LMFDB - Embedded newform 668.2.e.a.9.13

Newspace parameters

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.13
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.13

$q$-expansion

$f(q)$	$=$	$q+(0.353640 + 2.65381i) q^{3} +(-1.27217 - 0.562563i) q^{5} +(-1.92428 + 4.13797i) q^{7} +(-4.02235 + 1.09139i) q^{9} +O(q^{10})$	\(q+(0.353640 + 2.65381i) q^{3} +(-1.27217 - 0.562563i) q^{5} +(-1.92428 + 4.13797i) q^{7} +(-4.02235 + 1.09139i) q^{9} +(-1.02081 + 1.30885i) q^{11} +(1.42096 - 2.77578i) q^{13} +(1.04305 - 3.57504i) q^{15} +(-2.44034 - 0.185090i) q^{17} +(2.03980 - 3.06846i) q^{19} +(-11.6619 - 3.64331i) q^{21} +(0.849459 + 0.337813i) q^{23} +(-2.06243 - 2.26745i) q^{25} +(-1.21010 - 2.88279i) q^{27} +(-4.52393 + 1.79908i) q^{29} +(-2.76400 + 0.638732i) q^{31} +(-3.83443 - 2.24618i) q^{33} +(4.77587 - 4.18167i) q^{35} +(8.57531 + 2.32676i) q^{37} +(7.86891 + 2.78932i) q^{39} +(-5.33729 + 2.60595i) q^{41} +(-0.373781 + 3.93828i) q^{43} +(5.73107 + 0.874387i) q^{45} +(0.147189 + 7.77648i) q^{47} +(-8.90922 - 10.5724i) q^{49} +(-0.371807 - 6.54166i) q^{51} +(0.188558 + 1.09630i) q^{53} +(2.03495 - 1.09080i) q^{55} +(8.86447 + 4.32811i) q^{57} +(-10.3888 + 0.787950i) q^{59} +(5.52223 - 5.62774i) q^{61} +(3.22394 - 18.7445i) q^{63} +(-3.36924 + 2.73188i) q^{65} +(-8.24417 + 3.64564i) q^{67} +(-0.596091 + 2.37377i) q^{69} +(11.0551 - 1.26074i) q^{71} +(-3.43668 + 2.57728i) q^{73} +(5.28802 - 6.27517i) q^{75} +(-3.45165 - 6.74267i) q^{77} +(-0.402907 + 1.07178i) q^{79} +(-3.56612 + 2.08901i) q^{81} +(-4.94246 + 6.85715i) q^{83} +(3.00039 + 1.60831i) q^{85} +(-6.37426 - 11.3694i) q^{87} +(0.517404 + 1.77340i) q^{89} +(8.75181 + 11.2212i) q^{91} +(-2.67253 - 7.10926i) q^{93} +(-4.32116 + 2.75608i) q^{95} +(5.32857 + 1.23138i) q^{97} +(2.67759 - 6.37874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148q - 2q^{5} - 14q^{9} + O(q^{10}) $	$ 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.353640	+	2.65381i	0.204174	+	1.53218i	0.731101	+	0.682269i	$0.239007\pi$
$3$	0.353640	+	2.65381i	0.204174	+	1.53218i	−0.526927	+	0.849910i	$0.676656\pi$
$4$		0			0
$5$	−1.27217	−	0.562563i	−0.568930	−	0.251586i	0.0999044	−	0.994997i	$-0.468146\pi$
$5$	−1.27217	−	0.562563i	−0.568930	−	0.251586i	−0.668835	+	0.743411i	$0.733207\pi$
$6$		0			0
$7$	−1.92428	+	4.13797i	−0.727308	+	1.56401i	0.0953327	+	0.995445i	$0.469608\pi$
$7$	−1.92428	+	4.13797i	−0.727308	+	1.56401i	−0.822640	+	0.568562i	$0.807500\pi$
$8$		0			0
$9$	−4.02235	+	1.09139i	−1.34078	+	0.363798i
$10$		0			0
$11$	−1.02081	+	1.30885i	−0.307786	+	0.394632i	−0.917335	−	0.398117i	$-0.869664\pi$
$11$	−1.02081	+	1.30885i	−0.307786	+	0.394632i	0.609549	+	0.792749i	$0.291351\pi$
$12$		0			0
$13$	1.42096	−	2.77578i	0.394102	−	0.769864i	−0.605562	−	0.795798i	$-0.707051\pi$
$13$	1.42096	−	2.77578i	0.394102	−	0.769864i	0.999664	+	0.0259349i	$0.00825627\pi$
$14$		0			0
$15$	1.04305	−	3.57504i	0.269314	−	0.923070i
$16$		0			0
$17$	−2.44034	−	0.185090i	−0.591869	−	0.0448909i	−0.223713	−	0.974655i	$-0.571818\pi$
$17$	−2.44034	−	0.185090i	−0.591869	−	0.0448909i	−0.368156	+	0.929764i	$0.620011\pi$
$18$		0			0
$19$	2.03980	−	3.06846i	0.467961	−	0.703953i	−0.520763	−	0.853701i	$-0.674352\pi$
$19$	2.03980	−	3.06846i	0.467961	−	0.703953i	0.988724	+	0.149748i	$0.0478463\pi$
$20$		0			0
$21$	−11.6619	−	3.64331i	−2.54484	−	0.795036i
$22$		0			0
$23$	0.849459	+	0.337813i	0.177124	+	0.0704389i	0.456412	−	0.889769i	$-0.349134\pi$
$23$	0.849459	+	0.337813i	0.177124	+	0.0704389i	−0.279287	+	0.960208i	$0.590098\pi$
$24$		0			0
$25$	−2.06243	−	2.26745i	−0.412486	−	0.453489i
$26$		0			0
$27$	−1.21010	−	2.88279i	−0.232884	−	0.554793i
$28$		0			0
$29$	−4.52393	+	1.79908i	−0.840073	+	0.334081i	−0.749660	−	0.661824i	$-0.769783\pi$
$29$	−4.52393	+	1.79908i	−0.840073	+	0.334081i	−0.0904136	+	0.995904i	$0.528819\pi$
$30$		0			0
$31$	−2.76400	+	0.638732i	−0.496429	+	0.114720i	−0.465941	−	0.884816i	$-0.654284\pi$
$31$	−2.76400	+	0.638732i	−0.496429	+	0.114720i	−0.0304875	+	0.999535i	$0.509706\pi$
$32$		0			0
$33$	−3.83443	−	2.24618i	−0.667489	−	0.391010i
$34$		0			0
$35$	4.77587	−	4.18167i	0.807269	−	0.706831i
$36$		0			0
$37$	8.57531	+	2.32676i	1.40977	+	0.382517i	0.883752	−	0.467955i	$-0.155009\pi$
$37$	8.57531	+	2.32676i	1.40977	+	0.382517i	0.526020	+	0.850472i	$0.323684\pi$
$38$		0			0
$39$	7.86891	+	2.78932i	1.26003	+	0.446649i
$40$		0			0
$41$	−5.33729	+	2.60595i	−0.833545	+	0.406981i	−0.805478	−	0.592625i	$-0.798092\pi$
$41$	−5.33729	+	2.60595i	−0.833545	+	0.406981i	−0.0280663	+	0.999606i	$0.508935\pi$
$42$		0			0
$43$	−0.373781	+	3.93828i	−0.0570010	+	0.600582i	0.920656	+	0.390375i	$0.127655\pi$
$43$	−0.373781	+	3.93828i	−0.0570010	+	0.600582i	−0.977657	+	0.210207i	$0.932586\pi$
$44$		0			0
$45$	5.73107	+	0.874387i	0.854338	+	0.130346i
$46$		0			0
$47$	0.147189	+	7.77648i	0.0214698	+	1.13432i	0.834126	+	0.551574i	$0.185972\pi$
$47$	0.147189	+	7.77648i	0.0214698	+	1.13432i	−0.812656	+	0.582743i	$0.801979\pi$
$48$		0			0
$49$	−8.90922	−	10.5724i	−1.27275	−	1.51034i
$50$		0			0
$51$	−0.371807	−	6.54166i	−0.0520634	−	0.916015i
$52$		0			0
$53$	0.188558	+	1.09630i	0.0259004	+	0.150589i	0.995599	−	0.0937150i	$-0.0298742\pi$
$53$	0.188558	+	1.09630i	0.0259004	+	0.150589i	−0.969699	+	0.244304i	$0.921441\pi$
$54$		0			0
$55$	2.03495	−	1.09080i	0.274393	−	0.147083i
$56$		0			0
$57$	8.86447	+	4.32811i	1.17413	+	0.573272i
$58$		0			0
$59$	−10.3888	+	0.787950i	−1.35251	+	0.102582i	−0.731832	−	0.681485i	$-0.761335\pi$
$59$	−10.3888	+	0.787950i	−1.35251	+	0.102582i	−0.620676	+	0.784067i	$0.713142\pi$
$60$		0			0
$61$	5.52223	−	5.62774i	0.707049	−	0.720558i	−0.262642	−	0.964893i	$-0.584594\pi$
$61$	5.52223	−	5.62774i	0.707049	−	0.720558i	0.969691	+	0.244335i	$0.0785697\pi$
$62$		0			0
$63$	3.22394	−	18.7445i	0.406178	−	2.36159i
$64$		0			0
$65$	−3.36924	+	2.73188i	−0.417903	+	0.338848i
$66$		0			0
$67$	−8.24417	+	3.64564i	−1.00719	+	0.445386i	−0.841189	−	0.540741i	$-0.818144\pi$
$67$	−8.24417	+	3.64564i	−1.00719	+	0.445386i	−0.165996	+	0.986126i	$0.553084\pi$
$68$		0			0
$69$	−0.596091	+	2.37377i	−0.0717609	+	0.285768i
$70$		0			0
$71$	11.0551	−	1.26074i	1.31200	−	0.149623i	0.570899	−	0.821020i	$-0.306595\pi$
$71$	11.0551	−	1.26074i	1.31200	−	0.149623i	0.741097	+	0.671397i	$0.234306\pi$
$72$		0			0
$73$	−3.43668	+	2.57728i	−0.402233	+	0.301648i	−0.781816	−	0.623510i	$-0.785706\pi$
$73$	−3.43668	+	2.57728i	−0.402233	+	0.301648i	0.379583	+	0.925158i	$0.376068\pi$
$74$		0			0
$75$	5.28802	−	6.27517i	0.610608	−	0.724594i
$76$		0			0
$77$	−3.45165	−	6.74267i	−0.393352	−	0.768399i
$78$		0			0
$79$	−0.402907	+	1.07178i	−0.0453305	+	0.120585i	−0.956766	−	0.290858i	$-0.906059\pi$
$79$	−0.402907	+	1.07178i	−0.0453305	+	0.120585i	0.911436	+	0.411443i	$0.134975\pi$
$80$		0			0
$81$	−3.56612	+	2.08901i	−0.396236	+	0.232112i
$82$		0			0
$83$	−4.94246	+	6.85715i	−0.542506	+	0.752670i	−0.989915	−	0.141659i	$-0.954756\pi$
$83$	−4.94246	+	6.85715i	−0.542506	+	0.752670i	0.447410	+	0.894329i	$0.352347\pi$
$84$		0			0
$85$	3.00039	+	1.60831i	0.325438	+	0.174446i
$86$		0			0
$87$	−6.37426	−	11.3694i	−0.683393	−	1.21893i
$88$		0			0
$89$	0.517404	+	1.77340i	0.0548448	+	0.187980i	0.982786	−	0.184746i	$-0.0591462\pi$
$89$	0.517404	+	1.77340i	0.0548448	+	0.187980i	−0.927942	+	0.372726i	$0.878423\pi$
$90$		0			0
$91$	8.75181	+	11.2212i	0.917439	+	1.17631i
$92$		0			0
$93$	−2.67253	−	7.10926i	−0.277129	−	0.737195i
$94$		0			0
$95$	−4.32116	+	2.75608i	−0.443342	+	0.282768i
$96$		0			0
$97$	5.32857	+	1.23138i	0.541034	+	0.125027i	0.486821	−	0.873502i	$-0.338157\pi$
$97$	5.32857	+	1.23138i	0.541034	+	0.125027i	0.0542136	+	0.998529i	$0.482735\pi$
$98$		0			0
$99$	2.67759	−	6.37874i	0.269108	−	0.641088i
$100$		0			0
$101$	1.81295	+	19.1019i	0.180396	+	1.90071i	0.386678	+	0.922215i	$0.373623\pi$
$101$	1.81295	+	19.1019i	0.180396	+	1.90071i	−0.206282	+	0.978493i	$0.566136\pi$
$102$		0			0
$103$	15.3371	−	10.6195i	1.51121	−	1.04637i	0.531245	−	0.847218i	$-0.321724\pi$
$103$	15.3371	−	10.6195i	1.51121	−	1.04637i	0.979969	−	0.199149i	$-0.0638177\pi$
$104$		0			0
$105$	12.7863	+	11.1955i	1.24781	+	1.09256i
$106$		0			0
$107$	3.90543	+	2.70413i	0.377552	+	0.261418i	0.742829	−	0.669481i	$-0.233483\pi$
$107$	3.90543	+	2.70413i	0.377552	+	0.261418i	−0.365277	+	0.930899i	$0.619026\pi$
$108$		0			0
$109$	−1.47392	−	0.940081i	−0.141176	−	0.0900434i	0.465267	−	0.885170i	$-0.345958\pi$
$109$	−1.47392	−	0.940081i	−0.141176	−	0.0900434i	−0.606443	+	0.795127i	$0.707404\pi$
$110$		0			0
$111$	−3.14222	+	23.5801i	−0.298246	+	2.23812i
$112$		0			0
$113$	−5.49114	+	8.97979i	−0.516563	+	0.844748i	−0.999523	−	0.0308949i	$-0.990164\pi$
$113$	−5.49114	+	8.97979i	−0.516563	+	0.844748i	0.482959	+	0.875643i	$0.339562\pi$
$114$		0			0
$115$	−0.890612	−	0.907629i	−0.0830500	−	0.0846368i
$116$		0			0
$117$	−2.68610	+	12.7160i	−0.248330	+	1.17559i
$118$		0			0
$119$	5.46178	−	9.74189i	0.500680	−	0.893038i
$120$		0			0
$121$	2.00807	+	7.99659i	0.182552	+	0.726963i
$122$		0			0
$123$	−8.80318	−	13.2426i	−0.793756	−	1.19405i
$124$		0			0
$125$	3.54740	+	10.6430i	0.317289	+	0.951935i
$126$		0			0
$127$	−12.5565	−	1.43197i	−1.11421	−	0.127067i	−0.463284	−	0.886210i	$-0.653329\pi$
$127$	−12.5565	−	1.43197i	−1.11421	−	0.127067i	−0.650924	+	0.759143i	$0.725618\pi$
$128$		0			0
$129$	−10.5836	+	0.400787i	−0.931837	+	0.0352874i
$130$		0			0
$131$	−0.0538156	+	0.946843i	−0.00470189	+	0.0827261i	−0.999882	−	0.0153335i	$-0.995119\pi$
$131$	−0.0538156	+	0.946843i	−0.00470189	+	0.0827261i	0.995181	+	0.0980596i	$0.0312636\pi$
$132$		0			0
$133$	8.77208	+	14.3452i	0.760636	+	1.24389i
$134$		0			0
$135$	−0.0822996	+	4.34815i	−0.00708322	+	0.374229i
$136$		0			0
$137$	9.93134	−	3.52040i	0.848491	−	0.300768i	0.125900	−	0.992043i	$-0.459818\pi$
$137$	9.93134	−	3.52040i	0.848491	−	0.300768i	0.722592	+	0.691275i	$0.242951\pi$
$138$		0			0
$139$	0.544827	+	0.514740i	0.0462116	+	0.0436597i	0.709510	−	0.704695i	$-0.248916\pi$
$139$	0.544827	+	0.514740i	0.0462116	+	0.0436597i	−0.663298	+	0.748355i	$0.730844\pi$
$140$		0			0
$141$	−20.5853	+	3.14069i	−1.73359	+	0.264494i
$142$		0			0
$143$	2.18255	+	4.69336i	0.182514	+	0.392479i
$144$		0			0
$145$	6.76729	+	0.256268i	0.561993	+	0.0212819i
$146$		0			0
$147$	24.9064	−	27.3822i	2.05425	−	2.25845i
$148$		0			0
$149$	−16.0245	−	12.9931i	−1.31278	−	1.06444i	−0.993144	−	0.116894i	$-0.962706\pi$
$149$	−16.0245	−	12.9931i	−1.31278	−	1.06444i	−0.319631	−	0.947542i	$-0.603559\pi$
$150$		0			0
$151$	12.4663	+	9.34887i	1.01449	+	0.760800i	0.971201	−	0.238263i	$-0.0765779\pi$
$151$	12.4663	+	9.34887i	1.01449	+	0.760800i	0.0432888	+	0.999063i	$0.486216\pi$
$152$		0			0
$153$	10.0179	−	1.91888i	0.809899	−	0.155132i
$154$		0			0
$155$	3.87559	+	0.742350i	0.311295	+	0.0596270i
$156$		0			0
$157$	3.85567	+	18.2527i	0.307716	+	1.45673i	0.807136	+	0.590366i	$0.201017\pi$
$157$	3.85567	+	18.2527i	0.307716	+	1.45673i	−0.499420	+	0.866360i	$0.666453\pi$
$158$		0			0
$159$	−2.84271	+	0.888094i	−0.225441	+	0.0704304i
$160$		0			0
$161$	−3.03246	+	2.86499i	−0.238991	+	0.225793i
$162$		0			0
$163$	−6.59214	+	19.7778i	−0.516336	+	1.54912i	0.289619	+	0.957142i	$0.406471\pi$
$163$	−6.59214	+	19.7778i	−0.516336	+	1.54912i	−0.805955	+	0.591976i	$0.798348\pi$
$164$		0			0
$165$	3.61442	+	5.01463i	0.281382	+	0.390388i
$166$		0			0
$167$	3.39197	−	12.4697i	0.262479	−	0.964938i
$167$	3.39197	−	12.4697i	0.262479	−	0.964938i
$168$		0			0
$169$	1.91549	+	2.65754i	0.147345	+	0.204426i
$170$		0			0
$171$	−4.85587	+	14.5686i	−0.371338	+	1.11409i
$172$		0			0
$173$	12.6351	−	11.9373i	0.960626	−	0.907577i	−0.0351511	−	0.999382i	$-0.511191\pi$
$173$	12.6351	−	11.9373i	0.960626	−	0.907577i	0.995777	+	0.0918047i	$0.0292635\pi$
$174$		0			0
$175$	13.3513	−	4.17110i	1.00926	−	0.315306i
$176$		0			0
$177$	−5.76497	−	27.2913i	−0.433322	−	2.05134i
$178$		0			0
$179$	−22.9885	−	4.40333i	−1.71824	−	0.329121i	−0.767957	−	0.640501i	$-0.778727\pi$
$179$	−22.9885	−	4.40333i	−1.71824	−	0.329121i	−0.950285	+	0.311380i	$0.899209\pi$
$180$		0			0
$181$	13.1961	−	2.52765i	0.980859	−	0.187879i	0.327438	−	0.944873i	$-0.393815\pi$
$181$	13.1961	−	2.52765i	0.980859	−	0.187879i	0.653422	+	0.756994i	$0.273333\pi$
$182$		0			0
$183$	16.8878	+	12.6648i	1.24839	+	0.936206i
$184$		0			0
$185$	−9.60027	−	7.78418i	−0.705826	−	0.572304i
$186$		0			0
$187$	2.73338	−	3.00509i	0.199884	−	0.219754i
$188$		0			0
$189$	14.2575	+	0.539911i	1.03708	+	0.0392727i
$190$		0			0
$191$	−3.06193	−	6.58439i	−0.221553	−	0.476429i	0.764125	−	0.645069i	$-0.223171\pi$
$191$	−3.06193	−	6.58439i	−0.221553	−	0.476429i	−0.985678	+	0.168639i	$0.946063\pi$
$192$		0			0
$193$	6.74809	−	1.02955i	0.485738	−	0.0741089i	0.0966675	−	0.995317i	$-0.469182\pi$
$193$	6.74809	−	1.02955i	0.485738	−	0.0741089i	0.389071	+	0.921208i	$0.372796\pi$
$194$		0			0
$195$	−8.44140	−	7.97524i	−0.604501	−	0.571119i
$196$		0			0
$197$	6.52278	−	2.31215i	0.464729	−	0.164734i	−0.0914274	−	0.995812i	$-0.529143\pi$
$197$	6.52278	−	2.31215i	0.464729	−	0.164734i	0.556157	+	0.831078i	$0.312275\pi$
$198$		0			0
$199$	0.0916647	−	4.84293i	0.00649794	−	0.343306i	−0.981727	−	0.190296i	$-0.939055\pi$
$199$	0.0916647	−	4.84293i	0.00649794	−	0.343306i	0.988225	−	0.153010i	$-0.0488967\pi$
$200$		0			0
$201$	−12.5903	−	20.5892i	−0.888052	−	1.45225i
$202$		0			0
$203$	1.26075	−	22.1818i	0.0884870	−	1.55686i
$204$		0			0
$205$	8.25593	−	0.312641i	0.576619	−	0.0218358i
$206$		0			0
$207$	−3.78551	−	0.431707i	−0.263111	−	0.0300057i
$208$		0			0
$209$	1.93390	+	5.80210i	0.133770	+	0.401340i
$210$		0			0
$211$	10.4817	+	15.7676i	0.721591	+	1.08549i	0.992424	+	0.122861i	$0.0392068\pi$
$211$	10.4817	+	15.7676i	0.721591	+	1.08549i	−0.270833	+	0.962626i	$0.587299\pi$
$212$		0			0
$213$	7.25530	+	28.8923i	0.497125	+	1.97966i
$214$		0			0
$215$	2.69104	−	4.79987i	0.183527	−	0.327348i
$216$		0			0
$217$	2.67564	−	12.6665i	0.181634	−	0.859855i
$218$		0			0
$219$	−8.05497	−	8.20887i	−0.544304	−	0.554704i
$220$		0			0
$221$	−3.98138	+	6.51084i	−0.267817	+	0.437967i
$222$		0			0
$223$	2.91796	−	21.8972i	0.195401	−	1.46634i	−0.569391	−	0.822067i	$-0.692821\pi$
$223$	2.91796	−	21.8972i	0.195401	−	1.46634i	0.764792	−	0.644277i	$-0.222842\pi$
$224$		0			0
$225$	10.7705	+	6.86952i	0.718033	+	0.457968i
$226$		0			0
$227$	13.6337	+	9.44002i	0.904903	+	0.626556i	0.927758	−	0.373182i	$-0.121733\pi$
$227$	13.6337	+	9.44002i	0.904903	+	0.626556i	−0.0228551	+	0.999739i	$0.507276\pi$
$228$		0			0
$229$	18.9957	+	16.6323i	1.25527	+	1.09909i	0.990890	+	0.134676i	$0.0429995\pi$
$229$	18.9957	+	16.6323i	1.25527	+	1.09909i	0.264383	+	0.964418i	$0.414832\pi$
$230$		0			0
$231$	16.6731	−	11.5445i	1.09701	−	0.759573i
$232$		0			0
$233$	−1.34582	−	14.1800i	−0.0881677	−	0.928964i	−0.924612	−	0.380911i	$-0.875610\pi$
$233$	−1.34582	−	14.1800i	−0.0881677	−	0.928964i	0.836444	−	0.548053i	$-0.184631\pi$
$234$		0			0
$235$	4.18751	−	9.97578i	0.273163	−	0.650748i
$236$		0			0
$237$	−2.98678	−	0.690215i	−0.194012	−	0.0448343i
$238$		0			0
$239$	4.05354	−	2.58539i	0.262202	−	0.167235i	−0.400101	−	0.916471i	$-0.631025\pi$
$239$	4.05354	−	2.58539i	0.262202	−	0.167235i	0.662303	+	0.749236i	$0.269579\pi$
$240$		0			0
$241$	−6.17134	−	16.4165i	−0.397531	−	1.05748i	−0.971174	−	0.238373i	$-0.923386\pi$
$241$	−6.17134	−	16.4165i	−0.397531	−	1.05748i	0.573643	−	0.819106i	$-0.305530\pi$
$242$		0			0
$243$	−12.5733	−	16.1210i	−0.806576	−	1.03416i
$244$		0			0
$245$	5.38639	+	18.4618i	0.344124	+	1.17948i
$246$		0			0
$247$	−5.61892	−	10.0222i	−0.357523	−	0.637696i
$248$		0			0
$249$	−19.9454	−	10.6914i	−1.26399	−	0.677541i
$250$		0			0
$251$	−2.52008	+	3.49634i	−0.159066	+	0.220687i	−0.883229	−	0.468941i	$-0.844636\pi$
$251$	−2.52008	+	3.49634i	−0.159066	+	0.220687i	0.724164	+	0.689628i	$0.242226\pi$
$252$		0			0
$253$	−1.30928	+	0.766968i	−0.0823139	+	0.0482189i
$254$		0			0
$255$	−3.20709	+	8.53124i	−0.200836	+	0.534247i
$256$		0			0
$257$	−9.27201	−	18.1125i	−0.578372	−	1.12983i	−0.977104	−	0.212760i	$-0.931755\pi$
$257$	−9.27201	−	18.1125i	−0.578372	−	1.12983i	0.398732	−	0.917067i	$-0.369450\pi$
$258$		0			0
$259$	−26.1293	+	31.0071i	−1.62360	+	1.92669i
$260$		0			0
$261$	16.2333	−	12.1739i	1.00482	−	0.753546i
$262$		0			0
$263$	−18.7799	+	2.14170i	−1.15802	+	0.132063i	−0.671087	−	0.741379i	$-0.734172\pi$
$263$	−18.7799	+	2.14170i	−1.15802	+	0.132063i	−0.486929	+	0.873441i	$0.661883\pi$
$264$		0			0
$265$	0.376864	−	1.50076i	0.0231505	−	0.0921908i
$266$		0			0
$267$	−4.52329	+	2.00024i	−0.276821	+	0.122413i
$268$		0			0
$269$	−21.5771	+	17.4953i	−1.31558	+	1.06671i	−0.322837	+	0.946455i	$0.604636\pi$
$269$	−21.5771	+	17.4953i	−1.31558	+	1.06671i	−0.992743	+	0.120256i	$0.961629\pi$
$270$		0			0
$271$	−0.543356	+	3.15916i	−0.0330065	+	0.191905i	−0.997350	−	0.0727469i	$-0.976823\pi$
$271$	−0.543356	+	3.15916i	−0.0330065	+	0.191905i	0.964344	+	0.264652i	$0.0852572\pi$
$272$		0			0
$273$	−26.6841	+	27.1939i	−1.61500	+	1.64585i
$274$		0			0
$275$	5.07309	−	0.384773i	0.305919	−	0.0232027i
$276$		0			0
$277$	12.2620	+	5.98697i	0.736754	+	0.359722i	0.768565	−	0.639772i	$-0.220971\pi$
$277$	12.2620	+	5.98697i	0.736754	+	0.359722i	−0.0318116	+	0.999494i	$0.510128\pi$
$278$		0			0
$279$	10.4207	−	5.58581i	0.623868	−	0.334414i
$280$		0			0
$281$	1.30313	+	7.57659i	0.0777380	+	0.451982i	0.998138	+	0.0610025i	$0.0194298\pi$
$281$	1.30313	+	7.57659i	0.0777380	+	0.451982i	−0.920400	+	0.390979i	$0.872137\pi$
$282$		0			0
$283$	0.0611089	+	1.07516i	0.00363255	+	0.0639119i	0.999693	−	0.0247603i	$-0.00788224\pi$
$283$	0.0611089	+	1.07516i	0.00363255	+	0.0639119i	−0.996061	+	0.0886721i	$0.971738\pi$
$284$		0			0
$285$	−8.84225	−	10.4929i	−0.523770	−	0.621546i
$286$		0			0
$287$	−0.512938	−	27.1001i	−0.0302778	−	1.59967i
$288$		0			0
$289$	−10.8845	−	1.66065i	−0.640267	−	0.0976853i
$290$		0			0
$291$	−1.38345	+	14.5765i	−0.0810993	+	0.854489i
$292$		0			0
$293$	−24.7562	+	12.0873i	−1.44627	+	0.706148i	−0.983597	−	0.180380i	$-0.942267\pi$
$293$	−24.7562	+	12.0873i	−1.44627	+	0.706148i	−0.462676	+	0.886527i	$0.653111\pi$
$294$		0			0
$295$	13.6596	+	4.84196i	0.795291	+	0.281910i
$296$		0			0
$297$	5.00841	+	1.35895i	0.290618	+	0.0788541i
$298$		0			0
$299$	2.14474	−	1.87790i	0.124033	−	0.108602i
$300$		0			0
$301$	−15.5772	−	9.12502i	−0.897857	−	0.525958i
$302$		0			0
$303$	−50.0517	+	11.5664i	−2.87539	+	0.664474i
$304$		0			0
$305$	−10.1911	+	4.05282i	−0.583543	+	0.232064i
$306$		0			0
$307$	3.94119	+	9.38899i	0.224936	+	0.535858i	0.994741	−	0.102421i	$-0.0326588\pi$
$307$	3.94119	+	9.38899i	0.224936	+	0.535858i	−0.769805	+	0.638279i	$0.779647\pi$
$308$		0			0
$309$	33.6059	+	36.9464i	1.91177	+	2.10181i
$310$		0			0
$311$	6.12273	+	2.43489i	0.347188	+	0.138070i	0.536620	−	0.843824i	$-0.319701\pi$
$311$	6.12273	+	2.43489i	0.347188	+	0.138070i	−0.189432	+	0.981894i	$0.560665\pi$
$312$		0			0
$313$	5.76287	+	1.80038i	0.325736	+	0.101764i	0.456693	−	0.889624i	$-0.349034\pi$
$313$	5.76287	+	1.80038i	0.325736	+	0.101764i	−0.130957	+	0.991388i	$0.541805\pi$
$314$		0			0
$315$	−14.6464	+	22.0325i	−0.825228	+	1.24139i
$316$		0			0
$317$	9.95103	+	0.754746i	0.558906	+	0.0423907i	0.352051	−	0.935981i	$-0.385484\pi$
$317$	9.95103	+	0.754746i	0.558906	+	0.0423907i	0.206855	+	0.978372i	$0.433677\pi$
$318$		0			0
$319$	2.26336	−	7.75765i	0.126724	−	0.434345i
$320$		0			0
$321$	−5.79513	+	11.3206i	−0.323453	+	0.631853i
$322$		0			0
$323$	−5.54573	+	7.11054i	−0.308573	+	0.395641i
$324$		0			0
$325$	−9.22456	+	2.50292i	−0.511686	+	0.138837i
$326$		0			0
$327$	1.97356	−	4.24396i	0.109138	−	0.234692i
$328$		0			0
$329$	−32.4621	−	14.3550i	−1.78969	−	0.791418i
$330$		0			0
$331$	2.65889	+	19.9531i	0.146146	+	1.09672i	0.898817	+	0.438324i	$0.144428\pi$
$331$	2.65889	+	19.9531i	0.146146	+	1.09672i	−0.752671	+	0.658397i	$0.771235\pi$
$332$		0			0
$333$	−37.0323			−2.02936
$334$		0			0
$335$	12.5389			0.685071
$336$		0			0
$337$	−2.47199	−	18.5505i	−0.134658	−	1.01051i	−0.920130	−	0.391612i	$-0.871917\pi$
$337$	−2.47199	−	18.5505i	−0.134658	−	1.01051i	0.785473	−	0.618896i	$-0.212420\pi$
$338$		0			0
$339$	−25.7726	−	11.3969i	−1.39977	−	0.618992i
$340$		0			0
$341$	1.98552	−	4.26967i	0.107522	−	0.231216i
$342$		0			0
$343$	30.0621	−	8.15683i	1.62320	−	0.440427i
$344$		0			0
$345$	2.09372	−	2.68449i	0.112722	−	0.144528i
$346$		0			0
$347$	12.7087	−	24.8259i	0.682237	−	1.33272i	−0.249069	−	0.968486i	$-0.580125\pi$
$347$	12.7087	−	24.8259i	0.682237	−	1.33272i	0.931306	−	0.364238i	$-0.118670\pi$
$348$		0			0
$349$	4.14212	−	14.1971i	0.221722	−	0.759952i	−0.770713	−	0.637183i	$-0.780100\pi$
$349$	4.14212	−	14.1971i	0.221722	−	0.759952i	0.992435	−	0.122769i	$-0.0391775\pi$
$350$		0			0
$351$	−9.72150	−	0.737336i	−0.518895	−	0.0393561i
$352$		0			0
$353$	20.0247	−	30.1232i	1.06581	−	1.60329i	0.307324	−	0.951605i	$-0.400567\pi$
$353$	20.0247	−	30.1232i	1.06581	−	1.60329i	0.758486	−	0.651689i	$-0.225939\pi$
$354$		0			0
$355$	−14.7731	−	4.61530i	−0.784077	−	0.244955i
$356$		0			0
$357$	27.7847	+	11.0494i	1.47052	+	0.584797i
$358$		0			0
$359$	18.4046	+	20.2341i	0.971360	+	1.06792i	0.997667	+	0.0682629i	$0.0217457\pi$
$359$	18.4046	+	20.2341i	0.971360	+	1.06792i	−0.0263072	+	0.999654i	$0.508375\pi$
$360$		0			0
$361$	2.09928	+	5.00104i	0.110488	+	0.263213i
$362$		0			0
$363$	−20.5113	+	8.15695i	−1.07657	+	0.428129i
$364$		0			0
$365$	5.82191	−	1.34538i	0.304733	−	0.0704206i
$366$		0			0
$367$	−14.0328	−	8.22033i	−0.732508	−	0.429098i	0.0914050	−	0.995814i	$-0.470864\pi$
$367$	−14.0328	−	8.22033i	−0.732508	−	0.429098i	−0.823913	+	0.566716i	$0.808214\pi$
$368$		0			0
$369$	18.6243	−	16.3071i	0.969543	−	0.848915i
$370$		0			0
$371$	−4.89932	−	1.32935i	−0.254360	−	0.0690162i
$372$		0			0
$373$	−24.8930	−	8.82390i	−1.28891	−	0.456884i	−0.400652	−	0.916230i	$-0.631216\pi$
$373$	−24.8930	−	8.82390i	−1.28891	−	0.456884i	−0.888257	+	0.459346i	$0.848084\pi$
$374$		0			0
$375$	−26.9899	+	13.1779i	−1.39375	+	0.680505i
$376$		0			0
$377$	−1.43445	+	15.1139i	−0.0738781	+	0.778404i
$378$		0			0
$379$	−12.2034	−	1.86187i	−0.626848	−	0.0956380i	−0.170381	−	0.985378i	$-0.554500\pi$
$379$	−12.2034	−	1.86187i	−0.626848	−	0.0956380i	−0.456467	+	0.889740i	$0.650885\pi$
$380$		0			0
$381$	−0.640298	−	33.8290i	−0.0328035	−	1.73311i
$382$		0			0
$383$	18.7732	+	22.2777i	0.959266	+	1.13834i	0.990318	+	0.138821i	$0.0443312\pi$
$383$	18.7732	+	22.2777i	0.959266	+	1.13834i	−0.0310519	+	0.999518i	$0.509886\pi$
$384$		0			0
$385$	0.597899	+	10.5196i	0.0304718	+	0.536127i
$386$		0			0
$387$	−2.79474	−	16.2491i	−0.142064	−	0.825986i
$388$		0			0
$389$	−0.868271	+	0.465422i	−0.0440231	+	0.0235978i	−0.494304	−	0.869289i	$-0.664577\pi$
$389$	−0.868271	+	0.465422i	−0.0440231	+	0.0235978i	0.450281	+	0.892887i	$0.351324\pi$
$390$		0			0
$391$	−2.01044	−	0.981605i	−0.101672	−	0.0496419i
$392$		0			0
$393$	−2.53178	+	0.192025i	−0.127711	+	0.00968638i
$394$		0			0
$395$	1.11551	−	1.13682i	0.0561273	−	0.0571997i
$396$		0			0
$397$	2.49924	−	14.5310i	0.125433	−	0.729288i	−0.852872	−	0.522120i	$-0.825141\pi$
$397$	2.49924	−	14.5310i	0.125433	−	0.729288i	0.978305	−	0.207169i	$-0.0664248\pi$
$398$		0			0
$399$	−34.9673	+	28.3525i	−1.75055	+	1.41940i
$400$		0			0
$401$	−30.0457	+	13.2865i	−1.50041	+	0.663495i	−0.981522	−	0.191347i	$-0.938714\pi$
$401$	−30.0457	+	13.2865i	−1.50041	+	0.663495i	−0.518889	+	0.854842i	$0.673654\pi$
$402$		0			0
$403$	−2.15454	+	8.57987i	−0.107325	+	0.427394i
$404$		0			0
$405$	5.71190	−	0.651397i	0.283826	−	0.0323682i
$406$		0			0
$407$	−11.7991	+	8.84858i	−0.584862	+	0.438608i
$408$		0			0
$409$	22.2793	−	26.4384i	1.10164	−	1.30729i	0.153961	−	0.988077i	$-0.450797\pi$
$409$	22.2793	−	26.4384i	1.10164	−	1.30729i	0.947682	−	0.319217i	$-0.103420\pi$
$410$		0			0
$411$	12.8546	+	25.1110i	0.634070	+	1.23863i
$412$		0			0
$413$	16.7304	−	44.5049i	0.823250	−	2.18994i
$414$		0			0
$415$	10.1452	−	5.94299i	0.498009	−	0.291730i
$416$		0			0
$417$	−1.17335	+	1.62790i	−0.0574592	+	0.0797186i
$418$		0			0
$419$	5.22057	+	2.79840i	0.255042	+	0.136711i	0.594989	−	0.803734i	$-0.297156\pi$
$419$	5.22057	+	2.79840i	0.255042	+	0.136711i	−0.339948	+	0.940444i	$0.610409\pi$
$420$		0			0
$421$	−17.7062	−	31.5817i	−0.862949	−	1.53920i	−0.842040	−	0.539416i	$-0.818645\pi$
$421$	−17.7062	−	31.5817i	−0.862949	−	1.53920i	−0.0209090	−	0.999781i	$-0.506656\pi$
$422$		0			0
$423$	−9.07925	−	31.1191i	−0.441448	−	1.51306i
$424$		0			0
$425$	4.61335	+	5.91507i	0.223780	+	0.286923i
$426$		0			0
$427$	12.6612	+	33.6802i	0.612716	+	1.62990i
$428$		0			0
$429$	−11.6835	+	7.45183i	−0.564083	+	0.359778i
$430$		0			0
$431$	9.62732	+	2.22477i	0.463732	+	0.107164i	0.450553	−	0.892750i	$-0.351227\pi$
$431$	9.62732	+	2.22477i	0.463732	+	0.107164i	0.0131784	+	0.999913i	$0.495805\pi$
$432$		0			0
$433$	7.08343	−	16.8747i	0.340408	−	0.810944i	−0.657917	−	0.753091i	$-0.728562\pi$
$433$	7.08343	−	16.8747i	0.340408	−	0.810944i	0.998325	−	0.0578538i	$-0.0184257\pi$
$434$		0			0
$435$	1.71310	+	18.0497i	0.0821367	+	0.865419i
$436$		0			0
$437$	2.76929	−	1.91746i	0.132473	−	0.0917246i
$438$		0			0
$439$	2.32757	+	2.03798i	0.111089	+	0.0972674i	0.712499	−	0.701673i	$-0.247563\pi$
$439$	2.32757	+	2.03798i	0.111089	+	0.0972674i	−0.601411	+	0.798940i	$0.705394\pi$
$440$		0			0
$441$	47.3746	+	32.8022i	2.25593	+	1.56201i
$442$		0			0
$443$	6.60000	+	4.20954i	0.313575	+	0.200001i	0.685150	−	0.728402i	$-0.259736\pi$
$443$	6.60000	+	4.20954i	0.313575	+	0.200001i	−0.371575	+	0.928403i	$0.621182\pi$
$444$		0			0
$445$	0.339424	−	2.54713i	0.0160902	−	0.120746i
$446$		0			0
$447$	28.8144	−	47.1208i	1.36287	−	2.22874i
$448$		0			0
$449$	9.90408	+	10.0933i	0.467403	+	0.476333i	0.906560	−	0.422077i	$-0.138699\pi$
$449$	9.90408	+	10.0933i	0.467403	+	0.476333i	−0.439157	+	0.898410i	$0.644723\pi$
$450$		0			0
$451$	2.03758	−	9.64588i	0.0959458	−	0.454207i
$452$		0			0
$453$	−20.4016	+	36.3892i	−0.958550	+	1.70972i
$454$		0			0
$455$	−4.82110	−	19.1987i	−0.226017	−	0.900051i
$456$		0			0
$457$	3.99718	+	6.01295i	0.186980	+	0.281274i	0.914311	−	0.405014i	$-0.132733\pi$
$457$	3.99718	+	6.01295i	0.186980	+	0.281274i	−0.727330	+	0.686287i	$0.759239\pi$
$458$		0			0
$459$	2.41948	+	7.25896i	0.112932	+	0.338819i
$460$		0			0
$461$	0.207477	+	0.0236611i	0.00966318	+	0.00110201i	0.118138	−	0.992997i	$-0.462308\pi$
$461$	0.207477	+	0.0236611i	0.00966318	+	0.00110201i	−0.108475	+	0.994099i	$0.534597\pi$
$462$		0			0
$463$	37.4153	−	1.41686i	1.73884	−	0.0658473i	0.850763	−	0.525550i	$-0.176140\pi$
$463$	37.4153	−	1.41686i	1.73884	−	0.0658473i	0.888073	+	0.459703i	$0.152044\pi$
$464$		0			0
$465$	−0.599494	+	10.5476i	−0.0278009	+	0.489134i
$466$		0			0
$467$	−4.37084	−	7.14773i	−0.202258	−	0.330757i	0.735822	−	0.677175i	$-0.236796\pi$
$467$	−4.37084	−	7.14773i	−0.202258	−	0.330757i	−0.938081	+	0.346417i	$0.887398\pi$
$468$		0			0
$469$	0.778477	−	41.1294i	0.0359467	−	1.89918i
$470$		0			0
$471$	−47.0758	+	16.6871i	−2.16914	+	0.768902i
$472$		0			0
$473$	−4.77304	−	4.50946i	−0.219465	−	0.207345i
$474$		0			0
$475$	−11.1645	+	1.70336i	−0.512263	+	0.0781557i
$476$		0			0
$477$	−1.95494	−	4.20393i	−0.0895108	−	0.192485i
$478$		0			0
$479$	−35.0242	−	1.32632i	−1.60030	−	0.0606011i	−0.777481	−	0.628907i	$-0.783503\pi$
$479$	−35.0242	−	1.32632i	−1.60030	−	0.0606011i	−0.822818	+	0.568306i	$0.807599\pi$
$480$		0			0
$481$	18.6437	−	20.4970i	0.850080	−	0.934581i
$482$		0			0
$483$	−8.67556	−	7.03439i	−0.394751	−	0.320076i
$484$		0			0
$485$	−6.08610	−	4.56417i	−0.276356	−	0.207248i
$486$		0			0
$487$	12.7672	−	2.44549i	0.578537	−	0.110816i	0.109488	−	0.993988i	$-0.465079\pi$
$487$	12.7672	−	2.44549i	0.578537	−	0.110816i	0.469049	+	0.883172i	$0.344597\pi$
$488$		0			0
$489$	−54.8179	−	10.5001i	−2.47895	−	0.474830i
$490$		0			0
$491$	0.549948	+	2.60345i	0.0248188	+	0.117492i	0.989053	−	0.147559i	$-0.0471415\pi$
$491$	0.549948	+	2.60345i	0.0248188	+	0.117492i	−0.964235	+	0.265051i	$0.914611\pi$
$492$		0			0
$493$	11.3729	−	3.55303i	0.512210	−	0.160020i
$494$		0			0
$495$	−6.99478	+	6.60851i	−0.314392	+	0.297030i
$496$		0			0
$497$	−16.0561	+	48.1717i	−0.720214	+	2.16079i
$498$		0			0
$499$	1.26358	+	1.75308i	0.0565655	+	0.0784787i	0.838569	−	0.544795i	$-0.183393\pi$
$499$	1.26358	+	1.75308i	0.0565655	+	0.0784787i	−0.782004	+	0.623274i	$0.785802\pi$
$500$		0			0
$501$	34.2919	+	4.59186i	1.53205	+	0.205149i
$502$		0			0
$503$	0.968050	+	1.34307i	0.0431632	+	0.0598844i	0.832265	−	0.554378i	$-0.187044\pi$
$503$	0.968050	+	1.34307i	0.0431632	+	0.0598844i	−0.789102	+	0.614263i	$0.789454\pi$
$504$		0			0
$505$	8.43962	−	25.3207i	0.375558	−	1.12675i
$506$		0			0
$507$	−6.37522	+	6.02317i	−0.283134	+	0.267498i
$508$		0			0
$509$	21.3547	−	6.67146i	0.946532	−	0.295707i	0.214304	−	0.976767i	$-0.431252\pi$
$509$	21.3547	−	6.67146i	0.946532	−	0.295707i	0.732228	+	0.681060i	$0.238481\pi$
$510$		0			0
$511$	−4.05161	−	19.1803i	−0.179233	−	0.848486i
$512$		0			0
$513$	−11.3141	−	2.16716i	−0.499529	−	0.0956822i
$514$		0			0
$515$	−25.4855	+	4.88162i	−1.12303	+	0.215110i
$516$		0			0
$517$	−10.3285	−	7.74567i	−0.454246	−	0.340654i
$518$		0			0
$519$	36.1477	+	29.3096i	1.58671	+	1.28655i
$520$		0			0
$521$	20.4042	−	22.4324i	0.893922	−	0.982781i	−0.106011	−	0.994365i	$-0.533808\pi$
$521$	20.4042	−	22.4324i	0.893922	−	0.982781i	0.999933	+	0.0115838i	$0.00368731\pi$
$522$		0			0
$523$	20.0969	+	0.761043i	0.878778	+	0.0332781i	0.473376	−	0.880860i	$-0.343035\pi$
$523$	20.0969	+	0.761043i	0.878778	+	0.0332781i	0.405402	+	0.914139i	$0.367132\pi$
$524$		0			0
$525$	15.7909	+	33.9568i	0.689171	+	1.48200i
$526$		0			0
$527$	6.86332	−	1.04713i	0.298971	−	0.0456138i
$528$		0			0
$529$	−16.1111	−	15.2214i	−0.700481	−	0.661798i
$530$		0			0
$531$	40.9274	−	14.5077i	1.77610	−	0.629581i
$532$		0			0
$533$	−0.350502	+	18.5181i	−0.0151819	+	0.802108i
$534$		0			0
$535$	−3.44712	−	5.63715i	−0.149032	−	0.243715i
$536$		0			0
$537$	3.55596	−	62.5644i	0.153451	−	2.69985i
$538$		0			0
$539$	22.9322	−	0.868412i	0.987761	−	0.0374051i
$540$		0			0
$541$	−2.26077	−	0.257822i	−0.0971979	−	0.0110847i	0.0645731	−	0.997913i	$-0.479431\pi$
$541$	−2.26077	−	0.257822i	−0.0971979	−	0.0110847i	−0.161771	+	0.986828i	$0.551721\pi$
$542$		0			0
$543$	11.3746	+	34.1261i	0.488130	+	1.46449i
$544$		0			0
$545$	1.34622	+	2.02511i	0.0576657	+	0.0867463i
$546$		0			0
$547$	6.32334	+	25.1810i	0.270367	+	1.07666i	0.941955	+	0.335738i	$0.108986\pi$
$547$	6.32334	+	25.1810i	0.270367	+	1.07666i	−0.671589	+	0.740924i	$0.734388\pi$
$548$		0			0
$549$	−16.0702	+	28.6636i	−0.685861	+	1.22333i
$550$		0			0
$551$	−3.70750	+	17.5513i	−0.157945	+	0.747709i
$552$		0			0
$553$	−3.65969	−	3.72962i	−0.155626	−	0.158599i
$554$		0			0
$555$	17.2627	−	28.2301i	0.732761	−	1.19830i
$556$		0			0
$557$	−0.203067	+	1.52387i	−0.00860423	+	0.0645685i	−0.995014	−	0.0997353i	$-0.968200\pi$
$557$	−0.203067	+	1.52387i	−0.00860423	+	0.0645685i	0.986410	+	0.164304i	$0.0525377\pi$
$558$		0			0
$559$	10.4007	+	6.63365i	0.439902	+	0.280574i
$560$		0			0
$561$	8.94157	+	6.19116i	0.377513	+	0.261391i
$562$		0			0
$563$	−23.3989	−	20.4877i	−0.986147	−	0.863453i	0.00448838	−	0.999990i	$-0.498571\pi$
$563$	−23.3989	−	20.4877i	−0.986147	−	0.863453i	−0.990635	+	0.136537i	$0.956403\pi$
$564$		0			0
$565$	12.0373	−	8.33468i	0.506415	−	0.350643i
$566$		0			0
$567$	−1.78206	−	18.7763i	−0.0748394	−	0.788532i
$568$		0			0
$569$	−3.89729	+	9.28441i	−0.163383	+	0.389223i	−0.982979	−	0.183720i	$-0.941186\pi$
$569$	−3.89729	+	9.28441i	−0.163383	+	0.389223i	0.819596	+	0.572942i	$0.194198\pi$
$570$		0			0
$571$	12.6184	+	2.91599i	0.528066	+	0.122031i	0.480764	−	0.876850i	$-0.340359\pi$
$571$	12.6184	+	2.91599i	0.528066	+	0.122031i	0.0473018	+	0.998881i	$0.484938\pi$
$572$		0			0
$573$	16.3909	−	10.4543i	0.684740	−	0.436734i
$574$		0			0
$575$	−0.985979	−	2.62282i	−0.0411182	−	0.109379i
$576$		0			0
$577$	17.8157	+	22.8427i	0.741679	+	0.950953i	0.999885	−	0.0151365i	$-0.00481828\pi$
$577$	17.8157	+	22.8427i	0.741679	+	0.950953i	−0.258207	+	0.966090i	$0.583132\pi$
$578$		0			0
$579$	5.11864	+	17.5441i	0.212723	+	0.729107i
$580$		0			0
$581$	−18.8640	−	33.6468i	−0.782613	−	1.39591i
$582$		0			0
$583$	−1.62738	−	0.872327i	−0.0673990	−	0.0361281i
$584$		0			0
$585$	10.5707	−	14.6657i	0.437045	−	0.606354i
$586$		0			0
$587$	33.1109	−	19.3961i	1.36663	−	0.800564i	0.374679	−	0.927155i	$-0.377753\pi$
$587$	33.1109	−	19.3961i	1.36663	−	0.800564i	0.991955	+	0.126591i	$0.0404035\pi$
$588$		0			0
$589$	−3.67807	+	9.78411i	−0.151552	+	0.403147i
$590$		0			0
$591$	8.44274	+	16.4926i	0.347288	+	0.678414i
$592$		0			0
$593$	−14.3869	+	17.0726i	−0.590799	+	0.701088i	−0.975011	−	0.222157i	$-0.928690\pi$
$593$	−14.3869	+	17.0726i	−0.590799	+	0.701088i	0.384212	+	0.923245i	$0.374473\pi$
$594$		0			0
$595$	−12.4287	+	9.32072i	−0.509528	+	0.382112i
$596$		0			0
$597$	12.8847	−	1.46939i	0.527334	−	0.0601383i
$598$		0			0
$599$	−7.93582	+	31.6023i	−0.324249	+	1.29123i	0.561658	+	0.827370i	$0.310164\pi$
$599$	−7.93582	+	31.6023i	−0.324249	+	1.29123i	−0.885907	+	0.463864i	$0.846463\pi$
$600$		0			0
$601$	−33.5540	+	14.8379i	−1.36870	+	0.605249i	−0.952643	−	0.304091i	$-0.901647\pi$
$601$	−33.5540	+	14.8379i	−1.36870	+	0.605249i	−0.416054	+	0.909340i	$0.636587\pi$
$602$		0			0
$603$	29.1821	−	23.6617i	1.18839	−	0.963577i
$604$		0			0
$605$	1.94399	−	11.3027i	0.0790343	−	0.459518i
$606$		0			0
$607$	−5.62927	+	5.73682i	−0.228485	+	0.232851i	−0.818449	−	0.574579i	$-0.805166\pi$
$607$	−5.62927	+	5.73682i	−0.228485	+	0.232851i	0.589964	+	0.807429i	$0.299142\pi$
$608$		0			0
$609$	59.3123	−	4.49860i	2.40346	−	0.182292i
$610$		0			0
$611$	21.7950	+	10.6415i	0.881730	+	0.430508i
$612$		0			0
$613$	−26.9527	+	14.4475i	−1.08861	+	0.583530i	−0.915885	−	0.401441i	$-0.868510\pi$
$613$	−26.9527	+	14.4475i	−1.08861	+	0.583530i	−0.172723	+	0.984970i	$0.555257\pi$
$614$		0			0
$615$	3.74932	+	21.7991i	0.151187	+	0.879026i
$616$		0			0
$617$	−2.70668	−	47.6218i	−0.108967	−	1.91718i	−0.333557	−	0.942730i	$-0.608249\pi$
$617$	−2.70668	−	47.6218i	−0.108967	−	1.91718i	0.224590	−	0.974453i	$-0.427896\pi$
$618$		0			0
$619$	−10.2087	−	12.1144i	−0.410323	−	0.486921i	0.519738	−	0.854326i	$-0.326029\pi$
$619$	−10.2087	−	12.1144i	−0.410323	−	0.486921i	−0.930061	+	0.367405i	$0.880246\pi$
$620$		0			0
$621$	−0.0540873	−	2.85760i	−0.00217045	−	0.114672i
$622$		0			0
$623$	−8.33391	−	1.27150i	−0.333891	−	0.0509416i
$624$		0			0
$625$	0.0264074	−	0.278238i	0.00105630	−	0.0111295i
$626$		0			0
$627$	−14.7138	+	7.18405i	−0.587612	+	0.286903i
$628$		0			0
$629$	−20.4960	−	7.26529i	−0.817229	−	0.289686i
$630$		0			0
$631$	10.9037	+	2.95854i	0.434070	+	0.117777i	0.472192	−	0.881496i	$-0.343463\pi$
$631$	10.9037	+	2.95854i	0.434070	+	0.117777i	−0.0381219	+	0.999273i	$0.512138\pi$
$632$		0			0
$633$	−38.1375	+	33.3925i	−1.51583	+	1.32723i
$634$		0			0
$635$	15.1684	+	8.88552i	0.601938	+	0.352611i
$636$		0			0
$637$	−42.0062	+	9.70720i	−1.66435	+	0.384613i
$638$		0			0
$639$	−43.0914	+	17.1366i	−1.70467	+	0.677913i
$640$		0			0
$641$	1.50318	+	3.58098i	0.0593720	+	0.141440i	0.949029	−	0.315190i	$-0.102068\pi$
$641$	1.50318	+	3.58098i	0.0593720	+	0.141440i	−0.889657	+	0.456630i	$0.849056\pi$
$642$		0			0
$643$	−2.89854	−	3.18667i	−0.114307	−	0.125670i	0.679931	−	0.733276i	$-0.262010\pi$
$643$	−2.89854	−	3.18667i	−0.114307	−	0.125670i	−0.794239	+	0.607606i	$0.792130\pi$
$644$		0			0
$645$	13.6896	+	5.44409i	0.539028	+	0.214361i
$646$		0			0
$647$	25.5138	+	7.97079i	1.00305	+	0.313364i	0.755243	−	0.655445i	$-0.227519\pi$
$647$	25.5138	+	7.97079i	1.00305	+	0.313364i	0.247807	+	0.968809i	$0.420290\pi$
$648$		0			0
$649$	9.57371	−	14.4017i	0.375801	−	0.565317i
$650$		0			0
$651$	34.5606	+	2.62128i	1.35454	+	0.102736i
$652$		0			0
$653$	−4.87425	+	16.7065i	−0.190744	+	0.653774i	0.807235	+	0.590230i	$0.200963\pi$
$653$	−4.87425	+	16.7065i	−0.190744	+	0.653774i	−0.997979	+	0.0635436i	$0.979760\pi$
$654$		0			0
$655$	0.601121	−	1.17427i	0.0234877	−	0.0458824i
$656$		0			0
$657$	11.0107	−	14.1175i	0.429568	−	0.550776i
$658$		0			0
$659$	3.13661	−	0.851065i	0.122185	−	0.0331528i	−0.200247	−	0.979745i	$-0.564174\pi$
$659$	3.13661	−	0.851065i	0.122185	−	0.0331528i	0.322432	+	0.946593i	$0.395500\pi$
$660$		0			0
$661$	−10.7185	+	23.0491i	−0.416901	+	0.896508i	0.579754	+	0.814791i	$0.303149\pi$
$661$	−10.7185	+	23.0491i	−0.416901	+	0.896508i	−0.996656	+	0.0817162i	$0.973960\pi$
$662$		0			0
$663$	−18.6865	−	8.26334i	−0.725725	−	0.320922i
$664$		0			0
$665$	−3.08948	−	23.1843i	−0.119805	−	0.899049i
$666$		0			0
$667$	−4.45065			−0.172330
$668$		0			0
$669$	59.1429			2.28660
$670$		0			0
$671$	1.72869	+	12.9726i	0.0667355	+	0.500802i
$672$		0			0
$673$	−13.5532	−	5.99332i	−0.522436	−	0.231026i	0.126365	−	0.991984i	$-0.459669\pi$
$673$	−13.5532	−	5.99332i	−0.522436	−	0.231026i	−0.648801	+	0.760958i	$0.724729\pi$
$674$		0			0
$675$	−4.04081	+	8.68940i	−0.155531	+	0.334455i
$676$		0			0
$677$	−2.23620	+	0.606754i	−0.0859441	+	0.0233194i	−0.304577	−	0.952488i	$-0.598515\pi$
$677$	−2.23620	+	0.606754i	−0.0859441	+	0.0233194i	0.218633	+	0.975807i	$0.429840\pi$
$678$		0			0
$679$	−15.3490	+	19.6800i	−0.589042	+	0.755248i
$680$		0			0
$681$	−20.2306	+	39.5198i	−0.775239	+	1.51440i
$682$		0			0
$683$	−6.46713	+	22.1660i	−0.247458	+	0.848159i	0.737497	+	0.675350i	$0.236007\pi$
$683$	−6.46713	+	22.1660i	−0.247458	+	0.848159i	−0.984955	+	0.172809i	$0.944716\pi$
$684$		0			0
$685$	−14.6148	−	1.10847i	−0.558401	−	0.0423525i
$686$		0			0
$687$	−37.4214	+	56.2929i	−1.42772	+	2.14771i
$688$		0			0
$689$	3.31104	+	1.03441i	0.126140	+	0.0394077i
$690$		0			0
$691$	47.0475	+	18.7099i	1.78977	+	0.711757i	0.994406	+	0.105627i	$0.0336851\pi$
$691$	47.0475	+	18.7099i	1.78977	+	0.711757i	0.795366	+	0.606130i	$0.207279\pi$
$692$		0			0
$693$	21.2426	+	23.3542i	0.806942	+	0.887154i
$694$		0			0
$695$	−0.403537	−	0.961334i	−0.0153070	−	0.0364655i
$696$		0			0
$697$	13.5071	−	5.37152i	0.511619	−	0.203461i
$698$		0			0
$699$	37.1552	−	8.58618i	1.40534	−	0.324759i
$700$		0			0
$701$	27.7970	+	16.2833i	1.04988	+	0.615011i	0.926092	−	0.377297i	$-0.123147\pi$
$701$	27.7970	+	16.2833i	1.04988	+	0.615011i	0.123787	+	0.992309i	$0.460496\pi$
$702$		0			0
$703$	24.6315	−	21.5669i	0.928993	−	0.813410i
$704$		0			0
$705$	27.9547	+	7.58503i	1.05284	+	0.285669i
$706$		0			0
$707$	−82.5317	−	29.2553i	−3.10392	−	1.10026i
$708$		0			0
$709$	24.1344	−	11.7837i	0.906386	−	0.442546i	0.0743274	−	0.997234i	$-0.476319\pi$
$709$	24.1344	−	11.7837i	0.906386	−	0.442546i	0.832058	+	0.554688i	$0.187162\pi$
$710$		0			0
$711$	0.450897	−	4.75080i	0.0169100	−	0.178169i
$712$		0			0
$713$	−2.56368	−	0.391139i	−0.0960104	−	0.0146483i
$714$		0			0
$715$	−0.136251	−	7.19856i	−0.00509549	−	0.269211i
$716$		0			0
$717$	8.29462	+	9.84304i	0.309768	+	0.367595i
$718$		0			0
$719$	−0.870650	−	15.3184i	−0.0324698	−	0.571280i	−0.972890	−	0.231267i	$-0.925713\pi$
$719$	−0.870650	−	15.3184i	−0.0324698	−	0.571280i	0.940421	−	0.340013i	$-0.110432\pi$
$720$		0			0
$721$	14.4302	+	83.8995i	0.537409	+	3.12458i
$722$		0			0
$723$	41.3838	−	22.1831i	1.53908	−	0.824998i
$724$		0			0
$725$	13.4096	+	6.54729i	0.498021	+	0.243160i
$726$		0			0
$727$	−35.8496	+	2.71904i	−1.32959	+	0.100844i	−0.721161	−	0.692767i	$-0.756391\pi$
$727$	−35.8496	+	2.71904i	−1.32959	+	0.100844i	−0.608425	+	0.793611i	$0.708199\pi$
$728$		0			0
$729$	29.6518	−	30.2183i	1.09821	−	1.11920i
$730$		0			0
$731$	1.64109	−	9.54155i	0.0606978	−	0.352907i
$732$		0			0
$733$	18.2241	−	14.7766i	0.673123	−	0.545788i	−0.231056	−	0.972940i	$-0.574218\pi$
$733$	18.2241	−	14.7766i	0.673123	−	0.545788i	0.904180	+	0.427152i	$0.140483\pi$
$734$		0			0
$735$	−47.0893	+	20.8233i	−1.73692	+	0.768079i
$736$		0			0
$737$	3.64415	−	14.5119i	0.134234	−	0.534551i
$738$		0			0
$739$	27.0443	−	3.08419i	0.994841	−	0.113454i	0.399335	−	0.916805i	$-0.369241\pi$
$739$	27.0443	−	3.08419i	0.994841	−	0.113454i	0.595506	+	0.803351i	$0.296952\pi$
$740$		0			0
$741$	24.6099	−	18.4558i	0.904068	−	0.677991i
$742$		0			0
$743$	−34.0462	+	40.4018i	−1.24903	+	1.48220i	−0.436039	+	0.899928i	$0.643619\pi$
$743$	−34.0462	+	40.4018i	−1.24903	+	1.48220i	−0.812994	+	0.582272i	$0.802164\pi$
$744$		0			0
$745$	13.0763	+	25.5442i	0.479080	+	0.935865i
$746$		0			0
$747$	12.3964	−	32.9760i	0.453562	−	1.20653i
$748$		0			0
$749$	−18.7047	+	10.9571i	−0.683456	+	0.400364i
$750$		0			0
$751$	−17.5201	+	24.3074i	−0.639319	+	0.886988i	−0.998936	−	0.0461119i	$-0.985317\pi$
$751$	−17.5201	+	24.3074i	−0.639319	+	0.886988i	0.359617	+	0.933100i	$0.382907\pi$
$752$		0			0
$753$	−10.1698	−	5.45136i	−0.370609	−	0.198659i
$754$		0			0
$755$	−10.5998	−	18.9064i	−0.385767	−	0.688073i
$756$		0			0
$757$	13.6888	+	46.9184i	0.497529	+	1.70528i	0.689856	+	0.723947i	$0.257674\pi$
$757$	13.6888	+	46.9184i	0.497529	+	1.70528i	−0.192326	+	0.981331i	$0.561603\pi$
$758$		0			0
$759$	−2.49840	−	3.20336i	−0.0906863	−	0.116275i
$760$		0			0
$761$	2.30305	+	6.12639i	0.0834857	+	0.222082i	0.971178	−	0.238355i	$-0.0766083\pi$
$761$	2.30305	+	6.12639i	0.0834857	+	0.222082i	−0.887692	+	0.460437i	$0.847693\pi$
$762$		0			0
$763$	6.72626	−	4.29007i	0.243507	−	0.155311i
$764$		0			0
$765$	−13.8239	−	3.19456i	−0.499805	−	0.115500i
$766$		0			0
$767$	−12.5749	+	29.9567i	−0.454052	+	1.08167i
$768$		0			0
$769$	−1.11672	−	11.7661i	−0.0402698	−	0.424296i	−0.992794	−	0.119833i	$-0.961764\pi$
$769$	−1.11672	−	11.7661i	−0.0402698	−	0.424296i	0.952524	−	0.304463i	$-0.0984769\pi$
$770$		0			0
$771$	44.7883	−	31.0115i	1.61301	−	1.11685i
$772$		0			0
$773$	37.0460	+	32.4368i	1.33245	+	1.16667i	0.972289	+	0.233783i	$0.0751104\pi$
$773$	37.0460	+	32.4368i	1.33245	+	1.16667i	0.360164	+	0.932889i	$0.382721\pi$
$774$		0			0
$775$	7.14885	+	4.94988i	0.256794	+	0.177805i
$776$		0			0
$777$	−91.5273	−	58.3770i	−3.28353	−	2.09426i
$778$		0			0
$779$	−2.89073	+	21.6929i	−0.103571	+	0.777228i
$780$		0			0
$781$	−9.63503	+	15.7564i	−0.344768	+	0.563808i
$782$		0			0
$783$	10.6608	+	10.8645i	0.380985	+	0.388265i
$784$		0			0
$785$	5.36325	−	25.3896i	0.191422	−	0.906192i
$786$		0			0
$787$	−16.3659	+	29.1911i	−0.583382	+	1.04055i	0.408423	+	0.912793i	$0.366079\pi$
$787$	−16.3659	+	29.1911i	−0.583382	+	1.04055i	−0.991806	+	0.127756i	$0.959222\pi$
$788$		0			0
$789$	−12.3250	−	49.0809i	−0.438780	−	1.74732i
$790$		0			0
$791$	−26.5917	−	40.0018i	−0.945491	−	1.42230i
$792$		0			0
$793$	−7.77454	−	23.3253i	−0.276082	−	0.828304i
$794$		0			0
$795$	4.11600	+	0.469398i	0.145980	+	0.0166478i
$796$		0			0
$797$

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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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