LMFDB - Embedded newform 177.10.a.b.1.14

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} -38982.3 q^{10} +71994.6 q^{11} +21481.1 q^{12} +20979.3 q^{13} +25646.9 q^{14} +200992. q^{15} -56032.2 q^{16} -100423. q^{17} +103073. q^{18} +125554. q^{19} +658059. q^{20} -132235. q^{21} +1.13103e6 q^{22} +759888. q^{23} +988988. q^{24} +4.20414e6 q^{25} +329583. q^{26} -531441. q^{27} -432944. q^{28} -1.44179e6 q^{29} +3.15757e6 q^{30} -973200. q^{31} +5.37112e6 q^{32} -5.83156e6 q^{33} -1.57764e6 q^{34} -4.05093e6 q^{35} -1.73997e6 q^{36} +6.01928e6 q^{37} +1.97245e6 q^{38} -1.69932e6 q^{39} +3.02970e7 q^{40} +6.93821e6 q^{41} -2.07740e6 q^{42} +5.22977e6 q^{43} -1.90928e7 q^{44} -1.62804e7 q^{45} +1.19378e7 q^{46} -3.13303e7 q^{47} +4.53861e6 q^{48} -3.76885e7 q^{49} +6.60467e7 q^{50} +8.13429e6 q^{51} -5.56368e6 q^{52} +5.51922e7 q^{53} -8.34890e6 q^{54} -1.78646e8 q^{55} -1.99327e7 q^{56} -1.01699e7 q^{57} -2.26504e7 q^{58} -1.21174e7 q^{59} -5.33028e7 q^{60} -1.66783e8 q^{61} -1.52889e7 q^{62} +1.07110e7 q^{63} +1.13068e8 q^{64} -5.20577e7 q^{65} -9.16133e7 q^{66} +9.31844e7 q^{67} +2.66321e7 q^{68} -6.15509e7 q^{69} -6.36397e7 q^{70} -4.01312e7 q^{71} -8.01080e7 q^{72} -2.58311e8 q^{73} +9.45624e7 q^{74} -3.40536e8 q^{75} -3.32968e7 q^{76} +1.17533e8 q^{77} -2.66962e7 q^{78} -3.62808e8 q^{79} +1.39037e8 q^{80} +4.30467e7 q^{81} +1.08999e8 q^{82} +5.97676e8 q^{83} +3.50684e7 q^{84} +2.49189e8 q^{85} +8.21592e7 q^{86} +1.16785e8 q^{87} -8.79034e8 q^{88} +6.86238e8 q^{89} -2.55763e8 q^{90} +3.42493e7 q^{91} -2.01521e8 q^{92} +7.88292e7 q^{93} -4.92196e8 q^{94} -3.11548e8 q^{95} -4.35061e8 q^{96} +2.73324e7 q^{97} -5.92083e8 q^{98} +4.72356e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) $	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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 $

$2$	15.7099	0.694287	0.347143	−	0.937812i	$-0.387152\pi$
$2$	15.7099	0.694287	0.347143	+	0.937812i	$0.387152\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−265.198	−0.517966
$5$	−2481.38	−1.77553	−0.887767	−	0.460293i	$-0.847744\pi$
$5$	−2481.38	−1.77553	−0.887767	+	0.460293i	$0.847744\pi$
$6$	−1272.50	−0.400847
$7$	1632.53	0.256992	0.128496	−	0.991710i	$-0.458985\pi$
$7$	1632.53	0.256992	0.128496	+	0.991710i	$0.458985\pi$
$8$	−12209.7	−1.05390
$9$	6561.00	0.333333
$10$	−38982.3	−1.23273
$11$	71994.6	1.48263	0.741315	−	0.671158i	$-0.234203\pi$
$11$	71994.6	1.48263	0.741315	+	0.671158i	$0.234203\pi$
$12$	21481.1	0.299048
$13$	20979.3	0.203726	0.101863	−	0.994798i	$-0.467520\pi$
$13$	20979.3	0.203726	0.101863	+	0.994798i	$0.467520\pi$
$14$	25646.9	0.178426
$15$	200992.	1.02511
$16$	−56032.2	−0.213746
$17$	−100423.	−0.291618	−0.145809	−	0.989313i	$-0.546579\pi$
$17$	−100423.	−0.291618	−0.145809	+	0.989313i	$0.546579\pi$
$18$	103073.	0.231429
$19$	125554.	0.221024	0.110512	−	0.993875i	$-0.464751\pi$
$19$	125554.	0.221024	0.110512	+	0.993875i	$0.464751\pi$
$20$	658059.	0.919666
$21$	−132235.	−0.148374
$22$	1.13103e6	1.02937
$23$	759888.	0.566206	0.283103	−	0.959090i	$-0.408636\pi$
$23$	759888.	0.566206	0.283103	+	0.959090i	$0.408636\pi$
$24$	988988.	0.608472
$25$	4.20414e6	2.15252
$26$	329583.	0.141444
$27$	−531441.	−0.192450
$28$	−432944.	−0.133113
$29$	−1.44179e6	−0.378539	−0.189269	−	0.981925i	$-0.560612\pi$
$29$	−1.44179e6	−0.378539	−0.189269	+	0.981925i	$0.560612\pi$
$30$	3.15757e6	0.711717
$31$	−973200.	−0.189267	−0.0946334	−	0.995512i	$-0.530168\pi$
$31$	−973200.	−0.189267	−0.0946334	+	0.995512i	$0.530168\pi$
$32$	5.37112e6	0.905503
$33$	−5.83156e6	−0.855997
$34$	−1.57764e6	−0.202467
$35$	−4.05093e6	−0.456298
$36$	−1.73997e6	−0.172655
$37$	6.01928e6	0.528004	0.264002	−	0.964522i	$-0.414957\pi$
$37$	6.01928e6	0.528004	0.264002	+	0.964522i	$0.414957\pi$
$38$	1.97245e6	0.153454
$39$	−1.69932e6	−0.117621
$40$	3.02970e7	1.87124
$41$	6.93821e6	0.383460	0.191730	−	0.981448i	$-0.438590\pi$
$41$	6.93821e6	0.383460	0.191730	+	0.981448i	$0.438590\pi$
$42$	−2.07740e6	−0.103014
$43$	5.22977e6	0.233278	0.116639	−	0.993174i	$-0.462788\pi$
$43$	5.22977e6	0.233278	0.116639	+	0.993174i	$0.462788\pi$
$44$	−1.90928e7	−0.767951
$45$	−1.62804e7	−0.591845
$46$	1.19378e7	0.393109
$47$	−3.13303e7	−0.936535	−0.468267	−	0.883587i	$-0.655122\pi$
$47$	−3.13303e7	−0.936535	−0.468267	+	0.883587i	$0.655122\pi$
$48$	4.53861e6	0.123406
$49$	−3.76885e7	−0.933955
$50$	6.60467e7	1.49447
$51$	8.13429e6	0.168366
$52$	−5.56368e6	−0.105523
$53$	5.51922e7	0.960807	0.480403	−	0.877048i	$-0.340490\pi$
$53$	5.51922e7	0.960807	0.480403	+	0.877048i	$0.340490\pi$
$54$	−8.34890e6	−0.133616
$55$	−1.78646e8	−2.63246
$56$	−1.99327e7	−0.270845
$57$	−1.01699e7	−0.127608
$58$	−2.26504e7	−0.262815
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−5.33028e7	−0.530969
$61$	−1.66783e8	−1.54229	−0.771147	−	0.636658i	$-0.780317\pi$
$61$	−1.66783e8	−1.54229	−0.771147	+	0.636658i	$0.780317\pi$
$62$	−1.52889e7	−0.131406
$63$	1.07110e7	0.0856639
$64$	1.13068e8	0.842425
$65$	−5.20577e7	−0.361722
$66$	−9.16133e7	−0.594307
$67$	9.31844e7	0.564945	0.282473	−	0.959275i	$-0.408845\pi$
$67$	9.31844e7	0.564945	0.282473	+	0.959275i	$0.408845\pi$
$68$	2.66321e7	0.151048
$69$	−6.15509e7	−0.326899
$70$	−6.36397e7	−0.316801
$71$	−4.01312e7	−0.187422	−0.0937108	−	0.995599i	$-0.529873\pi$
$71$	−4.01312e7	−0.187422	−0.0937108	+	0.995599i	$0.529873\pi$
$72$	−8.01080e7	−0.351301
$73$	−2.58311e8	−1.06461	−0.532305	−	0.846553i	$-0.678674\pi$
$73$	−2.58311e8	−1.06461	−0.532305	+	0.846553i	$0.678674\pi$
$74$	9.45624e7	0.366586
$75$	−3.40536e8	−1.24276
$76$	−3.32968e7	−0.114483
$77$	1.17533e8	0.381024
$78$	−2.66962e7	−0.0816628
$79$	−3.62808e8	−1.04798	−0.523992	−	0.851723i	$-0.675558\pi$
$79$	−3.62808e8	−1.04798	−0.523992	+	0.851723i	$0.675558\pi$
$80$	1.39037e8	0.379513
$81$	4.30467e7	0.111111
$82$	1.08999e8	0.266231
$83$	5.97676e8	1.38234	0.691169	−	0.722693i	$-0.257096\pi$
$83$	5.97676e8	1.38234	0.691169	+	0.722693i	$0.257096\pi$
$84$	3.50684e7	0.0768528
$85$	2.49189e8	0.517778
$86$	8.21592e7	0.161962
$87$	1.16785e8	0.218549
$88$	−8.79034e8	−1.56255
$89$	6.86238e8	1.15936	0.579682	−	0.814843i	$-0.303177\pi$
$89$	6.86238e8	1.15936	0.579682	+	0.814843i	$0.303177\pi$
$90$	−2.55763e8	−0.410910
$91$	3.42493e7	0.0523559
$92$	−2.01521e8	−0.293275
$93$	7.88292e7	0.109273
$94$	−4.92196e8	−0.650224
$95$	−3.11548e8	−0.392436
$96$	−4.35061e8	−0.522792
$97$	2.73324e7	0.0313476	0.0156738	−	0.999877i	$-0.495011\pi$
$97$	2.73324e7	0.0313476	0.0156738	+	0.999877i	$0.495011\pi$
$98$	−5.92083e8	−0.648433
$99$	4.72356e8	0.494210
$100$	−1.11493e9	−1.11493
$101$	−1.63234e9	−1.56087	−0.780433	−	0.625240i	$-0.785001\pi$
$101$	−1.63234e9	−1.56087	−0.780433	+	0.625240i	$0.785001\pi$
$102$	1.27789e8	0.116894
$103$	1.28691e9	1.12663	0.563315	−	0.826242i	$-0.309526\pi$
$103$	1.28691e9	1.12663	0.563315	+	0.826242i	$0.309526\pi$
$104$	−2.56152e8	−0.214707
$105$	3.28125e8	0.263444
$106$	8.67064e8	0.667075
$107$	8.46105e8	0.624018	0.312009	−	0.950079i	$-0.398998\pi$
$107$	8.46105e8	0.624018	0.312009	+	0.950079i	$0.398998\pi$
$108$	1.40937e8	0.0996825
$109$	−6.07335e8	−0.412106	−0.206053	−	0.978541i	$-0.566062\pi$
$109$	−6.07335e8	−0.412106	−0.206053	+	0.978541i	$0.566062\pi$
$110$	−2.80652e9	−1.82768
$111$	−4.87562e8	−0.304843
$112$	−9.14741e7	−0.0549309
$113$	−1.20739e9	−0.696620	−0.348310	−	0.937379i	$-0.613244\pi$
$113$	−1.20739e9	−0.696620	−0.348310	+	0.937379i	$0.613244\pi$
$114$	−1.59768e8	−0.0885969
$115$	−1.88557e9	−1.00532
$116$	3.82360e8	0.196070
$117$	1.37645e8	0.0679086
$118$	−1.90363e8	−0.0903885
$119$	−1.63944e8	−0.0749435
$120$	−2.45406e9	−1.08036
$121$	2.82527e9	1.19819
$122$	−2.62014e9	−1.07079
$123$	−5.61995e8	−0.221391
$124$	2.58091e8	0.0980338
$125$	−5.58564e9	−2.04634
$126$	1.68269e8	0.0594753
$127$	4.29748e9	1.46587	0.732937	−	0.680296i	$-0.238149\pi$
$127$	4.29748e9	1.46587	0.732937	+	0.680296i	$0.238149\pi$
$128$	−9.73718e8	−0.320618
$129$	−4.23611e8	−0.134683
$130$	−8.17823e8	−0.251139
$131$	6.42427e8	0.190591	0.0952956	−	0.995449i	$-0.469620\pi$
$131$	6.42427e8	0.190591	0.0952956	+	0.995449i	$0.469620\pi$
$132$	1.54652e9	0.443377
$133$	2.04971e8	0.0568015
$134$	1.46392e9	0.392234
$135$	1.31871e9	0.341702
$136$	1.22614e9	0.307337
$137$	4.33548e9	1.05146	0.525732	−	0.850650i	$-0.323792\pi$
$137$	4.33548e9	1.05146	0.525732	+	0.850650i	$0.323792\pi$
$138$	−9.66960e8	−0.226962
$139$	−3.46178e9	−0.786563	−0.393281	−	0.919418i	$-0.628660\pi$
$139$	−3.46178e9	−0.786563	−0.393281	+	0.919418i	$0.628660\pi$
$140$	1.07430e9	0.236347
$141$	2.53775e9	0.540709
$142$	−6.30458e8	−0.130124
$143$	1.51040e9	0.302050
$144$	−3.67627e8	−0.0712486
$145$	3.57763e9	0.672108
$146$	−4.05805e9	−0.739145
$147$	3.05277e9	0.539219
$148$	−1.59630e9	−0.273488
$149$	−1.39148e9	−0.231280	−0.115640	−	0.993291i	$-0.536892\pi$
$149$	−1.39148e9	−0.231280	−0.115640	+	0.993291i	$0.536892\pi$
$150$	−5.34979e9	−0.862831
$151$	4.41234e9	0.690673	0.345336	−	0.938479i	$-0.387765\pi$
$151$	4.41234e9	0.690673	0.345336	+	0.938479i	$0.387765\pi$
$152$	−1.53298e9	−0.232938
$153$	−6.58878e8	−0.0972061
$154$	1.84644e9	0.264540
$155$	2.41488e9	0.336050
$156$	4.50658e8	0.0609237
$157$	−1.34294e10	−1.76404	−0.882021	−	0.471211i	$-0.843817\pi$
$157$	−1.34294e10	−1.76404	−0.882021	+	0.471211i	$0.843817\pi$
$158$	−5.69968e9	−0.727602
$159$	−4.47056e9	−0.554722
$160$	−1.33278e10	−1.60775
$161$	1.24054e9	0.145510
$162$	6.76261e8	0.0771430
$163$	1.05500e10	1.17060	0.585298	−	0.810818i	$-0.300978\pi$
$163$	1.05500e10	1.17060	0.585298	+	0.810818i	$0.300978\pi$
$164$	−1.84000e9	−0.198619
$165$	1.44703e10	1.51985
$166$	9.38943e9	0.959739
$167$	1.91306e9	0.190328	0.0951642	−	0.995462i	$-0.469662\pi$
$167$	1.91306e9	0.190328	0.0951642	+	0.995462i	$0.469662\pi$
$168$	1.61455e9	0.156372
$169$	−1.01644e10	−0.958496
$170$	3.91474e9	0.359486
$171$	8.23761e8	0.0736748
$172$	−1.38693e9	−0.120830
$173$	−1.79045e10	−1.51969	−0.759846	−	0.650103i	$-0.774726\pi$
$173$	−1.79045e10	−1.51969	−0.759846	+	0.650103i	$0.774726\pi$
$174$	1.83468e9	0.151736
$175$	6.86338e9	0.553180
$176$	−4.03401e9	−0.316906
$177$	9.81506e8	0.0751646
$178$	1.07807e10	0.804931
$179$	−7.61767e9	−0.554605	−0.277302	−	0.960783i	$-0.589440\pi$
$179$	−7.61767e9	−0.554605	−0.277302	+	0.960783i	$0.589440\pi$
$180$	4.31753e9	0.306555
$181$	−2.33571e10	−1.61758	−0.808788	−	0.588101i	$-0.799876\pi$
$181$	−2.33571e10	−1.61758	−0.808788	+	0.588101i	$0.799876\pi$
$182$	5.38054e8	0.0363500
$183$	1.35094e10	0.890443
$184$	−9.27803e9	−0.596727
$185$	−1.49362e10	−0.937489
$186$	1.23840e9	0.0758670
$187$	−7.22994e9	−0.432362
$188$	8.30874e9	0.485093
$189$	−8.67592e8	−0.0494581
$190$	−4.89440e9	−0.272463
$191$	−1.50832e10	−0.820057	−0.410029	−	0.912073i	$-0.634481\pi$
$191$	−1.50832e10	−0.820057	−0.410029	+	0.912073i	$0.634481\pi$
$192$	−9.15853e9	−0.486374
$193$	−1.68362e10	−0.873446	−0.436723	−	0.899596i	$-0.643861\pi$
$193$	−1.68362e10	−0.873446	−0.436723	+	0.899596i	$0.643861\pi$
$194$	4.29389e8	0.0217642
$195$	4.21667e9	0.208840
$196$	9.99492e9	0.483757
$197$	−1.40072e10	−0.662601	−0.331301	−	0.943525i	$-0.607487\pi$
$197$	−1.40072e10	−0.662601	−0.331301	+	0.943525i	$0.607487\pi$
$198$	7.42068e9	0.343123
$199$	7.08429e9	0.320227	0.160113	−	0.987099i	$-0.448814\pi$
$199$	7.08429e9	0.320227	0.160113	+	0.987099i	$0.448814\pi$
$200$	−5.13314e10	−2.26855
$201$	−7.54794e9	−0.326171
$202$	−2.56440e10	−1.08369
$203$	−2.35376e9	−0.0972814
$204$	−2.15720e9	−0.0872077
$205$	−1.72164e10	−0.680847
$206$	2.02173e10	0.782205
$207$	4.98563e9	0.188735
$208$	−1.17552e9	−0.0435455
$209$	9.03922e9	0.327697
$210$	5.15482e9	0.182905
$211$	−1.28875e10	−0.447609	−0.223804	−	0.974634i	$-0.571848\pi$
$211$	−1.28875e10	−0.447609	−0.223804	+	0.974634i	$0.571848\pi$
$212$	−1.46369e10	−0.497665
$213$	3.25063e9	0.108208
$214$	1.32922e10	0.433248
$215$	−1.29771e10	−0.414194
$216$	6.48875e9	0.202824
$217$	−1.58878e9	−0.0486400
$218$	−9.54119e9	−0.286120
$219$	2.09232e10	0.614653
$220$	4.73767e10	1.36352
$221$	−2.10681e9	−0.0594101
$222$	−7.65956e9	−0.211649
$223$	−1.54290e10	−0.417799	−0.208899	−	0.977937i	$-0.566988\pi$
$223$	−1.54290e10	−0.417799	−0.208899	+	0.977937i	$0.566988\pi$
$224$	8.76850e9	0.232707
$225$	2.75834e10	0.717507
$226$	−1.89681e10	−0.483654
$227$	7.87485e9	0.196846	0.0984229	−	0.995145i	$-0.468620\pi$
$227$	7.87485e9	0.196846	0.0984229	+	0.995145i	$0.468620\pi$
$228$	2.69704e9	0.0660968
$229$	2.02461e10	0.486499	0.243250	−	0.969964i	$-0.421787\pi$
$229$	2.02461e10	0.486499	0.243250	+	0.969964i	$0.421787\pi$
$230$	−2.96222e10	−0.697979
$231$	−9.52018e9	−0.219984
$232$	1.76038e10	0.398943
$233$	1.16127e10	0.258126	0.129063	−	0.991636i	$-0.458803\pi$
$233$	1.16127e10	0.258126	0.129063	+	0.991636i	$0.458803\pi$
$234$	2.16240e9	0.0471481
$235$	7.77425e10	1.66285
$236$	3.21351e9	0.0674334
$237$	2.93874e10	0.605054
$238$	−2.57554e9	−0.0520323
$239$	3.57480e10	0.708697	0.354349	−	0.935113i	$-0.384703\pi$
$239$	3.57480e10	0.708697	0.354349	+	0.935113i	$0.384703\pi$
$240$	−1.12620e10	−0.219112
$241$	3.30065e10	0.630264	0.315132	−	0.949048i	$-0.397951\pi$
$241$	3.30065e10	0.630264	0.315132	+	0.949048i	$0.397951\pi$
$242$	4.43848e10	0.831888
$243$	−3.48678e9	−0.0641500
$244$	4.42305e10	0.798855
$245$	9.35196e10	1.65827
$246$	−8.82890e9	−0.153709
$247$	2.63404e9	0.0450284
$248$	1.18825e10	0.199469
$249$	−4.84117e10	−0.798093
$250$	−8.77499e10	−1.42075
$251$	−1.11796e10	−0.177785	−0.0888926	−	0.996041i	$-0.528333\pi$
$251$	−1.11796e10	−0.177785	−0.0888926	+	0.996041i	$0.528333\pi$
$252$	−2.84054e9	−0.0443710
$253$	5.47078e10	0.839474
$254$	6.75130e10	1.01774
$255$	−2.01843e10	−0.298939
$256$	−7.31880e10	−1.06503
$257$	6.82071e10	0.975283	0.487642	−	0.873044i	$-0.337857\pi$
$257$	6.82071e10	0.975283	0.487642	+	0.873044i	$0.337857\pi$
$258$	−6.65490e9	−0.0935089
$259$	9.82664e9	0.135693
$260$	1.38056e10	0.187360
$261$	−9.45957e9	−0.126180
$262$	1.00925e10	0.132325
$263$	−1.28524e11	−1.65647	−0.828236	−	0.560379i	$-0.810655\pi$
$263$	−1.28524e11	−1.65647	−0.828236	+	0.560379i	$0.810655\pi$
$264$	7.12017e10	0.902138
$265$	−1.36953e11	−1.70594
$266$	3.22007e9	0.0394365
$267$	−5.55853e10	−0.669359
$268$	−2.47124e10	−0.292622
$269$	−1.82550e9	−0.0212567	−0.0106283	−	0.999944i	$-0.503383\pi$
$269$	−1.82550e9	−0.0212567	−0.0106283	+	0.999944i	$0.503383\pi$
$270$	2.07168e10	0.237239
$271$	1.42806e11	1.60836	0.804182	−	0.594383i	$-0.202604\pi$
$271$	1.42806e11	1.60836	0.804182	+	0.594383i	$0.202604\pi$
$272$	5.62694e9	0.0623322
$273$	−2.77419e9	−0.0302277
$274$	6.81100e10	0.730017
$275$	3.02675e11	3.19139
$276$	1.63232e10	0.169323
$277$	−1.25742e11	−1.28328	−0.641640	−	0.767006i	$-0.721745\pi$
$277$	−1.25742e11	−1.28328	−0.641640	+	0.767006i	$0.721745\pi$
$278$	−5.43843e10	−0.546100
$279$	−6.38517e9	−0.0630890
$280$	4.94607e10	0.480894
$281$	6.80928e10	0.651513	0.325756	−	0.945454i	$-0.394381\pi$
$281$	6.80928e10	0.651513	0.325756	+	0.945454i	$0.394381\pi$
$282$	3.98679e10	0.375407
$283$	−1.28817e11	−1.19381	−0.596904	−	0.802313i	$-0.703603\pi$
$283$	−1.28817e11	−1.19381	−0.596904	+	0.802313i	$0.703603\pi$
$284$	1.06427e10	0.0970780
$285$	2.52354e10	0.226573
$286$	2.37282e10	0.209709
$287$	1.13268e10	0.0985461
$288$	3.52399e10	0.301834
$289$	−1.08503e11	−0.914959
$290$	5.62043e10	0.466636
$291$	−2.21392e9	−0.0180986
$292$	6.85038e10	0.551432
$293$	1.18257e11	0.937394	0.468697	−	0.883359i	$-0.344724\pi$
$293$	1.18257e11	0.937394	0.468697	+	0.883359i	$0.344724\pi$
$294$	4.79587e10	0.374373
$295$	3.00678e10	0.231155
$296$	−7.34938e10	−0.556465
$297$	−3.82609e10	−0.285332
$298$	−2.18600e10	−0.160575
$299$	1.59419e10	0.115351
$300$	9.03095e10	0.643706
$301$	8.53774e9	0.0599506
$302$	6.93174e10	0.479525
$303$	1.32220e11	0.901166
$304$	−7.03508e9	−0.0472430
$305$	4.13852e11	2.73839
$306$	−1.03509e10	−0.0674889
$307$	1.20165e11	0.772070	0.386035	−	0.922484i	$-0.373844\pi$
$307$	1.20165e11	0.772070	0.386035	+	0.922484i	$0.373844\pi$
$308$	−3.11696e10	−0.197357
$309$	−1.04240e11	−0.650461
$310$	3.79376e10	0.233315
$311$	1.52314e11	0.923246	0.461623	−	0.887076i	$-0.347267\pi$
$311$	1.52314e11	0.923246	0.461623	+	0.887076i	$0.347267\pi$
$312$	2.07483e10	0.123961
$313$	−1.43895e11	−0.847416	−0.423708	−	0.905799i	$-0.639272\pi$
$313$	−1.43895e11	−0.847416	−0.423708	+	0.905799i	$0.639272\pi$
$314$	−2.10975e11	−1.22475
$315$	−2.65781e10	−0.152099
$316$	9.62161e10	0.542820
$317$	4.34701e10	0.241782	0.120891	−	0.992666i	$-0.461425\pi$
$317$	4.34701e10	0.241782	0.120891	+	0.992666i	$0.461425\pi$
$318$	−7.02322e10	−0.385136
$319$	−1.03801e11	−0.561233
$320$	−2.80566e11	−1.49575
$321$	−6.85345e10	−0.360277
$322$	1.94888e10	0.101026
$323$	−1.26086e10	−0.0644547
$324$	−1.14159e10	−0.0575517
$325$	8.82000e10	0.438524
$326$	1.65739e11	0.812729
$327$	4.91941e10	0.237930
$328$	−8.47137e10	−0.404130
$329$	−5.11475e10	−0.240682
$330$	2.27328e11	1.05521
$331$	1.33209e11	0.609968	0.304984	−	0.952358i	$-0.401349\pi$
$331$	1.33209e11	0.609968	0.304984	+	0.952358i	$0.401349\pi$
$332$	−1.58503e11	−0.716003
$333$	3.94925e10	0.176001
$334$	3.00539e10	0.132142
$335$	−2.31226e11	−1.00308
$336$	7.40940e9	0.0317144
$337$	4.38081e10	0.185020	0.0925102	−	0.995712i	$-0.470511\pi$
$337$	4.38081e10	0.185020	0.0925102	+	0.995712i	$0.470511\pi$
$338$	−1.59681e11	−0.665471
$339$	9.77989e10	0.402194
$340$	−6.60845e10	−0.268191
$341$	−7.00651e10	−0.280613
$342$	1.29412e10	0.0511514
$343$	−1.27406e11	−0.497011
$344$	−6.38540e10	−0.245853
$345$	1.52732e11	0.580421
$346$	−2.81279e11	−1.05510
$347$	−2.17392e11	−0.804935	−0.402467	−	0.915434i	$-0.631847\pi$
$347$	−2.17392e11	−0.804935	−0.402467	+	0.915434i	$0.631847\pi$
$348$	−3.09711e10	−0.113201
$349$	9.21736e10	0.332577	0.166288	−	0.986077i	$-0.446822\pi$
$349$	9.21736e10	0.332577	0.166288	+	0.986077i	$0.446822\pi$
$350$	1.07823e11	0.384066
$351$	−1.11493e10	−0.0392070
$352$	3.86691e11	1.34253
$353$	−4.92901e11	−1.68956	−0.844781	−	0.535113i	$-0.820269\pi$
$353$	−4.92901e11	−1.68956	−0.844781	+	0.535113i	$0.820269\pi$
$354$	1.54194e10	0.0521858
$355$	9.95810e10	0.332773
$356$	−1.81989e11	−0.600511
$357$	1.32795e10	0.0432686
$358$	−1.19673e11	−0.385055
$359$	1.26242e11	0.401123	0.200562	−	0.979681i	$-0.435723\pi$
$359$	1.26242e11	0.401123	0.200562	+	0.979681i	$0.435723\pi$
$360$	1.98779e11	0.623747
$361$	−3.06924e11	−0.951148
$362$	−3.66937e11	−1.12306
$363$	−2.28847e11	−0.691775
$364$	−9.08286e9	−0.0271185
$365$	6.40970e11	1.89025
$366$	2.12232e11	0.618223
$367$	−4.99871e11	−1.43834	−0.719169	−	0.694835i	$-0.755477\pi$
$367$	−4.99871e11	−1.43834	−0.719169	+	0.694835i	$0.755477\pi$
$368$	−4.25782e10	−0.121024
$369$	4.55216e10	0.127820
$370$	−2.34646e11	−0.650886
$371$	9.01027e10	0.246919
$372$	−2.09054e10	−0.0565998
$373$	−3.99849e11	−1.06956	−0.534781	−	0.844991i	$-0.679606\pi$
$373$	−3.99849e11	−1.06956	−0.534781	+	0.844991i	$0.679606\pi$
$374$	−1.13582e11	−0.300183
$375$	4.52437e11	1.18145
$376$	3.82534e11	0.987018
$377$	−3.02477e10	−0.0771181
$378$	−1.36298e10	−0.0343381
$379$	6.91858e11	1.72243	0.861213	−	0.508245i	$-0.169705\pi$
$379$	6.91858e11	1.72243	0.861213	+	0.508245i	$0.169705\pi$
$380$	8.26221e10	0.203269
$381$	−3.48096e11	−0.846323
$382$	−2.36956e11	−0.569355
$383$	−2.13034e11	−0.505888	−0.252944	−	0.967481i	$-0.581399\pi$
$383$	−2.13034e11	−0.505888	−0.252944	+	0.967481i	$0.581399\pi$
$384$	7.88712e10	0.185109
$385$	−2.91645e11	−0.676520
$386$	−2.64495e11	−0.606422
$387$	3.43125e10	0.0777594
$388$	−7.24850e9	−0.0162370
$389$	2.17993e11	0.482692	0.241346	−	0.970439i	$-0.422411\pi$
$389$	2.17993e11	0.482692	0.241346	+	0.970439i	$0.422411\pi$
$390$	6.62436e10	0.144995
$391$	−7.63105e10	−0.165116
$392$	4.60166e11	0.984299
$393$	−5.20366e10	−0.110038
$394$	−2.20052e11	−0.460035
$395$	9.00266e11	1.86073
$396$	−1.25268e11	−0.255984
$397$	−1.38887e11	−0.280612	−0.140306	−	0.990108i	$-0.544809\pi$
$397$	−1.38887e11	−0.280612	−0.140306	+	0.990108i	$0.544809\pi$
$398$	1.11294e11	0.222329
$399$	−1.66026e10	−0.0327943
$400$	−2.35567e11	−0.460092
$401$	−7.87148e11	−1.52022	−0.760111	−	0.649794i	$-0.774855\pi$
$401$	−7.87148e11	−1.52022	−0.760111	+	0.649794i	$0.774855\pi$
$402$	−1.18577e11	−0.226457
$403$	−2.04171e10	−0.0385585
$404$	4.32895e11	0.808475
$405$	−1.06815e11	−0.197282
$406$	−3.69773e10	−0.0675412
$407$	4.33356e11	0.782834
$408$	−9.93175e10	−0.177441
$409$	−1.03924e12	−1.83637	−0.918187	−	0.396148i	$-0.870347\pi$
$409$	−1.03924e12	−1.83637	−0.918187	+	0.396148i	$0.870347\pi$
$410$	−2.70468e11	−0.472703
$411$	−3.51174e11	−0.607063
$412$	−3.41287e11	−0.583556
$413$	−1.97819e10	−0.0334575
$414$	7.83238e10	0.131036
$415$	−1.48306e12	−2.45439
$416$	1.12682e11	0.184474
$417$	2.80404e11	0.454122
$418$	1.42005e11	0.227516
$419$	−1.85571e11	−0.294136	−0.147068	−	0.989126i	$-0.546984\pi$
$419$	−1.85571e11	−0.294136	−0.147068	+	0.989126i	$0.546984\pi$
$420$	−8.70183e10	−0.136455
$421$	−5.98397e11	−0.928368	−0.464184	−	0.885739i	$-0.653652\pi$
$421$	−5.98397e11	−0.928368	−0.464184	+	0.885739i	$0.653652\pi$
$422$	−2.02462e11	−0.310769
$423$	−2.05558e11	−0.312178
$424$	−6.73881e11	−1.01260
$425$	−4.22194e11	−0.627714
$426$	5.10671e10	0.0751274
$427$	−2.72277e11	−0.396357
$428$	−2.24386e11	−0.323220
$429$	−1.22342e11	−0.174389
$430$	−2.03869e11	−0.287569
$431$	1.23001e12	1.71696	0.858478	−	0.512850i	$-0.171410\pi$
$431$	1.23001e12	1.71696	0.858478	+	0.512850i	$0.171410\pi$
$432$	2.97778e10	0.0411354
$433$	−5.20413e11	−0.711463	−0.355732	−	0.934588i	$-0.615768\pi$
$433$	−5.20413e11	−0.711463	−0.355732	+	0.934588i	$0.615768\pi$
$434$	−2.49595e10	−0.0337701
$435$	−2.89788e11	−0.388042
$436$	1.61064e11	0.213457
$437$	9.54072e10	0.125145
$438$	3.28702e11	0.426746
$439$	−7.79982e11	−1.00229	−0.501146	−	0.865363i	$-0.667088\pi$
$439$	−7.79982e11	−1.00229	−0.501146	+	0.865363i	$0.667088\pi$
$440$	2.18122e12	2.77436
$441$	−2.47274e11	−0.311318
$442$	−3.30978e10	−0.0412477
$443$	−1.51957e12	−1.87458	−0.937291	−	0.348548i	$-0.886675\pi$
$443$	−1.51957e12	−1.87458	−0.937291	+	0.348548i	$0.886675\pi$
$444$	1.29301e11	0.157898
$445$	−1.70282e12	−2.05849
$446$	−2.42389e11	−0.290072
$447$	1.12710e11	0.133530
$448$	1.84587e11	0.216496
$449$	9.46589e11	1.09914	0.549570	−	0.835448i	$-0.314792\pi$
$449$	9.46589e11	1.09914	0.549570	+	0.835448i	$0.314792\pi$
$450$	4.33333e11	0.498156
$451$	4.99514e11	0.568530
$452$	3.20199e11	0.360825
$453$	−3.57399e11	−0.398760
$454$	1.23713e11	0.136667
$455$	−8.49856e10	−0.0929596
$456$	1.24172e11	0.134487
$457$	−1.31278e12	−1.40789	−0.703943	−	0.710256i	$-0.748579\pi$
$457$	−1.31278e12	−1.40789	−0.703943	+	0.710256i	$0.748579\pi$
$458$	3.18065e11	0.337770
$459$	5.33691e10	0.0561219
$460$	5.00051e11	0.520720
$461$	−9.37640e10	−0.0966901	−0.0483450	−	0.998831i	$-0.515395\pi$
$461$	−9.37640e10	−0.0966901	−0.0483450	+	0.998831i	$0.515395\pi$
$462$	−1.49561e11	−0.152732
$463$	−4.76737e11	−0.482131	−0.241065	−	0.970509i	$-0.577497\pi$
$463$	−4.76737e11	−0.482131	−0.241065	+	0.970509i	$0.577497\pi$
$464$	8.07865e10	0.0809111
$465$	−1.95606e11	−0.194018
$466$	1.82435e11	0.179214
$467$	1.50733e12	1.46650	0.733249	−	0.679960i	$-0.238003\pi$
$467$	1.50733e12	1.46650	0.733249	+	0.679960i	$0.238003\pi$
$468$	−3.65033e10	−0.0351743
$469$	1.52126e11	0.145186
$470$	1.22133e12	1.15449
$471$	1.08778e12	1.01847
$472$	1.47950e11	0.137207
$473$	3.76515e11	0.345865
$474$	4.61674e11	0.420081
$475$	5.27848e11	0.475760
$476$	4.34777e10	0.0388181
$477$	3.62116e11	0.320269
$478$	5.61598e11	0.492039
$479$	−4.82675e11	−0.418933	−0.209467	−	0.977816i	$-0.567173\pi$
$479$	−4.82675e11	−0.418933	−0.209467	+	0.977816i	$0.567173\pi$
$480$	1.07955e12	0.928235
$481$	1.26280e11	0.107568
$482$	5.18529e11	0.437584
$483$	−1.00484e11	−0.0840104
$484$	−7.49257e11	−0.620621
$485$	−6.78221e10	−0.0556588
$486$	−5.47771e10	−0.0445385
$487$	−1.54778e12	−1.24690	−0.623448	−	0.781865i	$-0.714269\pi$
$487$	−1.54778e12	−1.24690	−0.623448	+	0.781865i	$0.714269\pi$
$488$	2.03637e12	1.62543
$489$	−8.54547e11	−0.675844
$490$	1.46918e12	1.15131
$491$	1.47468e12	1.14507	0.572534	−	0.819881i	$-0.305961\pi$
$491$	1.47468e12	1.14507	0.572534	+	0.819881i	$0.305961\pi$
$492$	1.49040e11	0.114673
$493$	1.44789e11	0.110389
$494$	4.13806e10	0.0312626
$495$	−1.17210e12	−0.877486
$496$	5.45306e10	0.0404550
$497$	−6.55153e10	−0.0481658
$498$	−7.60544e11	−0.554105
$499$	−8.77017e11	−0.633222	−0.316611	−	0.948556i	$-0.602545\pi$
$499$	−8.77017e11	−0.633222	−0.316611	+	0.948556i	$0.602545\pi$
$500$	1.48130e12	1.05993
$501$	−1.54957e11	−0.109886
$502$	−1.75631e11	−0.123434
$503$	−1.48585e12	−1.03495	−0.517474	−	0.855699i	$-0.673128\pi$
$503$	−1.48585e12	−1.03495	−0.517474	+	0.855699i	$0.673128\pi$
$504$	−1.30778e11	−0.0902815
$505$	4.05047e12	2.77137
$506$	8.59455e11	0.582836
$507$	8.23314e11	0.553388
$508$	−1.13968e12	−0.759273
$509$	−1.72731e12	−1.14062	−0.570308	−	0.821431i	$-0.693176\pi$
$509$	−1.72731e12	−1.14062	−0.570308	+	0.821431i	$0.693176\pi$
$510$	−3.17094e11	−0.207550
$511$	−4.21700e11	−0.273596
$512$	−6.51234e11	−0.418815
$513$	−6.67247e10	−0.0425362
$514$	1.07153e12	0.677126
$515$	−3.19333e12	−2.00037
$516$	1.12341e11	0.0697613
$517$	−2.25561e12	−1.38853
$518$	1.54376e11	0.0942096
$519$	1.45027e12	0.877395
$520$	6.35610e11	0.381220
$521$	7.82017e11	0.464993	0.232496	−	0.972597i	$-0.425311\pi$
$521$	7.82017e11	0.464993	0.232496	+	0.972597i	$0.425311\pi$
$522$	−1.48609e11	−0.0876048
$523$	−2.13367e12	−1.24701	−0.623504	−	0.781820i	$-0.714291\pi$
$523$	−2.13367e12	−1.24701	−0.623504	+	0.781820i	$0.714291\pi$
$524$	−1.70371e11	−0.0987197
$525$	−5.55934e11	−0.319379
$526$	−2.01911e12	−1.15007
$527$	9.77320e10	0.0551937
$528$	3.26755e11	0.182966
$529$	−1.22372e12	−0.679411
$530$	−2.15152e12	−1.18442
$531$	−7.95020e10	−0.0433963
$532$	−5.43579e10	−0.0294212
$533$	1.45559e11	0.0781207
$534$	−8.73240e11	−0.464727
$535$	−2.09951e12	−1.10797
$536$	−1.13776e12	−0.595398
$537$	6.17031e11	0.320201
$538$	−2.86784e10	−0.0147582
$539$	−2.71336e12	−1.38471
$540$	−3.49720e11	−0.176990
$541$	−8.84532e11	−0.443941	−0.221971	−	0.975053i	$-0.571249\pi$
$541$	−8.84532e11	−0.443941	−0.221971	+	0.975053i	$0.571249\pi$
$542$	2.24347e12	1.11667
$543$	1.89192e12	0.933907
$544$	−5.39386e11	−0.264061
$545$	1.50703e12	0.731709
$546$	−4.35823e10	−0.0209867
$547$	1.54270e12	0.736783	0.368391	−	0.929671i	$-0.379909\pi$
$547$	1.54270e12	0.736783	0.368391	+	0.929671i	$0.379909\pi$
$548$	−1.14976e12	−0.544622
$549$	−1.09426e12	−0.514098
$550$	4.75501e12	2.21574
$551$	−1.81023e11	−0.0836663
$552$	7.51520e11	0.344520
$553$	−5.92294e11	−0.269323
$554$	−1.97540e12	−0.890964
$555$	1.20983e12	0.541259
$556$	9.18060e11	0.407412
$557$	2.50149e12	1.10116	0.550580	−	0.834782i	$-0.314406\pi$
$557$	2.50149e12	1.10116	0.550580	+	0.834782i	$0.314406\pi$
$558$	−1.00310e11	−0.0438018
$559$	1.09717e11	0.0475248
$560$	2.26982e11	0.0975317
$561$	5.85625e11	0.249624
$562$	1.06973e12	0.452337
$563$	4.12189e12	1.72906	0.864528	−	0.502584i	$-0.167617\pi$
$563$	4.12189e12	1.72906	0.864528	+	0.502584i	$0.167617\pi$
$564$	−6.73008e11	−0.280069
$565$	2.99601e12	1.23687
$566$	−2.02371e12	−0.828845
$567$	7.02749e10	0.0285546
$568$	4.89991e11	0.197524
$569$	−1.93214e12	−0.772738	−0.386369	−	0.922344i	$-0.626271\pi$
$569$	−1.93214e12	−0.772738	−0.386369	+	0.922344i	$0.626271\pi$
$570$	3.96446e11	0.157307
$571$	1.99421e12	0.785071	0.392536	−	0.919737i	$-0.371598\pi$
$571$	1.99421e12	0.785071	0.392536	+	0.919737i	$0.371598\pi$
$572$	−4.00555e11	−0.156451
$573$	1.22174e12	0.473460
$574$	1.77944e11	0.0684193
$575$	3.19468e12	1.21877
$576$	7.41841e11	0.280808
$577$	1.57088e12	0.590001	0.295000	−	0.955497i	$-0.404680\pi$
$577$	1.57088e12	0.590001	0.295000	+	0.955497i	$0.404680\pi$
$578$	−1.70457e12	−0.635244
$579$	1.36373e12	0.504284
$580$	−9.48782e11	−0.348129
$581$	9.75722e11	0.355249
$582$	−3.47805e10	−0.0125656
$583$	3.97354e12	1.42452
$584$	3.15391e12	1.12200
$585$	−3.41551e11	−0.120574
$586$	1.85781e12	0.650820
$587$	1.24412e12	0.432504	0.216252	−	0.976338i	$-0.430617\pi$
$587$	1.24412e12	0.432504	0.216252	+	0.976338i	$0.430617\pi$
$588$	−8.09589e11	−0.279297
$589$	−1.22189e11	−0.0418326
$590$	4.72363e11	0.160488
$591$	1.13458e12	0.382553
$592$	−3.37274e11	−0.112859
$593$	−2.93383e12	−0.974292	−0.487146	−	0.873321i	$-0.661962\pi$
$593$	−2.93383e12	−0.974292	−0.487146	+	0.873321i	$0.661962\pi$
$594$	−6.01075e11	−0.198102
$595$	4.06808e11	0.133065
$596$	3.69018e11	0.119795
$597$	−5.73828e11	−0.184883
$598$	2.50446e11	0.0800865
$599$	2.07249e12	0.657767	0.328884	−	0.944370i	$-0.393328\pi$
$599$	2.07249e12	0.657767	0.328884	+	0.944370i	$0.393328\pi$
$600$	4.15785e12	1.30975
$601$	−4.76700e12	−1.49043	−0.745213	−	0.666827i	$-0.767652\pi$
$601$	−4.76700e12	−1.49043	−0.745213	+	0.666827i	$0.767652\pi$
$602$	1.34127e11	0.0416229
$603$	6.11383e11	0.188315
$604$	−1.17014e12	−0.357745
$605$	−7.01058e12	−2.12743
$606$	2.07716e12	0.625668
$607$	3.17116e11	0.0948133	0.0474066	−	0.998876i	$-0.484904\pi$
$607$	3.17116e11	0.0948133	0.0474066	+	0.998876i	$0.484904\pi$
$608$	6.74367e11	0.200138
$609$	1.90654e11	0.0561654
$610$	6.50158e12	1.90123
$611$	−6.57288e11	−0.190796
$612$	1.74733e11	0.0503494
$613$	−5.57634e12	−1.59506	−0.797530	−	0.603279i	$-0.793860\pi$
$613$	−5.57634e12	−1.59506	−0.797530	+	0.603279i	$0.793860\pi$
$614$	1.88779e12	0.536038
$615$	1.39453e12	0.393087
$616$	−1.43505e12	−0.401562
$617$	−4.78857e12	−1.33022	−0.665108	−	0.746747i	$-0.731615\pi$
$617$	−4.78857e12	−1.33022	−0.665108	+	0.746747i	$0.731615\pi$
$618$	−1.63760e12	−0.451606
$619$	1.27618e12	0.349384	0.174692	−	0.984623i	$-0.444107\pi$
$619$	1.27618e12	0.349384	0.174692	+	0.984623i	$0.444107\pi$
$620$	−6.40423e11	−0.174062
$621$	−4.03836e11	−0.108966
$622$	2.39284e12	0.640998
$623$	1.12030e12	0.297947
$624$	9.52168e10	0.0251410
$625$	5.64890e12	1.48083
$626$	−2.26058e12	−0.588350
$627$	−7.32177e11	−0.189196
$628$	3.56146e12	0.913713
$629$	−6.04477e11	−0.153975
$630$	−4.17540e11	−0.105600
$631$	4.94728e12	1.24232	0.621161	−	0.783683i	$-0.286661\pi$
$631$	4.94728e12	1.24232	0.621161	+	0.783683i	$0.286661\pi$
$632$	4.42978e12	1.10447
$633$	1.04389e12	0.258427
$634$	6.82911e11	0.167866
$635$	−1.06637e13	−2.60271
$636$	1.18559e12	0.287327
$637$	−7.90678e11	−0.190271
$638$	−1.63070e12	−0.389657
$639$	−2.63301e11	−0.0624739
$640$	2.41617e12	0.569269
$641$	5.38898e12	1.26080	0.630399	−	0.776271i	$-0.282891\pi$
$641$	5.38898e12	1.26080	0.630399	+	0.776271i	$0.282891\pi$
$642$	−1.07667e12	−0.250136
$643$	−1.02124e12	−0.235602	−0.117801	−	0.993037i	$-0.537585\pi$
$643$	−1.02124e12	−0.235602	−0.117801	+	0.993037i	$0.537585\pi$
$644$	−3.28989e11	−0.0753693
$645$	1.05114e12	0.239135
$646$	−1.98080e11	−0.0447501
$647$	−3.44500e12	−0.772895	−0.386447	−	0.922311i	$-0.626298\pi$
$647$	−3.44500e12	−0.772895	−0.386447	+	0.922311i	$0.626298\pi$
$648$	−5.25589e11	−0.117100
$649$	−8.72384e11	−0.193022
$650$	1.38561e12	0.304461
$651$	1.28691e11	0.0280823
$652$	−2.79783e12	−0.606328
$653$	6.88490e12	1.48180	0.740898	−	0.671617i	$-0.234400\pi$
$653$	6.88490e12	1.48180	0.740898	+	0.671617i	$0.234400\pi$
$654$	7.72836e11	0.165191
$655$	−1.59411e12	−0.338401
$656$	−3.88763e11	−0.0819630
$657$	−1.69478e12	−0.354870
$658$	−8.03524e11	−0.167102
$659$	−4.67100e12	−0.964773	−0.482386	−	0.875958i	$-0.660230\pi$
$659$	−4.67100e12	−0.964773	−0.482386	+	0.875958i	$0.660230\pi$
$660$	−3.83751e12	−0.787231
$661$	3.71454e12	0.756830	0.378415	−	0.925636i	$-0.376469\pi$
$661$	3.71454e12	0.756830	0.378415	+	0.925636i	$0.376469\pi$
$662$	2.09270e12	0.423492
$663$	1.70652e11	0.0343005
$664$	−7.29745e12	−1.45685
$665$	−5.08611e11	−0.100853
$666$	6.20424e11	0.122195
$667$	−1.09560e12	−0.214331
$668$	−5.07339e11	−0.0985835
$669$	1.24975e12	0.241216
$670$	−3.63255e12	−0.696425
$671$	−1.20075e13	−2.28665
$672$	−7.10248e11	−0.134353
$673$	1.00851e12	0.189502	0.0947511	−	0.995501i	$-0.469794\pi$
$673$	1.00851e12	0.189502	0.0947511	+	0.995501i	$0.469794\pi$
$674$	6.88221e11	0.128457
$675$	−2.23425e12	−0.414253
$676$	2.69557e12	0.496468
$677$	9.99402e12	1.82848	0.914242	−	0.405168i	$-0.132787\pi$
$677$	9.99402e12	1.82848	0.914242	+	0.405168i	$0.132787\pi$
$678$	1.53641e12	0.279238
$679$	4.46208e10	0.00805608
$680$	−3.04253e12	−0.545688
$681$	−6.37863e11	−0.113649
$682$	−1.10072e12	−0.194826
$683$	−2.94151e12	−0.517222	−0.258611	−	0.965981i	$-0.583265\pi$
$683$	−2.94151e12	−0.517222	−0.258611	+	0.965981i	$0.583265\pi$
$684$	−2.18460e11	−0.0381610
$685$	−1.07580e13	−1.86691
$686$	−2.00153e12	−0.345068
$687$	−1.63994e12	−0.280881
$688$	−2.93035e11	−0.0498623
$689$	1.15789e12	0.195741
$690$	2.39940e12	0.402978
$691$	5.36780e12	0.895664	0.447832	−	0.894118i	$-0.352196\pi$
$691$	5.36780e12	0.895664	0.447832	+	0.894118i	$0.352196\pi$
$692$	4.74826e12	0.787149
$693$	7.71135e11	0.127008
$694$	−3.41521e12	−0.558856
$695$	8.59001e12	1.39657
$696$	−1.42591e12	−0.230330
$697$	−6.96759e11	−0.111824
$698$	1.44804e12	0.230904
$699$	−9.40631e11	−0.149029
$700$	−1.82016e12	−0.286528
$701$	−6.20303e12	−0.970226	−0.485113	−	0.874451i	$-0.661222\pi$
$701$	−6.20303e12	−0.970226	−0.485113	+	0.874451i	$0.661222\pi$
$702$	−1.75154e11	−0.0272209
$703$	7.55746e11	0.116702
$704$	8.14030e12	1.24900
$705$	−6.29714e12	−0.960047
$706$	−7.74344e12	−1.17304
$707$	−2.66485e12	−0.401130
$708$	−2.60294e11	−0.0389327
$709$	1.11494e13	1.65708	0.828541	−	0.559928i	$-0.189171\pi$
$709$	1.11494e13	1.65708	0.828541	+	0.559928i	$0.189171\pi$
$710$	1.56441e12	0.231040
$711$	−2.38038e12	−0.349328
$712$	−8.37878e12	−1.22186
$713$	−7.39523e11	−0.107164
$714$	2.08619e11	0.0300408
$715$	−3.74787e12	−0.536300
$716$	2.02019e12	0.287266
$717$	−2.89558e12	−0.409166
$718$	1.98325e12	0.278495
$719$	−1.13389e13	−1.58231	−0.791154	−	0.611616i	$-0.790520\pi$
$719$	−1.13389e13	−1.58231	−0.791154	+	0.611616i	$0.790520\pi$
$720$	9.12224e11	0.126504
$721$	2.10092e12	0.289535
$722$	−4.82175e12	−0.660370
$723$	−2.67352e12	−0.363883
$724$	6.19425e12	0.837848
$725$	−6.06148e12	−0.814813
$726$	−3.59517e12	−0.480291
$727$	9.02273e12	1.19793	0.598967	−	0.800773i	$-0.295578\pi$
$727$	9.02273e12	1.19793	0.598967	+	0.800773i	$0.295578\pi$
$728$	−4.18174e11	−0.0551780
$729$	2.82430e11	0.0370370
$730$	1.00696e13	1.31238
$731$	−5.25191e11	−0.0680282
$732$	−3.58267e12	−0.461219
$733$	−1.56301e12	−0.199984	−0.0999920	−	0.994988i	$-0.531882\pi$
$733$	−1.56301e12	−0.199984	−0.0999920	+	0.994988i	$0.531882\pi$
$734$	−7.85294e12	−0.998619
$735$	−7.57508e12	−0.957402
$736$	4.08145e12	0.512701
$737$	6.70877e12	0.837605
$738$	7.15141e11	0.0887438
$739$	−5.73629e12	−0.707507	−0.353754	−	0.935339i	$-0.615095\pi$
$739$	−5.73629e12	−0.707507	−0.353754	+	0.935339i	$0.615095\pi$
$740$	3.96104e12	0.485587
$741$	−2.13357e11	−0.0259971
$742$	1.41551e12	0.171433
$743$	5.90927e12	0.711352	0.355676	−	0.934609i	$-0.384251\pi$
$743$	5.90927e12	0.711352	0.355676	+	0.934609i	$0.384251\pi$
$744$	−9.62483e11	−0.115164
$745$	3.45279e12	0.410645
$746$	−6.28159e12	−0.742583
$747$	3.92135e12	0.460779
$748$	1.91737e12	0.223949
$749$	1.38129e12	0.160368
$750$	7.10774e12	0.820269
$751$	6.05076e11	0.0694113	0.0347056	−	0.999398i	$-0.488951\pi$
$751$	6.05076e11	0.0694113	0.0347056	+	0.999398i	$0.488951\pi$
$752$	1.75550e12	0.200180
$753$	9.05550e11	0.102644
$754$	−4.75189e11	−0.0535421
$755$	−1.09487e13	−1.22631
$756$	2.30084e11	0.0256176
$757$	1.87357e12	0.207366	0.103683	−	0.994610i	$-0.466937\pi$
$757$	1.87357e12	0.207366	0.103683	+	0.994610i	$0.466937\pi$
$758$	1.08690e13	1.19586
$759$	−4.43133e12	−0.484670
$760$	3.80392e12	0.413590
$761$	9.68739e12	1.04707	0.523535	−	0.852004i	$-0.324613\pi$
$761$	9.68739e12	1.04707	0.523535	+	0.852004i	$0.324613\pi$
$762$	−5.46856e12	−0.587591
$763$	−9.91491e11	−0.105908
$764$	4.00005e12	0.424762
$765$	1.63493e12	0.172593
$766$	−3.34675e12	−0.351232
$767$	−2.54214e11	−0.0265228
$768$	5.92823e12	0.614893
$769$	−1.11147e13	−1.14611	−0.573057	−	0.819516i	$-0.694243\pi$
$769$	−1.11147e13	−1.14611	−0.573057	+	0.819516i	$0.694243\pi$
$770$	−4.58172e12	−0.469699
$771$	−5.52478e12	−0.563080
$772$	4.46493e12	0.452415
$773$	5.13307e12	0.517094	0.258547	−	0.965999i	$-0.416756\pi$
$773$	5.13307e12	0.517094	0.258547	+	0.965999i	$0.416756\pi$
$774$	5.39047e11	0.0539874
$775$	−4.09147e12	−0.407401
$776$	−3.33721e11	−0.0330374
$777$	−7.95958e11	−0.0783422
$778$	3.42466e12	0.335127
$779$	8.71122e11	0.0847541
$780$	−1.11826e12	−0.108172
$781$	−2.88923e12	−0.277877
$782$	−1.19883e12	−0.114638
$783$	7.66225e11	0.0728498
$784$	2.11177e12	0.199629
$785$	3.33235e13	3.13212
$786$	−8.17491e11	−0.0763979
$787$	−6.86470e12	−0.637875	−0.318937	−	0.947776i	$-0.603326\pi$
$787$	−6.86470e12	−0.637875	−0.318937	+	0.947776i	$0.603326\pi$
$788$	3.71468e12	0.343205
$789$	1.04105e13	0.956365
$790$	1.41431e13	1.29188
$791$	−1.97110e12	−0.179026
$792$	−5.76734e12	−0.520850
$793$	−3.49899e12	−0.314205
$794$	−2.18191e12	−0.194825
$795$	1.10932e13	0.984928
$796$	−1.87874e12	−0.165866
$797$	9.50994e12	0.834863	0.417432	−	0.908708i	$-0.362930\pi$
$797$	9.50994e12	0.834863	0.417432	+	0.908708i	$0.362930\pi$
$798$	−2.60826e11	−0.0227687
$799$	3.14629e12	0.273111
$800$	2.25809e13	1.94911
$801$	4.50241e12	0.386455
$802$	−1.23660e13	−1.05547
$803$	−1.85970e13	−1.57842
$804$	2.00170e12	0.168946
$805$	−3.07825e12	−0.258358
$806$	−3.20750e11	−0.0267707
$807$	1.47865e11	0.0122726
$808$	1.99305e13	1.64500
$809$	−1.84582e13	−1.51503	−0.757516	−	0.652816i	$-0.773587\pi$
$809$	−1.84582e13	−1.51503	−0.757516	+	0.652816i	$0.773587\pi$
$810$	−1.67806e12	−0.136970
$811$	−7.97245e12	−0.647139	−0.323570	−	0.946204i	$-0.604883\pi$
$811$	−7.97245e12	−0.647139	−0.323570	+	0.946204i	$0.604883\pi$
$812$	6.24213e11	0.0503884
$813$	−1.15673e13	−0.928589
$814$	6.80798e12	0.543511
$815$	−2.61785e13	−2.07843
$816$	−4.55782e11	−0.0359875
$817$	6.56620e11	0.0515602
$818$	−1.63264e13	−1.27497
$819$	2.24710e11	0.0174520
$820$	4.56576e12	0.352655
$821$	−1.51036e13	−1.16021	−0.580103	−	0.814543i	$-0.696988\pi$
$821$	−1.51036e13	−1.16021	−0.580103	+	0.814543i	$0.696988\pi$
$822$	−5.51691e12	−0.421476
$823$	−2.55362e13	−1.94025	−0.970125	−	0.242607i	$-0.921997\pi$
$823$	−2.55362e13	−1.94025	−0.970125	+	0.242607i	$0.921997\pi$
$824$	−1.57129e13	−1.18736
$825$	−2.45167e13	−1.84255
$826$	−3.10772e11	−0.0232291
$827$	2.06767e13	1.53712	0.768558	−	0.639780i	$-0.220974\pi$
$827$	2.06767e13	1.53712	0.768558	+	0.639780i	$0.220974\pi$
$828$	−1.32218e12	−0.0977584
$829$	2.61708e13	1.92452	0.962258	−	0.272137i	$-0.0877304\pi$
$829$	2.61708e13	1.92452	0.962258	+	0.272137i	$0.0877304\pi$
$830$	−2.32988e13	−1.70405
$831$	1.01851e13	0.740902
$832$	2.37209e12	0.171624
$833$	3.78480e12	0.272358
$834$	4.40513e12	0.315291
$835$	−4.74703e12	−0.337934
$836$	−2.39719e12	−0.169736
$837$	5.17199e11	0.0364244
$838$	−2.91531e12	−0.204214
$839$	−1.97813e13	−1.37824	−0.689122	−	0.724645i	$-0.742004\pi$
$839$	−1.97813e13	−1.37824	−0.689122	+	0.724645i	$0.742004\pi$
$840$	−4.00632e12	−0.277644
$841$	−1.24284e13	−0.856708
$842$	−9.40078e12	−0.644554
$843$	−5.51552e12	−0.376151
$844$	3.41775e12	0.231846
$845$	2.52217e13	1.70184
$846$	−3.22930e12	−0.216741
$847$	4.61233e12	0.307925
$848$	−3.09254e12	−0.205368
$849$	1.04342e13	0.689246
$850$	−6.63263e12	−0.435814
$851$	4.57398e12	0.298959
$852$	−8.62062e11	−0.0560480
$853$	−9.83550e12	−0.636101	−0.318050	−	0.948074i	$-0.603028\pi$
$853$	−9.83550e12	−0.636101	−0.318050	+	0.948074i	$0.603028\pi$
$854$	−4.27746e12	−0.275185
$855$	−2.04407e12	−0.130812
$856$	−1.03307e13	−0.657655
$857$	−2.31797e13	−1.46789	−0.733947	−	0.679207i	$-0.762324\pi$
$857$	−2.31797e13	−1.46789	−0.733947	+	0.679207i	$0.762324\pi$
$858$	−1.92198e12	−0.121076
$859$	−4.78226e12	−0.299684	−0.149842	−	0.988710i	$-0.547877\pi$
$859$	−4.78226e12	−0.299684	−0.149842	+	0.988710i	$0.547877\pi$
$860$	3.44150e12	0.214538
$861$	−9.17473e11	−0.0568956
$862$	1.93233e13	1.19206
$863$	−7.08844e11	−0.0435013	−0.0217506	−	0.999763i	$-0.506924\pi$
$863$	−7.08844e11	−0.0435013	−0.0217506	+	0.999763i	$0.506924\pi$
$864$	−2.85443e12	−0.174264
$865$	4.44281e13	2.69827
$866$	−8.17564e12	−0.493960
$867$	8.78875e12	0.528252
$868$	4.21341e11	0.0251939
$869$	−2.61202e13	−1.55377
$870$	−4.55255e12	−0.269412
$871$	1.95494e12	0.115094
$872$	7.41540e12	0.434320
$873$	1.79328e11	0.0104492
$874$	1.49884e12	0.0868868
$875$	−9.11871e12	−0.525893
$876$	−5.54880e12	−0.318369
$877$	−1.86698e13	−1.06572	−0.532859	−	0.846204i	$-0.678883\pi$
$877$	−1.86698e13	−1.06572	−0.532859	+	0.846204i	$0.678883\pi$
$878$	−1.22535e13	−0.695878
$879$	−9.57880e12	−0.541204
$880$	1.00099e13	0.562677
$881$	−1.11188e12	−0.0621825	−0.0310912	−	0.999517i	$-0.509898\pi$
$881$	−1.11188e12	−0.0621825	−0.0310912	+	0.999517i	$0.509898\pi$
$882$	−3.88465e12	−0.216144
$883$	−2.83915e13	−1.57169	−0.785843	−	0.618426i	$-0.787771\pi$
$883$	−2.83915e13	−1.57169	−0.785843	+	0.618426i	$0.787771\pi$
$884$	5.58723e11	0.0307724
$885$	−2.43549e12	−0.133457
$886$	−2.38723e13	−1.30150
$887$	−2.15452e13	−1.16868	−0.584339	−	0.811510i	$-0.698646\pi$
$887$	−2.15452e13	−1.16868	−0.584339	+	0.811510i	$0.698646\pi$
$888$	5.95300e12	0.321275
$889$	7.01575e12	0.376718
$890$	−2.67512e13	−1.42918
$891$	3.09913e12	0.164737
$892$	4.09176e12	0.216405
$893$	−3.93365e12	−0.206997
$894$	1.77066e12	0.0927078
$895$	1.89024e13	0.984719
$896$	−1.58962e12	−0.0823963
$897$	−1.29130e12	−0.0665978
$898$	1.48708e13	0.763118
$899$	1.40315e12	0.0716449
$900$	−7.31507e12	−0.371644
$901$	−5.54258e12	−0.280189
$902$	7.84732e12	0.394723
$903$	−6.91557e11	−0.0346125
$904$	1.47419e13	0.734170
$905$	5.79578e13	2.87206
$906$	−5.61471e12	−0.276854
$907$	2.80098e13	1.37429	0.687143	−	0.726522i	$-0.258865\pi$
$907$	2.80098e13	1.37429	0.687143	+	0.726522i	$0.258865\pi$
$908$	−2.08840e12	−0.101959
$909$	−1.07098e13	−0.520288
$910$	−1.33512e12	−0.0645406
$911$	1.11071e13	0.534281	0.267141	−	0.963658i	$-0.413921\pi$
$911$	1.11071e13	0.534281	0.267141	+	0.963658i	$0.413921\pi$
$912$	5.69841e11	0.0272758
$913$	4.30294e13	2.04949
$914$	−2.06236e13	−0.977477
$915$	−3.35220e13	−1.58101
$916$	−5.36924e12	−0.251990
$917$	1.04878e12	0.0489804
$918$	8.38424e11	0.0389647
$919$	−1.57365e13	−0.727758	−0.363879	−	0.931446i	$-0.618548\pi$
$919$	−1.57365e13	−0.727758	−0.363879	+	0.931446i	$0.618548\pi$
$920$	2.30223e13	1.05951
$921$	−9.73339e12	−0.445755
$922$	−1.47302e12	−0.0671307
$923$	−8.41925e11	−0.0381826
$924$	2.52474e12	0.113944
$925$	2.53059e13	1.13654
$926$	−7.48951e12	−0.334737
$927$	8.44344e12	0.375544
$928$	−7.74401e12	−0.342768
$929$	2.12139e13	0.934435	0.467217	−	0.884142i	$-0.345257\pi$
$929$	2.12139e13	0.934435	0.467217	+	0.884142i	$0.345257\pi$
$930$	−3.07295e12	−0.134704
$931$	−4.73195e12	−0.206427
$932$	−3.07968e12	−0.133701
$933$	−1.23374e13	−0.533036
$934$	2.36800e13	1.01817
$935$	1.79402e13	0.767673
$936$	−1.68061e12	−0.0715691
$937$	4.96097e12	0.210251	0.105126	−	0.994459i	$-0.466476\pi$
$937$	4.96097e12	0.210251	0.105126	+	0.994459i	$0.466476\pi$
$938$	2.38989e12	0.100801
$939$	1.16555e13	0.489256
$940$	−2.06172e13	−0.861299
$941$	2.81479e13	1.17029	0.585143	−	0.810930i	$-0.301038\pi$
$941$	2.81479e13	1.17029	0.585143	+	0.810930i	$0.301038\pi$
$942$	1.70890e13	0.707110
$943$	5.27227e12	0.217117
$944$	6.78962e11	0.0278273
$945$	2.15283e12	0.0878145
$946$	5.91502e12	0.240130
$947$	3.56313e13	1.43965	0.719824	−	0.694156i	$-0.244222\pi$
$947$	3.56313e13	1.43965	0.719824	+	0.694156i	$0.244222\pi$
$948$	−7.79350e12	−0.313397
$949$	−5.41919e12	−0.216889
$950$	8.29245e12	0.330314
$951$	−3.52108e12	−0.139593
$952$	2.00171e12	0.0789832
$953$	2.49292e13	0.979018	0.489509	−	0.871998i	$-0.337176\pi$
$953$	2.49292e13	0.979018	0.489509	+	0.871998i	$0.337176\pi$
$954$	5.68881e12	0.222358
$955$	3.74273e13	1.45604
$956$	−9.48030e12	−0.367081
$957$	8.40787e12	0.324028
$958$	−7.58278e12	−0.290860
$959$	7.07778e12	0.270218
$960$	2.27258e13	0.863574
$961$	−2.54925e13	−0.964178
$962$	1.98385e12	0.0746830
$963$	5.55129e12	0.208006
$964$	−8.75326e12	−0.326455
$965$	4.17771e13	1.55083
$966$	−1.57859e12	−0.0583273
$967$	−4.82176e13	−1.77332	−0.886659	−	0.462424i	$-0.846980\pi$
$967$	−4.82176e13	−1.77332	−0.886659	+	0.462424i	$0.846980\pi$
$968$	−3.44958e13	−1.26278
$969$	1.02129e12	0.0372130
$970$	−1.06548e12	−0.0386432
$971$	2.25803e12	0.0815161	0.0407580	−	0.999169i	$-0.487023\pi$
$971$	2.25803e12	0.0815161	0.0407580	+	0.999169i	$0.487023\pi$
$972$	9.24690e11	0.0332275
$973$	−5.65146e12	−0.202140
$974$	−2.43156e13	−0.865703
$975$	−7.14420e12	−0.253182
$976$	9.34521e12	0.329659
$977$	4.23005e13	1.48532	0.742660	−	0.669669i	$-0.233564\pi$
$977$	4.23005e13	1.48532	0.742660	+	0.669669i	$0.233564\pi$
$978$	−1.34249e13	−0.469229
$979$	4.94054e13	1.71891
$980$	−2.48012e13	−0.858927
$981$	−3.98473e12	−0.137369
$982$	2.31671e13	0.795005
$983$	3.49372e13	1.19343	0.596716	−	0.802453i	$-0.296472\pi$
$983$	3.49372e13	1.19343	0.596716	+	0.802453i	$0.296472\pi$
$984$	6.86181e12	0.233325
$985$	3.47572e13	1.17647
$986$	2.27463e12	0.0766415
$987$	4.14295e12	0.138958
$988$	−6.98543e11	−0.0233231
$989$	3.97404e12	0.132084
$990$	−1.84136e13	−0.609227
$991$	4.83227e13	1.59155	0.795774	−	0.605594i	$-0.207064\pi$
$991$	4.83227e13	1.59155	0.795774	+	0.605594i	$0.207064\pi$
$992$	−5.22717e12	−0.171382
$993$	−1.07899e13	−0.352165
$994$	−1.02924e12	−0.0334409
$995$	−1.75788e13	−0.568573
$996$	1.28387e13	0.413385
$997$	−1.14216e13	−0.366098	−0.183049	−	0.983104i	$-0.558597\pi$
$997$	−1.14216e13	−0.366098	−0.183049	+	0.983104i	$0.558597\pi$
$998$	−1.37779e13	−0.439637
$999$	−3.19889e12	−0.101614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.14	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.14	✓	21	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} -38982.3 q^{10} +71994.6 q^{11} +21481.1 q^{12} +20979.3 q^{13} +25646.9 q^{14} +200992. q^{15} -56032.2 q^{16} -100423. q^{17} +103073. q^{18} +125554. q^{19} +658059. q^{20} -132235. q^{21} +1.13103e6 q^{22} +759888. q^{23} +988988. q^{24} +4.20414e6 q^{25} +329583. q^{26} -531441. q^{27} -432944. q^{28} -1.44179e6 q^{29} +3.15757e6 q^{30} -973200. q^{31} +5.37112e6 q^{32} -5.83156e6 q^{33} -1.57764e6 q^{34} -4.05093e6 q^{35} -1.73997e6 q^{36} +6.01928e6 q^{37} +1.97245e6 q^{38} -1.69932e6 q^{39} +3.02970e7 q^{40} +6.93821e6 q^{41} -2.07740e6 q^{42} +5.22977e6 q^{43} -1.90928e7 q^{44} -1.62804e7 q^{45} +1.19378e7 q^{46} -3.13303e7 q^{47} +4.53861e6 q^{48} -3.76885e7 q^{49} +6.60467e7 q^{50} +8.13429e6 q^{51} -5.56368e6 q^{52} +5.51922e7 q^{53} -8.34890e6 q^{54} -1.78646e8 q^{55} -1.99327e7 q^{56} -1.01699e7 q^{57} -2.26504e7 q^{58} -1.21174e7 q^{59} -5.33028e7 q^{60} -1.66783e8 q^{61} -1.52889e7 q^{62} +1.07110e7 q^{63} +1.13068e8 q^{64} -5.20577e7 q^{65} -9.16133e7 q^{66} +9.31844e7 q^{67} +2.66321e7 q^{68} -6.15509e7 q^{69} -6.36397e7 q^{70} -4.01312e7 q^{71} -8.01080e7 q^{72} -2.58311e8 q^{73} +9.45624e7 q^{74} -3.40536e8 q^{75} -3.32968e7 q^{76} +1.17533e8 q^{77} -2.66962e7 q^{78} -3.62808e8 q^{79} +1.39037e8 q^{80} +4.30467e7 q^{81} +1.08999e8 q^{82} +5.97676e8 q^{83} +3.50684e7 q^{84} +2.49189e8 q^{85} +8.21592e7 q^{86} +1.16785e8 q^{87} -8.79034e8 q^{88} +6.86238e8 q^{89} -2.55763e8 q^{90} +3.42493e7 q^{91} -2.01521e8 q^{92} +7.88292e7 q^{93} -4.92196e8 q^{94} -3.11548e8 q^{95} -4.35061e8 q^{96} +2.73324e7 q^{97} -5.92083e8 q^{98} +4.72356e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \)	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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