LMFDB - Embedded newform 177.12.a.c.1.14

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

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			1.14
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} -19480.2 q^{10} -671806. q^{11} +491242. q^{12} +1.37666e6 q^{13} +186616. q^{14} -920832. q^{15} +4.03264e6 q^{16} -4.33060e6 q^{17} -303550. q^{18} +8.25438e6 q^{19} -7.66062e6 q^{20} +8.82141e6 q^{21} +3.45352e6 q^{22} -6.13520e7 q^{23} -5.08362e6 q^{24} -3.44683e7 q^{25} -7.07696e6 q^{26} -1.43489e7 q^{27} +7.33874e7 q^{28} -7.51187e7 q^{29} +4.73368e6 q^{30} +2.73144e8 q^{31} -6.35751e7 q^{32} +1.63249e8 q^{33} +2.22621e7 q^{34} -1.37564e8 q^{35} -1.19372e8 q^{36} -5.71706e8 q^{37} -4.24329e7 q^{38} -3.34530e8 q^{39} +7.92759e7 q^{40} -9.81972e8 q^{41} -4.53478e7 q^{42} +1.36438e9 q^{43} +1.35810e9 q^{44} +2.23762e8 q^{45} +3.15389e8 q^{46} -1.13219e9 q^{47} -9.79931e8 q^{48} -6.59485e8 q^{49} +1.77190e8 q^{50} +1.05234e9 q^{51} -2.78303e9 q^{52} -3.65087e9 q^{53} +7.37628e7 q^{54} -2.54576e9 q^{55} -7.59449e8 q^{56} -2.00581e9 q^{57} +3.86159e8 q^{58} -7.14924e8 q^{59} +1.86153e9 q^{60} +4.73749e9 q^{61} -1.40414e9 q^{62} -2.14360e9 q^{63} -7.93203e9 q^{64} +5.21678e9 q^{65} -8.39206e8 q^{66} -1.18157e10 q^{67} +8.75463e9 q^{68} +1.49085e10 q^{69} +7.07170e8 q^{70} -2.10973e10 q^{71} +1.23532e9 q^{72} -4.85638e9 q^{73} +2.93894e9 q^{74} +8.37580e9 q^{75} -1.66868e10 q^{76} +2.43880e10 q^{77} +1.71970e9 q^{78} -3.22186e10 q^{79} +1.52814e10 q^{80} +3.48678e9 q^{81} +5.04798e9 q^{82} -3.61907e10 q^{83} -1.78331e10 q^{84} -1.64105e10 q^{85} -7.01379e9 q^{86} +1.82538e10 q^{87} -1.40544e10 q^{88} -1.60558e10 q^{89} -1.15028e9 q^{90} -4.99758e10 q^{91} +1.24028e11 q^{92} -6.63739e10 q^{93} +5.82020e9 q^{94} +3.12794e10 q^{95} +1.54487e10 q^{96} +1.28235e11 q^{97} +3.39018e9 q^{98} -3.96695e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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 $

$2$	−5.14065	−0.113593	−0.0567967	−	0.998386i	$-0.518089\pi$
$2$	−5.14065	−0.113593	−0.0567967	+	0.998386i	$0.518089\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−2021.57	−0.987097
$5$	3789.43	0.542299	0.271150	−	0.962537i	$-0.412596\pi$
$5$	3789.43	0.542299	0.271150	+	0.962537i	$0.412596\pi$
$6$	1249.18	0.0655832
$7$	−36302.1	−0.816380	−0.408190	−	0.912897i	$-0.633840\pi$
$7$	−36302.1	−0.816380	−0.408190	+	0.912897i	$0.633840\pi$
$8$	20920.3	0.225721
$9$	59049.0	0.333333
$10$	−19480.2	−0.0616017
$11$	−671806.	−1.25772	−0.628860	−	0.777519i	$-0.716478\pi$
$11$	−671806.	−1.25772	−0.628860	+	0.777519i	$0.716478\pi$
$12$	491242.	0.569900
$13$	1.37666e6	1.02835	0.514174	−	0.857686i	$-0.328099\pi$
$13$	1.37666e6	1.02835	0.514174	+	0.857686i	$0.328099\pi$
$14$	186616.	0.0927354
$15$	−920832.	−0.313097
$16$	4.03264e6	0.961456
$17$	−4.33060e6	−0.739740	−0.369870	−	0.929083i	$-0.620598\pi$
$17$	−4.33060e6	−0.739740	−0.369870	+	0.929083i	$0.620598\pi$
$18$	−303550.	−0.0378645
$19$	8.25438e6	0.764785	0.382393	−	0.924000i	$-0.375100\pi$
$19$	8.25438e6	0.764785	0.382393	+	0.924000i	$0.375100\pi$
$20$	−7.66062e6	−0.535302
$21$	8.82141e6	0.471337
$22$	3.45352e6	0.142869
$23$	−6.13520e7	−1.98758	−0.993792	−	0.111251i	$-0.964514\pi$
$23$	−6.13520e7	−1.98758	−0.993792	+	0.111251i	$0.964514\pi$
$24$	−5.08362e6	−0.130320
$25$	−3.44683e7	−0.705911
$26$	−7.07696e6	−0.116814
$27$	−1.43489e7	−0.192450
$28$	7.33874e7	0.805846
$29$	−7.51187e7	−0.680078	−0.340039	−	0.940411i	$-0.610440\pi$
$29$	−7.51187e7	−0.680078	−0.340039	+	0.940411i	$0.610440\pi$
$30$	4.73368e6	0.0355657
$31$	2.73144e8	1.71357	0.856785	−	0.515674i	$-0.172458\pi$
$31$	2.73144e8	1.71357	0.856785	+	0.515674i	$0.172458\pi$
$32$	−6.35751e7	−0.334936
$33$	1.63249e8	0.726145
$34$	2.22621e7	0.0840297
$35$	−1.37564e8	−0.442722
$36$	−1.19372e8	−0.329032
$37$	−5.71706e8	−1.35539	−0.677694	−	0.735344i	$-0.737021\pi$
$37$	−5.71706e8	−1.35539	−0.677694	+	0.735344i	$0.737021\pi$
$38$	−4.24329e7	−0.0868746
$39$	−3.34530e8	−0.593717
$40$	7.92759e7	0.122408
$41$	−9.81972e8	−1.32370	−0.661848	−	0.749638i	$-0.730227\pi$
$41$	−9.81972e8	−1.32370	−0.661848	+	0.749638i	$0.730227\pi$
$42$	−4.53478e7	−0.0535408
$43$	1.36438e9	1.41533	0.707666	−	0.706548i	$-0.249748\pi$
$43$	1.36438e9	1.41533	0.707666	+	0.706548i	$0.249748\pi$
$44$	1.35810e9	1.24149
$45$	2.23762e8	0.180766
$46$	3.15389e8	0.225777
$47$	−1.13219e9	−0.720082	−0.360041	−	0.932937i	$-0.617237\pi$
$47$	−1.13219e9	−0.720082	−0.360041	+	0.932937i	$0.617237\pi$
$48$	−9.79931e8	−0.555097
$49$	−6.59485e8	−0.333523
$50$	1.77190e8	0.0801869
$51$	1.05234e9	0.427089
$52$	−2.78303e9	−1.01508
$53$	−3.65087e9	−1.19917	−0.599583	−	0.800312i	$-0.704667\pi$
$53$	−3.65087e9	−1.19917	−0.599583	+	0.800312i	$0.704667\pi$
$54$	7.37628e7	0.0218611
$55$	−2.54576e9	−0.682061
$56$	−7.59449e8	−0.184274
$57$	−2.00581e9	−0.441549
$58$	3.86159e8	0.0772524
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.86153e9	0.309057
$61$	4.73749e9	0.718181	0.359091	−	0.933303i	$-0.383087\pi$
$61$	4.73749e9	0.718181	0.359091	+	0.933303i	$0.383087\pi$
$62$	−1.40414e9	−0.194650
$63$	−2.14360e9	−0.272127
$64$	−7.93203e9	−0.923410
$65$	5.21678e9	0.557672
$66$	−8.39206e8	−0.0824853
$67$	−1.18157e10	−1.06917	−0.534587	−	0.845113i	$-0.679533\pi$
$67$	−1.18157e10	−1.06917	−0.534587	+	0.845113i	$0.679533\pi$
$68$	8.75463e9	0.730195
$69$	1.49085e10	1.14753
$70$	7.07170e8	0.0502904
$71$	−2.10973e10	−1.38773	−0.693867	−	0.720103i	$-0.744095\pi$
$71$	−2.10973e10	−1.38773	−0.693867	+	0.720103i	$0.744095\pi$
$72$	1.23532e9	0.0752404
$73$	−4.85638e9	−0.274181	−0.137090	−	0.990559i	$-0.543775\pi$
$73$	−4.85638e9	−0.274181	−0.137090	+	0.990559i	$0.543775\pi$
$74$	2.93894e9	0.153963
$75$	8.37580e9	0.407558
$76$	−1.66868e10	−0.754917
$77$	2.43880e10	1.02678
$78$	1.71970e9	0.0674423
$79$	−3.22186e10	−1.17803	−0.589017	−	0.808121i	$-0.700485\pi$
$79$	−3.22186e10	−1.17803	−0.589017	+	0.808121i	$0.700485\pi$
$80$	1.52814e10	0.521397
$81$	3.48678e9	0.111111
$82$	5.04798e9	0.150363
$83$	−3.61907e10	−1.00848	−0.504240	−	0.863563i	$-0.668227\pi$
$83$	−3.61907e10	−1.00848	−0.504240	+	0.863563i	$0.668227\pi$
$84$	−1.78331e10	−0.465255
$85$	−1.64105e10	−0.401161
$86$	−7.01379e9	−0.160772
$87$	1.82538e10	0.392643
$88$	−1.40544e10	−0.283894
$89$	−1.60558e10	−0.304779	−0.152390	−	0.988320i	$-0.548697\pi$
$89$	−1.60558e10	−0.304779	−0.152390	+	0.988320i	$0.548697\pi$
$90$	−1.15028e9	−0.0205339
$91$	−4.99758e10	−0.839522
$92$	1.24028e11	1.96194
$93$	−6.63739e10	−0.989330
$94$	5.82020e9	0.0817966
$95$	3.12794e10	0.414743
$96$	1.54487e10	0.193376
$97$	1.28235e11	1.51622	0.758110	−	0.652127i	$-0.226123\pi$
$97$	1.28235e11	1.51622	0.758110	+	0.652127i	$0.226123\pi$
$98$	3.39018e9	0.0378861
$99$	−3.96695e10	−0.419240
$100$	6.96803e10	0.696803
$101$	1.34185e11	1.27039	0.635196	−	0.772351i	$-0.280919\pi$
$101$	1.34185e11	1.27039	0.635196	+	0.772351i	$0.280919\pi$
$102$	−5.40970e9	−0.0485146
$103$	6.70298e10	0.569723	0.284861	−	0.958569i	$-0.408052\pi$
$103$	6.70298e10	0.569723	0.284861	+	0.958569i	$0.408052\pi$
$104$	2.88002e10	0.232120
$105$	3.34281e10	0.255606
$106$	1.87679e10	0.136217
$107$	2.12026e11	1.46143	0.730716	−	0.682682i	$-0.239187\pi$
$107$	2.12026e11	1.46143	0.730716	+	0.682682i	$0.239187\pi$
$108$	2.90074e10	0.189967
$109$	−1.09209e11	−0.679846	−0.339923	−	0.940453i	$-0.610401\pi$
$109$	−1.09209e11	−0.679846	−0.339923	+	0.940453i	$0.610401\pi$
$110$	1.30869e10	0.0774776
$111$	1.38925e11	0.782534
$112$	−1.46393e11	−0.784914
$113$	3.74403e10	0.191165	0.0955825	−	0.995422i	$-0.469529\pi$
$113$	3.74403e10	0.191165	0.0955825	+	0.995422i	$0.469529\pi$
$114$	1.03112e10	0.0501571
$115$	−2.32489e11	−1.07787
$116$	1.51858e11	0.671303
$117$	8.12907e10	0.342782
$118$	3.67518e9	0.0147886
$119$	1.57210e11	0.603909
$120$	−1.92640e10	−0.0706725
$121$	1.66011e11	0.581860
$122$	−2.43538e10	−0.0815807
$123$	2.38619e11	0.764236
$124$	−5.52180e11	−1.69146
$125$	−3.15646e11	−0.925115
$126$	1.10195e10	0.0309118
$127$	5.88565e11	1.58079	0.790395	−	0.612597i	$-0.209875\pi$
$127$	5.88565e11	1.58079	0.790395	+	0.612597i	$0.209875\pi$
$128$	1.70978e11	0.439830
$129$	−3.31544e11	−0.817142
$130$	−2.68176e10	−0.0633479
$131$	−3.19444e11	−0.723440	−0.361720	−	0.932287i	$-0.617810\pi$
$131$	−3.19444e11	−0.723440	−0.361720	+	0.932287i	$0.617810\pi$
$132$	−3.30020e11	−0.716775
$133$	−2.99651e11	−0.624356
$134$	6.07405e10	0.121451
$135$	−5.43742e10	−0.104366
$136$	−9.05974e10	−0.166975
$137$	−2.28257e11	−0.404074	−0.202037	−	0.979378i	$-0.564756\pi$
$137$	−2.28257e11	−0.404074	−0.202037	+	0.979378i	$0.564756\pi$
$138$	−7.66396e10	−0.130352
$139$	4.86391e11	0.795068	0.397534	−	0.917587i	$-0.369866\pi$
$139$	4.86391e11	0.795068	0.397534	+	0.917587i	$0.369866\pi$
$140$	2.78096e11	0.437010
$141$	2.75123e11	0.415739
$142$	1.08454e11	0.157638
$143$	−9.24852e11	−1.29337
$144$	2.38123e11	0.320485
$145$	−2.84657e11	−0.368806
$146$	2.49649e10	0.0311451
$147$	1.60255e11	0.192560
$148$	1.15575e12	1.33790
$149$	−3.60386e11	−0.402016	−0.201008	−	0.979590i	$-0.564422\pi$
$149$	−3.60386e11	−0.402016	−0.201008	+	0.979590i	$0.564422\pi$
$150$	−4.30571e10	−0.0462959
$151$	−8.20006e11	−0.850049	−0.425024	−	0.905182i	$-0.639734\pi$
$151$	−8.20006e11	−0.850049	−0.425024	+	0.905182i	$0.639734\pi$
$152$	1.72684e11	0.172628
$153$	−2.55718e11	−0.246580
$154$	−1.25370e11	−0.116635
$155$	1.03506e12	0.929268
$156$	6.76276e11	0.586056
$157$	−1.34208e11	−0.112287	−0.0561435	−	0.998423i	$-0.517880\pi$
$157$	−1.34208e11	−0.112287	−0.0561435	+	0.998423i	$0.517880\pi$
$158$	1.65625e11	0.133817
$159$	8.87162e11	0.692339
$160$	−2.40914e11	−0.181636
$161$	2.22721e12	1.62262
$162$	−1.79243e10	−0.0126215
$163$	1.82174e12	1.24009	0.620046	−	0.784566i	$-0.287114\pi$
$163$	1.82174e12	1.24009	0.620046	+	0.784566i	$0.287114\pi$
$164$	1.98513e12	1.30662
$165$	6.18620e11	0.393788
$166$	1.86044e11	0.114557
$167$	1.74140e12	1.03743	0.518713	−	0.854948i	$-0.326411\pi$
$167$	1.74140e12	1.03743	0.518713	+	0.854948i	$0.326411\pi$
$168$	1.84546e11	0.106391
$169$	1.03046e11	0.0574982
$170$	8.43608e10	0.0455692
$171$	4.87413e11	0.254928
$172$	−2.75819e12	−1.39707
$173$	4.58319e11	0.224861	0.112430	−	0.993660i	$-0.464136\pi$
$173$	4.58319e11	0.224861	0.112430	+	0.993660i	$0.464136\pi$
$174$	−9.38366e10	−0.0446017
$175$	1.25127e12	0.576292
$176$	−2.70915e12	−1.20924
$177$	1.73727e11	0.0751646
$178$	8.25371e10	0.0346210
$179$	−4.11251e10	−0.0167269	−0.00836345	−	0.999965i	$-0.502662\pi$
$179$	−4.11251e10	−0.0167269	−0.00836345	+	0.999965i	$0.502662\pi$
$180$	−4.52352e11	−0.178434
$181$	3.53519e12	1.35264	0.676318	−	0.736610i	$-0.263575\pi$
$181$	3.53519e12	1.35264	0.676318	+	0.736610i	$0.263575\pi$
$182$	2.56908e11	0.0953642
$183$	−1.15121e12	−0.414642
$184$	−1.28350e12	−0.448640
$185$	−2.16644e12	−0.735026
$186$	3.41205e11	0.112381
$187$	2.90932e12	0.930386
$188$	2.28881e12	0.710790
$189$	5.20895e11	0.157112
$190$	−1.60797e11	−0.0471120
$191$	8.11282e11	0.230934	0.115467	−	0.993311i	$-0.463164\pi$
$191$	8.11282e11	0.230934	0.115467	+	0.993311i	$0.463164\pi$
$192$	1.92748e12	0.533131
$193$	−1.33845e12	−0.359779	−0.179890	−	0.983687i	$-0.557574\pi$
$193$	−1.33845e12	−0.359779	−0.179890	+	0.983687i	$0.557574\pi$
$194$	−6.59212e11	−0.172233
$195$	−1.26768e12	−0.321972
$196$	1.33320e12	0.329220
$197$	7.58650e12	1.82170	0.910850	−	0.412737i	$-0.135427\pi$
$197$	7.58650e12	1.82170	0.910850	+	0.412737i	$0.135427\pi$
$198$	2.03927e11	0.0476229
$199$	1.86054e12	0.422618	0.211309	−	0.977419i	$-0.432227\pi$
$199$	1.86054e12	0.422618	0.211309	+	0.977419i	$0.432227\pi$
$200$	−7.21087e11	−0.159339
$201$	2.87122e12	0.617288
$202$	−6.89801e11	−0.144308
$203$	2.72696e12	0.555202
$204$	−2.12738e12	−0.421578
$205$	−3.72112e12	−0.717839
$206$	−3.44577e11	−0.0647168
$207$	−3.62277e12	−0.662528
$208$	5.55159e12	0.988711
$209$	−5.54534e12	−0.961886
$210$	−1.71842e11	−0.0290352
$211$	7.60940e12	1.25256	0.626278	−	0.779600i	$-0.284578\pi$
$211$	7.60940e12	1.25256	0.626278	+	0.779600i	$0.284578\pi$
$212$	7.38051e12	1.18369
$213$	5.12665e12	0.801209
$214$	−1.08995e12	−0.166009
$215$	5.17022e12	0.767533
$216$	−3.00183e11	−0.0434401
$217$	−9.91569e12	−1.39892
$218$	5.61403e11	0.0772261
$219$	1.18010e12	0.158298
$220$	5.14645e12	0.673260
$221$	−5.96179e12	−0.760710
$222$	−7.14164e11	−0.0888907
$223$	1.12582e13	1.36708	0.683539	−	0.729914i	$-0.260440\pi$
$223$	1.12582e13	1.36708	0.683539	+	0.729914i	$0.260440\pi$
$224$	2.30791e12	0.273435
$225$	−2.03532e12	−0.235304
$226$	−1.92468e11	−0.0217151
$227$	6.67768e12	0.735332	0.367666	−	0.929958i	$-0.380157\pi$
$227$	6.67768e12	0.735332	0.367666	+	0.929958i	$0.380157\pi$
$228$	4.05490e12	0.435851
$229$	−4.01035e12	−0.420812	−0.210406	−	0.977614i	$-0.567479\pi$
$229$	−4.01035e12	−0.420812	−0.210406	+	0.977614i	$0.567479\pi$
$230$	1.19515e12	0.122439
$231$	−5.92627e12	−0.592810
$232$	−1.57150e12	−0.153508
$233$	−1.74443e12	−0.166416	−0.0832080	−	0.996532i	$-0.526517\pi$
$233$	−1.74443e12	−0.166416	−0.0832080	+	0.996532i	$0.526517\pi$
$234$	−4.17887e11	−0.0389378
$235$	−4.29036e12	−0.390500
$236$	1.44527e12	0.128509
$237$	7.82912e12	0.680138
$238$	−8.08162e11	−0.0686002
$239$	−9.98034e12	−0.827860	−0.413930	−	0.910309i	$-0.635844\pi$
$239$	−9.98034e12	−0.827860	−0.413930	+	0.910309i	$0.635844\pi$
$240$	−3.71338e12	−0.301029
$241$	−5.80164e12	−0.459682	−0.229841	−	0.973228i	$-0.573821\pi$
$241$	−5.80164e12	−0.459682	−0.229841	+	0.973228i	$0.573821\pi$
$242$	−8.53407e11	−0.0660955
$243$	−8.47289e11	−0.0641500
$244$	−9.57718e12	−0.708914
$245$	−2.49907e12	−0.180870
$246$	−1.22666e12	−0.0868122
$247$	1.13635e13	0.786465
$248$	5.71424e12	0.386789
$249$	8.79434e12	0.582246
$250$	1.62263e12	0.105087
$251$	−1.51372e13	−0.959048	−0.479524	−	0.877529i	$-0.659191\pi$
$251$	−1.51372e13	−0.959048	−0.479524	+	0.877529i	$0.659191\pi$
$252$	4.33345e12	0.268615
$253$	4.12166e13	2.49983
$254$	−3.02561e12	−0.179567
$255$	3.98776e12	0.231610
$256$	1.53659e13	0.873448
$257$	−2.53545e13	−1.41066	−0.705332	−	0.708877i	$-0.749202\pi$
$257$	−2.53545e13	−1.41066	−0.705332	+	0.708877i	$0.749202\pi$
$258$	1.70435e12	0.0928220
$259$	2.07541e13	1.10651
$260$	−1.05461e13	−0.550476
$261$	−4.43568e12	−0.226693
$262$	1.64215e12	0.0821780
$263$	−9.49565e12	−0.465338	−0.232669	−	0.972556i	$-0.574746\pi$
$263$	−9.49565e12	−0.465338	−0.232669	+	0.972556i	$0.574746\pi$
$264$	3.41521e12	0.163906
$265$	−1.38347e13	−0.650307
$266$	1.54040e12	0.0709227
$267$	3.90155e12	0.175965
$268$	2.38863e13	1.05538
$269$	2.00720e13	0.868868	0.434434	−	0.900704i	$-0.356948\pi$
$269$	2.00720e13	0.868868	0.434434	+	0.900704i	$0.356948\pi$
$270$	2.79519e11	0.0118552
$271$	−1.65588e12	−0.0688172	−0.0344086	−	0.999408i	$-0.510955\pi$
$271$	−1.65588e12	−0.0688172	−0.0344086	+	0.999408i	$0.510955\pi$
$272$	−1.74638e13	−0.711228
$273$	1.21441e13	0.484698
$274$	1.17339e12	0.0459002
$275$	2.31560e13	0.887839
$276$	−3.01387e13	−1.13273
$277$	−2.74139e13	−1.01002	−0.505012	−	0.863112i	$-0.668512\pi$
$277$	−2.74139e13	−1.01002	−0.505012	+	0.863112i	$0.668512\pi$
$278$	−2.50037e12	−0.0903146
$279$	1.61289e13	0.571190
$280$	−2.87788e12	−0.0999318
$281$	2.30957e13	0.786404	0.393202	−	0.919452i	$-0.371367\pi$
$281$	2.30957e13	0.786404	0.393202	+	0.919452i	$0.371367\pi$
$282$	−1.41431e12	−0.0472253
$283$	3.22107e13	1.05481	0.527405	−	0.849614i	$-0.323165\pi$
$283$	3.22107e13	1.05481	0.527405	+	0.849614i	$0.323165\pi$
$284$	4.26498e13	1.36983
$285$	−7.60089e12	−0.239452
$286$	4.75434e12	0.146919
$287$	3.56477e13	1.08064
$288$	−3.75405e12	−0.111645
$289$	−1.55178e13	−0.452784
$290$	1.46332e12	0.0418939
$291$	−3.11611e13	−0.875390
$292$	9.81752e12	0.270643
$293$	−6.10603e13	−1.65191	−0.825957	−	0.563734i	$-0.809364\pi$
$293$	−6.10603e13	−1.65191	−0.825957	+	0.563734i	$0.809364\pi$
$294$	−8.23814e11	−0.0218735
$295$	−2.70916e12	−0.0706014
$296$	−1.19603e13	−0.305940
$297$	9.63968e12	0.242048
$298$	1.85262e12	0.0456664
$299$	−8.44612e13	−2.04393
$300$	−1.69323e13	−0.402299
$301$	−4.95298e13	−1.15545
$302$	4.21537e12	0.0965600
$303$	−3.26071e13	−0.733462
$304$	3.32869e13	0.735307
$305$	1.79524e13	0.389469
$306$	1.31456e12	0.0280099
$307$	4.45828e13	0.933052	0.466526	−	0.884507i	$-0.345505\pi$
$307$	4.45828e13	0.933052	0.466526	+	0.884507i	$0.345505\pi$
$308$	−4.93021e13	−1.01353
$309$	−1.62883e13	−0.328930
$310$	−5.32088e12	−0.105559
$311$	2.92875e13	0.570822	0.285411	−	0.958405i	$-0.407870\pi$
$311$	2.92875e13	0.570822	0.285411	+	0.958405i	$0.407870\pi$
$312$	−6.99845e12	−0.134014
$313$	−1.04478e14	−1.96576	−0.982881	−	0.184239i	$-0.941018\pi$
$313$	−1.04478e14	−1.96576	−0.982881	+	0.184239i	$0.941018\pi$
$314$	6.89916e11	0.0127551
$315$	−8.12303e12	−0.147574
$316$	6.51323e13	1.16283
$317$	9.29865e13	1.63153	0.815763	−	0.578386i	$-0.196317\pi$
$317$	9.29865e13	1.63153	0.815763	+	0.578386i	$0.196317\pi$
$318$	−4.56059e12	−0.0786452
$319$	5.04651e13	0.855348
$320$	−3.00579e13	−0.500764
$321$	−5.15223e13	−0.843758
$322$	−1.14493e13	−0.184320
$323$	−3.57464e13	−0.565743
$324$	−7.04879e12	−0.109677
$325$	−4.74513e13	−0.725922
$326$	−9.36491e12	−0.140866
$327$	2.65377e13	0.392509
$328$	−2.05431e13	−0.298786
$329$	4.11009e13	0.587860
$330$	−3.18011e12	−0.0447317
$331$	3.70812e13	0.512979	0.256489	−	0.966547i	$-0.417434\pi$
$331$	3.70812e13	0.512979	0.256489	+	0.966547i	$0.417434\pi$
$332$	7.31622e13	0.995467
$333$	−3.37587e13	−0.451796
$334$	−8.95192e12	−0.117845
$335$	−4.47748e13	−0.579813
$336$	3.55736e13	0.453170
$337$	−1.33995e14	−1.67928	−0.839642	−	0.543140i	$-0.817235\pi$
$337$	−1.33995e14	−1.67928	−0.839642	+	0.543140i	$0.817235\pi$
$338$	−5.29724e11	−0.00653142
$339$	−9.09800e12	−0.110369
$340$	3.31751e13	0.395984
$341$	−1.83500e14	−2.15519
$342$	−2.50562e12	−0.0289582
$343$	9.57218e13	1.08866
$344$	2.85431e13	0.319470
$345$	5.64949e13	0.622306
$346$	−2.35606e12	−0.0255427
$347$	−3.33468e13	−0.355830	−0.177915	−	0.984046i	$-0.556935\pi$
$347$	−3.33468e13	−0.355830	−0.177915	+	0.984046i	$0.556935\pi$
$348$	−3.69015e13	−0.387577
$349$	−1.75315e13	−0.181250	−0.0906250	−	0.995885i	$-0.528886\pi$
$349$	−1.75315e13	−0.181250	−0.0906250	+	0.995885i	$0.528886\pi$
$350$	−6.43236e12	−0.0654630
$351$	−1.97536e13	−0.197906
$352$	4.27101e13	0.421256
$353$	−1.18278e14	−1.14853	−0.574265	−	0.818670i	$-0.694712\pi$
$353$	−1.18278e14	−1.14853	−0.574265	+	0.818670i	$0.694712\pi$
$354$	−8.93068e11	−0.00853821
$355$	−7.99469e13	−0.752568
$356$	3.24579e13	0.300847
$357$	−3.82020e13	−0.348667
$358$	2.11410e11	0.00190007
$359$	−5.70555e13	−0.504984	−0.252492	−	0.967599i	$-0.581250\pi$
$359$	−5.70555e13	−0.504984	−0.252492	+	0.967599i	$0.581250\pi$
$360$	4.68116e12	0.0408028
$361$	−4.83555e13	−0.415103
$362$	−1.81732e13	−0.153651
$363$	−4.03408e13	−0.335937
$364$	1.01030e14	0.828690
$365$	−1.84029e13	−0.148688
$366$	5.91797e12	0.0471006
$367$	−1.20150e14	−0.942019	−0.471010	−	0.882128i	$-0.656110\pi$
$367$	−1.20150e14	−0.942019	−0.471010	+	0.882128i	$0.656110\pi$
$368$	−2.47410e14	−1.91098
$369$	−5.79845e13	−0.441232
$370$	1.11369e13	0.0834941
$371$	1.32534e14	0.978976
$372$	1.34180e14	0.976564
$373$	−1.94635e14	−1.39580	−0.697899	−	0.716197i	$-0.745881\pi$
$373$	−1.94635e14	−1.39580	−0.697899	+	0.716197i	$0.745881\pi$
$374$	−1.49558e13	−0.105686
$375$	7.67020e13	0.534115
$376$	−2.36857e13	−0.162538
$377$	−1.03413e14	−0.699357
$378$	−2.67774e12	−0.0178469
$379$	−1.10895e14	−0.728444	−0.364222	−	0.931312i	$-0.618665\pi$
$379$	−1.10895e14	−0.728444	−0.364222	+	0.931312i	$0.618665\pi$
$380$	−6.32336e13	−0.409391
$381$	−1.43021e14	−0.912670
$382$	−4.17052e12	−0.0262326
$383$	4.20665e12	0.0260821	0.0130411	−	0.999915i	$-0.495849\pi$
$383$	4.20665e12	0.0260821	0.0130411	+	0.999915i	$0.495849\pi$
$384$	−4.15476e13	−0.253936
$385$	9.24165e13	0.556821
$386$	6.88050e12	0.0408686
$387$	8.05651e13	0.471777
$388$	−2.59237e14	−1.49665
$389$	3.28723e14	1.87114	0.935572	−	0.353137i	$-0.114885\pi$
$389$	3.28723e14	1.87114	0.935572	+	0.353137i	$0.114885\pi$
$390$	6.51669e12	0.0365739
$391$	2.65691e14	1.47030
$392$	−1.37966e13	−0.0752833
$393$	7.76249e13	0.417678
$394$	−3.89995e13	−0.206933
$395$	−1.22090e14	−0.638847
$396$	8.01947e13	0.413830
$397$	1.75916e14	0.895277	0.447639	−	0.894215i	$-0.352265\pi$
$397$	1.75916e14	0.895277	0.447639	+	0.894215i	$0.352265\pi$
$398$	−9.56441e12	−0.0480066
$399$	7.28152e13	0.360472
$400$	−1.38998e14	−0.678703
$401$	2.10376e14	1.01322	0.506608	−	0.862176i	$-0.330899\pi$
$401$	2.10376e14	1.01322	0.506608	+	0.862176i	$0.330899\pi$
$402$	−1.47599e13	−0.0701199
$403$	3.76027e14	1.76215
$404$	−2.71266e14	−1.25400
$405$	1.32129e13	0.0602555
$406$	−1.40184e13	−0.0630673
$407$	3.84076e14	1.70470
$408$	2.20152e13	0.0964031
$409$	−2.70328e14	−1.16792	−0.583960	−	0.811783i	$-0.698497\pi$
$409$	−2.70328e14	−1.16792	−0.583960	+	0.811783i	$0.698497\pi$
$410$	1.91290e13	0.0815418
$411$	5.54664e13	0.233292
$412$	−1.35506e14	−0.562371
$413$	2.59532e13	0.106284
$414$	1.86234e13	0.0752589
$415$	−1.37142e14	−0.546898
$416$	−8.75216e13	−0.344431
$417$	−1.18193e14	−0.459033
$418$	2.85067e13	0.109264
$419$	6.14097e12	0.0232306	0.0116153	−	0.999933i	$-0.496303\pi$
$419$	6.14097e12	0.0232306	0.0116153	+	0.999933i	$0.496303\pi$
$420$	−6.75774e13	−0.252308
$421$	2.97576e14	1.09660	0.548298	−	0.836283i	$-0.315276\pi$
$421$	2.97576e14	1.09660	0.548298	+	0.836283i	$0.315276\pi$
$422$	−3.91173e13	−0.142282
$423$	−6.68548e13	−0.240027
$424$	−7.63772e13	−0.270677
$425$	1.49269e14	0.522191
$426$	−2.63543e13	−0.0910121
$427$	−1.71981e14	−0.586309
$428$	−4.28626e14	−1.44257
$429$	2.24739e14	0.746729
$430$	−2.65783e13	−0.0871867
$431$	2.17247e14	0.703605	0.351803	−	0.936074i	$-0.385569\pi$
$431$	2.17247e14	0.703605	0.351803	+	0.936074i	$0.385569\pi$
$432$	−5.78640e13	−0.185032
$433$	8.84686e13	0.279322	0.139661	−	0.990199i	$-0.455399\pi$
$433$	8.84686e13	0.279322	0.139661	+	0.990199i	$0.455399\pi$
$434$	5.09731e13	0.158909
$435$	6.91717e13	0.212930
$436$	2.20773e14	0.671074
$437$	−5.06423e14	−1.52008
$438$	−6.06648e12	−0.0179816
$439$	−8.15963e13	−0.238845	−0.119422	−	0.992844i	$-0.538104\pi$
$439$	−8.15963e13	−0.238845	−0.119422	+	0.992844i	$0.538104\pi$
$440$	−5.32580e13	−0.153956
$441$	−3.89419e13	−0.111174
$442$	3.06475e13	0.0864117
$443$	1.83777e14	0.511765	0.255883	−	0.966708i	$-0.417634\pi$
$443$	1.83777e14	0.511765	0.255883	+	0.966708i	$0.417634\pi$
$444$	−2.80846e14	−0.772436
$445$	−6.08422e13	−0.165282
$446$	−5.78747e13	−0.155291
$447$	8.75738e13	0.232104
$448$	2.87949e14	0.753853
$449$	7.52236e14	1.94536	0.972679	−	0.232156i	$-0.0745779\pi$
$449$	7.52236e14	1.94536	0.972679	+	0.232156i	$0.0745779\pi$
$450$	1.04629e13	0.0267290
$451$	6.59695e14	1.66484
$452$	−7.56884e13	−0.188698
$453$	1.99261e14	0.490776
$454$	−3.43276e13	−0.0835289
$455$	−1.89380e14	−0.455272
$456$	−4.19622e13	−0.0996670
$457$	5.85789e14	1.37468	0.687341	−	0.726335i	$-0.258778\pi$
$457$	5.85789e14	1.37468	0.687341	+	0.726335i	$0.258778\pi$
$458$	2.06158e13	0.0478014
$459$	6.21394e13	0.142363
$460$	4.69994e14	1.06396
$461$	−5.91350e14	−1.32279	−0.661393	−	0.750040i	$-0.730034\pi$
$461$	−5.91350e14	−1.32279	−0.661393	+	0.750040i	$0.730034\pi$
$462$	3.04649e13	0.0673394
$463$	−5.70931e14	−1.24706	−0.623531	−	0.781799i	$-0.714303\pi$
$463$	−5.70931e14	−1.24706	−0.623531	+	0.781799i	$0.714303\pi$
$464$	−3.02926e14	−0.653865
$465$	−2.51519e14	−0.536513
$466$	8.96750e12	0.0189038
$467$	1.31858e14	0.274704	0.137352	−	0.990522i	$-0.456141\pi$
$467$	1.31858e14	0.274704	0.137352	+	0.990522i	$0.456141\pi$
$468$	−1.64335e14	−0.338359
$469$	4.28935e14	0.872853
$470$	2.20553e13	0.0443582
$471$	3.26125e13	0.0648289
$472$	−1.49564e13	−0.0293864
$473$	−9.16597e14	−1.78009
$474$	−4.02468e13	−0.0772592
$475$	−2.84515e14	−0.539871
$476$	−3.17812e14	−0.596117
$477$	−2.15580e14	−0.399722
$478$	5.13054e13	0.0940394
$479$	−2.92049e14	−0.529189	−0.264595	−	0.964360i	$-0.585238\pi$
$479$	−2.92049e14	−0.529189	−0.264595	+	0.964360i	$0.585238\pi$
$480$	5.85420e13	0.104867
$481$	−7.87048e14	−1.39381
$482$	2.98242e13	0.0522168
$483$	−5.41211e14	−0.936823
$484$	−3.35604e14	−0.574352
$485$	4.85938e14	0.822245
$486$	4.35562e12	0.00728702
$487$	−3.11946e14	−0.516025	−0.258012	−	0.966142i	$-0.583068\pi$
$487$	−3.11946e14	−0.516025	−0.258012	+	0.966142i	$0.583068\pi$
$488$	9.91095e13	0.162109
$489$	−4.42682e14	−0.715967
$490$	1.28469e13	0.0205456
$491$	−8.87961e14	−1.40425	−0.702127	−	0.712052i	$-0.747766\pi$
$491$	−8.87961e14	−1.40425	−0.702127	+	0.712052i	$0.747766\pi$
$492$	−4.82387e14	−0.754375
$493$	3.25309e14	0.503081
$494$	−5.84159e13	−0.0893373
$495$	−1.50325e14	−0.227354
$496$	1.10149e15	1.64752
$497$	7.65877e14	1.13292
$498$	−4.52086e13	−0.0661394
$499$	9.86386e14	1.42723	0.713615	−	0.700538i	$-0.247057\pi$
$499$	9.86386e14	1.42723	0.713615	+	0.700538i	$0.247057\pi$
$500$	6.38102e14	0.913177
$501$	−4.23160e14	−0.598959
$502$	7.78151e13	0.108942
$503$	7.18036e13	0.0994311	0.0497156	−	0.998763i	$-0.484169\pi$
$503$	7.18036e13	0.0994311	0.0497156	+	0.998763i	$0.484169\pi$
$504$	−4.48447e13	−0.0614248
$505$	5.08487e14	0.688933
$506$	−2.11880e14	−0.283964
$507$	−2.50402e13	−0.0331966
$508$	−1.18983e15	−1.56039
$509$	8.78462e14	1.13966	0.569830	−	0.821763i	$-0.307009\pi$
$509$	8.78462e14	1.13966	0.569830	+	0.821763i	$0.307009\pi$
$510$	−2.04997e13	−0.0263094
$511$	1.76297e14	0.223836
$512$	−4.29153e14	−0.539048
$513$	−1.18441e14	−0.147183
$514$	1.30339e14	0.160242
$515$	2.54005e14	0.308960
$516$	6.70240e14	0.806598
$517$	7.60613e14	0.905661
$518$	−1.06690e14	−0.125692
$519$	−1.11371e14	−0.129824
$520$	1.09136e14	0.125878
$521$	1.11109e15	1.26806	0.634031	−	0.773308i	$-0.281399\pi$
$521$	1.11109e15	1.26806	0.634031	+	0.773308i	$0.281399\pi$
$522$	2.28023e13	0.0257508
$523$	1.16878e15	1.30609	0.653047	−	0.757318i	$-0.273491\pi$
$523$	1.16878e15	1.30609	0.653047	+	0.757318i	$0.273491\pi$
$524$	6.45779e14	0.714105
$525$	−3.04059e14	−0.332722
$526$	4.88138e13	0.0528593
$527$	−1.18288e15	−1.26760
$528$	6.58324e14	0.698157
$529$	2.81126e15	2.95049
$530$	7.11196e13	0.0738706
$531$	−4.22156e13	−0.0433963
$532$	6.05767e14	0.616299
$533$	−1.35185e15	−1.36122
$534$	−2.00565e13	−0.0199884
$535$	8.03458e14	0.792533
$536$	−2.47188e14	−0.241335
$537$	9.99340e12	0.00965728
$538$	−1.03183e14	−0.0986978
$539$	4.43046e14	0.419479
$540$	1.09921e14	0.103019
$541$	1.01970e15	0.945991	0.472996	−	0.881065i	$-0.343173\pi$
$541$	1.01970e15	0.945991	0.472996	+	0.881065i	$0.343173\pi$
$542$	8.51229e12	0.00781719
$543$	−8.59051e14	−0.780944
$544$	2.75319e14	0.247766
$545$	−4.13838e14	−0.368680
$546$	−6.24287e13	−0.0550586
$547$	−6.38269e14	−0.557280	−0.278640	−	0.960396i	$-0.589884\pi$
$547$	−6.38269e14	−0.557280	−0.278640	+	0.960396i	$0.589884\pi$
$548$	4.61438e14	0.398860
$549$	2.79744e14	0.239394
$550$	−1.19037e14	−0.100853
$551$	−6.20058e14	−0.520114
$552$	3.11891e14	0.259022
$553$	1.16960e15	0.961723
$554$	1.40925e14	0.114732
$555$	5.26446e14	0.424367
$556$	−9.83276e14	−0.784809
$557$	4.12961e14	0.326366	0.163183	−	0.986596i	$-0.447824\pi$
$557$	4.12961e14	0.326366	0.163183	+	0.986596i	$0.447824\pi$
$558$	−8.29129e13	−0.0648835
$559$	1.87829e15	1.45545
$560$	−5.54747e14	−0.425658
$561$	−7.06966e14	−0.537159
$562$	−1.18727e14	−0.0893304
$563$	9.63114e14	0.717598	0.358799	−	0.933415i	$-0.383186\pi$
$563$	9.63114e14	0.717598	0.358799	+	0.933415i	$0.383186\pi$
$564$	−5.56180e14	−0.410375
$565$	1.41878e14	0.103669
$566$	−1.65584e14	−0.119820
$567$	−1.26578e14	−0.0907089
$568$	−4.41362e14	−0.313241
$569$	−1.13387e15	−0.796980	−0.398490	−	0.917173i	$-0.630466\pi$
$569$	−1.13387e15	−0.796980	−0.398490	+	0.917173i	$0.630466\pi$
$570$	3.90736e13	0.0272001
$571$	4.38349e14	0.302219	0.151109	−	0.988517i	$-0.451715\pi$
$571$	4.38349e14	0.302219	0.151109	+	0.988517i	$0.451715\pi$
$572$	1.86966e15	1.27668
$573$	−1.97141e14	−0.133330
$574$	−1.83252e14	−0.122753
$575$	2.11470e15	1.40306
$576$	−4.68378e14	−0.307803
$577$	−2.55059e14	−0.166025	−0.0830127	−	0.996548i	$-0.526454\pi$
$577$	−2.55059e14	−0.166025	−0.0830127	+	0.996548i	$0.526454\pi$
$578$	7.97715e13	0.0514333
$579$	3.25243e14	0.207719
$580$	5.75455e14	0.364047
$581$	1.31380e15	0.823303
$582$	1.60188e14	0.0994385
$583$	2.45268e15	1.50822
$584$	−1.01597e14	−0.0618884
$585$	3.08046e14	0.185891
$586$	3.13890e14	0.187647
$587$	9.94768e14	0.589132	0.294566	−	0.955631i	$-0.404825\pi$
$587$	9.94768e14	0.589132	0.294566	+	0.955631i	$0.404825\pi$
$588$	−3.23967e14	−0.190075
$589$	2.25463e15	1.31051
$590$	1.39268e13	0.00801985
$591$	−1.84352e15	−1.05176
$592$	−2.30549e15	−1.30315
$593$	−7.78691e14	−0.436078	−0.218039	−	0.975940i	$-0.569966\pi$
$593$	−7.78691e14	−0.436078	−0.218039	+	0.975940i	$0.569966\pi$
$594$	−4.95542e13	−0.0274951
$595$	5.95736e14	0.327500
$596$	7.28547e14	0.396829
$597$	−4.52112e14	−0.243999
$598$	4.34185e14	0.232177
$599$	−1.46914e15	−0.778425	−0.389213	−	0.921148i	$-0.627253\pi$
$599$	−1.46914e15	−0.778425	−0.389213	+	0.921148i	$0.627253\pi$
$600$	1.75224e14	0.0919945
$601$	−2.17016e15	−1.12897	−0.564484	−	0.825444i	$-0.690925\pi$
$601$	−2.17016e15	−1.12897	−0.564484	+	0.825444i	$0.690925\pi$
$602$	2.54615e14	0.131251
$603$	−6.97706e14	−0.356392
$604$	1.65770e15	0.839080
$605$	6.29089e14	0.315542
$606$	1.67622e14	0.0833164
$607$	2.68103e15	1.32058	0.660289	−	0.751012i	$-0.270434\pi$
$607$	2.68103e15	1.32058	0.660289	+	0.751012i	$0.270434\pi$
$608$	−5.24773e14	−0.256154
$609$	−6.62652e14	−0.320546
$610$	−9.22870e13	−0.0442412
$611$	−1.55865e15	−0.740494
$612$	5.16952e14	0.243398
$613$	−9.22855e14	−0.430627	−0.215313	−	0.976545i	$-0.569077\pi$
$613$	−9.22855e14	−0.430627	−0.215313	+	0.976545i	$0.569077\pi$
$614$	−2.29185e14	−0.105989
$615$	9.04232e14	0.414445
$616$	5.10203e14	0.231765
$617$	−1.46067e15	−0.657635	−0.328817	−	0.944394i	$-0.606650\pi$
$617$	−1.46067e15	−0.657635	−0.328817	+	0.944394i	$0.606650\pi$
$618$	8.37323e13	0.0373642
$619$	−3.42114e15	−1.51312	−0.756559	−	0.653925i	$-0.773121\pi$
$619$	−3.42114e15	−1.51312	−0.756559	+	0.653925i	$0.773121\pi$
$620$	−2.09245e15	−0.917277
$621$	8.80334e14	0.382511
$622$	−1.50557e14	−0.0648416
$623$	5.82857e14	0.248816
$624$	−1.34904e15	−0.570832
$625$	4.86904e14	0.204222
$626$	5.37085e14	0.223298
$627$	1.34752e15	0.555345
$628$	2.71311e14	0.110838
$629$	2.47583e15	1.00264
$630$	4.17577e13	0.0167635
$631$	1.76224e15	0.701298	0.350649	−	0.936507i	$-0.385961\pi$
$631$	1.76224e15	0.701298	0.350649	+	0.936507i	$0.385961\pi$
$632$	−6.74022e14	−0.265907
$633$	−1.84908e15	−0.723163
$634$	−4.78011e14	−0.185331
$635$	2.23033e15	0.857262
$636$	−1.79346e15	−0.683405
$637$	−9.07890e14	−0.342978
$638$	−2.59424e14	−0.0971619
$639$	−1.24578e15	−0.462578
$640$	6.47908e14	0.238519
$641$	−4.50632e15	−1.64476	−0.822381	−	0.568938i	$-0.807355\pi$
$641$	−4.50632e15	−1.64476	−0.822381	+	0.568938i	$0.807355\pi$
$642$	2.64858e14	0.0958453
$643$	2.77063e15	0.994073	0.497036	−	0.867730i	$-0.334422\pi$
$643$	2.77063e15	0.994073	0.497036	+	0.867730i	$0.334422\pi$
$644$	−4.50246e15	−1.60169
$645$	−1.25636e15	−0.443135
$646$	1.83760e14	0.0642647
$647$	−1.33400e15	−0.462577	−0.231288	−	0.972885i	$-0.574294\pi$
$647$	−1.33400e15	−0.462577	−0.231288	+	0.972885i	$0.574294\pi$
$648$	7.29445e13	0.0250801
$649$	4.80290e14	0.163741
$650$	2.43931e14	0.0824600
$651$	2.40951e15	0.807670
$652$	−3.68277e15	−1.22409
$653$	1.99299e15	0.656876	0.328438	−	0.944526i	$-0.393478\pi$
$653$	1.99299e15	0.656876	0.328438	+	0.944526i	$0.393478\pi$
$654$	−1.36421e14	−0.0445865
$655$	−1.21051e15	−0.392321
$656$	−3.95994e15	−1.27268
$657$	−2.86764e14	−0.0913935
$658$	−2.11286e14	−0.0667771
$659$	5.11300e15	1.60253	0.801265	−	0.598310i	$-0.204161\pi$
$659$	5.11300e15	1.60253	0.801265	+	0.598310i	$0.204161\pi$
$660$	−1.25059e15	−0.388707
$661$	−3.34905e15	−1.03232	−0.516160	−	0.856492i	$-0.672639\pi$
$661$	−3.34905e15	−1.03232	−0.516160	+	0.856492i	$0.672639\pi$
$662$	−1.90621e14	−0.0582710
$663$	1.44871e15	0.439196
$664$	−7.57119e14	−0.227635
$665$	−1.13551e15	−0.338588
$666$	1.73542e14	0.0513211
$667$	4.60868e15	1.35171
$668$	−3.52036e15	−1.02404
$669$	−2.73575e15	−0.789283
$670$	2.30172e14	0.0658629
$671$	−3.18267e15	−0.903271
$672$	−5.60822e14	−0.157868
$673$	−2.67235e15	−0.746124	−0.373062	−	0.927806i	$-0.621692\pi$
$673$	−2.67235e15	−0.746124	−0.373062	+	0.927806i	$0.621692\pi$
$674$	6.88822e14	0.190756
$675$	4.94583e14	0.135853
$676$	−2.08315e14	−0.0567563
$677$	−3.40990e15	−0.921520	−0.460760	−	0.887525i	$-0.652423\pi$
$677$	−3.40990e15	−0.921520	−0.460760	+	0.887525i	$0.652423\pi$
$678$	4.67697e13	0.0125372
$679$	−4.65520e15	−1.23781
$680$	−3.43313e14	−0.0905505
$681$	−1.62268e15	−0.424544
$682$	9.43307e14	0.244816
$683$	7.32941e15	1.88693	0.943464	−	0.331476i	$-0.107547\pi$
$683$	7.32941e15	1.88693	0.943464	+	0.331476i	$0.107547\pi$
$684$	−9.85341e14	−0.251639
$685$	−8.64964e14	−0.219129
$686$	−4.92072e14	−0.123665
$687$	9.74516e14	0.242956
$688$	5.50204e15	1.36078
$689$	−5.02603e15	−1.23316
$690$	−2.90421e14	−0.0706899
$691$	7.68618e15	1.85602	0.928008	−	0.372561i	$-0.121520\pi$
$691$	7.68618e15	1.85602	0.928008	+	0.372561i	$0.121520\pi$
$692$	−9.26525e14	−0.221959
$693$	1.44008e15	0.342259
$694$	1.71424e14	0.0404199
$695$	1.84315e15	0.431165
$696$	3.81875e14	0.0886279
$697$	4.25253e15	0.979191
$698$	9.01231e13	0.0205888
$699$	4.23896e14	0.0960804
$700$	−2.52954e15	−0.568856
$701$	−3.51387e14	−0.0784038	−0.0392019	−	0.999231i	$-0.512482\pi$
$701$	−3.51387e14	−0.0784038	−0.0392019	+	0.999231i	$0.512482\pi$
$702$	1.01547e14	0.0224808
$703$	−4.71908e15	−1.03658
$704$	5.32878e15	1.16139
$705$	1.04256e15	0.225455
$706$	6.08025e14	0.130465
$707$	−4.87121e15	−1.03712
$708$	−3.51201e14	−0.0741947
$709$	−4.65146e15	−0.975067	−0.487534	−	0.873104i	$-0.662103\pi$
$709$	−4.65146e15	−0.975067	−0.487534	+	0.873104i	$0.662103\pi$
$710$	4.10979e14	0.0854868
$711$	−1.90248e15	−0.392678
$712$	−3.35891e14	−0.0687952
$713$	−1.67579e16	−3.40587
$714$	1.96383e14	0.0396063
$715$	−3.50466e15	−0.701395
$716$	8.31374e13	0.0165111
$717$	2.42522e15	0.477965
$718$	2.93303e14	0.0573629
$719$	−2.87911e15	−0.558791	−0.279395	−	0.960176i	$-0.590134\pi$
$719$	−2.87911e15	−0.558791	−0.279395	+	0.960176i	$0.590134\pi$
$720$	9.02352e14	0.173799
$721$	−2.43332e15	−0.465110
$722$	2.48579e14	0.0471530
$723$	1.40980e15	0.265397
$724$	−7.14665e15	−1.33518
$725$	2.58921e15	0.480075
$726$	2.07378e14	0.0381602
$727$	9.82747e15	1.79474	0.897372	−	0.441275i	$-0.145474\pi$
$727$	9.82747e15	1.79474	0.897372	+	0.441275i	$0.145474\pi$
$728$	−1.04551e15	−0.189498
$729$	2.05891e14	0.0370370
$730$	9.46030e13	0.0168900
$731$	−5.90858e15	−1.04698
$732$	2.32726e15	0.409292
$733$	8.35206e15	1.45788	0.728940	−	0.684578i	$-0.240013\pi$
$733$	8.35206e15	1.45788	0.728940	+	0.684578i	$0.240013\pi$
$734$	6.17648e14	0.107007
$735$	6.07275e14	0.104425
$736$	3.90046e15	0.665714
$737$	7.93787e15	1.34472
$738$	2.98078e14	0.0501210
$739$	−8.08774e15	−1.34984	−0.674920	−	0.737890i	$-0.735822\pi$
$739$	−8.08774e15	−1.34984	−0.674920	+	0.737890i	$0.735822\pi$
$740$	4.37962e15	0.725542
$741$	−2.76133e15	−0.454066
$742$	−6.81313e14	−0.111205
$743$	7.31920e15	1.18584	0.592919	−	0.805262i	$-0.297975\pi$
$743$	7.31920e15	1.18584	0.592919	+	0.805262i	$0.297975\pi$
$744$	−1.38856e15	−0.223313
$745$	−1.36566e15	−0.218013
$746$	1.00055e15	0.158553
$747$	−2.13702e15	−0.336160
$748$	−5.88141e15	−0.918381
$749$	−7.69699e15	−1.19308
$750$	−3.94299e14	−0.0606720
$751$	−8.16956e15	−1.24790	−0.623949	−	0.781465i	$-0.714473\pi$
$751$	−8.16956e15	−1.24790	−0.623949	+	0.781465i	$0.714473\pi$
$752$	−4.56572e15	−0.692327
$753$	3.67834e15	0.553706
$754$	5.31611e14	0.0794423
$755$	−3.10736e15	−0.460981
$756$	−1.05303e15	−0.155085
$757$	6.90771e15	1.00997	0.504983	−	0.863129i	$-0.331499\pi$
$757$	6.90771e15	1.00997	0.504983	+	0.863129i	$0.331499\pi$
$758$	5.70073e14	0.0827465
$759$	−1.00156e16	−1.44327
$760$	6.54373e14	0.0936162
$761$	4.39006e15	0.623527	0.311764	−	0.950160i	$-0.399080\pi$
$761$	4.39006e15	0.623527	0.311764	+	0.950160i	$0.399080\pi$
$762$	7.35223e14	0.103673
$763$	3.96450e15	0.555013
$764$	−1.64007e15	−0.227954
$765$	−9.69025e14	−0.133720
$766$	−2.16249e13	−0.00296276
$767$	−9.84211e14	−0.133879
$768$	−3.73390e15	−0.504285
$769$	−2.32170e14	−0.0311323	−0.0155661	−	0.999879i	$-0.504955\pi$
$769$	−2.32170e14	−0.0311323	−0.0155661	+	0.999879i	$0.504955\pi$
$770$	−4.75081e14	−0.0632512
$771$	6.16115e15	0.814447
$772$	2.70577e15	0.355137
$773$	3.33082e15	0.434075	0.217037	−	0.976163i	$-0.430361\pi$
$773$	3.33082e15	0.434075	0.217037	+	0.976163i	$0.430361\pi$
$774$	−4.14157e14	−0.0535908
$775$	−9.41481e15	−1.20963
$776$	2.68271e15	0.342243
$777$	−5.04326e15	−0.638845
$778$	−1.68985e15	−0.212550
$779$	−8.10557e15	−1.01234
$780$	2.56270e15	0.317818
$781$	1.41733e16	1.74538
$782$	−1.36583e15	−0.167016
$783$	1.07787e15	0.130881
$784$	−2.65946e15	−0.320668
$785$	−5.08571e14	−0.0608932
$786$	−3.99042e14	−0.0474455
$787$	8.86494e15	1.04668	0.523341	−	0.852123i	$-0.324685\pi$
$787$	8.86494e15	1.04668	0.523341	+	0.852123i	$0.324685\pi$
$788$	−1.53367e16	−1.79819
$789$	2.30744e15	0.268663
$790$	6.27623e14	0.0725688
$791$	−1.35916e15	−0.156063
$792$	−8.29896e14	−0.0946313
$793$	6.52193e15	0.738540
$794$	−9.04323e14	−0.101698
$795$	3.36184e15	0.375455
$796$	−3.76123e15	−0.417165
$797$	1.00296e16	1.10475	0.552373	−	0.833597i	$-0.313722\pi$
$797$	1.00296e16	1.10475	0.552373	+	0.833597i	$0.313722\pi$
$798$	−3.74318e14	−0.0409472
$799$	4.90307e15	0.532673
$800$	2.19133e15	0.236435
$801$	−9.48076e14	−0.101593
$802$	−1.08147e15	−0.115095
$803$	3.26254e15	0.344842
$804$	−5.80438e15	−0.609323
$805$	8.43985e15	0.879948
$806$	−1.93303e15	−0.200168
$807$	−4.87751e15	−0.501641
$808$	2.80720e15	0.286755
$809$	−1.25713e16	−1.27544	−0.637722	−	0.770266i	$-0.720123\pi$
$809$	−1.25713e16	−1.27544	−0.637722	+	0.770266i	$0.720123\pi$
$810$	−6.79231e13	−0.00684463
$811$	9.04964e15	0.905768	0.452884	−	0.891570i	$-0.350395\pi$
$811$	9.04964e15	0.905768	0.452884	+	0.891570i	$0.350395\pi$
$812$	−5.51276e15	−0.548038
$813$	4.02378e14	0.0397316
$814$	−1.97440e15	−0.193643
$815$	6.90334e15	0.672501
$816$	4.24369e15	0.410628
$817$	1.12621e16	1.08242
$818$	1.38966e15	0.132668
$819$	−2.95102e15	−0.279841
$820$	7.52251e15	0.708577
$821$	1.28377e16	1.20115	0.600577	−	0.799567i	$-0.294938\pi$
$821$	1.28377e16	1.20115	0.600577	+	0.799567i	$0.294938\pi$
$822$	−2.85134e14	−0.0265005
$823$	−1.64147e16	−1.51542	−0.757710	−	0.652591i	$-0.773682\pi$
$823$	−1.64147e16	−1.51542	−0.757710	+	0.652591i	$0.773682\pi$
$824$	1.40228e15	0.128598
$825$	−5.62691e15	−0.512594
$826$	−1.33417e14	−0.0120731
$827$	1.04782e16	0.941900	0.470950	−	0.882160i	$-0.343911\pi$
$827$	1.04782e16	0.941900	0.470950	+	0.882160i	$0.343911\pi$
$828$	7.32371e15	0.653979
$829$	8.00579e15	0.710157	0.355079	−	0.934836i	$-0.384454\pi$
$829$	8.00579e15	0.710157	0.355079	+	0.934836i	$0.384454\pi$
$830$	7.05000e14	0.0621241
$831$	6.66158e15	0.583138
$832$	−1.09197e16	−0.949586
$833$	2.85597e15	0.246721
$834$	6.07590e14	0.0521431
$835$	6.59891e15	0.562596
$836$	1.12103e16	0.949474
$837$	−3.91931e15	−0.329777
$838$	−3.15686e13	−0.00263884
$839$	−8.86181e15	−0.735921	−0.367961	−	0.929841i	$-0.619944\pi$
$839$	−8.86181e15	−0.735921	−0.367961	+	0.929841i	$0.619944\pi$
$840$	6.99325e14	0.0576957
$841$	−6.55770e15	−0.537494
$842$	−1.52974e15	−0.124566
$843$	−5.61225e15	−0.454031
$844$	−1.53830e16	−1.23639
$845$	3.90486e14	0.0311813
$846$	3.43677e14	0.0272655
$847$	−6.02656e15	−0.475019
$848$	−1.47227e16	−1.15295
$849$	−7.82720e15	−0.608995
$850$	−7.67338e14	−0.0593175
$851$	3.50753e16	2.69395
$852$	−1.03639e16	−0.790871
$853$	−1.60165e16	−1.21436	−0.607182	−	0.794563i	$-0.707700\pi$
$853$	−1.60165e16	−1.21436	−0.607182	+	0.794563i	$0.707700\pi$
$854$	8.84093e14	0.0666009
$855$	1.84702e15	0.138248
$856$	4.43564e15	0.329876
$857$	−1.70481e16	−1.25974	−0.629871	−	0.776699i	$-0.716892\pi$
$857$	−1.70481e16	−1.25974	−0.629871	+	0.776699i	$0.716892\pi$
$858$	−1.15530e15	−0.0848236
$859$	−5.84317e15	−0.426272	−0.213136	−	0.977023i	$-0.568368\pi$
$859$	−5.84317e15	−0.426272	−0.213136	+	0.977023i	$0.568368\pi$
$860$	−1.04520e16	−0.757629
$861$	−8.66238e15	−0.623907
$862$	−1.11679e15	−0.0799250
$863$	−9.32399e15	−0.663044	−0.331522	−	0.943447i	$-0.607562\pi$
$863$	−9.32399e15	−0.663044	−0.331522	+	0.943447i	$0.607562\pi$
$864$	9.12233e14	0.0644585
$865$	1.73677e15	0.121942
$866$	−4.54786e14	−0.0317292
$867$	3.77082e15	0.261415
$868$	2.00453e16	1.38087
$869$	2.16446e16	1.48164
$870$	−3.55587e14	−0.0241875
$871$	−1.62663e16	−1.09948
$872$	−2.28467e15	−0.153456
$873$	7.57215e15	0.505406
$874$	2.60334e15	0.172671
$875$	1.14586e16	0.755245
$876$	−2.38566e15	−0.156256
$877$	−1.09528e16	−0.712899	−0.356450	−	0.934315i	$-0.616013\pi$
$877$	−1.09528e16	−0.712899	−0.356450	+	0.934315i	$0.616013\pi$
$878$	4.19458e14	0.0271312
$879$	1.48377e16	0.953733
$880$	−1.02661e16	−0.655771
$881$	2.13492e16	1.35523	0.677616	−	0.735416i	$-0.263013\pi$
$881$	2.13492e16	1.35523	0.677616	+	0.735416i	$0.263013\pi$
$882$	2.00187e14	0.0126287
$883$	2.06137e15	0.129233	0.0646163	−	0.997910i	$-0.479418\pi$
$883$	2.06137e15	0.129233	0.0646163	+	0.997910i	$0.479418\pi$
$884$	1.20522e16	0.750894
$885$	6.58325e14	0.0407617
$886$	−9.44734e14	−0.0581332
$887$	1.88858e16	1.15493	0.577465	−	0.816415i	$-0.304042\pi$
$887$	1.88858e16	1.15493	0.577465	+	0.816415i	$0.304042\pi$
$888$	2.90634e15	0.176634
$889$	−2.13662e16	−1.29053
$890$	3.12769e14	0.0187749
$891$	−2.34244e15	−0.139747
$892$	−2.27593e16	−1.34944
$893$	−9.34554e15	−0.550708
$894$	−4.50186e14	−0.0263655
$895$	−1.55841e14	−0.00907098
$896$	−6.20684e15	−0.359068
$897$	2.05241e16	1.18006
$898$	−3.86699e15	−0.220980
$899$	−2.05182e16	−1.16536
$900$	4.11455e15	0.232268
$901$	1.58105e16	0.887072
$902$	−3.39126e15	−0.189115
$903$	1.20357e16	0.667098
$904$	7.83262e14	0.0431500
$905$	1.33964e16	0.733533
$906$	−1.02433e15	−0.0557489
$907$	1.85358e16	1.00270	0.501351	−	0.865244i	$-0.332836\pi$
$907$	1.85358e16	1.00270	0.501351	+	0.865244i	$0.332836\pi$
$908$	−1.34994e16	−0.725843
$909$	7.92352e15	0.423464
$910$	9.73537e14	0.0517160
$911$	−3.24212e16	−1.71190	−0.855948	−	0.517062i	$-0.827026\pi$
$911$	−3.24212e16	−1.71190	−0.855948	+	0.517062i	$0.827026\pi$
$912$	−8.08872e15	−0.424530
$913$	2.43131e16	1.26839
$914$	−3.01134e15	−0.156155
$915$	−4.36243e15	−0.224860
$916$	8.10723e15	0.415382
$917$	1.15965e16	0.590602
$918$	−3.19437e14	−0.0161715
$919$	3.51960e15	0.177116	0.0885580	−	0.996071i	$-0.471774\pi$
$919$	3.51960e15	0.177116	0.0885580	+	0.996071i	$0.471774\pi$
$920$	−4.86374e15	−0.243297
$921$	−1.08336e16	−0.538698
$922$	3.03992e15	0.150260
$923$	−2.90440e16	−1.42707
$924$	1.19804e16	0.585161
$925$	1.97058e16	0.956784
$926$	2.93496e15	0.141658
$927$	3.95805e15	0.189908
$928$	4.77568e15	0.227783
$929$	1.92092e16	0.910799	0.455400	−	0.890287i	$-0.349496\pi$
$929$	1.92092e16	0.910799	0.455400	+	0.890287i	$0.349496\pi$
$930$	1.29297e15	0.0609444
$931$	−5.44364e15	−0.255074
$932$	3.52649e15	0.164269
$933$	−7.11687e15	−0.329564
$934$	−6.77838e14	−0.0312046
$935$	1.10247e16	0.504548
$936$	1.70062e15	0.0773733
$937$	−3.60925e16	−1.63248	−0.816242	−	0.577710i	$-0.803946\pi$
$937$	−3.60925e16	−1.63248	−0.816242	+	0.577710i	$0.803946\pi$
$938$	−2.20501e15	−0.0991504
$939$	2.53882e16	1.13493
$940$	8.67328e15	0.385461
$941$	−4.08149e16	−1.80333	−0.901666	−	0.432433i	$-0.857655\pi$
$941$	−4.08149e16	−1.80333	−0.901666	+	0.432433i	$0.857655\pi$
$942$	−1.67649e14	−0.00736414
$943$	6.02460e16	2.63096
$944$	−2.88303e15	−0.125171
$945$	1.97390e15	0.0852020
$946$	4.71191e15	0.202207
$947$	1.40417e16	0.599095	0.299548	−	0.954081i	$-0.403164\pi$
$947$	1.40417e16	0.599095	0.299548	+	0.954081i	$0.403164\pi$
$948$	−1.58271e16	−0.671362
$949$	−6.68560e15	−0.281953
$950$	1.46259e15	0.0613258
$951$	−2.25957e16	−0.941962
$952$	3.28887e15	0.136315
$953$	3.95272e16	1.62886	0.814432	−	0.580259i	$-0.197049\pi$
$953$	3.95272e16	1.62886	0.814432	+	0.580259i	$0.197049\pi$
$954$	1.10822e15	0.0454058
$955$	3.07430e15	0.125235
$956$	2.01760e16	0.817177
$957$	−1.22630e16	−0.493835
$958$	1.50132e15	0.0601124
$959$	8.28621e15	0.329878
$960$	7.30406e15	0.289116
$961$	4.91990e16	1.93632
$962$	4.04594e15	0.158328
$963$	1.25199e16	0.487144
$964$	1.17284e16	0.453750
$965$	−5.07196e15	−0.195108
$966$	2.78218e15	0.106417
$967$	2.10761e16	0.801577	0.400788	−	0.916171i	$-0.368736\pi$
$967$	2.10761e16	0.801577	0.400788	+	0.916171i	$0.368736\pi$
$968$	3.47300e15	0.131338
$969$	8.68638e15	0.326632
$970$	−2.49804e15	−0.0934016
$971$	1.84689e16	0.686648	0.343324	−	0.939217i	$-0.388447\pi$
$971$	1.84689e16	0.686648	0.343324	+	0.939217i	$0.388447\pi$
$972$	1.71286e15	0.0633223
$973$	−1.76570e16	−0.649078
$974$	1.60361e15	0.0586171
$975$	1.15307e16	0.419111
$976$	1.91046e16	0.690500
$977$	5.17619e16	1.86033	0.930166	−	0.367140i	$-0.119663\pi$
$977$	5.17619e16	1.86033	0.930166	+	0.367140i	$0.119663\pi$
$978$	2.27567e15	0.0813292
$979$	1.07863e16	0.383327
$980$	5.05206e15	0.178536
$981$	−6.44865e15	−0.226615
$982$	4.56470e15	0.159514
$983$	2.53882e16	0.882242	0.441121	−	0.897448i	$-0.354581\pi$
$983$	2.53882e16	0.882242	0.441121	+	0.897448i	$0.354581\pi$
$984$	4.99198e15	0.172504
$985$	2.87485e16	0.987907
$986$	−1.67230e15	−0.0571467
$987$	−9.98752e15	−0.339401
$988$	−2.29722e16	−0.776317
$989$	−8.37073e16	−2.81309
$990$	7.72767e14	0.0258259
$991$	−1.27518e16	−0.423806	−0.211903	−	0.977291i	$-0.567966\pi$
$991$	−1.27518e16	−0.423806	−0.211903	+	0.977291i	$0.567966\pi$
$992$	−1.73651e16	−0.573937
$993$	−9.01072e15	−0.296168
$994$	−3.93711e15	−0.128692
$995$	7.05040e15	0.229185
$996$	−1.77784e16	−0.574733
$997$	−2.78396e15	−0.0895033	−0.0447516	−	0.998998i	$-0.514250\pi$
$997$	−2.78396e15	−0.0895033	−0.0447516	+	0.998998i	$0.514250\pi$
$998$	−5.07067e15	−0.162124
$999$	8.20336e15	0.260845

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.14	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.14	✓	27	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} -19480.2 q^{10} -671806. q^{11} +491242. q^{12} +1.37666e6 q^{13} +186616. q^{14} -920832. q^{15} +4.03264e6 q^{16} -4.33060e6 q^{17} -303550. q^{18} +8.25438e6 q^{19} -7.66062e6 q^{20} +8.82141e6 q^{21} +3.45352e6 q^{22} -6.13520e7 q^{23} -5.08362e6 q^{24} -3.44683e7 q^{25} -7.07696e6 q^{26} -1.43489e7 q^{27} +7.33874e7 q^{28} -7.51187e7 q^{29} +4.73368e6 q^{30} +2.73144e8 q^{31} -6.35751e7 q^{32} +1.63249e8 q^{33} +2.22621e7 q^{34} -1.37564e8 q^{35} -1.19372e8 q^{36} -5.71706e8 q^{37} -4.24329e7 q^{38} -3.34530e8 q^{39} +7.92759e7 q^{40} -9.81972e8 q^{41} -4.53478e7 q^{42} +1.36438e9 q^{43} +1.35810e9 q^{44} +2.23762e8 q^{45} +3.15389e8 q^{46} -1.13219e9 q^{47} -9.79931e8 q^{48} -6.59485e8 q^{49} +1.77190e8 q^{50} +1.05234e9 q^{51} -2.78303e9 q^{52} -3.65087e9 q^{53} +7.37628e7 q^{54} -2.54576e9 q^{55} -7.59449e8 q^{56} -2.00581e9 q^{57} +3.86159e8 q^{58} -7.14924e8 q^{59} +1.86153e9 q^{60} +4.73749e9 q^{61} -1.40414e9 q^{62} -2.14360e9 q^{63} -7.93203e9 q^{64} +5.21678e9 q^{65} -8.39206e8 q^{66} -1.18157e10 q^{67} +8.75463e9 q^{68} +1.49085e10 q^{69} +7.07170e8 q^{70} -2.10973e10 q^{71} +1.23532e9 q^{72} -4.85638e9 q^{73} +2.93894e9 q^{74} +8.37580e9 q^{75} -1.66868e10 q^{76} +2.43880e10 q^{77} +1.71970e9 q^{78} -3.22186e10 q^{79} +1.52814e10 q^{80} +3.48678e9 q^{81} +5.04798e9 q^{82} -3.61907e10 q^{83} -1.78331e10 q^{84} -1.64105e10 q^{85} -7.01379e9 q^{86} +1.82538e10 q^{87} -1.40544e10 q^{88} -1.60558e10 q^{89} -1.15028e9 q^{90} -4.99758e10 q^{91} +1.24028e11 q^{92} -6.63739e10 q^{93} +5.82020e9 q^{94} +3.12794e10 q^{95} +1.54487e10 q^{96} +1.28235e11 q^{97} +3.39018e9 q^{98} -3.96695e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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