LMFDB - Embedded newform 1617.2.a.l.1.1

Newspace parameters

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$12.9118100068$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

$f(q)$	$=$	$q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} +2.23607 q^{5} -2.61803 q^{6} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} +2.23607 q^{5} -2.61803 q^{6} -7.47214 q^{8} +1.00000 q^{9} -5.85410 q^{10} -1.00000 q^{11} +4.85410 q^{12} -3.47214 q^{13} +2.23607 q^{15} +9.85410 q^{16} -6.00000 q^{17} -2.61803 q^{18} +4.23607 q^{19} +10.8541 q^{20} +2.61803 q^{22} -2.47214 q^{23} -7.47214 q^{24} +9.09017 q^{26} +1.00000 q^{27} -10.2361 q^{29} -5.85410 q^{30} -8.47214 q^{31} -10.8541 q^{32} -1.00000 q^{33} +15.7082 q^{34} +4.85410 q^{36} -0.527864 q^{37} -11.0902 q^{38} -3.47214 q^{39} -16.7082 q^{40} -6.00000 q^{41} -0.472136 q^{43} -4.85410 q^{44} +2.23607 q^{45} +6.47214 q^{46} -11.4721 q^{47} +9.85410 q^{48} -6.00000 q^{51} -16.8541 q^{52} -12.9443 q^{53} -2.61803 q^{54} -2.23607 q^{55} +4.23607 q^{57} +26.7984 q^{58} +11.9443 q^{59} +10.8541 q^{60} +6.94427 q^{61} +22.1803 q^{62} +8.70820 q^{64} -7.76393 q^{65} +2.61803 q^{66} +0.708204 q^{67} -29.1246 q^{68} -2.47214 q^{69} +4.47214 q^{71} -7.47214 q^{72} +1.00000 q^{73} +1.38197 q^{74} +20.5623 q^{76} +9.09017 q^{78} -2.47214 q^{79} +22.0344 q^{80} +1.00000 q^{81} +15.7082 q^{82} -12.4721 q^{83} -13.4164 q^{85} +1.23607 q^{86} -10.2361 q^{87} +7.47214 q^{88} +13.4164 q^{89} -5.85410 q^{90} -12.0000 q^{92} -8.47214 q^{93} +30.0344 q^{94} +9.47214 q^{95} -10.8541 q^{96} +6.94427 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{6} - 6 q^{8} + 2 q^{9} - 5 q^{10} - 2 q^{11} + 3 q^{12} + 2 q^{13} + 13 q^{16} - 12 q^{17} - 3 q^{18} + 4 q^{19} + 15 q^{20} + 3 q^{22} + 4 q^{23} - 6 q^{24} + 7 q^{26} + 2 q^{27} - 16 q^{29} - 5 q^{30} - 8 q^{31} - 15 q^{32} - 2 q^{33} + 18 q^{34} + 3 q^{36} - 10 q^{37} - 11 q^{38} + 2 q^{39} - 20 q^{40} - 12 q^{41} + 8 q^{43} - 3 q^{44} + 4 q^{46} - 14 q^{47} + 13 q^{48} - 12 q^{51} - 27 q^{52} - 8 q^{53} - 3 q^{54} + 4 q^{57} + 29 q^{58} + 6 q^{59} + 15 q^{60} - 4 q^{61} + 22 q^{62} + 4 q^{64} - 20 q^{65} + 3 q^{66} - 12 q^{67} - 18 q^{68} + 4 q^{69} - 6 q^{72} + 2 q^{73} + 5 q^{74} + 21 q^{76} + 7 q^{78} + 4 q^{79} + 15 q^{80} + 2 q^{81} + 18 q^{82} - 16 q^{83} - 2 q^{86} - 16 q^{87} + 6 q^{88} - 5 q^{90} - 24 q^{92} - 8 q^{93} + 31 q^{94} + 10 q^{95} - 15 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^6 - 6 * q^8 + 2 * q^9 - 5 * q^10 - 2 * q^11 + 3 * q^12 + 2 * q^13 + 13 * q^16 - 12 * q^17 - 3 * q^18 + 4 * q^19 + 15 * q^20 + 3 * q^22 + 4 * q^23 - 6 * q^24 + 7 * q^26 + 2 * q^27 - 16 * q^29 - 5 * q^30 - 8 * q^31 - 15 * q^32 - 2 * q^33 + 18 * q^34 + 3 * q^36 - 10 * q^37 - 11 * q^38 + 2 * q^39 - 20 * q^40 - 12 * q^41 + 8 * q^43 - 3 * q^44 + 4 * q^46 - 14 * q^47 + 13 * q^48 - 12 * q^51 - 27 * q^52 - 8 * q^53 - 3 * q^54 + 4 * q^57 + 29 * q^58 + 6 * q^59 + 15 * q^60 - 4 * q^61 + 22 * q^62 + 4 * q^64 - 20 * q^65 + 3 * q^66 - 12 * q^67 - 18 * q^68 + 4 * q^69 - 6 * q^72 + 2 * q^73 + 5 * q^74 + 21 * q^76 + 7 * q^78 + 4 * q^79 + 15 * q^80 + 2 * q^81 + 18 * q^82 - 16 * q^83 - 2 * q^86 - 16 * q^87 + 6 * q^88 - 5 * q^90 - 24 * q^92 - 8 * q^93 + 31 * q^94 + 10 * q^95 - 15 * q^96 - 4 * q^97 - 2 * q^99

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 $

$2$	−2.61803	−1.85123	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−2.61803	−1.85123	−0.925615	+	0.378467i	$0.876451\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.85410	2.42705
$5$	2.23607	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	−2.61803	−1.06881
$7$	0	0
$7$	0	0
$8$	−7.47214	−2.64180
$9$	1.00000	0.333333
$10$	−5.85410	−1.85123
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.85410	1.40126
$13$	−3.47214	−0.962997	−0.481499	−	0.876447i	$-0.659907\pi$
$13$	−3.47214	−0.962997	−0.481499	+	0.876447i	$0.659907\pi$
$14$	0	0
$15$	2.23607	0.577350
$16$	9.85410	2.46353
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−2.61803	−0.617077
$19$	4.23607	0.971821	0.485910	−	0.874009i	$-0.338488\pi$
$19$	4.23607	0.971821	0.485910	+	0.874009i	$0.338488\pi$
$20$	10.8541	2.42705
$21$	0	0
$22$	2.61803	0.558167
$23$	−2.47214	−0.515476	−0.257738	−	0.966215i	$-0.582977\pi$
$23$	−2.47214	−0.515476	−0.257738	+	0.966215i	$0.582977\pi$
$24$	−7.47214	−1.52524
$25$	0	0
$26$	9.09017	1.78273
$27$	1.00000	0.192450
$28$	0	0
$29$	−10.2361	−1.90079	−0.950395	−	0.311045i	$-0.899321\pi$
$29$	−10.2361	−1.90079	−0.950395	+	0.311045i	$0.899321\pi$
$30$	−5.85410	−1.06881
$31$	−8.47214	−1.52164	−0.760820	−	0.648963i	$-0.775203\pi$
$31$	−8.47214	−1.52164	−0.760820	+	0.648963i	$0.775203\pi$
$32$	−10.8541	−1.91875
$33$	−1.00000	−0.174078
$34$	15.7082	2.69393
$35$	0	0
$36$	4.85410	0.809017
$37$	−0.527864	−0.0867803	−0.0433902	−	0.999058i	$-0.513816\pi$
$37$	−0.527864	−0.0867803	−0.0433902	+	0.999058i	$0.513816\pi$
$38$	−11.0902	−1.79906
$39$	−3.47214	−0.555987
$40$	−16.7082	−2.64180
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−0.472136	−0.0720001	−0.0360000	−	0.999352i	$-0.511462\pi$
$43$	−0.472136	−0.0720001	−0.0360000	+	0.999352i	$0.511462\pi$
$44$	−4.85410	−0.731783
$45$	2.23607	0.333333
$46$	6.47214	0.954264
$47$	−11.4721	−1.67338	−0.836692	−	0.547674i	$-0.815513\pi$
$47$	−11.4721	−1.67338	−0.836692	+	0.547674i	$0.815513\pi$
$48$	9.85410	1.42232
$49$	0	0
$50$	0	0
$51$	−6.00000	−0.840168
$52$	−16.8541	−2.33724
$53$	−12.9443	−1.77803	−0.889016	−	0.457876i	$-0.848610\pi$
$53$	−12.9443	−1.77803	−0.889016	+	0.457876i	$0.848610\pi$
$54$	−2.61803	−0.356269
$55$	−2.23607	−0.301511
$56$	0	0
$57$	4.23607	0.561081
$58$	26.7984	3.51880
$59$	11.9443	1.55501	0.777506	−	0.628876i	$-0.216485\pi$
$59$	11.9443	1.55501	0.777506	+	0.628876i	$0.216485\pi$
$60$	10.8541	1.40126
$61$	6.94427	0.889123	0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427	0.889123	0.444561	+	0.895748i	$0.353360\pi$
$62$	22.1803	2.81691
$63$	0	0
$64$	8.70820	1.08853
$65$	−7.76393	−0.962997
$66$	2.61803	0.322258
$67$	0.708204	0.0865209	0.0432604	−	0.999064i	$-0.486225\pi$
$67$	0.708204	0.0865209	0.0432604	+	0.999064i	$0.486225\pi$
$68$	−29.1246	−3.53188
$69$	−2.47214	−0.297610
$70$	0	0
$71$	4.47214	0.530745	0.265372	−	0.964146i	$-0.414505\pi$
$71$	4.47214	0.530745	0.265372	+	0.964146i	$0.414505\pi$
$72$	−7.47214	−0.880600
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	1.38197	0.160650
$75$	0	0
$76$	20.5623	2.35866
$77$	0	0
$78$	9.09017	1.02926
$79$	−2.47214	−0.278137	−0.139069	−	0.990283i	$-0.544411\pi$
$79$	−2.47214	−0.278137	−0.139069	+	0.990283i	$0.544411\pi$
$80$	22.0344	2.46353
$81$	1.00000	0.111111
$82$	15.7082	1.73468
$83$	−12.4721	−1.36899	−0.684497	−	0.729015i	$-0.739978\pi$
$83$	−12.4721	−1.36899	−0.684497	+	0.729015i	$0.739978\pi$
$84$	0	0
$85$	−13.4164	−1.45521
$86$	1.23607	0.133289
$87$	−10.2361	−1.09742
$88$	7.47214	0.796532
$89$	13.4164	1.42214	0.711068	−	0.703123i	$-0.248212\pi$
$89$	13.4164	1.42214	0.711068	+	0.703123i	$0.248212\pi$
$90$	−5.85410	−0.617077
$91$	0	0
$92$	−12.0000	−1.25109
$93$	−8.47214	−0.878520
$94$	30.0344	3.09782
$95$	9.47214	0.971821
$96$	−10.8541	−1.10779
$97$	6.94427	0.705084	0.352542	−	0.935796i	$-0.385317\pi$
$97$	6.94427	0.705084	0.352542	+	0.935796i	$0.385317\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−3.52786	−0.351036	−0.175518	−	0.984476i	$-0.556160\pi$
$101$	−3.52786	−0.351036	−0.175518	+	0.984476i	$0.556160\pi$
$102$	15.7082	1.55534
$103$	7.41641	0.730760	0.365380	−	0.930858i	$-0.380939\pi$
$103$	7.41641	0.730760	0.365380	+	0.930858i	$0.380939\pi$
$104$	25.9443	2.54405
$105$	0	0
$106$	33.8885	3.29155
$107$	19.9443	1.92809	0.964043	−	0.265747i	$-0.0856186\pi$
$107$	19.9443	1.92809	0.964043	+	0.265747i	$0.0856186\pi$
$108$	4.85410	0.467086
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	5.85410	0.558167
$111$	−0.527864	−0.0501026
$112$	0	0
$113$	6.47214	0.608847	0.304424	−	0.952537i	$-0.401536\pi$
$113$	6.47214	0.608847	0.304424	+	0.952537i	$0.401536\pi$
$114$	−11.0902	−1.03869
$115$	−5.52786	−0.515476
$116$	−49.6869	−4.61331
$117$	−3.47214	−0.320999
$118$	−31.2705	−2.87868
$119$	0	0
$120$	−16.7082	−1.52524
$121$	1.00000	0.0909091
$122$	−18.1803	−1.64597
$123$	−6.00000	−0.541002
$124$	−41.1246	−3.69310
$125$	−11.1803	−1.00000
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.09017	−0.0963583
$129$	−0.472136	−0.0415693
$130$	20.3262	1.78273
$131$	4.47214	0.390732	0.195366	−	0.980730i	$-0.437410\pi$
$131$	4.47214	0.390732	0.195366	+	0.980730i	$0.437410\pi$
$132$	−4.85410	−0.422495
$133$	0	0
$134$	−1.85410	−0.160170
$135$	2.23607	0.192450
$136$	44.8328	3.84438
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	6.47214	0.550945
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	−11.4721	−0.966128
$142$	−11.7082	−0.982531
$143$	3.47214	0.290355
$144$	9.85410	0.821175
$145$	−22.8885	−1.90079
$146$	−2.61803	−0.216670
$147$	0	0
$148$	−2.56231	−0.210620
$149$	15.6525	1.28230	0.641150	−	0.767415i	$-0.278457\pi$
$149$	15.6525	1.28230	0.641150	+	0.767415i	$0.278457\pi$
$150$	0	0
$151$	−6.94427	−0.565117	−0.282558	−	0.959250i	$-0.591183\pi$
$151$	−6.94427	−0.565117	−0.282558	+	0.959250i	$0.591183\pi$
$152$	−31.6525	−2.56735
$153$	−6.00000	−0.485071
$154$	0	0
$155$	−18.9443	−1.52164
$156$	−16.8541	−1.34941
$157$	−3.41641	−0.272659	−0.136330	−	0.990664i	$-0.543531\pi$
$157$	−3.41641	−0.272659	−0.136330	+	0.990664i	$0.543531\pi$
$158$	6.47214	0.514895
$159$	−12.9443	−1.02655
$160$	−24.2705	−1.91875
$161$	0	0
$162$	−2.61803	−0.205692
$163$	−18.1246	−1.41963	−0.709815	−	0.704389i	$-0.751221\pi$
$163$	−18.1246	−1.41963	−0.709815	+	0.704389i	$0.751221\pi$
$164$	−29.1246	−2.27425
$165$	−2.23607	−0.174078
$166$	32.6525	2.53432
$167$	−18.4721	−1.42942	−0.714708	−	0.699423i	$-0.753441\pi$
$167$	−18.4721	−1.42942	−0.714708	+	0.699423i	$0.753441\pi$
$168$	0	0
$169$	−0.944272	−0.0726363
$170$	35.1246	2.69393
$171$	4.23607	0.323940
$172$	−2.29180	−0.174748
$173$	−5.52786	−0.420276	−0.210138	−	0.977672i	$-0.567391\pi$
$173$	−5.52786	−0.420276	−0.210138	+	0.977672i	$0.567391\pi$
$174$	26.7984	2.03158
$175$	0	0
$176$	−9.85410	−0.742781
$177$	11.9443	0.897786
$178$	−35.1246	−2.63270
$179$	−5.52786	−0.413172	−0.206586	−	0.978428i	$-0.566235\pi$
$179$	−5.52786	−0.413172	−0.206586	+	0.978428i	$0.566235\pi$
$180$	10.8541	0.809017
$181$	−0.472136	−0.0350936	−0.0175468	−	0.999846i	$-0.505586\pi$
$181$	−0.472136	−0.0350936	−0.0175468	+	0.999846i	$0.505586\pi$
$182$	0	0
$183$	6.94427	0.513335
$184$	18.4721	1.36178
$185$	−1.18034	−0.0867803
$186$	22.1803	1.62634
$187$	6.00000	0.438763
$188$	−55.6869	−4.06139
$189$	0	0
$190$	−24.7984	−1.79906
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	8.70820	0.628460
$193$	25.8885	1.86350	0.931749	−	0.363103i	$-0.118283\pi$
$193$	25.8885	1.86350	0.931749	+	0.363103i	$0.118283\pi$
$194$	−18.1803	−1.30527
$195$	−7.76393	−0.555987
$196$	0	0
$197$	−8.47214	−0.603615	−0.301807	−	0.953369i	$-0.597590\pi$
$197$	−8.47214	−0.603615	−0.301807	+	0.953369i	$0.597590\pi$
$198$	2.61803	0.186056
$199$	−24.4721	−1.73478	−0.867392	−	0.497626i	$-0.834205\pi$
$199$	−24.4721	−1.73478	−0.867392	+	0.497626i	$0.834205\pi$
$200$	0	0
$201$	0.708204	0.0499529
$202$	9.23607	0.649847
$203$	0	0
$204$	−29.1246	−2.03913
$205$	−13.4164	−0.937043
$206$	−19.4164	−1.35281
$207$	−2.47214	−0.171825
$208$	−34.2148	−2.37237
$209$	−4.23607	−0.293015
$210$	0	0
$211$	18.9443	1.30418	0.652089	−	0.758143i	$-0.273893\pi$
$211$	18.9443	1.30418	0.652089	+	0.758143i	$0.273893\pi$
$212$	−62.8328	−4.31538
$213$	4.47214	0.306426
$214$	−52.2148	−3.56933
$215$	−1.05573	−0.0720001
$216$	−7.47214	−0.508414
$217$	0	0
$218$	−15.7082	−1.06389
$219$	1.00000	0.0675737
$220$	−10.8541	−0.731783
$221$	20.8328	1.40137
$222$	1.38197	0.0927515
$223$	−18.0000	−1.20537	−0.602685	−	0.797980i	$-0.705902\pi$
$223$	−18.0000	−1.20537	−0.602685	+	0.797980i	$0.705902\pi$
$224$	0	0
$225$	0	0
$226$	−16.9443	−1.12712
$227$	−26.8328	−1.78096	−0.890478	−	0.455026i	$-0.849630\pi$
$227$	−26.8328	−1.78096	−0.890478	+	0.455026i	$0.849630\pi$
$228$	20.5623	1.36177
$229$	−15.4164	−1.01874	−0.509372	−	0.860546i	$-0.670122\pi$
$229$	−15.4164	−1.01874	−0.509372	+	0.860546i	$0.670122\pi$
$230$	14.4721	0.954264
$231$	0	0
$232$	76.4853	5.02151
$233$	13.4164	0.878938	0.439469	−	0.898258i	$-0.355167\pi$
$233$	13.4164	0.878938	0.439469	+	0.898258i	$0.355167\pi$
$234$	9.09017	0.594243
$235$	−25.6525	−1.67338
$236$	57.9787	3.77409
$237$	−2.47214	−0.160582
$238$	0	0
$239$	17.3607	1.12297	0.561485	−	0.827487i	$-0.310230\pi$
$239$	17.3607	1.12297	0.561485	+	0.827487i	$0.310230\pi$
$240$	22.0344	1.42232
$241$	19.0000	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$241$	19.0000	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$242$	−2.61803	−0.168294
$243$	1.00000	0.0641500
$244$	33.7082	2.15795
$245$	0	0
$246$	15.7082	1.00152
$247$	−14.7082	−0.935861
$248$	63.3050	4.01987
$249$	−12.4721	−0.790390
$250$	29.2705	1.85123
$251$	−3.94427	−0.248960	−0.124480	−	0.992222i	$-0.539726\pi$
$251$	−3.94427	−0.248960	−0.124480	+	0.992222i	$0.539726\pi$
$252$	0	0
$253$	2.47214	0.155422
$254$	−41.8885	−2.62832
$255$	−13.4164	−0.840168
$256$	−14.5623	−0.910144
$257$	7.76393	0.484301	0.242150	−	0.970239i	$-0.422147\pi$
$257$	7.76393	0.484301	0.242150	+	0.970239i	$0.422147\pi$
$258$	1.23607	0.0769542
$259$	0	0
$260$	−37.6869	−2.33724
$261$	−10.2361	−0.633597
$262$	−11.7082	−0.723335
$263$	−4.41641	−0.272327	−0.136164	−	0.990686i	$-0.543477\pi$
$263$	−4.41641	−0.272327	−0.136164	+	0.990686i	$0.543477\pi$
$264$	7.47214	0.459878
$265$	−28.9443	−1.77803
$266$	0	0
$267$	13.4164	0.821071
$268$	3.43769	0.209991
$269$	16.4721	1.00432	0.502162	−	0.864774i	$-0.332538\pi$
$269$	16.4721	1.00432	0.502162	+	0.864774i	$0.332538\pi$
$270$	−5.85410	−0.356269
$271$	−5.29180	−0.321454	−0.160727	−	0.986999i	$-0.551384\pi$
$271$	−5.29180	−0.321454	−0.160727	+	0.986999i	$0.551384\pi$
$272$	−59.1246	−3.58496
$273$	0	0
$274$	−15.7082	−0.948967
$275$	0	0
$276$	−12.0000	−0.722315
$277$	−18.9443	−1.13825	−0.569125	−	0.822251i	$-0.692718\pi$
$277$	−18.9443	−1.13825	−0.569125	+	0.822251i	$0.692718\pi$
$278$	20.9443	1.25615
$279$	−8.47214	−0.507214
$280$	0	0
$281$	5.18034	0.309033	0.154517	−	0.987990i	$-0.450618\pi$
$281$	5.18034	0.309033	0.154517	+	0.987990i	$0.450618\pi$
$282$	30.0344	1.78852
$283$	−4.70820	−0.279874	−0.139937	−	0.990160i	$-0.544690\pi$
$283$	−4.70820	−0.279874	−0.139937	+	0.990160i	$0.544690\pi$
$284$	21.7082	1.28814
$285$	9.47214	0.561081
$286$	−9.09017	−0.537513
$287$	0	0
$288$	−10.8541	−0.639584
$289$	19.0000	1.11765
$290$	59.9230	3.51880
$291$	6.94427	0.407080
$292$	4.85410	0.284065
$293$	9.88854	0.577695	0.288847	−	0.957375i	$-0.406728\pi$
$293$	9.88854	0.577695	0.288847	+	0.957375i	$0.406728\pi$
$294$	0	0
$295$	26.7082	1.55501
$296$	3.94427	0.229256
$297$	−1.00000	−0.0580259
$298$	−40.9787	−2.37383
$299$	8.58359	0.496402
$300$	0	0
$301$	0	0
$302$	18.1803	1.04616
$303$	−3.52786	−0.202670
$304$	41.7426	2.39410
$305$	15.5279	0.889123
$306$	15.7082	0.897978
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	0	0
$309$	7.41641	0.421905
$310$	49.5967	2.81691
$311$	12.9443	0.734002	0.367001	−	0.930220i	$-0.380385\pi$
$311$	12.9443	0.734002	0.367001	+	0.930220i	$0.380385\pi$
$312$	25.9443	1.46881
$313$	−26.3607	−1.48999	−0.744997	−	0.667068i	$-0.767549\pi$
$313$	−26.3607	−1.48999	−0.744997	+	0.667068i	$0.767549\pi$
$314$	8.94427	0.504754
$315$	0	0
$316$	−12.0000	−0.675053
$317$	26.9443	1.51334	0.756671	−	0.653796i	$-0.226825\pi$
$317$	26.9443	1.51334	0.756671	+	0.653796i	$0.226825\pi$
$318$	33.8885	1.90038
$319$	10.2361	0.573110
$320$	19.4721	1.08853
$321$	19.9443	1.11318
$322$	0	0
$323$	−25.4164	−1.41421
$324$	4.85410	0.269672
$325$	0	0
$326$	47.4508	2.62806
$327$	6.00000	0.331801
$328$	44.8328	2.47548
$329$	0	0
$330$	5.85410	0.322258
$331$	−16.0000	−0.879440	−0.439720	−	0.898135i	$-0.644922\pi$
$331$	−16.0000	−0.879440	−0.439720	+	0.898135i	$0.644922\pi$
$332$	−60.5410	−3.32262
$333$	−0.527864	−0.0289268
$334$	48.3607	2.64618
$335$	1.58359	0.0865209
$336$	0	0
$337$	11.4164	0.621891	0.310946	−	0.950428i	$-0.399354\pi$
$337$	11.4164	0.621891	0.310946	+	0.950428i	$0.399354\pi$
$338$	2.47214	0.134466
$339$	6.47214	0.351518
$340$	−65.1246	−3.53188
$341$	8.47214	0.458792
$342$	−11.0902	−0.599688
$343$	0	0
$344$	3.52786	0.190210
$345$	−5.52786	−0.297610
$346$	14.4721	0.778027
$347$	0.944272	0.0506912	0.0253456	−	0.999679i	$-0.491931\pi$
$347$	0.944272	0.0506912	0.0253456	+	0.999679i	$0.491931\pi$
$348$	−49.6869	−2.66350
$349$	2.41641	0.129347	0.0646737	−	0.997906i	$-0.479399\pi$
$349$	2.41641	0.129347	0.0646737	+	0.997906i	$0.479399\pi$
$350$	0	0
$351$	−3.47214	−0.185329
$352$	10.8541	0.578526
$353$	4.23607	0.225463	0.112732	−	0.993625i	$-0.464040\pi$
$353$	4.23607	0.225463	0.112732	+	0.993625i	$0.464040\pi$
$354$	−31.2705	−1.66201
$355$	10.0000	0.530745
$356$	65.1246	3.45160
$357$	0	0
$358$	14.4721	0.764876
$359$	−20.9443	−1.10540	−0.552698	−	0.833381i	$-0.686402\pi$
$359$	−20.9443	−1.10540	−0.552698	+	0.833381i	$0.686402\pi$
$360$	−16.7082	−0.880600
$361$	−1.05573	−0.0555646
$362$	1.23607	0.0649663
$363$	1.00000	0.0524864
$364$	0	0
$365$	2.23607	0.117041
$366$	−18.1803	−0.950302
$367$	25.4164	1.32673	0.663363	−	0.748298i	$-0.269129\pi$
$367$	25.4164	1.32673	0.663363	+	0.748298i	$0.269129\pi$
$368$	−24.3607	−1.26989
$369$	−6.00000	−0.312348
$370$	3.09017	0.160650
$371$	0	0
$372$	−41.1246	−2.13221
$373$	−16.9443	−0.877341	−0.438671	−	0.898648i	$-0.644550\pi$
$373$	−16.9443	−0.877341	−0.438671	+	0.898648i	$0.644550\pi$
$374$	−15.7082	−0.812252
$375$	−11.1803	−0.577350
$376$	85.7214	4.42074
$377$	35.5410	1.83046
$378$	0	0
$379$	−25.6525	−1.31768	−0.658840	−	0.752283i	$-0.728952\pi$
$379$	−25.6525	−1.31768	−0.658840	+	0.752283i	$0.728952\pi$
$380$	45.9787	2.35866
$381$	16.0000	0.819705
$382$	−31.4164	−1.60740
$383$	−8.94427	−0.457031	−0.228515	−	0.973540i	$-0.573387\pi$
$383$	−8.94427	−0.457031	−0.228515	+	0.973540i	$0.573387\pi$
$384$	−1.09017	−0.0556325
$385$	0	0
$386$	−67.7771	−3.44976
$387$	−0.472136	−0.0240000
$388$	33.7082	1.71127
$389$	20.8328	1.05627	0.528133	−	0.849162i	$-0.322892\pi$
$389$	20.8328	1.05627	0.528133	+	0.849162i	$0.322892\pi$
$390$	20.3262	1.02926
$391$	14.8328	0.750128
$392$	0	0
$393$	4.47214	0.225589
$394$	22.1803	1.11743
$395$	−5.52786	−0.278137
$396$	−4.85410	−0.243928
$397$	−9.41641	−0.472596	−0.236298	−	0.971681i	$-0.575934\pi$
$397$	−9.41641	−0.472596	−0.236298	+	0.971681i	$0.575934\pi$
$398$	64.0689	3.21148
$399$	0	0
$400$	0	0
$401$	−8.47214	−0.423078	−0.211539	−	0.977370i	$-0.567848\pi$
$401$	−8.47214	−0.423078	−0.211539	+	0.977370i	$0.567848\pi$
$402$	−1.85410	−0.0924742
$403$	29.4164	1.46534
$404$	−17.1246	−0.851981
$405$	2.23607	0.111111
$406$	0	0
$407$	0.527864	0.0261652
$408$	44.8328	2.21956
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	35.1246	1.73468
$411$	6.00000	0.295958
$412$	36.0000	1.77359
$413$	0	0
$414$	6.47214	0.318088
$415$	−27.8885	−1.36899
$416$	37.6869	1.84775
$417$	−8.00000	−0.391762
$418$	11.0902	0.542438
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	0	0
$421$	29.4721	1.43638	0.718192	−	0.695845i	$-0.244970\pi$
$421$	29.4721	1.43638	0.718192	+	0.695845i	$0.244970\pi$
$422$	−49.5967	−2.41433
$423$	−11.4721	−0.557794
$424$	96.7214	4.69720
$425$	0	0
$426$	−11.7082	−0.567264
$427$	0	0
$428$	96.8115	4.67956
$429$	3.47214	0.167636
$430$	2.76393	0.133289
$431$	−17.3607	−0.836235	−0.418117	−	0.908393i	$-0.637310\pi$
$431$	−17.3607	−0.836235	−0.418117	+	0.908393i	$0.637310\pi$
$432$	9.85410	0.474106
$433$	12.5836	0.604729	0.302364	−	0.953192i	$-0.402224\pi$
$433$	12.5836	0.604729	0.302364	+	0.953192i	$0.402224\pi$
$434$	0	0
$435$	−22.8885	−1.09742
$436$	29.1246	1.39482
$437$	−10.4721	−0.500950
$438$	−2.61803	−0.125095
$439$	−8.12461	−0.387767	−0.193883	−	0.981025i	$-0.562108\pi$
$439$	−8.12461	−0.387767	−0.193883	+	0.981025i	$0.562108\pi$
$440$	16.7082	0.796532
$441$	0	0
$442$	−54.5410	−2.59425
$443$	9.05573	0.430251	0.215125	−	0.976586i	$-0.430984\pi$
$443$	9.05573	0.430251	0.215125	+	0.976586i	$0.430984\pi$
$444$	−2.56231	−0.121602
$445$	30.0000	1.42214
$446$	47.1246	2.23142
$447$	15.6525	0.740337
$448$	0	0
$449$	−25.4164	−1.19947	−0.599737	−	0.800197i	$-0.704728\pi$
$449$	−25.4164	−1.19947	−0.599737	+	0.800197i	$0.704728\pi$
$450$	0	0
$451$	6.00000	0.282529
$452$	31.4164	1.47770
$453$	−6.94427	−0.326270
$454$	70.2492	3.29696
$455$	0	0
$456$	−31.6525	−1.48226
$457$	−11.4164	−0.534037	−0.267019	−	0.963691i	$-0.586038\pi$
$457$	−11.4164	−0.534037	−0.267019	+	0.963691i	$0.586038\pi$
$458$	40.3607	1.88593
$459$	−6.00000	−0.280056
$460$	−26.8328	−1.25109
$461$	−16.4721	−0.767184	−0.383592	−	0.923503i	$-0.625313\pi$
$461$	−16.4721	−0.767184	−0.383592	+	0.923503i	$0.625313\pi$
$462$	0	0
$463$	−2.70820	−0.125861	−0.0629305	−	0.998018i	$-0.520045\pi$
$463$	−2.70820	−0.125861	−0.0629305	+	0.998018i	$0.520045\pi$
$464$	−100.867	−4.68264
$465$	−18.9443	−0.878520
$466$	−35.1246	−1.62712
$467$	−23.8328	−1.10285	−0.551426	−	0.834224i	$-0.685916\pi$
$467$	−23.8328	−1.10285	−0.551426	+	0.834224i	$0.685916\pi$
$468$	−16.8541	−0.779081
$469$	0	0
$470$	67.1591	3.09782
$471$	−3.41641	−0.157420
$472$	−89.2492	−4.10803
$473$	0.472136	0.0217088
$474$	6.47214	0.297275
$475$	0	0
$476$	0	0
$477$	−12.9443	−0.592677
$478$	−45.4508	−2.07887
$479$	−21.8885	−1.00011	−0.500057	−	0.865993i	$-0.666687\pi$
$479$	−21.8885	−1.00011	−0.500057	+	0.865993i	$0.666687\pi$
$480$	−24.2705	−1.10779
$481$	1.83282	0.0835692
$482$	−49.7426	−2.26572
$483$	0	0
$484$	4.85410	0.220641
$485$	15.5279	0.705084
$486$	−2.61803	−0.118756
$487$	−21.8885	−0.991865	−0.495932	−	0.868361i	$-0.665174\pi$
$487$	−21.8885	−0.991865	−0.495932	+	0.868361i	$0.665174\pi$
$488$	−51.8885	−2.34888
$489$	−18.1246	−0.819623
$490$	0	0
$491$	−10.8885	−0.491393	−0.245697	−	0.969347i	$-0.579017\pi$
$491$	−10.8885	−0.491393	−0.245697	+	0.969347i	$0.579017\pi$
$492$	−29.1246	−1.31304
$493$	61.4164	2.76606
$494$	38.5066	1.73249
$495$	−2.23607	−0.100504
$496$	−83.4853	−3.74860
$497$	0	0
$498$	32.6525	1.46319
$499$	22.1246	0.990434	0.495217	−	0.868769i	$-0.335089\pi$
$499$	22.1246	0.990434	0.495217	+	0.868769i	$0.335089\pi$
$500$	−54.2705	−2.42705
$501$	−18.4721	−0.825274
$502$	10.3262	0.460883
$503$	−10.5836	−0.471899	−0.235950	−	0.971765i	$-0.575820\pi$
$503$	−10.5836	−0.471899	−0.235950	+	0.971765i	$0.575820\pi$
$504$	0	0
$505$	−7.88854	−0.351036
$506$	−6.47214	−0.287722
$507$	−0.944272	−0.0419366
$508$	77.6656	3.44586
$509$	−35.5279	−1.57474	−0.787372	−	0.616478i	$-0.788559\pi$
$509$	−35.5279	−1.57474	−0.787372	+	0.616478i	$0.788559\pi$
$510$	35.1246	1.55534
$511$	0	0
$512$	40.3050	1.78124
$513$	4.23607	0.187027
$514$	−20.3262	−0.896552
$515$	16.5836	0.730760
$516$	−2.29180	−0.100891
$517$	11.4721	0.504544
$518$	0	0
$519$	−5.52786	−0.242646
$520$	58.0132	2.54405
$521$	23.7639	1.04112	0.520558	−	0.853826i	$-0.325724\pi$
$521$	23.7639	1.04112	0.520558	+	0.853826i	$0.325724\pi$
$522$	26.7984	1.17293
$523$	−3.29180	−0.143940	−0.0719701	−	0.997407i	$-0.522929\pi$
$523$	−3.29180	−0.143940	−0.0719701	+	0.997407i	$0.522929\pi$
$524$	21.7082	0.948327
$525$	0	0
$526$	11.5623	0.504140
$527$	50.8328	2.21431
$528$	−9.85410	−0.428845
$529$	−16.8885	−0.734285
$530$	75.7771	3.29155
$531$	11.9443	0.518337
$532$	0	0
$533$	20.8328	0.902369
$534$	−35.1246	−1.51999
$535$	44.5967	1.92809
$536$	−5.29180	−0.228571
$537$	−5.52786	−0.238545
$538$	−43.1246	−1.85923
$539$	0	0
$540$	10.8541	0.467086
$541$	21.4164	0.920763	0.460382	−	0.887721i	$-0.347713\pi$
$541$	21.4164	0.920763	0.460382	+	0.887721i	$0.347713\pi$
$542$	13.8541	0.595085
$543$	−0.472136	−0.0202613
$544$	65.1246	2.79219
$545$	13.4164	0.574696
$546$	0	0
$547$	−13.4164	−0.573644	−0.286822	−	0.957984i	$-0.592599\pi$
$547$	−13.4164	−0.573644	−0.286822	+	0.957984i	$0.592599\pi$
$548$	29.1246	1.24414
$549$	6.94427	0.296374
$550$	0	0
$551$	−43.3607	−1.84723
$552$	18.4721	0.786226
$553$	0	0
$554$	49.5967	2.10716
$555$	−1.18034	−0.0501026
$556$	−38.8328	−1.64688
$557$	−8.12461	−0.344251	−0.172125	−	0.985075i	$-0.555063\pi$
$557$	−8.12461	−0.344251	−0.172125	+	0.985075i	$0.555063\pi$
$558$	22.1803	0.938969
$559$	1.63932	0.0693359
$560$	0	0
$561$	6.00000	0.253320
$562$	−13.5623	−0.572091
$563$	4.47214	0.188478	0.0942390	−	0.995550i	$-0.469958\pi$
$563$	4.47214	0.188478	0.0942390	+	0.995550i	$0.469958\pi$
$564$	−55.6869	−2.34484
$565$	14.4721	0.608847
$566$	12.3262	0.518110
$567$	0	0
$568$	−33.4164	−1.40212
$569$	−12.4721	−0.522859	−0.261430	−	0.965223i	$-0.584194\pi$
$569$	−12.4721	−0.522859	−0.261430	+	0.965223i	$0.584194\pi$
$570$	−24.7984	−1.03869
$571$	−10.5836	−0.442910	−0.221455	−	0.975171i	$-0.571081\pi$
$571$	−10.5836	−0.442910	−0.221455	+	0.975171i	$0.571081\pi$
$572$	16.8541	0.704705
$573$	12.0000	0.501307
$574$	0	0
$575$	0	0
$576$	8.70820	0.362842
$577$	−34.9443	−1.45475	−0.727375	−	0.686241i	$-0.759260\pi$
$577$	−34.9443	−1.45475	−0.727375	+	0.686241i	$0.759260\pi$
$578$	−49.7426	−2.06902
$579$	25.8885	1.07589
$580$	−111.103	−4.61331
$581$	0	0
$582$	−18.1803	−0.753599
$583$	12.9443	0.536097
$584$	−7.47214	−0.309199
$585$	−7.76393	−0.320999
$586$	−25.8885	−1.06945
$587$	−14.0557	−0.580142	−0.290071	−	0.957005i	$-0.593679\pi$
$587$	−14.0557	−0.580142	−0.290071	+	0.957005i	$0.593679\pi$
$588$	0	0
$589$	−35.8885	−1.47876
$590$	−69.9230	−2.87868
$591$	−8.47214	−0.348497
$592$	−5.20163	−0.213786
$593$	37.4164	1.53651	0.768254	−	0.640145i	$-0.221126\pi$
$593$	37.4164	1.53651	0.768254	+	0.640145i	$0.221126\pi$
$594$	2.61803	0.107419
$595$	0	0
$596$	75.9787	3.11221
$597$	−24.4721	−1.00158
$598$	−22.4721	−0.918954
$599$	25.3050	1.03393	0.516966	−	0.856006i	$-0.327061\pi$
$599$	25.3050	1.03393	0.516966	+	0.856006i	$0.327061\pi$
$600$	0	0
$601$	−5.83282	−0.237926	−0.118963	−	0.992899i	$-0.537957\pi$
$601$	−5.83282	−0.237926	−0.118963	+	0.992899i	$0.537957\pi$
$602$	0	0
$603$	0.708204	0.0288403
$604$	−33.7082	−1.37157
$605$	2.23607	0.0909091
$606$	9.23607	0.375190
$607$	22.7082	0.921698	0.460849	−	0.887479i	$-0.347545\pi$
$607$	22.7082	0.921698	0.460849	+	0.887479i	$0.347545\pi$
$608$	−45.9787	−1.86468
$609$	0	0
$610$	−40.6525	−1.64597
$611$	39.8328	1.61146
$612$	−29.1246	−1.17729
$613$	19.4164	0.784221	0.392111	−	0.919918i	$-0.371745\pi$
$613$	19.4164	0.784221	0.392111	+	0.919918i	$0.371745\pi$
$614$	41.8885	1.69048
$615$	−13.4164	−0.541002
$616$	0	0
$617$	−40.2492	−1.62037	−0.810186	−	0.586172i	$-0.800634\pi$
$617$	−40.2492	−1.62037	−0.810186	+	0.586172i	$0.800634\pi$
$618$	−19.4164	−0.781042
$619$	−27.4164	−1.10196	−0.550979	−	0.834519i	$-0.685746\pi$
$619$	−27.4164	−1.10196	−0.550979	+	0.834519i	$0.685746\pi$
$620$	−91.9574	−3.69310
$621$	−2.47214	−0.0992034
$622$	−33.8885	−1.35881
$623$	0	0
$624$	−34.2148	−1.36969
$625$	−25.0000	−1.00000
$626$	69.0132	2.75832
$627$	−4.23607	−0.169172
$628$	−16.5836	−0.661757
$629$	3.16718	0.126284
$630$	0	0
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	18.4721	0.734782
$633$	18.9443	0.752967
$634$	−70.5410	−2.80154
$635$	35.7771	1.41977
$636$	−62.8328	−2.49148
$637$	0	0
$638$	−26.7984	−1.06096
$639$	4.47214	0.176915
$640$	−2.43769	−0.0963583
$641$	31.5279	1.24528	0.622638	−	0.782510i	$-0.286061\pi$
$641$	31.5279	1.24528	0.622638	+	0.782510i	$0.286061\pi$
$642$	−52.2148	−2.06075
$643$	−5.41641	−0.213602	−0.106801	−	0.994280i	$-0.534061\pi$
$643$	−5.41641	−0.213602	−0.106801	+	0.994280i	$0.534061\pi$
$644$	0	0
$645$	−1.05573	−0.0415693
$646$	66.5410	2.61802
$647$	4.41641	0.173627	0.0868135	−	0.996225i	$-0.472332\pi$
$647$	4.41641	0.173627	0.0868135	+	0.996225i	$0.472332\pi$
$648$	−7.47214	−0.293533
$649$	−11.9443	−0.468854
$650$	0	0
$651$	0	0
$652$	−87.9787	−3.44551
$653$	5.88854	0.230437	0.115218	−	0.993340i	$-0.463243\pi$
$653$	5.88854	0.230437	0.115218	+	0.993340i	$0.463243\pi$
$654$	−15.7082	−0.614239
$655$	10.0000	0.390732
$656$	−59.1246	−2.30843
$657$	1.00000	0.0390137
$658$	0	0
$659$	32.8885	1.28116	0.640578	−	0.767893i	$-0.278695\pi$
$659$	32.8885	1.28116	0.640578	+	0.767893i	$0.278695\pi$
$660$	−10.8541	−0.422495
$661$	4.00000	0.155582	0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000	0.155582	0.0777910	+	0.996970i	$0.475213\pi$
$662$	41.8885	1.62804
$663$	20.8328	0.809080
$664$	93.1935	3.61661
$665$	0	0
$666$	1.38197	0.0535501
$667$	25.3050	0.979812
$668$	−89.6656	−3.46927
$669$	−18.0000	−0.695920
$670$	−4.14590	−0.160170
$671$	−6.94427	−0.268081
$672$	0	0
$673$	−18.5836	−0.716345	−0.358172	−	0.933655i	$-0.616600\pi$
$673$	−18.5836	−0.716345	−0.358172	+	0.933655i	$0.616600\pi$
$674$	−29.8885	−1.15126
$675$	0	0
$676$	−4.58359	−0.176292
$677$	−43.4164	−1.66863	−0.834314	−	0.551289i	$-0.814136\pi$
$677$	−43.4164	−1.66863	−0.834314	+	0.551289i	$0.814136\pi$
$678$	−16.9443	−0.650741
$679$	0	0
$680$	100.249	3.84438
$681$	−26.8328	−1.02824
$682$	−22.1803	−0.849329
$683$	9.52786	0.364574	0.182287	−	0.983245i	$-0.441650\pi$
$683$	9.52786	0.364574	0.182287	+	0.983245i	$0.441650\pi$
$684$	20.5623	0.786219
$685$	13.4164	0.512615
$686$	0	0
$687$	−15.4164	−0.588173
$688$	−4.65248	−0.177374
$689$	44.9443	1.71224
$690$	14.4721	0.550945
$691$	−6.58359	−0.250452	−0.125226	−	0.992128i	$-0.539966\pi$
$691$	−6.58359	−0.250452	−0.125226	+	0.992128i	$0.539966\pi$
$692$	−26.8328	−1.02003
$693$	0	0
$694$	−2.47214	−0.0938410
$695$	−17.8885	−0.678551
$696$	76.4853	2.89917
$697$	36.0000	1.36360
$698$	−6.32624	−0.239452
$699$	13.4164	0.507455
$700$	0	0
$701$	−13.4164	−0.506731	−0.253365	−	0.967371i	$-0.581537\pi$
$701$	−13.4164	−0.506731	−0.253365	+	0.967371i	$0.581537\pi$
$702$	9.09017	0.343086
$703$	−2.23607	−0.0843349
$704$	−8.70820	−0.328203
$705$	−25.6525	−0.966128
$706$	−11.0902	−0.417384
$707$	0	0
$708$	57.9787	2.17897
$709$	22.4164	0.841866	0.420933	−	0.907092i	$-0.361703\pi$
$709$	22.4164	0.841866	0.420933	+	0.907092i	$0.361703\pi$
$710$	−26.1803	−0.982531
$711$	−2.47214	−0.0927123
$712$	−100.249	−3.75700
$713$	20.9443	0.784369
$714$	0	0
$715$	7.76393	0.290355
$716$	−26.8328	−1.00279
$717$	17.3607	0.648346
$718$	54.8328	2.04634
$719$	4.63932	0.173017	0.0865087	−	0.996251i	$-0.472429\pi$
$719$	4.63932	0.173017	0.0865087	+	0.996251i	$0.472429\pi$
$720$	22.0344	0.821175
$721$	0	0
$722$	2.76393	0.102863
$723$	19.0000	0.706618
$724$	−2.29180	−0.0851739
$725$	0	0
$726$	−2.61803	−0.0971644
$727$	−4.58359	−0.169996	−0.0849980	−	0.996381i	$-0.527088\pi$
$727$	−4.58359	−0.169996	−0.0849980	+	0.996381i	$0.527088\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.85410	−0.216670
$731$	2.83282	0.104775
$732$	33.7082	1.24589
$733$	−29.0557	−1.07320	−0.536599	−	0.843837i	$-0.680291\pi$
$733$	−29.0557	−1.07320	−0.536599	+	0.843837i	$0.680291\pi$
$734$	−66.5410	−2.45607
$735$	0	0
$736$	26.8328	0.989071
$737$	−0.708204	−0.0260870
$738$	15.7082	0.578227
$739$	43.4164	1.59710	0.798549	−	0.601930i	$-0.205601\pi$
$739$	43.4164	1.59710	0.798549	+	0.601930i	$0.205601\pi$
$740$	−5.72949	−0.210620
$741$	−14.7082	−0.540319
$742$	0	0
$743$	12.3050	0.451425	0.225712	−	0.974194i	$-0.427529\pi$
$743$	12.3050	0.451425	0.225712	+	0.974194i	$0.427529\pi$
$744$	63.3050	2.32087
$745$	35.0000	1.28230
$746$	44.3607	1.62416
$747$	−12.4721	−0.456332
$748$	29.1246	1.06490
$749$	0	0
$750$	29.2705	1.06881
$751$	12.1246	0.442433	0.221217	−	0.975225i	$-0.428997\pi$
$751$	12.1246	0.442433	0.221217	+	0.975225i	$0.428997\pi$
$752$	−113.048	−4.12242
$753$	−3.94427	−0.143737
$754$	−93.0476	−3.38859
$755$	−15.5279	−0.565117
$756$	0	0
$757$	−11.5836	−0.421013	−0.210506	−	0.977592i	$-0.567511\pi$
$757$	−11.5836	−0.421013	−0.210506	+	0.977592i	$0.567511\pi$
$758$	67.1591	2.43933
$759$	2.47214	0.0897329
$760$	−70.7771	−2.56735
$761$	−13.5279	−0.490385	−0.245192	−	0.969474i	$-0.578851\pi$
$761$	−13.5279	−0.490385	−0.245192	+	0.969474i	$0.578851\pi$
$762$	−41.8885	−1.51746
$763$	0	0
$764$	58.2492	2.10738
$765$	−13.4164	−0.485071
$766$	23.4164	0.846069
$767$	−41.4721	−1.49747
$768$	−14.5623	−0.525472
$769$	−1.00000	−0.0360609	−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000	−0.0360609	−0.0180305	+	0.999837i	$0.505740\pi$
$770$	0	0
$771$	7.76393	0.279611
$772$	125.666	4.52281
$773$	20.3475	0.731850	0.365925	−	0.930644i	$-0.380753\pi$
$773$	20.3475	0.731850	0.365925	+	0.930644i	$0.380753\pi$
$774$	1.23607	0.0444295
$775$	0	0
$776$	−51.8885	−1.86269
$777$	0	0
$778$	−54.5410	−1.95539
$779$	−25.4164	−0.910637
$780$	−37.6869	−1.34941
$781$	−4.47214	−0.160026
$782$	−38.8328	−1.38866
$783$	−10.2361	−0.365807
$784$	0	0
$785$	−7.63932	−0.272659
$786$	−11.7082	−0.417618
$787$	−38.1246	−1.35900	−0.679498	−	0.733678i	$-0.737802\pi$
$787$	−38.1246	−1.35900	−0.679498	+	0.733678i	$0.737802\pi$
$788$	−41.1246	−1.46500
$789$	−4.41641	−0.157228
$790$	14.4721	0.514895
$791$	0	0
$792$	7.47214	0.265511
$793$	−24.1115	−0.856223
$794$	24.6525	0.874884
$795$	−28.9443	−1.02655
$796$	−118.790	−4.21041
$797$	45.7639	1.62104	0.810521	−	0.585710i	$-0.199184\pi$
$797$	45.7639	1.62104	0.810521	+	0.585710i	$0.199184\pi$
$798$	0	0
$799$	68.8328	2.43513
$800$	0	0
$801$	13.4164	0.474045
$802$	22.1803	0.783215
$803$	−1.00000	−0.0352892
$804$	3.43769	0.121238
$805$	0	0
$806$	−77.0132	−2.71267
$807$	16.4721	0.579847
$808$	26.3607	0.927365
$809$	−14.8197	−0.521032	−0.260516	−	0.965470i	$-0.583893\pi$
$809$	−14.8197	−0.521032	−0.260516	+	0.965470i	$0.583893\pi$
$810$	−5.85410	−0.205692
$811$	27.5410	0.967096	0.483548	−	0.875318i	$-0.339348\pi$
$811$	27.5410	0.967096	0.483548	+	0.875318i	$0.339348\pi$
$812$	0	0
$813$	−5.29180	−0.185591
$814$	−1.38197	−0.0484379
$815$	−40.5279	−1.41963
$816$	−59.1246	−2.06978
$817$	−2.00000	−0.0699711
$818$	36.6525	1.28152
$819$	0	0
$820$	−65.1246	−2.27425
$821$	−33.5410	−1.17059	−0.585295	−	0.810821i	$-0.699021\pi$
$821$	−33.5410	−1.17059	−0.585295	+	0.810821i	$0.699021\pi$
$822$	−15.7082	−0.547887
$823$	−45.5410	−1.58746	−0.793730	−	0.608270i	$-0.791864\pi$
$823$	−45.5410	−1.58746	−0.793730	+	0.608270i	$0.791864\pi$
$824$	−55.4164	−1.93052
$825$	0	0
$826$	0	0
$827$	0.167184	0.00581357	0.00290678	−	0.999996i	$-0.499075\pi$
$827$	0.167184	0.00581357	0.00290678	+	0.999996i	$0.499075\pi$
$828$	−12.0000	−0.417029
$829$	34.8328	1.20979	0.604897	−	0.796304i	$-0.293214\pi$
$829$	34.8328	1.20979	0.604897	+	0.796304i	$0.293214\pi$
$830$	73.0132	2.53432
$831$	−18.9443	−0.657170
$832$	−30.2361	−1.04825
$833$	0	0
$834$	20.9443	0.725241
$835$	−41.3050	−1.42942
$836$	−20.5623	−0.711162
$837$	−8.47214	−0.292840
$838$	7.85410	0.271315
$839$	20.5279	0.708701	0.354350	−	0.935113i	$-0.384702\pi$
$839$	20.5279	0.708701	0.354350	+	0.935113i	$0.384702\pi$
$840$	0	0
$841$	75.7771	2.61300
$842$	−77.1591	−2.65908
$843$	5.18034	0.178420
$844$	91.9574	3.16531
$845$	−2.11146	−0.0726363
$846$	30.0344	1.03261
$847$	0	0
$848$	−127.554	−4.38023
$849$	−4.70820	−0.161585
$850$	0	0
$851$	1.30495	0.0447332
$852$	21.7082	0.743711
$853$	54.7214	1.87362	0.936812	−	0.349834i	$-0.113762\pi$
$853$	54.7214	1.87362	0.936812	+	0.349834i	$0.113762\pi$
$854$	0	0
$855$	9.47214	0.323940
$856$	−149.026	−5.09361
$857$	50.7214	1.73261	0.866304	−	0.499517i	$-0.166489\pi$
$857$	50.7214	1.73261	0.866304	+	0.499517i	$0.166489\pi$
$858$	−9.09017	−0.310333
$859$	−15.4164	−0.526001	−0.263001	−	0.964796i	$-0.584712\pi$
$859$	−15.4164	−0.526001	−0.263001	+	0.964796i	$0.584712\pi$
$860$	−5.12461	−0.174748
$861$	0	0
$862$	45.4508	1.54806
$863$	35.3050	1.20179	0.600897	−	0.799326i	$-0.294810\pi$
$863$	35.3050	1.20179	0.600897	+	0.799326i	$0.294810\pi$
$864$	−10.8541	−0.369264
$865$	−12.3607	−0.420276
$866$	−32.9443	−1.11949
$867$	19.0000	0.645274
$868$	0	0
$869$	2.47214	0.0838615
$870$	59.9230	2.03158
$871$	−2.45898	−0.0833194
$872$	−44.8328	−1.51823
$873$	6.94427	0.235028
$874$	27.4164	0.927374
$875$	0	0
$876$	4.85410	0.164005
$877$	−21.8885	−0.739124	−0.369562	−	0.929206i	$-0.620492\pi$
$877$	−21.8885	−0.739124	−0.369562	+	0.929206i	$0.620492\pi$
$878$	21.2705	0.717845
$879$	9.88854	0.333532
$880$	−22.0344	−0.742781
$881$	22.5967	0.761304	0.380652	−	0.924718i	$-0.375700\pi$
$881$	22.5967	0.761304	0.380652	+	0.924718i	$0.375700\pi$
$882$	0	0
$883$	4.23607	0.142555	0.0712775	−	0.997457i	$-0.477292\pi$
$883$	4.23607	0.142555	0.0712775	+	0.997457i	$0.477292\pi$
$884$	101.125	3.40119
$885$	26.7082	0.897786
$886$	−23.7082	−0.796493
$887$	28.3607	0.952258	0.476129	−	0.879375i	$-0.342039\pi$
$887$	28.3607	0.952258	0.476129	+	0.879375i	$0.342039\pi$
$888$	3.94427	0.132361
$889$	0	0
$890$	−78.5410	−2.63270
$891$	−1.00000	−0.0335013
$892$	−87.3738	−2.92549
$893$	−48.5967	−1.62623
$894$	−40.9787	−1.37053
$895$	−12.3607	−0.413172
$896$	0	0
$897$	8.58359	0.286598
$898$	66.5410	2.22050
$899$	86.7214	2.89232
$900$	0	0
$901$	77.6656	2.58742
$902$	−15.7082	−0.523026
$903$	0	0
$904$	−48.3607	−1.60845
$905$	−1.05573	−0.0350936
$906$	18.1803	0.604001
$907$	−14.1115	−0.468563	−0.234282	−	0.972169i	$-0.575274\pi$
$907$	−14.1115	−0.468563	−0.234282	+	0.972169i	$0.575274\pi$
$908$	−130.249	−4.32247
$909$	−3.52786	−0.117012
$910$	0	0
$911$	−31.4164	−1.04087	−0.520436	−	0.853901i	$-0.674231\pi$
$911$	−31.4164	−1.04087	−0.520436	+	0.853901i	$0.674231\pi$
$912$	41.7426	1.38224
$913$	12.4721	0.412767
$914$	29.8885	0.988625
$915$	15.5279	0.513335
$916$	−74.8328	−2.47255
$917$	0	0
$918$	15.7082	0.518448
$919$	1.88854	0.0622973	0.0311487	−	0.999515i	$-0.490083\pi$
$919$	1.88854	0.0622973	0.0311487	+	0.999515i	$0.490083\pi$
$920$	41.3050	1.36178
$921$	−16.0000	−0.527218
$922$	43.1246	1.42023
$923$	−15.5279	−0.511106
$924$	0	0
$925$	0	0
$926$	7.09017	0.232997
$927$	7.41641	0.243587
$928$	111.103	3.64715
$929$	−52.4853	−1.72199	−0.860993	−	0.508616i	$-0.830157\pi$
$929$	−52.4853	−1.72199	−0.860993	+	0.508616i	$0.830157\pi$
$930$	49.5967	1.62634
$931$	0	0
$932$	65.1246	2.13323
$933$	12.9443	0.423776
$934$	62.3951	2.04163
$935$	13.4164	0.438763
$936$	25.9443	0.848015
$937$	−42.7214	−1.39565	−0.697823	−	0.716270i	$-0.745848\pi$
$937$	−42.7214	−1.39565	−0.697823	+	0.716270i	$0.745848\pi$
$938$	0	0
$939$	−26.3607	−0.860248
$940$	−124.520	−4.06139
$941$	−51.1935	−1.66886	−0.834430	−	0.551114i	$-0.814203\pi$
$941$	−51.1935	−1.66886	−0.834430	+	0.551114i	$0.814203\pi$
$942$	8.94427	0.291420
$943$	14.8328	0.483023
$944$	117.700	3.83081
$945$	0	0
$946$	−1.23607	−0.0401880
$947$	0.111456	0.00362184	0.00181092	−	0.999998i	$-0.499424\pi$
$947$	0.111456	0.00362184	0.00181092	+	0.999998i	$0.499424\pi$
$948$	−12.0000	−0.389742
$949$	−3.47214	−0.112710
$950$	0	0
$951$	26.9443	0.873728
$952$	0	0
$953$	−28.4853	−0.922729	−0.461365	−	0.887211i	$-0.652640\pi$
$953$	−28.4853	−0.922729	−0.461365	+	0.887211i	$0.652640\pi$
$954$	33.8885	1.09718
$955$	26.8328	0.868290
$956$	84.2705	2.72550
$957$	10.2361	0.330885
$958$	57.3050	1.85144
$959$	0	0
$960$	19.4721	0.628460
$961$	40.7771	1.31539
$962$	−4.79837	−0.154706
$963$	19.9443	0.642695
$964$	92.2279	2.97046
$965$	57.8885	1.86350
$966$	0	0
$967$	46.2492	1.48727	0.743637	−	0.668583i	$-0.233099\pi$
$967$	46.2492	1.48727	0.743637	+	0.668583i	$0.233099\pi$
$968$	−7.47214	−0.240164
$969$	−25.4164	−0.816493
$970$	−40.6525	−1.30527
$971$	−24.8885	−0.798711	−0.399356	−	0.916796i	$-0.630766\pi$
$971$	−24.8885	−0.798711	−0.399356	+	0.916796i	$0.630766\pi$
$972$	4.85410	0.155695
$973$	0	0
$974$	57.3050	1.83617
$975$	0	0
$976$	68.4296	2.19038
$977$	−13.5279	−0.432795	−0.216397	−	0.976305i	$-0.569431\pi$
$977$	−13.5279	−0.432795	−0.216397	+	0.976305i	$0.569431\pi$
$978$	47.4508	1.51731
$979$	−13.4164	−0.428790
$980$	0	0
$981$	6.00000	0.191565
$982$	28.5066	0.909681
$983$	−38.8328	−1.23857	−0.619287	−	0.785165i	$-0.712578\pi$
$983$	−38.8328	−1.23857	−0.619287	+	0.785165i	$0.712578\pi$
$984$	44.8328	1.42922
$985$	−18.9443	−0.603615
$986$	−160.790	−5.12060
$987$	0	0
$988$	−71.3951	−2.27138
$989$	1.16718	0.0371143
$990$	5.85410	0.186056
$991$	13.2918	0.422228	0.211114	−	0.977461i	$-0.432291\pi$
$991$	13.2918	0.422228	0.211114	+	0.977461i	$0.432291\pi$
$992$	91.9574	2.91965
$993$	−16.0000	−0.507745
$994$	0	0
$995$	−54.7214	−1.73478
$996$	−60.5410	−1.91832
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	−57.9230	−1.83352
$999$	−0.527864	−0.0167009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.l.1.1	yes	2
3.2	odd	2		4851.2.a.bg.1.2		2
7.6	odd	2		1617.2.a.k.1.1	✓	2
21.20	even	2		4851.2.a.bh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.k.1.1	✓	2	7.6	odd	2
1617.2.a.l.1.1	yes	2	1.1	even	1	trivial
4851.2.a.bg.1.2		2	3.2	odd	2
4851.2.a.bh.1.2		2	21.20	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} +2.23607 q^{5} -2.61803 q^{6} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} +2.23607 q^{5} -2.61803 q^{6} -7.47214 q^{8} +1.00000 q^{9} -5.85410 q^{10} -1.00000 q^{11} +4.85410 q^{12} -3.47214 q^{13} +2.23607 q^{15} +9.85410 q^{16} -6.00000 q^{17} -2.61803 q^{18} +4.23607 q^{19} +10.8541 q^{20} +2.61803 q^{22} -2.47214 q^{23} -7.47214 q^{24} +9.09017 q^{26} +1.00000 q^{27} -10.2361 q^{29} -5.85410 q^{30} -8.47214 q^{31} -10.8541 q^{32} -1.00000 q^{33} +15.7082 q^{34} +4.85410 q^{36} -0.527864 q^{37} -11.0902 q^{38} -3.47214 q^{39} -16.7082 q^{40} -6.00000 q^{41} -0.472136 q^{43} -4.85410 q^{44} +2.23607 q^{45} +6.47214 q^{46} -11.4721 q^{47} +9.85410 q^{48} -6.00000 q^{51} -16.8541 q^{52} -12.9443 q^{53} -2.61803 q^{54} -2.23607 q^{55} +4.23607 q^{57} +26.7984 q^{58} +11.9443 q^{59} +10.8541 q^{60} +6.94427 q^{61} +22.1803 q^{62} +8.70820 q^{64} -7.76393 q^{65} +2.61803 q^{66} +0.708204 q^{67} -29.1246 q^{68} -2.47214 q^{69} +4.47214 q^{71} -7.47214 q^{72} +1.00000 q^{73} +1.38197 q^{74} +20.5623 q^{76} +9.09017 q^{78} -2.47214 q^{79} +22.0344 q^{80} +1.00000 q^{81} +15.7082 q^{82} -12.4721 q^{83} -13.4164 q^{85} +1.23607 q^{86} -10.2361 q^{87} +7.47214 q^{88} +13.4164 q^{89} -5.85410 q^{90} -12.0000 q^{92} -8.47214 q^{93} +30.0344 q^{94} +9.47214 q^{95} -10.8541 q^{96} +6.94427 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 3 q^{6} - 6 q^{8} + 2 q^{9} - 5 q^{10} - 2 q^{11} + 3 q^{12} + 2 q^{13} + 13 q^{16} - 12 q^{17} - 3 q^{18} + 4 q^{19} + 15 q^{20} + 3 q^{22} + 4 q^{23} - 6 q^{24} + 7 q^{26} + 2 q^{27} - 16 q^{29} - 5 q^{30} - 8 q^{31} - 15 q^{32} - 2 q^{33} + 18 q^{34} + 3 q^{36} - 10 q^{37} - 11 q^{38} + 2 q^{39} - 20 q^{40} - 12 q^{41} + 8 q^{43} - 3 q^{44} + 4 q^{46} - 14 q^{47} + 13 q^{48} - 12 q^{51} - 27 q^{52} - 8 q^{53} - 3 q^{54} + 4 q^{57} + 29 q^{58} + 6 q^{59} + 15 q^{60} - 4 q^{61} + 22 q^{62} + 4 q^{64} - 20 q^{65} + 3 q^{66} - 12 q^{67} - 18 q^{68} + 4 q^{69} - 6 q^{72} + 2 q^{73} + 5 q^{74} + 21 q^{76} + 7 q^{78} + 4 q^{79} + 15 q^{80} + 2 q^{81} + 18 q^{82} - 16 q^{83} - 2 q^{86} - 16 q^{87} + 6 q^{88} - 5 q^{90} - 24 q^{92} - 8 q^{93} + 31 q^{94} + 10 q^{95} - 15 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 3 * q^6 - 6 * q^8 + 2 * q^9 - 5 * q^10 - 2 * q^11 + 3 * q^12 + 2 * q^13 + 13 * q^16 - 12 * q^17 - 3 * q^18 + 4 * q^19 + 15 * q^20 + 3 * q^22 + 4 * q^23 - 6 * q^24 + 7 * q^26 + 2 * q^27 - 16 * q^29 - 5 * q^30 - 8 * q^31 - 15 * q^32 - 2 * q^33 + 18 * q^34 + 3 * q^36 - 10 * q^37 - 11 * q^38 + 2 * q^39 - 20 * q^40 - 12 * q^41 + 8 * q^43 - 3 * q^44 + 4 * q^46 - 14 * q^47 + 13 * q^48 - 12 * q^51 - 27 * q^52 - 8 * q^53 - 3 * q^54 + 4 * q^57 + 29 * q^58 + 6 * q^59 + 15 * q^60 - 4 * q^61 + 22 * q^62 + 4 * q^64 - 20 * q^65 + 3 * q^66 - 12 * q^67 - 18 * q^68 + 4 * q^69 - 6 * q^72 + 2 * q^73 + 5 * q^74 + 21 * q^76 + 7 * q^78 + 4 * q^79 + 15 * q^80 + 2 * q^81 + 18 * q^82 - 16 * q^83 - 2 * q^86 - 16 * q^87 + 6 * q^88 - 5 * q^90 - 24 * q^92 - 8 * q^93 + 31 * q^94 + 10 * q^95 - 15 * q^96 - 4 * q^97 - 2 * q^99

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