LMFDB - Embedded newform 177.12.a.c.1.12

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			1.12
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)

$f(q)$	$=$	$q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +96507.1 q^{10} +814898. q^{11} +470228. q^{12} +2.09899e6 q^{13} -612233. q^{14} +2.20704e6 q^{15} +3.51337e6 q^{16} -428820. q^{17} -627434. q^{18} +2.07408e7 q^{19} +1.75754e7 q^{20} -1.40013e7 q^{21} -8.65883e6 q^{22} -2.39961e7 q^{23} -1.02845e7 q^{24} +3.36629e7 q^{25} -2.23032e7 q^{26} -1.43489e7 q^{27} -1.11497e8 q^{28} +2.13616e8 q^{29} -2.34512e7 q^{30} +1.63056e8 q^{31} -1.24009e8 q^{32} -1.98020e8 q^{33} +4.55649e6 q^{34} -5.23316e8 q^{35} -1.14265e8 q^{36} +2.02526e8 q^{37} -2.20385e8 q^{38} -5.10055e8 q^{39} -3.84397e8 q^{40} -7.88296e8 q^{41} +1.48773e8 q^{42} +5.39420e8 q^{43} -1.57691e9 q^{44} -5.36310e8 q^{45} +2.54974e8 q^{46} +4.74636e8 q^{47} -8.53748e8 q^{48} +1.34255e9 q^{49} -3.57690e8 q^{50} +1.04203e8 q^{51} -4.06175e9 q^{52} +1.49336e9 q^{53} +1.52467e8 q^{54} -7.40128e9 q^{55} +2.43858e9 q^{56} -5.04003e9 q^{57} -2.26980e9 q^{58} -7.14924e8 q^{59} -4.27083e9 q^{60} +2.95600e9 q^{61} -1.73258e9 q^{62} +3.40231e9 q^{63} -5.87769e9 q^{64} -1.90640e10 q^{65} +2.10410e9 q^{66} +1.73111e10 q^{67} +8.29807e8 q^{68} +5.83105e9 q^{69} +5.56058e9 q^{70} +2.37102e10 q^{71} +2.49913e9 q^{72} +1.89758e10 q^{73} -2.15198e9 q^{74} -8.18008e9 q^{75} -4.01355e10 q^{76} +4.69531e10 q^{77} +5.41967e9 q^{78} +2.68055e10 q^{79} -3.19100e10 q^{80} +3.48678e9 q^{81} +8.37617e9 q^{82} +1.55416e10 q^{83} +2.70938e10 q^{84} +3.89474e9 q^{85} -5.73170e9 q^{86} -5.19086e10 q^{87} +3.44889e10 q^{88} -5.66575e10 q^{89} +5.69865e9 q^{90} +1.20940e11 q^{91} +4.64347e10 q^{92} -3.96226e10 q^{93} -5.04332e9 q^{94} -1.88378e11 q^{95} +3.01343e10 q^{96} -7.99557e10 q^{97} -1.42655e10 q^{98} +4.81189e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.6257	−0.234796	−0.117398	−	0.993085i	$-0.537455\pi$
$2$	−10.6257	−0.234796	−0.117398	+	0.993085i	$0.537455\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1935.10	−0.944871
$5$	−9082.46	−1.29978	−0.649888	−	0.760030i	$-0.725184\pi$
$5$	−9082.46	−1.29978	−0.649888	+	0.760030i	$0.725184\pi$
$6$	2582.03	0.135560
$7$	57618.4	1.29575	0.647876	−	0.761746i	$-0.275658\pi$
$7$	57618.4	1.29575	0.647876	+	0.761746i	$0.275658\pi$
$8$	42323.0	0.456648
$9$	59049.0	0.333333
$10$	96507.1	0.305182
$11$	814898.	1.52561	0.762805	−	0.646628i	$-0.223821\pi$
$11$	814898.	1.52561	0.762805	+	0.646628i	$0.223821\pi$
$12$	470228.	0.545521
$13$	2.09899e6	1.56791	0.783957	−	0.620815i	$-0.213198\pi$
$13$	2.09899e6	1.56791	0.783957	+	0.620815i	$0.213198\pi$
$14$	−612233.	−0.304237
$15$	2.20704e6	0.750426
$16$	3.51337e6	0.837652
$17$	−428820.	−0.0732496	−0.0366248	−	0.999329i	$-0.511661\pi$
$17$	−428820.	−0.0732496	−0.0366248	+	0.999329i	$0.511661\pi$
$18$	−627434.	−0.0782653
$19$	2.07408e7	1.92168	0.960841	−	0.277099i	$-0.0893731\pi$
$19$	2.07408e7	1.92168	0.960841	+	0.277099i	$0.0893731\pi$
$20$	1.75754e7	1.22812
$21$	−1.40013e7	−0.748102
$22$	−8.65883e6	−0.358207
$23$	−2.39961e7	−0.777387	−0.388693	−	0.921367i	$-0.627073\pi$
$23$	−2.39961e7	−0.777387	−0.388693	+	0.921367i	$0.627073\pi$
$24$	−1.02845e7	−0.263646
$25$	3.36629e7	0.689416
$26$	−2.23032e7	−0.368140
$27$	−1.43489e7	−0.192450
$28$	−1.11497e8	−1.22432
$29$	2.13616e8	1.93394	0.966972	−	0.254883i	$-0.0820371\pi$
$29$	2.13616e8	1.93394	0.966972	+	0.254883i	$0.0820371\pi$
$30$	−2.34512e7	−0.176197
$31$	1.63056e8	1.02293	0.511467	−	0.859303i	$-0.329102\pi$
$31$	1.63056e8	1.02293	0.511467	+	0.859303i	$0.329102\pi$
$32$	−1.24009e8	−0.653325
$33$	−1.98020e8	−0.880812
$34$	4.55649e6	0.0171987
$35$	−5.23316e8	−1.68419
$36$	−1.14265e8	−0.314957
$37$	2.02526e8	0.480145	0.240072	−	0.970755i	$-0.422829\pi$
$37$	2.02526e8	0.480145	0.240072	+	0.970755i	$0.422829\pi$
$38$	−2.20385e8	−0.451203
$39$	−5.10055e8	−0.905236
$40$	−3.84397e8	−0.593540
$41$	−7.88296e8	−1.06262	−0.531310	−	0.847177i	$-0.678300\pi$
$41$	−7.88296e8	−1.06262	−0.531310	+	0.847177i	$0.678300\pi$
$42$	1.48773e8	0.175651
$43$	5.39420e8	0.559565	0.279783	−	0.960063i	$-0.409738\pi$
$43$	5.39420e8	0.559565	0.279783	+	0.960063i	$0.409738\pi$
$44$	−1.57691e9	−1.44151
$45$	−5.36310e8	−0.433258
$46$	2.54974e8	0.182527
$47$	4.74636e8	0.301872	0.150936	−	0.988544i	$-0.451771\pi$
$47$	4.74636e8	0.301872	0.150936	+	0.988544i	$0.451771\pi$
$48$	−8.53748e8	−0.483618
$49$	1.34255e9	0.678972
$50$	−3.57690e8	−0.161872
$51$	1.04203e8	0.0422907
$52$	−4.06175e9	−1.48148
$53$	1.49336e9	0.490511	0.245255	−	0.969459i	$-0.421128\pi$
$53$	1.49336e9	0.490511	0.245255	+	0.969459i	$0.421128\pi$
$54$	1.52467e8	0.0451865
$55$	−7.40128e9	−1.98295
$56$	2.43858e9	0.591702
$57$	−5.04003e9	−1.10948
$58$	−2.26980e9	−0.454082
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−4.27083e9	−0.709055
$61$	2.95600e9	0.448117	0.224058	−	0.974576i	$-0.428069\pi$
$61$	2.95600e9	0.448117	0.224058	+	0.974576i	$0.428069\pi$
$62$	−1.73258e9	−0.240181
$63$	3.40231e9	0.431917
$64$	−5.87769e9	−0.684254
$65$	−1.90640e10	−2.03794
$66$	2.10410e9	0.206811
$67$	1.73111e10	1.56644	0.783218	−	0.621747i	$-0.213577\pi$
$67$	1.73111e10	1.56644	0.783218	+	0.621747i	$0.213577\pi$
$68$	8.29807e8	0.0692114
$69$	5.83105e9	0.448825
$70$	5.56058e9	0.395440
$71$	2.37102e10	1.55961	0.779803	−	0.626025i	$-0.215319\pi$
$71$	2.37102e10	1.55961	0.779803	+	0.626025i	$0.215319\pi$
$72$	2.49913e9	0.152216
$73$	1.89758e10	1.07133	0.535666	−	0.844430i	$-0.320061\pi$
$73$	1.89758e10	1.07133	0.535666	+	0.844430i	$0.320061\pi$
$74$	−2.15198e9	−0.112736
$75$	−8.18008e9	−0.398035
$76$	−4.01355e10	−1.81574
$77$	4.69531e10	1.97681
$78$	5.41967e9	0.212546
$79$	2.68055e10	0.980111	0.490055	−	0.871691i	$-0.336977\pi$
$79$	2.68055e10	0.980111	0.490055	+	0.871691i	$0.336977\pi$
$80$	−3.19100e10	−1.08876
$81$	3.48678e9	0.111111
$82$	8.37617e9	0.249499
$83$	1.55416e10	0.433079	0.216540	−	0.976274i	$-0.430523\pi$
$83$	1.55416e10	0.433079	0.216540	+	0.976274i	$0.430523\pi$
$84$	2.70938e10	0.706860
$85$	3.89474e9	0.0952081
$86$	−5.73170e9	−0.131384
$87$	−5.19086e10	−1.11656
$88$	3.44889e10	0.696667
$89$	−5.66575e10	−1.07550	−0.537752	−	0.843103i	$-0.680726\pi$
$89$	−5.66575e10	−1.07550	−0.537752	+	0.843103i	$0.680726\pi$
$90$	5.69865e9	0.101727
$91$	1.20940e11	2.03163
$92$	4.64347e10	0.734530
$93$	−3.96226e10	−0.590591
$94$	−5.04332e9	−0.0708782
$95$	−1.88378e11	−2.49776
$96$	3.01343e10	0.377197
$97$	−7.99557e10	−0.945377	−0.472688	−	0.881230i	$-0.656716\pi$
$97$	−7.99557e10	−0.945377	−0.472688	+	0.881230i	$0.656716\pi$
$98$	−1.42655e10	−0.159420
$99$	4.81189e10	0.508537
$100$	−6.51409e10	−0.651409
$101$	−1.15204e10	−0.109069	−0.0545345	−	0.998512i	$-0.517367\pi$
$101$	−1.15204e10	−0.109069	−0.0545345	+	0.998512i	$0.517367\pi$
$102$	−1.10723e9	−0.00992969
$103$	6.79276e9	0.0577353	0.0288677	−	0.999583i	$-0.490810\pi$
$103$	6.79276e9	0.0577353	0.0288677	+	0.999583i	$0.490810\pi$
$104$	8.88356e10	0.715985
$105$	1.27166e11	0.972365
$106$	−1.58680e10	−0.115170
$107$	−2.79927e9	−0.0192945	−0.00964726	−	0.999953i	$-0.503071\pi$
$107$	−2.79927e9	−0.0192945	−0.00964726	+	0.999953i	$0.503071\pi$
$108$	2.77665e10	0.181840
$109$	−1.89624e11	−1.18045	−0.590225	−	0.807239i	$-0.700961\pi$
$109$	−1.89624e11	−1.18045	−0.590225	+	0.807239i	$0.700961\pi$
$110$	7.86435e10	0.465589
$111$	−4.92139e10	−0.277212
$112$	2.02434e11	1.08539
$113$	−3.78979e11	−1.93501	−0.967507	−	0.252844i	$-0.918634\pi$
$113$	−3.78979e11	−1.93501	−0.967507	+	0.252844i	$0.918634\pi$
$114$	5.35536e10	0.260502
$115$	2.17943e11	1.01043
$116$	−4.13366e11	−1.82733
$117$	1.23943e11	0.522638
$118$	7.59654e9	0.0305678
$119$	−2.47079e10	−0.0949133
$120$	9.34084e10	0.342680
$121$	3.78748e11	1.32749
$122$	−3.14095e10	−0.105216
$123$	1.91556e11	0.613505
$124$	−3.15529e11	−0.966541
$125$	1.37738e11	0.403689
$126$	−3.61517e10	−0.101412
$127$	−5.74444e11	−1.54286	−0.771431	−	0.636313i	$-0.780459\pi$
$127$	−5.74444e11	−1.54286	−0.771431	+	0.636313i	$0.780459\pi$
$128$	3.16425e11	0.813985
$129$	−1.31079e11	−0.323065
$130$	2.02567e11	0.478499
$131$	−3.55520e11	−0.805142	−0.402571	−	0.915389i	$-0.631883\pi$
$131$	−3.55520e11	−0.805142	−0.402571	+	0.915389i	$0.631883\pi$
$132$	3.83188e11	0.832253
$133$	1.19505e12	2.49002
$134$	−1.83942e11	−0.367793
$135$	1.30323e11	0.250142
$136$	−1.81489e10	−0.0334493
$137$	4.73661e11	0.838502	0.419251	−	0.907870i	$-0.362293\pi$
$137$	4.73661e11	0.838502	0.419251	+	0.907870i	$0.362293\pi$
$138$	−6.19587e10	−0.105382
$139$	8.42358e11	1.37694	0.688470	−	0.725265i	$-0.258283\pi$
$139$	8.42358e11	1.37694	0.688470	+	0.725265i	$0.258283\pi$
$140$	1.01267e12	1.59134
$141$	−1.15336e11	−0.174286
$142$	−2.51937e11	−0.366189
$143$	1.71046e12	2.39203
$144$	2.07461e11	0.279217
$145$	−1.94015e12	−2.51369
$146$	−2.01630e11	−0.251544
$147$	−3.26239e11	−0.392004
$148$	−3.91908e11	−0.453675
$149$	8.19778e11	0.914474	0.457237	−	0.889345i	$-0.348839\pi$
$149$	8.19778e11	0.914474	0.457237	+	0.889345i	$0.348839\pi$
$150$	8.69188e10	0.0934569
$151$	−1.77194e12	−1.83686	−0.918431	−	0.395580i	$-0.870543\pi$
$151$	−1.77194e12	−1.83686	−0.918431	+	0.395580i	$0.870543\pi$
$152$	8.77815e11	0.877532
$153$	−2.53214e10	−0.0244165
$154$	−4.98908e11	−0.464148
$155$	−1.48095e12	−1.32958
$156$	9.87005e11	0.855331
$157$	1.14069e12	0.954376	0.477188	−	0.878801i	$-0.341656\pi$
$157$	1.14069e12	0.954376	0.477188	+	0.878801i	$0.341656\pi$
$158$	−2.84826e11	−0.230126
$159$	−3.62888e11	−0.283196
$160$	1.12631e12	0.849176
$161$	−1.38261e12	−1.00730
$162$	−3.70494e10	−0.0260884
$163$	−1.12504e12	−0.765837	−0.382919	−	0.923782i	$-0.625081\pi$
$163$	−1.12504e12	−0.765837	−0.382919	+	0.923782i	$0.625081\pi$
$164$	1.52543e12	1.00404
$165$	1.79851e12	1.14486
$166$	−1.65140e11	−0.101685
$167$	1.15989e12	0.690995	0.345498	−	0.938420i	$-0.387710\pi$
$167$	1.15989e12	0.690995	0.345498	+	0.938420i	$0.387710\pi$
$168$	−5.92575e11	−0.341619
$169$	2.61360e12	1.45835
$170$	−4.13841e10	−0.0223545
$171$	1.22473e12	0.640561
$172$	−1.04383e12	−0.528717
$173$	6.58060e11	0.322859	0.161429	−	0.986884i	$-0.448390\pi$
$173$	6.58060e11	0.322859	0.161429	+	0.986884i	$0.448390\pi$
$174$	5.51563e11	0.262165
$175$	1.93960e12	0.893312
$176$	2.86304e12	1.27793
$177$	1.73727e11	0.0751646
$178$	6.02023e11	0.252524
$179$	9.77714e11	0.397667	0.198834	−	0.980033i	$-0.436285\pi$
$179$	9.77714e11	0.397667	0.198834	+	0.980033i	$0.436285\pi$
$180$	1.03781e12	0.409373
$181$	−1.86516e12	−0.713646	−0.356823	−	0.934172i	$-0.616140\pi$
$181$	−1.86516e12	−0.713646	−0.356823	+	0.934172i	$0.616140\pi$
$182$	−1.28507e12	−0.477018
$183$	−7.18309e11	−0.258720
$184$	−1.01559e12	−0.354992
$185$	−1.83944e12	−0.624080
$186$	4.21016e11	0.138669
$187$	−3.49444e11	−0.111750
$188$	−9.18465e11	−0.285230
$189$	−8.26760e11	−0.249367
$190$	2.00164e12	0.586463
$191$	−5.90311e12	−1.68034	−0.840171	−	0.542322i	$-0.817545\pi$
$191$	−5.90311e12	−1.68034	−0.840171	+	0.542322i	$0.817545\pi$
$192$	1.42828e12	0.395054
$193$	2.99243e12	0.804376	0.402188	−	0.915557i	$-0.368250\pi$
$193$	2.99243e12	0.804376	0.402188	+	0.915557i	$0.368250\pi$
$194$	8.49582e11	0.221971
$195$	4.63255e12	1.17660
$196$	−2.59796e12	−0.641540
$197$	3.54798e12	0.851955	0.425977	−	0.904734i	$-0.359930\pi$
$197$	3.54798e12	0.851955	0.425977	+	0.904734i	$0.359930\pi$
$198$	−5.11295e11	−0.119402
$199$	−7.86492e12	−1.78650	−0.893248	−	0.449564i	$-0.851579\pi$
$199$	−7.86492e12	−1.78650	−0.893248	+	0.449564i	$0.851579\pi$
$200$	1.42471e12	0.314820
$201$	−4.20659e12	−0.904382
$202$	1.22412e11	0.0256089
$203$	1.23082e13	2.50591
$204$	−2.01643e11	−0.0399592
$205$	7.15967e12	1.38117
$206$	−7.21776e10	−0.0135560
$207$	−1.41694e12	−0.259129
$208$	7.37453e12	1.31337
$209$	1.69017e13	2.93174
$210$	−1.35122e12	−0.228307
$211$	−2.88185e12	−0.474371	−0.237186	−	0.971464i	$-0.576225\pi$
$211$	−2.88185e12	−0.474371	−0.237186	+	0.971464i	$0.576225\pi$
$212$	−2.88980e12	−0.463469
$213$	−5.76158e12	−0.900438
$214$	2.97441e10	0.00453028
$215$	−4.89926e12	−0.727309
$216$	−6.07289e11	−0.0878819
$217$	9.39503e12	1.32547
$218$	2.01488e12	0.277165
$219$	−4.61111e12	−0.618534
$220$	1.43222e13	1.87363
$221$	−9.00089e11	−0.114849
$222$	5.22930e11	0.0650882
$223$	−6.94038e12	−0.842764	−0.421382	−	0.906883i	$-0.638455\pi$
$223$	−6.94038e12	−0.842764	−0.421382	+	0.906883i	$0.638455\pi$
$224$	−7.14521e12	−0.846547
$225$	1.98776e12	0.229805
$226$	4.02690e12	0.454334
$227$	1.00179e13	1.10315	0.551576	−	0.834125i	$-0.314027\pi$
$227$	1.00179e13	1.10315	0.551576	+	0.834125i	$0.314027\pi$
$228$	9.75293e12	1.04832
$229$	3.77275e12	0.395879	0.197939	−	0.980214i	$-0.436575\pi$
$229$	3.77275e12	0.395879	0.197939	+	0.980214i	$0.436575\pi$
$230$	−2.31579e12	−0.237245
$231$	−1.14096e13	−1.14131
$232$	9.04085e12	0.883131
$233$	1.02994e13	0.982552	0.491276	−	0.871004i	$-0.336531\pi$
$233$	1.02994e13	0.982552	0.491276	+	0.871004i	$0.336531\pi$
$234$	−1.31698e12	−0.122713
$235$	−4.31086e12	−0.392365
$236$	1.38345e12	0.123012
$237$	−6.51374e12	−0.565867
$238$	2.62537e11	0.0222853
$239$	−2.28705e13	−1.89709	−0.948543	−	0.316650i	$-0.897442\pi$
$239$	−2.28705e13	−1.89709	−0.948543	+	0.316650i	$0.897442\pi$
$240$	7.75413e12	0.628595
$241$	−7.49749e11	−0.0594049	−0.0297024	−	0.999559i	$-0.509456\pi$
$241$	−7.49749e11	−0.0594049	−0.0297024	+	0.999559i	$0.509456\pi$
$242$	−4.02444e12	−0.311689
$243$	−8.47289e11	−0.0641500
$244$	−5.72015e12	−0.423412
$245$	−1.21936e13	−0.882511
$246$	−2.03541e12	−0.144048
$247$	4.35349e13	3.01303
$248$	6.90102e12	0.467121
$249$	−3.77662e12	−0.250038
$250$	−1.46355e12	−0.0947846
$251$	−9.91526e12	−0.628201	−0.314101	−	0.949390i	$-0.601703\pi$
$251$	−9.91526e12	−0.628201	−0.314101	+	0.949390i	$0.601703\pi$
$252$	−6.58379e12	−0.408106
$253$	−1.95544e13	−1.18599
$254$	6.10384e12	0.362258
$255$	−9.46421e11	−0.0549684
$256$	8.67529e12	0.493133
$257$	1.74196e13	0.969186	0.484593	−	0.874740i	$-0.338968\pi$
$257$	1.74196e13	0.969186	0.484593	+	0.874740i	$0.338968\pi$
$258$	1.39280e12	0.0758544
$259$	1.16692e13	0.622148
$260$	3.68907e13	1.92559
$261$	1.26138e13	0.644648
$262$	3.77764e12	0.189044
$263$	−1.75510e13	−0.860093	−0.430047	−	0.902807i	$-0.641503\pi$
$263$	−1.75510e13	−0.860093	−0.430047	+	0.902807i	$0.641503\pi$
$264$	−8.38081e12	−0.402221
$265$	−1.35634e13	−0.637554
$266$	−1.26982e13	−0.584647
$267$	1.37678e13	0.620943
$268$	−3.34986e13	−1.48008
$269$	1.86255e13	0.806250	0.403125	−	0.915145i	$-0.367924\pi$
$269$	1.86255e13	0.806250	0.403125	+	0.915145i	$0.367924\pi$
$270$	−1.38477e12	−0.0587323
$271$	4.14769e13	1.72375	0.861877	−	0.507117i	$-0.169289\pi$
$271$	4.14769e13	1.72375	0.861877	+	0.507117i	$0.169289\pi$
$272$	−1.50660e12	−0.0613577
$273$	−2.93885e13	−1.17296
$274$	−5.03295e12	−0.196877
$275$	2.74318e13	1.05178
$276$	−1.12836e13	−0.424081
$277$	−1.00078e13	−0.368721	−0.184361	−	0.982859i	$-0.559021\pi$
$277$	−1.00078e13	−0.368721	−0.184361	+	0.982859i	$0.559021\pi$
$278$	−8.95060e12	−0.323300
$279$	9.62830e12	0.340978
$280$	−2.21483e13	−0.769080
$281$	2.85559e12	0.0972325	0.0486163	−	0.998818i	$-0.484519\pi$
$281$	2.85559e12	0.0972325	0.0486163	+	0.998818i	$0.484519\pi$
$282$	1.22553e12	0.0409216
$283$	3.51199e13	1.15008	0.575040	−	0.818125i	$-0.304986\pi$
$283$	3.51199e13	1.15008	0.575040	+	0.818125i	$0.304986\pi$
$284$	−4.58815e13	−1.47363
$285$	4.57758e13	1.44208
$286$	−1.81748e13	−0.561638
$287$	−4.54204e13	−1.37689
$288$	−7.32263e12	−0.217775
$289$	−3.40880e13	−0.994634
$290$	2.06154e13	0.590205
$291$	1.94292e13	0.545813
$292$	−3.67199e13	−1.01227
$293$	−8.00808e11	−0.0216649	−0.0108324	−	0.999941i	$-0.503448\pi$
$293$	−8.00808e11	−0.0216649	−0.0108324	+	0.999941i	$0.503448\pi$
$294$	3.46651e12	0.0920411
$295$	6.49327e12	0.169216
$296$	8.57153e12	0.219257
$297$	−1.16929e13	−0.293604
$298$	−8.71067e12	−0.214715
$299$	−5.03676e13	−1.21888
$300$	1.58292e13	0.376091
$301$	3.10805e13	0.725058
$302$	1.88281e13	0.431288
$303$	2.79946e12	0.0629710
$304$	7.28702e13	1.60970
$305$	−2.68478e13	−0.582451
$306$	2.69056e11	0.00573291
$307$	−3.85316e13	−0.806410	−0.403205	−	0.915110i	$-0.632104\pi$
$307$	−3.85316e13	−0.806410	−0.403205	+	0.915110i	$0.632104\pi$
$308$	−9.08588e13	−1.86783
$309$	−1.65064e12	−0.0333335
$310$	1.57361e13	0.312181
$311$	−4.84093e13	−0.943510	−0.471755	−	0.881730i	$-0.656379\pi$
$311$	−4.84093e13	−0.943510	−0.471755	+	0.881730i	$0.656379\pi$
$312$	−2.15871e13	−0.413374
$313$	2.56504e13	0.482615	0.241307	−	0.970449i	$-0.422424\pi$
$313$	2.56504e13	0.482615	0.241307	+	0.970449i	$0.422424\pi$
$314$	−1.21206e13	−0.224084
$315$	−3.09013e13	−0.561395
$316$	−5.18712e13	−0.926078
$317$	−9.07687e13	−1.59261	−0.796307	−	0.604893i	$-0.793216\pi$
$317$	−9.07687e13	−1.59261	−0.796307	+	0.604893i	$0.793216\pi$
$318$	3.85592e12	0.0664934
$319$	1.74075e14	2.95045
$320$	5.33839e13	0.889376
$321$	6.80223e11	0.0111397
$322$	1.46912e13	0.236510
$323$	−8.89408e12	−0.140763
$324$	−6.74726e12	−0.104986
$325$	7.06581e13	1.08095
$326$	1.19543e13	0.179816
$327$	4.60787e13	0.681533
$328$	−3.33631e13	−0.485244
$329$	2.73477e13	0.391151
$330$	−1.91104e13	−0.268808
$331$	6.45071e13	0.892387	0.446194	−	0.894936i	$-0.352779\pi$
$331$	6.45071e13	0.892387	0.446194	+	0.894936i	$0.352779\pi$
$332$	−3.00745e13	−0.409204
$333$	1.19590e13	0.160048
$334$	−1.23246e13	−0.162243
$335$	−1.57227e14	−2.03602
$336$	−4.91916e13	−0.626649
$337$	−1.01245e14	−1.26884	−0.634422	−	0.772987i	$-0.718762\pi$
$337$	−1.01245e14	−1.26884	−0.634422	+	0.772987i	$0.718762\pi$
$338$	−2.77713e13	−0.342416
$339$	9.20920e13	1.11718
$340$	−7.53668e12	−0.0899593
$341$	1.32874e14	1.56060
$342$	−1.30135e13	−0.150401
$343$	−3.65749e13	−0.415973
$344$	2.28299e13	0.255524
$345$	−5.29602e13	−0.583371
$346$	−6.99232e12	−0.0758059
$347$	−8.83024e13	−0.942238	−0.471119	−	0.882070i	$-0.656150\pi$
$347$	−8.83024e13	−0.942238	−0.471119	+	0.882070i	$0.656150\pi$
$348$	1.00448e14	1.05501
$349$	−8.87236e13	−0.917275	−0.458637	−	0.888624i	$-0.651662\pi$
$349$	−8.87236e13	−0.917275	−0.458637	+	0.888624i	$0.651662\pi$
$350$	−2.06095e13	−0.209746
$351$	−3.01182e13	−0.301745
$352$	−1.01055e14	−0.996720
$353$	−9.74142e13	−0.945936	−0.472968	−	0.881080i	$-0.656817\pi$
$353$	−9.74142e13	−0.945936	−0.472968	+	0.881080i	$0.656817\pi$
$354$	−1.84596e12	−0.0176483
$355$	−2.15347e14	−2.02714
$356$	1.09638e14	1.01621
$357$	6.00401e12	0.0547982
$358$	−1.03888e13	−0.0933707
$359$	−1.64288e14	−1.45407	−0.727035	−	0.686600i	$-0.759102\pi$
$359$	−1.64288e14	−1.45407	−0.727035	+	0.686600i	$0.759102\pi$
$360$	−2.26982e13	−0.197847
$361$	3.13692e14	2.69286
$362$	1.98185e13	0.167561
$363$	−9.20357e13	−0.766426
$364$	−2.34031e14	−1.91962
$365$	−1.72347e14	−1.39249
$366$	7.63250e12	0.0607465
$367$	−9.07931e13	−0.711852	−0.355926	−	0.934514i	$-0.615834\pi$
$367$	−9.07931e13	−0.711852	−0.355926	+	0.934514i	$0.615834\pi$
$368$	−8.43070e13	−0.651179
$369$	−4.65481e13	−0.354207
$370$	1.95452e13	0.146532
$371$	8.60452e13	0.635580
$372$	7.66736e13	0.558033
$373$	2.01891e14	1.44783	0.723917	−	0.689887i	$-0.242340\pi$
$373$	2.01891e14	1.44783	0.723917	+	0.689887i	$0.242340\pi$
$374$	3.71308e12	0.0262386
$375$	−3.34702e13	−0.233070
$376$	2.00880e13	0.137849
$377$	4.48377e14	3.03226
$378$	8.78487e12	0.0585505
$379$	−1.71894e13	−0.112913	−0.0564566	−	0.998405i	$-0.517980\pi$
$379$	−1.71894e13	−0.112913	−0.0564566	+	0.998405i	$0.517980\pi$
$380$	3.64529e14	2.36006
$381$	1.39590e14	0.890772
$382$	6.27244e13	0.394537
$383$	−4.50671e13	−0.279426	−0.139713	−	0.990192i	$-0.544618\pi$
$383$	−4.50671e13	−0.279426	−0.139713	+	0.990192i	$0.544618\pi$
$384$	−7.68914e13	−0.469955
$385$	−4.26450e14	−2.56941
$386$	−3.17966e13	−0.188864
$387$	3.18522e13	0.186522
$388$	1.54722e14	0.893259
$389$	−2.49811e14	−1.42196	−0.710982	−	0.703210i	$-0.751749\pi$
$389$	−2.49811e14	−1.42196	−0.710982	+	0.703210i	$0.751749\pi$
$390$	−4.92239e13	−0.276262
$391$	1.02900e13	0.0569433
$392$	5.68207e13	0.310051
$393$	8.63915e13	0.464849
$394$	−3.76996e13	−0.200036
$395$	−2.43460e14	−1.27392
$396$	−9.31147e13	−0.480502
$397$	−2.26483e14	−1.15262	−0.576311	−	0.817230i	$-0.695508\pi$
$397$	−2.26483e14	−1.15262	−0.576311	+	0.817230i	$0.695508\pi$
$398$	8.35699e13	0.419462
$399$	−2.90398e14	−1.43762
$400$	1.18270e14	0.577491
$401$	9.58388e13	0.461580	0.230790	−	0.973004i	$-0.425869\pi$
$401$	9.58388e13	0.461580	0.230790	+	0.973004i	$0.425869\pi$
$402$	4.46978e13	0.212345
$403$	3.42253e14	1.60387
$404$	2.22931e13	0.103056
$405$	−3.16686e13	−0.144419
$406$	−1.30782e14	−0.588378
$407$	1.65039e14	0.732514
$408$	4.41019e12	0.0193120
$409$	3.12553e14	1.35035	0.675174	−	0.737658i	$-0.264069\pi$
$409$	3.12553e14	1.35035	0.675174	+	0.737658i	$0.264069\pi$
$410$	−7.60762e13	−0.324293
$411$	−1.15100e14	−0.484109
$412$	−1.31446e13	−0.0545524
$413$	−4.11928e13	−0.168692
$414$	1.50560e13	0.0608425
$415$	−1.41156e14	−0.562906
$416$	−2.60294e14	−1.02436
$417$	−2.04693e14	−0.794977
$418$	−1.79591e14	−0.688361
$419$	−1.31239e14	−0.496462	−0.248231	−	0.968701i	$-0.579849\pi$
$419$	−1.31239e14	−0.496462	−0.248231	+	0.968701i	$0.579849\pi$
$420$	−2.46078e14	−0.918759
$421$	2.15819e14	0.795311	0.397656	−	0.917535i	$-0.369824\pi$
$421$	2.15819e14	0.795311	0.397656	+	0.917535i	$0.369824\pi$
$422$	3.06216e13	0.111380
$423$	2.80268e13	0.100624
$424$	6.32037e13	0.223991
$425$	−1.44353e13	−0.0504995
$426$	6.12206e13	0.211419
$427$	1.70320e14	0.580648
$428$	5.41685e12	0.0182308
$429$	−4.15643e14	−1.38104
$430$	5.20579e13	0.170769
$431$	1.68529e14	0.545820	0.272910	−	0.962040i	$-0.412014\pi$
$431$	1.68529e14	0.545820	0.272910	+	0.962040i	$0.412014\pi$
$432$	−5.04130e13	−0.161206
$433$	−2.96714e14	−0.936816	−0.468408	−	0.883512i	$-0.655172\pi$
$433$	−2.96714e14	−0.936816	−0.468408	+	0.883512i	$0.655172\pi$
$434$	−9.98283e13	−0.311215
$435$	4.71457e14	1.45128
$436$	3.66941e14	1.11537
$437$	−4.97699e14	−1.49389
$438$	4.89961e13	0.145229
$439$	1.22210e14	0.357728	0.178864	−	0.983874i	$-0.442758\pi$
$439$	1.22210e14	0.357728	0.178864	+	0.983874i	$0.442758\pi$
$440$	−3.13244e14	−0.905511
$441$	7.92762e13	0.226324
$442$	9.56403e12	0.0269661
$443$	3.82613e14	1.06546	0.532732	−	0.846284i	$-0.321165\pi$
$443$	3.82613e14	1.06546	0.532732	+	0.846284i	$0.321165\pi$
$444$	9.52337e13	0.261929
$445$	5.14589e14	1.39791
$446$	7.37460e13	0.197878
$447$	−1.99206e14	−0.527972
$448$	−3.38663e14	−0.886622
$449$	−6.61570e13	−0.171088	−0.0855442	−	0.996334i	$-0.527263\pi$
$449$	−6.61570e13	−0.171088	−0.0855442	+	0.996334i	$0.527263\pi$
$450$	−2.11213e13	−0.0539574
$451$	−6.42382e14	−1.62115
$452$	7.33361e14	1.82834
$453$	4.30582e14	1.06051
$454$	−1.06447e14	−0.259016
$455$	−1.09844e15	−2.64066
$456$	−2.13309e14	−0.506644
$457$	7.89022e14	1.85161	0.925806	−	0.377999i	$-0.123388\pi$
$457$	7.89022e14	1.85161	0.925806	+	0.377999i	$0.123388\pi$
$458$	−4.00879e13	−0.0929508
$459$	6.15309e12	0.0140969
$460$	−4.21741e14	−0.954724
$461$	6.71616e14	1.50233	0.751167	−	0.660113i	$-0.229491\pi$
$461$	6.71616e14	1.50233	0.751167	+	0.660113i	$0.229491\pi$
$462$	1.21235e14	0.267976
$463$	−3.32485e14	−0.726234	−0.363117	−	0.931744i	$-0.618287\pi$
$463$	−3.32485e14	−0.726234	−0.363117	+	0.931744i	$0.618287\pi$
$464$	7.50509e14	1.61997
$465$	3.59871e14	0.767636
$466$	−1.09438e14	−0.230699
$467$	−7.51124e14	−1.56484	−0.782418	−	0.622754i	$-0.786014\pi$
$467$	−7.51124e14	−1.56484	−0.782418	+	0.622754i	$0.786014\pi$
$468$	−2.39842e14	−0.493825
$469$	9.97436e14	2.02971
$470$	4.58057e13	0.0921258
$471$	−2.77188e14	−0.551010
$472$	−3.02577e13	−0.0594505
$473$	4.39573e14	0.853679
$474$	6.92128e13	0.132863
$475$	6.98197e14	1.32484
$476$	4.78121e13	0.0896808
$477$	8.81817e13	0.163504
$478$	2.43014e14	0.445428
$479$	−3.43615e14	−0.622625	−0.311312	−	0.950308i	$-0.600769\pi$
$479$	−3.43615e14	−0.622625	−0.311312	+	0.950308i	$0.600769\pi$
$480$	−2.73693e14	−0.490272
$481$	4.25101e14	0.752826
$482$	7.96657e12	0.0139480
$483$	3.35975e14	0.581565
$484$	−7.32913e14	−1.25430
$485$	7.26194e14	1.22878
$486$	9.00300e12	0.0150622
$487$	−4.61203e14	−0.762926	−0.381463	−	0.924384i	$-0.624580\pi$
$487$	−4.61203e14	−0.762926	−0.381463	+	0.924384i	$0.624580\pi$
$488$	1.25107e14	0.204631
$489$	2.73385e14	0.442156
$490$	1.29565e14	0.207210
$491$	−1.06056e15	−1.67721	−0.838604	−	0.544742i	$-0.816628\pi$
$491$	−1.06056e15	−1.67721	−0.838604	+	0.544742i	$0.816628\pi$
$492$	−3.70679e14	−0.579683
$493$	−9.16025e13	−0.141661
$494$	−4.62586e14	−0.707448
$495$	−4.37038e14	−0.660984
$496$	5.72876e14	0.856863
$497$	1.36614e15	2.02086
$498$	4.01290e13	0.0587080
$499$	−9.38857e13	−0.135846	−0.0679229	−	0.997691i	$-0.521637\pi$
$499$	−9.38857e13	−0.135846	−0.0679229	+	0.997691i	$0.521637\pi$
$500$	−2.66535e14	−0.381434
$501$	−2.81853e14	−0.398946
$502$	1.05356e14	0.147499
$503$	−1.60080e14	−0.221673	−0.110836	−	0.993839i	$-0.535353\pi$
$503$	−1.60080e14	−0.221673	−0.110836	+	0.993839i	$0.535353\pi$
$504$	1.43996e14	0.197234
$505$	1.04634e14	0.141765
$506$	2.07778e14	0.278466
$507$	−6.35106e14	−0.841981
$508$	1.11160e15	1.45781
$509$	−6.92627e14	−0.898569	−0.449284	−	0.893389i	$-0.648321\pi$
$509$	−6.92627e14	−0.898569	−0.449284	+	0.893389i	$0.648321\pi$
$510$	1.00563e13	0.0129064
$511$	1.09335e15	1.38818
$512$	−7.40220e14	−0.929771
$513$	−2.97608e14	−0.369828
$514$	−1.85095e14	−0.227561
$515$	−6.16950e13	−0.0750430
$516$	2.53651e14	0.305255
$517$	3.86780e14	0.460539
$518$	−1.23993e14	−0.146078
$519$	−1.59909e14	−0.186402
$520$	−8.06846e14	−0.930619
$521$	−3.38413e14	−0.386224	−0.193112	−	0.981177i	$-0.561858\pi$
$521$	−3.38413e14	−0.386224	−0.193112	+	0.981177i	$0.561858\pi$
$522$	−1.34030e14	−0.151361
$523$	4.64109e14	0.518634	0.259317	−	0.965792i	$-0.416503\pi$
$523$	4.64109e14	0.518634	0.259317	+	0.965792i	$0.416503\pi$
$524$	6.87966e14	0.760755
$525$	−4.71323e14	−0.515754
$526$	1.86491e14	0.201946
$527$	−6.99216e13	−0.0749296
$528$	−6.95718e14	−0.737813
$529$	−3.76998e14	−0.395670
$530$	1.44120e14	0.149695
$531$	−4.22156e13	−0.0433963
$532$	−2.31254e15	−2.35275
$533$	−1.65463e15	−1.66610
$534$	−1.46292e14	−0.145795
$535$	2.54242e13	0.0250785
$536$	7.32657e14	0.715310
$537$	−2.37584e14	−0.229593
$538$	−1.97908e14	−0.189304
$539$	1.09404e15	1.03585
$540$	−2.52188e14	−0.236352
$541$	1.77314e15	1.64497	0.822485	−	0.568787i	$-0.192587\pi$
$541$	1.77314e15	1.64497	0.822485	+	0.568787i	$0.192587\pi$
$542$	−4.40720e14	−0.404731
$543$	4.53233e14	0.412024
$544$	5.31776e13	0.0478558
$545$	1.72225e15	1.53432
$546$	3.12272e14	0.275406
$547$	3.74364e14	0.326861	0.163431	−	0.986555i	$-0.447744\pi$
$547$	3.74364e14	0.326861	0.163431	+	0.986555i	$0.447744\pi$
$548$	−9.16578e14	−0.792276
$549$	1.74549e14	0.149372
$550$	−2.91481e14	−0.246954
$551$	4.43057e15	3.71643
$552$	2.46787e14	0.204955
$553$	1.54449e15	1.26998
$554$	1.06339e14	0.0865742
$555$	4.46983e14	0.360313
$556$	−1.63004e15	−1.30103
$557$	−1.23516e15	−0.976153	−0.488077	−	0.872801i	$-0.662301\pi$
$557$	−1.23516e15	−0.976153	−0.488077	+	0.872801i	$0.662301\pi$
$558$	−1.02307e14	−0.0800603
$559$	1.13224e15	0.877350
$560$	−1.83860e15	−1.41076
$561$	8.49150e13	0.0645191
$562$	−3.03425e13	−0.0228298
$563$	1.76993e15	1.31874	0.659370	−	0.751818i	$-0.270823\pi$
$563$	1.76993e15	1.31874	0.659370	+	0.751818i	$0.270823\pi$
$564$	2.23187e14	0.164677
$565$	3.44206e15	2.51508
$566$	−3.73172e14	−0.270034
$567$	2.00903e14	0.143972
$568$	1.00349e15	0.712190
$569$	7.58600e13	0.0533206	0.0266603	−	0.999645i	$-0.491513\pi$
$569$	7.58600e13	0.0533206	0.0266603	+	0.999645i	$0.491513\pi$
$570$	−4.86398e14	−0.338595
$571$	9.69490e14	0.668413	0.334206	−	0.942500i	$-0.391532\pi$
$571$	9.69490e14	0.668413	0.334206	+	0.942500i	$0.391532\pi$
$572$	−3.30991e15	−2.26016
$573$	1.43446e15	0.970146
$574$	4.82621e14	0.323289
$575$	−8.07778e14	−0.535943
$576$	−3.47072e14	−0.228085
$577$	9.50265e14	0.618554	0.309277	−	0.950972i	$-0.399913\pi$
$577$	9.50265e14	0.618554	0.309277	+	0.950972i	$0.399913\pi$
$578$	3.62207e14	0.233536
$579$	−7.27161e14	−0.464407
$580$	3.75438e15	2.37511
$581$	8.95484e14	0.561163
$582$	−2.06448e14	−0.128155
$583$	1.21694e15	0.748328
$584$	8.03112e14	0.489221
$585$	−1.12571e15	−0.679312
$586$	8.50911e12	0.00508683
$587$	9.57183e14	0.566872	0.283436	−	0.958991i	$-0.408526\pi$
$587$	9.57183e14	0.566872	0.283436	+	0.958991i	$0.408526\pi$
$588$	6.31304e14	0.370394
$589$	3.38192e15	1.96576
$590$	−6.89952e13	−0.0397313
$591$	−8.62159e14	−0.491876
$592$	7.11550e14	0.402194
$593$	−1.68405e15	−0.943091	−0.471546	−	0.881842i	$-0.656304\pi$
$593$	−1.68405e15	−0.943091	−0.471546	+	0.881842i	$0.656304\pi$
$594$	1.24245e14	0.0689370
$595$	2.24408e14	0.123366
$596$	−1.58635e15	−0.864060
$597$	1.91117e15	1.03143
$598$	5.35188e14	0.286187
$599$	1.09435e15	0.579840	0.289920	−	0.957051i	$-0.406371\pi$
$599$	1.09435e15	0.579840	0.289920	+	0.957051i	$0.406371\pi$
$600$	−3.46206e14	−0.181762
$601$	−3.67077e15	−1.90962	−0.954812	−	0.297211i	$-0.903944\pi$
$601$	−3.67077e15	−1.90962	−0.954812	+	0.297211i	$0.903944\pi$
$602$	−3.30251e14	−0.170241
$603$	1.02220e15	0.522145
$604$	3.42888e15	1.73560
$605$	−3.43996e15	−1.72544
$606$	−2.97461e13	−0.0147853
$607$	8.87977e14	0.437385	0.218693	−	0.975794i	$-0.429821\pi$
$607$	8.87977e14	0.437385	0.218693	+	0.975794i	$0.429821\pi$
$608$	−2.57206e15	−1.25548
$609$	−2.99089e15	−1.44679
$610$	2.85275e14	0.136757
$611$	9.96256e14	0.473309
$612$	4.89993e13	0.0230705
$613$	1.31161e15	0.612031	0.306015	−	0.952027i	$-0.401004\pi$
$613$	1.31161e15	0.612031	0.306015	+	0.952027i	$0.401004\pi$
$614$	4.09423e14	0.189342
$615$	−1.73980e15	−0.797418
$616$	1.98720e15	0.902707
$617$	2.24011e14	0.100856	0.0504280	−	0.998728i	$-0.483941\pi$
$617$	2.24011e14	0.100856	0.0504280	+	0.998728i	$0.483941\pi$
$618$	1.75391e13	0.00782658
$619$	1.97391e15	0.873031	0.436515	−	0.899697i	$-0.356212\pi$
$619$	1.97391e15	0.873031	0.436515	+	0.899697i	$0.356212\pi$
$620$	2.86578e15	1.25629
$621$	3.44318e14	0.149608
$622$	5.14380e14	0.221532
$623$	−3.26451e15	−1.39359
$624$	−1.79201e15	−0.758272
$625$	−2.89469e15	−1.21412
$626$	−2.72552e14	−0.113316
$627$	−4.10711e15	−1.69264
$628$	−2.20734e15	−0.901762
$629$	−8.68473e13	−0.0351704
$630$	3.28347e14	0.131813
$631$	3.02278e15	1.20294	0.601471	−	0.798895i	$-0.294582\pi$
$631$	3.02278e15	1.20294	0.601471	+	0.798895i	$0.294582\pi$
$632$	1.13449e15	0.447566
$633$	7.00290e14	0.273878
$634$	9.64477e14	0.373939
$635$	5.21736e15	2.00538
$636$	7.02222e14	0.267584
$637$	2.81800e15	1.06457
$638$	−1.84966e15	−0.692753
$639$	1.40006e15	0.519868
$640$	−2.87392e15	−1.05800
$641$	−3.09596e15	−1.13000	−0.564998	−	0.825092i	$-0.691123\pi$
$641$	−3.09596e15	−1.13000	−0.564998	+	0.825092i	$0.691123\pi$
$642$	−7.22781e12	−0.00261556
$643$	−3.64598e15	−1.30814	−0.654069	−	0.756435i	$-0.726939\pi$
$643$	−3.64598e15	−1.30814	−0.654069	+	0.756435i	$0.726939\pi$
$644$	2.67549e15	0.951769
$645$	1.19052e15	0.419912
$646$	9.45054e13	0.0330505
$647$	−4.64520e15	−1.61076	−0.805380	−	0.592759i	$-0.798039\pi$
$647$	−4.64520e15	−1.61076	−0.805380	+	0.592759i	$0.798039\pi$
$648$	1.47571e14	0.0507387
$649$	−5.82591e14	−0.198618
$650$	−7.50789e14	−0.253802
$651$	−2.28299e15	−0.765260
$652$	2.17706e15	0.723617
$653$	3.83555e15	1.26417	0.632085	−	0.774899i	$-0.282199\pi$
$653$	3.83555e15	1.26417	0.632085	+	0.774899i	$0.282199\pi$
$654$	−4.89616e14	−0.160021
$655$	3.22900e15	1.04650
$656$	−2.76957e15	−0.890106
$657$	1.12050e15	0.357111
$658$	−2.90588e14	−0.0918406
$659$	−1.15381e15	−0.361631	−0.180816	−	0.983517i	$-0.557874\pi$
$659$	−1.15381e15	−0.361631	−0.180816	+	0.983517i	$0.557874\pi$
$660$	−3.48029e15	−1.08174
$661$	−2.01622e15	−0.621485	−0.310742	−	0.950494i	$-0.600578\pi$
$661$	−2.01622e15	−0.621485	−0.310742	+	0.950494i	$0.600578\pi$
$662$	−6.85430e14	−0.209529
$663$	2.18722e14	0.0663082
$664$	6.57769e14	0.197765
$665$	−1.08540e16	−3.23647
$666$	−1.27072e14	−0.0375787
$667$	−5.12594e15	−1.50342
$668$	−2.24449e15	−0.652901
$669$	1.68651e15	0.486570
$670$	1.67064e15	0.478048
$671$	2.40884e15	0.683651
$672$	1.73629e15	0.488754
$673$	−2.29558e15	−0.640928	−0.320464	−	0.947261i	$-0.603839\pi$
$673$	−2.29558e15	−0.640928	−0.320464	+	0.947261i	$0.603839\pi$
$674$	1.07579e15	0.297920
$675$	−4.83026e14	−0.132678
$676$	−5.05757e15	−1.37796
$677$	1.43072e15	0.386649	0.193325	−	0.981135i	$-0.438073\pi$
$677$	1.43072e15	0.386649	0.193325	+	0.981135i	$0.438073\pi$
$678$	−9.78538e14	−0.262310
$679$	−4.60692e15	−1.22497
$680$	1.64837e14	0.0434766
$681$	−2.43435e15	−0.636905
$682$	−1.41188e15	−0.366423
$683$	3.67944e15	0.947256	0.473628	−	0.880725i	$-0.342944\pi$
$683$	3.67944e15	0.947256	0.473628	+	0.880725i	$0.342944\pi$
$684$	−2.36996e15	−0.605247
$685$	−4.30200e15	−1.08986
$686$	3.88632e14	0.0976688
$687$	−9.16777e14	−0.228561
$688$	1.89518e15	0.468721
$689$	3.13456e15	0.769079
$690$	5.62737e14	0.136973
$691$	−6.73841e15	−1.62715	−0.813576	−	0.581459i	$-0.802482\pi$
$691$	−6.73841e15	−1.62715	−0.813576	+	0.581459i	$0.802482\pi$
$692$	−1.27341e15	−0.305060
$693$	2.77253e15	0.658937
$694$	9.38271e14	0.221234
$695$	−7.65068e15	−1.78971
$696$	−2.19693e15	−0.509876
$697$	3.38037e14	0.0778366
$698$	9.42747e14	0.215372
$699$	−2.50276e15	−0.567277
$700$	−3.75331e15	−0.844064
$701$	3.41642e14	0.0762294	0.0381147	−	0.999273i	$-0.487865\pi$
$701$	3.41642e14	0.0762294	0.0381147	+	0.999273i	$0.487865\pi$
$702$	3.20026e14	0.0708486
$703$	4.20057e15	0.922686
$704$	−4.78972e15	−1.04390
$705$	1.04754e15	0.226532
$706$	1.03509e15	0.222102
$707$	−6.63788e14	−0.141326
$708$	−3.36178e14	−0.0710208
$709$	−2.14634e15	−0.449929	−0.224965	−	0.974367i	$-0.572227\pi$
$709$	−2.14634e15	−0.449929	−0.224965	+	0.974367i	$0.572227\pi$
$710$	2.28820e15	0.475964
$711$	1.58284e15	0.326704
$712$	−2.39791e15	−0.491127
$713$	−3.91271e15	−0.795216
$714$	−6.37966e13	−0.0128664
$715$	−1.55352e16	−3.10910
$716$	−1.89197e15	−0.375744
$717$	5.55753e15	1.09528
$718$	1.74566e15	0.341410
$719$	−3.75354e15	−0.728505	−0.364252	−	0.931300i	$-0.618675\pi$
$719$	−3.75354e15	−0.728505	−0.364252	+	0.931300i	$0.618675\pi$
$720$	−1.88425e15	−0.362920
$721$	3.91388e14	0.0748106
$722$	−3.33319e15	−0.632274
$723$	1.82189e14	0.0342974
$724$	3.60925e15	0.674303
$725$	7.19092e15	1.33329
$726$	9.77940e14	0.179954
$727$	−4.00725e15	−0.731825	−0.365912	−	0.930649i	$-0.619243\pi$
$727$	−4.00725e15	−0.731825	−0.365912	+	0.930649i	$0.619243\pi$
$728$	5.11856e15	0.927738
$729$	2.05891e14	0.0370370
$730$	1.83130e15	0.326951
$731$	−2.31314e14	−0.0409880
$732$	1.39000e15	0.244457
$733$	5.72837e15	0.999906	0.499953	−	0.866053i	$-0.333351\pi$
$733$	5.72837e15	0.999906	0.499953	+	0.866053i	$0.333351\pi$
$734$	9.64736e14	0.167140
$735$	2.96305e15	0.509518
$736$	2.97574e15	0.507886
$737$	1.41068e16	2.38977
$738$	4.94604e14	0.0831664
$739$	3.82007e15	0.637568	0.318784	−	0.947827i	$-0.396726\pi$
$739$	3.82007e15	0.637568	0.318784	+	0.947827i	$0.396726\pi$
$740$	3.55949e15	0.589675
$741$	−1.05790e16	−1.73958
$742$	−9.14287e14	−0.149232
$743$	1.15911e16	1.87796	0.938981	−	0.343969i	$-0.111771\pi$
$743$	1.15911e16	1.87796	0.938981	+	0.343969i	$0.111771\pi$
$744$	−1.67695e15	−0.269692
$745$	−7.44559e15	−1.18861
$746$	−2.14523e15	−0.339946
$747$	9.17718e14	0.144360
$748$	6.76208e14	0.105590
$749$	−1.61289e14	−0.0250009
$750$	3.55643e14	0.0547239
$751$	7.92089e15	1.20991	0.604956	−	0.796259i	$-0.293190\pi$
$751$	7.92089e15	1.20991	0.604956	+	0.796259i	$0.293190\pi$
$752$	1.66757e15	0.252863
$753$	2.40941e15	0.362692
$754$	−4.76430e15	−0.711962
$755$	1.60936e16	2.38751
$756$	1.59986e15	0.235620
$757$	1.94070e15	0.283747	0.141874	−	0.989885i	$-0.454687\pi$
$757$	1.94070e15	0.283747	0.141874	+	0.989885i	$0.454687\pi$
$758$	1.82648e14	0.0265116
$759$	4.75171e15	0.684732
$760$	−7.97272e15	−1.14060
$761$	−3.75428e15	−0.533225	−0.266613	−	0.963804i	$-0.585904\pi$
$761$	−3.75428e15	−0.533225	−0.266613	+	0.963804i	$0.585904\pi$
$762$	−1.48323e15	−0.209150
$763$	−1.09258e16	−1.52957
$764$	1.14231e16	1.58771
$765$	2.29980e14	0.0317360
$766$	4.78868e14	0.0656081
$767$	−1.50062e15	−0.204125
$768$	−2.10810e15	−0.284710
$769$	8.90458e15	1.19404	0.597020	−	0.802227i	$-0.296351\pi$
$769$	8.90458e15	1.19404	0.597020	+	0.802227i	$0.296351\pi$
$770$	4.53131e15	0.603288
$771$	−4.23297e15	−0.559560
$772$	−5.79064e15	−0.760032
$773$	−4.45228e14	−0.0580223	−0.0290112	−	0.999579i	$-0.509236\pi$
$773$	−4.45228e14	−0.0580223	−0.0290112	+	0.999579i	$0.509236\pi$
$774$	−3.38451e14	−0.0437946
$775$	5.48894e15	0.705228
$776$	−3.38396e15	−0.431704
$777$	−2.83563e15	−0.359198
$778$	2.65440e15	0.333871
$779$	−1.63499e16	−2.04202
$780$	−8.96443e15	−1.11174
$781$	1.93214e16	2.37935
$782$	−1.09338e14	−0.0133701
$783$	−3.06515e15	−0.372188
$784$	4.71686e15	0.568742
$785$	−1.03603e16	−1.24048
$786$	−9.17966e14	−0.109145
$787$	1.81740e15	0.214580	0.107290	−	0.994228i	$-0.465783\pi$
$787$	1.81740e15	0.214580	0.107290	+	0.994228i	$0.465783\pi$
$788$	−6.86568e15	−0.804987
$789$	4.26489e15	0.496575
$790$	2.58692e15	0.299112
$791$	−2.18362e16	−2.50730
$792$	2.03654e15	0.232222
$793$	6.20463e15	0.702608
$794$	2.40652e15	0.270631
$795$	3.29591e15	0.368092
$796$	1.52194e16	1.68801
$797$	−5.13538e15	−0.565655	−0.282828	−	0.959171i	$-0.591272\pi$
$797$	−5.13538e15	−0.565655	−0.282828	+	0.959171i	$0.591272\pi$
$798$	3.08567e15	0.337546
$799$	−2.03533e14	−0.0221120
$800$	−4.17451e15	−0.450413
$801$	−3.34557e15	−0.358501
$802$	−1.01835e15	−0.108377
$803$	1.54633e16	1.63443
$804$	8.14016e15	0.854524
$805$	1.25575e16	1.30926
$806$	−3.63667e15	−0.376583
$807$	−4.52599e15	−0.465489
$808$	−4.87579e14	−0.0498061
$809$	−9.92930e14	−0.100740	−0.0503700	−	0.998731i	$-0.516040\pi$
$809$	−9.92930e14	−0.100740	−0.0503700	+	0.998731i	$0.516040\pi$
$810$	3.36499e14	0.0339091
$811$	8.87864e15	0.888652	0.444326	−	0.895865i	$-0.353443\pi$
$811$	8.87864e15	0.888652	0.444326	+	0.895865i	$0.353443\pi$
$812$	−2.38175e16	−2.36776
$813$	−1.00789e16	−0.995210
$814$	−1.75364e15	−0.171991
$815$	1.02181e16	0.995417
$816$	3.66104e14	0.0354249
$817$	1.11880e16	1.07531
$818$	−3.32108e15	−0.317056
$819$	7.14141e15	0.677209
$820$	−1.38546e16	−1.30503
$821$	−1.02137e16	−0.955643	−0.477821	−	0.878457i	$-0.658573\pi$
$821$	−1.02137e16	−0.955643	−0.477821	+	0.878457i	$0.658573\pi$
$822$	1.22301e15	0.113667
$823$	−1.93889e16	−1.79000	−0.895001	−	0.446063i	$-0.852826\pi$
$823$	−1.93889e16	−1.79000	−0.895001	+	0.446063i	$0.852826\pi$
$824$	2.87490e14	0.0263647
$825$	−6.66594e15	−0.607246
$826$	4.37700e14	0.0396083
$827$	−1.63787e16	−1.47231	−0.736153	−	0.676815i	$-0.763360\pi$
$827$	−1.63787e16	−1.47231	−0.736153	+	0.676815i	$0.763360\pi$
$828$	2.74192e15	0.244843
$829$	−1.53869e16	−1.36490	−0.682450	−	0.730932i	$-0.739086\pi$
$829$	−1.53869e16	−1.36490	−0.682450	+	0.730932i	$0.739086\pi$
$830$	1.49988e15	0.132168
$831$	2.43188e15	0.212881
$832$	−1.23372e16	−1.07285
$833$	−5.75711e14	−0.0497344
$834$	2.17500e15	0.186657
$835$	−1.05346e16	−0.898139
$836$	−3.27064e16	−2.77012
$837$	−2.33968e15	−0.196864
$838$	1.39450e15	0.116567
$839$	−3.30349e15	−0.274336	−0.137168	−	0.990548i	$-0.543800\pi$
$839$	−3.30349e15	−0.274336	−0.137168	+	0.990548i	$0.543800\pi$
$840$	5.38204e15	0.444029
$841$	3.34311e16	2.74014
$842$	−2.29321e15	−0.186736
$843$	−6.93909e14	−0.0561372
$844$	5.57666e15	0.448219
$845$	−2.37380e16	−1.89553
$846$	−2.97803e14	−0.0236261
$847$	2.18228e16	1.72009
$848$	5.24673e15	0.410877
$849$	−8.53414e15	−0.663999
$850$	1.53385e14	0.0118571
$851$	−4.85984e15	−0.373258
$852$	1.11492e16	0.850798
$853$	8.53780e15	0.647330	0.323665	−	0.946172i	$-0.395085\pi$
$853$	8.53780e15	0.647330	0.323665	+	0.946172i	$0.395085\pi$
$854$	−1.80976e15	−0.136334
$855$	−1.11235e16	−0.832585
$856$	−1.18473e14	−0.00881080
$857$	3.51817e15	0.259969	0.129985	−	0.991516i	$-0.458507\pi$
$857$	3.51817e15	0.259969	0.129985	+	0.991516i	$0.458507\pi$
$858$	4.41648e15	0.324262
$859$	2.39282e16	1.74561	0.872806	−	0.488067i	$-0.162298\pi$
$859$	2.39282e16	1.74561	0.872806	+	0.488067i	$0.162298\pi$
$860$	9.48054e15	0.687213
$861$	1.10371e16	0.794949
$862$	−1.79073e15	−0.128156
$863$	4.05306e15	0.288220	0.144110	−	0.989562i	$-0.453968\pi$
$863$	4.05306e15	0.288220	0.144110	+	0.989562i	$0.453968\pi$
$864$	1.77940e15	0.125732
$865$	−5.97681e15	−0.419644
$866$	3.15278e15	0.219961
$867$	8.28339e15	0.574252
$868$	−1.81803e16	−1.25240
$869$	2.18438e16	1.49527
$870$	−5.00954e15	−0.340755
$871$	3.63358e16	2.45604
$872$	−8.02546e15	−0.539050
$873$	−4.72130e15	−0.315126
$874$	5.28838e15	0.350760
$875$	7.93621e15	0.523081
$876$	8.92295e15	0.584434
$877$	−1.35224e16	−0.880147	−0.440074	−	0.897962i	$-0.645048\pi$
$877$	−1.35224e16	−0.880147	−0.440074	+	0.897962i	$0.645048\pi$
$878$	−1.29857e15	−0.0839932
$879$	1.94596e14	0.0125082
$880$	−2.60034e16	−1.66102
$881$	−5.26571e15	−0.334264	−0.167132	−	0.985935i	$-0.553451\pi$
$881$	−5.26571e15	−0.334264	−0.167132	+	0.985935i	$0.553451\pi$
$882$	−8.42361e14	−0.0531399
$883$	9.43476e15	0.591490	0.295745	−	0.955267i	$-0.404432\pi$
$883$	9.43476e15	0.591490	0.295745	+	0.955267i	$0.404432\pi$
$884$	1.74176e15	0.108518
$885$	−1.57786e15	−0.0976971
$886$	−4.06551e15	−0.250167
$887$	1.48332e16	0.907097	0.453549	−	0.891232i	$-0.350158\pi$
$887$	1.48332e16	0.907097	0.453549	+	0.891232i	$0.350158\pi$
$888$	−2.08288e15	−0.126588
$889$	−3.30985e16	−1.99917
$890$	−5.46785e15	−0.328225
$891$	2.84138e15	0.169512
$892$	1.34303e16	0.796304
$893$	9.84435e15	0.580101
$894$	2.11669e15	0.123966
$895$	−8.88004e15	−0.516878
$896$	1.82319e16	1.05472
$897$	1.22393e16	0.703718
$898$	7.02961e14	0.0401709
$899$	3.48313e16	1.97830
$900$	−3.84651e15	−0.217136
$901$	−6.40384e14	−0.0359297
$902$	6.82573e15	0.380639
$903$	−7.55257e15	−0.418612
$904$	−1.60395e16	−0.883620
$905$	1.69402e16	0.927580
$906$	−4.57522e15	−0.249004
$907$	−4.11603e15	−0.222658	−0.111329	−	0.993784i	$-0.535511\pi$
$907$	−4.11603e15	−0.222658	−0.111329	+	0.993784i	$0.535511\pi$
$908$	−1.93856e16	−1.04234
$909$	−6.80270e14	−0.0363563
$910$	1.16716e16	0.620016
$911$	2.40095e15	0.126775	0.0633873	−	0.997989i	$-0.479810\pi$
$911$	2.40095e15	0.126775	0.0633873	+	0.997989i	$0.479810\pi$
$912$	−1.77075e16	−0.929361
$913$	1.26649e16	0.660710
$914$	−8.38387e15	−0.434751
$915$	6.52401e15	0.336278
$916$	−7.30062e15	−0.374055
$917$	−2.04845e16	−1.04326
$918$	−6.53806e13	−0.00330990
$919$	−2.76545e16	−1.39165	−0.695826	−	0.718210i	$-0.744962\pi$
$919$	−2.76545e16	−1.39165	−0.695826	+	0.718210i	$0.744962\pi$
$920$	9.22402e15	0.461410
$921$	9.36318e15	0.465581
$922$	−7.13637e15	−0.352742
$923$	4.97676e16	2.44533
$924$	2.20787e16	1.07839
$925$	6.81763e15	0.331020
$926$	3.53287e15	0.170517
$927$	4.01106e14	0.0192451
$928$	−2.64903e16	−1.26349
$929$	1.34456e16	0.637519	0.318759	−	0.947836i	$-0.396734\pi$
$929$	1.34456e16	0.637519	0.318759	+	0.947836i	$0.396734\pi$
$930$	−3.82386e15	−0.180238
$931$	2.78456e16	1.30477
$932$	−1.99304e16	−0.928384
$933$	1.17635e16	0.544736
$934$	7.98119e15	0.367417
$935$	3.17381e15	0.145250
$936$	5.24565e15	0.238662
$937$	4.76557e15	0.215550	0.107775	−	0.994175i	$-0.465627\pi$
$937$	4.76557e15	0.215550	0.107775	+	0.994175i	$0.465627\pi$
$938$	−1.05984e16	−0.476568
$939$	−6.23305e15	−0.278638
$940$	8.34192e15	0.370734
$941$	2.65555e16	1.17331	0.586653	−	0.809839i	$-0.300445\pi$
$941$	2.65555e16	1.17331	0.586653	+	0.809839i	$0.300445\pi$
$942$	2.94530e15	0.129375
$943$	1.89160e16	0.826068
$944$	−2.51179e15	−0.109053
$945$	7.50902e15	0.324122
$946$	−4.67075e15	−0.200440
$947$	−5.12655e15	−0.218726	−0.109363	−	0.994002i	$-0.534881\pi$
$947$	−5.12655e15	−0.218726	−0.109363	+	0.994002i	$0.534881\pi$
$948$	1.26047e16	0.534671
$949$	3.98300e16	1.67976
$950$	−7.41880e15	−0.311067
$951$	2.20568e16	0.919496
$952$	−1.04571e15	−0.0433420
$953$	−1.77624e16	−0.731966	−0.365983	−	0.930622i	$-0.619267\pi$
$953$	−1.77624e16	−0.731966	−0.365983	+	0.930622i	$0.619267\pi$
$954$	−9.36988e14	−0.0383900
$955$	5.36148e16	2.18407
$956$	4.42566e16	1.79250
$957$	−4.23002e16	−1.70344
$958$	3.65113e15	0.146190
$959$	2.72915e16	1.08649
$960$	−1.29723e16	−0.513481
$961$	1.17882e15	0.0463947
$962$	−4.51698e15	−0.176761
$963$	−1.65294e14	−0.00643151
$964$	1.45084e15	0.0561299
$965$	−2.71786e16	−1.04551
$966$	−3.56996e15	−0.136549
$967$	−2.69583e16	−1.02529	−0.512646	−	0.858600i	$-0.671335\pi$
$967$	−2.69583e16	−1.02529	−0.512646	+	0.858600i	$0.671335\pi$
$968$	1.60297e16	0.606195
$969$	2.16126e15	0.0812693
$970$	−7.71629e15	−0.288512
$971$	−9.08427e15	−0.337741	−0.168871	−	0.985638i	$-0.554012\pi$
$971$	−9.08427e15	−0.337741	−0.168871	+	0.985638i	$0.554012\pi$
$972$	1.63958e15	0.0606135
$973$	4.85353e16	1.78417
$974$	4.90058e15	0.179132
$975$	−1.71699e16	−0.624084
$976$	1.03855e16	0.375366
$977$	−2.83300e16	−1.01819	−0.509093	−	0.860712i	$-0.670019\pi$
$977$	−2.83300e16	−1.01819	−0.509093	+	0.860712i	$0.670019\pi$
$978$	−2.90489e15	−0.103817
$979$	−4.61701e16	−1.64080
$980$	2.35959e16	0.833859
$981$	−1.11971e16	−0.393483
$982$	1.12691e16	0.393802
$983$	−1.34904e16	−0.468791	−0.234395	−	0.972141i	$-0.575311\pi$
$983$	−1.34904e16	−0.468791	−0.234395	+	0.972141i	$0.575311\pi$
$984$	8.10723e15	0.280156
$985$	−3.22244e16	−1.10735
$986$	9.73337e14	0.0332614
$987$	−6.64550e15	−0.225831
$988$	−8.42441e16	−2.84693
$989$	−1.29440e16	−0.434999
$990$	4.64382e15	0.155196
$991$	1.42310e15	0.0472967	0.0236483	−	0.999720i	$-0.492472\pi$
$991$	1.42310e15	0.0472967	0.0236483	+	0.999720i	$0.492472\pi$
$992$	−2.02205e16	−0.668309
$993$	−1.56752e16	−0.515220
$994$	−1.45162e16	−0.474490
$995$	7.14328e16	2.32204
$996$	7.30812e15	0.236254
$997$	2.29775e16	0.738720	0.369360	−	0.929286i	$-0.379577\pi$
$997$	2.29775e16	0.738720	0.369360	+	0.929286i	$0.379577\pi$
$998$	9.97597e14	0.0318961
$999$	−2.90603e15	−0.0924039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.12	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +96507.1 q^{10} +814898. q^{11} +470228. q^{12} +2.09899e6 q^{13} -612233. q^{14} +2.20704e6 q^{15} +3.51337e6 q^{16} -428820. q^{17} -627434. q^{18} +2.07408e7 q^{19} +1.75754e7 q^{20} -1.40013e7 q^{21} -8.65883e6 q^{22} -2.39961e7 q^{23} -1.02845e7 q^{24} +3.36629e7 q^{25} -2.23032e7 q^{26} -1.43489e7 q^{27} -1.11497e8 q^{28} +2.13616e8 q^{29} -2.34512e7 q^{30} +1.63056e8 q^{31} -1.24009e8 q^{32} -1.98020e8 q^{33} +4.55649e6 q^{34} -5.23316e8 q^{35} -1.14265e8 q^{36} +2.02526e8 q^{37} -2.20385e8 q^{38} -5.10055e8 q^{39} -3.84397e8 q^{40} -7.88296e8 q^{41} +1.48773e8 q^{42} +5.39420e8 q^{43} -1.57691e9 q^{44} -5.36310e8 q^{45} +2.54974e8 q^{46} +4.74636e8 q^{47} -8.53748e8 q^{48} +1.34255e9 q^{49} -3.57690e8 q^{50} +1.04203e8 q^{51} -4.06175e9 q^{52} +1.49336e9 q^{53} +1.52467e8 q^{54} -7.40128e9 q^{55} +2.43858e9 q^{56} -5.04003e9 q^{57} -2.26980e9 q^{58} -7.14924e8 q^{59} -4.27083e9 q^{60} +2.95600e9 q^{61} -1.73258e9 q^{62} +3.40231e9 q^{63} -5.87769e9 q^{64} -1.90640e10 q^{65} +2.10410e9 q^{66} +1.73111e10 q^{67} +8.29807e8 q^{68} +5.83105e9 q^{69} +5.56058e9 q^{70} +2.37102e10 q^{71} +2.49913e9 q^{72} +1.89758e10 q^{73} -2.15198e9 q^{74} -8.18008e9 q^{75} -4.01355e10 q^{76} +4.69531e10 q^{77} +5.41967e9 q^{78} +2.68055e10 q^{79} -3.19100e10 q^{80} +3.48678e9 q^{81} +8.37617e9 q^{82} +1.55416e10 q^{83} +2.70938e10 q^{84} +3.89474e9 q^{85} -5.73170e9 q^{86} -5.19086e10 q^{87} +3.44889e10 q^{88} -5.66575e10 q^{89} +5.69865e9 q^{90} +1.20940e11 q^{91} +4.64347e10 q^{92} -3.96226e10 q^{93} -5.04332e9 q^{94} -1.88378e11 q^{95} +3.01343e10 q^{96} -7.99557e10 q^{97} -1.42655e10 q^{98} +4.81189e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 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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