LMFDB - Embedded newform 177.8.a.a.1.1

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
Defining polynomial:	$x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} - 226132003872 x^{7} - 3353576629440 x^{6} + 16796366777600 x^{5} + 99470801612800 x^{4} - 494039551757568 x^{3} - 493048066650624 x^{2} + 3193975642099712 x - 2385018853548032$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$19.7363$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-19.7363 q^{2} -27.0000 q^{3} +261.522 q^{4} -90.5952 q^{5} +532.880 q^{6} -807.818 q^{7} -2635.23 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-19.7363 q^{2} -27.0000 q^{3} +261.522 q^{4} -90.5952 q^{5} +532.880 q^{6} -807.818 q^{7} -2635.23 q^{8} +729.000 q^{9} +1788.01 q^{10} +4971.97 q^{11} -7061.09 q^{12} -2921.19 q^{13} +15943.4 q^{14} +2446.07 q^{15} +18534.9 q^{16} -29331.0 q^{17} -14387.8 q^{18} +8907.94 q^{19} -23692.6 q^{20} +21811.1 q^{21} -98128.3 q^{22} -21320.0 q^{23} +71151.2 q^{24} -69917.5 q^{25} +57653.6 q^{26} -19683.0 q^{27} -211262. q^{28} +144361. q^{29} -48276.4 q^{30} +124102. q^{31} -28500.9 q^{32} -134243. q^{33} +578885. q^{34} +73184.5 q^{35} +190649. q^{36} +249110. q^{37} -175810. q^{38} +78872.3 q^{39} +238739. q^{40} +769960. q^{41} -430470. q^{42} -214862. q^{43} +1.30028e6 q^{44} -66043.9 q^{45} +420778. q^{46} +826532. q^{47} -500442. q^{48} -170973. q^{49} +1.37991e6 q^{50} +791936. q^{51} -763956. q^{52} +791662. q^{53} +388470. q^{54} -450437. q^{55} +2.12879e6 q^{56} -240514. q^{57} -2.84915e6 q^{58} +205379. q^{59} +639701. q^{60} -2.23090e6 q^{61} -2.44931e6 q^{62} -588900. q^{63} -1.80996e6 q^{64} +264646. q^{65} +2.64947e6 q^{66} -60136.4 q^{67} -7.67069e6 q^{68} +575640. q^{69} -1.44439e6 q^{70} +3.73452e6 q^{71} -1.92108e6 q^{72} +476492. q^{73} -4.91652e6 q^{74} +1.88777e6 q^{75} +2.32962e6 q^{76} -4.01645e6 q^{77} -1.55665e6 q^{78} +1.82860e6 q^{79} -1.67917e6 q^{80} +531441. q^{81} -1.51962e7 q^{82} +4.01281e6 q^{83} +5.70408e6 q^{84} +2.65724e6 q^{85} +4.24058e6 q^{86} -3.89775e6 q^{87} -1.31023e7 q^{88} +5.38781e6 q^{89} +1.30346e6 q^{90} +2.35979e6 q^{91} -5.57565e6 q^{92} -3.35075e6 q^{93} -1.63127e7 q^{94} -807017. q^{95} +769525. q^{96} -1.52550e7 q^{97} +3.37437e6 q^{98} +3.62457e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 6q^{2} - 432q^{3} + 974q^{4} - 68q^{5} + 162q^{6} - 2343q^{7} + 819q^{8} + 11664q^{9} + O(q^{10}) $	\( 16q - 6q^{2} - 432q^{3} + 974q^{4} - 68q^{5} + 162q^{6} - 2343q^{7} + 819q^{8} + 11664q^{9} - 3479q^{10} + 898q^{11} - 26298q^{12} - 8172q^{13} - 13315q^{14} + 1836q^{15} + 3138q^{16} - 44985q^{17} - 4374q^{18} - 40137q^{19} + 130657q^{20} + 63261q^{21} + 109394q^{22} - 2833q^{23} - 22113q^{24} + 285746q^{25} - 129420q^{26} - 314928q^{27} + 112890q^{28} + 144375q^{29} + 93933q^{30} - 141759q^{31} - 36224q^{32} - 24246q^{33} - 341332q^{34} - 78859q^{35} + 710046q^{36} - 297971q^{37} + 329075q^{38} + 220644q^{39} - 203048q^{40} + 659077q^{41} + 359505q^{42} - 1431608q^{43} + 254916q^{44} - 49572q^{45} + 873113q^{46} - 1574073q^{47} - 84726q^{48} + 1893545q^{49} + 302533q^{50} + 1214595q^{51} - 4972548q^{52} + 587736q^{53} + 118098q^{54} - 4624036q^{55} - 5798506q^{56} + 1083699q^{57} - 6991380q^{58} + 3286064q^{59} - 3527739q^{60} - 6117131q^{61} - 11570258q^{62} - 1708047q^{63} - 19063011q^{64} - 5335514q^{65} - 2953638q^{66} - 16518710q^{67} - 17284669q^{68} + 76491q^{69} - 39189486q^{70} - 10882582q^{71} + 597051q^{72} - 21097441q^{73} - 16717030q^{74} - 7715142q^{75} - 40864952q^{76} - 3404601q^{77} + 3494340q^{78} - 3784458q^{79} - 27466195q^{80} + 8503056q^{81} - 24990117q^{82} - 1951425q^{83} - 3048030q^{84} - 23238675q^{85} - 35910572q^{86} - 3898125q^{87} - 27843055q^{88} + 10499443q^{89} - 2536191q^{90} + 699217q^{91} - 20062766q^{92} + 3827493q^{93} - 59358988q^{94} - 29236333q^{95} + 978048q^{96} - 25158976q^{97} + 2120460q^{98} + 654642q^{99} + O(q^{100}) \)

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 $

$2$	−19.7363	−1.74446	−0.872230	−	0.489096i	$-0.837327\pi$
$2$	−19.7363	−1.74446	−0.872230	+	0.489096i	$0.837327\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	261.522	2.04314
$5$	−90.5952	−0.324123	−0.162062	−	0.986781i	$-0.551814\pi$
$5$	−90.5952	−0.324123	−0.162062	+	0.986781i	$0.551814\pi$
$6$	532.880	1.00716
$7$	−807.818	−0.890165	−0.445083	−	0.895490i	$-0.646826\pi$
$7$	−807.818	−0.890165	−0.445083	+	0.895490i	$0.646826\pi$
$8$	−2635.23	−1.81971
$9$	729.000	0.333333
$10$	1788.01	0.565420
$11$	4971.97	1.12630	0.563150	−	0.826355i	$-0.309589\pi$
$11$	4971.97	1.12630	0.563150	+	0.826355i	$0.309589\pi$
$12$	−7061.09	−1.17961
$13$	−2921.19	−0.368773	−0.184386	−	0.982854i	$-0.559030\pi$
$13$	−2921.19	−0.368773	−0.184386	+	0.982854i	$0.559030\pi$
$14$	15943.4	1.55286
$15$	2446.07	0.187133
$16$	18534.9	1.13128
$17$	−29331.0	−1.44795	−0.723977	−	0.689824i	$-0.757688\pi$
$17$	−29331.0	−1.44795	−0.723977	+	0.689824i	$0.757688\pi$
$18$	−14387.8	−0.581487
$19$	8907.94	0.297948	0.148974	−	0.988841i	$-0.452403\pi$
$19$	8907.94	0.297948	0.148974	+	0.988841i	$0.452403\pi$
$20$	−23692.6	−0.662229
$21$	21811.1	0.513937
$22$	−98128.3	−1.96479
$23$	−21320.0	−0.365376	−0.182688	−	0.983171i	$-0.558480\pi$
$23$	−21320.0	−0.365376	−0.182688	+	0.983171i	$0.558480\pi$
$24$	71151.2	1.05061
$25$	−69917.5	−0.894944
$26$	57653.6	0.643309
$27$	−19683.0	−0.192450
$28$	−211262.	−1.81873
$29$	144361.	1.09915	0.549575	−	0.835444i	$-0.314790\pi$
$29$	144361.	1.09915	0.549575	+	0.835444i	$0.314790\pi$
$30$	−48276.4	−0.326445
$31$	124102.	0.748190	0.374095	−	0.927390i	$-0.377953\pi$
$31$	124102.	0.748190	0.374095	+	0.927390i	$0.377953\pi$
$32$	−28500.9	−0.153757
$33$	−134243.	−0.650270
$34$	578885.	2.52590
$35$	73184.5	0.288523
$36$	190649.	0.681047
$37$	249110.	0.808510	0.404255	−	0.914646i	$-0.367531\pi$
$37$	249110.	0.808510	0.404255	+	0.914646i	$0.367531\pi$
$38$	−175810.	−0.519757
$39$	78872.3	0.212911
$40$	238739.	0.589812
$41$	769960.	1.74472	0.872358	−	0.488867i	$-0.162590\pi$
$41$	769960.	1.74472	0.872358	+	0.488867i	$0.162590\pi$
$42$	−430470.	−0.896542
$43$	−214862.	−0.412116	−0.206058	−	0.978540i	$-0.566064\pi$
$43$	−214862.	−0.412116	−0.206058	+	0.978540i	$0.566064\pi$
$44$	1.30028e6	2.30119
$45$	−66043.9	−0.108041
$46$	420778.	0.637383
$47$	826532.	1.16123	0.580614	−	0.814179i	$-0.302813\pi$
$47$	826532.	1.16123	0.580614	+	0.814179i	$0.302813\pi$
$48$	−500442.	−0.653145
$49$	−170973.	−0.207606
$50$	1.37991e6	1.56119
$51$	791936.	0.835977
$52$	−763956.	−0.753454
$53$	791662.	0.730423	0.365211	−	0.930925i	$-0.380997\pi$
$53$	791662.	0.730423	0.365211	+	0.930925i	$0.380997\pi$
$54$	388470.	0.335721
$55$	−450437.	−0.365060
$56$	2.12879e6	1.61985
$57$	−240514.	−0.172020
$58$	−2.84915e6	−1.91742
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	639701.	0.382338
$61$	−2.23090e6	−1.25842	−0.629210	−	0.777236i	$-0.716621\pi$
$61$	−2.23090e6	−1.25842	−0.629210	+	0.777236i	$0.716621\pi$
$62$	−2.44931e6	−1.30519
$63$	−588900.	−0.296722
$64$	−1.80996e6	−0.863057
$65$	264646.	0.119528
$66$	2.64947e6	1.13437
$67$	−60136.4	−0.0244273	−0.0122137	−	0.999925i	$-0.503888\pi$
$67$	−60136.4	−0.0244273	−0.0122137	+	0.999925i	$0.503888\pi$
$68$	−7.67069e6	−2.95837
$69$	575640.	0.210950
$70$	−1.44439e6	−0.503317
$71$	3.73452e6	1.23831	0.619157	−	0.785268i	$-0.287475\pi$
$71$	3.73452e6	1.23831	0.619157	+	0.785268i	$0.287475\pi$
$72$	−1.92108e6	−0.606572
$73$	476492.	0.143359	0.0716796	−	0.997428i	$-0.477164\pi$
$73$	476492.	0.143359	0.0716796	+	0.997428i	$0.477164\pi$
$74$	−4.91652e6	−1.41041
$75$	1.88777e6	0.516696
$76$	2.32962e6	0.608748
$77$	−4.01645e6	−1.00259
$78$	−1.55665e6	−0.371415
$79$	1.82860e6	0.417277	0.208638	−	0.977993i	$-0.433097\pi$
$79$	1.82860e6	0.417277	0.208638	+	0.977993i	$0.433097\pi$
$80$	−1.67917e6	−0.366674
$81$	531441.	0.111111
$82$	−1.51962e7	−3.04359
$83$	4.01281e6	0.770327	0.385164	−	0.922848i	$-0.374145\pi$
$83$	4.01281e6	0.770327	0.385164	+	0.922848i	$0.374145\pi$
$84$	5.70408e6	1.05005
$85$	2.65724e6	0.469316
$86$	4.24058e6	0.718920
$87$	−3.89775e6	−0.634595
$88$	−1.31023e7	−2.04955
$89$	5.38781e6	0.810116	0.405058	−	0.914291i	$-0.367251\pi$
$89$	5.38781e6	0.810116	0.405058	+	0.914291i	$0.367251\pi$
$90$	1.30346e6	0.188473
$91$	2.35979e6	0.328269
$92$	−5.57565e6	−0.746514
$93$	−3.35075e6	−0.431968
$94$	−1.63127e7	−2.02571
$95$	−807017.	−0.0965717
$96$	769525.	0.0887715
$97$	−1.52550e7	−1.69711	−0.848556	−	0.529106i	$-0.822527\pi$
$97$	−1.52550e7	−1.69711	−0.848556	+	0.529106i	$0.822527\pi$
$98$	3.37437e6	0.362160
$99$	3.62457e6	0.375433
$100$	−1.82850e7	−1.82850
$101$	−1.51903e7	−1.46703	−0.733517	−	0.679671i	$-0.762123\pi$
$101$	−1.51903e7	−1.46703	−0.733517	+	0.679671i	$0.762123\pi$
$102$	−1.56299e7	−1.45833
$103$	−7.35870e6	−0.663546	−0.331773	−	0.943359i	$-0.607647\pi$
$103$	−7.35870e6	−0.663546	−0.331773	+	0.943359i	$0.607647\pi$
$104$	7.69802e6	0.671061
$105$	−1.97598e6	−0.166579
$106$	−1.56245e7	−1.27419
$107$	−3.56527e6	−0.281352	−0.140676	−	0.990056i	$-0.544928\pi$
$107$	−3.56527e6	−0.281352	−0.140676	+	0.990056i	$0.544928\pi$
$108$	−5.14753e6	−0.393202
$109$	1.51208e7	1.11836	0.559179	−	0.829047i	$-0.311116\pi$
$109$	1.51208e7	1.11836	0.559179	+	0.829047i	$0.311116\pi$
$110$	8.88996e6	0.636833
$111$	−6.72598e6	−0.466794
$112$	−1.49728e7	−1.00703
$113$	−2.38727e7	−1.55642	−0.778212	−	0.628002i	$-0.783873\pi$
$113$	−2.38727e7	−1.55642	−0.778212	+	0.628002i	$0.783873\pi$
$114$	4.74687e6	0.300082
$115$	1.93149e6	0.118427
$116$	3.77536e7	2.24572
$117$	−2.12955e6	−0.122924
$118$	−4.05342e6	−0.227109
$119$	2.36941e7	1.28892
$120$	−6.44595e6	−0.340528
$121$	5.23332e6	0.268552
$122$	4.40297e7	2.19526
$123$	−2.07889e7	−1.00731
$124$	3.24553e7	1.52866
$125$	1.34119e7	0.614195
$126$	1.16227e7	0.517619
$127$	6.26438e6	0.271372	0.135686	−	0.990752i	$-0.456676\pi$
$127$	6.26438e6	0.271372	0.135686	+	0.990752i	$0.456676\pi$
$128$	3.93701e7	1.65933
$129$	5.80127e6	0.237935
$130$	−5.22314e6	−0.208511
$131$	−2.94087e7	−1.14295	−0.571474	−	0.820620i	$-0.693628\pi$
$131$	−2.94087e7	−1.14295	−0.571474	+	0.820620i	$0.693628\pi$
$132$	−3.51075e7	−1.32859
$133$	−7.19600e6	−0.265222
$134$	1.18687e6	0.0426124
$135$	1.78319e6	0.0623776
$136$	7.72938e7	2.63486
$137$	−4.62523e6	−0.153678	−0.0768390	−	0.997044i	$-0.524483\pi$
$137$	−4.62523e6	−0.153678	−0.0768390	+	0.997044i	$0.524483\pi$
$138$	−1.13610e7	−0.367993
$139$	−1.29866e7	−0.410152	−0.205076	−	0.978746i	$-0.565744\pi$
$139$	−1.29866e7	−0.410152	−0.205076	+	0.978746i	$0.565744\pi$
$140$	1.91393e7	0.589493
$141$	−2.23164e7	−0.670435
$142$	−7.37056e7	−2.16019
$143$	−1.45241e7	−0.415349
$144$	1.35119e7	0.377093
$145$	−1.30784e7	−0.356260
$146$	−9.40419e6	−0.250084
$147$	4.61626e6	0.119861
$148$	6.51478e7	1.65190
$149$	−6.03191e7	−1.49384	−0.746918	−	0.664917i	$-0.768467\pi$
$149$	−6.03191e7	−1.49384	−0.746918	+	0.664917i	$0.768467\pi$
$150$	−3.72577e7	−0.901356
$151$	−9.08405e6	−0.214714	−0.107357	−	0.994221i	$-0.534239\pi$
$151$	−9.08405e6	−0.214714	−0.107357	+	0.994221i	$0.534239\pi$
$152$	−2.34745e7	−0.542180
$153$	−2.13823e7	−0.482652
$154$	7.92699e7	1.74898
$155$	−1.12430e7	−0.242506
$156$	2.06268e7	0.435007
$157$	5.23075e7	1.07874	0.539368	−	0.842070i	$-0.318663\pi$
$157$	5.23075e7	1.07874	0.539368	+	0.842070i	$0.318663\pi$
$158$	−3.60898e7	−0.727923
$159$	−2.13749e7	−0.421710
$160$	2.58205e6	0.0498361
$161$	1.72227e7	0.325245
$162$	−1.04887e7	−0.193829
$163$	1.85380e7	0.335280	0.167640	−	0.985848i	$-0.446385\pi$
$163$	1.85380e7	0.335280	0.167640	+	0.985848i	$0.446385\pi$
$164$	2.01361e8	3.56470
$165$	1.21618e7	0.210768
$166$	−7.91980e7	−1.34380
$167$	1.04169e7	0.173074	0.0865369	−	0.996249i	$-0.472420\pi$
$167$	1.04169e7	0.173074	0.0865369	+	0.996249i	$0.472420\pi$
$168$	−5.74772e7	−0.935219
$169$	−5.42151e7	−0.864007
$170$	−5.24442e7	−0.818703
$171$	6.49389e6	0.0993158
$172$	−5.61911e7	−0.842011
$173$	7.37218e7	1.08252	0.541259	−	0.840856i	$-0.317948\pi$
$173$	7.37218e7	1.08252	0.541259	+	0.840856i	$0.317948\pi$
$174$	7.69272e7	1.10703
$175$	5.64806e7	0.796648
$176$	9.21549e7	1.27416
$177$	−5.54523e6	−0.0751646
$178$	−1.06335e8	−1.41321
$179$	−9.01187e7	−1.17444	−0.587218	−	0.809429i	$-0.699777\pi$
$179$	−9.01187e7	−1.17444	−0.587218	+	0.809429i	$0.699777\pi$
$180$	−1.72719e7	−0.220743
$181$	5.95539e7	0.746509	0.373255	−	0.927729i	$-0.378242\pi$
$181$	5.95539e7	0.746509	0.373255	+	0.927729i	$0.378242\pi$
$182$	−4.65736e7	−0.572651
$183$	6.02343e7	0.726549
$184$	5.61831e7	0.664880
$185$	−2.25682e7	−0.262057
$186$	6.61314e7	0.753551
$187$	−1.45833e8	−1.63083
$188$	2.16156e8	2.37255
$189$	1.59003e7	0.171312
$190$	1.59275e7	0.168465
$191$	8.79003e7	0.912795	0.456398	−	0.889776i	$-0.349139\pi$
$191$	8.79003e7	0.912795	0.456398	+	0.889776i	$0.349139\pi$
$192$	4.88690e7	0.498286
$193$	9.19947e7	0.921112	0.460556	−	0.887631i	$-0.347650\pi$
$193$	9.19947e7	0.921112	0.460556	+	0.887631i	$0.347650\pi$
$194$	3.01077e8	2.96054
$195$	−7.14545e6	−0.0690094
$196$	−4.47131e7	−0.424168
$197$	−9.51132e7	−0.886357	−0.443179	−	0.896433i	$-0.646149\pi$
$197$	−9.51132e7	−0.886357	−0.443179	+	0.896433i	$0.646149\pi$
$198$	−7.15356e7	−0.654928
$199$	−9.84642e7	−0.885712	−0.442856	−	0.896593i	$-0.646035\pi$
$199$	−9.84642e7	−0.885712	−0.442856	+	0.896593i	$0.646035\pi$
$200$	1.84249e8	1.62854
$201$	1.62368e6	0.0141031
$202$	2.99800e8	2.55918
$203$	−1.16618e8	−0.978425
$204$	2.07109e8	1.70802
$205$	−6.97547e7	−0.565503
$206$	1.45234e8	1.15753
$207$	−1.55423e7	−0.121792
$208$	−5.41440e7	−0.417185
$209$	4.42900e7	0.335578
$210$	3.89986e7	0.290590
$211$	−1.85405e8	−1.35873	−0.679364	−	0.733802i	$-0.737744\pi$
$211$	−1.85405e8	−1.35873	−0.679364	+	0.733802i	$0.737744\pi$
$212$	2.07037e8	1.49236
$213$	−1.00832e8	−0.714940
$214$	7.03654e7	0.490807
$215$	1.94655e7	0.133576
$216$	5.18692e7	0.350204
$217$	−1.00252e8	−0.666013
$218$	−2.98428e8	−1.95093
$219$	−1.28653e7	−0.0827685
$220$	−1.17799e8	−0.745869
$221$	8.56814e7	0.533966
$222$	1.32746e8	0.814303
$223$	−5.33953e7	−0.322431	−0.161215	−	0.986919i	$-0.551541\pi$
$223$	−5.33953e7	−0.322431	−0.161215	+	0.986919i	$0.551541\pi$
$224$	2.30236e7	0.136869
$225$	−5.09699e7	−0.298315
$226$	4.71160e8	2.71512
$227$	−7.79437e7	−0.442273	−0.221137	−	0.975243i	$-0.570977\pi$
$227$	−7.79437e7	−0.442273	−0.221137	+	0.975243i	$0.570977\pi$
$228$	−6.28998e7	−0.351461
$229$	−2.50546e7	−0.137868	−0.0689340	−	0.997621i	$-0.521960\pi$
$229$	−2.50546e7	−0.137868	−0.0689340	+	0.997621i	$0.521960\pi$
$230$	−3.81205e7	−0.206591
$231$	1.08444e8	0.578847
$232$	−3.80424e8	−2.00014
$233$	2.23037e8	1.15513	0.577567	−	0.816344i	$-0.304002\pi$
$233$	2.23037e8	1.15513	0.577567	+	0.816344i	$0.304002\pi$
$234$	4.20295e7	0.214436
$235$	−7.48799e7	−0.376381
$236$	5.37111e7	0.265994
$237$	−4.93722e7	−0.240915
$238$	−4.67634e8	−2.24847
$239$	−1.46524e8	−0.694249	−0.347124	−	0.937819i	$-0.612842\pi$
$239$	−1.46524e8	−0.694249	−0.347124	+	0.937819i	$0.612842\pi$
$240$	4.53376e7	0.211699
$241$	−5.35245e7	−0.246316	−0.123158	−	0.992387i	$-0.539302\pi$
$241$	−5.35245e7	−0.246316	−0.123158	+	0.992387i	$0.539302\pi$
$242$	−1.03286e8	−0.468478
$243$	−1.43489e7	−0.0641500
$244$	−5.83429e8	−2.57113
$245$	1.54893e7	0.0672900
$246$	4.10297e8	1.75722
$247$	−2.60218e7	−0.109875
$248$	−3.27037e8	−1.36149
$249$	−1.08346e8	−0.444749
$250$	−2.64702e8	−1.07144
$251$	−3.32032e8	−1.32532	−0.662661	−	0.748919i	$-0.730573\pi$
$251$	−3.32032e8	−1.32532	−0.662661	+	0.748919i	$0.730573\pi$
$252$	−1.54010e8	−0.606244
$253$	−1.06002e8	−0.411523
$254$	−1.23636e8	−0.473398
$255$	−7.17456e7	−0.270960
$256$	−5.45345e8	−2.03157
$257$	3.09916e8	1.13888	0.569441	−	0.822032i	$-0.307160\pi$
$257$	3.09916e8	1.13888	0.569441	+	0.822032i	$0.307160\pi$
$258$	−1.14496e8	−0.415069
$259$	−2.01236e8	−0.719708
$260$	6.92108e7	0.244212
$261$	1.05239e8	0.366383
$262$	5.80419e8	1.99383
$263$	−8.42828e7	−0.285689	−0.142845	−	0.989745i	$-0.545625\pi$
$263$	−8.42828e7	−0.285689	−0.142845	+	0.989745i	$0.545625\pi$
$264$	3.53762e8	1.18331
$265$	−7.17208e7	−0.236747
$266$	1.42022e8	0.462670
$267$	−1.45471e8	−0.467721
$268$	−1.57270e7	−0.0499084
$269$	−1.91871e8	−0.601001	−0.300501	−	0.953782i	$-0.597154\pi$
$269$	−1.91871e8	−0.601001	−0.300501	+	0.953782i	$0.597154\pi$
$270$	−3.51935e7	−0.108815
$271$	−7.09645e6	−0.0216595	−0.0108298	−	0.999941i	$-0.503447\pi$
$271$	−7.09645e6	−0.0216595	−0.0108298	+	0.999941i	$0.503447\pi$
$272$	−5.43646e8	−1.63804
$273$	−6.37145e7	−0.189526
$274$	9.12851e7	0.268085
$275$	−3.47628e8	−1.00798
$276$	1.50542e8	0.431000
$277$	−2.59631e8	−0.733968	−0.366984	−	0.930227i	$-0.619610\pi$
$277$	−2.59631e8	−0.733968	−0.366984	+	0.930227i	$0.619610\pi$
$278$	2.56308e8	0.715493
$279$	9.04702e7	0.249397
$280$	−1.92858e8	−0.525030
$281$	−4.92572e7	−0.132433	−0.0662167	−	0.997805i	$-0.521093\pi$
$281$	−4.92572e7	−0.132433	−0.0662167	+	0.997805i	$0.521093\pi$
$282$	4.40443e8	1.16955
$283$	−1.62830e8	−0.427053	−0.213526	−	0.976937i	$-0.568495\pi$
$283$	−1.62830e8	−0.427053	−0.213526	+	0.976937i	$0.568495\pi$
$284$	9.76658e8	2.53005
$285$	2.17895e7	0.0557557
$286$	2.86652e8	0.724559
$287$	−6.21988e8	−1.55309
$288$	−2.07772e7	−0.0512522
$289$	4.49966e8	1.09657
$290$	2.58120e8	0.621482
$291$	4.11884e8	0.979828
$292$	1.24613e8	0.292903
$293$	−5.14011e8	−1.19381	−0.596905	−	0.802312i	$-0.703603\pi$
$293$	−5.14011e8	−1.19381	−0.596905	+	0.802312i	$0.703603\pi$
$294$	−9.11079e7	−0.209093
$295$	−1.86064e7	−0.0421973
$296$	−6.56462e8	−1.47126
$297$	−9.78633e7	−0.216757
$298$	1.19048e9	2.60594
$299$	6.22799e7	0.134741
$300$	4.93694e8	1.05568
$301$	1.73569e8	0.366852
$302$	1.79286e8	0.374560
$303$	4.10137e8	0.846993
$304$	1.65108e8	0.337062
$305$	2.02109e8	0.407883
$306$	4.22007e8	0.841966
$307$	1.27895e8	0.252272	0.126136	−	0.992013i	$-0.459742\pi$
$307$	1.27895e8	0.252272	0.126136	+	0.992013i	$0.459742\pi$
$308$	−1.05039e9	−2.04844
$309$	1.98685e8	0.383098
$310$	2.21896e8	0.423042
$311$	6.02895e8	1.13653	0.568264	−	0.822846i	$-0.307615\pi$
$311$	6.02895e8	1.13653	0.568264	+	0.822846i	$0.307615\pi$
$312$	−2.07846e8	−0.387437
$313$	−8.09308e8	−1.49179	−0.745897	−	0.666061i	$-0.767979\pi$
$313$	−8.09308e8	−1.49179	−0.745897	+	0.666061i	$0.767979\pi$
$314$	−1.03236e9	−1.88181
$315$	5.33515e7	0.0961744
$316$	4.78219e8	0.852555
$317$	9.39100e7	0.165579	0.0827893	−	0.996567i	$-0.473617\pi$
$317$	9.39100e7	0.165579	0.0827893	+	0.996567i	$0.473617\pi$
$318$	4.21861e8	0.735655
$319$	7.17759e8	1.23797
$320$	1.63974e8	0.279737
$321$	9.62624e7	0.162439
$322$	−3.39912e8	−0.567376
$323$	−2.61278e8	−0.431415
$324$	1.38983e8	0.227016
$325$	2.04243e8	0.330031
$326$	−3.65873e8	−0.584882
$327$	−4.08260e8	−0.645684
$328$	−2.02902e9	−3.17489
$329$	−6.67688e8	−1.03368
$330$	−2.40029e8	−0.367675
$331$	9.98609e8	1.51355	0.756776	−	0.653674i	$-0.226773\pi$
$331$	9.98609e8	1.51355	0.756776	+	0.653674i	$0.226773\pi$
$332$	1.04944e9	1.57389
$333$	1.81601e8	0.269503
$334$	−2.05591e8	−0.301920
$335$	5.44807e6	0.00791746
$336$	4.04266e8	0.581406
$337$	1.07195e9	1.52570	0.762851	−	0.646575i	$-0.223799\pi$
$337$	1.07195e9	1.52570	0.762851	+	0.646575i	$0.223799\pi$
$338$	1.07001e9	1.50722
$339$	6.44564e8	0.898602
$340$	6.94927e8	0.958878
$341$	6.17030e8	0.842687
$342$	−1.28165e8	−0.173252
$343$	8.03388e8	1.07497
$344$	5.66210e8	0.749934
$345$	−5.21502e7	−0.0683737
$346$	−1.45500e9	−1.88841
$347$	−1.06764e9	−1.37174	−0.685869	−	0.727725i	$-0.740578\pi$
$347$	−1.06764e9	−1.37174	−0.685869	+	0.727725i	$0.740578\pi$
$348$	−1.01935e9	−1.29657
$349$	−1.09465e9	−1.37843	−0.689216	−	0.724556i	$-0.742045\pi$
$349$	−1.09465e9	−1.37843	−0.689216	+	0.724556i	$0.742045\pi$
$350$	−1.11472e9	−1.38972
$351$	5.74979e7	0.0709703
$352$	−1.41706e8	−0.173176
$353$	−2.65164e8	−0.320851	−0.160426	−	0.987048i	$-0.551287\pi$
$353$	−2.65164e8	−0.320851	−0.160426	+	0.987048i	$0.551287\pi$
$354$	1.09442e8	0.131122
$355$	−3.38330e8	−0.401366
$356$	1.40903e9	1.65518
$357$	−6.39740e8	−0.744158
$358$	1.77861e9	2.04876
$359$	−7.74082e8	−0.882992	−0.441496	−	0.897263i	$-0.645552\pi$
$359$	−7.74082e8	−0.882992	−0.441496	+	0.897263i	$0.645552\pi$
$360$	1.74041e8	0.196604
$361$	−8.14520e8	−0.911227
$362$	−1.17537e9	−1.30226
$363$	−1.41300e8	−0.155049
$364$	6.17138e8	0.670699
$365$	−4.31679e7	−0.0464660
$366$	−1.18880e9	−1.26744
$367$	6.18045e8	0.652663	0.326331	−	0.945255i	$-0.394187\pi$
$367$	6.18045e8	0.652663	0.326331	+	0.945255i	$0.394187\pi$
$368$	−3.95164e8	−0.413342
$369$	5.61301e8	0.581572
$370$	4.45413e8	0.457148
$371$	−6.39519e8	−0.650197
$372$	−8.76294e8	−0.882571
$373$	−2.27726e7	−0.0227212	−0.0113606	−	0.999935i	$-0.503616\pi$
$373$	−2.27726e7	−0.0227212	−0.0113606	+	0.999935i	$0.503616\pi$
$374$	2.87820e9	2.84492
$375$	−3.62122e8	−0.354606
$376$	−2.17810e9	−2.11310
$377$	−4.21707e8	−0.405337
$378$	−3.13813e8	−0.298847
$379$	−9.75855e8	−0.920763	−0.460382	−	0.887721i	$-0.652287\pi$
$379$	−9.75855e8	−0.920763	−0.460382	+	0.887721i	$0.652287\pi$
$380$	−2.11053e8	−0.197310
$381$	−1.69138e8	−0.156677
$382$	−1.73483e9	−1.59233
$383$	−8.32929e8	−0.757552	−0.378776	−	0.925488i	$-0.623655\pi$
$383$	−8.32929e8	−0.757552	−0.378776	+	0.925488i	$0.623655\pi$
$384$	−1.06299e9	−0.958012
$385$	3.63871e8	0.324964
$386$	−1.81564e9	−1.60684
$387$	−1.56634e8	−0.137372
$388$	−3.98951e9	−3.46744
$389$	−1.77468e8	−0.152861	−0.0764304	−	0.997075i	$-0.524352\pi$
$389$	−1.77468e8	−0.152861	−0.0764304	+	0.997075i	$0.524352\pi$
$390$	1.41025e8	0.120384
$391$	6.25336e8	0.529048
$392$	4.50552e8	0.377784
$393$	7.94035e8	0.659881
$394$	1.87718e9	1.54621
$395$	−1.65663e8	−0.135249
$396$	9.47903e8	0.767063
$397$	−1.50894e9	−1.21033	−0.605166	−	0.796099i	$-0.706893\pi$
$397$	−1.50894e9	−1.21033	−0.605166	+	0.796099i	$0.706893\pi$
$398$	1.94332e9	1.54509
$399$	1.94292e8	0.153126
$400$	−1.29591e9	−1.01243
$401$	1.77996e9	1.37850	0.689248	−	0.724525i	$-0.257941\pi$
$401$	1.77996e9	1.37850	0.689248	+	0.724525i	$0.257941\pi$
$402$	−3.20455e7	−0.0246023
$403$	−3.62525e8	−0.275912
$404$	−3.97258e9	−2.99736
$405$	−4.81460e7	−0.0360137
$406$	2.30160e9	1.70682
$407$	1.23857e9	0.910625
$408$	−2.08693e9	−1.52124
$409$	1.01746e9	0.735335	0.367667	−	0.929957i	$-0.380157\pi$
$409$	1.01746e9	0.735335	0.367667	+	0.929957i	$0.380157\pi$
$410$	1.37670e9	0.986497
$411$	1.24881e8	0.0887260
$412$	−1.92446e9	−1.35572
$413$	−1.65909e8	−0.115890
$414$	3.06747e8	0.212461
$415$	−3.63541e8	−0.249681
$416$	8.32568e7	0.0567013
$417$	3.50639e8	0.236801
$418$	−8.74122e8	−0.585403
$419$	−1.28968e9	−0.856514	−0.428257	−	0.903657i	$-0.640872\pi$
$419$	−1.28968e9	−0.856514	−0.428257	+	0.903657i	$0.640872\pi$
$420$	−5.16762e8	−0.340344
$421$	5.35636e8	0.349851	0.174925	−	0.984582i	$-0.444032\pi$
$421$	5.35636e8	0.349851	0.174925	+	0.984582i	$0.444032\pi$
$422$	3.65921e9	2.37025
$423$	6.02542e8	0.387076
$424$	−2.08621e9	−1.32916
$425$	2.05075e9	1.29584
$426$	1.99005e9	1.24718
$427$	1.80216e9	1.12020
$428$	−9.32397e8	−0.574841
$429$	3.92151e8	0.239802
$430$	−3.84176e8	−0.233019
$431$	−2.75089e9	−1.65502	−0.827509	−	0.561452i	$-0.810243\pi$
$431$	−2.75089e9	−1.65502	−0.827509	+	0.561452i	$0.810243\pi$
$432$	−3.64822e8	−0.217715
$433$	8.00172e8	0.473670	0.236835	−	0.971550i	$-0.423890\pi$
$433$	8.00172e8	0.473670	0.236835	+	0.971550i	$0.423890\pi$
$434$	1.97860e9	1.16183
$435$	3.53117e8	0.205687
$436$	3.95441e9	2.28496
$437$	−1.89917e8	−0.108863
$438$	2.53913e8	0.144386
$439$	7.72445e8	0.435754	0.217877	−	0.975976i	$-0.430087\pi$
$439$	7.72445e8	0.435754	0.217877	+	0.975976i	$0.430087\pi$
$440$	1.18700e9	0.664305
$441$	−1.24639e8	−0.0692020
$442$	−1.69104e9	−0.931483
$443$	2.85561e9	1.56058	0.780289	−	0.625419i	$-0.215072\pi$
$443$	2.85561e9	1.56058	0.780289	+	0.625419i	$0.215072\pi$
$444$	−1.75899e9	−0.953724
$445$	−4.88110e8	−0.262577
$446$	1.05383e9	0.562467
$447$	1.62861e9	0.862466
$448$	1.46212e9	0.768263
$449$	1.99990e9	1.04267	0.521334	−	0.853352i	$-0.325434\pi$
$449$	1.99990e9	1.04267	0.521334	+	0.853352i	$0.325434\pi$
$450$	1.00596e9	0.520398
$451$	3.82822e9	1.96507
$452$	−6.24324e9	−3.17999
$453$	2.45269e8	0.123965
$454$	1.53832e9	0.771528
$455$	−2.13786e8	−0.106399
$456$	6.33811e8	0.313027
$457$	−1.08512e9	−0.531829	−0.265915	−	0.963997i	$-0.585674\pi$
$457$	−1.08512e9	−0.531829	−0.265915	+	0.963997i	$0.585674\pi$
$458$	4.94485e8	0.240505
$459$	5.77321e8	0.278659
$460$	5.05127e8	0.241962
$461$	−3.43732e9	−1.63405	−0.817027	−	0.576600i	$-0.804379\pi$
$461$	−3.43732e9	−1.63405	−0.817027	+	0.576600i	$0.804379\pi$
$462$	−2.14029e9	−1.00978
$463$	−2.83083e9	−1.32550	−0.662750	−	0.748840i	$-0.730611\pi$
$463$	−2.83083e9	−1.32550	−0.662750	+	0.748840i	$0.730611\pi$
$464$	2.67572e9	1.24345
$465$	3.03562e8	0.140011
$466$	−4.40194e9	−2.01508
$467$	−1.27289e9	−0.578337	−0.289169	−	0.957278i	$-0.593379\pi$
$467$	−1.27289e9	−0.578337	−0.289169	+	0.957278i	$0.593379\pi$
$468$	−5.56924e8	−0.251151
$469$	4.85793e7	0.0217443
$470$	1.47785e9	0.656581
$471$	−1.41230e9	−0.622809
$472$	−5.41221e8	−0.236907
$473$	−1.06829e9	−0.464167
$474$	9.74426e8	0.420266
$475$	−6.22821e8	−0.266646
$476$	6.19652e9	2.63344
$477$	5.77121e8	0.243474
$478$	2.89184e9	1.21109
$479$	−1.83875e9	−0.764448	−0.382224	−	0.924070i	$-0.624842\pi$
$479$	−1.83875e9	−0.764448	−0.382224	+	0.924070i	$0.624842\pi$
$480$	−6.97153e7	−0.0287729
$481$	−7.27699e8	−0.298156
$482$	1.05638e9	0.429689
$483$	−4.65013e8	−0.187780
$484$	1.36863e9	0.548689
$485$	1.38203e9	0.550073
$486$	2.83194e8	0.111907
$487$	−1.80837e9	−0.709473	−0.354736	−	0.934966i	$-0.615429\pi$
$487$	−1.80837e9	−0.709473	−0.354736	+	0.934966i	$0.615429\pi$
$488$	5.87893e9	2.28996
$489$	−5.00527e8	−0.193574
$490$	−3.05701e8	−0.117385
$491$	3.14661e9	1.19966	0.599829	−	0.800128i	$-0.295235\pi$
$491$	3.14661e9	1.19966	0.599829	+	0.800128i	$0.295235\pi$
$492$	−5.43676e9	−2.05808
$493$	−4.23425e9	−1.59152
$494$	5.13575e8	0.191672
$495$	−3.28368e8	−0.121687
$496$	2.30021e9	0.846412
$497$	−3.01681e9	−1.10230
$498$	2.13835e9	0.775846
$499$	2.26779e9	0.817056	0.408528	−	0.912746i	$-0.366042\pi$
$499$	2.26779e9	0.817056	0.408528	+	0.912746i	$0.366042\pi$
$500$	3.50752e9	1.25489
$501$	−2.81257e8	−0.0999242
$502$	6.55308e9	2.31197
$503$	1.65622e9	0.580270	0.290135	−	0.956986i	$-0.406300\pi$
$503$	1.65622e9	0.580270	0.290135	+	0.956986i	$0.406300\pi$
$504$	1.55188e9	0.539949
$505$	1.37616e9	0.475500
$506$	2.09210e9	0.717885
$507$	1.46381e9	0.498834
$508$	1.63827e9	0.554451
$509$	5.27031e9	1.77143	0.885715	−	0.464229i	$-0.153668\pi$
$509$	5.27031e9	1.77143	0.885715	+	0.464229i	$0.153668\pi$
$510$	1.41599e9	0.472678
$511$	−3.84919e8	−0.127613
$512$	5.72373e9	1.88466
$513$	−1.75335e8	−0.0573400
$514$	−6.11660e9	−1.98673
$515$	6.66663e8	0.215071
$516$	1.51716e9	0.486135
$517$	4.10949e9	1.30789
$518$	3.97165e9	1.25550
$519$	−1.99049e9	−0.624992
$520$	−6.97403e8	−0.217507
$521$	−1.06833e9	−0.330957	−0.165478	−	0.986213i	$-0.552917\pi$
$521$	−1.06833e9	−0.330957	−0.165478	+	0.986213i	$0.552917\pi$
$522$	−2.07703e9	−0.639141
$523$	−4.88919e9	−1.49445	−0.747225	−	0.664572i	$-0.768614\pi$
$523$	−4.88919e9	−1.49445	−0.747225	+	0.664572i	$0.768614\pi$
$524$	−7.69102e9	−2.33520
$525$	−1.52498e9	−0.459945
$526$	1.66343e9	0.498374
$527$	−3.64002e9	−1.08335
$528$	−2.48818e9	−0.735637
$529$	−2.95028e9	−0.866500
$530$	1.41550e9	0.412995
$531$	1.49721e8	0.0433963
$532$	−1.88191e9	−0.541887
$533$	−2.24920e9	−0.643404
$534$	2.87106e9	0.815920
$535$	3.22997e8	0.0911927
$536$	1.58473e8	0.0444507
$537$	2.43320e9	0.678061
$538$	3.78682e9	1.04842
$539$	−8.50070e8	−0.233827
$540$	4.66342e8	0.127446
$541$	2.76671e9	0.751231	0.375615	−	0.926776i	$-0.377431\pi$
$541$	2.76671e9	0.751231	0.375615	+	0.926776i	$0.377431\pi$
$542$	1.40058e8	0.0377842
$543$	−1.60796e9	−0.430997
$544$	8.35960e8	0.222633
$545$	−1.36987e9	−0.362486
$546$	1.25749e9	0.330620
$547$	−5.33645e9	−1.39411	−0.697054	−	0.717018i	$-0.745506\pi$
$547$	−5.33645e9	−1.39411	−0.697054	+	0.717018i	$0.745506\pi$
$548$	−1.20960e9	−0.313986
$549$	−1.62633e9	−0.419473
$550$	6.86089e9	1.75837
$551$	1.28596e9	0.327489
$552$	−1.51694e9	−0.383869
$553$	−1.47718e9	−0.371445
$554$	5.12416e9	1.28038
$555$	6.09341e8	0.151299
$556$	−3.39629e9	−0.837998
$557$	−4.61945e8	−0.113265	−0.0566326	−	0.998395i	$-0.518036\pi$
$557$	−4.61945e8	−0.113265	−0.0566326	+	0.998395i	$0.518036\pi$
$558$	−1.78555e9	−0.435063
$559$	6.27653e8	0.151977
$560$	1.35647e9	0.326400
$561$	3.93748e9	0.941561
$562$	9.72156e8	0.231025
$563$	5.71818e9	1.35045	0.675224	−	0.737612i	$-0.264047\pi$
$563$	5.71818e9	1.35045	0.675224	+	0.737612i	$0.264047\pi$
$564$	−5.83622e9	−1.36979
$565$	2.16276e9	0.504473
$566$	3.21366e9	0.744976
$567$	−4.29308e8	−0.0989072
$568$	−9.84131e9	−2.25338
$569$	−5.60950e9	−1.27653	−0.638265	−	0.769816i	$-0.720348\pi$
$569$	−5.60950e9	−1.27653	−0.638265	+	0.769816i	$0.720348\pi$
$570$	−4.30043e8	−0.0972636
$571$	3.21411e9	0.722494	0.361247	−	0.932470i	$-0.382351\pi$
$571$	3.21411e9	0.722494	0.361247	+	0.932470i	$0.382351\pi$
$572$	−3.79837e9	−0.848615
$573$	−2.37331e9	−0.527003
$574$	1.22757e10	2.70930
$575$	1.49064e9	0.326991
$576$	−1.31946e9	−0.287686
$577$	2.42295e9	0.525085	0.262543	−	0.964920i	$-0.415439\pi$
$577$	2.42295e9	0.525085	0.262543	+	0.964920i	$0.415439\pi$
$578$	−8.88068e9	−1.91293
$579$	−2.48386e9	−0.531804
$580$	−3.42029e9	−0.727889
$581$	−3.24162e9	−0.685718
$582$	−8.12907e9	−1.70927
$583$	3.93612e9	0.822675
$584$	−1.25567e9	−0.260873
$585$	1.92927e8	0.0398426
$586$	1.01447e10	2.08255
$587$	−8.83936e9	−1.80380	−0.901898	−	0.431949i	$-0.857826\pi$
$587$	−8.83936e9	−1.80380	−0.901898	+	0.431949i	$0.857826\pi$
$588$	1.20725e9	0.244894
$589$	1.10549e9	0.222921
$590$	3.67221e8	0.0736114
$591$	2.56806e9	0.511739
$592$	4.61723e9	0.914651
$593$	−2.57682e9	−0.507450	−0.253725	−	0.967276i	$-0.581656\pi$
$593$	−2.57682e9	−0.507450	−0.253725	+	0.967276i	$0.581656\pi$
$594$	1.93146e9	0.378123
$595$	−2.14657e9	−0.417769
$596$	−1.57748e10	−3.05211
$597$	2.65853e9	0.511366
$598$	−1.22917e9	−0.235050
$599$	−6.40768e9	−1.21817	−0.609084	−	0.793106i	$-0.708463\pi$
$599$	−6.40768e9	−1.21817	−0.609084	+	0.793106i	$0.708463\pi$
$600$	−4.97471e9	−0.940240
$601$	2.70821e9	0.508887	0.254443	−	0.967088i	$-0.418108\pi$
$601$	2.70821e9	0.508887	0.254443	+	0.967088i	$0.418108\pi$
$602$	−3.42562e9	−0.639958
$603$	−4.38394e7	−0.00814244
$604$	−2.37568e9	−0.438691
$605$	−4.74114e8	−0.0870439
$606$	−8.09459e9	−1.47754
$607$	−8.53113e9	−1.54827	−0.774134	−	0.633022i	$-0.781814\pi$
$607$	−8.53113e9	−1.54827	−0.774134	+	0.633022i	$0.781814\pi$
$608$	−2.53885e8	−0.0458114
$609$	3.14867e9	0.564894
$610$	−3.98888e9	−0.711535
$611$	−2.41446e9	−0.428229
$612$	−5.59193e9	−0.986125
$613$	−2.93110e9	−0.513947	−0.256973	−	0.966418i	$-0.582725\pi$
$613$	−2.93110e9	−0.513947	−0.256973	+	0.966418i	$0.582725\pi$
$614$	−2.52418e9	−0.440079
$615$	1.88338e9	0.326493
$616$	1.05843e10	1.82443
$617$	7.69933e9	1.31964	0.659819	−	0.751425i	$-0.270633\pi$
$617$	7.69933e9	1.31964	0.659819	+	0.751425i	$0.270633\pi$
$618$	−3.92131e9	−0.668300
$619$	1.43713e9	0.243545	0.121772	−	0.992558i	$-0.461142\pi$
$619$	1.43713e9	0.243545	0.121772	+	0.992558i	$0.461142\pi$
$620$	−2.94030e9	−0.495473
$621$	4.19642e8	0.0703166
$622$	−1.18989e10	−1.98263
$623$	−4.35237e9	−0.721137
$624$	1.46189e9	0.240862
$625$	4.24725e9	0.695869
$626$	1.59728e10	2.60237
$627$	−1.19583e9	−0.193746
$628$	1.36796e10	2.20401
$629$	−7.30664e9	−1.17069
$630$	−1.05296e9	−0.167772
$631$	−7.31824e9	−1.15959	−0.579794	−	0.814763i	$-0.696867\pi$
$631$	−7.31824e9	−1.15959	−0.579794	+	0.814763i	$0.696867\pi$
$632$	−4.81878e9	−0.759325
$633$	5.00593e9	0.784462
$634$	−1.85344e9	−0.288845
$635$	−5.67523e8	−0.0879580
$636$	−5.59000e9	−0.861612
$637$	4.99444e8	0.0765595
$638$	−1.41659e10	−2.15959
$639$	2.72246e9	0.412771
$640$	−3.56674e9	−0.537826
$641$	1.21948e10	1.82883	0.914414	−	0.404779i	$-0.132652\pi$
$641$	1.21948e10	1.82883	0.914414	+	0.404779i	$0.132652\pi$
$642$	−1.89986e9	−0.283368
$643$	1.07659e10	1.59702	0.798510	−	0.601982i	$-0.205622\pi$
$643$	1.07659e10	1.59702	0.798510	+	0.601982i	$0.205622\pi$
$644$	4.50411e9	0.664521
$645$	−5.25567e8	−0.0771204
$646$	5.15667e9	0.752585
$647$	−1.11488e10	−1.61831	−0.809156	−	0.587594i	$-0.800075\pi$
$647$	−1.11488e10	−1.61831	−0.809156	+	0.587594i	$0.800075\pi$
$648$	−1.40047e9	−0.202191
$649$	1.02114e9	0.146632
$650$	−4.03100e9	−0.575726
$651$	2.70680e9	0.384523
$652$	4.84810e9	0.685023
$653$	1.17825e10	1.65593	0.827965	−	0.560780i	$-0.189498\pi$
$653$	1.17825e10	1.65593	0.827965	+	0.560780i	$0.189498\pi$
$654$	8.05755e9	1.12637
$655$	2.66429e9	0.370456
$656$	1.42711e10	1.97376
$657$	3.47363e8	0.0477864
$658$	1.31777e10	1.80322
$659$	−1.18824e10	−1.61736	−0.808680	−	0.588249i	$-0.799818\pi$
$659$	−1.18824e10	−1.61736	−0.808680	+	0.588249i	$0.799818\pi$
$660$	3.18057e9	0.430627
$661$	−3.51347e9	−0.473185	−0.236592	−	0.971609i	$-0.576031\pi$
$661$	−3.51347e9	−0.473185	−0.236592	+	0.971609i	$0.576031\pi$
$662$	−1.97089e10	−2.64033
$663$	−2.31340e9	−0.308286
$664$	−1.05747e10	−1.40178
$665$	6.51923e8	0.0859648
$666$	−3.58414e9	−0.470138
$667$	−3.07778e9	−0.401603
$668$	2.72425e9	0.353614
$669$	1.44167e9	0.186155
$670$	−1.07525e8	−0.0138117
$671$	−1.10920e10	−1.41736
$672$	−6.21637e8	−0.0790213
$673$	−7.05934e8	−0.0892712	−0.0446356	−	0.999003i	$-0.514213\pi$
$673$	−7.05934e8	−0.0892712	−0.0446356	+	0.999003i	$0.514213\pi$
$674$	−2.11563e10	−2.66152
$675$	1.37619e9	0.172232
$676$	−1.41784e10	−1.76529
$677$	−1.39303e10	−1.72544	−0.862720	−	0.505681i	$-0.831241\pi$
$677$	−1.39303e10	−1.72544	−0.862720	+	0.505681i	$0.831241\pi$
$678$	−1.27213e10	−1.56757
$679$	1.23232e10	1.51071
$680$	−7.00245e9	−0.854021
$681$	2.10448e9	0.255346
$682$	−1.21779e10	−1.47003
$683$	−2.00962e9	−0.241347	−0.120673	−	0.992692i	$-0.538505\pi$
$683$	−2.00962e9	−0.241347	−0.120673	+	0.992692i	$0.538505\pi$
$684$	1.69829e9	0.202916
$685$	4.19024e8	0.0498106
$686$	−1.58559e10	−1.87524
$687$	6.76474e8	0.0795981
$688$	−3.98244e9	−0.466219
$689$	−2.31260e9	−0.269360
$690$	1.02925e9	0.119275
$691$	−1.48060e9	−0.170712	−0.0853558	−	0.996351i	$-0.527203\pi$
$691$	−1.48060e9	−0.170712	−0.0853558	+	0.996351i	$0.527203\pi$
$692$	1.92799e10	2.21173
$693$	−2.92799e9	−0.334198
$694$	2.10712e10	2.39294
$695$	1.17653e9	0.132940
$696$	1.02715e10	1.15478
$697$	−2.25837e10	−2.52627
$698$	2.16043e10	2.40462
$699$	−6.02201e9	−0.666917
$700$	1.47709e10	1.62766
$701$	−9.38403e9	−1.02891	−0.514454	−	0.857518i	$-0.672005\pi$
$701$	−9.38403e9	−1.02891	−0.514454	+	0.857518i	$0.672005\pi$
$702$	−1.13480e9	−0.123805
$703$	2.21906e9	0.240894
$704$	−8.99908e9	−0.972061
$705$	2.02176e9	0.217304
$706$	5.23337e9	0.559712
$707$	1.22710e10	1.30590
$708$	−1.45020e9	−0.153572
$709$	5.90748e9	0.622501	0.311251	−	0.950328i	$-0.399252\pi$
$709$	5.90748e9	0.622501	0.311251	+	0.950328i	$0.399252\pi$
$710$	6.67738e9	0.700167
$711$	1.33305e9	0.139092
$712$	−1.41981e10	−1.47418
$713$	−2.64585e9	−0.273371
$714$	1.26261e10	1.29815
$715$	1.31581e9	0.134624
$716$	−2.35680e10	−2.39954
$717$	3.95614e9	0.400825
$718$	1.52775e10	1.54034
$719$	−1.54549e10	−1.55065	−0.775327	−	0.631560i	$-0.782415\pi$
$719$	−1.54549e10	−1.55065	−0.775327	+	0.631560i	$0.782415\pi$
$720$	−1.22412e9	−0.122225
$721$	5.94450e9	0.590665
$722$	1.60756e10	1.58960
$723$	1.44516e9	0.142211
$724$	1.55746e10	1.52522
$725$	−1.00934e10	−0.983678
$726$	2.78873e9	0.270476
$727$	−1.56689e8	−0.0151240	−0.00756201	−	0.999971i	$-0.502407\pi$
$727$	−1.56689e8	−0.0151240	−0.00756201	+	0.999971i	$0.502407\pi$
$728$	−6.21860e9	−0.597355
$729$	3.87420e8	0.0370370
$730$	8.51975e8	0.0810581
$731$	6.30211e9	0.596726
$732$	1.57526e10	1.48444
$733$	7.57137e9	0.710086	0.355043	−	0.934850i	$-0.384466\pi$
$733$	7.57137e9	0.710086	0.355043	+	0.934850i	$0.384466\pi$
$734$	−1.21979e10	−1.13854
$735$	−4.18211e8	−0.0388499
$736$	6.07640e8	0.0561790
$737$	−2.98996e8	−0.0275125
$738$	−1.10780e10	−1.01453
$739$	−7.72084e9	−0.703734	−0.351867	−	0.936050i	$-0.614453\pi$
$739$	−7.72084e9	−0.703734	−0.351867	+	0.936050i	$0.614453\pi$
$740$	−5.90208e9	−0.535419
$741$	7.02589e8	0.0634363
$742$	1.26217e10	1.13424
$743$	5.80399e9	0.519118	0.259559	−	0.965727i	$-0.416423\pi$
$743$	5.80399e9	0.519118	0.259559	+	0.965727i	$0.416423\pi$
$744$	8.82999e9	0.786058
$745$	5.46462e9	0.484187
$746$	4.49446e8	0.0396362
$747$	2.92534e9	0.256776
$748$	−3.81384e10	−3.33202
$749$	2.88009e9	0.250450
$750$	7.14696e9	0.618596
$751$	1.00286e10	0.863975	0.431987	−	0.901880i	$-0.357813\pi$
$751$	1.00286e10	0.863975	0.431987	+	0.901880i	$0.357813\pi$
$752$	1.53197e10	1.31367
$753$	8.96486e9	0.765176
$754$	8.32294e9	0.707093
$755$	8.22971e8	0.0695938
$756$	4.15827e9	0.350015
$757$	−1.32049e10	−1.10637	−0.553184	−	0.833059i	$-0.686587\pi$
$757$	−1.32049e10	−1.10637	−0.553184	+	0.833059i	$0.686587\pi$
$758$	1.92598e10	1.60623
$759$	2.86207e9	0.237593
$760$	2.12667e9	0.175733
$761$	2.09392e10	1.72232	0.861161	−	0.508332i	$-0.169738\pi$
$761$	2.09392e10	1.72232	0.861161	+	0.508332i	$0.169738\pi$
$762$	3.33817e9	0.273316
$763$	−1.22148e10	−0.995523
$764$	2.29878e10	1.86497
$765$	1.93713e9	0.156439
$766$	1.64390e10	1.32152
$767$	−5.99952e8	−0.0480101
$768$	1.47243e10	1.17293
$769$	1.74920e10	1.38706	0.693532	−	0.720426i	$-0.256054\pi$
$769$	1.74920e10	1.38706	0.693532	+	0.720426i	$0.256054\pi$
$770$	−7.18147e9	−0.566886
$771$	−8.36774e9	−0.657533
$772$	2.40586e10	1.88196
$773$	1.87442e10	1.45962	0.729808	−	0.683652i	$-0.239610\pi$
$773$	1.87442e10	1.45962	0.729808	+	0.683652i	$0.239610\pi$
$774$	3.09138e9	0.239640
$775$	−8.67689e9	−0.669589
$776$	4.02003e10	3.08826
$777$	5.43337e9	0.415523
$778$	3.50256e9	0.266659
$779$	6.85876e9	0.519834
$780$	−1.86869e9	−0.140996
$781$	1.85679e10	1.39471
$782$	−1.23418e10	−0.922902
$783$	−2.84146e9	−0.211532
$784$	−3.16896e9	−0.234861
$785$	−4.73881e9	−0.349644
$786$	−1.56713e10	−1.15114
$787$	−1.93622e10	−1.41594	−0.707968	−	0.706245i	$-0.750388\pi$
$787$	−1.93622e10	−1.41594	−0.707968	+	0.706245i	$0.750388\pi$
$788$	−2.48742e10	−1.81095
$789$	2.27564e9	0.164943
$790$	3.26957e9	0.235937
$791$	1.92848e10	1.38547
$792$	−9.55156e9	−0.683182
$793$	6.51689e9	0.464071
$794$	2.97809e10	2.11138
$795$	1.93646e9	0.136686
$796$	−2.57505e10	−1.80963
$797$	2.19937e10	1.53884	0.769420	−	0.638744i	$-0.220546\pi$
$797$	2.19937e10	1.53884	0.769420	+	0.638744i	$0.220546\pi$
$798$	−3.83461e9	−0.267123
$799$	−2.42430e10	−1.68141
$800$	1.99271e9	0.137604
$801$	3.92771e9	0.270039
$802$	−3.51299e10	−2.40473
$803$	2.36910e9	0.161465
$804$	4.24628e8	0.0288146
$805$	−1.56029e9	−0.105419
$806$	7.15491e9	0.481318
$807$	5.18051e9	0.346988
$808$	4.00298e10	2.66958
$809$	9.05373e9	0.601185	0.300592	−	0.953753i	$-0.402816\pi$
$809$	9.05373e9	0.601185	0.300592	+	0.953753i	$0.402816\pi$
$810$	9.50224e8	0.0628244
$811$	−2.27877e9	−0.150012	−0.0750062	−	0.997183i	$-0.523898\pi$
$811$	−2.27877e9	−0.150012	−0.0750062	+	0.997183i	$0.523898\pi$
$812$	−3.04980e10	−1.99906
$813$	1.91604e8	0.0125051
$814$	−2.44448e10	−1.58855
$815$	−1.67946e9	−0.108672
$816$	1.46784e10	0.945724
$817$	−1.91398e9	−0.122789
$818$	−2.00809e10	−1.28276
$819$	1.72029e9	0.109423
$820$	−1.82424e10	−1.15540
$821$	1.34643e10	0.849148	0.424574	−	0.905393i	$-0.360424\pi$
$821$	1.34643e10	0.849148	0.424574	+	0.905393i	$0.360424\pi$
$822$	−2.46470e9	−0.154779
$823$	1.64535e10	1.02887	0.514434	−	0.857530i	$-0.328002\pi$
$823$	1.64535e10	1.02887	0.514434	+	0.857530i	$0.328002\pi$
$824$	1.93919e10	1.20746
$825$	9.38595e9	0.581955
$826$	3.27443e9	0.202165
$827$	1.52598e10	0.938165	0.469082	−	0.883154i	$-0.344585\pi$
$827$	1.52598e10	0.938165	0.469082	+	0.883154i	$0.344585\pi$
$828$	−4.06465e9	−0.248838
$829$	−1.06615e10	−0.649946	−0.324973	−	0.945723i	$-0.605355\pi$
$829$	−1.06615e10	−0.649946	−0.324973	+	0.945723i	$0.605355\pi$
$830$	7.17496e9	0.435558
$831$	7.01004e9	0.423757
$832$	5.28725e9	0.318272
$833$	5.01479e9	0.300604
$834$	−6.92032e9	−0.413090
$835$	−9.43722e8	−0.0560972
$836$	1.15828e10	0.685633
$837$	−2.44270e9	−0.143989
$838$	2.54536e10	1.49415
$839$	−1.09099e10	−0.637757	−0.318878	−	0.947796i	$-0.603306\pi$
$839$	−1.09099e10	−0.637757	−0.318878	+	0.947796i	$0.603306\pi$
$840$	5.20716e9	0.303126
$841$	3.59025e9	0.208132
$842$	−1.05715e10	−0.610300
$843$	1.32994e9	0.0764605
$844$	−4.84874e10	−2.77607
$845$	4.91163e9	0.280045
$846$	−1.18920e10	−0.675238
$847$	−4.22757e9	−0.239056
$848$	1.46734e10	0.826312
$849$	4.39641e9	0.246559
$850$	−4.04742e10	−2.26054
$851$	−5.31103e9	−0.295410
$852$	−2.63698e10	−1.46072
$853$	−3.09781e10	−1.70897	−0.854483	−	0.519480i	$-0.826126\pi$
$853$	−3.09781e10	−1.70897	−0.854483	+	0.519480i	$0.826126\pi$
$854$	−3.55680e10	−1.95415
$855$	−5.88315e8	−0.0321906
$856$	9.39531e9	0.511980
$857$	4.23395e9	0.229781	0.114890	−	0.993378i	$-0.463348\pi$
$857$	4.23395e9	0.229781	0.114890	+	0.993378i	$0.463348\pi$
$858$	−7.73960e9	−0.418324
$859$	1.85088e10	0.996329	0.498165	−	0.867082i	$-0.334007\pi$
$859$	1.85088e10	0.996329	0.498165	+	0.867082i	$0.334007\pi$
$860$	5.09064e9	0.272915
$861$	1.67937e10	0.896674
$862$	5.42924e10	2.88711
$863$	−1.05929e10	−0.561020	−0.280510	−	0.959851i	$-0.590504\pi$
$863$	−1.05929e10	−0.561020	−0.280510	+	0.959851i	$0.590504\pi$
$864$	5.60984e8	0.0295905
$865$	−6.67884e9	−0.350869
$866$	−1.57924e10	−0.826298
$867$	−1.21491e10	−0.633107
$868$	−2.62180e10	−1.36076
$869$	9.09175e9	0.469979
$870$	−6.96923e9	−0.358813
$871$	1.75670e8	0.00900812
$872$	−3.98467e10	−2.03509
$873$	−1.11209e10	−0.565704
$874$	3.74827e9	0.189907
$875$	−1.08344e10	−0.546735
$876$	−3.36455e9	−0.169108
$877$	−9.90824e9	−0.496018	−0.248009	−	0.968758i	$-0.579776\pi$
$877$	−9.90824e9	−0.496018	−0.248009	+	0.968758i	$0.579776\pi$
$878$	−1.52452e10	−0.760156
$879$	1.38783e10	0.689247
$880$	−8.34879e9	−0.412985
$881$	1.77972e9	0.0876873	0.0438437	−	0.999038i	$-0.486040\pi$
$881$	1.77972e9	0.0876873	0.0438437	+	0.999038i	$0.486040\pi$
$882$	2.45991e9	0.120720
$883$	3.07682e10	1.50397	0.751985	−	0.659180i	$-0.229096\pi$
$883$	3.07682e10	1.50397	0.751985	+	0.659180i	$0.229096\pi$
$884$	2.24076e10	1.09097
$885$	5.02372e8	0.0243626
$886$	−5.63591e10	−2.72236
$887$	−6.77910e9	−0.326167	−0.163083	−	0.986612i	$-0.552144\pi$
$887$	−6.77910e9	−0.326167	−0.163083	+	0.986612i	$0.552144\pi$
$888$	1.77245e10	0.849431
$889$	−5.06048e9	−0.241566
$890$	9.63348e9	0.458056
$891$	2.64231e9	0.125144
$892$	−1.39640e10	−0.658771
$893$	7.36270e9	0.345985
$894$	−3.21428e10	−1.50454
$895$	8.16432e9	0.380662
$896$	−3.18039e10	−1.47707
$897$	−1.68156e9	−0.0777925
$898$	−3.94707e10	−1.81889
$899$	1.79155e10	0.822374
$900$	−1.33297e10	−0.609499
$901$	−2.32202e10	−1.05762
$902$	−7.55549e10	−3.42799
$903$	−4.68637e9	−0.211802
$904$	6.29101e10	2.83225
$905$	−5.39530e9	−0.241961
$906$	−4.84071e9	−0.216252
$907$	3.35163e10	1.49153	0.745763	−	0.666211i	$-0.232085\pi$
$907$	3.35163e10	1.49153	0.745763	+	0.666211i	$0.232085\pi$
$908$	−2.03840e10	−0.903626
$909$	−1.10737e10	−0.489011
$910$	4.21935e9	0.185610
$911$	2.19745e10	0.962953	0.481476	−	0.876459i	$-0.340101\pi$
$911$	2.19745e10	0.962953	0.481476	+	0.876459i	$0.340101\pi$
$912$	−4.45791e9	−0.194603
$913$	1.99516e10	0.867619
$914$	2.14163e10	0.927755
$915$	−5.45694e9	−0.235491
$916$	−6.55233e9	−0.281683
$917$	2.37569e10	1.01741
$918$	−1.13942e10	−0.486109
$919$	1.02526e10	0.435741	0.217871	−	0.975978i	$-0.430089\pi$
$919$	1.02526e10	0.435741	0.217871	+	0.975978i	$0.430089\pi$
$920$	−5.08992e9	−0.215503
$921$	−3.45317e9	−0.145650
$922$	6.78399e10	2.85054
$923$	−1.09093e10	−0.456656
$924$	2.83605e10	1.18267
$925$	−1.74172e10	−0.723571
$926$	5.58701e10	2.31228
$927$	−5.36449e9	−0.221182
$928$	−4.11443e9	−0.169002
$929$	−3.38955e10	−1.38703	−0.693517	−	0.720440i	$-0.743940\pi$
$929$	−3.38955e10	−1.38703	−0.693517	+	0.720440i	$0.743940\pi$
$930$	−5.99119e9	−0.244243
$931$	−1.52301e9	−0.0618557
$932$	5.83292e10	2.36010
$933$	−1.62782e10	−0.656175
$934$	2.51221e10	1.00889
$935$	1.32117e10	0.528591
$936$	5.61185e9	0.223687
$937$	−5.25645e9	−0.208739	−0.104370	−	0.994539i	$-0.533283\pi$
$937$	−5.25645e9	−0.208739	−0.104370	+	0.994539i	$0.533283\pi$
$938$	−9.58776e8	−0.0379321
$939$	2.18513e10	0.861288
$940$	−1.95827e10	−0.768999
$941$	2.78632e10	1.09010	0.545052	−	0.838402i	$-0.316510\pi$
$941$	2.78632e10	1.09010	0.545052	+	0.838402i	$0.316510\pi$
$942$	2.78736e10	1.08646
$943$	−1.64156e10	−0.637477
$944$	3.80668e9	0.147280
$945$	−1.44049e9	−0.0555263
$946$	2.10840e10	0.809720
$947$	2.23930e10	0.856817	0.428409	−	0.903585i	$-0.359074\pi$
$947$	2.23930e10	0.856817	0.428409	+	0.903585i	$0.359074\pi$
$948$	−1.29119e10	−0.492223
$949$	−1.39193e9	−0.0528670
$950$	1.22922e10	0.465154
$951$	−2.53557e9	−0.0955969
$952$	−6.24393e10	−2.34546
$953$	−4.95205e9	−0.185336	−0.0926680	−	0.995697i	$-0.529540\pi$
$953$	−4.95205e9	−0.185336	−0.0926680	+	0.995697i	$0.529540\pi$
$954$	−1.13902e10	−0.424731
$955$	−7.96334e9	−0.295858
$956$	−3.83191e10	−1.41845
$957$	−1.93795e10	−0.714744
$958$	3.62901e10	1.33355
$959$	3.73635e9	0.136799
$960$	−4.42729e9	−0.161506
$961$	−1.21114e10	−0.440211
$962$	1.43621e10	0.520122
$963$	−2.59909e9	−0.0937840
$964$	−1.39978e10	−0.503258
$965$	−8.33428e9	−0.298554
$966$	9.17763e9	0.327575
$967$	2.63566e9	0.0937338	0.0468669	−	0.998901i	$-0.485076\pi$
$967$	2.63566e9	0.0937338	0.0468669	+	0.998901i	$0.485076\pi$
$968$	−1.37910e10	−0.488688
$969$	7.05452e9	0.249077
$970$	−2.72761e10	−0.959581
$971$	2.95178e10	1.03471	0.517353	−	0.855772i	$-0.326918\pi$
$971$	2.95178e10	1.03471	0.517353	+	0.855772i	$0.326918\pi$
$972$	−3.75255e9	−0.131067
$973$	1.04908e10	0.365103
$974$	3.56905e10	1.23765
$975$	−5.51455e9	−0.190543
$976$	−4.13494e10	−1.42362
$977$	3.98464e9	0.136697	0.0683483	−	0.997662i	$-0.478227\pi$
$977$	3.98464e9	0.136697	0.0683483	+	0.997662i	$0.478227\pi$
$978$	9.87856e9	0.337682
$979$	2.67880e10	0.912434
$980$	4.05079e9	0.137483
$981$	1.10230e10	0.372786
$982$	−6.21024e10	−2.09275
$983$	−2.75939e10	−0.926566	−0.463283	−	0.886210i	$-0.653329\pi$
$983$	−2.75939e10	−0.926566	−0.463283	+	0.886210i	$0.653329\pi$
$984$	5.47836e10	1.83302
$985$	8.61680e9	0.287289
$986$	8.35684e10	2.77634
$987$	1.80276e10	0.596798
$988$	−6.80528e9	−0.224490
$989$	4.58086e9	0.150577
$990$	6.48078e9	0.212278
$991$	7.84374e8	0.0256015	0.0128008	−	0.999918i	$-0.495925\pi$
$991$	7.84374e8	0.0256015	0.0128008	+	0.999918i	$0.495925\pi$
$992$	−3.53702e9	−0.115039
$993$	−2.69624e10	−0.873850
$994$	5.95408e10	1.92292
$995$	8.92038e9	0.287080
$996$	−2.83348e10	−0.908683
$997$	8.21987e9	0.262683	0.131342	−	0.991337i	$-0.458072\pi$
$997$	8.21987e9	0.262683	0.131342	+	0.991337i	$0.458072\pi$
$998$	−4.47579e10	−1.42532
$999$	−4.90324e9	−0.155598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.a.1.1	✓	16
3.2	odd	2		531.8.a.b.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.1	✓	16	1.1	even	1	trivial
531.8.a.b.1.16		16	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-19.7363 q^{2} -27.0000 q^{3} +261.522 q^{4} -90.5952 q^{5} +532.880 q^{6} -807.818 q^{7} -2635.23 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-19.7363 q^{2} -27.0000 q^{3} +261.522 q^{4} -90.5952 q^{5} +532.880 q^{6} -807.818 q^{7} -2635.23 q^{8} +729.000 q^{9} +1788.01 q^{10} +4971.97 q^{11} -7061.09 q^{12} -2921.19 q^{13} +15943.4 q^{14} +2446.07 q^{15} +18534.9 q^{16} -29331.0 q^{17} -14387.8 q^{18} +8907.94 q^{19} -23692.6 q^{20} +21811.1 q^{21} -98128.3 q^{22} -21320.0 q^{23} +71151.2 q^{24} -69917.5 q^{25} +57653.6 q^{26} -19683.0 q^{27} -211262. q^{28} +144361. q^{29} -48276.4 q^{30} +124102. q^{31} -28500.9 q^{32} -134243. q^{33} +578885. q^{34} +73184.5 q^{35} +190649. q^{36} +249110. q^{37} -175810. q^{38} +78872.3 q^{39} +238739. q^{40} +769960. q^{41} -430470. q^{42} -214862. q^{43} +1.30028e6 q^{44} -66043.9 q^{45} +420778. q^{46} +826532. q^{47} -500442. q^{48} -170973. q^{49} +1.37991e6 q^{50} +791936. q^{51} -763956. q^{52} +791662. q^{53} +388470. q^{54} -450437. q^{55} +2.12879e6 q^{56} -240514. q^{57} -2.84915e6 q^{58} +205379. q^{59} +639701. q^{60} -2.23090e6 q^{61} -2.44931e6 q^{62} -588900. q^{63} -1.80996e6 q^{64} +264646. q^{65} +2.64947e6 q^{66} -60136.4 q^{67} -7.67069e6 q^{68} +575640. q^{69} -1.44439e6 q^{70} +3.73452e6 q^{71} -1.92108e6 q^{72} +476492. q^{73} -4.91652e6 q^{74} +1.88777e6 q^{75} +2.32962e6 q^{76} -4.01645e6 q^{77} -1.55665e6 q^{78} +1.82860e6 q^{79} -1.67917e6 q^{80} +531441. q^{81} -1.51962e7 q^{82} +4.01281e6 q^{83} +5.70408e6 q^{84} +2.65724e6 q^{85} +4.24058e6 q^{86} -3.89775e6 q^{87} -1.31023e7 q^{88} +5.38781e6 q^{89} +1.30346e6 q^{90} +2.35979e6 q^{91} -5.57565e6 q^{92} -3.35075e6 q^{93} -1.63127e7 q^{94} -807017. q^{95} +769525. q^{96} -1.52550e7 q^{97} +3.37437e6 q^{98} +3.62457e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q - 6q^{2} - 432q^{3} + 974q^{4} - 68q^{5} + 162q^{6} - 2343q^{7} + 819q^{8} + 11664q^{9} + O(q^{10}) \)	\( 16q - 6q^{2} - 432q^{3} + 974q^{4} - 68q^{5} + 162q^{6} - 2343q^{7} + 819q^{8} + 11664q^{9} - 3479q^{10} + 898q^{11} - 26298q^{12} - 8172q^{13} - 13315q^{14} + 1836q^{15} + 3138q^{16} - 44985q^{17} - 4374q^{18} - 40137q^{19} + 130657q^{20} + 63261q^{21} + 109394q^{22} - 2833q^{23} - 22113q^{24} + 285746q^{25} - 129420q^{26} - 314928q^{27} + 112890q^{28} + 144375q^{29} + 93933q^{30} - 141759q^{31} - 36224q^{32} - 24246q^{33} - 341332q^{34} - 78859q^{35} + 710046q^{36} - 297971q^{37} + 329075q^{38} + 220644q^{39} - 203048q^{40} + 659077q^{41} + 359505q^{42} - 1431608q^{43} + 254916q^{44} - 49572q^{45} + 873113q^{46} - 1574073q^{47} - 84726q^{48} + 1893545q^{49} + 302533q^{50} + 1214595q^{51} - 4972548q^{52} + 587736q^{53} + 118098q^{54} - 4624036q^{55} - 5798506q^{56} + 1083699q^{57} - 6991380q^{58} + 3286064q^{59} - 3527739q^{60} - 6117131q^{61} - 11570258q^{62} - 1708047q^{63} - 19063011q^{64} - 5335514q^{65} - 2953638q^{66} - 16518710q^{67} - 17284669q^{68} + 76491q^{69} - 39189486q^{70} - 10882582q^{71} + 597051q^{72} - 21097441q^{73} - 16717030q^{74} - 7715142q^{75} - 40864952q^{76} - 3404601q^{77} + 3494340q^{78} - 3784458q^{79} - 27466195q^{80} + 8503056q^{81} - 24990117q^{82} - 1951425q^{83} - 3048030q^{84} - 23238675q^{85} - 35910572q^{86} - 3898125q^{87} - 27843055q^{88} + 10499443q^{89} - 2536191q^{90} + 699217q^{91} - 20062766q^{92} + 3827493q^{93} - 59358988q^{94} - 29236333q^{95} + 978048q^{96} - 25158976q^{97} + 2120460q^{98} + 654642q^{99} + O(q^{100}) \)

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