LMFDB - Embedded newform 1470.2.g.k.589.2

Newspace parameters

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.g (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1698758656.6
Defining polynomial:	$x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64$
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.2
Root			$2.16053i$ of defining polynomial
Character	$\chi$	$=$	1470.589
Dual form			1470.2.g.k.589.6

$q$-expansion

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.0743018 - 2.23483i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(0.0743018 - 2.23483i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(-2.23483 - 0.0743018i) q^{10} -3.05545 q^{11} -1.00000i q^{12} +1.64124i q^{13} +(2.23483 + 0.0743018i) q^{15} +1.00000 q^{16} +2.90685i q^{17} +1.00000i q^{18} -2.21016 q^{19} +(-0.0743018 + 2.23483i) q^{20} +3.05545i q^{22} +1.78984i q^{23} -1.00000 q^{24} +(-4.98896 - 0.332104i) q^{25} +1.64124 q^{26} -1.00000i q^{27} -5.58667 q^{29} +(0.0743018 - 2.23483i) q^{30} +0.944547 q^{31} -1.00000i q^{32} -3.05545i q^{33} +2.90685 q^{34} +1.00000 q^{36} +10.7123i q^{37} +2.21016i q^{38} -1.64124 q^{39} +(2.23483 + 0.0743018i) q^{40} +6.67982 q^{41} +10.5021i q^{43} +3.05545 q^{44} +(-0.0743018 + 2.23483i) q^{45} +1.78984 q^{46} -11.3765i q^{47} +1.00000i q^{48} +(-0.332104 + 4.98896i) q^{50} -2.90685 q^{51} -1.64124i q^{52} +5.78984i q^{53} -1.00000 q^{54} +(-0.227026 + 6.82843i) q^{55} -2.21016i q^{57} +5.58667i q^{58} +5.97792 q^{59} +(-2.23483 - 0.0743018i) q^{60} +0.445811 q^{61} -0.944547i q^{62} -1.00000 q^{64} +(3.66790 + 0.121947i) q^{65} -3.05545 q^{66} -1.26561i q^{67} -2.90685i q^{68} -1.78984 q^{69} -14.8523 q^{71} -1.00000i q^{72} +7.91636i q^{73} +10.7123 q^{74} +(0.332104 - 4.98896i) q^{75} +2.21016 q^{76} +1.64124i q^{78} -14.2990 q^{79} +(0.0743018 - 2.23483i) q^{80} +1.00000 q^{81} -6.67982i q^{82} +0.874366i q^{83} +(6.49632 + 0.215984i) q^{85} +10.5021 q^{86} -5.58667i q^{87} -3.05545i q^{88} -17.5083 q^{89} +(2.23483 + 0.0743018i) q^{90} -1.78984i q^{92} +0.944547i q^{93} -11.3765 q^{94} +(-0.164219 + 4.93933i) q^{95} +1.00000 q^{96} +10.4476i q^{97} +3.05545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) $	$ 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + 8q^{16} - 24q^{19} - 4q^{20} - 8q^{24} + 4q^{25} + 16q^{29} + 4q^{30} + 32q^{31} - 8q^{34} + 8q^{36} + 24q^{41} - 4q^{45} + 8q^{46} - 4q^{50} + 8q^{51} - 8q^{54} - 40q^{59} + 24q^{61} - 8q^{64} + 28q^{65} - 8q^{69} - 40q^{71} + 16q^{74} + 4q^{75} + 24q^{76} + 16q^{79} + 4q^{80} + 8q^{81} + 28q^{85} + 8q^{86} - 88q^{89} - 24q^{94} + 24q^{95} + 8q^{96} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$	0.0743018	−	2.23483i	0.0332288	−	0.999448i
$5$	0.0743018	−	2.23483i	0.0332288	−	0.999448i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	−2.23483	−	0.0743018i	−0.706716	−	0.0234963i
$11$	−3.05545			−0.921254			−0.460627	−	0.887594i	$-0.652375\pi$
$11$	−3.05545			−0.921254			−0.460627	+	0.887594i	$0.652375\pi$
$12$		−	1.00000i		−	0.288675i
$13$			1.64124i			0.455198i	0.973755	+	0.227599i	$0.0730875\pi$
$13$			1.64124i			0.455198i	−0.973755	+	0.227599i	$0.926912\pi$
$14$		0			0
$15$	2.23483	+	0.0743018i	0.577031	+	0.0191846i
$16$	1.00000			0.250000
$17$			2.90685i			0.705014i	0.935809	+	0.352507i	$0.114671\pi$
$17$			2.90685i			0.705014i	−0.935809	+	0.352507i	$0.885329\pi$
$18$			1.00000i			0.235702i
$19$	−2.21016			−0.507045			−0.253522	−	0.967330i	$-0.581589\pi$
$19$	−2.21016			−0.507045			−0.253522	+	0.967330i	$0.581589\pi$
$20$	−0.0743018	+	2.23483i	−0.0166144	+	0.499724i
$21$		0			0
$22$			3.05545i			0.651425i
$23$			1.78984i			0.373208i	0.982435	+	0.186604i	$0.0597481\pi$
$23$			1.78984i			0.373208i	−0.982435	+	0.186604i	$0.940252\pi$
$24$	−1.00000			−0.204124
$25$	−4.98896	−	0.332104i	−0.997792	−	0.0664208i
$26$	1.64124			0.321873
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−5.58667			−1.03742			−0.518710	−	0.854951i	$-0.673587\pi$
$29$	−5.58667			−1.03742			−0.518710	+	0.854951i	$0.673587\pi$
$30$	0.0743018	−	2.23483i	0.0135656	−	0.408023i
$31$	0.944547			0.169646			0.0848228	−	0.996396i	$-0.472968\pi$
$31$	0.944547			0.169646			0.0848228	+	0.996396i	$0.472968\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	3.05545i		−	0.531886i
$34$	2.90685			0.498521
$35$		0			0
$36$	1.00000			0.166667
$37$			10.7123i			1.76109i	0.473960	+	0.880546i	$0.342824\pi$
$37$			10.7123i			1.76109i	−0.473960	+	0.880546i	$0.657176\pi$
$38$			2.21016i			0.358535i
$39$	−1.64124			−0.262809
$40$	2.23483	+	0.0743018i	0.353358	+	0.0117481i
$41$	6.67982			1.04321			0.521607	−	0.853186i	$-0.325333\pi$
$41$	6.67982			1.04321			0.521607	+	0.853186i	$0.325333\pi$
$42$		0			0
$43$			10.5021i			1.60156i	0.598957	+	0.800781i	$0.295582\pi$
$43$			10.5021i			1.60156i	−0.598957	+	0.800781i	$0.704418\pi$
$44$	3.05545			0.460627
$45$	−0.0743018	+	2.23483i	−0.0110763	+	0.333149i
$46$	1.78984			0.263898
$47$		−	11.3765i		−	1.65944i	−0.558183	−	0.829718i	$-0.688501\pi$
$47$		−	11.3765i		−	1.65944i	0.558183	−	0.829718i	$-0.311499\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	−0.332104	+	4.98896i	−0.0469666	+	0.705545i
$51$	−2.90685			−0.407040
$52$		−	1.64124i		−	0.227599i
$53$			5.78984i			0.795296i	0.917538	+	0.397648i	$0.130173\pi$
$53$			5.78984i			0.795296i	−0.917538	+	0.397648i	$0.869827\pi$
$54$	−1.00000			−0.136083
$55$	−0.227026	+	6.82843i	−0.0306121	+	0.920745i
$56$		0			0
$57$		−	2.21016i		−	0.292742i
$58$			5.58667i			0.733566i
$59$	5.97792			0.778259			0.389129	−	0.921183i	$-0.372776\pi$
$59$	5.97792			0.778259			0.389129	+	0.921183i	$0.372776\pi$
$60$	−2.23483	−	0.0743018i	−0.288516	−	0.00959232i
$61$	0.445811			0.0570802			0.0285401	−	0.999593i	$-0.490914\pi$
$61$	0.445811			0.0570802			0.0285401	+	0.999593i	$0.490914\pi$
$62$		−	0.944547i		−	0.119958i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.66790	+	0.121947i	0.454946	+	0.0151257i
$66$	−3.05545			−0.376100
$67$		−	1.26561i		−	0.154619i	−0.997007	−	0.0773094i	$-0.975367\pi$
$67$		−	1.26561i		−	0.154619i	0.997007	−	0.0773094i	$-0.0246329\pi$
$68$		−	2.90685i		−	0.352507i
$69$	−1.78984			−0.215472
$70$		0			0
$71$	−14.8523			−1.76264			−0.881321	−	0.472518i	$-0.843345\pi$
$71$	−14.8523			−1.76264			−0.881321	+	0.472518i	$0.843345\pi$
$72$		−	1.00000i		−	0.117851i
$73$			7.91636i			0.926540i	0.886217	+	0.463270i	$0.153324\pi$
$73$			7.91636i			0.926540i	−0.886217	+	0.463270i	$0.846676\pi$
$74$	10.7123			1.24528
$75$	0.332104	−	4.98896i	0.0383481	−	0.576075i
$76$	2.21016			0.253522
$77$		0			0
$78$			1.64124i			0.185834i
$79$	−14.2990			−1.60876			−0.804380	−	0.594115i	$-0.797503\pi$
$79$	−14.2990			−1.60876			−0.804380	+	0.594115i	$0.797503\pi$
$80$	0.0743018	−	2.23483i	0.00830719	−	0.249862i
$81$	1.00000			0.111111
$82$		−	6.67982i		−	0.737663i
$83$			0.874366i			0.0959741i	0.998848	+	0.0479871i	$0.0152806\pi$
$83$			0.874366i			0.0959741i	−0.998848	+	0.0479871i	$0.984719\pi$
$84$		0			0
$85$	6.49632	+	0.215984i	0.704625	+	0.0234268i
$86$	10.5021			1.13248
$87$		−	5.58667i		−	0.598954i
$88$		−	3.05545i		−	0.325712i
$89$	−17.5083			−1.85587			−0.927935	−	0.372741i	$-0.878418\pi$
$89$	−17.5083			−1.85587			−0.927935	+	0.372741i	$0.878418\pi$
$90$	2.23483	+	0.0743018i	0.235572	+	0.00783210i
$91$		0			0
$92$		−	1.78984i		−	0.186604i
$93$			0.944547i			0.0979450i
$94$	−11.3765			−1.17340
$95$	−0.164219	+	4.93933i	−0.0168485	+	0.506765i
$96$	1.00000			0.102062
$97$			10.4476i			1.06079i	0.847750	+	0.530396i	$0.177957\pi$
$97$			10.4476i			1.06079i	−0.847750	+	0.530396i	$0.822043\pi$
$98$		0			0
$99$	3.05545			0.307085
$100$	4.98896	+	0.332104i	0.498896	+	0.0332104i
$101$	15.4549			1.53782			0.768912	−	0.639355i	$-0.220798\pi$
$101$	15.4549			1.53782			0.768912	+	0.639355i	$0.220798\pi$
$102$			2.90685i			0.287821i
$103$			3.12563i			0.307978i	0.988073	+	0.153989i	$0.0492120\pi$
$103$			3.12563i			0.307978i	−0.988073	+	0.153989i	$0.950788\pi$
$104$	−1.64124			−0.160937
$105$		0			0
$106$	5.78984			0.562359
$107$			4.78249i			0.462341i	0.972913	+	0.231170i	$0.0742555\pi$
$107$			4.78249i			0.462341i	−0.972913	+	0.231170i	$0.925745\pi$
$108$			1.00000i			0.0962250i
$109$	9.10355			0.871962			0.435981	−	0.899956i	$-0.356401\pi$
$109$	9.10355			0.871962			0.435981	+	0.899956i	$0.356401\pi$
$110$	6.82843	+	0.227026i	0.651065	+	0.0216460i
$111$	−10.7123			−1.01677
$112$		0			0
$113$			14.3982i			1.35447i	0.735766	+	0.677236i	$0.236822\pi$
$113$			14.3982i			1.35447i	−0.735766	+	0.677236i	$0.763178\pi$
$114$	−2.21016			−0.207000
$115$	4.00000	+	0.132989i	0.373002	+	0.0124012i
$116$	5.58667			0.518710
$117$		−	1.64124i		−	0.151733i
$118$		−	5.97792i		−	0.550312i
$119$		0			0
$120$	−0.0743018	+	2.23483i	−0.00678279	+	0.204011i
$121$	−1.66421			−0.151292
$122$		−	0.445811i		−	0.0403618i
$123$			6.67982i			0.602299i
$124$	−0.944547			−0.0848228
$125$	−1.11289	+	11.1248i	−0.0995396	+	0.995034i
$126$		0			0
$127$			8.45405i			0.750176i	0.926989	+	0.375088i	$0.122387\pi$
$127$			8.45405i			0.750176i	−0.926989	+	0.375088i	$0.877613\pi$
$128$			1.00000i			0.0883883i
$129$	−10.5021			−0.924663
$130$	0.121947	−	3.66790i	0.0106955	−	0.321696i
$131$	8.32106			0.727015			0.363507	−	0.931591i	$-0.381579\pi$
$131$	8.32106			0.727015			0.363507	+	0.931591i	$0.381579\pi$
$132$			3.05545i			0.265943i
$133$		0			0
$134$	−1.26561			−0.109332
$135$	−2.23483	−	0.0743018i	−0.192344	−	0.00639488i
$136$	−2.90685			−0.249260
$137$		−	9.86701i		−	0.842996i	−0.906829	−	0.421498i	$-0.861505\pi$
$137$		−	9.86701i		−	0.842996i	0.906829	−	0.421498i	$-0.138495\pi$
$138$			1.78984i			0.152362i
$139$	−16.9632			−1.43880			−0.719399	−	0.694597i	$-0.755583\pi$
$139$	−16.9632			−1.43880			−0.719399	+	0.694597i	$0.755583\pi$
$140$		0			0
$141$	11.3765			0.958075
$142$			14.8523i			1.24638i
$143$		−	5.01473i		−	0.419353i
$144$	−1.00000			−0.0833333
$145$	−0.415100	+	12.4853i	−0.0344722	+	1.03685i
$146$	7.91636			0.655163
$147$		0			0
$148$		−	10.7123i		−	0.880546i
$149$	−8.04810			−0.659326			−0.329663	−	0.944099i	$-0.606935\pi$
$149$	−8.04810			−0.659326			−0.329663	+	0.944099i	$0.606935\pi$
$150$	−4.98896	−	0.332104i	−0.407347	−	0.0271162i
$151$	−9.97792			−0.811991			−0.405996	−	0.913875i	$-0.633075\pi$
$151$	−9.97792			−0.811991			−0.405996	+	0.913875i	$0.633075\pi$
$152$		−	2.21016i		−	0.179267i
$153$		−	2.90685i		−	0.235005i
$154$		0			0
$155$	0.0701816	−	2.11091i	0.00563712	−	0.169552i
$156$	1.64124			0.131404
$157$			12.6676i			1.01099i	0.862831	+	0.505493i	$0.168689\pi$
$157$			12.6676i			1.01099i	−0.862831	+	0.505493i	$0.831311\pi$
$158$			14.2990i			1.13757i
$159$	−5.78984			−0.459164
$160$	−2.23483	−	0.0743018i	−0.176679	−	0.00587407i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$		−	23.5646i		−	1.84572i	−0.385134	−	0.922861i	$-0.625845\pi$
$163$		−	23.5646i		−	1.84572i	0.385134	−	0.922861i	$-0.374155\pi$
$164$	−6.67982			−0.521607
$165$	−6.82843	−	0.227026i	−0.531592	−	0.0176739i
$166$	0.874366			0.0678639
$167$		−	18.0818i		−	1.39921i	−0.714528	−	0.699607i	$-0.753358\pi$
$167$		−	18.0818i		−	1.39921i	0.714528	−	0.699607i	$-0.246642\pi$
$168$		0			0
$169$	10.3063			0.792795
$170$	0.215984	−	6.49632i	0.0165652	−	0.498245i
$171$	2.21016			0.169015
$172$		−	10.5021i		−	0.800781i
$173$		−	1.93845i		−	0.147377i	−0.997281	−	0.0736887i	$-0.976523\pi$
$173$		−	1.93845i		−	0.147377i	0.997281	−	0.0736887i	$-0.0234771\pi$
$174$	−5.58667			−0.423525
$175$		0			0
$176$	−3.05545			−0.230313
$177$			5.97792i			0.449328i
$178$			17.5083i			1.31230i
$179$	24.4463			1.82720			0.913602	−	0.406609i	$-0.133289\pi$
$179$	24.4463			1.82720			0.913602	+	0.406609i	$0.133289\pi$
$180$	0.0743018	−	2.23483i	0.00553813	−	0.166575i
$181$	−16.9788			−1.26202			−0.631012	−	0.775773i	$-0.717360\pi$
$181$	−16.9788			−1.26202			−0.631012	+	0.775773i	$0.717360\pi$
$182$		0			0
$183$			0.445811i			0.0329553i
$184$	−1.78984			−0.131949
$185$	23.9402	+	0.795944i	1.76012	+	0.0585189i
$186$	0.944547			0.0692576
$187$		−	8.88174i		−	0.649497i
$188$			11.3765i			0.829718i
$189$		0			0
$190$	4.93933	+	0.164219i	0.358337	+	0.0119137i
$191$	0.741377			0.0536442			0.0268221	−	0.999640i	$-0.491461\pi$
$191$	0.741377			0.0536442			0.0268221	+	0.999640i	$0.491461\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	6.11091i		−	0.439873i	−0.975514	−	0.219936i	$-0.929415\pi$
$193$		−	6.11091i		−	0.439873i	0.975514	−	0.219936i	$-0.0705850\pi$
$194$	10.4476			0.750093
$195$	−0.121947	+	3.66790i	−0.00873281	+	0.262663i
$196$		0			0
$197$		−	20.6832i		−	1.47362i	−0.676100	−	0.736810i	$-0.736331\pi$
$197$		−	20.6832i		−	1.47362i	0.676100	−	0.736810i	$-0.263669\pi$
$198$		−	3.05545i		−	0.217142i
$199$	−12.0702			−0.855632			−0.427816	−	0.903866i	$-0.640717\pi$
$199$	−12.0702			−0.855632			−0.427816	+	0.903866i	$0.640717\pi$
$200$	0.332104	−	4.98896i	0.0234833	−	0.352773i
$201$	1.26561			0.0892692
$202$		−	15.4549i		−	1.08741i
$203$		0			0
$204$	2.90685			0.203520
$205$	0.496323	−	14.9283i	0.0346647	−	1.04264i
$206$	3.12563			0.217773
$207$		−	1.78984i		−	0.124403i
$208$			1.64124i			0.113799i
$209$	6.75303			0.467117
$210$		0			0
$211$	2.95153			0.203192			0.101596	−	0.994826i	$-0.467605\pi$
$211$	2.95153			0.203192			0.101596	+	0.994826i	$0.467605\pi$
$212$		−	5.78984i		−	0.397648i
$213$		−	14.8523i		−	1.01766i
$214$	4.78249			0.326924
$215$	23.4706	+	0.780329i	1.60068	+	0.0532180i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	9.10355i		−	0.616570i
$219$	−7.91636			−0.534938
$220$	0.227026	−	6.82843i	0.0153061	−	0.460372i
$221$	−4.77083			−0.320921
$222$			10.7123i			0.718963i
$223$		−	11.7678i		−	0.788027i	−0.919105	−	0.394014i	$-0.871086\pi$
$223$		−	11.7678i		−	0.788027i	0.919105	−	0.394014i	$-0.128914\pi$
$224$		0			0
$225$	4.98896	+	0.332104i	0.332597	+	0.0221403i
$226$	14.3982			0.957756
$227$		−	13.2365i		−	0.878540i	−0.898355	−	0.439270i	$-0.855237\pi$
$227$		−	13.2365i		−	0.878540i	0.898355	−	0.439270i	$-0.144763\pi$
$228$			2.21016i			0.146371i
$229$	−25.2448			−1.66822			−0.834111	−	0.551597i	$-0.814019\pi$
$229$	−25.2448			−1.66822			−0.834111	+	0.551597i	$0.814019\pi$
$230$	0.132989	−	4.00000i	0.00876900	−	0.263752i
$231$		0			0
$232$		−	5.58667i		−	0.366783i
$233$			3.32842i			0.218052i	0.994039	+	0.109026i	$0.0347732\pi$
$233$			3.32842i			0.218052i	−0.994039	+	0.109026i	$0.965227\pi$
$234$	−1.64124			−0.107291
$235$	−25.4246	−	0.845296i	−1.65852	−	0.0551410i
$236$	−5.97792			−0.389129
$237$		−	14.2990i		−	0.928819i
$238$		0			0
$239$	−24.8713			−1.60879			−0.804396	−	0.594094i	$-0.797511\pi$
$239$	−24.8713			−1.60879			−0.804396	+	0.594094i	$0.797511\pi$
$240$	2.23483	+	0.0743018i	0.144258	+	0.00479616i
$241$	10.3535			0.666931			0.333465	−	0.942762i	$-0.391782\pi$
$241$	10.3535			0.666931			0.333465	+	0.942762i	$0.391782\pi$
$242$			1.66421i			0.106979i
$243$			1.00000i			0.0641500i
$244$	−0.445811			−0.0285401
$245$		0			0
$246$	6.67982			0.425890
$247$		−	3.62740i		−	0.230806i
$248$			0.944547i			0.0599788i
$249$	−0.874366			−0.0554107
$250$	11.1248	+	1.11289i	0.703595	+	0.0703851i
$251$	16.5502			1.04464			0.522321	−	0.852749i	$-0.325066\pi$
$251$	16.5502			1.04464			0.522321	+	0.852749i	$0.325066\pi$
$252$		0			0
$253$		−	5.46878i		−	0.343819i
$254$	8.45405			0.530454
$255$	−0.215984	+	6.49632i	−0.0135254	+	0.406816i
$256$	1.00000			0.0625000
$257$			24.4546i			1.52543i	0.646732	+	0.762717i	$0.276135\pi$
$257$			24.4546i			1.52543i	−0.646732	+	0.762717i	$0.723865\pi$
$258$			10.5021i			0.653835i
$259$		0			0
$260$	−3.66790	−	0.121947i	−0.227473	−	0.00756283i
$261$	5.58667			0.345806
$262$		−	8.32106i		−	0.514077i
$263$		−	12.5091i		−	0.771346i	−0.922635	−	0.385673i	$-0.873969\pi$
$263$		−	12.5091i		−	0.771346i	0.922635	−	0.385673i	$-0.126031\pi$
$264$	3.05545			0.188050
$265$	12.9393	+	0.430196i	0.794857	+	0.0264267i
$266$		0			0
$267$		−	17.5083i		−	1.07149i
$268$			1.26561i			0.0773094i
$269$	18.9666			1.15641			0.578207	−	0.815890i	$-0.303753\pi$
$269$	18.9666			1.15641			0.578207	+	0.815890i	$0.303753\pi$
$270$	−0.0743018	+	2.23483i	−0.00452186	+	0.136008i
$271$	19.6638			1.19449			0.597247	−	0.802058i	$-0.296261\pi$
$271$	19.6638			1.19449			0.597247	+	0.802058i	$0.296261\pi$
$272$			2.90685i			0.176254i
$273$		0			0
$274$	−9.86701			−0.596088
$275$	15.2435	+	1.01473i	0.919219	+	0.0611904i
$276$	1.78984			0.107736
$277$			6.13998i			0.368915i	0.982840	+	0.184458i	$0.0590529\pi$
$277$			6.13998i			0.368915i	−0.982840	+	0.184458i	$0.940947\pi$
$278$			16.9632i			1.01738i
$279$	−0.944547			−0.0565486
$280$		0			0
$281$	−12.1330			−0.723793			−0.361897	−	0.932218i	$-0.617871\pi$
$281$	−12.1330			−0.723793			−0.361897	+	0.932218i	$0.617871\pi$
$282$		−	11.3765i		−	0.677462i
$283$		−	17.4172i		−	1.03535i	−0.855578	−	0.517674i	$-0.826798\pi$
$283$		−	17.4172i		−	1.03535i	0.855578	−	0.517674i	$-0.173202\pi$
$284$	14.8523			0.881321
$285$	−4.93933	−	0.164219i	−0.292581	−	0.00972747i
$286$	−5.01473			−0.296527
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	8.55023			0.502955
$290$	12.4853	+	0.415100i	0.733161	+	0.0243755i
$291$	−10.4476			−0.612448
$292$		−	7.91636i		−	0.463270i
$293$		−	23.7521i		−	1.38762i	−0.720160	−	0.693808i	$-0.755932\pi$
$293$		−	23.7521i		−	1.38762i	0.720160	−	0.693808i	$-0.244068\pi$
$294$		0			0
$295$	0.444170	−	13.3596i	0.0258606	−	0.777829i
$296$	−10.7123			−0.622640
$297$			3.05545i			0.177295i
$298$			8.04810i			0.466214i
$299$	−2.93756			−0.169883
$300$	−0.332104	+	4.98896i	−0.0191740	+	0.288038i
$301$		0			0
$302$			9.97792i			0.574165i
$303$			15.4549i			0.887863i
$304$	−2.21016			−0.126761
$305$	0.0331245	−	0.996313i	0.00189671	−	0.0570487i
$306$	−2.90685			−0.166174
$307$			7.90812i			0.451340i	0.974204	+	0.225670i	$0.0724572\pi$
$307$			7.90812i			0.451340i	−0.974204	+	0.225670i	$0.927543\pi$
$308$		0			0
$309$	−3.12563			−0.177811
$310$	−2.11091	−	0.0701816i	−0.119891	−	0.00398604i
$311$	−10.0772			−0.571424			−0.285712	−	0.958316i	$-0.592230\pi$
$311$	−10.0772			−0.571424			−0.285712	+	0.958316i	$0.592230\pi$
$312$		−	1.64124i		−	0.0929169i
$313$			20.3844i			1.15219i	0.817381	+	0.576097i	$0.195425\pi$
$313$			20.3844i			1.15219i	−0.817381	+	0.576097i	$0.804575\pi$
$314$	12.6676			0.714875
$315$		0			0
$316$	14.2990			0.804380
$317$			0.321063i			0.0180327i	0.999959	+	0.00901634i	$0.00287003\pi$
$317$			0.321063i			0.0180327i	−0.999959	+	0.00901634i	$0.997130\pi$
$318$			5.78984i			0.324678i
$319$	17.0698			0.955726
$320$	−0.0743018	+	2.23483i	−0.00415360	+	0.124931i
$321$	−4.78249			−0.266932
$322$		0			0
$323$		−	6.42459i		−	0.357474i
$324$	−1.00000			−0.0555556
$325$	0.545062	−	8.18807i	0.0302346	−	0.454193i
$326$	−23.5646			−1.30512
$327$			9.10355i			0.503428i
$328$			6.67982i			0.368832i
$329$		0			0
$330$	−0.227026	+	6.82843i	−0.0124973	+	0.375893i
$331$	−16.6084			−0.912880			−0.456440	−	0.889754i	$-0.650876\pi$
$331$	−16.6084			−0.912880			−0.456440	+	0.889754i	$0.650876\pi$
$332$		−	0.874366i		−	0.0479871i
$333$		−	10.7123i		−	0.587031i
$334$	−18.0818			−0.989394
$335$	−2.82843	−	0.0940371i	−0.154533	−	0.00513780i
$336$		0			0
$337$			1.91118i			0.104108i	0.998644	+	0.0520542i	$0.0165769\pi$
$337$			1.91118i			0.104108i	−0.998644	+	0.0520542i	$0.983423\pi$
$338$		−	10.3063i		−	0.560591i
$339$	−14.3982			−0.782005
$340$	−6.49632	−	0.215984i	−0.352313	−	0.0117134i
$341$	−2.88602			−0.156287
$342$		−	2.21016i		−	0.119512i
$343$		0			0
$344$	−10.5021			−0.566238
$345$	−0.132989	+	4.00000i	−0.00715986	+	0.215353i
$346$	−1.93845			−0.104212
$347$			7.90812i			0.424530i	0.977212	+	0.212265i	$0.0680840\pi$
$347$			7.90812i			0.424530i	−0.977212	+	0.212265i	$0.931916\pi$
$348$			5.58667i			0.299477i
$349$	23.5273			1.25939			0.629693	−	0.776844i	$-0.283181\pi$
$349$	23.5273			1.25939			0.629693	+	0.776844i	$0.283181\pi$
$350$		0			0
$351$	1.64124			0.0876029
$352$			3.05545i			0.162856i
$353$		−	22.9718i		−	1.22267i	−0.791373	−	0.611333i	$-0.790634\pi$
$353$		−	22.9718i		−	1.22267i	0.791373	−	0.611333i	$-0.209366\pi$
$354$	5.97792			0.317723
$355$	−1.10355	+	33.1924i	−0.0585704	+	1.76167i
$356$	17.5083			0.927935
$357$		0			0
$358$		−	24.4463i		−	1.29203i
$359$	−11.0264			−0.581950			−0.290975	−	0.956731i	$-0.593980\pi$
$359$	−11.0264			−0.581950			−0.290975	+	0.956731i	$0.593980\pi$
$360$	−2.23483	−	0.0743018i	−0.117786	−	0.00391605i
$361$	−14.1152			−0.742906
$362$			16.9788i			0.892386i
$363$		−	1.66421i		−	0.0873483i
$364$		0			0
$365$	17.6918	+	0.588200i	0.926029	+	0.0307878i
$366$	0.445811			0.0233029
$367$		−	10.1446i		−	0.529546i	−0.964311	−	0.264773i	$-0.914703\pi$
$367$		−	10.1446i		−	0.529546i	0.964311	−	0.264773i	$-0.0852970\pi$
$368$			1.78984i			0.0933020i
$369$	−6.67982			−0.347738
$370$	0.795944	−	23.9402i	0.0413791	−	1.24459i
$371$		0			0
$372$		−	0.944547i		−	0.0489725i
$373$		−	26.5021i		−	1.37223i	−0.727493	−	0.686115i	$-0.759315\pi$
$373$		−	26.5021i		−	1.37223i	0.727493	−	0.686115i	$-0.240685\pi$
$374$	−8.88174			−0.459264
$375$	−11.1248	−	1.11289i	−0.574483	−	0.0574692i
$376$	11.3765			0.586699
$377$		−	9.16907i		−	0.472231i
$378$		0			0
$379$	−29.4142			−1.51091			−0.755453	−	0.655203i	$-0.772583\pi$
$379$	−29.4142			−1.51091			−0.755453	+	0.655203i	$0.772583\pi$
$380$	0.164219	−	4.93933i	0.00842424	−	0.253382i
$381$	−8.45405			−0.433114
$382$		−	0.741377i		−	0.0379322i
$383$			3.64249i			0.186123i	0.995660	+	0.0930613i	$0.0296653\pi$
$383$			3.64249i			0.186123i	−0.995660	+	0.0930613i	$0.970335\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−6.11091			−0.311037
$387$		−	10.5021i		−	0.533854i
$388$		−	10.4476i		−	0.530396i
$389$	23.7938			1.20639			0.603196	−	0.797593i	$-0.293894\pi$
$389$	23.7938			1.20639			0.603196	+	0.797593i	$0.293894\pi$
$390$	3.66790	+	0.121947i	0.185731	+	0.00617503i
$391$	−5.20280			−0.263117
$392$		0			0
$393$			8.32106i			0.419742i
$394$	−20.6832			−1.04201
$395$	−1.06244	+	31.9558i	−0.0534572	+	1.60787i
$396$	−3.05545			−0.153542
$397$		−	9.76129i		−	0.489905i	−0.969535	−	0.244953i	$-0.921228\pi$
$397$		−	9.76129i		−	0.489905i	0.969535	−	0.244953i	$-0.0787724\pi$
$398$			12.0702i			0.605024i
$399$		0			0
$400$	−4.98896	−	0.332104i	−0.249448	−	0.0166052i
$401$	9.97792			0.498273			0.249137	−	0.968468i	$-0.419853\pi$
$401$	9.97792			0.498273			0.249137	+	0.968468i	$0.419853\pi$
$402$		−	1.26561i		−	0.0631229i
$403$			1.55023i			0.0772224i
$404$	−15.4549			−0.768912
$405$	0.0743018	−	2.23483i	0.00369209	−	0.111050i
$406$		0			0
$407$		−	32.7309i		−	1.62241i
$408$		−	2.90685i		−	0.143910i
$409$	−35.1837			−1.73972			−0.869862	−	0.493295i	$-0.835792\pi$
$409$	−35.1837			−1.73972			−0.869862	+	0.493295i	$0.835792\pi$
$410$	−14.9283	−	0.496323i	−0.737256	−	0.0245116i
$411$	9.86701			0.486704
$412$		−	3.12563i		−	0.153989i
$413$		0			0
$414$	−1.78984			−0.0879660
$415$	1.95406	+	0.0649669i	0.0959211	+	0.00318910i
$416$	1.64124			0.0804684
$417$		−	16.9632i		−	0.830691i
$418$		−	6.75303i		−	0.330302i
$419$	−18.6274			−0.910009			−0.455004	−	0.890489i	$-0.650362\pi$
$419$	−18.6274			−0.910009			−0.455004	+	0.890489i	$0.650362\pi$
$420$		0			0
$421$	31.6464			1.54235			0.771176	−	0.636622i	$-0.219669\pi$
$421$	31.6464			1.54235			0.771176	+	0.636622i	$0.219669\pi$
$422$		−	2.95153i		−	0.143678i
$423$			11.3765i			0.553145i
$424$	−5.78984			−0.281180
$425$	0.965377	−	14.5021i	0.0468277	−	0.703458i
$426$	−14.8523			−0.719595
$427$		0			0
$428$		−	4.78249i		−	0.231170i
$429$	5.01473			0.242113
$430$	0.780329	−	23.4706i	0.0376308	−	1.13185i
$431$	−14.8046			−0.713111			−0.356556	−	0.934274i	$-0.616049\pi$
$431$	−14.8046			−0.713111			−0.356556	+	0.934274i	$0.616049\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			4.24731i			0.204113i	0.994779	+	0.102056i	$0.0325422\pi$
$433$			4.24731i			0.204113i	−0.994779	+	0.102056i	$0.967458\pi$
$434$		0			0
$435$	−12.4853	−	0.415100i	−0.598623	−	0.0199025i
$436$	−9.10355			−0.435981
$437$		−	3.95583i		−	0.189233i
$438$			7.91636i			0.378258i
$439$	2.22880			0.106375			0.0531874	−	0.998585i	$-0.483062\pi$
$439$	2.22880			0.106375			0.0531874	+	0.998585i	$0.483062\pi$
$440$	−6.82843	−	0.227026i	−0.325532	−	0.0108230i
$441$		0			0
$442$			4.77083i			0.226925i
$443$		−	4.64213i		−	0.220554i	−0.993901	−	0.110277i	$-0.964826\pi$
$443$		−	4.64213i		−	0.220554i	0.993901	−	0.110277i	$-0.0351738\pi$
$444$	10.7123			0.508384
$445$	−1.30089	+	39.1280i	−0.0616683	+	1.85485i
$446$	−11.7678			−0.557220
$447$		−	8.04810i		−	0.380662i
$448$		0			0
$449$	3.69059			0.174170			0.0870849	−	0.996201i	$-0.472245\pi$
$449$	3.69059			0.174170			0.0870849	+	0.996201i	$0.472245\pi$
$450$	0.332104	−	4.98896i	0.0156555	−	0.235182i
$451$	−20.4099			−0.961064
$452$		−	14.3982i		−	0.677236i
$453$		−	9.97792i		−	0.468803i
$454$	−13.2365			−0.621222
$455$		0			0
$456$	2.21016			0.103500
$457$			2.72972i			0.127691i	0.997960	+	0.0638455i	$0.0203365\pi$
$457$			2.72972i			0.127691i	−0.997960	+	0.0638455i	$0.979664\pi$
$458$			25.2448i			1.17961i
$459$	2.90685			0.135680
$460$	−4.00000	−	0.132989i	−0.186501	−	0.00620062i
$461$	11.8072			0.549918			0.274959	−	0.961456i	$-0.411336\pi$
$461$	11.8072			0.549918			0.274959	+	0.961456i	$0.411336\pi$
$462$		0			0
$463$			2.40561i			0.111798i	0.998436	+	0.0558990i	$0.0178025\pi$
$463$			2.40561i			0.111798i	−0.998436	+	0.0558990i	$0.982198\pi$
$464$	−5.58667			−0.259355
$465$	2.11091	+	0.0701816i	0.0978909	+	0.00325459i
$466$	3.32842			0.154186
$467$			14.6612i			0.678437i	0.940708	+	0.339219i	$0.110163\pi$
$467$			14.6612i			0.678437i	−0.940708	+	0.339219i	$0.889837\pi$
$468$			1.64124i			0.0758663i
$469$		0			0
$470$	−0.845296	+	25.4246i	−0.0389906	+	1.17275i
$471$	−12.6676			−0.583693
$472$			5.97792i			0.275156i
$473$		−	32.0888i		−	1.47545i
$474$	−14.2990			−0.656774
$475$	11.0264	+	0.734003i	0.505925	+	0.0336783i
$476$		0			0
$477$		−	5.78984i		−	0.265099i
$478$			24.8713i			1.13759i
$479$	−11.8934			−0.543422			−0.271711	−	0.962379i	$-0.587590\pi$
$479$	−11.8934			−0.543422			−0.271711	+	0.962379i	$0.587590\pi$
$480$	0.0743018	−	2.23483i	0.00339140	−	0.102006i
$481$	−17.5815			−0.801645
$482$		−	10.3535i		−	0.471591i
$483$		0			0
$484$	1.66421			0.0756458
$485$	23.3486	+	0.776274i	1.06021	+	0.0352488i
$486$	1.00000			0.0453609
$487$			35.5018i			1.60874i	0.594129	+	0.804370i	$0.297497\pi$
$487$			35.5018i			1.60874i	−0.594129	+	0.804370i	$0.702503\pi$
$488$			0.445811i			0.0201809i
$489$	23.5646			1.06563
$490$		0			0
$491$	−0.978284			−0.0441493			−0.0220747	−	0.999756i	$-0.507027\pi$
$491$	−0.978284			−0.0441493			−0.0220747	+	0.999756i	$0.507027\pi$
$492$		−	6.67982i		−	0.301150i
$493$		−	16.2396i		−	0.731395i
$494$	−3.62740			−0.163204
$495$	0.227026	−	6.82843i	0.0102040	−	0.306915i
$496$	0.944547			0.0424114
$497$		0			0
$498$			0.874366i			0.0391813i
$499$	−11.7340			−0.525287			−0.262644	−	0.964893i	$-0.584594\pi$
$499$	−11.7340			−0.525287			−0.262644	+	0.964893i	$0.584594\pi$
$500$	1.11289	−	11.1248i	0.0497698	−	0.497517i
$501$	18.0818			0.807837
$502$		−	16.5502i		−	0.738674i
$503$			17.3618i			0.774125i	0.922054	+	0.387062i	$0.126510\pi$
$503$			17.3618i			0.774125i	−0.922054	+	0.387062i	$0.873490\pi$
$504$		0			0
$505$	1.14833	−	34.5392i	0.0511000	−	1.53697i
$506$	−5.46878			−0.243117
$507$			10.3063i			0.457720i
$508$		−	8.45405i		−	0.375088i
$509$	−25.8293			−1.14486			−0.572432	−	0.819952i	$-0.694000\pi$
$509$	−25.8293			−1.14486			−0.572432	+	0.819952i	$0.694000\pi$
$510$	6.49632	+	0.215984i	0.287662	+	0.00956394i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			2.21016i			0.0975808i
$514$	24.4546			1.07864
$515$	6.98527	+	0.232240i	0.307808	+	0.0102337i
$516$	10.5021			0.462331
$517$			34.7604i			1.52876i
$518$		0			0
$519$	1.93845			0.0850884
$520$	−0.121947	+	3.66790i	−0.00534773	+	0.160848i
$521$	−24.7466			−1.08417			−0.542083	−	0.840325i	$-0.682364\pi$
$521$	−24.7466			−1.08417			−0.542083	+	0.840325i	$0.682364\pi$
$522$		−	5.58667i		−	0.244522i
$523$		−	1.61574i		−	0.0706515i	−0.999376	−	0.0353258i	$-0.988753\pi$
$523$		−	1.61574i		−	0.0706515i	0.999376	−	0.0353258i	$-0.0112469\pi$
$524$	−8.32106			−0.363507
$525$		0			0
$526$	−12.5091			−0.545424
$527$			2.74566i			0.119603i
$528$		−	3.05545i		−	0.132972i
$529$	19.7965			0.860716
$530$	0.430196	−	12.9393i	0.0186865	−	0.562049i
$531$	−5.97792			−0.259420
$532$		0			0
$533$			10.9632i			0.474868i
$534$	−17.5083			−0.757656
$535$	10.6881	+	0.355347i	0.462085	+	0.0153630i
$536$	1.26561			0.0546660
$537$			24.4463i			1.05494i
$538$		−	18.9666i		−	0.817708i
$539$		0			0
$540$	2.23483	+	0.0743018i	0.0961719	+	0.00319744i
$541$	24.7530			1.06422			0.532108	−	0.846677i	$-0.321400\pi$
$541$	24.7530			1.06422			0.532108	+	0.846677i	$0.321400\pi$
$542$		−	19.6638i		−	0.844634i
$543$		−	16.9788i		−	0.728630i
$544$	2.90685			0.124630
$545$	0.676410	−	20.3449i	0.0289742	−	0.871481i
$546$		0			0
$547$			44.0524i			1.88354i	0.336253	+	0.941772i	$0.390840\pi$
$547$			44.0524i			1.88354i	−0.336253	+	0.941772i	$0.609160\pi$
$548$			9.86701i			0.421498i
$549$	−0.445811			−0.0190267
$550$	1.01473	−	15.2435i	0.0432682	−	0.649986i
$551$	12.3474			0.526018
$552$		−	1.78984i		−	0.0761808i
$553$		0			0
$554$	6.13998			0.260863
$555$	−0.795944	+	23.9402i	−0.0337859	+	1.01621i
$556$	16.9632			0.719399
$557$			2.06979i			0.0877000i	0.999038	+	0.0438500i	$0.0139624\pi$
$557$			2.06979i			0.0877000i	−0.999038	+	0.0438500i	$0.986038\pi$
$558$			0.944547i			0.0399859i
$559$	−17.2365			−0.729028
$560$		0			0
$561$	8.88174			0.374987
$562$			12.1330i			0.511799i
$563$			9.84493i			0.414914i	0.978244	+	0.207457i	$0.0665188\pi$
$563$			9.84493i			0.414914i	−0.978244	+	0.207457i	$0.933481\pi$
$564$	−11.3765			−0.479038
$565$	32.1776	+	1.06981i	1.35372	+	0.0450074i
$566$	−17.4172			−0.732101
$567$		0			0
$568$		−	14.8523i		−	0.623188i
$569$	−13.7561			−0.576686			−0.288343	−	0.957527i	$-0.593104\pi$
$569$	−13.7561			−0.576686			−0.288343	+	0.957527i	$0.593104\pi$
$570$	−0.164219	+	4.93933i	−0.00687836	+	0.206886i
$571$	19.2071			0.803791			0.401896	−	0.915685i	$-0.368351\pi$
$571$	19.2071			0.803791			0.401896	+	0.915685i	$0.368351\pi$
$572$			5.01473i			0.209676i
$573$			0.741377i			0.0309715i
$574$		0			0
$575$	0.594414	−	8.92945i	0.0247888	−	0.372384i
$576$	1.00000			0.0416667
$577$			37.3072i			1.55312i	0.630043	+	0.776560i	$0.283037\pi$
$577$			37.3072i			1.55312i	−0.630043	+	0.776560i	$0.716963\pi$
$578$		−	8.55023i		−	0.355643i
$579$	6.11091			0.253961
$580$	0.415100	−	12.4853i	0.0172361	−	0.518423i
$581$		0			0
$582$			10.4476i			0.433066i
$583$		−	17.6906i		−	0.732669i
$584$	−7.91636			−0.327581
$585$	−3.66790	−	0.121947i	−0.151649	−	0.00504189i
$586$	−23.7521			−0.981192
$587$			19.5459i			0.806748i	0.915035	+	0.403374i	$0.132163\pi$
$587$			19.5459i			0.806748i	−0.915035	+	0.403374i	$0.867837\pi$
$588$		0			0
$589$	−2.08760			−0.0860180
$590$	−13.3596	−	0.444170i	−0.550008	−	0.0182862i
$591$	20.6832			0.850795
$592$			10.7123i			0.440273i
$593$		−	28.9424i		−	1.18852i	−0.804273	−	0.594260i	$-0.797445\pi$
$593$		−	28.9424i		−	1.18852i	0.804273	−	0.594260i	$-0.202555\pi$
$594$	3.05545			0.125367
$595$		0			0
$596$	8.04810			0.329663
$597$		−	12.0702i		−	0.494000i
$598$			2.93756i			0.120126i
$599$	9.73170			0.397627			0.198813	−	0.980037i	$-0.436291\pi$
$599$	9.73170			0.397627			0.198813	+	0.980037i	$0.436291\pi$
$600$	4.98896	+	0.332104i	0.203673	+	0.0135581i
$601$	33.4038			1.36257			0.681284	−	0.732019i	$-0.261422\pi$
$601$	33.4038			1.36257			0.681284	+	0.732019i	$0.261422\pi$
$602$		0			0
$603$			1.26561i			0.0515396i
$604$	9.97792			0.405996
$605$	−0.123654	+	3.71923i	−0.00502724	+	0.151208i
$606$	15.4549			0.627814
$607$		−	43.2358i		−	1.75489i	−0.479680	−	0.877444i	$-0.659247\pi$
$607$		−	43.2358i		−	1.75489i	0.479680	−	0.877444i	$-0.340753\pi$
$608$			2.21016i			0.0896337i
$609$		0			0
$610$	−0.996313	−	0.0331245i	−0.0403395	−	0.00134117i
$611$	18.6716			0.755371
$612$			2.90685i			0.117502i
$613$		−	1.79023i		−	0.0723067i	−0.999346	−	0.0361534i	$-0.988490\pi$
$613$		−	1.79023i		−	0.0723067i	0.999346	−	0.0361534i	$-0.0115105\pi$
$614$	7.90812			0.319146
$615$	14.9283	+	0.496323i	0.601967	+	0.0200137i
$616$		0			0
$617$			38.2665i			1.54055i	0.637712	+	0.770275i	$0.279881\pi$
$617$			38.2665i			1.54055i	−0.637712	+	0.770275i	$0.720119\pi$
$618$			3.12563i			0.125731i
$619$	−0.132989			−0.00534526			−0.00267263	−	0.999996i	$-0.500851\pi$
$619$	−0.132989			−0.00534526			−0.00267263	+	0.999996i	$0.500851\pi$
$620$	−0.0701816	+	2.11091i	−0.00281856	+	0.0847760i
$621$	1.78984			0.0718239
$622$			10.0772i			0.404058i
$623$		0			0
$624$	−1.64124			−0.0657022
$625$	24.7794	+	3.31371i	0.991177	+	0.132548i
$626$	20.3844			0.814724
$627$			6.75303i			0.269690i
$628$		−	12.6676i		−	0.505493i
$629$	−31.1391			−1.24160
$630$		0			0
$631$	−25.1850			−1.00260			−0.501299	−	0.865274i	$-0.667145\pi$
$631$	−25.1850			−1.00260			−0.501299	+	0.865274i	$0.667145\pi$
$632$		−	14.2990i		−	0.568783i
$633$			2.95153i			0.117313i
$634$	0.321063			0.0127510
$635$	18.8934	+	0.628151i	0.749761	+	0.0249274i
$636$	5.78984			0.229582
$637$		0			0
$638$		−	17.0698i		−	0.675800i
$639$	14.8523			0.587547
$640$	2.23483	+	0.0743018i	0.0883395	+	0.00293704i
$641$	−24.5906			−0.971270			−0.485635	−	0.874162i	$-0.661412\pi$
$641$	−24.5906			−0.971270			−0.485635	+	0.874162i	$0.661412\pi$
$642$			4.78249i			0.188750i
$643$			9.15126i			0.360891i	0.983585	+	0.180445i	$0.0577539\pi$
$643$			9.15126i			0.360891i	−0.983585	+	0.180445i	$0.942246\pi$
$644$		0			0
$645$	−0.780329	+	23.4706i	−0.0307254	+	0.924152i
$646$	−6.42459			−0.252772
$647$			31.9268i			1.25517i	0.778548	+	0.627585i	$0.215957\pi$
$647$			31.9268i			1.25517i	−0.778548	+	0.627585i	$0.784043\pi$
$648$			1.00000i			0.0392837i
$649$	−18.2652			−0.716973
$650$	−8.18807	−	0.545062i	−0.321163	−	0.0213791i
$651$		0			0
$652$			23.5646i			0.922861i
$653$			3.06244i			0.119843i	0.998203	+	0.0599213i	$0.0190850\pi$
$653$			3.06244i			0.119843i	−0.998203	+	0.0599213i	$0.980915\pi$
$654$	9.10355			0.355977
$655$	0.618270	−	18.5962i	0.0241578	−	0.726613i
$656$	6.67982			0.260803
$657$		−	7.91636i		−	0.308847i
$658$		0			0
$659$	9.16636			0.357071			0.178535	−	0.983934i	$-0.442864\pi$
$659$	9.16636			0.357071			0.178535	+	0.983934i	$0.442864\pi$
$660$	6.82843	+	0.227026i	0.265796	+	0.00883696i
$661$	31.4181			1.22202			0.611012	−	0.791621i	$-0.290763\pi$
$661$	31.4181			1.22202			0.611012	+	0.791621i	$0.290763\pi$
$662$			16.6084i			0.645503i
$663$		−	4.77083i		−	0.185284i
$664$	−0.874366			−0.0339320
$665$		0			0
$666$	−10.7123			−0.415093
$667$		−	9.99927i		−	0.387173i
$668$			18.0818i			0.699607i
$669$	11.7678			0.454968
$670$	−0.0940371	+	2.82843i	−0.00363297	+	0.109272i
$671$	−1.36215			−0.0525854
$672$		0			0
$673$			6.45100i			0.248668i	0.992240	+	0.124334i	$0.0396794\pi$
$673$			6.45100i			0.248668i	−0.992240	+	0.124334i	$0.960321\pi$
$674$	1.91118			0.0736158
$675$	−0.332104	+	4.98896i	−0.0127827	+	0.192025i
$676$	−10.3063			−0.396397
$677$			6.01384i			0.231131i	0.993300	+	0.115565i	$0.0368680\pi$
$677$			6.01384i			0.231131i	−0.993300	+	0.115565i	$0.963132\pi$
$678$			14.3982i			0.552961i
$679$		0			0
$680$	−0.215984	+	6.49632i	−0.00828261	+	0.249123i
$681$	13.2365			0.507225
$682$			2.88602i			0.110511i
$683$			8.92208i			0.341394i	0.985324	+	0.170697i	$0.0546019\pi$
$683$			8.92208i			0.341394i	−0.985324	+	0.170697i	$0.945398\pi$
$684$	−2.21016			−0.0845075
$685$	−22.0511	−	0.733137i	−0.842530	−	0.0280117i
$686$		0			0
$687$		−	25.2448i		−	0.963148i
$688$			10.5021i			0.400391i
$689$	−9.50252			−0.362017
$690$	4.00000	+	0.132989i	0.152277	+	0.00506279i
$691$	47.6581			1.81300			0.906499	−	0.422207i	$-0.138745\pi$
$691$	47.6581			1.81300			0.906499	+	0.422207i	$0.138745\pi$
$692$			1.93845i			0.0736887i
$693$		0			0
$694$	7.90812			0.300188
$695$	−1.26040	+	37.9099i	−0.0478095	+	1.43800i
$696$	5.58667			0.211762
$697$			19.4172i			0.735480i
$698$		−	23.5273i		−	0.890521i
$699$	−3.32842			−0.125892
$700$		0			0
$701$	31.0788			1.17383			0.586914	−	0.809649i	$-0.300343\pi$
$701$	31.0788			1.17383			0.586914	+	0.809649i	$0.300343\pi$
$702$		−	1.64124i		−	0.0619446i
$703$		−	23.6759i		−	0.892953i
$704$	3.05545			0.115157
$705$	0.845296	−	25.4246i	0.0318357	−	0.957546i
$706$	−22.9718			−0.864556
$707$		0			0
$708$		−	5.97792i		−	0.224664i
$709$	12.1815			0.457485			0.228742	−	0.973487i	$-0.426539\pi$
$709$	12.1815			0.457485			0.228742	+	0.973487i	$0.426539\pi$
$710$	33.1924	+	1.10355i	1.24569	+	0.0414155i
$711$	14.2990			0.536254
$712$		−	17.5083i		−	0.656149i
$713$			1.69059i			0.0633131i
$714$		0			0
$715$	−11.2071	−	0.372603i	−0.419121	−	0.0139346i
$716$	−24.4463			−0.913602
$717$		−	24.8713i		−	0.928836i
$718$			11.0264i			0.411501i
$719$	31.9896			1.19301			0.596505	−	0.802609i	$-0.296556\pi$
$719$	31.9896			1.19301			0.596505	+	0.802609i	$0.296556\pi$
$720$	−0.0743018	+	2.23483i	−0.00276906	+	0.0832873i
$721$		0			0
$722$			14.1152i			0.525314i
$723$			10.3535i			0.385053i
$724$	16.9788			0.631012
$725$	27.8717	+	1.85536i	1.03513	+	0.0689063i
$726$	−1.66421			−0.0617646
$727$			22.9992i			0.852995i	0.904489	+	0.426497i	$0.140253\pi$
$727$			22.9992i			0.852995i	−0.904489	+	0.426497i	$0.859747\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	0.588200	−	17.6918i	0.0217703	−	0.654801i
$731$	−30.5282			−1.12912
$732$		−	0.445811i		−	0.0164776i
$733$		−	17.6001i		−	0.650076i	−0.945701	−	0.325038i	$-0.894623\pi$
$733$		−	17.6001i		−	0.650076i	0.945701	−	0.325038i	$-0.105377\pi$
$734$	−10.1446			−0.374446
$735$		0			0
$736$	1.78984			0.0659745
$737$			3.86701i			0.142443i
$738$			6.67982i			0.245888i
$739$	0.174100			0.00640437			0.00320218	−	0.999995i	$-0.498981\pi$
$739$	0.174100			0.00640437			0.00320218	+	0.999995i	$0.498981\pi$
$740$	−23.9402	−	0.795944i	−0.880060	−	0.0292595i
$741$	3.62740			0.133256
$742$		0			0
$743$			53.6360i			1.96771i	0.178957	+	0.983857i	$0.442728\pi$
$743$			53.6360i			1.96771i	−0.178957	+	0.983857i	$0.557272\pi$
$744$	−0.944547			−0.0346288
$745$	−0.597988	+	17.9862i	−0.0219086	+	0.658962i
$746$	−26.5021			−0.970313
$747$		−	0.874366i		−	0.0319914i
$748$			8.88174i			0.324749i
$749$		0			0
$750$	−1.11289	+	11.1248i	−0.0406369	+	0.406221i
$751$	29.0931			1.06162			0.530812	−	0.847490i	$-0.321887\pi$
$751$	29.0931			1.06162			0.530812	+	0.847490i	$0.321887\pi$
$752$		−	11.3765i		−	0.414859i
$753$			16.5502i			0.603125i
$754$	−9.16907			−0.333918
$755$	−0.741377	+	22.2990i	−0.0269815	+	0.811543i
$756$		0			0
$757$			34.0842i			1.23881i	0.785072	+	0.619405i	$0.212626\pi$
$757$			34.0842i			1.23881i	−0.785072	+	0.619405i	$0.787374\pi$
$758$			29.4142i			1.06837i
$759$	5.46878			0.198504
$760$	−4.93933	−	0.164219i	−0.179168	−	0.00595684i
$761$	−7.62959			−0.276572			−0.138286	−	0.990392i	$-0.544159\pi$
$761$	−7.62959			−0.276572			−0.138286	+	0.990392i	$0.544159\pi$
$762$			8.45405i			0.306258i
$763$		0			0
$764$	−0.741377			−0.0268221
$765$	−6.49632	−	0.215984i	−0.234875	−	0.00780892i
$766$	3.64249			0.131609
$767$			9.81119i			0.354262i
$768$			1.00000i			0.0360844i
$769$	37.8241			1.36397			0.681986	−	0.731365i	$-0.261117\pi$
$769$	37.8241			1.36397			0.681986	+	0.731365i	$0.261117\pi$
$770$		0			0
$771$	−24.4546			−0.880710
$772$			6.11091i			0.219936i
$773$		−	25.2349i		−	0.907636i	−0.891094	−	0.453818i	$-0.850062\pi$
$773$		−	25.2349i		−	0.907636i	0.891094	−	0.453818i	$-0.149938\pi$
$774$	−10.5021			−0.377492
$775$	−4.71231	−	0.313688i	−0.169271	−	0.0112680i
$776$	−10.4476			−0.375046
$777$		0			0
$778$		−	23.7938i		−	0.853048i
$779$	−14.7635			−0.528956
$780$	0.121947	−	3.66790i	0.00436640	−	0.131332i
$781$	45.3804			1.62384
$782$			5.20280i			0.186052i
$783$			5.58667i			0.199651i
$784$		0			0
$785$	28.3100	+	0.941227i	1.01043	+	0.0335938i
$786$	8.32106			0.296802
$787$			22.7193i			0.809855i	0.914349	+	0.404928i	$0.132703\pi$
$787$			22.7193i			0.809855i	−0.914349	+	0.404928i	$0.867297\pi$
$788$			20.6832i			0.736810i
$789$	12.5091			0.445337
$790$	31.9558	+	1.06244i	1.13694	+	0.0377999i
$791$		0			0
$792$			3.05545i			0.108571i

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.g (of order \(2\), degree \(1\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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