LMFDB - Embedded newform 177.12.a.b.1.8

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:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} -198873. q^{10} +281821. q^{11} +45976.7 q^{12} -286281. q^{13} -389554. q^{14} +1.02171e6 q^{15} -4.54600e6 q^{16} +5.87036e6 q^{17} -2.79296e6 q^{18} -8.24249e6 q^{19} +795526. q^{20} +2.00134e6 q^{21} -1.33299e7 q^{22} -1.83373e7 q^{23} +2.13644e7 q^{24} -3.11496e7 q^{25} +1.35408e7 q^{26} +1.43489e7 q^{27} +1.55828e6 q^{28} -3.47171e7 q^{29} -4.83262e7 q^{30} +3.33154e7 q^{31} +3.49627e7 q^{32} +6.84824e7 q^{33} -2.77663e8 q^{34} +3.46289e7 q^{35} +1.11723e7 q^{36} -6.02333e8 q^{37} +3.89862e8 q^{38} -6.95664e7 q^{39} +3.69665e8 q^{40} +1.14101e9 q^{41} -9.46617e7 q^{42} -9.42291e8 q^{43} +5.33217e7 q^{44} +2.48277e8 q^{45} +8.67338e8 q^{46} -1.01733e9 q^{47} -1.10468e9 q^{48} -1.90950e9 q^{49} +1.47335e9 q^{50} +1.42650e9 q^{51} -5.41657e7 q^{52} -1.59817e9 q^{53} -6.78690e8 q^{54} +1.18494e9 q^{55} +7.24102e8 q^{56} -2.00292e9 q^{57} +1.64209e9 q^{58} -7.14924e8 q^{59} +1.93313e8 q^{60} -5.49619e9 q^{61} -1.57579e9 q^{62} +4.86326e8 q^{63} +7.65650e9 q^{64} -1.20369e9 q^{65} -3.23915e9 q^{66} -9.28126e9 q^{67} +1.11070e9 q^{68} -4.45597e9 q^{69} -1.63791e9 q^{70} +5.67711e9 q^{71} +5.19155e9 q^{72} -3.15638e9 q^{73} +2.84898e10 q^{74} -7.56935e9 q^{75} -1.55951e9 q^{76} +2.32107e9 q^{77} +3.29043e9 q^{78} +3.09935e10 q^{79} -1.91140e10 q^{80} +3.48678e9 q^{81} -5.39688e10 q^{82} +6.71075e9 q^{83} +3.78663e8 q^{84} +2.46825e10 q^{85} +4.45695e10 q^{86} -8.43625e9 q^{87} +2.47775e10 q^{88} +8.36957e10 q^{89} -1.17433e10 q^{90} -2.35781e9 q^{91} -3.46950e9 q^{92} +8.09565e9 q^{93} +4.81190e10 q^{94} -3.46563e10 q^{95} +8.49593e9 q^{96} +1.29155e11 q^{97} +9.03174e10 q^{98} +1.66412e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) $	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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 $

$2$	−47.2991	−1.04517	−0.522586	−	0.852587i	$-0.675033\pi$
$2$	−47.2991	−1.04517	−0.522586	+	0.852587i	$0.675033\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	189.204	0.0923849
$5$	4204.59	0.601712	0.300856	−	0.953670i	$-0.402728\pi$
$5$	4204.59	0.601712	0.300856	+	0.953670i	$0.402728\pi$
$6$	−11493.7	−0.603430
$7$	8235.98	0.185215	0.0926074	−	0.995703i	$-0.470480\pi$
$7$	8235.98	0.185215	0.0926074	+	0.995703i	$0.470480\pi$
$8$	87919.4	0.948614
$9$	59049.0	0.333333
$10$	−198873.	−0.628892
$11$	281821.	0.527610	0.263805	−	0.964576i	$-0.415022\pi$
$11$	281821.	0.527610	0.263805	+	0.964576i	$0.415022\pi$
$12$	45976.7	0.0533385
$13$	−286281.	−0.213848	−0.106924	−	0.994267i	$-0.534100\pi$
$13$	−286281.	−0.213848	−0.106924	+	0.994267i	$0.534100\pi$
$14$	−389554.	−0.193581
$15$	1.02171e6	0.347398
$16$	−4.54600e6	−1.08385
$17$	5.87036e6	1.00276	0.501379	−	0.865228i	$-0.332826\pi$
$17$	5.87036e6	1.00276	0.501379	+	0.865228i	$0.332826\pi$
$18$	−2.79296e6	−0.348391
$19$	−8.24249e6	−0.763684	−0.381842	−	0.924228i	$-0.624710\pi$
$19$	−8.24249e6	−0.763684	−0.381842	+	0.924228i	$0.624710\pi$
$20$	795526.	0.0555891
$21$	2.00134e6	0.106934
$22$	−1.33299e7	−0.551443
$23$	−1.83373e7	−0.594063	−0.297031	−	0.954868i	$-0.595997\pi$
$23$	−1.83373e7	−0.594063	−0.297031	+	0.954868i	$0.595997\pi$
$24$	2.13644e7	0.547683
$25$	−3.11496e7	−0.637943
$26$	1.35408e7	0.223508
$27$	1.43489e7	0.192450
$28$	1.55828e6	0.0171111
$29$	−3.47171e7	−0.314307	−0.157154	−	0.987574i	$-0.550232\pi$
$29$	−3.47171e7	−0.314307	−0.157154	+	0.987574i	$0.550232\pi$
$30$	−4.83262e7	−0.363091
$31$	3.33154e7	0.209005	0.104502	−	0.994525i	$-0.466675\pi$
$31$	3.33154e7	0.209005	0.104502	+	0.994525i	$0.466675\pi$
$32$	3.49627e7	0.184196
$33$	6.84824e7	0.304616
$34$	−2.77663e8	−1.04805
$35$	3.46289e7	0.111446
$36$	1.11723e7	0.0307950
$37$	−6.02333e8	−1.42800	−0.713999	−	0.700147i	$-0.753118\pi$
$37$	−6.02333e8	−1.42800	−0.713999	+	0.700147i	$0.753118\pi$
$38$	3.89862e8	0.798181
$39$	−6.95664e7	−0.123465
$40$	3.69665e8	0.570792
$41$	1.14101e9	1.53808	0.769039	−	0.639202i	$-0.220735\pi$
$41$	1.14101e9	1.53808	0.769039	+	0.639202i	$0.220735\pi$
$42$	−9.46617e7	−0.111764
$43$	−9.42291e8	−0.977482	−0.488741	−	0.872429i	$-0.662544\pi$
$43$	−9.42291e8	−0.977482	−0.488741	+	0.872429i	$0.662544\pi$
$44$	5.33217e7	0.0487432
$45$	2.48277e8	0.200571
$46$	8.67338e8	0.620898
$47$	−1.01733e9	−0.647032	−0.323516	−	0.946223i	$-0.604865\pi$
$47$	−1.01733e9	−0.647032	−0.323516	+	0.946223i	$0.604865\pi$
$48$	−1.10468e9	−0.625761
$49$	−1.90950e9	−0.965695
$50$	1.47335e9	0.666761
$51$	1.42650e9	0.578942
$52$	−5.41657e7	−0.0197563
$53$	−1.59817e9	−0.524935	−0.262467	−	0.964941i	$-0.584536\pi$
$53$	−1.59817e9	−0.524935	−0.262467	+	0.964941i	$0.584536\pi$
$54$	−6.78690e8	−0.201143
$55$	1.18494e9	0.317469
$56$	7.24102e8	0.175697
$57$	−2.00292e9	−0.440913
$58$	1.64209e9	0.328505
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	1.93313e8	0.0320944
$61$	−5.49619e9	−0.833196	−0.416598	−	0.909091i	$-0.636778\pi$
$61$	−5.49619e9	−0.833196	−0.416598	+	0.909091i	$0.636778\pi$
$62$	−1.57579e9	−0.218446
$63$	4.86326e8	0.0617383
$64$	7.65650e9	0.891334
$65$	−1.20369e9	−0.128675
$66$	−3.23915e9	−0.318376
$67$	−9.28126e9	−0.839838	−0.419919	−	0.907562i	$-0.637942\pi$
$67$	−9.28126e9	−0.839838	−0.419919	+	0.907562i	$0.637942\pi$
$68$	1.11070e9	0.0926397
$69$	−4.45597e9	−0.342982
$70$	−1.63791e9	−0.116480
$71$	5.67711e9	0.373428	0.186714	−	0.982414i	$-0.440216\pi$
$71$	5.67711e9	0.373428	0.186714	+	0.982414i	$0.440216\pi$
$72$	5.19155e9	0.316205
$73$	−3.15638e9	−0.178203	−0.0891013	−	0.996023i	$-0.528399\pi$
$73$	−3.15638e9	−0.178203	−0.0891013	+	0.996023i	$0.528399\pi$
$74$	2.84898e10	1.49250
$75$	−7.56935e9	−0.368317
$76$	−1.55951e9	−0.0705529
$77$	2.32107e9	0.0977212
$78$	3.29043e9	0.129042
$79$	3.09935e10	1.13324	0.566619	−	0.823980i	$-0.308251\pi$
$79$	3.09935e10	1.13324	0.566619	+	0.823980i	$0.308251\pi$
$80$	−1.91140e10	−0.652165
$81$	3.48678e9	0.111111
$82$	−5.39688e10	−1.60756
$83$	6.71075e9	0.187000	0.0935001	−	0.995619i	$-0.470194\pi$
$83$	6.71075e9	0.187000	0.0935001	+	0.995619i	$0.470194\pi$
$84$	3.78663e8	0.00987908
$85$	2.46825e10	0.603371
$86$	4.45695e10	1.02164
$87$	−8.43625e9	−0.181465
$88$	2.47775e10	0.500498
$89$	8.36957e10	1.58876	0.794379	−	0.607422i	$-0.207796\pi$
$89$	8.36957e10	1.58876	0.794379	+	0.607422i	$0.207796\pi$
$90$	−1.17433e10	−0.209631
$91$	−2.35781e9	−0.0396078
$92$	−3.46950e9	−0.0548825
$93$	8.09565e9	0.120669
$94$	4.81190e10	0.676260
$95$	−3.46563e10	−0.459517
$96$	8.49593e9	0.106346
$97$	1.29155e11	1.52710	0.763551	−	0.645748i	$-0.223454\pi$
$97$	1.29155e11	1.52710	0.763551	+	0.645748i	$0.223454\pi$
$98$	9.03174e10	1.00932
$99$	1.66412e10	0.175870
$100$	−5.89363e9	−0.0589363
$101$	−6.81221e10	−0.644941	−0.322471	−	0.946579i	$-0.604513\pi$
$101$	−6.81221e10	−0.644941	−0.322471	+	0.946579i	$0.604513\pi$
$102$	−6.74721e10	−0.605094
$103$	−1.61545e11	−1.37306	−0.686528	−	0.727103i	$-0.740866\pi$
$103$	−1.61545e11	−1.37306	−0.686528	+	0.727103i	$0.740866\pi$
$104$	−2.51697e10	−0.202859
$105$	8.41482e9	0.0643433
$106$	7.55919e10	0.548647
$107$	2.70987e11	1.86783	0.933916	−	0.357493i	$-0.116368\pi$
$107$	2.70987e11	1.86783	0.933916	+	0.357493i	$0.116368\pi$
$108$	2.71488e9	0.0177795
$109$	1.06839e11	0.665093	0.332546	−	0.943087i	$-0.392092\pi$
$109$	1.06839e11	0.665093	0.332546	+	0.943087i	$0.392092\pi$
$110$	−5.60465e10	−0.331810
$111$	−1.46367e11	−0.824455
$112$	−3.74407e10	−0.200745
$113$	−2.41918e11	−1.23520	−0.617599	−	0.786493i	$-0.711894\pi$
$113$	−2.41918e11	−1.23520	−0.617599	+	0.786493i	$0.711894\pi$
$114$	9.47365e10	0.460830
$115$	−7.71008e10	−0.357455
$116$	−6.56863e9	−0.0290373
$117$	−1.69046e10	−0.0712826
$118$	3.38153e10	0.136070
$119$	4.83482e10	0.185726
$120$	8.98285e10	0.329547
$121$	−2.05889e11	−0.721628
$122$	2.59965e11	0.870834
$123$	2.77266e11	0.888010
$124$	6.30342e9	0.0193089
$125$	−3.36273e11	−0.985569
$126$	−2.30028e10	−0.0645272
$127$	1.39360e11	0.374298	0.187149	−	0.982332i	$-0.440075\pi$
$127$	1.39360e11	0.374298	0.187149	+	0.982332i	$0.440075\pi$
$128$	−4.33749e11	−1.11579
$129$	−2.28977e11	−0.564349
$130$	5.69337e10	0.134487
$131$	−7.67488e11	−1.73812	−0.869059	−	0.494708i	$-0.835275\pi$
$131$	−7.67488e11	−1.73812	−0.869059	+	0.494708i	$0.835275\pi$
$132$	1.29572e10	0.0281419
$133$	−6.78849e10	−0.141446
$134$	4.38995e11	0.877776
$135$	6.03312e10	0.115799
$136$	5.16118e11	0.951230
$137$	4.82437e11	0.854039	0.427020	−	0.904242i	$-0.359564\pi$
$137$	4.82437e11	0.854039	0.427020	+	0.904242i	$0.359564\pi$
$138$	2.10763e11	0.358476
$139$	5.67488e11	0.927630	0.463815	−	0.885932i	$-0.346480\pi$
$139$	5.67488e11	0.927630	0.463815	+	0.885932i	$0.346480\pi$
$140$	6.55194e9	0.0102959
$141$	−2.47212e11	−0.373564
$142$	−2.68522e11	−0.390296
$143$	−8.06799e10	−0.112828
$144$	−2.68437e11	−0.361283
$145$	−1.45971e11	−0.189122
$146$	1.49294e11	0.186252
$147$	−4.64007e11	−0.557545
$148$	−1.13964e11	−0.131925
$149$	1.25807e12	1.40340	0.701699	−	0.712474i	$-0.252425\pi$
$149$	1.25807e12	1.40340	0.701699	+	0.712474i	$0.252425\pi$
$150$	3.58023e11	0.384954
$151$	−1.00010e11	−0.103674	−0.0518370	−	0.998656i	$-0.516508\pi$
$151$	−1.00010e11	−0.103674	−0.0518370	+	0.998656i	$0.516508\pi$
$152$	−7.24674e11	−0.724441
$153$	3.46639e11	0.334252
$154$	−1.09784e11	−0.102135
$155$	1.40078e11	0.125761
$156$	−1.31623e10	−0.0114063
$157$	−2.12968e12	−1.78183	−0.890914	−	0.454171i	$-0.849935\pi$
$157$	−2.12968e12	−1.78183	−0.890914	+	0.454171i	$0.849935\pi$
$158$	−1.46596e12	−1.18443
$159$	−3.88355e11	−0.303071
$160$	1.47004e11	0.110833
$161$	−1.51026e11	−0.110029
$162$	−1.64922e11	−0.116130
$163$	−9.65551e11	−0.657269	−0.328635	−	0.944457i	$-0.606588\pi$
$163$	−9.65551e11	−0.657269	−0.328635	+	0.944457i	$0.606588\pi$
$164$	2.15884e11	0.142095
$165$	2.87940e11	0.183291
$166$	−3.17413e11	−0.195447
$167$	−2.58660e12	−1.54095	−0.770477	−	0.637468i	$-0.779982\pi$
$167$	−2.58660e12	−1.54095	−0.770477	+	0.637468i	$0.779982\pi$
$168$	1.75957e11	0.101439
$169$	−1.71020e12	−0.954269
$170$	−1.16746e12	−0.630626
$171$	−4.86711e11	−0.254561
$172$	−1.78286e11	−0.0903046
$173$	2.46099e12	1.20741	0.603707	−	0.797207i	$-0.293690\pi$
$173$	2.46099e12	1.20741	0.603707	+	0.797207i	$0.293690\pi$
$174$	3.99027e11	0.189663
$175$	−2.56547e11	−0.118157
$176$	−1.28116e12	−0.571850
$177$	−1.73727e11	−0.0751646
$178$	−3.95873e12	−1.66053
$179$	−3.79982e12	−1.54551	−0.772755	−	0.634705i	$-0.781122\pi$
$179$	−3.79982e12	−1.54551	−0.772755	+	0.634705i	$0.781122\pi$
$180$	4.69750e10	0.0185297
$181$	−3.35194e12	−1.28252	−0.641260	−	0.767323i	$-0.721588\pi$
$181$	−3.35194e12	−1.28252	−0.641260	+	0.767323i	$0.721588\pi$
$182$	1.11522e11	0.0413969
$183$	−1.33557e12	−0.481046
$184$	−1.61220e12	−0.563536
$185$	−2.53256e12	−0.859243
$186$	−3.82917e11	−0.126120
$187$	1.65439e12	0.529065
$188$	−1.92484e11	−0.0597760
$189$	1.18177e11	0.0356446
$190$	1.63921e12	0.480275
$191$	−4.77645e12	−1.35963	−0.679816	−	0.733382i	$-0.737941\pi$
$191$	−4.77645e12	−1.35963	−0.679816	+	0.733382i	$0.737941\pi$
$192$	1.86053e12	0.514612
$193$	8.03275e11	0.215923	0.107962	−	0.994155i	$-0.465568\pi$
$193$	8.03275e11	0.215923	0.107962	+	0.994155i	$0.465568\pi$
$194$	−6.10893e12	−1.59608
$195$	−2.92498e11	−0.0742903
$196$	−3.61285e11	−0.0892157
$197$	−4.58933e12	−1.10201	−0.551004	−	0.834502i	$-0.685755\pi$
$197$	−4.58933e12	−1.10201	−0.551004	+	0.834502i	$0.685755\pi$
$198$	−7.87115e11	−0.183814
$199$	−5.47173e12	−1.24289	−0.621445	−	0.783458i	$-0.713454\pi$
$199$	−5.47173e12	−1.24289	−0.621445	+	0.783458i	$0.713454\pi$
$200$	−2.73865e12	−0.605162
$201$	−2.25535e12	−0.484881
$202$	3.22211e12	0.674075
$203$	−2.85929e11	−0.0582144
$204$	2.69900e11	0.0534855
$205$	4.79748e12	0.925480
$206$	7.64093e12	1.43508
$207$	−1.08280e12	−0.198021
$208$	1.30143e12	0.231779
$209$	−2.32290e12	−0.402927
$210$	−3.98013e11	−0.0672499
$211$	2.55759e12	0.420996	0.210498	−	0.977594i	$-0.432492\pi$
$211$	2.55759e12	0.420996	0.210498	+	0.977594i	$0.432492\pi$
$212$	−3.02380e11	−0.0484960
$213$	1.37954e12	0.215598
$214$	−1.28174e13	−1.95221
$215$	−3.96195e12	−0.588162
$216$	1.26155e12	0.182561
$217$	2.74385e11	0.0387108
$218$	−5.05337e12	−0.695136
$219$	−7.67001e11	−0.102885
$220$	2.24196e11	0.0293293
$221$	−1.68058e12	−0.214437
$222$	6.92303e12	0.861697
$223$	1.33635e12	0.162271	0.0811357	−	0.996703i	$-0.474145\pi$
$223$	1.33635e12	0.162271	0.0811357	+	0.996703i	$0.474145\pi$
$224$	2.87952e11	0.0341158
$225$	−1.83935e12	−0.212648
$226$	1.14425e13	1.29099
$227$	−7.63779e12	−0.841057	−0.420528	−	0.907279i	$-0.638155\pi$
$227$	−7.63779e12	−0.841057	−0.420528	+	0.907279i	$0.638155\pi$
$228$	−3.78962e11	−0.0407337
$229$	1.86050e13	1.95225	0.976123	−	0.217219i	$-0.0696985\pi$
$229$	1.86050e13	1.95225	0.976123	+	0.217219i	$0.0696985\pi$
$230$	3.64680e12	0.373602
$231$	5.64019e11	0.0564194
$232$	−3.05230e12	−0.298156
$233$	−7.86554e12	−0.750362	−0.375181	−	0.926951i	$-0.622420\pi$
$233$	−7.86554e12	−0.750362	−0.375181	+	0.926951i	$0.622420\pi$
$234$	7.99573e11	0.0745026
$235$	−4.27747e12	−0.389326
$236$	−1.35267e11	−0.0120275
$237$	7.53141e12	0.654275
$238$	−2.28682e12	−0.194115
$239$	−4.25283e12	−0.352768	−0.176384	−	0.984321i	$-0.556440\pi$
$239$	−4.25283e12	−0.352768	−0.176384	+	0.984321i	$0.556440\pi$
$240$	−4.64471e12	−0.376528
$241$	−1.92766e13	−1.52734	−0.763672	−	0.645605i	$-0.776605\pi$
$241$	−1.92766e13	−1.52734	−0.763672	+	0.645605i	$0.776605\pi$
$242$	9.73836e12	0.754225
$243$	8.47289e11	0.0641500
$244$	−1.03990e12	−0.0769748
$245$	−8.02864e12	−0.581070
$246$	−1.31144e13	−0.928123
$247$	2.35967e12	0.163312
$248$	2.92907e12	0.198265
$249$	1.63071e12	0.107965
$250$	1.59054e13	1.03009
$251$	8.11676e12	0.514254	0.257127	−	0.966378i	$-0.417224\pi$
$251$	8.11676e12	0.514254	0.257127	+	0.966378i	$0.417224\pi$
$252$	9.20150e10	0.00570369
$253$	−5.16783e12	−0.313433
$254$	−6.59160e12	−0.391206
$255$	5.99784e12	0.348356
$256$	4.83543e12	0.274862
$257$	4.14442e12	0.230585	0.115293	−	0.993332i	$-0.463219\pi$
$257$	4.14442e12	0.230585	0.115293	+	0.993332i	$0.463219\pi$
$258$	1.08304e13	0.589842
$259$	−4.96080e12	−0.264486
$260$	−2.27744e11	−0.0118876
$261$	−2.05001e12	−0.104769
$262$	3.63015e13	1.81663
$263$	−3.40304e10	−0.00166767	−0.000833835	−	1.00000i	$-0.500265\pi$
$263$	−3.40304e10	−0.00166767	−0.000833835		1.00000i	$0.500265\pi$
$264$	6.02093e12	0.288963
$265$	−6.71964e12	−0.315859
$266$	3.21090e12	0.147835
$267$	2.03380e13	0.917270
$268$	−1.75606e12	−0.0775884
$269$	−5.28454e12	−0.228754	−0.114377	−	0.993437i	$-0.536487\pi$
$269$	−5.28454e12	−0.228754	−0.114377	+	0.993437i	$0.536487\pi$
$270$	−2.85361e12	−0.121030
$271$	4.46026e13	1.85366	0.926828	−	0.375485i	$-0.122524\pi$
$271$	4.46026e13	1.85366	0.926828	+	0.375485i	$0.122524\pi$
$272$	−2.66866e13	−1.08684
$273$	−5.72947e11	−0.0228676
$274$	−2.28189e13	−0.892618
$275$	−8.77859e12	−0.336585
$276$	−8.43088e11	−0.0316864
$277$	−2.25119e13	−0.829419	−0.414709	−	0.909954i	$-0.636117\pi$
$277$	−2.25119e13	−0.829419	−0.414709	+	0.909954i	$0.636117\pi$
$278$	−2.68416e13	−0.969533
$279$	1.96724e12	0.0696682
$280$	3.04455e12	0.105719
$281$	2.16093e13	0.735792	0.367896	−	0.929867i	$-0.380078\pi$
$281$	2.16093e13	0.735792	0.367896	+	0.929867i	$0.380078\pi$
$282$	1.16929e13	0.390439
$283$	5.07251e13	1.66111	0.830553	−	0.556940i	$-0.188025\pi$
$283$	5.07251e13	1.66111	0.830553	+	0.556940i	$0.188025\pi$
$284$	1.07413e12	0.0344991
$285$	−8.42147e12	−0.265302
$286$	3.81609e12	0.117925
$287$	9.39734e12	0.284875
$288$	2.06451e12	0.0613986
$289$	1.89263e11	0.00552241
$290$	6.90430e12	0.197665
$291$	3.13848e13	0.881673
$292$	−5.97202e11	−0.0164632
$293$	−3.09748e13	−0.837986	−0.418993	−	0.907989i	$-0.637617\pi$
$293$	−3.09748e13	−0.837986	−0.418993	+	0.907989i	$0.637617\pi$
$294$	2.19471e13	0.582730
$295$	−3.00596e12	−0.0783362
$296$	−5.29568e13	−1.35462
$297$	4.04382e12	0.101539
$298$	−5.95056e13	−1.46679
$299$	5.24963e12	0.127039
$300$	−1.43215e12	−0.0340269
$301$	−7.76069e12	−0.181044
$302$	4.73038e12	0.108357
$303$	−1.65537e13	−0.372357
$304$	3.74703e13	0.827719
$305$	−2.31092e13	−0.501344
$306$	−1.63957e13	−0.349351
$307$	−1.07004e13	−0.223944	−0.111972	−	0.993711i	$-0.535717\pi$
$307$	−1.07004e13	−0.223944	−0.111972	+	0.993711i	$0.535717\pi$
$308$	4.39156e11	0.00902797
$309$	−3.92554e13	−0.792735
$310$	−6.62554e12	−0.131441
$311$	−7.06656e13	−1.37729	−0.688646	−	0.725098i	$-0.741794\pi$
$311$	−7.06656e13	−1.37729	−0.688646	+	0.725098i	$0.741794\pi$
$312$	−6.11623e12	−0.117121
$313$	6.79714e12	0.127889	0.0639444	−	0.997953i	$-0.479632\pi$
$313$	6.79714e12	0.127889	0.0639444	+	0.997953i	$0.479632\pi$
$314$	1.00732e14	1.86232
$315$	2.04480e12	0.0371486
$316$	5.86410e12	0.104694
$317$	−8.25941e12	−0.144918	−0.0724591	−	0.997371i	$-0.523085\pi$
$317$	−8.25941e12	−0.144918	−0.0724591	+	0.997371i	$0.523085\pi$
$318$	1.83688e13	0.316761
$319$	−9.78399e12	−0.165832
$320$	3.21924e13	0.536326
$321$	6.58499e13	1.07839
$322$	7.14338e12	0.115000
$323$	−4.83864e13	−0.765789
$324$	6.59715e11	0.0102650
$325$	8.91754e12	0.136423
$326$	4.56697e13	0.686960
$327$	2.59618e13	0.383991
$328$	1.00317e14	1.45904
$329$	−8.37875e12	−0.119840
$330$	−1.36193e13	−0.191570
$331$	1.06786e14	1.47728	0.738638	−	0.674102i	$-0.235469\pi$
$331$	1.06786e14	1.47728	0.738638	+	0.674102i	$0.235469\pi$
$332$	1.26970e12	0.0172760
$333$	−3.55672e13	−0.475999
$334$	1.22344e14	1.61056
$335$	−3.90239e13	−0.505340
$336$	−9.09810e12	−0.115900
$337$	8.51744e13	1.06744	0.533721	−	0.845661i	$-0.320793\pi$
$337$	8.51744e13	1.06744	0.533721	+	0.845661i	$0.320793\pi$
$338$	8.08911e13	0.997376
$339$	−5.87860e13	−0.713142
$340$	4.67003e12	0.0557424
$341$	9.38897e12	0.110273
$342$	2.30210e13	0.266060
$343$	−3.20118e13	−0.364076
$344$	−8.28456e13	−0.927253
$345$	−1.87355e13	−0.206376
$346$	−1.16403e14	−1.26195
$347$	−2.09947e13	−0.224025	−0.112013	−	0.993707i	$-0.535730\pi$
$347$	−2.09947e13	−0.224025	−0.112013	+	0.993707i	$0.535730\pi$
$348$	−1.59618e12	−0.0167647
$349$	−1.57991e14	−1.63340	−0.816702	−	0.577059i	$-0.804200\pi$
$349$	−1.57991e14	−1.63340	−0.816702	+	0.577059i	$0.804200\pi$
$350$	1.21344e13	0.123494
$351$	−4.10782e12	−0.0411550
$352$	9.85320e12	0.0971835
$353$	−1.49722e13	−0.145386	−0.0726931	−	0.997354i	$-0.523159\pi$
$353$	−1.49722e13	−0.145386	−0.0726931	+	0.997354i	$0.523159\pi$
$354$	8.21711e12	0.0785600
$355$	2.38699e13	0.224696
$356$	1.58356e13	0.146777
$357$	1.17486e13	0.107229
$358$	1.79728e14	1.61532
$359$	−1.43233e14	−1.26772	−0.633859	−	0.773448i	$-0.718530\pi$
$359$	−1.43233e14	−1.26772	−0.633859	+	0.773448i	$0.718530\pi$
$360$	2.18283e13	0.190264
$361$	−4.85517e13	−0.416787
$362$	1.58544e14	1.34046
$363$	−5.00310e13	−0.416632
$364$	−4.46107e11	−0.00365916
$365$	−1.32713e13	−0.107227
$366$	6.31714e13	0.502776
$367$	−1.84151e14	−1.44382	−0.721908	−	0.691989i	$-0.756735\pi$
$367$	−1.84151e14	−1.44382	−0.721908	+	0.691989i	$0.756735\pi$
$368$	8.33613e13	0.643875
$369$	6.73755e13	0.512693
$370$	1.19788e14	0.898057
$371$	−1.31625e13	−0.0972257
$372$	1.53173e12	0.0111480
$373$	5.36309e13	0.384607	0.192303	−	0.981336i	$-0.438404\pi$
$373$	5.36309e13	0.384607	0.192303	+	0.981336i	$0.438404\pi$
$374$	−7.82511e13	−0.552964
$375$	−8.17144e13	−0.569019
$376$	−8.94434e13	−0.613783
$377$	9.93886e12	0.0672139
$378$	−5.58968e12	−0.0372548
$379$	7.87457e13	0.517263	0.258631	−	0.965976i	$-0.416728\pi$
$379$	7.87457e13	0.517263	0.258631	+	0.965976i	$0.416728\pi$
$380$	−6.55712e12	−0.0424525
$381$	3.38645e13	0.216101
$382$	2.25922e14	1.42105
$383$	1.66808e14	1.03425	0.517123	−	0.855911i	$-0.327003\pi$
$383$	1.66808e14	1.03425	0.517123	+	0.855911i	$0.327003\pi$
$384$	−1.05401e14	−0.644203
$385$	9.75913e12	0.0588000
$386$	−3.79942e13	−0.225677
$387$	−5.56414e13	−0.325827
$388$	2.44368e13	0.141081
$389$	4.34698e13	0.247437	0.123719	−	0.992317i	$-0.460518\pi$
$389$	4.34698e13	0.247437	0.123719	+	0.992317i	$0.460518\pi$
$390$	1.38349e13	0.0776462
$391$	−1.07647e14	−0.595701
$392$	−1.67882e14	−0.916072
$393$	−1.86500e14	−1.00350
$394$	2.17071e14	1.15179
$395$	1.30315e14	0.681882
$396$	3.14859e12	0.0162477
$397$	2.89431e13	0.147298	0.0736492	−	0.997284i	$-0.476535\pi$
$397$	2.89431e13	0.147298	0.0736492	+	0.997284i	$0.476535\pi$
$398$	2.58808e14	1.29903
$399$	−1.64960e13	−0.0816636
$400$	1.41606e14	0.691435
$401$	−3.82520e14	−1.84230	−0.921149	−	0.389211i	$-0.872748\pi$
$401$	−3.82520e14	−1.84230	−0.921149	+	0.389211i	$0.872748\pi$
$402$	1.06676e14	0.506784
$403$	−9.53758e12	−0.0446952
$404$	−1.28890e13	−0.0595829
$405$	1.46605e13	0.0668568
$406$	1.35242e13	0.0608441
$407$	−1.69750e14	−0.753426
$408$	1.25417e14	0.549193
$409$	1.21169e14	0.523494	0.261747	−	0.965136i	$-0.415701\pi$
$409$	1.21169e14	0.523494	0.261747	+	0.965136i	$0.415701\pi$
$410$	−2.26916e14	−0.967285
$411$	1.17232e14	0.493080
$412$	−3.05650e13	−0.126850
$413$	−5.88810e12	−0.0241129
$414$	5.12154e13	0.206966
$415$	2.82160e13	0.112520
$416$	−1.00092e13	−0.0393899
$417$	1.37899e14	0.535568
$418$	1.09871e14	0.421128
$419$	−1.03303e14	−0.390784	−0.195392	−	0.980725i	$-0.562598\pi$
$419$	−1.03303e14	−0.390784	−0.195392	+	0.980725i	$0.562598\pi$
$420$	1.59212e12	0.00594436
$421$	3.23588e13	0.119245	0.0596225	−	0.998221i	$-0.481010\pi$
$421$	3.23588e13	0.119245	0.0596225	+	0.998221i	$0.481010\pi$
$422$	−1.20972e14	−0.440013
$423$	−6.00726e13	−0.215677
$424$	−1.40510e14	−0.497960
$425$	−1.82859e14	−0.639702
$426$	−6.52509e13	−0.225338
$427$	−4.52665e13	−0.154320
$428$	5.12719e13	0.172560
$429$	−1.96052e13	−0.0651414
$430$	1.87396e14	0.614731
$431$	2.59343e14	0.839941	0.419970	−	0.907538i	$-0.362040\pi$
$431$	2.59343e14	0.839941	0.419970	+	0.907538i	$0.362040\pi$
$432$	−6.52301e13	−0.208587
$433$	3.06156e14	0.966629	0.483314	−	0.875447i	$-0.339433\pi$
$433$	3.06156e14	0.966629	0.483314	+	0.875447i	$0.339433\pi$
$434$	−1.29782e13	−0.0404594
$435$	−3.54710e13	−0.109190
$436$	2.02143e13	0.0614445
$437$	1.51145e14	0.453676
$438$	3.62785e13	0.107533
$439$	8.75264e12	0.0256203	0.0128101	−	0.999918i	$-0.495922\pi$
$439$	8.75264e12	0.0256203	0.0128101	+	0.999918i	$0.495922\pi$
$440$	1.04179e14	0.301155
$441$	−1.12754e14	−0.321898
$442$	7.94897e13	0.224124
$443$	3.44516e14	0.959376	0.479688	−	0.877439i	$-0.340750\pi$
$443$	3.44516e14	0.959376	0.479688	+	0.877439i	$0.340750\pi$
$444$	−2.76933e13	−0.0761672
$445$	3.51906e14	0.955974
$446$	−6.32079e13	−0.169602
$447$	3.05711e14	0.810252
$448$	6.30587e13	0.165088
$449$	9.04044e11	0.00233795	0.00116897	−	0.999999i	$-0.499628\pi$
$449$	9.04044e11	0.00233795	0.00116897	+	0.999999i	$0.499628\pi$
$450$	8.69996e13	0.222254
$451$	3.21560e14	0.811505
$452$	−4.57719e13	−0.114114
$453$	−2.43024e13	−0.0598562
$454$	3.61260e14	0.879049
$455$	−9.91360e12	−0.0238325
$456$	−1.76096e14	−0.418256
$457$	3.24415e13	0.0761311	0.0380656	−	0.999275i	$-0.487880\pi$
$457$	3.24415e13	0.0761311	0.0380656	+	0.999275i	$0.487880\pi$
$458$	−8.80000e14	−2.04043
$459$	8.42333e13	0.192981
$460$	−1.45878e13	−0.0330234
$461$	4.71969e14	1.05574	0.527871	−	0.849324i	$-0.322990\pi$
$461$	4.71969e14	1.05574	0.527871	+	0.849324i	$0.322990\pi$
$462$	−2.66776e13	−0.0589679
$463$	−4.86816e14	−1.06333	−0.531666	−	0.846954i	$-0.678434\pi$
$463$	−4.86816e14	−1.06333	−0.531666	+	0.846954i	$0.678434\pi$
$464$	1.57824e14	0.340662
$465$	3.40389e13	0.0726079
$466$	3.72033e14	0.784258
$467$	−5.28154e14	−1.10032	−0.550158	−	0.835060i	$-0.685433\pi$
$467$	−5.28154e14	−1.10032	−0.550158	+	0.835060i	$0.685433\pi$
$468$	−3.19843e12	−0.00658544
$469$	−7.64403e13	−0.155551
$470$	2.02321e14	0.406913
$471$	−5.17512e14	−1.02874
$472$	−6.28557e13	−0.123499
$473$	−2.65557e14	−0.515729
$474$	−3.56229e14	−0.683830
$475$	2.56750e14	0.487187
$476$	9.14769e12	0.0171582
$477$	−9.43702e13	−0.174978
$478$	2.01155e14	0.368703
$479$	−1.62930e14	−0.295227	−0.147613	−	0.989045i	$-0.547159\pi$
$479$	−1.62930e14	−0.295227	−0.147613	+	0.989045i	$0.547159\pi$
$480$	3.57219e13	0.0639893
$481$	1.72437e14	0.305374
$482$	9.11766e14	1.59634
$483$	−3.66992e13	−0.0635254
$484$	−3.89551e13	−0.0666676
$485$	5.43045e14	0.918875
$486$	−4.00760e13	−0.0670478
$487$	−5.50531e14	−0.910694	−0.455347	−	0.890314i	$-0.650485\pi$
$487$	−5.50531e14	−0.910694	−0.455347	+	0.890314i	$0.650485\pi$
$488$	−4.83221e14	−0.790382
$489$	−2.34629e14	−0.379475
$490$	3.79747e14	0.607318
$491$	−8.05489e14	−1.27383	−0.636915	−	0.770934i	$-0.719790\pi$
$491$	−8.05489e14	−1.27383	−0.636915	+	0.770934i	$0.719790\pi$
$492$	5.24599e13	0.0820388
$493$	−2.03802e14	−0.315174
$494$	−1.11610e14	−0.170689
$495$	6.99695e13	0.105823
$496$	−1.51452e14	−0.226530
$497$	4.67565e13	0.0691643
$498$	−7.71313e13	−0.112842
$499$	−7.88458e14	−1.14084	−0.570421	−	0.821352i	$-0.693220\pi$
$499$	−7.88458e14	−1.14084	−0.570421	+	0.821352i	$0.693220\pi$
$500$	−6.36244e13	−0.0910518
$501$	−6.28545e14	−0.889670
$502$	−3.83916e14	−0.537484
$503$	−3.07198e14	−0.425398	−0.212699	−	0.977118i	$-0.568225\pi$
$503$	−3.07198e14	−0.425398	−0.212699	+	0.977118i	$0.568225\pi$
$504$	4.27575e13	0.0585658
$505$	−2.86425e14	−0.388069
$506$	2.44434e14	0.327592
$507$	−4.15579e14	−0.550948
$508$	2.63675e13	0.0345795
$509$	1.05222e15	1.36508	0.682540	−	0.730849i	$-0.260875\pi$
$509$	1.05222e15	1.36508	0.682540	+	0.730849i	$0.260875\pi$
$510$	−2.83692e14	−0.364092
$511$	−2.59959e13	−0.0330058
$512$	6.59607e14	0.828515
$513$	−1.18271e14	−0.146971
$514$	−1.96027e14	−0.241001
$515$	−6.79229e14	−0.826184
$516$	−4.33234e13	−0.0521374
$517$	−2.86706e14	−0.341380
$518$	2.34642e14	0.276434
$519$	5.98020e14	0.697100
$520$	−1.05828e14	−0.122063
$521$	5.34501e14	0.610015	0.305008	−	0.952350i	$-0.401341\pi$
$521$	5.34501e14	0.610015	0.305008	+	0.952350i	$0.401341\pi$
$522$	9.69636e13	0.109502
$523$	2.58752e14	0.289151	0.144575	−	0.989494i	$-0.453818\pi$
$523$	2.58752e14	0.289151	0.144575	+	0.989494i	$0.453818\pi$
$524$	−1.45212e14	−0.160576
$525$	−6.23410e13	−0.0682177
$526$	1.60961e12	0.00174300
$527$	1.95574e14	0.209581
$528$	−3.11321e14	−0.330158
$529$	−6.16553e14	−0.647089
$530$	3.17833e14	0.330127
$531$	−4.22156e13	−0.0433963
$532$	−1.28441e13	−0.0130674
$533$	−3.26650e14	−0.328915
$534$	−9.61971e14	−0.958705
$535$	1.13939e15	1.12390
$536$	−8.16003e14	−0.796682
$537$	−9.23357e14	−0.892300
$538$	2.49954e14	0.239088
$539$	−5.38135e14	−0.509510
$540$	1.14149e13	0.0106981
$541$	7.12237e14	0.660753	0.330377	−	0.943849i	$-0.392824\pi$
$541$	7.12237e14	0.660753	0.330377	+	0.943849i	$0.392824\pi$
$542$	−2.10966e15	−1.93739
$543$	−8.14522e14	−0.740464
$544$	2.05244e14	0.184704
$545$	4.49212e14	0.400194
$546$	2.70999e13	0.0239005
$547$	−9.55842e14	−0.834557	−0.417278	−	0.908779i	$-0.637016\pi$
$547$	−9.55842e14	−0.834557	−0.417278	+	0.908779i	$0.637016\pi$
$548$	9.12793e13	0.0789004
$549$	−3.24544e14	−0.277732
$550$	4.15219e14	0.351789
$551$	2.86155e14	0.240031
$552$	−3.91766e14	−0.325358
$553$	2.55261e14	0.209892
$554$	1.06479e15	0.866885
$555$	−6.15413e14	−0.496084
$556$	1.07371e14	0.0856991
$557$	−1.03837e15	−0.820634	−0.410317	−	0.911943i	$-0.634582\pi$
$557$	−1.03837e15	−0.820634	−0.410317	+	0.911943i	$0.634582\pi$
$558$	−9.30488e13	−0.0728153
$559$	2.69760e14	0.209032
$560$	−1.57423e14	−0.120791
$561$	4.02016e14	0.305456
$562$	−1.02210e15	−0.769029
$563$	3.89162e14	0.289958	0.144979	−	0.989435i	$-0.453689\pi$
$563$	3.89162e14	0.289958	0.144979	+	0.989435i	$0.453689\pi$
$564$	−4.67737e13	−0.0345117
$565$	−1.01716e15	−0.743233
$566$	−2.39925e15	−1.73614
$567$	2.87171e13	0.0205794
$568$	4.99128e14	0.354239
$569$	1.80300e15	1.26730	0.633649	−	0.773621i	$-0.281556\pi$
$569$	1.80300e15	1.26730	0.633649	+	0.773621i	$0.281556\pi$
$570$	3.98328e14	0.277287
$571$	8.23896e12	0.00568033	0.00284017	−	0.999996i	$-0.499096\pi$
$571$	8.23896e12	0.00568033	0.00284017	+	0.999996i	$0.499096\pi$
$572$	−1.52650e13	−0.0104236
$573$	−1.16068e15	−0.784984
$574$	−4.44486e14	−0.297743
$575$	5.71199e14	0.378978
$576$	4.52109e14	0.297111
$577$	−1.90100e15	−1.23741	−0.618706	−	0.785622i	$-0.712343\pi$
$577$	−1.90100e15	−1.23741	−0.618706	+	0.785622i	$0.712343\pi$
$578$	−8.95199e12	−0.00577187
$579$	1.95196e14	0.124663
$580$	−2.76184e13	−0.0174721
$581$	5.52696e13	0.0346352
$582$	−1.48447e15	−0.921500
$583$	−4.50397e14	−0.276961
$584$	−2.77507e14	−0.169046
$585$	−7.10770e13	−0.0428915
$586$	1.46508e15	0.875840
$587$	−4.79622e14	−0.284047	−0.142023	−	0.989863i	$-0.545361\pi$
$587$	−4.79622e14	−0.284047	−0.142023	+	0.989863i	$0.545361\pi$
$588$	−8.77922e13	−0.0515087
$589$	−2.74602e14	−0.159613
$590$	1.42179e14	0.0818748
$591$	−1.11521e15	−0.636245
$592$	2.73821e15	1.54774
$593$	2.57962e15	1.44462	0.722312	−	0.691568i	$-0.243080\pi$
$593$	2.57962e15	1.44462	0.722312	+	0.691568i	$0.243080\pi$
$594$	−1.91269e14	−0.106125
$595$	2.03284e14	0.111753
$596$	2.38033e14	0.129653
$597$	−1.32963e15	−0.717583
$598$	−2.48303e14	−0.132778
$599$	6.39537e14	0.338858	0.169429	−	0.985542i	$-0.445808\pi$
$599$	6.39537e14	0.338858	0.169429	+	0.985542i	$0.445808\pi$
$600$	−6.65492e14	−0.349390
$601$	1.81544e14	0.0944436	0.0472218	−	0.998884i	$-0.484963\pi$
$601$	1.81544e14	0.0944436	0.0472218	+	0.998884i	$0.484963\pi$
$602$	3.67074e14	0.189222
$603$	−5.48049e14	−0.279946
$604$	−1.89223e13	−0.00957792
$605$	−8.65678e14	−0.434212
$606$	7.82973e14	0.389177
$607$	−1.87669e15	−0.924387	−0.462194	−	0.886779i	$-0.652937\pi$
$607$	−1.87669e15	−0.924387	−0.462194	+	0.886779i	$0.652937\pi$
$608$	−2.88179e14	−0.140667
$609$	−6.94808e13	−0.0336101
$610$	1.09304e15	0.523991
$611$	2.91244e14	0.138366
$612$	6.55856e13	0.0308799
$613$	2.34801e13	0.0109564	0.00547820	−	0.999985i	$-0.498256\pi$
$613$	2.34801e13	0.0109564	0.00547820	+	0.999985i	$0.498256\pi$
$614$	5.06120e14	0.234060
$615$	1.16579e15	0.534326
$616$	2.04067e14	0.0926997
$617$	−2.75414e15	−1.23999	−0.619993	−	0.784607i	$-0.712865\pi$
$617$	−2.75414e15	−1.23999	−0.619993	+	0.784607i	$0.712865\pi$
$618$	1.85675e15	0.828544
$619$	1.04827e15	0.463631	0.231816	−	0.972760i	$-0.425533\pi$
$619$	1.04827e15	0.463631	0.231816	+	0.972760i	$0.425533\pi$
$620$	2.65033e13	0.0116184
$621$	−2.63120e14	−0.114327
$622$	3.34242e15	1.43951
$623$	6.89316e14	0.294262
$624$	3.16248e14	0.133818
$625$	1.07085e14	0.0449148
$626$	−3.21499e14	−0.133666
$627$	−5.64465e14	−0.232630
$628$	−4.02944e14	−0.164614
$629$	−3.53592e15	−1.43194
$630$	−9.67172e13	−0.0388267
$631$	−1.74350e15	−0.693841	−0.346921	−	0.937894i	$-0.612773\pi$
$631$	−1.74350e15	−0.693841	−0.346921	+	0.937894i	$0.612773\pi$
$632$	2.72492e15	1.07501
$633$	6.21495e14	0.243062
$634$	3.90662e14	0.151464
$635$	5.85951e14	0.225219
$636$	−7.34784e13	−0.0279992
$637$	5.46653e14	0.206512
$638$	4.62774e14	0.173323
$639$	3.35228e14	0.124476
$640$	−1.82374e15	−0.671385
$641$	−4.25280e15	−1.55223	−0.776114	−	0.630593i	$-0.782812\pi$
$641$	−4.25280e15	−1.55223	−0.776114	+	0.630593i	$0.782812\pi$
$642$	−3.11464e15	−1.12711
$643$	3.10107e15	1.11263	0.556315	−	0.830971i	$-0.312215\pi$
$643$	3.10107e15	1.11263	0.556315	+	0.830971i	$0.312215\pi$
$644$	−2.85747e13	−0.0101651
$645$	−9.62753e14	−0.339576
$646$	2.28863e15	0.800382
$647$	5.81472e13	0.0201630	0.0100815	−	0.999949i	$-0.496791\pi$
$647$	5.81472e13	0.0201630	0.0100815	+	0.999949i	$0.496791\pi$
$648$	3.06556e14	0.105402
$649$	−2.01480e14	−0.0686889
$650$	−4.21792e14	−0.142585
$651$	6.66756e13	0.0223497
$652$	−1.82686e14	−0.0607218
$653$	−2.69946e15	−0.889722	−0.444861	−	0.895600i	$-0.646747\pi$
$653$	−2.69946e15	−0.889722	−0.444861	+	0.895600i	$0.646747\pi$
$654$	−1.22797e15	−0.401337
$655$	−3.22697e15	−1.04585
$656$	−5.18703e15	−1.66705
$657$	−1.86381e14	−0.0594009
$658$	3.96307e14	0.125253
$659$	3.01895e15	0.946205	0.473103	−	0.881007i	$-0.343134\pi$
$659$	3.01895e15	0.946205	0.473103	+	0.881007i	$0.343134\pi$
$660$	5.44795e13	0.0169333
$661$	1.80854e15	0.557469	0.278735	−	0.960368i	$-0.410085\pi$
$661$	1.80854e15	0.557469	0.278735	+	0.960368i	$0.410085\pi$
$662$	−5.05090e15	−1.54401
$663$	−4.08380e14	−0.123805
$664$	5.90005e14	0.177391
$665$	−2.85428e14	−0.0851094
$666$	1.68230e15	0.497501
$667$	6.36618e14	0.186718
$668$	−4.89397e14	−0.142361
$669$	3.24732e14	0.0936874
$670$	1.84579e15	0.528168
$671$	−1.54894e15	−0.439602
$672$	6.99723e13	0.0196968
$673$	1.28360e15	0.358381	0.179191	−	0.983814i	$-0.442652\pi$
$673$	1.28360e15	0.358381	0.179191	+	0.983814i	$0.442652\pi$
$674$	−4.02867e15	−1.11566
$675$	−4.46962e14	−0.122772
$676$	−3.23578e14	−0.0881601
$677$	5.87526e15	1.58778	0.793888	−	0.608064i	$-0.208054\pi$
$677$	5.87526e15	1.58778	0.793888	+	0.608064i	$0.208054\pi$
$678$	2.78053e15	0.745356
$679$	1.06372e15	0.282842
$680$	2.17007e15	0.572366
$681$	−1.85598e15	−0.485584
$682$	−4.44090e14	−0.115254
$683$	−2.70362e15	−0.696037	−0.348018	−	0.937488i	$-0.613145\pi$
$683$	−2.70362e15	−0.696037	−0.348018	+	0.937488i	$0.613145\pi$
$684$	−9.20878e13	−0.0235176
$685$	2.02845e15	0.513885
$686$	1.51413e15	0.380522
$687$	4.52101e15	1.12713
$688$	4.28365e15	1.05944
$689$	4.57526e14	0.112256
$690$	8.86172e14	0.215699
$691$	3.12375e15	0.754305	0.377152	−	0.926151i	$-0.376903\pi$
$691$	3.12375e15	0.754305	0.377152	+	0.926151i	$0.376903\pi$
$692$	4.65630e14	0.111547
$693$	1.37057e14	0.0325737
$694$	9.93029e14	0.234145
$695$	2.38605e15	0.558166
$696$	−7.41710e14	−0.172141
$697$	6.69815e15	1.54232
$698$	7.47285e15	1.70719
$699$	−1.91133e15	−0.433222
$700$	−4.85398e13	−0.0109159
$701$	3.98398e15	0.888930	0.444465	−	0.895796i	$-0.353394\pi$
$701$	3.98398e15	0.888930	0.444465	+	0.895796i	$0.353394\pi$
$702$	1.94296e14	0.0430141
$703$	4.96473e15	1.09054
$704$	2.15776e15	0.470276
$705$	−1.03943e15	−0.224778
$706$	7.08169e14	0.151954
$707$	−5.61052e14	−0.119453
$708$	−3.28698e13	−0.00694408
$709$	−5.06410e15	−1.06157	−0.530784	−	0.847507i	$-0.678103\pi$
$709$	−5.06410e15	−1.06157	−0.530784	+	0.847507i	$0.678103\pi$
$710$	−1.12902e15	−0.234846
$711$	1.83013e15	0.377746
$712$	7.35847e15	1.50712
$713$	−6.10915e14	−0.124162
$714$	−5.55698e14	−0.112072
$715$	−3.39226e14	−0.0678900
$716$	−7.18943e14	−0.142782
$717$	−1.03344e15	−0.203671
$718$	6.77478e15	1.32498
$719$	−5.40287e15	−1.04861	−0.524307	−	0.851529i	$-0.675676\pi$
$719$	−5.40287e15	−1.04861	−0.524307	+	0.851529i	$0.675676\pi$
$720$	−1.12866e15	−0.217388
$721$	−1.33048e15	−0.254311
$722$	2.29645e15	0.435614
$723$	−4.68421e15	−0.881812
$724$	−6.34202e14	−0.118486
$725$	1.08142e15	0.200510
$726$	2.36642e15	0.435452
$727$	5.20866e15	0.951232	0.475616	−	0.879653i	$-0.342225\pi$
$727$	5.20866e15	0.951232	0.475616	+	0.879653i	$0.342225\pi$
$728$	−2.07297e14	−0.0375725
$729$	2.05891e14	0.0370370
$730$	6.27720e14	0.112070
$731$	−5.53159e15	−0.980177
$732$	−2.52696e14	−0.0444414
$733$	1.03525e16	1.80706	0.903529	−	0.428527i	$-0.140967\pi$
$733$	1.03525e16	1.80706	0.903529	+	0.428527i	$0.140967\pi$
$734$	8.71020e15	1.50904
$735$	−1.95096e15	−0.335481
$736$	−6.41121e14	−0.109424
$737$	−2.61565e15	−0.443107
$738$	−3.18680e15	−0.535852
$739$	7.37617e15	1.23108	0.615540	−	0.788105i	$-0.288938\pi$
$739$	7.37617e15	1.23108	0.615540	+	0.788105i	$0.288938\pi$
$740$	−4.79172e14	−0.0793811
$741$	5.73400e14	0.0942882
$742$	6.22573e14	0.101618
$743$	1.70163e15	0.275693	0.137846	−	0.990454i	$-0.455982\pi$
$743$	1.70163e15	0.275693	0.137846	+	0.990454i	$0.455982\pi$
$744$	7.11764e14	0.114468
$745$	5.28967e15	0.844440
$746$	−2.53670e15	−0.401980
$747$	3.96263e14	0.0623334
$748$	3.13018e14	0.0488776
$749$	2.23184e15	0.345950
$750$	3.86502e15	0.594723
$751$	−1.60833e15	−0.245672	−0.122836	−	0.992427i	$-0.539199\pi$
$751$	−1.60833e15	−0.245672	−0.122836	+	0.992427i	$0.539199\pi$
$752$	4.62480e15	0.701285
$753$	1.97237e15	0.296905
$754$	−4.70099e14	−0.0702501
$755$	−4.20501e14	−0.0623819
$756$	2.23597e13	0.00329303
$757$	2.14689e15	0.313893	0.156947	−	0.987607i	$-0.449835\pi$
$757$	2.14689e15	0.313893	0.156947	+	0.987607i	$0.449835\pi$
$758$	−3.72460e15	−0.540629
$759$	−1.25578e15	−0.180961
$760$	−3.04696e15	−0.435905
$761$	5.84822e15	0.830631	0.415316	−	0.909677i	$-0.363671\pi$
$761$	5.84822e15	0.830631	0.415316	+	0.909677i	$0.363671\pi$
$762$	−1.60176e15	−0.225863
$763$	8.79920e14	0.123185
$764$	−9.03725e14	−0.125610
$765$	1.45747e15	0.201124
$766$	−7.88987e15	−1.08097
$767$	2.04669e14	0.0278406
$768$	1.17501e15	0.158692
$769$	−1.22144e16	−1.63787	−0.818934	−	0.573888i	$-0.805435\pi$
$769$	−1.22144e16	−1.63787	−0.818934	+	0.573888i	$0.805435\pi$
$770$	−4.61598e14	−0.0614561
$771$	1.00709e15	0.133128
$772$	1.51983e14	0.0199480
$773$	1.07268e16	1.39792	0.698959	−	0.715162i	$-0.253647\pi$
$773$	1.07268e16	1.39792	0.698959	+	0.715162i	$0.253647\pi$
$774$	2.63179e15	0.340546
$775$	−1.03776e15	−0.133333
$776$	1.13553e16	1.44863
$777$	−1.20548e15	−0.152701
$778$	−2.05608e15	−0.258615
$779$	−9.40477e15	−1.17461
$780$	−5.53419e13	−0.00686331
$781$	1.59993e15	0.197024
$782$	5.09159e15	0.622610
$783$	−4.98152e14	−0.0604885
$784$	8.68056e15	1.04667
$785$	−8.95442e15	−1.07215
$786$	8.82126e15	1.04883
$787$	−5.89767e15	−0.696337	−0.348169	−	0.937432i	$-0.613196\pi$
$787$	−5.89767e15	−0.696337	−0.348169	+	0.937432i	$0.613196\pi$
$788$	−8.68321e14	−0.101809
$789$	−8.26938e12	−0.000962829 0
$790$	−6.16377e15	−0.712684
$791$	−1.99243e15	−0.228777
$792$	1.46309e15	0.166833
$793$	1.57346e15	0.178177
$794$	−1.36898e15	−0.153952
$795$	−1.63287e15	−0.182361
$796$	−1.03528e15	−0.114824
$797$	−1.19466e16	−1.31590	−0.657949	−	0.753062i	$-0.728576\pi$
$797$	−1.19466e16	−1.31590	−0.657949	+	0.753062i	$0.728576\pi$
$798$	7.80248e14	0.0853526
$799$	−5.97212e15	−0.648816
$800$	−1.08907e15	−0.117506
$801$	4.94214e15	0.529586
$802$	1.80928e16	1.92552
$803$	−8.89534e14	−0.0940215
$804$	−4.26722e14	−0.0447957
$805$	−6.35000e14	−0.0662059
$806$	4.51119e14	0.0467141
$807$	−1.28414e15	−0.132071
$808$	−5.98925e15	−0.611800
$809$	−6.72785e15	−0.682589	−0.341295	−	0.939956i	$-0.610865\pi$
$809$	−6.72785e15	−0.682589	−0.341295	+	0.939956i	$0.610865\pi$
$810$	−6.93428e14	−0.0698769
$811$	9.15322e15	0.916134	0.458067	−	0.888918i	$-0.348542\pi$
$811$	9.15322e15	0.916134	0.458067	+	0.888918i	$0.348542\pi$
$812$	−5.40990e13	−0.00537813
$813$	1.08384e16	1.07021
$814$	8.02902e15	0.787459
$815$	−4.05974e15	−0.395486
$816$	−6.48486e15	−0.627487
$817$	7.76683e15	0.746487
$818$	−5.73116e15	−0.547142
$819$	−1.39226e14	−0.0132026
$820$	9.07704e14	0.0855004
$821$	−1.32950e16	−1.24395	−0.621973	−	0.783039i	$-0.713669\pi$
$821$	−1.32950e16	−1.24395	−0.621973	+	0.783039i	$0.713669\pi$
$822$	−5.54498e15	−0.515353
$823$	3.17979e15	0.293562	0.146781	−	0.989169i	$-0.453109\pi$
$823$	3.17979e15	0.293562	0.146781	+	0.989169i	$0.453109\pi$
$824$	−1.42029e16	−1.30250
$825$	−2.13320e15	−0.194327
$826$	2.78502e14	0.0252022
$827$	2.13503e16	1.91921	0.959606	−	0.281346i	$-0.0907810\pi$
$827$	2.13503e16	1.91921	0.959606	+	0.281346i	$0.0907810\pi$
$828$	−2.04870e14	−0.0182942
$829$	−1.86561e16	−1.65489	−0.827447	−	0.561543i	$-0.810208\pi$
$829$	−1.86561e16	−1.65489	−0.827447	+	0.561543i	$0.810208\pi$
$830$	−1.33459e15	−0.117603
$831$	−5.47040e15	−0.478865
$832$	−2.19191e15	−0.190610
$833$	−1.12094e16	−0.968358
$834$	−6.52252e15	−0.559760
$835$	−1.08756e16	−0.927209
$836$	−4.39503e14	−0.0372244
$837$	4.78040e14	0.0402230
$838$	4.88615e15	0.408436
$839$	−8.22682e15	−0.683190	−0.341595	−	0.939847i	$-0.610967\pi$
$839$	−8.22682e15	−0.683190	−0.341595	+	0.939847i	$0.610967\pi$
$840$	7.39825e14	0.0610370
$841$	−1.09952e16	−0.901211
$842$	−1.53054e15	−0.124632
$843$	5.25105e15	0.424810
$844$	4.83907e14	0.0388937
$845$	−7.19070e15	−0.574195
$846$	2.84138e15	0.225420
$847$	−1.69570e15	−0.133656
$848$	7.26527e15	0.568950
$849$	1.23262e16	0.959040
$850$	8.64908e15	0.668599
$851$	1.10452e16	0.848321
$852$	2.61015e14	0.0199181
$853$	−1.84247e16	−1.39695	−0.698474	−	0.715635i	$-0.746137\pi$
$853$	−1.84247e16	−1.39695	−0.698474	+	0.715635i	$0.746137\pi$
$854$	2.14106e15	0.161291
$855$	−2.04642e15	−0.153172
$856$	2.38250e16	1.77185
$857$	−1.62127e16	−1.19801	−0.599004	−	0.800746i	$-0.704437\pi$
$857$	−1.62127e16	−1.19801	−0.599004	+	0.800746i	$0.704437\pi$
$858$	9.27309e14	0.0680839
$859$	−1.84274e16	−1.34431	−0.672157	−	0.740408i	$-0.734632\pi$
$859$	−1.84274e16	−1.34431	−0.672157	+	0.740408i	$0.734632\pi$
$860$	−7.49618e14	−0.0543373
$861$	2.28355e15	0.164473
$862$	−1.22667e16	−0.877883
$863$	2.70048e15	0.192036	0.0960179	−	0.995380i	$-0.469389\pi$
$863$	2.70048e15	0.192036	0.0960179	+	0.995380i	$0.469389\pi$
$864$	5.01676e14	0.0354485
$865$	1.03474e16	0.726514
$866$	−1.44809e16	−1.01029
$867$	4.59910e13	0.00318836
$868$	5.19148e13	0.00357629
$869$	8.73459e15	0.597907
$870$	1.67774e15	0.114122
$871$	2.65705e15	0.179597
$872$	9.39317e15	0.630916
$873$	7.62650e15	0.509034
$874$	−7.14902e15	−0.474170
$875$	−2.76954e15	−0.182542
$876$	−1.45120e14	−0.00950506
$877$	−2.01065e15	−0.130870	−0.0654349	−	0.997857i	$-0.520843\pi$
$877$	−2.01065e15	−0.130870	−0.0654349	+	0.997857i	$0.520843\pi$
$878$	−4.13992e14	−0.0267776
$879$	−7.52688e15	−0.483812
$880$	−5.38673e15	−0.344089
$881$	−1.38461e16	−0.878939	−0.439469	−	0.898258i	$-0.644833\pi$
$881$	−1.38461e16	−0.878939	−0.439469	+	0.898258i	$0.644833\pi$
$882$	5.33315e15	0.336439
$883$	2.49585e16	1.56471	0.782357	−	0.622830i	$-0.214017\pi$
$883$	2.49585e16	1.56471	0.782357	+	0.622830i	$0.214017\pi$
$884$	−3.17972e14	−0.0198108
$885$	−7.30449e14	−0.0452274
$886$	−1.62953e16	−1.00271
$887$	−1.78428e16	−1.09115	−0.545574	−	0.838063i	$-0.683688\pi$
$887$	−1.78428e16	−1.09115	−0.545574	+	0.838063i	$0.683688\pi$
$888$	−1.28685e16	−0.782089
$889$	1.14777e15	0.0693256
$890$	−1.66448e16	−0.999158
$891$	9.82647e14	0.0586233
$892$	2.52842e14	0.0149914
$893$	8.38537e15	0.494128
$894$	−1.44599e16	−0.846853
$895$	−1.59767e16	−0.929951
$896$	−3.57235e15	−0.206661
$897$	1.27566e15	0.0733460
$898$	−4.27605e13	−0.00244356
$899$	−1.15661e15	−0.0656917
$900$	−3.48013e14	−0.0196454
$901$	−9.38183e15	−0.526382
$902$	−1.52095e16	−0.848163
$903$	−1.88585e15	−0.104526
$904$	−2.12693e16	−1.17173
$905$	−1.40935e16	−0.771708
$906$	1.14948e15	0.0625601
$907$	1.58086e16	0.855174	0.427587	−	0.903974i	$-0.359364\pi$
$907$	1.58086e16	0.855174	0.427587	+	0.903974i	$0.359364\pi$
$908$	−1.44510e15	−0.0777010
$909$	−4.02254e15	−0.214980
$910$	4.68904e14	0.0249090
$911$	2.08974e15	0.110342	0.0551711	−	0.998477i	$-0.482430\pi$
$911$	2.08974e15	0.110342	0.0551711	+	0.998477i	$0.482430\pi$
$912$	9.10529e15	0.477884
$913$	1.89123e15	0.0986631
$914$	−1.53446e15	−0.0795702
$915$	−5.61553e15	−0.289451
$916$	3.52015e15	0.180358
$917$	−6.32101e15	−0.321925
$918$	−3.98416e15	−0.201698
$919$	−2.87166e16	−1.44510	−0.722551	−	0.691318i	$-0.757030\pi$
$919$	−2.87166e16	−1.44510	−0.722551	+	0.691318i	$0.757030\pi$
$920$	−6.77865e15	−0.339086
$921$	−2.60020e15	−0.129294
$922$	−2.23237e16	−1.10343
$923$	−1.62525e15	−0.0798566
$924$	1.06715e14	0.00521230
$925$	1.87624e16	0.910981
$926$	2.30259e16	1.11137
$927$	−9.53906e15	−0.457686
$928$	−1.21380e15	−0.0578941
$929$	1.56332e16	0.741243	0.370621	−	0.928784i	$-0.379145\pi$
$929$	1.56332e16	0.741243	0.370621	+	0.928784i	$0.379145\pi$
$930$	−1.61001e15	−0.0758877
$931$	1.57390e16	0.737486
$932$	−1.48819e15	−0.0693222
$933$	−1.71717e16	−0.795179
$934$	2.49812e16	1.15002
$935$	6.95602e15	0.318344
$936$	−1.48624e15	−0.0676196
$937$	−3.51956e16	−1.59192	−0.795958	−	0.605351i	$-0.793033\pi$
$937$	−3.51956e16	−1.59192	−0.795958	+	0.605351i	$0.793033\pi$
$938$	3.61556e15	0.162577
$939$	1.65171e15	0.0738367
$940$	−8.09316e14	−0.0359679
$941$	3.43286e15	0.151675	0.0758373	−	0.997120i	$-0.475837\pi$
$941$	3.43286e15	0.151675	0.0758373	+	0.997120i	$0.475837\pi$
$942$	2.44778e16	1.07521
$943$	−2.09231e16	−0.913715
$944$	3.25004e15	0.141105
$945$	4.96887e14	0.0214478
$946$	1.25606e16	0.539026
$947$	1.10249e16	0.470380	0.235190	−	0.971949i	$-0.424429\pi$
$947$	1.10249e16	0.470380	0.235190	+	0.971949i	$0.424429\pi$
$948$	1.42498e15	0.0604452
$949$	9.03614e14	0.0381082
$950$	−1.21440e16	−0.509194
$951$	−2.00704e15	−0.0836686
$952$	4.25074e15	0.176182
$953$	2.73506e15	0.112708	0.0563542	−	0.998411i	$-0.482052\pi$
$953$	2.73506e15	0.112708	0.0563542	+	0.998411i	$0.482052\pi$
$954$	4.46363e15	0.182882
$955$	−2.00830e16	−0.818107
$956$	−8.04653e14	−0.0325904
$957$	−2.37751e15	−0.0957429
$958$	7.70644e15	0.308563
$959$	3.97334e15	0.158181
$960$	7.82276e15	0.309648
$961$	−2.42986e16	−0.956317
$962$	−8.15611e15	−0.319168
$963$	1.60015e16	0.622611
$964$	−3.64722e15	−0.141104
$965$	3.37744e15	0.129923
$966$	1.73584e15	0.0663950
$967$	−3.35304e16	−1.27524	−0.637622	−	0.770350i	$-0.720082\pi$
$967$	−3.35304e16	−1.27524	−0.637622	+	0.770350i	$0.720082\pi$
$968$	−1.81016e16	−0.684546
$969$	−1.17579e16	−0.442129
$970$	−2.56855e16	−0.960382
$971$	3.35993e16	1.24918	0.624590	−	0.780953i	$-0.285266\pi$
$971$	3.35993e16	1.24918	0.624590	+	0.780953i	$0.285266\pi$
$972$	1.60311e14	0.00592650
$973$	4.67381e15	0.171811
$974$	2.60396e16	0.951833
$975$	2.16696e15	0.0787637
$976$	2.49856e16	0.903060
$977$	2.84370e16	1.02203	0.511016	−	0.859571i	$-0.329269\pi$
$977$	2.84370e16	1.02203	0.511016	+	0.859571i	$0.329269\pi$
$978$	1.10977e16	0.396616
$979$	2.35872e16	0.838245
$980$	−1.51905e15	−0.0536821
$981$	6.30871e15	0.221698
$982$	3.80989e16	1.33137
$983$	2.38776e16	0.829749	0.414875	−	0.909879i	$-0.363825\pi$
$983$	2.38776e16	0.829749	0.414875	+	0.909879i	$0.363825\pi$
$984$	2.43770e16	0.842379
$985$	−1.92962e16	−0.663091
$986$	9.63965e15	0.329411
$987$	−2.03604e15	−0.0691896
$988$	4.46460e14	0.0150876
$989$	1.72791e16	0.580686
$990$	−3.30949e15	−0.110603
$991$	−4.58544e16	−1.52397	−0.761984	−	0.647596i	$-0.775774\pi$
$991$	−4.58544e16	−1.52397	−0.761984	+	0.647596i	$0.775774\pi$
$992$	1.16480e15	0.0384978
$993$	2.59491e16	0.852906
$994$	−2.21154e15	−0.0722886
$995$	−2.30064e16	−0.747861
$996$	3.08538e14	0.00997430
$997$	8.37516e15	0.269259	0.134629	−	0.990896i	$-0.457016\pi$
$997$	8.37516e15	0.269259	0.134629	+	0.990896i	$0.457016\pi$
$998$	3.72934e16	1.19238
$999$	−8.64283e15	−0.274818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.8	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.8	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} -198873. q^{10} +281821. q^{11} +45976.7 q^{12} -286281. q^{13} -389554. q^{14} +1.02171e6 q^{15} -4.54600e6 q^{16} +5.87036e6 q^{17} -2.79296e6 q^{18} -8.24249e6 q^{19} +795526. q^{20} +2.00134e6 q^{21} -1.33299e7 q^{22} -1.83373e7 q^{23} +2.13644e7 q^{24} -3.11496e7 q^{25} +1.35408e7 q^{26} +1.43489e7 q^{27} +1.55828e6 q^{28} -3.47171e7 q^{29} -4.83262e7 q^{30} +3.33154e7 q^{31} +3.49627e7 q^{32} +6.84824e7 q^{33} -2.77663e8 q^{34} +3.46289e7 q^{35} +1.11723e7 q^{36} -6.02333e8 q^{37} +3.89862e8 q^{38} -6.95664e7 q^{39} +3.69665e8 q^{40} +1.14101e9 q^{41} -9.46617e7 q^{42} -9.42291e8 q^{43} +5.33217e7 q^{44} +2.48277e8 q^{45} +8.67338e8 q^{46} -1.01733e9 q^{47} -1.10468e9 q^{48} -1.90950e9 q^{49} +1.47335e9 q^{50} +1.42650e9 q^{51} -5.41657e7 q^{52} -1.59817e9 q^{53} -6.78690e8 q^{54} +1.18494e9 q^{55} +7.24102e8 q^{56} -2.00292e9 q^{57} +1.64209e9 q^{58} -7.14924e8 q^{59} +1.93313e8 q^{60} -5.49619e9 q^{61} -1.57579e9 q^{62} +4.86326e8 q^{63} +7.65650e9 q^{64} -1.20369e9 q^{65} -3.23915e9 q^{66} -9.28126e9 q^{67} +1.11070e9 q^{68} -4.45597e9 q^{69} -1.63791e9 q^{70} +5.67711e9 q^{71} +5.19155e9 q^{72} -3.15638e9 q^{73} +2.84898e10 q^{74} -7.56935e9 q^{75} -1.55951e9 q^{76} +2.32107e9 q^{77} +3.29043e9 q^{78} +3.09935e10 q^{79} -1.91140e10 q^{80} +3.48678e9 q^{81} -5.39688e10 q^{82} +6.71075e9 q^{83} +3.78663e8 q^{84} +2.46825e10 q^{85} +4.45695e10 q^{86} -8.43625e9 q^{87} +2.47775e10 q^{88} +8.36957e10 q^{89} -1.17433e10 q^{90} -2.35781e9 q^{91} -3.46950e9 q^{92} +8.09565e9 q^{93} +4.81190e10 q^{94} -3.46563e10 q^{95} +8.49593e9 q^{96} +1.29155e11 q^{97} +9.03174e10 q^{98} +1.66412e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \)	\( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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