LMFDB - Embedded newform 177.10.a.d.1.14

Newspace parameters

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

Newform invariants

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

$f(q)$	$=$	$q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} -9846.43 q^{10} -86127.8 q^{11} -23395.6 q^{12} +43784.4 q^{13} -122968. q^{14} -53388.8 q^{15} -30835.3 q^{16} -393685. q^{17} +98013.0 q^{18} +166782. q^{19} +190377. q^{20} -666752. q^{21} -1.28664e6 q^{22} +1.77150e6 q^{23} -969039. q^{24} -1.51868e6 q^{25} +654084. q^{26} +531441. q^{27} +2.37754e6 q^{28} +3.21566e6 q^{29} -797561. q^{30} -2.76369e6 q^{31} +5.66464e6 q^{32} -6.97635e6 q^{33} -5.88115e6 q^{34} +5.42556e6 q^{35} -1.89504e6 q^{36} -427809. q^{37} +2.49151e6 q^{38} +3.54654e6 q^{39} +7.88536e6 q^{40} +1.68281e7 q^{41} -9.96042e6 q^{42} +206120. q^{43} +2.48767e7 q^{44} -4.32449e6 q^{45} +2.64639e7 q^{46} -1.61351e7 q^{47} -2.49766e6 q^{48} +2.74040e7 q^{49} -2.26872e7 q^{50} -3.18885e7 q^{51} -1.26465e7 q^{52} -8.10150e6 q^{53} +7.93905e6 q^{54} +5.67687e7 q^{55} +9.84771e7 q^{56} +1.35093e7 q^{57} +4.80379e7 q^{58} -1.21174e7 q^{59} +1.54205e7 q^{60} +3.93336e7 q^{61} -4.12860e7 q^{62} -5.40069e7 q^{63} +1.00410e8 q^{64} -2.88593e7 q^{65} -1.04218e8 q^{66} +3.07030e8 q^{67} +1.13710e8 q^{68} +1.43491e8 q^{69} +8.10509e7 q^{70} -2.50251e8 q^{71} -7.84922e7 q^{72} -1.16174e8 q^{73} -6.39091e6 q^{74} -1.23013e8 q^{75} -4.81724e7 q^{76} +7.08961e8 q^{77} +5.29808e7 q^{78} -3.26619e8 q^{79} +2.03242e7 q^{80} +4.30467e7 q^{81} +2.51390e8 q^{82} +4.90102e8 q^{83} +1.92581e8 q^{84} +2.59486e8 q^{85} +3.07917e6 q^{86} +2.60469e8 q^{87} +1.03039e9 q^{88} -6.22951e8 q^{89} -6.46024e7 q^{90} -3.60412e8 q^{91} -5.11670e8 q^{92} -2.23859e8 q^{93} -2.41038e8 q^{94} -1.09929e8 q^{95} +4.58836e8 q^{96} +6.21194e8 q^{97} +4.09381e8 q^{98} -5.65085e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) $	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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 $

$2$	14.9387	0.660205	0.330102	−	0.943945i	$-0.392917\pi$
$2$	14.9387	0.660205	0.330102	+	0.943945i	$0.392917\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−288.835	−0.564130
$5$	−659.121	−0.471629	−0.235814	−	0.971798i	$-0.575776\pi$
$5$	−659.121	−0.471629	−0.235814	+	0.971798i	$0.575776\pi$
$6$	1210.04	0.381169
$7$	−8231.50	−1.29580	−0.647900	−	0.761726i	$-0.724352\pi$
$7$	−8231.50	−1.29580	−0.647900	+	0.761726i	$0.724352\pi$
$8$	−11963.4	−1.03265
$9$	6561.00	0.333333
$10$	−9846.43	−0.311371
$11$	−86127.8	−1.77368	−0.886842	−	0.462073i	$-0.847106\pi$
$11$	−86127.8	−1.77368	−0.886842	+	0.462073i	$0.847106\pi$
$12$	−23395.6	−0.325701
$13$	43784.4	0.425182	0.212591	−	0.977141i	$-0.431810\pi$
$13$	43784.4	0.425182	0.212591	+	0.977141i	$0.431810\pi$
$14$	−122968.	−0.855493
$15$	−53388.8	−0.272295
$16$	−30835.3	−0.117627
$17$	−393685.	−1.14322	−0.571608	−	0.820527i	$-0.693680\pi$
$17$	−393685.	−1.14322	−0.571608	+	0.820527i	$0.693680\pi$
$18$	98013.0	0.220068
$19$	166782.	0.293601	0.146800	−	0.989166i	$-0.453102\pi$
$19$	166782.	0.293601	0.146800	+	0.989166i	$0.453102\pi$
$20$	190377.	0.266060
$21$	−666752.	−0.748130
$22$	−1.28664e6	−1.17099
$23$	1.77150e6	1.31998	0.659988	−	0.751276i	$-0.270561\pi$
$23$	1.77150e6	1.31998	0.659988	+	0.751276i	$0.270561\pi$
$24$	−969039.	−0.596198
$25$	−1.51868e6	−0.777566
$26$	654084.	0.280707
$27$	531441.	0.192450
$28$	2.37754e6	0.730999
$29$	3.21566e6	0.844266	0.422133	−	0.906534i	$-0.361281\pi$
$29$	3.21566e6	0.844266	0.422133	+	0.906534i	$0.361281\pi$
$30$	−797561.	−0.179770
$31$	−2.76369e6	−0.537479	−0.268739	−	0.963213i	$-0.586607\pi$
$31$	−2.76369e6	−0.537479	−0.268739	+	0.963213i	$0.586607\pi$
$32$	5.66464e6	0.954988
$33$	−6.97635e6	−1.02404
$34$	−5.88115e6	−0.754757
$35$	5.42556e6	0.611136
$36$	−1.89504e6	−0.188043
$37$	−427809.	−0.0375268	−0.0187634	−	0.999824i	$-0.505973\pi$
$37$	−427809.	−0.0375268	−0.0187634	+	0.999824i	$0.505973\pi$
$38$	2.49151e6	0.193837
$39$	3.54654e6	0.245479
$40$	7.88536e6	0.487025
$41$	1.68281e7	0.930053	0.465026	−	0.885297i	$-0.346045\pi$
$41$	1.68281e7	0.930053	0.465026	+	0.885297i	$0.346045\pi$
$42$	−9.96042e6	−0.493919
$43$	206120.	0.00919416	0.00459708	−	0.999989i	$-0.498537\pi$
$43$	206120.	0.00919416	0.00459708	+	0.999989i	$0.498537\pi$
$44$	2.48767e7	1.00059
$45$	−4.32449e6	−0.157210
$46$	2.64639e7	0.871454
$47$	−1.61351e7	−0.482317	−0.241158	−	0.970486i	$-0.577527\pi$
$47$	−1.61351e7	−0.482317	−0.241158	+	0.970486i	$0.577527\pi$
$48$	−2.49766e6	−0.0679122
$49$	2.74040e7	0.679097
$50$	−2.26872e7	−0.513353
$51$	−3.18885e7	−0.660036
$52$	−1.26465e7	−0.239858
$53$	−8.10150e6	−0.141034	−0.0705171	−	0.997511i	$-0.522465\pi$
$53$	−8.10150e6	−0.141034	−0.0705171	+	0.997511i	$0.522465\pi$
$54$	7.93905e6	0.127056
$55$	5.67687e7	0.836520
$56$	9.84771e7	1.33810
$57$	1.35093e7	0.169511
$58$	4.80379e7	0.557389
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	1.54205e7	0.153610
$61$	3.93336e7	0.363731	0.181865	−	0.983323i	$-0.441787\pi$
$61$	3.93336e7	0.363731	0.181865	+	0.983323i	$0.441787\pi$
$62$	−4.12860e7	−0.354846
$63$	−5.40069e7	−0.431933
$64$	1.00410e8	0.748114
$65$	−2.88593e7	−0.200528
$66$	−1.04218e8	−0.676074
$67$	3.07030e8	1.86142	0.930710	−	0.365757i	$-0.119190\pi$
$67$	3.07030e8	1.86142	0.930710	+	0.365757i	$0.119190\pi$
$68$	1.13710e8	0.644923
$69$	1.43491e8	0.762088
$70$	8.10509e7	0.403475
$71$	−2.50251e8	−1.16873	−0.584365	−	0.811491i	$-0.698656\pi$
$71$	−2.50251e8	−1.16873	−0.584365	+	0.811491i	$0.698656\pi$
$72$	−7.84922e7	−0.344215
$73$	−1.16174e8	−0.478801	−0.239400	−	0.970921i	$-0.576951\pi$
$73$	−1.16174e8	−0.478801	−0.239400	+	0.970921i	$0.576951\pi$
$74$	−6.39091e6	−0.0247754
$75$	−1.23013e8	−0.448928
$76$	−4.81724e7	−0.165629
$77$	7.08961e8	2.29834
$78$	5.29808e7	0.162066
$79$	−3.26619e8	−0.943451	−0.471725	−	0.881746i	$-0.656369\pi$
$79$	−3.26619e8	−0.943451	−0.471725	+	0.881746i	$0.656369\pi$
$80$	2.03242e7	0.0554764
$81$	4.30467e7	0.111111
$82$	2.51390e8	0.614025
$83$	4.90102e8	1.13354	0.566768	−	0.823878i	$-0.308194\pi$
$83$	4.90102e8	1.13354	0.566768	+	0.823878i	$0.308194\pi$
$84$	1.92581e8	0.422043
$85$	2.59486e8	0.539174
$86$	3.07917e6	0.00607003
$87$	2.60469e8	0.487437
$88$	1.03039e9	1.83159
$89$	−6.22951e8	−1.05244	−0.526222	−	0.850347i	$-0.676392\pi$
$89$	−6.22951e8	−1.05244	−0.526222	+	0.850347i	$0.676392\pi$
$90$	−6.46024e7	−0.103790
$91$	−3.60412e8	−0.550951
$92$	−5.11670e8	−0.744638
$93$	−2.23859e8	−0.310314
$94$	−2.41038e8	−0.318428
$95$	−1.09929e8	−0.138471
$96$	4.58836e8	0.551362
$97$	6.21194e8	0.712450	0.356225	−	0.934400i	$-0.384064\pi$
$97$	6.21194e8	0.712450	0.356225	+	0.934400i	$0.384064\pi$
$98$	4.09381e8	0.448343
$99$	−5.65085e8	−0.591228
$100$	4.38648e8	0.438648
$101$	6.76739e8	0.647105	0.323553	−	0.946210i	$-0.395123\pi$
$101$	6.76739e8	0.647105	0.323553	+	0.946210i	$0.395123\pi$
$102$	−4.76373e8	−0.435759
$103$	−1.66672e9	−1.45914	−0.729568	−	0.683908i	$-0.760279\pi$
$103$	−1.66672e9	−1.45914	−0.729568	+	0.683908i	$0.760279\pi$
$104$	−5.23813e8	−0.439062
$105$	4.39470e8	0.352840
$106$	−1.21026e8	−0.0931114
$107$	−6.75823e8	−0.498432	−0.249216	−	0.968448i	$-0.580173\pi$
$107$	−6.75823e8	−0.498432	−0.249216	+	0.968448i	$0.580173\pi$
$108$	−1.53499e8	−0.108567
$109$	−2.20524e8	−0.149636	−0.0748181	−	0.997197i	$-0.523838\pi$
$109$	−2.20524e8	−0.149636	−0.0748181	+	0.997197i	$0.523838\pi$
$110$	8.48051e8	0.552275
$111$	−3.46525e7	−0.0216661
$112$	2.53821e8	0.152422
$113$	−3.21303e9	−1.85379	−0.926897	−	0.375315i	$-0.877535\pi$
$113$	−3.21303e9	−1.85379	−0.926897	+	0.375315i	$0.877535\pi$
$114$	2.01812e8	0.111912
$115$	−1.16763e9	−0.622538
$116$	−9.28795e8	−0.476276
$117$	2.87270e8	0.141727
$118$	−1.81018e8	−0.0859513
$119$	3.24062e9	1.48138
$120$	6.38714e8	0.281184
$121$	5.06005e9	2.14596
$122$	5.87594e8	0.240137
$123$	1.36308e9	0.536966
$124$	7.98249e8	0.303208
$125$	2.28834e9	0.838351
$126$	−8.06794e8	−0.285164
$127$	−1.49943e9	−0.511458	−0.255729	−	0.966748i	$-0.582316\pi$
$127$	−1.49943e9	−0.511458	−0.255729	+	0.966748i	$0.582316\pi$
$128$	−1.40030e9	−0.461079
$129$	1.66957e7	0.00530825
$130$	−4.31120e8	−0.132389
$131$	5.72810e9	1.69938	0.849688	−	0.527285i	$-0.176790\pi$
$131$	5.72810e9	1.69938	0.849688	+	0.527285i	$0.176790\pi$
$132$	2.01501e9	0.577690
$133$	−1.37286e9	−0.380448
$134$	4.58664e9	1.22892
$135$	−3.50284e8	−0.0907650
$136$	4.70983e9	1.18054
$137$	6.47967e9	1.57149	0.785743	−	0.618553i	$-0.212281\pi$
$137$	6.47967e9	1.57149	0.785743	+	0.618553i	$0.212281\pi$
$138$	2.14358e9	0.503134
$139$	7.53691e9	1.71249	0.856243	−	0.516574i	$-0.172793\pi$
$139$	7.53691e9	1.71249	0.856243	+	0.516574i	$0.172793\pi$
$140$	−1.56709e9	−0.344760
$141$	−1.30695e9	−0.278466
$142$	−3.73844e9	−0.771600
$143$	−3.77106e9	−0.754138
$144$	−2.02310e8	−0.0392091
$145$	−2.11951e9	−0.398180
$146$	−1.73549e9	−0.316107
$147$	2.21972e9	0.392077
$148$	1.23566e8	0.0211700
$149$	−8.64441e8	−0.143680	−0.0718402	−	0.997416i	$-0.522887\pi$
$149$	−8.64441e8	−0.143680	−0.0718402	+	0.997416i	$0.522887\pi$
$150$	−1.83766e9	−0.296384
$151$	6.27824e8	0.0982747	0.0491373	−	0.998792i	$-0.484353\pi$
$151$	6.27824e8	0.0982747	0.0491373	+	0.998792i	$0.484353\pi$
$152$	−1.99529e9	−0.303186
$153$	−2.58297e9	−0.381072
$154$	1.05910e10	1.51737
$155$	1.82161e9	0.253490
$156$	−1.02436e9	−0.138482
$157$	3.90127e9	0.512458	0.256229	−	0.966616i	$-0.417520\pi$
$157$	3.90127e9	0.512458	0.256229	+	0.966616i	$0.417520\pi$
$158$	−4.87927e9	−0.622870
$159$	−6.56222e8	−0.0814261
$160$	−3.73369e9	−0.450400
$161$	−1.45821e10	−1.71042
$162$	6.43063e8	0.0733561
$163$	2.75564e9	0.305758	0.152879	−	0.988245i	$-0.451146\pi$
$163$	2.75564e9	0.305758	0.152879	+	0.988245i	$0.451146\pi$
$164$	−4.86053e9	−0.524671
$165$	4.59826e9	0.482965
$166$	7.32150e9	0.748365
$167$	2.26288e9	0.225132	0.112566	−	0.993644i	$-0.464093\pi$
$167$	2.26288e9	0.225132	0.112566	+	0.993644i	$0.464093\pi$
$168$	7.97665e9	0.772554
$169$	−8.68742e9	−0.819220
$170$	3.87639e9	0.355965
$171$	1.09426e9	0.0978670
$172$	−5.95346e7	−0.00518670
$173$	−8.51022e9	−0.722326	−0.361163	−	0.932503i	$-0.617620\pi$
$173$	−8.51022e9	−0.722326	−0.361163	+	0.932503i	$0.617620\pi$
$174$	3.89107e9	0.321808
$175$	1.25011e10	1.00757
$176$	2.65578e9	0.208634
$177$	−9.81506e8	−0.0751646
$178$	−9.30609e9	−0.694828
$179$	−5.31698e9	−0.387103	−0.193551	−	0.981090i	$-0.562001\pi$
$179$	−5.31698e9	−0.387103	−0.193551	+	0.981090i	$0.562001\pi$
$180$	1.24906e9	0.0886866
$181$	5.56101e9	0.385124	0.192562	−	0.981285i	$-0.438320\pi$
$181$	5.56101e9	0.385124	0.192562	+	0.981285i	$0.438320\pi$
$182$	−5.38409e9	−0.363740
$183$	3.18602e9	0.210000
$184$	−2.11932e10	−1.36307
$185$	2.81978e8	0.0176987
$186$	−3.34416e9	−0.204870
$187$	3.39072e10	2.02771
$188$	4.66039e9	0.272089
$189$	−4.37456e9	−0.249377
$190$	−1.64221e9	−0.0914190
$191$	3.29917e10	1.79372	0.896860	−	0.442315i	$-0.145843\pi$
$191$	3.29917e10	1.79372	0.896860	+	0.442315i	$0.145843\pi$
$192$	8.13323e9	0.431924
$193$	−2.35302e10	−1.22072	−0.610362	−	0.792122i	$-0.708976\pi$
$193$	−2.35302e10	−1.22072	−0.610362	+	0.792122i	$0.708976\pi$
$194$	9.27984e9	0.470362
$195$	−2.33760e9	−0.115775
$196$	−7.91523e9	−0.383099
$197$	2.75263e10	1.30212	0.651059	−	0.759027i	$-0.274325\pi$
$197$	2.75263e10	1.30212	0.651059	+	0.759027i	$0.274325\pi$
$198$	−8.44164e9	−0.390331
$199$	2.17126e10	0.981459	0.490729	−	0.871312i	$-0.336730\pi$
$199$	2.17126e10	0.981459	0.490729	+	0.871312i	$0.336730\pi$
$200$	1.81687e10	0.802951
$201$	2.48694e10	1.07469
$202$	1.01096e10	0.427222
$203$	−2.64697e10	−1.09400
$204$	9.21049e9	0.372346
$205$	−1.10918e10	−0.438640
$206$	−2.48987e10	−0.963328
$207$	1.16228e10	0.439992
$208$	−1.35011e9	−0.0500130
$209$	−1.43646e10	−0.520755
$210$	6.56512e9	0.232946
$211$	1.08182e10	0.375736	0.187868	−	0.982194i	$-0.439842\pi$
$211$	1.08182e10	0.375736	0.187868	+	0.982194i	$0.439842\pi$
$212$	2.33999e9	0.0795616
$213$	−2.02704e10	−0.674766
$214$	−1.00959e10	−0.329067
$215$	−1.35858e8	−0.00433623
$216$	−6.35787e9	−0.198733
$217$	2.27493e10	0.696465
$218$	−3.29435e9	−0.0987905
$219$	−9.41007e9	−0.276436
$220$	−1.63968e10	−0.471906
$221$	−1.72373e10	−0.486075
$222$	−5.17664e8	−0.0143041
$223$	2.01070e10	0.544472	0.272236	−	0.962230i	$-0.412237\pi$
$223$	2.01070e10	0.544472	0.272236	+	0.962230i	$0.412237\pi$
$224$	−4.66285e10	−1.23747
$225$	−9.96409e9	−0.259189
$226$	−4.79986e10	−1.22388
$227$	−2.29052e8	−0.00572555	−0.00286278	−	0.999996i	$-0.500911\pi$
$227$	−2.29052e8	−0.00572555	−0.00286278	+	0.999996i	$0.500911\pi$
$228$	−3.90196e9	−0.0956260
$229$	−3.35826e10	−0.806964	−0.403482	−	0.914988i	$-0.632200\pi$
$229$	−3.35826e10	−0.806964	−0.403482	+	0.914988i	$0.632200\pi$
$230$	−1.74429e10	−0.411003
$231$	5.74259e10	1.32695
$232$	−3.84704e10	−0.871828
$233$	−1.09191e10	−0.242709	−0.121355	−	0.992609i	$-0.538724\pi$
$233$	−1.09191e10	−0.242709	−0.121355	+	0.992609i	$0.538724\pi$
$234$	4.29144e9	0.0935690
$235$	1.06350e10	0.227474
$236$	3.49991e9	0.0734435
$237$	−2.64561e10	−0.544702
$238$	4.84107e10	0.978014
$239$	2.51977e10	0.499540	0.249770	−	0.968305i	$-0.419645\pi$
$239$	2.51977e10	0.499540	0.249770	+	0.968305i	$0.419645\pi$
$240$	1.64626e9	0.0320293
$241$	1.20750e10	0.230574	0.115287	−	0.993332i	$-0.463221\pi$
$241$	1.20750e10	0.230574	0.115287	+	0.993332i	$0.463221\pi$
$242$	7.55907e10	1.41677
$243$	3.48678e9	0.0641500
$244$	−1.13609e10	−0.205191
$245$	−1.80626e10	−0.320282
$246$	2.03626e10	0.354507
$247$	7.30245e9	0.124834
$248$	3.30632e10	0.555025
$249$	3.96983e10	0.654447
$250$	3.41849e10	0.553483
$251$	3.53064e10	0.561464	0.280732	−	0.959786i	$-0.409423\pi$
$251$	3.53064e10	0.561464	0.280732	+	0.959786i	$0.409423\pi$
$252$	1.55991e10	0.243666
$253$	−1.52575e11	−2.34122
$254$	−2.23996e10	−0.337667
$255$	2.10184e10	0.311292
$256$	−7.23287e10	−1.05252
$257$	−7.46059e10	−1.06678	−0.533389	−	0.845870i	$-0.679082\pi$
$257$	−7.46059e10	−1.06678	−0.533389	+	0.845870i	$0.679082\pi$
$258$	2.49413e8	0.00350453
$259$	3.52151e9	0.0486272
$260$	8.33555e9	0.113124
$261$	2.10980e10	0.281422
$262$	8.55705e10	1.12194
$263$	−5.39550e10	−0.695394	−0.347697	−	0.937607i	$-0.613036\pi$
$263$	−5.39550e10	−0.695394	−0.347697	+	0.937607i	$0.613036\pi$
$264$	8.34612e10	1.05747
$265$	5.33987e9	0.0665157
$266$	−2.05088e10	−0.251174
$267$	−5.04590e10	−0.607629
$268$	−8.86809e10	−1.05008
$269$	−1.57685e11	−1.83614	−0.918069	−	0.396421i	$-0.870252\pi$
$269$	−1.57685e11	−1.83614	−0.918069	+	0.396421i	$0.870252\pi$
$270$	−5.23280e9	−0.0599235
$271$	−1.52312e11	−1.71543	−0.857715	−	0.514126i	$-0.828117\pi$
$271$	−1.52312e11	−1.71543	−0.857715	+	0.514126i	$0.828117\pi$
$272$	1.21394e10	0.134474
$273$	−2.91933e10	−0.318091
$274$	9.67980e10	1.03750
$275$	1.30801e11	1.37916
$276$	−4.14453e10	−0.429917
$277$	−1.28972e11	−1.31624	−0.658122	−	0.752911i	$-0.728649\pi$
$277$	−1.28972e11	−1.31624	−0.658122	+	0.752911i	$0.728649\pi$
$278$	1.12592e11	1.13059
$279$	−1.81326e10	−0.179160
$280$	−6.49084e10	−0.631087
$281$	−2.04040e11	−1.95225	−0.976127	−	0.217199i	$-0.930308\pi$
$281$	−2.04040e11	−1.95225	−0.976127	+	0.217199i	$0.930308\pi$
$282$	−1.95241e10	−0.183844
$283$	−5.36671e10	−0.497358	−0.248679	−	0.968586i	$-0.579996\pi$
$283$	−5.36671e10	−0.497358	−0.248679	+	0.968586i	$0.579996\pi$
$284$	7.22812e10	0.659315
$285$	−8.90428e9	−0.0799461
$286$	−5.63348e10	−0.497886
$287$	−1.38520e11	−1.20516
$288$	3.71657e10	0.318329
$289$	3.63999e10	0.306944
$290$	−3.16628e10	−0.262880
$291$	5.03167e10	0.411333
$292$	3.35550e10	0.270106
$293$	2.48437e11	1.96930	0.984650	−	0.174538i	$-0.0558432\pi$
$293$	2.48437e11	1.96930	0.984650	+	0.174538i	$0.0558432\pi$
$294$	3.31599e10	0.258851
$295$	7.98681e9	0.0614008
$296$	5.11806e9	0.0387519
$297$	−4.57718e10	−0.341346
$298$	−1.29136e10	−0.0948584
$299$	7.75641e10	0.561230
$300$	3.55305e10	0.253254
$301$	−1.69668e9	−0.0119138
$302$	9.37889e9	0.0648814
$303$	5.48158e10	0.373606
$304$	−5.14277e9	−0.0345355
$305$	−2.59256e10	−0.171546
$306$	−3.85862e10	−0.251586
$307$	−1.85724e11	−1.19329	−0.596645	−	0.802506i	$-0.703500\pi$
$307$	−1.85724e11	−1.19329	−0.596645	+	0.802506i	$0.703500\pi$
$308$	−2.04772e11	−1.29656
$309$	−1.35005e11	−0.842433
$310$	2.72125e10	0.167356
$311$	−2.85134e11	−1.72834	−0.864168	−	0.503204i	$-0.832154\pi$
$311$	−2.85134e11	−1.72834	−0.864168	+	0.503204i	$0.832154\pi$
$312$	−4.24288e10	−0.253493
$313$	1.05330e11	0.620301	0.310150	−	0.950688i	$-0.399621\pi$
$313$	1.05330e11	0.620301	0.310150	+	0.950688i	$0.399621\pi$
$314$	5.82801e10	0.338327
$315$	3.55971e10	0.203712
$316$	9.43388e10	0.532229
$317$	2.12753e11	1.18334	0.591668	−	0.806181i	$-0.298469\pi$
$317$	2.12753e11	1.18334	0.591668	+	0.806181i	$0.298469\pi$
$318$	−9.80312e9	−0.0537579
$319$	−2.76958e11	−1.49746
$320$	−6.61825e10	−0.352832
$321$	−5.47416e10	−0.287770
$322$	−2.17838e11	−1.12923
$323$	−6.56595e10	−0.335650
$324$	−1.24334e10	−0.0626811
$325$	−6.64947e10	−0.330607
$326$	4.11657e10	0.201863
$327$	−1.78624e10	−0.0863925
$328$	−2.01322e11	−0.960415
$329$	1.32816e11	0.624986
$330$	6.86922e10	0.318856
$331$	2.45717e11	1.12515	0.562574	−	0.826747i	$-0.309811\pi$
$331$	2.45717e11	1.12515	0.562574	+	0.826747i	$0.309811\pi$
$332$	−1.41558e11	−0.639461
$333$	−2.80685e9	−0.0125089
$334$	3.38045e10	0.148633
$335$	−2.02370e11	−0.877899
$336$	2.05595e10	0.0880006
$337$	2.46465e11	1.04093	0.520463	−	0.853884i	$-0.325759\pi$
$337$	2.46465e11	1.04093	0.520463	+	0.853884i	$0.325759\pi$
$338$	−1.29779e11	−0.540853
$339$	−2.60255e11	−1.07029
$340$	−7.49485e10	−0.304164
$341$	2.38030e11	0.953318
$342$	1.63468e10	0.0646122
$343$	1.06595e11	0.415826
$344$	−2.46591e9	−0.00949431
$345$	−9.45783e10	−0.359423
$346$	−1.27132e11	−0.476883
$347$	−1.08361e10	−0.0401227	−0.0200614	−	0.999799i	$-0.506386\pi$
$347$	−1.08361e10	−0.0401227	−0.0200614	+	0.999799i	$0.506386\pi$
$348$	−7.52324e10	−0.274978
$349$	1.74996e11	0.631411	0.315706	−	0.948857i	$-0.397759\pi$
$349$	1.74996e11	0.631411	0.315706	+	0.948857i	$0.397759\pi$
$350$	1.86750e11	0.665202
$351$	2.32688e10	0.0818263
$352$	−4.87883e11	−1.69385
$353$	−1.94568e11	−0.666937	−0.333469	−	0.942761i	$-0.608219\pi$
$353$	−1.94568e11	−0.666937	−0.333469	+	0.942761i	$0.608219\pi$
$354$	−1.46624e10	−0.0496240
$355$	1.64946e11	0.551206
$356$	1.79930e11	0.593715
$357$	2.62490e11	0.855275
$358$	−7.94289e10	−0.255567
$359$	−5.27532e10	−0.167619	−0.0838097	−	0.996482i	$-0.526709\pi$
$359$	−5.27532e10	−0.167619	−0.0838097	+	0.996482i	$0.526709\pi$
$360$	5.17359e10	0.162342
$361$	−2.94872e11	−0.913798
$362$	8.30744e10	0.254260
$363$	4.09864e11	1.23897
$364$	1.04099e11	0.310808
$365$	7.65726e10	0.225816
$366$	4.75951e10	0.138643
$367$	−8.20938e10	−0.236218	−0.118109	−	0.993001i	$-0.537683\pi$
$367$	−8.20938e10	−0.236218	−0.118109	+	0.993001i	$0.537683\pi$
$368$	−5.46247e10	−0.155265
$369$	1.10409e11	0.310018
$370$	4.21239e9	0.0116848
$371$	6.66875e10	0.182752
$372$	6.46581e10	0.175057
$373$	1.57190e11	0.420469	0.210235	−	0.977651i	$-0.432577\pi$
$373$	1.57190e11	0.420469	0.210235	+	0.977651i	$0.432577\pi$
$374$	5.06530e11	1.33870
$375$	1.85356e11	0.484022
$376$	1.93032e11	0.498062
$377$	1.40796e11	0.358967
$378$	−6.53503e10	−0.164640
$379$	6.72895e11	1.67522	0.837608	−	0.546272i	$-0.183953\pi$
$379$	6.72895e11	1.67522	0.837608	+	0.546272i	$0.183953\pi$
$380$	3.17514e10	0.0781155
$381$	−1.21454e11	−0.295291
$382$	4.92854e11	1.18422
$383$	6.60882e11	1.56939	0.784693	−	0.619885i	$-0.212821\pi$
$383$	6.60882e11	1.56939	0.784693	+	0.619885i	$0.212821\pi$
$384$	−1.13424e11	−0.266204
$385$	−4.67291e11	−1.08396
$386$	−3.51511e11	−0.805928
$387$	1.35235e9	0.00306472
$388$	−1.79422e11	−0.401914
$389$	5.11385e11	1.13234	0.566168	−	0.824290i	$-0.308425\pi$
$389$	5.11385e11	1.13234	0.566168	+	0.824290i	$0.308425\pi$
$390$	−3.49208e10	−0.0764351
$391$	−6.97413e11	−1.50902
$392$	−3.27846e11	−0.701267
$393$	4.63976e11	0.981136
$394$	4.11208e11	0.859664
$395$	2.15281e11	0.444959
$396$	1.63216e11	0.333529
$397$	4.60522e11	0.930450	0.465225	−	0.885192i	$-0.345973\pi$
$397$	4.60522e11	0.930450	0.465225	+	0.885192i	$0.345973\pi$
$398$	3.24358e11	0.647964
$399$	−1.11202e11	−0.219652
$400$	4.68291e10	0.0914631
$401$	9.41887e11	1.81907	0.909535	−	0.415628i	$-0.136438\pi$
$401$	9.41887e11	1.81907	0.909535	+	0.415628i	$0.136438\pi$
$402$	3.71518e11	0.709516
$403$	−1.21007e11	−0.228526
$404$	−1.95466e11	−0.365051
$405$	−2.83730e10	−0.0524032
$406$	−3.95424e11	−0.722264
$407$	3.68462e10	0.0665607
$408$	3.81496e11	0.681584
$409$	−5.60303e11	−0.990075	−0.495037	−	0.868872i	$-0.664846\pi$
$409$	−5.60303e11	−0.990075	−0.495037	+	0.868872i	$0.664846\pi$
$410$	−1.65697e11	−0.289592
$411$	5.24853e11	0.907298
$412$	4.81407e11	0.823142
$413$	9.97441e10	0.168699
$414$	1.73630e11	0.290485
$415$	−3.23037e11	−0.534608
$416$	2.48023e11	0.406043
$417$	6.10490e11	0.988704
$418$	−2.14588e11	−0.343805
$419$	3.78397e11	0.599770	0.299885	−	0.953975i	$-0.403052\pi$
$419$	3.78397e11	0.599770	0.299885	+	0.953975i	$0.403052\pi$
$420$	−1.26934e11	−0.199047
$421$	−5.95120e11	−0.923284	−0.461642	−	0.887066i	$-0.652739\pi$
$421$	−5.95120e11	−0.923284	−0.461642	+	0.887066i	$0.652739\pi$
$422$	1.61610e11	0.248063
$423$	−1.05863e11	−0.160772
$424$	9.69219e10	0.145638
$425$	5.97883e11	0.888927
$426$	−3.02813e11	−0.445484
$427$	−3.23775e11	−0.471322
$428$	1.95201e11	0.281180
$429$	−3.05456e11	−0.435402
$430$	−2.02955e9	−0.00286280
$431$	4.27432e11	0.596650	0.298325	−	0.954464i	$-0.403572\pi$
$431$	4.27432e11	0.596650	0.298325	+	0.954464i	$0.403572\pi$
$432$	−1.63871e10	−0.0226374
$433$	−3.45341e11	−0.472121	−0.236060	−	0.971738i	$-0.575856\pi$
$433$	−3.45341e11	−0.472121	−0.236060	+	0.971738i	$0.575856\pi$
$434$	3.39846e11	0.459809
$435$	−1.71680e11	−0.229890
$436$	6.36949e10	0.0844142
$437$	2.95454e11	0.387546
$438$	−1.40574e11	−0.182504
$439$	−1.03278e12	−1.32714	−0.663569	−	0.748115i	$-0.730959\pi$
$439$	−1.03278e12	−1.32714	−0.663569	+	0.748115i	$0.730959\pi$
$440$	−6.79149e11	−0.863829
$441$	1.79798e11	0.226366
$442$	−2.57503e11	−0.320909
$443$	8.02607e11	0.990116	0.495058	−	0.868860i	$-0.335147\pi$
$443$	8.02607e11	0.990116	0.495058	+	0.868860i	$0.335147\pi$
$444$	1.00088e10	0.0122225
$445$	4.10600e11	0.496363
$446$	3.00373e11	0.359463
$447$	−7.00197e10	−0.0829539
$448$	−8.26527e11	−0.969407
$449$	1.00537e12	1.16739	0.583695	−	0.811973i	$-0.301606\pi$
$449$	1.00537e12	1.16739	0.583695	+	0.811973i	$0.301606\pi$
$450$	−1.48851e11	−0.171118
$451$	−1.44937e12	−1.64962
$452$	9.28034e11	1.04578
$453$	5.08538e10	0.0567389
$454$	−3.42174e9	−0.00378004
$455$	2.37555e11	0.259844
$456$	−1.61618e11	−0.175044
$457$	1.37752e11	0.147732	0.0738662	−	0.997268i	$-0.476466\pi$
$457$	1.37752e11	0.147732	0.0738662	+	0.997268i	$0.476466\pi$
$458$	−5.01681e11	−0.532761
$459$	−2.09220e11	−0.220012
$460$	3.37253e11	0.351193
$461$	−1.33388e11	−0.137551	−0.0687754	−	0.997632i	$-0.521909\pi$
$461$	−1.33388e11	−0.137551	−0.0687754	+	0.997632i	$0.521909\pi$
$462$	8.57869e11	0.876056
$463$	9.07405e11	0.917671	0.458835	−	0.888521i	$-0.348267\pi$
$463$	9.07405e11	0.917671	0.458835	+	0.888521i	$0.348267\pi$
$464$	−9.91560e10	−0.0993088
$465$	1.47550e11	0.146353
$466$	−1.63118e11	−0.160238
$467$	6.91974e11	0.673230	0.336615	−	0.941642i	$-0.390718\pi$
$467$	6.91974e11	0.673230	0.336615	+	0.941642i	$0.390718\pi$
$468$	−8.29734e10	−0.0799526
$469$	−2.52732e12	−2.41203
$470$	1.58874e11	0.150180
$471$	3.16003e11	0.295868
$472$	1.44965e11	0.134439
$473$	−1.77527e10	−0.0163075
$474$	−3.95221e11	−0.359614
$475$	−2.53289e11	−0.228294
$476$	−9.36002e11	−0.835691
$477$	−5.31540e10	−0.0470114
$478$	3.76421e11	0.329798
$479$	−4.51704e11	−0.392053	−0.196026	−	0.980599i	$-0.562804\pi$
$479$	−4.51704e11	−0.392053	−0.196026	+	0.980599i	$0.562804\pi$
$480$	−3.02429e11	−0.260038
$481$	−1.87314e10	−0.0159557
$482$	1.80385e11	0.152226
$483$	−1.18115e12	−0.987514
$484$	−1.46152e12	−1.21060
$485$	−4.09442e11	−0.336012
$486$	5.20881e10	0.0423521
$487$	−5.57074e11	−0.448779	−0.224389	−	0.974500i	$-0.572039\pi$
$487$	−5.57074e11	−0.448779	−0.224389	+	0.974500i	$0.572039\pi$
$488$	−4.70566e11	−0.375605
$489$	2.23207e11	0.176530
$490$	−2.69832e11	−0.211451
$491$	1.62345e12	1.26059	0.630294	−	0.776356i	$-0.282934\pi$
$491$	1.62345e12	1.26059	0.630294	+	0.776356i	$0.282934\pi$
$492$	−3.93703e11	−0.302919
$493$	−1.26596e12	−0.965179
$494$	1.09089e11	0.0824159
$495$	3.72459e11	0.278840
$496$	8.52192e10	0.0632222
$497$	2.05994e12	1.51444
$498$	5.93041e11	0.432069
$499$	4.33241e11	0.312808	0.156404	−	0.987693i	$-0.450010\pi$
$499$	4.33241e11	0.312808	0.156404	+	0.987693i	$0.450010\pi$
$500$	−6.60953e11	−0.472939
$501$	1.83293e11	0.129980
$502$	5.27433e11	0.370681
$503$	4.25950e11	0.296690	0.148345	−	0.988936i	$-0.452605\pi$
$503$	4.25950e11	0.296690	0.148345	+	0.988936i	$0.452605\pi$
$504$	6.46108e11	0.446034
$505$	−4.46053e11	−0.305193
$506$	−2.27928e12	−1.54568
$507$	−7.03681e11	−0.472977
$508$	4.33088e11	0.288529
$509$	2.93128e11	0.193565	0.0967826	−	0.995306i	$-0.469145\pi$
$509$	2.93128e11	0.193565	0.0967826	+	0.995306i	$0.469145\pi$
$510$	3.13988e11	0.205516
$511$	9.56284e11	0.620430
$512$	−3.63546e11	−0.233800
$513$	8.86347e10	0.0565035
$514$	−1.11452e12	−0.704292
$515$	1.09857e12	0.688171
$516$	−4.82230e9	−0.00299454
$517$	1.38968e12	0.855478
$518$	5.26068e10	0.0321039
$519$	−6.89328e11	−0.417035
$520$	3.45256e11	0.207074
$521$	2.47094e12	1.46924	0.734619	−	0.678480i	$-0.237361\pi$
$521$	2.47094e12	1.46924	0.734619	+	0.678480i	$0.237361\pi$
$522$	3.15177e11	0.185796
$523$	8.42425e11	0.492350	0.246175	−	0.969225i	$-0.420826\pi$
$523$	8.42425e11	0.492350	0.246175	+	0.969225i	$0.420826\pi$
$524$	−1.65447e12	−0.958669
$525$	1.01259e12	0.581721
$526$	−8.06019e11	−0.459102
$527$	1.08802e12	0.614455
$528$	2.15118e11	0.120455
$529$	1.33706e12	0.742335
$530$	7.97709e10	0.0439140
$531$	−7.95020e10	−0.0433963
$532$	3.96531e11	0.214622
$533$	7.36809e11	0.395441
$534$	−7.53793e11	−0.401159
$535$	4.45449e11	0.235075
$536$	−3.67314e12	−1.92219
$537$	−4.30675e11	−0.223494
$538$	−2.35561e12	−1.21223
$539$	−2.36025e12	−1.20450
$540$	1.01174e11	0.0512033
$541$	2.49463e12	1.25204	0.626020	−	0.779807i	$-0.284683\pi$
$541$	2.49463e12	1.25204	0.626020	+	0.779807i	$0.284683\pi$
$542$	−2.27535e12	−1.13253
$543$	4.50442e11	0.222351
$544$	−2.23008e12	−1.09176
$545$	1.45352e11	0.0705727
$546$	−4.36111e11	−0.210005
$547$	−1.57770e12	−0.753496	−0.376748	−	0.926316i	$-0.622958\pi$
$547$	−1.57770e12	−0.753496	−0.376748	+	0.926316i	$0.622958\pi$
$548$	−1.87155e12	−0.886522
$549$	2.58068e11	0.121244
$550$	1.95400e12	0.910526
$551$	5.36314e11	0.247877
$552$	−1.71665e12	−0.786967
$553$	2.68856e12	1.22252
$554$	−1.92668e12	−0.868990
$555$	2.28402e10	0.0102184
$556$	−2.17692e12	−0.966064
$557$	−1.90613e12	−0.839081	−0.419541	−	0.907737i	$-0.637809\pi$
$557$	−1.90613e12	−0.839081	−0.419541	+	0.907737i	$0.637809\pi$
$558$	−2.70877e11	−0.118282
$559$	9.02485e9	0.00390919
$560$	−1.67299e11	−0.0718864
$561$	2.74648e12	1.17070
$562$	−3.04809e12	−1.28889
$563$	6.38448e11	0.267817	0.133908	−	0.990994i	$-0.457247\pi$
$563$	6.38448e11	0.267817	0.133908	+	0.990994i	$0.457247\pi$
$564$	3.77491e11	0.157091
$565$	2.11778e12	0.874303
$566$	−8.01719e11	−0.328358
$567$	−3.54339e11	−0.143978
$568$	2.99387e12	1.20688
$569$	1.23249e12	0.492923	0.246462	−	0.969153i	$-0.420732\pi$
$569$	1.23249e12	0.492923	0.246462	+	0.969153i	$0.420732\pi$
$570$	−1.33019e11	−0.0527808
$571$	−3.41184e12	−1.34316	−0.671578	−	0.740934i	$-0.734383\pi$
$571$	−3.41184e12	−1.34316	−0.671578	+	0.740934i	$0.734383\pi$
$572$	1.08921e12	0.425432
$573$	2.67233e12	1.03560
$574$	−2.06932e12	−0.795653
$575$	−2.69035e12	−1.02637
$576$	6.58791e11	0.249371
$577$	2.65784e12	0.998247	0.499124	−	0.866531i	$-0.333655\pi$
$577$	2.65784e12	0.998247	0.499124	+	0.866531i	$0.333655\pi$
$578$	5.43768e11	0.202646
$579$	−1.90595e12	−0.704786
$580$	6.12188e11	0.224625
$581$	−4.03428e12	−1.46883
$582$	7.51667e11	0.271564
$583$	6.97765e11	0.250150
$584$	1.38984e12	0.494432
$585$	−1.89346e11	−0.0668427
$586$	3.71133e12	1.30014
$587$	4.49754e11	0.156352	0.0781761	−	0.996940i	$-0.475090\pi$
$587$	4.49754e11	0.156352	0.0781761	+	0.996940i	$0.475090\pi$
$588$	−6.41133e11	−0.221182
$589$	−4.60933e11	−0.157804
$590$	1.19313e11	0.0405371
$591$	2.22963e12	0.751778
$592$	1.31916e10	0.00441418
$593$	−4.61485e12	−1.53254	−0.766270	−	0.642519i	$-0.777889\pi$
$593$	−4.61485e12	−1.53254	−0.766270	+	0.642519i	$0.777889\pi$
$594$	−6.83773e11	−0.225358
$595$	−2.13596e12	−0.698661
$596$	2.49680e11	0.0810544
$597$	1.75872e12	0.566645
$598$	1.15871e12	0.370526
$599$	3.35316e11	0.106422	0.0532112	−	0.998583i	$-0.483054\pi$
$599$	3.35316e11	0.106422	0.0532112	+	0.998583i	$0.483054\pi$
$600$	1.47166e12	0.463584
$601$	−4.48338e12	−1.40175	−0.700874	−	0.713285i	$-0.747207\pi$
$601$	−4.48338e12	−1.40175	−0.700874	+	0.713285i	$0.747207\pi$
$602$	−2.53462e10	−0.00786554
$603$	2.01443e12	0.620473
$604$	−1.81337e11	−0.0554397
$605$	−3.33519e12	−1.01209
$606$	8.18879e11	0.246657
$607$	−5.01602e10	−0.0149972	−0.00749859	−	0.999972i	$-0.502387\pi$
$607$	−5.01602e10	−0.0149972	−0.00749859	+	0.999972i	$0.502387\pi$
$608$	9.44760e11	0.280385
$609$	−2.14405e12	−0.631621
$610$	−3.87296e11	−0.113255
$611$	−7.06468e11	−0.205072
$612$	7.46050e11	0.214974
$613$	−3.93106e11	−0.112444	−0.0562222	−	0.998418i	$-0.517906\pi$
$613$	−3.93106e11	−0.112444	−0.0562222	+	0.998418i	$0.517906\pi$
$614$	−2.77448e12	−0.787815
$615$	−8.98432e11	−0.253249
$616$	−8.48162e12	−2.37337
$617$	−1.85080e12	−0.514135	−0.257068	−	0.966393i	$-0.582756\pi$
$617$	−1.85080e12	−0.514135	−0.257068	+	0.966393i	$0.582756\pi$
$618$	−2.01680e12	−0.556178
$619$	1.79639e12	0.491803	0.245902	−	0.969295i	$-0.420916\pi$
$619$	1.79639e12	0.491803	0.245902	+	0.969295i	$0.420916\pi$
$620$	−5.26143e11	−0.143002
$621$	9.41448e11	0.254029
$622$	−4.25954e12	−1.14105
$623$	5.12782e12	1.36376
$624$	−1.09359e11	−0.0288750
$625$	1.45788e12	0.382176
$626$	1.57349e12	0.409525
$627$	−1.16353e12	−0.300658
$628$	−1.12682e12	−0.289093
$629$	1.68422e11	0.0429013
$630$	5.31775e11	0.134492
$631$	5.34615e12	1.34248	0.671242	−	0.741238i	$-0.265761\pi$
$631$	5.34615e12	1.34248	0.671242	+	0.741238i	$0.265761\pi$
$632$	3.90749e12	0.974250
$633$	8.76272e11	0.216931
$634$	3.17825e12	0.781244
$635$	9.88308e11	0.241218
$636$	1.89540e11	0.0459349
$637$	1.19987e12	0.288740
$638$	−4.13740e12	−0.988631
$639$	−1.64190e12	−0.389576
$640$	9.22966e11	0.217458
$641$	7.05261e12	1.65002	0.825010	−	0.565119i	$-0.191170\pi$
$641$	7.05261e12	1.65002	0.825010	+	0.565119i	$0.191170\pi$
$642$	−8.17770e11	−0.189987
$643$	6.00675e12	1.38577	0.692883	−	0.721050i	$-0.256340\pi$
$643$	6.00675e12	1.38577	0.692883	+	0.721050i	$0.256340\pi$
$644$	4.21182e12	0.964901
$645$	−1.10045e10	−0.00250352
$646$	−9.80869e11	−0.221597
$647$	2.10525e12	0.472318	0.236159	−	0.971714i	$-0.424111\pi$
$647$	2.10525e12	0.472318	0.236159	+	0.971714i	$0.424111\pi$
$648$	−5.14987e11	−0.114738
$649$	1.04364e12	0.230914
$650$	−9.93347e11	−0.218268
$651$	1.84269e12	0.402104
$652$	−7.95924e11	−0.172487
$653$	−1.86207e12	−0.400763	−0.200381	−	0.979718i	$-0.564218\pi$
$653$	−1.86207e12	−0.400763	−0.200381	+	0.979718i	$0.564218\pi$
$654$	−2.66842e11	−0.0570367
$655$	−3.77551e12	−0.801475
$656$	−5.18899e11	−0.109400
$657$	−7.62216e11	−0.159600
$658$	1.98411e12	0.412619
$659$	−3.37856e12	−0.697826	−0.348913	−	0.937155i	$-0.613449\pi$
$659$	−3.37856e12	−0.697826	−0.348913	+	0.937155i	$0.613449\pi$
$660$	−1.32814e12	−0.272455
$661$	−5.46765e12	−1.11402	−0.557011	−	0.830505i	$-0.688052\pi$
$661$	−5.46765e12	−1.11402	−0.557011	+	0.830505i	$0.688052\pi$
$662$	3.67070e12	0.742828
$663$	−1.39622e12	−0.280636
$664$	−5.86331e12	−1.17054
$665$	9.04884e11	0.179430
$666$	−4.19308e10	−0.00825846
$667$	5.69655e12	1.11441
$668$	−6.53598e11	−0.127004
$669$	1.62867e12	0.314351
$670$	−3.02315e12	−0.579593
$671$	−3.38772e12	−0.645143
$672$	−3.77691e12	−0.714455
$673$	3.35135e12	0.629727	0.314863	−	0.949137i	$-0.398041\pi$
$673$	3.35135e12	0.629727	0.314863	+	0.949137i	$0.398041\pi$
$674$	3.68187e12	0.687224
$675$	−8.07091e11	−0.149643
$676$	2.50923e12	0.462147
$677$	7.13136e12	1.30474	0.652369	−	0.757901i	$-0.273775\pi$
$677$	7.13136e12	1.30474	0.652369	+	0.757901i	$0.273775\pi$
$678$	−3.88788e12	−0.706610
$679$	−5.11336e12	−0.923192
$680$	−3.10435e12	−0.556776
$681$	−1.85532e10	−0.00330565
$682$	3.55587e12	0.629385
$683$	−1.19390e12	−0.209930	−0.104965	−	0.994476i	$-0.533473\pi$
$683$	−1.19390e12	−0.209930	−0.104965	+	0.994476i	$0.533473\pi$
$684$	−3.16059e11	−0.0552097
$685$	−4.27089e12	−0.741158
$686$	1.59239e12	0.274530
$687$	−2.72019e12	−0.465901
$688$	−6.35577e9	−0.00108149
$689$	−3.54720e11	−0.0599652
$690$	−1.41288e12	−0.237292
$691$	6.77087e12	1.12978	0.564889	−	0.825167i	$-0.308919\pi$
$691$	6.77087e12	1.12978	0.564889	+	0.825167i	$0.308919\pi$
$692$	2.45805e12	0.407486
$693$	4.65149e12	0.766113
$694$	−1.61878e11	−0.0264892
$695$	−4.96774e12	−0.807657
$696$	−3.11610e12	−0.503350
$697$	−6.62496e12	−1.06325
$698$	2.61421e12	0.416861
$699$	−8.84449e11	−0.140128
$700$	−3.61074e12	−0.568401
$701$	4.91860e12	0.769326	0.384663	−	0.923057i	$-0.374318\pi$
$701$	4.91860e12	0.769326	0.384663	+	0.923057i	$0.374318\pi$
$702$	3.47607e11	0.0540221
$703$	−7.13507e10	−0.0110179
$704$	−8.64811e12	−1.32692
$705$	8.61436e11	0.131332
$706$	−2.90660e12	−0.440315
$707$	−5.57058e12	−0.838519
$708$	2.83493e11	0.0424026
$709$	9.93757e11	0.147697	0.0738486	−	0.997269i	$-0.476472\pi$
$709$	9.93757e11	0.147697	0.0738486	+	0.997269i	$0.476472\pi$
$710$	2.46408e12	0.363909
$711$	−2.14295e12	−0.314484
$712$	7.45264e12	1.08680
$713$	−4.89587e12	−0.709459
$714$	3.92127e12	0.564656
$715$	2.48558e12	0.355673
$716$	1.53573e12	0.218376
$717$	2.04101e12	0.288409
$718$	−7.88066e11	−0.110663
$719$	−1.06186e13	−1.48179	−0.740896	−	0.671620i	$-0.765599\pi$
$719$	−1.06186e13	−1.48179	−0.740896	+	0.671620i	$0.765599\pi$
$720$	1.33347e11	0.0184921
$721$	1.37196e13	1.89075
$722$	−4.40500e12	−0.603294
$723$	9.78077e11	0.133122
$724$	−1.60621e12	−0.217260
$725$	−4.88358e12	−0.656473
$726$	6.12285e12	0.817972
$727$	6.74440e12	0.895444	0.447722	−	0.894173i	$-0.352235\pi$
$727$	6.74440e12	0.895444	0.447722	+	0.894173i	$0.352235\pi$
$728$	4.31177e12	0.568937
$729$	2.82430e11	0.0370370
$730$	1.14390e12	0.149085
$731$	−8.11463e10	−0.0105109
$732$	−9.20234e11	−0.118467
$733$	−5.61091e12	−0.717903	−0.358952	−	0.933356i	$-0.616866\pi$
$733$	−5.61091e12	−0.717903	−0.358952	+	0.933356i	$0.616866\pi$
$734$	−1.22638e12	−0.155952
$735$	−1.46307e12	−0.184915
$736$	1.00349e13	1.26056
$737$	−2.64438e13	−3.30157
$738$	1.64937e12	0.204675
$739$	−3.89121e12	−0.479938	−0.239969	−	0.970781i	$-0.577137\pi$
$739$	−3.89121e12	−0.479938	−0.239969	+	0.970781i	$0.577137\pi$
$740$	−8.14449e10	−0.00998438
$741$	5.91498e11	0.0720728
$742$	9.96227e11	0.120654
$743$	8.15319e12	0.981472	0.490736	−	0.871308i	$-0.336728\pi$
$743$	8.15319e12	0.981472	0.490736	+	0.871308i	$0.336728\pi$
$744$	2.67812e12	0.320444
$745$	5.69772e11	0.0677638
$746$	2.34821e12	0.277596
$747$	3.21556e12	0.377845
$748$	−9.79357e12	−1.14389
$749$	5.56303e12	0.645868
$750$	2.76898e12	0.319554
$751$	5.69916e12	0.653779	0.326890	−	0.945063i	$-0.393999\pi$
$751$	5.69916e12	0.653779	0.326890	+	0.945063i	$0.393999\pi$
$752$	4.97532e11	0.0567337
$753$	2.85982e12	0.324161
$754$	2.10331e12	0.236991
$755$	−4.13812e11	−0.0463492
$756$	1.26352e12	0.140681
$757$	1.69661e13	1.87781	0.938903	−	0.344181i	$-0.111844\pi$
$757$	1.69661e13	1.87781	0.938903	+	0.344181i	$0.111844\pi$
$758$	1.00522e13	1.10599
$759$	−1.23586e13	−1.35170
$760$	1.31513e12	0.142991
$761$	1.54543e13	1.67039	0.835197	−	0.549951i	$-0.185354\pi$
$761$	1.54543e13	1.67039	0.835197	+	0.549951i	$0.185354\pi$
$762$	−1.81437e12	−0.194952
$763$	1.81524e12	0.193898
$764$	−9.52914e12	−1.01189
$765$	1.70249e12	0.179725
$766$	9.87274e12	1.03612
$767$	−5.30552e11	−0.0553540
$768$	−5.85862e12	−0.607673
$769$	1.60580e12	0.165586	0.0827929	−	0.996567i	$-0.473616\pi$
$769$	1.60580e12	0.165586	0.0827929	+	0.996567i	$0.473616\pi$
$770$	−6.98074e12	−0.715637
$771$	−6.04308e12	−0.615904
$772$	6.79633e12	0.688647
$773$	2.75508e11	0.0277541	0.0138771	−	0.999904i	$-0.495583\pi$
$773$	2.75508e11	0.0277541	0.0138771	+	0.999904i	$0.495583\pi$
$774$	2.02024e10	0.00202334
$775$	4.19717e12	0.417925
$776$	−7.43161e12	−0.735708
$777$	2.85242e11	0.0280749
$778$	7.63945e12	0.747573
$779$	2.80662e12	0.273064
$780$	6.75180e11	0.0653121
$781$	2.15536e13	2.07296
$782$	−1.04185e13	−0.996260
$783$	1.70894e12	0.162479
$784$	−8.45011e11	−0.0798804
$785$	−2.57141e12	−0.241690
$786$	6.93121e12	0.647750
$787$	−1.60435e13	−1.49078	−0.745388	−	0.666630i	$-0.767736\pi$
$787$	−1.60435e13	−1.49078	−0.745388	+	0.666630i	$0.767736\pi$
$788$	−7.95055e12	−0.734564
$789$	−4.37035e12	−0.401486
$790$	3.21603e12	0.293764
$791$	2.64481e13	2.40215
$792$	6.76036e12	0.610529
$793$	1.72220e12	0.154652
$794$	6.87961e12	0.614287
$795$	4.32530e11	0.0384029
$796$	−6.27134e12	−0.553670
$797$	−1.39687e13	−1.22629	−0.613147	−	0.789969i	$-0.710097\pi$
$797$	−1.39687e13	−1.22629	−0.613147	+	0.789969i	$0.710097\pi$
$798$	−1.66122e12	−0.145015
$799$	6.35216e12	0.551393
$800$	−8.60281e12	−0.742566
$801$	−4.08718e12	−0.350815
$802$	1.40706e13	1.20096
$803$	1.00058e13	0.849242
$804$	−7.18316e12	−0.606266
$805$	9.61137e12	0.806685
$806$	−1.80768e12	−0.150874
$807$	−1.27725e13	−1.06009
$808$	−8.09613e12	−0.668230
$809$	1.35440e13	1.11167	0.555837	−	0.831292i	$-0.312398\pi$
$809$	1.35440e13	1.11167	0.555837	+	0.831292i	$0.312398\pi$
$810$	−4.23856e11	−0.0345968
$811$	−1.41243e12	−0.114650	−0.0573248	−	0.998356i	$-0.518257\pi$
$811$	−1.41243e12	−0.114650	−0.0573248	+	0.998356i	$0.518257\pi$
$812$	7.64537e12	0.617158
$813$	−1.23373e13	−0.990404
$814$	5.50435e11	0.0439437
$815$	−1.81630e12	−0.144204
$816$	9.83291e11	0.0776384
$817$	3.43771e10	0.00269942
$818$	−8.37021e12	−0.653652
$819$	−2.36466e12	−0.183650
$820$	3.20368e12	0.247450
$821$	2.53017e13	1.94359	0.971796	−	0.235825i	$-0.0757792\pi$
$821$	2.53017e13	1.94359	0.971796	+	0.235825i	$0.0757792\pi$
$822$	7.84064e12	0.599002
$823$	−1.45843e13	−1.10812	−0.554058	−	0.832478i	$-0.686922\pi$
$823$	−1.45843e13	−1.10812	−0.554058	+	0.832478i	$0.686922\pi$
$824$	1.99397e13	1.50677
$825$	1.05949e13	0.796257
$826$	1.49005e12	0.111376
$827$	1.46399e13	1.08834	0.544168	−	0.838976i	$-0.316845\pi$
$827$	1.46399e13	1.08834	0.544168	+	0.838976i	$0.316845\pi$
$828$	−3.35707e12	−0.248213
$829$	−1.65806e13	−1.21929	−0.609643	−	0.792676i	$-0.708687\pi$
$829$	−1.65806e13	−1.21929	−0.609643	+	0.792676i	$0.708687\pi$
$830$	−4.82575e12	−0.352951
$831$	−1.04467e13	−0.759934
$832$	4.39641e12	0.318085
$833$	−1.07885e13	−0.776355
$834$	9.11994e12	0.652747
$835$	−1.49151e12	−0.106179
$836$	4.14898e12	0.293774
$837$	−1.46874e12	−0.103438
$838$	5.65277e12	0.395971
$839$	1.08528e13	0.756161	0.378081	−	0.925773i	$-0.376584\pi$
$839$	1.08528e13	0.756161	0.378081	+	0.925773i	$0.376584\pi$
$840$	−5.25758e12	−0.364358
$841$	−4.16666e12	−0.287214
$842$	−8.89033e12	−0.609556
$843$	−1.65272e13	−1.12713
$844$	−3.12466e12	−0.211964
$845$	5.72606e12	0.386368
$846$	−1.58145e12	−0.106143
$847$	−4.16518e13	−2.78073
$848$	2.49812e11	0.0165895
$849$	−4.34704e12	−0.287150
$850$	8.93161e12	0.586873
$851$	−7.57863e11	−0.0495345
$852$	5.85478e12	0.380656
$853$	−1.79309e12	−0.115966	−0.0579830	−	0.998318i	$-0.518467\pi$
$853$	−1.79309e12	−0.115966	−0.0579830	+	0.998318i	$0.518467\pi$
$854$	−4.83678e12	−0.311169
$855$	−7.21247e11	−0.0461569
$856$	8.08517e12	0.514703
$857$	−3.89475e12	−0.246641	−0.123321	−	0.992367i	$-0.539354\pi$
$857$	−3.89475e12	−0.246641	−0.123321	+	0.992367i	$0.539354\pi$
$858$	−4.56312e12	−0.287454
$859$	2.04353e13	1.28059	0.640296	−	0.768128i	$-0.278812\pi$
$859$	2.04353e13	1.28059	0.640296	+	0.768128i	$0.278812\pi$
$860$	3.92405e10	0.00244620
$861$	−1.12202e13	−0.695801
$862$	6.38529e12	0.393911
$863$	1.13116e13	0.694184	0.347092	−	0.937831i	$-0.387169\pi$
$863$	1.13116e13	0.694184	0.347092	+	0.937831i	$0.387169\pi$
$864$	3.01042e12	0.183787
$865$	5.60927e12	0.340670
$866$	−5.15896e12	−0.311696
$867$	2.94839e12	0.177214
$868$	−6.57078e12	−0.392897
$869$	2.81310e13	1.67338
$870$	−2.56469e12	−0.151774
$871$	1.34431e13	0.791442
$872$	2.63823e12	0.154521
$873$	4.07565e12	0.237483
$874$	4.41371e12	0.255860
$875$	−1.88365e13	−1.08634
$876$	2.71795e12	0.155946
$877$	−1.74232e13	−0.994554	−0.497277	−	0.867592i	$-0.665667\pi$
$877$	−1.74232e13	−0.994554	−0.497277	+	0.867592i	$0.665667\pi$
$878$	−1.54284e13	−0.876182
$879$	2.01234e13	1.13698
$880$	−1.75048e12	−0.0983977
$881$	2.59628e13	1.45198	0.725990	−	0.687705i	$-0.241382\pi$
$881$	2.59628e13	1.45198	0.725990	+	0.687705i	$0.241382\pi$
$882$	2.68595e12	0.149448
$883$	−5.63113e12	−0.311725	−0.155863	−	0.987779i	$-0.549816\pi$
$883$	−5.63113e12	−0.311725	−0.155863	+	0.987779i	$0.549816\pi$
$884$	4.97872e12	0.274209
$885$	6.46932e11	0.0354498
$886$	1.19899e13	0.653679
$887$	1.90980e13	1.03593	0.517966	−	0.855401i	$-0.326690\pi$
$887$	1.90980e13	1.03593	0.517966	+	0.855401i	$0.326690\pi$
$888$	4.14563e11	0.0223734
$889$	1.23426e13	0.662747
$890$	6.13384e12	0.327701
$891$	−3.70752e12	−0.197076
$892$	−5.80760e12	−0.307153
$893$	−2.69105e12	−0.141609
$894$	−1.04601e12	−0.0547665
$895$	3.50453e12	0.182569
$896$	1.15265e13	0.597466
$897$	6.28269e12	0.324026
$898$	1.50189e13	0.770716
$899$	−8.88709e12	−0.453775
$900$	2.87797e12	0.146216
$901$	3.18944e12	0.161233
$902$	−2.16517e13	−1.08909
$903$	−1.37431e11	−0.00687843
$904$	3.84389e13	1.91431
$905$	−3.66538e12	−0.181635
$906$	7.59690e11	0.0374593
$907$	1.92812e13	0.946021	0.473010	−	0.881057i	$-0.343167\pi$
$907$	1.92812e13	0.946021	0.473010	+	0.881057i	$0.343167\pi$
$908$	6.61581e10	0.00322996
$909$	4.44008e12	0.215702
$910$	3.54877e12	0.171550
$911$	−2.56601e13	−1.23431	−0.617156	−	0.786841i	$-0.711715\pi$
$911$	−2.56601e13	−1.23431	−0.617156	+	0.786841i	$0.711715\pi$
$912$	−4.16564e11	−0.0199391
$913$	−4.22114e13	−2.01053
$914$	2.05784e12	0.0975336
$915$	−2.09998e12	−0.0990420
$916$	9.69981e12	0.455233
$917$	−4.71509e13	−2.20205
$918$	−3.12548e12	−0.145253
$919$	−6.69649e12	−0.309690	−0.154845	−	0.987939i	$-0.549488\pi$
$919$	−6.69649e12	−0.309690	−0.154845	+	0.987939i	$0.549488\pi$
$920$	1.39689e13	0.642862
$921$	−1.50437e13	−0.688946
$922$	−1.99265e12	−0.0908117
$923$	−1.09571e13	−0.496922
$924$	−1.65866e13	−0.748571
$925$	6.49706e11	0.0291796
$926$	1.35555e13	0.605850
$927$	−1.09354e13	−0.486379
$928$	1.82156e13	0.806264
$929$	6.76027e12	0.297778	0.148889	−	0.988854i	$-0.452430\pi$
$929$	6.76027e12	0.297778	0.148889	+	0.988854i	$0.452430\pi$
$930$	2.20421e12	0.0966228
$931$	4.57049e12	0.199384
$932$	3.15382e12	0.136919
$933$	−2.30959e13	−0.997855
$934$	1.03372e13	0.444470
$935$	−2.23490e13	−0.956324
$936$	−3.43674e12	−0.146354
$937$	−5.69718e12	−0.241453	−0.120726	−	0.992686i	$-0.538522\pi$
$937$	−5.69718e12	−0.241453	−0.120726	+	0.992686i	$0.538522\pi$
$938$	−3.77549e13	−1.59243
$939$	8.53172e12	0.358131
$940$	−3.07176e12	−0.128325
$941$	−3.10428e13	−1.29065	−0.645324	−	0.763909i	$-0.723278\pi$
$941$	−3.10428e13	−1.29065	−0.645324	+	0.763909i	$0.723278\pi$
$942$	4.72069e12	0.195333
$943$	2.98110e13	1.22765
$944$	3.73643e11	0.0153138
$945$	2.88336e12	0.117613
$946$	−2.65202e11	−0.0107663
$947$	1.01142e13	0.408653	0.204327	−	0.978903i	$-0.434500\pi$
$947$	1.01142e13	0.408653	0.204327	+	0.978903i	$0.434500\pi$
$948$	7.64144e12	0.307282
$949$	−5.08660e12	−0.203577
$950$	−3.78381e12	−0.150721
$951$	1.72330e13	0.683200
$952$	−3.87689e13	−1.52974
$953$	3.44106e13	1.35137	0.675685	−	0.737190i	$-0.263848\pi$
$953$	3.44106e13	1.35137	0.675685	+	0.737190i	$0.263848\pi$
$954$	−7.94052e11	−0.0310371
$955$	−2.17455e13	−0.845970
$956$	−7.27796e12	−0.281805
$957$	−2.24336e13	−0.864560
$958$	−6.74789e12	−0.258835
$959$	−5.33374e13	−2.03633
$960$	−5.36078e12	−0.203708
$961$	−1.88017e13	−0.711116
$962$	−2.79823e11	−0.0105340
$963$	−4.43407e12	−0.166144
$964$	−3.48768e12	−0.130074
$965$	1.55093e13	0.575729
$966$	−1.76449e13	−0.651961
$967$	1.44722e13	0.532251	0.266125	−	0.963938i	$-0.414256\pi$
$967$	1.44722e13	0.532251	0.266125	+	0.963938i	$0.414256\pi$
$968$	−6.05356e13	−2.21601
$969$	−5.31842e12	−0.193787
$970$	−6.11654e12	−0.221836
$971$	−2.63133e12	−0.0949922	−0.0474961	−	0.998871i	$-0.515124\pi$
$971$	−2.63133e12	−0.0949922	−0.0474961	+	0.998871i	$0.515124\pi$
$972$	−1.00710e12	−0.0361890
$973$	−6.20401e13	−2.21904
$974$	−8.32197e12	−0.296286
$975$	−5.38607e12	−0.190876
$976$	−1.21286e12	−0.0427847
$977$	−3.44811e13	−1.21075	−0.605376	−	0.795940i	$-0.706977\pi$
$977$	−3.44811e13	−1.21075	−0.605376	+	0.795940i	$0.706977\pi$
$978$	3.33442e12	0.116546
$979$	5.36534e13	1.86670
$980$	5.21709e12	0.180680
$981$	−1.44686e12	−0.0498787
$982$	2.42523e13	0.832246
$983$	1.43917e13	0.491612	0.245806	−	0.969319i	$-0.420947\pi$
$983$	1.43917e13	0.491612	0.245806	+	0.969319i	$0.420947\pi$
$984$	−1.63071e13	−0.554496
$985$	−1.81432e13	−0.614116
$986$	−1.89118e13	−0.637216
$987$	1.07581e13	0.360836
$988$	−2.10920e12	−0.0704225
$989$	3.65142e11	0.0121361
$990$	5.56406e12	0.184092
$991$	−4.60608e13	−1.51705	−0.758525	−	0.651644i	$-0.774080\pi$
$991$	−4.60608e13	−1.51705	−0.758525	+	0.651644i	$0.774080\pi$
$992$	−1.56553e13	−0.513286
$993$	1.99031e13	0.649604
$994$	3.07729e13	0.999839
$995$	−1.43112e13	−0.462884
$996$	−1.14662e13	−0.369193
$997$	−4.62562e13	−1.48266	−0.741330	−	0.671141i	$-0.765804\pi$
$997$	−4.62562e13	−1.48266	−0.741330	+	0.671141i	$0.765804\pi$
$998$	6.47207e12	0.206517
$999$	−2.27355e11	−0.00722204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.14	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+14.9387 q^{2} +81.0000 q^{3} -288.835 q^{4} -659.121 q^{5} +1210.04 q^{6} -8231.50 q^{7} -11963.4 q^{8} +6561.00 q^{9} -9846.43 q^{10} -86127.8 q^{11} -23395.6 q^{12} +43784.4 q^{13} -122968. q^{14} -53388.8 q^{15} -30835.3 q^{16} -393685. q^{17} +98013.0 q^{18} +166782. q^{19} +190377. q^{20} -666752. q^{21} -1.28664e6 q^{22} +1.77150e6 q^{23} -969039. q^{24} -1.51868e6 q^{25} +654084. q^{26} +531441. q^{27} +2.37754e6 q^{28} +3.21566e6 q^{29} -797561. q^{30} -2.76369e6 q^{31} +5.66464e6 q^{32} -6.97635e6 q^{33} -5.88115e6 q^{34} +5.42556e6 q^{35} -1.89504e6 q^{36} -427809. q^{37} +2.49151e6 q^{38} +3.54654e6 q^{39} +7.88536e6 q^{40} +1.68281e7 q^{41} -9.96042e6 q^{42} +206120. q^{43} +2.48767e7 q^{44} -4.32449e6 q^{45} +2.64639e7 q^{46} -1.61351e7 q^{47} -2.49766e6 q^{48} +2.74040e7 q^{49} -2.26872e7 q^{50} -3.18885e7 q^{51} -1.26465e7 q^{52} -8.10150e6 q^{53} +7.93905e6 q^{54} +5.67687e7 q^{55} +9.84771e7 q^{56} +1.35093e7 q^{57} +4.80379e7 q^{58} -1.21174e7 q^{59} +1.54205e7 q^{60} +3.93336e7 q^{61} -4.12860e7 q^{62} -5.40069e7 q^{63} +1.00410e8 q^{64} -2.88593e7 q^{65} -1.04218e8 q^{66} +3.07030e8 q^{67} +1.13710e8 q^{68} +1.43491e8 q^{69} +8.10509e7 q^{70} -2.50251e8 q^{71} -7.84922e7 q^{72} -1.16174e8 q^{73} -6.39091e6 q^{74} -1.23013e8 q^{75} -4.81724e7 q^{76} +7.08961e8 q^{77} +5.29808e7 q^{78} -3.26619e8 q^{79} +2.03242e7 q^{80} +4.30467e7 q^{81} +2.51390e8 q^{82} +4.90102e8 q^{83} +1.92581e8 q^{84} +2.59486e8 q^{85} +3.07917e6 q^{86} +2.60469e8 q^{87} +1.03039e9 q^{88} -6.22951e8 q^{89} -6.46024e7 q^{90} -3.60412e8 q^{91} -5.11670e8 q^{92} -2.23859e8 q^{93} -2.41038e8 q^{94} -1.09929e8 q^{95} +4.58836e8 q^{96} +6.21194e8 q^{97} +4.09381e8 q^{98} -5.65085e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \)	\( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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