294	−0.596468	−	0.802637i	$-0.703430\pi$
$347$	−1.11797e14	−1.19294	−0.596468	+	0.802637i	$0.703430\pi$
$348$	3.85826e13	0.405234
$349$	4.24021e13	0.438376	0.219188	−	0.975683i	$-0.429659\pi$
$349$	4.24021e13	0.438376	0.219188	+	0.975683i	$0.429659\pi$
$350$	−3.19527e14	−3.25187
$351$	5.27813e12	0.0528800
$352$	7.83786e14	7.73059
$353$	6.48229e13	0.629459	0.314729	−	0.949181i	$-0.398086\pi$
$353$	6.48229e13	0.629459	0.314729	+	0.949181i	$0.398086\pi$
$354$	1.55605e13	0.148767
$355$	−4.13799e13	−0.389524
$356$	9.42219e13	0.873327
$357$	−6.75024e13	−0.616089
$358$	−9.60861e13	−0.863583
$359$	−1.73150e14	−1.53251	−0.766253	−	0.642539i	$-0.777881\pi$
$359$	−1.73150e14	−1.53251	−0.766253	+	0.642539i	$0.777881\pi$
$360$	−4.97282e13	−0.433450
$361$	−1.12783e14	−0.968175
$362$	2.92884e14	2.47627
$363$	−7.83786e13	−0.652696
$364$	−1.81927e14	−1.49225
$365$	−6.92165e12	−0.0559240
$366$	−2.30510e13	−0.183461
$367$	3.72946e13	0.292403	0.146202	−	0.989255i	$-0.453295\pi$
$367$	3.72946e13	0.292403	0.146202	+	0.989255i	$0.453295\pi$
$368$	−6.58402e14	−5.08544
$369$	−1.63449e13	−0.124376
$370$	1.51742e14	1.13762
$371$	−3.10985e14	−2.29711
$372$	−2.49454e14	−1.81553
$373$	1.37448e14	0.985690	0.492845	−	0.870117i	$-0.335957\pi$
$373$	1.37448e14	0.985690	0.492845	+	0.870117i	$0.335957\pi$
$374$	2.34338e14	1.65595
$375$	−5.34867e13	−0.372455
$376$	8.65062e14	5.93628
$377$	9.77549e12	0.0661091
$378$	−1.06391e14	−0.709087
$379$	1.57972e14	1.03769	0.518843	−	0.854870i	$-0.326363\pi$
$379$	1.57972e14	1.03769	0.518843	+	0.854870i	$0.326363\pi$
$380$	2.75459e13	0.178339
$381$	−1.83922e13	−0.117367
$382$	2.50913e14	1.57824
$383$	−5.56921e13	−0.345303	−0.172651	−	0.984983i	$-0.555233\pi$
$383$	−5.56921e13	−0.345303	−0.172651	+	0.984983i	$0.555233\pi$
$384$	−6.00761e14	−3.67181
$385$	−1.54542e14	−0.931136
$386$	−2.72175e14	−1.61666
$387$	−5.77318e13	−0.338069
$388$	7.55812e14	4.36354
$389$	−3.02915e14	−1.72424	−0.862119	−	0.506705i	$-0.830863\pi$
$389$	−3.02915e14	−1.72424	−0.862119	+	0.506705i	$0.830863\pi$
$390$	−1.91709e13	−0.107594
$391$	−1.14682e14	−0.634636
$392$	1.71464e15	9.35623
$393$	−7.67265e12	−0.0412844
$394$	−6.79582e13	−0.360589
$395$	1.21856e14	0.637619
$396$	2.75056e14	1.41938
$397$	9.36275e13	0.476492	0.238246	−	0.971205i	$-0.423428\pi$
$397$	9.36275e13	0.476492	0.238246	+	0.971205i	$0.423428\pi$
$398$	1.79692e14	0.901927
$399$	3.87317e13	0.191741
$400$	−8.30233e14	−4.05387
$401$	−5.56083e13	−0.267822	−0.133911	−	0.990993i	$-0.542754\pi$
$401$	−5.56083e13	−0.267822	−0.133911	+	0.990993i	$0.542754\pi$
$402$	1.00105e14	0.475566
$403$	−6.32030e13	−0.296183
$404$	−5.98448e14	−2.76649
$405$	−8.34916e12	−0.0380750
$406$	−1.97044e14	−0.886482
$407$	−5.51611e14	−2.44830
$408$	−2.86789e14	−1.25583
$409$	−3.48651e14	−1.50630	−0.753152	−	0.657847i	$-0.771467\pi$
$409$	−3.48651e14	−1.50630	−0.753152	+	0.657847i	$0.771467\pi$
$410$	5.93668e13	0.253065
$411$	2.41757e13	0.101683
$412$	−6.52483e14	−2.70791
$413$	−5.91819e13	−0.242361
$414$	−1.80752e14	−0.730433
$415$	−7.73765e13	−0.308563
$416$	−3.69792e14	−1.45527
$417$	2.22411e14	0.863791
$418$	−1.34459e14	−0.515371
$419$	−4.27942e13	−0.161885	−0.0809427	−	0.996719i	$-0.525793\pi$
$419$	−4.27942e13	−0.161885	−0.0809427	+	0.996719i	$0.525793\pi$
$420$	2.87780e14	1.07446
$421$	3.12067e14	1.15000	0.574998	−	0.818155i	$-0.305003\pi$
$421$	3.12067e14	1.15000	0.574998	+	0.818155i	$0.305003\pi$
$422$	−8.56590e14	−3.11569
$423$	1.45240e14	0.521453
$424$	−1.32124e15	−4.68242
$425$	−1.44612e14	−0.505902
$426$	−3.76128e14	−1.29892
$427$	8.76709e13	0.298884
$428$	−6.91376e14	−2.32688
$429$	6.96897e13	0.231555
$430$	2.09690e14	0.687862
$431$	−3.26508e13	−0.105747	−0.0528735	−	0.998601i	$-0.516838\pi$
$431$	−3.26508e13	−0.105747	−0.0528735	+	0.998601i	$0.516838\pi$
$432$	−2.76438e14	−0.883969
$433$	−1.89246e14	−0.597507	−0.298753	−	0.954330i	$-0.596571\pi$
$433$	−1.89246e14	−0.597507	−0.298753	+	0.954330i	$0.596571\pi$
$434$	1.27398e15	3.97163
$435$	−1.54633e13	−0.0476003
$436$	1.68095e15	5.10950
$437$	6.58027e13	0.197513
$438$	−6.29152e13	−0.186487
$439$	−4.27860e14	−1.25241	−0.626206	−	0.779658i	$-0.715393\pi$
$439$	−4.27860e14	−1.25241	−0.626206	+	0.779658i	$0.715393\pi$
$440$	−6.56585e14	−1.89802
$441$	2.87882e14	0.821868
$442$	−1.10561e14	−0.311731
$443$	−1.32504e14	−0.368983	−0.184492	−	0.982834i	$-0.559064\pi$
$443$	−1.32504e14	−0.368983	−0.184492	+	0.982834i	$0.559064\pi$
$444$	1.02718e15	2.82514
$445$	−3.77626e13	−0.102584
$446$	3.78259e14	1.01496
$447$	7.91829e13	0.209865
$448$	4.18772e15	10.9635
$449$	8.62016e13	0.222926	0.111463	−	0.993769i	$-0.464446\pi$
$449$	8.62016e13	0.222926	0.111463	+	0.993769i	$0.464446\pi$
$450$	−2.27924e14	−0.582267
$451$	−2.15809e14	−0.544626
$452$	−2.34440e14	−0.584480
$453$	−7.77131e13	−0.191405
$454$	7.65631e14	1.86300
$455$	7.29134e13	0.175285
$456$	1.64555e14	0.390844
$457$	4.74379e14	1.11323	0.556616	−	0.830770i	$-0.312099\pi$
$457$	4.74379e14	1.11323	0.556616	+	0.830770i	$0.312099\pi$
$458$	−9.88833e14	−2.29278
$459$	−4.81507e13	−0.110315
$460$	4.88920e14	1.10680
$461$	−4.42982e14	−0.990903	−0.495451	−	0.868636i	$-0.664997\pi$
$461$	−4.42982e14	−0.990903	−0.495451	+	0.868636i	$0.664997\pi$
$462$	−1.40473e15	−3.10500
$463$	−5.34414e14	−1.16730	−0.583650	−	0.812005i	$-0.698376\pi$
$463$	−5.34414e14	−1.16730	−0.583650	+	0.812005i	$0.698376\pi$
$464$	−5.11983e14	−1.10511
$465$	9.99770e13	0.213260
$466$	−2.95612e13	−0.0623161
$467$	1.21405e14	0.252927	0.126463	−	0.991971i	$-0.459637\pi$
$467$	1.21405e14	0.252927	0.126463	+	0.991971i	$0.459637\pi$
$468$	−1.29772e14	−0.267196
$469$	−3.80732e14	−0.774762
$470$	−5.27533e14	−1.06099
$471$	−1.37521e14	−0.273372
$472$	−2.51439e14	−0.494028
$473$	−7.62261e14	−1.48036
$474$	1.10762e15	2.12623
$475$	8.29760e13	0.157448
$476$	1.65967e15	3.11302
$477$	−2.21831e14	−0.411312
$478$	−1.59804e15	−2.92911
$479$	−6.62655e14	−1.20072	−0.600360	−	0.799730i	$-0.704976\pi$
$479$	−6.62655e14	−1.20072	−0.600360	+	0.799730i	$0.704976\pi$
$480$	5.84952e14	1.04784
$481$	2.60252e14	0.460888
$482$	1.58627e15	2.77728
$483$	6.87460e14	1.18998
$484$	1.92708e15	3.29799
$485$	−3.02917e14	−0.512559
$486$	−7.58907e13	−0.126966
$487$	5.28395e13	0.0874076	0.0437038	−	0.999045i	$-0.486084\pi$
$487$	5.28395e13	0.0874076	0.0437038	+	0.999045i	$0.486084\pi$
$488$	3.72477e14	0.609243
$489$	−4.96658e14	−0.803265
$490$	−1.04563e15	−1.67224
$491$	1.03937e14	0.164369	0.0821845	−	0.996617i	$-0.473810\pi$
$491$	1.03937e14	0.164369	0.0821845	+	0.996617i	$0.473810\pi$
$492$	4.01868e14	0.628456
$493$	−8.91787e13	−0.137912
$494$	6.34381e13	0.0970179
$495$	−1.10238e14	−0.166726
$496$	3.31021e15	4.95115
$497$	1.43054e15	2.11612
$498$	−7.03323e14	−1.02895
$499$	−4.90518e14	−0.709745	−0.354872	−	0.934915i	$-0.615476\pi$
$499$	−4.90518e14	−0.709745	−0.354872	+	0.934915i	$0.615476\pi$
$500$	1.31507e15	1.88197
$501$	3.99273e14	0.565149
$502$	−2.55794e15	−3.58113
$503$	−8.18094e14	−1.13287	−0.566434	−	0.824107i	$-0.691677\pi$
$503$	−8.18094e14	−1.13287	−0.566434	+	0.824107i	$0.691677\pi$
$504$	1.71915e15	2.35476
$505$	2.39848e14	0.324963
$506$	−2.38655e15	−3.19847
$507$	4.02615e14	0.533760
$508$	4.52206e14	0.593042
$509$	7.21617e14	0.936179	0.468089	−	0.883681i	$-0.344943\pi$
$509$	7.21617e14	0.936179	0.468089	+	0.883681i	$0.344943\pi$
$510$	1.74890e14	0.224455
$511$	2.39288e14	0.303812
$512$	5.49103e15	6.89715
$513$	2.76280e13	0.0343324
$514$	2.50362e15	3.07802
$515$	2.61504e14	0.318082
$516$	1.41944e15	1.70822
$517$	1.91768e15	2.28338
$518$	−5.24588e15	−6.18023
$519$	8.67662e14	1.01142
$520$	3.09779e14	0.357300
$521$	−1.08925e15	−1.24313	−0.621567	−	0.783361i	$-0.713504\pi$
$521$	−1.08925e15	−1.24313	−0.621567	+	0.783361i	$0.713504\pi$
$522$	−1.40555e14	−0.158730
$523$	−3.51576e13	−0.0392880	−0.0196440	−	0.999807i	$-0.506253\pi$
$523$	−3.51576e13	−0.0392880	−0.0196440	+	0.999807i	$0.506253\pi$
$524$	1.88646e14	0.208605
$525$	8.66874e14	0.948593
$526$	−5.88277e14	−0.637031
$527$	5.76581e14	0.617877
$528$	−3.64994e15	−3.87079
$529$	2.15143e14	0.225798
$530$	8.05721e14	0.836889
$531$	−4.22156e13	−0.0433963
$532$	−9.52287e14	−0.968844
$533$	1.01819e14	0.102525
$534$	−3.43248e14	−0.342082
$535$	2.77092e14	0.273324
$536$	−1.61757e15	−1.57927
$537$	2.60681e14	0.251913
$538$	−2.22050e15	−2.12397
$539$	3.80104e15	3.59886
$540$	2.05279e14	0.192388
$541$	1.64963e14	0.153039	0.0765193	−	0.997068i	$-0.475619\pi$
$541$	1.64963e14	0.153039	0.0765193	+	0.997068i	$0.475619\pi$
$542$	3.35928e15	3.08497
$543$	−7.94593e14	−0.722347
$544$	3.37350e15	3.03589
$545$	−6.73695e14	−0.600182
$546$	6.62756e14	0.584513
$547$	−6.81655e14	−0.595161	−0.297580	−	0.954697i	$-0.596180\pi$
$547$	−6.81655e14	−0.595161	−0.297580	+	0.954697i	$0.596180\pi$
$548$	−5.94404e14	−0.513793
$549$	6.25373e13	0.0535170
$550$	−3.00939e15	−2.54967
$551$	5.11692e13	0.0429215
$552$	2.92073e15	2.42564
$553$	−4.21266e15	−3.46392
$554$	−3.44371e14	−0.280365
$555$	−4.11677e14	−0.331852
$556$	−5.46838e15	−4.36463
$557$	−7.11492e14	−0.562298	−0.281149	−	0.959664i	$-0.590715\pi$
$557$	−7.11492e14	−0.562298	−0.281149	+	0.959664i	$0.590715\pi$
$558$	9.08753e14	0.711144
$559$	3.59637e14	0.278676
$560$	−3.81878e15	−2.93016
$561$	−6.35757e14	−0.483054
$562$	2.41820e15	1.81946
$563$	−2.17339e14	−0.161935	−0.0809676	−	0.996717i	$-0.525801\pi$
$563$	−2.17339e14	−0.161935	−0.0809676	+	0.996717i	$0.525801\pi$
$564$	−3.57099e15	−2.63484
$565$	9.39595e13	0.0686553
$566$	−2.53839e15	−1.83683
$567$	2.88638e14	0.206846
$568$	6.07778e15	4.31349
$569$	3.02105e14	0.212344	0.106172	−	0.994348i	$-0.466141\pi$
$569$	3.02105e14	0.212344	0.106172	+	0.994348i	$0.466141\pi$
$570$	−1.00349e14	−0.0698555
$571$	−2.19838e15	−1.51567	−0.757835	−	0.652446i	$-0.773743\pi$
$571$	−2.19838e15	−1.51567	−0.757835	+	0.652446i	$0.773743\pi$
$572$	−1.71344e15	−1.17002
$573$	−6.80725e14	−0.460385
$574$	−2.05237e15	−1.37480
$575$	1.47277e15	0.977148
$576$	2.98718e15	1.96308
$577$	1.90112e15	1.23749	0.618746	−	0.785591i	$-0.287641\pi$
$577$	1.90112e15	1.23749	0.618746	+	0.785591i	$0.287641\pi$
$578$	−2.06108e15	−1.32890
$579$	7.38410e14	0.471591
$580$	3.80192e14	0.240519
$581$	2.67498e15	1.67630
$582$	−2.75340e15	−1.70920
$583$	−2.92894e15	−1.80108
$584$	1.01663e15	0.619289
$585$	5.20106e13	0.0313859
$586$	1.38431e15	0.827555
$587$	−2.00692e15	−1.18856	−0.594278	−	0.804260i	$-0.702562\pi$
$587$	−2.00692e15	−1.18856	−0.594278	+	0.804260i	$0.702562\pi$
$588$	−7.07809e15	−4.15280
$589$	−3.30832e14	−0.192297
$590$	1.53333e14	0.0882976
$591$	1.84370e14	0.105186
$592$	−1.36305e16	−7.70445
$593$	2.77378e15	1.55336	0.776678	−	0.629898i	$-0.216903\pi$
$593$	2.77378e15	1.55336	0.776678	+	0.629898i	$0.216903\pi$
$594$	−1.00202e15	−0.555970
$595$	−6.65166e14	−0.365668
$596$	−1.94685e15	−1.06042
$597$	−4.87503e14	−0.263099
$598$	1.12598e15	0.602108
$599$	−5.49930e14	−0.291380	−0.145690	−	0.989330i	$-0.546540\pi$
$599$	−5.49930e14	−0.291380	−0.145690	+	0.989330i	$0.546540\pi$
$600$	3.68298e15	1.93361
$601$	5.12826e14	0.266785	0.133392	−	0.991063i	$-0.457413\pi$
$601$	5.12826e14	0.266785	0.133392	+	0.991063i	$0.457413\pi$
$602$	−7.24918e15	−3.73687
$603$	−2.71583e14	−0.138726
$604$	1.91072e15	0.967148
$605$	−7.72341e14	−0.387395
$606$	2.18013e15	1.08363
$607$	2.20659e15	1.08689	0.543443	−	0.839446i	$-0.317120\pi$
$607$	2.20659e15	1.08689	0.543443	+	0.839446i	$0.317120\pi$
$608$	−1.93565e15	−0.944840
$609$	5.34579e14	0.258593
$610$	−2.27144e14	−0.108890
$611$	−9.04766e14	−0.429843
$612$	1.18387e15	0.557406
$613$	9.83359e14	0.458859	0.229430	−	0.973325i	$-0.426314\pi$
$613$	9.83359e14	0.458859	0.229430	+	0.973325i	$0.426314\pi$
$614$	5.73970e15	2.65438
$615$	−1.61062e14	−0.0738209
$616$	2.26988e16	10.3112
$617$	−1.71714e15	−0.773105	−0.386553	−	0.922267i	$-0.626334\pi$
$617$	−1.71714e15	−0.773105	−0.386553	+	0.922267i	$0.626334\pi$
$618$	2.37697e15	1.06069
$619$	−2.02666e15	−0.896359	−0.448179	−	0.893944i	$-0.647927\pi$
$619$	−2.02666e15	−0.896359	−0.448179	+	0.893944i	$0.647927\pi$
$620$	−2.45811e15	−1.07757
$621$	4.90379e14	0.213073
$622$	1.98214e15	0.853662
$623$	1.30549e15	0.557299
$624$	1.72205e15	0.728671
$625$	1.57716e15	0.661510
$626$	−1.09889e15	−0.456874
$627$	3.64786e14	0.150337
$628$	3.38119e15	1.38131
$629$	−2.37419e15	−0.961474
$630$	−1.04837e15	−0.420865
$631$	3.83119e15	1.52466	0.762328	−	0.647190i	$-0.224056\pi$
$631$	3.83119e15	1.52466	0.762328	+	0.647190i	$0.224056\pi$
$632$	−1.78978e16	−7.06084
$633$	2.32392e15	0.908869
$634$	2.72255e15	1.05556
$635$	−1.81237e14	−0.0696611
$636$	5.45412e15	2.07831
$637$	−1.79334e15	−0.677480
$638$	−1.85582e15	−0.695059
$639$	1.02043e15	0.378905
$640$	−5.91988e15	−2.17933
$641$	4.21125e15	1.53706	0.768532	−	0.639811i	$-0.220988\pi$
$641$	4.21125e15	1.53706	0.768532	+	0.639811i	$0.220988\pi$
$642$	2.51866e15	0.911438
$643$	−2.64381e15	−0.948570	−0.474285	−	0.880371i	$-0.657293\pi$
$643$	−2.64381e15	−0.948570	−0.474285	+	0.880371i	$0.657293\pi$
$644$	−1.69024e16	−6.01280
$645$	−5.68888e14	−0.200654
$646$	−5.78726e14	−0.202392
$647$	5.49441e15	1.90523	0.952615	−	0.304178i	$-0.0983819\pi$
$647$	5.49441e15	1.90523	0.952615	+	0.304178i	$0.0983819\pi$
$648$	1.22630e15	0.421633
$649$	−5.57392e14	−0.190027
$650$	1.41984e15	0.479972
$651$	−3.45630e15	−1.15855
$652$	1.22112e16	4.05880
$653$	1.82652e15	0.602009	0.301004	−	0.953623i	$-0.402678\pi$
$653$	1.82652e15	0.602009	0.301004	+	0.953623i	$0.402678\pi$
$654$	−6.12364e15	−2.00139
$655$	−7.56060e13	−0.0245036
$656$	−5.33270e15	−1.71386
$657$	1.70689e14	0.0543995
$658$	1.82373e16	5.76392
$659$	3.20680e15	1.00508	0.502542	−	0.864553i	$-0.332398\pi$
$659$	3.20680e15	1.00508	0.502542	+	0.864553i	$0.332398\pi$
$660$	2.71040e15	0.842444
$661$	3.71622e15	1.14550	0.572748	−	0.819732i	$-0.305878\pi$
$661$	3.71622e15	1.14550	0.572748	+	0.819732i	$0.305878\pi$
$662$	−1.04523e15	−0.319517
$663$	2.99952e14	0.0909342
$664$	1.13649e16	3.41696
$665$	3.81661e14	0.113804
$666$	−3.74198e15	−1.10661
$667$	9.08217e14	0.266378
$668$	−9.81684e15	−2.85563
$669$	−1.02621e15	−0.296070
$670$	9.86427e14	0.282263
$671$	8.25710e14	0.234344
$672$	−2.02223e16	−5.69247
$673$	−9.23544e14	−0.257854	−0.128927	−	0.991654i	$-0.541153\pi$
$673$	−9.23544e14	−0.257854	−0.128927	+	0.991654i	$0.541153\pi$
$674$	6.79866e15	1.88276
$675$	6.18358e14	0.169851
$676$	−9.89901e15	−2.69702
$677$	6.35740e15	1.71807	0.859037	−	0.511913i	$-0.171063\pi$
$677$	6.35740e15	1.71807	0.859037	+	0.511913i	$0.171063\pi$
$678$	8.54056e14	0.228941
$679$	1.04721e16	2.78452
$680$	−2.82601e15	−0.745375
$681$	−2.07715e15	−0.543450
$682$	1.19987e16	3.11401
$683$	8.71631e14	0.224398	0.112199	−	0.993686i	$-0.464211\pi$
$683$	8.71631e14	0.224398	0.112199	+	0.993686i	$0.464211\pi$
$684$	−6.79285e14	−0.173478
$685$	2.38227e14	0.0603522
$686$	2.14873e16	5.40006
$687$	2.68270e15	0.668821
$688$	−1.88357e16	−4.65849
$689$	1.38188e15	0.339052
$690$	−1.78112e15	−0.433535
$691$	1.27484e15	0.307840	0.153920	−	0.988083i	$-0.450810\pi$
$691$	1.27484e15	0.307840	0.153920	+	0.988083i	$0.450810\pi$
$692$	−2.13330e16	−5.11056
$693$	3.81103e15	0.905752
$694$	−1.00135e16	−2.36107
$695$	2.19163e15	0.512686
$696$	2.27120e15	0.527115
$697$	−9.28865e14	−0.213881
$698$	3.79791e15	0.867640
$699$	8.01995e13	0.0181780
$700$	−2.13136e16	−4.79312
$701$	5.91734e15	1.32031	0.660157	−	0.751128i	$-0.270490\pi$
$701$	5.91734e15	1.32031	0.660157	+	0.751128i	$0.270490\pi$
$702$	4.72756e14	0.104661
$703$	1.36227e15	0.299233
$704$	3.94412e16	8.59607
$705$	1.43119e15	0.309498
$706$	5.80611e15	1.24583
$707$	−8.29177e15	−1.76539
$708$	1.03794e15	0.219276
$709$	3.23355e15	0.677836	0.338918	−	0.940816i	$-0.389939\pi$
$709$	3.23355e15	0.677836	0.338918	+	0.940816i	$0.389939\pi$
$710$	−3.70636e15	−0.770950
$711$	−3.00497e15	−0.620237
$712$	5.54647e15	1.13600
$713$	−5.87204e15	−1.19343
$714$	−6.04611e15	−1.21937
$715$	6.86720e14	0.137435
$716$	−6.40931e15	−1.27289
$717$	4.33549e15	0.854442
$718$	−1.55088e16	−3.03315
$719$	2.65230e13	0.00514770	0.00257385	−	0.999997i	$-0.499181\pi$
$719$	2.65230e13	0.00514770	0.00257385	+	0.999997i	$0.499181\pi$
$720$	−2.72401e15	−0.524663
$721$	−9.04044e15	−1.72801
$722$	−1.01018e16	−1.91622
$723$	−4.30356e15	−0.810152
$724$	1.95365e16	3.64993
$725$	1.14524e15	0.212344
$726$	−7.02029e15	−1.29182
$727$	−5.21215e15	−0.951871	−0.475935	−	0.879480i	$-0.657890\pi$
$727$	−5.21215e15	−0.951871	−0.475935	+	0.879480i	$0.657890\pi$
$728$	−1.07093e16	−1.94106
$729$	2.05891e14	0.0370370
$730$	−6.19964e14	−0.110686
$731$	−3.28085e15	−0.581355
$732$	−1.53759e15	−0.270415
$733$	9.36385e15	1.63449	0.817246	−	0.576290i	$-0.195500\pi$
$733$	9.36385e15	1.63449	0.817246	+	0.576290i	$0.195500\pi$
$734$	3.34044e15	0.578728
$735$	2.83678e15	0.487804
$736$	−3.43565e16	−5.86383
$737$	−3.58584e15	−0.607463
$738$	−1.46399e15	−0.246166
$739$	3.30993e15	0.552427	0.276214	−	0.961096i	$-0.410920\pi$
$739$	3.30993e15	0.552427	0.276214	+	0.961096i	$0.410920\pi$
$740$	1.01218e16	1.67681
$741$	−1.72107e14	−0.0283008
$742$	−2.78545e16	−4.54647
$743$	2.07299e15	0.335860	0.167930	−	0.985799i	$-0.446292\pi$
$743$	2.07299e15	0.335860	0.167930	+	0.985799i	$0.446292\pi$
$744$	−1.46844e16	−2.36159
$745$	7.80266e14	0.124561
$746$	1.23111e16	1.95089
$747$	1.90811e15	0.300152
$748$	1.56312e16	2.44081
$749$	−9.57933e15	−1.48486
$750$	−4.79075e15	−0.737167
$751$	−1.02918e16	−1.57206	−0.786032	−	0.618185i	$-0.787868\pi$
$751$	−1.02918e16	−1.57206	−0.786032	+	0.618185i	$0.787868\pi$
$752$	4.73864e16	7.18547
$753$	6.93968e15	1.04464
$754$	8.75580e14	0.130844
$755$	−7.65783e14	−0.113605
$756$	−7.09668e15	−1.04517
$757$	−3.89227e15	−0.569083	−0.284541	−	0.958664i	$-0.591841\pi$
$757$	−3.89227e15	−0.569083	−0.284541	+	0.958664i	$0.591841\pi$
$758$	1.41494e16	2.05380
$759$	6.47470e15	0.933018
$760$	1.62152e15	0.231978
$761$	−5.49549e14	−0.0780532	−0.0390266	−	0.999238i	$-0.512426\pi$
$761$	−5.49549e14	−0.0780532	−0.0390266	+	0.999238i	$0.512426\pi$
$762$	−1.64737e15	−0.232295
$763$	2.32903e16	3.26054
$764$	1.67368e16	2.32627
$765$	−4.74476e14	−0.0654751
$766$	−4.98828e15	−0.683428
$767$	2.62979e14	0.0357723
$768$	−2.86336e16	−3.86713
$769$	−9.22049e15	−1.23640	−0.618200	−	0.786021i	$-0.712138\pi$
$769$	−9.22049e15	−1.23640	−0.618200	+	0.786021i	$0.712138\pi$
$770$	−1.38422e16	−1.84292
$771$	−6.79231e15	−0.897880
$772$	−1.81551e16	−2.38289
$773$	−1.14476e16	−1.49186	−0.745931	−	0.666023i	$-0.767995\pi$
$773$	−1.14476e16	−1.49186	−0.745931	+	0.666023i	$0.767995\pi$
$774$	−5.17098e15	−0.669110
$775$	−7.40452e15	−0.951345
$776$	4.44916e16	5.67596
$777$	1.42320e16	1.80282
$778$	−2.71317e16	−3.41263
$779$	5.32967e14	0.0665647
$780$	−1.27877e15	−0.158589
$781$	1.34733e16	1.65918
$782$	−1.02720e16	−1.25608
$783$	3.81326e14	0.0463027
$784$	9.39248e16	11.3251
$785$	−1.35513e15	−0.162254
$786$	−6.87231e14	−0.0817106
$787$	1.22123e16	1.44191	0.720953	−	0.692984i	$-0.243704\pi$
$787$	1.22123e16	1.44191	0.720953	+	0.692984i	$0.243704\pi$
$788$	−4.53307e15	−0.531494
$789$	1.59599e15	0.185826
$790$	1.09145e16	1.26198
$791$	−3.24827e15	−0.372976
$792$	1.61915e16	1.84628
$793$	−3.89572e14	−0.0441149
$794$	8.38612e15	0.943079
$795$	−2.18592e15	−0.244126
$796$	1.19861e16	1.32940
$797$	1.80565e15	0.198890	0.0994449	−	0.995043i	$-0.468293\pi$
$797$	1.80565e15	0.198890	0.0994449	+	0.995043i	$0.468293\pi$
$798$	3.46915e15	0.379496
$799$	8.25389e15	0.896709
$800$	−4.33229e16	−4.67436
$801$	9.31229e14	0.0997879
$802$	−4.98077e15	−0.530076
$803$	2.25368e15	0.238208
$804$	6.67735e15	0.700965
$805$	6.77421e15	0.706287
$806$	−5.66102e15	−0.586208
$807$	6.02422e15	0.619579
$808$	−3.52282e16	−3.59856
$809$	8.60818e15	0.873362	0.436681	−	0.899616i	$-0.356154\pi$
$809$	8.60818e15	0.873362	0.436681	+	0.899616i	$0.356154\pi$
$810$	−7.47825e14	−0.0753585
$811$	−1.06066e16	−1.06160	−0.530801	−	0.847497i	$-0.678109\pi$
$811$	−1.06066e16	−1.06160	−0.530801	+	0.847497i	$0.678109\pi$
$812$	−1.31436e16	−1.30664
$813$	−9.11372e15	−0.899907
$814$	−4.94072e16	−4.84570
$815$	−4.89405e15	−0.476762
$816$	−1.57097e16	−1.52010
$817$	1.88250e15	0.180931
$818$	−3.12283e16	−2.98129
$819$	−1.79805e15	−0.170507
$820$	3.95999e15	0.373008
$821$	8.25760e14	0.0772621	0.0386311	−	0.999254i	$-0.487700\pi$
$821$	8.25760e14	0.0772621	0.0386311	+	0.999254i	$0.487700\pi$
$822$	2.16540e15	0.201253
$823$	1.15919e16	1.07018	0.535089	−	0.844796i	$-0.320278\pi$
$823$	1.15919e16	1.07018	0.535089	+	0.844796i	$0.320278\pi$
$824$	−3.84090e16	−3.52236
$825$	8.16447e15	0.743758
$826$	−5.30086e15	−0.479685
$827$	2.58865e15	0.232698	0.116349	−	0.993208i	$-0.462881\pi$
$827$	2.58865e15	0.232698	0.116349	+	0.993208i	$0.462881\pi$
$828$	−1.20568e16	−1.07663
$829$	−5.98108e15	−0.530554	−0.265277	−	0.964172i	$-0.585463\pi$
$829$	−5.98108e15	−0.530554	−0.265277	+	0.964172i	$0.585463\pi$
$830$	−6.93052e15	−0.610712
$831$	9.34278e14	0.0817844
$832$	−1.86085e16	−1.61820
$833$	1.63601e16	1.41331
$834$	1.99211e16	1.70962
$835$	3.93443e15	0.335433
$836$	−8.96892e15	−0.759636
$837$	−2.46544e15	−0.207446
$838$	−3.83303e15	−0.320405
$839$	3.32964e15	0.276507	0.138254	−	0.990397i	$-0.455851\pi$
$839$	3.32964e15	0.276507	0.138254	+	0.990397i	$0.455851\pi$
$840$	1.69405e16	1.39762
$841$	−1.14943e16	−0.942114
$842$	2.79515e16	2.27609
$843$	−6.56055e15	−0.530749
$844$	−5.71378e16	−4.59240
$845$	3.96736e15	0.316803
$846$	1.30090e16	1.03207
$847$	2.67005e16	2.10456
$848$	−7.23751e16	−5.66776
$849$	6.88664e15	0.535815
$850$	−1.29528e16	−1.00129
$851$	2.41794e16	1.85709
$852$	−2.50892e16	−1.91456
$853$	3.33387e15	0.252772	0.126386	−	0.991981i	$-0.459662\pi$
$853$	3.33387e15	0.252772	0.126386	+	0.991981i	$0.459662\pi$
$854$	7.85259e15	0.591554
$855$	2.72246e14	0.0203774
$856$	−4.06985e16	−3.02673
$857$	−1.32025e16	−0.975578	−0.487789	−	0.872962i	$-0.662196\pi$
$857$	−1.32025e16	−0.975578	−0.487789	+	0.872962i	$0.662196\pi$
$858$	6.24203e15	0.458296
$859$	6.99654e15	0.510412	0.255206	−	0.966887i	$-0.417857\pi$
$859$	6.99654e15	0.510412	0.255206	+	0.966887i	$0.417857\pi$
$860$	1.39871e16	1.01388
$861$	5.56806e15	0.401039
$862$	−2.92449e15	−0.209296
$863$	1.32866e15	0.0944829	0.0472415	−	0.998883i	$-0.484957\pi$
$863$	1.32866e15	0.0944829	0.0472415	+	0.998883i	$0.484957\pi$
$864$	−1.44250e16	−1.01927
$865$	8.54991e15	0.600307
$866$	−1.69505e16	−1.18259
$867$	5.59170e15	0.387649
$868$	8.49792e16	5.85402
$869$	−3.96761e16	−2.71594
$870$	−1.38503e15	−0.0942111
$871$	1.69181e15	0.114354
$872$	9.89506e16	6.64627
$873$	7.46996e15	0.498586
$874$	5.89388e15	0.390920
$875$	1.82208e16	1.20095
$876$	−4.19668e15	−0.274874
$877$	−1.42791e15	−0.0929400	−0.0464700	−	0.998920i	$-0.514797\pi$
$877$	−1.42791e15	−0.0929400	−0.0464700	+	0.998920i	$0.514797\pi$
$878$	−3.83230e16	−2.47879
$879$	−3.75563e15	−0.241404
$880$	−3.59664e16	−2.29743
$881$	−1.51201e16	−0.959813	−0.479907	−	0.877320i	$-0.659329\pi$
$881$	−1.51201e16	−0.959813	−0.479907	+	0.877320i	$0.659329\pi$
$882$	2.57853e16	1.62665
$883$	1.84942e16	1.15945	0.579726	−	0.814812i	$-0.303160\pi$
$883$	1.84942e16	1.15945	0.579726	+	0.814812i	$0.303160\pi$
$884$	−7.37485e15	−0.459479
$885$	−4.15991e14	−0.0257570
$886$	−1.18682e16	−0.730296
$887$	−2.94266e15	−0.179954	−0.0899769	−	0.995944i	$-0.528679\pi$
$887$	−2.94266e15	−0.179954	−0.0899769	+	0.995944i	$0.528679\pi$
$888$	6.04660e16	3.67485
$889$	6.26552e15	0.378440
$890$	−3.38235e15	−0.203036
$891$	2.71848e15	0.162180
$892$	2.52313e16	1.49601
$893$	−4.73594e15	−0.279076
$894$	7.09232e15	0.415367
$895$	2.56874e15	0.149518
$896$	2.04656e17	11.8394
$897$	−3.05478e15	−0.175639
$898$	7.72098e15	0.441218
$899$	−4.56618e15	−0.259343
$900$	−1.52034e16	−0.858238
$901$	−1.26065e16	−0.707307
$902$	−1.93298e16	−1.07793
$903$	1.96670e16	1.09007
$904$	−1.38005e16	−0.760272
$905$	−7.82990e15	−0.428735
$906$	−6.96068e15	−0.378832
$907$	−2.56315e16	−1.38655	−0.693274	−	0.720674i	$-0.743832\pi$
$907$	−2.56315e16	−1.38655	−0.693274	+	0.720674i	$0.743832\pi$
$908$	5.10705e16	2.74598
$909$	−5.91468e15	−0.316104
$910$	6.53078e15	0.346926
$911$	3.34196e16	1.76462	0.882308	−	0.470673i	$-0.155989\pi$
$911$	3.34196e16	1.76462	0.882308	+	0.470673i	$0.155989\pi$
$912$	9.01398e15	0.473091
$913$	2.51937e16	1.31433
$914$	4.24896e16	2.20332
$915$	6.16241e14	0.0317640
$916$	−6.59589e16	−3.37947
$917$	2.61377e15	0.133118
$918$	−4.31281e15	−0.218336
$919$	−4.49904e15	−0.226404	−0.113202	−	0.993572i	$-0.536111\pi$
$919$	−4.49904e15	−0.226404	−0.113202	+	0.993572i	$0.536111\pi$
$920$	2.87808e16	1.43969
$921$	−1.55718e16	−0.774301
$922$	−3.96774e16	−1.96121
$923$	−6.35673e15	−0.312338
$924$	−9.37009e16	−4.57665
$925$	3.04897e16	1.48038
$926$	−4.78669e16	−2.31033
$927$	−6.44872e15	−0.309411
$928$	−2.67161e16	−1.27426
$929$	−1.33707e16	−0.633967	−0.316984	−	0.948431i	$-0.602670\pi$
$929$	−1.33707e16	−0.633967	−0.316984	+	0.948431i	$0.602670\pi$
$930$	8.95483e15	0.422086
$931$	−9.38714e15	−0.439855
$932$	−1.97185e15	−0.0918514
$933$	−5.37752e15	−0.249019
$934$	1.08741e16	0.500596
$935$	−6.26473e15	−0.286707
$936$	−7.63917e15	−0.347560
$937$	−1.85921e16	−0.840931	−0.420465	−	0.907309i	$-0.638133\pi$
$937$	−1.85921e16	−0.840931	−0.420465	+	0.907309i	$0.638133\pi$
$938$	−3.41017e16	−1.53342
$939$	2.98129e15	0.133274
$940$	−3.51885e16	−1.56386
$941$	−1.87091e16	−0.826629	−0.413314	−	0.910588i	$-0.635629\pi$
$941$	−1.87091e16	−0.826629	−0.413314	+	0.910588i	$0.635629\pi$
$942$	−1.23176e16	−0.541060
$943$	9.45979e15	0.413111
$944$	−1.37733e16	−0.597989
$945$	2.84423e15	0.122769
$946$	−6.82749e16	−2.92995
$947$	4.41173e16	1.88228	0.941140	−	0.338016i	$-0.109756\pi$
$947$	4.41173e16	1.88228	0.941140	+	0.338016i	$0.109756\pi$
$948$	7.38825e16	3.13398
$949$	−1.06329e15	−0.0448424
$950$	7.43207e15	0.311623
$951$	−7.38625e15	−0.307915
$952$	9.76979e16	4.04932
$953$	−3.80973e16	−1.56994	−0.784970	−	0.619534i	$-0.787322\pi$
$953$	−3.80973e16	−1.56994	−0.784970	+	0.619534i	$0.787322\pi$
$954$	−1.98692e16	−0.814074
$955$	−6.70785e15	−0.273253
$956$	−1.06596e17	−4.31739
$957$	5.03482e15	0.202754
$958$	−5.93533e16	−2.37648
$959$	−8.23573e15	−0.327869
$960$	2.94356e16	1.16515
$961$	4.11396e15	0.161913
$962$	2.33105e16	0.912196
$963$	−6.83312e15	−0.265873
$964$	1.05811e17	4.09360
$965$	7.27627e15	0.279904
$966$	6.15751e16	2.35522
$967$	1.55457e15	0.0591241	0.0295620	−	0.999563i	$-0.490589\pi$
$967$	1.55457e15	0.0591241	0.0295620	+	0.999563i	$0.490589\pi$
$968$	1.13439e17	4.28992
$969$	1.57008e15	0.0590393
$970$	−2.71319e16	−1.01446
$971$	−5.03856e16	−1.87327	−0.936636	−	0.350303i	$-0.886079\pi$
$971$	−5.03856e16	−1.87327	−0.936636	+	0.350303i	$0.886079\pi$
$972$	−5.06220e15	−0.187144
$973$	−7.57668e16	−2.78521
$974$	4.73277e15	0.172998
$975$	−3.85202e15	−0.140011
$976$	2.04035e16	0.737448
$977$	−2.81652e16	−1.01226	−0.506130	−	0.862457i	$-0.668925\pi$
$977$	−2.81652e16	−1.01226	−0.506130	+	0.862457i	$0.668925\pi$
$978$	−4.44851e16	−1.58983
$979$	1.22955e16	0.436958
$980$	−6.97473e16	−2.46481
$981$	1.66134e16	0.583820
$982$	9.30948e15	0.325321
$983$	5.44935e16	1.89365	0.946827	−	0.321744i	$-0.104269\pi$
$983$	5.44935e16	1.89365	0.946827	+	0.321744i	$0.104269\pi$
$984$	2.36563e16	0.817475
$985$	1.81678e15	0.0624314
$986$	−7.98764e15	−0.272958
$987$	−4.94777e16	−1.68138
$988$	4.23156e15	0.143000
$989$	3.34130e16	1.12289
$990$	−9.87389e15	−0.329985
$991$	3.81179e15	0.126684	0.0633422	−	0.997992i	$-0.479824\pi$
$991$	3.81179e15	0.126684	0.0633422	+	0.997992i	$0.479824\pi$
$992$	1.72732e17	5.70898
$993$	2.83571e15	0.0932053
$994$	1.28132e17	4.18825
$995$	−4.80384e15	−0.156157
$996$	−4.69143e16	−1.51663
$997$	2.43014e16	0.781283	0.390641	−	0.920543i	$-0.372253\pi$
$997$	2.43014e16	0.781283	0.390641	+	0.920543i	$0.372253\pi$
$998$	−4.39352e16	−1.40474
$999$	1.01520e16	0.322805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.27	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.27	✓	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)

\(f(q)\)	\(=\)	\(q+89.5689 q^{2} -243.000 q^{3} +5974.59 q^{4} -2394.52 q^{5} -21765.2 q^{6} +82780.6 q^{7} +351700. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+89.5689 q^{2} -243.000 q^{3} +5974.59 q^{4} -2394.52 q^{5} -21765.2 q^{6} +82780.6 q^{7} +351700. q^{8} +59049.0 q^{9} -214474. q^{10} +779652. q^{11} -1.45182e6 q^{12} -367842. q^{13} +7.41457e6 q^{14} +581867. q^{15} +1.92654e7 q^{16} +3.35571e6 q^{17} +5.28895e6 q^{18} -1.92545e6 q^{19} -1.43062e7 q^{20} -2.01157e7 q^{21} +6.98326e7 q^{22} -3.41753e7 q^{23} -8.54631e7 q^{24} -4.30944e7 q^{25} -3.29472e7 q^{26} -1.43489e7 q^{27} +4.94580e8 q^{28} -2.65752e7 q^{29} +5.21172e7 q^{30} +1.71821e8 q^{31} +1.00530e9 q^{32} -1.89455e8 q^{33} +3.00567e8 q^{34} -1.98219e8 q^{35} +3.52793e8 q^{36} -7.07509e8 q^{37} -1.72460e8 q^{38} +8.93856e7 q^{39} -8.42151e8 q^{40} -2.76802e8 q^{41} -1.80174e9 q^{42} -9.77694e8 q^{43} +4.65810e9 q^{44} -1.41394e8 q^{45} -3.06105e9 q^{46} +2.45966e9 q^{47} -4.68150e9 q^{48} +4.87530e9 q^{49} -3.85992e9 q^{50} -8.15437e8 q^{51} -2.19770e9 q^{52} -3.75673e9 q^{53} -1.28522e9 q^{54} -1.86689e9 q^{55} +2.91140e10 q^{56} +4.67883e8 q^{57} -2.38031e9 q^{58} -7.14924e8 q^{59} +3.47642e9 q^{60} +1.05908e9 q^{61} +1.53898e10 q^{62} +4.88811e9 q^{63} +5.05882e10 q^{64} +8.80803e8 q^{65} -1.69693e10 q^{66} -4.59928e9 q^{67} +2.00490e10 q^{68} +8.30460e9 q^{69} -1.77543e10 q^{70} +1.72811e10 q^{71} +2.07675e10 q^{72} +2.89063e9 q^{73} -6.33708e10 q^{74} +1.04719e10 q^{75} -1.15037e10 q^{76} +6.45401e10 q^{77} +8.00617e9 q^{78} -5.08894e10 q^{79} -4.61314e10 q^{80} +3.48678e9 q^{81} -2.47928e10 q^{82} +3.23140e10 q^{83} -1.20183e11 q^{84} -8.03529e9 q^{85} -8.75709e10 q^{86} +6.45778e9 q^{87} +2.74204e11 q^{88} +1.57705e10 q^{89} -1.26645e10 q^{90} -3.04502e10 q^{91} -2.04183e11 q^{92} -4.17525e10 q^{93} +2.20309e11 q^{94} +4.61051e9 q^{95} -2.44288e11 q^{96} +1.26505e11 q^{97} +4.36676e11 q^{98} +4.60377e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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