LMFDB - Embedded newform 177.12.a.c.1.11

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			1.11
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)

$f(q)$	$=$	$q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +104401. q^{10} +413614. q^{11} +463710. q^{12} -2.15678e6 q^{13} -227168. q^{14} +2.14620e6 q^{15} +3.35534e6 q^{16} -6.59896e6 q^{17} -697998. q^{18} +772293. q^{19} +1.68541e7 q^{20} -4.66995e6 q^{21} -4.88919e6 q^{22} +4.19889e7 q^{23} -1.13641e7 q^{24} +2.91781e7 q^{25} +2.54945e7 q^{26} -1.43489e7 q^{27} -3.66730e7 q^{28} -4.25227e7 q^{29} -2.53695e7 q^{30} -6.05374e7 q^{31} -1.35439e8 q^{32} -1.00508e8 q^{33} +7.80040e7 q^{34} -1.69735e8 q^{35} -1.12682e8 q^{36} -5.85646e8 q^{37} -9.12901e6 q^{38} +5.24097e8 q^{39} -4.13040e8 q^{40} -2.62066e8 q^{41} +5.52019e7 q^{42} -1.36297e9 q^{43} -7.89288e8 q^{44} -5.21527e8 q^{45} -4.96337e8 q^{46} -9.55377e8 q^{47} -8.15348e8 q^{48} -1.60800e9 q^{49} -3.44904e8 q^{50} +1.60355e9 q^{51} +4.11572e9 q^{52} -3.76739e9 q^{53} +1.69614e8 q^{54} -3.65309e9 q^{55} +8.98740e8 q^{56} -1.87667e8 q^{57} +5.02646e8 q^{58} -7.14924e8 q^{59} -4.09554e9 q^{60} -1.01945e9 q^{61} +7.15592e8 q^{62} +1.13480e9 q^{63} -5.27076e9 q^{64} +1.90489e10 q^{65} +1.18807e9 q^{66} -1.22341e10 q^{67} +1.25926e10 q^{68} -1.02033e10 q^{69} +2.00638e9 q^{70} -2.13614e10 q^{71} +2.76147e9 q^{72} +7.12398e8 q^{73} +6.92272e9 q^{74} -7.09028e9 q^{75} -1.47374e9 q^{76} +7.94880e9 q^{77} -6.19517e9 q^{78} +4.14934e10 q^{79} -2.96347e10 q^{80} +3.48678e9 q^{81} +3.09779e9 q^{82} -4.23677e9 q^{83} +8.91154e9 q^{84} +5.82828e10 q^{85} +1.61112e10 q^{86} +1.03330e10 q^{87} +1.93430e10 q^{88} +7.44660e9 q^{89} +6.16480e9 q^{90} -4.14487e10 q^{91} -8.01263e10 q^{92} +1.47106e10 q^{93} +1.12932e10 q^{94} -6.82098e9 q^{95} +3.29116e10 q^{96} +1.19796e11 q^{97} +1.90076e10 q^{98} +2.44235e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.8207	−0.261202	−0.130601	−	0.991435i	$-0.541691\pi$
$2$	−11.8207	−0.261202	−0.130601	+	0.991435i	$0.541691\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1908.27	−0.931773
$5$	−8832.11	−1.26395	−0.631975	−	0.774989i	$-0.717755\pi$
$5$	−8832.11	−1.26395	−0.631975	+	0.774989i	$0.717755\pi$
$6$	2872.42	0.150805
$7$	19217.9	0.432182	0.216091	−	0.976373i	$-0.430669\pi$
$7$	19217.9	0.432182	0.216091	+	0.976373i	$0.430669\pi$
$8$	46765.7	0.504583
$9$	59049.0	0.333333
$10$	104401.	0.330146
$11$	413614.	0.774347	0.387173	−	0.922007i	$-0.373451\pi$
$11$	413614.	0.774347	0.387173	+	0.922007i	$0.373451\pi$
$12$	463710.	0.537960
$13$	−2.15678e6	−1.61108	−0.805540	−	0.592542i	$-0.798124\pi$
$13$	−2.15678e6	−1.61108	−0.805540	+	0.592542i	$0.798124\pi$
$14$	−227168.	−0.112887
$15$	2.14620e6	0.729741
$16$	3.35534e6	0.799975
$17$	−6.59896e6	−1.12721	−0.563607	−	0.826043i	$-0.690587\pi$
$17$	−6.59896e6	−1.12721	−0.563607	+	0.826043i	$0.690587\pi$
$18$	−697998.	−0.0870674
$19$	772293.	0.0715545	0.0357773	−	0.999360i	$-0.488609\pi$
$19$	772293.	0.0715545	0.0357773	+	0.999360i	$0.488609\pi$
$20$	1.68541e7	1.17771
$21$	−4.66995e6	−0.249521
$22$	−4.88919e6	−0.202261
$23$	4.19889e7	1.36029	0.680145	−	0.733078i	$-0.261917\pi$
$23$	4.19889e7	1.36029	0.680145	+	0.733078i	$0.261917\pi$
$24$	−1.13641e7	−0.291321
$25$	2.91781e7	0.597568
$26$	2.54945e7	0.420817
$27$	−1.43489e7	−0.192450
$28$	−3.66730e7	−0.402696
$29$	−4.25227e7	−0.384974	−0.192487	−	0.981299i	$-0.561655\pi$
$29$	−4.25227e7	−0.384974	−0.192487	+	0.981299i	$0.561655\pi$
$30$	−2.53695e7	−0.190610
$31$	−6.05374e7	−0.379782	−0.189891	−	0.981805i	$-0.560813\pi$
$31$	−6.05374e7	−0.379782	−0.189891	+	0.981805i	$0.560813\pi$
$32$	−1.35439e8	−0.713538
$33$	−1.00508e8	−0.447069
$34$	7.80040e7	0.294431
$35$	−1.69735e8	−0.546256
$36$	−1.12682e8	−0.310591
$37$	−5.85646e8	−1.38843	−0.694217	−	0.719765i	$-0.744249\pi$
$37$	−5.85646e8	−1.38843	−0.694217	+	0.719765i	$0.744249\pi$
$38$	−9.12901e6	−0.0186902
$39$	5.24097e8	0.930157
$40$	−4.13040e8	−0.637768
$41$	−2.62066e8	−0.353264	−0.176632	−	0.984277i	$-0.556520\pi$
$41$	−2.62066e8	−0.353264	−0.176632	+	0.984277i	$0.556520\pi$
$42$	5.52019e7	0.0651753
$43$	−1.36297e9	−1.41387	−0.706935	−	0.707278i	$-0.749923\pi$
$43$	−1.36297e9	−1.41387	−0.706935	+	0.707278i	$0.749923\pi$
$44$	−7.89288e8	−0.721516
$45$	−5.21527e8	−0.421316
$46$	−4.96337e8	−0.355311
$47$	−9.55377e8	−0.607626	−0.303813	−	0.952732i	$-0.598260\pi$
$47$	−9.55377e8	−0.607626	−0.303813	+	0.952732i	$0.598260\pi$
$48$	−8.15348e8	−0.461866
$49$	−1.60800e9	−0.813219
$50$	−3.44904e8	−0.156086
$51$	1.60355e9	0.650797
$52$	4.11572e9	1.50116
$53$	−3.76739e9	−1.23744	−0.618719	−	0.785613i	$-0.712348\pi$
$53$	−3.76739e9	−1.23744	−0.618719	+	0.785613i	$0.712348\pi$
$54$	1.69614e8	0.0502684
$55$	−3.65309e9	−0.978735
$56$	8.98740e8	0.218072
$57$	−1.87667e8	−0.0413120
$58$	5.02646e8	0.100556
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−4.09554e9	−0.679954
$61$	−1.01945e9	−0.154545	−0.0772723	−	0.997010i	$-0.524621\pi$
$61$	−1.01945e9	−0.154545	−0.0772723	+	0.997010i	$0.524621\pi$
$62$	7.15592e8	0.0991999
$63$	1.13480e9	0.144061
$64$	−5.27076e9	−0.613598
$65$	1.90489e10	2.03632
$66$	1.18807e9	0.116775
$67$	−1.22341e10	−1.10703	−0.553514	−	0.832840i	$-0.686714\pi$
$67$	−1.22341e10	−1.10703	−0.553514	+	0.832840i	$0.686714\pi$
$68$	1.25926e10	1.05031
$69$	−1.02033e10	−0.785364
$70$	2.00638e9	0.142683
$71$	−2.13614e10	−1.40510	−0.702551	−	0.711633i	$-0.747956\pi$
$71$	−2.13614e10	−1.40510	−0.702551	+	0.711633i	$0.747956\pi$
$72$	2.76147e9	0.168194
$73$	7.12398e8	0.0402205	0.0201102	−	0.999798i	$-0.493598\pi$
$73$	7.12398e8	0.0402205	0.0201102	+	0.999798i	$0.493598\pi$
$74$	6.92272e9	0.362662
$75$	−7.09028e9	−0.345006
$76$	−1.47374e9	−0.0666726
$77$	7.94880e9	0.334659
$78$	−6.19517e9	−0.242959
$79$	4.14934e10	1.51716	0.758578	−	0.651583i	$-0.225895\pi$
$79$	4.14934e10	1.51716	0.758578	+	0.651583i	$0.225895\pi$
$80$	−2.96347e10	−1.01113
$81$	3.48678e9	0.111111
$82$	3.09779e9	0.0922733
$83$	−4.23677e9	−0.118061	−0.0590304	−	0.998256i	$-0.518801\pi$
$83$	−4.23677e9	−0.118061	−0.0590304	+	0.998256i	$0.518801\pi$
$84$	8.91154e9	0.232497
$85$	5.82828e10	1.42474
$86$	1.61112e10	0.369306
$87$	1.03330e10	0.222265
$88$	1.93430e10	0.390722
$89$	7.44660e9	0.141356	0.0706778	−	0.997499i	$-0.477484\pi$
$89$	7.44660e9	0.141356	0.0706778	+	0.997499i	$0.477484\pi$
$90$	6.16480e9	0.110049
$91$	−4.14487e10	−0.696280
$92$	−8.01263e10	−1.26748
$93$	1.47106e10	0.219267
$94$	1.12932e10	0.158713
$95$	−6.82098e9	−0.0904413
$96$	3.29116e10	0.411962
$97$	1.19796e11	1.41644	0.708218	−	0.705993i	$-0.249499\pi$
$97$	1.19796e11	1.41644	0.708218	+	0.705993i	$0.249499\pi$
$98$	1.90076e10	0.212414
$99$	2.44235e10	0.258116
$100$	−5.56798e10	−0.556798
$101$	−7.85276e10	−0.743455	−0.371728	−	0.928342i	$-0.621234\pi$
$101$	−7.85276e10	−0.743455	−0.371728	+	0.928342i	$0.621234\pi$
$102$	−1.89550e10	−0.169990
$103$	6.24296e10	0.530622	0.265311	−	0.964163i	$-0.414525\pi$
$103$	6.24296e10	0.530622	0.265311	+	0.964163i	$0.414525\pi$
$104$	−1.00863e11	−0.812924
$105$	4.12455e10	0.315381
$106$	4.45330e10	0.323221
$107$	−2.62553e11	−1.80970	−0.904848	−	0.425735i	$-0.860016\pi$
$107$	−2.62553e11	−1.80970	−0.904848	+	0.425735i	$0.860016\pi$
$108$	2.73816e10	0.179320
$109$	−2.15266e11	−1.34008	−0.670040	−	0.742325i	$-0.733723\pi$
$109$	−2.15266e11	−1.34008	−0.670040	+	0.742325i	$0.733723\pi$
$110$	4.31819e10	0.255648
$111$	1.42312e11	0.801613
$112$	6.44826e10	0.345735
$113$	1.01778e11	0.519662	0.259831	−	0.965654i	$-0.416333\pi$
$113$	1.01778e11	0.519662	0.259831	+	0.965654i	$0.416333\pi$
$114$	2.21835e9	0.0107908
$115$	−3.70851e11	−1.71934
$116$	8.11449e10	0.358709
$117$	−1.27356e11	−0.537026
$118$	8.45087e9	0.0340056
$119$	−1.26818e11	−0.487162
$120$	1.00369e11	0.368215
$121$	−1.14235e11	−0.400387
$122$	1.20506e10	0.0403674
$123$	6.36820e10	0.203957
$124$	1.15522e11	0.353871
$125$	1.73551e11	0.508654
$126$	−1.34141e10	−0.0376290
$127$	6.78964e11	1.82359	0.911793	−	0.410651i	$-0.134698\pi$
$127$	6.78964e11	1.82359	0.911793	+	0.410651i	$0.134698\pi$
$128$	3.39682e11	0.873811
$129$	3.31202e11	0.816298
$130$	−2.25171e11	−0.531892
$131$	3.24480e11	0.734846	0.367423	−	0.930054i	$-0.380240\pi$
$131$	3.24480e11	0.734846	0.367423	+	0.930054i	$0.380240\pi$
$132$	1.91797e11	0.416567
$133$	1.48418e10	0.0309246
$134$	1.44615e11	0.289158
$135$	1.26731e11	0.243247
$136$	−3.08605e11	−0.568773
$137$	6.17045e11	1.09233	0.546165	−	0.837678i	$-0.316087\pi$
$137$	6.17045e11	1.09233	0.546165	+	0.837678i	$0.316087\pi$
$138$	1.20610e11	0.205139
$139$	−7.24498e11	−1.18428	−0.592142	−	0.805834i	$-0.701717\pi$
$139$	−7.24498e11	−1.18428	−0.592142	+	0.805834i	$0.701717\pi$
$140$	3.23900e11	0.508987
$141$	2.32157e11	0.350813
$142$	2.52505e11	0.367016
$143$	−8.92073e11	−1.24753
$144$	1.98129e11	0.266658
$145$	3.75565e11	0.486588
$146$	−8.42102e9	−0.0105057
$147$	3.90744e11	0.469512
$148$	1.11757e12	1.29371
$149$	−6.77062e11	−0.755273	−0.377636	−	0.925954i	$-0.623263\pi$
$149$	−6.77062e11	−0.755273	−0.377636	+	0.925954i	$0.623263\pi$
$150$	8.38117e10	0.0901162
$151$	−1.64182e12	−1.70197	−0.850987	−	0.525187i	$-0.823995\pi$
$151$	−1.64182e12	−1.70197	−0.850987	+	0.525187i	$0.823995\pi$
$152$	3.61168e10	0.0361052
$153$	−3.89662e11	−0.375738
$154$	−9.39600e10	−0.0874136
$155$	5.34673e11	0.480025
$156$	−1.00012e12	−0.866696
$157$	7.23872e10	0.0605639	0.0302819	−	0.999541i	$-0.490359\pi$
$157$	7.23872e10	0.0605639	0.0302819	+	0.999541i	$0.490359\pi$
$158$	−4.90479e11	−0.396284
$159$	9.15475e11	0.714435
$160$	1.19621e12	0.901876
$161$	8.06939e11	0.587893
$162$	−4.12161e10	−0.0290225
$163$	−4.95381e11	−0.337216	−0.168608	−	0.985683i	$-0.553927\pi$
$163$	−4.95381e11	−0.337216	−0.168608	+	0.985683i	$0.553927\pi$
$164$	5.00093e11	0.329162
$165$	8.87700e11	0.565073
$166$	5.00815e10	0.0308377
$167$	8.26483e11	0.492372	0.246186	−	0.969223i	$-0.420823\pi$
$167$	8.26483e11	0.492372	0.246186	+	0.969223i	$0.420823\pi$
$168$	−2.18394e11	−0.125904
$169$	2.85953e12	1.59558
$170$	−6.88940e11	−0.372145
$171$	4.56031e10	0.0238515
$172$	2.60092e12	1.31741
$173$	2.96785e11	0.145609	0.0728046	−	0.997346i	$-0.476805\pi$
$173$	2.96785e11	0.145609	0.0728046	+	0.997346i	$0.476805\pi$
$174$	−1.22143e11	−0.0580561
$175$	5.60742e11	0.258258
$176$	1.38782e12	0.619458
$177$	1.73727e11	0.0751646
$178$	−8.80237e10	−0.0369224
$179$	−2.19982e12	−0.894737	−0.447369	−	0.894350i	$-0.647639\pi$
$179$	−2.19982e12	−0.894737	−0.447369	+	0.894350i	$0.647639\pi$
$180$	9.95216e11	0.392571
$181$	2.19331e12	0.839206	0.419603	−	0.907708i	$-0.362169\pi$
$181$	2.19331e12	0.839206	0.419603	+	0.907708i	$0.362169\pi$
$182$	4.89951e11	0.181870
$183$	2.47727e11	0.0892263
$184$	1.96364e12	0.686380
$185$	5.17249e12	1.75491
$186$	−1.73889e11	−0.0572731
$187$	−2.72942e12	−0.872854
$188$	1.82312e12	0.566170
$189$	−2.75756e11	−0.0831735
$190$	8.06284e10	0.0236234
$191$	−1.37402e12	−0.391120	−0.195560	−	0.980692i	$-0.562652\pi$
$191$	−1.37402e12	−0.391120	−0.195560	+	0.980692i	$0.562652\pi$
$192$	1.28080e12	0.354261
$193$	−5.84943e12	−1.57235	−0.786174	−	0.618006i	$-0.787941\pi$
$193$	−5.84943e12	−1.57235	−0.786174	+	0.618006i	$0.787941\pi$
$194$	−1.41607e12	−0.369976
$195$	−4.62888e12	−1.17567
$196$	3.06850e12	0.757735
$197$	3.23289e12	0.776295	0.388148	−	0.921597i	$-0.373115\pi$
$197$	3.23289e12	0.776295	0.388148	+	0.921597i	$0.373115\pi$
$198$	−2.88702e11	−0.0674203
$199$	−7.57931e12	−1.72162	−0.860811	−	0.508924i	$-0.830043\pi$
$199$	−7.57931e12	−1.72162	−0.860811	+	0.508924i	$0.830043\pi$
$200$	1.36454e12	0.301523
$201$	2.97287e12	0.639143
$202$	9.28248e11	0.194192
$203$	−8.17197e11	−0.166379
$204$	−3.06000e12	−0.606396
$205$	2.31460e12	0.446508
$206$	−7.37958e11	−0.138600
$207$	2.47940e12	0.453430
$208$	−7.23672e12	−1.28882
$209$	3.19431e11	0.0554080
$210$	−4.87549e11	−0.0823782
$211$	2.14129e12	0.352469	0.176235	−	0.984348i	$-0.443608\pi$
$211$	2.14129e12	0.352469	0.176235	+	0.984348i	$0.443608\pi$
$212$	7.18920e12	1.15301
$213$	5.19081e12	0.811236
$214$	3.10354e12	0.472696
$215$	1.20379e13	1.78706
$216$	−6.71037e11	−0.0971071
$217$	−1.16340e12	−0.164135
$218$	2.54459e12	0.350032
$219$	−1.73113e11	−0.0232213
$220$	6.97108e12	0.911959
$221$	1.42325e13	1.81603
$222$	−1.68222e12	−0.209383
$223$	5.58025e12	0.677606	0.338803	−	0.940857i	$-0.389978\pi$
$223$	5.58025e12	0.677606	0.338803	+	0.940857i	$0.389978\pi$
$224$	−2.60285e12	−0.308379
$225$	1.72294e12	0.199189
$226$	−1.20308e12	−0.135737
$227$	−4.01000e12	−0.441572	−0.220786	−	0.975322i	$-0.570862\pi$
$227$	−4.01000e12	−0.441572	−0.220786	+	0.975322i	$0.570862\pi$
$228$	3.58120e11	0.0384934
$229$	−2.06203e11	−0.0216372	−0.0108186	−	0.999941i	$-0.503444\pi$
$229$	−2.06203e11	−0.0216372	−0.0108186	+	0.999941i	$0.503444\pi$
$230$	4.38370e12	0.449095
$231$	−1.93156e12	−0.193215
$232$	−1.98860e12	−0.194252
$233$	−6.77586e12	−0.646408	−0.323204	−	0.946329i	$-0.604760\pi$
$233$	−6.77586e12	−0.646408	−0.323204	+	0.946329i	$0.604760\pi$
$234$	1.50543e12	0.140272
$235$	8.43800e12	0.768009
$236$	1.36427e12	0.121307
$237$	−1.00829e13	−0.875930
$238$	1.49907e12	0.127248
$239$	−1.19720e12	−0.0993066	−0.0496533	−	0.998767i	$-0.515812\pi$
$239$	−1.19720e12	−0.0993066	−0.0496533	+	0.998767i	$0.515812\pi$
$240$	7.20124e12	0.583775
$241$	2.15690e13	1.70898	0.854490	−	0.519468i	$-0.173870\pi$
$241$	2.15690e13	1.70898	0.854490	+	0.519468i	$0.173870\pi$
$242$	1.35033e12	0.104582
$243$	−8.47289e11	−0.0641500
$244$	1.94540e12	0.144001
$245$	1.42020e13	1.02787
$246$	−7.52763e11	−0.0532740
$247$	−1.66566e12	−0.115280
$248$	−2.83108e12	−0.191632
$249$	1.02954e12	0.0681625
$250$	−2.05149e12	−0.132862
$251$	−1.46993e13	−0.931306	−0.465653	−	0.884967i	$-0.654181\pi$
$251$	−1.46993e13	−0.931306	−0.465653	+	0.884967i	$0.654181\pi$
$252$	−2.16550e12	−0.134232
$253$	1.73672e13	1.05334
$254$	−8.02580e12	−0.476324
$255$	−1.41627e13	−0.822575
$256$	6.77926e12	0.385356
$257$	−1.15394e13	−0.642021	−0.321011	−	0.947076i	$-0.604023\pi$
$257$	−1.15394e13	−0.642021	−0.321011	+	0.947076i	$0.604023\pi$
$258$	−3.91502e12	−0.213219
$259$	−1.12549e13	−0.600057
$260$	−3.63505e13	−1.89739
$261$	−2.51092e12	−0.128325
$262$	−3.83557e12	−0.191943
$263$	2.68522e13	1.31590	0.657951	−	0.753060i	$-0.271423\pi$
$263$	2.68522e13	1.31590	0.657951	+	0.753060i	$0.271423\pi$
$264$	−4.70034e12	−0.225584
$265$	3.32740e13	1.56406
$266$	−1.75440e11	−0.00807757
$267$	−1.80952e12	−0.0816117
$268$	2.33459e13	1.03150
$269$	−2.32608e12	−0.100690	−0.0503451	−	0.998732i	$-0.516032\pi$
$269$	−2.32608e12	−0.100690	−0.0503451	+	0.998732i	$0.516032\pi$
$270$	−1.49805e12	−0.0635367
$271$	−1.78154e13	−0.740398	−0.370199	−	0.928952i	$-0.620711\pi$
$271$	−1.78154e13	−0.740398	−0.370199	+	0.928952i	$0.620711\pi$
$272$	−2.21417e13	−0.901743
$273$	1.00720e13	0.401997
$274$	−7.29387e12	−0.285319
$275$	1.20685e13	0.462724
$276$	1.94707e13	0.731781
$277$	1.49786e13	0.551866	0.275933	−	0.961177i	$-0.411013\pi$
$277$	1.49786e13	0.551866	0.275933	+	0.961177i	$0.411013\pi$
$278$	8.56404e12	0.309337
$279$	−3.57467e12	−0.126594
$280$	−7.93777e12	−0.275632
$281$	−3.35026e13	−1.14076	−0.570380	−	0.821381i	$-0.693204\pi$
$281$	−3.35026e13	−1.14076	−0.570380	+	0.821381i	$0.693204\pi$
$282$	−2.74424e12	−0.0916331
$283$	−5.75554e12	−0.188478	−0.0942390	−	0.995550i	$-0.530042\pi$
$283$	−5.75554e12	−0.188478	−0.0942390	+	0.995550i	$0.530042\pi$
$284$	4.07633e13	1.30924
$285$	1.65750e12	0.0522163
$286$	1.05449e13	0.325858
$287$	−5.03636e12	−0.152674
$288$	−7.99751e12	−0.237846
$289$	9.27436e12	0.270611
$290$	−4.43943e12	−0.127098
$291$	−2.91104e13	−0.817780
$292$	−1.35945e12	−0.0374764
$293$	−2.09331e13	−0.566319	−0.283159	−	0.959073i	$-0.591383\pi$
$293$	−2.09331e13	−0.566319	−0.283159	+	0.959073i	$0.591383\pi$
$294$	−4.61885e12	−0.122637
$295$	6.31429e12	0.164552
$296$	−2.73882e13	−0.700581
$297$	−5.93491e12	−0.149023
$298$	8.00331e12	0.197279
$299$	−9.05607e13	−2.19154
$300$	1.35302e13	0.321467
$301$	−2.61934e13	−0.611050
$302$	1.94074e13	0.444559
$303$	1.90822e13	0.429234
$304$	2.59130e12	0.0572418
$305$	9.00394e12	0.195336
$306$	4.60606e12	0.0981435
$307$	4.90108e13	1.02572	0.512862	−	0.858471i	$-0.328585\pi$
$307$	4.90108e13	1.02572	0.512862	+	0.858471i	$0.328585\pi$
$308$	−1.51685e13	−0.311826
$309$	−1.51704e13	−0.306355
$310$	−6.32019e12	−0.125384
$311$	−3.13688e13	−0.611386	−0.305693	−	0.952130i	$-0.598888\pi$
$311$	−3.13688e13	−0.611386	−0.305693	+	0.952130i	$0.598888\pi$
$312$	2.45098e13	0.469342
$313$	8.03328e13	1.51147	0.755734	−	0.654879i	$-0.227280\pi$
$313$	8.03328e13	1.51147	0.755734	+	0.654879i	$0.227280\pi$
$314$	−8.55664e11	−0.0158194
$315$	−1.00227e13	−0.182085
$316$	−7.91807e13	−1.41364
$317$	−9.56777e13	−1.67875	−0.839373	−	0.543556i	$-0.817077\pi$
$317$	−9.56777e13	−1.67875	−0.839373	+	0.543556i	$0.817077\pi$
$318$	−1.08215e13	−0.186612
$319$	−1.75880e13	−0.298104
$320$	4.65520e13	0.775556
$321$	6.38003e13	1.04483
$322$	−9.53855e12	−0.153559
$323$	−5.09633e12	−0.0806572
$324$	−6.65373e12	−0.103530
$325$	−6.29307e13	−0.962729
$326$	5.85573e12	0.0880814
$327$	5.23098e13	0.773695
$328$	−1.22557e13	−0.178251
$329$	−1.83603e13	−0.262605
$330$	−1.04932e13	−0.147598
$331$	4.55274e13	0.629823	0.314911	−	0.949121i	$-0.398025\pi$
$331$	4.55274e13	0.629823	0.314911	+	0.949121i	$0.398025\pi$
$332$	8.08492e12	0.110006
$333$	−3.45818e13	−0.462812
$334$	−9.76958e12	−0.128609
$335$	1.08053e14	1.39923
$336$	−1.56693e13	−0.199610
$337$	−1.39734e13	−0.175121	−0.0875603	−	0.996159i	$-0.527907\pi$
$337$	−1.39734e13	−0.175121	−0.0875603	+	0.996159i	$0.527907\pi$
$338$	−3.38015e13	−0.416768
$339$	−2.47320e13	−0.300027
$340$	−1.11219e14	−1.32754
$341$	−2.50391e13	−0.294083
$342$	−5.39059e11	−0.00623006
$343$	−6.89025e13	−0.783641
$344$	−6.37403e13	−0.713415
$345$	9.01168e13	0.992660
$346$	−3.50820e12	−0.0380334
$347$	−5.88577e13	−0.628046	−0.314023	−	0.949415i	$-0.601677\pi$
$347$	−5.88577e13	−0.628046	−0.314023	+	0.949415i	$0.601677\pi$
$348$	−1.97182e13	−0.207101
$349$	4.78263e13	0.494455	0.247227	−	0.968957i	$-0.420481\pi$
$349$	4.78263e13	0.494455	0.247227	+	0.968957i	$0.420481\pi$
$350$	−6.62834e12	−0.0674575
$351$	3.09474e13	0.310052
$352$	−5.60193e13	−0.552526
$353$	−8.23195e13	−0.799359	−0.399680	−	0.916655i	$-0.630879\pi$
$353$	−8.23195e13	−0.799359	−0.399680	+	0.916655i	$0.630879\pi$
$354$	−2.05356e12	−0.0196332
$355$	1.88666e14	1.77598
$356$	−1.42101e13	−0.131711
$357$	3.08168e13	0.281263
$358$	2.60033e13	0.233707
$359$	−2.06967e14	−1.83182	−0.915909	−	0.401386i	$-0.868529\pi$
$359$	−2.06967e14	−1.83182	−0.915909	+	0.401386i	$0.868529\pi$
$360$	−2.43896e13	−0.212589
$361$	−1.15894e14	−0.994880
$362$	−2.59264e13	−0.219202
$363$	2.77591e13	0.231164
$364$	7.90955e13	0.648775
$365$	−6.29198e12	−0.0508366
$366$	−2.92830e12	−0.0233061
$367$	1.12211e14	0.879773	0.439886	−	0.898053i	$-0.355019\pi$
$367$	1.12211e14	0.879773	0.439886	+	0.898053i	$0.355019\pi$
$368$	1.40887e14	1.08820
$369$	−1.54747e13	−0.117755
$370$	−6.11422e13	−0.458386
$371$	−7.24013e13	−0.534798
$372$	−2.80718e13	−0.204307
$373$	8.02486e13	0.575491	0.287746	−	0.957707i	$-0.407094\pi$
$373$	8.02486e13	0.575491	0.287746	+	0.957707i	$0.407094\pi$
$374$	3.22636e13	0.227991
$375$	−4.21730e13	−0.293672
$376$	−4.46789e13	−0.306598
$377$	9.17120e13	0.620224
$378$	3.25962e12	0.0217251
$379$	2.22349e13	0.146056	0.0730279	−	0.997330i	$-0.476734\pi$
$379$	2.22349e13	0.146056	0.0730279	+	0.997330i	$0.476734\pi$
$380$	1.30163e13	0.0842708
$381$	−1.64988e14	−1.05285
$382$	1.62418e13	0.102161
$383$	2.88958e14	1.79160	0.895800	−	0.444457i	$-0.146603\pi$
$383$	2.88958e14	1.79160	0.895800	+	0.444457i	$0.146603\pi$
$384$	−8.25427e13	−0.504495
$385$	−7.02047e13	−0.422992
$386$	6.91441e13	0.410700
$387$	−8.04820e13	−0.471290
$388$	−2.28603e14	−1.31980
$389$	−2.50047e14	−1.42331	−0.711654	−	0.702530i	$-0.752054\pi$
$389$	−2.50047e14	−1.42331	−0.711654	+	0.702530i	$0.752054\pi$
$390$	5.47164e13	0.307088
$391$	−2.77083e14	−1.53334
$392$	−7.51992e13	−0.410336
$393$	−7.88487e13	−0.424263
$394$	−3.82149e13	−0.202770
$395$	−3.66474e14	−1.91761
$396$	−4.66067e13	−0.240505
$397$	1.55567e14	0.791715	0.395857	−	0.918312i	$-0.370447\pi$
$397$	1.55567e14	0.791715	0.395857	+	0.918312i	$0.370447\pi$
$398$	8.95924e13	0.449691
$399$	−3.60657e12	−0.0178543
$400$	9.79024e13	0.478039
$401$	5.47621e13	0.263746	0.131873	−	0.991267i	$-0.457901\pi$
$401$	5.47621e13	0.263746	0.131873	+	0.991267i	$0.457901\pi$
$402$	−3.51413e13	−0.166946
$403$	1.30566e14	0.611859
$404$	1.49852e14	0.692732
$405$	−3.07957e13	−0.140439
$406$	9.65981e12	0.0434586
$407$	−2.42231e14	−1.07513
$408$	7.49910e13	0.328381
$409$	2.94979e14	1.27442	0.637212	−	0.770689i	$-0.280088\pi$
$409$	2.94979e14	1.27442	0.637212	+	0.770689i	$0.280088\pi$
$410$	−2.73600e13	−0.116629
$411$	−1.49942e14	−0.630657
$412$	−1.19133e14	−0.494420
$413$	−1.37393e13	−0.0562653
$414$	−2.93082e13	−0.118437
$415$	3.74197e13	0.149223
$416$	2.92111e14	1.14957
$417$	1.76053e14	0.683746
$418$	−3.77588e12	−0.0144727
$419$	9.05972e13	0.342719	0.171359	−	0.985209i	$-0.445184\pi$
$419$	9.05972e13	0.342719	0.171359	+	0.985209i	$0.445184\pi$
$420$	−7.87077e13	−0.293864
$421$	−5.24734e13	−0.193369	−0.0966847	−	0.995315i	$-0.530824\pi$
$421$	−5.24734e13	−0.193369	−0.0966847	+	0.995315i	$0.530824\pi$
$422$	−2.53114e13	−0.0920657
$423$	−5.64141e13	−0.202542
$424$	−1.76185e14	−0.624390
$425$	−1.92545e14	−0.673586
$426$	−6.13588e13	−0.211897
$427$	−1.95918e13	−0.0667914
$428$	5.01022e14	1.68623
$429$	2.16774e14	0.720264
$430$	−1.42296e14	−0.466784
$431$	−2.30277e14	−0.745806	−0.372903	−	0.927870i	$-0.621638\pi$
$431$	−2.30277e14	−0.745806	−0.372903	+	0.927870i	$0.621638\pi$
$432$	−4.81455e13	−0.153955
$433$	4.93132e14	1.55697	0.778485	−	0.627664i	$-0.215989\pi$
$433$	4.93132e14	1.55697	0.778485	+	0.627664i	$0.215989\pi$
$434$	1.37522e13	0.0428724
$435$	−9.12624e13	−0.280932
$436$	4.10787e14	1.24865
$437$	3.24277e13	0.0973349
$438$	2.04631e12	0.00606545
$439$	−3.84393e14	−1.12518	−0.562589	−	0.826737i	$-0.690195\pi$
$439$	−3.84393e14	−1.12518	−0.562589	+	0.826737i	$0.690195\pi$
$440$	−1.70839e14	−0.493853
$441$	−9.49507e13	−0.271073
$442$	−1.68237e14	−0.474351
$443$	6.90847e14	1.92381	0.961903	−	0.273390i	$-0.0881448\pi$
$443$	6.90847e14	1.92381	0.961903	+	0.273390i	$0.0881448\pi$
$444$	−2.71570e14	−0.746922
$445$	−6.57692e13	−0.178666
$446$	−6.59622e13	−0.176992
$447$	1.64526e14	0.436057
$448$	−1.01293e14	−0.265186
$449$	1.63534e14	0.422915	0.211457	−	0.977387i	$-0.432179\pi$
$449$	1.63534e14	0.422915	0.211457	+	0.977387i	$0.432179\pi$
$450$	−2.03663e13	−0.0520286
$451$	−1.08394e14	−0.273549
$452$	−1.94219e14	−0.484207
$453$	3.98963e14	0.982635
$454$	4.74008e13	0.115340
$455$	3.66080e14	0.880062
$456$	−8.77639e12	−0.0208454
$457$	−3.63750e14	−0.853620	−0.426810	−	0.904341i	$-0.640363\pi$
$457$	−3.63750e14	−0.853620	−0.426810	+	0.904341i	$0.640363\pi$
$458$	2.43746e12	0.00565167
$459$	9.46878e13	0.216932
$460$	7.07684e14	1.60203
$461$	−4.90161e14	−1.09644	−0.548218	−	0.836335i	$-0.684694\pi$
$461$	−4.90161e14	−1.09644	−0.548218	+	0.836335i	$0.684694\pi$
$462$	2.28323e13	0.0504683
$463$	3.68532e13	0.0804971	0.0402485	−	0.999190i	$-0.487185\pi$
$463$	3.68532e13	0.0804971	0.0402485	+	0.999190i	$0.487185\pi$
$464$	−1.42678e14	−0.307970
$465$	−1.29926e14	−0.277143
$466$	8.00951e13	0.168843
$467$	−1.25519e14	−0.261496	−0.130748	−	0.991416i	$-0.541738\pi$
$467$	−1.25519e14	−0.261496	−0.130748	+	0.991416i	$0.541738\pi$
$468$	2.43029e14	0.500387
$469$	−2.35113e14	−0.478438
$470$	−9.97427e13	−0.200605
$471$	−1.75901e13	−0.0349666
$472$	−3.34340e13	−0.0656911
$473$	−5.63743e14	−1.09483
$474$	1.19186e14	0.228795
$475$	2.25340e13	0.0427587
$476$	2.42004e14	0.453924
$477$	−2.22461e14	−0.412479
$478$	1.41517e13	0.0259391
$479$	1.91334e14	0.346694	0.173347	−	0.984861i	$-0.444542\pi$
$479$	1.91334e14	0.346694	0.173347	+	0.984861i	$0.444542\pi$
$480$	−2.90679e14	−0.520699
$481$	1.26311e15	2.23688
$482$	−2.54960e14	−0.446389
$483$	−1.96086e14	−0.339420
$484$	2.17992e14	0.373070
$485$	−1.05805e15	−1.79030
$486$	1.00155e13	0.0167561
$487$	1.83560e14	0.303646	0.151823	−	0.988408i	$-0.451486\pi$
$487$	1.83560e14	0.303646	0.151823	+	0.988408i	$0.451486\pi$
$488$	−4.76755e13	−0.0779806
$489$	1.20378e14	0.194692
$490$	−1.67877e14	−0.268481
$491$	1.00643e15	1.59160	0.795799	−	0.605561i	$-0.207051\pi$
$491$	1.00643e15	1.59160	0.795799	+	0.605561i	$0.207051\pi$
$492$	−1.21523e14	−0.190042
$493$	2.80605e14	0.433948
$494$	1.96892e13	0.0301114
$495$	−2.15711e14	−0.326245
$496$	−2.03124e14	−0.303816
$497$	−4.10521e14	−0.607260
$498$	−1.21698e13	−0.0178042
$499$	2.56147e14	0.370627	0.185313	−	0.982679i	$-0.440670\pi$
$499$	2.56147e14	0.370627	0.185313	+	0.982679i	$0.440670\pi$
$500$	−3.31183e14	−0.473951
$501$	−2.00835e14	−0.284271
$502$	1.73756e14	0.243259
$503$	1.31881e15	1.82624	0.913121	−	0.407689i	$-0.133665\pi$
$503$	1.31881e15	1.82624	0.913121	+	0.407689i	$0.133665\pi$
$504$	5.30697e13	0.0726906
$505$	6.93565e14	0.939689
$506$	−2.05292e14	−0.275134
$507$	−6.94865e14	−0.921206
$508$	−1.29565e15	−1.69917
$509$	9.41159e14	1.22100	0.610499	−	0.792017i	$-0.290969\pi$
$509$	9.41159e14	1.22100	0.610499	+	0.792017i	$0.290969\pi$
$510$	1.67413e14	0.214858
$511$	1.36908e13	0.0173826
$512$	−7.75804e14	−0.974467
$513$	−1.10816e13	−0.0137707
$514$	1.36403e14	0.167697
$515$	−5.51385e14	−0.670680
$516$	−6.32023e14	−0.760605
$517$	−3.95157e14	−0.470513
$518$	1.33040e14	0.156736
$519$	−7.21188e13	−0.0840675
$520$	8.90836e14	1.02749
$521$	1.96814e14	0.224620	0.112310	−	0.993673i	$-0.464175\pi$
$521$	1.96814e14	0.224620	0.112310	+	0.993673i	$0.464175\pi$
$522$	2.96808e13	0.0335187
$523$	1.74097e14	0.194551	0.0972753	−	0.995258i	$-0.468987\pi$
$523$	1.74097e14	0.194551	0.0972753	+	0.995258i	$0.468987\pi$
$524$	−6.19196e14	−0.684710
$525$	−1.36260e14	−0.149105
$526$	−3.17411e14	−0.343716
$527$	3.99484e14	0.428096
$528$	−3.37239e14	−0.357644
$529$	8.10259e14	0.850389
$530$	−3.93321e14	−0.408535
$531$	−4.22156e13	−0.0433963
$532$	−2.83223e13	−0.0288147
$533$	5.65218e14	0.569136
$534$	2.13898e13	0.0213171
$535$	2.31889e15	2.28736
$536$	−5.72134e14	−0.558588
$537$	5.34556e14	0.516577
$538$	2.74958e13	0.0263005
$539$	−6.65091e14	−0.629713
$540$	−2.41838e14	−0.226651
$541$	1.76596e15	1.63830	0.819152	−	0.573576i	$-0.194444\pi$
$541$	1.76596e15	1.63830	0.819152	+	0.573576i	$0.194444\pi$
$542$	2.10590e14	0.193394
$543$	−5.32975e14	−0.484516
$544$	8.93753e14	0.804310
$545$	1.90126e15	1.69379
$546$	−1.19058e14	−0.105003
$547$	−9.13558e14	−0.797638	−0.398819	−	0.917030i	$-0.630580\pi$
$547$	−9.13558e14	−0.797638	−0.398819	+	0.917030i	$0.630580\pi$
$548$	−1.17749e15	−1.01780
$549$	−6.01978e13	−0.0515149
$550$	−1.42657e14	−0.120865
$551$	−3.28400e13	−0.0275467
$552$	−4.77165e14	−0.396281
$553$	7.97416e14	0.655687
$554$	−1.77057e14	−0.144149
$555$	−1.25691e15	−1.01320
$556$	1.38254e15	1.10348
$557$	2.06801e15	1.63437	0.817183	−	0.576379i	$-0.195535\pi$
$557$	2.06801e15	1.63437	0.817183	+	0.576379i	$0.195535\pi$
$558$	4.22550e13	0.0330666
$559$	2.93962e15	2.27786
$560$	−5.69518e14	−0.436992
$561$	6.63249e14	0.503943
$562$	3.96023e14	0.297969
$563$	−8.03448e14	−0.598634	−0.299317	−	0.954154i	$-0.596759\pi$
$563$	−8.03448e14	−0.598634	−0.299317	+	0.954154i	$0.596759\pi$
$564$	−4.43018e14	−0.326878
$565$	−8.98911e14	−0.656826
$566$	6.80343e13	0.0492309
$567$	6.70087e13	0.0480202
$568$	−9.98980e14	−0.708991
$569$	−2.72353e15	−1.91432	−0.957162	−	0.289553i	$-0.906493\pi$
$569$	−2.72353e15	−1.91432	−0.957162	+	0.289553i	$0.906493\pi$
$570$	−1.95927e13	−0.0136390
$571$	1.83330e15	1.26396	0.631981	−	0.774984i	$-0.282242\pi$
$571$	1.83330e15	1.26396	0.631981	+	0.774984i	$0.282242\pi$
$572$	1.70232e15	1.16242
$573$	3.33887e14	0.225813
$574$	5.95331e13	0.0398789
$575$	1.22516e15	0.812865
$576$	−3.11233e14	−0.204533
$577$	1.93168e15	1.25738	0.628692	−	0.777655i	$-0.283591\pi$
$577$	1.93168e15	1.25738	0.628692	+	0.777655i	$0.283591\pi$
$578$	−1.09629e14	−0.0706842
$579$	1.42141e15	0.907795
$580$	−7.16681e14	−0.453390
$581$	−8.14219e13	−0.0510238
$582$	3.44104e14	0.213606
$583$	−1.55824e15	−0.958205
$584$	3.33158e13	0.0202946
$585$	1.12482e15	0.678774
$586$	2.47443e14	0.147924
$587$	−9.17137e14	−0.543156	−0.271578	−	0.962416i	$-0.587546\pi$
$587$	−9.17137e14	−0.543156	−0.271578	+	0.962416i	$0.587546\pi$
$588$	−7.45645e14	−0.437479
$589$	−4.67526e13	−0.0271751
$590$	−7.46391e13	−0.0429814
$591$	−7.85593e14	−0.448194
$592$	−1.96504e15	−1.11071
$593$	6.89190e14	0.385956	0.192978	−	0.981203i	$-0.438185\pi$
$593$	6.89190e14	0.385956	0.192978	+	0.981203i	$0.438185\pi$
$594$	7.01545e13	0.0389251
$595$	1.12007e15	0.615748
$596$	1.29202e15	0.703743
$597$	1.84177e15	0.993979
$598$	1.07049e15	0.572434
$599$	−2.08381e15	−1.10410	−0.552052	−	0.833809i	$-0.686155\pi$
$599$	−2.08381e15	−1.10410	−0.552052	+	0.833809i	$0.686155\pi$
$600$	−3.31582e14	−0.174084
$601$	3.29466e15	1.71396	0.856980	−	0.515350i	$-0.172338\pi$
$601$	3.29466e15	1.71396	0.856980	+	0.515350i	$0.172338\pi$
$602$	3.09623e14	0.159607
$603$	−7.22409e14	−0.369010
$604$	3.13304e15	1.58585
$605$	1.00894e15	0.506069
$606$	−2.25564e14	−0.112117
$607$	2.77434e15	1.36654	0.683270	−	0.730166i	$-0.260557\pi$
$607$	2.77434e15	1.36654	0.683270	+	0.730166i	$0.260557\pi$
$608$	−1.04598e14	−0.0510569
$609$	1.98579e14	0.0960590
$610$	−1.06432e14	−0.0510223
$611$	2.06054e15	0.978934
$612$	7.43581e14	0.350103
$613$	3.15429e15	1.47187	0.735934	−	0.677053i	$-0.236743\pi$
$613$	3.15429e15	1.47187	0.735934	+	0.677053i	$0.236743\pi$
$614$	−5.79340e14	−0.267921
$615$	−5.62447e14	−0.257791
$616$	3.71731e14	0.168863
$617$	−3.58310e15	−1.61321	−0.806604	−	0.591092i	$-0.798697\pi$
$617$	−3.58310e15	−1.61321	−0.806604	+	0.591092i	$0.798697\pi$
$618$	1.79324e14	0.0800206
$619$	9.09822e14	0.402400	0.201200	−	0.979550i	$-0.435516\pi$
$619$	9.09822e14	0.402400	0.201200	+	0.979550i	$0.435516\pi$
$620$	−1.02030e15	−0.447275
$621$	−6.02495e14	−0.261788
$622$	3.70800e14	0.159695
$623$	1.43108e14	0.0610914
$624$	1.75852e15	0.744103
$625$	−2.95754e15	−1.24048
$626$	−9.49586e14	−0.394799
$627$	−7.76217e13	−0.0319898
$628$	−1.38134e14	−0.0564318
$629$	3.86465e15	1.56506
$630$	1.18475e14	0.0475611
$631$	−3.37498e15	−1.34311	−0.671553	−	0.740957i	$-0.734372\pi$
$631$	−3.37498e15	−1.34311	−0.671553	+	0.740957i	$0.734372\pi$
$632$	1.94047e15	0.765531
$633$	−5.20332e14	−0.203498
$634$	1.13097e15	0.438492
$635$	−5.99668e15	−2.30492
$636$	−1.74698e15	−0.665691
$637$	3.46810e15	1.31016
$638$	2.07901e14	0.0778653
$639$	−1.26137e15	−0.468368
$640$	−3.00011e15	−1.10445
$641$	−2.46885e14	−0.0901106	−0.0450553	−	0.998984i	$-0.514346\pi$
$641$	−2.46885e14	−0.0901106	−0.0450553	+	0.998984i	$0.514346\pi$
$642$	−7.54161e14	−0.272911
$643$	4.89646e14	0.175680	0.0878399	−	0.996135i	$-0.472004\pi$
$643$	4.89646e14	0.175680	0.0878399	+	0.996135i	$0.472004\pi$
$644$	−1.53986e15	−0.547783
$645$	−2.92521e15	−1.03176
$646$	6.02419e13	0.0210678
$647$	−5.07765e15	−1.76072	−0.880358	−	0.474310i	$-0.842697\pi$
$647$	−5.07765e15	−1.76072	−0.880358	+	0.474310i	$0.842697\pi$
$648$	1.63062e14	0.0560648
$649$	−2.95703e14	−0.100811
$650$	7.43882e14	0.251467
$651$	2.82707e14	0.0947634
$652$	9.45322e14	0.314209
$653$	5.94866e13	0.0196064	0.00980318	−	0.999952i	$-0.496880\pi$
$653$	5.94866e13	0.0196064	0.00980318	+	0.999952i	$0.496880\pi$
$654$	−6.18336e14	−0.202091
$655$	−2.86585e15	−0.928807
$656$	−8.79320e14	−0.282602
$657$	4.20664e13	0.0134068
$658$	2.17031e14	0.0685930
$659$	−2.60850e15	−0.817561	−0.408781	−	0.912633i	$-0.634046\pi$
$659$	−2.60850e15	−0.817561	−0.408781	+	0.912633i	$0.634046\pi$
$660$	−1.69397e15	−0.526520
$661$	−1.10457e15	−0.340474	−0.170237	−	0.985403i	$-0.554453\pi$
$661$	−1.10457e15	−0.340474	−0.170237	+	0.985403i	$0.554453\pi$
$662$	−5.38163e14	−0.164511
$663$	−3.45849e15	−1.04849
$664$	−1.98136e14	−0.0595715
$665$	−1.31085e14	−0.0390871
$666$	4.08779e14	0.120887
$667$	−1.78548e15	−0.523677
$668$	−1.57716e15	−0.458779
$669$	−1.35600e15	−0.391216
$670$	−1.27725e15	−0.365481
$671$	−4.21661e14	−0.119671
$672$	6.32491e14	0.178042
$673$	−5.41044e15	−1.51060	−0.755301	−	0.655378i	$-0.772509\pi$
$673$	−5.41044e15	−1.51060	−0.755301	+	0.655378i	$0.772509\pi$
$674$	1.65175e14	0.0457419
$675$	−4.18674e14	−0.115002
$676$	−5.45676e15	−1.48672
$677$	2.10769e15	0.569598	0.284799	−	0.958587i	$-0.408073\pi$
$677$	2.10769e15	0.569598	0.284799	+	0.958587i	$0.408073\pi$
$678$	2.92348e14	0.0783677
$679$	2.30223e15	0.612159
$680$	2.72564e15	0.718900
$681$	9.74429e14	0.254942
$682$	2.95979e14	0.0768151
$683$	−6.58986e15	−1.69653	−0.848266	−	0.529570i	$-0.822353\pi$
$683$	−6.58986e15	−1.69653	−0.848266	+	0.529570i	$0.822353\pi$
$684$	−8.70231e13	−0.0222242
$685$	−5.44981e15	−1.38065
$686$	8.14472e14	0.204689
$687$	5.01074e13	0.0124922
$688$	−4.57322e15	−1.13106
$689$	8.12542e15	1.99361
$690$	−1.06524e15	−0.259285
$691$	1.29015e15	0.311538	0.155769	−	0.987794i	$-0.450214\pi$
$691$	1.29015e15	0.311538	0.155769	+	0.987794i	$0.450214\pi$
$692$	−5.66347e14	−0.135675
$693$	4.69368e14	0.111553
$694$	6.95737e14	0.164047
$695$	6.39885e15	1.49687
$696$	4.83231e14	0.112151
$697$	1.72936e15	0.398204
$698$	−5.65338e14	−0.129153
$699$	1.64653e15	0.373204
$700$	−1.07005e15	−0.240638
$701$	−1.53913e15	−0.343419	−0.171710	−	0.985148i	$-0.554929\pi$
$701$	−1.53913e15	−0.343419	−0.171710	+	0.985148i	$0.554929\pi$
$702$	−3.65819e14	−0.0809863
$703$	−4.52290e14	−0.0993488
$704$	−2.18006e15	−0.475137
$705$	−2.05043e15	−0.443410
$706$	9.73071e14	0.208794
$707$	−1.50914e15	−0.321308
$708$	−3.31518e14	−0.0700364
$709$	−3.68366e15	−0.772191	−0.386096	−	0.922459i	$-0.626177\pi$
$709$	−3.68366e15	−0.772191	−0.386096	+	0.922459i	$0.626177\pi$
$710$	−2.23016e15	−0.463889
$711$	2.45014e15	0.505718
$712$	3.48246e14	0.0713257
$713$	−2.54190e15	−0.516614
$714$	−3.64275e14	−0.0734665
$715$	7.87889e15	1.57682
$716$	4.19786e15	0.833693
$717$	2.90919e14	0.0573347
$718$	2.44649e15	0.478475
$719$	−6.47613e15	−1.25692	−0.628459	−	0.777843i	$-0.716314\pi$
$719$	−6.47613e15	−1.25692	−0.628459	+	0.777843i	$0.716314\pi$
$720$	−1.74990e15	−0.337043
$721$	1.19977e15	0.229326
$722$	1.36994e15	0.259865
$723$	−5.24128e15	−0.986680
$724$	−4.18544e15	−0.781950
$725$	−1.24073e15	−0.230048
$726$	−3.28131e14	−0.0603804
$727$	−3.09368e15	−0.564984	−0.282492	−	0.959270i	$-0.591161\pi$
$727$	−3.09368e15	−0.564984	−0.282492	+	0.959270i	$0.591161\pi$
$728$	−1.93838e15	−0.351331
$729$	2.05891e14	0.0370370
$730$	7.43754e13	0.0132786
$731$	8.99418e15	1.59373
$732$	−4.72731e14	−0.0831387
$733$	2.14364e15	0.374179	0.187089	−	0.982343i	$-0.440095\pi$
$733$	2.14364e15	0.374179	0.187089	+	0.982343i	$0.440095\pi$
$734$	−1.32640e15	−0.229798
$735$	−3.45109e15	−0.593439
$736$	−5.68692e15	−0.970619
$737$	−5.06018e15	−0.857224
$738$	1.82921e14	0.0307578
$739$	4.32853e15	0.722430	0.361215	−	0.932483i	$-0.382362\pi$
$739$	4.32853e15	0.722430	0.361215	+	0.932483i	$0.382362\pi$
$740$	−9.87052e15	−1.63518
$741$	4.04756e14	0.0665569
$742$	8.55831e14	0.139690
$743$	−2.87609e15	−0.465976	−0.232988	−	0.972480i	$-0.574850\pi$
$743$	−2.87609e15	−0.465976	−0.232988	+	0.972480i	$0.574850\pi$
$744$	6.87952e14	0.110639
$745$	5.97989e15	0.954626
$746$	−9.48591e14	−0.150320
$747$	−2.50177e14	−0.0393536
$748$	5.20848e15	0.813303
$749$	−5.04571e15	−0.782118
$750$	4.98512e14	0.0767076
$751$	−1.56156e15	−0.238528	−0.119264	−	0.992863i	$-0.538053\pi$
$751$	−1.56156e15	−0.238528	−0.119264	+	0.992863i	$0.538053\pi$
$752$	−3.20561e15	−0.486086
$753$	3.57194e15	0.537690
$754$	−1.08410e15	−0.162004
$755$	1.45008e16	2.15121
$756$	5.26217e14	0.0774989
$757$	−1.93821e15	−0.283383	−0.141691	−	0.989911i	$-0.545254\pi$
$757$	−1.93821e15	−0.283383	−0.141691	+	0.989911i	$0.545254\pi$
$758$	−2.62831e14	−0.0381501
$759$	−4.22023e15	−0.608144
$760$	−3.18988e14	−0.0456352
$761$	9.78831e15	1.39025	0.695124	−	0.718890i	$-0.255349\pi$
$761$	9.78831e15	1.39025	0.695124	+	0.718890i	$0.255349\pi$
$762$	1.95027e15	0.275006
$763$	−4.13697e15	−0.579159
$764$	2.62200e15	0.364435
$765$	3.44154e15	0.474914
$766$	−3.41567e15	−0.467970
$767$	1.54193e15	0.209745
$768$	−1.64736e15	−0.222486
$769$	−5.57344e13	−0.00747357	−0.00373678	−	0.999993i	$-0.501189\pi$
$769$	−5.57344e13	−0.00747357	−0.00373678	+	0.999993i	$0.501189\pi$
$770$	8.29865e14	0.110486
$771$	2.80406e15	0.370671
$772$	1.11623e16	1.46507
$773$	1.11036e16	1.44703	0.723514	−	0.690310i	$-0.242526\pi$
$773$	1.11036e16	1.44703	0.723514	+	0.690310i	$0.242526\pi$
$774$	9.51350e14	0.123102
$775$	−1.76637e15	−0.226945
$776$	5.60234e15	0.714710
$777$	2.73494e15	0.346443
$778$	2.95572e15	0.371771
$779$	−2.02392e14	−0.0252776
$780$	8.83317e15	1.09546
$781$	−8.83536e15	−1.08804
$782$	3.27530e15	0.400511
$783$	6.10154e14	0.0740883
$784$	−5.39538e15	−0.650555
$785$	−6.39332e14	−0.0765497
$786$	9.32043e14	0.110818
$787$	−1.02810e15	−0.121388	−0.0606939	−	0.998156i	$-0.519331\pi$
$787$	−1.02810e15	−0.121388	−0.0606939	+	0.998156i	$0.519331\pi$
$788$	−6.16924e15	−0.723331
$789$	−6.52509e15	−0.759737
$790$	4.33197e15	0.500883
$791$	1.95595e15	0.224589
$792$	1.14218e15	0.130241
$793$	2.19874e15	0.248984
$794$	−1.83890e15	−0.206798
$795$	−8.08558e15	−0.903009
$796$	1.44634e16	1.60416
$797$	−1.08662e16	−1.19690	−0.598450	−	0.801160i	$-0.704217\pi$
$797$	−1.08662e16	−1.19690	−0.598450	+	0.801160i	$0.704217\pi$
$798$	4.26320e13	0.00466359
$799$	6.30449e15	0.684925
$800$	−3.95184e15	−0.426387
$801$	4.39714e14	0.0471185
$802$	−6.47324e14	−0.0688911
$803$	2.94658e14	0.0311446
$804$	−5.67305e15	−0.595537
$805$	−7.12698e15	−0.743067
$806$	−1.54337e15	−0.159819
$807$	5.65237e14	0.0581335
$808$	−3.67240e15	−0.375135
$809$	−1.24954e16	−1.26774	−0.633872	−	0.773438i	$-0.718536\pi$
$809$	−1.24954e16	−1.26774	−0.633872	+	0.773438i	$0.718536\pi$
$810$	3.64025e14	0.0366829
$811$	1.56653e15	0.156792	0.0783958	−	0.996922i	$-0.475020\pi$
$811$	1.56653e15	0.156792	0.0783958	+	0.996922i	$0.475020\pi$
$812$	1.55943e15	0.155028
$813$	4.32915e15	0.427469
$814$	2.86333e15	0.280826
$815$	4.37526e15	0.426223
$816$	5.38044e15	0.520622
$817$	−1.05261e15	−0.101169
$818$	−3.48685e15	−0.332882
$819$	−2.44751e15	−0.232093
$820$	−4.41688e15	−0.416044
$821$	−3.01669e15	−0.282256	−0.141128	−	0.989991i	$-0.545073\pi$
$821$	−3.01669e15	−0.282256	−0.141128	+	0.989991i	$0.545073\pi$
$822$	1.77241e15	0.164729
$823$	6.25430e15	0.577404	0.288702	−	0.957419i	$-0.406776\pi$
$823$	6.25430e15	0.577404	0.288702	+	0.957419i	$0.406776\pi$
$824$	2.91956e15	0.267743
$825$	−2.93264e15	−0.267154
$826$	1.62408e14	0.0146966
$827$	−1.65925e16	−1.49153	−0.745764	−	0.666210i	$-0.767915\pi$
$827$	−1.65925e16	−1.49153	−0.745764	+	0.666210i	$0.767915\pi$
$828$	−4.73138e15	−0.422494
$829$	2.08080e16	1.84578	0.922890	−	0.385063i	$-0.125820\pi$
$829$	2.08080e16	1.84578	0.922890	+	0.385063i	$0.125820\pi$
$830$	−4.42325e14	−0.0389773
$831$	−3.63981e15	−0.318620
$832$	1.13679e16	0.988554
$833$	1.06111e16	0.916671
$834$	−2.08106e15	−0.178596
$835$	−7.29959e15	−0.622333
$836$	−6.09561e14	−0.0516277
$837$	8.68646e14	0.0730891
$838$	−1.07092e15	−0.0895188
$839$	−6.74798e15	−0.560381	−0.280190	−	0.959944i	$-0.590398\pi$
$839$	−6.74798e15	−0.560381	−0.280190	+	0.959944i	$0.590398\pi$
$840$	1.92888e15	0.159136
$841$	−1.03923e16	−0.851795
$842$	6.20270e14	0.0505085
$843$	8.14114e15	0.658618
$844$	−4.08615e15	−0.328421
$845$	−2.52557e16	−2.01673
$846$	6.66851e14	0.0529044
$847$	−2.19536e15	−0.173040
$848$	−1.26409e16	−0.989919
$849$	1.39860e15	0.108818
$850$	2.27601e15	0.175942
$851$	−2.45906e16	−1.88867
$852$	−9.90548e15	−0.755889
$853$	−1.85964e16	−1.40996	−0.704982	−	0.709225i	$-0.749045\pi$
$853$	−1.85964e16	−1.40996	−0.704982	+	0.709225i	$0.749045\pi$
$854$	2.31588e14	0.0174461
$855$	−4.02772e14	−0.0301471
$856$	−1.22785e16	−0.913142
$857$	1.07425e16	0.793798	0.396899	−	0.917862i	$-0.370086\pi$
$857$	1.07425e16	0.793798	0.396899	+	0.917862i	$0.370086\pi$
$858$	−2.56241e15	−0.188134
$859$	1.75952e16	1.28361	0.641803	−	0.766869i	$-0.278187\pi$
$859$	1.75952e16	1.28361	0.641803	+	0.766869i	$0.278187\pi$
$860$	−2.29716e16	−1.66514
$861$	1.22383e15	0.0881466
$862$	2.72203e15	0.194806
$863$	2.42553e16	1.72484	0.862418	−	0.506197i	$-0.168949\pi$
$863$	2.42553e16	1.72484	0.862418	+	0.506197i	$0.168949\pi$
$864$	1.94340e15	0.137321
$865$	−2.62124e15	−0.184043
$866$	−5.82915e15	−0.406684
$867$	−2.25367e15	−0.156237
$868$	2.22009e15	0.152937
$869$	1.71622e16	1.17480
$870$	1.07878e15	0.0733799
$871$	2.63861e16	1.78351
$872$	−1.00671e16	−0.676182
$873$	7.07382e15	0.472146
$874$	−3.83317e14	−0.0254241
$875$	3.33529e15	0.219831
$876$	3.30346e14	0.0216370
$877$	2.26640e16	1.47516	0.737579	−	0.675261i	$-0.235969\pi$
$877$	2.26640e16	1.47516	0.737579	+	0.675261i	$0.235969\pi$
$878$	4.54378e15	0.293899
$879$	5.08673e15	0.326964
$880$	−1.22573e16	−0.782964
$881$	1.05560e16	0.670090	0.335045	−	0.942202i	$-0.391248\pi$
$881$	1.05560e16	0.670090	0.335045	+	0.942202i	$0.391248\pi$
$882$	1.12238e15	0.0708048
$883$	2.13315e16	1.33733	0.668663	−	0.743566i	$-0.266867\pi$
$883$	2.13315e16	1.33733	0.668663	+	0.743566i	$0.266867\pi$
$884$	−2.71595e16	−1.69213
$885$	−1.53437e15	−0.0950042
$886$	−8.16627e15	−0.502502
$887$	−1.91504e16	−1.17111	−0.585555	−	0.810633i	$-0.699123\pi$
$887$	−1.91504e16	−1.17111	−0.585555	+	0.810633i	$0.699123\pi$
$888$	6.65532e15	0.404481
$889$	1.30483e16	0.788121
$890$	7.77435e14	0.0466680
$891$	1.44218e15	0.0860385
$892$	−1.06486e16	−0.631375
$893$	−7.37831e14	−0.0434784
$894$	−1.94481e15	−0.113899
$895$	1.94291e16	1.13090
$896$	6.52798e15	0.377646
$897$	2.20063e16	1.26528
$898$	−1.93308e15	−0.110466
$899$	2.57421e15	0.146206
$900$	−3.28783e15	−0.185599
$901$	2.48608e16	1.39486
$902$	1.28129e15	0.0714515
$903$	6.36500e15	0.352790
$904$	4.75970e15	0.262213
$905$	−1.93716e16	−1.06071
$906$	−4.71600e15	−0.256666
$907$	−2.80117e16	−1.51530	−0.757651	−	0.652660i	$-0.773653\pi$
$907$	−2.80117e16	−1.51530	−0.757651	+	0.652660i	$0.773653\pi$
$908$	7.65217e15	0.411445
$909$	−4.63698e15	−0.247818
$910$	−4.32731e15	−0.229874
$911$	3.77581e16	1.99370	0.996848	−	0.0793409i	$-0.0252816\pi$
$911$	3.77581e16	1.99370	0.996848	+	0.0793409i	$0.0252816\pi$
$912$	−6.29687e14	−0.0330486
$913$	−1.75239e15	−0.0914200
$914$	4.29977e15	0.222967
$915$	−2.18796e15	−0.112778
$916$	3.93492e14	0.0201609
$917$	6.23583e15	0.317587
$918$	−1.11927e15	−0.0566632
$919$	3.75954e16	1.89190	0.945952	−	0.324306i	$-0.105131\pi$
$919$	3.75954e16	1.89190	0.945952	+	0.324306i	$0.105131\pi$
$920$	−1.73431e16	−0.867549
$921$	−1.19096e16	−0.592203
$922$	5.79402e15	0.286391
$923$	4.60717e16	2.26373
$924$	3.68594e15	0.180033
$925$	−1.70880e16	−0.829683
$926$	−4.35629e14	−0.0210260
$927$	3.68640e15	0.176874
$928$	5.75921e15	0.274694
$929$	4.12183e15	0.195436	0.0977178	−	0.995214i	$-0.468846\pi$
$929$	4.12183e15	0.195436	0.0977178	+	0.995214i	$0.468846\pi$
$930$	1.53581e15	0.0723903
$931$	−1.24185e15	−0.0581895
$932$	1.29302e16	0.602306
$933$	7.62262e15	0.352984
$934$	1.48371e15	0.0683033
$935$	2.41066e16	1.10324
$936$	−5.95588e15	−0.270975
$937$	−4.76398e15	−0.215478	−0.107739	−	0.994179i	$-0.534361\pi$
$937$	−4.76398e15	−0.215478	−0.107739	+	0.994179i	$0.534361\pi$
$938$	2.77919e15	0.124969
$939$	−1.95209e16	−0.872646
$940$	−1.61020e16	−0.715610
$941$	2.23412e16	0.987106	0.493553	−	0.869716i	$-0.335698\pi$
$941$	2.23412e16	0.987106	0.493553	+	0.869716i	$0.335698\pi$
$942$	2.07926e14	0.00913334
$943$	−1.10039e16	−0.480541
$944$	−2.39881e15	−0.104148
$945$	2.43551e15	0.105127
$946$	6.66381e15	0.285971
$947$	1.86498e16	0.795701	0.397850	−	0.917450i	$-0.369756\pi$
$947$	1.86498e16	0.795701	0.397850	+	0.917450i	$0.369756\pi$
$948$	1.92409e16	0.816168
$949$	−1.53648e15	−0.0647984
$950$	−2.66367e14	−0.0111686
$951$	2.32497e16	0.969224
$952$	−5.93075e15	−0.245814
$953$	2.56240e15	0.105593	0.0527966	−	0.998605i	$-0.483186\pi$
$953$	2.56240e15	0.105593	0.0527966	+	0.998605i	$0.483186\pi$
$954$	2.62963e15	0.107740
$955$	1.21355e16	0.494355
$956$	2.28458e15	0.0925312
$957$	4.27388e15	0.172110
$958$	−2.26169e15	−0.0905572
$959$	1.18583e16	0.472085
$960$	−1.13121e16	−0.447768
$961$	−2.17437e16	−0.855766
$962$	−1.49308e16	−0.584277
$963$	−1.55035e16	−0.603232
$964$	−4.11596e16	−1.59238
$965$	5.16628e16	1.98737
$966$	2.31787e15	0.0886573
$967$	−7.38874e15	−0.281012	−0.140506	−	0.990080i	$-0.544873\pi$
$967$	−7.38874e15	−0.281012	−0.140506	+	0.990080i	$0.544873\pi$
$968$	−5.34229e15	−0.202029
$969$	1.23841e15	0.0465675
$970$	1.25068e16	0.467631
$971$	3.36438e16	1.25083	0.625417	−	0.780291i	$-0.284929\pi$
$971$	3.36438e16	1.25083	0.625417	+	0.780291i	$0.284929\pi$
$972$	1.61686e15	0.0597733
$973$	−1.39233e16	−0.511826
$974$	−2.16980e15	−0.0793130
$975$	1.52922e16	0.555832
$976$	−3.42062e15	−0.123632
$977$	5.16295e16	1.85557	0.927786	−	0.373112i	$-0.121709\pi$
$977$	5.16295e16	1.85557	0.927786	+	0.373112i	$0.121709\pi$
$978$	−1.42294e15	−0.0508538
$979$	3.08002e15	0.109458
$980$	−2.71013e16	−0.957739
$981$	−1.27113e16	−0.446693
$982$	−1.18966e16	−0.415729
$983$	6.14908e15	0.213681	0.106841	−	0.994276i	$-0.465927\pi$
$983$	6.14908e15	0.213681	0.106841	+	0.994276i	$0.465927\pi$
$984$	2.97814e15	0.102913
$985$	−2.85533e16	−0.981198
$986$	−3.31694e15	−0.113348
$987$	4.46156e15	0.151615
$988$	3.17854e15	0.107415
$989$	−5.72296e16	−1.92327
$990$	2.54985e15	0.0852159
$991$	3.09087e16	1.02725	0.513624	−	0.858015i	$-0.328303\pi$
$991$	3.09087e16	1.02725	0.513624	+	0.858015i	$0.328303\pi$
$992$	8.19910e15	0.270989
$993$	−1.10631e16	−0.363628
$994$	4.85262e15	0.158618
$995$	6.69413e16	2.17604
$996$	−1.96464e15	−0.0635120
$997$	−2.95763e16	−0.950869	−0.475435	−	0.879751i	$-0.657709\pi$
$997$	−2.95763e16	−0.950869	−0.475435	+	0.879751i	$0.657709\pi$
$998$	−3.02783e15	−0.0968084
$999$	8.40338e15	0.267204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.11	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +104401. q^{10} +413614. q^{11} +463710. q^{12} -2.15678e6 q^{13} -227168. q^{14} +2.14620e6 q^{15} +3.35534e6 q^{16} -6.59896e6 q^{17} -697998. q^{18} +772293. q^{19} +1.68541e7 q^{20} -4.66995e6 q^{21} -4.88919e6 q^{22} +4.19889e7 q^{23} -1.13641e7 q^{24} +2.91781e7 q^{25} +2.54945e7 q^{26} -1.43489e7 q^{27} -3.66730e7 q^{28} -4.25227e7 q^{29} -2.53695e7 q^{30} -6.05374e7 q^{31} -1.35439e8 q^{32} -1.00508e8 q^{33} +7.80040e7 q^{34} -1.69735e8 q^{35} -1.12682e8 q^{36} -5.85646e8 q^{37} -9.12901e6 q^{38} +5.24097e8 q^{39} -4.13040e8 q^{40} -2.62066e8 q^{41} +5.52019e7 q^{42} -1.36297e9 q^{43} -7.89288e8 q^{44} -5.21527e8 q^{45} -4.96337e8 q^{46} -9.55377e8 q^{47} -8.15348e8 q^{48} -1.60800e9 q^{49} -3.44904e8 q^{50} +1.60355e9 q^{51} +4.11572e9 q^{52} -3.76739e9 q^{53} +1.69614e8 q^{54} -3.65309e9 q^{55} +8.98740e8 q^{56} -1.87667e8 q^{57} +5.02646e8 q^{58} -7.14924e8 q^{59} -4.09554e9 q^{60} -1.01945e9 q^{61} +7.15592e8 q^{62} +1.13480e9 q^{63} -5.27076e9 q^{64} +1.90489e10 q^{65} +1.18807e9 q^{66} -1.22341e10 q^{67} +1.25926e10 q^{68} -1.02033e10 q^{69} +2.00638e9 q^{70} -2.13614e10 q^{71} +2.76147e9 q^{72} +7.12398e8 q^{73} +6.92272e9 q^{74} -7.09028e9 q^{75} -1.47374e9 q^{76} +7.94880e9 q^{77} -6.19517e9 q^{78} +4.14934e10 q^{79} -2.96347e10 q^{80} +3.48678e9 q^{81} +3.09779e9 q^{82} -4.23677e9 q^{83} +8.91154e9 q^{84} +5.82828e10 q^{85} +1.61112e10 q^{86} +1.03330e10 q^{87} +1.93430e10 q^{88} +7.44660e9 q^{89} +6.16480e9 q^{90} -4.14487e10 q^{91} -8.01263e10 q^{92} +1.47106e10 q^{93} +1.12932e10 q^{94} -6.82098e9 q^{95} +3.29116e10 q^{96} +1.19796e11 q^{97} +1.90076e10 q^{98} +2.44235e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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