LMFDB - Embedded newform 177.12.a.c.1.10

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			1.10
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +509431. q^{10} -548740. q^{11} +137357. q^{12} +1.36786e6 q^{13} +343630. q^{14} +3.21483e6 q^{15} -2.71715e6 q^{16} +5.04723e6 q^{17} -2.27377e6 q^{18} -5.16583e6 q^{19} +7.47818e6 q^{20} +2.16852e6 q^{21} +2.11300e7 q^{22} -9.48085e6 q^{23} -2.44524e7 q^{24} +1.26198e8 q^{25} -5.26712e7 q^{26} -1.43489e7 q^{27} +5.04431e6 q^{28} -1.29431e8 q^{29} -1.23792e8 q^{30} -9.27006e7 q^{31} -1.01457e8 q^{32} +1.33344e8 q^{33} -1.94351e8 q^{34} +1.18062e8 q^{35} -3.33777e7 q^{36} -3.97993e7 q^{37} +1.98918e8 q^{38} -3.32389e8 q^{39} -1.33127e9 q^{40} +9.65170e7 q^{41} -8.35020e7 q^{42} -6.50542e8 q^{43} +3.10178e8 q^{44} -7.81204e8 q^{45} +3.65074e8 q^{46} -1.60481e9 q^{47} +6.60267e8 q^{48} -1.89769e9 q^{49} -4.85945e9 q^{50} -1.22648e9 q^{51} -7.73187e8 q^{52} -3.48155e9 q^{53} +5.52525e8 q^{54} +7.25970e9 q^{55} -8.97992e8 q^{56} +1.25530e9 q^{57} +4.98393e9 q^{58} -7.14924e8 q^{59} -1.81720e9 q^{60} +5.15750e9 q^{61} +3.56957e9 q^{62} -5.26950e8 q^{63} +9.47145e9 q^{64} -1.80964e10 q^{65} -5.13460e9 q^{66} -5.22349e9 q^{67} -2.85297e9 q^{68} +2.30385e9 q^{69} -4.54614e9 q^{70} +1.67408e10 q^{71} +5.94193e9 q^{72} +2.13806e10 q^{73} +1.53253e9 q^{74} -3.06662e10 q^{75} +2.92001e9 q^{76} +4.89693e9 q^{77} +1.27991e10 q^{78} -3.48354e10 q^{79} +3.59472e10 q^{80} +3.48678e9 q^{81} -3.71653e9 q^{82} -6.02784e10 q^{83} -1.22577e9 q^{84} -6.67736e10 q^{85} +2.50500e10 q^{86} +3.14518e10 q^{87} -5.52181e10 q^{88} -5.21245e10 q^{89} +3.00814e10 q^{90} -1.22067e10 q^{91} +5.35910e9 q^{92} +2.25262e10 q^{93} +6.17956e10 q^{94} +6.83426e10 q^{95} +2.46540e10 q^{96} -1.33295e11 q^{97} +7.30733e10 q^{98} -3.24026e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−38.5064	−0.850880	−0.425440	−	0.904987i	$-0.639881\pi$
$2$	−38.5064	−0.850880	−0.425440	+	0.904987i	$0.639881\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−565.255	−0.276003
$5$	−13229.8	−1.89329	−0.946644	−	0.322280i	$-0.895551\pi$
$5$	−13229.8	−1.89329	−0.946644	+	0.322280i	$0.895551\pi$
$6$	9357.06	0.491256
$7$	−8923.95	−0.200686	−0.100343	−	0.994953i	$-0.531994\pi$
$7$	−8923.95	−0.200686	−0.100343	+	0.994953i	$0.531994\pi$
$8$	100627.	1.08573
$9$	59049.0	0.333333
$10$	509431.	1.61096
$11$	−548740.	−1.02732	−0.513662	−	0.857993i	$-0.671711\pi$
$11$	−548740.	−1.02732	−0.513662	+	0.857993i	$0.671711\pi$
$12$	137357.	0.159351
$13$	1.36786e6	1.02177	0.510884	−	0.859650i	$-0.329318\pi$
$13$	1.36786e6	1.02177	0.510884	+	0.859650i	$0.329318\pi$
$14$	343630.	0.170760
$15$	3.21483e6	1.09309
$16$	−2.71715e6	−0.647819
$17$	5.04723e6	0.862152	0.431076	−	0.902316i	$-0.358134\pi$
$17$	5.04723e6	0.862152	0.431076	+	0.902316i	$0.358134\pi$
$18$	−2.27377e6	−0.283627
$19$	−5.16583e6	−0.478625	−0.239312	−	0.970943i	$-0.576922\pi$
$19$	−5.16583e6	−0.478625	−0.239312	+	0.970943i	$0.576922\pi$
$20$	7.47818e6	0.522554
$21$	2.16852e6	0.115866
$22$	2.11300e7	0.874129
$23$	−9.48085e6	−0.307146	−0.153573	−	0.988137i	$-0.549078\pi$
$23$	−9.48085e6	−0.307146	−0.153573	+	0.988137i	$0.549078\pi$
$24$	−2.44524e7	−0.626844
$25$	1.26198e8	2.58454
$26$	−5.26712e7	−0.869401
$27$	−1.43489e7	−0.192450
$28$	5.04431e6	0.0553901
$29$	−1.29431e8	−1.17179	−0.585895	−	0.810387i	$-0.699257\pi$
$29$	−1.29431e8	−1.17179	−0.585895	+	0.810387i	$0.699257\pi$
$30$	−1.23792e8	−0.930089
$31$	−9.27006e7	−0.581558	−0.290779	−	0.956790i	$-0.593914\pi$
$31$	−9.27006e7	−0.581558	−0.290779	+	0.956790i	$0.593914\pi$
$32$	−1.01457e8	−0.534510
$33$	1.33344e8	0.593125
$34$	−1.94351e8	−0.733588
$35$	1.18062e8	0.379957
$36$	−3.33777e7	−0.0920011
$37$	−3.97993e7	−0.0943552	−0.0471776	−	0.998887i	$-0.515023\pi$
$37$	−3.97993e7	−0.0943552	−0.0471776	+	0.998887i	$0.515023\pi$
$38$	1.98918e8	0.407252
$39$	−3.32389e8	−0.589918
$40$	−1.33127e9	−2.05559
$41$	9.65170e7	0.130105	0.0650523	−	0.997882i	$-0.479279\pi$
$41$	9.65170e7	0.130105	0.0650523	+	0.997882i	$0.479279\pi$
$42$	−8.35020e7	−0.0985884
$43$	−6.50542e8	−0.674837	−0.337418	−	0.941355i	$-0.609554\pi$
$43$	−6.50542e8	−0.674837	−0.337418	+	0.941355i	$0.609554\pi$
$44$	3.10178e8	0.283545
$45$	−7.81204e8	−0.631096
$46$	3.65074e8	0.261344
$47$	−1.60481e9	−1.02067	−0.510336	−	0.859975i	$-0.670479\pi$
$47$	−1.60481e9	−1.02067	−0.510336	+	0.859975i	$0.670479\pi$
$48$	6.60267e8	0.374018
$49$	−1.89769e9	−0.959725
$50$	−4.85945e9	−2.19914
$51$	−1.22648e9	−0.497763
$52$	−7.73187e8	−0.282011
$53$	−3.48155e9	−1.14355	−0.571775	−	0.820411i	$-0.693745\pi$
$53$	−3.48155e9	−1.14355	−0.571775	+	0.820411i	$0.693745\pi$
$54$	5.52525e8	0.163752
$55$	7.25970e9	1.94502
$56$	−8.97992e8	−0.217890
$57$	1.25530e9	0.276334
$58$	4.98393e9	0.997053
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−1.81720e9	−0.301697
$61$	5.15750e9	0.781853	0.390927	−	0.920422i	$-0.372155\pi$
$61$	5.15750e9	0.781853	0.390927	+	0.920422i	$0.372155\pi$
$62$	3.56957e9	0.494836
$63$	−5.26950e8	−0.0668955
$64$	9.47145e9	1.10262
$65$	−1.80964e10	−1.93450
$66$	−5.13460e9	−0.504678
$67$	−5.22349e9	−0.472661	−0.236330	−	0.971673i	$-0.575945\pi$
$67$	−5.22349e9	−0.472661	−0.236330	+	0.971673i	$0.575945\pi$
$68$	−2.85297e9	−0.237957
$69$	2.30385e9	0.177331
$70$	−4.54614e9	−0.323298
$71$	1.67408e10	1.10117	0.550586	−	0.834779i	$-0.314404\pi$
$71$	1.67408e10	1.10117	0.550586	+	0.834779i	$0.314404\pi$
$72$	5.94193e9	0.361909
$73$	2.13806e10	1.20710	0.603552	−	0.797323i	$-0.293751\pi$
$73$	2.13806e10	1.20710	0.603552	+	0.797323i	$0.293751\pi$
$74$	1.53253e9	0.0802850
$75$	−3.06662e10	−1.49219
$76$	2.92001e9	0.132102
$77$	4.89693e9	0.206170
$78$	1.27991e10	0.501949
$79$	−3.48354e10	−1.27371	−0.636857	−	0.770982i	$-0.719766\pi$
$79$	−3.48354e10	−1.27371	−0.636857	+	0.770982i	$0.719766\pi$
$80$	3.59472e10	1.22651
$81$	3.48678e9	0.111111
$82$	−3.71653e9	−0.110703
$83$	−6.02784e10	−1.67970	−0.839850	−	0.542818i	$-0.817357\pi$
$83$	−6.02784e10	−1.67970	−0.839850	+	0.542818i	$0.817357\pi$
$84$	−1.22577e9	−0.0319795
$85$	−6.67736e10	−1.63230
$86$	2.50500e10	0.574205
$87$	3.14518e10	0.676533
$88$	−5.52181e10	−1.11539
$89$	−5.21245e10	−0.989458	−0.494729	−	0.869047i	$-0.664733\pi$
$89$	−5.21245e10	−0.989458	−0.494729	+	0.869047i	$0.664733\pi$
$90$	3.00814e10	0.536987
$91$	−1.22067e10	−0.205055
$92$	5.35910e9	0.0847732
$93$	2.25262e10	0.335763
$94$	6.17956e10	0.868469
$95$	6.83426e10	0.906175
$96$	2.46540e10	0.308599
$97$	−1.33295e11	−1.57605	−0.788024	−	0.615644i	$-0.788896\pi$
$97$	−1.33295e11	−1.57605	−0.788024	+	0.615644i	$0.788896\pi$
$98$	7.30733e10	0.816611
$99$	−3.24026e10	−0.342441
$100$	−7.13342e10	−0.713342
$101$	−1.75528e11	−1.66180	−0.830902	−	0.556419i	$-0.812175\pi$
$101$	−1.75528e11	−1.66180	−0.830902	+	0.556419i	$0.812175\pi$
$102$	4.72272e10	0.423537
$103$	7.57783e10	0.644080	0.322040	−	0.946726i	$-0.395631\pi$
$103$	7.57783e10	0.644080	0.322040	+	0.946726i	$0.395631\pi$
$104$	1.37643e11	1.10936
$105$	−2.86890e10	−0.219369
$106$	1.34062e11	0.973023
$107$	2.53729e10	0.174887	0.0874437	−	0.996169i	$-0.472130\pi$
$107$	2.53729e10	0.174887	0.0874437	+	0.996169i	$0.472130\pi$
$108$	8.11079e9	0.0531169
$109$	−1.49235e11	−0.929018	−0.464509	−	0.885568i	$-0.653769\pi$
$109$	−1.49235e11	−0.929018	−0.464509	+	0.885568i	$0.653769\pi$
$110$	−2.79545e11	−1.65498
$111$	9.67123e9	0.0544760
$112$	2.42477e10	0.130008
$113$	−2.95296e11	−1.50774	−0.753869	−	0.657025i	$-0.771815\pi$
$113$	−2.95296e11	−1.50774	−0.753869	+	0.657025i	$0.771815\pi$
$114$	−4.83370e10	−0.235127
$115$	1.25429e11	0.581515
$116$	7.31616e10	0.323418
$117$	8.07705e10	0.340589
$118$	2.75292e10	0.110775
$119$	−4.50412e10	−0.173022
$120$	3.23499e11	1.18680
$121$	1.58041e10	0.0553926
$122$	−1.98597e11	−0.665263
$123$	−2.34536e10	−0.0751159
$124$	5.23994e10	0.160512
$125$	−1.02359e12	−3.00000
$126$	2.02910e10	0.0569200
$127$	−7.67775e10	−0.206212	−0.103106	−	0.994670i	$-0.532878\pi$
$127$	−7.67775e10	−0.206212	−0.103106	+	0.994670i	$0.532878\pi$
$128$	−1.56929e11	−0.403690
$129$	1.58082e11	0.389617
$130$	6.96828e11	1.64603
$131$	3.86066e11	0.874317	0.437159	−	0.899384i	$-0.355985\pi$
$131$	3.86066e11	0.874317	0.437159	+	0.899384i	$0.355985\pi$
$132$	−7.53733e10	−0.163705
$133$	4.60996e10	0.0960534
$134$	2.01138e11	0.402178
$135$	1.89833e11	0.364364
$136$	5.07888e11	0.936060
$137$	8.37523e11	1.48263	0.741317	−	0.671155i	$-0.234202\pi$
$137$	8.37523e11	1.48263	0.741317	+	0.671155i	$0.234202\pi$
$138$	−8.87129e10	−0.150887
$139$	7.87009e10	0.128647	0.0643233	−	0.997929i	$-0.479511\pi$
$139$	7.87009e10	0.128647	0.0643233	+	0.997929i	$0.479511\pi$
$140$	−6.67350e10	−0.104870
$141$	3.89969e11	0.589285
$142$	−6.44628e11	−0.936965
$143$	−7.50598e11	−1.04968
$144$	−1.60445e11	−0.215940
$145$	1.71234e12	2.21854
$146$	−8.23292e11	−1.02710
$147$	4.61139e11	0.554097
$148$	2.24968e10	0.0260424
$149$	4.99227e11	0.556896	0.278448	−	0.960451i	$-0.410180\pi$
$149$	4.99227e11	0.556896	0.278448	+	0.960451i	$0.410180\pi$
$150$	1.18085e12	1.26967
$151$	1.27434e12	1.32103	0.660514	−	0.750814i	$-0.270338\pi$
$151$	1.27434e12	1.32103	0.660514	+	0.750814i	$0.270338\pi$
$152$	−5.19822e11	−0.519655
$153$	2.98034e11	0.287384
$154$	−1.88563e11	−0.175426
$155$	1.22641e12	1.10106
$156$	1.87884e11	0.162819
$157$	−5.95494e11	−0.498229	−0.249115	−	0.968474i	$-0.580140\pi$
$157$	−5.95494e11	−0.498229	−0.249115	+	0.968474i	$0.580140\pi$
$158$	1.34139e12	1.08378
$159$	8.46016e11	0.660228
$160$	1.34225e12	1.01198
$161$	8.46067e10	0.0616400
$162$	−1.34264e11	−0.0945422
$163$	6.18612e11	0.421101	0.210551	−	0.977583i	$-0.432474\pi$
$163$	6.18612e11	0.421101	0.210551	+	0.977583i	$0.432474\pi$
$164$	−5.45567e10	−0.0359093
$165$	−1.76411e12	−1.12296
$166$	2.32110e12	1.42922
$167$	−1.69328e12	−1.00876	−0.504381	−	0.863481i	$-0.668279\pi$
$167$	−1.69328e12	−1.00876	−0.504381	+	0.863481i	$0.668279\pi$
$168$	2.18212e11	0.125799
$169$	7.88694e10	0.0440080
$170$	2.57121e12	1.38889
$171$	−3.05037e11	−0.159542
$172$	3.67722e11	0.186257
$173$	−2.92929e12	−1.43717	−0.718587	−	0.695438i	$-0.755211\pi$
$173$	−2.92929e12	−1.43717	−0.718587	+	0.695438i	$0.755211\pi$
$174$	−1.21110e12	−0.575649
$175$	−1.12619e12	−0.518683
$176$	1.49101e12	0.665519
$177$	1.73727e11	0.0751646
$178$	2.00713e12	0.841910
$179$	1.28881e12	0.524199	0.262099	−	0.965041i	$-0.415585\pi$
$179$	1.28881e12	0.524199	0.262099	+	0.965041i	$0.415585\pi$
$180$	4.41579e11	0.174185
$181$	−1.05813e12	−0.404860	−0.202430	−	0.979297i	$-0.564884\pi$
$181$	−1.05813e12	−0.404860	−0.202430	+	0.979297i	$0.564884\pi$
$182$	4.70036e11	0.174477
$183$	−1.25327e12	−0.451403
$184$	−9.54031e11	−0.333476
$185$	5.26535e11	0.178642
$186$	−8.67405e11	−0.285694
$187$	−2.76962e12	−0.885708
$188$	9.07128e11	0.281709
$189$	1.28049e11	0.0386221
$190$	−2.63163e12	−0.771046
$191$	2.32669e12	0.662301	0.331150	−	0.943578i	$-0.392563\pi$
$191$	2.32669e12	0.662301	0.331150	+	0.943578i	$0.392563\pi$
$192$	−2.30156e12	−0.636599
$193$	−2.14235e12	−0.575872	−0.287936	−	0.957650i	$-0.592969\pi$
$193$	−2.14235e12	−0.575872	−0.287936	+	0.957650i	$0.592969\pi$
$194$	5.13272e12	1.34103
$195$	4.39743e12	1.11688
$196$	1.07268e12	0.264887
$197$	−5.43248e12	−1.30447	−0.652235	−	0.758017i	$-0.726168\pi$
$197$	−5.43248e12	−1.30447	−0.652235	+	0.758017i	$0.726168\pi$
$198$	1.24771e12	0.291376
$199$	4.38801e12	0.996726	0.498363	−	0.866968i	$-0.333935\pi$
$199$	4.38801e12	0.996726	0.498363	+	0.866968i	$0.333935\pi$
$200$	1.26990e13	2.80610
$201$	1.26931e12	0.272891
$202$	6.75897e12	1.41399
$203$	1.15504e12	0.235162
$204$	6.93271e11	0.137384
$205$	−1.27690e12	−0.246326
$206$	−2.91795e12	−0.548035
$207$	−5.59835e11	−0.102382
$208$	−3.71667e12	−0.661920
$209$	2.83470e12	0.491702
$210$	1.10471e12	0.186656
$211$	−2.77223e12	−0.456327	−0.228163	−	0.973623i	$-0.573272\pi$
$211$	−2.77223e12	−0.456327	−0.228163	+	0.973623i	$0.573272\pi$
$212$	1.96796e12	0.315623
$213$	−4.06801e12	−0.635762
$214$	−9.77018e11	−0.148808
$215$	8.60651e12	1.27766
$216$	−1.44389e12	−0.208948
$217$	8.27255e11	0.116711
$218$	5.74650e12	0.790483
$219$	−5.19549e12	−0.696922
$220$	−4.10358e12	−0.536832
$221$	6.90388e12	0.880918
$222$	−3.72405e11	−0.0463526
$223$	1.79436e12	0.217887	0.108944	−	0.994048i	$-0.465253\pi$
$223$	1.79436e12	0.217887	0.108944	+	0.994048i	$0.465253\pi$
$224$	9.05394e11	0.107269
$225$	7.45189e12	0.861514
$226$	1.13708e13	1.28290
$227$	−1.07806e12	−0.118713	−0.0593567	−	0.998237i	$-0.518905\pi$
$227$	−1.07806e12	−0.118713	−0.0593567	+	0.998237i	$0.518905\pi$
$228$	−7.09562e11	−0.0762691
$229$	9.89002e12	1.03777	0.518886	−	0.854843i	$-0.326347\pi$
$229$	9.89002e12	1.03777	0.518886	+	0.854843i	$0.326347\pi$
$230$	−4.82984e12	−0.494800
$231$	−1.18995e12	−0.119032
$232$	−1.30243e13	−1.27224
$233$	−1.08290e13	−1.03307	−0.516534	−	0.856267i	$-0.672778\pi$
$233$	−1.08290e13	−1.03307	−0.516534	+	0.856267i	$0.672778\pi$
$234$	−3.11018e12	−0.289800
$235$	2.12313e13	1.93243
$236$	4.04114e11	0.0359326
$237$	8.46501e12	0.735380
$238$	1.73438e12	0.147221
$239$	1.53403e13	1.27247	0.636233	−	0.771497i	$-0.280492\pi$
$239$	1.53403e13	1.27247	0.636233	+	0.771497i	$0.280492\pi$
$240$	−8.73518e12	−0.708125
$241$	−5.27094e12	−0.417633	−0.208816	−	0.977955i	$-0.566961\pi$
$241$	−5.27094e12	−0.417633	−0.208816	+	0.977955i	$0.566961\pi$
$242$	−6.08561e11	−0.0471324
$243$	−8.47289e11	−0.0641500
$244$	−2.91530e12	−0.215794
$245$	2.51060e13	1.81704
$246$	9.03116e11	0.0639146
$247$	−7.06611e12	−0.489043
$248$	−9.32819e12	−0.631412
$249$	1.46476e13	0.969776
$250$	3.94148e13	2.55264
$251$	−2.06077e13	−1.30564	−0.652820	−	0.757513i	$-0.726414\pi$
$251$	−2.06077e13	−1.30564	−0.652820	+	0.757513i	$0.726414\pi$
$252$	2.97861e11	0.0184634
$253$	5.20253e12	0.315538
$254$	2.95643e12	0.175462
$255$	1.62260e13	0.942410
$256$	−1.33548e13	−0.759131
$257$	−2.21773e13	−1.23389	−0.616946	−	0.787006i	$-0.711630\pi$
$257$	−2.21773e13	−1.23389	−0.616946	+	0.787006i	$0.711630\pi$
$258$	−6.08716e12	−0.331517
$259$	3.55167e11	0.0189358
$260$	1.02291e13	0.533929
$261$	−7.64278e12	−0.390597
$262$	−1.48660e13	−0.743939
$263$	−1.25777e12	−0.0616375	−0.0308188	−	0.999525i	$-0.509811\pi$
$263$	−1.25777e12	−0.0616375	−0.0308188	+	0.999525i	$0.509811\pi$
$264$	1.34180e13	0.643971
$265$	4.60600e13	2.16507
$266$	−1.77513e12	−0.0817300
$267$	1.26663e13	0.571264
$268$	2.95260e12	0.130456
$269$	−9.80514e12	−0.424440	−0.212220	−	0.977222i	$-0.568069\pi$
$269$	−9.80514e12	−0.424440	−0.212220	+	0.977222i	$0.568069\pi$
$270$	−7.30978e12	−0.310030
$271$	−2.77249e13	−1.15223	−0.576114	−	0.817369i	$-0.695432\pi$
$271$	−2.77249e13	−1.15223	−0.576114	+	0.817369i	$0.695432\pi$
$272$	−1.37141e13	−0.558518
$273$	2.96622e12	0.118388
$274$	−3.22500e13	−1.26154
$275$	−6.92501e13	−2.65516
$276$	−1.30226e12	−0.0489438
$277$	−1.02150e13	−0.376358	−0.188179	−	0.982135i	$-0.560259\pi$
$277$	−1.02150e13	−0.376358	−0.188179	+	0.982135i	$0.560259\pi$
$278$	−3.03049e12	−0.109463
$279$	−5.47388e12	−0.193853
$280$	1.18802e13	0.412529
$281$	−2.51699e13	−0.857031	−0.428516	−	0.903534i	$-0.640963\pi$
$281$	−2.51699e13	−0.857031	−0.428516	+	0.903534i	$0.640963\pi$
$282$	−1.50163e13	−0.501411
$283$	4.75093e13	1.55580	0.777900	−	0.628388i	$-0.216285\pi$
$283$	4.75093e13	1.55580	0.777900	+	0.628388i	$0.216285\pi$
$284$	−9.46281e12	−0.303927
$285$	−1.66073e13	−0.523180
$286$	2.89028e13	0.893156
$287$	−8.61313e11	−0.0261102
$288$	−5.99091e12	−0.178170
$289$	−8.79741e12	−0.256695
$290$	−6.59362e13	−1.88771
$291$	3.23907e13	0.909932
$292$	−1.20855e13	−0.333165
$293$	−2.75677e13	−0.745811	−0.372906	−	0.927869i	$-0.621639\pi$
$293$	−2.75677e13	−0.745811	−0.372906	+	0.927869i	$0.621639\pi$
$294$	−1.77568e13	−0.471470
$295$	9.45828e12	0.246485
$296$	−4.00489e12	−0.102444
$297$	7.87382e12	0.197708
$298$	−1.92235e13	−0.473851
$299$	−1.29684e13	−0.313831
$300$	1.73342e13	0.411848
$301$	5.80540e12	0.135431
$302$	−4.90703e13	−1.12404
$303$	4.26534e13	0.959442
$304$	1.40363e13	0.310062
$305$	−6.82325e13	−1.48027
$306$	−1.14762e13	−0.244529
$307$	−2.04562e13	−0.428118	−0.214059	−	0.976821i	$-0.568669\pi$
$307$	−2.04562e13	−0.428118	−0.214059	+	0.976821i	$0.568669\pi$
$308$	−2.76801e12	−0.0569035
$309$	−1.84141e13	−0.371860
$310$	−4.72245e13	−0.936868
$311$	3.95899e13	0.771617	0.385809	−	0.922579i	$-0.373923\pi$
$311$	3.95899e13	0.771617	0.385809	+	0.922579i	$0.373923\pi$
$312$	−3.34473e13	−0.640489
$313$	−7.17027e13	−1.34909	−0.674546	−	0.738233i	$-0.735661\pi$
$313$	−7.17027e13	−1.34909	−0.674546	+	0.738233i	$0.735661\pi$
$314$	2.29303e13	0.423933
$315$	6.97143e12	0.126652
$316$	1.96909e13	0.351550
$317$	5.35317e10	0.000939258 0	0.000469629	−	1.00000i	$-0.499851\pi$
$317$	5.35317e10	0.000939258 0	0.000469629		1.00000i	$0.499851\pi$
$318$	−3.25770e13	−0.561775
$319$	7.10241e13	1.20381
$320$	−1.25305e14	−2.08758
$321$	−6.16560e12	−0.100971
$322$	−3.25790e12	−0.0524482
$323$	−2.60731e13	−0.412647
$324$	−1.97092e12	−0.0306670
$325$	1.72621e14	2.64080
$326$	−2.38205e13	−0.358306
$327$	3.62640e13	0.536369
$328$	9.71223e12	0.141258
$329$	1.43213e13	0.204835
$330$	6.79295e13	0.955502
$331$	−1.17536e14	−1.62599	−0.812996	−	0.582269i	$-0.802165\pi$
$331$	−1.17536e14	−1.62599	−0.812996	+	0.582269i	$0.802165\pi$
$332$	3.40726e13	0.463603
$333$	−2.35011e12	−0.0314517
$334$	6.52022e13	0.858335
$335$	6.91055e13	0.894883
$336$	−5.89219e12	−0.0750604
$337$	1.37448e14	1.72256	0.861279	−	0.508133i	$-0.169664\pi$
$337$	1.37448e14	1.72256	0.861279	+	0.508133i	$0.169664\pi$
$338$	−3.03698e12	−0.0374455
$339$	7.17569e13	0.870493
$340$	3.77441e13	0.450521
$341$	5.08685e13	0.597448
$342$	1.17459e13	0.135751
$343$	3.45805e13	0.393290
$344$	−6.54621e13	−0.732688
$345$	−3.04793e13	−0.335738
$346$	1.12797e14	1.22286
$347$	1.18508e14	1.26455	0.632276	−	0.774744i	$-0.282121\pi$
$347$	1.18508e14	1.26455	0.632276	+	0.774744i	$0.282121\pi$
$348$	−1.77783e13	−0.186725
$349$	5.65533e13	0.584680	0.292340	−	0.956314i	$-0.405566\pi$
$349$	5.65533e13	0.584680	0.292340	+	0.956314i	$0.405566\pi$
$350$	4.33655e13	0.441337
$351$	−1.96272e13	−0.196639
$352$	5.56733e13	0.549114
$353$	−8.08290e13	−0.784886	−0.392443	−	0.919776i	$-0.628370\pi$
$353$	−8.08290e13	−0.784886	−0.392443	+	0.919776i	$0.628370\pi$
$354$	−6.68959e12	−0.0639561
$355$	−2.21477e14	−2.08484
$356$	2.94636e13	0.273094
$357$	1.09450e13	0.0998944
$358$	−4.96273e13	−0.446030
$359$	3.39630e13	0.300598	0.150299	−	0.988641i	$-0.451976\pi$
$359$	3.39630e13	0.300598	0.150299	+	0.988641i	$0.451976\pi$
$360$	−7.86103e13	−0.685197
$361$	−8.98045e13	−0.770919
$362$	4.07446e13	0.344487
$363$	−3.84041e12	−0.0319809
$364$	6.89988e12	0.0565958
$365$	−2.82861e14	−2.28540
$366$	4.82590e13	0.384090
$367$	−7.35188e13	−0.576415	−0.288207	−	0.957568i	$-0.593059\pi$
$367$	−7.35188e13	−0.576415	−0.288207	+	0.957568i	$0.593059\pi$
$368$	2.57609e13	0.198975
$369$	5.69923e12	0.0433682
$370$	−2.02750e13	−0.152003
$371$	3.10691e13	0.229495
$372$	−1.27331e13	−0.0926716
$373$	−1.36850e14	−0.981398	−0.490699	−	0.871329i	$-0.663258\pi$
$373$	−1.36850e14	−0.981398	−0.490699	+	0.871329i	$0.663258\pi$
$374$	1.06648e14	0.753631
$375$	2.48732e14	1.73205
$376$	−1.61488e14	−1.10817
$377$	−1.77043e14	−1.19730
$378$	−4.93071e12	−0.0328628
$379$	−1.56486e14	−1.02792	−0.513960	−	0.857814i	$-0.671822\pi$
$379$	−1.56486e14	−1.02792	−0.513960	+	0.857814i	$0.671822\pi$
$380$	−3.86310e13	−0.250107
$381$	1.86569e13	0.119056
$382$	−8.95926e13	−0.563538
$383$	−2.72767e14	−1.69121	−0.845607	−	0.533806i	$-0.820761\pi$
$383$	−2.72767e14	−1.69121	−0.845607	+	0.533806i	$0.820761\pi$
$384$	3.81337e13	0.233070
$385$	−6.47852e13	−0.390339
$386$	8.24944e13	0.489998
$387$	−3.84138e13	−0.224946
$388$	7.53457e13	0.434995
$389$	−3.21230e14	−1.82849	−0.914247	−	0.405157i	$-0.867217\pi$
$389$	−3.21230e14	−1.82849	−0.914247	+	0.405157i	$0.867217\pi$
$390$	−1.69329e14	−0.950334
$391$	−4.78520e13	−0.264806
$392$	−1.90959e14	−1.04200
$393$	−9.38139e13	−0.504787
$394$	2.09185e14	1.10995
$395$	4.60864e14	2.41151
$396$	1.83157e13	0.0945149
$397$	3.76608e14	1.91664	0.958322	−	0.285690i	$-0.0922227\pi$
$397$	3.76608e14	1.91664	0.958322	+	0.285690i	$0.0922227\pi$
$398$	−1.68967e14	−0.848094
$399$	−1.12022e13	−0.0554565
$400$	−3.42900e14	−1.67432
$401$	−6.97557e13	−0.335958	−0.167979	−	0.985791i	$-0.553724\pi$
$401$	−6.97557e13	−0.335958	−0.167979	+	0.985791i	$0.553724\pi$
$402$	−4.88765e13	−0.232197
$403$	−1.26801e14	−0.594217
$404$	9.92182e13	0.458663
$405$	−4.61293e13	−0.210365
$406$	−4.44764e13	−0.200095
$407$	2.18395e13	0.0969333
$408$	−1.23417e14	−0.540435
$409$	3.30559e14	1.42814	0.714069	−	0.700075i	$-0.246850\pi$
$409$	3.30559e14	1.42814	0.714069	+	0.700075i	$0.246850\pi$
$410$	4.91687e13	0.209594
$411$	−2.03518e14	−0.855999
$412$	−4.28340e13	−0.177768
$413$	6.37995e12	0.0261271
$414$	2.15572e13	0.0871147
$415$	7.97468e14	3.18016
$416$	−1.38778e14	−0.546144
$417$	−1.91243e13	−0.0742742
$418$	−1.09154e14	−0.418379
$419$	−3.91370e14	−1.48051	−0.740254	−	0.672327i	$-0.765295\pi$
$419$	−3.91370e14	−1.48051	−0.740254	+	0.672327i	$0.765295\pi$
$420$	1.62166e13	0.0605464
$421$	2.19574e14	0.809150	0.404575	−	0.914505i	$-0.367419\pi$
$421$	2.19574e14	0.809150	0.404575	+	0.914505i	$0.367419\pi$
$422$	1.06749e14	0.388279
$423$	−9.47625e13	−0.340224
$424$	−3.50338e14	−1.24158
$425$	6.36952e14	2.22827
$426$	1.56645e14	0.540957
$427$	−4.60253e13	−0.156907
$428$	−1.43421e13	−0.0482695
$429$	1.82395e14	0.606036
$430$	−3.31406e14	−1.08714
$431$	1.17139e14	0.379382	0.189691	−	0.981844i	$-0.439251\pi$
$431$	1.17139e14	0.379382	0.189691	+	0.981844i	$0.439251\pi$
$432$	3.89881e13	0.124673
$433$	1.68180e14	0.530995	0.265497	−	0.964112i	$-0.414464\pi$
$433$	1.68180e14	0.530995	0.265497	+	0.964112i	$0.414464\pi$
$434$	−3.18546e13	−0.0993069
$435$	−4.16099e14	−1.28087
$436$	8.43556e13	0.256412
$437$	4.89764e13	0.147007
$438$	2.00060e14	0.592997
$439$	4.29459e14	1.25709	0.628546	−	0.777772i	$-0.283650\pi$
$439$	4.29459e14	1.25709	0.628546	+	0.777772i	$0.283650\pi$
$440$	7.30523e14	2.11176
$441$	−1.12057e14	−0.319908
$442$	−2.65844e14	−0.749556
$443$	−4.46499e14	−1.24337	−0.621684	−	0.783268i	$-0.713551\pi$
$443$	−4.46499e14	−1.24337	−0.621684	+	0.783268i	$0.713551\pi$
$444$	−5.46671e12	−0.0150356
$445$	6.89595e14	1.87333
$446$	−6.90942e13	−0.185396
$447$	−1.21312e14	−0.321524
$448$	−8.45228e13	−0.221281
$449$	−2.27812e14	−0.589145	−0.294573	−	0.955629i	$-0.595177\pi$
$449$	−2.27812e14	−0.589145	−0.294573	+	0.955629i	$0.595177\pi$
$450$	−2.86946e14	−0.733045
$451$	−5.29628e13	−0.133659
$452$	1.66917e14	0.416141
$453$	−3.09665e14	−0.762696
$454$	4.15122e13	0.101011
$455$	1.61491e14	0.388228
$456$	1.26317e14	0.300023
$457$	4.70956e13	0.110520	0.0552600	−	0.998472i	$-0.482401\pi$
$457$	4.70956e13	0.110520	0.0552600	+	0.998472i	$0.482401\pi$
$458$	−3.80830e14	−0.883020
$459$	−7.24222e13	−0.165921
$460$	−7.08996e13	−0.160500
$461$	−7.29447e13	−0.163169	−0.0815847	−	0.996666i	$-0.525998\pi$
$461$	−7.29447e13	−0.163169	−0.0815847	+	0.996666i	$0.525998\pi$
$462$	4.58209e13	0.101282
$463$	−3.70200e14	−0.808613	−0.404306	−	0.914624i	$-0.632487\pi$
$463$	−3.70200e14	−0.808613	−0.404306	+	0.914624i	$0.632487\pi$
$464$	3.51684e14	0.759108
$465$	−2.98017e14	−0.635696
$466$	4.16984e14	0.879017
$467$	−3.41187e14	−0.710803	−0.355402	−	0.934714i	$-0.615656\pi$
$467$	−3.41187e14	−0.710803	−0.355402	+	0.934714i	$0.615656\pi$
$468$	−4.56559e13	−0.0940037
$469$	4.66142e13	0.0948566
$470$	−8.17541e14	−1.64426
$471$	1.44705e14	0.287653
$472$	−7.19408e13	−0.141349
$473$	3.56978e14	0.693275
$474$	−3.25957e14	−0.625720
$475$	−6.51919e14	−1.23703
$476$	2.54598e13	0.0477547
$477$	−2.05582e14	−0.381183
$478$	−5.90701e14	−1.08272
$479$	−3.09598e14	−0.560986	−0.280493	−	0.959856i	$-0.590498\pi$
$479$	−3.09598e14	−0.560986	−0.280493	+	0.959856i	$0.590498\pi$
$480$	−3.26166e14	−0.584268
$481$	−5.44397e13	−0.0964091
$482$	2.02965e14	0.355355
$483$	−2.05594e13	−0.0355878
$484$	−8.93337e12	−0.0152885
$485$	1.76346e15	2.98392
$486$	3.26261e13	0.0545840
$487$	9.11010e14	1.50700	0.753501	−	0.657447i	$-0.228364\pi$
$487$	9.11010e14	1.50700	0.753501	+	0.657447i	$0.228364\pi$
$488$	5.18984e14	0.848878
$489$	−1.50323e14	−0.243123
$490$	−9.66742e14	−1.54608
$491$	−4.54520e14	−0.718795	−0.359398	−	0.933185i	$-0.617018\pi$
$491$	−4.54520e14	−0.718795	−0.359398	+	0.933185i	$0.617018\pi$
$492$	1.32573e13	0.0207322
$493$	−6.53268e14	−1.01026
$494$	2.72091e14	0.416117
$495$	4.28678e14	0.648340
$496$	2.51881e14	0.376744
$497$	−1.49394e14	−0.220990
$498$	−5.64028e14	−0.825163
$499$	4.96092e14	0.717809	0.358904	−	0.933374i	$-0.383150\pi$
$499$	4.96092e14	0.717809	0.358904	+	0.933374i	$0.383150\pi$
$500$	5.78589e14	0.828009
$501$	4.11467e14	0.582409
$502$	7.93528e14	1.11094
$503$	−7.22327e14	−1.00025	−0.500126	−	0.865952i	$-0.666713\pi$
$503$	−7.22327e14	−1.00025	−0.500126	+	0.865952i	$0.666713\pi$
$504$	−5.30255e13	−0.0726301
$505$	2.32220e15	3.14627
$506$	−2.00331e14	−0.268485
$507$	−1.91653e13	−0.0254080
$508$	4.33989e13	0.0569152
$509$	−5.21265e14	−0.676256	−0.338128	−	0.941100i	$-0.609794\pi$
$509$	−5.21265e14	−0.676256	−0.338128	+	0.941100i	$0.609794\pi$
$510$	−6.24805e14	−0.801878
$511$	−1.90800e14	−0.242249
$512$	8.35635e14	1.04962
$513$	7.41240e13	0.0921113
$514$	8.53970e14	1.04989
$515$	−1.00253e15	−1.21943
$516$	−8.93564e13	−0.107536
$517$	8.80625e14	1.04856
$518$	−1.36762e13	−0.0161121
$519$	7.11818e14	0.829752
$520$	−1.82099e15	−2.10034
$521$	9.18931e14	1.04876	0.524379	−	0.851485i	$-0.324297\pi$
$521$	9.18931e14	1.04876	0.524379	+	0.851485i	$0.324297\pi$
$522$	2.94296e14	0.332351
$523$	6.36992e13	0.0711827	0.0355913	−	0.999366i	$-0.488669\pi$
$523$	6.36992e13	0.0711827	0.0355913	+	0.999366i	$0.488669\pi$
$524$	−2.18225e14	−0.241314
$525$	2.73664e14	0.299462
$526$	4.84323e13	0.0524461
$527$	−4.67881e14	−0.501391
$528$	−3.62315e14	−0.384238
$529$	−8.62923e14	−0.905662
$530$	−1.77361e15	−1.84221
$531$	−4.22156e13	−0.0433963
$532$	−2.60580e13	−0.0265111
$533$	1.32021e14	0.132937
$534$	−4.87733e14	−0.486077
$535$	−3.35677e14	−0.331112
$536$	−5.25625e14	−0.513180
$537$	−3.13180e14	−0.302646
$538$	3.77561e14	0.361147
$539$	1.04134e15	0.985948
$540$	−1.07304e14	−0.100566
$541$	−1.62321e15	−1.50588	−0.752939	−	0.658090i	$-0.771365\pi$
$541$	−1.62321e15	−1.50588	−0.752939	+	0.658090i	$0.771365\pi$
$542$	1.06759e15	0.980408
$543$	2.57124e14	0.233746
$544$	−5.12074e14	−0.460828
$545$	1.97434e15	1.75890
$546$	−1.14219e14	−0.100734
$547$	1.15177e15	1.00562	0.502810	−	0.864397i	$-0.332299\pi$
$547$	1.15177e15	1.00562	0.502810	+	0.864397i	$0.332299\pi$
$548$	−4.73414e14	−0.409212
$549$	3.04545e14	0.260618
$550$	2.66658e15	2.25922
$551$	6.68619e14	0.560847
$552$	2.31830e14	0.192532
$553$	3.10870e14	0.255617
$554$	3.93345e14	0.320236
$555$	−1.27948e14	−0.103139
$556$	−4.44861e13	−0.0355069
$557$	−3.76631e14	−0.297654	−0.148827	−	0.988863i	$-0.547550\pi$
$557$	−3.76631e14	−0.297654	−0.148827	+	0.988863i	$0.547550\pi$
$558$	2.10779e14	0.164945
$559$	−8.89847e14	−0.689526
$560$	−3.20791e14	−0.246144
$561$	6.73017e14	0.511364
$562$	9.69203e14	0.729231
$563$	5.16229e14	0.384632	0.192316	−	0.981333i	$-0.438400\pi$
$563$	5.16229e14	0.384632	0.192316	+	0.981333i	$0.438400\pi$
$564$	−2.20432e14	−0.162645
$565$	3.90669e15	2.85458
$566$	−1.82942e15	−1.32380
$567$	−3.11159e13	−0.0222985
$568$	1.68458e15	1.19557
$569$	1.67695e14	0.117870	0.0589349	−	0.998262i	$-0.481230\pi$
$569$	1.67695e14	0.117870	0.0589349	+	0.998262i	$0.481230\pi$
$570$	6.39486e14	0.445163
$571$	2.56075e15	1.76550	0.882752	−	0.469839i	$-0.155688\pi$
$571$	2.56075e15	1.76550	0.882752	+	0.469839i	$0.155688\pi$
$572$	4.24279e14	0.289717
$573$	−5.65386e14	−0.382379
$574$	3.31661e13	0.0222167
$575$	−1.19647e15	−0.793831
$576$	5.59280e14	0.367541
$577$	1.11755e15	0.727442	0.363721	−	0.931508i	$-0.381506\pi$
$577$	1.11755e15	0.727442	0.363721	+	0.931508i	$0.381506\pi$
$578$	3.38757e14	0.218416
$579$	5.20592e14	0.332480
$580$	−9.67910e14	−0.612324
$581$	5.37921e14	0.337093
$582$	−1.24725e15	−0.774243
$583$	1.91046e15	1.17479
$584$	2.15147e15	1.31058
$585$	−1.06857e15	−0.644833
$586$	1.06153e15	0.634596
$587$	−3.26597e15	−1.93420	−0.967102	−	0.254390i	$-0.918125\pi$
$587$	−3.26597e15	−1.93420	−0.967102	+	0.254390i	$0.918125\pi$
$588$	−2.60661e14	−0.152933
$589$	4.78875e14	0.278348
$590$	−3.64204e14	−0.209729
$591$	1.32009e15	0.753136
$592$	1.08141e14	0.0611251
$593$	1.98254e15	1.11025	0.555125	−	0.831767i	$-0.312671\pi$
$593$	1.98254e15	1.11025	0.555125	+	0.831767i	$0.312671\pi$
$594$	−3.03193e14	−0.168226
$595$	5.95884e14	0.327581
$596$	−2.82191e14	−0.153705
$597$	−1.06629e15	−0.575460
$598$	4.99368e14	0.267033
$599$	−3.00851e14	−0.159406	−0.0797028	−	0.996819i	$-0.525397\pi$
$599$	−3.00851e14	−0.159406	−0.0797028	+	0.996819i	$0.525397\pi$
$600$	−3.08585e15	−1.62011
$601$	−4.02711e14	−0.209500	−0.104750	−	0.994499i	$-0.533404\pi$
$601$	−4.02711e14	−0.209500	−0.104750	+	0.994499i	$0.533404\pi$
$602$	−2.23545e14	−0.115235
$603$	−3.08442e14	−0.157554
$604$	−7.20327e14	−0.364608
$605$	−2.09085e14	−0.104874
$606$	−1.64243e15	−0.816370
$607$	1.62300e14	0.0799431	0.0399715	−	0.999201i	$-0.487273\pi$
$607$	1.62300e14	0.0799431	0.0399715	+	0.999201i	$0.487273\pi$
$608$	5.24107e14	0.255829
$609$	−2.80674e14	−0.135771
$610$	2.62739e15	1.25954
$611$	−2.19515e15	−1.04289
$612$	−1.68465e14	−0.0793189
$613$	2.80499e15	1.30888	0.654439	−	0.756114i	$-0.272905\pi$
$613$	2.80499e15	1.30888	0.654439	+	0.756114i	$0.272905\pi$
$614$	7.87695e14	0.364277
$615$	3.10286e14	0.142216
$616$	4.92764e14	0.223844
$617$	2.73536e15	1.23153	0.615766	−	0.787929i	$-0.288847\pi$
$617$	2.73536e15	1.23153	0.615766	+	0.787929i	$0.288847\pi$
$618$	7.09062e14	0.316408
$619$	−3.03415e14	−0.134196	−0.0670979	−	0.997746i	$-0.521374\pi$
$619$	−3.03415e14	−0.134196	−0.0670979	+	0.997746i	$0.521374\pi$
$620$	−6.93232e14	−0.303895
$621$	1.36040e14	0.0591102
$622$	−1.52446e15	−0.656554
$623$	4.65157e14	0.198571
$624$	9.03150e14	0.382160
$625$	7.37982e15	3.09532
$626$	2.76101e15	1.14792
$627$	−6.88831e14	−0.283884
$628$	3.36606e14	0.137513
$629$	−2.00876e14	−0.0813485
$630$	−2.68445e14	−0.107766
$631$	1.28691e15	0.512137	0.256068	−	0.966659i	$-0.417573\pi$
$631$	1.28691e15	0.512137	0.256068	+	0.966659i	$0.417573\pi$
$632$	−3.50539e15	−1.38290
$633$	6.73652e14	0.263460
$634$	−2.06131e12	−0.000799196 0
$635$	1.01575e15	0.390419
$636$	−4.78214e14	−0.182225
$637$	−2.59577e15	−0.980615
$638$	−2.73488e15	−1.02430
$639$	9.88527e14	0.367057
$640$	2.07613e15	0.764301
$641$	2.70651e15	0.987848	0.493924	−	0.869505i	$-0.335562\pi$
$641$	2.70651e15	0.987848	0.493924	+	0.869505i	$0.335562\pi$
$642$	2.37415e14	0.0859145
$643$	−5.18247e15	−1.85942	−0.929708	−	0.368298i	$-0.879941\pi$
$643$	−5.18247e15	−1.85942	−0.929708	+	0.368298i	$0.879941\pi$
$644$	−4.78243e13	−0.0170128
$645$	−2.09138e15	−0.737658
$646$	1.00398e15	0.351113
$647$	3.11247e15	1.07927	0.539637	−	0.841898i	$-0.318561\pi$
$647$	3.11247e15	1.07927	0.539637	+	0.841898i	$0.318561\pi$
$648$	3.50865e14	0.120636
$649$	3.92308e14	0.133746
$650$	−6.64703e15	−2.24700
$651$	−2.01023e14	−0.0673830
$652$	−3.49673e14	−0.116225
$653$	−1.22125e15	−0.402516	−0.201258	−	0.979538i	$-0.564503\pi$
$653$	−1.22125e15	−0.402516	−0.201258	+	0.979538i	$0.564503\pi$
$654$	−1.39640e15	−0.456385
$655$	−5.10755e15	−1.65533
$656$	−2.62251e14	−0.0842842
$657$	1.26251e15	0.402368
$658$	−5.51461e14	−0.174290
$659$	4.37350e14	0.137075	0.0685377	−	0.997649i	$-0.478167\pi$
$659$	4.37350e14	0.137075	0.0685377	+	0.997649i	$0.478167\pi$
$660$	9.97170e14	0.309940
$661$	−1.38090e15	−0.425650	−0.212825	−	0.977090i	$-0.568266\pi$
$661$	−1.38090e15	−0.425650	−0.212825	+	0.977090i	$0.568266\pi$
$662$	4.52591e15	1.38352
$663$	−1.67764e15	−0.508598
$664$	−6.06564e15	−1.82369
$665$	−6.09886e14	−0.181857
$666$	9.04943e13	0.0267617
$667$	1.22712e15	0.359910
$668$	9.57135e14	0.278422
$669$	−4.36028e14	−0.125797
$670$	−2.66101e15	−0.761438
$671$	−2.83013e15	−0.803216
$672$	−2.20011e14	−0.0619317
$673$	−4.15651e15	−1.16050	−0.580252	−	0.814437i	$-0.697046\pi$
$673$	−4.15651e15	−1.16050	−0.580252	+	0.814437i	$0.697046\pi$
$674$	−5.29263e15	−1.46569
$675$	−1.81081e15	−0.497396
$676$	−4.45813e13	−0.0121464
$677$	1.94680e15	0.526119	0.263060	−	0.964780i	$-0.415268\pi$
$677$	1.94680e15	0.526119	0.263060	+	0.964780i	$0.415268\pi$
$678$	−2.76310e15	−0.740685
$679$	1.18952e15	0.316292
$680$	−6.71923e15	−1.77223
$681$	2.61968e14	0.0685393
$682$	−1.95877e15	−0.508356
$683$	−3.57495e15	−0.920358	−0.460179	−	0.887826i	$-0.652215\pi$
$683$	−3.57495e15	−0.920358	−0.460179	+	0.887826i	$0.652215\pi$
$684$	1.72424e14	0.0440340
$685$	−1.10802e16	−2.80705
$686$	−1.33157e15	−0.334643
$687$	−2.40328e15	−0.599158
$688$	1.76762e15	0.437172
$689$	−4.76225e15	−1.16844
$690$	1.17365e15	0.285673
$691$	−2.73596e15	−0.660663	−0.330331	−	0.943865i	$-0.607160\pi$
$691$	−2.73596e15	−0.660663	−0.330331	+	0.943865i	$0.607160\pi$
$692$	1.65580e15	0.396665
$693$	2.89159e14	0.0687233
$694$	−4.56333e15	−1.07598
$695$	−1.04119e15	−0.243565
$696$	3.16490e15	0.734529
$697$	4.87143e14	0.112170
$698$	−2.17767e15	−0.497492
$699$	2.63144e15	0.596442
$700$	6.36583e14	0.143158
$701$	3.17495e15	0.708415	0.354208	−	0.935167i	$-0.384751\pi$
$701$	3.17495e15	0.708415	0.354208	+	0.935167i	$0.384751\pi$
$702$	7.55775e14	0.167316
$703$	2.05596e14	0.0451607
$704$	−5.19737e15	−1.13275
$705$	−5.15920e15	−1.11569
$706$	3.11244e15	0.667844
$707$	1.56641e15	0.333501
$708$	−9.81998e13	−0.0207457
$709$	4.33573e15	0.908883	0.454441	−	0.890777i	$-0.349839\pi$
$709$	4.33573e15	0.908883	0.454441	+	0.890777i	$0.349839\pi$
$710$	8.52827e15	1.77395
$711$	−2.05700e15	−0.424572
$712$	−5.24514e15	−1.07428
$713$	8.78880e14	0.178623
$714$	−4.21453e14	−0.0849981
$715$	9.93022e15	1.98736
$716$	−7.28504e14	−0.144681
$717$	−3.72770e15	−0.734659
$718$	−1.30779e15	−0.255773
$719$	5.63989e15	1.09462	0.547308	−	0.836931i	$-0.315653\pi$
$719$	5.63989e15	1.09462	0.547308	+	0.836931i	$0.315653\pi$
$720$	2.12265e15	0.408836
$721$	−6.76242e14	−0.129258
$722$	3.45805e15	0.655959
$723$	1.28084e15	0.241120
$724$	5.98110e14	0.111743
$725$	−1.63340e16	−3.02854
$726$	1.47880e14	0.0272119
$727$	−5.36267e15	−0.979358	−0.489679	−	0.871903i	$-0.662886\pi$
$727$	−5.36267e15	−0.979358	−0.489679	+	0.871903i	$0.662886\pi$
$728$	−1.22832e15	−0.222633
$729$	2.05891e14	0.0370370
$730$	1.08920e16	1.94460
$731$	−3.28343e15	−0.581812
$732$	7.08418e14	0.124589
$733$	4.25039e15	0.741920	0.370960	−	0.928649i	$-0.379029\pi$
$733$	4.25039e15	0.741920	0.370960	+	0.928649i	$0.379029\pi$
$734$	2.83095e15	0.490460
$735$	−6.10075e15	−1.04907
$736$	9.61895e14	0.164172
$737$	2.86634e15	0.485575
$738$	−2.19457e14	−0.0369011
$739$	−1.19448e16	−1.99358	−0.996790	−	0.0800612i	$-0.974488\pi$
$739$	−1.19448e16	−1.99358	−0.996790	+	0.0800612i	$0.974488\pi$
$740$	−2.97627e14	−0.0493057
$741$	1.71706e15	0.282349
$742$	−1.19636e15	−0.195273
$743$	6.10708e15	0.989453	0.494727	−	0.869049i	$-0.335268\pi$
$743$	6.10708e15	0.989453	0.494727	+	0.869049i	$0.335268\pi$
$744$	2.26675e15	0.364546
$745$	−6.60466e15	−1.05436
$746$	5.26959e15	0.835052
$747$	−3.55938e15	−0.559900
$748$	1.56554e15	0.244458
$749$	−2.26426e14	−0.0350975
$750$	−9.57780e15	−1.47377
$751$	1.08674e15	0.165999	0.0829996	−	0.996550i	$-0.473550\pi$
$751$	1.08674e15	0.165999	0.0829996	+	0.996550i	$0.473550\pi$
$752$	4.36051e15	0.661210
$753$	5.00766e15	0.753811
$754$	6.81730e15	1.01876
$755$	−1.68592e16	−2.50109
$756$	−7.23803e13	−0.0106598
$757$	8.46368e15	1.23746	0.618731	−	0.785603i	$-0.287647\pi$
$757$	8.46368e15	1.23746	0.618731	+	0.785603i	$0.287647\pi$
$758$	6.02570e15	0.874636
$759$	−1.26421e15	−0.182176
$760$	6.87712e15	0.983857
$761$	−2.19644e15	−0.311963	−0.155982	−	0.987760i	$-0.549854\pi$
$761$	−2.19644e15	−0.311963	−0.155982	+	0.987760i	$0.549854\pi$
$762$	−7.18412e14	−0.101303
$763$	1.33176e15	0.186441
$764$	−1.31517e15	−0.182797
$765$	−3.94291e15	−0.544101
$766$	1.05033e16	1.43902
$767$	−9.77913e14	−0.133023
$768$	3.24521e15	0.438284
$769$	5.08350e15	0.681661	0.340830	−	0.940125i	$-0.389292\pi$
$769$	5.08350e15	0.681661	0.340830	+	0.940125i	$0.389292\pi$
$770$	2.49465e15	0.332132
$771$	5.38909e15	0.712388
$772$	1.21098e15	0.158943
$773$	1.19595e16	1.55856	0.779282	−	0.626674i	$-0.215584\pi$
$773$	1.19595e16	1.55856	0.779282	+	0.626674i	$0.215584\pi$
$774$	1.47918e15	0.191402
$775$	−1.16987e16	−1.50306
$776$	−1.34131e16	−1.71116
$777$	−8.63056e13	−0.0109326
$778$	1.23694e16	1.55583
$779$	−4.98590e14	−0.0622713
$780$	−2.48567e15	−0.308264
$781$	−9.18634e15	−1.13126
$782$	1.84261e15	0.225318
$783$	1.85720e15	0.225511
$784$	5.15631e15	0.621728
$785$	7.87824e15	0.943292
$786$	3.61244e15	0.429513
$787$	1.14735e16	1.35467	0.677335	−	0.735675i	$-0.263135\pi$
$787$	1.14735e16	1.35467	0.677335	+	0.735675i	$0.263135\pi$
$788$	3.07074e15	0.360038
$789$	3.05639e14	0.0355864
$790$	−1.77462e16	−2.05191
$791$	2.63520e15	0.302582
$792$	−3.26058e15	−0.371797
$793$	7.05472e15	0.798872
$794$	−1.45018e16	−1.63083
$795$	−1.11926e16	−1.25000
$796$	−2.48034e15	−0.275100
$797$	−1.37704e16	−1.51679	−0.758393	−	0.651798i	$-0.774015\pi$
$797$	−1.37704e16	−1.51679	−0.758393	+	0.651798i	$0.774015\pi$
$798$	4.31357e14	0.0471868
$799$	−8.09985e15	−0.879973
$800$	−1.28037e16	−1.38146
$801$	−3.07790e15	−0.329819
$802$	2.68604e15	0.285860
$803$	−1.17324e16	−1.24009
$804$	−7.17483e14	−0.0753188
$805$	−1.11933e15	−0.116702
$806$	4.88265e15	0.505607
$807$	2.38265e15	0.245050
$808$	−1.76629e16	−1.80426
$809$	4.97789e15	0.505043	0.252521	−	0.967591i	$-0.418740\pi$
$809$	4.97789e15	0.505043	0.252521	+	0.967591i	$0.418740\pi$
$810$	1.77628e15	0.178996
$811$	9.30004e15	0.930830	0.465415	−	0.885093i	$-0.345905\pi$
$811$	9.30004e15	0.930830	0.465415	+	0.885093i	$0.345905\pi$
$812$	−6.52890e14	−0.0649056
$813$	6.73715e15	0.665240
$814$	−8.40960e14	−0.0824786
$815$	−8.18408e15	−0.797266
$816$	3.33252e15	0.322461
$817$	3.36059e15	0.322993
$818$	−1.27286e16	−1.21517
$819$	−7.20792e14	−0.0683516
$820$	7.21772e14	0.0679867
$821$	1.83634e16	1.71817	0.859085	−	0.511834i	$-0.171034\pi$
$821$	1.83634e16	1.71817	0.859085	+	0.511834i	$0.171034\pi$
$822$	7.83676e15	0.728352
$823$	1.65501e16	1.52793	0.763964	−	0.645259i	$-0.223251\pi$
$823$	1.65501e16	1.52793	0.763964	+	0.645259i	$0.223251\pi$
$824$	7.62535e15	0.699294
$825$	1.68278e16	1.53296
$826$	−2.45669e14	−0.0222311
$827$	1.94784e16	1.75094	0.875471	−	0.483270i	$-0.160551\pi$
$827$	1.94784e16	1.75094	0.875471	+	0.483270i	$0.160551\pi$
$828$	3.16449e14	0.0282577
$829$	−9.00331e15	−0.798643	−0.399321	−	0.916811i	$-0.630754\pi$
$829$	−9.00331e15	−0.798643	−0.399321	+	0.916811i	$0.630754\pi$
$830$	−3.07077e16	−2.70593
$831$	2.48226e15	0.217291
$832$	1.29556e16	1.12662
$833$	−9.57807e15	−0.827428
$834$	7.36409e14	0.0631984
$835$	2.24017e16	1.90988
$836$	−1.60233e15	−0.135711
$837$	1.33015e15	0.111921
$838$	1.50703e16	1.25973
$839$	8.51024e15	0.706726	0.353363	−	0.935486i	$-0.385038\pi$
$839$	8.51024e15	0.706726	0.353363	+	0.935486i	$0.385038\pi$
$840$	−2.88689e15	−0.238174
$841$	4.55191e15	0.373092
$842$	−8.45500e15	−0.688489
$843$	6.11628e15	0.494807
$844$	1.56702e15	0.125948
$845$	−1.04342e15	−0.0833199
$846$	3.64897e15	0.289490
$847$	−1.41035e14	−0.0111165
$848$	9.45988e15	0.740813
$849$	−1.15448e16	−0.898241
$850$	−2.45267e16	−1.89599
$851$	3.77331e14	0.0289808
$852$	2.29946e15	0.175472
$853$	−1.47084e16	−1.11519	−0.557593	−	0.830115i	$-0.688275\pi$
$853$	−1.47084e16	−1.11519	−0.557593	+	0.830115i	$0.688275\pi$
$854$	1.77227e15	0.133509
$855$	4.03556e15	0.302058
$856$	2.55320e15	0.189880
$857$	−5.31834e15	−0.392990	−0.196495	−	0.980505i	$-0.562956\pi$
$857$	−5.31834e15	−0.392990	−0.196495	+	0.980505i	$0.562956\pi$
$858$	−7.02339e15	−0.515664
$859$	1.44436e16	1.05369	0.526845	−	0.849962i	$-0.323375\pi$
$859$	1.44436e16	1.05369	0.526845	+	0.849962i	$0.323375\pi$
$860$	−4.86487e15	−0.352639
$861$	2.09299e14	0.0150747
$862$	−4.51061e15	−0.322809
$863$	−1.88206e16	−1.33836	−0.669180	−	0.743100i	$-0.733355\pi$
$863$	−1.88206e16	−1.33836	−0.669180	+	0.743100i	$0.733355\pi$
$864$	1.45579e15	0.102866
$865$	3.87538e16	2.72098
$866$	−6.47600e15	−0.451813
$867$	2.13777e15	0.148203
$868$	−4.67610e14	−0.0322126
$869$	1.91156e16	1.30852
$870$	1.60225e16	1.08987
$871$	−7.14498e15	−0.482949
$872$	−1.50171e16	−1.00866
$873$	−7.87094e15	−0.525350
$874$	−1.88591e15	−0.125086
$875$	9.13447e15	0.602059
$876$	2.93678e15	0.192353
$877$	−1.11677e16	−0.726885	−0.363443	−	0.931617i	$-0.618399\pi$
$877$	−1.11677e16	−0.726885	−0.363443	+	0.931617i	$0.618399\pi$
$878$	−1.65370e16	−1.06964
$879$	6.69896e15	0.430594
$880$	−1.97257e16	−1.26002
$881$	−2.25647e16	−1.43239	−0.716195	−	0.697900i	$-0.754118\pi$
$881$	−2.25647e16	−1.43239	−0.716195	+	0.697900i	$0.754118\pi$
$882$	4.31490e15	0.272204
$883$	1.02568e16	0.643026	0.321513	−	0.946905i	$-0.395809\pi$
$883$	1.02568e16	0.643026	0.321513	+	0.946905i	$0.395809\pi$
$884$	−3.90245e15	−0.243136
$885$	−2.29836e15	−0.142308
$886$	1.71931e16	1.05796
$887$	−4.84262e15	−0.296143	−0.148071	−	0.988977i	$-0.547307\pi$
$887$	−4.84262e15	−0.296143	−0.148071	+	0.988977i	$0.547307\pi$
$888$	9.73188e14	0.0591460
$889$	6.85159e14	0.0413839
$890$	−2.65538e16	−1.59398
$891$	−1.91334e15	−0.114147
$892$	−1.01427e15	−0.0601376
$893$	8.29018e15	0.488518
$894$	4.67130e15	0.273578
$895$	−1.70506e16	−0.992460
$896$	1.40042e15	0.0810150
$897$	3.15133e15	0.181191
$898$	8.77224e15	0.501292
$899$	1.19983e16	0.681464
$900$	−4.21222e15	−0.237781
$901$	−1.75721e16	−0.985913
$902$	2.03941e15	0.113728
$903$	−1.41071e15	−0.0781909
$904$	−2.97148e16	−1.63699
$905$	1.39987e16	0.766517
$906$	1.19241e16	0.648963
$907$	2.75849e16	1.49222	0.746108	−	0.665825i	$-0.231920\pi$
$907$	2.75849e16	1.49222	0.746108	+	0.665825i	$0.231920\pi$
$908$	6.09378e14	0.0327653
$909$	−1.03648e16	−0.553934
$910$	−6.21846e15	−0.330335
$911$	3.00066e16	1.58440	0.792202	−	0.610259i	$-0.208934\pi$
$911$	3.00066e16	1.58440	0.792202	+	0.610259i	$0.208934\pi$
$912$	−3.41083e15	−0.179014
$913$	3.30772e16	1.72560
$914$	−1.81348e15	−0.0940392
$915$	1.65805e16	0.854636
$916$	−5.59038e15	−0.286429
$917$	−3.44523e15	−0.175464
$918$	2.78872e15	0.141179
$919$	−1.72784e16	−0.869495	−0.434748	−	0.900552i	$-0.643162\pi$
$919$	−1.72784e16	−0.869495	−0.434748	+	0.900552i	$0.643162\pi$
$920$	1.26216e16	0.631366
$921$	4.97086e15	0.247174
$922$	2.80884e15	0.138838
$923$	2.28990e16	1.12514
$924$	6.72627e14	0.0328533
$925$	−5.02261e15	−0.243865
$926$	1.42551e16	0.688032
$927$	4.47463e15	0.214693
$928$	1.31316e16	0.626333
$929$	−2.08626e16	−0.989194	−0.494597	−	0.869122i	$-0.664684\pi$
$929$	−2.08626e16	−0.989194	−0.494597	+	0.869122i	$0.664684\pi$
$930$	1.14756e16	0.540901
$931$	9.80314e15	0.459348
$932$	6.12112e15	0.285130
$933$	−9.62034e15	−0.445493
$934$	1.31379e16	0.604808
$935$	3.66413e16	1.67690
$936$	8.12770e15	0.369786
$937$	−1.02457e16	−0.463418	−0.231709	−	0.972785i	$-0.574432\pi$
$937$	−1.02457e16	−0.463418	−0.231709	+	0.972785i	$0.574432\pi$
$938$	−1.79495e15	−0.0807116
$939$	1.74238e16	0.778899
$940$	−1.20011e16	−0.533356
$941$	2.75473e16	1.21713	0.608565	−	0.793504i	$-0.291746\pi$
$941$	2.75473e16	1.21713	0.608565	+	0.793504i	$0.291746\pi$
$942$	−5.57207e15	−0.244758
$943$	−9.15064e14	−0.0399611
$944$	1.94256e15	0.0843388
$945$	−1.69406e15	−0.0731228
$946$	−1.37460e16	−0.589894
$947$	4.25827e16	1.81681	0.908403	−	0.418095i	$-0.137302\pi$
$947$	4.25827e16	1.81681	0.908403	+	0.418095i	$0.137302\pi$
$948$	−4.78489e15	−0.202967
$949$	2.92456e16	1.23338
$950$	2.51031e16	1.05256
$951$	−1.30082e13	−0.000542281 0
$952$	−4.53237e15	−0.187855
$953$	2.07111e16	0.853476	0.426738	−	0.904375i	$-0.359663\pi$
$953$	2.07111e16	0.853476	0.426738	+	0.904375i	$0.359663\pi$
$954$	7.91622e15	0.324341
$955$	−3.07816e16	−1.25393
$956$	−8.67120e15	−0.351205
$957$	−1.72588e16	−0.695018
$958$	1.19215e16	0.477332
$959$	−7.47402e15	−0.297544
$960$	3.04491e16	1.20527
$961$	−1.68151e16	−0.661790
$962$	2.09628e15	0.0820326
$963$	1.49824e15	0.0582958
$964$	2.97942e15	0.115268
$965$	2.83428e16	1.09029
$966$	7.91670e14	0.0302810
$967$	−5.37393e14	−0.0204384	−0.0102192	−	0.999948i	$-0.503253\pi$
$967$	−5.37393e14	−0.0204384	−0.0102192	+	0.999948i	$0.503253\pi$
$968$	1.59033e15	0.0601411
$969$	6.33576e15	0.238242
$970$	−6.79046e16	−2.53895
$971$	1.89251e16	0.703612	0.351806	−	0.936073i	$-0.385568\pi$
$971$	1.89251e16	0.703612	0.351806	+	0.936073i	$0.385568\pi$
$972$	4.78934e14	0.0177056
$973$	−7.02323e14	−0.0258176
$974$	−3.50797e16	−1.28228
$975$	−4.19470e16	−1.52467
$976$	−1.40137e16	−0.506499
$977$	−5.54836e15	−0.199409	−0.0997044	−	0.995017i	$-0.531790\pi$
$977$	−5.54836e15	−0.199409	−0.0997044	+	0.995017i	$0.531790\pi$
$978$	5.78839e15	0.206868
$979$	2.86028e16	1.01649
$980$	−1.41913e16	−0.501508
$981$	−8.81216e15	−0.309673
$982$	1.75020e16	0.611608
$983$	4.72330e16	1.64135	0.820675	−	0.571396i	$-0.193598\pi$
$983$	4.72330e16	1.64135	0.820675	+	0.571396i	$0.193598\pi$
$984$	−2.36007e15	−0.0815553
$985$	7.18704e16	2.46974
$986$	2.51550e16	0.859610
$987$	−3.48007e15	−0.118261
$988$	3.99415e15	0.134977
$989$	6.16769e15	0.207273
$990$	−1.65069e16	−0.551659
$991$	−6.68696e15	−0.222241	−0.111120	−	0.993807i	$-0.535444\pi$
$991$	−6.68696e15	−0.222241	−0.111120	+	0.993807i	$0.535444\pi$
$992$	9.40508e15	0.310848
$993$	2.85614e16	0.938767
$994$	5.75263e15	0.188036
$995$	−5.80523e16	−1.88709
$996$	−8.27965e15	−0.267661
$997$	8.23312e15	0.264692	0.132346	−	0.991204i	$-0.457749\pi$
$997$	8.23312e15	0.264692	0.132346	+	0.991204i	$0.457749\pi$
$998$	−1.91027e16	−0.610769
$999$	5.71077e14	0.0181587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.10	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +509431. q^{10} -548740. q^{11} +137357. q^{12} +1.36786e6 q^{13} +343630. q^{14} +3.21483e6 q^{15} -2.71715e6 q^{16} +5.04723e6 q^{17} -2.27377e6 q^{18} -5.16583e6 q^{19} +7.47818e6 q^{20} +2.16852e6 q^{21} +2.11300e7 q^{22} -9.48085e6 q^{23} -2.44524e7 q^{24} +1.26198e8 q^{25} -5.26712e7 q^{26} -1.43489e7 q^{27} +5.04431e6 q^{28} -1.29431e8 q^{29} -1.23792e8 q^{30} -9.27006e7 q^{31} -1.01457e8 q^{32} +1.33344e8 q^{33} -1.94351e8 q^{34} +1.18062e8 q^{35} -3.33777e7 q^{36} -3.97993e7 q^{37} +1.98918e8 q^{38} -3.32389e8 q^{39} -1.33127e9 q^{40} +9.65170e7 q^{41} -8.35020e7 q^{42} -6.50542e8 q^{43} +3.10178e8 q^{44} -7.81204e8 q^{45} +3.65074e8 q^{46} -1.60481e9 q^{47} +6.60267e8 q^{48} -1.89769e9 q^{49} -4.85945e9 q^{50} -1.22648e9 q^{51} -7.73187e8 q^{52} -3.48155e9 q^{53} +5.52525e8 q^{54} +7.25970e9 q^{55} -8.97992e8 q^{56} +1.25530e9 q^{57} +4.98393e9 q^{58} -7.14924e8 q^{59} -1.81720e9 q^{60} +5.15750e9 q^{61} +3.56957e9 q^{62} -5.26950e8 q^{63} +9.47145e9 q^{64} -1.80964e10 q^{65} -5.13460e9 q^{66} -5.22349e9 q^{67} -2.85297e9 q^{68} +2.30385e9 q^{69} -4.54614e9 q^{70} +1.67408e10 q^{71} +5.94193e9 q^{72} +2.13806e10 q^{73} +1.53253e9 q^{74} -3.06662e10 q^{75} +2.92001e9 q^{76} +4.89693e9 q^{77} +1.27991e10 q^{78} -3.48354e10 q^{79} +3.59472e10 q^{80} +3.48678e9 q^{81} -3.71653e9 q^{82} -6.02784e10 q^{83} -1.22577e9 q^{84} -6.67736e10 q^{85} +2.50500e10 q^{86} +3.14518e10 q^{87} -5.52181e10 q^{88} -5.21245e10 q^{89} +3.00814e10 q^{90} -1.22067e10 q^{91} +5.35910e9 q^{92} +2.25262e10 q^{93} +6.17956e10 q^{94} +6.83426e10 q^{95} +2.46540e10 q^{96} -1.33295e11 q^{97} +7.30733e10 q^{98} -3.24026e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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