LMFDB - Embedded newform 3630.2.a.bi.1.2

Newspace parameters

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.9856959337$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
Defining polynomial:	$x^{2} - x - 1$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +1.61803 q^{13} -1.38197 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} +1.00000 q^{18} -1.61803 q^{19} -1.00000 q^{20} +1.38197 q^{21} -1.85410 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.61803 q^{26} -1.00000 q^{27} -1.38197 q^{28} +9.70820 q^{29} +1.00000 q^{30} -4.76393 q^{31} +1.00000 q^{32} -2.47214 q^{34} +1.38197 q^{35} +1.00000 q^{36} +1.61803 q^{37} -1.61803 q^{38} -1.61803 q^{39} -1.00000 q^{40} -6.32624 q^{41} +1.38197 q^{42} -5.23607 q^{43} -1.00000 q^{45} -1.85410 q^{46} -0.381966 q^{47} -1.00000 q^{48} -5.09017 q^{49} +1.00000 q^{50} +2.47214 q^{51} +1.61803 q^{52} +5.09017 q^{53} -1.00000 q^{54} -1.38197 q^{56} +1.61803 q^{57} +9.70820 q^{58} -12.3820 q^{59} +1.00000 q^{60} -6.76393 q^{61} -4.76393 q^{62} -1.38197 q^{63} +1.00000 q^{64} -1.61803 q^{65} +14.1803 q^{67} -2.47214 q^{68} +1.85410 q^{69} +1.38197 q^{70} -13.7082 q^{71} +1.00000 q^{72} +6.94427 q^{73} +1.61803 q^{74} -1.00000 q^{75} -1.61803 q^{76} -1.61803 q^{78} -4.47214 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.32624 q^{82} -12.9443 q^{83} +1.38197 q^{84} +2.47214 q^{85} -5.23607 q^{86} -9.70820 q^{87} -11.8541 q^{89} -1.00000 q^{90} -2.23607 q^{91} -1.85410 q^{92} +4.76393 q^{93} -0.381966 q^{94} +1.61803 q^{95} -1.00000 q^{96} -2.94427 q^{97} -5.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} + O(q^{10}) $	$ 2q + 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + 2q^{8} + 2q^{9} - 2q^{10} - 2q^{12} + q^{13} - 5q^{14} + 2q^{15} + 2q^{16} + 4q^{17} + 2q^{18} - q^{19} - 2q^{20} + 5q^{21} + 3q^{23} - 2q^{24} + 2q^{25} + q^{26} - 2q^{27} - 5q^{28} + 6q^{29} + 2q^{30} - 14q^{31} + 2q^{32} + 4q^{34} + 5q^{35} + 2q^{36} + q^{37} - q^{38} - q^{39} - 2q^{40} + 3q^{41} + 5q^{42} - 6q^{43} - 2q^{45} + 3q^{46} - 3q^{47} - 2q^{48} + q^{49} + 2q^{50} - 4q^{51} + q^{52} - q^{53} - 2q^{54} - 5q^{56} + q^{57} + 6q^{58} - 27q^{59} + 2q^{60} - 18q^{61} - 14q^{62} - 5q^{63} + 2q^{64} - q^{65} + 6q^{67} + 4q^{68} - 3q^{69} + 5q^{70} - 14q^{71} + 2q^{72} - 4q^{73} + q^{74} - 2q^{75} - q^{76} - q^{78} - 2q^{80} + 2q^{81} + 3q^{82} - 8q^{83} + 5q^{84} - 4q^{85} - 6q^{86} - 6q^{87} - 17q^{89} - 2q^{90} + 3q^{92} + 14q^{93} - 3q^{94} + q^{95} - 2q^{96} + 12q^{97} + q^{98} + 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	−1.38197	−0.522334	−0.261167	−	0.965294i	$-0.584107\pi$
$7$	−1.38197	−0.522334	−0.261167	+	0.965294i	$0.584107\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	1.61803	0.448762	0.224381	−	0.974502i	$-0.427964\pi$
$13$	1.61803	0.448762	0.224381	+	0.974502i	$0.427964\pi$
$14$	−1.38197	−0.369346
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.47214	−0.599581	−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214	−0.599581	−0.299791	+	0.954005i	$0.596917\pi$
$18$	1.00000	0.235702
$19$	−1.61803	−0.371202	−0.185601	−	0.982625i	$-0.559423\pi$
$19$	−1.61803	−0.371202	−0.185601	+	0.982625i	$0.559423\pi$
$20$	−1.00000	−0.223607
$21$	1.38197	0.301570
$22$	0	0
$23$	−1.85410	−0.386607	−0.193303	−	0.981139i	$-0.561920\pi$
$23$	−1.85410	−0.386607	−0.193303	+	0.981139i	$0.561920\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	1.61803	0.317323
$27$	−1.00000	−0.192450
$28$	−1.38197	−0.261167
$29$	9.70820	1.80277	0.901384	−	0.433020i	$-0.142552\pi$
$29$	9.70820	1.80277	0.901384	+	0.433020i	$0.142552\pi$
$30$	1.00000	0.182574
$31$	−4.76393	−0.855627	−0.427814	−	0.903867i	$-0.640716\pi$
$31$	−4.76393	−0.855627	−0.427814	+	0.903867i	$0.640716\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.47214	−0.423968
$35$	1.38197	0.233595
$36$	1.00000	0.166667
$37$	1.61803	0.266003	0.133002	−	0.991116i	$-0.457538\pi$
$37$	1.61803	0.266003	0.133002	+	0.991116i	$0.457538\pi$
$38$	−1.61803	−0.262480
$39$	−1.61803	−0.259093
$40$	−1.00000	−0.158114
$41$	−6.32624	−0.987992	−0.493996	−	0.869464i	$-0.664464\pi$
$41$	−6.32624	−0.987992	−0.493996	+	0.869464i	$0.664464\pi$
$42$	1.38197	0.213242
$43$	−5.23607	−0.798493	−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607	−0.798493	−0.399246	+	0.916844i	$0.630728\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−1.85410	−0.273372
$47$	−0.381966	−0.0557155	−0.0278577	−	0.999612i	$-0.508869\pi$
$47$	−0.381966	−0.0557155	−0.0278577	+	0.999612i	$0.508869\pi$
$48$	−1.00000	−0.144338
$49$	−5.09017	−0.727167
$50$	1.00000	0.141421
$51$	2.47214	0.346168
$52$	1.61803	0.224381
$53$	5.09017	0.699189	0.349594	−	0.936901i	$-0.386319\pi$
$53$	5.09017	0.699189	0.349594	+	0.936901i	$0.386319\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.38197	−0.184673
$57$	1.61803	0.214314
$58$	9.70820	1.27475
$59$	−12.3820	−1.61199	−0.805997	−	0.591919i	$-0.798370\pi$
$59$	−12.3820	−1.61199	−0.805997	+	0.591919i	$0.798370\pi$
$60$	1.00000	0.129099
$61$	−6.76393	−0.866033	−0.433016	−	0.901386i	$-0.642551\pi$
$61$	−6.76393	−0.866033	−0.433016	+	0.901386i	$0.642551\pi$
$62$	−4.76393	−0.605020
$63$	−1.38197	−0.174111
$64$	1.00000	0.125000
$65$	−1.61803	−0.200692
$66$	0	0
$67$	14.1803	1.73240	0.866202	−	0.499694i	$-0.166554\pi$
$67$	14.1803	1.73240	0.866202	+	0.499694i	$0.166554\pi$
$68$	−2.47214	−0.299791
$69$	1.85410	0.223208
$70$	1.38197	0.165177
$71$	−13.7082	−1.62686	−0.813432	−	0.581660i	$-0.802404\pi$
$71$	−13.7082	−1.62686	−0.813432	+	0.581660i	$0.802404\pi$
$72$	1.00000	0.117851
$73$	6.94427	0.812766	0.406383	−	0.913703i	$-0.366790\pi$
$73$	6.94427	0.812766	0.406383	+	0.913703i	$0.366790\pi$
$74$	1.61803	0.188093
$75$	−1.00000	−0.115470
$76$	−1.61803	−0.185601
$77$	0	0
$78$	−1.61803	−0.183206
$79$	−4.47214	−0.503155	−0.251577	−	0.967837i	$-0.580949\pi$
$79$	−4.47214	−0.503155	−0.251577	+	0.967837i	$0.580949\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.32624	−0.698616
$83$	−12.9443	−1.42082	−0.710409	−	0.703789i	$-0.751490\pi$
$83$	−12.9443	−1.42082	−0.710409	+	0.703789i	$0.751490\pi$
$84$	1.38197	0.150785
$85$	2.47214	0.268141
$86$	−5.23607	−0.564620
$87$	−9.70820	−1.04083
$88$	0	0
$89$	−11.8541	−1.25653	−0.628266	−	0.777998i	$-0.716235\pi$
$89$	−11.8541	−1.25653	−0.628266	+	0.777998i	$0.716235\pi$
$90$	−1.00000	−0.105409
$91$	−2.23607	−0.234404
$92$	−1.85410	−0.193303
$93$	4.76393	0.493997
$94$	−0.381966	−0.0393968
$95$	1.61803	0.166007
$96$	−1.00000	−0.102062
$97$	−2.94427	−0.298946	−0.149473	−	0.988766i	$-0.547758\pi$
$97$	−2.94427	−0.298946	−0.149473	+	0.988766i	$0.547758\pi$
$98$	−5.09017	−0.514185
$99$	0	0
$100$	1.00000	0.100000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	2.47214	0.244778
$103$	−3.14590	−0.309975	−0.154987	−	0.987916i	$-0.549534\pi$
$103$	−3.14590	−0.309975	−0.154987	+	0.987916i	$0.549534\pi$
$104$	1.61803	0.158661
$105$	−1.38197	−0.134866
$106$	5.09017	0.494401
$107$	17.8885	1.72935	0.864675	−	0.502331i	$-0.167524\pi$
$107$	17.8885	1.72935	0.864675	+	0.502331i	$0.167524\pi$
$108$	−1.00000	−0.0962250
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	−1.61803	−0.153577
$112$	−1.38197	−0.130584
$113$	−3.52786	−0.331874	−0.165937	−	0.986136i	$-0.553065\pi$
$113$	−3.52786	−0.331874	−0.165937	+	0.986136i	$0.553065\pi$
$114$	1.61803	0.151543
$115$	1.85410	0.172896
$116$	9.70820	0.901384
$117$	1.61803	0.149587
$118$	−12.3820	−1.13985
$119$	3.41641	0.313182
$120$	1.00000	0.0912871
$121$	0	0
$122$	−6.76393	−0.612378
$123$	6.32624	0.570418
$124$	−4.76393	−0.427814
$125$	−1.00000	−0.0894427
$126$	−1.38197	−0.123115
$127$	−10.3820	−0.921251	−0.460625	−	0.887595i	$-0.652375\pi$
$127$	−10.3820	−0.921251	−0.460625	+	0.887595i	$0.652375\pi$
$128$	1.00000	0.0883883
$129$	5.23607	0.461010
$130$	−1.61803	−0.141911
$131$	−3.05573	−0.266980	−0.133490	−	0.991050i	$-0.542618\pi$
$131$	−3.05573	−0.266980	−0.133490	+	0.991050i	$0.542618\pi$
$132$	0	0
$133$	2.23607	0.193892
$134$	14.1803	1.22499
$135$	1.00000	0.0860663
$136$	−2.47214	−0.211984
$137$	−11.4164	−0.975370	−0.487685	−	0.873020i	$-0.662158\pi$
$137$	−11.4164	−0.975370	−0.487685	+	0.873020i	$0.662158\pi$
$138$	1.85410	0.157832
$139$	5.38197	0.456492	0.228246	−	0.973603i	$-0.426701\pi$
$139$	5.38197	0.456492	0.228246	+	0.973603i	$0.426701\pi$
$140$	1.38197	0.116797
$141$	0.381966	0.0321673
$142$	−13.7082	−1.15037
$143$	0	0
$144$	1.00000	0.0833333
$145$	−9.70820	−0.806222
$146$	6.94427	0.574712
$147$	5.09017	0.419830
$148$	1.61803	0.133002
$149$	−8.94427	−0.732743	−0.366372	−	0.930469i	$-0.619400\pi$
$149$	−8.94427	−0.732743	−0.366372	+	0.930469i	$0.619400\pi$
$150$	−1.00000	−0.0816497
$151$	3.52786	0.287094	0.143547	−	0.989644i	$-0.454149\pi$
$151$	3.52786	0.287094	0.143547	+	0.989644i	$0.454149\pi$
$152$	−1.61803	−0.131240
$153$	−2.47214	−0.199860
$154$	0	0
$155$	4.76393	0.382648
$156$	−1.61803	−0.129546
$157$	−3.38197	−0.269910	−0.134955	−	0.990852i	$-0.543089\pi$
$157$	−3.38197	−0.269910	−0.134955	+	0.990852i	$0.543089\pi$
$158$	−4.47214	−0.355784
$159$	−5.09017	−0.403677
$160$	−1.00000	−0.0790569
$161$	2.56231	0.201938
$162$	1.00000	0.0785674
$163$	−17.8885	−1.40114	−0.700569	−	0.713584i	$-0.747071\pi$
$163$	−17.8885	−1.40114	−0.700569	+	0.713584i	$0.747071\pi$
$164$	−6.32624	−0.493996
$165$	0	0
$166$	−12.9443	−1.00467
$167$	−8.56231	−0.662571	−0.331286	−	0.943531i	$-0.607482\pi$
$167$	−8.56231	−0.662571	−0.331286	+	0.943531i	$0.607482\pi$
$168$	1.38197	0.106621
$169$	−10.3820	−0.798613
$170$	2.47214	0.189604
$171$	−1.61803	−0.123734
$172$	−5.23607	−0.399246
$173$	4.43769	0.337392	0.168696	−	0.985668i	$-0.446044\pi$
$173$	4.43769	0.337392	0.168696	+	0.985668i	$0.446044\pi$
$174$	−9.70820	−0.735977
$175$	−1.38197	−0.104467
$176$	0	0
$177$	12.3820	0.930686
$178$	−11.8541	−0.888503
$179$	−17.8541	−1.33448	−0.667239	−	0.744844i	$-0.732524\pi$
$179$	−17.8541	−1.33448	−0.667239	+	0.744844i	$0.732524\pi$
$180$	−1.00000	−0.0745356
$181$	20.3607	1.51340	0.756699	−	0.653764i	$-0.226811\pi$
$181$	20.3607	1.51340	0.756699	+	0.653764i	$0.226811\pi$
$182$	−2.23607	−0.165748
$183$	6.76393	0.500004
$184$	−1.85410	−0.136686
$185$	−1.61803	−0.118960
$186$	4.76393	0.349308
$187$	0	0
$188$	−0.381966	−0.0278577
$189$	1.38197	0.100523
$190$	1.61803	0.117385
$191$	−0.291796	−0.0211136	−0.0105568	−	0.999944i	$-0.503360\pi$
$191$	−0.291796	−0.0211136	−0.0105568	+	0.999944i	$0.503360\pi$
$192$	−1.00000	−0.0721688
$193$	−9.70820	−0.698812	−0.349406	−	0.936971i	$-0.613617\pi$
$193$	−9.70820	−0.698812	−0.349406	+	0.936971i	$0.613617\pi$
$194$	−2.94427	−0.211386
$195$	1.61803	0.115870
$196$	−5.09017	−0.363584
$197$	−1.38197	−0.0984610	−0.0492305	−	0.998787i	$-0.515677\pi$
$197$	−1.38197	−0.0984610	−0.0492305	+	0.998787i	$0.515677\pi$
$198$	0	0
$199$	4.94427	0.350490	0.175245	−	0.984525i	$-0.443928\pi$
$199$	4.94427	0.350490	0.175245	+	0.984525i	$0.443928\pi$
$200$	1.00000	0.0707107
$201$	−14.1803	−1.00020
$202$	−4.00000	−0.281439
$203$	−13.4164	−0.941647
$204$	2.47214	0.173084
$205$	6.32624	0.441844
$206$	−3.14590	−0.219185
$207$	−1.85410	−0.128869
$208$	1.61803	0.112190
$209$	0	0
$210$	−1.38197	−0.0953647
$211$	−3.41641	−0.235195	−0.117598	−	0.993061i	$-0.537519\pi$
$211$	−3.41641	−0.235195	−0.117598	+	0.993061i	$0.537519\pi$
$212$	5.09017	0.349594
$213$	13.7082	0.939271
$214$	17.8885	1.22284
$215$	5.23607	0.357097
$216$	−1.00000	−0.0680414
$217$	6.58359	0.446923
$218$	−4.00000	−0.270914
$219$	−6.94427	−0.469250
$220$	0	0
$221$	−4.00000	−0.269069
$222$	−1.61803	−0.108595
$223$	5.38197	0.360403	0.180202	−	0.983630i	$-0.442325\pi$
$223$	5.38197	0.360403	0.180202	+	0.983630i	$0.442325\pi$
$224$	−1.38197	−0.0923365
$225$	1.00000	0.0666667
$226$	−3.52786	−0.234670
$227$	−18.1803	−1.20667	−0.603336	−	0.797487i	$-0.706162\pi$
$227$	−18.1803	−1.20667	−0.603336	+	0.797487i	$0.706162\pi$
$228$	1.61803	0.107157
$229$	−20.4721	−1.35284	−0.676418	−	0.736518i	$-0.736469\pi$
$229$	−20.4721	−1.35284	−0.676418	+	0.736518i	$0.736469\pi$
$230$	1.85410	0.122256
$231$	0	0
$232$	9.70820	0.637375
$233$	29.7082	1.94625	0.973125	−	0.230279i	$-0.0739640\pi$
$233$	29.7082	1.94625	0.973125	+	0.230279i	$0.0739640\pi$
$234$	1.61803	0.105774
$235$	0.381966	0.0249167
$236$	−12.3820	−0.805997
$237$	4.47214	0.290496
$238$	3.41641	0.221453
$239$	0.180340	0.0116652	0.00583261	−	0.999983i	$-0.498143\pi$
$239$	0.180340	0.0116652	0.00583261	+	0.999983i	$0.498143\pi$
$240$	1.00000	0.0645497
$241$	23.3820	1.50616	0.753082	−	0.657926i	$-0.228566\pi$
$241$	23.3820	1.50616	0.753082	+	0.657926i	$0.228566\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−6.76393	−0.433016
$245$	5.09017	0.325199
$246$	6.32624	0.403346
$247$	−2.61803	−0.166582
$248$	−4.76393	−0.302510
$249$	12.9443	0.820310
$250$	−1.00000	−0.0632456
$251$	−26.5066	−1.67308	−0.836540	−	0.547906i	$-0.815425\pi$
$251$	−26.5066	−1.67308	−0.836540	+	0.547906i	$0.815425\pi$
$252$	−1.38197	−0.0870557
$253$	0	0
$254$	−10.3820	−0.651422
$255$	−2.47214	−0.154811
$256$	1.00000	0.0625000
$257$	−22.9443	−1.43122	−0.715612	−	0.698498i	$-0.753852\pi$
$257$	−22.9443	−1.43122	−0.715612	+	0.698498i	$0.753852\pi$
$258$	5.23607	0.325983
$259$	−2.23607	−0.138943
$260$	−1.61803	−0.100346
$261$	9.70820	0.600923
$262$	−3.05573	−0.188784
$263$	14.8541	0.915943	0.457972	−	0.888967i	$-0.348576\pi$
$263$	14.8541	0.915943	0.457972	+	0.888967i	$0.348576\pi$
$264$	0	0
$265$	−5.09017	−0.312687
$266$	2.23607	0.137102
$267$	11.8541	0.725459
$268$	14.1803	0.866202
$269$	−29.2361	−1.78255	−0.891277	−	0.453459i	$-0.850190\pi$
$269$	−29.2361	−1.78255	−0.891277	+	0.453459i	$0.850190\pi$
$270$	1.00000	0.0608581
$271$	30.6525	1.86201	0.931003	−	0.365012i	$-0.118935\pi$
$271$	30.6525	1.86201	0.931003	+	0.365012i	$0.118935\pi$
$272$	−2.47214	−0.149895
$273$	2.23607	0.135333
$274$	−11.4164	−0.689690
$275$	0	0
$276$	1.85410	0.111604
$277$	−25.2705	−1.51836	−0.759179	−	0.650882i	$-0.774399\pi$
$277$	−25.2705	−1.51836	−0.759179	+	0.650882i	$0.774399\pi$
$278$	5.38197	0.322789
$279$	−4.76393	−0.285209
$280$	1.38197	0.0825883
$281$	27.8885	1.66369	0.831846	−	0.555007i	$-0.187285\pi$
$281$	27.8885	1.66369	0.831846	+	0.555007i	$0.187285\pi$
$282$	0.381966	0.0227457
$283$	9.70820	0.577093	0.288546	−	0.957466i	$-0.406828\pi$
$283$	9.70820	0.577093	0.288546	+	0.957466i	$0.406828\pi$
$284$	−13.7082	−0.813432
$285$	−1.61803	−0.0958441
$286$	0	0
$287$	8.74265	0.516062
$288$	1.00000	0.0589256
$289$	−10.8885	−0.640503
$290$	−9.70820	−0.570085
$291$	2.94427	0.172596
$292$	6.94427	0.406383
$293$	18.0344	1.05358	0.526792	−	0.849994i	$-0.323395\pi$
$293$	18.0344	1.05358	0.526792	+	0.849994i	$0.323395\pi$
$294$	5.09017	0.296865
$295$	12.3820	0.720906
$296$	1.61803	0.0940463
$297$	0	0
$298$	−8.94427	−0.518128
$299$	−3.00000	−0.173494
$300$	−1.00000	−0.0577350
$301$	7.23607	0.417080
$302$	3.52786	0.203006
$303$	4.00000	0.229794
$304$	−1.61803	−0.0928006
$305$	6.76393	0.387302
$306$	−2.47214	−0.141323
$307$	26.8328	1.53143	0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328	1.53143	0.765715	+	0.643180i	$0.222385\pi$
$308$	0	0
$309$	3.14590	0.178964
$310$	4.76393	0.270573
$311$	7.88854	0.447318	0.223659	−	0.974667i	$-0.428200\pi$
$311$	7.88854	0.447318	0.223659	+	0.974667i	$0.428200\pi$
$312$	−1.61803	−0.0916031
$313$	−7.70820	−0.435693	−0.217847	−	0.975983i	$-0.569903\pi$
$313$	−7.70820	−0.435693	−0.217847	+	0.975983i	$0.569903\pi$
$314$	−3.38197	−0.190855
$315$	1.38197	0.0778650
$316$	−4.47214	−0.251577
$317$	22.0902	1.24071	0.620354	−	0.784322i	$-0.286989\pi$
$317$	22.0902	1.24071	0.620354	+	0.784322i	$0.286989\pi$
$318$	−5.09017	−0.285443
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−17.8885	−0.998441
$322$	2.56231	0.142792
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	1.61803	0.0897524
$326$	−17.8885	−0.990755
$327$	4.00000	0.221201
$328$	−6.32624	−0.349308
$329$	0.527864	0.0291021
$330$	0	0
$331$	23.3262	1.28213	0.641063	−	0.767488i	$-0.278494\pi$
$331$	23.3262	1.28213	0.641063	+	0.767488i	$0.278494\pi$
$332$	−12.9443	−0.710409
$333$	1.61803	0.0886677
$334$	−8.56231	−0.468509
$335$	−14.1803	−0.774755
$336$	1.38197	0.0753924
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−10.3820	−0.564705
$339$	3.52786	0.191607
$340$	2.47214	0.134070
$341$	0	0
$342$	−1.61803	−0.0874933
$343$	16.7082	0.902158
$344$	−5.23607	−0.282310
$345$	−1.85410	−0.0998215
$346$	4.43769	0.238572
$347$	−26.1803	−1.40543	−0.702717	−	0.711469i	$-0.748030\pi$
$347$	−26.1803	−1.40543	−0.702717	+	0.711469i	$0.748030\pi$
$348$	−9.70820	−0.520414
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	−1.38197	−0.0738692
$351$	−1.61803	−0.0863643
$352$	0	0
$353$	6.65248	0.354076	0.177038	−	0.984204i	$-0.443349\pi$
$353$	6.65248	0.354076	0.177038	+	0.984204i	$0.443349\pi$
$354$	12.3820	0.658094
$355$	13.7082	0.727556
$356$	−11.8541	−0.628266
$357$	−3.41641	−0.180815
$358$	−17.8541	−0.943619
$359$	−20.7639	−1.09588	−0.547939	−	0.836518i	$-0.684587\pi$
$359$	−20.7639	−1.09588	−0.547939	+	0.836518i	$0.684587\pi$
$360$	−1.00000	−0.0527046
$361$	−16.3820	−0.862209
$362$	20.3607	1.07013
$363$	0	0
$364$	−2.23607	−0.117202
$365$	−6.94427	−0.363480
$366$	6.76393	0.353556
$367$	−36.3607	−1.89801	−0.949006	−	0.315258i	$-0.897909\pi$
$367$	−36.3607	−1.89801	−0.949006	+	0.315258i	$0.897909\pi$
$368$	−1.85410	−0.0966517
$369$	−6.32624	−0.329331
$370$	−1.61803	−0.0841176
$371$	−7.03444	−0.365210
$372$	4.76393	0.246998
$373$	7.14590	0.370001	0.185000	−	0.982738i	$-0.440771\pi$
$373$	7.14590	0.370001	0.185000	+	0.982738i	$0.440771\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−0.381966	−0.0196984
$377$	15.7082	0.809014
$378$	1.38197	0.0710807
$379$	9.74265	0.500446	0.250223	−	0.968188i	$-0.419496\pi$
$379$	9.74265	0.500446	0.250223	+	0.968188i	$0.419496\pi$
$380$	1.61803	0.0830034
$381$	10.3820	0.531884
$382$	−0.291796	−0.0149296
$383$	27.4508	1.40267	0.701336	−	0.712830i	$-0.252587\pi$
$383$	27.4508	1.40267	0.701336	+	0.712830i	$0.252587\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−9.70820	−0.494135
$387$	−5.23607	−0.266164
$388$	−2.94427	−0.149473
$389$	12.4721	0.632362	0.316181	−	0.948699i	$-0.397599\pi$
$389$	12.4721	0.632362	0.316181	+	0.948699i	$0.397599\pi$
$390$	1.61803	0.0819323
$391$	4.58359	0.231802
$392$	−5.09017	−0.257092
$393$	3.05573	0.154141
$394$	−1.38197	−0.0696224
$395$	4.47214	0.225018
$396$	0	0
$397$	28.3262	1.42165	0.710827	−	0.703367i	$-0.248321\pi$
$397$	28.3262	1.42165	0.710827	+	0.703367i	$0.248321\pi$
$398$	4.94427	0.247834
$399$	−2.23607	−0.111943
$400$	1.00000	0.0500000
$401$	−17.3262	−0.865231	−0.432616	−	0.901579i	$-0.642409\pi$
$401$	−17.3262	−0.865231	−0.432616	+	0.901579i	$0.642409\pi$
$402$	−14.1803	−0.707251
$403$	−7.70820	−0.383973
$404$	−4.00000	−0.199007
$405$	−1.00000	−0.0496904
$406$	−13.4164	−0.665845
$407$	0	0
$408$	2.47214	0.122389
$409$	37.2148	1.84015	0.920076	−	0.391739i	$-0.128126\pi$
$409$	37.2148	1.84015	0.920076	+	0.391739i	$0.128126\pi$
$410$	6.32624	0.312431
$411$	11.4164	0.563130
$412$	−3.14590	−0.154987
$413$	17.1115	0.842000
$414$	−1.85410	−0.0911241
$415$	12.9443	0.635409
$416$	1.61803	0.0793306
$417$	−5.38197	−0.263556
$418$	0	0
$419$	−35.7984	−1.74887	−0.874433	−	0.485147i	$-0.838766\pi$
$419$	−35.7984	−1.74887	−0.874433	+	0.485147i	$0.838766\pi$
$420$	−1.38197	−0.0674330
$421$	9.05573	0.441349	0.220675	−	0.975347i	$-0.429174\pi$
$421$	9.05573	0.441349	0.220675	+	0.975347i	$0.429174\pi$
$422$	−3.41641	−0.166308
$423$	−0.381966	−0.0185718
$424$	5.09017	0.247201
$425$	−2.47214	−0.119916
$426$	13.7082	0.664165
$427$	9.34752	0.452358
$428$	17.8885	0.864675
$429$	0	0
$430$	5.23607	0.252506
$431$	20.1803	0.972053	0.486026	−	0.873944i	$-0.338446\pi$
$431$	20.1803	0.972053	0.486026	+	0.873944i	$0.338446\pi$
$432$	−1.00000	−0.0481125
$433$	7.12461	0.342387	0.171193	−	0.985237i	$-0.445238\pi$
$433$	7.12461	0.342387	0.171193	+	0.985237i	$0.445238\pi$
$434$	6.58359	0.316023
$435$	9.70820	0.465473
$436$	−4.00000	−0.191565
$437$	3.00000	0.143509
$438$	−6.94427	−0.331810
$439$	2.18034	0.104062	0.0520310	−	0.998645i	$-0.483431\pi$
$439$	2.18034	0.104062	0.0520310	+	0.998645i	$0.483431\pi$
$440$	0	0
$441$	−5.09017	−0.242389
$442$	−4.00000	−0.190261
$443$	−24.8328	−1.17984	−0.589921	−	0.807461i	$-0.700841\pi$
$443$	−24.8328	−1.17984	−0.589921	+	0.807461i	$0.700841\pi$
$444$	−1.61803	−0.0767885
$445$	11.8541	0.561938
$446$	5.38197	0.254843
$447$	8.94427	0.423050
$448$	−1.38197	−0.0652918
$449$	−16.3820	−0.773113	−0.386556	−	0.922266i	$-0.626336\pi$
$449$	−16.3820	−0.773113	−0.386556	+	0.922266i	$0.626336\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−3.52786	−0.165937
$453$	−3.52786	−0.165754
$454$	−18.1803	−0.853246
$455$	2.23607	0.104828
$456$	1.61803	0.0757714
$457$	25.8885	1.21102	0.605508	−	0.795840i	$-0.292970\pi$
$457$	25.8885	1.21102	0.605508	+	0.795840i	$0.292970\pi$
$458$	−20.4721	−0.956600
$459$	2.47214	0.115389
$460$	1.85410	0.0864479
$461$	29.2361	1.36166	0.680830	−	0.732442i	$-0.261619\pi$
$461$	29.2361	1.36166	0.680830	+	0.732442i	$0.261619\pi$
$462$	0	0
$463$	−5.61803	−0.261092	−0.130546	−	0.991442i	$-0.541673\pi$
$463$	−5.61803	−0.261092	−0.130546	+	0.991442i	$0.541673\pi$
$464$	9.70820	0.450692
$465$	−4.76393	−0.220922
$466$	29.7082	1.37621
$467$	24.9443	1.15428	0.577142	−	0.816644i	$-0.304168\pi$
$467$	24.9443	1.15428	0.577142	+	0.816644i	$0.304168\pi$
$468$	1.61803	0.0747936
$469$	−19.5967	−0.904894
$470$	0.381966	0.0176188
$471$	3.38197	0.155833
$472$	−12.3820	−0.569926
$473$	0	0
$474$	4.47214	0.205412
$475$	−1.61803	−0.0742405
$476$	3.41641	0.156591
$477$	5.09017	0.233063
$478$	0.180340	0.00824855
$479$	−37.0132	−1.69117	−0.845587	−	0.533837i	$-0.820749\pi$
$479$	−37.0132	−1.69117	−0.845587	+	0.533837i	$0.820749\pi$
$480$	1.00000	0.0456435
$481$	2.61803	0.119372
$482$	23.3820	1.06502
$483$	−2.56231	−0.116589
$484$	0	0
$485$	2.94427	0.133693
$486$	−1.00000	−0.0453609
$487$	−4.36068	−0.197601	−0.0988006	−	0.995107i	$-0.531501\pi$
$487$	−4.36068	−0.197601	−0.0988006	+	0.995107i	$0.531501\pi$
$488$	−6.76393	−0.306189
$489$	17.8885	0.808948
$490$	5.09017	0.229950
$491$	−13.3262	−0.601405	−0.300702	−	0.953718i	$-0.597221\pi$
$491$	−13.3262	−0.601405	−0.300702	+	0.953718i	$0.597221\pi$
$492$	6.32624	0.285209
$493$	−24.0000	−1.08091
$494$	−2.61803	−0.117791
$495$	0	0
$496$	−4.76393	−0.213907
$497$	18.9443	0.849767
$498$	12.9443	0.580047
$499$	26.6869	1.19467	0.597335	−	0.801992i	$-0.296226\pi$
$499$	26.6869	1.19467	0.597335	+	0.801992i	$0.296226\pi$
$500$	−1.00000	−0.0447214
$501$	8.56231	0.382536
$502$	−26.5066	−1.18305
$503$	−19.7984	−0.882766	−0.441383	−	0.897319i	$-0.645512\pi$
$503$	−19.7984	−0.882766	−0.441383	+	0.897319i	$0.645512\pi$
$504$	−1.38197	−0.0615577
$505$	4.00000	0.177998
$506$	0	0
$507$	10.3820	0.461079
$508$	−10.3820	−0.460625
$509$	1.41641	0.0627812	0.0313906	−	0.999507i	$-0.490006\pi$
$509$	1.41641	0.0627812	0.0313906	+	0.999507i	$0.490006\pi$
$510$	−2.47214	−0.109468
$511$	−9.59675	−0.424535
$512$	1.00000	0.0441942
$513$	1.61803	0.0714379
$514$	−22.9443	−1.01203
$515$	3.14590	0.138625
$516$	5.23607	0.230505
$517$	0	0
$518$	−2.23607	−0.0982472
$519$	−4.43769	−0.194793
$520$	−1.61803	−0.0709555
$521$	21.6738	0.949545	0.474772	−	0.880109i	$-0.342530\pi$
$521$	21.6738	0.949545	0.474772	+	0.880109i	$0.342530\pi$
$522$	9.70820	0.424917
$523$	−15.7082	−0.686872	−0.343436	−	0.939176i	$-0.611591\pi$
$523$	−15.7082	−0.686872	−0.343436	+	0.939176i	$0.611591\pi$
$524$	−3.05573	−0.133490
$525$	1.38197	0.0603139
$526$	14.8541	0.647670
$527$	11.7771	0.513018
$528$	0	0
$529$	−19.5623	−0.850535
$530$	−5.09017	−0.221103
$531$	−12.3820	−0.537332
$532$	2.23607	0.0969458
$533$	−10.2361	−0.443373
$534$	11.8541	0.512977
$535$	−17.8885	−0.773389
$536$	14.1803	0.612497
$537$	17.8541	0.770461
$538$	−29.2361	−1.26046
$539$	0	0
$540$	1.00000	0.0430331
$541$	32.9443	1.41638	0.708192	−	0.706019i	$-0.249511\pi$
$541$	32.9443	1.41638	0.708192	+	0.706019i	$0.249511\pi$
$542$	30.6525	1.31664
$543$	−20.3607	−0.873760
$544$	−2.47214	−0.105992
$545$	4.00000	0.171341
$546$	2.23607	0.0956949
$547$	14.7639	0.631260	0.315630	−	0.948882i	$-0.397784\pi$
$547$	14.7639	0.631260	0.315630	+	0.948882i	$0.397784\pi$
$548$	−11.4164	−0.487685
$549$	−6.76393	−0.288678
$550$	0	0
$551$	−15.7082	−0.669192
$552$	1.85410	0.0789158
$553$	6.18034	0.262815
$554$	−25.2705	−1.07364
$555$	1.61803	0.0686817
$556$	5.38197	0.228246
$557$	−29.3262	−1.24259	−0.621296	−	0.783576i	$-0.713394\pi$
$557$	−29.3262	−1.24259	−0.621296	+	0.783576i	$0.713394\pi$
$558$	−4.76393	−0.201673
$559$	−8.47214	−0.358333
$560$	1.38197	0.0583987
$561$	0	0
$562$	27.8885	1.17641
$563$	17.3050	0.729317	0.364658	−	0.931141i	$-0.381186\pi$
$563$	17.3050	0.729317	0.364658	+	0.931141i	$0.381186\pi$
$564$	0.381966	0.0160837
$565$	3.52786	0.148418
$566$	9.70820	0.408066
$567$	−1.38197	−0.0580371
$568$	−13.7082	−0.575183
$569$	−8.14590	−0.341494	−0.170747	−	0.985315i	$-0.554618\pi$
$569$	−8.14590	−0.341494	−0.170747	+	0.985315i	$0.554618\pi$
$570$	−1.61803	−0.0677720
$571$	−16.5066	−0.690779	−0.345389	−	0.938459i	$-0.612253\pi$
$571$	−16.5066	−0.690779	−0.345389	+	0.938459i	$0.612253\pi$
$572$	0	0
$573$	0.291796	0.0121900
$574$	8.74265	0.364911
$575$	−1.85410	−0.0773214
$576$	1.00000	0.0416667
$577$	33.1246	1.37900	0.689498	−	0.724288i	$-0.257831\pi$
$577$	33.1246	1.37900	0.689498	+	0.724288i	$0.257831\pi$
$578$	−10.8885	−0.452904
$579$	9.70820	0.403459
$580$	−9.70820	−0.403111
$581$	17.8885	0.742142
$582$	2.94427	0.122044
$583$	0	0
$584$	6.94427	0.287356
$585$	−1.61803	−0.0668975
$586$	18.0344	0.744996
$587$	−18.8328	−0.777313	−0.388657	−	0.921383i	$-0.627061\pi$
$587$	−18.8328	−0.777313	−0.388657	+	0.921383i	$0.627061\pi$
$588$	5.09017	0.209915
$589$	7.70820	0.317611
$590$	12.3820	0.509757
$591$	1.38197	0.0568465
$592$	1.61803	0.0665008
$593$	29.4164	1.20799	0.603994	−	0.796989i	$-0.293575\pi$
$593$	29.4164	1.20799	0.603994	+	0.796989i	$0.293575\pi$
$594$	0	0
$595$	−3.41641	−0.140059
$596$	−8.94427	−0.366372
$597$	−4.94427	−0.202356
$598$	−3.00000	−0.122679
$599$	−17.7082	−0.723538	−0.361769	−	0.932268i	$-0.617827\pi$
$599$	−17.7082	−0.723538	−0.361769	+	0.932268i	$0.617827\pi$
$600$	−1.00000	−0.0408248
$601$	23.9098	0.975302	0.487651	−	0.873039i	$-0.337854\pi$
$601$	23.9098	0.975302	0.487651	+	0.873039i	$0.337854\pi$
$602$	7.23607	0.294920
$603$	14.1803	0.577468
$604$	3.52786	0.143547
$605$	0	0
$606$	4.00000	0.162489
$607$	−28.3607	−1.15112	−0.575562	−	0.817758i	$-0.695217\pi$
$607$	−28.3607	−1.15112	−0.575562	+	0.817758i	$0.695217\pi$
$608$	−1.61803	−0.0656199
$609$	13.4164	0.543660
$610$	6.76393	0.273864
$611$	−0.618034	−0.0250030
$612$	−2.47214	−0.0999302
$613$	−18.5836	−0.750584	−0.375292	−	0.926907i	$-0.622458\pi$
$613$	−18.5836	−0.750584	−0.375292	+	0.926907i	$0.622458\pi$
$614$	26.8328	1.08288
$615$	−6.32624	−0.255099
$616$	0	0
$617$	40.9443	1.64835	0.824177	−	0.566332i	$-0.191638\pi$
$617$	40.9443	1.64835	0.824177	+	0.566332i	$0.191638\pi$
$618$	3.14590	0.126547
$619$	−18.7426	−0.753331	−0.376665	−	0.926349i	$-0.622929\pi$
$619$	−18.7426	−0.753331	−0.376665	+	0.926349i	$0.622929\pi$
$620$	4.76393	0.191324
$621$	1.85410	0.0744025
$622$	7.88854	0.316302
$623$	16.3820	0.656330
$624$	−1.61803	−0.0647732
$625$	1.00000	0.0400000
$626$	−7.70820	−0.308082
$627$	0	0
$628$	−3.38197	−0.134955
$629$	−4.00000	−0.159490
$630$	1.38197	0.0550588
$631$	−11.7082	−0.466096	−0.233048	−	0.972465i	$-0.574870\pi$
$631$	−11.7082	−0.466096	−0.233048	+	0.972465i	$0.574870\pi$
$632$	−4.47214	−0.177892
$633$	3.41641	0.135790
$634$	22.0902	0.877313
$635$	10.3820	0.411996
$636$	−5.09017	−0.201838
$637$	−8.23607	−0.326325
$638$	0	0
$639$	−13.7082	−0.542288
$640$	−1.00000	−0.0395285
$641$	−18.4508	−0.728765	−0.364382	−	0.931249i	$-0.618720\pi$
$641$	−18.4508	−0.728765	−0.364382	+	0.931249i	$0.618720\pi$
$642$	−17.8885	−0.706005
$643$	23.4164	0.923453	0.461726	−	0.887022i	$-0.347230\pi$
$643$	23.4164	0.923453	0.461726	+	0.887022i	$0.347230\pi$
$644$	2.56231	0.100969
$645$	−5.23607	−0.206170
$646$	4.00000	0.157378
$647$	22.8328	0.897651	0.448825	−	0.893620i	$-0.351843\pi$
$647$	22.8328	0.897651	0.448825	+	0.893620i	$0.351843\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	1.61803	0.0634645
$651$	−6.58359	−0.258031
$652$	−17.8885	−0.700569
$653$	−9.14590	−0.357907	−0.178953	−	0.983858i	$-0.557271\pi$
$653$	−9.14590	−0.357907	−0.178953	+	0.983858i	$0.557271\pi$
$654$	4.00000	0.156412
$655$	3.05573	0.119397
$656$	−6.32624	−0.246998
$657$	6.94427	0.270922
$658$	0.527864	0.0205783
$659$	5.27051	0.205310	0.102655	−	0.994717i	$-0.467266\pi$
$659$	5.27051	0.205310	0.102655	+	0.994717i	$0.467266\pi$
$660$	0	0
$661$	−43.4853	−1.69138	−0.845691	−	0.533673i	$-0.820811\pi$
$661$	−43.4853	−1.69138	−0.845691	+	0.533673i	$0.820811\pi$
$662$	23.3262	0.906600
$663$	4.00000	0.155347
$664$	−12.9443	−0.502335
$665$	−2.23607	−0.0867110
$666$	1.61803	0.0626975
$667$	−18.0000	−0.696963
$668$	−8.56231	−0.331286
$669$	−5.38197	−0.208079
$670$	−14.1803	−0.547834
$671$	0	0
$672$	1.38197	0.0533105
$673$	−3.59675	−0.138644	−0.0693222	−	0.997594i	$-0.522084\pi$
$673$	−3.59675	−0.138644	−0.0693222	+	0.997594i	$0.522084\pi$
$674$	20.0000	0.770371
$675$	−1.00000	−0.0384900
$676$	−10.3820	−0.399306
$677$	30.3607	1.16686	0.583428	−	0.812165i	$-0.301711\pi$
$677$	30.3607	1.16686	0.583428	+	0.812165i	$0.301711\pi$
$678$	3.52786	0.135487
$679$	4.06888	0.156149
$680$	2.47214	0.0948021
$681$	18.1803	0.696672
$682$	0	0
$683$	−9.12461	−0.349144	−0.174572	−	0.984644i	$-0.555854\pi$
$683$	−9.12461	−0.349144	−0.174572	+	0.984644i	$0.555854\pi$
$684$	−1.61803	−0.0618671
$685$	11.4164	0.436199
$686$	16.7082	0.637922
$687$	20.4721	0.781061
$688$	−5.23607	−0.199623
$689$	8.23607	0.313769
$690$	−1.85410	−0.0705845
$691$	36.5066	1.38878	0.694388	−	0.719601i	$-0.255675\pi$
$691$	36.5066	1.38878	0.694388	+	0.719601i	$0.255675\pi$
$692$	4.43769	0.168696
$693$	0	0
$694$	−26.1803	−0.993792
$695$	−5.38197	−0.204150
$696$	−9.70820	−0.367989
$697$	15.6393	0.592381
$698$	−10.0000	−0.378506
$699$	−29.7082	−1.12367
$700$	−1.38197	−0.0522334
$701$	−38.0689	−1.43784	−0.718921	−	0.695092i	$-0.755364\pi$
$701$	−38.0689	−1.43784	−0.718921	+	0.695092i	$0.755364\pi$
$702$	−1.61803	−0.0610688
$703$	−2.61803	−0.0987410
$704$	0	0
$705$	−0.381966	−0.0143857
$706$	6.65248	0.250369
$707$	5.52786	0.207897
$708$	12.3820	0.465343
$709$	6.65248	0.249839	0.124919	−	0.992167i	$-0.460133\pi$
$709$	6.65248	0.249839	0.124919	+	0.992167i	$0.460133\pi$
$710$	13.7082	0.514460
$711$	−4.47214	−0.167718
$712$	−11.8541	−0.444251
$713$	8.83282	0.330792
$714$	−3.41641	−0.127856
$715$	0	0
$716$	−17.8541	−0.667239
$717$	−0.180340	−0.00673492
$718$	−20.7639	−0.774903
$719$	11.8885	0.443368	0.221684	−	0.975119i	$-0.428845\pi$
$719$	11.8885	0.443368	0.221684	+	0.975119i	$0.428845\pi$
$720$	−1.00000	−0.0372678
$721$	4.34752	0.161910
$722$	−16.3820	−0.609674
$723$	−23.3820	−0.869585
$724$	20.3607	0.756699
$725$	9.70820	0.360554
$726$	0	0
$727$	31.6312	1.17314	0.586568	−	0.809900i	$-0.300479\pi$
$727$	31.6312	1.17314	0.586568	+	0.809900i	$0.300479\pi$
$728$	−2.23607	−0.0828742
$729$	1.00000	0.0370370
$730$	−6.94427	−0.257019
$731$	12.9443	0.478761
$732$	6.76393	0.250002
$733$	19.5279	0.721278	0.360639	−	0.932705i	$-0.382559\pi$
$733$	19.5279	0.721278	0.360639	+	0.932705i	$0.382559\pi$
$734$	−36.3607	−1.34210
$735$	−5.09017	−0.187754
$736$	−1.85410	−0.0683431
$737$	0	0
$738$	−6.32624	−0.232872
$739$	−25.3820	−0.933691	−0.466845	−	0.884339i	$-0.654610\pi$
$739$	−25.3820	−0.933691	−0.466845	+	0.884339i	$0.654610\pi$
$740$	−1.61803	−0.0594801
$741$	2.61803	0.0961759
$742$	−7.03444	−0.258242
$743$	13.8541	0.508258	0.254129	−	0.967170i	$-0.418211\pi$
$743$	13.8541	0.508258	0.254129	+	0.967170i	$0.418211\pi$
$744$	4.76393	0.174654
$745$	8.94427	0.327693
$746$	7.14590	0.261630
$747$	−12.9443	−0.473606
$748$	0	0
$749$	−24.7214	−0.903299
$750$	1.00000	0.0365148
$751$	50.2492	1.83362	0.916810	−	0.399323i	$-0.130755\pi$
$751$	50.2492	1.83362	0.916810	+	0.399323i	$0.130755\pi$
$752$	−0.381966	−0.0139289
$753$	26.5066	0.965953
$754$	15.7082	0.572059
$755$	−3.52786	−0.128392
$756$	1.38197	0.0502616
$757$	−4.85410	−0.176425	−0.0882127	−	0.996102i	$-0.528116\pi$
$757$	−4.85410	−0.176425	−0.0882127	+	0.996102i	$0.528116\pi$
$758$	9.74265	0.353869
$759$	0	0
$760$	1.61803	0.0586923
$761$	−27.8885	−1.01096	−0.505479	−	0.862839i	$-0.668684\pi$
$761$	−27.8885	−1.01096	−0.505479	+	0.862839i	$0.668684\pi$
$762$	10.3820	0.376099
$763$	5.52786	0.200122
$764$	−0.291796	−0.0105568
$765$	2.47214	0.0893803
$766$	27.4508	0.991840
$767$	−20.0344	−0.723402
$768$	−1.00000	−0.0360844
$769$	10.2016	0.367880	0.183940	−	0.982937i	$-0.441115\pi$
$769$	10.2016	0.367880	0.183940	+	0.982937i	$0.441115\pi$
$770$	0	0
$771$	22.9443	0.826318
$772$	−9.70820	−0.349406
$773$	−20.7984	−0.748066	−0.374033	−	0.927415i	$-0.622025\pi$
$773$	−20.7984	−0.748066	−0.374033	+	0.927415i	$0.622025\pi$
$774$	−5.23607	−0.188207
$775$	−4.76393	−0.171125
$776$	−2.94427	−0.105693
$777$	2.23607	0.0802185
$778$	12.4721	0.447148
$779$	10.2361	0.366745
$780$	1.61803	0.0579349
$781$	0	0
$782$	4.58359	0.163909
$783$	−9.70820	−0.346943
$784$	−5.09017	−0.181792
$785$	3.38197	0.120708
$786$	3.05573	0.108994
$787$	−4.18034	−0.149013	−0.0745065	−	0.997221i	$-0.523738\pi$
$787$	−4.18034	−0.149013	−0.0745065	+	0.997221i	$0.523738\pi$
$788$	−1.38197	−0.0492305
$789$	−14.8541	−0.528820
$790$	4.47214	0.159111
$791$	4.87539	0.173349
$792$	0	0
$793$	−10.9443	−0.388642
$794$	28.3262	1.00526
$795$	5.09017	0.180530
$796$	4.94427	0.175245
$797$	−28.7426	−1.01812	−0.509058	−	0.860732i	$-0.670006\pi$
$797$	−28.7426	−1.01812	−0.509058	+	0.860732i	$0.670006\pi$
$798$	−2.23607	−0.0791559
$799$	0.944272	0.0334059
$800$	1.00000	0.0353553
$801$	−11.8541	−0.418844
$802$	−17.3262	−0.611811
$803$	0	0
$804$	−14.1803	−0.500102
$805$	−2.56231	−0.0903094
$806$	−7.70820	−0.271510
$807$	29.2361	1.02916
$808$	−4.00000	−0.140720
$809$	41.5066	1.45929	0.729647	−	0.683824i	$-0.239684\pi$
$809$	41.5066	1.45929	0.729647	+	0.683824i	$0.239684\pi$
$810$	−1.00000	−0.0351364
$811$	7.27051	0.255302	0.127651	−	0.991819i	$-0.459256\pi$
$811$	7.27051	0.255302	0.127651	+	0.991819i	$0.459256\pi$
$812$	−13.4164	−0.470824
$813$	−30.6525	−1.07503
$814$	0	0
$815$	17.8885	0.626608
$816$	2.47214	0.0865421
$817$	8.47214	0.296403
$818$	37.2148	1.30118
$819$	−2.23607	−0.0781345
$820$	6.32624	0.220922
$821$	−17.2361	−0.601543	−0.300771	−	0.953696i	$-0.597244\pi$
$821$	−17.2361	−0.601543	−0.300771	+	0.953696i	$0.597244\pi$
$822$	11.4164	0.398193
$823$	44.0902	1.53689	0.768443	−	0.639918i	$-0.221032\pi$
$823$	44.0902	1.53689	0.768443	+	0.639918i	$0.221032\pi$
$824$	−3.14590	−0.109593
$825$	0	0
$826$	17.1115	0.595384
$827$	−3.70820	−0.128947	−0.0644734	−	0.997919i	$-0.520537\pi$
$827$	−3.70820	−0.128947	−0.0644734	+	0.997919i	$0.520537\pi$
$828$	−1.85410	−0.0644345
$829$	39.3050	1.36512	0.682559	−	0.730831i	$-0.260867\pi$
$829$	39.3050	1.36512	0.682559	+	0.730831i	$0.260867\pi$
$830$	12.9443	0.449302
$831$	25.2705	0.876624
$832$	1.61803	0.0560952
$833$	12.5836	0.435996
$834$	−5.38197	−0.186362
$835$	8.56231	0.296311
$836$	0	0
$837$	4.76393	0.164666
$838$	−35.7984	−1.23663
$839$	−7.12461	−0.245969	−0.122984	−	0.992409i	$-0.539247\pi$
$839$	−7.12461	−0.245969	−0.122984	+	0.992409i	$0.539247\pi$
$840$	−1.38197	−0.0476824
$841$	65.2492	2.24997
$842$	9.05573	0.312081
$843$	−27.8885	−0.960532
$844$	−3.41641	−0.117598
$845$	10.3820	0.357150
$846$	−0.381966	−0.0131323
$847$	0	0
$848$	5.09017	0.174797
$849$	−9.70820	−0.333185
$850$	−2.47214	−0.0847936
$851$	−3.00000	−0.102839
$852$	13.7082	0.469635
$853$	51.8115	1.77399	0.886996	−	0.461776i	$-0.152788\pi$
$853$	51.8115	1.77399	0.886996	+	0.461776i	$0.152788\pi$
$854$	9.34752	0.319866
$855$	1.61803	0.0553356
$856$	17.8885	0.611418
$857$	−50.7639	−1.73406	−0.867031	−	0.498253i	$-0.833975\pi$
$857$	−50.7639	−1.73406	−0.867031	+	0.498253i	$0.833975\pi$
$858$	0	0
$859$	21.9656	0.749455	0.374728	−	0.927135i	$-0.377736\pi$
$859$	21.9656	0.749455	0.374728	+	0.927135i	$0.377736\pi$
$860$	5.23607	0.178548
$861$	−8.74265	−0.297949
$862$	20.1803	0.687345
$863$	−6.85410	−0.233316	−0.116658	−	0.993172i	$-0.537218\pi$
$863$	−6.85410	−0.233316	−0.116658	+	0.993172i	$0.537218\pi$
$864$	−1.00000	−0.0340207
$865$	−4.43769	−0.150886
$866$	7.12461	0.242104
$867$	10.8885	0.369794
$868$	6.58359	0.223462
$869$	0	0
$870$	9.70820	0.329139
$871$	22.9443	0.777437
$872$	−4.00000	−0.135457
$873$	−2.94427	−0.0996485
$874$	3.00000	0.101477
$875$	1.38197	0.0467190
$876$	−6.94427	−0.234625
$877$	25.6180	0.865060	0.432530	−	0.901620i	$-0.357621\pi$
$877$	25.6180	0.865060	0.432530	+	0.901620i	$0.357621\pi$
$878$	2.18034	0.0735829
$879$	−18.0344	−0.608287
$880$	0	0
$881$	−16.7984	−0.565952	−0.282976	−	0.959127i	$-0.591322\pi$
$881$	−16.7984	−0.565952	−0.282976	+	0.959127i	$0.591322\pi$
$882$	−5.09017	−0.171395
$883$	−37.3050	−1.25541	−0.627706	−	0.778451i	$-0.716006\pi$
$883$	−37.3050	−1.25541	−0.627706	+	0.778451i	$0.716006\pi$
$884$	−4.00000	−0.134535
$885$	−12.3820	−0.416215
$886$	−24.8328	−0.834275
$887$	−43.7426	−1.46873	−0.734367	−	0.678752i	$-0.762521\pi$
$887$	−43.7426	−1.46873	−0.734367	+	0.678752i	$0.762521\pi$
$888$	−1.61803	−0.0542977
$889$	14.3475	0.481201
$890$	11.8541	0.397350
$891$	0	0
$892$	5.38197	0.180202
$893$	0.618034	0.0206817
$894$	8.94427	0.299141
$895$	17.8541	0.596797
$896$	−1.38197	−0.0461682
$897$	3.00000	0.100167
$898$	−16.3820	−0.546673
$899$	−46.2492	−1.54250
$900$	1.00000	0.0333333
$901$	−12.5836	−0.419220
$902$	0	0
$903$	−7.23607	−0.240801
$904$	−3.52786	−0.117335
$905$	−20.3607	−0.676812
$906$	−3.52786	−0.117205
$907$	−5.88854	−0.195526	−0.0977629	−	0.995210i	$-0.531169\pi$
$907$	−5.88854	−0.195526	−0.0977629	+	0.995210i	$0.531169\pi$
$908$	−18.1803	−0.603336
$909$	−4.00000	−0.132672
$910$	2.23607	0.0741249
$911$	20.6525	0.684247	0.342124	−	0.939655i	$-0.388854\pi$
$911$	20.6525	0.684247	0.342124	+	0.939655i	$0.388854\pi$
$912$	1.61803	0.0535785
$913$	0	0
$914$	25.8885	0.856317
$915$	−6.76393	−0.223609
$916$	−20.4721	−0.676418
$917$	4.22291	0.139453
$918$	2.47214	0.0815926
$919$	−40.0689	−1.32175	−0.660875	−	0.750496i	$-0.729815\pi$
$919$	−40.0689	−1.32175	−0.660875	+	0.750496i	$0.729815\pi$
$920$	1.85410	0.0611279
$921$	−26.8328	−0.884171
$922$	29.2361	0.962839
$923$	−22.1803	−0.730075
$924$	0	0
$925$	1.61803	0.0532006
$926$	−5.61803	−0.184620
$927$	−3.14590	−0.103325
$928$	9.70820	0.318687
$929$	22.0344	0.722927	0.361463	−	0.932386i	$-0.382277\pi$
$929$	22.0344	0.722927	0.361463	+	0.932386i	$0.382277\pi$
$930$	−4.76393	−0.156215
$931$	8.23607	0.269926
$932$	29.7082	0.973125
$933$	−7.88854	−0.258259
$934$	24.9443	0.816202
$935$	0	0
$936$	1.61803	0.0528871
$937$	−3.63932	−0.118891	−0.0594457	−	0.998232i	$-0.518933\pi$
$937$	−3.63932	−0.118891	−0.0594457	+	0.998232i	$0.518933\pi$
$938$	−19.5967	−0.639856
$939$	7.70820	0.251548
$940$	0.381966	0.0124584
$941$	−28.9443	−0.943556	−0.471778	−	0.881717i	$-0.656388\pi$
$941$	−28.9443	−0.943556	−0.471778	+	0.881717i	$0.656388\pi$
$942$	3.38197	0.110190
$943$	11.7295	0.381965
$944$	−12.3820	−0.402999
$945$	−1.38197	−0.0449554
$946$	0	0
$947$	59.3050	1.92715	0.963576	−	0.267435i	$-0.0861760\pi$
$947$	59.3050	1.92715	0.963576	+	0.267435i	$0.0861760\pi$
$948$	4.47214	0.145248
$949$	11.2361	0.364738
$950$	−1.61803	−0.0524960
$951$	−22.0902	−0.716323
$952$	3.41641	0.110726
$953$	49.2361	1.59491	0.797456	−	0.603377i	$-0.206178\pi$
$953$	49.2361	1.59491	0.797456	+	0.603377i	$0.206178\pi$
$954$	5.09017	0.164800
$955$	0.291796	0.00944230
$956$	0.180340	0.00583261
$957$	0	0
$958$	−37.0132	−1.19584
$959$	15.7771	0.509469
$960$	1.00000	0.0322749
$961$	−8.30495	−0.267902
$962$	2.61803	0.0844088
$963$	17.8885	0.576450
$964$	23.3820	0.753082
$965$	9.70820	0.312518
$966$	−2.56231	−0.0824408
$967$	46.7426	1.50314	0.751571	−	0.659652i	$-0.229296\pi$
$967$	46.7426	1.50314	0.751571	+	0.659652i	$0.229296\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	2.94427	0.0945349
$971$	−18.7984	−0.603269	−0.301634	−	0.953424i	$-0.597532\pi$
$971$	−18.7984	−0.603269	−0.301634	+	0.953424i	$0.597532\pi$
$972$	−1.00000	−0.0320750
$973$	−7.43769	−0.238442
$974$	−4.36068	−0.139725
$975$	−1.61803	−0.0518186
$976$	−6.76393	−0.216508
$977$	28.8328	0.922443	0.461222	−	0.887285i	$-0.347411\pi$
$977$	28.8328	0.922443	0.461222	+	0.887285i	$0.347411\pi$
$978$	17.8885	0.572013
$979$	0	0
$980$	5.09017	0.162600
$981$	−4.00000	−0.127710
$982$	−13.3262	−0.425257
$983$	−3.96556	−0.126482	−0.0632408	−	0.997998i	$-0.520144\pi$
$983$	−3.96556	−0.126482	−0.0632408	+	0.997998i	$0.520144\pi$
$984$	6.32624	0.201673
$985$	1.38197	0.0440331
$986$	−24.0000	−0.764316
$987$	−0.527864	−0.0168021
$988$	−2.61803	−0.0832908
$989$	9.70820	0.308703
$990$	0	0
$991$	−8.94427	−0.284124	−0.142062	−	0.989858i	$-0.545373\pi$
$991$	−8.94427	−0.284124	−0.142062	+	0.989858i	$0.545373\pi$
$992$	−4.76393	−0.151255
$993$	−23.3262	−0.740236
$994$	18.9443	0.600876
$995$	−4.94427	−0.156744
$996$	12.9443	0.410155
$997$	−57.7771	−1.82982	−0.914909	−	0.403659i	$-0.867738\pi$
$997$	−57.7771	−1.82982	−0.914909	+	0.403659i	$0.867738\pi$
$998$	26.6869	0.844760
$999$	−1.61803	−0.0511923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bi.1.2		2
11.2	odd	10		330.2.m.d.301.1	yes	4
11.6	odd	10		330.2.m.d.91.1	✓	4
11.10	odd	2		3630.2.a.bc.1.1		2
33.2	even	10		990.2.n.a.631.1		4
33.17	even	10		990.2.n.a.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.91.1	✓	4	11.6	odd	10
330.2.m.d.301.1	yes	4	11.2	odd	10
990.2.n.a.91.1		4	33.17	even	10
990.2.n.a.631.1		4	33.2	even	10
3630.2.a.bc.1.1		2	11.10	odd	2
3630.2.a.bi.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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