LMFDB - Embedded newform 950.2.u.g.149.1

Newspace parameters

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.1
Character	$\chi$	$=$	950.149
Dual form			950.2.u.g.899.1

$q$-expansion

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +(-3.22960 + 5.59384i) q^{11} +(-1.55443 + 0.897451i) q^{12} +(2.01005 - 5.52256i) q^{13} +(0.236417 - 1.34079i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-1.64480 + 1.96020i) q^{17} -0.221676i q^{18} +(3.83851 + 2.06538i) q^{19} +(1.87199 + 1.57079i) q^{21} +(-2.20918 - 6.06967i) q^{22} +(-8.29626 + 1.46285i) q^{23} +(0.311682 - 1.76763i) q^{24} +(2.93849 + 5.08962i) q^{26} +(-4.31871 - 2.49341i) q^{27} +(0.875137 + 1.04295i) q^{28} +(-3.41558 + 2.86601i) q^{29} +(0.701264 + 1.21462i) q^{31} +(0.342020 - 0.939693i) q^{32} +(11.4175 + 2.01322i) q^{33} +(-0.444341 - 2.51998i) q^{34} +(0.169813 + 0.142490i) q^{36} +4.42962i q^{37} +(-4.04953 + 1.61287i) q^{38} -10.5486 q^{39} +(5.15407 - 1.87593i) q^{41} +(-2.40658 + 0.424346i) q^{42} +(6.74986 + 1.19018i) q^{43} +(6.06967 + 2.20918i) q^{44} +(4.21212 - 7.29560i) q^{46} +(6.11821 + 7.29140i) q^{47} +(1.15374 + 1.37498i) q^{48} +(-2.57320 + 4.45691i) q^{49} +(4.31591 + 1.57086i) q^{51} +(-5.78770 - 1.02053i) q^{52} +(-4.35841 + 0.768506i) q^{53} +(4.68608 - 1.70559i) q^{54} -1.36147 q^{56} +(1.12716 - 7.74218i) q^{57} -4.45872i q^{58} +(7.87687 + 6.60948i) q^{59} +(1.12233 + 6.36503i) q^{61} +(-1.38122 - 0.243546i) q^{62} +(0.103223 - 0.283604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-8.88125 + 7.45226i) q^{66} +(4.31929 + 5.14753i) q^{67} +(2.21604 + 1.27943i) q^{68} +(7.56034 + 13.0949i) q^{69} +(0.336459 - 1.90815i) q^{71} +(-0.218308 + 0.0384936i) q^{72} +(2.14907 + 5.90451i) q^{73} +(-3.39328 - 2.84730i) q^{74} +(1.36746 - 4.13885i) q^{76} -8.79403i q^{77} +(6.78052 - 8.08071i) q^{78} +(-3.37355 + 1.22787i) q^{79} +(-1.66978 + 9.46980i) q^{81} +(-1.87593 + 5.15407i) q^{82} +(-11.6908 + 6.74970i) q^{83} +(1.22185 - 2.11631i) q^{84} +(-5.25046 + 4.40566i) q^{86} +(6.93077 + 4.00148i) q^{87} +(-5.59384 + 3.22960i) q^{88} +(-1.78165 - 0.648469i) q^{89} +(1.38942 + 7.87979i) q^{91} +(2.88126 + 7.91619i) q^{92} +(1.61815 - 1.92844i) q^{93} -9.51825 q^{94} -1.79490 q^{96} +(-0.0793596 + 0.0945771i) q^{97} +(-1.76017 - 4.83603i) q^{98} +(-0.248638 - 1.41010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36q + 36q^{9} + O(q^{10}) $	$ 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−0.613893	−	1.68666i	−0.354431	−	0.973792i	−0.980929	−	0.194368i	$-0.937734\pi$
$3$	−0.613893	−	1.68666i	−0.354431	−	0.973792i	0.626497	−	0.779423i	$-0.284488\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	1.68666	+	0.613893i	0.688575	+	0.250621i
$7$	−1.17907	+	0.680736i	−0.445646	+	0.257294i	−0.705990	−	0.708222i	$-0.749498\pi$
$7$	−1.17907	+	0.680736i	−0.445646	+	0.257294i	0.260343	+	0.965516i	$0.416164\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.169813	+	0.142490i	−0.0566045	+	0.0474968i
$10$		0			0
$11$	−3.22960	+	5.59384i	−0.973762	+	1.68661i	−0.289803	+	0.957086i	$0.593590\pi$
$11$	−3.22960	+	5.59384i	−0.973762	+	1.68661i	−0.683960	+	0.729520i	$0.739744\pi$
$12$	−1.55443	+	0.897451i	−0.448726	+	0.259072i
$13$	2.01005	−	5.52256i	0.557487	−	1.53168i	−0.265784	−	0.964033i	$-0.585631\pi$
$13$	2.01005	−	5.52256i	0.557487	−	1.53168i	0.823270	−	0.567650i	$-0.192147\pi$
$14$	0.236417	−	1.34079i	0.0631851	−	0.358341i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.64480	+	1.96020i	−0.398923	+	0.475418i	−0.927691	−	0.373348i	$-0.878210\pi$
$17$	−1.64480	+	1.96020i	−0.398923	+	0.475418i	0.528768	+	0.848766i	$0.322654\pi$
$18$		−	0.221676i		−	0.0522494i
$19$	3.83851	+	2.06538i	0.880615	+	0.473832i
$19$	3.83851	+	2.06538i	0.880615	+	0.473832i
$20$		0			0
$21$	1.87199	+	1.57079i	0.408502	+	0.342774i
$22$	−2.20918	−	6.06967i	−0.470999	−	1.29406i
$23$	−8.29626	+	1.46285i	−1.72989	+	0.305026i	−0.947971	−	0.318356i	$-0.896869\pi$
$23$	−8.29626	+	1.46285i	−1.72989	+	0.305026i	−0.781918	+	0.623382i	$0.785758\pi$
$24$	0.311682	−	1.76763i	0.0636217	−	0.360817i
$25$		0			0
$26$	2.93849	+	5.08962i	0.576286	+	0.998156i
$27$	−4.31871	−	2.49341i	−0.831137	−	0.479857i
$28$	0.875137	+	1.04295i	0.165385	+	0.197099i
$29$	−3.41558	+	2.86601i	−0.634257	+	0.532205i	−0.902248	−	0.431217i	$-0.858084\pi$
$29$	−3.41558	+	2.86601i	−0.634257	+	0.532205i	0.267992	+	0.963421i	$0.413640\pi$
$30$		0			0
$31$	0.701264	+	1.21462i	0.125951	+	0.218153i	0.922104	−	0.386942i	$-0.126469\pi$
$31$	0.701264	+	1.21462i	0.125951	+	0.218153i	−0.796153	+	0.605095i	$0.793135\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	11.4175	+	2.01322i	1.98753	+	0.350456i
$34$	−0.444341	−	2.51998i	−0.0762038	−	0.432173i
$35$		0			0
$36$	0.169813	+	0.142490i	0.0283022	+	0.0237484i
$37$			4.42962i			0.728225i	0.931355	+	0.364112i	$0.118628\pi$
$37$			4.42962i			0.728225i	−0.931355	+	0.364112i	$0.881372\pi$
$38$	−4.04953	+	1.61287i	−0.656920	+	0.261642i
$39$	−10.5486			−1.68913
$40$		0			0
$41$	5.15407	−	1.87593i	0.804931	−	0.292971i	0.0934025	−	0.995628i	$-0.470226\pi$
$41$	5.15407	−	1.87593i	0.804931	−	0.292971i	0.711528	+	0.702658i	$0.248003\pi$
$42$	−2.40658	+	0.424346i	−0.371344	+	0.0654780i
$43$	6.74986	+	1.19018i	1.02934	+	0.181501i	0.662719	−	0.748868i	$-0.269402\pi$
$43$	6.74986	+	1.19018i	1.02934	+	0.181501i	0.366625	+	0.930369i	$0.380513\pi$
$44$	6.06967	+	2.20918i	0.915037	+	0.333046i
$45$		0			0
$46$	4.21212	−	7.29560i	0.621043	−	1.07568i
$47$	6.11821	+	7.29140i	0.892433	+	1.06356i	0.997609	+	0.0691065i	$0.0220148\pi$
$47$	6.11821	+	7.29140i	0.892433	+	1.06356i	−0.105176	+	0.994454i	$0.533541\pi$
$48$	1.15374	+	1.37498i	0.166528	+	0.198461i
$49$	−2.57320	+	4.45691i	−0.367600	+	0.636701i
$50$		0			0
$51$	4.31591	+	1.57086i	0.604349	+	0.219965i
$52$	−5.78770	−	1.02053i	−0.802610	−	0.141522i
$53$	−4.35841	+	0.768506i	−0.598674	+	0.105562i	−0.464769	−	0.885432i	$-0.653863\pi$
$53$	−4.35841	+	0.768506i	−0.598674	+	0.105562i	−0.133905	+	0.990994i	$0.542752\pi$
$54$	4.68608	−	1.70559i	0.637695	−	0.232102i
$55$		0			0
$56$	−1.36147			−0.181934
$57$	1.12716	−	7.74218i	0.149296	−	1.02548i
$58$		−	4.45872i		−	0.585458i
$59$	7.87687	+	6.60948i	1.02548	+	0.860481i	0.990306	−	0.138900i	$-0.0443566\pi$
$59$	7.87687	+	6.60948i	1.02548	+	0.860481i	0.0351753	+	0.999381i	$0.488801\pi$
$60$		0			0
$61$	1.12233	+	6.36503i	0.143699	+	0.814958i	0.968402	+	0.249393i	$0.0802310\pi$
$61$	1.12233	+	6.36503i	0.143699	+	0.814958i	−0.824703	+	0.565566i	$0.808658\pi$
$62$	−1.38122	−	0.243546i	−0.175415	−	0.0309304i
$63$	0.103223	−	0.283604i	0.0130049	−	0.0357307i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−8.88125	+	7.45226i	−1.09321	+	0.917309i
$67$	4.31929	+	5.14753i	0.527685	+	0.628871i	0.962380	−	0.271707i	$-0.0875882\pi$
$67$	4.31929	+	5.14753i	0.527685	+	0.628871i	−0.434695	+	0.900578i	$0.643144\pi$
$68$	2.21604	+	1.27943i	0.268734	+	0.155153i
$69$	7.56034	+	13.0949i	0.910158	+	1.57644i
$70$		0			0
$71$	0.336459	−	1.90815i	0.0399303	−	0.226456i	−0.958312	−	0.285725i	$-0.907766\pi$
$71$	0.336459	−	1.90815i	0.0399303	−	0.226456i	0.998242	+	0.0592685i	$0.0188768\pi$
$72$	−0.218308	+	0.0384936i	−0.0257278	+	0.00453651i
$73$	2.14907	+	5.90451i	0.251529	+	0.691071i	0.999622	+	0.0274772i	$0.00874737\pi$
$73$	2.14907	+	5.90451i	0.251529	+	0.691071i	−0.748093	+	0.663594i	$0.769030\pi$
$74$	−3.39328	−	2.84730i	−0.394461	−	0.330992i
$75$		0			0
$76$	1.36746	−	4.13885i	0.156858	−	0.474758i
$77$		−	8.79403i		−	1.00217i
$78$	6.78052	−	8.08071i	0.767743	−	0.914960i
$79$	−3.37355	+	1.22787i	−0.379554	+	0.138146i	−0.524750	−	0.851257i	$-0.675841\pi$
$79$	−3.37355	+	1.22787i	−0.379554	+	0.138146i	0.145195	+	0.989403i	$0.453619\pi$
$80$		0			0
$81$	−1.66978	+	9.46980i	−0.185531	+	1.05220i
$82$	−1.87593	+	5.15407i	−0.207162	+	0.569172i
$83$	−11.6908	+	6.74970i	−1.28323	+	0.740876i	−0.977438	−	0.211221i	$-0.932256\pi$
$83$	−11.6908	+	6.74970i	−1.28323	+	0.740876i	−0.305797	+	0.952097i	$0.598923\pi$
$84$	1.22185	−	2.11631i	0.133315	−	0.230909i
$85$		0			0
$86$	−5.25046	+	4.40566i	−0.566172	+	0.475074i
$87$	6.93077	+	4.00148i	0.743057	+	0.429004i
$88$	−5.59384	+	3.22960i	−0.596305	+	0.344277i
$89$	−1.78165	−	0.648469i	−0.188855	−	0.0687376i	0.245861	−	0.969305i	$-0.420929\pi$
$89$	−1.78165	−	0.648469i	−0.188855	−	0.0687376i	−0.434716	+	0.900567i	$0.643151\pi$
$90$		0			0
$91$	1.38942	+	7.87979i	0.145651	+	0.826026i
$92$	2.88126	+	7.91619i	0.300392	+	0.825320i
$93$	1.61815	−	1.92844i	0.167795	−	0.199970i
$94$	−9.51825			−0.981732
$95$		0			0
$96$	−1.79490			−0.183191
$97$	−0.0793596	+	0.0945771i	−0.00805774	+	0.00960285i	−0.770058	−	0.637974i	$-0.779773\pi$
$97$	−0.0793596	+	0.0945771i	−0.00805774	+	0.00960285i	0.762001	+	0.647576i	$0.224217\pi$
$98$	−1.76017	−	4.83603i	−0.177804	−	0.488513i
$99$	−0.248638	−	1.41010i	−0.0249891	−	0.141720i
$100$		0			0
$101$	−12.8307	−	4.66998i	−1.27670	−	0.464680i	−0.387359	−	0.921929i	$-0.626613\pi$
$101$	−12.8307	−	4.66998i	−1.27670	−	0.464680i	−0.889339	+	0.457249i	$0.848835\pi$
$102$	−3.97757	+	2.29645i	−0.393838	+	0.227382i
$103$	5.95330	+	3.43714i	0.586596	+	0.338672i	0.763751	−	0.645512i	$-0.223356\pi$
$103$	5.95330	+	3.43714i	0.586596	+	0.338672i	−0.177154	+	0.984183i	$0.556689\pi$
$104$	4.50203	−	3.77765i	0.441460	−	0.370429i
$105$		0			0
$106$	2.21282	−	3.83272i	0.214929	−	0.372267i
$107$	−7.65580	+	4.42008i	−0.740114	+	0.427305i	−0.822111	−	0.569328i	$-0.807204\pi$
$107$	−7.65580	+	4.42008i	−0.740114	+	0.427305i	0.0819969	+	0.996633i	$0.473870\pi$
$108$	−1.70559	+	4.68608i	−0.164121	+	0.450918i
$109$	1.65245	−	9.37152i	0.158276	−	0.897629i	−0.797453	−	0.603381i	$-0.793820\pi$
$109$	1.65245	−	9.37152i	0.158276	−	0.897629i	0.955729	−	0.294248i	$-0.0950691\pi$
$110$		0			0
$111$	7.47124	−	2.71931i	0.709139	−	0.258106i
$112$	0.875137	−	1.04295i	0.0826927	−	0.0985493i
$113$		−	11.0799i		−	1.04231i	−0.853462	−	0.521154i	$-0.825502\pi$
$113$		−	11.0799i		−	1.04231i	0.853462	−	0.521154i	$-0.174498\pi$
$114$	5.20633	+	5.84003i	0.487617	+	0.546969i
$115$		0			0
$116$	3.41558	+	2.86601i	0.317128	+	0.266102i
$117$	0.445578	+	1.22422i	0.0411937	+	0.113179i
$118$	−10.1263	+	1.78554i	−0.932203	+	0.164373i
$119$	0.604958	−	3.43088i	0.0554564	−	0.314509i
$120$		0			0
$121$	−15.3607	−	26.6055i	−1.39643	−	2.41868i
$122$	−5.59731	−	3.23161i	−0.506757	−	0.292576i
$123$	−6.32809	−	7.54153i	−0.570585	−	0.679997i
$124$	1.07440	−	0.901527i	0.0964838	−	0.0809595i
$125$		0			0
$126$	0.150903	+	0.261371i	0.0134435	+	0.0232848i
$127$	−3.14395	+	8.63792i	−0.278980	+	0.766491i	0.718499	+	0.695528i	$0.244830\pi$
$127$	−3.14395	+	8.63792i	−0.278980	+	0.766491i	−0.997479	+	0.0709633i	$0.977393\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−2.13626	−	12.1153i	−0.188087	−	1.06670i
$130$		0			0
$131$	0.0847217	+	0.0710900i	0.00740217	+	0.00621116i	0.646481	−	0.762930i	$-0.276240\pi$
$131$	0.0847217	+	0.0710900i	0.00740217	+	0.00621116i	−0.639079	+	0.769141i	$0.720684\pi$
$132$		−	11.5937i		−	1.00910i
$133$	−5.93185	+	0.177782i	−0.514357	+	0.0154157i
$134$	−6.71962			−0.580487
$135$		0			0
$136$	−2.40454	+	0.875181i	−0.206188	+	0.0750461i
$137$	13.4434	−	2.37043i	1.14855	−	0.202520i	0.433205	−	0.901295i	$-0.357383\pi$
$137$	13.4434	−	2.37043i	1.14855	−	0.202520i	0.715341	+	0.698776i	$0.246271\pi$
$138$	−14.8910	−	2.62568i	−1.26760	−	0.223513i
$139$	2.27126	+	0.826670i	0.192645	+	0.0701172i	0.436541	−	0.899684i	$-0.356203\pi$
$139$	2.27126	+	0.826670i	0.192645	+	0.0701172i	−0.243896	+	0.969801i	$0.578425\pi$
$140$		0			0
$141$	8.54216	−	14.7955i	0.719380	−	1.24600i
$142$	1.24546	+	1.48428i	0.104517	+	0.124558i
$143$	24.4007	+	29.0796i	2.04048	+	2.43176i
$144$	0.110838	−	0.191977i	0.00923648	−	0.0159981i
$145$		0			0
$146$	−5.90451	−	2.14907i	−0.488661	−	0.177858i
$147$	9.09694	+	1.60404i	0.750303	+	0.132299i
$148$	4.36232	−	0.769195i	0.358581	−	0.0632274i
$149$	−2.08531	+	0.758990i	−0.170835	+	0.0621789i	−0.426022	−	0.904713i	$-0.640085\pi$
$149$	−2.08531	+	0.758990i	−0.170835	+	0.0621789i	0.255187	+	0.966892i	$0.417863\pi$
$150$		0			0
$151$	−11.6771			−0.950267			−0.475133	−	0.879914i	$-0.657600\pi$
$151$	−11.6771			−0.950267			−0.475133	+	0.879914i	$0.657600\pi$
$152$	2.29156	+	3.70793i	0.185870	+	0.300753i
$153$		−	0.567236i		−	0.0458583i
$154$	6.73662	+	5.65269i	0.542852	+	0.455507i
$155$		0			0
$156$	1.83175	+	10.3884i	0.146657	+	0.831734i
$157$	4.10004	+	0.722948i	0.327219	+	0.0576975i	0.334844	−	0.942273i	$-0.391316\pi$
$157$	4.10004	+	0.722948i	0.327219	+	0.0576975i	−0.00762562	+	0.999971i	$0.502427\pi$
$158$	1.22787	−	3.37355i	0.0976843	−	0.268385i
$159$	3.97181	+	6.87937i	0.314985	+	0.545569i
$160$		0			0
$161$	8.78604	−	7.37236i	0.692437	−	0.581024i
$162$	−6.18097	−	7.36620i	−0.485623	−	0.578743i
$163$	−4.15894	−	2.40117i	−0.325753	−	0.188074i	0.328201	−	0.944608i	$-0.393558\pi$
$163$	−4.15894	−	2.40117i	−0.325753	−	0.188074i	−0.653954	+	0.756534i	$0.726891\pi$
$164$	−2.74242	−	4.75002i	−0.214147	−	0.370914i
$165$		0			0
$166$	2.34415	−	13.2943i	0.181941	−	1.03184i
$167$	−3.80840	+	0.671525i	−0.294703	+	0.0519641i	−0.319045	−	0.947740i	$-0.603362\pi$
$167$	−3.80840	+	0.671525i	−0.294703	+	0.0519641i	0.0243418	+	0.999704i	$0.492251\pi$
$168$	0.835798	+	2.29634i	0.0644832	+	0.177166i
$169$	−16.4998	−	13.8450i	−1.26921	−	1.06500i
$170$		0			0
$171$	−0.946128	+	0.196221i	−0.0723522	+	0.0150054i
$172$		−	6.85399i		−	0.522612i
$173$	−7.41704	+	8.83929i	−0.563907	+	0.672039i	−0.970369	−	0.241629i	$-0.922318\pi$
$173$	−7.41704	+	8.83929i	−0.563907	+	0.672039i	0.406461	+	0.913668i	$0.366763\pi$
$174$	−7.52033	+	2.73718i	−0.570115	+	0.207505i
$175$		0			0
$176$	1.12163	−	6.36108i	0.0845460	−	0.479484i
$177$	6.31237	−	17.3431i	0.474467	−	1.30359i
$178$	1.64198	−	0.947998i	0.123072	−	0.0710555i
$179$	4.18981	−	7.25696i	0.313161	−	0.542411i	−0.665884	−	0.746055i	$-0.731945\pi$
$179$	4.18981	−	7.25696i	0.313161	−	0.542411i	0.979045	+	0.203645i	$0.0652788\pi$
$180$		0			0
$181$	−8.13969	+	6.83001i	−0.605018	+	0.507671i	−0.893054	−	0.449949i	$-0.851442\pi$
$181$	−8.13969	+	6.83001i	−0.605018	+	0.507671i	0.288036	+	0.957620i	$0.406998\pi$
$182$	−6.92937	−	4.00067i	−0.513639	−	0.296550i
$183$	10.0466	−	5.80042i	0.742668	−	0.428780i
$184$	−7.91619	−	2.88126i	−0.583590	−	0.212409i
$185$		0			0
$186$	0.437142	+	2.47915i	0.0320528	+	0.181780i
$187$	−5.65298	−	15.5314i	−0.413386	−	1.13577i
$188$	6.11821	−	7.29140i	0.446216	−	0.531780i
$189$	6.78942			0.493857
$190$		0			0
$191$	10.8514			0.785179			0.392589	−	0.919714i	$-0.371579\pi$
$191$	10.8514			0.785179			0.392589	+	0.919714i	$0.371579\pi$
$192$	1.15374	−	1.37498i	0.0832641	−	0.0992303i
$193$	−0.662240	−	1.81949i	−0.0476691	−	0.130970i	0.913574	−	0.406674i	$-0.133311\pi$
$193$	−0.662240	−	1.81949i	−0.0476691	−	0.130970i	−0.961243	+	0.275704i	$0.911089\pi$
$194$	−0.0214389	−	0.121586i	−0.00153922	−	0.00872936i
$195$		0			0
$196$	4.83603	+	1.76017i	0.345431	+	0.125726i
$197$	−10.6122	+	6.12697i	−0.756090	+	0.436529i	−0.827890	−	0.560890i	$-0.810459\pi$
$197$	−10.6122	+	6.12697i	−0.756090	+	0.436529i	0.0718004	+	0.997419i	$0.477126\pi$
$198$	1.24002	+	0.715925i	0.0881242	+	0.0508785i
$199$	0.331678	−	0.278311i	0.0235121	−	0.0197290i	−0.630956	−	0.775819i	$-0.717337\pi$
$199$	0.331678	−	0.278311i	0.0235121	−	0.0197290i	0.654468	+	0.756090i	$0.272893\pi$
$200$		0			0
$201$	6.03053	−	10.4452i	0.425361	−	0.736747i
$202$	11.8248	−	6.82705i	0.831990	−	0.480350i
$203$	2.07621	−	5.70433i	0.145721	−	0.400365i
$204$	0.797549	−	4.52312i	0.0558396	−	0.316682i
$205$		0			0
$206$	−6.45971	+	2.35114i	−0.450070	+	0.163812i
$207$	1.20037	−	1.43055i	0.0834317	−	0.0994300i
$208$			5.87698i			0.407496i
$209$	−23.9503	+	14.8017i	−1.65668	+	1.02385i
$210$		0			0
$211$	−10.5293	−	8.83513i	−0.724867	−	0.608235i	0.203860	−	0.979000i	$-0.434651\pi$
$211$	−10.5293	−	8.83513i	−0.724867	−	0.608235i	−0.928727	+	0.370765i	$0.879096\pi$
$212$	1.51366	+	4.15875i	0.103959	+	0.285624i
$213$	−3.42495	+	0.603911i	−0.234674	+	0.0413793i
$214$	1.53508	−	8.70585i	0.104936	−	0.595120i
$215$		0			0
$216$	−2.49341	−	4.31871i	−0.169655	−	0.293851i
$217$	−1.65368	−	0.954751i	−0.112259	−	0.0648127i
$218$	6.11683	+	7.28975i	0.414284	+	0.493724i
$219$	8.63959	−	7.24948i	0.583809	−	0.489874i
$220$		0			0
$221$	7.51918	+	13.0236i	0.505795	+	0.876062i
$222$	−2.71931	+	7.47124i	−0.182508	+	0.501437i
$223$	−22.1729	−	3.90968i	−1.48481	−	0.261812i	−0.628310	−	0.777963i	$-0.716253\pi$
$223$	−22.1729	−	3.90968i	−1.48481	−	0.261812i	−0.856497	+	0.516151i	$0.827364\pi$
$224$	0.236417	+	1.34079i	0.0157963	+	0.0895852i
$225$		0			0
$226$	8.48769	+	7.12202i	0.564593	+	0.473750i
$227$			18.8403i			1.25048i	0.780433	+	0.625239i	$0.214998\pi$
$227$			18.8403i			1.25048i	−0.780433	+	0.625239i	$0.785002\pi$
$228$	−7.82029	+	0.234380i	−0.517911	+	0.0155222i
$229$	4.51829			0.298577			0.149289	−	0.988794i	$-0.452302\pi$
$229$	4.51829			0.298577			0.149289	+	0.988794i	$0.452302\pi$
$230$		0			0
$231$	−14.8325	+	5.39859i	−0.975908	+	0.355201i
$232$	−4.39098	+	0.774248i	−0.288282	+	0.0508319i
$233$	−10.5997	−	1.86901i	−0.694406	−	0.122443i	−0.184705	−	0.982794i	$-0.559133\pi$
$233$	−10.5997	−	1.86901i	−0.694406	−	0.122443i	−0.509701	+	0.860351i	$0.670244\pi$
$234$	−1.22422	−	0.445578i	−0.0800295	−	0.0291284i
$235$		0			0
$236$	5.14126	−	8.90493i	0.334668	−	0.579662i
$237$	4.14200	+	4.93624i	0.269052	+	0.320643i
$238$	2.23935	+	2.66875i	0.145156	+	0.172990i
$239$	11.7010	−	20.2668i	0.756876	−	1.31095i	−0.187560	−	0.982253i	$-0.560058\pi$
$239$	11.7010	−	20.2668i	0.756876	−	1.31095i	0.944436	−	0.328695i	$-0.106609\pi$
$240$		0			0
$241$	19.6353	+	7.14665i	1.26482	+	0.460356i	0.885383	−	0.464862i	$-0.153896\pi$
$241$	19.6353	+	7.14665i	1.26482	+	0.460356i	0.379435	+	0.925218i	$0.376118\pi$
$242$	30.2547	+	5.33471i	1.94484	+	0.342928i
$243$	2.26419	−	0.399237i	0.145248	−	0.0256111i
$244$	6.07344	−	2.21055i	0.388812	−	0.141516i
$245$		0			0
$246$	9.84477			0.627679
$247$	19.1218	−	17.0469i	1.21669	−	1.08467i
$248$			1.40253i			0.0890606i
$249$	18.5613	+	15.5748i	1.17628	+	0.987014i
$250$		0			0
$251$	−3.10917	−	17.6330i	−0.196249	−	1.11298i	−0.910628	−	0.413226i	$-0.864402\pi$
$251$	−3.10917	−	17.6330i	−0.196249	−	1.11298i	0.714379	−	0.699759i	$-0.246709\pi$
$252$	−0.297220	−	0.0524079i	−0.0187231	−	0.00330139i
$253$	18.6107	−	51.1324i	1.17004	−	3.21466i
$254$	−4.59614	−	7.96075i	−0.288388	−	0.499502i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.312965	+	0.372978i	0.0195222	+	0.0232657i	0.775717	−	0.631081i	$-0.217388\pi$
$257$	0.312965	+	0.372978i	0.0195222	+	0.0232657i	−0.756195	+	0.654346i	$0.772944\pi$
$258$	10.6541	+	6.15112i	0.663292	+	0.382952i
$259$	−3.01540	−	5.22282i	−0.187368	−	0.324531i
$260$		0			0
$261$	0.171632	−	0.973373i	0.0106238	−	0.0602503i
$262$	−0.108916	+	0.0192049i	−0.00672886	+	0.00118648i
$263$	7.54785	+	20.7375i	0.465420	+	1.27873i	0.921356	+	0.388719i	$0.127082\pi$
$263$	7.54785	+	20.7375i	0.465420	+	1.27873i	−0.455936	+	0.890013i	$0.650695\pi$
$264$	8.88125	+	7.45226i	0.546603	+	0.458655i
$265$		0			0
$266$	3.67673	−	4.65834i	0.225435	−	0.285621i
$267$			3.40313i			0.208268i
$268$	4.31929	−	5.14753i	0.263843	−	0.314435i
$269$	16.6789	−	6.07061i	1.01693	−	0.370131i	0.220838	−	0.975310i	$-0.429121\pi$
$269$	16.6789	−	6.07061i	1.01693	−	0.370131i	0.796089	+	0.605179i	$0.206899\pi$
$270$		0			0
$271$	1.89657	−	10.7560i	0.115208	−	0.653380i	−0.871438	−	0.490505i	$-0.836812\pi$
$271$	1.89657	−	10.7560i	0.115208	−	0.653380i	0.986647	−	0.162875i	$-0.0520766\pi$
$272$	0.875181	−	2.40454i	0.0530656	−	0.145797i
$273$	12.4375	−	7.18082i	0.752755	−	0.434603i
$274$	−6.82538	+	11.8219i	−0.412337	+	0.714188i
$275$		0			0
$276$	11.5831	−	9.71939i	0.697222	−	0.585039i
$277$	7.84590	+	4.52983i	0.471414	+	0.272171i	0.716832	−	0.697246i	$-0.245592\pi$
$277$	7.84590	+	4.52983i	0.471414	+	0.272171i	−0.245417	+	0.969418i	$0.578925\pi$
$278$	−2.09320	+	1.20851i	−0.125542	+	0.0724816i
$279$	−0.292156	−	0.106336i	−0.0174909	−	0.00636618i
$280$		0			0
$281$	2.65688	+	15.0679i	0.158496	+	0.898876i	0.955520	+	0.294928i	$0.0952956\pi$
$281$	2.65688	+	15.0679i	0.158496	+	0.898876i	−0.797023	+	0.603948i	$0.793593\pi$
$282$	5.84318	+	16.0540i	0.347957	+	0.956003i
$283$	6.33163	−	7.54574i	0.376376	−	0.448548i	−0.544291	−	0.838897i	$-0.683201\pi$
$283$	6.33163	−	7.54574i	0.376376	−	0.448548i	0.920667	+	0.390349i	$0.127646\pi$
$284$	−1.93759			−0.114975
$285$		0			0
$286$	−37.9607			−2.24466
$287$	−4.79999	+	5.72041i	−0.283335	+	0.337665i
$288$	0.0758175	+	0.208307i	0.00446759	+	0.0122746i
$289$	1.81501	+	10.2935i	0.106766	+	0.605498i
$290$		0			0
$291$	0.208237	+	0.0757922i	0.0122071	+	0.00444302i
$292$	5.44163	−	3.14173i	0.318447	−	0.183856i
$293$	−7.08299	−	4.08936i	−0.413792	−	0.238903i	0.278625	−	0.960400i	$-0.410121\pi$
$293$	−7.08299	−	4.08936i	−0.413792	−	0.238903i	−0.692418	+	0.721497i	$0.743455\pi$
$294$	−7.07617	+	5.93761i	−0.412690	+	0.346288i
$295$		0			0
$296$	−2.21481	+	3.83616i	−0.128733	+	0.222972i
$297$	27.8955	−	16.1055i	1.61866	−	0.934534i
$298$	0.758990	−	2.08531i	0.0439671	−	0.120799i
$299$	−8.59717	+	48.7570i	−0.497187	+	2.81969i
$300$		0			0
$301$	−8.76875	+	3.19157i	−0.505423	+	0.183959i
$302$	7.50588	−	8.94516i	0.431915	−	0.514736i
$303$			24.5078i			1.40794i
$304$	−4.31343	−	0.627978i	−0.247392	−	0.0360170i
$305$		0			0
$306$	0.434528	+	0.364612i	0.0248403	+	0.0208435i
$307$	−2.06799	−	5.68175i	−0.118026	−	0.324275i	0.866586	−	0.499028i	$-0.166309\pi$
$307$	−2.06799	−	5.68175i	−0.118026	−	0.324275i	−0.984612	+	0.174753i	$0.944087\pi$
$308$	−8.66043	+	1.52707i	−0.493474	+	0.0870127i
$309$	2.14259	−	12.1512i	0.121888	−	0.691259i
$310$		0			0
$311$	−16.5582	−	28.6797i	−0.938932	−	1.62628i	−0.767468	−	0.641087i	$-0.778484\pi$
$311$	−16.5582	−	28.6797i	−0.938932	−	1.62628i	−0.171463	−	0.985191i	$-0.554849\pi$
$312$	−9.13537	−	5.27431i	−0.517188	−	0.298599i
$313$	−3.96728	−	4.72802i	−0.224244	−	0.267244i	0.642179	−	0.766555i	$-0.278031\pi$
$313$	−3.96728	−	4.72802i	−0.224244	−	0.267244i	−0.866423	+	0.499312i	$0.833586\pi$
$314$	−3.18927	+	2.67611i	−0.179981	+	0.151022i
$315$		0			0
$316$	1.79503	+	3.10908i	0.100978	+	0.174900i
$317$	5.61135	−	15.4171i	0.315165	−	0.865908i	−0.676428	−	0.736509i	$-0.736473\pi$
$317$	5.61135	−	15.4171i	0.315165	−	0.865908i	0.991593	−	0.129399i	$-0.0413049\pi$
$318$	−7.82293	−	1.37939i	−0.438688	−	0.0773525i
$319$	−5.00103	−	28.3623i	−0.280004	−	1.58798i
$320$		0			0
$321$	12.1550	+	10.1992i	0.678425	+	0.569266i
$322$			11.4694i			0.639163i
$323$	−10.3622	+	4.12710i	−0.576566	+	0.229638i
$324$	9.61589			0.534216
$325$		0			0
$326$	4.51272	−	1.64249i	0.249936	−	0.0909694i
$327$	−16.8210	+	2.96599i	−0.930202	+	0.164020i
$328$	5.40152	+	0.952434i	0.298249	+	0.0525894i
$329$	−12.1773	−	4.43218i	−0.671357	−	0.244354i
$330$		0			0
$331$	−8.53392	+	14.7812i	−0.469066	+	0.812447i	−0.999375	−	0.0353579i	$-0.988743\pi$
$331$	−8.53392	+	14.7812i	−0.469066	+	0.812447i	0.530308	+	0.847805i	$0.322076\pi$
$332$	8.67725	+	10.3411i	0.476226	+	0.567544i
$333$	−0.631178	−	0.752208i	−0.0345883	−	0.0412208i
$334$	1.93358	−	3.34906i	0.105801	−	0.183252i
$335$		0			0
$336$	−2.29634	−	0.835798i	−0.125275	−	0.0455965i
$337$	−18.5701	−	3.27441i	−1.01158	−	0.178368i	−0.356792	−	0.934184i	$-0.616130\pi$
$337$	−18.5701	−	3.27441i	−1.01158	−	0.178368i	−0.654785	+	0.755816i	$0.727241\pi$
$338$	21.2117	−	3.74020i	1.15377	−	0.203440i
$339$	−18.6880	+	6.80187i	−1.01499	+	0.369427i
$340$		0			0
$341$	−9.05922			−0.490584
$342$	0.457845	−	0.850905i	0.0247574	−	0.0460117i
$343$		−	16.5370i		−	0.892913i
$344$	5.25046	+	4.40566i	0.283086	+	0.237537i
$345$		0			0
$346$	−2.00370	−	11.3636i	−0.107720	−	0.610909i
$347$	−5.32560	−	0.939047i	−0.285893	−	0.0504107i	0.0288626	−	0.999583i	$-0.490811\pi$
$347$	−5.32560	−	0.939047i	−0.285893	−	0.0504107i	−0.314756	+	0.949173i	$0.601923\pi$
$348$	2.73718	−	7.52033i	0.146728	−	0.403132i
$349$	−18.1540	−	31.4436i	−0.971761	−	1.68314i	−0.690235	−	0.723586i	$-0.742493\pi$
$349$	−18.1540	−	31.4436i	−0.971761	−	1.68314i	−0.281526	−	0.959554i	$-0.590841\pi$
$350$		0			0
$351$	−22.4508	+	18.8385i	−1.19834	+	1.00552i
$352$	4.15190	+	4.94804i	0.221297	+	0.263731i
$353$	1.06514	+	0.614958i	0.0566916	+	0.0327309i	0.528078	−	0.849196i	$-0.322913\pi$
$353$	1.06514	+	0.614958i	0.0566916	+	0.0327309i	−0.471386	+	0.881927i	$0.656246\pi$
$354$	9.22807	+	15.9835i	0.490466	+	0.849513i
$355$		0			0
$356$	−0.329236	+	1.86719i	−0.0174495	+	0.0989610i
$357$	−6.15810	+	1.08584i	−0.325921	+	0.0574687i
$358$	2.86600	+	7.87426i	0.151473	+	0.416168i
$359$	11.5897	+	9.72494i	0.611683	+	0.513263i	0.895177	−	0.445711i	$-0.147049\pi$
$359$	11.5897	+	9.72494i	0.611683	+	0.513263i	−0.283494	+	0.958974i	$0.591494\pi$
$360$		0			0
$361$	10.4684	+	15.8560i	0.550967	+	0.834527i
$362$		−	10.6256i		−	0.558470i
$363$	−35.4445	+	42.2411i	−1.86036	+	2.21709i
$364$	7.51881	−	2.73662i	0.394093	−	0.143438i
$365$		0			0
$366$	−2.01447	+	11.4246i	−0.105298	+	0.597174i
$367$	0.723196	−	1.98697i	0.0377505	−	0.103719i	−0.919385	−	0.393358i	$-0.871313\pi$
$367$	0.723196	−	1.98697i	0.0377505	−	0.103719i	0.957136	+	0.289640i	$0.0935354\pi$
$368$	7.29560	−	4.21212i	0.380310	−	0.219572i
$369$	−0.607928	+	1.05296i	−0.0316475	+	0.0548151i
$370$		0			0
$371$	4.61572	−	3.87305i	0.239636	−	0.201079i
$372$	−2.18013	−	1.25870i	−0.113035	−	0.0652605i
$373$	4.36262	−	2.51876i	0.225888	−	0.130416i	−0.382786	−	0.923837i	$-0.625035\pi$
$373$	4.36262	−	2.51876i	0.225888	−	0.130416i	0.608674	+	0.793421i	$0.291702\pi$
$374$	15.5314	+	5.65298i	0.803111	+	0.292308i
$375$		0			0
$376$	1.65283	+	9.37364i	0.0852380	+	0.483409i
$377$	8.96223	+	24.6235i	0.461579	+	1.26818i
$378$	−4.36415	+	5.20100i	−0.224468	+	0.267510i
$379$	−37.2812			−1.91501			−0.957503	−	0.288423i	$-0.906869\pi$
$379$	−37.2812			−1.91501			−0.957503	+	0.288423i	$0.906869\pi$
$380$		0			0
$381$	16.4993			0.845282
$382$	−6.97514	+	8.31264i	−0.356879	+	0.425312i
$383$	−5.09082	−	13.9869i	−0.260129	−	0.714698i	−0.999158	−	0.0410250i	$-0.986938\pi$
$383$	−5.09082	−	13.9869i	−0.260129	−	0.714698i	0.739029	−	0.673673i	$-0.235285\pi$
$384$	0.311682	+	1.76763i	0.0159054	+	0.0902042i
$385$		0			0
$386$	1.81949	+	0.662240i	0.0926096	+	0.0337071i
$387$	−1.31581	+	0.759681i	−0.0668862	+	0.0386168i
$388$	0.106921	+	0.0617308i	0.00542808	+	0.00313391i
$389$	−23.6259	+	19.8245i	−1.19788	+	1.00514i	−0.198191	+	0.980163i	$0.563507\pi$
$389$	−23.6259	+	19.8245i	−1.19788	+	1.00514i	−0.999688	+	0.0249764i	$0.992049\pi$
$390$		0			0
$391$	10.7782	−	18.6684i	0.545078	−	0.944102i
$392$	−4.45691	+	2.57320i	−0.225108	+	0.129966i
$393$	0.0678943	−	0.186538i	0.00342482	−	0.00940960i
$394$	2.12787	−	12.0678i	0.107201	−	0.607966i
$395$		0			0
$396$	−1.34550	+	0.489721i	−0.0676138	+	0.0246094i
$397$	−14.2405	+	16.9711i	−0.714708	+	0.851756i	−0.994105	−	0.108420i	$-0.965421\pi$
$397$	−14.2405	+	16.9711i	−0.714708	+	0.851756i	0.279397	+	0.960176i	$0.409865\pi$
$398$			0.432975i			0.0217031i
$399$	3.94138	+	9.89586i	0.197316	+	0.495413i
$400$		0			0
$401$	23.8011	+	19.9715i	1.18857	+	0.997330i	0.999883	+	0.0152927i	$0.00486799\pi$
$401$	23.8011	+	19.9715i	1.18857	+	0.997330i	0.188688	+	0.982037i	$0.439576\pi$
$402$	4.12513	+	11.3337i	0.205743	+	0.565273i
$403$	8.11741	−	1.43132i	0.404357	−	0.0712990i
$404$	−2.37101	+	13.4467i	−0.117962	+	0.668997i
$405$		0			0
$406$	3.03521	+	5.25714i	0.150635	+	0.260907i
$407$	−24.7786	−	14.3059i	−1.22823	−	0.709118i
$408$	2.95226	+	3.51836i	0.146159	+	0.174185i
$409$	−1.56037	+	1.30931i	−0.0771554	+	0.0647411i	−0.680550	−	0.732702i	$-0.738259\pi$
$409$	−1.56037	+	1.30931i	−0.0771554	+	0.0647411i	0.603394	+	0.797443i	$0.293815\pi$
$410$		0			0
$411$	−12.2509	−	21.2192i	−0.604292	−	1.04667i
$412$	2.35114	−	6.45971i	0.115833	−	0.318247i
$413$	−13.7867	−	2.43097i	−0.678399	−	0.119620i
$414$	0.324279	+	1.83908i	0.0159374	+	0.0903857i
$415$		0			0
$416$	−4.50203	−	3.77765i	−0.220730	−	0.185215i
$417$		−	4.33832i		−	0.212448i
$418$	4.05624	−	27.8613i	0.198397	−	1.36274i
$419$	11.2236			0.548308			0.274154	−	0.961686i	$-0.411602\pi$
$419$	11.2236			0.548308			0.274154	+	0.961686i	$0.411602\pi$
$420$		0			0
$421$	9.19144	−	3.34541i	0.447964	−	0.163045i	−0.108181	−	0.994131i	$-0.534502\pi$
$421$	9.19144	−	3.34541i	0.447964	−	0.163045i	0.556144	+	0.831086i	$0.312280\pi$
$422$	13.5362	−	2.38680i	0.658932	−	0.116187i
$423$	−2.07791	−	0.366391i	−0.101031	−	0.0178146i
$424$	−4.15875	−	1.51366i	−0.201967	−	0.0735099i
$425$		0			0
$426$	1.73889	−	3.01185i	0.0842496	−	0.145925i
$427$	−5.65620	−	6.74080i	−0.273723	−	0.326210i
$428$	5.68234	+	6.77195i	0.274666	+	0.327335i
$429$	34.0679	−	59.0073i	1.64481	−	2.84890i
$430$		0			0
$431$	4.58045	+	1.66715i	0.220633	+	0.0803037i	0.449971	−	0.893043i	$-0.351434\pi$
$431$	4.58045	+	1.66715i	0.220633	+	0.0803037i	−0.229339	+	0.973347i	$0.573656\pi$
$432$	4.91106	+	0.865953i	0.236284	+	0.0416632i
$433$	19.6135	−	3.45838i	0.942563	−	0.166199i	0.318808	−	0.947819i	$-0.396717\pi$
$433$	19.6135	−	3.45838i	0.942563	−	0.166199i	0.623755	+	0.781620i	$0.285606\pi$
$434$	1.79434	−	0.653088i	0.0861313	−	0.0313492i
$435$		0			0
$436$	−9.51609			−0.455738
$437$	−34.8666	−	11.5198i	−1.66790	−	0.551066i
$438$			11.2782i			0.538892i
$439$	16.3249	+	13.6982i	0.779145	+	0.653780i	0.943033	−	0.332699i	$-0.107959\pi$
$439$	16.3249	+	13.6982i	0.779145	+	0.653780i	−0.163888	+	0.986479i	$0.552404\pi$
$440$		0			0
$441$	−0.198103	−	1.12350i	−0.00943348	−	0.0534999i
$442$	−14.8099	−	2.61138i	−0.704435	−	0.124211i
$443$	−2.11541	+	5.81205i	−0.100506	+	0.276139i	−0.979747	−	0.200239i	$-0.935828\pi$
$443$	−2.11541	+	5.81205i	−0.100506	+	0.276139i	0.879241	+	0.476377i	$0.158050\pi$
$444$	−3.97537	−	6.88554i	−0.188662	−	0.326773i
$445$		0			0
$446$	17.2475	−	14.4723i	0.816691	−	0.685285i
$447$	2.56031	+	3.05126i	0.121099	+	0.144320i
$448$	−1.17907	−	0.680736i	−0.0557058	−	0.0321617i
$449$	20.3687	+	35.2797i	0.961260	+	1.66495i	0.719345	+	0.694653i	$0.244442\pi$
$449$	20.3687	+	35.2797i	0.961260	+	1.66495i	0.241914	+	0.970298i	$0.422225\pi$
$450$		0			0
$451$	−6.15197	+	34.8896i	−0.289685	+	1.64288i
$452$	−10.9116	+	1.92400i	−0.513237	+	0.0904975i
$453$	7.16847	+	19.6952i	0.336804	+	0.925362i
$454$	−14.4325	−	12.1103i	−0.677353	−	0.568366i
$455$		0			0
$456$	4.84724	−	6.14134i	0.226993	−	0.287595i
$457$		−	14.7073i		−	0.687978i	−0.938974	−	0.343989i	$-0.888222\pi$
$457$		−	14.7073i		−	0.687978i	0.938974	−	0.343989i	$-0.111778\pi$
$458$	−2.90430	+	3.46121i	−0.135709	+	0.161732i
$459$	11.9910	−	4.36437i	0.559692	−	0.203711i
$460$		0			0
$461$	−2.43148	+	13.7896i	−0.113245	+	0.642245i	0.874359	+	0.485280i	$0.161282\pi$
$461$	−2.43148	+	13.7896i	−0.113245	+	0.642245i	−0.987604	+	0.156966i	$0.949829\pi$
$462$	5.39859	−	14.8325i	0.251165	−	0.690071i
$463$	1.96929	−	1.13697i	0.0915206	−	0.0528394i	−0.453541	−	0.891235i	$-0.649840\pi$
$463$	1.96929	−	1.13697i	0.0915206	−	0.0528394i	0.545062	+	0.838396i	$0.316506\pi$
$464$	2.22936	−	3.86136i	0.103495	−	0.179259i
$465$		0			0
$466$	8.24507	−	6.91843i	0.381945	−	0.320490i
$467$	−25.5178	−	14.7327i	−1.18082	−	0.681749i	−0.224618	−	0.974447i	$-0.572114\pi$
$467$	−25.5178	−	14.7327i	−1.18082	−	0.681749i	−0.956205	+	0.292698i	$0.905447\pi$
$468$	1.12824	−	0.651392i	0.0521531	−	0.0301106i
$469$	−8.59685	−	3.12900i	−0.396966	−	0.144484i
$470$		0			0
$471$	−1.29762	−	7.35917i	−0.0597912	−	0.339093i
$472$	3.51683	+	9.66242i	0.161875	+	0.444749i
$473$	−28.4571	+	33.9138i	−1.30846	+	1.55936i
$474$	−6.44381			−0.295974
$475$		0			0
$476$	−3.48381			−0.159680
$477$	0.630612	−	0.751534i	0.0288738	−	0.0344104i
$478$	8.00397	+	21.9907i	0.366093	+	1.00583i
$479$	−3.55187	−	20.1437i	−0.162289	−	0.920387i	−0.951816	−	0.306671i	$-0.900785\pi$
$479$	−3.55187	−	20.1437i	−0.162289	−	0.920387i	0.789527	−	0.613716i	$-0.210326\pi$
$480$		0			0
$481$	24.4628	+	8.90374i	1.11541	+	0.405976i
$482$	−18.0960	+	10.4477i	−0.824248	+	0.475880i
$483$	−17.8283	−	10.2932i	−0.811217	−	0.468357i
$484$	−23.5339	+	19.7473i	−1.06972	+	0.897606i
$485$		0			0
$486$	−1.14956	+	1.99109i	−0.0521450	+	0.0903178i
$487$	−25.2182	+	14.5597i	−1.14275	+	0.659765i	−0.947109	−	0.320912i	$-0.896011\pi$
$487$	−25.2182	+	14.5597i	−1.14275	+	0.659765i	−0.195637	+	0.980676i	$0.562677\pi$
$488$	−2.21055	+	6.07344i	−0.100067	+	0.274932i
$489$	−1.49680	+	8.48877i	−0.0676876	+	0.383875i
$490$		0			0
$491$	−15.6448	+	5.69426i	−0.706042	+	0.256978i	−0.669988	−	0.742372i	$-0.733701\pi$
$491$	−15.6448	+	5.69426i	−0.706042	+	0.256978i	−0.0360537	+	0.999350i	$0.511479\pi$
$492$	−6.32809	+	7.54153i	−0.285293	+	0.339998i
$493$		−	11.4092i		−	0.513846i
$494$	0.767422	+	25.6057i	0.0345279	+	1.15205i
$495$		0			0
$496$	−1.07440	−	0.901527i	−0.0482419	−	0.0404798i
$497$	0.902240	+	2.47888i	0.0404710	+	0.111193i
$498$	−23.8620	+	4.20752i	−1.06928	+	0.188543i
$499$	−5.09005	+	28.8671i	−0.227862	+	1.29227i	0.629276	+	0.777182i	$0.283351\pi$
$499$	−5.09005	+	28.8671i	−0.227862	+	1.29227i	−0.857138	+	0.515087i	$0.827760\pi$
$500$		0			0
$501$	3.47058	+	6.01123i	0.155054	+	0.268562i
$502$	15.5062	+	8.95251i	0.692075	+	0.399570i
$503$	4.54061	+	5.41129i	0.202456	+	0.241277i	0.857713	−	0.514128i	$-0.171884\pi$
$503$	4.54061	+	5.41129i	0.202456	+	0.241277i	−0.655258	+	0.755405i	$0.727440\pi$
$504$	0.231196	−	0.193997i	0.0102983	−	0.00864129i
$505$		0			0
$506$	27.2070	+	47.1238i	1.20950	+	2.09491i
$507$	−13.2226	+	36.3288i	−0.587237	+	1.61342i
$508$	9.05263	+	1.59622i	0.401646	+	0.0708209i
$509$	−2.11320	−	11.9846i	−0.0936661	−	0.531207i	−0.995148	−	0.0983900i	$-0.968631\pi$
$509$	−2.11320	−	11.9846i	−0.0936661	−	0.531207i	0.901482	−	0.432817i	$-0.142480\pi$
$510$		0			0
$511$	−6.55331	−	5.49888i	−0.289901	−	0.243256i
$512$			1.00000i			0.0441942i
$513$	−11.4276	−	18.4908i	−0.504540	−	0.816389i
$514$	−0.486888			−0.0214757
$515$		0			0
$516$	−11.5603	+	4.20761i	−0.508915	+	0.185230i
$517$	−60.5463	+	10.6760i	−2.66282	+	0.469528i
$518$	5.93918	+	1.04724i	0.260952	+	0.0460130i
$519$	19.4621	+	7.08363i	0.854292	+	0.310937i
$520$		0			0
$521$	−12.6575	+	21.9234i	−0.554535	+	0.960483i	0.443405	+	0.896322i	$0.353770\pi$
$521$	−12.6575	+	21.9234i	−0.554535	+	0.960483i	−0.997940	+	0.0641611i	$0.979563\pi$
$522$	0.635324	+	0.757150i	0.0278074	+	0.0331396i
$523$	27.7800	+	33.1069i	1.21473	+	1.44766i	0.858150	+	0.513399i	$0.171614\pi$
$523$	27.7800	+	33.1069i	1.21473	+	1.44766i	0.356583	+	0.934263i	$0.383942\pi$
$524$	0.0552982	−	0.0957793i	0.00241571	−	0.00418414i
$525$		0			0
$526$	−20.7375	−	7.54785i	−0.904200	−	0.329102i
$527$	−3.53434	−	0.623200i	−0.153958	−	0.0271470i
$528$	−11.4175	+	2.01322i	−0.496884	+	0.0876140i
$529$	45.0750	−	16.4060i	1.95978	−	0.713302i
$530$		0			0
$531$	−2.27939			−0.0989169
$532$	1.20514	+	5.81086i	0.0522493	+	0.251933i
$533$		−	32.2344i		−	1.39623i
$534$	−2.60695	−	2.18749i	−0.112814	−	0.0946619i
$535$		0			0
$536$	1.16685	+	6.61753i	0.0504002	+	0.285834i
$537$	−14.8121	−	2.61177i	−0.639189	−	0.112706i
$538$	−6.07061	+	16.6789i	−0.261722	+	0.719076i
$539$	−16.6208	−	28.7881i	−0.715909	−	1.23999i
$540$		0			0
$541$	−16.8919	+	14.1740i	−0.726240	+	0.609388i	−0.929104	−	0.369819i	$-0.879420\pi$
$541$	−16.8919	+	14.1740i	−0.726240	+	0.609388i	0.202864	+	0.979207i	$0.434975\pi$
$542$	7.02047	+	8.36667i	0.301555	+	0.359379i
$543$	16.5168	+	9.53597i	0.708803	+	0.409228i
$544$	1.27943	+	2.21604i	0.0548550	+	0.0950117i
$545$		0			0
$546$	−2.49387	+	14.1435i	−0.106728	+	0.605284i
$547$	23.6615	−	4.17215i	1.01169	−	0.178388i	0.356855	−	0.934160i	$-0.383849\pi$
$547$	23.6615	−	4.17215i	1.01169	−	0.178388i	0.654836	+	0.755771i	$0.272738\pi$
$548$	−4.66884	−	12.8275i	−0.199443	−	0.547965i
$549$	−1.09754	−	0.920946i	−0.0468419	−	0.0393050i
$550$		0			0
$551$	−19.0301	+	3.94673i	−0.810712	+	0.168137i
$552$			15.1207i			0.643579i
$553$	3.14179	−	3.74424i	0.133603	−	0.159221i
$554$	−8.51330	+	3.09859i	−0.361695	+	0.131646i
$555$		0			0
$556$	0.419711	−	2.38030i	0.0177997	−	0.100947i
$557$	−1.55843	+	4.28175i	−0.0660328	+	0.181424i	−0.968320	−	0.249711i	$-0.919664\pi$
$557$	−1.55843	+	4.28175i	−0.0660328	+	0.181424i	0.902288	+	0.431135i	$0.141887\pi$
$558$	0.269253	−	0.155453i	0.0113984	−	0.00658085i
$559$	20.1404	−	34.8842i	0.851848	−	1.47544i
$560$		0			0
$561$	−22.7259	+	19.0693i	−0.959486	+	0.805105i
$562$	−13.2505	−	7.65018i	−0.558939	−	0.322703i
$563$	−19.9237	+	11.5030i	−0.839684	+	0.484792i	−0.857157	−	0.515056i	$-0.827771\pi$
$563$	−19.9237	+	11.5030i	−0.839684	+	0.484792i	0.0174729	+	0.999847i	$0.494438\pi$
$564$	−16.0540	−	5.84318i	−0.675996	−	0.246042i
$565$		0			0
$566$	1.71048	+	9.70062i	0.0718969	+	0.407747i
$567$	−4.47765	−	12.3022i	−0.188043	−	0.516645i
$568$	1.24546	−	1.48428i	0.0522583	−	0.0622790i
$569$	39.2546			1.64564			0.822819	−	0.568303i	$-0.192400\pi$
$569$	39.2546			1.64564			0.822819	+	0.568303i	$0.192400\pi$
$570$		0			0
$571$	−20.4203			−0.854563			−0.427282	−	0.904119i	$-0.640529\pi$
$571$	−20.4203			−0.854563			−0.427282	+	0.904119i	$0.640529\pi$
$572$	24.4007	−	29.0796i	1.02024	−	1.21588i
$573$	−6.66159	−	18.3026i	−0.278292	−	0.764601i
$574$	−1.29671	−	7.35402i	−0.0541237	−	0.306951i
$575$		0			0
$576$	−0.208307	−	0.0758175i	−0.00867946	−	0.00315906i
$577$	19.1093	−	11.0328i	0.795531	−	0.459300i	−0.0463754	−	0.998924i	$-0.514767\pi$
$577$	19.1093	−	11.0328i	0.795531	−	0.459300i	0.841906	+	0.539624i	$0.181434\pi$
$578$	−9.05191	−	5.22613i	−0.376510	−	0.217378i
$579$	−2.66231	+	2.23394i	−0.110642	+	0.0928396i
$580$		0			0
$581$	9.18953	−	15.9167i	0.381246	−	0.660337i
$582$	−0.191913	+	0.110801i	−0.00795503	+	0.00459284i
$583$	9.77706	−	26.8622i	0.404924	−	1.11252i
$584$	−1.09111	+	6.18799i	−0.0451504	+	0.256061i
$585$		0			0
$586$	7.68549	−	2.79729i	0.317485	−	0.115555i
$587$	−1.82311	+	2.17270i	−0.0752478	+	0.0896768i	−0.802355	−	0.596847i	$-0.796420\pi$
$587$	−1.82311	+	2.17270i	−0.0752478	+	0.0896768i	0.727107	+	0.686524i	$0.240864\pi$
$588$		−	9.23728i		−	0.380939i
$589$	0.183143	+	6.11073i	0.00754629	+	0.251788i
$590$		0			0
$591$	16.8489	+	14.1379i	0.693070	+	0.581554i
$592$	−1.51502	−	4.16248i	−0.0622669	−	0.171077i
$593$	41.3185	−	7.28557i	1.69675	−	0.299183i	0.760192	−	0.649698i	$-0.225105\pi$
$593$	41.3185	−	7.28557i	1.69675	−	0.299183i	0.936557	+	0.350515i	$0.113994\pi$
$594$	−5.59337	+	31.7216i	−0.229499	+	1.30155i
$595$		0			0
$596$	1.10957	+	1.92183i	0.0454498	+	0.0787213i
$597$	−0.673031	−	0.388574i	−0.0275453	−	0.0159033i
$598$	−31.8238	−	37.9262i	−1.30137	−	1.55092i
$599$	23.2333	−	19.4950i	0.949286	−	0.796546i	−0.0298911	−	0.999553i	$-0.509516\pi$
$599$	23.2333	−	19.4950i	0.949286	−	0.796546i	0.979177	+	0.203008i	$0.0650716\pi$
$600$		0			0
$601$	−16.4125	−	28.4274i	−0.669482	−	1.15958i	−0.978049	−	0.208374i	$-0.933183\pi$
$601$	−16.4125	−	28.4274i	−0.669482	−	1.15958i	0.308568	−	0.951202i	$-0.400150\pi$
$602$	3.19157	−	8.76875i	0.130078	−	0.357388i
$603$	−1.46695	−	0.258662i	−0.0597387	−	0.0105335i
$604$	2.02770	+	11.4997i	0.0825060	+	0.467915i
$605$		0			0
$606$	−18.7741	−	15.7533i	−0.762644	−	0.639934i
$607$			7.07201i			0.287044i	0.989647	+	0.143522i	$0.0458428\pi$
$607$			7.07201i			0.287044i	−0.989647	+	0.143522i	$0.954157\pi$
$608$	3.25368	−	2.90062i	0.131954	−	0.117636i
$609$	−10.8958			−0.441521
$610$		0			0
$611$	52.5651	−	19.1321i	2.12656	−	0.774003i
$612$	−0.558619	+	0.0984995i	−0.0225808	+	0.00398161i
$613$	−20.7853	−	3.66501i	−0.839510	−	0.148028i	−0.262670	−	0.964886i	$-0.584603\pi$
$613$	−20.7853	−	3.66501i	−0.839510	−	0.148028i	−0.576840	+	0.816857i	$0.695714\pi$
$614$	5.68175	+	2.06799i	0.229297	+	0.0834572i
$615$		0			0
$616$	4.39702	−	7.61585i	0.177161	−	0.306852i
$617$	18.8083	+	22.4149i	0.757195	+	0.902390i	0.997667	−	0.0682659i	$-0.0217466\pi$
$617$	18.8083	+	22.4149i	0.757195	+	0.902390i	−0.240472	+	0.970656i	$0.577302\pi$
$618$	7.93114	+	9.45197i	0.319037	+	0.380214i
$619$	−8.81402	+	15.2663i	−0.354265	+	0.613606i	−0.986992	−	0.160770i	$-0.948602\pi$
$619$	−8.81402	+	15.2663i	−0.354265	+	0.613606i	0.632727	+	0.774375i	$0.281936\pi$
$620$		0			0
$621$	39.4767	+	14.3683i	1.58414	+	0.576581i
$622$	32.6134	+	5.75062i	1.30768	+	0.230579i
$623$	2.54213	−	0.448246i	0.101848	−	0.0179586i
$624$	9.91246	−	3.60784i	0.396816	−	0.144429i
$625$		0			0
$626$	6.17199			0.246682
$627$	39.6682	+	31.3093i	1.58420	+	1.25037i
$628$		−	4.16329i		−	0.166133i
$629$	−8.68293	−	7.28584i	−0.346211	−	0.290505i
$630$		0			0
$631$	5.98586	+	33.9475i	0.238293	+	1.35143i	0.835566	+	0.549390i	$0.185140\pi$
$631$	5.98586	+	33.9475i	0.238293	+	1.35143i	−0.597273	+	0.802038i	$0.703749\pi$
$632$	−3.53552	−	0.623407i	−0.140635	−	0.0247978i
$633$	−8.43797	+	23.1831i	−0.335379	+	0.921447i
$634$	8.20325	+	14.2084i	0.325793	+	0.564289i
$635$		0			0
$636$	6.08516	−	5.10605i	0.241292	−	0.202468i
$637$	19.4413	+	23.1692i	0.770292	+	0.917998i
$638$	24.9414	+	14.3999i	0.987438	+	0.570097i
$639$	0.214758	+	0.371972i	0.00849570	+	0.0147150i
$640$		0			0
$641$	8.27820	−	46.9480i	0.326969	−	1.85434i	−0.168489	−	0.985704i	$-0.553889\pi$
$641$	8.27820	−	46.9480i	0.326969	−	1.85434i	0.495458	−	0.868632i	$-0.335000\pi$
$642$	−15.6262	+	2.75531i	−0.616715	+	0.108744i
$643$	3.24102	+	8.90463i	0.127813	+	0.351164i	0.987050	−	0.160414i	$-0.0512831\pi$
$643$	3.24102	+	8.90463i	0.127813	+	0.351164i	−0.859236	+	0.511579i	$0.829061\pi$
$644$	−8.78604	−	7.37236i	−0.346219	−	0.290512i
$645$		0			0
$646$	3.49912	−	10.5907i	0.137671	−	0.416686i
$647$		−	16.8594i		−	0.662810i	−0.943489	−	0.331405i	$-0.892477\pi$
$647$		−	16.8594i		−	0.662810i	0.943489	−	0.331405i	$-0.107523\pi$
$648$	−6.18097	+	7.36620i	−0.242812	+	0.289372i
$649$	−62.4116	+	22.7160i	−2.44987	+	0.891679i
$650$		0			0
$651$	−0.595156	+	3.37530i	−0.0233260	+	0.132288i
$652$	−1.64249	+	4.51272i	−0.0643250	+	0.176732i
$653$	9.34245	−	5.39386i	0.365598	−	0.211078i	−0.305936	−	0.952052i	$-0.598969\pi$
$653$	9.34245	−	5.39386i	0.365598	−	0.211078i	0.671534	+	0.740974i	$0.265636\pi$
$654$	8.54023	−	14.7921i	0.333949	−	0.578417i
$655$		0			0
$656$	−4.20164	+	3.52559i	−0.164046	+	0.137651i
$657$	−1.20628	−	0.696444i	−0.0470613	−	0.0271709i
$658$	11.2227	−	6.47941i	0.437505	−	0.252594i
$659$	−18.6209	−	6.77745i	−0.725367	−	0.264012i	−0.0471644	−	0.998887i	$-0.515018\pi$
$659$	−18.6209	−	6.77745i	−0.725367	−	0.264012i	−0.678202	+	0.734875i	$0.737241\pi$
$660$		0			0
$661$	−4.06094	−	23.0307i	−0.157952	−	0.895792i	−0.956037	−	0.293247i	$-0.905264\pi$
$661$	−4.06094	−	23.0307i	−0.157952	−	0.895792i	0.798084	−	0.602546i	$-0.205847\pi$
$662$	−5.83754	−	16.0385i	−0.226883	−	0.623355i
$663$	17.3504	−	20.6774i	0.673833	−	0.803043i
$664$	−13.4994			−0.523878
$665$		0			0
$666$	0.981938			0.0380493
$667$	24.1439	−	28.7736i	0.934857	−	1.11412i
$668$	1.32265	+	3.63394i	0.0511747	+	0.140601i
$669$	7.01750	+	39.7982i	0.271312	+	1.53869i
$670$		0			0
$671$	−39.2296	−	14.2784i	−1.51444	−	0.551212i
$672$	2.11631	−	1.22185i	0.0816386	−	0.0471341i
$673$	19.0320	+	10.9881i	0.733628	+	0.423560i	0.819748	−	0.572724i	$-0.194113\pi$
$673$	19.0320	+	10.9881i	0.733628	+	0.423560i	−0.0861200	+	0.996285i	$0.527447\pi$
$674$	14.4450	−	12.1208i	0.556399	−	0.466874i
$675$		0			0
$676$	−10.7695	+	18.6533i	−0.414210	+	0.717434i
$677$	40.2317	−	23.2278i	1.54623	−	0.892716i	0.547804	−	0.836607i	$-0.315464\pi$
$677$	40.2317	−	23.2278i	1.54623	−	0.892716i	0.998425	−	0.0561091i	$-0.0178695\pi$
$678$	6.80187	−	18.6880i	0.261224	−	0.717707i
$679$	0.0291884	−	0.165536i	0.00112015	−	0.00635268i
$680$		0			0
$681$	31.7772	−	11.5660i	1.21770	−	0.443208i
$682$	5.82315	−	6.93976i	0.222980	−	0.265737i
$683$		−	13.4198i		−	0.513496i	−0.966478	−	0.256748i	$-0.917349\pi$
$683$		−	13.4198i		−	0.513496i	0.966478	−	0.256748i	$-0.0826511\pi$
$684$	0.357534	+	0.897681i	0.0136706	+	0.0343237i
$685$		0			0
$686$	12.6681	+	10.6298i	0.483669	+	0.405846i
$687$	−2.77375	−	7.62081i	−0.105825	−	0.290752i
$688$	−6.74986	+	1.19018i	−0.257336	+	0.0453753i
$689$	−4.51650	+	25.6143i	−0.172065	+	0.975828i
$690$		0			0
$691$	20.9252	+	36.2436i	0.796033	+	1.37877i	0.922181	+	0.386759i	$0.126405\pi$
$691$	20.9252	+	36.2436i	0.796033	+	1.37877i	−0.126148	+	0.992011i	$0.540261\pi$
$692$	9.99296	+	5.76944i	0.379875	+	0.219321i
$693$	1.25306	+	1.49334i	0.0476000	+	0.0567275i
$694$	4.14258	−	3.47604i	0.157250	−	0.131949i
$695$		0			0
$696$	4.00148	+	6.93077i	0.151676	+	0.262710i
$697$	−4.80023	+	13.1885i	−0.181822	+	0.499551i
$698$	35.7564	+	6.30481i	1.35340	+	0.238641i
$699$	3.35468	+	19.0253i	0.126886	+	0.719605i
$700$		0			0
$701$	20.5106	+	17.2104i	0.774674	+	0.650028i	0.941901	−	0.335890i	$-0.109037\pi$
$701$	20.5106	+	17.2104i	0.774674	+	0.650028i	−0.167228	+	0.985918i	$0.553481\pi$
$702$		−	29.3075i		−	1.10614i
$703$	−9.14886	+	17.0031i	−0.345056	+	0.641286i
$704$	−6.45921			−0.243441
$705$		0			0
$706$	−1.15574	+	0.420656i	−0.0434970	+	0.0158316i
$707$	18.3073	−	3.22806i	0.688515	−	0.121404i
$708$	−18.1757	−	3.20488i	−0.683086	−	0.120447i
$709$	−17.7455	−	6.45882i	−0.666445	−	0.242566i	−0.0134283	−	0.999910i	$-0.504274\pi$
$709$	−17.7455	−	6.45882i	−0.666445	−	0.242566i	−0.653016	+	0.757344i	$0.726497\pi$
$710$		0			0
$711$	0.397914	−	0.689208i	0.0149230	−	0.0258473i
$712$	−1.21872	−	1.45242i	−0.0456736	−	0.0544317i
$713$	−7.59468	−	9.05099i	−0.284423	−	0.338962i
$714$	3.12655	−	5.41535i	0.117008	−	0.202664i
$715$		0			0
$716$	−7.87426	−	2.86600i	−0.294275	−	0.107107i
$717$	−41.3662	−	7.29398i	−1.54485	−	0.272399i
$718$	−14.8995	+	2.62718i	−0.556044	+	0.0980455i
$719$	30.3154	−	11.0339i	1.13057	−	0.411496i	0.292074	−	0.956396i	$-0.405655\pi$
$719$	30.3154	−	11.0339i	1.13057	−	0.411496i	0.838501	+	0.544900i	$0.183432\pi$
$720$		0			0
$721$	−9.35914			−0.348553
$722$	−18.8754	−	2.17281i	−0.702468	−	0.0808637i
$723$		−	37.5052i		−	1.39483i
$724$	8.13969	+	6.83001i	0.302509	+	0.253835i
$725$		0			0
$726$	−9.57529	−	54.3042i	−0.355372	−	2.01542i
$727$	17.6378	+	3.11002i	0.654150	+	0.115344i	0.490866	−	0.871235i	$-0.336680\pi$
$727$	17.6378	+	3.11002i	0.654150	+	0.115344i	0.163284	+	0.986579i	$0.447791\pi$
$728$	−2.73662	+	7.51881i	−0.101426	+	0.278666i
$729$	12.3605	+	21.4090i	0.457796	+	0.792926i
$730$		0			0
$731$	−13.4352	+	11.2735i	−0.496918	+	0.416964i
$732$	−7.45688	−	8.88676i	−0.275614	−	0.328464i
$733$	41.4082	+	23.9071i	1.52945	+	0.883027i	0.999385	+	0.0350693i	$0.0111652\pi$
$733$	41.4082	+	23.9071i	1.52945	+	0.883027i	0.530063	+	0.847958i	$0.322168\pi$
$734$	1.05724	+	1.83120i	0.0390235	+	0.0675907i
$735$		0			0
$736$	−1.46285	+	8.29626i	−0.0539215	+	0.305804i
$737$	−42.7440	+	7.53693i	−1.57450	+	0.277626i
$738$	−0.415848	−	1.14253i	−0.0153076	−	0.0420572i
$739$	2.75913	+	2.31519i	0.101496	+	0.0851656i	0.692124	−	0.721779i	$-0.256675\pi$
$739$	2.75913	+	2.31519i	0.101496	+	0.0851656i	−0.590627	+	0.806944i	$0.701120\pi$
$740$		0			0
$741$	−40.4910	−	21.7870i	−1.48747	−	0.800364i
$742$			6.02540i			0.221199i
$743$	1.99911	−	2.38245i	0.0733403	−	0.0874036i	−0.728127	−	0.685443i	$-0.759609\pi$
$743$	1.99911	−	2.38245i	0.0733403	−	0.0874036i	0.801467	+	0.598039i	$0.204053\pi$
$744$	2.36558	−	0.861001i	0.0867264	−	0.0315658i
$745$		0			0
$746$	−0.874756	+	4.96099i	−0.0320271	+	0.181635i
$747$	1.02349	−	2.81202i	0.0374476	−	0.102886i
$748$	−14.3138	+	8.26410i	−0.523366	+	0.302165i
$749$	6.01781	−	10.4231i	0.219886	−	0.380854i
$750$		0			0
$751$	15.5562	−	13.0532i	0.567654	−	0.476318i	−0.313213	−	0.949683i	$-0.601405\pi$
$751$	15.5562	−	13.0532i	0.567654	−	0.476318i	0.880866	+	0.473365i	$0.156961\pi$
$752$	−8.24304	−	4.75912i	−0.300593	−	0.173547i
$753$	−27.8321	+	16.0689i	−1.01426	+	0.585582i
$754$	−24.6235	−	8.96223i	−0.896736	−	0.326385i
$755$		0			0
$756$	−1.17897	−	6.68627i	−0.0428787	−	0.243177i
$757$	−13.3721	−	36.7396i	−0.486018	−	1.33532i	−0.904258	−	0.426987i	$-0.859575\pi$
$757$	−13.3721	−	36.7396i	−0.486018	−	1.33532i	0.418239	−	0.908337i	$-0.362647\pi$
$758$	23.9639	−	28.5591i	0.870408	−	1.03731i
$759$	−97.6677			−3.54511
$760$		0			0
$761$	4.22431			0.153131			0.0765656	−	0.997065i	$-0.475605\pi$
$761$	4.22431			0.153131			0.0765656	+	0.997065i	$0.475605\pi$
$762$	−10.6055	+	12.6392i	−0.384197	+	0.457868i
$763$	4.43118	+	12.1746i	0.160419	+	0.440748i
$764$	−1.88432	−	10.6865i	−0.0681724	−	0.386625i
$765$		0			0
$766$	13.9869	+	5.09082i	0.505368	+	0.183939i
$767$	52.3341	−	30.2151i	1.88968	−	1.09101i
$768$	−1.55443	−	0.897451i	−0.0560907	−	0.0323840i
$769$	−28.9268	+	24.2725i	−1.04313	+	0.875288i	−0.992354	−	0.123422i	$-0.960613\pi$
$769$	−28.9268	+	24.2725i	−1.04313	+	0.875288i	−0.0507735	+	0.998710i	$0.516169\pi$
$770$		0			0
$771$	0.436958	−	0.756833i	0.0157367	−	0.0272567i
$772$	−1.67685	+	0.968131i	−0.0603512	+	0.0348438i
$773$	1.32574	−	3.64243i	0.0476834	−	0.131009i	−0.913565	−	0.406693i	$-0.866682\pi$
$773$	1.32574	−	3.64243i	0.0476834	−	0.131009i	0.961248	+	0.275684i	$0.0889042\pi$
$774$	0.263834	−	1.49628i	0.00948333	−	0.0537827i
$775$		0			0
$776$	−0.116016	+	0.0422263i	−0.00416473	+	0.00151584i
$777$	−6.95798	+	8.29220i	−0.249616	+	0.297481i
$778$		−	30.8414i		−	1.10572i
$779$	23.6585	+	3.44436i	0.847653	+	0.123407i
$780$		0			0
$781$	9.58727	+	8.04468i	0.343060	+	0.287861i
$782$	7.37273	+	20.2564i	0.263648	+	0.724368i
$783$	21.8970	−	3.86104i

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +(-3.22960 + 5.59384i) q^{11} +(-1.55443 + 0.897451i) q^{12} +(2.01005 - 5.52256i) q^{13} +(0.236417 - 1.34079i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-1.64480 + 1.96020i) q^{17} -0.221676i q^{18} +(3.83851 + 2.06538i) q^{19} +(1.87199 + 1.57079i) q^{21} +(-2.20918 - 6.06967i) q^{22} +(-8.29626 + 1.46285i) q^{23} +(0.311682 - 1.76763i) q^{24} +(2.93849 + 5.08962i) q^{26} +(-4.31871 - 2.49341i) q^{27} +(0.875137 + 1.04295i) q^{28} +(-3.41558 + 2.86601i) q^{29} +(0.701264 + 1.21462i) q^{31} +(0.342020 - 0.939693i) q^{32} +(11.4175 + 2.01322i) q^{33} +(-0.444341 - 2.51998i) q^{34} +(0.169813 + 0.142490i) q^{36} +4.42962i q^{37} +(-4.04953 + 1.61287i) q^{38} -10.5486 q^{39} +(5.15407 - 1.87593i) q^{41} +(-2.40658 + 0.424346i) q^{42} +(6.74986 + 1.19018i) q^{43} +(6.06967 + 2.20918i) q^{44} +(4.21212 - 7.29560i) q^{46} +(6.11821 + 7.29140i) q^{47} +(1.15374 + 1.37498i) q^{48} +(-2.57320 + 4.45691i) q^{49} +(4.31591 + 1.57086i) q^{51} +(-5.78770 - 1.02053i) q^{52} +(-4.35841 + 0.768506i) q^{53} +(4.68608 - 1.70559i) q^{54} -1.36147 q^{56} +(1.12716 - 7.74218i) q^{57} -4.45872i q^{58} +(7.87687 + 6.60948i) q^{59} +(1.12233 + 6.36503i) q^{61} +(-1.38122 - 0.243546i) q^{62} +(0.103223 - 0.283604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-8.88125 + 7.45226i) q^{66} +(4.31929 + 5.14753i) q^{67} +(2.21604 + 1.27943i) q^{68} +(7.56034 + 13.0949i) q^{69} +(0.336459 - 1.90815i) q^{71} +(-0.218308 + 0.0384936i) q^{72} +(2.14907 + 5.90451i) q^{73} +(-3.39328 - 2.84730i) q^{74} +(1.36746 - 4.13885i) q^{76} -8.79403i q^{77} +(6.78052 - 8.08071i) q^{78} +(-3.37355 + 1.22787i) q^{79} +(-1.66978 + 9.46980i) q^{81} +(-1.87593 + 5.15407i) q^{82} +(-11.6908 + 6.74970i) q^{83} +(1.22185 - 2.11631i) q^{84} +(-5.25046 + 4.40566i) q^{86} +(6.93077 + 4.00148i) q^{87} +(-5.59384 + 3.22960i) q^{88} +(-1.78165 - 0.648469i) q^{89} +(1.38942 + 7.87979i) q^{91} +(2.88126 + 7.91619i) q^{92} +(1.61815 - 1.92844i) q^{93} -9.51825 q^{94} -1.79490 q^{96} +(-0.0793596 + 0.0945771i) q^{97} +(-1.76017 - 4.83603i) q^{98} +(-0.248638 - 1.41010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36q + 36q^{9} + O(q^{10}) \)	\( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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