LMFDB - Embedded newform 930.2.o.e.161.7

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.7
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.17

$q$-expansion

$f(q)$	$=$	$q-1.00000i q^{2} +(0.500302 - 1.65822i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.65822 - 0.500302i) q^{6} +(-1.28701 - 2.22916i) q^{7} +1.00000i q^{8} +(-2.49940 - 1.65922i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.500302 - 1.65822i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.65822 - 0.500302i) q^{6} +(-1.28701 - 2.22916i) q^{7} +1.00000i q^{8} +(-2.49940 - 1.65922i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.56707 - 4.44629i) q^{11} +(-0.500302 + 1.65822i) q^{12} +(4.59412 + 2.65242i) q^{13} +(-2.22916 + 1.28701i) q^{14} +(1.26238 - 1.18591i) q^{15} +1.00000 q^{16} +(-2.59376 - 4.49252i) q^{17} +(-1.65922 + 2.49940i) q^{18} +(-0.264764 - 0.458584i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-4.34033 + 1.01889i) q^{21} +(-4.44629 - 2.56707i) q^{22} +3.03318 q^{23} +(1.65822 + 0.500302i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.65242 - 4.59412i) q^{26} +(-4.00181 + 3.31444i) q^{27} +(1.28701 + 2.22916i) q^{28} -8.44680 q^{29} +(-1.18591 - 1.26238i) q^{30} +(0.790363 + 5.51138i) q^{31} -1.00000i q^{32} +(-6.08863 - 6.48126i) q^{33} +(-4.49252 + 2.59376i) q^{34} -2.57401i q^{35} +(2.49940 + 1.65922i) q^{36} +(0.580888 - 0.335376i) q^{37} +(-0.458584 + 0.264764i) q^{38} +(6.69674 - 6.29106i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-9.85425 - 5.68936i) q^{41} +(1.01889 + 4.34033i) q^{42} +(-6.69156 + 3.86337i) q^{43} +(-2.56707 + 4.44629i) q^{44} +(-1.33493 - 2.68663i) q^{45} -3.03318i q^{46} +6.75256i q^{47} +(0.500302 - 1.65822i) q^{48} +(0.187231 - 0.324294i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-8.74726 + 2.05341i) q^{51} +(-4.59412 - 2.65242i) q^{52} +(0.822328 - 1.42431i) q^{53} +(3.31444 + 4.00181i) q^{54} +(4.44629 - 2.56707i) q^{55} +(2.22916 - 1.28701i) q^{56} +(-0.892896 + 0.209606i) q^{57} +8.44680i q^{58} +(10.4486 - 6.03251i) q^{59} +(-1.26238 + 1.18591i) q^{60} -7.06279i q^{61} +(5.51138 - 0.790363i) q^{62} +(-0.481936 + 7.70698i) q^{63} -1.00000 q^{64} +(2.65242 + 4.59412i) q^{65} +(-6.48126 + 6.08863i) q^{66} +(3.98360 - 6.89980i) q^{67} +(2.59376 + 4.49252i) q^{68} +(1.51751 - 5.02968i) q^{69} -2.57401 q^{70} +(8.45327 + 4.88050i) q^{71} +(1.65922 - 2.49940i) q^{72} +(-3.21521 - 1.85630i) q^{73} +(-0.335376 - 0.580888i) q^{74} +(1.68621 - 0.395836i) q^{75} +(0.264764 + 0.458584i) q^{76} -13.2153 q^{77} +(-6.29106 - 6.69674i) q^{78} +(8.75345 - 5.05381i) q^{79} +(0.866025 + 0.500000i) q^{80} +(3.49396 + 8.29411i) q^{81} +(-5.68936 + 9.85425i) q^{82} +(-3.97145 + 6.87875i) q^{83} +(4.34033 - 1.01889i) q^{84} -5.18752i q^{85} +(3.86337 + 6.69156i) q^{86} +(-4.22595 + 14.0067i) q^{87} +(4.44629 + 2.56707i) q^{88} +14.8905 q^{89} +(-2.68663 + 1.33493i) q^{90} -13.6547i q^{91} -3.03318 q^{92} +(9.53451 + 1.44676i) q^{93} +6.75256 q^{94} -0.529528i q^{95} +(-1.65822 - 0.500302i) q^{96} -6.46323 q^{97} +(-0.324294 - 0.187231i) q^{98} +(-13.7935 + 6.85371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) $	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.500302	−	1.65822i	0.288850	−	0.957375i
$3$	0.500302	−	1.65822i	0.288850	−	0.957375i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.65822	−	0.500302i	−0.676966	−	0.204247i
$7$	−1.28701	−	2.22916i	−0.486443	−	0.842543i	0.513436	−	0.858128i	$-0.328372\pi$
$7$	−1.28701	−	2.22916i	−0.486443	−	0.842543i	−0.999879	+	0.0155847i	$0.995039\pi$
$8$			1.00000i			0.353553i
$9$	−2.49940	−	1.65922i	−0.833132	−	0.553074i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.56707	−	4.44629i	0.774000	−	1.34061i	−0.161355	−	0.986897i	$-0.551586\pi$
$11$	2.56707	−	4.44629i	0.774000	−	1.34061i	0.935355	−	0.353711i	$-0.115080\pi$
$12$	−0.500302	+	1.65822i	−0.144425	+	0.478687i
$13$	4.59412	+	2.65242i	1.27418	+	0.735648i	0.975772	−	0.218790i	$-0.0702109\pi$
$13$	4.59412	+	2.65242i	1.27418	+	0.735648i	0.298408	+	0.954438i	$0.403544\pi$
$14$	−2.22916	+	1.28701i	−0.595768	+	0.343967i
$15$	1.26238	−	1.18591i	0.325946	−	0.306201i
$16$	1.00000			0.250000
$17$	−2.59376	−	4.49252i	−0.629079	−	1.08960i	−0.987737	−	0.156127i	$-0.950099\pi$
$17$	−2.59376	−	4.49252i	−0.629079	−	1.08960i	0.358658	−	0.933469i	$-0.383234\pi$
$18$	−1.65922	+	2.49940i	−0.391083	+	0.589113i
$19$	−0.264764	−	0.458584i	−0.0607410	−	0.105206i	0.834056	−	0.551680i	$-0.186013\pi$
$19$	−0.264764	−	0.458584i	−0.0607410	−	0.105206i	−0.894797	+	0.446474i	$0.852680\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−4.34033	+	1.01889i	−0.947138	+	0.222339i
$22$	−4.44629	−	2.56707i	−0.947953	−	0.547301i
$23$	3.03318			0.632462			0.316231	−	0.948682i	$-0.397583\pi$
$23$	3.03318			0.632462			0.316231	+	0.948682i	$0.397583\pi$
$24$	1.65822	+	0.500302i	0.338483	+	0.102124i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.65242	−	4.59412i	0.520182	−	0.900982i
$27$	−4.00181	+	3.31444i	−0.770149	+	0.637864i
$28$	1.28701	+	2.22916i	0.243221	+	0.421272i
$29$	−8.44680			−1.56853			−0.784265	−	0.620426i	$-0.786960\pi$
$29$	−8.44680			−1.56853			−0.784265	+	0.620426i	$0.786960\pi$
$30$	−1.18591	−	1.26238i	−0.216517	−	0.230479i
$31$	0.790363	+	5.51138i	0.141953	+	0.989873i
$31$	0.790363	+	5.51138i	0.141953	+	0.989873i
$32$		−	1.00000i		−	0.176777i
$33$	−6.08863	−	6.48126i	−1.05989	−	1.12824i
$34$	−4.49252	+	2.59376i	−0.770461	+	0.444826i
$35$		−	2.57401i		−	0.435087i
$36$	2.49940	+	1.65922i	0.416566	+	0.276537i
$37$	0.580888	−	0.335376i	0.0954974	−	0.0551355i	−0.451491	−	0.892276i	$-0.649108\pi$
$37$	0.580888	−	0.335376i	0.0954974	−	0.0551355i	0.546988	+	0.837140i	$0.315774\pi$
$38$	−0.458584	+	0.264764i	−0.0743922	+	0.0429504i
$39$	6.69674	−	6.29106i	1.07234	−	1.00738i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−9.85425	−	5.68936i	−1.53898	−	0.888528i	−0.998899	−	0.0469123i	$-0.985062\pi$
$41$	−9.85425	−	5.68936i	−1.53898	−	0.888528i	−0.540077	−	0.841616i	$-0.681605\pi$
$42$	1.01889	+	4.34033i	0.157218	+	0.669728i
$43$	−6.69156	+	3.86337i	−1.02045	+	0.589159i	−0.914235	−	0.405184i	$-0.867207\pi$
$43$	−6.69156	+	3.86337i	−1.02045	+	0.589159i	−0.106218	+	0.994343i	$0.533874\pi$
$44$	−2.56707	+	4.44629i	−0.387000	+	0.670304i
$45$	−1.33493	−	2.68663i	−0.198999	−	0.400499i
$46$		−	3.03318i		−	0.447218i
$47$			6.75256i			0.984961i	0.870323	+	0.492481i	$0.163910\pi$
$47$			6.75256i			0.984961i	−0.870323	+	0.492481i	$0.836090\pi$
$48$	0.500302	−	1.65822i	0.0722124	−	0.239344i
$49$	0.187231	−	0.324294i	0.0267473	−	0.0463278i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−8.74726	+	2.05341i	−1.22486	+	0.287535i
$52$	−4.59412	−	2.65242i	−0.637090	−	0.367824i
$53$	0.822328	−	1.42431i	0.112955	−	0.195644i	−0.804005	−	0.594622i	$-0.797302\pi$
$53$	0.822328	−	1.42431i	0.112955	−	0.195644i	0.916961	+	0.398978i	$0.130635\pi$
$54$	3.31444	+	4.00181i	0.451038	+	0.544578i
$55$	4.44629	−	2.56707i	0.599538	−	0.346143i
$56$	2.22916	−	1.28701i	0.297884	−	0.171983i
$57$	−0.892896	+	0.209606i	−0.118267	+	0.0277630i
$58$			8.44680i			1.10912i
$59$	10.4486	−	6.03251i	1.36029	−	0.785366i	0.370632	−	0.928780i	$-0.379141\pi$
$59$	10.4486	−	6.03251i	1.36029	−	0.785366i	0.989663	+	0.143414i	$0.0458079\pi$
$60$	−1.26238	+	1.18591i	−0.162973	+	0.153100i
$61$		−	7.06279i		−	0.904297i	−0.891943	−	0.452149i	$-0.850658\pi$
$61$		−	7.06279i		−	0.904297i	0.891943	−	0.452149i	$-0.149342\pi$
$62$	5.51138	−	0.790363i	0.699946	−	0.100376i
$63$	−0.481936	+	7.70698i	−0.0607182	+	0.970988i
$64$	−1.00000			−0.125000
$65$	2.65242	+	4.59412i	0.328992	+	0.569831i
$66$	−6.48126	+	6.08863i	−0.797787	+	0.749458i
$67$	3.98360	−	6.89980i	0.486675	−	0.842945i	−0.513208	−	0.858264i	$-0.671543\pi$
$67$	3.98360	−	6.89980i	0.486675	−	0.842945i	0.999883	+	0.0153191i	$0.00487642\pi$
$68$	2.59376	+	4.49252i	0.314539	+	0.544798i
$69$	1.51751	−	5.02968i	0.182686	−	0.605503i
$70$	−2.57401			−0.307653
$71$	8.45327	+	4.88050i	1.00322	+	0.579208i	0.909199	−	0.416362i	$-0.136695\pi$
$71$	8.45327	+	4.88050i	1.00322	+	0.579208i	0.0940192	+	0.995570i	$0.470028\pi$
$72$	1.65922	−	2.49940i	0.195541	−	0.294557i
$73$	−3.21521	−	1.85630i	−0.376312	−	0.217264i	0.299901	−	0.953970i	$-0.403047\pi$
$73$	−3.21521	−	1.85630i	−0.376312	−	0.217264i	−0.676212	+	0.736707i	$0.736380\pi$
$74$	−0.335376	−	0.580888i	−0.0389867	−	0.0675269i
$75$	1.68621	−	0.395836i	0.194707	−	0.0457072i
$76$	0.264764	+	0.458584i	0.0303705	+	0.0526032i
$77$	−13.2153			−1.50603
$78$	−6.29106	−	6.69674i	−0.712322	−	0.758257i
$79$	8.75345	−	5.05381i	0.984841	−	0.568598i	0.0811125	−	0.996705i	$-0.474153\pi$
$79$	8.75345	−	5.05381i	0.984841	−	0.568598i	0.903728	+	0.428107i	$0.140819\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	3.49396	+	8.29411i	0.388218	+	0.921568i
$82$	−5.68936	+	9.85425i	−0.628284	+	1.08822i
$83$	−3.97145	+	6.87875i	−0.435923	+	0.755041i	−0.997371	−	0.0724712i	$-0.976911\pi$
$83$	−3.97145	+	6.87875i	−0.435923	+	0.755041i	0.561447	+	0.827513i	$0.310245\pi$
$84$	4.34033	−	1.01889i	0.473569	−	0.111170i
$85$		−	5.18752i		−	0.562665i
$86$	3.86337	+	6.69156i	0.416598	+	0.721569i
$87$	−4.22595	+	14.0067i	−0.453069	+	1.50167i
$88$	4.44629	+	2.56707i	0.473976	+	0.273650i
$89$	14.8905			1.57839			0.789195	−	0.614143i	$-0.210498\pi$
$89$	14.8905			1.57839			0.789195	+	0.614143i	$0.210498\pi$
$90$	−2.68663	+	1.33493i	−0.283195	+	0.140714i
$91$		−	13.6547i		−	1.43140i
$92$	−3.03318			−0.316231
$93$	9.53451	+	1.44676i	0.988683	+	0.150022i
$94$	6.75256			0.696473
$95$		−	0.529528i		−	0.0543284i
$96$	−1.65822	−	0.500302i	−0.169242	−	0.0510619i
$97$	−6.46323			−0.656242			−0.328121	−	0.944636i	$-0.606415\pi$
$97$	−6.46323			−0.656242			−0.328121	+	0.944636i	$0.606415\pi$
$98$	−0.324294	−	0.187231i	−0.0327587	−	0.0189132i
$99$	−13.7935	+	6.85371i	−1.38630	+	0.688823i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			8.88476i			0.884067i	0.896999	+	0.442034i	$0.145743\pi$
$101$			8.88476i			0.884067i	−0.896999	+	0.442034i	$0.854257\pi$
$102$	2.05341	+	8.74726i	0.203318	+	0.866107i
$103$	−5.26044	+	9.11135i	−0.518327	+	0.897768i	0.481447	+	0.876475i	$0.340111\pi$
$103$	−5.26044	+	9.11135i	−0.518327	+	0.897768i	−0.999773	+	0.0212926i	$0.993222\pi$
$104$	−2.65242	+	4.59412i	−0.260091	+	0.450491i
$105$	−4.26828	−	1.28778i	−0.416542	−	0.125675i
$106$	−1.42431	−	0.822328i	−0.138342	−	0.0798715i
$107$	−11.2096	+	6.47185i	−1.08367	+	0.625657i	−0.931884	−	0.362756i	$-0.881836\pi$
$107$	−11.2096	+	6.47185i	−1.08367	+	0.625657i	−0.151786	+	0.988413i	$0.548503\pi$
$108$	4.00181	−	3.31444i	0.385075	−	0.318932i
$109$	−1.35138			−0.129439			−0.0647193	−	0.997904i	$-0.520615\pi$
$109$	−1.35138			−0.129439			−0.0647193	+	0.997904i	$0.520615\pi$
$110$	−2.56707	−	4.44629i	−0.244760	−	0.423937i
$111$	−0.265508	−	1.13103i	−0.0252009	−	0.107353i
$112$	−1.28701	−	2.22916i	−0.121611	−	0.210636i
$113$	4.08230	+	2.35692i	0.384030	+	0.221720i	0.679570	−	0.733610i	$-0.262166\pi$
$113$	4.08230	+	2.35692i	0.384030	+	0.221720i	−0.295540	+	0.955330i	$0.595500\pi$
$114$	0.209606	+	0.892896i	0.0196314	+	0.0836274i
$115$	2.62681	+	1.51659i	0.244951	+	0.141423i
$116$	8.44680			0.784265
$117$	−7.08158	−	14.2521i	−0.654692	−	1.31761i
$118$	−6.03251	−	10.4486i	−0.555338	−	0.961873i
$119$	−6.67636	+	11.5638i	−0.612021	+	1.06005i
$120$	1.18591	+	1.26238i	0.108258	+	0.115239i
$121$	−7.67968	−	13.3016i	−0.698152	−	1.20924i
$122$	−7.06279			−0.639435
$123$	−14.3643	+	13.4941i	−1.29519	+	1.21673i
$124$	−0.790363	−	5.51138i	−0.0709767	−	0.494937i
$125$			1.00000i			0.0894427i
$126$	7.70698	+	0.481936i	0.686593	+	0.0429343i
$127$	13.5026	−	7.79574i	1.19816	−	0.691760i	0.238018	−	0.971261i	$-0.423502\pi$
$127$	13.5026	−	7.79574i	1.19816	−	0.691760i	0.960146	+	0.279500i	$0.0901688\pi$
$128$			1.00000i			0.0883883i
$129$	3.05853	+	13.0289i	0.269288	+	1.14713i
$130$	4.59412	−	2.65242i	0.402931	−	0.232632i
$131$	16.4069	−	9.47252i	1.43348	−	0.827618i	0.436093	−	0.899902i	$-0.356362\pi$
$131$	16.4069	−	9.47252i	1.43348	−	0.827618i	0.997384	+	0.0722837i	$0.0230287\pi$
$132$	6.08863	+	6.48126i	0.529947	+	0.564121i
$133$	−0.681505	+	1.18040i	−0.0590940	+	0.102354i
$134$	−6.89980	−	3.98360i	−0.596052	−	0.344131i
$135$	−5.12289	+	0.869482i	−0.440908	+	0.0748331i
$136$	4.49252	−	2.59376i	0.385231	−	0.222413i
$137$	−2.98906	+	5.17720i	−0.255373	+	0.442318i	−0.964997	−	0.262262i	$-0.915531\pi$
$137$	−2.98906	+	5.17720i	−0.255373	+	0.442318i	0.709624	+	0.704580i	$0.248865\pi$
$138$	−5.02968	−	1.51751i	−0.428155	−	0.129179i
$139$		−	20.6001i		−	1.74728i	−0.486573	−	0.873640i	$-0.661753\pi$
$139$		−	20.6001i		−	1.74728i	0.486573	−	0.873640i	$-0.338247\pi$
$140$			2.57401i			0.217544i
$141$	11.1972	+	3.37832i	0.942977	+	0.284506i
$142$	4.88050	−	8.45327i	0.409562	−	0.709382i
$143$	23.5869	−	13.6179i	1.97243	−	1.13878i
$144$	−2.49940	−	1.65922i	−0.208283	−	0.138269i
$145$	−7.31514	−	4.22340i	−0.607489	−	0.350734i
$146$	−1.85630	+	3.21521i	−0.153629	+	0.266093i
$147$	−0.444079	−	0.472716i	−0.0366271	−	0.0389890i
$148$	−0.580888	+	0.335376i	−0.0477487	+	0.0275677i
$149$	20.8920	−	12.0620i	1.71154	−	0.988160i	0.779057	−	0.626953i	$-0.215698\pi$
$149$	20.8920	−	12.0620i	1.71154	−	0.988160i	0.932486	−	0.361206i	$-0.117635\pi$
$150$	−0.395836	−	1.68621i	−0.0323199	−	0.137679i
$151$			16.5788i			1.34916i	0.738201	+	0.674581i	$0.235676\pi$
$151$			16.5788i			1.34916i	−0.738201	+	0.674581i	$0.764324\pi$
$152$	0.458584	−	0.264764i	0.0371961	−	0.0214752i
$153$	−0.971266	+	15.5322i	−0.0785222	+	1.25570i
$154$			13.2153i			1.06492i
$155$	−2.07122	+	5.16818i	−0.166364	+	0.415118i
$156$	−6.69674	+	6.29106i	−0.536169	+	0.503688i
$157$	14.6508			1.16926			0.584631	−	0.811300i	$-0.301239\pi$
$157$	14.6508			1.16926			0.584631	+	0.811300i	$0.301239\pi$
$158$	−5.05381	−	8.75345i	−0.402059	−	0.696387i
$159$	−1.95041	−	2.07619i	−0.154678	−	0.164652i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.90372	−	6.76144i	−0.307656	−	0.532876i
$162$	8.29411	−	3.49396i	0.651647	−	0.274511i
$163$	22.4774			1.76056			0.880281	−	0.474452i	$-0.157354\pi$
$163$	22.4774			1.76056			0.880281	+	0.474452i	$0.157354\pi$
$164$	9.85425	+	5.68936i	0.769488	+	0.444264i
$165$	−2.03228	−	8.65725i	−0.158213	−	0.673966i
$166$	6.87875	+	3.97145i	0.533895	+	0.308244i
$167$	−8.21327	−	14.2258i	−0.635562	−	1.10083i	−0.986396	−	0.164388i	$-0.947435\pi$
$167$	−8.21327	−	14.2258i	−0.635562	−	1.10083i	0.350833	−	0.936438i	$-0.385898\pi$
$168$	−1.01889	−	4.34033i	−0.0786089	−	0.334864i
$169$	7.57064	+	13.1127i	0.582357	+	1.00867i
$170$	−5.18752			−0.397864
$171$	−0.0991442	+	1.58549i	−0.00758174	+	0.121245i
$172$	6.69156	−	3.86337i	0.510226	−	0.294579i
$173$	−2.51861	−	1.45412i	−0.191486	−	0.110554i	0.401192	−	0.915994i	$-0.368596\pi$
$173$	−2.51861	−	1.45412i	−0.191486	−	0.110554i	−0.592678	+	0.805439i	$0.701929\pi$
$174$	14.0067	+	4.22595i	1.06184	+	0.320368i
$175$	1.28701	−	2.22916i	0.0972885	−	0.168509i
$176$	2.56707	−	4.44629i	0.193500	−	0.335152i
$177$	−4.77578	−	20.3442i	−0.358969	−	1.52916i
$178$		−	14.8905i		−	1.11609i
$179$	−2.85826	−	4.95065i	−0.213637	−	0.370029i	0.739213	−	0.673471i	$-0.235197\pi$
$179$	−2.85826	−	4.95065i	−0.213637	−	0.370029i	−0.952850	+	0.303442i	$0.901864\pi$
$180$	1.33493	+	2.68663i	0.0994997	+	0.200249i
$181$	−13.2525	−	7.65134i	−0.985051	−	0.568719i	−0.0812595	−	0.996693i	$-0.525894\pi$
$181$	−13.2525	−	7.65134i	−0.985051	−	0.568719i	−0.903791	+	0.427974i	$0.859228\pi$
$182$	−13.6547			−1.01215
$183$	−11.7117	−	3.53353i	−0.865751	−	0.261206i
$184$			3.03318i			0.223609i
$185$	0.670752			0.0493146
$186$	1.44676	−	9.53451i	0.106081	−	0.699104i
$187$	−26.6334			−1.94763
$188$		−	6.75256i		−	0.492481i
$189$	12.5388	+	4.65498i	0.912061	+	0.338600i
$190$	−0.529528			−0.0384160
$191$	4.31841	+	2.49324i	0.312470	+	0.180404i	0.648031	−	0.761614i	$-0.275593\pi$
$191$	4.31841	+	2.49324i	0.312470	+	0.180404i	−0.335562	+	0.942018i	$0.608926\pi$
$192$	−0.500302	+	1.65822i	−0.0361062	+	0.119672i
$193$	8.08463	+	14.0030i	0.581945	+	1.00796i	0.995249	+	0.0973645i	$0.0310413\pi$
$193$	8.08463	+	14.0030i	0.581945	+	1.00796i	−0.413304	+	0.910593i	$0.635625\pi$
$194$			6.46323i			0.464033i
$195$	8.94508	−	2.09985i	0.640571	−	0.150373i
$196$	−0.187231	+	0.324294i	−0.0133737	+	0.0231639i
$197$	−4.30925	+	7.46384i	−0.307021	+	0.531777i	−0.977709	−	0.209963i	$-0.932666\pi$
$197$	−4.30925	+	7.46384i	−0.307021	+	0.531777i	0.670688	+	0.741740i	$0.265999\pi$
$198$	6.85371	+	13.7935i	0.487072	+	0.980262i
$199$	4.91862	+	2.83976i	0.348671	+	0.201306i	0.664100	−	0.747644i	$-0.268815\pi$
$199$	4.91862	+	2.83976i	0.348671	+	0.201306i	−0.315429	+	0.948949i	$0.602148\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−9.44840	−	10.0577i	−0.666438	−	0.709414i
$202$	8.88476			0.625130
$203$	10.8711	+	18.8293i	0.763000	+	1.32155i
$204$	8.74726	−	2.05341i	0.612430	−	0.143767i
$205$	−5.68936	−	9.85425i	−0.397362	−	0.688251i
$206$	9.11135	+	5.26044i	0.634818	+	0.366512i
$207$	−7.58112	−	5.03272i	−0.526924	−	0.349798i
$208$	4.59412	+	2.65242i	0.318545	+	0.183912i
$209$	−2.71867			−0.188054
$210$	−1.28778	+	4.26828i	−0.0888655	+	0.294539i
$211$	0.695561	+	1.20475i	0.0478844	+	0.0829382i	0.888974	−	0.457957i	$-0.151419\pi$
$211$	0.695561	+	1.20475i	0.0478844	+	0.0829382i	−0.841090	+	0.540896i	$0.818085\pi$
$212$	−0.822328	+	1.42431i	−0.0564777	+	0.0978222i
$213$	12.3221	−	11.5757i	0.844298	−	0.793151i
$214$	6.47185	+	11.2096i	0.442407	+	0.766271i
$215$	−7.72674			−0.526960
$216$	−3.31444	−	4.00181i	−0.225519	−	0.272289i
$217$	11.2685	−	8.85503i	0.764959	−	0.601118i
$218$			1.35138i			0.0915269i
$219$	−4.68674	+	4.40282i	−0.316700	+	0.297515i
$220$	−4.44629	+	2.56707i	−0.299769	+	0.173072i
$221$		−	27.5189i		−	1.85112i
$222$	−1.13103	+	0.265508i	−0.0759098	+	0.0178197i
$223$	11.5712	−	6.68062i	0.774863	−	0.447368i	−0.0597434	−	0.998214i	$-0.519028\pi$
$223$	11.5712	−	6.68062i	0.774863	−	0.447368i	0.834607	+	0.550846i	$0.185695\pi$
$224$	−2.22916	+	1.28701i	−0.148942	+	0.0859917i
$225$	0.187231	−	2.99415i	0.0124821	−	0.199610i
$226$	2.35692	−	4.08230i	0.156780	−	0.271550i
$227$	13.4583	+	7.77017i	0.893261	+	0.515724i	0.875008	−	0.484109i	$-0.160856\pi$
$227$	13.4583	+	7.77017i	0.893261	+	0.515724i	0.0182532	+	0.999833i	$0.494190\pi$
$228$	0.892896	−	0.209606i	0.0591335	−	0.0138815i
$229$	12.6066	−	7.27845i	0.833071	−	0.480974i	−0.0218323	−	0.999762i	$-0.506950\pi$
$229$	12.6066	−	7.27845i	0.833071	−	0.480974i	0.854903	+	0.518788i	$0.173617\pi$
$230$	1.51659	−	2.62681i	0.100001	−	0.173207i
$231$	−6.61166	+	21.9139i	−0.435015	+	1.44183i
$232$		−	8.44680i		−	0.554559i
$233$			2.89624i			0.189739i	0.995490	+	0.0948694i	$0.0302434\pi$
$233$			2.89624i			0.189739i	−0.995490	+	0.0948694i	$0.969757\pi$
$234$	−14.2521	+	7.08158i	−0.931690	+	0.462937i
$235$	−3.37628	+	5.84788i	−0.220244	+	0.381474i
$236$	−10.4486	+	6.03251i	−0.680147	+	0.392683i
$237$	−4.00096	−	17.0436i	−0.259890	−	1.10710i
$238$	11.5638	+	6.67636i	0.749570	+	0.432764i
$239$	−2.74446	+	4.75354i	−0.177524	+	0.307481i	−0.941032	−	0.338318i	$-0.890142\pi$
$239$	−2.74446	+	4.75354i	−0.177524	+	0.307481i	0.763508	+	0.645799i	$0.223476\pi$
$240$	1.26238	−	1.18591i	0.0814866	−	0.0765502i
$241$	−4.61436	+	2.66410i	−0.297237	+	0.171610i	−0.641201	−	0.767373i	$-0.721564\pi$
$241$	−4.61436	+	2.66410i	−0.297237	+	0.171610i	0.343964	+	0.938983i	$0.388230\pi$
$242$	−13.3016	+	7.67968i	−0.855059	+	0.493668i
$243$	15.5015	−	1.64420i	0.994422	−	0.105475i
$244$			7.06279i			0.452149i
$245$	0.324294	−	0.187231i	0.0207184	−	0.0119618i
$246$	13.4941	+	14.3643i	0.860355	+	0.915835i
$247$		−	2.80906i		−	0.178736i
$248$	−5.51138	+	0.790363i	−0.349973	+	0.0501881i
$249$	9.41957	+	10.0270i	0.596941	+	0.635435i
$250$	1.00000			0.0632456
$251$	0.392937	+	0.680586i	0.0248019	+	0.0429582i	0.878160	−	0.478367i	$-0.158771\pi$
$251$	0.392937	+	0.680586i	0.0248019	+	0.0429582i	−0.853358	+	0.521325i	$0.825438\pi$
$252$	0.481936	−	7.70698i	0.0303591	−	0.485494i
$253$	7.78638	−	13.4864i	0.489526	−	0.847883i
$254$	−7.79574	−	13.5026i	−0.489148	−	0.847230i
$255$	−8.60205	−	2.59533i	−0.538681	−	0.162526i
$256$	1.00000			0.0625000
$257$	−10.4435	−	6.02954i	−0.651446	−	0.376113i	0.137564	−	0.990493i	$-0.456073\pi$
$257$	−10.4435	−	6.02954i	−0.651446	−	0.376113i	−0.789010	+	0.614380i	$0.789406\pi$
$258$	13.0289	−	3.05853i	0.811146	−	0.190416i
$259$	−1.49521	−	0.863261i	−0.0929080	−	0.0536405i
$260$	−2.65242	−	4.59412i	−0.164496	−	0.284915i
$261$	21.1119	+	14.0151i	1.30679	+	0.867514i
$262$	−9.47252	−	16.4069i	−0.585214	−	1.01362i
$263$	−2.04756			−0.126258			−0.0631291	−	0.998005i	$-0.520108\pi$
$263$	−2.04756			−0.126258			−0.0631291	+	0.998005i	$0.520108\pi$
$264$	6.48126	−	6.08863i	0.398894	−	0.374729i
$265$	1.42431	−	0.822328i	0.0874949	−	0.0505152i
$266$	1.18040	+	0.681505i	0.0723751	+	0.0417858i
$267$	7.44975	−	24.6917i	0.455917	−	1.51111i
$268$	−3.98360	+	6.89980i	−0.243337	+	0.421473i
$269$	−13.5077	+	23.3961i	−0.823581	+	1.42648i	0.0794184	+	0.996841i	$0.474694\pi$
$269$	−13.5077	+	23.3961i	−0.823581	+	1.42648i	−0.902999	+	0.429642i	$0.858640\pi$
$270$	0.869482	+	5.12289i	0.0529150	+	0.311769i
$271$		−	3.17938i		−	0.193134i	−0.995327	−	0.0965668i	$-0.969214\pi$
$271$		−	3.17938i		−	0.193134i	0.995327	−	0.0965668i	$-0.0307861\pi$
$272$	−2.59376	−	4.49252i	−0.157270	−	0.272399i
$273$	−22.6425	−	6.83148i	−1.37039	−	0.413460i
$274$	5.17720	+	2.98906i	0.312766	+	0.180576i
$275$	5.13414			0.309600
$276$	−1.51751	+	5.02968i	−0.0913431	+	0.302751i
$277$		−	16.5427i		−	0.993955i	−0.867763	−	0.496978i	$-0.834443\pi$
$277$		−	16.5427i		−	0.993955i	0.867763	−	0.496978i	$-0.165557\pi$
$278$	−20.6001			−1.23551
$279$	7.16918	−	15.0865i	0.429208	−	0.903206i
$280$	2.57401			0.153827
$281$			1.55339i			0.0926672i	0.998926	+	0.0463336i	$0.0147537\pi$
$281$			1.55339i			0.0926672i	−0.998926	+	0.0463336i	$0.985246\pi$
$282$	3.37832	−	11.1972i	0.201176	−	0.666785i
$283$	−3.03122			−0.180187			−0.0900936	−	0.995933i	$-0.528717\pi$
$283$	−3.03122			−0.180187			−0.0900936	+	0.995933i	$0.528717\pi$
$284$	−8.45327	−	4.88050i	−0.501609	−	0.289604i
$285$	−0.878074	−	0.264924i	−0.0520126	−	0.0156927i
$286$	−13.6179	−	23.5869i	−0.805242	−	1.39472i
$287$			29.2889i			1.72887i
$288$	−1.65922	+	2.49940i	−0.0977707	+	0.147278i
$289$	−4.95516	+	8.58260i	−0.291480	+	0.504859i
$290$	−4.22340	+	7.31514i	−0.248006	+	0.429560i
$291$	−3.23357	+	10.7175i	−0.189555	+	0.628269i
$292$	3.21521	+	1.85630i	0.188156	+	0.108632i
$293$	−6.74006	+	3.89138i	−0.393759	+	0.227337i	−0.683787	−	0.729681i	$-0.739668\pi$
$293$	−6.74006	+	3.89138i	−0.393759	+	0.227337i	0.290029	+	0.957018i	$0.406335\pi$
$294$	−0.472716	+	0.444079i	−0.0275694	+	0.0258992i
$295$	12.0650			0.702453
$296$	0.335376	+	0.580888i	0.0194933	+	0.0337634i
$297$	4.46404	+	26.3016i	0.259030	+	1.52617i
$298$	−12.0620	−	20.8920i	−0.698734	−	1.21024i
$299$	13.9348	+	8.04526i	0.805870	+	0.465270i
$300$	−1.68621	+	0.395836i	−0.0973535	+	0.0228536i
$301$	17.2241	+	9.94437i	0.992783	+	0.573184i
$302$	16.5788			0.954002
$303$	14.7329	+	4.44507i	0.846383	+	0.255362i
$304$	−0.264764	−	0.458584i	−0.0151852	−	0.0263016i
$305$	3.53139	−	6.11655i	0.202207	−	0.350233i
$306$	15.5322	+	0.971266i	0.887917	+	0.0555236i
$307$	−5.71957	−	9.90659i	−0.326433	−	0.565399i	0.655368	−	0.755310i	$-0.272513\pi$
$307$	−5.71957	−	9.90659i	−0.326433	−	0.565399i	−0.981801	+	0.189911i	$0.939180\pi$
$308$	13.2153			0.753013
$309$	12.4768	+	13.2814i	0.709782	+	0.755552i
$310$	5.16818	+	2.07122i	0.293533	+	0.117637i
$311$		−	7.22744i		−	0.409831i	−0.978780	−	0.204915i	$-0.934308\pi$
$311$		−	7.22744i		−	0.409831i	0.978780	−	0.204915i	$-0.0656919\pi$
$312$	6.29106	+	6.69674i	0.356161	+	0.379129i
$313$	11.2641	−	6.50334i	0.636686	−	0.367591i	−0.146651	−	0.989188i	$-0.546849\pi$
$313$	11.2641	−	6.50334i	0.636686	−	0.367591i	0.783337	+	0.621598i	$0.213516\pi$
$314$		−	14.6508i		−	0.826793i
$315$	−4.27086	+	6.43347i	−0.240636	+	0.362485i
$316$	−8.75345	+	5.05381i	−0.492420	+	0.284299i
$317$	−19.7129	+	11.3812i	−1.10718	+	0.639233i	−0.938099	−	0.346368i	$-0.887415\pi$
$317$	−19.7129	+	11.3812i	−1.10718	+	0.639233i	−0.169086	+	0.985601i	$0.554082\pi$
$318$	−2.07619	+	1.95041i	−0.116427	+	0.109374i
$319$	−21.6835	+	37.5569i	−1.21404	+	2.10278i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	5.12359	+	21.8258i	0.285971	+	1.21820i
$322$	−6.76144	+	3.90372i	−0.376801	+	0.217546i
$323$	−1.37347	+	2.37891i	−0.0764217	+	0.132366i
$324$	−3.49396	−	8.29411i	−0.194109	−	0.460784i
$325$			5.30484i			0.294259i
$326$		−	22.4774i		−	1.24491i
$327$	−0.676098	+	2.24089i	−0.0373883	+	0.123921i
$328$	5.68936	−	9.85425i	0.314142	−	0.544110i
$329$	15.0525	−	8.69058i	0.829873	−	0.479127i
$330$	−8.65725	+	2.03228i	−0.476566	+	0.111873i
$331$	4.25023	+	2.45387i	0.233614	+	0.134877i	0.612238	−	0.790673i	$-0.290269\pi$
$331$	4.25023	+	2.45387i	0.233614	+	0.134877i	−0.378624	+	0.925550i	$0.623603\pi$
$332$	3.97145	−	6.87875i	0.217962	−	0.377521i
$333$	−2.00833	−	0.125586i	−0.110056	−	0.00688206i
$334$	−14.2258	+	8.21327i	−0.778402	+	0.449410i
$335$	6.89980	−	3.98360i	0.376977	−	0.217647i
$336$	−4.34033	+	1.01889i	−0.236785	+	0.0555849i
$337$			27.0752i			1.47488i	0.675414	+	0.737439i	$0.263965\pi$
$337$			27.0752i			1.47488i	−0.675414	+	0.737439i	$0.736035\pi$
$338$	13.1127	−	7.57064i	0.713239	−	0.411789i
$339$	5.95067	−	5.59018i	0.323196	−	0.303617i
$340$			5.18752i			0.281333i
$341$	26.5341	+	10.6339i	1.43690	+	0.575858i
$342$	1.58549	+	0.0991442i	0.0857333	+	0.00536110i
$343$	−18.9820			−1.02493
$344$	−3.86337	−	6.69156i	−0.208299	−	0.360785i
$345$	3.82904	−	3.59708i	0.206149	−	0.193660i
$346$	−1.45412	+	2.51861i	−0.0781738	+	0.135401i
$347$	10.2487	+	17.7512i	0.550178	+	0.952936i	0.998261	+	0.0589439i	$0.0187733\pi$
$347$	10.2487	+	17.7512i	0.550178	+	0.952936i	−0.448084	+	0.893992i	$0.647893\pi$
$348$	4.22595	−	14.0067i	0.226535	−	0.750836i
$349$	−20.0539			−1.07346			−0.536732	−	0.843753i	$-0.680341\pi$
$349$	−20.0539			−1.07346			−0.536732	+	0.843753i	$0.680341\pi$
$350$	−2.22916	−	1.28701i	−0.119154	−	0.0687934i
$351$	−27.1761	+	4.61246i	−1.45055	+	0.246195i
$352$	−4.44629	−	2.56707i	−0.236988	−	0.136825i
$353$	−4.20458	−	7.28255i	−0.223787	−	0.387611i	0.732168	−	0.681125i	$-0.238509\pi$
$353$	−4.20458	−	7.28255i	−0.223787	−	0.387611i	−0.955955	+	0.293513i	$0.905175\pi$
$354$	−20.3442	+	4.77578i	−1.08128	+	0.253830i
$355$	4.88050	+	8.45327i	0.259030	+	0.448653i
$356$	−14.8905			−0.789195
$357$	15.8351	+	16.8563i	0.838085	+	0.892129i
$358$	−4.95065	+	2.85826i	−0.261650	+	0.151064i
$359$	22.0093	+	12.7070i	1.16160	+	0.670652i	0.951688	−	0.307067i	$-0.0993476\pi$
$359$	22.0093	+	12.7070i	1.16160	+	0.670652i	0.209916	+	0.977719i	$0.432681\pi$
$360$	2.68663	−	1.33493i	0.141598	−	0.0703569i
$361$	9.35980	−	16.2116i	0.492621	−	0.853245i
$362$	−7.65134	+	13.2525i	−0.402145	+	0.696536i
$363$	−25.8991	+	6.07979i	−1.35935	+	0.319106i
$364$			13.6547i			0.715701i
$365$	−1.85630	−	3.21521i	−0.0971633	−	0.168292i
$366$	−3.53353	+	11.7117i	−0.184700	+	0.612178i
$367$	14.9832	+	8.65053i	0.782114	+	0.451554i	0.837179	−	0.546929i	$-0.184203\pi$
$367$	14.9832	+	8.65053i	0.782114	+	0.451554i	−0.0550648	+	0.998483i	$0.517537\pi$
$368$	3.03318			0.158115
$369$	15.1898	+	30.5704i	0.790748	+	1.59143i
$370$		−	0.670752i		−	0.0348707i
$371$	−4.23336			−0.219785
$372$	−9.53451	−	1.44676i	−0.494341	−	0.0750109i
$373$	−14.4940			−0.750471			−0.375236	−	0.926929i	$-0.622438\pi$
$373$	−14.4940			−0.750471			−0.375236	+	0.926929i	$0.622438\pi$
$374$			26.6334i			1.37718i
$375$	1.65822	+	0.500302i	0.0856302	+	0.0258355i
$376$	−6.75256			−0.348236
$377$	−38.8056	−	22.4044i	−1.99859	−	1.15389i
$378$	4.65498	−	12.5388i	0.239426	−	0.644925i
$379$	−9.90778	−	17.1608i	−0.508929	−	0.881490i	−0.999947	−	0.0103407i	$-0.996708\pi$
$379$	−9.90778	−	17.1608i	−0.508929	−	0.881490i	0.491018	−	0.871149i	$-0.336625\pi$
$380$			0.529528i			0.0271642i
$381$	−6.17168	−	26.2906i	−0.316185	−	1.34691i
$382$	2.49324	−	4.31841i	0.127565	−	0.220949i
$383$	−1.97590	+	3.42236i	−0.100964	+	0.174874i	−0.912082	−	0.410008i	$-0.865526\pi$
$383$	−1.97590	+	3.42236i	−0.100964	+	0.174874i	0.811118	+	0.584882i	$0.198859\pi$
$384$	1.65822	+	0.500302i	0.0846208	+	0.0255309i
$385$	−11.4448	−	6.60766i	−0.583282	−	0.336758i
$386$	14.0030	−	8.08463i	0.712734	−	0.411497i
$387$	23.1350	+	1.44669i	1.17602	+	0.0735393i
$388$	6.46323			0.328121
$389$	−9.71945	−	16.8346i	−0.492796	−	0.853547i	0.507170	−	0.861846i	$-0.330692\pi$
$389$	−9.71945	−	16.8346i	−0.492796	−	0.853547i	−0.999966	+	0.00829898i	$0.997358\pi$
$390$	−2.09985	−	8.94508i	−0.106330	−	0.452952i
$391$	−7.86734	−	13.6266i	−0.397868	−	0.689128i
$392$	0.324294	+	0.187231i	0.0163793	+	0.00945661i
$393$	−7.49914	−	31.9454i	−0.378281	−	1.61143i
$394$	7.46384	+	4.30925i	0.376023	+	0.217097i
$395$	10.1076			0.508569
$396$	13.7935	−	6.85371i	0.693150	−	0.344412i
$397$	11.9703	+	20.7332i	0.600772	+	1.04057i	0.992704	+	0.120574i	$0.0384735\pi$
$397$	11.9703	+	20.7332i	0.600772	+	1.04057i	−0.391932	+	0.919994i	$0.628193\pi$
$398$	2.83976	−	4.91862i	0.142344	−	0.246548i
$399$	1.61641	+	1.72064i	0.0809216	+	0.0861399i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	20.4973			1.02359			0.511793	−	0.859109i	$-0.328981\pi$
$401$	20.4973			1.02359			0.511793	+	0.859109i	$0.328981\pi$
$402$	−10.0577	+	9.44840i	−0.501632	+	0.471243i
$403$	−10.9875	+	27.4163i	−0.547324	+	1.36571i
$404$		−	8.88476i		−	0.442034i
$405$	−1.12120	+	8.92989i	−0.0557128	+	0.443730i
$406$	18.8293	−	10.8711i	0.934480	−	0.539522i
$407$		−	3.44373i		−	0.170699i
$408$	−2.05341	−	8.74726i	−0.101659	−	0.433054i
$409$	7.58719	−	4.38047i	0.375163	−	0.216600i	−0.300549	−	0.953766i	$-0.597170\pi$
$409$	7.58719	−	4.38047i	0.375163	−	0.216600i	0.675712	+	0.737166i	$0.263837\pi$
$410$	−9.85425	+	5.68936i	−0.486667	+	0.280977i
$411$	7.08951	+	7.54669i	0.349700	+	0.372251i
$412$	5.26044	−	9.11135i	0.259163	−	0.448884i
$413$	−26.8949	−	15.5278i	−1.32341	−	0.764071i
$414$	−5.03272	+	7.58112i	−0.247345	+	0.372592i
$415$	−6.87875	+	3.97145i	−0.337665	+	0.194951i
$416$	2.65242	−	4.59412i	0.130045	−	0.225245i
$417$	−34.1596	−	10.3063i	−1.67280	−	0.504701i
$418$			2.71867i			0.132974i
$419$		−	17.8444i		−	0.871754i	−0.900006	−	0.435877i	$-0.856438\pi$
$419$		−	17.8444i		−	0.871754i	0.900006	−	0.435877i	$-0.143562\pi$
$420$	4.26828	+	1.28778i	0.208271	+	0.0628374i
$421$	−8.25775	+	14.3028i	−0.402458	+	0.697078i	−0.994022	−	0.109180i	$-0.965177\pi$
$421$	−8.25775	+	14.3028i	−0.402458	+	0.697078i	0.591564	+	0.806258i	$0.298511\pi$
$422$	1.20475	−	0.695561i	0.0586462	−	0.0338594i
$423$	11.2040	−	16.8773i	0.544757	−	0.820603i
$424$	1.42431	+	0.822328i	0.0691708	+	0.0399358i
$425$	2.59376	−	4.49252i	0.125816	−	0.217919i
$426$	−11.5757	−	12.3221i	−0.560843	−	0.597009i
$427$	−15.7441	+	9.08985i	−0.761909	+	0.439889i
$428$	11.2096	−	6.47185i	0.541835	−	0.312829i
$429$	−10.7809	−	45.9253i	−0.520507	−	2.21729i
$430$			7.72674i			0.372617i
$431$	−10.7198	+	6.18908i	−0.516354	+	0.298117i	−0.735442	−	0.677588i	$-0.763025\pi$
$431$	−10.7198	+	6.18908i	−0.516354	+	0.298117i	0.219087	+	0.975705i	$0.429692\pi$
$432$	−4.00181	+	3.31444i	−0.192537	+	0.159466i
$433$			1.18613i			0.0570017i	0.999594	+	0.0285008i	$0.00907333\pi$
$433$			1.18613i			0.0570017i	−0.999594	+	0.0285008i	$0.990927\pi$
$434$	−8.85503	−	11.2685i	−0.425055	−	0.540908i
$435$	−10.6631	+	10.0171i	−0.511257	+	0.480285i
$436$	1.35138			0.0647193
$437$	−0.803076	−	1.39097i	−0.0384163	−	0.0665391i
$438$	4.40282	+	4.68674i	0.210375	+	0.223941i
$439$	8.22962	−	14.2541i	0.392778	−	0.680312i	−0.600036	−	0.799973i	$-0.704847\pi$
$439$	8.22962	−	14.2541i	0.392778	−	0.680312i	0.992815	+	0.119660i	$0.0381806\pi$
$440$	2.56707	+	4.44629i	0.122380	+	0.211969i
$441$	−1.00604	+	0.499881i	−0.0479068	+	0.0238039i
$442$	−27.5189			−1.30894
$443$	−20.9565	−	12.0992i	−0.995671	−	0.574851i	−0.0887065	−	0.996058i	$-0.528273\pi$
$443$	−20.9565	−	12.0992i	−0.995671	−	0.574851i	−0.906965	+	0.421207i	$0.861607\pi$
$444$	0.265508	+	1.13103i	0.0126004	+	0.0536763i
$445$	12.8955	+	7.44525i	0.611308	+	0.352939i
$446$	−6.68062	−	11.5712i	−0.316337	−	0.547911i
$447$	−9.54918	−	40.6783i	−0.451661	−	1.92402i
$448$	1.28701	+	2.22916i	0.0608053	+	0.105318i
$449$	32.2944			1.52406			0.762032	−	0.647539i	$-0.224202\pi$
$449$	32.2944			1.52406			0.762032	+	0.647539i	$0.224202\pi$
$450$	−2.99415	−	0.187231i	−0.141146	−	0.00882617i
$451$	−50.5931	+	29.2099i	−2.38233	+	1.37544i
$452$	−4.08230	−	2.35692i	−0.192015	−	0.110860i
$453$	27.4913	+	8.29440i	1.29165	+	0.389705i
$454$	7.77017	−	13.4583i	0.364672	−	0.631631i
$455$	6.82736	−	11.8253i	0.320071	−	0.554380i
$456$	−0.209606	−	0.892896i	−0.00981571	−	0.0418137i
$457$		−	19.0886i		−	0.892929i	−0.894801	−	0.446464i	$-0.852683\pi$
$457$		−	19.0886i		−	0.892929i	0.894801	−	0.446464i	$-0.147317\pi$
$458$	−7.27845	−	12.6066i	−0.340100	−	0.589070i
$459$	25.2699	+	9.38137i	1.17950	+	0.437885i
$460$	−2.62681	−	1.51659i	−0.122476	−	0.0707114i
$461$	12.8115			0.596691			0.298345	−	0.954458i	$-0.403565\pi$
$461$	12.8115			0.596691			0.298345	+	0.954458i	$0.403565\pi$
$462$	21.9139	+	6.61166i	1.01953	+	0.307602i
$463$			20.6891i			0.961503i	0.876857	+	0.480751i	$0.159636\pi$
$463$			20.6891i			0.961503i	−0.876857	+	0.480751i	$0.840364\pi$
$464$	−8.44680			−0.392133
$465$	7.53375	+	6.02018i	0.349369	+	0.279179i
$466$	2.89624			0.134166
$467$			23.8528i			1.10378i	0.833918	+	0.551889i	$0.186093\pi$
$467$			23.8528i			1.10378i	−0.833918	+	0.551889i	$0.813907\pi$
$468$	7.08158	+	14.2521i	0.327346	+	0.658804i
$469$	−20.5077			−0.946957
$470$	5.84788	+	3.37628i	0.269743	+	0.155736i
$471$	7.32983	−	24.2943i	0.337741	−	1.11942i
$472$	6.03251	+	10.4486i	0.277669	+	0.480937i
$473$			39.6702i			1.82404i
$474$	−17.0436	+	4.00096i	−0.782838	+	0.183770i
$475$	0.264764	−	0.458584i	0.0121482	−	0.0210413i
$476$	6.67636	−	11.5638i	0.306011	−	0.530026i
$477$	−4.41858	+	2.19550i	−0.202313	+	0.100525i
$478$	4.75354	+	2.74446i	0.217422	+	0.125529i
$479$	−2.62035	+	1.51286i	−0.119727	+	0.0691243i	−0.558667	−	0.829392i	$-0.688687\pi$
$479$	−2.62035	+	1.51286i	−0.119727	+	0.0691243i	0.438941	+	0.898516i	$0.355354\pi$
$480$	−1.18591	−	1.26238i	−0.0541292	−	0.0576197i
$481$	3.55823			0.162241
$482$	2.66410	+	4.61436i	0.121347	+	0.210178i
$483$	−13.1650	+	3.09047i	−0.599029	+	0.140621i
$484$	7.67968	+	13.3016i	0.349076	+	0.604618i
$485$	−5.59732	−	3.23162i	−0.254161	−	0.146740i
$486$	−1.64420	−	15.5015i	−0.0745822	−	0.703162i
$487$	−33.0749	−	19.0958i	−1.49877	−	0.865314i	−0.498768	−	0.866735i	$-0.666214\pi$
$487$	−33.0749	−	19.0958i	−1.49877	−	0.865314i	−0.999999	+	0.00142186i	$0.999547\pi$
$488$	7.06279			0.319717
$489$	11.2455	−	37.2724i	0.508538	−	1.68552i
$490$	−0.187231	−	0.324294i	−0.00845825	−	0.0146501i
$491$	−12.7244	+	22.0394i	−0.574245	+	0.994622i	0.421878	+	0.906653i	$0.361371\pi$
$491$	−12.7244	+	22.0394i	−0.574245	+	0.994622i	−0.996123	+	0.0879695i	$0.971962\pi$
$492$	14.3643	−	13.4941i	0.647593	−	0.608363i
$493$	21.9089	+	37.9474i	0.986729	+	1.70907i
$494$	−2.80906			−0.126385
$495$	−15.3724	−	0.961271i	−0.690937	−	0.0432059i
$496$	0.790363	+	5.51138i	0.0354884	+	0.247468i
$497$		−	25.1249i		−	1.12701i
$498$	10.0270	−	9.41957i	0.449321	−	0.422101i
$499$	−7.16472	+	4.13656i	−0.320737	+	0.185178i	−0.651721	−	0.758459i	$-0.725953\pi$
$499$	−7.16472	+	4.13656i	−0.320737	+	0.185178i	0.330984	+	0.943636i	$0.392619\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−27.6987	+	6.50223i	−1.23748	+	0.290498i
$502$	0.680586	−	0.392937i	0.0303760	−	0.0175376i
$503$	12.4153	−	7.16797i	0.553570	−	0.319604i	−0.196991	−	0.980405i	$-0.563117\pi$
$503$	12.4153	−	7.16797i	0.553570	−	0.319604i	0.750561	+	0.660802i	$0.229784\pi$
$504$	−7.70698	−	0.481936i	−0.343296	−	0.0214671i
$505$	−4.44238	+	7.69443i	−0.197683	+	0.342398i
$506$	−13.4864	−	7.78638i	−0.599544	−	0.346147i
$507$	25.5314	−	5.99347i	1.13389	−	0.266179i
$508$	−13.5026	+	7.79574i	−0.599082	+	0.345880i
$509$	−17.7292	+	30.7078i	−0.785832	+	1.36110i	0.142668	+	0.989771i	$0.454432\pi$
$509$	−17.7292	+	30.7078i	−0.785832	+	1.36110i	−0.928501	+	0.371331i	$0.878902\pi$
$510$	−2.59533	+	8.60205i	−0.114923	+	0.380905i
$511$			9.55629i			0.422745i
$512$		−	1.00000i		−	0.0441942i
$513$	2.57948	+	0.957625i	0.113887	+	0.0422802i
$514$	−6.02954	+	10.4435i	−0.265952	+	0.460642i
$515$	−9.11135	+	5.26044i	−0.401494	+	0.231803i
$516$	−3.05853	−	13.0289i	−0.134644	−	0.573567i
$517$	30.0238	+	17.3343i	1.32045	+	0.762360i
$518$	−0.863261	+	1.49521i	−0.0379295	+	0.0656959i
$519$	−3.67131	+	3.44891i	−0.161153	+	0.151390i
$520$	−4.59412	+	2.65242i	−0.201466	+	0.116316i
$521$	−13.5448	+	7.82011i	−0.593410	+	0.342605i	−0.766445	−	0.642310i	$-0.777976\pi$
$521$	−13.5448	+	7.82011i	−0.593410	+	0.342605i	0.173035	+	0.984916i	$0.444643\pi$
$522$	14.0151	−	21.1119i	0.613425	−	0.924042i
$523$			26.2117i			1.14616i	0.819500	+	0.573078i	$0.194251\pi$
$523$			26.2117i			1.14616i	−0.819500	+	0.573078i	$0.805749\pi$
$524$	−16.4069	+	9.47252i	−0.716738	+	0.413809i
$525$	−3.05255	−	3.24939i	−0.133224	−	0.141815i
$526$			2.04756i			0.0892780i
$527$	22.7100	−	17.8459i	0.989263	−	0.777380i
$528$	−6.08863	−	6.48126i	−0.264973	−	0.282060i
$529$	−13.7998			−0.599992
$530$	−0.822328	−	1.42431i	−0.0357196	−	0.0618682i
$531$	−36.1245	−	2.25895i	−1.56767	−	0.0980302i
$532$	0.681505	−	1.18040i	0.0295470	−	0.0511769i
$533$	−30.1811	−	52.2752i	−1.30729	−	2.26429i
$534$	−24.6917	−	7.44975i	−1.06852	−	0.322382i
$535$	−12.9437			−0.559605
$536$	6.89980	+	3.98360i	0.298026	+	0.172065i
$537$	−9.63928	+	2.26281i	−0.415965	+	0.0976474i
$538$	23.3961	+	13.5077i	1.00868	+	0.582360i
$539$	−0.961271	−	1.66497i	−0.0414049	−	0.0717154i
$540$	5.12289	−	0.869482i	0.220454	−	0.0374166i
$541$	−2.17123	−	3.76069i	−0.0933487	−	0.161685i	0.815570	−	0.578659i	$-0.196424\pi$
$541$	−2.17123	−	3.76069i	−0.0933487	−	0.161685i	−0.908918	+	0.416974i	$0.863090\pi$
$542$	−3.17938			−0.136566
$543$	−19.3179	+	18.1476i	−0.829009	+	0.778788i
$544$	−4.49252	+	2.59376i	−0.192615	+	0.111206i
$545$	−1.17033	−	0.675690i	−0.0501314	−	0.0289434i
$546$	−6.83148	+	22.6425i	−0.292360	+	0.969011i
$547$	−3.95664	+	6.85310i	−0.169174	+	0.293017i	−0.938130	−	0.346285i	$-0.887443\pi$
$547$	−3.95664	+	6.85310i	−0.169174	+	0.293017i	0.768956	+	0.639302i	$0.220777\pi$
$548$	2.98906	−	5.17720i	0.127686	−	0.221159i
$549$	−11.7187	+	17.6527i	−0.500144	+	0.753399i
$550$		−	5.13414i		−	0.218920i
$551$	2.23641	+	3.87357i	0.0952741	+	0.165020i
$552$	5.02968	+	1.51751i	0.214078	+	0.0645894i
$553$	−22.5315	−	13.0086i	−0.958137	−	0.553180i
$554$	−16.5427			−0.702833
$555$	0.335578	−	1.11225i	0.0142445	−	0.0472126i
$556$			20.6001i			0.873640i
$557$	23.6372			1.00154			0.500770	−	0.865580i	$-0.333050\pi$
$557$	23.6372			1.00154			0.500770	+	0.865580i	$0.333050\pi$
$558$	−15.0865	−	7.16918i	−0.638663	−	0.303496i
$559$	−40.9891			−1.73365
$560$		−	2.57401i		−	0.108772i
$561$	−13.3248	+	44.1641i	−0.562572	+	1.86461i
$562$	1.55339			0.0655256
$563$	9.05588	+	5.22841i	0.381660	+	0.220351i	0.678540	−	0.734563i	$-0.262613\pi$
$563$	9.05588	+	5.22841i	0.381660	+	0.220351i	−0.296880	+	0.954915i	$0.595946\pi$
$564$	−11.1972	−	3.37832i	−0.471488	−	0.142253i
$565$	2.35692	+	4.08230i	0.0991562	+	0.171744i
$566$			3.03122i			0.127412i
$567$	13.9922	−	18.4632i	0.587615	−	0.775380i
$568$	−4.88050	+	8.45327i	−0.204781	+	0.354691i
$569$	−5.12252	+	8.87246i	−0.214747	+	0.371953i	−0.953194	−	0.302358i	$-0.902226\pi$
$569$	−5.12252	+	8.87246i	−0.214747	+	0.371953i	0.738447	+	0.674311i	$0.235559\pi$
$570$	−0.264924	+	0.878074i	−0.0110964	+	0.0367785i
$571$	27.0944	+	15.6430i	1.13387	+	0.654638i	0.944904	−	0.327346i	$-0.106154\pi$
$571$	27.0944	+	15.6430i	1.13387	+	0.654638i	0.188962	+	0.981984i	$0.439488\pi$
$572$	−23.5869	+	13.6179i	−0.986216	+	0.569392i
$573$	6.29485	−	5.91352i	0.262971	−	0.247041i
$574$	29.2889			1.22250
$575$	1.51659	+	2.62681i	0.0632462	+	0.109546i
$576$	2.49940	+	1.65922i	0.104141	+	0.0691343i
$577$	−12.2866	−	21.2810i	−0.511498	−	0.885941i	−0.999911	−	0.0133282i	$-0.995757\pi$
$577$	−12.2866	−	21.2810i	−0.511498	−	0.885941i	0.488413	−	0.872613i	$-0.337576\pi$
$578$	8.58260	+	4.95516i	0.356989	+	0.206108i
$579$	27.2648	−	6.40038i	1.13309	−	0.265991i
$580$	7.31514	+	4.22340i	0.303745	+	0.175367i
$581$	20.4451			0.848207
$582$	10.7175	+	3.23357i	0.444253	+	0.134036i
$583$	−4.22194	−	7.31262i	−0.174855	−	0.302858i
$584$	1.85630	−	3.21521i	0.0768143	−	0.133046i
$585$	0.993232	−	15.8835i	0.0410651	−	0.656701i
$586$	3.89138	+	6.74006i	0.160751	+	0.278429i
$587$	28.3116			1.16855			0.584273	−	0.811557i	$-0.301380\pi$
$587$	28.3116			1.16855			0.584273	+	0.811557i	$0.301380\pi$
$588$	0.444079	+	0.472716i	0.0183135	+	0.0194945i
$589$	2.31817	−	1.82166i	0.0955187	−	0.0750603i
$590$		−	12.0650i		−	0.496709i
$591$	10.2208	+	10.8799i	0.420426	+	0.447538i
$592$	0.580888	−	0.335376i	0.0238744	−	0.0137839i
$593$			26.2219i			1.07680i	0.842689	+	0.538401i	$0.180972\pi$
$593$			26.2219i			1.07680i	−0.842689	+	0.538401i	$0.819028\pi$
$594$	26.3016	−	4.46404i	1.07917	−	0.183162i
$595$	−11.5638	+	6.67636i	−0.474070	+	0.273704i
$596$	−20.8920	+	12.0620i	−0.855771	+	0.494080i
$597$	7.16975	−	6.73541i	0.293438	−	0.275662i
$598$	8.04526	−	13.9348i	0.328995	−	0.569836i
$599$	−29.8917	−	17.2580i	−1.22134	−	0.705141i	−0.256136	−	0.966641i	$-0.582450\pi$
$599$	−29.8917	−	17.2580i	−1.22134	−	0.705141i	−0.965204	+	0.261500i	$0.915783\pi$
$600$	0.395836	+	1.68621i	0.0161600	+	0.0688393i
$601$	−23.6671	+	13.6642i	−0.965403	+	0.557375i	−0.897832	−	0.440339i	$-0.854858\pi$
$601$	−23.6671	+	13.6642i	−0.965403	+	0.557375i	−0.0675710	+	0.997714i	$0.521525\pi$
$602$	9.94437	−	17.2241i	0.405302	−	0.702004i
$603$	−21.4049	+	10.6357i	−0.871675	+	0.433117i
$604$		−	16.5788i		−	0.674581i
$605$		−	15.3594i		−	0.624447i
$606$	4.44507	−	14.7329i	0.180568	−	0.598483i
$607$	11.0332	−	19.1100i	0.447822	−	0.775651i	−0.550422	−	0.834887i	$-0.685533\pi$
$607$	11.0332	−	19.1100i	0.447822	−	0.775651i	0.998244	+	0.0592358i	$0.0188664\pi$
$608$	−0.458584	+	0.264764i	−0.0185980	+	0.0107376i
$609$	36.6619	−	8.60633i	1.48561	−	0.348746i
$610$	−6.11655	−	3.53139i	−0.247652	−	0.142982i
$611$	−17.9106	+	31.0221i	−0.724585	+	1.25502i
$612$	0.971266	−	15.5322i	0.0392611	−	0.627852i
$613$	24.3755	−	14.0732i	0.984517	−	0.568411i	0.0808859	−	0.996723i	$-0.474225\pi$
$613$	24.3755	−	14.0732i	0.984517	−	0.568411i	0.903631	+	0.428312i	$0.140892\pi$
$614$	−9.90659	+	5.71957i	−0.399797	+	0.230823i
$615$	−19.1869	+	4.50411i	−0.773692	+	0.181623i
$616$		−	13.2153i		−	0.532461i
$617$	−24.9200	+	14.3875i	−1.00324	+	0.579221i	−0.909205	−	0.416348i	$-0.863310\pi$
$617$	−24.9200	+	14.3875i	−1.00324	+	0.579221i	−0.0940345	+	0.995569i	$0.529976\pi$
$618$	13.2814	−	12.4768i	0.534256	−	0.501891i
$619$		−	14.4354i		−	0.580208i	−0.956995	−	0.290104i	$-0.906310\pi$
$619$		−	14.4354i		−	0.580208i	0.956995	−	0.290104i	$-0.0936899\pi$
$620$	2.07122	−	5.16818i	0.0831820	−	0.207559i
$621$	−12.1382	+	10.0533i	−0.487090	+	0.403425i
$622$	−7.22744			−0.289794
$623$	−19.1642	−	33.1933i	−0.767796	−	1.32986i
$624$	6.69674	−	6.29106i	0.268084	−	0.251844i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.50334	−	11.2641i	−0.259926	−	0.450205i
$627$	−1.36015	+	4.50815i	−0.0543193	+	0.180038i
$628$	−14.6508			−0.584631
$629$	−3.01337	−	1.73977i	−0.120151	−	0.0693691i
$630$	6.43347	+	4.27086i	0.256316	+	0.170155i
$631$	18.2779	+	10.5528i	0.727633	+	0.420099i	0.817556	−	0.575850i	$-0.195329\pi$
$631$	18.2779	+	10.5528i	0.727633	+	0.420099i	−0.0899227	+	0.995949i	$0.528662\pi$
$632$	5.05381	+	8.75345i	0.201030	+	0.348194i
$633$	2.34573	−	0.550657i	0.0932343	−	0.0218866i
$634$	11.3812	+	19.7129i	0.452006	+	0.782898i
$635$	15.5915			0.618729
$636$	1.95041	+	2.07619i	0.0773390	+	0.0823262i
$637$	1.72033	−	0.993232i	0.0681619	−	0.0393533i
$638$	37.5569	+	21.6835i	1.48689	+	0.858458i
$639$	−13.0302	−	26.2241i	−0.515468	−	1.03741i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	13.7198	−	23.7633i	0.541898	−	0.938594i	−0.456898	−	0.889519i	$-0.651039\pi$
$641$	13.7198	−	23.7633i	0.541898	−	0.938594i	0.998795	−	0.0490748i	$-0.0156273\pi$
$642$	21.8258	−	5.12359i	0.861397	−	0.202212i
$643$			34.0135i			1.34136i	0.741747	+	0.670680i	$0.233998\pi$
$643$			34.0135i			1.34136i	−0.741747	+	0.670680i	$0.766002\pi$
$644$	3.90372	+	6.76144i	0.153828	+	0.266438i
$645$	−3.86571	+	12.8127i	−0.152212	+	0.504498i
$646$	2.37891	+	1.37347i	0.0935971	+	0.0540383i
$647$	12.8461			0.505031			0.252516	−	0.967593i	$-0.418742\pi$
$647$	12.8461			0.505031			0.252516	+	0.967593i	$0.418742\pi$
$648$	−8.29411	+	3.49396i	−0.325823	+	0.137256i
$649$		−	61.9435i		−	2.43149i
$650$	5.30484			0.208073
$651$	−9.04592	−	23.1159i	−0.354537	−	0.905985i
$652$	−22.4774			−0.880281
$653$			0.0217666i			0.000851794i	1.00000		0.000425897i	$0.000135567\pi$
$653$			0.0217666i			0.000851794i	−1.00000		0.000425897i	$0.999864\pi$
$654$	2.24089	+	0.676098i	0.0876256	+	0.0264375i
$655$	18.9450			0.740244
$656$	−9.85425	−	5.68936i	−0.384744	−	0.222132i
$657$	4.95606	+	9.97438i	0.193354	+	0.389138i
$658$	−8.69058	−	15.0525i	−0.338794	−	0.586808i
$659$			42.3998i			1.65166i	0.563917	+	0.825832i	$0.309294\pi$
$659$			42.3998i			1.65166i	−0.563917	+	0.825832i	$0.690706\pi$
$660$	2.03228	+	8.65725i	0.0791063	+	0.336983i
$661$	3.57820	−	6.19762i	0.139176	−	0.241059i	−0.788009	−	0.615664i	$-0.788888\pi$
$661$	3.57820	−	6.19762i	0.139176	−	0.241059i	0.927185	+	0.374604i	$0.122221\pi$
$662$	2.45387	−	4.25023i	0.0953724	−	0.165190i
$663$	−45.6325	−	13.7678i	−1.77222	−	0.534696i
$664$	−6.87875	−	3.97145i	−0.266947	−	0.154122i
$665$	−1.18040	+	0.681505i	−0.0457740	+	0.0264276i
$666$	−0.125586	+	2.00833i	−0.00486635	+	0.0778213i
$667$	−25.6207			−0.992036
$668$	8.21327	+	14.2258i	0.317781	+	0.550413i
$669$	−5.28887	−	22.5299i	−0.204479	−	0.871056i
$670$	−3.98360	−	6.89980i	−0.153900	−	0.266563i
$671$	−31.4032	−	18.1307i	−1.21231	−	0.699926i
$672$	1.01889	+	4.34033i	0.0393044	+	0.167432i
$673$	−15.4883	−	8.94220i	−0.597032	−	0.344696i	0.170841	−	0.985299i	$-0.445351\pi$
$673$	−15.4883	−	8.94220i	−0.597032	−	0.344696i	−0.767873	+	0.640602i	$0.778685\pi$
$674$	27.0752			1.04290
$675$	−4.87129	−	1.80845i	−0.187496	−	0.0696073i
$676$	−7.57064	−	13.1127i	−0.291179	−	0.504336i
$677$	−16.7056	+	28.9349i	−0.642048	+	1.11206i	0.342927	+	0.939362i	$0.388582\pi$
$677$	−16.7056	+	28.9349i	−0.642048	+	1.11206i	−0.984975	+	0.172698i	$0.944752\pi$
$678$	−5.59018	−	5.95067i	−0.214690	−	0.228534i
$679$	8.31822	+	14.4076i	0.319224	+	0.552912i
$680$	5.18752			0.198932
$681$	19.6179	−	18.4295i	0.751759	−	0.706218i
$682$	10.6339	−	26.5341i	0.407193	−	1.01604i
$683$			19.4433i			0.743979i	0.928237	+	0.371990i	$0.121324\pi$
$683$			19.4433i			0.743979i	−0.928237	+	0.371990i	$0.878676\pi$
$684$	0.0991442	−	1.58549i	0.00379087	−	0.0606226i
$685$	−5.17720	+	2.98906i	−0.197811	+	0.114206i
$686$			18.9820i			0.724734i
$687$	−5.76215	−	24.5460i	−0.219840	−	0.936489i
$688$	−6.69156	+	3.86337i	−0.255113	+	0.147290i
$689$	7.55575	−	4.36231i	0.287851	−	0.166191i
$690$	−3.59708	−	3.82904i	−0.136939	−	0.145769i
$691$	−10.6087	+	18.3747i	−0.403572	+	0.699007i	−0.994154	−	0.107970i	$-0.965565\pi$
$691$	−10.6087	+	18.3747i	−0.403572	+	0.699007i	0.590582	+	0.806978i	$0.298898\pi$
$692$	2.51861	+	1.45412i	0.0957430	+	0.0552772i
$693$	33.0303	+	21.9272i	1.25472	+	0.832945i
$694$	17.7512	−	10.2487i	0.673827	−	0.389034i
$695$	10.3001	−	17.8402i	0.390704	−	0.676718i
$696$	−14.0067	−	4.22595i	−0.530921	−	0.160184i
$697$			59.0273i			2.23582i
$698$			20.0539i			0.759053i
$699$	4.80260	+	1.44899i	0.181651	+	0.0548060i
$700$	−1.28701	+	2.22916i	−0.0486443	+	0.0842543i
$701$	28.4019	−	16.3979i	1.07273	−	0.619338i	0.143801	−	0.989607i	$-0.454068\pi$
$701$	28.4019	−	16.3979i	1.07273	−	0.619338i	0.928925	+	0.370268i	$0.120734\pi$
$702$	4.61246	+	27.1761i	0.174086	+	1.02570i
$703$	−0.307596	−	0.177591i	−0.0116012	−	0.00669796i
$704$	−2.56707	+	4.44629i	−0.0967500	+	0.167576i
$705$	8.00793	+	8.52432i	0.301596	+	0.321045i
$706$	−7.28255	+	4.20458i	−0.274082	+	0.158242i
$707$	19.8056	−	11.4347i	0.744865	−	0.430048i
$708$	4.77578	+	20.3442i	0.179485	+	0.764582i
$709$		−	49.3472i		−	1.85327i	−0.375960	−	0.926636i	$-0.622687\pi$
$709$		−	49.3472i		−	1.85327i	0.375960	−	0.926636i	$-0.377313\pi$
$710$	8.45327	−	4.88050i	0.317245	−	0.183162i
$711$	−30.2637	−	1.89246i	−1.13498	−	0.0709729i
$712$			14.8905i			0.558045i
$713$	2.39732	+	16.7170i	0.0897802	+	0.626057i
$714$	16.8563	−	15.8351i	0.630831	−	0.592615i
$715$	27.2358			1.01856
$716$	2.85826	+	4.95065i	0.106818	+	0.185015i
$717$	6.50937	+	6.92913i	0.243097	+	0.258773i
$718$	12.7070	−	22.0093i	0.474223	−	0.821378i
$719$	3.77117	+	6.53187i	0.140641	+	0.243598i	0.927738	−	0.373232i	$-0.121750\pi$
$719$	3.77117	+	6.53187i	0.140641	+	0.243598i	−0.787097	+	0.616829i	$0.788417\pi$
$720$	−1.33493	−	2.68663i	−0.0497499	−	0.100125i
$721$	27.0809			1.00854
$722$	−16.2116	−	9.35980i	−0.603335	−	0.348336i
$723$	2.10910	+	8.98449i	0.0784382	+	0.334137i
$724$	13.2525	+	7.65134i	0.492525	+	0.284360i
$725$	−4.22340	−	7.31514i	−0.156853	−	0.271677i
$726$	6.07979	+	25.8991i	0.225642	+	0.961207i
$727$	20.0826	+	34.7841i	0.744822	+	1.29007i	0.950278	+	0.311403i	$0.100799\pi$
$727$	20.0826	+	34.7841i	0.744822	+	1.29007i	−0.205456	+	0.978666i	$0.565868\pi$
$728$	13.6547			0.506077
$729$	5.02899	−	26.5275i	0.186259	−	0.982501i
$730$	−3.21521	+	1.85630i	−0.119000	+	0.0687048i
$731$	34.7126	+	20.0413i	1.28389	+	0.741255i
$732$	11.7117	+	3.53353i	0.432875	+	0.130603i
$733$	7.73727	−	13.4013i	0.285783	−	0.494990i	−0.687016	−	0.726642i	$-0.741080\pi$
$733$	7.73727	−	13.4013i	0.285783	−	0.494990i	0.972799	+	0.231652i	$0.0744132\pi$
$734$	8.65053	−	14.9832i	0.319297	−	0.553038i
$735$	−0.148226	−	0.631424i	−0.00546740	−	0.0232904i
$736$		−	3.03318i		−	0.111805i
$737$	−20.4524	−	35.4245i	−0.753372	−	1.30488i
$738$	30.5704	−	15.1898i	1.12531	−	0.559143i
$739$	20.8170	+	12.0187i	0.765767	+	0.442116i	0.831362	−	0.555731i	$-0.187561\pi$
$739$	20.8170	+	12.0187i	0.765767	+	0.442116i	−0.0655955	+	0.997846i	$0.520895\pi$
$740$	−0.670752			−0.0246573
$741$	−4.65804	−	1.40538i	−0.171117	−	0.0516278i
$742$			4.23336i			0.155412i
$743$	16.5869			0.608516			0.304258	−	0.952590i	$-0.401591\pi$
$743$	16.5869			0.608516			0.304258	+	0.952590i	$0.401591\pi$
$744$	−1.44676	+	9.53451i	−0.0530407	+	0.349552i
$745$	24.1241			0.883837
$746$			14.4940i			0.530663i
$747$	21.3396	−	10.6032i	0.780776	−	0.387951i
$748$	26.6334			0.973814
$749$	28.8536	+	16.6586i	1.05429	+	0.608693i
$750$	0.500302	−	1.65822i	0.0182684	−	0.0605497i
$751$	−15.3278	−	26.5485i	−0.559318	−	0.968768i	−0.997553	−	0.0699074i	$-0.977730\pi$
$751$	−15.3278	−	26.5485i	−0.559318	−	0.968768i	0.438235	−	0.898860i	$-0.355604\pi$
$752$			6.75256i			0.246240i
$753$	1.32515	−	0.311077i	0.0482911	−	0.0113363i
$754$	−22.4044	+	38.8056i	−0.815921	+	1.41322i
$755$	−8.28939	+	14.3576i	−0.301682	+	0.522528i
$756$	−12.5388	−	4.65498i	−0.456031	−	0.169300i
$757$	15.7629	+	9.10072i	0.572913	+	0.330771i	0.758312	−	0.651892i	$-0.226024\pi$
$757$	15.7629	+	9.10072i	0.572913	+	0.330771i	−0.185399	+	0.982663i	$0.559358\pi$
$758$	−17.1608	+	9.90778i	−0.623308	+	0.359867i
$759$	−18.4679	−	19.6588i	−0.670343	−	0.713570i
$760$	0.529528			0.0192080
$761$	−18.2034	−	31.5292i	−0.659873	−	1.14293i	−0.980648	−	0.195778i	$-0.937277\pi$
$761$	−18.2034	−	31.5292i	−0.659873	−	1.14293i	0.320775	−	0.947155i	$-0.396057\pi$
$762$	−26.2906	+	6.17168i	−0.952406	+	0.223576i
$763$	1.73923	+	3.01244i	0.0629645	+	0.109058i
$764$	−4.31841	−	2.49324i	−0.156235	−	0.0902022i
$765$	−8.60725	+	12.9657i	−0.311196	+	0.468774i
$766$	3.42236	+	1.97590i	0.123655	+	0.0713922i
$767$	64.0030			2.31101
$768$	0.500302	−	1.65822i	0.0180531	−	0.0598359i
$769$	15.0861	+	26.1298i	0.544017	+	0.942265i	0.998668	+	0.0515956i	$0.0164307\pi$
$769$	15.0861	+	26.1298i	0.544017	+	0.942265i	−0.454651	+	0.890670i	$0.650236\pi$
$770$	−6.60766	+	11.4448i	−0.238124	+	0.412442i
$771$	−15.2232	+	14.3010i	−0.548251	+	0.515038i
$772$	−8.08463	−	14.0030i	−0.290972	−	0.503979i
$773$	−14.9673			−0.538336			−0.269168	−	0.963093i	$-0.586749\pi$
$773$	−14.9673			−0.538336			−0.269168	+	0.963093i	$0.586749\pi$
$774$	1.44669	−	23.1350i	0.0520002	−	0.831572i
$775$	−4.37781	+	3.44017i	−0.157256	+	0.123574i
$776$		−	6.46323i		−	0.232016i

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.500302 - 1.65822i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.65822 - 0.500302i) q^{6} +(-1.28701 - 2.22916i) q^{7} +1.00000i q^{8} +(-2.49940 - 1.65922i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.500302 - 1.65822i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.65822 - 0.500302i) q^{6} +(-1.28701 - 2.22916i) q^{7} +1.00000i q^{8} +(-2.49940 - 1.65922i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.56707 - 4.44629i) q^{11} +(-0.500302 + 1.65822i) q^{12} +(4.59412 + 2.65242i) q^{13} +(-2.22916 + 1.28701i) q^{14} +(1.26238 - 1.18591i) q^{15} +1.00000 q^{16} +(-2.59376 - 4.49252i) q^{17} +(-1.65922 + 2.49940i) q^{18} +(-0.264764 - 0.458584i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-4.34033 + 1.01889i) q^{21} +(-4.44629 - 2.56707i) q^{22} +3.03318 q^{23} +(1.65822 + 0.500302i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.65242 - 4.59412i) q^{26} +(-4.00181 + 3.31444i) q^{27} +(1.28701 + 2.22916i) q^{28} -8.44680 q^{29} +(-1.18591 - 1.26238i) q^{30} +(0.790363 + 5.51138i) q^{31} -1.00000i q^{32} +(-6.08863 - 6.48126i) q^{33} +(-4.49252 + 2.59376i) q^{34} -2.57401i q^{35} +(2.49940 + 1.65922i) q^{36} +(0.580888 - 0.335376i) q^{37} +(-0.458584 + 0.264764i) q^{38} +(6.69674 - 6.29106i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-9.85425 - 5.68936i) q^{41} +(1.01889 + 4.34033i) q^{42} +(-6.69156 + 3.86337i) q^{43} +(-2.56707 + 4.44629i) q^{44} +(-1.33493 - 2.68663i) q^{45} -3.03318i q^{46} +6.75256i q^{47} +(0.500302 - 1.65822i) q^{48} +(0.187231 - 0.324294i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-8.74726 + 2.05341i) q^{51} +(-4.59412 - 2.65242i) q^{52} +(0.822328 - 1.42431i) q^{53} +(3.31444 + 4.00181i) q^{54} +(4.44629 - 2.56707i) q^{55} +(2.22916 - 1.28701i) q^{56} +(-0.892896 + 0.209606i) q^{57} +8.44680i q^{58} +(10.4486 - 6.03251i) q^{59} +(-1.26238 + 1.18591i) q^{60} -7.06279i q^{61} +(5.51138 - 0.790363i) q^{62} +(-0.481936 + 7.70698i) q^{63} -1.00000 q^{64} +(2.65242 + 4.59412i) q^{65} +(-6.48126 + 6.08863i) q^{66} +(3.98360 - 6.89980i) q^{67} +(2.59376 + 4.49252i) q^{68} +(1.51751 - 5.02968i) q^{69} -2.57401 q^{70} +(8.45327 + 4.88050i) q^{71} +(1.65922 - 2.49940i) q^{72} +(-3.21521 - 1.85630i) q^{73} +(-0.335376 - 0.580888i) q^{74} +(1.68621 - 0.395836i) q^{75} +(0.264764 + 0.458584i) q^{76} -13.2153 q^{77} +(-6.29106 - 6.69674i) q^{78} +(8.75345 - 5.05381i) q^{79} +(0.866025 + 0.500000i) q^{80} +(3.49396 + 8.29411i) q^{81} +(-5.68936 + 9.85425i) q^{82} +(-3.97145 + 6.87875i) q^{83} +(4.34033 - 1.01889i) q^{84} -5.18752i q^{85} +(3.86337 + 6.69156i) q^{86} +(-4.22595 + 14.0067i) q^{87} +(4.44629 + 2.56707i) q^{88} +14.8905 q^{89} +(-2.68663 + 1.33493i) q^{90} -13.6547i q^{91} -3.03318 q^{92} +(9.53451 + 1.44676i) q^{93} +6.75256 q^{94} -0.529528i q^{95} +(-1.65822 - 0.500302i) q^{96} -6.46323 q^{97} +(-0.324294 - 0.187231i) q^{98} +(-13.7935 + 6.85371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) \)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about