LMFDB - Embedded newform 177.12.a.c.1.2

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			1.2
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)

$f(q)$	$=$	$q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +1.00465e6 q^{10} +614467. q^{11} -1.13182e6 q^{12} +1.74232e6 q^{13} +5.37472e6 q^{14} +2.98124e6 q^{15} +7.96101e6 q^{16} -1.11473e6 q^{17} -4.83543e6 q^{18} +1.46733e7 q^{19} -5.71431e7 q^{20} +1.59492e7 q^{21} -5.03177e7 q^{22} +5.31182e7 q^{23} +5.19304e7 q^{24} +1.01688e8 q^{25} -1.42676e8 q^{26} -1.43489e7 q^{27} -3.05708e8 q^{28} -1.59287e8 q^{29} -2.44129e8 q^{30} +4.50702e7 q^{31} -2.14246e8 q^{32} -1.49315e8 q^{33} +9.12837e7 q^{34} +8.05238e8 q^{35} +2.75033e8 q^{36} +7.33231e8 q^{37} -1.20157e9 q^{38} -4.23385e8 q^{39} +2.62184e9 q^{40} -3.90985e7 q^{41} -1.30606e9 q^{42} +9.67989e8 q^{43} +2.86201e9 q^{44} -7.24442e8 q^{45} -4.34976e9 q^{46} +1.84099e9 q^{47} -1.93453e9 q^{48} +2.33058e9 q^{49} -8.32704e9 q^{50} +2.70880e8 q^{51} +8.11525e9 q^{52} +3.64445e9 q^{53} +1.17501e9 q^{54} -7.53858e9 q^{55} +1.40265e10 q^{56} -3.56561e9 q^{57} +1.30438e10 q^{58} -7.14924e8 q^{59} +1.38858e10 q^{60} +1.84441e9 q^{61} -3.69073e9 q^{62} -3.87566e9 q^{63} +1.24009e9 q^{64} -2.13757e10 q^{65} +1.22272e10 q^{66} -1.36376e10 q^{67} -5.19211e9 q^{68} -1.29077e10 q^{69} -6.59397e10 q^{70} -2.07952e10 q^{71} -1.26191e10 q^{72} +1.69766e10 q^{73} -6.00431e10 q^{74} -2.47101e10 q^{75} +6.83441e10 q^{76} -4.03303e10 q^{77} +3.46703e10 q^{78} +3.36122e10 q^{79} -9.76695e10 q^{80} +3.48678e9 q^{81} +3.20171e9 q^{82} +2.76507e10 q^{83} +7.42870e10 q^{84} +1.36761e10 q^{85} -7.92671e10 q^{86} +3.87067e10 q^{87} -1.31315e11 q^{88} -1.44161e10 q^{89} +5.93234e10 q^{90} -1.14357e11 q^{91} +2.47409e11 q^{92} -1.09521e10 q^{93} -1.50755e11 q^{94} -1.80019e11 q^{95} +5.20617e10 q^{96} +1.18137e11 q^{97} -1.90848e11 q^{98} +3.62837e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−81.8884	−1.80950	−0.904748	−	0.425947i	$-0.859941\pi$
$2$	−81.8884	−1.80950	−0.904748	+	0.425947i	$0.859941\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	4657.72	2.27428
$5$	−12268.5	−1.75572	−0.877861	−	0.478915i	$-0.841030\pi$
$5$	−12268.5	−1.75572	−0.877861	+	0.478915i	$0.841030\pi$
$6$	19898.9	1.04471
$7$	−65634.7	−1.47603	−0.738013	−	0.674786i	$-0.764236\pi$
$7$	−65634.7	−1.47603	−0.738013	+	0.674786i	$0.764236\pi$
$8$	−213706.	−2.30580
$9$	59049.0	0.333333
$10$	1.00465e6	3.17697
$11$	614467.	1.15037	0.575187	−	0.818022i	$-0.304929\pi$
$11$	614467.	1.15037	0.575187	+	0.818022i	$0.304929\pi$
$12$	−1.13182e6	−1.31305
$13$	1.74232e6	1.30149	0.650744	−	0.759297i	$-0.274457\pi$
$13$	1.74232e6	1.30149	0.650744	+	0.759297i	$0.274457\pi$
$14$	5.37472e6	2.67086
$15$	2.98124e6	1.01367
$16$	7.96101e6	1.89805
$17$	−1.11473e6	−0.190415	−0.0952076	−	0.995457i	$-0.530351\pi$
$17$	−1.11473e6	−0.190415	−0.0952076	+	0.995457i	$0.530351\pi$
$18$	−4.83543e6	−0.603165
$19$	1.46733e7	1.35951	0.679756	−	0.733438i	$-0.262086\pi$
$19$	1.46733e7	1.35951	0.679756	+	0.733438i	$0.262086\pi$
$20$	−5.71431e7	−3.99300
$21$	1.59492e7	0.852184
$22$	−5.03177e7	−2.08160
$23$	5.31182e7	1.72084	0.860419	−	0.509587i	$-0.170202\pi$
$23$	5.31182e7	1.72084	0.860419	+	0.509587i	$0.170202\pi$
$24$	5.19304e7	1.33125
$25$	1.01688e8	2.08256
$26$	−1.42676e8	−2.35504
$27$	−1.43489e7	−0.192450
$28$	−3.05708e8	−3.35689
$29$	−1.59287e8	−1.44209	−0.721043	−	0.692891i	$-0.756337\pi$
$29$	−1.59287e8	−1.44209	−0.721043	+	0.692891i	$0.756337\pi$
$30$	−2.44129e8	−1.83423
$31$	4.50702e7	0.282749	0.141374	−	0.989956i	$-0.454848\pi$
$31$	4.50702e7	0.282749	0.141374	+	0.989956i	$0.454848\pi$
$32$	−2.14246e8	−1.12872
$33$	−1.49315e8	−0.664168
$34$	9.12837e7	0.344556
$35$	8.05238e8	2.59149
$36$	2.75033e8	0.758092
$37$	7.33231e8	1.73833	0.869163	−	0.494526i	$-0.164658\pi$
$37$	7.33231e8	1.73833	0.869163	+	0.494526i	$0.164658\pi$
$38$	−1.20157e9	−2.46003
$39$	−4.23385e8	−0.751415
$40$	2.62184e9	4.04834
$41$	−3.90985e7	−0.0527046	−0.0263523	−	0.999653i	$-0.508389\pi$
$41$	−3.90985e7	−0.0527046	−0.0263523	+	0.999653i	$0.508389\pi$
$42$	−1.30606e9	−1.54202
$43$	9.67989e8	1.00414	0.502070	−	0.864827i	$-0.332572\pi$
$43$	9.67989e8	1.00414	0.502070	+	0.864827i	$0.332572\pi$
$44$	2.86201e9	2.61627
$45$	−7.24442e8	−0.585241
$46$	−4.34976e9	−3.11385
$47$	1.84099e9	1.17088	0.585440	−	0.810716i	$-0.300922\pi$
$47$	1.84099e9	1.17088	0.585440	+	0.810716i	$0.300922\pi$
$48$	−1.93453e9	−1.09584
$49$	2.33058e9	1.17865
$50$	−8.32704e9	−3.76839
$51$	2.70880e8	0.109936
$52$	8.11525e9	2.95994
$53$	3.64445e9	1.19706	0.598528	−	0.801102i	$-0.295752\pi$
$53$	3.64445e9	1.19706	0.598528	+	0.801102i	$0.295752\pi$
$54$	1.17501e9	0.348238
$55$	−7.53858e9	−2.01974
$56$	1.40265e10	3.40342
$57$	−3.56561e9	−0.784915
$58$	1.30438e10	2.60945
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.38858e10	2.30536
$61$	1.84441e9	0.279604	0.139802	−	0.990179i	$-0.455353\pi$
$61$	1.84441e9	0.279604	0.139802	+	0.990179i	$0.455353\pi$
$62$	−3.69073e9	−0.511633
$63$	−3.87566e9	−0.492009
$64$	1.24009e9	0.144366
$65$	−2.13757e10	−2.28505
$66$	1.22272e10	1.20181
$67$	−1.36376e10	−1.23403	−0.617017	−	0.786950i	$-0.711659\pi$
$67$	−1.36376e10	−1.23403	−0.617017	+	0.786950i	$0.711659\pi$
$68$	−5.19211e9	−0.433057
$69$	−1.29077e10	−0.993526
$70$	−6.59397e10	−4.68930
$71$	−2.07952e10	−1.36786	−0.683930	−	0.729548i	$-0.739731\pi$
$71$	−2.07952e10	−1.36786	−0.683930	+	0.729548i	$0.739731\pi$
$72$	−1.26191e10	−0.768599
$73$	1.69766e10	0.958465	0.479232	−	0.877688i	$-0.340915\pi$
$73$	1.69766e10	0.958465	0.479232	+	0.877688i	$0.340915\pi$
$74$	−6.00431e10	−3.14549
$75$	−2.47101e10	−1.20237
$76$	6.83441e10	3.09191
$77$	−4.03303e10	−1.69798
$78$	3.46703e10	1.35968
$79$	3.36122e10	1.22899	0.614494	−	0.788922i	$-0.289360\pi$
$79$	3.36122e10	1.22899	0.614494	+	0.788922i	$0.289360\pi$
$80$	−9.76695e10	−3.33245
$81$	3.48678e9	0.111111
$82$	3.20171e9	0.0953688
$83$	2.76507e10	0.770507	0.385254	−	0.922811i	$-0.374114\pi$
$83$	2.76507e10	0.770507	0.385254	+	0.922811i	$0.374114\pi$
$84$	7.42870e10	1.93810
$85$	1.36761e10	0.334316
$86$	−7.92671e10	−1.81699
$87$	3.87067e10	0.832588
$88$	−1.31315e11	−2.65253
$89$	−1.44161e10	−0.273655	−0.136827	−	0.990595i	$-0.543691\pi$
$89$	−1.44161e10	−0.273655	−0.136827	+	0.990595i	$0.543691\pi$
$90$	5.93234e10	1.05899
$91$	−1.14357e11	−1.92103
$92$	2.47409e11	3.91366
$93$	−1.09521e10	−0.163245
$94$	−1.50755e11	−2.11870
$95$	−1.80019e11	−2.38693
$96$	5.20617e10	0.651668
$97$	1.18137e11	1.39683	0.698413	−	0.715695i	$-0.253890\pi$
$97$	1.18137e11	1.39683	0.698413	+	0.715695i	$0.253890\pi$
$98$	−1.90848e11	−2.13277
$99$	3.62837e10	0.383458
$100$	4.73632e11	4.73632
$101$	−3.07269e10	−0.290905	−0.145453	−	0.989365i	$-0.546464\pi$
$101$	−3.07269e10	−0.290905	−0.145453	+	0.989365i	$0.546464\pi$
$102$	−2.21819e10	−0.198929
$103$	4.65828e10	0.395932	0.197966	−	0.980209i	$-0.436566\pi$
$103$	4.65828e10	0.395932	0.197966	+	0.980209i	$0.436566\pi$
$104$	−3.72344e11	−3.00097
$105$	−1.95673e11	−1.49620
$106$	−2.98438e11	−2.16607
$107$	−1.33118e11	−0.917542	−0.458771	−	0.888555i	$-0.651710\pi$
$107$	−1.33118e11	−0.917542	−0.458771	+	0.888555i	$0.651710\pi$
$108$	−6.68331e10	−0.437684
$109$	1.35886e11	0.845921	0.422960	−	0.906148i	$-0.360991\pi$
$109$	1.35886e11	0.845921	0.422960	+	0.906148i	$0.360991\pi$
$110$	6.17322e11	3.65470
$111$	−1.78175e11	−1.00362
$112$	−5.22518e11	−2.80158
$113$	1.99811e11	1.02020	0.510102	−	0.860114i	$-0.329608\pi$
$113$	1.99811e11	1.02020	0.510102	+	0.860114i	$0.329608\pi$
$114$	2.91982e11	1.42030
$115$	−6.51679e11	−3.02131
$116$	−7.41913e11	−3.27970
$117$	1.02882e11	0.433830
$118$	5.85440e10	0.235576
$119$	7.31651e10	0.281058
$120$	−6.37108e11	−2.33731
$121$	9.22580e10	0.323359
$122$	−1.51036e11	−0.505943
$123$	9.50093e9	0.0304290
$124$	2.09924e11	0.643048
$125$	−6.48505e11	−1.90068
$126$	3.17372e11	0.890288
$127$	−2.45066e11	−0.658208	−0.329104	−	0.944294i	$-0.606747\pi$
$127$	−2.45066e11	−0.658208	−0.329104	+	0.944294i	$0.606747\pi$
$128$	3.37226e11	0.867493
$129$	−2.35221e11	−0.579740
$130$	1.75042e12	4.13479
$131$	−3.48684e11	−0.789659	−0.394830	−	0.918754i	$-0.629196\pi$
$131$	−3.48684e11	−0.789659	−0.394830	+	0.918754i	$0.629196\pi$
$132$	−6.95469e11	−1.51050
$133$	−9.63078e11	−2.00668
$134$	1.11676e12	2.23298
$135$	1.76039e11	0.337889
$136$	2.38225e11	0.439059
$137$	7.91794e10	0.140168	0.0700840	−	0.997541i	$-0.477673\pi$
$137$	7.91794e10	0.140168	0.0700840	+	0.997541i	$0.477673\pi$
$138$	1.05699e12	1.79778
$139$	5.35686e11	0.875646	0.437823	−	0.899061i	$-0.355750\pi$
$139$	5.35686e11	0.875646	0.437823	+	0.899061i	$0.355750\pi$
$140$	3.75057e12	5.89377
$141$	−4.47359e11	−0.676007
$142$	1.70288e12	2.47514
$143$	1.07060e12	1.49720
$144$	4.70090e11	0.632684
$145$	1.95421e12	2.53190
$146$	−1.39019e12	−1.73434
$147$	−5.66332e11	−0.680496
$148$	3.41518e12	3.95343
$149$	−1.13785e12	−1.26928	−0.634642	−	0.772806i	$-0.718852\pi$
$149$	−1.13785e12	−1.26928	−0.634642	+	0.772806i	$0.718852\pi$
$150$	2.02347e12	2.17568
$151$	7.52312e11	0.779875	0.389937	−	0.920841i	$-0.372497\pi$
$151$	7.52312e11	0.779875	0.389937	+	0.920841i	$0.372497\pi$
$152$	−3.13577e12	−3.13476
$153$	−6.58239e10	−0.0634717
$154$	3.30259e12	3.07249
$155$	−5.52944e11	−0.496428
$156$	−1.97201e12	−1.70892
$157$	1.57758e12	1.31991	0.659954	−	0.751306i	$-0.270576\pi$
$157$	1.57758e12	1.31991	0.659954	+	0.751306i	$0.270576\pi$
$158$	−2.75245e12	−2.22385
$159$	−8.85602e11	−0.691121
$160$	2.62847e12	1.98172
$161$	−3.48639e12	−2.54000
$162$	−2.85527e11	−0.201055
$163$	1.11569e12	0.759470	0.379735	−	0.925095i	$-0.376015\pi$
$163$	1.11569e12	0.759470	0.379735	+	0.925095i	$0.376015\pi$
$164$	−1.82110e11	−0.119865
$165$	1.83187e12	1.16610
$166$	−2.26427e12	−1.39423
$167$	1.00214e12	0.597020	0.298510	−	0.954407i	$-0.403510\pi$
$167$	1.00214e12	0.597020	0.298510	+	0.954407i	$0.403510\pi$
$168$	−3.40844e12	−1.96496
$169$	1.24353e12	0.693874
$170$	−1.11991e12	−0.604944
$171$	8.66444e11	0.453171
$172$	4.50862e12	2.28369
$173$	1.17842e12	0.578156	0.289078	−	0.957306i	$-0.406651\pi$
$173$	1.17842e12	0.578156	0.289078	+	0.957306i	$0.406651\pi$
$174$	−3.16963e12	−1.50657
$175$	−6.67423e12	−3.07392
$176$	4.89178e12	2.18347
$177$	1.73727e11	0.0751646
$178$	1.18051e12	0.495177
$179$	−1.28029e12	−0.520735	−0.260368	−	0.965510i	$-0.583844\pi$
$179$	−1.28029e12	−0.520735	−0.260368	+	0.965510i	$0.583844\pi$
$180$	−3.37424e12	−1.33100
$181$	2.22754e12	0.852302	0.426151	−	0.904652i	$-0.359869\pi$
$181$	2.22754e12	0.852302	0.426151	+	0.904652i	$0.359869\pi$
$182$	9.36450e12	3.47610
$183$	−4.48192e11	−0.161430
$184$	−1.13516e13	−3.96790
$185$	−8.99563e12	−3.05202
$186$	8.96848e11	0.295391
$187$	−6.84967e11	−0.219049
$188$	8.57479e12	2.66290
$189$	9.41786e11	0.284061
$190$	1.47415e13	4.31913
$191$	1.46958e11	0.0418320	0.0209160	−	0.999781i	$-0.493342\pi$
$191$	1.46958e11	0.0418320	0.0209160	+	0.999781i	$0.493342\pi$
$192$	−3.01343e11	−0.0833496
$193$	−7.03816e12	−1.89188	−0.945941	−	0.324338i	$-0.894859\pi$
$193$	−7.03816e12	−1.89188	−0.945941	+	0.324338i	$0.894859\pi$
$194$	−9.67407e12	−2.52755
$195$	5.19429e12	1.31928
$196$	1.08552e13	2.68058
$197$	4.74360e12	1.13905	0.569527	−	0.821973i	$-0.307127\pi$
$197$	4.74360e12	1.13905	0.569527	+	0.821973i	$0.307127\pi$
$198$	−2.97121e12	−0.693865
$199$	−6.90796e12	−1.56913	−0.784563	−	0.620049i	$-0.787113\pi$
$199$	−6.90796e12	−1.56913	−0.784563	+	0.620049i	$0.787113\pi$
$200$	−2.17312e13	−4.80196
$201$	3.31394e12	0.712470
$202$	2.51618e12	0.526392
$203$	1.04547e13	2.12856
$204$	1.26168e12	0.250025
$205$	4.79679e11	0.0925347
$206$	−3.81459e12	−0.716438
$207$	3.13657e12	0.573613
$208$	1.38707e13	2.47029
$209$	9.01626e12	1.56395
$210$	1.60233e13	2.70737
$211$	2.87436e12	0.473139	0.236569	−	0.971615i	$-0.423977\pi$
$211$	2.87436e12	0.473139	0.236569	+	0.971615i	$0.423977\pi$
$212$	1.69748e13	2.72244
$213$	5.05323e12	0.789734
$214$	1.09008e13	1.66029
$215$	−1.18758e13	−1.76299
$216$	3.06644e12	0.443751
$217$	−2.95817e12	−0.417345
$218$	−1.11275e13	−1.53069
$219$	−4.12532e12	−0.553370
$220$	−3.51126e13	−4.59344
$221$	−1.94223e12	−0.247823
$222$	1.45905e13	1.81605
$223$	−9.28787e11	−0.112782	−0.0563910	−	0.998409i	$-0.517959\pi$
$223$	−9.28787e11	−0.112782	−0.0563910	+	0.998409i	$0.517959\pi$
$224$	1.40619e13	1.66602
$225$	6.00455e12	0.694187
$226$	−1.63622e13	−1.84606
$227$	2.76808e11	0.0304815	0.0152408	−	0.999884i	$-0.495149\pi$
$227$	2.76808e11	0.0304815	0.0152408	+	0.999884i	$0.495149\pi$
$228$	−1.66076e13	−1.78511
$229$	2.06500e12	0.216683	0.108341	−	0.994114i	$-0.465446\pi$
$229$	2.06500e12	0.216683	0.108341	+	0.994114i	$0.465446\pi$
$230$	5.33650e13	5.46705
$231$	9.80027e12	0.980330
$232$	3.40405e13	3.32515
$233$	1.37762e13	1.31423	0.657117	−	0.753788i	$-0.271776\pi$
$233$	1.37762e13	1.31423	0.657117	+	0.753788i	$0.271776\pi$
$234$	−8.42489e12	−0.785013
$235$	−2.25861e13	−2.05574
$236$	−3.32991e12	−0.296085
$237$	−8.16776e12	−0.709556
$238$	−5.99138e12	−0.508573
$239$	1.12934e13	0.936776	0.468388	−	0.883523i	$-0.344835\pi$
$239$	1.12934e13	0.936776	0.468388	+	0.883523i	$0.344835\pi$
$240$	2.37337e13	1.92399
$241$	1.59171e13	1.26116	0.630581	−	0.776123i	$-0.282817\pi$
$241$	1.59171e13	1.26116	0.630581	+	0.776123i	$0.282817\pi$
$242$	−7.55487e12	−0.585116
$243$	−8.47289e11	−0.0641500
$244$	8.59075e12	0.635897
$245$	−2.85927e13	−2.06939
$246$	−7.78016e11	−0.0550612
$247$	2.55657e13	1.76939
$248$	−9.63176e12	−0.651961
$249$	−6.71912e12	−0.444853
$250$	5.31051e13	3.43927
$251$	1.23833e12	0.0784569	0.0392284	−	0.999230i	$-0.487510\pi$
$251$	1.23833e12	0.0784569	0.0392284	+	0.999230i	$0.487510\pi$
$252$	−1.80517e13	−1.11896
$253$	3.26394e13	1.97961
$254$	2.00681e13	1.19102
$255$	−3.32329e12	−0.193018
$256$	−3.01546e13	−1.71409
$257$	−2.89910e13	−1.61299	−0.806494	−	0.591242i	$-0.798638\pi$
$257$	−2.89910e13	−1.61299	−0.806494	+	0.591242i	$0.798638\pi$
$258$	1.92619e13	1.04904
$259$	−4.81253e13	−2.56581
$260$	−9.95618e13	−5.19684
$261$	−9.40573e12	−0.480695
$262$	2.85532e13	1.42889
$263$	2.19744e13	1.07686	0.538432	−	0.842669i	$-0.319017\pi$
$263$	2.19744e13	1.07686	0.538432	+	0.842669i	$0.319017\pi$
$264$	3.19095e13	1.53144
$265$	−4.47119e13	−2.10170
$266$	7.88649e13	3.63107
$267$	3.50312e12	0.157995
$268$	−6.35201e13	−2.80653
$269$	1.88848e13	0.817476	0.408738	−	0.912652i	$-0.365969\pi$
$269$	1.88848e13	0.817476	0.408738	+	0.912652i	$0.365969\pi$
$270$	−1.44156e13	−0.611409
$271$	−2.90121e13	−1.20573	−0.602863	−	0.797845i	$-0.705973\pi$
$271$	−2.90121e13	−1.20573	−0.602863	+	0.797845i	$0.705973\pi$
$272$	−8.87440e12	−0.361418
$273$	2.77887e13	1.10911
$274$	−6.48387e12	−0.253633
$275$	6.24837e13	2.39572
$276$	−6.01205e13	−2.25955
$277$	4.19714e13	1.54638	0.773188	−	0.634177i	$-0.218661\pi$
$277$	4.19714e13	1.54638	0.773188	+	0.634177i	$0.218661\pi$
$278$	−4.38665e13	−1.58448
$279$	2.66135e12	0.0942496
$280$	−1.72084e14	−5.97545
$281$	3.40504e13	1.15941	0.579706	−	0.814826i	$-0.303167\pi$
$281$	3.40504e13	1.15941	0.579706	+	0.814826i	$0.303167\pi$
$282$	3.66336e13	1.22323
$283$	2.11301e12	0.0691951	0.0345976	−	0.999401i	$-0.488985\pi$
$283$	2.11301e12	0.0691951	0.0345976	+	0.999401i	$0.488985\pi$
$284$	−9.68580e13	−3.11089
$285$	4.37447e13	1.37809
$286$	−8.76698e13	−2.70917
$287$	2.56622e12	0.0777934
$288$	−1.26510e13	−0.376241
$289$	−3.30293e13	−0.963742
$290$	−1.60027e14	−4.58147
$291$	−2.87073e13	−0.806457
$292$	7.90724e13	2.17981
$293$	−1.32074e13	−0.357311	−0.178656	−	0.983912i	$-0.557175\pi$
$293$	−1.32074e13	−0.357311	−0.178656	+	0.983912i	$0.557175\pi$
$294$	4.63760e13	1.23135
$295$	8.77104e12	0.228576
$296$	−1.56695e14	−4.00822
$297$	−8.81693e12	−0.221389
$298$	9.31763e13	2.29676
$299$	9.25490e13	2.23965
$300$	−1.15093e14	−2.73451
$301$	−6.35336e13	−1.48214
$302$	−6.16057e13	−1.41118
$303$	7.46664e12	0.167954
$304$	1.16814e14	2.58043
$305$	−2.26281e13	−0.490908
$306$	5.39021e12	0.114852
$307$	2.80769e13	0.587608	0.293804	−	0.955866i	$-0.405079\pi$
$307$	2.80769e13	0.587608	0.293804	+	0.955866i	$0.405079\pi$
$308$	−1.87847e14	−3.86168
$309$	−1.13196e13	−0.228592
$310$	4.52797e13	0.898285
$311$	−1.42706e13	−0.278139	−0.139069	−	0.990283i	$-0.544411\pi$
$311$	−1.42706e13	−0.278139	−0.139069	+	0.990283i	$0.544411\pi$
$312$	9.04797e13	1.73261
$313$	−6.35564e13	−1.19582	−0.597910	−	0.801564i	$-0.704002\pi$
$313$	−6.35564e13	−1.19582	−0.597910	+	0.801564i	$0.704002\pi$
$314$	−1.29186e14	−2.38837
$315$	4.75485e13	0.863831
$316$	1.56556e14	2.79506
$317$	8.71235e13	1.52866	0.764328	−	0.644828i	$-0.223071\pi$
$317$	8.71235e13	1.52866	0.764328	+	0.644828i	$0.223071\pi$
$318$	7.25205e13	1.25058
$319$	−9.78765e13	−1.65894
$320$	−1.52141e13	−0.253466
$321$	3.23477e13	0.529743
$322$	2.85495e14	4.59612
$323$	−1.63568e13	−0.258872
$324$	1.62404e13	0.252697
$325$	1.77173e14	2.71043
$326$	−9.13618e13	−1.37426
$327$	−3.30203e13	−0.488393
$328$	8.35556e12	0.121526
$329$	−1.20832e14	−1.72825
$330$	−1.50009e14	−2.11004
$331$	7.31864e13	1.01246	0.506229	−	0.862399i	$-0.331039\pi$
$331$	7.31864e13	1.01246	0.506229	+	0.862399i	$0.331039\pi$
$332$	1.28789e14	1.75235
$333$	4.32965e13	0.579442
$334$	−8.20638e13	−1.08030
$335$	1.67313e14	2.16662
$336$	1.26972e14	1.61749
$337$	−7.55866e13	−0.947284	−0.473642	−	0.880717i	$-0.657061\pi$
$337$	−7.55866e13	−0.947284	−0.473642	+	0.880717i	$0.657061\pi$
$338$	−1.01831e14	−1.25556
$339$	−4.85540e13	−0.589015
$340$	6.36993e13	0.760327
$341$	2.76942e13	0.325267
$342$	−7.09517e13	−0.820011
$343$	−2.31859e13	−0.263698
$344$	−2.06865e14	−2.31534
$345$	1.58358e14	1.74436
$346$	−9.64987e13	−1.04617
$347$	9.47376e13	1.01090	0.505452	−	0.862854i	$-0.331326\pi$
$347$	9.47376e13	1.01090	0.505452	+	0.862854i	$0.331326\pi$
$348$	1.80285e14	1.89354
$349$	−6.81483e12	−0.0704556	−0.0352278	−	0.999379i	$-0.511216\pi$
$349$	−6.81483e12	−0.0704556	−0.0352278	+	0.999379i	$0.511216\pi$
$350$	5.46542e14	5.56224
$351$	−2.50004e13	−0.250472
$352$	−1.31647e14	−1.29845
$353$	−8.85389e13	−0.859752	−0.429876	−	0.902888i	$-0.641443\pi$
$353$	−8.85389e13	−0.859752	−0.429876	+	0.902888i	$0.641443\pi$
$354$	−1.42262e13	−0.136010
$355$	2.55125e14	2.40158
$356$	−6.71462e13	−0.622366
$357$	−1.77791e13	−0.162269
$358$	1.04841e14	0.942269
$359$	1.09759e14	0.971449	0.485724	−	0.874112i	$-0.338556\pi$
$359$	1.09759e14	0.971449	0.485724	+	0.874112i	$0.338556\pi$
$360$	1.54817e14	1.34945
$361$	9.88156e13	0.848274
$362$	−1.82410e14	−1.54224
$363$	−2.24187e13	−0.186691
$364$	−5.32642e14	−4.36896
$365$	−2.08278e14	−1.68280
$366$	3.67018e13	0.292106
$367$	−1.27385e14	−0.998745	−0.499373	−	0.866387i	$-0.666436\pi$
$367$	−1.27385e14	−0.998745	−0.499373	+	0.866387i	$0.666436\pi$
$368$	4.22874e14	3.26624
$369$	−2.30873e12	−0.0175682
$370$	7.36638e14	5.52261
$371$	−2.39202e14	−1.76689
$372$	−5.10116e13	−0.371264
$373$	−1.67487e14	−1.20111	−0.600554	−	0.799584i	$-0.705053\pi$
$373$	−1.67487e14	−1.20111	−0.600554	+	0.799584i	$0.705053\pi$
$374$	5.60908e13	0.396368
$375$	1.57587e14	1.09736
$376$	−3.93429e14	−2.69981
$377$	−2.77529e14	−1.87686
$378$	−7.71214e13	−0.514008
$379$	8.74232e13	0.574263	0.287132	−	0.957891i	$-0.407298\pi$
$379$	8.74232e13	0.574263	0.287132	+	0.957891i	$0.407298\pi$
$380$	−8.38478e14	−5.42853
$381$	5.95511e13	0.380016
$382$	−1.20341e13	−0.0756949
$383$	1.33470e14	0.827541	0.413770	−	0.910381i	$-0.364212\pi$
$383$	1.33470e14	0.827541	0.413770	+	0.910381i	$0.364212\pi$
$384$	−8.19459e13	−0.500847
$385$	4.94792e14	2.98118
$386$	5.76344e14	3.42335
$387$	5.71588e13	0.334713
$388$	5.50249e14	3.17676
$389$	−2.38319e14	−1.35655	−0.678276	−	0.734808i	$-0.737272\pi$
$389$	−2.38319e14	−1.35655	−0.678276	+	0.734808i	$0.737272\pi$
$390$	−4.25352e14	−2.38722
$391$	−5.92126e13	−0.327674
$392$	−4.98059e14	−2.71773
$393$	8.47302e13	0.455910
$394$	−3.88446e14	−2.06111
$395$	−4.12370e14	−2.15776
$396$	1.68999e14	0.872088
$397$	3.31386e14	1.68650	0.843249	−	0.537523i	$-0.180640\pi$
$397$	3.31386e14	1.68650	0.843249	+	0.537523i	$0.180640\pi$
$398$	5.65682e14	2.83933
$399$	2.34028e14	1.15855
$400$	8.09536e14	3.95281
$401$	−2.88745e14	−1.39066	−0.695330	−	0.718691i	$-0.744742\pi$
$401$	−2.88745e14	−1.39066	−0.695330	+	0.718691i	$0.744742\pi$
$402$	−2.71373e14	−1.28921
$403$	7.85270e13	0.367994
$404$	−1.43117e14	−0.661599
$405$	−4.27776e13	−0.195080
$406$	−8.56122e14	−3.85161
$407$	4.50546e14	1.99972
$408$	−5.78886e13	−0.253491
$409$	3.50854e14	1.51582	0.757911	−	0.652358i	$-0.226220\pi$
$409$	3.50854e14	1.51582	0.757911	+	0.652358i	$0.226220\pi$
$410$	−3.92802e13	−0.167441
$411$	−1.92406e13	−0.0809260
$412$	2.16970e14	0.900459
$413$	4.69238e13	0.192162
$414$	−2.56849e14	−1.03795
$415$	−3.39232e14	−1.35280
$416$	−3.73285e14	−1.46902
$417$	−1.30172e14	−0.505555
$418$	−7.38328e14	−2.82996
$419$	−8.89563e13	−0.336511	−0.168256	−	0.985743i	$-0.553813\pi$
$419$	−8.89563e13	−0.336511	−0.168256	+	0.985743i	$0.553813\pi$
$420$	−9.11388e14	−3.40277
$421$	−1.68005e14	−0.619113	−0.309556	−	0.950881i	$-0.600181\pi$
$421$	−1.68005e14	−0.619113	−0.309556	+	0.950881i	$0.600181\pi$
$422$	−2.35377e14	−0.856142
$423$	1.08708e14	0.390293
$424$	−7.78839e14	−2.76017
$425$	−1.13354e14	−0.396551
$426$	−4.13801e14	−1.42902
$427$	−1.21057e14	−0.412703
$428$	−6.20026e14	−2.08674
$429$	−2.60156e14	−0.864408
$430$	9.72487e14	3.19012
$431$	−1.33060e14	−0.430946	−0.215473	−	0.976510i	$-0.569129\pi$
$431$	−1.33060e14	−0.430946	−0.215473	+	0.976510i	$0.569129\pi$
$432$	−1.14232e14	−0.365280
$433$	−3.10508e14	−0.980370	−0.490185	−	0.871619i	$-0.663071\pi$
$433$	−3.10508e14	−0.980370	−0.490185	+	0.871619i	$0.663071\pi$
$434$	2.42240e14	0.755183
$435$	−4.74873e14	−1.46179
$436$	6.32919e14	1.92386
$437$	7.79419e14	2.33950
$438$	3.37816e14	1.00132
$439$	5.94518e14	1.74024	0.870122	−	0.492837i	$-0.164040\pi$
$439$	5.94518e14	1.74024	0.870122	+	0.492837i	$0.164040\pi$
$440$	1.61104e15	4.65710
$441$	1.37619e14	0.392885
$442$	1.59046e14	0.448435
$443$	−6.10093e14	−1.69893	−0.849465	−	0.527645i	$-0.823075\pi$
$443$	−6.10093e14	−1.69893	−0.849465	+	0.527645i	$0.823075\pi$
$444$	−8.29889e14	−2.28251
$445$	1.76864e14	0.480462
$446$	7.60569e13	0.204078
$447$	2.76496e14	0.732821
$448$	−8.13931e13	−0.213088
$449$	3.25417e14	0.841560	0.420780	−	0.907163i	$-0.361756\pi$
$449$	3.25417e14	0.841560	0.420780	+	0.907163i	$0.361756\pi$
$450$	−4.91703e14	−1.25613
$451$	−2.40247e13	−0.0606300
$452$	9.30661e14	2.32023
$453$	−1.82812e14	−0.450261
$454$	−2.26674e13	−0.0551562
$455$	1.40299e15	3.37280
$456$	7.61991e14	1.80985
$457$	−5.63579e14	−1.32256	−0.661281	−	0.750139i	$-0.729987\pi$
$457$	−5.63579e14	−1.32256	−0.661281	+	0.750139i	$0.729987\pi$
$458$	−1.69100e14	−0.392087
$459$	1.59952e13	0.0366454
$460$	−3.03534e15	−6.87130
$461$	1.78681e14	0.399691	0.199846	−	0.979827i	$-0.435956\pi$
$461$	1.78681e14	0.399691	0.199846	+	0.979827i	$0.435956\pi$
$462$	−8.02529e14	−1.77390
$463$	5.69718e14	1.24441	0.622207	−	0.782853i	$-0.286236\pi$
$463$	5.69718e14	1.24441	0.622207	+	0.782853i	$0.286236\pi$
$464$	−1.26808e15	−2.73715
$465$	1.34365e14	0.286613
$466$	−1.12811e15	−2.37810
$467$	−3.81172e13	−0.0794105	−0.0397052	−	0.999211i	$-0.512642\pi$
$467$	−3.81172e13	−0.0794105	−0.0397052	+	0.999211i	$0.512642\pi$
$468$	4.79197e14	0.986648
$469$	8.95101e14	1.82147
$470$	1.84954e15	3.71985
$471$	−3.83352e14	−0.762049
$472$	1.52783e14	0.300189
$473$	5.94797e14	1.15514
$474$	6.68845e14	1.28394
$475$	1.49209e15	2.83127
$476$	3.40782e14	0.639203
$477$	2.15201e14	0.399019
$478$	−9.24798e14	−1.69509
$479$	−8.91177e13	−0.161480	−0.0807400	−	0.996735i	$-0.525728\pi$
$479$	−8.91177e13	−0.161480	−0.0807400	+	0.996735i	$0.525728\pi$
$480$	−6.38718e14	−1.14415
$481$	1.27753e15	2.26241
$482$	−1.30343e15	−2.28207
$483$	8.47193e14	1.46647
$484$	4.29712e14	0.735407
$485$	−1.44936e15	−2.45244
$486$	6.93831e13	0.116079
$487$	−1.20100e15	−1.98670	−0.993350	−	0.115137i	$-0.963269\pi$
$487$	−1.20100e15	−1.98670	−0.993350	+	0.115137i	$0.963269\pi$
$488$	−3.94161e14	−0.644711
$489$	−2.71112e14	−0.438480
$490$	2.34141e15	3.74455
$491$	−4.53460e14	−0.717118	−0.358559	−	0.933507i	$-0.616732\pi$
$491$	−4.53460e14	−0.717118	−0.358559	+	0.933507i	$0.616732\pi$
$492$	4.42526e13	0.0692040
$493$	1.77562e14	0.274595
$494$	−2.09353e15	−3.20170
$495$	−4.45146e14	−0.673245
$496$	3.58805e14	0.536672
$497$	1.36488e15	2.01900
$498$	5.50218e14	0.804959
$499$	−2.32270e13	−0.0336079	−0.0168039	−	0.999859i	$-0.505349\pi$
$499$	−2.32270e13	−0.0336079	−0.0168039	+	0.999859i	$0.505349\pi$
$500$	−3.02055e15	−4.32266
$501$	−2.43520e14	−0.344689
$502$	−1.01405e14	−0.141967
$503$	−1.06144e15	−1.46985	−0.734926	−	0.678148i	$-0.762783\pi$
$503$	−1.06144e15	−1.46985	−0.734926	+	0.678148i	$0.762783\pi$
$504$	8.28250e14	1.13447
$505$	3.76973e14	0.510749
$506$	−2.67279e15	−3.58209
$507$	−3.02178e14	−0.400608
$508$	−1.14145e15	−1.49695
$509$	4.13158e14	0.536005	0.268002	−	0.963418i	$-0.413636\pi$
$509$	4.13158e14	0.536005	0.268002	+	0.963418i	$0.413636\pi$
$510$	2.72139e14	0.349265
$511$	−1.11426e15	−1.41472
$512$	1.77867e15	2.23415
$513$	−2.10546e14	−0.261638
$514$	2.37403e15	2.91870
$515$	−5.71501e14	−0.695148
$516$	−1.09559e15	−1.31849
$517$	1.13122e15	1.34695
$518$	3.94091e15	4.64283
$519$	−2.86355e14	−0.333799
$520$	4.56810e15	5.26887
$521$	1.20058e15	1.37019	0.685097	−	0.728452i	$-0.259760\pi$
$521$	1.20058e15	1.37019	0.685097	+	0.728452i	$0.259760\pi$
$522$	7.70220e14	0.869816
$523$	−2.39919e14	−0.268105	−0.134052	−	0.990974i	$-0.542799\pi$
$523$	−2.39919e14	−0.268105	−0.134052	+	0.990974i	$0.542799\pi$
$524$	−1.62407e15	−1.79590
$525$	1.62184e15	1.77473
$526$	−1.79945e15	−1.94858
$527$	−5.02413e13	−0.0538397
$528$	−1.18870e15	−1.26063
$529$	1.86873e15	1.96128
$530$	3.66139e15	3.80302
$531$	−4.22156e13	−0.0433963
$532$	−4.48574e15	−4.56373
$533$	−6.81222e13	−0.0685945
$534$	−2.86865e14	−0.285891
$535$	1.63316e15	1.61095
$536$	2.91443e15	2.84543
$537$	3.11111e14	0.300647
$538$	−1.54645e15	−1.47922
$539$	1.43207e15	1.35589
$540$	8.19941e14	0.768452
$541$	−1.53994e15	−1.42862	−0.714312	−	0.699827i	$-0.753260\pi$
$541$	−1.53994e15	−1.42862	−0.714312	+	0.699827i	$0.753260\pi$
$542$	2.37576e15	2.18176
$543$	−5.41292e14	−0.492077
$544$	2.38827e14	0.214926
$545$	−1.66712e15	−1.48520
$546$	−2.27557e15	−2.00693
$547$	−1.77377e15	−1.54870	−0.774349	−	0.632759i	$-0.781923\pi$
$547$	−1.77377e15	−1.54870	−0.774349	+	0.632759i	$0.781923\pi$
$548$	3.68795e14	0.318781
$549$	1.08911e14	0.0932015
$550$	−5.11669e15	−4.33505
$551$	−2.33726e15	−1.96053
$552$	2.75845e15	2.29087
$553$	−2.20612e15	−1.81402
$554$	−3.43697e15	−2.79816
$555$	2.18594e15	1.76208
$556$	2.49507e15	1.99146
$557$	−1.34692e15	−1.06448	−0.532242	−	0.846592i	$-0.678650\pi$
$557$	−1.34692e15	−1.06448	−0.532242	+	0.846592i	$0.678650\pi$
$558$	−2.17934e14	−0.170544
$559$	1.68655e15	1.30688
$560$	6.41051e15	4.91879
$561$	1.66447e14	0.126468
$562$	−2.78834e15	−2.09795
$563$	−5.37127e14	−0.400204	−0.200102	−	0.979775i	$-0.564127\pi$
$563$	−5.37127e14	−0.400204	−0.200102	+	0.979775i	$0.564127\pi$
$564$	−2.08367e15	−1.53743
$565$	−2.45137e15	−1.79120
$566$	−1.73031e14	−0.125208
$567$	−2.28854e14	−0.164003
$568$	4.44404e15	3.15401
$569$	8.67485e14	0.609740	0.304870	−	0.952394i	$-0.401387\pi$
$569$	8.67485e14	0.609740	0.304870	+	0.952394i	$0.401387\pi$
$570$	−3.58218e15	−2.49365
$571$	6.22355e14	0.429081	0.214541	−	0.976715i	$-0.431175\pi$
$571$	6.22355e14	0.429081	0.214541	+	0.976715i	$0.431175\pi$
$572$	4.98655e15	3.40504
$573$	−3.57107e13	−0.0241517
$574$	−2.10143e14	−0.140767
$575$	5.40146e15	3.58375
$576$	7.32262e13	0.0481219
$577$	−2.49549e15	−1.62438	−0.812191	−	0.583392i	$-0.801725\pi$
$577$	−2.49549e15	−1.62438	−0.812191	+	0.583392i	$0.801725\pi$
$578$	2.70471e15	1.74389
$579$	1.71027e15	1.09228
$580$	9.10215e15	5.75824
$581$	−1.81485e15	−1.13729
$582$	2.35080e15	1.45928
$583$	2.23939e15	1.37706
$584$	−3.62800e15	−2.21002
$585$	−1.26221e15	−0.761684
$586$	1.08154e15	0.646553
$587$	−4.10477e14	−0.243097	−0.121549	−	0.992585i	$-0.538786\pi$
$587$	−4.10477e14	−0.243097	−0.121549	+	0.992585i	$0.538786\pi$
$588$	−2.63781e15	−1.54764
$589$	6.61330e14	0.384400
$590$	−7.18247e14	−0.413607
$591$	−1.15270e15	−0.657633
$592$	5.83725e15	3.29943
$593$	3.87690e14	0.217112	0.108556	−	0.994090i	$-0.465377\pi$
$593$	3.87690e14	0.217112	0.108556	+	0.994090i	$0.465377\pi$
$594$	7.22005e14	0.400603
$595$	−8.97625e14	−0.493460
$596$	−5.29976e15	−2.88670
$597$	1.67863e15	0.905935
$598$	−7.57870e15	−4.05264
$599$	−3.99439e14	−0.211642	−0.105821	−	0.994385i	$-0.533747\pi$
$599$	−3.99439e14	−0.211642	−0.105821	+	0.994385i	$0.533747\pi$
$600$	5.28068e15	2.77241
$601$	−1.59334e15	−0.828896	−0.414448	−	0.910073i	$-0.636025\pi$
$601$	−1.59334e15	−0.828896	−0.414448	+	0.910073i	$0.636025\pi$
$602$	5.20267e15	2.68192
$603$	−8.05288e14	−0.411345
$604$	3.50406e15	1.77365
$605$	−1.13187e15	−0.567728
$606$	−6.11432e14	−0.303913
$607$	−1.83861e15	−0.905631	−0.452816	−	0.891604i	$-0.649580\pi$
$607$	−1.83861e15	−0.905631	−0.452816	+	0.891604i	$0.649580\pi$
$608$	−3.14369e15	−1.53451
$609$	−2.54050e15	−1.22892
$610$	1.85298e15	0.888295
$611$	3.20759e15	1.52389
$612$	−3.06589e14	−0.144352
$613$	−2.85879e15	−1.33398	−0.666992	−	0.745065i	$-0.732418\pi$
$613$	−2.85879e15	−1.33398	−0.666992	+	0.745065i	$0.732418\pi$
$614$	−2.29917e15	−1.06327
$615$	−1.16562e14	−0.0534249
$616$	8.61882e15	3.91520
$617$	4.04258e15	1.82008	0.910040	−	0.414520i	$-0.136051\pi$
$617$	4.04258e15	1.82008	0.910040	+	0.414520i	$0.136051\pi$
$618$	9.26947e14	0.413636
$619$	1.66600e15	0.736847	0.368423	−	0.929658i	$-0.379898\pi$
$619$	1.66600e15	0.736847	0.368423	+	0.929658i	$0.379898\pi$
$620$	−2.57545e15	−1.12901
$621$	−7.62188e14	−0.331175
$622$	1.16860e15	0.503291
$623$	9.46197e14	0.403922
$624$	−3.37057e15	−1.42623
$625$	2.99096e15	1.25450
$626$	5.20454e15	2.16383
$627$	−2.19095e15	−0.902945
$628$	7.34793e15	3.00183
$629$	−8.17356e14	−0.331004
$630$	−3.89367e15	−1.56310
$631$	−2.22420e15	−0.885140	−0.442570	−	0.896734i	$-0.645933\pi$
$631$	−2.22420e15	−0.885140	−0.442570	+	0.896734i	$0.645933\pi$
$632$	−7.18311e15	−2.83379
$633$	−6.98471e14	−0.273167
$634$	−7.13441e15	−2.76610
$635$	3.00659e15	1.15563
$636$	−4.12488e15	−1.57180
$637$	4.06063e15	1.53400
$638$	8.01496e15	3.00184
$639$	−1.22793e15	−0.455953
$640$	−4.13725e15	−1.52308
$641$	−3.13841e15	−1.14549	−0.572743	−	0.819735i	$-0.694121\pi$
$641$	−3.13841e15	−1.14549	−0.572743	+	0.819735i	$0.694121\pi$
$642$	−2.64890e15	−0.958568
$643$	−2.20899e15	−0.792563	−0.396281	−	0.918129i	$-0.629700\pi$
$643$	−2.20899e15	−0.792563	−0.396281	+	0.918129i	$0.629700\pi$
$644$	−1.62386e16	−5.77666
$645$	2.88581e15	1.01786
$646$	1.33943e15	0.468428
$647$	−2.86406e15	−0.993137	−0.496568	−	0.867998i	$-0.665407\pi$
$647$	−2.86406e15	−0.993137	−0.496568	+	0.867998i	$0.665407\pi$
$648$	−7.45145e14	−0.256200
$649$	−4.39297e14	−0.149766
$650$	−1.45084e16	−4.90451
$651$	7.18836e14	0.240954
$652$	5.19655e15	1.72724
$653$	2.31705e15	0.763681	0.381841	−	0.924228i	$-0.375290\pi$
$653$	2.31705e15	0.763681	0.381841	+	0.924228i	$0.375290\pi$
$654$	2.70398e15	0.883744
$655$	4.27782e15	1.38642
$656$	−3.11263e14	−0.100036
$657$	1.00245e15	0.319488
$658$	9.89478e15	3.12726
$659$	−1.43478e14	−0.0449691	−0.0224846	−	0.999747i	$-0.507158\pi$
$659$	−1.43478e14	−0.0449691	−0.0224846	+	0.999747i	$0.507158\pi$
$660$	8.53235e15	2.65202
$661$	3.98885e15	1.22953	0.614766	−	0.788710i	$-0.289250\pi$
$661$	3.98885e15	1.22953	0.614766	+	0.788710i	$0.289250\pi$
$662$	−5.99312e15	−1.83204
$663$	4.71961e14	0.143081
$664$	−5.90911e15	−1.77663
$665$	1.18155e16	3.52317
$666$	−3.54549e15	−1.04850
$667$	−8.46102e15	−2.48159
$668$	4.66769e15	1.35779
$669$	2.25695e14	0.0651147
$670$	−1.37010e16	−3.92049
$671$	1.13333e15	0.321649
$672$	−3.41705e15	−0.961879
$673$	−5.12540e14	−0.143102	−0.0715509	−	0.997437i	$-0.522795\pi$
$673$	−5.12540e14	−0.143102	−0.0715509	+	0.997437i	$0.522795\pi$
$674$	6.18967e15	1.71411
$675$	−1.45911e15	−0.400789
$676$	5.79202e15	1.57806
$677$	2.83003e15	0.764809	0.382405	−	0.923995i	$-0.375096\pi$
$677$	2.83003e15	0.764809	0.382405	+	0.923995i	$0.375096\pi$
$678$	3.97601e15	1.06582
$679$	−7.75390e15	−2.06175
$680$	−2.92265e15	−0.770865
$681$	−6.72644e13	−0.0175985
$682$	−2.26783e15	−0.588568
$683$	1.48113e15	0.381312	0.190656	−	0.981657i	$-0.438938\pi$
$683$	1.48113e15	0.381312	0.190656	+	0.981657i	$0.438938\pi$
$684$	4.03565e15	1.03064
$685$	−9.71411e14	−0.246096
$686$	1.89866e15	0.477160
$687$	−5.01795e14	−0.125102
$688$	7.70617e15	1.90591
$689$	6.34981e15	1.55796
$690$	−1.29677e16	−3.15641
$691$	6.00640e15	1.45039	0.725195	−	0.688544i	$-0.241750\pi$
$691$	6.00640e15	1.45039	0.725195	+	0.688544i	$0.241750\pi$
$692$	5.48873e15	1.31489
$693$	−2.38147e15	−0.565994
$694$	−7.75791e15	−1.82923
$695$	−6.57205e15	−1.53739
$696$	−8.27184e15	−1.91978
$697$	4.35844e13	0.0100358
$698$	5.58056e14	0.127489
$699$	−3.34762e15	−0.758774
$700$	−3.10867e16	−6.99093
$701$	1.87164e15	0.417613	0.208806	−	0.977957i	$-0.433042\pi$
$701$	1.87164e15	0.417613	0.208806	+	0.977957i	$0.433042\pi$
$702$	2.04725e15	0.453227
$703$	1.07589e16	2.36327
$704$	7.61996e14	0.166075
$705$	5.48842e15	1.18688
$706$	7.25031e15	1.55572
$707$	2.01675e15	0.429384
$708$	8.09169e14	0.170945
$709$	6.18607e15	1.29676	0.648382	−	0.761315i	$-0.275446\pi$
$709$	6.18607e15	1.29676	0.648382	+	0.761315i	$0.275446\pi$
$710$	−2.08918e16	−4.34565
$711$	1.98476e15	0.409663
$712$	3.08080e15	0.630992
$713$	2.39405e15	0.486565
$714$	1.45590e15	0.293625
$715$	−1.31346e16	−2.62866
$716$	−5.96323e15	−1.18430
$717$	−2.74429e15	−0.540848
$718$	−8.98798e15	−1.75783
$719$	−3.83167e14	−0.0743668	−0.0371834	−	0.999308i	$-0.511839\pi$
$719$	−3.83167e14	−0.0743668	−0.0371834	+	0.999308i	$0.511839\pi$
$720$	−5.76729e15	−1.11082
$721$	−3.05745e15	−0.584407
$722$	−8.09186e15	−1.53495
$723$	−3.86786e15	−0.728133
$724$	1.03752e16	1.93837
$725$	−1.61975e16	−3.00323
$726$	1.83583e15	0.337817
$727$	−5.51247e15	−1.00672	−0.503358	−	0.864078i	$-0.667902\pi$
$727$	−5.51247e15	−1.00672	−0.503358	+	0.864078i	$0.667902\pi$
$728$	2.44387e16	4.42951
$729$	2.05891e14	0.0370370
$730$	1.70555e16	3.04502
$731$	−1.07905e15	−0.191203
$732$	−2.08755e15	−0.367135
$733$	5.39658e15	0.941991	0.470995	−	0.882136i	$-0.343895\pi$
$733$	5.39658e15	0.941991	0.470995	+	0.882136i	$0.343895\pi$
$734$	1.04314e16	1.80722
$735$	6.94803e15	1.19476
$736$	−1.13803e16	−1.94235
$737$	−8.37987e15	−1.41960
$738$	1.89058e14	0.0317896
$739$	−4.28606e15	−0.715342	−0.357671	−	0.933848i	$-0.616429\pi$
$739$	−4.28606e15	−0.715342	−0.357671	+	0.933848i	$0.616429\pi$
$740$	−4.18991e16	−6.94113
$741$	−6.21245e15	−1.02156
$742$	1.95879e16	3.19718
$743$	−3.44325e15	−0.557866	−0.278933	−	0.960311i	$-0.589981\pi$
$743$	−3.44325e15	−0.557866	−0.278933	+	0.960311i	$0.589981\pi$
$744$	2.34052e15	0.376410
$745$	1.39596e16	2.22851
$746$	1.37152e16	2.17340
$747$	1.63275e15	0.256836
$748$	−3.19038e15	−0.498177
$749$	8.73715e15	1.35432
$750$	−1.29045e16	−1.98566
$751$	−1.02592e16	−1.56709	−0.783547	−	0.621332i	$-0.786592\pi$
$751$	−1.02592e16	−1.56709	−0.783547	+	0.621332i	$0.786592\pi$
$752$	1.46561e16	2.22239
$753$	−3.00914e14	−0.0452971
$754$	2.27264e16	3.39617
$755$	−9.22973e15	−1.36924
$756$	4.38657e15	0.646034
$757$	−8.42991e15	−1.23252	−0.616262	−	0.787541i	$-0.711354\pi$
$757$	−8.42991e15	−1.23252	−0.616262	+	0.787541i	$0.711354\pi$
$758$	−7.15895e15	−1.03913
$759$	−7.93136e15	−1.14293
$760$	3.84711e16	5.50376
$761$	−1.18345e16	−1.68088	−0.840439	−	0.541907i	$-0.817703\pi$
$761$	−1.18345e16	−1.68088	−0.840439	+	0.541907i	$0.817703\pi$
$762$	−4.87654e15	−0.687638
$763$	−8.91885e15	−1.24860
$764$	6.84487e14	0.0951376
$765$	8.07559e14	0.111439
$766$	−1.09296e16	−1.49743
$767$	−1.24563e15	−0.169439
$768$	7.32757e15	0.989631
$769$	−8.62931e15	−1.15713	−0.578564	−	0.815637i	$-0.696387\pi$
$769$	−8.62931e15	−1.15713	−0.578564	+	0.815637i	$0.696387\pi$
$770$	−4.05178e16	−5.39444
$771$	7.04482e15	0.931260
$772$	−3.27818e16	−4.30266
$773$	−3.26142e15	−0.425030	−0.212515	−	0.977158i	$-0.568165\pi$
$773$	−3.26142e15	−0.425030	−0.212515	+	0.977158i	$0.568165\pi$
$774$	−4.68064e15	−0.605662
$775$	4.58308e15	0.588842
$776$	−2.52466e16	−3.22079
$777$	1.16945e16	1.48137
$778$	1.95156e16	2.45467
$779$	−5.73704e14	−0.0716526
$780$	2.41935e16	3.00040
$781$	−1.27779e16	−1.57355
$782$	4.84882e15	0.592924
$783$	2.28559e15	0.277529
$784$	1.85538e16	2.23715
$785$	−1.93545e16	−2.31739
$786$	−6.93842e15	−0.824967
$787$	2.49094e15	0.294105	0.147053	−	0.989129i	$-0.453021\pi$
$787$	2.49094e15	0.294105	0.147053	+	0.989129i	$0.453021\pi$
$788$	2.20943e16	2.59052
$789$	−5.33978e15	−0.621728
$790$	3.37684e16	3.90446
$791$	−1.31145e16	−1.50585
$792$	−7.75402e15	−0.884175
$793$	3.21356e15	0.363902
$794$	−2.71367e16	−3.05171
$795$	1.08650e16	1.21342
$796$	−3.21753e16	−3.56862
$797$	2.02263e15	0.222790	0.111395	−	0.993776i	$-0.464468\pi$
$797$	2.02263e15	0.222790	0.111395	+	0.993776i	$0.464468\pi$
$798$	−1.91642e16	−2.09640
$799$	−2.05221e15	−0.222953
$800$	−2.17861e16	−2.35063
$801$	−8.51257e14	−0.0912183
$802$	2.36449e16	2.51639
$803$	1.04316e16	1.10259
$804$	1.54354e16	1.62035
$805$	4.27728e16	4.45954
$806$	−6.43045e15	−0.665884
$807$	−4.58901e15	−0.471970
$808$	6.56651e15	0.670768
$809$	7.96662e15	0.808272	0.404136	−	0.914699i	$-0.367572\pi$
$809$	7.96662e15	0.808272	0.404136	+	0.914699i	$0.367572\pi$
$810$	3.50299e15	0.352997
$811$	−2.21596e15	−0.221793	−0.110896	−	0.993832i	$-0.535372\pi$
$811$	−2.21596e15	−0.221793	−0.110896	+	0.993832i	$0.535372\pi$
$812$	4.86952e16	4.84092
$813$	7.04995e15	0.696126
$814$	−3.68945e16	−3.61849
$815$	−1.36878e16	−1.33342
$816$	2.15648e15	0.208665
$817$	1.42036e16	1.36514
$818$	−2.87309e16	−2.74287
$819$	−6.75266e15	−0.640344
$820$	2.23421e15	0.210449
$821$	7.19699e15	0.673385	0.336692	−	0.941615i	$-0.390692\pi$
$821$	7.19699e15	0.673385	0.336692	+	0.941615i	$0.390692\pi$
$822$	1.57558e15	0.146435
$823$	2.87425e15	0.265354	0.132677	−	0.991159i	$-0.457643\pi$
$823$	2.87425e15	0.265354	0.132677	+	0.991159i	$0.457643\pi$
$824$	−9.95501e15	−0.912939
$825$	−1.51835e16	−1.38317
$826$	−3.84252e15	−0.347717
$827$	8.45798e15	0.760302	0.380151	−	0.924924i	$-0.375872\pi$
$827$	8.45798e15	0.760302	0.380151	+	0.924924i	$0.375872\pi$
$828$	1.46093e16	1.30455
$829$	4.09434e15	0.363190	0.181595	−	0.983373i	$-0.441874\pi$
$829$	4.09434e15	0.363190	0.181595	+	0.983373i	$0.441874\pi$
$830$	2.77792e16	2.44788
$831$	−1.01991e16	−0.892800
$832$	2.16064e15	0.187890
$833$	−2.59798e15	−0.224434
$834$	1.06596e16	0.914799
$835$	−1.22948e16	−1.04820
$836$	4.19952e16	3.55685
$837$	−6.46709e14	−0.0544150
$838$	7.28449e15	0.608915
$839$	2.31251e15	0.192040	0.0960201	−	0.995379i	$-0.469389\pi$
$839$	2.31251e15	0.192040	0.0960201	+	0.995379i	$0.469389\pi$
$840$	4.18164e16	3.44993
$841$	1.31718e16	1.07961
$842$	1.37576e16	1.12028
$843$	−8.27426e15	−0.669387
$844$	1.33880e16	1.07605
$845$	−1.52563e16	−1.21825
$846$	−8.90196e15	−0.706234
$847$	−6.05533e15	−0.477286
$848$	2.90135e16	2.27208
$849$	−5.13461e14	−0.0399498
$850$	9.28242e15	0.717558
$851$	3.89479e16	2.99138
$852$	2.35365e16	1.79607
$853$	−2.06938e15	−0.156899	−0.0784496	−	0.996918i	$-0.524997\pi$
$853$	−2.06938e15	−0.156899	−0.0784496	+	0.996918i	$0.524997\pi$
$854$	9.91320e15	0.746785
$855$	−1.06300e16	−0.795642
$856$	2.84480e16	2.11566
$857$	1.04644e16	0.773248	0.386624	−	0.922237i	$-0.373641\pi$
$857$	1.04644e16	0.773248	0.386624	+	0.922237i	$0.373641\pi$
$858$	2.13038e16	1.56414
$859$	7.94158e15	0.579354	0.289677	−	0.957124i	$-0.406452\pi$
$859$	7.94158e15	0.579354	0.289677	+	0.957124i	$0.406452\pi$
$860$	−5.53139e16	−4.00952
$861$	−6.23590e14	−0.0449140
$862$	1.08961e16	0.779796
$863$	1.14766e16	0.816122	0.408061	−	0.912955i	$-0.366205\pi$
$863$	1.14766e16	0.816122	0.408061	+	0.912955i	$0.366205\pi$
$864$	3.07419e15	0.217223
$865$	−1.44574e16	−1.01508
$866$	2.54270e16	1.77397
$867$	8.02611e15	0.556417
$868$	−1.37783e16	−0.949156
$869$	2.06536e16	1.41379
$870$	3.88866e16	2.64511
$871$	−2.37611e16	−1.60608
$872$	−2.90396e16	−1.95052
$873$	6.97588e15	0.465608
$874$	−6.38254e16	−4.23332
$875$	4.25644e16	2.80545
$876$	−1.92146e16	−1.25852
$877$	−2.61506e16	−1.70209	−0.851046	−	0.525090i	$-0.824031\pi$
$877$	−2.61506e16	−1.70209	−0.851046	+	0.525090i	$0.824031\pi$
$878$	−4.86841e16	−3.14896
$879$	3.20941e15	0.206294
$880$	−6.00147e16	−3.83357
$881$	9.22917e14	0.0585862	0.0292931	−	0.999571i	$-0.490674\pi$
$881$	9.22917e14	0.0585862	0.0292931	+	0.999571i	$0.490674\pi$
$882$	−1.12694e16	−0.710923
$883$	6.31286e15	0.395769	0.197885	−	0.980225i	$-0.436593\pi$
$883$	6.31286e15	0.395769	0.197885	+	0.980225i	$0.436593\pi$
$884$	−9.04634e15	−0.563618
$885$	−2.13136e15	−0.131968
$886$	4.99596e16	3.07421
$887$	2.29576e16	1.40393	0.701966	−	0.712211i	$-0.252306\pi$
$887$	2.29576e16	1.40393	0.701966	+	0.712211i	$0.252306\pi$
$888$	3.80770e16	2.31415
$889$	1.60848e16	0.971532
$890$	−1.44831e16	−0.869394
$891$	2.14251e15	0.127819
$892$	−4.32603e15	−0.256497
$893$	2.70133e16	1.59182
$894$	−2.26419e16	−1.32604
$895$	1.57072e16	0.914267
$896$	−2.21337e16	−1.28044
$897$	−2.24894e16	−1.29306
$898$	−2.66479e16	−1.52280
$899$	−7.17910e15	−0.407748
$900$	2.79675e16	1.57877
$901$	−4.06259e15	−0.227938
$902$	1.96735e15	0.109710
$903$	1.54387e16	0.855712
$904$	−4.27006e16	−2.35238
$905$	−2.73285e16	−1.49641
$906$	1.49702e16	0.814745
$907$	−1.33216e16	−0.720636	−0.360318	−	0.932830i	$-0.617332\pi$
$907$	−1.33216e16	−0.720636	−0.360318	+	0.932830i	$0.617332\pi$
$908$	1.28929e15	0.0693234
$909$	−1.81439e15	−0.0969684
$910$	−1.14888e17	−6.10307
$911$	−4.14245e15	−0.218729	−0.109364	−	0.994002i	$-0.534882\pi$
$911$	−4.14245e15	−0.218729	−0.109364	+	0.994002i	$0.534882\pi$
$912$	−2.83859e16	−1.48981
$913$	1.69904e16	0.886371
$914$	4.61506e16	2.39317
$915$	5.49864e15	0.283426
$916$	9.61818e15	0.492797
$917$	2.28858e16	1.16556
$918$	−1.30982e15	−0.0663098
$919$	−2.51113e16	−1.26367	−0.631836	−	0.775102i	$-0.717698\pi$
$919$	−2.51113e16	−1.26367	−0.631836	+	0.775102i	$0.717698\pi$
$920$	1.39267e17	6.96653
$921$	−6.82268e15	−0.339256
$922$	−1.46319e16	−0.723239
$923$	−3.62319e16	−1.78025
$924$	4.56469e16	2.22954
$925$	7.45604e16	3.62017
$926$	−4.66534e16	−2.25176
$927$	2.75067e15	0.131977
$928$	3.41265e16	1.62771
$929$	2.94286e16	1.39535	0.697675	−	0.716415i	$-0.254218\pi$
$929$	2.94286e16	1.39535	0.697675	+	0.716415i	$0.254218\pi$
$930$	−1.10030e16	−0.518625
$931$	3.41974e16	1.60239
$932$	6.41658e16	2.98893
$933$	3.46777e15	0.160584
$934$	3.12136e15	0.143693
$935$	8.40350e15	0.384589
$936$	−2.19866e16	−1.00032
$937$	−1.14822e16	−0.519347	−0.259673	−	0.965697i	$-0.583615\pi$
$937$	−1.14822e16	−0.519347	−0.259673	+	0.965697i	$0.583615\pi$
$938$	−7.32984e16	−3.29594
$939$	1.54442e16	0.690407
$940$	−1.05200e17	−4.67532
$941$	−3.44099e16	−1.52034	−0.760171	−	0.649724i	$-0.774885\pi$
$941$	−3.44099e16	−1.52034	−0.760171	+	0.649724i	$0.774885\pi$
$942$	3.13921e16	1.37893
$943$	−2.07684e15	−0.0906961
$944$	−5.69152e15	−0.247105
$945$	−1.15543e16	−0.498733
$946$	−4.87070e16	−2.09021
$947$	1.75216e16	0.747563	0.373782	−	0.927517i	$-0.378061\pi$
$947$	1.75216e16	0.747563	0.373782	+	0.927517i	$0.378061\pi$
$948$	−3.80431e16	−1.61373
$949$	2.95788e16	1.24743
$950$	−1.22185e17	−5.12317
$951$	−2.11710e16	−0.882570
$952$	−1.56358e16	−0.648062
$953$	2.42597e16	0.999713	0.499856	−	0.866108i	$-0.333386\pi$
$953$	2.42597e16	0.999713	0.499856	+	0.866108i	$0.333386\pi$
$954$	−1.76225e16	−0.722023
$955$	−1.80295e15	−0.0734455
$956$	5.26014e16	2.13049
$957$	2.37840e16	0.957787
$958$	7.29771e15	0.292197
$959$	−5.19691e15	−0.206892
$960$	3.69702e15	0.146339
$961$	−2.33771e16	−0.920053
$962$	−1.04615e17	−4.09382
$963$	−7.86048e15	−0.305847
$964$	7.41375e16	2.86823
$965$	8.63476e16	3.32162
$966$	−6.93753e16	−2.65357
$967$	−9.87645e15	−0.375626	−0.187813	−	0.982205i	$-0.560140\pi$
$967$	−9.87645e15	−0.375626	−0.187813	+	0.982205i	$0.560140\pi$
$968$	−1.97161e16	−0.745599
$969$	3.97471e15	0.149460
$970$	1.18686e17	4.43768
$971$	9.14735e15	0.340087	0.170043	−	0.985437i	$-0.445609\pi$
$971$	9.14735e15	0.340087	0.170043	+	0.985437i	$0.445609\pi$
$972$	−3.94643e15	−0.145895
$973$	−3.51596e16	−1.29248
$974$	9.83476e16	3.59492
$975$	−4.30530e16	−1.56487
$976$	1.46834e16	0.530704
$977$	−2.21369e16	−0.795603	−0.397801	−	0.917472i	$-0.630227\pi$
$977$	−2.21369e16	−0.795603	−0.397801	+	0.917472i	$0.630227\pi$
$978$	2.22009e16	0.793428
$979$	−8.85823e15	−0.314805
$980$	−1.33177e17	−4.70636
$981$	8.02394e15	0.281974
$982$	3.71331e16	1.29762
$983$	1.98996e16	0.691513	0.345756	−	0.938324i	$-0.387622\pi$
$983$	1.98996e16	0.691513	0.345756	+	0.938324i	$0.387622\pi$
$984$	−2.03040e15	−0.0701631
$985$	−5.81968e16	−1.99986
$986$	−1.45403e16	−0.496879
$987$	2.93623e16	0.997805
$988$	1.19078e17	4.02408
$989$	5.14178e16	1.72796
$990$	3.64523e16	1.21823
$991$	2.64736e16	0.879849	0.439925	−	0.898035i	$-0.355005\pi$
$991$	2.64736e16	0.879849	0.439925	+	0.898035i	$0.355005\pi$
$992$	−9.65610e15	−0.319145
$993$	−1.77843e16	−0.584542
$994$	−1.11768e17	−3.65337
$995$	8.47502e16	2.75495
$996$	−3.12958e16	−1.01172
$997$	3.83411e16	1.23265	0.616327	−	0.787491i	$-0.288620\pi$
$997$	3.83411e16	1.23265	0.616327	+	0.787491i	$0.288620\pi$
$998$	1.90203e15	0.0608133
$999$	−1.05211e16	−0.334541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.2	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-81.8884 q^{2} -243.000 q^{3} +4657.72 q^{4} -12268.5 q^{5} +19898.9 q^{6} -65634.7 q^{7} -213706. q^{8} +59049.0 q^{9} +1.00465e6 q^{10} +614467. q^{11} -1.13182e6 q^{12} +1.74232e6 q^{13} +5.37472e6 q^{14} +2.98124e6 q^{15} +7.96101e6 q^{16} -1.11473e6 q^{17} -4.83543e6 q^{18} +1.46733e7 q^{19} -5.71431e7 q^{20} +1.59492e7 q^{21} -5.03177e7 q^{22} +5.31182e7 q^{23} +5.19304e7 q^{24} +1.01688e8 q^{25} -1.42676e8 q^{26} -1.43489e7 q^{27} -3.05708e8 q^{28} -1.59287e8 q^{29} -2.44129e8 q^{30} +4.50702e7 q^{31} -2.14246e8 q^{32} -1.49315e8 q^{33} +9.12837e7 q^{34} +8.05238e8 q^{35} +2.75033e8 q^{36} +7.33231e8 q^{37} -1.20157e9 q^{38} -4.23385e8 q^{39} +2.62184e9 q^{40} -3.90985e7 q^{41} -1.30606e9 q^{42} +9.67989e8 q^{43} +2.86201e9 q^{44} -7.24442e8 q^{45} -4.34976e9 q^{46} +1.84099e9 q^{47} -1.93453e9 q^{48} +2.33058e9 q^{49} -8.32704e9 q^{50} +2.70880e8 q^{51} +8.11525e9 q^{52} +3.64445e9 q^{53} +1.17501e9 q^{54} -7.53858e9 q^{55} +1.40265e10 q^{56} -3.56561e9 q^{57} +1.30438e10 q^{58} -7.14924e8 q^{59} +1.38858e10 q^{60} +1.84441e9 q^{61} -3.69073e9 q^{62} -3.87566e9 q^{63} +1.24009e9 q^{64} -2.13757e10 q^{65} +1.22272e10 q^{66} -1.36376e10 q^{67} -5.19211e9 q^{68} -1.29077e10 q^{69} -6.59397e10 q^{70} -2.07952e10 q^{71} -1.26191e10 q^{72} +1.69766e10 q^{73} -6.00431e10 q^{74} -2.47101e10 q^{75} +6.83441e10 q^{76} -4.03303e10 q^{77} +3.46703e10 q^{78} +3.36122e10 q^{79} -9.76695e10 q^{80} +3.48678e9 q^{81} +3.20171e9 q^{82} +2.76507e10 q^{83} +7.42870e10 q^{84} +1.36761e10 q^{85} -7.92671e10 q^{86} +3.87067e10 q^{87} -1.31315e11 q^{88} -1.44161e10 q^{89} +5.93234e10 q^{90} -1.14357e11 q^{91} +2.47409e11 q^{92} -1.09521e10 q^{93} -1.50755e11 q^{94} -1.80019e11 q^{95} +5.20617e10 q^{96} +1.18137e11 q^{97} -1.90848e11 q^{98} +3.62837e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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